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

Abstract

The borehole thermal resistance – that is, the thermal resistance between the fluid in the U-tube and the borehole wall – is both a key performance characteristic of a closed-loop borehole ground heat exchanger and an important design parameter. Lower borehole thermal resistance leads to better system performance and/or lower total borehole length and possibly lower installation costs. Borehole thermal resistance may be determined using in situ thermal response testing, but for design purposes, it is important to be able to predict the borehole thermal resistance prior to installation. Due to the complexity of calculating it, numerous simplified methods have been proposed. This paper reviews published methods for calculating borehole thermal resistance for grouted boreholes with single U-tubes and compares their results against a rigorous analytical method.Another quantity that is particularly important for deep boreholes is the internal thermal resistance – that is, the thermal resistance between the upward-flowing and downward-flowing fluid paths in the borehole. Short-circuiting between the two legs has the effect of reducing the total heat transfer and can be quantified as an adjustment to the borehole thermal resistance, resulting in an effective borehole thermal resistance. A few simplified methods for calculating internal thermal resistance are compared against a rigorous analytical method.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.