StudentPocketHandbook[1]

8/11/2019 StudentPocketHandbook[1]

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Pocket

Handbook


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The AIChEPocket Handbook

Thomas R. Hanley, Editor

American Institute of Chemical Engineers

New York, New York 100163 Park Ave. 19th Floor


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TheAIChE Pocket Handbook is a publication ofAIChE and its Student Chapters Committee.

Copyright 1985 by the

American Institute of Chemical Engineers

ISBN 0-8169-0342-5

Reprinted, 1988, 1990, 1992, 1993, 2001, 2004, 2005


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TABLE OF CONTENTS

Inorganic Chemistry...................................................... 1

Organic Chemistry......................................................... 6Physical Chemistry........................................................ 10Fluid Flow....................................................................... 14Heat Transfer.................................................................. 18Distillation ...................................................................... 23Mass Transfer ................................................................. 26Thermodynamics ........................................................... 29Kinetics and Reactor Design ........................................ 34Conversion Factors ....................................................... 40Physical Constants ........................................................ 44Greek Alphabet .............................................................. 48Mathematics ................................................................... 48Chemical Process Safety .............................................. 51

Biochemical Engineering.............................................. 53


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Foreword

The purpose of this handbook is to make readily avail-able in a limited number of pages some of the more im-

portant chemical, biological, physical, safety, and mathe-matical data and concepts that are fundamental to the

practice of the chemical engineering profession.With these principles you should be able to solve many

chemical engineering problems.

Good Luck!

AIChE would like to thank Professors David Murhammer,Chuck Coronella, Galen Suppes, and Joseph F. Louvar fortheir work on this Handbook.


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INORGANIC CHEMISTRY

I. COMMON DEFINITIONS

Atomic numberthe number of protons in the nucleusof an atom.

Avogadros numberthe number of molecules(6.023 1023) in one gram-mole of a substance.

Equilibrium constants for the reaction aAbBcC dD

where reaction is in solution,

([ ] refers to molarity)

where reaction is in the gas phase,

(p partial pressure)

Gram equivalent weightA. (nonredox reaction) the mass in grams of a

substance equivalent to 1 gram-atom of hydrogen,0.5 gram-atom of oxygen, or 1 gram-ion of the

hydroxyl ion. It can be determined by dividingthe molecular weight by the number of hydrogenatoms or hydroxyl ions (or their equivalent)supplied or required by the molecule in a givenreaction.

B. (redox reaction) the molecular weight in gramsdivided by the change in oxidation state.

Ion product of water (Kw)the product of thehydrogen ion and hydroxyl ion concentrations ingram-ions per liter;

Kw [H][OH]

Kp

pcCpdD

paApbB

Kc[C]c[D]d

[A]a[B]b

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Mass numberthe number of protons plus the numberof neutrons in the nucleus of an atom.

Molality (m)(gram moles of solute)/(kilograms ofsolvent).

Molarity (M)(gram moles of solute)/(liters ofsolution).

Normality (N)(gram equivalents of solute)/(liters ofsolution).

Oxidationthe loss of electrons by an atom or groupof atoms.

pHthe negative logarithm (base 10) of the hydrogenion concentration in gram ions per liter;

Reductionthe gain of electrons by an atom or groupof atoms.

Solubility product (S.P. or Ksp)for the slightly solublesolid,AaBb , dissolving

AaBb (solid) aA (aq) bB(aq)

whereA is any cation andB is anyanion

S.P. orKsp [A]a[B]b a constant at a giventemperature

II. PROPERTIES OF CHEMICAL ELEMENTS

Atomic Atomic Common

Name Symbol Number Weight Valence

Actinium Ac 89 (227) 3Aluminum Al 13 26.9815 3Americium Am 95 (243) 6,5,4,3Antimony Sb 51 121.75 3,5

pH log10[H]

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Atomic Atomic CommonName Symbol Number Weight Valence

Argon Ar 18 39.948 0Arsenic As 33 74.9216 3,5Astatine At 85 (210) 1,3,5,7Barium Ba 56 137.34 2Berkelium Bk 97 (247) 4,3Beryllium Be 4 9.0122 2Bismuth Bi 83 208.980 3,5Boron B 5 10.811 3

Bromine Br 35 79.904 1,5Cadmium Cd 48 112.40 2Calcium Ca 20 40.08 2Californium Cf 98 (249) 3Carbon C 6 12.01115 4,2Cerium Ce 58 140.12 3,4Cesium Cs 55 132.905 1

Chlorine Cl 17 35.453 1,3,5,7Chromium Cr 24 51.996 6,2,3Cobalt Co 27 58.9332 2,3Copper Cu 29 63.546 2,1Curium Cm 96 (247) 3Dysprosium Dy 66 162.50 3Einsteinium Es 99 (254)

Erbium Er 68 167.26 3Europium Eu 63 151.96 3,2Fermium Fm 100 (253) Fluorine F 9 18.9984 1Francium Fr 87 (223) 1Gadolinium Gd 64 157.25 3Gallium Ga 31 69.72 3Germanium Ge 32 72.59 4Gold Au 79 196.967 3,1Hafnium Hf 72 178.49 4Helium He 2 4.0026 0Holmium Ho 67 164.930 3

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Atomic Atomic CommonName Symbol Number Weight Valence

Protactinium Pa 91 (231) 5,4

Radium Ra 88 (226) 2Radon Rn 86 (222) Rhenium Re 75 186.2 7,6,4,

2,1Rhodium Rh 45 102.905 2,3,4Rubidium Rb 37 85.47 1Ruthenium Ru 44 101.07 2,3,4,6,8

