16
- s m . Societyof PetroleumEn@eers SPE 39425 The Effect of Near-Wellbore Fracture Geometry on Fracture Execution and Post-Treatment Production of Deviated and Horizontal Wells Z. Chen, SPE, BJ Services Company and M. J. Economies, SPE, Texas A&M University Copylght 1998, Society of Petroleum Engineers, Inc. This paper was prepared for presentatbn at the 1998 International Sympsium on Formation Damage Control in Lafayette, Louialana, USA., 18-19 February, 1998. ~s papar was selected for Presentafon by an SPE Prcgram Committee folW!W review of information contained in an abstract submitted by the auther(s). Centents of the paper, as presented, have not bean reviewed by the Seciety of Petroleum Engineers and are subjad to correction by the auther(s) The material, as presented, doss not necessarily reflest any position of the Swiely of Petroleum Enginasrs, its officers, or membsrs. Papers presented et SPE meatinga are subject to wblical~ review by Editorial Committees of the Seciety of Petroleum En%ineara. Permission to *Y is restricted to an abstract of not more than 3W words. Illustrations may not be mpied, The abstrasl shwld retain mnsplcuous atinowledgmenl of where and by whom the papr is presented. Writs librarian, SPE, P, 0. Sax 833836, Rtiardson, TX 750S3-3836, U. S.A., Telex, t63245 SPEUT. Abstract The near-wellbore fracture geometry is important to hydraulic fracture execution and the subsequent post- treatment well performance. A fracture from an arbitrarily- oriented well “cuts” the wellbore at an angle and this limits the communication between the wellbore and reservoir, The stress concentration around the wellbore firther complicates the near-wellbore fracture geometry. The fracture width at the wellbore can be much smaller than the maximum width, or it may even close when the fracturing pressure decreases below some critical value. The limited communication path may cause a “screenout” during fracture execution or large reduction in the subsequent production because of choked fracture effects. This paper fwst discusses fracturing conditions for an optimal communication path between the wellbore and the reservoir. The near-wellbore fracture geomet~ is then determined. The effects of this fracture geometry on fracture execution and production are discussed. Critical fracturing pressures are also calculated for different wellbore orientations and in-situ principal stress magnitudes. Guidelines are provided to enhance the success of fracturing treatments. Introduction Unless deliberate actions are taken during drilling, the orientation of deviated and horizontal wells rarely coincides with the principal stress directions. Fracturing these wells involves different mechanisms compared to those for vertical wells. Several researchers [1-6] have demonstrated that fracturing a deviated or horizontal well often results in multiple fracture initiations, near-wellbore fracture reorientation, starter fractures eventual link-up, and near- wellbore fracture width reduction. Yew et al. [1, 2] studied the deviated-well fracture initiation and demonstrated theoretically that fracture reorientation occurs in the very near-wellbore region. The influence of the wellbore on stress distribution decreases rapidly with distance r (proportional to l/#). Abass et al. [3] and Hallam et al. [4] explored this phenomenon experimentally and showed that the creation of nonplanar fracture geometries such as multiple, T-shape, and reoriented fractures depends on the wellbore direction relative to the in-situ stress field. An optimum wellbore azimuth is necessary to avoid the creation of undesirable fracture geometry. Sousa [5] attempted to solve this problem numerically using fracture mechanics principles. Narrowed near-wellbore fracture width and fracture tortuosity can lead to proppant bridging and premature screenouts. Even if brought to successful execution, tortuous fractures with narrowed near-wellbore width are likely to be choked with considerable reduction in the post- treatment production performance. In this paper, the following problems are addressed The eflects of well orientation and in-situ principal stresses onfracture initiation. The study is based on stress analysis. Generalized type curves are developed to guide perforation design and provide information on optimal well orientation for fracturing. Fracture tortuosity in the near-wellbore region. During propagation the fracture turns and adjusts toward the dmection of minimum resistance. This path has a great impact on the near-well fracture geome@. A simple-to-use 75

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  • -s m

    l .

    Societyof PetroleumEn@eers

    SPE 39425

    The Effect of Near-Wellbore Fracture Geometry on Fracture Execution andPost-Treatment Production of Deviated and Horizontal Wells

    Z. Chen, SPE, BJ Services Company and M. J. Economies, SPE, Texas A&M University

    Copylght 1998, Society of Petroleum Engineers, Inc.

    This paper was prepared for presentatbn at the 1998 International Sympsium onFormation Damage Control in Lafayette, Louialana, USA., 18-19 February, 1998.

    ~s papar was selected for Presentafon by an SPE Prcgram Committee folW!W reviewof information contained in an abstract submitted by the auther(s). Centents of the paper,as presented, have not bean reviewed by the Seciety of Petroleum Engineers and aresubjad to correction by the auther(s) The material, as presented, doss not necessarilyreflest any position of the Swiely of Petroleum Enginasrs, its officers, or membsrs.Papers presented et SPE meatinga are subject to wblical~ review by EditorialCommittees of the Seciety of Petroleum En%ineara. Permission to *Y is restricted to anabstract of not more than 3W words. Illustrations may not be mpied, The abstrasl shwldretain mnsplcuous atinowledgmenl of where and by whom the papr is presented.Writs librarian, SPE, P, 0. Sax 833836, Rtiardson, TX 750S3-3836, U. S.A., Telex,t63245 SPEUT.

