A hysteresis model for the unfrozen liquid content in freezing porous media

The description of the freezing characteristics of porous media is one of the most conspicuous ingredients in flow and heat transport models that involve freezing and thawing processes. Unfrozen liquid content (ULC) shows strong hysteresis during freezing and thawing cycles in different types of soils and other porous media. We discuss the possible mechanisms of hysteresis in porous media and develop a numerical model for the unfrozen liquid content that is capable of describing the hysteresis phenomenon in freezing and thawing cycles. We present a coupled finite element model as the framework for the numerical simulation of fluid flow and heat transport in partially frozen porous media. The implementation aspects of the ULC model as well as its integration into numerical codes are discussed in detail. We investigate the potential impact of the hysteresis phenomenon on the numerical simulation of transport processes in porous media through benchmark examples and validate the behavior of the model against available laboratory measurement data.