Performance of Fractured Horizontal Wells in High-Permeability Reservoirs P. Valkó, SPE and M. J. Economides, SPE, Texas A&M University

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1 SPE 349 Performance of Fractured Horizontal Wells in Hig-Permeability Reservoirs P. Valkó, SPE and M. J. Economides, SPE, Texas A&M University Copyrigt 995, Society of Petroleum Engineers, Inc. Tis paper was prepared for presentation at te Society of Petroleum engineers International Symposium on Formation amage control, to be eld in Lafayette, Louisiana, 4-5 February 996. Tis paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by te autor(s). Contents of te paper, as presented, ave not been reviewed by te Society of Petroleum Engineers and are subject to correction by te autor(s). Te material, as presented, does not necessarily reflect any position of te Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of te Society of Petroleum Engineers. Permission to copy is restricted to an abstract of not more tan 300 words. Illustrations may not be copied. Te abstract sould contain conspicuous acknowledgment of were and by wom te paper was presented. Write Librarian, SPE, P.O. Box , Ricardson, TX , U.S.A., fax Abstract Two of te most important recent developments in petroleum production are orizontal wells and ig-permeability fracturing. Tis work combines tem wit potentially considerable incremental production economics. Hydraulic fractures ave a distinctly defined azimut, in almost all cases of interest; tey are vertical and normal to te minimum orizontal stress direction. Horizontal wells can tus be drilled eiter normal or longitudinal to te fracture azimut. Te first configuration as been already considered in te literature and in practice, and is applicable for relatively low-permeability formations. Te emergence of ig-permeability fracturing, also apparently successful in a number of fields, often results in low dimensionless conductivity ydraulic fractures. Te possibility of fracturing orizontal wells longitudinally may ave te net effect of installing a ig-conductivity streak in an oterwise limited conductivity flow conduit. A rigorous model was constructed to describe tis configuration. Tis paper presents comparative production rates and cumulative productions for longitudinally fractured orizontal wells vis a vis vertical fractured wells and unfractured orizontal wells. Te range of attractiveness of te individual options is presented in te framework of discounted revenues. Introduction Horizontal wells and ig-permeability fracturing are peraps te most important recent development in petroleum engineering. Te productivity index of a orizontal well as been well studied in te literature. -5 Te issue of areal permeability anisotropy 6 and its economic impact 7 ave also been considered. Hydraulic fractures are, in almost all cases of interest, vertical and normal to te minimum orizontal stress direction. Horizontal wells can tus be drilled eiter normal or longitudinal to te fracture azimut. Te first configuration results in transverse fractures and as been found to be applicable for relatively low-permeability formations. 8 For te case of transverse ydraulic fractures a skin effect, introduced by Mukerjee and Economides, 5 accounts for te extra pressure drop wen fluid converges from linear to radial flow witin te fracture. Tis calculation points to a substantial reduction in te performance of suc transverse fractures, compared to te performance from a fracture completed from a vertical well. Tere is muc less information available on te oter configuration, involving longitudinally fractured orizontal wells. Te study by Larsen and Hegre, 9 a first step taken in tat direction, contains several assumptions restricting te generality of te results. In particular, tose autors neglect te orizontal flow and te vertical distribution of pressure in te fracture in te fracture. Te longitudinally fractured orizontal well deserves furter attention. Te reason is connected wit te specific limitations involved in ig-permeability fracturing. Indeed, igpermeability fracturing, 0, also apparently successful in a number of fields, often results in low dimensionless conductivity ydraulic fractures. Te possibility of fracturing orizontal wells longitudinally may ave te net effect of installing a ig-conductivity streak in an oterwise limited conductivity flow conduit. A rigorous model was constructed to describe tis configuration. Tis paper uses te concept of discounted revenue (R) to compare te economic attractiveness of te individual options. iscounted revenue is te economic indicator fully representing bot te cumulative production differences and teir distribution in time. It can be used to obtain suc economic indicators 3 as net present value (PV), discounted revenue-to-investment ratio (RI) and incremental discounted revenue-to-investment ratio (IRI). Te latter indicators contain te information on te costs of realizing an individual option. Costs are important from te point of view of any real life economic decision but tey may vary from location to location. Te discounted revenue indicator is, owever, caracteristic for te given configuration and reflects tat

