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Reciprocating Compressor Power Calculation Part 1 (Two-Stage Compression)


Many of readers in of this technical blog asked me how to calculate reciprocating compressor power. Long time ago I wrote how to estimate centrifugal compressor power.

In this post I want to share how to calculate reciprocating compressor power. This calculation is used for estimation only. For more accurate results, you should consult a compressor manufacturer.

You will find that the method used in this calculation rely on graphical methods. So, please be patient in using this method.

I used calculation method as stated in GPSA.

Let’s start using example. I used example as used in GPSA.

Example

Compress 2 MMscfd of gas measured at 14.65 psia and 60oF. Intake pressure is 100 psia, and intake temperature is 100oF. Discharge pressure is 900 psia. The gas has a specific gravity of 0.80 (23 MW). What is the required horse power?

Solution

Step 1 – Calculate Overall Compression Ratio

Overall compression ratio is ratio of discharge pressure in absolute pressure and suction pressure in absolute pressure. So,

Pressure ratio = 900 psia/100 psia = 9

Step 2 – Decide Number of Stage

Number of compression stage is determined by the overall compression ratio. The compression ratio per stage is generally limited by the discharge temperature and usually does not exceed 4.

For this example, we use number of stage 2. In the next post, we will compare if we use 3 compression ratio and 4 compression ratio.

Step 3 – Determine Compression Ratio Per Stage

For two-stage compressor, ratio per stage is = (overall compression ratio) ^ (1/2)

So, we get ratio per stage for two-stage compressor is = (9)^(1/2) = 3

 

If number of stage is 3, then ratio per stage is = (overall compression ratio) ^ (1/3)

And if number of stage is 4, then ratio per stage is = (overall compression ratio) ^ (1/4)

Step 4 – Determine 1st Stage Discharge Pressure

1st stage discharge pressure = compression ratio per stage x suction pressure

So, 1st stage discharge pressure = 3 x 100 psia = 300 psia

Step 5 – Determine Suction Pressure for 2nd Stage

Suction pressure for 2nd stage is not the same as 1st stage discharge pressure. We must consider pressure drop between first stage discharge pressure and second stage suction. Let say, pressure drop is 5 psi.

Then 2nd stage suction pressure = 1st stage discharge pressure – pressure drop = 300 – 5 = 295 psi

Step 6 – Determine Compression Ratio for 2nd Stage

As we considered pressure drop between 1st stage discharge pressure and 2nd stage suction pressure, compression ratio of 2nd stage is no longer the same as compression ratio of 1st stage.

Compression ratio for 2nd stage compression in 2-stage compression = discharge pressure / 2nd stage suction pressure.

So we get compression ratio is 900 / 295 = 3.05

How if number of compression is 3?

Then compression ratio for 2nd stage = (discharge pressure/2nd stage suction pressure)^(1/2)

How about 4-stage of compression?

Then, compression ratio for 2nd stage = (discharge pressure/2nd stage suction pressure)^(1/3)

Step 7 – Determine k value (heat-capacity ratio)

K value or heat-capacity ratio is function of molecular weight and temperature. We will determine K value by curve. For most compression application, 150oF curve will be adequate. This should be checked after determining the average cylinder temperature.

So, for molecular weight 23 and temperature of 150oF, we get K value of 1.21.

Heat-capacity ratio (k-value)
Heat-capacity ratio (k-value)

Step 8 – Determine discharge temperature of 1st stage compression

Discharge temperature of compressor is function of compression ratio and K value. We can determine discharge temperature by chart. For compression ratio 3 at first stage compression, K value of 1.21, and suction temperature of 100oF, we get discharge temperature of 1st stage compression is 220oF.

Theoretical discharge temperature of compression
Theoretical discharge temperature of compression

Step 9 – Determine cylinder temperature of 1st stage compression

Cylinder temperature of 1st stage compression is average of suction temperature (100oF) and discharge temperature of 1st stage compression (220oC). Therefore, cylinder temperature of 1st stage compression is 160oF.

Step 10 – Determine discharge temperature of 2nd stage compression

Step 10 is the same as Step 8. Assuming inter-stage cooling to 120oF.

For compression ratio 3.05 at first stage compression, K value of 1.21, and suction temperature of 120oF, we get discharge temperature of 2nd stage compression is 244oF.

Theoretical discharge temperature of compression
Theoretical discharge temperature of compression

Step 11 – Determine cylinder temperature of 2nd stage compression

The method used is the same as Step 9. Cylinder temperature is average of suction temperature at 2nd stage (120oF) and discharge temperature (244oF). Therefore, cylinder temperature is 182oF.

Step 12 – Estimate compressibility factor (Z factor) at suction and discharge condition at each compression stage

From calculation above, we get:

1st stage (P suction = 100 psia, T suction = 100oF)

1st stage (P discharge = 300 psia, T discharge = 220oF) ____ see Step 4 and Step 8

 

2nd stage (P suction = 295 psia, T suction = 120oF) ____ see Step 5 and Step 10. Assuming inter-stage cooling to 120oF

2nd stage (P discharge = 900 psia, T discharge = 244oF ____ (see step 11)

 

Based on operating condition above, we will check compressibility factor based on charts. Please note that each chart is function of gas molecular weight. So, ensure you use proper chart.

In this example, molecular weight of gas is 23. So, I will use compressibility factor for gas with molecular weight 23.20.

Compressibility factor for gas with MW 23.20
Compressibility factor for gas with MW 23.20

1st stage, Z factor at suction condition = 0.98 (red line)

1st stage, Z factor at discharge condition = 0.97 (green line)

Average Z factor = (0.98 + 0.97)/2 = 0.975

 

Calculate the same thing for 2nd stage

2nd stage, Z factor at suction condition = 0.92 (blue line)

1st stage, Z factor at discharge condition = 0.90 (pink line)

Average Z factor = (0.92 + 0.90)/2 = 0.91

Step 13 – Estimate BHP per MMcfd from Chart

BHP per MMcfd is a function of compression ratio and K value. BHP per MMcfd read from figure below use a pressure base of 14.4 psia.

BHP per MMcfd
BHP per MMcfd

For compression ratio 3, and k value 1.21, we get BHP per MMcfd is 63 (1st stage) (red line)

For compression ratio 3.05, and k value 1.21, we get BHP per MMcfd is 64.5 (2nd stage) (yellow line)

Step 14 – Check correction factor for low intake pressure and for specific gravity

Based on figure below, for ratio of compression 3 and 3.05, correction factor for low intake pressure is 1.

Correction factor for low intake pressure
Correction factor for low intake pressure

Based on figure below, for ratio of compression 3 and 3.05, correction factor for specific gravity is 1.

Correction factor for specific gravity
Correction factor for specific gravity

Step 15 (Last Step) – Calculate BHP for each stage and total BHP

BHP = (BHP/MMcfd) x (PL/14.4) x (TS/TL) x (Z average) x (MMcfd)

PL is pressure base, which is 14.65 psia

Ts is suction temperature, which is 100oF (560oR)

TL is temperature base, which is 60oF (520oR)

For 1st stage, BHP is 63 x (14.65/14.4) x (560/520) x 2 = 134.6

 

For 2nd stage, T suction is 120oF (580oR)

Using the same equation, BHP is 64.5 x (14.65/14.4) x (580/520) x 2 = 133.2

Total BHP is 134.6 + 133.2 = 267.81

Based on calculation above, we can illustrate the results below.

I also tried using Ariel Commercial to check if the result is similar. I found that the BHP is 288.58 which is about 8% higher than above calculation.

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