ESP system selection and performance calculations

Proper sizing and selection of an electrical submersible pump (ESP) system is essential to efficient and cost-effective performance. Selection and sizing of proper ESP equipment for a particular application should be based on a nine-step design procedure. This page outlines the procedure as a manual process to illustrate the ESP design steps. While it is accurate for simple water and light-crude designs, there are commercially available ESP design software programs that give accurate designs for wells with:

• High gas/oil ratios (GOR)
• Viscous crudes
• High temperature
• Operation on variable speed controllers (VSC)

This nine-step procedure helps the engineer design the appropriate submersible pumping system for a particular well. Each of the nine steps is explained below, including gas calculations and variable-speed operations. Specific examples are worked through in ESP design.

Step one: basic data

The design of a submersible pumping unit, under most conditions, is not a difficult task, especially if reliable data are available. Although, if the information, especially that pertaining to the well’s capacity, is poor, the design will usually be marginal. Bad data often result in a misapplied pump and costly operation. A misapplied pump may operate outside the recommended range, overload or underload the motor, or draw down the well at a rapid rate that may result in formation damage. On the other extreme, the pump may not be large enough to provide the desired production rate.

Too often, data from other wells in the same field or in a nearby area are used, assuming that wells from the same producing horizon have similar characteristics. Unfortunately, for the engineer sizing the submersible installations, oil wells are much like fingerprints (i.e., no two are quite alike).

The actual selection procedure can vary significantly depending on the well-fluid properties. The three major types of ESP applications are wells with single-phase flow of oil and/or water, wells with multiphase flow of liquids and gas (especially high free-gas rates), and wells producing highly-viscous fluids typically much greater than 10 cp. A list of required data is outlined next.

• Well data: Casing or liner size, weight, grade; tubing size, weight, grade type and thread, plus condition; pump setting depth (measured and vertical); perforated or openhole interval; well plugback total depth (measured and vertical).
• Production data: Wellhead tubing pressure; wellhead casing pressure; present production rate; producing fluid level and/or pump-intake pressure at datum point; static fluid level and/or static bottomhole pressure at datum point; datum point; bottomhole temperature; desired production rate (target); GOR; and water cut.
• Well-fluid conditions: Specific gravity of water; oil °API or specific gravity; specific gravity of gas; bubblepoint pressure of gas; viscosity of oil (dead); and other available pressure/volume/temperature (PVT) data.
• Power sources: Available primary voltage, frequency, and power source capabilities.
• Possible production problems: Sand, scale deposition, corrosion, paraffin/asphaltenes, emulsion, gas, high reservoir temperature.

Step two: production capacity

The following is a simplification of procedures for predicting well performance. This discussion assumes little or no well skin. A damaged wellbore or other factors affects the well flow performance.

Productivity index

When the well flowing pressure (P_wf) is greater than bubblepoint pressure (P_b), the fluid flow is single-phase flow, and the inflow performance relationship is a straight line with slope J, as given by the productivity index (PI).

....................(1)

Inflow performance relationships

If P_wf is less than P_b, resulting in multiphase flow in the reservoir, the inflow-performance-relationship (IPR) method should be used. The relationship is given by Eq. 2.

....................(2)

This relationship was first used by Gilbert and further developed by Vogel. Vogel developed a dimensionless reference curve that can be used to determine the IPR curve for a particular well. Others have developed variations of the IPR equation. (See Reservoir inflow performance) .

Step three: gas calculations

The presence of free gas at the pump intake and in the discharge tubing makes the process of equipment selection much more complicated and voluminous. As the fluid (liquid/gas mixture) flows through the pump stages from the intake to the discharge and through the discharge tubing, the pressure and, consequently, fluid properties (such as volume, density, etc.) are undergoing continuous change. Also, the presence of free gas in the discharge tubing may create a significant "gas lift" effect and considerably reduce the required discharge pressure or TDH of the pump.

Ideally, a well is produced with a submergence pressure above the bubblepoint pressure to keep gases in solution at the pump intake. This is typically not feasible, so the gases must be either handled by the pump or separated from the other fluids prior to the pump intake.

It is essential to determine the effect of the gas on the fluid volume to select the proper pump and any auxiliary equipment. The following calculations yield the approximate percent free gas by volume.

If the solution GOR (R_s), the gas volume factor (B_g), and the formation volume factor (B_o) are not available from reservoir data, they must be calculated, and there are a number of multiphase correlations to select from. The correlation selected will affect the design, so select the one that best matches the conditions. Standings correlations for solution GOR and formation volume factor are shown next.

