Modeling the methane hydrate formation in an aqueous film submitted to steady cooling

This work mathematically models the thermal evolution in a hydrate forming system which is subjected to an imposed steady cooling. The study system is a cylindrical thin film of aqueous solution at 19 Mpa where methane is the hydrate forming molecule. The model accounts for both the stochastic nature of crystallization that causes sub-cooling and the heat source term due to the exothermicity of hydrate formation. The model equation is based on the resolution of the continuity equation in terms of a heat balance. The inclusion of the heat source term has to be considered in order to account for the influence of crystallization. The rate of heat released during the crystallization is governed by the probability of nucleation. The results provided by the model equation subjected to boundary conditions allow the depiction of temperature evolution in the dispersed phase. The most important point in the temperature-time curve is the onset time of hydrate crystallization. Three time intervals were found to characterize the temperature evolution during the steady cooling: (1) linear cooling, (2) hydrate formation with a release of heat, and (3) the last interval of steady cooling.