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Reference HandbookVersion 1.0
PE Chemica l
This document may be printed from the NCEES Web site
for your personal use, but it may not be copied, reproduced,
distributed electronically or in print, or posted online
All NCEES material is copyrighted under the laws of the United States. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means without the prior written permission of NCEES. Requests for permissions should be addressed in writing to [email protected].
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Using the Handbook for the April 2017 Paper ExamThe Principles and Practice of Engineering (PE) Chemical exam is an open-book pencil-and-paper exam through April 2017. The PE Chemical Reference Handbook is a resource you may use on exam day. Additional references that adhere to policies in the NCEES Examinee Guide are still allowed in the exam room for the April 2017 exam.
The PE Chemical Reference Handbook contains charts, formulas, tables, and other information that may help you answer questions on the PE Chemical exam. However, it does not contain all information required to answer every question; theories, conversions, formulas, and definitions that examinees are expected to know have not been included.
This Handbook is intended solely for use on the NCEES PE Chemical exam. You may bring your personal copy of the Handbook into the exam room as long as it is bound and remains bound according to the policies in the NCEES Examinee Guide.
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1.2.1 Material Balances With No ReactionBalanced equation at steady state with no reaction: Input = Output
1.2.2 Material Balances With Reaction
1.2.2.1 GeneralBalanced equation at steady state with reaction: Input + Generation = Output + Consumption
Common Flow Configurations
PROCESS WITH BYPASS
PROCESS WITH PURGE PROCESS WITH RECYCLEAND PURGE
PROCESS WITH RECYCLE
1.2.2.2 Combustion Reactions Theoretical (stoichiometric) air is the air required for complete combustion.
Molar air-fuel ratio Moles of fuel
Moles of airFA =c m
Percent theoretical air FAFA
100
Theoretical
Actual #=c
c
m
m
Percent excess air 100FA
FA
FA
Theoretical
Actual Theoretical #=−c
c
cm
m
m
Gross or higher heating value (HHV) is the heat of combustion assuming all water generated is condensed as a liquid.
Net or lower heating value (LHV) is the heat of combustion assuming that no water is condensed.
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Major Components of Air
Element Volume, %Nitrogen 78.09Oxygen 20.94Argon 0.93
Selected Properties of AirProperty Amount
Molecular weight of air 28.965 lbmolelbm
Absolute viscosity (m)
at 80°F 0.045 hr ftlbm-
at 100°F 0.047 hr ftlbm-
Density
at 80°F 0.0734 ftlbm3
at 100°F 0.0708 ftlbm3
The dry adiabatic lapse rate ΓAD is 0.98°C per 100 m (5.4°F per 1000 ft). This is the rate at which dry air cools adiabatically with altitude. The actual (environmental) lapse rate Γ is compared to ΓAD to determine stability.
Stability of Adiabatic Lapse RateLapse Rate Stability Condition
Γ > ΓAD Unstable
Γ = ΓAD Neutral
Γ < ΓAD Stable
1.2.2.3 Heat of ReactionCalculate standard state heat of reaction h 0D R
t from standard heat of formation h 0D ft at 298 K (25°C) and 1 atm, using
h h h0 0 0D D D= −R f ftstanproducts reac
t t t/ /
Calculate hRDt at temperature T using
h h h hR R f f0D D D D= + +
tstanproducts reac
t t t t/ /
where hfDt includes the sensible and latent heat changes between T and 298K
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 5
1.2.2.4 Standard Heat of Formation and CombustionThe standard heat of formation and combustion at 25°C are shown in the tables below. The products of combustion are H2O (l) and CO2 (g). Solids are listed as s in the tables below.
Alkanes
Name Formula Phaseh f0D t hc0D− t
HHV
molkJ
lbmolBtu
molkJ
lbmolBtu
Methane CH4 g –74.6 –32,070 890.7 382,900Ethane C2H6 g –84.00 –36,110 1560 670,700n-Propane C3H8 g –104.6 –44,970 2219 954,100Isobutane C4H10 g –134.3 –57,740 2868 1,233,000n-Butane C4H10 g –125.5 –53,960 2877 1,237,000n-Pentane C5H12 g –146.9 –63,160 3535 1,520,000n-Pentane C5H12 l –173.5 –74,600 3509 1,507,000Cyclohexane C6H12 g –124.0 –53,310 — —Cyclohexane C6H12 l –157.0 –67,500 3930 1,690,000n-Hexane C6H14 g –167.2 –71,890 4199 1,805,000n-Hexane C6H14 l –198.8 –85,470 4163 1,790,000Methylcyclohexane C7H14 g –154.78 –66,540 4601 1,978,000Methylcyclohexane C7H14 l –190.2 –81,760 4565 1,963,000n-Heptane C7H16 g –187.9 –80,790 — —n-Heptane C7H16 l –225.0 –96,740 4817 2,071,000n-Octane C8H18 g –208.4 –89,600 — —n-Octane C8H18 l –250.0 –107,500 5430 2,335,000n-Nonane C9H20 g –228.3 –98,160 — —n-Nonane C9H20 l –274.7 –118,100 6125 2,633,000n-Decane C10H22 g –249.7 –107,400 — —n-Decane C10H22 l –301.0 –129,400 6779 2,915,000
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Alkenes and Alkynes
Name Formula Phaseh f0D t hc0D− t
HHV
molkJ
lbmolBtu
molkJ
lbmolBtu
Acetylene C2H2 g 226.8 97,510 — —Ethylene C2H4 g 52.3 22,500 1411 606,600Propylene C3H6 g 20.4 8770 2058 884,8001,3-Butadiene C4H6 g 109 46,900 2540 1,092,0001,3-Butadiene C4H6 l 91 39,100 2522 1,084,0001-Butene C4H8 g –0.630 –270 2717 1,168,0001-Pentene C5H10 g –22 –9500 — —1-Pentene C5H10 l –49 –21,000 3350 1,440,0001-Hexene C6H12 g –42 –1800 — —1-Hexene C6H12 l –73 –31,000 — —
Aromatics
Name Formula Phaseh f0D t hc0D− t
HHV
molkJ
lbmolBtu
molkJ
lbmolBtu
Benzene C6H6 g 82.9 35,600 — —Benzene C6H6 l 49 21,000 3270 1,406,000Toluene C7H8 g 50 21,000 — —Toluene C7H8 l 12 5200 3920 1,685,000Styrene C8H8 g 147 63,200 — —Styrene C8H8 l 103 44,300 4390 1,887,000Ethylbenzene C8H10 g 49 21,000 — —Ethylbenzene C8H10 l 6.8 2900 4567 1,964,000p-Xylene C8H12 g 17.9 7700 — —p-Xylene C8H12 l –24.4 –10,500 4552 1,957,000o-Xylene C8H12 g 19 8200 — —o-Xylene C8H12 l –24.4 –10,500 4552 1,957,000
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 7
Other Organic Compounds
Name Formula Phaseh f0D t hc0D− t
HHV
molkJ
lbmolBtu
molkJ
lbmolBtu
Methanol CH4O g –205 –88,100 764 328,500Methanol CH4O l –239 –103,000 726 312,100Acetaldehyde C2H4O g –171 –73,500 — —Acetaldehyde C2H4O l –196 –84,300 — —Ethylene oxide C2H4O g –53 –22,700 1306 561,500Ethylene oxide C2H4O l –96 –41,200 1263 543,000Acetic Acid C2H4O2 l –484 –208,000 875 376,000Ethanol C2H6O g –234 –100,600 1366 587,300Ethanol C2H6O l –276 –119,000 1367 587,700Ethylene glycol C2H6O2 l –460 –197,800 1190 511,600
Inorganic Compounds
Name Formula Phaseh f0D t hc0D− t
HHV
molkJ
lbmolBtu
molkJ
lbmolBtu
Ammonia NH3 g –45.9 –19,700 383.0 164,700Calcium carbide CaC2 s –62.8 –27,000 — —Calcium carbonate CaCO2 s –1207 –518,900 — —Calcium chloride CaCl2 s –795.0 –342,000 — —Calcium chloride CaCl2 6H2O s –2607 1,121,000 — —Calcium hydroxide Ca(OH)2 s –986.6 –424,200 — —Calcium oxide CaO s –635.6 –273,200 — —Carbon C, graphite s 0 0 393.5 169,200Carbon monoxide CO g –110.5 –47,510 283.0 121,700Carbon dioxide CO2 g –393.5 –169,200 — —Hydrochloric acid HCl g –92.31 –39,690 — —Hydrogen H2 g 0 0 286.0 123,000Hydrogen sulfide H2S g –20.6 –8860 546.3 234,900Iron oxide FeO s –269.0 –115,700 — —Iron oxide Fe2O3 s –822.2 –353,500 — —Iron oxide Fe3O4 s –1117 –480,300 — —Nitric acid HNO3 g –134.3 –57,740 — —Nitric oxide NO g 90.29 38,820 — —Nitrogen dioxide NO2 g 33.10 14,200 — —Nitrogen trioxide NO3 g 71.13 30,580 — —Sodium carbonate NaCO3 s –1131 –486,300 — —
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Inorganic Compounds (cont'd)
Name Formula Phaseh f0D t hc0D− t
HHV
molkJ
lb molBtu
molkJ
lb molBtu
Sodium carbonate NaCO3 10H2O s –4082 1,755,000 — —Sodium chloride NaCl s –411.0 –176,700 — —Sodium hydroxide NaOH s –426.7 –183,500 — —Sulfur oxide SO g 5.01 2150 — —Sulfur dioxide SO2 g –296.8 –127,600 — —Sulfur trioxide SO3 g –395.8 –170,200 — —Sulfur trioxide SO3 l –442.5 –190,300 — —Water H2O g –241.83 –103,970 — —Water H2O l –285.83 –122,890 — —
1.3 State Functions and Thermodynamics
1.3.1 NomenclatureIntensive properties are independent of mass.
Extensive properties are proportional to mass.
1.3.2 Properties of State FunctionsFor a single-phase pure component, specifying any two intensive properties specifies the remaining intensive properties.
State Functions
Component Property U.S. Units SI UnitsAbsolute pressure P psia PaAbsolute temperature T °R K
Specific volume v mV=
lbmft3
kgm3
Specific internal energy u mU=
lbmBtu
kgJ
Specific enthalpy h = u + P v = mH
lbmBtu
kgJ
Specific entropy s mS= lbm-°R
Btukg KJ:
Specific Gibbs free energy g = h – T s lbmBtu
kgJ
Heat Capacity at Constant Pressure
lbm °RBtu or kg K
kJc Th
-pP :2
2= c m
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 9
Heat Capacity at Constant Volume
lbm °RBtu or kg K
kJc Tu
-vv :2
2= c mThe steam tables in Chapter 8 provide T, P, v, u, h, and s data for saturated water and superheated steam.
Thermal and physical property tables for selected gases, liquids, and solids are included in Chapter 8.
1.4 First Law of ThermodynamicsThe First Law of Thermodynamics states that energy is neither created nor destroyed but can change from one form into another. The net energy crossing the system boundary is equal to the change in energy inside the system.
Heat Q q mQ=c m is energy transferred due to temperature difference and is considered positive if it is inward (added
to the system). Work W w mW=b l is considered positive if it is outward (subtracted from the system).
Changes in state functions are computed by changes in Q and W, which are path-dependent. The common paths are
Isobaric DP = 0Isochoric DV = 0Isothermal DT = 0Isenthalpic DH = 0Adiabatic DQ = 0Adiabatic and reversible (isentropic)
DS = 0
Efficiencies are used to correct irreversible processes.
1.4.1 Closed Thermodynamic SystemsIn a closed thermodynamic system, no mass crosses the system boundary:
Q – W = DU + DKE + DPE
where
DU = change in internal energy
DKE = change in kinetic energy
DPE = change in potential energy
Energy can cross the system boundary only in the form of heat or work. Work can be shaft work (ws) or other work forms, such as electrical.
Reversible work is
P dvw = #The table below displays the work, heat, and internal energy changes in closed systems for each of the four appli-cable paths for 1 mole of ideal gas. These changes assume constant heat capacities and neglect kinetic and potential energy changes.
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Closed System Energy Changes for 1 Mole of Ideal Gas
Path Work (W) Heat (Q) Change in Internal Energy (DU)
Isochoric (DV = 0) 0 c TVDt c TVDt
Isobaric (DP = 0) P(V2 – V1) c TPDt ( )c T P V VP 2 1D − −t
Isothermal (DT = 0)ln
ln
RT PP
RT VV2
1
1
2
e
e o
o ln
ln
RT PP
RT VV2
1
1
2
e
e o
o0
Isentropic (Ds = 0) kk RT
PP
1 1kk
1
1
21
− −−
e o> H 0 kRT
PP
1 1kk
1
1
21
− − −−
e o> H
where k ccV
P= tt
For ideal gas in an isentropic process:
TT
VV
PPk k
k
1
2
2
11
1
21
= =− −
e e eo o o
1.4.2 Open Thermodynamic SystemsIn an open thermodynamic system, mass does cross the system boundary. Flow work (Pv) is defined as the work for mass entering and leaving the system.
Reversible flow work = vw d P K E P Erev - D D= + +#The First Law applies whether or not processes are reversible.
Open System First Law (energy balance):
m h
Vg Z m h
Vg Z Q W dt
d m u2 2i ii
i e ee
e in nets s2 2
- -+ + + + + =o o o o_ i= =G G/ /
where
subscripts i and e refer to inlet and exit states of the system
Wneto = rate of net or shaft work
mo = mass flow rate
h = enthalpy
g = acceleration of gravity
Z = elevation
V = velocity
ms = mass of fluid within the system
us = specific internal energy of system
Qin = rate of heat transfer (neglecting kinetic and potential energy of the system)
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 11
The table below displays the work, heat, and internal enthalpy changes in open systems for each of the five appli-cable paths for 1 mole of ideal gas. These changes assume constant heat capacities and neglect kinetic and potential energy changes.
Open System Energy Changes for 1 Mole of Ideal Gas
Path Work (W) Heat (Q) Change in Enthalpy (DH)
Isochoric (DV = 0) –V(P2 – P1) c TVDt c T V P PV 2 1D + −t _ iIsobaric (DP = 0) 0 c TPDt c TPDt
Isothermal (DT = 0)ln
ln
RT PP
RT VV2
1
1
2
e
e o
o ln
ln
RT PP
RT VV2
1
1
2
e
e o
o0
Isentropic (DS = 0) kk RT
PP
1 1kk
1
1
21
− −−
e o> H 0 kk RT
PP
1 1kk
1
1
21
− −−
e o> H
Isenthalpic (DH = 0) 0 0 0
The actual work required is
ww
actual isrevh=
where his = isentropic efficiency
In the polytropic process, the only condition for process path is reversibility.
Pvn = constant
where n = empirical constant
w nn P v P v
n MWnR T T
1 1rev2 2 1 1 2 1
-
-
-
-= =_^ ^
_hi
hi
w nnMWRT
PP
1 1revnn
1
1
2
1
- -= −−
e^o
h> H
The actual work required is
ww
actual polyrevh=
where hpoly = polytropic efficiency
Polytropic efficiencies are always higher than isentropic efficiencies for the same compression stage.
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For multistage compression, the pressure ratio PR is
PR P
P m
1
21
= e owhere m = number of stages
The temperature drop on isenthalpic expansion (Joule-Thomson) is
T PJTnD D=
assuming the Joule-Thomson coefficient PT
JTH2
2n = c m is constant.
1.4.3 Steady-Flow SystemsThe system does not change state with time. This assumption is valid for the steady operation of turbines, pumps, compressors, throttling valves, nozzles, and heat exchangers, including boilers and condensers. The letter V denotes velocity in the following three equations:
m h
Vg Z m h
Vg Z Q W m m2 2 0i i
ii e e
ee s i e
2 2- -/ / / /+ + + + + = =o o o o od dn n
For a single fluid-flow stream at steady state, the equation reduces to:
h V g Z w q2 0
2-D
DD+ + + =o o
If the fluid is incompressible with negligible friction losses, the equation reduces to:
P V g Z w q2 0s
2-t
D DD+ + + =o o
1.5 Behavior of Single-Component Systems
1.5.1 Ideal Systems
1.5.1.1 Ideal Gas LawFor an ideal gas,
andP v RT PPvv
TT
2
1
2
1
2
1= =t tt
where 1 and 2 indicate separate system states.
Alternatively,
andPV n RT MWmRT
PPVV
nnTT
2
1
2
121
2
1= = =
For ideal gases, c c Rp v− =t t . These are independent of both pressure and volume, as are u and h.
Assuming constant heat capacities, or average heat capacities over the temperature range T1 to T2, the following apply:
u c T h c Tv PD D D D= =
ln
lnln
lns c T
TMW
R PP
s c TT
MW
R vv
vP1
2 1
2
1
2 12
D D= − = −ee
ed
oo
on
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 13
1.5.2 Nonideal Systems
1.5.2.1 Compressibility and the Theorem of Corresponding StatesThe compressibility factor is a dimensionless number defined by the equation:
Z RTP v= t
Theorem of Corresponding States
To first approximation, all fluids have the same compressibility factor when compared at the same reduced tem-perature and reduced pressure.
Reduced temperature (Tr) and reduced pressure (Pr) are defined as
andT TT P P
Pr c r c
= =
Compressibility Factor Chart
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4REDUCED PRESSURE, Pr
0.5
0.5
0.6
0.7
0.8
0.9
1.0
1.0 2.0 3.0 4.0 5.0 10 20 30
1.1
1.2
1.3
1.4
1.5
0.0
COMPRESSIBILITY FACTOR CHART
COMP
RESS
IBILI
TY FA
CTOR
, Z
GENERALIZED COMPRESSIBILITY FACTORS(Ze = 0.27)
15.00
5.003.00
2.002.00
1.801.70
1.60
1.50
1.50
1.401.35
1.30
1.30
1.25
1.20
1.20
1.10
1.10
1.081.06
1.04
1.02
1.00
1.00
0.50
0.50
0.60
0.70 0.9
00.8
0 1.00
2.00 3.0
05.0
0
10.00
15.00
0.95
0.95
0.90
0.90
0.90
0.85
0.85
SATURATED LIQUID
SATURATED GAS
0.80
0.80
0.75
1.15
Tr
GENERALIZED COMPRESSIBILITY FACTORS(Ze = 0.27)
15.00
5.003.00
2.002.00
1.801.70
1.60
1.50
1.50
1.401.35
1.30
1.30
1.25
1.20
1.20
1.10
1.10
1.081.06
1.04
1.02
1.00
1.00
0.50
0.50
0.60
0.70 0.9
00.8
0 1.00
2.00 3.0
05.0
0
10.00
15.00
0.95
0.95
0.90
0.90
0.90
0.85
0.85
SATURATED LIQUID
SATURATED GAS
0.80
0.80
0.75
1.15
Tr
From de Nevers, Noel, Physical and Chemical Engineers, 2nd ed., New York: Wiley & Sons, 2012, p. 94.
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1.5.2.2 Equations of State
Virial Equation of State
Z RTP v
vB
vC
vD1 2 3 g= = + + + +t
t t t
where B, C, D = virial equation coefficients, accounting for two-body, three-body, and four-body interactions, respectively
Alternatively,
Z RTP v B P C P D P1 2 3g= = + + +l l lt
where , ,B C Dl l l= virial equation coefficients
The two sets of virial coefficients are related by:
B RTB=l
( )C
RTC B
2
2= −l
( )D
RTD BC B3 2
3
3= − +l
Generic Cubic Equation of State
( ) ( )( )
P v bRT
v b v ba Te v
= − − + +t t t
where
a(T) = substance-dependent constant
b = substance-dependent constant
e = constant for generic cubic equation of state
s = constant for generic cubic equation of state
For the Van der Waals equation, a(T) = a and .0e v= =
1.5.3 Phase Equilibrium for a Pure Component
1.5.3.1 Phase RuleFor nonreacting systems, the degrees of freedom F (for example, temperature, pressure, and composition) are
F = 2 – p + N
where
p = number of phases
N = number of chemical species
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 15
1.5.3.2 Phase DiagramsThe pressure-temperature relationship for a pure fluid is often shown in a P-T plot. The intersection of the solid-liquid-vapor lines is the triple point where the three phases coexist. The critical point is where vapor and liquid properties become identical.
Four kinds of diagrams are often used for calculations involving a pure fluid. These indicate the qualitative behavior of fluid properties as shown.
Calculations Involving a Pure Fluid
PRES
SURE
PRES
SURE
ENTHALPY
ENTH
ALPY
ENTROPYENTROPY
T-S DIAGRAM FOR PURE FLUID MOLLIER DIAGRAM FOR PURE FLUID
P-h DIAGRAM FOR PURE FLUIDPRESSURE-TEMPERATURE FOR PURE FLUID
TEMPERATURE
VAPOR
VAPORPRESSURECURVE
LIQUID
CRITICALPOINT
CRITICALPOINT
CRITICALPOINT
CRITICALPOINT
CONST. T
CONST. PCONS
T. P
CONST. H
CONST. H
CONST. V
CONST. S
CONST. T
CONST. T
CONST. T
FUSIONCURVE
SOLID TRIPLE POINT
SUBLIMATION CURVE
TEMP
ERAT
URE
CONS
T. QU
ALITY
CONST. QUALITY
CONST. QUALITY
SAT. VAPOR
SAT. VAPOR
SAT.
LIQUID
SAT.
LIQUID
SAT. LIQ
UID
SAT. LIQUID
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1.5.3.3 Compressibility and Expansivity Volume expansivity: V T
V1P2
2b = c m
Isothermal compressibility: V P
V1T2
2l =− c m
For real liquids, assume that k and b are independent of pressure and temperature:
VdV dT dPb l= −
ln VV T T P P1
22 1 2 1b l= − − −e _ _o i i
For incompressible liquids: dV = 0
dTdP
V lb=c m
1.5.3.4 Vapor PressureVapor pressure is the pressure in a closed system containing a pure fluid with both liquid and vapor in equilibrium at a given temperature. The equilibrium phases are saturated.
The Antoine Equation expresses the temperature dependence of vapor pressure:
ln P A T CBsat = − +
where
Psat = saturation pressure or vapor pressure
A, B, and C = constants for a given species
T = absolute temperature in K or °R
1.5.3.5 Latent HeatThe Clapeyron Equation relates enthalpy change to temperature, vapor pressure, and volume in the phase change of a two-phase, single-species system.
d Td P
T vhsat
DD=
where
hD = specific latent heat for the phase change
vD = specific volume change for the phase change
For the phase transition from liquid to vapor of an ideal gas, the Clapeyron equation becomes the Clausius- Clapeyron equation:
( )ln
d T
d PRh
1
satvapD
= −c m
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 17
1.5.3.6 Properties for Two-Phase (Vapor-Liquid) SystemsQuality x (for liquid-vapor systems at saturation) is defined as the mass fraction of the vapor phase:
x m mmv l
v= +
where
mv = mass of vapor
ml = mass of liquid
Specific volume of a two-phase system can be represented as
v = xvv + (1 – x) vl or v = vv + xDvvap
where
vv = specific volume of saturated vapor
vl = specific volume of saturated liquid
Dvvap = specific volume change upon vaporization
= vv – vl
Similar expressions exist for u, h, and s:
u = xuv + (1 – x) ul or u = ul + xDuvap
h = xhv + (1 – x) hl or h = hl + xDhvap
s = xsv + (1 – x) sl or s = sl + xDsvap
The energy difference between two phases in equilibrium at a given temperature (or pressure) is the latent heat. The three types of latent heat are
Latent heat of fusion (melting): Dhfusion = hl – hs
Latent heat of sublimation: Dhsubl = hv – hs
Latent heat of vaporization: Dhvap = hv – hl
1.6 Behavior of Multicomponent SystemsThe properties of a mixture can be estimated using the properties of its pure components, based on either a mass-fraction average or a mole-fraction average. The one exception is entropy, which must be estimated based only on a mole-fraction average, as shown below. Use volumes when computing the density of a mixture:
When i = 1, 2, …, n constituents, the mole fraction is
x nn
n n x 1ii
i i/ /= = =
where
ni = number of moles of component i
n = total moles in the mixture
Mass fraction: w mm
ii= m = mi/ wi/ = 1
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18 NCEES
Molecular weight: MW = n
m = x MWi i/ To convert mole fractions xi to mass fractions wi:
w x MWx MW
ni
i i
i i= _ i/
To convert mass fractions to mole fractions:
x
MWw
MWw
n
i
i
ii
i
=/
To convert a component from a wet basis to a dry basis:
( )w ww1–Dry
H O
Weti
i
2
=
where
wH O2 = the weight fraction of water in the mixture
1.6.1 Ideal Mixtures
1.6.1.1 Ideal Gas Mixtures
Dalton’s Law of Partial Pressures
p V n RTi i=
results in orP p p p pnii
n
i1
g= = + +=/ and y P
pnn
ii i= =
where
pi = partial pressure of component i
ni = moles of component i
yi = mole fraction of component i in gas phase
Amagat’s Law of Partial Volumes
pV n RTi i=
results in: orV V V V Vnii
n
i1
g= = + +=/ and y V
Vnn
ii i= =
where Vi = partial volume of component i
Other properties include:
( ) ( ) ( )u y u h v h s y s smixi i i i i i= = = +// /
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 19
where
ui and hi are evaluated at T
si is evaluated at T and Pr
To calculate the molar volume of an ideal gas or liquid mixture:
v x vmix i in
=t t_ i/
This equation applies to internal energy, enthalpy, and volume but not to density, which is the reciprocal of specific volume.
For terms involving entropy, include the entropy of mixing:
nlns R x x1
mix i i= d n/
When mixing pure components:
nnlns x s R x x1
mix i i i i= +t t_ di n//
and Gibbs free energy is
nnlng x g RT x x1
mix i i i i= +t t_ di n//
1.6.1.2 Raoult’s LawAssuming a vapor phase that is an ideal gas and a liquid phase that is an ideal solution:
p y P x P sati i i i= =
where
xi = mole fraction of component i in liquid phase
P sati = vapor pressure of pure component i
1.6.1.3 Henry’s LawThe partial pressure of a component in the gas phase is proportional to the concentration of the component in the liquid phase:
pi = yi P = xi Hi
where Hi = Henry’s law constant for component i
1.6.2 Nonideal Mixtures
1.6.2.1 Fugacity Coefficients and Activity Coefficients
Fugacity
The criterion for the vapor-liquid equilibrium of mixtures is
f fV Li i=t t
where
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f Vit = fugacity of component i in the vapor phase
f Lit = fugacity of component i in the liquid phase
Vapor Fugacity of Pure Component
f PVi iz=
where iz = fugacity coefficient of pure component i in vapor phase
The fugacity coefficient of a pure component is a function of temperature and pressure and may be determined from any of:
The residual Gibbs free energy (GR) ln RTGR
z =
An equation of state ( )ln Z P
dP1P
z = −0#
A generalized correlation, e.g., ( ) ( )ln ln ln0 1z z ~ z= +
where w = the accentric factor
Liquid Fugacity of Pure Component
f PL sat sati i i /z= ( )exp RT
v P PL sati i/ = −t= G
wheresatiz = fugacity coefficient of pure component i at saturation
/ = Poynting correction factor
v Lit = molar volume of pure component i in the liquid phase
Vapor Fugacity of Mixture
f P y PVi i i i iz z= =t t t
where izt = fugacity coefficient of component i in the vapor phase
The fugacity coefficient of a component in a mixture may be determined from an equation of state and a mixing rule.
For a pure component, using the virial equation: ln RTB P
iz =
For a mixture, using the virial equation: ln y B B RTP
mi j ijjz = −a k/where
B y y Bm i j ijji
= //
Bm = second virial coefficient of the mixture
Bij = virial coefficient that characterizes a bimolecular interaction between i and j
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 21
For i = j, Bij = Bji = Bii
For i j=Y , Bij must be obtained from measured values or mixing rules.
Liquid Fugacity of Mixture
f x f x PL L sat sati i i i i i i i /c c z= =t
where gi = activity coefficient of component i
Activity coefficients are normally based on experimental measurements and fitted to an activity coefficient model, for example the Van Laar model:
ln lnandA A xA x A A x
A x1 11 12
21 2
12 12
2 2112 1
21 22
c c= + = +− −
e eo o
where A12 and A21 = Van Laar constants, typically fitted from experimental data
Gamma/Phi Approach to Vapor-Liquid Equilibrium (VLE)
y P x Psat sati i i i i i i i/z c z=t
Special cases:
Ideal vapor phase, ideal liquid solution, and low pressure:
Assume , , ,and then y P x P1 1 1 sati i i i i i/z c= = = =t
Ideal vapor phase, nonideal liquid solution, and low pressure:
Assume ,and then y P x P1 1 sati i i i i i/z c= = =t
Nonideal vapor phase, nonideal liquid solution, and moderate pressure:
Assume , then y P x P1 sat sati i i i i i i/ z c z= =t
1.6.2.2 Heat of SolutionIdeal mixing applies to gases at low pressures; liquids and high-pressure gases involve nonideal mixing. In these cases, make calculations on a mole or mass basis instead of on a mole-fraction or mass-fraction basis. For the heat of a solution for a binary mixture on a molar basis:
nh n h n h n h1 1 2 2D= + +ix, actualmt t t t
where
n = total moles of solution
n1 = moles of component 1
n2 = moles of component 2
This equation also applies to solids or gases dissolving into liquids. The hD t value must be known.
Heats of solutions often appear in charts, and enthalpies of mixing are presented as a function of composition. For evolved or absorbed heat:
n h nh n h n h1mix1-D = + 2,ix final 2m mixt t t t_ i
where hmix1 and hmix2 can be either mixtures or pure components. This is calculated on a mass basis if the data are on a mass basis.
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1.6.3 Phase Equilibrium for Multicomponent Systems
1.6.3.1 Vapor-Liquid Equilibrium in Binary, Fully Miscible Systems
Typical Vapor-Liquid Equilibrium Diagrams for Binary, Fully Miscible Systems
L
L
V–L
V–L
V
V
x-y x x
TP y
1.6.3.2 AzeotropesAn azeotrope is a mixture that produces a liquid and vapor of equal composition when boiled. No separation of such a mixture is possible by simple distillation.
For a positive azeotrope (minimum-boiling azeotrope):
• A positive deviation from Raoult’s Law is exhibited on a P-xy diagram, with the P-x curve lying above that for ideal behavior.
• The P-x curve and the P-y curve exhibit maxima at a point for which x = y.• A T-xy diagram exhibits a minima at the point for which x = y, which represents a boiling point lower than that
of any other composition.• A positive deviation from ideal-solution behavior results when liquid-phase intermolecular forces between like
molecules are stronger than between unlike molecules.
Positive Azeotrope Diagrams
L
V–LV–L
V
x - y
LV–L
V–LV
x - y x - y
P T y
For a negative azeotrope (maximum-boiling azeotrope):
• A negative deviation from Raoult’s Law is exhibited on a P-xy diagram, with the P-x curve lying below that for ideal behavior.
• The P-x curve and the P-y curve exhibit minima at a point for which x = y.• The T-xy diagram exhibits a maxima at the point for which x = y, which represents a boiling point higher than
that of any other composition.• A negative deviation from ideal-solution behavior results when liquid-phase intermolecular forces between
unlike molecules are stronger than between like molecules.
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 23
Negative Azeotrope Diagrams
L
V–LV–L
Vy
LV–L
V–L
V
TP
x - y x - y x - y
Lever Rule for a Binary Phase System
For a vapor-liquid mixture of A and B, the relative amounts of the liquid and vapor phases in a mixture with an overall composition of xF are given by the following equations:
A a bb
y xy x
A a ba
y xx x
LA A
A F
VA A
F A
= + = −−
= + = −−
P
L
V
0 1xA
CONCENTRATION OF COMPONENT A
xF yA
a b
1.6.3.3 Liquid-Liquid Equilibrium for Partially Miscible and Immiscible SystemsMany mixtures of chemical species, when mixed in certain ranges of composition, form two liquid phases of differ-ent compositions at thermodynamic equilibrium.
The criterion for the liquid-liquid equilibrium of mixtures is
f fi i=a bt t
where
fiat = fugacity of component i in the liquid phase designated a
fibt = fugacity of component i in the liquid phase designated b
If each species exists as a liquid at the system temperature, then:
x xi i i ic c=a a b b
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A solubility diagram is a T-x diagram at a constant pressure for a binary system. It depicts curves that indicate the compositions of coexisting liquid phases. Such diagrams may show:
• A lower critical solution temperature, above which two liquid phases are possible and below which a single liquid phase exists for all compositions.
• An upper critical solution temperature, below which two liquid phases are possible and above which a single liquid phase exists for all compositions.
• When liquid-liquid equilibrium curves intersect a vapor-liquid equilibrium bubble point curve and where only the lower critical solution temperature exists.
• When liquid-liquid equilibrium curves intersect a solid-liquid equilibrium freezing point curve and where only the upper critical solution temperature exists.
Upper and Lower Critical Solution Temperatures
x
T
x
T
LOWER CRITICALSOLUTION TEMPERATURE
UPPER CRITICALSOLUTION TEMPERATURE
Phase Diagrams
Most of the ternary or pseudoternary systems used in extraction are of two types:
Type I System: One binary pair has limited miscibility.
Type II System: Two binary pairs have limited miscibility.
Examples of type I and II systems are shown below.
Example: Type I System Components A + B + C1.00000.90000.80000.70000.60000.50000.40000.30000.20000.10000.0000
0.0000 0.0500
TIE
LINES
COMPONENT C LAYER
0.1000 0.1500
COMPONENT ALAYER
WEIGHT FRACTION COMPONENT B
WT.
FRAC
TION
COM
PONE
NT C
0.2000 0.2500 0.3000 0.3500
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 25
Type I System Type II System
Lever Rule for a Ternary Two-Phase System
In the following ternary phase diagram, two phases contain partially miscible components A, B, and C. One phase is rich in component B and one is lean in component B. The fraction of the B-lean phase is a b
a+ , where a and b
represent the length of the tie line on each side of the overall composition, denoted by the heavy black dot.
Ternary Phase Diagram
b100% B 100% A
100% C
a
1.6.3.4 Vapor-Liquid-Liquid EquilibriumThe gamma-phi approach to vapor-liquid equilibrium applies to each liquid phase. Assuming that and1 1/z = = :
andy P x P y P x P* * * *sat sati i i i i i i ic c= =a a b b
For a binary system,
P y P y P x P x P* * * * * sat sat1 2 1 1 1 2 2 2c c= + = +b b a a and y
Px P**
sat
11 1 1c=b b
where
P* = three-phase equilibrium pressure
y*1 = three-phase equilibrium concentration of component 1 in the vapor phase
PLAITPOINT
a c
e z
f
d
b
MOL FRACTION MOL FRACTION
TWO LIQUID PHASESTWO LIQUID PHASES
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x1b = concentration of component 1 in the liquid phase
x2a = concentration of component 2 in the liquid phase
1cb = activity coefficient of component 1
2ca = activity coefficient of component 2
a = liquid phase rich in component 2
b = liquid phase rich in component 1
In an immiscible system, , , , andx x1 1 2 2c cb b a a all are equal to 1. As a result:
andP P P y P PP* *sat satsat sat
sat
1 2 11 2
1= + =+
For the range in which the vapor is in equilibrium with pure-liquid component 1:
y PP sat
11=
And similarly, for the range in which the vapor is in equilibrium with pure-liquid component 2:
y PP sat
22=
Vapor-Liquid-Liquid Equilibrium Diagrams
L1 – L2
L1 – L2
L1L1L2 L2
V–L1
V–L1
V–L2 V–L2
V
V
x x x
P T y
1.7 Power CyclesThe most efficient means of converting heat into work is the Carnot cycle. Thermal efficiency is defined as
QWin
outh =
For the Carnot cycle,
QW
QQ
TT T
1in
out
in
out
H
H C--
h = = =
where
TC = temperature of working fluid entering the engine
TH = temperature at which heat is emitted from the engine
Refrigeration cycles are the reverse of heat-engine cycles. Heat is moved from low to high temperature, requiring work, W. Cycles can be used for refrigeration or in heat pumps.
The Coefficient of Performance (COP) is defined as
COP WQ
HPH= for heat pumps
Chapter 1: Mass/Energy Balances and Thermodynamics
NCEES 27
COP W
Qref
L= for refrigerators and air conditioners
The upper limit of COP is based on the reversed Carnot cycle:
COP T TT
CH L
H
-= _ i for heat pumps
COP T TT
CH L
L
-= _ i for refrigerators and air conditioners
1 ton of refrigeration = 12,000 hrBtu = 3516 W
Common Thermodynamic Cycles
P T
T
h h( () )3 4
CARNOT CYCLE
RANKINE CYCLE REFRIGERATION
CONDENSER
CONDENSER
CONDENSER
COP HPCOP
EVAPORATOR
EVAPORATOR
EXPANSIONVALVE
COMPRESSOR
COMPRESSOR
REVERSED CARNOT
v s
s
T
s
T
s
33
3
3
3
3
wT
3η
η
1
1
1
1
1
1 1
12 2
2
2
TURBINE
TURBINEEXPANSIONVALVE
= = =
BOILER
BOILER
PUMP
ref
=p p2 3
=p p2 3
=h h4 3
2
4
4
4
2
2
4
4
4 4T = TL
TL
TL TL
THTH
TH
s = c s = cs = cq = 0
s = cq = 0q = 0
s = cq = 0s = c
T = TH
=
q in
q in
q out
q out
wC
PUMP
— h h1 4— h h2 3—
h h2 1— h h2 1—h h3 2—
h h2 1——
CONDENSER
—
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Combustion Cycles
OTTO CYCLE(GASOLINE ENGINE)
BRAYTON CYCLE(GAS TURBINE)
P 3
2 41
s = c
s = c
v
T 3
42
1s
v = c q = 0
v = c
FUEL GAS
AIR1
EXHAUSTGAS
W
H.P./L.P. TURBINE
AXIALCOMPRESSOR
COMBUSTIONCHAMBER
43
2
P12P
1T4T ––– ==
)(( )2T3T – )(11η
( k – 1 )kr
vr
–
=
= 1η 1 – k
1v2
k =ĉv
âp
q = 0
29
2 HEAT TRANSFER
2.1 Symbols and Definitions
SymbolsSymbol Description Units (U.S.) Units (SI)
A Area ft2 m2
C Heat-capacity rate hr FBtu-c K
Ws Kkg m3
2
:
:=
Cs Heat-capacity ratio CCmax
mine o dimensionless
cp Heat capacity lbm FBtu-c kg K
Js Km2
2
: :=
D Diameter ft or in. m
d Wall thickness, width ft or in. m
F Correction factor for heat-exchanger configuration dimensionless
Fij Shape factor (radiation) dimensionless
f Moody friction factor dimensionless
g Acceleration of gravity secft2 s
m2
h Convection heat-transfer coefficient hr ft FBtu- -2 c m K
Ws Kkg
2 3: :=
hfusionD Latent heat of fusion lbmBtu
kgJ
sm2
2=
hsublD Latent heat of sublimation lbmBtu
kgJ
sm2
2=
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Symbols (cont'd)Symbol Description Units (U.S.) Units (SI)
hvapD Latent heat of vaporization lbmBtu
kgJ
sm2
2=
jH Colburn factor for heat transfer dimensionless
k Thermal conductivity hr ft FBtu- -c m K
Ws Kkg m3: :
:=
L Length ft or in. m
m Mass lbm kg
mo Mass flow rate hrlbm s
kg
NTU Number of thermal transfer units dimensionless
n Number of tubes (in shell-and-tube heat exchangers) dimensionless
P Pressure psi = inlbf2 Pa
mN
m skg
2 2:= =
P Thermal efficiency dimensionless
Q Heat Btu Js
kg m2
2:=
Qo Rate of heat transfer hrBtu
Ws
kg m3
2:=
qo Heat flux (rate of heat transfer per area) -hr ftBtu
2 mW
skg
2 3=
qlo Heat-transfer rate per unit length -hr ftBtu
mW
skg m
3:=
qgeno Heat-generation rate (per volume) hr ftBtu
3- mW
m skg
3 3:=
R Heat-transfer resistance Btuhr F-c
WK
kg ms K
2
3
::=
R Heat-capacity ratio CCshell
tubee o dimensionless
Rf Fouling factor -Btu
hr ft F-o2W
m Kkgs K2 3: :=
r Radius ft or in. m
T Temperature F Rorc c C or Kc
TlmD Log-mean temperature difference F Rorc c K
t Time hr s
U Overall heat-transfer coefficient hr ft FBtu- -2 c m K
Ws Kkg
2 3: :=
Chapter 2: Heat Transfer
NCEES 31
Symbols (cont'd)Symbol Description Units (U.S.) Units (SI)
UD Change in internal energy Btu Js
kg m2
2:=
u Velocity secft
sm
V Volume ft3 m3
x Distance ft or in. m
a Adsorptivity (radiation) dimensionless
a Thermal diffusivity hrft2 s
m2
b Coefficient of thermal expansion R1
K1
g Surface tension in.lbf
mN
skg2=
d Thickness ft or in. m
e Emissivity of a body (radiation) dimensionless
e Heat exchanger effectiveness dimensionless
e Void fraction (packed bed) dimensionless
q, f Angle dimensionless
m Dynamic viscosity cP or secftlbm- Pa s m s
kg: :=
n Kinematic viscosity hrft2
sm2
r Density ftlbm3 m
kg3
r Reflectivity (radiation) dimensionless
v Stefan-Boltzmann Constant ft hr RBtu- -2 4c m K
W2 4:
t Time constant hr s
t Transmissivity (radiation) dimensionless
2.2 Heat-Transfer Mechanisms
2.2.1 Heat Transfer Without Phase Change
2.2.1.1 Heat Capacity/Specific Heat (Cp)
Q mc dtdT
p=o
c m T
Up DD=
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Heat transferred in or out of a flowing material:
Q mc TpD=o o
2.2.1.2 Thermal Conductivity (k), Thermal Diffusivity (a), and Kinematic Viscosity (n)Thermal conductivity is a measure of the rate at which a substance transfers thermal energy:
k Tq
dD
= o
Thermal diffusivity is a measure of the rate at which a thermal disturbance is transmitted through a substance:
ckp
a t=
Kinematic viscosity (also called momentum diffusivity) is the ratio of the dynamic viscosity m to the density of the fluid r:
v tn=
2.2.1.3 Conduction
Fourier’s Law of Conduction
Total heat flux: Q k A dxdT= −o
Heat flux per area: q AQ
k dxdT= = −o
o
Heat flux per unit length: q LQ=loo
Conduction Through a Plane Wall T1
Q
T2
k
δ
( )Q k A T T1 2d
= −o
where
T1 = temperature of one surface of wall
T2 = temperature of the other surface of wall
Conduction Through a Composite Wall
( )Q
k
A T T
i
ii
1 2d
=−
o
/
Chapter 2: Heat Transfer
NCEES 33
Conduction Through a Cylindrical Wall
( )
lnQ
rrk L T T2
12
1 2r= −o
d n
T1Q
T2
r2
r1k
Cylinder (Length = L)
where L = cylinder length
Conduction Through a Spherical Wall
( )Q r r
k r rT T
42 1
1 21 2
r= − −o
Conduction Through a Cube With Thick Walls (Approximation)
.Q A A T T0 725 outer inner
inner outer.d
-o e o
where AA
2inner
outer $
Steady Conduction With Internal Energy Generation
For a plane wall:
−δ +δ0
T1
T(x)
gen
T2
k
q1 q2
q
dxd T
kq
T x kq x T T x T T
0
2 1 2 2
gen
gen
2
2
2
2
22 1 1 2
d
d d
+ =
= − + − + +
o
o^ e d c dh o n m n
and
q q q
q k dxdT q k dx
dT2 gen1 2
1 2
d+ =
= =d d− +
o o o
o oc cm m
For a long circular cylinder:
T0
kr0
qʹ 0
genq
( )
r drd r dr
dTkq
T r kq r
rr T
q r q
1 0
4 1
gen
gen
gen
02
02
2
0
0 02r
+ =
= − +
=l
o
o
o o
c
f
m
p
where q 0lo = heat transfer rate per unit length in hr ftBtu or m
W-
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Transient Conduction Using the Lumped Capacitance Model
The lumped capacitance model is valid if
As
Body
ρ, V, c , T P
T h,Fluid
∞ Bi k A
hV 1<<s
=
where
Bi = Biot number
V = volume of body
As = surface area of body
For constant fluid temperature T3 and uniform body temperature T:
Heat transfer rate at the body surface is
( )Q h A T T V c dtdT
s pt= − =3o
Temperature variation of the body with time is
( )expT T T T ti x
− = − −3 3 c m
where
t = h AV c
s
pt = time constant
Ti = initial temperature of the body in K or °R
Total heat transferred to the body at time t is
( ) ( ) expQ V c T T V c T T t1total i ip pt t x= − = − − −3 d c mn
= VELOCITY= DENSITY= COLBURN FACTOR= SPECIFIC HEAT OF THE FLUID= INSIDE DIAMETER OF TUBES= FILM COEFFICIENT= THERMAL CONDUCTIVITY= LENGTH OF PATH= VISCOSITY AT THE BULK TEMPERATURE= VISCOSITY AT THE TUBE WALL TEMPERATURE
uρjHcpdh ikLµµw
j H=k
kc p
h id
wµµ
µ
−−
1/30.1
4
=Red.u.ρµ
Source: Donald Q. Kern, Process Heat Transfer, New York: McGraw-Hill, 1990, p. 834.
a = absorptivity (ratio of energy absorbed to incident energy)
r = reflectivity (ratio of energy reflected to incident energy)
t = transmissivity (ratio of energy transmitted to incident energy)
a + r + t = 1
Opaque body: t = 0
Gray body: t = 0 and a = e with 0 < a < 1 and 0 < e < 1
Black body: t = 0 and a = e = 1
Real bodies are frequently approximated as gray bodies.
A black body is one that absorbs all energy incident upon it. It also emits radiation at the maximum rate for a body of its size and temperature.
Shape Factor Fij (Also Called View Factor or Configuration Factor)
Reciprocity relations:
j jiA F A Fi ij =
where
Ai = surface area of surface i
Fij = fraction of the radiation leaving surface i that is intercepted by surface j; F0 1ij# #
Summation rule for N surfaces:
j 1=
F 1ij =N
/
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Net energy exchange by radiation between two bodies:
When the body is small in comparison to its surroundings
Q A T T12 14
24fv= −o ` j
where T = absolute temperature in K or °R
When both bodies are black bodies
Q AF T T12 12 14
24v= −o ` j
Net energy exchange by radiation between two diffuse gray surfaces that form an enclosure:
Q
A A F A
T T1 1 112
1 1
1
1 12 2
2
14
24
2ff
ff
v= −
+ +−
−o
` j
A2, T2, ε2
A2, T2, ε2
A1, T1, ε1
A1, T1, ε1
12Q 12Q
For radiative heat loss at night, neglect any return radiation from the clear night sky, i.e., set T2 to 0 K or 0oR.
One-dimensional geometry with a thin, low-emissivity shield inserted between two parallel plates:
Q
A A F A A A F A
T T1 1 1 1 1 112
1 1
1
1 13 31
31
32
32
3 32 2 2
2
14
24
3 3ff
ff
ff
ff
v= −
+ +−
+−
+ +−
−o
` j
A3, T3
A2 , T2 ,A1, T1,
ε3,2
ε2ε1
ε3,1
RADIATION SHIELD
12Q
Energy transfer by radiation from reradiating surfaces:
Q
AA F A F A F
A
T T1
1 11 1
R R
1 1
1
1 12 1 1 2 2
1 2 2
2
14
24
ff
ff
v= −
++ +
+−
−
−
o
d
` j
n
A2 , T2 , ε2
A1 , T1 , ε1 AR , TR , εR12Q
Reradiating surfaces are considered to be insulated or adiabatic.
Chapter 2: Heat Transfer
NCEES 43
Radiation Heat Transfer—Special Considerations
Heat input from solar radiation:
Q A F qp solar12a=o o
where a = absorptivity
Ap = projected area perpendicular to the source
Simplified Equation for the Radiation Heat-Transfer Coefficient
This equation is in the same form as the equations for the conduction and convection heat-transfer coefficients and is used when there is a combination of heat-transfer coefficients. The radiation heat-transfer coefficient must be calculated at the system temperatures.
Q h A T Trad rad 1 2= −o _ iwhere h F T T T Trad 12 1
222
1 2v= + +` _j i
2.2.1.7 Combination of Heat-Transfer MechanismsOverall heat-transfer coefficient Uov:
Heat flux relations: ...T Q R Q R Q Ri i1 1 2 2D = = = =o o o
Heat Transfer from Fins
For a straight fin with uniform cross-section (assuming negligible heat transfer from the tip):
tanhQ h P k A T T L P
Ak Ah P
c bc
c= − +3o ` dj n= G
Circular (pin) fin: P = p D and A D4c
2r=
Rectangular fin: P = 2 (w + l) and A w lc =
where
P = perimeter of the exposed fin cross-section
Ac = fin cross-sectional area
L = length of the fin
D = diameter of a circular fin
w = width of a rectangular fin
l = height of a rectangular fin
Tb = temperature at the base of the fin
T∞ = bulk fluid temperature
Pin Fin: Rectangular Fin:
t
T ,h
w
Ac= wtP = 2( w+L)
∞
Lt
L
D
2
= πP D
4πD=
Tb Tb
Ac
T , h∞
t
T ,h
w
Ac= wtP = 2 ( w+L)
∞
Lt
Tb
Chapter 2: Heat Transfer
NCEES 45
2.2.2 Heat Transfer With Phase Change
2.2.2.1 Latent and Sensible HeatSensible heat: Q mc Tsensible pD=
Latent heat: Q m hlatent phase changeD=
Heat-transfer rate during phase change: Q m hlatent phase changeD=o o
Rate of phase change: dtdm
hQ
phase changeD=
o
2.2.2.2 Vaporization and Evaporation
Boiling
Evaporation is occurring at a solid-liquid interface when Ts > Tsat:
q h T T h Ts sat eD= − =o ` j
where
Ts = temperature of solid
Tsat,liquid = saturation temperature of liquid at system pressure
DTe = excess temperature
Pool boiling: Liquid is quiescent; motion near the solid surface is caused by free convection and mixing induced by bubble growth and detachment.
Forced convection boiling: Fluid motion is induced by external means in addition to free convection and bubble-induced mixing.
Sub-cooled boiling: Liquid temperature is below the saturation temperature; bubbles forming at the heating surface may condense in the liquid.
Saturated boiling: Liquid temperature slightly exceeds the saturation temperature; bubbles forming at the heated surface are propelled through the liquid by buoyant forces.
PE Chemical Reference Handbook
46 NCEES
Typical Boiling Curve for Water at One AtmosphereSurface Heat Flux as a Function of the Excess Temperature
107
∆Te =Ts–Tsat (°C)
C
P
B
AONB
1 5 10 30 120 1,000
q"MAX
q"s(W
/m2 )
q"MIN
106
105
104
103
FREECONVECTION
ISOLATEDBUBBLES
JETS ANDCOLUMNS
NUCLEATE
BOILING REGIMES
TRANSITION FILM
∆Te,A ∆Te,B ∆Te,C ∆Te,D
- CRITICAL HEAT FLUX, q"MAX
q"MIN-LEIDENFROST POINT,
D
Free convection boiling: There is insufficient vapor in contact with the liquid phase to cause boiling at the satura-tion temperature.
Nucleate boiling: Isolated bubbles form at nucleation sites and separate from the surface; vapor escapes as jets or columns.
Equation for nucleate-boiling heat flux (Rohsenow):
( )Prq h g
C hc T T/,
nucleate liq vapliq vap
sf vap liqn
p liq s sat1 2 3
nc
t tD
D= − −
o` j> >H H
where
g = surface tension of vapor-liquid interface
Ts = surface temperature of heater
Tsat = saturation temperature of fluid
Csf = experimental constant that depends on surface-fluid combination
n = experimental constant that depends on fluid
Peak heat flux: The maximum (or critical) heat flux (CHF) in nucleate pool boiling:
q C h g/
max cr vap vap liq vap2 1 4
c t t tD= −o ` j9 C
where Ccr = constant whose value depends on the heater geometry, but generally about 0.15
Chapter 2: Heat Transfer
NCEES 47
The critical heat flux is independent of the fluid-heating surface combination, as well as the viscosity, thermal conductivity, and specific heat of the liquid. It increases with pressure up to about one-third of the critical pressure, and then starts to decrease and becomes zero at the critical pressure. The critical heat flux is proportional to the latent heat of vaporization; large maximum heat fluxes can be obtained using fluids with a large enthalpy of vapor-ization, such as water.
Values of the coefficient Ccr for maximum heat flux:
L Lg
Kg A
* liq vap
liq vap heater1
c
t t
t t
c
=−
=−`
`
j
j
Maximum Heat Flux vs. Heater Geometry
Heater Geometry CcrCharacteristic Dimension (L) Range of L*
Minimum heat flux: This occurs at the Leidenfrost point and is of practical interest because it represents the lower limit for the heat flux in the film boiling regime.
Minimum heat flux for a large horizontal plate:
.
)q h
g0 09min vap vap
liq vap
liq vap2
41
tt t
v t tD=
+
−o `
`jjR
T
SSSSSSSS
V
X
WWWWWWWW
Transition boiling: Rapid bubble formation results in vapor film on surface and oscillation between film and nucleate boiling.
Film boiling: Surface is completely covered by a vapor blanket; includes significant radiation through the vapor film.
Heat flux for film boiling on a horizontal cylinder or sphere of diameter D:
( )( ) . ( )
( )q CD T T
g k h c T TT T
0 4 ,film film
vap s sat
vap vap liq vap vap vap s sats sat
p3 4
1
n
t t t D=−
− + −−o
8 B* 4
For horizontal cylinders: Cfilm = 0.62
For spheres: Cfilm = 0.67
PE Chemical Reference Handbook
48 NCEES
2.2.2.3 Condensation
Heat-Transfer Coefficient for the Condensation of a Pure Vapor
Evaluate all liquid properties at the average temperature between the saturated temperature and the surface tem-perature,
where
rl = density of the liquid phase of the fluid
ml = viscosity of the liquid phase of the fluid
kl = thermal conductivity of the liquid phase of the fluid
Nu = average Nusselt number
h = average heat-transfer coefficient
Tsat = saturation temperature of the fluid
Ts = temperature of the vertical surface
P = wetted perimeter (width of a vertical plate, or pd, for a vertical tube)
mo = condensate generation rate
L = length of the vertical surface
D = tube outside diameter
Condensation Film CoefficientsGeometry Correlation Conditions
Condensation on a vertical or angled surface, laminar flow
. ( )Nu kh L
k T Tg h L
0 943.
l l sat s
l vap2 3 0 25
n
t D= =−L > H Vertical surface
. ( )cos
Nu kh L
k T Tg h L
0 943.
l l sat s
l vap2 3 0 25
n
t iD= =−L > H Inclined surface, angle q
measured from the vertical
Condensation on the out-side of a horizontal tube, laminar flow
. ( )Nu kh D
k T Tg h D
0 729.
l l sat s
l vap2 3 0 25
n
t D= =−D > H Single tube or horizontal
layer of tubes
. ( )Nu kh D
N k T Tg h D
0 729.
l l sat s
l vap2 3 0 25
n
t D= =−D > H
Tube bank with N layers of horizontal tubes, arranged vertically over one another
Condensation on a tall vertical surface or on the outside of a tall vertical tube, turbulent flow
. ReNu kh D g h D
0 0076 hl
l vap52
2
2 3 31
n
t D= =D > H
Condensation Reynolds number:
Re 4 1800
Q
Pm
m h hh A T T
>h l
vap vap
sat s
n
D D
=
= =−
o
oo ` j
Condensation on a sphere . ( )Nu kh D
k T Tg h D
0 815.
l l sat s
l vap2 3 0 25
n
t D= =−D > H
Chapter 2: Heat Transfer
NCEES 49
2.3 Heat-Transfer Applications
2.3.1 Heat-Exchange Equipment Design
2.3.1.1 Overall Heat-Transfer CoefficientEnergy balance around a heat exchanger:
( ) ( )Q m c T T m c T Tcold p,cold cold,out cold,in hot p,hot hot,in hot,out= − = −o o o
Rate of heat transfer in a heat exchanger:
Q U AF TlmD=o
Heat-transfer area in a shell-and-tube heat exchanger:
A n D Lo or=
where n = total number of tubes
Mass flow rate in a shell-and-tube heat exchanger
m nD
u4passi2
r t=o
where npass = number of tubes in each pass
Overall heat-transfer coefficient for concentric tube and shell-and-tube heat exchangers:
ln
ln
U A h A AR
k LDD
AR
h A
U h DD R D
DkD
DD R h
1 12
1
1 12
1
ov ref i i i
fi
o
fo
o o
ov i i
ofi
i
o o
i
ofo
o
i
o
r= + + + +
= + + + +e e
e
eo o
o
o
where
Ai = inside area of the tubes
Ao = outside area of the tubes
Aref = reference areas for the overall heat-transfer coefficient U (usually the outside area)
Di = inside diameter of the tubes
Do = outside diameter of the tubes
hi = convection heat-transfer coefficient for inside the tubes
ho = convection heat-transfer coefficient for outside the tubes
Rfi = fouling factor for inside the tubes
Rfo = fouling factor for outside the tubes
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50 NCEES
2.3.1.2 Fouling FactorsFouling factors are defined as:
R h h1 1
ffouled clean
= −
A table of fouling factors is shown in section 2.4.
Fouling factors increase with time. The following approximations are used:
Linear: ( )R t R a t,f f initial= +
Falling-rate: [ ( )] ( )R t R b t,f f initial2 2= +
Asymptotic: ( )R t R e1,f ft= −3 x−a k
where a, b, and t = empirical constants
2.3.1.3 Log-Mean Temperature Difference
Temperature Profiles for Counter- and Co-Current Heat Exchangers Without Phase Change
For countercurrent flow in heat exchangers:
U OV
Δ A
Δ AHOT FLUID
COLD FLUID
A
T
(THOT – TCOLD)ΔQ =
TCOLD, OUT
TCOLD, IN
TCOLD
THOT, OUT
THOT
THOT, IN
ΔQ
lnT
T TT T
T T T T
, ,
, ,
, , , ,lm
hot in cold out
hot out cold in
hot out cold in hot in cold outD =
−−
− − −`
f
`j
p
j
Chapter 2: Heat Transfer
NCEES 51
For co-current (parallel) flow in heat exchangers:
(THOT – TCOLD)U OV
Δ A
Δ A
ΔQ
T
HOT FLUID
A
ΔQ =
COLD FLUID
TCOLD, OUT
TCOLD
TCOLD, IN
THOT, OUT
THOT
THOT, IN
lnT
T TT T
T T T T
, ,
, ,
, , , ,lm
hot in cold out
hot out cold in
hot out cold in hot in cold outD =
−−
− − −`
f
`j
p
j
Temperature Profiles for Evaporation and Condensation:
During the phase change of a pure substance, the temperature remains constant.
Evaporation:
THOT, OUT
THOT, IN
TEVAP
THOT
(THOT − TEVAP)
Δ A
T
A
U OV Δ AΔQ =
COLD FLUID
HOT FLUID
TCOLD, IN = TCOLD, OUT = TEVAP
Δ A
COLD FLUIDΔQ
lnT
T TT T
T T
,
,
, ,lm
hot out evap
hot in evap
hot in hot outD =
−−
−`
f
j
p
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52 NCEES
Condensation:
TCOLD, IN
TCOLD, OUT
TCOLD
TCOND
(TCOND – TCOLD)
THOT, IN = THOT, OUT = TCOND
HOT FLUID
Δ A
T
A
ΔQ
U OV Δ AΔQ =
TCOLDTTΔ ACOLD FLUID
lnT
T TT T
T T
,
,
, ,lm
cond cold out
cond cold in
cold out cold inD =
−−
−`
f
j
p
Temperature Approach
Minimum temperature difference between a hot and a cold fluid:
Tapproach = (Thot - Tcold)min
Co-current: Tapproach = Thot, out - Tcold, out
Countercurrent, with Cmin = Chot Tapproach = Thot, out - Tcold, in
Countercurrent, with Cmin = Ccold Tapproach = Thot, in - Tcold, out
Evaporation Tapproach = Thot, out - Tevap
Condensation Tapproach = Tcond - Tcold, out
where C mcp= =o heat-capacity rate
for T 0approach "
Constant heat-transfer coefficient U0v A " 3
Constant heat-transfer rate Qo m mmin"o o
Constant flow rate mo Q Qmax"o o
Chapter 2: Heat Transfer
NCEES 53
2.3.1.4 F-Factor (Log-Mean Temperature Correction Factor or LMTC Factor)
T F Tlogmean meanD D=
Temperature efficiency:
P T TT T
, ,
, ,
shell in tube out
tube out tube in= −−
Ratio of heat-capacity rates:
R T TT T
CC
, ,
, ,
tube out tube in
shell in shell out
shell
tube= −−
=
where C mcp= =o heat-capacity rate
Charts of the F-factors for various configurations are shown at the end of section 2.4.
2.3.1.5 Equipment Selection
Types of Evaporators
EvaporatorsType and Schematic Description and Applications Advantages and Disadvantages
Forced-Circulation Evaporator
V
S
G
C
PF
Description:
Circulating pump withdraws liquor from the flash chamber and forces it past the heat-ing surfaces. Typically, heating tubes are submerged and hydrostatic heads prevents boiling ; evaporation occurs in the flash cham-ber. Higher heat-transfer rates can be achieved if boiling is allowed in the tubes but then scal-ing and salt formation may occur. The forced circulation keeps solids in suspension. Tube velocities are limited by erosion and typically are 4–10 ft/s.
• High heat-transfer coefficients• Positive circulation• Relative freedom from salting, scaling,
and foulingDisadvantages:
• High cost• Power required for circulating pump• High hold-up and residence time
Difficulties:
• Plugging of tube inlets by detached salt deposits
• Corrosion/erosion• Salting due to boiling in the tubes• Poor circulation due to high head
losses
PE Chemical Reference Handbook
54 NCEES
EvaporatorsType and Schematic Description and Applications Advantages and Disadvantages
Short-Tube Vertical Evaporator
V
S
G
CP
F
Description:
Circulation past the heating surface is gener-ated by boiling in the tubes. The liquid then returns to the chamber through a central well. For crystallizing solutions, a propeller placed in the lower end of the central well will keep solids in suspension. Best heat transfer is achieved when liquid level is halfway up the tubes. Scaling occurs in the tubes where evaporation takes place but can be mechani-cally cleaned, because the tubes are relatively wide (2–3") and short (4–6').
Liquid is fed to the top of vertical tubes. Tubes are narrow (1–2") and long (20–35'). The liquid flows down the walls as a film. Pressure drop in the tubes is low and the temperature of the liquid is essentially the same as that of the vapor head. Vapor-liquid separation typically occurs at the bottom. To ensure proper wetting of the tubes, external recirculation is usually required unless feed-to-evaporation rates are high.
Applications:
• Heat-sensitive materials• Foaming liquids• Low temperature operation• Large evaporation loads
Advantages:
• Low hold-up• Cheapest per unit of capacity• Small floor space• Good heat-transfer coefficients at all
temperaturesDisadvantages:
• High head room• Not suitable for scaling or salting
liquids• External recirculation usually required
Difficulties:
• Poor feed distribution• Plugging of the feed distributor if
solids are present in the liquid
Chapter 2: Heat Transfer
NCEES 55
EvaporatorsType and Schematic Description and Applications Advantages and Disadvantages
Long-Tube Vertical Evaporator (Rising Film)
V
S
ENT’T
G
C
P
F
Description:
Liquid enters the long, vertical heating tubes from the bottom and rises up, propelled by the vapors generated by the evaporation. Boiling occurs in the tubes. On top of the tubes is a small vapor head with almost no liquid hold-up, where the liquid and vapor separate. The product line can be connected to the feed line to create recirculation.
Applications:
• Black liquid (pulp and paper)• High temperature differences• High evaporation loads
Advantages:
• Good heat-transfer coefficients at reasonable temperatures
• Simple construction and compactness enables use of corrosion-resistant alloys
• Low cost• Low hold-up• Small floor space
Disadvantages:
• High head room• Not suitable for scaling or salting
liquids• Poor heat-transfer coefficients at lower
temperaturesDifficulties:
• Sensitivity to changes in operating conditions
Horizontal Tube Evaporator
V SG
CF
Description:
The evaporating liquid is on the shell side and the heating medium on the tube side. This evaporator is mainly used for boiler feedwater. It has low entrainment and can be designed for high steam and vapor temperatures and pres-sures. Tubes can be designed so that they de-form when shocked (sprayed with cold water while still heated with steam), which causes the scale to crack off, making this evaporator suitable for severe scaling applications, such as hard water.
• Large vapor-liquid disengaging area• Good heat-transfer coefficients• Semiautomatic descaling (bent-tube
type)• Low cost (straight-tube type)• Minimal head room required
Disadvantages:
• Not suitable for salting liquids• Not suitable for scaling liquids
(straight-tube type)• High cost (bent-tube type)• Typically small capacity
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56 NCEES
EvaporatorsType and Schematic Description and Applications Advantages and Disadvantages
Wiped Film (Agitated Film) Evaporator
S
FV
C
P
BLADES
Description:
The liquid is spread on the tube wall by a rotating assembly of blades that maintain close clearance from the wall or ride on the film. The heating surface is one large-diameter tube that may be straight or tapered, horizontal or vertical. The expensive construction limits application to the most difficult materials.
Applications:
• Extremely viscous materials• Heat-sensitive materials in which
exposure to high temperature must be minimized
Advantages:
• Very short residence time• Ability to handle extremely viscous
materials• High feed-to-product ratios without
need for recirculationDisadvantages:
• Low heat-transfer coefficients• High installation costs• High operating costs
Submerged Combustion Evaporator
V + G
P
F
Description:
Heat transfer is provided by bubbling com-bustion gases through the liquid; thus no heat-transfer surfaces are used. The evapora-tor consists of a tank holding the liquid, a burner, and a gas distributor. The vapor from the evaporation is mixed with the combustion gases, making it impossible to recover the heat from the vapor.
• No surface on which scale can form• Use of special alloys or nonmetallic
materials is possibleDisadvantages:
• High entrainment losses• No heat recovery from the vapor,
resulting in high fuel costs• Cannot control crystal size in crystal-
lization applications
Source of first 5 schematics: Robert H. Perry and Cecil H. Chilton, Chemical Engineer's Handbook, 5th ed., New York: McGraw-Hill, 1973, Figure 11-16.
Source of Wiped Film Evaporator schematic: www.cherd.ichemejournals.com/cms/attachment/ 2020819194/2041009035/gr1.jpg.
Source of Combustion Evaporator schematic: www.china-ogpe.com/buyingguide_content/ Submerged_combustion_evaporator__1307.html
Heat-Transfer Calculations for Evaporators
While the general heat-transfer equations apply, evaporators have some special considerations:
Heat-transfer coefficient: Depends strongly on the temperature difference.
Heat-transfer area: Surface area through which the heat transfer takes place, measured on the liquid side.
Chapter 2: Heat Transfer
NCEES 57
Apparent temperature difference: The temperature difference can be difficult to determine because it varies along the length of the evaporator tubes. The apparent temperature difference is calculated as the difference between the heating-medium and boiling-liquid temperatures. Heating-medium temperature is the saturation temperature of the steam at steam pressure. (Superheat or subcooling are not considered.) Boiling-liquid temperature is the saturation temperature of the liquid at vapor head pressure—thus assuming a negligible boiling-point rise.
Temperature corrected for boiling-point rise: Boiling-point rise is the difference between the boiling point of the solution and the boiling point of the pure solvent at the same pressure. The temperature corrected for the boiling-point rise is the apparent temperature difference minus the boiling-point rise. This is typically used as the basis for the calculation of heat-transfer coefficients and also as a basis for comparing efficiencies of different evaporator types.
