Theoretical Compressor Discharge Temperature Equations By Gpsa 13Th Edition

Just one remark and question that I would like to add;

The Isentropic exponent shall be calculated in the average suction and discharge temperature e.g. (Cp/Cv)@((Ts+Td)/2).

The question that I have in this regard,

In process simulation software's' like HYSYS, the exponent is calculated in the mean temperature or just suction temperature is considered?

If the mean temperature is used in HYSYS, then there should be a sort of iteration embedded in the compressor icon of HYSYS.

Regards,

Amir

working frequently with compressors I add my comment hoping to answer your question,

I have a different software (Prode Properties)

Prode has several methods to simulate compression stages including a proprietary method able to solve a compression stage with phase equilibria such as the case of wet gas,

for gas phase (without phase equilibria) generally I prefer the Huntington method which is a iterative method, you may find the details in the paper Evaluation of Polytropic calculation methods for turbomachinery performace (I did a copy and paste from Prode Properties operating manual), the other "classic" method is the ASME PTC10 (Schultz) procedure, results are quite close also if I consider Huntington (and Prode method) more accurate.

When a client requires a   formulation as that in GPSA manual I create a Excel page (Prode works directly in Excel) and (for GPSA formulation) I use the properties calculated at average values (p,t).

as you noted, the limits of these methods are that for real fluids properties as cp, cv density etc. are not constant, ASME PTC 10 introduces specific corrections while in Prode method values are recalculated at each step.

This equation is also used for predefining expander outlet temperature, but it assumes no liquid formation.

T₂ = T₁+T₁* [(P₂ / P₁)^_(k-1)/k - 1] * η_isen

Hello Ankur,

Thanks a lot for your interesting article.

I am a process design engineer working on refining projects and I often specify compressors for various units.

 I do not have the 13^th edition of the GPSA, but only the 12^th.

In the 12^th edition, the delta temperature of reciprocating compressors is calculated with the adiabatic method where DT=T1*[r^((k-1)/k)-1]

For centrifugal compressor, the delta temperature can be calculated with 2 methods:

• Isentropic method where DT ideal= T1*[r^((k-1)/k)-1] and DT actual= DT ideal / ηis
• Polytropic method where DT poly= T1*[r^((n-1)/n)-1]

In the 13^th edition, the formalism of the delta temperature calculations for the adiabatic and polytropic method seems to be inspired of the isentropic method of the 12^th edition with a DT ideal and a DT actual.

The power consumed by the compressor can be calculated by: Power = W*H/η where W is the mass flow rate, η the efficiency and H the head which is directly proportional to DT.

In the 13^th edition, has this formula changed to Power = W*H, without mentioning the efficiency that is already included in the head term (H)?

If not, the thing I would like to point out is that as the power consumed in a compressor is proportional to the delta temperature, the power calculated in the 13^th edition will then be higher than in the 12^th edition: Power 13^th = Power 12^th / η. Is it correct?

For a centrifugal compressor for example, the polytropic efficiency is often close to 76%. It means that the calculated power of the compressor will be (1/0.76=1.32) 32% higher when calculated with the 13^th edition compared to the 12^th. It seems to be a very huge difference for the same compressor! In my opinion, this will lead to an unnecessary very large oversizing of the driver for the service required.

Could you please give your opinion about this Ankur please?

Thanks

Flyou,

I had only extracted bits of information in my blog entry.
 
Here is what exactly the 13th Edition of GPSA has to say about discharge temperature for centrifugal compressors:
 
Isentropic Process:
 
The approximate theoretical discharge temperature can be
calculated from:

ΔT_ideal = T₁*[(P₂/P₁)^(k-1)/k – 1]

T₂^ideal = T₁ + ΔT_ideal

The actual discharge temperature can be approximated:

ΔT_actual = T₁*[(P₂/P₁)^(k-1)/k – 1] / η_is

T₂ = T₁ + ΔT_actual

GP = (w)*(H_is) / (η_is)*(3600)

Polytropic Process:

The approximate theoretical discharge temperature can be
calculated from:

ΔT_ideal = T₁*[(P₂/P₁)^(n-1)/n – 1]

T₂^ideal = T₁ + ΔT_ideal

The actual discharge temperature can be approximated:

