Low-conductivity Fractures in an Unsaturated Porous Medium

Many flows observed in subsurface rock formations are unsaturated flows through a medium containing fractures. In cases where the fracture voids are small and nonconnective, one finds that little flow occurs within those voids. Under these conditions, the fractures act as barriers which impede background flow in the underlying matrix. From a computational point of view, discrete modeling of these fractures in flow simulations is impractical not only due to the small size of the fractures, but also because the fractures often represent singularities in the flow field. In general, the background flow through unsaturated porous media is highly nonlinear because of the strong dependence of the hydraulic conductivity on the suction head. For analytical studies, a two-parameter exponential model for the conductivity has been used in conjunction with a Kirchhoff transformation to cast the nonlinear governing equation into a linear form which is more amenable to solution. In this research, simple problems were analyzed using a boundary element numerical implementation of this transformation approach which was applied to characterize the influence of fractures upon the effective hydraulic conductivity of the medium.