T [k

3.70

Figure 2. Plot of methane hydrate in seawater stability data (o) from Dickens and Quinby-Hunt (1994); their linear fit (—) to equation (5) and the second order polynomial fit (—) to equation (7). Curvature in the data is apparent for even this small range.

where, T is in degrees K and P is pressure in MPa (Fig. 2). This relationship is based upon the Clausius-Clapeyron equation:

where AH is the enthalpy of formation, z is the compressibility and R is the gas constant. Sloan (1990, 1998) has pointed out that this equation predicts straight lines over limited temperature ranges (assuming AH and z are constant). This statement raises the obvious questions, what is the extent of this limited temperature range, and how straight is straight? Fitting a simple second order polynomial to their data we obtain:

1 / T = 3.83 x 10-3 - 4.09 x 10"4 log10P + 8.64 x 10"5 (log10P)2. (7)

This equation reveals significant curvature for even this limited temperature range (Fig. 2). When plotted in linear temperature vs pressure space, the offset between the data and equation (5) becomes more apparent (Fig. 3).

Figure 3. Plot of data from Dickens and Quinby-Hunt (1994) in linear temperature and pressure space; the linear fit (—) to equation (5) and the second order polynomial fit (—) to equation (7) are also shown. Although the offset between the linear fit and the data is small (<0.5°C), it is poorest at the ends of the line as well as at the mid-point of the data.

Figure 3. Plot of data from Dickens and Quinby-Hunt (1994) in linear temperature and pressure space; the linear fit (—) to equation (5) and the second order polynomial fit (—) to equation (7) are also shown. Although the offset between the linear fit and the data is small (<0.5°C), it is poorest at the ends of the line as well as at the mid-point of the data.

Extrapolation of these equations to higher P-T conditions reveals an ever increasing discrepancy between them (Fig. 4). After converting pressure to depth, and thereby introducing the error due to variations in gravity with latitude, Brown et al. (1996) fit the data of Dickens and Quinby-Hunt (1994) to a different second-order polynomial and obtained the following equation:

where, T is temperature in degrees C and z is depth in kilometers. This equation is also plotted in figure 4 after adjusting depth back to pressure, etc. Without data on the stability of methane hydrates in seawater at high temperature and pressures, it is impossible to tell which equation (5, 7 or 8) is correct. Dickens and Quinby-Hunt (1994, 1997) have found that there is a 1.1 - 1.2°C difference between the predictions for methane hydrate in pure water and seawater of 33.5 salinity at equivalent pressures. Handa (1990) fit the stability data for methane hydrates in pure water at 0.2 to 40 Mpa to obtain:

In (P/P0) = -1205.907 + 44097.00/T + 186.7594 InT, (9)

Figure 4. Plot of the linear fit (Eq. 5, —), the second-order polynomial fit (Eq. 7, ---) and equation 8 converted to absolute pressure (—-). Also shown is the stability data for methane hydrate in seawater (o) from Dickens and Quinby-Hunt (1994) and the freshwater stability data calculated at 1 °C intervals with equation 9 offset by 1.15°C (+).

Temperature [°C]

Figure 4. Plot of the linear fit (Eq. 5, —), the second-order polynomial fit (Eq. 7, ---) and equation 8 converted to absolute pressure (—-). Also shown is the stability data for methane hydrate in seawater (o) from Dickens and Quinby-Hunt (1994) and the freshwater stability data calculated at 1 °C intervals with equation 9 offset by 1.15°C (+).

where T is in degrees K and P0 = 1.01325 bar. Applying the mean offset to equation (9) for methane hydrate stability in pure water, allows us to test these three predictions at higher pressures (Fig. 4). Clearly, equation (8), when converted to pressure, is the closest extrapolation to the freshwater data from equation (9) adjusted to seawater.

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