Hydrate lattice

One important difference between the present and the previous case should be noted. For the hydroquinone clathrates, where the wall of a cavity consists of 12 OH groups, 6 adjacent carbon atoms, and 6 CH groups in ortho position to the OH groups, it seemed best to consider the product z qjk) as one unknown. For hydrates one may not do this the walls of both types of cavities consist exclusively of tetrahedrally-coordinated water molecules. Hence, one should use the same value of (,eg/k) —characteristic for a water molecule in a hydrate lattice—for both types of cavities and multi-... 

Chemical potential of hydrate lattice, 22 Chlorine, frequency, 189 hydrate, 3... 

The fact that solutes are excluded from the hydrate lattice motivated work on using hydrates for the desalination of seawater and the concentration of aqueous solutions in general. Most of that work occurred in the 1960s and 70s and was reviewed by Englezos... 

Davidson and Ripmeester (1984) discuss the mobility of water molecules in the host lattices, on the basis of NMR and dielectric experiments. Water mobility comes from molecular reorientation and diffusion, with the former being substantially faster than the water mobility in ice. Dielectric relaxation data suggest that Bjerrum defects in the hydrate lattice, caused by guest dipoles, may enhance water diffusion rates. 

Proton NMR spectroscopy and dielectic constant measurements provide evidence about the motion of the water molecules in crystal structures, as reviewed by Davidson and Ripmeester (1984). At very low temperatures (<50 K) molecular motion is frozen in so that hydrate lattices become rigid. The hydrate proton NMR analysis suggests that the first-order contribution to motion is due to reorientation of water molecules in the structure the second-order contribution is due to translational diffusion at these low temperatures. 

Pandit and King (1982) and Bathe et al. (1984) presented measurements using transducer techniques, which are somewhat different from the accepted values of Kiefte et al. (1985). The reason for the discrepancy of the sonic velocity values from those in Table 2.8 and above is not fully understood. It should be noted that compressional velocity values can vary significantly depending on the hydrate composition and occupancy. This has been demonstrated by lattice-dynamics calculations, which showed that the adiabatic elastic moduli of methane hydrate is larger than that of a hypothetical empty hydrate lattice (Shpakov et al., 1998). 

In the hydrate lattice structure, the water molecules are largely restricted from translation or rotation, but they do vibrate anharmonically about a fixed position. This anharmonicity provides a mechanism for the scattering of phonons (which normally transmit energy) providing a lower thermal conductivity. Tse et al. (1983, 1984) and Tse and Klein (1987) used molecular dynamics to show that frequencies of the guest molecule translational and rotational energies are similar to those of the low-frequency lattice (acoustic) modes. Tse and White (1988) indicate that a resonant coupling explains the low thermal conductivity. 

Hydrate dissociation is of key importance in gas production from natural hydrate reservoirs and in pipeline plug remediation. Hydrate dissociation is an endothermic process in which heat must be supplied externally to break the hydrogen bonds between water molecules and the van der Waals interaction forces between the guest and water molecules of the hydrate lattice to decompose the hydrate to water and gas (e.g., the methane hydrate heat of dissociation is 500 J/gm-water). The different methods that can be used to dissociate a hydrate plug (in the pipeline) or hydrate core (in oceanic or permafrost deposits) are depressurization, thermal stimulation, thermodynamic inhibitor injection, or a combination of these methods. Thermal stimulation and depressurization have been well quantified using laboratory measurements and state-of-the-art models. Chapter 7 describes the application of hydrate dissociation to gas evolution from a hydrate reservoir, while Chapter 8 describes the industrial application of hydrate dissociation. Therefore in this section, discussion is limited to a brief review of the conceptual picture, correlations, and laboratory-scale phenomena of hydrate dissociation. 

In particular, the extension of the van der Waals and Platteeuw method addresses the first assumption listed at the beginning of Section 5.1.1—namely that encaged molecules do not distort the cavity. In the development of the statistical thermodynamic hydrate model (Equation 5.23), the free energy of water in the standard hydrate (empty hydrate lattice), gt, is assumed to be known at a given temperature (T) and volume (v). Since the model was developed at constant volume, the assumption requires that the volume of the empty hydrate lattice, 7, be equal to the volume of the equilibrium hydrate, v11, so that the only energy change is due to occupation of the hydrate cavities, as shown in Figure 5.3. 

The reader may be confused by the suggestion that the empty hydrate lattice being distorted by the addition of guests. Yet the method is pragmatically justified because it would be impossible to measure the empty lattice energies for all possible combinations of hydrate components. So we simply use methane for si (or propane for sll, or methane + neohexane for sH) as a reference case. With these references, the deviation occurs because an empty methane lattice is not the same as an empty CO2 or xenon lattice, and thus we try to account for that by using this activity term. This point is further discussed in Section 5.1.6. 

