A hybrid immersed boundary-lattice Boltzmann/finite difference method for coupled dynamics of fluid flow, advection, diffusion and adsorption in fractured and porous media

In this paper, a hybrid immersed boundary-lattice Boltzmann/finite difference method is extended to simulate the coupled dynamics of fluid flow, advection, diffusion and adsorption in fractured and porous media which can describe gas migration and adsorption in the cleat-matrix system of coal. The numerical method includes three important components: fluid solver, advection-diffusion solver, and immersed boundary method for fluid-solid interaction with coupled mass exchange. In the fluid solver, the single-relaxation time lattice Boltzmann method is adopted for the fluid dynamics, and immersed boundary method is employed to achieve the no-slip boundary conditions at the fluid-solid interface. The advection-diffusion equation is solved by using the finite difference method, with immersed boundary method for the Neumann boundary conditions. This integrated method is extremely efficient for flows involving complex geometries and large deformation problems, as usually encountered in geosciences. Benchmark studies including the lid driven cavity flow, heat transfer around a stationary cylinder, and gas migration with adsorption in a channel are conducted to validate the efficiency and accuracy of the current solver. It is found that results predicted by our solver are in good agreement with published data achieved by other numerical or analytical methods, showing that the current method is robust and capable to solve the fluid-solid interaction and mass exchange involving complex geometries in geosciences. Finally, this method is employed to model gas migration in the cleat-matrix system of coal, involving the process of kinetic adsorption. This contribution is the first development of its kind for solving problems in geosciences. It is held in a generic numerical formulation so that can be applied to many fields of geosciences involving fluid flow and reaction diffusion through fractured rocks, gas storage in geological formations, groundwater contaminant studies, geothermal and resource applications.