Phase-field modeling of proppant-filled fractures in a poroelastic medium

Phase-field Modeling of Pressurized Fractures in a Poroelastic Medium

In this paper we present an incremental formulation of the phase field model for a fluid filled crack in a poroelastic medium. The mathematical model represents a linear elasticity system with fading elastic moduli as the crack grows that is coupled with an elliptic variational inequality for the phase field variable. The convex constraint of the variational inequality assures the irreversibili...

Phase-field modeling of a fluid-driven fracture in a poroelastic medium

A Phase-Field Method for Propagating Fluid-Filled Fractures Coupled to a Surrounding Porous Medium

The recently introduced phase-field approach for pressurized fractures in a porous medium offers various attractive computational features for numerical simulations of cracks such as joining, branching, and non-planar propagation in possibly heterogeneous media. In this study, the pressurized phase-field framework is extended to fluid-filled fractures in which the pressure is computed from a ge...

Partially Saturated Flow in a Poroelastic Medium

The formulation and existence theory is presented for a system modeling diffusion of a slightly compressible fluid through a partially saturated poroelastic medium. Nonlinear effects of density, saturation, porosity and permeability variations with pressure are included, and the seepage surface is determined by a variational inequality on the boundary.

Indentation of a Sharp Penetrometer in a Poroelastic Medium

Solution is developed for the build!up\ steady and post!arrest dissipative pore ~uid pressure _elds that develop around a conical penetrometer advanced in a poroelastic medium[ The analog with cone penetrometer testing is direct\ and is used to enable continuous distributions of permeability and di}usivity to be determined\ with depth[ Solution for a point normal dislocation migrating in a poro...