Velocity fluctuations in slow flow through porous media

Abstract

In this thesis, I study the spatial statistical properties of slow flow through porous media on the pore scale by a combination of numerical simulation and theoretical arguments. I demonstrate that the flow patterns undergo a transition from swirls to strongly focused and channel-like patterns for decreasing porosities. Not only is the flow in low-porosity media strongly focused, but the flow also possesses long-tailed, non-Gaussian velocity probability density distributions. A main result of our simulations is that the statistics of the flow through a single channel captures the entire flow, insofar as the patterns and probability distributions are concerned. I have constructed a simplified, phenomenological model for the fast part of the flow in random porous media. This model yields the desired exponential velocity distributions. For high porosities, I find that the statistical properties of the velocity fluctuations behave in a similar way as those observed in dilute suspensions flows: the swirls have a power-law dependency on the solid volume fraction, the correlation length is finite and has also a power-law dependency. I demonstrate that this scaling behavior is consistent with the predictions of theories. Finally, I study creeping flow through a single rough walled channel by numerical simulation and present a theory that predicts scale dependency of the permeability for tight fractures.