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Onset and Nonlinear Regimes of Convection of Ternary Mixture in a Rectangular Porous Cavity Taking into Account the Soret Effect

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Abstract

The onset and nonlinear regimes of the Soret-induced convection in a mixture of dodecane, isobutylbenzene, and tetralin, taken in equal mass fractions and placed in a rectangular porous cavity with rigid impermeable boundaries elongated in the horizontal direction and heated from below, have been numerically investigated. The vertical boundaries of the cavity are thermally insulated. The components of the mixture under consideration are representatives of the main groups of chemical compounds that are oil components. The values of the porosity and permeability of the medium were chosen to be close to the values of real media, such as sand, sandstone, or limestone. The area of such a configuration simulates a hydrocarbon field. Due to the Soret effect (thermal diffusion), the light components of the mixture with positive separation ratios (dodecane and isobutylbenzene) are accumulated in the hot region, whereas the heavy component (tetralin) is accumulated in the cold region. In the case of heating from below (provided by the presence of geothermal gradient under natural conditions), this process may induce convection. It was found that a steady flow occurs in the cavity at a certain value of Rayleigh number; this flow becomes oscillatory with an increase in the Rayleigh number. With a further increase in the Rayleigh number, irregular oscillations arise. Several monotonic and oscillatory regimes, characterized by different spatial scales (from one to ten vortices), were found in the range of Rayleigh numbers under consideration. The oscillations of instantaneous flow characteristics in oscillatory regimes have a complex shape. A steady-state flow regime with an asymmetric structure was found. The ranges of Rayleigh numbers in which the found regimes may exist and the time dependences of the integral characteristics during the formation of steady flows were determined. The effect of supercriticality on the flow structure and concentration distributions of mixture components were analyzed.

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REFERENCES

  1. Smorodin, B.L., Cherepanov, I.N., Myznikova, B.I., and Shliomis, M.I., Traveling-wave convection in colloids stratified by gravity, Phys. Rev. E, 2011, vol. 84, p. 026305. https://doi.org/10.1103/PhysRevE.84.026305

    Article  ADS  Google Scholar 

  2. Cherepanov, I.N., Colloid flow in a horizontal cell subjected to heating from sidewall, Vychisl. Mekh. Splosh. Sred, 2016, vol. 9, no. 2, pp. 135–144. https://doi.org/10.7242/1999-6691/2016.9.2.12

    Article  Google Scholar 

  3. Lyubimova, T.P. and Parshakova, Ya.N., Numerical investigation heat and mass transfer during vertical Bridgman crystal growth under rotational vibrations, J. Cryst. Growth, 2014, vol. 385, pp. 82–87. https://doi.org/10.1016/j.jcrysgro.2013.04.063

    Article  ADS  Google Scholar 

  4. Lyubimova, T.P. and Skuridin, R.V., Control of thermo- and solutocapillary flows in FZ crystal growth by high-frequency vibrations, Vychisl. Mekh. Splosh. Sred, 2016, vol. 9, no. 1, pp. 109–120. https://doi.org/10.7242/1999-6691/2016.9.1.10

    Article  MATH  Google Scholar 

  5. Lyubimova, T.P., Lepikhin, A.P., Parshakova, Ya.N., and Tsiberkin, K.B., Numerical modeling of liquid-waste infiltration from storage facilities into surrounding groundwater and surface-water bodies, J. Appl. Mech. Tech. Phys., 2016, vol. 57, pp. 1208–1216. https://doi.org/10.1134/S0021894416070099

    Article  ADS  MathSciNet  Google Scholar 

  6. Lyubimova, T.P., Lyubimov, D.V., Baydina, D.T., Kolchanova, E.A., and Tsiberkin, K.B., Instability of plane-parallel flow of incompressible liquid over a saturated porous medium, Phys. Rev. E, 2016, vol. 94, p. 013104. https://doi.org/10.1103/PhysRevE.94.013104

    Article  ADS  Google Scholar 

  7. Lebedev, D.V., Solodovnichenko, V.S., Ryzhkov, I.I., and Simunin, M.M., Effect of electric field on ion transport in nanoporous membranes with conductive surface, Pet. Chem., 2018, vol. 58, pp. 474–481. http://dx.doi.org/%2010.1134/S0965544118060075

