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Polytropic Efficiency As A Function Of Inlet Volume Flow

21 February 2011

Posted by ankur2061

After a 2 month hiatus I am back on my blog and wih something really special.

Since the past 1 year or so the subject of compressors has intrigued me and led me to a quest in understanding more of this fascinating subject which all chemical engineers have to deal at one time or the other in their professional careers. A lot of reading on the subject went into this and subsequently led to the development of a spreadsheet on "Centrifugal Compressors Head & Power Calculations" which is on sale at the "Cheresources" online store. This spreadsheet has seen a good response from professional engineers who probably don't have access to simulation software such as HYSYS or from engineers who have ventured to understand the basic thermodynamic equations governing compression of gases rather than depending on a simulation software where the backend calculations are not provided. Mind you, I have not provided a treatise on thermodynamics of gas compression but a simple calculation tool which is fairly in agreement with the simulation software existing today.

There are some novel features in the spreadsheet which are not there in some software (e.g. HYSYS), such as calculation of number of stages and two different methods of calculating the rotational speed of the compressor

In the spreadsheet the polytropic efficiency as a function of inlet volume flow has been picked up from a table as published in the book "Pipeline Rules of Thumb Handbook" by E.W. McAllister.

However, how the Polytropic efficiency is related to the inlet volume flow was something that was still not very clear to me. Further study of the subject revealed that there are charts available in some chemical engineering texts which relate polytropic efficiency to the inlet volume flow. Following are the known sources for such charts:

1. Figure 3.6, Page 83 in Coulson And Richardson Volume 6

2. Figure 7.27 (a), Page 158 in Chemical Process Equipment - Selection & Deign by Stanley M. Walas

3. Figure 2 in the article titled "What Process Engineers Need to Know About Compressors" by William Dimoplon, "Hydrocarbon Processing", May 1978

As I had mentioned earlier in one of my blogs I like to use math more than reading charts and I decided to find out if there was a way that the inlet volume flow (m³/h or cfm)(x-axis) versus polytropic efficiency (y-axis) chart could be regressed into an equation form for ease of use.

Further searching led me to a published source from a company standard wherein the relationship between inlet volume flow and polytropic efficiency was expressed as an empirical equation. However, the units used in this equation were metric units and there was no direct means available to find the corresponding equation in English units. In order to find the corresponding equation in English units I regressed the data from the metric unit equation in an excel spreadsheet with the corresponding conversion of flow rate from m³/h to cfm. Next I introduced a trendline on the excel spreadsheet and using the equation option generated the corresponding English unit equation.

The purpose of this entry was to share these equations with all of you. Below are the equations:

Metric Units:

n_p = 0.0992 +0.2463*log₁₀Q₁-0.02167*(log₁₀Q₁)²

where:

n_P = polytropic efficiency
Q₁ = inlet volume flow, m³/h

English Units:

n_p = 0.027*log_eQ₁+0.4984

where:

n_P = polytropic efficiency
Q₁ = inlet volume flow, ft³/min

Note: Above equations provide fairly good results for inlet volume flow rates ranging from 1000 cfm to 100,000 cfm (1700 m³/h to 170,000 m³/h)

I am sure that there will be some questions and further debate on this matter and I am looking forward to it from our knowledgable forum members.

Regards,
Ankur.

20 Comments

breizh

Feb 23 2011 06:27 AM

thanks for the Math ,
Breizh

sheiko

Feb 23 2011 10:07 AM

Works good in my spreadsheet. Thanks!
But i did not find your above mentionned spreadsheet in the website. Could you please provide the link?

Chris Haslego

Feb 23 2011 02:55 PM

You can find the spreadsheet in the online store here:

http://www.cheresour...|&cat=33&shop=1

shivaprasad

Feb 25 2011 09:34 PM

My one of the intresting topic is compressors, calculating no. of stages, efficiency, type of compressors...etc

I just want to know more about this topic....

Can you please provide the article "What Process Engineers Need to Know About Compressors" by William Dimoplon, "Hydrocarbon Processing", May 1978

And can you please provide the spreadsheet? where i can give inputs/get the results..

Regards,
Shivaprasad

Root

Mar 11 2011 01:59 PM

Thanks ankur.

