# Development Considerations of AREVA NP Inc.'s Realistic LBLOCA Analysis Methodology

Authors: Robert P. Martin; Larry D. O'Dell
Journal: Science and Technology of Nuclear Installations
 (2008-01-21)

---

## Abstract

The AREVA NP Inc. realistic large-break loss-of-coolant-accident (LOCA) analysis methodology references the 1988 amended 10 CFR 50.46 allowing best-estimate calculations of emergency core cooling system performance. This methodology
conforms to the code scaling, applicability, and uncertainty (CSAU) methodology developed by the
Technical Program Group for the United States Nuclear Regulatory Commission in the late
1980s. In addition, several practical considerations were revealed with the move to a production
application. This paper describes the methodology development within the CSAU framework and utility objectives, lessons
learned, and insight about current LOCA issues.


---

## Body

## 1. Introduction

The objective of any methodology for measuring the
performance of an emergency core-cooling system (ECCS) during a loss-of-coolant
accident (LOCA) is to provide a statement of assurance that the ECCS will
preserve fuel integrity. For large-break LOCA analysis, the key measure (among
several) is peak cladding temperature (PCT) relative to 2200°F
(1200°C). Traditionally, LOCA analyses performed in
the U.S. for Nuclear Power Plant design-basis safety analysis were required to
comply with the U.S. Code of Federal Regulations Title 10, Part 50 (10 CFR 50), Appendix K, a conservative,
deterministic approach. Following several research and development advances in
two-phase flow and heat transfer phenomena specifically related to the LOCA, regulations
were updated in 1988 to allow best-estimate approaches. Several events leading
up to the rule change included the close of the 2D/3D program [1] and the development
of NUREG-1230, Compendium of ECCS Research [2]. In addition, during the rule-making process, a
committee of experts was convened to develop a paradigm for performing
best-estimate LOCA evaluations. These experts came from the USNRC, national
laboratories, and academia. This Technical Program Group (TPG) produced the code
scaling, applicability and uncertainty (CSAU) methodology, which is documented
in NUREG-5249 [3]. Today, the CSAU methodology is well known in the LOCA
community and many papers have been inspired from both the content and the
conclusion developed from that original work. Accompanying NUREG-5249, the
USNRC released Regulatory Guide 1.157, best-estimate calculations of emergency core
cooling system performance, which provides specific detail describing
acceptable best-estimate LOCA methodologies [4].An AREVA NP predecessor company, Siemens Power Corporation,
developed and submitted to the USNRC a best-estimate LBLOCA methodology during
the early 1990s; however, the USNRC could not provide resources to support the
review for several years. As a consequence, Siemens Power Corporation decided
to reinvent this methodology and resubmitted a realistic large-break LOCA
(RLBLOCA) methodology in August 2001 [5]. In April 2003, AREVA NP received
approval of an S-RELAP5-based realistic large-break LOCA methodology from the
USNRC [6].


## 2. Evolution of BE Methods Since 1988

The development of this methodology is a product of the
lessons learned since the 1988 rule change both internal to AREVA NP and by the
thermal-hydraulic community at large. This is despite the fact that in May 1990
in a special issue of “Nuclear
Engineering and Design” [7], the editor declared “the closure of the
large-break LOCA issue.” This bold statement did not go unchallenged. In
January 1992, a special issue of “Nuclear Engineering and Design” [8]
was published providing comment and criticism, in the form of “Letters to the
Editor,” of the existing technical understanding of LOCA, in general, and the
CSAU methodology, specifically. Several areas were identified as being
incomplete. These can be generally associated in the following categories [9]:(i)
defining “best-estimate
methods;”(ii)
merits of engineering judgment;(iii)
methods for the convolution
of uncertainty;(iv)
data to quantify
uncertainties. In order to produce an acceptable, usable methodology,
resolution of these and other issues was necessary. “Resolution” is, of course,
a negotiated condition involving the methodology developers, an applicant, and the
regulatory reviewers. Nonetheless, this paper presents insights from AREVA NP’s
experience in the process from the 1988 rule change until USNRC approval in
2003.


### 2.1. Defining “Best-Estimate” Methods

In the context of thermal-hydraulic safety analysis
performed to support nuclear power plant operation, no consensus appears to
have been established for defining “best estimate.” The difficulty stems from the many types of
uncertainty contributing to a plant-scale accident scenario. Sources of uncertainty
associated with a large-break loss-of-coolant accident (LOCA) analysis begin
with that which can be observed—measurable quantities reflecting the design or
condition of a system, structure, or component. In this context,
“best-estimate” can be simply characterized as a preferred state for which any perturbation
is followed by a return to its preferred or “best-estimate” state for the
system, structure, or component.The original problem tackled by the TPG in NUREG-5249 was
for a double-ended large-break LOCA at a Westinghouse 4-loop PWR operating at steady-state
full power. Several uncertainties associated with this problem were recognized
in that reference including those associated with code models, the impact of
test facility scaling, epistemic uncertainty resulting in compensating errors,
nodalization, and, to a lesser extent, the user effect. On the surface, the TPG
appeared to establish a well-defined description; however, even this
description, supported by the discussion on uncertainty presented in
NUREG-5249, disguises other uncertainties that are much more difficult to
quantify and include into a definition for “best-estimate methods.” To identify these additional uncertainty
contributors, this application statement can be dissected.Beginning with “double-ended large-break LOCA,” this
identifies a scenario with a particular break configuration. This vision of the large-break LOCA problem
either ignores the spectrum of breaksizes associated with LOCAs or addresses
this uncertainty with conservatism. Incorporating
conservatism into the definition of “best-estimate methods” appears to
undermine the original move to best-estimate methods. One of the primary
criticisms of the Appendix K deterministic approach was that certain so-called
“conservative” models could result in nonconservative behavior during a simulation.
Best-estimate methods certainly should avoid this situation; however, the
question of breaksize is just one element of the broader uncertainty category associated
with the nature of the initiating event. The communicative nature of the break
(i.e., guillotine or longitudinal split), break orientation (i.e., necking for
guillotine break and directional nature of split breaks), break location (i.e.,
cold or hot leg; pressurizer or other loops, attached pipe), and the assumed
single failure (a regulatory requirement) also contribute to the initiating
event uncertainty.The descriptor “Westinghouse 4-loop PWR” identifies a plant
design; however, the nature of nuclear power plant development is such that
even among Westinghouse 4-loop PWRs there can be significant differences. Component
choices, such as reactor coolant pumps, steam generators, core/reactor vessel
design (i.e., bypass flows, fuel assembly design, upper head design), and
containment response features (i.e., sprays, ice, fan coolers, passive
structure surface area), represent elements of the design uncertainty. In
addition, operational and maintenance history can impact the performance of
“equivalent” systems, structures, and components. As a consequence, there are no “identical”
plants.“Operating at steady-state full power” encompasses all
uncertainties associated with plant operating state and event response. In
analysis space, these are often initial or boundary conditions. A plant’s
technical specifications and limiting condition of operation define the
operational space enveloping acceptable plant states. Frequently, there is
significant latitude for “acceptable” states for system variables, including
core axial power and fuel burnup that can have a strong influence on the
acceptance criteria metrics. The challenge for a “best-estimate” analysis is to
balance the value of defining the likely plant state at the time of an accident
with the need to support the plant’s operational envelope. Dozens of analysis
parameters fall into this category.In recognizing the complexity of the uncertainty problem
associated with LOCA safety analysis, the term “best-estimate” as applied to
this problem has evolved into “best-estimate plus uncertainty” (BEPU). The
problem has always been the management of uncertainty. At the time the CSAU methodology was being
developed, a relatively narrow view of uncertainty was necessary because of
limitations in computational ability and limited appreciation of advanced
statistical methods. This original CSAU view on uncertainty was criticized as
being incomplete with relevant contributors to the LOCA safety analysis problem
being treated implicitly and, as a consequence, wrong. As such, the conversation
moved from BE to BEPU—with the emphasis on uncertainty management.


### 2.2. The Role of Engineering Judgment

Engineering judgment has always been a necessary part of any
engineering task. Engineers, through the expression of their experience, have
often applied engineering judgment to make big engineering challenges workable.
Confirmation is, of course, necessary when safety is a concern. In developing
the CSAU methodology, the TPG formalized this often unappreciated aspect of engineering.
Doing so started a debate as to the extent that engineering
judgment should play in the LOCA safety analysis problem.The manifestation of engineering judgment in the CSAU
process is the phenomenological identification and ranking table (PIRT). As the
name implies, the PIRT reflects qualitative engineering judgment as to the
importance of various phenomena relevant to the problem of interest. The intent of the PIRT is to provide a
technical basis during the BEPU methodology development process for the many
decisions, including the management of uncertainty, required to complete the
task.Resistance to this formalized use of engineering judgment inspired
several criticisms, including the following.(i)
Who is qualified to be a part
of a PIRT team?(ii)
How do PIRT teams deal with
differences of opinion?(iii)
Should uncertainty with the
ranking process be incorporated into the PIRT?(iv)
Even after the PIRT is
developed, engineering judgment is required to use the results.(v)
How can the absence of
knowledge (i.e., unmodeled parameters) be treated in this context? Despite the initial criticism, the PIRT exercise has found a
degree of acceptance. Its foremost value
has been in establishing an understanding of the processes and phenomena of
interest among a group of peers. Once
consensus is achieved, decisions impacting the solution of the task at hand may
begin.In the original CSAU large-break LOCA sample problem, the
TPG,applying a PIRT they developed for
this problem, established a precedent that the large-break LOCA problem can be
well characterized by explicitly addressing a minimum set of very important
processes and phenomena. Beyond that set of large-break LOCA contributors,
other phenomenological or process parameters were treated as “nominal.” This
application of engineering judgment has not found universal acceptance for two
reasons: (1) there is a lack of consensus of “important” parameters and (2) it
ignores traditional licensing measures defined in plant technical
specifications and limiting condition of operation.To satisfy this criticism, the BEPU approach recognizes the
value of “realistic conservatism,” that is, the explicit treatment of
uncertainty by characterizing the uncertainty parameter such that the key
output variables are penalized relative to the acceptance criteria. For parameters
with low large-break LOCA importance, this may be a trivial distinction;
however, as importance increases, scrutiny over that which is proclaimed
conservative also increases. Nonetheless, the acceptance of “realistic
conservatism” represents a significant departure from the original concept of
BE methods; yet, it is absolutely necessary for the complex LOCA analysis
problem where engineering judgment is involved.


