**2. Model setup and simulation matrix**

#### **2.1. 2D DEM model capabilities**

A two-dimensional DEM code was used in all the simulations presented. The code used was a general-purpose program based on the distinct element method for discontinuum modeling. The code can simulate the response of discontinuous media (such as a jointed rock mass) subjected to either static or dynamic loading. The discontinuous medium is represented as an assemblage of discrete blocks, and discontinuities are treated as boundary conditions between blocks. Large displacements along discontinuities and rotations of blocks are allowed. Individual blocks behave as either rigid or deformable material. Deformable blocks are subdivided into a mesh of finite-difference elements, and each element responds according to a prescribed linear or nonlinear stress-strain law. The relative motion of the discontinuities is also governed by linear or nonlinear force-displacement relations for movement in both the normal and shear directions. The basic formulation of the code assumes a two-dimensional plane-strain state. This condition is associated with long structures or excavations with a 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 direction if the out-of-plane stress becomes a major or minor principal stress.

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


#### **2.2. Model setup**

**•** 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

**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

**•** The stress shadow effect, that is the increase in the principal stresses around a hydraulic fracture, causes a stabilization of natural fractures. This can only be overcome by increasing the fluid pressure within the natural fractures (suggesting a desire to increase the net pressure, which would also increase the stress shadow). Decreasing stage spacing, or overlapping hydraulic fractures from different wells, will tend to increase the stress shadow

**•** Because the stress shadow effect does not extend horizontally beyond the tip of the hydraulic fracture (the x-direction in Figure 3), when two fractures are simultaneous created from parallel wellbores, the fractures will not 'see' each other until the tip regions are very near

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

A two-dimensional DEM code was used in all the simulations presented. The code used was a general-purpose program based on the distinct element method for discontinuum modeling. The code can simulate the response of discontinuous media (such as a jointed rock mass) subjected to either static or dynamic loading. The discontinuous medium is represented as an assemblage of discrete blocks, and discontinuities are treated as boundary conditions between blocks. Large displacements along discontinuities and rotations of blocks are allowed. Individual blocks behave as either rigid or deformable material. Deformable blocks are subdivided into a mesh of finite-difference elements, and each element responds according to a prescribed linear or nonlinear stress-strain law. The relative motion of the discontinuities is also governed by linear or nonlinear force-displacement relations for movement in both the normal and shear directions. The basic formulation of the code assumes a two-dimensional plane-strain state. This condition is associated with long structures or excavations with a

to each other (and increase the potential for screenout during a stimulation).

networks, different fracture friction angles, and different stress ratio conditions.

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

nature of stress shadows suggests the following for a multi-well completion strategy:

effect and impair the stimulation of natural fractures.

**2. Model setup and simulation matrix**

**2.1. 2D DEM model capabilities**

spacing.

518 Effective and Sustainable Hydraulic Fracturing

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.

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

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 (their fracture half length).

Fig 4

**DFN #1 DFN #2**

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521

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

**DFN #1 DFN #2**

**Set#2 Gap Length** 5m 5m **Set#2 Spacing, mean** 3m 3m **Set#2 Spacing, st. deviation** 1m 1m **Fracture Normal Stiffness** 2e11 Pa 2e11 Pa **Fracture Shear Stiffness** 2e11 Pa 2e11 Pa **Initial Fracture Aperture** 0.1 mm 0.1 mm

**Case Name** '180°' '145°' **Vertical Stress, Sv** 55.2 MPa 55.2 MPa 55.2 MPa

**Pore Pressure** 27.6 MPa 27.6 MPa 27.6 MPa

For any numerical modeling, assumptions need to be made for the problem being simulated.

**•** 2D, plane strain condition exists (i.e., effects above and below the vertical centerline of a

**•** Hydraulic fracturing is a quasi-static process and both fracture propagation and injection rate effects can be ignored for the cases being simulated (i.e., the hydraulic fracturing process can be represented by static simulations of the fracture at specific lengths under a given net

**•** Events within the formation at the tip of the hydraulic fracture can be simulated without fluid flow within the natural fractures (i.e., the behavior within the formation at the tip is dominated by the changes in total stress and pore pressure changes are negligible).

**•** Net injection pressure was a constant 4 MPa within the hydraulic fractures Xf1 and Xf2 for

**•** Simulations were conducted first for single hydraulic fractures (without influence from a second, nearby hydraulic fracture). Then simulations were conducted for dual hydraulic fractures and compared to results from two hydraulic fractures acting independent of each

For the simulations described in this paper, the following assumptions were made:

vertical hydraulic fracture do not impact the results).

