“…Because of the extensive presence of fluid flow and reactive transport, predicting the spatially distributed permeability with reasonably good accuracy is crucial to the Earth science community and beyond. Previous researchers have built upon pioneering treatments of the relation between k r and the saturation level of an additional nonwetting fluid phase (e.g., Brooks & Corey, 1964; van Genuchten, 1980), to consider how k r varies with the saturation level of a solid, such as hydrate (e.g., Brooks & Corey, 1964; Kleinberg et al., 2003; Kumar et al., 2010; Liang et al., 2011; Murphy et al., 2020; Ordonez et al., 2009) or ice (e.g., Chamberlain & Gow, 1979; Horiguchi & Miller, 1983; Watanabe & Osada, 2016). Empirical correlations based on these findings are commonly employed in the oil industry (see Lee, 2008).…”