Laboratory Investigation of Heterogeneous Metamorphic Rocks and Their Spatial Distribution of Thermal Conductivity

Assessing the variation in the thermal conductivity of heterogeneous rock materials can be critical when upscaling models to simulate geothermal system operation, especially for petrothermal systems, where conduction dominates over convection. This study’s objective was to evaluate heterogeneity effects when assessing the thermal conductivity of geological materials, in this case, metamorphic rocks from Kuujjuaq (Canada), where the installation of a ground-coupled heat pump system is expected. Four core samples of gneissic rocks were analyzed in detail and compared to results obtained from a thermal response test. Thermal conductivity measurements in dry conditions were performed on the cylindrical surface of the samples with an optical thermal conductivity scanner. The 2D thermal conductivity spatial distribution was obtained by linear interpolation and used for numerical modeling to simulate steady-state conductive heat transfer along the sample vertical direction. Then, the effective thermal conductivity was computed according to Fourier’s law, using the simulated temperature to investigate the effect of scale variation with the heterogeneity. Results indicate the importance of distinguishing between the sample section’s effective thermal conductivity and local average thermal conductivity. Significant scale effects were identified with a variation ratio comprised between −10% and +16% when varying the length of the sample section. The representative elementary volume for the effective thermal conductivity was determined equivalent to half of the sample length. This volume gave a thermal conductivity that is equal to the harmonic mean of the laboratory-assessed values with a relative error <5%. A comparison between the in situ and laboratory-assessed thermal conductivity indicates that the thermal conductivity inferred from the thermal response test is adequate for sizing a geothermal system, assuming a range of variability equivalent to 1.5 times its standard deviation.