Flow in unsaturated fractured porous media: Hydraulic conductivity of rough surfaces

The general trend in models for flow in unsaturated fractured porous media is to regard desaturated fractures as nonparticipating elements that impede flow. Mounting experimental and theoretical evidence shows that fractures retain and conduct liquid in the form of film and partially filled corner f low to a relatively low degree of saturation. A simple geometrical model fo r rough fracture surfaces is developed offering a tractable geometry for ca lculations of surface liquid storage due to adsorbed films and capillary me nisci. Assuming that under slow laminar flow the equilibrium liquid configu rations on the fracture surface are not modified significantly, the average hydraulic conductivities for film and corner flows were derived and used a s building blocks for a representative fracture roughness element and an as semblage of statistically distributed surface roughness elements. Calculati ons for a single representative element yielded excellent agreement with su rface storage and unsaturated hydraulic conductivity measurements of Tokuna ga and Wan [1997]. A statistical representation of surface roughness using a gamma distribution of pit depths resulted in closed-form expressions for unsaturated hydraulic conductivity averaged across the fracture length (tra nsverse to flow) or weighted by the liquid cross section occupying the frac ture surface. An important attribute of the surface roughness model is the direct link between fracture surface and matrix processes unified by the ma tric potential. The proposed model represents a first step toward developme nt of a comprehensive approach for liquid retention and hydraulic conductiv ity of unsaturated fractured porous media based on details of liquid config uration for different matric potentials.