First-Order Adjoint Sensitivity and Uncertainty Analysis of the OECD/NEA PERP Reactor Physics Benchmark

Abstract

The application of the “nth-order Comprehensive Adjoint Sensitivity Analysis Methodology for Linear Systems” (nth-CASAM-L), which was presented in Volume 1 of this monograph, will be illustrated in this chapter for the particular case n = 1 by using as a paradigm “linear system” for the subcritical polyethylene-reflected plutonium (acronym: PERP) metal fundamental physics benchmark. This benchmark is included in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project Handbook. This benchmark has been selected to serve as a paradigm illustrative “linear system” for the application of the nth-CASAM-L because the PERP benchmark is modeled by the linear neutron transport equation, the solution of which is a representative of “large-scale computations.” The numerical model of the PERP benchmark includes 21,976 parameters, of which the following 7477 parameters have nonzero (but imprecisely known) nominal values: 180 group-averaged total microscopic cross sections, 120 fission process parameters, 60 fission spectrum parameters, 10 parameters describing the experiment’s nuclear sources, 6 isotopic number densities, and 7101 nonzero group-averaged scattering microscopic cross sections (the remaining scattering cross sections, out of a total of 21,600, have zero nominal values). This chapter presents the derivation of the expressions of the first-order sensitivities of the PERP’s total leakage response with respect to the following uncertain model parameters: (i) microscopic total cross sections, (ii) microscopic scattering cross sections, (iii) microscopic fission cross sections, (iv) fission spectrum parameters, (v) spontaneous source parameters, and (vi) isotopic number densities. Several of these sensitivities turn out to have very large values, the significance of which is also discussed. The comparisons of the CPU times required for the computation of these 7477 first-order sensitivities highlight the overwhelming advantages of computing the first-order sensitivities exactly and efficiently by using the nth-CASAM-L (with n = 1), rather than attempting to obtain approximate values for these first-order sensitivities by using finite difference schemes.