Multi-Effect Evaporators
Multi-effect evaporators reduce the energy needed for evaporation by using the steam generated in one stage as the heating medium for another stage.
The temperature difference for heat transfer in each effect is:
T T T, ,cond steam evap liquidD = −
where the condensation temperature of the steam is determined by the pressure in the effect where the steam was generated:
atT T P,cond steam sat n 1= −
The evaporation temperature of the liquid is determined by the pressure in the current effect:
atT T P,evap liquid sat n=
Different feed arrangements are common:
1. In the forward feed configuration, the product and vapor flow are parallel. This configuration is used when the feed is near the boiling point or when the product is heat-sensitive or prone to scaling and requires low temperature differences. One additional advantage is that flow of the product from one effect can be achieved by pressure difference alone, so that no intermediate liquor pumps are needed.
Forward Feed Configuration
VAPOR TOCONDENSER
THICKLIQUOR
FEED
CONDENSATE
STEAM
I I I I I I I V
Source: McCabe, Smith, Harriott, Unit Operations of Chemical Engineering, New York: McGraw-Hill, 1993, Figure 16-10.
PE Chemical Reference Handbook
58 NCEES
2. In the backward feed configuration, the product and vapor flow are countercurrent. It is used when the feed is cold, because most of the feed preheating is done by the vapor generated in the previous effect. It is pre-ferred for highly viscous liquor, because the temperature in the effect will be higher as the liquor becomes more concentrated.
Backward Feed Configuration
VAPOR TOCONDENSER
CONDENSATE
STEAM
THICK LIQUOR FEED
I I I I I I I V
Source: McCabe, Smith, Harriott, Unit Operations of Chemical Engineering, New York: McGraw-Hill, 1993, p. 485.
2.3.1.6 InsulationHeat loss from cylindrical, insulated pipe:
( )
lnQ
rr
h rk
k L T T2ins
ins
12
1
2
r=+
−
3
3o
d n
Surface temperature of the insulation:
ln
lnT
kh r
rr
T T kh r
rr
12
212
12
12
=+
+
3
33
d
d
n
n
Critical insulation radius (where heat loss is at a minimum): ddrQ
02
=o
r h
k, crit
ins2 =
3
1 ln
2 ( )Q
h rk
k L T Tmin
1
ins 1
ins
r=+
−
3
3o
e o
ln
lnT
h rk
T T h rk
1, crit
ins
ins
2
1
11=
+
+
3
33
e
e
o
o
Chapter 2: Heat Transfer
NCEES 59
where
T1 = surface temperature of the pipe
T2 = surface temperature of the insulation
T∞ = temperature of surroundings
r1 = outer radius of the pipe
r2 = outer radius of the insulation
kins = thermal conductivity of the insulation
h∞ = convective heat-transfer coefficient for the surroundings
2.3.2 Heat-Exchange Equipment Analysis
2.3.2.1 Pressure Drop
Single-Phase Heat Transfer
Tube-side pressure drop for a shell-and-tube exchanger (including pressure drop in the tubes, in the heads for a multipass exchanger, and at the inlet and outlet nozzles):
. .P n f D
L u1 5 2 2 5 2tubeside
w
tm 2
nn t
D = + +c dm n> H* 4where
ut = velocity in the tubes
f = Moody friction factor
m = 0.25 for laminar flow (Re < 2,100)
m = 0.14 for turbulent flow (Re > 2,100)
Condensation
Surface temperature for the condensation of a superheated vapor:
T T T hU1surface coolant vapor= + −c m
where
h = sensible heat-transfer coefficient for the vapor
U = overall heat-transfer coefficient, based on h
Condensation only occurs if T Tsurface sat# .
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60 NCEES
Evaporation
In rising film evaporators, the pressure drop in the tubes is comprised of frictional pressure drop and acceleration pressure drop from the increased velocity of the flow due to volume change during evaporation. If the inlet flow is liquid, the acceleration pressure drop is calculated from:
gP y Am 1 1 1
a cross vap liq c
2
t tD = −od dn nwhere
DPa = acceleration pressure drop
y = vapor fraction (by weight)
Across = cross-sectional area of the tube
2.3.2.2 Performance Evaluations (Number of Thermal Transfer Units)
Heat-Exchanger Effectiveness (e):
maximum possible heat transfer rateactual heat transfer rate
( )( )
( )( )
QQ
C T TC T T
C T TC T T
, ,
, ,
, ,
, ,
max
min minhot in cold in
hot hot in hot out
hot in cold in
cold cold out cold in
f
f
= = −−
= −−
= −−
o
o
Chot = Cmin Ccold = Cmin
T TT T
, ,
, ,hot
hot in cold in
hot in hot outf = −
−T T
T T, ,
, ,cold
hot in cold in
cold out cold inf = −
−
Heat-capacity rate is C:
C mcp= o
Cmin = smaller of Chot and Ccold
Cmax = larger of Chot and Ccold
Ratio of heat-capacity rates is C{ :
C CCmax
min={
where
C0 1# #{
C 0={ for exchangers with phase change (condensation or evaporation)
Number of Transfer Units (NTU)
NTU C
U Amin
=
Chapter 2: Heat Transfer
NCEES 61
Heat-Exchanger Effectiveness and NTU RelationsFlow Geometry Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
Double Pipe
Co-Current
e ( )expC
NTU C1
1 1f =
+− − +
{
{8 B
NTU ( )lnNTU C
C11 1f
=+
− − +{
{8 B
1.0 0.00
0.25
0.500.751.00
0.8
0.6
0.4
0.2
0.0
0 1 2 3
NTU
4 5
C
TUBEFLUID
SHELL FLUID
Countercurrent
e( )( )
expexpC NTU C
NTU C1 11 1
f =− − −
− − −{ {
{88
BB
:C NTUNTU1 1f= = +
{
NTU lnNTU C C11
11
ff=
− −−
{ {d n :C NTU1 1 ff= = −
{
1.0
0.000.250.500.751.00
0.8
0.6
0.4
0.2
0.0
0 1 2 3
NTU
4 5
C
TUBEFLUID
SHELL FLUID
PE Chemical Reference Handbook
62 NCEES
Heat-Exchanger Effectiveness and NTU Relations (cont'd)Flow Geometry Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
Cross-Flow
Both Fluids, Unmixed
eNTU( )exp exp
CNTU C1 1
.
.
0 22
0 78f = −
− −− {
{> H
1.0
0.000.250.500.751.00
0.8
0.6
0.4
0.2
0.0
0 1 2 3 4 5NTU
C
COLD FLUID
HOTFLUID
Both Fluids, Mixed
e ( ) ( )exp expNTU NTU CC
NTU1
11
11
f = − − +− −
−{{
1.0 0.00
0.25
0.500.751.00
0.8
0.6
0.4
0.2
0.0
0 1 2 3NTU
4 5
C
COLD FLUID
HOTFLUID
Chapter 2: Heat Transfer
NCEES 63
Heat-Exchanger Effectiveness and NTU Relations (cont'd)Flow Geometry Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
Cmax Mixed Cmin Unmixed
e ( )exp expC C NTU1 1 1f = − − − −{{8 B% /
NTU ( )ln lnNTU C C1 1 1 f= − + −{{< F
1.0 0.000.25
0.500.751.00
0.8
0.6
0.4
0.2
0.0
0 1 2 3NTU
4 5
C
MIXEDFLUID
C
C
min
max
UNMIXEDFLUID
Cmax Unmixed Cmin Mixed
e ( )exp expC NTU C1 1 1f = − − − −{{8 B( 2
NTU ( )lnNTU C C1 1 1 f= − + −{{8 B
1.0 0.000.250.50
0.751.00
0.8
0.6
0.4
0.2
0.0
0 1 2 3NTU
4 5
C Cmin
Cmax
MIXED FLUID
UNMIXEDFLUID
PE Chemical Reference Handbook
64 NCEES
Heat-Exchanger Effectiveness and NTU Relations (cont'd)Flow Geometry Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
Shell-and-Tube
One shell pass; 2, 4, 6 tube passes
eexp
expC C
NTU C
NTU C2 1 11 1
1 12
2
f = + + +− − +
+ − +{ {
{
{``
jj
NTU lnNTUC C C
C C
11
2 1 1
2 1 1
f
f= −+ − − + +
− − − +{ { {
{ {R
T
SSSSSSSS
V
X
WWWWWWWW
1.0 0.00
0.250.500.751.00
0.8
0.6
0.4
0.2
0.0
0 1 2 3NTU
4 5
C
TUBE FLUID
SHELL FLUID
Two shell passes; 2, 4, 6 tube passes
1.0 0.000.250.500.751.00
0.8
0.6
0.4
0.2
0.0
0 1 2 3NTU
4 5
C
SHELL FLUID
TUBE FLUID
Chapter 2: Heat Transfer
NCEES 65
Heat-Exchanger Effectiveness and NTU Relations (cont'd)Flow Geometry Effectiveness and Transfer Unit Equations, Schematic, and Graphical Solution
All Exchangers With Evaporation and Condensation
C 0={
e ( )exp NTU1f = − −
NTU ( )lnNTU 1 f= − −
1.0
0.8
0.6
0.4
0.2
0.0
0 1 2 3 4 5
= ø
NTU
C
2.4 Tables and Graphs
2.4.1 Tables of Heat-Transfer Data
2.4.1.1 Heat Capacity
Typical Ranges of Heat Capacity at Ambient Temperatures
Typical Values of Heat-Transfer Coefficients Without Phase Change
System Description hr ft FBtu- -2 c m K
W2 :
Air and gas (free convection) 0.2–4 1–20Air and gas (flowing—low pressure) 2–20 10–100Air and gas (flowing—high pressure) 20–60 100–360Liquid (free convection) 10–175 50–1000Oils and heavy organics (flowing) 35–200 200–1200Molten salts and brines 100–200 500–1000Heat-transfer fluids and refrigerants 175–450 1000–2700Water (flowing) 150–450 900–2700
Typical Values of Heat-Transfer Coefficients With Phase Change
Typical Overall Heat-Transfer Coefficients for Plate ExchangersPlate Exchangers
hr ft FBtu- -2 c m K
W2 :Hot Fluid Cold Fluid
Light organic Light organic 450–900 2500–5000Light organic Viscous organic 45–90 250–500Viscous organic Viscous organic 20–35 100–200Light organic Process water 450–600 2500–3500Viscous organic Process water 45–90 250–500Light organic Cooling water 350–800 2000–4500Viscous organic Cooling water 45–80 250–450Condensing steam Light organic 450–600 2500–3500Condensing steam Viscous organic 45–90 250–500Process water Process water 900–1300 5000–7500Process water Cooling water 90–1200 500–7000Dilute aqueous solutions Cooling water 900–1200 5000–7000
Condensing steam Process water 600–800 3500–4500
Typical Overall Heat-Transfer Coefficients in Evaporators
System hr ft FBtu- -2 c m K
W2 :
Agitated filmNewtonian liquid, m = 1 cP 400 2000Newtonian liquid, m = 100 cP 300 1500Newtonian liquid, m = 10,000 cP 120 700Vertical long tubeNatural circulation 200–600 1000–3500Forced circulation 400–1000 2000–6000
PE Chemical Reference Handbook
72 NCEES
Representative Values for Fouling FactorsValues for /F C125 50# c c , unless specified otherwise
Material / , , )1 ( 1tC dd P EG z n#- -c m
Wm K2 :
Seawater, brine, salt water 0.0005 0.00009Seawater, brine, salt water (> 125°F/50°C) 0.0010 0.00018River water (brackish) 0.0020 0.00035River water (muddy, silty) 0.0030 0.00053Hard water 0.0033 0.00059City/well water 0.0010 0.00018Untreated boiler feedwater (> 125°F/50°C) 0.0010 0.00018Treated boiler feedwater 0.0010 0.00018Untreated cooling tower water 0.0020 0.00035Treated cooling tower water 0.0010 0.00018Distilled water 0.0005 0.00009Fuel oil 0.0050 0.00088Asphalt and residue 0.0100 0.00176Vegetable oil and heavy gas oil 0.0030 0.00054Light hydrocarbons 0.0010 0.00018Heavy hydrocarbons 0.0040 0.00072Quenching liquids 0.0040 0.00070Refrigerating liquids, brines 0.0010 0.00018Heat-transfer media 0.0010 0.00018Polymer forming liquids 0.0050 0.00090Vaporizing liquids (organic and inorganic) 0.0020 0.00035Condensing organic liquids 0.0010 0.00018Steam (clean) 0.0005 0.00009Steam (oil-bearing) 0.0010 0.00018Organic vapors and liquids (including condensing) 0.0010 0.00018Alcohol vapors 0.0005 0.00009Industrial air or other dirty (oil-bearing) gases 0.0020 0.00035Diesel exhaust (> 125°F/50°C) 0.0100 0.00176
Chapter 2: Heat Transfer
NCEES 73
2.4.1.5 Nucleate Boiling Heat-Transfer Data
Relative Magnitude of Nucleate Boiling Heat-Transfer Coefficients at 1 atm, Referenced to Value for Water
Fluid hhwater
Water 1.0Water with 20% sugar 0.87Water with 10% Na2SO4 0.94Water with 26% glycerin 0.83Water with 55% glycerin 0.75Water with 24% NaCl 0.61Isopropanol 0.70Methanol 0.53Toluene 0.36Carbon-tetrachloride 0.35n-Butanol 0.32
Source: Holman, J.P., Heat Transfer, New York: McGraw-Hill,1981, p. 430.
Maximum Heat Flux in Nucleate Boiling (Burnout Heat Flux)
Overall Heat-Transfer Coefficients for Various Applications (U.S. Units): hr ft FBtu- -2 c
CONDENSATIONAQUEOUS VAPOURS
BOILING AQUEOUS
DILUTE AQUEOUSBOILING ORGANICS
CONDENSATION ORGANIC VAPORS
PARAFFINSHEAVY ORGANICS
MOLTEN SALTS
RESIDUE
BRINESAIR
AND GAS
COOLING TOWER WATER SERVICE FLUID COEFFICIENT, Btuft2 °F hr
THERMAL FUID
CONDENSATE STEAM CONDENSINGHOT HEATTRANSFER OIL
RIVER, WELL,SEAWATER
ESTIMATED OVERALL COEFFICIENT, U,
PROCESS FLUID COEFFICIENT, U
,
BOILINGWATER
REFRIGERANTS
AIR AND GASLOW PRESSURE
OILS
100
AIR AND GASHIGH PRESSURE
Btuft2 °F hr
Btu
ft2 °F hr
200 300 400 500 600 700 800 900
100
200
300
400
500
600
100
150
50
200
250
300
350
400
Source: Towler, Sinnot. Chemical Engineering Design. Oxford: Butterworth-Heinermann: 2013, p. 1052, Figure 19.1. (Converted to U.S. units)
Overall Heat-Transfer Coefficients for Various Applications (SI Units): m KW2 :
CONDENSATIONAQUEOUS VAPOURS
BOILING AQUEOUS
DILUTE AQUEOUSBOILING ORGANICS
CONDENSATION ORGANIC VAPORS
PARAFFINSHEAVY ORGANICS
MOLTEN SALTS
RESIDUE
BRINESAIR
AND GAS
1000 1500 25002000 35003000 45004000
500
250
500
750
1000
1250
1500
1750
2000
2250
COOLING TOWER WATER SERVICE FLUID COEFFICIENT, W/m2°K
THERMAL FUID
CONDENSATE STEAM CONDENSINGHOT HEATTRANSFER OIL
RIVER, WELL,SEAWATER
ESTIMATED OVERALL COEFFICIENT, U, W/m2 °K
PROCESS FLUID COEFFICIENT, U
, W/m
2 °K
BOILINGWATER
REFRIGERANTS
AIR AND GASLOW PRESSURE
OILSAIR AND GAS
HIGH PRESSURE500
1000
1500
2000
2500
Source: Towler, Sinnot. Chemical Engineering Design. Oxford: Butterworth-Heinermann: 2013, p. 1052, Figure 19.1.
Chapter 2: Heat Transfer
NCEES 77
2.4.3 Heat-Exchanger Design Information
TEMA Heat Exchanger Types
FRONT-ENDSTATIONARY HEAD TYPES SHELL TYPES REAR-END
HEAD TYPES
FIXED TUBE SHEETLIKE "A" STATIONARY HEADONE-PASS SHELL
PASS SHELLWITH LONGITUDINAL BAFFLE
DOUBLE SPLIT FLOW
DIVIDED FLOW
KETTLE-TYPE REBOILER
CROSS FLOWSPECIAL HIGH-PRESSURE CLOSURE
CHANNEL INTEGRAL WITH TUBESHEET AND REMOVABLE COVER
CHANNEL INTEGRAL WITH TUBESHEET AND REMOVABLE COVER
BONNET (INTEGRAL COVER)
CHANNELAND REMOVABLE COVER
REMOVABLETUBE
BUNDLEONLY
SPLIT FLOW
FIXED TUBE SHEETLIKE "B" STATIONARY HEAD
FIXED TUBE SHEETLIKE ''N" STATIONARY HEAD
OUTSIDE PACKED FLOATING HEAD
FLOATING HEADWITH BACKING DEVICE
PULL-THROUGH FLOATING HEAD
U-TUBE BUNDLE
EXTERNALLY SEALEDFLOATING TUBE SHEET
AE
F
G
H
J
K
X
L
M
N
P
S
T
U
W
B
C
N
D
PE Chemical Reference Handbook
78 NCEES
2.4.4 F-Factor Charts1.0 0.9 0.8
F = MTD CORRECTION FACTOR
0.7 0.6 0.50
0.10.2
0.30.4
0.5P
= TEM
PERA
TURE
EFF
ICIE
NCY
MTD
CORR
ECTI
ON FA
CTOR
1 SHE
LL P
ASS
2 OR
MORE
TUB
E PA
SSES
T 2
T 1
T 1P
=––
t 1
t 1
t 2
t 2t 1
F-FACTORS CHARTS
0.60.7
0.80.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.5
1.6
2.0
3.0
4.0
6.0
8.0
15.020.0
R = 10.0
2.5
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.5
1.6
2.0
3.0
4.0
6.0
8.0
15.020.0
R = 10.0
2.5
1.0
T 2R
=––
t 1T 1
T 2F
ΔΔ =
t LOG
t M
Chapter 2: Heat Transfer
NCEES 79
1.0 0.9 0.8
F = MTD CORRECTION FACTOR
0.7 0.6 0.50
0.10.2
0.30.4
0.5P
= TEM
PERA
TURE
EFF
ICIE
NCY
MTD
CORR
ECTI
ON FA
CTOR
2 SHE
LL P
ASS
4 OR
MORE
TUB
E PA
SSES
T 2
T 1
T 1P
=––
t 1t 1
t 2
t 2t 1
F-FACTORS CHARTS
0.60.7
0.80.9
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.8
1.6
2.0
3.0
4.0
6.0
8.0
15.020.0
R = 10.0
2.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.8
1.6
2.0
3.0
4.0
6.0
8.0
15.020.0
R = 10.0
2.61.0
T 2R
FΔ
Δ=
=––
t 1t L
OGt M
T 1T 2
PE Chemical Reference Handbook
80 NCEES
1.0 0.9 0.8
F = MTD CORRECTION FACTOR
0.7 0.6 0.50
0.10.2
0.30.4
0.5P
= TEM
PERA
TURE
EFF
ICIE
NCY
MTD
CORR
ECTI
ON FA
CTOR
3 SHE
LL P
ASSE
S6 O
R MO
RE T
UBE
PASS
ES
T 2
T 1
T 1P
=––
t 1t 1
t 2
t 2t 1
0.60.7
0.80.9
0.2
2.0
8.0
15.020.0
R = 10.0
2.5
0.2
0.40.4
0.60.6
0.80.8
1.01.0
1.21.2
1.41.4
1.81.8
1.61.6
2.0
3.03.0
5.05.0
4.04.0
8.0
15.020.0
R = 10.0
2.5
1.0
T 2R
FΔ
Δ=
=––
t 1t L
OGt M
T 1T 2
Chapter 2: Heat Transfer
NCEES 81
1.0 0.9 0.8
F = MTD CORRECTION FACTOR
0.7 0.6 0.50
0.1
4SH
ELLS
0.20.3
0.40.5
P = T
EMPE
RATU
RE E
FFIC
IENC
Y
MTD
CORR
ECTI
ON FA
CTOR
4 SHE
LL P
ASSE
S8 O
R MO
RE T
UBE
PASS
ES
T 2T 1
T 1P
=––
t 1t 1
t 2
t 2t 1
0.60.7
0.80.9
2.0
8.0
15.020.0
R = 10.0
2.5
0.20.2
0.40.4
0.60.6
0.80.8
1.01.0
1.21.2
1.41.4
1.81.8
1.61.6
2.0
3.03.0
6.06.0
4.04.0
8.0
15.020.0
R = 10.0
2.51.0
T 2R
FΔ
Δ=
=––
t 1t L
OGt M
T 1T 2
PE Chemical Reference Handbook
82 NCEES
1.0 0.9 0.8
F = MTD CORRECTION FACTOR
0.7 0.6 0.50
0.1
5SH
ELLS
0.20.3
0.40.5
P = T
EMPE
RATU
RE E
FFIC
IENC
Y
MTD
CORR
ECTI
ON FA
CTOR
5 SHE
LL P
ASSE
S10
OR
MORE
TUB
E PA
SSES
T 2
T 1
T 1P
=––
t 1t 1
t 2
t 2t 1
0.60.7
0.80.9
2.0
8.0
15.020.0
R = 10.0
2.5
0.20.20.40.4
0.60.6
0.80.8
1.01.0
1.21.2
1.41.4
1.81.8
1.61.6
2.0
3.03.0
6.06.0
4.04.0
8.0
15.020.0
R = 10.0
2.5
1.0
T 2R
FΔ
Δ=
=––
t 1t L
OGt M
T 1T 2
Chapter 2: Heat Transfer
NCEES 83
1.0 0.9 0.8
F = MTD CORRECTION FACTOR
0.7 0.6 0.50
0.1
6SH
ELLS
0.20.3
0.40.5
P = T
EMPE
RATU
RE E
FFIC
IENC
Y
MTD
CORR
ECTI
ON FA
CTOR
6 SHE
LL P
ASSE
S12
OR
MORE
TUB
E PA
SSES
T 2T 1
T 1P
=––
t 1t 1
t 2
t 2t 1
0.60.7
0.80.9
1.0
T 2R
FΔ
Δ=
=––
t 1t L
OGt M
T 1T 2
2.0
8.0
15.0R = 20.0
10.0
2.5
0.20.20.40.4
0.60.6
0.80.8
1.01.0
1.21.2
1.41.4
1.81.8
1.61.6
2.0
3.03.0
6.06.0
4.04.0
8.0
15.0R = 20.0
10.0
2.5
PE Chemical Reference Handbook
84 NCEES
1.0
F = MTD CORRECTION FACTOR
0.9 0.8 0.7
00.1
0.20.3
0.40.5
P = T
EMPE
RATU
RE E
FFIC
IENC
Y
MTD
CORR
ECTI
ON FA
CTOR
1 DIV
IDED
FLO
W S
HELL
PAS
S2 O
R MO
RE T
UBE
PASS
ES
T 2
T 1T 1
T 1P
=––
t 1
t 1
t 2
t 2t 1
0.60.7
0.80.9
1.0
T 2R
FΔ
Δ=
=––
t 1t L
OGt M
T 1T 2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
5.0
6.0
8.0
15.020.0
R = 10.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.2
1.4
1.6
1.8
2.0
2.5
3.0
5.0
6.0
8.0
15.020.0
R = 10.0
85
3 KINETICS
3.1 Symbols and Definitions
SymbolsSymbol Description Units (U.S.) Units (SI)
CA or [A] Concentration of component Aft
lb mole3 liter
mol
FA Molar feed of A slb moleec s
mol
g rDV Gibbs free energy of reaction (molar) lb moleBtu
molJ
hrDt Heat of reaction lb mole
BtumolJ
K Equilibrium constant varies varies
k Reaction rate constantsecft
lb mole n
3
1-
d^n
h
slitermol n1-c
^m
h
M Molar ratio of initial reactant concentrations dimensionless
n Moles of reactant or product lb mole g mol
n Reaction order dimensionless
P Pressure (PA = partial pressure of A) inlbf2 Pascal
rA Rate of reaction – based on component Aft seclb mole-3 L s
g mol:
SAB Selectivity to A relative to B dimensionless
SV Space velocity = space time1
sec1 1
sT Temperature °F or °R °C or K
t Time sec s
PE Chemical Reference Handbook
86 NCEES
Symbols (con't)Symbol Description Units (U.S.) Units (SI/metric)
V Reactor volume ft3 L
XA Fractional conversion of component A dimensionless
YA Yield of A relative to reactant use dimensionless
eAFractional volume change at full conversion of A dimensionless
x Space time = space velocity1 sec s
3.1.1 Reaction Parameters – NomenclatureA chemical reaction may be expressed by the general equation:
aA bB cC dD*+ +
The rate of reaction of any component is defined as the number of moles of that component formed per unit time per unit volume:
r V dtdn1
AA− = − (negative because A is consumed)
r dtdC
AA− = − if V is constant
The rate of reaction is frequently expressed as
, , ...r k f C CA B− =A _ iThe fractional conversion XA is defined as the moles of A reacted per mole of A fed:
X CC C
AAo
Ao A=−
if V is constant
3.1.2 Temperature DependenceThe Arrhenius equation gives the dependence of k on temperature:
k Ae R TEa
=−
where
A = pre-exponential or frequency factor
Ea = activation energy molJ or mol
calc mR = universal gas constant
For values of rate constant ki at two temperatures Ti:
lnET TRT T
kk
a1 2
1 2
2
1=−_ ei o or ln k
kRE
T TT Ta
2
1
1 2
1 2=−e o
Chapter 3: Kinetics
NCEES 87
3.1.3 Reaction OrderIf r k C CA A B
x y− = , then the reaction is x order with respect to A and y order with respect to B.
The overall order is n = x + y.
3.2 Rate Equations in Differential Form for Irreversible Reactions
3.2.1 Zero-Order A R( )"
r d t
d CC d t
d XkA
AAo
A− = − = = and d td X
CkA
Ao=
3.2.2 First-Order A R"^ h r d t
d CC d t
d XkCA
AAo
AA− = − = = and d t
d XCkC
k X1A
Ao
AA= = −_ i
3.2.3 Second-Order A R2 "^ h r d t
d CC d t
d XkCA
AAo
AA2− = − = = and d t
d XCkC
kC X1Ao
AAo
AA
22= = −_ i
3.2.4 Second-Order A bB R"+_ i r d t
d CkC CA
AA B− = − = k bC X M X1Ao A A
2= − −_ _i i when bM CC
1Ao
Bo !=
and
r k bC X1A Ao A2 2− = −_ i when M = 1
Integrated forms of these equations are presented in Section 3.5 for constant and variable volume batch, plug flow, and CSTR reactors.
3.3 Chemical Equilibrium Constants from Rate Constants for Reversible Reactions
3.3.1 Gaseous Phase ReactionsFor general reactions: aA bB cC dD*+ +
At equilibrium: r rFWD REV=
where
r k P PFWD Aa
Bb
1=
r k P PREV Cc
Dd
2=
The equilibrium constant is defined as
KP PP P
kk
PAa
Bb
Cc
Dd
2
1= =
LeChatelier's Principle describes the qualitative effect of pressure on equilibrium: For a gaseous reaction, increas-ing pressure will shift the equilibrium to the side of the reaction in the reaction equation with fewer moles.
Changes in pressure have negligible effect on liquid or solid phase reactions.
PE Chemical Reference Handbook
88 NCEES
3.3.2 Liquid Phase ReactionsGeneral reaction: aA bB cC dD*+ +
At equilibrium: r rFWD REV=
where
r k C CFWD Aa
Bb
1=
r k C CREV Cc
Dd
2=
The equilibrium constant is defined as
KC CC C
kk
cAa
Bb
Cc
Dd
2
1= =
When a + b = c + d, KP = Kc , and both are dimensionless.
When they are not equal:
KP has units of pressure to the power (c + d – a – b).
Kc has units of concentration to the power (c + d – a – b).
Thus:
KP = Kc (R T)(c+d-a-b)
3.3.3 Effect of Temperature on Chemical Equilibrium ConstantsThe change of the equilibrium constant with temperature is a function of the heat of reaction:
lnKd T
dRTh r2
D=^ h V
The integrated equation is
ln KK
R Th d T1 rT
1
22
1
2 D=Te oV#
Over a range where h rDV is nearly constant, this simplifies to:
ln KK
RhT T1 1r
1
22 1
D= − −d nV
3.3.4 Relationship Between Gibbs Free Energy and the Equilibrium Constant
ln lnorg RT K K RTg
rrD
D= − = −V V
Chapter 3: Kinetics
NCEES 89
3.4 Reactor Equations
3.4.1 Batch Reactor
Constant Volume
For a well-mixed, constant-volume batch reactor:
Cr d td C
d td X
AA
AoA− = − = and t C r
d XAo
A
AXA= −0#
Variable Volume
For a well-mixed, variable-volume batch reactor:
rX
Cd td X
1AA A
Ao A
f− =
+_ i and t Cr Xd X1Ao
A A A
XAA
f=
− +0 _ _i i#
where eA = fractional volume change at full conversion of A
3.4.2 Half-LifeThe half-life of a reaction, t
21 , is the batch time required to reach 50% conversion.
For r dtd C
kCAA
An− =− = t
21 occurs when C C2
1A Ao=
For n = 1 (first order) lnt k
221 =
For n 1=Y ( )
tn k C12 1
( )Aon
n
21 1
1=
−−
−
−
3.4.3 Flow Reactors, Steady State (Space Time, Space Velocity)For flow reactors, space time t is defined as the reactor volume divided by the inlet volumetric feed rate. Space velocity SV is the reciprocal of space time, that is, SV = 1/t.
3.4.3.1 Plug-Flow ReactorFor a plug-flow reactor, for all values of Af :
FC V
Cr
d XAo
Ao PFRAo
A
AXAx = =
−0 _ i#
where FAo = moles of A fed per unit time
For a constant volume plug-flow reactor ( 0Af = ):
rd C
A
A
C
C
Ao
Ax =− −#
PE Chemical Reference Handbook
90 NCEES
3.4.3.2 Continuous Stirred Tank Reactor (CSTR)For a well-mixed CSTR for all values of eA:
FC V
rC X
Ao
Ao CSTR
A
Ao Ax = =−_ i
where - rA is evaluated at exit stream conditions
For a constant volume CSTR ( 0Af = ):
rC C
A
Ao Ax =−−_ i
3.4.3.3 Continuous Stirred Tank Reactors in SeriesWith a first-order reaction A R" , with no change in volume:
NN reactors individualx x=−
kN
CC
1N reactorsA
AoN1
N
x = −- e o> H or CC
Nk
1A
Ao NN
N
x= +d n
where
N = number of CSTRs (equal volume) in series
CAN = concentration of A leaving the Nth CSTR
3.5 Integrated Reactor Equations for Irreversible Reactions
3.5.1 Zero-Order Reactions ,A R r kA" − =_ iConstant Volume
Batch reactor:
k t C X C CA A A A= = −q q
Plug-flow reactor or CSTR:
k C X C CA A A Ax = = −q q
Variable Volume
,V V X V V X1 A A A Af fD= + =q q_ i
Batch reactor:
ln lnk tC X C
VV1
AAo
A A AAo
of f f= + =_ i
Plug-flow reactor or CSTR:
k C XA Ax = q
Chapter 3: Kinetics
NCEES 91
3.5.2 First-Order Reactions ,A R r k CA A" − =_ i
Constant Volume
Batch reactor:
ln ln lnk t CC
X X11 1
A
Ao
AA= = − = − −_ i
Plug-flow reactor:
ln ln lnk CC
X X11 1
A
Ao
AAx = = − =− −_ i
CSTR:
k CC C
XX
1A
Ao A
A
Ax =−
= −
Variable Volume
,V V X V V X1 A A A Af fD= + =q q_ iBatch reactor:
ln ln lnk t X X VV
11 1 1
AA A of
D= − = − − = − −_ di n
Plug-flow reactor:
lnk X X1 1A A A Ax f f= − + − −_ _i iCSTR:
k XX X
11
A
A A Ax
f= −
+_ i
3.5.3 Second-Order Reactions ,A R r k C2 A A2" − =` j
Constant Volume
Batch reactor:
k t C C C XX1 11A Ao Ao A
A= − =−_ i or C
Ck tC11
Ao
A
Ao= +
Plug-flow reactor:
k C C C XX1 11A Ao Ao A
Ax = − =−_ i or C
Ck C11
Ao
A
Aox= +
CSTR:
kC
C CC X
X1A
Ao A
Ao A
A2 2x =−
=−_ i
PE Chemical Reference Handbook
92 NCEES
Variable Volume
V = Vo (1 + eA XA), DV = Vo eA XA
Batch reactor:
lnk t C XX
X111
1Ao A
A AA A
ff=
−+
+ −_ _i i> H
Plug-flow reactor:
lnk C X X XX1 2 1 1 1 1Ao
A A A A A AA
A2 2x f f f f= + − + + + −_ _ _i i i= G
CSTR:
kC XX X
1
1
Ao A
A A A2
2
xf
=−
+__ i
i
3.5.4 Second-Order Reactions ,A bB R r k C CA A B"+ − =_ iConstant Volume
Batch reactor:
ln lnbk t C M M CC
M XM X
11Ao
A
B
A
A− = =−−^ _h i when bM C
C1
Ao
Bo !=
bk tC k t C C
C CXX
1Bo AoA
Ao A
A
A= =−
= − when M = 1
Plug-flow reactor:
ln lnbk t C M MCC
M XM X
11Ao
A
B
A
A− = =−−^ _h i when bM C
C1
Ao
Bo !=
bk C k C C
C CXX
1Bo AoA
Ao A
A
Ax x= =−
= − when M = 1
CSTR:
b bk
C C M CC C
C X M XX
1 1A Ao A
Ao A
Ao A A
Ax =− +
−=
− −^ _ _h i i8 B when bM CC
1Ao
Bo !=
b bk
CC C
C XX1A
Ao A
Ao A
A2 2x =
−=
−_ i when M = 1
Chapter 3: Kinetics
NCEES 93
3.6 Complex Reactions
3.6.1 First-Order Reversible Reactions ( )A Rk
k
2
1
r d t
d Ck C k CA
AA R1 2− = − = −
K k
kCCA
CR
2
1
eq
eq= = and M CCAo
oR=
d td X
M Xk M X X1A
AA A
1
eqeq
= ++ −^ ah k
ln lnXX
C CC C
M XM
k t1 1A
A
Ao A
A A
A1
eq eq
eq
eq
− − = − −−
=++f
a^p h
k
At equilibrium, when X XA Aeq= , then -ln(0)"∞ and t"∞.
3.6.2 Reactions of Shifting OrderFrom zero order at high CA to first order at low CA:
r k C
k C1A
A
A
2
1− = +
ln CC
k C C k tA
AoAo A2 1+ − =e `o j
ln
C CCC
k C Ck t
Ao A
A
A
Ao A
o
21
− = − + −
e o
where
kk2
1 = zero-order rate constant
k1 = first-order rate constant
This form of the rate equation is used for elementary enzyme-catalyzed reactions and for elementary surface- catalyzed reactions.
3.6.3 Plug-Flow Reactors With Recycle
First Order (eA = 0)
( )lnRk
R CC RC
1 1 A
Ao Ax+ = +
+
PE Chemical Reference Handbook
94 NCEES
Second Order (eA = 0)
RkC
C C RCC C C
1Ao
A Ao A
Ao Ao Ax+ =
+
−
`` j
j
where R = recycle ratio, defined as the fraction of the reactor outlet stream that is recycled
3.7 Yield and SelectivityYield Y is defined as the molar ratio of the desired product formed to the reactant that is consumed.
Selectivity S is defined as the molar ratio of the formation of desired product to undesired product.
3.7.1 Two Irreversible Reactions in Parallel A DD"k (desired) and A UU"k (undesired)
r d td C
k C k CAA
D A U Ax y− = − = +
r d td C
k CDD
D Ax= =
r d td C
k CUU
U Ay= =
YD = instantaneous fractional yield of D d Cd C
A
D= −
overall fractional yield of DY N NN
DAo A
D= = −
where andN NA D are the final values measured at the reactor outlet
overall selectivity to D over US NN
DUU
D= =
where andN ND U are the final values measured at the reactor outlet
3.7.2 Two First-Order Irreversible Reactions in Series A D UD U
" "k k (D = desired, U = undesired)
r d td C
k CAA
D A− = − =
r d td C
k C k CDD
D A U D= = −
r d td C
k CUU
U D= =
The maximum yield of D in a plug-flow reactor is ln
at timeCC
kk
k k kkk
1max
logAo
D
U
D
mean U D
D
Uk kkU DU
x= = =−
−e `
eo
oj
The maximum yield of D in a CSTR is
at timeCC
kK
k k1
1 1,maxmax
Ao
D
D
UD U2
1 2 x=
+
=
e o> H
95
4 FLUIDS
4.1 Symbols and Definitions
SymbolsSymbol Description Units (U.S.) Units (SI)
A Area ft2 m2 Ar Archimedes diameter dimensionless
cp Specific heat (constant pressure) lbm FBtu-c kg K
J:
cv Specific heat (constant volume) lbm FBtu-c kg K
J:
D Diameter ft or in. mDH Hydraulic diameter ft or in. md Diameter (minor) ft or in. mF Force lbf Nf Friction factor (Moody or Darcy) dimensionless
fFanning Fanning friction factor dimensionless
gc Gravitational conversion factorseclbf
lbm ft--2 —
H Total head ft mh Height ft mhf Head loss ft m
hf, fittingHead loss in fitting ft m
hL Head loss (general) ft mK Loss coefficient dimensionless
PE Chemical Reference Handbook
96 NCEES
Symbols (con't)Symbol Description Units (U.S.) Units (SI)
KE Kinetic energy Btu J
k Ratios of specific heats (cp/cv) dimensionless
L Length or thickness ft or in. m
MW Molecular weight lb molelb
kmolkg
Ma Mach number dimensionlessm Mass lbm kg
mo Mass flow rate hrlbm
skg
Ns Specific speed rpm rpm
NPSHaNet positive suction head available
ft m
NPSHrNet positive suction head required
ft m
P Pressure ftlbf2 Pa
P Wetted perimeter ft mPE Potential energy Btu J
Pvap Vapor pressure psi Pa
R Radius ft or in. m
R Universal gas constant lb mole RBtu or lb mole R
psi ft- -
- 3
c c mol KJ:
RD Relative density dimensionlessRe Reynolds number dimensionlessr Radius (minor) ft or in. mS Rotational speed rpm rpm
SG Specific gravity dimensionlessT Temperature °F or °R °C or Kt Time hr s
u Velocity secft
sm
usound Local speed of sound secft
sm
V Volume ft3 m3
Vo Volumetric flowrate secft3
sm3
Wo Power hp W
X Distance ft or in. mx Length, distance, or position ft or in. my Length ft or in. mz Length or elevation difference ft or in. ma Angle radian radian
Chapter 4: Fluids
NCEES 97
Symbols (con't)Symbol Description Units (U.S.) Units (SI)
d Thickness of a film ft me Absolute roughness ft m
ePorosity or void fraction 0 11 1e^ h dimensionless
h Efficiency dimensionlessq Angle radian radian
μ Dynamic viscosity seccP ftlbmor - Pa s s m
kgor: :
n3Infinite, plastic, or high shear viscosity seccP ft
lbmor - Pa s s mkg
or: :
n Kinematic viscosityhrft2
sm2
r Density ftlbm3 m
kg3
s Surface tension ftlbf
mN
τ Stress ftlbf2 Pa
τ0 Yield stress of fluidftlbf2 Pa
Φ Sphericity of particle (0 < Φ ≤ 1, where Φ = 1 is a perfect sphere) dimensionless
4.2 Mechanical-Energy Balance
4.2.1 General
4.2.1.1 Stress, Pressure, and ViscosityDefinitions:
Stress is
lim AF
A 0x
DD=
"D^ hwhere x = surface stress at a point
Pressure is
P nx= −
where nx = stress normal at a point
Newton’s Law of Viscosity relates shear stress (τt = stress tangential to the boundary) to the velocity gradient or shear rate (du/dy), using a constant of proportionality known as the dynamic (absolute) viscosity (μ) of the fluid:
dydu
tx n=
PE Chemical Reference Handbook
98 NCEES
Kinematic viscosity is
v tn=
Temperature dependence on viscosity is
For liquids (Andrade Equation): DeTB
n =
where
D and B = empirical constants
T = absolute temperature
For gases (Sutherland's Equation): T SCT 2
3
n = +
where
C and S = empirical constants
T = absolute temperature
4.2.1.2 Fluid Types and Characteristics FLUID TYPES AND CHARACTERISTICS
SHEA
R ST
RESS
(
)
SHEAR RATE (du/dy)
BINGHAM PLASTIC
DILATANTNEWTONIAN
PSEUDOPLASTIC
1
0
τ
τ
Chapter 4: Fluids
NCEES 99
Classifications of FluidsFluid
Classification Fluid Type Behavior Examples
Time-Independent Viscosity
Newtonian
Viscosity is constant.
dydu
tx n=
The term μ is reserved for Newtonian fluids.
Water, light oil, blood plasma
Pseudoplastic (shear thinning)
Apparent viscosity (m) decreases with increased shear stress.
m dydu
t
n
x = d nn = power law index, n < 1
m is also known as the consistency coefficient or consistency index
Molasses, latex paint, whole blood
Dilatant (shear thickening)
Apparent viscosity (m) increases with increased shear stress.
m dydu
t
n
x = d nn = power law index, n > 1
Corn starch suspensions
Time-Dependent Viscosity
Thixotropic Apparent viscosity (m) decreases with duration of stress. Yogurt, plastisols
Rheopectic Apparent viscosity (m) increases with duration of stress.
Gypsum paste, kaolin clay suspensions
Viscoplastic Bingham plastic
Behaves as a rigid body until a minimum stress (yield stress) is applied, then reacts as a Newto-nian fluid at stresses above the yield stress.
dydu
t 0x x h= +
h = fluid viscosity 0x = yield stress
Mayonnaise, river mud, slurries
Viscoelastic Kelvin material Maxwell material
The materials exhibit both viscous and elastic characteristics during deformation under stress. Silicone putty
4.2.1.3 Surface Tension and Capillary RiseSurface tension g is the force per unit contact length
LF
c =
where
F = surface force at the interface
L = length of interface
PE Chemical Reference Handbook
100 NCEES
The capillary rise, h, is approximated bycosh g d
g4 ctc b= e o
where
h = height of the liquid in the vertical tube
b = angle made by the liquid with the wetted tube wall
d = the diameter of the capillary tube
4.2.2 Conservation of MassConservation of mass for flow from point 1 to point 2 is
m m1 2=o o
The continuity equation is
ρ1 A1 u1 = ρ2 A2 u2
For an incompressible fluid, ρ1 = ρ2, therefore:
A1 u1 = A2 u2 and V V1 2=o o
4.2.2.1 The Bernoulli EquationThe Bernoulli equation states, in energy per unit mass
ttan. c nlbmft lbf
sft or kg
Nmsm o s
P g u g z32 2 2- c
2
2
2
2 2
t= = + + =
For one-dimensional flows (with uniform velocity profiles) through conduits with flow from point 1 to point 2, expressed in:
Energy Per Unit Mass (Energy Basis)
lossP g u
g z wP g u
g z2 2c
inc1 1
2
12 2
2
2t t+ + + = + + +
where
win = net shaft work in = power/mass flow rate
Energy Per Unit Volume (Pressure Basis)
lossP gu
gg z
w P gu
gg z
2 2c c inc c1
12
12
22
2t tt
t tt+ + + = + + + ^ h
Height of Fluid (Head Basis)
gP g
gu
z h gP g
gu
z h2 2c
sc
L1 1
2
12 2
2
2t t+ + + = + + +
where
hs = shaft work head
hL = head loss
Chapter 4: Fluids
NCEES 101
4.2.2.2 The Impulse-Momentum PrincipleThe resultant force in a given direction acting on a fluid equals the rate of change of momentum of the fluid,
where
F V u V u2 2 2 1 1 1t t= −o o// /F/ = result of all external forces acting on the control volume
V u1 1 1to/ = rate of momentum of the fluid flow entering the control volume in the same direction as the force
V u2 2 2t =o/ rate of momentum of the fluid flow leaving the control volume in the same direction as the force
4.2.2.3 Energy Line and Hydraulic Grade Line
Energy Line (or Energy Grade Line)
The Energy Line (EL) represents the total head available to a fluid and can be expressed as:
For inviscid incompressible flow:
EL gP g
gu z2
c2
t= + + = constant along a streamline
For incompressible flow with losses:
EL gP g
gu z h2
cL
2
t= + + −
Hydraulic Grade Line (or Hydraulic Gradient Line)
The Hydraulic Grade Line (HGL) represents the total head available to a fluid, minus the velocity head, and can be expressed as:
For inviscid incompressible flow:
HGL gP g
zct= +
For incompressible flow with losses:
HGL gP g
z hcLt= + −
Note: The energy or hydraulic grade lines do not represent “sources” or “sinks” of energy such as the effects of pumps or turbines.
Energy Line and Hydraulic Grade Line for Incompressible Fluid Between Two Points (With Losses)
DATUM
HYDRAULIC GRADE LINE
1
2
z1
z2
1 cP 1 g cg
12
2u 1
2
2 g
2 cP 2 g cg
22
2u 2
2
2 g
h L
FLOW
ENERGY LINE
PE Chemical Reference Handbook
102 NCEES
4.3 Flow Behavior
4.3.1 VelocityVelocity is defined as the rate of change of position with respect to time
u dtdx=
where x = position
Velocity of a Newtonian fluid in a thin film is
u t uyd
=^ h dydu u
d=
BOUNDARY
THIN FILM
δy
u
The velocity distribution for laminar flow in circular tubes or between planes is
u r u Rr1max
2= −^ ch m= G
where r = distance from the centerline
R = radius of the tube or half the distance between the parallel planes
u = local velocity at r
umax = velocity at the centerline of the duct
u = average velocity in the duct
Flow Conditions
Fully turbulent flow Circular tubes in laminar flow
Parallel planes in laminar flow
uumax = 1.18 2 1.5
The shear stress distribution is
Rr
wxx =
where τ and τw = shear stresses at radii r and R, respectively
4.3.2 Reynolds NumberDimensionless number describing flow behavior with the general definition:
Re viscous forcesinertial forces=
Chapter 4: Fluids
NCEES 103
4.3.2.1 Hydraulic DiameterDH = hydraulic diameter (also known as the characteristic length)
tional areasecwetted perimetercrossD P
A4 4H #= =
Hydraulic Diameters for Various Flow Configurations
Around any object (or an any object through a fluid)
FLUID APPROACH VELOCITY (uO)
FLUIDSTREAMLINES
PROJECTED AREA (Ap)
P = PERIMETER OF SHAPE PRESENTED NORMAL TOTHE APPROACH VELOCITY
PA4 p
4.3.2.2 Newtonian Fluid Re
D uHnt=
where u = approach velocity
Various Forms of Reynolds Numbers and Their UnitsReynolds
Number FormHydraulic Diameter
D
Fluid Velocity
u
Fluid Density
ρ
Fluid Viscosity
μ
Volumetric Flow rate
Vo
Mass Flow rate
mo
Kinematic Viscosity
νD uHnt ft
secft
ftlbm3 secft
lbm-
D uHnt m s
mmkg3
Pa s ormN s
2::
or m s
kg:
.D u32 2Hnt ft
secft
ftlbm3
secft
lbf-2
.D u
123 9 Hnt in.
secft
ftlbm3 cP
, DV22 700Hnto in.
ftlbm3
cPsecft3
Chapter 4: Fluids
NCEES 105
Various Forms of Reynolds Numbers and Their Units (cont'd)
Reynolds Number Form
Hydraulic Diameter
D
Fluid Velocity
u
Fluid Density
ρ
Fluid Viscosity
μ
Volumetric Flow rate
Vo
Mass Flow rate
mo
Kinematic Viscosity
ν
. DV50 6Hnto in.
ftlbm3 cP gpm
. Dm6 31Hno in. cP
hrlbm
. DV35 42Hnto in.
ftlbm3 cP
hrbarrels
vD uH ft
secft
secft2
vD uH m m/s
sm2
vD u12H in.
secft
secft2
7740 vD uH in.
secft cS
, , D vV1 419 000H
o in.secft3 cS
3160 D vVH
o in. gpm cS
4.3.2.3 Power Law Fluid Re
K nn
D u
43 1 8( )
( )x
nn
n n
1
2 t=
+ −
−
f d
`_ in
j
p
where
n = power law index
K = consistency index
4.3.2.4 Bingham PlasticBingham plastic flow through a pipe:
ReD
VD g
V
124
4
cBP 3
0r nn
r x
t=+3
3o
o
f p
where
n3 = infinite viscosity, or plastic viscosity, or high shear limiting viscosity
0x = yield stress of the fluid
PE Chemical Reference Handbook
106 NCEES
Viscosity as a Function of Temperature for a Variety of Gases and Liquids
SAE 10 LUBRICATING OIL (21° API)
35° API DISTILLATE
CARBON TETRACHLORIDE
ETHYL ALCOHOL (100%)GASOLINEWATER
BENZENEACETONE (LIQUID)
N - PENTANE (LIQUID)
n - PENTANE
AMMONIA (LIQUID)
AIR AT ATMOSPHERE PRESSURE
OXYGEN (1 ATM)
CHLORINE CARBON DIOXIDE CARBON DIOXIDE
METHANEMETHANE
PROPANE
AMMONIA VAPOR
WATER VAPOR (1 ATM)
WATER VAPOR HYDROGEN
SAE 10 LUBRICATING OIL (21° API)
35° API DISTILLATE
CARBON TETRACHLORIDE
ETHYL ALCOHOL (100%)GASOLINEWATER
BENZENEACETONE (LIQUID)
N - PENTANE (LIQUID)
n - PENTANE
AMMONIA (LIQUID)
AIR AT ATMOSPHERE PRESSURE
OXYGEN (1 ATM)
CHLORINE CARBON DIOXIDE CARBON DIOXIDE
METHANEMETHANE
PROPANE
AMMONIA VAPOR
WATER VAPOR (1 ATM)
WATER VAPOR HYDROGEN
VISC
OSIT
Y, CE
NTIP
OISE
S (cP
)
TEMPERATURE, °F
0 100 200 300 400 500 600 700
10080
60
40
30
20
8
6
4
3
2
10
0.8
0.6
0.4
0.3
0.2
1
0.08
0.06
0.04
0.03
0.02
0.1
0.008
0.006
0.004
0.1
Source: G.G. Brown et al, Unit Operations, New York: Wiley, 1951, p. 586.
Chapter 4: Fluids
NCEES 107
4.3.2.5 Critical Reynolds NumberThe critical Reynolds number (Rec ) is the minimum Reynolds number at which flow is expected to become turbulent, as shown in the following table:
* Approximated from the loss coefficient equation using friction factors for fully turbulent flow for pipe sizes 1" through 24"
PE Chemical Reference Handbook
112 NCEES
4.3.5.2 Loss Coefficients for Contraction and ExpansionNotes:
1. Reynolds Number (Re) and friction factor (f) are based on inlet velocity.2. D
db =
Contraction: CONTRACTION
D dFLOW
When θ < 45° and
Re < 2500, then . . Re sinK 1 6 1 2 160 1 1 24bi= + −c e cm o m
Re > 2500, then . . . sinK f1 6 0 6 1 92 124
2
b
b i= + −` fj pWhen θ > 45° and
Re < 2500, then . . Re sinK 1 6 1 2 160 1 1 2421
bi= + −c e cm o m< F
Re > 2500, then . . sinK f0 6 0 48 1
24
2 21
b
b i= + −` f cj p m< F
Expansion: EXPANSION
DDFLOW
When θ < 45° and
Re < 4000, then . sinK 5 2 1 24b
i= −` cj m
Re >4000, then . . sinK f2 6 1 3 2 1 24b
i= + −` ` cj j m
When θ > 45° and
Re < 4000, then K 2 1 4b= −` j
Re > 4000, then .K f1 3 2 1 4 2b= + −` `j j
Chapter 4: Fluids
NCEES 113
4.3.5.3 Loss Coefficients for Pipe Entrance and Exit
Loss Coefficients
Fitting Type Configuration
Loss Coefficient
Re IDKK
K 1 1inches
1= + +3d n
K1 K∞
Entrance
Inward projecting or reentrant FLOW 160 1.0
Sharp-edged
FLOW 160 0.5
Rounded
r
dFLOW
160
r/d K∞
0.02 0.280.04 0.240.06 0.150.10 0.090.15 & up 0.04
Exit All geometries 0.0 1.0
4.3.5.4 Valve Flow Coefficient (Cv)
Valve flow coefficient (Cv ) is a value of the relationship between the pressure drop across a valve and the corre-sponding flow rate:
C V PSG
v D= o
Also:
CKad
v
2=
where
a = constant, . .in psigpm
orm Pasm
29 9 0 03522 2
3
d = effective diameter of the valve, in inches or meters
K = loss coefficient
Note: Values of Cv are not interchangeable between unit systems.
PE Chemical Reference Handbook
114 NCEES
The estimated flow rate with a known K value is
VKad
SGP
gpm
2 D=o
where ΔP = pressure drop (psi or Pa)
4.3.6 Particle FlowThe force exerted by a fluid that opposes the weight of an immersed object (buoyant force) can be expressed in terms of differential densities:
F ggV
G c
p f pt t=
−` j
where
FG = buoyant force
rp = particle density
rf = fluid density
Vp = volume of particle
The force exerted by a fluid flowing past a solid body (drag force) can be expressed in terms of a drag coefficient (CD):
F gC u A
2Dc
D f P2t= 3
where
FD = drag force
u3 = approach velocity
AP = the projected area of object with axes perpendicular to the flow
4.3.6.1 Stokes Law or Stokes FlowFor a sphere moving through a fluid at Re << 1:
ReC 24D =
where
ReD upnt
= 3
Dp = the particle diameter
In Stokes flow, viscosity can be determined using:
u
D g18 t
p p f2
nt t
=−` j
where ut = terminal (or settling) velocity of particle
Chapter 4: Fluids
NCEES 115
Drag Coefficients
For spheres in a flowing fluid with Reynolds numbers (1 < Re < 2×105), the Dallavalle equation applies:
. .ReC 0 632 4 8
D
2
= +e o
For cylinders in a flowing fluid with Reynolds numbers (1 < Re < 2×105) and with the axis normal to the flow, this equation applies:
. .ReC 1 05 1 9
D
2
= +e o
Drag Coefficients for Spheres and Flat Disks
EFFECT OF SURFACE ROUGHNESS OR MAIN-STREAM TURBULENCE
4.3.6.2 Terminal Velocity (ut)For a sphere of diameter Dp, equation applies for any Reynolds number (Newton's Law of falling particles):
u C
g D3
4t
f D
p sphere f
t
t t=
−` j
For a small sphere of diameter Dp, following Stokes Law:
u
D g18t
p sphere f2
nt t
=−_ i
4.3.6.3 Reynolds Numbers for Particles in a FluidReynolds number when particle velocity (ut) is unknown and Dp, rs, r, and μ are known:
. . .Re Ar14 42 1 827 3 79821 2
= + −_ i; Ewhere the Archimedes number (Ar) is:
Ar
D gp f p f2
3
n
t t t=
−` j
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116 NCEES
Reynolds number when particle diameter (Dp ) is unknown and ut, ρs, ρ, and μ are known:
. . .
Re ReC1 0 00433 0 203 0 0658D 2
1
= + −d n
where Re
Cu
g3
4D
f t
p f2 3t
n t t=
−` j
Reynolds number when fluid viscosity (μ) is unknown and Dp, ut, rs, and r are known:
..
Re C 0 6324 8
D
2
= −e o Use known quantities to solve for CD.
4.3.6.4 Settling OperationsFree Settling: Particle-to-particle interactions are negligible.
Hindered Settling: Particle settling is at a reduced rate relative to the settling velocity of a single particle caused by interactions with neighboring particles.
Approximate Regions of Free and Hindered Settling for Given Solids' Concentration and Density
50
40
30
20
100.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
HINDERED
FREE
wt. %
SOL
IDS
PARTICLE
PARTICLE FLUID—
If upwards fluid velocity ( uf ) is less than the settling velocity of the particle (us ), then the particles will settle.
For settling operations, the settling velocity (us ) equals the terminal velocity (ut).
Chapter 4: Fluids
NCEES 117
4.3.6.5 Settling DiameterFor Stokes flow, the smallest diameter spherical particle (Dp ) that will settle is
Dg
u18p
p f
f
t t
n=−` j
For general flow up to Re < 2×105, the smallest diameter spherical particle that will settle is
D uRe
p f ftn=
where the Reynolds number can be estimated using
. . .Re Re
C1 0 00433 0 203 0 0658D 21
= + −d n where ReC
ug3
4D
f t
p f2 3t
n t t=
−` j
4.3.6.6 Flow Through Porous Media and Packed BedsA porous, fixed bed of solid particles can be characterized by:
L = length of particle bed
ds = average particle diameter (diameter of a sphere with the same volume of the particle)
Φ = sphericity of particle (0 –1)
e = porosity or void fraction of the particle bed (dimensionless)
Porosity (e) or void fraction:
Total volumeTotal volume Volume of solids
AA
AA1 solid voidse =
−=
−=
_ i
where
Asolid = area of the solid phase in a cross-section of area A
Avoids = void area in a cross-section of area A
Interstitial velocity (actual velocity of fluid within the pores or voids):
u AV u
i e e= =o
where u = approach velocity (or superficial velocity)
Sphericity of a particle (shape factor):
surface area of particlesurface area of sphere with same volume as particle
U =
Friction loss through porous media:
h f dL
gu
43 1
sf
2
3e
e=−d e_n i o
Reynolds number for flow through porous media:
Re d u32
11
nt
e= −e_ i o
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118 NCEES
Use the Ergun equation to estimate the pressure loss through a packed bed (DP) under laminar and turbulent conditions:
4.3.6.7 FluidizationFor a fluid passing vertically through a bed of particles, ΔP increases as fluid velocity u increases. The net upward force FB on the bed is
FB = AΔP
where A = cross-sectional area of the bed
At fluidization, net upward force (fluid drag force) equals the weight of the bed (FB = WB), while the fluid velocity above the bed is less than the terminal velocity of the particles (ut).
The Reynolds number for a fluidized bed can be approximated by:
Re C C Ar C1 2 1= + −
where
Ar = Archimedes number
.C 3 5180 1
1e
=−_ i
.C 1 752
3e=
where ϵ = minimum bed void fraction (porosity) at the point of fluidization
The minimum bed void fraction for bed height H at the first indication of fluidization is
H Am
1particles
particlese t
= −
Chapter 4: Fluids
NCEES 119
4.3.7 Two-Phase Flow
4.3.7.1 Flow PatternsBubble or Froth Flow: Bubbles of gas are dispersed throughout the liquid. Gas bubbles move at roughly the same velocity as the liquid.
BUBBLE FLOWPlug Flow: Alternate plugs of liquid and gas move along the upper portion of the pipe, with mostly liquid moving along the lower portion.
PLUG FLOW
Stratified Flow: Gas flow moves on top and over the liquid forming a distinct, relatively smooth, liquid-gas inter-face.
STRATIFIED FLOW
Wavy Flow: Similar to stratified flow, the fast-moving gas flow creates waves in the liquid phase.
WAVY FLOW
Slug Flow: High velocity gas picks up waves to form frothy slugs of liquid. These slugs move at higher velocity than the bulk liquid phase and can create dangerous vibrations that can damage equipment.
SLUG FLOW
Annular Flow:As gas velocity increases, liquid forms around the inside of the pipe wall, with the high-velocity gas flowing through the center.
ANNULAR FLOW
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120 NCEES
Dispersed Flow (or Spray Flow or Mist Flow): Liquid is entrained as fine droplets in the gas phase.
DISPERSED FLOW4.3.7.2 Flow Regimes
Flow Patterns for Horizontal Two-Phase Flow
DISPERSED
100,000
10,000
1,000
1000 1 10 100 1,000 10,000
ANNULARBUBBLE OR
FROTH
SLUG
PLUG
STRATIFIED
By
Bx
WAVE
Source: O. Baker, Oil and Gas Journal, Nov. 10, 1958, p. 156.
Baker parameters for the previous chart:
B W
W531G
L
LLx
L
L G
32
21
31
t
t t
cn= e _ fo i p
R
T
SSSSSSSSS
V
X
WWWWWWWWW
.B AW2 16
1G
L Gy 2
1t t
= d f_n i pwhere
A = internal pipe cross-sectional area, in ft2
WG = gas flow rate, in hrlbm
WL = liquid flow rate, in hrlbm
ρL = liquid density, in ftlbm3
ρG = gas density, in ftlbm3
μL = liquid viscosity, in cP
gL = liquid surface tension, in cmdyn
Chapter 4: Fluids
NCEES 121
4.3.8 Jet PropulsionThe force produced by jetting action is
F m u u2 1= −o _ iJET PROPULSION
m, u1
m, u2
Therefore, according to the conservation of mass:
F gV u V u
c2 2 2 1 1 1t t=
−o o
Jet Forces on PlatesJet on a Vertical Plate Jet on a Horizontal Plate Jet on an Inclined Plate
JET FORCES ON PLATES
JET ON A VERTICAL PLATE JET ON A HORIZONTAL PLATE JET ON AN INCLINED PLATE
h
F gmuc
jetx =
− oF g
m u g h2c
jety
23=
− −o sinF g
muc
jet i=
− o
4.3.9 Open-Channel Flow
4.3.9.1 Specific Energy (or Specific Head) E g
u y22
a= +
where
E = specific energy (or head)
u = fluid velocity
y = depth of liquid
Critical Depth: The depth of flow for a given discharge where the specific energy is at q minimum.
y gq
c
2 31
= e o
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122 NCEES
where
yc = critical depth
q = unit discharge BVoc m
Vo = total discharge, volumetric flow rate
B = channel width
Specific Energy Diagram
y
E
CHAN
NEL D
EPTH
SPECIFIC ENERGYEmin
yc
4.3.9.2 Froude Number Fr g y
ug AV T
h
2
3= =o
where
yh = hydraulic depth = TA
A = cross-sectional area of flow
T = width of fluid surface
Supercritical flow: Fr > 1
Subcritical flow: Fr < 1
Critical flow: Fr = 1
Chapter 4: Fluids
NCEES 123
4.3.9.3 Hydraulic Jump
Hydraulic Jump
FLOW DIRECTION
HYDRAULIC JUMPSUPERCRITICAL FLOW
(Fr1 > 1)
SUBCRITICAL FLOW(Fr2 < 1)
(2)
(1)y1
y2
yy
Fr21 1 1 8
12
12= − + +` j
where
y1 = flow depth at upstream supercritical flow location
y2 = flow depth at downstream subcritical flow location
Fr1 = Froude number at upstream supercritical flow location
Fr2 = Froude number at downstream subcritical flow location
4.3.9.4 Manning Equation v AR S3
221
hl=
Ho
where
vo = discharge volumetric flow rate
k = 1.0 for SI units; 1.49 for U.S. units
A = cross-sectional area of flow
RH = hydraulic radius
S = slope of hydraulic surface
h = Manning's roughness coefficient
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124 NCEES
Manning's Roughness Coefficients
Material hCast iron pipe 0.013Wrought iron pipe 0.015Riveted steel pipe 0.016Corrugated storm pipe 0.024Glass 0.010Vitrified sewer pipe 0.014Concrete pipe 0.013Excavated canal—earth, uniform 0.023Natural channel—uniform cross-section 0.050
4.3.10 Compressible Flow
4.3.10.1 Isentropic Flow RelationshipsIn an ideal gas for an isentropic process, the following relationships exist between static properties at any two points in the flow:
PP
TT k
k k
1
2
1
2 1
12tt= =
−e d^o nh
where k = ratio of specific heats = ccv
p
The stagnation temperature T0 at a point in the flow is related to the static temperature:
T T cu2 p
0
2= +
Energy relation between two points is
hu
hu
2 2112
222
+ = +
The relationship between the static and stagnation properties (T0, P0, and r0) at any point in the flow can be expressed as a function of the Mach number (Ma):
MaTT k1 2
10 2= + −
MaPP
TT k1 2
1kk
kk
0 0 1 2 1= = + −− −d c^ ^n mh h
MaTT k1 2
1kk
k0 0 1 2 11
tt = = + −− −d c^ ^n mh h
Chapter 4: Fluids
NCEES 125
Compressible flows are often accelerated or decelerated through a nozzle or diffuser. For subsonic flows, the velo-city decreases as the flow cross-sectional area increases and vice versa. For supersonic flows, the velocity increases as the flow cross-sectional area increases and decreases as the flow cross-sectional area decreases, The point at which the Mach number is sonic is called the throat; its area is represented by the variable A*. The following area ratio holds for any Mach number:
MaMa
AA
k
k1
21 1
1 21 1
*
kk
2 2 11
=+
+ − −+
__
^^i
i
hhR
T
SSSSSSSSS
V
X
WWWWWWWWW
where
A = area (length2)
A* = area at the sonic point (Ma = 1.0)
4.3.10.2 Net Expansion Factors of Gases for Orifices and Nozzles
Expansion Factors for Compressible Flow-Through Orifices and Nozzles
Y —
EXP
ANSI
ON FA
CTOR
PRESSURE RATIO –
SQUAREEDGEORIFICE
SQUAREEDGEORIFICE
=====
0.20.50.60.70.75
β
=====
0.20.50.60.70.75
β
WHERE IS P1 THE ABSOLUTE UPSTREAM PRESSURE
1.0
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
ΔP—P1
0 0.2 0.4 0.6
k = 1.3 approximately [CO2, SO2, H2O (steam),H2S, NH3, N2O, Cl2, CH4, C2H2, and C2H4]
k = 1.4 approximately [Air H2, O2, N2,CO, NO, and HCl]
Y —
EXP
ANSI
ON FA
CTOR
PRESSURE RATIO –
SQUAREEDGEORIFICE
SQUAREEDGEORIFICE
=====
0.20.50.60.70.75
β
=====
0.20.50.60.70.75
β
1.0
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
ΔP—P1
0 0.2 0.4 0.6
where Pl = absolute upstream pressure
PE Chemical Reference Handbook
126 NCEES
4.3.10.3 Net Expansion Factors of Gases for Pipes
Expansion Factors for Compressible Flow-Through Pipes
k = 1.3 approximately [CO2, SO2, H2O (steam), H2S, NH3, N2O, Cl2, CH4, C2H2, and C2H4]
1.0
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.550 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
K = 100
K = 40
K = 20
K = 15
K = 10
K = 8.0
K = 6.0K = 4.0
K = 3.0K = 2.0K = 1.5
K = 1.2
K = 100
K = 40
K = 20
K = 15
K = 10
K = 8.0
K = 6.0K = 4.0
K = 3.0K = 2.0K = 1.5
K = 1.2
PRESSURE RATIO – ΔP—P1
Y
k = 1.4 approximately [Air, H2, O2, N2, CO, NO, HCl]
WHERE P1 IS THE ABSOLUTE UPSTREAM PRESSUREwhere Pl = absolute upstream pressure
Chapter 4: Fluids
NCEES 127
4.3.10.4 Critical Pressure Ratio, rc , for Compressible Flow
Critical Pressure Ratio Through Nozzles and Venturi Tubes (Only)
β
0.64
0.60
0.62
0.58
0.56
0.54
0.85
0.80
0.75
0.70
0.650.60
0.500.400.200
k = CP / CV
r c =
P 2 /P
1
1.25 1.30 1.35 1.40 1.45
where P1 and P2 = absolute pressures upstream and downstream of the nozzle or venturi tube, respectively
4.3.10.5 Choked FlowChoked flow is a limiting condition where the mass flow will not increase with a further decrease in the down-stream pressure environment while upstream pressure is fixed. Choked flow occurs when the Mach number is 1.0 at the minimum cross-section area.
