Development and Validation of a Numerical Model for Non-isothermal Multiphase Flow in Partially Frozen Porous Media

A general numerical model for the simultaneous transport of water, air, and heat in geological media under transient freezing conditions will be presented. The code solves conservation equations for air (as gas and dissolved in liquid water) and water (ice, liquid and vapor phases) using an integrated finite difference method with fully implicit time stepping. Key physical processes represented include advection as gas or liquid, vapor and aqueous phase diffusion, and heat conduction. Key relationships among liquid and ice saturations, interfacial pressures, and temperatures are based on empirical unfrozen soil moisture retention curves combined with thermodynamic relationships between ice/liquid capillary pressure and temperature. Saturated, partially saturated and partially frozen, and fully dry conditions are accommodated; phase disappearance/reappearance is handled with a variable substitution approach. Simulations of freezing-induced moisture redistribution agree well with published laboratory data on freezing-induced moisture redistribution (cryosuction). However, the comparison is sensitive to the assumed relationship between thermal conductivity and ice content, which is uncertain. Acknowledgment: This work was supported by SwRI(TM) Southwest Initiative for Mars (SwIM) under project number R9313 and by NASA Mars Fundamental Research Program award NNX06AB19G. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the author and do not necessarily reflect the views of the National Aeronautics and Space Administration.