Comparing Analytical and Numerical Solutions to A Comprehensive Hydrate Kinetic Growth Model

Gas hydrate formation in subsea pipelines poses a significant risk to flow assurance, with deposits capable of restricting or completely blocking hydrocarbon transport. While the thermodynamic stability regions of methane hydrates are well established, accurately predicting their kinetic growth remains challenging due to a limited knowledge and research around the controlling mechanisms. Intrinsic kinetics dominate the early stages of hydrate formation, with heat and mass transfer constraints becoming increasingly important as growth progresses. Existing kinetic growth models do not account for the summation of all influencing growth mechanism hence necessitating this work. To address this issue, we employ the transport equation to complete an already existing growth model. The second-order partial differential nature of the new model's expression together with its practical inhomogeneous boundary conditions needs a solution. This new model is then solved via two solution techniques: analytical and numerical. Firstly, in the analytical solution, we employ the separable variable technique to solve our model, while for the numerical solution, Taylor's series expansion and the Crank-Nicolson method were implemented for increased stability and accuracy. The numerical and analytical solutions to the proposed comprehensive model are then implemented and compared, with discrepancies explained. The work delivers novel growth expressions and enhances understanding of the coupled effects of intrinsic kinetics, heat transfer, and mass transfer in methane hydrate formation. The outcomes provide both theoretical insight and practical tools to support the design of hydrate management strategies in production systems.