Analytic solutions of radionuclide transport with the limited diffusion from the fracture into a porous rock matrix

To identify the effect of the limiting zone for the matrix diffusion from an open fracture into surrounding medium recently found from field studies, full analytic solutions are derived. The solutions are then verified with existing solutions and a numerical inversion of the Laplace transform approach. The relevant field data are collected and then numerical evaluations are pursued for these complicated analytic solutions with multiple integrals. Numerical results illustrate that for given data sets the effect of limiting zone for the rock matrix diffusion can be negligible so that the current infinite rock model may underestimate the radionuclide transport through fractured porous rock.