spe-19545-ms predicting wellbore trajectory

8/18/2019 SPE-19545-MS Predicting Wellbore Trajectory

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S PSPE 9545 Society o f et ro leum Engineers

An Analysis of Predicted Wellbore Trajectory Using a Three-Dimensional Model of a Bottomhole Assembly With Bent SubBent Housing and Eccentric Contact CapabilitiesJ.B. Williams* and M.C. Apostal, * * DAD Corp., and G.A. Haduch, Jordan, Apostal,Ritter Assocs.

*SPE Member* *SPE Member with Jordan, Apostal, Ritter Assocs.

Copyright 1989, Society of Petroleum Engineers, Inc.

This paper was prepared for presentation at the 64th Annual Techn ical Conference and Exhibition of the Society of Petroleum Engineers held in San Antonio, TX, October 8-11 1989.

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author s). Contents of the paper,s presented, have not been reviewed by the .Society of Petroleum Engineers and are subject to correction by the author s). The material, as presented, does not necessarily reflect

any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are sub ject to publication review by Editorial Comm ittees of the Societyof Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustr ations may not be copied. The abstract should contain con spicuous ack nowledg mentof where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836. Telex, 730989 SPEDAL.

ABSTRACT

Bent subs and bent housing motors are one of themost important class of tools available to aid drillingengineers in deviation and directional control of wellbores.Even though such tools may spend very little actual timedrilling a hole, the quality of their performance oftendetermines the difference between success or failure of a

well as far as execution of the trajectory plan (or design) ofthe well is concerned.

Despite the importance of bent subs and benthousing motors to the drilling community the previous lack

INTRODUCTION

Apparently, the earliest attempts at explaining· thestructural behavior of drill strings and Bottom Hole Assemblies (i.e., BHA s) in terms of beam mechanics and elasticbending theory dates back to the early work ofCapelushnikov [1] and Clark [2] in the 1930 s. Drilling mechanics did not, however, really come into its own as a discipline until the 1950 s when Lubinski and Woods [3,4,5] intheir pioneering work carried out buckling studies on rotarydrill strings and addressed such questions as the factors f-fecting inclination and dog-legging in rotary boreholes andh f bili i lli h l d i i


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housing motors to the drilling community the previous lack th f t bili i t lli h l d i ti

N ANALYSIS OF PREDICTED WELLBORE TRAJECTORY USING A THREE-DIMENSIONALMODEL OF ABOTTOMHOLE ASSEMBLY WITH BENT SUB, BENT HOUSING, ND ECCENTRIC CONT CT CAPABILITIES SPE 19545

Millheim and Apostal [11] were the firSt to implement complex three-dimensional dynamic models of a rotating BHA to study the effect BHA dynamics has on the tra

jectory of a bit. This work was instrumental in demonstrating that the intermittent contact and dynamic torque andfriction effects associated with a rotating BHA were important factors in directional (especially azimuth) responses ofa drilling BHA. Previously, these responses had been attributed to formation effects. More recent efforts in this areaare represented by the studies of Mitchell and Allen [12]and Birades [13]. Dunayevsky, Judzis and Mills [14,15]implemented analytical models of the entire drill string (notjust the BHA) to investigate the onset of drill string precession in directional boreholes [14] and the dynamic stabilityof drill strings under fluctuating weight on bit [15].

A common characteristic of the BHA analysis algorithms described in [8-13] is the assumption that the interaction between a BHA s bit and stabilizers and the formation can be dealt with via implementation of simplified contact, torque and friction models imposed on the bit andstabilizer nodes of the finite element model. Though this ap- .proach is adequate for analyzing the overall static and dynamic response of a BHA, the resulting solution provides little insight into the complex behavior which results from theinteraction between the teeth (or cutters) of the bit, theblades of the stabilizers, and the formation.

