NUREG/CR-6759

ORNL/TM-2001/69

Parametric Study of

the Effect of Control Rods

for PWR Burnup Credit

Prepared by

C. E. Sanders and J. C. Wagner, ORNL

Oak Ridge National Laboratory

U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001
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NUREG/CR–6759

ORNL/TM–2001/69

Parametric Study of

the Effect of Control Rods

for PWR Burnup Credit

Manuscript Completed: October 2001

Date Published: February 2002

Prepared by

C. E. Sanders and J. C. Wagner, ORNL

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831–6370

R. Y. Lee, NRC Project Manager

Prepared for

Division of System Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555–0001

NRC Job Code W6479

iii

ABSTRACT

The Interim Staff Guidance on burnup credit for pressurized water reactor (PWR) spent nuclear fuel (SNF), issued

by the United States Nuclear Regulatory Commission’s (U.S. NRC) Spent Fuel Project Office, recommends the use

of analyses that provide an “adequate representation of the physics” and notes particular concern with the “need to

consider the more reactive actinide compositions of fuels burned with fixed absorbers or with control rods fully

or partly inserted.” In the absence of readily available information on the extent of control rod (CR) usage in U.S.

PWRs and the subsequent reactivity effect of CR exposure on discharged SNF, NRC staff has indicated a need for

greater understanding in these areas. In response, this report presents a parametric study of the effect of CR

exposure on the reactivity of discharged SNF for various CR designs, including Axial Power Shaping Rods, fuel

enrichments, and exposure conditions (i.e., burnup and axial insertion). The study is performed in two parts. In the

first part, two-dimensional assembly calculations are performed, effectively assuming full axial CR insertion.

These calculations bound the effect of CR exposure and facilitate comparisons of the various CR designs. In the

second part, three-dimensional calculations are performed to quantify the reactivity effect of CR exposure in a

burnup credit cask environment and determine the effect of partly inserted CRs. The reactivity effect as a function

of axial insertion depth is shown for the various CR designs considered. The results from the study demonstrate

that the reactivity effect increases with increasing CR exposure (e.g., burnup) and decreasing initial fuel enrichment

(for a fixed burnup). Further, CR exposure is shown to have a larger effect on discharge reactivity when it occurs

later in the assembly burnup. For variations in CR design, there exists a direct relationship between the reactivity

worth of the CRs and their effect on discharge reactivity – higher reactivity worth CRs result in larger effects on

discharge reactivity. The effects are quantified and typical operating conditions are reviewed, enabling an increased

understanding of the effect of CR exposure on the reactivity of discharged SNF. The report concludes with a

discussion of the issues for consideration and preliminary recommendations to address the effect of CR exposure in

burnup credit criticality safety analyses.

v

CONTENTS

Page

ABSTRACT.....................................................................................................................................................iii

LIST OF FIGURES.........................................................................................................................................vii

LIST OF TABLES ...........................................................................................................................................ix

FOREWORD...................................................................................................................................................xi

ACKNOWLEDGEMENTS............................................................................................................................xiii

1 INTRODUCTION.....................................................................................................................................1

2 REVIEW OF CONTROL ROD DESIGNS AND OPERATIONAL PRACTICES .....................................3

2.1 CONTROL ROD DESIGNS............................................................................................................3

2.1.1 Westinghouse Designs..........................................................................................................3

2.1.2 Babcock & Wilcox Designs..................................................................................................3

2.1.3 Combustion Engineering Designs..........................................................................................3

2.2 CONTROL ROD DESIGNS INVESTIGATED ...............................................................................3

2.2.1 Hybrid Ag-In-Cd/B4C Control Rod Design (Westinghouse 17 × 17) .....................................4

2.2.2 Ag-In-Cd Control Rod Design (B&W 15 × 15) ....................................................................4

2.2.3 CE Ag-In-Cd/B4C Control Rod Design (CE 14 × 14)...........................................................4

2.2.4 Axial Power Shaping Rod Design (B&W 15 × 15)...............................................................4

2.3 CONTROL RODS OPERATIONAL PRACTICES..........................................................................4

3 REACTIVITY EFFECT OF CONTROL RODS........................................................................................7

3.1 INTRODUCTION AND BACKGROUND.......................................................................................7

3.2 TWO-DIMENSIONAL ANALYSES ...............................................................................................7

3.2.1 Code Description..................................................................................................................7

3.2.2 Calculations.........................................................................................................................8

3.2.3 B&W Ag-In-Cd Control Rods ..............................................................................................9

3.2.4 Westinghouse Hybrid Ag-In-Cd/B4C Control Rods .............................................................17

3.2.5 CE Ag-In-Cd/B4C Control Rods.........................................................................................24

3.2.6 B&W Gray Axial Power Shaping Rods ..............................................................................29

3.2.7 Cooling Time.....................................................................................................................35

3.2.8 Summary of Two-Dimensional Analyses ............................................................................36

3.3 THREE-DIMENSIONAL ANALYSES..........................................................................................38

3.3.1 Code Description................................................................................................................39

3.3.2 Reactivity Behavior with CRs Present for a Rail-Type Cask ...............................................39

3.3.2.1 Full-Axial Insertion Analyses..............................................................................41

3.3.2.2 Partial-Axial Insertion Analyses..........................................................................46

4 DISCUSSION AND IMPLICATIONS ....................................................................................................51

5 RECOMMENDATIONS.........................................................................................................................53

6 REFERENCES........................................................................................................................................55

vii

LIST OF FIGURES

Figure Page

1 B&W 15 × 15 assembly lattice representing the CR locations..............................................................10

2 HELIOS calculational model of a B&W 15 × 15 assembly containing 16 CRs ....................................11

3 Comparison of kinf values (out-of-reactor conditions) as a function of burnup. The results correspond

to 4 wt % 235U enriched B&W 15 × 15 fuel and Ag-In-Cd CRs............................................................12

4 Comparison of ∆k values as a function of burnup for various CR exposures with initial fuel

enrichments of 3, 4, and 5 wt % 235U, for B&W 15 × 15 fuel and Ag-In-Cd CRs..................................14

5 Comparison of ∆k values as a function of burnup for 5 GWd/MTU CR exposures at various times

during the burnup with 4 wt % 235U B&W 15 × 15 fuel and Ag-In-Cd CRs..........................................15

6 Comparison of ∆k values as a function of burnup with CR exposure during the first 15 GWd/MTU

(1 cycle) for various initial fuel enrichments. The results correspond to B&W 15 × 15 fuel and

Ag-In-Cd CRs.....................................................................................................................................16

7 Westinghouse 17 × 17 assembly lattice representing the CR locations..................................................18

8 HELIOS calculational model of a Westinghouse 17 × 17 assembly containing 24 CRs.........................19

9 Comparison of kinf values (out-of-reactor conditions) as a function of burnup with and without CR

exposure. The results correspond to 4 wt % 235U enriched Westinghouse 17 × 17 fuel and

