An Approximate Solution for Predicting the Heat Extraction from a Closed-loop Dipole Well Circulation in an Enhanced Geothermal Reservoir

Abstract

This paper investigates the heat extraction from an enhanced geothermal reservoir (EGR) using a closed-loop circulation through one fracture in the reservoir connecting one injection and one production well. Based on the fact that heat conduction is very slow, the one-fracture system serving as both injection and outlet is economically not viable, but represents one fracture in an array of such fractures. In this paper, we will employ a few simplifications to make this complex problem tractable theoretically. Heat exchange between the well and its surrounding formation is assumed to be radial and horizontal. Vertical heat conduction dominates the vicinity of an infinite fractured reservoir and flow-induced heat advection transfers injected cool water to outlet hot water. Mathematically, the closed-loop is divided into three portions, i.e. the injection and production wells and the fracture connecting them, with suitable governing equations for temperature change and connection conditions. Semi-analytical solutions in the Laplace space for each portion are found and the Stehfest method is used to obtain the physical values in the time domain. The results produce useful insights for future geothermal reservoir design. For example, the fluid viscosity does not affect greatly the bottom-hole temperature of the injection well and thus the outlet temperature of the EGR system. The flow rates and the well separation distance are two important factors for outlet temperature. Compared to fully numerical methods, this model is more efficient and can be used as a design and optimization tool.