Page 291 - Handbook Of Multiphase Flow Assurance

290 10. Research methods in flow assurance

Computer modeling of hydrates: Solid solution models
An extensive review of the effort of the hydrate computational community was presented
by Tse at the First Conference on Natural Gas Hydrates in the New York Academy of Sciences
in 1993 (Tse, 1994). He emphasized the success of the van der Waals and Platteeuw solid
solution model (van der Waals and Platteeuw, 1959) in describing the stability of clathrate
hydrates. That model uses statistical thermodynamics and Langmiur adsorption theory to
calculate the adsorption of guest molecules in hydrate cavities assumed to be spherical. The
model is used to predict temperature and pressure of hydrate stability based on empirical
Langmiur constants.
The spherical cell approximation used in the original model can be replaced by localized
water sites (Tester et al., 1972). Tse stated that the dissociation pressure and guest occupancy
calculated with this method for several clathrate hydrates are similar to those calculated with
the spherical cell approximation. Rodger (1989) discussed the possibility of including the
effects of hydrate lattice thermal motion on the small cavity potential in sI in the model of
cavity-guest interactions.

Potential models

Proper choice of the potential model determines the success of a simulation. TIP4P
(Jorgensen et al., 1983) and SPC (Berendsen et al., 1981) potentials for water are the most
accurate in predicting such properties of liquid water as density, structure (in terms of radial
distribution functions), and intermolecular energy (Jorgensen et al., 1983). These models are
comparable to or better than other models in predicting heat of vaporization, heat capacity,
thermal expansivity, and isothermal compressibility of liquid water.
The TIP4P and SPC models predict dielectric relaxation times, which is a measure of the
hydrogen-bond rearrangement dynamics, of 6.3 and 11 ps (Ohmine and Tanaka, 1993) which
compare favorably with the experimental value of 8–9 ps (Bertolini et al., 1982).
Water molecules show the strongest preference for participation in 4 hydrogen bonds in
the ST2 (Stillinger and Rahman, 1974) potential model which uses a tetrahedral charge distri-
bution. Radial distribution function for this potential shows the greater structure than for the
potentials with 3-point charge distributions.
Recently, a new potential model (Kumagai et al., 1994) was developed for water in
clathrate hydrates which includes 2-body guest-guest, host-host and guest-host inter-
actions and 3-body intramolecular host interactions. This potential is being used with
some success in Japan to model hydrates (Itoh et al., 1996). However, this potential model
does not explicitly include the hydrogen bonding host-host or guest-host interactions.
The long-range attractive part of the potential is represented by Coulombic charge-charge
attraction.

Structures of liquid water and hydrate

The classic work on the structure of water molecules in liquid water by Rahman and
Stillinger (1973) used the ST2 potential model to estimate the hydrogen-bond connectivity