Comprehensive study and comparison of equilibrium and kinetic models in simulation of hydrate reaction in porous media

Abstract

Coupling hydrate reaction in fluid transport in porous media is essential for simulation of gas hydrate production, as well as carbon sequestration in deep-sea sediments. It can be conceptualized as multiphase, multicomponent, and non-isothermal reactive transport. Two types of models have been developed for the description of hydrate reaction in numerical models. The equilibrium model (EM) assumes instantaneous chemical equilibrium among species, and thus ignores reaction kinetics. The kinetic model (KM) incorporates reaction kinetics by introducing a term of reaction rate dependent on fugacity difference. Although KM achieves a more accurate description of the reaction, it is potentially more computationally intensive due to the increased degree of freedom in the nonlinear equation system. Although several previous studies have investigated the similarities and differences between these two models, inconsistencies exist in their studies, and the mechanisms to distinguish these two models are still not well understood. In our study, in order to identify the reasons for these inconsistencies and elucidate the mechanisms that control the differences between the two reaction models, we provide a comprehensive investigation and comparison of these two models via theoretical analysis and numerical experiments. Through comparing the basic assumptions, mathematical model and the equation systems, we pointed out the basic difference of these two models, which results from the different calculations of physical parameters. Dimensionless analysis of the governing equations of KM yields several characteristic numbers, representing the relative strength of different physical processes. We performed numerical experiments to investigate the effect of characteristic numbers on the difference between the two models, and the results indicate that there exist critical values for these characteristic numbers, lower than which lead to an obvious gap between the results of EM and KM. It turns out that the relative strength of the hydrate reaction and other physical processes controls the magnitude of difference between these two models. EM is essentially a special case of KM when the time scale of the hydrate reaction is sufficiently smaller than other physical processes, such as convective and diffusive transport of mass and heat. Comparison between the time and iteration steps in the two reaction models provides insights into the computational efficiency of the two models.