    AbstractThe near-wellbore fracture geometry is important tohydraulic fracture execution and the subsequent post-treatment well performance. A fracture from an arbitrarily-oriented well cuts the wellbore at an angle and this limitsthe communication between the wellbore and reservoir, Thestress concentration around the wellbore firthercomplicates the near-wellbore fracture geometry. Thefracture width at the wellbore can be much smaller than themaximum width, or it may even close when the fracturingpressure decreases below some critical value. The limitedcommunication path may cause a screenout duringfracture execution or large reduction in the subsequentproduction because of choked fracture effects. This paperfwst discusses fracturing conditions for an optimalcommunication path between the wellbore and thereservoir. The near-wellbore fracture geomet~ is thendetermined. The effects of this fracture geometry onfracture execution and production are discussed. Criticalfracturing pressures are also calculated for differentwellbore orientations and in-situ principal stressmagnitudes. Guidelines are provided to enhance the successof fracturing treatments.

    IntroductionUnless deliberate actions are taken during drilling, theorientation of deviated and horizontal wells rarely coincideswith the principal stress directions. Fracturing these wells

    involves different mechanisms compared to those forvertical wells. Several researchers [1-6] have demonstratedthat fracturing a deviated or horizontal well often results inmultiple fracture initiations, near-wellbore fracturereorientation, starter fractures eventual link-up, and near-wellbore fracture width reduction.

    Yew et al. [1, 2] studied the deviated-well fractureinitiation and demonstrated theoretically that fracturereorientation occurs in the very near-wellbore region. Theinfluence of the wellbore on stress distribution decreasesrapidly with distance r (proportional to l/#). Abass et al.[3] and Hallam et al. [4] explored this phenomenonexperimentally and showed that the creation of nonplanarfracture geometries such as multiple, T-shape, andreoriented fractures depends on the wellbore directionrelative to the in-situ stress field. An optimum wellboreazimuth is necessary to avoid the creation of undesirablefracture geometry. Sousa [5] attempted to solve thisproblem numerically using fracture mechanics principles.

    Narrowed near-wellbore fracture width and fracturetortuosity can lead to proppant bridging and prematurescreenouts. Even if brought to successful execution,tortuous fractures with narrowed near-wellbore width arelikely to be choked with considerable reduction in the post-treatment production performance.

    In this paper, the following problems are addressed

    The eflects of well orientation and in-situ principal stressesonfracture initiation. The study is based on stress analysis.Generalized type curves are developed to guide perforationdesign and provide information on optimal well orientationfor fracturing.

    Fracture tortuosity in the near-wellbore region. Duringpropagation the fracture turns and adjusts toward thedmection of minimum resistance. This path has a greatimpact on the near-well fracture geome@. A simple-to-use

    75

  • 2 The Effect of Near-Wellbore Fracture Geometry on Fracture Execution and SPE 39425Post-Treatment Production_ o~_Deviated and Horizontal Wells

    criterion is presented to predict the fracture orientation andwidth.

    The choke efiect of near wellbore fracture on fracturingexecution and post-treatment well production. The effectsof narrowed near-wellbore fracture width on hydraulicfracturing and post-treatment production are investigated inthis section.

    It is, of course, obvious that these effects will be differentfor different well deviations and perforation orientations(phasing). Certainly, a perfectly vertical well or a horizontalwell in the longitudinal to the fracture direction and using180perforation phasing that can be oriented, will eliminatemany of the problems addressed in this paper.

    Fracture Initiation in an Arbitrarily-OrientedWellboreAn arbitrarily-oriented wellbore is defined within twocoordinate systems as shown in Fig. 1. A global coordinatesystem (a) corresponds to the in-situ stresses while a localcoordinate system (b) is defined by the wellboreorientation. Two angles are used to describe the orientationof a deviated wellbore in the global coordinate system:angle a, formed between the in-situ minimum horizontalstress and the projection of the wellbore on the horizontalplane; and angle p, with which the wellbore deviates fromthe vertical direction. Fracture initiation is discussed in thelocal coordinate system, and the fracture initiation positionangle 6 is relative to the reference axis m.

    For any wellbore, the magnitude and orientation of the in-situ stresses result in the local stress concentrations. Theseinduced stress concentrations are significantly differentfrom the far field stress values. An arbitrarily-orientedwellbore complicates the state of stresses firther. Analyticalsolutions of stresses around a deviated wellbore werepresented by several authors [7-9], and later by Yew et al.[2]. A 3D-view of stress component distribution around adeviated wellbore is shown in Fig. 2. There are twoimportant points that are warranted here. First, the near wellstress concentrations happen within a few wellborediameters (approximate five). Second, there are specificangles (two each) at which stresses ae and IS, exhibitminima and maxima. This is an important issue and isexpounded upon below.

    Not only the wellbore orientation but also the position ofthe perforation has a great impact on fracture initiation andits orientation. Figure 3 shows an example calculation ofthe effect of the perforation position angle O(defined in thelocal coordinates of Fig. 1 (b)) on the fracture initiation

    pressure and the fracture orientation angle y for a deviatedwellbore defined by a=60 and /3=60. The breakdownpressure Pbd is normalized @bd~)by the absolute rn=imUrnhorizontal stress, m,mm=9000 psi. At different fractureinitiation positions, the initiation pressure changesconsiderably, and the worst perforation position can resultin initiation pressure that is twice as high as the minimum.There are two positions with minimum fracture initiationpressures, each 180 apart. Another two positions worthstudying are the positions with the fracture orientationangle y =0, which implies that the fracture is aligned withthe wellbore and a fractire along the wellbore can becreated in spite of well orientation. Creating such a fracturemay not necessarily be good for a highly deviated wellbecause of the ensuing fracture tortuosity.

