**1. Introduction**

Much has now been written about the boom in shale gas and shale oil developments in the United States and around the world. In its recent assessment for example, the Energy Infor‐ mation Agency (EIA 2012) noted that North Dakota has become the second largest oil producer in the United States due to production from the Bakken shale. In addition, the EIA (EIA 2013) has predicted that the United States will continue to add more than 230,000 bpd of oil pro‐ duction per year through the end of the decade and become a net exporter of natural gas within the decade. Expenditures on shale gas and shale oil developments have also rapidly increased. For example, more than \$54 billion dollars was spend in drilling and development operations in the seven major US shale developments in 2012 (Clover Global Solutions 2012), with the bulk being spent in the Eagle Ford and Bakken plays.

Shale developments, notably beginning in the Barnett in the 1990s, have been driven by: 1) the application of horizontal wells; 2) the application and improvements in hydraulic fracturing; and 3) significant commodity prices (GWPC 2009 and King 2010). Because of the low perme‐ ability in most shale developments (nano-darcy permeability in shale gas plays and microdarcies in shale oil plays), hydraulic fracturing is a key technology because, as noted by King (2010), the presence of, and the ability to open and maintain flow in, both the primary and secondary natural fracture systems is critical. King further noted the importance of maximizing the fracture-to-shale contact area and optimizing the development, placement, and length of small fractures to enhance and stabilize well production (i.e., optimizing the stimulation of the natural fracture system - that is, increasing natural fracture 'complexity').

Because the stimulation of the natural fracture system is critical to many shale developments, a number of different multi-well completion schemes have been devised in an effort to improve the ability to enhance the stimulation of natural fractures. Three of the common completions schemes are shown in Figure 1. In simultaneous fracturing (plot A in Figure 1), the concept is that hydraulic fracturing both wells at the same time enhances the stimulation of the natural fractures. In the sequential (zipper) frac concept (plot B), the residual stress field from well #1 is thought to enhance the stimulation of the natural fractures when well #2 is stimulated. Finally, in the modified zipper-frac concept (plot C, Figure 1), the sequential stimulation of offsetting stages is thought to enhance the stimulation of the natural fractures.

Nagel et al. (2012c) summarized five 'conditions' for natural fracture shear to occur:

fracture friction, fracture normal stress, or fracture pore pressure;

the fracture friction coefficient, or fracture pore pressure;

**Well #1 Well #2 Well #1 Well #2**

**5.** A variety of combinations of the above.

the fracture friction coefficient, or fracture normal stress; and

are unchanged;

frac); and C) Modified zipper-frac.

**1.** The shear stress along the fracture grows to exceed the shear strength with no change in

**Figure 1.** Common shale completion schemes. A) Simultaneous hydraulic fracturing; B) Sequential fracturing (zipper-

**A B C**

Quantitative Evaluation of Completion Techniques on Influencing Shale Fracture 'Complexity'

**Well #1**

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**Well #2**

**2.** Due to thermal or chemical changes, fracture friction is reduced while the shear stress along the fracture is unchanged and the fracture normal stress and fracture pore pressure

**3.** The fracture normal stress decreases with no change in the shear stress along the fracture,

**4.** The fracture pore pressure increases with no change in the shear stress along the fracture,

Of these, conditions 3 and 4 (and, by default, condition 5) are believed to be most relevant to the behavior of fractured shale plays during hydraulic fracturing. The impact of these condi‐ tions is shown graphically in Figure 2. Figure 2 is a schematic representation of the results of a direct shear test on a fractured rock sample. The x-axis represents the shear displacement along the fracture during the test, and the y-axis represents the shear stress imparted to the

#### **1.1. Natural fracture behavior**

A critical component to understanding the efficacy of multi-well completion techniques on increasing shale complexity is the understanding of the geomechanical behavior of natural fractures. The authors have written extensively about the mechanical behavior of natural fractures and the results of numerical modeling (both continuum and distinct element modeling) of the response of natural fractures to hydraulic fracture stimulation (Nagel et al. 2012a, Nagel et al. 2012b, Nagel et al. 2012c, Nagel et al. 2011a, Nagel et al. 2011b, and Nagel and Sanchez-Nagel 2011). Of first interest in evaluating the impact of multi-well completion schemes on the stimulation of natural fractures is the basic behavior of natural fracture shear and deformation.

