Fresh look from the back-end [what kinds of reactor parameters we need for the transient modeling]

Evgeny Ivanov

Items to be discussed

• General remarks, questions & reasoning

• Conservative values appearance with best-estimated calculations and uncertainty estimation

• Codes and models qualification

• Algorithms are usually used and dimension reduction

• General analysis through DiD principles

• Accidental state and CDI concept

• The most penalized concept

• Conclusions

Performance-based regulation

▌ A regulatory approach that focuses on desired, measurable outcomes, rather than prescriptive processes, techniques, or procedures. Performance-based regulation leads to defined results without specific direction regarding how those results are to be obtained. At the NRC, performance-based regulatory actions focus on identifying performance measures that ensure an adequate safety margin and offer incentives for licensees to improve safety without formal regulatory intervention by the agency.

3/20

Adding value through knowledge

Basic data uncertainty

(XS covariance data)Basic data uncertainty

(XS covariance data)

DiscretizationDiscretization

simplifications simplifications

coupling couplingR

efe

rent

calc

ula

tions

from static to transient

TSO specific needs in reactor’s physics

modelingTOOLS

▌ world mainstream of tools => complex, powerful, universal;

▌ quality control =>culture and special approaches;

▌ principles of DIS => level of maturity must be enough high;

RESULTS: Conservative values

▌ models and codes => best estimated;

▌ simplifications => to be addressed;

▌ uncertainties & discrepancies => to be propagated and associated with safety margins;

NOTE:

▌ To be applied any tool should be qualified for TSO specific needs

Logic Flow Diagram of

Defense in Depth

Source term conservative estimation & ultimately worst

consequences

Analysis of an accuracy of reactor parameters prediction, estimation of

a balance of reactivity etc

Control and monitoring system efficiency and sufficiency analysis

Simulation of an accidental events & analysis of safety measures

capabilities

Simulation of an accidental coupled process & analysis of loads on

barriers

Levels 1÷3

Prevention of abnormal operation;

Control of abnormal operation and detection failures;

Control of Accidents within the Design Basis

▌ Evaluation of the reactor parameters

Criticality, reactivity balance, and coefficients;

control rod worth, power distribution and dpa

Burn-up, reactivity swing, doses and dpa Main kinetic parameters etc

▌ Validation of calculations and uncertainty analysis

Both experimental based benchmarks and precise calculations

Perturbation theory and simplification of transient models for S/U analysis

Association of uncertainties with “safety margins”

Neutronics tools:

ERANOS 2.2 => basic design oriented code

MORET5, MCNP6 => high accurate Monte-Carlo code

SCALE6 => high accurate Monte-Carlo code + sensitivity analysis

Benchmarks and referent calculations with:

MORET5, MCNPX => referent calculations

ERANOS 2.2 and SCALE 6 => sensitivity analysis for uncertainty propagation

IRPhE Handbook => benchmarks for validation of calculational tools

Parameters to be studied Qualification principles

Level 4

Control of severe plant conditions including prevention of

accident progression and mitigation of consequences of

Severe Accidents

▌ Multi-physics modeling Generation of the initial data for transient

analysis – effective XS generation; kinetic parameters and reactivity feedbacks evaluation

Reconstruction of transient power distributions

▌ Uncertainty propagation on transient parameters

Development of relevant benchmarks Simplification of processes for S/U analysis

Neutronics tools:

SIMMER-III (TWODANT) => coupled processes calculations

ERANOS 2.2 => XS generation and simplified models preparation

Benchmarks and referent calculations with:

ERANOS 2.2 and SCALE 6 => propagation of uncertainties came from the lacks of the physical data and from the simplifications

Parameters to be studied Qualification principles

MORET5 [IRSN] referent Monte-Carlo tool

Arbitrary 3D geometry MORET5, MCNP6, SCALE6

•Criticality calculations for all kinds of reactors

•Reactivity feedbacks analysis (including using of correlated trajectories)

•Point kinetic parameters calculations

•Multi-components spectra calculations,

power distribution

•[Sensitivity analysis with SCALE]

VESTA

•Depletion studies

•Source term estimation

Qualification procedure notes:

Precise and high accurate codes could be validated against evaluated experimentally based benchmarks

SCALE 6 M-C calculations and S/U analysis

•M-C high accurate

criticality/reactivity

study

•Burn-up and kinetic

parameters

calculations ( eff, )

