6 replies to this topic

[eirik]

Hi,

I am interesting in finding the discharge pressure of a compressor.

I have:
inlet pressure: 300kPa
inlet temperature: 25C
outlet temperature: 81.74C
polytropic efficiency: 80%
flow: 20000 kgmole/hr


Does anybody have a good approximation method?

[ankur2061]

eirik,

The discharge pressure is normally an input and not a calculated result. However, you can calculate it as a function of the inlet and outlet pressure as follows:

T₂ = T₁*(P_d / P_s)^n-1/n ...........................(1)

where:

T₂ = absolute discharge temperature, K
T₁ = absolute suction temperature, K
P_d = absolute discharge pressure, kPaa
P_s = absolute suction pressure, kPaa
n = polytropic exponent

n can be calculated as follows:

n-1 / n = k-1 / (k*n_poly).........................(2)
where:

k = C_p / C_v at the inlet conditions

n_poly = polytropic efficiency, %

In your case the suction & discharge temperatures are known, the suction presssure P_s is known and you can calculate the polytropic exponent as per equation 2. Now using equation 1 you can calculate the discharge pressure P_d. As I mentioned earlier for compressor calculations the discharge pressure is an input.

Regards,
Ankur.

Edited by ankur2061, 26 November 2011 - 08:54 AM.

[eirik]

Hi Ankur,

Thank you for your reply

I am currently trying to copy for my own part hysys simulations for three different cases.
First case involves finding the polytropic efficiency, knowing p1,p2,t1,t2.
The second case involves finding the discharge temperature, knowing p1,p2,t1,np
For the third case I'm trying to find the dicharge pressure, knowing p1,t1,t2,np.

I've solved my two first cases with good accuracy compared to hysys results. But for the last case I'm having trouble. I've tried to use your method, but it is not accurate enough, i think.

This is why; correct me if I'm wrong.


Once having p1,p2,t1,t2. (p2 from above)

-I make two independent streams in hysys with the known information.
-Having this I can enter each stream and read enthalpy (h) and entropy (s).
-I make a new stream with p2 and entropy s1. This stream should then be the isentropic outlet.

-With this information i find the isentropic head

His=Z1*R*t1*(k/(k-1))*((p2/p1)^((k-1)/k)-1)

-Further on i find the polytropic head factor, also known as schultz correction factor

f=(h2s-h1)/His here h2s is the enthalpy of the outlet isentropic state

-I contiune to find the polytropic head. Now knowing the polytropic exponent

n-1 / n = k-1 / (k*n_poly)

Hp=( Z1*R*t1*(n/(n-1))*((p2/p1)^((n-1)/n)-1) ) *f

-Now just for curiosity I try to find the polytropic efficiency. Not really necessary, because it is already know.

using the following eq I find that the polytropic efficiency is significantly lower than 80%

np=Hp/(h2-h1)




Regards,

Eirik

[pavanayi]

Eirik,
Check the values of k that you have used in equation as mentioned by Ankur and the ones computed by hysys when you did the steps as mentioned in your second post.

[eirik]

Hi Pavanayi,

The K values I use are withdrawn from Hysys, this means that I end up using same k values as hysys in the equations above .

The reason for not getting the same results is that Hysys does not use the K values as explained above..
I'm sure the method above gives a fairly good approximation, and that an exact approximation involves more complex relations

I know that the isentropic and the polytropic exponent that hysys ends up using can be found using the simple relation

p₁V₁^k=p₂V_2s^k -> k=(log10(p1/p2))/(log10(V2s/V1))

p₁V₁^n=p₂V₂^n -> n=(log10(p1/p2))/(log10(V2/V1))

where s denotes isentropic outlet condition.

The question is therefore what is the link between k values from (k=Cp/Cv) and the isentropic exponent hysys expresses for a compression.

Once having a correct k value it is possible to calculate correct n value from the relation given by Ankur.

n-1 / n = k-1 / (k*n_poly)

this relation is also given in several compressor books

Regards,

Eirik

[P K Dwivedi]

Dear Readers,

Usually compressor prefromance curves received from supplier show isentropic head (kJ/kg), plotted against volumetric flow rate at compressor suction conditions (am3/s).

Has anybody set up an excel sheet to calculate the compressor discharge pressure (kPaa), knowing the following:

Isentropic Head (kJ/kg), Gas Mol Wt, Average Compressibility, Suction and Discharge Temperatures (deg K), Suction Pressure (kPaa), Sp. Heat ratio (k)?


Kind Regards,
P K Dwivedi
pkdwivedi2303@yahoo.co.uk

[breizh]

Hi ,

Consider this Xcel sheet .

Hope this helps

Breizh

Note : using the search button you should find additional xcel sheets.