Solution GOR

....................(3)

Or, in metric,

....................(4)

Note: pump-intake pressure should be substituted for bubblepoint pressure when calculating pump-intake conditions.

Gas volume factor

The gas volume factor, B_g, is expressed in reservoir scf/bbl gas (m³/m³).

....................(5)

Or, in metric,

....................(6)

Formation volume factor

The formation volume factor, B_o , represents the increased volume that a barrel of oil occupies in the formation as compared to the stock-tank barrel of oil (STBO).

....................(7)

where

....................(8)

Or, in metric,

....................(9)

Total volume of fluids

When these three variables: R_s, B_o, and B_g are known, the volumes of oil, water, and free gas can be determined and percentages of each calculated. The total volume of gas (both free and in solution) can be determined as

....................(10)

The gas in solution at submergence pressure can be determined as

....................(11)

The free gas equals the total gas minus the solution gas. The volume of oil (V_o) at the pump intake is equal to stock-tank barrels multiplied by B_o, the formation volume factor. The volume of gas (V_g) at the pump intake is equal to the amount of free gas multiplied by B_g, the gas volume factor. The volume of water (V_w) in the formation is approximately the same as stock tank barrels. Total fluid volume (V_t) can now be determined.

....................(12)

The percentage of free gas to total volume of fluids can now be calculated as

....................(13)

Step four: total dynamic head

The next step is to determine the total dynamic head (TDH) required to pump the desired capacity. The total pump head refers to feet (meters) of liquid being pumped and is calculated to be the sum of: net well lift, H_L; well-tubing friction loss, F_t; and wellhead pressure head, H_wh. The simplified equation is written as

....................(14)

Step five: pump type

Refer to the manufacturer’s catalog for pump types, ranges, and pump-performance curves (60 Hz and 50 Hz). On the basis of expected fluid production rate and casing size, select the pump type that will, at the expected producing rate, be operating within the pump’s operating range and near to the pump’s peak efficiency.

Where two or more pump types have similar efficiencies at the desired volume, certain conditions determine the pump choice:

• Pump prices and corresponding motor sizes and prices may differ somewhat. Normally, the larger-diameter pump and motor are less expensive and operate at higher efficiencies.
• When the well’s capacity is not known, or cannot be closely estimated, a pump with a "steep" characteristic curve should be chosen. If the desired volume falls at a point where two pump types have approximately equal efficiency, choose the pump type that requires the greatest number of stages. Such a pump will produce a capacity nearest the desired volume even if the well lift is substantially more or less than expected.
• If gas is present in the produced fluid, a gas separator may be required to achieve efficient operation. Note that the free gas is vented up the casing annulus. Refer to Step 3 to determine the effect of gas on the produced volume. The adjusted volume affects pump selection and the size of the other system components.
• In wells where the fluid is quite viscous and/or tends to emulsify, or in other extraordinary circumstances, some pump corrections may be necessary to ensure a more efficient operation. In such cases, contact the manufacturer for engineering recommendations.

Variable-speed submersible pumping (VSSP) system and pump selection

Under the previous or other pumping conditions, also consider the VSSP system. Such systems must be justified. For instance, if the production rate is not accurately known, a VSSP system may be applicable. A VSC effectively converts a single pump into a family of pumps, so a pump can be selected for an estimated range and adjusted for the desired production level, once more data are collected.

Review Step 9 when considering the VSSP system. Variable-frequency performance curves are included in most manufacturers’ information. The VSSP system with the VSC may provide additional economies of capital expenditure and operating expenses and should be considered in Step 6. The VSC and transformers for the VSSP system are discussed in Steps 8 and 9.

Step 6: optimum size of components

ESP components are built in a number of sizes and can be assembled in a variety of combinations. These combinations must be carefully determined to operate the submersible pumping system within production requirements, material strength, and temperature limits. While sizing components, refer to the manufacturer for the following information: equipment combinations in various casings, maximum loading limits, maximum diameter of units, velocity of a fluid passing a motor, shaft HP limitations at various frequencies.