### 2.3. Convolution of Uncertainty

A constraint, recognized early by the TPG during the development
of the CSAU method, stemmed from the application of statistics to convolve
parameter uncertainty of several individual large-break LOCA contributors into
a single uncertainty statement for PCT.
Specifically, the broader the set of uncertainty contributors
considered, the more than number of required LOCA simulations
grows exponentially. This is the nature of the response surface methods that the TPG considered
state-of-the-art for this application. There is no doubt that this practical constraint
influenced their acceptance of the relatively small number of large-break LOCA
contributors considered in their uncertainty analysis sample problem. Later,
Westinghouse would introduce a clever extension to the response surface
approach to expand the number of large-break LOCA contributors that could be
considered [10].When introduced in 1989, a few organizations in the
international thermal-hydraulic community—in particular, Germany’s GRS—recognized that this obvious limitation could
be eliminated by considering nonparametric statistical approaches. This
counterpoint was not universally appreciated either because there was a lack of
understanding or nonacceptance of nonparametric statistics lack of a definitive
uncertainty statement. The uncertainty statement from a nonparametric
statistical approach is expressed as an inequality characterized with a
confidence level.Today, nonparametric-ordered
statistics (e.g., Wilk’s method) have become the method of choice. However, consensus with regard to its
implementation within regulatory guidelines is still evolving. Current regulation in the U.S. and other
countries recognize a multivariant acceptance criterion for large-break LOCA
analysis. As a consequence, a debate over the required number of calculations
necessary to provide an acceptable uncertainty statement has resulted in
several journal articles on the subject [11–15]. Much of this
debate is on the semantics used to present the uncertainty statement. Specifically,
should the acceptance criterion be measured individually or is it sufficient to
consider the outcome of an analysis as a single statement concerning whether the
entire acceptance criterion has been satisfied.
AREVA NP’s position is with the latter.


### 2.4. Completeness of the Experimental Database

Driven by the recognized gap in knowledge of LOCA phenomena
apparent in the early 1970s that resulted in the early Appendix K rule making,
governments around the world invested heavily in experimental programs to
rectify this situation. By the late 1980s, a large body of research on many
facets of the large-break LOCA problem was completed. Coupled with the CSAU
approach for performing BE analysis, was this body of work sufficient to
declare the closure of the large-break LOCA problem? Undermining the closure position was the view
that so much of the thermal-hydraulic phenomenological database was populated empirically
and, as such, there remains much yet to be characterized.While statistics appeared to be the answer to the analyst,
the experimentalist was saying that in many areas data was insufficient for
deriving statistical measures. In addition, the possibility of unknown
phenomena or undesirable interplay between competing phenomena made any declaration
of closure irresponsible. The TPG’s response was simply that a sufficient
amount of experimentation focused on both separate and integral effects existed
and that uncertainty associated with scale could be determined. In areas this
may be large; however, if it turns out that uncertainty is too penalizing, this
would be a motivation for new test programs.


### 2.5. AREVA NP’s BEPU Paradigm

Constraining factors that can limit a nuclear power plant’s
efficiency include engineering design limits, equipment operability, and
regulatory requirements. The acceptance of BE methods has revealed margin for
improving plant operating performance. Figure1 illustrates this view of the plant
operating margin provided by BE methods relative to the traditional Appendix K
deterministic methods. Margin is characterized by the separation between the
design or the licensing
limit and the nominal operating point.
With regard to regulatory limits, this is measured by recognized metrics
relative to the regulatory acceptance criteria, for example, PCT < 2200°F.Figure 1
Illustration of plant operating margin.Deterministic methods provide a single “analysis of record” that
quantifies the acceptance criteria metrics (PCT, total oxidation, and local
hydrogen generation). Over the operating history of current generation nuclear
power plants, utilities have nearly exhausted the availability of margin
provided by this original method and, as a result, the apparent margin is
small.In contrast, BE methods strive to identify the acceptance
criteria metrics associated with the real state of the plant. Practical
limitations associated with the state of knowledge required to perform analyses
force analysts to apply conservatisms that make the calculated BE value
bounding of the real state. In addition,
the real margin is never realized because the design basis limits reserve
margin to cover uncertainties associated with the actual limits.For the purpose of reporting plant operating performance
margin relative to licensing limits, the goal is not to define this margin
relative to the actual state; rather, it is to convolve all key phenomenological
and process uncertainties to identify the calculated BEPU value—a conservative estimate of margin
incorporating realistic models of the physical processes and associated
phenomena.In preparing the AREVA NP large-break LOCA methodology, the
challenge of addressing the expectations of Regulatory Guide 1.157 and the CSAU
process—balanced with the known criticisms of the CSAU
process—moved the AREVA NP methodology development
team towards nonparametric statistical methods and the “realistic conservatism”
concept of uncertainty management. By taking this step, the focus of the
methodology moves towards the resolution of individual uncertainty
contributors.The main advantage of nonparametric statistical methods is
that the number of treatable uncertainty contributors is independent of the
number of plant calculations. This characteristic provides flexibility during
the development process to explicitly address as many or as few analysis
contributors as necessary to resolve the outcome of the PIRT. As this is a
product of engineering judgment, the uncertainty associated with this exercise
can be reduced by explicitly addressing additional analysis contributors. In
addition, this methodology characteristic provides the opportunity to
incorporate customer requests for the explicit treatment of plant process
uncertainty.For the remainder of this paper, a description is provided of
how AREVA NP’s RLBLOCA methodology conforms to the basic principles of the CSAU
methodology while incorporating realistic conservatisms and nonparametric
statistics.


## 2.1. Defining “Best-Estimate” Methods

In the context of thermal-hydraulic safety analysis
performed to support nuclear power plant operation, no consensus appears to
have been established for defining “best estimate.” The difficulty stems from the many types of
uncertainty contributing to a plant-scale accident scenario. Sources of uncertainty
associated with a large-break loss-of-coolant accident (LOCA) analysis begin
with that which can be observed—measurable quantities reflecting the design or
condition of a system, structure, or component. In this context,
“best-estimate” can be simply characterized as a preferred state for which any perturbation
is followed by a return to its preferred or “best-estimate” state for the
system, structure, or component.The original problem tackled by the TPG in NUREG-5249 was
for a double-ended large-break LOCA at a Westinghouse 4-loop PWR operating at steady-state
full power. Several uncertainties associated with this problem were recognized
in that reference including those associated with code models, the impact of
test facility scaling, epistemic uncertainty resulting in compensating errors,
nodalization, and, to a lesser extent, the user effect. On the surface, the TPG
appeared to establish a well-defined description; however, even this
description, supported by the discussion on uncertainty presented in
NUREG-5249, disguises other uncertainties that are much more difficult to
quantify and include into a definition for “best-estimate methods.” To identify these additional uncertainty
contributors, this application statement can be dissected.Beginning with “double-ended large-break LOCA,” this
identifies a scenario with a particular break configuration. This vision of the large-break LOCA problem
either ignores the spectrum of breaksizes associated with LOCAs or addresses
this uncertainty with conservatism. Incorporating
conservatism into the definition of “best-estimate methods” appears to
undermine the original move to best-estimate methods. One of the primary
criticisms of the Appendix K deterministic approach was that certain so-called
“conservative” models could result in nonconservative behavior during a simulation.
Best-estimate methods certainly should avoid this situation; however, the
question of breaksize is just one element of the broader uncertainty category associated
with the nature of the initiating event. The communicative nature of the break
(i.e., guillotine or longitudinal split), break orientation (i.e., necking for
guillotine break and directional nature of split breaks), break location (i.e.,
cold or hot leg; pressurizer or other loops, attached pipe), and the assumed
single failure (a regulatory requirement) also contribute to the initiating
event uncertainty.The descriptor “Westinghouse 4-loop PWR” identifies a plant
design; however, the nature of nuclear power plant development is such that
even among Westinghouse 4-loop PWRs there can be significant differences. Component
choices, such as reactor coolant pumps, steam generators, core/reactor vessel
design (i.e., bypass flows, fuel assembly design, upper head design), and
containment response features (i.e., sprays, ice, fan coolers, passive
structure surface area), represent elements of the design uncertainty. In
addition, operational and maintenance history can impact the performance of
“equivalent” systems, structures, and components. As a consequence, there are no “identical”
plants.“Operating at steady-state full power” encompasses all
uncertainties associated with plant operating state and event response. In
analysis space, these are often initial or boundary conditions. A plant’s
technical specifications and limiting condition of operation define the
operational space enveloping acceptable plant states. Frequently, there is
significant latitude for “acceptable” states for system variables, including
core axial power and fuel burnup that can have a strong influence on the
acceptance criteria metrics. The challenge for a “best-estimate” analysis is to
balance the value of defining the likely plant state at the time of an accident
with the need to support the plant’s operational envelope. Dozens of analysis
parameters fall into this category.In recognizing the complexity of the uncertainty problem
associated with LOCA safety analysis, the term “best-estimate” as applied to
this problem has evolved into “best-estimate plus uncertainty” (BEPU). The
problem has always been the management of uncertainty. At the time the CSAU methodology was being
developed, a relatively narrow view of uncertainty was necessary because of
limitations in computational ability and limited appreciation of advanced
statistical methods. This original CSAU view on uncertainty was criticized as
being incomplete with relevant contributors to the LOCA safety analysis problem
being treated implicitly and, as a consequence, wrong. As such, the conversation
moved from BE to BEPU—with the emphasis on uncertainty management.


