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Cp/cv Of Gas Mixture


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#1 CHEMSTRONG

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Posted 21 March 2022 - 01:18 AM

Hi,

 

 For a Centrifugal Compressor, we know that performance changes if there is a change in inlet Molecular Weight. K value which is Cp/Cv of Gas mixture, if it will change based on change in Gas Composition and also Gas Molecular Weight and Gas Temperature ?? Also K value changes if density of gas changes ?

 

Please guide me how K value changes based on other process Variables. K value is important as it is in Polytropic Efficiency formula . So it is one of the factors in Efficiency Determination

 

Best Regards,

CHEMCSTRONG 



#2 PaoloPemi

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Posted 21 March 2022 - 02:43 AM

there are many threads at cheresources forum discussing how to utilize polytropic efficiency for solving centrifugal compressor models,

inside each compressor stage you can assume constant composition while fluid properties change due to different operating conditions,

you should adopt assumptions based on ideal fluid behavior only in preliminary estimates,

for all other cases it's better to adopt rigorous models which consider real fluid properties changes,

there are many software applications available, as example I have Prode Properies but you can obtain similar results with commercial and free process simulators (see dwsim or equivalents)



#3 CHEMSTRONG

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Posted 26 March 2022 - 02:30 AM

I am using ASPEN PLUS for estimating K value ( Cp/Cv) for Compressor Gas). but i found that for heavier feeds, K value is higher around 1.32 and for lighter feeds , it is lower around 1.26 only.

IS it correct? As K value affects Polytropic Efficiency directly, how to know that value of K is correct only. Please advice on this



#4 PaoloPemi

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Posted 26 March 2022 - 07:44 AM

it depends from the procedure you utilize to calculate the efficiency...
as said the basic model based on ideal gas behaviour
Tout = Tin * (Pout / Pin) ^ (k-1) / k
in general it is not very accurate,
but if you solve the compressor with a simulator it is the software which calculates fluid properties (including heat capacity), you can start, for example, with ASME PTC 10 (based on Schultz "The Polytropic Analysis of Centrifugal Compressors") and the software will include correction factors for fluid properties...
But there are many other methods (I am familiar with ASME PTC, Huntington and proprietary methods in Prode for solving vapor+liquid) which include additional complexity / accuracy...

see also the many threads available at cheresources forum :-)



#5 CHEMSTRONG

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Posted 26 March 2022 - 10:07 AM

Dear Sir, 

 

I agree with your points but We use Polytropic efficiency equation as Eff= (k-1)/K)* In(T2/IT1))/ (In(P2/P1)) . with this equation, for heavier feeds, I get from HYSYS Compressor steady state model , K Value , T and P from PFD or H & MB directly. For some feeds with Heavier feeds, i get K value as 1.26 for first stage and K value increases from 1st stage to 5th Stage always . is it due to heavier feed in later stages of compressor . Also as pressure increases, K value increases? 

Also for heavier feeds, I get efficiency more than 100 percent , 

 

Also it temp increases beyond certain temp range,  K value is stable and stable plot after 200 Deg C

 

Also K value taken for calculation should be  K value at compressor discharge or it should be average of suction and discharge K values ?

 

Please advice



#6 PaoloPemi

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Posted 26 March 2022 - 12:19 PM

if you wish to obtain consistent results you need to adopt a more accurate model or,

with your basic model, solve in sequence several small steps (with fluid properties calculated at  intermediate condition),
as discussed in previous post ASME PTC-10 could be a good starting point, see this paper for the equations

https://oaktrust.lib...3234/t34-13.pdf

 

Schultz's method includes correction factors which improve the accuracy (compared to the basic method you adopt)


 



#7 CHEMSTRONG

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Posted 26 March 2022 - 11:42 PM

I want to know basic concept first. Shall I use average K value of suction and discharge values or just K values at compressor discharge ?

 

Regards,

CHEMSTRONG



#8 CHEMSTRONG

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Posted 26 March 2022 - 11:44 PM

For my process simulation model of compressor, K values varies from 1st stage to second to third , is it logical ?



#9 CHEMSTRONG

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Posted 26 March 2022 - 11:56 PM

Why we use K/K-1 ratio in Efficiency formula of compressor  and not only K ? K is anyways just a scaling factor right ?



#10 breizh

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Posted 27 March 2022 - 12:20 AM

Hi,

I believe you need to go to basics and find a good thermo book .  

Consider the document attached to support your work .

Breizh 



#11 PingPong

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Posted 27 March 2022 - 02:33 AM

@ CHEMSTRONG

Again you opened a new topic about a question that is related to those in other topics you already have.

As a result others here don't see the relation with what you said in other topics.

 

This is all about that ethylene plant charge gas compressor you mentioned before in your other topics.

 

You earlier wrote in one of those other topics that that CGC has water injection.

That decreases the CGC outlet temperature and as a consequence that outlet temperature cannot be used anymore to calculate compressor polytropic efficiency in the way you do.

If you would use it to calculate polytropic efficiency then indeed you could get a number higher than 100 % but that is obviously nonsens.



#12 CHEMSTRONG

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Posted 27 March 2022 - 06:53 AM

Dear Sir,( Ping-Pong),

 

I am not using it in Efficiency Formula temp which you said. 