Mass velocity of gas at choked flow:
m C A k P g k 1
2d c
kk
1 111
t= +−+
c mwhere
Cd = discharge
r1 = density of gas before restriction
P1 = pressure of gas before restriction (absolute)
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128 NCEES
4.4 Flow Applications
4.4.1 Pumps
Types and Subtypes of Pumps
PUMPS
POSITIVE DISPLACEMENT
KINETIC
RECIPROCATING
BLOW CASE
ROTARY
CENTRIFUGAL
SPECIAL EFFECT
VANE SCREWCIRCUMFERENTIAL PISTONGEAR
FLEXIBLE MEMBER LOBE
CANNED PUMPOVERHUNG IMPELLERIMPELLER BETWEEN BEARINGSTURBINE TYPEREGENERATIVE TURBINE
REVERSE CENTRIFUGALROTATING CASING
STEAMPOWERCONTROLLED VOLUMEPISTON
4.4.1.1 Affinity Laws for Pumps, Fans, and CompressorsFor small changes in impeller diameter (changes not to exceed 20%):
DD
VV
HH
2
1
2
1
2
1= =oo
and B PB P
DD
2
1
2313
=
For variations in speed (constant impeller diameter):
SS
VV
HH
2
1
2
1
2
1= =oo
and B PB P
SS
2 2313
=1
where
B P = brake power
D = impeller or wheel diameter
H = head (height of fluid)
Vo = volumetric capacity
S = speed (rpm)
Chapter 4: Fluids
NCEES 129
4.4.1.2 Pump Similitude
Predicting Performance of Homologous Pumps
Volume capacity estimate:
VV
SS
DD
DD
HH .
2
1
2
1
2
13
2
12
2
10 5
= =o
o e e eo o o
Pressure or head estimate:
HH
SS
DD
2
1
2
12
2
12
= e eo o
Brake power estimate:
B PB P
SS
DD
DD
HH .
2
121
2
13
2
15
21
2
12
2
11 5
tt
tt= =e e e eo o o o
Impeller or wheel speed estimate:
SS
DD
HH
VV
HH. . .
2
1
1
2
2
10 5
1
20 5
2
10 75
= = o
oe e eo o o
4.4.1.3 Pump HeadPump head (Hp) is a variation of the head-basis Bernoulli equation:
H g
P P gg
u uz z h2p
d s c d sd s f
2 2
t=−
+−
+ − −` ` `j j j
where
Ps = suction pressure at suction reference point (absolute)
Pd = discharge pressure at discharge reference point (absolute)
us = velocity at the pump suction
ud = velocity at the pump suction
zs = elevation at the suction reference point
zd = elevation at the discharge reference point
hf = friction loss in the pipe between the reference points
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130 NCEES
Centrifugal PumpPUMP HEAD
CENTRIFUGAL PUMP
PsSUCTIONREFERENCE POINT
DISCHARGEREFERENCE POINTPd
UdUs
ZdZs
Pump Head in Common Units
Pump Head Calculations
Component
U.S. Units SI Units
.H SG
p pg
u uz z h
2 312p
d s d sd s f
2 2
=−
+−
+ − −_ `
_i j
i Hp p
gu u
z z h2pd s d s
d s f
2 2
t=−
+−
+ − −` ` `j j j
Hp ft mp psi Pau
secft
sm
z ft mg .
secft32 2 2
.sm9 81 2
hf ft m
r ftlbm3 m
kg3
Chapter 4: Fluids
NCEES 131
4.4.1.4 Pump CurveA pump curve, head-capacity curve, or H-Q curve is provided by pump manufacturers.
Pump Curve for a Fixed Impeller Diameter and Pump Speed
POW
ER
TOTA
L HEA
D
VOLUMETRIC CAPACITY
BEP
BRAKE POWER
HEAD
EFFIC
IENCY
NPSHr
where BEP = best operating point
4.4.1.5 Net-Positive Suction Head (NPSH)NPSH: Total suction head minus the vapor pressure of the liquid being pumped (units are in height of liquid (absolute) and the referenced datum is the suction nozzle.)
NPSHa: Net-positive suction head available to the pump
NPSHr: Net-positive suction head required by the pump (provided by the pump manufacturer)
For suction lift:
NPSHa = ha – hvap – hst – hL
For flooded suction:
NPSHa = ha – hvap + hst – hL
where
ha = absolute pressure (in height of liquid) on the surface of the liquid supply level
hvap = vapor pressure (in height of liquid) of the liquid at the temperature being pumped
hst = static height of liquid supply, either above or below the pump centerline or impeller eye
hL = suction line losses in height of liquid
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132 NCEES
4.4.1.6 Pump PowerPower required to move the fluid, or water power (WP):
U.S. units ( ) ,
( ) ( )horsepower
Flowrate gpm ft ftlbm
WPH
246 7803# # t
=d n
Metric units ( )W Flowrate s mmkg
smWP m H g
33 2# # #t= c ^ e dm h o n
Power required at the pump shaft, or brake power (BP):
BP WPpumph=
Power required by the pump driver, or supplied power (SP):
SP WPpump driver transmissionh h h=
4.4.1.7 Temperature Rise in a Centrifugal Pump
cT VBP 1
p
pump
t
hD =
−o
` j
4.4.1.8 Specific Speed (Ns ) at the BEP N
HSV
.
.
s 0 75
0 5=o
where head (H) and flow rate Vo^ hare taken at the BEP
4.4.1.9 Suction-Specific Speed (Ns ) at the BEP N
NPSHSV
.
.
sa0 75
0 5=
o
_ i
4.4.1.10 System CurvesSystem curves are developed from different flow rates through a given system, using the Bernoulli equation.
Note: The velocity head terms are usually omitted because the changes in gu2
2 are negligible.
Hs = pressure head + static head (hs ) + pipe losses* (hf )
*Include friction, entrance, and exit losses:
H g
P P gh hs
B A cs ft=
−+ +
_ i
Chapter 4: Fluids
NCEES 133
Simple Pumping System
PB
PA PUMPSTAT
IC H
EAD
(HS)
System Curve Plot
TOTA
L HEA
D
CAPACITY
STATIC HEAD (hs )
PRESSURE HEAD
SYSTEM CURVE
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134 NCEES
4.4.1.11 Pumps in Parallel and SeriesOperating Point: Centrifugal pumps operate at the intersection of the pump curve and the system curve.
For pumps in parallel, capacities are added horizontally. For pumps in series, heads are added vertically:
Pumps Operating in Parallel
SYSTEM CURVE
CAPACITY
TOTA
L HEA
D
OPERATINGPOINT
COMBINED (A+B)PUMP CURVE
PUMP B
PUMP A
A B
A+B
Pumps Operating in Series
TOTA
L HEA
D
OPERATINGPOINT
COMBINED (A+B)PUMP CURVE
PUMP B
PUMP A
SYSTEMCURVE
A
B A+B
CAPACITY
Chapter 4: Fluids
NCEES 135
4.4.2 Fans, Compressors, and Turbines
4.4.2.1 FansTypical backward curved fans:
CONSTANT N, D, ρ
FLOW RATE
POWER
Δ
f
pW PV
fhD=oo
where
Wo = fan power
DP = pressure rise
hf = fan efficiency
4.4.2.2 CompressorsCompressors consume power to add energy to the working fluid. This addition of energy results in an increase in fluid pressure (head).
For an adiabatic compressor with DPE = 0 and negligible DKE:
W•
INLET
EXIT
COMPRESSORin
W m h hcomp e i=− −o o ` j
For an ideal gas with constant specific heats:
W mc T Tcomp p e i=− −o o ` j
Per unit mass:
W c T Tcomp p e i=− −o ` j
Compressor Isentropic Efficiency
ww
T TT T
C as
e i
es ih = = −−
where
wa = actual compressor work per unit mass
ws = isentropic compressor work per unit mass
Tes = isentropic exit temperature
For a compressor where DKE is included:
W m h hu u m c T T u u2 2comp e i
e ip e i
e i2 2 2 2
= − − +− = − − +
−o o od d `n j n
PE Chemical Reference Handbook
136 NCEES
Adiabatic compression:
WkmP k
PP
1 1compi C
i
i
e k1 1
t h=
− −−
o o
_ ei o> H = MW kmRT k P
1 1C
i
ie k1 1
h t- --o
_ di n> H
where
Wcompo = fluid or gas power
Pi = inlet or suction pressure
Pe = exit or discharge pressure
ri = inlet gas density
hC = isentropic compressor efficiency
Isothermal compression:
ln lnMWW
mRTPP mP P
comp C
i
i
ei Ci
ie
h t h t= =o o o
where
, , , andW P Pcomp e i Cho = as defined for adiabatic compression, above
R = univeral gas constant
Ti = inlet temperature of gas
4.4.2.3 TurbinesTurbines produce power by extracting energy from a working fluid. The energy loss shows up as a decrease in fluid pressure (head).
For an adiabatic turbine with DPE = 0 and negligible DKE:
W•
INLET
EXIT
TURBINEout
W m h hturb i e= −o o ` j
For an ideal gas with constant specific heats:
W mc T Tturb i ep= −o o ` j
Per unit mass:
w c T Tturb i ep= −` j
Turbine isentropic efficiency:
ww
T TT T
T sa
i es
i eh = = −−
For a turbine where DKE is included:
W m h hu u m c T T u u2 2turb e i
e ip e i
e i2 2 2 2
= − +− = − +
−o o od d `n j n
Chapter 4: Fluids
NCEES 137
4.4.3 Control Valves
4.4.3.1 Control Valve Flow CharacteristicsFlow characteristic of a control valve: The relationship between valve capacity and valve stem travel (or valve lift).
Control Valve Flow Versus Stem Travel
0 20 40 60 80 100
20
40
60
80
100
PERCENT OF RATED STEM TRAVEL
PERC
ENT
OF M
AXIM
UM F
LOW
QUICK OPENING
LINEAR
MODIFIEDPARABOLIC
EQUAL PERCENTAGE
Linear: Flow capacity increases linearly with stem travel.
Equal Percentage: Flow capacity increases exponentially with stem travel. Equal increments of stem travel produce equal percentage changes in the existing CV.
Modified Parabolic: Valve characteristic is approximately midway between linear and equal-percentage characteristics. It provides fine throttling at low flow capacities and approximately linear characteristics at higher flow capacities.
Quick Opening: Provides large changes in flow for very small changes in early stem travel.
PE Chemical Reference Handbook
138 NCEES
4.4.3.2 Control Valve Sizing (Traditional Method)
Control Valve Sizing Equations for Liquids (Incompressible Flow)Equation Use Notes
V C SGP
VD=o
Basic sizing equation; does not consider viscosity effects or valve recovery capabilities
CV is the flow coefficient for a control valve. The value of CV is dependent on the type of valve and also varies with stem travel or per-centage of valve opening. The units and values for the flow coefficient are provided by the manufacturer.
C V PSG
V D= o
Flow coefficient For Newtonian fluids of viscosities similar to water.
C C FV Corr V V=−Corrected flow coefficient for viscosity
Use the appropriate FV to predict pressure drop, select valve size, or predict flow rate.
P K P r pmax m C v1D = −_ i
Maximum allowable differential pressure
where:
Km = valve recovery coefficient (provided by manufacturer)
P1 = valve body inlet pressure (absolute)
pv = liquid vapor pressure (absolute) at the valve body inlet temperature
rC = critical pressure ratio
The critical pressure ratio is provided by the manufacturer or, in the absence of correlation data, the equation below can be used.
. .r pp
0 96 0 28C cv= −
Critical pressure ratio (when manufacturer data is not available)
pc is the critical pressure of the fluid (absolute).
,ReCV17 250
Vn
t=o Control valve Reynolds number For engineering units only, where Vo is in gpm,
ΔP is in psi, μ is in cP, and ρ is in ftlbm3
.
Chapter 4: Fluids
NCEES 139
4.4.4 Mixing
4.4.4.1 Tank Mixing
Tank Mixing
BAFF
LE
IMPE
LLER
BAFF
LE
LIQUIDLEVEL
TANK
D
NW
BAFF
LE
BAFF
LE
H
T
B
TDNVBW
WHERE:======
TANK DIAMETERIMPELLER DIAMETERROTATIONAL SPEEDTANK VOLUMEBAFFLE WIDTHIMPELLER WIDTH
Impeller Reynolds number
Re D N2nt=
Flow Number
NNDq
Q 3=
where q = volumetric flow rate through the impeller
Power Number
NN DPg
Pc
3 5t=
where P = impeller power
Ratio of tangential liquid velocity at blade tips to blade tip velocity (K):
Power required to suspend particles to a maximum height (Z) using a turbine impeller is
P g V u DT e1 .
m m t m32 2
14 35t f= − b_ ci m
where
.TZ E 0 1b = − − , with E = clearance between impeller and tank floor
rm , Vm = density and volume, respectively, of solid-liquid suspension, not including the clear liquid in zone above height Z
ut = terminal velocity of particles
em = volume fraction of liquid in zone occupied by suspension
Chapter 4: Fluids
NCEES 141
and
x1 1 1 1m liquid solids solids liquidst t t t= + −d n
with xsolids = mass fraction of the solid particles in the solid-liquid suspension
Suspension of Particles in a Tank
Z
E
TANK
SOLID-LIQUIDSUSPENSION
CLEAR LIQUID
T
D
4.4.4.2 Blending of Miscible Liquids in a Tank
Correlation of Blending Times for Miscible Liquids in a Turbine-Agitated, Baffled Vessel
Re = _________ND2p
CORRELATION OF BLENDING TIMES FOR MISCIBLELIQUIDS IN A TURBINE-AGITATED BAFFLED VESSEL
1000
100
fT
10
11 10610510410310210
μ
Blending time factor (fT) (for miscible Newtonian fluids only):
fH T
t N D g DT
21
23
2 32
61
21
=_ i
where t = blend time (sec)
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4.4.5 Air Lift
Air Lift Operation
AIR INLETNO AIR
LIQUID LIQUID
LIQUIDAND AIR
AIR INLETNO AIR
LIQUID LIQUID
LIQUIDAND AIR
Common Air Lift TermsDISCHARGE LEVEL
GROUND LEVEL
STATIC WATERLEVEL
PUMPING WATERLEVEL
AIR INLET
PUMPINGSUBMERGENCE
STARTINGSUBMERGENCE
DRAW-DOWN
TOTALPUMPING
LIFT
TOTALSTARTING
LIFTSTATICLEVEL
LIFTABOVE
GROUND
DISCHARGE LEVEL
GROUND LEVEL
STATIC WATERLEVEL
PUMPING WATERLEVEL
AIR INLET
PUMPINGSUBMERGENCE
STARTINGSUBMERGENCE
DRAW-DOWN
TOTALPUMPING
LIFT
TOTALSTARTING
LIFTSTATICLEVEL
LIFTABOVE
GROUND
Air lifts are used to pump liquids and mixtures of liquids and solids. The air required to pump is
logV
C SL
3434a
10
= +
Chapter 4: Fluids
NCEES 143
where
Va = quantity of free air required per gallon of liquid pumped gallon pumpedft3e o
C = constant found for outside airline (VA) and inside airline (VC) in figure below
S = pumping submergence (%) in figure below
L = total pumping lift (ft)
Constant in Formula for Va
INSIDE AIRLINE – VCOUTSIDE AIRLINE – VA375
350
325
300
275
250
225
200
175
150
12530 35 40 45 50 55
CONSTANT IN FORMULASUBMERGENCE – PERCENT
VALU
ES O
F CO
NSTA
NT “C
”
60 65 70 75 80
Approximate Percent Submergence for Optimum Efficiency70
60
50
40
30
TOTAL PUMPING LIFT – FEET
SUBM
ERGE
NCE
– PE
RCEN
T
30 100 200 300 400 500 600 700 800 900
Use for either system with straight or tapered pipe. Graphs only available in U.S. units; SI not available.
Source: Gibbs, C.W., editor, New Compressed Air and Gas Data, 2nd ed., Davidson, N.C.: Ingersoll-Rand Company, 1971, p. 31–8.
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4.4.6 Solids Handling
4.4.6.1 Granular Media Storage
Vertical Normal Stress Profile in a Silo
BULK SOLIDS
HYDROSTATIC
PRESSURE
Z
Source: Chase, George G., Solids Notes 10, Akron: University of Akron, p.10-10.
Compressive normal stress (Pv) in silos can be calculated by the Janssen equation:
expP K gg D
DK z
4 1 4c
V nt n= − −d n= G
where
r = granular bulk density
μ = solids coefficient of friction
D = silo diameter
K = lateral pressure ratio, where PW = K PV (Janssen's assumption that vertical normal stress is proportional to the lateral normal stress)
z = bed depth at which pressure is being measured
Sources: Don McGlinchey, editor, Bulk Solids Handling: Equipment Selection and Operation, and J.M. Rotter, Silo and Hopper Design for Strength, Oxford: Blackwell Publishing Ltd., 2008.
Chapter 4: Fluids
NCEES 145
4.4.6.2 Pneumatic TransportPneumatic transport (or pneumatic conveying) is using gas to transport particulate solids through a pipeline (such as flour, pulverized coal, powdered clay).
Flow Regimes:
Dilute Phase—Particles are fully suspended at loadings less than 1%.
Dense Phase—Particles are not suspended (or periodically suspended) with loadings greater than 20%.
Pressure Systems
BLOWER
BLOWER
POSITIVE PRESSURE SYSTEM (PUSH)
DISCHARGE HOPPERS
DISCHARGEHOPPER
NEGATIVE PRESSURE SYSTEM (PULL)
FILTERFEED
HOPPER
FEED HOPPERS
FILTER
FILTER
FILTER
A “PUSH-PULL” SYSTEM USES BLOWERS TO SIMULTANEOUSLYPUSH (POSITIVE PRESSURE) AND PULL THE SOLIDS (NEGATIVE PRESSURE)
Characteristics of Pneumatic Conveying Flow RegimesDilute Phase Dense Phase
High velocity Low velocityParticles subject to attrition Low particle attritionLow pressure High pressureLow cost/simple operation Complex operationLow loadings High solids loading
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146 NCEES
Flows in Pneumatic Transport
DILUTE PHASE
DILUTE PHASE
DILUTE PHASEFLOW
CONTINUOUS DENSEPHASE FLOW
PLUG FLOW
DISCRETE PLUG FLOW
DUNE FLOW
DISCONTINUOUS DENSEPHASE FLOW
SALTATING FLOW
DENSE PHASE
PRES
SURE
GRA
DIEN
T
HIGH VELOCITYPARTICLES SUBJECT TO ATTRITIONLOW PRESSURELOW COST / SIMPLE OPERATIONLOW LOADINGS
DENSE PHASE
CHARACTERISTICS OF PNEUMATICCONVEYING FLOW REGIMES
Saltation—Settling of solid particles in the bottom of the pipe during dilute phase pneumatic transport
Superficial gas velocity u g_ i—The gas volumetric flow Vgo` j divided by the pipe cross-sectional area (A): u A
Vg
g=o
Superficial solids velocity u s^ h—The solids volumetric flow Vso_ i divided by the pipe cross-sectional area: u A
Vs
s=o
where Vm
s sst=o o
, with andms sto as the mass flow rate and density of the solid particles, respectively
Actual gas velocity (ug): u A
Vg
gf
=o
where e = void fraction
Actual particle velocity (us): u
AV1ss
f=
−o
_ i
Chapter 4: Fluids
NCEES 147
Relationships
In vertical pipes, the minimum gas velocity (umin) to suspend particles is when the net upward force on the bed provided by the gas equals the net weight of the solids bed (see Section 4.3.6.7):
F WB B=
Practical minimum gas velocity:
u u C
g D2 2 3
4 1min
D
gstt
= =−te o
where ReC 24D =
Mass flowrate of the solid particles:
m Au 1s s sf t= −o _ i
Mass flowrate of the gas:
m Aug gg ft=o
Solids loading (R):
R mmgs= oo
Concentration (volume fraction) of solids:u
u us
sC V VV
ss g
s
g= + =
+o o
o
Dilute phase pressure drop: The total pressure drop is the sum of the contributions from the carrier gas pressure drop, acceleration of the solid particles, the friction of the solid particles against the pipe wall and fittings, the lift-ing of the solid particles through the vertical sections, and miscellaneous factors.
P P P P P P Pgf sa sf sb sv miscD D D D D D D= + + + + +` j
Carrier gas pressure drop ( DPgf ): For the purpose of this equation, compressible flow equations are not used. Treat the gas as an incompressible fluid:
P g Df Lu2gf
c
g g2t
D =
Acceleration of solids pressure drop (DPsa):
P Agm u
sac
s sD = o
where A = pipe cross-sectional area
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Solids friction in straight pipe pressure drop (DPsf ):
P D gR u L2sf
c
s g g actual2m t
D =
where
ls = solids friction factor (if unknown, assume 0.2)
R = solids loading
Lactual = actual length of pipe (not equivalent length)
Solid friction in bends pressure drop (DPsb):
P L LP
sb eqactual
sDD= e o
Vertical lift pressure drop (DPsv):
P g uR g Z u
sv c s
g gtD =
where Z = total length of vertical pipe where the flow is upwards
Miscellaneous pressure drop (DPmisc):
where Pmisc /D additional pressure drop for other components, interferences, and other special conditions
Saltation velocity ( usalt ):
Rg Du
101 salta
b
= f p (Rizk correlation)
where
D = inside diameter of conveying pipe
a = 1440 Dp + 1.96 (SI units)
= 439 Dp + 1.96 (U.S. units)
b = 1100 Dp + 2.5 (SI units)
= 325 Dp + 2.5 (U.S. units)
Dp = mean particle diameter
Chapter 4: Fluids
NCEES 149
4.4.7 Cyclone
Cyclone SeparatorFINES + AIR
IMMERSION TUBE(OR GAS OUTLET TUBE)
FEED(DIRTY AIR)
CONICALSECTION
CYCLONEBODY
De
s
a
Dh
z
H
B
TAILS
b
where
a = height of tangential inlet
b = width of tangential inlet
De = diameter of immersion tube
s = immersion length of outlet tube
D = cyclone diameter
h = length of cylindrical section
z = length of conical section
H = cyclone height
B = diameter of tail outlet
Particle Removal Efficiency
DD
1
1
p
pc2h =
+ f p
where
Dpc = diameter of particle collected with 50% efficiency
Dp = diameter of particle of interest
h = fractional particle collection efficiency
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Effective Number of Turns N H h z1
2e = +c mwhere
Ne = number of effective turns the gas makes in the cyclone
h = length of body of cyclone
z = length of cone of cyclone
Cyclone 50% Particle Efficiency for Particle Diameter
DN u
b2
9.
pce i p g
0 5
r t t
n=−` j> H
where
Dpc = diameter of particle that is collected with 50% efficiency, in meters
Cyclone Ratio of Dimensions to Body Diameter (D) CapacityDimension High Efficiency Conventional High Throughput
Inlet height, a 0.44 0.50 0.80Inlet width, b 0.21 0.25 0.35Cylindrical section length, h 1.40 1.75 1.70Cone length, z 2.50 2.00 2.00Immersion length, s 0.50 0.60 0.85Gas exit diameter, D 0.40 0.50 0.75Tails outlet diameter, B 0.40 0.40 0.40Cyclone height, H 3.90 3.75 3.70
Source: Adapted from D.C. Cooper and F.C. Alley. Air Pollution Control: A Design Approach, 2nd ed., Illinois: Waveland Press, 1986.
4.4.8 Special Flow Applications
4.4.8.1 Submerged Orifice
Submerged Orifice Operating Under Steady-Flow Conditions
1 – 2
A A
V
h1h
h h
2
2
V A u C A g h h22 2 1 2= = −o _ iwhere u2 = velocity of fluid exiting the orifice
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152 NCEES
4.4.8.2 Orifice Discharging Freely into Atmosphere
Orifice Discharging Into Atmosphere
2A0A
h
Atm
Torricelli's equation:
u gh2=
V CA gh20=o
where
h = distance from the liquid surface to the centerline of the orifice opening
A0 = cross-sectional area of flow
4.5 Flow and Pressure Measurement Techniques
4.5.1 Manometers and Barometers
4.5.1.1 Simple Manometer
Simple Manometer
z1
2zAz FLUID 2
( fluid 2)
PA
Patm
P2
P1
ρ
FLUID 1( fluid 1) ρ
P P P P gg z z z zA atm A c fluid fluid A2 2 2 1 1 1t t− = − = − − −_ _i i9 C
Chapter 4: Fluids
NCEES 153
4.5.1.2 Manometer With Multiple Fluids
Manometer With Multiple Fluids
zAPA
zBPB
z2P2 z2P2
z1P1z1P1z3P3 z3P3
FLUID 1 (ρfluid 2)
FLUID 3 (ρfluid 2)
FLUID 4 (ρfluid 4)FLUID 2 (ρfluid 2)
A
P P P P P P P P P P
P P gg z z z z z z z z
A B A B
A B c fluid A fluid fluid fluid B
1 1 2 2 3 3
1 1 2 2 1 3 3 2 4 3t t t t
− = − + − + − + −
− = − + − + − + −
___ _
__
_ _i
ii j
ij
j j9 C
4.5.1.3 Inclined U-Tube Manometer
Inclined U-Tube Manometer
MANOMETERFLUID
P2P1
Δ h
X
θ
sinP P g
gX g
gh
c m mc1 2 : : :t i t D− = =
where
x = difference in tube fill length
rm = density of the manometer fluid (densities of the fluids on each side of the manometer are equal)
q = angle of inclination (horizontal = 0°)
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4.5.1.4 BarometersAnother device that works on the same principle as the manometer is the simple barometer.
P P P gg h
P gg h
atm A v c B c
t t= = + = +
where Pv = vapor pressure of the barometer fluid
BarometerPV PB
PA
h ρ
4.5.2 Flow Measurement Devices (Summary)
Flow Measurement DevicesClass Meter Type Description Advantages Drawbacks
Mec
hani
cal Rotary
pistonRotary piston spins within a chamber of known volume. For each rotation, an amount of fluid passes through the piston chamber. The rotations are counted and the flow rate is determined from the rate of rotations.
• Accurate; suitable for fuel metering
• Suitable for low volume metering and laboratory or bench scale testing
• High permanent pressure drop at high flows
• Clear liquids only• High cost
Gear Two rotating gears with synchronized, close-fitting teeth. A fixed quantity of liquid passes through the meter for each revolution. Permanent magnets in the rotating gears transmit a signal to a transducer for flow measurement.
OPERATION OF AN OVAL GEAR METER
Operation of an oval gear meter
• Accurate; suitable for fuel metering
• Suitable for low volume metering and laboratory or bench scale testing
• High permanent pressure drop at high flows
• Clear liquids only• High cost
Chapter 4: Fluids
NCEES 155
Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
Mec
hani
cal (
cont
'd) Nutating
DiskAlso known as a wobbly plate meter. Fluid enters a chamber of known volume. When the chamber is filled, the fluid is released, which causes the disk to perform a nutating action (wobble in a circular path without actually spinning on its axis). The motion is detected by either gearing or magnetic transducers. The flow rate is determined from the rate of motions.
SHAFTHOLE
NUTATING DISK
OUTLETINLET
• Accurate and repeatable; used for water service metering
• Good for hot liquids
• Accuracy is ad-versely affected by viscosities below the meter's desig-nated threshold
Helical Counter-rotation of the gears carries known volumes of liquid axially down the length of the gears. The rotation rate is measured using sensors, which in turn correlates to flow rate.
Source: Flowserve Corp., Irving, TX
• Used for heavy and high-viscous liquids
• Highest accuracy of any positive displacement flow-meter
• Can only measure liquids
• Low corrosion al-lowance
• Cannot handle abrasive fluids
Rotameter (variable area)
Fluid flows upward through a clear tapered tube and suspends a bob. The higher the flow rate, the higher the bob suspends in the tube. The bob is the indicator and the reading is obtained from the scale marked on the tube.
FLOW
FLOW
PIPE
TAPERED TUBE
BOB
• Simple operation with few moving parts and no exter-nal power source
• Inexpensive and widely available
• Accurate provided the fluid properties remain unchanged
• Resistant to shock and chemical ac-tion
• Cannot be read by machine
• Must be mounted vertically
• Changes in fluid properties gives erroneous results
• Not suited for large pipes (< 6 inches)
• Readout uncertainty near bottom of the scale
• Some fluids may obscure reading.
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Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
Mec
hani
cal (
cont
'd) Turbine (or
Woltmann Type)
Fluid flows past a turbine wheel positioned in the center of the pipe with the shaft in line with the pipe. The rotational speed is proportional to the flow rate. Shaft rotation is detected electronically.
FLOW
METERHOUSING
TURBINEROTORSUPPORT
ELECTRONICPICKUP
• Simple and du-rable structure; can be installed vertically or hori-zontally
• Can be designed to detect flow in either direction
• Operates under a wide range of temperatures and pressures
• Low pressure drop across the flow meter
• Effective in ap-plications with steady, high-speed flows
• Can be used for gasses but not suit-able for steam
• Cannot tolerate cavitation
• Accuracy ad-versely affected by entrained gas
• Sensitive to chang-es in fluid viscosity
• Long straight runs of pipe upstream and downstream of the meter are needed
• Bearings are prone to wear (though some are provided “bearingless”)
• Not suitable for steam
Paddle Wheel Type
Fluid flows past a paddle wheel positioned off-center of the pipe with the shaft perpendicular with the pipe. The rotational speed is proportional to the flow rate. Shaft rotation is detected electronically.
FLOW ROTATION
PADDLE WHEEL
DETECTOR(MOUNTED
EXTERNALLY)
Other meters in this class: Single Jet Multi Jet Pelton Wheel
• Simple and du-rable structure; can be installed vertically or hori-zontally
• Easy installation into existing sys-tems for insertion models
• Can be designed to detect flow in either direction
• Operates under a wide range of temperatures and pressures
• Low pressure drop across the flow meter
• Effective in ap-plications with steady, high-speed flows
• Requires a full pipe of liquid
• Not suitable for steam
• Bearings are prone to wear
Chapter 4: Fluids
NCEES 157
Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
Pres
sure Venturi The meter constricts the fluid flow and sensors
measure the differential pressure before and within the constriction. The differential pressure is then converted to a corresponding flow rate.
FLOW
PRESSURE MEASUREMENT
• Highly accurate over a wide range of flows
• No moving parts• Low pressure drop
• Flow must be derived from pres-sure drop
• Pipe must be full (mostly used for liquid service)
• Occupies space ( DL of approxi-
mately 50)• Cannot measure
fluids in reverse flow
Orifice Plate (also square-edge orifice plate)
Flow is restricted using a plate with a hole drilled through it. Sensors measure the differential pres-sure before and after the meter (two tap configura-tions are shown). The differential pressure is then converted to a corresponding flow rate.
FLOW
dP MEASUREMENT(FOR FLANGE TAP OPTION)
dP
dP
dP MEASUREMENT(FOR VENA CONTRACTATAP OPTION)
Note: Orifices may be drilled in the middle of the plate (concentric) or off-center (eccentric) to ac-commodate certain fluid types and flow regimes. Orifices may also be round or segmented.
• Accurate over a wide range of flows, but not suit- able for trade use (2–4% of full scale)
• No moving parts• Low cost; price
does not drama-tically increase with pipe size
• Low maintenance (orifice plates can be replaced dur-ing maintenance operations)
• Easy to convert to different applica-tions or fluids by replacing the orifice plate
• In common use
• Flow must be derived from pres-sure drop
• Accuracy reduced at low flows
• Plate materials prone to wear and corrosion, which adversely effects accuracy
• Accuracy effected by high-viscous fluids
• Moderate to high permanent pres-sure drop
• Pipe must be full (for liquids)
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158 NCEES
Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
Pres
sure
(con
t'd) Nozzle Similar to a venturi meter, but the inlet section is
in the shape of an ellipse and there is no exit sec-tion.
FLOW
dP MEASUREMENTdP
• More accurate than orifice plates
• High flow capa-city and high velocity applica-tions
• Less susceptible to wear and corro-sion than orifice plates
• Can operate in higher turbulence
• Tolerant of fluids containing sus-pended solids
• Less expensive than the venturi meter
• Physically smaller than the venturi meter
• Can indicate a reverse-flow condition
• Flow must be derived from pres-sure drop
• More expensive than orifice plates
• Takes up slightly more room than orifice plates
• Higher permanent pressure drop than venturi meters
• Pipe must be full (for liquids)
Dall Tube Similar to the venturi meter but more compact at the expense of some loss in accuracy and addi-tional permanent pressure loss.
FLOW
dP
• Similar perfor-mance as the venturi meter
• Shorter length than the venturi meter
• Low unrecover-able pressure loss
• Accurate to within 1% of full scale
• More expensive than orifice plates or flow nozzle meters
• Sensitive to turbu-lence
• More complex to manufacture
• Accuracy depen-dent on actual flow data
• Cannot indicate a reverse-flow condition
Chapter 4: Fluids
NCEES 159
Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
Pres
sure
(con
t'd) Wedge Similar in principle to the orifice meter, a wedge
placed in the flow stream creates the differential pressure element. The fluid is forced downward, similar to a segmented orifice plate, but is guided along a sloping wedge shape rather than a sharp edge. The differential pressure is then converted to a corresponding flow rate.
FLOW
WEDGE
dP
• Well suited for sludge, slurry, or high-viscous fluid service
• Differential pres-sure to flow rate dependent on em-pirical data unique to each model and application
• High permanent pressure drop
Pitot Tube The pitot tube is primarily used for gas or air service. The Pitot tube measures the total pres-sure (dynamic and static pressures combined). The static tube measures the static pressure only. The difference between the two measurements reveals that the dynamic pressure is converted into flow rate.
STATIC TUBE
PITOT TUBE
dP
FLOW
Note: The pitot tube (impact tube) and the static tube are sometimes provided within a single ele-ment.
• Essentially no pressure drop
• Easy to install and use
• Instrument can be removed when not in service
• Can be used to measure gas velocities and to establish a velo-city profile
• Low accuracy (dif-ferential pressure between static and dynamic is small and therefore prone to error)
• Accuracy depen-dent on placement within the flow cross-section
• Low rangeability• Requires clean
fluids (tube easily plugs)
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160 NCEES
Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
Pres
sure
(con
t'd) Annubar The annubar or averaging pitot-tube flow meter
measures the difference between the total pressure (upstream) and the static pressure (downstream) to derive the flow rate.
dP
FLOW DOWNSTREAMSENSINGPORTS
SIMPLIFIED CROSS-SECTIONOF SENSING (IMPACT) TUBE
UPSTREAMSENSINGPORTS
ANNUBAR(IMPACT TUBE)
FLOW
Note: Temperature elements can be made integral with the impact tube to provide temperature com-pensation and corrections.
• Accurate (1% of full scale)
• Compact design (sensing lines not required)
• Not suitable for dirty or viscous fluids
• Element must be centered within the pipe
Cone (or V-Cone)
A cone is inserted in the flow stream to create a differential pressure similar to a venturi meter or Dall tube meter, which is then correlated to flow rate.
FLOW
dP
• Excellent accu-racy (0.5% of full scale)
• Suitable for fluids with suspended solids
• Compact design (0–2 pipe dia-meters)
• Suitable for gas flow measurement
• Moderate perma-nent pressure drop
• Requires exten-sive calibration to achieve rated accuracy
• Must operate within rated β-ratio range
Chapter 4: Fluids
NCEES 161
Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
The
rmal Thermal
Mass Meters
A known amount of heat is applied to the heating element. Some of this heat is lost to the flowing fluid. As flow increases, more heat is lost. The amount of heat lost is sensed using temperature el-ements (comparing the upstream and downstream values). The fluid flow is derived from the known heat input and the temperature measurements.
HEATING ELEMENT DOWNSTREAMTEMPERATUREELEMENT
UPSTREAMTEMPERATUREELEMENT
FLOW
T2T1 ==
• Used primarily for gas service (stack flow measurement and emissions monitoring)
• Low pressure drop• The temperature
and heating ele-ments come in a single element assembly for a compact design
• Detects low flows (laminar flows)
• Can be used as a velocity meter
• Results are in true mass flow
• Thermal properties of the gas must be known
• Moderate accuracy• Not for steam
service
Vort
ex Vortex Shedding
Vortices (or eddy currents) created by an obstruc-tion are detected by ultrasonic or optical transduc-ers. The rate of vortex formation and subsequent shedding caused by the bluff body or obstruction is proportional to the fluid velocity.
RECEIVINGTRANSDUCER
EDDYS (VORTICES)
TRANSMITTINGTRANSDUCER
BLUFF BODY(STRUT)
FLOWFLOW
• Can be used for liquids, gases, and steam
• Low wear• Low cost to install
and maintain• Low sensitivity to
variations in pro-cess conditions
• Stable long-term accuracy and repeatability
• Applicable to a wide range of pro-cess temperatures
• Available for a wide variety of pipe sizes
• Not suitable for low flow rates
• Minimum length of straight pipe is required upstream and downstream of the meter
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Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
Mag
netic Mag Meter The operation of a magnetic flow meter or mag
meter is based upon Faraday's Law, which states that the voltage induced across any conductor as it moves at right angles through a magnetic field is proportional to the velocity of that conductor.
E u B D\ # #
where
E = voltage generated in a conductor
u = velocity of the conductor
B = magnetic field strength
D = length of the conductor
The flowmeter applies a magnetic field through the entire cross-section of the flow tube. The velocity is then determined by the meter by measuring the magnetic strength.
• Ideal for dirty water or other con-ductive fluids
• Suitable for fluids with two-phase flow
• No pressure drop (models are avail-able for full pipe bores)
• Accurate• Measures true
volumetric flow
• Does not work on nonconductive fluids (e.g., hydro-carbons)
• Expensive• Does not correlate
to mass flow until fluid or bulk slurry density is known
Ultr
ason
ic For a simple Doppler system, sound waves are used to determine the velocity of a fluid flowing in a pipe. At zero flow, the frequencies of an ultrason-ic wave transmitted into a pipe and its reflections from the fluid are the same. At flow, the frequency of the reflected wave is different because of the Doppler effect. As fluid velocity increases, the frequency shift increases linearly. A transmitter evaluates the frequency shift to determine the flow rate.
For a Transit time system, ultrasonic waves are sent and received between transducers in both directions in the pipe. At zero flow, it takes the same time to travel upstream and downstream be-tween the transducers. At flow, the upstream wave travels more slowly and takes more time than the downstream wave. As fluid velocity increases, the difference between the upstream and downstream times also increases. A transmitter evaluates the delay times to determine the flow rate.
Note: Either method can be deployed as a clamp-on unit (dry) or be installed integral to the fluid (wet).
• Sufficiently ac-curate for custody transfer
• Clamp-on systems suitable for field testing and verifi-cation of installed flow meters
• Expensive• Sensitive to stray
vibrations• Unwanted
attenuation can occur
• Fluid must be able to transmit ultra-sonic waves
Chapter 4: Fluids
NCEES 163
Flow Measurement Devices (cont'd)Class Meter Type Description Advantages Drawbacks
Impu
lse Coriolis A Coriolis flow meter uses the natural phenom-
enon in which an object begins to “drift” as it travels from or toward the center of a rotation occurring in the surrounding environment. Coriolis flow meters generate this effect by diverting the fluid flow through a pair of parallel U-tubes with an induced vibration (by an actuator, not shown) perpendicular to the flow. The vibration simulates a rotation of the pipe and the resulting Coriolis “drift” in the fluid causes the U-tubes to twist and deviate from their parallel alignment. The force producing this deviation is proportional to the mass flow rate through the U-tubes.
FLOWVIBRATIONVIBRATION
NO DEFLECTION DEFLECTION
• Suitable for highly viscous fluids
• Insensitive to tem-perature and fluid properties
• Measures mass flow rate directly
• Not accurate for gases at low flow rates
• High permanent pressure drop
4.5.3 Orifice, Nozzle, and Venturi Meters
4.5.3.1 Square-Edge Orifice Meter (Vena Contracta Taps)
FLOW
SQUARE-EDGE ORIFICE METER
d2
Re
104
0.60
0.62
0.64
0.66
0.58105 105 107 108
d2d2
2
d1
C orific
e
DISCHARGE COEFFICIENTCorifice FOR SQUARE-EDGEORIFICE METERS
d2
d1——β = = 0.7
0.60.5
0.40.2
PE Chemical Reference Handbook
164 NCEES
Flow Coefficient (C) and Orifice Loss Coefficient
CC
KC11orifice
4 2 4
2,
b b
b=−
−
Incompressible Flow
V C Ag P2
orificectD=o
Compressible Flow
V Y C Ag P2
orificectD=o
where Y = net expansion factor
4.5.3.2 Flow Nozzle Meter
FLOW
NOZZLE METER Re
1040.94
0.96
0.98
1.00
105 105 107 108
C orific
e
d2
d2 d1
d2
2
d2
d1——β = = 0.8
0.60.4
0.2
DISCHARGE COEFFICIENTCorifice FOR NOZZLE METERS
Flow Coefficient (C)
C
C1nozzle
4b=
−
Incompressible Flow
V C A
g P2nozzle
ctD=o
Compressible Flow
V Y C A
g P2nozzle
ctD=o
where Y = net expansion factor
Chapter 4: Fluids
NCEES 165
4.5.3.3 Venturi Flow Nozzle MeterThe Venturi discharge coefficient is a function of the specific geometry of the meter.
FLOW
PRESSURE MEASUREMENT
Flow Coefficient (C)
C
C1venturi
4b=
−
Incompressible Flow
V C A
g P2venturi
ctD=o
Compressible Flow
V Y C A
g P2venturi
ctD=o
where Y = net expansion factor
4.5.3.4 Pitot Tube Flow Meter
STATIC TUBE
PITOT TUBE(OR IMPACT TUBE)
FLOW
P1 P2
P1 measures the static pressure. Assuming elevation effects are negligible, P2 is the stagnation pressure:
P gu2 c
1
2t+
Therefore:
u
g P P2 c 2 1t=
−_ i
PE Chemical Reference Handbook
166 NCEES
4.5.3.5 Permanent Pressure Drop PERMANENT PRESSURE DROP
FLOW
P1
P 1
P 2
P 2
FLOW RESTRICTION
PERMANENTPRESSURE
DROP
P VC
P vc
P = P 2 – P 1 (P vc – P 1) (1 – 1.9 )
VENA CONTRACTA
The fraction of the orifice differential pressure that is permanently lost can be approximated by the relation, 1 – β1.9. Therefore, the permanent pressure drop for orifice meters for incompressible fluids is
A Area ft2 or in2 m2 A Absorption factor dimensionless
a Effective interfacial mass-transfer area per unit volumeftft3
2
mm3
2
B Bottom product flow rate hrlb mole
smol
c Concentration ftlb mole
3 mmol
3
cp Heat capacity lbm FBtu-c kg K
Js Km2
2
: :=
D Distillate flow rate hrlb mole
smol
DAB Mass diffusivity (diffusion coefficient)hrft2
sm2
D, d Diameter ft or in. mE Efficiency dimensionless
F Molar feed flow hrlb mole
smol
f Ratio of vapor phase flow to feed flow (fraction vaporized) dimensionlessf Darcy friction factor dimensionless
f Fugacity of a pure component inlbf
2 Pa mN
m skg
2 2:= =
ft Fugacity of a component in a mixture inlbf
2 Pa mN
m skg
2 2:= =
PE Chemical Reference Handbook
178 NCEES
Symbols (cont'd)Symbol Description Units (U.S.) Units (SI)
G Gas flow rate (stripper/absorber) hrlb mole
smol
GS Gas flow rate, solute-free basis hrlb mole
smol
g Gravitational accelerationsecft
2 sm2
gt Molar Gibbs free energy lb moleBtu
molJ
H Henry’s Law constant inlbf
2 Pa mN
m skg
2 2:= =
HD Heat input hrBtu
W sJ
skg m
3
2:= =
h Height ft or in. mh Head loss, pressure drop ft or in. m
h Specific enthalpy lbmBtu kg
Jsm2
2
=
ht Molar specific enthalpy lb moleBtu
molJ
hD Specific enthalpy change lbmBtu kg
Jsm2
2
=
hvapD Heat of vaporization lbmBtu
kgJ
sm2
2
=
HTU Height of a transfer unit ft or in. mj Colburn Factor dimensionless
jA Molar flux of component A per area ft hrlb mole-2 m s
mol2 :
K Distribution coefficient for phase equilibrium dimensionless
k Mass transfer coefficient hrft
sm
kc Convective mass transfer coefficient hrft
sm
L Liquid flow (for a flash, in a column, stripper, or absorber) hrlb mole
smol
LS Liquid flow rate, solute-free basis hrlb mole
smol
l Length, distance ft or in. m
m Mass lbm kgm General phase equilibrium coefficient dimensionlessm Slope of the operating line or slope of the equilibrium line dimensionless
MW Molecular weight lb molelbm
molkg
N Number of stages dimensionlessn Number of moles lb mole mol
Chapter 5: Mass Transfer
NCEES 179
Symbols (cont'd)Symbol Description Units (U.S.) Units (SI)
no Molar flow per area ft hrlb mole-2 m s
mol2 :
NTU Number of transfer units dimensionless
P Pressure inlbf
2 Pa mN
m skg
2 2:= =
Pc Critical pressure inlbf
2 Pa mN
m skg
2 2:= =
Pr Reduced pressure dimensionless
P* Three-phase equilibrium pressure inlbf
2 Pa mN
m skg
2 2:= =
p Partial pressure inlbf
2 Pa mN
m skg
2 2:= =
psat Saturation pressure, or vapor pressure inlbf
2 Pa mN
m skg
2 2:= =
/ Poynting correction factor dimensionless
q Ratio of liquid phase flow to feed flow dimensionless
Qo Heat duty hrBtu W s
Js
kg m3
2:= =
q Ratio of liquid phase flow to feed flow (fraction not vaporized) dimensionless
R Reflux ratio dimensionless
R Universal gas constant lb mole RBtu
-c mol KJ:
S Boil-up ratio dimensionlessS Stripping factor dimensionlessT Temperature °R or °F K or °CTc Critical temperature °R or °F K or °CTr Reduced temperature dimensionless
u Velocity secft s
m
V Volume ft3 m3
V Vapor flow (for a flash, in a column, stripper, or absorber) hrlb mole
smol
vt Molar volume lb moleft3
molm3
v Specific volume lbmft3
kgm3
vD Specific volume change during phase change lb moleft3
molm3
X Mole ratio in liquid phase (solute-free basis) dimensionlessx Mole fraction in liquid phase dimensionlessY Mole ratio in vapor phase (solute-free basis) dimensionless
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180 NCEES
Symbols (cont'd)Symbol Description Units (U.S.) Units (SI)
y Mole fraction in vapor phase dimensionlessZ Compressibility factor dimensionlessz Mole fraction in the feed dimensionlessz Distance or length ft or in. m
a Interfacial area per unit volumeftft3
2
mm
3
2
aij Relative volatility for components i and j dimensionless
d Film thickness ft or in. mg Activity coefficient dimensionless
g Surface tension inlbf m
Nskg2=
e Void fraction dimensionless
m Dynamic viscosity seccP ftlbmor - Pa s m s
kg: :=
r Density ftlbm
3 mkg
3
zFugacity coefficient of a pure component in the vapor phase dimensionless
ztFugacity coefficient of a component in a mixture in the vapor phase dimensionless
dz Volume fraction of the dispersed phase (holdup) dimensionless
5.2 Phase Equilibria
5.2.1 Phase Equilibrium Applications
5.2.1.1 Distribution of Components Between Phases in a Vapor/Liquid EquilibriumAssume Dalton’s Law and Raoult’s Law apply. The distribution coefficient is defined as:
K xy
Pp sat
i ii i= =
where Ki = distribution coefficient for component i
The relative volatility is defined as:
KK
y xy x
ij j
ij i
i ja = =
where aij = relative volatility for components i and j
For a binary system, the following expressions may be derived:
( ) ( )y xx
K x K KK x
1 111 12
1 12
2 1 1 2
1 1aa= + − = + −
( ) ( )x yy
K y K KK y
111 1 1
1
1 1 2 1
2 1
2 2a a= + − = + −
Chapter 5: Mass Transfer
NCEES 181
5.2.1.2 Dew PointThe dew point is defined as the point where the vapor reaches saturation and the liquid phase begins to form. It may be determined by iterative calculations from one of the following three relationships, given the vapor composition and either pressure or temperature:
or orx Ky
x py P
P
py1 1 1
i
n n n
sat
n
ni i
i
ii
i i
i
i
isati
i1 1 1 1
1
= = = = == = = =
= f p/ / / /
/
If ,Ky
1>n
i
i
i 1=/ increase temperature or decrease total pressure.
If ,Ky
1<n
i
i
i 1=/ decrease temperature or increase total pressure.
5.2.1.3 Bubble PointSimilarly, the bubble point is defined as the temperature/pressure combination in which the first bubble of vapor is formed in a liquid. It may be determined by iterative calculations from one of the following three relationships, given the liquid composition and either pressure or temperature:
or ory K x y Px p
P x p1 1,,
n n nsat
n
sat
n
ii
i ii
ii
i i
ii i
i1 1 1 1 1= = = = =
= = = = =/ / / / /
If ,K x 1>
n
i ii 1=/ decrease temperature or increase total pressure.
If ,K x 1<n
i ii 1=/ increase temperature or decrease total pressure.
5.2.1.4 Single-Stage FlashA single-stage flash determines the distribution of components between the liquid and vapor phase. It may be determined by iterative calculations from one of the following two relationships, given the feed composition, the relative proportions of vapor and liquid resulting from the flash, and either pressure or temperature:
( ) ( )orx f Kz
y f Kz K
1 1 1 1 1 1n n n n
ii i
i
ii
i i
i i
i1 1 1 1= + − = = + − =
= = = =/ / / /
where
zi = mole fraction of component in the feed
f = ratio of vapor phase flow to the feed flow
The lever rule may be applied to binary single-stage flash calculations as follows:
FV f y x
z x
FL f y x
y z1
i i
i i
i i
i i
= = −−
= − = −−
F, zi, fi
L, xi
V, yi
T, Ptot
PE Chemical Reference Handbook
182 NCEES
5.2.2 Diffusion
5.2.2.1 Fick’s Law of Diffusion: Molar Flux j D dz
Past single spheres Re Sc .0 5ll = 1.8–600,000 Sc = 0.6–3200
.Sh Sh Re Sc0 347 . .0
0 5 0 62= + ll_ i
. . ( ). . ( )
Sh Gr Sc Sc Gr ScGr Sc Gr Sc
2 0 0 0254 102 0 0 569 10<
. .
.
M M
M M0 0 333 0 244 8
0 250 8
2=
++* 4
Through fixed beds of pellets3
Rell = 90–4000 Sc = 0.6
.j j Re2 06 .M H
0 575f= = −
ll^ h
Rell = 5000–10,300 Sc = 0.6
. .j j Re0 95 20 4 .M H
0 815f= = −
ll^ h
Rell =0.0016–55 Sc = 168–70,600
.j Re1 09 /M
2 3f= −
ll^ h
Rell = 5–1500 Sc = 168–70,600
.j Re0 250 .M
0 31f= −
ll^ h
1. Average mass-transfer coefficients throughout, for constant solute concentrations at the phase surface. Generally, fluid properties are evaluated at the average conditions between the phase surface and the bulk fluid. The heat-mass-transfer analogy is valid throughout.
2. Mass-transfer data for this case scatter badly but are reasonably well represented by setting jM = jH.
PE Chemical Reference Handbook
186 NCEES
3. For fixed beds, the relation between e and dp is –
a d6 1
p
f=^ h
, where a is the specific solid surface, surface per volume of bed. For mixed sizes:
d
n d
n dp
i pii
i piin
n
2
1
3
1=
=
=
/
/
4. For small rates of flow or long contact times:
.Dk
Sh 3 41,
AB
L avav .
d=
For large Reynold numbers of short contact times:
k l
D6,l av
AB21
rtdC= e o
Sh l Re Sc23
av21
rd= c m
Total absorption rate from the average kL:
N lu
c c k c c, , , ,A avy
A l A L av A i A M0d
= − = −r
r r` `j j
ln
c c
c c
c c
c c c c,
, ,
,
, , ,A i A M
A i A l
A i A
A i A A i A l
0
0− =
−
−
− − −r
r
r` `
``
`j jjj
jR
T
SSSSSSS
V
X
WWWWWWWwhere
a = specific surface of a fixed bed of pellets, pellet surface/volume of bed
cA,i = concentration of A at the interface
cA0 = concentration of A at the approach, or initial, value
c A = bulk-average concentration of A
c ,A l = bulk-average concentration of A across length l
DAB = molecular diffusivity of A in B
dc = diameter of a cylinder
de = equivalent diameter of a noncircular duct = 4 (cross-sectional area)/perimeter
dp = diameter of a sphere; for a nonspherical particle, diameter of a sphere of the same surface as the particle
G = mass velocity
GrM = Grashof number for mass transfer gl3 2
ttntD d n
k = mass-transfer coefficient
kl,av = average mass-transfer coefficient across length l
l = length
Chapter 5: Mass Transfer
NCEES 187
NA,av = average mass-transfer flux of A at, and relative to, a phase boundary
ni = a number, demensionless
Nu = Nusselt number khd
Pr = Prandtl number k
cpn
Pr0 = Prandtl number at the approach, or initial, value
Pri = Prandtl number at the interface
Re = Reynolds number dGn or lGn
Re' = Reynolds number for flow outside a cylinder d Gcn
Re'' = Reynolds number for flow past a sphere d Gpn
Ree = Reynolds number for flow in a noncircular duct d Gen
Rex = Reynolds number with x as the length dimension xGn
Sc = Schmidt number DABtn
Sh = Sherwood number Dk lAB
Sh0 = Sherwood number at the approach, or initial, value
Shi = Sherwood number at the interface
u y = bulk average velocity in the y direction (parallel to the direction of flow)
C = mass flow rate per unit width
d = thickness of a layer
e = void fraction
Source: Treybal, Robert, Mass Transfer Operations, New York: McGraw-Hill, 1987, pp. 74–75.
5.2.2.4 Mass Transfer with ReactionConsider a reaction between a dissolving gas A and a liquid phase reactant B, with q moles of B reacting per mole of A, so that:
A B Productsn m "+
q nm=
where
q = number of moles of B reacting per mole of A
CAL and CBL = molar concentrations of A and B, respectively, in the liquid
PE Chemical Reference Handbook
188 NCEES
The rate of reaction of A, JL, is then given by
J k C CL nm ALn
BLm=
where knm = reaction velocity constant, in mol
mm n3 1+ −
d nJL has units, moles/sec/unit volume of liquid. Alternatively,
J k C Cnm ALn
BLm
Lf=
JL is the rate of reaction and has units of s mmol
3:, n and m are the orders of reaction in A and B, and Lf is the liquid
hold-up fraction. A "reaction time" tR can be defined as
( )nt
k C C21
( )Rnm AL
nBLm1=
+−
The mass transfer of A in the liquid is given by
( )J k a C C*L AL AL= −
where
J = reaction rate in moles/sec/unit volume of reactor
C*AL = dissolved gas concentration in liquid bulk in
mmol3
kL = interphase mass-transfer coefficient in sm
a = gas-liquid interphase surface area/unit dispersion volume in m1
J is the rate of reaction and has units of s mmol
3:. A mass-transfer "diffusion time," tD, can be defined as
tkD
DL
AL2=
where DAL = diffusivity of A in the liquid
If a fast reaction is occurring near the interface within the "diffusion film," it will enhance the mass-transfer rate and the equation for the mass transfer of A into liquid, above, becomes
( )J k a C C* *L AL AL= −
( )n
k D k C C C1
2** ( )
LAL nm AL AL
nBLm1 2
1
=+− −
= Gwhere k*L = enhanced liquid-film mass-transfer coefficient in s
m
Chapter 5: Mass Transfer
NCEES 189
Various Gas-Liquid Reaction Regimes and Parameters of ImportanceRegime Conditions Important Variables Concentration Profiles
I Kinetic control
Slow reaction
.tt
0 02RD 1
Rate \ Le \ knm
\ C*AL
n` j \ C*
BLm` j
Independent of a (if a is adequate) Independent of kL
GAS
LIQUID
FILM BULKCBL
CAL
CAL*
II Diffusion control
Moderately fast reaction in bulk of liquid, C 0AL .
. tt
0 02 2RD1 1
Design so that
a kD
100L
L
AL2e
Rate \ a \ kL
\ C*AL
Independent of knm Independent of Le (if Le is adequate)
CBL
CAL
CAL*
III Fast reaction
Reaction in film, C 0AL . (pseudo first order in A' )
tt
qCC
2 *RD
AL
BL1 1
C C*BL AL22
Rate \ a
\ knm
\ C*AL
n21+
` cj m
Independent of kL Independent of Le
CBL
CAL
CAL*
IV Very fast reaction
General case of III tt
2RD1
C C*BL AL+
Rate \ a
depends on
k k C C*L nm AL BL
Independent of Le
CBL
CAL
CAL*
V Instantaneous reaction
Reaction at interface; controlled by transfer of B to interface from bulk, J k aL\
tt
qCC
*RD
AL
BL22
Rate \ a \ kL
Independent of C*AL
Independent of knm Independent of Le
CBL
CAL
CAL*
5.2.2.5 Mass Transfer Between Phases for Dilute Systems( ) ( ) ( ) ( )n k x x k y y k c c k p pA L i G i L i G i= − = − = − = −l lo
andk k k k PL L L G Gt= =l lr
yi
y
xi
x
T, ptot
MASS TRANSFER BETWEEN PHASES:LIQUID PHASE INTERFACE VAPOR PHASE
Lkl = liquid-phase mass-transfer coefficient (concentration basis)
kG = gas-phase mass-transfer coefficient (mole fraction basis)
k Gl = gas-phase mass-transfer coefficient (partial pressure basis)
LM = molar-liquid mass velocity, in moles/time/area
GM = molar-gas mass velocity, in moles/time/area
HTUL = height of a transfer unit based on liquid phase resistance
HTUG = height of a transfer unit based on vapor phase resistance
pi = partial pressure
Ltr = average molar density of liquid phase
In most types of separation equipment, the interfacial area for mass transfer cannot be accurately determined and transfer coefficients based on volume of the device are used:
andK a k a k am
K a mk a k a1 1 1 1 1G G L L G L
= + = +
where
a = effective interfacial mass-transfer area per unit volume, in ftft or
Overall Mass Transfer Coefficients KL and KG for Dilute Systems
( ) ( )n K x x K y yA L
eqG
eq= − = −o
where
xeq = liquid mole fraction in equilibrium with vapor phase
yeq = vapor mole fraction in equilibrium with liquid phase
Overall Mass-Transfer Coefficients for Dilute SystemsGas Phase Liquid Phase
Equilibrium: y = m • x K k km1 1
G G L= + K mk k
1 1 1L G L
= +
Use for: High solubility, low m; gas-phase resistance is controlling
Low solubility, high m; liquid-phase resistance is controlling
Chapter 5: Mass Transfer
NCEES 191
5.2.2.6 Mass Transfer Between Phases for Concentrated Systems ( ) ( ) ( ) ( )n x
k x xy
k y yx
K x xy
K y yA BM
L iBM
G i
BMeq
Leq
BMeq
Geq
=−
=−
=−
=−
ot t t t
( ) ( )
lnx
xx
x x
11
1 1BM
i
i
=
−−
− − −
__ i
j
( ) ( )
lnx
xx
x x
11
1 1BMeq
eq
eq=
−−
− − −
__ i
i ( ) ( )
lny
yy
y y
11
1 1BM
i
i
=
−
−− − −
`` j
j
( ) ( )
lny
y
yy y
1
11 1
BMeq
eq
eq=
−
−− − −
`` j
j k k y k P yG G BM G BM= = lt
Lk k x k P xL L BM L BM= = lt
x xy y
kk
k xk y
G HTU xL HTU y
i
i
G
L
G BM
L BM
M L BM
M G BM−−
= = =t
t
where
kGt = gas-phase mass-transfer coefficient for concentrated systems
KGt = overall gas-phase mass-transfer coefficient for concentrated systems
kLt = liquid-phase mass-transfer coefficient for concentrated systems
KLt = overall liquid-phase mass-transfer coefficient for concentrated systems
xBM = logarithmic-mean solvent concentration between bulk and interface
yBM = logarithmic-mean gas concentration between bulk and interface
LM = molar-liquid mass velocity, in moles/time/area
GM = molar-gas mass velocity, in moles/time/area
HTUL = height of a transfer unit based on liquid-phase resistance
HTUG = height of a transfer unit based on vapor-phase resistance
Overall Mass-Transfer Coefficients KLt and KG
t for Concentrated Systems
( )( )
K yy
k yx
k x xy y1 1 1
G BMeqBM
G BMeqBM
L i
eqi= + −
−t t t
( )( )
K xx
k xy
k y yx x1 1 1
L BMeqBM
L BMeqBM
G i
ieq
= + −−
t t t
PE Chemical Reference Handbook
192 NCEES
5.2.2.7 Height of a Transfer Unit HTU k a y
Gk aG
GG BM
M
G
M= = t
HTU k a x
Lk aL
L BM
M
L
ML = = t
HTU K a yG
K aG
yy
HTU LmG
yx
HTUOGG BM
eqM
G
M
BMeqBM
G M
M
BMeqBM
L= = = +t
HTU K a xL
K aL
xx
HTU mGL
xy
HTUOLL BM
eqM
L
M
BMeqBM
LM
M
BMeqBM
G= = = +t
where
HTUG = height of a transfer unit based on vapor-phase resistance
HTUOG = height of a overall vapor-phase mass-transfer unit
HTUL = height of a transfer unit based on liquid-phase resistance
HTUOL = height of a overall liquid-phase mass-transfer unit
Height Equivalent to One Theoretical Plate (HETP)
If equilibrium line and operating line are parallel L
mG1
M
M =e o, then:
HETP = HTU
If equilibrium line and operating line are straight, but not parallel, then:
lnHETPHTU
LmGLmG
1OG
M
M
M
M
=−
e o
5.3 Continuous Vapor-Liquid Contactors
5.3.1 Material and Energy Balances for Trayed and Packed Units
5.3.1.1 Theoretical StageAn ideal theoretical stage has the following characteristics:
1. It operates in steady state and has a liquid product and a vapor product.2. All vapor and liquid entering the stage are intimately contacted and perfectly mixed.3. Total vapor leaving the stage is in equilibrium with total liquid leaving the stage.
For a single binary distillation stage, the following balances and equilibrium relationships apply.
Chapter 5: Mass Transfer
NCEES 193
Overall mass balance:
Fn STAGE n(zn)
(yn)
(xn)
ΔHn
(yn+1)
(xn–1)
Vn+1
Vn
Ln
Ln–1F V L V Ln n n n n1 1+ + = ++ −
Component mass balance:
z F y V x L y V x Ln n n n n n n n n n1 1 1 1+ + = ++ + − −
Energy balance:
h F h V h L H h V h L, , , , ,f n n V n n L n n n V n n L n n1 1 1 1 D+ + + = ++ + − −t t t o t t
where
ht = molar specific enthalpy
Fn = feed flow to stage n
Vn = vapor flow leaving stage n
Ln = liquid flow leaving stage n
HnD o = heat input to stage n
Phase equilibrium:
y K xn n=
For binary system with relative volatility a12:
yx
x1 1n
n
n
12
12
a
a=+ −_ i
5.3.1.2 Constant Molal OverflowWhen the molar heats of vaporization of the components are nearly equal, the molar flow rates of the vapor and liquid are nearly constant in each section of the column.
In the rectifying section, the following assumptions then apply:
andL L L L V V Vn n0 1 1= = = = =
And in the stripping section, the following assumptions then apply:
andL L L V V VN m N m= = = =l l
where
L = liquid flow in the rectifying section
V = vapor flow in the rectifying section
Ll = liquid flow in the stripping section
V l = vapor flow in the stripping section
N = total number of stages
m = stage in stripping section
n = stage in rectifying section
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194 NCEES
5.3.1.3 Column Material Balance
Stage Model for Distillation
V1
V1
V2
Vn
Vn+1
Vf+1
VM+1
VN+1
STAGE N
STAGE M
STAGE f (FEED)
STAGE n
STAGE 1
STAGE MODELFOR DISTILLATION
RECT
IFYI
NG S
ECTI
ONST
RIPP
ING
SECT
ION
CONDENSERSTAGE 0
VfzF
F
VM
VN
L0
Qc
L0 D
Ln-1
Lf-1
LM-1
LN-1
REBOILERSTAGE N+1
LN
LN
B
LM
Lf
Ln
L1
XD
•
QR
XB
•
Chapter 5: Mass Transfer
NCEES 195
Overall mass balance:
F = D + B
Component mass balance:
z F x D x BF D B= +
Ratios:
FD
x xz xD B
F B= −−
FB
x xx zD B
D F= −−
For the rectifying section, the following balances apply:
D V L V L0 n n1 1= − = −+
x D y V x L y V x LD n n n n1 1 0 0 1 1= − = −+ +
For the stripping section, the following balances apply:
B L V L VN N m m1 1= − = −− +
x B x L y V x L y VB N N N N m m m m1 1 1 1= − = −− − + +
To calculate the composition on each stage (for constants L, Ll, V, and V l), for the
Rectifying section: y V
L x Vx D
L DL x L D
x DRR x R
x1 1n n
Dn
Dn
D1 = + = + + + = + + ++
Stripping section: y V
L x Vx B
L BL x L B
x BSS x S
x
BLBL
xBLx1
1 1m m
Bm
Bm
Bm
B1 = − = − − − = + − =
−−
−+ l
ll l
ll l
l
l
Reflux ratio (also called external reflux ratio):
R DL
DV D= = −
Boil-up ratio:
S BV
BL 1= = −l l
Slope of the operating line, for the
Rectifying section: slope VL
RR1= = +
Stripping section: slope VL
SS
BLBL
11
= = + =−l
ll
l
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196 NCEES
5.3.1.4 Graphical Solution for Binary Distillation (McCabe-Thiele Diagram)
McCabe-Thiele Diagram for Binary Distillation With Constant Molal Overflow and Constant Relative Volatility
xNxB
y1
y = x
y - INTERCEPT (x = 0)
x - INTERCEPT (y = 1)
xD
zF
xI
yI
q LINE
EQUILIBRIUM CURVE
yN+1
yNy = M
OLE
FRAC
TION
IN V
APOR
x = MOLE FRACTION IN LIQUID
STRIPPINGOPERATING LINE
RECTIFYING OPERATING LINE
C
D
AE
B
00
1
1
Equations for the McCabe-Thiele DiagramName Equations
Equilibrium Line ( )y xx
1 1aa= + −
Operating Line for the Rectifying Section
A
y VL x V
x DL DL x L D
x DRR x R
x1 1n n
Dn
Dn
D1 = + = + + + = + + ++
Slope: VL
RR
1= +y-Intercept (x = 0):
y Rx
L Dx D
1D D
x 0 = + = +=
Reflux Ratio:
R yx
1xD0
= −=
Operating Line for the Stripping Section
B
y V
L x Vx B
L BL x L B
x BSS x S
x
BLBL
xBLx1
1 1m m
Bm
Bm
Bm
B1 = − = − − − = + − =
−−
−+ l
ll l
ll l
l
l
BL f R f x x
x x1 1
D F
F B= − + + − −−l ` `j j
Slope:
VL
SS 1= +
ll
x-Intercept (y = 1):
xBL
x BL 1B
y 1 =+ −
= l
lBoil-up Ratio:
S xx x1 y
y B
1
1= −−
=
=
Chapter 5: Mass Transfer
NCEES 197
Equations for the McCabe-Thiele Diagram (cont'd)Name Equations
Feed Line
Cy f
fx fz
qqx q
z11 1
F F=−
+ = − − −
Slope:
ff
qq1
1−
= −
Intercept:
For x f1F $ -
x fz
qz
1yF F
0 = − ==
For x f1F # -
y fz f
qq z1
1xF F
1 =+ −
= −−
=
Feed Quality:
For y = 0 intercept:
f xz
q xz
1yF
yF
0 0= − =
= =
For x = 1 intercept
f yz
q yz y
11
1x
F
x
F x
1 1
1= −−
= −−
= =
=
Intersection of Feed Line/ Operating Lines
D
x f
zRx
R ff R
1 11
IF D= − + + −
+e ^o h
y f
zfz
Rx
R ff R
1 11 1
IF F D= + − + + −
− +e ` ^o j h
Intersection of Feed Line/ Equilibrium Line
E
For constant a:
x f
zff
fz
ff
fz
21
11
1 1 1 41
11
1 1 1 1 1F F F
2
a a
aa a
a
a=− − + − −
− −+ − + − −
− −−
− −_ ` _ ` _ `i j i j i j> >H H
y x ff
fz1 F= − +e o
Operating Line for Total Reflux y x=
Operating Line for Minimum Reflux R y x
x ymin
F F
D F= −−
Circled A, B, C, D, and E in table above refer to the previous graph, "Binary Distillation With Constant Molal Overflow."
