Damage evolution and fluid flow in poroelastic rock

Abstract

We present a formulation for mechanical modeling of the interaction between fracture and fluid flow. Our model combines the classic Biot poroelastic theory and a damage rheology model. The model provides an internally consistent framework for simulating coupled evolution of fractures and fluid flow together with gradual transition from brittle fracture to cataclastic flow in high-porosity rocks. The theoretical analysis, based on thermodynamic principles, leads to a system of coupled kinetic equations for the evolution of damage and porosity. A significant advantage of the model is the ability to reproduce the entire yield curve, including positive and negative slopes, in high-porosity rocks by a unified formulation. A transition from positive to negative values in the yield curve, referred to as a yield cap, is determined by the competition between the two thermodynamic forces associated with damage and porosity evolution. Numerical simulations of triaxial compression tests reproduce the gradual transition from localized brittle failure to distributed cataclastic flow with increasing pressure in high-porosity rocks and fit well experimentally measured yield stress for Berea sandstone samples. We modified a widely used permeability porosity relation by accounting for the effect of damage intensity on the connectivity. The new damage-permeability relation, together with the coupled kinetics of damage and porosity evolution, reproduces a wide range of realistic features of rock behavior. We constrain the model variables by comparisons of the theoretical predictions with laboratory results reporting porosity and permeability variation in rock samples during isotropic and anisotropic loading. The new damage-porosity-permeability relation enables simulation of coupled evolution of fractures and fluid flow and provides a possible explanation for permeability measurements in high-porosity rocks, referred to as the “apparent permeability paradox.”