Modeling a Positive Displacement Pump With Slip

It’s often necessary for a process system to model positive displacement (PD) pumps.

First, we will review the operation of a PD pump. Figure 1 shows a PD pump operating curve.

The X-axis displays the pump speed and the Y-axis displays the pump capacity.  There are multiple pump curves based on the pump’s discharge pressure.  As you can see from the curve, as the discharge pressure increases, the capacity of the pump decreases for a given pump speed.  This is caused by slip or leakage of fluid in the pump. The greater the differential pressure across the pump, the greater the pump slip.

A PD pump can be modeled in PIPE-FLO by combining a pump operating at a fixed flow rate with a component in parallel with the pump to allow for the pump slip.  See Figure 2 below:

The pump provides the motive flow. It passes a set flow rate regardless of the pump’s discharge pressure. Since the PD pump slip increases with increasing discharge pressure, that must be factored into the model. The slip can be added by installing a component in parallel with the pump. To determine the appropriate component characteristics to model the pump slip, we must look at the PD pump curve and see how the discharge pressure affects the flow rate through the pump at a given speed.

As you can see from the example PD pump curve, as the pump speed increases the flow rate increases. Further, as the pump discharge pressure increases for a given pump speed, the flow rate through the pump decreases (due to the pump slip).

From the pump curve in Figure 1, we can get the following data for the pump when it is running at 460 rpm:

We can see with a differential pressure of 50 psi across the pump, the slip is 2 gpm, and with a dP of 100 psi the slip increases to 6 gpm. With this information we can design the slip component in PIPE-FLO:

Notice that the slip through the PD pump is constant for all pump speeds. As a result, the slip component will work for the entire range of operation for the pump. One additional note concerning PD pumps: the operating curve for a PD pump is a function of fluid viscosity. As the viscosity increases, the slip through the pump decreases. As a result, you must change your slip component to match the viscosity of the process fluid through the pump.

Note: When designing the inlet and outlet component pipelines, you should make them short (< 1′) so that the pressure drop through them is insignificant.

Once the component installation is complete, set the pump flow rate to the desired value. During the system calculation, as the pump discharge pressure increases, the flow rate through the slip component will also increase, passing more fluid back to the pump suction. To obtain the required flow rate out to the system, you will need to compensate for the pump slip by increasing the set flow rate through the pump.