Testing the EPRI Reactivity Depletion Decrement

Testing the EPRI Reactivity Depletion Decrement

Uncertainty Methodsby

Elliot M. Sykora

B.S. Physics, Massachusetts Institute of Technology (2014)

Submitted to the Department of Nuclear Science and Engineering

in partial fulfillment of the requirements for the degree of

Master of Science in Nuclear Science and Engineering

at the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

September 2015

c�Massachusetts Institute of Technology 2015. All rights reserved.

Author ........................................................................................................................

Department of Nuclear Science and EngineeringAugust 12, 2015

Certified by ................................................................................................................

Kord SmithKEPCO Professor of the Practice of Nuclear Science and Engineering

Thesis Supervisor

Certified by ................................................................................................................

Benoit ForgetProfessor of Nuclear Science and Engineering

Thesis Reader

Accepted by ................................................................................................................

Chair, Department Committee on Graduate Students

1

Testing the EPRI Reactivity Depletion Decrement

Uncertainty Methodsby

Elliot M. Sykora

Submitted to the Department of Nuclear Science and Engineeringon August 12, 2015, in partial fulfillment of the

requirements for the degree ofMaster of Science in Nuclear Science and Engineering.

AbstractAn EPRI study[1], published in 2011, used measured flux map data (taken over 44operational cycles of the Catawba and McGuire nuclear power plants) to determinefuel assembly reactivity decrements versus burnup. The analytical techniques usedto infer measured assembly reactivities required perturbation calculations using 3Dnodal diffusion core models. Subsequently, questions have arisen within the NuclearRegulatory Commission (NRC) as to potential uncertainties in measured assemblyreactivity decrements that might have arisen from approximations of the 2-groupnodal methods and perturbation techniques employed. Subsequently, Gunow[2] usedfull-core, multi-group, neutron transport models to replace the nodal diffusion coremodels, and he demonstrated that measured reactivity decrements were independentof the core model. In this thesis, two cycles of the BEAVRS PWR reactor benchmarkare used to test the EPRI methodology, now including testing of not only the nodalcore diffusion model, but also the perturbation technique itself. By changing the per-turbation technique from assembly reactivity to assembly-average fuel temperature,it is demonstrated that measured reactivity decrements are almost independent of theperturbation technique - with a level of precision greater then the 250 pcm reactivitydecrement uncertainty assigned in the EPRI study. These new results demonstratethat the reactivity decrements and uncertainties derived by nodal diffusion and bur-nup perturbation in the original EPRI study hold up to further scrutiny, and theyremain credible for licensing application of burnup credit in Spent Fuel Pool (SFP)criticality analysis.

Thesis Supervisor: Kord SmithTitle: KEPCO Professor of the Practice of Nuclear Science and Engineering

Thesis Reader: Benoit ForgetTitle: Professor of Nuclear Science and Engineering

2

Acknowledgments

I would like to express my gratitude to my research advisor Professor Kord Smith for

the useful comments, remarks and engagement through the learning process of this

master’s thesis. Furthermore, I would like to thank Professor Benoit Forget for his

support throughout this project and for introducing me to the topic. Also, I would

like to thank Geoff Gunow for providing assistance in building the SIMULATE-3

and CASMO-5 models. This work was supported by the Electric Power Research

Institute.

3

Contents

1 Introduction 16

2 Background 18

2.1 Description of Method of Characteristics . . . . . . . . . . . . . . . . 18

2.2 Description of Nodal Methods . . . . . . . . . . . . . . . . . . . . . . 20

3 Methods and Measurement Data 23

3.1 Descriptions of Full Core Modeling . . . . . . . . . . . . . . . . . . . 23

3.2 BEAVRS Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.1 Cycle 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2.2 Cycle 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Generating Tilt Corrected Data . . . . . . . . . . . . . . . . . . . . . 29

3.4 Setup of the Gap Test . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.5 Standard Model Considerations . . . . . . . . . . . . . . . . . . . . . 32

3.5.1 HFP Approximations & Influence on Results . . . . . . . . . . 32

3.5.2 CASMO-5 MxN Considerations . . . . . . . . . . . . . . . . . 35

3.6 Methods to Infer Reactivity Decrement Uncertainties . . . . . . . . . 35

4 Tilt Correction, Gap Test, and Early Cycle Results 41

4.1 Results of Tilt Corrected Data . . . . . . . . . . . . . . . . . . . . . . 41

4.2 Gap Test Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2.1 Magnitude of Simulated Tilt . . . . . . . . . . . . . . . . . . . 43

4.2.2 HZP Comparisons to Calculations . . . . . . . . . . . . . . . . 45

4.2.3 HFP Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5 Standard Model HFP Results 60

5.1 HFP results Cycle 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.2 HFP results Cycle 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4

6 Inferring Reactivity Decrements Results 65

6.1 Reporting Results in Reactivity . . . . . . . . . . . . . . . . . . . . . 65

6.2 Perturbing Sub-batch Burnup in SIMULATE-3 and CASMO-5 MxN 68

6.2.1 Cycle 1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.2.2 Cycle 2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.3 Perturbing Burnup vs Fuel Temperatures in CASMO-5 MxN . . . . 75

6.3.1 Cycle 1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.3.2 Cycle 2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.4 Summary of Calculated Reactivity Decrements . . . . . . . . . . . . . 84

7 Summary 86

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

References 88

8 Appendix 89

8.1 Detailed Maps of the Full Cycle Depletion Points . . . . . . . . . . . 89

8.1.1 CASMO-5 MxN Cycle 1 . . . . . . . . . . . . . . . . . . . . . 89

8.1.2 CASMO-5 MxN Cycle 2 . . . . . . . . . . . . . . . . . . . . . 99

8.1.3 SIMULATE-3 3D Cycle 1 . . . . . . . . . . . . . . . . . . . . 109

8.1.4 SIMULATE-3 3D Cycle 2 . . . . . . . . . . . . . . . . . . . . 119

5

List of Figures

2.1 The picture on the left shows the unique material regions in an assem-

bly such as fuel, cladding, and coolant. The picture on the right shows

how these regions are discretized into source regions. [3] . . . . . . . . 20

2.2 SIMULATE-3 radial discretization for the quarter core model. There

are four nodes per assembly. [2] . . . . . . . . . . . . . . . . . . . . . 22

3.1 BEAVRS Cycle 1 layout of fuel assemblies showing the assembly en-

richment distribution by color and the burnable poison locations by

number. [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2 Scale view of burnable poison pins in cycle 1. [4] . . . . . . . . . . . . 27

3.3 BEAVRS Cycle 2 fresh fuel enrichment locations shown in color, burn-

able poison positions in the fresh fuel are labeled by number, and the

once burned shuffled assemblies are labeled by their cycle 1 locations. [4] 28

3.4 CASMO-5 MxN HZP minus BEAVRS Data. RMS is 0.0498. . . . . . 30

3.5 Full power points (above 80% power) used in cycle depletion. The List

of full power points here (in GWd/T) are 0.88, 1.02, 1.51, 2.16, 3.30,

4.61, 6.49, 7.51, 8.70, 9.80, 11.08, 12.34, 12.92. We do not use the 9.80

GWd/T data because the measurement occurred when the reactor was

at full power for a very brief period. . . . . . . . . . . . . . . . . . . . 34

3.6 Full power points used in cycle depletion. The list of full power points

here (in GWd/T) are 1.14, 1.4, 2.11, 3.20, 4.04, 5.23, 6.52, 7.71, 8.73,

9.36, 10.43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.7 Reactivity of an assembly with 2.4% enriched fuel and 12 burnable

poisons as a function of burnup. . . . . . . . . . . . . . . . . . . . . . 38

3.8 exposure reactivity coefficient of an assembly with 2.4% enriched fuel

and 12 burnable poisons as a function of burnup. . . . . . . . . . . . 39

3.9 The temperature reactivity coefficient of an assembly with 2.4% en-

riched fuel and 12 burnable poisons as a function of temperature at a

beginning, middle, and end of cycle statepoint. . . . . . . . . . . . . . 40

6

4.1 Planar peripheral assembly fractional tilt of measured fission rates for

cycle 1. Positive tilt in the x direction means that the measurements

were higher on the east side of the core. Positive tilt in the y direction

means that the measurements were higher on the south side of the core. 42

4.2 Planar peripheral assembly fractional tilt of measured fission rates for

cycle 2. Positive tilt in the x direction means that the measurements

were higher on the east side of the core. Positive tilt in the y direction

means that the measurements were higher on the south side of the

core. Cycle 2 has a very small tilt at BOC and it too goes away with

depletion. Early Cycle 1 displays the only truly significant tilts. . . . 43

4.3 HZP CASMO-5 MxN with a 0.5 cm southeast gap minus no gap shows

the distribution of tilt. The top number shows the fission rates of the

gap case. The next line shows the fractional difference of the gap minus

no gap case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.4 CASMO-5 MxN HZP minus BEAVRS Data. RMS is 0.0498. . . . . . 46

4.5 CASMO-5 MxN HZP minus tilt corrected data. RMS is 0.0149. . . . 47

4.6 CASMO-5 MxN HZP Manual Baffle with a 0.5cm Gap minus BEAVRS

Data. RMS is 0.0282. . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.7 CASMO-5 MxN HFP 1.02 GWd/T Manual Baffle with No Gap minus

BEAVRS Data. RMS is 0.0306. . . . . . . . . . . . . . . . . . . . . . 50

4.8 CASMO-5 MxN HFP 1.02 GWd/T with a 0.5 cm southeast gap minus

no gap shows the distribution of tilt. The top number shows the fission

rates of the gap case. The next line shows the fractional difference of

the gap minus no gap case. . . . . . . . . . . . . . . . . . . . . . . . 51

4.9 CASMO-5 MxN HFP 1.02 GWd/T Manual Baffle with 0.5 cm gap

minus BEAVRS Data. RMS is 0.0305. . . . . . . . . . . . . . . . . . 52



7





4.12 CASMO-5 MxN HFP 2.16 GWd/T Manual Baffle with 0.5 cm gap

minus BEAVRS Data. RMS is 0.0225. . . . . . . . . . . . . . . . . . 55







4.15 CASMO-5 MxN HFP 3.3 GWd/T Manual Baffle with 0.5 cm gap minus


5.1 Normalized fission rate RMS error of CASMO-5 MxN and SIMULATE-

3 2D vs BEAVRS data and tilt corrected data in cycle 1. Data is folded

into an octant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.2 Normalized fission rate RMS error of SIMULATE-3 2D and SIMULATE-


into an octant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3 Normalized fission rate RMS error of CASMO-5 MxN and SIMULATE-


to quarter core. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.4 Normalized fission rate RMS error of SIMULATE-3 2D and SIMULATE-


to quarter core. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

8

6.1 RMS difference of CASMO-5 MxN compared to BEAVRS data for the

2.4% enriched fuel sub-batch in Cycle 1. The sub-batch reactivity was

perturbed via changing the sub-batch exposure as shown on the x-axis.

The circle represents the initial unperturbed point. . . . . . . . . . . 66


2.4% enriched fuel sub-batch in Cycle 1. The sub-batch reactivity was

perturbed via changing the sub-batch fuel temperature as shown on

the x-axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.3 RMS difference of CASMO-5 MxN compared to BEAVRS data for

the 2.4% enriched fuel sub-batch in Cycle 1. The sub-batch reactivity

(represented in pcm) was perturbed via changing the sub-batch fuel

temperature in three cases and via changing the sub-batch exposure in

three cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.4 RMS difference of CASMO-5 MxN and SIMULATE-3 compared to

BEAVRS data for the 2.4% enriched fuel sub-batch in Cycle 1. The

sub-batch reactivity (represented in pcm) was perturbed via changing

the sub-batch exposure. . . . . . . . . . . . . . . . . . . . . . . . . . 70






BEAVRS data for the 3.1% enriched fuel sub-batch in Cycle 1 while

starting from the optimal perturbation point of the 2.4% enriched sub-

batch. The sub-batch reactivity (represented in pcm) was perturbed

via changing the sub-batch exposure. . . . . . . . . . . . . . . . . . . 72

9










BEAVRS data for the fresh, 3.2% and 3.4% enriched, fuel sub-batch in

Cycle 2. The sub-batch reactivity (represented in pcm) was perturbed

via changing the sub-batch exposure. . . . . . . . . . . . . . . . . . . 75





three cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78





three cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79


the 3.1% enriched fuel sub-batch in Cycle 1 while starting from the

optimal perturbation point of the 2.4% enriched sub-batch. The sub-

batch reactivity (represented in pcm) was perturbed via changing the

sub-batch fuel temperature in three cases and via changing the sub-

batch exposure in three cases. . . . . . . . . . . . . . . . . . . . . . . 80

10





three cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82





three cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83


fresh, 3.2% and 3.4% enriched, fuel sub-batch in Cycle 2. The sub-

batch reactivity (represented in pcm) was perturbed via changing the

sub-batch fuel temperature in three cases and via changing the sub-

batch exposure in three cases. . . . . . . . . . . . . . . . . . . . . . . 84

8.1 The difference in fission rates of CASMO-5 MxN compared to BEAVRS

data at 1.02 GWd/T exposure in Cycle 1. The RMS difference is 0.0227. 89













11










data at 2.11 GWd/T exposure in Cycle 2. The RMS difference is 0.0213.100

















8.21 The difference in fission rates of SIMULATE-3 3D compared to BEAVRS


12





























13











14

List of Tables

2.1 Variables in the neutron transport equation. . . . . . . . . . . . . . . 19

3.1 CASMO-5 MxN Simulation Parameters. . . . . . . . . . . . . . . . . 35

6.1 Summary Table of exposure reactivity coefficients and temperature

reactivity coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.2 Inferred Fuel Batch Reactivity Bias by perturbing sub-batch burnup in

SIMULATE-3 and sub-batch burnup and fuel temperature in CASMO-

5 MxN. The differences in the biases inferred by the two methods is

shown in the far right columns. . . . . . . . . . . . . . . . . . . . . . 85

15

1 Introduction

The storage of spent nuclear fuel is an important issue in the nuclear industry. Since

no long term storage solution has been approved in the United States, the utilities

must continue to safely use spent fuel pools (SFP) and dry casks for storage. Crit-

icality analyses of these storage methods rely on lattice physics codes to accurately

predict nuclide inventories in each spent fuel assembly. Current procedures for defin-

ing the uncertainty in these calculations follow the NRC Kopp Memo which directs

analysts to add 5% of the calculated reactivity decrement to compensate for deple-

tion uncertainties.[1] The technical basis for the Kopp Memo was simply engineering

judgment of the SFP criticality analyses. Given the improvements in methods used in

SFP criticality analysis, a firm technical basis for the Kopp Memo criteria is desired

by the NRC. Doing so will help maintain the desired safety margin while not being

unnecessarily conservative. An unnecessarily conservative safety margin will increase

spent fuel storage costs, making nuclear power less competitive without improving

safety.

