Transport Equations for Fractured Porous Media: Fid-Bau Portal

Transport Equations for Fractured Porous Media

Shapiro, Allen M.

Abstract With the advent of analyzing geological settings as possible sites for hazardous waste isolation, the modeling of transport phenomena in fractured rock has been a topic of increasing interest. In studies to date, the means by which transport phenomena in fractured rock have been mathematically visualized has taken two distinct routes. The need for different conceptualizations of fractured rock has arisen due to the diverse nature of fracturing in rock formations. Usually, the length scale of a given transport problem, in relation to the intensity of fracturing, varies from one rock formation to the next. In some instances, there may exist only a few significant fractures (of a given fracture family) over the length scale of the transport problem. In other situations, the length scale of the transport problem may encompass large numbers of interconnected fractures. These observations have led to conceptualizations of fractured rock as either a system of individual and possibly interconnected fractures in a permeable or impermeable host rock, or as one or more overlapping fluid continua, in a manner similar to the mathematical treatment of granular porous materials. The assumptions implicit in the use of each of these conceptualizations are discussed in this chapter along with a selective review of the recent literature. A detailed analysis of the discrete fracture and continuum conceptualizations of fractured rock is provided by developing the appropriate equations of mass, momentum and energy transport for each conceptualization.