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`SPE 127986
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`Optimizing Fracture Spacing and Sequencing in Horizontal Well Fracturing
`N.P. Roussel, SPE, M.M. Sharma, SPE, The University of Texas at Austin
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`Copyright 2010, Society of Petroleum Engineers
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`This paper was prepared for presentation at the 2010 SPE International Symposium and Exhibition on Formation Damage Control held in Lafayette, Louisiana, USA, 10–12 February 2010.
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`This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been
`reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its
`officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to
`reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
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`Abstract
`The opening of propped fractures results in the redistribution of local earth stresses. In this paper, the extent of stress
`reversal and reorientation has been calculated for fractured horizontal wells using a three-dimensional numerical model of the
`stress interference induced by the creation of one or more propped fractures. The results have been analyzed for their impact
`on simultaneous and sequential fracturing of horizontal wells.
`Horizontal wells with multiple fractures are now commonly used in unconventional (low permeability) gas reservoirs.
`The spacing between perforations and the number and orienation of transverse fractures all have a major impact on well
`production.
`Our results demonstrate that a transverse fracture initiated from a horizontal well may deviate away from the previous
`fracture. The effect of the reservoir’s mechanical properties on the spatial extent of stress reorientation caused by an opened
`crack has been quantified. The paper takes into account the presence of layers that bound the pay zone, but which have
`different mechanical properties from the pay zone. The fracture vertical growth into the bounding layers is also examined.
`It is shown that stress interference, or reorientation, increases with the number of fractures created and also depends on
`the sequence of fracturing. Three fracturing sequences are investigated for a typical field case in the Barnett shale: (a)
`consecutive fracturing, (b) alternate fracturing and (c) simultaneous fracturing of adjacent wells. The numerical calculation of
`the fracture spacing required to avoid fracture deviation during propagation, for all three fracturing techniques, demonstrate
`the potential advantages of alternate fracture sequencing and zipper-fracs to improve the performance of stimulation
`treatments in horizontal wells.
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`Introduction
`For the past few years, most new wells drilled in the Barnett shale, and other shale plays, have been horizontal wells.
`Slickwater fracturing is the primary technique used to hydraulically fracture these wells. The horizontal well is generally
`fractured multiple times, one fracture at a time, starting from the toe. More recently, new stimulation techniques have been
`investigated to improve the reservoir volume effectively stimulated (Mayerhofer et al., 2008). Simultaneous fracturing of two
`or more parallel adjacent wells, also referred to as simul-fracs or zipper-fracs, aim to generate a more complex fracture
`network in the reservoir (Mutalik et al., 2008; Waters et al., 2009).
`When placing multiple transverse fractures in shales, it is crucial to minimize the spacing between fractures in order to
`achieve commercial production rates and an optimum depletion of the reservoir (Cipolla et al., 2009), but the spacing of
`perforation clusters is limited by the stress perturbation caused by the opening of propped fractures (Soliman et al., 1997).
`The geometry and width of fractures are strongly influenced by fracture spacing and number, due to mechanical interactions
`(Cheng, 2009). The center fractures, subject to most stress interference, may exhibit a decrease in their width and
`conductivity. Stress distributions and fracture mechanics must be well understood and quantified to avoid screen-outs,
`propagation of longitudinal fractures, or simply deviation from their orthogonal orientation. The presence of natural fractures
`also impacts fracture propagation increasing fracture path complexity, depending on their preferential orientation and on the
`importance of the net pressure relative to the horizontal stress contrast. (Olson et al., 2009).
`Previous studies in the literature on fracture-induced stress interference mostly focus on the effect of a single fracture
`(Siebrits et al., 1998). Using analytical solutions, Soliman et al. (2004) calculated the effect of multiple fractures on the
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`expected net pressure and the stress contrast: both quantities increase substantially with the number of sequential fractures
`and a smaller fracture spacing. The stress field in the horizontal plane and the fracture geometries were numerically
`calculated, based on a displacement discontinuity method for three transverse fractures assuming a homogeneous single-layer
`formation with the bounding layers not playing any role except to act as barriers to fracture propagation (Cheng, 2009).
