Use of an analytical solution for calculating temperatures in repository host rock

In many concepts considered for deep geological disposal of nuclear High Level Waste, a bentonite clay buffer will be used as a protecting and isolating barrier between the waste canisters and the surrounding host rock. The temperature development in the nearfield rock, and in particular the temperature at the buffer/rock interface, contributes to control the temperature within the buffer and at the canister/buffer interface. The temperature at the buffer/rock interface is a time-dependent boundary condition for coupled Thermo-Hydro-Mechanical-Chemical processes in the buffer, and is consequently important when analysing the T-H-M-C development of the buffer. In this paper, an analytical method for calculating the rock temperature development at any point within, or around, a repository consisting of thousands of regularly distributed waste canisters is presented. Examples are given that demonstrate the robustness of the analytical solution by applying it to a KBS-3 type repository, in which canisters are positioned in vertical deposition holes in the floor of horizontal deposition tunnels. It is shown that the analytical solution can be used to determine the rock temperature at the buffer/rock interface, or at any other point in the repository host rock, quite easily and with good accuracy. It is furthermore shown that this can be done for different assumptions regarding repository layout and extension, depth below ground surface, rock thermal properties, initial canister power and fuel decay characteristics, thus allowing for fast and accurate sensitivity analyses. The mathematical approach, the essence of which is superposition of a global solution and a quasi-stationary local double-periodic solution, is presented in a principal and descriptive way. Results from verification calculations, performed with independent numerical methods, are presented and compared with corresponding analytical results. The relevance, validity and limitations of the analytical solution are discussed.