A Modeling Approach for Simulating Geothermal Energy Utilization by Borehole Heat Exchangers and Borehole Heat Exchanger Arrays

Michael Rembe1
1Rembe Consulting PartG mbB, Germany
Published in 2023

Decarbonization of the heating sector requires the exploitation of climate-neutral energy sources and the use of natural heat storage. Shallow and deep geothermal energy can make a valuable contribution to this. The dimensioning and design of geothermal boreholes and larger borehole heat exchanger arrays requires efficient and flexible simulation tools. They should meet a wide range of configurations (expansion of the geothermal borehole, different types of borehole heat exchangers, flexible arrangement of borehole heat exchangers, etc.).

The COMSOL Multiphysics® software is generally very well suited to meet a wide range of requirements, to consider different types of heat exchangers and to flexibly arrange many boreholes. However, due to the strongly varying dimensions of lengths (depth of the boreholes, length of the completion material), diameters (diameter of the borehole, of the completion, of the borehole heat exchangers) and the dimensions of the surrounding rock to be considered, the simulation with the Method of Finite Elements is a great challenge due to the required resolution of the mesh (diameter/length). With COMSOL Multiphysics®, a closed-form methodology has been developed to deal with the disproportions and multiplex requirements.

The simulation model represents the geothermal heat utilization from the heat pump up to the surrounding rock (Figure 1). The governing differential equations of the different physics are described by COMSOL Multiphysics®, the Pipe Flow Module and the Subsurface Flow Module. Three different geometry spaces (3D, 3D, 1D) represent the different compartments (Figure 2). The coupling of the computational variables is done independently from mesh by non-local coupling operators. Global ODEs and PDEs simulate the heat pump and calculate auxiliary variables. Events ensure the correct consideration of the temporal operating regime of the geothermal system.

The seasonal heat extraction and injection may cause phase change of pore water of the surrounding rock, what is considered, too. The analysis of geothermal heat utilization is performed at different time scales. A detailed operating regime (for example, hourly) can be analyzed as well as long-term utilization (several tens of years). This supports efficient planning from a rough to a detailed calculation. In a 2023 performed study for the Stadtwerke Sondershausen GmbH, the geothermal site potential for a borehole heat exchanger array of 216 boreholes with a depth of 150m to 400m and with different types of heat exchanger was investigated. Due to the planned long utilization time of 75a, the temperature changes in the surrounding rock were calculated by transient compact analyses based on years (Figure 3). For the analysis of short-term temperature changes by peak loads, simulations were performed based on months and days (Figure 4). Model verification and refinement is foreseen by simulation of a longer-term geothermal response test.