Ag-In-Cd/B4C CRs. ............................................................................................................................20

10 Comparison of ∆k values as a function of burnup for various CR exposures with initial fuel

enrichments of 3, 4, and 5 wt % 235U. The results correspond to Westinghouse 17 × 17 fuel and the

B4C axial segment of the hybrid Ag-In-Cd/B4C CRs............................................................................22

11 Comparison of ∆k values as a function of burnup for 5 GWd/MTU CR exposures at various times

during the burnup with initial fuel enrichment of 4 wt % 235U. The results correspond to

Westinghouse 17 × 17 fuel and B4C CRs.............................................................................................23

12 CE 14 × 14 assembly lattice representing the CR locations ..................................................................25

13 HELIOS calculational model of a CE 14 × 14 assembly containing five CRs .......................................26

14 Comparison of kinf (out-of-reactor conditions) as a function of burnup with and without CR exposure.

The results correspond to 4 wt % 235U enriched CE 14 × 14 fuel and the B4C axial segment of the

Ag-In-Cd/B4C CRs. ............................................................................................................................27

15 Comparison of ∆k values as a function of burnup for various CR exposures with initial fuel

enrichments of 3, 4, and 5 wt % 235U. The results correspond to CE 14 × 14 fuel and the B4C axial

segment of the Ag-In-Cd/B4C CRs. .....................................................................................................28

16 B&W 15 × 15 assembly lattice representing the APSR locations..........................................................31
viii

LIST OF FIGURES (continued)

Figure Page

17 Comparison of kinf values (out-of-reactor conditions) as a function of burnup with and without APSR

exposure. The results correspond to 4 wt % 235U enriched B&W 15 × 15 fuel and gray APSRs. ..........32

18 Comparison of ∆k values as a function for various APSR exposures with initial fuel enrichments of

3, 4, and 5 wt % 235U. The results correspond to B&W 15 × 15 fuel and gray APSRs. ........................33

19 Comparison of ∆k values as a function of burnup with APSR exposure during the first 30 GWd/MTU

(2 cycles) for various initial fuel enrichments. The results correspond to B&W 15 × 15 fuel and gray

APSRs................................................................................................................................................34

20 Comparison of ∆k values as a function of burnup for 15 GWd/MTU APSR exposures at various times

during the burnup with initial fuel enrichment of 4 wt % 235U. The results correspond to B&W

15 × 15 fuel and gray APSRs..............................................................................................................35

21 Comparison of ∆k values as a function of burnup for various cooling times for 45 GWd/MTU CR

exposures with initial fuel enrichment of 4 wt % 235U. The results correspond to Westinghouse

17 × 17 fuel and the B4C segment of the Ag-In-Cd/B4C CRs................................................................36

22 Comparison of ∆k values for an infinite assembly array (45 GWd/MTU, 0-year cooling time) with

various CR exposures. The results correspond to fuel with 4.0 wt % 235U initial enrichment. ...............37

23 Relationship between the effect of CR exposure on discharge reactivity (in terms of ∆k) and CR initial

reactivity worth (in terms of ∆k/k) for each of the CR and APSR designs considered. The results

correspond to fuel with 45 GWd/MTU burnup and 4.0 wt % 235U initial enrichment that have

experienced different CR exposure durations.CR exposure durations are continuous, beginning at zero

burnup and continuing until the specified burnup exposure (e.g., 5 GWd/MTU exposure occurs from

0–5 GWd/MTU.)................................................................................................................................38

24 Cross-sectional view of one quarter of the KENO V.a calculational model of the GBC-32 cask loaded

with Westinghouse 17 × 17 assemblies................................................................................................40

25 Illustration of (a) partially inserted control rods and (b) a cross section of the criticality model. ............47

26 ∆k as a function of axial depth of CR insertion for the GBC-32 cask. Results correspond to 4 wt %

235U enriched Westinghouse 17 × 17 fuel and B4C/Ag-In-Cd CRs. .......................................................48

27 ∆k as a function of axial depth of CR insertion for the GBC-32 cask. Results correspond to 4 wt %

235U enriched B&W 15 × 15 fuel and Ag-In-Cd CRs............................................................................49

28 ∆k as a function of axial depth of CR insertion for the GBC-32. Results correspond to 4 wt % 235U

enriched CE 14 × 14 fuel and B4C CRs. ..............................................................................................50
ix

LIST OF TABLES

Table Page

1 Summary of parameters used for the depletion calculations.......................................................................8

2 B&W 15 × 15 fuel assembly and CR specifications .................................................................................9

3 Summary of maximum positive ∆k values observed for B&W Ag-In-Cd CR cases considered ................ 15

4 Westinghouse 17 × 17 fuel assembly and CR specifications ................................................................... 17

5 Summary of maximum positive ∆k values observed for B4C axial segment of the Westinghouse hybrid

Ag-In-Cd/B4C CR cases considered ....................................................................................................... 23

6 CE 14 × 14 fuel assembly and CR specifications.................................................................................... 24

7 Summary of maximum positive ∆k values observed for the B4C axial segment of the CE Ag-In-Cd/B4C

CR cases considered............................................................................................................................... 29

8 B&W 15 × 15 fuel assembly and APSR specifications........................................................................... 30

9 Summary of maximum positive ∆k values observed for B&W APSR cases considered............................ 34

10 Nuclides associated with the various classifications of burnup credit....................................................... 41

11 Value of keff for various CR exposures for actinide-only burnup credit in the GBC-32 cask.

Results correspond to Westinghouse 17 × 17 fuel with 4 wt % 235U enrichment and B4C CRs fully

inserted during depletion......................................................................................................................... 42

12 Value of keff for various CR exposures for actinide + fission product burnup credit in the GBC-32 cask.

Results correspond to Westinghouse 17 × 17 fuel with 4 wt % 235U enrichment and B4C CRs fully

inserted during depletion......................................................................................................................... 42

13 Value of keff for various CR exposures for actinide-only burnup credit in the GBC-32 cask.

Results correspond to Westinghouse 17 × 17 fuel with 4 wt % 235U enrichment and B4C

(top part, approximately 160 cm)/ Ag-In-Cd (lower part, approximately 102 cm) CRs fully inserted

during depletion ..................................................................................................................................... 43

14 Value of keff for various CR exposures for actinide + fission product burnup credit in the GBC-32 cask.

Results correspond to Westinghouse 17 × 17 fuel with 4 wt % 235U enrichment and B4C

(top part, approximately 160 cm)/ Ag-In-Cd (lower part, approximately 102 cm) CRs fully inserted

during depletion ..................................................................................................................................... 43

15 Value of keff for various CR exposures for actinide-only burnup credit in the GBC-32 cask.

Results correspond to B&W 15 × 15 fuel with 4 wt % 235U enrichment and Ag-In-Cd CRs fully

inserted during depletion......................................................................................................................... 44
x

