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
𝑧𝑎𝑣𝑔 − Average Compressibility Factor
𝑘 = (𝑐𝑝/𝑐𝑣) − Specific Heat Ratio
𝑛𝑎 − 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
𝑇𝑓 − 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