reducing economic risk in areally anisotropic formations...

n Sooistyof PetroleumEngineers

SPE 30647

Reducing Economic Risk In Areally Anisotropic Formations With Multiple-LateralHorizontal Wells

J. Smith*. SPE and M. J. Economies. SPE, Texas A&M University, and T. P. Rick, SPE, Mining University Leoben*NO-WwithtiOt2iloil Corp.

Cc@gM 1995, Sociefy of Pdrdeum Engineers, Inc.

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AbstractWell orientation is critical to horizontal well perfonnamx inareally anisotropic reservoirs. A horizontal well, drilled normalto the direction of maximum permeability, will have higherproductivity than one drilled in any other arbitmry direction.Currently, horizontal permeability magnitudes and evenindications of direction rue rarely measured in the field. Basedon well performance modeling and economic evaluation, thisstudy attempts to determine the relative attractiveness ofhorizontal wells with multiple-laterals. The work exposes theeconomic risk in ignoring horizontrd permeability magnitudesand directions and demonstrates the importance of &Jequatemervoir testing. A new rationalization for multiple-latemlhorizontal wells is the reduction of the economic riskassociated with poor reservoir characterizadon in arealIyanisotropic formations while inm%sing the incremental netpresent value (NPV) over single-horizontal wells.

IntroductionHorizontal wells are proliferating throughout the petroleum

in&~&y as a m_JO -V .,.W-twnc fn int-.rrwcf= well nrnflmtivitv nnii fmh2Mk— .. . . y- ----- .-., —-- .-_.--

ineremental recovery aonomics. Multiple latemls from thesame vertical section provide greater nxrvoir exposure, softenthe risk of economic uncertainty, reduce the number of wellsneeded to drain a particular reservoir, and speed up the reservoirdrainage proms. Very importantly, they may also rcznedypoor production from a horizontal well drilled in the wrong

orientation in formations with large rmal anisotropy. For ahorizontal weii driiied without adequate fommtiori ewiuaticxt, risecond Iatteral will increase the chance to intersect frequentlycritical natnral fractures.

Traditionally, petroleum engineers have not been tooconcerned about horizontal permeability anisotropy. For avertical well this is forgiving because in cylindrical flow theaverage permeability, kH, is in the horizontal plane and is

simply J-. ‘ Several studies” have shown that large

permeability anisotropies in the horizontal plane am commonin many reservoirs. Naturally ffactured formations, which ategenerally exeellent candkkdes for horizontal wells, are likely toexhibit horizontal permeability anisotropy. In this situation,two principal horizontal permeabilities can be identifkxk kHM

and kn~.

The dwtion to drill a horizontal well is often based on theshape of the presumed drainage area when instead.ifbe decidingparameter should be the horizontal permeability anisotropy.This beeomes increasingly important with increasingpermeability anisotropy. Warpinski2 and Buchsteiner et aL4note eases where permeability ratios in the horizontal plane an?as much as 50:1.

This is an extreme case. However, ratios of 3:1 or 4:1 rnecommon2’4. The well trajectory with respect to thepermeability dinxtions is then central to the success of thehorizontal well project and thus, it is essential to know thepreftmed permeability direction before drilling a horizontalwell. Several means exist for this purpose.

It is also important to evaluate the risk of economicuncertainty when the horizontal permeability components rmnot known versus the additional costs of performing tests touc,G’IlullG&* ,.*I “0. paus”wm..-h.+-:.. + . . . -..-, ;. *omTn.a*m

Using a versatile productivity index model, this paper willdemonstrate the advantages of multiple-lateral horizontal wellsover conventional single-horizontal well completions inanisotropic formations. The model allows for arbhmrypositioning of wells and is useful in evaluating the economicsof drilling multiple-lateral horizontal wells for various well

171

2 ECONOMIC RISK IN MULTIPLE-LATERAL HORIZONTAL WELLS SPE 30647

configurations. Economic compmisons are simple once theproductivity of multiple-laterals with time is compared with abase case, such as a verticai weii or a singie-horizcm-d weii.Net present value (NW) calculations can weigh the discountedincremental benefits of multiple-laterals against theincremental costs of drilling, completing, and stimulating anyalternative configuration.

Estimating Directional PermeabilitiesPermeability anisotropy and direction can be determined with

stress measurements in a verticat pilot before a horizontal wellis directedj or by ex~riments with directional CORSobtained inthe vertical pilot.

Horizontal well tests or multi-well interference tests are, ofcourse, the best techniques to measure permeabilityrmisomopy. Ressure transient tests at a well are mostcommonly used to measum permeability magnitudes mddirections directly, while interference testa are seldom used inthe field.