Samarium Sm 62 150.35 3,2Scandium Sc 21 44.956 3Selenium Se 34 78.96 2,4,5Silicon Si 14 28.086 4Silver Ag 47 107.870 1Sodium Na 11 22.9898 1Strontium Sr 38 87.62 2

Sulfur S 16 32.064 2,4,6Tantalum Ta 73 180.948 5Technetium Tc 43 (98) 7Tellurium Te 52 127.60 2,4,6Terbium Tb 65 158.924 3,4Thallium Tl 81 204.37 3,1Thorium Th 90 232.038 4

Thulium Tm 69 168.934 3,2Tin Sn 50 118.69 4,2Titanium Ti 22 47.90 4,3Tungsten W 74 183.85 6,5,4,3,2Uranium U 92 238.03 6,5,4,3Vanadium V 23 50.942 5,4,3,2Xenon Xe 54 131.30 0Ytterbium Yb 70 173.04 3,2Yttrium Y 39 88.905 3Zinc Zn 30 65.37 2Zirconium Zr 40 91.22 4

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III. COMMON ANIONS

Name Symbol Name Symbol

Arsenite AsO3 Hydroxide OH

Arsenate AsO4 Hypochlorite OClAcetate C2H3O2

Iodide I

Bicarbonate HCO3 Iodate IO3

Bisulfate HSO4 Molybdate MoO4

Bromate BrO3 Nitrate NO3

Bromide Br Nitrite NO2

Carbonate CO3 Oxalate C2O4

Chlorate ClO3 Perchlorate ClO4

Chloride Cl Peroxide O2

Chromate CrO4 Permanganate MnO4

Cyanamide CN2 Phosphate PO4

Cyanide CN Sulfate SO4

Dichromate Cr 2O7 Sulfide S

Dithionate S2O6 Sulfite SO3

Ferricyanide Fe(CN)6 Thiocyanate CNSFerrocyanide Fe(CN)6

Thiosulfate S2O3

Formate CHO2

ORGANIC CHEMISTRY

Note: For conciseness the following symbols areused:

R H atom or saturated hydrocarbon groupR hydrocarbon group onlyX halogenn an integer

I. GENERAL CLASSES OF COMPOUNDS

A. The straight and branched chain types of com-pounds

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Type or Name General Formula

1. Alkane or paraffin(also saturated

hydrocarbons)

2. Alkene or olefin(unsaturatedhydrocarbons)

3. Alkyne

4. Alcohol

5. Ether

6. Aldehyde

7. Ketone

8. Carboxylic Acid

9. Grignard reagent

10. Acyl halide

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11. Anhydride

12. Ester

13. Amide

14. Amine (base)

15. Nitrile

B. Cyclic Compounds

1. Cycloparaffin

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II. PERTINENT NOTES

A. Markovnikovs (Markownikoffs) Rule for the additionof acids to acids to olefins: the negative group ofthe acid adds to the carbon atom having the fewesthydrogen atoms.

4. Naphthalenic

3. Aromatic

2. Cycloalkene

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B. Mechanisms1. Free radical (unshared electron)

(no charge)

2. Carbonium ion (deficient in electrons)( positive charge)(carbon with six electrons)

3. Carbanion(excess of electrons)

(negative charge)(carbon with eight electrons)

PHYSICAL CHEMISTRY

1. Amagats Law of Partial VolumesThe volume

of a mixture of gases is equal to the sum of the par-tial volumes of each component gas. The partial

volume of a component gas is the volume whichthat component would occupy at the same temper-ature and pressure.

2. Boiling Point Elevation (Tb)The following equa-

tions hold for a dilute solution of a nonionic non-volatile solute.

where Hv molal heat of vaporizationKb molal boiling point elevation con-

stantm molality

Ma solvent molecular weight

KbR(Tbp)

2Ma

Hv(1000)

TbKbm

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6. Faradays LawsFirst Law: The mass of a substance reacting

at the electrodes is directly proportional to thequantity of electricity passed through the solu-tion.

Second Law: The masses of different sub-stances produced during electrolysis are directly

proportional to their equivalent weights; 96,496coulombs of electricity 1 faraday electricity toyield 1 gram equivalent of any substance.

7. Freezing Point Depression (Tf)The follow-ing equations hold for a dilute solution of anonionic solute in which the solid phase is puresolvent.

where Hf molal heat of fusion of solventKf molal freezing point lowering con-

stant

m molalityMa solvent molecular weightR ideal-gas constant

Tf p solvent freezing point, absolute tem-perature

8. Gibbs Phase RuleAt equilibrium the number

of independent variables (F) required to spec-ify the system is equal to the number of compo-nents (C) minus the number of phases (P) plustwo, or symbolically FCP 2. This form

KfR(Tfp)2Ma

Hf(1000)

TfKfm

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of the phase rule applies to non-reactive sys-tems.

9. Grahams Law of DiffusionThe rate of diffusionof a gas is inversely proportional to the square rootof its density.

10. Henrys LawAt a constant temperature, the con-centration of a gas dissolved in a liquid is directly

proportional to the partial pressure of the gas abovethe liquid.

