Mechanics of an Electric SubmersiblePump Failure Mode

Maston L. Powers, SPE, Consultant

SummaryThe occurrence of electric submersible pump (ESP) failurescaused by spinning diffusers is tolerably frequent in moderate-operating-cost circumstances. However, extremely high well-servicing expenses are associated with many ESP applications.Examples include deep wells, arctic locations, offshore wells thatmust be killed with high-density fluids, and seafloor completions.In these or other high-cost circumstances, early pump failures ofany mode cannot be tolerated.

Longitudinal compressive force is imposed on the diffuserstack of ESPs during assembly to prevent diffuser rotation. If thisis done improperly, the diffusers can spin because of torque trans-ferred from the impellers, resulting in early pump failure. Thispaper analyzes the mechanics of the spinning-diffuser failure modeand demonstrates why some pumps with inadequate compressiveforce can pass common pump tests but fail in this mode. Equationsare developed to calculate the restraining force as it changes undervarying conditions and the minimum value required to preventdiffuser spinning. Testing procedures are proposed to emulate theeffects of well conditions conducive to diffuser spinning, therebydetecting the defective pumps currently being missed. Practicalexamples are included that illustrate the utility of the conceptspresented herein.

IntroductionLongitudinal compression is imposed on the diffuser stack of ESPsduring assembly to prevent diffuser rotation. If this is done im-properly, the diffusers can spin because of transferred impellertorque, resulting in an impeded flow condition and early pumpfailure. Examination of pumps that have failed in this mode maydisclose evidence of high temperature and diffusers with circum-ferential wear and/or shortening because of wear caused by rela-tive movement at the contact with adjacent diffusers. This mode offailure begins at or near the pump top and progresses downward,as wear further loosens the diffuser stack and the head, developedby upper stages, deteriorates.

Some pumps that pass API performance specifications duringcommon testing procedures subsequently fail because of diffuserspinning. A possible explanation for a portion of these occurrencesis that an otherwise strong pump might meet test standards in spiteof an incipient diffuser-spin condition. It should be pointed out thata spinning diffuser is audible when horizontal testing is employedand would not go unnoticed. Most cases of tested pumps failing inthe subject mode are probably the result of service conditions.

The assumption of floating impeller pumps is made throughoutthis paper. However, the effects described here are equally appli-cable to pumps with a fixed impeller design.

Restraining the Diffuser StackImpellers transfer torque to diffusers by three means: the mechani-cal drag of thrust-washer contact, which increases with increasingimpeller thrust; disk friction and other hydraulic drag; and thedynamic portion of the head generated by the impeller. Torque ofa single impeller is defined in Eq. 1.

I = 5,252PI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)At shutoff, it is known that generated head is 12 dynamic and 12static.1 A reasonable estimate of maximum transferable torquewould be one-half that calculated with Eq. 1, with PI at maximumvalue. This assumption is made herein, although experimental datawould be more desirable.

Diffuser rotation is prevented by frictional contact betweenstages and with the pump head and base. The contribution oflateral contact with the housing is neglected here. The static torquecapacity of a diffuser/diffuser contact (or a diffuser/head or dif-fuser/base contact) is expressed in Eq. 2. The minus sign in thisequation reflects the fact that FN is a compressive force and, there-fore, negative.

C = dDKSFN24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)Once spinning has begun, it will continue unless FN doubles, or

possibly triples, because the value of KK is 12 to 13 of KS. Valuesof KS (and KK) should vary somewhat, depending on the fluidwetting the diffuser surfaces; thus, the value of KS when a pump isin service may be different from that during testing. This would affectthe minimum value of |FN| required to prevent diffuser spinningand could account for the subsequent failure of some tested pumps.

The initiation of diffuser spinning can be illustrated by envi-sioning the diffuser stack as a torqued shaft restrained at the endswith couples distributed throughout its length. The interstage con-tacts would be equally spaced planes of weakness. Fig. 1 illustratesthe couples (D) imposed by each diffuser, the interstage torquetransfers (i), and the end reactive torques for a six-stage pump.Also shown is a plane view of a longitudinal line along the diffuserstack, demonstrating (in great exaggeration) the distortion causedby the distributed torque. Note that i is zero at midpump andincreases toward the ends, where it assumes values of nD/2. Theequation for torque capacity (C) of the interstage contacts wasderived from Eq. 2 by substituting the appropriate value of FN. Atthe pump top, FNFDR. This is augmented by an additional force,at subsequently lower contacts, equal to the sum of the pressure-based force and the buoyed weight of all stages listed previously.Eq. 3 (in which 0nn) was, thus, derived.