To address this limitation, Baird, Apostal andWormley, together with Caskey and Stone [16,17,18,20],undertook the development of a three dimensional transientdynamic finite element computer program (GEODYN2) ca

pable of simulating the behaviorof

a rotating BHA interacting with a non-uniform formation. GEODYN2 facilitates avery detailed analysis/simulation of the behavior of a BHAwith a polycrystalline diamond compact (PDC) bit and various stabilizer designs Working along somewhat different

A limitation of all models addressed above is theassumption of an initially straight centerline of theundeformed string, a limitation which precludes the use of

bent tools (i.e., bent subs or bent housing motors) in theBHA. To date, with the exception of the study by Brett,Gray, Bell and Dunbar [28], very little information isprovided in the open literature concerning analytical ornumerical models for dealing with bent subs in the BHA.Brett et. al. directly modify the computational scheme ofMillheim and Apostal [11] by implementing a series of

· coordinate transformations, to achieve the desired result of aslope discontinuity in the centerline of the undeformedBHA. The work described herein, has the same ultimategoals as that of Brett et. al. but achieves the result from adecidedly more powerful mathematical approach.

DESCRIPI'ION OF MATHEMATICAL MODEL

Background of The BRA Model

The BHA model described in this paper is based onthe finite element method and has been designed to accountfor the static and rotational response of a bottomhole

assembly drilling in an arbitrary curved three-dimensionalwellbore [31,32].

The nonlinear solution algorithm incorporated in themodel is designed to accommodate intermittentcontact/friction, large displacement, buoyancy, and otherdiverse effects which characterize the interaction of arotating bottomhole assembly with the formation.

The mo


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SPE 19545 WILLIAMS , APOSTAL, HADUCH

twenty 20) Wlz A drillahead simulation for a one hundredfoot 100) interval normally takes from 5 - 5 minutesdepending on the assembly and wellbore configuration. This

proportional increase in time is due to the drillaheadalgorithm. This makes rig site use of the program acceptablefor drilling operations.

Modification of The BHA Mo4e1 to .Accommodate the New Tools

Bent tools and their associated hardware e ~ g .kickpads, eccennic stabilizers, etc.) are characterized byinherent geometrical and thus structural) asymtnetry · n

their construction which causes them to provide abottomhole assembly with a predilection for deformation in aprescribed direction or plane). Modification of the abovedescribed BHA model to accommodate the presence ofthese components not only mandated significant expansionof the existing drilling component library but requiredaddition of some significant new analytical capability aswell.

An important difference between creating a structurale.g. finite element) model of a conventional rotary

bottomhole assembly and one with a bent tool in it is thediscontinuity in slope in the undeformed centerline of theassembly which occurs at every bent tool location. nconstructing a finite element model of an assembly, thisslope discontinuity can be enforced in a number of waysincluding local to global coordinate transformation whichturns the bottomhole assembly into a space structure), theuse of Lagrange multipliers and the implementation of

penalty function models both ofh ~ h

enforce the bent toolangle as a geomenic constraint acting on the fmite elementmodel).

The kick pads, eccennic contact stabilizers, etc.,

some type of measuring device such as a steering tool orMWDcollar.

The objective of this procedure is frrst the orientationof the steering tool or similar functioning component) withrespect to the high side of the hole or some otherconvenient reference direction) followed by the subsequentalignment of the bend s) and accompanying eccentr iccomponents with respect to the steering tool. Control of thedrill string through torque applied at the surface is then usedto keep the assembly properly oriented as it drills ahead.Consequently, any finite element algorithms purporting toaccurately model such a hole deflection process must be able

to constrain any resulting solution to reflect the aboveorientation process. n effect, the orientation process isinflicting a constraint on the solution; a constraint which isbest handled by either a Lagrange multiplier or penaltyfunction technique.

Since the Lagrange multiplier and penalty functionmethods both excel at dealing with ll the analyticalproblems addressed above, either of these techniques i ~ aviable candidate for implementation in the mathematical

formulation of the new bent tool analysis capability beingaddressed here. The authors, having had a great deal ofexperience implementing both these approaches, have foundthat, in most situations, the penalty function method is themost effective means of accommodating the constraintswhich invariably inflict themselves on a static or dynamicbottomhole assembly analysis. The authors experience withthis technique dates back to the earliest versions of theBHA Model where the procedure was implemented torepresent the intermittent contact and friction effects

characterizing the rotational behavior of standardassemblies. n incorporating the new bent tool capabilities,the areas addressed by the penalty function method wereexpanded to include modeling the structural behavior of theb t t l d th i i t d h d ll th

3


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4N ANALYSIS·OF PREDICTED WELLBORE TRAJECTORY USING A THREE-DIMENSIONAL MODEL OF A

BOTTOMHOLE ASSEMBLY WITH BENT SUB, ~ N THOUSING, ND ECCENTRIC CONTACT CAPABILITIES SPE 19545

collars. In the case of a bent housing motor, it is a simplematter (using this procedure) to intersperse a bend in themidst of the motor. It should also be noted that there is no

limit to the number of bends which a user can introduce intothe model of a bottomhole assembly. n this way, the modelcan be used to evaluate any one of the commerciallyavailable steerable systems presently being used by thedrilling industry.

