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This paper was prepared for presentation at the 1997 SPE Production OperationsSymposium, held in Oklahoma City, Oklahoma, 911 March 1997.

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AbstractThe progressing cavity (PC) pump is well established as thepump of choice for handling abrasive solids. PC pump designcan be optimized to achieve the best wear performanceavailable for a given size. The wear optimization of the PCpumps is achieved through geometric design for minimuminternal fluid velocities and by selecting proper materials ofconstruction.

Wear causes PC pump failure by gradually reducing thevolumetric efficiency and increasing pump slippage. Thispaper focuses on the parameters that influence pump wear,describes wear mechanisms, reviews design techniques forwear optimization , and presents field data to support some ofthe claims.

BackgroundPump Design Parameters. Figure 1. shows the cross sectionof a progressing cavity pump.

Figure 1.Definitions:

Ps Stator Pitch D Rotor/Stator Minor Diameter Ecc Rotor EccentricityA progressing cavity pump consists of a helical steel rotorwhich turns within a stationary tube with a helical elastomeric

lining (stator).As the rotor turns inside the stator, fluid moves through the

pump from cavity to cavity. As one cavity diminishes, theopposing cavity increases at exactly the same rate whichresults in a pulsationless positive displacement flow throughthe pump. The cavities are separated from each other by aseries of seal lines which are created between the rotor andstator. The pressure capability of a pump is a function of thenumber of times the progressing seal lines are repeated. PCpump manufacturers rate the pressure capability of a pump as afunction of the number of pump stages. Although somewhatarbitrary, each stage is between one to one and a half of astator pitch length and is capable of handling 100 psidifferential. If cavity pressure increases beyond the seal limits,the seal lines will open, and fluid will slip from one cavity tothe other at a very high speed. The PC pump slippage isgenerally a function of pressure differential across the pumpand it changes depending on the compression fit of the rotorand stator.

Flow Rate. Pump flow rate is a function of design parameterssuch as stator pitch (Ps ), rotor diameter (D), and pumpeccentricity (Ecc). Equation 1. defines this function:

Fluid Velocity. Nominally, for each rotation of the rotor, fluidwill move one pitch length of the stator. Therefore, fluidnominal velocity in the axial direction of the pump is definedby Equation 2:Equation 2. Assumes that the fluid particles travel along a

SPE 37455

Progressing Cavity (PC) Pump Design Optimization for Abrasive ApplicationsR & M Energy Systems, a Unit of Robbins and Myers Inc.

Vfluid= C*Ps * NWhere:Vfluid nominal fluid velocityN number of revolutions per unit timeC conversion factor

Equation 2.

Q = K*PS*4*Ecc*D*Nwhere:Q flow rateN number of revolutions per unit timeK conversion factor

Equation 1.Ps Ecc

DCavity

2 SPE 37455

straight line. In reality, fluid does not travel in a straight lineand calculation of the maximum velocity must consider thelongest fluid path along a circular helix defined by the statorpitch and diameter. The theoretical maximum velocity within aPC pump is therefore defined by Equation 3.

Wear PhenomenonAbrasive wear of PC pumps is one of the most common modesof failure in down-hole applications. High speed particles(sand) traveling through pump cavities abrade both rotor andstator. This causes the seal lines between the rotor and statorto become less effective and results in higher pump slippage.The increase in the pump slippage will reduce pumpvolumetric efficiency and will gradually destroy the pump.

There are many factors that contribute to rotor and statorwear. Among the most important are particle size,concentration and hardness, pump rotational speed and numberof stages, and velocity of the solids traveling through thepump.

Particle Size. There is little or no uniformity in the size ofsand grains that find their way into the pump. Coarser grains(less than 20 mesh) can do more damage to the PC pumpscompared to finer powder-like sands (higher than 100 mesh .)However, high concentration of very fine powder-like sand canalso abrade rotors and stators. Larger sand particles can noteasily pass through the pump seal lines. These particles areoften partially embedded in the inner surface of the stator(Figure 2.) and continually rub against the rotor during pumpoperation.

Figure 2. Particles embedded on the stator surfaceThe rubbing of the rotor against the sand particles

combined with the high speed impact of hard particles with therotor contribute to the formation of wear patterns similar to

Figure 3.

Figure 3. Deep grooves on the rotor crest resulting fromextreme abrasive conditions

Pump Rotational Speed and Number of Stages. Equations1., 2. and 3. show that PC pump internal velocity and flow rateincrease as pump speed increases. As these parametersincrease, the rate of particle impact to the rotor and statorincreases which will accelerate rotor and stator wear. Ingeneral, the more abrasive the fluid, the slower the pump mustoperate. The amount of wear in an abrasive application isclosely proportional to the speed squared of the pump. Onedetrimental effect that speed reduction may have on pump lifemay best be shown by the performance curves of Figure 4 for aspeed A and B where B is one half of A.

