A Statistical Thermodynamic Approach to Hydrate Phase Equilibria

The object of Chapter 4 was to provide an overview of phase equilibria concepts, which are more easily obtained through phase diagrams and the approximate, historical methods. With Chapter 4 as background, the subject of the present chapter is the phase equilibrium calculation method that is both most accurate and most comprehensive. 

The statistical thermodynamic method discussed here provides a bridge between the molecular crystal structures of Chapter 2 and the macroscopic thermodynamic properties of Chapter 4. It also affords a comprehensive means of correlation and prediction of all of the hydrate equilibrium regions of the phase diagram, without separate prediction schemes for two-, three-, and four-phase regions, inhibition, and so forth as in Chapter 4. However, for a qualitative understanding of trends and an approximation (or a check) of prediction schemes in this chapter, the previous chapter is a valuable tool. 

Section 5.1 presents the fundamental method as the heart of the chapter— the statistical thermodynamics approach to hydrate phase equilibria. The basic statistical thermodynamic equations are developed, and relationships to measurable, macroscopic hydrate properties are given. The parameters for the method are determined from both macroscopic (e.g., temperature and pressure) and microscopic (spectroscopic, diffraction) measurements. A Gibbs free energy calculation algorithm is given for multicomponent, multiphase systems for comparison with the methods described in Chapter 4. Finally, Section 5.1 concludes with ab initio modifications to the method, along with an assessment of method accuracy. 

Section 5.2 shows the prediction method of phase diagrams of the major components of natural gas, namely methane, ethane, and propane hydrates and their mixtures at the common deep-ocean temperature of 277 K. Many of the commonly observed phenomena in natural gas systems are illustrated, while the power of the method is shown to go beyond that of Chapter 4, to illustrate future needs. 

The method presented in this chapter serves as a link between molecular properties (e.g., cavities and their occupants as measured by diffraction and spectroscopy) and macroscopic properties (e.g., pressure, temperature, and density as measured by pressure guages, thermocouples, etc.) As such Section 5.3 includes a brief overview of molecular simulation [molecular dynamics (MD) and Monte Carlo (MC)] methods which enable calculation of macroscopic properties from microscopic parameters. Chapter 2 indicated some results of such methods for structural properties. In Section 5.3 molecular simulation is shown to predict qualitative trends (and in a few cases quantitative trends) in thermodynamic properties. Quantitative simulation of kinetic phenomena such as nucleation, while tenable in principle, is prevented by the capacity and speed of current computers however, trends may be observed. 

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C A Statistical Thermodynamic Approach to Hydrate Phase Equilibria... 

A Statistical Thermodynamic Approach to Hydrate Phase Equilibria and the ideal gas chemical potential fx is calculated by... 

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