Page 296 - Handbook Of Multiphase Flow Assurance

Experimental and computer study of the effect of kinetic inhibitors on clathrate hydrates 295

simulations in modern computers are typically limited to times of the order of hundreds
−4
of microseconds (10 s) or tens of milliseconds for supercomputers. This time frame al-
lows the use of supercomputers for simulated growth. However, with the advent of GPUs
and parallel programming such as CUDA, the task is now becoming within reach of more
researchers.
Since in a real crystal growth the preferred growth sites are steps or kinks, an idea may be
recommended for future work that the hydrate growth be stimulated in a crystal kink site.
This could be attempted using a (2 × 2 × 2) periodic MD simulation box composed of 7 crystal-
line hydrate unit cells and one melted unit cell. However, such a simulation is not currently
feasible because of the reasons mentioned above.
Computer modeling of crystal growth has been done since 1972 when growth of the {001}
face of a Kossel crystal surface had been simulated using the Monte Carlo (MC) method
(Gilmer and Bennema, 1972). In 1993 Clancy (Baez and Clancy, 1994) used the SPC/E
(Berendsen et al., 1987) potential in an attempt to utilize the memory effect of a recently
melted hydrate (Makogon, 1981) for hydrate growth. A simulation box with ca. 3000 water
molecules and a stoichiometric number of guests was seeded with a spherical crystal of hy-
drate (245 water molecules + guests) and the simulation was allowed to proceed. After 1/5th
of the simulation time the number of water molecules in a hydrate cluster had stabilized at
ca. 400 molecules.
An experimental study and computer modeling of the memory effect of hydrate lattices
was performed on sI and sII by Handa and colleagues (Handa et al., 1991). They discovered
that a compressed empty hydrate lattice was able to recover its crystalline structure after
pressure was released. It was proposed from the MD results that under pressure the water
molecules collapse around the guest molecules, and repulsive guest-host forces are responsi-
ble for the recovery of crystal structure when pressure is released.
Recently, hydrate growth was modeled with some success by Hirai (Hirai et al., 1996b).
He used the Kumagai (Kumagai et al., 1994) two- and three-body potential to model
host-host and guest-host interactions in a periodic box with side of two unit cells length.
Positions of the Ar guest molecules were held constant. He observed the formation of sI
hydrate lattice around guests in the simulation box after a 165 ps MD simulation. As the
simulation progressed, the number of pentagonal hydrogen bonded rings increased to ca.
330, and number of hexagonal rings decreased to ca. 50. This distribution in 8 sI hydrate
unit cells is 384:48.
2
A number of commercial software packages are available. The Cerius program utilizes the
Bravais Friedel Donnay Harker method to predict the faces on a growing crystal. This method
is a geometrical calculation that uses the crystal lattice and symmetry to generate a list of
possible faces and their relative growth rates. From this, crystal morphology can be deduced.
Bravais and Friedel (Bravais, 1913; Friedel, 1907) observed that the center-to-face distance for
a given plane tended to be related to the inverse-plane spacing:
1
D ~
d
where

D—crystal center-to-face distance,
d—lattice-plane spacing (thickness of unit cell in a direction normal to plane).