Approximate reduced permeability of marine sediments due to hydrate growth using a floating random walk method

Near the base of the hydrate stability zone (BHSZ), methane-rich pore fluid migrates upward, supplying the growth of hydrates in the pore space between marine sediment particles. As the hydrate saturation (i.e., pore volume fraction occupied by hydrate crystals) increases and limits pore liquid content, the relative permeability (i.e., the ratio of permeability of hydrate-bearing sediment to that of hydrate-free sediment) decreases. When exceeds the percolation threshold, hydrate crystals grow beyond individual pores, and decreases in are even more significant. Previous workers have measured the relation between and hydrate fraction, and various empirical correlations have been developed for predicting relative permeability in hydrology and the oil industry. However, predictions from different formulae can differ by orders of magnitude, causing great uncertainty in modeling results. More sophisticated approaches have included the use of computational fluid mechanics to solve Poisson's equation in the pore space, which gives more accurate results, but at high computational expense. We present a floating random walk method combined with Monte Carlo integration to approximate the porous flow field and calculate the permeability. In packed spherical particles, the method compares favorably with the Kozeny-Carman relation. We further extend this method using Monte Carlo method to simulate the growth of hydrate in irregular pores and predict the evolution of sediment permeability with(). Our results can provide insight into the coupling between phase transitions and permeability change, which play important roles in hydrate formation and dissociation, as well as in the thawing and freezing of permafrost.