LIST OF TABLES (continued)

Table Page

16 Value of keff for various CR exposures for actinide + fission product burnup credit in the GBC-32 cask.

Results correspond to B&W 15 × 15 fuel with 4 wt % 235U enrichment and Ag-In-Cd CRs fully

inserted during depletion......................................................................................................................... 44

17 Value of keff for various CR exposures for actinide-only burnup credit in the GBC-32 cask.

Results correspond to CE 14 × 14 fuel with 4 wt % 235U enrichment and B4C CRs fully inserted

during depletion. .................................................................................................................................... 45

18 Value of keff for various CR exposures for actinide + fission product burnup credit in the GBC-32 cask.

Results correspond to CE 14 × 14 fuel with 4 wt % 235U enrichment and B4C CRs fully inserted

during depletion ..................................................................................................................................... 45
xi

FOREWORD

In 1999 the United States Nuclear Regulatory Commission (NRC) issued initial recommended guidance

for using reactivity credit due to fuel irradiation (i.e., burnup credit) in the criticality safety analysis of

spent pressurized-water-reactor (PWR) fuel in storage and transportation packages. This guidance was

issued by the NRC Spent Fuel Project Office (SFPO) as Revision 1 to Interim Staff Guidance 8 (ISG8R1)

and published in the Standard Review Plan for Transportation Packages for Spent Nuclear Fuel,

NUREG-1617 (March 2000). With this initial guidance as a basis, the NRC Office of Nuclear

Regulatory Research initiated a program to provide the SFPO with technical information that would:

• enable realistic estimates of the subcritical margin for systems with spent nuclear fuel (SNF) and

an increased understanding of the phenomena and parameters that impact the margin, and

• support the development of technical bases and recommendations for effective implementation of

burnup credit and provide realistic SNF acceptance criteria while maintaining an adequate

margin of safety.

The ISG8R1 recommends that consideration be given to the increased reactivity of SNF resulting from

the presence of control rods (CRs) in the fuel during a portion of the irradiation. This report presents a

parametric study that quantifies the changes in the SNF neutron multiplication factor as a function of the

CR insertion (axial depth into fuel as well as burnup duration) and discusses the behavior that causes the

changes. The results provide a basis for efficiently and effectively estimating the impact of CR exposure

within typical domestic PWR operations (CRs resting at the top of the fuel and full-axial insertions of

short burnup duration).

Farouk Eltawila, Director

Division of Systems Analysis and Regulatory Effectiveness

xiii

ACKNOWLEDGEMENTS

This work was supported by the Office of Nuclear Regulatory Research, Nuclear Regulatory Commission under

Project JCN W6479, Development and Applicability of Criticality Safety Software for Licensing Review. The

authors acknowledge review and useful comments by Carl J. Withee of the Spent Fuel Project Office.

The thorough review of the manuscript by our colleagues R. M. Westfall, S. M. Bowman, M. D. DeHart,

J. C. Gehin, R. T. Primm, and C. V. Parks is much appreciated. Also, the authors are grateful to W. C. Carter and

J. B. Anderson for their careful preparation of this report. In addition, thanks to S. K. Lichtenwalter for her

consultation.

1

1 INTRODUCTION

The concept of taking credit for the reduction in reactivity due to the fuel burnup is commonly referred to as

burnup credit. The reduction in reactivity that occurs with fuel burnup is due to the change in concentration (net

reduction) of fissile nuclides and the production of actinide and fission-product neutron absorbers. The change in

the concentration of these nuclides with fuel burnup, and consequently the reduction in reactivity, is dependent

upon the depletion environment (e.g., the neutron spectrum). In contrast to criticality safety analyses that employ

the “fresh-fuel assumption,” the utilization of credit for fuel burnup therefore necessitates consideration of all

possible fuel operating conditions, including exposure to control rods (CRs).

The Interim Staff Guidance1 on burnup credit (ISG-8) for pressurized water reactor (PWR) spent nuclear fuel

(SNF), issued by the United States Nuclear Regulatory Commission’s (U.S. NRC) Spent Fuel Project Office,

recommends the use of analyses that provide an “adequate representation of the physics” and notes particular

concern with the “need to consider the more reactive actinide compositions of fuels burned with fixed absorbers

or with control rods fully or partly inserted.” In the absence of readily available information on the extent of CR

usage in U.S. PWRs and the subsequent reactivity effect of CR exposure on discharged SNF, NRC staff has

indicated2 a need for greater understanding in these areas. In response, this report presents a parametric study of

the effect of CR exposure on the reactivity of discharged SNF for various CR designs, including axial power

shaping rods (APSRs), fuel enrichments, and exposure conditions (i.e., burnup and axial insertion). Herein,

APSRs are included in the general classification of CRs, but are discussed separately where differences exist

(e.g., usage/operations). The effects of fixed absorbers, such as burnable poison rods (BPRs) and integral

burnable absorbers (IBAs), on the reactivity of SNF are addressed elsewhere.3,4

The presence of CRs/APSRs increases the reactivity of burned fuel by hardening the neutron spectrum (due to

removal of thermal neutrons by capture and displacement of moderator) and suppressing burnup in localized

regions. The former effect results in an increased production of fissile plutonium isotopes and a decrease in 235U

fission, while the latter effect can lead to axial burnup distributions characterized by significantly under-burned

regions. Consequently, an assembly exposed to CRs can have a higher reactivity for a given burnup than an

assembly that has not been exposed to CRs. Although the axial burnup distribution is an important concern for

burnup credit evaluations, the effect of CR/APSR insertion on the axial burnup distribution is not addressed here

because it is considered in the selection of bounding axial burnup profile(s).5,6 Instead, this study examines the

effect of CR/APSR insertion on reactivity due to the impact of spectral hardening on the spent-fuel isotopics.

Currently in the United States, PWRs operate with the CRs withdrawn or nearly withdrawn and use soluble boron

to control the change in reactivity with burnup. In contrast, French PWR operations involve long periods of CR

insertion for reactor control, low-power operations and load following.7 Similarly, some early domestic

operations included notable CR insertions (usually in conjunction with an assembly’s first cycle of burnup).8

Axial power shaping rods, on the other hand, are inserted during “normal” reactor operation, but are relatively

few in number (e.g., in the Three Mile Island Unit-1 reactor, eight assemblies/core may contain APSRs, while 24

assemblies/core may contain CRs9

). Fuel shuffling between cycles reduces the probability that a fuel assembly

will be exposed to CR/APSR insertions for more than one cycle.

