Thermodynamic framework for non-local transport-damage modeling of fluid driven fracture in porous media

Abstract

We present a novel non-local damage transport model for hydraulic fracture in porous media. The new model is sought to provide an enhanced description for the long-range damage and transport interactions in the fracture process zone. The non-local model is derived from thermodynamic principles, where a new thermodynamic potential expression for non-local transport is introduced. The thermodynamically consistent model is reduced to a gradient non-local permeability relationship that simultaneously provides a non-local transport description and regularized damage growth via a permeability-stress relationship. The analogy of the proposed model to Darcy-Brinkman fluid flow is demonstrated and discussed. A monolithic 3-field (u−P−κ˜) mixed finite element framework is then used to discretize and solve the nonlinear coupled physics poromechanics problem. The hydraulic fracture continuum models previously presented in the literature rely on using different fluid flow laws inside and outside the fracture zone, which introduces a discontinuity in the continuum model. Our model prescribes Darcy type fluid flow all over the domain with a non-linear permeability constitutive law that allows for elevated fluid velocity in the crack zone, which preserves the continuity of all quantities within the domain. The numerical examples confirm the capability of the proposed model in capturing the essential features of hydraulic fracture simulation. The significance of the non-local transport modeling is demonstrated through modeling hydraulic fracturing in materials with pre-existing high permeability zones. The incorporation of non-local transport effects in hydraulic fracture modeling is proved to uncover possible flow paths through pre-existing high permeability zones. The proposed model can act as a platform for quantifying the fluid leak-off from hydraulic fracture and can be further used to analyze the hydraulic fracture interaction with neighboring geological material.