Shape of a Crack-Like Reservoir in a Hot Dry Rock for Extraction of Geothermal Energy

Abstract

The extraction of geothermal energy from hot dry rocks in the earth's crust has received wide attention. An abundand amount of geothermal energy could be recovered from hot dry rocks by circulating fluid through crack-like reservoirs which are created by a hydraulic fracturing technique. During the extraction of geothermal energy, the surfaces of the crack-like reservoirs are cooled by the fluid and the thermal contraction of the rock occurs. When the stress intensity factors at the border of the crack-like reservoir attain the fracture toughness of rock, the reservoir begins to propagate at the border. Therefore, in the design of crack-like geothermal reservoirs, the fracture mechanics study of a water-filled crack including thermoelastic effect is needed to control the mechanical behavior of the reservoirs.
This paper is concerned with the shape of a vertical two-dimensional crack-like reservoir in the earth's crust on the basis of the theory of quasi-static thermoelasticity. The surrounding rock is assumed to be a continuum which is homogeneous and isotropic with respect to thermal and elastic constants. By using the singular point method, a set of singular integral equations for density functions derived. The singular integral equations are solved by means of the collocation method and the inversion formula. Numerical calculations are carried out to find the shape of the crack-like reservoir, and the opening displacement of the reservoir against time is shown. The variation of the volume of the reservoir is also plotted against time. An approximate formula is also proposed to estimate the volume of the reservoir.