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ESP design

This page walks through the suggested 9-step process for selecting and sizing an electrical submersible pump system for artificial lift. The process is manual for illustrative purposes. A number of computer programs are available to automate this process.

Design example 1

Step one: basic data

Well data. K55 casing from surface to 5,600 ft: 7 in. and 26 lbm/ft; K55 liner from 5,530 to 6,930 ft: 5 in. and 15 lbm/ft; J55 EUE API tubing: 2 7/8 in. and 6.5 lbm/ft; perforations and true vertical depth (TVD): 6,750 to 6,850 ft; and pump setting TVD (just above liner top): 5,500 ft.

Production data. Tubing pressure: 100 psi; casing pressure: 100 psi; present production rate: 850 BFPD; pump-intake pressure: 2,600 psi; static bottomhole pressure: 3,200 psi; datum point: 6,800 ft; bottomhole temperature: 160°F; minimum desired production rate: 2,300 BFPD; GOR: 300 scf/STB; and water cut: 75%.

Well fluid conditions. Specific gravity of water: 1.085; oil °API or SG: 32; SG of gas: 0.7; bubblepoint pressure of gas: 1,500 psi; viscosity of oil: N/A; PVT data: none.

Power sources. Available primary voltage: 12,470 V; frequency: 60 Hz; power source capabilities: N/A.

Possible problems. There were no reported problems.

Step two: production capacity

Determine the well productivity at the test pressure and production rate. In this case, the maximum production rate is desired without resulting in severe gas-interference problems. The pump-intake pressure at the desired production rate can be calculated from the present production conditions.

Because the well flowing pressure (2,600 psi) is greater than bubblepoint pressure (1,500 psi), the constant-productivity index (PI) method will most probably give satisfactory results. First, one can determine the PI using the test data:

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

and

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

Next, we can determine the new well flowing pressure (Pwf) at the estimated production rate (Qd).

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

and

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

The well flowing pressure of 1,580 psi is still above the bubblepoint pressure of 1,500 psi; therefore, the PI approach should give good results. The pump-intake pressure can be determined by correcting the flowing bottomhole pressure for the difference in the pump setting depth and datum point, and by considering the friction-loss datum point and friction loss in the casing annulus. In the given example, as the pump is set 1,300 ft above the perforations, the friction loss, because of flow of fluid through the annulus from perforations to pump setting depth, is small, as compared to the flowing pressure, and can be neglected.

Because there is both water and oil in the produced fluids, it is necessary to calculate a composite SG of the produced fluids. To find the composite SG, water cut is 75%; therefore,

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

Oil is 25%; therefore,

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

The composite SG is the sum of the weighted percentages:

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

The pressure, because of the difference in perforation depth and pump setting depth (6,800 to 5,500 ft = 1,300 ft), can be determined as:

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

and

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

Therefore, the pump intake pressure is

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

Step three: gas calculations

In this third step, one must determine the total fluid mixture, inclusive of water, oil, and free gas that is ingested by the pump. Use actual pressure volume temperature (PVT) data if available. For this example, Standing’s correlation was used. [1]

Determine the solution GOR (Rs) at the pump-intake pressure by substituting the pump-intake pressure for the bubblepoint pressure (Pb) in Standing’s equation. This relationship can also be found as a monograph in many textbooks.

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

and

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

Determine the formation volume factor (Bo) with Rs and the following Standing’s equation (can also be found as a monograph).

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

where

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

Therefore,

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

and

....................(16)

Determine the gas volume factor (Bg) as

....................(17)

By assuming 0.85 Z factor (use actual PVT data if available),

....................(18)

Next, determine the total volume of fluids and the percentage of free gas released at the pump intake. Using the producing GOR and oil volume, determine the total volume of gas (Vg).

....................(19)

Using the solution GOR (Rs) at the pump intake, determine the solution gas volume (VSG).

....................(20)

The difference represents the volume of free gas (VFG) released from solution by the decrease in pressure from bubblepoint pressure of 1,500 psi to the pump-intake pressure of 1,000 psi.

....................(21)

The volume of oil (Vo) at the pump intake is

....................(22)

The volume of free gas at the pump intake (VIG) in barrels is

....................(23)

Next, is the equation for the volume of water (Vw) at the pump intake.

