Benchmark for Uncertainty Analysis in Best-Estimate Modelling for Design, Operation and Safety Analysis of Light Water Reactors (LWR-UAM)

The goal of the benchmark was to determine the uncertainty in light water reactor (LWR) systems and processes in all stages of calculations. It was estimated through a simulation process of nine exercises in three phases provided by the benchmarking framework.

Coupled multiphysics and multi-scale light water reactor analysis

There had been an increasing demand from nuclear research, industry, safety and regulation for best estimate predictions to be provided with their confidence bounds. Consequently, an in-depth discussion on uncertainty analysis in modelling was organised at the June 2005 Nuclear Science Committee (NSC) meeting, with three presentations covering relevant topics. Furthermore, discussions were held at the 2005 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2005) in Avignon and the Washington American Nuclear Society (ANS) meetings, which led to a proposal for launching an Expert Group on Uncertainty Analysis in Modelling. Following the endorsement by the Nuclear Science Committee (NSC), a workshop on Uncertainty Analysis in Modelling UAM-2006 was held from 28-29 April 2006 at University of Pisa, Italy to define future actions and a programme of work. Following the presentation made by Professor J. Aragonés of the results from the workshop at the 1-2 June 2006 meeting of the NSC, the creation of the Expert Group on Uncertainty Analysis in Modelling (UAM) was endorsed. This expert group reported to the Working Party on Scientific issues in Reactor Systems (WPRS). Because it addresses multi-scale/multi-physics aspects of uncertainty analysis, it also works in close co-ordination with the benchmark groups on coupled neutronics-thermal-hydraulics and coupled core-plant problems, and the Committee on the Safety of Nuclear Installations (CSNI) Working Group on the Analysis and Management of Accidents (WGAMA).


The first phase focused on understanding uncertainties in prediction of key reactor core parameters associated with LWR stand-alone neutronics core simulation. Such uncertainties normally occur due to input data uncertainties, modelling errors and numerical approximations. Input data for core neutronics calculations primarily include the lattice averaged few group cross-sections.

The second phase focused on the prediction of key reactor parameters associated with LWR stand-alone simulations. Fuel performance, thermal-hydraulics and neutron kinetics simulations are all included without considering any coupling effects between the three physics models.

The third phase focused on the prediction of key reactor parameters associated with LWR multi-physics simulations. Coupled fuel rod, thermal-hydraulics and neutron kinetics simulations were included with taking into account coupling/feedback effects between the three phenomena.

The exercises in all phases were based on three main types of LWRs selected in UAM: a pressurised water reactor (PWR), a boiling water reactor (BWR) and a water-water energetic reactor (VVER). These three main types of LWRs were selected based on previous benchmark experience and available data from the following representative reactors:

  • PWR– Three Mile Island Unit 1
  • BWR – Peach Bottom-2
  • VVER-1000 – Kozloduy Unit 6 and Kalinin Unit 3
Publications and reports

Reference systems and scenarios

Reference systems and scenarios for coupled code analysis were defined to study the uncertainty effects in all stages of calculations. Measured data from plant operation were available for the chosen scenarios.

The coupled code transient benchmarks developed, such as the BWR Turbine Trip (TT), VVER-1000 Coolant Transients (V1000CT) and BWR Full Bundle Test (BFBT) were used as a framework for the uncertainty analysis in best-estimate modelling for design and operation of LWRs. Such an approach facilitated the proposed benchmark activities since many organisations had already developed input decks and tested their codes on the above mentioned coupled code benchmarks.

From the LWR transient benchmark problems, the Peach Bottom 2 BWR Turbine Trip was chosen as the first reference system-scenario, although provisions were made to address the other LWR systems and scenarios such as TMI-1 PWR MSLB, PWR-RIA-ATWS, BWR-CRDA-ATWS (with boron modelling), VVER-1000CT, etc. The Peach Bottom 2 BWR Turbine Trip is well documented, not only in the NEA/NRC BWR TT benchmark specifications, but also in a series of EPRI and Peco reports, which include the design, operation and measured steady-state and transient neutronics and thermal-hydraulics data. The presence of cycle depletion, steady-state and transient measured data on both the integral parameter level and the local distribution level is a very important feature of the Peach Bottom 2 BWR Turbine Trip.

The interaction was made with the OECD/NEA/NRC BWR Full Bundle Test (BFBT) benchmark and the uncertainty analysis exercises performed in its framework. The interaction was also be extended to the CSNI BEMUSE-3 benchmark through the NEA internal co-operation among the NSC and CSNI Committees.

