15 replies to this topic

[Ranga v]

How to calculate the polytropic efficency of a four stage centrifugal air compressor?

[ankur2061]

Ranga,

As a mathematical equation polytropic efficiency can be defined as follows:

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

where:

n= polytropic exponent, dimensionless
k = C_p/C_v =average (suction/discharge) ratio of specific heats, dimensionless

However, the tricky part is to calculate the polytropic exponent. For practical purpose as a first approximation an average polytropic efficiency of 75% (0.75) is considered per stage of compression & the polytropic exponent calculated based on the above equation knowing the average specific heat ratios.

Alternatively, if you know the discharge temperature (T₂) of the compression stage based on field measured values then you can calculate the exponent value as follows:

exponent (n or gamma) = ln(P₂/P₁) / (ln(P₂/P₁) - ln(T₂/T₁))

where:

P₁ = stage suction pressure, absolute units
P₂ = stage discharge pressure, absolute units
T₁ = stage suction temperature, absolute units
T₂ = stage discharge temperature, absolute units

Here again the pitfall is that if you don't know the discharge temperature from actual measurement then to calculate the discharge temperature you require the exponent value using the equation:

T₂ = T₁* (P₂/P₁)^n-1/n

So if you are doing some sizing calcualtions it is always a practical approach to consider a 75% polytropic efficiency for starting the calculations.

Hope this helps.

Regards,
Ankur.

Edited by Art Montemayor, 12 March 2011 - 07:33 PM.

[Root]

Dear Ankur,

For me ploytropic exponent answer is negative with above eqution, could you please elaborate further? P₂ = 45 psia; P₁ = 14.4 psia; T₁ = 40 oF and T₂ = 100 ^oF.

Thanks
Toor

[ankur2061]

Toor,

You forgot to add 460 to 40 and 100 respectively. All pressure and temperature are in absolute units. I get a value of polytropic exponent as 1.11 with your values.

Regards,
Ankur.

[Root]

Thanks for correction.

Toor

Hi

I am also looking at the n value, polytropic efficiency and hence power comsumption of a 4 stage centrifugal compressor. The compressor is not jacket cooled but does have an intercooler between each stage. I have all of the pressure and temperature readings from actual measurement and come up with the attached values for n (or gamma) and efficiency. Although when I calculate the power consumption it appears correct (21.4MW calculated vs. 26.24MW actual consumed) I am a bit confused by the values of n above 1.4? Is this expected? Please have a look at my spreadsheet and give your feedback, thanks.

Attached Files

•  Comp Data.xls   25KB   402 downloads

[ankur2061]

Alistair,

Your calculations are right, no questions about it. However, the specific heat ratio (k = C_p/C_v) is considered constant for all the stages. Since Specific heat at constant pressure (C_p) is a function of temperature, you should recheck the C_p values at the outlet of each stage for your gas composition and then recalculate the specific heat ratio at the outlet of each stage as

k = C_p/C_v = C_p / (C_p-(8.314 / MW))

where:

C_p = specific heat at constant pressure, KJ/kg-K

MW = Molecular weight of gas or gas mixture, kg / kmole

For large changes in temperature there is a variation in the specific heat ratio due to the change in the value of C_p which is a temperature dependent property. This is specially required for estimating efficiency and power characteristics of existing compressors. For initial power and head calculations of new compressor an average specific heat value may be considered since the actual sizing is done by the compressor vendor and the initial estimation is only done for the purpose of having a conservative estimate of the power requirement for the particular compressor.

For more accurate power calculations where iterative procedures are adopted for variation in temperature across the stages simulation software such as HYSYS and PROII should be utilized if available.

Regards,
Ankur.

Edited by ankur2061, 14 March 2011 - 05:12 AM.

Thanks Ankur

I have done as you advised and calculated the power when using Cp at each outlet stage; the power requirement goes from 21.38MW to 21.50MW. Not a big change numerically but when you put costs to this it is quite significant!

Can you comment on the high n value? So this compressor consumes more power than a theoretical isentropic compressor? So heat gets transferred from the compressor casing to the air? Is this the norm?

Also, I noted that the theoretical discharge temperature per stage (from T₂ = T₁ * [P₂/P₁]^(k-1)/k ) is lower than the actual outlet temperatures - again is this because of heat being transferred from the casing to the air?

