Fractal scaling and fluid flow in fracture networks in rock
- Geological Survey, St. Petersburg, FL (United States)
Recovery of oil and gas resources and injection of toxic waste materials requires quantitative models to describe and predict the movement of fluids in rock. Existing models based on pore-space flow are inappropriate for study of the more rapid process of fluid flow through fracture networks. This type of flow is not a simple function of the fracture characteristics at any particular scale, but rather the integration of fracture contributions at all scales. The mathematical constructs of fractal geometry are well suited to quantify and model relationships within complex systems that are statistically self-similar over a wide range of scales. Analyses show that fracture traces mapped on two-dimensional slices through three-dimensional nature fracture networks in rock follow a fractal scaling law over six orders of magnitude. Detailed measurements of 17 two-dimensional samples of fracture networks (at diverse scales in rocks of dissimilar age, lithology, and tectonic setting) show similar fractal dimensions in the range 1.3-1.7. The range in fractal dimension implies that a single physical process of rock fracturing operates over a wide range of scales, from microscopic cracks to large, regional fault systems. The knowledge that rock-fracture networks are fractal allows the use of data from a one-dimensional drill-hole sample to predict the two- and three-dimensional scaling of the fracture system. The spacing of fractures in drill holes is a fractal Cantor distribution, and the range of fractal dimension is 0.4-0.6, which is an integer dimension less than that of fracture-trace patterns exposed on two-dimensional, planar sections. A reconstruction of the fracture history at the point of initial connectivity across the network (percolation) has a fractal dimension of 1.35 as compared to a dimension of 1.9 for the percolation cluster in a two-dimensional model. Paleo flow was mapped based on the deposition of aqueous minerals on the fracture surface.
- OSTI ID:
- 425412
- Report Number(s):
- CONF-960527-; TRN: 96:004994-0042
- Resource Relation:
- Conference: Annual convention of the American Association of Petroleum Geologists, Inc. and the Society for Sedimentary Geology: global exploration and geotechnology, San Diego, CA (United States), 19-22 May 1996; Other Information: PBD: 1996; Related Information: Is Part Of 1996 AAPG annual convention. Volume 5; PB: 231 p.
- Country of Publication:
- United States
- Language:
- English
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