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A hydro-mechanical-damage fully coupled numerical method is developed for simulations of complicated quasi-brittle fracking in poroelastic media. A unified fluid continuity equation with crack-width dependent permeability, based on the Biot’s poroelastic theory, is used for simultaneous modeling of fluid flow in both fractures and porous media. The fluid pressure is coupled into the governing equations of the phase-field regularized cohesive zone model, which can automatically predict quasi-brittle multi-crack initiation, nucleation, and propagation without remeshing, crack tracking, or auxiliary fields as needed by other methods. An alternate minimization Newton–Raphson iterative algorithm is implemented within the finite element framework to solve the above three-fields coupled problem with nodal degrees of freedom of displacements, fluid pressures, and damages. The method is first validated by three problems with analytical solutions, a problem with experimental results, and a two-crack merging problem with numerical results in published literature, in terms of time evolutions of injected fluid pressures, crack widths and lengths, and final crack paths. Horizontal wellbore fracking problems with parallel hydraulic cracks and random natural fractures are then simulated, with the effects of spacing, number, and angle of perforations investigated in detail. It is found that the developed method is capable of modeling complex multi-crack fracking in both homogeneous media and heterogeneous media with natural fractures, and is thus promising for fracking design optimization of practical exploitation of shale gas and oil.
Li et al. (2022) studied this question.