Diffusion,Percolation And Heat Conduction In Fractal Porous Media

Fractal theory would offer a new sight on heat and mass transfer in porous media. This paper mainly deals with the research on the mass diffusion, dispersion and heat conduction in fractal porous media.Firstly, heat conduction in fractal porous media is analyzed and simulated by use of finite volume method in this paper. Fractal porous media can be simplified as a kind of binary mixture with different thermal conductivities. The calculated results show that heat transfer in fractal porous media is very complicated, the thermal coupling effect of matrix with pore structure is studied. When heat transfer in pore structure is neglected, the effective thermal conductivity for random Sierpinski Carpet is scaled up with the percent of matrix, which is described by the classic Archie's law. All these results are helpful to understand heat conduction mechanism in porous media.Then, Brownian motion in fractal sierpinski carpet is discussed in the third chapter. The random walk in fractal sierpinski carpet is demonstrated as a scaled process. The Fick law is not applicable in fractal media. The spectral dimension is estimated by Monte Cario(random walk) method. The calculated results show that mass diffusion in fractal media is non-homogeneous and nonlinear. The diffusion coefficient is scaled up with porosity percent. The gas diffusion is simulated using diffusion equation in fractal porous media .Dispersion process in porous media is analyzed and simulated by use of Monte Carlo method in this paper. Many unusual phenomena near the percolation threshold caused by random pore removal or blockage is found. First, the grid pressure distribution is Anomalous ; Secondly, the dispersion is much slowly than in Euclidean space. Thirdly, there is a preferential path for dispersion flow near the percolation threshold; Fourth, the longitudinal dispersivity is scaled with grid length. At last, the probability density function shows multi-fractal characteristic, which is Gauss distribution in Euclidean space.The experimental study is designed to observe the flow process by use of morphological method in different kind of soils. Macropore geometry is subsequently characterized by using fractal dimensions of staining patterns on horizontal cross-sections. The results prove that water flow in structured clay soils is strongly influenced by the presence of macro-pores and their geometries. The preferential flow is found widely in the un-destructed soils.A math-physical model of vertical transport of organic carbon in soil is introduced. Numerical simulation of distribution of SOC in soil profiles is conducted ? Influence of some parameters are analyzed, such as: D(diffusion rates), v (coefficient of convection).Double or three compartments model of SOC is used. It is found that the diffusion process for different compartments of organic carbon in soil is very differently. This model could also calculated the accumulation of SOC in soil per year, which is helpful to understand the dynamic process of organic carbon storage in soil.The analytical and experimental results obtained in this work will be greatly valuable and significant for the understanding of heat and mass transfer mechanism in fractal porous media.