    At issue is whether fracture initiation at the minimuminitiation pressure path or a non-tortuous fracture initiationalong the wellbore are preferable. Figure 4 shows the extentto which a fractire will turn to reach its final orientation.When a fracture initiates at the minimum pressure thefracture turn will be determined by the minimum in-situprincipal stress magnitude and direction. Figure 4 showsthat the fracture initiates with an orientation angle (Y27)with the wellbore direction, while the final fractureorientation has an angle (~30) with the wellbore. Thisimplies that the fracture will turn only a little (3) to reachits final position producing a small tortuosity. Thereorientation curve on Fig. 4 denotes the degree oftortuosity. If the perforation phase is designed to force thefracture to initiate along the wellbore, the fracture initiationpressure will be much higher and this fracture willexperience a large turn and re-orientation to reach its finalorientation. This study shows that the optimalcommunication path between wellbore and reservoir islikely to be created when the fracture initiates at theminimum pressure.

    The optimal fracture initiation pressure and the optimalperforation position vary with well orientation. A study wasdone to demonstrate how the well orientation affectsfracture initiation. Figures 5 and 6 generalize the results ofour study. These figures show the effects of well orientationon optimal initiation pressure, optimal perforation positionand the fracture orientation with wellbore direction.

    Figure 5 shows that the wellbore deviation angle a reachesa critical value at 45 and all optimal initiation pressurecurves converge to one point, indicating that all deviatedand horizontal wells have the same optimal initiationpressure as a vertical well no matter what is the value of thewellbore deviation angle P. If a is smaller than 45, the

    76

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    SPE 39425 Z. Chen and M. J. Economies 3

    optimal initiation pressure increases as the angle P increasesuntil p =60 and then the pressure decreases. When a islarger than 45 the optimal initiation pressure decreasesmonotonically as the wellbore orientation from verticalapproaches the horizontal,

    Figure 6 also compares the effects of well deviation onoptimal initiation pressures. The difference here is that thewellbore deviation angle a takes several discrete values butthe angle p changes form 0 (vertical well) to 90(horizontal well). From these results the followingobservations can be made:

    (1)

    (2)

    (3)

    (4)

    (5)

    (6)

    (7)

    When P is smaller than 20 the optimal initiationpressure doesnt change much and is approximatelyequal to the vertical well initiation pressure no matterwhat value the angle a is.

    For angle a smaller than 30 two distinguishing trendsare found, the optimal initiation pressure increases firstwith angle P until P reaches 60 and then the initiationpressure decreases with p.

    For angle a larger than 30 the optimal initiationpressure decreases with the angle P monotonically.

    For a smaller than 45 the deviated well optimalinitiation pressure is higher than that of a vertical well.The curve labeled &O provides the high limit offracture initiation pressure.

    For a larger than 45 the deviated well optimalinitiation pressure is lower than that of a vertical well.The curve labeled a=90 provides the low limit offracture initiation pressure.

    The maximum optimal initiation pressure is on thecurve labeled wO.The angle a=O represents the planenormal to the in-situ maximum horizontal stressdirection. When a well stays on this plane the optimalinitiation pressure increases rapidly, reaches amaximum at P =50 and then decreases slowly. Adeviated or horizontal well should not be drilled on thisor near this plane if the well is to be fractured.

    The curve labeled as a =90 represents the plane normalto the in-situ minimum horizontal stress, A well on thisplane has the lowest optimal fracture initiation pressureand no fracture reorientation. This plane is the bestchoice to drill a deviated well that is to be fractured.

    Near-Well Fracture GeometryFracture propagation in the near-wellbore region isconsidered the result of mixed stress mode I-II-III load[6,10]. The near-well fracture propagation is characterizedas the process of fracture turning followed by adjustment ofthe fracture orientation towards the minimum resistancedirection. This turning and twisting create the undesirablefracture tortuosity which is harmful both during the fractureexecution and the post-treatment performance of thefractured well.

    Rigorous description of the near-well fracture geometryneeds a non-planar, filly 3-D fracturing model. Chen andEconomies [6] developed a simplified model to predictthe fracture reorientation. In that model the maximumtangential stress criterion (o-criterion) is used to investigatethe fracture extension.

    As the fracture propagates and reorients, the propagationangle em at the fracture tip changes as shown in Fig. 7. Acomputer program was developed to calculate the changeof em along the fracture. Afier the first @wis calculated bythe program, the fracture extends by a length k~ At thenew fracture tip, a new em is calculated and the fiac~reextends another Ay. These procedures are repeated untilthe desired fracture length is obtained (actually until, thefracture follows the path perpendicular, i.e., normal, to theminimum far-field stress).

    Closure Pressure and Net Pressure in FractureThe closure pressure along the fracture path is the stressperpendicular to the fracture path. It is this stress thatcauses the closure of the fracture,

    o= = o,l~ +OOm~+2~@l,ml. ....................................... (1)

    wherecc : closure pressure,11,ml : are the direction cosines of the closure

    pressure Ocwith or and cr~respectively.

    The net pressure in the fracture is the pressure differencebetween the fluid pressure and the closure pressure. mefracture width along the fracture is calculated based on thisnet pressure in the fracture. Figure 8 shows a typical netpressure distribution and the corresponding fracture width.Notice that in the near-wellbore region the fluid pressurewithin the fracture is smaller than the closure pressure,resulting in a negative net pressure, The phenomenon doesnot mean that the near- wellbore fracture is closed; thefracture width along the fracture results from the netpressure in the entire fracture.

