Numerical simulation of Coaxial Borehole Heat exchangers using supercritical CO2 as a working fluid

Geothermal heat is an almost emission-free energy source, and it has become an important replacement for fossil fuels used to heat buildings. A promising geothermal system is the Coaxial Borehole Heat Exchanger (CBHE). It is a tube-in-tube system, where the “cold” fluid is injected into the annulus of the coaxial. The fluid becomes heated from the surrounding rocks on its way down the well, and the “hot” fluid returns to the surface through the inner tube. Here, we present numerical methods for deep coaxial borehole heat exchangers using compressible working fluids, such as supercritical CO2.

Pressure and the temperature in compressible fluids become coupled. A usual numerical approach is to decouple the temperature- and the pressure equations, where these equations are solved separately. We compare a fully coupled numerical scheme with three different schemes of decoupled pressure and temperature. These four schemes are (1) fully coupled and implicit temperature and pressure; (2) serially coupled implicit temperature and explicit pressure; and (3) serially coupled explicit temperature and pressure. These finite-difference schemes were tested using Ramey’s approximation of the heat flow from the rock. The final scheme was: (4) the coupling of a 1-dimensional pipe simulator with a transient temperature equation for the well bore and the transient conductive cooling of the rock.

Benchmarking of the numerical schemes was done by comparing their results. Schemes (1), (2) and (4) were in excellent agreement. The serially coupled explicit scheme (3) could produce useful results, considering its simplicity and speed and the uncertainties associated with rock properties. The testing of the schemes was done assuming a constant flow rate and quasi-stationary state of the fluid in the well.

For a constant mass flow rate, scheme (2) is recommended. Scheme (4) showed that just a few residence times were enough to establish a quasi-stationary state in the fluid. The CO2 test cases demonstrated the thermosiphon effect, and also showed how the temperature increased with increasing pressure — an effect directly related to the thermal expansibility of the fluid.

Reference:

M. Wangen, Numerical solutions for coaxial borehole heat exchangers using CO2 as a working fluid, Applied Thermal Engineering, 264 (2025) 125295, DOI: doi.org/10.1016/j.applthermaleng.2024.125295