Fault zones have the potential to act as leakage pathways through low permeability structural seals in geological reservoirs. Faults may facilitate migration of groundwater contaminants and stored anthropogenic carbon dioxide (CO $_2$ ), where the waste fluids would otherwise remain securely trapped. We present an analytical model that describes the dynamics of leakage through a fault zone cutting multiple aquifers and seals. Current analytical models for a buoyant plume in a semi-infinite porous media are combined with models for a leaking gravity current and a new model motivated by experimental observation, to account for increased pressure gradients within the fault due to an increase in Darcy velocity directly above the fault. In contrast to previous analytical fault models, we verify our results using a series of analogous porous medium tank experiments, with good matching of observed leakage rates and fluid distribution. We demonstrate the utility of the model for the assessment of CO $_2$ storage security, by application to a naturally occurring CO $_2$ reservoir, showing the dependence of the leakage rates and fluid distribution on the fault/aquifer permeability contrast. The framework developed within this study can be used for quick assessment of fluid leakage through fault zones, given a set of input parameters relating to properties of the fault, aquifer and fluids, and can be incorporated into basin-scale models to improve computational efficiency. The results show the utility of using analytical methods and reduced-order modelling in complex geological systems, as well as the value of laboratory porous medium experiments to verify results.

The rate of carbon dioxide (CO 2) dissolution in saline aquifers is the least well-constrained of the secondary trapping mechanisms enhancing the long-term security of geological carbon storage. CO 2 injected into a heterogeneous saline reservoir will preferentially travel along high permeability layers increasing the CO 2-water interfacial area which increases dissolution rates. We provide a conservative, first-principles analysis of the quantity of CO 2 dissolved and the rate at which free-phase CO 2 propagates in layered reservoirs. At early times, advection dominates the propagation of CO 2. This transitions to diffusion dominated propagation as the interfacial area increases and diffusive loss slows propagation. As surrounding water-filled layers become CO 2 saturated, propagation becomes advection dominated. For reservoirs with finely bedded strata, ∼10% of the injected CO 2 can dissolve in a year. The maximum fraction of CO 2 that dissolves is determined by the volumetric ratio of water in low permeability layers and CO 2 in high permeability layers. Plain Language Summary To limit global warming to 2 • C, it is likely that large amounts of carbon dioxide (CO 2) will need to be stored underground. A significant fraction of the total possible storage space for CO 2 is in salt water reservoirs, kilometers beneath the surface. It is important that once the CO 2 has been injected underground, it is securely trapped, otherwise, there is a risk that it could leak back to the surface. After the CO 2 is injected into these reservoirs, it can dissolve in the surrounding water, greatly reducing the risk of leakage, although complete dissolution of all the injected CO 2 may take millions of years. However, preferential flow of CO 2 along more permeable layers in geological formations creates a complex front between the water and CO 2 which increases the surface area available for dissolution. This study calculates the minimum amount of injected CO 2 that can dissolve in such a reservoir and how far it travels. Using injection of CO 2 for enhanced oil recovery at the Salt Creek Field in Wyoming as an example, we find that in one year around 10% of the total injected CO 2 can dissolve into the surrounding water by this process and become trapped.

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