optimization of drilling parameters with the performance of multilobe positive displacement motor...

5/28/2018 Optimization of Drilling Parameters With the Performance of Multilobe Positive Displacement Motor (PDM)

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m....ociety of Petroleum ElADC/SPE 47791Optimization of Drilling Parameters with the Performance of MultilobePositive Displacement Motor PDMG.Robello Samuel*, EnerTech-Landmark Graphics, Stefan Miska, University of Tulsa* SPE MemberCopwght 19S8, lADC/SPE Asia Pacific Drilling TefinologyThis paper was ~psred fw presentaticm at the 1998 lADC/SPE Asia Pacific DriffingConferenM held inJakarta, Indowsia, 7-9 Septembr 1998.This paper was selasted fw presentation by an lADC/SPE Program Committee fol lowingreview of info imatim untained in m abstract submit tad by the author(s) . Contents of thepaper, as presented, have not been reviewed by the International Association of Dri ll ingCcfdfactws or the Society of Petroleum Engineers and are subject to Wedicm by thsauthor(s). The material, as presented, does not necessarily reflect any position of the IADC orSPE, their of ti~ rs, w members. Papers psented at the lADC/SPE meetings are subjest topublication review by Editorial Committees of the IADC and SPE. Electronic reprodudfon,disbibution, or slorage of any part of this papar for commercial purposes without the writtencnnsent of the Society of Petroleum Engineers isprohibited, Permission to reproduce in print isrestricted to an abstract of not more than 300 words; i llustrations may not bs copied. Theabstrad must cQntain Cnnsplcuous acknowledgment of wbre and by whom the paper waspresentd write Librar ian, SPE, PO. Box 833836, Richardson, TX 75083-3836, U.S.A., fsx01-972-9S3-9435.

AbstractRecent increase in application of coiled tubing for horizontalwells and in particular underbalanced drilling triggered thenecessity of a powefil downhole motor. More oftendownhole motor stalling and motor replacement is a problemwhen using with coiled tubing drilling system. To enhance thetechnology and make the system effective, optimization ofdrilling parameters is essentially required. The frequent motorreplacement during the operation incrementally increases theoperating cost despite deriving potential benefits from coiledtubing drilling. The key to improved coiled tubing drillingsystem is a unified system approach that encompasses motorand bit. This paper presents an analytical study on theoptimization of motor performance and drilling parameters. Anew simple test called wear o~f test is defined to establish anoperating window. The practical usefulness of the theory,backed by the fundamental and optimal analysis for rollercone and diamond bits, is demonstrated with numericalexamples.IntroductionOptimization of the downhole motor is very important to havea better trade off between premature bearing failures anddownhole operating hours of the motor. The motor operationalso has to be tuned and sized to achieve maximum rate ofpenetration (ROP). This helps not only to prevent downholefailures of motors but also frequent pulIing out of the coiledtubing. This optimization should result in accelerating the rateof penetration without worsening the health and operation ofthe motor. This objective imposes neither the condition of

maximum rock destructive ability nor maximum horsof the motor. The optimization is carried out with the ofunction of maximum ROP and a constraint of net ththe motor bearing, Common equations are derived forthrust acting on the motor bearing. This optimization nresult in increased rate of penetration but also increasedthe motor bearing and thus increasing the downhole ophours of the motor. It also enables us to calculate theflowrate and optimal horsepower of the motor.Roller Cone BitsThe average rate of penetration as a function of eighand bit rotational speed is given by

RoP=K, f) y. ,The power required for drilling can be given by the foempirical relationship ~)HPb=Kb~.V b. (2The above equations are based on the following assump

the formation is microscopically homogeneou hole cleaning is adequate. hole drilled isverticalThe power developed by the motor is calculated frproduct of torque and angular velocity and is givenfollowing relation ()~NHP. = 550 60 (Combining the two equations and solving for torquefollowing relationship is achieved

