Analytical and numerical models for determining geothermal energy potential

Abstract

Comparison of analytical theories on heat extraction from hot dry rock (HDR) has been presented in the literature by various authors.. In this paper a physical model, it is proposed to analyze the phenomenon of heat exchange between water and hot dry rock as a homogeneous and isotropic impermeable medium. Cold water enters a vertical fracture from below, extracts heat from the rock, during the ascent of through the fracture. The equations governing the heat exchange are the conduction equation in the rock, and convection in the fluid. The study of this phenomenon, is conducted in two parts, a single fracture through the rock, and the case of multiple fractures with an infinite series of parallel fractures with equal distance. In addition to comparing the analytical solutions in the literature, the comparison was extended with numerical solutions solved by numerical methods based on reverse – Laplace transform, and the resulting solutions from software models built on finite element method (FEM). These solutions, are given in dimensionless terms, describing the trend of the temperature as a function of time, and in the case of multi – fracture as a function of the spacing between the fractures themselves. Finally, a comparison between single fracture, and multi – fracture is presented, to show that in the case of multi – fracture the system is much more efficient for heat extraction than in the case of single fracture, for the same flow rate, as the multi – fracture presents a greater surface area of heat exchange between rock and fluid.