A numerical method for estimating the effective thermal conductivity coefficient of hydrate-bearing rock samples using synchrotron microtomography data

We propose a numerical method for estimating the effective thermal conductivity coefficient of hydrate-bearing rock samples using synchrotron-based microtomography data. The construction of a three-phase digital three-dimensional model of samples using machine learning methods with subsequent averaging of mixed-phase thermal conductivity, and application of numerical simulation of the heat transfer process is performed. Unlike the existing analogs, the proposed approach is not based on phenomenological models, but it realizes continuum models, which allow to achieve more physically correct results. Mapping the micro-CT data to a digital model is performed by an algorithm that takes a stack of segmented images as input and generates a discrete grid model with separation into the phases present in the samples. To discretize the mathematical model of the heat transfer process, a multiscale discontinuous Galerkin method is proposed. To calculate the effective thermal conductivity coefficient, a numerical homogenization algorithm based on Fourier's law is implemented. The dependence of the effective thermal conductivity coefficient on the volume fraction of components in the hydrate-bearing samples is shown. We compared the computational results with published experimental, theoretical, and numerical data. A good agreement of the numerical simulation results and published estimates was found at the hydrate saturation more than 15%, and divergence at the hydrate saturation less than 15% for some estimates.