**5. Predicting the shape of the stimulated reservoir volume**

little improvement with further stimulation. It is important to note that this result does not take into account the possibility of injecting proppant to maintain the conductivity of fractures

**Figure 9.** Relative well productivity for wells of all orientations based on the fractures observed in all three wells. (a) Ambient condition. (b) After 20-MPa stimulation. Natural fractures are shown as poles to the fracture surfaces (black dots). Green circles are computed optimal orientations of wells with highest productivity from natural fractures based

(a) (b)

**Figure 10.** Reservoir flow properties changes with time due to natural fracture stimulation for studied fault block. The blue curves are showing the productivity changes when pressure increases during stimulation, the green curves are showing productivity changes during flowback and production. (a) no stimulation (b) 30-MPa stimulation (c) 50-MPa stimulation (d) number of stimulated (shear slip) natural fractures. Fracture properties: cohesion=0, sliding fric‐

which open at pressures above 40 MPa.

on the fracture and stress analysis.

1028 Effective and Sustainable Hydraulic Fracturing

tion=0.6.

Fracture stimulation modeling showed that the shear slip of natural fractures could be effective in improving reservoir properties. Next, we need to reproduce the affected productive volume in the reservoir using the "shear stimulation" concept to enable more accurate production prediction. At the present no commercial simulator can fully model this process in 3D, although some research simulators have been developed. It was decided to use two different commercial models to simulate both fracture network stimulation created by low-viscosity frac fluid and the growth of the main hydraulic fracture. A commercial dual-porosity, dualpermeability simulator is used to simulate the flow property changes of natural fractures due to the shear slip. A commercial hydraulic fracturing design and evaluation simulator is used to model the geometry and conductivity of the principal hydraulic fracture filled with proppant. The modeling in two separate simulators is coupled by the fluid volume used for stimulation. The fluid volume leaked off in the shear-dilated natural fracture network was estimated in the dual-permeability, dual-porosity flow simulator. By adjusting the pressuredependent leak-off coefficient, the fluid volume leaked off in the hydraulic fracturing simu‐ lator was matched with the fluid volume leaked into natural fractures networks estimated by the flow simulator. The prediction of the stimulated reservoir volume is discussed in the rest of this section and the hydraulic fracturing design will be discussed in next section.

To predict the extent and properties of the stimulated volume by a dual-permeability, dualporosity simulator, a finely gridded model (Model A) was created based on the original reservoir model. The main function of this model is to simulate the change in flow properties in every single frac stage during and immediately after injection. The model is initialized with average known reservoir characteristics such as matrix porosity and permeability, fracture permeability and initial pressure, characterized from core and log analysis. Although different cases have been tested in the study, only one of the most realistic cases will be discussed here: the average matrix porosity used in the initial model is ~7.4%, matrix permeability is 0.07 mD in all directions, and the initial fracture permeability is ~ 0.2 mD. The initial fracture permea‐ bility is set close to the lower bound of fracture permeability based on core and log analysis. The orientations of the principal flow directions were chosen to correspond to the principal directions of the fracture sets and of bedding, which also approximately corresponded to the principal stress directions.

The relative magnitudes of the permeability enhancements in different directions were constrained by the geomechanical analysis. A set of permeability-pressure tables for different directions were then used to describe the hysteretic rock behavior that results from shear fracture activation. Although the fracture properties during stimulation can be estimated as described in the previous section, it is better to calibrate and constrain the permeabilitypressure relationship based on real lab or in-situ tests, e.g., using a pre-stimulation injectivity test [4]. The injectivity test should ideally be conducted in the open hole using slow injection to evaluate the potential natural fractures being stimulated, as permeability changes could then be interpreted based on the flow-rate/pressure changes along with the reservoir pressure. Because the D3 well has already been cased it was impossible to conduct such a test in the field before the actual treatment is carried out. Consequently, it was decided to produce a perme‐ ability-pressure table based on experience from shale gas reservoirs. Based on this table, on fracture density in different directions and on the stress anisotropy, a composite transmissi‐ bility multiplier was produced for the prediction of properties and extent of the stimulated reservoir volume. Transmissibility multipliers were different for each of the I, J and K direc‐ tions; those directions were aligned as discussed above with the primary structural fabric and stresses. The propagation of the pressure and fluid front in these directions can be controlled by modifying these multipliers.

Figure 11 shows diagrammatically the relationship between the permeability multiplier and the pore pressure (green curve). A slow increase in the permeability multiplier with increasing pressure occurs until fractures begin to slip. Above this pressure, the injectivity increases rapidly as an increased number of fractures are stimulated. During decreasing injection pressure in the injectivity test, the injectivity should decrease more slowly, retaining behind a permanent injectivity increase. The post-stimulation response can also be extrapolated to pressures below the original reservoir pressure. This makes it possible to predict the reservoir's response to depletion, which could lead to improved predictions of production decline. When the pressure during stimulation exceeds the minimum horizontal stress, extensional hydro‐ fracs are created, and the permeability-pressure relationship does not follow the green line. Three different flow paths (A, B, C) were assumed for conditions with pressure above Shmin, and the intermediate path, B was chosen to be used in the simulation.

The result of this modeling work is a 3D induced permeability map that describes the stimu‐ lated rock volume as discrete blocks, each with a unique permeability. The stimulated rock volume is therefore described not as a geometrical shape with identical flow properties throughout, but as a rock body with variable induced permeability, as shown in Figure 12.