PE Chemical Reference Handbook
198 NCEES
5.3.1.5 Feed ConditionsThe feed condition is defined by
q = mole fraction liquid in feed
= molar enthalpy of vaporizationm lar enthalpy to c nvert feed to saturated vap rq q q
f = mole fraction vapor in feed
q + f = 1
L L q F L f F1= + = + −l ` j
V V q F V f F1= + − = +l l` j
Feed ConditionsFeed Condition Values for f and q Flows at Feed Location Feed Line in McCabe-Thiele
Subcooled Liquid f < 0( )
f hc T T
vap
pL b F
D= −
−
q > 1( )
q hc T T
1vap
pL b F
D= +
−
F
L V
V 'L '
Bubble Point (Saturated Liquid)
f = 0
q = 1F
L V
V 'L '
Partially Vaporized 0 < f < 1
0 < q < 1
F
L
V 'L '
V
Chapter 5: Mass Transfer
NCEES 199
Feed Conditions (cont'd)Feed Condition Values for f and q Flows at Feed Location Feed Line in McCabe-Thiele
Dew Point (Saturated Vapor)
f = 1
q = 0
F
L V
V 'L '
Superheated Vapor f > 1( )
f hc T T
1vap
pV F d
D= +
−
q < 0 ( )
q hc T T
vap
pV F d
D= −
−
F
LV
V 'L '
where
cpL = heat capacity of the liquid
cpV = heat capacity of the vapor
TF = temperature of the feed
Tb = bubble point temperature of the liquid
Td = dew point temperature of the vapor
PE Chemical Reference Handbook
200 NCEES
5.3.1.6 Condensers
Types of CondensersTotal Condenser Partial Condenser
A total condenser does not represent a theo-retical stage.
A partial condenser represents a theoretical stage.
L1
V1
V1 y1
y1
x0
L0x0
x1
NOT A THEORETICAL STAGE
“STAGE” 0
STAGE 1
D
L1
V1
V1
V2
V2
y2
y2
y0 x0=
x1
A THEORETICAL STAGE
STAGE 1
STAGE 2 D
x N–1
y
yN
x N
ab
c
x
The triangle indicated by abc represents the top stage of the distillation column.
y
yN
yN+1
x N+1
ba
d c
e
x N–1x Nx
The triangle indicated by cde represents the top stage of the distillation column and the triangle indicated by abc represents the partial condenser.
Heat Duty: ( )Q V h D R h1TC vap vap1D D= = +o Heat Duty: Q L h D R hPC vap vap1D D= =o
For subcooled reflux:
If the reflux is subcooled, a portion of the vapor entering the top stage of the column will condense, providing heat to increase the liquid temperature to the bubble point. The additional amount of liquid that is condensed inside the column is determined by:
L hL c T T
vap
ER pR R1D
D=
−_ i
Chapter 5: Mass Transfer
NCEES 201
Effective reflux ratio (also called internal reflux ratio) for the stages in the column:
DL
DL L
D
L c hT T
1ER
ER pRvap
R1
D D=
+=
+−_ i> H
The temperature of the top stage in the column, T1, may be estimated as equal to the bubble point of the external reflux.
where
T1 = temperature of top stage
TR = temperature of the reflux
LER = external reflux (LER = RD)
DL = rate of liquid condensed on top stage of the column
cpR = heat capacity of the reflux
5.3.1.7 Reboilers
Types of ReboilersReboiler Without Mixing Reboiler With Mixing
If the vapor effluent from the reboiler is in equili-brium with the bottom product, then the reboiler represents a theoretical stage. Other examples: kettle reboiler, internal heating coil.
If liquid effluent from the reboiler mixes with the liquid from the bottom stage of the column, the reboiler does not represent a theoretical stage.
THEORETICALSTAGE
Vap
BOTTOMPRODUCT
HOTSTREAM
STAGEN+1
LNXN
LN+1XN+1
LNXN
VN+1YN+1
Liq
NOT ATHEORETICAL
STAGEVap
LIQUIDFROMTRAYS
BOTTOMPRODUCT
HOTSTREAM
Liq
Heat Duty: Q V h S B hR N vap vap1D D= =+o Heat Duty: Q V h S B hR R vap vapD D= =o
Heat Duty: Q B R f x xx x
f h1RD F
F BvapD= + − −
−−o ` j= G
PE Chemical Reference Handbook
202 NCEES
5.3.1.8 Minimum Flow Rates and Reflux
Underwood Method With No Distributed Nonkey Components
The Underwood method assumes constant relative volatilities and constant molal overflows, and it requires a trial-and-error solution.
First, by trial-and-error, find a value for φ that is between the relative volatilities of the light key and heavy key components. The relative volatilities are based on a characteristic temperature for the column, such as the bubble-point temperature of the distillate or the flashed feed temperature at the column pressure. The heavy key is the reference component j for the relative volatilities of each component i.
qz
f1 F
ij
ij ii/a {
a− = − =/
Second, calculate the value of φ from:
Rx
1minD
ij
ij ia {
a+ = −/
where
zfi = concentration of component i in the feed
q = moles of feed to stripping section per mole of feed
aij = relative volatility between components i and j
φ = adjustable parameter, which has no physical significance
fi = fraction of component i in the feed that is vaporized
5.3.1.9 Minimum and Theoretical Stages
Minimum Theoretical Stages: Fenske Equation
The Fenske equation applies when the relative volatility is constant across the column. If the relative volatility varies across the column, a geometric mean of the range of values for the relative volatility may be used as an approximation. For example:
/top botij
1 2a a a= ` j
or/
top mid botij1 3
a a a a= ` jFor a binary separation, the Fenske equation for the number of stages (including any theoretical stages represented by the condenser and reboiler) at total reflux is
N
ln
ln xx
xx
11
,min
D
DBB
1 2a=
−−= G
For a multicomponent separation —where 1 and 2 are the two components with the light key indicated by i and the heavy key indicated by j—the Fenske equation is
N
ln xxxx
minDD
B
B
ij
ji
i
j
a=> H
where Nmin = minimum number of stages, including any theoretical stages represented by the condenser and reboiler
Chapter 5: Mass Transfer
NCEES 203
Estimated Number of Theoretical Stages: Gilliland Correlation
Gilliland Correlation
1.0
1.0
0.80.60.4
0.2
0.2
0.10.080.06
0.6
0.04
0.40.04
R – RminR + 1
0.02
0.020.01
0.100.01
N –
N min
N +
1
Source: McCabe, Warren L., Julian C. Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed, New York: McGraw-Hill, 1993, p. 609.
Estimated Number of Theoretical Stages: Underwood Correlation
The Underwood correlation can be used for constant volatility and partial reflux.
Intersection of feed line with operating lines: x fx
Rx
R ff R
1 11
IF D= − + + −
+e ^o h
lnNx K K xx K K x
RI D
D I
1 2
1 2=− −
− −__ _
_ii i
i lnNx K K xx K K x
SB I
I B
1 2
1 2=− −
− −__
__ii
ii
PE Chemical Reference Handbook
204 NCEES
where
K1 , K2 = distribution coefficients of components 1 and 2
b = intercept of the operating line with the vertical axis
NR = number of stages in the rectifying section
NS = number of stages in the stripping section
5.3.1.10 Multicomponent Distillation
Key and Nonkey Components
Key components are the two components in a mixture that characterize the degree of separation or that may provide the basis for a separation to be achieved.
Light key: The more volatile of the two key components. Present in both the distillate and bottoms product, and recovered predominantly in the distillate product.
Heavy key: The less volatile of the two key components. Present in both the distillate and bottoms product, and recovered predominantly in the bottoms product.
Nonkey: Other components in the mixture to be separated.
Light nonkey: Components more volatile than the light key component. Present almost completely in the distillate product.
Heavy nonkey: Components less volatile than the heavy key component. Present almost completely in the bottoms product.
Distributed key: Components having volatility between that of the light key and heavy key. Present in both the distillate and bottoms product. Also called intermediate key.
5.3.1.11 Absorption and StrippingFor dilute solutions ( )x 1solvent . , use solute-free basis for the concentrations (X, Y) and the flow rates (GS, LS):
Absorption and Stripping (cont'd)Absorber Stripper
Efficiency
Ey y xy y
GLGL
EA
A A1
min
ineq
in
in out
act
N
N
1
1
=−
−=
=−−
+
+
_c
cim
m
Efficiency
Ex x xx x
LGLG
ES
S S1
min
ineq
in
in out
act
N
N
1
1
=−
−=
=−−
+
+
_c
cim
m
Theoretical Stages
ln
ln
for
N AA AEA E
N EE A1 1
A
A
=−+
= + =
c mTheoretical Stages
ln
ln
for
N SS S ES E
N EE S1 1
S
S
=−+
= + =
d n
NTU (Number of Transfer Units)
ln
NTU YY Y
Y
Y Y XY Y X
Y Y X Y Y X
OYlm
in out
lm
outeq
in
ineq
out
ineq
out outeq
in
D
D
=−
=
−−
− − −___
_iii
i8
>8B
HB
NTU (Number of Transfer Units)
ln
NTU XX X
X
X X YX X Y
X X Y X X Y
OXlm
in out
lm
outeq
in
ineq
out
ineq
out outeq
in
D
D
=−
=
−−
− − −___
_iii
i8
>8B
HB
where
DYlm = log mean concentration difference in the vapor phase (solute-free basis)
DXlm = log mean concentration difference in the liquid phase (solute-free basis)
NTUOY = overall number of transfer units based on the gas phase
NTUOX = overall number of transfer units based on the liquid phase
5.3.2 Design Parameters for Trayed Units
5.3.2.1 Primary Tray Unit Design Parameters• Number of passes• Tray spacing• Tray type• Outlet weir type and height• Downcomer type and area• Clearance under downcomer• Hole size, valve size, or bubble cap size and style• Fractional hole area for sieve and valve trays• Tray pressure drop• Tray efficiency• Tray capacity• Tray hydraulics (flooding)
Chapter 5: Mass Transfer
NCEES 207
Starting Dimensions for Cross-Flow Sieve TraysDimension (units) Vacuum Atmospheric Pressure
Source: Albright, Lyle F., Editor, Albright's Chemical Engineering Handbook, Chapter 12, "Distillation," by James R. Fair, Boca Raton, FL: CRC Press, 2009, p. 1027.
5.3.2.2 Tray Selection
Criteria for Selecting a Distillation Column DeviceCriterion Details
Vapor-Handling Capacity Entrainment flooding. At incipient flooding, the minimum column diameter is fixed.Liquid-Handling Capacity Fixes the size of downcomers. Downcomer backup can lead to flooding.
Mass-Transfer Efficiency Sets required height for a given number of theoretical stages. Efficiency can be a function of column diameter.
Flexibility Of concern when the column must be operated under a wide range of feed rates or when future capacity needs must be considered in the initial design.
Pressure Drop Low pressure drop is critical for vacuum columns, especially when a low bottoms temperature must be maintained.
Cost Consider total cost of the system, including auxiliary equipment; a more expensive device may lead to lower operating costs.
Design Limitations Device should be proven commercially. Also, the user needs to understand how the device was designed (if by a vendor).
Special Concerns Fouling, corrosion, ease of installation or removal, potential foaming problems, adequate residence time for reactions, special heat-transfer needs.
Source: Albright, Lyle F., Editor, Albright's Chemical Engineering Handbook, Chapter 12, "Distillation," by James R. Fair, Boca Raton, FL: CRC Press, 2009, p. 1008.
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208 NCEES
5.3.2.3 Common Types of Distillation Trays
Bubble Cap Tray (left) and Various Caps (right)
Sieve Tray (left) and Dual-Flow Tray (right)
Bubble Cap Trays
Chapter 5: Mass Transfer
NCEES 209
Sieve Trays
Valve Trays
5.3.2.4 Comparison of Common Types of Distillation Trays
Comparison of the Common Tray TypesFeature Sieve Trays Valve Trays Bubble-Cap Trays Dual-Flow Trays
Capacity High High to very high Moderately high Very highEfficiency High High Moderately high Lower than other types
Turndown
About 2:1; not gener-ally suitable for operation under variable loads
About 4–5:1; some special designs achieve (or claim) 10:1 or more
Excellent; better than valve trays; good at extremely low liquid rates
Low; even lower than sieve trays; unsuitable for variable load operation
Entrainment Moderate ModerateHigh; about 3 times higher than sieve trays
Low to moderate
Pressure Drop Moderate
Moderate; early designs somewhat higher; recent designs same as sieve trays
High Low to moderate
Cost Low About 20 percent higher than sieve trays
High; about 2–3 times the cost of sieve trays
Low
Maintenance Low Low to moderate Relatively high Low
Fouling Tendency Low Low to moderate High; tends to col-lect solids
Extremely low; suitable where fouling is extensive and for slurry handling
Effects of Corrosion Low Low to moderate High Very low
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210 NCEES
Comparison of the Common Tray Types (cont'd)Feature Sieve Trays Valve Trays Bubble-Cap Trays Dual-Flow Trays
Availability of Design Information Well-known Proprietary, but infor-
mation readily available Well-known Some information available
Other Instability sometimes occurs in large diameter (> 8 ft) columns
Main Applications
Most columns when turn-down is not critical
Most columns, services where turndown is important
Extremely low-flow conditions; where leakage must be minimized
Capacity revamps where ef-ficiency and turndown can be sacrificed; highly fouling and corrosive services
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, pp. 266–267.
5.3.2.5 Tray EfficiencyThe point efficiency is the ratio of the change of composition at a point to the change that would occur on a theoretical stage:
E y yy y
intOG
n n
n n
po1
1eq= −−
−
−f p The Murphree tray efficiency applies to an entire tray instead of to a single point on a tray:
E y yy y
MVneq
n
n n
tray1
1= −−
−
−f p Overall column efficiency:
E NN
OC a
t=
The overall column efficiency is related to the Murphree efficiency by:
lnln
withEE
m LV1 1
OCMV
m
mm=
+ −=
_ i8 B
where
EOC = overall column efficiency
EOG = point efficiency for a tray
EMV = Murphree tray efficiency
Nt = number of theoretical stages in a column
Na = number of actual stages in a column
yneq = vapor mole fraction in equilibrium with the liquid
l = ratio of slope of equilibrium curve to operating line
Chapter 5: Mass Transfer
NCEES 211
5.3.2.6 Hydraulic Model for Trays
The Hydraulic Model for Trays
LIQUID AND GAS
FROTH
LIQUID WITH BUBBLES
TRAY BELOW
TRAY ABOVE
AB
AN
ADB
ADT
hwhcl
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992. As shown in Green, Don W., and Robert H. Perry, Perry's Chemical Engineers'
Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-27.
Tray Area DefinitionsTray Area Symbol Definition
Total tower cross-sectional area AT The inside cross-section area of the empty tower without downcomers or trays
Net area AN
Total cross-section area minus the area at top of the downcomer; also referred to as free area; represents smallest area available for vapor flow in the intertray spacing
Bubbling area AB
Total tower cross-section area minus total downcomer area, downcomer seal area, and any other nonperforated regions; also referred to as the active area (Aa); represents the area available to vapor flow near the tray floor
Hole area Ah Total area of perforations on the tray; smallest area available for vapor passage
Slot area AS
Total vertical curtain area for all valves through which vapor passes in a hori-zontal direction as it leaves the valves, based on the narrowest opening of the valves; smallest area available for vapor flow on a valve tray
Open slot area ASo Slot area when all valves are fully opened
Fractional hole area AfRatio of hole area to bubbling area (in sieve trays) or slot area to bubbling area (in valve trays)
Downcomer top area ADT Area at top of downcomerDowncomer bottom area ADB Area at bottom of downcomer
PE Chemical Reference Handbook
212 NCEES
5.3.2.7 Definitions of Vapor LoadSeveral different parameters are used for characterization of the vapor load.
The vapor load (Vload), in sft or s
m3 3, is
V CFSloadL G
Gt tt= −
where
CFS = vapor flow rate at conditions, in secft or s
m3 3
rL, rG = densities of the liquid and gas phases, respectively
The F-factor for gas loading, in
sec ftlbft or
s mkgft
. .
3
0 5
3
0 5d en o
, is
F u Gt=
where u = superficial linear gas velocity
The C-factor for gas loading, in secft or s
m , is
C uL G
Gt tt= −
In practice, the F-factor and the C-factor may be based on bubbling area AB, net area AN, or some other area, depending on the source of data and correlations. Care must be taken to use the correct area basis, depending on the source.
These terms are related as follows:
C AV Fload
L Gt t= =
−
5.3.2.8 Definitions of Liquid Load The tray liquid load QL, in in.
gpmor hr m
m3
: , isgpm
Q LL W=
where
gpm = liquid volumetric flow rate, in mingal
or sm3
LW = outlet weir length, in inches or meters
The downcomer liquid load QD, in in.gpm
or secft or s
m , isgpm
Q ADDT
=
Chapter 5: Mass Transfer
NCEES 213
5.3.2.9 Flow Regimes on Trays
Flow Regimes
SPRAY
FROTH
EMULSION
FLOODING
Cs, V
APOR
LOAD
/A, ft
/sBUBBLE
LIQUID FLOW RATE PER WEIR LENGTH
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992. As shown in Green, Don W., and Robert H. Perry, Perry's Chemical Engineers'
Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-29.
Tray Performance Diagram
AREA OFSATISFACTORY OPERATION
EXCE
SSIVE
ENTR
AINMEN
T
VAPO
R FL
OW R
ATE
ENTRAINMENT FLOODING
DOWNCOMER FLOODING
DUMP POINT
LIQUID FLOW RATE
EXCESSIVE WEEPING
WEEP POINT
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, pp. 266–269.
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214 NCEES
5.3.2.10 Flooding
Effect of Design Parameters on FloodingDesign Parameters That
Lower Flooding PointSpray Entrainment
FloodingFroth Entrainment
FloodingDowncomer Backup
FloodingDowncomer Choke
FloodingLow bubbling area X X XLow fractional hole area (< 8%) X X X
Low tray spacing X X XHigh weirs (> 4 in) X XSmall weir length X XSmall clearance under downcomer X
Small downcomer top area X
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 274.
Entrainment Flooding
The correlations for entrainment given below are based on C-factors, specifically the Souders and Brown constant
CSB at the entrainment flood point, in secft or s
m .
C u, ,SB flood S floodL G
Gt tt= −
where uS,flood = superficial gas velocity at the entrainment flood point
Fair’s Entrainment Flooding Correlation
C u 20
, ,
. .
SB flood N floodL G
G0 2 0 5
v t tt= −c em o
where uN,flood = superficial gas velocity at the entrainment flood point based on the net area AN.
CSB,flood and uN,flood are based on the net area AN. The correlation is applicable to sieve trays, valve trays, and
bubble cap trays.
These restrictions apply:
1. System is nonfoaming or low-foaming.2. Weir height is less than 15 percent of tray spacing.3. Sieve-tray perforations are 13 mm (1/2 in.) or less in diameter.4. Ratio of slot (bubble cap), perforation (sieve), or full valve opening (valve plate) area Ah to active area Aa
is 0.1 or greater. Otherwise the value of uN,flood should be corrected using the table below:
AAa
h uN,flood Correction Factor
0.10 1.000.08 0.900.06 0.80
Chapter 5: Mass Transfer
NCEES 215
Fair's Entrainment Flooding Correlation
0.7
1.0 2.00.7
0.60.5
0.50.5
0.5, ft
/s0.2
20 σ
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.07
0.07
0.060.05
0.05
0.04
0.030.020.01 0.03
LG
C
gl
F
g
gl
=
=Unf
–
lv
sbflo
od,
_
PLATE SPACING36"
24"
18"
12"
9"6"
PLATE SPACING36"
24"
18"
12"
9"6"
ρ
ρ
ρ
ρρ
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 278.
Kister and Haas Entrainment Flooding Correlation
.C d
hS0 144
. . .
SBLH
LG
ct
2 0 125 0 1 0 5
tc
tt= e d do n n
where
dH = hole diameter
hct = clear liquid height at transition from froth to spray regime
g = surface tension
S = tray spacing
CSB and uflood are based on the net area AN. For surface tensions greater than 25 cmdyne
, use the value of 25 cmdyne
. The correlation applies to nonfoaming systems.
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216 NCEES
Recommended Range of Application: The Kister and Haas Entrainment Flood Correlation
Liquid viscosity 0.05–2.0 cPTray spacing 14–36 in. 4, 5Hole diameter 1/8–1 in.Fractional hole area 0.06–0.20 5Weir height 0–3 in.
1. At pressures above 150 psia, downcomer flood is often the capacity limitation. This limitation is not predicted by the correlation. Caution is required.
2. At high liquid loads (above 7–10 in.gpm
), downcomer flood is often the capacity limitation. This limitation is not predicted by the correlation. Caution is required.
3. Equation does not apply for liquid loads lower than 0.5 in.gpm
of weir. For this reason, this correlation must not be extended to lower liquid rates.
4. At lower tray spacing, entrainment flooding may be related to lifting of the froth envelope and to froth height rather than to spray height. This correlation must not be extended to lower tray spacing.
5. The correlation does not apply when the following three conditions occur simultaneously: (a) ratio of flow-path length to tray spacing is high, > 3; (b) liquid rate is high, < 6 in.
gpm of
weir; and (c) fractional hole area is high, > 11%. Under these conditions, entrainment flooding is related to vapor channeling and vapor cross-flow rather than to spray height.
5.3.2.11 Downcomer Backup FloodingThe downcomer backup is determined by a pressure balance for the downcomer:
hdc = ht + hw + how + hhg + hda
Chapter 5: Mass Transfer
NCEES 217
where
hdc = height of clear liquid in downcomer, in inch liquid or mm liquid
ht = total tray pressure drop
hw = height of weir at tray outlet
how = height of liquid crest over weir
hhg = liquid hydraulic gradient across tray
hda = head loss due to liquid flow under downcomer apron
The height of aerated liquid in the downcomer is determined by:
hh
dcdc
dcz
=l
where
h dcl = height of aerated liquid in downcomer
dcz = relative froth density (froth density to liquid density)
To prevent downcomer backup flooding, the following criterion must be met:
h S hdc W1 +l
Criteria for Downcomer Aeration FactorsFoaming Tendency
Bolles's Criteria1 Glitsch's Criteria2 Fair et al.'s Criteria3
Examples dcz Examples dcz Examples dcz
Low Low molecular weight hydrocar-bons4 and alcohols 0.6 .
ftlb1 0<G 3t 0.6
Rapid bubble rise systems, such as low gas density, low liquid viscosity systems
0.5
Moderate Distillation of medium molecular weight hydrocarbons 0.5 . .
ftlb1 0 3 0< <G 3t 0.5
High Mineral oil absorbers 0.4 .ftlb3 0>G 3t 0.4
Very high Amines, glycols 0.3
Slow bubble rise systems, such as high gas density, high liquid viscosity, foam-ing systems
0.2–0.3
Notes:1. "Distillation Theory and Practice: an Intensive Course," University of New South Wales/
University of Sydney, August 9–11, 1977.2. Glitsch, Inc. Ballast Tray Design Manual, 6th ed., Wichita, KS: Koch-Glitsch LP, 1993.3. Perry, R.H. and D.W. Green (eds). Perry's Chemical Engineers' Handbook, 7th ed., New
York: McGraw-Hill, 1997.4. The author believes that "low molecular weight hydrocarbons" refers to light hydrocarbons
at near atmospheric pressure or under vacuum. The foam stability of light hydrocarbon distillation at medium and high pressure is best inferred from the Glitsch criterion.
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992.
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218 NCEES
5.3.2.12 Downcomer Choke Flooding
Glitsch Correlation
The maximum clear liquid velocity at the downcomer entrance to avoid downcomer choke flooding is the lowest of the three following correlations:
.
Q SFQ SF
Q S SF
250
41
7 5
,
,
,
max
max
max
D
D L G
D L G
1
2
3
t t
t t
=
= −
= −
``` `
jjj j
where
S = tray spacing
SF = system factor
QD,max = maximum downcomer liquid load, in ftgpm
or sft or s
m2
Koch and Nutter Correlations
The maximum downcomer velocity is calculated from:
.Q tS SF S448 8 12 30,maxD R
#= d nwhere tR = apparent residence time, or the ratio of downcomer volume to the clear liquid flow in the downcomer, in seconds
Koch and Nutter Correlations14
12
10
8
6
4
2
00 10 20 30 40
5.13 SEC
4 SEC
†R FOR THEKOCH CORRELATION (8)
†R FOR THENUTTER CORRELATION (9)
5.13 sec
4 sec
†R FOR THEKOCH CORRELATION
†R FOR THENUTTER CORRELATION
lb/ft3
KOCH AND NUTTER CORRELATIONS
,GLρ ρ–
RESI
DENC
E TI
ME
, se
c† R
70 80
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 289.
Chapter 5: Mass Transfer
NCEES 219
Generalized Criteria for Maximum Downcomer Velocity
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992.
Recommended Minimum Residence Time in the DowncomerFoaming Tendency Examples Residence
Time, secLow Low molecular weight hydrocarbons, alcohols 3Medium Medium molecular weight hydrocarbons 4High Mineral oil absorbers 5Very high Amines and glycols 7
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 315.
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The hydraulic gradient is
h g Rf u L12
hg h
f f=
where
f = friction factor
uf = velocity of the aerated liquid across the tray, in secft or s
m
Lf = length of flow path across the tray, in feet or meters
g = acceleration due to gravity
Rh = hydraulic radius, in feet or meters
Rh, the hydraulic radius of the aerated mass, is
R h D
h D
hh
DD L
2 12
2
hf f
f f
f tl
fT W
{
= +
=
=+
where
LW = outlet weir length
h1 = pressure drop through the aerated liquid on the tray, in inches or millimeters of liquid
hf = froth height on tray, in inches or millimeters
Df = average of tower diameter and weir length, in inches or millimeters
DT = tower diameter, in inches or millimeters
jt = froth density on tray
The velocity of the aerated mass across the tray uf is also equal to the velocity of the clear liquid across the tray:
.u hQ
DL
37 41
fl
L
f
w=
The friction factor is correlated with the Reynold number:
ReR u
h lh f Lnt=
where ml = viscosity of the liquid
Chapter 5: Mass Transfer
NCEES 225
Friction Factor for Froth Cross-Flow on Sieve Trays0.5
0.2
0.1
0.05
0.02 0.4 0.7 1.0 1.50.4 0.7 1.0 1.5
0.01103
μ
104
REYNOLDS MODULUS =
hw , in.
l
105
FRIC
TION
FAC
TOR,
f
Rh Uf lρ
Source: Kister, Henry Z., Distillation Design, New York: McGraw-Hill, 1992, p. 317.
For a segmental downcomer, the head loss is
.h Agpm
0 03 100dada
= e owhere Ada = area under the downcomer apron, in ft2 or m2
5.3.2.15 General Considerations for Column SizingTray sizing calculations are performed at points where the column loading is expected to be the highest and lowest in each section. Typically, these are
• The top tray• Above every feed, product draw-off, and point of heat addition or removal• Below every feed, product drawoff, and point of heat addition or removal• The bottom tray• At any point in the column where the calculated vapor or liquid loading peaks
Source: Eckert, Foote, Nemunaitis, and Rollison, Akron, OH: Norton Chemical Process Products Division, 1972 (revised 2001).
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244 NCEES
5.3.3.15 Flooding Velocities
Flooding in Gas Absorption Packed Towers
0.01
1.0
0.1
0.01
.001
.0001
.000010.10 1.0 10 100
Ggc
ap
L
LG
30.2
G
L
G2 μL
where
ap = packing area, in ftft3
2
e = void fraction in packing
mL = viscosity of liquid in centipoise
gc = gravitational constant, 32.2
rG = density of gas phase, in ftlb3
rL = density of liquid phase, in ftlb3
Chapter 5: Mass Transfer
NCEES 245
5.4 Miscellaneous Mass Transfer Processes (Continuous, Batch, and Semicontinuous)
5.4.1 Membrane Separation Processes
5.4.1.1 General Background
Fluid Stream SchematicPERMEATE OR FILTRATETMP
FEEDFEED CHANNEL
RETENTATE
ΔP
Normal flow filtration (NFF) refers to the situation in which retentate flow is zero and all the feed stream flows to the membrane surface are normal.
Tangential flow filtration (TFF) refers to the situation in which the feed stream flows are tangential to the membrane surface and exit the module as a retentate stream, creating a velocity gradient at the membrane surface.
Permeation flux J in ft dayft2
3 or m smol2 indicates the productivity of a membrane:
membrane areavolumetric permeate flow rate
J =
Permeability L indicates the sensitivity of productivity or flux to transmembrane pressure (TMP):
transmembrane pressurefluxL =
TMP may refer to a module average. Pure-component permeability (e.g., water permeability) refers to membrane properties, while the more industrially relevant process permeability includes fouling and polarization effects.
The recovery or conversion ratio CR indicates the efficiency of a membrane module:
feed flow ratepermeate flow rate
CR =
Solutes entrained by the permeate flow are retained by the membrane. They accumulate on the membrane surface and form a region of high concentration called the polarization boundary layer. A steady state is reached between back transport away from the membrane surface, tangential convective transport along the membrane surface, and normal convective flow towards the membrane.
The local transmission or sieving coefficient S indicates the passage of a single component through a membrane. The concentrations may change within a module:
( )( )locallocal
S ccf
p=
The observed passage Sobs indicates the transmission coefficient based on the concentration in the permeate stream exiting a module and in the feed stream entering a module. The observed passage characterizes the module:
))ule
ule((modmod
S cc
obsf
p=
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246 NCEES
The intrinsic passage Sint indicates the transmission coefficient based on the concentration in the permeate stream exiting a module and in the feed stream at the membrane wall. The intrinsic passage characterizes the membrane:
S cc
int w
p=
where
cf = concentration in feed
cp = concentration in permeate
cw = concentration at wall of membrane
The retention or rejection R is the complement to the transmission coefficient or passage:
R = 1 – S
The multiple-component separation factor aij defines the selectivity for component separation:
cccc
SS
ijj
i
jf
jp
if
ip
a = =f
f p
p where
cif = concentration of component i in feed
cip = concentration of component i in permeate
Component transport through membranes can be considered as mass transfer in series:
1. Transport through a polarization layer above the membrane that may include static or dynamic cake layers2. Partitioning between the upstream polarization layer and membrane phases at the membrane surface3. Transport through the membrane4. Partitioning between the membrane and the downstream fluid
A simplified model of polarization can be used as the basis for analysis:
Polarization in Tangential Flow Filtration
REGIONS: CONCENTRATIONS: FLOW VECTORS:
TANGENTIAL FLOW
PERMEATENORMAL FLOW
PERMEATE
Cb
Cw
Cp
POLARIZATIONBOUNDARYLAYER
BULK SOLUTIONS
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 20-38.
Chapter 5: Mass Transfer
NCEES 247
5.4.1.2 Gas SeparationThe flux for permeation is
J z p p, ,ii
i feed i permeatet= −c `m j
where:
Ji = permeation flux of component i, in ft hrft2
3 or m smol2
ri = permeability of component i, in
ft hr psift ft2
3 or m sPamol2
z = membrane thickness
pi = partial pressure of component i
Stage cut q is defined by
feed volume flow ratepermeate volume flow rate
LV
i = =
where
V = molar permeate flow rate, in hrlb mole or s
mol
L = molar feed flow rate, in hrlb mole or s
mol
Selectivity is
xxyy
ij
ji
ji
a =e
e o
o
where
aij = separation factor
xi = mole fraction of component i in the feed or reject
yi = mole fraction of component i in the permeate
The pressure ratio U is
PPpermeate
feedU =
The ratio of permeation flux for two components i and j is
JJ
xy
x y
j
iij
jj
ii
a
U
U=
−
−
e
d n
o
R
T
SSSSSSSSSSS
V
X
WWWWWWWWWWW
At stage cut 0U = , the permeate composition as a function of feed composition is
y x x x
21
11 1
11
14
i i ii
2
a a a
aUU U U
= + + − − + + − −−
c c c _m m m i> H For membrane modules, the partial pressure driving force is a point function dependent on the partial pressures at a point on the membrane and is not constant. To take this into account, the equation may be used in iterative calcula-tions for approximating the performance of membrane modules.
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248 NCEES
The limiting case for a >> F is
y x PP
xi i permeate
feedi, U=
The limiting case for a << F is
yxx
1 1ii
i,a
a
+ −_ i
Flow Paths in Gas PermeatorsPERMEATE
MEMBRANE
FEED
FEED
FEED
SPIRAL WOUND MODULES(a)
HOLLOW-FIBER MODULES WITH COUNTERCURRENT FLOW
(HOLLOW-FIBER WALL)MEMBRANE
PERMEATE
(b)
HOLLOW-FIBER MODULES WITH CROSS FLOW(c)
FEED (HOLLOW-FIBER WALL)MEMBRANE
PERMEATE
5.4.1.3 Material Balances for Membrane Modules
MEMBRANE MODULE
MEMBRANE
REJECT
PERMEATE
INCREMENT
FEEDL0 x0 PF LN xN PF
VN yN PP
n-1 n
Overall and component balances for a module are
L0 = LN + VN
x0 L0 = xN LN + yN VN
Overall and component balances for an increment of module area are
Ln–1 + Vn–1 = Ln + Vn
xn–1 Ln–1 + yn–1 Vn–1 = xn Ln + yn Vn
These may be expressed as
V V V y xL x x
n n nn n
n n n1
1 1D = − =
−−
−− −_ i
Chapter 5: Mass Transfer
NCEES 249
where y y y
V V Vy V y V y V
21
n n n
n n
n n n n nn
1
1
1 1/
D
D
= +
= −−
−
−
− −
` j
At any point along the membrane, the permeate composition is
yV y Vn nN1 D=/
and the permeate composition for the overall module is
y V y VN N n nN1 D=/
Area for Membrane Modules
Based on a stepwise incremental solution, the membrane area is
A A J
y VN n
N
i av
n nN
g1 1
D= = _ i> H/ /
where J z x P y P x P y P z x x P y y P21
21
i avi
n F n P n F n Pi
n n F n n Pg 1 1 1 1t t= − + − = + − +− − − −_ c c ` ` c c _ `i m m j j m m i j9 9C C
The overall module area can be approximated as
A Jy V
Ni av
n n
g
= _ i
where J z x P y P x P y P z x x P y y P2
121
i avi
F P N F n Pi
n F n Pg 0 0 0 0t t= − + − = + − +_ c c ` ` c c _ `i m m j j m m j j9 9C C
Procedure for Incremental Calculation
Given aij, PF, PP, L0, and x0:
1. Select increment Dx2. For the initial point 0, calculate y0 and (Ji)0
3. Determine xn
4. Calculate yn and y n
5. Calculate DVn and Vn
6. Calculate y Vn nD
7. Calculate Ln
8. Calculate (Ji)n, (Ji)avg, and An
9. After the final increment, calculate (Ji)N and AN
Source: McCabe, Warren L., Julian C. Smith, and Peter Harriott, Unit Operations of Chemical Engineering, 5th ed., New York: McGraw-Hill, 1993, p. 872.
where
aw = activity of water
cs = concentration of solute
Chapter 5: Mass Transfer
NCEES 251
Flux Across Membrane
The flux of solvent JW (water, for example) is
J RTc D v
zP
ww w w rD D= −c m
where
J = permeation flux in ft hrft2
3 or m sm2
3
c = concentration in ft
lb mole3 or
mmol3
D = effective diffusivity in hrft2 or s
m2
v = partial specific volume in lbmft3 or kg
m3
DP = friction losses in psi or Pa
z = membrane thickness in ft or m
Dp = differential osmotic pressure in psi or Pa
The flux of solute is
J D S zc
s s ssD= c m
where:
Ss = distribution coefficient of the solute
Polarization Factor
The polarization factor is the relative concentration difference across the polarization boundary layer and is
cc c
kJ f
ssi s
c
wC =−
=
where
f = fraction of solute rejected
kc = mass transfer coefficient based on concentration, in hrft or s
m
Pressure Drop
The internal flow in a hollow-fiber membrane is laminar, and the internal pressure drop DPf with one closed end is
PDJ L128
2fw3
2nD =
where
L = length
D = diameter
m = viscosity
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252 NCEES
5.4.2 Liquid-Liquid Extraction
5.4.2.1 Partition Ratio The equilibrium partition ratio in mole fraction units is
K xyo
extract
raffinate
i ii
i
ic
c= =
where
yi = mole fraction of solute i in the extract phase
xi = mole fraction of solute i in the raffinate phase
gi = activity coefficient of solute i in the indicated phase
The equilibrium partition ratio in mass ratio units Kil is
K XY
mm
mm
feed solventsoluteraffinate
extraction solventsoluteextract
ii
i= =ll
le
e o
o
where
Yi l = ratio of mass solute i to mass extract solvent in extract phase
Xil = ratio of mass solute i to mass extract solvent in raffinate phase
m = mass flow rate, in hrlbm or s
kg
The advantage of using the solute-free basis is that the feed solvent and extraction solvent flows do not change during the extraction.
5.4.2.2 Extraction Factor On a McCabe-Thiele type of diagram, E is the slope of the equilibrium line divided by the slope of the operating
line SF .
m FSE i i=
where
E i = extraction factor
mi = local slope of the equilibrium line
S = mass flow rate of the solvent phase, in hrlbm or s
kg
F = mass flow rate of the feed phase, in hrlbm or s
kg
For dilute systems with straight equilibrium lines, the slope of the equilibrium line is equal to the partition ratio:
m Ki i= l
Chapter 5: Mass Transfer
NCEES 253
5.4.2.3 Separation FactorThe separation factor indicates the relative enrichment of a given component in the extract phase after one theoretical stage of extraction.
XXYY
XYXY
KK
raffinate
extractij
j
i
j
i
j
j
i
i
j
ia = = =l
l
l
l
l
l
l
l
l
l
l
f
f
f
f
p
p p
p
where ija l = separation factor for solute i with respect to solute j (mass ratio basis)
Equilibrium Lines
Plotting equilibrium data in terms of mass ratios on logarithmic scales often gives a straight line.
Hand-Type Ternary Diagram for Water + Acetic Acid + MIBK at 25oC
WATER LAYER
PLAIT POINT
864
2
2
.8
.8
1
1
.6
.6
.4
.4
.2
WT.
ACET
IC A
CID
WT.
MIBK
.2
.08
.08
.1
.1.01.01
.06
.06
.04
.04
.02
.02
Y
X
MIBK LAYER
LIQUID - L
IQUID EQUILIBRIUM
LIQUID - L
IQUID EQUILIBRIUM
WT. ACETIC ACIDWT. WATER
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-27.
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254 NCEES
5.4.2.4 Liquid-Liquid Extraction: Process Calculations
Countercurrent Extraction Cascade
2
n
Y2
Y1YE ' oreXF ' f
XR ' r YS ' s
X1
X n–1
Xr–1
r –1
r
Yn+1
Yr
Yn
Xn
1FEED STAGE
RAFFINATE STAGE
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-11.
Theoretical (Equilibrium) Stage Calculations With McCabe-Thiele Method
McCabe-Thiele Graphical Stage Calculation Using Bancroft Coordinates
PARTIAL STAGEX
X
Yr s
'
'
X Yf e'
SLOPE =
WT. SOLUTEWT. FEED-SOLVENT
2
1
3
4
20
2
0r
OPERATING LINE
EQUILIBRIUM LIN
E
F 'S '
Y 'W
T. SO
LUTE
WT.
EXTR
ACTI
ON-S
OLVE
NT
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-45.
Chapter 5: Mass Transfer
NCEES 255
For immiscible feed and extraction solvents, the operating line for the feed end (stage 1 to stage n) is
Y SF X S
E Y F Xn n
e f1 = +
−+l l
l ll
l l l l
where
fX l = mass ratio of solute in feed
eY l = mass ratio of solute in extract
El = mass flow rate of extraction solvent only
F l = mass flow rate of feed solvent only
Sl = mass flow rate of extraction solvent only
For immiscible feed and extraction solvents, the operating line for the raffinate end (stage n to stage r) is
For straight equilibrium and operating lines, the number of theoretical stages N is approximated by:
//
,ln
lnforN
X Y mX Y m
m FS
1 1 1
1E
E EE E
r s
f s
=−−
− += =
l l l
l l l
lll Y
f cp m
where
N = number of theoretical stages
ml = local slope of equilibrium line in mass ratio units
Sl= mass flow rate of the solvent only (solute-free basis), in hrlbm or s
kg
F l= mass flow rate of the feed solvent (solute-free basis), in hrlbm or s
kg
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256 NCEES
An alternate form is
//
// forX Y m
X Y m1 1
1 1EE E E
r s
f sN
−−
= −− =
l l l
l l lY
//
forX Y mX Y m
N 1 1Er s
f s−−
= + =l l l
l l l
Graphical solutions to the KSB equation are shown below. Note that the term for the abscissa is the inverse of the term used in the KSB equation.
Graphical Solutions to the KSB Equation
1.00.80.60.4
0.2
.001.0008.0006.0004
.0002
.01.008.006.004
.002
0.1.08.06.04
.02
.0001
.00001
.00008
.00006
.00004
.00002
N = 1
2
3
4
6
8
1 2 4 6 8 10ε, EXTRACTION FACTOR
10
15
X
–
Y/m
sr X
–
Y/m
sf
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-46.
Chapter 5: Mass Transfer
NCEES 257
In general, these equations are valid for any concentration range in which equilibrium can be represented by a linear relationship Y = m X + b (written here in general form for any system of units). For applications that involve dilute feeds, the section of the equilibrium line of interest is a straight line that extends through the origin where Yi = 0 at Xi = 0. In this case, b = 0 and the slope of the equilibrium line is equal to the partition ratio where m = K.
The KSB equation also may be used to represent a linear segment of the equilibrium curve at higher solute concen-trations. In this case, the linear segment is represented by a straight line that does not extend through the origin, and m is the local slope of the equilibrium line, so .andb m K0= =Y Y
Furthermore, a series of KSB equations may be used to model a highly curved equilibrium line by dividing the analysis into linear segments and matching concentrations where the segments meet. For equilibrium lines with moderate curvature, an approximate average slope of the equilibrium line may be obtained from the geometric mean of the slopes at low and high solute concentrations:
m m m maverage geometric mean low high. =
Stage Efficiency
(%) actual stages
theoretical stages100o #p =
c cc c
,*
, ,md
d n d
d n d n
1
1p =
−−
+
+
(%)
[ ( )]ln
ln 1 1100E
Eo
md #pp=
+ −
where
op = overall stage efficiency
mdp = Murphree stage efficiency based on the dispersed phase
Mass Transfer Between Phases
( ) ( )( ) ( )
n k y y n k y yn k x x n k x x
int
int
y y
x x
= − = −
= − = −
*
*
o o
o o where
no = molar flow per area
xint = mole fraction of solute i in the raffinate phase at the interface
x* = mole fraction of solute i in the raffinate phase in equilibrium with the extract phase
yint = mole faction solute i in the extract phase at the interface
y* = mole fraction of solute i in the extract phase in equilibrium with the raffinate phase
( ) ( )( )
NTU y y yy dy
11
intG
my
y 1
s
e= − −−#
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258 NCEES
For dilute solutions:
( )NTU
x xx x
*OLm
r
1=
−−f
where
xf = mole fraction of solute i in the feed
xr = mole fraction of solute i in the raffinate
NTUG = number of transfer units based on gas phase
NTUOL = number of trasnsfer units based on liquid phase
( )lm = log mean
Rate-Based Calculations With Mass-Transfer Units
In most cases, the dominant mass-transfer resistance resides in the feed (raffinate) phase, because the slope of the equilibrium line usually is greater than one. In that case, the overall mass-transfer coefficient based on the raffinate phase may be written:
k k m k1 1 1or r er
vole
= +
where
ke = extract phase mass-transfer coefficient, in hrft or s
m
kr = raffinate phase mass-transfer coefficient, in hrft or s
m
kor = overall mass-transfer coefficient based on the raffinate phase, in hrft or s
m
mervol = local slope of equilibrium line (volumetric concentration basis)
The required contacting height of an extraction column is related to the height of a transfer unit and the number of transfer units by:
Z k aV
X XdX HTU NTUt
or
req
x
x
or orout
in
= − =#
where
Zt = total height of extractor
Vr = liquid velocity of raffinate phase, in secft or s
m
a = interfacial area per unit volume, in ftft or
mm
3
2
3
2
Xeq = mass ratio in equilibrium with composition of extract phase
HTUor = height of overall transfer units (based on raffinate phase)
NTUor = number of transfer units (based on raffinate phase)
Chapter 5: Mass Transfer
NCEES 259
For straight equilibrium and operating lines, the number of transfer units is approximated by the Colburn equation:
ln
NTUX m
YX m
Y
1 1
1 1 1
E
E E
or
r
f
s
s
=−
−
−− +
ll
l
ll
lJ
L
KKKKKKKKKcN
P
OOOOOOOOOm
where
,m FS 1E E= =lll
Y
An alternate form is
exp
X mY
X mY NTU
1 1
1 1 1
E
E E
r
f or
s
s
−
−=
−
− −
ll
l
ll
l c m< F
The height of a transfer unit is
HTU HTU
HTUEor r
e= +
HTU A k a
Qr
col r
r=
HTU A k a
Qe
col e
e=
where
HTUr = height of a transfer unit due to resistance in the raffinate phase, in ft or m
HTUe = height of a transfer unit due to resistance in the extract phase, in ft or m
Acol = column cross-sectional area, in ft2 or m2
Qr = volumetric flow rate of the raffinate phase, in minft or s
m3 3
Qe = volumetric flow rate of the extract phase, in minft or s
m3 3
The relation between overall raffinate phase transfer units from the Colburn equation and the number of theoretical stages from the KSB equation is
ln for
for
NTU N
NTU NX m
YX m
Y
1 1 1
1 1
E
E E
E
or
or
r
f
s
s
#=−
=
= =−
−− =
ll
l
ll
l
Y
PE Chemical Reference Handbook
260 NCEES
Extraction Factor
The solute reduction factor FR, or extraction factor, is an indication of process performance.
For a single-stage batch process or for one theoretical stage of a continuous process, the extraction factor is
forF X
XN
1 1
1
1E
E ER out
in= =−
−=
c
c m
m
The required solvent-to-feed ratio is approximated by
forFS
KF
N1
1R=−
=
where K = distribution coefficient for phase equilibrium
For any extraction configuration, the concentration of solute in the extract is
forY
FSX
F Y1 1 0outin
R in= − =cdm
n For cross-flow extraction, in which the raffinate phase for each stage is contacted with fresh solvent, the extraction factor is
F N1 ER
No= +
p
c m
FS
KNF 1R
N1o= −pc m
For multi-stage countercurrent extraction, the extraction factor is
F
1 1
1
E
E ER
No
=−
−pc
c m
m
For countercurrent extraction without discrete stages, the extraction factor is
For liquid distributors, the liquid should issue from the hole as a jet that breaks up into drops. As a general guide-line, the maximum recommended design velocity corresponds to a Weber number (We) of about 12. The minimum Weber number that ensures jetting in all the holes is about 2. It is common practice to specify a Weber number between 8 and 12 for a new design.
u dWe
,maxoo d
. tc
where
uo,max = maximum velocity through an orifice or nozzle
We = Weber number
g = surface tension
do = orifice or nozzle diameter
rd = density of the dispersed phase
Drop Size, Dispersed-Phase Holdup, and Interfacial Area
For the general case where the dispersed phase travels through the column as drops, an average liquid-liquid inter-facial area can be calculated from the Sauter mean drop diameter and dispersed-phase holdup.
The drop diameter is
.d g1 15P htcD
=
where
dp = Sauter mean drop diameter
Dr = density difference between the raffinate and the extract
h = parameter, specifically:
h = 1.0 for no mass transfer
h = 1.0 for transfer from continuous to dispersed phase
h = 1.4 for transfer from dispersed to continuous phase
The dispersed-phase holdup is
,exp
cos
uu
u a d
61
42d
sod
d
c
dp p
2
z
f rz
f z
rg
g=− −
−
=
−
d
c
`n
m
j>
= G
H
where
dz = volume fraction of the dispersed phase (holdup)
z = tortuosity factor
ud = liquid velocity of the dispersed phase
Chapter 5: Mass Transfer
NCEES 263
uc = liquid velocity of the continuous phase
uso = slip velocity at low dispersed-phase flow rate
e = void fraction
aP = interfacial area
The interfacial area is
a d6
pp
dfz=
Drop Velocity
The average velocity of a dispersed drop udrop is
uu
dropd
dfz
=
Interstitial Velocity of Continuous Phase
The interstitial velocity of the continuous phase uic is
uu1ic
d
c
f z=
−` jSlip Velocity and Characteristic Slip Velocity
The relative velocity between the counterflowing phases is referred to as the slip velocity us:
u u us drop ic= +
The characteristic slip velocity uso obtained at low dispersed-phase flow rate is
Re
g d18Stokes
c
c P2
3
n
t tD=
where
Re = Reynolds Number
rc = density of the continuous phase
Dr = density difference between the two phases
mc = viscosity of the continuous phase
For ReStokes < 2:
u
g d18so
c
p2
ntD
=
For ReStokes > 2:Re
u dsop c
ctn=
where
. . .ReP
H H0 94 0 857 59 3..
0 1490 757 #= −
. . .ReP
H H3 42 0 857 59 3..
0 1490 441 2= −
PE Chemical Reference Handbook
264 NCEES
P
gcc
4
2 3
n t
t c
D=
H d g P
34 .
.pcw
2 0 140 149
ctnnD= f dp n
P , H = dimensionless groups
mw = reference viscosity equal to 0.9c P or 9 #10-4Pa s
g = surface tension in in.lbf
The slip velocity at higher holdup is estimated from:
u u 1s so d. z-` j
Flooding Velocity
It is generally recommended that flow velocities be limited to 50 percent of the calculated flooding velocities.
.
.u
uu
u
1 0 925
0 178cf
cfdf
so=+ d n
where
ucf = continuous phase flooding velocity
udf = dispersed phase flooding velocity
Drop Coalescence Rate
Problems with coalescence are most likely when the superficial dispersed-phase flooding velocity udf is greater than about 12 percent of the characteristic slip velocity.
Mass Transfer Coefficients and Efficiency
.k a m k a
D m D
g
0 081
1
/ /
/
oc dcvol
od
c c
cdc d d
d
d dc
1 2 1 2
2
3 3 1 4
#
tn
tn
z zct
tD
= =+
−
e
`
d
f
eo
j
n
p
o
where
Dc = solute diffusion coefficient for the continuous phase
Dd = solute diffusion coefficient for the dispersed phase
koc = overall mass-transfer coefficient based on the continuous phase
kod = overall mass-transfer coefficient based on the dispersed phase
mdc = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase concentration
Chapter 5: Mass Transfer
NCEES 265
mdcvol = local slope of equilibrium line for dispersed-phase concentration plotted versus continuous-phase
concentration on volumetric concentration basis
γ = interfacial tension
μc = viscosity of continuous phase
μd = viscosity of dispersed phase
rc = density of continuous phase
rd = density of dispersed phase
φd = volume fraction of dispersed phase (holdup)
With the height of one transfer unit (based on the continuous phase):
Little benefit is gained from a packed height greater than 10 ft (3 m). Redistributing the dispersed phase about every 5 to 10 ft (1.5 to 3 m) is recommended to generate new droplets and constrain backmixing.
Minimum Packing Size
For a given application, a minimum packing size or dimension exists below which random packing is too small for good extraction performance. The critical packing dimension dc is
.d g2 4c tvD
=
Packing Holdup
For standard commercial packings of 0.5 in (1.27 cm) and larger, φd varies linearly with the liquid velocity of the dispersed phase (ud) up to values of φd = 0.10 (for low values of ud). As ud increases further, φd increases sharply up to a “lower transition point” resembling loading in gas-liquid contact. At still higher values of ud, an upper transition point occurs, the drops of dispersed phase tend to coalesce, and ud can increase without a corresponding increase in φd. This regime ends in flooding. Below the upper transition point, the dispersed-phase holdup is
u uu1 1
d
d
d
cso dz z
f z+ − = −` j
Packing Flooding: Siebert, Reeves, and Fair Correlation
= ft./hr. (SUPERFICIAL VELOCITY)= CONTINUOUS PHASE= DISPERSE PHASE= sq. ft. AREA OF PACKING/ c ft.= DIFFERENCE= VOID FRACTION IN PACKING
VISCOSITY IN (CENTIPOISE)= DENSITY (POUNDS PER / CUBIC FOOT)
μ'c =
'
γ =
γ
F = PACKING FACTOR (DIMENSIONLESS)
LIQUID – LIQUID PACKED TOWERS
A MODIFIED CRAWFORD-WILKE CORRELATION
10 22
22
0.50.5
0.5 0.5=
++
1.50.2c
cD
DC
CC
c F
4 6 10
103
32
102
10
CC
C
INTERFACIAL SURFACE TENSION (DYNES / cm)
Pressure Drop
In general, the pressure drop through a packed extractor is due to the hydrostatic head pressure. The resistance to flow caused by the packing itself normally is negligible; typical packings are large and flooding velocities are much lower than those needed to develop significant DP from resistance to flow between the packing elements.
Mass Transfer Coefficients
D
1d
cd
d d
d 21
z
nn
tn
=+
e
d
o
n For φd < 6:
.k
u
1
0 00375d
cd
s
nn
=+d n
Chapter 5: Mass Transfer
NCEES 267
For φd > 6:
.k u D0 023d sd d
d 21
tn=
−
e o
.Dk d
Dd u
0 698 1c
c p
c c
c
c
p s cd
52
21
tn
nt
z= −e e `o o j
k k km1 1
od d c
dcvol
= +
where
kc = continuous-phase mass-transfer coefficient
kd = dispersed-phase mass-transfer coefficient
Packing Data
Random and Structured Packings Used in Packed Extractors
Packing Surface Area ap1 mm3
2Void Fraction1 (e)
Metal Random PackingKoch-Glitsch IMTP® 25 Koch-Glitsch IMTP® 40 Koch-Glitsch IMTP® 50 Koch-Glitsch IMTP® 60 Sulzer I-Ring #25 Sulzer I-Ring #40 Sulzer I-Ring #50 Nutter Ring® NR 0.7 Nutter Ring® NR 1 Nutter Ring® NR 1.5 Nutter Ring® NR 2 Nutter Ring® NR 2.5 HY-PAK® #1 in. HY-PAK® #1-1/2 in. HY-PAK® #2 in. FLEXIRING® 1 in. FLEXIRING® 1-1/2 in. FLEXIRING® 2 in. CMR® 1 CMR® 2 CMR® 3 BETARING® #1 BETARING® #2 FLEXIMAX® 200 FLEXIMAX® 300 FLEXIMAX® 400
Random and Structured Packings Used in Packed Extractors (cont'd)
Packing Surface Area ap1 mm3
2Void Fraction1 (e)
Plastic Random PackingSuper INTALOX® Saddles #1 Super INTALOX® Saddles #2 BETARING® #1 BETARING® #2 SNOWFLAKE® FLEXIRING® 1 in. FLEXIRING® 1-1/2 in. FLEXIRING® 2 in.
204 105 167 114 93 205 119 99
0.896 0.934 0.942 0.940 0.949 0.922 0.925 0.932
Ceramic Random PackingINTALOX® Saddles 1 in. INTALOX® Saddles 1-1/2 in. INTALOX® Saddles 2 in.
1. Typical value for standard wall thickness. Values will vary depending upon thickness.2. SMV structured packings also are available with horizontal dual-flow perforated plates
installed between elements (typically designated SMVP packing). These plates generally reduce backmixing and improve mass-transfer performance at the expense of a reduction in the open cross-sectional area and somewhat reduced capacity.
Source: Green, Don W., and Robert H. Perry, Perry's Chemical Engineers' Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 15-71.
Perforations usually are in the range of 0.125 to 0.25 in (0.32 to 0.64 cm) in diameter, set 0.5 to 0.75 in (1.27 to 1.81 cm) apart, on square or triangular pitch. Hole size appears to have relatively little effect on the mass-transfer rate except that, in systems of high interfacial tension, smaller holes produce somewhat better mass transfer. The entire hole area is normally set at 15 to 25 percent of the column cross-section, although adjustments may be need-ed. It is common practice to set the velocity of liquid exiting the holes to correspond to a Weber number between 8 and 12. This normally gives velocities in the range of 0.5 to 1.0 sec
ft (15 to 30 scm ).
The velocity of the continuous phase in the downcomer (or upcomer) udow, which sets the downcomer cross- sectional area, should be set lower than the terminal velocity of some arbitrarily small droplet of dispersed phase, such as a diameter of 1/32 or 1/16 in (0.08 or 0.16 cm). Otherwise, recirculation of entrained dispersed phase around a tray will result in flooding. The terminal velocity ut of these small drops can be calculated using Stokes’ Law:
ug d18t
c
p2
ntD
=
Downcomer area typically is in the range of 5 to 20 percent of the total cross-sectional area, depending upon the ratio of continuous- to dispersed-phase volumetric flow rates.
For large columns, tray spacing between 18 and 24 in. (45 and 60 cm) is generally recommended.
The height of the coalesced layer at each tray, h, is
hg
P P g L1 d
o dow d
z t
z t
D
D D D=−
+ −` j
where
DPo = orifice pressure drop
DPdow = pressure drop for flow through a downcomer (or upcomer)
L = downcomer (or upcomer) length
The orifice pressure drop DPo is
. .log ReforP Re u d g
du d
21 1 0 71 3 2
.
o d oo
o do o d
22
2 0 2
tvt v
nt
D D= − + =−
d dn nwhere do = diameter of orifice in ft
The pressure drop through the downcomer is
.P
u2
4 5dow
dow c2 t
D =
where udow = velocity in downcomer (or upcomer)
For large columns, the design should specify that the height of the coalesced layer is at least 1 in. (2.5 cm) to en-sure that all holes are adequately covered.
PE Chemical Reference Handbook
270 NCEES
For segmental downcomers, the area of the downcomer is
A SH H S6 3 42 2= +_ i
where
A = area of segmental downcomer (or upcomer)
H = height of segmental downcomer (or upcomer)
S = chord length of segmental downcomer (or upcomer)
Chord length S is
S H D H8 2 2col
21
= −d n= Gwhere Dcol = column diameter
Sieve Tray Flooding Velocity
Velocity of the continuous phase at the flood point is
u
B uu C
L A.
cf
cfdf
2
0 5
=+
−
d n
R
T
SSSSSSSS
V
X
WWWWWWWW
where
A d g6o tcD
= .
Bg f1 11
ha
d2t
t
D=
.C
g f22 7
da
c2t
t
D=
where
fha = fractional hole area
fda = fractional downcomer area
The cross-flow velocity of the continuous phase uc flow is
u z hL
ucflowfp
c. -
where
Lfp = length of flow path
z = sieve tray spacing
Sieve Tray Efficiency
The sieve tray efficiency is approximated by
. d
zuu0 21 .
. .
oo c
d0 35
0 5 0 42
pv
= f dp n
Chapter 5: Mass Transfer
NCEES 271
5.4.3 Adsorption
5.4.3.1 Adsorption EquilibriumFor a single adsorbate in a gas stream, the equilibrium capacit of the adsorbent may be related to the concentration of the adsorbate in the bulk stream by the Freundlich equation:
W = a pn
where
W = unit mass of adsorbentmass f ads rbateq q
p = partial pressure of adsorbate in the bulk gas stream
a, n = empirical coefficients derived from log-log plot of data for W vs. p
Both coefficients are a function of temperature.
The Freundlich equation can be used for liquid-solid adsorption by entering concentration instead of partial pressure.
5.4.3.2 Adsorption OperationAdsorption in typical commercial operations is conducted by passing the gas or liquid stream through a usually vertical fixed bed of adsorbent particles. Adsorption beds are usually oriented vertically.
Adsorption beds have three zones that characterize the operation:
1. Equilibrium zone where adsorbate is in equilibrium with inlet concentration2. Mass transfer zone where adsorbate is diffusing into adsorbent3. Active zone where no adsorption has occurred
The length of the mass transfer zone (MTZ) is a function of the fluid velocity along with adsorbent porosity and uniformity of pore size.
PE Chemical Reference Handbook
272 NCEES
Adsorption Concentration Profiles Across Bed
EQUILIBRIUMZONE
MASSTRANSFER
ZONE
LOy OUT
y IN
ACTIVEZONE
CONCENTRATION PROFILE AT A GIVEN TIME DURING ADSORPTION OPERATION
BED LENGTH
VAPO
R PH
ASE
CONC
ENTR
ATIO
N
Three performance regimes for adsorption beds characterize the operation. Considering a given point in a bed:
1. Dry, when the mass transfer zone is below the point in the bed and the concentration has a low value2. Break-through,when the mass transfer zone reaches the point in the bed and the concentration increases3. Saturated, when the concentration at the point in the bed increases to the value of the inlet concentration
Adsorption Outlet Composition Versus Time
DRY BREAK-THROUGH
TIME0
SATURATED
y OUT
y IN
CONCENTRATION PROFILE AS A FUNCTION OF TIME AT A GIVEN POINT IN THE BED. ADSORPTION STEP.
VAPO
R PH
ASE
CONC
ENTR
ATIO
N
Chapter 5: Mass Transfer
NCEES 273
5.4.3.3 Adsorption RegenerationAdsorption processes can be nonregenerative or regenerative. Nonregenerative adsorption is a batch process. For regenerative adsorption, adsorbent beds are cycled between adsorption and desorption (regeneration) modes and multiple beds are required for continuous operation.
During regeneration, stripping the adsorbate is accomplished by passing a pure fluid through the bed at a lower pressure for pressure swing adsorption (PSA) or at a higher temperature for temperature swing adsorption (TSA). For TSA, the pressure may be slightly lowered in addition to the temperature increase. Often a split stream from the fluid exiting the adsorbing bed is used as the pure fluid for regenerating adsorption beds.
The regeneration of adsorption beds leaves a residual concentration of adsorbate in the adsorbent. This reduces the working capacity of regenerated adsorbent in comparison with the capacity of fresh adsorbent.
Working capacity W W Wsat regen= −l
where
Wsat = amount adsorbed on the bed at break-through
Wregen = amount of adsorbate remaining on the bed after regeneration
5.4.3.4 Characteristics of Typical Adsorption Systems
Adsorption System Characteristics
System Type:TSA PSA
Gas Phase Liquid Phase Gas PhaseConfiguration of systemNumber of beds 2 to 4 2 to 4 2 to 16Time on adsorption 4 to 8 hours 4 to 8 hours Minutes to hoursFlow direction on adsorption Down Up Up
Flow direction on regeneration Up Down; treated vaporized liquid when feasible Down
Common adsorbents
Hydrophobic Activated carbons for removing VOCs from gas
Activated carbons for water purification
Activated carbon for air separations; heavy hydrocarbons from light hydrocarbons
Hydrophilic Silica gel, activated alumina, mol sieve for dehydration and removing slightly polar organics
5.4.4 Leaching
5.4.4.1 Single-Stage LeachingLeaching is the removal of a soluble substance from an insoluble solid via liquid extraction. The desired compo-nent diffuses into the solvent by mass transfer.
Two common methods of leaching are:
• Percolation of liquids through stationary solid beds• Dispersion of solids in each leaching stage by mechanical agitation
PE Chemical Reference Handbook
274 NCEES
5.4.4.2 Multistage LeachingFor multistage leaching processes, the most common setup is continuous countercurrent leaching, where a liquid solvent overflows from stage to stage in a direction opposite to the flow of the solid. The stages are numbered in the direction of flow of the solid.
• The flow rates of contained liquid in the solid slurry streams are shown as L-values.• The concentrations of solute in the solid slurries are shown as x-values.• Feed solid slurries enter at stage 1, containing a liquid flow of La with a solute concentration of Xa.• Leached solid slurries exit at stage N, containing a liquid flow of Lb with a solute concentration of Xb.• It is assumed that the solids flow rate is constant from stage to stage.• The flow rates of overflow solvent from each stage are shown as V-values.• The concentrations of solute in the solvent streams are shown as y-values.• Lean solvent enters the process at stage N, at a mass flow rate of Vb and a solute concentration of yb.• The concentrated solvent, or leachate, exits at a mass flow rate of Va and a solute concentration of Ya.
Multistage Leaching Diagram
Va VbVNYa
V2 Vn Vn+1 Vn+2
xa xbxN-1
NnONE
STAGELEACHATE LEAN
SOLVENT
FEEDSOLIDS
LEACHEDSOLIDS
STAGE STAGE STAGE
x1 xn-1 xn xn+1n+1La LbLN-1L1 Ln-1 Ln Ln+1
YbYNY2 Yn Yn+1 Yn+2
Leaching Calculations
Inputs = Outputs:
La + Vn+1= Va + Ln
Component balance:
( ) ( ) ( ) ( )L x V y V y L xa a n n a a n n1 1+ = ++ +
Leaching Operating Line
Y V
LX V
V Y L Xn n
nn n
a a a a1 1 1= +
−+
+ +
Note: If the density of liquid Ln is constant from stage to stage, then the overflow and underflow rates are both con-stant and the operating line is straight.