    77

  • 4 The Effect of Near-Wellbore Fracture Geometry on Fracture Execution and SPE 39425Post-Treatment Production of Deviated and Horizontal Wells

    Narrowed Near-Wellbore Fracture WidthDue to the stress concentration around the wellbore, theclosure pressure in this zone is often larger than the fluidpressure in the fracture after the initiated fracture hasturned. This causes a negative net pressure as shown in Fig.8. The negative net pressure tends to close the fracture. Itisbecause of this negative net pressure near the wellbore,that the fracture width at the wellbore, in contrast to theconventional belie$ is always smaller than the maximum@acture width along the fracture. (Except for open-holefracturing and 180 oriented perforations in perfectlyvertical wells).

    If the fluid pressure in the fracture is not large enough toovercome the closure pressure, the fracture cannot beopened. While the negative stress is very near the weEbore,at a short distance away from the wellbore the net pressurealong the fracture changes from negative to positive. It isthis positive net pressure that keeps the fracture openoverall.

    The width of the fracture at the wellbore is a complicatedissue because of this negative net pressure. A positive netpressure in part of the fracture may not assure the openingof the tiacture at the wellbore. When the net pressure in thefracture is not large enough to open the fracture to a criticalwidth, the fracture at the wellbore could be closed. Thefinal fracture geometry is the result of the combinationeffect of all the net pressures along the fracture.

    The fracture width near the wellbore is important both forthe hydraulic fracture execution and the post-fractured wellperformance, If at a critical moment during the fractureexecution the fracture width at the wellbore is smaller thanthe dimension of the proppant, the proppant cannot becarried into the fracture and will accumulate at the fractureinlet with a proppant screenout occurring. Thisphenomenon could be the cause of many unsuccessfulfracturing jobs.

    Even with a successful fracturing execution (successfullypumping proppant into formation), the near wellbore stressconcentration can reduce the fracture width. This reducedfracture width causes a choke effect and is very harmfilto the post-fractured well performance.

    The fracture width is calculated by the England and Greensolution for a crack between x=-L and x=L opened by anequal opposite normal pressure distribution, p(x), on eachside of the crack as exerted by a fluid. The fracture widthalong the length is calculated by the following doubleintegral [14]:

    4(1 - v)Lf xL2&L2 2 Ap(xL,)~~lw(x) =

    d !Jv /Jw...........(2)

    where x, XL2and XLI are all dimensionless lengths definedas the fraction of fracture half length x~ @(xL]) is the netpressure distribution in the fracture, defined as the pressuredifference between the fluid pressure and the closurepressure.

    The net pressure, @(XL]), changes because both the fluidpressure and the closure pressure have different valuesalong the fracture. Solving the fracture width model aboveis cumbersome except for Ap constant along the fracture,which is the assumption of the KGD model where thedouble integral was solved. With ~ varying along fracture,a universal analytical solution for different net pressuredistributions is impractical. Numerical calculation of thisdouble integral encounters singularities. Chen andEconomies [6] developed a transformation to removethese singularities before numerical computation.

    Choke Effects on Fracturing Execution and PostTreatment Well ProductionAs we discussed in the previous section, the fracture of anarbitrarily oriented wellbore has two distinguishingcharacteristics:(1) The fracture does not align itself with the wellbore but

    cuts the wellbore at an angle y This cut mayreduce tremendously the contact between the wellboreand the reservoir.

    (2) The near-wellbore stress concentration may causesevere near-wellbore fracture width reduction andfracture tortuosity.

    This section and the next section discuss the choke effectscaused in a fracture by the reduced near-wellbore fracturefluid flow capacity.

    A choke dissipates large amounts of potential energy (i.e.,pressure loss) over a short distance. Figure 10 is aschematic of the tiow characteristics as fluid passesthrough a narrowed near-wellbore fracture path. Itillustrates the combined effect of a sudden flow contraction,a small flow restriction, and an abrupt enlargement. As thefluid approaches the orifice-like short path, the fluidcontracts to form a high-velocity jet. The jet converges to aminimum called the throat, and then the jet expands towardthe larger fracture wall. After leaving this narrowed near-wellbore short path (choke), the stream of fluid returns to a

    78

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    SPE 39425 Z. Chen and M. J. Economies 5

    flow geometry similar to what it was before entering thechoke. An area of turbulence just beyond the choke exitalso contributes to the pressure loss.

    An important characteristic about the general nature ofcompressible flow is that there exists a maximum flow ratethrough the choke for given upstream conditions. If thechoke flow phenomenon occurs in the near-wellbore part ofthe fracture the flow rate will remain unchanged aslong asthe ratio of wellbore pressure to the reservoir pressure isless than or equal to the critical pressure ratio, no matterhow low the wellbore pressure drop~. This analysis impliesthat l~choke$ow occurs (pl /p I=0.5), half of thefracturingpressure will be lost.

    For gas flow (note that some highly compressible fracturingfluids and post-fractured well production fluid with highgas oil ratio have similar characteristics when subjected tochoke flow), the critical downstream pressure is reachedwhen the velocity at the flow throat reaches sonic velocity.Analytical equations for the critical pressure ratio can bederived using assumptions of ideal gas, no friction losses,and adiabatic flow, In general, the pressure ratio is about0.5, or the upstream pressure should be double thedownstream pressure for critical flow conditions to exist.

