Improving the Rigor and Consistency of the Thermodynamic Theory for Clathrate Hydrates through Incorporation of Movement of Water Molecules of Hydrate Lattice

Abstract

Current applications of statistical thermodynamic theories for clathrate hydrates do not incorporate the translational and rotational movement of water molecules of the hydrate lattice in a rigorous manner. Previous studies have shown that the movement of water molecules has a significant effect on the properties of clathrate hydrates. In this Article, a method is presented to incorporate the effect of water movement with as much rigor as possible. This method is then used to calculate the Langmuir constant of the guest species in a clathrate hydrate. Unlike previous studies on modeling of clathrate hydrate thermodynamics, the method presented in this paper does not regress either the intermolecular potentials or the properties of the empty hydrate from clathrate phase equilibria data. Also the properties of empty hydrate used in the theory do not depend on the nature and composition of the guest molecules. The predicted phase equilibria from the resulting theory are shown to be highly accurate and thermodynamically consistent by comparing them with the phase equilibria computed directly from molecular simulations.

Storage of Methane in Clathrate Hydrates: Monte Carlo Simulations of sI Hydrates and Comparison with Experimental Measurements

“…We observe that the corresponding equilibrium curve is shifted considerably toward the temperature range 220–260 K. SPC/E is known to underpredict significantly the melting point of ice (i.e., it predicts a melting point of ice equal to 214 K), which is reflected, as well, in the calculation of the three-phase hydrate equilibrium. On the other hand, the results reported by and Ravipati and Punnathanam for the TIP4P/Ice water model, as well as, those by Jensen et al using the same model are closer to the calculations of the thermodynamic models that are considered for comparison. It should be noted that the TIP4P/Ice water model is significantly more accurate in the calculation of the melting point of ice, predicting a value equal to 270 ± 3 K…”

“…Therefore, the occupancy results correspond to the equilibrium conditions that are calculated by their methodology. The error in the calculation of the equilibrium temperature results in shifting the corresponding occupancy curves by several K. A more pronounced effect is observed in Figure c for the case of the results reported by and Ravipati and Punnathanam for the SPC/E water model. We observe that the corresponding equilibrium curve is shifted considerably toward the temperature range 220–260 K. SPC/E is known to underpredict significantly the melting point of ice (i.e., it predicts a melting point of ice equal to 214 K), which is reflected, as well, in the calculation of the three-phase hydrate equilibrium.…”

“…In Figure , we present the cavity occupancies, as a function of temperature, for the small cavities, θ S (Figure a), the large cavities, θ L (Figure b), and the total cavity occupancy of the hydrate unit cell, θ T , (Figure c) along the hydrate equilibrium curve P eq = f ( T ), for the sI CH 4 hydrates. Comparison is made for cavity occupancies calculated using the following three methods: The thermodynamic model of Sun and Duan The commercial simulators CSMHyd and CSMGem The Langmuir-type fitted curves to the occupancy results obtained in the current study with the GCMC simulations with reported results from MC simulations obtained by Papadimitriou et al, Jensen et al, and Ravipati and Punnathanam. − It should be noted that the simulations reported in the current study using TIP4P/Ice and the results of Papadimitriou et al using SPC/E are based on the assumption that the three-phase P , T , equilibrium conditions are known and calculating subsequently the cage occupancies at the known conditions. On the other hand, the studies of Jensen et al and Ravipati and Punnathanam − make an effort to calculate the three-phase equilibrium conditions.…”

“…Comparison is made for cavity occupancies calculated using the following three methods: The thermodynamic model of Sun and Duan The commercial simulators CSMHyd and CSMGem The Langmuir-type fitted curves to the occupancy results obtained in the current study with the GCMC simulations with reported results from MC simulations obtained by Papadimitriou et al, Jensen et al, and Ravipati and Punnathanam. − It should be noted that the simulations reported in the current study using TIP4P/Ice and the results of Papadimitriou et al using SPC/E are based on the assumption that the three-phase P , T , equilibrium conditions are known and calculating subsequently the cage occupancies at the known conditions. On the other hand, the studies of Jensen et al and Ravipati and Punnathanam − make an effort to calculate the three-phase equilibrium conditions. Therefore, the occupancy results correspond to the equilibrium conditions that are calculated by their methodology.…”

“…This issue is of particular interest to studies related to gas mixture separation processes. A number of studies have been reported that use MC simulations for CH 4 hydrates. − …”