Application of the Variational Fracture Model to Hydraulic Fracturing in Poroelastic Media

Abstract

Hydraulic fracturing has persisted through the use of simple numerical models to describe fracture geometry and propagation. Field tests provide evidence of interaction and merging of multiple fractures, complex fracture geometry and propagation paths. These complicated behaviors suggest that the simple models are incapable of serving as predictive tools for treatment designs. In addition, other commonly used models are designed without considering poroelastic effects even though a propagating hydraulic fracture induces deformation of the surrounding porous media. A rigorous hydraulic fracturing model capable of reproducing realistic fracture behaviors should couple rock deformation, fracture propagation and fluid flow in the both the fracture and reservoir. In this dissertation, a fully coupled hydraulic fracturing simulator is developed by coupling reservoir-fracture flow models with a mechanical model for reservoir deformation. Reservoir-fracture deformation is modeled using the variational fracture model which provides a unified framework for simultaneous description of fracture deformation and propagation, and reservoir deformation. Its numerical implementation is based on a phase-field regularized model. This approach avoids the need for explicit knowledge of fracture location and permits the use of a single computational domain for fracture and reservoir representation. The first part of this work involves verification of the variational fracture model by solving the classical problem of fracture propagation in impermeable reservoirs due to injection of an inviscid fluid. Thereafter, the developed reservoir-fracture model is coupled to the mechanical model. Iterative solution of the variational fracture model and the coupled flow model provides a simplified framework for simultaneous modeling of rock deformation and fluid flow during hydraulic fracturing. Since the phase field technique for fracture representation removes the limitation of knowing a priori, fracture direction, the numerical solutions provide a means of evaluating the role of reservoir and fluid properties on fracture geometry and propagation paths. First, the proposed approach is validated for simple idealized scenarios for which closed form solutions exist in the literature. Further simulations highlight the role of fluid viscosity and reservoir properties on fracture length, fracture width and fluid pressure. Numerical results show stress shadowing effect on multiple hydraulic fracture propagation. Finally, the effect of in situ stress on fracture propagation direction is reproduced while the role of varying reservoir mechanical properties on fracture height growth is investigated.