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Hydraulic Fracturing is a widely used method for enhancing oil exploitation in petroleum industry. In this method, some artificial fractures are induced in the reservoir by fluid injection and the overall rock permeability is increased. The geometry of the induced fracture is dominated by the rock's mechanical properties, in-situ stresses, and local heterogeneities such as natural fractures and weak bedding planes. From the mathematical point of view it is a coupled hydro-mechanical problem, where equations for fluid flow through porous media and fractures (fluid mass balance) and medium deformation and fracture propagation (mechanical problem) have to be solved simultaneously considering the constitutive equations that describe the material behavior. When a fracture propagates through a continuous media, discontinuities in the displacement and fluid pressure fields are introduced.

The selection of an appropriate fracture propagation model is a critical task in modeling of hydraulic fracturing. From the numerical point of view, the strong discontinuity approach can be introduced in two distinct ways. The first one is a technique to embed the discontinuities into the finite element, the discontinuity path is placed inside the elements, irrespective of size and specific orientation of them. In addition, mesh refinement is not necessary to capture these discontinuities and the simulation can be done with relatively coarse meshes in a reasonable computational time. The second way is to introduce solid finite elements with high aspect ratio, finite elements which have one edge much smaller than the others. These elements have similar kinematic fields of the strong discontinuity approach and can be used as interface elements.

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