Reciprocating Compressor Sizing Fundamentals

1. Overview

Preliminary compressor sizing is a critical early step in project development. Accurate estimates enable proper equipment selection, facility layout planning, and budgetary cost development. The methodology presented here uses industry-standard empirical formulas, providing quick yet reliable estimates for reciprocating compressor applications.

Key Principle: This methodology uses simplified empirical formulas derived from extensive field experience. While not a substitute for detailed engineering analysis, these methods provide estimates typically within 10-15% of final specifications.

Reciprocating compressors are positive displacement machines that use pistons driven by a crankshaft to compress gas. They are characterized by:

High efficiency across wide operating ranges
Ability to handle high compression ratios per stage
Flexibility in capacity control through unloading
Robust construction suitable for remote locations
Lower flow rates than centrifugal machines at equivalent power

2. Compression Ratio

The compression ratio (CR) is the fundamental parameter for compressor sizing. It represents the ratio of absolute discharge pressure to absolute suction pressure:

Compression Ratio: CR = P_discharge / P_suction Where both pressures must be in absolute units (psia). Add 14.7 psi to gauge pressure at sea level.

Important: Compression ratio must be calculated using absolute pressures (psia), not gauge pressures (psig). Add 14.7 psi (at sea level) to convert gauge to absolute pressure.

Typical Compression Ratios

Application	Typical CR Range	Notes
Gas gathering	2:1 to 6:1	Often single or two-stage
Gas lift	3:1 to 10:1	Multiple stages common
Pipeline transmission	1.2:1 to 2:1	Low ratio, high volume
Gas processing	3:1 to 15:1	Depends on process
Underground storage	2:1 to 8:1	Variable seasonally

3. Stage Determination

The number of compression stages required depends on the overall compression ratio. Higher ratios require multiple stages to limit discharge temperatures and improve efficiency. The following formula provides a quick determination:

Number of Stages: n = INT[ln(CR) / ln(3.5) + 0.90] Where: n = Number of stages (rounded down to integer) CR = Overall compression ratio 3.5 = Maximum practical ratio per stage 0.90 = Margin factor for typical applications

Why 3.5:1 Maximum Per Stage?

The 3.5:1 ratio limit is based on practical considerations:

Temperature

Discharge limits

Higher ratios cause excessive temperatures that damage valves and packings.

Efficiency

Volumetric losses

Efficiency drops significantly at higher ratios due to re-expansion.

Mechanical

Rod loading

Higher pressure differentials require larger, more expensive components.

Stage Count vs. Ratio

Overall CR	Stages	Ratio/Stage
Up to 3.5	1	Up to 3.5:1
3.5 to 12	2	1.87 to 3.46:1
12 to 42	3	2.29 to 3.48:1
42 to 150	4	2.55 to 3.50:1

4. Power Estimation

The following simplified formula estimates brake horsepower accounting for typical efficiencies and real gas effects:

Estimated BHP: BHP = 21 × CR^(1/n) × n × Q × 1.154 Where: 21 = Empirical constant (hp per stage per MMscfd per ratio) CR^(1/n) = Geometric mean compression ratio per stage n = Number of stages Q = Flow rate (MMscfd at standard conditions) 1.154 = Correction factor for real gas behavior

Understanding the Formula

The 21 constant is derived from thermodynamic analysis of typical natural gas compression, accounting for:

Adiabatic compression work
Mechanical efficiency losses (~90-95%)
Volumetric efficiency effects
Valve pressure drops

Power per MMscfd Rule of Thumb: A common industry benchmark is 80-120 hp per MMscfd for typical gas gathering applications with moderate compression ratios. Higher ratios require more power per unit flow.

5. Interstage Pressures

For multi-stage compression, interstage pressures should be distributed to achieve equal compression ratios in each stage. This minimizes total power consumption and balances discharge temperatures.

