FieldEngineersKitEngineering Reference & ASME Code Basis
1. Core Formula & Variable Definitions
GPSA Engineering Data Book — Section 13 Compressors and Expanders (polytropic head & power) · API Standard 617 — Axial and Centrifugal Compressors and Expander-compressors (Clause 4.1 & Annex E context) · ASME PTC 10 — Performance Test Codes on Compressors and Exhausters (acceptance context)
Pressure ratio: rp = P2 / P1
Polytropic exponent: (n−1)/n = (k−1)/(k·ηp)
Polytropic head: Hp = (Zavg·R·T1/M)·(n/(n−1))·[rp(n−1)/n − 1]
Gas power & T₂: Pgas = ṁ·Hp/ηp · T2 = T1·rp(n−1)/n
GPSA Engineering Data Book Sec. 13 · API 617 · ASME PTC 10 screening
R = 8.314462618 kJ/(kmol·K). M in kg/kmol (= g/mol numeric). ρ₁ = P₁ M /(Z R T₁) with absolute suction pressure. Screening only — confirm OEM performance maps, multi-stage layout, and real-gas EOS.
- r_p (Pressure ratio) — P₂/P₁ absolute suction and discharge pressures.
- (n−1)/n (Polytropic exponent factor) — (k−1)/(k·η_p) with k = Cp/Cv and polytropic efficiency η_p.
- H_p (Polytropic head) — Specific polytropic work (kJ/kg or ft·lbf/lb) from GPSA-style relation.
- P_gas (Gas power) — ṁ·H_p/η_p (kW or hp). Mass flow from Q₁·ρ₁ at suction.
- T₂ (Discharge temperature) — T₁ · r_p^((n−1)/n) absolute temperatures.
- Z_avg (Average compressibility) — User/screening Z between suction and discharge (not a full EOS solve).
2. Screening Rules Matching This Calculator
GPSA polytropic head with (n−1)/n = (k−1)/(k η_p), gas power = ṁ H_p / η_p, and T₂ = T₁ r_p^((n−1)/n). OEM maps, PTC 10 tests, and full EOS Z are out of scope.
Hero ≈ 1902 kW · 219.6 °C with H_p ≈ 270.2 kJ/kg, r_p = 5 (high T₂ and high r_p alerts).
API 617 single-stage screening cue for seals/gas quality — recommend intercooled multi-stage above this band.
Single-stage centrifugal duties above ≈ 4.5 warrant stage split for stress and efficiency.
No impeller aerodynamics, surge control, or Lee–Kesler/RK Z solve. Confirm with vendor rating.
Quick Reference Lookup Table
| Quantity | Value | Unit | Notes |
|---|---|---|---|
| r_p | 5.00 | — | P₂/P₁ |
| (n−1)/n | 0.2917 | — | (k−1)/(k η_p) |
| H_p | 270.2 | kJ/kg | GPSA polytropic head |
| T₂ | 219.6 | °C | High-temp alert (>150 °C) |
| ρ₁ | 3.800 | kg/m³ | P M /(Z R T) at suction |
| ṁ | 19 002 | kg/h | Q₁ · ρ₁ |
| P_gas | 1902 | kW | ṁ H_p / η_p |
| Air 1.013→7 bar · 1000 m³/h · 72% | 114 kW · 358 °C | kW / °C | H_p ≈ 244.5 kJ/kg |
| NG 70→350 psia · 3000 ICFM · 75% | 2510 hp · 427 °F | hp / °F | Same r_p = 5 polytropic path |
| N₂ 15→90 psia · 1500 ICFM · 70% | 370 hp · 641 °F | hp / °F | H_p ≈ 77 200 ft·lbf/lb |
Hero reports polytropic gas power and discharge temperature. Default NG duty asserts H_p ≈ 270.2 kJ/kg, T₂ ≈ 219.6 °C, P_gas ≈ 1902 kW (suction density included). Spec LLM heroes that omit ρ₁ are discarded.
3. Applicability & Gas / Regime Limits
Fluid and single-stage regime limits for this screening tool. Metallurgy is not computed — select materials from PMS / API 617 separately.
| Group / Regime | Range / Condition | Limit / Criterion | Engineering Notes |
|---|---|---|---|
| Lean natural gas / air / nitrogen (constant k, Z) | T₁ −50–200 °C screening | Z_avg 0.5–1.5 user/screen | Uses handbook MW and k defaults. Custom gas requires user M, k, and Z_avg. |
| Single-stage high pressure ratio | r_p > 4.5 warn | Mechanical / efficiency screen | Split stages when r_p exceeds the single-stage screen to limit temperature rise and casing stress. |
| High discharge temperature | T₂ > 150 °C (302 °F) | Seal / O-ring / packing screen | API 617 context recommends intercooling / multi-stage when discharge temperature exceeds this band. |
| High-pressure real-gas band | P₂ > 50 bar(a) | Constant-Z may understate H_p | Confirm Z_avg with Lee–Kesler or Redlich–Kwong EOS — not solved inside this calculator. |
Code Applicability & Safety Boundaries
- Not a substitute for OEM performance maps or ASME PTC 10 acceptance tests
- T₂ > 150 °C and r_p > 4.5 trigger screening warnings
- Constant Z_avg — no full EOS integration
4. Step-by-Step Worked Example
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Worked Example — Natural Gas 5→25 bar(a)
Screen a single-stage centrifugal compressor raising lean natural gas from 5 bar(a) to 25 bar(a) at 35 °C suction with 5000 m³/h inlet volume flow, η_p = 75%, M = 18.5, k = 1.28, Z_avg = 0.95.
Pressure ratio and polytropic factor
Polytropic head
Discharge temperature
Suction density, mass flow, gas power
5. How to calculate compressor polytropic gas power
- 1
Select gas and enter M, k, Z_avg
Choose air, natural gas, nitrogen, or custom. Confirm molecular weight, specific heat ratio, and average compressibility.
- 2
Enter absolute suction and discharge pressures
Use bar(a) or psia. Discharge must exceed suction. Pressure ratio r_p = P₂/P₁ drives head and T₂.
- 3
Set suction temperature, inlet volume flow, and η_p
Enter T₁, Q₁ (m³/h or ICFM), and polytropic efficiency percent (typically 60–88%).
- 4
Read P_gas, T₂, H_p, and screening alerts
Hero shows gas power and discharge temperature. Review T₂ > 150 °C and r_p > 4.5 warnings before OEM selection.
6. Frequently Asked Questions & Technical References
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FEK uses the GPSA form H_p = (Z_avg·R·T₁/M)·(n/(n−1))·[r_p^((n−1)/n) − 1] with (n−1)/n = (k−1)/(k·η_p).
Inlet volume flow Q₁ is converted with ρ₁ = P₁ M /(Z R T₁) so ṁ = Q₁·ρ₁. Omitting density understates power at elevated suction pressure.
When r_p > 4.5 or T₂ > 150 °C (302 °F), API 617 screening practice recommends splitting stages with intercooling to protect seals and limit mechanical stress.
No. This is GPSA/API 617 screening only. Confirm head, power, and surge margin on the vendor map and ASME PTC 10 when required.