Figure 4. Effect of wear on progressing cavity pumpperformance

Since wear is assumed proportional to speed squared, itwould take four times as long for a pump to wear at speed Bcompared to the same pump running at speed A. Although itwould take almost four times as long to reach the same amountof wear at half the speed, the reduction in the volumetric

VMAX= C*N*(Ps2 + 2 (D + 4Ecc)2)1/2where:VMAX theoretical maximum velocityC conversion factor

Equation 3.

SPE 37455 PROGRESSING CAVITY (PC) PUMP DESIGN OPTIMIZATION FOR ABRASIVE APPLICATIONS 3

efficiency1 would be doubled. In most applications, this effectwill negate the usefulness of the longer life expected by speedreduction. To compensate for this effect, using more pumpstages for an abrasive application is recommended. This helpsmaintain high volumetric efficiencies under pressure at eventhe lower speeds, reducing the effect of wear on flow rate andthereby increasing the time between pump replacement.Therefore, abrasive wear of PC pumps can be improved bydecreasing pump rotational speed and by increasing thenumber of pump stages.

Sand Concentration. Most wells produce some amount ofsand for varying periods of time which reduces rotor and statorlife of a PC pump. Sand cuts of 10 to 30 percent by volumeare considered to be heavy sand concentrations. In general,wear is directly proportional to the number of particles thatcome in contact with the rotor and stator. Therefore, in theabsence of other failure mechanisms and for otherwiseidentical operating conditions, change in wear life isproportional to the change in sand concentration.Particle Hardness. The degree of particle hardness alsoaffects rotor and stator wear. If sand grains are harder than thesurface of the rotor, shear on the rotor surface will causeabrasion. Generally, rotor wear is accelerated as the particlehardness increases. Some times, the affect of rotor wear isaccelerated when corrosion induced rotor surface cracks arealso present. For example, in sour wells, the effects of hardiron-sulfide particles are accelerated due to rotor surfacecorrosion cracks induced by the presence of H2S.

Particle Velocity. Velocity of the solids traveling through thepump is the most important parameter that causes rotor andstator wear. Particle speed within a PC pump can be separatedinto two categories: 1) predictable pump internal velocity and2) unpredictable particle speed due to pump slippage. Toreduce wear in PC pumps, pump internal velocity and slippagemust be minimized. This can be accomplished throughgeometrical design optimization and proper selection of thepump for the application. Pump slippage accelerates wear by causing fluid andparticles to travel at higher speed between rotor and stator seallines. Compression fit between the rotor and stator can beoptimized to reduce pump slippage and improve wear life. Thefollowing paragraphs describe pump design optimization,materials of construction, and pump selection techniques thatcan increase pump life in abrasive applications.

PC Pump Design for Abrasive ApplicationsWear in PC pumps increases as a function of fluid and particlespeed within the pump. The goal for PC pump designoptimization is to minimize the particle internal velocity whilemeeting pump flow and lift requirements. Equation 1.

1 volumetric efficiency is defined as the flow rate at the

pressure divided by the flow rate at zero pressure differential.

describes flow rate as a function of pump rotor diameter (D),eccentricity (Ecc), and stator pitch (Ps). Flow rate can also bedescribed by Equation 4.

Equation 4 illustrates that pump cross sectional area (Acavity)must be maximized in order to minimize fluid velocity for adesired pump flow rate. Figure 5. shows the relationshipbetween pump design parameters and Acavity . From Figure 5.,the maximum possible pump cross sectional area and thereforeminimum pump internal velocity is achieved when the ratio ofrotor diameter to pump eccentricity (D/Ecc) is equal to 4.

0

20

40

60

80

100

0 2 4 6 8 10 12

D/E

% M

AX

FLO

W

Figure 5. Relationship between pump design parametersand PC pump maximum possible flow rate

Figure 6. Stator pitch length which minimizes velocityFigure 6. describes a more complicated relationship betweenthe pump design parameters. This figure shows the statorpitch length (Ps) which minimizes the Vmax (Equation 3.) andtherefore provides the best wear performance for a requiredpump capacity.

Figure 7. further demonstrates the necessary relationship

Q = Acavity * VfluidWhere:Acavity Area of the pump cavity cross section or (D*4Ecc)Vfluid Nominal velocity of the fluid and particles inside the pump

Equation 4.

0

3

6

9

12

15

0 2 4 6 8 10 12

D/E

Ps/D

4 SPE 37455

between the stator pitch, pump eccentricity, and pumpdiameter to achieve lowest internal velocity.

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12

Ps / D

INTE

RN

AL

VELO

CITY

( V /

Vmin

)

D/E=4D/E=6D/E=10

Figure 7. Relationship between pump internal velocityand design parameters

Pump design optimization is typically conducted using Figures5 and 6 as the starting point. However, manufacturinglimitations, well casing size, pump pressure and flowrequirements often constrain pump geometrical parameters.For example, most PC pump rotors are designed with the D/Eratio of larger than four (4) to insure adequate rotor strength tomeet torsional and bending stresses. Also, stator pitch istypically lengthened beyond the optimized value to increasethe pump capacity per revolution (at the expense of higherinternal velocity.) Consequently, it is not always possible tooptimize a pump solely based on the wear performance, andoften pump wear resistance is compromised in order to meetother design requirements.