Pump

Refer to the manufacturer’s performance curve of the selected pump type, and determine the number of stages required to produce the anticipated capacity against the previously calculated total dynamic head. Usually, performance curves for 60-Hz, 50-Hz, and variable-frequency operations are provided in the manufacturer’s catalog. The pump characteristic curves are stage performance curves based on water with a specific gravity of 1.0. At the intersection of the desired production rate (bottom scale) and the head-capacity curve (vertical scale), read the head value on the left scale. Divide this value into the TDH to determine the number of stages: total stages = TDH/(head/stage).

Separator

Refer to the manufacturer’s catalog for gas-separator information. Make the necessary adjustments in HP requirements and housing length.

Motor

To select the proper motor size for a predetermined pump size, the BHP required by the pump must be determined. The HP per stage is obtained by referring to the performance curve for the selected pump. The BHP required to drive a given pump is easily calculated by the following formula: BHP = total stages × (BHP/stage) × SG.

Refer to the manufacturer’s information for motor specifications. Select a motor size that closely meets the design conditions. The maximum load conditions should not exceed 110% of rating. Minimum operating loads should not put the motor into an idle condition, otherwise protection monitoring is nullified. Manufacturers should be contacted for specific operating ranges. Typically, operators try to select a motor that operates in the range from 70 to 100% of its rating.

Seal selection

Refer to a manufacturer’s catalog for selection of the proper seal section.

Step 7: electric cable

ESP electric cables are normally available in conductor sizes 1, 2, 4, and 6. These sizes are offered in both round and flat configurations. Several types of armor and insulation are available for protection against corrosive fluids and severe environments.

Cable selection involves the determination of cable size, cable type, and cable length.

Cable size

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

Refer to the cable voltage drop curve (samples are shown in Fig 1 ) for voltage drop in cable. At the selected motor amperage and the given downhole temperature, the selection of a cable size that gives a voltage drop of less than 30 volts per 1,000 ft (305 m) can be used as a guideline. This curve determines the necessary surface voltage (motor voltage plus voltage drop in the cable) required to operate the motor.

• 

  Fig. 1-ESP-power-cable voltage drop (after Centrilift).

Finally, check the manufacturer’s information to determine if the size selected can be used with the proposed tubing and well casing sizes. The cable diameter plus tubing-collar diameter must be less than the ID of the casing. To determine the optimum cable size, consider future equipment requirements that may require the use of a larger-sized cable.

Where power cost is a major concern, kilowatt-hour loss curves can be used to justify the cable selection. Although power rates vary widely, this information is valuable in determining the economics of various cable sizes.

Optimization procedures are based on finding the least value of total operating costs over the expected life of the cable. The total operating cost is the sum of the capital and operating expenses and these vary with cable size. Since an increase of the conductor size involves increased capital costs but decreased operating costs, a cable providing the minimum of total costs can surely be found. It is easy to see that, contrary to the rules previously used, the smallest possible size may not be the best selection.

Cable type

Selection of the cable type is primarily based on fluid conditions, bottomhole temperature, and space limitations within the casing annulus. Carefully select the type of cable for hostile environments. Refer to the manufacturers catalog for cable specifications. Where there is not sufficient space to run round cable, use electric cable with a flat configuration. The flat cable configuration induces a voltage imbalance. If it is significant, a transition splice may be required. Verify this with the manufacturer.

Cable length

The total cable length should be about 100 ft (30 m) longer than the measured pump setting depth to make surface connections a safe distance from the wellhead. Check the voltage available at the motor terminal block to avoid the possibility of low voltage starts. The available motor terminal voltage is the surface supply voltage minus the cable voltage drop.

Cable venting

In all wells, it is necessary to vent gases from the cable prior to the motor controller to avoid explosive conditions. A cable venting box is available to protect the motor controller from such gases.

Step 8: accessory and optional equipment

Downhole accessory equipment

Flat cable (motor lead extension). Select a length at least 6 ft (1.8 m) longer than the pump intake (standard or gas separator) and seal section for the motor series chosen. Refer to the manufacturer’s information for dimensions.

Flat cable guard (optional). Choose the required number for 6-ft (1.8-m) guard sections to at least equal the flat-cable length. Do not use guards for installation of a 400 series pump and seal section with 5 1/2-in. outside diameter (OD) and 20-lbm casing, and a 513 series pump and seal section with 6 5/8-in. OD and 26-lbm casing.

Cable bands. Use one 30-in. (76-cm) cable band every 2 ft (60 cm) for clamping flat cables to pumps. The 22-in. (56-cm) length can be used for all tubing/cable combinations through 3½-OD tubing. For 4 1/2-in.- and 5 1/2-in.-OD tubing, use 30-in. (76-cm) bands. One band is required for each 15 ft (5 m) of setting depth. Refer to the manufacturer’s information for dimensions.

