## ESP Design – Hand Calculations

This article walks through the suggested nine step procedure for selecting and designing an electric submersible pump. This nine step procedure for ESP design is a basic hand-design of simple water and light crude oil. For more complicated well conditions, such as high GOR, viscous oil, high-temperature wells, etc. a number of computer programs are available to automate this process.

## Step 1: Basic Data:

As detailed in the article “Step 1: Basic data ”, step 1 of the nine step design procedure is the most important step because all the others design steps will depend on the basic data selected in this step.

In this example, a high water cut well is considered. This is the simplest type of well for sizing submersible equipment.

• Well Profile:

Vertical Well

Casing: 7” 26#

Tubing: 3 ½” 9,2# N80 NU

Top perforation: 2003m

Pump Intake depth: 1713m

## 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”).

## Step 8 – Downhole and Surface Accessory Equipment

This article “Downhole and Surface Accessory Equipment” is the step 8 of the nine-step procedure to design an ESP with an efficient and cost-effective performance. The required downhole and surface accessory equipment are discussed and recommended practices are highlighted.

## Downhole Accessory Equipment:

• ### Motor Lead Extension (MLE):

API RP 11S4 defines the Motor Lead Extension as a “special power cable extending from the pothead on the motor to above the end of the pump where it connects with the power cable. A low-profile cable (flat configuration) is usually needed in this area due to limited clearance between the pump housing and the well casing”. It is recommended to select a length at least 6 ft. (1.8 m) longer than the upper end of the pump. The length of MLE has to be select in a way to avoid a splice over a tubing collar. Doing so could allow the cable to catch on the wellbore casing and damage the equipment.

• ### Banding Cable Protectors:

Cable protectors are used to protect the Motor Lead Cables from damage during installation, operation and pulling. The figures below show an example of cable protectors.

## ESP design – Step 7: Electric Cables

The AC current is carried from the surface to the motor using either copper or aluminum cable conductors. For ESP applications, four sizes of conductors have been standardized: #1, #2, #4 and #6 AWG (AWG stands for “American Wire Gauge”). Electric Cables are available in either flat or round configurations.

An electric submersible cable is mainly compounded by a cable conductor, insulation, jacket, braid & covering and armor. These cable compounds are for protection against corrosive fluids and severe environments.

Cable selection involves the determination of Cable Size, Type and Length.

### Cable Size:

The proper cable size is dependent on combined factors of voltage drop, amperage and available space between tubing collars and casing.

• Cable Voltage Drop:

The following graph shows an example of Cable Voltage drop plot to determine the voltage drop in cable. At the selected motor amperage and the given downhole temperature, the selection of a cable size that will give a voltage drop of less than 30 volts per 1000 feet is recommended. This curve will also enable you to determine the necessary surface voltage (motor voltage plus voltage drop in cable) required to operate the motor.

## 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)]