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Acta Mechanica
Published in: Acta Mechanica 8/2023

11-04-2023 | Original Paper

Cleaning porous media by an external vertical flow

Authors: Boris S. Maryshev, Lyudmila S. Klimenko

Published in: Acta Mechanica | Issue 8/2023

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Abstract

The paper is devoted to the study of the cleaning process of a clogged porous medium. A flow through a closed domain of porous media is generated by the prescribed pressure drop between the boundaries. The porous media initially contain an immobilized solute which is removed by an external flow. As a result, the porosity and permeability of the media increase. The solute immobilization is modelled within the framework of the mobile/immobile media model taking into account saturation of a solid matrix of the media with the solute. The porosity is assumed as a linear function of the immobile solute concentration, and the dependence of permeability variation due to porosity change is modelled on the base of the Kozeny–Carman expression. The direction of an external flux is assumed to be the same as the gravity force direction. This assumption allows us to obtain a one-dimensional solution for the cleaning process taking into account the buoyancy force. The equation for the flow into the clogged porous media is derived in the general case. The one-dimensional problem of the porous media cleaning by a vertical external flow is formulated and solved. The dependences of the cleaning time on the system parameters are obtained and discussed. The question about the stability of the one-dimensional solution is described, and critical values of the governing parameters are defined in a particular case.
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Literature
1.
Adin, A., Rebhun, M.: Deep-bed filtration: accumulation-detachment model parameters. Chem. Eng. Sci. 42(5), 1213–1219 (1987)CrossRef
2.
Barthe, L., Desportes, S., Steinmetz, D., Hemati, M.: Metallic salt deposition on porous particles by dry impregnation in fluidized bed: effect of drying conditions on metallic nanoparticles distribution. Chem. Eng. Res. Des. 87(7), 915–922 (2009)CrossRef
3.
Beiki, H.: Developing convective mass transfer of nanofluids in fully developed flow regimes in a circular tube: modeling using fuzzy inference system and ANFIS. Int. J. Heat Mass Transf. 173, 121285 (2021)CrossRef
4.
Bromly, M., Hinz, C.: Non-Fickian transport in homogeneous unsaturated repacked sand. Water Resour. Res. 40, W07402 (2004)CrossRef
5.
Butcher, J.C.: Numerical Methods for Ordinary Differential Equations. Wiley, New York (2016)CrossRefMATH
6.
Carman, P.C.: Fluid flow through granular beds. Trans. Inst. Chem. Eng. 15, 150–166 (1937)
7.
Conte, S.D., De Boor, C.: Elementary Numerical Analysis: An Algorithmic Approach. SIAM, Philadelphia (2017)CrossRefMATH
8.
Darcy, H.: Les fontaines publiques de la ville de Dijon: exposition et application... Victor Dalmont (1856)
9.
Deans, H.A.: A mathematical model for dispersion in the direction of flow in porous media. Soc. Petrol. Eng. J. 3(01), 49–52 (1963)CrossRef
10.
11.
Elimelech, M., Gregory, J., Jia, X.: Particle Deposition and Aggregation: Measurement, Modelling and Simulation. Butterworth-Heinemann, Oxford (2013)
12.
Gouze, P., Le Borgne, T., Leprovost, R., Lods, G., Poidras, T., Pezard, P.: Non-Fickian dispersion in porous media: 1. Multiscale measurements using single-well injection withdrawal tracer tests. Water Resour. Res. 44(6), W06426 (2008)CrossRef
13.
Gresho, P., Sani, R.: The stability of a fluid layer subjected to a step change in temperature: transient vs. frozen time analyses. Int. J. Heat Mass Transf. 14(2), 207–221 (1971)CrossRefMATH
14.
Gruesbeck, C., Collins, R.: Entrainment and deposition of fine particles in porous media. Soc. Petrol. Eng. J. 22(06), 847–856 (1982)CrossRef
15.
Herzig, J., Leclerc, D., Goff, P.L.: Flow of suspensions through porous media-application to deep filtration. Ind. Eng. Chem. 62(5), 8–35 (1970)CrossRef
16.
