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 60^oF. Intake pressure is 100 psia, and intake temperature is 100^oF. 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 1^st Stage Discharge Pressure

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

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

Step 5 – Determine Suction Pressure for 2^nd Stage

Suction pressure for 2^nd stage is not the same as 1^st 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 2^nd stage suction pressure = 1^st stage discharge pressure – pressure drop = 300 – 5 = 295 psi

Step 6 – Determine Compression Ratio for 2^nd Stage

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

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

So we get compression ratio is 900 / 295 = 3.05

How if number of compression is 3?

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

How about 4-stage of compression?

Then, compression ratio for 2^nd stage = (discharge pressure/2^nd 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, 150^oF curve will be adequate. This should be checked after determining the average cylinder temperature.

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

Step 8 – Determine discharge temperature of 1^st 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 100^oF, we get discharge temperature of 1^st stage compression is 220^oF.

Step 9 – Determine cylinder temperature of 1^st stage compression

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

Step 10 – Determine discharge temperature of 2^nd stage compression

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

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

Step 11 – Determine cylinder temperature of 2^nd stage compression

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

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

From calculation above, we get:

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

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

 

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

2^nd stage (P discharge = 900 psia, T discharge = 244^oF ____ (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.

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

1^st 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 2^nd stage

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

1^st 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.

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

For compression ratio 3.05, and k value 1.21, we get BHP per MMcfd is 64.5 (2^nd 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.

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

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

BHP = (BHP/MMcfd) x (P_L/14.4) x (T_S/T_L) x (Z _average) x (MMcfd)

P_L is pressure base, which is 14.65 psia

T_s is suction temperature, which is 100^oF (560^oR)

T_L is temperature base, which is 60^oF (520^oR)

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

 

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

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.