11. Raoults Law

where papartial pressure of component A invapor

xa mole fraction ofA in liquid solutionPavapor pressure of pure liquidA

12. vant Hoff Reaction Isochore

at constant pressure

where H heat of reaction

K

reaction equilibrium constantR ideal-gas constantT absolute temperature

If His constant,

13. Molar Humiditymoles vapor/mole vaporfree gas

Yya

1ya

pa

Ppa

lnaK2K1

b HR

c T2T1T1T2

d

d(lnK)

dT

H

RT 2

paxaPa

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Humiditypounds vapor/pound vapor-free gas

Relative Saturationratio of partial pressure ofvapor to partial pressure of vapor at saturation(vapor pressure)

Percentage of Saturationratio of vapor con-centration to vapor concentration at saturation(ratio of molar humidity to saturated molar humidity)

where papartial pressure of component A ingas

Pavapor pressure of pure liquid A

P total pressureMa molecular weight of AMb molecular weight of Bya mole fraction of a gas

FLUID FLOW

I. DEFINITIONS AND GENERAL EQUATIONS

Mass velocity

GV

Hp 100Y

Ysat 100

pa(PPa)

Pa(Ppa)

Hr 100pa

Pa

Y YMa

Mb

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Simple manometer equation

Hagen-Poiseuille equation (laminar flow in long hori-zontal tube)

Average velocity,

Reynolds number,NRe

Mechanical energy balance

where 1 for turbulent flow (NRe 4,000) 0.5 for laminar flow (NRe 2,100)

Hydraulic radius

Equivalent diameter,De

De 4 (hydraulic radius,rH)

rHs, cross-sectional area

Lp, the wetted perimeter

Pa

a

g

gc

Za

V2a

2gca

Ws

Pb

b

g

gc

Zb

V2b

2gcb

Hf

NReDV

DV

Vq, volumetric flow rate

s, cross-sectional area

V

PaPb32LV

gcD2

PaPbRmg

gc (a b)

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II. FRICTION

Skin friction

Fanning friction factor,f(flow in smooth pipes)

laminar

turbulent

Friction of valves and fittings (Add to length of pipe toget total equivalent length.)

Equivalent

Fittings and Valves resistance,pipe diameters

45-degree elbows 1590-degree elbows (standard radius) 3290-degree square elbows 60180-degree close return bends 75Ts (used as elbow, entering run) 60Ts (used as elbow, entering branch) 90Couplings NegligibleUnions NegligibleGate valves (open) 7Globe valves (open) 300Angle valves (open) 170

Friction loss from sudden expansion of cross sec-tion

HfeV2a

2gca1 sa

sbb2

1

f..5 4.0 log (NRef.

.5) 0.4

f16

DV

16NRe

Hfs

2fLV2

Dgc

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Friction loss from sudden contraction of cross section

Values of Kc are given on page 6-18, Perrys ChemicalEngineers Handbook, 7th ed., Don W. Green, ed.,McGraw-Hill Book Co., New York, NY, 1997.

III. MEASUREMENT OF FLOWING FLUIDS

Venturi meter

(b is at throatof meter)

Orifice meter, design equation (NRe 20,000)

Pilot tube (manometer measurespsP)

IV. SYMBOLS USED

Cu , Cp coefficients of velocityD diameterg acceleration of gravity 32.2 ft/s2 9.81 m/s2

gc Newtons conversion factor 32.2 ft-lbm/(lbf-s2) 1 m-kg/(N-s2)

Hf head loss due to frictionHfs head loss due to skin frictionHfc head loss due to contraction of cross section

VCp

B

2gc(psP)

Vo0.61

21 4B2gc(papb)

2VsbV2aCvB2gc(papb)

HfcKcV

2b

2gc

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Hfe head loss due to expansion of cross sectionKe expansion loss coefficientKc contraction loss coefficientL length of pipePpressure

Pa upstream pressurePb downstream pressure

pa, pbpressure in arms of manometerps static pressure

Rm manometer readings cross-sectional areaVvelocity

average velocityVa upstream velocityVb downstream velocityWs shaft work done by pump

Z elevation kinetic energy correction factor ratio of diameter of orifice to diameter of

pipe fluid density, lbm/ft

3

a density of manometer fluid

b

density of fluid above manometer kinematic viscosity viscosity

HEAT TRANSFER

I. CONDUCTION

Fouriers Law (constantk)steady state

qkAT

x

T

R

V

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unsteady state

Resistance in Series

Radial Heat Flow Through a Cylinder

where Am logarithmic mean area normal to heatflow

rm logarithmic mean radiusrm (rori)ln [rori]

II. CONVECTION

qhAT

where hkx, heat transfer coefficientk thermal conductivity of the fluid

x thickness of the laminar film

III. COMBINED CONDUCTION AND CONVECTION

qUAavg(T)

where U overall heat transfer coefficientT overall temperature difference

qk(2rm)LT

(rori)

kAmT

r

T

RARBRC

q T

xA

kAA

xB

kBA

xC

kCA

T

t

k

Cpx

2T

x2

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where Ar reference area, usually the areaof the solid through which heat isbeing conducted

hFi, hFo inside and outside fouling fac-tors

IV. RADIATION

where q12 net radiation between surfaces 1 and2, Btu/hr

T1,T2 absolute temperature of surfaces 1,

2, R.A area of either surface, sq ft Stefan-Boltzman Constant 1.712

109 Btu/hr-sq ft-R 4

F geometric view factor

V. EMPIRICAL, DIMENSIONLESS CORRELATION

Turbulent Flow in Clean Smooth Pipes

where NRe the Reynolds NumberDG

NPr the Prandtl NumberCpk

Laminar Flow in Clean Smooth Pipes

hiD

k 1.86(NRe)

0.33(NPr)0.33(w)

0.14(DL)0.33

hiD

k 0.023(NRe)

0.8(NPr)0.33(w)

0.14[1 (DL)0.7]

q12 AF(T41T

42)

1U

Ar

UAr

1

hiAi

Ar

xm

kmAm

Ar

1

hoAo

Ar

1

hFiAi

Ar

1

hFoAo

Ar

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where the Reynolds and Prandtl Numbers are as definedfor turbulence

VI. HEAT TRANSFER TO AND FROM FLUIDS FLOWINGNORMAL TO A SINGLE TUBE

where NRe the Reynolds NumberDoGf

The subscript f calls attention to the fact that thecorrelation is based on the mean film temperature,Tf, which is defined as the arithmetic mean of theaverage fluid temperature and the wall tempera-ture.

