A Numerical Method for Estimating the Effective Thermal Conductivity Coefficient of Hydrate-Bearing Rock Samples Using Synchrotron Microtomography Data

• Published in: Mathematical models and computer simulations 2024, Vol.16 (6), p.896-905
• Main Authors: Fokin, M. I., Markov, S. I., Shtanko, E. I.
• Format: Article
• Language: English
• Subjects: Algorithms; Computer simulation; Continuum modeling; Digital imaging; Estimates; Galerkin method; Heat conductivity; Heat transfer; Image segmentation; Machine learning; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Microtomography; Numerical analysis; Numerical methods; Numerical models; Simulation and Modeling; Thermal conductivity; Thermal simulation; Three dimensional models
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048224700649

We propose a numerical method for estimating the effective thermal conductivity coefficient of hydrate-bearing rock samples using synchrotron-based microtomography data. A three-phase digital three-dimensional model of samples using machine learning methods is constructed, followed the averaging of mixed-phase thermal conductivity and application of numerical simulation of the heat transfer process. Unlike the existing analogs, the proposed approach is not based on phenomenological models but it realizes continuum models, which allow us to achieve more physically correct results. The microCT data are mapped to a digital model 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 compare the computational results with the published experimental, theoretical, and numerical data. Close agreement of the numerical simulation results and published estimates is found at hydrate saturation of more than 15% and divergence at the hydrate saturation less than 15% for some estimates.