2 PERFORMACE OF FRACTURE HORIZOTAL WELLS I HIGH-PERMEABILITY RES. SPE 349 aspect of te economic attractiveness wic depends only on te productivity of an individual configuration. Overview of Individual Configurations In te following comparison we consider tree different isotropic formations wit permeability k = md, k =0 md and k 3 =00 md. Te formation and production caracteristics are selected according to Table. Table Formation and Production Caracteristics Symb Parameter Value Unit k reservoir permeability k = k =0 k 3 =00 reservoir tickness 75 ft µ fluid viscosity cp B formation volume factor. res. bbl/stb φ reservoir porosity 0. c t reservoir total compress. 0-5 psi - r w well radius 0.38 ft p drawdown 000 psi md Table 3 Individual Configurations in an Infinite Acting Reservoir C Vertical well given C Horizontal well + L given C3 Vertical well finite conductivity fracture + f =, + x f, F C given C4 Horizontal well + f = given finite conductivity fracture + x f,=l/ given +F C given C5 Infinite conductivity fracture + f = given + x f given Fig. Fig. Bot Figs. and Figures and illustrate te relative geometry of te fracture and te well. w Te discounted revenue is calculated from R = n j Price...() j j= ( + i) x f were j is te production in year j from te given configuration and te economic parameters are given in Table. Figure - Vertical well intersected by a longitudinal vertical fracture Table Economic Parameters Symb Parameter Value Unit i discount rate 0.5 n time orizon 3 year Price price of oil 8 $/bbl w An overview of te different configurations considered are given in Table 3. x f Figure - Horizontal well intersected by a longitudinal vertical fracture

3 SPE 349 P. VALKÓ A M.J. ECOOMIES 3 To deal wit comparable situations several assumptions are made and several parameters are fixed. Some of tese assumptions are quite reasonable oters are necessary in order to make te treatment as simple as possible. Because of te nature of te assumptions te results sould be considered as guidelines for te real situations. For all configurations infinite acting reservoir (no boundary effects) is assumed. ear wellbore effects are neglected. Te vertical well is fully penetrating and so is te fracture. In te case of fractured orizontal well te fracture total lengt equals te well lengt. Te flow in te entire system obeys arcy s law, te pressure gradients are small, and gravity effects are negligible. In accordance wit similar studies, it is assumed tat flow enters te fracture only troug te fracture faces and not troug te tips, te flow inside te fracture is incompressible, te flow entering te intersected wellbore comes totally from te fracture, and tere is no pressure drop witin te wellbore. As far as te fracture extent is considered, we assume tat te total propped volume and te fracture permeability are given as sown in Table 4. R/R(F C =.) ominal optimum Figure 3 - iscounted revenue divided by discounted revenue at F C =.. Vertical well, fixed propped volume of fracture. Terefore, we consider te fracture alf-lengts for te individual permeabilities as depicted in Table 5. F C Table 4 Fixed Fracture Parameters Symb Parameter Value Unit V f total propped volume,000 ft 3 k f fracture permeability 50,000 md Tere is only one way to place te given amount of proppant into te formation if we wis to maximize production from a vertical well. Te optimal fracture extent is determined from te condition tat te dimensionless fracture conductivity F C Table 5 (ominal-) Optimal Fracture Extent (F C =.) k, md x f ft w, in For te sake of comparison we consider te same fracture in bot te case of vertical well and tat of te orizontal well. To maintain consistency, we select te lengt of te orizontal well according to L=x f,, even for te case were fracture is not present. kf w =...() Te above specifications determine all te necessary input kx f parameters to calculate R for all te five configurations in te tree formations, i.e. altogeter 5 cases. sould be equal to.. Tis result was first obtained by Pratts 4 for pseudo-radial flow. Strictly speaking, te optimal Calculation Metods fracture extent is somewat iger for transient flow and Te details of te calculation procedures differ from depends on te time orizon considered, but fixing F C =. is configuration to configuration. a good approximation of te optimum, as illustrated by Fig. 3. Configuration (C: vertical well) is calculated by standard In te following for eac permeability we select te alflengt of te fracture intersected by a vertical well so tat Configuration (C: orizontal well) is calculated eiter reservoir engineering metods. F C =. be obtained. from te uniform flux orizontal well solution 6 using te Gringarten et al. 7 or from te Kucuk 8 approximation or by If = f and F C =., it follows 5 tat te Wilkinson and Hammon 9 metod. From our point of view x f = V k (cumulative production) tese metods are equivalent. f f...(3) Configuration 3 (C3: vertical well intersected by a finite 4. k conductivity fracture) is calculated from te Cinco-Ley and Meng 0 metod. Configuration 4 (C4: orizontal well intersected by a finite conductivity fracture) is calculated by te metod described by us elsewere.