## 2.2. The Role of Engineering Judgment

Engineering judgment has always been a necessary part of any
engineering task. Engineers, through the expression of their experience, have
often applied engineering judgment to make big engineering challenges workable.
Confirmation is, of course, necessary when safety is a concern. In developing
the CSAU methodology, the TPG formalized this often unappreciated aspect of engineering.
Doing so started a debate as to the extent that engineering
judgment should play in the LOCA safety analysis problem.The manifestation of engineering judgment in the CSAU
process is the phenomenological identification and ranking table (PIRT). As the
name implies, the PIRT reflects qualitative engineering judgment as to the
importance of various phenomena relevant to the problem of interest. The intent of the PIRT is to provide a
technical basis during the BEPU methodology development process for the many
decisions, including the management of uncertainty, required to complete the
task.Resistance to this formalized use of engineering judgment inspired
several criticisms, including the following.(i)
Who is qualified to be a part
of a PIRT team?(ii)
How do PIRT teams deal with
differences of opinion?(iii)
Should uncertainty with the
ranking process be incorporated into the PIRT?(iv)
Even after the PIRT is
developed, engineering judgment is required to use the results.(v)
How can the absence of
knowledge (i.e., unmodeled parameters) be treated in this context? Despite the initial criticism, the PIRT exercise has found a
degree of acceptance. Its foremost value
has been in establishing an understanding of the processes and phenomena of
interest among a group of peers. Once
consensus is achieved, decisions impacting the solution of the task at hand may
begin.In the original CSAU large-break LOCA sample problem, the
TPG,applying a PIRT they developed for
this problem, established a precedent that the large-break LOCA problem can be
well characterized by explicitly addressing a minimum set of very important
processes and phenomena. Beyond that set of large-break LOCA contributors,
other phenomenological or process parameters were treated as “nominal.” This
application of engineering judgment has not found universal acceptance for two
reasons: (1) there is a lack of consensus of “important” parameters and (2) it
ignores traditional licensing measures defined in plant technical
specifications and limiting condition of operation.To satisfy this criticism, the BEPU approach recognizes the
value of “realistic conservatism,” that is, the explicit treatment of
uncertainty by characterizing the uncertainty parameter such that the key
output variables are penalized relative to the acceptance criteria. For parameters
with low large-break LOCA importance, this may be a trivial distinction;
however, as importance increases, scrutiny over that which is proclaimed
conservative also increases. Nonetheless, the acceptance of “realistic
conservatism” represents a significant departure from the original concept of
BE methods; yet, it is absolutely necessary for the complex LOCA analysis
problem where engineering judgment is involved.


## 2.3. Convolution of Uncertainty

A constraint, recognized early by the TPG during the development
of the CSAU method, stemmed from the application of statistics to convolve
parameter uncertainty of several individual large-break LOCA contributors into
a single uncertainty statement for PCT.
Specifically, the broader the set of uncertainty contributors
considered, the more than number of required LOCA simulations
grows exponentially. This is the nature of the response surface methods that the TPG considered
state-of-the-art for this application. There is no doubt that this practical constraint
influenced their acceptance of the relatively small number of large-break LOCA
contributors considered in their uncertainty analysis sample problem. Later,
Westinghouse would introduce a clever extension to the response surface
approach to expand the number of large-break LOCA contributors that could be
considered [10].When introduced in 1989, a few organizations in the
international thermal-hydraulic community—in particular, Germany’s GRS—recognized that this obvious limitation could
be eliminated by considering nonparametric statistical approaches. This
counterpoint was not universally appreciated either because there was a lack of
understanding or nonacceptance of nonparametric statistics lack of a definitive
uncertainty statement. The uncertainty statement from a nonparametric
statistical approach is expressed as an inequality characterized with a
confidence level.Today, nonparametric-ordered
statistics (e.g., Wilk’s method) have become the method of choice. However, consensus with regard to its
implementation within regulatory guidelines is still evolving. Current regulation in the U.S. and other
countries recognize a multivariant acceptance criterion for large-break LOCA
analysis. As a consequence, a debate over the required number of calculations
necessary to provide an acceptable uncertainty statement has resulted in
several journal articles on the subject [11–15]. Much of this
debate is on the semantics used to present the uncertainty statement. Specifically,
should the acceptance criterion be measured individually or is it sufficient to
consider the outcome of an analysis as a single statement concerning whether the
entire acceptance criterion has been satisfied.
AREVA NP’s position is with the latter.


## 2.4. Completeness of the Experimental Database

Driven by the recognized gap in knowledge of LOCA phenomena
apparent in the early 1970s that resulted in the early Appendix K rule making,
governments around the world invested heavily in experimental programs to
rectify this situation. By the late 1980s, a large body of research on many
facets of the large-break LOCA problem was completed. Coupled with the CSAU
approach for performing BE analysis, was this body of work sufficient to
declare the closure of the large-break LOCA problem? Undermining the closure position was the view
that so much of the thermal-hydraulic phenomenological database was populated empirically
and, as such, there remains much yet to be characterized.While statistics appeared to be the answer to the analyst,
the experimentalist was saying that in many areas data was insufficient for
deriving statistical measures. In addition, the possibility of unknown
phenomena or undesirable interplay between competing phenomena made any declaration
of closure irresponsible. The TPG’s response was simply that a sufficient
amount of experimentation focused on both separate and integral effects existed
and that uncertainty associated with scale could be determined. In areas this
may be large; however, if it turns out that uncertainty is too penalizing, this
would be a motivation for new test programs.


## 2.5. AREVA NP’s BEPU Paradigm

Constraining factors that can limit a nuclear power plant’s
efficiency include engineering design limits, equipment operability, and
regulatory requirements. The acceptance of BE methods has revealed margin for
improving plant operating performance. Figure1 illustrates this view of the plant
operating margin provided by BE methods relative to the traditional Appendix K
deterministic methods. Margin is characterized by the separation between the
design or the licensing
limit and the nominal operating point.
With regard to regulatory limits, this is measured by recognized metrics
relative to the regulatory acceptance criteria, for example, PCT < 2200°F.Figure 1
Illustration of plant operating margin.Deterministic methods provide a single “analysis of record” that
quantifies the acceptance criteria metrics (PCT, total oxidation, and local
hydrogen generation). Over the operating history of current generation nuclear
power plants, utilities have nearly exhausted the availability of margin
provided by this original method and, as a result, the apparent margin is
small.In contrast, BE methods strive to identify the acceptance
criteria metrics associated with the real state of the plant. Practical
limitations associated with the state of knowledge required to perform analyses
force analysts to apply conservatisms that make the calculated BE value
bounding of the real state. In addition,
the real margin is never realized because the design basis limits reserve
margin to cover uncertainties associated with the actual limits.For the purpose of reporting plant operating performance
margin relative to licensing limits, the goal is not to define this margin
relative to the actual state; rather, it is to convolve all key phenomenological
and process uncertainties to identify the calculated BEPU value—a conservative estimate of margin
incorporating realistic models of the physical processes and associated
phenomena.In preparing the AREVA NP large-break LOCA methodology, the
challenge of addressing the expectations of Regulatory Guide 1.157 and the CSAU
process—balanced with the known criticisms of the CSAU
process—moved the AREVA NP methodology development
team towards nonparametric statistical methods and the “realistic conservatism”
concept of uncertainty management. By taking this step, the focus of the
methodology moves towards the resolution of individual uncertainty
contributors.The main advantage of nonparametric statistical methods is
that the number of treatable uncertainty contributors is independent of the
number of plant calculations. This characteristic provides flexibility during
the development process to explicitly address as many or as few analysis
contributors as necessary to resolve the outcome of the PIRT. As this is a
product of engineering judgment, the uncertainty associated with this exercise
can be reduced by explicitly addressing additional analysis contributors. In
addition, this methodology characteristic provides the opportunity to
incorporate customer requests for the explicit treatment of plant process
uncertainty.For the remainder of this paper, a description is provided of
how AREVA NP’s RLBLOCA methodology conforms to the basic principles of the CSAU
methodology while incorporating realistic conservatisms and nonparametric
statistics.


## 3. Reconciling AREVA NP’s RLBLOCA Methodology with CSAU

The development of AREVA NP’s RLBLOCA methodology was
primarily an exercise in complying with the main themes of the CSAU
methodology. AREVA NP’s interpretation of the CSAU approach is that it
represents a framework for deriving a quantifiable degree of assurance from a
best-estimate analysis tool. This framework, graphically presented in Figure2,
consists of three elements and 14 steps that build on a qualitative
understanding of (in this case) the large-break LOCA problem to define the
necessary tasks to derive a quantitative solution. Highlighted components in
Figure 2 represent steps that overlap with deterministic Appendix K
methodologies. The CSAU framework outlines a procedure that leads from the
identification and characterization of the dominant phenomena influencing the
key acceptance parameter, PCT, to quantify a best-estimate of the consequences
of a LBLOCA and its associated uncertainty. As with Appendix-K-derived
methodologies, the final result is a calculation that provides a PCT to be
measured against the 10 CFR 50.46 acceptance criteria and a statement of total
uncertainty associated with that result.Figure 2
The CSAU methodology framework.


