Reports: AC9
45967-AC9 Modeling the Phase Behavior of Gas Hydrate Forming Systems
This project is concerned with the molecular modeling of the phase behavior of gas hydrate forming systems. This is a problem of great technological and environmental importance that also addresses fundamental science, especially the solution thermodynamics and phase behavior of mixtures of water with hydrophobic species. In recent work we have initiated research that provides a new perspective in this field, through calculations of the entire phase diagram for a hydrate forming systems including all fluid, ice and hydrate phases. Our work has two key features. First we have sought to learn about the origin of hydrate stability by investigating what are perhaps the simplest molecular models that could describe the essential features of the water + alkane system. Second we have developed a methodology for calculating the free energy and chemical potentials for molecular models of hydrate phases from Monte Carlo simulations. The PRF award is allowing us to exploit these developments for a wider range of systems.
Initially we have focused on studying the influence of molecular shape upon the phase behavior of hydrate systems. This is being done through calculations of the phase diagrams for the water + methane, water + ethane and water + propane systems. Among the issues of interest here are the difference in the average occupancies of the small cavities in the structure-I hydrate between methane and ethane hydrates, and the onset of stability of the structure-II hydrate for propane. One aspect of the work has been to study the effect of explicitly treating the molecular shape in the models of the alkanes and we do this through interaction site models. Our approach requires a theory of the thermodynamics of the fluid phase mixtures and for this purpose we have extended the perturbation theory of Nezbeda and coworkers for mixtures of water and alkanes to the case of nonspherical models of alkanes. We have tested this theory against Monte Carlo simulations and the agreement is very good. In computing the phase diagrams we are able to take advantage of earlier work by our group on calculating the solid-fluid phase behavior for molecular models of n-alkanes.
We have made calculations of the phase behavior for hydrates in which the alkanes are treated by spherical and nonspherical molecular models. We find that predictions of the hydrate occupancy can be quite sensitive to the treatment of the molecular shape of the guest molecules and this strongly impacts the predicted phase diagram. For example we have made calculations of the water + ethane phase diagram using two models of ethane one where it is treated as spherical and one where it is treated as a two-site molecule. We have found that incorporation of the nonspherical shape improves the agreement with experiment. In particular it allows us to correctly describe the low occupancy of the small cavities in the structure-I Hydrate. The small cavity occupancy is over predicted if the ethane is treated as spherical.
We have also investigated the accuracy of the van der Waals and Platteeuw (vdWP) theory for our molecular models. We are doing this by comparing calculations of the hydrate occupancies from the theory with the (essentially exact) results obtained from Monte Carlo simulations of our models. The occupancies of the large and small cavities can be tracked separately in these calculations. We have discovered an interesting feature of this theory associated with the molecular shape of the guest molecule in the hydrate. We are finding that the vdWP theory is less accurate when the guest molecule is comparable in size to the cavity, as is the case for ethane in the small cavities of the structure-I hydrate. This inaccuracy is associated with the assumption in the vdWP theory that the hydrate framework is rigid. We have found that the motions of the water molecules in the framework have a significant effect on the calculated occupancy because these motions change the configuration space available to the guest molecules. This acts to reduce the occupancy relative to that predicted by the vdWP theory and this effect is larger for guest molecules with nonspherical shape where the orientations make a significant contribution to the configuration space.
