Module 2

Centrifugal compressor performance characteristics

In compressor performance diagrams, curves are drawn for constant speed of rotation which relate polytropic head or pressure ratio or discharge pressure to actual inlet (or outlet) volume flow or mass flow for reference inlet conditions i.e.

Y axis could represent polytropic Head Pressure Ratio (P2/P1) Discharge Pressure (P2)

X axis could represent Actual inlet flow Actual outlet flow Standard inlet flow Standard outlet flow Mass flow

Figure 2-1 represents a family of such curves for a particular impeller design.

Centrifugal compressor impellers can be designed, to some extent, to achieve more nearly the characteristic required to suit the system requirements. But in actual practice, manufacturers usually offer standardized impeller designs.

Figure 2-1 compressor performance curve

There are two basic relations that we have to always remember about centrifugal compressors:

(1) The head produced is proportional to the square of the speed i.e. H = C N2

(2) The flow rate is linearly proportional to the speed i.e. Q = C N

Where

Q = Actual inlet volume flowH = HeadN = Compressor speedC = Constant

Thus, we may conclude that it is possible to change the design inlet gas conditions and still maintain the design inlet flow.

Centrifugal compressor head flow characteristic

Centrifugal compressor performance is typically shown on a graph of head vs. flow, with the head on the vertical scale and flow on the horizontal scale. Lines representing head and flow points for constant compressor operating speeds are plotted on the graph.

In the graph shown in Figure 2-2, head and flow are represented as 0 -100 % of the total range, and the speed line represents 100% speed for the purposes of demonstration. When a head/flow map is prepared for a particular compressor application, the actual values for the anticipated head/flow range and rpm for the compressor are used.

Figure 2-2 simplified head/ flow curve

Using the simplified curve In Figure 5, it can be seen that if any two of the three variables of head, speed, or flow are known that the third variable can be determined. If flow is determined to be 60% of the total rang and we know the compressor is operating at 100% speed, head can be determined by entering the graph at 60%, proceeding vertically to the 100% speed line, then drawing a horizontal line to read head: approximately 75%.

Within the stable flow range of a centrifugal compressor, with the compressor operating at constant speed, flow will increase if head requirements decrease, flow will decrease if head increase.

This relationship is illustrated in Figure 2-3

Figure 2-3 head/flow relationship for a centrifugal compressor

At point A, the compressor is operating at 100% speed with a flow of 60% and a head of 75%. If the compressor pressure ratio increases and the head require Increase to 90% with speed kept constant, compressor operation will move to point B with a flow of 44%. If head requirements continue to Increase, flow will continue to decrease until the compressor is operating at point C. This point represents the maximum head capability and the minimum stable flow for this compressor operating speed. If flow is allowed to decrease further, the compressor will no longer be able to maintain stable operation.

Unstable compressor operation is called surge. The peak of the compressor speed line is known as the surge limit point.

This head/flow relationship will exist at any constant compressor operating speed, as seen from the additional speed lines added to the graph In Figure 2-4. For each constant speed flow will decrease as head requirements increase, until the maximum compressor head-making capability for that speed is reached (surge point). If head requirements decrease, flow will increase.

Figure 2-4 Head/Flow Graph with Multiple Speed Lines

Compressor horsepower requirements

Centrifugal compressors are primarily designed to be driven by a two shaft turbine, though some models can be driven by electric motor

You learned that a two shaft turbine has a gas producer rotor that drives the engine compressor and accessories, and a power turbine rotor which drives the centrifugal compressor. The two rotors are mechanically independent of each other.

Figure 2-5 Gas Producer and Power Turbines

The speed of the gas producer (Ngp) determines the available output horsepower from the turbine. Generally, gas producer speed will be either manually or automatically set to remain constant for a constant utput horsepower. However, if a particular application requires a constant flow or a constant discharge pressure the package may be equipped with a governing system which will allow gas producer speed, and therefore horsepower, to vary with the process. For the purposes of this example, assume that gas producer speed remains constant unless changed by the operator.

With the gas producer turbine supplying a constant output horsepower, the power turbine is free to rotate at whatever speed is required in. order to produce the required pressure ratio1 up to 100% speed. For a constant horsepower the speed at which the power turbine and therefore the compressor will rotate is determined by head requirements and mass flow.

A simple way of relating head, mass flow, and horsepower is as follows:

Horsepower = head x mass flow x constant

Where constant = all terms other than head and flow

Part of the horsepower available to the operating compressor is used to increase the pressure ratio through head. A1other part of the horsepower is used to move the gas

through the compressor, with a small amount of horsepower being consumed by mechanical losses.Now, assume that available horsepower and horsepower consumed by mechanical losses are fixed; no additional horsepower is available.

