Compressor head and power
Isentropic or polytropic head, gas and shaft power and discharge temperature for a gas compressor — one stage or several with intercooling.
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How this calculator works
The head per stage is H = (Z·R·T1/MW)·(1/e)·(re − 1), with e = (k − 1)/k for isentropic head or e = (n − 1)/n for polytropic head, where (n − 1)/n = (k − 1)/(k·ηp). Gas power is mass flow × head ÷ efficiency of the same kind (Branan, Rules of Thumb for Chemical Engineers, compressors). Discharge temperature is T1·r(n−1)/n for polytropic, or T1·[1 + (r(k−1)/k − 1)/ηis] for isentropic. With more than one stage the pressure ratio is split equally, which gives close to the least total work with full intercooling (Silla, Chemical Process Engineering, ch. 5).
The example is 100,000 Nm³/h of natural gas (MW 18, k 1.27, Z 0.95) from 20 to 60 bar a at 35 °C with 78 % polytropic efficiency: head 173.2 kJ/kg, discharge 142.6 °C, shaft power about 5,050 kW. As a hand check, air (k 1.4) from 1 to 4 bar a at 30 °C with 80 % isentropic efficiency needs 148.0 kJ/kg and leaves at 214.2 °C.
Limits: ideal gas with an average Z and constant k; no intercooler pressure drop, side streams or liquid knock-out. For gases near their critical point or with large Z changes, use a process simulator. References: Branan (compressors, horsepower calculation); Silla (polytropic compression, optimum stage ratio); Perry's §10 (compressors); GPSA Engineering Data Book Section 13.