Fractal Analyses of Anisotropic Fracture Surfaces

Cox, B.L.; Wang, J. S. Y.

doi:10.1142/9789814503792_0023

Cited by 2 publications

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“…It was confirmed by experiments that the fractal type of fracture openings belongs to the self-affine fractals. 29 The most commonly used mathematical model for describing self-affine fractals is the fractional Brownian motion (fBm) model. 30 While the Modified Successive Random addition (MSRA) algorithm 31 is relatively simple and computationally efficient, here, we adopt the MSRA algorithm to generate the fracture openings.…”

Section: Stochastic Modeling Of the Fracture Propertiesmentioning

confidence: 99%

Effect of Fractal Fractures on Permeability in Three-Dimensional Digital Rocks

Liu

Yan²,

Liu

et al. 2019

Fractals

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The fracture has great impact on the flow behavior in fractured reservoirs. Fracture traces are usually self-similar and scale-independent, which makes the fractal theory become a powerful tool to characterize fracture. To obtain three-dimensional (3D) digital rocks reflecting the properties of fractured reservoirs, we first generate discrete fracture networks by stochastic modeling based on the fractal theory. These fracture networks are then added to the existing digital rocks of rock matrixes. We combine two low-permeable cores as rock matrixes with a group of discrete fracture networks with fractal characteristics. Various types of fractured digital rocks are obtained by adjusting different fracture parameters. Pore network models are extracted from the 3D fractured digital rock. Then the permeability is predicted by Darcy law to investigate the impacts of fracture properties to the absolute permeability. The permeability of fractured rock is subject to exponential increases with fracture aperture. The relationship between the permeability and the fractal dimension of fracture centers is exponential, as well as the relationship between permeability and the fractal dimension of fracture lengths.

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Section: Stochastic Modeling Of the Fracture Propertiesmentioning

confidence: 99%

Effect of Fractal Fractures on Permeability in Three-Dimensional Digital Rocks

Liu

Yan²,

Liu

et al. 2019

Fractals

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A fractal filtering technique for processing regional geochemical maps for mineral exploration

Cheng²

2001

GEEA

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A regional geochemical map interpolated from point data, usually sampled in surficial media such as stream sediments or lake sediments, may contain a large amount of information critical for mineral exploration and environmental studies. The geochemical map is, however, not 'ready-to-use' for such tasks as the determination of a local 'anomaly' or the characterization of a regional trend of one or more chemical elements as may be required for the purpose of mineral resource prediction. This becomes possible only after the map has been clearly divided into different components. Fractal filtering, a recently developed technique for decomposing a map or image into different components, helps to separate the anomaly from background or to extract other meaningful patterns from the geochemical map using both frequency and spatial information.The fractal filters are formed by applying the fractal concentration-area model to the power spectrum of the processed geochemical field. They often constitute a group of irregularly shaped filters in the frequency domain that can separate the domain of wave numbers into distinct regions, each with a power spectrum following a similar power-law or fractal property. The corresponding patterns of the separate components are obtained after transformation back to the spatial domain.The fractal filter can be applied to decompose the original geochemical field into a set of map components with distinct scaling ranges and anisotropy. The analysis of relationships among these decomposed maps can provide useful information for the interpretation and evaluation of anomalies or trends.This paper briefly introduces the theory behind the fractal filtering technique. A case study of regional geochemical data of lake sediments from western Meguma Terrain, Southern Nova Scotia, Canada, is used to illustrate application of this technique to process the regional geochemical maps of the study area for the prediction of the turbidite-hosted gold deposits.

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Fractal Analyses of Anisotropic Fracture Surfaces

Cited by 2 publications

References 0 publications

Effect of Fractal Fractures on Permeability in Three-Dimensional Digital Rocks

Effect of Fractal Fractures on Permeability in Three-Dimensional Digital Rocks

A fractal filtering technique for processing regional geochemical maps for mineral exploration

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