C = dDKSFDR nhUdi2 dS24 + fBWU24. . . . . . . (3)Eq. 3 shows that the contact between the top diffuser and the

pump head (n0) has the least torque capacity, with C increas-ing at each successively lower interstage contact. Therefore, dif-fuser spinning should begin at the top stage, where i is maximumand C is minimum. The previous analysis assumes that KS has thesame value at all interstage, diffuser/head, and diffuser/base con-tacts. Because some variation in KS occurs, spinning should beginnear the top of the diffuser stack but not necessarily with the top stage.

Fig. 2 graphically illustrates i and C for a pump with adequateFDR, and C for a pump for which FDR0. Diffuser spinning mayoccur at any contact for which C falls below the i curve. As thehead developed by upper stages declines, C of the lower stages isdiminished, and diffuser spinning progresses downward.

Effects of Varying Conditions on Reactive ForceDuring assembly, reactive forces are imposed on the diffuser stackand pump housing by installing a spacer, called a compressionring, between the pump head and the top stage. The compressionring is cut to a length equal to the housing free space, with the headinstalled plus tL, which is approximately 0.2% of the diffuser-stack length. This is performed at a comfortable temperature with

Copyright 2002 Society of Petroleum Engineers

This paper (SPE 75295) was revised for publication from paper SPE 39813, first presentedat the 1998 SPE Permian Basin Oil and Gas Recovery Conference, Midland, Texas, 2527March. Original manuscript received for review 22 April 1998. Revised manuscript received1 September 1999. Paper peer approved 11 October 2001.

62 February 2002 SPE Production & Facilities

the pump horizontal and without external stress on the pump orinternal pressure. Some or all these conditions will change duringpump testing. Service conditions may vary greatly from thosepresent at the time of assembly or during testing.

Pump Testing. When a pump is tested in a test well, the housingand diffuser stack are subjected to forces resulting from internalpressure and weight. The resulting length changes cause a reduc-tion of the equal but opposite reactive forces FHR and FDR. (FDRis the only force acting at the top of the diffuser stack to preventspinning.) Tensile forces and elongations are considered positivehere, and compressive forces and contractions are considerednegative. During horizontal testing, weight is not a factor, andlongitudinal forces imposed on the housing because of internalpressure and temperature changes are only partially effective be-cause a portion of the housing is restrained between vise clamps.Another difference between the two testing methods is that hori-zontal testing is performed with fresh water, and diesel is commonlyused for test-well testing. These fluids have different densities andlubricities, which affect pressure-based forces and coefficients offriction, respectively. Fluid temperature should be more consistentwith test-well tests. Because of the previously described differ-ences, different results may be obtained from the two test methods.

Well Conditions. When a pump is placed in service, the housingis subjected to an effective tensile force equal to the buoyed weightof the motor(s), seal section, gas separator, lower pumps, and itsown buoyed weight less 12 the buoyed housing weight. Further-more, it is stressed by a tensile force equal to the developed pres-sure plus that developed by lower pumps times the internal cross-sectional area of the housing. Impeller thrust is an integral part ofthis pressure-based force and need not be considered separately inregard to either housing or diffuser stresses. It is demonstrated ina later section that the head applicable to this pressure-based forceis shut-in (or maximum) head for pump installations equipped withcheck valves. The diffuser stack is subjected to an average com-pressive force equal to hU(n+1)/2 times the housing/shaft annulararea. This force is augmented by an average compressive forceequal to 12 the buoyed stack weight, including impellers. Super-imposed pressure from lower stages and lower pumps affects dif-fuser length only to the extent of bulk volume compression.

Except for some arctic applications,2 wellbore temperatures aregreater than those present during pump assembly and testing. Thenet result of a temperature increase is an increase in reactive forces,because the carbon steel housing has a coefficient of linear thermalexpansion of 6.7106 F1, while that of the iron alloy diffusersis approximately 10.5106 F1. Wellbore temperature may alsoaffect KS and KK to the extent that fluid lubricity is altered.

