期刊
CHEMICAL ENGINEERING JOURNAL
卷 414, 期 -, 页码 -出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cej.2021.128745
关键词
Self-affine fracture; Triple-effect advection-diffusion model; Fractal topography; Lattice Boltzmann simulation; Hurst exponent
资金
- National Natural Science Foundation of China [41972175]
- Science and Technology Major Project of Shanxi Province, China [20181101013-1]
- Program for Innovative Research Team (in Science and Technology) in Universities of Henan Province, China [21IRTSTHN007]
- Program for Innovative Research Team (in Science and Technology) of Henan Polytechnic University [T2020-4]
The study clarifies the triple effects of surface geometries on the advection-diffusion process and establishes a model to consider the joint effect of hydraulic tortuosity, surface tortuosity, and stationary roughness in rough fractures. The results show the significant influence of self-affine properties of fractures on the advection-diffusion process.
The surface geometry of a natural fracture may feature self-affine properties, which affects the advection-diffusion process significantly. A good understanding of the underlying mechanisms of controlling such a process is of fundamental importance for a clear description of complex hydrodynamic problems. However, the effects of hydraulic tortuosity, surface roughness, scale-invariance properties, and size effect on self-affine fractures have not been fully verified. In this work, we clarify the presence of triple effects of surface geometries on the advection-diffusion process by analytical derivations, quantify their physical implications based on Poiseuille flow and Fick's law, establish a triple-effect advection-diffusion model for rough fractures by taking into consideration the joint effect of hydraulic tortuosity (tau), surface tortuosity (tau(s)), and stationary roughness (f(sigma)), and then reformulate the triple-effect model into a scaling form as per the size effect in self-affine fractures. For validation, we propose a novel Weierstrass-Mandelbrot function to model self-affine fractures according to the fractal topography theory, simulate the advection-diffusion process at the pore scale by the lattice Boltzmann method, and verify the triple-effect model and its scaling form systematically. The results indicate that the advection-diffusion process is composed of effective molecular diffusion and advection-induced dispersion, with the former inversely proportional to tau(2) and the latter inversely proportional to tau(2)tau(6)(s)f(sigma). Moreover, tau(s) and tau are both scaled by H - 1 (H is the Hurst exponent) with the mean aperture in self-affine fractures. Theoretical analysis and numerical simulations demonstrate that our model enables the generalization of several conventional models reported in the literature.
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