However, there m! many complications associated withanalyzing horizontal well transient tests beyond the fact thatthey are done after the drilling of the horizontal well. Oneproblem is the unavoidable presence of large wellbore storageeffects caused by the longer borehole, even with a downholeshut-in. Wellbore storage often masks early-time tmnsientbehavior, which inhibits the determination of verticalpermeability, the permeability normal to the well, and thedamage skin effect.

A vertical pilot is essential in determining the desirability oftiliing a iiorizoiitai weii. First, a prtiai pefietiitiorl &+listemtest should be run. This can be accomplished by drilling onlypartially into the net pay or by drilling through the net pay andthen packing off only a small portion of the interval. Sphericrdflow emerges when a negative one-hatf slope straight line isseen on the early-time pressure derivative curve. This flowregime, properly interpret@ provides the spherical

permeability, ~=”. Nex4 a second tes~ conducted with

the endre pay thickness open to flow, should provide thehorizontal permeability, kH. Knowledge of the vertical mlhorizontal permeabilit.ies and the reservoir Wlckness candetermine the desirability of drilling a horizontal well in thetested formation.

Once the decision to drill a horizontal well is made, the nextstep is to determine the proper well dwection. This will bebased on the horizontal-to-horizontal permeability anisotropy.Figs. 1 and 2 show that horizontal well d~tion is importantand that a well shouId be oriented normal to the maximumhorizontal permeabMy dmtion.

Every reservoir is subject to a stress field, which can bedesaibed with * principal stfesse~ a vertical, 0., aminimum horizontal, cr~tin,and a maximum horizontal, a~-.Measurements can identify the maximum and minimum

horizontal stress directions, usually coinciding with themaximum and minimum horizontal permeability dimtionsm:. 2\(l-lg. lx m

~). I 16. ~ ~n~~~te~ ~~w the ~QrizQnt~ stre~~

components affect the state of fissures in the formation.Fhues perpendicular to the maximum stress dmtion amcompacted, wldle fissures perpendicular to the minimum stressm left relatively open. Larger fissure widths imply largerpermeability along those fissures. This idea illustrates why themaximum and minimum stress components normally coincidewith the maximum and minimum permealilities, mpectively.The measmement of stresses in a verticai piiot iioie wouid beinvaluable for the proper steering of a horizontal well.

Warpinski2 and Deimbacher e~ al.3 expounded upon therelationship between stress components and penneabilhycomponents. For example, a hydraulically frachued verticalwell would generally intersect the fracture plane longitudinally.The fracture itself is normal to the minimum stress direction,which corresponds to the path of least resistance during fracturepropagation. This path also implies that the minimumpermeability is normal to the fmcture plane.

l--.—-. ~~—x 1- A.--. *.1 ..,.11 ●b Am ‘rOr dn ~uriuucu UOI MUUUZJ WG1l, ~ ~. ,1.. =- .Zw. -,..-opil hnri.nntal

suess direction has a large bearing on the principal horizontalpermeability direction. The drilling of the horizontal well, itsdirection and (if it will be tiactud hydraulically) the type offractunx it will accept must consider the stress directions.

Econornides5 discussed several techniques to determine thestress magnitude and direction:

1. A fracture injection test6 is the best technique fwestimating the closure pressure, which should be very near themhim,lm ctrf=cc fnr a cinok+ laver. In almost d (XW3S$ thisU,.1.ul”u. “uW””.“. . “-..~-- .-, --- ---corresponds to the minimum horizontal stress.

2. A four-arm caliper log detects open-hole wellboreeccentricity. Knowing that stresses are compressive in natme,it is relatively easy to conclude that the smaller axis of theellipse should be normal to the minimum stress. A hydraulicfmcture would be along the minimum axis of the wellboreellipse (Fig. 3).

3. Laboratory analysis of directionally obtained ccnes isusually quite accurate and very useful. Techniques include

- measurements of strain, i.e., the disappeamnce orappearance of fissure, such as differential strain curve analysis(DSCA) and anelastic strain recovery (ASR)

- an acoustic technique, i.e., the differential wave velocityanalysis (DWVA)

Productivity ModelRedkting the performance of horizontal wells requires a

model that can account for both vertical-to-horizontal mlhorizontal-to-horizontal permeability anisotropies and anyreservoir or well configuration, including partial completion.

