The Influence of Layering and Time-Dependent Injection Rates on Gravity-Driven Flows in Porous Media

Abstract

The geological storage of both carbon dioxide and hydrogen in underground porous rock formations, such as saline aquifers and depleted oil fields, has been proposed to mitigate both the negative effects of increased carbon dioxide concentration in the atmosphere in the case of carbon storage and make up for intermittency in the renewable energy supply in the case of hydrogen storage. Understanding the flow processes of both fluids once injected into these formations is of great importance in understanding the efficacy of such storage. In this thesis, we study idealised geological flow problems related to geological carbon and hydrogen storage in the limit where buoyancy forces dominate. In particular, we explore the influence that both layering of the rock formation, as well as time-dependent injection rates, have on the evolution of the flows. We give a brief introduction to carbon and hydrogen storage, as well as gravity-driven flows in porous media in chapter 1. Chapters 2, 3 and 4 consider flow through layered porous media. In chapter 2 we investigate the controls on the spreading of a plume in the thin layer limit of a cross-bedded formation where the along-slope extent of the invading fluid is much larger than each individual layer. Rather surprisingly, it is found that a buoyant plume may rise above the lower boundary of the formation when certain conditions are met. We provide experimental validation of the model developed and then consider the implications of our results in an anticline setting. Chapters 3 and 4 conversely consider flows in the thick layer limit. Flow occurs in two thick adjacent rock layers. In Chapter 3 we study the effect that differing permeabilities in each layer have on the flow, finding similarity solutions which we validate with numerics and experiments. In chapter 4 we extend this model to consider not only a change in permeability but also a change in the elevation of the cap rock at the interface between two regions. We consider a finite release of fluid around this change in elevation and show numerically that the fluid is ultimately found to drain into the deeper layer due to buoyancy forces. The transient behaviour before the fluid fully drains into this deeper region is shown to depend on the change in elevation and the permeability ratio of the layers. In chapters 5 and 6 we study currents supplied with decaying and periodic injection rates, respectively. In particular, in chapter 5, we study how gravity currents evolve when supplied by either power law or exponentially decaying fluxes in time. We show that early and late regimes exist where the current behaves according to well-known analytic solutions. Experimental and numerical results are provided. In chapter 6, to gain insight into how hydrogen may behave in an anticline, we study the cyclic injection and extraction of hydrogen along a shallow incline. In particular, we investigate the controls on how much hydrogen can be extracted in each cycle without producing ambient fluid. In chapter 7, we first summarise the work presented in this thesis. Then we outline some potential ways our work could be expanded, namely the addition of residual trapping to the models developed, the extension of our models to the axisymmetric case, and the use of an invasion percolation model to study the effect layering has on flows dominated by capillary forces.