Materials of Construction for Abrasive ApplicationsRotor Coating. Rotor wear is the primary cause of pumpfailure in abrasive applications. To date, the majority of PCpump rotors are hard chrome plated. Hard chrome is adequatefor medium to low abrasive environments. However, life of achrome plated rotor can be reduced by as much as 50% in highflowing wells that produce more than 10% sand. Alternative rotor coatings using thermal spray processeshave been successfully used by PC pump manufacturers toimprove rotor life in abrasive applications. Field trials of theserotors have shown to double or triple the life of chrome platedrotors in similar applications. The alternative coatings aretypically more expensive than chrome and operators mustcarefully weigh the economic benefits of using these rotors fortheir specific applications.Stator. Elastomeric stators give PC pumps an advantage overother down-hole pumps in handling abrasive slurries. Theflexibility of the elastomer allows large abrasive particles to gothrough the pump or to imbed rather than abrade the stator.The PC pump stator elastomer can be optimized for best wearresistance while meeting other mechanical and physicalproperties.

The elastomer wear resistance optimization involvescreating a balance between the elastomers cross-link density,

physical strength, tear resistance, and fracture properties. Asthe hard particles stress the elastomer upon contact with thestator, energy is either converted to heat or stored elastically inthe polymeric chains of the rubber. The elastic energy storedwithin the rubber becomes available as a driving force for therubber fracture propagation. Once the fracture has occurred,tear properties of the rubber will control fracture propagationwithin the rubber. The elastomer for PC pumps used in abrasive applicationsmust be soft enough to allow the passage of large particlesthrough the seal lines without damaging the rubber. Optimumhardness range of the elastomer for maximum life in abrasiveapplications is between 50 to 65 durometer (shore A.) Inaddition, physical and mechanical properties of the rubbermust be optimized to allow hard particles to imbed inside therubber without allowing the small surface fractures topropagate. As in design optimization, it is not always possibleto select the most wear resistant elastomer for an application.For example, although the most abrasion resistant rubbercompound is a high grade of natural rubber, its lack of oilresistance eliminates its use in oilfield applications. Statorelastomer selection must take into consideration other down-hole conditions such as temperature, water cut, aromaticsconcentration, or H2S presence. The abrasion resistance of astator elastomer is some times compromised to meet thesedown-hole conditions.

Pump Selection Selecting a PC pump for an abrasive application involvesseveral steps. First, the pump must be rated for the applicationflow requirements. The user must then select a pump whichcan produce the desired volume at lowest fluid internalvelocity and at lowest possible pump rotational speed. Theuser must also consider de-rating pump pressure per stage tomaximize pump life for the application. Once these criteria areconsidered, the materials of construction must be selected formaximum wear life.

Material selection can greatly influence the life of a PCpump. To select the right material for an application, all down-hole conditions which may contribute to rotor and statorfailure must be considered. Materials for the pump must beselected to achieve the best overall performance for theapplication. For those applications where abrasion is theprimary concern, stator material must have superior wearproperties as described in the previous section. Hard chromeor other wear resistant rotor coatings must also be consideredto improve rotor life in abrasive applications. Selection of thepump material may also require an economic justificationsince some of the alternative materials might be moreexpensive than others.

Field ResultsNew elastomers and rotor coatings for abrasive applicationshave been studied in many different locations in Canada andthe United States. Figure 8 shows the improvement in pump

SPE 37455 PROGRESSING CAVITY (PC) PUMP DESIGN OPTIMIZATION FOR ABRASIVE APPLICATIONS 5

life obtained using pumps optimized for abrasive applicationsin the sandy (3 to 20 percent by volume) Lloydminster regionin Canada2.

0

50

100

150

200

250

300

350

400

Figure 8. Improvement in average pump life of tendifferent wells in Lloydminster Canada using more

abrasive resistant elastomerSummaryProgressing cavity pumps can be optimized to provide longerlife in abrasive applications. Wear optimization of PC pumpsis achieved through pump geometric design, proper selectionof stator elastomers and wear resistant rotor coatings, andproper sizing of the pump for the application. Down-holeconditions such as concentration, size, and hardness of thesand particles influence pump wear. PC pump life can beextended by reducing particle velocity through the pump, byrunning the pump at lower speed, and by adding more stages tothe pump. Field results show that the life of PC pumps can beincreased significantly if pumps are optimized for the abrasiveconditions.

AcknowledgmentsAuthor wishes to thank Moyno@ Oilfield Products for theopportunity to prepare this paper. Author also expressesappreciation to Mr. Dave J. Bourke for providing valuabletechnical comments.

2The data was obtained in December 1996 and all of thepumps shown in this Figure were still in operation.

AVG PUMP LIFEWITHOUT

OPTIMIZATION

SERVICE DAYS

1 2 3 4 5 6 7 8 9 10