Groundwater age in fractured porous media: Analytical solution for parallel fractures

We present an analytical solution to describe mean groundwater age in a conceptualized 2D system involving parallel fractures in a porous matrix. The solution is obtained by a perturbative approach and takes into account advection and longitudinal mechanical dispersion in the fracture, molecular diffusion in both media and constraints at the water inflow boundary. Far from the inflow boundary, the solution for the age of water in the porous matrix is one-dimensional, and depends on the distance between the fractures and the diffusion coefficient. In the fractures and far from the inflow boundary, the contribution of the porous medium to the age of water depends only on the ratio of fluid volume in the respective regions, a result consistent with known behavior in ideal aquitard–aquifer systems. The analytical solution developed in this paper is also suitable for evaluating the accuracy of numerical models