Derivation of a Langmuir type of model to describe the intrinsic growth rate of gas hydrates during crystallisation from gas mixtures

Gas hydrates are crystalline water based solids composed of a three-dimensional network of water molecules. They form a network of cavities in which molecules of light gases can be encapsulated depending on their size and affinity. Gas hydrates can, by their nature, not be classified as chemical compounds since they do not possess a definite stoechiometry. In contrast they have to be regarded as solid solution phases, the stoechiometry of which is not fixed but depends on the composition of the surrounding liquid. At equilibrium, the composition dependence of the hydrate phase can be described by means of the classical van der Waals and Platteeuw model (van der Waals and Platteeuw, 1959). In the framework of the model, Langmuir constants are used for expressing the relative ability of light components to get enclathrated within the cavities. The work consists in considering again the enclathration of host species, not at thermodynamic equilibrium, but during the crystallisation process taking place under non-equilibrium conditions. It aims at proposing a new formulation for the hydrate composition as a function of new intrinsic constants which are based on Langmuir kinetic constants.