Gas Hydrate Equilibria

In pressure applications of the FREZCHEM model, the molar volumes of the neutral species CC 2(aq), 02(aq), and CH aq) are constants independent of temperature and pressure (Appendix B). This is similar to how solids are handled in the FREZCHEM model (see previous section). Of the gas-phase gases, only C02(g) and CHi(g) at high pressures in gas hydrate equilibria are assumed to be compressible (see the following section on gas hydrate chemistry). That means that other gas constituents such as H2O, O2, HC1, HNO3, and H2SO4 are only validly parameterized for low pressures (a few bars). 

Two gas hydrates are now part of the FREZCHEM model C02-6H2 0 and CH46H2O (Table 3.2). Gas hydrate equilibrium for C02-6H20 is described by the reaction 

To estimate a gas hydrate solubility product requires knowing j g, Pg, and aw (Eq. 3.36). The gas partial pressure, Pg, is experimentally measured. The activity of water, aw, is calculated by the FREZCHEM model (Eq. 2.37), as is the gas fugacity coefficient ( j g) using a model developed by Duan et al. (1992b). The equation used to calculate gas fugacity coefficients is given by 

There is an abundance of experimental gas partial pressures for gas hydrate equilibria across a broad range of temperatures (Fig. 3.10 Sloan 1998). The lower temperature limit in our model database for these systems is 180 K (Fig. 3.10) because this is the lower limit of our model s ability to estimate aw (Fig. 3.1, Eq. 3.11), which is needed to calculate the solubility product of gas hydrates (Eq. 3.36). In our model, the upper temperature limit for methane hydrate is at 298 K (25 °C), which is the upper temperature limit for FREZCHEM the upper temperature limit for carbon dioxide hydrate is at 283K (10 °C), which is the temperature where liquid C02(l) becomes the thermodynamically stable phase. 

Given gas partial pressures (Fig. 3.10), a model to calculate fi (Eq. 3.37), and a model to calculate aw (Eq. 2.37), the solubility product (Eq. 3.36) can be calculated for gas hydrates (Fig. 3.11). The actual solubility product calculations are made at the experimental gas partial pressures, which vary widely (Fig. 3.10). Equation 2.29 was used to adjust all these pressure-dependent estimates (Kp) to a hypothetical 1.0 atm total pressure (iTP0), which is what is presented in Fig. 3.11. 

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Another mixture problem is how to deal with mixed solid-phase gas hydrates. Both methane and carbon dioxide form structure I gas hydrates. Thus CH4-CO2 gas mixtures will ultimately lead to CH4-CO2 gas hydrates. Equilibria for the simple gas hydrates can be represented by... 

To explore how pressure affects gas hydrate equilibria, you need to select the Pressure Pathway (Table A.l), plus you need to specify gas-phase... 

This appendix contains a complete listing of all parameters used in the FREZCHEM model (version 9.2). Tables B.1-B.6 deal primarily with model parameterizations as a function of temperature at 1.01 bar pressure. Tables B.7-B.11 list volumetric parameters used in developing a pressure dependence for the model. Table B.12 deals with gas hydrate equilibria. 

Tohidi-Kalorazi, B. Gas Hydrate Equilibria in the Presence of Electrolyte Solutions. Ph.D. Thesis, Heriot-Watt University, 1995. 

Finally, gas-solid equilibria should be studied to avoid plugging problems due in particular to hydrate formation. 

As already remarked in the introduction, the formulation of the laws governing heterogeneous equilibria by Bakhuis Roozeboom1 was partly based on his studies on gas hydrates. Although the general laws he derived are certainly correct, and have marked an important step in the development of physical chemistry, Roozeboom and his contempories were mistaken in the nature of the phase diagram of gas hydrates gas hydrates are not stoichiometric... 

Equilibrium Flash Calculations in Systems Containing Gas Hydrates. Fluid Phase Equilibria, 53,97-104. 

Mooijer van Heuvel, M.M. Peters. C.J. de Swaan Arons, J. (2000). Influence of water-insoluble organic components on the gas hydrate equilibrium conditions of methane. Fluid Phase Equilibria, 172, 73-91. 

The virial isotherm equation, which can represent experimental isotherm contours well, gives Henry s law at low pressures and provides a basis for obtaining the fundamental constants of sorption equilibria. A further step is to employ statistical and quantum mechanical procedures to calculate equilibrium constants and standard energies and entropies for comparison with those measured. In this direction moderate success has already been achieved in other systems, such as the gas hydrates 25, 26) and several gas-zeolite systems 14, 17, 18, 27). In the present work AS6 for krypton has been interpreted in terms of statistical thermodynamic models. 

Sloan, E.D. Phase Equilibria of Natural Gas Hydrates, paper presented at 63rd Annual GPA Convention, New Orleans, March 19-21, 1984. 

A Estimation Techniques for Phase Equilibria of Natural Gas Hydrates... 

Substantially different from ice, the phase equilibria of natural gas hydrates represents the most important set of hydrate properties. In contrast to kinetic phenomena, hydrate phase equilibria are well defined and determine a boundary to the kinetic problem. This chapter addresses hydrate phase equilibria with approximate methods that provide an understanding of the phenomena involved. 

