A hybrid numerical-semi-analytical method for computer simulations of groundwater flow and heat transfer in geothermal borehole fields

The formulation of a hybrid numerical-semi-analytical method for cost-effective simulations of heat transfer in fields of vertical geothermal boreholes, in the presence of groundwater flow, is presented. An amalgamation of a co-located control-volume finite element method and a finite volume method is used to solve 1) a volume-averaged continuity and the Darcy-Brinkman-Frochheimer equations to obtain the distribution of the groundwater flow; and 2) an unsteady three-dimensional volume-averaged advection-conduction equation to calculate the related ground temperature distribution, assuming local thermodynamic equilibrium between the groundwater and the soil particles. The bulk temperature distribution of the working fluid (flowing inside the legs of a U-tube pipe inserted inside each borehole and kept in place by grout) and the related heat extraction (or addition) rate are obtained using a semi-analytical method to solve a quasi-steady quasi-one-dimensional model. The conditions of no-slip, impermeability, equality of temperature, and continuity of heat flux are used at the interface between each borehole and the groundwater-saturated soil in the borehole field. The proposed method is applied to test and demonstration problems to demonstrate its capabilities.