The eccentric stabilizer model currently provides for amaximum of eight blades, of varying diameter, distributedcircumferentially in a uniform manner about a cylindricalbody. As in the case of an ordinary stabilizer or reamer, all

blades (or rollers) for this component are assumed to havethe same length. During the solution process, the blades aremodeled by a series of contact points (or vectors) whichoverlay the cross-section of the cylindrical body so that boththe body outer diameter and the blades (contact vectors)provide a mechanism for contact with the wellbore wall.

Rather than being visualized as a component in itsown right, the kick pad alluded to earlier is really just anappendage attached to a component (e.g. PDM, bent

housing, turbine, etc.). The kick pad is modeled by a singleoriented contact vector emanating from a reference nodedefined during mesh generation. n practice, thisconfiguration acts like a stabilizer with a single, very short,blade since both the component and attached kick pad canact as contact mechanisms.

A steering tool, or MWD, is modeled as a referencepoint at a specific location in the drilling assembly. It has nolength, outer diameter, or inner diameter but rather is usedto orient some defined plane of the assembly with respect tothe high side of the hole. In this way, the user has thecapability to orient a bend, series of bends, kick pad, oreccentric stabilizer from zero 0) to one hundred eighty

bit and the bit tilt for a typical Bent Sub Assembly,respectively, with an orientation zero 0) degrees from highside. As expected, the lateral (building) force at the bit

increases as bent sub angle is increased. This conflmls theearlier assumption that the build rate should increase as theangle of the bent sub is increased. Figure 2, however,illustrates a unique characteristic of the Bent Sub Assemblywhich had not been expected. For all assemblies, the value

·of bit tilt is found to decrease as the bent sub angle isincreased.

This is an important result because it may explainwhy s o ~Bent Sub Assemblies do not build faster when

the angle of the bent sub is increased. In the case of the12-l/4 hole size, Figure 2 shows that the effect on the buildrate may not be very noticeable. However, the 9-7/8 and8-l/2 hole size plots given in that figure demonstrate thatwhen the angle of the bent sub is greater than one 1)degree, the building tendency of the assembly being modeledwill be offset by a dropping tendency due, in large part, tothe negative (downward) tilt at the bit

Figures 3 and 4 show the effect of bent sub angle on

the lateral force at the bit and bit tilt, respectively, when thesame Bent Sub Assembly modeled in Figures 1 and 2 is reoriented straight down, i.e., the plane of bend is oriented onehundred eighty (180) degrees from the high side of the hole.Referring to Figures 3 and 4 we fmd that, again, the behaviorof the lateral force is as expected. Increasing bent sub angleincreases the value of the lateral (dropping) force at the bit.

n interesting effect of bent sub angle on bit tilt forthe Bent Sub Assembly can be seen in Figure 4 where weobserve a reversal in behavior an inflection point) at a bentsub angle of approximately one 1) degree for allassemblies. The effects of this phenomenon can haveadverse effects on drilling performance. Correlating


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SPE 1951.5 WILLIAMS. APOSTAL, H DUCH

model correctly predicted a build and turn response of theassembly.

BENT HOUSING ASSEMBLY

The use of a Bent Housing Assembly as analternative to the side loading concept of the Bent SubAssembly was proposed by Emery [36] in 1985. Bycreating a bend in the assembly close to the bit, it wastheorized that two objectives could be accomplished, (i) bittilt could be controlled, and (ii) the side loading of the bit andresultant power loss to the motor could be eliminated.Analyses were undertaken with the new ·bent tool model tovalidate the above statements.

Figures and 6 show the effect of bent housing angleon the lateral force at the bit (Figure 5) and bit tilt (Figure6) for typical, but comparative, Bent Housing and, Bent SubAssemblies. The bends in the assembly were located at 5.8ft. (Bent Housing) and 26.5 ft. (Bent Sub) from the bit,respectively. Under the given conditions, the model predictsthat bit side force is minimized and bit tilt continuouslyincreases in the range of zero (0) to one (1) degree of bent

housing angle. At bent housing angles greater than one1)

degree however, the model predicts a dramatic increase inbit side force while the value of bit tilt levels of f in magnitudeto a value of approximately 0.9 degrees.