•Sensitivity calculations

•XS uncertainty

propagation on KD, ,

eff,

•Benchmarks

evaluation, GLLSM

application for

qualification of tools

ERANOS 2.2 design oriented

codes’ package

Qualification procedure notes:

Tool was intended to be used in reactor physics analysis of Sodium Cooled Fast Reactors;

Code could be qualified trough validation against as other precise or high accurate (Monte-Carlo) codes as against experimentally based benchmarks

3D transient simulation with the process

oriented SIMMER tool

ts

shape step

reactivity step = fuel-pin heat transfer

fluid-dynamics step = amplitude projection

tr

tf

ts

tr

ts

ts

shape step

reactivity step = fuel-pin heat transfer

fluid-dynamics step = amplitude projection

tr

tf

ts

tr

ts

( , , , , ) ( ) ( , , , )t r z E N t t r z E

1 1 1

4V E t r

r

r r zt r z E E t r z E dEt SE( )

( ) ( )( , , , ' ) ( , , , ') 'z

zp

p f dd

IGD

d d

E

kt r z E t r z E dE E C

( )( , , , ') ( , , , ') ' ( )

4

1

400

1

)()()()(

)()()( 0

rntcrntf

rnv

rndt

tdf

asiias

eff

asas

Qualification procedure notes:

Reactor physics processes could be described roughly and should be adjustedby definition

Code could be qualified trough validation against high accurate other static or kinetic codes with calibrated uncertainties

IRSN Neutronics Codes’ Status

The Diagram of Codes and Models Qualification

1. Determining of the principal components responsible for expected errors, and Development of an application object to study of the processes of interest

2. Selection/development of errors’ propagation technique

3. Selection of relevant benchmarks

4. Performing of the S/U analysis

the application object

Calibration and S/U estimation

Errors’ propagation

Precise codes (MCNP etc)

Design oriented codes (ERANOS, DANTSYS etc)

Process oriented codes (SIMMER etc)

1

2

3

Problem oriented benchmarks’ library

International Handbook of Evaluated Reactor

Physics Benchmark Experiments (IRPhEP)

Evaluated parameters:

▌ keff

▌ Reactivity data,

▌ Power distribution,

▌ Reaction rates distribution,

▌ Spectra,

▌ Beta effective,

▌ and other important for reactor physics characteristics

“Extensively peer-reviewed set of reactor physics-related integral data that can be used by reactor designers and safety analysts to validate the analytical tools used to design next-generation reactors and establish the safety basis for operation of these reactors...”

Fast Systems:

BFS-1 (Russia)

ZPR, ZPPR (USA),

ZEBRA (UK)

JOYO (Japan),

SNEAK (Germany),

etc

Example: States and processes to be analyzed

Asymptotic= semi-static Transition

An accidental state concept for CDA

modeling accuracy

{ }

Qualification procedure notes:

How to associate the accidental configuration with available experimental (numerical) benchmarks?

Neutronics similarity could be done by so-called representativity factor;

But for TH and mechanic model Core Disruptive Index (CDI) could be used

CDI parameter as a criteria

core disruptive index (CDI) defined as volumetric

fraction of melted fuel and fuel particles was used as

parameter for definition of accidental configuration

Stages to be selected for CDA study

Sodium boiling off

Steel run off

Melted fuel collapse

core disruptive index (CDI) is a

volumetric fraction of melted fuel

and fuel particles

evaluated k eff bias

-0,5%

0,0%

0,5%

1,0%

1,5%

2,0%

0 0,1 0,2 0,3 0,4 0,5 0,6CDI

bias

Representativity factors

<(Sk-S0

k)TC (Sk-S

0k)>

Bias vs CDI

evaluated k eff bias

-0,5%

0,0%

0,5%

1,0%

1,5%

2,0%

0 0,1 0,2 0,3 0,4 0,5 0,6CDI

bias

CDI bias eff

0 0,00% 0,49% 0,327%

0,2 0,68% 0,48% 0,330%

0,3 0,31% 0,49% 0,329%

0,45 1,02% 0,48% 0,333%

0,65 1,34% 0,47% 0,359%

Benchmark-to-application

transition

1 2 3 4 50.03

0.02

0.01

0

0.01

bias ib ib

bias ib ib

0

ib

0 2 4 6 80.98

0.99

1

1.01

1.02

1.03

keffib

1

keffib

CORib

Z

keffib

INIib

Z

ib

...\W_CORR.csv

WCOR

...\P_CORR.csv

P

Several criticality

benchmarks data:

•keff

•keff

Application objects data

after benchmarks

discrepancies

propagation:

•keff

•keff

Uncertainty propagation approach

W

WCOR

Criticality analysis for generation of XS covariance matrices

k( FPu)

k( FU5)

k( FU8)

eff=REGR( 1, 1, 2, 2,…, n, n)

eff=REGR( 1, 1, 2, 2,…, n, n)

T=REGR( 1, 1, 2, 2,…, n, n)

Technique of selection of

benchmarks could be used only

after separation of all methodical

uncertainties (mesh, dimensions,

homogenization etc.)

Dimensions’ reduction for transient

models S/U analysis

0.00E+00

1.00E+09

2.00E+09

3.00E+09

4.00E+09

5.00E+09

6.00E+09

- 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Power shield

Power noshield

5.05GW

1.58GW

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.2 0.4 0.6 0.8 1

Dop

ple

r e

ffe

ct

(pcm

/°C

)

-420

-410

-400

-390

-380

-370

-360

-350

Void

Eff

ect

(pcm

/%)

SIMMER 100°

APOLLO 100°

SIMMER 400°

APOLLO 400°

SIMMER 600°

APOLLO 600°

SIMMER 800°

APOLLO 800°

SIMMER 20%

APOLLO 20%

0.760.750.66 0.720.46

Objective: validation of transient models against high accurate referent

calculations

Problem: only steady state (or partially decoupled) results are available

Solution: parametric studies with 3D coupled model and generation of

simplified (lumped model) for S/U analysis

IBRAE-IRSN Seminar on Sodium Fast Reactors, September 15-16, 2010

PHX (experienced) SFR (innovative)

An application object for Levels 1-3

[the most penalized configuration]

DISTRMARG

Phénix sodium worth distribution

Core without blankets, sodium worth distribution

SNR-300 sodium worth distribution

0

500

1000

1500

2000

1st Configuration 2nd Configuration

Rea

ctiv

ity

(p

cm)

The most penalizing area The fissile core

The core with plenum Total reactor

MPV +CORE + PLENUM BLANKET

SVR in the decision making

Void effects for sodium cooled monolithic reactors (core volume≈10m3)

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

40

SPX type ISFR (H/R=0,1)

Vo

id e

ffe

cts

(pcm

)

Core voided Core + Plenum voided TOTAL void effect

Ref. Slessarev, “Intrinsically secure fast reactors for long-lived waste free and proliferation resistant nuclear power”, Annals of Nuclear Energy Volume 35, Issue 4,

April 2008, Pages 636-646

Conservative way of studies =>

The most penalized configuration

Data supplying for SAS4A-like codes

12

34

56

78

910

1112

1314

1516

1718S

1

S3

S5

0,000E+00

2,000E-06

4,000E-06

6,000E-06

8,000E-06

1,000E-05

1,200E-05

1,400E-05

1,600E-05

1,800E-05

effect

layer number

derivation

1,600E-05-1,800E-05

1,400E-05-1,600E-05

1,200E-05-1,400E-05

1,000E-05-1,200E-05

8,000E-06-1,000E-05

6,000E-06-8,000E-06

4,000E-06-6,000E-06

2,000E-06-4,000E-06

0,000E+00-2,000E-06

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

S1 S3 S5

-8,000E-06

-7,000E-06

-6,000E-06

-5,000E-06

-4,000E-06

-3,000E-06

-2,000E-06

-1,000E-06

0,000E+00

1,000E-060,000E+00-1,000E-06

-1,000E-06-0,000E+00

-2,000E-06--1,000E-06

-3,000E-06--2,000E-06

-4,000E-06--3,000E-06

-5,000E-06--4,000E-06

-6,000E-06--5,000E-06

-7,000E-06--6,000E-06

-8,000E-06--7,000E-06

12

34

56

78

910

1112

1314

1516

1718

S1

S3

S5

-2,000E-05

-1,800E-05

-1,600E-05

-1,400E-05

-1,200E-05

-1,000E-05

-8,000E-06

-6,000E-06

-4,000E-06

-2,000E-06

0,000E+00

2,000E-06

effect dK/K/kg

layer number

derivation

0,000E+00-2,000E-06

-2,000E-06-0,000E+00

-4,000E-06--2,000E-06

-6,000E-06--4,000E-06

-8,000E-06--6,000E-06

-1,000E-05--8,000E-06

-1,200E-05--1,000E-05

-1,400E-05--1,200E-05

-1,600E-05--1,400E-05

-1,800E-05--1,600E-05

-2,000E-05--1,800E-05

dK/K/kg (MOX) dK/K/kg (SS) dK/K/kg (Na)