....................(24)

The total volume (Vt) of oil, water, and gas at the pump intake can now be determined by

....................(25)

The ratio or percentage of free gas present at the pump intake to the total volume of fluid is

....................(26)

As this value is less than 10% by volume, it has only a minor effect on the pump performance, especially if most of the free gas is vented up the annulus. Use of a gas separation component is not essential in this case.

The composite specific gravity (SG), including gas, is determined by first calculating the total mass of produced fluid (TMPF) from the original data given.

....................(27)

and

....................(28)

Now that the total volume of fluid entering the first pump stage is known (2,550 BFPD) and the composite SG has been determined, we can continue to the next step of designing the ESP system.

Step four: total dynamic head (TDH)

Sufficient data are now available to determine the TDH required by the pump.

....................(29)

and

....................(30)

The TDH required is based on the normal pumping conditions for the well application. If the well is killed with a heavier-gravity fluid, a higher head is required to pump the fluid out, until the well is stabilized on its normal production. More HP is also required to lift the heavier kill fluid and should be considered when selecting the motor rating for the application. Ft = tubing friction loss. Refer to Fig. 1[2].

Friction loss per 1,000 ft of 2 7/8-in. tubing (new) is 49 ft/1,000 ft of depth at 2,440 B/D (405 m3/d) or 4.5 m/100 m. Using the desired pump setting depth,

....................(31)

....................(32)

and

....................(33)

Step five: pump-type selection

From the manufacturer’s catalog information, select the pump type with the highest efficiency at the calculated capacity 2,440 B/D (405 m3/d) that will fit the casing. Select the 513 series GC-2200 pump (Fig. 2).

The head in feet (meters) for one stage is 2,550 B/D (405 m3/d) and is 41.8 ft (13 m). The BHP per stage is 1.16. To determine the total number of stages required, divide the TDH by the head/stage taken from the curve. The number of stages = TDH/(head/stage). The number of stages = (3,556 /41.8) = 85 stages.

Refer to the manufacturer’s information for the GC-2200 pump. The housing no. 9 can house a maximum of 84 stages, 93 stages for a housing no. 10. Because the 84-stage pump is only one stage less than the calculated requirement, it should be adequate and the pump will cost less. Once the maximum number of pump stages is decided, calculate the total BHP required as

....................(34)

and

....................(35)

Step six: optimum size of components

Gas separator. If a gas separator was required, refer to a catalog to select the appropriate separator and determine its HP requirement. In this example, one was not needed. If gas interference causes operating problems, a gas separator can be added on the next ESP repair.

Seal section. Normally, the seal section series is the same as that of the pump, although there are exceptions and special adapters available to connect the units together. Here, the 513 series GSB seal section is selected.

The HP requirement for the seal depends on the TDH produced by the pump. The manufacturer’s information shows a requirement of 3.0 hp for the 513 series seal operating against a TDH of 3,556 ft. Therefore, the total HP requirement for this example is 91.5 hp for the pump, plus 3.0 hp for the seal, or 94.5 hp total.

Motor. Generally, a 500 series motor should be used with the 513 series pump. When a motor is selected, consideration should be given to choose as large a diameter unit as possible for the casing to optimize the initial cost, motor efficiency, operating costs, and repair costs. In this example select the 100-hp 562 series motor from the catalog. The motor voltage can be selected on the basis of considerations discussed next.

The high-voltage, consequently low-current, motors have lower cable losses and require smaller conductor-size cables. High-voltage motors have superior starting characteristics—a feature that can be extremely important if excessive voltage losses are expected during starting. Although, the higher the motor voltage, the more expensive is the motor.

In some cases, the savings, because of smaller cable, may be offset by the difference in motor-controller cost, and it may be necessary to make an economic analysis for the various voltage motors. However, for this example, the high-voltage motor (100 hp; 2,145 V; 27 amps) is an excellent choice. Check the manufacturers catalog and equipment information to assure that all operating parameters are well within their recommended ranges (e.g., thrust bearing, shaft HP, housing burst pressure, and fluid velocity).