Eq. A-10 (derived in Appendix A) defines DR2the diffuserstack contractive strain at other than assembly conditions. Thisequation requires values for housing and diffuser strains resulting

from pressure, temperature changes, and weight. (Weight-basedstrains are relatively small.) Equations for these quantities aredeveloped in Appendix B. Substituting values of DR2 into Eq. 4(Hooks Law) results in the normal force exerted on the top dif-fuser. This is required for calculating torque capacity with Eqs. 2or 3. The quantity AD (in Eq. 4) is the diffuser effective elastic areaand would need to be determined experimentally for each pump type.

FDR2 = DR2 AD ED. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

Head Applicable to Stress CalculationsMaximum head occurs at shutoff. However, most ESP perfor-mance curves are relatively flat for the first 10 to 15% of bestefficiency point (BEP) flow rate, and some are reasonably flat to50%, as shown in Fig. 3. Also, if a check valve is installed, flowbegins when the developed head equals the net lift (Eq. C-1), atwhich time fluid acceleration begins. Eq. C-7 defines qT, the flowrate when pump speed reaches T (assumed to be 3,500 rpm on 60Hz power). The latter equation was developed so that the maxi-mum head generated during start-up can be estimated, as demon-strated in the following example.

A 400-series ESP is designed to operate at the BEP, pumping1,500 B/D from a depth of 5,000 ft. The controller will restart thepump after 1 hour downtime, at which time pI450 psi and pS20 psi. Terminal speed is reached in 20 cycles. Other variables aredT1.995 in., 0.433 psi/ft, and hST6,500 ft. Applying Eq.C-7 results in qT184 B/D, or 12.3% of the 1,500-B/D operatingrate. Most pumps would develop head very close to shutoff at12.3% of BEP flow rate. Therefore, it is concluded that approxi-

Fig. 1Schematic of a six-stage pump.

Fig. 2Plot of i and c vs. diffuser location.

Fig. 3Typical ESP performance curve.

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mating head may be developed at start-up in installations equippedwith check valves.

Practical Applications. The following examples illustrate the util-ity of the concepts presented. In Example 1, a 400-series ESP isselected to be set at 3,000 ft and produce 2,200 B/D with 100-psisurface-tubing pressure and 60 psi pump-inlet pressure; power is60 Hz. The well is equipped with 2.875-in. tubing, and a checkvalve is installed. Other well data are 133-ft tubing friction loss,100F formation temperature, and 1.0 fluid specific gravity. Pumpdata include 21.5 ft/stage operating head, 30.5 ft/stage shut-inhead, maximum PI0.6 hp/stage for 1.0 specific gravity fluid, dS0.6875 in., di3.5 in., eH0.25 in., AH2.9452 in.2, AD1.0in.2, EH29.5106 psi, ED15.0106 psi, H0.29, D0.27,KTH6.7106 F1, KTD10.5106 F1, KS0.24, and 73Fassembly temperature. A 150-stage, 350-lbm pump was selected,as was a 100-hp motor and a seal section, weighing 950 and 100 lbm,respectively. Single-impeller torque was calculated with Eq. 1 tobe 0.90 lbf-ft, and it was assumed that half this was transferred tothe diffusers. Total restraining torque at the pump head (and base)is then equal to 0.45n/2 or 33.75 lbf-ft. The minimum |FN| requiredto prevent the initiation of diffuser spinning can be computed fromEq. 5 (a rearrangement of Eq. 2) by substituting this value for C,dD3.5 in. and KS0.24. The result is 964 lbf. Thus, |FDR2|must equal to or exceed 964 lbf to prevent diffuser spinning.

