MethodsX (Jan 2023)
An X–FEM technique for numerical simulation of variable-density flow in fractured porous media
Abstract
Solute transport is one of the major topics in geological studies. Fracture is a significant characteristic of natural porous media, where the solute can transport due to its higher density with respect to the density of fluid. As the solute migrates in the medium, the density of the fluid changes with time. In this paper, the mass transport problem in the fractured porous media is modeled using the extended finite element method (X–FEM). An advection-diffusion equation is adopted to define the transport phenomenon in conjunction with the continuity equation of fluid. Transport regimes including diffusion, dispersion and advection are taken into the computational model. The presence of fractures within a porous medium substantially affects the transport behavior. In order to resolve the issue of discontinuity in the field variables, the X–FEM is implemented to discretize the discontinuity of medium. The Newmark integration scheme is adopted to discretize the governing equations in time domain. The nonlinear equations are solved by the Newton-Raphson iterative technique in a fully coupled manner. Finally, in order to illustrate the performance of the proposed computational model, two conventional problems, including the Schincariol problem and the Elder problem as well as the fractured Elder problem are solved numerically. Different patterns of fractures including horizontal and vertical intersecting cracks are adopted to study the effect of fracture density as well as the capability and versatility of the proposed computational model. The method is described in details and the pitfalls of the whole approach are demonstrated. • The density-driven fluid flow in naturally fractured porous media is modeled using an enhanced–FEM technique. • The effect of fractures (faults) in the porous medium is investigated by modeling the transport of saltwater in the fractured Elder problem. • The proposed computational model provides an accurate prediction of subsurface hydrology for a field-scale closed desert basin.
