UC Berkeley

This study investigates the effect of the non-uniform nuclide composition in spent fuel on material accountancy in the pyroprocess. High-fidelity depletion simulations are performed using the Monte Carlo code SERPENT in order to determine nuclide composition as a function of axial and radial position within fuel rods and assemblies, and burnup. For improved accuracy, the simulations use short burnups step (25 days or less), Xe-equilibrium treatment (to avoid oscillations over burnup steps), axial moderator temperature distribution, and 30 axial meshes.

Analytical solutions of the simplified depletion equations are built to understand the axial non-uniformity of nuclide composition in spent fuel. The cosine shape of axial neutron flux distribution dominates the axial non-uniformity of the nuclide composition. Combined cross sections and time also generate axial non-uniformity, as the exponential term in the analytical solution consists of the neutron flux, cross section and time. The axial concentration distribution for a nuclide having the small cross section gets steeper than that for another nuclide having the great cross section because the axial flux is weighted by the cross section in the exponential term in the analytical solution. Similarly, the non-uniformity becomes flatter as increasing burnup, because the time term in the exponential increases.

Based on the developed numerical recipes and decoupling of the results between the axial distributions and the predetermined representative radial distributions by matching the axial height, the axial and radial composition distributions for representative spent nuclear fuel assemblies, the Type-0, -1, and -2 assemblies after 1, 2, and 3 depletion cycles, is obtained. These data are appropriately modified to depict processing for materials in the head-end process of pyroprocess that is chopping, voloxidation and granulation. The expectation and standard deviation of the Pu-to-244Cm-ratio by the single granule sampling calculated by the central limit theorem and the Geary-Hinkley transformation. Then, the uncertainty propagation through the key-pyroprocess is conducted to analyze the Material Unaccounted For (MUF), which is a random variable defined as a receipt minus a shipment of a process, in the system. Finally, the Type-I error for the Pu MUF is evaluated for spent fuel assemblies with respect the size of granules and powders which are the key parameters to evaluate the uncertainty in determining ratio by sampling. The main observations of this calculation are the following: (1) the probabilities of Type-I error for the Pu MUF are occasionally greater than 5% when the size of powder particles and granules are large and small; (2) the possibility of Type-I error greater than 5% increases by increasing the depletion period, because the increasing production of Pu and 244Cm with increasing burnup propagates the uncertainty through the system; (3) the major contributor to the uncertainty of ratio is the non-uniformity of 244Cm; (4) Pu generation in the Type-2 spent fuel assemblies is greater that in the others due to higher gadolinia bearing fuel (GBF) loading in the assembly, therefore, the area indicating the probability of Type-I error greater than or equal to 5% is the widest among the figures for the Type-0 and -1 spent fuel assemblies.

The random variable, LOPu, is defined for evaluating the non-detection probability at each Key Measurement Point (KMP) as the original Pu mass minus the Pu mass after a missing scenario. A number of assemblies for the LOPu to be 8 kg is considered in this calculation. The probability of detection for the 8 kg LOPu is evaluated with respect the size of granule and powder using the event tree analysis and the hypothesis testing method. We can observe there are possible cases showing the probability of detection for the 8 kg LOPu less than 95%. In order to enhance the detection rate, a new Material Balance Area (MBA) model is defined for the key-pyroprocess. The probabilities of detection for all spent fuel types based on the new MBA model are greater than 99%. Furthermore, it is observed that the probability of detection significantly increases by increasing granule sample sizes to evaluate the Pu-to-244Cm-ratio before the key-pyroprocess.

Based on these observations, even though the Pu material accountability in pyroprocess is affected by the non-uniformity of nuclide composition when the Pu-to-244Cm-ratio method is being applied, that is surmounted by decreasing the uncertainty of measured ratio by increasing sample sizes and modifying the MBAs and KMPs.