Numerical Construction And Flow Simulation In Networks Of Fractures Using Fractal Geometry

Abstract

Abstract Present models for the representation of naturally fractured systems rely on the double-porosity Warren-Root model or on random arrays of fractures. However field observation in outcrops has demonstrated the existence of multiple length scales in many naturally fractured media. The existing models fail to capture this important fractal property. In this paper, we use concepts from the theory property. In this paper, we use concepts from the theory of fragmentation and from fractal geometry for the numerical construction of networks of fractures that have fractal characteristics. The method is based mainly on the work of Barnsley and allows for great flexibility in the development of patterns. Numerical techniques are developed for the simulation of unsteady single phase flow in such networks. It is found that the pressure transient response of finite fractals behaves according to the analytical predictions of Chang and Yortsos, provided that there exists predictions of Chang and Yortsos, provided that there exists a power law in the mass-radius relationship around the test well location. Otherwise, finite size effects become significant and interfere severely with the identification of the underlying fractal structure. Introduction Fractal geometry is a relatively new approach for the description and modeling of complex objects and processes. In general, fractal images are the result of the repetition of a given geometric shape into itself over a cascade of different length scales. When coupled with random noise, the resulting complexity makes fractal images suitable for the description of a variety of natural objects. Although this should not imply that every suds object is fractal, nonetheless fractals constitute a very convenient method to describe many physical processes. In particular, the application of fractures to porous media is very promising. The review by Sahimi and Yortsos classifies promising. The review by Sahimi and Yortsos classifies the fractal patterns that result from various porous media processes, such as percolation, viscous fingering and fracturing. Networks of fractures in a rock are natural candidates for a fractal geometry description. This particular alternative is explored in this paper. Conventionally, naturally fractured systems have been represented by the Warren and Root double porosity model or by a random array of fractures. Although capturing important properties, neither of the two geometries can account for fractal characteristics recently attributed to naturally fractured systems. The relation of fractals to fracture networks was first explored in 1985, in a study of nuclear waste disposal. That study revealed that many fracture patterns at Yucca Mountain, NV, were self-repetitive over a range of scales, spanning from 0.2 to 15 meters, within which several generations of fractures were detected. Additional support for the fractal character of fracture networks can be found in recent studies of the fracture patterns of the Monterey formation and of the Geysers geothermal field. Prominent fractal features in the latter include the existence of a cascade of fracture scales and a self-similar structure. It was recently proposed that the fracturing of disordered media, such as natural rocks, can be modeled using fractals. Indeed, fractal structures have been related to the fracture resistance of the material and to the particular fracturing process it undergoes. particular fracturing process it undergoes.