VII. HEAT TRANSFER TO AND FROM FLUIDS FLOWING

PERPENDICULAR TO TUBE BANKS

(b andn depend on geometry)

where NRe the Reynolds NumberDGmaxf

VIII. HEAT TRANSFER FROM CONDENSING VAPORS

Vertical Tubes

Horizontal Tubes

havg 0.725 ck3f

2fg

ToDofd 0.25

havg 1.13

ck3f

2fg

ToLfd

0.25

havgDo

kfb(NRe)

n

hoDo

kf 0.35 0.56(NRe)

0.52

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IX. NOTATION

A area, sq. ft.b empirical constant

Cp specific heat at constant pressure, Btu/lb-FD diameter, ftG mass velocity, lbm/sq ft-sec

Gmax mass velocity through minimum cross section intube bundle

g acceleration of gravity, 32.2 ft/sec2

h heat transfer coefficient, Btu/sq ft-hr-Fk thermal conductivity, Btu/sq ft-(F/ft)-hrL length of tube or cylinder, ftq heat flow per unit of time, Btu/hr

R resistancer radius, ftT temperature, Ft time, hr

U over-all heat transfer coefficient, Btu/sq ft-hrF

x distance in direction of heat flow; thickness oflayer, ft

latent heat of condensation or vaporization,

Btu/lbmviscosity,lbm/ft-sec density, lbm/ft

3

Subscripts

avg averagef filmi insideo outsider reference

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w wallm mean or log mean

DISTILLATION

I. FLASH (OR EQUILIBRIUM) DISTILLATION

FzFyVxL (component material balance)FVL (over-all material balance)

II. DIFFERENTIAL (SIMPLE OR RAYLEIGH) DISTILLATION

When the relative volatility is constant y x

[1 ( 1)x] can be substituted to give

For binary system following Raoults Law

where pipartial pressure of component i

III. CONTINUOUS DISTILLATION (BINARY SYSTEM)

WHERE CONSTANT MOLAL OVERFLOW IS ASSUMED

Total Material Balance

FzFDxDBxB

FDB

(yx)a

(yx)b

pa

pb

lnW

Wo

1( 1)

ln cx(1xo)xo(1x)

d ln c 1xo1x

d

lnW

Wo

x

xo

dx

yx

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where yn concentration of vapor above platen

yn1 concentration of vapor entering fromplate belown

y*n concentration of vapor in equilibriumwith liquid leaving platen

IV. NOTATION

relative volatilityB moles of bottoms productD moles of overhead productF moles of feedL molar liquid downflow

RD ratio of reflux to overhead productV molar vapor upflowW weight in still potx mole fraction of the more volatile component in

the liquid phasey mole fraction of the more volatile component in

the vapor phasezD mole fraction of the more volatile component in

the feed

Subscripts

B bottoms productD overhead productF feedm any plate in stripping section of column

m 1plate below platemn any plate in stripping section of column

n 1plate below plateno original charge in still pot

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MASS TRANSFER

I. DIFFUSION

1. Molecular Diffusion

2. Unidirectional Diffusion of a GasA Through a SecondStagnant GasB (NB 0)

in which (pB)lm is the log mean of and

3. Equimolar Countercurrent Diffusion (NB NA)

(gases)

4. Unsteady State Diffusion

II. CONVECTION

1. Two-Film Theory

kG(pAGpA)kL(CACAL)

NA

AkG(pAGpAi)kL(CAiCAL)

pA

tD

2pA

z2

NA

A

D

RT

(pA2pA1)

z2z1

pB1pB2

NA

A

DP

RT(pB)lm

(pA2pA1)

x2x1

NA

A

pA

P cNA

A

NB

Ad D

RTpA

z

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2. Overall Coefficients

3. Transfer Unit

HTUheight of a transfer unit

NTUnumber of transfer units

For dilute solutions (straight operating and equilib-rium line)

ZNTGHTGNTLHTL tower height

4. Dimensionless Group Equation (Sherwood)

(NSh) 0.023(NRe)0.8(NSc)

13

NTGy1y2

(yy*)lm

NTL x2

x1

dx

xx

*

12

ln1x11x2

NTG y2

y1

dy

y*y

12

ln1y21y1

HTL L

KLa

HTG G

KGa

1KL

1

HkG

1kL

1KG

1

kG

H

kL

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III. MOMENTUM, HEAT, AND MASS TRANSFER ANALOGY

where f Fanning friction factor

IV. NOTATION

A area perpendicular to direction of diffusiona interfacial area per unit volumeC concentration in liquid phased tube diameter

D molecular diffusivityG gas mass velocity, mass/(time)(area)

H Henrys Law constant,piHCih heat transfer coefficientk film coefficient of mass transferK overall coefficient of mass transferL liquid mass velocity, mass/(time)(area)N moles of a substance per unit timeppartial pressureP total pressureR gas constant

NRe Reynolds numberdu

NSc Schmidt numberDNSh Sherwood numberkdD

t timeT absolute temperatureuvelocity

jMkc

G(NSc)

0.667

jH h

CpG c Cp

kd 0.667 c w

d 0.14

0.5fjHjD

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lm logarithm mean average

Greek Letters

densityviscosity

Subscripts

A, B components of mixtureG gas phase

L liquid phasei interface

x mole fraction of liquidy mole fraction of gasz length in direction of travel* equilibrium concentration

THERMODYNAMICS

I. DEFINITIONS

Systeman arbitrarily chosen portion of space which is

under consideration.

