Boundary Layer Flow, Heat, and Chemical Transfer near Vertical Heated Boreholes in Water-Saturated Rock: A Mechanism for Developing a Large Scale Underground Hydrothermal Experiment (DUSEL)

We investigate a means of developing a large-scale hydrothermal experiment at the DUSEL site in the Homestake Mine, South Dakota, or elsewhere, by considering boundary layer flow, heat, and chemical transfer near an internally heated vertical borehole or borehole array emplaced in a water-saturated porous medium with homogeneous permeability. We use scale analysis to determine the relationships between vertical fluid velocity u, boundary layer thickness δ and the Rayleigh number Ra for both a single borehole maintained at constant temperature and a linear array of boreholes maintained at constant heat flux. For a single borehole, u ~ (a/y)Ra and δ ~ yRa^-1/2, whereas for the borehole array u ~(a/y) Ra^-1/3 and δ ~ yRa^-1/3, where y is the borehole height and a is the thermal diffusivity. We find that for y = 100 m, optimum initial permeability lies between ~ 10^-10 -10^-12 m^2 and the optimum heat flux is ~ 60 W/m^2. We also use scale analysis to determine the permeability change resulting from thermoelastic stresses generated by heating the rock near the boreholes and find that these stresses do not significantly impact the permeability so long as the initial porosity is ~ 5%, or the initial crack aspect ratios are less than or equal to 10^-2. Finally, we use scale analysis to investigate mineral dissolution within the boundary layer flow adjacent to the boreholes. Using the above velocity scaling and assuming linear reaction kinetics, and a crustal porosity of 5%, thermodynamic equilibrium may be obtained at the top of a 100 m high borehole provided reaction rate constants are in the range of ~ 10^-7 - 10^-8 s-1.