4 4 PERFORMACE OF FRACTURE HORIZOTAL WELLS I HIGH-PERMEABILITY RES. SPE 349 Configuration 5 (C5: infinite conductivity fracture) is a ypotetical configuration. It is included into te comparison because it provides an upper bound on te production from a fracture of given extent, regardless of te way te well intersects te fracture. Infinite conductivity fracture production is calculated from te uniform flux fracture solution 6 using te Gringarten et al. 7 approximation. Virtually te same results are obtained using one of te above finite conductivity metods but wit a very large dimensionless fracture conductivity. ote tat te infinite conductivity fracture idealization refers to bot te vertical well and te orizontal well cases. In all tese calculations te dimensionless cumulative production ( ) = q t' dt'...(4) t xf 0 w In Table 6 sown are te discounted revenues for te 5 cases. For a given permeability all values lie between te vertical well (C) and te infinite conductivity fracture (C5) cases. One can consider tat interval as a window of opportunity. Figure 4 sows ow te different configurations make use of tis window of opportunity. Table 6 iscounted Revenue (R) in Million US$ Configuration k, md 0 00 C: Vertical well C: Horizontal well C3: Vertical well, finite conductivity fracture C4: Horizontal well, finite conductivity fracture C5: Infinite conductivity fracture is calculated using te integration rule of Laplacetransformation: = 3 s p w...(5). were s is te Laplace variable and p w is te Laplace transform of te dimensionless constant rate solution. Te dimensionless cumulative production is defined as α Bµ = πk p, ( p ) α k cx φµ i wf const t f....(6) R, million $ C: Vertical well C: Horizontal well C3: Fractured vertical well C4: Fractured orizontal well C5: Infinite conductivity fracture 0 00 k, md for te fractured wells; and α B k µ α = k( p p ) cl....(7) π i wf const φµ t / 4, for te unfractured orizontal well. For te orizontal well intersecting a finite conductivity fracture ( case C5) te solution depends on te dimensionless tickness (or fracture eigt) defined by te ratio of te formation tickness to te fracture alf-lengt: =...(8) x f In our calculations te dimensionless tickness (fracture eigt) is not an independent variable, because for every permeability it is determined by te optimal alf-lengt of te fracture. Figure 4 - iscounted revenue for te different configurations and different permeabilities. At and 0 millidarcies te orizontal well is more productive tan te fractured vertical well. If te orizontal well is longitudinally fractured, te well-fracture system fills out te window of opportunity, i.e., beaves as an infinite conductivity fractured well. At 00 md te fractured vertical well is more beneficial tan te unfractured orizontal well and te fractured orizontal well - toug still more productive tan te fractured vertical well - already does not beave as an infinite conductivity fractured well. Te surprising infinite conductivity beavior of a fracture wit F C =. for configuration 4 is explained by Figure 5, were we plot te constant rate dimensionless pressure for fixed F C. Results and iscussion

