Uncertainty quantification in the calculation of keff using sensitity and stochastic sampling method

Abstract

The sensitivity and uncertainty analysis(S/U) method based on the first order perturbation theory is commonly employed to calculate the uncertainties in-nuclear reactor's integral parameters, such as the neutron effective multiplication factor(keff), due to uncertainties in nuclear data. However, this method is only theoretically suitable for the linear model because of its first order approximation. Moreover, S/U method is difficult to incorporate into a neutronics code, because the adjoint angular flux is needed to obtain the sensitivity coefficient of an integral parameter to nuclear data. Meanwhile, the sampling approach based on parametric random sampling of input parameters, an easy implemented method, evaluates the uncertainties in the integral parameters by performing a set of neutronics simulations inputted with a set of stochastic nuclear data sampled from a multinomial normal distribution with nuclear cross section mean values and covariance data. The sampling approach is considered as a more exact method, as linear approximation is not needed. With the increase of computational power, the sampling methods with consuming more time are now possible. The sampling approach is incorporated into SURE, a sensitivity and uncertainty analysis code developed in IAPCM, as a functional module. A careful verification of the new function is necessary before it is used to analyze complicated problems, such as multi-physical coupling calculations of nuclear reactor. Two simple fast criticality benchmark experiments, namely Godiva(HEU-MET-FAST-001) and Jezebel(PU-MET-FAST-001), are selected to verify the sampling module of SURE. The uncertainties in nuclear data are given by multigroup covariance matrices processed from ENDF/B-VⅡ. 1 data. The uncertainties in the computed value of keff resulting from uncertainties in the nuclear data are calculated with both S/U and sampling methods. The uncertainties due to reaction cross sections for each nuclide in two benchmarks given by two methods with the multigroup covariance matrices are in good agreement. Since the S/U module of SURE code is verified extensively, the correctness of the sampling function of the code is confirmed as well. The distribution of the keff from the sampling approach obeys the normal distribution pretty well, which indicates that keff varies linearly with the nuclear data under its uncertainty range, since the nuclear data used in calculations are assumed to be normal distribution in the sampling method. The results from the sampling method also support the S/U method with linear approximation as a suitable uncertainty quantification method for keff calculation.