## Step 9 – Variable Speed Submersible Pumping System

Compared to conventional ESP installations with constant motor speeds, installations running at variable frequencies have several advantages. The most important benefit of a Variable Speed Submersible Pumping System is the wide flexibility of the variable frequency ESP system that permits perfect matching of the lift capacity of the ESP system and the well’s productivity. Therefore, it operates over a much broader range of capacity, head, and efficiency.

NB: Variable Frequency Drive basics (also, named: Variable Speed Drive) are presented and discussed in the article “Variable Frequency Drive Basics”.

Since a submersible pump motor is an induction motor, its speed is proportional to the frequency of the electrical power supply. This relationship between variables involved in pump performance (such as head, flow rate, shaft speed) and power is known as “Affinity Laws” (also called “Pump Laws”).

## ESP design – Step 6: Optimum Size of Compounds

ESP compounds have different sizes and can be assembled in a variety of combinations. These combinations must be carefully determined to operate the ESP with production requirement, downhole conditions, material strength and temperature limits, etc. to select the optimum size of compounds.

### Pump:

To determine the required number of stages of the pump to produce the anticipated capacity; just divide the Total Dynamic Head (TDH) by the Head developed by Stage.

Refer to the article “ESP design – Step 4: Total Dynamic Head” to review how the TDH is calculated.

The Head developed per stage is deducted from the published performance curve which shows the discharge head developed by the pump. It is an experimental curve given by the manufacturer and obtained with fresh water at 60 F under controlled conditions detailed in API R11 S2. Refer to the articles “Pump Performance Curves – part 01” and “Pump Performance Curves – part 02” for more details.

Once calculated, divide the TDH by the Head developed per stage to get the Total Number of Stages required to produce the anticipated capacity.

Total Stages = TDH / [(Head / stage)]