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`Three-Dimensional Model of Stress Interference around a Propped-Open fracture
`The results presented here are organized to highlight the important conclusions that we can reach based on the
`simulations. The validity of numerical simulations is verified through comparison with existing analytical models (Sneddon
`et al., 1946) for simple fracture geometries. The important addition to existing models consists in the evaluation of the impact
`of the layers bounding the pay zone on the width of the fracture, which eventually affects the stress interference caused by a
`propped fracture. The identified dimensionless parameters are the fracture aspect ratio (hf/Lf), the Poisson’s ratio of the pay
`zone (νp), the fracture containment (hp/hf), and the ratio of Young’s moduli (Eb/Ep). Their effects on the stress contrast
`generated by the propped-open fracture, and consequently the spatial extent of the stress reversal region, are discussed in the
`following sections.
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`Model Formulation
`The geometry of the simulated fracture is shown in Figure 1. The model includes the presence of layers bounding the
`reservoir and cases where the fracture is not fully contained (hf>hp) are accounted for. The layers bounding the pay zone may
`have mechanical properties (Eb, νb) differing from the pay zone (Ep, νp).
`The pay zone is homogeneous, isotropic, and purely elastic. Hooke’s law relates the components of the strain and stress
`tensors:
`⎛
`σij = 2Gεij + K −
`⎝
`Where,
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` (1)
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`⎞
`G
`εkkδij
`⎠
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`23
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`K
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`=
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`E
`(
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`−
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`3 1 2v
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`)
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` ,
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`G
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`=
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`E
`(
`2 1
`+
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`)
` v
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`A symmetry boundary condition is set up at the fracture center plane, forbidding any deformation in the direction normal
`to the fracture face. Displacement is allowed along the face of the fracture where a constant pressure, equal to the net pressure
`pnet plus the minimum in-situ horizontal stress Shmin, is imposed. The far-field boundaries are located at a distance from the
`fracture equal to at least three times the fracture half-length Lf. A zero-displacement boundary condition normal to the
`“block” faces is applied at outside boundaries. In-situ stresses are initialized prior to the opening of the fracture:
`Sxx = Shmax
`Syy = Shmin
`Szz = Sv
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`Model Validation
`Sneddon et al. (1946) derived analytical expressions of the additional normal and shear stresses versus the distance
`normal to the fracture for two geometries: semi-infinite (Figure 2) and penny-shaped fractures (Figure 3).
`The results of the three-dimensional numerical model were compared to analytical solutions by plotting the additional
`stress in the direction parallel (ΔSxx) and perpendicular (ΔSyy) to the fracture as a function of the net extension pressure (pnet).
`The net extension pressure is the stress remaining as the fracture closes on the proppant minus the minimum horizontal stress.
`In the present study, net pressure is assumed to be constant along the fracture (uniform proppant distribution). Stress
`distributions are plotted versus the distance normal to the fracture face (y) normalized by the fracture half-height (hf).
`Figures 2 and 3 show that the additional stress in the horizontal plane is always higher in the direction perpendicular to
`the fracture than parallel to the fracture. As is true initially, the direction of maximum horizontal stress is parallel to the crack,
`and the stresses are reoriented in the vicinity of the fracture. The numerical results agree well with the analytical solution
`indicating that the numerical results are correct for this simple case.
`The additional stress normal to the fracture (ΔSyy) decreases monotonically with distance away from the fracture. On the
`other hand, ΔSxx becomes negative at some distance normal to the fracture and then passes through a minimum.
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`Comparison of Stress Reorientation due to Poroelastic and Mechanical Effects
`Stress reorientation around fractured wells can occur due to both the fracture opening and due to poroelastic effects. In the
`fracturing of horizontal wells, since the production or injection of fluids is minimal, poroelastic effects can be neglected.
`However, in other cases where significant volumes of fluids have been produced from a well, poroelastic effects can be
`dominant.
`The structure of stress reorientation around a single fracture due to poroelastic effects has been well described in the
`literature (Siebrits et al., 1998; Roussel et al., 2009). In the vicinity of the fracture, the direction of maximum horizontal
`stress is rotated 90 degrees from its in-situ direction (for producing wells). Stress reorientation is not just limited to the stress
`reversal region. The stress distribution resulting from the mechanical opening of a fracture differs from that due to poroelastic
`stresses. It was shown that outside the stress reversal region, it is the direction of maximum horizontal stress which is
`oriented perpendicular to the fracture (Figure 4).