Because of the variability in CR and APSR usage, estimating the effect of CRs and APSRs in a generic manner is

difficult. Therefore parametric analyses were performed for a variety of exposure scenarios to establish an

increased understanding of the effect of CR exposure on the reactivity of discharged SNF. Effects are quantified

and typical operating conditions are reviewed. Although many of the scenarios considered are not representative

of actual reactor operations, it should be possible to estimate the reactivity effect of specific CR exposure

conditions based on inspection of the calculated results and trends shown in this report.
Introduction Section 1

2

The study described in this report is performed in two parts. In the first part, two-dimensional (2-D) calculations

are performed, effectively assuming full axial CR exposure (i.e., fully inserted). These calculations are intended

to bound the effect of CR exposure and facilitate comparisons of the various CR designs. Several CR designs

(including APSRs) that have been widely used in U.S. commercial PWRs are included in this study. In the second

part, three-dimensional (3-D) calculations are performed to quantify the reactivity effect in a burnup credit cask

environment and to determine the effect of partly inserted CRs and gain a better understanding of reality. The

reactivity effect as a function of axial insertion depth is shown for the various CR designs considered. Note that

the effect of the CRs is determined based on their effect on the depletion isotopics alone (i.e., the CRs are not

included in the criticality models, since these models represent out-of-reactor conditions).
Section 2 Review of Control Rods

3

2 REVIEW OF CONTROL ROD DESIGNS AND

OPERATIONAL PRACTICES

2.1 CONTROL ROD DESIGNS

Several different CR designs have been used in commercial nuclear reactors. However, all CR designs are similar

in that they contain thermal neutron absorbing material in rods sized to fit within the assembly guide tubes. The

Westinghouse, Combustion Engineering (CE), and Babcock & Wilcox (B&W) CR designs, including B&W

APSRs, were considered in this report. Note that B&W is the only U.S. PWR fuel vendor known to use APSRs.

2.1.1 Westinghouse Designs

Westinghouse has manufactured various types of CRs for 14 × 14, 15 × 15, and 17 × 17 fuel lattices.10 Fulland part-length silver-indium-cadmium (Ag-In-Cd) CRs with stainless steel cladding have been manufactured for

the 16 CR locations in the 14 × 14 fuel assembly designs. For the 20 CR locations in the 15 × 15 fuel assembly

designs, full-length Ag-In-Cd CRs with stainless steel cladding are used. For the 24 CR locations in the 17 × 17

fuel assembly designs, the following four different CR designs, all with stainless steel cladding, have been used:

(1) full-length “hybrid” CRs, using 102 in. (~259 cm) of boron carbide (B4C) and 40 in. (~102 cm) of Ag-In-Cd,

(2) full-length Ag-In-Cd CRs, (3) full-length hafnium (Hf) CRs (many reactors have been replacing these with

Ag-In-Cd rods because of irradiation induced swelling), and (4) part-length CRs, using 36 in. (~91 cm) of

Ag-In-Cd with a 106 in. (~269 cm) aluminum oxide spacer.

2.1.2 Babcock & Wilcox Designs

Babcock & Wilcox has manufactured two main types of CRs for 15 × 15 fuel assembly designs with 16 CR

locations: (1) Ag-In-Cd CRs with stainless steel cladding and (2) gray/black APSRs with stainless steel cladding.

The APSRs consist of either part-length Ag-In-Cd absorber (black APSRs) or Inconel absorber (gray APSRs).11

The absorber region in the black APSRs is 36 in. (~91 cm) tall while the absorber region in the gray APSRs is

63 in. (~160 cm) tall.

2.1.3 Combustion Engineering Designs

Combustion Engineering has manufactured a variety of CR assemblies, referred to as control element assemblies

(CEAs), for use in the five CR locations present in their 14 × 14 and 16 × 16 fuel assembly designs.10,12 For the

14 × 14 fuel assembly designs, the following different CEAs with Inconel cladding have been used: (1) fulllength CEAs with B4C in the central rod and axial regions of Inconel, Ag-In-Cd, and B4C in the remaining four

rods, (2) part-length CEAs with one B4C rod and four stainless steel rods, (3) part-length CEAs with one rod of

Al2O3 and four rods of Ag-In-Cd and B4C, and (3) part-length CEAs with one rod of Al2O3, two rods of Ag-In-Cd

and B4C, and two rods with stainless steel and Al2O3. Similar variations of full- and part-length CEAs have been

manufactured for the 16 × 16 fuel assembly design.

2.2 CONTROL ROD DESIGNS INVESTIGATED

As evident from the preceding discussion, the variation in CR designs is significant. However, the variation in

CR absorber materials is more limited, namely B4C, Ag-In-Cd, Hf, and Inconel. Rather than attempt to
Review of Control Rods Section 2

4

investigate each of the numerous CR designs, which in many cases involve relatively minor differences, analyses

in this report focused on investigating unique CR designs and materials to establish greater understanding. The

effects of CR designs that use the same absorber material are expected to be similar. The CR designs analyzed in

this report are the (1) Westinghouse 17 × 17 hybrid Ag-In-Cd/B4C CR design, (2) B&W 15 × 15 Ag-In-Cd CR

design, (3) CE 14 × 14 B4C CR design, and (4) B&W 15 × 15 gray APSR design. Additional information about

the specific CR designs analyzed in this report is provided in the following subsections. Detailed specifications

are given in the respective analysis sections.

2.2.1 Hybrid Ag-In-Cd/B4C Control Rod Design (Westinghouse 17 × 17)

The hybrid Ag-In-Cd/B4C rod cluster control assembly (RCCA) developed by Westinghouse and analyzed in this

report, consists of B4C pellets and Ag-In-Cd cylinders encapsulated in stainless steel cladding. Inside each

RCCA, the B4C absorber pellets are stacked on top of the Ag-In-Cd absorber. The total length of the absorber

column is 142 in. (~361 cm), where B4C constitutes 102 in. (~259 cm) and the Ag-In-Cd constitutes 40 in.

(~102 cm). The absorber column is sitting on an Inconel coil spring (in the lower part of the absorber rod). The

hold-down spring is designed to restrain the absorber material against longitudinal movement during transport,

handling, and operation while allowing for differential expansion between the absorber and the clad.13

2.2.2 Ag-In-Cd Control Rod Design (B&W 15 × 15)

The Ag-In-Cd RCCA developed by B&W and analyzed in this report, consists of Ag-In-Cd cylinders

encapsulated in stainless steel cladding. The 134-in. long absorber column sits on a lower-end plug made of

stainless steel. The upper end plug (also known as the spring spacer) is also made of stainless steel and designed

to restrain the absorber material against longitudinal movement during transport, handling, and operation.11

2.2.3 CE Ag-In-Cd/B4C Control Rod Design (CE 14 × 14)

The CEA developed by CE and analyzed in this report, consists of five Inconel tubes (fingers) that are stacked

with cylindrical B4C pellets.12 The lower 8 in. (~20 cm) of the fingers are filled with Ag-In-Cd material. The

CEAs are 161 in. (~409 cm) long, with 134 in. (~340 cm) and 124 in. (~315 cm) of B4C in the center and outer

fingers, respectively. A plenum is positioned above the poison pellet column to allow expansion volume. The

plenum also contains a spring that prevents the absorber material from moving during shipping and handling.