    Critical pressure ratios and critical flow conditions areobserved for all types of compressible flow, includinggas/liquid mixture flow. For incompressible liquid flow thesimilar nozzle effects are easily present.

    Nozzle Phenomenon at the Fracture InletAlthough the choke flow phenomenon is not likely tohappen for incompressible liquid flow such as thefrequently-used hydraulic fracturing fluids, the similarnozzle phenomenon is likely to exist and it would cause aconsiderably large pressure loss when the fluid flowsthrough a local narrowed path like the near-wellborefracture. The following analysis starts with the energyconservation of fluid flow to reveal the nozzle phenomenain the near-wellbore fracture and their effects on hydraulicfracture execution.

    The pressure drop across this narrow short restriction isderived in the Appendix (A.2) as:

    -w .. . . .. .. . . .. ... .. . .. . .. . ...(3)Where

    Ap: pressure loss, psi,qi: fracturing fluid rate, bb~min,P fluid density, lbm/fi3,

    fracture width, in,;: fracture-wellbore contact length, fi,

    Since the viscous tilctional effects are essentially negligiblefor flow through short distances, Eq. (3) is valid for bothNewtonian and non-Newtonian fluids.

    Figures 11 and Fig. 12 show the pressure drop across therestriction at different fluid injection rates with the fractirehaving a limited, 2-fiiong, contact with the wellbore, thefracture width at the wellbore is 0.05 in, and the fluiddensity is 70 lb /R.

    Figure 11 indicates that the pressure loss due to a restrictionat the near-wellbore inlet to a fracture can be substantial.With an injection rate of 15 bbl/min, the pressure 10SSwould be 500 psi. A 30 bbl/min injection rate can result in apressure loss as high as 1500 psi.

    Figure 12 investigates the pressure 10SS for severalfracturing fluid injection rates at different fracture widths. Itshows that when the width of the narrowed fracture issmaller than 0.1 inch, the pressure loss is large and verysensitive to the fracture width.

    Post-Treatment Well ProductionAfter the fracture is successfully created, Eq. (4) which isderived in the Appendix, can be used to calculate thepressure loss across the short narrowed near-wellborefracture during production. The dominant term in theequation is the production rate and the pressure lossincreases rapidly as the production rate increases.

    515~2Ap=, -, =kwh . .. . .. . .. .. . ... . .. .. . . . . . .. .. ......(4)

    fff

    Where the units are the same with Eq. (3) except:q: production rate, bbllday,kf: fracture permeability, md.

    Figure 13 plots the pressure loss with production rate forper unit fracture-wellbore contact length. The calculationassumes that the fracture permeability-width productk~~l0,000 md-ft.

    The figure indicates that for this case when the productionrate is larger than 50 bbl/day/ft the pressure loss is no-longer negligible. Another observation is that for a givenreservoir pressure, the pressure which can be lost duringthis short path is limited, implying that the nozzlephenomenon will certainly constrain the production rate.

    79

  • 6 The Effect of Near-Wellbore Fracture Geometry on Fracture Execution and SPE 39425Post-Treatment Production of Deviated and Horizontal Wells

    If the pressure drop is represented in terms of a productionrate dependent skin, then we define the following skinfactor due to nozzle effect:

    kh 3.65kh~&. .. . . .. . ..... . .. . . ........(5) = 141.2q Bp B@fwihf

    where B: volume factor; p:viscosity, cp; k: reservoirpermeability, md; h: reservoir thickness, fi.

    The skin in Eq. (5) is added to the dimensionless pressureof, e.g., the Cinco-Ley and Samaniego [20] solution forfinite conductivity fractures:

    kh(p) Pw )pD+sn= ... .. . .. .... . . .. . . . .. . .. . .. .............(6)141 .2qBp

    Equation (6) is quite instructive on the importance of wellto fracture connectivity and point source fracturing on awell performance. Based on the findings of this work,minimizing tortuosity, i.e., allowing the near-wellborefracture width to be as large as possible is important for allreservoirs. For example, Fig. 8 suggests that the near-wellfracture width can be as little as 407. of the maximum,thus, adding a skin value to the dimensionless pressuresolution.

    However, the restriction to flow provided by a reduced h~(nozzle phenomenon) is far more severe in highpermeability reservoirs. A 100-md reservoir, and candidatefor high permeability fracturing (frac&pack), canexperience a skin effect that may be much larger than thatin a low-permeability reservoir. Note that the skin is alsorate-dependent, similar to other rate-dependent skins suchas turbulence effects.

    The following simple calculation compares the effect ofthis skin on different reservoirs.

    Case 1: reservoir with 0.1 md permeability, 60 h thick,1000 ft fracture half-length and 1000 psi pressuredrawdown, C@=100, at 180days, the production ratewould be:Without Sn: 35 STB/day, with Sn: 34 STB/day.

    Case 2: reservoir with 100 md permeability, 60 ft thick, 100ft fracture half-length, 1000 psi pressure drawdown, C~=l,at 180days, and assume the that wellbore-reservoir fracturecontact length is reduced to 1 ft for eve~ 4 ft thick ofreservoir. The production rate would be:Whhout Sn: 1900 STB/day, with Sn: 423 STB/day.

    This extra skin causes about 2% production reduction in alow-permeability reservoir (Case 1), while for the higher-permeability reservoir (Case 2) the production reduction isfar larger (77.4%).

    Conclusions1.

    2.

    3.

    4.

