Abstract
We present the results of the numerical investigation of the Soret-induced convection in a ternary liquid mixture consisting of dodecane, isobutylbenzene and tetralin, taken in equal portions. The mixture is placed into a square porous cavity with rigid impermeable boundaries heated from below. The lateral boundaries are adiabatic. The problem under consideration is a model of natural hydrocarbon reservoir with porous medium, and the components of mixture are representatives of the main groups of chemical compounds comprising oil. Due to the thermodiffusion effect, dodecane and isobutylbenzene as the lighter components of this mixture with positive separation ratios are accumulated in the warmer domain of the cavity, and the heavy component, tetralin, is accumulated in the colder domain, which may lead to the development of convection. The calculations are performed for the parameters of porous medium close to the real parameters of oil fields and temperature gradient that correspond to geothermal gradient. They provide data on the temporal evolution of the characteristics of the flow and component separation. We also analyze the onset and development of single-vortex and two-vortex instability modes with the growth of the Rayleigh number \(Ra_{\mathrm{{por}}}\). It is found that at a certain value of the supercriticality, the stationary flow regime is replaced by the oscillatory regime. At even higher values of the Rayleigh number, the chaotic oscillations take place. The transitions between single-vortex and two-vortex flows are also observed. For porosity equal to 0.1, the two oscillatory regimes at different oscillation amplitudes are excited. With the porosity growth, the region of the existence of the oscillatory regimes becomes narrower.
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Abahri, O., Sadaoui, D., Mansouri, K., Mojtabi, A., Mojtabi, M.C.: Thermogravitational separation in horizontal annular porous cellmogravitational separation in horizontal annular porous cell. Mech. Ind. 18, 106 (2017)
Benano-Melly, L.B., Caltagirone, J.-P., Faissat, B., Montel, F., Costeseque, P.: Modeling Soret coefficient measurement experiments in porous media considering thermal and solutal convection. Int. J. Heat Mass Transf. 44, 1285–1297 (2001)
Blanco, P., Bou Ali, M.M., Platten, J.K., Nezquia, D.A., Madariaga, J.A., Santamaría, C.: Thermodiffusion coefficients of binary and ternary hydrocarbon mixtures. J. Chem. Phys. 132, 114506 (2010)
Bonté, D., Van Wees, J.-D., Verweij, J.M.: Subsurface temperature of the onshore Netherlands: new temperature dataset and modelling. Geol. Mijnb. Neth. J. Geosci. 91, 491515 (2012)
Charrier-Mojtabi, M.C., Elhajjar, B., Mojtabi, A.: Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer. Phys. Fluids 19, 124104 (2007)
Collell, J., Galliero, G., Vermorel, R., Ungerer, P., Yiannourakou, M., Montel, F., Pujol, M.: Transport of multicomponent hydrocarbon mixtures in shales organic matter by molecular simulations. J. Phys. Chem. C 119(39), 22587 (2015)
Faissat, B., Knudsen, K., Stenby, E.H., Montel, F.: Fundamental statements about thermal diffusion for a multicomponent mixture in a porous medium. Fluid Phase Equilibria 100, 209–222 (1994)
Forster, S., Bobertz, B., Bohling, B.: Permeability of sands in the coastal areas of the southern Baltic Sea: mapping a grain-size related sediment property. Aquat. Geochem. 9, 171–190 (2003)
Guillou-Frottier, L., Carré, C., Bourgine, B., Bouchot, V., Genter, A.: Structure of hydrothermal convection in the Upper Rhine Graben as inferred from corrected temperature data and basin-scale numerical models. J. Volcanol. Geotherm. Res. 256, 2949 (2013)
Hoover, D.B., Reran, W.D., Hill, P.L.: The geophysical expression of selected mineral deposit models. Open-File report 92-557, United States department of the interior geological survey (1992)
