Nonlinear regimes of binary mixture convection in a two-layer porous medium of different configurations
DOI:
https://doi.org/10.7242/1999-6691/2022.15.2.11Keywords:
convection, diffusion, thermal diffusion, binary mixture, hydrocarbon mixture, porous medium, two-layer mediumAbstract
The results of modeling the convection of a binary mixture of liquid hydrocarbons in a two-layer porous medium are presented. The simulation area is a horizontally elongated rectangular cavity divided into two layers. In one of the considered cases, these sublayers are of equal height, and in the other case, the interface between the layers has the shape of a convex downward circular arc, which imitates a synclinal geological fold. The layers have different permeability. In the cavity, there is a geothermal temperature gradient with an average temperature characteristic of a depth of 2000 m, which corresponds to the average oil depth. The composition of the mixture, the thermal conditions and the geometry used make up the reservoir model of the hydrocarbon deposit. The problem is solved in terms of the Darcy–Boussinesq model with allowance for the effect of thermal diffusion. The emergence and establishment of nonlinear convection regimes, as well as the distribution of the concentration of mixture components for different values of the permeability of the layers and their dependence on which of these layers is more permeable, are considered in simulations. It is found that in the case of a small difference in the permeabilities of the layers, a stationary regime is established in the cavity of any of the considered configurations. With a significant difference in permeability of the layers in the cavity, either quasi-periodic oscillations of a complex shape or irregular oscillations can be observed. A "local" occurrence of convection is shown for a large permeability difference, followed by a weak penetration of the flow into a less permeable layer, as well as a "large-scale" occurrence of convection in the case of an insignificant permeability difference.
Downloads
References
Szulczewski M., Hesse M., Juanes R. Carbon dioxide dissolution in structural and stratigraphic traps. J. Fluid Mech., 2013, vol. 736, pp. 287-315. https://doi.org/10.1017/jfm.2013.511
Simmons C., Bauer-Gottwein P., Graf T., Kinzelbach W., Kooi H., Li L., Werner A. Variable density groundwater flow: From modelling to applications. Groundwater modelling in arid and semi-arid areas, ed. H. Wheater, S. Mathias, X. Li. Cambridge University Press, 2010. Pp. 87-118. https://doi.org/10.1017/CBO9780511760280.008
Baghooee H., Montel F., Galliero G., Yan W., Shapiro A. A new approach to thermal segregation in petroleum reservoirs: Algorithm and case studies. J. Petrol. Sci. Eng., 2021, vol. 201, 108367. https://doi.org/10.1016/j.petrol.2021.108367
Parameswari K., Mudgal B.V. Assessment of contaminant migration in an unconfined aquifer around an open dumping yard: Perungudi a case study. Environ. Earth Sci., 2015, vol. 74, pp. 6111-6122. https://doi.org/10.1007/s12665-015-4634-x
Kozeny J. Uber Kapillare Leitung des Wassers im Boden: Sitzungsber [On capillary flow of water in soil: session report]. Sitz. Akad. Wiss. Wien., 1927, vol. 136, pp. 271-306.
Carman P.C. Fluid fow through granular beds. AIChE, 1937, vol. 15, pp. 150-166.
