Number of compressor stages
The fewest stages for a total pressure ratio, limited by the ratio per stage and by the discharge temperature; the pressure ratio and discharge temperature of each stage.
ε_T = (1 + η_s · (T_max / T_1 − 1))^(k/(k−1))ε_T = (T_max / T_1)^(k · η_p / (k−1))N = ⌈ln(p_2 / p_1) / ln(min(ε_max, ε_T))⌉ε = (p_2 / p_1)^(1/N)The stages have equal pressure ratios and the gas is cooled to T_1 after each stage. The temperature is usually the limit: the heavier the gas (the lower k), the less it heats up and the higher the stage ratio it allows. Pressure losses in the coolers raise the stage ratios by a few percent.
Source: GPSA Engineering Data Book, Section 13; API 618 — discharge temperature limit
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Air 1.40; natural gas 1.26–1.30; rich associated gas 1.15–1.25.
Set by the machine design; usually 3–4 for reciprocating compressors.
API 618: predicted discharge temperature not above 150 °C, 135 °C for hydrogen-rich gases.
Unit converter for this formulaPressure · Temperature · Fraction and percent
- MPa1
- kPa1,000
- bar10
- atm9.86923
- kgf/cm²10.1972
- mmHg7,500.62
- MPa(g)0.898675
- barg8.98675
- psi145.038
- psia145.038
- psig130.342
- ksi0.145038
psi and psia are absolute pressure; gauge units (barg, MPa(g), psig) are above atmospheric (101.325 kPa = 14.696 psi). Pressure differences in the formulas do not depend on this.
- ε — Pressure ratio per stage–
- T_2 — Stage discharge temperature–
- ε_T — Pressure ratio limit set by the temperature–
More in Compressors
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.