Contaminant transport in finite fractured porous medium: integral transforms and lumped-differential formulations

Mass transfer within saturated porous media with discrete finite fractures is examined, by simultaneously solving the convection–diffusion equation for the contaminant transport along the fracture and the two-dimensional diffusion equation for contamination within the porous matrix. A lumped-differential formulation based on Hermite integration is proposed for the porous matrix thus eliminating the dependence on the transverse direction. The resulting coupled partial differential equations are then handled through the generalized integral transform technique (GITT), which yields analytical expressions for the space dependence and numerical estimates for the concentration fields as a function of time. Different analytical filtering strategies are proposed and analyzed in terms of convergence rates. An illustrative example is considered for both the constant and time-variable contamination physical situations.