3rd TAGRA

Transient heat transfer in a U-tube geothermal borehole heat exchanger embedded in saturated sand was investigated numerically. The energy equation was solved by the finite element method on a two-dimensional cross-section of the borehole (fluid, pipe wall, grout and sand), following the setup of the COMSOL Multiphysics Heat Transfer module. Geometry, thermal properties and heat load (57.7 W/m for 52 h) were taken from the laboratory reference data set of Beier et al. [6]. After 52 h the borehole-wall temperature (30.09 °C) differs by only 0.1% from the infinite line-source analytical solution, and refining the mesh changes the response by less than 0.03%. The borehole thermal resistance was 0.206 m·K/W for the nominal pipe spacing (53 mm) and 0.175 m·K/W for an effective spacing of 68.8 mm, i.e. errors of 19.1% and 1.4% relative to the experimental value of 0.173 m·K/W. The ground conductivity estimated from the fluid-temperature slope (2.43 W/m·K) deviates by 13.9% from the measured 2.82 W/m·K. A parametric study showed that grout conductivity is the most influential parameter: raising it from 0.5 to 2.0 W/m·K lowers the borehole resistance by about 62%.