ABSTRACT:

A number of problems involving flow through rock masses need to be analyzed by fracture flow models rather than equivalent porous medium models. The authors, and others, have developed two- and three-dimensional fracture flow models. In this paper, computational comparisons are made. They show that different fracture geometries lead to considerably different conductivities, that three dimensional modelling leads to higher conductivities than two dimensional modelling, and that equivalent porous medium or even stochastic continuum approaches are not generally applicable to fracture flow problems. Possible approaches for modeling channeling in fractures are presented.

RESUME:

C'est bien connu que les problèmes d'ecoulement en masses rocheuses doivent etre analyses avec des modèles d'ecoulement en fissures au lieu de modèles utilisant une masse poreuse equivalent. Les auteurs et des autres chercheurs ont developpe des mod les d'ecoulement en fissures en deux et trois dimensions, dont quelques-uns sont compares sur la base de resultats calcules. Ces resultats montrent que des geometries de fissures differentes causent des conductivites très differentes, que les modèles en trois dimensions donnent des conductivites fortement superieures au modèles en deux dimensions, et que les modèles quasiporeux ou represantant un continu stochastique ne sont generalement pas appliquable aux problèmes d'ecoulement en fissures. Si, au lieu d'ecoulement en fissures il y a ecoulement canalise a l'interieur des fissures, c'est possible d'utiliser des modèles plus simples qui Sont presentes succinctement ci-après.

ZUSAMMENFASSUNG:

Es ist bekannt, dass das Durchstroemen von Fels meistens mit Kluftdurchstroemungsmodellen anstatt von Modellen fuer ein equivalentes poroeses Medium analysiert werden muss. Die Verfasser und andere Autoren haben zwei- und dreidimensionale Kluftdurchstroemungsmodelle enwickelt, von denen einige in diesem Artikel rechnerisch verglichen werden. Die Resultate zeigen, dass verschiedene Kluftgeometrien zu sehr verschiedenen Konduktivitaeten fuehren, dass dreidimensionale Modelle wesentlich hoehere Konduktivitaeten haben als zweidimensionale Modelle, und dass Modelle fuer ein equivalentes poroeses Medium oder auch stochastische Kontinuummodelle generell nicht fuer Kluftdurchstroemungsprobeleme anwendbar sind. Wenn anstatt von eigentlichem Kluftdurschstroemen kanalisiertes Durchstroemen auftritt, koennen einfachere Modelle, die hier skizziert sind, angewendet werden.

INTRODUCTION

The conventional assumption for hydrologic analysis in rock is that flow can be modeled by a porous medium. This is a reasonable assumption where flow is dominated by the rock matrix rather than fracture or joint porosity (the terms fracture and joint will be used interchangeably), or where jointing is sufficiently intense that a representative elementary volume can be defined. However, for an increasing number of practical problems in petroleum extraction, hazardous and nuclear waste disposal, and water resources engineering, the porous medium approximation is not reasonable. Discrete fracture flow models (e.g., Long et al., 1982, Rouleau, 1983, Dershowitz, 1984) were developed to directly model flow in fractured rock masses. This paper describes the development and application of three dimensional discrete fracture flow models, and the use of those models in conjunction with conventional continuum approaches.

THEORETICAL BACKGROUND

As in many rock mechanics applications, the first problem in hydrologic modeling of fractured rock masses is to characterize fracture system geometry. Fracture geometry conceptual models developed for other rock mechanics applications by Baecher et al. (1978) and Veneziano (1978) have been applied to the problem of discrete fracture flow modeling in two dimensions by Long (1983), Rouleau (1984), and Dershowitz (1984), and more recently in three dimensional models by Long et al. (1985) and Dershowitz et al (1986). Figures 1 through 3 illustrate three three dimensional discrete fracture system models: the Baecher (disk) model; the polygonal fracture model by Veneziano (1978) and the further developed polygonal model by Dershowitz (1984). In all of these models, as in most rock mechanics models, the fracture system is described by distributions of fracture orientation (dip and azimuth), size (trace length or fracture area), and intensity (fractures per unit volume). The polygonal fracture models require, in addition, the definition of an area persistence measure defining the degree of fracture coplanarity (as the percentage of a fracture plane consisting of open fractures), and the Dershowitz model also a fracture termination measure (the percentage of fracture terminations occurring at intersections with other fractures). Other three-dimensional fracture system models are the orthogonal model used by Snow (1965) and mosaic tesselation models discussed by. Dershowitz (1984) and Dershowitz et a1. (1987). The variety of fracture system models reflect the variety of geometries encountered in nature. Each of the above mentioned models can represent typical geometries and can also be explained by particular joint genesis mechanisms.

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