Polytropic Head β’ Discharge Temperature β’ Stages β’ Power β’ Z-effect β’ Anti-surge (Screening)
Scope: Polytropic compression screening for centrifugal/axial style estimation.
Anti-surge is an approximate control-line estimate; real surge line must come from OEM map.
Suction / Discharge Conditions
Gas Properties
Performance Assumptions
Flow
Staging Limits (Design Rules)
Anti-surge (Screening)
Compression Results
Overall Pressure Ratio, PR:-
Polytropic Exponent used, n:-
Avg Compressibility, Zavg:-
Polytropic Head, Hp:-
Discharge Temperature, T2:-
Staging Estimate
Stages Required (by PR & T2):-
Estimated Stage PR:-
Estimated T2 per Stage:-
Power
Gas Power (shaft), Pgas:-
Driver Power, Pdriver:-
Anti-surge (Screening)
Estimated Surge Control Flow:-
Recommended Min Operating Flow:-
Formulas (screening):
1) Overall pressure ratio: PR = P2/P1
2) If n is blank, an effective polytropic exponent is derived from k and Ξ·p using:
(nβ1)/n = (kβ1)/(kΒ·Ξ·p) β n = 1 / (1 β (kβ1)/(kΒ·Ξ·p))
3) Polytropic head (per kg): Hp = (n/(nβ1)) Β· (ZavgΒ·RspecΒ·T1) Β· (PR((nβ1)/n) β 1)
4) Discharge temperature (polytropic path): T2 = T1 Β· PR((nβ1)/n)
5) Specific gas constant: Rspec = Ru/MW, with Ru=8314.462618 J/(kmolΒ·K)
6) Power: Pgas = αΉ(kg/s) Β· Hp (W); Driver power = Pgas /(Ξ·mΒ·Ξ·d) Note: Zavg is taken as (Z1+Z2)/2 for screening. For rigorous work use an EOS and OEM map.
Technical Notes
Purpose: This tool is intended for preliminary/screening estimates for compressor polytropic head,
discharge temperature, staging and power. Final selection and surge control must be based on the OEM compressor map
and validated real-gas properties (EOS) for the specified composition and operating envelope.
Variable Definitions
P1, P2 = suction & discharge absolute pressure (bar(a)) T1 = suction temperature (Β°C), converted internally to Kelvin (K) T2 = estimated discharge temperature (Β°C) along a polytropic path PR = overall pressure ratio = P2/P1 (dimensionless) MW = molecular weight (kg/kmol) k = Cp/Cv at suction (dimensionless) Z1, Z2 = compressibility factors at suction & discharge (dimensionless); Zavg=(Z1+Z2)/2 (screening) Ξ·p = polytropic efficiency (dimensionless, 0β1) n = polytropic exponent (dimensionless). If provided by user it is treated as the actual exponent. αΉ = mass flow rate (kg/h), converted internally to kg/s Hp = polytropic head per unit mass (J/kg, shown as kJ/kg) Pgas = gas power at shaft (kW), Pdriver = required driver power (kW) including Ξ·m and Ξ·d
Formulas / Logic
1) Polytropic exponent:
If n is blank, an effective n is derived from k and Ξ·p using:
(nβ1)/n = (kβ1)/(kΒ·Ξ·p). This is a common compressor screening relationship linking efficiency to the effective polytropic path.
2) Discharge temperature (screening):
T2 = T1 Β· PR^((nβ1)/n) (Kelvin). (For rigorous prediction, use EOS + vendor polytropic correlations).
5) Staging estimate:
Stages are estimated from (a) maximum allowable per-stage PR and (b) temperature limit per-stage based on intercooling assumption.
This is a design-rule check only; OEM maps and mechanical limits govern final stage count/casing selection.
6) Anti-surge screening:
If suction volumetric flow is not provided, Q1 is estimated from ideal-gas density with Z1:
Ο1 = P1Β·MW / (Z1Β·RuΒ·T1). Then Q1 = αΉ/Ο1. The surge control flow and minimum operating flow are screening heuristics;
actual surge and control lines must be derived from the OEM map and control philosophy.
Assumptions / Notes / References
β’ Preliminary estimation tool; not a substitute for OEM performance curves or test procedures.
β’ Real-gas behavior is approximated via user-provided Z1 and Z2; for high pressure/complex mixtures, use an EOS (e.g., PengβRobinson) from a simulator.
β’ Applicable industry references for terminology and compressor practice include API 617 (axial & centrifugal compressors) and performance/testing practices such as ASME PTC 10 (compressor performance test code).
β’ Temperature limits depend on gas, seals, metallurgy, lube oil, and vendor limitsβalways confirm allowable T2 with project/vendor data sheets.
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