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Effects of Intra-REV Pore Distribution Modeling in the Flow of Non-Newtonian Fluids in Porous Media

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Abstract

Motivated by some discrepancies in the comparison between the rheometric viscosity function of shear-thinning fluids and the apparent Darcy viscosity function obtained in porous media simulations/experiments, we propose a model for the flow in porous media with a non-uniform pore distribution in the pore scale, i.e., inside the Representative Elementary Volume (REV). Since different pore sizes inside the REV would lead to different characteristic shear rates, the heterogeneity of the pores in the elementary scale can be responsible for the mentioned discrepancies. Indeed, simulations in a plug of a porous medium have shown that the apparent viscosity function decreases as we increase the standard deviation distribution of the diameter of idealized cylindrical pores. The ratio of the mobility of the heterogeneous pore distribution to the mobility of the homogeneous one is plotted as a function of the power-law index of the non-Newtonian viscosity function. The dimensionless analysis has shown to be a powerful tool in the investigation, collapsing the information in several cases. In addition, our results reveal that a non-uniform pore size distribution can be an important source of the discrepancy between the viscosity function obtained in a rheometric device and the one obtained from the Darcy equation, as reported in the literature.

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Funding

The funding was provided by Petrobras (Grant No. 2017/00428-1) and CAPES (Grant No. PROEX 803/2018).

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Authors and Affiliations

  1. Department of Mechanical Engineering, COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 24210-240, Brazil

    Allan B. G. Motta & Roney L. Thompson

  2. Petrobras Research Center (CENPES), Petrobras Av. Horácio Macedo 950, Cidade Universitária, Ilha do Fundão, Rio de Janeiro, RJ, 21941-598, Brazil

    Mateus P. Schwalbert & Raphael J. Leitão

  3. Escola de Química, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 21941-909, Brazil

    Luiz F. L. R. Silva

  4. Wikki Brasil LTDA, Parque Tecnológico da UFRJ, Rio de Janeiro, RJ, 21941-907, Brazil

    Jovani L. Favero & Rodrigo A. C. Dias

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  1. Allan B. G. Motta
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  2. Roney L. Thompson
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  3. Mateus P. Schwalbert
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  4. Luiz F. L. R. Silva
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Correspondence to Roney L. Thompson.

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Motta, A.B.G., Thompson, R.L., Schwalbert, M.P. et al. Effects of Intra-REV Pore Distribution Modeling in the Flow of Non-Newtonian Fluids in Porous Media. Transp Porous Med 145, 505–525 (2022). https://doi.org/10.1007/s11242-022-01861-w

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