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. . . SPE 13949 Horizontal Radial Drilling System . . ......-, Copyright 19S5,SocietyofPetroleumEngineers ThispaWr wasprsssnladattheSPE 19S5Osllforrrla RsglonslMsetlng,hetdInSSkSmf18kI, CSIlfOrnla, Msroh27-S9, 19S6.The Mat@slIssubkotto corrsdbnbytheauthar.Permlsslon tocopyISrestricted toansbstraclofnotmorothanSW word$.writeSPE, P.O.SoxS39S3S, Rlehardson, Texss 760S3-3S36. Telex:730S89SPL5DAL. ABSTRACT : 2. Drill a 100-200 foot hole rapidly, A high pressure, water jet drilling systexn has approximately 4 inches in diameter, through an unconsolidated formation, been developed using a new force system to con- currently drill a bore hole and place a iwtal tube 3. Place a 1% inch OD production tube within in the bore hole. the 4 inch diameter bore hole in the . formation while drilling is in progress. The first commercial application has been hori- zontal radials for shallow heavy oil” reservoirs. 4. Cutoff the production tube, as required, Many radials may be placed at the same elevation. downhole. Logging, and comtpleiion techniques have been develop- ed. 5. Log the individual production tube in 1. Introduction three dimensions, 6. Provide perforacio:lti and sand controls Over the past f%ve years Mchtel Investments Inc & if desired. Patrolphysice Ltd. have been developing a new drklling’systern. The initial goal of the work B. System Technology Summary has been to provide multiple horizontal drain holee or injection radiala Ln unconsolidated Early in the ayetem development, a decision wa heavy oil reservoirs viaexiating wells. In thie made to employ a 10 to 12 inch radius turn paperwe shall diacues the technology which has from the verttcal to thehotizontal so ae to been developed to achieva that goal. We will be”able to peneerate shallow or thin formation also comment on other application of this and to minimige underreaming, technology, An eractable whipstock containing a combination of slides M thiB paper the tarm “radial” rafers to the and rollers has been developed to effect this bending and straightening process. approximately 4 inch radial bore drilled into the formation. The term “production tube” refers The drill system uses 8,000-10,000 paiwatsr to the 1* inch metal ERWtube placed in that bore. for water jet drilling and canbe adapted to commonly used additives* The drill bores an A. System Technical Objectives approximately 4-inch diamater rad%al within which it progressively places a 14 inch OD The following Project Technical objectives carbon steel production tube 86 it proceeds through the formation. The jet drill head evolved from the primary goal,~ does not rotate and delivers in e%cese of 1,000 hydraulic horsepower to the formation. 1. Provide multiple, generally hori~ontal radials of predetermined direction, 100 For drill propulsion, a totalky new pueh-pull to 200 feet in length from a single process has been developed. Specifically, esfeting oil well, all from the earn% depth. the drill penetrates the formation in aelE- regulated movements propelled by internal static fluid pressure. Forward velocities can be controlled from a low of 6 feet per minute ko a high of 120 feet per minute, As the drill moves thrOUgh the formation, the References and illustrations at end of paper, anterior portion of the 14 inch tube ia 887 I

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    SPE 13949

    Horizontal Radial Drilling System. . .... ..-,

    Copyright19S5,Societyof PetroleumEngineers

    ThispaWr wasprsssnladat theSPE 19S5OsllforrrlaRsglonslMsetlng,hetdInSSkSmf18kI,CSIlfOrnla,Msroh27-S9, 19S6.TheMat@slIssubkottocorrsdbnbytheauthar.PermlsslontocopyISrestrictedtoan sbstraclofnotmorothanSW word$.write SPE, P.O.SoxS39S3S,Rlehardson,Texss760S3-3S36.Telex:730S89SPL5DAL.