5 SPE 349 P. VALKÓ A M.J. ECOOMIES Vertical Well 0 + = p Horizontal Well, F C = Figure 5 - imensionless pressure at constant flowrate production, F C =0., several dimensionless ticknesses. Te plot sows tat for small dimensionless tickness, (i.e., were te fractured orizontal well extends far enoug) te dimensionless pressure needed to obtain a given flowrate is muc less tan for a vertical well intersected by te same fracture. As a consequence, at small dimensionless ticknesses te cumulative production curve is almost indistinguisable from te infinite conductivity curve already at F C = as seen from Fig. 6. H =0.5 t xf F C 0 0. H F C Figure 7 - imensionless cumulative production at constant drawdown, fixed dimensionless tickness, =, several fracture conductivities Te above results sow clearly, tat a dimensionless fracture conductivity of order one is no more necessary if te fracture is intersected by a orizontal well instead of a vertical well. In te following we consider configuration C4: orizontal well wit a longitudinal fracture; but reduce te fracture conductivity by a factor of ten (witout canging te lengt or any oter parameter.) One can consider tis calculation as placing only one tent of te proppant into te fracture (assuming tat te proppant bed permeability is maintained in te narrower fracture as well.) Figure 8 sows te discounted revenues, not only for a ten-fold reduction of te F C, but also for a one undred-fold reduction. (For comparison te fractured vertical well case is also sown.) 00 t xf Figure 6 - imensionless cumulative production at constant drawdown, fixed dimensionless tickness, =0.5, several fracture conductivities. Te influence of te dimensionless fracture conductivity sows only at larger dimensionless ticknesses, as illustrated by Fig. 7. t xf R, million $ C3: Fractured vertical well, F C =. C4: Fractured orizontal well, F C =. C4: Fractured orizontal well, F C =0. C4: Fractured orizontal well, F C = k, md Figure 8 - iscounted revenue for te longitudinally fractured orizontal well, several dimensionless fracture

6 6 PERFORMACE OF FRACTURE HORIZOTAL WELLS I HIGH-PERMEABILITY RES. SPE 349 Te important result is tat te orizontal well fractured wit tenfold less proppant still outperforms te fractured vertical well for k= and 0 md, and it is competitive at 00 md. In fact for te and 0 millidarcies range even te undred times reduced fracture widt is more tan enoug. Te competitive widts (providing nearly equivalent productivity as te optimal fracture for a vertical well) are sown in Table 7. Table 7 Competitive fracture widt for configuration C4: fractured orizontal well k, md w, in It is no longer true, tat ig-permeability fracturing only means wide fractures wic can be obtained only by tip screen-out tecnique. Te combination of orizontal wells wit moderate-widt fracturing may provide te optimal configuration. Conclusions Te possibility of fracturing orizontal wells longitudinally may ave te net effect of installing a ig-conductivity streak in an oterwise limited conductivity flow conduit. A rigorous model predicts almost infinite conductivity fracture beavior in contrast to te finite conductivity beaviour of a vertical well intersected by a similar fracture. Comparative discounted revenue calculations for longitudinally fractured orizontal wells vis a vis vertical fractured wells and unfractured orizontal wells sow a wide range of attractiveness for te longitudinally fractured orizontal well. Te key advantage is tat orders of magnitude less fracture widt (tan tat suggested for te fractured vertical well) migt be sufficient to acieve a certain production goal. omenclature B = formation volume factor, -, -, res. bbl/stb c t = reservoir total compressibility, Lt/m, Pa-, psi- R = discounted revenue, $ = reservoir tickness, L, m, ft f = fracture eigt, L, m, ft k = reservoir permeability, L, m, md k f = fracture permeability, L, m, md F C = dimensionless frac. conductivity = dimensionless eigt (/x f ), p = pressure, m/lt, Pa, psi p = pressure drawdown, m/lt, Pa, psi q = flow rate, L 