    Book  Google Scholar 

  8. Maryshev, B., Lyubimova, T., and Lyubimov, D., Two-dimensional thermal convection in porous enclosure subjected to the horizontal seepage and gravity modulation, Phys. Fluid, 2013, vol. 25, p. 084105. https://doi.org/10.1063/1.4817375

    Article  ADS  Google Scholar 

  9. Maryshev, B.S., Lyubimova, T.P., and 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., 2016, vol. 102, pp. 113–121. https://doi.org/10.1016/j.ijheatmasstransfer.2016.06.016

    Article  Google Scholar 

  10. Soboleva, E.B., Density-driven convection in an inhomogeneous geothermal reservoir, Int. J. Heat Mass. Transf., 2018, vol. 127, pp. 784–798. https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.019

    Article  Google Scholar 

  11. Maryshev, B.S., On the horizontal pressure filtration of the mixture through a porous medium with clogging, Vestn. Perm. Univ., Fiz., 2016, no. 3 (34), pp. 12–21. https://doi.org/10.17072/1994-3598-2016-3-12-21

  12. Gubkin, I.M., Uchenie o nefti (The Doctrine of Oil), Moscow: Nauka, 1975.

  13. Collell, J., Galliero, G., Vermorel, R., Ungerer, P., Yiannourakou, M., Montel, F., and Pujol, M., Transport of multicomponent hydrocarbon mixtures in shales organic matter by molecular simulations, J. Phys. Chem. C, 2015, vol. 119, no. 39, pp. 22587–22595. https://doi.org/10.1021/acs.jpcc.5b07242

    Article  Google Scholar 

  14. Shevtsova, V., Melnikov, D., Mialdun, A., and Legros, J.C., Development of convection in binary mixture with Soret effect, Micrograv. Sci. Technol., 2006, vol. 18, pp. 38–41. https://doi.org/10.1007/BF02870376

    Article  ADS  Google Scholar 

  15. Goldobin, D.S., On thermal diffusion and gauge transformations for thermodynamic fluxes and forces, Vychisl. Mekh. Splosh. Sred, 2016, vol. 9, no. 1, pp. 52–58. https://doi.org/10.7242/1999-6691/2016.9.1.5

    Article  Google Scholar 

  16. Bratsun, D.A., Stepkina, O.S., Kostarev, K.G., Mizev, A.I., and Mosheva, E.A., Development of concentration-dependent diffusion instability in reactive miscible fluids under influence of constant or variable inertia, Micrograv. Sci. Technol., 2016, vol. 28, pp. 575–585. https://doi.org/10.1007/s12217-016-9513-x

    Article  ADS  Google Scholar 

  17. Smorodin, B.L., Ishutov, S.M., and Myznikova, B.I., On the convection of a binary mixture in a horizontal layer under high-frequency vibrations, Micrograv. Sci. Technol., 2018, vol. 30, pp. 95–102. https://doi.org/10.1007/s12217-017-9582-5

    Article  ADS  Google Scholar 

  18. Blanco, P., Bou-Ali, M.M., Platten, J.K., de Mezquia, D.A., Madariaga, J.A., and Santamaria, C., Thermodiffusion coefficients of binary and ternary hydrocarbon mixtures, J. Chem. Phys., 2010, vol. 132, p. 114506. https://doi.org/10.1063/1.3354114

    Article  ADS  Google Scholar 

  19. Bou-Ali, M.M., Ahadi, A., de Mezquia, D.A., Galand, Q., Gebhardt, M., Khlybov, O., Köhler, W., Larrañaga, M., Legros, J.C., Lyubimova, T., Mialdun, A., Ryzhkov, I., Saghir, M.Z., Shevtsova, V., and Varenbergh, S.V., Benchmark values for the Soret, thermodiffusion and molecular diffusion coefficients of the ternary mixture tetralin+isobutylbenzene+n-dodecane with 0.8-0.1-0.1 mass fraction, Eur. Phys. J. E, 2015, vol. 38, p. 30. https://doi.org/10.1140/epje/i2015-15030-7

    Article  Google Scholar 

  20. Platten, J.K. and Legros, J.C., Convection in Liquids, Berlin: Springer, 1984.

    Book  Google Scholar 

  21. Ryzhkov, I.I., Termodiffuziya v smesyakh: uravneniya, simmetrii, resheniya i ikh ustoichivost’ (Thermal Diffusion in Mixtures: Equations, Symmetries and Solutions and Their Stability), Novosibirsk: Sib. Otdel. RAN, 2013.