Step seven: electric cable

Determine cable size. The cable size is selected on the basis of its current-carrying capability. Using the motor amps (27) and the cable voltage-drop chart in the catalog, select a cable size with a voltage drop of less than 30 V/1,000 ft. All conductor sizes 1 through 6 fall in this category. The no. 6 cable has a voltage drop of 18.5 × 1.201 = 22.2 V/1,000 ft (305 m), and based on \$0.06/kW-hr. results in a monthly I 2 R loss of \$255. A no. 4 cable has 14.1 V/1,000 ft and costs \$158/month. The operating cost savings of \$97/month is divided into the added cost of the no. 4 over the no. 6 cable to calculate a payout. A no. 6 cable size was selected for this example.

Cable type. Because of the gassy conditions and the bottomhole temperature, the polypropylene ("poly") cable should be used. Check to be sure the cable diameter plus tubing collar diameter is smaller than the casing inside diameter (ID).

Cable length. The pump setting depth is 5,500 ft (1676.4 m), with 100 ft (30.5 m) of cable for surface connections; the total cable length should be 5,600 ft (1707 m). Check to verify that the cable length is within the manufacturer’s recommended maximum length,

Cable venting. A cable vent box must be installed between the wellhead and the motor controller to prevent gas migration to the controller.

Step eight: accessory and miscellaneous equipment

Flat cable-motor lead extension. As described in ESP system selection and performance calculations, calculate the length for the MLE. Pump length = 14.8 ft (4.51 m); seal length = 6.3 ft (1.92 m); plus, 6 ft = 6.0 ft (1.83 m) = 213.1 ft (8.26 m); select 35 ft (10.7 m) of 562 series flat cable.

Flat guards. Cable guards are available in 6-ft sections; therefore, six sections are sufficient.

Cable bands. The pump and seal section is approximately 20 ft (6 m) long. Twenty-two-inch (56 cm) bands are required to clamp to the housing with bands spaced at 2-ft (61 cm) intervals (10 bands). On the production-tubing string above the pump, the same length cable bands can be used. The bands should be spaced at 15-ft (4.5-m) intervals. The setting depth of 5,500 ft requires 367 bands.

Downhole accessory equipment. Refer to the manufacturer’s catalog for the accessories listed next.

Swaged nipple. The pump outlet is 2 7/8 in., per the manufacturer’s information, so a swaged nipple is not required for the 2 7/8-in. tubing.

Check valve. The 2 7/8-in.-EUE, 8-round, thread check valve is recommended.

Drain valve. The 2 7/8-in.-EUE, 8-round, thread drain valve should be used (in conjunction with the check valve) to eliminate pulling a wet string.

Motor controller. The motor-controller selection is based on its voltage, amperage, and KVA rating. Therefore, before selecting the controller, one must first determine the motor controller voltage. Assume the controller voltage is the same as the surface voltage going downhole. The surface voltage (SV) is the sum of the motor voltage and the total voltage loss in the cable. (Adjust taps on the transformer to closely achieve this value.)

....................(36)

The motor amperage is 27 amps; the KVA can now be calculated.

....................(37)

and

....................(38)

The 6H-CG motor controller suits these requirements.

Transformer. The transformer selection is based on the available primary power supply (12,470 V), the secondary voltage requirement (2,269 V) and the KVA requirement (106 KVA). Choose three 313.5 KVA single-phase transformers as shown in the manufacturer’s catalog.

Surface cable. Select 50 ft (15.2 m) of no. 1 cable for surface connection to transformers.

Design example 2

Step one: variable-speed pumping system

Use the previous example, and design a new system using a VSC. To help justify the use of a VSC, two new conditions were added. First, assume that we need to maintain a constant oil production (575 BOPD), although, reservoir data indicate we should see an increase in water cut (75 to 80%) over the next few months. Next, to satisfy our economic justification in using the VSC, we must optimize the initial cost and size of the downhole assembly.

To maintain oil production as the water cut increases, we must determine the maximum desired flow rate with 80% water.

....................(39)

and

....................(40)

Step two: production capacity

We can now calculate the pump intake pressure at the maximum rate of 2,875 B/D. First, make the assumption that even though the water cut changes, the well’s PI will remain constant. Now, determine the new well flowing pressure (Pwf) at the maximum desired production rate (Qd).

....................(41)

and

....................(42)

The new well flowing pressure of 1,175 psi is slightly below the bubblepoint pressure of 1,500 psi; therefore, the PI approach should still give good results.

The pump-intake pressure can be determined the same as before, although, a new composite specific gravity must be calculated.