ΔT_actual = T₁*[(P₂/P₁)^(n-1)/n – 1] / η_p

T₂ = T₁ + ΔT_actual

GP = (w)*(H_p) / (η_p)*(3600) 

The various terms are defined as follows:

P₁ = Pressure at compressor inlet, kPa(abs)

P₂ = Pressure at compressor outlet, kPa(abs)

T₁ = Temperature at compressor inlet, K

T₂ = Temperature at compressor outlet, K

k = isentropic exponent (C_p / C_v)

n = polytropic exponent

η_is = isentropic efficiency

η_p = polytropic efficiency

GP = Gas Power excluding mechanical losses, kW

w = mass flow of compressor, kg/h

H_is = Isentropic Head, kN.m / kg

H_p = Polytropic Head, kN.m / kg

Hope this clarifies what is mentioned in the GPSA 13th edition.

Regards,

Ankur.

Thank you Ankur for your clarifications.


My point is that if we take for example the polytropic method for the calculation of a centrifugal compressor, as you said, the Delta Temperature of the 13th edition is higher than the Delta Temperature of the 12th edition:


ΔT(13th)= ΔT(12th) / ηp


As the polytropic Head of the compressor is proportional to ΔT, it means that:


Hp(13th)= Hp(12th) / ηp


Finally, as the Gas Power is proportional to Hp, it means that:


GP(13th)= GP(12th) / ηp


For the example of a centrifugal compressor with a polytropic efficiency ηp of 0.76, the Gas Power calculated (but also the ΔT and the Head) with the 13th edition will be (1/0.76=1.32) 32% higher than when calculated with the 12th edition. This makes a very large difference in the consumed power for a same compressor calculated either with the 12th or 13th edition.


Is this correct? Do you get my point?
Thank you for your answer, sorry if the first post was not so clear :-D

Flyou,

The polytropic head equation does not take into account ΔT, the only input to the head equation whether polytropic or isentropic for temperature is the inlet or suction temperature of the gas being compressed.

So what you are proposing is not correct. Refer the equation below:

H_poly = (8314 / MW)*T₁*Z_avg*(n / n-1)*[(P₂/P₁)^(n-1)/n – 1]  

Regards,

Ankur.

Ankur,

Sorry to insist but I do not totally agree with you since the polytropic head equation you have just written above can also be written as follows:

H_poly = (8314 / MW)*Z_avg*(n / n-1)*T₁*[(P₂/P₁)^(n-1)/n – 1]

H_poly = (8314 / MW)*Z_avg*(n / n-1)*ΔT_{ideal (13th) =} (8314 / MW)*Z_avg*(n / n-1)*ΔT_{actual (12th)}

Correct me if i am wrong but if i well understand what is said in the 13th edition is that the Gas Power and the Polytropic Head is the same as in the 12th edition whereas the ΔT_actual is different:

ΔT_actual(13th) = ΔT_actual(12th) / η_{p =} ΔT_ideal(13th) / η_p

If it is the case, then i do not understand how the discharge temperature could be higher with the same energy consumed?

Flyou,

I do not have the 12th edition of GPSA engineering databook. Before I bought the 13th Edition I was refering the 11th Edition, so I am unable to comment on what is written in the 12th edition of GPSA databook. I have written what is there in the 13th edition and you have the 12th edition with you. Hence you can come to  a better understanding better than me for comparing the 12th and 13th edition.

Regards,

Ankur.

I think that the 12th edition GPSA engineering databook polytropic equations are the same than in the 11th edition and also the same than in the old texts and literature for compressors you are talking about at the beggining of your blog article:

ΔT = T₁*[(P₂/P₁)^(n-1)/n – 1] ------------------------------------------------------(1a)

H_p = (8314 / MW)*Z_avg*(n / n-1)*T₁*[(P₂/P₁)^(n-1)/n – 1] ----------------------(2a)

GP = (w)*(H_p) / (η_p)*(3600) -------------------------------------------------------(3a)

For the 13th edition, the actual outlet temperature equation seems to be different whereas the Polytropic Head and the Gas Power equations remain the same:

ΔT_ideal = T₁*[(P₂/P₁)^(n-1)/n – 1] ------------------------------------------------- (1b1)

ΔT_actual = T₁*[(P₂/P₁)^(n-1)/n – 1] / η_p ------------------------------------------ (1b2)

H_p = (8314 / MW)*Z_avg*(n / n-1)*T₁*[(P₂/P₁)^(n-1)/n – 1] ----------------------(2b)

GP = (w)*(H_p) / (η_p)*(3600) -------------------------------------------------------(3b)

My only concern was that i did not not understand how the discharge temperature can be higher in the 13th edition while the gas power calculated is exactly the same than in the old texts.

