Compressor power and discharge temperature
Gas compression power in one stage or several stages with intercooling — from the isentropic or polytropic efficiency with the gas compressibility — the pressure ratio per stage and the discharge temperature.
ε = (p_2 / p_1)^(1/N)T_2 = T_1 · (1 + (ε^((k−1)/k) − 1) / η_s)T_2 = T_1 · ε^((k−1)/(k · η_p))P = N · Z · p_st · Q_st · (T_1 / T_st) · k / (k − 1) · (T_2 / T_1 − 1)Pressures are absolute, the flow rate is at standard conditions (20 °C, 101.325 kPa). The stages have equal pressure ratios and the gas is cooled to T_1 before each of them, which gives the least total power; pressure losses in the coolers and valves are not included. The motor rating adds the mechanical losses and a 10–15 % margin. API 618 limits the discharge temperature of reciprocating compressors (150 °C) — see the "Number of compressor stages" calculator.
Source: GPSA Engineering Data Book, Section 13 Compressors and Expanders; API 617, API 618
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Gas volume at 20 °C and 101.325 kPa. For air compressors 1 m³/min ≈ 1.44 thousand m³/d.
Absolute = gauge + 0.101 MPa.
With intercooling, the gas is cooled to this temperature before every stage.
Air and nitrogen 1.40; methane 1.30; natural gas 1.26–1.30; rich associated gas 1.15–1.25; CO₂ 1.29.
(Z_1 + Z_2) / 2; below 1 MPa Z ≈ 1, natural gas at 5–10 MPa and 20–40 °C 0.82–0.92.
Reciprocating compressors: isentropic efficiency about 75–85 %; centrifugal: polytropic about 70–85 %. Mechanical losses (2–5 %) are not included.
Unit converter for this formulaGas rate · Pressure · Temperature · Power · Fraction and percent
- Sm³/d1
- 10³ Sm³/d0.001
- 10⁶ Sm³/d1·10⁻⁶
- Sm³/h0.0416667
- 10⁹ Sm³/yr3.65·10⁻⁷
- scf/d34.7793
- Mscf/d0.0347793
- MMscf/d3.47793·10⁻⁵
Gas at standard conditions, 101.325 kPa: Sm³ at 20 °C (GOST 2939, used in Kazakhstan), Sm³ (15 °C) per ISO 13443 and SPE, Nm³ at 0 °C, scf at 60 °F. Gas volumes convert by the ideal-gas law, so 1 Sm³ = 34.78 scf (not 35.31 as for a geometric volume).
- ε — Pressure ratio per stage–
- T_2 — Stage discharge 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.