Variable speed drive units (VSD) designed specifically for use with electrical submersible pumps (ESP) have been available for several years. pumps (ESP) have been available for several years. The ability to vary the operating speed of the ESP greatly expands the operating range of the unit. To take full advantage of the capabilities of an ESP operating on a VSD, it is necessary to understand the concepts of sizing and the operational limitations of the equipment.
Until the appearance of the VSD, there were only two methods of changing the performance of an ESP from the surface. The unit could be choked or it could be cycled. Neither of these methods can increase the production from the unit and both had possible detrimental effects. The VSD offers the possible detrimental effects. The VSD offers the opportunity to increase or decrease the production rate from an ESP. To understand the limitations of units operated with VSD's, it is necessary to develop a general understanding of the design details of the VSD, the pump and the motor.
The VSD belongs to a family of inverter drives. They are classified as nonsinusoidal power sources. The voltage source type is the most commonly used with the ESP. The device operates by rectifying the incoming AC power. The DC is then used to construct a stepped pseudo sine wave whose frequency is adjustable. For efficient operation, the motor flux density must be kept at the designed saturation level. The VSD accomplishes this by holding the ratio of voltage to frequency constant. As the frequency increases, the voltage is increased accordingly. The VSD efficiency ranges from 85 to 96 percent depending on design and application.
The pump is a multistage centrifugal device. The hydraulic performance of the pump is governed by four factors, the physical design of the stage, the properties of the fluid flowing through the pump, the number of stages and the RPM at which the pump operates. The performance of a particular stage is given in the form of a stage performance curve. The X axis represents the flow rate through the stage and the Y axis represents the differential head that the stage will produce. This curve represents the stage performance for water (sp.gr.=1) and a rotational speed of 3500 RPM. The efficiency and the required input horsepower are also represented.
The pump performance is dependent on the specific fluid properties which are accounted for by using performance correction factors. For the sake of simplicity, these factors are not included in this discussion.
The total pump performance is a multiple of the single stage performance for a specified flow rate. Except for cases involving high viscosity or gas cut fluid, all the stages can be considered to be operating at the same point on the stage performance curve.
Total Differential Head - Head per Stage x Number of Stages (1)
Total Required HP - HP per Stage x Number of Stages (2)
The relation between rotational speed and hydraulic performance is given by three affinity laws;
The flow through a pump is directly related to the speed.
The head produced by a pump is directly related to the square of the speed.