### 3.1. Requirements and Code Capabilities

The first CSAU element sets a foundation of understanding to
guide methodology development. Its
emphasis is on defining the problem and capturing a knowledge base that will be
used to provide the fundamental technical basis for decisions downstream in the
methodology development process. Steps 1, 2, 4, and 5 shown in Figure 2 identify
the problem through specification of the event scenario, plant type, computer
code and version, and computer code documentation, respectively. Historically,
this information represented all that would normally be required for evaluation
methodologies (EM) based on 10 CFR 50 Appendix K. Table 1 summarizes the AREVA choices. Of
particular note is the primary analysis tool S-RELAP5. S-RELAP5 is a modified version of RELAP5/MOD2
[16] with several updates including:Table 1
AREVA NP’s choices for CSAU steps 1, 2, 4 and 5.
PIRT stepAREVA methodologySpecify scenarioLarge-break LOCASelection NPPWestinghouse and CE PWRs withcold leg SISelect frozen codeRODEX3A (fuel performance) S-RELAP5 (RCS and ContainmentThermal-Hydraulics)Provide documentation[5, 18–24](i)
multidimensional modeling capability
(two-dimensional hydrodynamics);(ii)
energy equations modified
to better conserve transported energy;(iii)
incorporation of a
derivative of the CONTEMPT [17] containment analysis code;(iv)
iterative evaluation for choked
junctions;(v)
bankoff CCFL model;(vi)
modeling of noncondensable
gases (e.g., nitrogen discharge form accumulators);(vii)
revised two-phase pump degradation based on EPRI data;(viii)
improvements to interphase friction and mass transfer models;(ix)
Sleicher-Rouse used for single-phase
vapor heat transfer. Step 3, identify and rank phenomena, marks a
significant departure from traditional evaluation methodology approaches by formulizing
engineering judgment to aid both methodology development and regulatory review.
This is particularly important given the substantial effort required to develop
a CSAU-based methodology. Step 3 acknowledges that plant behavior is not
equally influenced by all processes and phenomena that occur during a
transient. This provides the basis to reduce the analysis effort to a
manageable set of phenomena ranked with respect to their influence or
importance on the primary safety criteria (i.e., PCT).The ranking process employed for the AREVA NP RLBLOCA
methodology was accomplished primarily through structured discussions among
AREVA NP engineers and recognized nuclear safety and thermal-hydraulics experts
from industry and academia. The experts assembled for this task had extensive
experience in both the experimental and computational areas of nuclear
thermal-hydraulics. The PIRT team started with the original LBLOCA PIRT
presented by the TPG [4]. This initial PIRT was reviewed by the three external
experts, who offered recommendations for the addition or deletion of phenomena
from the PIRT and revisions to the ranking of the phenomena based on the
evolution of LBLOCA understanding since the publication of the CSAU methodology
and lessons learned from early applications of BE methods. Following this
review, a peer review was held with the three experts and four additional AREVA
NP personnel to derive a final PIRT that incorporated the input from all seven
participants. This final PIRT also merited from approximately 300 code
sensitivity studies that served as a validation of the engineering judgment
statements. The outcome of these meetings was an AREVA NP-proprietary phenomena
identification and ranking table (PIRT) for large-break LOCAs that has many
similarities with the original TPG large-break LOCA PIRT [4]. AREVA NP identified the PIRT parameters shown
in Table 2 as dominant in a large-break LOCA and must be explicitly
addressed in a CSAU-based methodology. Following PIRT development nearly 100
unique sensitivity studies were performed to assess consistency between the
PIRT and S-RELAP5 large-break LOCA model response. The outcome of those studies
served to motivate further code model upgrades and validate PIRT selections.Table 2
Key LBLOCA phenomena identified by AREVA.
PIRT parametersHeat transferVoid distributionAxial power distributionEntrainmentSpacer effectsBreak flowCold leg condensationInterfacial heat transferUpper tie plate
CCFLCore multidimensional
flowECCS bypassSteam bindingAccumulator nitrogen
dischargeCSAU, Step 6, serves to establish a computer code’s
applicability to the analysis problem. This is done by defining a cross
reference of phenomena and plant components to the computer code’s models and
correlations and nodalization capability. With regard to the dominant PIRT
parameters, code applicability also must be supported by the documentation
provided in Step 5.


### 3.2. Assessment and Ranging of Parameters

The second CSAU element establishes the methodology’s
pedigree to perform a best-estimate analysis. This is done by code-to-data
comparisons, sensitivity studies, and uncertainty analysis. It builds from
Element 1 that defines a framework for the performance of sensitivity
studies and identification of experimental test programs by relevance to the
dominant large-break LOCA phenomena. Step 7 defines the code’s assessment
matrix. Thermal-hydraulic computer codes like S-RELAP5 include a large number
of closure-relationships to address the broad spectrum of possible
thermal-hydraulic phenomenological processes. For this reason, it is neither
practical nor necessary to assess every code model and correlation to support
the subset of important phenomena anticipated during a LBLOCA. The PIRT and the
subsequent sensitivity studies were used by AREVA NP to identify the most
useful experimental programs for code assessment from the rather extensive knowledge
base of experiments supporting PWR LOCA phenomena. Proprietary restrictions
reduce this set considerably; however, sufficient data remains in the public
domain to support qualification of a best-estimate LOCA code for PWR
applications. The AREVA NP RLBLOCA assessment matrix is characterized in Table3,
which identifies the test program, the number of specific tests applied to the
AREVA NP RLBLOCA assessment matrix, and the primary phenomenon of interest. The
particular tests were selected to address the following:Table 3
Summary of S-RELAP5 assessment matrix.
Test facilityTests usedKey phenomena of interestReferencesTHTF heat transfer35Heat transfer[25–28]THTF level swell3Void distribution[29]GE level swell1Void distribution[30]FRIGG-227Void distribution[31]Bennet tube2Heat transfer[32]Flecht and flech-seaset9Heat transfer,
nodalization, axial power distribution,[33, 34]scalability, entrainmentPDTF/SMART4Spacer effects[35]Marviken9Break flow[36]W/EPRI 1/3 scale9Cold leg condensation,
interfacial heat transfer[37]MiniLoop CCFL3Upper tie plate
CCFL[38]Multidimensional flow3Core flow distribution[39]UPTF14ECCS bypass,
steam binding, CCFL, scalability,[40–45]nodalizationCCTF4Steam binding,
nodalization, scalability[43–50]SCTF6Nodalization[51]ACHILLES1Accumulator
nitrogen discharge[52]LOFT4Overall code
performance, nodalization, scalability[53–57]Semiscale2Blowdown heat
transfer, nodalization, scalability,[58–60]compensating errors(i)
important LOCA phenomena
defined in the PIRT;(ii)
nodalization validation
(defined in CSAU Step 8);(iii)
code/model scaling (defined
in CSAU Step 10);(iv)
verification of no
important compensating effects;(v)
establishing a broad range of
applicability. The CSAU methodology acknowledges that system nodalization
is similar to any code model or correlation in that code results are sensitive
to model permutations. This is addressed in Step 8, nuclear power plant nodalization
definition. System nodalization presents an inherent code uncertainty. Unlike
code models and correlations, quantification of nodalization-based code
uncertainty is deemed to be of lesser importance relative to the practical
requirements of model accuracy and calculation efficiency or economics. The
objective is to define the minimum noding needed to capture the important
phenomena. The selection process used to arrive at this objective becomes the
standard nodalization procedure. The standard nodalization procedure is applied
to every code assessment and LBLOCA analysis; thus, minimizing nodalization as
a contributor to uncertainty.Code assessment using the test matrix from Step 7 and
the nuclear power plant nodalization of Step 8 is used to accomplish Step 9, code, and experiment
accuracy. Code accuracy is quantified for bias and deviations through
confirmatory code uncertainty analysis and benchmarks. This step also serves as
a validation for Step 6, code applicability, and sets up the tasks of element 3,
sensitivity, and uncertainty analysis. The demonstration of code accuracy—or for a conservative EM, code adequacy—has always been a required component of LOCA
evaluation methodologies. With a CSAU-based evaluation methodology, the
emphasis is focused on evaluating the important individual contributors (i.e.,
phenomena) to the overall code uncertainty.For the dominant LBLOCA phenomenon (e.g., critical flow,
film boiling, condensation, fuel stored energy, etc.), sets of separate effects
tests were used to derive the S-RELAP5 code uncertainty as it relates to each
individual phenomenon. From the code-to-data comparisons, such as that seen in
Figure3 comparing S-RELAP5 results (xc)
to Marviken critical flow test data (xm),
code bias (μx) and
the statistical standard deviation (σ) were evaluated.Figure 3
Calculated versus measured results for Marviken critical flow tests.While uncertainty quantification obviously requires data,
the process for quantification begins with a clear qualitative understanding of
the assumptions associated with measured values. This is the nature of probability and
statistics in general. For example, heat transfer is fundamentally dependent on
geometry, power, temperatures, fluid properties, and mass flow. In a nuclear
power reactor core, heat transfer is complicated by multidimensional effects
resulting from core and fuel design and radial and axial power variations. In
addition, potentially dramatic changes in fluid properties can occur as a consequence
of both phenomenological (e.g., phase change) and plant process response (e.g.,
safety injection). However, what we know about core heat transfer has been
gathered from data taken from prototypical systems of likely different scale skewed
by limitations in measurement capabilities and data reduction techniques.The quality of the data, characterized by both quantitative
limitations such as the domain of system conditions during testing and
qualitative limits associated with measurement factors and data reduction, must
be addressed. The ideal nature of measured data would have the following
characteristics.(i)
Phenomenon
of interest is measurable independent of other phenomena.(ii)
Phenomenological
dependencies with a particular system condition are measurable independent
of changes of other system conditions.(iii)
Detailed
dimensional variations are measurable.(iv)
Scale
distortion is eliminated. Since real data often does not have these characteristics,
data reduction techniques have been devised and applied to compensate. Such
methods often involve the elimination of “tainted” data and/or the averaging of
data. The cost of such techniques is typically seen in the loss of some data
and/or the broadening of uncertainty measures. Some examples from a hypothetical
reflood heat transfer test are as follows:(a)
the elimination of temperature
data for heater rods near a “cold” vessel wall (possible excessive radiation)—a consequence of scale distortion;(b)
insufficient number of
thermocouples to track radial and/or axial temperature variation in the
simulated fuel assembly resulting in the need to track computed average
temperature results or just the peak temperature results by eliminating data not considered “peak”;(c)
tracking a total heat
transfer measure rather than separate heat transfer mechanisms and other
influencing phenomena (i.e., combinations of radiation and convection between
walls and liquid and vapor fluids, interfacial drag); that is, tracking the convolution
of multiple phenomena to produce an “aggregate phenomenon”;(d)
binning temperature data
over a segment of a test condition range (e.g., pressure, void fraction) to
assure an adequate depth of data necessary to generate meaningful uncertainty
measures. Such limitations in data are manageable; however, the
implications of such limits should be addressed in the implementation of the
uncertainty measures used in BEPU methodologies.Completeness requires that the treatment of each important
LBLOCA phenomena be addressed; however, a full quantification of uncertainty
for each phenomenon is not necessary and, given the availability of data, may
not be possible. “Phenomenological
treatment” should describe a method in which the parameter range of each LBLOCA
contributor is covered. The use of
statistics provides various methods for describing ranges of uncertainty for a
given problem; however, the CSAU process does allow for methodology
conservatisms to satisfy the objective of defining uncertainty treatment for
individual code models and correlations. The practical limitations of economics
and data availability are considered
when accepting a conservative phenomenological treatment. The trade off is the
reduction in margin relative to the LBLOCA acceptance criteria. Again,
engineering judgment can play a role in how to approach this step. Table 4
provides a summary of the parameters for which code uncertainty was quantified.
While in most cases AREVA NP developed proprietary analyses to quantify
parameter uncertainty, quantified uncertainty for a few parameters appears in
open literature. In those cases (i.e., metal-water reaction and decay heat),
the values used in the AREVA NP RLBLOCA methodology are provided.Table 4
Summary of uncertainty quantification exercise.
PIRT ParameterBiasσMin or−2σMax or+2σBreak SizeN/AN/A0.12Break discharge coefficients############Critical heat flux###0.0######Film boling HTC###Special###N/ADispersed film boiling###Special###N/ATmin,############Power (inc. radial and axial shapes)Treated as a sampled plant parameterStored energy (centerline temperature)############Metal-water reaction constant10.1820.6361.364Metal-water reaction exponent10.01340.97321.0268Decay heat uncertainty10.0030.941.06Condensation interface HTC###Uniform######Steam Generator Inlet Interphase Friction###0.0######Hot wall (CHF multiplier)###binary######Containment pressure (volume)###uniformmin free volumemax free volumeGiven quantified uncertainty measures, the integrity of the statistics
requires the demonstration of sufficient density and breadth of data within the
range-of-applicability. Validation of
uncertainty ranges or standard deviation is provided by reserving “control
sets” of data and reevaluating statistics. Data from integral effects tests (e.g.,
CCTF, LOFT, and semiscale) was used to demonstrate the acceptability of the
code biases developed from the separate effects tests. Figure4 shows a comparison of a CCTF
Test 54 assessment before and after the evaluation of code biases.Figure 4
Comparison of CCTF Test 54 assessment before
and after the evaluation of code biases.Beyond the uncertainty quantification exercise, the primary
challenge of Element 2 is to demonstrate sufficient range of applicability
of the computer code models and correlations.
Code models and correlations are best assessed using separate effects
test data developed for the explicit purpose of investigating the phenomena
described by the code model or correlation.
Establishing a sufficient range of applicability is complicated by the
fact that conditions present during a PWR LBLOCA span thermal-hydraulic ranges
(pressures, temperatures, flows, etc.) that exceed the ranges of any individual
separate effects test. Given this inherent limitation, the logical approach to
establish the pedigree of a particular code model or correlation must
incorporate a broader body of knowledge on the phenomena of interest. Applying
an analogy from vector space analysis, the “applicability space” will not only
include data from various separate effects test programs, but also analytical
solutions and data from various integral effects tests. It is the collection of
this full body of phenomenological knowledge: the analytical model, the
statistical description of uncertainty from separate effects tests, and
validation with integral effects tests—as incorporated within a calculational
framework such as S-RELAP5 that provides the technical basis supporting the
declared range of applicability of a code model or correlation.An added complexity to the
applicability question is test scalability. This is addressed in Step 10. In the long history of thermal-hydraulic code
models and correlations development, computer code models and correlations have
often been “tuned” to particular data sets. This approach to computer code
development can create a results bias and uncertainty associated with the
scaling of the problem of interest. Scaling uncertainty can be evaluated using
data from a suite of test programs generated at various scales. For the
specific application to the PWR LBLOCA, there is a motivation to acquire full-scale
data for the dominant LBLOCA phenomena.
Fortunately, many hydraulic phenomena can be assessed using tests
performed at the full-scale upper plenum test facility (UPTF). In addition,
heat transfer phenomena can be assessed applying data from the many reflood
tests that have been performed with full-scale assemblies. The AREVA NP RLBLOCA methodology utilized the
available full-scale data wherever possible.
In addition, code-to-data comparisons from scaled test facilities did
not show a significant scale bias. With this approach to the scaling issue, no
additional accounting for scale is necessary.


