A 3D space-marching analytical model for geothermal borehole systems with multiple heat exchangers

We present a novel, three-dimensional (3D), space-marching analytical framework that accurately predicts and evaluates the thermal performance of a geothermal borehole system with single or multiple N-by-N heat exchangers. The procedure for this model which is associated with the key novelties of this work is threefold. First, a radial temperature profile in a single borehole arrangement is solved through an exact solution using the Green’s function. A time-dependent convective boundary is prescribed around the borehole wall. Second, an axial temperature distribution in this single borehole is calculated by a space-marching algorithm, which updates the convective boundary at every depth by obtaining the heat transfer fluid (HTF) temperature via an energy balance. Third, the single borehole in 2D is extended to a N-by-N arrangement in 3D by the thermal superposition with algebraic equation based on each borehole’s location. The developed 3D model is verified with numerical results using the finite element method and validated against a field-scaled experimental data in the literature in regards to the HTF temperature. Further, the influences of borehole distance, ground thermal conductivity and mass flow rate of the HTF are studied. It can be concluded that this 3D space-marching analytical framework is capable of predicting transient temperature profile of any N-by-N geothermal boreholes subjected to a time-dependent boundary in an accurate and computationally efficient manner, which in turn facilitates the thermal design and implementation of geothermal systems for energy extraction.