`The extent of the stress reversal region (Lf’) is not limited to 0.58 Lf as is the case for poroelastic effects (Siebrits et al.,
`1998), but may extend to a distance larger than the fracture half-length (Lf). How far the stress reversal region extends in the
`reservoir depends mainly on fracture width and height as well as the Young’s modulus in the pay zone. The reoriented stress
`region (outside the stress reversal region) is confined to the vicinity of the fracture, contrary to poroelastic stress
`reorientation, which can be observed far inside the reservoir.
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`Effect of Fracture Dimensions
`The additional stresses in the parallel and normal directions are plotted versus the dimensionless distance y/hf normal to
`the fracture in Figure 5. Both components increase as the fracture length increases compared to its height. The quantity of
`practical interest, though, is the difference between the additional stress in the direction perpendicular to and in the direction
`parallel to the fracture (Figure 6). This difference represents the stress contrast that is generated by the opening of the
`fracture:
`(Generated StressContrast GSC
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`)
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`S
`− Δ
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` (3)
`
`S
`S
`S
`= Δ − Δ = Δ
`yy
`xx
`//
`⊥
`In most situations the creation of the fracture generates large additional stresses perpendicular to the fracture face. This
`alters the stress contrast and may cause the direction of maximum stress to rotate 90 degrees in the vicinity of the fracture.
`The stress contrast generated by the open crack decreases with distance from the fracture (Figure 6). At some distance from
`the fracture, it becomes smaller than the in-situ stress contrast and the direction of maximum stress is oriented as initially.
`The areal extent of the stress reversal region is directly proportional to the fracture height, as the distance to the fracture is
`normalized by the fracture half-height in our analysis. Figure 6 also shows that as the fracture length increases, the GSC is
`higher. For instance, assuming the in-situ stress contrast is equal to 0.2 pnet, the maximum distance of stress reversal Lf’ is
`increased by 36% for a semi-infinite fracture compared to a penny-shaped fracture.
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`Effect of Poisson’s Ratio in the Pay Zone
`The effect of the Poisson’s ratio in the pay zone on the stress reorientation around the fracture depends on the fracture
`geometry. In the limiting case of a penny-shaped fracture (hf = Lf), the GSC is independent of the Poisson’s ratio. This can be
`explained by the fact that the deformation in the horizontal x-y plane is exactly the same as that in the vertical x-z plane. In
`the more general case where the fracture length differs from the fracture height, Poisson’s ratio will play a role.
`It is shown in Figure 7 that an opened crack generates more stress contrast in a rock with a low Poisson’s ratio. A low
`Poisson’s ratio implies that the deformation in the direction parallel to the fracture is small compared to the deformation
`along the normal to the fracture. When νp = 0, all the deformation occurs along the in-situ direction of minimum horizontal
`stress (εxx = 0), thus maximizing the stress contrast generated.
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`Effect of the Bounding Layers’ Mechanical Properties
`Models of stress interference available in the literature (Sneddon et al., 1946; Cheng, 2009) assume homogeneous
`mechanical properties and do not accurately model layered rocks. The rocks bounding gas reservoirs often have different
`mechanical properties than the reservoir and can play an important role in stress reorientation. Figure 8 shows that the GSC
`decreases, if the Young’s modulus of the bounding layers is higher than in the pay zone. The effect of the bounding layers’
`Young’s modulus was analyzed for a fracture penetration factor hp/hf equal to 0.75. The width of an opened crack is
`proportional to the Young’s modulus. The relationship between maximum fracture width w0 (at the center of the fracture) and
`net pressure for a semi-infinite fracture is given in Equation 4 (Palmer, 1993). If the fracture penetrates into a weaker
`bounding layer (lower Young’s modulus), the fracture width is negatively affected (Figure 9). Thus, a smaller stress contrast
`is generated by the fracture.
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`(
`4 1
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`=
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`p h (4)
`net
`f
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`w
`0
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`)2
`ν−
`E
` The effect of the Poisson’s ratio in the bounding layers was also analyzed (Figure 10). It is shown that the GSC is
`independent of this value, and rather depends only on the Poisson’s ratio inside the pay zone.
