CMG: A Graph-Based Approach for Generating Pore Networks to Represent the Uncertainty of the Subsurface's Pore Structure

地下流动和输运过程的预测是地学研究的重要内容。定量预测可以通过模拟孔隙网络，即基于图形的多孔介质表示来获得。这一概念最关键的部分是表示地下孔隙结构的不确定性，即寻找能够充分代表多孔介质的拓扑和度量特征的孔隙网络。细化通常用于从多孔介质的数字图像中获得孔隙网络。然而，它通常会产生多孔性介质的模糊分隔成孔隙和颗粒。这项建议开发了一种双重方法，用于将孔隙空间细分(图像)为孔隙并定义相应的孔隙网络。孔隙网络和颗粒基质将从多孔介质的数字图像中获得，并由一对细胞复合体表示，它们唯一地确定孔隙、颗粒以及由颗粒形成的孔和孔喉。这些网络将被用来分析地下系统孔隙结构的不确定性，并模拟多相流动。地下水被滥用的污染源从泄漏的下水道、垃圾填埋场、小作坊和车库到大型工业工厂。评估这种污染源产生的污染、评估对人类和生态健康的风险，以及规划清理战略，都可以通过使用数学模型来促进。这些模型描述了流体流动和污染物在这样的系统中如何传输和反应。地下系统建模的一个关键问题是它们非常复杂的孔隙几何结构。这项研究将开发一种新的、数学上严格的方法，通过孔隙网络(在最简单的情况下：由管子连接的球体)来表示这些复杂的孔隙几何形状，该网络充分和唯一地表示原始土壤的连通性和几何形状。这种新的方法利用数学图论中的先进概念，将孔隙空间的拓扑(连通性)与固相的拓扑联系起来。由此产生的网络将回答许多与地下危险化学品和液体的命运和运输有关的问题。

Predicting flow and transport processes in the subsurface is of major interest in the geosciences. Quantitative predictions may be derived by simulating pore networks, i.e., graph-based representations of porous media. The most crucial part of this concept is to represent the uncertainty of the pore structure of the subsurface, that is, to find pore networks, which adequately represent the topological and metric characteristics of a porous medium. Thinning is commonly used to obtain pore networks from digital images of porous media. However, it typically yields ambiguous partitions of the porous medium into pores and grains. This proposal develops a dual approach for subdividing (an image of) a pore space into pores and defining a corresponding pore network. The pore network and the grain matrix will be derived from digital images of porous media and be represented by a dual pair of cellular complexes, which uniquely determine the pores, the grains, and the formation of pores and pore throats by grains. The networks will be used to analyze the uncertainty in pore structure of subsurface systems and to simulate multiphase flow.Groundwater is abused with pollution sources ranging from leaking sewers, landfills, small workshops and garages, to large industrial plants. Evaluating the contamination that occurs from such sources, assessing the risk to human and ecological health, and planning cleanup strategies can all be facilitated by the use of mathematical models. These models describe how fluids flow and contaminants are transported and react in such systems. A key problem in modeling subsurface systems is their very complex pore geometry. This research will develop a novel and mathematically rigorous approach for representing these complex pore geometries by pore networks (in the simplest case: spheres connected by tubes) that adequately and uniquely represent the connectivity and geometry of the original soils. This new approach relates the topology (connectivity) of the pore space to the topology of the solid phase by using advanced concepts from mathematical graph theory. The resulting networks will answer many questions that are concerned with the fate and transport of hazardous chemicals and liquids in the subsurface.