172

SPE 30647 J. SMITH, M.J. ECONOMIES, T.P. FRICK 3

Economies e? al.’ attempted to resolve these problems bypresenting performance relationships for complex wellconfigurations in horizontal wells. Their model accounts fortransient and boundary-dominatai flow behavior and usesanalytical solutions for arbitrarily oriented single- mdmultiple-horizontal wells as well as vertical and slant wells.

The model requires a list of input parameters:

Reservoir Data (x,, y,, h, k=,kp kZ)

Production Data Q.J@BO,@,c,)

Borehole Trajectory (lengths and directions)

Well Completion (r., open/closed segments,s)

The transformations developed by Bessona m used forpermeability anisotropy with kX,ky, and k, in the x-, y-, and z-directions, respectively and can be found in Ref. 7. Next+ the~~yt~~n ~~bp@e obt~n~ ~~ma~~s@!~Ss nres.sllresf~~ ~ point~.--- .-.

sourceof unit length within a bounded no-flow mxervoir. Fora line source with uniform flux, the solution is integrated fcrthe point sources along any arbitrary well trajectory. Using aline source with constant pressure, the well is split intosegments and each segment is treated as a line source withuniform flux. Nextt a rate is assigned for each segment so theindividual rates sum to one, the solutions m superposed Wim%viauairates are adjusted so die pressure at “tileinidpoim ofeach segment is the same. Careful switching of early- and late-time semi-analytical solutions allows for very accmatecalculations of the composite dimensionless pressure for anywell configuration.

The productivity index, J, is related to the dimensionlesspmssum under transient conditions (in oilfield units)’:

J=q= e(k z)(1)

F - Pti 8fJ7.22Bp pD + ~ s27r L

The generalized solution to the dimensionless pressure, p~,~r~ti~ ~i~b ~r]y-t~m.~ &~ns~~n! behav~of and ~ds with

pseudosteady state if all drainage kandaries rue felt. At thatmoment the dimensionless pressure can be decomposed from a3-dimensional contribution into one 2-dimensional and one 1-dimensional contribution. The horizontal plane can bechmcmmd with shape factors, while the vertical effects cmbe accounted for by a vertical skin effect. Thus, underpseudosteady-state flow conditions, pDis:

‘.CH ~ ‘e——

‘D=4zh 27r Lsx ’(2)

where the skin effec~ s,, is (after Kuchuk et al.g)

[)hh; sSx =ln —

27rrw 6L “(3)

and s,, describing eccentricity effects in the vertical direction,~~

which is negligible if the well is plwed near the verticalmiddle of the reservoir.

These equations m sufficient for the prediction of anysingle- or multiple-well configuration, and the generalsolutions desnibed in the Appendix of Ref. 7 can handle allsituations for infinite-acting, mixed and no-flow boundaries.

Effect Of Areal AnisotropyTo illustrate the impact of areal anisotropy, consider a 2000-

ft-long single-horizontal well in a 100-ft-thiclc formation withan index of anisotropy, l-i, equal to 3. The averagehorizontalpermeability is 10-md, but the horizontal penneabiitymagnitudes and directions are uncertain. Four horizontalpermeability anisotropy ratios will be examkt 1:1(isotropic), 5:1, 10:1, and 50:1. The importance of weIlorientation will be determined by rotating the horizontal wellin the horizontal plane. Fig. 4 shows the two wellconfigurations mfened to throughout the rest of the papa asingle-horizontal well and a multiple-lateral “cross”configuration. Economic calculations am made using the NPVcriterion and the inputs listed in Table 1.

Horizontal well productivity is greatest when the well isdrilled normal to the maximum horizontal permeabilitydirection. Fig. 5 shows that for a single-horizontal well driUedin the optimal dmtion, cumulative production accelerates asareal anisotropy increases. For a given horizontal permeabilitywith increasing anxd anisotropy ratio, the reservoir dminageprocess speeds up, making the high areal anisotropy ratio casesmore attractive than the isotropic case. As the deviation fromthe optimal well direction incn%ises, horizontal wellproductivity decreases, resulting in a deceleration of cumulativeproduction. Fig. 1 shows the critical importance of wellorientation for the highly anisotropic case.

Changes in the areal anisotropy ratio and well orientationA-----m....m..:,+-mkl.aaffa,+ m r.mn,,lntk,a im-vh,r.i;nn T&x/ alcnIJttVG a WIIMUGUUJIVUK.%.Lo.. WW..KMJ.u ~.uu?wuv... A ., --have similar effects on the NPV calculations. Fig. 2 showsthin-year NPV’s for a single-horizontal well as the wellorientation is rotated in the horizontal plane from the optimaldirection (0°) to 90°. NPV decmses as the horizontal well

173

.


orientation deviates from the optimal direction. Similarly,Fig. 6 shows that when single-horizontal wells are drilled inthe optimal direction, NPV incmses as areal anisotropyincreases.