### 3.3. Sensitivity and Uncertainty Analysis

Given the inherent uncertainty and complexity of the
thermal-hydraulic processes appearing during a large-break LOCA, a
best-estimate statement of assurance must be provided statistically. This CSAU element
focuses on setting-up, executing, and evaluating a RLBLOCA analysis. As a
statistics-based methodology, the problem setup involves implementing the bias
and uncertainty for the LBLOCA contributors identified from CSAU Elements 1
and 2. Execution involves the
convolution of these uncertainty contributors and the final result is evaluated
from the number of calculations necessary to provide a statistically meaningful
set.While the CSAU methodology through Step 9 is focused on
phenomenological contributors to uncertainty, it recognizes in Step11
that there is also uncertainty associated with the measurable states that
define a plant’s operating condition, such as pressures, temperatures, levels.For utility customers interested in
plant-specific application of an approved methodology, this step may be the
most important step; however, the CSAU methodology [4] discussion provides the
least amount of direction. In response to the limited amount of guidance
provided by the TPG, the AREVA NP approach has been detailed and reported in [61].The key challenge to addressing the uncertainty associated
with plant state is reconciling the requirement for analyses to support a
plant’s licensing basis through the plant’s design and control specifications while
still being “best-estimate.” Traditional deterministic analyses explicitly
utilize a plant’s technical specifications when it is clearly conservative to
do so; otherwise, a best-estimate value is considered to bound the technical
specification. Since no provision is made for BE methods to exempt the use of
conservative technical specification in safety analysis, the concept of
“realistic conservatism” is unavoidable. That is, this condition is a function
of the regulatory process for plant licensing and not an artifact of the
developed safety analysis methodology.AREVA NP’s approach to identify which plant parameters to
explicitly treat as an uncertainty parameter, either as a direct bias or
sampled, considers the interests of several constituents. The primary regulatory interest requires that
the plant be analyzed at technical specification limits. Precedence established
by Appendix K methods provides the list of those parameters that are expected
to be treated in this fashion. A second interest has been inferred by AREVA NP
given the emphasis in the CSAU methodology on important phenomenological
contributors to LOCA acceptance criteria. AREVA NP chose to recognize that plant
response to an off-normal event is driven by phenomena. Specifically, plant parameters were
correlated to phenomena and the importance of a plant parameter was made in
relation to any associated phenomenological parameter. For example, accumulator
pressure will affect ECCS bypass and initial flow rate will affect break flow.
In effect, the inclusion of a plant parameter’s operational and measurement
uncertainty implicitly broadens the range and distribution of PIRT parameters. The
third interest in this regard is the customer. In this situation, the customer
may be interested in an analysis of some process or condition for which an
expanded operational variance is desired, for reasons beyond the normal support of a plant’s limits of
operation. The uncertainty treatment for these parameters is handled just like
other sampled parameters.Table5 presents the list of plant parameters treated
in the AREVA NP RLBLOCA 3- and 4-loop sample problems and their relation to
important PIRT parameters. Generally, the impact of plant parameters will be
much less than PIRT parameters. Most plant parameters represent initial
conditions; hence, their impact diminishes with time. Typically, limiting
LBLOCA safety analyses show PCT during late reflood; hence, the impact of plant
initial state is likely very small. The ECCS parameters will influence the
simulation throughout the event; hence, greater importance should be given to
these plant parameters.Table 5
Treated process parameters and relation to
PIRT.
Process
parameterInfluenced
phenomenon (PIRT subset)Fuel state (burnup and power peaking)Stored energyCore powerStored energyPower peaking, axial shapeStored energyLoop flow rateFlow split, DNBCore inlet temperatureDNBUpper head temperatureFlow reversal, stagnationPressurizer pressure, levelEarly quench, critical flow in surge lineAccumulator pressure, temperature, levelAccumulator discharge, condensation,
noncondensable gasesContainment volume, heat transfer, spraysBackpressure, critical flowSteam generator feedwater temperatureCore heat transferOffsite power and diesel start delayCore heat transfer via pumped ECCThe objective of CSAU Steps 12 and 13 is to combine the bias
and uncertainty of the important individual contributors as identified in Step
9 and Step 11 through the running of a large set of plant simulations. RLBLOCA
simulations using the AREVA NP methodology involves two computer codes: RODEX3A
and S-RELAP5. As stated in the introduction, RODEX3A is a fuel performance code
that provides fuel material property characteristics that determine a fuel
pin’s initial stored energy versus burnup. S-RELAP5, a derivative of
RELAP5/MOD2 and the CONTEMPT codes, uses the RODEX3A results to initialize the
fuel heat structure models as a part of calculating the steady-state solution
that initializes the LBLOCA transient simulation. S-RELAP5 is then executed for the transient
simulation of the fuel and coolant system response to the break and containment
back pressure condition.The convolution of the many LBLOCA uncertainty contributors
(Tables4 and 5) to PCT is an inherently statistical approach. The
two common approaches are generally classified as either parametric or
nonparametric. The response surface method, a parametric method, was the
approach demonstrated in the CSAU sample problem [4]. The objective of that
method is the development of a response surface describing peak clad
temperature sensitivity to the dominant LBLOCA uncertainty contributors. The number
of calculations required for that approach is dependent on the number of LBLOCA
uncertainty contributors considered. AREVA NP chose to apply a nonparametric
approach originally recommended in the German Gesellschaft fur Anlagen und
Reaktorsicherheit (GRS) methodology [62]. This statistical method is often
referred to as Wilks’ method [63]. The nonparametric approach decouples the
association between the number of uncertainty parameters and the number of
required calculations. The desired quantification of PCT uncertainty is the
identification of a specific result that represents coverage of the results
domain at or above 95% with a 95% confidence. The 95/95 coverage/confidence has
been recognized by the USNRC having sufficient conservatism for LBLOCA
analyses.The minimum number of sampled cases is given by Wilks’
formula for one-sided tolerance limits. Beginning with the probability statement(1)P[F(xk)>β]=n!(k−1)!(n−k)!∫β1ξk−1(1−ξ)n−kdξ, where the P[F(xk)>β] is the “probability that the result from a
given sample case (F(xk))
exceeds the β percentile” case. When k=n, that is, the largest value of all of the samples, this relationship reduces to
(2)γ=1−βn, where β is the coverage, γ is the confidence, and n is the minimum number
of sampled calculations. For the 95/95 coverage/confidence condition, n=59. This means in a random sample of 59 calculations, one case,
the highest PCT case, will bound the 95/95 coverage/confidence condition for
PCT. A disadvantage of this method is that there may be significant
conservatism as a result of bounding the 95/95 condition. Applying Somerville’s
generalization of Wilk’s formula on nonparametric tolerance limits [64] can
improve the fidelity in the final result through the performance of additional
calculations.Each calculation is setup by first sampling every LBLOCA
uncertainty contributor over its derived range. A minimum of 59 calculations
are performed. The PCT results from each calculation are sorted to identify the
highest PCT. The highest PCT result from 59 calculations bounds the 95/95
condition.Included in the AREVA NP RLBLOCA methodology, topical reports are sample
problems demonstrating application of this methodology on both a 3- and
4-loop Westinghouse pressurized water reactor. Some results from the 3-loop
sample problem were presented in [65], which culminated in a PCT of 1853°F. For
this problem, more than 30 uncertainty parameters were statistically treated
using a Monte Carlo sampling procedure for the creation of 59 code input file
sets. Each set included four input files describing models for the fuel
performance evaluation, thermal-hydraulic steady-state initialization,
thermal-hydraulic transient response, and simultaneous containment response.The final step in the CSAU process
is to identify the total uncertainty. If any PCT gains or penalties were
identified during the CSAU process, they are to be applied in Step 14. In
addition, the total uncertainty can be quantified relative to a “best-estimate”
figure-of-merit. The total uncertainty does not have meaning in relationship to
regulatory acceptance criteria. As such, the importance of this measure is
somewhat diminished from what the TPG originally envisioned. AREVA NP chose to define
total uncertainty using the 50/50 condition, also evaluated from nonparametric
statistics. The 50/50 condition is provided by the calculation providing(n+1)/2 for an odd-numbered sized sample space. For the sample
problem, the 50/50 condition was identified as 1500°F; hence, the 95/95
condition represents about 350°F uncertainty.