Section 4.2 deals with the most useful hydrate equilibria—calculations of temperatures and pressures at which hydrates form from gas and free water. In this section, two historical methods, namely, the gas gravity method (Section 4.2.1) and the Kvs, value method (Section 4.2.2), for calculating the pressure-temperature equilibrium of three phases (liquid water-hydrate-vapor, Lw-H-V)1 are discussed. With the gas gravity method in Section 4.2.1.1, a method is given for limits to expansion, as for flow through a valve. In Section 4.2.2 a distribution coefficient (KVSi) method is provided to determine whether a component prefers residing in the hydrate or the vapor phase. These methods provide initial estimates for the calculation and provide a qualitative understanding of the equilibria. A statistical... 

Patil, S.L., Measurements of Multiphase Gas Hydrates Phase Equilibria Effect of Inhibitors and Heavier Hydrocarbon Components, M.S. Thesis, University of Alaska (1987). Patwardhan, V.S., Kumar, A., AIChE J., 32,1419 (1986). 

Although a typical natural gas is mainly comprised of the first three normal paraffins, the phase equilibria of each component with water will differ from that of a natural gas with water. However, a comparison of predictions with data for methane, ethane, and propane simple gas hydrates is given as a basis for understanding the phase equilibria of water with binary and ternary mixtures of those gases. 

Schroeder s (1927) hydrate monograph (Katz, Personal Communication, 1988), Hammerschmidt (1934) constructed a Pyrex tube flow apparatus for visual observation of simulated pipeline formations. After the gas flow stopped, slow heating enabled visual confirmation of hydrate disappearance, with measurement of temperatures and pressures. While numerous hydrate equilibria data were obtained using the above apparatus, Hammerschmidt reported a correlation rather than data, thereby inhibiting analysis of his data by others. 

Figure 6.2 Kobayashi s ball mill hydrate apparatus for three-phase and for two-phase hydrate equilibria. (Reproduced, from Aoyagi, K., Song, K.Y., Kobyahshi, R., Sloan, E.D., Dharmawardhana, P.D., Gas Proc. Assn. Res. Report, No. 45, Julsa, OK (December 1980). With permission from the Gas Processors Association.)...

More recently, Tohidi and coworkers (Burgass et al., 2002 Mohammadi et al., 2003) have applied a novel method for measuring gas hydrate phase equilibria (Lw-H-V), which is based on a Quartz Crystal Microbalance (QCM). Figure 6.3 shows a schematic of the QCM set up and the QCM placed in a high pressure cell. The QCM consists of a thin disk of quartz sandwiched between two electrodes. The crystal will oscillate at a particular resonant frequency when an electric current is passed across the electrodes. This frequency is a function of the properties of the crystal. Any mass (from hydrate formation) attached to the surface of the crystal disk will cause a change in the resonant frequency, and hence be detected. The pressure and temperature of the system is measured using conventional methods, namely, a pressure transducer and a thermocouple in the high pressure cell. 

Therefore, key advantages of the QCM method are that much smaller samples (one drop of water) and hence shorter times (15 min/temperature step versus several hours for conventional methods) are required for these hydrate phase equilibria measurements. The authors applied this system to measure dissociation temperatures of gas hydrates, such as methane, nitrogen, and oxygen hydrates. 

Data for Natural Gas Hydrate Phase Equilibria and Thermal Properties... 

John, V.T., Improved Predictions of Gas Hydrate Phase Equilibria, Ph.D. Thesis, University of Pittsburgh, Pittsburgh, PA (1982). 

The FREZCHEM model was designed to characterize aqueous electrolyte solutions. To work properly, there must always be ions in solution, even if only hypothetical. To simulate pure water, pure gas hydrate, pure ice, or other nonion equilibria, you need to add minor concentrations of ions (e.g., Na = Cl = 1 x 10 6m). Such minor concentrations do not significantly affect the thermodynamic properties, but they do allow for proper model calculations. 

Sulfur dioxide is quite soluble in water such solutions, which possess acidic properties, have long been referred to as solutions of sulfurous acid (H2S03). However, H2S03 either is not present or is present only in infinitesimal quantities in such solutions. The so-called hydrate H2S03- 6H20 is really a gas hydrate S02—7H20. The equilibria in aqueous solutions of S02 are best represented as... 

The chemical reactions involved in this process were outlined in the patent, which laid the basis for this industry. However, many improvements in practice have been achieved from a more detailed knowledge of the gas phase kinetics of the sulfur dioxide oxidation step, as well as from a better understanding of the gas-liquid equilibria associated with the hydration step. 

Servio, P. Lagers, F. Peters, C. Englezos, P. Gas hydrate phase equilibrium in the system methane-carbon dioxide-neohexane and water. Fluid Phase Equilibria 1999, 158-160, 795-800. 

Bishnoi, P.R. Gupta, A.K. Englezos, P. Kalogerakis, N. Multiphase equilibrium flash calculations for systems containing gas hydrates. Fluid Phase Equilibria 1989, 53, 97-104. 

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