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Centrifugal Compressor Power Calculation

In this post I want to share you how to calculate centrifugal compressor power since there are so many process engineers are looking for it (and I also don’t know how).

To calculate centrifugal compressor power, we need these gas properties: compressibility factor (Z), molecular weight (MW), inlet gas temperature, inlet gas pressure, outlet gas pressure, adiabatic component (Cp/Cv), and mass flow rate.

Let’s start with an example while I show you step-by-step of the calculation method. In this example, we have these gas properties (I use US units).

Compressibility factor (Z) = 0.9972

Molecular weight (MW) = 18.15

Gas constant (R) = 1544/molecular weight

Inlet temperature (T1)  = 546 deg R

Inlet pressure (P1) = 15 psia (don’t forget to use absolute pressure)

Outlet pressure (P2) = 60 psia

K (Cp/Cv) = 1,274

Flow (W) = 0,184 lb/min

The required data to calculate centrifugal compressor power is head. We can use either adiabatic head or polytropic head as long as we use adiabatic efficiency and polytropic efficiency in companion.

In this example, we will calculate power requirement by using adiabatic head, polytropic head, and by process simulator. We want to know if those methods give the same results or not.

Centrifugal Compressor Power Calculation using Adiabatic Head

To calculate adiabatic head and power we use equation below.

Centrifugal Compressor Power Calculation
Adiabatic head and centrifugal compressor power calculation

From the data above, adiabatic head (Had) is 74,808.54 ft.lbf/lbm.

To calculate power, we need adiabatic efficiency (Ea). Adiabatic efficiency is function of type of compressor, rpm, volumetric flow, and adiabatic head. We can determine adiabatic efficiency by using figure below.

Adiabatic efficiency
Adiabatic efficiency

Figure above shows that for centrifugal compressor, adiabatic efficiency is ranging from 60% to 80%. For preliminary calculation we choose 70% adiabatic efficiency.

By using the second equation, we get power requirement is 0.594 hp.

Centrifugal Compressor Power Calculation using Polytropic Head

To calculate power by using polytropic head, we need polytropic efficiency. Polytropic efficiency is a function of adiabatic efficiency. Relationship between those efficiency is expressed in equation below.

Relationship between adiabatic efficienct and polytropic efficiency
Relationship between adiabatic efficiency and polytropic efficiency

From equation above, we get polytropic efficiency is 73.99%. Please note you can change (N-1)/N with (K-1)/KEp.

To calculate polytropic head and power using polytropic data, use equation below.

Centrifugal Compressor Power Calculation using Polytropic head
Centrifugal Compressor Power Calculation using Polytropic head

By using the equation, we get polytropic head is 79,075.11 ft lbf/lbm. And power requirement is 0.594 hp, which is exactly the same as previous method.

Centrifugal Compressor Power Calculation using Process Simulator

By using process simulator, we get power requirement 0.589 hp, which is slightly below calculation. But overall, the method is correct.

I think I spend too much time calculating power requirement using both adiabatic approach and polytropic approach. So, it is better to use adiabatic approach only if you are sure enough with the calculation.

One thing that you might need to correct is adiabatic efficiency. In this example, I guessed adiabatic efficiency. It will be more accurate if you calculate specific speed to get exact value of adiabatic efficiency based on graph.

References:

  1. Rules of thumb of Chemical Engineers – Carl Brannan
  2. Perry’s Chemical Engineers’ Handbook

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