A Simplified Numerical Model as a Design Tool for Vertical Single U-Tube Ground Heat Exchangers

Ground heat exchangers (GHEs) are commonly modeled using the finite-element (FE) method for the design and evaluation of the GHE performance. However, one of the disadvantages of these FE models is the huge computational time involved due to the complex transient three-dimensional (3D) transport phenomena of GHEs. Thus, it is essential to develop an FE model that can provide the inlet and outlet fluid temperature and 3D temperature field with high accuracy and yet with minimal computational time. The primary objective of this study was to create a streamlined numerical model that could serve as an effective and practical design tool for simulating vertical GHEs, emphasizing a high degree of numerical accuracy while minimizing computational time. A computationally efficient 3D transient FE model was developed in COMSOL Multiphysics, which uses an equivalent 1D pipe flow instead of fully modeling the borehole grout. The proposed model prioritizes the simulation of fluid and borehole wall temperatures with an accuracy comparable to the conventional model, but it sacrifices the simulation accuracy of the borehole grout to reduce computational time and offer more convenient meshing. The proposed model was compared with a conventional model and verified against field measurements of outlet fluid temperature and spatial subsurface soil temperature at different depths and radial distances from a 132.5-m GHE operated in a full-scale geothermal bridge de-icing system. Two FE mesh cases––optimum and extrafine––were designed in order to compare the models. The results indicated that the computational time was greatly reduced, by 95% and 81% for the two mesh cases, respectively, while the same level of accuracy in the temperature evaluation was maintained. Also, the required number of model elements was decreased by 90% and 67% for the optimum and extrafine-mesh cases.