Sensitivity and Uncertainty Analysis of Nuclear Reactor Reactivity Coefficients Due to Nuclear Covariance Data by Monte Carlo Second-Order Perturbation Techniques

Abstract

The uncertainty quantification of the reactivity coefficients such as the fuel temperature coefficient (FTC) and the moderator density coefficient (MCD) is crucial for the nuclear reactor safety margin evaluation. For the nuclear data sensitivity and uncertainty (S/U) analysis of the reactivity coefficient, this study proposes a new method to efficiently estimate the sensitivities of the reactivity coefficient to cross sections by the Monte Carlo (MC) perturbation techniques. A perturbation formulation for the reactivity coefficient has been derived based on the differential operator sampling method accompanied with the fission source perturbation method (DOS/FSP). In the new formulation, the sensitivity of the reactivity coefficient is expressed by reactivity derivatives with respect to two different variables. The proposed MC second-order perturbation (MC2P) method is implemented into Seoul National University MC code, McCARD.

The proposed MC2P method is verified via sensitivities of the density coefficient and the temperature coefficient in two-group homogeneous infinite medium problems by comparing its results with analytic solutions. The sensitivities estimated by MC2P method agree with the analytic solutions within three standard deviations. The effectiveness of the MC2P method is examined for a 235U density coefficient problem in Godiva by comparisons with direct subtraction-based approach in which the sensitivities of the reactivity coefficients are estimated by subtracting the first-order k sensitivities in nominal and perturbed systems. From the comparison results, one can see that the new method can predict the cross section sensitivities of the reactivity coefficient more accurately from much smaller number of MC history simulations. Then the proposed method is applied to quantify the uncertainties of the MDC of a LWR pin cell problem and the FTC of a CANDU 6 lattice cell problem due to the nuclear covariance data. The MDC uncertainty of the LWR pin cell problem are estimated as 0.44%. The FTC uncertainty of the CANDU 6 bundle problem is estimated as 1.24%.