1. Overview
Reciprocating compressor sizing translates process requirements (flow, pressures, gas composition) into a specific machine configuration (frame, cylinders, speed, driver). The process involves iterative matching of available cylinder bores and strokes to the required displaced volume while satisfying constraints on rod load, discharge temperature, and power.
Frame
Crankcase Assembly
Determines throw count, stroke, rod load limit
Cylinder
Compression Element
Bore diameter, MAWP, valve area
Piston
Displacement Member
Single or double-acting, rod diameter
Valves
Flow Control
Plate, ring, or poppet type; determine losses
Frame Classifications
| Category | Speed (RPM) | HP Range | Throws | Application |
|---|---|---|---|---|
| Slow-speed integral | 200-400 | 500-12,000 | 2-10 | Pipeline, process (integral engine-compressor) |
| Low-speed separable | 400-600 | 200-5,000 | 2-6 | Gas gathering, process |
| Medium-speed | 600-1,000 | 100-3,000 | 2-6 | General purpose, skid-mounted |
| High-speed separable | 1,000-1,800 | 50-2,000 | 2-6 | Wellhead, fuel gas, small gathering |
Sizing philosophy: Select the smallest, least expensive machine that meets all design requirements with adequate margin. A good sizing provides 10-15% capacity margin and does not exceed 90% of any mechanical limit (rod load, speed, power).
2. Sizing Process
The sizing process follows a systematic sequence from process requirements to final machine specification.
Step-by-Step Sizing Procedure
| Step | Action | Key Inputs | Output |
|---|---|---|---|
| 1 | Define process conditions | Flow (MMSCFD), P_s, P_d, T_s, gas comp | Design basis |
| 2 | Determine gas properties | MW, k, Z at suction and discharge | Thermodynamic data |
| 3 | Select number of stages | Overall ratio, max T_discharge | Stage count, interstage P |
| 4 | Calculate required capacity | ACFM at each stage suction | Displacement needed |
| 5 | Select frame and speed | HP estimate, throw count | Frame model, RPM |
| 6 | Select cylinder bore | Required displacement, MAWP | Bore diameter, stroke |
| 7 | Check volumetric efficiency | Clearance, ratio, k | Actual capacity |
| 8 | Check rod loads | Pressures, piston area, inertia | Combined rod load |
| 9 | Calculate power | Head, mass flow, efficiency | BHP per stage and total |
| 10 | Verify discharge temperature | T_1, ratio, k, efficiency | T_2 within limits |
Flow Conversion
Standard to actual volume flow:
ACFM = SCFM * (P_std / P_actual) * (T_actual / T_std) * (Z_actual / Z_std)
Where:
SCFM = Standard cubic feet per minute
ACFM = Actual cubic feet per minute at suction
P_std = 14.696 psia
T_std = 520 R (60 deg F)
Z_std = 1.0 (ideal at standard conditions)
MMSCFD to SCFM:
SCFM = MMSCFD * 1,000,000 / 1,440
Required displacement:
PD = ACFM / eta_v
Where eta_v = volumetric efficiency (0.50-0.92 typical)
Displacement from cylinder geometry:
PD = (pi/4) * D^2 * Stroke * RPM * N_act / 1,728
Where:
D = Bore diameter (in)
Stroke = Piston stroke (in)
N_act = Number of acting ends (1 or 2 per cylinder)
1,728 = in^3 to ft^3 conversion
3. Cylinder Selection
Cylinders are selected from manufacturer catalogs based on bore diameter, MAWP rating, valve area, and compatibility with the selected frame. Key considerations include single vs double-acting operation and available bore sizes.