    ABSTRACT: 2. Drill a 100-200 foot hole rapidly,

    A high pressure, water jet drilling systexn hasapproximately 4 inches in diameter,through an unconsolidated formation,

    been developed using a new force system to con-currently drill a bore hole and place a iwtal tube 3. Place a 1% inch OD production tube withinin the bore hole. the 4 inch diameter bore hole in the .

    formation while drilling is in progress.The first commercial application has been hori-

    zontal radials for shallow heavy oil reservoirs. 4. Cutoff the production tube, as required,Many radials may be placed at the same elevation. downhole.Logging, and comtpleiion techniques have been develop-ed. 5. Log the individual production tube in

    1. Introductionthree dimensions,

    6. Provide perforacio:lti and sand controlsOver the past f%ve years Mchtel Investments Inc & if desired.Patrolphysice Ltd. have been developing a newdrkllingsystern. The initial goal of the work B. System Technology Summaryhas been to provide multiple horizontal drainholee or injection radiala Ln unconsolidated Early in the ayetem development, a decision waheavy oil reservoirs viaexiating wells. In thie made to employ a 10 to 12 inch radius turnpaperwe shall diacues the technology which has from the verttcal to thehotizontal so ae tobeen developed to achieva that goal. We will beable to peneerate shallow or thin formationalso comment on other application of this and to minimige underreaming,technology,

    An eractablewhipstock containing a combination of slides

    M thiB paper the tarm radial rafers to theand rollers has been developed to effect thisbending and straightening process.

    approximately 4 inch radial bore drilled into theformation. The term production tube refers The drill system uses 8,000-10,000 paiwatsrto the 1* inch metal ERWtube placed in thatbore.

    for water jet drilling and canbe adapted tocommonly used additives* The drill bores an

    A. System Technical Objectivesapproximately 4-inch diamater rad%al withinwhich it progressively places a 14 inch OD

    The following Project Technical objectivescarbon steel production tube 86 it proceedsthrough the formation. The jet drill head

    evolved from the primary goal,~ does not rotate and delivers in e%cese of1,000 hydraulic horsepower to the formation.

    1. Provide multiple, generally hori~ontalradials of predetermined direction, 100 For drill propulsion, a totalky new pueh-pullto 200 feet in length from a single process has been developed. Specifically,esfeting oil well, all from the earn%depth.

    the drill penetrates the formation in aelE-regulated movements propelled by internalstatic fluid pressure. Forward velocitiescan be controlled from a low of 6 feet perminute ko a high of 120 feet per minute, Asthe drill moves thrOUgh the formation, the

    References and illustrations at end of paper, anterior portion of the 14 inch tube ia

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  • l2 HORIZONTALMDIAL DRILLING SYSTEM SPE 13949

    maintained in tension. The internal static In consolidated formation materials thepressure provides a pulling force of 4000- array of nozzlee creates an alternating8000 pounds. This tension force tends to pattern of compressive and tensile forceskeep the production tube straight which aids in the rock such that spalling occurs con-directivity for the system. tinuously, even in very highly consoli-

    dated cobbles and rocks as are oftefiMethods hava been developed to provide found bedded in oil formations nearregulation of the forward speed of the drill Bakersfield. The combined jets also washwhich in turn tends to control drill away cuttings from the area around theinclination or vertical trajectory. Among drill head. The measured nozzle velocltythese are a cable tail restraint attached to coefficient of the drill head is in excessthe tail of the radial. of 80 percent.

    The drill eystem has been principally tested 2. Pulling Force .in unconsolidated California reservoirs of500 to 2,600 feet depth, such as Bakersfield The production tube is 1% inch OD, 1.03(Kern River), Taft, and Brea (Olinda). The inch ID A-606 carbon eteel, .electricdrill has penetrated through cobbles of hard resistance welded reeled tubing (ERW).crystalline rocks for short distances, as When the area of the nozzles is eub-confirmed by experiments dow shallow tracted, the net internal cross sectionscaissons where drilling progress can be seen of the drill head is about .8 square inch.directly. No work has yet been done in Hence, excluding the jet reaction force,continuous consolidated formations. The at 8000 psi. net drill head pressure, thesystem hae effectively penetrated thick gross force from fluid static pressure oncement. h important part of the system is the backside of the drill head is aboutto Log tha drill trajectory. Normal logging 6000 pounds. his force literally pulleequipment will not bend around a 12 inch the radial through the formation. TMeradius. Hence, entirely new flexible force also initially aids in moving thelogging and electronic packaging systems l% inch tube through the whipstock.suitable for downhole application have beendeveloped and are being applied. This To understand why this pulling forcetechnology ie being extended to provide existe, consider a simple elon$atedthree-dimensional trajectory maPs of the vessel with closed ends$ which is filledradial location. with a preaeuriied fluid. The axial