## 3.1. Requirements and Code Capabilities

The first CSAU element sets a foundation of understanding to
guide methodology development. Its
emphasis is on defining the problem and capturing a knowledge base that will be
used to provide the fundamental technical basis for decisions downstream in the
methodology development process. Steps 1, 2, 4, and 5 shown in Figure 2 identify
the problem through specification of the event scenario, plant type, computer
code and version, and computer code documentation, respectively. Historically,
this information represented all that would normally be required for evaluation
methodologies (EM) based on 10 CFR 50 Appendix K. Table 1 summarizes the AREVA choices. Of
particular note is the primary analysis tool S-RELAP5. S-RELAP5 is a modified version of RELAP5/MOD2
[16] with several updates including:Table 1
AREVA NP’s choices for CSAU steps 1, 2, 4 and 5.
PIRT stepAREVA methodologySpecify scenarioLarge-break LOCASelection NPPWestinghouse and CE PWRs withcold leg SISelect frozen codeRODEX3A (fuel performance) S-RELAP5 (RCS and ContainmentThermal-Hydraulics)Provide documentation[5, 18–24](i)
multidimensional modeling capability
(two-dimensional hydrodynamics);(ii)
energy equations modified
to better conserve transported energy;(iii)
incorporation of a
derivative of the CONTEMPT [17] containment analysis code;(iv)
iterative evaluation for choked
junctions;(v)
bankoff CCFL model;(vi)
modeling of noncondensable
gases (e.g., nitrogen discharge form accumulators);(vii)
revised two-phase pump degradation based on EPRI data;(viii)
improvements to interphase friction and mass transfer models;(ix)
Sleicher-Rouse used for single-phase
vapor heat transfer. Step 3, identify and rank phenomena, marks a
significant departure from traditional evaluation methodology approaches by formulizing
engineering judgment to aid both methodology development and regulatory review.
This is particularly important given the substantial effort required to develop
a CSAU-based methodology. Step 3 acknowledges that plant behavior is not
equally influenced by all processes and phenomena that occur during a
transient. This provides the basis to reduce the analysis effort to a
manageable set of phenomena ranked with respect to their influence or
importance on the primary safety criteria (i.e., PCT).The ranking process employed for the AREVA NP RLBLOCA
methodology was accomplished primarily through structured discussions among
AREVA NP engineers and recognized nuclear safety and thermal-hydraulics experts
from industry and academia. The experts assembled for this task had extensive
experience in both the experimental and computational areas of nuclear
thermal-hydraulics. The PIRT team started with the original LBLOCA PIRT
presented by the TPG [4]. This initial PIRT was reviewed by the three external
experts, who offered recommendations for the addition or deletion of phenomena
from the PIRT and revisions to the ranking of the phenomena based on the
evolution of LBLOCA understanding since the publication of the CSAU methodology
and lessons learned from early applications of BE methods. Following this
review, a peer review was held with the three experts and four additional AREVA
NP personnel to derive a final PIRT that incorporated the input from all seven
participants. This final PIRT also merited from approximately 300 code
sensitivity studies that served as a validation of the engineering judgment
statements. The outcome of these meetings was an AREVA NP-proprietary phenomena
identification and ranking table (PIRT) for large-break LOCAs that has many
similarities with the original TPG large-break LOCA PIRT [4]. AREVA NP identified the PIRT parameters shown
in Table 2 as dominant in a large-break LOCA and must be explicitly
addressed in a CSAU-based methodology. Following PIRT development nearly 100
unique sensitivity studies were performed to assess consistency between the
PIRT and S-RELAP5 large-break LOCA model response. The outcome of those studies
served to motivate further code model upgrades and validate PIRT selections.Table 2
Key LBLOCA phenomena identified by AREVA.
PIRT parametersHeat transferVoid distributionAxial power distributionEntrainmentSpacer effectsBreak flowCold leg condensationInterfacial heat transferUpper tie plate
CCFLCore multidimensional
flowECCS bypassSteam bindingAccumulator nitrogen
dischargeCSAU, Step 6, serves to establish a computer code’s
applicability to the analysis problem. This is done by defining a cross
reference of phenomena and plant components to the computer code’s models and
correlations and nodalization capability. With regard to the dominant PIRT
parameters, code applicability also must be supported by the documentation
provided in Step 5.


