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### Predicting centrifugal compressor performance

When a plant revamp is planned, assessing an existing centrifugal compressor to meet new performance requirements is essential.

**TEK SUTIKNO**

Fluor EnterprisesFluor Enterprises

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**Article Summary**

Among various types of compressors commonly used in process plants, the centrifugal type is widely used and suitable in certain applications such as high gas flow rates. For some processing plants such as hydroprocessing units, the capital cost for the centrifugal compressor recycling the reactor loop gas stream is often the highest relative to those for the remaining equipment types or items. The compressor driver also requires the highest rate of mechanical or electrical energy consumption. When an existing plant needs to be revamped for expansion, repurposing or other goals, assessing the capabilities of the existing centrifugal compressor to meet the new performance requirements is an essential step for identifying cost-effective revamp options without the need for a new compressor and the associated systems. In cases where the compressor needs to be modified to meet the new requirements, the performance of this modified compressor at off-
design or upset conditions will also need to be predicted for evaluating overpressure risk levels and identifying any additional modification scope necessary for the connected systems.

While the compressor vendor may be requested to provide modification options for reusing the existing compressor to meet new performances needed for a revamp project, the vendor typically requires a new commercial contract and probably considers the option for a new compressor replacement is more lucrative than the reuse option, in addition to the time period required to complete the evaluation of the existing compressor. To maximise the potential reuse of an existing compressor in a new revamp project, the ability to predict the compressor performance can certainly be essential for assessing or pre-screening the modification options more effectively and in a more timely fashion, especially when several options need to be evaluated at a time and additional options may come up later.

This article discusses a correlation method for predicting the performance of an existing centrifugal compressor in new operating conditions and presents the results from specific examples. This method utilises parameters reported in the literature and mainly involves correlating an available set of performance data to predict the performances at new operating conditions.

The performance curves provided by the vendor for an existing centrifugal compressor typically include the polytropic head (H) versus the volume flow rate (Q) at suction and polytropic efficiency (η) versus Q. Figures 1 and 2 show these typical performance curves provided by the vendor except that heads and flow rates are presented as ratios based on the rated or design operating points. The left vertical axis of Figure 1 shows the polytropic head ratios and right vertical axis discharge pressures Pd ratios. The polytropic heads plotted versus the actual volumetric flow rate at the suction condition in Figure 1 are typically derived by assuming an essentially adiabatic polytropic compression path represented as Equation 1 describing the pressure (P) and specific volume (v) relation for this path:

P1 v1n = P2v2n (1)

For ideal gas following Cp – Cv = R, where R is the gas constant, Cp heat capacity at constant pressure, and Cv heat capacity at constant volume, Equation 2 can be derived to describe a reversible, adiabatic process, and kideal equals to Cp/Cv, or ideal gas heat capacity ratio:

P1v1k = P2v2k (2)

The polytropic exponent n describing the adiabatic Pvn compression path can be estimated by Equation 3 where η is the polytropic efficiency shown in Figure 2 as a function of the inlet volumetric flow rate. k may be estimated from molecular weight and temperature correlations or obtained from a commercial simulation program. The average of ks at compressor suction and discharge is generally used for estimating the k value:

(3)

The compressor discharge pressure Pd in psia at a given rotation speed (N) can be estimated using Equation 4. As shown, a number of gas properties and suction conditions are needed to predict the discharge pressure, Pd:

(4)

where:

Ps – Suction pressure, psia

n – polytropic exponent

H – head in lbf-ft/lbm

MW – molecular weight, lbm/lb mole

Zavg – average compressibility factor

Ts – suction temperature, °R

Flow and head coefficients

The head data in Figure 1 can be used to generate plots of head coefficient (ψ) versus flow coefficient (φ) and η versus φ. Equations 5 and 6 define φ and ψ respectively:

(5)

(6)

where:

Q – inlet volumetric flow rate, acfm

N – rotational speed, rpm

d – impeller diameter (or effective), IN

I – number of impellers

Figures 3 and 4 respectively show the plots of head coefficient ψ versus flow coefficient φ and polytropic efficiency η versus φ. These are derived from the existing set of curves provided by the vendor for the base case or design case of the existing compressor. As will be discussed next, these figures can be used to predict the new performance of the compressor when one (or more) of the operating parameters has changed.

One of the operating conditions affecting compressor performance is the suction pressure. Reducing the suction pressure decreases the gas density and increases the inlet volumetric flow rate, Q. As indicated in Figures 1 and 3, higher flow rates decrease the polytropic head and the associated discharge pressure. For a system where the discharge pressure is controlled to stay constant, the compressor delivers less mass flow rate as the suction pressure is reduced. Conversely, the compressor in the same constant discharge pressure system delivers more mass flow rate when the suction pressure increases.

