# The Importance of Determining Number of Stages in Reciprocating Compressor and Bonus Calculation Spreadsheet

Three previous posts show comparison of number of stages in determining reciprocating compressor power.

Estimate reciprocating compressor power (2-stage compression)

Estimate reciprocating compressor power (3-stage compression)

Estimate reciprocating compressor power (2-stage compression)

Let’s summarize the results.

We can see that the more stages we use, the higher total BHP is. Next question is, how to determine number of stages?

Many references mentioned that number of stages of reciprocating compressor is determined by allowable discharge temperature. If the calculated discharge temperature using one stage is too high, it is obvious to add more stages.

In almost all multi-stage applications [1], the gas will be cooled between stages. In this case, increasing the number of stages, up to a limit, will increase the efficiency of compressor. This is because with intercooling, the compression more closely approximates an isothermal compression with resulting lower power requirement. An alternative way of looking at this is on a pressure-volume diagram below.

The work required to compress gas is given by the area of the pressure vs volume diagram. Figure above shows a single- and a two-stage compression for a given application. The diagram for single stage compression is 1-2-3-4-1. For two-stage compression, it is 1-5-6-7-3-8-4-1. As the interstage gas is cooled (5-6), its volume decreases. The work done as given by the areas of the diagrams is obviously less in the two-stage case than in the single-stage case. Further, if any liquids are condensed out of the gas in the intercoolers, the liquids must be separated from the gas and the mass of gas compressed from the interstage to the final discharge is reduced with a further resulting power reduction. However, as stages are added, the number of compressor valves the gas must flow through in series, and the amount of interstage piping and coolers increase. If too many stages are used, the pressure losses in the valves and piping will offset the gains from intercooling and the efficiency will be reduced.

The cost of compressor to do a given task usually increases as the number of stages is increased because of the additional compressor cylinders, coolers, and piping.

In other reference [2], the maximum compression ratio per stage is usually about 3:1 to 4:1. Higher compression ratios can result it reduced volumetric and mechanical efficiencies and greater mechanical stress. The outlet temperature also limits the compression ratio. The mechanical design limit is usually 350oF to 400oF, but lower temperature may be required depending on the gas properties. In addition, the pressure rise per stage is often limited by compressor valve design considerations to 1000 psi or less.

API 618 recommended that the discharge temperature should be limited to 300oF [3]. Higher temperatures cause problems with lubricant coking and valve deterioration. In non-lube service, the ring material is also a factor in setting the temperature limit. Packing life may be significantly shortened by the dual requirement to seal both high pressure and high temperature gases. For this reason, at higher discharge pressures, a temperature closer to 250oF or 275oF may be the practical limit.

In summary and for most field applications, the use of 300oF maximum would be a good average.

So, back to the case we use. We can conclude that 2-stage reciprocating compressor is suitable for the case. The discharge temperature for each stage is below 275-300oF.

I hope you find this post useful.

# Bonus

Here is the spreadsheet calculation for reciprocating compressor power based on GPSA.

Compressor Calculation R1

# References:

[1] Hanlon, Paul C., “Compressor Handbook”, McGraw-Hill, 2001

[2] Dimoplon, William, “What Process Engineers Need to Know About Compressors”

[3] GPSA Engineering Data Book