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`Effect of Fracture Containment
`The bounding layers’ mechanical properties do not affect the extent of stress reorientation if the fracture is fully
`contained. In the Barnett Shale, fractures are generally well contained in the pay zone even though “out-of-zone” growth has
`been measured in the field (Maxwell et al., 2002). From the relationship between fracture width and Young’s modulus
`(equation 4), it can be deduced that the further the fracture penetrates into the bounding layers, the more the stress
`reorientation will be affected by their mechanical properties. For instance, in the case where the Young’s modulus is higher
`in the layers bounding the pay zone, the maximum width of the crack, and consequently the generated stress contrast,
`decreases as the fracture height increases (Figures 9 and 10).
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`Application of the Model to Multiple Hydraulic Fractures in Horizontal wells
`The quantification of the extent of the stress reversal region around a propped-open fracture is critical in the design of
`multiple hydraulic fractures in horizontal wells. In low permeability reservoirs such as shales in which the slow depletion
`allows for short spacing between sequential fractures, great attention should be given to avoid stress interference between
`transverse fractures. The model of mechanical stress reorientation presented in the previous section of the paper is applied to
`the case of the Barnett shale. Values of the reservoir and fracture parameters are provided in Table 1. The dimensions of the
`opened cracks (height, length and width) are similar for all fractures.
`Poroelastic effects due to the leak-off of the fracturing fluid into the reservoir are neglected in this study, due to the very
`low permeability of the shale and the small amount of fluid leak-off during fracturing.
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`Definition of the Minimum Fracture Spacing
`The minimum fracture spacing can be defined as the distance between two adjacent fractures that allows the refracture not
`to change orientation by 90o from the original stress field. This is shown as S90 in Figure 11. No refracturing should be done
`within S90. In this stress reversal region, the direction of maximum horizontal stress is parallel to the horizontal well, which
`would lead the refracture to either grow longitudinal to the well, or screen out as the change in fracture orientation is very
`rapid. The gain in production and new reserves will be very limited.
`Even when refracturing is done past S90, refracture propagation will still be affected by previous fractures. Stress
`reorientation extends past the stress reversal region, causing a fracture to deviate from its normal trajectory. The fracture
`spacing needed to limit fracture deviation to less than 5o is shown as the area outside the S5 region (Figure 11). The distance
`from the fracture to the S5 or S10 contours represents the minimum fracture spacing so that the refracture may not be subject
`to stress reorientation angles higher than 5 and 10o. Note that the presence of natural fractures, and their effect on fracture
`propagation, is not modeled. In the situation where the natural fractures are mainly oriented perpendicular to the direction of
`maximum horizontal stress (as in the Barnett shale), the direction of propagation of hydraulic fractures may significantly
`deviate from the preferential direction, in particular when stress anisotropy is low (Olson et al., 2008).
`In very low permeability reservoirs such as the Barnett shale, it is desirable to minimize fracture spacing while at the same
`time ensuring transverse fracture growth, to efficiently access gas in the reservoir. This implies that the optimal fracture
`spacing should be just beyond the S5 contour.
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`Sequential Fracturing
`The stress interference caused by one transverse fracture is shown in Figure 11. Horizontal wells are, however, fractured
`multiple times. Thus, the values for the minimum fracture spacing provided in Figure 11 are under-estimates (S90=140 ft,
`S10=320 ft, and S5=450 ft). The stress perturbation caused by each fracture is cumulative with the effect of all prior fractures.
`Therefore, stress interference (or reorientation) increases with the number of fractures and also depends on the sequence of
`fracturing. In this section, we will investigate and compare two fracturing sequences (Figure 12): (a) a conventional
`consecutive fracturing from toe to heel and (b) sequencing the fractures alternately.
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`Effect of fracture width and in-situ stress contrast
`The values of the fracture width and of the horizontal stress contrast chosen for the base case (Table 1) are respectively 4
`mm and 100 psi. As the fracture width increases, the stress contrast generated by the propped-open fracture increases. Thus,
`depending on the horizontal contrast present in-situ and the fracture design, the stress interference caused by the opening of
`multiple fractures will be affected. In Figure 13, the distance between the fracture and the isotropic point (minimum fracture
`spacing S90) is plotted against fracture width for different values of the in-situ stress contrast.
