12 replies to this topic

[SickPuppy0]

Hello . I've rewritten for conciseness.

 

Context: I need to develop a thermodynamics model to evaluate compressor performance, power, efficiency, etc. This has been done using the Peng-Robinsons EOS and all my calculations have been validated with HYSYS.

 

Problem: For polytropic compression we have the following thermodynamic law:  dH = vdP + Tds. I have performed a numerical integration by breaking the compression pathway into smaller segment sizes of constant pressure ratio and across a path of constant polytropic efficiency yielding: vdP = 18,350 kJ, Tds = 350 kJ, dH = 21,350kW. 

 

Questions:

- why does vdP + Tds != dH ? Is there some other source of inefficiencies I'm failing to consider?

- does dH = required shaft power ? Excluding mechanical inefficiencies on the shaft / gear box.

- calculating polytropic efficiency via ((k-1)/k)/((n-1)/n yields 80.06% polytropic efficiency. Thus required shaft power is 18,350kJ/0.8006 = 22,798kJ which exceeds dH. Is it possible for shaft power to be greater than dH??

- calculating polytropic efficiency via 1-TdS / dH yields 86.8% polytropic efficiency.

 

Any feedback on what I'm missing would be highly appreciated. Thank you!

Edited by SickPuppy0, 29 December 2022 - 04:06 AM.

[breizh]

Hi,

You may find pointers in the link attached:

https://www.scienced...opic-efficiency

Good luck

Breizh 

[SickPuppy0]

Hi Breizh, thank you for sharing the article and spreadsheet. I will endeavour to compare my models predictions against it. FYI - I have rewritten my original post for conciseness and clarity, if you have any more feedback or suggestions it would be highly appreciated. Thank you.

[breizh]

Hi,

A few thermo relations:

H=U+PV 

dH=dU+PdV+VdP

TdS=dU+PdV  therefore  dH=TdS+VdP

 

dH=Cp*dT+[v-dV/dT) p=cte]*dP

dS=Cp*dT/T-[dV/dT) P=cte ]*dP = Cv*dT/T+[dP/dV) T=cte]*dT

 

Good luck

Breizh 

[Bobby Strain]

Why are you doing this? HYSYS has a perfectly good model for polytropic compression.

Bobby

[SickPuppy0]

A instantaneous power calc is to be implemented in the field for the operators. This must be validated first against historic performance. I'm analysing years worth of data and I've found it easy to implement in python. Does HYSYS have the capacity to perform such an analysis over many timestamps? Say tens of thousands of datapoints?

 

Regarding my original question on dH = vdP + Tds. I have evaluated polytropic efficiency for a different composition and differentsuction/discharge conditions. Calculating polytropic efficiency via (vdP - Tds)/dH matches the manufacturers reported polytropic efficiency by 0.2%.

 

My question is, is efficiency = (vdP - Tds)/dH thermodynamically correct?

 

Thanks.

Edited by SickPuppy0, 30 December 2022 - 05:47 AM.

[PaoloPemi]

normally you calculate polytopic head, from that value , mass flow and efficiency you can estimate power, consider 90-95% mechanical eff. to estimate the power required,for realtime operations with Python (or similar programming tools) you may also consider a thermodynamic library as Prode Properties, it includes a method to solve polytropic stages including phase equilibria, the adopted method for single phase is based on integration of 4 poles function (with accuracy equivalent to multistep methods) and direct integration for multiphase, there are Excel, OpenOffice, Python examples provided...but you can adapt to most programming languages, by the way, I would suggest LK(Plocker) or GERG 2008 models which provide more accurate values than Peng Robinson

Edited by PaoloPemi, 30 December 2022 - 07:21 AM.

[breizh]

Hi,

This is what you need.

Good luck

Breizh 

[SickPuppy0]

Thank you! I will check out Prode properties and the methods you have suggested.

If someone could also please enlighten me... if compressor power is just "enthalpy change + mechanical losses", what is the point in evaluating polytropic head or polytropic efficiency ??? Why can't I just use the enthalpy delta??

Thanks again

[SickPuppy0]

Thanks Breizh, I did see that paper where they state efficiency = 1 - TdS/dH. This greatly overestimates efficiency. However (vdP-TdS)/dH matches HYSYS and the manufacturers datasheet almost perfectly.

Perhaps peng-robinsons is not the best EOS as Paolo suggests.

I may just extract enthalpy as a function of T&P from HYSYS and use a lookup interpolation table. I don't see why I need efficiency now if "shaft power = enthalpy + mechanical losses" only.

Regards

Thanks again

Edited by SickPuppy0, 30 December 2022 - 08:57 AM.

[breizh]

Hi,

 Other documents to support your work.

Good luck

Breizh

[SickPuppy0]

Realised my mistake! Entropic contribution is on a mol basis, and PdV is on a kg basis. Getting decent results from PdV+TdS now. Cheers!

[latexman]

Units matter!