A coupled fluid-diffusion and elasto-damage model for numerical simulation of hydraulic fracture

The study of hydraulic fracturing is still an important research topic today for the appropriate use and management of natural resources. This has led to the development of increasingly efficient and accurate numerical models, suitable for the study and analyses on this topic. The present work aims to develop a coupled fluid diffusion and rock deformation with damage model in order to simulate hydraulic fracture propagation in porous media. In the proposed model, a nonlocal integral-type continuum damage formulation is applied to describe the damage evolution under dynamic excitation. Furthermore, the mathematical representation of the solid is based on Biot’s theory and the definition of the effective stress for poro-damage-elasticity, together with generalized Darcy’s law for the fluid phase. Through the Galerkin method, the discrete coupled multi-field formulation of the partial differential equations was developed. The numerical solution of the initial-boundary value coupled problem in space was obtained by using the wellknown Finite Element Method (FEM) with inf-sup stable discretization while, for temporal integration, one–step generalized trapezoidal method. The fully coupled equations were solved monolithically using a Newton procedure, and the numerical results are validated against available experimental and numerical data.