Philip Johnson

Apr 19 2011 09:58 AM

Very interesting and useful - I will definately use this. As always, Ankur, you are a treasure trove of useful and hard-to-find equations. I don't have any of your references so I can't personally follow-up my questions about this, so perhaps you can shed some light Ankur. My understand of polytropic efficiency is that real compressors aren't adiabatic (no heat transfer during compression), nor do they achieve the lofty goal of being isothermal (the case for infinite, continuous heat transfer during compression). Rather they lie somewhere between the two extremes because some heat transfer occurs during the compression process. The polytropic efficiency accounts for this non-ideal behavior. So I always assumed that the type of compressor was critical to determining the polytropic efficiency, since type and geometry would influence heat transfer during compression. I know this is true for some oil-bath screw compressors as they can approach isothermal performance. But maybe most recips and dynamic compressors have about the same polytropic efficiency at the same flow rates...did the authors restrict their equations to certain types or sizes of compressors?

Juned Ansari

Jun 14 2011 04:53 AM

Dear Ankur!
Nice to read your article.

What is the effect of speed on the performance of a centrifugal compressor, reciprocating compressor or Roots blower/screw compressor?

I mean to say, for example:

For a roots blower pushing ambient air, T1=20C, P1=atmospheric, T2=75C, P2=5m of water column gauge, power is 100kW (Input power to motor, assume motor eff as 90%) at 1300RPM. What would be the performance at 1480 RPM? Can we apply the affinity laws as used for pumps in this case as well. I believe, not. Please help!

Is there any equation for Cp which is a function of temp?

Also,
Can you please provide me the Isentropic Efficiency and Inlet flow for this data.

Atm pressure= 0.87908bar

Suction Temperature C

Differential Temperature
mK

Suction Pressure m(H2O)

Discharge Pressure m(H2O)

Power
KW

Drive Efficiency %

Speed
RPM

35.0000

62377.4178

0.1758

7.5228

396.3885

94.10

3570

35.0000

61027.0290

0.1758

7.5158

425.9360

94.23

3570

35.0000

57050.5520

0.1758

7.5088

505.2313

94.50

3570

35.0000

55161.5601

0.1758

7.1713

555.8407

94.62

3570

35.0000

55424.3351

0.1758

7.0307

590.9562

94.68

3570

35.0000

51832.8928

0.1758

6.6792

612.0670

94.70

3570

35.0000

44214.2352

0.1758

3.1638

622.2444

94.71

3570

ankur2061

Jun 15 2011 02:23 AM

Juned,

You need to arrive at the answers using your own efforts. I will only provide you guidelines to do your own work. You need to get your gas compression fundamentals refreshed. There are several standard chemical engineering textbooks which deal about gas compression and its thermodynamics. Also there are several specialized textbooks on compressors if you are looking for indepth study of gas compression. To name a few:

Compressors, Selection and Sizing by Royce N. Brown

Compressor Handbook by Paul C. Hanlon

Centrifugal machines (pumps are compressors) have similar affinity laws. Some free web resources about affinity laws for compressors are provided below:

http://compressorcal...ators/view/126/

http://books.google....ressors&f=false

http://books.google....ressors&f=false

Hope this helps.

Regards,
Ankur.

izzathaikal87

Sep 20 2011 08:52 PM

thanks for your information, actually when we deal with compressor
what we need to determine first?

blueminded

Dec 22 2011 04:24 AM

i was searching for such an equation for a long time:
n_p = 0.0992 +0.2463*log₁₀Q₁-0.02167*(log₁₀Q₁)²

but i have a question about it :

shouldn't the equation contain SPEED term [ rpm]?

1.my knowledge says that: poly. effeciency is a function of the flow coeffecient phi=4*60*Q/(3,14² *d³ * N * 3600 )
where
phi: flow coefficent
Q:inlet volume [m³/h]
d: diameter [m]
N: speed [rpm]

2. poly. effeciency in your function keeps in increasing while the volume increases. in fact, poly. eff. increases till it reaches its maximum , and then starts to decrease.

I hope that you can answer this question.
thank you

ankur2061

Dec 22 2011 08:32 AM

blueminded,

In my blog entry I have mentioned the resources where the relationship between the poytropic efficiency and the inlet volume flow has been depicted as a curve. The equation is just applies curve fitting techniques to represent the polytropic efficiency as a fucntion of inlet volume flow. I am not aware of polytropic efficiency as a function of volume coefficient as shown in your reply. Can you refer the source of your information.

