多孔介质分形模型的难点与探索

对分形理论的一些关键而又复杂的概念，如谱维数，Hurst数，稳定分布进行了讨论，谱维数是联系分形介质中静态结构参数和动程的桥梁，而Hurst数的大小划分各种类型的分形布朗运动，这也同时决定了分形介质中扩散过程的快慢，物质在分形结构中的扩散密度分布函数属于稳定分布，并对应用于分形介质扩散动力学各种方法的实质进行了分析，分数微分扩散方程可以得到扩散密度分布函数，但目前仍然是一种近似解，随机模拟方法比较直观，但决定过程的扩散密度分布函数目前只能采用预估的方法，而传统的差分方法比较实用，却能以给出对分形介质网格之间的扩散系数，因此，将分形理论应用于实际的多孔介质仍然有很多难点，有待未来更深入的研究。

Important problems of fractal model in porous media

Fractal theory would offer promise for new sight on heat and mass transfer in porous media. Some confused conceptions in fractal percolation theory, spectral dimension, Hurst number and stable distribution are discussed. Spectral dimension links static structure exponents with dynamic processes in fractals. Hurst number corresponds to different kind of fractional Brownian motion, which means the different mode of the particle diffusion. Diffusion probability density function in fractals is described by stable distribution.Three general dynamic methods, fractional fractal equation, random walk model and a finite difference theory, are analysed. Diffusion probability density function can be solved by fractional fractal equation,but it only provides an approximate solution. Random walk model is easily understood, but the important probability density function must be estimated through other methods. The classic finite difference approach is widely used, which is limited by ambiguity of diffusion coefficient between the grids or pores. Therefore, these are still many difficulties and complexities for the fractal model in porous media,and further study is needed in the future.