Tracing diffusion in porous media with fractal properties

Vladimirov, I. G. and Klimenko, A. Y. (2010) Tracing diffusion in porous media with fractal properties. Multiscale Modeling and Simulation, 8 4: 1178-1211. doi:10.1137/090760234

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Author Vladimirov, I. G.
Klimenko, A. Y.
Title Tracing diffusion in porous media with fractal properties
Journal name Multiscale Modeling and Simulation   Check publisher's open access policy
ISSN 1540-3459
Publication date 2010
Sub-type Article (original research)
DOI 10.1137/090760234
Open Access Status File (Publisher version)
Volume 8
Issue 4
Start page 1178
End page 1211
Total pages 34
Place of publication Philadelphia, PA, United States
Publisher Society for Industrial and Applied Mathematics
Collection year 2011
Language eng
Formatted abstract
This work is concerned with conditional averaging methods which can be used for modeling of transport in porous media with volume reactions in the fluid phase and surface reactions at the fluid/solid interface. The model under consideration takes into account convection, diffusion within the pores and on larger scales, and homogeneous and heterogeneous reactions. Near the interface with fractal properties, the fluid flow is slow, and diffusion, as a transport mechanism, dominates over convection. Following the conditional moment closure paradigm, we employ a diffusion tracer as a reference scalar field that makes the conditional averaging sensitive to the proximity of a point to the interface. The resulting conditionally averaged reactive transport equations are governed by the probability density function (PDF) of the diffusion tracer, and this makes the study of its behavior an important problem. We consider a hitting time stochastic interpretation of the diffusion tracer, establish integral equations relating it to a subsidiary distance tracer, and obtain distance-diffusion inequalities. Assuming that the fluid/solid interface and pores themselves possess fractal properties which are quantified, in particular, by a variant of the Minkowski-Bouligand fractal dimension, we investigate the interplay between the interface and network scenarios of fractality in the scaling laws of the diffusion tracer PDF. We also discuss and employ several hypotheses, including a lognormal cascade hypothesis on the behavior of the diffusion tracer at different length scales.
© 2010 Society for Industrial and Applied Mathematics.
Keyword Reactive transport
Porous media
Contact distribution
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

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Created: Sun, 26 Sep 2010, 00:02:24 EST