CMG: Multiphase Porous Medium Dynamics: Pore to Field Scale

多相多孔介质系统在自然和工程系统中经常出现。对于这项工作来说，一个具有启发性的例子是由天然材料组成的多孔介质系统，例如由多种流体相占据的土壤或含水层材料。目前用于描述这类系统的模型并不自然地遵循孔隙尺度的表示，而是由经验的、专门的滞后关系封闭的，这些关系旨在描述流体压力、饱和度和渗透率之间的相互依存关系。在这项工作中，我们将提出并评估一套基于严格多尺度分析的新模型。我们将使用多尺度理论、模拟和实验来模拟与表面物理和化学相关的现象，这些现象隐藏在当前多相模型的压力-饱和度关系或现象学方面。我们将通过添加固、气、液相之间的界面接触来推广标准模型。这种概括很自然地属于Gray和Hassanizadeh导出的模型。闭合关系是这项工作的核心部分，它将结合孔隙尺度数值模拟、多尺度平均方法和系数的尺度特性分析及其对宏观尺度模型行为的影响，以及实验。先进的模型将：求解新的数值方法，推广现有的方法，特别是新的快速线性求解与高阶精确时间步进算法；用数学方法分析了物理初始边界条件下的适定性。最后，我们将使用实验实验室数据对新模型进行基准测试。多相地下流动问题对社会提出了严峻的技术挑战。目前多孔介质系统的流动和输送模型在解决包括污染物修复、水资源恢复和保护在内的挑战方面发挥了至关重要的作用。尽管如此，需要在流动和运输的基本模型方面取得进展，同时认识和解决与模型发展相关的新的数值挑战。这项工作将推进此类模型的严格科学和数学基础，并产生更逼真的模拟多孔介质系统中输运现象的模拟器。我们希望这项工作能够改善地下水系统中污染物运输和回收的模拟。

Multiphase porous medium systems occur routinely in natural and engineered systems. A motivating example class of problems for this work are porous medium systems comprised of natural materials, such as soils or aquifer materials that are occupied by multiple fluid phases. Models currently used to describe such systems do not follow naturally from pore scale representations, but rather are closed by empirical, ad hoc hysteretic relations that are intended to describe the interdependence among fluid pressures, saturations, and permeabilies. In this work, we will advance and evaluate a novel set of models based in rigorous multi-scale analysis. We will use multi-scale theory, simulation, and experiment to model phenomena associated with surface physics and chemistry that are buried in pressure-saturation relations or phenomenological aspects of current multiphase models. We will generalize standard models by the addition of interfacial contacts between solid, gas, and liquid phases. This generalization falls naturally into the class of models derived by Gray and Hassanizadeh. Closure relations represent a central piece of this work and will combine pore-scale numerical simulations, multi-scale averaging methods and analysis of scaling properties of coefficients and their consequences for macroscale model behavior, and experiments. The advanced models will be: solved with new numerical methods that generalize existing approaches, in particular new fast linear solvers with high-order accurate time-stepping algorithms; and analyzed mathematically for well-posedness with physically conceived initial-boundary conditions. Finally, we will benchmark the new models using experimental laboratory data.Multiphase subsurface flow problems present critical technological challenges to society. Current flow and transport models of porous medium systems have served vital roles in addressing the challenges, including remediation of contaminants, as well as recovery and protection of water resources. Nonetheless, advances in the fundamental models for flow and transport are needed, along with recognition and resolution of new numerical challenges associated with model developments. This work will advance the rigorous scientific and mathematical bases of such models and result in more realistic simulators for modeling transport phenomena in porous medium systems. We expect this work to lead to improved simulation of contaminant transport and recovery from groundwater systems.