The idea was to:

  • subdivide the complex system/scenario into several steps (exercises)
  • identify input, output and assumptions for each step
  • calculate the uncertainty in each step
  • propagate the uncertainty for the evaluation of the overall system/scenario

The investigation of uncertainty effects was initiated for each step of calculation and therefore it is proposed to have a sequence of exercises as described below:

  1. derivation of the multi-group microscopic cross-section libraries (nuclear data, selection of multi-group structure)
  2. derivation of the few-group macroscopic cross-section libraries (energy collapsing, spatial homogenisation.)
  3. criticality (steady-state) stand-alone neutronics calculations (keff calculations, diffusion approximation)
  4. fuel thermal properties relevant for transients performance
  5. neutron kinetics stand-alone performance (kinetics data, space-time dependence treatment) in PWR rod ejection and BWR control rod drop accidents
  6. thermal-hydraulic fuel bundle performance – interaction with the OECD/NRC BFBT benchmark and the available experimental data as well as the uncertainty analysis exercises being performed in the framework of the BFBT benchmark
  7. coupled neutronics/thermal-hydraulics core performance (coupled steady-state, coupled depletion, and coupled core transient with boundary conditions) – interaction with the Peach Bottom Cycles 1, 2 and 3 operating and measured data
  8. thermal-hydraulics BWR system performance – interaction with the Peach Bottom Turbine Trip and BEMUSE-3 experimental data
  9. coupled neutronics kinetics thermal-hydraulic core/thermal-hydraulic system BWR performance – interaction with the Peach Bottom Turbine Trip experimental data and Peach Bottom stability performance – interaction with EOC2 and EOC3 experimental data

The recommendation was to use experimental data as much as possible (two interactions with known experimental data are indicated above, but others could be added). The host institution identified input (I), output (O) or target of the analysis, as well as assumptions for each step and target uncertainty parameters (U). The uncertainty from one step would be propagated to the others (as much as it was feasible and realistic).

The above-described approach based on the introduction of the nine exercises allowed the development of a benchmark framework which mixed information from the available integral facility and nuclear power plant (NPP) experimental data with analytical and numerical benchmarking. Such an approach compared and assessed the uncertainty methods on representative applications and simultaneously benefitted from different approaches to be able to make recommendations and provide guidelines.

The nine exercises were carried out in three phases each covering two years. The first phase included the first three exercises (neutronics), with the final specifications discussed and adopted at a first workshop, held in May 2007 in Paris, France. A second workshop was held from for 2-4 April 2008 to discuss the preliminary results of phase I, the output parameters and formats for phase II and the priorities for phases II and III. The 2008 workshop was held in Garching, Germany.

The work of the group mainly addressed the scientific aspects of the methodologies developed and demonstrated their validity. The work interfaced with the activities of the CSNI, which later addressed any licensing issues.

To summarise, uncertainty analysis in modelling (UAM) was further developed and validated on scientific grounds in support of its performance, in addition to LWR best-estimate calculations for design and safety analysis. There was a need for efficient and powerful analysis methods suitable for such complex coupled multi-physics and multi-scale simulations. The proposed sequence of benchmarks addressed this need by combining the expertise in reactor physics, thermal-hydraulics, and uncertainty and sensitivity analysis, and contributed to the introduction of advanced/optimised uncertainty methods in best-estimate reactor simulations. Such a task could only be launched within the framework of a programme of international co-operation that benefitted from the coordination of the NSC interfacing with the acitivities of the CSNI.

Exercises programmed for UAM Expert Group on Uncertainty Analysis in Modelling

Phase I (Neutronics Phase)

  • Exercise I-1: Derivation of the multi-group microscopic cross-section libraries (nuclear data and covariance data, selection of multi-group structure, etc.).
  • Exercise I-2: Derivation of the few-group macroscopic cross-section libraries (energy collapsing, spatial homogenisation of cross-sections and covariance data, etc.).
  • Exercise I-3: Criticality (steady state) stand-alone neutronics calculations with confidence bounds (keff calculations, diffusion approximation, etc.).

Phase II (Core Phase)

  • Exercise II-1: Fuel thermal properties relevant for transient performance.
  • Exercise II-2: Neutron kinetics stand-alone performance (kinetics data, space-time dependence treatment, etc.).
  • Exercise II-3: Thermal-hydraulic fuel bundle performance.

Phase III (System Phase)

  • Exercise III-1: Coupled neutronics/thermal-hydraulics core performance (coupled steady state, coupled depletion, and coupled core transient with boundary conditions)
  • Exercise III-2: Thermal-hydraulics system performance
  • Exercise III-3: Coupled neutronics kinetics thermal-hydraulic core/thermal-hydraulic system performance

For the core and systems applications, three main LWRs types were selected based on previous benchmark experiences and available data:

boiling water reactor (BWR) Peach Bottom-2, pressurised water reactor (PWR) Three Mile Island and VVER-1000 (Kozloduy-6, Kalinin-3).

Related data

External publication

Global Sensitivity Analysis - The Primer, by A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, S. Tarantola, Wiley, 2008, ISBN 978-0-470-05997-5


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Ian Hill