Simulation of dynamic pulsing fracking in poroelastic media by a hydro-damage-mechanical coupled cohesive phase field model

Abstract

This study develops a hydro-damage-mechanical fully coupled numerical method capable of modelling complex fluid-driven transient dynamic crack propagation in quasi-brittle poroelastic media. In this method, the fluid flow in both fractures and porous media is described by a fluid continuity equation with the modified Darcy-Poiseuille law based on the Biot's poroelastic theory. The fluid pressure and the inertial force of solids are coupled by governing equations of the mesh-insensitive phase-field regularized cohesive zone model that can simulate quasi-brittle multi-crack initiation, propagation, branching and merging without remeshing or crack tracking. The resultant displacement-pressure-damage coupled multiphysics system of equations is solved using an alternative minimization Newton-Raphson iterative algorithm with an implicit Newmark integration scheme within the finite element framework. The new method was first validated by a few 2D problems, including crack branching and deflecting in solids, fracking in a concrete cube, and consolidation and stress wave propagation in poroelastic media, subjected to various impulsive loadings. It was then applied to pressure pulsing fracking of a 40 m granite rock reservoir with extensive parametric studies of fluid viscosity and pulsing injection rate, mode and period. It was found that pulsing injection with higher fluid rates and lower fluid viscosities resulted in more developed crack patterns, and in particular, there existed an optimal pulsing injection period that could promote fracking under relatively low injection pressures. 3D horizontal well problems with multiple non-planar crack propagation and bifurcation were also successfully simulated to demonstrate the capacity and potential of the new method for engineering design and optimization of pressure pulsing fracking.