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`Consecutive fracturing (1-2-3-4-5…)
`When a horizontal well is consecutively fractured, the stress perturbation ahead of the latest fracture increases with each
`additional fracture (Soliman et al., 2004) until it reaches a limit, corresponding to the case where the refracture is placed just
`outside of the stress reversal region (Figure 14). The deviation of the refracture from the stress interference generated by
`previous fractures is not modeled for simplicity. The calculation of the stress perturbation ahead of the modeled second
`fracture of Figure 14 provides a good estimate of the minimum distance of refracturing, when taking into account the effect
`of multiple fractures (Figure 15). The extent of stress reorientation for refracturing are summarized by the values below:
`S90 = 230 ft
`S10 = 430 ft
`S5 = 600 ft
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`In order to limit refracture deviation, the horizontal well corresponding to the values given in Table 1 should be
`refractured every 430 to 600 ft, which is equal to 1.4 to 2 fracture heights. This calculation corroborates typical values of the
`recommended fracture spacing found in the literature (Ketter et al., 2008).
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`Alternate fracturing sequence (1-3-2-5-4…)
`If the sequence of fracture placement was altered to conduct fractures in the sequence 1-3-2-5-4, it is shown here that the
`fractures could be placed much closer to each other. This proximity helps to most efficiently drain the reservoir by ensuring
`that the fractures remain transverse. We recognize that this fracturing sequence may not be possible with current downhole
`tools and that special tools may need to be developed. However, our goal is to demonstrate the significant benefits of this
`alternate fracturing sequence compared to the sequential fractures currently being pumped.
`The new strategy consists of placing the second fracture at the location of what would traditionally be the third fracture.
`Perforations for the second fracture are placed at a distance greater than S5. This ensures that its deviation from a transverse
`or perpendicular trajectory is minimal. In the first calculation (S = 600 ft, Figure 16), the direction of maximum horizontal
`stress is reversed along the whole interval separating the fractures. When the fracture spacing is increased to 650 ft, there is
`an interval where the stress distribution will force the third fracture to grow along a normal path intersecting the horizontal
`well at the middle point between previous fractures, where the reorientation angle is exactly equal to zero (Figure 17).
`However, the width of the acceptable interval for the new perforations is extremely narrow (20 ft). For a 700-ft spacing, the
`width of the refracturing interval is considerably increased (220 ft, Figure 18). If the third fracture were to be initiated in this
`interval, the stress reorientation would favor transverse fracture growth. The location of this third fracture does not have to be
`exactly at the mid-point between the previous fractures. In fact, even if the fracture is initiated at some distance from the
`middle, it will follow a trajectory (as seen in the stress profiles, Figure 18) that will force it to become transverse.
`For the last simulation, the fracture spacing is equal to 350 ft (1.17 times the fracture height) which is smaller than the
`recommended value for consecutive fracturing (S5=600 ft). The practical advantage of this fracturing sequence, in addition to
`the fact that minimum fracture spacing is decreased compared to consecutive fracturing, is that stress reorientation is playing
`to our advantage, forcing the middle fracture to propagate in the optimum direction.
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`Impact of Adjacent Wells (Zipper-fracs)
`The technique of zipper-fracs consists of simultaneously fracturing two parallel horizontal wells. In the particular case
`that was modeled, the spacing between adjacent wells is equal to the fracture length (Figure 19). It is shown that the extent of
`stress reversal around each individual fracture is unchanged compared to the case of the single fracture (S90=140 ft).
`However, the reoriented zone outside the stress reversal region significantly shrank (S10=250<320 ft and S5=325<450 ft).
`This is due to the symmetry along the plane x =500 ft (middle plane between adjacent wells), where the reorientation angle is
`equal to zero.
`The worst case scenario for the stress reorientation ahead of the last fracture was calculated for zipper-fracs (second
`fractures placed at isotropic point), similar to the case described in Figure 14. If stress reversal remain unchanged compared
`to the consecutive fracturing of a single horizontal well, the fracture spacing needed to minimize fracture deviation (S10, S5) is
`significantly reduced (Figure 20):
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`S90, zipper-fracs = 230 ft
`S10, zipper-fracs = 330 ft = 77% S10, singlewell
`S5, zipper-fracs = 400 ft = 67% S5, singlewell
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`Conclusions
` A comprehensive and quantitative study of stress reorientation around fractured horizontal wells has been presented. A
`three-dimensional numerical model was introduced, taking into account the presence of layers bounding the pay zone as well
`as fracture containment. It was shown that the stress contrast generated by the opening of a propped fracture is a function of
`the fracture dimensions (w0, hf, Lf), the Poisson’s ratio in the pay zone (νp), the ratio of Young’s moduli of the reservoir and
`bounding layers (Ep/Eb) and the fracture penetration into the bounding layers (hf/hp).
