USMS019307 Fundamentals Electrical of Submersible Pumpingin Oil Wells Delft U. of Technology A.W. Grupping,

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Copyright 1SS9 Sodoty of P@olaum Englnaors nlismanuscfiptwaatothomof~

Enginaersfordwrhtii andposaibkpublication inanSPEjoumal. Thematerial issubjact tocorraction bythe uthor(s). q Pwniaaion oopy reatrkted to is to anabatraot more ofnot than :~Ign Wnh,SPE SookOrder Dept., Library Tachnidan, Sex833S36, P.O. 5M3483S U.S.A. hkBX7309S9 SPEDAL. *

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FUNDAMENTALS OF ELECTRICAL SUBMERSIBLE PUMPING IN om

A.W. Grupping, SPE, Delft U. of TechnologySUMMARY This paper analyzes the performance of electrical submersible pumps in oil wells. Pump performance is matched to well performance in a pressure versus production rate diagram. This allows the effect of changes of res&voir characteristics and pumping parameters to be analyzed quantitatively. INTRODUCTION . ,. .

Electrical sulxnersible pumping can be an attractive alternative for other artificial lift methods such as beam punping and gaslift. It is specifically applicable in situations where gas/liquid ratiois are low and well capacities are high, as is the case in strong waterdrive fields and wat,?rflood projects. Wells equipped with a submersible pump may be analyzed in a way similar to flowing and gaslift wellsl. . Equilibrium conditons are established in a pressure versus production rate diagram; this allows a quantitative . interpretation of the influence of changing well parameters on the production rate and pump intake pressure (annulus fluid level). The effect of remedial measures such as choking the well, altering the motor frequency or changing the pump depth can also be analyzed quantitatively. THE PUMPING SYS!IZ?4 Fig. 1 shows a submersible pumping system. A centrifugal pump/electric motor combination is attached to the lower end of a tubing string at depth D Electric power is fed P from the surface to the motor through an electric cable, clamped to the outside of the tubing. The motor is located

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below the pump; so-that it is cooled by the well fluids. A centrifugal gas/liquid separator may be added upstream of the pump intake, the gas being vented through the annulus to the surface. Production is pumped through the tubing to the surface. The wellhead pressure pwh is required to move the fluids through the flowline to the flow station. The well may be equipped with a flow bean to regulate the.production rate. ~is causes an additional backpressure at the surface. A producing fluid level establishes itself in the annulus, the depth of wt..chdepends on the production rate q, the annultlsgrad.,t and the annulus back-pressure p= at the surface. Theannulus may be open to the atmosphere or connected to the flowline with a back-pressure valve insealled. THE PRESSURE-PRODUmION RATE DIAGRAM

Fig. 2 shows the pintake pressure curve and the load curve in a pressure-production rate diagram. The pmp intake pressure curve is obtained by subtracting the pressure losses in the conduit below the pump (Dw - p)*9f] from the flowing bottomhole pressure at [ various production rates. This curve is n pseudo wellhead pressure curve similar to wellhead pressure curves established in flowing and gaslift well analysisl. At zdro production rate the pump intake pressure equals the static bottomhole pressure pw5 minus the pressure caused by the static fluid column between pump depth I)p and well depth Dw. The load curve indicates the pressure required at various production rates to move the fluids from the pump through the tubing into the flowline. The load curve consists of three elements: The pressure caused by the static head of the tubing contents Ht, friction losses in the tubing

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Hf and the back-pressure at the wellhead pwh. Its curvature reflects the friction losses which increase proportional to the square of the production rate. . The vertical distance between the two curves at a certain production rate q equals the required pressure increase the pump must deliver at this production rate2. It is usually expressed in metres water column with a density of 1.0 g/cm3 and is called Total Dynamic Head (~H). Fig. 3 shows a pressure versus depth diagram of an electrical submersible punping system.

THE HEAD-CAPACITY dRVEThe head-capacity curve of an electrical submersible pURP has the shape as shown in Fig. 4. When pumping large volumes the pump can produce only a

small head, i.e. it can give only a small pressure increaseto the fluid flow; when punping small volumes it can produce a large head. Fig. 4 also shows the efficiency curve. Pump efficiencyis defined as: ~ = delivered hvdraulic Dower . (1) consumed electric power Because hydraulic power is proportional to the product of the pumped volume and the head, E is zero both when q.= O and when H = 0. Somewhere in-between pump efficiency reaches a maximum value. lheead an electrical submersible pump can attain h increases with the number of stages (impellers). MATCHING FUMP PERFORMANCE ICWELL PZRFORidANCE Fig. 5 explains how equilibrium conditions for a given well and pump (head-capacity curve) may be determined. In Fig. 5a, for a given pump depth and tubing size, both the pump intake pressure curve and the load curve are

