Enhanced saturation of liquid-saturated porous medium with atmosphere gases due to surface temperature oscillations

Abstract

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.