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1 Introduction

The main objective of a safety analysis is to demonstrate that all safety requirements are met, i.e. that sufficient margins exist between real values of important parameters and their threshold values at which damage of the barriers against release of radioactivity would occur.

Historically, the existence of a consistent safety margin in respect to the licensing limits has been demonstrated using conservative approach. These approaches were introduced to circumvent uncertainties due to limited capability for modelling and understanding of physical phenomena at the early stages of safety analysis. However the use of conservative assumption maybe so conservative that important safety issues can be masked. Another drawback connected with the use of the conservative approach is the impossibility to assess the exact safety margins, resulting in economical penalties for the owner of the plant. Therefore, it may be preferable to use a more realistic approach together with an evaluation of the related uncertainties to compare with acceptance criteria. This type of analysis is referred to as a Best Estimate Plus Uncertainty (BEPU) approach and can provide more realistic information about the physical behaviour, identifying the most relevant safety issues and supplying information about the actual existing margins between the results of calculations and acceptance criteria.

Various options exist for combining computer codes types and input data for safety analysis. In [Error! Bookmark not defined.] four options are identified.

• Option 1 approach is the “very conservative” or Appendix K (of 10 CFR 50.46, USA) analysis in the case of LOCA. Many regulatory bodies prescribe the conservative models/correlations to be used for safety analysis and the conservative assumption for the initial and boundary condition to be used for the analysis.

• The second approach is called “realistic conservative”, is similar to the first one except for the fact that best estimate computer codes are used instead of conservative codes. However, it must be noted that in certain countries option 2 is considered a conservative analysis.

• The option 3 assumes that the initial and boundary conditions are taken as realistic with consideration of their uncertainties. From the point of view of the computer

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codes used and assumptions regarding availability of systems, the approach is the same as option 2. In several countries, such as the USA, option 3 is best estimate analysis with uncertainty evaluation or Best Estimate Plus Uncertainty (BEPU). A summary of the main methods used for the uncertainty evaluation is given in chapter 3. More emphasis will be dedicated to the GRS methodology and the CIAU method, considering that two application of these methods have been performed during this thesis work and the results are presented in chapter 4. In real practice, the mixture of option 2 and option 3 is employed. By the way all options mentioned make conservative assumptions regarding the availability of the systems.

• The option 4 is the most rigorous approach. It consists in a realistic analysis for quantifying the availability of systems, significant from safety point of view. The availability is usually quantified based on PSA based assumptions. This option would also contribute towards risk informed regulation.

Recent advances in the best estimate codes and the introduction of new uncertainty evaluation methods are gradually replacing the conventional conservative evaluation methods.

Thermal-hydraulic system code calculations are affected by unavoidable errors arising from several causes: including the unavoidable approximations in the constitutive equations, the limited capabilities of numerical solution methods, the uncertainties in the knowledge of boundary and initial conditions, and errors in setting up the nodalization, etc... These can be characterized by hundreds of parameters that are typically part of the input deck for a system code calculation suitable for predicting a transient scenario in a NPP. This happens notwithstanding the high code performance level and the systematic qualification processes, nowadays in progress or completed. It is necessary to remind, in this connection, that the user choices strongly affect the code results, through the so called "user effect".

The BE codes, as already mentioned, are applied to the safety:

• in combination with a reasonably conservative selection of input data and a sufficient evaluation of the uncertainties of the results;

• with realistic initial and boundary conditions.

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Both options are considered acceptable and suggested by the existing IAEA Safety Standards [Error! Bookmark not defined.]. The option 2 is still more typically used at present for safety analysis in many countries. The international activity aims at the code validations as well as various evaluations of data uncertainties, and sensitivity studies helps to establish confidence in calculated results.

This thesis work has to be considered in the framework of the development and application of the uncertainty methods for the licensing of water cooled reactors. The objective of this work is provide a proof of the application of uncertainty methodology during the licensing of a nuclear reactor and contributes to further development of the uncertainty analysis methods.

1.1 Historical background

The majority of the actual NPP plant were designed on the traditional defence in depth philosophy, and licensed with the use of a conservative approach (see section 2.6) for the demonstration of the safety in relation of the DBA, intended as a minimum set of enveloping scenarios whose positive-conservative evaluation could ensure that an adequate level of protection is provided by the designers. This kind of procedures, that governed analysis, were established in 1974 when USNRC published rules for LOCA analysis in 10CFR 50.46 and Appendix K [i].

