How is reciprocating compressor capacity calculated?

Reciprocating compressor capacity is determined by the piston's swept volume, rotational speed (RPM), number of cylinders, and the volumetric efficiency. The volumetric efficiency accounts for the clearance volume and compression ratio, which reduces the effective gas intake into the cylinder.

What is volumetric efficiency and why is it important for reciprocating compressors?

Volumetric efficiency (Ev) is a measure of how effectively a compressor cylinder draws in gas, comparing the actual volume of gas drawn into the cylinder to the piston's swept volume. It is crucial because clearance volume, compression ratio, and gas properties significantly reduce the effective capacity, directly impacting the compressor's overall performance and output.

How to estimate power consumption for a reciprocating compressor?

The power required for a reciprocating compressor involves calculating the theoretical (indicated) power based on suction pressure, volumetric capacity, isentropic exponent, and compression ratio. This indicated power is then divided by the compressor's overall efficiency (including mechanical and volumetric) to determine the actual shaft power required.

Reciprocating compressor capacity

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Section summary
1. Reciprocating compressor capacity calculation formula
2. Usual values
3. Other relations (mass flowrate, power)
4. Multistage compression

1. Reciprocating compressor capacity calculation formula

In a reciprocating compressor, the capacity depends on the volume displaced by the piston during its movement. The swept volume of one piston can be calculated the following way

\\[ V_d = St \cdot \frac{(\pi D^2)}{4} \\] Reciprocating compressor swept volume

Not all the cylinder volume can be used for the compression as there is always the clearance at the end of the cylinder that remains with some air inside. This phenomena can be quantified by defining the volumetric efficiency of the compressor

\\[ E_v = \frac{V_s}{V_d} \\] Reciprocating compressor volumetric efficiency

Ev should be calculated rigourously thanks to the actual volume and swept volume, but for quick estimations, the volumetric efficiency can be estimated thanks to the following expression

\\[ E_v = 0.97 - c \cdot (\tau^{1/k} - 1) - L \\] Estimation of Reciprocating compressor volumetric efficiency

The volumetric capacity of a single piston can then be calculated thanks to

\\[ Q_v = 60 \cdot N \cdot V_d \cdot E_v \\] Calculation of reciprocating compressor capacity

This value needs to be multiplied by the number of cylinders to find out the capacity of the reciprocating compressor.

With

V_d=Swept volume (m3)
V_s=Actual volume capacity (m3)
V_c=Clearance volume (m3)
c=clearance=V_c/V_d=Swept volume (m3)
E_v=volumetric efficiency (-)

τ=compression ration = p_discharge / p_suction(-)

St=Piston Stroke (m)
k=isentropic coeffient (-)
D=Cylinder internal diameter (m)

⚠️ ENGINEERING NOTICE & EDUCATIONAL DISCLAIMER: This interactive calculator is provided exclusively for preliminary estimation and educational purposes. It is not intended for detailed design or equipment procurement without certified vendor rating. No warranty, expressed or implied, is provided, and no liability is assumed.

Reciprocating Compressor Sizing Calculator

Piston Stroke (m)

Cylinder Diameter (m)

RPM

Number of Cylinders

Clearance (c)

Suction Pressure (bar abs)

bar abs

Discharge Pressure (bar abs)

bar abs

Suction Temperature (°C)

°C

Isentropic Exponent (k)

Lubrication Factor (L)

Molar Mass (M, kg/kmol)

kg/kmol

Overall Efficiency (η)

⚙️ Practical Plant Engineering Rules of Thumb & Safety Limits:

Compression Ratio: For single-stage reciprocating compressors, the compression ratio (P_discharge/P_suction) typically ranges from 3:1 to 5:1. Ratios above 5:1 often necessitate multi-stage compression with intercooling to manage discharge temperatures and improve efficiency.
Volumetric Efficiency: A good volumetric efficiency for industrial reciprocating compressors is usually in the range of 75-90%. Lower values indicate significant losses, often due to high clearance volume, high compression ratio, or gas leakage. If Ev drops below 0.65, consider it problematic.
Clearance Volume: Typical clearance values (c) range from 0.04 (4%) for high-pressure applications to 0.16 (16%) for low-pressure, high-volume machines. Higher clearance reduces volumetric efficiency but increases operational flexibility.
Intercooling: For multi-stage compressors, intercoolers are essential to reduce the gas temperature between stages, decreasing the work required, managing discharge temperatures, and preventing material overstressing. Aim to cool the gas back to near suction temperature before the next stage.
Piston Speed: Reciprocating compressor piston speeds are generally limited to 3-5 m/s (600-1000 ft/min) to minimize wear, vibration, and dynamic stresses.
Overall Efficiency: Industrial reciprocating compressors (excluding motor/drive) usually have an overall efficiency (mechanical + volumetric) ranging from 65% to 85%, depending on size, design, and maintenance.

2. Usual values

For air k=1.4
L=0.04 for lubricated compressors (only for estimation)
c must be defined according to the compressor type but should range from 0.04 to 0.16

3. Other relations (mass flowrate, power)

The mass capacity of the compressor can be calculated, per cylinder with

\\[ Q_M = 12 \cdot \frac{P \cdot M}{T} \cdot Q_v \\] Calculation of reciprocating compressor mass capacity

The power necessary to perform the compression can be calculated the following way by using the mass capacity, the pressures and temperatures reach and taking into account the efficiency of the compressor :

\\[ P_i = \frac{Q_{vs} P_s}{36} \frac{k}{k-1} \left( \left(\frac{P_d}{P_s}\right)^{(k-1)/k} - 1 \right) \\] Calculation of reciprocating compressor power consumption

\\[ P_{shaft} = \frac{P_i}{\eta_{overall}} \\] Calculation of reciprocating compressor power consumption

The overall efficiency of the reciprocating compressor can be determined thanks to the following graph :

A reciprocating compressor has a cooling system built-in. This particularity, which cannot be implemented for centrifugal compressors, allows to have a discharge temperature close (but not equal) to the isentropic discharge temperature.

4. Multistage compression

Reciprocating compressors are often used in multistage compression with intercoolers in order to maintain the temperatures in a range manageable for the machine. If the compression ratio is > 3, multistage compression is then advised.

Figure 1 : Principle of operation of a reciprocating compressor, 2 stages, 2 cylinders double effect