Transfer and accumulation of gases dissolved in water saturating a nonisothermal massif of a porous medium with water freezing zones

Abstract

A one-dimensional problem of gas transport through a bubbly medium under the influence of a temperature wave is investigated taking into account freezing of the near-surface layer. Such freezing means the presence of a phase transition under the action of a temperature wave on the massif of the porous medium when the temperature goes below the freezing point of water. In this case, the Stefan problem is to be solved in order to obtain a nonstationary temperature distribution. With the knowledge of the temperature distribution in the massif at each moment of time, it is possible to take into consideration the influence of the temperature wave on the gas transport process. This process is described within the framework of the bubbly medium approximation. The calculation of the solubility of gas in water is based on the scaled particle theory. It is shown that a temperature wave causes the rise of an average flow of gases generated in the porous massif toward the surface, which leads to the effect of gas accumulation in the near-surface layer. The distribution of the gas concentration in the near-surface layer is obtained and the depth of this layer is estimated. In addition, the influence of the parameters of the problem on the accumulation effect is examined. The gas accumulation rate is found to be constant if the surface of the massif is at a temperature below the freezing point all year round and to decrease with an increase in the average surface temperature. At the same time, the accumulation rate increases with the intensification of gas generation in the porous massif.