Calculation of the Number of Required Stages in Leaching With Constant Overflow
The equilibrium line for leaching is
Xe = Ye
Chapter 5: Mass Transfer
NCEES 275
The first stage of the leaching process is calculated initially as a mass balance to set up the flow of slurried solids through the rest of the stages. Therefore, the following calculation determines the total number of stages N, in the format of N–1:
ln
lnN
x xy yy xy x
1
b a
b a
a a
b b
− =
−−
−−e
e o
o
5.4.5 Batch Distillation
5.4.5.1 Rayleigh Equation
lnndn
nn
y xdxf
n
n
x
x
0
f f
0 0
= = −# #where
nf = moles in still at end of run
n0 = initial moles in still
xf = mole fraction in liquid phase at end of run
x0 = initial mole fraction in liquid phase in still
5.4.5.2 Relative Volatility Equation
xyxy
11ija =
−−d
c m
n
where
aij = relative volatility
y = mole fraction of light component in vapor phase
Rearranging:
( )y xx
1 1aa= + −
Therefore,
ln lnnn
nn
AA
AB BB
0 0a=
where
nx = moles of liquid "x" left in the still at any time
0 = time zero
aAB = relative volatility
PE Chemical Reference Handbook
276 NCEES
5.4.5.3 Operating Line for Batch Distillation With Reflux y R
Rx R
x1 1n
D
Dn
D
D1 = + + ++
where
RD = reflux ratio based on the distillate rate
x = liquid composition
5.4.5.4 Batch Distillation Apparatus
Batch Distillation Apparatus
N
N-1
N-2
COLUMN
DISTILLATEACCUMULATOR
CONDENSER
REBOILER
QR•
QC•
1
2
3
Chapter 5: Mass Transfer
NCEES 277
5.4.6 Crystallization
5.4.6.1 Saturation and Supersaturation
The Solubility-Supersolubility Diagram
LABILE
TEMPERATURE
STABLEMETASTABLE
CONC
ENTR
ATIO
N
C"B"
C'
B'
B
D CA
Diagram regions:
• Stable (unsaturated) zone, where crystallization is impossible.• Metastable (supersaturated) zone, between the solubility and supersolubility curves, where spontaneous crys-
tallization is improbable. However, if a crystal seed were placed in such a metastable solution, growth would occur on it.
• Unstable or Labile (supersaturated) zone, where spontaneous crystallization is probable, but not inevitable.
5.4.6.2 Expressions of SupersaturationDc = c – c*
where
c = concentration
c* = saturation concentration
Dc = driving-force concentration
PE Chemical Reference Handbook
278 NCEES
*S cc=
where
S = supersaturation ratio
s *cc S 1D= = −
where s = relative supersaturation (100s is % supersaturation)
5.4.6.3 Expression of SupercoolingDq = q* – q
where
q = temperature of the solution
q* = saturation temperature of the solution
The supersaturation and supercooling are related by the local slope of the solubility curve *dd ci
by*c d
d ci iD D= c m
5.4.6.4 Nucleation
Diagram of NucleationNUCLEATION
PRIMARY
HOMOGENEOUS(SPONTANEOUS)
HETEROGENEOUS(INDUCED BY FOREIGN PARTICLES)
SECONDARY(INDUCED BY CRYSTALS)
Gibbs Energy of Nucleation
G
r3
4crit
c2rc
D =
where
Gr3
4crit
c2rc
D = = Gibbs free energy for the critical radius of a stable nucleus
g = interfacial tension between the developing crystal surface and the supersaturated solution
rc = critical radius of a stable nucleus
Chapter 5: Mass Transfer
NCEES 279
Homogeneous Nucleation Rate (Arrhenius Form)
( )lnJ A
k T Sv
316
EXP 3 3 2
3 2rc= −> H where
J = nucleation rate
A = rate constant
k = Boltzmann constant (k NRc= , where N is Avogadro's number)
v = number of moles of ions produced from one mole of electrolyte (for non electrolytes, v = 1)
T = absolute temperature
S = supersaturation ratio
Heterogenous Nucleation Rate
J k cmaxnnD=
where
J = nucleation rate
kn = nucleation rate constant
Dcmax = maximum allowable metastable zone width
n = the observed order of the nucleation (a fitting parameter)
5.4.6.5 Crystal GrowthR K c A dt
dm G dtdL
dtdr v1 3 3 6 6
G Gg
c c c cbat
bat
bat
batD= = = = = = r
where
RG = mass deposition rate, in m skg2 :
KG = mass-transfer coefficient with units that are dependent on g (if g = 1), in sm
g = the order (a fitting parameter)
Dcg = concentration driving force for mass transfer, in mkg3
A = b L2 = particle area, in m2
m = a rc L3 = particle mass, in kg
t = time, in s
a = volume shape factor
b = surface shape factor
G = overall linear growth rate, in sm
rc = crystal density, in mkg3
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280 NCEES
L = some characteristic size of the crystal, in m
r = radius corresponding to the equivalent sphere, in m
vr = mean linear velocity of growth, in sm
Some Mean Overall Crystal Growth Rates Expressed as a Linear Velocity1
Crystallizing Substance Cc S smvr b l
( ) ( )NH SO Al SO H O244 2 4 2 4 3 2: : 15 30 30 40
5.4.7.1 Factors for Selection of Filter MediaThe filter media in any process filter need to meet the following requirements to be of value in a chemical process:
• The septum must obviously be able to retain the solids to be filtered, producing a reasonably clear filtrate• The removed solids must not plug off the media upon initial or subsequent use.• The media must be chemically resistant to the chemicals in the filtrate and the filter cake.• The septum must be strong enough physically to withstand the operating conditions.• The media must allow the cake to be discharged cleanly and completely.• The cost of the media must be reasonable enough not to add significantly to the overall plant or production
cost.
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5.4.7.2 Filtration EquationsTotal pressure drop:
( ) ( )p p p p p p p p pa b a b c mD D D− = − = − + − = − −l l
where
- Dp = overall pressure drop
pa = filter inlet pressure
p' = septum inlet pressure
pb = filter outlet pressure
- Dpc = pressure drop over cake
- Dpm = pressure drop over medium
Therefore, P p pb aD = −
Filter cake pressure drop:
( )( )
dLdp
g Du150 1
c s p2 3
2
z f
n f=−
where
dLdp
= pressure gradient at thickness L
µ = viscosity of filtrate
u = linear velocity of filtrate, based on filter area
e = porosity of cake
gc = gravitational conversion factor
Dp = nominal diameter of solid particles
D sv6
s p p
pz = for nonspherical particles
1sz = for spherical particles
or
. ( )
dLdp
g
u vs
4 17 1
c
p
p
3
22
f
n f
=− f p
where
sp = surface of single particle
vp = volume of single particle
Filter medium resistance:
R u
p p gup g
mb c m c
n nD=
−=
−l` j
Chapter 5: Mass Transfer
NCEES 283
5.4.8 Drying of Solids
5.4.8.1 Moisture (Solvent) Percentage ContentTypically calculated on a dry solid/dry air basis:
X = % moisture in solid = mmsw
where
X = moisture (solvent) content in solid, moisture mass/dry solid mass
mw = moisture (solvent) content, mass of water or solvent, in lbm
ms = mass of dry solid, in lbm
Y = % moisture in air = m
maw
where
Y = moisture (solvent) content in air, moisture mass/dry air mass
mw = moisture (solvent) content, mass of water or solvent, in lbm
ma = mass of dry air, in lbm
5.4.8.2 Rate of DryingRate of drying is dictated by the state of the solvent, such as:
• "Free" solvent on surface of solids• "Bound" solvent, which must reach the surface through diffusion or capillary action• "Solvated" solvent, which is chemically bound to the solids (sometimes labile to removal, sometimes not) that
are not generally considered in drying analyses
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Drying Curve
FALLINGRATE II
N, D
RYIN
G RA
TEFALLINGRATE I
CONSTANT RATE
X * XC
X, MOISTURE (SOLVENT) CONTENT lb/lb DRY SOLID
where
X* = equilibrium moisture content: the moisture content of the solid when it reaches equilibrium with the surrounding air; depending upon the specific conditions of the surrounding air
Xc = critical moisture content: the moisture content that marks the instant when the liquid content on the surface of the solid is no longer sufficient to maintain a continuous liquid film on the surface
Constant Rate: Rate of drying independent of moisture content. During this period the solid is so wet that the entire surface of the solid is covered with a continuous film of liquid.
Falling Rate I: Only part of the solid surface is saturated as the entire solid surface can no longer be main-tained at saturation conditions by the movement of moisture within the solid. The rate of drying is linear with regard to X.
Falling Rate II: The entire solid surface is unsaturated and the drying rate is limited by the rate of internal moisture movement.
5.4.8.3 Specific Drying ApplicationsDrying of slab using gas from one side only:*
1. For drying during the constant rate periodRate of drying can be determined based on the balance between the heat transfer to the material and the rate of vapor removal from the surface.
Nh A T
k A pCt
gmD
D= =
* Source: McCabe, Warren L., and Julian C. Smith, Unit Operations in Chemical Engineering, 3rd ed., New York: McGraw-Hill, 1976.
Chapter 5: Mass Transfer
NCEES 285
where
DT = gas dry bulb temperature—temperature at surface of solid
Dp = vapor pressure of water at surface temperature—partial pressure of water vapor in the gas
A = surface area, in ft2
kg = mass-transfer coefficient, in hr ft atmlbm- -2
Nc = constant drying rate, in ft hrlbm-2
l = latent heat of evaporation, in lbmBtu
ht = total heat-transfer coefficient, in hr ft FBtu- -2 c
When the air is flowing parallel to the surface:
ht = 0.0128 G0.8
When the air is flowing perpendicular to the surface, the equation is
ht = 0.37 G0.37
where G = mass velocity, in ft hrlbm-2
( )t ANm X X
C
s 1 2=−
where
t = drying time
X1 = moisture content in solid at time 1
X2 = moisture content in solid at time 2
2. For falling rate period I
( )( ) lnt A N N
m X XNNs
1 2
1 22
1= −−> H
where
N1 = drying rate at time 1, in ft hrlb-2
N2 = drying rate at time 2, in ft hrlb-2
ms = mass of dry solids, in lb
3. For falling rate period II, rate curve must be integrated: t A
mNdXs
x
x
2
1= d n #
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5.4.8.4 Dryer Design and Performance1. Tray dryers
To determine the tray area for a specific production rate:
( )A L
P t tT
d=+
where
P = production rate, in mass of dry solids per hour
t = drying time
td = downtimefor loading and unloading trays
LT = tray loading in mass of dry solids per square area of tray, in ftlbm2
( )t k T TW d
12 f a s
s p2m t
= −
where
dp = drop diameter, in ft
W = moisture content in the drop, in lbm dry solidlbm
kf = thermal conductivity of the gas film, in hr ft FBtu- -c
Ta –Ts = temperature difference between drop and gas, in °F
Sources: 1 Perry, Robert H., and Cecil H. Chilton, Perry's Chemical Engineers' Handbook, 6th ed.
2 Schweitzer, Philip A., Handbook of Separation Techniques for Chemical Engineers, 2nd ed.
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5.4.9 Adiabatic Humidification and Cooling
Adiabatic Humidification and CoolingLENGTH OR HEIGHT
Z
GAS INTERFACE
ADRIABATICSAT'N
TG1
Y '2
Y '2
Y 'as
Y 'as
Y '
T – dT
Y 'as
Y '1
L'1 L'2L' L'+ dL'
Y'1 Y ' Y ' dY '+G's1
ds = adz
G 's1G 's1
G 's1
Y '1
Y '2
TG
TG TG2G
dTG
TG1
TG2 TG1
TG2
Tas
Tas Tas Tas
TasTas
Tas
BULK GAS
BULK GAS
ABS
HUMI
DITY
ABS
HUMI
DITY
TEMP
ERAT
URE
SENSIBLE RATE OF TRANSFER
RATE OF MASS TRANSFER
TEMPERATURE
zO
O
dz
dY '
MATERIAL BALANCE
INTERFACIAL SERVICE
SAT'N HUMIDITY
dZ
PSYCHOMETRIC RELATIONS
SENSIBLE HEAT TRANSFER
MASS TRANSFER
FLOW MODEL
INTERFACE AND BULK LIQUID
L'2 – L'1 = G 's (Y '2 – Y '1)
G'sdY '1 = kYa (Y 'as – Y ')dz
dL' = G'sdY'
G's Cs1 dTG = hg a (TG – Tas) dz
Chapter 5: Mass Transfer
NCEES 291
where
Ll = solute-free liquid flow rate
G sl = dry-gas mass flow rate
Y 1l = initial humidity
Y 2l = final humidity
Y asl = saturation humidity at liquid-gas interface
TG = temperature of bulk gas
Tas = temperature at liquid-gas interface
CS1 = specific heat capacity at the liquid-gas interface
hg = gas heat-transfer coefficient
Since Y asl is constant:
ln Y YY Y
Gk a z
as
as
s
y
2
1−−
=l ll l
lf p
where
ky = overall mass-transfer coefficient
a = interstitial surface per unit volume, in ftft3
2
z = height, in ft
G Y Y k a Z Ys y lm2 1 D− =l l l l_ ^i h
where Y lmD l^ h = logarithmic mean of humidity difference
or
lnlmNTU YY Y
Y YY Y
tGas
as2 1
2
1
D=
−= −
−l
l ll ll l
^ h > H and
HTU k aG
NTUz
tGy
s
tG= =l
where
NTUtG = number of gas-phase transfer units
HTUtG = height of transfer unit
5.4.9.1 Air-Water Systems Y y29
18A A= r
where YA = molal humidity
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AY yy1AA=
−rr
where yAr = mole fraction of water vapor
Y yy
2918 1
AAA= −rre o
Relative humidity = 100 APP
A
where AP = partial pressure of water at a given temperature
PA = vapor pressure of water at a given temperature
A
AY PP Y P
P1 1A AS
A
A=−
= −
where Yas = saturation humidity
% saturation = A
A( )Y
YP PP P
10011
100as
A
A
A=−
−
^_ i
h at total pressure of one atmosphere
Humid heat CPH = 0.24 + 0.46YA
CPH = CPy (1 + YA)
where CPy = specific heat of water vapor at constant pressure
CPH = humid heat capacity
5.4.9.2 Adiabatic Saturation Temperature t t C Y YAS y
PH
RAS A0 0
m= − −` j
where
tAS = adiabatic saturation temperature
ty0 = initial inlet temperature
lR = heat of vaporization at reference temperature
YA0 = initial inlet humidity
CPH = humid heat capacity
YAS = humidity at saturation
t t C Y YWB y
PH
RWB A
m= − −` j
where
YWB = humidity at wet bulb temperature
tWB = wet bulb temperature
Chapter 5: Mass Transfer
NCEES 293
Humidity Chart for the Air-Water System at One Atmosphere
12
25
0.22 0.24
140° ADRIABATIC SITUATION LINES
SATURATED VOLUME VS. TEMPERATURE
SPECIFIC VOLUME VS TEMPERATURE
HUMI
D HE
AT V
S HU
MIDI
TY
PERC
ENT
SATU
RATIO
N 135°
130°
125°
120°
115°
110°105°
100°95°
90°85°
80°75°
70°65°60°55°50°45°
140° ADRIABATIC SITUATION LINES
SATURATED VOLUME VS. TEMPERATURE
SPECIFIC VOLUME VS TEMPERATURE
HUMI
D HE
AT V
S HU
MIDI
TY
PERC
ENT
SATU
RATIO
N
0.26 0.28 0.15
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0
0.30
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
135°
130°
125°
120°
115°
110°105°
100°95°
90°85°
80°75°
70°65°60°55°50°45°
40 60 80 100 120 140TEMPERATURE, F°
160 180 200 220 240 250
13
14
15
16
17
12
19
20
21
22
HUMI
DITY
, LB
WAT
ER V
APOR
/LB D
RY A
IR
VOLU
ME,C
U FT
/LB D
RY A
IRHUMID HEAT, BTU/LB DRY AIR (°F)
Source: G.G. Brown et al., Unit Operations, New York: John Wiley & Sons, Inc., 1950, p. 545.
Cooling Tower Operating Diagram
80
60Hy vs tx
txHY
11
CpxLGB
Hy8 vs t4
tx0
Hy0
SLOPE =
TOP OF TOWER
BOTTOM OFTOWER
CpxLmaxGB
Hy vs tx
txHY
11
CpxLGB
Hy8 vs t4
tx0
Hy0
40
20
050 60
SLOPE =
70 80
TOP OF TOWER
BOTTOM OFTOWER
90t, °F
H, B
TU/LB
DRY
AIR
100 110
CpxLmaxGB
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H GC L t H G
C L tyB
Pxx y0
B
Pxx0= + −e eo o
where
Hy = enthalpy of vapor phase
CPx = specific of liquid phase
L = liquid phase mass velocity
GB = dry air mass velocity
tx = liquid phase temperature
Hy0 = initial enthalpy of vapor phase
tx0 = liquid phase inlet temperature
295
6 PLANT DESIGN AND OPERATION
6.1 Terms and Definitions
DefinitionsTerm Description
Boiling point The temperature at which the vapor pressure of a liquid equals the atmospheric pressure of 14.7 pounds per square inch (psia), 101 kPa, or 760 mm of mercury. For purposes of this classification, when an accurate boiling point is not available for a material or when a mixture does not have a constant boiling point, use the 20%-evaporated point of a distillation performed in accordance with ASTM D 86. Boiling point is commonly expressed in °F or °C.
Combustible dust
A finely divided solid material that is 420 microns or less in diameter and that, when dispersed in air in the proper proportions, can be ignited by a flame, spark, or other source of ignition. Will pass through a U.S. No. 40 standard sieve.
Combustible liquid
A liquid having a closed-cup flash point at or above 100°F (38°C). Subdivided into:
Class II: Closed-cup flash point at or above 100°F (38°C) and below 140°F (60°C)
Class IIIA: Closed-cup flash point at or above 140°F (60°C) and below 200°F (93°C)
Class IIIB: Closed-cup flash point at or above 200°F (93°C)
This category does not include compressed gases or cryogenic fluids.Deflagration An exothermic reaction, such as the extremely rapid oxidation of a flammable dust or vapor in air, in
which the reaction progresses through the unburned material at a rate less than the velocity of sound. A deflagration can have an explosive effect.
Detonation An exothermic reaction characterized by the presence of a shock wave in the material that establishes and maintains the reaction. The reaction zone progresses through the material at a rate greater than the velocity of sound. The principal heating mechanism is one of shock compression. A detonation has an explosive effect.
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Definitions (cont'd)Term Description
Explosion An effect produced by the sudden, violent expansion of gases, which may be accompanied by a shock wave, a disruption of enclosing materials or structures, or both. An explosion could result from:
• Chemical changes such as rapid oxidation, deflagration or detonation, decomposition of molecules, or runaway polymerization (usually detonations)
• Physical changes such as pressure tank ruptures• Atomic changes such as nuclear fission or fusion
Flammable gas
A material that is a gas at 68°F (20°C) or less at 14.7 psia (101 kPa) of pressure—therefore a material that has a boiling point of 68°F (20°C) or less at 14.7 psia (101 kPa)—and which either:
• Ignites at 14.7 psia (101 kPa) when in a mixture of 13% or less by volume with air• Has a flammable range mixed in air at 14.7 psia (101 kPa) and 63°F (20°C)
These levels shall be determined at the specified pressure and temperature in accordance with ASTM E 681.
Flammable liquefied gas
A liquefied compressed gas that, under a charged pressure, is partially liquid at a temperature of 68°F (20°C) and that is flammable.
Flammable liquid
A liquid having a closed-cup flash point below 100°F (38°C). Flammable liquids are further catego-rized into a group known as Class I liquids and subdivided into:
Class IA: Closed-cup flash point below 73°F (23°C) and boiling point below 100°F (38°C)
Class IB: Closed-cup flash point below 73°F (23°C) and boiling point at or above 100°F (38°C)
Class IC: Closed-cup flash point at or above 73°F (23°C) and boiling point below 100°F (38°C). The category of flammable liquids does not include compressed gases or cryogenic fluids.
Flammable material
A material capable of being readily ignited from a common source of heat or at a temperature of 600°F (316°C).
Flammable solid
A solid, other than a blasting agent or explosive, that:
Is capable of causing fire through friction, absorption or moisture, spontaneous chemical change, or retained heat from manufacturing or processing
or
Has an ignition temperature below 212°F (100°C)
or
Burns so vigorously and persistently when ignited as to create a serious hazard
A chemical shall be considered a flammable solid in accordance with the test method of CPSC 16 CFR: Part 1500.44 if it ignites and burns with a self-sustained flame at a rate greater than 0.1 inch (2.5 mm) per second along its major axis.
Flammable vapors or fumes
The concentration of flammable constituents in air that exceeds 25% of their lower flammable limit (LFL).
Flash point The minimum temperature in degrees Fahrenheit (or Centigrade) at which a liquid will give off suf-ficient vapors to form an ignitable mixture with air near the surface or in the container, but will not sustain combustion. The flash point of a liquid shall be determined by appropriate test procedure and apparatus as specified in ASTM D 56, ASTM D 93, or ASTM D 3278.
Chapter 6: Plant Design and Operation
NCEES 297
Definitions (cont'd)Term Description
Highly toxic A material that produces a lethal dose or lethal concentration that falls within any of these categories:
• A chemical that has a median lethal dose (LD50) of 50 milligrams or less per kilogram of body weight when administered orally to albino rats weighing between 200 and 300 grams each
• A chemical that has a median lethal dose (LD50) of 200 milligrams or less per kilogram of body weight when administered by continuous contact for 24 hours (or less if death occurs within 24 hours) with the bare skin of albino rabbits weighing between 2 and 3 kilograms each
• A chemical that has a median lethal concentration (LC50) in air of 200 parts per million by vol-ume or less of gas or vapor, or 2 milligrams per liter or less of mist, fume, or dust when admin-istered by continuous inhalation for 1 hour (or less if death occurs within 1 hour) to albino rats weighing between 200 and 300 grams each
Mixtures of these materials with ordinary materials, such as water, may not warrant classification as highly toxic.
Immediately dangerous to life and health (IDLH)
The concentration of air-borne contaminants that poses a threat of death, immediate or delayed per-manent adverse health effects, or effects that could prevent escape from such an environment. This concentration level of contaminants is established by the National Institute for Occupational Safety and Health (NIOSH) based on both toxicity and flammability. Generally it is expressed in parts per-million by volume (ppm/v) or milligrams per cubic meter (mg/m3).
Organic peroxide
An organic compound that contains the bivalent -O-O- structure and that may be considered a struc-tural derivative of hydrogen peroxide in which one or both of the hydrogen atoms have been replaced by an organic radical. Organic peroxides can pose an explosion hazard (detonation or deflagration) or can be shock sensitive. They also can decompose into various unstable compounds over an extended period of time.
Class I: Formulations that are capable of deflagration but not detonation
Class II: Formulations that burn very rapidly and pose a moderate reactivity hazard
Class III: Formulations that burn rapidly and pose a moderate reactivity hazard
Class IV: Formulations that burn in the same manner as ordinary combustibles and pose a mini-mal reactivity hazard
Class V: Formulations that burn with less intensity than ordinary combustibles or do not sustain combustion and pose no reactivity hazard
Unclassified detonable: Organic peroxides that are capable of detonation. These pose an extremely high explosion hazard through rapid explosive decomposition.
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Definitions (cont'd)Term Description
Oxidizer A material that readily yields oxygen or other oxidizing gas or that readily reacts to promote or initi-ate combustion of combustible materials and, if heated or contaminated, can result in vigorous self-sustained decomposition.
Class 4: An oxidizer that can undergo an explosive reaction due to contamination or exposure to thermal or physical shock and that causes a severe increase in the burning rate of combustible materials with which it comes into contact. Additionally, the oxidizer causes a severe increase in the burning rate and can cause spontaneous ignition of combustibles.
Class 3: An oxidizer that causes a severe increase in the burning rate of combustible materials with which it comes into contact.
Class 2: An oxidizer that causes a moderate increase in the burning rate of combustible materials with which it comes into contact.
Class 1: An oxidizer that does not moderately increase the burning rate of combustible materials.Oxidizing gas A gas that can support and accelerate combustion of other materials more than air does.Physical hazard
A chemical for which there is evidence that it is one of the following:
• Combustible liquid• Cryogenic fluid• Explosive or flammable solid, liquid, or gas• Solid or liquid organic peroxide• Solid or liquid oxidizer• Oxidizing gas• Pyrophoric solid, liquid, or gas• Unstable (reactive) solid, liquid, or gas material• Water-reactive solid or liquid material
Toxic A chemical falling within any of these categories:
• Has a median lethal dose (LD50) of more than 50 milligrams per kilogram but not more than 500 milligrams per kilogram of body weight when administered orally to albino rats weighing between 200 and 300 grams each.
• A chemical that has a median lethal dose (LD50) of more than 200 milligrams per kilogram but not more than 1000 milligrams per kilogram of body weight when administered by continuous contact for 24 hours (or less if death occurs within 24 hours) with the bare skin of albino rabbits weighing between 2 and 3 kilograms each.
• A chemical that has a median lethal concentration (LC50) in air of more than 200 parts per mil-lion but not more than 2000 part per million by volume or less of gas or vapor, or more than 2 milligrams per liter but not more than 20 milligrams per liter of mist, fume, or dust, when ad-ministered by continuous inhalation for 1 hour (or less if death occurs within 1 hour) to albino rats weighing between 200 and 300 grams each.
Chapter 6: Plant Design and Operation
NCEES 299
Definitions (cont'd)Term Description
Unstable (reactive) material
A material, other than an explosive, that in the pure state or as commercially produced will vigor-ously polymerize, decompose, condense, or become self-reactive and undergo other violent chemical changes, including explosion, when it is either:
• Exposed to heat, friction, or shock• In the absence of an inhibitor• In the presence of contaminants• In contact with incompatible materials
Unstable (reactive) materials are subdivided into:
Class 4: Materials that in themselves are readily capable of detonation or explosive decomposi-tion or explosive reaction at normal temperatures and pressures. Includes materials that are sensitive to mechanical or localized thermal shock at normal temperatures and pressures
Class 3: Materials that in themselves are capable of detonation or of explosive decomposition or explosive reaction but which require a strong initiating source or which must be heated under confinement before initiation. Includes materials that are sensitive to thermal or mechanical shock at elevated temperatures and pressures
Class 2: Materials that in themselves are normally unstable and readily undergo violent chemi-cal change but do not detonate; includes materials that can undergo chemical change with rapid release of energy at normal temperatures and pressures and that can undergo violent chemical change at elevated temperatures and pressures
Class 1: Materials that in themselves are normally stable but that can become unstable at elevated temperatures and pressures
Water-reactive material
A material that explodes; violently reacts; produces flammable, toxic, or other hazardous gases; or evolves enough heat to cause autoignition or ignition of combustibles upon exposure to water or moisture. Water-reactive materials are subdivided into:
Class 3: Materials that react explosively with water without requiring heat or confinement
Class 2: Materials that react violently with water or have the ability to boil water. Materials that produce flammable, toxic, or other hazardous gases, or evolve enough heat to cause autoignition or ignition of combustibles upon exposure to water or moisture
Class 1: Materials that react with water with some release of energy, but not violently
Source: International Code Council, International Building Code, 2015.
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6.2 Economic Considerations
NomenclatureAbbreviation Definition
A Uniform amount per interest periodBV Book valueC Cost, present worthDj Depreciation in year j
F Future worth, value, or amountG Uniform gradient amount per interest periodi Interest rate per interest periodm Number of compounding periods per interest periodn Number of interest periods, or the expected life of an assetP Present worth, value, or amountr Nominal annual interest rateSn Expected salvage value in year n
Subscriptse Effective
j At time j
n At time n
6.2.1 Cost Estimation and Project Evaluation
Basic EquationsFactor Name Converts Symbol Formula
Single payment Compound amount to F given P (F/P, i%, n) F = P (1 + i)n
Single payment Present worth to P given F (P/F, i%, n) P = F (1 + i)-n
Uniform series Sinking fund to A given F (A/F, i%, n) ( )A F i
i1 1n= + −d n
Capital recovery to A given P (A/P, i%, n)( )( )A P ii i1 11
n
n=
+ −+f p
Uniform series Compound amount to F given A (F/A, i%, n) ( )F A i
i1 1n= + −d n
Uniform series Present worth to P given A (P/A, i%, n)
( )( )P A i i
i1
1 1n
n=
++ −f p
Uniform gradient Present worth to P given G (P/G, i%, n)
( )( )
( )P Gi ii
i in
11 1
1n
n
n2=+
+ −− +f p
Uniform gradient* Future worth to F given G (F/G, i%, n) ( )F G
ii
in1 1n
2=+ −
−f p
Uniform gradient Uniform series to A given G (A/G, i%, n)
( )A G i in1
1 1n= − + −d n
Chapter 6: Plant Design and Operation
NCEES 301
Basic Equations (cont'd)Factor Name Converts Symbol Formula
Interest rate to ic given r,m i mr1 1e
m= + −c m
Book value initial costBV D jR= −
* GF
iAF n
AF
GA#=
−=
Depreciation Methods
Method Description Formula Stipulations
Straight line
Annual depreciation cost d n
V Vs=−
where d = annual depreciation, in $ per year V = original value of the property at start the service-life period, completely installed and ready for use, in $ Vs = salvage value of property at end of service life, in $ n = service life, in years Va = asset or book value a = number of years in actual use i = annual interest rate expressed as a fraction R = uniform annual payments made at end of each year (annual depreciation cost), in $ V - Vs = total amount of the annuity accumulated in an estimated service life of n years (original value of property minus salvage value at end of service life), in $
Book value V V ada = −
Declining balance (or fixed percentage)
Fixed percentage factor f V
V1 sn1
= − d n
Book value V V f1aa= −` j
Sinking fund
Depreciation for year a d
n nn a V V
12 1
a s=+
− +−
__ `i
i j
Book value V V V Vii
1 11 1
a s n
a
= − −+ −+ −` __j
ii
Source: Peters, Max S., and Klaus D. Timmerhaus, Plant Design and Economics for Chemical Engineers, 4th ed., New York: McGraw-Hill, Inc., 1991, pp. 278 and 280.
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6.2.1.1 Cost IndiciesCost indices are used to update historical cost data to the present. If a purchase cost is available for an item of equipment in year M, the equivalent current cost can be found using:
$ ( )Current Cost in year Index in yearCurrent IndexM M= d n
Cost IndexYear Equipment Index Labor Index Material Index
6.2.1.2 Scaling Equipment CostsThe cost of Unit A at one capacity related to the cost of a similar Unit B with X times the capacity of Unit A is approximately X n times the cost of Unit B, or:
Cost of Unit A Cost of Unit B Capacity of Unit BCapacity of Unit A n
= e o
Typical Scaling Factors (n) for Equipment Cost vs. CapacityEquipment Size Range Exponent
Crystallizer, growth 0.65Crystallizer, forced circulation 0.55Crystallizer, batch 0.70Dryer, drum, single vacuum 10 to 102 ft2 0.76Dryer, drum, single atmospheric 10 to 102 ft2 0.40Dust collector, cyclone 0.80Dust collector, cloth filter 0.68
Dust collector, precipitator 0.75
Evaporator, forced circulation 0.70
Evaporator, vertical and horizontal tube 0.53
Fan, centrifugal 103 to 104 minft3 0.44
Fan, centrifugal 2 x 104 to 7 x 104minft3 1.17
Filter, plate and press 0.58Filter, pressure leaf 0.55Heat exchanger, shell and tube, floating head, carbon steel 100 to 400 ft2 0.60Heat exchanger, shell and tube, fixed sheet, carbon steel 100 to 400 ft2 0.44Mill, ball and roller 0.65Mill, hammer 0.85Motor, squirrel cage, induction, 440 volts, explosion proof 5 to 10 hp 0.69Motor, squirrel cage, induction, 440 volts, explosion proof 20 to 200 hp 0.99Pump, centrifugal, carbon steel 0.67Pump, centrifugal, stainless steel 0.70Pump, reciprocating, cast iron, horizontal, including motor 2 to 100 gpm 0.34Reactor, stainless steel, 300 psi 100 to 1000 gal 0.56Tanks and vessels, pressure, carbon steel 0.60Tanks and vessels, horizontal, carbon steel 0.50Tanks and vessels, stainless steel 0.68Tray, bubble cap, carbon steel 3- to 10-ft diameter 1.20Tray, sieve, carbon steel 3- to 10-ft diameter 0.86
Source: Guthrie, K.M., "Data and Techniques for Preliminary Capital Cost Estimating," Chemical Engineering, New York: Chemical Engeering, 1969.
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6.3 Design
6.3.1 Process DesignNote: The symbology used in this reference is intended to be used for the Chemical PE exam. It does not necessarily correspond to a particular standard.
6.3.1.1 Piping and Instrumentation Diagram (P&ID) Equipment Tag Nomenclature
Mechanical Function CodesCode Equipment or FunctionAG AgitatorAX Packaged unitBL BlowerBX BoilerCL ColumnCM CompressorCR Crane and winchCV ConveyorDR DryerEX ExpanderFA FanFI FilterFL FlareFX Fired furnace, heaterGN GeneratorHV HVACHX Unfired heat transfer equipment, e.g., heat
Measured or Initiating Variable Modifier Readout or
Passive Function Output Function Modifier
A Analysis AlarmB Burner, combustionC ControlD Differential
E Voltage Sensor (primary element)
F Flow rate Ratio (fraction) G Glass, viewing deviceH Hand HighI Current (electrical) IndicateJ Power Scan
K Time, time schedule Time rate of change Control station
L Level Light LowM Momentary Middle, intermediateO Orifice, restrictionP Pressure, vacuum Point (test) connectionQ Quantity Integrate, totalizeR Radiation RecordS Speed, frequency Safety SwitchT Temperature TransmitU Multivariable Multifunction Multifunction Multifunction
V Vibration, mechanical analysis
Valve, damper, louver
W Weight, force WellX Unclassified X axis Unclassified Unclassified Unclassified
Y Event, state, or presence Y axis Relay, compute,
convert
Z Position, dimension Z axisDriver, actuator, unclassified final control element
Source: Instrumentation Symbols and Identification (ANSI/ISA-5.1-2009), Research Triangle Park, NC: American National Standard, 2009.
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General Instrument or Function Symbols
COMPUTERFUNCTION
PROGRAMMABLELOGIC CONTROL
SHARED DISPLAY,SHARED CONTROL
DISCRETEINSTRUMENTS
PRIMARYLOCATION
ACCESSIBLE TOOPERATOR
FIELDMOUNTED
AUXILIARYLOCATION
**NORMALLY**NORMALLYACCESSIBLE TO
OPERATOR
*IP1
* Abbreviations of the user's choice—such as IP1 (Instrument Panel #1), IC2 (Instrument Console #2), CC3 (Computer Console #3), etc.—may be used when it is necessary to specify instrument or function location.
** Normally inaccessible or behind-the-panel devices or functions may be depicted by using the same symbol but with dashed horizontal lines, as in:
Additional General Instrument or Function Symbols
PILOT LIGHT DIAPHRAGM SEAL INTERLOCK LOGIC
*
* This diamond is approximately half the size of the larger symbols.
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Actuator Symbols
WITH OR WITHOUT POSITIONER OR OTHER
PILOT
DIAPHRAGMSPRING –OPPOSED OR
UNSPECIFIED ACTUATOR
DIAPHRAGMPRESSURE–BALANCED
ROTARY MOTOR (SHOWN TYPICALLY WITH ELECTRIC
SIGNAL, MAY BE HYDRAULIC OR PNEUMATIC)
PREFERRED FOR DIAGRAM ASSEMBLED
WITH PILOT*, ASSEMBLY IS ACTUATED BY ONE
INPUT (SHOWN TYPICALLY WITH ELECTRIC INPUT)
CYLINDER WITHOUT POSITION OR OR OTHER PILOT
SPRING-OPPOSEDSINGLE-ACTING
PREFERRED FOR ANY CYLINDER THAT IS ASSEMBLED WITH A PILOT* SO THAT ASSEMBLY IS ACTUATED
BY ONE CONTROLLED INPUT
M
SOLENOID
SI
I
PREFERRED ALTERNATIVE. A BUBBLE WITH INSTRUMENT TAGGING, E.G. TY-I MAY BE USED INSTEAD OF THE INTERLOCK SYMBOL
CYLINDER WITH POSITIONER AND OVERRIDING PILOT VALVE
S
SINGLE-ACTING CYLINDER(IMPLIED I/P)
FOR PRESSURE RELIEFOR SAFETY VALVES ONLY.
SPRING WEIGHT DENOTES A SPRING WEIGHT OR INTEGRAL PILOT
HAND ACTUATOROR HANDWHEEL
DOUBLE-ACTING
* Pilot may be positioned solenoid valve signal converter, etc.
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Symbols for Self-Actuated Regulators, Valves, and Other Devices
LEVEL REGULATOR WITH MECHANICAL LINKAGE
BACKPRESSUREREGULATOR
SELF-CONTAINED
VACUUM RELIEF VALVE,GENERAL SYMBOL
PSVXX
PRESSURE RELIEF ORSAFETY VALVE,
GENERAL SYMBOL
PSVXX
AUTOMATIC REGULATOR WITH INTEGRAL FLOW
INDICATION
FICVXX
AUTOMATIC REGULATOR WITHOUT INDICATION
FCVXX
FLOW SIGHT GLASS, PLAIN OR WITH PADDLE WHEEL FLAPPER, ETC.
RESTRICTION ORIFICE (ORIFICE PLATE, CAPILLARY TUBE OR MULTI-STAGE
TYPE. ETC.) IN PROCESS LINE
ROXX
HAND CONTROL VALVE IN PROCESS LINE
HVXX
LCVXX
TANK
PRESSURE-REDUCING REGULATOR, SELF- CONTAINED, WITH
HANDWHEEL ADJUST-ABLE SETPOINT
PCVXX PCV
XX
FLOW
HAND
LEVE
LPR
ESSU
RE
FGXX
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RUPTURE DISK OR SAFETY HEAD FOR PRESSURE RELIEF
RUPTURE DISK OR SAFETY HEAD FOR
VACUUM RELIEF
PSEXX
PSEXX
PILOT-OPERATEDRELIEF VALVE
P
PRES
SURE
(CON
TD.)
6.3.2 Process Equipment Design
Comparison of the Common Tray Types
Property Sieve Tray Fixed Valve Tray Moving Valve TrayCapacity High High High to very highEfficiency High High High
TurndownAbout 2:1 Not generally suitable for operation under variable loads
About 2.5:1 Not generally suitable for operation under variable loads
About 4:1 to 5:1 Some special designs achieve 8:1 or more
Entrainment Moderate Moderate ModeratePressure drop Moderate Moderate Slightly higherCost Low Low About 20% higherMaintenance Low Low ModerateFouling tendency Low to very low Low to very low ModerateEffects of corrosion Low Very low Moderate
Main applications
(1) Most columns when turndown is not critical (2) High fouling and corro-sion potential
(1) Most columns when turndown is not critical (2) High fouling and corro-sion potential
(1) Most columns (2) Services where turn-down is important
Source: Green, Don W., and Robert H. Perry, Chemical Engineer's Handbook, 8th ed., New York: McGraw-Hill, 2008, p. 14-29.
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6.3.2.1 Equipment Relief Installation Practices
Installation Practices for Equipment ReliefSystem Recommendations
VESSEL
For rupture disc in corrosive service, or for highly toxic materials where spring-loaded reliefs may weep.
P For two rupture discs in extremely corrosive service. The first may need to be replaced periodically.
For rupture disc and spring-loaded relief. Normal relief may go through spring-loaded device and rupture disc is backup for larger reliefs.
P For two reliefs in series. The rupture disc protects against toxicity or corrosion. The spring-loaded relief closes and minimizes losses.
For two rupture discs with special valve that keeps one valve always directly connected to vessel. This design is good for polymerization reactors that require periodic cleaning.
VESSEL
A
B
CA. Pressure drop not more than 3% of set pressure.
B. Long radius elbow.
C. If distance is greater than 10 feet, support weight and reaction forces below the long radius elbow.
PIPE
For orifice area of a single safety relief in vapor service; should not exceed 2% of the cross-sectional area of the protected line. May require multiple valves with staggered settings.
A
A. Process lines; should not be connected to safety-valve inlet piping.
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Installation Practices for Equipment Relief (cont'd)System Recommendations
A
B
A. Turbulence-causing device.
B. Dimension shown below:
Device Causing the Turbulence Minimum Number of Straight-Pipe Diameters
Regulator or valve 252 ells or bends not in same plane 202 ells or bends in same plane 151 ell or bend 10Pulsation damper 10
Source: Crowl, D.A., and J.F. Louvar, Chemical Process Safety: Fundamentals With Applications, 2nd ed., New York: Prentice Hall, 2002, pp. 369–370, Figure 8-11.
6.3.3 Siting Considerations
6.3.3.1 Fixed FacilitiesBuilding Siting Evaluation: The procedures used to evaluate the hazards and establish the design criteria for new buildings and the suitability of existing buildings at their specific locations.
Facility: The physical location where the management system activity is performed. In early life-cycle stages, a facility may be the company's central research laboratory or the engineering offices of a technology vendor. In later stages, the facility may be a typical chemical plant, storage terminal, distribution center, or corporate office. Site is used synonymously with facility when describing to Risk Management Plan (RMP) audit criteria.
Fixed Facility: A portion of or a complete plant, unit, site, complex, or any combination thereof that is generally not moveable. In contrast, mobile facilities, such as ships (e.g., transport vessels, floating platform storage and offloading vessels, drilling platforms), trucks, and trains, are designed to be moveable.
Siting: The process of locating a complex, site, plant, or unit.
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Guiding Principles for Location of Fixed Facility
API Recommended Practice 752 is based on the following guiding principles:
a. Locate personnel away from process areas consistent with safe and effective operations.b. Minimize the use of buildings intended for occupancy in close proximity to process areas.c. Manage the occupancy of buildings in close proximity to process areas.d. Design, construct, install, modify, and maintain buildings intended for occupancy to protect occupants against explosion, fire, and toxic material releases.e. Manage the use of buildings intended for occupancy as an integral part of the design, construction, mainte- nance, and operation of a facility.
Source: "Management of Hazards Associated with Location of Process Plant Permanent Buildings," Section of API Recommended Practice 752, 3rd ed., December 2009.
Overall Building Siting Evaluation Flow Chart
NO NO
NO
NO
YES
START
STOP
IS BUILDINGWITHIN THE SCOPE OF
API752?
IS BUILDING INCLUDED IN THE SITING VALUATION?
IS BUILDINGIMPACTED BY
EXPLOSION, FIRE OR TOXICS?
DESIGN BUILDING (INCLUDING
EXTENSIONS AND MODIFICATIONS TO
EXISTING BUILDINGS) TO MEET BUILDING SITING EVALUATION
CHOOSE BUILDING SITING EVALUATION APPROACH(ES) AND
CRITERIA
ARE BUILDING SITING
EVALUATION CRITERIA MET?
CARRY OUT BUILDING SITING EVALUATION
INCLUDE BUILDING IN MITIGATION PLAN.
DEVELOP AND IMPLEMENT
MITIGATION PLAN.
IMPLEMENT MANAGEMENT OF
BUILDING OCCUPANCYAND/OR MANAGEMENT
OF CHANGE
NO
YES YES
YES
YESIS IT A NEW
BUILDING ORMODIFICATION TO
EXISTINGBUILDING?
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Building Siting Evaluation for ExplosionsSTART
STOP
YES
NO NO
NO
NO
YES
YESYESCOULD BUILDINGBE IMPACTED
BY EXPLOSION?
IS IT A NEWBUILDING OR
MODIFICATION TOEXISTING
BUILDING?
DETERMINEBLAST LOADSON BUILDING
DETERMINEBLAST LOADSON BUILDING
DESIGN BUILDING (INCLUDING EXTENSIONS AND MODIFICATIONS TO EXISTING BUILDINGS) TO MEET BUILDING SITING
EVALUATION FOR EXPLOSION
COMPLETE A BUILDING DAMAGE LEVEL
ASSESSMENT ORA DETAILED STRUCTURAL
ANALYSIS
CARRY OUT MORE DETAILED ANALYSIS?
DOES BUILDINGMEET BUILDING SITING
CRITERIA FOR EXPLOSION?
INCLUDE BUILDING AND MITIGATION PLAN
BUILDING SITING EVALUATION FOR EXPLOSION NOT
REQUIRED.
IMPLEMENT MANAGE-MENT OF THE BUILDING
OCCUPANCY AND/OR MANAGEMENT OF
CHANGE
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Building Siting Evaluation for Fire
START
STOP
NO NO
NO
NO
YES YES YES
YES
YES
NO
COULD BUILDING BE IMPACTED BY
FIRE?ARE SEPARATION DISTANCES MET?
BUILDING SITING EVALUATION FOR FIRE
NOT REQUIRED.
INCLUDE BUILDING IN MITIGATION PLANAND IMPLEMENT MITIGATION PLAN
CARRY OUT MORE DETAILED ANALYSIS.IF NEEDED, INCLUDE
BUILDING IN MITIGATION PLAN AND IMPLEMENT
MITIGATION PLAN
INCLUDE BUILDING AND MITIGATION PLAN AN AND IMPLEMENT MITIGATION
PLAN
CARRY OUT MORE DETAILED ANALYSISIF NEEDED, INCLUDE
BUILDING IN MITIGATION PLAN AND IMPLEMENT
MITIGATION PLAN
IMPLEMENT MANAGEMENT OF
BUILDING OCCUPANCY AND/OR MANAGEMENT
OF CHANGE
DOES BUILDINGMEET BUILDING
SITING EVALUATION CRITERIA?
DESIGN BUILDINGTO MEET BUILDINGSITING EVALUATION
CRITERIA.
IS IT A NEW BUILDING OR
MODIFICATIONS TO EXISTING
BUILDING?
DETERMINE FIRE EFFECTS AT BUILDING AND SELECT THE FIRE
PROTECTION CONCEPT
IS A SPACING TABLE APPROACH
USED?
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Building Siting Evaluation for Toxic Material Release
START
STOP
NONO
NO
NO
YES YES
YES
YES
BUILDING SITING EVALUATION FOR TOXIC
NOT REQUIRED
IS THERE POTENTIAL FOR A TOXIC
RELEASE?
IS IT ASSUMED THAT BUILDING IS IMPACTED?
PERFORM TOXIC GAS DISPERSING MODELING.
SELECT PROTECTION CONCEPT FOR TOXIC
MATERIAL.
DESIGN AND BUILDING TO MEET BUILDING
SITING THE EVALUATION CRITERIA.
IMPLEMENT MANAGEMENT OF
BUILDING OCCUPANCY AND MANAGEMENT OF
CHANGE.
INCLUDE BUILDING A MITIGATION PLAN AND
IMPLEMENT MITIGATION PLAN
CARRY OUT MORE DETAILED ANALYSIS . IF
NEEDED, INCLUDE BUILDING IN MITIGATION PLAN AND IMPLEMENT
MITIGATION PLAN.
ARE BUILDING SITING EVALUATION CRITERIA
EXCEEDED?
IS IT A NEW BUILDING OR MODIFICATION TO EXISTING
BUILDING?
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6.3.3.2 Portable BuildingsPortable Building: Any rigid structure that can be moved easily to another location within the facility, regardless of the length of time it is kept at the site. Examples of portable buildings include wood framed trailers (single- and double-wide), container boxes, semi-trailers, and portable structures designed to be blast resistant. Lightweight fabric enclosures, such as tents, are excluded.
Guiding Principles for Siting Portable Buildings
API Recommended Practice 753 is based on the following guiding principles:
a. Locate personnel away from covered process areas consistent with safe and effective operations.b. Minimize the use of occupied portable buildings in close proximity to covered process areas.c. Manage the occupancy of portable buildings, especially during periods of increased risk including start-up or planned shut-down operations.d. Design, construct, install, and maintain occupied portable buildings to protect occupants against potential hazards.e. Manage the use of portable buildings as an integral part of the design, construction, maintenance, and opera- tion of a facility.
Source: "Management of Hazards Associated with Location of Process Plant Portable Buildings," Section of API Recommended Practice 753, 1st ed., June 2007.
6.3.3.3 Typical Clearances to Railroads
Typical Clearances to RailroadsNO CONSTRUCTION ACTIVITIES OR OTHER OBSTRUCTION SHALL BE PLACED IN WITHIN THESE LIMITS
12'-0"15'-0"
21'-6
"
UPRR*BNSF**
C L TRACK
TOPOF RAIL
*Union Pacific Railroad**Burlington Northern Santa Fe Railway
(NORMAL TO RAILROAD)MINIMUM CONSTRUCTION CLEARANCE ENVELOPE
Source: State of California Department of Transportation, Standard Drawing XS11-010, July 2014.
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6.3.3.4 Building Occupancy
Maximum Allowable Quantity per Control Area of Hazardous Materials Posing a Physical Hazarda,j,m,n,p
Material Class
Group When the Maximum
Allowable Quantity Is Exceeded
Storageb Used in Closed Systemsb Used in Open Systemsb
For SI: 1 cubic foot = 0.028 m3, 1 pound = 0.454 kg, 1 gallon = 3.7785 L NL = not limited; N/A = not applicable; UD = unclassified detonable
Source: International Code Council, International Building Code, 2012 ed. All footnote references are to the IBC.
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a. For use of control areas, see Section 414.2.b. The aggregate quantity in use and storage shall not exceed the quantity listed for storage.c. The quantities of alcoholic beverages in retail and wholesale sales occupancies shall not be limited provided the liquids are packaged in individual containers not exceeding 1.3 gallons. In retail and wholesale sales occupancies, the quantities of medicines, foodstuffs, consumer or industrial products, and cosmetics containing not more than 50 percent by volume of water-miscible liquids, with the remainder of the solutions not being flammable, shall not be limited, provided that such materials are packaged in individual containers not exceeding 1.3 gallons. d. Maximum allowable quantities shall be increased 100% in buildings equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1. Where Note e also applies, the increase for both notes shall be applied accumulatively.e. Maximum allowable quantities shall be increased 100% when stored in approved storage cabinets, day boxes, gas cabinets, or exhausted enclosures or in listed safety cans in accordance with Section 5003.9.10 of the Inter- national Fire Code. Where Note d also applies, the increase for both notes shall be applied accumulatively.f. The permitted quantities shall not be limited in a building equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1.g. Permitted only in buildings equipped throughout with an automatic sprinkler system in accordance with Section 903.3.1.1.h. Containing not more than the maximum allowable quantity per control area of Class IA, IB, or IC flammable liquids.i. The maximum allowable quantity shall not apply to fuel oil storage complying with Section 603.3.2 of the International Fire Code.j. Quantities in parentheses indicate quantity units in parentheses at the head of each column.k. A maximum quantity of 200 pounds of solid or 20 gallons of liquid Class 3 oxidizers is allowed when such materials are necessary for maintenance purposes, operation, or sanitation of equipment. Storage containers and the manner of storage shall be approved.l. Net weight of the pyrotechnic composition of the fireworks. Where the net weight of the pyrotechnic composi- tion of the fireworks is not known, 25% of the gross weight of the fireworks, including packaging, shall be used.m. For gallons of liquids, divide the amount in pounds by 10 in accordance with Section 5003.1.2 of the Interna- tional Fire Code.n. For storage and display quantities in Group M and storage quantities in Group S occupancies complying with Section 414.2.5, see Tables 414.2.5(1) and 414.2.5(2). o. Densely packed baled cotton that complies with the packing requirements of ISO 8115 shall not be included in this material class.p. The following shall not be included in determining the maximum allowable quantities: 1. Liquid or gaseous fuel in fuel tanks on vehicles 2. Liquid or gaseous fuel in fuel tanks on motorized equipment operated in accordance with this code 3. Gaseous fuels in piping systems and fixed appliances regulated by the International Fuel Gas Code 4. Liquid fuels in piping systems and fixed appliances regulated by the International Mechanical Codeq. Where manufactured, generated, or used in such a manner that the concentration and conditions create a fire or explosion hazard based on information prepared in accordance with Section 414.1.3.
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Maximum Allowable Quantity Per Control Area of Hazardous Material Posing a Health Hazarda,b,c,i
MaterialLiquefied (150)h Storaged Used in Closed Systemsd Used in Open Systemsd
For SI: 1 cubic foot = 0.028 m3, 1 pound = 0.454 kg, 1 gallon = 3.785 L
a. For use of control areas, see Section 414.2.b. In retail and wholesale occupancies, the quantities of medicines, foodstuffs, consumer or industrial products, and cosmetics containing not more than
50% by volume of water-miscible liquids—with the remainder of the solutions not being flammable—shall not be limited, provided that such materials are packaged in individual containers not exceeding 1.3 gallons.
c. For storage and display quantities in Group M and storage quantities in Group S, occupancies complying with Section 414.2.5, see Tables 414.2.5(1) and 414.2.5(2).
d. The aggregate quantity in use and storage shall not exceed the quantity listed for storage.e. Maximum allowable quantities shall be increased 100% in buildings equipped throughout with an approved automatic sprinkler system in accordance
with Section 903.3.1.1. Where Note f below also applies, the increase for both notes shall be applied accumulatively.f. Maximum allowable quantities shall be increased 100% when stored in approved storage cabinets, gas cabinets, or exhausted enclosures as specified
in the International Fire Code. Where Note e above also applies, the increase for both notes shall be applied accumulatively.g. Allowed only when stored in approved exhausted gas cabinets or exhausted enclosures as specified in the International Fire Code.h. Quantities in parentheses indicate quantity units in parentheses at the head of each column.i. For gallons of liquids, divide the amount in pounds by 10 in accordance with Section 5003.1.2 of the International Fire Code.
Source: International Building Code, 2012 edition. All footnote references are to the IBC.
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International Building Code Area Classification DescriptionsOccupancy
Class Description
A Assembly Group A occupancy includes, among others, the use of a building or structure, or a portion thereof, for the gathering of persons for purposes such as civic, social or religious functions; recreation, food or drink consumption or awaiting transportation.
B Business Group B occupancy includes, among others, the use of a building or structure, or a portion thereof, for office, professional or service-type transactions, including storage of records and accounts. Business occupancies shall include, but not be limited to, the following:
Airport traffic control towers Ambulatory care facilities Animal hospitals, kennels, and pounds Banks Barber and beauty shops Car wash Civic administration Clinic, outpatient Dry cleaning and laundries: pick-up and delivery stations and self-service Educational occupancies for students above the 12th grade Electronic data processing Laboratories: testing and research Motor vehicle showrooms Post offices Print shops Professional services (architects, attorneys, dentists, physicians, engineers, etc.) Radio and television stations telephone exchanges Training and skill development not within a school or academic program
F Factory Industrial Group F occupancy includes, among others, the use of a building or structure, or a portion thereof, for assembling, disassembling, fabricating, finishing, manufacturing, packaging, repair, or processing operations that are not classified as a Group H hazardous or Group S storage occupancy.
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International Building Code Area Classification Descriptions (cont'd)Occupancy
Class Description
F-1 Factory Industrial uses which are not classified as Factory Industrial F-2 Low Hazard. Examples include:
Aircraft (manufacturing, not to include repair) Appliances Athletic equipment Automobiles and other motor vehicles Bakeries Beverages over 16-percent alcohol content Bicycles Boats Brooms or brushes Business machines Cameras and photo equipment Canvas or similar fabric Carpets and rugs (including cleaning) Clothing Construction and agricultural machinery Disinfectants Dry cleaning and dyeing Electric generation plants Electronics Engines (including rebuilding) Food processing and commercial kitchens not associated with restaurants, cafeterias and similar dining facilities Furniture Hemp products Jute products Laundries Leather products Machinery Metals Millwork (sash and door) Motion pictures and television filming (without spectators) Musical instruments Optical goods Paper mills or products Photographic film Plastic products Printing or publishing Recreational vehicles Refuse incineration Shoes Soaps and detergents Textiles Tobacco Trailers Wood: distillation Woodworking (cabinet) Upholstering
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International Building Code Area Classification Descriptions (cont'd)Occupancy
Class Description
F-2 Factory industrial uses that involve the fabrication or manufacturing of noncombustible materials which during finishing, packing or processing do not involve a significant fire hazard. Examples include:
Beverages up to and including 16-percent alcohol content Brick and masonry Ceramic products Foundries Glass products Gypsum Ice Metal products (fabrication and assembly)
H High-Hazard Group H occupancy includes, among others, the use of a building or structure, or a portion thereof, that involves the manufacturing, processing, generation or storage of materials that constitute a physical or health hazard in quantities in excess of those allowed in control areas comply-ing with Section 414, based on the maximum allowable quantity limits for control areas set forth in Tables 307.1(1) and 307.1(2). Hazardous occupancies are classified in Groups H-1, H-2, H-3, H-4 and H-5 and shall be in accordance with this section, with the requirements of Section 415 and the Interna-tional Fire Code. Hazardous materials stored, or used on top of roofs or canopies shall be classified as outdoor storage or use and shall comply with the International Fire Code.
H-1 Buildings and structures containing materials that pose a detonation hazard. Examples include: Deton-able pyrophoric materials, explosives, organic peroxides (unclassified detonable), Class 4 oxidizers, Class 3 detonable and Class 4 unstable (reactive) materials.
H-2 Buildings and structures containing materials that pose a deflagration hazard or a hazard from acceler-ated burning. Examples include:
Class I, II, or IIIA flammable or combustible liquids which are used or stored in normally open containers or systems, or in closed containers or systems pressurized at more than 15 psi (103.4 kPa) gage Combustible dusts where manufactured, generated or used in such a manner that the concentration and conditions create a fire or explosion hazard based on information prepared in accordance with Section 414.1.3 Cryogenic fluids, flammable Flammable gases Organic peroxides, Class I Oxidizers, Class 3, that are used or stored in normally open containers or systems or in closed containers or systems pressurized at more than 15 psi (103.4 kPa) gage Pyrophoric liquids, solids, and gases, nondetonable Unstable (reactive) materials, Class 3, nondetonable Water-reactive materials, Class 3
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International Building Code Area Classification Descriptions (cont'd)Occupancy
Class Description
H-3 Buildings and structures containing materials that readily support combustion or that pose a physical hazard. Examples include:
Class I, II, or IIIA flammable or combustible liquids that are used or stored in normally closed containers or systems pressurized at 15 pounds psi (103.4 kPa) gauge or less Combustible fibers, other than densely packed baled cotton Consumer fireworks, 1.4G (Class C, Common) Cryogenic fluids, oxidizing Flammable solids Organic peroxides, Class II and III Oxidizers, Class 2 Oxidizers, Class 3, that are used or stored in normally closed containers or systems pressurized at 15 pounds psi (103.4 kPa) gage or less Oxidizing gases Unstable (reactive) materials, Class 2 Water-reactive materials, Class 2
H-4 Buildings and structures that contain materials that are health hazards. Examples include:
Corrosives Highly toxic materials Toxic materials
H-5 Semiconductor fabrication facilities and comparable research and development areas in which hazard-ous production materials (HPM) are used and the aggregate quantity of materials is in excess of those listed in Tables 307.1(1) and 307.1(2).
I Institutional Group I occupancy includes, among others, the use of a building or structure, or a portion thereof, in which care or supervision is provided to persons who are or are not capable of self-preserva-tion without physical assistance or in which persons are detained for penal or correctional purposes or in which the liberty of the occupants is restricted.
M Mercantile Group M occupancy includes, among others, the use of a building or structure, or a portion thereof, for the display and sale of merchandise and involves stocks of goods, wares, or merchandise incidental to such purposes and accessible to the public. Mercantile occupancy shall include, but not be limited to, the following:
Department stores Drug stores Markets Motor fuel-dispensing facilities Retail or wholesale stores Sales rooms
R Residential Group R includes among others, the use of a building or structure, or a portion thereof, for sleeping purposes when not classified as an Institution Group I or when not regulated by the Interna-tional Residential Code.
S Storage Group S occupancy includes among others, the use of a building or structure, or a portion thereof, for storage that is not classified as a hazardous occupancy.
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International Building Code Area Classification Descriptions (cont'd)Occupancy
Class Description
S-1 Moderate hazard Storage Group S-1. Buildings occupied for storage uses that are not classifies as Group S-2, including, but not limited to, storage of the following:
Aerosols, levels 2 and 3 Aircraft hangars (storage and repair) Bags: cloth, burlap and paper Bamboos and rattan Baskets Belting: canvas and leather Books and paper in rolls or packs Boots and shoes Buttons, including cloth covered, pearl or bone Cardboard and cardboard boxes Clothing, woolen wearing apparel Cordage Dry boats (indoor) Furniture Furs Glues, mucilage, pastes and size Grains Horns and combs, other than celluloid Leather Linoleum Lumber Motor vehicle repair garages complying with the maximum allowable quantities of hazardous materials listed in Table 307.1(1) (see Section 406.8) Photo engravings Resilient flooring Silks Soaps Sugar Tires, bulk storage of Tobacco, cigars, cigarettes and snuff Upholstery and mattresses Wax candles
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International Building Code Area Classification Descriptions (cont'd)Occupancy
Class Description
S-2 Low-hazard storage, Group S-2. Includes among others, buildings used for the storage of noncombus-tible materials such as products on wood pallets or in paper cartons with or without single thickness divisions; or in paper wrappings. Such products are permitted to have a negligible amount of plastic trim such as knobs, handles or film wrapping. Group S-2 storage shall include, but not be limited to, storage of the following:
Asbestos Beverages up to and including 16-percent alcohol in metal, glass or ceramic containers Cement in bags Chalk and crayons Dairy products in nonwaxed coated paper containers Dry cell batteries Electrical coils Electrical motors Empty cans Food products Foods in noncombustible containers Fresh fruits and vegetables in nonplastic trays or containers Frozen foods Glass Glass bottles, empty or filled with noncombustible liquids Gypsum board Inert pigments Ivory Meats Metal cabinets Metal desks with plastic tops and trim Metal parts Metals Mirrors Oil-filled and other types of distribution transformers Parking garages, open or enclosed Porcelain and pottery Stoves Talc and soapstones Washers and dryers
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332 NCEES
International Building Code Area Classification Descriptions (cont'd)Occupancy
Class Description
U General. Buildings and structures of an accessory character and miscellaneous structures not classified in any specific occupancy shall be constructed, equipped and maintained to conform to the require-ments of this code commensurate with the fire and life hazard incidental to their occupancy. Group U shall include, but not be limited to, the following:
Agricultural buildings Aircraft hangars, accessory to a one- or two-family residence (see Section 412.5) Barns Carports Fences more than 6 feet (1829 mm) in height Grain silos, accessory to a residential occupancy Greenhouses Livestock shelters Private garages Retaining wall Sheds Stables Tanks Towers
6.3.3.5 Area Separation Requirements
Required Separation of Occupancies (Hours)
OccupancyA, E I-1, I-3,
I-4 I-2 Ra F-2, S-2b, U
B, F-1, M, S-1 H-1 H-2 H-3, H-4 H-5
S NS S NS S NS S NS S NS S NS S NS S NS S NS S NSA, E N N 1 2 2 NP 1 2 N 1 1 2 NP NP 3 4 2 3 2 NP
S = Buildings equipped throughout with an automatic sprinkler system installed in accordance with Section 903.3.1.1 NS = Buildings not equipped throughout with an automatic sprinkler system installed in accordance with Section 903.3.1.1 N = No separation requirement NP = Not permitteda. See Section 420.b. The required separation from areas used only for private or pleasure vehicles shall be reduced by 1 hour but to
not less than 1 hour.c. See Section 406.3.4.d. Separation is not required between occupancies of the same classification.
Chapter 6: Plant Design and Operation
NCEES 333
6.3.3.6 Wind DirectionPrevailing winds should be considered in both plant siting and layout:
a. For siting, it is undesirable to locate a plant where prevailing winds would carry any fugitive emissions into nearby residential areas.
b. In laying out a plant, safety considerations dictate that process units be located such that:1. Prevailing winds would not carry potentially flammable releases to an area of the plant where there
could be a source of ignition.2. Prevailing winds would not carry potentially hazardous or toxic releases to an area of the plant where
workers are in enclosed areas, e.g., offices, control rooms, or enclosed process buildings.
6.3.4 Instrumentation and Process Control
6.3.4.1 First-Order Control System ModelsThe transfer function model for a first-order system is
( )( )R sY s
sK1x
= +
where
K = steady-state gain
t = time constant
The step response of a first-order system to a step input of magnitude M is
( ) ( )y t y e KM e1/ /t t0= + −x x− −
In the chemical process industry, y0 is typically taken to be zero, and y(t) is referred to as a deviation variable.
For systems with time delay (dead time or transport lag) q, the transfer function is
( )( )R sY s
sKe
1s
x= +
i−
The step response for t ≥ q to a step of magnitude M is
( ) ( ) ( )y t y e KM e u t1( )/ ( )/t t0 i= + − −i x i x− − − −8 B
where
u(t) = unit step function
6.3.4.2 Second-Order Control System ModelsOne standard second-order control system model is
( )( )R sY s
s sK2 n n
n2 2
2
g~ ~
~=+ +
PE Chemical Reference Handbook
334 NCEES
where
K = steady-state gain
z = the damping ratio
wn = the undamped natural (z = 0) frequency
1d n2~ ~ g= − , the damped natural frequency
1 2r n2~ ~ g= − , the damped resonant frequency
If the damping ratio z is less than unity, the system is said to be underdamped; if z is equal to unity, it is said to be critically damped; and if z is greater than unity, the system is said to be overdamped.
For a unit step input to a normalized, underdamped, second-order control system, the time required to reach a peak value tp and the value of that peak Mp are determined by
t1
pn
2~ g
r=−
M e1 /p
1 2= + rg g− −
The percent overshoot (%OS) of the response is determined by
%OS e100 / 1 2= rg g− −
For an underdamped, second-order system, the logarithmic decrement is
nm xx1 1
12
k mk
2dg
rg= =−+
d nwhere xk and xk+m are the amplitudes of oscillation at cycles k and k + m, respectively.
The period of oscillation t is related to wd by
wdt = 2p
The time required for the output of a second-order system to settle to within 2% of its final value (2% settling time) is defined to be
T 4s
ng~=
An alternative form commonly employed in the chemical process industry is
Source: Perry, R.H., Properties of Materials, 8th ed., New York: McGraw-Hill, 2008.
PE Chemical Reference Handbook
338 NCEES
6.3.5.2 Gasket Materials
Important Properties of Gasket Materials*
Material Max Service Temp °F Important Properties
Rubber (straight):
Natural 225Good mechanical properties. Impervious to water. Fair to good resistance to acids, alkalies. Poor resistance to oils, gasoline. Poor weathering, aging properties.
Styrene-butadiene (SBR) 250 Better water resistance than natural rubber. Fair to good resistance to acids, alkalies. Unsuitable with gasoline, oils, and solvents.
Butyl 300 Very good resistance to water, alkalies, many acids. Poor resistance to oils, gasoline, most solvents (except oxygenated).
Nitrile 300 Very good resistance to water. Excellent resistance to oils, gasoline. Fair to good resistance to acids, alkalies.
Polysulfide 150Excellent resistance to oils, gasoline, aliphatic, and aromatic hydro-carbon solvents. Very good resistance to water. Good resistance to alkalies. Fair acid resistance. Poor mechanical properties.
Neoprene 250Excellent mechanical properties. Good resistance to nonaromatic petroleum, fatty oils, solvents (except aromatic, chlorinated, or ketone types). Good water and alkali resistance. Fair acid resistance.
Silicone 600Excellent heat resistance. Fair water resistance. Poor resistance to steam at high pressures. Fair to good acid, alkali resistance. Poor (except fluorosilicone rubber) resistance to oils, solvents.
Acrylic 450Good heat resistance but poor cold resistance. Good resistance to oils, aliphatic and aromatic hydrocarbons. Poor resistance to water, alkalies, some acids.
Chlorosulfonated polyethylene (Hypalon) 250
Excellent resistance to oxidizing chemicals, ozone, weathering. Relatively good resistance to oils, grease. Poor resistance to aromat-ic or chlorinated hydrocarbons. Good mechanical properties.
Floroelastomer (Viton, Fluorel 2141, Kel-F) 450
Can be used at high temperatures with many fuels, lubricants, hy-draulic fluids, solvents. Highly resistant to ozone, weathering. Good mechanical properties.
Asbestos:Compressed asbestos-rubber sheet To 700 Large number of combinations available; properties vary widely
depending on materials used.Asbestos-rubber woven sheet To 250 Same as above.
Asbestos-rubber (beater addition process) 400 Same as above.
Asbestos composites To 1000 Same as above.
Asbestos-TFE To 500 Combines heat resistance and sealing properties of asbestos with chemical resistance of TFE.