Thus, for wells drilled perpendicular to the maximumhorizontal permeability direction, areal anisotropy is favorable,but as the well deviates from this optimal ditection, arealanisotropy becomes a detriment. in some instances the successor failure of a horizontal well completion may @end solelyon the decision at which direction to drill the horizontal well.There am large ranges of possible economic outcomes whenthe horizontal permeability magnitudes and directions ate notknown. These problems are magnified with increasing mealanisotropy. The range of possible economic outcomes will betermed the risk of economicuncertainty.

Table 2 shows the risk of economic uncertainty for single-horizontal wells for various anisotropy ratios. In the isotropicreservoir, the NPV is independent of the well orientation, butm the horizont~ anisotropy ratios increase, the risk of

economic uncertainty grows. In fac~ the range of possibleNPV’S rises to over $2 million in the most anisotropic case.Not only do the high anisotropy cases have the most positiveeconomic potential when drilled comedy, they also have thepotential to lose the most when orientated incorrectly. .

New Approach Using Multiple-LateralHorizontal Wells

Previous work10 has shown that horizontal wells withmultiple-laterals increase productivity and incremental NPV inlow- to moderate-permeability reservoirs over single-horizontalwell completions. This study will extend that work byshowing the impact of well orientation in amlly anisotropicmmvoirs and presenting a new application using multiple-laterals in risk managemen~ while still increasing productivityand incremental NPV.

Using the same analytical simulator discussed earlier,Remanto and Economides10 presented a series of parametricstudies for a mnge of reservoir permeabilities and permeabilityanisotropies for various multiple well configurations. The

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magnitudes of horizontal anisotropy: (kl=O. 1, 1, and lo-red),(ky=kx, O.lkx, and O.OlkX), and (kZ=O.lkl). The k=value wasusedas the basis for the calculations, while ky values wemvaried to account for various horizontal anisotropy ratios mlto determine the effects of increasing areal anisotropy. Thevertical permeability was left constant.

Remanto and Economides10 examined four wellconfigurations: (1) a 2,000-ft horizontal well rdong k=, (2) a2,000-ft horizontal well along k,, (3) a “ems” configurationfif fn,,r 19t~lC wh h-h farrq tu~~ e@@~~[ of ~w() z9000-f~“. X“UI -... -0 . . . . ...1. .“. . .

wells intersecting orthogonally at the reservoir middle, and (4)a “star” configuration with eight laterals which form theequivalent of four 2,000-ft wells intersecting at 45° angles at

the teservoir center. In summarizing their results, they foundthat multiple-laterals in low- to moderate-permeabilityreservoirs can produce with higher production rates @+~mfm, .wi* Mgh= ~~i.u!a~ve yoductions at ~!y times

compamd to single-horizontal wells. They also found thatmultiple-laterals in higher-permeability reservoirs have nxkedincremental benefits.

Bo’h iligh- 1,.... -—aA!.:l ;*.,aiid lUw -pa lllGauuALy avh;hhreserwxtt “-a”..

productivity improvements with multiple-laterals diningtransient conditions. However, once pseudmteady state isfeache4tie~ in productivity index is dtiished.Multiple wells in the same drainage area will interfm witheach other. Although high-permeability formations see largerabsolute productivity increases, they also experienceinterference effects earlier. Themfom, the relative economicbenefit of multi-well configurations in high-permeabilityreservoirs begins to diminish quickly, while low permeabilityformations exhibit interference effects much later and dativeeconomic benefits are both higher and prolonged.

Consider a case study comparing single-horizontalcompletions to a multiple-lateral “ems” cotilguration inareally anisotropic reservoirs. The study involves fourhorizontal anisotropy ratios: 1:1 (isotropic), 5:1, 101, md501, and shows the effect of well orientation by rotating bothconfigurations within the horizontal plane. For the sittgle-horizonta.1well, rotation of 90° displays all possibilities; thisexample looks at 0°, 30°, 45°, 60°, and 90°. lle “ems”configuration needs to be mated only by 45°; the studyincludes 0°, 15°, 30°, and 45°.

The economic base case is a 2,000-ft-long single-horizontalwell that is oriented in the optimal direction, pqendicular tothe dmtion of maximum horizontal permeability. Thereservoir has a horizontal pemwaMlity equal to 10-md with anindex of anisotropy equal to 3. The thickness is 100-ft.

