Thermo‐hydro‐mechanical modeling of fracturing porous media with two‐phase fluid flow using X‐FEM technique

Abstract

In this paper, a fully coupled thermo-hydro-mechanical model is presented for two-phase fluid flow and heat transfer in fractured/fracturing porous media using the extended finite element method. In the fractured porous medium, the traction, heat, and mass transfer between the fracture space and the surrounding media are coupled. The wetting and nonwetting fluid phases are water and gas, which are assumed to be immiscible, and no phase-change is considered. The system of coupled equations consists of the linear momentum balance of solid phase, wetting and nonwetting fluid continuities, and thermal energy conservation. The main variables used to solve the system of equations are solid phase displacement, wetting fluid pressure, capillary pressure, and temperature. The fracture is assumed to impose the strong discontinuity in the displacement field and weak discontinuities in the fluid pressure, capillary pressure, and temperature fields. The mode I fracture propagation is employed using a cohesive fracture model. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. It is shown that the effect of thermal expansion on the effective stress can influence the rate of fracture propagation and the injection pressure in hydraulic fracturing process. Moreover, the effect of thermal loading is investigated properly on fracture opening and fluids flow in unsaturated porous media, and the convective heat transfer within the fracture is captured successfully. It is shown how the proposed computational model is capable of modeling the fully coupled thermal fracture propagation in unsaturated porous media.

Modeling non‐isothermal two‐phase fluid flow with phase change in deformable fractured porous media using extended finite element method

“…The above system of equations is then discretized in time using the generalized Newmark scheme. 45 Indeed, the governing equations are fully coupled; however, couplings of the hydromechanical and thermal partitions are not strong in the scope of this study. Hence, the staggered solution method is implemented, in which the hydromechanical equations and the energy conservation equation are solved separately and consecutively in an iterative manner to achieve the convergence of the final solution for the fully coupled system of equations at each time step.…”

“…The above system of equations is then discretized in time using the generalized Newmark scheme 45 . Indeed, the governing equations are fully coupled; however, couplings of the hydromechanical and thermal partitions are not strong in the scope of this study.…”

“…Iranmanesh and Pak 44 proposed the element free Galerkin (EFG) method together with the extrinsic enrichment strategy to model discontinuities in the THM problems. Recently, Khoei and Mortazavi 45 developed a coupled THM model for fracturing porous media with two‐phase fluid flow using the X‐FEM, where the evaporation and condensation of water was disregarded. In the present study, the work of Khoei and Mortazavi 45 is extended to investigate the influence of phase change in nonisothermal process of fractured unsaturated porous media.…”

“…Recently, Khoei and Mortazavi 45 developed a coupled THM model for fracturing porous media with two‐phase fluid flow using the X‐FEM, where the evaporation and condensation of water was disregarded. In the present study, the work of Khoei and Mortazavi 45 is extended to investigate the influence of phase change in nonisothermal process of fractured unsaturated porous media. To this end, a computational model is presented for the analysis of coupled thermo‐hydro‐mechanical process with phase change, that is, evaporation and condensation, in fractured porous media using the X‐FEM.…”

Preconditioners for multiphase poromechanics with strong capillarity

“…Modeling multiphase poromechanics with capillarity requires the solution of a coupled system of nonlinear algebraic equations 31,44–49 . Here, we consider fully‐implicit methods in which all governing variables are updated simultaneously.…”