Stochastic Cellular Automata Modeling of CO₂ Hydrate Growth and Morphology

Carbon dioxide (CO₂) hydrates are important in a diverse range of applications and technologies in the environmental and energy fields. The development of such technologies relies on fundamental understanding, which necessitates not only experimental but also computational studies of the growth behavior of CO₂ hydrates and the factors affecting their crystal morphology. As experimental observations show that the morphology of CO₂ hydrate particles differs depending on growth conditions, a detailed understanding of the relation between the hydrate structure and growth conditions would be helpful. To this end, this work adopts a modeling approach based on hybrid probabilistic cellular automata to investigate variations in CO₂ hydrate crystal morphology during hydrate growth from stagnant liquid water presaturated with CO₂. The model, which uses free energy density profiles as inputs, correlates the variations in growth morphology to the system subcooling ΔT, i.e., the temperature deficiency from the triple CO₂-hydrate-water equilibrium temperature under a given pressure, and properties of the growing hydrate-water interface, such as surface tension and curvature. The model predicts that when ΔT is large, parabolic needle-like or dendrite crystals emerge from planar fronts that deform and lose stability. In agreement with chemical diffusion-limited growth, the position of such planar fronts versus time follows a power law. In contrast, the tips of the emerging parabolic crystals steadily grow in proportion to time. The modeling framework is computationally fast and produces complex growth morphology phenomena under diffusion-controlled growth from simple, easy-to-implement rules, opening the way for employing it in multiscale modeling of gas hydrates.