Carbon capture and storage has been identified as a key technology in the global effort to reduce carbon emissions and mitigate the adverse effects of climate change. In this thesis we present a series of theoretical and experimental studies pertaining to surface tension effects in the geological sequestration of carbon dioxide. The aim of the thesis is to further our understanding of the role of surface tension, or capillarity, in geological flows. We consider a number of important problems related to carbon storage and present simplified models which consider the key dynamical controls in each case.

In chapters 2 and 3, we explore injection of CO2 into layers of permeable storage rock, where the layers are separated by thin low permeability mudstones and the formation takes the shape of an anticline. We assume that the mudstone layers are continuous and have a capillary entry pressure. We show that discrete pools of CO2 may form below the mudstone horizons and that the pool depth is a function of both the capillary entry pressure and the flux of CO2 into a given layer. We assume that the maximum pool depth before CO2 spills into the neighbouring aquifer is equal to the vertical deformation of the anticline. We then develop a dynamic model for rate of filling in each layer and show that spilling may occur from the system both during and after injection. The model is then applied to a two layered anticline and we show that there is a critical injection flux as a function of capillary pressure, above which spilling will occur before the capacity of the anticline is reached. We then extend our model to a system with more than two layers, and consider injection into several of the storage layers. We then discuss with an example how the choice of injection strategy may depend on the uncertainty in properties of the mudstone.

Motivated by CO2 migration through fractures and micro-fractures, in chapters 4 and 5 we consider capillary driven flows in non-uniform channels. In chapter 4, we develop a model for the capillary driven exchange of two immiscible fluids in a v-shaped wedge. We present a suite of analytical and numerical solutions, which consider capillary flow with and without gravitational forces. Our solutions demonstrate that unconfined flows in non-uniform channels may transition from a gravity current at early times to a capillary current at later times. We also identify the analogue between our exact model for fluid saturation as a function of capillary pressure and the classical empirical models. In chapter 5, we present a general model for capillary driven flow in a channel of arbitrary cross-sectional shape, as well as a series of capillary flow experiments in a v-shaped channel.

We conclude with a summary of our findings and identify some areas for further investigation in chapter 6.