Prediction of Bent Housing Assembly Performance

Data from a horizontal well [37 ,38] was used tosimulate. the predicted performance of a 1-7/8 degree benthousing motor in a 7-7 8 hole. This case is unique in thatthe directional work was performed with a positive displacement motor using air as the drilling medium. The BentHousing Assembly configuration used in the analysis isdefined in Table 3 while the results of the analysis are givenin Figure 7. As shown in Figure 7, the results of the

Figures 8 and 9 show the effect of variation ofeccentric stabilizer diameter on the bit side force and bit tilt,respectively. The blades in the model used to generate theresults shown in Figures 8 and 9 are located at 2 ft. and25 ft. distances from the bit. The lower blade is orientedone hundred eighty degrees from high side with the upperblade oriented zero degrees from high side. In carrying outthe computer runs used to generate the curves of Figures 8and 9, the blade diameter was increased in 0.125 in.increments for both blades simultaneously. For this holesize and assembly, the computer results indicate that theside force at the bit increases at a rate of approximately 2.5kips I 0.125 in. of blade diameter. It is unlikely that bit side

forces on the orderof

10 - 20 kips could be achieved duringdrilling operations. The results plotted in Figures 8 and 9stand as a representation of the type of analysis that can beperformed with a computer model of this type.

A unique and rather unanticipated effect of thepresence of the eccentric stabilizers on bit tilt can be seen inFigure 9. In carrying out the computer runs comprising thisanalysis, it was not expected that (see Figure 9) the bit tiltwould continue to decrease with increasing blade diameter,

especially to the point where the bit tilt would eventuallypoint down (i.e., maintain a measurable negative value).This example demonstrates the usefulness of the new benttooVeccentric stabilizer computer model in optimizing thesize of blade diameter for this class of assembly.

APPLICATIONS OF THE MODEL

A model of this type has many applications in thefield of directional drilling or deviation control, some of which

are listed below:

1. Orientation of a bottomhole assembly (0 - 180 ·degrees left or right of high side) for achievingoptimum performance n a well deflection scenario


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6AN ANALYSIS OF PREDICTED WELLBORE TRAJECTORY USING A THREE-DIMENSIONAL MODEL OF A

BOTTOMHOLE ASSEMBLY WITH BENT SUB BENT HOUSING AND ECCENTRIC CONTACT CAPABILITIES SPE 19545

CONCLUSIONS

1

2.

A three-dimensional finite element model of a

bottomhole assembly has been modified to simulatethe nonlinear behavior of a bottomhole assembly thatcontains bends and eccentric contact points along itslength.

Results obtained by performing analyses (using theabove described new computer model) on bottomholeassemblies that contain bends and eccentricstabilization show that the behavior of theseassemblies is predictable and not always consistent

with prior expectations.ACKNOWLEDGMENTS

NOMENCLATURE

A: Vector A-~ Matrix C

a: Variational Operator

)T: Transpose of the Vector or Matrix ( )

7t: Total Potential Energy

A

7t: Modified Total Potential Energy

U: Elastic Strain Energy

V: Potential Energy Due to Applied Loads

F: Functional

REFERENCES

1.

2.

3.

4.

5.

6.

7.

8.

9.

Capelushnikov, M., Why Holes go Crooked in Drilling, World Petroleum, May 1930.

Clark, L.V.W., A Theoretical Examination ofStraight and Directed Drilling Techniques, Instituteof Petroleum Technologists, Vol. 22, January 1936.

Lubinski, A., A Study of the Buckling of Rotary Drilling Strings, Drilling and Production Practices, 1950.

Lubinski, A. and Woods, H.B., Factors Affecting

Angle of Inclination and Dog-Legging in Rotary BoreHoles, Spring Meeting, Mid-Continent District, Division of Production, Tulsa, March 1953.

Woods, fl.B. and Lubinski, A., Use of Stabilizers inDrill-Collar String, Oil and Gas Journal, April 4,1955.

Huang, T. and Dareing, D.W., Buckling and Frequencies of Long Vertical Pipes, Journal of the Engi

neering Mechanics Division of the ASCE, February1969.

