Modeling of Heat Exchange and Temperature Distribution Between Stored Nuclear Waste Canisters and the Surrounding Earth in a Nuclear Waste Repository, 14-9419

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Principal Investigators
Martin J. Sablik
Sitakanta Mohanty
Alex Sun

Inclusive Dates:  10/1/03 - Current

Background - One objective in a high-level radioactive waste repository is to keep the various parts of the repository at moderate temperatures without undue or uncontrolled heating. One thus needs to be able to estimate the temperatures at the surface of the radioactive waste packages and in the surrounding medium (e.g., at the wall of the tunnel surrounding the waste package). The need is for a fast, adaptable analytical model that can estimate temperatures not only at these two places but across the entire repository. Finite difference or finite element computations may not be suitable because these are time-consuming when the model has to be executed hundreds to thousands of times. One way to approach this problem is to develop first a mathematical model for the heat exchange and temperature distribution of a single waste package. This model has already been developed using a model of three confocal prolate spheroids, with the inner spheroid representing the waste-package heat source, the middle spheroid representing the tunnel, and the outer spheroid representing the surrounding earth.

Approach - The purpose of this project is to estimate the effects of many waste packages distributed in a repository. The waste packages are laid end-to-end in a tunnel with a small spacing between each package. In a repository, there are a number of tunnels parallel to each other, with each tunnel having waste packages end-to-end. The spheroidal model is such that the distribution from the inner spheroid heat source can be spatially superimposed on the distribution from a second spheroid heat source displaced with respect to the first heat source. As long as the temperature distribution is solved outside the heat sources, a superposed solution can be obtained. An objective of this project is to obtain such a solution for many waste packages and compare it to the finite difference simulation results, confirming that the spheroidal solution gives reasonable results.The approach is to first explore ways to superpose the single waste-package spheroidal solution in such a way as to most efficiently compute the total effect of the whole repository. The effect of different tunnel separations, different tunnel diameters, and different spacings between waste packages are to be examined. The effects of thermal conductivity and other parameter changes are also to be investigated. Finally, the spheroidal superposition approach (SSA) is to be validated via comparison to a finite difference solution for the same geometry.

Accomplishments - An SSA solution for three tunnels and various numbers of waste packages has been constructed, using an efficient computer algorithm. Computations have been started to compare the SSA temperatures at desired places and times to the temperatures computed by a finite difference (FD) algorithm. A two-dimensional FD model was developed as the first step, but since the SSA computation is three-dimensional, a three-dimensional FD model has also been developed. Efforts are being made so as to keep the parameters in the computations as closely corresponding as possible. Both computations appear to yield maximum temperatures at roughly the same time (in years), but the calculations need further scrutiny to get temperatures to closely match.

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