Nield D.A., Bejan A. Convection in porous media. Springer, 2013. 778 p. https://doi.org/10.1007/978-1-4614-5541-7
Klimenko L.S., Maryshev B.S. Numerical simulation of microchannel blockage by the random walk method. Chem. Eng. J., 2020, vol. 381, 122644. https://doi.org/10.1016/j.cej.2019.122644
Maryshev B.S., Klimenko L.S. Porous media cleaning by pulsating filtration flow. Microgravity Sci. Technol., 2022, vol. 34, 5. https://doi.org/10.1007/s12217-021-09922-3
Nield D.A., Kuznetsov A.V. The onset of convection in an anisotropic heterogeneous porous medium: A new hydrodynamic boundary condition. Transp. Porous Med., 2019, vol. 127, pp. 549-558. https://doi.org/10.1007/s11242-018-1210-3
Kolchanova E.A., Kolchanov N.V. Onset of solutal convection in layered sorbing porous media with clogging. Int. J. Heat Mass Trans., 2022, vol. 183, 122110. https://doi.org/10.1016/j.ijheatmasstransfer.2021.122110
Hewitt D.R., Neufeld J.A., Lister J.R. High Rayleigh number convection in a porous medium containing a thin low-permeability layer. J. Fluid Mech., 2014, vol. 756, pp. 844-869. https://doi.org/10.1017/jfm.2014.478
Zech A., Zehner B., Kolditz O., Attinger S. Impact of heterogeneous permeability distribution on the groundwater flow systems of a small sedimentary basin. J. Hydrol., 2016, vol. 532, pp. 90-101. https://doi.org/10.1016/j.jhydrol.2015.11.030
Salibindla A.K.R., Subedi R., Shen V.C., Masuk A.U.M., Ni R. Dissolution-driven convection in a heterogeneous porous medium. J. Fluid Mech., 2018, vol. 857, pp. 61-79. https://doi.org/10.1017/jfm.2018.732
Soboleva E. Density-driven convection in an inhomogeneous geothermal reservoir. Int. J. Heat Mass Tran., 2018, vol. 127, pp. 784-798. https://doi.org/10.1016/j.ijheatmasstransfer.2018.08.019
Zubova N.A., Lyubimova T.P. Convection of ternary mixture in anisotropic porous medium. AIP Conf. Proc., 2021, vol. 2371, 050013. https://doi.org/10.1063/5.0059568
Zubova N.A., Lyubimova T.P. Nonlinear convection regimes of a ternary mixture in a two-layer porous medium. Vychisl. mekh. splosh. sred – Computational Continuum Mechanics, 2021, vol. 14, no. 1, pp. 110-121. https://doi.org/10.7242/1999-6691/2021.14.1.10
De Paoli M., Zonta F., Soldati A. Dissolution in anisotropic porous media: Modelling convection regimes from onset to shutdown. Phys. Fluid., 2017, vol. 29, 026601. https://doi.org/10.1063/1.4975393
Li Q., Cai W.H., Li B.X., Chen C.-Y. Numerical study of density-driven convection in laminated heterogeneous porous media. Journal of Mechanics, 2020, vol. 36, pp. 665-673. https://doi.org/10.1017/jmech.2020.32
Barbier E. Geothermal energy technology and current status: An overview. Renew. Sustain. Energ. Rev., 2002, vol. 6, pp. 3-65. https://doi.org/10.1016/S1364-0321(02)00002-3
Kocberber S., Collins R.E. Proc. of the SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana, USA, September 23-26, 1990. P. 175-201. https://doi.org/10.2118/20547-MS
Schmitt R.W. Double diffusion in oceanography. Annu. Rev. Fluid Mech., 1994, vol. 26, pp. 255-285. https://doi.org/10.1146/ANNUREV.FL.26.010194.001351
Pedersen K.S., Hjermstad H.P. Proc. of the SPE Annual Technical Conference and Exhibition. Houston, Texas, USA, September 28-30, 2015. SPE-175085-MS. https://doi.org/10.2118/175085-MS
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, 2015, vol. 119, pp. 22587-22595. http://dx.doi.org/10.1021/acs.jpcc.5b07242
Mialdun A., Minetti C., Gaponenko Yu., Shevtsova V., Dubois F. Analysis of the thermal performance of SODI instrument for DCMIX configuration. Microgravity Sci. Technol., 2013, vol. 25, pp. 83-94. http://dx.doi.org/ 10.1007/s12217-012-9337-2
Alkhasov A.B. Vozobnovlyayemaya energetika [Renewable energy]. Moscow, Fizmatlit, 2012. 256 p.
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. Aquatic Geochemistry, 2003, vol. 9, pp. 171-190. https://doi.org/10.1023/B:AQUA.0000022953.52275.8b
Iscan A.G., 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
Gebhardt M., Kohler W., Mialdun A., Yasnou V., Shevtsova V. Diffusion, thermal diffusion, and Soret coefficients and optical contrast factors of the binary mixtures of dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene. J. Chem. Phys., 2013, vol. 138, 114503. https://doi.org/10.1063/1.4795432
McKibbin R., O’Sullivan M.J. Onset of convection in a layered porous medium heated from below. J. Fluid Mech., 1980, vol. 96, pp. 375-393. https://doi.org/10.1017/S0022112080002170
McKibbin R., O’Sullivan M.J. Heat transfer in a layered porous medium heated from below. J. Fluid Mech., 1981, vol. 111, pp. 141-173. ]https://doi.org/10.1017/S0022112081002334
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.