Multistage compressors with intercooling are common in processes demanding high pressure ratio compression. Their widespread application mainly stems from the energy savings multistage compression provides over single stage, even though they are more capital intensive, less reliable and require more floor space.

Key considerations made in designing multistage compressors include deciding the number of stages and fixing the interstage pressures. Limits associated with allowable gas discharge temperature and material temperature limits of the components decide the number of compression stages. The values for interstage pressures are chosen to achieve the minimum energy demand condition.

The procedure involves differentiating the general equation for the work done by any two consecutive stages of a multistage compressor with respect to the interstage pressure. Equating the derivative to zero gives the minimum work condition. The result shows that the work done by the compressor is minimized when the pressure ratio across each stage is equal. The pressure ratio across any stage is defined as the ratio of the discharge pressure to the suction pressure, with both values expressed in absolute units.

The result shows that, for any multistage compressor, the minimum work condition is achieved when:

*PR _{stage} = (PR_{overall})*

^{1/n}

where, *PR _{stage}* is the pressure ratio across each stage;

*PR*is the ratio of the final stage discharge pressure to the first stage suction pressure; and n is the total number of compression stages.

_{overall}The interstage pressure, *P _{i}*, is obtained using the equation:

*P _{i}=P_{s-u} ×PR_{stage}*

where, *P _{s-u}* is the suction pressure of upstream stage. (Note: Each pressure value is in absolute units.)

Multistage compressors are thus designed and built to achieve the above conditions. Optimum energy consumption is indicated when such compressors operate with the same pressure ratio across each stage.

Thus, the interstage pressures of any multistage compressor provide an important indicator. When the pressure ratio across each stage is the same, the interstage pressure values for this condition can be calculated and then compared with actual pressure indications on the compressor. When there is a good match for every stage, the gas compression is efficient.

Interstage pressures, along with consumed motor current, can help determine the mechanical health of the compressor stages. A change in actual values of interstage pressures from the expected values is a definite indicator of underperformance of the stages.

As an example, consider a 2-stage reciprocating compressor handling air. It takes suction from atmosphere and discharges at 6 barg. Using the above equations, the expected interstage pressure is 1.6 barg (2.6 bara). Values higher or lower than this value clearly warrant a look at the health of the stages.

Interstage pressure below that expected implies that mass flow rate from the upstream (low pressure – LP) stage is lower than normal. The interstage volume (volume between the two stages) is fixed. When mass delivered in this volume is less than normal, the interstage pressure will be lower. The inference is that the LP stage isn’t performing as expected and needs further analysis to identify the cause.

On the other hand, interstage pressure greater than the expected value reveals that the high pressure (HP) stage can’t intake the normal mass flow rate being discharged by the LP stage. Underperformance of the HP stage would lead to accumulation of mass in the interstage, resulting in a higher interstage pressure.

This brings us to a simple and easy to remember rule. If the interstage pressure is *Lower*, there is a problem with the LP stage, when it is *Higher*, the HP stage needs attention.

Maintenance personnel and field operators often mark the expected values of the interstage pressures and motor current on the pressure and ampere meter gauges. Deviations from the normal values are the first indicators of sub-optimal performance and compressor health issues.

The interstage pressure parameter is thus a useful early-warning parameter in multistage compressors.

Paresh Girdhar is a guest contributor to Chemical Processing

*Editor’s note: This article was written by a colleague of our regular columnist, Alan Rossiter. Paresh Girdhar is a rotating machinery specialist with extensive experience in maintenance, operation and reliability enhancement of rotating equipment in the petrochemical and refining industry. In his current role as principal engineer at the Asset Technology Centre in SABIC, KSA, he provides technical support on turbomachines to all SABIC affiliates. He has also authored books on performance evaluation of pumps and compressors, predictive maintenance techniques and centrifugal pumps.*