T=KXKh ~ di. (However, the torque capability of the multilobe motorby the relation(2)T= KyApK, D:phq. (

where ()+iKY=O.O1 Ki = I .(2 -i~ (Equating Eq. 4 and Eq. 5 the relationship between thedrop across the motor in terms of the \VOB can be oand isgiven by


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2 Robello, Miska IAD

(7)where

[1K,,. = ~KyKi

Figure 1 shows the variation of pressure drop for variousweights on bit for different configurations of the motor. At astall torque, pressure drop across the motor deforms the statorof the power section and breaks the seal lines. At this pointmaximum torque is produced while rpm is equal to zero.Equation 7 could be useful to calculate the stall WOBcorresponding to stall pressure drop and vice versa.Bearing ThrustThe bearing section of the motor is a critical part in the motorassembly, which transmits the drilling thrust and rotationalpower to the drill bit. The endurance of the thrust bearing hastremendous implication on the life of the motor besides thepower section. ~erefore, the thrust on the bearing of themotor is an important consideration and constraint in theoptimal operation of the motor, which dictates the optimalselection of WOB and speed of the motor. Generally, it givesone of the best criteria to be optimized not only to have betteroperatin conditions of the motor, but also for the system as a3~whole ( - . Figure 2 illustrates the forces acting on the bearingsection.The axial thrust on the bearings is composed of the followingthree components:a. hydraulic thrust created by the pressure drop acting

on the cross sectional area (hydraulic thrust - HTa)b. hydraulic thrust created due to the pressure dropacross the bit (hydraulic thrust - HTb)c. thrust due to the radial force (mechanical thrust - Mnd. self-weight of the shafi and the U-joint. (weightthrust - W~.The hydraulic thrust can be approximately given asHTa=Apx Ac, (8)HTb = Aph X Ac . (9)HT= @x Ac+Aphx Ac. (lo)

Unbalance exists due to the fact that the center of mass of theshafi does not coincide with the axis of the rotation. Theunbalance force ismore pronounced at the lower pair motor ascompared to the higher pair motor due to the largereccentricity. The unbalance is measured in terms of anequivalent mass of the shafi with the eccentricity of the shafi.This unbalance force has two components, axial FY andtangential F.. me axial component tends to impart thrust onthe top bearings in addition to the HT and WT.The tangential force is given by(45)

FX =4n2Arprl,, n,,N2e. (11)The axial component can be calculated from the followingequation considering Fig. 3

()rDhFY=FX .PhSubstituting Eq. 11in Eq. 12Fy=8.9x105 A,p,[,, n, N2e~.

PhThe thrust due to weight of the rotating elements itransmission parts is given by

WT= (Ar/,,n,,pr + W,,).The net axial thrust (NT) on the bearing can be gi

NT= HT+MT-t WTNT=(Ap+Ap~)Ac +8.9x 10s A, I,n,epr N2 ~

Ph+ (.4,1,,p, + It~,,1The pressure drop across the bit can be given as

Aph = PQ210858A,~Substituting Eq. 7 and Eq, 16 in Eq. 15,the net thbearing ismodified as

+ 8.9x 10-5A,l,,n,,eprN2~ + (.4r/Ph

In addition, the flow rate can be given by thequation(z) in terms of the configuration and pdimensions aswhere

K,i = 0,0034- .2OptimizationThe following optimization is carried out usingmultiplier method with the objective function of REq. 1 and constraint of net thrust on the beariEq. 17. The objective function isEq. 1

With the objective function of Eq. 19 and constraithe Lagrange functions are solved which yields.(),c +NfJ p[ = 9.where[ )[

AcKr, xd;W(,;t4.= : ~,q1 h pm = 17,8x 1051,eprn, Ar + P,D;P5429 A


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47791 Optimization of Dr il ling Parameters with the Performance of Multi lobe Positive Displacement Motor PDM

