Anomalous diffusion in simulations of pumping tests on fractal lattices
Published:January 01, 2005
Shaun Sellers, John A. Barker, 2005. "Anomalous diffusion in simulations of pumping tests on fractal lattices", Understanding the Micro to Macro Behaviour of Rock–Fluid Systems, R. P. Shaw
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The recent interest in fractals in the geosciences literature has led to several proposed theoretical models for the hydraulic testing of fractured-rock systems that exhibit a fractal-like geometric structure. There is, however, no agreement on the correct form of the resulting model equations. In order to gain some insight into the range of possible behaviours to be expected from pumping tests on such systems, as well as the type of theoretical models needed, extensive simulations of pressure diffusion for transient groundwater flow, modelled by random walks on both deterministic and random fractal lattices were performed. For simplicity, the focus was on measurements of the random-walk dimension for generalized Sierpinski carpets, a proposed model for porous and fractured media. In addition to the expected anomalous slow down in diffusion in fractals as measured by the random-walk dimension, the simulations show further novel and unexpected anomalous behaviour due to the presence of internal boundaries at all scales. None of the proposed theoretical models for pumping tests on fractals appears consistent with all of the observed anomalous behaviours. The simulations suggest that interpretation of experimental pumping tests in terms of well-defined non-integer dimensions can be difficult, even when finite-size effects are negligible.
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Understanding the Micro to Macro Behaviour of Rock–Fluid Systems
Understanding how fluids flow through though rocks is very important in a number of fields. Almost all of the world's oil and gas are produced from underground reservoirs. Knowledge of how they got where they are, what keeps them there and how they migrate through the rock is very important in the search for new resources, as well as for maximising the extraction of as much of the contained oil/gas as possible. Similar understanding is important for managing groundwater resources and for predicting how hazardous or radioactive waste or carbon dioxide will behave if stored or disposed of underground. Unravelling the complex behaviour of fluids as they flow through rock is difficult, but important. We cannot see through rock, so we need to predict how and where fluids flow. Understanding the type of rock, its porosity, the character and pattern of fractures within it and how fluids flows through it are important. Some contributors to this volume have been trying to understand real rocks in real situations and others have been working on computer models and laboratory simulations. Put together, these approaches have yielded very useful results, many of which are discussed in this volume.