The dimensionless time and dnensionless mte me detimdas:

= 0.000264Et

tD (5)G)%%*

d

887.22qBpqll =

~x,Ap .(6)

Figs. 7 to 13 show the advantages of multiple-lateralhorizontal wells, the effect of areal anisotropy, and the types ofmervoirs in which they are most useful. Fig. 710 gmphsdimensionless production rate as a function of dimensionless

xIW ~,e=~ i= *Ae m %imnmtiini3 Case D is a well w— U.....-.”-..permeability, whereas Case E is a well drilled normal to themaximum pmneability. Cases F and G are for the “cross” *

174

SPE30647 J. SMITH, M.J. ECONOMIES, T,P. FRICK 5

“star” configurations, respectively. This illustration shows thatmultiple-lateral wells have higher productivities at early time.However, as time advances the productivity advantagedecreases, until at Pseudosteady-state, they vanish. Cases D andE in Fig. 7 show the effect of well orientation on productivityfor single horizontal wells. Fig. 8 illustrates the effect of wellorientation in more detail. At early time, the highestproductivity results when the well is drilled in the optimaldwtion. As the well direction deviates from the optimaldirection, the productivity demases. The productivityadvantage lasts until pseudostcady-state is mackd butdminishes as the curves converge at pseudosteady-state. Atlate time, productivities diverge due to the depletion of then%ervoir.

Fig. 910illustrates the effect of permeability magnitude onproductivity increases in multiple-latemls. This figure plotsthe cumulative production ratio vs time and shows howproductivity zuivantages last much longer in low-permeabilityreservoirs. The cumulative production ratio is the ratio of theproduction fmm the muhiple-laterat well over the productionof the base case for a single-horizontal well oriented in thedirection ptapendicular to the maximum permeability. Thisfigure is for the “cross” configumtion. Therefore, at early time,we would expect the “cress” configuration to produce twice theamount of the base case. Fig. 9 shows that this is true, Thecumulative production ratio is constant at a value of 2 at earlytime for all three cases and then begins to decrease over timeuntil they eventually converge at a value of 1. Productionratios for wells in the high-permeability formations begin todecrease earlier than those in low-permeability formations. Theproductivity advantage lasts much longer in the latter.

Fig. 10 shows that, for all Permetillity orientations thecross configuration in anisotropic formations is better than forthe isotropic case . This demonstrates that for the crossconfiguration, the productivity is rdways greater than theisotropic case regardless of well orientation, where the single-horizontal well is much better when drilled correctly — butworse when drilled incorrectly. Fig. 11 graphs production mtevs time, showing that high-pemneability formations posemuch higher increases in production whesever multiple-lateralsan? used but, once again, the benefits disappm much soonerthan in low-permeability formations. Of course, the decisionto drill multiple-laterals must be made on a reservoir-by-mservoir basis where permeability and completion costs havebeen accounted for to determine the incremental economicl.a..G t. eknl.= hnri rmfnl .w~!!~ ~~ rithrw OomdetinpUcll!sll la over ixllglw=uul Iz”,,uu “-1”1 “ U.pww” .

options.Fig. 12 is a 3-dimensional graph that shows the effects of

well orientation on NPV as a function of increasing anisotropyand deviation for a singie horizontal weii. As the figure shows,the NPV in the isotropic case is independent of wellorientation. As the anisotropy ratio increases, if the wells mdrilled Colmctly, there ate increases in NPV fmm the isotropiccawx however, as the well deviates from the optimrd direction,

the net-pment-value &creases, until at 90° the NPV decmseswith increasing horizontal anisotropy.

Although all the cases shown have the same ultimatecumulative pmductiou drilling a well in the optimal dinxtionwill increase the production rate at early times and result in ahigher NPV than any other well orientation. Poor wellorientation results in delayed recovery. As well orientationdeviates from this optimal direction, production rates at earlytime decrease, slowing down the increase in cumulativeproduction, and thereby decmsing the NPV. Increasinganisotropy ratios results in increasing the range of possibleeconomic outcomes, depending upon the direction thehorizontal well is drilled.

Fig. 13 shows another 3dimensional graph of NPV as afunction of well orientation and incnmsing areal anisotropy fcrthe “cross” configuration. For this case, the isotropic case isonce more independent of well orientation. Another similarityis that the NPV increases as the areal anisotropy ratioincreases. However, in this case, as the well is rotated in thereservoir, the NPV decmses ahnost imperceptibly. In f=regardless of well orientation, NPV increases with increasingaxeal anisotropy ratios.