The optimum speed is located in such a way that the weight onbit balances the net thrust load on the bearings so as to haveextended bearing life and also maximum ROP. From Eq. 2optimum weight thus calculated can be used to calculate thepressure drop across the motor. The relation between theoptimum weight on bit and the pressure drop across the motoris given as [1


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4 Robello, Miska lAD

the motor. For the same pressure drop, the lower pair motorresults in a higher speed coupled with the lower weight on bit,as compared to that of the higher pair motor. The decrease inrotational speed is more pronounced at the lower configurationmotor than the higher pair motor, which obviously calls forhigher optimum weight on bit. These calculations also dependon the rotational speed, weight exponents and formationfactors, which vary for different formations. The formationfactor for horsepower calculation ranges from 4x10sfor veryhard to 14x10-5for very sofi formations. So the calculationsand results should be handled with due circumspection. Thesensitivity of the change in eccentricity of the shaft on the rateof penetration is far less when compared to that of change inmud density and nozzle area.Diamond BitsRuggedness and high rotational speed capability makediamond bits more attractive and preferable than roller conebits to operate with the downhole motor. The motor operationwas optimized for roller cone bits to achieve the maximumrate of penetration with the constraint of net thrust acting onthe bearing of the motor. The same philosophy of optimizationwas carried out for diamond bits, In the case of diamonddrilling, the restricted mud flow area results in a pressuregradient over surface of the bit face causing a force called thehydraulic [ifi G)or pump-off force as shown in Fig,7. Thiscauses a reduction of effective weight on bit. Therefore, thepump-off force needs to be accounted for the calculations. Themechanical weight on bit is the difference between the appliedweight and the pump-off force acting on the face of the bit.The average rate of penetration for a diamond bit Tis furthersimplified and given as

(23)W=w. -wpWp=Aph Ah.

The power required for drilling can be given by the followingempirical relationship

()HPh = p ; nWNd, (24)The relationship between the pressure drop across the motor interms of the WOB can be obtained and is given by(25)

whereK~ =

()K~ .KVK,

OptimizationThe optimization is carried out with the objective function ofEq. 23 and the constraint of net thrust. Therefore, theLagrange function is formulated as below:

L(Dr, Ph)= ROP(D, ,P , ]+~T(D, ,P .)Taking respective derivatives and solving yields

()@t,N,,., =t P,,where [)4Ci,d,W,,,,0,, = 1.5x D;7P,te/;P: ~5429A()p,, = 17.8x 10-lteprn,A, i ,,The optimum speed is found in such a way thaapplied on bit balances the net thrtlst load acbearings.

IllustrationThe following numerical example explains the ithe calculations of the optimum drilling parameter

d~= 6 W 4P,,,,,,= 550 psi d, =0x.Y=3.5s=0.4p =0.12

Motor details: Same as in previous illustrationArea of the cross section of the cavity

Area of the cross section of the shaft is given by.4, = ~ D? = 4.63 in2K~ 8.34The optimum bit rotational speed and weight on biteratively and found to beN,)P,=518W,,p,= 10900 Ibs.The corresponding flow rate is 240 gpm.The average optimal rate of penetration is found tROP(,P,= 195 ftihrand the corresponding horsepower is calculated

Hp= 0.12X10900 X5I8XZX4X6.25 =60x12x3x.530x2Analysis:Estimation of optimum parameters for rollediamond bits by the above method calls foranalysis. Upon comparison of the parameters, ithe rate of penetration is lower for diamond bits tcone bits. On the other hand, the operating hlower for the diamond bits than the roller cone brequirements have not changed much as comparedparameters, The graphical representation of tspeed and weight are shown in Fig,8.Wear-off TestThe evaluation of drilling parameters dependsoperating efficiency of the motor. The efficiency


