Unit-response function for ground heat exchanger with parallel, series or mixed borehole arrangement

•A matrix approach enables to compute fluid temperature for BHE arrangements.•Pure parallel, pure series and mixed BHE arrangements can be modeled.•The approach is general and can be used with any analytical model.•Computation is very efficient as only a few time steps need to be computed.•Results are compared to those of a full 3D finite element model.

A novel approach is presented that allows to predict fluid temperatures entering a Ground Heat Exchanger (GHE) for parallel, series and mixed arrangements of boreholes. The method determines at each time step the heat transfer rates occurring at each borehole so as to reproduce the fluid temperature at the GHE inlet for a specific borehole arrangement. The analytical finite line source model is used to compute the borehole wall temperatures, whereas the fluid temperatures are assumed to vary linearly along the pipes. The method requires to solve a linear system of equations at a small number of time steps. The different systems of equations for each arrangement are determined. A comprehensive 3D finite element numerical model shows good agreement with the computed fluid temperatures. The proposed approach is computationally very efficient. The fluid temperature unit response function can be convolved with any desired heat load to estimate fluid temperatures at the GHE inlet for a wide variety of scenarios.