The best choice for the standard hydrate is one that is well-characterized and not too different from the real state of the system. If the standard state is well-defined, small perturbations from this standard state can be accounted for correctly. With this in mind, we turn to the three most well-known hydrates of si, sll, and sH, namely methane, propane, and methane+neohexane. Note that the standard states for si, sll, and sH are the empty hydrate lattices of these and not the actual hydrates. Therefore for the reference hydrates, the activity coefficients for methane, propane, and methane + neohexane hydrates will be unity. 

The compressibility coefficient, k, and reference volume, vo, are solely dependent on the composition of the guest(s) in the hydrate lattice while the thermal expansion coefficients, a, a2, ando 3 are solely dependent on the hydrate structure. 

Neutron spectroscopy (also referred to as inelastic neutron scattering) has been used to measure the extent of guest-host interactions in a hydrate lattice, which help to explain the anomalous thermal behavior of hydrates (e.g., low thermal... 

Figure 5 Multiscale approach to understand rate of CO2 diffusion into and CH4 diffusion out of a structure I hydrate, (left) Molecular simulation for individual hopping rates, (middle) Mesoscale kinetic Monte Carlo simulation of hopping on the hydrate lattice to determine dependence of diffusion constants on vacancy, CO2 and CH4 concentrations, (right) Macroscopic coupled non-linear diffusion equations to describe rate of CO2 infusion and methane displacement. Graph from Stockie. ...

A different model presented by Christiansen and Sloan is based on the fact that water molecules form labile water clusters around dissolved gas molecules. The number of water molecules in each water cluster shell depends on the size of the dissolved gas molecules, e.g. 20 for methane and 24 for ethane or 28 for propane. The clusters of the dissolved species combine to form unit cells. The formation rate of a particular hydrate structure depends on the availability of labile clusters with required coordination numbers. With a mixture of methane and propane dissolved in the liquid water phase, hydrates should form more rapidly than if either methane or propane alone are dissolved in the water phase. This cluster nucleation hypothesis is based on the assumption that the guest molecule has to be dissolved in the liquid phase before getting encased into a hydrate lattice. 

In order to proof the applicability of the mentioned approaches and to study the incorporation of different gases in the hydrate lattices depending on their properties (solubility, dimension, etc.) we performed investigations on gas hydrates which have been synthesized from gas mixtures as a free gas phase and water. The gas mixtures contain besides methane the isomers of butane (n-butane iso-butane) and pentane (iso-pentane, 2,2-dimethylpropane), respectively. The exact compositions of the gas mixtures are given in table 1. The experiments and results are described in detail in the diploma thesis of M. Luzi. ... 

Natural gas could possibly be stored at low pressures and temperatures in the form of a hydrate. The relative density of gas in the hydrate lattice exceeds its liquid density. According to the calculations of Parent, a natural gas with a volume of 4.42 m at 15°C and atmospheric pressure only needs 0.028 m volume for storage in the hydrate state. Thus, only 1/156 of the volume in the free state is needed. Rogers and Zhong conducted a study on storing natural gas... 

Define the following terms enthalpy of solution, hydration, heat of hydration, lattice energy, heat of dilution. 

The water sequestered in the hydrate lattice is preferentially enriched in 0 and deuterium (D), thus the isotopic composition of the water in the pore spaces collected from gas hydrate bearing sediment can provide additional information on the abundance and the characteristics of these deposits. Pore fluid samples that had been modified by hydrate decomposition upon core recovery during ODP Legs 146 (Kastner et al. 1998), and 164 (Matsumoto and Borowski 2000) provided the first field data to derive the oxygen isotope fractionation factor for in situ hydrate formation. A more comprehensive sampling... 

Fig. 14.19 Isotopic fractionation between water in the pore fluid and water in the hydrate lattice as a function of chloride anomalies (ACl). Hydrate dissociation causes chloride dilution and O, D enrichment. The fractionation factors = 1.0025 and = 1.022 are based on data from low-chloride pore waters recovered from Hydrate Ridge during ODP Leg 204. They are in agreement with previous estimates from Legs 146 and 164, as well as with experimentally determined values during hydrate formation shown hy open circles. Samples collected from pore water hrines deviate considerably from expected values (from Tomaru et al., submitted).

A clathrate hydrate is a crystalline inclusion compound in which small guest molecules, usually hydrophobic, are trapped in polyhedral cages formed by hydrogen-bonded water molecules. True clathrates are formed by guests that interact with the hydrate lattice only by weak, nondirectional forces. In such cases, the water molecules form a completely hydrogen-bonded network, and the inaterials effectively are ices. A number of structures are known for true clathrate hydrates, including the three major families of clathrate hydrate structures that will be discussed later. 

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