Page 195 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap13 Final Proof page 191 3.1.2007 9:07pm Compositor Name: SJoearun

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Table 13.2 Result Given by Computer Program ReciprocatingCompressorPower.xls for the First-
Stage Compression
ReciprocatingCompressorPower.xls
Description: This spreadsheet calculates stage power of reciprocating compressor.
Instruction: (1) Update parameter valves in the ‘‘Input data’’ in blue; (2) click ‘‘Solution’’ button; (3) view
result in the Solution section.
Input data
Gas flow rate (q g ): 32 MMscf/day
Stage inlet temperature (T 1 ): 70 8F
Stage inlet pressure ( p 1 ): 100 psia
Gas-specific gravity (g g ): 0:65(air ¼ 1)
Stage outlet pressure ( p 2 ): 341 psia
Gas-specific heat ratio (k): 1.25
Overall efficiency (E o ): 0.8
Base temperature (T b ): 60 8F
Base pressure ( p b ): 14.7 psia
Solution
z ¼ Hall–Yarborogh Method ¼ 0:9574
p 2
r ¼ " Z 1 (k 1)=k # ¼ 3:41
p 1 k 3:027p b p 2
Hp MM ¼ T 1 1 ¼ 60 hp
k 1 T b p 1
Hp b ¼ q MM Hp MM ¼ 2,401 hp
E o
z 1 (k 1)=k
p 2
T 2 ¼ T 1 ¼ 210:33 F
p 1

T avg ¼ T 1 þ T 2 ¼ 140:16 F
2
C p ¼ 9:50 btu=lbm-mol F
3
C
Cooler load ¼ 2:640 10 q MM C p T avg T 1 ¼ 56,319,606 btu=day
n
pV ¼ constant, (13:30)
4. Calculate polytropic ratio (n 1)=n:
where n denotes the polytropic exponent. The isentropic
exponent k applies to the ideal frictionless adiabatic pro- R p ¼ n 1 ¼ k 1 1 (13:35)
cess, while the polytropic exponent n applies to the actual n k E p
process with heat transfer and friction. The n is related to k 5. Calculate discharge temperature by
through polytropic efficiency E p :
T 2 ¼ T 1 r : (13:36)
R p
n 1 k 1 1
¼ (13:31) 6. Estimate gas compressibility factor values at inlet and
n k E p
discharge conditions.
The polytropic efficiency of centrifugal compressors is 7. Calculate gas capacity at the inlet condition (q 1 ) by real
nearly proportional to the logarithm of gas flow rate in
gas law:
the range of efficiency between 0.7 and 0.75. The polytro-
pic efficiency chart presented by Rollins (1973) can z 1 p b T 1
be represented by the following correlation (Guo and q 1 ¼ q (13:37)
z 2 p 1 T b
Ghalambor, 2005):
8. Repeat steps 2 through 7 until the value of q 1 converges
E p ¼ 0:61 þ 0:03 log (q 1 ), (13:32) within an acceptable deviation.
9. Calculate gas horsepower by
where q 1 ¼ gas capacity at the inlet condition, cfm.
There is a lower limit of gas flow rate below which severe R p
q 1 p 1 z 1 þ z 2 r 1
gas surge occurs in the compressor. This limit is called surge Hp g ¼ : (13:38)
limit. The upper limit of gas flow rate is called stone-wall 229E p 2z 1 R p
limit, which is controlled by compressor horsepower.
Some manufacturers present compressor specifications
The procedure of preliminary calculations for selection
using polytropic head in lb f -ft=lb m defined as
of centrifugal compressors is summarized as follows:
r R p 1
1. Calculate compression ratio based on the inlet and z 1 þ z 2 , (13:39)
H g ¼ RT 1
discharge pressures: 2 R p
where R is the gas constant given by 1,544=MW a in
p 2
r ¼ (13:33) psia-ft =lb m -8R. The polytropic head relates to the gas
3
p 1
horsepower by
2. Based on the required gas flow rate under standard
condition (q), estimate the gas capacity at inlet condi- Hp g ¼ M F H g , (13:40)
tion (q 1 ) by ideal gas law: 33,000E p
where M F is mass flow rate in lb m = min.
p b T 1
q 1 ¼ q (13:34)
p 1 T b 10. Calculate gas horsepower by
3. Find a value for the polytropic efficiency E p from the
manufacturer’s manual based on q 1 . Hp b ¼ Hp g þ DHp m , (13:41)