Hydraulic characteristic of the fractured heat exchange region in the subsurface system for extracting energy directly from Magma

In magma energy extraction, a fluid flows down through a tube set in a borehole in a magma body. About the tube, a solidified layer of cylindrical shape forms with an inner region fractured by thermal contraction during drilling the borehole. The fluid flows out from the lower end of the tube into the fractured region and flows up through the fractured region. The heat is exchanged in the fractured region by direct contact between the fluid and the solidified magma. Regarding hydraulic characteristic of the fractured heat exchange region, there is almost no direct information available so far. To this end, we have introduced a set of radial cracks emanating from the inner surface of the solidified layer to model the fluid flow paths in the fractured region and have examined crack growth behavior with respect to the temperature difference between the outer and inner surfaces of the solidified layer. Finally, we have discussed the hydraulic characteristic by introducing the hydraulic conductance, which is defined as Q- η/ΔP, where Q, η and ΔP are volumetric flow rate, fluid viscosity and pressure difference per unit distance in the flow direction, respectively. It is found that the hydraulic conductance decreases significantly as the temperature difference decreases. The effect of several factors on hydraulic conductance is examined. It is shown that the depth of the heat extraction system is most influential. A shallower system is highly preferable to enhance the fluid flow thorough the fractured region.