`Based on the simulation results obtained, we can summarize our recommendations as follows:
`(cid:190) To avoid longitudinal fractures, the minimum fracture spacing must be larger than S90. The model presented
`here allows us to obtain reliable estimates of S90 for a given set of reservoir and fracture properties.
`(cid:190) To ensure transverse fractures and avoid deviation of the fracture from its orthogonal path, the fracture spacing
`should be larger than S5.
`(cid:190) The alternate fracturing technique, allows the fracture spacing needed to ensure transverse fractures to be
`reduced by almost a factor of 2 (see Figure 17). Values of the minimum and recommended fracture spacing are
`given in Table 2, for the Barnett shale case values of Table 1.
`It is possible, using this model, to estimate values of the minimum and optimum fracture spacing based on the
`recommendation listed above. Values for the recommended fracture spacing for an example case of the Barnett shale are
`presented in Table 2 for three possible fracturing sequences: (a) consecutive fracturing, (b) alternate fracturing and (c)
`simultaneous fracturing of adjacent wells. The last two techniques make it possible to shrink the stress reorientation region,
`thus significantly reducing the fracture spacing needed to limit fracture deviation from the desired orthogonal path. A
`technique that consists of sequencing the fractures alternately, results in the smallest fracture spacing (340 ft). It also presents
`the important advantage of forcing the “third fracture” to propagate along the orthogonal plane midway between the previous
`two fractures. The development of technologies allowing this fracturing technique to be applied in the field may prove
`beneficial to the performance of stimulation treatments in horizontal wells.
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`Acknowledgments
`The authors would like to acknowledge the financial support provided by the Department of Energy / RPSEA and the
`companies supporting the Fracturing and Sand Control Joint Industry Project at the University of Texas at Austin (Anadarko,
`BP, BJ Services, ConocoPhillips, Halliburton, Shell, Schlumberger and Total).
`
`Nomenclature
`Ep = Young’s modulus of the pay zone
`Eb = Young’s modulus of the bounding layers
`νp = Poisson’s ratio in the pay zone
`νb = Poisson’s ratio in the bounding layers
`K = dry bulk modulus
`G = shear modulus
`Lf = fracture half-length
`hf = fracture half-height
`hp = pay zone half-thickness
`w0 = maximum fracture width
`SV = vertical in-situ stress
`Shmax = maximum horizontal in-situ stress
`Shmin = minimum horizontal in-situ stress
`pnet = net extension pressure
`S90 = distance between fracture and isotropic point (=Lf’)
`S10 = distance between fracture and end of 10-degree stress reorientation region
`S5 = distance between fracture and end of 5-degree stress reorientation region
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`References
`Cheng, Y., “Boundary Element Analysis of the Stress Distribution around Multiple Fractures: Implications for the Spacing of Perforation
`Clusters of Hydraulically Fractured Horizontal Wells”, SPE 125769, SPE Eastern Regional Meeting, Charleston, WV, 23-25
`September, 2009.
`Cipolla, C.L., Lolon, E.P., Mayerhofer, M.J. and Warpinski, N.R., “Fracture Design Considerations in Horizontal Wells Drilled in
`Unconventional Gas Reservoirs”, SPE 119366, SPE Hydraulic Fracturing Conference held in The Woodlands, TX, 19-21 January,
`2009.
`Ketter, A.A., Heinze, J.R., Daniels, J.L., and Waters, G., “A Field Study in Optimizing Completion Strategies for Fracture Initiation in
`Barnett Shale Horizontal Wells”, SPE 103232, SPE Production & Operations, August 2008.
`Maxwell, S.C., Urbancic, T.I., Steinsberger, N. and Zinno, R., “Microseismic Imaging of Hydraulic Fracture Complexity in the Barnett
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