WCCM 2020: Nonlocal Continuum Modeling of Fluid Fracture in Porous Media

Abstract:

Fluid-driven fracture in porous media is achieved by applying large pressure on a deformable porous solid skeleton. The fracture process involves coupled mechanical failure as well as changes to transport properties (e.g. permeability) of the porous material. In this research, we propose a continuum non-local formulation for coupled damage and transport in porous media. The formulation is motivated from experimental observations and is based on thermodynamics principles. The non-local damage represents the extended micro-fracture network surrounding the macro-fracture. The non-local transport represents the long-range sub-scale capillary networks leading to fluid dissipation away from the macro-fracture. The non-local damage and transport contributions are introduced as contributors to the overall Free Energy, which is then used to derive the state laws and constitutive relationships. The non-local transportation definition proves analogous to the Darcy-Brinkman fluid flow which realizes second-order porosity and transport effects. The constitutive model definition features a stress-dependent damage and permeability functions that allow for capturing the material non-linear deformation and transport effects. A mixed finite element formulation is developed and the non-linear system of equations is solved monolithically in an implicit scheme.

The developed model is used to analyze benchmark problems such as hydraulic fracturing of geomaterials and damage enhanced consolidation. The model response is consistent with findings from previous studies, and the solution demonstrates mesh-independence. The developed continuum model allows for the exploration of physical phenomena beyond the capabilities of discrete fracture modeling, for example, quantifying the fluid leakoff from the sides of the macro-fracture.