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Centrifugal Compressor – Required Adiabatic Horsepower

Contents

Introduction

This application uses a compression unit that calculates a natural gas-fired turbine to turn a centrifugal compressor. The centrifugal compressor is like a large fan inside a case, which pumps the gas as the fan turns.

Size of the fan and speed within the case controls the pumping action.

Adiabatic Compressor Horsepower:

HP = 0.0857 \left( \frac{k}{k – 1} \right) Q T_1z_{\text{avg}}\frac{1}{n_a} \left[ \left( \frac{P_2}{P_1} \right)^{\frac{k-1}{k}} – 1 \right] \text{ in [HP]} \~\ or\~\HP = 0.0857 \left( \frac{k}{k – 1} \right) T_1z_{\text{avg}} \frac{1}{n_a} \left[\left( \frac{P_2}{P_1} \right)^{\frac{k-1}{k}} – 1 \right] \text{ in [HP/MMSCFD]} \~\ z_{\text{avg}} = \frac{z_1 + z_2}{2} \~\ n_a = \left( \frac{T_1}{T_2 – T_1} \right) \left[ \left( \frac{z_1}{z_2} \right) \left( \frac{P_2}{P_1} \right)^{\frac{k-1}{k}} – 1 \right]

HP = 0.0857 \left( \frac{k}{k - 1} \right) Q T_1z_{\text{avg}}\frac{1}{n_a} \left[ \left( \frac{P_2}{P_1} \right)^{\frac{k-1}{k}} - 1 \right] \text{ in [HP]} \\~\\ or\\~\\HP = 0.0857 \left( \frac{k}{k - 1} \right) T_1z_{\text{avg}}  \frac{1}{n_a} \left[\left( \frac{P_2}{P_1} \right)^{\frac{k-1}{k}} - 1 \right] \text{ in [HP/MMSCFD]} \\~\\ z_{\text{avg}} = \frac{z_1 + z_2}{2} \\~\\ n_a = \left( \frac{T_1}{T_2 - T_1} \right) \left[ \left( \frac{z_1}{z_2} \right) \left( \frac{P_2}{P_1} \right)^{\frac{k-1}{k}} - 1 \right]

Where:
𝐻𝑃 βˆ’ Adiabatic Compressor Horsepower
𝑄 βˆ’ Gas Flow Rate (MMSCFD)
𝑇1βˆ’Suction Temperature (°𝑅)
𝑇2 βˆ’ Discharge Temperature (°𝑅)
𝑧1 βˆ’ Compressibility of Gas at Suction Conditions
𝑧2 βˆ’ Compressibility of Gas at Discharge Conditions
π‘§π‘Žπ‘£π‘” βˆ’ Average Compressibility Factor
π‘˜ = (𝑐𝑝/𝑐𝑣) βˆ’ Specific Heat Ratio
π‘›π‘Ž βˆ’ Compressor Adiabatic (Isentropic) Efficiency
𝑃1 βˆ’ Gas Suction Pressure (psia)
𝑃2 βˆ’ 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 βˆ’ Compressibility Factor
𝑃 βˆ’ Pressure
𝑇𝑓 βˆ’ Gas Flowing Temperature (°𝑅)

Brake Horsepower

BHP=\frac{HP}{n_m}

BHP=\frac{HP}{n_m}

Where:
π‘›π‘š βˆ’ Mechanical Efficiency π‘›π‘š = 0.95/0.98

Case Guide

Part 1: Create Case

  1. Select the Required Adiabatic Horsepower application from the Compressor Module
  2. To create a new case, click the β€œAdd Case” button
  3. Enter Case Name, Location, Date and any necessary notes.
  4. Fill out all required Parameters.
  5. Make sure the values you are inputting are in the correct units.
  6. Click the CALCULATE button to overview results.

Input Parameters

  • Suction Temperature Upstream (Β°F)
  • Base Temperature (Β°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)
  • Z1 – Compressibility Factor at Suction Conditions
  • Z2 – Compressibility Factor at Discharge Conditions

Part 2: Outputs/Reports

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

Results

  • Discharge Temperature (Β°F)
  • Zavg – Average Compressibility Factor
  • Adiabatic Head (ft lbf/lbm)
  • Adiabatic GHP per Unit of the Flowrate (HP/MMSCFD)
  • GHP – Adiabatic Gas Horsepower (HP)
  • BHP – Adiabatic Brake Horsepower (HP)
  • ACFM – Actual Flow Rate for Sizing (ftΒ³/min)

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
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