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SPE 19307

drawn in a pressure-production rate diagram. The headcapacity curve of the selected pump is then superimposed on the pump intake pressure cuxve. Equilibrium is achieved yhere the head-capacity curve intersects with the load tune. The resuitant production rate q andpump intake pressure pp may then be read from the diagram. The hatched area representsthe pump diagram, the shape of which is now distorted. . Fig. 5b shows an alternative method of establishing equilibrium in a submersible pumping system. Here, the pumpintake pressure curve has been subtracted from the load curve and the resultantcue has been intersected

with the head-capacity curve of the pur@. The advantageof determiningequilibriumin this way is that the original,shape the head-capacitycurve is of preserved. PUMP SELECTIONL

Selection of a suitable electrical submersible pump for a given well with known characteristics and tubing size requires the construction of a family of load curves-and pump intake pressure curves for various depths in the pressure-production rate diagram2. . This has been carried out in Fig. 6 for a well producing from a depth of 4000 ft. The pump intake pressure curve at 4000 ft coincides with the wellss P? line. At various pump depths the pressure differential between the load curve and the pump intake pressure curve gives the required Total Dynamic Head for different production rates. For proper pump selection it is necessary to either specify the pump depth or the required production rate.o

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If the requiredproductionrate is ql and the minim-am

intakepressure is pp, the pump must be installedat 2300 ft and it must generate ahead equivalentto the pressuredifferenceA-B.Again with pump intake pressure pp, if the desired pump depth is 2000 ft, the maximum obtainable production rate for which the pump must generatea head equivalent is q-y

to the pressuredifferenceC-D. The advantageof pumping larger volumes from greater depths must, of course, always be weighed against the higher equipmentcosts and increasedfrictionlosses. VARIABLESPEED DRIVE An electricalsubmersiblepwith variable speed drive is identicalto a standardpunp system,with the exception of a variable frequencycontrol panel installedat the surfacewith which the frequencyand thereby the speed of the motor and pump can be changed. By alteringthe frequencyf of the motor the head-capacity curve will move to another position in the pump diagram. .- the basic pump curve at 50 Hz or 60 Hz is known, pump Ifcurves at other frequencies can be determined. The pumped volume per unit of time q is proportional to . the rotational speed of the impellers and thus to the frequency f of the electric current. Because the head H is proportional ta the impulse (1/2~v2), it is proportional to f2. The required power is proportional to q.H and thus to f3. Changing from frequency fl to frequency f2 gives the following relationships:

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= fl/f2

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q qz = (f*/fl) qlH 2 . (f2/fl)2,H 1

(2) (3)

Hi/H. = (fl/f2)2 L

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For every point on a pump curve with frequency fl the production rate ql and head HI are known so that for a Pcurve with frequency f2 the corresponding values of q2 and H2 can be calculated. An example of two headcapacity curves for a one-stage pump is given in Fig. 7. With variable speed drive the frequency can be altered to adapt the head-capacity curve of an installed pump to changing well conditions. In the example shown in Fig. 8 a well is producing with a productivity index PT1 at the maximum rate ql with minimum punp intake pressure ppl. The frequency is fl. When the productivity index increases to P12, the wells production rate increases to q2 and the pump intakepressure to pp2 as the head-capacity curve moves from position I to position II. With variable spee@

the frequencymay be adjusted to adapt the pump to the changedwell conditions.In the example shown a frequencyf2 has been chosen which results in a larger head-capacity diagram such that the well producesat its maximum rate q3 with the originalminimum pump intake pressureppl. It should be noted that the power supplied by the motor increases in proportion to the frequency f, while the powerdrive

required by the pump increasesproportional to f3. If the punpmotor combination is well matched at the original . frequency, there is only limited scope for a frequency increase to adapt the system to improved well conditions. THE RECOMMENDED RANGE Electrical submersible pumps must be operated within their recommended capacity range, as specified by the manufacturer. The recommended range is usually drawn in the pump diagram, see Fig. 9. When operated outside this range there will be increased wear in the thrust bearings which carry the shaft

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loadz at low rates loss of motor cooling may occur. In many practicalsituationsa wells reservoirpressure and/or productivityindex change with time. As a result, the productionrate may change to a value which isoutside the reconunended range of thepump. Remedial measures are then necessary: Dependent on circumstances

the frequencyof the electric motor may be changed,or a flow bean may be installed.In some cases it may be necessaryto install another punp with a differentcapacity range.

Fig. 10 gives an example of a well with a productivity index PI1, wmintake pressure c-e a (1), a headcapacityqurve (1) and a-load cume (l), producingat the rate ql and pump intake pressure PP3. When the wells productivity index increases to Pr2, a new equilibriumestablishesitself with the pump intake pressure cume and head-capacity curve in position (2). Production increases to q2 and the pump intakepressure rises to pp2e The productionrate is now outside the recommendedrange of the pump and it must thereforebereduced.,. This canjbe done in several ways: A simple . method is toinstall a flow bearsin the wellhea~ which moves the load cutve to ahigher position in the pressure-production rate diagram. In +he example shown. the choking effect equals the pressure differ~nce A-B. The production rate decreases to q3 and the pump intake pressure increases to pp3. EXAMPLE CALCULATION See Table 1 for reservoir, well and pump da*a. For simplicity, friction losses in the well below the pump and in the tubing have been neglected.

