Upscaling of constitutive relations in unsaturated heterogeneous tuff matrix

When numerical models are used for modeling large-scale flow and transport processes in the subsurface, upscaling is generally needed to determine large-scale hydraulic properties from small-scale measurements. This study is focused on the upscaling of constitutive relations (among relative permeability, capillary pressure, and saturation) for unsaturated tuff matrix (or a porous medium with a large air entry value). Unsaturated flow in tuff matrix is of interest at a number of existing and proposed waste disposal sites, as well as in connection with environmental contamination in arid and semiarid regions. Based on the notion that a large air entry value corresponds to a spatially uniform capillary pressure distribution, even at a relatively large scale for steadystate unsaturated flow, we present an upscaling approach for constitutive relations of tuff matrix. Numerical experiments were used to verify and demonstrate the usefulness of the approach.