A. Closed systemone in which matter does not passthrough its boundaries.

B. Open systemone in which matter flows across itsboundaries.

C. Isolated systemone in which there is no interchange

of energy or matter with the surroundings.

Boundariesthe envelope separating the system fromthe surroundings.

Universea system and its surroundings.

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Total energy,Ethe sum of the various forms of energyof the system: e.g., U, internal energy; Ek, kinetic en-ergy;Ep, potential energy; Hence,

EUEpEk

II. FIRST LAW

In an isolated system EE2E1 0

In a closed system EQW

In an open system E g(HEpEk)QW

where the summed terms refer to leaving () and enter-ing () streamsIn a steady state open system

Esystem 0

Hence for the entering and leaving streams

H Ek EpQW

III. SECOND LAW

For any real process the total entropy of the universealways increases

Ssystem Ssurroundings 0

IV. THERMODYNAMIC FUNCTIONS: DEFINITIONS

AND RELATIONSHIPS

Definition of entropy

From First and Second Laws, with changes inEk,

S dQrevT

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Ep, and composition negligible,

Also

P, V, T, S, U, H, G, A are state functions. Q and Ware pathfunctions and have no total derivatives.

V. PERFECT-GAS RELATIONSHIPS

For any path:

For any path:

For monoatomic gas: Cp 2.5R and Cv 1.5R

For diatomic gas: Cp 3.5R and Cv 2.5R

Adiabatic (Q 0) and reversible path for system withEp Ek 0.

(per mole)

Isothermal path, flow or nonflow

P2

P1

V1

V2

Wflow H [Wnonflow] (per mole)

Wnonflow URT1

1c aP2

P1b(1) 1 d

(P2P1) (V1V2) (T2T1)

(1)

U T2

T1

CvdTor (UV)T 0

H T2

T1

CpdTor (HP)T 0

Cp (HT)p; Cv (UT)v; (CpCv)

dAdUd(TS) SdTPdV

dGdHd(TS) SdTVdP

dHdUd(PV) TdSVdP

dUdQrevPdVTdSPdV

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At actual conditions

VIII. NOTATION

AUTS, Helmholtz work functiona activityC heat capacity

E total energy of the systemEk kinetic energy of the systemEppotential energy of the system reversible voltage of cell

F faradays per equivalentf fugacity

GHTS, Gibbs free energygc Newtons conversion factorHUPV, enthalpyh enthalpy per pound

K equilibrium constant for the reaction as writ-ten

Ka equilibrium constant in terms of activity

Kf equilibrium constant in terms of fugacityKp equilibrium constant in terms of partial pres-

suren number of equivalents for the reaction as

writtenPpressureQ heat, defined as positive when absorbed by

systemR gas constantS entropyT absolute temperature

G nF nFRT lnarRa

sS

aaAabB

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U internal energy of the systemuvelocityVvolumev specific volume

W work, defined as positive when done by systemon surroundings

final state minus initial state (CpCv)

Superscript

standard state

KINETICS AND REACTOR DESIGN

I. RATE OR REACTION

The rate of reaction of any component A based on unitvolume of fluid is

and where density remains unchanged

Frequently, the rate can be described as a temperature-dependent term times a concentration-dependentterm, or

rAk (T)f(CA, CB . . .)

A. Order, Molecularity, Elementary Reactions

Where the rate can be expressed as

rAdCA

dt

rA1

VdNa

dt

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the reaction is ath order with respect to A andnth order overall;nab

NOTE:a, b, . . . are empirically observed and arenot necessarily equal to the stoichiometric coeffi-cients. In the special case where a, b, . . . are thestoichiometric coefficients, the reaction is elementary:unimolecular (n 1), bimolecular (n 2), trimolecular(n 3)

B. Rate Constant k and Temperature Dependency of aReaction

k (conc)1n(time)1

From Arrheniuss Law the variation with temper-ature is

whereEis the activation energy of the reaction

II. HOMOGENEOUS, CONSTANT FLUID DENSITY,

BATCH KINETICS

A. Irreversible First-order Reaction

For the reactionASproducts, with rate

the integrated form is

lnCA

CA0 ln(1XA)kt

dCA

dt

kCAordXA

dt

k(1XA)

kkoeERTor ln

k2

k1

E

R c 1

T1

1

T2d

rAkCaAC

bB. . .

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B. Irreversible Second-order Reaction

For the reactionABSproducts, with rate

WhenMCB0CA0 1, the integrated form is

When CA0CB0 , the integrated form is

C. Irreversible nth-order Reaction

For the reaction with rate

the integrated form forn 1 is

D. Reversible First-order Reaction

For the reactionA R,Kk1k2 with rate

the integrated form is

lnXAeXA

XAe ln

CACAe

CA0CAe (k1k2)t

dCA

dt

dCR

dtk1CAk2CR

12

C1nA C1nA0 (n 1)kt

dCA

dtkCnA

1

CA

1

CA0

1

CA0

XA

1XAkt

lnCBCA0

CB0CA ln

MXA

M(1XA) (CB0CA0)kt

dCA

dt kCACB

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E. Integration of Rate in General

For the reaction with rate

which is to be solved analytically or graphically.

