**6. Constraining the hydraulic fracture propagation in the horizontal direction**

 A major shortcoming in most of the current hydraulic fracture simulators is the assumption that shale reservoirs at the scale of the wellbore are subjected to a homogeneous stress environment. Hence, hydraulic fracture stages were designed based on a constant stress field, in terms of magnitude and orientation. Unfortunately, lateral stress gradients, and their effects on microseismicity, have evidenced a more complex situation. The origins of these lateral stress gradients are numerous and include variation of the rock geomechanical properties, pressure depletion around existing wells, and proximity to faults and their associated natural fracture systems.

 A decoupled approach using a plane strain framework to capture the lateral stress gradients was used by Aimene and Ouenes [11]. Their geomechanical modeling uses as input the three key factors affecting the lateral stress gradients: rock elastic properties, reservoir pressure, and natural fractures. The elastic properties and reservoir pressure models derived in previous sections from surface drilling data are used as inputs for the geomechanical model. The model uses explicit fractures to describe the distribution of the natural fractures then simulates the proper initial stress conditions resulting from the various sources of stress variability followed by the simulation of hydraulic fracturing in this heterogeneous stress medium. Since microseismic data is limited to only a few wells, the geomechanical approach used to capture the lateral stress gradients must be able to predict microseismicity rather than use it as calibration. The resulting geomechanical simulation predicts the differential stress, stress rotations and strain which serves as a reasonable proxy for microseismic events for validation as shown in **Figure 5**.

#### **Figure 5.**

*Differential stress (A) and strain (C) validated with microseismicity (B) and the resulting geomechanically constrained hydraulic fractures (D).* 

 This geomechanical approach combines the advantages of the particle-based numerical method, Material Point Method (MPM), a meshless numerical method, and the CFM approach to solve for a general continuum mechanics problem where all reservoir realities (natural fractures, variable rock properties and reservoir pressure heterogeneity), can be accounted for when estimating the stress field prior to stimulation and its subsequent perturbation during hydraulic fracturing. A direct benefit of this geomechanical approach is the quick estimation of the differential stress.