    forces on the cloeed ende balance out,For aand control of highly deviated or eo there ia no reaction force on thehorizontal wells in unconsolidated formations, vessel. Now if a hole is cut in one endan integrated technology of radial completion of the vessel, the pressurized fluid exitsis being developed. Operational appli- through the hole and eacerta a reactioncatlona examined for the aystern involve force on the vessel, Next, coneider thateither production~ injections or boCh. The a tube with one end closed ie placed ininitial economic objective for the system that hole and that a seal iei provided inwas to provide a capability to get a quick the hole so the tube will slide withproduction response, Hence, a huff-and-puff respect to ehe vessel. The result ieapproach was initially applied. The that the tube will be ejected much like atechnology is applicable also to @team drive projectile by the static force on iteor injection. closed end. This is the principla which

    has been epplied to provides pulling

    11. Systems Theory and Functioningforce on the production tube,

    A. Drilling and PropulsionBy placing suitable nouleo or holes inthe cloeed end of the tube, or drillhead,

    The basic cutting, drilling and propulsion the water jet cutting ~ystem just de-scribed is provided. Thus for this

    systems uses hydraulic forcae, These forces drilling syetem, both the static andconcurrently (a) cue the formation, (b) pullforward the drill head attached to the pro- dynamic propertied of the pressurizedduction tube and (c) push forward the tail of water jet cutting fluid are concurrentlyapplied.the production tube, These forces andfunctions will be separately discuseed. In our dril.%in8 system, tha production

    1. Cutting tube begins vertically, proceede arounda 900 whipakock turn and entars the

    The basic cuttin~ mechanism ie an array of formation horizontally. Aa I.ater

    nozzles in the drill head. Each nozzle indescribed these same fluid preesure

    the array achieves about 900-1000 feet per forces are furthar exploited to controlthe eyatem. TM cmrall drilling systeatsecond exit velocity, The combination ofwater jete cuts a cavity of about 4 configuration ie shown in Mgure 1,inches diamster in unccmeolidated forma-t ions,

    3. Pushing Force

    The production tube wall ie .109 ittcheaBRA-

  • WADEANDWAYNEDICKINSONSPE 13949 3

    thick. A simple configuration of the underreaming tools has been developed. Thesesystem is shown in Figure 1 - Overall create a space of up to four feet inDrlK1.ing System. Therein the posterior diameter. Such a large underreamed holeof the production tube is vertical and diameter is not possible with conventionalcontained in a sealed chamber made up of mechanical underreamerB within the constraintsthe string of drill pipe down to the of the casing sizes characteristic of thewhipstock. This string operationally typical older existing wells in California.terminates in a high pressure, slidingseal system riding against the OD of the No of the mosttime consuming tasks in placing1% incil production tube. radiala involve the large diameter (48 inch)

    underreaming and repeatedly tripping of theWithin the vertical tubing string holding whipstock to the surface to provide thethe whipstock and containing the production mulitple radials. The second-generationtube, the high pressure water is at 9000-10000 psi. The water exerts a force on

    whipstock, which is just coming out ofresearch, requires only one-half that diameter

    the cross-section of the tail of the .109 of underreaming. These new tools alaoInch thick production tube of about 3500 -pounds. This force helps pueh it through

    permit placing multiple radials withouttripping to the surface between radials. The

    the eeallwhipstock system. This force is new tool is a repeater, rather than a singlereduced by any net cable restraint forces. shot .The result is a total pushlpull forwardgross forca on the projection tube of C. Control of Directionabout 9500 pounds less net cable restraintforcee. As later discussed, other re- The jet drilling system creates a generallystraint or pushing force systems can be round radial bore in the formation of aboutapplied to control or enhance the groesforward directed force.

    4 inches diameter. Of couree, consolidatedareas or formation inhornogeneitles affect theradial section. But, because the production

    B. Whipstock tube Is under tension ae it enters the for-mation, it hcs a natural tendency to go

    Tl% next major component of the syecem @ the straight, as doee the resulting bore hole.whipstock. The whipstock provided twoseparate capabilities or functions that are The velocity of the production tube and thetotally integrated into on@ tool The irst volumetric flow rate of the high preesureset of components coneiets of the slidee and water both have a strong bearing on radialwheele which enable the production tube to pitch or inclination. Typical velocities ofmove initially from the vertical, around the 20-120 feet per minute cause the radial to900 whipatock turn, through the straightener rise. Conversely, lower velocities cause theand out horizontally into the formation. The trajectory to droop downward. The precisesecond eet of components functions only during downhol.e effecte are not experimentally known.the paesage of the tube through the formation. But one model ia that at higher velocitiesWhile moving out into the formation the pro-duction tube automatically lifts itself off

    the larger cuttings are probably not edurrifieout of the way faat enough and may pile up

    the bending wheels and elides, which reducesfriction.

