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.