A Multiscale Approach for Gas Hydrates Considering Structure, Agglomeration, and Transportability under Multiphase Flow Conditions: II. Growth Kinetic Model

In the second part of this series, we introduce the mathematical model for the growth kinetics of gas hydrates in oil continuous flow. Mathematical description of the capillary filling-up process is given (porosity evolution), coupled with growth phenomena already described in the literature (gas absorption by the oil bulk, mass transfer particle/bulk, outer growth due to permeation). The range of closure parameters reported in the literature for CH4 hydrates is used to understand the limiting steps of crystallization, the evolution of porosity being the controlling factor in the asymptotic trend of the gas consumed over time. Furthermore, gas absorption by the bulk and mass transfer particle/bulk is shown to be negligible for oil-continuous flow when considering a gas that is much more soluble in oil than in water. The model is simplified for engineering purposes, giving rise to an explicit semi-empirical equation for the gas consumption rate because of hydrate formation based on two independent parameters that are experimentally regressed. A criterion for the existence of wet or dry particles (the water layer covering the particles in oil-continuous flow) is proposed in means of the competition of crystal integration in the outer surface versus water permeation through the porous hydrate.