Chapter 21 Performance Curves for Performance Curves for Individual Unit Operations (Fluid Flow Equipment) Department of Chemical Engineering West Virginia University Copyright J. A. Shaeiwitz and R. Turton - 2012 1
Chapter 21 Performance Curves forPerformance Curves for
Individual Unit Operations(Fluid Flow Equipment)
Department of Chemical EngineeringWest Virginia University
Copyright J. A. Shaeiwitz and R. Turton - 2012 1
OutlineOutline
• Flow in pipesFlow in pipes– laminar vs. turbulent
• NPSH• NPSH
• Pump and system curves– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors
Copyright J. A. Shaeiwitz and R. Turton - 2012 2
OutlineOutline
• Flow in pipesFlow in pipes– laminar vs. turbulent
• NPSH• NPSH
• Pump and system curves– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors
Copyright J. A. Shaeiwitz and R. Turton - 2012 3
Key RelationshipsKey Relationships
2
• Turbulent flow
22
4
2∝Δ⇒=Δ
mm
vPDfLvP frfrρ
&&
2
2
32
4==
mfL
Dm
Amv
ρπρ
&
&&
552
32 −∝Δ⇒=Δ DPDmfLP frfr ρπ&
Copyright J. A. Shaeiwitz and R. Turton - 2012 4
Key RelationshipsKey Relationships
• Laminar flow
LLL
DPvDv Δ==
128321284
42
μππ
&
&
vDPD
LvD
LvP frfr ∝∝Δ⇒==Δ − and12832 442 πμμ &
Copyright J. A. Shaeiwitz and R. Turton - 2012 5
Example 1Example 1
• Increase velocity by 25% ‐ turbulent flow ‐effect on ΔP
ld12
25.1
old1 new2
2 =
==
vv
2 22
1
∝Δ⇒=Δ vPDfLvP
v
frfrρ
5625.125.1 22
22
1
2 ===ΔΔ
vv
PP
D ff
11Δ vP
Copyright J. A. Shaeiwitz and R. Turton - 2012 6
Example 2Example 2
• Double diameter – turbulent flow‐ effect on ΔP
2
old1 new2
2 =
==
DD
32 552
21
∝Δ⇒=Δ −DPDmfLP
D
frfrρπ
&
32103125.05.0 5
5
51
1
2 ====ΔΔ
DD
PP
Dρπ
3221Δ DP
Copyright J. A. Shaeiwitz and R. Turton - 2012 7
OutlineOutline
• Flow in pipesFlow in pipes– laminar vs. turbulent
• NPSH• NPSH
• Pump and system curves– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors
Copyright J. A. Shaeiwitz and R. Turton - 2012 8
NPSHNPSH
NPSH N P i i S i H d• NPSH = Net Positive Suction Head
• There is pressure drop upon entering pump, p p p g p p,before mechanism that increases pressure
• If fluid is too close to vapor pressure at pump• If fluid is too close to vapor pressure at pump inlet, it could flash upon entering pump
• Pumps are designed to handle liquids and do not behave well with vapor
Copyright J. A. Shaeiwitz and R. Turton - 2012 9
NPSHNPSH
• NPSHA = Pinlet – P *NPSHR
• NPSHA= NPSH “available”
NPSHR
• NPSHR = NPSH “required”i f i li d b f
v&
– information supplied by pump manufacturer
Copyright J. A. Shaeiwitz and R. Turton - 2012 10
NPSHNPSH
• Common situation
• Apply MEB
1202
2WezgvP
sf −→Δ=−+Δ+Δ
+Δρ
2
02
2
212
fL
DfLvghPP
=+−−
ρ
ρ
*2*
2
2
2
12
PfLvghPPPNPSH
DfLvghPP
+==
−+=
ρρ
ρρ
Copyright J. A. Shaeiwitz and R. Turton - 2012 11
** 12 PD
ghPPPNPSH A −−+=−= ρ
NPSHNPSH
52
2
1 *32 PD
vfLghPNPSH A πρρ −−+=
&
2
form of
vbaNPSH A −= &NPSH
1
32*
fLb
PghPavbaNPSH A
ρρ −+=
NPSHA
5232
DfLb
πρ
=v&
this is for turbulent flowf l i fl t i ht li
Copyright J. A. Shaeiwitz and R. Turton - 2012 12
for laminar flow – straight linewith negative slope
NPSHNPSH
2
1
2
32*
fLPghPavbaNPSH A
ρ −+=−= &• How to increase NPSHA
• base case is line (1)increase a line (2)
5232
DfLb
πρ
=– increase a – line (2)
• increase h• increase P1• decrease P*
– decrease T
– decrease b – line (3) NPSHA
• decrease L• increase D
– suction line usually larger D1
32
Copyright J. A. Shaeiwitz and R. Turton - 2012 13
v&
NPSHNPSHNPSHA > NPSHRpump operates appropriately
R
NPSHA < NPSHRpump will cavitateinappropriate pump operationbut it will operate
NPSHbut it will operate
v&
A
v&
Copyright J. A. Shaeiwitz and R. Turton - 2012 14
OutlineOutline
• Flow in pipesFlow in pipes– laminar vs. turbulent
• NPSH• NPSH
• Pump and system curves– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors
Copyright J. A. Shaeiwitz and R. Turton - 2012 15
Pump and System CurvesPump and System Curves
• Pump curve (centrifugal pump shown)• Pump curve (centrifugal pump shown)
• Supplied by manufacturer
• Can be measured in lab
• centrifugal is sometimes called “constant head” pump
ΔP in pressure unitsor head developedor head developed