    The. in-situ stress and wellbore orientation influencegreatly the fracture initiation and near wellborepropagation of deviated and horizontal wells.The narrowed near-wellbore fracture will cause highfracturing pressures and will also limit the post-treatment productivity of a well.For low-permeability reservoirs, point-sourcefracturing is the indicated way to avoid tortuosity.Little reduction in the post-treatment well performancecan be anticipated from the limited well-to-fractureconnection.However, narrowed, tortuous and limited well-to-fracture contact can have a devastating effect on high-permeability fracturing. Point-source is notrecommended. To afford a non-tortuous and largecontact an S-shape well is recommended where thewell is turned vertical into the formation even if it isinitiated as a deviated well from the surface.

    Nomenclaturea =wellbore deviation angle formed between the

    in-sip minburn horizontal stress and theprojection of the wellbore on the horizontal plane

    P = wellbore deviation angle with which thewellbore deviates from the vertical direction

    Y = angle between the starter fracture andwellbore

    6 = fracture initiation angle relative to thereference axis xx

    em = the angle where rPodisappearsc = absolute earth stress perpendicular to the

    plane of the fracture~r = stress in the direction of r~,min = minimum in-situ horizontal stress~,mm = maximum in-situ horizontal stress~e = stress in the direction of 6cr~ = maximum tangential stresso~ = critical stress of materialOc = closure pressure11 = direction cosines of the closure pressure ~c

    with ~rXf = fracture half lengthm] = direction cosines of the closure pressure cc

    with GOPbd = fracture initiation pressure

    80

  • .. .. = -.. . ... .

    SPE 39425 Z. Chen and M. J. Economies 7

    PbdN = normalized fraCtUreinitiation pressure@bdN=Pb~G,mox)

    cfD = fracture conductivityPm = minimum fracture extension pressure~(x) = net pressure in fracturer = radial distance from wellborew(x) = fracture width at position xx = dimensionless distance defined as the fraction

    of fracture half lengthXL1 = dimensionless distance defined as the fraction

    of fracture half lengthXL2 = dimensionless distance defined as the fraction

    of fracture half length

    References1.

    2.

    3.

    4.

    5.

    6.

    7.

    8.

    9.

    10.

    Yew, C.H. and Li, Y.: On Fracture Design ofDeviated Wells~ paper SPE 19722, presented at the1989 SPE Annual Technical Conference andExhibition, San Antonio, Texas, Oct. 8-11, 1989.Yew, C.H. and Li. Y.: Fracturing of a Deviated Well:SPE PE, NOV.1988,429-437.Abass, H.H., Hedayati, S., and Meadows, D.L.:Nonplanar Fracture Propagation From a HorizontalWellbore: Experimental Studyj paper SPE 24823,presented at the 67th SPE Annual TechnicalConference and Exhibition, Washington, DC, Oct. 4-7,1992.Halkun, S.D,, and Last, N.C.: Geometry of HydraulicFractures From Modestly Deviated Wellbores, paperSPE 20656, presented at the 65th SPE AnnualTechnical Conference and Exhibition, New Orleans,LA, Sept. 23-26, 1990.Sousa, J.L,: Three-Dimensional Simulation of NearWellbore Phenomena Related to hydraulic FractureFrom Perforated Wellbore~ 1992 DoctoralDissertation, Cornell University.Chen, Z, and Economies, M. J.: Fracturing Pressureand Near-Well Fracture Geometry of ArbitrarilyOriented and Horizontal Wells; paper SPE 30531,presented at the 1995 SPE Annual TechnicalConference and Exhibition, Dallas, Texas, Oct. 22-25,1995.Deily, F.H., and Owens, T.C.: Stress Around a Wellbore; paper SPE 2557, 1969.Bradley, W.B.: Failure of Inclined Boreholes, J.Energy Res. Tech., Trans., AIME (Dec. 1979) 102,232-239.Richardson, R.M.: Hydraulic Fracture in ArbitrarilyOriented Boreholes: an Analytic Solution, Proc.,Workshop on Hydraulic Fracturing StressMeasurements, Monterey, California (Dec. 1981).Kassir, M.K., and Sib, G.C.: Mechanics of Fracture,volume 2, Three-dimensional crack problems,

    11.

    2.

    3.

    4.

    Noordhoff International Publishing, Leyden, TheNetherlands, 1975.Perkins, T.K. and Kern, L.R.: Widths of HydraulicFractures, JPT, Sept. 1961, 937-49; Trans.,- AIME,222.Valko, P. and Economies, M. J.: Hydraulic FractureMechanics, John Wiley & Sons Ltd, 1995.Economies, M.J., Nolte, K.G.: Reservoir Stimulation,Second Edition, Prentice Hall, Englewood Cliffs, NewJersey, 1989.Sib, G.C.: Mechanics of Fracture Initiation and

    15.

    16.

    17.

    18.

    19.

    20,

    21.

    22.

    Propagation, Khrwer Academic Publishers, 1991.Gdout~s, E.E.: Problems of retied mode CrackPropagation, Martinus Nijhoff Publishers, The Hague,The Netherlands ISBN 9024730554.Weng, X.W.: Fracture Initiation and PropagationFrom Deviated Wellbores, paper SPE 26597,presented at the 68th SPE Annual TechnicalConference and Exhibition, Houston, Texas, Oct. 3-6,1993.Behrrnann, L.A., Elbel, J.L.: Effect of Perforation onFracture Initiationfl paper SPE 20661, presented at the65th SPE Annual Technical Conference andExhibition, New Orleans, LA, Sept. 23-26, 1990.Yew, C.H., Mear, M.E., Chang, C.C., and Zhang, X.C.:On Perforating and Fracturing of Deviated CasedWellbores, paper SPE 26514, presented at the 68thSPE Annual Technical Conference and Exhibition,Houston, TX, Oct. 3-6, 1993.Barry, K.A.: Fracture Mechanics of Rock AcademicPress Geology Series, 1987.Chen, Zhongming: Real-Time Visualization of 3-Dimensional Fracture Initiation and Propagation inDeviated and Horizontal Wells; 1995 DoctoralDissertation, Texas A&M University.Cinco-Ley, H., and Samaniego, F.: Trmsient PressureAnalysis for Fractured Wells: JPT, 1749-1766.September, 1981.M. J. Economies, A. D. Hill, and C. E. Economies:Petroleum Production System, PTR Prentice Hall,1994.

