Compressor and Pump Power Calculator

Isentropic / Polytropic compression - Multi-stage - Pump power - API 617 / ASME PTC 10

COMPRESSOR

PUMP

/// gas properties and presets

Molecular weight MW

g/mol

Heat capacity ratio γ (Cp/Cv)

Gas compressibility Z (inlet)

/// operating conditions

Inlet pressure P1

bar(a)

Outlet pressure P2

bar(a)

Inlet temperature T1

°C

Mass flow rate

kg/s

Isentropic efficiency η_is

Mechanical efficiency η_mech

Polytropic efficiency η_p (if known)

Driver efficiency (motor/turbine)

P-V diagram: isentropic vs polytropic vs isothermal compression

/// multi-stage compression with intercooling

Optimal staging: For minimum total work with perfect intercooling, the compression ratio per stage is equal: r_stage = (P_final/P_inlet)^(1/N_stages). Intercooling reduces discharge temperature and improves efficiency by approaching isothermal compression.

Inlet pressure P1

bar(a)

Final outlet pressure Pn

bar(a)

Inlet temperature T1

°C

Number of stages

stages

Molecular weight MW

g/mol

γ (Cp/Cv)

Mass flow rate

kg/s

Isentropic efficiency

Intercooler outlet T

°C

Pressure and temperature profile - multi-stage compression

/// pump power calculation

Pump power: Unlike compressors, liquids are incompressible (density constant). Hydraulic power = rho x g x Q x H. Pump efficiency and motor efficiency are applied to get shaft power and installed motor power. NPSH check is critical to avoid cavitation.

/// liquid properties

Liquid density

kg/m3

Liquid viscosity

Vapor pressure

bar(a)

/// hydraulic parameters

Flow rate Q

m3/hr

Total head H

Pump efficiency η_pump

Motor efficiency η_motor

Service factor

Speed (RPM)

RPM

/// NPSH check

Atmospheric pressure

bar(a)

Suction head (positive = above)

Suction friction loss

NPSHr (pump datasheet)

/// compressor performance map

Performance map: Shows discharge temperature, power, and efficiency as functions of compression ratio and inlet conditions. Used for operating envelope definition and surge margin calculation.

Inlet pressure P1

bar(a)

Inlet temperature T1

°C

Mass flow rate

kg/s

γ (Cp/Cv)

g/mol

Isentropic efficiency

Discharge temperature vs compression ratio (at various inlet T)

Shaft power vs compression ratio

/// intercooling analysis - power savings

Intercooling benefit: Cooling gas between stages reduces volumetric flow entering the next stage, reducing compression work. Perfect intercooling (back to T1) minimizes work. Each stage of intercooling saves typically 10-25% of compression power vs single-stage at the same total ratio.

Inlet pressure P1

bar(a)

Final pressure Pn

bar(a)

Inlet temperature T1

°C

g/mol

Mass flow

kg/s

Isentropic efficiency per stage

Intercooler outlet T (all stages)

°C

Total shaft power vs number of stages (same total ratio)

/// key formulas - compressor

Compression ratio (per stage): r = P2/P1
Isentropic discharge T: T2s = T1 x (P2/P1)^((γ-1)/γ) [K]
Actual discharge T (isentropic): T2 = T1 + (T2s - T1) / η_is [K]
Isentropic head: H_is = Z1 x R x T1 / MW x (γ/(γ-1)) x ((P2/P1)^((γ-1)/γ) - 1) [J/kg]
Isentropic power: W_is = m_dot x H_is [W]
Shaft power: W_shaft = W_is / η_is [W]
Installed motor power: W_motor = W_shaft / (η_mech x η_driver) [W]
Polytropic exponent n: n/(n-1) = γ/(γ-1) x η_p (for compressors)
Polytropic head: H_p = Z1 x R x T1 / MW x (n/(n-1)) x ((P2/P1)^((n-1)/n) - 1)
Discharge T (polytropic): T2_p = T1 x (P2/P1)^((n-1)/n) [K]
Isothermal power: W_iso = m_dot x Z x R x T1 / MW x ln(P2/P1)
Optimal stage ratio: r_stage = (Pn/P1)^(1/N) for N stages
Intercooling saving: W_N_stages / W_1_stage (at equal total ratio)

/// key formulas - pump

Hydraulic power: W_hyd = rho x g x Q x H [W] (Q in m3/s)
Shaft power: W_shaft = W_hyd / η_pump
Motor input power: W_motor = W_shaft / η_motor
Motor selected (IEC): P_motor ≥ W_shaft x service_factor
Specific speed Ns (US units): Ns = N (rpm) x sqrt(Q (gpm)) / H (ft)^0.75
Ns < 4,000: radial | 4,000 to 9,000: mixed flow | > 9,000: axial (approximate boundaries)
NPSHa: P_atm/(rho x g) - P_vapor/(rho x g) ± Z_s - H_f_suction [m]
NPSHa must exceed NPSHr by ≥ 0.5m minimum (ISO 9906)
Affinity laws: Q ~ N | H ~ N^2 | P ~ N^3 (speed change)
VFD savings: P_new/P_old = (N_new/N_old)^3
Torque: T = W_shaft / omega = W_shaft x 60 / (2 x pi x N_RPM) [N.m]

/// typical compressor parameters

Type	Compression ratio/stage	η_is typical	η_p typical	Typical application
Reciprocating (low speed)	2-8	80-88%	82-90%	Gas injection, CNG, HPHT
Reciprocating (high speed)	2-6	75-85%	78-87%	Gas gathering, pipelines
Centrifugal (single stage)	1.2-3.5	72-82%	76-85%	Refrigeration, pipeline boost
Centrifugal (multi-stage)	1.2-3.5/stage	74-84%	78-87%	Gas reinjection, LNG, refinery
Axial compressor	1.1-1.4	85-92%	87-93%	Air separation, large gas turbines
Screw (dry)	2-5	65-75%	68-78%	Instrument air, small gas
Screw (oil-flooded)	2-8	70-80%	73-82%	Industrial air, refrigerants

/// common gas properties

Gas	MW (g/mol)	γ (Cp/Cv)	R (J/kg.K)	Notes
Methane CH4	16.04	1.307	518.3	Main component natural gas
Natural gas (typical)	17-20	1.25-1.30	415-490	Varies by composition
Air (dry)	28.97	1.400	287.1	N2/O2 mixture
Hydrogen H2	2.016	1.405	4124	Very high R, low MW
Nitrogen N2	28.01	1.400	296.8	Inert, similar to air
CO2	44.01	1.289	188.9	Near-critical at 73 bar, 31°C
Ethane C2H6	30.07	1.188	276.5	LNG / NGL component
Propane C3H8	44.10	1.131	188.6	LPG, refrigerant R290
H2S	34.08	1.320	243.9	Sour gas - NACE MR0175
Ammonia NH3	17.03	1.310	488.2	Refrigerant, fertilizer

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