A semi-analytical method for simulating matrix diffusion in numerical transport models

Abstract

A semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates.

Experimental Analysis of Mass Exchange Across a Heterogeneity Interface: Role of Counter‐Current Transport and Non‐Linear Diffusion

“…Further analytical solutions considered various fracture‐matrix configurations to represent natural systems more realistically (Sudicky & Frind, 1982; West et al., 2004). It was shown that the ratio of transversal dispersion flux in the fracture to the longitudinal diffusion flux in the matrix is the main controlling factor of the fracture‐matrix mass exchange rate (Falta & Wang, 2017; Houseworth et al., 2013; Roubinet et al., 2012). These studies assumed the interface coupling condition, the advective mass exchange across the interface and the dispersion in the matrix due to flow in the channel were negligible.…”

Impact of diffuse layer processes on contaminant forward and back diffusion in heterogeneous sandy-clayey domains

“…Due to the low hydraulic conductivity, advective flow is typically slow in such media, making them rather inaccessible for the groundwater flow. Therefore, mass transport in these low-permeability zones is known to be mainly controlled by diffusive mechanisms (e.g., Gillham et al, 1984;Mackay end Cherry, 1989;Harrison et al, 1992;Haggerty and Gorelick, 1995;Ball et al, 1997;Gusawa and Freyberg, 2000;LaBolle and Fogg, 2001;Parker et al 2004;Rasa et al, 2011;Rezaei et al, 2013;Yang et al, 2014;Parker and Kim, 2015;Falta and Wang., 2017;Lari et al, 2019). Thus, the presence of such low permeability regions within or at the boundary of a permeable aquifer can significantly enhance the persistence of contaminant plumes because the low-conductive regions can act as effective traps for the contaminants.…”

Two-Dimensional Solute Transport with Multiple Point Sources in Semi-infinite Porous Media

“…Singh et al [10] obtained analytical solutions for onedimensional solute dispersion with uniform and time varying dispersion in a semi-infinite aquifer using the Laplace transform technique. Falta and Wang [11] presented a semianalytical solution of one-dimensional advection-dispersion equation with matrix diffusion process by assuming the low permeability in semi-infinite domain. Yadav and Kumar [12] established a mathematical model for two-dimensional solute transport in a semi-infinite heterogeneous porous medium with spatially and temporally dependent coefficients for pulse type input concentration of varying nature.…”