Fischer, F.J., Analysis of Drill Strings in CurvedBoreholes, Society of Petroleum Engineers ofAIME, Paper No. SPE5071, 1974.

Nicholson, R.W., Jr., Analysis of Constrained Directional Drilling Assemblies, Ph.D. Dissertation, TheUniversity of Tulsa, Department of Petroleum Engineering, 1972.

Wolfson, L., Three-Dimensional Analysis of Constrained Directional Drilling Assemblies in a Curved


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SPE 19545 WILLIAMS APOSTAL H DUCH

14. Dunayevsky, V.A., Judzis, A., and Mills, W.H.,"Onset of Drill String Precision in a Directional Borehole," SPE 13027, 59th Annual Technical Conferenceof the SPE, Houston, TX, 1984.

15. Dunayevsky, V.A., Judzis, A. and Mills, W.H.,"Dynamic Stability of Drill Strings Under FluctuatingWeights-On-Bit," SPE14329, Presented at the 60thAnnual Technical Conference of the SPE, Las Vegas,NV, September 1985.

16. Baird, J.A., Apostal, M.C., Wormley, D.N.,"Analyzing the Dynamic Behavior of Some TypicalRotary Bottom Hole Assemblies During Start Up,"Geothermal Resources ·Council Transactions, Vol. 9 -Part I, 1985.

17. Baird, J.A., Caskey, B.C., Wormley, D.N. and S t ~ n eC.M., "OEODYN2: A Bottom Hole Assembly -Geological Formation Dynamic Interaction ComputerProgram," SPE 14328, Presented at the 60th AnnualTechnical Conference of the SPE, Las Vegas, NV,

September 1985.

18. Baird., J.A., Apostal, M.C., and Wormley, D.N.,"Phase 2 Theoretical Description - A Geological Formation - r i l l String Dynamic Interaction Finite Element Program (GEODYN2), Sandia Laboratories,Contract No. 68-3061, Report No. SAND86-7084,1986.

19. Brakel, J.D., and Azar, J.J., "Prediction of Wellbore

Trajectory Considering Bottomhole Assembly andDrill Bit Dynamics," SPE IADC 16172, presented atthe SPE IADC Drilling Conference, New Orleans,LA, March 1987.

24. Toutain, P., "Analyzing Drill String Behavior,'' ThreePart Series Appearing in World Oil, June, July andSeptember 1981.

25. Walker, B.H. and Friedman, M.B., "Three-Dimensional Force and Deflection Analysis of a VariableCross Section Drill String,'' Journal of Pressure Vessel Technology of the ASME., May 1977.

26. Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, NY1955.

27. Andersen, C.T., "Formulation of a Beam Finite Ele~ e n tFor Torsion-Flexure Coupling and Axial ForceFlexure Coupling, M.S. Thesis, The University of Tulsa, Discipline of Mechanical Engineering, 1985.

28. Brett, J.F., Gray, J.A., Bell, R.K. and Dunbar, M.E.,"A Method of Modeling the Directional Behavior ofBottomhole Assemblies Including Those With BentSubs and Downhole Motors," IADC/SPE/4767, Presented at the 1986 IADC/SPE Dt;illing Conference,Dallas, TX, February 1986.

29. Baird, J.A., Caskey, B.C., Tinianow, M.A., and Stone,C.M., "GEODYN: A Geological Formation/DrillString Dynamics Computer Program," Paper SPE13023 Presented at the 59th Annual Technical Conference and Exhibition, Houston, TX, Sept. 16-19,1984.

30. Millheim, K.K., and Warren, T.M., "Side CuttingCharacteristics of Rock Bits and Stabilizers WhileDrilling," Paper SPE 7518 Presented at the SPEAIME 53rd Annual Fall Technical Conference andExhibition Houston TX Oct 1 3 1978

7


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8N ANALYSIS OF PREDICTED WELLBORE TRAJECTORY USING A THREE-DIMENSIONAL MODEL OF A

BOTTOMHOLE ASSEMBLY WITH BENT SUB, BENT HOUSING, ND ECCENTRIC CONT CT CAPABILITIES SPE 19545

38.

39.

