Using temperature profiles to estimate vertical flux within the geothermal zone.

In the 1970 and 1980s salt beds in the Paradox Basin of south eastern Utah and south western Colorado were considered for storage of hazardous waste by the U.S. Department of Energy. Numerous geologic and hydrologic studies were undertaken to study the salts. The most favorable locations identified were anticlines where salts beds covered a depth interval of up to 4,000 m. The table DOE6_Temperature_Log.xls contains temperature measurements at several depths in borehole DOE6 in the Salt Valley anticline of eastern Utah (Sass et al., 1983).

Following the approach of Stallman (1967) (as shown in Figure 8.4b) plot the data with dimensionless depth (z/L) on the y axis and dimensionless depth minus dimensionless temperature (T(z) - T₀)/(T_L - T₀) on the x axis, where L is thickness of the measurement interval, z=0 at the top of the interval, and T₀ and T_L are temperatures at the top and bottom of the interval, respectively.

Determine the value of B in Equation (8.4) that most closely matches the plotted data. The function, f, in Equation (8.4) is given as: f(B, z/L) = [exp(Bz/L) - 1]/[exp(B) - 1] The best fit value of B can be determined through visual inspection or by application of a formal parameter estimation routine, such as PEST.

The interval over which the temperature measurements were made is within the unsaturated caprock. Thermal conductivity is estimated at 3 W/mK on the basis of data provided in Sass et al. (1983) and Rush et al. (1980). No data on volumetric water content are provided, but for purposes of this exercise assume a value of 0.02. Determine values of vertical velocity and flux for the best-fit value of B.

References

Stallman, R.W., 1967, Flow in the zone of aeration. In Advances in Hydrosciences, Vol. 4., ed. V.T. Chow, New York: Academic Press, 151-197.

Rush, F.E., Hart, I.M., Whitfield, M.S., Giles, T.F., and D'Epagnier, T.E., 1980, Results of hydraulic test in wells DOE-1, 2, and 3, Salt Valley, Grand County, Utah, U.S. Geological Survey Open-File Report 80-205.

Sass, J.H., Lachenbruch, A.H., and Smith, E.P., 1983, Temperature profiles from Salt Valley, Utah, thermal conductivity of 10 samples from drill hole DOE 3, and preliminary estimates of heat flow, U.S. Geological Survey Open-File Report 83-455.

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