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Gas Compression Stages – Process Design & Optimization
Jayanthi Vijay Sarathy, M.E, CEng, MIChemE, Chartered Chemical Engineer, IChemE, UK
The following tutorial demonstrates how to
estimate the required number of compression
stages and optimize the individual pressure
ratio in a multistage centrifugal compression
system. A schematic of a 2-Stage compressor
unit is as follows,
Fig 1. Two Stage Compressor Unit
A schematic of a 3-Stage Compressor Unit is
as follows,
Fig 2. Three Stage Compressor Unit
General Notes
1. When vapours are compressed, its
temperature increases & therefore
requires provisions for gas cooling.
2. High gas temperatures can affect lube oil
characteristics causing them to carbonize
and turn in sludge. This results in fouling
causing the bearing pads and seals to wear
out and performance degradation.
3. As per API 617 (7th Edition, 2002), Clause
2.7.1.3, it states, As a design criteria,
bearing metal temperatures shall not
exceed 100°C (212°F) at specified
operating conditions with a maximum inlet
oil temperature of 50°C (120°F). Vendors
shall provide bearing temperature alarm
and shutdown limits on the datasheets.
However clause No. 2.7.1.3.1 of the said
document also says, In the event that the
above design criteria cannot be met,
purchaser and vendor shall mutually agree
on acceptable bearing metal temperatures.
4. During gas recycling, (either by cold
recycling or hot recycling), the compressor
discharge temperature rises above the
temperature pertaining to normal running
conditions. Quantitatively, the rise in
temperature depends on the pressure ratio
of each stage. The maximum discharge
temperature is typically limited to, in the
range of 1500C to 1600C to avoid damage
to the bearings and seals. To ensure these
limits are not crossed, the compressor
discharge temperature at normal running
conditions must be operated at lower
temperatures with a margin of 200C to
250C. This means typical compressor
discharge temperatures (under normal
running conditions) should be limited to
the range of 1200C to 1350C.
5. Individual compressor pressure ratios
must also be optimized to obtain the
lowest amount of power required to meet
the final discharge pressure. This also
enables to reduce the suction scrubber
volumes and air cooler duties to save on
material and operating costs.
Case Study
A multistage compression system receives 30
MMScfd of hydrocarbon vapours at 2 bara,
300C and is required to be raised to 15 bara.
The Polytropic efficiency [] for all
compressors is assumed to be 82%. An
optimization study is performed for a 2-Stage
and 3-Stage centrifugal compression system.
The vapour composition is as follows,

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Table 1. Gas Composition
Components Mole Fraction [-]
Methane [C1] 0.5232
Ethane [C2] 0.3001
Propane [C3] 0.1096
iso-Butane [iC4] 0.0106
n-Butane [nC4] 0.0346
Iso-Pentane [iC5] 0.0076
n-Pentane [nC5] 0.0092
n-Hexane [C6] 0.0052
Total 1.0000
MW [kg/kmol] [PR EoS] 26.53
Density [1 atm, 15.60C] [kg/m3] 1.128
Methodology
The number of compressors can be chosen by
first estimating preliminary discharge
pressures based on equal pressure ratio as,
𝑋 𝑛
= [
𝑃 𝐿𝑎𝑠𝑡
𝑃 𝐹𝑖𝑟𝑠𝑡
] (1)
Where,
PFirst = First Compressor Pressure [bara]
PLast = Last Compressor Pressure [bara]
n = Number of stages [-]
X = Maximum number of Stages [-]
Rewriting the expression,
𝑛 × 𝑙𝑛𝑋 = 𝑙𝑛 [
𝑃 𝐿𝑎𝑠𝑡
𝑃 𝐹𝑖𝑟𝑠𝑡
] (2)
Or, 𝑛 =
𝑙𝑛[
𝑃 𝐿𝑎𝑠𝑡
𝑃 𝐹𝑖𝑟𝑠𝑡
]
𝑙𝑛𝑋
(3)
The separation ratio is computed as,
𝑅 = [
𝑃 𝐿𝑎𝑠𝑡
𝑃 𝐹𝑖𝑟𝑠𝑡
]
1
𝑛⁄
(4)
The intermediate pressure is computed as,
𝑃𝑖 = 𝑃𝑓𝑖𝑟𝑠𝑡 × 𝑅 𝑖
(5)
Where,
Pi = Intermediate Pressure at Stage ‘i’
Therefore considering a maximum number of
stages of 3, for a two stage compressor unit,
the first compressor discharge pressure [P1]
and Pressure ratio [R] is,
𝑛 =
𝑙𝑛[
15
2
]
𝑙𝑛[3]
= 1.83 ~ 2 𝑆𝑡𝑎𝑔𝑒𝑠 (6)
𝑅 = [
15
2
]
1
2⁄
= 2.7386 (7)
𝑃1 = 2 × 2.73861
= 5.48 𝑏𝑎𝑟𝑎 (8)
For a three stage compressor unit, the LP
compressor discharge pressure [P1] and MP
compressor discharge pressure [P2] is,
𝑅 = [
15
2
]
1
3⁄
= 1.9574 (9)
𝑃1 = 2 × 1.95741
= 3.91 𝑏𝑎𝑟𝑎 (10)
𝑃2 = 2 × 1.95742
= 7.66 𝑏𝑎𝑟𝑎 (11)
Using these preliminary values, to arrive at
optimized discharge pressures, the following
iterative procedure is adopted.
1. Keeping all preliminary estimated
discharge pressures fixed, the LP
compressor discharge pressure is varied
for a range to obtain total absorbed power
& total cooler duty of all compressors, and
sizing each suction scrubber. Making a plot
of the above values, the discharge pressure
corresponding to the lowest duty is chosen
[1st Iteration of LP Compressor].
2. The LP compressor initial estimated
discharge pressure is now replaced with
the 1st Iteration’s optimized pressure.
3. Following further, the MP compressor
discharge pressure is also varied for a
given range to similarly obtain an
optimized discharge pressure
corresponding to the lowest total
compressor duty and cooler duty. [1st
Iteration of 2nd stage].
4. The MP compressor initial estimate
pressure is now replaced with the
optimized value, [1st Iteration of 2nd stage].