....................(43)

....................(44)

The composite SG is the sum of the weighted percentages:

....................(45)

The pressure because of the difference in perforation depth and pump setting depth (6,800 &plus; 5,500 ft &equals; 12,300 ft) can be determined as

....................(46)

and

....................(47)

Therefore, the pump-intake pressure (PIP) can now be determined as

....................(48)

Step three: gas calculations

Next, determine the total fluid mixture that will be ingested by the pump at the new maximum desired flow rate (2,875 B/D). Determine the solution GOR (Rs) at the pump-intake pressure or by substituting the pump-intake pressure for the bubblepoint pressure (Pb) in Standing’s equation. [1]

....................(49)

and

....................(50)

Determine the formation volume factor (Bo) with the Rs from Standing’s monograph or use Standing’s equation[1]

....................(51)

where

....................(52)

and

....................(53)

Therefore,

....................(54)

Determine the gas volume factor (Bg) as

....................(55)

Assuming a 0.85 Z factor,

....................(56)

Next, determine the total volume of fluids, and the percentage of free gas released at the pump intake. Using the producing GOR and oil volume, determine the total volume of gas (TG).

....................(57)

or

....................(58)

Using the solution GOR (Rs) at the pump intake, determine the solution gas volume (VSG).

....................(59)

The difference represents the volume of free gas (VFG) released from solution by the decrease in pressure from the bubblepoint pressure of 1,500 psi to the pump intake pressure of 1,000 psi.

....................(60)

The volume of oil (Vo) at the pump intake is

....................(61)

and

....................(62)

The volume of free gas at the pump intake is

....................(63)

and

....................(64)

The volume of water (Vw) at the pump intake is

....................(65)

and

....................(66)

The total volume (Vt) or oil, water, and gas at the pump intake can now be determined

....................(67)

....................(68)

and

....................(69)

The ratio or percentage of free gas present at the pump intake to the total volume of fluid is

....................(70)

and

....................(71)

As this value is greater than 10% by volume, there is significant free gas to affect pump performance; therefore, it is recommended that a gas separator be installed. Next, we must assume the gas separator’s efficiency. At 15% free gas, a 90% efficiency of separation is used on the basis of the manufacturer’s gas-separator performance information.

The percentage of gas not separated is 10%.

....................(72)

and

....................(73)

Total volume of fluid mixture ingested into the pump is

....................(74)

....................(75)

....................(76)

and

....................(77)

The amount of free gas entering the first pump stage as a percent of the total fluid mixture is

....................(78)

and

....................(79)

As the free gas represents only 2% by volume of fluid being pumped, it has little significant effect on the well fluid composite SG and may be ignored for conservative motor sizing.

Now that the total volume of fluid entering the first pump stage is known (2,973 BFPD) and the composite SG has been determined, we can continue to the next step of designing the ESP system.

Sufficient data are now available to determine the TDH required at the maximum desired flow rate (2,973 B/D). The TDH for the minimum desired flow rate (2,550 B/D) was previously determined to be 3,556 ft.

....................(80)

where HL = the vertical distance in feet between the estimated producing fluid level and the surface, and

....................(81)

From Fig. 1 , friction loss per 1,000 ft of 2 7/8-in. tubing (new) is 60 ft/1,000 ft of depth at 2,973 B/D (405 m3 /d), or 4.5 m/100 m. Using the desired pump setting depth,

....................(82)

Hwh = the discharge pressure head (desired wellhead pressure). Using the composite SG,

....................(83)

and

....................(84)

or

....................(85)

Step five: pump-type selection

The hydraulic requirements for our variable speed pumping system have been determined. Those requirements are the minimum hydraulic requirement (flow rate 2,550 B/D; total dynamic head 3,556 ft) and maximum hydraulic requirement (flow rate 2,973 B/D; total dynamic head 4,746 ft).

In the economic justification for using the VSC, the size of the downhole unit was determined. This was done using the guidelines discussed next.

As the operating frequency increases, the number of stages required to generate the required lift decreases. The closer the operation is to the best efficiency point, the lower the power requirement and power cost.

A fixed frequency motor of a particular frame size has a maximum output torque, provided that the specified voltage is supplied to its terminals. The same torque can be achieved at other speeds by varying the voltage in proportion to the frequency. This way the magnetizing current and flux density will remain constant, and so the available torque will be a constant (at no-slip RPM). As a result, power output rating is directly proportional to speed because power rating is obtained by multiplying the rated torque with speed. Using the variable-speed performance curves, select a pump that will fit in the casing so the maximum flow rate (2,973 B/D) falls at its BEP. The GC-2200 satisfies these conditions at 81 Hz.

