The fractal geometry of flow paths in natural fractures in rock and the approach to percolation |
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| Authors: | D D Nolte L J Pyrak-Nolte N G W Cook |
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| Institution: | (1) Department of Physics, University of California, 94720 Berkeley, CA, USA;(2) Present address: AT&T Bell Laboratories, Crawfords Corner Rd., 07733 Holmdel, New Jersey, USA;(3) Department of Material Science and Mineral Engineering, University of California, 94720 Berkeley, CA, USA |
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| Abstract: | The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold. |
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| Keywords: | Fractals fractures fluid flow percolation rock mechanics geohydrology |
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