Reciprocating Compression

Compressor Flow Prediction Fundamentals

Industry-standard volumetric efficiency models and capacity calculation methods for reciprocating compressor selection, station design, and performance monitoring.

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5 Correlations

Theoretical, Worthington, Cooper-Bessemer, NGPSA

Key Variable

Volumetric Efficiency

EVs determines actual flow from displacement

Common Term

Clearance Term T

T = CL * (R^(1/k) - 1) shared by all models

Contents

1. Introduction

Accurate flow prediction is essential for reciprocating compressor selection, station design, and performance monitoring. Multiple industry-standard correlations exist for estimating volumetric efficiency, each developed from different operational databases and making different assumptions about mechanical losses. This guide covers the five most widely used models and their practical application.

Core Relationship

Q = f(PD, EVs)

Flow depends on displacement and volumetric efficiency

Critical Factor

EVs Model Selection

Different models predict different capacities

Common Term

Clearance Re-expansion

All models share the same clearance term T

Difference

Non-clearance Losses

Models differ in how they estimate mechanical losses

Key insight: All five volumetric efficiency models share the same clearance re-expansion term. They differ only in how they account for non-clearance losses such as valve pressure drop, ring leakage, and gas heating effects. Selecting the appropriate model for your compressor type and operating conditions is the single most important factor in flow prediction accuracy.

2. The General Flow Equation

The standard equation for predicting reciprocating compressor flow converts cylinder displacement to standard-condition flow using pressure, temperature, and compressibility corrections along with the volumetric efficiency.

Standard flow prediction equation: Q = 0.00144 * (Ps / Pb) * (Tb / Ts) * (Zb / Zs) * PD * EVs Where: Q = Flow in MMSCFD 0.00144 = Unit conversion (1440 min/day / 1,000,000) Ps = Suction pressure (psia) Pb = Base pressure (typically 14.73 psia) Tb = Base temperature (typically 519.67 R) Ts = Suction temperature (R) Zb = Base compressibility (typically 1.0) Zs = Suction compressibility PD = Piston displacement (CFM) EVs = Suction volumetric efficiency (fraction)

Equation Components

TermPurposeTypical Value
0.00144Converts CFM to MMSCFD (1440 min/day / 10^6)Constant
Ps / PbPressure ratio to base conditions5 - 100+
Tb / TsTemperature ratio to base conditions0.85 - 1.05
Zb / ZsCompressibility correction for real gas1.0 - 1.15
PDPiston displacement from cylinder geometry10 - 5,000+ CFM
EVsSuction volumetric efficiency0.50 - 0.95
Accuracy depends on EVs: The pressure, temperature, and compressibility terms can be calculated precisely from operating conditions. The accuracy of flow prediction depends primarily on the volumetric efficiency model selected for EVs.

3. The Clearance Term

The clearance term T represents the fraction of cylinder capacity lost to re-expansion of gas trapped in the clearance volume. This term is common to all five volumetric efficiency models.

Clearance term definition: T = CL * (R^(1/k) - 1) Where: CL = Clearance fraction (clearance volume / swept volume) R = Compression ratio (Pd / Ps) k = Ratio of specific heats (Cp / Cv) For the theoretical model: EVs + T = 1 (All capacity loss is due to clearance re-expansion) Physical meaning: CL = fraction of swept volume occupied by clearance R^(1/k) = isentropic expansion ratio of clearance gas R^(1/k) - 1 = additional volume fraction consumed CL * (R^(1/k) - 1) = total fraction of stroke lost

Clearance Term Values

CLR = 1.5R = 2.0R = 3.0R = 4.0R = 5.0
8%0.0140.0300.0580.0850.108
12%0.0200.0460.0870.1270.162
16%0.0270.0610.1160.1690.216
20%0.0340.0760.1450.2120.270
25%0.0420.0950.1810.2650.338
30%0.0510.1140.2180.3170.405

Values calculated for k = 1.27 (natural gas). T = CL * (R^(1/k) - 1).

In practice, additional losses from valve pressure drop, ring leakage, heating effects, and cylinder geometry reduce EVs below the theoretical prediction of (1 - T). The five models described below differ in how they estimate these non-clearance losses.

4. Five Industry Volumetric Efficiency Models

Each model represents a different approach to accounting for the non-clearance losses that reduce actual volumetric efficiency below the theoretical value.

