Hydromechanical modeling of hydraulic fracturing in poroelastic media using the extended finite element method

The process of hydraulic fracturing involves pumping a viscous fluid down a well into the underground formation at a high enough injection rate to fracture the formation and drive the fracture hydraulically. Interest in hydraulic fracturing is mainly because of its practical applications in a broad range of engineering areas. Hydraulic fracturing is the most commonly used stimulation technique of potential reservoirs. Although the main industrial use of hydraulic fracturing is to enhance the extraction of natural resources from hydrocarbon-bearing reservoirs, this technique is also applied for waste disposal, geothermal energy production, and so on. Obviously, investing in improving our scientific understanding of hydraulic fracturing not only enables greater access to formerly inaccessible resources, but also helps ensure that natural resources extraction does not come at the expense of public health and environment. Aiming at this goal, the objective of this research is to devise a reliable and robust simulation tool for hydro-mechanical modeling of hydraulic fracturing. For this purpose, a fully coupled numerical model is developed using the extended finite element method in conjunction with a cohesive crack model, which provides an effective means to describe the coupled hydro-mechanical processes occurring during the hydraulic fracture propagation and the nonlinear fracture processes developing along the fracture process zone

Hydro-mechanical modeling of two-phase fluid flow in deforming, partially saturated porous media with propagating cohesive cracks using the extended finite element method

In the present paper, a fully coupled numerical model is developed for the hydromechanical analysis of deforming, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non-wetting pore fluids. The governing equations involving the coupled two-phase fluid flow and deformation processes in partially saturated porous media containing cohesive cracks are derived within the framework of the generalized Biot theory. The displacement of the solid phase, the pressure of the wetting phase and the capillary pressure are taken as the primary unknowns of the three-phase formulation. A softening cohesive law is employed to describe the nonlinear behavior of the material in the fracture process zone. In order to account for the flux of the two fluid phases through the fracture faces, the mass balance equation for each flowing fluid inside the fully damaged zone and the cohesive zone is averaged over its cross section. The resulting equations provide mass couplings to the standard equations of the multiphase system. The effect of cracking and therefore change of porosity on the permeability of the damaged zone is also taken into account. To arrive at the discrete equations, the extended finite element method (XFEM) is utilized to discretize the weak form of the balance equations of mass and linear momentum in spatial domain along with the Generalized Newmark scheme for time domain discretization. By exploiting the partition of unity property of finite element shape functions, the evolving cohesive crack is simulated independently of the underlying finite element mesh and without continuous remeshing of the domain as the crack grows by adding enriched degrees of freedom to nodes whose support is bisected by the crack. For the numerical solution, the unconditionally stable direct time-stepping procedure is applied to solve the resulting system of strongly coupled non-linear algebraic equations using a Newton-Raphson iterative procedure. Finally, numerical simulations are presented to demonstrate the capability of the proposed method and the significant influence of the hydro-mechanical coupling between the continuum porous medium and the discontinuity on the results

Hydro-mechanical modeling of two-phase fluid flow in deforming, partially saturated porous media with propagating cohesive cracks using the extended finite element method

In the present paper, a fully coupled numerical model is developed for the hydromechanical analysis of deforming, progressively fracturing porous media interacting with the flow of two immiscible, compressible wetting and non-wetting pore fluids. The governing equations involving the coupled two-phase fluid flow and deformation processes in partially saturated porous media containing cohesive cracks are derived within the framework of the generalized Biot theory. The displacement of the solid phase, the pressure of the wetting phase and the capillary pressure are taken as the primary unknowns of the three-phase formulation. A softening cohesive law is employed to describe the nonlinear behavior of the material in the fracture process zone. In order to account for the flux of the two fluid phases through the fracture faces, the mass balance equation for each flowing fluid inside the fully damaged zone and the cohesive zone is averaged over its cross section. The resulting equations provide mass couplings to the standard equations of the multiphase system. The effect of cracking and therefore change of porosity on the permeability of the damaged zone is also taken into account. To arrive at the discrete equations, the extended finite element method (XFEM) is utilized to discretize the weak form of the balance equations of mass and linear momentum in spatial domain along with the Generalized Newmark scheme for time domain discretization. By exploiting the partition of unity property of finite element shape functions, the evolving cohesive crack is simulated independently of the underlying finite element mesh and without continuous remeshing of the domain as the crack grows by adding enriched degrees of freedom to nodes whose support is bisected by the crack. For the numerical solution, the unconditionally stable direct time-stepping procedure is applied to solve the resulting system of strongly coupled non-linear algebraic equations using a Newton-Raphson iterative procedure. Finally, numerical simulations are presented to demonstrate the capability of the proposed method and the significant influence of the hydro-mechanical coupling between the continuum porous medium and the discontinuity on the results

Flow Liquefaction Instability as a Mechanism for Lower End of Liquefaction Charts

The state-of-the-practice uses the “simplified procedure” for evaluating liquefaction susceptibility of soils. Based on this procedure, liquefaction charts have been developed that correlate soil resistance to earthquake-induced stresses. These charts are based on case histories of past earthquakes and have proven to be useful while evaluating liquefaction susceptibility at a new site. However, these charts are inherently empirical, which makes extrapolation into regimes with insufficient data difficult. In addition, they do not inform an engineer about the effects of liquefaction. This work hypothesizes that the lower end of liquefaction charts corresponds to soils that are susceptible to unstable flow liquefaction. A numerical investigation is undertaken, the results of which support this hypothesis. This implies that if test data at a new site correspond to the lower end of liquefaction charts, then the site may be susceptible to flow liquefaction. This in turn could provide an engineer with some predictive power regarding the effects of liquefaction