Finally, i think i have found the answer i wanted: the actual outlet temperature equation of the 13th edition is only used to determine a conservative value of the outlet temperature. Nevertheless, the calculation of the polytropic head and gas power does not takes into account this actual outlet temperature but only the ideal outlet temperature otherwise the polytropic head equation for the 13th edition would have been:

H_p = (8314 / MW)*Z_avg*(n / n-1)*T₁*[(P₂/P₁)^(n-1)/n – 1]/ η_p ------------------(2c)

And the power consumed would have been 1/η_p higher than in the old texts which is not the case.

Thanks again Ankur for your article and your help.

Regards,

Flyou

Please Help Me, I want to Conclude the size of header of air compressor with air velocity aproxximately 57 m/s and pressure inlet to header is 6,5 bar,and flow rate is about 5773 m3/s

Could any1 can explain that how to calculate the discharge temperature at block discharge case and fire case for PSV sizing. I go through the API 520 & 521 but block discharge case relieving temperature is not discussed.

W8 for your reply.

Hello ankur,

                   I have one doubt. Actually i was trying to use the equation 

Delta T = T1 * [(P2/P1)^(K-1)/K -1]/poly effici to fit in DCS for my compressor surge control. For that , i manually try to estimate the discharge temperature in excel spreadsheet. But i ended up in high discharge temperature which is not matching with my design value. I have doubt on K. The specific heat ratio which i have calculated in hysys based on suction condtion (Temperature, pressure). S it correct? or do u recommend some other condition.

Hello ankur,

                   I have one doubt. Actually i was trying to use the equation 

Delta T = T1 * [(P2/P1)^(K-1)/K -1]/poly effici to fit in DCS for my compressor surge control. For that , i manually try to estimate the discharge temperature in excel spreadsheet. But i ended up in high discharge temperature which is not matching with my design value. I have doubt on K. The specific heat ratio which i have calculated in hysys based on suction condtion (Temperature, pressure). S it correct? or do u recommend some other condition.

For polytropic process (centrifugal compressors follow this) the following formulas are used as per GPSA 13th edition:

ΔT_actual = T₁*[(P₂/P₁)^(n-1)/n – 1] / η_poly

and actual discharge temperature T2 as:

T₂ = T₁ + ΔT_actual

'n' is called as the polytropic exponent and can be calculated as follows:

n / (n-1) = [k / (k-1)]*η_poly

Choosing the right value of η_poly is very important. For determining η_poly refer the following link:

http://www.cheresour...et-volume-flow/

Hope this helps.

Regards,

Ankur.

Thanks ankur. One more thing i want to add up. The formula u have mentioned here is almost matching with my results for stage compression ratio 1.6. But, when i was trying to find the discharge temperature of gas for the compressor stage whose design stage compression ratio 13.6. The above formula found inconsistent (values are not matching). S there any solution? i know the compression ratio which i have mentioned is very high. But, compression ratio value is real.

raj1,

You want to have a compression ratio of 13.6 in one stage. Sorry, you can't do this my friend because the temperatures would be abnormally high. You provide multi-stage compression for this very reason.You work with a temperature to fix the stage compression ratio. As a rule of thumb you fix the stage compression ratio in such a manner that the outlet temperature from the stage does not exceed 150 deg C. When moving from one stage to another,you provide inter-stage coolers to reduce the temperature of the gas which is entering the next stage.

For gases like hydrogen and acetylene, the stage outlet temperature is maintained even lower than 150 deg C.

Hope this explains that a compression ratio of 13.6 per stage
would not be practically possible to implement.

Regards,
Ankur

Dear ankur, i agree with ur answer. But in my case inlet temperature is very less (as its is the refrigerant). So for the same power, i can be able to pressurise more for the required power and outlet temperature is coming around 35.5°F. I have attached  table for your reference.