Yost II, A.B., Overbey, W.K., and Carden, R.S.,Drilling a 2,000-ft. Horizontal Well in the Devonian

Shale, Paper SPE 16681 Presented at the 62nd An

nual Technical Conference and Exhibition, Dallas, TX,Sept. 27-30, 1987.

Warren, T.M., Factors Affecting Torque for a RollerCone Bit, JPT (Sept. 1984), 1500-1508.

APPENPIX

Generation and Solution of the Constrained Finite Ele

ment Model of the BHA

Notwithstanding the fact that time and space do notpermit an exhaustive treatment of the subject, one notesthat the prominence of the penalty function method in generating and solving constrained finite element models of bottom hole assemblies in the BHA analysis model describedhere dictates that we stop for a moment to provide a briefmathematical review of the ideas involved. Though the finiteelement models implemented in the BHA analysis model

module are formulated using the more general Principle ofVirtual Work, the concepts involved here are more conciselyand elegantly explained using the Principal of Minimum Potential Energy as a variational framework for the direct formulation of the element stiffness equations.

The Total Potential Energy functional 1t of an elasticbody is given by

x = U V 1)

where U is the strain energy arising from deformation ofthe body and where V is the potential energy attributableto the presence of any applied loads. The Principal of Minimum Potential Energy states that Among all displacements

o =od ~

(5)

In the constrained minimization problem defined by (3) and(5)above, ~ must not only satisfy the specified boundary

conditions and be sufficiently continuous, but must satisfyany of the constraints imposed on the body as well.

The constraints in the BHA solution algorithm arisefrom many sources including contact and friction effects, definition of specialized drilling tool behavior, orientation ofsteering tools, etc. The penalty function method, which isemployed in the BHA model solution algorithm to deal withthese constraints, involves the reduction of conditional extremum problems to extremum problems without constraints bythe introduction of a penalty function associated with theconstraints. As applied to the problem defined by (3) and(5) above, the technique involves seeking the minimum of a

AModified Potential Energy Functional 1t obtained byadding a quadratic term associated with the constraint in(5) (i.e., the constraint is satisfied in the least squaresense):

\

1t F + 0 2 ) dvv

(6)

where ( is a weighting parameter bounded by 0 < Y< oo •We note that the stationary condition

(7)

attempts to yield a kinematically admissible solution for u

which simultaneously satisfies both equilibrium and the constraint conditions of (5) as well.


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SPE 19545 WILLIAMS. APOSTAL. HADUCH

\

where ; is the Jacobian matrix given by

(11)

In introducing the standard fmite element approximations,

we assume that the modified Total Potential Energy ~ ofthe elastic body under consideration can be approximated bythe sum of the energy contributions of the N individual discrete (finite) elements used to model the body. It thereforefollows from (6), (8) and (10) that, in building a finite ele

ment model, we assume thatN7t J::l Ie=1 ve

( F 1 o 2 dv2

(12)

In considering the deformation of an arbitrary element e ofthe assemblage, we note that we can employ the elementshape functions to relate E (at any ·point ~ within the ele-

ment) to e (the nodal degrees of freedom of the element)

via an expression of the form

u = B (x) e1


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1

N ANALYSIS OF PREDICTED WELLBORE TRAJECTORY USING A THREE-DIMENSIONAL MODEL 0F ABOTTOMHOLE ASSEMBLY WITH BENT SUB. BENT HOUSING. ND ECCENTRIC CONT CT r A P A R T T T T T ~ ~

analysis including (but not limited to) displacement field -tialization (for the Newton-Raphson solution process), identification of solution convergence or divergence, solution in

crement sizing, identification and circumventionof

limit andbifurcation buckling points, convergence acceleration, penaltyfunction parameter control, etc.

BENT SUB ASSEMBLY(DRILLED FROM 10,571' - 10,698' MD)

15 - 6-1/4 X 2-1/4 DRILL COLLARS1 - 6-1/4 X 2-1/4 NONMAGNETIC DRILL COLLAR1 - 1.00 DEGREE BENT SUB1 - 6-1/2 POSITIVE DISPLACE:MENT MOTOR1 - 8-1/2 DRILL BIT (IADC 837)

TABLE 1

ACTUAL VERSUS PREDICfED RATES FOR BUILD AND TURN

SPE 19545


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:

5 DEG./ ORIENTED0 OFF HIGHSIDE STATICBIT TILT DEGREES

0 . 3 . . . .