If process head requirement: increase, more horsepower will have to be used to produce heed. This means that there will be less horsepower available to produce flow, so flow will decrease.If process head requirements decrease, less of the available horsepower will be used to produce head, so more horsepower will be available to produce flow. Flow will increase.

The amount of horsepower being consumed by the compressor does not change, only the proportion of horsepower which is being used to produce head as opposed to flow changes.

Horsepower and compressor speed

The graph shown In Figure 2-6 is slightly different from those shown earlier in the lesson.It shows lines of constant speed, and flow is represented along the horizontal scale. A hypothetical pressure ratio of 1.0 to 3.0 is represented along the vertical scale. Last, the dashed lines that have been added represent levels constant horsepower.

Figure 2-6 Performance Horsepower Map with Lines of Constant

For the purposes of explaining the compressor head/cfm relationship, the previous examples assumed a constant compressor speed.

The example in Figure 2-6 assumes that available horsepower remains constant, with compressor speed variable.

At point A, the compressor pressure ratio is 2.2, and flow is at 58%. This pressure ratio and flow require 90% of the horsepower available from the driver. This point fans slightly more than half way between the 801 and 90% speed lines, so we know that the compressor is operating at about 86% speed.

How, what will happen if pressure ratio increases to 2.9 but the available horsepower doer not increase? The compressor will have to use more horsepower to compress gas, so less horsepower will be available to produce flow.

Compressors performance maps

Map Accuracy

Compressor performance maps are computer predictions of performance for a particular compressor under specific conditions of pressure, temperature and gas composition (specific gravity and ratio of specific heats). These base conditions are assumed to remain constant. If the map is used to predict compressor performance when actual site conditions are different than those on which the map is based, some inaccuracy may occur, therefore, on every compressor performance map the base operating conditions used for computation of the map are clearly printed in the heading area.

This prediction of performance is based on computed data for each Individual stage configuration and computer data for all of the stages operating together.

Due to machining tolerance for aerodynamic components, actual compressor performance may vary somewhat from the performance predicted by the map. Figure 2-7 shows the results of testing seven identical compressors under identical conditions, at two different speeds. Note that, while all compressors fall within a reasonable margin of the prediction, there is some variation.

Figure 2-7 Compressor Test Performance

Dimensional maps

An example dimensional performance map is shown In Figure 2-8 base conditions of suction pressure and temperature, specific gravity, and ratio of specific heats are shown in the upper left corner.

The dimensional map shows, on coordinates of pressure and standard volumetric flow, lines of constant speed (rpm), horsepower lines, and a single line showing the surge limit points for all compressor operating speeds.

If a dimensional map is based on a constant suction pressure, as shown In Figure 2, the vertical scale will show a range of discharge pressure. Dimensional maps can also be based on a constant discharge pressure. In this case, the vertical scale will show the range of suction pressure. In order to have the vertical scale plotted in the customery ascending order, the dimensional map appears to be upside down when plotted for a constant base discharge pressure. This is shown in Figure 3.

In English Engineering units, pressure is expressed in psia and standard volumetric flow is expressed in mmscfd.

The dimensional map enables the user to predict what power and speed will be needed if flow and pressure conditions are known. If the maximum power available is known, the curve also enables the user to predict maximum possible flow and pressure.In the example In Figure 2, flow is 65 mmscfd and discharge pressure is 1200 psia. To read compressor speed and power requirements, a line was drawn vertically from the 65 mmscfd point at the base of the map and horizontally from the 1200 psia point at the left of the map. The intersection of these two points represents compressor operating point.

Interpolating between the 3000 and 4000 horsepower lines, we can see that required horsepower for this flow and pressure is approximately 3750 hp.

Figure 2-8 example dimensional performance map

Figure 2-8a lower suction pressure

Figure 2-8b higher suction temperature

Figure 2-8c higher suction pressure

Figure 2-8d lower suction temperature

Interpolating between the 14,000 and 15,000 rpm lines, compressor speed for this operating point can be read as approximately 14,120 rpm.

If changes in site specific gravity suction temperature or base pressure occur, relatively significant changes occur in the dimensional map. This makes the use of the dimensional map relatively inaccurate for site condition more than just a few percent different than one base condition shown on the map.

If base conditions have changed, either the semi-dimensional or head vs. capacity map should be used as described in the following pages.

Semi-dimensional performance map

An example semi-dimensional map for a compressor is shown in Figure 2-9. This map is the same as the dimensional map, except that all of the values for discharge pressure, horsepower, and flow have been divided by the map base pressure.

