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

项目摘要合作研究：在高度非均匀多孔介质中传输现象的数学和实验分析这个项目的重点是在高度非均匀多孔介质中溶质扩散的描述。传统的模型通常捕捉溶质的净运动和扩散，但它们通常不捕捉溶质羽流的“尾巴”，因为它们通过地下移动。通常，尾矿的产生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之间的相互作用。这种介质通常被物理学家和水文学家描述为包含两种或多种类型的离散区域。该研究将结合理论和实验来理解溶质在高度非均匀多孔介质中的运移，特别关注拖尾现象。理论的发展和随后的实验验证通常是由完全不同的研究小组进行的。相比之下，这个研究小组的成员谁拥有整合新的数学理论和精心控制的实验室实验证明记录。这项工作还提供了一个机会，增加稀疏的数据库的特点良好的溶质运移实验提供给水文和数学界的目的，测试和验证描述性理论的溶质运移在异质地下系统。这项研究的主要目的是提高对高度非均匀多孔介质中拖尾现象的认识。这个项目要解决的问题是真正的跨学科，需要在数学和地球科学的交叉点进行新的实质性基础研究。跨学科的研究团队（包括代表数学，地球科学，统计学和工程学的成员）带来了现代数据收集技术的平衡观点;地下水文学;放大方法;统计学;随机过程;数值方法;和质量，动量和能量传输的偏微分方程。我们的研究成果旨在为数学和地球科学提供实质性贡献。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，对公共健康以及我们持续获得饮用、农业和工业淡水构成威胁。这项研究旨在提高我们的基本科学的理解相关的地下修复方案的有效设计的运输过程。促进培训和学习。了解和管理地下异质性是学生和从业人员掌握地下水水文学最具挑战性的概念之一。拟议的研究提供了多种机会，以提高本科生和研究生的学习在一个令人兴奋的和集中的跨学科环境。加强网络和伙伴关系。这项建议扩大了现有的合作，并侧重于一个跨学科的地球科学家和数学家小组，具有广泛的各种专业知识。对拟议研究的支持将为PI提供独特的机会，以便在共同感兴趣的问题上进行跨学科合作。

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.