  22. Charrier-Mojtabi, M.C., Elhajjar, B., and Mojtabi, A., Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer, Phys. Fluid, 2007, vol. 19, p. 124104. https://doi.org/10.1063/1.2821460

    Article  ADS  MATH  Google Scholar 

  23. Lyubimova, T. and Zubova, N., Nonlinear regimes of the Soret-induced convection of ternary fluid in a square porous cavity, Transp. Porous Med., 2019, vol. 127, pp. 559–572. https://doi.org/10.1007/s11242-018-1211-2

    Article  MathSciNet  Google Scholar 

  24. Nield, D.A. and Bejan, A., Convection in Porous Media, 4th ed., New York: Springer, 2013.

    Book  Google Scholar 

  25. Ryzhkov, I.I. and Shevtsova, V.M., Long-wave instability of a multicomponent fluid layer with the Soret effect, Phys. Fluid, 2009, vol. 21, p. 014102. https://doi.org/10.1063/1.3054154

    Article  ADS  MATH  Google Scholar 

  26. Lyubimova, T.P. and Zubova, N.A., Onset of convection in a ternary mixture in a square cavity heated from above at various gravity levels, Micrograv. Sci. Technol., 2014, vol. 26, pp. 241–247. https://doi.org/10.1007/s12217-014-9383-z

    Article  ADS  Google Scholar 

  27. Lyubimova, T.P. and Zubova, N.A., Onset and nonlinear regimes of the ternary mixture convection in a square cavity, Eur. Phys. J. E, 2015, vol. 38, p. 19. https://doi.org/10.1140/epje/i2015-15019-2

    Article  Google Scholar 

  28. Forster, S., Bobertz, B., and Bohling, B., Permeability of sands in the coastal areas of the southern Baltic Sea: Mapping a grain-size related sediment property, Aquat. Geochem., 2003, vol. 9, pp. 171–190. https://doi.org/10.1023/B:AQUA.0000022953.52275.8b

    Article  Google Scholar 

  29. Iscan, A.G. and Kok, M.V., Porosity and permeability determinations in sandstone and limestone rocks using thin section analysis approach, Energy Sources, Part A, 2009, vol. 31, pp. 568–575. https://doi.org/10.1080/15567030802463984

    Article  Google Scholar 

  30. Shevtsova, V.M., Melnikov, D.E., and Legros, J.C., Onset of convection in Soret-driven instability, Phys. Rev. E, 2006, vol. 73, p. 047302. https://doi.org/10.1103/PhysRevE.73.047302

    Article  ADS  Google Scholar 

  31. Kim, M.C., Choi, C.K., and Yeo, J.-K., The onset of Soret-driven convection in a binary mixture heated from above, Phys. Fluid, 2007, vol. 19, p. 084103. https://doi.org/10.1063/1.2756824

    Article  ADS  MATH  Google Scholar 

  32. Lyubimova, T., Zubova, N., and Shevtsova, V., Onset and non-linear regimes of Soret-induced convection in binary mixtures heated from above, Eur. Phys. J. E, 2017, vol. 40, p. 27. https://doi.org/10.1140/epje/i2017-11517-5

    Article  Google Scholar 

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Funding

This study was supported by the Perm Krai Government (Program for Supporting Perm Krai Scientific Schools, agreement no. S-26/788).

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Authors and Affiliations

  1. Institute of Continuous Media Mechanics, Ural Branch, Russian Academy of Sciences, Perm, Russia

    T. P. Lyubimova & N. A. Zubova

  2. Perm State University, Perm, Russia

    T. P. Lyubimova

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  1. T. P. Lyubimova
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  2. N. A. Zubova
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Correspondence to T. P. Lyubimova or N. A. Zubova.

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Translated by Yu. Sin’kov

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Lyubimova, T.P., Zubova, N.A. Onset and Nonlinear Regimes of Convection of Ternary Mixture in a Rectangular Porous Cavity Taking into Account the Soret Effect. J Appl Mech Tech Phy 61, 1160–1173 (2020). https://doi.org/10.1134/S0021894420070068

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