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47791 Optimization of Dri ll ing Parameters with the Performance of Mult ilobe Positive Displacement Motor PDM

drops as the operating time of the motor increases.Accordingly, the optimum parameters estimated for the samemotor also change. This necessitates establishing a method toestimate the efficiency of the motor while the motor is inoperation. This will help to delineate the safe operatingenvelope so that maximum rate of penetration and operatinglife of motor is achieved. The Fig, 9 shows a typical plotrepresenting the operating parameters for maximum rate ofpenetration rate. The operating efficiency of the motor relativeto the new motor can be estimated in the field by conducting asimple test, called the wear oJf test, by observing the hookload and the standpipe pressure. The equation 7 relates to thepressure drop across the motor and the efficiency of the motor.Whh the bit off bottom as shown in the first sketch of Fig.10,the standpipe pressure, p~b~l~s noted. Afier applying desiredamount of weight on bit as seen in the second sketch ofFig.10, the standpipe pressure, pWObfl)s noted. The differencebetween these standpipe pressures gives the pressure dropacross the motor and is related by

@M(l)= ~ ,b l) ~w,,b l) (28)Afier drilling a certain number of hours, the above mentionedprocedure is repeated for the same flow rate and weight on bitand is shown in the third and fourth sketch of Fig. 10. Thedifference between the standpipe pressures at this desiredpoint gives the new pressure drop across the motor, and isgiven by@m(2) = ~,,b 2) - ~ v,,b(2) . (29)

From Eq, 7 the operating efficiency is given by(30) fiPm~

The efficiency of a new motor for the particular configurationcan be estimated either by the analytical equation presented inthis paper or obtained from the bench test performancecharacteristic curves provided by the manufacturer. Using theef~ciency of a new motor, subsequent change in the operatingefficiency of the motor can be evaluated. Equation 29 alsohelps to monitor performance of the motor. me wearcoefficient takes into consideration the change in the diameterand pitch due to wear. This coefficient can be avoided bymeasuring the pitch and diameter downhole so that realisticefficiency can be monitored in real time. The above procedureis valid for roller cone bits. For diamond bits the pump-offforce changes as the bit wears out. To effectively isolate thepump-off effect, the procedure needs to be modified asfollows. 1.2.3.

4.5.6.

Note down the off bottom stand pipe pressure.Note down the drill-off standpipe pressure.Apply the desired weight on bit and note downthe on bottom stand pipe pressure and calculatethe effective weight.Repeat steps 1 and 2 at the desired depth.Apply the same effective weight on bit taking itto account of the new pump-off force.The difference in the standpipe pressures in both

the cases gives the pressure drop acmotor,Wear EstimationIt needs to be highlighted here that the ivear oJJ testbe helpful to monitor the wear on the motor to avoipernicious effect on the motor operation. The weamotor can be given as a finction of pressure drop amotor and the cumulative operating time in hours(45

WE= @, t).The relative wear on the motor can be estimatedfollowing equation , \

AcknowledgmentThe authors wish to thank the U, S. Department of Epermission to publish this paper. The sL~pportof(Tulsa University Drilling Research Projects)companies is also gratefully acknowledged. Thewould like to express their appreciation to ELandmark Graphics Corp., and The University of Tulopportunity to present this paper,Summarv

The comprehensive optimization of PDM with thparameters using roller cone and diamond bitsis applicable for multilobe motors. Generalizedrelations between bit rotational speed and weigwill help the user to prevent the operation of tbeyond the capability of the motor,The theory presents a quantifiable basis for meffects of the operating parameters on differentconfigurations of the motor under use.The wear off test gives an operating window ofso that the driller-can stay with in-the operatingof operation and also gives an estimate of the wpower section of the motor while drilling.