III. BATCH REACTION WITH CHANGING FLUID DENSITY

Where density change is proportional to the frac-tional conversion of any reactant A (isothermal sys-tems),

where

The rate for any reactantA is then

Integrating in the general case

tCA0XA

0

dXA

(1 AXA)(rA)

ra 1

VdNA

dt

CA0

(1 AXA)dXA

dtkf(CA, CB, . . .)

AVXA 1VXA 0

VXA 0

CA

CA0

1XA1 AXA

tCA0XA

0

dXA

(rA)

CA

CA0

dCA

kf(CA, CB, . . .)

rA dCA

dtkf(CA, CB, . . .),

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IV. FLOW REACTORS

A. Capacity Measures

Space time: time required to process one reactor

volume of entering feed mean residence time

B. Design Equation for Plug Flow (Ideal Tubular)Reactor

In general

For irreversible first-order reactions (isothermal)

For reversible first-order reactionsA rR

(isothermal)

where

C. Design Equation for Back-Mix (Ideal Stirred

N 1k2

k2(1 A)

k1AXA

N

N A

N2ln(1NXA)

12

k (1 A) ln (1XA) AXA

CA0XA

0

dXA

(rA)or

V

FA0

XA

0

dXA

(rA)

V

v

VCA0

FA0 (units of time)

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vvolumetric feed rate, volume of feed/time

XA fraction of reactant A converted, dimen-sionless

Greek Symbols

A measure of density change with reaction, dimen-sionless

space time based on entering feed, time

Subscripts

e equilibrium value

CONVERSION FACTORS

Acceleration1 ft /s2 0.3048 m/s2

0.6318 (mile/hr)/sec 1.097 km/hr-s 30.48 cm /s2

1 rev/min2 2.778 104 rev/s2

0.001745 rad/s2

0.01667 rev/min-s

Density

1 lbm/ft3 16.02 kg/m3

5.787 104 lbm/in3

0.01602 g/cc

Flow

1 ft3/min 4.719 104 m3/s 0.1247 gal/s

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0.4720 liter/s 472 cc/s

Length

1 ft 0.3048 m 1.894 104 mile 13 yd 12 in 30.48 cm 3.05 105 microns ()

1 1010 m 108 cm 1 104 microns ()

Angle

1 rad 12circle

0.1592 rev 0.637 quad 57.3 deg 3,438 min 2.063 105 s

Mass

1 lbm 0.4536 kg 4.464 104 long ton 5 104 short ton 4.536 104 metric ton 0.4536 kg 453.6 g 0.0311 slug

Pressure

1 lbf/ in2 abs 6.895 103 N/m2

6.895 103 Pascal

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Viscosity

1 centipoise 0.001 Pa-s 0.001 N-s/m2

0.01 g /cm-s 6.72 104 lbm/ft-s 2.42 lbm/ft-hr

Volume

1 ft3 0.02832 m3

0.03704 yd3

0.80357 bushel (U.S.) 7.481 gal (U.S.) 6.229 gal (British) 25.714 qt (dry, U.S.) 29.92 qt (liq., U.S.)

1.728 103 in3 28.32 liters 2.832 104 cm3

2.832 104 ml 59.8 pt (U.S. liq.)

Work and Energy

1 Btu 1054 J 2.93 104 kW-hr 3.93 104 hp-hr 0.252 kg cal 0.293 W-hr

10.41 liter-atm 252 g cal 778 ft-lbf 0.3676 ft3-atm 1.054 1010 ergs

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Mole fraction (x) to mass fraction (w)

Mass fraction (w) to mole fraction (x)

whereMi molecular weight of i

PHYSICAL CONSTANTS

Gas constants

R 0.0821 atm-liter/g-mole-K 1.987 g-cal/g-mole-K

1.987 Btu/lbm-mole-R 8.314 joules/g-mole-K 1.546 ft-lbf/ lbm-mole-R 10.73 (psi)-ft3/lbm-mole-R 0.7302 atm-ft3/lbm-mole-R

Acceleration of gravity (standard)

g 32.17 ft/s2 980.7 cm /s2

Avogadros number

N 6.023 1023 molecules/g-mole

Boltzmanns constant

K 1.3805 1016 erg/molecule-K

Newtons conversion constant

gc 32.17 lbm-ft/lbf-s2 1.000 kg-m/N-s2

xAwAMA

wAMAwBMB

wAxAMA

xAMAxBMB

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Plancks constant

h 6.624 1027 erg-s

Stefan-Boltzmann constant 1.355 1012 cal/s-cm2-K4

1.712 109 Btu /hr-sq ft-R4

Velocity of light

c 186,000 miles/s 3 1010 cm/s

Velocity of sound in dry air, 0C and 1 atm

33,136 cm /s 1,089 ft /s

Heat of fusion of water at 1 atm, 0C

79.7 cal /g 144 Btu /lbm

Heat of vaporization of water at 1 atm, 100C

540 cal /g 972 Btu/lbm

Ton of refrigeration 12,000 Btu /hr

1 lbm-mole of perfect gas occupies 359 ft3

at stan-dard conditions (32F, 14.7 psi abs)

1 g-mole of perfect gas occupies 22.4 liters at 0C and760 mm Hg

Thermochemistry

F 96,500 coulombs/gram equivalent

joules volts coulombs

coulombs amperes seconds

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Dimensionless Groups

Name Symbol Formula

Fanning friction factor f pgcd2LV2

Heat transfer factor jH (hcpG)(Cpk)23Mass transfer factor jM (kcG)(D)