Each finger is sealed with an Inconel cap at the bottom and an Inconel end fitting at the top.12

2.2.4 Axial Power Shaping Rod Design (B&W 15 × 15)

The APSRs developed by B&W consist of part-length absorber rods encapsulated in stainless steel cladding. As

mentioned, the APSRs can either be gray (Inconel) or black (Ag-In-Cd). The gray APSRs are only considered in

this report due to the fact that the black APSRs are very similar to the Ag-In-Cd CR that is analyzed in this

report.

2.3 CONTROL RODS OPERATIONAL PRACTICES

Because the effect of CRs on reactivity is dependent on the duration and extent (i.e., axial insertion) of CR

exposure and the fraction of burnup without CRs inserted, it is important to understand typical operational

practices. However, because of operational variability, the extent of CR usage varies, making it difficult to truly
Section 2 Review of Control Rods

5

characterize “typical” operational practice. With this in mind, some general observations related to “typical” CR

operational practices are given in this section.

During full-power operation CRs are typically inserted into the upper portion of the fuel assemblies – above the

active fuel region. It is fairly common for the CRs to be inserted about 20 cm for the majority of the entire

burnup cycle.7, 14–16 This insertion depth is above the active fuel region, so the fuel is not exposed to the CRs.

When inserted into the active fuel region, CRs are either inserted into a small region of the upper portion of the

active fuel or fully inserted during reactor shutdown. Note, however, that some early domestic operations included

notable CR insertions (usually in conjunction with an assembly’s first cycle of burnup).8

Axial power shaping rods are utilized in the active fuel region during “normal” reactor operation. The APSRs are

typically inserted into fuel assemblies that have been previously irradiated (second or third cycle).9,11 The APSRs

remain partially inserted until the end (or near the end) of the burnup cycle.

Section 3 Reactivity Effects of Control Rods

7

3 REACTIVITY EFFECT OF CONTROL RODS

3.1 INTRODUCTION AND BACKGROUND

Since the presence of the CRs hardens the spectrum during depletion, the production of fissile plutonium increases

while the depletion of 235U decreases. This occurrence increases the reactivity of the fuel at discharge and beyond.

Hence, an assembly exposed to CRs can have a higher reactivity for a given burnup than an assembly that has not

been exposed to CRs.

Due to the great variability in CR and APSR usage, as mentioned earlier, estimating the effect of CRs and APSRs

in a generic manner is difficult. Therefore parametric analyses were performed for a variety of exposure

scenarios to establish an increased understanding of the effect of CR exposure on the reactivity of discharged

SNF. Although many of the scenarios considered are not representative of current U.S. PWR reactor operations,

it should be possible to estimate the reactivity effect of actual CR exposure conditions based on inspection of the

calculated results and trends.

The study is performed in two parts. In the first part, 2-D calculations are performed with the intent to bound the

effect of CR exposure, effectively assuming full axial CR exposure (i.e., fully inserted). In the second part, 3-D

calculations are performed to determine the effect of partial CR insertion conditions. Note that the effect of the

CRs is determined based on their effect on the depletion isotopics alone (i.e., the CRs are not included in the

criticality models).

The following sections describe the calculational methods used for this evaluation and present detailed analyses to

demonstrate the reactivity effect of CRs as a function of burnup. The analyses include variations in the type of

CR, composition, duration of exposure, axial depth of insertion, and initial fuel assembly enrichment.

3.2 TWO-DIMENSIONAL ANALYSES

3.2.1 Code Description

The 2-D calculations presented in the following subsections were performed using the HELIOS-1.6 code

package,17 which primarily consists of three programs: AURORA, HELIOS, and ZENITH. HELIOS is a 2-D,

generalized-geometry transport theory code based on the method of collision probabilities with current coupling.

AURORA, the input processor, is used to define the geometry, materials, and calculational parameters. ZENITH,

the output processor, reads the results saved by HELIOS (in a binary database) and outputs the results in text

format. The HELIOS code system also contains the ORION program for viewing and checking model geometries

and materials.

HELIOS was employed for this analysis because of its capability to explicitly model the relatively complicated,

heterogeneous assembly lattices associated with CRs. The various structures within each of the assembly models

were coupled using angular current discretization (interface currents). All calculations are for an infinite array of

fuel assemblies and utilize the 45-group neutron cross-section library, based on ENDF/B-VI, which is distributed

with the HELIOS-1.6 code package.

It should be pointed out that since there is a balance between the number of neutrons produced (from fissions) and

the number of neutrons lost (either by absorption or leakage) in a critical reactor, concerns have arisen that when

performing calculations this balance may not be accurately described and consequently the spectrum in the

computational model may not agree with critical reactor conditions. In general, for the systems considered in this
Reactivity Effects of Control Rods Section 3

8

report, the calculated neutron multiplication factor, k, is not equal to unity. However, the systems are assumed to

be part of a critical reactor (i.e., k = 1). The HELIOS code, by default, compensates for this difference by

approximating the criticality spectrum based on an adjustment of the net out-leakage if k > 1 or the net in-leakage

if k < 1. A few calculations were performed with a user specified buckling value to override the use of the

HELIOS calculated criticality spectrum and assess the spectral variations and consequent affects on reactivity.

The conclusion from these calculations is that, for the purpose of the studies presented in this report, the default

criticality spectrum calculated by HELIOS is the most appropriate one to use.

3.2.2 Calculations

All depletion calculations were performed with HELIOS using the properties and parameters given in Table 1.

Using the isotopic compositions from the depletion calculations, branch or restart calculations were performed

with HELIOS to determine the infinite neutron-multiplication factor, kinf, as a function of burnup for

out-of-reactor conditions (i.e., 20°C with no soluble boron present), zero cooling time, and the full nuclide set.

Note that all of the 2-D analyses presented in this section include all of the nuclides available in the HELIOS

45-group cross-section library that is distributed as part of the HELIOS-1.6 code package. For each unique CR

assembly design considered, a depletion calculation was performed for (1) the uncontrolled assembly condition

(i.e., no CRs present) and (2) conditions in which the CRs were assumed to be present for various periods of

burnup. Subsequently, separate criticality calculations were performed for out-of-reactor conditions using the

isotopic compositions from the depletion calculations. The ∆k values between these sets of conditions are reported

to assess the effect of CRs on the reactivity of discharge SNF.