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

-0.5

f · · · · · · · · · · · · · · · · · ~ · · · · · · · · · · · · · · · · · · · = = = · · · · · · · · · · · · · · . 1 . 2 . : . 1 l 4 . ~Q l ~. : ~ / 8 . ~ . M Q I Q R ...............................

0 0.5 1 1.5 2 2.5 3BENTSUB ANGLE DEGREES

FJGURE 2

5 DEG. fORIENTED 180 OFF HIGH SIDE STATIC

BIT TILT DEGREES

3.5

0.5 r - - - - - - - - - - - - - - - - - - - - - - - - - -

0.4

0.3

0.2

9-718 HOLE, 7-3/4 MOTOR0.1

0

-0.1

-0.20 0.5 1.5 2 2.5 3 3.5

BENTSUB ANGLE DEGREES

FIGURE4

5 DEG I ORIENTED 180 OFF HIGH SIDE STATIC

BIT SIDE FORCE LBS.0 . .

-500 f · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ~

8 1 1 2 ~ H O L E

-1000 r · - · · · · · - · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · - ~ ~ - - - · · · · · · · · · · · · · · · · · · · · · · - ~ · - · · · · · · · · · ·

-1500 f-···············································-············'···················· '=

9-718 . HOLE

-2000 ~ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ~ · · · · · · · · · ·......

-2500 1 - · · · · · · · · · · · · · · - - · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · - · · · · · · · · · · · · · · · · · · - · · · · · · · · · · · · · · · · · · · · · · · · · · · · - ~ · - · · · · · · · · · · · · · · · · · · · ·12-114 HOLE

9-5/8 MOTOR-3000 - - - - - - - - - - - - - - - - - - - . L . . - . - - - - l . . . . . - - - - - - - - - - . - - J

0 0.5 1 ~ 2 ~ 5 3 3.5

14

12

10

8

6

4

2

0

-2

BENTSUB ANGLE DEGREES

FJGURE 3

5 DEG I ORIENTED 0 OFF HIGH SfDE STATIC12-114 HOLE SIZE WITH 9-5/8 MOTOR

BIT SIDE FORCE LBS. (Thousands)

BENT HOUSING I

···············-···················-···················································································· ··················································-:I

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·· . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . .

··········································-······························································· ·································································

BENT SUB

____j__ _ I I I I

0 0.5 1.5 2 2.5 3 3.5BEND ANGLE DEGREES

FIGURES

.· _-

- .

~

0V \

\ \


13/13

ND

en

BIT TILT DEGREES1

5 DEG./ ORIENTED 0 OFF HIGH SIDE/ STATIC

12-1/4 HOLE WITH 9-5/8 MOTOR

0.8

0.6

0.4

0.2

BENT HOUSING................................... ···································································································································

......................................................................................................................................................................

.......................................................................................................................................................................

-0.20.5 1.5 2 2.5 3 3.5

25

20

15

10

5

BEND ANGLE DEGREES

FIGURE 6

5 DEG./ E N T R ~BLADES ORIENTED 180 AND 0/STATfC

9-7/8 HOLE SIZE WITH 7-3/4 MOTOR

B1T SIDE FORCE DEGREES Thousands)

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ~ · · · · · · · · · · · ·························

--············································································-· .........................................................................................

9.75 10 1 0.25 1 0.5 1 0.75

STABILIZER DIAMETER /INCHES

FIGURES

7-718 HOLE SIZE /1 7/8 DEGREE BENT HOUS1NG MOTOR

HOLE ANGLE DEGREES9 0 . ~

8 5 1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ~ ~ · · · · · · · · · · · ·

ACTUAL

8 0 1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ~ ~ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·

7 5 ~ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·

70 1-·············································································································································································1

65 1 I I I I I • 3909I I I I I I

3a

9I I I I • I I

3 9 9 8

3869

MEASURED DEPTH FEET

FIGURE7

5 DEGJECCENTRIC BLADES ORIENTED 180 AND 0/STATIC

9-7/8 HOLE SIZE WITH 7-3/4 MOTOR

BIT TILT DEGREES0.4

0.2 ~ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·

-0.2

-0.4

9.75 10 10.25 10.5 10.75

STABILIZER DIAMETER /INCHES

FIGURE 9

~1 11

~z:

l

spe-19545-ms predicting wellbore trajectory

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