Cork compositions 250
Low cost. Truly compressible materials that permit substantial deflections with negligible side flow. Conform well to irregular surfaces. High resistance to oils. Good resistance to water, many chemicals. Should not be used with inorganic acids, alkalies, oxidiz-ing solutions, live steam.
Chapter 6: Plant Design and Operation
NCEES 339
Important Properties of Gasket Materials* (cont'd)
Material Max Service Temp °F Important Properties
Cork rubber 300 Controlled compressibility properties. Good conformability, fatigue resistance. Chemical resistance depends on kind of rubber used.
Plastics:
TFE (solid) (tetrafluoro- ethylene, Teflon) 500
Excellent resistance to almost all chemicals and solvents. Good heat resistance; exceptionally good low-temperature properties. Rela-tively low compressibility and resilience.
TFE (filled) To 500 Selectively improved mechanical and physical properties. However, fillers may lower resistance to specific chemicals.
TFE composite To 500 Chemical and heat resistance comparable with solid TFE. Inner gasket material provides better resiliency and deformability.
CFE (chlorotrifluoro- ethylene, Kel-F) 350 Higher cost than TFE. Better chemical resistance than most other
gasket materials, although not quite as good as TFE.
Vinyl 212 Good compressibility, resiliency. Resistant to water, oils, gasoline, and many acids and alkalies. Relatively narrow temperature range.
Polyethylene 150 Resists most solvents. Poor heat resistance.Plant fiber:
Neoprene-impregnated wood fiber 175 Nonporous; recommended for glycol, oil, and gasoline to 175°F.
SBR-bonded cotton 230 Good water resistance.Nitrile rubber-cellulose fiber Resists oil at high temperatures.
Vegetable fiber, glue binder 212 Resists oil and water to 212°F.
Vulcanized fiber Low cost. Good mechanical properties. Resists gasoline, oils, greases, waxes, many solvents.
Inorganic fibers To 2200 Excellent heat resistance. Poor mechanical properties.Felt:
Pure felt
Resilient, compressible, and strong, but not impermeable. Resists medium-strength mineral acids and dilute mineral solutions if not intermittently dried. Resists oils, greases, waxes, most solvents. Damaged by alkalies.
TFE-impregnated 300 Good chemical and heat resistance.Petrolatum- or paraffin-impregnated High water repellency.
Rubber-impregnated Many combinations available; properties vary widely depending on materials used.
PE Chemical Reference Handbook
340 NCEES
Important Properties of Gasket Materials* (cont'd)
Material Max Service Temp °F Important Properties
Metal:Lead 500 Good chemical resistance. Best conformability of metal gaskets.Tin Good resistance to neutral solutions. Attacked by acids and alkalies.
Aluminum 800 High corrosion resistance. Slightly attacked by strong acids and alkalies.
Copper, brass Good corrosion resistance at moderate temperatures.Nickel 1400 High corrosion resistance.
Monel 1500 High corrosion resistance. Good against most acids and alkalies, but attacked by strong hydrochloric and strong oxidizing acids.
Inconel 2000 Excellent heat, oxidation resistance.Stainless steel High corrosion resistance. Properties depend on type used.
Metal composites Many combinations available; properties vary widely depending on materials used.
Leather 220 Low cost. Limited chemical and heat resistance. Not recommended against pressurized steam, acid, or alkali solutions.
Glass fabric High strength and heat resistance. Can be impregnated with TFE for high chemical resistance.
Packing and Sealing Materials
Rubber (straight) 600 See Gasket Materials for properties. Mainly used for ring-type seals, although some types are available as spiral packings.
Rubber composites:
Cotton-reinforced 350High strength. Chemical resistance depends on type of rubber used; however, most types are noted for high resistance to water, aqueous solutions.
Asbestos-reinforced 450 High strength combined with good heat resistance.Asbestos:
Plain, braided asbestos 500 Heat resistance combined with resistance to water, brine, oil, many chemicals. Can be reinforced with wire.
Impregnated asbestos To 750
Environmental properties vary widely depending on type of asbestos and impregnant used. Neoprene-cemented type resists hot oils, gaso-line, and solvents. Oil-and-wax-impregnated type resists caustics. Wax-impregnated blue asbestos type has high acid resistance. TFE-impregnated has good all-around chemical resistance.
Asbestos composites To 1200 End properties vary widely depending on secondary material used.Metals:
Copper To 1500
Properties depend on other construction materials and form of cop-per used. Packing made of copper foil over asbestos core resists steam and alkalies to 1000°F. Packing of braided copper tinsel resists water, steam, and gases to 1500°F.
Aluminum To 1000 Resists hot petroleum derivatives, gases, foodstuffs, many organic acids.
Lead 550 Many types are available.
Chapter 6: Plant Design and Operation
NCEES 341
Important Properties of Gasket Materials* (cont'd)
Material Max Service Temp °F Important Properties
Organic fiber:Flax 300 Good water resistance. Jute 300 Good water resistance. Ramie 300 Good resistance to water, brine, cold oil.Cotton 300 Good resistance to water, alcohol, dilute aqueous solutions. Rayon 300 Good resistance to water, dilute aqueous solutions. Felt 300 See Gasket Materials.
Leather To 210 Good mechanical properties for sealing. Resistant to alcohol, gaso-line, many oils and solvents, synthetic hydraulic fluids, water.
TFE To 500 Available in many forms, all of which have high chemical resis-tance.
Carbon graphite 700 Good bearing and self-lubricating properties. Good resistance to chemicals, heat.
* From Materials in Engineering Design, New York: Reinhold, 1959, p. 11-126.
Source: Perry, R.H., and D. Green, Chemical Engineer's Handbook, 6th ed., New York: McGraw-Hill, 1984.
6.3.5.3 CorrosionCorrosion is a natural process that converts a refined metal to a more stable form such as its oxide, hydroxide, or sulfide. It is the gradual destruction of a material by chemical reaction with its environment. Corrosion effects must be taken into account during the design of any system, unit, facility, or plant.
Use the following corrosion data charts to assist in narrowing the field of choice of materials. Once the choice has been narrowed, the effects of contaminants, aeration, galvanic coupling, erosion, and so on must be taken into account. Field testing is best for final suitability decisions.
PE Chemical Reference Handbook
342 NCEES
Source: All corrosion data from Perry, John H., Perry's Chemical Engineers' Handbook, 6th ed., New York: McGraw-Hill, 1963, pp. 23-13 to 23-30.
Detailed Corrosion Data on Construction Materials
ASPHALTIC RESINSSATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
COPPER, AL BRONZE, TIN BRONZE< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
EPOXY RESINSSATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
FURANE RESINSSATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
GLASS< 0.005 IN. PER YR. 0.005 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
HASTELLOY B< 0.002 IN. PER YR.< 0.02 IN. PER YR.. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
HASTELLOY C< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
HASTELLOY D< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
ACID
,AC
ETIC
ACID
,BO
RIC
ACID
,CH
ROMI
C
ACID
,CI
TRIC
ACID
,FO
RMIC
ACID
,HY
DROC
HLOR
IC
ACID
,HY
DROF
LUOR
IC
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
ALUMINUM< 0.005 IN. PER YR. 0.005 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
AIR FREE AIR FREE AIR FREE
CARBON-FILLEDCEMENT
AERATED500 F
400 F 450 F
AERATED ORNON-AERATED
AERATED ORAIR-FREE
1,500 F
NOTE SYMBOLS ON VERTICAL HEAVY LINES REPRESENT 100% CONCENTRATION. SYMBOLS ON
HORIZONTAL HEAVY LINES REPRESENT 300 F. TEMPERATURE.
AIR FREE AIR FREE AIR FREE
CARBON-FILLEDCEMENT
AERATED500 F
400 F 450 F
AERATED ORNON-AERATED
AERATED ORAIR-FREE
1500 F
12½ 25 37½
12½ 25 37½
Chapter 6: Plant Design and Operation
NCEES 343
Detailed Corrosion Data on Construction Materials (cont'd)
IRON, CAST
MONEL
NEOPRENE
NICKEL
PHENOLIC RESINS
POLYETHYLENE
RUBBER (NATURAL, GR-S)
RUBBER, BUTYL
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
SATISFACTORYFOR LIMITED USE ONLYUNSATISFACTORY
===
SATISFACTORYSATISFACTORY FOR LIMITED USEGENERALLY UNSATISFACTORY
===
SATISFACTORYSATISFACTORY FOR LIMITED USEGENERALLY UNSATISFACTORY
===
COMPLETE RESISTANCE SOME ATTACK ATTACK OR DECOMPOSITION
===
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
ACID
,AC
ETIC
ACID
,BO
RIC
ACID
,CH
ROMI
C
ACID
,CI
TRIC
ACID
,FO
RMIC
ACID
,HY
DROC
HLOR
IC
ACID
,HY
DROF
LUOR
IC
AIR FREE
AIR FREE AIR FREE AIR FREE AIR FREE
AIR FREE AIR FREE AIR FREEAERATED
AERATED
HARD RUBBER
HARD RUBBER HARDRUBBER
SOFT GR-SCANNOT BE USED
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
PE Chemical Reference Handbook
344 NCEES
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
STAINLESS STEEL, 18-8
STAINLESS STEEL, TYPE 316
STAINLESS STEEL, 12% Cr
STAINLESS STEEL, 17% Cr
STEEL
STYRENE COPOLYMERS, HIGH IMPACT
ZIRCONIUM
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR. 0.002 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR.0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
ACID
,AC
ETIC
ACID
,BO
RIC
ACID
,CH
ROMI
C
ACID
,CI
TRIC
ACID
,FO
RMIC
ACID
,HY
DROC
HLOR
IC
ACID
,HY
DROF
LUOR
IC
STRESS CORROSION
Chapter 6: Plant Design and Operation
NCEES 345
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
ALUMINUM
ASPHALTIC RESINS
COPPER, AL BRONZE, TIN BRONZE
EPOXY RESINS
FURANE RESINS
GLASS
HASTELLOY B
HASTELLOY C
HASTELLOY D
= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED SERVICE= UNSATISFACTORY
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= NOT RECOMMENDED
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
ACID
,NI
TRIC
ACID
,OX
ALIC
ACID
,PH
OSPH
ORIC
ACID
,SU
LFUR
IC
ALUM
INUM
CHLO
RIDE
ALUM
INUM
PO
TASS
IUM
SULF
ATE
(ALU
M)
AMMO
NIA,
AQUE
OUS
AIR FREE DRYAIR FREE AERATED,NO VELOCITY
AERATED
600 F
250 PSIHCI AND
TECH
TECHSLUDGE-
400 F
IN ETHANOL
NOTRECOMMENDED
IN ETHANOL
IN ETHANOL
300
200
PE Chemical Reference Handbook
346 NCEES
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
ACID
,NI
TRIC
ACID
,OX
ALIC
ACID
,PH
OSPH
ORIC
ACID
,SU
LFUR
IC
ALUM
INUM
CHLO
RIDE
ALUM
INUM
PO
TASS
IUM
SULF
ATE
(ALU
M)
AMMO
NIA,
AQUE
OUS
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
SATISFACTORYFOR LIMITED USEUNSATISFACTORY
===
SATISFACTORYSATISFACTORY FOR LIMITED SERVICE
===
SATISFACTORYSATISFACTORY FOR LIMITED SERVICEGENERALLY UNSATISFACTORY
GENERALLY UNSATISFACTORY
===
COMPLETE RESISTANCE SOME ATTACK ATTACK OR DECOMPOSITION
===
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
IRON, CAST
MONEL
NEOPRENE
NICKEL
PHENOLIC RESINS
POLYETHYLENE
RUBBER (NATURAL, GR-S)
RUBBER, BUTYL
AIR FREE,NO VELOCITY
AIR FREEAIR FREE
AERATED
AERATED
IN ETHANOL
AERATED,NO VELOCITY
AERATED,NO VELOCITY
Chapter 6: Plant Design and Operation
NCEES 347
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
STAINLESS STEEL, 18-8
STAINLESS STEEL, TYPE 316
STAINLESS STEEL, 12% Cr
STAINLESS STEEL, 17% Cr
STEEL
STYRENE COPOLYMERS, HIGH IMPACT
ZIRCONIUM
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR. 0.002 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
ACID
,NI
TRIC
ACID
,OX
ALIC
ACID
,PH
OSPH
ORIC
ACID
,SU
LFUR
IC
ALUM
INUM
CHLO
RIDE
ALUM
INUM
PO
TASS
IUM
SULF
ATE
(ALU
M)
AMMO
NIA,
AQUE
OUS
AIR FREE,NO VELOCITY
STRESSCRACKS
IN ETHANOL
PE Chemical Reference Handbook
348 NCEES
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
ALUMINUM
ASPHALTIC RESINS
COPPER, AL BRONZE, TIN BRONZE
EPOXY RESINS
FURANE RESINS
GLASS
HASTELLOY B
HASTELLOY C
HASTELLOY D
< 0.005 IN. PER YR. 0.005 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
SATISFACTORYSATISFACTORY FOR LIMITED USENOT RECOMMENDED
===
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
< 0.005 IN. PER YR. 0.005 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
AMMO
NIUM
CARB
ONAT
E
AMMO
NIUM
CHLO
RIDE
CALC
IUM
CHLO
RIDE
CALC
IUM
HYPO
CHLO
RITE
Chapter 6: Plant Design and Operation
NCEES 349
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
AVOID HCI
AND Fe, NI IONS
IRON, CAST
MONEL
NEOPRENE
NICKEL
PHENOLIC RESINS
POLYETHYLENE
RUBBER (NATURAL, GR–S)
RUBBER, BUTYL
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
SATISFACTORYFOR LIMITED USE ONLYUNSATISFACTORY
===
SATISFACTORYSATISFACTORY FOR LIMITED SERVICEGENERALLY UNSATISFACTORY
===
SATISFACTORYSATISFACTORY FOR LIMITED SERVICEGENERALLY UNSATISFACTORY
===
COMPLETE RESISTANCESOME ATTACKATTACK OR DECOMPOSITION
===
AMMO
NIUM
CARB
ONAT
E
AMMO
NIUM
CHLO
RIDE
CALC
IUM
CHLO
RIDE
CALC
IUM
HYPO
CHLO
RITE
PE Chemical Reference Handbook
350 NCEES
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
STAINLESS STEEL, 18-8
STAINLESS STEEL, TYPE 316
STAINLESS STEEL, 12% Cr
STAINLESS STEEL, 17% Cr
STEEL pH > 7pH > 7
ZIRCONIUM< 0.002 IN. PER YR. 0.002 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
STYRENE COPOLYMERS, HIGH IMPACTSATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
====
AMMO
NIUM
CARB
ONAT
E
AMMO
NIUM
CHLO
RIDE
CALC
IUM
CHLO
RIDE
CALC
IUM
HYPO
CHLO
RITE
Chapter 6: Plant Design and Operation
NCEES 351
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
AIR FREE
0.09% HCI
COPP
ERSU
LFAT
E
ETHA
NOL
ETHY
LENE
GLYC
OL
FERR
ICCH
LORI
DE
FERR
OUS
CHLO
RIDE
FERR
OUS
SULF
ATE
GLYC
ERIN
E
ALUMINUM
ASPHALTIC RESINS
COPPER, AL BRONZE, TIN BRONZE
EPOXY RESINS
FURANE RESINS
GLASS
HASTELLOY B
HASTELLOY C
HASTELLOY D
= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= < 0.002 IN. PER YR.= 0.002 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= NOT RECOMMENDED
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
PE Chemical Reference Handbook
352 NCEES
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
PITS
COPP
ERSU
LFAT
E
ETHA
NOL
ETHY
LENE
GLYC
OL
FERR
OUS
CHLO
RIDE
FERR
OUS
SULF
ATE
FERR
ICCH
LORI
DE
GLYC
ERIN
E
IRON, CAST
MONEL
NEOPRENE
NICKEL
PHENOLIC RESINS
POLYETHYLENE
RUBBER (NATURAL, GR–S)
RUBBER, BUTYL
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
SATISFACTORYFOR LIMITED USE ONLYUNSATISFACTORY
===
SATISFACTORYSATISFACTORY FOR LIMITED SERVICEGENERALLY UNSATISFACTORY
===
SATISFACTORYSATISFACTORY FOR LIMITED SERVICEGENERALLY UNSATISFACTORY
===
COMPLETE RESISTANCESOME ATTACKATTACK OR DECOMPOSITION
===
Chapter 6: Plant Design and Operation
NCEES 353
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
DRYDISCOLORSDISCOLORS
COPP
ERSU
LFAT
E
ETHA
NOL
ETHY
LENE
GLYC
OL
FERR
ICCH
LORI
DE
FERR
OUS
CHLO
RIDE
FERR
OUS
SULF
ATE
GLYC
ERIN
E
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= 0.002 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
STAINLESS STEEL, 18-8
STAINLESS STEEL, TYPE 316
STAINLESS STEEL, 12% Cr
STAINLESS STEEL, 17% Cr
STEEL
STYRENE COPOLYMERS, HIGH IMPACT
ZIRCONIUM
PE Chemical Reference Handbook
354 NCEES
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
AIR FREEAIR FREE AIR FREE
HYDR
OGEN
PERO
XIDE
MAGN
ESIU
MCH
LORI
DE
MAGN
ESIU
MSU
LFAT
E
METH
ANOL
NICK
ELCH
LORI
DE
NICK
ELSU
LFAT
E
PHEN
OL
POTA
SSIU
MHY
DROX
IDE
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
ALUMINUM
ASPHALTIC RESINS
COPPER, AL BRONZE, TIN BRONZE
EPOXY RESINS
FURANE RESINS
GLASS
HASTELLOY B
HASTELLOY C
HASTELLOY D
Chapter 6: Plant Design and Operation
NCEES 355
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
DRY
AIRFREE
SULFER FREE
ALKALINEDISCOLORS
AIR FREE
AIR FREE,PITS
DRY
HYDR
OGEN
PERO
XIDE
MAGN
ESIU
M CH
LORI
DE
MAGN
ESIU
MSU
LFAT
E
METH
ANOL
NICK
ELNI
TRAT
E
NICK
ELSU
LFAT
E
PHEN
OL
POTA
SSIU
MHY
DROX
IDE
IRON, CAST
MONEL
NEOPRENE
NICKEL
PHENOLIC RESINS
POLYETHYLENE
RUBBER (NATURAL, GR-S)
RUBBER, BUTYL
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED SERVICE= GENERALLY UNSATISFACTORY
= SATISFACTORY= SATISFACTORY FOR LIMITED SERVICE= GENERALLY UNSATISFACTORY
= COMPLETE RESISTANCE= SOME ATTACK= ATTACK OR DECOMPOSITION
= SATISFACTORY= FOR LIMITED USE ONLY= UNSATISFACTORY
PE Chemical Reference Handbook
356 NCEES
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
PITS
STRESSCRACKS
ALKALINE
STRESS CRACKS
DISCOLORS,SULFUR FREE
AIR FREE
800 F.
800 F.
pH > 7 pH > 7
HYDR
OGEN
PERO
XIDE
MAGN
ESIU
M CH
LORI
DE
MAGN
ESIU
MSU
LFAT
E
METH
ANOL
NICK
ELNI
TRAT
E
NICK
ELSU
LFAT
E
PHEN
OL
POTA
SSIU
MHY
DROX
IDE
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= 0.002 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
STAINLESS STEEL, 18-8
STAINLESS STEEL, TYPE 316
STAINLESS STEEL, 12% Cr
STAINLESS STEEL, 17% Cr
STEEL
STYRENE COPOLYMERS, HIGH IMPACT
ZIRCONIUM
Chapter 6: Plant Design and Operation
NCEES 357
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
PITS AIR FREE
10 20 30
POTA
SSIU
MSU
LFAT
E
SODI
UMCA
RBON
ATE
SODI
UMCH
LORI
DE
SODI
UMHY
DROX
IDE
SODI
UMNI
TRAT
E
ZINC
CHLO
RIDE
ZINC
SULF
ATE
= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.005 IN. PER YR.= 0.005 - 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
ALUMINUM
ASPHALTIC RESINS
COPPER, AL BRONZE, TIN BRONZE
EPOXY RESINS
FURANE RESINS
GLASS
HASTELLOY B
HASTELLOY C
HASTELLOY D
PE Chemical Reference Handbook
358 NCEES
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
AIR FREE
AIR FREE
DRY950 F.
1300 F.
1300 F.
DRY
600 F.STRESS CRACKS
400F.
POTA
SSIU
MSU
LFAT
E
SODI
UMCA
RBON
ATE
SODI
UMCH
LORI
DE
SODI
UMHY
DROX
IDE
SODI
UMNI
TRAT
E
ZINC
CHLO
RIDE
ZINC
SULF
ATE
= SATISFACTORY= SATISFACTORY FOR LIMITED USE= UNSATISFACTORY
= SATISFACTORY= FOR LIMITED USE ONLY= UNSATISFACTORY
= COMPLETE RESISTANCE= SOME ATTACK= ATTACK OR DECOMPOSITION
= SATISFACTORY= SATISFACTORY FOR LIMITED SERVICE= GENERALLY UNSATISFACTORY
= SATISFACTORY= SATISFACTORY FOR LIMITED SERVICE= GENERALLY UNSATISFACTORY
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
= < 0.002 IN. PER YR.= < 0.02 IN. PER YR.= 0.02 - 0.05 IN. PER YR.= > 0.05 IN. PER YR.
Chapter 6: Plant Design and Operation
NCEES 359
Detailed Corrosion Data on Construction Materials (cont'd)
KEY TO CHARTS
CONCENTRATION, %
300
200
100
00 50 100TE
MPER
ATUR
E, °F
STRESS CRACKSAT HIGHER TEMPS.
DRYpH > 7
STRESSCRACKS
POTA
SSIU
MSU
LFAT
E
SODI
UMCA
RBON
ATE
SODI
UMCH
LORI
DE
SODI
UMHY
DROX
IDE
SODI
UMNI
TRAT
E
ZINC
CHLO
RIDE
ZINC
SULF
ATE
STAINLESS STEEL, 18-8
STAINLESS STEEL, TYPE 316
STAINLESS STEEL, 12% Cr
STAINLESS STEEL, 17% Cr
STEEL
STYRENE COPOLYMERS, HIGH IMPACT
ZIRCONIUM
SATISFACTORYSATISFACTORY FOR LIMITED USEUNSATISFACTORY
===
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR. 0.002 - 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
====
< 0.002 IN. PER YR.< 0.02 IN. PER YR. 0.02 - 0.05 IN. PER YR.> 0.05 IN. PER YR.
ALLOY 20 STAINLESS STEELNICKEL IRON CHROMIUM ALLOY 825TITANIUMGOLD, PLATINUMGRAPHITE
MOST NOBLE – CATHODIC LEAST NOBLE – ANODICMOST NOBLE – CATHODIC LEAST NOBLE – ANODIC
Note: Unshaded symbols show ranges exhibited by stainless steels in acidic water such as may exist in crevices or in stagnant, low-velocity, or poorly aerated water.
Cathode The electrode at which reduction occursAnode The electrode at which oxidation occursOxidation The loss of electronsReduction The gaining of electronsCation Positive ionAnion Negative ion
Chapter 6: Plant Design and Operation
NCEES 361
6.3.5.6 Standard Oxidation Potentials
Standard Oxidation Potentials for Corrosion Reactions*
Corrosion Reaction Potential (Eo) Volts vs. Normal Hydrogen Electrode
Au Au e33" ++ − -1.498
H O O H e2 4 42 2" + ++ − -1229
Pt Pt e22" ++ − -1.200
Pd Pd e22" ++ − -0.987
Ag Ag e" ++ − -0.799
2Hg Hg e222" ++ − -0.788
Fe Fe e2 3" ++ + − -0.771
OH O H O e4 2 42 2" + +− −^ h -0.401
Cu Cu e22" ++ − -0.337
Sn Sn e22 4" ++ + − -0.150
H H e2 22 " ++ − +0.000
Pb Pb e22" ++ − +0.126
Sn Sn e22" ++ − +0.136
Ni Ni e22" ++ − +0.250
Co Co e22" ++ − +0.277
Cd Cd e22" ++ − +0.403
Fe Fe e22" ++ − +0.440
Cr Cr e33" ++ − +0.744
Zn Zn e22" ++ − +0.763
Al Al e33" ++ − +1.662
Mg Mg e22" ++ − +2.363
Na Na e" ++ − +2.714
K K e" ++ − +2.925
*Measured at 25°C. Reactions are written as anode half-cells. Arrows are reversed for cathode half-cells.
Note: In some chemistry texts, the reactions and the signs of the values (in this table) are reversed; for example, the half-cell potential of zinc is given as –0.763 volt for the reaction Zn e Zn22 "++ − . When the potential Eo is positive, the reaction
proceeds spontaneously as written.
Source: Republished with permission of Houghton Mifflin Harcourt, from Flinn, Richard A., and Paul K. Trojan, Engineering Materials and Their Applications, 3rd ed., 1986. Permission conveyed through Copyright Clearance Center, Inc.
PE Chemical Reference Handbook
362 NCEES
6.4 Operation
6.4.1 Process and Equipment Reliability
6.4.1.1 Operating ProceduresThe main types of process operating procedures are
1. Standard Operating Procedures (SOP)—Written instructions documenting step-by-step instructions for safely performing a task within operating limits. The SOP covers all modes of operation. The purpose of the standard operating procedure is to ensure operations are always carried out correctly and in the same manner. An SOP should be available at the place where the work is done.
2. Startup/Shutdown Procedures—Written procedures for startup and shut-down phased so that interlinked plant operations can resume or stop in a safe and controlled manner.
3. Emergency or Abnormal Operating Procedures—Written instructions documenting step-by-step instructions for reaching a safe state following a process in an upset condition.The emergency procedures should cover the PPE, the level of intervention which is safe, and when to evacuate. The procedures will also need to tie in with site emergency plans.
4. Temporary Operating Procedures—Written instructions for a finite period of time. At the conclusion of this time, the facility returns to using the Standard Operating Procedures. Temporary operating procedures should include an expiration date.
5. Maintenance Procedures—Written instructions that address material control and maintenance practices needed to ensure system operability and integrity. These procedures specify the required maintenance, testing, and inspection frequencies.
Source: Guidelines for Engineering Design for Process Safety, 2nd ed., 5.3.2 "Testing Instrumentation," Center for Chemical Process Safety/AlChE, 2012, pp. 135–137.
The zones for safe operation of process equipment are defined as
1. Normal Operating Zone: The minimum or maximum values of an operating parameter that define the boundaries of normal operations. Some examples of operating parameters to be defined include• High and low pressure
• High and low temperature
• High and low level
• High and low pH
• High and low flow
2. Troubleshooting Zone: An area that provides time for troubleshooting, so that operations personnel can make adjustments in time to return the operating parameters to the Normal Operating Zone. Human factors and process response time generally indicate zone size. Immediate actions, and in some cases predeter-mined actions, to avoid Safe Operating Limit (SOL) deviation are taken in this zone.
3. Buffer Zone: The upper and lower area of the known safe zone provides a buffer to ensure no operating parameter can reach the Unknown/Unacceptable Operation Zone. Factors that influence Buffer Zone size may include engineering judgment, reliability of instrumentation, operating experience, probability and consequence of human error, and so on. A process will not be operated intentionally in this zone.
Chapter 6: Plant Design and Operation
NCEES 363
4. Safe Operating Limit (SOL): A value for an operating parameter that defines the equipment or process unit's safe-operating envelope, beyond which a process will not intentionally be operated due to the risk of imminent, catastrophic equipment failure or loss of containment. Operational or mechanical corrective ac-tion ceases and immediate predetermined actions are taken at these operating parameter values in order to bring equipment and process units to a safe state. Each SOL should be documented in the plant's Process Safety Information.
5. Unacceptable or Unknown Operating Zone: An area beyond the Safe Operating Limit. A process will not be intentionally operated in this zone.
Operation Zones for Process Equipment
SAFE OPERATING LIMIT
EQUIPMENT LIMIT
INSTRUMENT RANGEUNACCEPTABLE/UNKNOWN
OPERATING ZONE
UNACCEPTABLE/UNKNOWNOPERATING ZONE
BUFFER ZONE
BUFFER ZONE
TROUBLESHOOTING ZONE
TROUBLESHOOTING ZONE
NORMALOPERATING ZONE
EQUIPMENT LIMIT
INSTRUMENT RANGE
SAFE OPERATING LIMIT
NEVER EXCEED LIMIT
NEVER EXCEED LIMIT
MAXIMUM NORMAL OPERATING LIMIT
MINIMUM NORMAL OPERATING LIMIT
Source: Smith, David J., Reliability, Maintainability and Risk—Practical Methods for Engineers, 5th ed., Appendix A1: "Terms Related to Failure," Amsterdam: Elsevier, 1997.
PE Chemical Reference Handbook
364 NCEES
6.4.1.2 Maintenance and Reliability
Maintenance and ReliabilityTerm Definition Example or Application
Availability
Availability (%) = Total TimeUp Time
The proportion of time that an item is capable of operating to specification within a large time interval.
The availability of a gas turbine generator was increased to 95% by minimizing the scheduled maintenance duration.
DiversityThe same performance of a function by two or more independent and dissimilar means.
In-line check valves of two different tech-nologies or separate manufacturers are installed to decrease the likelihood of reverse flow from waste-water treatment back to the process.
Failure Modes and Effects Analysis (FMEA)
A qualitative tool for analysis identify-ing all the ways a particular component can fail and the effects of the failure on the system.
An FMEA identifies internal spring failure from excessive wear on a solenoid valve. The local and system consequences are documented. A recommendation is made for regular inspection to prevent this point of failure.
Mean Time Between Failures (MTBF)
The total cumulative functioning time of a population divided by the number of failures, MTBF is used for items that involve repair and excludes downtime.
MTBF Number of FailuresTotal Up Time=
For 10,000 total hours of recorded uptime, the MTBF for 4 power supplies is 2500 hours.
Predictive Maintenance
The aim of predictive maintenance is, first, to predict when equipment failure may occur and, second, to prevent oc-currence of that failure by performing maintenance.
A plant predictive maintenance program could use regular vibration analyses and motor current signature analyses to deter-mine equipment conditions and predict failure.
Preventive MaintenanceActions carried out for the purpose of keeping equipment or instrumentation in a specified condition.
A preventive maintenance program for a centrifugal pump at a plant could include monthly inspection of the gland packing, bearing lubrication, and pump mountings.
Redundancy
The provision of more than one means of achieving a function.
Active/Duty: All items remain operating prior to failure.
Standby: Replicated items do not oper-ate until needed.
An active pump runs continuously for long periods of time without having to go through the start-up process. The standby pump remains dormant and is tested regu-larly to ensure reliability.
Reliability
The probability that the system will not leave the operational state. The avail-ability for a given system is always greater than or equal to the reliability.
Safety-instrumented function; probability of failure on demand.
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6.4.1.3 Decision-Tree Approach to Determine the Optimum Maintenance Period
Decision Tree for Optimum Maintenance
YES YES YES
NO NO NOIS IMPACT AND FREQUENCY OF FAILURE ON AVAILABILITY AND COST ACCEPTABLE?
6.4.2 Process Improvement and TroubleshootingThe variety and complexity of modern processing industries requires that engineers be able to find ways to improve the processes of their facilities for the benefit of their employers or clients. Process improvement allows for the optimization of utilities, raw materials, and other resources to maximize production and minimize the cost per unit produced.
Engineers who are tasked with process improvement and troubleshooting focus their knowledge and training to make a facility or process work more efficiently and economically.
Work in this area will focus on one of the following types of activities:
• Optimum balance of process variables• Increased capacity—Debottleneck and/or add equipment• Improved product quality—Control contamination and deterioration• Improved mechanical performance—Reduce corrosion and fouling• Decreased utility and raw material consumption—Steam, power, water, chemicals, and so on• More efficient maintenance• Improved safety practices
The use of data is paramount to any of the activities listed above. The modern process-industries plant typically has an abundance of data that is part of the control systems. This data is collected from all aspects and areas of the facility.
One of the most common methods of using data to improve a process is the DMAIC method. The five phases in the DMAIC method are
1. Define the problem and system by setting goals and understanding the requirements of the customer and the system.
2. Measure the key aspects of the process and gather the data that is available and relevant to the issue, project, or problem to be solved. This data can be used to determine the "as is" state of the process.
3. Analyze the data to investigate the process and determine the cause-and-effect relationships in the process. Seek out the root cause(s) of the problem being evaluated.
4. Improve or optimize the current process based on data analysis techniques to create a new, future-state process and run pilot trials to establish the process capability.
5. Control the new process to ensure that any deviations are corrected quickly before they result in defects or issues.
Data analysis can be a complex activity and techniques in this area include
5 Whys Analysis of varianceRegression analysis CorrelationCause-and-effect diagraming Control/run chartsDesign of experiments Pareto analysisTaguchi loss function Value stream mappingGeneral linear modeling Axiomatic designCost-benefit analysis Root-cause analysis
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One of the most useful techniques for troubleshooting is root-cause analysis (RCA). RCA is a method of problem-solving used to identify the root cause(s) of faults or problems.
A factor is considered a root cause if removal from the problem-fault sequence prevents the final undesirable event from recurring. A causal factor is one that affects an event's outcome and, if removed, might benefit the process but does not prevent the recurrence of the problem being addressed. RCA is applied to methodically identify and correct the root causes of events, rather than to simply address the symptomatic result. Focusing correction on root causes has the goal of entirely preventing problem recurrence. RCA is typically used as a reactive method for identifying event causes, revealing problems, and solving them. Analysis is most typically done after an event has occurred; however, it can also be used as a predictive tool.
The basic steps in root-cause analysis are:
1. Define the problem or describe the event to prevent in the future.2. Gather data and evidence, classifying it along a time line.3. Data-mine for clusters of similar problems that are close to the problem or event.4. Ask why this happens and identify the causes, giving each sequential step toward the problem or event.5. Classify all causes into either "causal" or "root."6. Identify any other items that affect the problem or event.7. Identify the corrective action(s) that will, with certainty, prevent recurrence of each harmful effect.8. Identify solutions that prevent recurrence and that are within the control of the institution.9. Implement the recommended root-cause corrections.10. Ensure effectiveness by observing the implemented solutions in operation.
Observation is one of the best ways to identify issues that need to be addressed when working and troubleshooting in any type of plant.
6.5 Safety, Health, and Environment
6.5.1 General
6.5.1.1 Definition of SafetySafety is the condition of protecting people from threats or failure that could harm their physical, emotional, occu-pational, psychological, or financial well-being. Safety is also the control of known threats to attain an acceptable level of risk. The United States relies on public codes and standards, engineering designs, and corporate policies to ensure that a structure or place does what it should do to maintain a steady state of safety—that is, long-term stability and reliability. Some safety/regulatory agencies that develop codes and standards commonly used in the United States are shown below.
Insurance, Safety, and Regulatory AgenciesAcronym Name Jurisdiction
ANSI American National Standards Institute Nonprofit standards organizationCGA Compressed Gas Association Nonprofit trade associationCSA Canadian Standards Association Nonprofit standards organizationFAA Federal Aviation Administration U.S. federal regulatory agencyFMG FM Global InsuranceIEC International Electrotechnical Commission Nonprofit standards organization
Insurance, Safety, and Regulatory Agencies (cont'd)Acronym Name Jurisdiction
MSHA Mine Safety and Health Administration Federal regulatory agencyNFPA National Fire Protection Association Nonprofit trade organizationOSHA Occupational Health and Safety Administration Federal regulatory agencyUL Underwriters Laboratories Nationally recognized testing laboratoryUSCG United States Coast Guard Federal regulatory agencyUSDOT United States Department of Transportation Federal regulatory agencyUSEPA United States Environmental Protection Agency Federal regulatory agency
6.5.1.2 Elements of Process Safety Management (PSM)The U.S. Occupational Safety and Health Administration (OSHA) 1910.119 defines all 14 elements of a process safety management plan:
1. Employee Participation—Consult with employees and their representatives on the development and conduct of hazard assessments and the development of chemical accident prevention plans, and provide access to these and other records required under the standard.
2. Process Safety Information—Develop and maintain written safety information identifying workplace chemical and process hazards, equipment used in the processes, and technology used in the processes.
3. Process Hazard Analysis—Perform a workplace hazard assessment including, as appropriate, identifica-tion of potential sources of accidental releases, identification of any previous release within the facility that had a potential for catastrophic consequences in the workplace, estimation of workplace effects of a range of releases, and estimation of the health and safety effects of such a range on employees. Establish a system to respond to the workplace hazard assessment findings, which shall address prevention, mitiga-tion, and emergency responses.
4. Operating Procedures—Develop and implement written operating procedures for the chemical processes, including procedures for each operating phase, operating limitations, and safety and health considerations.
5. Training—Provide written safety and operating information for employees and employee training in oper-ating procedures, by emphasizing hazards and safe practices that must be developed and made available.
6. Contractors—Ensure contractors and contract employees are provided with appropriate information and training.
7. Pre-startup Safety Review—Conduct pre-startup safety reviews of all newly installed or modified equip-ment.
8. Mechanical Integrity—Establish maintenance systems for critical process-related equipment, including written procedures, employee training, appropriate inspections, and testing of such equipment to ensure ongoing mechanical integrity. Establish a quality-assurance program to ensure that initial process-related equipment, maintenance materials, and spare parts are fabricated and installed consistent with design specifications.
9. Hot-Work Permit—A permit must be issued for hot-work operations conducted on or near a covered process. The permit must document that the fire prevention and protection requirements have been imple-mented prior to beginning the hot-work operations; it must indicate the date(s) authorized for hot work and identify the object on which hot work is to be performed. The permit must be kept on file until completion of the hot work.
10. Management of Change—Establish and implement written procedures managing change to process chemicals, technology, equipment, and facilities.
11. Incident Investigation—Investigate every incident that results in or could have resulted in a major accident in the workplace, with any findings to be reviewed by operating personnel and modifications made if appropriate.
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12. Emergency Planning and Response—Develop and implement an emergency action plan for the entire plant in accordance with the provisions of other OSHA rules. Include in the emergency action plan proce-dures for handling small releases of hazardous chemicals.
13. Compliance Audits—Employers must certify that they have evaluated compliance with the provisions of PSM at least every three years. This will verify that the procedures and practices developed under the standards are adequate and are being followed.
14. Trade Secrets—Employers must make available all information necessary to comply with PSM to those persons responsible for compiling the process safety information, those developing the process hazard analysis, those responsible for developing the operating procedures, and those performing incident inves-tigations, emergency planning and response, and compliance audits, without regard to the possible trade-secret status of such information.
6.5.1.3 Safety, Health, and PreventionA traditional preventive approach to both accidents and occupational illness involves recognizing, evaluating, and controlling hazards and work conditions that may cause physical injuries or adverse health effects.
Hazard is the capacity to cause harm. It is an inherent quality of a material or a condition. For example, a rotating saw blade or an uncontrolled high-pressure jet of water has the capability (hazard) to slice through flesh. A toxic chemical or a pathogen has the capability (hazard) to cause illness.
Risk is the chance or the probability that a person will experience harm and is not the same as a hazard. Risk al-ways involves both probability and severity elements. The hazard associated with a rotating saw blade or the water jet continues to exist, but the probability of causing harm, and thus the risk, can be reduced by installing a guard or by controlling the jet's path. Risk is expressed by the equation:
Risk = Hazard # Probability
When people discuss the hazards of disease-causing agents, the term exposure is typically used more than probabil-ity. If a certain type of chemical has a toxicity hazard, the risk of illness rises with the degree to which that chemi-cal contacts your body or enters your lungs. In that case, the equation becomes:
Risk = Hazard # Exposure
Organizations evaluate hazards using multiple techniques and data sources.
6.5.1.4 Job Safety AnalysisJob safety analysis (JSA) is known by many names, including activity hazard analysis (AHA), or job hazard analy-sis (JHA). Hazard analysis helps integrate accepted safety and health principles and a specific task. In a JSA, each basic step of the job is reviewed, potential hazards identified, and recommendations documented as to the safest way to do the job. JSA techniques work well when used on a task that the analysts understand well. JSA analysts look for specific types of potential accidents and ask basic questions about each step, such as these:
Can the employee strike against or otherwise make injurious contact with the object? Can the employee be caught in, on, or between objects? Can the employee strain muscles by pushing, pulling, or lifting? Is exposure to toxic gases, vapors, dust, heat, electrical currents, or radiation possible?
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6.5.2 Protection Systems
6.5.2.1 Major Types of Relief Devices
Relief Devices
BONNET
ADJUSTING SCREW
STEM SPINDLE
VENT (PLUGGED)
CAP
SPRING
SEATING SURFACE
ADJUSTING RINGBODY
NOZZLE
BONNET
ADJUSTING SCREW
STEM SPINDLE
VENT (UNPLUGGED)
CAP
SPRING
DISK
DISK
BELLOWS
SEATING SURFACE
ADJUSTING RINGBODY
NOZZLE
Conventional pressure relief valve (PRV) with a single adjusting ring for blowdown control
Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, Part 1, December 2008, Figure 1.
BONNET
ADJUSTING SCREW
STEM SPINDLE
VENT (PLUGGED)
CAP
SPRING
SEATING SURFACE
ADJUSTING RINGBODY
NOZZLE
BONNET
ADJUSTING SCREW
STEM SPINDLE
VENT (UNPLUGGED)
CAP
SPRING
DISK
DISK
BELLOWS
SEATING SURFACE
ADJUSTING RINGBODY
NOZZLE
Balance-Bellows PRV
Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, Part 1, December 2008, Figure 2.
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PILOT EXHAUST
PILOT VALVE
SEAT
SEAT
INTERNALPRESSURE PICKUP
MAIN VALVE
OUTLET
INLET
SET PRESSUREADJUSTMENT SCREW
SPINDLE
EXTERNAL BLOWDOWNADJUSTMENT
PILOT SUPPLY LINE
OPTIONALPILOT FILTER
PISTON
Pop-Action Pilot-Operated Valve (Flow-ing Type)
Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, Part 1, December 2008, Figure 10.
DISC
CARRIERASSEMBLY
Rupture Disk Assembly
Source: Chemical Process Safety: Funda-mentals with Applications, 2nd ed., New York: Prentice Hall, 2002, p. 362, Figure 8-7.
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6.5.2.2 Pressure-Level Relationships for Pressure Relief Valves
Pressure-Level Relationships for PRVs
PRESSURE VESSEL REQUIREMENTSVESSEL
PRESSURE
121120
116
115
110
105
100
95
90
85
TYPICAL CHARACTERISTICS OFPRESSURE RELIEF VALVES
MAXIMUM ALLOWABLE ACCUMULATED PRESSURE (FIRE EXPOSURE ONLY)
MAXIMUM ALLOWABLE ACCUMULATIVE PRESSURE FOR MULTI-VALVE INSTALLATION (OTHER THAN FIRE EXPOSURE)
MAXIMUM ALLOWABLE ACCUMULATED PRESSURE FOR SINGLE–VALVE INSTALLATION(OTHER THAN FIRE EXPOSURE))
MAXIMUM ALLOWABLE WORKING PRESSURE OR DESIGN PRESSURE(SEE NOTE 4)
MAXIMUM EXPECTEDOPERATING PRESSURE(SEE NOTES 5 AND 6)
LEAK TEST PRESSURE (TYPICAL)
CLOSING PRESSURE FORA SINGLE VALVE
BLOWDOWN (TYPICAL)(SEE NOTE 6)
MAXIMUM ALLOWABLE SET PRESSURE FOR SINGLE VALVE
MAXIMUM ALLOWABLE SET PRESSURE FOR ADDITIONAL VALVES (PROCESS)
OVERPRESSURE (MAXIMUM)
THE MAXIMUM ALLOWABLE SET PRESSURE FOR SUPPLEMENTAL VALVES (FIRE EXPOSURE)
SINGLE–VALVE MAXIMUM RELIEVING PRESSURE FOR PROCESS SIZING
MULTIPLE VALVES AND MAXIMUM RELIEVING PRESSURE FOR PROCESS SIZING
MAXIMUM RELIEVING PRESSUREFOR FIRE SIZING
SIMMER(TYPICAL)
PERC
ENT
OF M
AXIM
UM A
LLOW
ABLE
WOR
KING
PRE
SSUR
E (G
AUGE
)
NOTES:
1. THIS FIGURE CONFORMS WITH THE REQUIREMENTS OF SECTION VIII OF THE ASME BOILER AND PRESSURE VESSEL CODE FOR MAWPS GREATER THAN 30 PSIG.
2. THE PRESSURE CONDITIONS SHOWN ARE FOR PRESSURE RELIEF VALVE INSTALLED A PRESSURE VESSEL.
3. ALLOWABLE SET-PRESSURE TOLERANCES WILL BE IN ACCORDANCE WITH THE APPLICABLE CODES.
4. THE MAXIMUM ALLOWABLE WORKING PRESSURE IS EQUAL TO OR GREATER THAN THE DESIGN PRESSURE FOR COINCIDENT DESIGN TEMPERATURE.
5. THE OPERATING PRESSURE MAYBE HIGHER OR LOWER THAN 90%.
6. SECTION VIII, DIVISION 1, APPENDIX M OF THE ASME CODE SHOULD BE REFERRED TO FOR GUIDANCE ON BLOWDOWN AND PRESSURE DIFFERENTIALS.
Source: "Sizing, Selection, and Installation of Pressure-relieving Devices in Refineries: Part 1—Sizing and Selection," API Standard 520, Part 1, December 2008.
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6.5.2.3 Designs for Preventing Fires and Explosions
Designs for Fire- and Explosion-PreventionFeature Explanation
Maintenance programsThe best way to prevent fires and explosions is to stop the release of flam mable materials. Preventive maintenance programs are designed to upgrade systems before failures occur.
FireproofingInsulate vessels, pipes, and structures to minimize damage resulting from fires. Add deluge systems and design to withstand some damage from fires and explosions, e.g., use multiple deluge systems with separate shutoffs.
Control rooms Design control rooms to withstand explosions.
Water supplies Provide supply for maximum demand. Consider many deluge systems run ning simul-taneously. Diesel-engine pumps are recommended.
Control valves for deluge Place shutoffs well away from process areas.
Manual fire protection Install hydrants, monitors, and deluge systems. Add good drainage.
Separate units Separate (space) plants on a site, and separate units within plants. Provide access from two sides.
Utilities Design steam, water, electricity, and air supplies to be available during emergencies. Place substations away from process areas.
Personnel areas Locate personnel areas away from hazardous process and storage areas.
Group unitsGroup units in rows. Design for safe operation and maintenance. Create islands of risk by concentrating hazardous process units in one area. Space units so hot work can be performed on one group while another is operating.
Isolation valves Install isolation valves for safe shutdowns. Install in safe and accessible locations at edge of unit or group.
Railroads and flares Process equipment should be separated from flares and railroads. Compressors Place gas compressors downwind and separated from fired heaters.
Dikes Locate flammable storage vessels at edge of unit. Dike vessels to con tain and carry away spills.
Block valves Place automated block valves to stop and/or control flows dur ing emergencies. Con-sider the ability to transfer hazardous materials from one area to another.
Online analyzersAdd appropriate online analyzers to (1) monitor the status of the process, (2) detect problems at their incipient stage, and (3) take appropriate action to minimize effects of problems while still in initial phase of development.
Fail-safe designs Design all controls to fail safely. Add safeguards for automated and safe shutdowns during emergencies.
Safety-instrumented systems (SIS)
Use SIS to automatically bring process to a safe state upon detection of potentially hazardous conditions.
Source: Chemical Process Safety: Fundamentals with Applications, 2nd ed., New York: Prentice Hall, 2002, p. 346, Figure 7-8.
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6.5.3 Industrial HygienePersonal protective equipment (PPE) is designed to protect employees from serious injuries or illnesses resulting from contact with chemical, radiological, physical, electrical, mechanical, or other workplace hazards. Besides face shields, safety glasses, hard hats, and safety shoes, PPE includes a variety of devices and garments, such as goggles, coveralls, gloves, vests, earplugs, and respirators.
6.5.3.1 RespiratorsAssigned protection factors (APFs)—Per 29 CFR 1910.134, employers must use the assigned protection factors (listed in the table that follows) to select a respirator that meets or exceeds the required level of employee protec-tion. When using a combination respirator (e.g., airline respirators with an air-purifying filter), employers must en-sure that the assigned protection factor is appropriate to the mode of operation in which the respirator is being used.
Immediately dangerous to life or health (IDLH)—An atmosphere that poses an immediate threat to life, would cause irreversible adverse health effects, or would impair an individual's ability to escape from a dangerous atmo-sphere.
Powered air-purifying respirator (PAPR)—An air-purifying respirator that uses a blower to force the ambient air through air-purifying elements to the inlet covering.
Supplied-air respirator (SAR) or airline respirator—An atmosphere-supplying respirator for which the source of breathing air is not designed to be carried by the user.
Workplace protection factor (WPF) study—A study, conducted under actual conditions of use in the work-place, that measures the protection provided by a properly selected, fit-tested, and functioning respirator, when the respirator is worn correctly and used as part of a comprehensive respirator program that is in compliance with OSHA's Respiratory Protection Standard at 29 CFR 1910.134. Measurements of Co and Ci are obtained only while the respirator is being worn during performance of normal work tasks (that is, samples are not collected when the respirator is not being worn). As the degree of protection afforded by the respirator increases, the WPF increases.
Simulated workplace protection factor (SWPF) study—A study, conducted in a controlled laboratory setting, in which Co and Ci sampling is performed while the respirator user performs a series of set exercises. The laboratory setting is used to control many of the variables found in workplace studies, while the exercises simulate the work activities of respirator users. This type of study is designed to determine the optimum performance of respirators by reducing the impact of sources of variability through maintenance of tightly controlled study conditions.
4. Self-contained breathing apparatus (SCBA) • Demand mode — 10 50 50 — • Pressure-demand or other positive-pressure mode (e.g., open or closed) — — 10,000 10,000 —
Notes:1. Employers may select respirators assigned for use in higher workplaces concentration of a hazardous
substance for use at lower concentrations of that substance, or when required respirator use is independent of concentration.
2. The assigned protection factors in this table are only effective when the employer implements a continu-ing, effective respirator program as required by this section (29 CFR 1910.134), including training, fit-testing, maintenance, and use requirements.
3. This APF category includes filtering face pieces, and half masks with elastomeric face pieces.4. The employer must have evidence provided by the respirator manufacturer that testing of these respira-
tors demonstrates performance at a level of protection of 1000 or greater to receive an APF of 1000. This level of performance can best be demonstrated by performing a WPF or SWPF study or equivalent testing. Absent such testing, all other PAPRs and SARs with helmets/hoods are to be treated as loose-fitting face piece respirators, and receive an APF of 25.
5. These APFs do not apply to respirators used solely for escape. Tor escape respirators used in associa-tion with specific substances covered by 29 CFR 1910 subpart Z, employers must refer to the appropriate substance-specific standards in that subpart. Escape respirators for other IDLH atmospheres are specified by 29 CFR 1910.134(d)(2)(ii).
Source: OSHA, "Assigned Protective Factors for the Revised Respiratory Protection Standard," OSHA 3352-02, 2009. www.OSHA.gov.
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6.5.3.2 Hazard AssessmentThe fire/hazard diamond below summarizes common hazard data available on the Safety Data Sheet (SDS) and is frequently shown on chemical labels.
BA C
DPosition A – Health Hazard (Blue) 0 = Normal material 1 = Slightly hazardous 2 = Hazardous 3 = Extreme danger 4 = Deadly
Position B – Flammability (Red) 0 = Will not burn 1 = Will ignite if preheated 2 = Will ignite if moderately heated 3 = Will ignite at most ambient temperature 4 = Burns readily at ambient conditions
Position C – Reactivity (Yellow) 0 = Stable and not reactive with water 1 = Unstable if heated 2 = Violent chemical change 3 = Shock short may detonate 4 = May detonate
Position D – (White) ALKALI = Alkali OXY = Oxidizer ACID = Acid Cor = Corrosive W = Use no water = Radiation
6.5.3.3 Globally Harmonized System (GHS)The Globally Harmonized System of Classification and Labeling of Chemicals, or GHS, is a system for standard-izing and harmonizing the classification and labeling of chemicals.
GHS is a comprehensive approach to:
• Defining health, physical, and environmental hazards of chemicals
• Creating classification processes that use available data on chemicals for comparison with the defined hazard criteria
• Communicating hazard information, as well as protective measures, on labels and Safety Data Sheets (SDSs), formerly called Material Safety Data Sheets (MSDSs).
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GHS label elements include:
• Precautionary statements and pictograms: Measures to minimize or prevent adverse effects
• Product identifier (ingredient disclosure): Name or number used for a hazardous product on a label or in the SDS
• Supplier identification: The name, address, and telephone number of the supplier
• Supplemental information: nonharmonized information
Other label elements include symbols, signal words, and hazard statements.
GHS Label ElementsGHS LABEL ELEMENTS
Product Name Or Identifier(Identify Hazardous Ingredients, Where Appropriate)
Signal Word
Physical, Health, Environmental,Hazard Statements
Supplemental Information
Precautionary Measures And Pictograms
First Eight Statements
Name and Address of Company
Telephone Number
Note: Pictograms for hazard statements must have red borders.
Source: A Guide to the Globally Harmonized System of Classification and Labeling of Chemicals (GHS), United States Department of Labor, Occupational Safety and Health Administration.
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HCS Quick Card
Product Identifier
Signal Word
Supplier Identification
HazardStatements
Hazard Pictograms
Company Name_______________________Street Address________________________City_______________________ State_____Postal Code______________Country_____Emergency Phone Number_____________
Highly flammable liquid and vapor.May cause liver and kidney damage.
Keep container tightly closed. Store in a cool, well-ventilated place that is locked.Keep away from heat/sparks/open flame. No smoking.Only use non-sparking tools.Use explosion-proof electrical equipment.Take precautionary measures against static discharge.Ground and bond container and receiving equipment.Do not breathe vapors.Wear protective gloves.Do not eat, drink or smoke when using this product.Wash hands thoroughly after handling.Dispose of in accordance with local, regional, national, international regulations as specified.
In Case of Fire: use dry chemical (BC) or Carbon Dioxide (CO2) fire extinguisher to extinguish.
First AidIf exposed call Poison Center.If on skin (or hair): Take off immediately any contaminated clothing. Rinse skin with water. Fill weight:____________ Lot Number:___________
Gross weight:__________ Fill Date:______________Expiration Date:________
Directions for Use______________________________________________________________________________________________________
PrecautionaryStatements} Supplemental Information
}
}
SAMPLE LABEL
EP
AM
PLESS
HiH ghMM
PPrrecae ututStStaatt
SAMnatioonnaal,l,
CC)) oor Cr Caarrbob n Dioxixidede ( (CCOO2)
tely ly aany ny ccoontanta
e}}
OS
HA
349
2-01
R 2
016
Note: Pictograms for hazard statements must have red borders.
Source: United States Department of Labor, Occupational Safety and Health Administration.
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HCS Pictograms and Hazards Card
Note: Pictograms for hazard statements must be printed with red borders.
Source: A Guide to the Globally Harmonized System of Classification and Labeling of Chemicals (GHS), United States Department of Labor, Occupational Safety and Health Administration.
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Acute Oral Toxicity
DANGERFATAL IF SWALLOWED
DANGERFATAL IF SWALLOWED
DANGERTOXIC IF SWALLOWED
WARNINGHARMFUL IF SWALLOWED
LD50
SIGNAL WORDHAZARD STATEMENT
CATEGORY 1 ≤ 5 mg/kg
CATEGORY 2 > 5 < 50 mg/kg
CATEGORY 3 50 < 300 mg/kg
CATEGORY 4 300 < 2000 mg/kg
CATEGORY 5 2000 > 5000 mg/kg
NO SYMBOL
WARNINGMAY BE HARMFULIF SWALLOWED
PICTOGRAM
6.5.3.4 Safety Data Sheets (SDS)Source: Appendix D to OSHA CFR 1910.1200 - Safety Data Sheets (Mandatory).
A safety data sheet (SDS) must include the information in the table below under the section number and heading indicated for Sections 1–11 and 16. If no relevant information is found for any given subheading within a section, the SDS must clearly indicate that no applicable information is available. Sections 12–15 may be included in the SDS, but are not mandatory.
Minimum Information for a Safety Data SheetHeading Subheading
1. Identification a. Product identifier used on the labelb. Other means of identificationc. Recommended use of the chemical and restrictions on used. Name, address, and telephone number of the chemical manufacturer, importer, or other responsible partye. Emergency phone number
2. Hazard(s) Identification a. Classification on the chemical in accordance with paragraph (d) of §1910.1200b. Signal word, hazard statement(s), symbol(s), and precautionary state- ment(s) in accordance with paragraph (f) of §1910.1200. (Hazard symbols may be provided as graphical reproductions in black and white or the name of the symbol, e.g., flame, skull and crossbones)c. Describe any hazards not otherwise classified that have been identified during the classification processd. Where an ingredient with unknown acute toxicity is used in a mixture at a concentration = 1% and the mixture is not classified based on testing of the mixture as a whole, a statement that X % of the mixture consists of ingredient(s) of unknown acute toxicity is required
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Minimum Information for a Safety Data Sheet (cont'd)Heading Subheading
3. Composition and Information on Ingredients
Except as provided for in paragraph (i) of §1910.1200 on trade secrets:
For Substances
a. Chemical nameb. Common name and synonymsc. CAS number and other unique identifiersd. Impurities and stabilizing additives that are themselves classified and that contribute to the classification of the substance For Mixtures In addition to the information required for substances:
a. The chemical name and concentration (exact percentage) or concentra- tion ranges of all ingredients that are classified as health hazards in accordance with paragraph (d) of §1910.1200 and either (1) Are present above their cut-off/concentration limits (2) Present a health risk below the cut-off/concentration limitsb. The concentration (exact percentage) shall be specified unless a trade secret claim is made in accordance with paragraph (i) of §1910.1200, when there is batch-to-batch variability in the production of a mixture, or for a group of substantially similar mixtures (See A.0.5.1.2) with similar chemical composition. In these cases, concentration ranges may be used. For All Chemicals for Which a Trade Secret Is Claimed When a trade secret is claimed in accordance with paragraph (i) of §1910.1200, a statement that the specific chemical identity and/or exact percentage (concentration) of composition has been withheld as a trade secret is required.
4. First-aid Measures a. Description of necessary measures, subdivided according to the differ ent routes of exposure, i.e., inhalation, skin and eye contact, and ingestionb. Most important symptoms/ effects, acute and delayedc. Indication of immediate medical attention and special treatment needed, if necessary
5. Fire-fighting Measures a. Suitable (and unsuitable) extinguishing mediab. Specific hazards arising from the chemical (e.g., nature of any hazard ous combustion products)c. Special protective equipment and precautions for fire-fighters
6. Accidental Release Measures a. Personal precautions, protective equipment, and emergency proceduresb. Methods and materials for containment and cleaning up
7. Handling and Storage a. Precautions for safe handlingb. Conditions for safe storage, including any incompatibilities
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Minimum Information for a Safety Data Sheet (cont'd)Heading Subheading
8. Exposure Controls and Personal Protection
a. OSHA permissible exposure limit (PEL), American Conference of Governmental Industrial Hygienists' (ACGIH) threshold limit value (TLV), and any other exposure limit used or recommended by the chemical manufacturer, importer, or employer preparing the safety data sheet, where availableb. Appropriate engineering controlsc. Individual protection measures, such as personal protective equipment
9. Physical and Chemical Properties a. Appearance (physical state, color, etc.)b. Odorc. Odor threshholdd. pHe. Melting point/freezing pointf. Initial boiling point and boiling rangeg. Flash pointh. Evaporation ratei. Flammability (solid, gas)j. Upper/lower flammability or explosive limitsk. Vapor pressurel. Vapor densitym. Relative densityn. Solubility(ies)o. Partition coefficient: n-octanol/waterp. Auto-ignition temperatureq. Decomposition temperaturer. Viscosity
10. Stability and Reactivity a. Reactivityb. Chemical stabilityc. Possibility of hazards reactionsd. Conditions to avoid (e.g., static discharge, shock, or vibration)e. Incompatible materialsf. Hazardous decomposition products
11. Toxicological Information Description of the various toxicological (health) effects and the available data used to identify those effects, including:
a. Information on the likely routes of exposure (inhalation, ingestion, skin and eye contactb. Symptoms related to the physical, chemical, and toxicological charac- teristicsc. Delayed and immediate effects and also chronic effects from short- and long-term exposured. Numerical measures of toxicity (such as acute toxicity estimates)e. Whether the hazardous chemical is listed in the National Toxicology Program (NTP) Report on Carcinogens (latest edition) or has been found to be a potential carcinogen in the International Agency for Research on Cancer (IARC) Monographs (latest editions), or by OSHA
12. Ecological Information (Non-mandatory)
a. Ecotoxicity (aquatic and terrestrial, where available)b. Persistence and degradabilityc. Bioaccumulative potentiald. Mobility in soile. Other adverse effects (such as hazardous to the ozone layer)
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Minimum Information for a Safety Data Sheet (cont'd)Heading Subheading
13. Disposal Considerations (Non-mandatory)
Description of waste residues and information on their safe handling and method of disposal, including disposal of any contaminated packaging.
14. Transport Information (Non-mandatory)
a. UN numberb. UN proper shipping namec. Transport hazard class(es)d. Packing group, if applicablee. Environmental hazards (e.g., Marine pollutant [Yes/No])f. Transport in bulk (according to Annex II of MARPOL 73/78 and IBC Code)g. Special precautions which a user needs to be aware of, or needs to comply with, in connection with transport or conveyance either within or outside their premises
15. Regulatory Information (Non-mandatory)
Safety, health, and environmental regulations specific for the product in question
16. Other Information, Including Date of Preparation or Last Revision
The date of preparation of the SDS or the last change to it
Source: U.S. Department of Labor, Occupational Safety & Health Administration, www.OSHA.gov.
6.5.3.5 PesticidesThis section establishes four toxicity categories for acute hazards of pesticide products. Category I is the highest category. Most human hazard, precautionary statements, and human personal protective equipment statements are based on the toxicity category of the pesticide product as sold or distributed. In addition, toxicity categories may be used for regulatory purposes other than labeling, such as classification for restricted use and requirements for child-resistant packaging. In certain cases, statements based on the toxicity category of the product as diluted for use are also permitted. A toxicity category is assigned for each of five types of acute exposure, as specified in the table below.
Acute Toxicity Categories for Pesticide ProductsHazard
Indicators I II III IV
Oral LD50Up to and including 50 mg/kg >50 through 500 mg/kg >500 through 5000 mg/kg > 5000 mg/kg
Dermal LD50Up to and including 200 mg/kg >200 through 2000 mg/kg >2000 through 20,000
mg/kg >20,000 mg/kg
Inhalation LC50Up to and including 0.2 mg/liter >0.2 through 2 mg/liter >2 through 20 mg/liter >20 mg/liter
Eye irritationCorrosive: corneal opacity not reversible within 7 days
Corneal opacity reversible within 7 days; irritation persisting for 7 days
No corneal opacity; irrita-tion reversible within 7 days
No irritation
Skin irritation Corrosive Severe irritation at 72 hours
Moderate irritation at 72 hours
Mild or slight irritation at 72 hours
Source: From Regulating Pesticides, U.S. Environmental Protection Agency.
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Pesticide Toxicity CategoriesToxicity Category Signal Word
I PoisonII WarningIII CautionIV Caution
Source: U.S. Environmental Protection Agency 40 CFR 156.
6.5.3.6 Fundamentals of Ventilation
Ventilation Definitions
Aerosol: An assemblage of small particles, solid or liquid, suspended in air. The diameter of the particles may vary from 100 microns down to 0.01 micron or less, e.g., dust, fog, smoke.
Air cleaner: A device designed for the purpose of removing atmospheric airborne impurities such as dusts, gases, mists, vapors, fumes, and smoke. (Air cleaners include air washers, air filters, electrostatic precipitators, and char-coal filters.)
Air filters: An air-cleaning device that removes light particulate loadings from normal atmospheric air before intro-ducing into the building. Usual range: loadings up to 3 grains per thousand cubic feet (0.003 grains per cubic foot). Note: Atmospheric air in heavy industrial areas and in-plant air in many industries have higher loadings than this, and dust collectors are then indicated for proper air cleaning.
Aspect ratio: The ratio of the width (W) to the length (L); AR = LW .
Aspect ratio of an elbow: The width (W) along the axis of the bend divided by the depth (D) in the plane of the
bend; AR = DW .
Blast gate: Sliding damper.
Capture velocity: The air velocity at any point in front of the hood or at the hood opening necessary to overcome opposing air currents and capture the contaminated air at that point by causing it to flow into the hood.
Density factor: The ratio of actual air density to density of standard air. The product of the density factor and the
density of standard air (0.075 ftlb3 ) gives the actual air density in pounds per cubic foot; Density = df # 0.075
ftlb3 .
Dust: Small solid particles created by breakup of larger particles by processes, such as crushing, grinding, drilling, and explosions. Dust particles already in existence in a mixture of materials may escape into the air through such operations as shoveling, conveying, screening, or sweeping.
Dust collector: An air-cleaning device to remove heavy particulate loadings from exhaust systems. Usual range of particulate loading: 0.003 grains per cubic foot or higher.
Entry loss: Loss in pressure caused by air flowing into a duct or hood (inches H2O).
Fumes: Small solid particles formed by the condensation of vapors of solid materials.
Gases: Formless fluids that tend to occupy an entire space uniformly at ordinary temperatures and pressures.
Hood: A shaped inlet designed to capture contaminated air and conduct it into the exhaust duct system.
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Hood flow coefficient: The ratio of flow caused by a given hood static pressure compared to the theoretical flow that would result if the static pressure could be converted to velocity pressure with 100 percent efficiency.
Inch of water: A unit of pressure equal to the pressure exerted by a column of liquid water one inch high at a stan-dard temperature.
Minimum design duct velocity: Minimum air velocity required to move the particles in the air stream (fpm).
Mists: Small droplets of materials that are ordinarily liquid at normal temperature and pressure.
Pressure, static: The potential pressure exerted in all directions by a fluid at rest. For a fluid in motion, it is mea-sured in a direction normal to the direction of flow. Usually expressed in inches of water gauge when dealing with air. (The tendency to either burst or collapse the pipe.)
Pressure, total: The algebraic sum of the velocity pressure and the static pressure (with due regard to sign).
Pressure, velocity: The kinetic pressure in the direction of flow necessary to cause a fluid at rest to flow at a given velocity. Usually expressed in inches of water gauge.
Replacement air: A ventilation term used to indicate the volume of controlled outdoor air supplied to a building to replace air being exhausted.
Slot velocity: Linear flow rate of contaminated air through a slot, fpm.
Smoke: An air suspension (aerosol) of particles, usually but not necessarily solid, often originating in a solid nucleus, formed from combustion or sublimation.
Standard air: Dry air at 70°F and 29.92 (in Hg) barometer. This is substantially equivalent to 0.075 ftlb3 . Specific
heat of dry air = 0.24 Btu/lb/°F.
Turn-down ratio: The degree to which the operating performance of a system can be reduced to satisfy part-load conditions. Usually expressed as a ratio; for example, 30:1 means the minimum operation point is 1/30th of full load.
Source: Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, pp. x–xi.