Table 3 shows that multiple-lateral horizontal wells have amuch lower risk of uncertainty than single-horizontal wellswith well orientation in areally anisotropic reservoirs. For thethee anisotropic cases, the &crease in the risk of uncertaintyranges from approximately $1 million in the 5:1 case (@xxdby a factor of 37) from $935,000 to $25,000; and $2 millionin the501 case (reduced by a factor of 13) from $2,123,000 to$159,000.

These data have shown that horizontal wells can reduce therisk of uncertainty resulting from not knowing the horizontalpermeability magnitudes and directions in amally anisotropicreservoirs. The incremental economics of single- and multiple-lateral horizontal wells over the selected base case appears inFigs. 14 and 15. Fig. 14 shows the incremental NPV for thesingle-horizontal well with increasing areal anisotropy mdvarious well orientations over the single-horizontal-well basecase. For single-horizontal wells, the positive incrementalNPV’S are modemte when the well is chilled in the optimaldirection, and the negative incremental NPV’s m @ativelylarger when drilled incornxtly.

Fig. 15 shows the incremental NPV for the “cross”configuration over the single well base case. Once again, theincreases in incremental NPV are modem~, however,~&tiJe~ of ‘Qli Qfi-enr~~Qn@ &@_ ~i~~P~ tie: meincremental NPV is positive for the cross configuration. Thiswould confm that the multiple-lateral configuration is themost attractive completion in this reservoir.

-r-Ll - A . . . . . . . _ -----A .-.. AC ●ha -n ma. -f :m-ma.t.l1iiulG * Mlu Ws a Wqhll mull U1 LUG A’I’AGS 8)1 U,v,vlllw,,uu

NPV with increasing areal anisotropy between a single-horizontal well and a “cross” configuration multiple-lateralwell.

175


Clearly, not only are multiple-lateral horizontal wellsattractive in low-permeability reservoirs, but they are alsobeneficial in modemte-perrneabfity reservoirs in reducing therisk of uncertainty associated with amally anisotropicmemoirs and in increasing the incremental NPV over single-well completion options.

Also, drilling a horizontal well normal to the direction ofmaximum permeability results in incmsed well productivity.For a given horizontal permeability, the highest productivityand NPV comes from the most anisotropic reservoirs whendrilled correctly. Horizontal well direction becomes criticalwith increasing areal anisotropy. NPV demases as deviationfrom the optimum well dtition increases. Choosing the

. .. ..~1 a~on to ~fi a h~~~fi-~ -we;! ~r m~u!t ~~ *&e

economic successor failure of a project.Poor reservoir chamctmm- tion (unknown directional

permeabilities) results in a high risk of uncertainty. The newapplication for multiple-lateral horizontal wells, developed inthis study, can reduce the risk of uncertainty and improveincremental economics.

ConciusioiisThis study found that drilling a single-horizontal well

normal to the direction of the maximum permeability resultsin increased well productivity over any other arlitmrydirection. Horizontal well direction becomes critical withincreasing meal anisotropy. For a given horizontalpermeability, the highest productivity and NPV come from themost anisotropic reservoirs when single-horizontal wells areoriented correctly. NPV decmses as deviation from theoptimal direction incnmes therefore, there is a large risk ofuncertainty associated with drilling a single-horizontal wellwithout an idea of the permeability component magnitudes mldirections. Choosing the correct di.mction to drill a horizontalwell can effect greatly the economic success or failure of aproject.

To improve well productivity and incremental economics,multiple-lateral horizontal wells should be considen% alongwith additional reservoir testing to reduce the risk of economicuncertainty associated with poor reservoir chwxerimtion.They can also be used to remedy single-horizontal wells thathave been drilled incornxtly.

NomenclatureBO = Fonnrd.ion volume factor, bbl/STB

[resm3/m3]cf/ =Oeometic shape factorcosts = Total costs for drilling, completing, and

stimulating well, $

~f s Tntnl eomnreccihilitv. nsi-’ [Pa-’]. .— ..-. =---- . . .. .. , ~-.

h = Formation thickness, ft [m]i = Discount rate, fraction

JkHkH,-

kH,dn

kvkxkykzk

iiL

;,NPVOOIPAf)PD

PiP

Pwf

4

rwsses=x.Y*z.

