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Uncertainty of Transient Processes Calculation for Nuclear Reactors


Analysis of the Methodical Part of Uncertainty of Neutron-Physics Calculation of Transient Processes for Next Generation Reactors and Fuel Cycles

Tech Area / Field

  • FIR-MOD/Modelling/Fission Reactors
  • INF-SOF/Software/Information and Communications

3 Approved without Funding

Registration date

Leading Institute
Kurchatov Research Center, Russia, Moscow


  • Pennsylvania State University / Department of Mechanical and Nuclear Engineering, USA, PA, University Park\nAgence de L'ocde Pour L'energie Nucleaire, France, Issy les Moulineaux\nGRS mbH Foeschungsgelande Hauptgelande, Germany, Garching

Project summary

The correct estimation of the calculational uncertainty of parameters of current and next generation Nuclear Energy Installations (NEI) is of particular importance for assessing their safety and efficiency. Errors in determination of the reactor and fuel cycles characteristics force designers to provide ‘reserves’ that inevitably make worse the NEI economics. Generally, the cross-sections (neutron date), methodical, technological and exploitation (operation) parts of the uncertainty give a contribution to the calculational uncertainty of the prediction of specific reactor characteristic.

The methods for estimating uncertainty of calculational predictions of the main NEI parameters have been developed much more completely for stationary states. There exist fewer and less developed theoretical methods and code tools for estimating these time dependent uncertainties for transients and accident conditions. For that reason, during the development of a reactor project too conservative approaches are used today that can lead to a loss of NEI competitiveness. On the other hand in definite moments of the running the accident processes, the big value of calculational prediction uncertainty of the reactor characteristics is quite permissible.

The present project aims at the estimation and analysis of the methodical part of uncertainty relative to the neutron-physics calculation of transient processes for next generation reactors and fuel cycles.

Firstly, the estimation of the methodical part of uncertainty for VVER-MOX and GT-MHR reactors with different fuels will be carried out. In order to achieve this task both existing codes for calculating neutron kinetics of JAR type as well as new codes being developed or planned based on the group Monte Carlo method (UNK-Time) and the deterministic PSN method (CONSUL-Time) and Surface Harmonics method (SUHAM-U-Time) will be used.

Code system JAR being developed at RRC KI is intended for stationary calculation of nuclear reactor neutronics in multi-group diffusion approximation through solution of a conditionally critical equation (eigenvalue problem) or an inhomogeneous equation with an external neutron source and with known group macroscopic and microscopic neutron constants for physical zones contained in the reactor model.

Code system UNK-MC realizes transport equation solution with Monte-Carlo method in multigroup approximation. Distinctive peculiarity of this code is the original geometric module. The feature of this geometric module is the following. Calculation region in the plane is pided to the set of identical small squares. Every square corresponds to the definite registration zone number and material number. Stepwise properties are given in axial direction.

Code system CONSUL is intended for calculations of nuclear reactor characteristics on the basis of correlated neutron, isotope and temperature distributions. The CONSUL complex ensures the calculation of all practically important characteristics of nuclear reactors

Code system SUHAM-U is intended for solving the neutron-physical problems in all volume of VVER and PWR reactor core. Code system SUHAM-U unites two code systems – UNK and SUHAM-2D. Code system SUHAM-U combines advantages of direct deterministic codes (calculational accuracy) and design codes (time expenditures).

At creation of the algorithms and codes for solution of space kinetic equation we will be based on the equations given in book of D. Bell, S. Glesston «Theory of Nuclear Reactor » in that form, which corresponds to the full numerical solution of time-dependence neutron transport equation. It is supposed that it will be the main way for solution of the transient processes in created codes. Codes UNK-MC, CONSUL and SUHAM-U will be used for calculation of the time-dependent form-function. It should be noted that solution of the time-dependent equations supposes the development of the codes UNK-MC, CONSUL and SUHAM-U for solution of the adjoint problem too.

