Heat Conduction in Radioactive Waste Repository

The paper presents some numerical tests for the temperature development around nuclear waste packages stored in vaults. We deal with two simplified models. In the first of them, a single long cylinder of the diameter 1 m is considered. It is filled with radioactive waste and surrounded by rock. The second model presents a long cuboidal package stored in a vault. The computation was carried out in Matlab using its tools for sparse matrices and iterative methods. 1 Radioactive waste and heat conduction. The radioactive waste and spent nuclear fuel repository management belongs to the actual issues of contemporary physics and engineering sciences. The extreme complexity of the task leads to considering and solving the separated aspects of the problem the results of which have to be taken into account in the design of storage and disposal facilities. In the presented paper, we consider the heat production as a consequence of high-level radioactivity. The paper presents numerical tests of the temperature development around waste packages stored in vaults which are built in the depth of about 300 m. The model of the repository is based on the well known Yucca Mountain repository project and on the data presented by some European projects [1, 2]. We deal with two models. In the first of them, a single long steel cylinder of the diameter 1 m is considered. It is filled with radioactive waste and surrounded by rock. The second model describes a long cuboidal package stored in a vault. The numerical formulation reduces to the one-dimensional task in the first case, while it leads to a two-dimensional problem in the second case. We consider the equation for the heat conduction [7] ∇k∇u+ q = ρc ∂u ∂t , (1) where k is the thermal conductivity [W/mK], q is the volumetric heat release [W/m], ρ is the density [kg/m] and c is the specific heat capacity [J/kgK]. The equation has to be fulfilled in some domain Ω the dimensions of which can be tens up to hundreds of meters. The temperature u(x, y, z, t) depends on three space variables and on the time. The function u(., ., ., 0) is given and it gives the initial condition u(x, y, z, t) = u0(x, y, z) (2) for all t = 0. The Dirichlet boundary condition u(x, y, z, t) = 10 (3) is considered in each point of the boundary of the domain Ω, i.e. the constant temperature 10 C sufficiently far from the heat source is considered. As follows from the character of the problem, the constant in the Dirichlet boundary condition changes additively the solution in the whole domain. The heat produced by the radioactive material corresponds to the approximate volumetric heat release 1036.10 W/m, where t is time measured in years. The characteristics of the radioactive packages, rock and air used in our tests can be found in Table 1. Table 1: Constants used for heat conduction k [W/mK] c [J/kgK] ρ [kg/m] Waste packages 3.1 509 5400 Rock 3.0 76