Analytical Solution to Temperature Field of the Repository for Deposing the High-Level Radioactive Waste Considering the Bentonite Pellet Layer

The spatiotemporal distribution of temperature fields serves as a critical basis for the thermal design and safety assessment of high-level radioactive waste repositories. Based on the multi-barrier concept of disposal systems, a two-dimensional axisymmetric three-layer thermal model was developed. The governing heat transfer equations were solved using the Laplace transform, Fourier transform, and their corresponding inverse transforms, yielding semi-analytical expressions for temperature distributions in the bentonite block layer, pellet layer, and host rock. Comparative analyses with numerical simulations and two-layer analytical solutions demonstrated the validity and superior capability of the three-layer model in addressing complex heat conduction phenomena. Utilizing the derived semi-analytical solutions, parametric studies were conducted to investigate the influence of geometric and thermal properties on buffer layer temperature maxima. Furthermore, the model was applied to determine optimal disposal container spacing for various nuclear waste types and to simulate the thermal response in Sweden􀆳s prototype repository. The results indicate: (1) inclusion of the bentonite pellet layer increases buffer peak temperature by 14.84 ℃ compared to its exclusion; (2) pellet layer thickness significantly affects temperature maxima due to its relatively low thermal conductivity; (3) buffer temperature variations become negligible when container spacing exceeds 20 m; (4) the proposed solution accurately predicts thermal behavior in prototype repository heating experiments.