23

Froude number NFr V2gL

Graetz number NGz wcpkLGrashof number NGr L

32gT2

Nusselt number NNu hdkPeclet number NPe LVcpk

Power number NPo Pgcn3d5Prandtl number NPr cpkReynolds number NRe LVSchmidt number NSc DSherwood number NSh KcLD

Notation

cp specific heat, Btu/lbm-FD molecular diffusivity, sq ft/hrd diameter, ftG mass velocity, lbm/sq ft-hrg acceleration of gravity, 32.2 ft/s2

gc conversion factor 32.2 ft-lbm/( lbf-s2 )

1 m-kg/(N-s2)h heat transfer coefficient, Btu/sq ft-hr-Fk thermal conductivity, Btu/sq ft-(F/ft)-hr

kc mass transfer coefficient, ft/hrL characteristic dimension, ftn rate of rotation, s1Ppower to agitator, ft-lbf/sppressure drop, lbf/sq ftT temperature, FV fluid velocity, ft /s

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w mass flow rate, lbm/s coefficient of bulk expansion, F1

density, lbm/ft3

viscosity lbm

/ft-hr

Abbreviations

atm atmosphereBtu British thermal unitcal calorie

cm centimetercu cubicft foot, feetg gram

hp horsepowerhr hour

in inchkg kilogramkm kilometerkW kilowattlbmpound-masslbfpound-forcem meter

min minuteml milliliterptpintqt quart

quad quadrantR degrees Rankine

rad radianrev revolution

s secondyd yard micron

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GREEK ALPHABET

, alpha , eta, beta , theta

, gamma , iota, delta , kappa, epsilon , lambda, zeta M, mu, nu , tau, xi , upsilon

,

omicron

, phi, pi , chi, rho , psi, sigma , omega

MATHEMATICS

Area of circle r2

Circumference of circle 2r

Surface of sphere 4r2

Volume of sphere (43)r3

Volume of cone or pyramid 13 (base area)(height)

dxn nxn1dx

daxadx

ax2 bxc 0 xb2b2 4ac

2a

a3 b3 (ab)(a2 abb2)

a3 b3 (ab)(a2 abb2)

a2 b2 (ab)(ab)

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Binomial series

Taylor series

f(x)f(a)f(a)xa

1! f(a)

(xa)2

2!

xn2y2 (y2 x2)

(xy)n xn nxn1yn(n 1)

2!

eaxdx eax

a

dxx logex lnxxndxxn

1(n 1) forn 1

udvuv vdu

(uv) dx udx vdx

dtanx sec2xdx

dcosx sinxdx

dsinx cosxdx

dax axlogeadx

deax aeaxdx

d cu

v d vduudv

v2

d(uv)udvvdu

d(uv)dudv

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CHEMICAL PROCESS SAFETY

Contributed by Joe Louvar

I. COMMON DEFINITIONS: GENERAL CONCEPTS

Chemical Process SafetyThe application of technologyand management practices a) to prevent accidents in

plants, and/or b) to reduce the potential for accidents.Process Safety ManagementAn OSHA regulation that

emphasizes the management of safety within plants.This is an especially important and effective regulation

that has 14 elements: 1) Employee Participation,2) Process Safety Information, 3) Operating Procedures,4) Process Hazards Analysis, 5) Mechanical Integrity,6) Management of Change, 7) Incident Investigation,8) Hot Work Permits, 9) Employee Training 10) Pre-Startup Review, 11) Emergency Planning, 12) Contrac-tors, 13) Audits, and 14) Trade Secretes.

Safety TechnologyDesign features and control featuresto reduce the potential for accidents.

Safety Design Featuresa) Inerting to control the concen-tration of a flammable gas to below the LFL, b) ground-ing and bonding to prevent static electricity chargingand discharging (spark) and potential fire, c) installing

relief valves to prevent vessel ruptures, d) installingdouble block and bleeds to prevent the backup of reac-tive chemicals into a monomer storage tank, e) installingan explosion suppression system to prevent dust explo-sions, f) installing containment systems to catch the re-lease from relief valves, etc.

Safety Control Featuresa) Monitoring the temperatureand pressure to prevent abnormal conditions, b) addingreactor safeguards to prevent runaway reactions,c) adding redundant controls to decrease the frequencyof accidents, d) adding more reliable instruments to re-duce the frequency of plant accidents, etc.

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II. COMMON DEFINITIONS: TERMS

Auto Ignition Temperature (AIT)A fixed temperatureabove which a flammable mixture is capable of extract-

ing enough energy from the environment to self-ignite.Boiling Liquid Expanding Vapor Explosion (BLEVE)ABLEVE occurs when a vessel ruptures which containsa liquid at a temperature above its atmospheric-

pressure boiling point. It is the explosive vaporizationof a large fraction of the vessel contents; possibly fol-lowed by the combustion or explosion of the vaporizedcloud if it is combustible (similar to a rocket).

DeflagrationAn explosion with a flame front moving inthe unburned gas at a speed below the speed of sound(1250 ft /s).

DetonationAn explosion with a shock wave moving ata speed greater than the speed of sound in the unre-

acted medium.Flash Point (FP)The FP of a liquid is the lowest tem-

perature at which it gives off enough vapor to form anignitable mixture with air.

Flammability Limits (LFL and UFL)A gas mixture willnot burn when the composition is lower than the lower

flammable limit (LFL). The mixture is also not com-bustible when the composition is above the upper flam-mability limit (UFL).

Flammability Limits of MixturesThey are computedwith the following equations:

UFLMIXTURE1

a a yiUFLib

LFLMIXTURE1

a a yiLFLib

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Lower Flammability Limit in the Presence of MistsLFLMISTS 0.1LFLTHEORETICAL

Mechanical ExplosionAn explosion due to the suddenfailure of a vessel containing a nonreactive gas at ahigh pressure.

