Application of the Cell Potential Method To Predict Phase Equilibria of Multicomponent Gas Hydrate Systems

Abstract

We present the application of a mathematical method reported earlier 1 by which the van der Waals-Platteeuw statistical mechanical model with the Lennard-Jones and Devonshire approximation can be posed as an integral equation with the unknown function being the intermolecular potential between the guest molecules and the host molecules. This method allows us to solve for the potential directly for hydrates for which the Langmuir constants are computed, either from experimental data or from ab initio data. Given the assumptions made in the van der Waals-Platteeuw model with the spherical-cell approximation, there are an infinite number of solutions; however, the only solution without cusps is a unique central-well solution in which the potential is at a finite minimum at the center to the cage. From this central-well solution, we have found the potential well depths and volumes of negative energy for 16 single-component hydrate systems: ethane (C 2 H 6 ), cyclopropane (C 3 H 6 ), methane (CH 4 ), argon (Ar), and chlorodifluoromethane (R-22) in structure I; and ethane (C 2 H 6 ), cyclopropane (C 3 H 6 ), propane (C 3 H 8 ), isobutane (C 4 H 10 ), methane (CH 4 ), argon (Ar), trichlorofluoromethane (R-11), dichlorodifluoromethane (R-12), bromotrifluoromethane (R-13B1), chloroform (CHCl 3 ), and 1,1,1,2-tetrafluoroethane (R-134a) in structure II. This method and the calculated cell potentials were validated by predicting existing mixed hydrate phase equilibrium data without any fitting parameters and calculating mixture phase diagrams for methane, ethane, isobutane, and cyclopropane mixtures. Several structural transitions that have been determined experimentally as well as some structural transitions that have not been examined experimentally were also predicted. In the methane-cyclopropane hydrate system, a structural transition from structure I to structure II and back to structure I is predicted to occur outside of the known structure II range for the cyclopropane hydrate. Quintuple (L w -sI-sII-L hc -V) points have been predicted for the ethane-propane-water (277.3 K, 12.28 bar, and x eth,waterfree ) 0.676) and ethane-isobutanewater (274.7 K, 7.18 bar, and x eth,waterfree ) 0.81) systems.

A simple van’t Hoff law for calculating Langmuir constants in clathrate hydrates

“…In the case of argon, methane, ethane, cyclo-propane, propane and iso-butane, the values of V min K;t calculated here are consistent with the well depth of the cell potentials used previously by Anderson et al [7,8], as shown in Table 5. However, it should be noted that the different potential energy surfaces show that, except for Ar, the five other molecules cannot freely rotate inside the clathrate cage.…”

“…It is thus obvious from Eq. (7) that, in contrast to the simplified central-well potential approach [8], any analytical integration would be intractable here due to the asymmetries of the host lattice cages and of the guest molecule itself.…”

“…Because such constants are not necessarily extracted from experiments in a large range of temperatures, we propose here to express them as a function of temperature through a simple van't Hoff law as already proposed by Bazant and Trout [19] and Anderson et al [8]:…”

“…The cell potential method has then been extended to other molecules like methane, propane, isobutane and small chlorofluorocarbon molecules, showing a good accuracy in reproducing both dissociation pressures and phase diagrams of hydrocarbon mixtures [7,8]. This method thus appears as a very interesting and quite simple approach for predictions of clathrate hydrate equilibrium properties.…”

“…However, it should be mentioned that, for some cases, the central-well potential does not satisfactorily reproduce the shape of the guest-water potential at the center of the clathrate cages. Although Anderson et al [8] claimed that this has no influence on the accuracy of the Langmuir constants calculated for Argon, the influence of this failure should be carefully analyzed each time it is evidenced. For other guests in clathrate hydrates, in particular, argon, hydrogen, nitrogen, methane, ethane, propane, cyclo-propane, and carbon dioxide, other workers [3][4][5][6]9] have explicitly taken into account the angledependence of the guest-water intermolecular potential in an atom-atom or site-site description to calculate the corresponding Langmuir constants.…”