Frozen barrier evolution in saturated porous media

Abstract

A numerical model capable of simulating the freezing of aqueous solution flow in saturated porous media is presented. This model is based on a finite-difference approximation of the coupled equations for liquid water flow, heat and solute transport and phase change. The phase change equation facilitates the condition for the special case when liquid water and ice can reside in the pore space simultaneously, leading to a `mushy' zone. Results are presented to show the evolution of multiple frozen regions growing by a chain of freezing pipes. Two different regimes for the evolution of frozen bodies are distinguished based on system parameters. For the regime with lower freezing rate separate frozen bodies exist at steady-state, while for higher freezing rate the regime is characterized by linked frozen bodies. The numerical solution for the first regime is tested by a semi-analytical solution for the case of fresh water. For the second regime the model is able to simulate the process up to the point when linking of the separate frozen bodies occurs. For both regimes freezing is hindered downgradient of the freeze pipe where solute becomes highly concentrated, and a wedge of unfrozen media forms. For the first regime the wedge eventually forms into a liquid `island' surrounded by ice-bearing porous media.