A hydro-thermo-damage-mechanical fully coupled cohesive phase-field model for fracking in quasi-brittle thermo-poroelastic media

A hydro-thermo-damage-mechanical fully coupled cohesive phase-field method is developed for modelling of fracking in quasi-brittle thermo-poroelastic media. A new sigmoid interpolation function is proposed to characterize the transitional behaviour from porous media to cracks for permeability, specific heat capacity, and thermal conductivity. A fluid continuity equation with the Darcy-Poiseuille law and an energy conservation equation with the Fourier’s law are then used to simulate fluid flow and heat transfer in cracking porous media, respectively. The fluid pressure and temperature of fluids and solids are fully incorporated into the governing equation of the phase-field regularized cohesive zone model to efficiently simulate complicated quasi-brittle hydro-thermal fracking, without the need of remeshing, crack tracking or auxiliary fields. The resultant displacement–pressure-temperature-damage coupled multiphysics system of equations is solved using a staggered Newton–Raphson iterative algorithm within the finite element framework. The method is first validated by five two-dimensional thermally or hydro-thermally induced fracture examples with analytical solutions, experimental data, and published numerical solutions. Three-dimensional fracking and fluid circulation problems in a vertical five-spot wellbore system with complex natural fracture networks, are then simulated as an application to energy harvesting in enhanced geothermal systems (EGS). It is found that the present method is capable of accurately and robustly modelling complicated hydraulic fracture propagation and fluid circulation problems and has the potential to be used for fracking design and optimization of EGS.