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Validity of triple-effect model for fluid flow in mismatched, self-affine fractures
Advances in Water Resources ( IF 4.016 ) Pub Date : 2020-04-18 , DOI: 10.1016/j.advwatres.2020.103585
Junling Zheng; Yi Jin; Xianhe Liu; Cheng Wang; Xiaokun Liu

Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2(H−1) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.
更新日期:2020-04-18

 

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