Enhanced saturation of liquid-saturated porous medium with atmosphere gases due to surface temperature oscillations
DOI:
https://doi.org/10.7242/1999-6691/2021.14.4.38Keywords:
diffusion transport, porous media, solubility of atmosphere gasesAbstract
We study the non-isothermal diffusion transport of a poorly soluble substance in a porous liquid-saturated medium being in contact with the reservoir of this substance. The surface temperature of a half-space porous medium oscillates in time, which creates a decaying temperature wave propagating deep into sediments. Since the solubility exponentially strongly depends on temperature, a decaying running solubility wave forms in the porous medium. In such a system, the zones of saturated solution and non-dissolved phase coexist with the zones of undersaturated solution. The effect is considered for the case of annual oscillation of the surface temperature of water-saturated ground being in contact with atmosphere. We reveal the phenomenon of formation of a near-surface bubbly horizon due to the temperature oscillation for one- and two-component solutes. In the case of a two-component solute, the solubility depends on the composition of the nondissolved phase, which necessitates the construction of a corresponding mathematical model of dissolution of multicomponent mixtures. We develop an analytical theory of the phenomenon of formation of the bubbly horizon. In both analytical theory and numerical simulations, the temperature dependence of the molecular diffusion coefficient is taken into account. In the presence of a propagating temperature wave, the nonlinear interaction between this dependence and the temperature dependence of the solubility creates an additional nonzero contribution to the mean-over-period mass flux. For multicomponent solutions, we report the formation of a diffusive boundary layer, which is not possible for single-component solutions. We construct an analytical theory for this boundary layer and derive effective boundary conditions for the problem of the diffusive transport beyond this layer. Theoretical results are in fair agreement with the results of numerical simulation.
Downloads
References
Donaldson J.H., Istok J.D., Humphrey M.D., O'Reilly K.T., Hawelka C.A., Mohr D.H. Development and testing of a kinetic model for oxygen transport in porous media in the presence of trapped gas. Groundwater, 1997, vol. 35, pp. 270-279. https://doi.org/10.1111/j.1745-6584.1997.tb00084.x
Donaldson J.H., Istok J.D., O'Reilly K.T. Dissolved gas transport in the presence of a trapped gas phase: Experimental evaluation of a two-dimensional kinetic model. Groundwater, 1998, vol. 36, pp. 133-142. https://doi.org/10.1111/J.1745-6584.1998.TB01073.X
Haacke R.R., Westbrook G.K., Riley M.S. Controls on the formation and stability of gas hydrate‐related bottom‐simulating reflectors (BSRs): A case study from the west Svalbard continental slope. Geophys. Res.: Solid Earth, 2008, vol. 113, B05104. https://doi.org/10.1029/2007JB005200
Goldobin D.S., Brilliantov N.V. Diffusive counter dispersion of mass in bubbly media. Rev. E, 2011, vol. 84, 056328. https://doi.org/10.1103/physreve.84.056328
Krauzin P.V., Goldobin D.S. Effect of temperature wave on diffusive transport of weakly soluble substances in liquid-saturated porous media. Phys. J. Plus, 2014, vol. 129, 221. https://doi.org/10.1140/epjp/i2014-14221-1
Goldobin D.S., Krauzin P.V. Formation of bubbly horizon in liquid-saturated porous medium by surface temperature oscillation. Rev. E, 2015, vol. 92, 063032. https://doi.org/10.1103/PhysRevE.92.063032
