Three-dimensional fluid flow and solute transport in rough-walled fractures

Abstract

Predicting fluid flow and solute transport through fractured rock is an important component of engineering analysis and design in many disciplines including groundwater contamination, drinking water supply, nuclear waste disposal, petroleum and gas production, mine and excavation stability, and geothermal production. Fractures largely influence the flow of fluids in a fractured rock environment by forming conduits that are typically orders of magnitude more conductive to fluid flow than the surrounding rock.

This thesis examines flow and transport through a single laboratory scale rock fracture, which is the necessary starting point for predicting flow and transport through large scale fractured rock systems. In the past, single fractures were idealized as a set of parallel plates in order to obtain a tractable mathematical description of fluid flow, namely the cubic law. However, it is now well established in the literature that single fractures are rough-walled conduits with variable aperture and points of contact. In fact, modern laboratory methods have directly mapped the void space of fracture samples, and provide the unique opportunity of simulating flow and transport at the scale of these measurements.

The primary objective of this investigation was to develop a numerical model to simulate three-dimensional small-scale fluid flow within a single fracture using the Navier-Stokes (NS) equations. The NS equations are the fundamental equations for fluid flow and form a complex non-linear system of equations that require numerical solution. In this work, the NS equations were solved using the finite volume method with a structured non-orthogonal grid mapped onto the three-dimensional void space. The fracture flow model was verified by comparing simulations to analytical and published results of fluid flow through parallel and sinusoidal plates. The flow model was applied to numerous synthetic or randomly generated rough-walled fractures, and the results clearly demonstrate for Reynolds numbers (Re) above unity, that the inertial forces may significantly influence the internal flow field within a fracture and the bulk flow rate across a fracture. Conversely, these simulations demonstrated that inertial forces may be neglected when Re was below unity. Two additional constraints involving the product of Re an d statistical roughness parameters were also used to delineate the influence of inertial forces. For simulations with Re below unity, the bulk flow rates were shown to be within 10% of a two-dimensional approximation commonly referred as the local cubic law.

The secondary objective of this investigation was to develop a numerical model to simulate three-dimensional small-scale solute transport within a single fracture using the flow field determined by the NS flow model. To accomplish this task, the random walk particle method (RWPM) which uses particle tracking methods to simulate advective transport of massless marker particles through the fracture flow field, and random displacements to simulate diffusive transport was employed. The fracture transport model was verified by comparing the simulation results to analytical solutions of solute transport through a set of parallel plates. Furthermore, the model simulations were compared to observations of solute breakthrough during tracer experiments on an actual rough-walled fracture, and a rough-walled transparent fracture replica. The model was successful in predicting the breakthrough curve for the actual fracture, and moderately successful for the transparent fracture replica.

By comparing the developed models to analytical solutions, simplified numerical simulations, and laboratory experiments, it was concluded that the models adequately describe fluid flow and contaminant transport through a single rough-walled fracture. Some examples of future applications of these models include: the comparison of the three-dimensional RWPM to the two-dimensional advection-dispersion equation for various synthetic fractures, high Reynolds number fluid flow and contaminant transport, and the dissolution of immiscible fluids trapped within a rough-walled fracture.