7 replies to this topic

[bdabhi]

Hi


Natural gas compressor has following condition:

P1 28.8 kg/cm2g

T1 297 K

P2 57.3 kg/cm2g

T2 370 K

By using this condition can i find polytroic constant for my centrifugal compressor as i have used PV^n as a basic formula for suction & discharge condition & derived n which comes as 1.47 but my Adaibatic constant k is 1.26 but k is always more than n as adiabatic work must be more than polytropic work . please help me to correct my n. something i am missing.

Regards,

[ankur2061]

bdabhi,

The polytropic constant or polytropic exponent is related to the adiabatic exponent through the polytropic effciency. In equation form this can be represented as follows:

n/(n-1) = (k/(k-1))*η_poly

where:
n = polytropic exponent
k = adiabatic exponent
η_poly = polytropic efiiciency

The polytropic effciency may be considered approximately as 77-78% for a wide range of inlet volume flows to the compressor. Alternatively polytropic efficiency may be approximated from the following emprical correlation:
η_poly = 0.0992 +0.2463*log₁₀Q₁-0.02167*(log₁₀Q₁)²

where:
η_poly = polytropic efficiency

Q₁ = inlet volume flow, m³/h (at inlet conditions of pressure and temperature)

The above should be able to provide you the polytropic exponent n.

Regards,
Ankur.

[S.AHMAD]

Dear bdabhi

Nothing wrong with your calculation except that you are not using absolute pressure you need to add 1.0332 to the pressure. My calculation shows n=1.49 Using this value in the polytropic relationship with adiabatic constant (k=1.26) namely

n/(n-1) = (k/(k-1))*ηpoly

then we have polytropic efficiency of 63% which is a reasonable figure. If you know the flowrate at inlet conditions then use the equation given by ankur and compare the two figures

Edited by S.AHMAD, 15 August 2011 - 04:14 AM.

[bdabhi]

Thanks Ankur

But as per polytropic constant formula n-1/n =LN(T2/T1)/LN(P2/P1) , value of N is more than adiabatic constant. I have aslo used the formula given by you for the above condition(Qi =7505 m3/hour @P 28.8 kg/cm2g & T 297K) which gives some illogical value like 1848 .0 for polytropic efficiency. i want to calculate efficiency after finding polytropic constant & based on polytropic constant i would like to calculate Polytropic power.

[S.AHMAD]

Using ankur's equation and flowrate of 7505 m3/h the calculated polytropic efficiency is .728 or 72.8% so ankur's equation is reliable and can be used for comparison.

[bdabhi]

Thanks S Ahmad

As per thermodynemics, value of n must be k>n>0, in this case why does the valyue of n is more than k ?

[ankur2061]

bdabhi,

Which thermodynamic textbook did you refer for this? You have got it all backward.

For a given compression process following a ideal thermodynamic isentropic (reversible adiabatic) path, the isentropic efficiency is greater than the polytropic efficiency. Essentially a polytropic path of compression deviates from the isentropic path in the sense that there are infinitesmal amount changes in the gas characteristics when the isentropic compression process is broken up into infinitesmal steps. A polytropic path is thus less efficient compared to an isentropic path.

If you put it in terms of the equation, the value of n will always be greater than k when determining the work done on the system due to the fact that a polytropic process requires more work (power) than an isentropic process for the same compression ratio and the same volumetric flow rate.

Regards,
Ankur.

Edited by ankur2061, 15 August 2011 - 07:41 AM.

[S.AHMAD]

As per thermodynemics, value of n must be k>n>0, in this case why does the valyue of n is more than k ?

Dear bdabhi
Ankur has explained the thermodynamic part. Let me share with you actual plant data which were obtained sometime ago while I was working in an ammonia plant. P1=31.5 barg, T1=39.4C, P2=49 barg and T2=97.2C. These data give poly eff = 75% and n=1.65. The value of n = 1.65,that is greater than k=1.42. It seems that for n>k is quite common in the industry.

Let say if we have k=1.42 and n=1.3, these data give a poly eff = 128%. We know very well that polytropic efficiency cannot be greater than 100%.

Edited by S.AHMAD, 15 August 2011 - 07:50 PM.