Turbomachinery, Pipeline Gas Compression & Process Engineering
Polytropic Centrifugal Gas Compressor Temp & Power Formula
Calculate Centrifugal Gas Compressor Polytropic Temperature Exponent, Discharge Temperature T2 (K), Polytropic Specific Enthalpy Rise (kJ/kg), and Gas Compression Power (kW).
Divide the isentropic exponent (k-1)/k by polytropic efficiency eta_p—or underpredict T2 seal limits!
In multistage pipeline and refinery centrifugal compressors (ASME PTC 10), stage impeller friction heats the gas continuously as it compresses, increasing the volume of subsequent stages (the preheat factor)! Consequently, Polytropic Temperature Exponent is (n - 1) / n = ((k - 1) / k) / eta_p, Actual Discharge Temperature is T_2 = T_1 * (P_2 / P_1)^(((k - 1) / k) / eta_p), and Gas Compression Power is W_gas = m_dot * c_p * (T_2 - T_1)! Using the textbook reversible isentropic exponent (k - 1) / k underpredicts discharge temperature by 20–35 K, risking dry-gas seal elastomer failure above ~420–450 K!
Verify on a Natural-Gas Pipeline Booster Stage—Suction_Temp T_1 = 300.0 K (26.85°C, B2), Stage_Pressure_Ratio P_2/P_1 = 3.00 (20 bar -> 60 bar, B3), Specific_Heat_Ratio k = 1.28 (B4), Polytropic_Efficiency eta_p = 0.80 (80.0%, B5 -> Polytropic Exponent = (0.28 / 1.28) / 0.80 = 0.2734 in E2), Gas_Cp = 2.25 kJ/(kg·K) (B6), and Mass_Flow = 12.0 kg/s (B7): Discharge Temperature T_2 reaches 300 * 3^0.2734375 = 405.12 K (131.97°C, E3), Specific Enthalpy Rise is 236.52 kJ/kg (E4), and Gas Power equals 2,838.25 kW (E5)!
| ASME PTC 10 Polytropic Compressor KPI (300 K, PR = 3.0, k = 1.28, eta_p = 80%) | Formula | Verified Output |
|---|---|---|
| Polytropic Temp Exponent (n-1)/n | ((k - 1) / k) / Polytropic_Efficiency | 0.2734 (0.2188 Isentropic) |
| Discharge Temperature T2 (K) | T1_K * Pressure_Ratio ^ ((n - 1) / n) | 405.12 K (381.50 K Isentropic) |
| Specific Enthalpy Rise (kJ/kg) | Cp_kJ_kgK * (T2_K - T1_K) | 236.52 kJ/kg |
| Gas Compression Power (kW) | Mass_Flow_kg_s * Cp_kJ_kgK * (T2_K - T1_K) | 2,838.25 kW (2,200.43 Ideal) |
Polytropic Discharge Temperature & Gas Power Formula
Validate Suction_Temp_K > 100, Pressure_Ratio > 1.0, Gas_k in (1.01, 1.67], Polytropic_Efficiency in (0.40, 1.0], Gas_Cp > 0, and Mass_Flow > 0!
=LET(t_in, B2, pr_r, B3, k_ga, B4, et_p, B5, cp_g, B6, m_fl, B7, IF(OR(t_in <= 100, pr_r <= 1, k_ga <= 1.01, k_ga > 1.67, et_p <= 0.4, et_p > 1, cp_g <= 0, m_fl <= 0), "Invalid Compressor Input", LET(ex_p, ((k_ga - 1) / k_ga) / et_p, t_ou, t_in * (pr_r ^ ex_p), ROUND(m_fl * cp_g * (t_ou - t_in), 2))))Reversible Isentropic Lower-Bound Check (Set Polytropic Efficiency = 1.00)
Set Polytropic_Efficiency B5 to 1.00 (reversible isentropic baseline): Discharge Temperature E3 drops by 23.62 K from 405.12 K to 381.50 K, and Ideal Gas Power E5 drops to 2,200.43 kW!
=IF(ISTEXT(E5), E5, ROUND(B2 * (B3 ^ (((B4 - 1) / B4) / B5)), 2))Try the example
Use the original values or change them to test your understanding.