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.

Abstract

It has been shown experimentally that small droplets, bouncing on a vibrated liquid bath, can "walk" across the surface due to their interaction with their own wave-field. Gunwale bobbing is a life-size instance of this phenomena in which a person standing on the gunwales of a canoe propels it by pumping it into oscillation with the legs. The canoe moves forward by surfing the resulting wave-field. After an initial transient, the canoe achieves a cruising velocity which satisfies a balance between the thrust generated from pushing downwards into the surface gradients of the wave-field and the resistance due to a combination of profile drag and wave drag. By superposing the linear wave theories of for steady cruising and of Helmholtz for an oscillating source, we demonstrate that such a balance can be sustained. We calculate the optimal parameter values to achieve maximum canoe velocity. We compare our theoretical result to accelerometer data taken from an enthusiastic gunwale bobber. We discuss the similarities and differences between gunwale bobbing and hydrodynamic quantum analogues, and possible applications to competitive sports.

We present a simple model for the development of shear layers between parallel flows in confining channels. Such flows are important across a wide range of topics from diffusers, nozzles and ducts to urban air flow and geophysical fluid dynamics. The model approximates the flow in the shear layer as a linear profile separating uniform-velocity streams. Both the channel geometry and wall drag affect the development of the flow. The model shows good agreement with both particle image velocimetry experiments and computational turbulence modelling. The simplicity and low computational cost of the model allows it to be used for benchmark predictions and design purposes, which we demonstrate by investigating optimal pressure recovery in diffusers with non-uniform inflow.

An asymmetric body with a sharp leading edge and a rounded trailing edge produces a smaller wave disturbance moving forwards than backwards, and this is reflected in the wave drag coefficient. This experimental fact is not captured by Michell's theory for wave drag (Michell 1898). In this study, we use a tow-tank experiment to investigate the effects of asymmetry on wave drag, and show that these effects can be replicated by modifying Michell's theory to include the growth of a symmetry-breaking boundary layer. We show that asymmetry can have either a positive or a negative effect on drag, depending on the depth of motion and the Froude number.