An improved method for upscaling borehole thermal energy storage using inverse finite element modelling


A finite element model of a pilot borehole thermal energy storage is developed.

We determine improved thermal conductivity estimates using inverse modelling of distributed storage temperature measurements.

Scaling effects are examined by comparing calibrated model predictions to a simple thermal response test based estimate.

The calibrated model yields improved storage energy balance predictions.


Dimensioning of large-scale borehole thermal energy storage (BTES) is inherently uncertain due to the natural variability of thermal conductivity and heat capacity in the storage volume. We present an improved method for upscaling a pilot BTES to full scale and apply the method to an operational storage in Brædstrup, Denmark. The procedure utilizes inverse 3D finite element method (FEM) modelling of distributed temperature measurements inside the BTES for inferring the thermal properties of the subsurface. We find that individual geological layers can be distinguished in terms of their heat capacities and thermal conductivities using inverse modelling. The depth integrated estimate of thermal conductivity differs significantly from that obtained from a single thermal response test (TRT) at the site. As such, we find significant scaling effects in terms of the subsurface thermal conductivity distribution which are expected to be further amplified in an expansion of the pilot BTES to full scale. The methodology presented in this paper therefore provides an improved basis for upscaling pilot BTES systems. The operational data and BTES temperature measurements are published with the present paper in the supplementary material.


  • Borehole thermal energy storage;
  • Numerical modelling;
  • Inverse modelling;
  • Model validation;
  • Thermal conductivity;
  • Dimensioning

Be the first to comment

Leave a Reply

Your email address will not be published.