Analysis of Radionuclide Transport Through Fractured Geologic Media by Percolation Theory

采用精确枚举法分析了二维和三维渗流团簇上的异常扩散，建立了反常扩散指数、分形维数和分形维数的广义表达式。通过这个公式，正常的菲克扩散也可以表示为一种特殊情况。本文采用实验和计算两种方法对二维空间中随机分布的裂缝网络中的质量输运进行了分析，以探讨裂缝网络中流动的影响。在实验工作中，在光敏树脂上实现了随机线网络。对突破曲线的分析表明，随机线网络的离散度等于相关长度，连通性越差的网络对应的相关长度或离散度越大。连接良好的网络的相关长度与分布的线的长度大致相同。在计算工作中，用蒙特卡罗方法模拟了示踪剂在随机线网络中的色散。研究发现，示踪剂分子向网络中死角孔和低流区扩散是示踪剂非菲克性分散的关键机制。固结玻璃微珠形成的多孔介质的导电性和渗透率特征长度可以通过玻璃微珠的原始半径分布来预测。

Anomalous diffusion on 2-dimensional, or 3-dimensional percolation clusters were analysed by the exact enumeration method, and a generalized formulation for anomalous diffuion in terms of anomalous diffusion exponent, fractal and fracton dimensions was established. By this formulation normal Fickian diffusion can also be expressed as a special case.Mass transport in randomly-distributed lines in a 2-dimensional space, which is considered as a simulation of geological fracture networks, was analyzed both experimentally and computationally, to investigate effects of flow in a network. In the experimental work, random-line networks were realized on photosensitive resin. Analysis of breakthrough curves reveals that dispersivity is equal to correlation length of random-line networks, and that networks of less connectivity indicates greater correlation length or dispersivity. Correlation length of well-connected networks is roughly in the same order as the length of lines distributed. In the computational work, tracer dispersion in the random-line network was simulated by the Monte Carlo method. Molecular diffusion of tracers into dead-end pores and low-flow regions in networks is found to be the key mechanism of non-Fickian behavior of tracer dispersion.Characteristic length of electrical conductivity and permeability of porous media made by consolidating glass beads can be predicted by the original radius distribution of glass beads.