## 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)]

## Pump Performance Curves – part 02

In the previous article “Pump Performance Curves – part 01“, we have discussed how pump performance curves are obtained? How there are plotted? What are the downthrust and the upthrust? and what is the recommended operating range of the pump? In this article, pump performance curve is further detailed and we will answer the following two questions :

• How the shape of the pump performance curve is related to changes in well performance?
• What are the tolerance limits of performance data?

### Shape of the pump performance curve:

The  ability  of  a  pump  to  adapt  to  changes  in  well  performance  depends  on  the characteristic  shape of  the pump performance  curve.

## Pump Performance Curve – part 01

The pump performance curves characterize the performance of ESP pumps. This article will detail the technical aspects related to these curves and will answers the following questions: How pump performance curve is obtained? How to plot it? What are the downthrust and the upthrust? What is the recommended operating range of the pump?

### Pump Curve:

The published pump performance curve describes the performance of particular pump (or stage). It shows the discharge head developed by the pump, brake horsepower (power consumption curve), and efficiency of the pump as a function of flow rate. It is an experimental curve given by the manufacturer and obtained with freshwater at 60 °F (S.G. = 1) under controlled conditions detailed in API RP11 S2. These curves are commonly available for both 50 Hz and 60 Hz operation and must represent the operation of one or more stages of each pump curve (the number of pump stages must be clearly indicated on the pump chart).

Typical Pump Curve

• The left vertical axis is scaled in feet and meters of head (or lift).
• The bottom horizontal axis is scaled in bbl/d and m3/d.
• The curve labeled Head-Capacity defines the lift (or head) the impeller can produce at all of the available flow rates.
• The first vertical axis on the right is scaled in horsepower. It is based on pumping water with a specific gravity of 1.00.