The 2-D calculations were done with an infinite radial array of assemblies to gain an understanding of behaviors

and trends and so that the results would be general (i.e., not dependent on storage cell specifications, such as

poison loading). Three-dimensional results for a specific SNF cask are provided in Section 3.3. A number of the

2-D calculations were repeated in Section 3.2.7 to assess the effect for variations in cooling time. The results

demonstrate that the calculated effects are not sensitive to variations in cooling time within the time frame of cask

storage and transportation.

Table 1 Summary of parameters used for the depletion calculations

Parameter Value used in analyses

Moderator temperature (K) 600

Fuel temperature (K) 1000

Fuel density (g/cm3

) 10.44 (UO2)

Clad temperature (K) 600

Clad density (g/cm3

) 5.78 (Zr)

Power density* (MW/MTU) 60

Moderator boron concentration (ppm) 650

*Various cases were also calculated using a power density of 30 MW/t

(which is a more realistic value). The results showed that the ∆k values

presented in the following sections are not sensitive to variations in the

power density.
Section 3 Reactivity Effects of Control Rods

9

3.2.3 B&W Ag-In-Cd Control Rods

The Ag-In-Cd RCCA consists of 16 CRs. Calculations were performed with a B&W 15 × 15 assembly in order

to investigate the reactivity effect of these CRs. Dimensional specifications for the fuel assembly and CRs are

given in Table 2 (Ref. 11). The 15 × 15 B&W assembly lattice considered is shown in Figure 1. Figure 2

displays the geometry of the B&W 15 × 15 assembly as modeled in HELIOS.

Table 2 B&W 15 × 15 fuel assembly and CR specifications

Parameter

Dimension

(cm)

Fuel assembly specifications

Rod pitch 1.44272

Assembly pitch 21.81

Cladding outside diameter 1.09220

Cladding inside diameter 0.95758

Pellet outside diameter 0.940

Guide/instrument tube outside diameter 1.34620

Guide/instrument tube inside diameter 1.26492

Array size 15 × 15

Number of fuel rods 208

Number of guide/instrument tubes 17

Control rod specifications

Absorber material Ag (80%)–In (15%)–Cd (5%)

Absorber pellet diameter 0.99568

Cladding (304 SS) outside diameter 1.11760

Cladding (304 SS) inside diameter 1.01092
Reactivity Effects of Control Rods Section 3

10

Guide tube/CR location

Fuel rod Instrument Tube

Figure 1 B&W 15 × 15 assembly lattice representing the CR locations
Section 3 Reactivity Effects of Control Rods

11

Figure 2 HELIOS calculational model of a B&W 15 × 15 assembly containing 16 CRs
Reactivity Effects of Control Rods Section 3

12

The criticality calculations are performed for out-of-reactor conditions with isotopic compositions from the

following conditions: (1) the uncontrolled condition (i.e., CRs not present during depletion) and (2) the controlled

condition (i.e., CRs present during depletion). The kinf values (out-of-reactor conditions) as a function of burnup

from the two conditions are compared in Figure 3. The ∆k values between these two conditions demonstrate the

effect of CR exposure on reactivity.

Figure 3 Comparison of kinf values (out-of-reactor conditions) as a function of burnup. The results

correspond to 4 wt % 235U enriched B&W 15 × 15 fuel and Ag-In-Cd CRs.

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

kinf

no control rods

control rods inserted
Section 3 Reactivity Effects of Control Rods

13

For each of the following initial enrichments: 3, 4, and 5 wt % 235U, calculations were performed for cases in

which the CRs were withdrawn at 5, 15, 30, and 45 GWd/MTU (full exposure). Three cycles of 15 GWd/MTU

per cycle were assumed for the analysis. The results (∆k as a function of burnup) are shown in Figure 4 for initial

enrichments of 3, 4, and 5 wt % 235U. It is evident from the figures that the reactivity effect of CRs increases with

increasing exposure and decreasing fuel enrichment. These results are consistent with a previous study3 that

examined the effect of BPR exposure on reactivity. The maximum positive ∆k values for the various CR

exposure cases considered are summarized in Table 3. For the cases considered here, the highest ∆k is

approximately 7% (the case when CRs are present during the entire depletion with 3 wt % 235U enriched fuel).

When studying the ∆k curves of the CRs a divergence in the behavior can be noted. This divergence appears at

the moment when the CRs are withdrawn from the fuel assembly. A ‘bump’ appears because of the change in the

rate at which Pu is being produced. When the CRs are withdrawn, the spectrum immediately softens because of

the removal of strong absorbers. This causes a greater reactivity worth of 235U, relative to that when CRs are

present. Because the reactivity worth of 235U is suddenly increased, the fission rate of 235U increases as well. This

effect is only temporary, and the fission rate will stabilize throughout the remainder of the depletion while the CRs

are withdrawn. This ‘bump’ is more apparent at higher initial fuel enrichments. The increased reactivity effect at

higher enrichment is because the reactivity worth of 235U is less at 3 wt % enriched 235U fuel than at 5 wt %

enriched 235U fuel. Consequently, the fission rates of 235U will be higher at 5 wt % enriched fuel and the effects

will be more apparent.

In addition to the calculations described above, the reactivity effect of CR exposure was studied for scenarios in

which the CRs were inserted for a burnup duration of 5 GWd/MTU throughout the assembly burnup. The results

(∆k as a function of burnup) are shown in Figure 5 for an initial enrichment of 4 wt % 235U. Figure 5 show that

CR exposure has a larger effect on discharge reactivity when it occurs later in the assembly burnup. Note that

these calculations were performed to investigate/demonstrate the behavior, and may not represent realistic

exposure conditions. However, some early U.S. PWR operations included significant CR insertions in

conjunction with an assembly’s first burnup cycle.8 Thus, it is expected that cases involving exposure during the

first cycle (i.e., within the first 15 GWd/MTU) are closer to reality than those involving exposure late in burnup.

Figure 6 compares the ∆k for various initial fuel enrichments in which the CRs are present for the first

15 GWd/MTU (approximating 1 cycle). It is interesting to note that, following the initial jump, there is an

increasing trend in the ∆k values after the CRs are withdrawn for the cases with 4 and 5 wt % 235U enrichment,

but a decreasing trend for the 3 wt % 235U enrichment case. While the CRs are inserted, they displace moderator

and absorb thermal neutrons, significantly hardening the neutron spectrum. The hardened neutron spectrum

results in reduced 235U depletion, higher production of fissile plutonium isotopes and increased plutonium fission.

