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Modeling Deep Bed Filtration Considering Limited Particle Retention

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Abstract

The classic deep bed filtration model (CDBFM) has been widely used for predicting transport and retention of particulate suspensions in porous media. In the CDBFM, the filtration coefficient function is assumed to be dependent of the retained particle concentration, and the boundary conditions are fixed at the porous media inlet cross section. However, if particle retention is limited, no more retention occurs (filtration coefficient equals zero) in regions where maximum retention (jamming limit) is reached. In this article, a model for deep bed filtration considering limited retention is proposed and analytical solutions are obtained. In cases where jamming limit is reached, the well-known CDBFM and the proposed model significantly differ from each other. Contrary to the CDBFM solutions, the obtained solutions show that concentrations along porous media are highly influenced by maximum retention front, which propagates with velocity independent of filtration coefficient.

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Acknowledgments

The authors are grateful for the financial support provided by Petrobras (T.C. 0050.0022723.06.4). J. A. Araújo acknowledges the Ph.D. scholarship provided by ANP/PRH 14.

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  1. Departamento de Engenharia de Petróleo, Universidade Federal do Rio Grande do Norte, Av. Salgado Filho 3000, Natal, RN, 59078-970, Brazil

    A. Santos & J. A. Araújo

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  1. A. Santos
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  2. J. A. Araújo
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Correspondence to A. Santos.

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Santos, A., Araújo, J.A. Modeling Deep Bed Filtration Considering Limited Particle Retention. Transp Porous Med 108, 697–712 (2015). https://doi.org/10.1007/s11242-015-0496-7

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  • DOI: https://doi.org/10.1007/s11242-015-0496-7

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