Mathematical Modeling of Pollutant Migration in Unsaturated Fractured Formations

利用双重孔隙的概念，建立了非饱和裂隙岩石中污染物运移的数学模型。该地层可视作两个重叠的连续体、多孔混合体和裂缝的复合体。这两种介质通过孔间交换机制进行通信，这种交换机制是两种介质中溶质浓度(对于物质传输问题)或压力(对于流体流动问题)的差异的函数。我们将研究这些媒体间交换术语的各种数学表示法。将对放射性废物给予特别关注。建议的模型是为评估污染物在非饱和裂隙地层中的运动而开发综合计算机模型的第一步。我们的目标是建立一个与现场一致的数学模型，用于变饱和裂隙岩石中的输运过程。利用参数摄动、渐近分析和变换技术获得近似解析解，以考察污染物在非饱和裂隙地层中运移的关键特征。

A mathematical model, using the dual-porosity concept, is proposed for the transport of contaminants in unsaturated fractured rocks. The formation is visualized as a composite of two overlapping continua, the porous mixtrix and the fractures. These two media communicate via interporosity exchange mechanisms that are functions of the difference in the solute concentration (for the specie transport problem) or the pressure (for the fluid flow problem) in the two media. We will examine various mathematical representations of these intermedia exchange terms. A special attention will be paid to radioactive waste. The proposed model is the first step towards developing a comprehensive computer model for assessing the movement of pollutants in unsaturated fractured formations. Our objective is the establishment of a field-consistent mathematical model for the transport process in a variably saturated fractured rock. Approximate analytical solutions using parameter perturbation, asymptotic analyses and transform techniques will be obtained in order to examine key characteristics of contaminant migration in unsaturated fractured formations.