A Multi‐Phase Heat Transfer Model for Water Infiltration Into Frozen Soil

Abstract

Water infiltration into frozen soil is a crucial process in many parts of the world as more than 50% of the exposed land in the Northern Hemisphere are experiencing seasonally frozen soils (T. Zhang et al., 2003). Frozen soil has a significantly reduced infiltration capacity depending on the ice content compared to unfrozen soil and therefore infiltration and surface runoff substantially depend on the ice content in the soil (Mohammed et al., 2018). If the liquid water cannot infiltrate into the soil, erosion and substantial surface water runoff might take place causing landslides and debris flow (Seyfried & Murdock, 1997). Also, the contribution of snowmelt to the groundwater resources can be an important factor in regions with otherwise little soil water storage (Hood & Hayashi, 2015). With the snow melt, contaminants originally stored in the snow are transported by the meltwater and infiltrate into groundwater resources (e.g., Feng et al., 2001;Jones et al., 1989). If water infiltrates into the soil and then freezes, frost heave might occur and damage roads, train tracks, pipelines and other critical infrastructure. In general, the vadose zone experiences complex interactions between soil, water, and air with chemical and biological activity within the vadose zone strongly effected by temperature and the availability of liquid water (Hayashi, 2013). Therefore, understanding the flow behavior under freezing conditions and the thermal interaction between soil and infiltrating water is crucial for hazard prevention and groundwater management. The thermal state of the involved phases is key for the hydraulic processes.Water infiltration into frozen soil is a multi-phase scenario with an -at least initially -local thermal non-equilibrium (LTNE) between the involved phases because the infiltrating water has a temperature above the freezing point, while the soil and its pore filling are frozen. LTNE situations are well-known for a saturated porous matrix (Gossler et al., 2020;Hamidi et al., 2019) and the LTNE concept has been recently extended to partially saturated soils (Heinze & Blöcher, 2019). In the context of geothermal energy exploration, the LTNE concept has gained more and more attention due to the obvious limitations and the oversimplification of models assuming local thermal equilibrium (LTE) (e.g., Gelet et al., 2013;Shaik et al., 2011;C. Xu et al., 2015). LTE models are based on the volumetric weighting of thermal parameters of the involved

Permafrost modelling with OpenFOAM®: New advancements of the permaFoam solver

“…It involves basic coupling between water flow and heat flow, in the sense of Yu et al [65]. The two primary variables that describe the physical state of water into the soil are the generalized water pressure h [m] (positive in saturated conditions, negative in unsaturated conditions -see [49]) and the soil temperature T [K] (defined by assuming local thermal equilibrium -see [15] for a discussion of this assumption). The two equations governing these primary variables are a modified Richards equation with a source term accounting for actual evapotranspiration (Eq.…”

“…In this patch, the temperature of start of infiltration is fixed at Tmelt+Tshif = 273. 15 Such a feature may help to ease significantly the numerical resolution of cases in particularly steep conditions at the period of initiation of thawing or freezing. The approximation related with the use of the 'thawing' option may generate additional errors in the numerical resolutions, so problem-wise trade off must be made between the accuracy of the simulation and the decrease of the computation time.…”

A Thermodynamic Nonequilibrium Model for Preferential Infiltration and Refreezing of Melt in Snow

“…The α i and α w terms in Equations 10 and 11 account for heat transfer between the ice and water phases regardless of if phase change occurs or not. Despite Equations 10 and 11 not explicitly including any Newton's law of cooling terms (Heinze, 2021), our model accounts for this heat transfer mechanism. We prove this point and describe the estimation of α i and α w in the following section.…”

“…The LTNE assumption allows us to mechanistically estimate the rate of ice‐water phase change as a function of both the ice and water temperatures. The LTNE model has been recently used to improve thermodynamic description of frozen soil (Hamidi et al., 2019; Heinze, 2021), and, to the best of our knowledge, has not been used to investigate the thermodynamics of snowpack. The thermodynamic component of this model can be readily used to investigate melting instead of refreezing.…”

Computational Modelling on Gasification Processes of Municipal Solid Wastes Including Molten Slag

“…The enthalpy-porosity method was most often used when interface tracking was important, as it is able to represent both solid and liquid phases in an Eulerian manner, and the solid-liquid interface is determined via the phase volume fraction. For others, the focus was on melting of multiple solids, such as through packed beds [17,22,23], and water infiltration into frozen soil [24]. For the present application of slagging gasifiers, which are operated at higher temperatures than conventional gasifiers, much of the available literature focuses on slag formation and its effects on gasifier performance.…”