    ahead of, or under the drill head, causing itto rise. Conversely, at lower velocities the

    In this process the metal production tubeeorted cuttings may be more thoroughly waehedout so that the drill would tend to droop as a

    movaa through a 12 inch radius~ 90 turn cantilever beam, and move progressivelyvery ra;idly. Ma re4wo~&for file sharp turn downward.radius io t;lcealol~.

    For actual operations, the drill is started at1. To aseure suitable placement in thin lower velocities and the velocity la progress-

    formationa ively increased as the radial progressesoutward.

    2. To minimize the diameter of an under-reamed hole or a slot for whipstock 1)$ Velocity Controlerection,

    To provide control of velocity, especially3. To keep the metal tube at high stress during progrese through the whipstock and

    under the combination of pushing~ during initial entry into the formation, apulling, and bending forces, plus cable restraint ie applied. This consists ofinternal fluid praasure. a cabla truck, a wellhead high pressure

    The reeult ia that the electric resistancegrease seal and a removable plu~ ac a tail ofthe production tube. The plug is removed

    welded production tube is highly stressed after a run to permit the entry of loggingand is in a plastic state. Hence, large tools. Of couree, the restraining cabledeformation of the tube can be accompllehed instrumentation gives a real-time indicationat Low incremental atrem, To provide a of production tube movement.space into which the whipstock can beerected, a series of high preaeure hydraulic

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    4 HORIZONTALRADIALDRILLING SYSTEM SPE 13949

    E. Instrumentation and Logging Equipment is in shallow, heavy oil reservoirs in the qanJoaquin Valley and the Los Angeles basin. Both

    1. Drilling Instrumentation huff and puff and pure injection commercial.applications have been done.

    To control the production tube duringdrilling, two variables are monitored For these reservoir the system has been appliedin real time. to provide more than three hundred radials in

    msny.wells. In general, four radials are pro-s) High preseure water pressure and flow vialed in each well. All are at the same depth,

    as shown in Figure 2 - Typical Vertical Radialb) Production tube displacement and Patterns. But, if desired, many more than four

    velocity in terms of cable movement radials can ba placed at the same eleVatiOn ae ;shown in Figure 3 -Typical Aerial Radial

    2. Logging Patterns.

    Because of the 12 Inch radiue turn through The drilling eyetem is not limited to horizontalthe whipstock~ the logging instrumenta- shallow, 100-200 foot radials, nor is it limitadtion must paes through this 1 inch to a 1$ inch production tube nor a 4 inch radialinternal diameter production tuba at a bore. The system can work vertically and we12 inch turn radius. Rigid conventional believe it can place very long and large tubes.instruments wont pass and no gyroscopes Hence, among the applications other than theare available which are small enough to initial one which may have potential valueare:pase through the tube. Hence, completelynew types of mechanical sensor instru- a) Offshore reservoirsments and packaging have been developad. b) Consolidated formation and long radiale

    c) In-situ coal gasification or gas drainageThe key to thesa new logging eysteks is radialea packaging concept which combines d) Waste disposalseveral conflicting propertied. The e) Mineral recovary by solution miningpackaging must be soft and yielding, yetsupportive around the electronic and Conclusion:seneors. The package must be suffi-ciently tough and strong to take A new concept of drilling a bore and placing aexternal abrasion, pressure and shock. tube within that bore has been developed and appliedThese resulting flexible logging systems in existing California oil wells. The technology hascurrently provide a reliable and repro- been successfully applied to providing multiple hori-ducible printout of inclination or pitch zontal radials at the same level in a single well.accurate to 1. Instruments in test are Suitable logging, and completion techniques are inexpected to do the sfame in yaw or hand. The technology has potentially broad appli-azimuth in the field. cation to many petroleum and other resource drilling

    needs.F. Sand Control and Downhole Completion

    The requirements of a 12 inch radius whipstock Acknowledgment:turn and a thin ERWproduction tuba createda need for a new procedure of tube in-situ This technology hae been developed by a teamofcutoff, in-situ perforation, graval pack- msny engineers and scientists, particularly: Randying and flexible lining of the production Anderson, Harvey Brush, Richard Cummings, Erictube. These technologies are in commercial Dickinson, Herman Dykstra, Harold Forsen, Daleusage or on test. Hackney, Charles Harper, Stanlay Hu&chison, RichardJensen, Donald Klucker, Rsif Kulunk, Charles Mackey,

