A robust 3D finite element framework for monolithically coupled thermo-hydro-mechanical analysis of fracture growth with frictional contact in porous media

This paper presents the formulation of a robust integrated framework for the coupled multiphysics and multiple fracture growth analysis in porous media. The finite element- based thermo-hydro-mechanical method for fracture growth with frictional contact (THMf-g) simultaneously solves monolithically coupled equations, incorporating contact and frictional constraints from fracture sliding. It also implements an adaptive process to update fields and geometries during fracture growth, effectively modeling emerging new surfaces. The thermohydro-mechanical fields are derived from fundamental principles of mass, momentum, and energy conservation and discretized numerically using the finite element method. Fractures are represented as sub-dimensional surfaces embedded within the volume of the porous medium. The growth of multiple fracture is modeled based on stress intensity factors at fracture tips, with fracture aperture and permeability emerging as dynamic properties of the system. The main novelty of this work lies in extending the implicitly solved monolithic coupling to include frictional and growth modeling for multiple non-planar fractures of emerging geometry in three dimensions. This includes the direct incorporation of cubic terms in the fracture flow equations and convection terms in the heat transfer equations, adopting an incremental method to solve these coupled, nonlinear equations. To ensure energy conservation, the heat equations are resolved using an implicit scheme, establishing a velocity dependency on pressure fields and introducing quadratic terms into the heat equation. Furthermore, the heat transfer equation has been revised to account for the work done on the fluid, enhancing the accuracy of thermal modeling. A contact mechanics leader-follower strategy tracks a conformal mesh split at each fracture, accounting explicitly for permeability changes during deformation and growth, effectively reducing computational complexity and cost. The iterative process for applying these constraints and the solution of the coupled THMf-g with friction and growth is described. The method does not require calibrated material properties or artificial length scale parameters, and relies on laboratory-measured properties with direct physical interpretation. A detailed algorithm is presented, including the updating of apertures and handling of new surfaces during the simulation, accounting for the variability of fracture permeability and its interplay with contact and friction during the non-linear solution. Several validating numerical experiments are benchmarked against analytical solutions, demonstrating the accuracy and reliability of the proposed framework in capturing complex fracture behavior and multiphysics interactions in porous media.