A mathematical model of the initial stage of the hydrate layer formation at the interface between water and a hydrate forming gas

Abstract

This paper proposes a concept and a corresponding theoretical framework describing the initial stage of the formation of a hydrate layer at the interface between water and a gas hydrate former. According to the presented model, this stage (the induction period) involves the dissolution of gas in water as well as the formation and growth of a hydrate in the bulk zone on impurity particles near the contact boundary. We have obtained an analytical solution for the characteristic time (induction time) during which the volume fraction of the hydrate phase at the contact boundary reaches unity, and thus nuclei are formed in the form of a film preceding the appearance of a hydrate layer at the gas-water interface. According to the derived formula, the induction period is inversely proportional to the static pressure and depends on the number of impurity particles per unit volume of water according to a power law with an exponent of –2/3. The study has found that the growth rate of the methane hydrate layer at the water-gas contact boundary is less than that of carbon dioxide hydrate and hydrogen sulfide.