0“~H,~OH,=PO4~~

A$

= Productivity index, STB/psi [m3/s/Pa]= Average horizontal permeability, md [m2]= Minimum horizontal permeability

componen~ md [m2]= Maximum horizontal permeability

componen~ md [m2]= Vertical ptmneability, md [m2]= Permeability in the xdiredion, md [m2]= Permeability in the ydmtiom md [m2]= Permeability in the z-direction, md [m2]= Average Permeability, md [m2]

= Average permeability, md [m2]= Length of horizontal section, ft [m]= Number of years= Cumulative oil production, STB [m’]= Net pment value= Original oil in place, Bbl [resm3]= Differential pressure, psi [Pa]= Dimensionless pressure, psi [Pa]= Initial reservoir pmsure, psi [Pa]= Average pressure in drainage volume of

well, psi [Pal= Average flowing bottomhole pressure, psi

[Pa]= Totai production rdie iilio a iimizon”d ‘well,

STB/d [m’/s]= Wellbore radius, ft [m]= Skin due to damage= Eccentricity skin= Vertical skin effect= Reservoir length, ft [m]= Reservoir width, ft [m]= Distance of well from middle of reservoir,

ft [m]= Vertical stress componeng psi {Pa]= Minimum horizontal stress componen~ psi {Pa]= Maximum horizontal stress component psi {Pa]= Viscosity, cp [Pa-s]= Porosity, fraction

= Summation of damage skin, i-uhderxe

skin, and other pseudoskin factors= Yearly incremental revenue, $

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~i~.~~~~, F.x,, Economies, M.J., Heinemann, Z.E.,

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27980 presented at the 1994 University of TulsaCentennial Petroleum Engineering Symposium in TUIW———UK, Aug. 29-3i .

Besson, J.: “Performance of Slanted and Horizontal Wellsin an Anisotropic Medium,” paper SPE 20965 presentedat the 1990 Europec, The Hague, Netherlands, Oct. 22-24.

Kuch@ FJ., Goode, P.A., Brice, B.W., Sherrard, D.W.,and Thambynayagam, R.K.M.: ‘Tressum TransientAnalysis and Inflow Performance for Horizontal Wells:paper SPE 18300, presented at the 1988 SPE AnnualConference, Houston, Oct. 2-5.

Retnanto, A. and Economies, M.J.: “Performance ofMultiple Horizontal Well LateraIs in Low- to Medium-l%enneabilityReservoirs;’ paper SPE 29647, presented attbe 1995 SPE California Regional Meeting, Bakersfield,Mar. 10-12.

Table 1 - Net Present Value InputsPrice of Oil $151STB

Discount Rate 259’0Single-HorizontalWell Costs $1,250,000“Croaa”HorizontalWell Costs $1,750,000

Table 2 - Risk of Economic Uncertain ty With Increasing Areal Anisotropy 1A.--l A.. L.- A, A,.., ~~~~~MI Wal ml Il=vll Upy TAA Rsnna d NPV (&l CICU)\,“.”. . .-., ,=” “. ..0 . ,- .---,

1:1 05:1 935101 1,31550:1 2,123

Table 3 - Reducing the Risk of Economic Uncertainty With Multiple-LateralHorizontal Wells Compared to Single-Horizontal Wells

Areal AnisotropyRatio NPV Ranges (Single) ($1000’s) NPV Ranges (“Cross’)($1000’s)1:1 0 05:1 --.

!MD 25f~:l f,~f~ 5850:1 159

Table 4- Reducing the Risk of Economic Uncertainty With a “Cross”Configuration Compared to a Sin9ie-Horizontal ‘Weii

I

Areal AnisotropyRatio IncrementalNPV Ratio (Single) IncrementalNPV Ratio (“Cross”)1:1 1 1.075:1 0.74-1.13 1.09-1.11

10:1 0.62-1.19 1.11-1.1450:1 0.34-1.28 1.13-1.21

177

.


O deu

30 deg

I ///1/’ r ! 60 ‘z ~

50J)O0

o ,0 1 2 3 4 5 6

Time (years)

Fiiure 1 Poor Well Oriitation Slows Down the Reeervoir Drainage Process on Cumulative Production for a Single-Horizontal Well.

$3J)oo

($500)

FI■Year2

clYear3

F~re 2 Net Preeent Value for a Sk@Aorizontal Well bxeaeaa ee Well DireotionOaviateeFrom the Optimal Orientation.

178

SPE30647 J. SMITH, M.J. ECONOMIES, T.P. FRICK 9

F~m 3 CcmoaptualRelationship BatwaarrStraaaandParrnaabtity Compananta.

