Application of Fractal Geometry to the Study of Networks of Fractures and Their Pressure Transient

Abstract

Typical models for the representation of naturally fractured systems generally rely on the double‐porosity Warren‐Root model or on random arrays of fractures. However, field observations have demonstrated the existence of multiple length scales in a variety of naturally fractured media. Present models fail to capture this important property of self‐similarity. We first use concepts from the theory of fragmentation and from fractal geometry to construct numerically a network of fractures that exhibits self‐similar behavior over a range of scales. The method is a combination of fragmentation concepts and the iterated function system approach and allows for great flexibility in the development of patterns. Next, numerical simulation of unsteady single‐phase flow in such networks is described. It is found that the pressure transient response of finite fractals behaves according to the analytical predictions of Chang and Yortsos (1990) provided that there exists a power law in the mass‐radius relationship around the test well location. Finite size effects can become significant and interfere with the identification of the fractal structure. The paper concludes by providing examples from actual well tests in fractured systems which are analyzed using fractal pressure transient theory.