Davie M.K., Buffett B.A. A numerical model for the formation of gas hydrate below the seafloor. Geophys. Res.: Solid Earth, 2001, vol. 106, pp. 497-514. http://dx.doi.org/10.1029/2000JB900363
Goldobin D.S. Non-Fickian diffusion affects the relation between the salinity and hydrate capacity profiles in marine sediments. Rendus Mec., 2013, vol. 341, pp. 386-392. http://dx.doi.org/10.1016/j.crme.2013.01.014
Goldobin D.S., Brilliantov N.V., Levesley J., Lovell M.A., Rochelle C.A., Jackson P.D., Haywood A.M., Hunter S.J., Rees J.G. Non-Fickian diffusion and the accumulation of methane bubbles in deep-water sediments. Phys. J. E, 2014, vol. 37, 45. http://dx.doi.org/10.1140/epje/i2014-14045-x
Petit J.R., Jouzel J., Raynaud D., Barkov N.I., Barnola J.-M., Basile I., Bender M., Chappellaz J., Davis M., Delaygue G., Delmotte M., Kotlyakov V.M., Legrand M., Lipenkov V.Y., Lorius C., Pépin L., Ritz C., Saltzman E., Stievenard M. Climate and atmospheric history of the past 420,000 years from the Vostok ice core, Antarctica. Nature, 1999, vol. 399, pp. 429-436. http://dx.doi.org/10.1038/20859
Hunter S.J. Goldobin D.S., Haywood A.M., Ridgwell A., Rees J.G. Sensitivity of the global submarine hydrate inventory to scenarios of future climate change. Earth Planetary Sci. Lett., 2013, vol. 367, pp. 105-115. http://dx.doi.org/10.1016/j.epsl.2013.02.017
Henry W. III. Experiments on the quantity of gases absorbed by water, at different temperatures, and under different pressures. Trans. R. Soc., 1803, vol. 93, pp. 29-43. http://dx.doi.org/10.1098/rstl.1803.0004
Pierotti R.A. A scaled particle theory of aqueous and nonaqueous solutions. Rev., 1976, vol. 76, pp. 717-726. http://dx.doi.org/10.1021/cr60304a002
Baranenko V.I., Sysoev V.S., Fal’kovskii L.N., Kirov V.S., Piontkovskii A.I., Musienko A.N. The solubility of nitrogen in water. Energy, 1990, vol. 68, pp. 162-165. http://dx.doi.org/10.1007/bf02069879
Baranenko V.I., Fal’kovskii L.N., Kirov V.S., Kurnyk L.N., Musienko A.N., Piontkovskii A.I. The solubility of oxygen and carbon dioxide in water. Energy, 1990, vol. 68, pp. 342-346. http://dx.doi.org/10.1007/bf02074362
Yamamoto S., Alcauskas J.B., Crozier T.E. Solubility of methane in distilled water and seawater. Chem. Eng. Data, 1976, vol. 21, pp. 78-80. http://dx.doi.org/10.1021/je60068a029
Verhallen P.T.H.M., Oomen L.J.P., van den Elsen A.J.J.M., Kruger J., Fortuin J.M.H. The diffusion coefficients of helium, hydrogen, oxygen and nitrogen in water determined from the permeability of a stagnant liquid layer in the quasi-steady state. Eng. Sci., 1984, vol. 39, pp. 1535-1541. http://dx.doi.org/10.1016/0009-2509(84)80082-2
Sachs W. The diffusional transport of methane in liquid water: method and result of experimental investigation at elevated pressure. Petrol. Sci. Eng., 1998, vol. 21, pp. 153-164. https://doi.org/10.1016/S0920-4105(98)00048-5
Zeebe R.E. On the molecular diffusion coefficients of dissolved CO2, HCO3-, and CO32- and their dependence on isotopic mass. Cosmochim. Acta, 2011, vol. 75, pp. 2483-2498. https://doi.org/10.1016/j.gca.2011.02.010
Yershov E.D. General geocryology. Cambridge University Press, 1998. 580 p. https://doi.org/10.1017/CBO9780511564505
Gregg S.J., Sing K.S.W. Adsorption, surface area and porosity. Academic Press, 1982. 303 p.
Bird R.B., Stewart W.E., Lightfoot E.N. Transport phenomena. Wiley, 2007. 928 p.
Frenkel J. Kinetic theory of liquids. Dover Publications, 1955. 488 p.
Maryshev B.S., Goldobin D.S. Accumulation of gases dissolved in water saturating a nonisothermal porous massif in the presence of water freezing zones. IOP Conf. Ser.: Earth Environ. Sci., 2018, vol. 193, 012044. https://doi.org/10.1088/1755-1315/193/1/012044
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
