Mathematical Model of Freezing of Rocks Saturated With Salt Solution Taking Into Account the Influence of Osmosis

Abstract

The paper presents a mathematical model of rocks freezing saturated with salt solution under impact of osmotic force. Osmosis is related to the salt concentration gradient, which is characteristic for solutions, and it is a powerful mechanism for the movement of solutions in poorly permeable porous media. A mathematical criterion for the formation of closed “pockets” with brines (cryopags) in frozen rocks has been obtained. This criterion is shown to be significantly depends on the osmosis coefficient. The model includes three layers of a porous medium saturated, respectively, with ice, ice and solution, and salt solution only. A special case was studied when there is only a second layer with a movable boundary, on which a phase transition from the second layer to the third one occurs. The investigated layer is saturated with a salt solution and ice in thermodynamic equilibrium. Other layers are replaced by boundary conditions. An approximate analytical solution of the problem is found in a self-similar formulation. The nature of the influence of osmotic force on the freezing process of rocks saturated with solution is shown. The characteristic patterns associated with the considered process are revealed. One of the features of the osmosis influence is the fact that it can cause the movement (migration) of the solution in the direction of increasing pressure, i.e. in the direction opposite to the driving force caused by the pressure gradient.