Three-phase numerical model of water migration in partially frozen geological media: model formulation,validation, and applications

Water in the subsurface of the Earth’s cold regions—and possibly the subsurface of Mars—resides in the liquid, vapor, and ice phases. However, relatively few simulations addressing full three-phase, nonisothermal water dynamics in below-freezing porous media have been undertaken. This paper presents a nonisothermal, three-phase approach to modeling water migration in partially frozen porous media. Conservation equations for water (as ice, liquid, and vapor) and a single gas species (in the gas phase and dissolved in water) are coupled to a heat transport equation and solved by a finite-volume method with fully implicit time stepping. Particular attention is given to the method of spatial differencing when the pore space is partially filled with ice. The numerical model is able to reproduce freezing-induced water redistribution observed in laboratory experiments. Simulations of Earth permafrost dynamics and of the formation and evolution of a planetary-scale cryosphere on Mars demonstrate the new capabilities.