A Fractal Study For Heat And Mass Transport Properties In Porous Media

Porous media widely exist in nature,engineering applications,organisms as well as industrial applications,and the heat and mass transfer processes in porous media involve many fields.Thus,the study for heat and mass transport properties of porous media has important engineering application prospects and scientific values.According to the fractal geometry theory,the microstructures of all natural porous media and most artificial porous media show certain fractal characteristics.Therefore,fractal geometry theory can be used to quantitatively characterize complicated porous space,and then study the heat and mass transport properties of porous media.In Chapter 1,this dissertation introduces porous media and the fractal geometry theory.Then this chapter outlines the fractal model of capillary bundles and the fractal-like tree branching network model,respectively,and the fractal characteristics of low permeability reservoirs are discussed.At last,the basis theory of the heat and mass transport in porous media is summarized briefly.In Chapter 2,the Fractal-Monte Carlo simulations is applied to study the heat-transfer properties of unsaturated fibrous media.Firstly,the Fractal-Monte Carlo method is used to simulate fibrous media.Then we build a theoretical model of the effective thermal conductivity of unsaturated fibrous media and analyze the variation of the dimensionless effective thermal conductivity with the structural parameters of fibrous media.The numerical simulation predictions of the theoretical model are in good agreement with the experimental data available.The proposed model of the dimensionless effective thermal conductivity is expressed as a function for structural parameters of unsaturated fibrous media,and there are no empirical constants.In Chapter 3,the fractal geometry theory is used to study the influence of the surface topography on the laminar flow resistance in cylindrical microchannels.Firstly,the roughness height fractal dimension is introduced to describe the roughness characteristics of the surface topography for the cylindrical microchannels in porous media,and we obtain the expression of relative roughness.Then we deduce the theoretical models of the friction factor and the Poiseuille number for laminar flow through the cylindrical microchannels with the roughened surface topography.The model predictions are in good agreement with the experimental data available.In addition,the transport channels of some porous media,such as plant nutrient transport systems,blood capillaries,etc.,show certain fractal characteristics,they can be described by the fractal-like tree branching microchannel network.Therefore,this chapter also studies the heat-transfer properties in this kind of porous media.Then we obtain the relative roughness expression of the fractal-like tree branching microchannel network.Subsequently,we deduce the model of the effective thermal conductivity of the fractal-like tree branching microchannel network with roughened surface.Later,we analyze the variation of the dimensionless effective thermal conductivity with the structural parameters of the branching microchannel network.In Chapter 4,the fractal geometry theory is used to study digital rock cores of low permeability reservoirs.Studying the pore structure characteristics of rock cores contributes to understand the fluid flow mechanisms as well as the heat and mass transport properties in the reservoir.Therefore,in this chapter,fractal geometry theory is used to quantitatively characterize the pore structures of 16 digital core samples of low permeability reservoirs.By determining the fractal dimension of pore size distribution,the maximum and minimum pore sizes,we get the porosity of the digital rock core sample,and the porosity predictions of 12 digital rock core samples are in good agreement with measurement date,indicating that it is effective to analyze and to predict the fractal parameters of digital rock core samples by using the fractal geometry theory.Finally,a standard or criterion is established whether the pore/particle size distribution in a digit rock core/porous medium is fractal or non-fractal.Finally,the main contents and innovations of present thesis are summarized,and some prospects are also made about the potential research works on heat and mass transport properties in porous media.