A Single Continuum Approximation of the Solute Transport in Fractured Porous Media

Abstract

Solute transport in fractured porous media is described by the single continuum model, i.e., equivalent porous medium model. In this model, one-dimensional solute transport in the fracture and two-dimensional solute transport in the porous rock matrix is considered. The network of fractures embedded in the porous rock matrix is idealized as two orthogonally intersecting families of equally spaced, parallel fractures directed at 45-degrees to the regional groundwater flow direction. Governing equations are solved by the finite element method, and upstream weighting technique is used in order to prevent the oscillation of solution in case of highly advection dominated transport. The breakthrough curves similar to those of the one-dimensional solute transport problem in ordinary porous media are obtained as a function of time according to volume or flux averaging of the concentration profile across the width of the flow region. The equivalent parameters, i.e., porosity and overall coefficient of longitudinal dispersivity are obtained by trial-and-error method. Analyses for the non-sorbing solute transport case show that within the range of considered parameters, and except for the region very close to the source, application of the single continuum model in the idealized fracture system is sufficient for modeling the solute transport in fractured porous media. And this numerical scheme is shown to be applicable to the sorbing solute and radionuclide transport.