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5. With the 1st iteration optimized pressures,
calculations are repeated similar to Step 2
Step 3 & Step 4, i.e., 2nd Iteration and so
forth, until a converged solution is reached.
Results
With the procedure applied for the calculated
initial estimates, the optimized results of 2-
Stage & 3-stage system [ = 82%] is,
Table 2. Optimized Compressor Stage Pressures
Stages-Pressure
Discharge
Pressure
Pressure
Ratio
- [bara] [-]
2 Stage LP [2S-LP] 8.12 4.060
2 Stage HP [2S-HP] 15.00 1.847
3 Stage LP [3S-LP] 6.15 3.075
3 Stage MP [3S-MP] 8.25 1.341
3 Stage HP [3S-HP] 15.00 1.818
The plots of total compressor absorbed
power, total cooler duty for two stage design
and three stage design is as follows,
Fig 3. Two Stages –Total Compressor & Cooler Duty
Fig 4. Two Stages – Total Compressor & Cooler Duty
Based on the optimized compression ratios,
the savings on the total compressor duty and
total air cooler duty is 1.59% and 1.68% for 2
stages respectively. For 3 stages, the
respective savings is 1.86% and 2.03%.
Table 3. Savings on Compressor & Air Cooler Duty
Parameter 2 Stage 3 Stage
Before Optimization
Total Comp. Duty [kW] 3,000 2,930
Total Cooler Duty [kW] 2,786 2,717
After Optimization
Total Comp. Duty [kW] 2,952 2,876
Total Cooler Duty[kW] 2,739 2,663
% Savings [Compressor] 1.59% 1.86%
% Savings [Air Cooler] 1.68% 2.03%
Based on the optimized compression ratios,
the suction scrubber sizes for both cases are,
Table 4. Suction Scrubber Sizes
Suction
Scrubber
[H/D = 3.0]
Head Design [2:1 Elliptical]
D
[mm]
H
[mm]
Vessel
Volume [m3]
2S-LP/3S-LP 2,400 7,200 34.08
Before Optimization
2S-HP 1,900 5,700 17.11
3S-MP 2,100 6,300 22.98
3S-HP 1,800 5,400 14.59
After Optimization
2S-HP 1,800 5,400 14.59
3S-MP 1,900 5,700 17.11
3S-HP 1,800 5,400 14.59
For 2S-HP & 3S-MP cases, the vessel volume
decreases by 14.7% and 25.5% respectively.
References
1. “Example problems for the calculation and
selection of compressors”, Intech GMBH,
(intech-gmbh.com/compr_calc_and_selec_examples/)
2. www.checalc.com

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Appendix A
Appendix B