Model 1: Theoretical (Ideal)

Theoretical volumetric efficiency: EVs = 1 - CL * (R^(1/k) - 1) EVs = 1 - T The baseline model assuming no mechanical losses beyond clearance re-expansion. Always gives the highest predicted EVs. Useful as an upper bound for screening calculations.

Model 2: Worthington Correlation

Worthington correlation: EVs = 1 - 0.01*R - CL * (R^(1/k) - 1) Adds a linear correction term (0.01 * R) to account for valve losses and ring leakage that increase with compression ratio. Developed from extensive manufacturer test data. The 0.01*R term typically ranges from 0.015 to 0.05 for compression ratios of 1.5 to 5.0.

Model 3: Cooper-Bessemer Correlation

Cooper-Bessemer correlation: EVs = 0.97 - 0.008*R*(Ps/Pb)^0.2 - CL * (R^(1/k) - 1) Includes a pressure-dependent loss term that accounts for the effect of suction pressure level on mechanical losses. The (Ps/Pb)^0.2 factor makes the loss correction sensitive to operating pressure, not just compression ratio. Most appropriate for large-bore, slow-speed compressors. Key feature: The 0.97 base factor (vs 1.00) accounts for a fixed 3% loss independent of operating conditions.

Model 4: NGPSA Slow Speed (< 500 RPM)

NGPSA slow speed correlation: EVs = 0.96 - 0.01*R - CL * (R^(1/k) - 1) Published in the GPSA Engineering Data Book for slow-speed reciprocating compressors. The 0.96 base factor and 0.01*R loss term reflect typical performance of integral and low-speed separable units. Application: Integral engine-compressors and low-speed separable units operating below 500 RPM.

Model 5: NGPSA High Speed (≥ 500 RPM)

NGPSA high speed correlation: EVs = 0.96 - 0.02*R - CL * (R^(1/k) - 1) Also from GPSA standards, but with a larger loss coefficient (0.02 vs 0.01) reflecting the increased valve losses and dynamic effects at higher operating speeds. Application: High-speed separable compressors operating at 500 RPM and above. The doubled loss coefficient (0.02 vs 0.01) reflects increased valve flutter, shorter valve opening time, and higher gas inertia effects at elevated speeds.

5. Comparison of Model Coefficients

All models share the same clearance term T = CL * (R^(1/k) - 1). They differ only in how they estimate the non-clearance losses.

ModelBase Factor (A)Loss TermClearance Term
Theoretical1.00None-T
Worthington1.00-0.01*R-T
Cooper-Bessemer0.97-0.008*R*(Ps/Pb)^0.2-T
NGPSA Slow Speed0.96-0.01*R-T
NGPSA High Speed0.96-0.02*R-T

EVs Comparison at Typical Conditions

Example: CL = 15%, k = 1.27, Ps = 300 psia, Pb = 14.73 psia

ModelR = 1.5R = 2.0R = 3.0R = 4.0
Theoretical94.4%89.1%79.4%70.3%
Worthington92.9%87.1%76.4%66.3%
Cooper-Bessemer89.2%83.2%72.0%61.5%
NGPSA Slow Speed88.9%83.1%72.4%62.3%
NGPSA High Speed87.4%81.1%69.4%58.3%

The spread between Theoretical and NGPSA High Speed increases with compression ratio, ranging from ~7% at R=1.5 to ~12% at R=4.0.

Model selection matters: At R = 3.0 with 15% clearance, the Theoretical model predicts 79.4% EVs while the NGPSA High Speed model predicts 69.4% -- a difference of 10 percentage points. This translates directly to a 10% difference in predicted flow, which can significantly affect station design and equipment selection.

6. Modified Curve-Fit Form

For field performance correlation, all five models can be expressed in a unified polynomial form that simplifies calibration to actual operating data.

Unified polynomial form: EVs = A + B*T + C*T^2 Where: A, B, C = Constants determined by the model or by regression of field test data T = CL * (R^(1/k) - 1) = clearance term Applications of the curve-fit form: 1. Calibrating predictions to actual performance data - Fit A, B, C to measured EVs vs T from field tests - Accounts for unit-specific mechanical condition 2. Developing unit-specific correlations - Each compressor can have its own calibrated constants - More accurate than generic industry correlations 3. Trending compressor degradation over time - Track changes in A, B, C coefficients - Declining A indicates increasing fixed losses - Changes in B indicate clearance-dependent degradation
Practical benefit: The curve-fit form allows engineers to start with an industry-standard model for initial design, then calibrate the constants to actual field performance data once the compressor is operating. This provides the most accurate flow prediction for ongoing performance monitoring and optimization.

