Design Optimization of the Spacing Parameters in the Canadian Deep Geological Repository Containing High Level Radioactive Nuclear Waste

Abstract

The Canadian Deep geological repository (DGR) is the facility designed to isolate and contain the highly radioactive nuclear waste at approximately 500m underground for approximately one million years. The reliability and safety of the DGR depends on the performance of the designed engineering barrier systems (EBS) as well as the environments at the site. In this thesis, surrogate models are utilized for optimizing the spacing of the current design of DGR by incorporating the thermal numerical model developed in finite element software COMSOL, which is hard to use for this purpose due to the long CPU time it takes. The temperature rise caused by the radioactive waste buried inside the repository is analyzed by COMSOL. The result indicates that the temperature peak will likely happen within the first 100 years. Other than the material properties, the peak temperature also depends on the design of spacing between container and placement rooms. Increasing spacing reduces the peak temperature and thus increases the probability of meeting the temperature constraint, however, it increases the cost and the overall footprint of the DGR. Optimizing the design directly using the simulation is computationally expensive due to long simulation times, for example, a single simulation may take minutes to hours. As a result, surrogate based optimization is used to solve the optimization problem as well as computing the probability of meeting the temperature constraint for a given spacing design. Using the surrogate-based optimization, the optimal design points based only on temperature constraint can be found with 19 COMSOL evaluations. The surrogate’s mean absolute error (MAE) at these design points are 1.1 C comparing to COMSOL results. Similarly, for the cost and multi-objective optimization problems, the surrogate converged with 16 and 25 COMSOL evaluations, the MAE for these optimal points are 0.4C and 0.091C. For these design problems, there are a total of 310 possible design combinations by varying the spacer width and the room spacing, the surrogate-based optimization greatly reduces the number of simulations comparing to an exhaustive simulation approach where all 310 points are evaluated for finding optimal designs. For the uncertainty analysis, three variables are fit to the model, the possible input combination will be 103 if 10 values are sampled for each variable. The resulting surrogate model converged with 75 evaluations, the number of simulations is an order of magnitude less than the exhaustive simulation approach. The surrogate model estimates the temperature of the sample design model with MAE of 0.6C. Comparing the surrogate prediction results to the results of the 320 known COMSOL evaluations from other fitting process yields a MAE of 1.0C. In these surrogate model experiments, the reduction in the total number of simulations are significant while the surrogate only slightly sacrifices the accuracy comparing to original model evaluation.