Contaminant Transport in Fractured Porous Media: Analytical Solution for a Two‐Member Decay Chain in a Single Fracture

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Abstract
An analytical solution is presented for the problem of radionuclide chain decay during transport through a discrete fracture situated in a porous rock matrix. The solution takes into account advection along the fracture, molecular diffusion from the fracture to the porous matrix, adsorption on the fracture face, adsorption in the rock matrix, and radioactive decay. The solution for the daughter product is in the form of a double integral which is evaluated by Gauss‐Legendre quadrature. Results show that the daughter product tends to advance ahead of the parent nuclide even when the half‐life of the parent is larger. This is attributed to the effect of chain decay in the matrix, which tends to reduce the diffusive loss of the daughter along the fracture. The examples also demonstrate that neglecting the parent nuclide and modeling its daughter as a single species can result in significant overestimation of arrival times at some point along the fracture. Although the analytical solution is restricted to a two‐member chain for practical reasons, it represents a more realistic description of nuclide transport along a fracture than available single‐species models. The solution may be of use for application to other contaminants undergoing different types of first‐order transformation reactions.