Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers

The simplified methods for calculating both borehole thermal resistance and internal thermal resistance are compared in parametric studies spanning the range of borehole diameters, pipe spacing, ground thermal conductivities and grout thermal conductivities found in practice. Many of the simplified methods work well with some combinations of parameters and poorly with others. The first-order multipole expressions are closed-form algebraic expressions that give results within 2% (for borehole thermal resistance) and 6% (for internal thermal resistance) over the entire range of parameters. This represents significantly better accuracy than any of the other simplified methods and, therefore, the first-order multipole algorithm is recommended for single U-tube applications when the tubes are symmetrically placed.