    Appendix

    A.1 Parameters for Sample CalculationTABLE 1- PARAMETERS COMMON TO

    ALL CALCULATIONSEffective stress cr,m;.,Psi 3000

    ......... .

    Effective stress ~h,~u,psi 5000Effective stress o, ,psi 7000Fluid ~res~llr~ n n~i 400(-)

    81

  • .

    ... -.

    8 The Effect of Near-Wellbore Fracture Geomet~ on Fracture Execution and SPE 39425Post-Treatment Production of Deviated and Horizontal Wells

    A.2 Energy Balance Analysis and the NozzlePhenomenon at the Fracture InletWhen fluid flows through a short narrowed, choke-likepath, there will be a considerable fluid velocity increaseand also pressure loss. Compressible fluid may lead to achoke phenomenon and incompressible fluid may result innozzle phenomenon. These phenomena are likely to existwhen the fluid flows through a local narrowed path such asthe near-wellbore contact into a fracture. The followinganalysis starts with the energy conservation of fluid flow toderive the equation describing the phenomenon.

    The law of conservation of energy states that the net energyrate out of a system is equal to the time rate of work donewithin the system.

    ener~ in - energy out = work done, (A-1)

    Consider the generalized flow system shown in Fig. A- 1.

    QHeat energy

    E,+plVl

    ?

    r

    w

    Work doneH,

    I

    2~E2+p2V2H,v

    Fig. A-1 Generalized flow system

    The work done by the fluid is equal to the energy per unitmass of fluid output by the fluid to fluid engine. Thus thelaw of conservation of energy yields:

    (E2-E, )+(P272 -P,7i)-g(H2 -H,)+

    +:(;;-;:) =W+Q (A-2)Simpli@ing this expression using differential notationsyields

    AE-gAH+ Au=~+ A(p~)=W+Q (A-3)

    Eq. (A-3) is the first law of thermodynamics applied to asteady flow process. The change in internal energy of the

    fluid and the heat gained by the fluid usually are consideredby using a friction pressure loss term, which can be definedin terms of Eq. (A-3) using the following expression:

    F= AE+~pd~-Q1

    (A-4)

    The friction 10SSterm can be used conveniently to accountfor the lost work or energy wasted by the viscous forceswithin the fluid. Substitution of Eq. (A-4) into (A-3) yields

    2

    ~

    A;2VdpgAH+ =W-F

    1 2(A-5)

    Equation (A-5) is the mechanical energy balance equation.This equation is a completely general expression conkiningno limiting assumptions other than the exclusion of phase

    boundaries. The first term in Eq. (A-5), ~~~p, may beI

    difficult to evaluate if tie fluid is compressible unless theexact path of compression or expansion is known.Fortunately, hydraulic fracturing deals primarily withessentially incompressible fluids having a constant specific

    volume, V..

    Since for incompressible fluids, tie term f~dp is given by1

    2

    J~dp = *1 P

    and Eq. (A-5) can be expressed by

    &.wAH+p+= pW pF.

    --.;.. ..Expressing this equation m practical

    1

    (A-6)

    (A-7)

    field units of pressurewith pounds per square inch, density with pounds per cubicfoot, velocity with feet per second, and length with feetgives

    PI +0.0069P(HZ HI ) 1.079x 10AP(~~ ~?)++@p APf=P2 (A-8)

    The hydraulic fracturing fluid flowing through a locallynarrowed, near-wellbore fracture path, can beapproximately represented by tie fluid flowing through ashort restriction as shown in Fig. 10.

    82

  • SPE 39425 Z. Chen and M. J, Economies 9

    As the fluid flows through the short constriction betweenPoint 1 and Point 2 as shown in Fig. IO, the pressure lossthrough this narrow fracture path can be calculated by Eq.(A-8). We assume that

    (1)

    (2)

    (3)

    the change in pressure due to a change inelevation is negligible;the upstream velocity u] is negligiblecompared with the velocity Uzat the outlet ofthe narrow restriction;the frictional pressure loss across the shortnarrow restriction is negligible.

    Thus, Eq. (A-8) reduces to

    p, 1.079xlo-4pu; =p2 (A-9)

    whereUz is the fluid velocity at the outlet of a shortrestriction, ft/see,p is the fluid density, lbm/ft3,p is the pressure, psi.

    If the injection rate of hydraulic fracturing fluid is qj(bbl/min) and the cross section area of this narrow path isA~(inz), then

    13.47qjzf2=

    Af(A-IO)

    Substituting (A- 10) into (A-9) and rearranging the equationyields pressure drop across this narrow short restriction:

    1.96 X 102~;Ap=pl Pz= A2

    t

    (A-11)

    Since the viscous frictional effects are essentially negligiblefor flow through short distances, Eq. (A-11) is valid forboth Newtonian and non-Newtonian fluids.

