Flow through partially frozen pores in granular media containing ice or gas hydrate plays an essential role in diverse phenomena including methane migration and frost heave. As freezing progresses, the frozen phase grows in the pore space and constricts flow paths so that the permeability decreases. Previous works have measured the relationship between permeability and volumetric fraction of the frozen phase, and various correlations have been proposed to predict permeability change in hydrology and the oil industry. However, predictions from different formulae can differ by orders of magnitude, causing great uncertainty in modeling results. We present a floating random walk method to approximate the porous flow field and estimate the effective permeability in isotropic granular media, without solving for the entire flow field in the pore space. In packed spherical particles, the method compares favorably with the Kozeny-Carman formula. We further extend this method with a probabilistic interpretation of the volumetric fraction of the frozen phase, simulate the effect of freezing in irregular pores, and predict the evolution of permeability. Our results can provide insight into the coupling between phase transitions and permeability change, which plays important roles in hydrate formation and dissociation, as well as in the thawing and freezing of permafrost and ice--bed coupling beneath glaciers.

At thermodynamic equilibrium, gas hydrates are arranged in the pore space of host sediments to minimize free energy, including the energy of interfaces. Through an analogy with frozen soil, we show that free energy minimization in hydrate-bearing sediments requires the presence of a water film of finite thickness separating hydrate from the sediment grains. The thickness of this premelted layer may be predicted from a balance of intermolecular forces acting across the film. Temperature and porewater salinity are the strongest determiners of premelted layer thickness. We show that, at temperatures and salinities typical of the subsurface or commonly used in laboratory investigations of hydrate-bearing porous media, the premelted layer varies in thickness from microns to sub-nanometer, with thicker layers corresponding to lower salinities and/or higher temperatures. Balance of intermolecular forces predicts that hydrate will be completely nonwetting on hydrophilic surfaces, including silica. We also show that flow through premelted layers may be a significant component of the permeability of hydrate-bearing sediments, particularly at moderate to high hydrate saturation (>60%); and that the electrical conductivity of the premelted layer at needs to be accounted for in assessments of hydrate abundance from subsurface resistivity logs. This work highlights the importance of considering premelted layers when predicting the effects of hydrate on sediment properties.

Freezing in porous media is associated with a host of dynamic phenomena that stem from the presence and mobility of premelted liquid at subzero temperatures. Accurate assessments of the progressive liquid---ice phase transition is required for predictive models of frost damage, glacier---till coupling, and many other cold regions processes, as well as for evaluating the capacity for water storage in near-surface extraterrestrial environments. We use a Monte Carlo approach to sample the pore space in a synthetic 3D packing of poly-dispersed spherical particles, and evaluate local geometrical constraints that allow us to assess changes in the relative proportions of pore fluid and ice. By approximating the phase boundary geometry in fine-grained pores while considering both the curvature of the liquid---ice interface and wetting interactions with matrix particles, our model predicts changes in phase equilibrium in granular media over a broad temperature range, where present accounting for the colligative effects of chloride and perchlorate solutes. In addition to formulating the constitutive behavior needed to better understand properties and processes in frozen soils, our results also provide insight into other aspects of phase equilibria in porous media, including the formation of methane hydrates in permafrost and marine sediments, and the partitioning between liquid water and vapor in the vadose zone.