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

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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.