Nomenclatureal =WOB exponent,a2= speed exponent,Ac= cross sectional area of the cavity, sq.in.,A, = area of the cross section of the shaft, sq,4. = total nozzle flow area, sq.in.,AP= effective pump-off area, sq,in.,D,,= diameter of the shaft, in.,Dll= diameter of the housing, in,,db=diameter of the bit, in.,e = eccentricity of the motor, in.,F,= axial force, Ibf,Fy = tangential force, Ibf,HP= horsepower, hp,i = winding ratio,k = housin~shafi wear coefficient,


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6 Robello, Miska lAD

kz =material property coefficient,kj = housing, shaft, pitch wear coefficient,kq = coefficient, (9.48),k,= coefficient, (1.8xIOC),K= constant,K,= constant, (5252)Ky = con-, (0.01)K,= constant, (0.028)Kb = formation hardness, teeth, bearing, mud coeff.,Kf = formation drillability factor, Wr,Ki= winding ratio coefficient,Kij =winding ratio coefficient,1,= length of the seal line of one cavity, in.,n$= number of stages,N= bit rotational speed per minute, rpm,Ph= pitch of the housing, in.,P,= pitch of the shaft, in.,Q = theoretical flow rate, cu.in,ROP =rate of penetration, ft/hr.,s = diamond size (carats/stone),T= theoretical torque, ft-lb,w.= weight of the U-joints, lbs,W = weight on bit (WOB), lbs,WP=pump-offforce, lbs,xx= average density of face stones (carats/inz),x = exponent, (1.5)y = exponent, (2.5)= pressure drop, psi,P,= density of the shafi, lbm/in3,q = overall efficiency,a = helix angle, deg.,pm= density of mud, ppg,P = coefficient of friction

Subscript 1,2 = condtion points,b = bit,d= diamond,f= final condition,i = initial condition,m =motor,ob = off-bottom,opt = optimum,rc = roller cone,stall = stall condition.

References1.2.

3.4.

Report, Smith Tool, Technical Services, Irvine, CAG. Robello Samuel, Stefan Miska, Len Volk AnalyticalStudy of the Performance of Positive Displacement Motor(PDM): Modeling for Incompressible Fluid SPE 39026LACPC, Brazil, 1997.Lucia F.V., How to Optimize Downhole MotorGuidance System Performance Pet. Engineer, June 1992.Miska S., Qui W., Robello G.S., Advanced HorizontalCoiled Tubing Drilling System Annual Report US.

Department of Energy -BDM -19985. G. Robello Samuel, TUDRP Advisory BoaReports, May, Nov. 1996,May, Nov. 19986. Winter W.J, Warren T.M., Determining

Weight-on-bit for Diamond Bits SPEFrancisco 1983.7. Peterson J.L., Diamond Drilling Model Veriand Laboratory Tests SPE 5072, AIME: HouFigures

o~1 3 5 7 9 11

winding number

Figure 1 IYOB and Pressure Drop Across the

power semion

Imsmissionsection

bea ring sect ion

bit

I Weightof rod1pressuredropacro1eight oftrnnsmissioI+ pressuredropacross

? WOB

Figure 2 Forces acting On the PDM Bearing SecRoller Cone Bits


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47791 Optimizat ion of Dri lling Parameters with the Performance of Mult ilobe Posi tive Displacement Motor PDM

@Figure 3 Unbalance Force Components

P

Figure 6 The Effect of ROP Opt , WOB Opt , RPM OPressure Drop

pw r section

dssion w t ionFigure 4 Load Weight on Biflhrust Load For Various Bit

Rotational Speeds

b ea r i n g s e ct i m

1eight ofrcd/ Weight o f b n n sm i ss i on s l

bit

Figure 5 The Effect of ROP Optimum on Pressure Drop AcrossThe Motor


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8 Robello, Miska lADC

r/

w.

Figure 8 Load Weight on Bit/Thrust Load For Various BitRotational Speeds

I._...-. l

RPM

Figure 9 Load Weight on Bit/Thrust Load ForVarious Rotational Speeds and Operating Efficiencies

P-, ,} .,..

rr.bo l,,m n.eight ppli d

.. ..;.,..

Figure 10 Wear-oj~Test

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optimization of drilling parameters with the performance of multilobe positive displacement motor...

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