Stability of a Penny-Shaped Geothermal Reservoir in the Earth’s Crust

The theoretical analysis of a penny-shaped geothermal reservoir in the earth’s crust subject to linear tectonic stress gradients has been made on the basis of the three-dimensional theory of elasticity. The condition for stability of a reservoir requires K₁ < K_c, where K₁ and K_c are, respectively, the stress intensity factor for the opening mode and the fracture toughness of the surrounding rock. From this condition the upper critical pressure being necessary for the reservoir stability is obtained and is shown graphically.