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TABLE 1 - RESER~ IR, WELL AND P 24P DATA JK)R EXAMPIJE SUBMERSIBLEPUMP CAMUL$TION Dspth @f reservoir, metres Reservoir pressure, bar Prod~ctivity index, m3/ (bar. ~) Pump depth, metres Wellhead pressure, bar Annulus pressure, bar 1,023 3.00 95 -* 4-*2 350 8.6

Minimumpump intakepressure, bar Gradientof punped fluids, bar/metreHead-capacity curve submersible pump

o 500104 Fig. 9

Calculatsthe productionrate, pump intake pressure and annulus +luid level at the initial reservoir pressure of 100 bar and productivityIndex of 4 m3/(bar.D). At the reduced reservoir pressure of 95 bar and productivity index of 2 m3/(bar.D) the annulus fluid level would be below the level of the pump intake. This can be preven+ed by? a) Choking the productionat the surface. b) Altering the frequsncyof the electriccurrent. c) Changing the depth of the pump.GF@FHICAL ANALYSIS .

A graphical analysis of the wellcs production behaviour is presen+ed in Fig. 11. Th~ pump intake pressures are obtained by subtracting the fluid column pressure between +he pump and the reservoir . from th~ bottomhole pressure at various production rates: - q/PI - (1023 - 350).(0.104)] bar. P = [ Ws The head-capeci+y curves areob+ained by adding to the pump L. take pressures at various production rates the corresponding pressures of the head-capacity curve of the pump (i?ig.9).

The heads are in metres water with a density of 1.0 g/crn3and can be converted to bars by dividing by ten.

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The load curve consists of the static head above the pump, friction losses in the tubing and the wellhead pressure: Load curve= (350).(0.104)*O + 8.6 = 45 bax Equilibrium exists at the intersectionof the head-capacity

curve and the load curve, i.e. at a productionrate of 70 m3/day and a pintake pressure of 100 - 70/4 - (1023 - 350).(0.104) = 12.5 bar.Because p= = O, the fluid level in the annulus above the pump is at ~50 - (12.5)/(0~104~ -= 230 metres depth.

At the reducedreservoirpressure of 95 bar and productivity index of 2 m3/(bar.D)the intersection the head-capacity of curve and load curve 3s at 57 m3/day and the p&p intake pressure is negative: ~5 - 57/2 - (1023 - 3SO).(0.104~ =-3.5 bar The system cannot operate under these conditionsbecause theannulus fluid level will be drawn down to the pump intake. SOLUTIONS ~

a) Installing a flow bean in the wellhead is one way tosolve this problem, Fig. 11 shows that at the required minimum pump inkake pressure of 5 bar the.well produces 40 m3/day. At that productionrate the load curve must intersect with the . head-capacity curve at a pressure of 65 bar. This can be achieved bv installing a flow bean with a choking 3 effect of 20 bat at a production rate of 40 m /day. b) The same result can be obtained by changing the frequency (50 Hz) of the electric current. For this solution the new head-capacity curve must intersect with the load curve at point A (40 m3/day~ 45 bar). The head is then: (45 - 5) = 40 bar. With equations (2) and (3) the following relationships are found: -

40 = (f,/So) ql .

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(45 - 5)

q

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By trial and error it Is found that the new frequency f2

is approximately Hz. The values of ql and HI are 42 47.6 xn3/day and 56.7 bar respectively; the corresponding point on the original head-capacitycurve is point B (47.6m3/day, 57.8 bar). Solutionb) is superior to solutiona) because i% results in lower operating (electricity) costs.,c) A third solution is to lower.the pump to a deeper level in the well. Fig. 12 shows the.result of installing the pump at a depth of S42.3 metres. The pump intake pr~ssure at zero production rate increases to: c - (1023 - 542.3). 95 (0.104~= 4S bar. The load curve increases to: (542.3).(0.104) + O + 8.6 q 65 bar.

Equilibriumexists at a productionrate of 57 m3/day. The accompanying pump intake pressure is: 95 - 57/2 - (1023.-542.3).(0.104)= 16.5 bar. Tf t-hepressure scale of Fig. 11 is increased by.20 bar.both figures are identical. This means that, inthis simplified case without friction losses, the system will produce 57 m3/day at any pump depth as long as there is suffiCien* pump submergence. ACKNOWLEDGEMENTS The author wishes to thank F.M. Kramer for reading through and commenting m the manuscript and A. Steenhuis for preparation of the illustrations.

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NOMENCLAWRE

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REFERENCES. 1.

Gilbert,W.E.: Flowingand Gas-lift Well Performance,.

Drill. & Prod. Prac. (1954) 126-57. 2. Grupping,A*W. and Ie, E.C. : *Pressure-Production Diagram matches SubmersiblePump Performance.to that of Wellw, Oil & Gas J. {Nov. 29, 1982).

3. Divine~D.L.: VariableSpeed SubmersiblePumps Find Wider Application[, & Gas J. (June11, 1979). Oil 4. Reds SubmergiblePump catalog (1980). 5. Senaroya,A.: CentrifugalPumps for the Practicing Engineer,PetroleumPublishingCo., Tulsa, okla. (1978).

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