Examination of the atom densities of 239Pu and 235U as a function of burnup reveals that the lower the initial 235U

enrichment, the greater the 239Pu fission while the CRs are present. Therefore, lower initial 235U enrichments have

less net buildup of 239Pu while the CRs are present (relative to higher initial 235U enrichments), because they have

an increased rate of 239Pu fission during this period. When the CRs are withdrawn, the spectrum softens because

of the removal of strong absorbers and added moderation. The reactivity worth of 235U increases and

consequently the fission rate increases. However, the higher initial 235U enrichment cases have significantly more

fissile plutonium built in relative to the case with no CR exposure. The increased fissile plutonium and

subsequent increased plutonium fission result in a small degree of conversion, and thus there is an increase in ∆k

after the CRs have been withdrawn for the 4 and 5 wt % 235U enriched cases. The reactivity worth of the 3 wt %

235U enriched case is not increasing because, due to the lower initial 235U enrichment, a significant portion of the

239Pu is being depleted while the CRs are still present, which results in less net buildup of 239Pu.
Reactivity Effects of Control Rods Section 3

14

Figure 4 Comparison of ∆k values as a function of burnup for various CR exposures with initial fuel

enrichments of 3, 4, and 5 wt % 235U, for B&W 15 × 15 fuel and Ag-In-Cd CRs

-0.010

0.000

0.010

0.020

0.030

0.040

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

5.0 wt% U-235

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

4.0 wt% U-235

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

CRs removed at 5 GWd/MTU CRs removed at 15 GWd/MTU

CRs removed at 30 GWd/MTU CRs present during entire depletion

3.0 wt% U-235

∆k [k(CR) –k(no_CR)] ∆k [k(CR) –k(no_CR)] ∆k [k(CR) –k(no_CR)]
Section 3 Reactivity Effects of Control Rods

15

Table 3 Summary of maximum positive ∆k values observed for B&W

Ag-In-Cd CR cases considered (discharge burnup of 45 GWd/MTU)

Enrichment (wt % 235 Burnup at U)

CR removal

(GWd/MTU) 34 5

5 0.0042 0.0026 0.0017

15 0.0177 0.0099 0.0063

30 0.0443 0.0266 0.0154

45 0.0697 0.048 0.0304

Figure 5 Comparison of ∆k values as a function of burnup for 5 GWd/MTU CR exposures at various

times during the burnup with 4 wt % 235U B&W 15 × 15 fuel and Ag-In-Cd CRs

-0.005

-0.003

0.000

0.003

0.005

0.008

0.010

0.013

0.015

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

∆k [k(CRs) - k(no_CRs)]

CRs inserted between 0 - 5 GWd/MTU

CRs inserted between 5 -10 GWd/MTU

CRs inserted between 10 - 15 GWd/MTU

CRs inserted between 20 - 25 GWd/MTU

CRs inserted between 40 - 45 GWd/MTU
Reactivity Effects of Control Rods Section 3

16

Figure 6 Comparison of ∆k values as a function of burnup with CR exposure during the first

15 GWd/MTU (1 cycle) for various initial fuel enrichments. The results correspond to B&W 15 × 15 fuel and

Ag-In-Cd CRs.

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

∆k [k(CRs) - k(no_CRs)]

3 wt % U-235

4 wt % U-235

5 wt % U-235
Section 3 Reactivity Effects of Control Rods

17

3.2.4 Westinghouse Hybrid Ag-In-Cd/B4C Control Rods

The hybrid Ag-In-Cd/B4C RCCA, developed by Westinghouse, consists of 24 Ag-In-Cd/B4C CRs. Each CR

contains Ag-In-Cd absorber with B4C absorber pellets stacked on top of the Ag-In-Cd. Calculations were

performed with a Westinghouse 17 × 17 assembly to investigate the reactivity effect of these CRs. Dimensional

specifications for the fuel assembly and CRs are given in Table 4. The 17 × 17 Westinghouse assembly lattice is

shown in Figure 7. Figure 8 displays the geometry of the Westinghouse 17 × 17 assembly as modeled in

HELIOS-1.6.

Table 4 Westinghouse 17 × 17 fuel assembly and CR specifications

Parameter

Dimension

(cm)

Fuel assembly specifications

Rod pitch 1.2598

Assembly pitch 21.5

Cladding outside diameter 0.8898

Cladding inside diameter 0.8001

Pellet outside diameter 0.7844

Guide/instrument tube outside diameter 1.204

Guide/instrument tube inside diameter 1.123

Array size 17 × 17

Number of fuel rods 264

Number of guide/instrument tubes 25

Control rod specifications (Ref. 13)

Absorber material Natural B4C/Ag-In-Cd

B4C pellet diameter 0.84836

B4C pellet axial height 259.08

Ag-In-Cd diameter 0.86614

Ag-In-Cd axial height 101.60

Cladding (304 SS) thickness 0.0470

Cladding inside diameter 0.87376

Cladding outside diameter 0.96774
Reactivity Effects of Control Rods Section 3

18

Guide tube/CR location

Fuel rod Instrument tube

Figure 7 Westinghouse 17 × 17 assembly lattice representing the CR locations
Section 3 Reactivity Effects of Control Rods

19

Figure 8 HELIOS calculational model of a Westinghouse 17 × 17 assembly containing 24 CRs

Analyses are presented in this section for the Westinghouse hybrid CR design with various initial fuel enrichments

and various CR exposure conditions to better understand the effect of these CRs on reactivity. Since it is not

possible to include the axial variation in absorber material in a 2-D model, separate models were developed to

compare the effect of the two-absorber materials. The first model represented the axial segment of the CR

corresponding to the B4C region, while the second model represented the axial segment of the CR corresponding

to the Ag-In-Cd region. The kinf values, as a function of burnup from calculations with and without CR exposure,

are compared in Figure 9. The ∆k values between these conditions demonstrate the effect of these CRs on
Reactivity Effects of Control Rods Section 3

20

reactivity and that the B4C region of the CR results in a larger positive reactivity effect, as compared to the

Ag-In-Cd region. Since the effect of Ag-In-Cd CRs was demonstrated in the previous section with B&W fuel, the

remainder of the calculations in this section will involve the axial segment corresponding to the B4C region. Note,

however, that the lower ~100 cms of these CRs contain Ag-In-Cd, and thus partial CR insertions may only

involve the Ag-In-Cd region.

Figure 9 Comparison of kinf values (out-of-reactor conditions) as a function of burnup with and without

CR exposure. The results correspond to 4 wt % 235U enriched Westinghouse 17 × 17 fuel and Ag-In-Cd/B4C

CRs.

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

kinf

no control rods

inserted B4C control rods

inserted Ag-In-Cd control rods
Section 3 Reactivity Effects of Control Rods

21

Calculations were performed with initial enrichments of 3, 4, and 5 wt % 235U and CR exposures of 5, 15, 30, and

45 GWd/MTU (full exposure). Three cycles of 15 GWd/MTU per cycle were assumed for the analysis. The

results (∆k as a function of burnup) are shown in Figure 10 for initial enrichments of 3, 4, and 5 wt % 235U.

Consistent with the results shown in the previous section, the reactivity effect of the CRs increases with increasing

exposure and decreasing fuel enrichment. Note, however, the larger reactivity effect of B4C absorber, relative to

the Ag-In-Cd absorber considered in the previous section. The maximum positive ∆k values for the various CR

cases considered are summarized in Table 5. For the cases considered here, the highest ∆k is approximately 10%

(the case when CRs are present during the entire depletion with 3 wt % 235U enriched fuel).