Iscan, A.G., Kok, M.V.: Porosity and permeability determinations in sandstone and limestone rocks using thin section analysis approach. Energy Sources Part A 31, 568–575 (2009)
Labrosse, G.: Free convection of binary liquid with variable Soret coefficient in thermogravitational column: the steady parallel base states. Phys. Fluids 15(9), 2694–2727 (2003)
Larabi, M.A., Mutschler, D., Mojtabi, A.: Thermal gravitational separation of ternary mixture n-dodecane/isobutylbenzene/tetralin components in a porous medium. J. Chem. Phys. 144, 244902 (2016)
Larraaga, M., Bou-Ali, M.M., Lizarraga, I., Madariaga, J.A., Santamaría, C.: Soret coefficients of the ternary mixture 1,2,3,4-tetrahydronaphthalene + isobutylbenzene + n-dodecane. J. Chem. Phys. 143, 024202 (2015)
Lipsey, L., Pluymaekers, M., Goldberg, T., Oversteeg, K., van Ghazaryan, L., Cloetingh, S., van Wees, J.-D.: Numerical modelling of thermal convection in the Luttelgeest carbonate platform, the Netherlands. Geothermics 64, 135151 (2016)
Lyubimova, T.P., Parshakova, Ya.N.: Numerical investigation heat and mass transfer during vertical Bridgman crystal growth under rotational vibrations. J. Cryst. Growth. 385, 82–87 (2014)
Lyubimova, T.P., Zubova, N.A.: Onset of convection in a ternary mixture in a square cavity heated from above at various gravity levels. Microgravity Sci. Technol. 26(4), 241–247 (2014)
Lyubimova, T.P., Zubova, N.A.: Onset and nonlinear regimes of the ternary mixture convection in a square cavity. Eur. Phys. J. E 38, 19 (2015)
Lyubimova, T.P., Lepikhin, A.P., Parshakova, Ya.N., Tsiberkin, K.B.: Numerical modeling of liquid-waste infiltration from storage facilities into surrounding groundwater and surface-water bodies. J. Appl. Mech. Tech. Phys. 57(7), 58–66 (2016a)
Lyubimova, T.P., Lyubimov, D.V., Baydina, D.T., Kolchanova, E.A., Tsiberkin, K.B.: Instability of plane-parallel flow of incompressible liquid over a saturated porous medium. Phys. Rev. E 94(1), 013104 (2016b)
Manger, G.E.: Porosity and Bulk Density of Sedimentary Rocks. Contributions to geochemistry. Geological survey bulletin 1144-e. United States government printing office, Washington (1963)
Martin, A., Bou-Ali, M.M.: Determination of thermal diffusion coefficient of nanofluid: fullerenetoluene. C. R. Méc. 339(5), 329–334 (2011)
Maryshev, B., Lyubimova, T., Lyubimov, D.: Two-dimensional thermal convection in porous enclosure subjected to the horizontal seepage and gravity modulation. Phys. Fluids 25(8), 084105 (2013)
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)
Nasrabadi, H., Hoteit, H., Firoozabadi, A.: An analysis of species separation in thermogravitational column filled with porous media. Transp. Porous Med. 67(3), 473–486 (2007)
Nield, D.A., Bejan, A.: Convection in Porous Media. Springer, New York (2013)
Pasquale, V., Chiozzi, P., Verdoya, M.: Evidence for thermal convection in the deep carbonate aquifer of the eastern sector of the Po Plain, Italy. Tectonophysics 594, 112 (2013)
Ryzhkov, I.I., Shevtsova, V.M.: Long-wave instability of a multicomponent fluid layer with the Soret effect. Phys. Fluids 21(1), 014102 (2009)
Soboleva, E.: Numerical simulation of haline convection in geothermal reservoirs. J. Phys. Conf. Ser. 891, 012105 (2017)
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The work was carried out under financial support of Russian Science Foundation (Grant 14-21-00090).
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Lyubimova, T., Zubova, N. Nonlinear Regimes of the Soret-Induced Convection of Ternary Fluid in a Square Porous Cavity. Transp Porous Med 127, 559–572 (2019). https://doi.org/10.1007/s11242-018-1211-2
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DOI: https://doi.org/10.1007/s11242-018-1211-2