4oo,oal

350,0(XI

300,000

250,000

200,0CNI

150,000

1OO,O(X)

50,000

SingleWell

+-

“cross” W(4I

F~m 4 Horizontal Well Configumtiona for UtisStudy.

50:110:

I

o 1 2 3 4 5 6T:—- 1..--—1Ime (ycsars)

Fwum 5 Increasing Araal Anisotropy Spasds Up Rasawoir Racovq for a Sh@d+orizontal Wall Drillad irrb Optfmd Dirastion

47nI/a

.


$3Doo

$2s00

$2/)00

w Soo

$lfloo

S500

solsdropic 5bl 10tol 5otol

Areal Anisotropy Ratios

Net present Value Increasesas Arasl Anisotropy Incrsnes for a Given I+orfzontalParmaabtiftyas a 6in~a-Horizontalia Drilfsd in the Optimal Direction

10°

‘“’*l I I I IL

Ik=O.1 k

k:=O.1 k:,0-2

1 t 111111 1 t , ,,,,, 1 1 111111 1 1 111111 1 t 111111 1 toll.

k\\

1 # LUJ

mva9w4n i-l I

■Yaar2❑Year3

Dimensionless Time, tD

Dimensionless Produotfon Rats vs Dimensionless Tfme for HorizontA40-Horizontal PermeabilityAnhotropy, f$=tl.llq(Caeea D, E, F, and G)’”

180


60 degI

90 deg

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+OO

Dimensionless Time, u

Figure &Dimensionless production Rate vs Dimensionless Time for Various Single-WeflOrientations(101 Anisotropy Ratio)

2.2

2.0

1.8

1.6

1.4

1.2

1.0

.

. —k=O.lmd ‘. \- – – -kx=l.Omd ‘, \

. . . . . kx=10 md *x , \

8, \.

● ✼

u, \,

,

●* Vt ‘ss.- k=k

. . . .

- ky=O:1 kz x

, t t , t , h, ,, , , I , , , ,, , , 1 , , , , ,_

10’ 102 3 104 105Time,’ }ours

Figure 9- Cumulative Production Ratio for Real Time for the “Croee” Configuration, +Iq .10

181

.


10

0 ‘eg 15 deg 30

I

45 deg

jeg

Isotropic

100 1000 lomo

Time,hours

Fiiura 10 Cumulative Production Ratio for Real Time for the “Croaa” Configuration (10:1 Anisotropy Ratio)

n

F~re 11

104

103

102

10’

m’lG-..a -

L.JL1

.-----

F: :---- ‘-. ----- --------- ----.. . ..=

Ill

----

E.

ky=O.l-k, ❑ D + F

k=o.lk~E+@z x

1 1 1 1 1 Ill # 1 I 1 1 # u

~. . . k =0.1 md

k~=10 md

Td

_llL

\

r----- -..

“.----- .--- .----- .-.. . .-..

J

----- . . .● .- \ .

10°10’ 102 103 104 105

Time, hours

Production Rata for Horizontal-to-l+orizontil PermeabilityMtaofropy, k#.llq (Caaea D, E, F, G)~”

182

.,

----- .,. ..-sr~ 3Vb4 I j. SMiTH, M.J. ECONOMIES, T.P. FIUCK

———--—-13

30002500

200015001000

~~

00-””

deg g g g

Well Deviation From theOptimal Direction

.Ratio

z

Fqure 12 Effeot of Well Orientation on Net PresentValue in AreallyAniaotropic Reaervoira(Single Horizontal Wefl)

o deg 15 deg 30 deg 6 deg

Well Deviation Fromthe Optimal Direction

❑ l:l

■ 5:1

❑ lal

❑ 501

❑ l:l

■ 5:1

‘n 101

El5(kl

Fsure 13 Effect of Weft Orientation on NPV in ArealtyAnbotropic Reaervoira(’trod’ Configuration)

183


1.4

1.2

1

Q8

Q6

a4

02

I

IsOtro

9 ,

n 1 1 m ,

I I I I i 1

Iic 5:1

05 10 15 20 ?5 30354045505660= m 75 80 s 90

Well Deviation From Optimal Direction

F-14 Inoramantal Nat Praaant Value Ratio Cornp#uedto the Single+lorizontal Wall Saea Caee (Singla+torizontal Wall)

1.s

1

II50:1 I I

I

5:1

Isotropic,

, 8

0 15 30 45

Well Deviation From the Optimal Direction

F~e 15 Incremental Net Preaant Value Ratio Compared to the Singla+lorizontal Wall Baae Caae (“Cross” Configuration)

reducing economic risk in areally anisotropic formations...

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