One of the challenges of the hydraulic fracturing operation is the determination of the fluid-driven vertical fracture extent. In cases such as cuttings re-injection and CO2 sequestration fractures must be contained mainly to the pay zone since fracture breakout into overlaying or underlying formations with water-bearing zone can lead to irreparable water damage to the formation, Cormack et. al, (1983). Numerical modelling of hydraulic fracturing can reduce uncertainties in the reservoir integrity. Parametric studies help define critical conditions and predict the most favorable scenarios. In this work, a fully coupled cohesive fracture model is used to simulate hydraulic fracturing processes considering the propagation of a vertical planar fluid-driven fracture for a transient analyses. This paper is focused on the pressure required for crack extension and on the resulting fracture geometry considering the injection procedure as a concentrated fluid flow. The influence of the vertical variation in tectonic stress, the elastic stiffness and the critical stress intensity factor on the fracture behavior are investigated. A finite element model with coupled cohesive elements was used for the simulation of rock fracture. Symmetrical (no vertical variation in tectonic stress) and asymmetrical (vertical variation in tectonic stress) tri-layered formations were studied and compared to the analytical solutions proposed by Simonson (1977) and Fung (1987). According to these results, the predicted pore pressure for crack propagation exhibits good agreement with the analytical solutions. As expected, the mechanism of fracture containment has proven to be the vertical variation in tectonic stresses and critical stress intensity factor. On the other hand, the contrasts in the elastic stiffness do not act as effective barriers to vertical fracture propagation.

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