Ives, K.: Research on deep filters. Trans. Inst. Chem. Eng. Chem. Eng. 43(8), T238 (1965)
17.
Iwasaki, T.: Some notes on sand filtration. J. Am. Water Works Assoc. 29(10), 1591–1597 (1937)CrossRef
18.
Kord, S., Mohammadzadeh, O., Miri, R., Soulgani, B.S.: Further investigation into the mechanisms of asphaltene deposition and permeability impairment in porous media using a modified analytical model. Fuel 117, 259–268 (2014)CrossRef
19.
Li, X., Huang, H., Meakin, P.: A three-dimensional level set simulation of coupled reactive transport and precipitation/dissolution. Int. J. Heat Mass Transf. 53(13–14), 2908–2923 (2010)CrossRefMATH
20.
Maryshev, B., Cartalade, A., Latrille, C., Néel, M.C.: Identifying space-dependent coefficients and the order of fractionality in fractional advection–diffusion equation. Transp. Porous Media 116(1), 53–71 (2017)MathSciNetCrossRef
21.
Maryshev, B.S., Lyubimova, T.P., Lyubimov, D.V.: Stability of homogeneous seepage of a liquid mixture through a closed region of the saturated porous medium in the presence of the solute immobilization. Int. J. Heat Mass Transf. 102, 113–121 (2016)CrossRef
22.
Molnar, I.L., Pensini, E., Asad, M.A., Mitchell, C.A., Nitsche, L.C., Pyrak-Nolte, L.J., Miño, G.L., Krol, M.M.: Colloid transport in porous media: a review of classical mechanisms and emerging topics. Transp. Porous Media 130(1), 129–156 (2019)MathSciNetCrossRef
24.
25.
Parvan, A., Jafari, S., Rahnama, M., Raoof, A., et al.: Insight into particle retention and clogging in porous media; a pore scale study using lattice Boltzmann method. Adv. Water Resour. 138, 103530 (2020)CrossRef
26.
Pham, N.H., Papavassiliou, D.V.: Hydrodynamic effects on the aggregation of nanoparticles in porous media. Int. J. Heat Mass Transf. 121, 477–487 (2018)CrossRef
27.
Qin, F., Moqaddam, A.M., Kang, Q., Derome, D., Carmeliet, J.: LBM simulation of self-assembly of clogging structures by evaporation of colloidal suspension in 2D porous media. Transp. Porous Media 128(3), 929–943 (2019)CrossRef
28.
Rajagopalan, R., Chu, R.Q.: Dynamics of adsorption of colloidal particles in packed beds. J. Colloid Interface Sci. 86(2), 299–317 (1982)CrossRef
29.
Rees, D.A.S., Selim, A., Ennis-King, J.: The instability of unsteady boundary layers in porous media. In: Emerging Topics in Heat and Mass Transfer in porous media, pp. 85–110. Springer (2008)
30.
Roth, E.J., Gilbert, B., Mays, D.C.: Colloid deposit morphology and clogging in porous media: fundamental insights through investigation of deposit fractal dimension. Environ. Sci. Technol. 49(20), 12263–12270 (2015)CrossRef
31.
Selim, H.: Prediction of contaminant retention and transport in soils using kinetic multireaction models. Environ. Health Perspect. 83, 69–75 (1989)CrossRef
32.
Selim, H., Davidson, J., Rao, P.: Transport of reactive solutes through multilayered soils. Soil Sci. Soc. Am. J. 41(1), 3–10 (1977)CrossRef
33.
Taylor, S.W., Jaffé, P.R.: Substrate and biomass transport in a porous medium. Water Resour. Res. 26(9), 2181–2194 (1990)CrossRef
23.
Van Genuchten, MTh., Wierenga, P.J.: Mass transfer studies in sorbing porous media I. Analytical solutions. Soil Sci. Soc. Am. J. 40(4), 473–480 (1976)CrossRef
34.
Völtz, C., Pesch, W., Rehberg, I.: Rayleigh–Taylor instability in a sedimenting suspension. Phys. Rev. E 65(1), 011404 (2001)CrossRef
35.
Yang, X.G., Ye, Q., Cheng, P.: In-plane transport effects on hydrogen depletion and carbon corrosion induced by anode flooding in proton exchange membrane fuel cells. Int. J. Heat Mass Transf. 55(17–18), 4754–4765 (2012)CrossRef
36.
Zheng, X.L., Shan, B.B., Chen, L., Sun, Y.W., Zhang, S.H.: Attachment–detachment dynamics of suspended particle in porous media: experiment and modeling. J. Hydrol. 511, 199–204 (2014)CrossRef
Metadata
Title
Cleaning porous media by an external vertical flow
Authors
Boris S. Maryshev
Lyudmila S. Klimenko
Publication date
11-04-2023
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 8/2023
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-023-03559-6

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