Regards,
Ankur.

blueminded

Feb 09 2012 02:29 AM

Hello Ankur,
Sorry for taking so long time to answer. i was busy doing another stuff.
It is just a missunderstanding. You mean probably the max. possible poly. effeciency as a function of volume inlet for "all" types of compressors.
i meant: eych compressor has a performance curve. in this performance curve, you can see the poly. effeciency as a function on volume inlet.
so now wonder we have different curves.

i have a question :
do you know where can i find data for specific heat Cp [J/kg °k] for real gases. This means that Cp is a function of Temperature AND PRESSURE.
Im searching for CH4 and C3H8

Best regards,

Blueminded

ankur2061

Feb 09 2012 02:51 AM

Blueminded,

Cp is at constant pressure, change in pressure of the real gas has little impact on the value of Cp. Change in temperature has a far greater effect on Cp values. Considering this, the Cp value at different temperatures becomes important for engineering calculations. For evaluating Cp value of the most commonly encountered hydrocarbon gases refer the attachment in the following link:

http://www.cheresour...vided-by-dippr/

Regards,
Ankur.

Sunil5

Dec 22 2012 07:31 AM

Hi, I would like to calculate the polytropic efficiency of compressors. The data I received is the Actual Volumetric Flow (m3/hr) Vs Power (KW). Is there any way that the efficiency can be predicted using the above curve points?

ankur2061

Dec 22 2012 08:14 AM

Hi, I would like to calculate the polytropic efficiency of compressors. The data I received is the Actual Volumetric Flow (m3/hr) Vs Power (KW). Is there any way that the efficiency can be predicted using the above curve points?

If you have a datasheet for your compressor it surely should mention the design case for your compressor wherein the volume flow rate at standard conditions (generally 15°C & 1.01325 bara) should be mentioned or alternatively the design case mass flow rate should be provided.

If you are provided the design case standard volume flow than convert it to the volume flow at the inlet conditions using ideal gas law P1*V1 / T1 = P2*V2 / T2
where the values of P,V, T with suffix 1 indicate at standard conditions and with suffix 2 indicate at actual inlet conditions. Solve for V2 to give you the actual volume flow or inlet volume flow. Then use the equation in my blog entry to calculate the polytropic efficiency.

If you are given the design case mass flow rate for your compressor then calculate the actual volume flow rate or inlet volume flow rate by dividing the mass flow rate with the gas density at actual conditions. The actual gas density can be calculated using the equation; rho = P*M / R*T*Z where P is absolute gas pressure at inlet conditions, M is mol wt. of the gas, R is universal gas constant, T is the absolute gas temperature at inlet conditions and Z is the compressibility factor of the gas at inlet temperature / pressure. The density as calculated when divided with the mass flow rate will give you the actual volume flow. Again use this actual volume flow to find out the polytropic effciency as per the equation given in the blog.

Regards,
Ankur.

Sunil5

Dec 22 2012 09:06 AM

Thanks Ankur,

I have understood that the equation for calculation of Polytropic eff from Vol Flow rate you have mentioned is nothing but the curve equation you have fitted. I am not sure how can the same equation give polytropic eff for all cases? I mean if compressor gas is methane or if compressor gas is butane then the equation which you are saying would give same answere... Am i missing anything here?
What about the power KW curve points? Don't we ve to use it somewhere to calculate the poly. eff.?
Correct me if i am wrong..

ankur2061

Dec 22 2012 11:34 AM

Sunil,

Your concept of polytropic efficiency is not correct. Polytropic efficiency is independent of gas properties. If you read through Heinz P Bloch's book "Compressors & Modern Process Applications it says the following in Chapter 5- Centrifugal Compressor performance:

As will be explained later by dimensionless numbers, polytropic efficiency is independent of the gas properties of the application under consideration.

Normally polytropic efficiencies are provided by the compressor manufacturer, but in cases where the poytropic efficiency is not provided the curve-fitting equation for polytropic efficiency versus inlet volume flow may be used with fair amount of accuracy.

Regards,
Ankur.

jatinder

May 01 2013 02:49 AM

You can find the spreadsheet in the online store here:

http://www.cheresour...|&cat=33&shop=1

Hello Chris,

I would like to ask if there is any other way for payment to download the paid excel files. I am interest to download the pipe sizing excel file. The problem is that as a student I do not hold credit card but normal bank transfer is no problem for me.

Thanks

Jatinder

bien

May 05 2014 01:45 AM

Thanks Ankur.

¨Further searching led me to a published source from a company standard wherein the relationship between inlet volume flow and polytropic efficiency was expressed as an empirical equation¨

Could someone kindly refer me to the source/company standard from where you got the empirical equation ?

Kind regards,
Bien

ankur2061

May 05 2014 10:35 PM

Thanks Ankur.

¨Further searching led me to a published source from a company standard wherein the relationship between inlet volume flow and polytropic efficiency was expressed as an empirical equation¨

Could someone kindly refer me to the source/company standard from where you got the empirical equation ?

Kind regards,
Bien

Snamprojetti

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Polytropic Efficiency As A Function Of Inlet Volume Flow

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