In 2011, EPRI sponsored a study focused on experimental quantification of PWR

fuel reactivity burnup decrement uncertainties. The reactivity decrement is defined as

the difference between the fuel assembly k-infinity at zero burnup and the k-infinity

at the calculated exposure point. The study used the Studsvik Core Management

System (CMS) suite to simulate core behavior, and used measured data from 44

PWR operating cycles from Catawba and McGuire nuclear power plants.[1] The EPRI

study used nodal methods (SIMULATE-3) to analyze the reactivity decrement biases,

but inherent assumptions in nodal methods may introduce biases and uncertainties.

Gunow’s thesis [2] quantified the bias introduced by nodal methods by comparing

reactivity decrements derived with nodal methods to multi-group transport methods,

which have far fewer assumptions. Specifically, he used a method of characteristics

(MOC) solver to solve the neutron transport equation. He approximated reactivity

decrement biases by perturbing fuel sub-batch reactivities by changing the exposure

of all assemblies in a sub-batch. [2] Gunow’s study modeled the BEAVRS PWR

16

and used in-core flux map data to compare the reactivity decrements inferred with

different core simulation tools.

To strengthen the confidence in these results, Gunow suggested three follow-on

tasks:

1) Improving thermal hydraulic modeling is needed in a full core MOC solver.

2) Comparing 3D nodal and transport methods.

3) Investigating different methods for perturbing sub-batch reactivity.

The Studsvik MOC solver does not have thermal hydraulic feedback and 3D transport

methods are still too computationally cumbersome.

The main goal of this study is to approximate reactivity decrement biases by

perturbing fuel sub-batch reactivities using fuel temperature. This method of ap-

proximating reactivity decrement biases would provide evidence that biases are inde-

pendent of the perturbation method. This study will supplement the EPRI work by

using different methods to test results and assumptions. The relationship between

fuel temperature and reactivity is found to be even more stable than that of fuel

burnup and reactivity particularly at the beginning of the cycle because burnable

poison depletion competes with fuel depletion when burnup perturbation was em-

ployed. Additionally, this study will investigate the tilt observed in the measured

data in order to better understand its cause and improve comparison to simulations.

The BEAVRS data is not symmetric which is probably caused by some asymmetry

in reactor fabrication or loading of the fuel assemblies. The asymmetry in the data

cannot be explained by neutron detector uncertainties alone. A new mechanism will

be proposed which simulates one potential cause of the tilt in the theoretically sym-

metric reactor. The preliminary work in this thesis is needed to independently verify

Gunow’s reactivity decrement biases that were based on perturbing the exposure of

sub-batches.

17

2 Background

As in the EPRI study, the Studsvik CMS codes were used for simulation.[1] In order

to understand how the core simulations are performed, we need to understand the

various methods used in the Studsvik CMS codes used in this study. The Studsvik

CMS codes used were SIMULATE-3, CMSLINK, CASMO-5 and its extension to full

core 2D modeling, CASMO-5 MxN. CASMO-5 is a lattice depletion code based on

MOC, SIMULATE-3 is a nodal code, and CMSLINK is a linking code that takes

CASMO-5 data and constructs a cross section library for SIMULATE-3. Section 2.1

contains a brief description of the method of characteristics (MOC) while Section 2.2

describes nodal diffusion methods. A more detailed explanation of MOC and nodal

methods can be found in Gunow’s thesis.[2]

2.1 Description of Method of Characteristics

The method of characteristics is a method of solving partial differential equations.

Specifically we want to apply it to the neutron transport equation which is described

in Eq. 2.1.

~⌦ ·r (~r, ~⌦, E) + ⌃T (~r, E) (~r, ~⌦, E) =

1Z

0

dE0Z

4⇡

d ~⌦0⌃S(~r, ~⌦0 ! ~⌦, E 0 ! E) (~r, ~⌦0, E 0)

= +�(~r, E)

4⇡keff

Z 1

0

dE 0⌫⌃F (~r, E 0)

Z

4⇡

d ~⌦0 (~r, ~⌦0, E 0)

(2.1)

18

Variable Description~r Spatial position vector~⌦ Angular direction vectorE Neutron Energy Angular neutron fluxkeff Effective neutron multiplication factor⌃T Neutron total cross section⌃S Neutron scattering cross section⌃F Neutron fission cross section� Energy spectrum of neutrons from fission⌫ Number of neutrons per fission

Table 2.1: Variables in the neutron transport equation.

This equation assumes that there is an isotropic distribution of emitted fission

neutrons and that there are no neutron-neutron collisions.

The equation is stated for continuous cross section, however, for the MOC calcu-

lation used in CASMO-5, one needs to use discrete multi-group cross sections. To

collapse continuous energy cross sections to group cross sections, one must specify

the energy interval for each neutron energy group. Then we can calculate the average

cross section over each energy interval weighted by the neutron scalar flux in order

to preserve reaction rates.

MOC is an iterative method that tracks angular flux in discrete directions over

the entire domain. These tracks cover the entire geometry that is sub-divided into

source regions. The neutron source, composed of in-scattering and fission, is assumed

to have a certain shape in a source region, such as a flat spatial distribution. Each

track segment contained in a source region contributes to that region’s scalar flux.

MOC needs very fine spacing and a large number of angles to cover the geometry with

a dense angular distribution and a fine enough mesh of neutron sources to account

for the flux gradients. Figure 2.1 shows how the unique materials in an assembly are

finely discretized into source regions.

19

Figure 2.1: The picture on the left shows the unique material regions in an assemblysuch as fuel, cladding, and coolant. The picture on the right shows how these regionsare discretized into source regions. [3]

2.2 Description of Nodal Methods

Nodal diffusion methods are a significant simplification of the neutron transport meth-

ods. However, they can have high accuracy and computational efficiency when con-

sistently formulated. Nodal methods avoid the explicit modeling of heterogeneous

regions by treating large nodes, such as a radial plane of an assembly, as a homo-

geneous region. These methods assume that the angular distribution of neutrons

are at most linearly anisotropic, which may not accurately describe angular distri-

butions that are near high absorbing or scattering regions. However, an equivalent

diffusion theory parameter, such as an assembly discontinuity factor (ADF), can be

computed for each homogeneous region that approximately captures the effect of the

truly heterogeneous geometry.

Nodal methods solve the 3D diffusion equation by transverse integrating over two

directions, thus leaving a set of coupled 1D diffusion equations. Higher-order or even

20

analytical spatial solutions are then used to solve each 1D diffusion equation. With

approximations to capture the effects of xenon, fuel temperature, and cross sections

between nodes, the coupled 1D equations can be solved accurately.

Nodal methods reduce the runtimes of a full core depletion by orders of magni-

tudes, but this method also introduces new assumptions. The nodal method relies on

2-group cross section data which may not describe neutronic behavior as accurately

as a full-core multi-group MOC calculation and must be generated by numerous 2D

lattice calculations using an MOC code. The nodal method also uses a coarse radial

discretization, with one node per quarter assembly shown in Figure 2.2. This study

evaluates the uncertainty on fuel assembly reactivity introduced by nodal methods as

compared to the full-core multi-group MOC transport method calculations.

21

Figure 2.2: SIMULATE-3 radial discretization for the quarter core model. There arefour nodes per assembly. [2]

22

3 Methods and Measurement Data

3.1 Descriptions of Full Core Modeling

Two models are used to calculate full core depletions: the nodal method and the 2D

MOC transport method. In this study, SIMULATE-3 is used as the nodal diffusion

code, and CASMO5 MxN as the full core MOC code. Each code can produce sim-

ulated fission rates that can be compared to measured data. The root-mean-square

(RMS) error of the fractional difference of simulated fission rates to measured fission

rates is used to summarize the accuracy of the model at a given statepoint. This is

needed to infer reactivity decrement bias by searching for assembly reactivity changes

that produce best agreement between measured and computed fission rates.

First, a standard library of a multi-group cross sections needs to be computed.

Nuclear data for use in CASMO-5 is collected from ENDF-B/VII data and contains

microscopic cross sections in 586 energy groups that are functions of material tem-

perature and background cross sections. CASMO-5 calculations condense the cross

sections to a few groups. Next, the neutron transport problem is solved for each

unique assembly using the few group cross sections using the 2D method of charac-

teristics (MOC). In this case, the group structure has 19 energy groups ranging from

10�5 eV to 20 MeV. This range covers a few groups for fast neutrons, and a significant

number of groups in the resonance region and thermal region.

Each unique assembly is simulated at various reactor conditions by varying fuel

temperature, moderator temperature, and boron concentration. Unique assemblies

are also modeled with a baffle and barrel present to produce radial and axial reflec-

tor data. This yields accurate two-group cross sections with assembly discontinuity

factors (ADFs) that are used by SIMULATE-3 to solve the full-core simulation.

CASMO-5 MxN takes orders of magnitude longer to solve the problem, but does so

with many fewer assumptions than the nodal method. This MOC solver eliminates the

diffusion approximation and it has increased spatial resolution and increased energy

resolution. The spatial resolution is increased by 2 or 3 orders of magnitude from

23

SIMULATE-3 and the energy resolution is increased from 2 groups to 35 groups. Since

CASMO-5 MxN does not have thermal hydraulic feedback, the thermal hydraulic

behavior is extracted from nodal results and input into CASMO-5 MxN cases for a

more realistic comparison.

These steps were followed to produce SIMULATE-3 2D results:

• Run CASMO-5 with the ’S3C’ edit for each unique assembly in order to create

two group cross sections and ADFs.

• Use the library created from CASMO-5 for a SIMULATE-3 3D calculation.

• For cycle 1, use the core axial buckling terms produced in the 3D calculation

for a SIMULATE-3 2D calculation.

• For cycle 2, the average core axial buckling term (as a function of core-averaged

burnup) from cycle 1 is mapped onto individual assembly burnups to produce

local assembly bucklings for a SIMULATE-3 2D calculation.

These steps were followed to produce CASMO-5 MxN results:

• Extract axially collapsed fuel and moderator temperature maps at every state-

point produced by the SIMULATE-3 3D calculation and place them into the

CASMO-5 MxN input file. The 3D results produce the most accurate temper-

ature maps.

• For cycle 1, compute the average core axial buckling term produced in the

SIMULATE-3 3D calculation and place this into the CASMO MxN input file.

• For cycle 2, the average core axial buckling term (as a function of core-averaged

burnup) from cycle 1 is mapped onto individual assembly burnups to produce

local assembly bucklings for a CASMO-5 MxN calculation.

24

3.2 BEAVRS Benchmark

Any full core model needs to be compared to a detailed and relevant benchmark

to validate its methods. The results of various CASMO-5 MxN and SIMULATE-3

simulations are compared against the BEAVRS benchmark to evaluate errors caused

by underlying assumptions in each program/method.

This benchmark specifies the radial geometry of each pin type used throughout

the core. It also specifies the configuration of these pin within an assembly, including

various configurations of burnable absorbers. On an assembly level, the benchmark

describes the locations of the various enriched assemblies, the locations of the instru-

ment tubes and control rod banks. Finally, the dimensions of the baffle, core barrel,

and neutron shield pads, as well as, all the material properties are specified in the

benchmark. Parameters that can change from cycle 1 to cycle 2 are discussed in this

section.

The benchmark has measured fission rates from 235U fission chambers from two

operating cycles of a PWR. The axial distribution of computed fission rates is axially

integrated into a 2D radial fission rate map to compare with the measured data in

each cycle. Since the measured fission rates are only known at the assemblies with an

instrument tube (58 locations), the simulated fission rates are renormalized to match

the sum of the 58 measured signals at these locations.

3.2.1 Cycle 1

Cycle 1 of the BEAVRS benchmark begins with all fresh fuel with enrichments of 1.6%,

2.4%, and 3.1% 235U fuel (by weight). The initial isotopic distribution is known with

high confidence because it is specified in the manufacturing of the fuel. Notice in

Figure 3.1 that the sub-batches of enriched assemblies are octant symmetric. Other

than the instrument tubes, the core is octant symmetric. These few instrument tubes

will not change the fission rate distribution significantly.[2] Since the core is loaded

octant symmetric, cycle 1 can be calculated in quarter core with either rotation or

reflected boundary conditions.