Method for definition of technological parameters influence of fuel production on the uncertainty in local power distribution in VVER-1000 core, which is variety of regression analysis, is elaborated. On the base of this method, approach to evaluation of technological part of uncertainty for Russian reactor of VVER-1000 type is realized. This method was discussed at the Russia-France meeting, which was on February 2000 in RRC Kurchatov Institute. Code system CONSUL intended for calculations of nuclear reactor characteristics on the base of correlated neutron, isotope and temperature distributions is used for core calculations. The study allowed us to conclude about degree of contribution on the uncertainty of the technological parameters such as tolerance for isotope composition of Pu, density, geometrical sizes of tablets and others. Besides, this method allows us to retrace the influence exchange of the technological parameters of fuel production on the distribution of the local power in the process of the fuel burn up and to estimate stability of the results at the exchange of core composition. Experience obtained in process of this estimation will be used for estimation of the calculational uncertainty of the initial stationary state.

Work on calculational uncertainty estimation will be carried out step by step. Division on the stages is carried out on the next base. Uncertainty of the neutron-physical characteristics of the initial stationary state may be defined by known methods (statistical method, method of perturbation theory and method of regression analysis). Then, positive or negative reactivity is introduced in the reactor by some way. If the way of the reactivity introduction is known absolutely exactly the calculational uncertainty of transient process on each time step is summed from the uncertainty of the initial stationary state and methodical uncertainty of the transient process calculation including uncertainty of prompt and delayed neutrons. As far as the way of the reactivity introduction has own uncertainty it is added to the other calculational uncertainties.

On the first stage selection of the existing and completely described transient benchmarks with given initial cross-sections, properties of the delayed neutrons and its precursors and reactivity introduction way will be carried out. As a rule, all these benchmarks are diffusion ones. So, they will be reformulated as transport benchmarks. These benchmarks have not uncertainties of the initial data. All calculational uncertainty is only connected with methodical part of the calculational uncertainty of the transient process for which the time-space distribution will be obtained.

On the second stage uncertainties of the initial cross-sections, parts of the delayed neutrons and its precursors and reactivity introduction way will be additionally introduced to benchmarks calculated on the first stage. It allows us to study interaction of the uncertainties of different types.

On the third stage more real situations, i.e. benchmarks based not on the given cross-sections but on the initial nuclear composition and temperatures of the materials, sizes of core construction which are known with given uncertainty will be supported. Benchmarks of the reactors VVER-MOX and GT-MHR will be among these ones.

Both statistical method with numerous direct calculations and perturbation theory with use of sensitivity coefficients will be applied for study of interactions of different parts of uncertainty.

Expected Results:

  • Method and algorithm for estimation of calculational prediction uncertainty of the transient processes with different part of calculational uncertainty of initial stationary state;
  • Set of benchmarks for calculation of both kinetic transient processes and calculational time-space distributions of uncertainty parts;
  • Results of the estimation of calculational prediction uncertainty of the transient processes of suggested benchmarks, study of interaction of the uncertainties of different types;
  • Codes for calculation of the transient processes based on the solution of the time-dependence neutron transport equation by three alternative methods including solution stationary adjoint task.

The completion of this project will be a considerable step forward for the analysis of the methodical part of uncertainty of neutronics calculations of transient processes for next generation reactors. This is achieved in the context of solving the transient neutron transport equation by different methods (Monte Carlo, PSN method and Surface Harmonics method).

In the future, not in the frame this project, work can be continued for estimating the calculation uncertainty of mutli-physics by coupling neutronics, thermal-hydraulics and thermo-mechanical processes in perspective reactors and fuel cycles and definition of the requirements for permissible values of uncertainties at different moments of transient processes running.

The staff of our researcher group accumulates the excellent knowledge in the field of reactor analysis and the highest mathematical qualification required for the fulfillment of all the listed project steps.

Project fulfillment supposes permanent contacts between Russian and foreign specialists, joint benchmark-calculations and analysis of results. It is supposed regular carrying out joint seminars, presentation of reports on international conferences.

Total project effort for three years will be 10180 person*days, in so doing, project effort of weapon scientists and engineers will be 6960 person*days


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