Two phase flows in karstic geometry

岩溶几何中的两相流

• 批准号: 1312701
• 负责人: Xiaoming Wang
• 金额: $ 25万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-01 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1312701&HistoricalAwards=false
• 关键词: Two; phase; flows; karstic; geometry

We propose to study two phase flow in karstic geometry utilizing a hierarchical family of physically motivated diffuse interface (phase field) models. These models embody several challenges: moving interface between two types of fluids which leads to strong nonlinearity of the resulting models, and different physics in different parts of the physical domain which leads to the coupling of subsystems of different types. Although these two difficult issues have been studied before in separate contexts, the physical need of two phase fluid flow in karstic geometry requires us to investigate the two issues in a coupled fashion. This is a challenge that has not been addressed so far. The PI and collaborators plan to investigate the models from several different angles. Firstly, we will investigate the mathematical well-posedeness of models. Secondly, we will study the sharp interface limit. Thirdly, we will design and implement accurate and efficient numerical methods for the models so that the results can be compared to experimental results. These are highly non-trivial tasks due to the highly nonlinear nature of the coupled systems, and the disparity of physical and mathematical mechanism in the porous media and in the conduit. The sharp interface limit is a highly nonlinear singular perturbation problem which is known to be a challenge. We will combine tools from partial differential equations, functional analysis, asymptotic analysis, numerical analysis and computation, and laboratory experiments to investigate these problems.Geometric configurations that contain both conduit (or vug) and porous media is termed karstic geometry. It is known that the study of multiphase flow in karstic geometry is of great importance in many applications such as groundwater study, fuel cell technology, petroleum engineering and carbon-dioxide sequestration. The successful completion of the investigation on the validity of the models proposed here will help us better understand several important two fluid phenomena in karstic geometry. We also believe that the methodologies to be developed may be expanded to investigate more complex models that involve phase transition, and large density ratio. The better understanding of these important problems could lead to better engineering processes and better science based environmental policies.

我们建议利用出色动机的分散界面（相位场）模型的分层家族研究术中的两相流。这些模型体现了几个挑战：两种类型的流体之间移动界面，从而导致了所得模型的强烈非线性，以及物理域的不同部分的不同物理，从而导致不同类型的子系统的耦合。尽管这两个困难的问题之前已经在不同的环境中进行了研究，但在喀斯坦几何形状中对两个相流量流的物理需求要求我们以耦合方式调查这两个问题。到目前为止，这是一个尚未解决的挑战。 PI和合作者计划从几个不同角度研究模型。首先，我们将研究模型的数学良好性。其次，我们将研究尖锐的界面限制。第三，我们将为模型设计和实施准确有效的数值方法，以便可以将结果与实验结果进行比较。由于耦合系统的高度非线性性质，以及多孔介质和导管中物理和数学机制的差异，这些都是高度非平凡的任务。尖锐的界面限制是一个高度非线性的奇异扰动问题，已知是一个挑战。我们将结合部分微分方程，功能分析，渐近分析，数值分析和计算以及实验室实验来研究这些问题。众所周知，在诸如地下水研究，燃料电池技术，石油工程和碳 - 二氧化碳固结化等许多应用中，术中多相流的研究非常重要。在此处提出的模型的有效性的成功完成将有助于我们更好地理解Karstic几何形状中几种重要的两种流体现象。我们还认为，可以扩展要开发的方法，以研究涉及相变和较大密度比的更复杂的模型。对这些重要问题的更好理解可能会导致更好的工程过程和更好的基于科学的环境政策。