Compressor-and-Turbine-Efficiency

Real-gas compressor performance (Peng–Robinson) and IAPWS-IF97 steam-table turbine performance from historical/field data

COMPRESSOR & STEAM TURBINE EFFICIENCY MONITOR

COMPRESSOR TYPE

Type Centrifugal Axial Screw / Rotary Reciprocating

Bore (mm)

Stroke (mm)

Speed (RPM)

No. of cylinders

Clearance volume (%)

Single-acting assumption. VEa = actual suction volumetric flow / swept volume. VEt = 100 − clearance%·(r^(1/k)−1), theoretical reference.

GAS PROPERTY SOURCE

Source Composition (PR-EOS) Manual input (k, Z, MW)

k (Cp/Cv)

MW (kg/kmol)

Z1 (suction)

Z2 (discharge)

k, Z1, Z2 taken as-entered (assumed constant across the operating range); MW is used for R_specific and reciprocating VE.

GAS COMPOSITION (MOL %)

REFERENCE CONDITIONS

Tag / Compressor ID

Gauge readings are converted to absolute using a fixed atmospheric reference of 1.0332 kg/cm²a, then ×98.0665 for kPa.

ADD OPERATING POINT

Timestamp

P1 suction (kg/cm²g)

P2 discharge (kg/cm²g)

T1 suction (°C)

T2 discharge (°C)

Mass flow (kg/hr)

REFERENCE

Real-gas: a_mix,b_mix from PR-EOS mixing rules (k_ij=0)

k = Cp°_mix(T) / (Cp°_mix(T) - R)

r = P2(abs)/P1(abs) | T2_ideal = T1·r^((k-1)/k)

η_isentropic = (T2_ideal−T1)/(T2_actual−T1)

η_polytropic from n: (n-1)/n = ln(T2a/T1)/ln(r)

Reciprocating: VEa = W·v1 / V_swept (v1 from PR-EOS Z1)

EFFICIENCY TREND

HISTORY LOG

Time	P1(g)	P2(g)	T1	T2	W	r	Z1	Z2	ηis %	n	ηp %	GHP	VEa%	VEt%

STEAM INLET

P0 inlet (kg/cm²g)

T0 inlet (°C)

EXTRACTION 1

Enable extraction 1 (HP→IP)

P1 (kg/cm²g)

State SuperheatedWet (dryness x)

T1 (°C, if superheated)

x1 (dryness, if wet)

Extraction 1 flow (kg/hr)

EXTRACTION 2

Enable extraction 2 (IP→LP)

P2 (kg/cm²g)

State SuperheatedWet (dryness x)

T2 (°C, if superheated)

x2 (dryness, if wet)

Extraction 2 flow (kg/hr)

CONDENSER EXHAUST

P_exh (kg/cm²a, absolute)

Determine exit condition from Measured T / dryness (x) Measured turbine power output

State Wet (dryness x)Superheated

Texh (°C, if superheated)

x_exh (dryness, if wet)

Condensing (LP) stage power output (kW)

Exit enthalpy is back-calculated from this power and the flow through the final (condensing) section: h_out = h_in − Power·3600/flow. Exit state (wet or superheated) and dryness fraction are then determined automatically.

Main steam flow at inlet (kg/hr)

REFERENCE

Properties via IAPWS-IF97 Region 1 (liquid), Region 2 (vapor), Region 4 (saturation)

η_section = (h_in−h_out,actual) / (h_in−h_out,s)

h_out,s at section exit P, using entropy of section's actual inlet state

Wet-steam isentropic point found from s vs saturation entropy at exit P

η_overall uses inlet entropy s0 projected to final exhaust pressure

EXPANSION PATH (h-s)

SECTION & OVERALL EFFICIENCY

EQUIPMENT TYPE

Type Pump (liquid) Fan / Blower (air)

Hydraulic power = Q·ΔP / 36.71 (Q in m³/hr, ΔP in kg/cm²) — independent of liquid density.

Air power = Q·ΔP·9.80665 / 3.6×10⁶ (Q in m³/hr, ΔP in mmWC).

ADD OPERATING POINT

Timestamp

P1 suction (kg/cm²g)

P2 discharge (kg/cm²g)

Flow, Q (m³/hr)

Specific gravity, SG

ΔP static (mmWC)

Flow, Q (m³/hr)

Measured input power (kW)

Motor efficiency (%, if input is electrical)

REFERENCE

Pump: ΔP = P2−P1 (kg/cm²)  |  Head H(m) = ΔP·10/SG

Hydraulic power (kW) = Q(m³/hr)·ΔP(kg/cm²) / 36.71

Fan: Air power (kW) = Q(m³/hr)·ΔP(mmWC)·9.80665 / 3,600,000

Shaft power = Measured input power × motor efficiency

η = Hydraulic/Air power ÷ Shaft power × 100

EFFICIENCY TREND

HISTORY LOG