## 3.2. Assessment and Ranging of Parameters

The second CSAU element establishes the methodology’s
pedigree to perform a best-estimate analysis. This is done by code-to-data
comparisons, sensitivity studies, and uncertainty analysis. It builds from
Element 1 that defines a framework for the performance of sensitivity
studies and identification of experimental test programs by relevance to the
dominant large-break LOCA phenomena. Step 7 defines the code’s assessment
matrix. Thermal-hydraulic computer codes like S-RELAP5 include a large number
of closure-relationships to address the broad spectrum of possible
thermal-hydraulic phenomenological processes. For this reason, it is neither
practical nor necessary to assess every code model and correlation to support
the subset of important phenomena anticipated during a LBLOCA. The PIRT and the
subsequent sensitivity studies were used by AREVA NP to identify the most
useful experimental programs for code assessment from the rather extensive knowledge
base of experiments supporting PWR LOCA phenomena. Proprietary restrictions
reduce this set considerably; however, sufficient data remains in the public
domain to support qualification of a best-estimate LOCA code for PWR
applications. The AREVA NP RLBLOCA assessment matrix is characterized in Table3,
which identifies the test program, the number of specific tests applied to the
AREVA NP RLBLOCA assessment matrix, and the primary phenomenon of interest. The
particular tests were selected to address the following:Table 3
Summary of S-RELAP5 assessment matrix.
Test facilityTests usedKey phenomena of interestReferencesTHTF heat transfer35Heat transfer[25–28]THTF level swell3Void distribution[29]GE level swell1Void distribution[30]FRIGG-227Void distribution[31]Bennet tube2Heat transfer[32]Flecht and flech-seaset9Heat transfer,
nodalization, axial power distribution,[33, 34]scalability, entrainmentPDTF/SMART4Spacer effects[35]Marviken9Break flow[36]W/EPRI 1/3 scale9Cold leg condensation,
interfacial heat transfer[37]MiniLoop CCFL3Upper tie plate
CCFL[38]Multidimensional flow3Core flow distribution[39]UPTF14ECCS bypass,
steam binding, CCFL, scalability,[40–45]nodalizationCCTF4Steam binding,
nodalization, scalability[43–50]SCTF6Nodalization[51]ACHILLES1Accumulator
nitrogen discharge[52]LOFT4Overall code
performance, nodalization, scalability[53–57]Semiscale2Blowdown heat
transfer, nodalization, scalability,[58–60]compensating errors(i)
important LOCA phenomena
defined in the PIRT;(ii)
nodalization validation
(defined in CSAU Step 8);(iii)
code/model scaling (defined
in CSAU Step 10);(iv)
verification of no
important compensating effects;(v)
establishing a broad range of
applicability. The CSAU methodology acknowledges that system nodalization
is similar to any code model or correlation in that code results are sensitive
to model permutations. This is addressed in Step 8, nuclear power plant nodalization
definition. System nodalization presents an inherent code uncertainty. Unlike
code models and correlations, quantification of nodalization-based code
uncertainty is deemed to be of lesser importance relative to the practical
requirements of model accuracy and calculation efficiency or economics. The
objective is to define the minimum noding needed to capture the important
phenomena. The selection process used to arrive at this objective becomes the
standard nodalization procedure. The standard nodalization procedure is applied
to every code assessment and LBLOCA analysis; thus, minimizing nodalization as
a contributor to uncertainty.Code assessment using the test matrix from Step 7 and
the nuclear power plant nodalization of Step 8 is used to accomplish Step 9, code, and experiment
accuracy. Code accuracy is quantified for bias and deviations through
confirmatory code uncertainty analysis and benchmarks. This step also serves as
a validation for Step 6, code applicability, and sets up the tasks of element 3,
sensitivity, and uncertainty analysis. The demonstration of code accuracy—or for a conservative EM, code adequacy—has always been a required component of LOCA
evaluation methodologies. With a CSAU-based evaluation methodology, the
emphasis is focused on evaluating the important individual contributors (i.e.,
phenomena) to the overall code uncertainty.For the dominant LBLOCA phenomenon (e.g., critical flow,
film boiling, condensation, fuel stored energy, etc.), sets of separate effects
tests were used to derive the S-RELAP5 code uncertainty as it relates to each
individual phenomenon. From the code-to-data comparisons, such as that seen in
Figure3 comparing S-RELAP5 results (xc)
to Marviken critical flow test data (xm),
code bias (μx) and
the statistical standard deviation (σ) were evaluated.Figure 3
Calculated versus measured results for Marviken critical flow tests.While uncertainty quantification obviously requires data,
the process for quantification begins with a clear qualitative understanding of
the assumptions associated with measured values. This is the nature of probability and
statistics in general. For example, heat transfer is fundamentally dependent on
geometry, power, temperatures, fluid properties, and mass flow. In a nuclear
power reactor core, heat transfer is complicated by multidimensional effects
resulting from core and fuel design and radial and axial power variations. In
addition, potentially dramatic changes in fluid properties can occur as a consequence
of both phenomenological (e.g., phase change) and plant process response (e.g.,
safety injection). However, what we know about core heat transfer has been
gathered from data taken from prototypical systems of likely different scale skewed
by limitations in measurement capabilities and data reduction techniques.The quality of the data, characterized by both quantitative
limitations such as the domain of system conditions during testing and
qualitative limits associated with measurement factors and data reduction, must
be addressed. The ideal nature of measured data would have the following
characteristics.(i)
Phenomenon
of interest is measurable independent of other phenomena.(ii)
Phenomenological
dependencies with a particular system condition are measurable independent
of changes of other system conditions.(iii)
Detailed
dimensional variations are measurable.(iv)
Scale
distortion is eliminated. Since real data often does not have these characteristics,
data reduction techniques have been devised and applied to compensate. Such
methods often involve the elimination of “tainted” data and/or the averaging of
data. The cost of such techniques is typically seen in the loss of some data
and/or the broadening of uncertainty measures. Some examples from a hypothetical
reflood heat transfer test are as follows:(a)
the elimination of temperature
data for heater rods near a “cold” vessel wall (possible excessive radiation)—a consequence of scale distortion;(b)
insufficient number of
thermocouples to track radial and/or axial temperature variation in the
simulated fuel assembly resulting in the need to track computed average
temperature results or just the peak temperature results by eliminating data not considered “peak”;(c)
tracking a total heat
transfer measure rather than separate heat transfer mechanisms and other
influencing phenomena (i.e., combinations of radiation and convection between
walls and liquid and vapor fluids, interfacial drag); that is, tracking the convolution
of multiple phenomena to produce an “aggregate phenomenon”;(d)
binning temperature data
over a segment of a test condition range (e.g., pressure, void fraction) to
assure an adequate depth of data necessary to generate meaningful uncertainty
measures. Such limitations in data are manageable; however, the
implications of such limits should be addressed in the implementation of the
uncertainty measures used in BEPU methodologies.Completeness requires that the treatment of each important
LBLOCA phenomena be addressed; however, a full quantification of uncertainty
for each phenomenon is not necessary and, given the availability of data, may
not be possible. “Phenomenological
treatment” should describe a method in which the parameter range of each LBLOCA
contributor is covered. The use of
statistics provides various methods for describing ranges of uncertainty for a
given problem; however, the CSAU process does allow for methodology
conservatisms to satisfy the objective of defining uncertainty treatment for
individual code models and correlations. The practical limitations of economics
and data availability are considered
when accepting a conservative phenomenological treatment. The trade off is the
reduction in margin relative to the LBLOCA acceptance criteria. Again,
engineering judgment can play a role in how to approach this step. Table 4
provides a summary of the parameters for which code uncertainty was quantified.
While in most cases AREVA NP developed proprietary analyses to quantify
parameter uncertainty, quantified uncertainty for a few parameters appears in
open literature. In those cases (i.e., metal-water reaction and decay heat),
the values used in the AREVA NP RLBLOCA methodology are provided.Table 4
Summary of uncertainty quantification exercise.
PIRT ParameterBiasσMin or−2σMax or+2σBreak SizeN/AN/A0.12Break discharge coefficients############Critical heat flux###0.0######Film boling HTC###Special###N/ADispersed film boiling###Special###N/ATmin,############Power (inc. radial and axial shapes)Treated as a sampled plant parameterStored energy (centerline temperature)############Metal-water reaction constant10.1820.6361.364Metal-water reaction exponent10.01340.97321.0268Decay heat uncertainty10.0030.941.06Condensation interface HTC###Uniform######Steam Generator Inlet Interphase Friction###0.0######Hot wall (CHF multiplier)###binary######Containment pressure (volume)###uniformmin free volumemax free volumeGiven quantified uncertainty measures, the integrity of the statistics
requires the demonstration of sufficient density and breadth of data within the
range-of-applicability. Validation of
uncertainty ranges or standard deviation is provided by reserving “control
sets” of data and reevaluating statistics. Data from integral effects tests (e.g.,
CCTF, LOFT, and semiscale) was used to demonstrate the acceptability of the
code biases developed from the separate effects tests. Figure4 shows a comparison of a CCTF
Test 54 assessment before and after the evaluation of code biases.Figure 4
Comparison of CCTF Test 54 assessment before
and after the evaluation of code biases.Beyond the uncertainty quantification exercise, the primary
challenge of Element 2 is to demonstrate sufficient range of applicability
of the computer code models and correlations.
Code models and correlations are best assessed using separate effects
test data developed for the explicit purpose of investigating the phenomena
described by the code model or correlation.
Establishing a sufficient range of applicability is complicated by the
fact that conditions present during a PWR LBLOCA span thermal-hydraulic ranges
(pressures, temperatures, flows, etc.) that exceed the ranges of any individual
separate effects test. Given this inherent limitation, the logical approach to
establish the pedigree of a particular code model or correlation must
incorporate a broader body of knowledge on the phenomena of interest. Applying
an analogy from vector space analysis, the “applicability space” will not only
include data from various separate effects test programs, but also analytical
solutions and data from various integral effects tests. It is the collection of
this full body of phenomenological knowledge: the analytical model, the
statistical description of uncertainty from separate effects tests, and
validation with integral effects tests—as incorporated within a calculational
framework such as S-RELAP5 that provides the technical basis supporting the
declared range of applicability of a code model or correlation.An added complexity to the
applicability question is test scalability. This is addressed in Step 10. In the long history of thermal-hydraulic code
models and correlations development, computer code models and correlations have
often been “tuned” to particular data sets. This approach to computer code
development can create a results bias and uncertainty associated with the
scaling of the problem of interest. Scaling uncertainty can be evaluated using
data from a suite of test programs generated at various scales. For the
specific application to the PWR LBLOCA, there is a motivation to acquire full-scale
data for the dominant LBLOCA phenomena.
Fortunately, many hydraulic phenomena can be assessed using tests
performed at the full-scale upper plenum test facility (UPTF). In addition,
heat transfer phenomena can be assessed applying data from the many reflood
tests that have been performed with full-scale assemblies. The AREVA NP RLBLOCA methodology utilized the
available full-scale data wherever possible.
In addition, code-to-data comparisons from scaled test facilities did
not show a significant scale bias. With this approach to the scaling issue, no
additional accounting for scale is necessary.


