Contaminant transport in fractured porous media: Steady-state solutions by a Fourier sine transform method (Q1114537)

The steady-state transport of a decaying contaminant in a fractured porous rock matrix by two-dimensional diffusion and vertical advection is treated by a Fourier sine transform technique for the cases of a single vertical fracture and a periodic array of fractures. The general case of unequal Peclet numbers in the fracture and matrix regions is reduced to a first-kind Fredholm integral equation in the transformed interfacial flux. The asymptotic behavior of the solution for large and small vertical positions relative to the contaminant source is analyzed. For the special case of equal Peclet numbers an exact analytical expression for the steady-state concentration has been derived for an arbitrary source distribution. A method of calculating an accurate analytical approximate solution to the general mismatched Peclet number case is proposed, and its accuracy verified by comparison of its predictions with the exact numerical solution obtained by a boundary integral method.