25

The burnable poisons are made of borosilicate glass (pyrex) 12.5% B2O3 and are

inserted into octant symmetric guide tube locations. Fig. 3.1 shows the enrichment

distribution and the number of burnable poisons in each assembly. Fig. 3.2 shows

the scale view of the burnable poison rods. This figure shows how the assemblies are

rotated to be octant symmetric with respect to the burnable poisons.

Figure 3.1: BEAVRS Cycle 1 layout of fuel assemblies showing the assembly enrich-ment distribution by color and the burnable poison locations by number. [4]

26

Figure 3.2: Scale view of burnable poison pins in cycle 1. [4]

3.2.2 Cycle 2

The 2.4% and 3.1% enriched fuel from cycle one (once burned) is shuffled in different

positions as shown in Fig. 3.3. Only one 1.6% enriched assembly from cycle 1 is kept

and placed at the core center. The poison pins are removed from the once-burned fuel

from cycle 1 feed fuel. The 3.2% and 3.4% enriched fresh fuel are placed throughout

the core, also shown in Fig. 3.3. All of the sub-batches of enriched assemblies in

the cycle 2 map are quarter core symmetric. However, it is not fully quarter core

27

symmetric because the center assembly came from an outside location which will

give it an unsymmetrical burnup distribution. More importantly, the cycle 2 core is

no longer octant symmetric. If octant symmetric, one could use reflective boundary

conditions to simulate in quarter core. Given this lack of octant symmetry, one must

run cycle 2 depletions in full core.

Figure 3.3: BEAVRS Cycle 2 fresh fuel enrichment locations shown in color, burnablepoison positions in the fresh fuel are labeled by number, and the once burned shuffledassemblies are labeled by their cycle 1 locations. [4]

28

3.3 Generating Tilt Corrected Data

The BEAVRS measured data is not symmetric as shown in the HZP case in Figure

3.4. The simulated fission rates are much higher than the measured fission rates

in the NW corner and are much lower in the SE corner. These data are expected

to be nearly symmetric since the core is constructed as such. There may be some

asymmetry in the real reactor or uncertainties in the detector measurements. The

simulated measurements on the other hand will always be symmetric since the model

is symmetric. Some of the differences between calculated and measured fission rates

can be removed by averaging, or folding rotationally symmetric assemblies. While

this method produces symmetric data, it ignores the cause of errors. This section

discusses what the asymmetry looks like and the following section discusses possible

reasons why the asymmetry exists.

29

Detector Fission Rate

Fractional Difference

# Symmetry Positions

Figure 3.4: CASMO-5 MxN HZP minus BEAVRS Data. RMS is 0.0498.

A tilt in the data is observed leading to high RMS errors. Since we are not sure

what phenomenon in the reactor is causing the tilt, we want to remove it from the data

so that we can compare how accurate our simulations are to a theoretically symmetric

reactor. In order to better evaluate the performance of the simulations, any errors

introduced by this asymmetry or tilt should be eliminated. We correct the measured

fission rates assuming deviations that take the form of a pure linear tilt. We need

30

to find a linear tilt such that the x-y tilt coefficients minimize the measured fission

rate deviations from a pure linear tilt. This corresponds to fitting a best fit plane

adjustment of the measured data. We use detector signals at symmetric locations

to deduce the orientation of the plane of tilt that minimizes deviations (RMS error)

of the symmetric detector fission rates relative to the plane. Then we create a new

data set called ’tilt corrected data’ that is the measured data made symmetric by

removing the tilt of the best fit plane. This new set of measured data will have been

filtered by a planar linear tilt and produce a much more symmetric distribution. We

want to compare all of our simulations with this new symmetric data set. This is a

systematic means to interpret what the fission rate map would look like without any

tilt in the data. This shows that much of the uncertainties are not coming from the

simulations. Some uncertainty might be coming from the fact the the reactor has

slightly different conditions than specified in the reactor plans.

3.4 Setup of the Gap Test

The tilt in the data from a real world reactor could be coming from a variety of

sources when building a real reactor. To test a possible core configuration that could

be causing a tilt in the measured data, a 0.5cm water gap is modeled in between the

fuel assemblies and the baffle in the southeast corner of the core. This is a possible

situation that may occur when loading the fuel from the northwest corner into the

southeast corner. The assemblies may not sit flush on the baffle and there will be

extra space somewhere between the assemblies or between the assemblies and the

baffle to allow for thermal expansion and swelling of the assemblies. We might expect

that the tilt will be the highest at the beginning of the cycle and it decreases as the

assemblies swell and fill in the gap between the baffle wall.

The test was performed using CASMO-5 MxN. This code will not allow the user

to place a gap between the assembly and the automatically-generated baffle. So, a

manual baffle was created by adding the extra water gap to the baffle model. With

the correct density adjustments, these regions replicate a steel baffle with a specified

31

amount of water gap. CASMO-5 MxN had to be run in full core because this added

gap eliminated the model symmetry.

3.5 Standard Model Considerations

3.5.1 HFP Approximations & Influence on Results

There are a number of approximations made in the HFP model for both SIMULATE-3

and CASMO-5 MxN. Each approximation contributes to a small increase in the RMS

error versus the measured data. We are forced to make most of these approximations

because of the limitations of the code or computational power and the assumptions are

discussed below. All of the influences of these assumptions, with the exception of the

thermal expansion approximation used in SIMULATE-3, are discussed in Gunow’s

thesis. The assumptions are stated here for completeness.

Thermal Hydraulic Feedback Thermal hydraulic feedback is important, but it is

not implemented in full core CASMO-5 MxN. However, SIMULATE-3 has a thermal

hydraulic feedback model. A full cycle depletion in SIMULATE-3 is used to obtain the

thermal hydraulic feedback behavior. These results are input into CASMO-5 MxN

as described in section 3.1. Using data from SIMULATE-3 as an input to CASMO-5

MxN is not ideal because full cycle depletion results from CASMO-5 MxN are not

completely independent of full cycle depletion results obtained using SIMULATE-3.

2D Modeling We need to model in 2D since 3D transport methods are too com-

putationally cumbersome. The 2D model requires an axial buckling parameter gener-

ated by 3D SIMULATE-3 cycle depletion to capture the axial leakage effect. The 2D

SIMULATE-3 model can take buckling terms at each depletion step but the CASMO-

5 MxN 2D model only allows one cycle-averaged buckling term for all burnup points.

Since partial rod insertions cannot be accurately modeled in two dimensions, we

are forced to neglect rod insertions. At full power there is only one bank slightly

inserted. Some errors are introduced at the point of insertion. Overall, this effect

32

only increases the total RMS errors by a small amount, since only five assemblies out

of 193 assemblies are significantly affected.

Baffle Thickness CASMO-5 MxN can only model an integer number of pin pitches

for the baffle. We must model the 2.22 cm thick baffle with the correct properties

under these restrictions. A good approximation is to preserve the product of baffle

thickness and material density. Two scenarios were used to test this. The first case was

limited to an integer number of 1.7 cm pin pitches. The second case was limited to an

integer number of 1.9 cm pin pitches. The baffle density was changed to accommodate

these restrictions. There was little difference in these cases, which suggests that either

approximation is valid.

SIMULATE-3 Geometry The assembly pitch was changed in the SIMULATE-

3 model in order to eliminate a 0.2cm water gap between the baffle and the outer

assembly around the entire core since it was included in the baffle/reflector nodes.

Since the volume of the assemblies would change in this situation, the power density

of the fuel rods is also changed in order to preserve the total core power.

Full power points Depletion steps are compared near full power to be consistent

with the original EPRI study. CASMO-5 MxN is run at full power for the full cycle

depletion. Flux map points that have a power above 80% are used. The chosen

measurement points for cycle 1 are shown in Figure 3.5 and for cycle 2 are shown by

green dots in Figure 3.6.

33

)XOO�3RZHU�3RLQWV

Figure 3.5: Full power points (above 80% power) used in cycle depletion. The Listof full power points here (in GWd/T) are 0.88, 1.02, 1.51, 2.16, 3.30, 4.61, 6.49, 7.51,8.70, 9.80, 11.08, 12.34, 12.92. We do not use the 9.80 GWd/T data because themeasurement occurred when the reactor was at full power for a very brief period.

Figure 3.6: Full power points used in cycle depletion. The list of full power pointshere (in GWd/T) are 1.14, 1.4, 2.11, 3.20, 4.04, 5.23, 6.52, 7.71, 8.73, 9.36, 10.43.

34

3.5.2 CASMO-5 MxN Considerations

CASMO-5 MxN is structured such that reflected boundary conditions can be used.

Given that cycle 1 is octant symmetric, it can be run with quarter core symmetry.

Cycle 2 is run in full core geometry and takes much longer to run than cycle 1.

Table 3.1 states the simulation parameters for a very detailed transport calculation.

Sensitivity analysis of each of these parameters was tested to determine the proper

balance between accuracy and computation time. The optimal parameters selected

are shown in Table 3.1.

Azimuthal Angles Ray Spacing Polar Angles Energy Groups GeometryCycle 1 64 0.05 3 35 quarter coreCycle 2 64 0.05 3 35 full core

Table 3.1: CASMO-5 MxN Simulation Parameters.

3.6 Methods to Infer Reactivity Decrement Uncertainties

The reactivity decrement is defined as the difference between the assembly k-infinity

at zero burnup and the k-infinity at the calculated exposure point. If the full cycle

depletion models were perfectly accurate, one would know the reactivity decrement

of all the fuel assemblies in the core with certainty. One would find the assembly

reactivity decrement from the depletion model and find the k-infinity vs exposure

curve for the specific type of assembly, as calculated by CASMO-5. A 2.4% enriched

assembly with 12 burnable poisons is shown as an example in Figure 3.7. However,

since the full cycle depletion models do not predict core behavior perfectly, we need

to infer the true reactivity of an assembly.

To determine the inferred reactivity of the fuel, a series of perturbations are applied

to a sub-batch of fuel. These perturbations change the reactivity of the sub-batch of

35

fuel via changing the exposure or temperature of an assembly. The fuel assembly sub-

batch is chosen by a common characteristic, such as having the same fuel enrichment.

When the fuel reactivity of a sub-batch is perturbed at a specified depletion point,

the RMS error of the new simulated point will change. The minimum RMS point,

along with its corresponding reactivity perturbation, is considered the most accurate

representation of the core behavior. The magnitude of the reactivity perturbation at

the minimum RMS point is used to infer the bias of the CASMO-5 predicted reactivity

decrement.

This study perturbed the fuel sub-batch exposures from +1 GWd/T to -1 GWd/T

in steps of 0.1 GWd/T. The sub-batch fuel temperatures were perturbed from -250K

to +250K in steps of 25K. In order to convert the exposure values or temperature

values to reactivity, the exposure reactivity coefficient or fuel temperature coefficient

of reactivity of the assemblies in the sub-batch is needed. The exposure reactivity co-

efficient is the derivative of the k-infinity vs burnup of an assembly at a given burnup

point. An example of a exposure reactivity coefficient curve derived from Figure 3.7

is shown in Figure 3.8. There are multiple unique assembly types within a sub-batch.

The exposure reactivity coefficient is computed for each unique assembly by using

the k-infinity vs exposure curve and the central difference approximation. The expo-

sure reactivity coefficient for the sub-batch is approximated as the weighted average

coefficient of the unique assemblies within the sub-batch. This average exposure re-

activity coefficient and the difference between the average exposure of the sub-batch

at the base point and at the minimum RMS point is used to determine the reactivity

decrement error. The sub-batch reactivity decrement error is described in Eq. 3.1

�klatticebias (Elattice

bias ) = �(Elatticemin � Elattice

base )dk

dE

��lattice

Elatticebase

(3.1)

where k is the lattice critical eigenvalue at the measured boron concentration, E

is exposure, Elatticebase is the average exposure of the fuel batch of interest at the base

point, and Elatticemin is the average exposure of the sub-batch after optimal perturbations

(smallest RMS error). The fuel temperature coefficient of reactivity is determined by

36

taking the derivative of k-infinity versus temperature at the given exposure point.

Then, the average fuel temperature coefficient for the sub-batch is approximated as

the weighted average coefficient of the unique assemblies within the sub-batch. The

average temperature reactivity coefficient and the average temperature of the sub-

batch at the base point and at the minimum RMS point is used to determine the

reactivity decrement error. The reactivity decrement error is described in Eq. 3.2.

�klatticebias (T lattice

bias ) = �(T latticemin � T lattice

base )dk

dT

��lattice

T latticebase

(3.2)

where k is the lattice critical eigenvalue at the measured boron concentration, T is

the fuel temperature, T latticebase is the average temperature of the fuel batch of interest at

the base point, and T latticemin is the average temperature of the sub-batch after optimal

perturbations (smallest RMS error). Figure 3.9 shows that the temperature reactiv-

ity coefficient is around -2.5 pcm/K at three different cycle points. The relationship

between fuel temperature and reactivity is more stable than fuel exposure and reac-

tivity at the beginning of the cycle because burnable poison depletion competes with

fuel depletion.

37

0 10 20 30 40 50 600.75

0.8

0.85

0.9

0.95

1

1.05

1.1

Burnup (GWd/T)

k−in

f

BP insertedBP pulled

Figure 3.7: Reactivity of an assembly with 2.4% enriched fuel and 12 burnable poisonsas a function of burnup.

38

5 10 15 20 25 30 35 40 45 50 55 60−1200

−1000

−800

−600

−400

−200

0

200

400

Burnup (GWd/T)

Expo

sure

Rea

ctiv

ity C

oeffi

cien

t (pc

m/G

Wd/

T)

BP insertedBP pulled

Figure 3.8: exposure reactivity coefficient of an assembly with 2.4% enriched fuel and12 burnable poisons as a function of burnup.