**Max. Horizontal Stress, SHmax** 44.8 MPa 44.8 MPa 44.8 MPa **Min. Horizontal Stress, Shmin** 37.9 MPa 43.5 MPa 37.9 MPa

**Table 1.** Mechanical Parameters Used For Model Construction

**Table 2.** Model Stress And Pore Pressure Data

**2.3. Modeling assumptions**

pressure).

all simulations.

other.

**Figure 4.** DEM model setup and dimensions. A) Full model - only the middle section in green contained fractures; B) Middle section natural fracture pattern for the '180°' model; and C) Middle section natural fracture pattern for the '145°' model. The location of simulated hydraulic fractures are represented by the black lines. Horizontal wellbores are located along the full length of the left and right sides of the model.


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**Table 1.** Mechanical Parameters Used For Model Construction


**Table 2.** Model Stress And Pore Pressure Data

#### **2.3. Modeling assumptions**

**225m**

520 Effective and Sustainable Hydraulic Fracturing

**AB C**

**Xf1**

**Well #2**

**Figure 4.** DEM model setup and dimensions. A) Full model - only the middle section in green contained fractures; B) Middle section natural fracture pattern for the '180°' model; and C) Middle section natural fracture pattern for the '145°' model. The location of simulated hydraulic fractures are represented by the black lines. Horizontal wellbores are

**Case Name** '180°' '145°' **Matrix Young's modulus** 27.6 GPa 27.6 GPa **Matrix Poisson's ratio** 0.25 0.25 **Fracture Set #1 Orientation** N180° N145° **Set#1 Trace Length, mean** 35m 35m **Set#1 Trace Length, st. deviation** 10m 10m

**Set#1 Gap Length** 5m 5m **Set#1 Spacing, mean** 2m 2m **Set#1 Spacing, st. deviation** 0.75m 0.75m **Fracture Set #2 Orientation** N90° N45° **Set#2 Trace Length, mean** 35m 35m **Set#2 Trace Length, st. deviation** 10m 10m

**DFN #1 DFN #2**

**Xf2**

**Well #1**

located along the full length of the left and right sides of the model.

**1200m**

Fig 4

For any numerical modeling, assumptions need to be made for the problem being simulated. For the simulations described in this paper, the following assumptions were made:


#### **2.4. Simulation matrix**

In total, nearly 100 simulations were performed in order to explore the behavior of the modified zipper-frac completion scheme. 20 simulations were performed to look at the shear results from a single hydraulic fracture with the '180°' (DFN#1 from Tables 1 and 2) varying the length of both fractures Xf1 and Xf2 separately (Xf1 represents the left-side hydraulic fracture - the solid black line in Figure 4 - and Xf2 represents the right-side hydraulic fracture – the dashed lines in Figure 4) from 25m to 125m in 25m increments with a friction angle of 15 degrees (10 simulations) and repeating these with a 25 degree friction angle (10 simulations). Then 60 simulations were performed to look at the efficacy of the modified zipper-frac completion by performing simulations with dual hydraulic fractures with both DFN models (the '180°' and '145°') varying the length of Xf2 (0m, 50, 75m, 100m, and 125m) for a constant Xf1 of 125m length for three separation spacings (20m, 35, and 45m, where separation is the horizontal offset of the Xf1 and Xf2 fractures as shown in Figure 4) and for two friction angles (15 degrees and 25 degrees in the '180°' model and 25 degrees and 35 degrees in the '145°' model). Finally, an additional 15 simulations were performed with the '180°' model varying the initial in-situ stress (see Table 2) and Xf2 length, and keeping the friction angle at 25 degrees.

**Figure 5.** Natural fracture shear (blue lines) for a 100m-long Xf1 hydraulic fracture. A) Shear for the 15° fracture fric‐

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**Figure 6.** Cumulative natural fracture shear (shaded area) from simulations at 25 to 125m hydraulic fracture half length. A) Shear for the 15° friction case with an area of 5740m2; and B) Shear for the 25° friction case with an area of

Figure 7 shows the growth of sheared natural fracture length as a function of hydraulic fracture half-length for the 15° and 25° natural fracture friction cases for all 20 single fracture simula‐ tions. Not surprisingly, given the slight variability in the statistics for natural fracture gener‐ ation, there are slight, insignificant differences between the results for the Xf1 and Xf2

tion case; and B) Shear for the 25° fracture friction case.

2220m2.

simulations.
