How to convert absolute discharge pressure to polytropic head?

Many of the compressor vendors provide performance curves in terms of absolute discharge pressure vs actual suction flow however, most of the process simulation software require compressor head data not discharge pressure (absolute).

Following are the steps to convert the discharge pressure to polytropic head:

Step1: Get the absolute discharge pressure (Pd) and efficiency (ε) vs. actual volumetric flowrate (v) data.

You may have to digitize the performance curve using Graph Digitizer programs. There are many available online such as GetData.

Step2: Find out the inlet conditions at each stage:

  • Suction Temperature: T1
  • Suction Pressure: Ps
  • Discharge Pressure: Pd
  • Average Isentropic Exponent, Cp/Cv: k
  • Molecular Weight: MW
  • Polytropic Efficiency: ηp

Step 3 : Calculate the polytropic exponent (n) using equation below:

 \frac {n}{n-1} = \frac {k}{k-1} \; \eta_p

Step 4 : Conversion of Absolute discharge pressure to Polytropic Head:

 H_p = \frac {Z_{avg} \; R \; T_1}{MW  \; m}  \; (r^m - 1)

where:

 m = \frac {n-1}{n}

 r = \frac {P_d}{P_s}

 Z_{avg} = \frac {Z_d + Z_s}{2}

Zs = Suction Compressibility Factor.

Zd = Discharge Compressibility Factor.

R = Universal gas Constant.

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2 thoughts on “How to convert absolute discharge pressure to polytropic head?

  1. jitesh zanwar

    Dear Sir,
    Your information looks useful to me. Please kinldy provide more details abouts below items:
    frackk, etap, and rest other. what are these variable and from were I will get these. Plz provide more details describtion about them.
    mail me.
    thanks

    Reply
    1. ckbadmin Post author

      Hi Jitesh,
      We are glad that you liked our article. There was some formula formatting issue on this articles which we have fixed.
      We apologize for any inconvenience it may have caused to you and also thank you for pointing it out.
      Please go over the updated article and let us know if you need any further assistance.
      We also have an app for converting the Absolute pressure to Polytropic or Isentropic heads here

      Thanks
      ChemKB Support

      Reply

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