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Type: Journal article
Title: A stochastic theory for deep bed filtration accounting for dispersion and size distributions
Author: Shapiro, A.
Bedrikovetski, P.
Citation: Physica A: Statistical Mechanics and its Applications, 2010; 389(13):2473-2494
Publisher: Elsevier Science BV
Issue Date: 2010
ISSN: 0378-4371
Statement of
A.A. Shapiro and P.G. Bedrikovetsky,
Abstract: We develop a stochastic theory for filtration of suspensions in porous media. The theory takes into account particle and pore size distributions, as well as the random character of the particle motion, which is described in the framework of the theory of continuous-time random walks (CTRW). In the limit of the infinitely many small walk steps we derive a system of governing equations for the evolution of the particle and pore size distributions. We consider the case of concentrated suspensions, where plugging the pores by particles may change porosity and other parameters of the porous medium. A procedure for averaging of the derived system of equations is developed for polydisperse suspensions with several distinctive particle sizes. A numerical method for solution of the flow equations is proposed. Sample calculations are applied to compare the roles of the particle size distribution and of the particle flight dispersion on the deposition profiles. It is demonstrated that the temporal flight dispersion is the most likely mechanism forming the experimentally observed hyperexponential character of the deposition profiles.
Keywords: Suspension
Porous medium
Size distribution
Random walk
Rights: Copyright © 2010 Elsevier B.V. All rights reserved.
DOI: 10.1016/j.physa.2010.02.049
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Appears in Collections:Aurora harvest 5
Australian School of Petroleum publications

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