To predict the performance curves of the same compressor at a lower suction pressure and other variations of parameters such as the rotational speed, flow coefficient φ is first calculated using Equation 5 for the required range of inlet volumetric flow rates, Q. Based on the calculated φ values, Figures 3 and 4, which are derived from the available performance curves, are used to predict the head coefficient ψ and the polytropic efficiency η.

While the compressor vendor may be requested to provide modification options for reusing the existing compressor to meet new performances needed for a revamp project, the vendor typically requires a new commercial contract and probably considers the option for a new compressor replacement is more lucrative than the reuse option, in addition to the time period required to complete the evaluation of the existing compressor. To maximise the potential reuse of an existing compressor in a new revamp project, the ability to predict the compressor performance can certainly be essential for assessing or pre-screening the modification options more effectively and in a more timely fashion, especially when several options need to be evaluated at a time and additional options may come up later.

This article discusses a correlation method for predicting the performance of an existing centrifugal compressor in new operating conditions and presents the results from specific examples. This method utilises parameters reported in the literature and mainly involves correlating an available set of performance data to predict the performances at new operating conditions.

**Existing performance data**The performance curves provided by the vendor for an existing centrifugal compressor typically include the polytropic head (H) versus the volume flow rate (Q) at suction and polytropic efficiency (η) versus Q. Figures 1 and 2 show these typical performance curves provided by the vendor except that heads and flow rates are presented as ratios based on the rated or design operating points. The left vertical axis of Figure 1 shows the polytropic head ratios and right vertical axis discharge pressures Pd ratios. The polytropic heads plotted versus the actual volumetric flow rate at the suction condition in Figure 1 are typically derived by assuming an essentially adiabatic polytropic compression path represented as Equation 1 describing the pressure (P) and specific volume (v) relation for this path:

P1 v1n = P2v2n (1)

For ideal gas following Cp – Cv = R, where R is the gas constant, Cp heat capacity at constant pressure, and Cv heat capacity at constant volume, Equation 2 can be derived to describe a reversible, adiabatic process, and kideal equals to Cp/Cv, or ideal gas heat capacity ratio:

P1v1k = P2v2k (2)

The polytropic exponent n describing the adiabatic Pvn compression path can be estimated by Equation 3 where η is the polytropic efficiency shown in Figure 2 as a function of the inlet volumetric flow rate. k may be estimated from molecular weight and temperature correlations or obtained from a commercial simulation program. The average of ks at compressor suction and discharge is generally used for estimating the k value:

(3)

The compressor discharge pressure Pd in psia at a given rotation speed (N) can be estimated using Equation 4. As shown, a number of gas properties and suction conditions are needed to predict the discharge pressure, Pd:

(4)

where:

Ps – Suction pressure, psia

n – polytropic exponent

H – head in lbf-ft/lbm

MW – molecular weight, lbm/lb mole

Zavg – average compressibility factor

Ts – suction temperature, °R

Flow and head coefficients

The head data in Figure 1 can be used to generate plots of head coefficient (ψ) versus flow coefficient (φ) and η versus φ. Equations 5 and 6 define φ and ψ respectively:

(5)

(6)

where:

Q – inlet volumetric flow rate, acfm

N – rotational speed, rpm

d – impeller diameter (or effective), IN

I – number of impellers

Figures 3 and 4 respectively show the plots of head coefficient ψ versus flow coefficient φ and polytropic efficiency η versus φ. These are derived from the existing set of curves provided by the vendor for the base case or design case of the existing compressor. As will be discussed next, these figures can be used to predict the new performance of the compressor when one (or more) of the operating parameters has changed.

**Operating conditions**One of the operating conditions affecting compressor performance is the suction pressure. Reducing the suction pressure decreases the gas density and increases the inlet volumetric flow rate, Q. As indicated in Figures 1 and 3, higher flow rates decrease the polytropic head and the associated discharge pressure. For a system where the discharge pressure is controlled to stay constant, the compressor delivers less mass flow rate as the suction pressure is reduced. Conversely, the compressor in the same constant discharge pressure system delivers more mass flow rate when the suction pressure increases.

To predict the performance curves of the same compressor at a lower suction pressure and other variations of parameters such as the rotational speed, flow coefficient φ is first calculated using Equation 5 for the required range of inlet volumetric flow rates, Q. Based on the calculated φ values, Figures 3 and 4, which are derived from the available performance curves, are used to predict the head coefficient ψ and the polytropic efficiency η.

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