| As we known,some processes,such as groundwater pollution and treatment,the contaminant control remediation in underground rock-soil mass and the diffusion of radioactive materials,belong to solute transport phenomena in porous media.At present,the research on problems of seepage through porous media has formed a mature theory system,while the study of solute transport in porous media is relatively insufficient.The main difficulty for the movement of solute in porous media is that it is affected by diffusion processes,pore structure and fluid flow.Therefore,it is of great and practical significance to find out how the structures and fluid flow affect solute transport,providing theoretical basis for production practices of human being.In order to understand the mechanism of fractal behavior,the concept of fractal topology was proposed by defining two dimensionless scale-invariant parameters:Scaling Lacunarity?P?and Scaling Coverage?F?to implement its mathematical description:??P,F?based on the intrinsic analysis of the scale invariance of fractal behavior,and a generalized model of fractal dimension for arbitrary fractals was finally given.The validity of the proposed fractal dimension model was then verified by comparing with box dimension estimation;based on the topological definition of fractal dimension and considering random characteristics of medium,we realized the fine simulation of porous media with Sierpinski Carpet model.On this basis,the fractal model of porosity was proposed and validated.In terms of diffusive mass transfer,the quantitative evaluation of effective diffusion coefficient was achieved at pore scale combining the definition of effective diffusion coefficient and the treatment of local concentration gradient by discrete LB.Based on the above research,this thesis emphatically analyzed the influence of reservoir pore structure on solute diffusion process.The results showed that,for regular porous media,the relationship among effective diffusion coefficient,diffusion tortuosity and porosity was???,???,while stochastic features of porous media would enlarge the dependency of diffusion tortuosity and porosity on effective diffusion coefficient;diffusion tortuosity of solute decreased with the porosity and pore,regression analysis following power-law distributions,and the power exponent varies with the media configuration;for fractal porous media,the relationship between diffusion tortuosity and porosity was about?d?0.9854?-0.2118.In terms of convective mass transfer,the numerical simulation was realized by means of a coupling LB model of NS and CDE.The longitudinal dispersion coefficient and dispersity were calculated based on the relationship of concentration and iteration time at different section of single fracture,and further analysis showed that the scale-dependent fractal dimension decreased first and then increased with aperture.Self-affine fractures with different aperture and roughness were constructed by Weierstrass-Mandelbrot fractal function,the discussions about solute transport with convection dominated and diffusion dominated under different roughness structures and hydraulic characteristics showed:when diffusion plays a main role,the dispersion tortuosity is always greater than hydraulic tortuosity;when advection dominates,the concentration breakthrough curves affected by the distribution of velocity show a long tailing and become more serious with the increase of roughness of fracture surface.This thesis focused on the topological fractal behavior of porous media,then a scale-invariant model of fractal dimension was put forward and applied to complicated media modeling,the numerical simulation of solute transport and the calculation of transport coefficients at the pore scale were implemented,which not only provided theoretical basis for the assessment and control of groundwater pollution,but also laid the foundation for further research on the mass transport influenced by multi-physics coupling problems of porous media. |
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