Mathematical modelling of buoyant flows in deformable porous media, applied to carbon sequestration, saltwater intrusion and subglacial hydrology

涉及可变形含水层中的两相浮力地下水流动的问题出现在几个重要的地球科学背景下。一个例子是超临界二氧化碳在含盐含水层中的流动，在固碳过程中被开采(Huppert和Neufeld，2014)；另一个例子是海水侵入淡水沿海水文系统，例如由于地下水过度开采，这可能威胁到沿海社区的饮用水供应(Mondal等人，2019年)。一个新出现的兴趣是海洋冰盖下海水的入侵，以及它与冰下水文系统中新鲜融水的相互作用。这是因为最近在南极冰盖下发现了咸水地下水系统(Gustafson等人，2022年)，其年龄和来源仍然是一个悬而未决的问题，最近的研究(Robel等人，2022年)表明，海洋冰盖下的咸水入侵可能显著加速冰下融化，并有助于此类冰盖的消融。数学模型可以为这些现象提供强大的物理洞察力，但在许多问题上需要进一步研究。目前对描述浮力流体注入弹性多孔介质的问题的解决方案受碳封存的推动，在注入地点附近包含非物理奇点，需要额外的物理和渐近分析来解决(Hewitt等人，2015)。盐水入侵的数学和数值模型几乎完全集中在稳态上(Ketabchi等人。2016年)，相应的动态问题仍未得到充分调查；例如，缺乏模型来描述海平面上升或地下水开采率的变化，其时间尺度与地下水运移的时间尺度相当。特别需要发展和建立现有的冰下咸水入侵的数学理论，这是最近才出现的一个调查专题。现有最好的模型(例如Robel等人，2022年)在对融化等物理效应的参数化方面高度简化，尚未纳入诸如接地线移动等动态现象，并且没有考虑冰盖下含水层在冰盖重量下的显著变形(例如Lemieux等人，2008年)。该项目建议使用数学建模和流体动力学技术来研究这些在数学上相似的问题。这将涉及构建物理激励的微分方程模型，建立在现有模型的基础上，并使用渐近分析技术将这些模型简化为更易于处理的形式，同时保留关键的物理学知识。下一阶段将是利用计算数学寻找解析和数值解，这将为上述未建模的现象和开放问题提供新的见解。该项目属于EPSRC连续介质力学研究领域。没有外部合作者参与。

Problems involving two-phase buoyant groundwater flows in deformable aquifers appear in several important geoscientific contexts. One example is the flow of supercritical carbon dioxide in saline aquifers, exploited during carbon sequestration (Huppert and Neufeld, 2014); another is the intrusion of seawater into freshwater coastal hydrological systems, for example due to groundwater over-extraction, which can threaten potable water supply to coastal communities (Mondal et al., 2019). A newly emerging interest is the intrusion of seawater beneath marine ice sheets, and its interaction with fresh meltwater in subglacial hydrological systems. This is motivated by the recent discovery of saline groundwater systems beneath the Antarctic ice sheet (Gustafson et al., 2022), whose age and origin remain an unresolved question, and recent research (Robel et al., 2022) suggesting that saltwater intrusion beneath marine ice sheets could significantly accelerate subglacial melting and contribute to the retreat of such ice sheets.Mathematical models can provide a powerful physical insight into these phenomena, but in many problems there is a need for further development. Current solutions to the problem, motivated by carbon sequestration, of describing buoyant fluid injection into an elasto-porous medium, contain unphysical singularities near to the injection site, which require additional physics and asymptotic analysis to resolve (Hewitt et al., 2015). Mathematical and numerical models of saltwater intrusion have focused almost exclusively on steady states (Ketabchi et al. 2016), with the corresponding dynamic problems remaining under-investigated; for instance, there are a lack of models to describe sea level rise, or changes in groundwater extraction rate, on a comparable timescale to groundwater transport. There is a particular need to develop and build upon the existing mathematical theory of subglacial saltwater intrusion, which has only emerged very recently as a topic of investigation. The best existing models (e.g. Robel et al., 2022) are highly simplistic in their parametrisation of physical effects such as melting, are yet to incorporate dynamic phenomena such as grounding line movement, and fail to consider the significant deformation of subglacial aquifers under the weight of an ice sheet (considered by e.g. Lemieux et al., 2008).This project proposes to investigate these mathematically similar problems using the techniques of mathematical modelling and fluid dynamics. This will involve constructing physically-motivated differential equation models, building on existing ones, and using the techniques of asymptotic analysis to reduce these models to a more tractable form while retaining the key physics. The next stage will be to find analytical and numerical solutions, using computational mathematics, which will provide new insights into the under-modelled phenomena and open problems considered above.This project falls within the EPSRC Continuum Mechanics research area. There are no external collaborators involved.