## 3.3. Sensitivity and Uncertainty Analysis

Given the inherent uncertainty and complexity of the
thermal-hydraulic processes appearing during a large-break LOCA, a
best-estimate statement of assurance must be provided statistically. This CSAU element
focuses on setting-up, executing, and evaluating a RLBLOCA analysis. As a
statistics-based methodology, the problem setup involves implementing the bias
and uncertainty for the LBLOCA contributors identified from CSAU Elements 1
and 2. Execution involves the
convolution of these uncertainty contributors and the final result is evaluated
from the number of calculations necessary to provide a statistically meaningful
set.While the CSAU methodology through Step 9 is focused on
phenomenological contributors to uncertainty, it recognizes in Step11
that there is also uncertainty associated with the measurable states that
define a plant’s operating condition, such as pressures, temperatures, levels.For utility customers interested in
plant-specific application of an approved methodology, this step may be the
most important step; however, the CSAU methodology [4] discussion provides the
least amount of direction. In response to the limited amount of guidance
provided by the TPG, the AREVA NP approach has been detailed and reported in [61].The key challenge to addressing the uncertainty associated
with plant state is reconciling the requirement for analyses to support a
plant’s licensing basis through the plant’s design and control specifications while
still being “best-estimate.” Traditional deterministic analyses explicitly
utilize a plant’s technical specifications when it is clearly conservative to
do so; otherwise, a best-estimate value is considered to bound the technical
specification. Since no provision is made for BE methods to exempt the use of
conservative technical specification in safety analysis, the concept of
“realistic conservatism” is unavoidable. That is, this condition is a function
of the regulatory process for plant licensing and not an artifact of the
developed safety analysis methodology.AREVA NP’s approach to identify which plant parameters to
explicitly treat as an uncertainty parameter, either as a direct bias or
sampled, considers the interests of several constituents. The primary regulatory interest requires that
the plant be analyzed at technical specification limits. Precedence established
by Appendix K methods provides the list of those parameters that are expected
to be treated in this fashion. A second interest has been inferred by AREVA NP
given the emphasis in the CSAU methodology on important phenomenological
contributors to LOCA acceptance criteria. AREVA NP chose to recognize that plant
response to an off-normal event is driven by phenomena. Specifically, plant parameters were
correlated to phenomena and the importance of a plant parameter was made in
relation to any associated phenomenological parameter. For example, accumulator
pressure will affect ECCS bypass and initial flow rate will affect break flow.
In effect, the inclusion of a plant parameter’s operational and measurement
uncertainty implicitly broadens the range and distribution of PIRT parameters. The
third interest in this regard is the customer. In this situation, the customer
may be interested in an analysis of some process or condition for which an
expanded operational variance is desired, for reasons beyond the normal support of a plant’s limits of
operation. The uncertainty treatment for these parameters is handled just like
other sampled parameters.Table5 presents the list of plant parameters treated
in the AREVA NP RLBLOCA 3- and 4-loop sample problems and their relation to
important PIRT parameters. Generally, the impact of plant parameters will be
much less than PIRT parameters. Most plant parameters represent initial
conditions; hence, their impact diminishes with time. Typically, limiting
LBLOCA safety analyses show PCT during late reflood; hence, the impact of plant
initial state is likely very small. The ECCS parameters will influence the
simulation throughout the event; hence, greater importance should be given to
these plant parameters.Table 5
Treated process parameters and relation to
PIRT.
Process
parameterInfluenced
phenomenon (PIRT subset)Fuel state (burnup and power peaking)Stored energyCore powerStored energyPower peaking, axial shapeStored energyLoop flow rateFlow split, DNBCore inlet temperatureDNBUpper head temperatureFlow reversal, stagnationPressurizer pressure, levelEarly quench, critical flow in surge lineAccumulator pressure, temperature, levelAccumulator discharge, condensation,
noncondensable gasesContainment volume, heat transfer, spraysBackpressure, critical flowSteam generator feedwater temperatureCore heat transferOffsite power and diesel start delayCore heat transfer via pumped ECCThe objective of CSAU Steps 12 and 13 is to combine the bias
and uncertainty of the important individual contributors as identified in Step
9 and Step 11 through the running of a large set of plant simulations. RLBLOCA
simulations using the AREVA NP methodology involves two computer codes: RODEX3A
and S-RELAP5. As stated in the introduction, RODEX3A is a fuel performance code
that provides fuel material property characteristics that determine a fuel
pin’s initial stored energy versus burnup. S-RELAP5, a derivative of
RELAP5/MOD2 and the CONTEMPT codes, uses the RODEX3A results to initialize the
fuel heat structure models as a part of calculating the steady-state solution
that initializes the LBLOCA transient simulation. S-RELAP5 is then executed for the transient
simulation of the fuel and coolant system response to the break and containment
back pressure condition.The convolution of the many LBLOCA uncertainty contributors
(Tables4 and 5) to PCT is an inherently statistical approach. The
two common approaches are generally classified as either parametric or
nonparametric. The response surface method, a parametric method, was the
approach demonstrated in the CSAU sample problem [4]. The objective of that
method is the development of a response surface describing peak clad
temperature sensitivity to the dominant LBLOCA uncertainty contributors. The number
of calculations required for that approach is dependent on the number of LBLOCA
uncertainty contributors considered. AREVA NP chose to apply a nonparametric
approach originally recommended in the German Gesellschaft fur Anlagen und
Reaktorsicherheit (GRS) methodology [62]. This statistical method is often
referred to as Wilks’ method [63]. The nonparametric approach decouples the
association between the number of uncertainty parameters and the number of
required calculations. The desired quantification of PCT uncertainty is the
identification of a specific result that represents coverage of the results
domain at or above 95% with a 95% confidence. The 95/95 coverage/confidence has
been recognized by the USNRC having sufficient conservatism for LBLOCA
analyses.The minimum number of sampled cases is given by Wilks’
formula for one-sided tolerance limits. Beginning with the probability statement(1)P[F(xk)>β]=n!(k−1)!(n−k)!∫β1ξk−1(1−ξ)n−kdξ, where the P[F(xk)>β] is the “probability that the result from a
given sample case (F(xk))
exceeds the β percentile” case. When k=n, that is, the largest value of all of the samples, this relationship reduces to
(2)γ=1−βn, where β is the coverage, γ is the confidence, and n is the minimum number
of sampled calculations. For the 95/95 coverage/confidence condition, n=59. This means in a random sample of 59 calculations, one case,
the highest PCT case, will bound the 95/95 coverage/confidence condition for
PCT. A disadvantage of this method is that there may be significant
conservatism as a result of bounding the 95/95 condition. Applying Somerville’s
generalization of Wilk’s formula on nonparametric tolerance limits [64] can
improve the fidelity in the final result through the performance of additional
calculations.Each calculation is setup by first sampling every LBLOCA
uncertainty contributor over its derived range. A minimum of 59 calculations
are performed. The PCT results from each calculation are sorted to identify the
highest PCT. The highest PCT result from 59 calculations bounds the 95/95
condition.Included in the AREVA NP RLBLOCA methodology, topical reports are sample
problems demonstrating application of this methodology on both a 3- and
4-loop Westinghouse pressurized water reactor. Some results from the 3-loop
sample problem were presented in [65], which culminated in a PCT of 1853°F. For
this problem, more than 30 uncertainty parameters were statistically treated
using a Monte Carlo sampling procedure for the creation of 59 code input file
sets. Each set included four input files describing models for the fuel
performance evaluation, thermal-hydraulic steady-state initialization,
thermal-hydraulic transient response, and simultaneous containment response.The final step in the CSAU process
is to identify the total uncertainty. If any PCT gains or penalties were
identified during the CSAU process, they are to be applied in Step 14. In
addition, the total uncertainty can be quantified relative to a “best-estimate”
figure-of-merit. The total uncertainty does not have meaning in relationship to
regulatory acceptance criteria. As such, the importance of this measure is
somewhat diminished from what the TPG originally envisioned. AREVA NP chose to define
total uncertainty using the 50/50 condition, also evaluated from nonparametric
statistics. The 50/50 condition is provided by the calculation providing(n+1)/2 for an odd-numbered sized sample space. For the sample
problem, the 50/50 condition was identified as 1500°F; hence, the 95/95
condition represents about 350°F uncertainty.


## 4. Regulatory Review

The unwritten “Element 4” in the CSAU process is the USNRC
regulatory review process. This process spanned over 20 months and required 139
formal “requests for additional information.”
Plant-specific elements of the generic review were addressed for the
first application and an additional 12 months and approximately 30 RAIs were
required. The bulk of the review focused on the explicit definition of the range
of applicability for the key LBLOCA phenemological and plant parameters. This
was provided following the methods previously discussed in the Element 2
section. In addition, the USNRC requested technical basis supporting the
treatment of fuel relocation, downcomer boiling and rod-to-rod radiation–phenomena not appearing on the AREVA NP PIRT. AREVA
NP responded to these concerns by supplying new sensitivity results and/or
detailed characterization of how the existing model was adequate.


## 5. Conclusion

The AREVA NP RLBLOCA methodology is a CSAU-based methodology
for performing best-estimate large-break LOCA analysis. The methodology
addresses all of the expressed steps of the CSAU process. The key challenge to
this process has been the defense of declared engineering judgment and the
demonstration of the methodologies range of applicability. This was
accomplished by careful characterization of dominant LOCA parameters and
emphasis on validation through sensitivity studies and the statistical nature
of the methodology.The generic AREVA NP RLBLOCA methodology was approved by the
USNRC in April 2003 and is now being applied to several nuclear power plants
serviced by AREVA NP Inc. While the CSAU
methodology represents a significant departure from traditional deterministic
methods, the AREVA NP methodology applying nonparametric statistics retains an
economical viability on par with existing methodologies. Throughout the 40+
staff-years of development effort at AREVA NP, the CSAU process has withstood
the technical questions and challenges to its foundation. The key benefits
realized by AREVA during this development are(i)
The move to a realistic
LOCA methodology brings a new clarity of understanding of the LBLOCA problem to
the industry by demonstrating contrast to the very conservative 10 CFR 50
Appendix K methodologies.(ii)
Through use of
statistically-based methods, there is improved characterization of the
conditions in which individual LBLOCA uncertainty contributors influence LBLOCA
response.(iii)
The reliance on
experimental data has revived the importance of the many test programs that
have long since been decommissioned.These rewards alone have validated the CSAU approach.



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*Source: 239718-2008-03-13.xml*