39

600 700 800 900 1000 1100 1200−5

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

−0.5

0

Fuel Temperature (K)

Tem

pera

ture

Rea

ctiv

ity C

oeffi

cien

t (pc

m/K

)

@ 2.1GWd/T@ 6.5GWd/T@ 11.0GWd/T

Figure 3.9: The temperature reactivity coefficient of an assembly with 2.4% enrichedfuel and 12 burnable poisons as a function of temperature at a beginning, middle,and end of cycle statepoint.

40

4 Tilt Correction, Gap Test, and Early Cycle Results

This section will discuss the results of tilt correcting the BEAVRS data and how the

baffle gap model can explain the tilt in the data. The models are tested against the

HZP and early HFP points.

4.1 Results of Tilt Corrected Data

Figure 4.1 and Figure 4.2 show the planar tilt coefficients found in cycle 1 and cycle 2,

respectively. The tilt coefficients describe the magnitude of linear peripheral assembly

fractional tilt of the best fit plane to the measured data in the x and y directions at a

given statepoint. The fractional tilt is defined as simulated�referencereference and the magnitude

of the tilt is quoted as the tilt at the most peripheral assemblies. The method used

to determine the tilt coefficients was described in section 3.3. The planar tilt is large

at HZP and decreases quickly with burnup. As depletion increases, the assemblies

that have higher fission rates will deplete more quickly, resulting in a reduced tilt

over time. The cause of the tilt is not known, and it is difficult to determine what

causes the tilt to change over time. Geometrical changes occurring throughout the

cycle depletion (e.g. reduction in inter-assembly gaps through swelling) could help

restore symmetry, explaining the reduction in measured tilt..

41

0 2 4 6 8 10 12 14−3

−2

−1

0

1

2

3

4

5

6

7

8

Cycle burnup (GWd/T)

Plan

ar T

ilt o

f Mea

sure

d Fi

ssio

n R

ate

X DirectionY Direction

Figure 4.1: Planar peripheral assembly fractional tilt of measured fission rates forcycle 1. Positive tilt in the x direction means that the measurements were higher onthe east side of the core. Positive tilt in the y direction means that the measurementswere higher on the south side of the core.

42

0 2 4 6 8 10 12 14−3

−2

−1

0

1

2

3

4

5

6

7

8

Cycle burnup (GWd/T)

Plan

ar T

ilt o

f Mea

sure

d Fi

ssio

n R

ate

X DirectionY Direction

Figure 4.2: Planar peripheral assembly fractional tilt of measured fission rates forcycle 2. Positive tilt in the x direction means that the measurements were higher onthe east side of the core. Positive tilt in the y direction means that the measurementswere higher on the south side of the core. Cycle 2 has a very small tilt at BOC and ittoo goes away with depletion. Early Cycle 1 displays the only truly significant tilts.

4.2 Gap Test Results

4.2.1 Magnitude of Simulated Tilt

Figure 4.3 shows a comparison of fission rates at HZP from the manually-created

baffle with no water gap versus the manually created baffle with a 0.5cm water gap

in the southeast corner. A manually created baffle with no gap is used for a direct

comparison rather than the CASMO-5 MxN generated baffle. The fission rates in-

crease by about 9% near the gap and continually decrease towards the opposite side

of the core. In the northwest corner the fission rates have dropped to about 3% below

43

the no gap reference. This test does not produce a purely linear tilt, but it shows

that a smooth and significant tilt can be introduced with only a 0.5cm water gap on

one edge of the baffle. The magnitude of the introduced tilt is comparable to the

approximately 6% planar tilt calculated at HZP in cycle 1. The 6% tilt means that

the overall difference between opposite sides of the core is 12%. The simulated gap

has the same net difference in tilt as observed in the measurement.




Figure 4.3: HZP CASMO-5 MxN with a 0.5 cm southeast gap minus no gap showsthe distribution of tilt. The top number shows the fission rates of the gap case. Thenext line shows the fractional difference of the gap minus no gap case.

44

4.2.2 HZP Comparisons to Calculations

The BEAVRS benchmark specifies the hot zero power (HZP) configuration. The

HZP simulation shown in Figure 4.4 shows a relatively high RMS difference vs the

measured data. Figure 4.5 is a comparison of CASMO-5 MxN HZP to tilt corrected

data. Correcting for the tilt is a systematic means to interpret what the fission

map would look like without any tilt. A comparison of Figure 4.4 and Figure 4.5

shows that the radial tilt in the measured fission rates causes a large portion of the

difference. There is still an in-out tilt present in Figure 4.5, but it is less significant.

A comparison of Figure 4.5 and Figure 4.6 shows that the correction of measured tilt

and the simulation of the gap yields much reduced measurement errors relative to the

uncorrected case. The comparison to the tilt corrected data was the most accurate at

a 1.49% RMS difference compared to the gap test simulation with an RMS of 2.82%.

However, a large portion of the tilt was corrected by simulating the gap at the baffle,

suggesting that the test is a plausible explanation for the tilt seen in the measured

data. If it was feasible to simulate smaller inter-assembly gaps throughout the SE

region of the core, it is expected that the induced tilt would be closer to linear and

show results even closer to the tilt corrected case.

Since the tilt exists in the data, especially at HZP, future comparisons will be

made to the tilt corrected data in addition to the uncorrected data to test if the

interpretation of the results would be any different if the tilt was corrected. Fission

rate tilts are most pronounced at HZP because there is no feedback.

45




Figure 4.4: CASMO-5 MxN HZP minus BEAVRS Data. RMS is 0.0498.

46




Figure 4.5: CASMO-5 MxN HZP minus tilt corrected data. RMS is 0.0149.

47




Figure 4.6: CASMO-5 MxN HZP Manual Baffle with a 0.5cm Gap minus BEAVRSData. RMS is 0.0282.

4.2.3 HFP Results

The linear tilt in the HFP data is rapidly diminished with depletion as shown in

Figure 4.1. The sensitivity to baffle gap also decreases with cycle depletion shown in

Figure 4.8, 4.11, and 4.14. Figure 4.8 shows a 5% increase in fission rate in the SW

corner and a 1.3% decrease in fission rate in the NE corner. The calculated tilt is

48

about 2%, or a net of 4% from the SW corner to the NE corner. The simulated baffle

gap is over-correcting the real tilt by about 2.3% at this point. Figure 4.11 shows

a 3.6% increase in fission rate in the SW corner and a 0.8% decrease in fission rate

in the NE corner. The calculated tilt is about 1.5%, or a net of 3% from the SW

corner to the NE corner. The simulated baffle gap is over-correcting the real tilt by

about 1.4% at this point. Figure 4.14 shows a 2.6% increase in fission rate in the SW

corner and a 0.2% decrease in fission rate in the NE corner. The calculated tilt is

about 1%, or a net of 2% from the SW corner to the NE corner. The simulated baffle

gap is over-correcting the real tilt by about 0.8% at this point. The sensitivity to

the baffle gap does not decrease as fast as the real tilt. However, by the 3.3 GWd/T

point the real tilt is small and the simulated tilt from the baffle gap has decreased to

the approximately correct level.

The simulations with and without tilt at three early cycle points are compared to

the measured data in Figure 4.7, 4.9, 4.10, 4.12, 4.13, and 4.15. At the 1.02 GWd/T

and 2.16 GWd/T points, the simulated baffle gap results have similar total errors to

the no gap case because the assemblies near the baffle gap were over corrected. If the

gap was reduced in size at these points, it would follow the more rapid reduction in

tilt that is in the measured data. At the 3.3GWd/T point, the baffle gap tilt is now

closely following the calculated tilt in the data. The comparison of Figure 4.13, and

4.15 shows a reduction in the total RMS error. Overall, the gap does not fix the tilt

perfectly because the magnitude of the induced tilt is reduced more slowly than the

measured tilt as burnup increases.

The assemblies that had higher than estimated fission rates will deplete faster

and, likewise, assemblies that have lower than estimated fission rates will deplete

slower. This feedback will reduce errors in the calculated vs measured fission rates as

depletion increases.

49




Figure 4.7: CASMO-5 MxN HFP 1.02 GWd/T Manual Baffle with No Gap minusBEAVRS Data. RMS is 0.0306.

50




Figure 4.8: CASMO-5 MxN HFP 1.02 GWd/T with a 0.5 cm southeast gap minusno gap shows the distribution of tilt. The top number shows the fission rates of thegap case. The next line shows the fractional difference of the gap minus no gap case.

51




Figure 4.9: CASMO-5 MxN HFP 1.02 GWd/T Manual Baffle with 0.5 cm gap minusBEAVRS Data. RMS is 0.0305.

52





53





54





55





56





57





Overall, it is important to show that this tilt is real and not just a measurement

error or uncertainty in order for the BEAVRS benchmark to be accepted. This tilt

helps justify eliminating early cycle depletion points in the original EPRI study.[1] It

shows that the RMS errors in the early cycle do not hinder interpretation of reactivity

decrement data.

58

The source of the tilt is not just a simple fuel assembly/baffle gap. The HFP

results show that the tilt in the measured data is reduced much faster than the tilt

modeled by the simple gap and the source of the tilt is still unknown. However, since

the tilt in the measured data is reduced to negligible levels with depletion it does not

affect the results of this study.

59

5 Standard Model HFP Results

5.1 HFP results Cycle 1

The HFP results show the baseline accuracy of simulations. A fission rate error

distribution plot similar to the plots provided for the the HZP point are made at

every HFP statepoint and shown in the Appendix, section 8.1 . Figure 5.1 displays

the RMS error at each statepoint as a summary of the results. This plot shows

how well the model predicts core behavior throughout a full cycle depletion. The

results show that the RMS errors with respect to BEAVRS data and tilt corrected

data decrease as depletion increases. The errors burn out because regions that were

predicted to have higher than actual reactivity will be depleted more quickly. The

data in Figure 5.1 was folded to an octant because the calculated core model is octant

symmetric. This reduces the RMS errors because some of the errors introduced by

the tilt are cancelled out between quadrants. The figure also shows a comparison to

tilt corrected data. The tilt corrected data gives better results than just folding in

the early cycle points. However, as the cycle depletion increases, the amount of tilt is

reduced so there is no longer a significant error reduction by using the tilt corrected

data.

Figure 5.1 compares CASMO-5 MxN to the SIMULATE 2D model. The SIMULATE-

3 2D model performs better than CASMO-5 MxN at the early cycle point, but by

the middle of the cycle the results are comparable. The SIMULATE-3 2D model is

compared to the CASMO-5 MxN model because CASMO-5 MxN is also a 2D model,

and the reactivity decrement bias studies are based on these two models. Figure 5.2

shows the RMS error of the SIMULATE-3 2D model in comparison to the 3D model.

The SIMULATE-3 2D model has a higher RMS than the 3D model as expected. No-

tice that the 3D model benefits greatly from comparing to tilt corrected data in the

early cycle but by the end of the cycle the difference is negligible.

60

0 2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Cycle 1

Cycle burnup (MWd/kg)

RMS

Diffe

renc

e (%

)

SIMULATE−3 2D vs BEAVRSSIMULATE−3 2D vs tilt correctedCASMO−5 MxN vs BEAVRSCASMO−5 MxN vs tilt corrected

Figure 5.1: Normalized fission rate RMS error of CASMO-5 MxN and SIMULATE-32D vs BEAVRS data and tilt corrected data in cycle 1. Data is folded into an octant.

61

0 2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Cycle 1


RM

S D

iffer

ence

(%)

SIMULATE−3 2D vs BEAVRSSIMULATE−3 2D vs tilt correctedSIMULATE−3 3D vs BEAVRSSIMULATE−3 3D vs tilt corrected

Figure 5.2: Normalized fission rate RMS error of SIMULATE-3 2D and SIMULATE-3 3D vs BEAVRS data and tilt corrected data in cycle 1. Data is folded into an octant.

5.2 HFP results Cycle 2

Figure 5.3 and 5.4 show the same RMS error graphs displayed in the previous section,

but for cycle 2 data. Notice that at the beginning of the cycle, RMS errors are

comparable between SIMULATE-3 2D and CASMO-5 MxN. The data are folded to

quarter core in this case, and we see that comparing to the tilt corrected data gives

a large error reduction in the beginning of the cycle and a moderate error reduction

towards the end of the cycle. There is a tilt in the data at the beginning of the

cycle that is reduced to negligible levels by mid cycle. The CASMO 5-MxN and

62

SIMULATE-3 2D cases compare well to each other and are both somewhat higher

than the SIMULATE-3 3D case throughout the depletion as expected.

0 2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Cycle 2


RMS

Diffe

renc

e (%

)

SIMULATE−3 2D vs BEAVRSSIMULATE−3 2D vs tilt correctedCASMO−5 MxN vs BEAVRSCASMO−5 MxN vs tilt corrected

Figure 5.3: Normalized fission rate RMS error of CASMO-5 MxN and SIMULATE-32D vs BEAVRS data and tilt corrected data in cycle 2. Data is folded to quartercore.

63

0 2 4 6 8 10 12 140

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5Cycle 2


RM

S D

iffer

ence

(%)

SIMULATE−3 2D vs BEAVRSSIMULATE−3 2D vs tilt correctedSIMULATE−3 3D vs BEAVRSSIMULATE−3 3D vs tilt corrected

Figure 5.4: Normalized fission rate RMS error of SIMULATE-3 2D and SIMULATE-33D vs BEAVRS data and tilt corrected data in cycle 2. Data is folded to quartercore.

