Natural convection of water contained in a vertical fracture or fault in which the temperature increases with depth is strongly influenced by the heat transport processes not only within the water itself but also by the heat transferred to and from the surrounding rock mass. The results of a linear stability analysis indicate that the critical Rayleigh number R* is time dependent. For spontaneous neutral stability, R*(t = O) • 10(h/a):, where h and a are the fault height and aperture, respectively. Since h >> a, R*(O) is several orders of magnitude greater than the value 4;r: that would pertain to the same situation without the influence of the surrounding rock masses, e.g., a porous bed with large horizontal dimensions. The resultant cell motion consists of rolls about axes parallel to the aperture. These rolls are of height h and closely spaced in the strike direction. Cases of spontaneous instabilities in fractures or faults are expected to be infrequent, but initially subcritical convection could be fostered by other means such as tectonic displacements at the fault. Because R* diminishes as time -x/:, eventually, this subcritical convection becomes unstable, and exponential growth ensues. As the heat of the surrounding rock is depleted and an isothermal state is approached, the convection eventually dampens until a period of thermal recovery allows its resumption.

Two hot dry rock geothermal energy reservoirs were created by hydraulic fracturing of Precambrian granitic rock on the west flank of the Valles Caldera, a dormant volcanic complex, in the Jemez Mountains of northern New Mexico. Heat was extracted in a closed‐loop mode of operation, injecting water into one well and extracting the heated water from a separate production well. The first reservoir was produced by fracturing the injection well at a depth of 2.75 km, where the indigenous rock temperature was 185°C. The relatively rapid decline in temperature of the water produced from the first reservoir, 100°C in 74 days, indicated an effective fracture radius of about 60 m with an average thermal power extracted of 4 MW. A second, larger reservoir was created by refracturing the injection well 180 m deeper. Downhole measurements of water temperature at the reservoir outlet as well as temperatures inferred from chemical geothermometry showed that the thermal decline of this reservoir was negligible; the effective heat transfer area of the new reservoir must be at least 45,000 m2, nearly 6 times larger than the first reservoir. In addition, reservoir residence time studies employing visible dye tracers indicated that the mean volume of the second reservoir is 9 times larger. Other measurements showed that flow impedances were low and that downhole water losses from these reservoirs should be manageable. The geochemistry of the produced water was essentially benign, with no scaling problems apparent. Moreover, the level of induced seismic activity was insignificantly small.

[1] If fluid is injected into joints in rock masses, the pressure required might result in changes in the joint space between rock blocks that accommodate the fluid transport. At one extreme, very low injection rate and pressure, the joint space is unaffected, and the fluid pressure follows the usual law of linear diffusion. At the opposite extreme, very high injection rates, as used, for example, during hydraulic fracturing, the pressure is so high as to overcome the original Earth stress holding the rock blocks in contact. They ''lift off,'' resulting in huge changes in joint space, and the flow equation then becomes so nonlinear that pressure pulses are no longer transmitted in a smooth, diffusive manner but more like a propagating shock wave. In between these extremes, at more modest pressure, the result is not liftoff, but nevertheless, the effective stress tending to close the joint space is reduced; this space dilates, and the effective permeability and storativity of the joint will increase. While the pressure wave will not propagate quite as sharply as it does for liftoff, nonlinearities greatly influence the results, exhibiting behavior far from that predicted by linear diffusion.

Instantaneous measurements of the wall shear stress were made in the laterally converging duct also used for mean measurements in part 1 and were analysed by conditional sampling and by conditional averaging. The sidewalls of the duct were adjusted to provide (i) a straight duct of constant rectangular cross-section and (ii) laterally (spanwise) converging ducts resulting in streamwise acceleration of the flow. The Reynolds number varied from 7600 to 47 200 and the dimensionless acceleration parameter Kv = (ν/V2)dV/dx ranged from 0 to 3·4 × 10−6, yielding a variation of the flow regime from fully turbulent to nearly laminar. The typical burst pattern, or conditionally averaged time history of the wall shear stress, resembled the time history of the streamwise velocity component deduced at y+ = 15 by Blackwelder and Kaplan using the same general technique. For fully developed flows, inner or wall scaling of the bursting frequency was found to be less dependent upon Reynolds number than outer scaling; other characteristics examined varied with both inner and outer scaling. For converging flows measurements of bursting characteristics essentially confirmed the indicated flow regimes deduced in part 1 and showed that the measured characteristic that was most affected by acceleration was the bursting frequency. All characteristics varied with acceleration, but the variation was generally less when normalized by wall variables rather than when normalized by outer variables.

This report was prepared a$ an account of work sponsored by Ule United States Government. Neither the United States nor the Untied Stater Department of Energy, nor any of their employees, nor any of their contraclorr, subcontractors. or their employees, makes any warranty, express or implied, or assumes any legal liability or reiponribillty for the accuracy, completeneu or urefulnesr of any information, apparatus, product or proeeu disclord. or reprerents that its u s would not infringe pnvatcly owned nghts. P I ~~ISTRIBUTION OF THIS DOCUMENT IS_ UNWTED distributed homogeneously. This additional porosity, 4 , was simply related t o the volumetric coefficient of thermal contraction of the rock and the cooling of the rock. The new permeability, k , of the thermal s t r e s s crack-altered rock 2 was calculated from the Kozeny formula. . '. .

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