The basic reason for developing the conservative method has been the need to circumvent the lacks of knowledge of the physical phenomena. It is approach based on the notions of consequences (maximisation) and criteria (restrictive). When questions were raised whether plants could be considered as safe, the usual answer was first that criteria had been set up to ensure that if they were satisfied, nothing reprehensible could occur, and secondly that plant behaviour was evaluated with large conservatisms so that to ensure that the plant was on the right side of the preceding criteria. This, of course, meant that some "distance" existed between the most severe state of the plant and the criteria. This "distance" which was the result of the combination of all kinds of conservatisms (without making any classification) appeared as an additional margin to the criteria, which already was guaranteeing by themselves the safety of the plant. The concept of safety margin was then created. This conceptual two-prong approach define a

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safety limit, and stay under it is what is most commonly understood as having “adequate safety margin” in the nuclear industry.

Problems raised by conservative approach are:

• no way to prove that the conservatism’s which are verified on scaled down experiments are also valid at full scale reactor size;

• due to nonlinearity, the additivity of several conservative measures cannot be verified;

• method un-adapted for Emergency Operating Procedures (EOP) studies (especially obvious after TMI2 accident);

• unknown margin between the calculated result and real value of the peak of specific key parameters results in economic penalizations, in other word is impossible to known how large is the safety margin.

Thus, nor the ‘safety margins’ could be established in a quantitative manner, neither the optimization of a safety solution could be demonstrated. All these limitations have been the motivation for developing best estimate codes.

Research during ‘70s and ‘80s provided a foundation sufficient for use of realistic and physically based analysis methods. Large number of experimental programs were completed internationally. A number of advanced computer codes (BE) were developed in parallel with experiments for replacing evaluation model: RELAP, TRAC, COBRA- TRAC, RETRAN, CATHARE, ATHLET etc. As a result of this huge effort, in September 1988, the NRC approved a revised rule for the acceptance of ECCSs [ii].

The revised rule of ECCS contains three key features: the existing acceptance criteria were retained; evaluation model methods based on Appendix K may continue to be used as an alternative to best estimate methodology; and an alternate ECCS performance, based on BE methods, may be used to provide more realistic estimates of plant safety margins, provided the licensee quantifies the uncertainty of the estimates and includes the uncertainty when comparing the calculated results with prescribed acceptance limits. The use of BE code do not overcame the uncertainties related on the status of the plant and, moreover, the code itself introduces error and uncertainty (see section 2.3 “Source of Uncertainty”), consequently a BE estimate analysis without the quantification of the error in predicted the results is a no sense.

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To support the revised ECCS rule and illustrate its application, USNRC and its contractors and consultants have developed and demonstrated an uncertainty evaluation methodology called CSAU. The CSAU was demonstrated to LBLOCA [iii], later in 1992 it was applied to SBLOCA [iv]. First non US CSAU application to plant was done in 1993 [v]. After pioneering CSAU method in the next five years several new original methods were developed. At special OECD/NEA workshop on uncertainty analysis methods, London 1-4 March 1994 [vi] eight new methods were presented: CSAU, UMAE method (Uncertainty Methodology based on Accuracy Extrapolation, Italy) [vii], AEA method (Atomic Energy Authority, UK), NE Method (Nuclear Energy, UK) [viii], GRS method (Gesellschaft für Anlagen-und Reaktorsicherheit, Germany) [ix], IPSN method (Institut de Protection et de Sureté Nucleairé, France), Tractebel method (Belgium) and Limit value approach (ABB, USA).

More importantly, these methods have progressed far beyond the capabilities of the early CSAU analysis. At present, uncertainty bands (both upper and lower) can be calculated for any desired quantity throughout the transient of interest, in addition to point values like the PCT. One method, namely the internal assessment of uncertainty (CIAU, University of Pisa) [18], also includes the capability to assess the calculation uncertainty in a code subroutine while the transient progresses.

1.2 Purpose of the thesis

The objective of this work is provide a proof of the application of uncertainty methodology during the licensing of a nuclear reactor and contributes to further development of the uncertainty analysis methods.

The GRS method has been applied as a support of the activity aiming to address a key safety issue for the ATUCHA-2 nuclear power plant, see section 4.2. Objective of this first activity is the quantification of the uncertainty associated to the prediction of the void average production in the CNA-2 reactor core using a BE code.

The second activity carried out during this thesis work is the simulation of two experiment performed on the LOBI/MOD1 test facility, with the BE code Relap5.33, plus the application of the CIAU method for take in to account the uncertainty.