64

6 Inferring Reactivity Decrements Results

As discussed in section 3.6, the exposure and fuel temperature of a sub-batch of

fuel was perturbed in order to infer the reactivity decrement. A sub-batch of fuel is

chosen by its enrichment. Assemblies with similar enrichment have similar properties.

A simulation may have errors due to under-predicting the absorption of the fuel

depletion isotopics or some other physical behavior. By perturbing the sub-batch

reactivity we can change the properties of the set of fuel assemblies. There will be

an optimal perturbation in these parameters that will produce the best fit to the

measured data. This amount of perturbation is the reactivity decrement bias of

the simulation. That is, how far off the simulation was from predicting the correct

reactivity of the fuel. All of the results in chapter 6 are compared to BEAVRS data

without the tilt correction. The investigation of the tilt in the data showed that it

is reduced quickly and will not affect the overall accuracy of the model substantially.

Also, the sub-batches used in this study are symmetric so perturbing to find a best

fit to the data could not remove the tilt. The results would be the same so we choose

to perform the reactivity decrement measurements on the original set of data to be

consistent with prior studies.

6.1 Reporting Results in Reactivity

This section explains the methods used to construct the graphs in the next sections

in terms of reactivity. Increasing burnup usually means that a sub-batch of fuel will

decrease in reactivity. This is not always true as shown in Figure 6.1 in the case of

the 2.4% enriched sub-batch at the early cycle point. Increasing temperature always

results in decreasing reactivity. So, if all the comparisons were observed only in

burnup space and temperature space, one may think that the perturbation of sub-

batch burnup and sub-batch temperature gave different results. Figure 6.1 shows

the 2.4% enriched sub-batch burnup perturbations in burnup space and Figure 6.2

shows the 2.4% enriched sub-batch temperature perturbation in temperature space.

65

Figure 6.3 shows both of these figures displayed with respect to reactivity in pcm,

defined as keff�1keff

. Reactivity is the more relevant value and is used going forward for

comparisons of all the results.

2 4 6 8 10 12 140

1

2

3

4

5

6

7

Sub−batch Burnup Average (GWd/T)

RMS

Diffe

renc

e (%

)

CASMO−5 2.16 GWd/TCASMO−5 6.49 GWd/TCASMO−5 11.08 GWd/T

Figure 6.1: RMS difference of CASMO-5 MxN compared to BEAVRS data for the2.4% enriched fuel sub-batch in Cycle 1. The sub-batch reactivity was perturbed viachanging the sub-batch exposure as shown on the x-axis. The circle represents theinitial unperturbed point.

66

−400 −300 −200 −100 0 100 200 300 4000

1

2

3

4

5

6

7Cycle 1: 2.4% sub−batch perturbations

Fuel Temperature Perturbation (K)

RMS

Diffe

renc

e (%

)

CASMO−5 2.16 GWd/TCASMO−5 6.49 GWd/TCASMO−5 11.08 GWd/T

Figure 6.2: RMS difference of CASMO-5 MxN compared to BEAVRS data for the2.4% enriched fuel sub-batch in Cycle 1. The sub-batch reactivity was perturbed viachanging the sub-batch fuel temperature as shown on the x-axis.

67

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)

CASMO−5 2.16 GWd/T exposure perturbationCASMO−5 6.49 GWd/T exposure perturbationCASMO−5 11.08 GWd/T exposure perturbationCASMO−5 2.16 GWd/T temperature perturbationCASMO−5 6.49 GWd/T temperature perturbationCASMO−5 11.08 GWd/T temperature perturbation

Figure 6.3: RMS difference of CASMO-5 MxN compared to BEAVRS data for the2.4% enriched fuel sub-batch in Cycle 1. The sub-batch reactivity (represented inpcm) was perturbed via changing the sub-batch fuel temperature in three cases andvia changing the sub-batch exposure in three cases.

6.2 Perturbing Sub-batch Burnup in SIMULATE-3 and CASMO-

5 MxN

This section compares the reactivity decrement bias of the SIMULATE-3 model and

the CASMO-5 MxN model. The reactivity was perturbed by changing the exposure

of a given sub-batch of fuel.

68

6.2.1 Cycle 1 Results

In cycle 1, perturbations of exposure were performed using both SIMULATE-3 and

CASMO-5 MxN at three statepoints representing the beginning, middle, and end

of cycle. The perturbation was done by replacing each assembly in the sub-batch

with the same assembly from a previous or future statepoint from a fine time-step

depletion. This changes the exposure of the sub-batch of fuel. In the first case,

the 2.4% enriched fuel sub-batch exposure was perturbed. Figure 6.4 shows that the

optimal reactivity perturbations were roughly the same whether they were done in the

SIMULATE-3 model or the CASMO-5 MxN model. The middle of cycle point covers

a much smaller range of pcm because the reactivity derivative of these assemblies

is small at this point since this sub-batch has a large number of burnable poisons.

However, the inferred reactivity can be determined as long as the minimum point is

found. Figure 6.5 shows the results of the 3.1% enriched fuel sub-batch perturbation.

The reactivity change of the 2.16 GWd/T point is somewhat larger in CASMO-5

MxN than in SIMULATE-3, but they are in the same direction. Lastly, Figure 6.6

shows a perturbation of the 3.1% enriched fuel sub-batch while using the optimal

perturbation for the 2.4% assembly as a starting point. There is not a large change in

reactivity because the 2.4% assembly was already at the optimal conditions, so there

was less room to improve the fit to the measured data. Similar reactivity errors are

calculated irrespective of which fuel batch is selected and which code is used.

69

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)

CASMO−5 2.16 GWd/TCASMO−5 6.49 GWd/TCASMO−5 11.08 GWd/TSIMULATE−3 2.16 GWd/TSIMULATE−3 6.49 GWd/TSIMULATE−3 11.08 GWd/T

Figure 6.4: RMS difference of CASMO-5 MxN and SIMULATE-3 compared toBEAVRS data for the 2.4% enriched fuel sub-batch in Cycle 1. The sub-batch reac-tivity (represented in pcm) was perturbed via changing the sub-batch exposure.

70

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)



71

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)


Figure 6.6: RMS difference of CASMO-5 MxN and SIMULATE-3 compared toBEAVRS data for the 3.1% enriched fuel sub-batch in Cycle 1 while starting from theoptimal perturbation point of the 2.4% enriched sub-batch. The sub-batch reactivity(represented in pcm) was perturbed via changing the sub-batch exposure.


In cycle 2, there are also three perturbations of exposure performed with both SIMULATE-

3 and CASMO-5 MxN. The first case is the 2.4% enriched assemblies shown in Figure

6.7. These are the same 2.4% enriched assemblies from cycle 1 located in different

positions due to the core shuffling. The curves are very flat and wide here, indicating

that the sub-batch now has a smaller reactivity slope and the reactor is less sensi-

tive to reactivity change for this sub-batch in cycle 2. The optimal perturbations

are similar when computed by CASMO-5 MxN vs SIMULATE-3. It is important

that the curves look approximately the same, but in this case we do not want to

72

credit the minimum value as a good indication of the true reactivity because it is

highly sensitive. The original EPRI study calculates a sensitive parameter which is

the RMS peak to the minimum. If this value is too small, the data point would not be

used. Figure 6.8 shows the 3.1% assembly perturbation results. SIMULATE-3 shows

a larger reactivity decrement bias at the early cycle point, but it is still in the same

direction as the CASMO-5 MxN bias. The other points match up closely. Lastly,

the fresh fuel containing 3.2% and 3.4% enriched bundles are perturbed as shown in

Figure 6.9. Again, SIMULATE-3 shows a larger bias at the early cycle point, but

it is in the same direction as CASMO-5 MxN. Overall, similar reactivity errors are

calculated irrespective of which fuel batch is selected and which core model was used.

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)



73

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)



74

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)


Figure 6.9: RMS difference of CASMO-5 MxN and SIMULATE-3 compared toBEAVRS data for the fresh, 3.2% and 3.4% enriched, fuel sub-batch in Cycle 2. Thesub-batch reactivity (represented in pcm) was perturbed via changing the sub-batchexposure.

6.3 Perturbing Burnup vs Fuel Temperatures in CASMO-5

MxN

This section compares the reactivity decrement bias of the CASMO-5 MxN model

perturbing exposure and perturbing fuel temperature. Both methods change the sub-

75

batch reactivity, and therefore, change the core fission rate distributions. We want

to investigate if the method of perturbation affects the inferred reactivity decrement

errors. Table 6.1 shows that the exposure reactivity coefficient of the heavy burnable

poison sub-batches changes dramatically from the beginning of the cycle to the end of

the cycle. The burnable poisons create a positive reactivity coefficient in the beginning

of the cycle. As they burn out, the relationship becomes constant. The exposure

reactivity coefficient also changes depending on the enrichment of the fuel. Finally, the

exposure reactivity coefficient increases with burnup, regardless of burnable poisons.

The temperature reactivity coefficient is nearly constant throughout the cycle for each

sub-batch. It is much easier to perform reactivity perturbation with these properties.

This section will test if the reactivity decrement results are independent of the method

of perturbation.

Cycle Enrichment-Cycle-Burnup-

Fuel--Burnup- k3inf dk/dE dK/dT

% "GWd/T GWd/T pcm/GWd/T pcm/K1 2.4 2.16 2.44 1.011 295.0 42.431 2.4 6.49 7.39 1.013 4141.0 42.441 2.4 11.08 12.62 0.995 4550.0 42.512 2.4 3.20 18.10 0.958 4742.5 42.502 2.4 6.52 20.88 0.938 4744.0 42.462 2.4 9.36 23.29 0.919 4724.3 42.421 3.1 2.16 1.87 1.139 4493.1 42.641 3.1 6.49 5.53 1.115 4699.0 42.571 3.1 11.08 9.52 1.087 4709.3 42.602 3.1 3.20 15.43 1.045 4771.8 42.652 3.1 6.52 19.09 1.015 4795.8 42.632 3.1 9.36 22.17 0.991 4791.0 42.592 3.2"/"3.4 3.20 3.29 1.160 4782.5 42.432 3.2"/"3.4 6.52 6.81 1.131 4836.0 42.452 3.2"/"3.4 9.36 9.85 1.106 4823.0 42.481 3.1"@"2.4min 2.16 2.15 1.075 499.1 42.541 3.1"@"2.4min 6.49 6.46 1.064 4420.0 42.511 3.1"@"2.4min 11.08 11.07 1.041 4629.7 42.56

Reactivity"Derivatives"Used"to"Convert"Exposure"and"Temperature"Perturbations"to"Reactivity

Table 6.1: Summary Table of exposure reactivity coefficients and temperature reac-tivity coefficients.

76


In cycle 1, three perturbations of temperature and exposure were performed using

CASMO-5 MxN. The exposure perturbation results for CASMO-5 MxN are the same

as the CASMO-5 MxN results in the previous section. They are displayed again to

compare to the temperature perturbation method. The temperature perturbation was

done by changing the assembly fuel temperature at each of the sub-batch locations

in a range from -250K to +250K. Figure 6.10 shows the perturbation of the 2.4%

sub-batch. Notice that the 0 pcm point is the same for the exposure perturbation

and the temperature perturbation at a given cycle point. The yellow curve has a

much narrower range than all the other curves because the 2.4% enriched sub-batch

as a small exposure reactivity coefficient at this cycle point. All the points show a

similar reactivity decrement bias. Figure 6.11 shows the results of the 3.1% enriched

sub-batch perturbations. All three cycle points show a similar reactivity decrement

bias. Lastly, Figure 6.12 shows the results of the 3.1% perturbation given a starting

point of the 2.4% minimum point. There is not a large change in reactivity here

because the 2.4% assembly was already at the optimal conditions, so there was less

room to improve the fit to the measured data. Similar reactivity errors are calculated

irrespective of which fuel batch is selected and which perturbation method is used.

77

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)



78

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)



79

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)


Figure 6.12: RMS difference of CASMO-5 MxN compared to BEAVRS data for the3.1% enriched fuel sub-batch in Cycle 1 while starting from the optimal perturbationpoint of the 2.4% enriched sub-batch. The sub-batch reactivity (represented in pcm)was perturbed via changing the sub-batch fuel temperature in three cases and viachanging the sub-batch exposure in three cases.


In cycle 2, three sub-batches were perturbed at the beginning, middle, and end of

cycle. Figure 6.13 shows the results of the 2.4% enriched (once burned) sub-batch

perturbation. The sub-batch is very insensitive to changes in reactivity by both

changing the exposure, and changing the fuel temperature. It is difficult to find a

80

minimum RMS point in these circumstances, but the shape of the graphs show good

agreement between both perturbation methods. Again, the sensitivity parameter in

the original EPRI study would exclude this data point because the slope of the curve

is so shallow. Figure 6.14 shows the results of the 3.1% enriched (once burned) sub-

batch. The curves at all burnup points look very similar because the perturbation in

exposure is more constant at these higher burnup points. The measured reactivity

bias is similar using either perturbation method. Figure 6.15 shows the 3.2% and

3.4% (fresh fuel) sub-batch results. Again, the perturbation in exposure is stable in

this sub-batch so all of the curve are similar to the temperature perturbation curves.

The measured reactivity bias is similar using either perturbation method.

81

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)



82

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)



83

−800 −600 −400 −200 0 200 400 600 8000

1

2

3

4

5

6

7

pcm

RMS

Diffe

renc

e (%

)


Figure 6.15: RMS difference of CASMO-5 MxN compared to BEAVRS data for thefresh, 3.2% and 3.4% enriched, fuel sub-batch in Cycle 2. The sub-batch reactivity(represented in pcm) was perturbed via changing the sub-batch fuel temperature inthree cases and via changing the sub-batch exposure in three cases.