Next, select the head per stage from the curve. It indicates 86 ft/stage. With the maximum TDH requirement of 4,746 ft, the number of pump stages required can be determined. The number of stages = the maximum TDH /head per stage and = 4,746 /86 = 55 stages. A 55-stage GC-2200 meets our maximum hydraulic requirement. To determine if it meets our minimum hydraulic requirement, divide the minimum TDH requirement by the number of stages. The minimum head per stage = 3,556 /55 = 64.7 ft/stage. Plotting the minimum head/stage (64.7 ft) and the minimum flow rate (2,550 B/D) on the curve indicates an operating frequency of 70 Hz. Note, the minimum hydraulic requirement is also near the pump’s BEP.

Next, using the VSC curve for the GC-2200 find the BHP/stage at the 60-Hz BEP (1.12 hp). To calculate the BHP at the maximum frequency use Eqs. 86 and 87.

....................(86)

and

....................(87)

Because a rotary gas separator was selected (which is a centrifugal machine using HP), it will add additional load to the motor. The HP requirement also changes by the cube function. Referring to the manufacturer’s information, the 513 series rotary gas separator requires 5 hp at 60 Hz.

....................(88)

Total BHP for the pump and separator = 157.6 + 12.8 = 170.4 hp. With Eqs. 89 and 90, the equivalent 60-Hz BHP for both the pump and gas separator can be calculated:

....................(89)

or

....................(90)

Select the appropriate model seal section and determine the HP requirement at the maximum TDH requirement. Select a motor that is capable of supplying total HP requirements of the pump, gas separator, and seal. In this example, a 562 series motor with 130 hp; 2,145 volts; and 35 amps was selected.

Using the technical data provided by the manufacturer, determine if any load limitations were exceeded (e.g., shaft loading, thrust bearing loading, housing burst pressure limitations, fluid velocity passing the motor, etc.).

Next, select the power cable and calculate the cable voltage drop. On the basis of the motor current (35 amps) and the temperature (160°F), no. 6 cable can be used. Adding 200 ft for surface connections, the cable voltage drop is written as

....................(91)

We can now calculate the required surface voltage (SV) at the maximum operating frequency as

....................(92)

and

....................(93)

Note that the surface voltage is greater than standard 3KV cable. Therefore, 4KV or higher cable construction should be selected. Sufficient data are available to calculate KVA.

....................(94)

and

....................(95)

Referring to the manufacturer’s catalog, select the model 2200-3VT, 200 KVA, NEMA3 (outdoor enclosure) VSC. All other accessory equipment should be selected as in the previous example.

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. 51 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

References

1. Electrical Submersible Pumps and Equipment, 11. 2001. Claremore, Oklahoma: Centrilift.
2. Saveth, K.J., Klein, S.T., and Fisher, K.B. 1987. A Comparative Analysis of Efficiency and Horsepower Between Progressing Cavity Pumps and Plunger Pumps. Presented at the SPE Production Operations Symposium, Oklahoma City, Oklahoma, 8-10 March 1987. SPE-16194-MS. http://dx.doi.org/10.2118/16194-MS

Noteworthy books

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

Noteworthy papers in OnePetro

Camilleri, L. A. P., & Macdonald, J. 2010. How 24/7 Real-Time Surveillance Increases ESP Run Life and Uptime. Society of Petroleum Engineers. http://dx.doi.org/10.2118/134702-MS

Camilleri, L., & Gambier, P. 2013. Does your ESP Completion Architecture Meet All Your Production Requirements? Society of Petroleum Engineers. http://dx.doi.org/10.2118/164249-MS

Cudmore, J. 2012. Using Real Time Automated Optimisation & Diagnosis to Manage an ArtificiallyLifted Reservoir - A Case Study. Society of Petroleum Engineers. http://dx.doi.org/10.2118/163296-MS

Durham, M. O., & Lea, J. F. 1996. Survey of Electrical Submersible Systems Design, Application, and Testing. Society of Petroleum Engineers. http://dx.doi.org/10.2118/29506-PA