AR Aspect ratio HVAC Heating, ventilation, and air conditioningAs Slot area "wg Inches water gaugeB Barometric pressure L LengthCc Hood flow coefficient mo Mass flow rate
CLR Centerline radius ME Mechanical efficiencydf Overall density factor mm wg Millimeters water gaugedfe Elevation density factor MRT Mean radiant temperaturedfm Moisture density factor Q Flow rate, in cfmdfp Pressure density factor sfpm Surface feet per minutedft Temperature density factor SP Static pressureF dl Loss per unit length (duct) SPgov Higher static pressure at junction of 2 ductsFel Elbow loss coefficient SPh Hood static pressureFen Entry loss coefficient SPs SP, system handling standard airFh Hood entry-loss coefficient TP Total pressureFs Slot loss coefficient V Velocity, in fpmgr Grains Vd Duct velocityH Height VP Velocity pressurehd Loss in straight duct run VPd Duct velocity pressurehe Overall hood entry loss VPr Resultant velocity pressurehel Elbow loss VPs Slot velocity pressurehen Entry loss Vs Slot velocityhh Hood entry loss Vt Duct transport velocity
hs Slot or opening entry loss ~ Moisture content, in lbm dry airlbm H O2
HEPA High-efficiency particulate air filter z Elevation, in feet above sea level
HV Humid volume, in lb dry airft mix3
Source: Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, pp. xii–xiii.
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Ventilation EquationsDescription Equation Units
Velocity pressure (VP) VP 2gV
4005V df
c
2 2t= = c m V in fpm VP in "wg
Total pressure (TP) TP = SP +VP "wg
Hood entry loss (hh) hh = Fh(VPd)
"wg
Values of Fh can be found in the Hood Loss Coefficients table on page 391.
Hood static pressure (SPh) SPh = – (VPd + hh) "wg
Velocity ContoursPlain Circular Opening—% of Opening Velocity Flanged Circular Opening—% of Opening Velocity
100% 60%
30%
15%
7.5%
100% 60%
30%
15%
0 50% OF DIAMETER
100
7.5%
0 50% OF DIAMETER
100
100% 60%
30%
15%
7.5%
100% 60%
30%
15%
7.5%
Source: Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, p. 6-23.
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Summary of Hood Airflow EquationsHood Type Description Aspect Ratio, W/L Airflow
X
L
W
Slot 0.2 or less Q = 3.7 LVXX
X
Flanged Slot 0.2 or less Q = 2.6 LVXX
W L
A = WL
XPlain opening 0.2 or greater
and round Q = VX(10X 2 + A)
X
Flanged opening 0.2 or greater and round Q = 0.75VX(10X 2 + A)
H
W
Booth To suit work Q = VA = VWH
D Canopy To suit work
Q = 1.4 PVD
P = Perimeter D = Height above work
X
LW Plain multiple-slot opening,
2 or more slots0.2 or greater Q = VX(10X 2 + A)
X
LW Flanged multiple-slot opening,
2 or more slots0.2 or greater Q = 0.75VX(10X 2 + A)
Source: Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, p. 6-27.
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6.5.3.7 Flow-Capture Velocity of Suspended Hoods (Small Side-Draft Hoods)
Freely Suspended Hood
SOURCE
H
L
X Q
Q = VX(10X 2 + A)
Large Hood
SOURCEX
2X
For a large hood with small X, measure X perpendicular to the hood face and not less than 2X from the edge of the opening.
Hood on Bench or Floor
SOURCE X Q
Q = VX(5X 2 + A)
Hood with Wide Flange
SOURCE
FLANGE WIDTH ≥ A
QX
Q = 0.75VX(10X 2 + A)
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whereQ = required exhaust airflow, in acfm or s
m3
X = distance from hood face to farthest point of contamination, in ft or m
A = hood face area, in ft2 or m2
VX = capture velocity at distance X, in fpm or sm , at distance X
Note: Airflow rate must increase as the square of distance of the source from the hood. Baffling by flanging or by placing on bench, floor, etc. has a beneficial effect.
Source: Hood illustrations in this section are from Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, p. 6-19.
6.5.3.8 Flow-Capture Velocity of Canopy Hood
45° MINIMUM
0.4D D
Q = 1.4 PDV
where P = Perimeter of tank, in ft or m
Not recommended if workers must bend over source. V ranges from 50 to 500 fpm or 0.25 to 2.50 sm , depending
on crossdrafts. Side curtains on two or three sides to create a semi-booth or booth are desirable.
Recommended Capture Velocities
Energy of Dispersion ExamplesVX
minft
sm
Little motion Evaporation from tanks, degreasing 75–100 0.38–0.51
High Barrel filling, conveyor loading, crushers 200–500 1.02–2.54Very high Grinding, abrasive blasting, tumbling 500–2000 2.54–10.2
Factors affecting choices within ranges:
• Strength of cross-drafts due to makeup air, traffic, etc.• Need for effectiveness in collection:
- Toxicity of contaminants produced by the source - Exposures from other sources, which reduce acceptable exposure from this source - Quantity of air contaminants generated: production rate, volatility, time generated
Source: Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Cincinnati: ACGIH, 2013, p. 6-22.
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Hood Type Efficiency
Hood Loss CoefficientsHood Type Description Hood Entry Loss (Fh) Coefficient
Plain opening 0.93
Flanged opening 0.49
Taper or cone hood 0.15–0.4
Bell mouth inlet 0.04
Orifice 0.55 when duct velocity = slot velocity
Typical grinding hood
Straight takeoff: 0.65
Tapered takeoff: 0.40
Source: ACGIH, Industrial Ventilation: A Manual of Recommended Practice for Design, 28th ed., Signature Publications, Cincinnati, Ohio, 2013.
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6.5.3.9 Electrical Safety
Probable Effects of Various Levels of Current on the Human BodyLevel of Current (milliamperes) Probable Effect
1 mA Perception level. Slight tingling sensation. Still dangerous under certain conditions.
5 mA Slight shock felt; not painful but disturbing. Average individual can let go. How-ever, strong involuntary reactions to shocks in this range may lead to injuries.
6 mA-16 mA Painful shock; begin to lose muscular control. Commonly referred to as the freezing current or "let-go" range.
17 mA-99 mA Extreme pain, respiratory arrest, severe muscular contractions. Individual cannot let go. Death is possible.
100 mA-2000 mA Ventricular fibrillation (uneven, uncoordinated pumping of the heart). Muscular contraction and nerve damage begins to occur. Death is likely.
>2000 mA Cardiac arrest, internal organ damage, and severe burns. Death is probable.
Sources: NIOSH, Worker Deaths by Electrocution; A Summary of NIOSH Surveillance and Investigative Findings, Ohio: U.S. Health and Human Services, 1998. And Greenwald, E.K., Electrical Hazards and Accidents—Their Cause and
Prevention, New York: Van Nostrand Reinhold, 1991.
6.5.3.10 Risk Assessment/Toxicology
The Dose-Response Curve
The dose-response curve relates toxic response (i.e., percentage of test population exhibiting a specified symptom
or dying) to the logarithm of the dosage (i.e., kg daymg: ingested). A typical dose-response curve is shown below.
Typical Dose-Response Curve
100
50
10
TOXICANT
TOXI
C RE
SPON
SE %
LOGARITHM OF LD50 DOSELD50LD10
where
LC50 = Median lethal concentration in air that, based on laboratory tests, is expected to kill 50% of a
group of test animals when administered as a single exposure over one or four hours.
LD50 = Median lethal single dose, based on laboratory tests, expected to kill 50% of a group of test
animals, usually by oral or skin exposure.
Similar definitions exist for LC10 and LD10, where the corresponding percentages are 10%.
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The following table lists the LD50 values for several chemicals:
Adapted from Williams, P.L., R.C. James, and S.M. Roberts. Principles of Toxicology: Environmental and Industrial Applications, 2nd ed., New York: Wiley, 2000.
a. Columns 3 and 4 list PELs from OSHA Table Z-1 in 29 CFR 1910.1000. Columns 5 and 6 list other occupa-tional exposure limits (OELs) from NIOSH and ACGIH®.
b. Occupational Safety and Health Administration (OSHA) Permissible Exposure Limits (PELs) from 29 CFR 1910.1000 Z-1 Table [58 FR 35340, June 30, 1993; 58 FR 40191, July 27, 1993, as amended at 61 FR 56831, Nov. 4, 1996; 62 FR 1600, Jan 10,1997; 62 FR 42018, Aug. 4, 1997; 71 FR 10373, Feb. 28, 2006; 71 FR 16673, Apr. 3, 2006; 71 FR 36008, June 23, 2006.]. PELs are 8-hour time-weighted averages (TWAs), unless otherwise indicated. OSHA enforces these limits under section 5(a)(2) of the OSH Act. In addition to the values listed in this table, the Z tables in 29 CFR 1910.1000 list skin absorption designations.
c. The CAS number is for information only. Enforcement is based on the substance name. For an entry covering more than one metal compound measured as the metal, the CAS number for the metal is given—not CAS num-bers for the individual compounds.
d. Parts of vapor or gas per million parts of contaminated air by volume at 25 oC and 760 torr.e. Milligrams of substance per cubic meter of air. When entry is in this column only, the value is exact; when
listed with a ppm entry, it is approximate.f. TWA indicates a time-weighted average concentration. A short-term exposure limit (STEL) is designated by
ST preceding the value; unless noted otherwise, the STEL is a 15-minute TWA exposure that should not be exceeded at any time during a work day. A ceiling REL is designated by C preceding the value; unless noted otherwise, the ceiling value should not be exceeded at any time.
g. National Institute for Occupational Safety and Health (NIOSH) Recommended Exposure Limits (RELs) from the NIOSH Pocket Guide to Chemical Hazards (http://www.cdc.gov/niosh/npg) (NIOSH 2007). RELs are for up to 10-hour time weighted averages (TWAs) during a 40-hour work week, unless otherwise indicated. NIOSH has established occupational exposure limits for compounds not included in the OSHA Z Tables. Please see the NIOSH Pocket Guide for additional limits, skin absorption and other designations, and explanations.
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h. ACGIH® Threshold Limit Values (TLVs®) (ACGIH® 2015). TLVs® are listed in the order of 8-hour time-weighted averages (TWAs), STELs (ST), and Ceilings (C), if available. ACGIH® has established TLVs® for compounds not included in the OSHA Z Tables. Please see ACGIH® Documentation for additional limits, skin absorption and other designations, and explanations. The 2015 TLV® and BEI® Book and Documentation of the Threshold Limit Values on Chemical Substances, 7th Edition, are available through the ACGIH® website at http://www.acgih.org. The TLVs® and BEIs® are copyrighted by ACGIH® and are not publicly available. Permission must be requested from ACGIH® to reproduce the TLVs® and BEIs®.
Carcinogens
For carcinogens, the EPA considers an acceptable risk to an individual to be a lifetime excess cancer risk within the range of 10-4 to 10-6. The added risk of cancer is calculated as follows:
Risk = dose # toxicity = CDI # CSF
where
CDI = Chronic daily intake
CSF = Cancer slope factor, the slope of the dose-response curve for carcinogenic materials
RESPONSE
DOSE
X
X X
NO THRESHOLD LINEARAT LOW DOSE
CARCINOGENIC DOSERESPONSE CURVE
X
X
Noncarcinogens
For noncarcinogens, a hazard index (HI) characterizes the risk from all pathways and exposure routes. The EPA considers that an HI > 1.0 represents an unacceptable risk of an adverse effect occurring.
HI RfDCDInoncarcinogen=
where
CDInoncarcinogen = chronic daily intake of noncarcinogenic compound
RfD = reference dose
RESPONSE
DOSE
XX
X X
X
X
NONCARCINOGENIC DOSERESPONSE CURVE
THRESHOLD
RfD
NOAEL
Dose is expressed as body weight exposure time
mass of chemical#d n
NOAEL = No observable adverse effect level (the dose below which no harmful effects are apparent)
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Reference Dose
Reference dose (RfD) is determined from the noncarcinogenic dose-response curve using the NOAEL:
RfD = lifetime (i.e., chronic) dose that a healthy person could be exposed to daily without adverse effects
UFNOAELRfD
and
=
WSHD RfD UFNOAEL W#
#= =
where
SHD = safe human dose (mg/day)
NOAEL = threshold dose per kg of test animal kgdaymg
from the dose-response curve
UF = the total uncertainty factor, depending on nature and reliability of the animal test data
W = the weight of the adult male (typically 70 kg)
Exposure
Residential Exposure Equations for Various Pathways
Pathway Exposure Equation
Ingestion in drinking water CDI BW ATCW IR EF ED=^^^ ^^^h h
hhhh
Ingestion while swimming CDI BW ATCW CR ET EF ED=^ ^
^^^^ ^h h
hhhh h
Dermal contact with water AD BW ATCW SA PC ET EF ED CF=^ ^ ^
^^^^ ^ ^h h h
hhhh h h
Ingestion of chemicals in soil CDI BW ATCS IR CF FI EF ED=^ ^
^^ ^
^^ ^h h h
hhhh h
Dermal contact with soil AD BW ATCW CF SA AF ABS EF ED=^ ^ ^
^^^^ ^ ^h h h
hhhh h h
Inhalation of airborne (vapor phase) chemicals CDI BW ATCA IR ET EF ED
=^ ^
^^^^ ^h h
hhhh h
Ingestion of contaminated fruits, vegetables, fish, and shellfish CDI BW AT
CF IR FI EF ED=^ ^
^^^^ ^h hhhhh h
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where
ABS = absorption factor for soil contaminant is unitless
AD = absorbed dose in kg daymg:
AF = soil-to-skin adherence factor in
cmmg
2
AT = averaging time in days
BW = body weight in kg
CA = contaminant concentration in air in mmg3
CDI = chronic daily intake in kg daymg:
CF = volumetric conversion factor for water is 1000 cm1L
3
= conversion factor for soil in mgkg10 6-
CR = contact rate in hrL
CS = chemical concentration in soil in kgmg
CW = chemical concentration in water in Lmg
ED = exposure duration in years
EF = exposure frequency in yeardays
or yearevents
ET = exposure time in dayhr or event
hr
FI = fraction ingested is unitless
IR = ingestion rate in dayL or day
mg soilor meal
kg
= inhalation rate in hr
m3
PC = Chemical-specific dermal permeability constant in hrcm
SA = skin surface area available for contact in cm2
Source: U.S. Environmental Protection Agency, Risk Assessment Guidance for Superfund: Volume 1, Human Health Evaluation Manual (part A), EPA/540/1-89/002,1989.
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6.5.3.11 Intake Rates
EPA Recommended Values for Estimating IntakeParameter Standard Value
Average body weight, female adult 65.4 kgAverage body weight, male adult 78 kgAverage body weight, childa
6-11 months 9 kg1-5 years 16 kg6-12 years 33 kg
Amount of water ingested, adult 2.3 L/dayAmount of water ingested, child 1.5 L/dayAmount of air breathed, female adult 11.3 m3/dayAmount of air breathed, male adult 15.2 m3/dayAmount of air breathed, child (3-5 years) 8.3 m3/dayAmount of fish consumed, adult 6 g/dayWater swallowing rate, while swimming 50 mL/hrInhalation rates
Exposure durationLifetime (carcinogens; for noncarcinogens use, actual exposure duration) 75 yearsAt one residence, 90th percentile 30 yearsNational median 5 years
Averaging time (ED) (365 days/year)
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EPA Recommended Values for Estimating Intake (cont'd)Parameter Standard Value
Exposure Frequency (EF)Swimming 7 days/yearEating fish and shellfish 48 days/yearOral ingestion 350 days/year
Exposure time (ET)Shower, 90th percentile 12 minShower, 50th percentile 7 min
aData in this category taken from Copeland, T., A. M. Holbrow, J. M. Otan, et al. "Use of probabilistic methods to understand the conservatism in California's approach to assessing health risks posed by contaminants."
Journal of the Air and Waste Management Association, Vol. 44, pp. 1399–1413, 1994.
Source: U.S. Environmental Protection Agency, Risk Assessment Guidance for Superfund: Volume 1, Human Health Evaluation Manual (part A), EPA/540/1-89/002,1989.
6.5.3.12 Concentrations of Vaporized LiquidsVaporization rate (Qm, mass/time) from a liquid surface:
Q R TMKA P
g L
sat
ms= = G
where
M = molecular weight of volatile substance
K = mass transfer coefficient
As = area of liquid surface
Psat = saturation vapor pressure of the pure liquid at TL
Rg = ideal gas constant
TL = absolute temperature of the liquid
Mass flow rate of liquid from a hole in the wall of a process unit:
( )Q A C g P2H c gm 0½t=
where
AH = area of hole
C0 = discharge coefficient
ρ = density of the liquid
gc = gravitational constant
Pg = gage pressure within the process unit
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Concentration (Cppm) of vaporized liquid in ventilated space:
( )×C kQ PM
Q R T 10ppm
V
gm6
= > H
where
T = absolute ambient temperature
k = nonideal mixing factor
QV = ventilation rate
P = absolute ambient pressure
Sweep-through concentration change in a vessel:
lnQ t V C CC C––
V2 0
1 0= = Gwhere
QV = volumetric flow rate
t = time
V = vessel volume
C0 = inlet concentration
C1 = initial concentration
C2 = final concentration
6.5.3.13 Noise Pollution
SPL (dB) = 10 logPP
1002
2f p
SPLtotal = log10 101010SPLR
Point Source Attenuation: logSPL dB rr10 10 21D =^ dh n
Line Source Attenuation: logSPL dB rr10 10 21D =^ dh n
where
SPL (dB) = sound pressure level, measured in decibels
P = sound pressure (Pa)
P0 = reference sound pressure (2 × 10–5 Pa)
SPLtotal = sum of multiple sources
∆ SPL (dB) = change in sound pressure level with distance, measured in decibels
r1 = distance from source to receptor at point 1
r2 = distance from source to receptor at point 2
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6.5.3.14 Permissible Noise Exposure (per OSHA Regulations)Noise dose D should not exceed 100%.
%D TC100ii#= !
where
Ci = time spent at specified sound pressure level (SPL) in hours
Ti = time permitted at SPL in hours
Ci! = 8 (hours)
Permissible Noise Level vs. Permissible Time of Exposure
If 50% ≤ D ≤ 100%, hearing conservation program is required.
Note: D = 100% is equivalent to 90 dBA time-weighted average (TWA). D = 50% is equivalent to TWA of 85 dBA.
Hearing conservation program requires: (1) testing employee hearing, (2) providing hearing protection at employee's request, and (3) monitoring noise exposure.
Exposure to impulsive or impact noise should not exceed 140 dB sound pressure level (SPL).
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6.5.4 Hazard Identification and Management
Terms and Definitions for Hazards Identification and ManagementTerm Definition
Alarm An audible and/or visible means of indication to the operator an equipment mal-function, process deviation, or abnormal condition requiring a timely response.
As Low as Reasonably Practicable (ALARP)
The concept that efforts to reduce risk should be continued until the incremental sacrifice (in terms of cost, time, effort, or other expenditure of resources) is grossly disproportionate to the incremental risk reduction achieved. The term as low as reasonably achievable (ALARA) is often used synonymously.
ConsequencesThe direct, undesirable result of an accident sequence usually involving a fire, ex-plosion, or release of toxic material. Consequence descriptions may be qualitative or quantitative estimates of the effects of an accident.
FrequencyNumber of occurrences of an event per unit time
e.g.,1 event in 1000 yr. 1 10 yrevents3#= −d n.
Failure Mode and Effect Analysis (FMEA)
A hazard identification technique in which all known failure modes of components or features of a system are considered in turn and undesired outcomes are noted. It is usually used in combination with fault tree analysis. It is a complicated proce-dure, usually carried out by experienced risk analysts.
Hazards and Operability Analysis (HAZOP)
A systematic qualitative technique to identify process hazards and potential operat-ing problems using a series of guide words to study process deviations. A HAZOP is used to question every part of a process to discover what deviations from the intention of the design can occur and what their causes and consequences may be. This is done systematically by applying suitable guide words. This is a systematic detailed review technique, for both batch and continuous plants, which can be applied to new or existing processes to identify hazards.
Independent Protection Layer (IPL)
A device, system, or action that is capable of preventing a postulated accident sequence from proceeding to a defined, undesirable endpoint. An IPL is indepen-dent of the event that initiated the accident sequence and independent of any other IPLs. IPLs are normally identified during layer of protection analysis.
Initiating Event
The minimum combination of failures or errors necessary to start the propagation of an incident sequence. It can be comprised of a single initiating cause, multiple causes, or initiating causes in the presence of enabling conditions. (The term initi-ating event is the usual term employed in Layer of Protection Analysis to denote an initiating cause or where appropriate, an aggregation of initiating causes with the same immediate effect, such as "BPCS failure resulting in high reactant flow.")
Layer of Protection Analysis (LOPA)
An approach that analyzes one incident scenario (cause-consequence pair) at a time, using predefined values for the initiating event frequency, independent protection layer failure probabilities, and consequence severity, in order to com-pare a scenario risk estimate to risk criteria for determining where additional risk reduction or more detailed analysis is needed. Scenarios are identified elsewhere, typically using a scenario-based hazard evaluation procedure such as the HAZOP study.
Lock-OutTag-Out (LOTO)Specific practices and procedures to safeguard employees from the unexpected energization or startup of machinery and equipment, or the release of hazardous energy during service or maintenance activities.
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Terms and Definitions for Hazards Identification and Management (cont'd)Term Definition
Process Hazard Analysis (PHA)
An organized effort to identify and evaluate hazards associated with processes and operations to enable their control. This review normally involves the use of qualita-tive techniques to identify and assess the significance of hazards. Conclusions and appropriate recommendations are developed. Occasionally, quantitative methods are used to help prioritized risk reduction.
Process Safety Management (PSM)
A management system that is focused on prevention of, preparedness for, mitiga-tion of, response to, and restoration from catastrophic releases of chemicals or energy from a process associated with a facility.
Quantitative Risk Analysis (QRA)
QRA is a technique that provides advanced quantitative means to supplement other hazard identification, analysis, assessment, control, and management meth ods to identify the potential for such incidents and to evaluate risk reduction and control strategies. QRA identifies those areas where operation, engineering, or manage-ment systems may be modified to reduce risk and may identify the most economi-cal way to do it. The primary goal of QRA is that appropriate management actions, based on results from a QRA study, help to make facilities handling haz ardous chemicals safer. QRA is one component of an organization's total process risk management. It allows the quantitative assessment of risk alternatives that can be balanced against other considerations.
Qualitative Risk Analysis (QRA)
The systematic development of numerical estimates of the expected frequency and/or consequence of potential accidents associated with a facility or operation. Using consequence and probability analyses and other factors such as population density and expected weather conditions, QRA predicts the fatality rate for a given event. This methodology is useful for eval uation of alternatives, but its value as an abso-lute measure of risk should be considered carefully.
Risk
A measure of human injury, environmental damage, or economic loss in terms of both the incident likelihood and the magnitude of the loss or injury. A simplified version of this relationship expresses risk as the product of the likelihood and the consequences (i.e., Risk = Consequence x Likelihood) of an incident.
Chapter 6: Plant Design and Operation
NCEES 405
6.5.4.1 Layers of Protection
Typical Risk Reduction Methods Found in Process Plants
COMMUNITY EMERGENCY RESPONSEEMERGENCY BROADCASTING
PLANT EMERGENCY RESPONSEEVACUATION PROCEDURES
MITIGATIONMECHANICAL MITIGATION SYSTEMS
SAFETY INSTRUMENTED CONTROL SYSTEMSSAFETY INSTRUMENTED MITIGATION SYSTEMS
OPERATOR SUPERVISION
PREVENTIONMECHANICAL PROTECTION SYSTEM
PROCESS ALARMS WITH OPERATOR CORRECTIVE ACTION
SAFETY INSTRUMENTED CONTROL SYSTEMSSAFETY INSTRUMENTED PREVENTION SYSTEMS
CONTROL AND MONITORINGBASIC PROCESS CONTROL SYSTEMS
MONITORING SYSTEMS ( PROCESS ALARMS)OPERATOR SUPERVISION
PROCESS
Source: ISA 84.00.00.
Hierarchy of Controls
Source: Controls for Noise Exposure, Atlanta: The National Institute for Occupational Safety and Health (NIOSH), 2016.
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6.5.4.2 Elements of Risk-Based Process Safety
Commitment to process safety Process safety culture Compliance with standards Workforce involvement Stakeholder outreach
Understanding hazards and risk Process knowledge management Hazards identification and risk analysis
Managing risk Operating procedures Safe work practices Asset integrity and reliability Contractors management Training and performance assurance Management of change Operational readiness Conduct of operations Emergency management
Learning from experience Incident investigation Measurements and metrics Auditing Management review and continuous improvement
6.5.4.3 Safety Instrumented Systems
Definitions of Safety Integrity TermsTerm Definition
Architecture
Arrangement of hardware and/or software elements in a system; for example:
(1) Arrangement of safety instrumented system (SIS) subsystems (2) Internal structure of an SIS subsystem (3) Arrangement of software programs
Average Probability of Failure on Demand (PFDavg)
Average probability that a safety-instrumented function will fail in such a way that it cannot respond to a potentially dangerous condition. PFD or PFDavg is applied to repairable systems.
Basic Process Control System (BPCS)
System that responds to input signals from the process, its associated equipment, other programmable systems, and/or an operator and generates output signals caus-ing the process and its associated equipment to operate in the desired manner but that does not perform any safety-instrumented functions with a claimed SIL 1$ .
Common Cause Failure Failure that is the result of one or more events and that causes failure of two or more separate channels in a multiple-channel system, leading to system failure.
MooNSafety instrumented system, or part thereof, made up of N independent channels that are so connected that M channels are sufficient to perform the safety-instru-mented function.
Mean Time to Fail (MTTF) Mean time to random failure for a component population. MTTF is applied to items that are not repaired, such as bearings and transistors.
Mean Time to Trip Spurious (MTTFS) Mean time for a safety function to fail in a mode that causes a spurious trip.
Safe Failure Fraction (SFF) Fraction of the overall random hardware failure rate of a device that results in either a safe failure or a detected dangerous failure.
Chapter 6: Plant Design and Operation
NCEES 407
Definitions of Safety Integrity Terms (cont'd)Term Definition
Safety Instrumented System (SIS)
Instrumented system used to implement one or more safety-instrumented func-tions.An SIS is composed of any combination of sensor(s), logic solver(s), and final element(s).
Safety Integrity Level (SIL)Discrete level (one out of four) for specifying the safety integrity requirements of the safety-instrumented functions to be allocated to the safety instrumented sys-tems. SIL 4 has the highest level of safety integrity; SIL 1, the lowest.
Safety Instrumented Function (SIF)
Safety function with a specified safety integrity level that is necessary to achieve functional safety and that can be either a safety instrumented protection function or a safety instrumented control function.
Systematic FailureFailure related in a deterministic way to a certain cause, which can only be elimi-nated by a modification of the design or of the manufacturing process, operational procedures, documentation, or other relevant factors.
Tolerable Risk Risk that is accepted in a given context based on the current values of society.
ValidationActivity of demonstrating that the safety-instrumented function(s) and safety in-strumented system(s) under consideration after installation meet in all respects the safety requirements specification.
VerificationActivity of demonstrating for each phase of the relevant safety life-cycle, by analy-sis and/or tests, that for specific inputs the outputs meet in all respects the objec-tives and requirements for the specific phase.
Source: The Instrumentation, Systems, and Automation Society (IHS), Functional Safety: Safety Instrumented Systems for the Process Industry Sector - Part 1: Framework, Definitions, System, Hardware and Software
Requirements (ANSI/ISA-84.00.01-2004 Part 1 IEC 61511-1 Mod), 2004.
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6.5.4.4 Functional Safety Life Cycle
SIS Safety Life-Cycle Phases and Functional Safety Assessment Stages
KEY:TYPICAL DIRECTION OF INFORMATION FLOW.
NO DETAILED REQUIREMENTS GIVEN IN THIS STANDARD.
REQUIREMENTS GIVEN IN THIS STANDARD.
NOTE 1 STAGES 1 THROUGH 5 INCLUSIVE ARE DEFINED IN 5.2.6.1.3.NOTE 2 ALL REFERENCES ARE TO PART 1 UNLESS OTHERWISE NOTED.
9
CLAUSES 7,12.4, AND
12.7
VERIFICATION
10 11
CLAUSE 5 CLAUSE 6.2
MANAGEMENT OF FUNCTION-AL SAFETY IN FUNCTIONAL
SAFETY ASSESSMENT AND AUDITING
SAFETY LIFE-CYCLE STRUCTURE
AND PLANNING 1
2
3
4
5
6
7
8
STAGE 4
STAGE 5DECOMMISSIONING
CLAUSE 18
MODIFICATIONCLAUSE 17
OPERATION AND MAINTENANCECLAUSE 16
INSTALLATION, COMMISSIONINGAND VALIDATION
CLAUSES 14 AND 15
DESIGN AND ENGINEERING OFSAFETY INSTRUMENTED SYSTEM
CLAUSES 11 AND 12
STAGE 3
STAGE 2
STAGE 1DESIGN AND DEVELOPMENT OF OTHER MEANS OF RISK
REDUCTIONCLAUSE 9
SAFETY REQUIREMENTS SPECIFICATION FOR SAFETY
INSTRUMENTED SYSTEM CLAUSES 10 AND 11
HAZARD AND RISK ASSESSMENT
CLAUSE 8
ALLOCATION OF SAFETY FUNCTIONS TO PROTEC-
TION LAYERSCLAUSE 9
Source: The Instrumentation, Systems, and Automation Society (IHS), Functional Safety: Safety Instrumented Systems for the Process Industry Sector - Part 1: Framework, Definitions, System, Hardware and Software
Requirements (ANSI/ISA-84.00.01-2004 Part 1 IEC 61511-1 Mod), 2004.
Chapter 6: Plant Design and Operation
NCEES 409
6.5.4.5 SIS Safety Life-Cycle Overview
The Safety Instrumented System (SIS) Safety Life-CycleSafety Life-Cycle Phase
or ActivityObjectives
Requirements Clause or Subclause
Inputs OutputsBox # in Previous
ImageTitle
1 Hazard and Risk Assessment
To determine the hazards and hazardous events of the process and associated equipment, the sequence of events leading to the hazard-ous event, the process risks associated with the hazardous event, the requirements for risk reduction, and the safety functions required to achieve the necessary risk reduction
8 Process design, layout, work force arrange-ments, safety targets
Description of hazards of the required safety function(s) and their associated risk reduction(s)
2 Allocation of Safety Functions to Protection Layers
Allocation of safety functions to protection layers and the associated safety integrity level for each safety-instru-mented function
9 Description of required safety-instrumented function(s) and associated safety integrity require-ments
Description of allocation of safety requirements (see Clause 9)
3 SIS Safety Requirements Specification
To specify the requirements for each SIS, in terms of the required safety-instrumented functions and their associated safety integrity, in order to achieve the required function-al safety
10 Description of allocation of safety require-ments (see Clause 9)
Design of the SIS in conformance with the SIS safety requirements; planning for the SIS integration test
5 SIS Installation Commissioning and Validation
To integrate and test the SIS
To validate that the SIS meets in all respects the require-ments for safety in terms of the required safety-instru-mented functions and the required safety integrity
12.3, 14, 15 SIS design
SIS integration test plan
SIS safety requirements
Plan for the safety validation of the SIS
Fully functioning SIS in confor-mance with the SIS design results of SIS integration tests
Results of the installation, commissioning, and validation activities
To ensure that the functional safety of the SIS is main-tained during operation and maintenance
16 SIS requirements
SIS design
Plan for SIS operation and maintenance
Results of the operation and maintenance activities
7 SIS Modification To make corrections, en-hancements, or adaptations to the SIS, ensuring that the required safety integrity level is achieved and maintained
17 Revised SIS safety require-ments
Results of SIS modification
8 Decommission-ing
To ensure proper review and sector organization, and to ensure SIF remains appropri-ate
18 As-built safety requirements and process informa-tion
SIF placed out of service
9 SIS Verification To test and evaluate the outputs of a given phase to ensure correctness and con-sistency with respect to the products and standards pro-vided as inputs to that phase
7, 12.7 Plan for the verification of the SIS for each phase
Results of the veri-fication of the SIS for each phase
10 SIS Functional Safety Assessment
To investigate and arrive at a judgment on the functional safety achieved by the SIS
5 Planning for SIS functional safety assessment
SIS safety requirement
Results of SIS functional safety assessment
6.5.4.6 Safety Integrity Levels: Probability of Failure on Demand
Demand Mode of OperationSafety Integrity
Level (SIL)Target Average Probability
of Failure on Demand Target Risk Reduction
4 to10 105 41$- - , ,to10 000 100 0002 #
3 to10 104 31$- - 1000 to 10,0002 #
2 to10 103 21$- - 100 to 10002 #
1 to10 102 11$- - to10 1002 #
Chapter 6: Plant Design and Operation
NCEES 411
6.5.4.7 Functional Safety Equations
Average Probability of Failure on Demand (PFDavg)
( )PF T PF t dt1
avg
T
0
= # (Rigorous version)
PF t
2avgm= (Approximation)
Safe Failure Fraction (SFF)
SFF
SD SU DD DU
SD SU DDm m m mm m m= + + +
+ +
where
l = failure rate (failures/year)
and subscripts indicate failure mode:
SD = safe detected
SU = safe undetected
DD = dangerous detected
DU = dangerous undetected
6.5.4.8 Management of ChangeManagement of Change (MOC)—A management system to identify, review, and approve all modifications to equip-ment, procedures, raw materials, and processing conditions, other than replacement in kind, prior to implementation, to help ensure that changes to processes are properly analyzed (for example, for potential adverse impacts), documented, and communicated to affected employees.
Key Principles:
• Maintain a dependable practice• Identify potential change situations• Evaluate possible impacts• Decide whether to allow the change• Complete follow-up activities
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6.5.4.9 Hazardous Waste Compatibility
Hazardous Waste Compatibility Chart
HEAT GENERATIONFIREINNOCUOUS & NON-FLAMMABLE GASTOXIC GAS GENERATIONFLAMMABLE GAS GENERATION EXPLOSIONPOLYMERIZATIONSOLUBILIZATION OF TOXIC MATERIALMAY BE HAZARDOUS BUT UNKNOWN
HFGGTGFEPSU
KEY
REACTIVITYCODE CONSEQUENCES
HEAT GENERATIONFIRE, AND TOXIC GASGENERATION
HF
GT
EXAMPLE
REACTIVITYGROUP
NAME
ACID, MINERALSNON-OXIDIZING
ACIDS, MINERALSOXIDIZING
ACIDS,ORGANIC
ALCOHOLS & GLYCOLS
AMINES ALIPHATIC &AROMATIC
CAUSTICS
CYAMIDES
CARBAMATES
AZO COMPOUNDS,DIAZO COMP, HYDRAZINES
DITHIOCARBAMATES
ESTERS
ETHERS
FLUORIDES, INORGANIC
CARBONS, AROMATIC
ISOCYANATES
KEYTONES
ORGANIC SULFIDESMETAPHORS & OTHER
OXIDIZING AGENTS,STRONG
REDUCING AGENTS,STRONG
EXTREMELY REACTIVE! DO NOT MIX WITH ANY CHEMICAL OR WASTE MATERIAL
WATER & MIXTURESCONTAINING WATER
WATER REACTIVESUBSTANCES
U.S. ENVIRONMENTAL PROTECTION AGENCY. APRIL 1980 EPA – 600/2–80–076
1 2 3 4 5 6 7 8 9 10 11
11
10
9
8
7
HS
S
SS
S
S
H H H H
HHH
H
H HG
HG
HG
HG
HG
GH
HG
HF
F
HF
HF
HF
F
H
H
HG
HT
HF
HF
HF
HFH
F
H
HG HH
G
G
G
H
EH
H
GH
EH
G
G
H
GH
GH
GH
GH
G GFH
G
GT
GF
GT GT
GT GT GT
GFGF GFGF
HGF
HGF
HGF
GTGTGFGFGFGF
GTGTGT
GT
HGT
HGT
HH H H
HH
H
H
GT
GFGFGF
H
H
H
GH H
FH
FH
FH
HFH
FH
FH
F UH
FH
FH
FH
FH
F
F F
HFH
FH
F
F
H
H
GTFH
H
H H
H
H
H
GF
GTGF
GF
FHGF
F
F
HGF
FHGF
FHGF
FHGF
HGF
GTHFGT
HFGT
GT
GT
GF
GF
HFGT GT
HFGT
HFGT
GTHGFH
H
GFGFHH
GFH
GFH
GFH
GFH
GFH
H H H
6
5
4
3
2
1
12
12
13
13
14
14
15
15
16
16
17
17
18
18
19
19
20
20
21
21
22 23 24 25 26 27 28 29 30 31 32 33 34
METAL, ALKALI & ALKALINEEARTH, ELEMENTAL
HALOGENATED ORGANICS
AMIDES
ALDEHYDES
NO.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
104
105
106
107
101 102 103 104
104
105
105
106
106
107
107
Source: U.S. Environmental Protection Agency, EPA 600/2-80-076, April 1980.
Chapter 6: Plant Design and Operation
NCEES 413
6.5.4.10 OSHA Highly Hazardous ChemicalsThe following is from 29 CFR 1910.119, Appendix A. It contains a list of toxic and reactive highly hazardous chemicals that present a potential for a catastrophic event at or above the threshold quantity.
* Chemical abstract service number ** Threshold quantity in pounds (amount necessary to be covered by OSHA CFR 1910.119 standard)
Chapter 6: Plant Design and Operation
NCEES 417
6.5.4.11 Hazardous Classification Based on NFPA 70
NFPA Hazardous Classification
GROUP AACETYLENE
CLASS IGASES OR VAPOR
CLASS IICOMBUSTIBLE DUST
DIVISION 2HAZARDOUS VAPORSCONTAINED BUT MAY
BE PRESENT
DIVISION 1HAZARDOUS VAPORS
PRESENTZONE 0, 1, OR 2
DIVISION 2STORED OR HANDLED
OTHER THANMANUFACTURE
DIVISION 1HANDLED,
MANUFACTURED ORUSED
DIVISION 2SURFACE
ACCUMULATED – NONAIR SUSPENDED
DIVISION 1AIR SUSPENDED
CLASS IIIFIBERS
GROUP BFLAMMABLE GAS, FLAMMABLE
OR COMBUSTIBLE VAPORMESG ≤ 0.45 MM MIC RATIO ≤ 0.40
GROUP CFLAMMABLE GAS, FLAMMABLE
OR COMBUSTIBLE VAPOR0.45 MM ≤MESG ≤ 0.75 MM 0.45 MM ≤ MIC RATIO ≤ 0.80
GROUP DFLAMMABLE GAS, FLAMMABLE
OR COMBUSTIBLE VAPOR0.75MM ≤ MESG
0.80MM ≤ MIC RATIO CLASS 1, ZONE 0: IGNITABLE CONCENTRATIONS PRESENT CONTINUOUSLY OR FOR LONG PERIODS OF TIMECLASS 1, ZONE 1: IGNITABLE CONCENTRATIONS LIKELY TO EXIST UNDER NORMAL OPERATIONCLASS 1, ZONE 2: IGNITABLE CONCENTRATIONS NOT LIKELY TO EXIST UNDER NORMAL OPERATION
MSEG: MAXIMUM EXPERIMENTAL SAFE GAPMIC: MINIMUM IGNITING CURRENT RATIO
GROUP GCOMBUSTIBLE DUSTS NOT
INCLUDED ELSEWHERE
GROUP FCOMBUSTIBLE CARBONACEOUS
DUSTS CONTAINING >8%AND TRAPPED VOLATILES
GROUP ECOMBUSTIBLE METAL DUSTS
Source: National Fire Protection Association, NFPA 70, Chapters 500 and 505, 2011.
Maximum Experimental Safe Gap (MESG): The maximum clearance between two parallel metal surfaces that has been found, under specified test conditions, to prevent an explosion in a test chamber from being propagated to a secondary chamber containing the same gas or vapor at the same concentration.
Minimum Igniting Current (MIC) Ratio: The ratio of the minimum current required from an inductive spark dis-charge to ignite the most easily ignitable mixture of a gas or vapor, divided by the minimum current required from an inductive spark discharge to ignite methane under the same test conditions.
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6.5.4.12 FlammabilityFlammable describes any solid, liquid, vapor, or gas that will ignite easily and burn rapidly. A flammable liquid is defined by NFPA and USDOT as a liquid with a flash point below 100°F (38°C). Flammability is further defined with lower and upper limits:
LFL = lower flammability limit (volume % in air) UFL = upper flammability limit (volume % in air)
A vapor-air mixture will only ignite and burn over the range of concentrations between LFL and UFL. Examples:
Predicting Lower Flammable Limits of Mixtures of Flammable Gases (Le Chatelier's Rule)
Based on an empirical rule developed by Le Chatelier, the lower flammable limit of mixtures of multiple flam-mable gases in air can be determined. A generalization of Le Chatelier's rule is
LFLC 1
i
i
i
n
1
$=
a k/where
Ci = the volume percent of fuel gas i in the fuel/air mixture
LFLi = the volume percent of fuel gas i at its lower flammable limit in air alone
If the indicated sum is greater than unity, the mixture is above the lower flammable limit. This can be restated in terms of the lower flammable limit concentration of the fuel mixture (LFLm):
C100LFLLFL
m
i
fi
i
n
1
=
=
a k/
where Cfi = the volume percent of fuel gas i in the fuel gas mixture.
THE SFPE HANDBOOK OF FIRE PROTECTION ENGINEERING, NATIONAL FIRE PROTECTION ASSOCIATION. 1988. WITH PERMISSION FROM THE SOCIETY OF FIRE PREVENTION ENGINEERS.
*
LOWERLIMIT
Source: National Fire Protection Association, The SFPA Handbook of Fire Protection Engineering, 1988. Used by permission of the Society of Fire Prevention Engineers.
Chapter 6: Plant Design and Operation
NCEES 419
6.5.4.13 Fundamental Burning Velocities
Fundamental Burning Velocities of Selected Gases and Vapors
* Gases that were critically examined as to their fundamental burning velocities, in studies by Andrews and Bradley (Andrews, G.E., and D. Bradley, "Determination of Burning Velocities: a Critical Review," Combustion and Flame,
Vol. 18, New York: Elsevier Scientific Publishing Co., 1972, pp. 133–153) or by France and Pritchard (France, D.H., and R. Pritchard, "Burning Velocity Measurements of Multicomponent Fuel Gas Mixtures," Gas Warnie International, Vol. 26,
No. 12, 1977).
Source: National Fire Protection Association 68, Standard on Explosion Protection by Deflagration Venting, 2013 ed., pp. 65–66. Used by permission.
Chapter 6: Plant Design and Operation
NCEES 421
The table below compares values from the Andrews/Bradley and France/Pritchard studies to those in the table above.
Comparison of Fundamental Burning Velocities for Selected Gases
Fundamental Burning Velocity scma k
Gas From Table AboveAndrews and Bradley France and
Pritchard (in Air)In Air In OxygenAcetylene 166 158 1140 -Ethylene 80 79 - 0Hydrogen 312 310 1400 347Methane 40 45 450 43Propane 46 - - 46
Flammability Properties of Gases 5L (0.005 m3) Sphere; E = 10J, normal conditions*
a. Measured at elevated temperatures and extrapolated to 25°C (77°F) at normal conditionsb. E = 100J - 200Jc. 200°C (392°F)
* W. Bartknecht, "Explosions-Schutz: Grundlagen und Anwendung," Springer-Verlag, Berlin, 1993 (German only).
Source: National Fire Protection Association 68, Standard on Explosion Protection by Deflagration Venting, 2013 ed., pp. 65–66.
6.5.4.14 Combustible DustCombustible dust is a solid material composed of distinct particles or pieces, regardless of size, shape, or chemical composition, that presents a fire or deflagration hazard when suspended in air or some other oxidizing medium over a range of concentrations. Combustible dusts are often either organic or metal dusts that are finely ground into very small particles, fibers, fines, chips, chunks, flakes, or a small mixture of these.
According to OSHA's Safety and Health Information Bulletin (SHIB) "Combustible Dust in Industry: Preventing and Mitigating the Effects of Fire and Explosions," dust particles with an effective diameter of less than 420 microns (those passing through a U.S. No. 40 standard sieve) should be deemed to meet the criterion of the defini-tion. However, larger particles can still pose a deflagration hazard (for instance, as larger particles are moved, they can abrade each other, creating smaller particles). In addition, particles can stick together (agglomerate) due to electrostatic charges accumulated through handling, causing them to become explosible when dispersed.
Types of dusts include, but are not limited to:
• Metal dust, such as aluminum and magnesium
• Wood dust
• Plastic or rubber dust
• Biosolids
• Coal dust
• Organic dust, such as flour, sugar, paper, soap, and dried blood
• Dusts from certain textiles
Kst is the dust deflagration index, which measures relative explosion severity compared to other dusts. The larger the value for Kst, the more severe the explosion. Kst provides the best "single number" estimate of the anticipated behavior of a dust deflagration.
MIE, the minimum ignition energy, predicts the ease and likelihood of ignition of a dispersed dust cloud.
MEC, the minimum explosible concentration, measures the minimum amount of dust dispersed in air required to spread an explo sion. The MEC is analogous to the Lower Flammable Limit (LFL) or Lower Explosive Limit (LEL) for gases and vapors in air.
Chapter 6: Plant Design and Operation
NCEES 423
Examples of Kst Values for Different Types of Dusts
Dust Explosion Class* Kst bar sm:c m* Characteristic Typical materials**
St 0 0 No explosion SilicaSt 1 > 0 and < 200 Weak explosion Powered milk, charcoal, sulfur, sugar, zincSt 2 > 200 and < 300 Strong explosion Cellulose, wood flour, poly methyl acrylateSt 3 > 300 Very strong explosion Anthraquinone, aluminum, magnesium
* OSHA CPL 03-00-008 - Combustible Dust National Emphasis Program ** NFPA 68, Standard on Explosion Prevention by Deflagration Venting
Source: U.S. Department of Labor, OSHA, "Hazard Communication Guidance for Combustible Dusts," OSHA 3371-08, 2009.
The actual class is sample-specific and will depend on varying characteristics of the material, such as particle size or moisture.
Source for next five tables: National Fire Protection Association 68, Standard on Explosion Protection by Deflagration Venting, 2013 ed., pp. 67–69. Used by permission.
Source: Jacobson, M., A.R. Cooper, and J. Nagy, Explosibility of Metal Powders, Bureau of Mines Report of Investigations 6516, Washington, D.C.: United States Department of the Interior, Bureau of Mines, 1964.
6.5.4.15 Relief Vent Sizing
Relief-Venting Flammable Liquids
20 200
14,090,0009,950,000
4,000,000
400,000
1000 2800EXPOSED WITH A SURFACE AREA, A (FT2)
HEAT
ABS
ORPT
ION,
Q (B
TU/H
R)
Q = 20,00
0A
Q = 21,000 (A)0.82
Q = 14,090,000
Q = 20,00
0A
Q = 199,300 (A)0.566Q = 963,400 (A)0.338
Q = 199,300 (A)0.566Q = 963,400 (A)0.338
Q = 21,000 (A)0.82
Q = 14,090,000
Source: National Fire Prevention Association, NFPA 30: Flammable and Combustible Liquid Code, 2008 ed., p. 110. Used by permission.
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Estimation of Emergency Relief Venting for Specific Liquids
.CFH
L MQ70 5=
where
CFH = cubic feet of free air per hour
70.5 = factor for converting pounds of gas to ft3 of air
Q = total heat input per hour (Btu)
L = latent heat of vaporization lbBtuc m
M = molecular weight
6.5.4.16 Pressure Relief Variables and Constants
Pressure Relief Variables and ConstantsSymbol Description Units (U.S.) Units (metric)
A Required effective discharge area of the device in2 mm2
C A function of the ratio of the ideal gas-specific heats k CCv
p=e o of the gas or vapor at inlet-relieving temperature lbf hr
lbm lbmole R-
- -cmm hr K Pakg kgmol K
2 : :
: :
Cp Specific heat at constant pressure lb FBtuc kgK
KJ
Cv Specific heat at constant volume lb FBtuc kgK
KJ
F2 Coefficient of subcritical flow
GlSpecific gravity of a liquid at flowing temperature referred to water at standard conditions
k Ratio of the specific heats CCv
pe o for an ideal gas at relieving tempera-
ture. The ideal-gas to specific-heat ratio is independent of pressure.dimensionless
Kb
Capacity correction factor due to back pressure; can be obtained from manufacturer's literature or estimated for preliminary sizing. The back-pressure correction factor applies to balanced-bellows valves only. For conventional and pilot-operated valves, use a value for Kb equal to 1.0.
dimensionless
Kc
Combination correction factor for installations with a rupture disk upstream of the pressure relief valve. Equals 1.0 when a rupture disk is not installed; equals 0.9 when a rupture disk is installed in com-bination with a PRV and the combination does not have a certified value.
dimensionless
Chapter 6: Plant Design and Operation
NCEES 429
Pressure Relief Variables and Constants (cont'd)Symbol Description Units (U.S.) Units (metric)
Kd for gas,
vapor, steam
Rated coefficient of discharge that should be obtained from the valve manufacturer. For preliminary sizing, an effective discharge coeffi-cient can be used as follows:
• 0.65 when a PRV is installed with or without a rupture disk in combination
• 0.62 when a PRV is not installed and sizing is for a rupture disk with minimum net flow area
dimensionless
Kd for liquid
Effective coefficient of discharge. For preliminary sizing, use the following values:
• 0.975 when a PRV is installed with or without a rupture disk in combination
• 0.62 when a PRV is not installed and sizing is for a rupture disk with minimum net flow area
dimensionless
KN Correction factor for the Napier equation (KN = 1.0) dimensionless
KSH
Superheat correction factor; can be obtained from the "Superheat Correction Factors" table on page 432. For saturated steam at any pressure, KSH = 1.0. For temperatures above 1200°F, use the critical vapor sizing equations.
dimensionless
Kv Correction factor due to viscosity dimensionless
KW
Correction factor due to back pressure. If the back pressure is atmo-spheric, use a value for KW of 1.0. Balanced-bellows valves in back-pressure service require the correction determined from the figure "Capacity Correction Factor, KW, Due to Back Pressure on Balanced-Bellows PRVs in Liquid Service." Conventional and pilot-operated valves require no special correction.
dimensionless
M
Molecular weight of the gas or vapor at inlet-relieving conditions. Various handbooks carry tables of molecular weights of materials; however, the composition of the flowing gas or vapor is seldom the same as that listed in such tables. This composition should be obtained from the process data.
P1Upstream relieving pressure; set pressure plus allowable overpres-sure plus atmospheric pressure psia kPa
P2 Back pressure psia kPa
Q Flow rate . .min
U S galminL
r Ratio of back pressure to upstream relieving pressure, PP1
2 dimensionless
Re Reynolds number dimensionlessT Relieving temperature of the inlet gas or vapor °R (°F + 460) K (°C + 273)m Absolute viscosity at the flowing temperature cPU Viscosity at the flowing temperature Saybolt universal seconds
V Required flow through the devicescfm at
14.7 psia and 60°F
minnormalm3 at 0°C
and 101.325 kPa
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430 NCEES
Pressure Relief Variables and Constants (cont'd)Symbol Description Units (U.S.) Units (metric)
W Required flow through the device. hlb
hkg
Z Compressibility factor for the deviation of the actual gas from a perfect gas, evaluated at inlet-relieving conditions. dimensionless
Pressure Relief EquationsDescription Units (U.S.)
(units per previous table)Units (metric)
(units per previous table)
Coefficient C C k k520 12 k
k11
= +−+
c^^m
hh .C k k0 03948 1
2 kk11
= +−+
c^^m
hh
Correction Factor KN
KN = 1.0
where , psiaP 1 5001 #
KN = 1.0
where , kPaP 10 3391 #
. ,
. ,K P
P0 2292 1 0610 1906 1 000
N1
1= −−
where P1 > 1,500 psia and , psia3 200#
. ,
. ,K P
P0 03324 1 0610 02764 1 000
N1
1= −−
where P1 > 10,339 kPa and , kPa22 057#
Coefficient F2F k
k rr
r1 1
1k kk
22 1
= − −−
−c c cm m m> H
Sizing for Gas or Vapor Service at Critical Flow Conditions
A C K P K KW
MT Z
d b c1=
Sizing for Subcritical Flow: Gas or Vapor, Conventional and Pilot-Operated PRVs
When the ratio of back pressure to inlet pressure exceeds the critical pressure ratio Pcf /P1, the flow through the pressure-relief device is subcritical. These equations may be used to calculate the required effective discharge area for a conventional PRV whose spring setting is adjusted to com-pensate for superimposed back pressure. Equations may also be used for sizing a pilot-operated PRV.
( )A F K KW
M P P PT Z
735 d c2 1 1 2= −
.( )A F K K
WM P P P
T Z17 9d c2 1 1 2
= −
Sizing for Steam-Relief Operating at Critical Flow Conditions .A P K K K K K
W51 5 d b c N SH1
= .A P K K K K KW190 5
d b c N SH1=
Chapter 6: Plant Design and Operation
NCEES 431
Pressure Relief Equations (cont'd)Description Units (U.S.) Units (metric)
Sizing for Liquid Relief: PRVs Requiring Capacity Certification
The ASME Code requires that capacity certification be obtained for PRVs de-signed for liquid service. The procedure for obtaining capacity certification includes testing to determine the rated coefficient of discharge for the liquid PRVs at 10% overpressure.
The sizing equations for pressure-relief devices in liquid service provided here as-sume that the liquid is incompressible (i.e., the density of the liquid does not change as the pressure decreases from the relieving pressure to the total back pressure).
Valves in liquid service that are designed in accordance with the ASME Code may be initially sized using these area equations.
A K K K KQ
P PG
38 d w c v 1 2
1= −.
A K K K KQ
P PG11 78
d w c v 1 2
1= −
Kv: Correction Factor Due to Viscosity . . .Re ReK 0 9935 2 878 342 75
. .
.
v 0 5 1 5
1 0= + +
−
d n
Re = Reynolds Number
When a PRV is sized for viscous liquid ser-vice, it should first be sized as if it were for a nonviscous application (i.e., Kv = 1.0), so that a preliminary required discharge area A can be obtained from the liquid relief area equations above.
From API 526 standard orifice sizes, use the next orifice size larger than A to deter-mine the Reynolds Number, Re, from either of the following relationships:
Second equation is not recommended for viscosities less than 100 Saybolt universal seconds (SSU)
After determining the Reynolds Number, Re, obtain the factor KV. Apply KV in the liquid relief area equations above to correct the preliminary required discharge area. If the corrected area exceeds the chosen standard orifice area, repeat the above calculations using the next larger standard orifice size.
( , )Re
AQ G2 800 l
n= ,
ReU A
Q12 700=
Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008.
Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008.
Chapter 6: Plant Design and Operation
NCEES 433
Capacity Correction Factor, KW, Due to Back Pressure on Balanced-Bellows PRVs in Liquid Service1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.500 10
PERCENT OF GAUGE BACKPRESSURE = (PB /PS) x 10020
K w
Kw = CORRECTION FACTOR DUE TO BACK PRESSURE.= BACK PRESSURE, IN PSIG.= SET PRESSURE, IN PSIG.
PBPS
30 40 50
NOTE: THE CURVE ABOUT REPRESENTS VALUES RECOMMENDED BY VARIOUS MANUFACTURERS.THIS CURVE MAY BE USED WHEN THE MANUFACTURER IS NOT KNOWN.OTHERWISE, THE MANUFACTURER SHOULD BE CONSULTED FOR THE APPLICABLE CORRECTION FACTOR.
Source: Sizing, Selection, and Installation of Pressure-Relieving Devices in Refineries: Part 1—Sizing and Selection, API Standard 520, 8th ed., December 2008.
6.5.5 Environmental Considerations
6.5.5.1 Air PollutionConcentrations in air can be converted from ppb to
mg3n
as follows:
mg
ppbMWRT
P3n =
_ i
where
ppb = parts per billion
P = pressure, in atm
R = ideal gas law constant = 0.0821 mol Kliter atm
::
T = absolute temperature, K = 273.15 + °C
MW = molecular weight, in molg
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6.5.5.2 Atmospheric Dispersion Modeling (Gaussian)σy and σz are functions of downwind distance and stability class:
exp exp expC uQ y z H z H
2 21
21
21
y z y z z2
2
2
2
2
2
r v v v v v= − −
−+ −
+f f ^ f ^p h p h p> Hwhere
C = steady-state concentration at a point (x, y, z) in mg3n
Q = emissions rate in sgn
σy = horizontal dispersion parameter, in meters
σz = vertical dispersion parameter, in meters
u = average wind speed at stack height in sm
x = downwind distance along plume center line, in meters
y = horizontal distance from plume center line, in meters
z = vertical distance from ground level, in meters
H = effective stack height (m) = h + ∆h
where h = physical stack height
∆h = plume rise
Maximum concentration at ground level and directly downwind from an elevated source:
expC uQ H
21
max y z z2
2
r v v v= −f _ i p
where variables are as above except for
Cmax = maximum ground-level concentrationH2zv = for neutral atmospheric conditions
Chapter 6: Plant Design and Operation
NCEES 435
6.5.5.3 Characteristic Hazardous WasteA waste is a characteristic waste if it meets any of the characteristics identified in 40 CFR 261 Subpart C (D code waste).
Hazardous Waste CharacteristicsCharacteristic
(D Code) [Subpart #] Definition
Ignitability (D001) [40 CFR 261.21]
(1) A liquid (other than an aqueous solution containing <24% alcohol by volume) that has flash point <140oF [Method Pensky-Martens or Setaflash].
(2) A nonliquid that is capable (under STP) of causing fire through friction, absorption of moisture, or spontaneous chemical changes and, when ignited, burns so vigorously and persistently that it creates a hazard.
(3) An ignitable compressed gas.
Corrosivity (D002) [40 CFR 261.22]
(1) An aqueous solution with a pH .or2 12 5# $ [Method 9040C in SW-846].
(2) A liquid that corrodes steel (SAE 1020) at a rate of > 1/4 inch per year at a test temperature of 130oF [Method 1110A in SW-846].
Reactivity (D003) [40 CFR 261.23]
(1) Normally unstable and readily undergoes violent change without detonating.
(2) Reacts violently with water.
(3) Forms potentially explosive mixtures with water.
(4) When mixed with water, generates toxic gases, vapors, or fumes in a quantity sufficient to present a danger to human health or the environment.
(5) A cyanide- or sulfide-bearing waste that, when exposed to pH conditions between 2 and 12.5, can generate toxic gases, vapors, or fumes in a quantity sufficient to present a danger to human health or the environment.
(6) Capable of detonation or explosive reaction if subjected to a strong initiating source or if heated under confinement.
(7) Readily capable of detonation or explosive decomposition or reaction at standard temperature and pressure.
(8) A forbidden explosive as defined in 49 CFR 173.54, or a Division 1.1, 1.2, or 1.3 explosive as defined in 49 CFR 173.50 and 173.53.
Toxicity (D004 to D043) [40 CFR 261.24]
A waste that contains constituents above the regulatory threshold listed in Table 1 of 40 CFR 261.24 using the Toxicity Characteristic Leaching Procedure (TCLP) test [Method 1311 in SW846].
Atmospheric Stability Under Various ConditionsSurface Wind Speeda in s
mDay: Solar Insulation Night: Cloudinesse
Strongb Moderatec Slightd Cloudy (<4/8) Clear (<3/8)<2 A A-Bf B E F2-3 A-B B C E F3-5 B B-C C D E5-6 C C-D D D D> 6 C D D D D
Source: Turner, D.B., Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed., Florida: Lewis Publishing/CRC Press, 1994.
a. Surface wind speed is measured at 10 m above the ground. b. Corresponds to a clear summer day with sun higher than 60° above the horizon. c. Corresponds to a summer day with a few broken clouds, or clear day with sun 35–60° above the horizon. d. Corresponds to a fall afternoon or a cloudy summer day with the sun 15–35°. e. Cloudiness is defined as the fraction of sky covered by the clouds. f. For A - B, B - C, or C - D conditions, average the values obtained for each.
A = Very unstable B = Moderately unstable C = Slightly unstable D = Neutral E = Slightly stable F = Stable Regardless of wind speed, Class D should be assumed for overcast conditions, day or night.
Chapter 6: Plant Design and Operation
NCEES 437
Standard Deviations of a Plume
Source: D.B. Turner, Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed. Florida: Lewis Publishing/CRC Press, 1994.
Source: Turner, D.B., Workbook of Atmospheric Dispersion Estimates: An Introduction to Dispersion Modeling, 2nd ed., CRC Press (Lewis Publishing), 1994.
Effective stack height is shown on curves numerically.
xmax = distance along plume center line to the point of maximum concentration
(Cu/Q)max = e[ ( ) ( ) ( ) ]ln ln lna b H c H d H2 3+ + +
H = effective stack height, stack height + plume rise, in meters
Values of Curve-Fit Constants for Estimating (Cu/Q)max from H as a Function of Atmospheric Stability
StabilityConstants
a b c dA –1.0563 –2.7153 0.1261 0B –1.8060 –2.1912 0.0389 0C –1.9748 –1.9980 0 0D –2.5302 –1.5610 –0.0934 0E –1.4496 –2.5910 0.2181 –0.0343F –1.0488 –3.2252 0.4977 –0.0765
Source: Table 1, Ranchoux, R.J.P., "Determination of Maximum Ground Level Concentration," Journal of the Air Pollution Control Association, vol. 26, no. 11, Lexington: Taylor & Francis Ltd, 1976, p. 1089, reprinted by permission of the Air
& Waste Management Association, www.awma.org, and Taylor & Francis Ltd, http://www.tandfonline.com. Journal's website can be found at htpp://informaworld.com.
Chapter 6: Plant Design and Operation
NCEES 439
6.5.5.4 Incineration
%DRE WW W 100
in
in out #=-
where
DRE = destruction and removal efficiency (%)
Win = mass feed rate of a particular POHC*, in hrkgor hrlb
Wout = mass emission rate of the same POHC*, in hrkgor hrlb
*POHC = principal organic hazardous contaminant
%CE 100CO COCO2
2 #=+
where
CO2 = volume concentration (dry) of CO2 , in parts per million (volume: ppmv)
Methyl Chloride 74-87-3 D GAS −46 632 8.1 17.4 1.7 IIA 1Methyl Ether 115-10-6 Cd GAS −41 350 3.4 27 1.6 IIB 0.85 0.84Methyl Ethyl Ketone 78-93-3 Dd I −6 404 1.4 11.4 2.5 92.4 IIB 0.53 0.92 0.84Naptha (Petroleum) 8030-30-6 Dd,h I 42 288 1.1 5.9 2.5 IIAn-Octane 111-65-9 Dd,g I 13 206 1 6.5 3.9 14 IIA 0.94n-Pentane 109-66-0 Dd,g I −40 243 1.5 7.8 2.5 513 IIA 0.28 0.97 0.93Process Gas > 30% H2 1333-74-0 Bi GAS 520 4 75 0.1 0.019 0.45Propane 74-98-6 Dd GAS 450 2.1 9.5 1.6 IIA 0.25 0.82 0.97
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hemical R
eference Handbook
442
NC
EES
Chemical CAS No.Class I
Division Group
TypeaFlash Point (°C)
AIT (°C)
% LFL
% UFL
Vapor Density (Air=1)
Vapor Pressureb
(mm Hg)
Class 1 Zone
Groupc
MIE (mJ)
MIC Ratio
MESG (mm)
1-Propanol 71-23-8 Dd I 15 413 2.2 13.7 2.1 20.7 IIA 0.89Propylene 115-07-1 Dd GAS 460 2.4 10.3 1.5 IIA 0.28 0.91Styrene 100-42-5 Dd I 31 490 0.9 6.8 3.6 6.1 IIA 1.21Tetrahydrofuran 109-99-9 Cd I −14 321 2 11.8 2.5 161.6 IIB 0.54 0.87Toluene 108-88-3 Dd I 4 480 1.1 7.1 3.1 28.53 IIA 0.24Triethylamine 121-44-8 Cd I –9 249 1.2 8 3.5 68.5 IIA 0.75 1.05Vinyl Acetate 108-05-4 Dd I −6 402 2.6 13.4 3 113.4 IIA 0.7 0.94Vinyl Chloride 75-01-4 Dd GAS −78 472 3.6 33 2.2 IIA 0.96Xylene 1330-20-7 Dd I 25 464 0.9 7 3.7 IIA 0.2 1.09
a. Type designates whether the material is a gas, flammable liquid, or combustible liquid.b. Vapor Pressure is reflected in units of mm Hg at 25°C (77°F), unless stated otherwise.c. Class I Zone Groups are based on 1996 IEC TR3 60079-20, Electrical apparatus for explosive gas atmospheres—Part 20: Data for flammable gases
and vapors, relating to the use of electrical apparatus, which contains additional data on MESG and group classifications.d. Material has been classified by test.e. When all conduits run into explosion-proof equipment are provided with explosion-proof seals installed within 450 mm (18 in.) of the enclosure,
equipment for the group classification shown in parentheses is permitted.f. For classification of areas involving ammonia, see ASHRAE 15, Safety Code for Mechanical Refrigeration, and ANSI/CGA G2.1, Safety Require-
ments for the Storage and Handling of Anhydrous Ammonia.g. Commercial grades of aliphatic hydrocarbon solvents are mixtures of several isomers of the same chemical formula (or molecular weight). The
autoignition temperatures of the individual isomers are significantly different. The electrical equipment should be suitable for the AIT of the solvent mixture.h. [deleted]i. Petroleum naphtha is a saturated hydrocarbon mixture whose boiling range is 20°C to 135°C (68°F to 275°F). It is also known as benzine, ligroin,
petroleum ether, and naphtha.j. Fuel and process gas mixtures found by test not to present hazards similar to those of hydrogen may be grouped based on the test results.k. [deleted]
Source: NFPA 497: "Recommended Practice for the Classification of Flammable Liquids, Gases, or Vapors and of Hazardous (Classified) Locations for Electrical Installations in Chemical Process Areas," 2008 ed., Table 4.4.2. Used by permission.
443
7 GENERAL INFORMATION
7.1 Terms, Symbols, and Definitions
SymbolsSymbol Description Units (U.S.) Units (SI)
A Area or surface area ft2 m2
a Acceleration secft2 s
m2
ci Molar concentration ftlb mole
3 mmol3
cp Heat capacitylbm FBtu-c kg K
Js Km2
2
: :=
D Diameter ft or in. m
DAB Mass diffusivity hrft2
sm2
d Distance or diameter or diagonal ft or in. m
f Moody friction factor dimensionless
f Frequency sec1
s1
g Gravitational accelerationsecft2 s
m2
h Height ft or in. m
h Convection heat-transfer coefficient hr ft FBtu- -2 c m K
Ws Kkg
2 3: :=
hm Mass-transfer coefficient hrft
sm
Dhfusion Latent heat of fusionlbmBtu
kgJ
sm2
2=
Dhvap Latent heat of vaporizationlbmBtu
kgJ
sm2
2=
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444 NCEES
Symbols (cont'd)Symbol Description Units (U.S.) Units (SI)
k Thermal conductivity - -hr ft FBtuc m K
Ws Kkg m3: :
:=
L Length ft or in. m
MW Molecular weight lbmolelbm
molkg
N Number of moles lbmole molm Mass lbm kg
P Pressure inlbf2 Pa
mN
m skg
2 2:= =
P Perimeter ft or in. m
P Probability dimensionless
r, R Radius ft or in. m
R Universal gas constant lb mole Rpsi ft
lb mole RBtuor-
--
3
c c mol KJ:
T Temperature °F or °R °C or Kt Time hr or sec s
u Velocity secft
sm
V Volume ft3 m3
Wi Mass ratio dimensionless
wi Mass fraction or weight fraction dimensionless
Xi Molar ratio dimensionless
xi Mole fraction dimensionless
x Distance ft or in. ma, b, q,
f, j Angle degree or radians
a Thermal diffusivityhrft2
sm2
β Coefficient of thermal expansion R1c K
1
gi Mass concentrationftlbm3 m
kg3
g Surface tension in.lbf
mN
skg2=
λ Molecular mean free path ft or in. m
μ Dynamic viscosity cP or -secft
lbf2 Pa s m s
kg: :=
n Kinematic viscosityhrft2
sm2
r Density ftlbm3 m
kg3
Chapter 7: General Information
NCEES 445
Symbols (cont'd)Symbol Description Units (U.S.) Units (SI)
t Shear stress inlbf2 m
Nm skg
2 2:=
ji Volume fraction dimensionless
fi Volume concentrationftft3
3
mm3
3
7.1.1 Constants
Physical ConstantsSymbol Value Units Description
co
6.706 • 108hrmiles
Speed of light2.998 • 108 s
m
G3.44 • 10–8
lbf secft- 4
4
Gravitational constant6.674 • 10–11
kgN m
2
2:
g32.174
secft2 Gravitational acceleration
(earth)9.8067 s
m2
gc 32.174 -lbf seclbm ft- 2
Gravitational conversion factor
k5.66 • 10–24
Rft lbf-c
Boltzmann constant 1.3806 • 10–23
KJ
s Kkg m2
2
:
:=
NA
2.731 • 1026lb mole1
Avogadro's Number6.022 • 1023
mol1
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446 NCEES
Physical Constants (cont'd)Symbol Value Units Description
R
8.314 mol KJ
mol Km Pa3
: ::=
Universal gas constant
83.14mol Kcm bar3
::
8314kmol Km Pa3
::
82.06mol Kcm atm3
::
0.0821 mol Kliter atm
::
62.36 mol Kliter Torr
::
62,360mol Kcm Torr3
::
10.73lb mole Rpsi ft
-- 3
c
1.987 lb mole RBtu
mol Kcal
- :c=
1545 lb mole Rft lbf
--c
0.7302lb mole Ratm ft
-- 3
c
v
1.71 • 10–9ft hr RBtu- -2 4c
Stefan-Boltzmann constant (radiation)
5.67 • 10–8m KW
s Kkg
2 4 3 4: :=
Mathematical ConstantsSymbol Value Description
p 3.14159 Archimedes constant (Pi)e 2.71828 Base of the natural logg 0.57722 Euler's constant
Chapter 7: General Information
NCEES 447
Standard ValuesNote: The definitions for STP (standard temperature and pressure) vary between industries.
