Abstract—
The Rayleigh–Taylor instability and the initial stage of density-driven convection in a porous medium is simulated numerically in reference to geologic problems. A two-layer fluid system in which the lower layer is formed by pure water and the upper layer by an aqueous solution of salts is considered. The upper layer is more dense and viscous. The determination of the characteristic time of the onset of convection in the numerical solution is discussed. The parameters which depend on and do not depend of the initial density fluctuations are revealed. The effect of the viscosity contrast on the onset and development of convection flow and mass transfer is analyzed. The quantitative discrepancies related to neglecting the viscosity contrast in geologic fluids are estimated.
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REFERENCES
Polubarinova-Kochina, P.Ya., Teoriya dvizheniya gruntovykh vod (Theory of Ground–Water Movement), Moscow: Nauka, 1977.
Bear, J. and Cheng, A., Modeling Groundwater Flow and Contaminant Transport, New York: Springer, 2010.
Afanas’ev, A.A. and Barmin, A.A., Unsteady one-dimensional water and steam flows through a porous medium with allowance for phase transitions, Fluid Dynamics, 2007, vol. 42, no. 4, pp. 627–636. https://doi.org/10.1134/S0015462807040126
Shargatov, V.A., Tsypkin, G.G., and Bogdanova, Yu.A., Fragmentation of flow through a porous medium with a capillary pressure gradient, Dokl. Ros. Akad. Nauk, 2018, vol. 480, no. 1, pp. 40–44.
Afanasyev, A.A. and Chernova, A.A., On solution of the Riemann problem describing injection of a heated salt solution into an aquifer, Fluid Dynamics, 2019, vol. 54, no. 4, pp. 510–519. https://doi.org/10.1134/S0015462819040013
Tsypkin, G.G., Instability of a light fluid over a heavy one under the motion of their interface in a porous medium, Fluid Dynamics, 2020, vol. 55, no. 2, pp. 213–219. https://doi.org/10.1134/S0015462820020135
Nield, D.A. and Bejan, A., Convection in Porous Media, New York: Springer, 2006.
Drazin, P.G., Introduction to Hydrodynamic Stability, Cambridge University Press, 2002.
Bestehorn, M. and Firoozabadi, A., Effect of fluctuations on the onset of density-driven convection in porous media, Phys. Fluids, 2012, vol. 24, p. 114102.
Homsy, G.M., Viscous fingering in porous media, Ann. Rev. Fluid Mech., 1987, vol. 19, pp. 271–311.
Manickam, O. and Homsy, G.M., Fingering instabilities in vertical miscible displacement flows in porous media, J. Fluid Mech., 1995, vol. 288, pp. 75–102.
Ghesmat, K. and Azaiez, J., Viscous fingering instability in porous media: Effect of anisotropic velocity-dependent dispersion tensor, Transport in Porous Media, 2008, vol. 73, pp. 297–318.
Moortgat, J., Viscous and gravitational fingering in multiphase compositional and compressible flow, Adv. Water Resources, 2016, vol. 89, pp. 53–66.
Teng, Y., Wang, P., Jiang, L., Liu, Yu, Song, Y., and Wei, Y., An experimental study of density-driven convection of fluid pairs with viscosity contrast in porous media, Int. J. Heat and Mass Transfer, 2020, vol. 152, p. 119514.
Aleksandrov, A.A., Dzhuraeva, E.V., and Utenkov, V.F., Viscosity of saline, Teplofiz. Vysok. Temp., 2012, vol. 50, no. 3, pp. 378–383.
Soboleva, E.B., Density-driven convection in an inhomogeneous geothermal reservoir, Int. J. Heat and Mass Transfer, 2018, vol. 127 (part C), pp. 784–798.
Soboleva, E.B., Method for numerically investigating the dynamics of saline water in soil, Mat. Modelirovanie, 2014, vol. 26, no. 2, pp. 50–64.
Soboleva, E.B. and Tsypkin, G.G., Numerical simulation of convective flows in a soil during the evaporation of water containing a dissolved admixture, Fluid Dynamics, 2014, vol. 49, no. 5, pp. 634–644. https://doi.org/10.1134/S001546281405010X
Soboleva, E.B. and Tsypkin, G.G., Regimes of haline convection during the evaporation of groundwater containing a dissolved admixture, Fluid Dynamics, 2016, vol. 51, no. 3, pp. 364–371. https://doi.org/10.1134/S001546281603008X
Soboleva, E.B., A method for numerical simulation of haline convective flows in porous media applied to geology, Comp. Math. Mathem. Phys., 2019, vol. 59, no. 11, pp. 1893–1903.
Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere Pub. Corp.; McGraw-Hill, 1980.
Leonard, B.P., A stable and accurate convective modeling procedure based on quadratic upstream interpolation, Computer Methods in Applied Mechanics and Engineering, 1979, vol. 19, no. 1, pp. 59–98.
Landau, L.D. and Lifshitz, E.M., Course of Theoretical Physics, vol. 6, Fluid Mechanics, (2nd ed.), Butterworth-Heinemann, 1987.
Kim Kim, M.Ch., Onset of buoyancy-driven convection in a variable viscosity liquid saturated in a porous medium, Chemical Engineering Science, 2014, vol. 113, pp. 77–87.
ACKNOWLEDGMENT
The author wishes to thank G.G. Tsypkin for useful discussions.
Funding
The work was carried out with support from the Russian Science Foundation under the grant no. 16–11–10195.
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Translated by E.A. Pushkar
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Soboleva, E.B. Onset of Rayleigh–Taylor Convection in a Porous Medium. Fluid Dyn 56, 200–210 (2021). https://doi.org/10.1134/S0015462821020105
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DOI: https://doi.org/10.1134/S0015462821020105