Activity Coefficient for Water in the Hydrate

Several methods have arisen to correct the assumptions in the above van der Waals and Platteeuw model, to address the inaccuracies at the high pressures of current applications. The two most prominent modern correction methods are (1) to use ab initio quantum mechanical corrections to relate to first principles as much possible, as briefly discussed in Section 5.1.9, and (2) to fit the existing 

Because there is a very large phase equilibrium data base, existing over 70 years as shown in Chapter 6, and because recent spectroscopic tools (e.g., Raman, NMR, and diffraction) have provided microscopic hydrate data, the latter approach was chosen in this monograph and the accompanying computer programs. While the latter method used in this book represents a theoretical advance, it is shown to compare favorably with the existing commercial hydrate programs in Section 5.1.8. 

Traditionally, the chemical potential of the standard hydrate is assumed to be at a given volume, independent of the hydrate guests. If the standard hydrate volume is not the volume of the equilibrium hydrate, there should be an energy change proportional to the difference in volume (AvH = v11 — 7). Note that, in the development of Equation 5.23, Av11 is assumed to be equal to zero (i.e., all hydrates of a given structure are at the same volume). 

Equation 5.23 is considered to be an ideal solid solution model. If we choose to extend our equations from one hydrate crystal to a large number Na (Avogadro s number) of crystals, we must replace the Boltzmann constant k with the universal gas constant R (=kN ). Ballard (2002) defined the chemical potential of water in hydrates as 

At the limit stated above, Equation 5.28 reduces to Equation 5.23 when Av11 = 0 (i.e., = 1). In the strictest sense, the activity coefficient accounts for the 

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