Flow diversion around cavities in fractured media

Flow diversion around subsurface cavities in unsaturated fractured media is important to numerous environmental and engineering applications. This paper provides analytical solutions to partial and complete flow diversion around cavities intersected by fractures under steady state conditions. It is focused on a typical trifracture junction located upstream from a cavity surface. Fractures are modeled as two-dimensional porous media with an exponential relationship between the capillary pressure and unsaturated hydraulic conductivity. The solutions show that the vertical distance between the fracture end and the nearest junction (Z) and the slope of the unsaturated hydraulic conductivity ((alpha)) are by far the most important determinants of flow diversion. In fact, the product of Z and (alpha) enters the threshold flux and liquid entry flux equations as a dimensionless sorptive length (s). This relationship between Z and (alpha) is shown to have important implications for uncertainty and scalability of calibrated model parameters. The solutions given in this paper are expected to be directly applicable to cavities on the order of the fracture spacing.