The table below contains several conditions as specified.Property Conditions U.S. Units SI Units
Molar standard volume, ideal gas (STP)
P = 1 atm = 14.696 psia T = 0°C = 32°F lb mole
ft3593 .
.
molm
molliter
0 0224
22 41
3
Molar standard volume, ideal gas (ambient)
P = 1 atm = 14.696 psia T = 15°C = 59°F
. molm0 023653
. molliter23 645
Standard cubic foot (scf) P = 1 atm = 14.696 psia T = 15.56°C = 60°F
. lbmoleft379 493
Density of air (STP) P = 1 atm = 14.696 psia T = 0°C = 32°F
.ftlbm0 0805 3 .
mkg
1 29 3
Density of air (ambient) P = 1 atm = 14.696 psia T = 15.6°C = 60°F .
ftlbm0 0764 3 .
mkg
1 22 3
Density of air (ambient) P = 1 atm = 14.696 psia T = 20°C = 68°F
.ftlbm0 0749 3 .
mkg
1 20 3
Density of mercury P = 1 atm = 14.696 psia T = 20°C = 68°F ft
lbm848 3 ,mkg
13 579 3
Density of water P = 1 atm= 14.696 psia T = 4°C = 32.9°F .
ftlbm62 4 3 1000
mkg3
Density of water P = 1 atm= 14.696 psia T = 15.6°C = 60°F .
Speed of sound in air (STP) P = 1 atm= 14.696 psia T = 0°C = 32°F 1090 sec
ftsm330
Speed of sound in air (ambient) P = 1 atm= 14.696 psia T = 20°C = 69°F 1130 sec
ftsm343
Energy of visible light Wavelength: 555 nm .cd sr hrBtu1 4 98 10 3: := − * .cd sr W1 1 46 10 3: := −
* cd • sr = candela steradian; see derived SI units for definition
7.1.2 Dimensional AnalysisA dimensionally homogeneous equation has the same dimensions on the left and the right sides of the equation. Dimensional analysis involves the development of equations that relate dimensionless groups of variables to describe physical phenomena.
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448 NCEES
7.1.2.1 Buckingham Pi TheoremThe number of independent dimensionless groups that may be used to describe a phenomenon known to involve n variables is equal to the number (n-r ), where r is the number of basic dimensions (e.g., mass, length, time) needed to express the variables dimensionally.
7.1.2.2 SimilitudeTo use a model to simulate the conditions of the prototype, the model must be geometrically, kinematically, and dynamically similar to the system that is modeled. Systems that have the same dimensionless numbers are similar.
Dimensionless Numbers1
Symbol Definition Name Description
Ar g D p f2
3
n
t t t−` jp f
p f Archimedes Ratio of buoyancy forces to viscous forces for a particle (p) in a fluid (f)
Bi kh L or k A
h V Biot Ratio of internal thermal resistance of a solid body to its surface thermal resistance (used for heat transfer)
Bim Dh LAB
m Biot (mass transfer)
Ratio of the internal species transfer resistance to the boundary layer species transfer resistance (used for mass transfer)
Bo ( ) g Lv12
ct t- Bond Ratio of buoyancy force to surface tension (used for boiling and
condensation)
Brk Tu2nD
Brinkman Ratio of viscous dissipation to enthalpy change (for use in high-speed flow)
Cf u21 2t
x Drag or friction coefficient
Ratio of surface shear stress to free-stream kinetic energy; dimension-less surface shear stress
Ca uReWe
cn = Capillary Ratio of viscous forces to surface tension (for use in two-phase flow)
Cauu Masound2
22= Cauchy Ratio of inertia forces to compression forces (for use in compressible
flow)
Ec c Tup
2
DEckert Kinetic energy of flow relative to boundary-layer enthalpy difference
(for use in high-speed flow)
Eu uP
2tD
Euler Ratio of pressure to inertia force
FoLD tAB
2 Fourier Dimensionless time; ratio of rate of heat conduction to rate of internal energy storage in a solid (for use in transient heat transfer problems)
Fom Lt2a Fourier
(mass transfer)Dimensionless time; ratio of rate of heat conduction to rate of internal energy storage in a solid (for use in transient mass transfer problems)
Frg Lu2
Froude Ratio of flow inertia to gravitational forces (for flow with a free surface)
f21
DL u
P2t
DFriction factor Ratio of shear force to inertia force; dimensionless pressure drop for
internal flow
Gavg L2
3Galilei Ratio of gravitational forces to viscous forces
Grv
g T L2
3bD Grashoff Ratio of buoyancy to viscous forces (for use in natural convection)
Chapter 7: General Information
NCEES 449
Dimensionless Numbers (cont'd)Symbol Definition Name Description
GzDx
Re Pr
Dx
u La
= Graetz Ratio of enthalpy flow rate to axial heat conduction
Jal hc T.
vap
p l
D
D
Jakob Ratio of sensible heat to latent heat (for use in film condensation and boiling)
Jav hc T.
vap
p v
D
D
jH St Pr 32 Colburn factor
(heat) Dimensionless heat transfer coefficient
jm St Scm 32 Colburn factor
(mass) Dimensionless mass transfer coefficient
Ka g3
4
tc
n Kapitza Ratio of surface tension forces to viscous forces (used for waves on a liquid film)
Kn Lm Knudsen Ratio of mean free path to a characteristic length (for use in non-
continuum flow)
Le DABa Lewis Ratio of molecular thermal diffusivity to mass diffusivity
Ma uusound Mach Dimensionless velocity; ratio of velocity to speed of sound (for use in
compressible flow)
Nukh L Nusselt
Dimensionless heat transfer coefficient; ratio of convection heat trans-fer to conduction in a fluid layer of thickness L (for use in convective heat transfer)
Pe u L Re Pra =3 Peclet Ratio of enthalpy flow rate to heat conduction rate (for use in forced convection heat transfer)
Pem Du L Re ScAB
=3 Peclet (mass transfer)
Ratio of enthalpy flow rate to heat conduction rate (for use in forced convection mass transfer)
Prkcpn Prandtl
Relative effectiveness of molecular transport of momentum and energy within the boundary layer; ratio of molecular momentum dif-fusivity to thermal conductivity (for use in convective heat transfer)
Rav
g T LPr2
3bD Raleigh Product of Grashoff and Prandtl numbers (for use in natural convec-tion)
Re u Dnt Reynolds Ratio of inertia and viscous forces (for use in forced convection and
fluid flow)
Sc DvAB Schmidt Ratio of molecular momentum diffusivity to mass diffusivity (for use
in convective mass transfer)
Sh Dh LAB
m Sherwood Ratio of convection mass transfer to diffusion in a slab of thickness L (for use in convective mass transfer)
Sk uP LnD Stokes Ratio of pressure force to viscous force
St Re PrNu
u chpt
=Stanton
Dimensionless heat transfer coefficient, ratio of actual convection heat flux to enthalpy energy heat flux (for use in forced convection heat transfer)
Stm Re ScSh
uhm=
Stanton (mass)
Dimensionless mass transfer coefficient (for use in forced convection mass transfer)
PE Chemical Reference Handbook
450 NCEES
Dimensionless Numbers (cont'd)Symbol Definition Name Description
Stehc Tfusion
p
D
D Stefan Ratio of sensible heat to latent heat for the solid/liquid transition (for use in melting and solidification)
Sr uL f Strouhal Time characteristics of fluid flow (for use in oscillating flow)
We u L2
ct Weber Ratio of inertial to surface tension forces (for use in liquid/vapor
phase change)
1Verify whether gravitational constant (gc) is required before using.
7.2 Units of Measurement
7.2.1 Metric Prefixes
Metric Prefixes and Their SymbolsMultiple Prefix Symbol
10–18 atto a10–15 femto f10–12 pico p10–9 nano n10–6 micro μ10–3 milli m10–2 centi c10–1 deci d101 deka da102 hecto h103 kilo k106 mega M109 giga G1012 tera T1015 peta P1018 exa E
7.2.2 Base and Derived SI Units
Base SI UnitsQuantity Name Symbol
Length meter mMass kilogram kgTime second sElectric current ampere ATemperature Kelvin KAmount of a substance mol molLuminous intensity candela cd
Chapter 7: General Information
NCEES 451
Derived SI Units With Special NamesQuantity Unit
Name Symbol Name Symbol Definition
Electric capacitance C farad F F VC
JA s
kg mA s2 2
2
2 4:::= = =
Electric charge Q coulomb C C A s:=
Electric conductance G siemens S S 1VA
JA s
kg mA s2
2
2 3:::
X= = = =
Energy or work or heat H joule J J N m skg m
2
2
::
= =
Force F newton N N skg m
2:
=
Frequency f hertz Hz Hz s1=
Inductance L henry H H s AV s
A skg m2 2
2
::
:
:X= = =
Electric potential E volt V V A sJ
A skg m2 3
2
: :
:= =
Power or energy flux P watt W W sJ
sN m
skg m
3
2: :
= = =
Pressure or stress P pascal Pa Pa mN
m skg
2 2:= =
Electric resistance R ohm Ω AV
A skg m2 3
2
:
:X = =
Illuminance lux lx lx mlm
mcd sr
2 2:= =
Luminous flux VU lumen lm lm cd sr:=
Magnetic flux UE weber Wb Wb V s s Akg m2
2
::
:= =
Magnetic flux density tesla T T mWb
mV s
s Akg
2 2 2:
:= = =
Note: Steradian or square radian (sr) is dimensionless and represents a solid angle in three-dimensional space (angle at the tip of a cone).
PE Chemical Reference Handbook
452 NCEES
7.2.3 Unit Conversion Tables (U.S. and Metric)
TimeTime Second (sec) Minute (min) Hour (hr) Day Week Year
Conversion Table for the Most Commonly Used Units of Cubic Expansion
Cubic Expansion m K
kg3 : m F
lbm-3 c cm C
g3 : c
m Kkg
1 3 := 1 0.03468 0.001
1m Flbm
-3 c= 28.833 1 0.02883
1cm Cg3 : c
= 1000 34.682 1
7.2.3.28 Temperature
Conversion Table for Temperature UnitsKelvin (K) Celsius (°C) Rankine (°R) Fahrenheit (°F)
T(K) = T(K) T(°C) + 273.15 95 T(°R) 9
5 T(°F) + 255.37
T(°C) = T(K) – 273.15 T(°C)95 T(°R) – 273.15 9
5 T(°F) – 17.78
T(°R) = 59 T(K) 5
9 T(°C) + 491.67°R T(°R) T(°F) + 459.67
T(°F) = 59 T(K) + 459.67 5
9 T(°C) + 32 T(°R) – 459.67 T(°F)
PE Chemical Reference Handbook
472 NCEES
7.3 General Engineering Relations
7.3.1 Measures of Composition
7.3.1.1 Fractions
Mole Fraction (or mole%): xi
x N
NA
A= N Nii=/ x 1ii =/
For binary systems:
x N NN
NN
11
AA B
a
a
B= + =
+ N x N1 1A B B= −c m x x 1A B+ =
Mass Fractions (Weight Fraction or wt%): wi
w m
mA
A= m mii=/ w 1ii =/
For binary systems:
w m mm
mm
11
AA B
A
AB
= + =+
m w m1 1A B B= −c m w w 1A B+ =
Conversion Between Mole Fraction and Mass Fraction
MW N
mA A
A= m N MWA A A= N MWm
A A
A=
xm MWMW
m
w MWMWw
A A
A
A
A
ii i i ii
= =/ /
wN MWMW
N
x MWMWx
A
A
A
A
A
ii
i ii
i
= =/ /
For binary systems:
xm m MW
MWm
w MWMW
1 1 1
1A
A B B
A
A
A B
A=
+=
+ −c m w
N N MWMW
N
x MWMW
1 1 1
1A
A B A
B
A
A A
B=
+=
+ −c m
Volume Fraction (%vol): i{
VV
*
*
ii{ = where V Vii=[ [/ 1ii{ =/
Volume fraction is the volume of a constituent of a mixture prior to mixing Vi[` j divided by the sum of volumes of all constituents prior to mixing V [` j.For mixtures of ideal gases: φi = xi
For ideal solutions (no volume change due to mixing): wi i i{ t
t=
Chapter 7: General Information
NCEES 473
Density and Average Molecular Weight (MW) of a Mixture:
MW x MWi ii=/
For ideal solutions (no change in volume due to mixing): w1ii
it t=/For solutions of components with similar densities (assume volume of the solution is proportional to the mass):
wi iit t=/
7.3.1.2 Ratios or Loading
Mole Ratio: Xi
Ratios are used primarily for dilute solution or when one component is not affected by the process. For solutions with a solvent it is also called "solute-free basis" and for combustion gases "dry basis."
Note: Component A is the basis (the solvent, the inert, or the predominant component).
X NN
xx
A Aii i= = X N
N 1AA ii = −
!/ X 1A =
For binary systems (A: Solvent, B: Solute):
X xx
xx1 1 1
1 1 1BB
B
BA
= − =−
= − xX1 11
B
B
=+
x X11
AB
= +
For dilute systems with xA→1: Xi→xi
Mass Ratio: Wi
W m
mww
A Aii i= = W m
m 1AA ii = −
!/ WA = 1
For binary systems (A: Solvent, B: Solute):
W w
w
ww1 1 1
1 1 1BB
B
BA
= − =−
= − wW1 11
B
B
=+
w W11
AB
= +
For dilute systems with wA→1: Wi→wi
Conversion Between Mole Ratio and Mass Ratio
W X MW
MWAi ii= X W MW
MWAi i i=
7.3.1.3 Concentrations
Molar Concentration: ci or [i]
c V
Ni
i=
For ideal gases: c x RTp
i i=
PE Chemical Reference Handbook
474 NCEES
Mass Concentration: gi
Vm
wiiic t= =
Volume Concentration: fi
VV
iiz =[
Volume fraction is the volume of a constituent of a mixture prior to mixing V *i divided by the volume of the mix-
ture (V).
For mixtures in which volume decreases on mixing:
V V*mixii 2/ 1ii 2z/
Ideal solution (no volume change due to mixing):
wi i i iz { t
t= =
1iiz =/ (ideal solutions only)
7.3.1.4 Molarity and Molality
Molarity (M)
Molarity Liters of solutionmoles of solute=
Note that molarity is temperature-dependent.
Molality (m)
Molality kg of solvent
moles of solute=
Note that molality is temperature-independent.
Chapter 7: General Information
NCEES 475
7.3.1.5 Special Measures of Composition
Normality (N)
Normality liters of solution
equivalent grams of the solute=
Gram equivalent weight is a measure of the reactive capacity of a given molecule and thus is reaction-dependent.
Note that normality is temperature-dependent.
pH and pOH
logpH H10=− +7 A or logpH H O10 3=− +8 BlogpOH OH10=− −7 A
and
logpK pH pOH K10= + =− where K H O OH3= + −8 7B AFor water at 20 Cc : K 10 14= − and pK = 14
Note that all concentrations are in moles/liter.
Proof (for Alcohol Content)
Proof abv ml of solution
ml of pure ethanol2 200= =
abv = alcohol % by volume (volume concentration)
For Dilute Solution (Can Be Based on Mass, Molar, or Volume)
ppm = parts per million = 10–6
ppb = parts per billion = 10–9
ppt = parts per trillion = 10–12
Percent: 1% = 10,000 ppm
Permil: 1a = 1000 ppm
PE C
hemical R
eference Handbook
476
NC
EES
7.3.1.6 Conversion Table Between Different Measures of Concentration
Multicomponent SystemsMole
Fraction xi
Mass Fraction
wi
Mole Ratio Xi
Mass Ratio Wi
Molar concentration
ci
Mass concentration
gi
Mole Fraction
xi =xi w MW
MWw
j j
ij
i
/ XX
1 A jj
i
+!/ MW
MWW MWMW
W
A Ai
j j
ij
i
+!
/ c MWit MW
MWi
itc
Mass Fraction
wi =x MWMWx
jj i
j
i
/ wi MW X MWX MW
A j jj A
i i+
!/ W
W1 jj A
i+
!/ c MWi i
titc
Mole Ratio Xi = x
xAi
wwMWMW
A A
i i Xi W MWMWAi i
ccAi
MWMW
A
A
i
icc
Mass Ration Wi = x
xMWMW
AAi
i ww
Ai X MW
MWAii Wi c MW
c MWA A
i iAicc
Molar concentration
ci = MWxit
MWw
i
it X cAi MWW A
i
ic ci MWiic
Mass concentration
gi = MWx MWi it wit X MW cAi i w Ai c c MWi i gi
Avg. MW MW = x MWj jj/ MW
w1
j
jj/ X
MW X MW1 A
A A
jj
j jj
+
+
!
!
//
MW X MWW
W1A A
A
j j
jj
jj
+!
!
//
Avg.* Density
r =x MWMW
i
j jj t/
w1
j
jj t/
*Ideal solutions only
C
hapter 7: General Inform
ation
NC
EES
477
Binary SystemsMole
Fraction xB
Mass Fraction
wB
Mole Ratio XB
Mass Ratio WB
Molar concentration
cB
Mass concentration
gB
Mole Fraction
xB =xB w w MW
MWw
1B BA
B
B
+ −_ i XX
1 B
B+ MW
MWW
W
A
BB
B
+c MWBt MW
MWB
Btc
Mass Fraction
wB = x x MWMW
x
1B BB
A
B
+ −_ i wBMWMW
X
X
B
AB
B
+ WW1 B
B+
c MWB Bt
Btc
Mole Ratio XB = x
x1 B
B- w
wMWMW
1 B
B
B
A- XB W MW
MWB B
A
ccAB
MWMW
A B
B Acc
Mass Ratio WB = x
xMWMW
1 B
B
A
B- w
w1 B
B- X MW
MWB A
B WB c MWc MWA A
B B
ABcc
Molar concentration
cB = MWxBt
MWw
B
Bt X cB A MWW
B
B Ac cB MWB
Bc
Mass concentration
gB = MWx MWB Bt wBt X c MWB A B wB Ac c MWB B gB
Avg. MW MW = x MW x MW1B B B A+ −_ i w w MW
MWMW
1B BA
B
B
+ −_ i XMW X MW
1 B
A B B+
+MW MW
WW
11
A B
B
B
+
+
Avg.* Density
r = x x MWMW
MWMW
1B BB
AAB
B B
tt
t
+ −_ i w w1B B AB
B
tt
t
+ −_ i X MWMWMWMW X
B B AB
B B
A
B
tt
t
+
+d n
W
W1
BA
B
B B
ttt
+
+_ i
*Ideal solutions only
Note: For mole and mass ratios, "A" is the basis component (e.g., the solvent).
PE Chemical Reference Handbook
478 NCEES
7.3.2 Density Definitions
7.3.2.1 Density and Relative DensityDensity is
Vm
t =
Relative density is
RDreftt=
where reft = density of a reference material
7.3.2.2 Specific Gravity
Specific Gravity (Relative Density) of Gas
SG
ir at ef emp, ress
as
a r t p
gt
t=
The reference temperatures are commonly either 0°C or 60°F and the reference pressure is commonly 14.696 psia (101,325 Pa).
For ideal gas:
28.96SG
molgMW
MW MWair
gas gas==
Specific Gravity (Relative Density) of Liquid
SGH O at ref temp2tt=
where 62.4ftlbm 1000
mkg
H O, ref 3 32t = =
The reference temperatures are commonly either 4°C or 60°F.
Specific Gravity (Realtive Density) in Baumé
For liquids lighter than water, using degrees Baumé or B°: BSG 130140= + c
For liquids heavier than water, using degrees Baumé or B°: 145 B145SG = − c
Specific Gravity (Relative Density) for Hydrocarbon Liquid
131.5 API141.5SG60 F = +c API 141.5 131.5SG60 F
= −c
where API = American Petroleum Institute gravity or API gravity
Chapter 7: General Information
NCEES 479
Specific Gravity (Relative Density) for Slurries
Bulk density and specific gravity of solids and liquid mixtures (slurries) are1 1 1 1bulk liquid solids solids liquidt t \ t t= + −d n
SG SG SG SG1 1 1 1bulk liquid
solids solids liquid\= + −e o
7.4 Mathematics
7.4.1 Algebra
7.4.1.1 Linear Algebra
Straight Line
General form: A x + B y + C = 0
Standard form: y = m x + b
Point-slope form: y - y1 = m (x - x1)
Two-point form: x xy y
x xy y
1
1
2 1
2 1−−
= −−
Intercept form: xx
yy
1 00
+ − =0
, where intercepts x0 ≠ 0, y0 ≠ 0
Slope: 2m x xy y2 1
= −− 1
Angle between lines with slopes m1 and m2: arctan m mm m1 2 1
2 1−a = +e o
Distance between two points (two-dimensional space): d y y x x12
2 12−= + −2` _j i
Intersection of two straight lines: x m mb b
y m mm b m b
i i1 2
2 1
1 2
1 2 2 1= −−
= −−
7.4.1.2 Polynomials
Quadratic Equation
Standard form: a x2 + b x + c = 0
Normal form: x2 + p x + q = 0
Roots: cx ab
ba
ab b a c
2 1 1 42
4,1 2 2
2!
!= − − =− −d n
xp p
q2 4,1 2
2
!= −
Vieta's Rule: p = – (x1 + x2) q = x1 x2
If (b2 – 4 a c) > 0, the roots are real and unequal.
If (b2 – 4 a c) = 0, the roots are real and equal.
If (b2 – 4 a c) < 0, the roots are imaginary and unequal.
If (b2 – 4 a c) = n2 (perfect square), the roots are rational and unequal.
PE Chemical Reference Handbook
480 NCEES
Expansion of General Algebraic Expressions
(a ± b)2 = a2 ± 2 a b + b2
(a ± b)3 = a3 ± 3 a2 b + 3 a ∙ b2 ± b3
(a ± b)4 = a4 ± 4 a3 b + 6 a2 b2 ± 4 a b3 + b4
a2 – b2 = (a + b) (a – b)
a3 + b3 = (a + b) (a2 – a b + b2)
a3 – b3 = (a – b) (a2 + a b + b2)
a4 + b4 = (a2 + b2) (a2 – b2) = (a2 + a b 2 + b2) (a2 – a b 2 + b2)
Quadratic Surface (Sphere)
Standard form: (x – h)2 + (y – k)2 + (z – m)2 = r2
Distance between two points in three-dimensional space: d x x y y z z2 12
2 12
2 12= − + − + −_ ` _i j i
7.4.1.3 Logarithms, Exponents, and Roots
Logarithms
General definition: logb(x) = c where: x = bc
Natural logarithm: ln(x) = c where: x = ec (base: e = 2.71828)
Base 10 logarithm: log(x) = c where: x = 10c (base: 10)
The radius of a sphere inscribed within a regular polyhedron is:
r AV3=
Paraboloid of Revolution d
h
V hd82r=
Chapter 7: General Information
NCEES 495
7.4.3 Calculus
7.4.3.1 DifferentiationFor any function y = f(x), the derivative D y dx
dyyx= = = l
itlimy xy
x 0 DD=
"Dl d n
itlimx
f x x f xx 0
-
D
D=+
"D
_^
^ih
h8 B* 4
where the slope of the curvey f x=l ^ h
Test for a Maximum
y f x= ^ h is a maximum for ,x a= if f a 0=l^ h and f a 01m^ h
Test for Minimum
y f x= ^ h is a minimum for ,x a= if f a 0=l^ h and f a 02m^ h
Test for a Point of Inflection
y = f(x) has a point of inflection at x = a, if ,f a 0=m^ h and if f xm^ h changes sign as x increases through x = a
L'Hôpital's Rule
If the fractional function g xf x^^hh assumes one of the indeterminate forms 0
0 or 33 (where a is finite or infinite), then:
itlim g xf x
x" a
^^hh
is equal to the first of the expressions
it it itlim lim limg xf x
g xf x
g xf x
x x x" " "a a al
l
m
m
n
n
^^
^^
^^
hh
hh
hh
which is not indeterminate, provided such first indicated limit exists.
Curvature K of a Function
P
s
+ Δ
ΔΔ
ααα
α
Y
O X
Q
y = f (x)
=
The curvature K of a curve at point P is the limit of its average curvature for the arc PQ as Q approaches P. This is also expressed as:
The curvature of a curve at a given point is the rate of change of its inclination with respect to its arc length.
itlimK s dsd
s 0
a aDD= =
"D
PE Chemical Reference Handbook
496 NCEES
Curvature in Rectangular Coordinates
Ky
y
1 2 23=
+ l
m
_ i9 CWhen it may be easier to differentiate the function with respect to y rather than x, the notation xlwill be used for the derivative.
x dydx=l
Kx
x
1 2 23=
+
−
l
m
^ h8 B
Radius of Curvature
The radius of curvature R at any point on a curve is defined as the absolute value of the reciprocal of the curvature K at that point.
R K1= K 0!_ i
Ryy1 2 2
3
= +m
l_ i9 C y 0!m_ i
List of Derivatives
u, v, and w represent functions of x.
a, c, and n represent constants.
Arguments of trigonometric functions are in radians. The following definitions are used:
arcsin u = sin-1 (u), sin sinu u
11 =−^ h
1. dxdc 0=
2. dxdx 1=
3. dxd cu c dx
du=^ h
4. dxd u v w
dxdu
dxdv
dxdw+ −
= + −_ i
5. dxd uv u dx
dv v dxdu= +
^ h
6. dxd uvw u v dx
dw uw dxdv v w dx
du= + +^ h
7. dxd vu
vv dxdu u dx
dv
2=−c m
8. dxd u
n u dxdun
n 1= −_ i
Chapter 7: General Information
NCEES 497
9. dxd f u
dud f u
dxdu=
^ ^h h7 7A A) 3
10. dxdu
dudx1=c m
11. log
logdxd u
e u dxdu1a
a=_ _i i
12. lndx
d uu dxdu1=
^ h
13. lndxd a a a dx
duuu=
_ ^i h
14. dxd e
e dxduu
u=_ i
15. lndxd u
vu dxdu u u dx
dvvv v1= +−_ ^i h
16. sin
cosdxd u
u dxdu=
^ h
17. cos
sindxd u
u dxdu= −
^ h
18. tan
secdxd u
u dxdu2=
^ h
19. cot
cscdxd u
u dxdu2= −
^ h
20. sec
sec tandxd u
u u dxdu=
^ h
21. csc
csc cotdxd u
u u dxdu= −
^ h
22. sindx
d uu dxdu
111
2=
−
−_ i sin u2 2
1# #r r- -c m
23. cosdx
d uu dxdu
111
2=−
−
−_ i cos u0 1# # r
-_ i
24. tandx
d uu dxdu
111
2=+
−_ i tan u2 2
11 1r r- -c m
25. cotdx
d uu dxdu
111
2= −+
−_ i cot u0 11 1 r-_ i
26. secdx
d uu u dx
du1
11
2=
−
−_ i sec secandu u0 2 2
1 11 # #r
rr- -- -c cm m
27. cscdx
d uu u dx
du1
11
2= −
−
−_ i csc cscandu u0 2 2
1 11 1# #r
rr- -- -c cm m
PE Chemical Reference Handbook
498 NCEES
Parametric Form of the Derivative
y x t dx
dydtdydxdt
xy= = =l oo_ ^ hi
y x tdxd y
xx y y x
2
2= =
−m p
o p o p_ ^ ^hi h
where
y dtdy
ydtd y
2
2
=
=
o
p
Derivative of Inverse Functions
The equation y = f(x) solved for x gives the inverse function x y{= _ i.f x
y1{
=ll
^ _h i7.4.3.2 Integration
The indefinite integral F(x) is a function such that F x f x=l] ]g g .f x dx F x C= +^ ^h h#
C is an unknown constant which disappears on differentiation.
The definite integral:
iti 1=
( )lim f x x f x dx F x F b F an
i i a
babD = = = −
"3
n
_ ^ ^ ^i h h h/ # Also, x 0i "D for all i.
To find the integral: Use the list of indefinite integrals (below), integration by parts (equation #6 in the list), integra-tion by substitution, and separation of rational fractions into partial fractions.
List of Indefinite Integrals
u, v, and w represent functions of x.
a, c, and n represent constants.
Arguments of trigonometric functions are in radians. The following definitions are used:
,sin sin sin sinarc u u u u11 1= =− −^ ^h h
Note: A constant of integration should be added to the integrals.
1. d f x f x=^ ^h h#2. dx x=#3. a f x dx a f x dx=^ ^h h##4. u x v x dx u x dx v x dx! !=^ ^ ^ ^h h h h7 A# ##
Chapter 7: General Information
NCEES 499
5. x dx mx
1m
m 1= +
+
# m 1-!_ i
6. u x dv x u x v x v x du x-=^ ^ ^ ^ ^ ^h h h h h h# #
7. lnax bdx
a ax b1+ = +# for a = 1 and b = 0: lnx
dx x=#8.
xdx x2#
9. lna dx aaxx
=#10. sin cosx dx x-=#11. cos sinx dx x=#
12. sin sinx dx x x2 4
22 -=#
13. cos sinx dx x x2 4
22 = +#
14. sin sin cosx x dx x x x-=#
15. cos cos sinx x dx x x x= +#
16. sin cos sinx x dx x22
=#
17. sin coscos cos
ax bx dxa ba b x
a ba b x
2 2- -=
−−
++
__
__
ii
ii# a b2 2!_ i
18. tan ln cos ln secx dx x x-= =#
19. cot ln csc ln sinx dx x x-= =#
20. tan tanx dx x x2 -=#21. cot cotx dx x x2 -= −#22. e dx a e
1ax ax= c m#
23. xe dx ae ax 1axax
2 -= e ^o h#
24. ln lnx dx x x 1= −^ h8 B# x 02^ h25. tan
a xdx
a ax1
2 21
+= −# a 0!_ i
26. tanax cdx
acx ca1
21
+= − c m# ,a c0 02 2_ i
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500 NCEES
27a. tanax bx c
dxac b ac b
ax b42
42
2 21
2+ +=
− −+−# ac b4 02 2-_ i
27b. lnax bx c
dxb ac ax b b ac
ax b b ac4
12 42 4
2 2 2
2
-
- -+ +
=− + +
+# b ac4 02 - 2_ i
27c. ax bx c
dxax b2
22 -+ +
= +# b ac4 02 - =_ i
7.4.3.3 Multivariable Calculus
Partial Derivatives
In a function of two independent variables x and y, a derivative with respect to one of the variables may be found if the other variable is assumed to remain constant. If y is kept fixed, the function
,z f x y= _ ibecomes a function of the single variable x, and its derivative (if it exists) can be found. This derivative is called the partial derivative of z with respect to x. The partial derivative with respect to x is denoted as follows:
( , )xz
xf x y
22
22=
Total Derivative
Given f(x,y), then the total derivative df is
df xf dx y
f dyy x2
222= +d en o
Chain Rule
Given ,f x y_ i where x g t= ^ h and y h t= ^ h, then
dtdf
xf
dtdx
yf
dtdy
y x22
22= +d en o
Identities in Partial Derivatives
xx 1z2
2 =c m
zx 0x2
2 =c m
Implicit Differentiation
If f (x,y,z) cannot be converted to an explicit expression in the form of ,z f x y= )_ i, then
xz
zfxf
,
,
y
x y
y z22
22
22
=−
cd
dm
n
n and y
z
zfyf
,
,
x
x y
x z22
22
22
=−
dd
en
n
o
Chapter 7: General Information
NCEES 501
Rules for changing the constant or the variable on a partial derivative:
Given f (x,y,z) = constant, then
xf
xf
yf
xy
z y x z22
22
22
22= +d d e dn n o n
zf
yf
zy
x x x22
22
22=d e dn o n
7.4.3.4 Differential EquationsA common class of ordinary linear differential equations is
...b dxd y x
b dxdy x
b y x f x1 0n n
n+ + + =
^ ^ ^ ^h h h hwhere bn, ... , bi, ... , b1, b0 are constants.
When the equation is a homogeneous differential equation, f(x) = 0, the solution is
. . .y x C e C e C e C e1 2hr x r x
ir x
nr x1 2 i n= + + + +^ h
where rn is the nth distinct root of the characteristic polynomial P(x) with
P r b r b r b r b11
1 0n
nn= + + +−
−n^ h
If the root r1 = r2, then C e2r x2 is replaced with C xe2
r x1 .
Higher orders of multiplicity imply higher powers of x. The complete solution for the differential equation is
y(x) = yh(x) + yp(x)
where yp(x) is any particular solution with f(x) present. If f(x) has er xn terms, then resonance is manifested. Further-more, specific f(x) forms result in specific yp(x) forms, some of which are
f(x) yp(x)A BAe xa ,Be rx
n!aa
sin cosA x A x1 2~ ~+ sin cosB x B x1 2~ ~+
Common First-Order Differential Equations and Their Solutions
Form Solution Substitution/Conditions
Linear, homogeneous ODE with constant coefficients
y a y 0+ =l
( )y x C e ax= − C is a constant that satisfies the initial condition.
Linear, homogeneous ODE
y p x y 0+ =l ^ h y(x) Ce( p(x)dx)= − # C is a constant that satisfies the initial condition.
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Common First-Order Differential Equations and Their Solutions (cont'd)Form Solution Substitution/Conditions
Linear, inhomogeneous ODE with constant coefficients
( )y y K p tx + =l
( ) ( )y t KA KB KA e1t= + − − x−a k
lntKB yKB KA
x = −−e o ,ttan
( ) ( )
time cons gain
p t B tA t y K A
K00 02
1
x
= =
= =
' 1
Comment: Solution is for a step function.
Implicit ODE, no y term
x f y= l_ i
( )( )
x f py p f p dp C
== +#
Substitution: y p=l
Comment: Elimination of p leads to a solution in parametric form.
Implicit ODE, no x term
y f y= l_ i
( )
( )
x pf p
dp C
y f p
= +
=
#y p=l
Comment: Elimination of p leads to a solution in parametric form.
Separable ODE
y dxdy
g yf x= =l^_hi
g y dy f x dx C= +_ ^i h# #Comment: The variables x and y can be separated into the left and right
sides of the equation.
Similarity ODE
y f xy=l c m
xdx
f u udu C=
−+^ h# #
:Substitution u xy
y u x dxdu
=
= +l
Comment: Check whether it is possible to transform to f xyc m.
Common Second-Order Differential Equations and Their SolutionsForm Solution Substitution
ODE, y and y' terms missing
y f x=m ^ h( )y x C C x f x dx dx1 2= + + ^ h; E##
Comment: Start the calculation with the inner integral.
ODE, y term missing
y p x f y 01+ =m l^ _h if udu p x dx C
y udx C
1 1
2
= − +
= +
^ ^h h# ##
: 'Substitution u y
y dxdu f y f u
=
= =m l_ ^i h
ODE, x term missing
( , )y f y y=m l
u dydu f y,u
xu ydy
C
=
= +_
_
i
i
#
Substitution:
( , )
Then substitute for .
where ( ) and ( )
u y
y dxdu u dy
du f y u
y dxdy
u
u u y y y x
=
= = =
=
= =
l
m
l
Chapter 7: General Information
NCEES 503
Common Second-Order Differential Equations and Their SolutionsForm Solution Substitution
Linear, homogeneous ODE with constant coefficients
y a y b y 0+ + =m l
Solution depends on the values of a and b. r a a b2
1 42!= − −,1 2 ` j( )y x C e C er x r x
1 21 2= + ( )overdampeda b42 2
( ) ( )y x C C x er x1 21= + ( )critically dampeda b42 =
( )[ ( ) ( )]cos sin
y x eC x C x
a b a21
21 4
x
1 2
2
b b
a b
=+
= − = −
a
( )underdampeda b42 1
7.4.3.5 The Fourier Transform and Its Inverse X f x t e dt
x t X f e df
2
2
j ft
j ft
=
=
3
3
3
3
r
r
−
+ −
−
+^
_
_
^
h
i
i
h##
We say that x(t) and X(f) form a Fourier transform pair:
x t X f*^ _h i
Fourier Transform Pairs
Fourier Transform Pairsx(t) X(f)1 fd_ itd^ h 1
u t^ h fj2
1 1f2d + r_ i
txPc m csin fx x_ i
csin Bt^ h B Bf1
Pd n
txKc m csin f2x x_ i
e u tat- ^ h a j f a21 02r+
te u tat- ^ ha f
a a22 02 2 2r+ _ i
e a t-
a fa a22 02 2 2r+ _ i
e at 2-^ ha e a
f 2r r-c m
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Fourier Transform Pairs (cont'd)x(t) X(f)
cos f t2r i+0` j e f f e f f2
1 j j0 0d d− + +i i−` `j j9 C
sin f t2r i+0` j j e f f e f f2
1 j j0 0d d− − +i i−` `j j9 C
t nTs
n
n
d −3
3
=−
=+
_ i/ f f kf f T1
s s
k
k
ss
d − =3
3
=−
=+
` j/
Fourier Transform Theorems
Fourier Transform Theorems
Linearity ax t by t+^ ^h h aX f bY f+_ _i i
Scale change x at^ h a X af1 c m
Time reversal x t-_ i X f-` j
Duality X t^ h x f-` j
Time shift x t t0-_ j X f e j ft2 0r-_ i
Frequency shift x t e j f t2 0r-^ h X f f0-` j
Modulation cosx t f t2r 0^ h X f f X f f21
21− + +
0 0` `j j
Multiplication x t y t:^ ^h h *X f Y f_ _i iConvolution *x t y t^ ^h h X f Y f:_ _i i
represents a powerful tool for the transient and frequency response of linear time invariant systems. Some useful Laplace transform pairs are
Chapter 7: General Information
NCEES 505
Laplace Transform Pairsf(t) F(s)
d(t), Impulse at t = 0 1
u(t), Step at t = 0 s1
t[u(t)], Ramp at t = 0 s12
e at-s a
1+_ i
te at-s1
2a+_ i
sine tt ba-
s 2 2a b
b
+ +_ i9 C
cose tt ba-
s
s2 2a b
a
+ +
+
__ii
9 C
dtd f t
n
n ^ h 0s F s s dt
d f1
0
1n n m
m
m
m
n− − −
=
−
^ ^h h/
f dtx x
0^ h# s F s
1c ^m h
x t h dt
x x x-0_ ^i h# H s X s^ ^h h
f t u tx x- -_ _i i e F ssx- ^ hitlim
t f t" 3 ^ h itlims sF s0" ^ h
itlimt f t0" ^ h itlim
s sF s" 3 ^ h
The last two transforms represent the Final Value Theorem (F.V.T.) and Initial Value Theorem (I.V.T.), respectively. It is assumed that the limits exist.
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7.4.4 Statistics and Probability
7.4.4.1 Mean, Median, and ModeIf X1, X2, ... , Xn represents the values of a discrete random sample of n items or observations, the arithmetic mean of these items or observations, denoted X , is defined as
...X n X X X n X1 1n i
i
n
1 21
= + + + =−
c _ cm j m/X " n for sufficiently large values of n.
The weighted arithmetic mean is
X ww X
wii i//=
where Xi = the value of the ith observation and wi = the weight applied to Xi.
The variance of the population is the arithmetic mean of the squared deviations from the population mean. If m is the arithmetic mean of a discrete population of size N, the population variance is defined by
i 1=
...N X X X
N X
1
1i
21
22
2 2
2
v n n n
n
= − + − + + −
= −
N
N
c
c _
_
_ `
m
m i
j
i j: D
/
Standard deviation formulas are
spopulation N X1i
2/ n= −c _m j
ssum = ... n2
22 2v v v+ + +1
sseries = nv
smean = nv
sproduct = A Bb a2 2 2 2v v+
The sample variance is s2 = n X X11
ii
n
1−
−=
2_ _i j= G/
The sample standard deviation is = n X X11
ii
n2
1− −
=c _m j/
The sample coefficient of variation is CV = Xs
The sample geometric mean is ...X X X Xnn1 2 3
The sample root-mean-square value is n X1i2/c m
When the discrete data are rearranged in increasing order and n is odd, the median is the value of the n21 th+c m
item.
When n is even, the median is the avarage of the andn n2 2 1th th
+c cm m items.
The mode of a set of data is the value that occurs with greatest frequency.
The sample range R is the largest sample value minus the smallest sample value.
Chapter 7: General Information
NCEES 507
7.4.4.2 Permutations and CombinationsA permutation is a particular sequence of a given set of objects. A combination is the set itself without reference to order.
The number of different permutations of n distinct objects taken r at a time is:
,!
!P n rn rn=−
_ _i iAn alternative notation for P(n,r) is nPr.
The number of different combinations of n distinct objects taken r at a time is:
, !,
! !!C n r r
P n rr n rn= =−
_ __i i
i8 B
nCr and rnb l are alternative notations for C(n,r).
The number of different permutations of n objects taken n at a time, given that ni are of type i, where i= 1, 2, ..., k and ,n ni/ = is
; , , ..., ! !... !!P n n n n n n nn
kk
1 21 2
=_ i
7.4.4.3 Probabilities
Property 1. General Character of Probability
The probability P(E) of an event E is a real number in the range of 0 to 1. The probability of an impossible event is 0 and that of an event certain to occur is 1.
Property 2. Law of Total Probability
,P A B P A P B P A B+ = + −^ ^ ^ _h h h iwhere P(A+B) = the probability that either A or B occurs alone or that both occur together
P(A) = the probability that A occurs
P(B) = the probability that B occurs
P(A,B) = the probability that both A and B occur simultaneously
Property 3. Law of Compound or Joint Probability
If neither P(A) nor P(B) is zero, then
P(A, B) = P(A) P(B | A) = P(B) P(A | B)
where
P(B | A) = the probability that B occurs given the fact that A has occurred
P(A | B) = the probability that A occurs given the fact that B has occurred
If either P(A) or P(B) is zero, then P(A, B) = 0.
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Bayes' Theorem:
|
|
|P B A
P A B P B
P B P A Bj
i ii
nj j
1
=
=
` `_`_
j jiji/
where P(Aj ) is the probability of event Aj within the population of A
P(Bj ) is the probability of event Bj within the population of B
7.4.4.4 Distributions and Expected ValuesA random variable X has a probability associated with each of its possible values. The probability is termed a discrete probability if X can assume only discrete values, or
, , , ...,X x x x xn1 2 3=
The discrete probability of any single event X = xi occurring is defined as P(xi) while the probability mass function of the random variable X is defined by
, , , ...,f x P X x k n1 2k k= = =_ _i j
Probability Density Function
If X is continuous, the probability density function, f, is defined such that
P a X b f x dxa
b
# # =^ ^h h#
See the table of probability and density functions.
Cumulative Distribution Function
The cumulative distribution function, F, of a discrete random variable, X, that has a probability distribution described by P(xi) is defined as
, , , ...,F x P x P X x m n1 2m k mk
m
1#= = =
=_ _ _i i i/
If X is continous, the cumulative distribution function F is defined by
F x f t dtx
=3−
^ ^h h#
which implies that F(a) is the probability that X a# .
Expected Values
Let X be a discrete random variable having probability mass function:
, , , ...,f x k n1 2k =_ iThe expected value of X is defined as
E X x f xk k
k
n
1
n = ==
^ h6 @ /
Chapter 7: General Information
NCEES 509
The variance of X is defined as
V X x f xkk
n
k2 2
1
−v n= ==_ _j i6 @ /
Let X be a continuous random variable having a density function f(X) and let Y = g(X) be some general function. The expected value of Y is
E Y E g X g x f x dx= =3
3
−
^ ^ ^h h h6 7@ A #
The mean or expected value of the random variable X is now defined as
E X xf x dxn = =3
3
−
^ h6 @ #
while the variance is
V X E X x f x dx2 2 2− −v n n= = =
3
3
−
_ _ ^i i h6 :@ D #
The standard deviation is V Xv = 6 @ .The coefficient of variation is defined as n
v .
Combinations of Random Variables
...Y a X a X a Xn n1 1 2 2= + + +
The expected value of Y is ...E Y a E X a E X a E Xy n n1 1 2 2n = = + + +^ _ _ _h i i i.If the random variables are statistically independent, then the variance of Y is
......
V Y a V X a V X a V Xa a a
y n n
n n
212
1 22
22
1212
22
22 2 2
v
v v v
= = + + +
= + + +^ _ _ _h i i i
Also, the standard deviation of Y is y y2v v= .
When Y = f(X1,X2,...,Xn) and Xi are independent, the standard deviation of Y is expressed as
...Xf
Xf
Xf
y x xn
x1
2
2
2 2
22
22
22
v v v v= + + + n21e e eo o o
Normal Distribution (Gaussian Distribution)
This is a unimodal distribution, the mode being x = m, with two points of inflection (each located at a distance s to either side of the mode). The averages of n observations tend to become normally distributed as n increases. The variate x is said to be normally distributed if its density function f (x) is given by an expression of the form
f x e21 x
21
2
v r= v
n−−^ dh n
where
m = the population mean
s = the standard deviation of the population
x3 3# #-
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When m = 0 and s2 = s = 1, the distribution is called a standardized or unit normal distribution. Then
f x e21 /x 22
r= −^ h
where x3 3# #-
It is noted that Z x=-vn follows a standardized normal distribution function.
A unit normal distribution table is included at the end of this section. In the table, the following notations are used:
F(x) = the area under the curve from –∞ to x
R(x) = the area under the curve from x to ∞
W(x) = the area under the curve between –x and x
F(-x) = 1 - F(x)
7.4.4.5 Confidence Intervals
Confidence Interval for the Mean n of a Normal Distribution
When standard devation v is known:
X Zn
X Zn/ /2 2- # #
vn
v+a a
When standard deviation v is not known:
X tns X t
ns
/ /2 2- # #n +a a
where t /a 2corresponds to n - 1 degrees of freedom.
Confidence Interval for the Difference Between Two Means m1 and m2
When standard deviations s1 and s2 are known:
X X Z n n X X Z n n/ /1 2 2 1
12
222
1 2 1 2 2 112
222
- - - -# #v v
n nv v+ + +a a
When standard deviations s1 and s2 are not known:
X X t n nn n n s n s
X X t n nn n n s n s
2
1 1 1 2 1
2
1 1 1 2 1
/
/
1 2 21 2
1 21 1
222
1 2
1 2 21 2
1 21 1
222
- - -
- --
-- -
# #n n+
+ +
+ + −
+ +
a
a
c
c
_
_
^
^
m
m
i
i
h
h
8
8
B
B
where t /2a corresponds to n1 + n2 - 2 degrees of freedom.
Confidence Intervals for the Variance 2v of a Normal Distribution
xn s
xn s1 1
/ , / ,n n2 12
22
1 2 12
2- -# #v
a a- - -
^ ^h h
Sample Size
z
n
X -vn= n x
z /22
nv= −a
re o
Chapter 7: General Information
NCEES 511
The Central Limit Theorem
Let X1, X2,...,Xn be a sequence of independent and identically distributed random variables having mean m and vari-ance s2.Then for a large n, the Central Limit Theorem asserts that the sum
...Y X X Xn1 2= + + + is approximately normal
yn n=r
and the standard deviation is nyvv=
r .
Probability and Density FunctionsKind of
DistributionProbability Density Function f(x)
Distribution Function F(x)Expected Mean (m),
Mean (x), Variance (s2)Form of the Density
Function
General (continuous)
Comment: General distribution for continuous values( )
( ) ( )
f x
F x f t dtx
=3−#
( )
( )
x x f x dx
x f x dx2 2 2v n
=
= −3
3
3
3
−
−
##
General (discrete)
Comment: General distribution for discrete values: n is the number in a random sample, xi is the discrete value of the random variable, and Pi is the probability.
( )
P
F x Pi
ii x<=/
( )
( )
x x P
x P
i iin
i iin1
2 2 21v n
=
= −=
=
//
Uniform
Comment: Random variable x = 0 only within the interval <a, b>, where each value is of equal probability. Use when only maximum and minimum values are known
but no other information about the distribution in between.
( )
( )
for
for outsidefor
for
for
f x b a a x b
F x
x a
b ax a a x b
b x
1
00
1
3
3
1 1
1 1
# #
# #
= −
=
−
−−
Z
[
\
]]]]]]]]Z
[
\
]]]]]]]]]]]
x a b
b a2
122
2
v
= +
=−_ i
f(x)
b - a
a μo b x
1
Binomial
Comment: If P(k) is the probability that in n random samples exactly k errors will occur, the error probability is p. Lot size is assumed to be .3
k x<
( )
( )
P k kn p p
F x xn p p
1
1
k n k
k n k
= −
= −
−
−
c `
`
m j
j/ ( )x n p
n p p12v
== −
P(k)n = 20
p = 0.1p = 0.2p = 0.5
0 5
0.30.20.1
10 15 k
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Probability and Density Functions (cont'd)Kind of
DistributionProbability Density Function f(x)
Distribution Function F(x)Expected Mean (m),
Mean (x), Variance (s2)Form of the Density
Function
Normal (Gaussian)
Comment: Often obtained in practice as measured values with a bell-shaped distribution occurring around a mean value. Special case of the binomial
distribution with . .andn p 0 5" 3 =
( )
( )
exp
exp
f x x
F x
t dt
21
21
21
21x
2
2
v r vn
v r vn
= − −
=
− −3−
d
d
n
n
>
>
H
H
#
m
2v
f(x)μ =
= 0.5
0.5=1
–2 –1 0 1 2x
0σ
σ=2σ
Standardized (unit normal)
Comment: Special case of the Normal (Gaussian) distribution. A unit normal table is included below.
( )
( )
exp
exp
f x x
F x t dt
21
2
21
2x
2
2r
r
= −
= −3−
d
d
n
n#012
n
v
==
---
Hypergeometric
Comment: Sample of dichotomous population (population of two types, e.g., defective/ not defective parts) without replacement. N is lot size, pN is number of defective parts
in the lot, P is the probability that in n random samples k will be defective.
k x#
( )
( )
( )
( )
P knN
kpN
n kN p
F xnN
kpN
n kN p
1
1
=−−
=−−
d
d
c
c
n
n
m
m
=
=
G
G/ ( )
x n p
n p NN n p1 1
2v
=
= −− −
0.3
0.4
0.2
0.1
P(k)
n = 20N = 100
p = 0.04
0 k5 10 15
p = 0.1p = 0.2
Poisson
Comment: P(k) is the probability that in n random samples k errors will occur. Used for curves in a random sampling valuation. Conditions: large value of random samples
with a small value for proportion defective.
k x#
( ) !( )
( ) !( )
P k kn p
e
F x kn p
e
kn p
kn p
=
=
$
$
−
−/x n p
n p2v
==
P(k)n.p = 1
n.p = 10
0.3
0.2
0.1
n.p = 5
0 5 10 15 k
Chapter 7: General Information
NCEES 513
Probability and Density Functions (cont'd)Kind of
DistributionProbability Density Function f(x)
Distribution Function F(x)Expected Mean (m),
Mean (x), Variance (s2)Form of the Density
Function
Exponential
Comment: Special case of the Poisson distribution for x = 0 that gives the probability without error. When used for reliability calculations, replace a x$^ h with failure rate r
multiplied by control time t.
( )
( )
f x a eax
F x e
001
a x
a x
2
$
=
= −
−
−
x a
a
1
122v
=
=
a = 2
a = 1
a = 0.5
0.5
0.5
0
2
1
21
f(x)
x
Geometric
Comment: Describes the number of trials needed to get the first success, with p as the success parameter.
n 1=
( , ) ( )
( ) ( )
f x p p p
F x p p
1
1
x
n
1
1
= −
= −
−
−x
/p
pp
1
122
n
v
=
=− ---
Negative Binomial
Comment: Describes the trial number of the kth success, with k as the stopping parameter and p as the success probability.
k x<
( ) ( )
( ) ( )
P k kn p p
F x kn p p
11 1
11 1
k n k
k n k
= −− −
= −− −
−
−x
c
c
m
m/
x k p
kpp
1
122v
=
=−` j ---
Gamma
Comment: Gamma distribution is widely used to model physical quantities that take positive values. The Gamma function is defined as
( ) ,wherek x e dx k x0 0k x10
$ $C =3 − −#
( )( )
( ) ( )
, where
f xb k
x e
F x k
k bx
bk
1
00
>>
/k
k x b1
C
C
C
=
=
− −
c mx b k
b k2 2v
==
---
Weibull
Comment: Note that when k = 1, the Weibull distribution reduces to the exponential distribution with parameter 1.
( )
( )where
f tbk t e
F t et
10 < <
kk b
t
bt
1k
k
3
=
= −
− −
−c
c
m
m x b k
b k
k
1 1
1 2
1 1
2 2
22
v
C
C
C
= +
= + −
+
c
c
c
m
m
m<
G
---
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514 NCEES
Probability and Density Functions (cont'd)Kind of
DistributionProbability Density Function f(x)
Distribution Function F(x)Expected Mean (m),
Mean (x), Variance (s2)Form of the Density
Function
Triangular
Comment: The triangular distribution is based on a simple geometric shape. The distribution arises naturally when uniformly distributed random variables are
transformed in various ways.
( )( ) ,
( ) ,
( )( ) ,
( )( ) ,
f x px a a x a p
pa x a p x a w
F x px a a x a p
pa x a p x a w
2
2
1
111
2
2
22
22
# #
# #
# #
# #
~~
~~ ~
~~
~~ ~
=− +
+ − + +
=− +
−−
+ − + +
Z
[
\
]]]]]]]]]]]]
Z
[
\
]]]]]]]]]]]]
( )
[ ( )]
x a p
p p
3 1
18 1 122
~
v~
= + +
= − −
Semicircle
Comment: The semicircular distribution is based on the shape of a semicircle with center a (location parameter) and radius r (scale parameter).
( ) ( )
( ) ( )
arcsin
where
f xr
r x a
F xr
x a r x a
rx a
a r x a r
2
21
1
22 2
22 2
# #
r
r
r
= − −
= + − − − +
−
− +
c m
x ar4
22
v
=
=---
U-Power Distribution
Comment: f(x) is symmetric about m.
( )
( )
where
f x ck
cx
F x cx
c x c
22 1
211
k
k
2
2 1
# #
n
n
n n
= + −
= + −
− −
+
d
d
n
n
> Hx
c kk2 32 12 2
n
v
=
= ++
---
Chapter 7: General Information
NCEES 515
Normal Distribution Tablex f(x) F(x) R(x) 2 R(x) W(x)
Sample Correlation Coefficient R and Coefficient of Determination R2
R
S SS
xx yy
xy= R S SSxx yy
xy22
=
7.4.4.7 Test StatisticsThe following definitions apply:
Zn
Xvar
o-vn= t
ns
Xvar
o- n=
where
Zvar = the standard normal Z score
tvar = the sample distribution test statistic
v = known standard deviation
on = population mean
X = hypothesized mean or sample mean
n = sample size
s = computed sample standard deviation
The Z score is applicable when the standard deviations are known. The test statistic is applicable when the standard deviations are computed at time of sampling.
Za corresponds to the appropriate probability under the normal probability curve for a given Zvar.
ta, n-1 corresponds to the appropriate probability under the t distribution with n-1 degrees of freedom for a given tvar.
Actinium Ac 89 ---* Holmium Ho 67 164.930Aluminum Al 13 26.9815 Hydrogen H 1 1.00797Americium Am 95 ---* Indium In 49 114.82Antimony Sb 51 121.75 Iodine I 53 126.9044Argon Ar 18 39.948 Iridium Ir 77 192.2Arsenic As 33 74.9216 Iron Fe 26 55.847Astatine At 85 ---* Krypton Kr 36 83.80Barium Ba 56 137.34 Lanthanum La 57 138.91Berkelium Bk 97 ---* Lead Pb 82 207.19Beryllium Be 4 9.0122 Lithium Li 3 6.939Bismuth Bi 83 208.980 Lutetium Lu 71 174.97Boron B 5 10.811 Magnesium Mg 12 24.312Bromine Br 35 79.904 Manganese Mn 25 54.9380Cadmium Cd 48 112.40 Mendelevium Md 101 ---*Calcium Ca 20 40.08 Mercury Hg 80 200.59Californium Cf 98 ---* Molybdenum Mo 42 95.94Carbon C 6 12.01115 Neodymium Nd 60 144.24Cerium Ce 58 140.12 Neon Ne 10 20.183Cesium Cs 55 132.905 Neptunium Np 93 ---*Chlorine Cl 17 35.453 Nickel Ni 28 58.71Chromium Cr 24 51.996 Niobium Nb 41 92.906Cobalt Co 27 58.9332 Nitrogen N 7 14.0067Copper Cu 29 63.546 Nobelium No 102 ---*Curium Cm 96 ---* Osmium Os 76 190.2Dysprosium Dy 66 162.50 Oxygen O 8 15.9994Einsteinium Es 99 ---* Palladium Pd 46 106.4Erbium Er 68 167.26 Phosphorus P 15 30.9738Europium Eu 63 151.96 Platinum Pt 78 195.09Fermium Fm 100 ---* Plutonium Pu 94 ---*Fluorine F 9 18.9984 Polonium Po 84 ---*Francium Fr 87 ---* Potassium K 19 39.102Gadolinium Gd 64 157.25 Praseodymium Pr 59 140.907Gallium Ga 31 69.72 Promethium Pm 61 ---*Germanium Ge 32 72.59 Protactinium Pa 91 ---*Gold Au 79 196.967 Radium Ra 88 ---*Hafnium Hf 72 178.49 Radon Rn 86 ---*Helium He 2 4.0026 Rhenium Re 75 186.2
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Table of Relative Atomic Mass (Atomic Weight) (cont'd)
Name
SymbolAtomic Number
Atomic Mass
Name
Symbol
Atomic Number
Atomic Mass
Rhodium Rh 45 102.905 Terbium Tb 65 158.924Rubidium Rb 37 85.47 Thallium Tl 81 204.37Ruthenium Ru 44 101.07 Thorium Th 90 232.038Samarium Sm 62 150.35 Thulium Tm 69 168.934Scandium Sc 21 44 .956 Tin Sn 50 118.69Selenium Se 34 78.96 Titanium Ti 22 47.90Silicon Si 14 28.086 Tungsten W 74 183.85Silver Ag 47 107.868 Uranium U 92 238.03Sodium Na 11 22.9898 Vanadium V 23 50.942Strontium Sr 38 87.62 Xenon Xe 54 131.30Sulfur S 16 32.064 Ytterbium Yb 70 173.04Tantalum Ta 73 180.948 Yttrium Y 39 88.905Technetium Tc 43 ---* Zinc Zn 30 65.37Tellurium Te 52 127.60 Zirconium Zr 40 91.22
* Multiple isotopes
Chapter 7: General Information
NCEES 521
7.5.3 Oxidation Number
Oxidation Number or Charge NumberName Symbol Charge Name Symbol Charge
Acetate C2H3O2 –1 Iron Fe +2, +3Aluminum Al +3 Lead Pb +2, +4Ammonium NH4 +1 Lithium Li +1Barium Ba +2 Magnesium Mg +2Borate BO3 –3 Mercury Hg +1, +2Boron B +3 Nickel Ni +2, +3Bromine Br –1 Nitrate NO3 –1Calcium Ca +2 Nitrite NO2 –1Carbon C +4, –4 Nitrogen N –3, +1, +2,
+3, +4, +5Carbonate CO3 –2 Oxygen O –2Chlorate ClO3 –1 Perchlorate ClO4 –1Chlorine Cl –1 Permanganate MnO4 –1Chlorite ClO2 –1 Phosphate PO4 –3Chromate CrO4 –2 Phosphorus P –3, +3, +5Chromium Cr +2, +3, +6 Potassium K +1Copper Cu +1, +2 Silicon Si +4, –4Cyanide CN –1 Silver Ag +1Dichromate Cr2O7 –2 Sodium Na +1Fluorine F –1 Sulfate SO4 –2Gold Au +1, +3 Sulfite SO3 –2Hydrogen H +1 Sulfur S –2, +4, +6Hydroxide OH –1 Tin Sn +2, +4Hypochlorite ClO –1 Zinc Zn +2
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7.5.4 Organic Compounds
Families of Organic Compounds
FAMILY Specific Example IUPAC Name Common
NameGeneral Formula Functional Group
Alkane CH3CH3 Ethane Ethane RH C–H and C–C bonds
Alkene H2C = CH2Ethene or ethylene Ethylene
RCH = CH2 RCH = CHR R2C = CHR R2C = CR2
C C=
Alkyne HC = CH Ethyne or acetylene Acetylene RC = CH
RC = CR C C=– –
Arene Benzene Benzene ArH Aromatic ring
Haloalkane CH3CH2Cl Chloroethane Ethyl chloride RX C X
Alcohol CH3CH2OH Ethanol Ethyl alcohol ROH C OH
Ether CH3OCH3Methoxy-methane
Dimethyl ether ROR C CO
Amine CH3NH2 Methanamine MethylamineRNH2 R2NH R3N
C N
AldehydeCH3CH
=
OEthanal Acetaldehyde
RCH
=
O
=
C HO
KetoneCH3CCH3
=
OAcetone Dimethyl
ketone R1CR2
=
O
=
C
O
Carboxylic Acid CH3COH
=
OEthanoic acid Acetic acid
RCOH
=
O
=
C OHO
EsterCH3COCH3
=
O Methyl ethanoate
Methyl acetate RCOR
=
O
CO
=
C
O
Chapter 7: General Information
NCEES 523
7.5.5 Industrial Chemicals
Common Names of Industrial ChemicalsCommon Name Chemical Name Molecular Formula
Source for tables in Section 8.4: "Table of Physical Properties for Hydrocarbons and Other Compounds of Interest to the Natural Gas and Natural Gas Liquids Industries," GPS Standard 2145-16, Tulsa, OK:
GPA Midstream Association, 2016, pp. 4–9, and NIST Chemistry Web Book, NIST Standard Reference Database Number 69, P.J. Linstrom and W.G. Mallard, eds.
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8.5 Physical Properties of Liquids and Gases—Temperature-Dependent Properties
8.5.1 U.S. Customary Units
Temperature-Dependent Physical Properties of Gases at 14.7 psia (U.S. Units)
Sources: These data are provide courtesy of the American Institute of Chemical Engineering (AIChE) and its thermophysical property research consortium, the Design Institute for Physical Properties (DIPPR®)
using DIPPR® 2016 version. Vapor densities were obtained using SRK equation of state with DIPPR 801 values for critical temperature, critical pressure, and acentric factor.
These data are provided for the sole purpose of the preparation for and taking of NCEES engineering exams with no warrantee expressed or implied.
* The vapor pressure of sulfur dioxide at 0˚F is 10.2 psia. Hypothetical vapor density at 0˚F and 14.7 psia is reported in the table.
** Extrapolated values
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8.5.2 SI Units
Temperature-Dependent Physical Properties of Gases at 0.1 MPa (SI Units)
Sources: These data are provide courtesy of the American Institute of Chemical Engineering (AIChE) and its thermophysical property research consortium, the Design Institute for Physical Properties (DIPPR®)
using DIPPR® 2016 version. Vapor densities were obtained using SRK equation of state with DIPPR 801 values for critical temperature, critical pressure, and acentric factor.
These data are provided for the sole purpose of the preparation for and taking of NCEES engineering exams with no warrantee expressed or implied.
Properties of Dry Atmospheric AirProperty U.S. Units* SI Units**
Molar mass 28.965 lb molelb 28.965 mol
g
NBP temperature –317.64 °F 78.903 KTriple point temperature –352.12 °F 59.75 KCritical temperature –221.12 °F 132.53 KCritical pressure 549.11 psia 3.7860 MPa
Critical density 21.393 ftlbm3 342.68
mkg3
Density of liquid at NBP54.637
ftlbm3
7.3039 gallbm 875.21
mkg3
Volume of liquid at NBP 0.13691 lbmgal
0.0011426 kgm3
Density of ideal gas 0.07633 ftlbm3 1.2250
mkg3
Volume of ideal gas 13.101 lbmft3 0.81631 kg
m3
Speed of sound in air p = 14.696 psia, T = 32°F p = 0.1 MPa, T = 0°C
1090 secft 330 s
m
Speed of sound in air p = 14.696 psia , T = 68°F p = 0.1 MPa, T = 20°C
1130 secft 343 s
m
* U.S. unit values are given at 60°F and 14.696 psia, except where noted otherwise. ** SI unit values are given at 15°C and 0.101325 MPa, except where noted otherwise.
Chapter 8: Physical Properties
NCEES 545
8.6.3 Temperature-Dependent Properties of Air (U.S. Customary Units)
Temperature-Dependent Properties of Air at 14.7 psia (U.S. Units)
Boiling temperature 212°F 373.15 KTriple point temperature 32°F 273.15 KTriple point pressure 0.0887 psia 611.657 PaCritical temperature 705.1°F 647.09 KCritical pressure 3200.1 psia 22.06 MPa
Critical density 20.102 ftlbm3 322.00
mkg3
Maximum density of liquid (4°C = 39°F)
62.426 ftlbm3
8.3455 gallbm 1000
mkg3
Minimum volume of liquid (4°C = 39°F) 0.11983 lbm
gal0.001 kg
m3
Heat of vaporization (100°C = 212°F)
970.17 lbmBtu 2257 kg
kJ
Density of ice (0°C = 32°F)
57.227 ftlbm3 916.7
mkg3
Latent heat of fusion (0°C = 32°F) 143.38 lbm
Btu 333.55 kgkJ
Dielectric constant (0°C = 32°F) 87.88 87.88
Dielectric constant (100°C = 212°F) 55.51 55.51
Refractive index 1.3325 1.3325
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8.8 Steam TablesSource for all tables in Section 8.8: GPSA Engineering Data Book, 13th ed., Vol. 2,
Tulsa, OK: GPSA, 2012, Figures 24-30 and 24-31 on pp. 24-35 through 24-38.
8.8.1 Properties of Saturated Steam (U.S. Customary Units)
Saturated Steam (U.S. Units)—Temperature Table
Temperature Pressure Specific Volume, v Specific Enthalpy, h Specific Entropy, s