## Gibbs Free Energy Minimizations

Several methods to estimate the P-T conditions of methane hydrate stability by searching for the state which minimizes the Gibbs Free Energy of the system have been developed. These programs are computationally intensive and require sophisticated computer programming. However, computer programs to carry-out these calculations are now readily available. Sloan (1990, 1998) presents a detailed description of CSMHYD, a PC-DOS based computer program. His textbook includes a floppy disk with an executable version of the program. In addition to calculations of the stability temperature at a given pressure (or vice-versa) in pure water, the program also includes a variable composition salt component to allow seawater and pore-water predictions. We refer the reader to the textbook for the details of how the program works. Output from CSMHYD is shown in figure 5 for a pure methane hydrate in equilibrium

Figure 5. Output from CSMHYD (—) and Multiflash (—) plotted with the seawater data (o) from Dickens and Quinby-Hunt (1994) and the predictions from equation (9) offset for seawater (+) as in Figure 4.

Temperature [°C]

Figure 5. Output from CSMHYD (—) and Multiflash (—) plotted with the seawater data (o) from Dickens and Quinby-Hunt (1994) and the predictions from equation (9) offset for seawater (+) as in Figure 4.

with seawater. A salinity of 33.5 was chosen for the CSMHYD predictions so that a direct comparison could be made with the seawater data and the stability conditions calculated using equation (9) and adjusted to seawater, as above in figure 4. Clearly, the CSMHYD predictions better fit with the seawater data than the freshwater predictions adjusted to seawater at P > 12MPa.

Zatsepina and Buffet (1997, 1998) present an alternate Gibbs Free Energy minimization routine based, in part, on a very fast simulated annealing algorithm (Ingber, 1989). Their results are quite similar to the CSMHYD program and compare favorably to a prediction from Handa (1990). Recently, they have begun exploring whether the equilibrium calculations are sufficient or whether additional complexities lay in meta-stable phases that persist in nature outside their stability fields as decomposition of the gas hydrate is impeded by the free energy required to create small bubbles (Buffet and Zatsepina, 1999).

A commercially available program, Multiflash (Infochem Computer Services Ltd., London), also calculates the P-T conditions for methane hydrate stability using the Gibbs Free Energy minimization approach. It is more sophisticated that CSMHYD, running in the Windows® operating system, and it performs a wider variety of calculations. The Multiflash P-T predictions for methane hydrate stability in seawater of salinity 33.5 are also shown in figure 5. They are slightly different from the CSMHYD program and compare quite favorably with both the seawater data and the higher P-T predictions from equation (9) adjusted to seawater as before.

Given the close correspondence between these computer programs and the predictions based upon equations (8) and (9), it is logical to ask why incur the additional expense of the programs if the equations work so well? For pure methane hydrates in freshwater or seawater of salinity 33.5, these equations are the simplest approach. However, if one is dealing with substantially different salinity, or different salt compositions, as may be found in pore-water, or with mixed gas compositions, then computer programs offer the ability to deal with these situations and to extend the predictions beyond the range of the data. This can be seen quite clearly in figure 6, where the differences between the predicted equilibrium P-T conditions for mixed gas hydrate stability in salinity 33.5 seawater, where the gas is a composite of methane and other natural gases, and pure methane hydrate in the same salinity seawater are plotted as a function of pressure. For this example, we progressively increased the complexity of the gas mixture, starting with methane + ethane, then adding carbon dioxide and hydrogen sulfide (see the figure caption for the percent composition). These differences (0.4-2.0°C) are larger than the effects described earlier and they vary with pressure. Also shown is the destabilizing effect of high salinity (40.0) on pure methane hydrate. These lines represent complex functions for which it will be difficult to derive simple mathematical expressions. Thus, it is in situations that address the complex real-world problems of mixed gas compositions and varied salinity that the computer programs will find their greatest use.

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Figure 6. Plot of the temperature differences as a function of pressure between the Multiflash predictions for methane hydrate stability in high salinity (40.0) seawater (—); and methane + 2% ethane (—), methane + 2% ethane + 2% C02 (••••), and methane + 2% ethane + 2% C02 + 2% H2S (—-) in seawater of salinity 33.5 relative to pure methane hydrate in seawater of salinity 33.5, respectively.

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