Swaged nipple, check valve, and drain valve (optional). Select these accessories on the basis of required ODs and type of threads.

Motor controllers

Motor controllers are typical state-of-the-art digital controls consisting of two components.

System unit. This unit performs all the shutdown and restart operations. It is mounted in the low-voltage compartment of the control panel.

Display unit (optional). This unit displays readings, set points, and alarms. It is normally mounted in the amp chart enclosure for easy access. It provides all the basic functions, such as underload, overload, phase imbalance, phase rotation, and many other parameters including password and communication protocols.

Single-phase and three-phase transformers

The type of transformer selected depends on the size of the primary power system and the required secondary voltage. Three-phase isolation stepup transformers are generally selected for increasing voltage from a low-voltage system, while a bank of three identical single-phase transformers is usually selected for reducing a high-voltage primary power source to the required surface voltage.

On existing systems, some ESP units operate without the use of an additional transformer. For new installation of units with higher voltages, it is usually less expensive to install three single-phase transformers, connected wye, to eliminate the auto-transformer.

In choosing the size of a stepup transformer or a bank of three single-phase transformers, Eq. 15 is used to calculate the total kilowatts/volts/amps (KVA) required.

....................(15)

Surface cable

Choose the approximate length required for connecting the controller to the primary power system or transformer. Two pieces are generally required for installations using an auto-transformer. Size should equal the well cable size, except in the case of stepup or auto-transformer, where the primary and secondary currents are not the same.

Wellheads and accessories

Select the wellhead on the basis of casing size, tubing size, maximum recommended load, surface pressure, and maximum setting depth. Electric cable passes through the wellhead where pressure fittings are not required.

Electric-feed-through (EFT) mandrels are also available. The electric cable is spliced to pigtails. The EFT wellheads seal against downhole pressure and prevent gas leaks at the surface.

Servicing equipment

Cable reels, reel supports, and cable guides. Select the size of cable reel required to handle the previously selected cable size. Select a set of cable-reel supports on the basis of cable-reel size. Cable guides are designed to handle cable sizes 1 through 6. Normally, customers retain one cable reel, one set of reel supports, and one cable guide wheel for future use.

Shipping cases. Select the type and length of the case required accommodating the previously selected motor, pump, gas separator, and seal.

Optional equipment

Bottomhole sensing device. The downhole sensor provides continuous measurement of parameters such as:

• Wellbore pressures
• Wellbore or ESP temperature
• Discharge flow rates
• Water contamination of the motor
• Equipment vibration

Automatic well monitoring. Motor controllers are available for the continuous monitoring of pump operations from a central location.

Step 9: variable speed submersible pumping system

The ESP system can be modified to include a variable-frequency controller so that it operates over a broader range of capacity, head, and efficiency. Most of the ESP manufacturers and several third parties have computerized pump-selection programs to assist in VSSP-system selection; what follows is a basic explanation of the principles involved.

Variable frequency. The VSC is commonly used to generate any frequency between 30 and 90 Hz. Pump-performance curves for frequencies other than 60 Hz can be generated with the affinity laws (Eqs. 2 through 4 in ESP centrifugal pumps). The output rating of the motor is also affected by the operating frequency (Eq. 3 in ESP motors).

A set of curves can be developed for an arbitrary series of frequencies with these equations, as shown in the variable-frequency performance curves at the end of this step (Fig. 2). Each curve represents a series of points derived from the 60-Hz curve for flow and corresponding head points, transformed using the previously mentioned equations.

• 

  Fig. 2-FC-1200 stage variable-speed performance curve [after Centrilift Graphics, Claremore, Oklahoma (2003)].

Suppose we are given the following data at a frequency of 60 Hz: rate = 1,200 B/D; head = 24.5 ft (from FC-1200 curve at 1,200 B/D); BHP = 0.34 BHP (from FC-1200 curve at 1,200 B/D). If a new frequency of 50 Hz is chosen, the data will be: new rate = (50/60) × 1,200 B/D = 1,000 B/D; new head = (50/60)² × 24.5 ft = 17 ft; and new BHP = (50/60)³ × 034 BHP = 0.20 BHP.

