Contaminant transport in fractured porous media: Steady state solutions by a boundary integral method

The problem of steady state transport of a decaying contaminant in a fractured porous rock matrix by two‐dimensional diffusion and vertical advection is solved using a powerful (and readily generalizable) numerical method. Worst case predictions of contaminant penetration are obtained by assuming that the uniform porous medium contains either a single vertical fracture or a periodic array of vertical fractures. The method requires construction of appropriate Green's functions, which are here obtained analytically in both the fracture and matrix regions. Application of Green's theorem in the plane then yields representations for the contaminant concentration in both regions in terms of integrals along their boundaries of known quantities and the unknown fracture‐matrix interfacial flux. This flux is given by a Fredholm integral equation which can be solved numerically to great accuracy using a simple discretization technique. At sufficiently large distances vertically from the source the concentration is observed to be exponentially decaying. Although the concentration can, in general, only be obtained numerically, an analytical method is developed which produces a uniformly valid and extremely accurate approximation to its vertical decay length. Also, an assessment of the accuracy of analytical approximations made by various authors to solution of the full problem is provided. The parameter space of validity of these simpler psuedo‐two‐dimensional models is determined.