Thanks again
Alistair

[ankur2061]

Alistair,

For compressor discharge temperature discussion check out the following link:

http://www.cheresour...ge-temperature/

Additionally check out the blog entry for polytropic efficiency as a function of inlet volume flow:

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

Regards,
Ankur.

[izzathaikal87]

thanks, but how about we dont know the final temperature?

[ankur2061]

izzathaikal87,

Your question is not clear. What is that you want to know? The compressor stage discharge temperature can be calculated as follows:

T₂ = T₁*(r_p)^(n-1)/n or T₂ = T₁*(r_p)^(k-1)/k

where:

T₂ = stage discharge temperature, K

T₁ = stage suction temperature, K

r_p = Pressure ratio (Discharge Pressure / Suction Pressure)

n = polytropic exponent

k = isentropic exponent = C_p/C_v

Relation between n & k is given as below:

n-1 / n = (k-1 / k)*(1 / η_poly)

where:

η_poly = polytropic efficiency

As you will notice that the key to calculating the accurate stage discharge temperature is the accurate evaluation of the k-value. If you use k-values based on the suction conditions this will provide a more conservative (read higher temperature). k-values normally decrease during compression.

The link below provides some guidelines about the impact of k-values on compressor performance and some guidelines to estimate more accurate k-values.

http://www.jmcampbel...or-performance/

Hope this helps.

Regards,
Ankur.

Edited by ankur2061, 21 September 2011 - 12:04 AM.

[eirik]

Ankur,

I see your explanations regarding polytropic relations of compression. I am currently using Hysys to find out more about compression. Therefore I want to know how hysys calculates certain values. I've tried to apply your explanations above, but still I'm not getting the numbers to agree with the numbers calculated by hysys.

I'm trying to understand how hysys calculates the isentropic exponent and the polytropic exponent. Do you now how?

E

[ankur2061]

eirik,

Have a look at the link below. This should provide you answers related to your observations about difference in HYSYS and the calculations I have presented above:

http://www.cheresour...ge-temperature/

Also note that the differences between what is calculated by HYSYS and by manual methods in terms of percentage is not very large.

You also need to provide what specific differences you are finding using an example which will provide a better understanding to the problem you are facing.

Regards,
Ankur.

[eirik]

Thanks for your answer Ankur,

I'm trying compress a gas mixture with the following input data
Composition
Methane: 0,27
Ethane: 0,34
Propane: 0,0223
n-Butane: 0,2290
Nitrogen: 0,1387

T1=25C
P1=300kPa
Mol. Flow=2e4kgmole/h

P2= 800kPa

and polytropic efficiency np=0,8

With this input I get an isentropic exponent being 1,15, and a polytropic exponent being 1,199. I understand that the polytropic exponent may be calculated from the relation
n-1 / n = (k-1 / k)*(1 / η_poly). This equation gives, with k=1,15, a fairly good approximation to the polytropic exponent given by hysys. I can accept that. But what I have trouble understanding is how hysys gets the isentropic exponent to be 1,15. I've calculated manually the k values of both streams, but neither of them gives an acceptable approximation to the result from hysys, nor does the average of k1 and k2.
I can't even see the connection between the k value and the isentropic exponent value, both calculated in hysys.

I also wonder what the difference is between Cp/(Cp-R) and Cp/Cv

E

[ankur2061]

eirik,

Presently I am on the way to board an aircraft so I will give a brief reply on the last part of your question which is the diffference between Cp / (Cp-R) and Cp/Cv as given in HYSYS.

Cp / (Cp-R) is the ideal gas heat capacity ratio whereas Cp/Cv is the real gas heat capacity ratio. Recently there has been a big discussion regarding this on the forum and the link is provided below:

http://www.cheresour...522-psv-sizing/

To quickly conclude if you have HYSYS available for compressor power and head calculations use it. It is a treied and tested simulation tool. If you are interested in trying to perform manal calculations then have a look at the link below:

http://www.cheresour...wer-calculator/

Hope this helps.

Regards,
Ankur

[eirik]

Ankur,

In the following thread you provide an equation of the specific heat capacity ratio. You also provide a spreadsheet in which there is a similar equation. Are both correct? You provide a source of the first, but do you have a source of the one in your spreadsheet? or have you made by yourself?

http://www.cheresour...0185#entry30185

Do you have any link or any tip in how I can get to the "March 14, 1977 edition of 'Chemical Engineering' magazine"

Kind regards,

Eirik