I have very basic query for experts like you that for K Value (Cp/Cv) . K values increases as pressure increases and also decreases as temp increases .

So for my compressor in Hysys , k values are getting affected  from stage 1 to stage5, they increases as we go from stage 1 to stage 5. IS this correct?

Also my another query is K value should be taken at compressor discharge or average of suction and discharge conditions ?

 

Please advice.

 

Regards,

CHEMSTRONG



#13 PingPong

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Posted 27 March 2022 - 08:07 AM

Cp/Cv ratio of a gas depends on its composition.

In general: The more atoms a molecule has the lower its Cp/Cv ratio.

Temp and pres also have some impact.

When dealing with gas mixtures of H2 and hydrocarbons this means that the higher the molecular weight of the gas mixture the lower its Cp/Cv ratio.

Stage 1 gas contains more heavy hydrocarbons than stage 5 gas (due to interstage condensation of heavier molecules) so Cp/Cv ratio is likely to increase from #1 to #5.

 

For hand calculations use average of suction and discharge for each stage.

 

Simulators like Hysys however will calculate power and outlet temperature using an EOS which allows isentropic calculations, with the end result corrected for non-isentropic behavior depending on the efficiency specified by the user. Consult the reference manual of your simulator.


Edited by PingPong, 27 March 2022 - 08:09 AM.


#14 CHEMSTRONG

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Posted 27 March 2022 - 10:58 AM

Dear PingPong Sir,

 

Thanks a lot for your expert advice. I am grateful to you.

 

When we say more atoms per molecule, means for Ethane, K will be higher as compared to Propane ?? is it right ? This is my first query .

 

Second query is in efficiency formula, why we have K/K-1 term instead of just K value, K/(K-1) is a scaling factor ?? 

I am getting Efficiency higher than 98 percent for heavier feed, without water wash effect, so it is a dry efficiency only, without water effect.

What can be the reason for higher efficiencies ? 

I have simulation model of compressor 5 stage, but i am fetching all process conditions from model to excel and calculating efficiency outside in excel . so it is excel calculation. 

 

Thirdly, for K, i am currently using K from compressor discharge after water addition ?

 

Please advice. 

 

Regards,

CHEMStrong 



#15 PingPong

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Posted 27 March 2022 - 04:08 PM


When we say more atoms per molecule, means for Ethane, K will be higher as compared to Propane ?? is it right ?

Yes.

 


Second query is in efficiency formula, why we have K/K-1 term instead of just K value, K/(K-1) is a scaling factor ?? 

You need to read a thermodynamics book in which the formula is derived and explained. It has to do with isentropic (= reversed adiabatic) compression.

 


I am getting Efficiency higher than 98 percent for heavier feed, without water wash effect, so it is a dry efficiency only, without water effect.

What can be the reason for higher efficiencies ? 

98 % efficiency is impossibly high. You must have done something wrong.
 



#16 CHEMSTRONG

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Posted 27 March 2022 - 11:07 PM

Dear PingPong Sir,

 

I have pressure ratio of compressor around 3 for all stages and discharge temp is 80-85 deg and suction temp is 35-40 Deg C and K value is around 1.24 . With this data and flow of around 110 MTPH, can i get such high efficiencies values? 

 

Please advice. 

 

As for other plants, i do not get such high efficiencies , only for this case, i get high efficiencies .

 

Regards,

CHEMSTRONG 



#17 PingPong

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Posted 28 March 2022 - 03:02 AM

The low discharge temperature of 80 - 85 oC is caused by water injection inside the compressor casing so as to reduce temperature to minimize fouling.

 

As I said before in post #11, you can't use those temperatures to simply calculate efficiency by hand as you do.

 

To do it correctly you would have to include the water injections in an Aspen simulation and then make runs with different specified efficiencies resulting in different discharge temperatures. The efficiency that gives the real discharge temperature that you measure in actual operation is then the real efficiency.

 

To do this you need to know exactly how much water is injected at exactly which points in the compressor. Do you know that? Probably not.


Edited by PingPong, 28 March 2022 - 03:03 AM.


#18 CHEMSTRONG

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Posted 28 March 2022 - 03:24 AM

Dear Sir,

 

In HYSYS process model, I have compressor discharge stream 1 which is having H & MB discharge T, P, and then i add mixer to it and mix water wash flow 2, and then mixer outlet stream 3 has lower temp than actual, but my efficiency calculation is on stream no 1 only which is temp without wash water only. 

 

So there is no artificial increase in temp here. 80 deg c temp is for stream no 1 only. i am using formula K-1/K * (In (T2+Delta T/T1)/In(p2/P1)



#19 PingPong

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Posted 28 March 2022 - 05:33 AM

In this way we get nowhere.

What exactly are you trying to simulate? Actual operation of an existing compressor? Or data from some H&MB from a design book?



#20 CHEMSTRONG

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Posted 28 March 2022 - 06:37 AM

H & MB data of compressor operation but we have H & MB data only. I am getting values of 1.38 for compressor.

Is that possible ?



#21 PingPong

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Posted 28 March 2022 - 06:51 AM

Post all H&MB data that you have for stage 1 (or another stage if you prefer).






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