Analysis of the Effect of Different Types of Errors on the Accuracy of Calculations of the Number of Reactions in Individual Volumes of the Core of a Water Cooled and Moderated Power Reactor

A method and numerical algorithm for evaluating the computational errors in calculating the number of fission rates in small individual volumes of a reactor core, viz., fuel element, group of fuel elements, fuel assemblies, are presented. The standard error was determined by a combination of the methods of the statistical theory of errors and linear perturbation theory. An algorithm developed for calculating the value function, sensitivity coefficients, and errors of functionals which is based on the use of the MCCG3D, TRIFON, and ERRORJ software is described. The standard error, due to, for example, the relative error ~1% (over the volume of a fuel element) in the microscopic fission and total cross section, of the computed fission rate in the most stressed fuel element in fuel assembly No. 10 PWR (ALMARAZ II, Spain), is evaluated as an example. The standard error of the fission reactions in this case is ε_ƒ,235_U = 5.573·10^–3, ε_ƒ,239_Pu = 1.193·10^–3, i.e., the total error is ~0.67%. For other isotopes, it is hundredths of a percent, i.e., approximately equal to its computational error. For the technological error ±1.2% of the density of the loaded PWR uranium-dioxide fuel, the computed uncertainty in the number of fissions is ±0.93%, and for the uncertainty ±0.5% in the fuel enrichment the error in the number fissions will be ±1.5%.