This map can be used when the actual base pressure at the site is different than the base pressure for the dimensional map. As stated previously, a variation in base pressure may make the dimensional map Inaccurate. If the base temperature, specific gravity and ratio of specific heats remain the same, the semi-dimensional map may be used when base pressure has changed by simply multiplying the operating point values for pressure, standard flow rate, and power by the actual base pressure.

As an example, assume that you want to use the semi-dimensional map in Figure 2-9 (based on a constant P1 of 500 psia) for an operating condition which actually has a suction pressure of 700 psia. All other conditions remain the same.

The desired P2 for this application is 1400 psia and the maximum power available is 3500 hp. You need to determine the maximum possible flow in mmscfd for this P2.

First, the 1400 psia/3500 hp point must be plotted on the map. To do this, divide both the horsepower and P2 values by the actual suction pressure of 700 psia.

Now the P2/P1 value and the hp/P1 value can be plotted on the map by drawing a horizontal line from 2.0 on the left side of the map to 5.0 hp, midway between the 4.0 and 6.0 hp lines. Draw a vertical line from this point to the base of the graph to read mmscfd/P1: 0.115

Figure 2-9 example semi-dimensional performance map

To determine the actual numerical value for mmscfd, multiply 0.115 by the actual suction pressure of 700 psia.

Thus, the maximum available flow for a P2 of 1400 and hp of 3500 at a suction pressure of 700 is 80.5 mmscfd.

In summary, this map may be used when temperature, ratio of specific heats, and specific gravity are the same as those listed on the map but base pressure has changed. If conditions other than pressure have changed, this map may no longer be accurate. In this case the head vs. capacity (inlet volume flow) map should be used.

Head versus capacity map

An example head versus capacity map (for a compressor) is shown In Figure 2-10The base operating conditions are printed in the upper left corner of the map.

The performance map shows, on coordinates of head and inlet flow, lines of constant speed (rpm), lines of constant adiabatic efficiency (η) and a single line showing the surge limit points for all compressor operating speeds. In English Engineering units, head is expressed in ft-lbf/lbm and Inlet flow is expressed in cubic feet per minute (cfm).This type of map is most often used to depict compressor performance because it is virtually unchanged by changes in the base conditions of pressure, temperature, and gas composition.

If any two values for the compressor operating point are known, the other two values may be determined from the map. In the example in Figure 2-10, cfm is known to be 1350 and compressor speed is 14,150 rpm. To determine head and efficiency for this operating point, the point must be plotted on the map. To do this, start by entering the base of the map at 1350 cfm. Draw a vertical line to 14,150 rpm. Since 14,150 rpm is not represented by a specific speed line, it is necessary to interpolate between the 14,000 and 15,000 rpm lines.) This point represents the compressor operating point of l350 cfm and l4,150 rpm. You can now read head and efficiency.

To read head, draw a horizontal line from the operating point to the left of the graph.Head for this point is approximately 37,500 ft-lbf/lbm. To read efficiency sees where the point lies in comparison to the efficiency line on the map. This point is almost directly on the 75% efficiency line. If the point were to fall between two lines, it would be necessary to interpolate.

Figure 2-10 example head vs. capacity map

Composite tandem performance maps

For all tandem compressor units, two types of composite performance maps:

Dimensional Semi-Dimensional

The composite map depicts the overall performance of multiple single body compressors operating on a single shaft at the same speed. The performance of each Individual compressor body continues to be affected by changes in:

Suction temperature Specific gravity Suction pressure first body or discharge pressure last body Ratio of specific heats

All of the base conditions which are assumed to remain constant for computation of the map are printed clearly in the heading area. In addition, assumptions are made for variations in flow rate between bodies for sidestreams entering or exiting, or for condensation drop out due to interstage cooling. These flow rate assumptions are also printed in the heading area.

It can be seen that the tandem composite performance map is based on many more assumed constant conditions than a single body map, and is thus much more susceptible to Inaccuracy when the base conditions change from the assumed base conditions. The composite map is produced for depiction of overall tandem unit performance for sales and general unit operation predictions. It should not be used for performance testing of the unit or surge control calibration.

For every tandem unit, also produces a head vs. flow map for each individual body. This map is produced for compressor performance evaluation, surge control calibration, etc.

It is important to note that the flow in MMSCFD will be related to the variable pressure. For example, if a curve is drawn on a constant suction pressure with a variable discharge pressure, the discharge flow should be divided by the factor tabulated in the inlet gas conditions to arrive at

Figure 2-11 example dimensional map for a tandem compressor package

Figure 2-12 example semi-dimensional map for a tandem compressor package