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``Velocity Fluctuations in Slow Flow Through Porous Media''
Department of Earth, Atmospheric, and Planetary Sciences, MIT 1998.
Abstract:
% $Log: abstract.tex,v $ % Revision 1.1 93/05/14 14:56:25 starflt % Initial revision % % Revision 1.1 90/05/04 10:41:01 lwvanels % Initial revision % % %% The text of your abstract and nothing else (other than comments) goes here. %% It will be single-spaced and the rest of the text that is supposed to go on %% the abstract page will be generated by the abstractpage environment. This %% file should be \input (not \include 'd) from cover.tex. In this thesis, I study the spatial statistical properties of slow flow through various 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 stream tube captures the entire flow, insofar 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. At the other side of the porosity spectrum--high porosities-- I find that the statistics properties velocity fluctuations behave in a similar way as the fluctuations 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.
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