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**Figure 1.** Common shale completion schemes. A) Simultaneous hydraulic fracturing; B) Sequential fracturing (zipperfrac); and C) Modified zipper-frac.

Nagel et al. (2012c) summarized five 'conditions' for natural fracture shear to occur:


**1. Introduction**

514 Effective and Sustainable Hydraulic Fracturing

bulk being spent in the Eagle Ford and Bakken plays.

**1.1. Natural fracture behavior**

and deformation.

Much has now been written about the boom in shale gas and shale oil developments in the United States and around the world. In its recent assessment for example, the Energy Infor‐ mation Agency (EIA 2012) noted that North Dakota has become the second largest oil producer in the United States due to production from the Bakken shale. In addition, the EIA (EIA 2013) has predicted that the United States will continue to add more than 230,000 bpd of oil pro‐ duction per year through the end of the decade and become a net exporter of natural gas within the decade. Expenditures on shale gas and shale oil developments have also rapidly increased. For example, more than \$54 billion dollars was spend in drilling and development operations in the seven major US shale developments in 2012 (Clover Global Solutions 2012), with the

Shale developments, notably beginning in the Barnett in the 1990s, have been driven by: 1) the application of horizontal wells; 2) the application and improvements in hydraulic fracturing; and 3) significant commodity prices (GWPC 2009 and King 2010). Because of the low perme‐ ability in most shale developments (nano-darcy permeability in shale gas plays and microdarcies in shale oil plays), hydraulic fracturing is a key technology because, as noted by King (2010), the presence of, and the ability to open and maintain flow in, both the primary and secondary natural fracture systems is critical. King further noted the importance of maximizing the fracture-to-shale contact area and optimizing the development, placement, and length of small fractures to enhance and stabilize well production (i.e., optimizing the stimulation of the

Because the stimulation of the natural fracture system is critical to many shale developments, a number of different multi-well completion schemes have been devised in an effort to improve the ability to enhance the stimulation of natural fractures. Three of the common completions schemes are shown in Figure 1. In simultaneous fracturing (plot A in Figure 1), the concept is that hydraulic fracturing both wells at the same time enhances the stimulation of the natural fractures. In the sequential (zipper) frac concept (plot B), the residual stress field from well #1 is thought to enhance the stimulation of the natural fractures when well #2 is stimulated. Finally, in the modified zipper-frac concept (plot C, Figure 1), the sequential stimulation of

A critical component to understanding the efficacy of multi-well completion techniques on increasing shale complexity is the understanding of the geomechanical behavior of natural fractures. The authors have written extensively about the mechanical behavior of natural fractures and the results of numerical modeling (both continuum and distinct element modeling) of the response of natural fractures to hydraulic fracture stimulation (Nagel et al. 2012a, Nagel et al. 2012b, Nagel et al. 2012c, Nagel et al. 2011a, Nagel et al. 2011b, and Nagel and Sanchez-Nagel 2011). Of first interest in evaluating the impact of multi-well completion schemes on the stimulation of natural fractures is the basic behavior of natural fracture shear

natural fracture system - that is, increasing natural fracture 'complexity').

offsetting stages is thought to enhance the stimulation of the natural fractures.

Of these, conditions 3 and 4 (and, by default, condition 5) are believed to be most relevant to the behavior of fractured shale plays during hydraulic fracturing. The impact of these condi‐ tions is shown graphically in Figure 2. Figure 2 is a schematic representation of the results of a direct shear test on a fractured rock sample. The x-axis represents the shear displacement along the fracture during the test, and the y-axis represents the shear stress imparted to the rock in order to achieve the given displacement. Four stress-displacement profiles are shown, which represent increasing effective normal stress on the fracture. As the effective normal stress is increased, both the peak shear stress necessary to initiate non-elastic displacements and the shear stress necessary to continue non-elastic displacements increase.

shadow. Figure 3 shows the stress shadow (increase in Shmin) from a single hydraulic fracture that was 300m long and 140m in height (along the x-z plane on the right side of the model) in

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**Figure 3.** Stress shadow contours from a single 300m long/140m high hydraulic fracture with a 5MPa net pressure applied on the x-z plane. The cut-away image was created by cutting along the y-z and x-y planes. The model shown is 1000m in each of the x and y-directions. The white area is a region of stress change greater than the color scale shown