    G. Well Head and Surface Equipment Sherman May, John Morrison, Irving Odgars, DavidRabb, Donald Shepley, Steve Soegaard, Audrey Sutton,

    Throughout the system development program, George Wang, and Archie Wilson. The authors arestandard oil field equipment has been used particularly gratefulto Bechtel Investments, Inc.where possible. Hence, the surface for their generous technical and financial. supportequipment is conventional. Pump power is of this effort and this publication,supplied by a 1600hp/10000 psi frac pump.The rigs used are generally double etand, Reference$work-over rtgs. Logging trucks araconventional. 1. Based upon reservoir etudies undertaken for

    Bechtel by Scientific Software Intercomp, a 100Equipment for measuring production tube foot, or at most a 200 foot radial, is all thatmovement, instrumentation for fluid pressures , is required for heavy oil production or steamflowe, cable tension, etc. are all conven- Injection. Longer radials are not useful intional oil field hardware and function wall theee typically low pressure reservoirs, Thisin thie application, is more fully discussed in the papert AnInnovative Methods of Drilling Horizontal

    111, System Application Borehole, by Larry E. Pendleton and A.Behrooz Rameeh on February 20, 1985 at the

    Theinitial application of the drilling system Heavy Oil end Oil Sands Technical SyIUposium~

    non

  • ..

    SPE 13949 5

    University of Calgary, Calgary, Alberta CN 25oOUniversity Dr., N.W., Calgary, ALST T2N1N4. A copyof this paper may be obtained from the Universityof Calgary or from the authors.

    -WORKOVER RIG

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    OIL FORMATION

    VERTICAL VIEW

    Pig.l-Overall drilling system,

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  • SPE Paper Number 13950.

  • Discussion of NumericalSimulation of C02 ~k.wd PerformanceP.A. ForsythJr., SPB,Computer Mm!elling GroupP.H. Sarnmon, SPE, ComputerModellirrgOroup

    This DiscussionaddressesChaserindTodds papty thatappearedht the &a. 1984 SP4?V (Pages597-605). In theirrecentpaper on C02 simulation, * a strtbilized implicitpressure, cxplich saturation (IMPES) time discretizstionwassuggested.TMsmethodispurportedtoincreasestablethneatepsizesfor lMPES-like simulators.Thistechniquewassuggestedby vanderHouwen2*3for parabolic &qua-tions. It SJSO was used in reservoir simuirition byMeijerink4 and Vinsome, S However, the maximumtimestepscalculatedby van der Houwen do not appiy tohyperbolic equations if upstream differencing is used.Upstream differencing resultsin a Jacobianthat isdefec-tive (not diagonalizable). [n fact, for a one-dimensionst!Bucidey-Leverett problem, it ispossibleto prove that tilestabilized IMPES method is never moreefficient thanordinarylMPBS.6 Consequently,the claims made byvariousauthors *4*$about increased stable titnesteps with

    .

    the stabilized IMPES method must be regarded as being,without theoretical basis,

    Referencest. Cfrw, C.A. and Todd, M, R,: *Nunrcrical Sinmlalimr of COt

    Flocd Performance,* Sac. Pet. EW J. (Deco19S4)S97-605,2. van der Houwen, P.J.: ExpliciI Rungc.Kune Formulas with ln-

    crcascdStability Eoundarics, Namer, MrM/I. (1972) 20, 149-64.3. vandw Houwcm,P.J.: Cwtwnwtinn qfltw~ro~iort Frmmtfm for fnitial

    Va/ae Prokhws, NortlI Hulkir, Ncw York City (1977).4. J.A. Meijcrink: A Ncw Srabili7ml Mctlmd 101 UscInlMPE!!.Type

    Numerical ReservoirSimulators,pqwrSPiS!i247presentedatthe1974SPE AnnualMectirrg,NousImI, Od, 6-%

    !!, Vinsome,P,K.W.: *A NumcricxdDcscriphn of Hot.Wntcr~ndSteam Drives by the Fhri[e-t)iffcrcncc Method, paperSPE5248prcacrrtcdat Ihc 1974SPE AnnualMcc\ing, Hrwstnn, OCI. 6-9,

    6. Sammon, P,H, and Forsyth,P. Jr.: tns[abiiityin Rungc-KuttaScfrarrrssforSirouiationof Oii Recovery, B/3(19S4) 24,373-79.

