Size Effect on Fracture Permeability Estimated by Using Synthetic Fractal Fracture.

概要

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It is prerequisite to clarify size effect on fracture permeability to estimate permeability of actual natural fractures or artificially created hydraulic fractures. However, aperture distributions, which are necessary for the estimation, are difficult to be measured for a large fracture. In this study, by creating a synthetic square fracture with various sizes from 41 mm to 656 mm in a side length, size effect on the fracture permeability is investigated by solving Reynolds equation to obtain a hydraulic aperture of the fracture. Synthetic fracture surfaces are createdd with a spectral synthesis method based on fractional Brownian motion (fBm) by giving a gradual phase difference between the Fourier components of the two fracture surfaces. When a fracture is closed to have a certain mean aperture, the hydraulic aperture decreases with the fracture size. This is due to the increase in the percentage of contact point with the fracture size because the standard deviation of the aperture increases with the fracture size. When a fracture is closed to have a certain percentage of contact point, the hydraulic aperture increases with the fracture size. This is, due to the increase in the mean aperture with the fracture size because the standard deviation of the aperture increases with the fracture size. Thus, size effect on fracture permeability is governed by size effect on the standard deviation of the aperture.
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