    The cross section area of this narrow fracture path A~(inz)can also written as wfiz(in-ft). For fracturing execution thepressure loss due to nozzle effect is given in the followingform:

    P=P-P2=W (A-12)For post-treatment production the fracture is filled withproppant. The fractures ability to conduct the fluid flow isdetermined by the fracture permeability k~ which has a unitof area. Incorporating kf into (A-11) and making properunits conversion yields:

    sls~zAp=pl-P2=kwh

    f.ff

    (A-13)

    Where the unik in Eqs. (A-12) and (A-13) areAp: pressure loss, psi,qi: fracturing fluid rate, bbl/min,9: production rate, bbl/dayP; fluid density, lbm/@,

    fracture width, in,y: fracture-wellbore contact length, ft,kf; fracture permeability, md.

    wellbore

    &

    Zz

    r

    //

    /I h,min \

    (a) Global coordinate system

    Fig. 1 Description

    (b) Local coordinate system

    of deviated well parameters

    83

  • 10 The Effect of Near-Wellbore Fracture Geometry on Fracture Execution and SPE 39425Post-Treatment Production of Deviated and_HoflZgnt?l W?IIS

    (b) or

    (c) o~

    Fig. 2 3-D view of stress components around a wellbore

    84

  • SPE 39425 Z. Chen and M. J. Economies 11

    PbdNand ~ With perforation angle 0

    2.5...llb.r.

    --n

    + PM2 n T

    1.5- -5

    a l?

    0.5

    0=1 : II \ 40

    01 60 120 1801 240 300 3fo1: Perforation! angle e;1

    II

    ,1 I I,1 ,1 I

    II

    1: /1I

    ,1:1

    I,1 I

    ,1 ,1 I

    II ,11

    ,1 ,1 I

    ,1 ,1 I

    ,1 ,1 1

    .1 ,! I

    ;!

    /

    I

    starter fractures

    +

    I1

    II

    / I1iI1 wellbore (front: O-180)

    ~------- --- ----~// --

    I II

    I

    I

    I

    \ IIII1

    wellbore (back: 180 -360)

    Fig. 3 Upper figure: Normalized fracture initiation pressure and orientation vs. perforation angleLower figure: Fracture projection on the wellbore corresponding to the minimum

    initiation pressure

    85

  • 12 The Effect of Near-Wellbore Fracture Geometry on Fracture Execution and SPE 39425Post-Treatment Production of Deviated and Horizontal Wells

    ,

    25000 40 ~

    reorientation -w

    Fig. 4

    20000

    15000

    10000

    5000

    Oj ! 400 50 100 150 200 250 300 350 400

    Perforation angle, 0

    Normalized fracture initiation pressure, fracture initiation orientation, and fracturereorientation angle vs. perforation angIe(Wellbore orientation: a=600, %600)

    1.8 , I

    *I:,u, ,,P ,? :w.!lb.r. ?, :,. y, 6,,..,.,, a, .,.

    1.4

    51.2

    m

    1

    0.8

    0.6 ~ I

    o 20 40 60 80 100

    Angle a

    Fig. 5 Normalized optimal fracture initiation pressure vs. well deviation angle a

    r+p=o+p=30+p=45+p=60+p=90

    86

  • SPE 39425 Z. Chen and M. J. Economies 13

    1.8

    1.6

    1.4

    1

    0.8

    0.6

    _ .-

    0 20 40 m 80 100

    Angle ~

    Fig. 6 Normalized optimal fracture initiation pressure vs. well deviation angle P

    fi-acture

    606~

    h,max

    Lh, min

    Fig. 7 Fracture propagation and reorientation

  • 14 The Effect of Near-Wellbore Fracture Geometry on Fracture Execution and SPE 39425Post-Treatment Production of Deviated and Horizontal Wells

    1000

    0

    -1000

    -2000

    -3000

    -5000

    -6000

    -7000

    0.2

    0.18

    0.16

    0.14

    0.12

    0.1

    0.08

    0.06

    0.04

    0.02

    0

    Fig. 8 Net pressure and corresponding fracture width along the fracture

    0.2

    0.18

    0.16

    0.14

    0.12

    0.1

    0.08

    0.06

    O.w

    0.02

    0-.

    0 5 10 15 20 25

    Fracture length, fi

    Fig. 9 Comparison of fracture width at the wellbore with maximum fracture width

    88

  • .-J

    SPE 39425 Z. Chen and M. J. Economies 15

    Wellbore\

    Locally narrowed

    -

    Fracture

    Fig. 10 Fracture fluid flow through a narrowed near-wellbore fracture path

    1600

    1200

    800

    400

    0

    0 10 20 30 40 50

    Injection rate, bbl/min

    Fig. 11 Pressure loss across the narrowed near-wellborefracture path

  • =

    16 The Effect of Near-Wellbore Fracture Geometry on Fracture Execution and SPE 39425Post-Treatment Production of Deviated and Horizontal Wells

    10000

    .-.+ q=l O bbVmin

    1000- - + q=20 bbVmin.-

    & + q=30 bbVminm~

    100g~A

    10-

    1- 1 1 I 10 0.05 0.1 0.15 0.2

    Narrowed fracture width, in

    Fig. 12 Pressure loss vs nmowed fracture width

    .

    4

    0 20 40 60Production rate, bbl/day/ft

    80 100

    0.25

    Fig. 13 Pressure loss vs production rate per foot ofwellbore-reservoir fracture contact length

    90