Fertilization of liquid-saturated porous medium with multicomponent gases due to surface temperature oscillation

TL;DR

This paper develops an analytical model for non-isothermal diffusive transport of multicomponent gases in porous media under temperature oscillations, revealing complex phenomena like bubbly horizon formation and diffusion boundary layers.

Contribution

It introduces a new analytical framework for multicomponent gas solubility and transport in porous media affected by temperature oscillations, including boundary layer analysis.

Findings

Formation of a near-surface bubbly horizon due to temperature oscillation

Existence of a diffusion boundary layer for multicomponent solutions

Derivation of effective boundary conditions for diffusive transport

Abstract

We study non-isothermal diffusive transport of a weakly-soluble two-component substance in a liquid-saturated porous medium being in contact with the reservoir of this substance. Particular attention is given to the example case of infiltration of nitrogen and oxygen from the atmosphere under the annual temperature oscillation. The surface temperature of the porous medium half-space oscillates in time, which results in a decaying solubility wave propagating deep into the porous medium. In such a system, the zones of saturated solution and nondissolved phase coexist with the zones of undersaturated solution; these zones migrate with time. Moreover, the solubility of a multicomponent substance depends on its composition, which results in a much more intricate mathematical model of solubility as compared to the single-component case. We describe the phenomenon of formation of a near-surface bubbly horizon due to the temperature oscillation. An analytical theory of the phenomenon is developed. For multicomponent solutions we report the formation of diffusion boundary layer, which is not possible for single-component solutions. We construct an analytical theory for this boundary layer; in particular, we derive effective boundary conditions for the problem of the diffusive transport beyond this layer.