Single-Acting vs Double-Acting
| Feature | Single-Acting | Double-Acting |
|---|---|---|
| Compression events/rev | 1 | 2 |
| Capacity per cylinder | Lower | ~1.8x single-acting |
| Rod loading | Unidirectional (tension only) | Alternating (reversal required) |
| Packing | Simpler | Full packing case required |
| Piston rod | Tail rod or plunger | Through-rod with packing |
| Typical application | High-speed, small capacity | Low/medium speed, larger capacity |
Cylinder Bore Selection
Required bore diameter (double-acting):
D = sqrt[(PD * 1,728 * 4) / (pi * Stroke * RPM * 2)]
Head-end vs crank-end areas:
A_HE = (pi/4) * D^2
A_CE = (pi/4) * (D^2 - d_rod^2)
Effective double-acting area:
A_eff = A_HE + A_CE = (pi/4) * (2*D^2 - d_rod^2)
Typical rod diameter:
d_rod = (0.25 to 0.35) * D_bore
Capacity ratio (CE/HE):
CE/HE = (D^2 - d_rod^2) / D^2
Typical: 0.85-0.93 depending on bore and rod size
Common Bore Sizes
| Bore (in) | Stroke (in) | MAWP (psi) | Approx PD/cyl (CFM at 900 RPM) | Frame Class |
|---|---|---|---|---|
| 3.0-5.0 | 3-5 | 3,000-6,000 | 10-60 | High-speed |
| 5.0-9.0 | 5-8 | 2,000-5,000 | 50-250 | Medium-speed |
| 9.0-15.0 | 6-12 | 1,000-3,000 | 200-800 | Low-speed separable |
| 15.0-30.0 | 10-18 | 500-2,000 | 500-3,000 | Slow-speed integral |
Sizing margin: Select a cylinder with 5-15% more displacement than calculated. This margin accounts for wear, valve losses, and operating variations. Excess capacity is controlled using clearance pockets or speed variation.
4. Clearance & Capacity Control
Clearance volume is the gas space remaining when the piston is at top dead center (TDC). It directly affects volumetric efficiency and provides the primary means of capacity control.
Clearance definition:
Cl = V_clearance / V_swept (dimensionless, typically 0.05-0.40)
Effect on volumetric efficiency:
eta_v = 1 - Cl * [r^(1/k) - 1] - L_v
Where:
Cl = Fractional clearance
r = Compression ratio
k = Specific heat ratio
L_v = Valve and leakage losses (0.03-0.10)
Types of clearance:
Fixed clearance: 5-15% (built into cylinder geometry)
Variable volume pocket (VVP): 0-100% additional clearance
Fixed volume pocket (FVP): Discrete step (e.g., 50% added)
Head-end unloader: 0% or 100% (on/off per end)
Capacity with added clearance:
As Cl increases, eta_v decreases, reducing capacity.
At maximum clearance, eta_v may reach 0 (no gas delivered).
Capacity Control Methods
| Method | Range | Efficiency | Cost | Application |
|---|---|---|---|---|
| Variable volume pockets | 50-100% | Excellent | Moderate | Process compressors |
| Fixed clearance pockets | Discrete steps | Good | Low | Field gas compressors |
| Head-end unloaders | 0/50/100% | Good at full steps | Low | All applications |
| Speed variation (VFD) | 50-100% | Excellent | High | Electric drive |
| Suction valve unloaders | 0/100% per end | Fair | Low | Gas engine driven |
| Bypass/recycle | 0-100% | Poor | Low | Emergency control only |
Clearance pocket sizing: To reduce capacity by X%, the additional clearance needed is approximately: delta_Cl = X / [r^(1/k) - 1] / 100. For r=3.0 and k=1.27, reducing capacity by 20% requires approximately 0.09 (9%) additional clearance.
5. Valve Losses & Derating
Compressor valves create pressure drops during suction and discharge strokes. These losses reduce effective capacity and increase power consumption. Valve losses are often the largest source of deviation between theoretical and actual performance.
Valve Pressure Drop
Valve pressure drop (per valve):
delta_P_valve = C_v * rho * v_valve^2 / 2
Where:
C_v = Valve resistance coefficient (1.5-4.0 depending on type)
rho = Gas density at valve conditions (lb/ft^3)
v_valve = Gas velocity through valve seat (ft/s)
