Fully analytical solution in time and space domains on temperature in multi-barrier nuclear waste repository

Abstract

Temperature evolution is one of the crucial factors in safe operation and geometric design of high-level radioactive waste disposal repositories. A three-dimensional two-layer axisymmetric heat transfer model was established to study the temperature evolution of the repository in the case of single canister. Applying a series of mathematical tools such as the finite Fourier sine transform, separation of variables and Duhamel's theorem, a fully analytical solution was obtained, which can visually and quickly represent the temperature evolution in both time and space. The validity of the model and solution was confirmed by comparing it with the existing line heat source solution, semi-analytical solution and finite element simulation results. The canister surface temperature was obtained by superimposing the temperature difference between the internal and external surfaces of buffer layer on the rock wall temperature. A single-panel calculation model was established, and dimensional and parameter analysis were carried out using the obtained fully analytical solution. According to the quantitative analysis using the obtained solution, increasing the canister spacing has a better effect on reducing the peak temperature than increasing the tunnel spacing. The effect of the two ways in reducing the peak temperature weakens with increasing the spacings.