FN = 24CdDKS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)The pump was tested in a test well at the 73F assembly tem-

perature with 0.85 specific gravity diesel. The weight of the testmotor and seal section were equal to those chosen for field instal-lation. When the pump was assembled, the value of t was belowspecification, 7.7525104. Substituting this value into Eq. A-10results in DR26.6667105. With this quantity known, Eq. 4 canbe applied, yielding FDR21,000 lbf. Diffuser spinning shouldnot occur during this test because |FDR2|>964. Before the pumpwas sent to the field, it was retested on a horizontal test bench with73F fresh water. During this test, only 50% of the housing wasfree to elastically react with the pressure-based force because ofthe housing interval restrained between clamps. Application of Eq.A-10 results in DR24.6569105. Substituting this value intoEq. 4 yields FDR2699 lbf. Because |FDR2|

In Example 4, all conditions and equipment are identical tothose in Example 3, except that the produced fluid temperature is100F and the fluid specific gravity is 1.15. This pump would passthe test-well and horizontal tests of Example 1 and the relaxed-housing test of Example 3. Service conditions result in FDR2481 lbf. Because |FDR2| is less than the threshold value (in thiscase 1.15964), diffuser spinning should occur. The value of

HD is 8.34874, which exceeds that of the relaxed-housing test by 3.8624105. The external force required to emu-late service conditions is calculated with Eq. 7 to be 3,356 lbf.Service conditions could likewise be emulated with a 530-psi suc-tion pressure or a 3,584-rpm testing speed.

Example 5 is similar to the tandem installation of Example 2,with all conditions and equipment the same except that the upperpump is the more tightly assembled one of Examples 3 and 4 (T8.7246104), which would pass the relaxed-housing test. Ser-vice conditions would result in FDR2690 lbf. Because690

WS weight of seal section, mL/t2, lbfWU weight of a single stage, mL/t2, lbf gradient, m/L3, psi/ft

T pump temperature minus assembly temperature, T, FD total change in D, dimensionlessDP change in D because of pressure-based force,

dimensionlessDR change in D caused by reactive force, dimensionlessDT change in D caused by thermal-based force, dimensionlessDW change in D caused by weight-based force, dimensionlessH total change in H, dimensionlessHP change in H because of pressure-based force,

dimensionlessHR change in H caused by reactive force, dimensionlessHT change in H because of thermal-based force, dimensionlessHW change in H caused by weight-based force, dimensionlessHE change in H because of FHE, dimensionless

strain, dimensionlessD diffuser strain, dimensionless

DR1 diffuser reactive strain at assembly, dimensionlessDR2 diffuser reactive strain at other-than-assembly

conditions, dimensionlessH housing strain, dimensionless

HR1 housing reactive strain at assembly, dimensionlesst compression ring length minus housing free space

with head installed divided by diffuser stack length,dimensionless

Poissons ratio, dimensionlessD Poissons ratio of diffuser material, dimensionlessH Poissons ratio of housing material, dimensionless density, m/L3, lbm/ft3C torque capacity of diffuser contact, mL2/t2, lbf-ftD torque transferred to one diffuser, mL2/t2, lbf-ftI torque of one impeller, mL2/t2, lbf-fti interstage torque transfer, mL2/t2, lbf-ft angular velocity, t1, rpmT terminal angular velocity, t1, rpm

References1. Stepanoff, A.J.: Centrifugal and Axial Flow Pumps, second edition,

John Wiley & Sons Inc., New York City (1948) 53.2. Andrew, J.H. and Augustine, B.G.: Initial Experience with ESPs on

the Alaskan North Slope, paper OTC 7062 presented at the 1992Offshore Technology Conference, Houston, 47 May.

3. Singer, F.L.: Strength of Materials, Harper & Brothers, New York City(1951) 17.

Appendix ADerivation of the Equation forDiffuser Reactive StrainDuring pump assembly, the housing and diffuser stack are sub-jected to the reactive forces FHR and FDR, respectively. Through-out this paper, tensile forces and elongations are considered posi-tive, and compressive forces and contractions negative. Eq. A-1defines the relationship between FHR and FDR.

FHR = FDR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-1)The initial values of these reactive forces result in the initial

reactive strains defined in Eq. A-2.

HR1 DR1 = 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-2)The reactive forces will assume different values during pump

testing and when the pump is in service. As long as they do not goto zero, the lengths of the pump housing and diffuser stack will beequal. Eq. A-3 is an obvious result.