Typical valve velocity limits:
Suction valves: 3,000-5,000 ft/min (50-83 ft/s)
Discharge valves: 4,000-6,000 ft/min (67-100 ft/s)
Effect on capacity:
Suction valve drop reduces effective suction pressure:
P_1_eff = P_1 - delta_P_suction
Discharge valve drop increases effective discharge pressure:
P_2_eff = P_2 + delta_P_discharge
Effective ratio: r_eff = P_2_eff / P_1_eff > r_nominal
Valve Types and Characteristics
| Valve Type | Lift (in) | Flow Area | Pressure Drop | Speed Limit (RPM) |
|---|---|---|---|---|
| Plate (channel) | 0.040-0.080 | Moderate | Moderate | 1,200 |
| Ring (concentric) | 0.030-0.060 | Good | Low | 1,000 |
| Poppet | 0.060-0.120 | Excellent | Very low | 1,800 |
| Plate (ported) | 0.040-0.060 | Good | Moderate | 900 |
Overall Derating Factors
Actual capacity vs theoretical:
Q_actual = Q_theoretical * eta_v * F_valve * F_leak * F_gas
Where:
eta_v = Volumetric efficiency (clearance effect)
F_valve = Valve loss factor (0.92-0.98)
F_leak = Piston ring leakage factor (0.95-0.99)
F_gas = Gas property deviation factor (0.97-1.03)
Typical combined derating:
New machine: Q_actual = 0.88-0.95 * Q_theoretical
Worn machine: Q_actual = 0.82-0.90 * Q_theoretical
Power increase from valve losses:
BHP_actual = BHP_ideal / (eta_isen * eta_mech)
eta_mech = 0.93-0.97 (bearing, oil pump, auxiliaries)
6. Worked Examples
Example 1: Single-Stage Cylinder Sizing
Given:
Flow: 5 MMSCFD natural gas (MW=18.5, k=1.27)
P_suction = 300 psia, P_discharge = 750 psia
T_suction = 90 deg F, Z_suction = 0.92
Frame: 4-throw, 900 RPM, 8-inch stroke
Step 1: Compression ratio
r = 750 / 300 = 2.5 (single-stage OK)
Step 2: Convert flow to ACFM at suction
SCFM = 5,000,000 / 1,440 = 3,472 SCFM
ACFM = 3,472 * (14.696/300) * ((90+459.67)/520) * (0.92/1.0)
ACFM = 3,472 * 0.04899 * 1.0571 * 0.92
ACFM = 165.6 ACFM
Step 3: Estimate volumetric efficiency
Cl = 0.12 (12% clearance)
eta_v = 1 - 0.12 * [2.5^(1/1.27) - 1] - 0.05
eta_v = 1 - 0.12 * [2.02 - 1] - 0.05
eta_v = 1 - 0.122 - 0.05 = 0.828 (82.8%)
Step 4: Required displacement
PD = 165.6 / 0.828 = 200.0 CFM
Step 5: Required bore (double-acting, 1 cylinder per stage)
PD = (pi/4) * D^2 * 8 * 900 * 2 / 1,728 * CE_factor
(CE factor ~0.93 for typical rod)
200.0 = (pi/4) * D^2 * 8 * 900 * 2 * 0.965 / 1,728
200.0 = D^2 * 6.33
D^2 = 31.6
D = 5.62 in
Select 6-inch bore cylinder from catalog.
Actual PD = 6^2 * 6.33 = 227.9 CFM (14% margin -- good)
Example 2: Two-Stage Configuration
Given:
Flow: 10 MMSCFD, P_1 = 100 psia, P_final = 900 psia
T_1 = 80 deg F, Natural gas (MW=19, k=1.26, Z_1=0.95)
Frame: 6-throw, 720 RPM, 10-inch stroke
Step 1: Overall ratio
R = 900/100 = 9.0 (need 2 stages)
r = sqrt(9.0) = 3.0 per stage
Step 2: Stage 1 (100 -> 300 psia)
SCFM = 10,000,000 / 1,440 = 6,944 SCFM
ACFM_1 = 6,944 * (14.696/100) * (540/520) * (0.95/1.0)
ACFM_1 = 6,944 * 0.14696 * 1.0385 * 0.95 = 1,006 ACFM
eta_v1 = 1 - 0.10 * [3.0^(1/1.26) - 1] - 0.05
eta_v1 = 1 - 0.10 * [2.46 - 1] - 0.05 = 1 - 0.146 - 0.05 = 0.804
PD_1 = 1,006 / 0.804 = 1,251 CFM
Need 3 throws (of 6) for Stage 1
Per-cylinder PD = 1,251 / 3 = 417 CFM
D_1 = sqrt[417 * 1,728 / (pi/4 * 10 * 720 * 2 * 0.965)]
D_1 = sqrt[417 / 8.11] = sqrt(51.4) = 7.17 in
Select 7.5-inch bore
Step 3: Stage 2 (300 -> 900 psia)
After intercooler: T = 100 deg F, Z_2 = 0.90
ACFM_2 = 6,944 * (14.696/300) * (560/520) * (0.90/1.0)
ACFM_2 = 6,944 * 0.04899 * 1.077 * 0.90 = 329.6 ACFM
eta_v2 = 1 - 0.10 * [3.0^(1/1.26) - 1] - 0.05 = 0.804
PD_2 = 329.6 / 0.804 = 410 CFM
Use remaining 3 throws for Stage 2
Per-cylinder PD = 410 / 3 = 136.7 CFM
D_2 = sqrt[136.7 / 8.11] = sqrt(16.9) = 4.11 in
Select 4.5-inch bore
Configuration: 3 x 7.5" (1st stage) + 3 x 4.5" (2nd stage)
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