Minimum Oxygen Concentration (MOC)A mixture ofgas will not burn if the oxygen concentration is belowthe minimum oxygen concentration.

Minimum Oxygen Concentration (MOC)It is estimatedusing the following equation:

OverpressureThe pressure on an object as a result ofan impacting shock wave.

Relief ValveA device that relieves the pressure within a

vessel when the pressure approaches the maximumallowable working pressure (MAWP). All vessels havereliefs.

RiskThis is the product of the frequency and the con-sequence of an accident scenario.

BIOCHEMICAL ENGINEERING

Contributed by David Murhammer

I. COMMON DEFINITIONS: GENERAL CONCEPTS

AerobesOrganisms whose growth requires the pres-ence of air or oxygen.

AnabolismMetabolism involved with the biosynthesis

of cellular components.AnaerobesOrganisms that grow in the absence of air oroxygen.

Biochemical EngineeringThe extension of chemicalengineering principles to biological systems with thegoal of producing useful products.

MOC (LFL%)aMolesofOxygenMolesofFuel

b

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BioreactorA vessel used for biological processes. Ex-amples include growing microorganisms and animalcells for the production of useful products.

BiotechnologyThe use or development of methods ofdirect genetic manipulation for a socially desirablegoal. Examples include the production of a particularchemical, production of better plants or seeds, andgene therapy.

CatabolismMetabolism involved with the breakdown ofmaterials for the production of intermediates and energy.

EnzymeA catalytic protein (and in some cases RNA)produced by living cells.

EukaryoteA cell or organism with a membrane-boundnucleus and well-developed organelles. Examples in-clude yeast, animals, and plants.

ProkaryoteA cell lacking a true nucleus. Examples in-

clude bacteria and blue-green algae.VirusA noncellular entity that consists minimally ofprotein and DNA or RNA and that can replicate only af-ter entry into specific types of living cells.

II. COMMON DEFINITIONS: TERMS

AntibioticsSubstances of microbial origin that in verysmall amounts have antimicrobial activity.

AntibodiesGlycoprotein molecules produced by B-lymphocytes in higher organisms in response to theintroduction of a foreign material (antigen). These mol-ecules react with antigens with great specificity.

Attachment DependentCells whose growth requiresattachment to a surface. Also referred to as Anchorage-Dependent.

Batch CultureA culture that once supplied with rawmaterials is run to completion.

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ChemostatA bioreactor in which the continuous addi-tion of fresh medium and removal of effluent results inconstant nutrient, product, and cell concentrationswhen operated under steady state conditions.

Death PhaseThe portion of the growth curve in culturein which there is a net decline in the number of viable(live) cells.

Exponential (Log) Growth PhaseA period of growth ina culture in which the number of cells or cell mass in-creases exponentially, i.e., the growth rate is propor-

tional to the population density:

where X cell number (cells/mL) or cell biomass(mg/mL), t is time, and is the specific growth rate (h1).

Fed-Batch CultureA culture to which nutrients are pe-riodically added during the operation of the culture.

Growth YieldYield of biomass based on substrate (e.g.,glucose or oxygen) utilization:

where YXSis the yield coefficient of biomass (X) basedon Substrate (S) and is usually given in terms of either(gm biomass/gm or mole substrate) or (cell number/gmor mole substrate).

KLaVolumetric mass transfer coefficient usually meas-ured in h1 and often used to compare the efficienciesof bioreactors in supplying oxygen. The resulting oxy-gen transfer rate is then given by

dCL

dtKLa(C*CL),

YX/S dX

dS,

dX

dt X,

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where CL is the dissolved oxygen concentration withinthe bioreactor, t in time, and C* is the equilibrium dis-solved oxygen concentration (i.e., solubility) under thespecified conditions.

Lag PhaseThe portion of the growth curve between in-oculation and the beginning of cell growth.

Media SterilizationRemoval of undesired microorgan-isms from the media through filtration or heat to pre-

vent their growth during the course of a bioreactor run.Michaelis-Menton KineticsCommon type of enzyme ki-

netics given by

where v is the reaction rate, vmax is the maximum reac-

tion rate,KM is the Michaelis Constant and is equal tothe substrate concentration at v 12vmax , and [S] isthe substrate concentration.

Perfusion CultureA bioreactor in which cells areretained, medium is added continuously or semi-continuously, and spent medium containing toxicmetabolites is removed.

Population Doubling Time (PDT)The time required forthe viable cell population to double. This term is com-monly used for animal cell cultures, and is related tothe specific growth rate () by

Power Number (Np)A dimensionless number com-monly used to determine the amount of power intro-duced to the bioreactor as a result of agitation. The

PDT

ln(2)

.

vvmax[S]

KM [S],

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Power Number is given by

wherePis the power input, is the density of the solu-tion being agitated,Nis the rotational speed of the im-

peller, andD is the impeller diameter.Monod EquationAn equation commonly used to model

the effect of the rate-limiting substrate concentrationon the specific growth rate. This equation is given by

where is the specific growth rate, m is the maximumspecific growth rate when [S]WKs, [S] is the sub-strate concentration, andKs is the saturation constant

or half-velocity constant and is equal to the substrateconcentration when 12m.

Stationary PhasePhase in growth curve following theexponential growth phase in which there is no netgrowth. This phase is commonly associated with nutri-ent depletion.

m[S]

Ks [S],

NP P

N3D5,

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American Institute of

Chemical Engineers

3 Park Avenue

New York, NY

10016-5991

212.591.8100

www.aiche.org

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