Numerical determination of pressure-dependent effective thermal conductivity in Berea sandstone

Within the scope of the present work, the pressure-dependent effective thermal conductivity of rock samples is simulated. Our workflow can be assigned to the field of digital rock physics. In a first step, a 3D micro-CT scan of a rock sample is taken. Subsequently, the resulting greyscale images are analysed and segmented depending on the occurring phases. Based on this data set, a computational mesh is created and the corresponding thermal conductivities are assigned to each phase. Finally the numerical simulations can be carried out.
For the representation of the pressure dependency we use the approach proposed by Saenger [1]. By making use of the watershed algorithm, boundaries between the individual grains of the rock sample are detected and assigned to an artificial contact phase. In the course of several simulations, the thermal conductivity of the contact phase is continuously increased. Starting with the thermal conductivity of the pore phase and ending with the thermal conductivity of the grain phase. A linear correlation is used to match the thermal conductivity of the contact phase with the pressure of a given experimental data set. This enables a direct comparison between simulation and measurement.
In a further step, the numerical model is calibrated to optimise the agreement between experimental data and simulation results. In particular, starting from two calibration points of the experimental data set, an adjustment of the thermal conductivities in the numerical model is carried out. While the thermal conductivity of the pore phase is held constant during the whole calibration process, thermal conductivities of the grain and contact phase are adjusted.

References
[1] Saenger et al. 2016. Analysis of high-resolution X-ray computed tomography images of Bentheim sandstone under elevated confining pressures. Geophysical Prospecting, 64(4), 848–859.