Published 1994 as part of Computer Applications 3
Copyright © 1994 The American Association of Petroleum Geologists.  All Rights Reserved.
 

The geometric characteristics of self-similar nested fractal structures are reviewed and the scaling laws are presented in terms of the fractal dimension, D. These scaling laws provide the basis for the determination of the "box dimension," equivalent to D, of a set of fractures from fracture maps or photographs. The results of this procedure are applied to a number of natural fracture sets, showing that fracture networks exhibit fractal characteristics over a wide range of scales. The widespread occurrence of fractal sets in fragmented materials is explained by a hierarchical model of fragmentation processes that leads to a fractal distribution of the resulting fragments. A method of generating synthetic fractal fracture networks based on a probabilistic form of iterated function systems is described and illustrated in realistic synthetic examples. The implications of a fractal character in fracture networks on flow processes in such networks is shown to result in "anomalous diffusion" of the pressure response in well tests, which results in pressure and pressure derivative plots with straight parallel lines on double logarithmic axes. The results of several well tests performed at The Geysers geothermal field are presented and shown to exhibit the characteristics expected for fractal fracture networks.