Temperature field due to time-dependent heat sources in a large rectangular grid. Application for the KBS-3 repository

摘要

In the KBS-3 concept canisters containing nuclear waste are deposited along parallel tunnels over a large rectangular area deep below the ground surface. The temperature field in rock due to such a rectangular grid of heat-releasing canisters is studied. An analytical solution for this problem for any heat source has been presented in a preceding paper. The complete solution is summarized in this paper. The solution is by superposition divided into two main parts. There is a global temperature field due to the large rectangular canister area, while a local field accounts for the remaining heat source problem. In this sequel to the first report, the local solution is discussed in detail. The local solution consists of three parts corresponding to line heat sources along tunnels, point heat sources along a tunnel and a line heat source along a canister. Each part depends on two special variables only. These parts are illustrated in dimensionless form. Inside the repository the local temperature field is periodic in the horizontal directions and has a short extent in the vertical direction. This allows us to look at the solution in a parallelepiped around a canister. The solution in the parallelepiped is valid for all canisters that are not too close to the repository edges. The total temperature field is calculated for the KBS-3 case. The temperature field is calculated using a heat release that is valid for the first 10 000 years after deposition. The temperature field is shown in 23 figures in order to illustrate different aspects of the complex thermal process. 6 refs, 23 figs.