FRACFLO: Analytical solutions for two-dimensional transport of a decaying species in a discrete planar fracture and equidistant multiple parallel fractures with rock matrix diffusion

Abstract

Analytical solutions based on the Laplace and Fourier transformation techniques are derived for the transient advective-dispersive transport of a single radionuclide through fractures (two-dimensional analysis) and rock (one-dimensional analysis). The longitudinal dispersion-free solution is also reported. The geometry considered consists of either a single planar fracture (infinite diffusion in the rock) or a system of equidistant parallel fracture planes with uniform aperture (finite diffusion in the rock). The solution assumes that the ground-water flow regime is under steady-state and isothermal conditions, and the streamlines along the direction of flow are parallel. The solution related to the single fracture case was verified by comparing its performance with available results from other works. Two sets of solutions were derived for the multiple parallel fracture case; the first, based on a series approximation, and the second, based on contour integration, were designed to cope efficiently with small and large Fourier numbers, respectively. The general solution requires, in both cases, the evaluation of a single integral, except in the case of the solution based on contour integration, where an additional one is required. This is performed using a Gauss-Legendre quadrature scheme. 34 refs., 65 figs., 77 tabs.