## 1 Introduction  
In accordance with international scientific consensus, the best solution for the final disposal of Canadian high-level radioactive waste, which is predominantly produced by the country's operation of nuclear power plants running CANDU reactors, is to isolate it within a deep geological repository (DGR) that will prevent radionuclide release into the biosphere for at least one million years. Designing and implementing such a repository are the responsibilities of the Nuclear Waste Management Organization (NWMO), and they have devised a plan for a DGR that will utilize a multiple-barrier system. It will employ five engineered and natural barriers for the isolation of the used nuclear fuel, as shown in Figure 1. The used CANDU fuel bundles (durable ceramic UO2 fuel pellets and the Zircaloy cladding that house them) provides the initial two barriers. The remaining three layers of the multiple-barrier system will be copper-coated carbon steel used fuel containers (UFCs) that consolidate 48 used fuel bundles per UFC, highly compacted bentonite buffer boxes for encasing the UFCs, and the host rock environment of the future repository approximately 500-800 m below ground surface. As a critical component for the containment of used nuclear fuel, the integrity of the UFCs is the focus of many research programs at NWMO. The copper coating of the UFCs has been designed to be 3 mm thick, more than double the expected corrosion allowancesfor uniform corrosion, under-deposit corrosion, and microbially induced corrosion over one million years [1; 2; 3]. These phenomena are partially influenced by the presence of groundwater and the dissolved chemical species it would contain at the final DGR site. Although the copper coating on the UFCs should outperform its design life, it is still best to limit the transport of corrosive species towards the containers. Bentonite is an excellent material to help achieve this because it swells when exposed to water, meaning it will resist flow and can act as a sealing material. However, these desired properties of bentonite are lost if it is subjected to elevated temperatures--it converts to illite, a non-swelling clay, at around 140 \({}^{\circ}\)C [4]. Furthermore, at around 125 \({}^{\circ}\)C, the electrochemical properties of copper change such that corrosion kinetics become more rapid [4]. Furthermore, elevated temperatures will increase diffusive transport through the engineered barriers [5]. In consideration of these drawbacks, NWMO has chosen the maximum temperature within Canada's DGR to be below 100 \({}^{\circ}\)C.  
The conceptual DGR designed by NWMO thus far has UFCs stacked into two staggered layers, organized in a series of parallel placement rooms [4]. The temperature evolution within the DGR will be caused by the heat generated during the radioactive decay of the used nuclear fuel. As such, the maximum evolved temperature will be directly affected by the emplacement density of the UFCs inside the repository. Previous computer modelling studies on DGRs, including the one proposed by NWMO, have determined the thermal evolution within an infinite DGR through modeling a unit cell within a placement room [7; 8; 9]. Others have further studied the minimum combinations of UFC spacing and placement room spacings to meet maximum temperature requirements [10; 11]. However, these studies were highly conservative, as the heat output of all UFCs was assumed to be identical at a maximum value. Should a UFC inventory of various ages (i.e., the time since the fuel they contain was discharged from a nuclear power reactor) be considered instead, the placement density of UFCs may be increased. This would be economically beneficial because for a given number of UFCs because a higher placement density would decrease the DGR footprint, thus requiring less material, land space, construction time, etc. In this paper, the arrangement of UFCs into a conceptual DGR in a crystalline rock environment, detailed by NWMO in [4], is studied.