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# GPSA Compressor performance calculations2

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## 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?

### RE: GPSA Compressor performance calculations

It seems to me that Fig 13-35 yields compressor head for the case when polytropic eff = 100% = isentropic eff, since there is no provision to account for polytropic or isentropic eff. It doesnt say this anywhere in the narratives though.
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

After cross checking the results in the example calc 13-4 with my excel spreadsheet on compressor performance, it is confirmed the graphs show performance for a machine isentropic eff of 70%, and not 100% as I previously assumed.

### RE: GPSA Compressor performance calculations

The same isentropic eff of 70% is implied in the numerical example 13-5 which refers to fig 13-36. In this example, the head of 70 000 ft.lbf/lb is the isentropic head. The corresponding polytropic head is 72813ft.lbf/lb with a polytropic eff of 73%.
To convert ft.lbf / lb to Nm/kg, multiply by 2.986.

### RE: GPSA Compressor performance calculations

(OP)
Thanks for the replies georgeverghese, very helpful!

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

Also take note of the eqn 13-36 in the GPSA. I dont have this Bloch book, so I cannot tell what the concern is about the n method for compressor calcs. Pls note that poly eff for a compressor at a reference speed and flow is independant of the gas properties and compression ratio, while the isentropic eff is dependant on all these variables. So for rating a given compressor for some other duty, use the polytropic eff values in the compressor flow/ head curves. This is why compressor manufacturers always show polytropic curves and not isentropic head curves.

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

### RE: GPSA Compressor performance calculations

(OP)
Thanks again georgeverghese!

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

(OP)
I've been able to source the HP curve from the vendor.... though I'd still be interested to hear if anyone had any thoughts on my original question above.

### RE: GPSA Compressor performance calculations

2
Good you've got the curves for the HP stage. The RV sizing should be based on max normal stage 1 suction press, max normal speed and max unfouled site rate rated driver power. As such, the modelling should be based on each of both stages in the model and not the composite head curve. Obviously the performance of the cooler, both hydraulic and thermal, will also vary for the RV flow rate. It would be much easier to get this whole model set up carefully on a process simulator so you can see when you get to relief conditions.

### RE: GPSA Compressor performance calculations

(OP)
Great advice thanks georgeverghese!

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