Experimental validation of heat and mass transfer numerical correlations for geothermal systems

Geothermal energy provides a sustainable and renewable solution to meet part of the global energy demand while simultaneously reducing carbon emissions. This study aims to propose an empirical correlation derived from numerical simulations based on Computational Fluid Dynamics (CFD) to describe the heat and mass transfer within a system consisting of an aquifer-well-Downhole Heat Exchanger (DHE). The generalized porous model is adopted for numerical simulations describe the behavior of the DHE, the well, and the aquifer by using a single domain approach and the same set of equations for both free-flow fluids and porous media. Additionally, sensitivity analyses are conducted to study the impact of the aquifer-well-DHE system under different thermal power conditions, geothermal aquifer permeabilities, heat exchanger lengths, filter tube and temperatures of the reservoir. Key findings include the development of empirical correlations between the Nusselt number and a "modified" Rayleigh number at the interface between the free-flow fluid and the porous medium, which can be used for designing the DHE with a lumped parameter model. Furthermore, another numerical correlation is built to describe the dimensionless geothermal mass flow rate involved in the natural convection phenomena. The numerical simulations are validated using experimental data from a system built on the island of Ischia, located in southern Italy. Unlike recent interface modeling approaches proposed in the available literature which remain far from being applicable for such geothermal systems, the correlations developed in this work explicitly capture the role of operating conditions and geometrical configurations through a Rayleigh-based formulation and can be directly embedded into lumped-parameter models of geothermal DHE system.