As shown, note both the long distance over which the stress change occurs – to the edge of the 1000m long block simulated – and the vertical spreading with distance. At large distances, the change in stress is seen to affect a total formation height more than double the original height of the created fracture. Note also the near-complete lack of stress change beyond the horizontal tip of the hydraulic fracture. Overall, the following can be summarized about stress shadows

**•** The increase in Shmin (stress shadow) extends significant distances behind a fracture and

**•** The increase in Shmin due to a hydraulic fracture is largely unaffected by either the in-situ rock mechanical properties or the stress ratio (though these do appear to affect changes in

**•** A horizontal shear stress field occurs with the fracture tip and does not extend back to the wellbore. This suggests that, at some distance behind the fracture tip, the effect of the stress

spreads out above and below the fracture but not beyond the tip of the fracture.

a model that is 1000m cube.

(from Nagel et al. 2013).

(Nagel and Sanchez-Nagel 2011):

the vertical stress and the SHmax stress).

shadow is to stabilize the natural fracture system.

The implications of this behavior are critical to understanding the behavior of natural fractures during hydraulic fracturing. As shown in Figure 2, as the normal stress acting on natural fractures increases (due, for example, to the inflation of an induced hydraulic fracture), greater shear stress is required to cause shear slippage and displacement along a natural fracture. Effectively, increasing the normal stress stabilizes the natural fractures. At the same time, as pressure increases within a natural fracture (due, for example, to bulk fluid flow into the natural fractures or pressure diffusion from the induced hydraulic fracture), less shear stress is required to cause shear slippage. Given this behavior for natural fractures, and the goal of increasing the shear stimulation of these during hydraulic fracturing, the evaluation of the impact of completion scheme on well stimulation should focus on whether or not the com‐ pletion scheme increases the shear of the natural fractures.

**Figure 2.** Shear-displacement profiles as a function of normal effective stress from direct shear testing of fractured rock.

#### **1.2. Hydraulic fracturing and stress shadows**

If increasing normal stress stabilizes natural fractures, then evaluating the stress changes from a hydraulic fracture is a required element of evaluations to optimize shale complexity. As far back as Sneddon's work on the evaluation of stress near a crack (Sneddon 1946), numerous authors have looked at the impact of stress field changes around hydraulic fractures (Nagel and Sanchez-Nagel 2011 and Warpinski et al. 2012). The stress field change, principally the increase in the minimum horizontal stress, Shmin, caused by a hydraulic fracture (typically the final, propped hydraulic fracture) is called the stress shadow effect or simply the stress shadow. Figure 3 shows the stress shadow (increase in Shmin) from a single hydraulic fracture that was 300m long and 140m in height (along the x-z plane on the right side of the model) in a model that is 1000m cube.

rock in order to achieve the given displacement. Four stress-displacement profiles are shown, which represent increasing effective normal stress on the fracture. As the effective normal stress is increased, both the peak shear stress necessary to initiate non-elastic displacements

The implications of this behavior are critical to understanding the behavior of natural fractures during hydraulic fracturing. As shown in Figure 2, as the normal stress acting on natural fractures increases (due, for example, to the inflation of an induced hydraulic fracture), greater shear stress is required to cause shear slippage and displacement along a natural fracture. Effectively, increasing the normal stress stabilizes the natural fractures. At the same time, as pressure increases within a natural fracture (due, for example, to bulk fluid flow into the natural fractures or pressure diffusion from the induced hydraulic fracture), less shear stress is required to cause shear slippage. Given this behavior for natural fractures, and the goal of increasing the shear stimulation of these during hydraulic fracturing, the evaluation of the impact of completion scheme on well stimulation should focus on whether or not the com‐

**Figure 2.** Shear-displacement profiles as a function of normal effective stress from direct shear testing of fractured

If increasing normal stress stabilizes natural fractures, then evaluating the stress changes from a hydraulic fracture is a required element of evaluations to optimize shale complexity. As far back as Sneddon's work on the evaluation of stress near a crack (Sneddon 1946), numerous authors have looked at the impact of stress field changes around hydraulic fractures (Nagel and Sanchez-Nagel 2011 and Warpinski et al. 2012). The stress field change, principally the increase in the minimum horizontal stress, Shmin, caused by a hydraulic fracture (typically the final, propped hydraulic fracture) is called the stress shadow effect or simply the stress

and the shear stress necessary to continue non-elastic displacements increase.

pletion scheme increases the shear of the natural fractures.

