## Centrifugal Compressor Performance Calculations

Centrifugal compressors are versatile, compact, and generally used in the range of 1,000 to 100,000 inlet cubic ft per minute (ICFM) for process and pipe line compression applications.

Centrifugal compressors can use either a horizontal or a vertical split case. The type of case used will depend on the pressure rating with vertical split casings generally being used for the higher pressure applications. Flow arrangements include straight through, double flow, and side flow configurations.

Centrifugal compressors may be evaluated using either the adiabatic or polytropic process method. An adiabatic process is one in which no heat transfer occurs. This doesn't imply a constant temperature, only that no heat is transferred into or out of the process system. Adiabatic is normally intended to mean adiabatic isentropic. A polytropic process is a variable-entropy process in which heat transfer can take place.

When the compressor is installed in the field, the power required from the driver will be the same whether the process is called adiabatic or polytropic during design. Therefore, the work input will be the same value for either process. It will be necessary to use corresponding values when making the calculations. When using adiabatic head, use adiabatic efficiency and when using polytropic head, use polytropic efficiency. Polytropic calculations are easier to make even though the adiabatic approach appears to be simpler and quicker.

The polytropic approach offers two advantages over the adiabatic approach. The polytropic approach is independent of the thermodynamic state of the gas being compressed, whereas the adiabatic efficiency is a function of the pressure ratio and therefore is dependent upon the thermodynamic state of the gas.

If the design considers all processes to be polytropic, an impeller may be designed, its efficiency curve determined, and it can be applied without correction regardless of pressure, temperature, or molecular weight of the gas being compressed. Another advantage of the polytropic approach is that the sum of the polytropic heads for each stage of compression equals the total polytropic head required to get from state point 1 to state point 2. This is not true for adiabatic heads.

### Sample Performance Calculations

Determine the compressor frame size, number of stages, rotational speed, power requirement, and discharge temperature required to compress 5,000 lbm/min of gas from 30 psia at 60°F to 100 psia. The gas mixture molar composition is as follows:

Ethane 5%

Propane 80% n-Butane 15%

The properties of this mixture are as follows:

MW = 45.5 Pc = 611 psia Tc = 676°R Cp = 17.76 ki = 1.126 Zj = 0.955

Before proceeding with the compressor calculations, let's review the merits of using average values of Z and k in calculating the polytropic head.

The inlet compressibility must be used to determine the actual volume entering the compressor to approximate the size of the compressor and to communicate with the vendor via the data sheets. The maximum value of 6 is of interest and will be at its maximum at the inlet to the compressor where the inlet compressibility occurs (although using the average compressibility will result in a conservative estimate of \$).

Compressibility will decrease as the gas is compressed. This would imply that using the inlet compressibility would be conservative since as the compressibility decreases, the head requirement also decreases. If the variation in compressibility is drastic, the polytropic head re quirement calculated by using the inlet compressibility would be practically useless. Compressor manufacturers calculate the performance for each stage and use the inlet compressibility for each stage. An accurate approximation may be substituted for the stage-by-stage calculation by calculating the polytropic head for the overall section using the average compressibility. This technique results in overestimating the first half of the impellers and underestimating the last half of the impellers, thereby calculating a polytropic head very near that calculated by the stage-by-stage technique.

Determine the inlet flow volume, Qi: Qi = m1[(Z1RT1)/(144P1)]

where m = mass flow

Zi = inlet compressibility factor R = gas constant = 1,545/MW Ti = inlet temperature °R Pi = inlet pressure

Qi = 5,000[(0.955)(1,545)(60 + 460)/(45.5)(144)(30)] = 19,517 ICFM

Refer to Tkble 3 and select a compressor frame that will handle a flow rate of 19,517 ICFM. A Frame C compressor will handle a range of 13,000 to 31,000 ICFM and would have the following nominal data:

Hpnon, = 10,000 ft-lb/lbm (nominal polytropic head)

Ifable 3

Typical Centrifugal Compressor Frame Data*

Ifable 3

Typical Centrifugal Compressor Frame Data*

 Frame Nominal Inla t Volume Row Nominal Polytropic Head Nominal Polytropic Efficiency (%) Nominal Rotational Speed (RPM) Nominal Impeller Diameter English (ICFM) Metric (m»/h) English (fMbf/lbm) Metric (k-Nm/kg) English (in) Metric (mm)
+1 0

### Responses

• lidya
Why roller bearing in the centrifugal compressor?
4 years ago
• DANIEL
Which process occurs practically polytropic or adiabitic?
4 years ago
• folcard
Why polytropic is used for centrifugal compressors?
2 months ago