Modeling of the Kinetics of the Gas Hydrates Formation on the Basis of a Stochastic Approach

Abstract

Recently, more attention has been paid to the development of gas hydrate deposits, the use of gas-hydrated technologies, suitable for energy-efficient transportation of natural gas, the separation of gas mixtures, production and storage of cold, desalinating of seawater, etc. Hydrate formation is one of the main processes of gas-hydrate technological installations. In the article a model is proposed that describes the kinetics of the formation of hydrate in disperse systems, which are characteristic for real conditions of operation of gas-hydrate installations, on the basis of a stochastic approach using Markov chains. An example of numerical calculations is presented on the basis of the proposed model of the dynamics of the total mass of gas hydrates, and changes in the velocity of their formation and size distribution at different values of the nucleation constants and growth rate of the gas hydrates, and results of these calculations are analyzed. It is shown that the rate of formation of hydrate has a maximum value in half the time period of the whole process. The obtained results of the calculations of the dynamics the total mass of gas hydrates are in good agreement with the results of calculations by the equation of kinetics Kolmogorov-Avrami. The proposed model can be applied to the inverse problem: the determination of the nucleation constants and the rate of growth of gas hydrates by the results of the dynamics of the formation of hydrate and the changes in the fractional composition of the generated gas hydrates.