Scaling laws for nucleation rates of gas hydrate

Formation of gas hydrates is a first-order phase transition that starts with nucleation. Nucleation rate is central to nucleation phenomena of any system as it defines the rate at which critical nuclei form in a unit volume or other measures of system size. For gas hydrates, a primary difficulty in the investigation of gas hydrate nucleation has been the inability of researchers to compare nucleation rates of gas hydrates across various systems of different scales and complexity, as it is not even clear which measure(s) of system size is most appropriate to use in a given circumstance. This inadequacy in turn has been limiting the capacity of researchers to investigate the nucleation process itself. Here we first derived general scaling laws of nucleation rates of gas hydrate systems and then applied it to compare the nucleation rate of methane hydrate determined by a High Pressure Automated Lag Time Apparatus (HP-ALTA) to that of a flow loop. The ratio of the nucleation rates of two systems (of the same guest gas and at the same driving force) scales linearly with the ratio of the system sizes (i.e., the ratio of most probable induction times scales linearly with the inverse of the ratio of the system sizes). Comparison of five conceivable measures of the system size for the scaling suggests that the total length of the three-phase-lines in the system is the most appropriate measure for scaling of the nucleation rate of methane hydrate.