6.4 Summary of Calculated Reactivity Decrements

Changing the method of simulation or the method of perturbation does not change

the measured reactivity bias. The results of the previous sections are summarized

in Table 6.2. It shows the SIMULATE-3 reactivity decrement biases determined

from exposure perturbations as well as the CASMO-5 MxN biases determined from

both exposure and temperature perturbations. Overall, similar reactivity errors are

84

calculated irrespective of which fuel batch is selected and how it is perturbed. It

is important to look at the summary statistics of the differences in these methods

rather than the nominal value of the biases in each case. This set of points is a small

set of possible points that could have been found in the EPRI study. We only want

the differences in the methods to evaluate possible uncertainty of the SIMULATE-3

EPRI biases. Overall, the calculated bias does not change significantly from either

code or method. The EPRI study uses a 250 pcm uncertainty of the bias regression

curves. The standard deviation of the differences of biases shown here are much lower

than the assigned uncertainty. The EPRI study was produced using SIMULATE-3

with exposure perturbations to find the reactivity decrement biases.

Cycle Enrichment-Cycle-Burnup-

Fuel--Burnup-

SIMULATE-Bias-(burnup-pert.)----------

Δk

CASMO-Bias-(burnup-pert.)-

Δk

CASMO-Bias-(temp.-pert.)--

Δk-

SIMULATE-A-CASMO-Bias-(burnup-pert.)-

Bias-Difference-(burnup-pert.-A-temp.-pert.)-

% "GWd/T GWd/T pcm pcm pcm pcm pcm1 2.4 2.16 2.44 0215 0251 0182 36 0691 2.4 6.49 7.39 66 66 90 0 0241 2.4 11.08 12.62 050 050 063 0 132 2.4 3.20 18.10 90 119 030 029 1492 2.4 6.52 20.88 0347 0230 0369 0117 1392 2.4 9.36 23.29 0197 0167 0302 030 1351 3.1 2.16 1.87 60 222 198 0162 241 3.1 6.49 5.53 0 0 0 0 01 3.1 11.08 9.52 14 14 0 0 142 3.1 3.20 15.43 432 255 300 177 0452 3.1 6.52 19.09 160 72 132 88 0602 3.1 9.36 22.17 198 119 65 79 542 3.2"/"3.4 3.20 3.29 0328 0242 0243 086 12 3.2"/"3.4 6.52 6.81 054 0 061 054 612 3.2"/"3.4 9.36 9.85 075 0 062 075 621 3.1"@"2.4min 2.16 2.15 0 182 66 0182 1161 3.1"@"2.4min 6.49 6.46 100 70 0 30 701 3.1"@"2.4min 11.08 11.07 0 14 0 014 14

S.D."of"Bias 188 152 169 88 67Mean"Bias 08 11 026 019 36

Fuel"Assembly"Reactivity"Decrement"Biases"for"BEAVRS"Cycle"1"and"Cycle"2"(CASMO05""with"ENDF0B/VII)

Table 6.2: Inferred Fuel Batch Reactivity Bias by perturbing sub-batch burnup inSIMULATE-3 and sub-batch burnup and fuel temperature in CASMO-5 MxN. Thedifferences in the biases inferred by the two methods is shown in the far right columns.

85

7 Summary

7.1 Conclusions

This study investigated using SIMULATE-3 with exposure perturbations and CASMO-

5 MxN with exposure and temperature perturbations to calculate reactivity decre-

ment biases. The results of this study show that similar reactivity decrement biases

are calculated irrespective of how it is perturbed. Overall, this is important because

it confirms that the EPRI study was valid in only using SIMULATE-3 with exposure

perturbations to calculate reactivity decrement biases.

An NRC information notice in 2011 stated that “Regarding the depletion uncer-

tainty, the Kopp letter states the following: A reactivity uncertainty due to uncer-

tainty in the fuel depletion calculations should be developed and combined with other

calculational uncertainties. In the absence of any other determination of the deple-

tion uncertainty, an uncertainty equal to 5 percent of the reactivity decrement to the

burnup of interest is an acceptable assumption.”[5] Perturbations in temperature and

burnup found reactivity decrement uncertainties that were well under the 250 pcm

mark set in the EPRI study. Therefore, the conclusions of the EPRI study are valid

and show that the Kopp memo is conservative, but given the uncertainty calculations

performed, the 5% decrement could possibly be lowered while maintaining the same

safety standards.

7.2 Future Work

Improved Thermal Hydraulic Modeling in an MOC Solver Currently CASMO-

5 MxN does not have a thermal hydraulic feedback model. To improve the accuracy

of the calculation, temperature maps were extracted from the SIMULATE-3 results

since it has a built in thermal hydraulic feedback model. However, this introduces

some dependency on SIMULATE-3, a nodal method. The main purpose of using a

MOC solver was to verify the reactivity decrements independently of the nodal model.

86

In order to show fully independent results, a thermal hydraulic feedback model should

be implemented into a MOC solver.

3D Transport Method The original EPRI study used 3D nodal methods to cal-

culate reactivity decrement uncertainties. Ideally, this study would use 3D MOC

methods in order to independently determine the reactivity decrement uncertainties.

However, since the 3D MOC model is computationally cumbersome, this study com-

pared the results of the 2D nodal method versus the 2D MOC method. The 2D

models are less accurate, but can be solved in a reasonable amount of time. A 3D

transport method would need to solve approximately 300 full core statepoints in a rea-

sonable timeframe in order to compare results to nodal methods using the BEAVRS

benchmark.

87

References

[1] K. Smith, et al., “Benchmarks for Quantifying Fuel Reactivity Depletion Un-

certainty,” Electric Power Research Institute (EPRI), Palo Alto, CA, Technical

Report Number 1022909, (2011).

[2] G. Gunow, "LWR Fuel Reactivity Depletion Verification Using 2D Full Core MOC

and Flux Map Data," Master’s thesis, Massachusetts Institute of Technology,

(2015).

[3] J. Rhodes, et al., “CASMO5 Overview USNRC Pre-Submittal Meeting,” (2015).

[4] N. Horelik, B. Herman, B. Forget, and K. Smith. "Benchmark for Evaluation and

Validation of Reactor Simulations (BEAVRS), v1.1.1," (2013).

[5] United States Nuclear Regulatory Commission Office of Nuclear Reactor Regu-

lation Office of New Reactors, "Nonconservative Criticality Safety Analyses for

Fuel Storage," (2011).

[6] J. Cronin, et al., “SIMULATE-3 Methodology Manual,” STUDSVIK/SOA-95/18,

Studsvik of America, Inc., (1995).

[7] J. Rhodes, et al., “CASMO-5 A Fuel Assembly Burnup Program User’s Manual,”

SSP-07/431 Rev 8, (2014).

[8] T. Bahadir, et al., “CMSLINK User’s Manual,” STUDSVIK/SOA-97/04, Studsvik

of America, Inc. (1997).

[9] L. Kopp, NRC memorandum from L. Kopp to T. Collins, "Guidance on the Regu-

latory Requirements for Criticality Analysis of Fuel Storage at Light-Water Reac-

tor Power Plants," dated August 19, 1998 (ADAMS Accession No. ML003728001).

88

8 Appendix

8.1 Detailed Maps of the Full Cycle Depletion Points

8.1.1 CASMO-5 MxN Cycle 1

H G F E D C B A

15

14

13

12

11

10

9

81.019-0.019

1

1.323-0.036

2

1.103-0.005

2

1.283-0.017

2

0.971-0.006

4

1.1600.002

2

0.6680.017

21.296-0.005

2

1.105-0.020

2

1.336-0.002

2

1.062-0.010

2

1.211-0.015

1

0.8050.021

2

0.6870.021

21.349-0.042

1

1.101-0.009

1

1.272-0.020

2

0.9640.021

2

1.125-0.005

3

0.6170.027

21.319-0.000

4

1.2280.025

2

0.499-0.022

31.1750.008

1

1.0040.032

2

0.7570.009

20.6920.061

1

0.5490.035

4

Figure 1: HZP 1.02 MWD/kg S3 21.6cm assembly version D vs beavrs RMS=0.0227

1

File Data% Differenceto Reference

# of Folds













Figure 8.1: The difference in fission rates of CASMO-5 MxN compared to BEAVRSdata at 1.02 GWd/T exposure in Cycle 1. The RMS difference is 0.0227.

