Collaborative Research: CDI-Type II--Revolutionary Advances in Modeling Transport Phenomena in Porous Medium Systems

美国的供水、地下能源开采、温室气体储存、全球气候变化、生物组织、混凝土材料和燃料电池设计都是涉及天然和工程多孔介质系统的关键领域的例子。尽管多孔介质过程的广泛存在和重要性，但对它们进行建模的基本方法，尽管已经很好地建立并几乎被普遍使用，但仍然存在严重缺陷。随着对日益复杂问题的可靠模拟器的需求，这些缺陷变得更加严重。这些缺陷包括：(A)人们熟知的多相流和输运的微观尺度物理与宏观尺度上对这些过程的模拟之间的脱节；(B)依赖准静态假设来描述诸如相对渗透率和毛细压力等量，即使对于动态效应很重要的系统；(C)缺乏一个方法学、严谨的理论框架来为一般和专门的应用建立守恒方程和热力学关系；以及(D)在能量传输、弥散和相相互作用的封闭方案中缺乏物理现实性。最终的结果是，对多孔介质系统的研究需要结合理论、计算和数学分析的变革性研究，以产生所需的严格的、多尺度的、基于物理的模型，以提高在广泛和重要的科学学科范围内的应用中对模拟的理解和可靠性。这个项目将结合理论、计算、数学分析和高分辨率的实验观测，来制定、求解和验证模型，这些模型捕捉到了在一定长度范围内多孔介质中多相流和传输现象的物理过程。这种多管齐下的方法将产生新一代多孔介质模型的基础基础，该模型将应用于涉及自然和工程系统的广泛科学领域。一般的基础性工作将通过对三个重要问题的具体研究来说明：非稀释密度相关的输运，两液相流和三液相流。在这项工作中集成的工具将包括高分辨率的孔隙结构和流体分布的成像，图像分析和数据提取，流体和固体的连续介质力学，经典和扩展的热力学，多尺度分析，高分辨率的格子-Boltzmann算法的发展和模拟，新模型的数学分析，时间和空间自适应的数值方法，以及求解非线性偏微分方程组的高级积分方法。该项目将通过短期课程、学生研究和科学推广为教育做出贡献。它将通过编写一本专著和分发用于模拟和分析多孔介质的工具，加强跨学科的基础多孔介质研究的基础设施。该项目将鼓励代表性不足的研究人员参与，并与少数族裔招募计划建立联系。这将有助于改善我们管理自然资源和为各种应用设计可渗透系统的能力。

The nation's water supply, subsurface energy extraction, storage of greenhouse gases, global climate change, biological tissues, concrete materials, and fuel cell design are all examples of critical areas involving natural and engineered porous medium systems. Despite the widespread occurrence and importance of porous medium processes, the basic approach to modeling them, although well-established and nearly universally used, is seriously flawed. The flaws have become more consequential with the need for reliable simulators of increasingly complex problems. These flaws include: (a) a disconnect between well-understood microscale physics of multiphase flow and transport and the modeling of these processes at the macroscale; (b) reliance upon quasi-static assumptions to describe quantities such as relative permeability and capillary pressure even for systems where dynamic effects are important; (c) lack of a methodical, rigorous, theoretical framework within which conservation equations and thermodynamic relations can be established for general and specialized applications; and (d) a lack of physical realism in closure schemes for energy transport, dispersion, and phase interactions. The end result is that the study of porous medium systems requires transformational research combining theory, computation, and mathematical analysis to produce the rigorous, multiscale, physics-based models needed to advance understanding and reliability of simulations in applications across a broad and important range of scientific disciplines. This project will combine theory, computation, mathematical analysis, and high-resolution experimental observation to formulate, solve, and validate models that capture the physics of multiphase flow and transport phenomena in porous media across a range of length scales. The multi-pronged approach will produce the foundational underpinnings of a new generation of porous medium models that will apply across a wide range of scientific fields involving both natural and engineered systems. The general foundational work will be illustrated by specific study of three important problems: non-dilute density dependent transport, two-fluidphase flow, and three-fluid-phase flow. The tools integrated in this work will include high-resolution imaging of pore structure and fluid distributions, image analysis and data extraction, continuum mechanics of fluids and solids, classical and extended thermodynamics, multiscale analysis, high-resolution lattice-Boltzmann algorithm development and simulation, mathematical analysis of new models, time and space adaptive numerical methods, and advanced integral methods for solving systems of nonlinear partial differential algebraic equations. This project will contribute to education through short courses, student research, and science outreach. It will enhance the infrastructure for fundamental porous media research across disciplines through the production of a monograph and the distribution of tools for modeling and analysis of porous media. The project will encourage the participation of underrepresented researchers and has linkages to minority recruitment programs. It will help improve our to manage natural resources and engineer porous systems for a variety of applications.