UPSCALING OF CONSTITUTIVE RELATIONS IN UNSATURATED HETEROGENEOUS TUFF MATRIX

Abstract

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 steady-state 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.