Collaborative Research: CMG: Mathematical and Experimental Analysis of Transport Phenomena in Highly Heterogeneous Porous Media

项目简介合作研究：高非均质多孔介质中输运现象的数学和实验分析该项目专注于描述溶质在高非均质多孔介质中的扩散。传统的模型经常捕捉到溶质的净运动和扩散，但它们通常不能捕捉到溶质羽流在地下移动时的“尾巴”。通常，尾矿是由于两种或两种以上具有明显不同物理性质的地质物质相互作用而产生的。这类介质通常被物理学家和水文学家描述为包含两种或两种以上类型的离散区域。这项研究将把理论和实验结合起来，以了解溶质在高度非均质多孔介质中的运移，特别是尾矿现象。通常，理论的发展和随后的实验验证是由完全不同的研究人员小组进行的。相比之下，这个研究团队的成员都有将新的数学理论和精心控制的实验室实验相结合的良好记录。这项工作还提供了一个机会，以增加水文学和数学界可用的具有良好特性的溶质运移实验的稀疏数据库，以测试和验证非均质地下系统中溶质运移的描述性理论。这项研究的广泛目标是更好地理解高度非均质多孔介质中的尾矿现象。这个项目要解决的问题确实是跨学科的，需要在数学和地球科学的交叉点上进行新的实质性的基础研究。跨学科研究小组(包括代表数学、地球科学、统计学和工程学的成员)带来了关于现代数据收集技术、地下水文学、提升尺度方法、统计学、随机过程、数值方法以及质量、动量和能量传输的偏微分方程式的平衡观点。我们的研究结果旨在为数学和地球科学做出实质性贡献。拟议的研究将产生以下更广泛的影响。对社会有益。地下污染是一个严重的问题，对公众健康和我们持续获得饮用水、农业和工业用淡水构成威胁。这项研究旨在提高我们对与有效设计地下补救方案相关的运输过程的基本科学理解。促进培训和学习。对于地下水水文学的学生和实践者来说，理解和管理地下水非均质性是最具挑战性的概念之一。拟议的研究提供了多种机会，在一个令人兴奋和专注的跨学科环境中改善本科生和研究生的学习。加强网络和伙伴关系。这项建议扩展了现有的合作，并集中了一个由具有各种专业知识的地球科学家和数学家组成的跨学科小组。对拟议研究的支持将为PI提供独特的机会，使他们能够就共同感兴趣的问题进行跨学科协作。

PROJECT ABSTRACTCollaborative Research: Mathematical and Experimental Analysis of Transport Phenomena in Highly Heterogeneous Porous MediaThis project is focused on the description of solute spreading in highly heterogeneous porous media. Conventional models often capture the net movement and spreading of solutes, but they do not typically capture the 'tails' of solute plumes as they move through the subsurface. Usually, tailing arises because of the interaction between two or more kinds of geologic material that have distinctly different physical properties. Such media are often represented by physicists and hydrologists as containing two or more types of discrete regions.The research will integrate theory and experiment for understanding solute transport through highly heterogeneous porous media, with a particular focus on tailing phenomena. Often the development of theory and subsequent experimental validation is conducted by entirely separate groups of researchers. In contrast, this research team consists of members who have a proven record of integrating new mathematical theory and carefully-controlled laboratory experiments. This work also provides an opportunity to increase the sparse database of well-characterized solute transport experiments available to the hydrology and mathematics communities for the purposes of testing and validating descriptive theories of solute transport in heterogeneous subsurface systems. The broad objective of the research is to develop an improved understanding of tailing phenomena in highly heterogeneous porous media. The problems to be addressed in this project are truly interdisciplinary, and require new and substantive basic research to be conducted at the intersection of mathematics and geosciences. The interdisciplinary research team (involving members representing mathematics, geosciences, statistics, and engineering) brings a balanced perspective on modern data collection technology; subsurface hydrology; upscaling methods; statistics; stochastic processes; numerical methods; and the partial differential equations of mass, momentum, and energy transport. The results from our research are intended to provide substantial contributions to both mathematics and to geosciences.The proposed research will have the following broader impacts. Benefits to society. Subsurface contamination is a serious problem that poses threats to public health and to our continuing access to fresh water for drinking, agriculture, and industry. This research seeks to improve our basic scientific understanding of transport processes relevant to the effective design of subsurface remediation schemes. Promoting training and learning. Understanding and managing subsurface heterogeneity is one of the most challenging concepts for students and practitioners to master in groundwater hydrology. The proposed research provides multiple opportunities to improve both undergraduate and graduate learning in an exciting and focused interdisciplinary environment. Enhancing networks and partnerships. This proposal expands on existing collaborations and focuses an interdisciplinary group of geoscientists and mathematicians with a wide variety of expertise. Support of the proposed research will provide the unique opportunity for the PI's to collaborate across disciplinary lines on problems of mutual interest.