Novel mathematical approaches for multiscale modelling of three-phase porous media flow

这是爱丁堡赫里奥特-瓦特大学数学系(MACS)和石油工程研究所(IPE)的联合竞标，将有两个系的研究人员参与。这两个系都建立了一个良好的跨学科环境，这要归功于目前由PI教授Dugald Duncan持有的弥合差距的赠款。所有被点名的调查人员都是爱丁堡工程和数学研究伙伴关系(www.erp.ac.uk)的两个主要联合研究所的成员，麦克斯韦尔数学科学研究所和爱丁堡地下科学与工程合作(ECosse)。这两个项目都是苏格兰资助委员会2200万英镑资助计划的一部分，该计划旨在促进爱丁堡各地数学和工程领域的跨学科研究。此外，麦克斯韦尔研究所是470万科学与创新补助金的合作伙伴，以建立跨学科的数值算法和智能软件中心(NAIS)。我们的提议旨在巩固现有的跨学科合作，以补充和加强Mac和IPE的世界领先研究概况。我们建议探索新的数学方法用于三相(如油、气、水)多孔介质流动的多尺度模拟的可行性。为此，我们将跨越工程学科(即石油、水文学和工业多孔介质应用)、物理和应用数学之间的传统界限，并评估了来自不同学科的专家团队。我们的研究将是高度推测和冒险的，因为我们根本不知道是否可以开发出一种合适的替代三相达西定律的方法，以使其能够以在日常工程应用中成功使用所需的数学健壮和高效的方式求解。然而，另一种选择是必要的，因为达西定律在某些流动状态下本质上是无效的，即当一个或多个相作为不连续的气泡和神经节运动时。然而，工程上最感兴趣的正是这种情况，例如，当预测少量有毒地下水污染物或残余石油在枯竭的碳氢化合物储集层中的迁移时。我们工作的高风险和投机性研究性质不一定会吸引资金，尽管它在许多应用中具有根本性的重要性：对于工业支持来说，这太过投机和蓝天，因为产品的交付时间是几个月，而不是几年，而且由于其活跃的、跨学科的和方法的范围，将很难从其他来源获得资金。然而，如果我们的初步研究表明，三相流动达西定律的替代方案是可行的，那么结果将对工程和数学学科产生重大影响：三相流动达西定律的可能替代或改进将对提高采油技术产生根本影响。这类技术旨在从不断衰落的油田中提取碳氢化合物，比如北海英国和世界各地的油田经常出现这种情况。它们也将是改善地下水污染物修复、预测地下二氧化碳储存以及各种其他工业多孔介质应用(例如木材加工)的关键。我们的研究还将解决重要的和具有挑战性的数学和计算问题，如开发有效和可靠的算法、升级方法、数值稳定性和收敛证明或误差估计，所有这些都必须能够处理三相流动固有的高度非线性物理和工业应用中参数的数量级变化和相关的不确定性。

This is a joint bid from the Department of Mathematics (MACS) and Institute of Petroleum Engineering (IPE) at Heriot-Watt University in Edinburgh and will involve researchers across both departments. Both departments have established a virbant cross-disciplinary environment thanks to the current Bridging the Gaps grant held by the PI, Prof. Dugald Duncan. All named investigators are members of two major joint research institutes of the Edinburgh Research Partnership in Engineering and Mathematics (www.erp.ac.uk), the Maxwell Institute of Mathematical Sciences and the Edinburgh Collaboration of Subsurface Science and Engineering (ECOSSE). Both are part of the 22M funding initiative of the Scottish Funding Council to foster interdisciplinary research in mathematics and engineering across Edinburgh. Furthermore the Maxwell Institute is a partner in the 4.7M Science and Innovation Grant to found the interdisciplinary Numerical Algorithms and Intelligent Software Centre (NAIS).Our proposal aims to consolidate existing and create new cross-disciplinary collaborations that will complement and enhance the world-leading research profiles of MACS and IPE. We propose to explore the feasibility of novel mathematical approaches for multiscale modelling of three-phase (e.g. oil, gas, water) porous media flow. For this we will cross traditional boundaries between engineering disciplines (i.e. petroleum, hydrology, and industrial porous media applications), physics, and applied mathematics and have assmebled a team of experts from the different disciplines. Our studies will be highly speculative and adventurous because we simply do not know if a suitable alternative to three-phase Darcy's law can be developed in such a way that it can be solved in the mathematically robust and efficient manner that is required for successful use in daily engineering applications. However, an alternative is required because Darcy's law is intrinsically not valid in certain flow regimes, that is when one or more phases move as discontinuous blobs and ganglia. Yet it is exactly this situation that is of most interest to engineering, for example when predicting the migration of small volumes of toxic groundwater contaminants or residual oil in a depleted hydrocarbon reservoir. The high risk and speculative research nature of our work would not necessarily attract funding despite being of fundamental importance in many applications: It is too speculative and blue sky for industrial support where lead time to product is months, not years and would struggle to be funded from other sources due to its novely, interdisciplinarity, and range of approaches. Yet, if our initial studies show that an alternative to Darcy's law for three phase-flow is feasible, the outcomes will have a major impact on engineering and mathematical disciplines: A possible alternative or improvement of Darcy's law for three-phase flow will have a fundamental influence in improving enhanced oil recovery techniques. Such techniques aim to extract hydrocarbons from declining oil fields such as they are frequent in the U.K. sector of the North Sea and world-wide. They will also be the key to improving the remediation of groundwater contaminants, predicting subsurface CO2 storage, and a variety of other industrial porous media applications (e.g., wood processing). Our research will also tackle important and challenging mathematical and computational issues, such as development of efficient and reliable algorithms, upscaling methods, numerical stability and convergence proofs, or error estimation, all of which must be able to cope with the highly non-linear physics inherent to three-phase flow and the orders-of-magnitude variation in parameter and associated uncertainties arising in industrial applications.