title: 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.
authors.affiliation: Department of Environmental Engineering and Earth Sciences, Clemson University, SC 29634-0919, United States. Electronic address: faltar@clemson.edu.
authors.forename: Ronald W
authors.initials: RW
authors.lastname: Falta
authors.affiliation: Department of Environmental Engineering and Earth Sciences, Clemson University, SC 29634-0919, United States.
authors.forename: Wenwen
authors.initials: W
authors.lastname: Wang
mesh_terms: D000538:Aluminum Silicates; D000077215:Clay; D003198:Computer Simulation; D004058:Diffusion; D060587:Groundwater; D062070:Hydrology / Q000379:methods*; D008962:Models, Theoretical; D010539:Permeability; D012822:Silicon Dioxide; D014874:Water Pollutants, Chemical
chemical_list: D000538:Aluminum Silicates; D014874:Water Pollutants, Chemical; D012822:Silicon Dioxide; D000077215:Clay
keywords: Matrix diffusion; Numerical modeling; Semi-analytical