Design of a laboratory borehole storage model

Abstract

This paper presents the design process of a 4x4 Laboratory Borehole Storage (LABS) model through analytical and numerical analyses. This LABS is intended to generate reference Thermal Response Functions (TRFs) as well as to be a validation tool for borehole heat transfer models. The objective of this design process is to determine suitable geometrical and physical parameters for the LABS. An analytical scaling analysis is first performed and important scaling constraints are derived. In particular, it is shown that the downscaling process leads to significantly higher values for Neumann and convective boundary conditions whereas the Fourier number is invariant. A numerical model is then used to verify the scaling laws, determine the size of the LABS, as well as to evaluate the influence of top surface convection and borehole radius on generated TRFs. An adequate shape for the LABS is found to be a quarter cylinder of radius and height 1.0 m, weighing around 1.2 tonnes. Natural convection on the top boundary proves to have a significant effect on the generated TRF with deviations of at least 15%. This convection effect is proposed as an explanation for the difference observed between experimental and analytical results in Cimmino and Bernier (2015). A numerical reproduction of their test leads to a relative difference of 1.1% at the last reported time. As small borehole radii are challenging to reproduce in a LABS, the effect of the borehole radius on TRFs is investigated. It is found that Eskilson's radius correction (1987) is not fully satisfactory and a new correction method must be undertaken.