Modeling mass transfer in fracture flows with the time domain-random walk method

Abstract

The time domain-random walk method was developed further for simulating mass transfer in fracture flows together with matrix diffusion in surrounding porous media. Specifically, a time domain-random walk scheme was developed for numerically approximating solutions of the advection-diffusion equation when the diffusion coefficient exhibits significant spatial variation or even discontinuities. The proposed scheme relies on second-order accurate, central-difference approximations of the advective and diffusive fluxes. The scheme was verified by comparing simulated results against analytical solutions in flow configurations involving a rectangular channel connected on one side with a porous matrix. Simulations with several flow rates, diffusion coefficients, and matrix porosities indicate good agreement between the numerical approximations and analytical solutions.

Breakthrough Investigation of Advective and Diffusive Transport in a Porous Matrix with a Crack

“…[14] derived an analytical solution for what they call velocity dispersion, i.e., dispersive effects caused by the velocity distributions. The topic is more recently been re-examined using domain-random walk numerical method [15]. Natarajan et al [16] explored a sinusodial fracture geometry.…”