Interstage Pressure: P_stage = P_suction × CR^(stage/n) Where: P_stage = Discharge pressure of the specified stage P_suction = First stage suction pressure (absolute) CR = Overall compression ratio stage = Stage number (1, 2, 3, ...) n = Total number of stages

Example: Three-Stage Compression

For a compressor with 65 psia suction, 565 psia discharge (CR = 8.69), three stages:

Stage 1 discharge: 65 × 8.69^(1/3) = 134 psia
Stage 2 discharge: 65 × 8.69^(2/3) = 275 psia
Stage 3 discharge: 65 × 8.69^(3/3) = 565 psia

6. Discharge Temperature

Discharge temperature is a critical parameter affecting equipment selection, material choices, and intercooler design. For isentropic (ideal) compression:

Discharge Temperature: T_d = T_s × CR^((k-1)/k) Where: T_d = Discharge temperature (absolute - Rankine) T_s = Suction temperature (absolute - Rankine) CR = Stage compression ratio k = Specific heat ratio (Cp/Cv) To convert: °R = °F + 459.67

Temperature Limits:

275°F: Typical limit for standard valves and packings
300°F: Maximum for many lubricants
350°F: Requires special materials and non-lubed design
400°F+: Generally avoided in reciprocating compressors

Specific Heat Ratio (k) Values

Gas Type	k Value	Notes
Natural Gas (typical)	1.27	0.65 SG
Lean Natural Gas	1.30	Higher methane content
Rich Natural Gas	1.22	Higher NGL content
Methane (pure)	1.31	Reference value
Carbon Dioxide	1.30	CO2 rich streams
Hydrogen	1.41	High temperature rise

7. Volumetric Efficiency

Volumetric efficiency (VE) is the ratio of actual gas volume displaced to the theoretical cylinder displacement. It accounts for various losses in the compression process:

Volumetric Efficiency: VE = α - Slippage - Clr × (CR^(1/k) × Zs/Zd - 1) Where: α = 0.97 (typical valve loss factor) Slippage = Piston ring leakage - 0.03-0.05 for oil-flooded - 0.06-0.12 for non-lubed Clr = Clearance volume as fraction of stroke Zs/Zd = Compressibility ratio (often ≈ 1)

Clearance Volume Effects

Clearance volume is the gas remaining in the cylinder at the end of the discharge stroke. This gas re-expands during the suction stroke, reducing the effective cylinder capacity.

Cylinder Type	Clearance Range	Typical
Normal Cylinders	8% - 30%	20%
Pipeline Cylinders	40% - 200%	60%

Pipeline Cylinders: Pipeline cylinders are designed for low compression ratios (typically 1.2-2.0:1) with high clearances. They trade volumetric efficiency for the ability to handle low ratios without excessive re-expansion work.

8. Practical Considerations

Intercooling

Multi-stage compressors require intercoolers between stages to:

Reduce gas temperature before next stage suction
Remove heat of compression
Condense liquids that may be present
Improve overall compression efficiency

Typical intercooler approach temperatures are 15-25°F above cooling medium (ambient air or cooling water) temperature.

Rod Loading

The piston rod must withstand combined gas and inertia loads. Rod load limits often determine maximum allowable pressures for a given frame size:

Gas load increases with pressure differential
Inertia load increases with speed and reciprocating mass
Combined load must not exceed frame rating

Speed Selection

Speed Range	RPM	Characteristics
Low speed	200-450	Long life, lower efficiency, larger frame
Medium speed	450-900	Balance of life and efficiency
High speed	900-1800	Compact, higher maintenance

Preliminary Estimates Only: This methodology provides estimates suitable for feasibility studies (±15-20%), budgetary cost estimates, equipment layout, and initial utility requirements. Detailed engineering analysis with actual gas compositions, site conditions, and manufacturer data is required for final equipment selection.

Reciprocating Compressor Sizing

3.5:1

21 hp/ratio

±10-15%

Contents

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