Page 106 - Handbook Of Multiphase Flow Assurance

102 5. Flow restrictions and blockages in operations

Gas hydrate formation
The formation of gas hydrate usually begins at the interface of water-gas-solid or water-
hydrocarbon-solid. This is called heterogeneous nucleation. The presence of a solid reduces
the time it takes to start the formation of the crystal, called an induction time. In reality this is
related to the reduction of the energy barrier as described in a book by Makogon (1974, 1981)
on pages 65 and 72 accordingly. Whether a small crystal nucleus continues to grow larger
than the critical radius or dissolve depends on the latent heat of crystallization Q, supercool-
ing at which crystallization occurs and nucleus' specific surface energy σ:
 (
[
2
logP bar] = β + 0 0497( T    C + k T    C  )
.
Crystals don't start to form as soon as the hydrate stability condition is reached. It takes ex-
tra cooling below the stability temperature to help organize the water molecules into a lattice
of cells which can trap gas molecules. This extra cooling is known as subcooling or supercool-
ing or propensity. These terms are used interchangeably. The greater the subcooling, or the
difference between hydrate equilibrium temperature and local temperature in the system, the
sooner the crystals will start to form.
Similarly Sloan (1990) in p. 83 also provides an expression referenced from prior publica-
tions for the critical size of hydrate crystal nuclei above which the crystal continues to grow
as a function of the surface tension σ and a change in Gibbs free energy.

2σ
r =−
cr ∆ g
Neither manuscript provided a clear indication of what the typical size for the critical
nucleus would be—whether it is of the order of magnitude of 10 Angstroms, 100, or 1000,
rightly so because the nucleus size depends on the process. Nonetheless knowing the order
of magnitude for this value is important for a general understanding of how hydrates form.
Koh et al. (1996, 2000) suggests the gas hydrate nucleus size is of the order of 1 nm. A molec-
ular modeling work by Walsh et al. (2009) with TIP4P-ICE confirms critical nucleus is of the
nanometer scale.
The importance of microbubbles and nanobubbles of gas for hydrate formation was de-
scribed by Makogon (1996), ICGH-2. The radius of such microbubbles was related to pressure
of gas in such bubbles and the surface tension through the Laplace's law and the van der
Waals equation. An example detailed calculation presented in that work showed the gas mi-
crobubble size at 4.3 nm or 0.0043 μm. Pressure inside such gas microbubbles was estimated
to be on the order of tens of MegaPascals or higher.
An important observation is made by Sloan (1990) in p. 74 that works by Angell and Speedy
and Angell (1976) indicated that concentration of hydrogen-bonded polyhedra is suggestive
of pre-nucleation phenomena.
Rahman and Stillinger (1973) showed that hydrogen-bonded water molecules is arranged
as polygons.
Makogon (1974, 1981) calculated from measurements the number of hydrogen bonds re-
maining in water after melting of ice and after dissociation of hydrate.
Number of hydrogen bonds in water is shown in Table 5.3.