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1.3 Structure of the thesis

The present work has been organized in five chapters including the present one dealing with introductory remarks and the organization of the performed work.

In chapter number two are first discussed the definition of: uncertainty, accuracy and sensitivity, in order to avoid misunderstanding. The aim of every safety analysis is, as already state, verify that a safety margins exist between the actual state of the plant and the threshold limit under every condition, so the second section of this chapter point out on the evolution of the safety margins concept. The chapter ended with a discussion of the four type of analysis today existing and accepted by the regulatory body for the deterministic safety analysis.

A state of the art on the uncertainty methods developed by the international community in the latest decade is provide in chapter 3. A revision of the various approach recognized by the IAEA to performed a safety analysis, either for design or licensing purpose is provided at the end of chapter 2. The salient features of three independent approaches for estimating the uncertainties are reviewed in respect with relevant topics to be considered and addressed by a consistent uncertainty methodology.

The uncertainty methods today used by the industry and the regulator are reviewed starting from the first pioneering approach, namely the CSAU. All the methodology developed in the recent year are less or more derived or connect by this first pioneering procedure. The description focuses mostly on the GRS method and the CIAU method, highlighting benefits and drawback of the two method. The goal of this part is to give the necessary information for understand the applications of these two methods done during these thesis work an presented in chapter 4. The chapter ended with a comparison with the two approach.

In chapter 4 the two activity carried out during this thesis work are reviewed.

Considering the importance of the quality of the computational tool used for a safety analysis, the first section of this chapter deal with this argument, highlighting the importance of high level quality of code, code user and uncertainty method and how achieve this quality. In section 4.2 the GRS activity is reviewed, starting with a description of the ATUCHA-2 NPP, necessary to understand the importance of the topic addressed, the chapter continues with a description of the objective, the procedures

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utilized and a discussion of the achieved results. The activity related to the CIAU application to two test performed on the LOBI/MOD1 facility is described in section 4.3.

The section started with a description of the facility: geometry and scaling criteria. The Relap5.33 model is after described and the procedures follows to achieve a validated nodalization is described. The results of the simulation are compared with the experimental data, both in steady-state and on-transient condition. The last section describe the results of the CIAU application and discuss the results.

Chapter 5 concludes the thesis summarizing the main achievements and giving the

recommendations for future works in the framework of the use of best estimate code for licensing of NPP.

[i] US-NRC 10CFR50.46 Appendix K, “Acceptance criteria for emergency core cooling systems for light-water nuclear power reactors.”, and Appendix K to10 CFR 50, “ECCS Evaluation Models” U.S. Federal Register, 39, 3,January 4, 1974

[ii] US-NRC, “Emergency Core Cooling Systems, Revisions to Acceptance Criteria”, Federal Register 53, 180, September 16, 1988.

[iii] Technical Program Group (BOYAK, B.E. et al.), “Quantifying Reactor Safety Margin Parts 1 to 6”, Nuclear Engineering and Design (NED), 119, 1990, pp. 1- 117.

[iv] G. ORTIZ, L.S. GHAN, “Uncertainty Analysis of Minimum Vessel Liquid Inventory During a Small-Break LOCA in a B&W plant”, NUREG/CR-5818, 1992.

[v] H. GLASERS, R. POCHARD, “Review on Uncertainty Methods for Thermal Hydraulic Computer Codes”, Proc. Int. Conf. on New Trends in Nuclear System Thermal-hydraulics, Pisa, Italy, May 30 –June 2, Vol. 1, 1994, pp. 447-455.

[vi] OECD/CSNI, “Report of a CSNI workshop on Uncertainty analysis methods, London 1-4 March1994”, NEA/CSNI/R(1994)20, Vol. 1 and 2, OECD/NEA/CSNI, Paris, 1994 .

[vii] D’AURIA, F., DEBRECIN, N., GALASSI, G.M., “Outline of the uncertainty methodology based on accuracy extrapolation”, Nucl. Technol. 109 1 (1995) 21–

38.

[viii] WICKETT, T., et al., “Report of the Uncertainty Methods Study for Advanced Best Estimate Thermal Hydraulic Code Applications”, 2 vol., Rep. NEA/CSNI R(97)35, OECD, Paris (1998).

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[ix] H. GLASERS “GRS Method for Uncertainty and Sensitivity Evaluation of Code Results and Applications ”. Science and Technology of Nuclear Installations Volume 2008, Article ID 798901, 7 pages.

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