Continuum percolation theory for transport properties in porous media
Continuum percolation theory for transport properties in porous media
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DOI：
10.1080/14786430500157094
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发表时间：
2005-10
影响因子：
1.6
通讯作者：
A. G. Hunt *
中科院分区：
文献类型：
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作者：
A. G. Hunt *
众所周知，输运性质在渗流阈值处根据幂律消失。在用连续体渗流描述的系统中，理论结果可以给出非普适幂。多孔介质被认为是一种系统，它代表了这种非普遍的渗透结果。本文表明，通过使用远离渗透阈值的关键路径分析（来自渗透理论）和使用靠近渗透阈值的输运性质的通用标度，可以完美地描述一系列性质，压力饱和度关系，电导率，空气渗透性，水力导电性和溶质扩散。大多数多孔介质的适当描述是截断随机分形，典型的孔径范围可达两个数量级。结果表明，在无限孔径范围的极端条件下，本文的理论处理从理论上得到了适当的非普适渗流指数。然而，孔隙大小的无限范围对应于孔隙率为1，这将要求在任意体积中具有无限大的固体表面积和零固体体积分数。由于许多原因，这不是一个真实的多孔介质模型。因此，认为典型的天然多孔介质构成了从渗流理论产生非普适指数的现实基础的论点是不成立的。
It is well-known that transport properties vanish according to power laws at a percolation threshold. In systems described by continuum percolation, theoretical results can give non-universal powers. Porous media have been argued to be systems, which typify such non-universal percolation results. It is shown here that the suite of properties, pressure saturation relationships, electrical conductivity, air permeability, hydraulic conductivity, and solute diffusion are perfectly described by using critical path analysis (from percolation theory) far from the percolation threshold and using universal scaling of transport properties near the percolation threshold. The appropriate description of most porous media is a truncated random fractal, with typical pore size ranges up to two orders of magnitude. It is shown that in the extreme condition of an infinite range of pore sizes, the present theoretical treatment generates the appropriate non-universal percolation exponents from theory. However, an infinite range of pore sizes corresponds to a porosity of 1, which would require in an arbitrary volume an infinite solid surface area with zero solid volume fraction. For a number of reasons this is not a realistic model of a porous medium. Thus the argument that typical natural porous media form a realistic basis to generate non-universal exponents from percolation theory is not supported.