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:  10/01/03 – 10/15/05

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 in the vicinity of the radioactive waste packages and in the surrounding medium (e.g., at the wall of the tunnel surrounding the waste package). Use of numerical models is constrained because the relatively small waste package spacing requires extensive discretization. A fast, adaptable analytical model is needed that can estimate temperatures close to the waste packages and at places across the entire repository. A mathematical model for the heat exchange and temperature distribution of a single waste package was developed based on 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 - This project aimed to determine the effects of superposition of the solutions for many waste packages distributed end-to-end in parallel tunnels in a repository. The spheroidal model mathematically is such that the temperature distribution from an inner spheroid heat source could be spatially superimposed on the distribution from a second spheroid heat source at a different location with respect to the first heat source. As long as the temperature distribution is solved outside the heat sources and boundary spheroids are confocal, a superposed solution can be obtained. The objective of this project was to obtain such a superposed solution for many waste packages and compare it to numerical simulation results, thus testing whether the spheroidal solution could give reasonable results. The approach was to develop algorithms for superposing the waste package spheroidal solutions with waste packages in different tunnels as well as in the same tunnel, thus obtaining a computational algorithm for an entire repository. The spheroidal superposition approach (SSA) was to be validated by comparing its results to numerical solutions for the same geometry. To reduce discretization in the numerical calculation, the waste packages in each tunnel were treated as being amalgamated into a single cylindrical heat source equal to the length of N separate waste packages in a given tunnel. Furthermore, three parallel tunnels containing cylindrical sources were considered. The SSA computation also treated the three tunnels with N waste packages per tunnel, but with a very small waste package separation of 0.125 meter.

Accomplishments - For comparison, a finite-volume (FV) numerical model was built and later validated through an alternative finite-element (FE) model. The FV solution matched well with the FE solution. The SSA solution produced solutions in somewhat the same range in time and temperature as the numerical solution, but did not produce a sufficiently good match. The inability of the SSA solution to match numerical solutions was attributed to the rather severe approximation used for the tunnel spheroid, which was constrained not to overlap the next waste package, and thus the small separation of 0.125 meter between waste packages was too much of a constraint.

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