CHAPTER 2: HYDRATE STRUCTURE AND THERMODYNAMIC
2.1 Gas hydrate theory
2.1.3 Hydrate kinetics
Various assumptions are made for the construction of ternary type C phase diagrams (Mooijer-van den Heuvel, 2004). They are as follows:
Water and guest component have immiscible Lw and Lg phases.
Water and additive component have immiscible Lw and La phases.
Guest component and additive component have immiscible Lg and La phases.
Water, guest component and additive component have immiscible Lw, La and Lg phases.
Based on a series of measurements performed on natural gas and carbon dioxide hydrates, Long and Sloan (1996) proposed that in non-stirred systems, the hydrate nucleation site is located at the gas- liquid interface. This proposal was reinforced by a number of other researchers based on their observations made on methane hydrate (Huo et al., 2001; Ostergaard et al., 2001) and carbon dioxide hydrate (Kimuro et al., 1993; Hirai et al., 1995) nucleation. According to Sloan and Koh (2007), the vapour-liquid interface is preferred for hydrate formation due to lower Gibbs free energy of nucleation, as well as the high concentration of water and former (guest) molecules. For systems where stirring occurs, the nuclei may form anywhere in the solution, depending on where the highest concentration of the dissolved former gas is present (Bishnoi and Natarajan, 1996).
Referring to Figure 2-11 below, for an isochoric system, nucleation occurs between points A and B.
The induction time is dependent on the time required for the nucleation process to occur. For systems in which hydrates have previously been formed, the induction time is reduced. This is known as the memory effect (Vysniauskas and Bishnoi, 1983). Therefore, the induction time is also dependent on water history and agitation, and consequently surface area.
Three models have been developed to describe the nucleation process. More information on these models can be found in the book of Sloan and Koh (2007), Natural Gas Hydrates: A Guide for Engineers.
Figure 2-11: Experimental pressure-temperature trace (Bishnoi and Natarajan, 1996).
2.1.3.2 Crystal growth
The hydrate crystal growth process applies to the growth of stable hydrate nuclei to form solid hydrate crystals. The transferal of heat and mass play a paramount role in the growth process; however, most of the nucleation parameters such as surface area, agitation, and gas composition continue to be significant during this process (Bishnoi and Natarajan, 1996).
Once the hydrate nuclei have reached critical size, they continue to grow to form gas hydrate crystals.
During the crystal growth phase, a large pressure drop is observed in the system. This is due to diffusion and absorption of the former gas into the crystal cavities. Consequently, stable gas hydrates are formed.
Numerous models for hydrate growth have been developed (Sloan and Koh, 2008). One such model is that of Englezos et al. (1987). This model is a mechanical model based on mass transfer and crystallization theories. It visualises the solid hydrate particle as being surrounded by an adsorption
“reaction” layer followed by a stagnant liquid diffusion layer. This is schematically represented in Figure 2-12 below.
Figure 2-12: Fugacity profile in the diffusion and absorption film surrounding a growing hydrate (Bishnoi and Natarajan, 1996).
The authors proposed two consecutive steps for the hydrate growth process; step one involves diffusion of the gas phase from the bulk of the solution (point fb) to the crystal-liquid interface through the laminar diffusion layer around the particle (point fs), while step two involves the
“reaction” at this interface, where the gas is absorbed into the hydrate structure, which is assumed to be spherical.
The reaction rates of the growth process are based on system fugacity instead of dissolved gas concentration. At equilibrium, the growth rate per particle can be expressed as (Bishnoi and Natarajan, 1996):
(2.3) where is the hydrate surface area per particle, is the difference in fugacity of the dissolved gas and its fugacity at the three phase equilibrium and is expressed in terms of the coefficients for diffusion ) and reaction ( as (Bishnoi and Natarajan, 1996):
(2.4)
2.1.3.3 Hydrate dissociation
The dissociation of hydrate crystals is an endothermic process. For such a process to occur, heat of some form must be provided by an external source in order to break the hydrogen bonds that are present between water molecules, as well as the van der Waals interaction forces present between the former (guest) molecules and the water molecules of the hydrate lattice. Thereafter, the hydrate dissociates into water and gas. The heat transfer that occurs during the hydrate dissociation process has been studied by Kamath et al. (1984). It was observed that the dissociation process is analogous to that of the nucleate boiling phenomena. Later, Kamath and Holder (1987) generalized this relationship and applied it to methane hydrate dissociation.
Kim et al. (1987) proposed two consecutive steps for the hydrate dissociation process: step one involves the destruction of the hydrate host lattice at the particle surface, while step two involves the desorption of the former (guest) molecule from the surface of the particle. Based on these ideas, an intrinsic kinetic model for hydrate dissociation was developed. This is represented schematically in Figure 2-13 below.
Figure 2-13: Dissociation of hydrate particles (Bishnoi and Natarajan, 1996).
At very low temperatures, the molecular motion within the hydrate lattice stops. Consequently the hydrate lattice becomes rigid. As temperature increases, the motion due to water molecule reorientation and diffusion causes the hydrate to dissociate. The trapped gas in the hydrate is then released which increases the system pressure.
At equilibrium, the dissociation rate for a hydrate particle is given as (Bishnoi and Natarajan, 1996):
(2.5)
where is the dissociation rate constant and is the fugacity of the gas obtained at the particle surface temperature and the experimental pressure.