No abstract

A 3D fully coupled hydromechanical model for the simulation of fluid-driven fracture propagation through poroelastic saturated media is presented and compared to several analytical or numerical benchmarks. The hydromechanical coupling in the porous matrix is derived within the framework of the generalized Biot theory and the fluid flow in the fractures satisfies the lubrication equation. The presence and propagation of fluid-driven fractures is handled with the extended finite element method and the propagation of the fluid-driven fractures is governed by a mixed linear cohesive law relying on a stable mortar formalism. A comparison between numerical results and a semi-analytical solution for plane fluid-driven fractures in porous media assess the validity of the proposed model. Then, a procedure for the propagation of fluid-driven fractures on non predefined paths is detailed. In particular, the fracture reorientation angle is computed exclusively from cohesive quantities. Various numerical experiments are performed to study the interferences between neighboring fluid-driven fractures as well as the reorientation of fluid-driven fractures under complex stress conditions. Finally, the model is extended to discontinuity junctions and an application to arrays of vertical fractures initiated from horizontal wells is presented.

In this paper, we present a robust procedure for the integration of functions discontinuous across arbitrary curved interfaces defined by means of level set functions for an application to linear and quadratic eXtended Finite Elements. It includes the possibility to have branching discontinuities between the different sub-domains. For the volume integration, integration subcells are built from the approximation mesh, in order to obtain an accurate approximation of the sub-domains. The set of subcells we get constitutes the integration mesh, which can also be used by the visualization tools. Then, we extract the faces of these integration subcells that coincide with the sub-domain boundaries, allowing us to perform surface integrations on the sub-domain boundaries. When combined with the eXtended Finite Element Method (XFEM) optimal convergence rates are obtained with curved geometries for both linear and quadratic elements.

No abstract