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.

Pressure-transient tests in naturally fractured reservoirs often exhibit nonuniform responses, Various models explain such nonuniformity; however, their relevance is often not justified on a geologic basis. Fractal geometry provides a method to account for a great variety of such transients under the assumption that the network of fractures is fractal. This paper presents an application to real well tests in various fractured reservoirs. The physical meaning of the fractal parameters is presented in the context of well testing. Examples showing a behavior similar to the finite-conductivity fracture model or to spherical flow are presented and explained by the alternative of fractal networks. A behavior that can be mistakenly interpreted as a double-porosity case is also analyzed.

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 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 [1] 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 offinite fractals behaves according to the analytical predictions of Chang and Yortsos [6], 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.

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