Analytical and Numerical Modelling of a Coaxial Borehole Heat Exchanger to Extract Geothermal Energy

Abstract

Unused wells in petroleum fields are readily available as a potential source of geothermal energy. To produce geothermal heat in a viable manner, borehole heat exchangers may be used in some of the available deep wells (> 500 m). Therefore, we aim to develop a rigorous modelling technique to evaluate such systems in deep oil and gas wells.
We examine a mathematical model based on unsteady-state heat conduction for the coupled borehole-reservoir system. Using the analytical technique, our paper presents cases evaluated using the Method of Characteristics. We briefly discuss the challenges encountered while using the above method for a non-linear hyperbolic system of partial differential equations in a practical scenario. Finally, we adopt a numerical technique based on the Finite Difference Scheme to analyse transient heat transfer in a coupled
wellbore-reservoir system. The paper also discusses a hypothetical case that uses borehole heat exchangers to supply geothermal heat in a greenhouse.
We conclude that the numerical technique based on the finite difference scheme is appropriate to study deep borehole heat exchanger systems. The hypothetical case study of a greenhouse demonstrates the feasibility of using such systems to supply geothermal heat. Future work should perform a detailed economic study and develop a more rigorous analytical method to optimise the design of multi-borehole
systems.