H = D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-3)

Equations for H and D follow.H = HP + HW + HT + HR. . . . . . . . . . . . . . . . . . . (A-4)D = DP + DW + DT + DR. . . . . . . . . . . . . . . . . . . (A-5)Eq. A-6 is an expression of Hooks law.F = AE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-6)Combining Eq. A-6 and the equality FHRFDR results in

Eq. A-7.HR = DRADEDAHEH. . . . . . . . . . . . . . . . . . . . . . . . . . (A-7)Eq. A-8 was derived by combining Eqs. A-3, A-4, A-5, and A-7.DR = AHEHAHEH + ADED

HP + HW + HT DP DW DT. . . . . (A-8)Eq. A-9 was derived from Eqs. A-1, A-2, and A-6.DR1 = AHEHtAHEH + ADED. . . . . . . . . . . . . . . . . . . . . . (A-9)Eq. A-10 was derived from Eqs. A-8 and A-9 by observing that

DR2=DR1+DR.

DR2 = AHEHAHEH + ADEDHP + HW + HT DP DW DT t.

. . . . . . . . . . . . . . . . . . . . . . . (A-10)Appendix BDerivation of Equations for StrainsResulting From Pressure, Weight, andTemperature ChangesEq. B-1 is the common equation for longitudinal strain undertriaxial loading.3

X = E1SX Sy + Sz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-1)

The common equation for longitudinal housing stress causedby pressure is as follows.

SHx = pT di24eH di + eH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-2)The pressure at the top of the pump section being analyzed is

expressed in Eq. B-3.pT = hP1 + hP2 + . . + hPn. . . . . . . . . . . . . . . . . . . . . . . . . . . (B-3)Eq. B-4 is based on the common is equation for hoop stressSHy = pM di2eH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-4)Pressure at the midpoint of the pump is expressed aspM = 0.5hP1 + hP2 + . . hPn. . . . . . . . . . . . . . . . . . . . . . . . . . (B-5)Stress normal to the housing surface (SHZ) would equal PC,

which, in many cases, could be neglected.Eq. B-6 defines HP and was derived from Eqs. B-1 through B-5.

HP = di2hP1 + hP2 + . . + hPn4eHEHdi + eH H di0.5hP1 + hP2 + . . + hPn2eH EH + H PCEH.

. . . . . . . . . . . . . . . . . . . . . . . . . (B-6)The following equations define HW and HT.HW = fBWP1 0.5WH1 + WP2 + . . + WPn + WM + WS + WG

AHEH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-7)HT = TKHT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-8)The average pressure-based longitudinal stress imposed on the

diffuser stack equals the product of hU(n+1)/2 times the annulararea between the housing and shaft divided by the effective elasticarea of the diffuser stack. Combining this and the relationshipSE yields Eq. B-9.

DP = hU n + 1di2 dS28ADED. . . . . . . . . . . . . . . (B-9)Superimposed pressure affects difuser length to the extent of

bulk volume compression. This is expressed in Eq. B-10.

DP = 1 pB kDB13 1. . . . . . . . . . . . . . . . . . . . . . . . . . (B-10)

66 February 2002 SPE Production & Facilities

Eq. B-11 expresses the total contraction caused by pressure-based forces and was derived by adding Eqs. B-9 and B-10 andsubstituting [hU(n1)/2+hP2+. .+hPn+pC/] for pB.

DP = hU n + 1di2 dS28AD ED 1

+ 1 KDB1hU n 12 + hP2 + . . . + hPn + pC1

3.

. . . . . . . . . . . . . . . . . . . . . . . (B-11)The following equationd define DW and DT.DW = fBnWU 2ADED. . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-12)DT = TKDT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-13)

Appendix CDerivation of Equations for InitialTerminal Speed Flow RateAssuming a check valve is employed, flow is initiated duringstartup when the following condition occurs.

hi = DP pI pS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (C-1)Eq. C-2 follows from the pump-affinity laws.

hS = hST T2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (C-2)For simplicity, it is assumed that increases linearly with t

during startup. Thus, t/tT/T for 0ttT . Note that hi occurs atti . With these two relationships, Eq. C-3 was derived by equatingEqs. C-1 and C-2.

ti = tT hST0.5 DP pI pS 0.5. . . . . . . . . . . . . . . . . . . . . . (C-3)Tubing fluid is accelerated during the interval ti