12

34

56

78

910

1112

1314

1516

1718

S1

S3

S5

-3,500E-04

-3,000E-04

-2,500E-04

-2,000E-04

-1,500E-04

-1,000E-04

-5,000E-05

0,000E+00

effect dK/K/kg

layer number

derivation

-5,000E-05-0,000E+00

-1,000E-04--5,000E-05

-1,500E-04--1,000E-04

-2,000E-04--1,500E-04

-2,500E-04--2,000E-04

-3,000E-04--2,500E-04

-3,500E-04--3,000E-04

12

34

56

78

910

1112

1314

1516

1718

S1

S3

S5

-3,000E-04

-2,500E-04

-2,000E-04

-1,500E-04

-1,000E-04

-5,000E-05

0,000E+00

effect dK/K/kg

layer number

derivation

-5,000E-05-0,000E+00

-1,000E-04--5,000E-05

-1,500E-04--1,000E-04

-2,000E-04--1,500E-04

-2,500E-04--2,000E-04

-3,000E-04--2,500E-04

KD (with coolant) KD (voided)

Example: SVR in the 2-nd zone

1

1 1

1 1

1

1

1

1

1

1

1 1

1 1 1 1

1 1

1

1

1

1

1

1

1

11

11

2 2 2 2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2 2 2 22

2

2

2

2

2

2

2

2

2

2

2

3 3 3 3 3

33

3

3

3

3

3

3

3

3

3

3

3

3

3 3 3 3 3

3

3

3

3

3

3

3

3

3

3

3

3

1

2

ABR Metallic-Fuel Core

3

Voided S.A.

= ai i+ bij i j

i is a volumetric part of void

ai, bij are coefficients to be found

Example: SVR in the 2-nd zone results

351.3 514.4 -695.7

514.4 162.1 -157.3

-695.7 -157.3 -110.7

The matrix of “interference”

= ai i+ bij i j

ai, bij are the discrepancies

ai

1 351.3 351.3

2 162.1 162.1

3 -110.7 -110.7

1-2 518.7 2.65

1-3 230.9 -4.84

2-3 50.9 -0.247

1-2-3 351.3 416.3

KD for voided vs non-voided core

Core 1 Core 2 KD, pcm

non-voided non-voided -268.7

voided non-voided -87.8

non-voided non-voided -157.6

voided voided -4.0

Sheet to be included => total Doppler constant for cases w/w/o voids

Conclusions & complementary calculations

▌ The needs in calculations should be specified from the “back-

end” (=transient analysis needs)

▌ Spatial void effect distribution (by sub-assembly layers) to feed

the SAS4A-kind calculations (CATHAR-LM and so on)

▌ KD for voided and non-voided cores separately

▌ Effective delayed neutron fraction by nuclides, neutron

generation lifetime

▌ Spatial power and materials’ worth distribution [for simplified

analysis with Bete-Tait or Nordheim-Fuchs models]

▌ The SVR for the most penalized area and configuration of the

area

Adjustment procedure, matrices evolution

)()( 112 HPkUHPkPWPS tt

kUHHUHWP tt 1111 )(

111 )( HUHWW t

tprior DWDkappl

DPkappltposter DWDk

appl

Two Points’ Lumped Parameters Model

The solution with more than one exponent appears with : Fourier decomposition, or the multi-point coupled kinetics

The spatial effect appears with multi-exponential prompt neutrons density decay

Decomposition of SNEAK 7A Model

I

II

Core

Reflector

C-R I-II

Noise Measurements

Reproduction

(Using Two-Point Kinetic

Model)

Only prompt neutrons are “seen” by detector

Prompt neutrons sub-criticality

Decomposition of SNEAK 7B Model

Core

Reflector

I

II

C-R I-II

Results

corecoreCfrec

- calculated with the two-point kinetic models

corecoresyssysnoisecorrnoise,