CMG: Mathematical and Experimental Analysis of Reactive Transport in Discontinuous Porous Media

污染物在地下的发生和运移是一个普遍存在的问题。由于我们的地下水资源既有限又宝贵，因此我们必须制定保护和修复这些资源的方法。地质材料中污染物运动的适当数学模型的发展使从业者和研究人员能够预测污染物的行为，这对地下水保护至关重要。在这个项目中，研究人员正在研究污染物在高度异质介质中的运动。在地质材料中，非均质性——基本上是材料的空间变异性——可能是巨大的，地下污染物通常是化学反应性的。大多数现有的数学模型不能很好地表示这种高度非均相材料中的输运和反应。在地下水预测中广泛使用的一种数学方法是把溶解的化学物质看作是随地下水移动的离散粒子云。该项目的目标是开发这种粒子模型的新表示，包括在遇到高度异质介质时粒子运动的数学表示，并添加允许表示反应的规则。研究人员在地球科学家、工程师和数学家之间形成了一个独特的合作来开展这项研究。这项工作将集中在(1)通过粒子模型来表示反应性污染物迁移所需的基本数学方法，以及(2)通过在高度非均质材料中进行的直接、大规模（米或更多）受控实验室实验来验证这些数学模型。这一努力的实际结果将是：(1)数学科学的新结果，进一步加深我们对基于颗粒的模型的理解；(2)水文学家和工程师可以使用新的模型来更准确地预测地下水系统中的污染物运输和反应。

The occurrence and transport of contaminants in the subsurface is a widespread problem. Because our groundwater resources are both limited and valuable, it is important that we develop methods to both protect and remediate these resources. The development of appropriate mathematical models for contaminant movement in geologic materials allows practitioners and researchers to predict contaminant behavior, which is critical for groundwater protection.In this project, the investators are studying the movement of contaminants in highly heterogeneous media. In geological materials heterogeneity- basically the spatial variability of the material- can be enormous, and subsurface contaminants are often chemically reactive. Most existing mathematical models do not well represent transport and reaction in such highly heterogeneous materials. One mathematical approach that has been used extensively in groundwater prediction is to treat dissolved chemical species as if they were a cloud of discrete particles moving with the groundwater. The goal of this project is to develop new representations of such particle models to include mathematical representations of particle motion when highly heterogeneous media are encountered, and to add rules that allow one to represent reactions. The investigators have formed a unique collaboration between geoscientists, engineers, and mathematicians to develop this research. The work will focus on (1) the fundamental mathematical methods necessary to represent reactive contaminant transport by particle models, and (2) validation of these mathematical models by direct, large-scale (meters or more) controlled laboratory experiments in highly heterogeneous materials. The practical results of this effort will be (1) new results in the mathematical sciences that further our understanding of particle-based models, and (2) new models that can be used by hydrologists and engineers to more accurately predict contaminant transport and reaction in groundwater systems.