Semi-analytical method for thermal field analysis of multiple arbitrarily shaped inhomogeneities in heterogeneous geological media

Abstract

Natural geological formations typically exhibit heterogeneous thermal properties due to the presence of multiple inhomogeneities, such as mineral inclusions, fractures, or pore clusters, which significantly influence subsurface heat transport. In this work, an effective semi-analytical approach is proposed to investigate the heterogeneous thermal field containing multiple inhomogeneities with arbitrary shapes and various conductivities. Temperature solutions for rectangular elements are constructed from integrated line element temperatures, from which temperature gradients and heat flux are analytically derived. The work features a unified formulation for both the interior and exterior thermal responses of inhomogeneities, avoiding separate treatment of field regions. By Combing the Numerical Equivalent Inclusion Method (NEIM) with two-dimensional Fast Fourier Transform (2D-FFT) algorithms, the proposed approach efficiently solves thermal fields involving both stiff and soft inhomogeneities in heterogeneous media. Furthermore, the method is applied to geostructures, analyzing the thermal distributions of multiple arbitrarily shaped inhomogeneities subjected to remote heat flux. The semi-analytical method demonstrates high accuracy, computational efficiency, and robustness, providing a valuable tool for geoscientific thermal studies.