    Authors Reply to Discussion ofNumerical Simulation of C02 PerformanceCUfiS A. ChaseJr., SPR,Ttxki, Dietrich& ChaseInc.Michael R, Todd, SPE, Todd, Dietrich& Chase10C.

    %rnmmtand Forsytht are, of course,correc: in theirclaimthatthevan,derHouwenl strtbilitylimit is tooop-timistic for the upstreamwe.ghted finite differencediscretizationof the hyperbolicBuckiey-Leveretteqtra-tioft,particularlyunderthepositivityrequirementof theirEq. 11. UsingthelinearBuckley-Leverettproblemtheyiihtstratethat, beginningat timezerowith a stepchangeboundarycondition,onecannotsignificantlyexceedthesingle-stagestabilitylimit, Their analysisalsoheipsex-plainseveralphenomenawe hrweobservedusingthem-restagediscretizationin actualreservoirsimulations,

    Recauseof timetruncationerror, onewouldneverat-temptin an actualreservoirsimulationprobiemto usetimestepsizesapproachingthe Euler stabilitylimit afterstepchangesat theIx)undaries(for example,turningonof waterinjectionweils),Instead,multiplestagesareap=pliedonly after frontshavemovedawayfrom the weiisand, becauseof the divergentnatureof the flow field,stabtiityin thewell regionislimitingratherthantimetrtrn-eationerror. For thisease,we illustratedin our paper3thatsignificantworkimprovementscanbeobtainedeventhough,a%SantmonandForsythhavepointedout, weex-ceededthestrictstabilitylimitsimposedbytheiranalysis,This work improvementalsocanbe demonstratedwiththe linwtr Bucldey-hwrett problemby comparingtheamountof work requiredbothwith attdwithoutntultiplcstagingper timestepto simulatea well into the steady-statcregion,The keytothiscomparison,however,istheuse of a timestepselectorto keepthetimestepsizebeiowthe single-stagestrrbievaluewhentimetruncationerroris important.- ,

    280

    :

    Why the m-stage method works,apparentlyin viola-tion of the stabilitylimitationspointedout by Ssutunonand Fotsyth, is perhapsa resultof the fact that in thequasistwtdy-stateregionh maynotbenecessaryto invokethe positivityrequirementexpressedby Bq, 11 in theirpaper.1 Violationof the positivitycondition,however,probablycausesthe oscillatorysolutionswe often haveobservedwith the m-stagemethod,Becausethe singlc-stagestabletimestepsizeseidomisknownexactlyin redreservoirsimulationproblems,but only estimated, agoodtimestepseiector,wilichcansensetheonsetof ht-stabilityand correctthe timestepsize, is a must,

    Finally, wc wouldlike to pointout thatthe simulatordescribedin our paper3 usesa two=pohttupstreamweighting4of transmissibilitimratherthansingle-pointweightingas analyzedby Sammonand Forsyth,Theiranalysisappliedtotwo-pointupstreamhygwrbolicsystemswould, no doubt, lead to very similar conclusionscon-cerningthe stabilitylimitationsof the m-stageprocess.

    References1.Samnron,P,}{. andForayth,P.: ltrsruttilltyIn RmIgc.KuItnScitsmcs

    for Simulation of Oil Recovery, BIT (t9S4)24,373-79.2, Vandur Houwcn,P.J,: Ccrrrsfractimtof lmegratioa Forwttrlasjor

    /nitial ValueProblems,NorthHollandpublishingCo., Anlsterdatn(1977).

    3. ChIM, C,A. andTakt, M.R.: Numcrfcal!lhnulalirtnof COI FloodPerformance,hc. Pet, Eng. J, (tlcc, 19S4)S97-60S.

    4, Todd,M, R,, ODcil, P.M., audHinmki, CJ,J.:Mctimis for hr.crctrsedAccuracyin NumericalReservoirSinwlrilors,Sot+PeLEng, J, (Dec. 1972)S1S-22.

    SOCIETY OF l%TRtlLEllM fiN(llNW?RSJOURNAL