Numerical Modeling of Vertical Geothermal Heat Exchangers using Finite Difference and Finite Element Techniques


This paper presents the development of a 2D finite difference modelling approach and a 3D finite element numerical model for simulating vertical geothermal heat exchangers (GHEs), explaining the theory governing the thermal processes, element discretization and the selection of the appropriate boundary conditions. Both of these models provide fully coupled solutions for the fluid flow in the circulation pipes and the thermal processes between the fluid and solid domains (pipes, grout and soil). The numerical models are verified with a field test and subsequently they are utilized to simulate the thermal performance of a borehole heat exchanger integrated with a single U-tube. Two different thermal operation cases are analyzed; a constant rate heat injection and a fluid injection at a constant temperature. A model validation study is also carried out for the constant rate heat injection case by comparing the numerical results with the available analytical solution for a finite line source. Furthermore, effective thermal conductivity of the ground back-calculated from the results of the numerical analyses is compared with the value used in the numerical models. Comparison of the results obtained from both numerical models and validating model predictions with the analytical solution confirms that both FE and FD models can accurately simulate the heat transfer mechanisms governing the thermal performance of GHE systems.


Civil, Architectural and Environmental Engineering

Keywords and Phrases

Finite Difference Analysis; Finite Element Analysis; Finite Line Source; Geothermal Heat Exchanger; Numerical Modeling

International Standard Serial Number (ISSN)

0960-3182; 1573-1529

Document Type

Article - Journal

Document Version


File Type





© 2015 Springer International Publishing, All rights reserved.

Publication Date

01 Apr 2015