7. HP/MMSCFD Relationship

When enthalpy data is available, horsepower per unit flow provides an additional performance metric that can be used for flow back-calculation and efficiency monitoring.

Horsepower per unit flow: HP/MMSCFD = (Hd - Hs) * SG / 0.7995 Where: Hd = Discharge enthalpy (BTU/lb) Hs = Suction enthalpy (BTU/lb) SG = Gas specific gravity 0.7995 = Unit conversion constant Flow from measured horsepower: Q = HPm / (HP/MMSCFD) Where: HPm = Measured indicated horsepower Q = Flow in MMSCFD Application: When indicated horsepower can be measured from PV cards or cylinder pressure data, the actual flow can be back-calculated without requiring a separate flow meter. This provides an independent check on flow measurement and volumetric efficiency estimates.

Typical HP/MMSCFD Values

Compression RatioSG = 0.60SG = 0.65SG = 0.70SG = 0.75
1.525 - 3528 - 3830 - 4032 - 43
2.045 - 6050 - 6553 - 7057 - 75
3.075 - 9582 - 10388 - 11095 - 118
4.0100 - 125108 - 135117 - 145125 - 155

Ranges reflect variation in gas composition, temperature, and compressor efficiency.

8. Model Selection Guide

Selecting the appropriate volumetric efficiency model depends on the compressor type, operating speed, and available data.

SituationRecommended ModelRationale
Screening / upper boundTheoreticalGives maximum possible EVs; useful for initial feasibility
High-speed separable (≥ 500 RPM)NGPSA High SpeedAccounts for increased valve and dynamic losses at speed
Integral / low-speed separable (< 500 RPM)NGPSA Slow SpeedMatches typical performance of slow-speed machines
Manufacturer data unavailableWorthingtonConservative general-purpose correlation
Large-bore, pressure effects significantCooper-BessemerIncludes suction pressure correction for better accuracy
Field data availableCurve-fit formCalibrated to actual unit performance; most accurate
Best practice: Always validate with field test data when available. Use an industry-standard model for initial design, then calibrate to actual performance once the compressor is operating. The difference between models can exceed 10% in predicted flow, making model selection a critical engineering decision.

9. Practical Considerations

Several factors beyond the volumetric efficiency model affect the accuracy of flow predictions in real-world applications.

Assumptions and Limitations

FactorAssumption in ModelsReal-World Impact
Valve conditionClean, properly seating valvesWorn or fouled valves reduce actual EVs below predicted
Ring conditionGood ring sealWorn rings increase leakage, reducing EVs 2-10%
Pulsation effectsSteady-state suction/discharge pressurePulsation alters effective pressures, changing actual ratio
Z-factor correctionIdeal gas re-expansion (basic models)Multiply re-expansion ratio by Zs/Zd for real gas effects
Gas propertiesKnown k and Z at operating conditionsTemperature effects on k and Z values affect predictions
Cylinder geometryAccurate clearance measurementActual clearance may differ from design due to wear or shims

Z-Factor Correction

Real gas correction to clearance term: For real gas behavior, the re-expansion follows: T_corrected = CL * ((Zs/Zd) * R^(1/k) - 1) Where: Zs = Compressibility factor at suction conditions Zd = Compressibility factor at discharge conditions Effect: If Zs > Zd (common at moderate pressures): Corrected T is larger, and EVs is lower than ideal If Zs < Zd (possible at very high pressures): Corrected T is smaller, and EVs is higher than ideal Magnitude: Typically 1-3 percentage points difference from ideal gas. Should always be included for accurate predictions.

Performance Degradation Indicators

ObservationLikely CauseAction
Gradual EVs decline over monthsRing wear, valve deposit buildupSchedule maintenance at next opportunity
Sudden EVs dropValve failure, ring breakageImmediate inspection required
EVs higher than predictedLower actual clearance, favorable Z ratioVerify clearance measurements
EVs varies with load stepPocket valve leakageCheck clearance pocket valve sealing

Related Calculator: Compressor Flow Prediction Calculator

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