Hydrate growth

After the stochastic nature of hydrate crystal nucleation, the quantification of the hydrate growth rate provides some relief for modeling hydrate formation. However, only a limited amount of accurate data exist for the crystal growth rate after nucleation. Most of the nucleation parameters (displacement from equilibrium conditions, surface area, agitation, water history, and gas composition) continue to be important in hydrate growth. 

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Knowledge concerning the mechanism of hydrates formation is important in designing inhibitor systems for hydrates. The process of formation is believed to occur in two steps. The first step is a nucleation step and the second step is a growth reaction of the nucleus. Experimental results of nucleation are difficult to reproduce. Therefore, it is assumed that stochastic models would be useful in the mechanism of formation. Hydrate nucleation is an intrinsically stochastic process that involves the formation and growth of gas-water clusters to critical-sized, stable hydrate nuclei. The hydrate growth process involves the growth of stable hydrate nuclei as solid hydrates [129]. 

A kinetic study in a well-stirred semi-batch reactor was conducted to determine the rate of methane as shown in Figure 4 (Lee et al., 2005b). As seen, the system with TBME has the shortest nucleation time and fastest hydrate growth rate followed by NH and MCH. This trend... 

Hydrate growth (Section 3.2), which may be controlled by kinetic, heat,... 

In order to verify which of the above nucleation mechanisms accurately represents hydrate nucleation, it is clear that experimental validation is required. This can then lead to such qualitative models being quantified. However, to date, there is very limited experimental verification of the above hypotheses (labile cluster or local structuring model, or some combination of both models), due to both their stochastic and microscopic nature, and the timescale resolution of most experimental techniques. Without experimental validation, these hypotheses should be considered as only conceptual aids. While the resolution of a nucleation theory is uncertain, the next step of hydrate growth has proved more tenable for experimental evidence, as discussed in Section 3.2. 

Figure 3.17 Probability of survival of CH3CCI2F hydrate free samples plotted vs. the induction time. The triple liquid-water/hydrate/liquid-CF CC F equilibrium temperature is 281.6 K. The sample is cooled to 277.2 K (within 90 s), and held at this temperature until nucleation occurs and hydrate growth is detected. (Reproduced and modified from Ohmura, R., Ogawa, M., Yasuka, K., Mori, Y.J., J. Phys. Chem. B, 107, 5289 (2003). With permission from the American Chemical Society.)...

On the molecular level, hydrate growth can be considered to be a combination of three factors (1) the kinetics of crystal growth at the hydrate surface, (2) mass transfer of components to the growing crystal surface, and (3) heat transfer of the exothermic heat of hydrate formation away from the growing crystal surface (see Section 3.2.3 for heat transfer models). 

A hypothesis picture of hydrate growth at a crystal is shown in Figure 3.21, modified from Elwell and Scheel (1975). This conceptual picture for crystal growth may be combined with either the labile cluster or local structuring hypotheses for nucleation. 

The reader should be warned that the above conceptual picture has little supporting evidence from hydrate growth experiments, other than the few single crystal growth studies in Section 3.2.2.1. Nevertheless, it is hoped that such a conceptual picture can promote some understanding of the phenomena involved, if only to serve as a basis for improvement. 

When the hydrate growth rate (dm/dt) is measured by the rate of gas consumption (drii/dt) the pseudo-steady-state approximation is made. That is, at any instant the rate of gas consumption by the hydrate is assumed equal to the rate of gas consumption from the gas phase. Frequently, experimenters monitor the amount of gas needed to keep the pressure constant in the hydrate vessel so that the driving force remains constant. In such cases, the rate of gas consumption from a separate supply reservoir is measured. 

Equation 3.17b may be regarded as the starting point for the models discussed in Section 3.2.3. In all hydrate growth models the coefficient K is a parameter fitted to kinetic data. 

Hydrate growth is typically initiated at the water-hydrocarbon interface (as discussed in Section 3.1.1.4). Measurements of the growth of a hydrate film (or shell) at the water-hydrocarbon interface provides insight into the growth mechanism(s), which can be incorporated into realistic hydrate growth models. 

The trends shown from the predicted curves, Csh and Cs, are in qualitative agreement with corresponding dissolved methane Raman peak intensities. Therefore, the Raman spectra (Figure 3.27a) support the proposed mechanism that hydrate growth occurs in part as a result of methane diffusing from the bulk aqueous phase to the hydrate film formed at the vapor-liquid interface. This decreases the methane concentration in the bulk water phase. Hydrate growth from an aqueous... 

In summary, the microimaging technique provides a powerful tool to study directly the mechanism of converting water droplets to hydrate particles. The results reported indicate that provided the gas hydrate former can diffuse into the interior droplet, hydrate growth can proceed in the bulk interior droplet away from the hydrate shell-water interface, as well by growing out from the hydrate shell resulting in shell thickening. 

Also in Bishnoi s laboratory, Dholabhai et al. (1993) studied the effect of electrolytes on methane hydrate formation kinetics. They found that after the equilibrium fugacity (or driving force) is adjusted for the presence of salt, hydrate growth kinetics are quantitatively described by the pure water kinetics model of Englezos. 

The appearance of metastable phases during hydrate growth can provide valuable insight into the molecular mechanism of hydrate growth, as well as an increased... 

Coexistence of si and sll carbon dioxide hydrate has been detected from x-ray diffraction measurements during hydrate growth (Staykova and Kuhs, 2003). Similarly, metastable sll hydrate phases were detected using NMR spectroscopy during si xenon hydrate formation (Moudrakovski et al., 2001a) and during si methane/ethane hydrate formation (Bowler et al., 2005 Takeya et al., 2003). 

Table 3.5 summarizes the different hydrate growth models that have been developed by various research groups. Three major correlations for hydrate growth exist ... 

The role of hydrate intrinsic kinetics has been more recently suggested to play a smaller role in hydrate growth in real systems than heat and mass transfer effects. In view of this, the discussion on the kinetics models is only briefly presented here. For a more thorough treatment, the reader is referred to the original references (Englezos et al., 1987a,b Malegaonkar et al., 1997). 

Englezos et al. (1987a,b) generated a kinetic model for methane, ethane, and their mixtures to match hydrate growth data at times less than 200 min in a high pressure stirred reactor. Englezos assumed that hydrate formation is composed of three steps (1) transport of gas from the vapor phase to the liquid bulk, (2) diffusion of gas from the liquid bulk through the boundary layer (laminar diffusion layer) around hydrate particles, and (3) an adsorption reaction whereby gas molecules are incorporated into the structured water framework at the hydrate interface. 

The data were modeled with one fitted parameter (K ) for hydrate growth of simple hydrate formers of methane, ethane, carbon dioxide. Since all these model components form si hydrate, the model should be used with caution for sll and sH. 

The state-of-the-art for hydrate growth may be summarized with only a few statements ... 

Hydrate growth data and modeling are more tenable than are nucleation phenomena. In particular, the growth data (after nucleation) appears to be linear for as much as 100 min in Englezos data. 

Metastable states can form during hydrate growth, which is not accounted for in the simulations or models. 

In addition there have been multiple studies (Sloan et al., 1976 Cady, 1983a,b Kobayashi et al., 1987 Woolridge et al., 1987) that demonstrate that hydrate growth can occur from a hydrocarbon fluid phase if a hydrate nucleus is either already present, absorbed at sites on a wall, or on a third surface. 

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