Introduction
Using the centrifugal compressor application resets when the head is developed by increasing gas velocity to create kinetic energy. As compression ratio drops, adiabatic efficiency drops.
One limitation of the calculation is that it does not consider the heat gained or lost.
Adiabatic Head:
H_a = z_s R_c T_s \frac{k}{k – 1} \left[ \left( \frac{P_d}{P_s} \right)^{\frac{k – 1}{k}} – 1 \right] \~\ R_c = \frac{1545.3}{MW}
H_a = z_s R_c T_s \frac{k}{k - 1} \left[ \left( \frac{P_d}{P_s} \right)^{\frac{k - 1}{k}} - 1 \right] \\~\\ R_c = \frac{1545.3}{MW}
Where:
𝐻𝑎 − Adiabatic Head (ft*lbf/lbm)
𝑧𝑠 − Compressibility Factor at Suction Conditions
𝑅𝑐 − Specific Gas Constant (ft*lbf/lbm°𝑅)
𝑀𝑊 − Molecular Mass of Gas (lb/lb*mol)
𝑇𝑠 − Gas Suction Temperature (°𝑅)
𝑘 = (𝑐𝑝/𝑐𝑣) − Specific Heat Ratio
𝑃𝑑 − Discharge Pressure (psia)
𝑃𝑠 − Suction 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)
Case Guide
Part 1: Create Case
- Select the Adiabatic Head 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)
- Pressure Upstream (psig)
- Pressure Downstream (psig)
- Specific Gravity
- Molecular Weight
- Gas Specific Heat Ratio
- Adiabatic 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
- Discharge Temperature (°F)
- Z1 – Compressibility Factor at Suction Conditions
- Adiabatic Head (ft-lbf/lbm)
- Adiabatic GHP per Unit of the Flowrate (HP/MMSCFD)
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