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的问题出现在几个重要的地球科学背景下。一个例子是在固碳过程中开采的盐水层中超临界二氧化碳的流动（Huppert和Neufeld，2014年）;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的海水入侵，其与冰下水文系统中的新鲜融水的相互作用。这是由于最近在南极冰盖下发现了含盐地下水系统（Gustafson等人，2022），其年龄和起源仍然是一个悬而未决的问题，和最近的研究（罗贝尔等人，2022年）表明，海水入侵下的海洋冰盖可能会显着加速冰下融化，并有助于这些冰盖的退缩。数学模型可以提供一个强大的物理洞察这些现象，但在许多问题有必要进一步发展。由碳封存激发的描述浮力流体注入弹性多孔介质的问题的当前解决方案在注入位点附近包含非物理奇异性，这需要额外的物理和渐近分析来解决（休伊特等人，2015）。盐水入侵的数学和数值模型几乎完全集中在稳定状态（Ketabchi et al. 2016），相应的动态问题仍然没有得到充分的研究;例如，缺乏模型来描述海平面上升，或地下水开采率的变化，与地下水运输的时间尺度相当。有一个特别需要发展和建立在现有的冰下盐水入侵的数学理论，这只是最近才出现作为一个调查的主题。现有的最佳模型（例如，Robel等人，2022）在物理效应（如融化）的参数化方面是高度简单化的，尚未纳入动态现象（如接地线移动），并且没有考虑冰盖重量下冰下含水层的显著变形（例如Lemieux等人，2008).该项目建议使用数学建模和流体动力学技术来研究这些数学上相似的问题。这将涉及构建物理动机的微分方程模型，建立在现有的基础上，并使用渐近分析的技术，以减少这些模型到一个更容易处理的形式，同时保留关键的物理。下一个阶段将是寻找分析和数值解，使用计算数学，这将提供新的见解下模型化的现象和上述考虑的开放问题。该项目属于EPSRC连续介质力学研究领域的福尔斯。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.