Copyright J. A. Shaeiwitz and R. Turton - 2012 16v&
Pump and System CurvesPump and System Curves
• System curvepump supplies pressure increase
)()( 323121 Δ−+Δ−+Δ=Δ −−− PPPP fr
to increase fluid pressure and to overcome all of these pressure losses
0)(h)0or0becould()0usually(n destinatio tosource
in-out
31
Δ<>Δ+>Δ=Δ
=Δ
−
PzgPP ρ
0)(valveacrossdroppressurefrictional
0)( pipesin drop pressure frictional0)(pumpacrosschange pressure
32
21
<=Δ
<=Δ>=Δ −
P
PP
fr
0)( valveacrossdroppressure frictional32 <=Δ −P
Copyright J. A. Shaeiwitz and R. Turton - 2012 17
Pump and System CurvesPump and System Curves
• To plot system curve – look at source to destination and frictional loss
31
31
)0or0becould()0usually(n destinatio tosourcein-out
)(
zgPP
PPP frsys
<>Δ+>Δ=Δ=Δ
Δ−+Δ=Δ −
ρ
52
2
31
2
31
31
so
322
)obecou d()usu y(des oosou ce
DvfLP
DfLvPP
g
sys&
+Δ=+Δ=Δ −−
−
πρρ
ρ
ΔPsys
( )2 form empirical
so
vbaP
PPP
sys
valvesyspump
&+=Δ
Δ−+Δ=Δ
v&
ΔPsys
Copyright J. A. Shaeiwitz and R. Turton - 2012 18
v&this is for turbulent flowfor laminar flow – straight line
Pump and System CurvesPump and System Curves
• Often expressed as head
sysvfLhfLvhh +=+= −−
32252
2
31
2
31&
sys DggD −−
so
523131 π
valvesyspump hhh += hsys
Copyright J. A. Shaeiwitz and R. Turton - 2012 19
v&
Pump and System CurvesPump and System Curves
ΔP
ΔPpump < ΔPsysimpossible operation
sys
ΔP
a = ΔPsource dest + ρgΔz if know this point2
{-ΔPvalve
ΔPpump
a ΔPsource-dest + ρgΔzwithcan find a and b
2vbaPsys &+=Δ
operatingv& v&
pumpa}-ΔPfr
ΔPpump > ΔPsysexcess pressure dissipated across partially closed valveas open and close valve, flowrate changes
operating v&
Copyright J. A. Shaeiwitz and R. Turton - 2012 20
as open and close valve, flowrate changesintersection point is fully open valve
OutlineOutline
• Flow in pipesFlow in pipes– laminar vs. turbulent
• NPSH• NPSH
• Pump and system curves– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors
Copyright J. A. Shaeiwitz and R. Turton - 2012 21
Pumps in Series and ParallelPumps in Series and Parallel
• Series– Pump curve
two pumps
Pump curve
– 2X head at same flowrate
ΔPpump
one pump
v&
Copyright J. A. Shaeiwitz and R. Turton - 2012 22
Pumps in Series and ParallelPumps in Series and Parallel
• ParallelP
two pumps
– Pump curve
– 2X flowrate at same head
ΔPpumpone pump
same head
v&
Copyright J. A. Shaeiwitz and R. Turton - 2012 23
Pumps in Series and ParallelPumps in Series and Parallel
• Which configuration
two pumpsseries
configuration maximizes flowrate?
ΔPpumpflowrate?– No general result
one pumptwo pumps parallel
result
Copyright J. A. Shaeiwitz and R. Turton - 2012 24
v&
OutlineOutline
• Flow in pipesFlow in pipes– laminar vs. turbulent
• NPSH• NPSH
• Pump and system curves– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors
Copyright J. A. Shaeiwitz and R. Turton - 2012 25
Centrifugal – variable speedCentrifugal variable speed
ΔPΔPpump
rpm 5
rpm 3
rpm 2
rpm 4
v& rpm 1
rpm increases with numbermore expensive pump
Copyright J. A. Shaeiwitz and R. Turton - 2012 26
p p pcost of “wasting” pressure across valve may be less than cost of pump
Positive Displacementfl l /flow regulation/pump curve
ΔP in pressure unitssometimes called “constant volume” pump
por head developed
v&
Copyright J. A. Shaeiwitz and R. Turton - 2012 27
OutlineOutline
• Flow in pipesFlow in pipes– laminar vs. turbulent
• NPSH• NPSH
• Pump and system curves– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors
Copyright J. A. Shaeiwitz and R. Turton - 2012 28
CompressorsCompressors
locus of maxima = surge line
can also draw systemPout /Pin
rpm 5
can also draw systemcurves on this graph –must change form of left-hand side to ratio
rpm 3
rpm 2
rpm 4
v& rpm 1
rpm 2
usually worth using speed control here because of compression costs
Copyright J. A. Shaeiwitz and R. Turton - 2012 29
usually worth using speed control here because of compression costs
OutlineOutline
• Flow in pipesFlow in pipes– laminar vs. turbulent
• NPSH• NPSH
• Pump and system curves– single vs. multiple pumps
– centrifugal vs. positive displacement
– compressors
Copyright J. A. Shaeiwitz and R. Turton - 2012 30