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

合作研究：高度非均质多孔介质中输运现象的数学与实验分析本项目重点描述溶质在高度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，但它们通常不会捕捉到溶质羽流在地下移动时的“尾巴”。通常，尾矿是由两种或两种以上物理性质截然不同的地质物质相互作用而产生的。这种介质通常被物理学家和水文学家描述为包含两种或更多类型的离散区域。该研究将结合理论和实验来理解溶质在高度非均质多孔介质中的运移，特别关注尾矿现象。通常理论的发展和随后的实验验证是由完全独立的研究小组进行的。相比之下，这个研究小组的成员在整合新的数学理论和精心控制的实验室实验方面有着良好的记录。这项工作还为水文学和数学界提供了一个机会，以增加具有良好特征的溶质输运实验的稀疏数据库，以测试和验证非均质地下系统中溶质输运的描述性理论。研究的主要目的是提高对高度非均质多孔介质中尾矿现象的理解。这个项目要解决的问题是真正的跨学科的，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）为现代数据收集技术带来了平衡的视角；地下水文;升级方法;统计数据;随机过程;数值方法;以及质量，动量和能量输运的偏微分方程。我们的研究结果旨在为数学和地球科学提供实质性的贡献。建议的研究将产生以下更广泛的影响。造福社会。地下污染是一个严重的问题，对公众健康和我们饮用水、农业和工业的持续获取构成威胁。本研究旨在提高我们对与有效设计地下修复方案相关的运输过程的基本科学认识。促进培训和学习。理解和管理地下非均质性是地下水水文学专业学生和实践者最难掌握的概念之一。拟议的研究提供了多种机会，以提高本科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。该提案扩展了现有的合作，并将重点放在具有广泛专业知识的地球科学家和数学家的跨学科小组上。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。

Collaborative 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.