## GPSA Compressor performance calculations

## GPSA Compressor performance calculations

(OP)

Hello,

I am completing a relief calculation for a PSV on the discharge of a compressor. I am using GPSA engineering handbook method for eveluating compressor performance.

I am having some difficulty interpreting the calculation methodology in GPSA Section 13, compressors. Specifically equation 13-33 and Fig. 13-35.

How do the terms Polytropic efficiency (ϒp) and isotropic efficiency (%) on Fig 13-35 relate to the terms in equation 13-33: n/(n-1) = [k/k-1]ηp ? The text above the equation states this is the equation for calculating polytropic efficiency, and for converting between polytropic and isotropic efficiency. But the symbols (and units for isotropic efficiency on the graph) don’t appear to match.

I've been tearing my hair out on this, asked loads of people on client and design side and no one has any experience of completing these calcs!

Does anyone out there know how to complete this part of the calculation?

I am completing a relief calculation for a PSV on the discharge of a compressor. I am using GPSA engineering handbook method for eveluating compressor performance.

I am having some difficulty interpreting the calculation methodology in GPSA Section 13, compressors. Specifically equation 13-33 and Fig. 13-35.

How do the terms Polytropic efficiency (ϒp) and isotropic efficiency (%) on Fig 13-35 relate to the terms in equation 13-33: n/(n-1) = [k/k-1]ηp ? The text above the equation states this is the equation for calculating polytropic efficiency, and for converting between polytropic and isotropic efficiency. But the symbols (and units for isotropic efficiency on the graph) don’t appear to match.

I've been tearing my hair out on this, asked loads of people on client and design side and no one has any experience of completing these calcs!

Does anyone out there know how to complete this part of the calculation?

## RE: GPSA Compressor performance calculations

To get the actual polytropic head, use the polytropic eff conversion expression in eqn 13-33 to get the polytropic exponent n (with isentropic exponent k), then use n to get Hp with eqn 13-34a.

## RE: GPSA Compressor performance calculations

## RE: GPSA Compressor performance calculations

To convert ft.lbf / lb to Nm/kg, multiply by 2.986.

## RE: GPSA Compressor performance calculations

I continued to do some digging on this and I think I've found the answer. In App B1 of "A Practical Guide to Compressor Technology, Second Edition, By Heinz P. Bloch", theres a run though of compressor performance calcs. It shows that polytropic efficiency np is either taken as a typical value, or i guess if its known then that can be used. then using the equation (k/(k-1))np the polytropic exponent n/(n-1) is calculated. In this equation method the conversion chart for polytropic and isentropic efficiency is not required, so I'm not entirely sure why it is referenced.

The graph for converting between isentropic and polytropic efficiency is for using the "mollier" method, which is for when fluid properties of the gas are available... and i believe this means gases with non ideal behaviour. The method using the polytropic efficiency is the "n-method".

I'm wondering why the GPSA recommends use of the "n-method" for all compressor performance calculations, when the textbook above suggests thats only for gases which are close to ideal behaviour.

## RE: GPSA Compressor performance calculations

In general, use the polytropic approach for centrofugal compressor calcs, and isentropic eff approach for expander calcs.

## RE: GPSA Compressor performance calculations

I have another question(s), perhaps you can help me..... I'm asking this after already asking lots of people in the client office I'm based in, and also people back at the design house.

I am wanting to complete compressor performance calculations using GPSA method. This is for relief valve sizing as i described above.

These compressors are relatively old (from early 70's) and the vendor at the time appears to have provided polytropic head curves for the LP Stage only, and also the combined LP and HP stage. It is the HP i am interested in though, as i want to check the PSV sizing for the HP discharge valves.

Is it valid to calculate the total polytropic head using average suction and discharge conditions across both the LP And HP stages together? I have tried this and it the answer is significantly higher than the maximum head the compressors can deliver. I'm not sure how valid this is as there is an interstage cooler and separation drum.

If it is not valid to calculate the maximum polytropic across both LP and HP stage, how can I determine the flowrate the HP stage can deliver for a given set of HP stage suction and discharge conditions, bearing in mind i dont have a HP stage only polytropic head curve?

## RE: GPSA Compressor performance calculations

## RE: GPSA Compressor performance calculations

## RE: GPSA Compressor performance calculations