Centrifugal Compressor – Required Polytropic Horsepower

Contents

Introduction

This application uses initial impeller speed and final impeller rotational speed to determine final flow rate, compression head and final shaft Horsepower (HP). One drawback is the difficulty to determine efficiency which is based on the ratio of specific heat for the gas being used in the compressor.

Polytropic Compressor Horsepower:

HP = 0.0857 \left( \frac{n}{n – 1} \right) Q T_1z_{\text{avg}}\frac{1}{n_p} \left[ \left( \frac{P_2}{P_1} \right)^{\frac{n-1}{n}} – 1 \right] \text{ in [HP]} \~\ or\~\HP = 0.0857 \left( \frac{n}{n – 1} \right) T_1z_{\text{avg}} \frac{1}{n_p} \left[\left( \frac{P_2}{P_1} \right)^{\frac{n-1}{n}} – 1 \right] \text{ in [HP/MMSCFD]} \~\ z_{\text{avg}} = \frac{z_1 + z_2}{2} \~\ n_p=\left(\frac{k-1}{k} \right)\left( \frac{n}{n-1} \right)

HP = 0.0857 \left( \frac{n}{n - 1} \right) Q T_1z_{\text{avg}}\frac{1}{n_p} \left[ \left( \frac{P_2}{P_1} \right)^{\frac{n-1}{n}} - 1 \right] \text{ in [HP]} \\~\\ or\\~\\HP = 0.0857 \left( \frac{n}{n - 1} \right) T_1z_{\text{avg}} \frac{1}{n_p} \left[\left( \frac{P_2}{P_1} \right)^{\frac{n-1}{n}} - 1 \right] \text{ in [HP/MMSCFD]} \\~\\ z_{\text{avg}} = \frac{z_1 + z_2}{2} \\~\\ n_p=\left(\frac{k-1}{k} \right)\left( \frac{n}{n-1} \right)

Where:
𝐻𝑃 − Polytropic Compressor Horsepower
𝑛 − Polytropic Gas Exponent
𝑄 − Gas Flow Rate (MMSCFD)
𝑇₁ − Suction Temperature (°𝑅)
𝑇₂ − Discharge Temperature (°𝑅)
𝑧₁ − Compressibility of Gas at Suction Conditions
𝑧₂ − Compressibility of Gas at Discharge Conditions
𝑧_𝑎𝑣𝑔 − Average Compressibility Factor
𝑘 = (𝑐𝑝/𝑐𝑣) − Specific Heat Ratio
𝑛_𝑎 − Compressor Polytropic Efficiency
𝑃₁ − Gas Suction Pressure (psia)
𝑃₂ − Gas Discharge Pressure (psia)

CNGA/GPSA Compressibility Factor Approximation:

Z=\frac{1}{\left[1+\left(\frac{3.444\times10^5P\times10^{1.785G}}{T_f^{3.825}} \right)\right]}

Z=\frac{1}{\left[1+\left(\frac{3.444\times10^5P\times10^{1.785G}}{T_f^{3.825}} \right)\right]}

Where:
𝑍 − Compressibility Factor
𝑃 − Pressure
𝑇_𝑓 − Gas Flowing Temperature (°𝑅)

Brake Horsepower

BHP=\frac{HP}{n_m}

BHP=\frac{HP}{n_m}

Where:
𝑛𝑚 − Mechanical Efficiency 𝑛𝑚 = 0.95/0.98

Case Guide

Part 1: Create Case

Select the Required Polytrophic Horsepower application from the Compressor Module
To create a new case, click the “Add Case” button
Enter Case Name, Location, Date and any necessary notes.
Fill out all required Parameters.
Make sure the values you are inputting are in the correct units.
Click the CALCULATE button to overview results.

Input Parameters

Suction Temperature Upstream (°F)
Base Temperature (°F)
Base Pressure (psi)
Suction Pressure Upstream (psig)
Discharge Pressure Downstream (psig)
Capacity/Required Flow Rate (MMSCFD)
Gas Specific Gravity (Relative to air)
Gas Molecular Weight
Gas Specific Heat Ratio
Adiabatic Efficiency (0.75 – 0.79)
Mechanical Efficiency (0.95 – 0.98)
Polytropic Efficiency
Compressibility Factor

Part 2: Outputs/Reports

If you need to modify an input parameter, click the CALCULATE button after the change.
To SAVE, fill out all required case details then click the SAVE button.
To rename an existing file, click the SAVE As button. Provide all case info then click SAVE.
To generate a REPORT, click the REPORT button.
The user may export the Case/Report by clicking the Export to Excel icon.
To delete a case, click the DELETE icon near the top of the widget.

Results

Polytopic Exponent
Discharge Temperature (°F)
Zavg – Average Compressibility Factor
Adiabatic Head (ft lbf/lbm)
Polytopic GHP per Unit of the Flowrate (HP/MMSCFD)
GHP – Adiabatic Gas Horsepower (HP)
BHP – Adiabatic Brake Horsepower (HP)
ACFM – Actual Flow Rate for Sizing (SCFM)

References

Engineering Data Book, Volume 1, Gas Processors Suppliers Association, Tenth Edition
Compressor Station Operation, Book T-2, GEOP, American Gas Association (A.G.A.)
Compressor Selection and Sizing, Royce N. Brown, Second Edition, Gulf Professional Publishing

Updated on January 4, 2024

Tagged: Calculations Pipeline Compressors

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