On thermohydrologic conditions near high‐level nuclear wastes emplaced in partially saturated fractured tuff: 2. Effective continuum approximation

Abstract

This paper presents an effective continuum approximation for modeling of fluid and heat flow in fractured porous media. The approximation is based on the thermohydrologic behavior observed in detailed simulations with explicit consideration of fracture effects (see the companion paper, part 1.) The crucial concept in the development of an effective continuum approximation is the notion of local thermodynamic equilibrium between rock matrix and fractures. Where applicable it provides a substantial simplification of the description of fluid and heat flow in fractured porous media. We derive formulas for effective continuum characteristic curves (relative permeabilities and capillary pressures) in terms of the properties of fracture and matrix continua, respectively. Numerical simulations demonstrate that under favorable conditions the effective continuum approximation closely matches predictions obtained from an explicit modeling of fracture effects. It is also demonstrated that the approximation breaks down under unfavorable conditions (very tight rock matrix). A simple criterion for the applicability of an effective continuum approximation is derived from consideration of diffusive processes. A quantitative evaluation shows the criterion to be consistent with results of our numerical simulations.