By performing these calculations at other production rates, a new curve for 50-Hz operation can be plotted. Start by locating the existing points on the one-stage 60-Hz curve:

• Q₁ rate, B/D: 0; 950; 1,200; 1550; and 1,875.
• H₁ head, ft: 32, 28.6, 24.5, 15, and 0.
• Efficiency, %: 1, 63.5, 64, 49, and 0.

Following the previous equations, calculate the corresponding values at 50 Hz:

• Q₁ rate, B/D: 0; 792; 1,000; 1,292; and 1,563.
• H₁ head, ft: 22.2, 19.9, 17, 10.4, and 0.
• Efficiency, %: 0, 63.5, 64, 49, and 0.

Plotting these coordinates gives the one-stage FC-1200 head-capacity performance curve an operation at 50 Hz. Similar calculations provide coordinates for curves at other frequencies, as shown by the FC-1200 variable-speed performance curve (Fig. 2). The vortex-shaped window is the recommended operating range for the pump. As long as the hydraulic requirement falls within this range, the pump is within the recommended operating range.

Nomenclature

Am	=	motor amperage, amps
Bg	=	gas volume factor, scf/bbl [m3/m3]
Bo	=	oil volume factor, bbl/STBO
C	=	constant = 3,960, where Q is in gal/min, and TDH is in ft [= 6,750, where Q is in m3/D, and TDH is in m]
D	=	diameter, in. [cm]
F	=	correlating function for Eq. 7
Ft	=	well-tubing friction loss
H	=	head, ft [m]
HL	=	net well lift
Hwh	=	wellhead pressure head, ft [m]
J	=	slope
N	=	rotating speed, rev/min
P	=	pressure, psi [kg/cm2]
Pb	=	bubblepoint pressure, psi [kg/cm2]
Pdischarge	=	pump-discharge pressure, psi [kg/cm2]
Pr	=	well static pressure, psi [kg/cm2]
Pwf	=	well flowing pressure, psi [kg/cm2]
Q	=	flow rate, B/D [m3/d]
Qd	=	estimated production rate
Qo	=	maximum production at Pwf = 0, B/D [m3/D]
Rs	=	solution gas/oil ratio, scf/bbl [m3/m3]
T	=	torque, ft-lbf
Tconductor	=	wellbore temperature at the ESP setting depth
TC	=	temperature, °C
TF	=	temperature, °F
TG	=	total volume of gas
TK	=	temperature, K
TR	=	temperature, °R
V	=	voltage, volts
VFG	=	volume of free gas
Vg	=	volume of gas
VIG	=	volume of free gas at the pump intake
Vo	=	volume of oil, bbl [m3]
Vs	=	surface voltage, volts
VSG	=	solution gas volume
Vt	=	total volume
Vw	=	volume of water
Z	=	gas-compressibility factor (typically 0.50 to 1.00)
ηm	=	motor efficiency
ηp	=	pump efficiency

Noteworthy papers in OnePetro

Takacs, G. (2011): How to Improve Poor System Efficiencies of ESP Installations Controlled by Surface Chokes. Journal of Petroleum Exploration and Production Technologies: Vol. 1, Issue 2, p 89-97. DOI 10.1007/s13202-011-0011-9

Clegg, J. D., Bucaram, S. M., & Hein, N. W. (1993, December 1). Recommendations and Comparisons for Selecting Artificial-Lift Methods(includes associated papers 28645 and 29092 ). Society of Petroleum Engineers. doi:10.2118/24834-PA

Lea, J. F., & Nickens, H. V. (1999, January 1). Selection of Artificial Lift. Society of Petroleum Engineers. doi:10.2118/52157-MS

Lee, H. K. (1988, January 1). Computer Modeling and Optimization for Submersible Pump Lifted Wells. Society of Petroleum Engineers. doi:10.2118/17586-MS

Romer, M. C., Johnson, M. E., Underwood, P. C., Albers, A. L., & Bacon, R. (2012, January 1). Offshore ESP Selection Criteria: An Industry Study. Society of Petroleum Engineers. doi:10.2118/146652-MS

Noteworthy books

Takács G. (2009): Electrical submersible pumps manual. ISBN 978-1-85617-557-9. Gulf Professional Publishing, An Imprint of Elsevier, 440p.

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

ESP design

Electrical submersible pumps

Alternate ESP configurations

Use of ESPs in harsh environments

PEH:Electrical_Submersible_Pumps

Page champions

Jose Caridad, BSME & MSc ME