3 /t, m 3 /s, STB/ i = discount rate n = number of years considered x f = fracture (alf-) lengt, L, m, ft w = fracture widt, L, m, in µ = fluid viscosity, m/lt, Pa s, cp φ = reservoir porosity Subscripts w = wellbore = dimensionless f = fracture References. Josi, S.. "Augmentation of Well Productivity wit Slant and Horizontal Wells." JPT (June 988) Babu,.K. and Ode, A.S. : "Productivity of a Horizontal Well," SPERE (ov. 989) Economides, M.J., eimbacer, F.X., Brand, C.W. and Hienemann, Z.E. "Compreensive Simulation of Horizontal Well Performance." SPEFE (ec. 99) Goode, P.A. and Wilkinson,.J. "Inflow Performance of Partially Open Horizontal Wells." JPT (Aug. 99) Mukerjee, H. and Economides, M.J. "A Parametric Comparison of Horizontal and Vertical Well Performance." SPEFE (Jun. 99) Economides, M.J., Brand, C.W. and Frick, T.P. : "Well Configurations in Anisotropic Reservoirs," paper SPE 7980, presented at te SPE University of Tulsa Centennial Symposium, Tulsa, OK, Aug. 9-3, Smit, J., Economides, M.J. and Frick, T.P. : "Reducing Risk in Areally Anisotropic Formations wit Multiple-Lateral Horizontal Wells," paper SPE 30647, presented at te SPE Annual Tecnical Conference and Exibition, allas, TX, Oct. -5, Brown, J.E. and Economides, M.J.: "An Analysis of Hydraulically Fractured Horizontal Wells," paper SPE 43, presented at te SPE Rocky Mountain Regional Meeting, Casper, WY, May 8-, Larsen, L. and Hegre, T.M.: Pressure-Transient Beavior of Horizontal Wells Wit Finite-Conductivity Vertical Fractures, paper SPE 076 presented at te International Arctic Tecnology Conference in Ancorage, Alaska, May 9-3, Smit, M.B., Miller, W.K. II. and Haga, J.:"Tip Screenout Fracturing: A Tecnique for soft, Unstable Formation," SPEPE (May 987) Roodart, L.P., Fokker, P.A., avies,.r., Slyapobersky, J. and Wong, G.K. : "Frac and Pack Stimulation: Application, esign, and Field Experience From te Gulf of Mexico to Borneo," paper SPE 6564 presented at te SPE Annual Tecnical Conference and Exibition, Houston, TX, Oct Valkó, P. and Economides, M. J.: Productivity of Longitudinally Fractured Horizontal Wells, paper SPE 3050, to be publised in SPEJ, Voneiff, G.W. and Holditc, S.A.: An Economic Assesment of applying Recent Advances in Fracturing Tecnology to Six

7 SPE 349 P. VALKÓ A M.J. ECOOMIES 7 Tigt Gas Formations, paper SPE 4888, presented at te SPE Annual Tecnical Conference and Exibition, Wasington, C, Oct Pratts, M.: Effect of Vertical Fractures on Reservoir Beavior - Incompressible Fluid Case, SPEJ (June 96) Valkó, P. and Economides, M.J.: Hydraulic Fracture Mecanics, Wiley, Cicester, Ragavan, R. and Ozkan, E.: A Metod for Computing Unsteady Flows in Porous Media, Longman Scientific & Tecnical, Harlow, Essex, UK, Gringarten, A.C., Ramey, H.J., Jr., and Ragavan, R.: Unsteady-Stae Pressure istributions Created by a Well Wit a Single Infinite-Conductivity Vertical Fracture, SPEJ, (August, 994), Kucuk, F. J.: ew Metods for Estimating Parameters of Low Permeability Reservoirs, paper SPE 6394, Wilkinson,. and Hammond P.S.: A Perturbation Metod for Mixed Boundary Value Problems in Pressure Transient Testing, Transport in Porous Media 5, , Cinco-Ley, H. and Meng, H.Z.: Pressure Transient Analysis of Wells wit Finite Conductivity Vertical Fracture in ouble Porosity Reservoirs, paper SPE 87 presented at te 63rd Annual Tecnical Conference and Exibition eld in Houston, TX, Oct. -5, 988. SI Metric Conversion Factors cp.0* E-03 = Pa s ft 3.048* E-0 = m in..54* E+00 = m md E-04 = µm psi E+00 = kpa bbl E-0 = m 3 *conversion factor is exact

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