The importance of input interactions in the uncertainty and sensitivity analysis of nuclear fuel behavior

The propagation of uncertainties in a PWR fuel rod under steady-state irradiation is analyzed by computational means. A hypothetical steady-state scenario of the Three Mile Island 1 reactor fuel rod is modeled with the fuel performance FRAPCON, using realistic input uncertainties for the fabrication and model parameters, boundary conditions and material properties. The uncertainty and sensitivity analysis is performed by extensive Monte Carlo sampling of the inputs' probability distribution and by applying correlation coefficient and Sobol' variance decomposition analyses. The latter includes evaluation of the second order and total effect sensitivity indices, allowing the study of interactions between input variables. The results show that the interactions play a large role in the propagation of uncertainties, and first order methods such as the correlation coefficient analyses are in general insufficient for sensitivity analysis of the fuel rod. Significant improvement over the first order methods can be achieved by using higher order methods. The results also show that both the magnitude of the uncertainties and their propagation depends not only on the output in question, but also on burnup. The latter is due to onset of new phenomena (such as the fission gas release) and the gradual closure of the pellet-cladding gap with increasing burnup. Increasing burnup also affects the importance of input interactions. Interaction effects are typically highest in the moderate burnup (of the order of 10-40 MWd/kgU) regime, which covers a large portion of the operating regime of typical nuclear power plants. The results highlight the importance of using appropriate methods that can account for input interactions in the sensitivity analysis of the fuel rod behavior.