Fractal theory and groundwater flow in fractured media

Numerous statistical models have been developed to study fluid flow in fractured media. However, the randomness assumption in these models is difficult to rationalize. In fact, experimentally and theoretically, it has been shown that rock fractures have predetermined paths of growth. Rock fracturing is a self-similar process in which properties of new fractures are controlled by the existing fractures. Unlike engineering materials, rock fracturing cannot be described by simple mathematical equations, neither by statistical models.; This research aims to develop a fractal model that overcomes limitations of the current statistical models. Iterated function systems (IFS) can create fractal objects. An arbitrary fracture set can be created by four “background” transformations and one “condensation set”. The challenge remains to identify the correct IFS whose attractor is “close” to limited field observations. An inverse fractal algorithm and associated graphical program provide the answer to this question. Subsequently, the fractal nature of fractures defines their hydraulic properties. Permeability tensors of all cells in a grid are calculated using “representative fractures”. The flow problem is then solved using a finite difference program (FLAC 2D). Limitations of the finite difference technique are discussed, as applied to fractured media. For a highly heterogeneous fracture network, it is recommended to use a discrete network model, as opposed to an equivalent continuum model.; In a physical experiment based on a Hele-Shaw model, good agreement was observed between the experiment and the fractal model. 30% difference in discharge was predicted due to the considerably smaller number of fractures in the experiment and the observations confirmed this prediction. As a practical example, some initial work on Yucca Mountain Project (YMP) showed that fracture patterns at this site have a fractal nature. The “shadow theorem of fractals” was used to simulate a fracture set with a fractal pattern.; This work opens new opportunities for fractal theory to be used in characterization of fractured media. The proposed model is a simple and easy to use technique that proved to be effective and accurate.