516 Effective and Sustainable Hydraulic Fracturing

**1.2. Hydraulic fracturing and stress shadows**

rock.

**Figure 3.** Stress shadow contours from a single 300m long/140m high hydraulic fracture with a 5MPa net pressure applied on the x-z plane. The cut-away image was created by cutting along the y-z and x-y planes. The model shown is 1000m in each of the x and y-directions. The white area is a region of stress change greater than the color scale shown (from Nagel et al. 2013).

As shown, note both the long distance over which the stress change occurs – to the edge of the 1000m long block simulated – and the vertical spreading with distance. At large distances, the change in stress is seen to affect a total formation height more than double the original height of the created fracture. Note also the near-complete lack of stress change beyond the horizontal tip of the hydraulic fracture. Overall, the following can be summarized about stress shadows (Nagel and Sanchez-Nagel 2011):


**•** Reducing fracture spacing results in a greater minimum Shmin stress increase in the interfracture region as the stress shadows from each fracture overlap more with reduced fracture spacing.

constant cross-section acted on by loads in the plane of the cross section. Discontinuities, therefore, are considered as planar features oriented normal to the plane of analysis. For planestrain analyses, blocks may exhibit plastic yield, and failure can occur in the out-of-plane

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**•** A rock mass is modeled as an assemblage of rigid or deformable blocks. The size, shape, and orientation of the blocks are defined by the imported Discrete Fracture Network (DFN)

**•** Discontinuities are regarded as distinct boundary interactions between blocks, and contin‐ uous and discontinuous joint patterns or joint properties can be generated on a statistical

**•** Fractures are created within, and propagate along, the static block boundary planes; however, propagation can be modeled explicitly based upon the stress intensity factor at the fracture tip. Fracture behavior is prescribed by the block interactions. Thus, natural fracture aperture is, for example, affected by shear displacement and fracture fluid pressure.

**•** Fluid flow is limited to flow within the fractures, and matrix fluid (and, for example, fluid

Figure 4 shows the setup and dimensions of the 2D model in planview at the centerline of the horizontal wellbores (located along the left and right sides of the model shown). Table 1 summarizes the model mechanical parameters while Table 2 summarizes the stress conditions used. The total model was 1200m long in the direction of Shmin (vertical or y-direction) and 225m wide in the direction of SHmax (horizontal or x-direction) as shown in plot A of Figure 4. In order to avoid boundary effects, the vertical boundaries were placed at a large distance (> 550m) from the simulated hydraulic fractures and roller boundaries were applied. The horizontal boundaries were considered to be symmetry planes at the wellbore locations (as

only half the fracture length was modelled) and roller boundaries were also applied.

have been rotated roughly 45° relative to the principal stresses.

Two different natural fracture patterns were employed. In plot B of Figure 4 (note that plot B and C represent the central core in green from plot A), the '180°' fracture pattern is shown. This pattern contains two fracture sets, which are nominally orthogonal to each other and aligned with the principal stress directions. The second fracture pattern, called the '145°' pattern, is shown in plot C. For the 145° pattern, the same two fracture sets from the 180° pattern

The simulated hydraulic fractures are shown in solid and dashed black lines in plots B and C. The solid line represents the first hydraulic fracture location (Xf1) and the dashed lines represent the location of the second hydraulic fracture (Xf2) at a distance of 20m, 35m, and 45m offset along the wellbore from Xf1. When fully propagated, Xf1 and Xf2 were 125m long

direction if the out-of-plane stress becomes a major or minor principal stress.

or by the internal fracture generator.

basis or from an imported DFN.

leakoff) is not considered.

(their fracture half length).

**2.2. Model setup**

The critical modeling features for the simulation of hydraulic fracturing include:

#### **1.3. Natural fracture behavior and stress shadows: Implications for completion strategies**

The combined consideration of the basic mechanical behavior of natural fractures and the nature of stress shadows suggests the following for a multi-well completion strategy:


#### **1.4. Numerical simulation of completion strategies: Modified zipper-frac**

In this paper, numerical simulation results are presented for the evaluation of the modified zipper-frac multi-well completion strategy. The simulations were conducted with a 2D discrete element model (DEM) under different well configurations for two different natural fracture networks, different fracture friction angles, and different stress ratio conditions.
