A Concept of Fuzzy Dual Permeability of Fractured Porous Media

Abstract

The interpretation of the results of hydrogeological field observations and the modeling of fractured porous subsurface media is often conducted using dual-porosity and/or dual-permeability concepts. These concepts, however, do not consider the effects of spatial and temporal variations and uncertainties, or fuzziness, in the evaluation of the subsurface flow characteristics of fractured porous media. The goal of the paper is to introduce a concept of fuzzy dual permeability of fractured porous media based on the fuzzy system analysis of the results of ponded infiltration tests in fractured basalt. The author revisited the results of the tests conducted in areas close to the Idaho National Laboratory (INL), Idaho, USA: small-scale (approximately 0.5 m2) ponded tests at the Hell’s Half Acre site, mesoscale (56 m2) ponded tests at the Box Canyon site, and a large-scale infiltration test (31,416 m2) at the Radioactive Waste Management Complex at INL. Methods of fuzzy clustering and fuzzy regression were applied to describe the time-depth waterfront penetration and to characterize the phenomena of rapid flow through a predominantly fractured component and slow flow through a predominantly porous matrix component. The concept of fuzzy dual permeability is presented using a series of fuzzy membership functions of the waterfront propagation with depth and time. To describe the time variation of the flux, a fuzzy Horton’s model is presented. The developed concept can be used for the uncertainty quantification in flow and transport in geologic media.