89

H G F E D C B A

15

14

13

12

11

10

9

81.044-0.006

1

1.339-0.020

2

1.113-0.018

2

1.292-0.010

2

0.980-0.005

4

1.154-0.012

2

0.6610.012

21.317-0.024

2

1.118-0.010

2

1.345-0.022

2

1.070-0.006

2

1.216-0.015

1

0.8030.007

2

0.6770.007

21.358-0.011

1

1.1070.004

1

1.276-0.009

2

0.9690.010

2

1.117-0.009

2

0.6120.031

21.321-0.007

4

1.2180.001

1

0.4950.009

31.1520.018

1

0.9910.037

1

0.7400.026

20.6810.037

1

0.5390.045

3


1


# of Folds





90

H G F E D C B A

15

14

13

12

11

10

9

81.072-0.003

1

1.353-0.015

1

1.131-0.019

2

1.303-0.020

1

1.000-0.001

3

1.159-0.018

2

0.6650.008

21.334-0.021

2

1.138-0.006

2

1.354-0.018

2

1.089-0.014

2

0.817-0.000

2

0.6800.003

21.367-0.010

1

1.1250.000

1

1.288-0.010

2

0.9880.007

2

1.1210.006

1

0.6150.029

21.330-0.010

4

1.2240.001

1

0.498-0.001

31.1580.019

1

1.0000.042

1

0.7410.022

20.6920.036

1

0.5400.028

4


1


# of Folds





91

H G F E D C B A

15

14

13

12

11

10

9

81.0810.023

1

1.3350.006

2

1.127-0.000

2

1.285-0.005

2

1.003-0.007

4

1.140-0.022

2

0.656-0.000

21.3220.005

2

1.1350.009

2

1.332-0.001

2

1.085-0.000

2

1.213-0.017

1

0.818-0.001

2

0.669-0.007

21.3440.000

1

1.1190.009

1

1.270-0.006

2

0.9890.000

2

1.102-0.019

2

0.6080.008

21.308-0.005

4

1.203-0.006

1

0.492-0.014

31.1400.023

1

0.9910.020

1

0.7280.008

20.6910.013

1

0.5300.007

4


1


# of Folds





92

H G F E D C B A

15

14

13

12

11

10

9

81.0960.023

1

1.3260.002

2

1.1310.005

2

1.287-0.011

2

1.028-0.009

4

1.154-0.025

2

0.6660.003

21.3180.004

2

1.1380.008

2

1.324-0.001

2

1.098-0.003

2

0.8430.001

2

0.679-0.003

21.333-0.005

1

1.1260.005

1

1.277-0.004

2

1.015-0.003

2

1.116-0.021

2

0.6190.008

21.311-0.006

3

1.217-0.006

1

0.501-0.016

31.1520.032

1

1.0140.013

1

0.7370.010

20.7150.011

1

0.5380.007

4


1


# of Folds





93

H G F E D C B A

15

14

13

12

11

10

9

81.1000.010

1

1.3020.005

2

1.1230.016

2

1.274-0.008

2

1.044-0.006

4

1.157-0.024

1

0.6710.005

21.2980.004

2

1.1290.019

2

1.2990.006

2

1.100-0.005

2

1.229-0.028

1

0.8610.003

2

0.681-0.004

21.3060.006

1

1.1220.012

1

1.268-0.005

2

1.0320.003

2

1.119-0.022

2

0.6240.011

21.295-0.003

4

0.507-0.016

21.1500.018

1

1.0260.003

1

0.7380.017

20.735-0.010

1

0.5390.004

4


1


# of Folds





94

H G F E D C B A

15

14

13

12

11

10

9

81.0740.015

1

1.2610.010

2

1.0950.015

2

1.2450.005

1

1.038-0.000

3

1.147-0.019

2

0.6660.010

21.2570.006

2

1.0980.020

2

1.2610.011

1

1.0810.007

1

1.214-0.017

1

0.8620.004

2

0.676-0.008

21.2660.008

1

1.0970.011

1

1.244-0.002

2

1.028-0.006

2

1.110-0.015

3

0.6220.006

11.268-0.005

3

1.205-0.021

1

0.504-0.019

31.137-0.006

1

0.7320.010

10.536-0.012

4


1


# of Folds





95

H G F E D C B A

15

14

13

12

11

10

9

81.0840.022

1

1.2610.023

2

1.0980.017

2

1.2480.003

2

1.0510.006

4

1.157-0.022

1

0.6700.008

21.2600.017

1

1.1010.027

2

1.2600.028

1

1.0880.009

2

1.224-0.017

1

0.874-0.005

2

0.680-0.020

21.2640.008

1

1.1010.021

1

1.250-0.003

2

1.041-0.010

2

1.120-0.015

3

0.627-0.007

21.271-0.007

3

1.215-0.025

1

0.510-0.026

21.146-0.014

1

0.7370.003

10.756-0.018

1

0.541-0.021

4


1


# of Folds





96

H G F E D C B A

15

14

13

12

11

10

9

81.0600.005

1

1.2190.001

2

1.230-0.002

2

1.0660.006

4

1.178-0.008

2

0.6860.015

11.218-0.000

2

1.0700.011

2

1.2250.011

1

1.0800.005

2

1.230-0.013

1

0.902-0.001

1

0.695-0.005

11.223-0.005

1

1.0810.007

1

1.2370.000

2

1.0590.008

1

1.141-0.011

3

0.6440.002

21.249-0.004

3

1.2240.000

1

0.524-0.013

31.1490.001

1

1.060-0.008

1

0.7490.002

20.786-0.006

1

0.551-0.000

3


1


# of Folds





97

H G F E D C B A

15

14

13

12

11

10

9

81.198-0.012

1

1.0610.010

2

1.224-0.000

1

1.0790.007

3

1.200-0.009

2

0.7040.020

21.197-0.010

2

1.0550.004

2

1.210-0.009

2

1.0780.004

1

0.9260.013

2

0.7120.006

21.205-0.009

1

1.072-0.001

1

1.2340.004

1

1.0720.005

2

1.164-0.011

2

0.6620.012

21.242-0.009

4

1.236-0.006

2

0.539-0.011

31.1560.009

1

1.077-0.005

1

0.7640.008

20.5630.004

4


1


# of Folds





98

8.1.2 CASMO-5 MxN Cycle 2

H G F E D C B A

15

14

13

12

11

10

9

81.2000.052

1

1.1630.037

2

1.1460.007

2

1.072-0.004

4

1.041-0.018

2

0.885-0.023

11.2000.052

1

1.1810.050

1

1.1860.024

1

1.2130.012

2

1.1320.027

1

0.885-0.050

11.1630.037

2

1.1820.021

1

1.2310.021

1

1.161-0.019

2

1.0710.016

1

0.764-0.002

21.1040.015

1

1.147-0.022

3

1.122-0.020

1

0.478-0.077

21.1460.007

2

1.119-0.003

1

1.087-0.008

1

1.0540.006

2

0.8380.001

11.072-0.004

4

1.133-0.038

1

0.9680.014

1

0.466-0.046

11.041-0.018

2

1.028-0.036

3

0.465-0.052

20.885-0.023

1

0.475-0.043

1


1


# of Folds





99

H G F E D C B A

15

14

13

12

11

10

9

81.1590.038

1

1.1340.027

2

1.1470.011

2

1.0670.005

4

1.037-0.018

2

0.875-0.006

11.1590.038

1

1.1460.027

2

1.1590.017

1

1.2080.012

2

1.1250.023

1

0.879-0.034

11.1340.027

2

1.1540.013

1

1.2280.014

1

1.182-0.017

2

1.0720.008

1

0.7670.008

21.1000.013

1

1.177-0.026

3

1.145-0.017

1

0.498-0.043

21.1470.011

2

1.113-0.002

1

1.115-0.019

1

1.061-0.002

2

0.8440.006

11.0670.005

4

1.145-0.023

1

0.9640.014

1

0.484-0.018

11.037-0.018

2

1.036-0.030

3

0.484-0.037

20.875-0.006

1

0.495-0.023

1


1


# of Folds





100

H G F E D C B A

15

14

13

12

11

10

9

81.1170.030

1

1.1170.011

2

1.1490.001

1

1.0680.008

3

1.037-0.015

2

0.8660.002

21.1250.031

2

1.1450.016

1

1.2080.008

2

1.061-0.010

1

0.873-0.019

11.1170.030

1

1.1420.011

1

1.2330.007

1

1.208-0.019

1

1.0850.010

2

0.7680.005

21.1170.011

2

1.1090.013

1

1.212-0.019

4

1.174-0.005

1

0.511-0.038

21.1490.001

1

1.1150.002

1

1.1490.018

1

1.0780.010

2

0.8520.017

11.0680.008

3

1.169-0.033

1

0.498-0.015

11.037-0.015

2

1.050-0.026

2

0.498-0.027

20.8660.002

2

0.871-0.005

1

0.509-0.025

1


1


# of Folds





101

H G F E D C B A

15

14

13

12

11

10

9

81.1070.033

1

1.0950.020

2

1.0960.006

1

1.1320.003

2

1.0510.004

4

1.021-0.010

2

0.8460.014

21.1070.033

1

1.1020.027

2

1.1220.013

1

1.1900.005

2

1.1080.008

1

0.853-0.017

11.0950.020

2

1.1190.009

1

1.2170.004

1

1.200-0.022

2

1.0710.005

1

0.7540.012

21.0960.006

1

1.0930.013

1

1.209-0.027

3

1.167-0.014

1

0.509-0.035

21.1320.003

2

1.098-0.005

1

1.1450.026

1

1.064-0.006

2

0.8360.018

11.0510.004

4

1.146-0.021

1

1.163-0.032

1

0.9470.015

1

0.496-0.015

11.021-0.010

2

1.039-0.022

3

0.495-0.027

20.8460.014

2

0.508-0.025

1


1


# of Folds





102

H G F E D C B A

15

14

13

12

11

10

9

81.0900.025

1

1.0840.022

1

1.0900.009

2

1.1360.002

2

1.0520.002

4

1.020-0.010

2

0.8350.014

21.0900.025

1

1.0880.025

2

1.1130.009

1

1.1930.000

2

1.1100.007

1

0.844-0.010

11.0840.022

1

1.1100.006

1

1.223-0.003

1

1.223-0.017

2

1.0810.004

2

0.7520.003

21.0900.009

2

1.1020.012

1

1.240-0.024

4

1.190-0.010

1

0.520-0.036

21.1360.002

2

1.101-0.005

1

1.1730.009

1

1.076-0.002

2

0.8390.018

11.0520.002

4

1.157-0.011

1

1.187-0.024

1

0.9460.023

1

0.507-0.011

11.020-0.010

2

1.049-0.019

3

0.507-0.030

20.8350.014

2

0.8430.007

1

0.519-0.019

1


1


# of Folds





103

H G F E D C B A

15

14

13

12

11

10

9

81.0800.020

1

1.0760.011

2

1.084-0.000

2

1.1350.002

2

1.0490.007

4

1.0160.000

2

0.8210.027

21.0800.020

1

1.0790.023

2

1.1060.008

1

1.193-0.004

2

1.1060.003

1

1.0440.004

1

0.832-0.000

11.0760.011

2

1.1030.001

1

1.224-0.009

1

1.233-0.022

2

1.080-0.001

2

0.7450.015

21.084-0.000

2

1.1030.004

1

1.257-0.029

4

1.199-0.013

1

0.526-0.030

21.1350.002

2

1.098-0.003

1

1.1860.007

1

1.075-0.001

2

0.8310.024

11.0490.007

4

1.161-0.007

1

1.196-0.023

1

0.9340.024

1

0.511-0.005

11.0160.000

2

1.050-0.014

3

0.511-0.024

20.8210.027

2

0.8310.016

1

0.526-0.012

1


1


# of Folds





104

H G F E D C B A

15

14

13

12

11

10

9

81.0670.018

1

1.0670.022

2

1.077-0.005

2

1.136-0.001

2

1.046-0.003

4

1.012-0.001

2

0.8100.025

21.0670.018

1

1.0680.009

2

1.0980.008

1

1.192-0.005

2

1.1040.002

1

1.041-0.003

1

0.821-0.004

11.0670.022

2

1.0950.011

1

1.2260.003

1

1.244-0.025

2

1.083-0.009

2

0.739-0.007

11.077-0.005

2

1.1070.026

1

1.275-0.031

4

1.210-0.008

1

0.533-0.010

11.136-0.001

2

1.097-0.002

1

1.2020.011

1

1.078-0.001

2

0.8280.025

11.046-0.003

4

1.165-0.003

1

1.209-0.027

1

0.9270.023

1

0.518-0.005

11.012-0.001

2

1.0530.003

3

0.518-0.021

20.8100.025

2

0.821-0.001

1

0.533-0.015

1


1


# of Folds





105

H G F E D C B A

15

14

13

12

11

10

9

81.0620.018

1

1.0630.009

2

1.0740.007

2

1.136-0.000

2

1.0460.002

4

1.011-0.004

2

0.8020.019

21.0620.018

1

1.0640.015

2

1.0940.007

1

1.192-0.003

2

1.1020.001

1

1.0400.002

1

0.8150.001

11.0630.009

2

1.0910.003

1

1.226-0.005

1

1.251-0.012

2

1.084-0.001

2

0.7360.019

21.0740.007

2

1.1070.003

1

1.285-0.028

4

1.216-0.003

1

0.538-0.026

21.136-0.000

2

1.096-0.006

1

1.2100.005

1

1.0780.000

2

0.8240.018

11.0460.002

4

1.168-0.003

1

1.215-0.019

1

0.9210.021

1

0.523-0.005

11.011-0.004

2

1.055-0.015

3

0.523-0.022

20.8020.019

2

0.8150.014

1

0.538-0.014

1


1


# of Folds





106

H G F E D C B A

15

14

13

12

11

10

9

81.0580.016

1

1.0610.010

2

1.0730.006

2

1.137-0.001

2

1.0450.003

4

1.011-0.003

2

0.7980.026

21.0580.016

1

1.0610.013

2

1.0910.006

1

1.192-0.005

2

1.1010.007

1

1.0400.003

1

0.811-0.002

11.0610.010

2

1.090-0.002

1

1.227-0.015

1

1.254-0.016

2

1.084-0.004

2

0.7330.012

21.0730.006

2

1.1080.006

1

1.290-0.025

4

1.219-0.002

1

0.541-0.037

21.137-0.001

2

1.096-0.009

1

1.2140.012

1

1.0780.002

2

0.8210.027

11.0450.003

4

1.171-0.000

1

1.219-0.021

1

0.9170.032

1

0.525-0.011

11.011-0.003

2

1.056-0.012

3

0.525-0.028

20.7980.026

2

0.8120.014

1

0.542-0.008

1


1


# of Folds





107

H G F E D C B A

15

14

13

12

11

10

9

81.0580.010

1

1.0620.002

2

1.0750.004

2

1.1430.001

2

1.0500.005

4

1.016-0.002

2

0.7970.028

21.0580.010

1

1.0620.008

2

1.0920.007

1

1.197-0.005

2

1.105-0.003

1

1.0440.006

1

0.8100.004

11.0620.002

2

1.0900.001

1

1.233-0.006

1

1.266-0.012

2

1.0900.003

2

0.7350.014

21.0750.004

2

1.1130.014

1

1.304-0.027

4

1.232-0.008

1

0.550-0.028

21.1430.001

2

1.100-0.004

1

1.228-0.001

1

1.084-0.004

2

0.8230.022

11.0500.005

4

1.231-0.016

1

0.9170.020

1

0.533-0.007

11.016-0.002

2

1.064-0.005

3

0.533-0.026

20.7970.028

2

0.8120.020

1

0.551-0.011

1


1


# of Folds





108

8.1.3 SIMULATE-3 3D Cycle 1

H G F E D C B A

15

14

13

12

11

10

9

81.0440.005

1

1.359-0.009

2

1.1210.012

2

1.303-0.001

2

0.973-0.003

4

1.156-0.002

2

0.655-0.002

21.3350.024

2

1.127-0.000

2

1.3620.016

2

1.0730.000

2

1.220-0.007

1

0.7910.004

2

0.672-0.001

21.377-0.021

1

1.1120.002

1

1.284-0.010

2

0.9600.017

2

1.117-0.012

3

0.6040.007

21.3300.008

4

1.2180.017

2

0.488-0.044

31.131-0.031

1

0.9810.009

2

0.730-0.029

20.6710.032

1

0.5310.002

4


1


# of Folds




Figure 8.21: The difference in fission rates of SIMULATE-3 3D compared to BEAVRSdata at 1.02 GWd/T exposure in Cycle 1. The RMS difference is 0.0162.

