Homework #3
Do problems 9.1, 9.2, & 9.5 on pages 209-210. In addition, add the following to 9.5:
Using a simulation program (Aspen Plus or HYSYS) check the compression power calculation. What
is the outlet temperature from the compressor?
CBEN 408 Spring 2016
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February 28, 2016
Solutions
Problem #9.1 (5 points)
A gas mixture has the following composition:
• C1 89 vol%
• C2 6
• C3 5
Using Appendix B.13 (B.14) what is the value of the heat capacity ratio, γ, at 150°F (65°C)?
Solution
The table below shows the pure component parameters used for the calculations and the results.
The requested values are highlighted in orange. 1,2
The ideal gas heat capacity for the gas is calculated as a mole average:
Cp =
(0.89)(8.94 ) + (0.06 )(13.77 ) + (0.05)(19.59)
∑ xi C p , i =
= 9.762 Btu/°R ⋅ lb.mol
and the heat capacity ratio is calculated from:
=
γ
Cp
9.762
=
= 1.255
C p − R 9.762 − 8.314
Note that the numbers shown may be slightly different from hand calculations because of the number of
digits retained in intermediate calculations.
2 The pure component parameters used are from Table B.1 in the Kidnay, et. al. text book.
1
CBEN 408 Spring 2016
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February 28, 2016
Problem #9.2 (10 points)
A field compressor boosts a raw gas stream from 8 psig (0.55 barg) to 450 psig (31.0 barg). The
maximum acceptable pressure ratio is 3.
a) How many stages will be required assuming the compression ratio is constant for all stages?
b) What is the compression ratio based upon the number of stages required?
Solution
Assuming an equal compression ratio in each stage:
1/ m
P 
=
RP  2 
 T1 
ln ( P2 / P1 )
m
⇒=
=
ln (R P )
 450 + 14.7 
ln 

 8 + 14.7=
 2.7
ln (3)
so (rounding up) 3 stages are required. Using 3 stages with equal compression ratios gives:
1/ m
1/3
 P2 
 450 + 14.7 
2.74
=
R P =
=



 8 + 14.7 
 P1 
CBEN 408 Spring 2016
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February 28, 2016
Problem #9.5 (15 points)
The sales gas from a gas plant is compressed from 330 to 1000 psig (22.7–69.0 bara) to meet
pipeline requirements using a centrifugal compressor. The compressor has an isentropic efficiency
of 75% and the gas turbine has a heat rate of 8,200 Btu/hp-h (11,600 kJ/kWh). Low pressure sales
gas is the fuel to the gas turbine. The gas is 99 vol% methane and 1 vol% ethane. Assuming the
suction temperature is 60°F (15.6°C) what fraction of low-pressure sales gas is consumed in
compressing the gas to pipeline specifications?
Solution
This problem has two major parts:
• How much power is required to compress a certain amount of product gas? You will
determine this power either by hand calculations (assuming ideal gas behavior) or using a
simulator (assuming real gas behavior as modeled by an equation of state). This power will
be produced by a gas turbine.
• How much fuel gas is needed to burn in the gas turbine to provide this power? You will
calculate this using the heat rate for the gas turbine. The final conversion to the gas flowrate
will be done using the LHV for the gas.
Total Produced Gas
from Process
Product Gas
Fuel Gas
Work from gas turbine
to compressor
Compressor
Gas Turbine
Hand calculations
The following are the steps needed to do the hand calculations for this. If necessary, use as a flow
basis 100 scf/hr through the compressor.
• Determine the following properties for the gas:
o Ideal gas heat capacity for the mixture at the inlet temperature (60°F) & use to
calculate the heat capacity ratio (γ).
o Lower heating value (LHV).
• Calculate the compression work required at isentropic conditions.
• Increase this compression work to account for the 75% efficiency. Calculate the outlet
temperature for these conditions.
• Use the heat rate for the gas turbine to determine the amount of fuel gas needed based on
its heating value. Convert to molar flowrate based on the gas’s LHV.
The table below shows the pure component parameters used for the calculations and the results. 1,1
Note that the numbers shown may be slightly different from hand calculations because of the number of
digits retained in intermediate calculations.
1
CBEN 408 Spring 2016
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February 28, 2016
The ideal gas heat capacity for the gas is calculated as a mole average:
=
Cp
xC
(0.99)( 8.44 ) + (0.01)(12.23)
∑=
i
p ,i
= 8.478 Btu/°R ⋅ lb.mol
and the heat capacity ratio is calculated from:
=
γ
Cp
8.478
=
= 1.306
C p − R 8.478 − 8.314
The LHV for the gas is also calculated as a mole average:
=
Cp
xC
(0.99)( 909.4 ) + (0.01)(1619)
∑=
i
p ,i
= 916.5 Btu/scf
Next, let’s determine the isentropic work of compression:
Wˆ s
=
( γ −1)/ γ

γ  P2 
 
− 1
( RT1 )
γ − 1  P1 


(1.306 −1)/1.306

1.306  1000 + 14.7 
=
− 1
(1.9859)(60 + 459.67 )


1.306 − 1  330 + 14.7 

= 1268 Btu/lb.mol
and converting to more useful units:
Wˆ s
Btu 

 1268

lb.mol 

0.001313 hp/(scf/hr)
=
scf  
Btu/hr 

379.5
2544.433


lb.mol  
hp 

Now, at 75% efficiency for the compression:
1
The pure component parameters used are from Tables B.1 & B.13 in the Kidnay, et. al. text book.
CBEN 408 Spring 2016
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February 28, 2016
Wˆ s 0.001313
Wˆ s ,=
=
= 0.001750 hp/(scf/hr)
act
ηIS
0.75
How much fuel is needed by the gas turbine? Let’s apply the basis of the 100 scf/hr through the
compressor:
(
N fuel ( L(V ) = ( (eat Rate ) Wˆ s ,act N gas
and
)

Btu/hr 
hp  
scf 
=  8200

 0.001750
  100
hp 
scf/hr  
hr 

= 1435 Btu/hr
=
N fuel ( L(V )
1435 Btu/hr
= 1.566 scf/hr
916.5 Btu/scf
So, the fuel gas requirement based on the produced gas (i.e., that going through the compressor &
that needed for fuel) is 1.54%. The ratio of the fuel gas to the gas through the compressor is 1.57%.
HYSYS results
HYSYS can be used to perform the compression calculations. The following image summarizes the
results using a basis of 100 MMscfd flow through the compressor. Note the compression required @
75% efficiency is 0.001654 hp/(scf/hr) (5.5% less than that calculated by hand).
Note that the net heating value above is 916.5 Btu/scf (the same as the hand calculation). So,
directly based on these HYSYS results, the rate of fuel gas required is 61,663 scf/hr fuel gas which is
CBEN 408 Spring 2016
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February 28, 2016
1.48 MMscfd. So, the ratio to the compressed gas is 1.48% & the fraction of total produced gas is
1.46%.
Aspen Plus results
Aspen Plus can be used to perform the compression calculations. The following images show the
results using a basis of 100 MMscfd flow through the compressor. Note the compression required @
75% efficiency is 0.001655 hp/(scf/hr) (5.5% less than that calculated by hand).
CBEN 408 Spring 2016
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February 28, 2016
Note that the net heating value above is 21488.9 Btu/lb which is 916.4 Btu/scf (0.01% lower than
the hand calculation). So, directly based on these Aspen Plus results, the rate of fuel gas required is
61,706 scf/hr fuel gas which is 1.48 MMscfd. So, the ratio to the compressed gas is 1.48% & the
fraction of total produced gas is 1.46%.
CBEN 408 Spring 2016
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February 28, 2016