109

H G F E D C B A

15

14

13

12

11

10

9

81.0610.010

1

1.363-0.003

2

1.132-0.001

2

1.3060.002

2

0.984-0.001

4

1.151-0.015

2

0.6530.000

21.341-0.006

2

1.1390.009

2

1.363-0.009

2

1.0830.005

2

1.221-0.011

1

0.7970.000

2

0.669-0.004

21.3780.004

1

1.1210.017

1

1.283-0.003

2

0.9680.009

2

1.108-0.017

2

0.6010.014

21.325-0.004

4

1.207-0.008

1

0.484-0.014

31.110-0.019

1

0.9740.021

1

0.721-0.000

20.6690.019

1

0.5240.017

3


1


# of Folds





110

H G F E D C B A

15

14

13

12

11

10

9

81.0800.005

1

1.369-0.004

1

1.148-0.004

2

1.317-0.010

1

1.0080.007

3

1.163-0.015

2

0.6620.005

21.349-0.010

2

1.1550.008

2

1.368-0.008

2

1.100-0.003

2

0.8180.001

2

0.677-0.001

21.381-0.001

1

1.1360.009

1

1.292-0.007

2

0.9890.007

2

1.1190.004

1

0.6100.021

21.330-0.011

4

1.213-0.008

1

0.491-0.014

31.105-0.027

1

0.9840.026

1

0.7260.002

20.6800.020

1

0.5270.003

4


1


# of Folds





111

H G F E D C B A

15

14

13

12

11

10

9

81.0750.017

1

1.3330.004

2

1.1320.004

2

1.291-0.000

2

1.0120.002

4

1.151-0.013

2

0.6580.003

21.3170.001

2

1.1370.010

2

1.333-0.000

2

1.0930.006

2

1.223-0.008

1

0.8260.008

2

0.673-0.002

21.343-0.001

1

1.1230.012

1

1.272-0.005

2

0.9940.006

2

1.107-0.014

2

0.6070.007

21.304-0.009

4

1.199-0.009

1

0.489-0.020

31.097-0.016

1

0.9850.015

1

0.720-0.003

20.6880.008

1

0.522-0.009

4


1


# of Folds





112

H G F E D C B A

15

14

13

12

11

10

9

81.0860.014

1

1.3260.002

2

1.1370.011

2

1.296-0.004

2

1.0390.002

4

1.168-0.013

2

0.6690.007

21.313-0.000

2

1.1400.010

2

1.3270.001

2

1.1060.004

2

0.8520.012

2

0.6840.005

21.334-0.004

1

1.1300.007

1

1.281-0.002

2

1.0210.002

2

1.123-0.014

2

0.6190.008

21.307-0.009

3

1.214-0.009

1

0.499-0.020

31.102-0.011

1

1.0050.004

1

0.729-0.001

20.7100.004

1

0.529-0.010

4


1


# of Folds





113

H G F E D C B A

15

14

13

12

11

10

9

81.080-0.008

1

1.289-0.006

2

1.1180.011

2

1.275-0.007

2

1.0530.003

4

1.173-0.010

1

0.6750.011

21.281-0.009

2

1.1190.011

2

1.2920.000

2

1.103-0.002

2

1.241-0.018

1

0.8740.018

2

0.6890.007

21.296-0.002

1

1.1180.008

1

1.269-0.004

2

1.0390.010

2

1.131-0.011

2

0.6260.014

21.290-0.007

4

0.508-0.014

21.116-0.012

1

1.0280.005

1

0.7370.016

20.737-0.007

1

0.536-0.001

4


1


# of Folds





114

H G F E D C B A

15

14

13

12

11

10

9

81.0630.004

1

1.2500.001

2

1.0880.008

2

1.2420.003

1

1.0410.002

3

1.156-0.011

2

0.6660.010

21.247-0.001

2

1.0890.012

2

1.2530.005

1

1.0790.005

1

1.221-0.012

1

0.8690.012

2

0.680-0.002

21.2570.001

1

1.0930.007

1

1.245-0.001

2

1.032-0.002

2

1.119-0.007

3

0.6200.004

11.268-0.004

3

1.214-0.014

1

0.505-0.018

31.139-0.004

1

0.7350.013

10.536-0.013

4


1


# of Folds





115

H G F E D C B A

15

14

13

12

11

10

9

81.0650.005

1

1.2420.008

2

1.0850.005

2

1.241-0.003

2

1.0530.008

4

1.169-0.011

1

0.6740.013

21.2410.002

1

1.0850.013

2

1.2460.017

1

1.0830.004

2

1.230-0.011

1

0.8860.008

2

0.689-0.006

21.248-0.004

1

1.0930.015

1

1.248-0.004

2

1.046-0.005

2

1.133-0.003

3

0.630-0.002

21.268-0.009

3

1.226-0.016

1

0.514-0.019

21.158-0.003

1

0.7440.012

10.764-0.007

1

0.543-0.018

4


1


# of Folds





116

H G F E D C B A

15

14

13

12

11

10

9

81.049-0.005

1

1.210-0.006

2

1.226-0.005

2

1.0650.004

4

1.186-0.001

2

0.6870.016

11.210-0.007

2

1.0630.004

2

1.2180.005

1

1.0770.002

2

1.233-0.011

1

0.9090.007

1

0.7020.006

11.216-0.011

1

1.0770.003

1

1.235-0.001

2

1.0590.008

1

1.150-0.003

3

0.6440.003

21.247-0.006

3

1.2290.005

1

0.526-0.008

31.148-0.000

1

1.065-0.004

1

0.7510.005

20.786-0.006

1

0.550-0.002

3


1


# of Folds





117

H G F E D C B A

15

14

13

12

11

10

9

81.202-0.009

1

1.0650.014

2

1.2260.001

1

1.0770.006

3

1.202-0.008

2

0.7010.015

21.201-0.006

2

1.0600.008

2

1.212-0.008

2

1.0790.005

1

0.9270.014

2

0.7160.011

21.209-0.006

1

1.0750.002

1

1.2350.005

1

1.0710.004

2

1.166-0.010

2

0.6570.005

21.242-0.008

4

1.236-0.006

2

0.537-0.015

31.144-0.002

1

1.074-0.008

1

0.7610.004

20.558-0.005

4


1


# of Folds





118

8.1.4 SIMULATE-3 3D Cycle 2

H G F E D C B A

15

14

13

12

11

10

9

81.1760.033

1

1.1590.033

2

1.1720.029

2

1.0830.006

4

1.052-0.007

2

0.889-0.019

11.1760.033

1

1.1720.042

1

1.1700.010

1

1.2240.021

2

1.1220.018

1

0.886-0.050

11.1590.033

2

1.1660.008

1

1.2410.029

1

1.176-0.006

2

1.0580.004

1

0.762-0.005

21.0970.009

1

1.169-0.002

3

1.125-0.016

1

0.484-0.063

21.1720.029

2

1.1230.000

1

1.081-0.015

1

1.029-0.018

2

0.824-0.016

11.0830.006

4

1.156-0.018

1

0.940-0.015

1

0.468-0.040

11.052-0.007

2

1.042-0.022

3

0.468-0.045

20.889-0.019

1

0.486-0.019

1


1


# of Folds





119

H G F E D C B A

15

14

13

12

11

10

9

81.1450.027

1

1.1320.026

2

1.1620.024

2

1.0730.011

4

1.046-0.009

2

0.875-0.006

11.1450.027

1

1.1430.025

2

1.1470.007

1

1.2130.016

2

1.1140.014

1

0.876-0.037

11.1320.026

2

1.1440.004

1

1.2350.019

1

1.194-0.007

2

1.0640.001

1

0.760-0.000

21.0960.009

1

1.197-0.009

3

1.152-0.011

1

0.497-0.046

21.1620.024

2

1.115-0.001

1

1.120-0.014

1

1.049-0.013

2

0.832-0.009

11.0730.011

4

1.157-0.013

1

0.948-0.002

1

0.482-0.022

11.046-0.009

2

1.050-0.016

3

0.482-0.040

20.875-0.006

1

0.498-0.019

1


1


# of Folds





120

H G F E D C B A

15

14

13

12

11

10

9

81.1150.028

1

1.1110.005

2

1.1630.013

1

1.0760.016

3

1.051-0.002

2

0.8710.008

21.1200.026

2

1.1330.006

1

1.2130.012

2

1.064-0.007

1

0.874-0.018

11.1150.028

1

1.1310.002

1

1.2370.010

1

1.216-0.012

1

1.0750.001

2

0.7650.002

21.1110.005

2

1.1020.006

1

1.225-0.008

4

1.177-0.003

1

0.512-0.037

21.1630.013

1

1.1170.004

1

1.1310.002

1

1.061-0.006

2

0.8390.002

11.0760.016

3

1.178-0.025

1

0.495-0.021

11.051-0.002

2

1.065-0.012

2

0.495-0.033

20.8710.008

2

0.8770.002

1

0.513-0.018

1


1


# of Folds





121

H G F E D C B A

15

14

13

12

11

10

9

81.0900.018

1

1.0910.017

2

1.089-0.000

1

1.1460.015

2

1.0590.012

4

1.0330.001

2

0.8480.015

21.0900.018

1

1.0950.021

2

1.1110.003

1

1.1960.010

2

1.1000.000

1

0.853-0.017

11.0910.017

2

1.108-0.001

1

1.2220.008

1

1.211-0.013

2

1.064-0.001

1

0.7510.008

21.089-0.000

1

1.0890.009

1

1.226-0.013

3

1.173-0.009

1

0.511-0.030

21.1460.015

2

1.101-0.003

1

1.1330.016

1

1.054-0.016

2

0.8280.008

11.0590.012

4

1.154-0.013

1

1.174-0.022

1

0.9340.001

1

0.495-0.016

11.0330.001

2

1.054-0.007

3

0.495-0.027

20.8480.015

2

0.512-0.015

1


1


# of Folds





122

H G F E D C B A

15

14

13

12

11

10

9

81.0820.017

1

1.0860.024

1

1.0880.007

2

1.1500.014

2

1.0590.009

4

1.0320.001

2

0.8370.016

21.0820.017

1

1.0880.025

2

1.1070.004

1

1.1990.005

2

1.1030.001

1

0.844-0.010

11.0860.024

1

1.1050.002

1

1.2290.002

1

1.230-0.011

2

1.073-0.004

2

0.749-0.002

21.0880.007

2

1.0980.008

1

1.253-0.013

4

1.192-0.008

1

0.521-0.035

21.1500.014

2

1.103-0.003

1

1.156-0.006

1

1.063-0.014

2

0.8290.006

11.0590.009

4

1.161-0.007

1

1.193-0.018

1

0.9310.007

1

0.505-0.015

11.0320.001

2

1.060-0.008

3

0.506-0.032

20.8370.016

2

0.8460.010

1

0.522-0.013

1


1


# of Folds





123

H G F E D C B A

15

14

13

12

11

10

9

81.0710.012

1

1.0770.012

2

1.081-0.002

2

1.1470.012

2

1.0550.013

4

1.0250.008

2

0.8210.027

21.0710.012

1

1.0780.023

2

1.1000.003

1

1.1980.001

2

1.100-0.003

1

1.0450.005

1

0.829-0.004

11.0770.012

2

1.097-0.004

1

1.230-0.004

1

1.241-0.016

2

1.074-0.007

2

0.7410.009

21.081-0.002

2

1.1000.002

1

1.271-0.017

4

1.203-0.009

1

0.527-0.029

21.1470.012

2

1.100-0.002

1

1.173-0.004

1

1.065-0.011

2

0.8230.014

11.0550.013

4

1.162-0.006

1

1.203-0.017

1

0.9230.013

1

0.511-0.006

11.0250.008

2

1.060-0.005

3

0.511-0.024

20.8210.027

2

0.8310.016

1

0.528-0.009

1


1


# of Folds





124

H G F E D C B A

15

14

13

12

11

10

9

81.0630.013

1

1.0710.025

2

1.078-0.004

2

1.1470.009

2

1.0540.004

4

1.0220.008

2

0.8100.026

21.0630.013

1

1.0710.012

2

1.0950.006

1

1.1990.000

2

1.099-0.002

1

1.043-0.001

1

0.820-0.006

11.0710.025

2

1.0930.009

1

1.2320.008

1

1.251-0.019

2

1.077-0.015

2

0.736-0.011

11.078-0.004

2

1.1030.023

1

1.286-0.022

4

1.212-0.006

1

0.534-0.009

11.1470.009

2

1.099-0.000

1

1.179-0.008

1

1.067-0.012

2

0.8180.013

11.0540.004

4

1.164-0.005

1

1.212-0.024

1

0.9150.011

1

0.517-0.008

11.0220.008

2

1.0610.010

3

0.517-0.024

20.8100.026

2

0.8220.000

1

0.534-0.013

1


1


# of Folds





125

H G F E D C B A

15

14

13

12

11

10

9

81.0590.015

1

1.0670.012

2

1.0750.007

2

1.1460.008

2

1.0530.009

4

1.0190.004

2

0.8020.019

21.0590.015

1

1.0660.018

2

1.0910.005

1

1.1980.003

2

1.097-0.003

1

1.0420.004

1

0.813-0.001

11.0670.012

2

1.0890.001

1

1.2320.000

1

1.257-0.008

2

1.078-0.007

2

0.7320.014

21.0750.007

2

1.1060.002

1

1.295-0.019

4

1.218-0.001

1

0.538-0.027

21.1460.008

2

1.098-0.004

1

1.190-0.012

1

1.069-0.008

2

0.8150.008

11.0530.009

4

1.165-0.006

1

1.218-0.016

1

0.9120.011

1

0.522-0.007

11.0190.004

2

1.062-0.008

3

0.522-0.023

20.8020.019

2

0.8140.013

1

0.539-0.012

1


1


# of Folds





126

H G F E D C B A

15

14

13

12

11

10

9

81.0560.014

1

1.0650.014

2

1.0750.008

2

1.1470.008

2

1.0530.010

4

1.0190.005

2

0.7980.026

21.0560.014

1

1.0640.015

2

1.0900.005

1

1.1990.001

2

1.0970.003

1

1.0410.003

1

0.809-0.004

11.0650.014

2

1.088-0.003

1

1.233-0.010

1

1.261-0.010

2

1.079-0.009

2

0.7300.007

21.0750.008

2

1.1050.003

1

1.300-0.016

4

1.220-0.001

1

0.542-0.035

21.1470.008

2

1.097-0.008

1

1.191-0.007

1

1.068-0.007

2

0.8130.018

11.0530.010

4

1.166-0.005

1

1.221-0.019

1

0.9080.022

1

0.524-0.013

11.0190.005

2

1.062-0.007

3

0.524-0.030

20.7980.026

2

0.8110.013

1

0.542-0.007

1


1


# of Folds





127

H G F E D C B A

15

14

13

12

11

10

9

81.0620.013

1

1.0670.007

2

1.0770.005

2

1.1500.006

2

1.0550.009

4

1.0200.002

2

0.7940.024

21.0620.013

1

1.0680.014

2

1.0920.006

1

1.202-0.002

2

1.100-0.008

1

1.0440.005

1

0.806-0.001

11.0670.007

2

1.0900.001

1

1.238-0.002

1

1.269-0.009

2

1.084-0.003

2

0.7300.007

21.0770.005

2

1.1090.011

1

1.313-0.019

4

1.233-0.008

1

0.549-0.031

21.1500.006

2

1.100-0.004

1

1.219-0.008

1

1.079-0.009

2

0.8160.014

11.0550.009

4

1.233-0.014

1

0.9120.015

1

0.533-0.006

11.0200.002

2

1.066-0.003

3

0.533-0.027

20.7940.024

2

0.8080.015

1

0.549-0.013

1


1


# of Folds





128

Documents

Testing the EPRI Reactivity Depletion Decrement