In addition to the calculations described above, the reactivity effect was studied for scenarios in which the CRs

were inserted for a burnup duration of 5 GWd/MTU throughout the assembly burnup. The results (∆k as a

function of burnup) are shown in Figure 11 for an initial enrichment of 4 wt % 235U. Consistent with the results

shown in the previous section, this figure shows that CR exposure has a larger effect on discharge reactivity when

it occurs later in the assembly burnup.
Reactivity Effects of Control Rods Section 3

22

Figure 10 Comparison of ∆k values as a function of burnup for various CR exposures with initial fuel

enrichments of 3, 4, and 5 wt % 235U. The results correspond to Westinghouse 17 × 17 fuel and the B4C axial

segment of the hybrid Ag-In-Cd/B4C CRs.

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

5.0 wt% U-235

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

4.0 wt% U-235

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

CRs removed at 5 GWd/MTU CRs removed at 15 GWd/MTU

CRs removed at 30 GWd/MTU CRs present during entire depletion

3.0 wt% U-235
Section 3 Reactivity Effects of Control Rods

23

Table 5 Summary of maximum positive ∆k values observed for B4C axial segment

of the Westinghouse hybrid Ag-In-Cd/B4C CR cases considered

(discharge burnup of 45 GWd/MTU)

Enrichment (wt % 235 Burnup at U)

CR removal

(GWd/MTU) 3.0 4.0 5.0

5 0.0086 0.0048 0.0041

15 0.0280 0.0174 0.0113

30 0.0698 0.0417 0.0256

45 0.1050 0.0739 0.0479

Figure 11 Comparison of ∆k values as a function of burnup for 5 GWd/MTU CR exposures at various

times during the burnup with initial fuel enrichment of 4 wt % 235U. The results correspond to Westinghouse

17 × 17 fuel and B4C CRs.

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

∆k [k(CRs) - k(no_CRs)]

CRs inserted between 0 - 5 GWd/MTU

CRs inserted between 5 - 10 GWd/MTU

CRs inserted between 10 - 15 GWd/MTU

CRs inserted between 20 - 25 GWd/MTU

CRs inserted between 40 - 45 GWd/MTU
Reactivity Effects of Control Rods Section 3

24

3.2.5 CE Ag-In-Cd/B4C Control Rods

Combustion Engineering has designed a CEA consisting of five Inconel fingers loaded with a stack of B4C

cylindrical pellets, with Ag-In-Cd in the lower 8 in. (20.32 cm) of the fingers. Calculations are presented in this

section to investigate the reactivity effect of these CE CRs within a CE 14 × 14 fuel assembly design.

Dimensional specifications for the fuel assembly and CRs used for this analysis are given in Table 6 (Ref. 12).

The 14 × 14 CE assembly lattice is shown in Figure 12, and Figure 13 displays the assembly as modeled in

HELIOS-1.6.

Table 6 CE 14 × 14 fuel assembly and CR specifications

Parameter

Dimension

(cm)

Fuel assembly specifications

Rod pitch 1.47

Assembly pitch 20.8

Cladding outside diameter 1.1176

Cladding inside diameter 0.97536

Pellet outside diameter 0.95631

Guide tube outside diameter 2.6289

Guide tube inside diameter 2.8321

Array size 14 × 14

Number of fuel rods 176

Number of guide/instrument tubes 5

Control rod specifications

Absorber material Natural B4C/Ag-In-Cd

B4C pellet diameter 2.1844

B4C axial height 340.36 (center finger) /

314.96 (outside fingers)

Ag-In-Cd diameter 2.1844

Ag-In-Cd axial height 20.32

Cladding (Inconel) thickness 0.1016

Cladding outside diameter 2.4079
Section 3 Reactivity Effects of Control Rods

25

Guide tube/CR location

Fuel rod

Figure 12 CE 14 × 14 assembly lattice representing the CR locations
Reactivity Effects of Control Rods Section 3

26

Figure 13 HELIOS calculational model of a CE 14 × 14 assembly containing five CRs

Analyses are presented in this section for the CE CEA with various initial fuel enrichments and CR exposures to

better understand the effect of these CRs on the reactivity of SNF. Since the primary material in these CRs is

B4C, and it is not possible to include the axial variation in absorber materials in a 2-D model, the calculations in

this section involve the axial segment corresponding to the B4C region. Based on results shown in the previous

sections, calculations with the Ag-In-Cd axial segment are expected to yield smaller effects. Note however, that

the lower ~20 cm of these CRs contain Ag-In-Cd, and thus, partial CR insertions may only involve the Ag-In-Cd

region. Figure 14 displays the kinf values versus burnup from calculations with and without CR exposure.
Section 3 Reactivity Effects of Control Rods

27

Figure 14 Comparison of kinf (out-of-reactor conditions) as a function of burnup with and without CR

exposure. The results correspond to 4 wt % 235U enriched CE 14 × 14 fuel and the B4C axial segment of the

Ag-In-Cd/B4C CRs.

Consistent with the analyses in the previous sections, calculations were performed with initial enrichments of 3, 4,

and 5 wt % 235U and CR exposures of 5, 15, 30, and 45 GWd/MTU (full exposure). Three cycles of

15 GWd/MTU per cycle were assumed for the analysis. The results (∆k as a function of burnup) are shown in

Figure 15 for initial enrichments of 3, 4, and 5 wt % 235U. The maximum positive ∆k values for the various CR

cases considered are summarized in Table 7. For the cases considered here, the highest ∆k is approximately 9%

(the case when CRs are present during the entire depletion at 3 wt % 235U fuel enrichment). Consistent with the

results shown in the previous sections, the reactivity effect of the CRs increases with increasing exposure and

decreasing fuel enrichment.

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

kinf

no control rods

control rods inserted
Reactivity Effects of Control Rods Section 3

28

Figure 15 Comparison of ∆k values as a function of burnup for various CR exposures with initial fuel

enrichments of 3, 4, and 5 wt % 235U. The results correspond to CE 14 × 14 fuel and the B4C axial segment of

the Ag-In-Cd/B4C CRs.

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

5.0 wt% U-235

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

4.0 wt% U-235

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(CR) - k(no_CR)]

CRs removed at 5 GWd/MTU CRs removed at 15 GWd/MTU

CRs removed at 30 GWd/MTU CRs present during entire depletion

3.0 wt% U-235
Section 3 Reactivity Effects of Control Rods

29

Table 7 Summary of maximum positive ∆k values observed for the

B4C axial segment of the CE Ag-In-Cd/B4C CR cases considered

(discharge burnup of 45 GWd/MTU)

Enrichment (wt % 235 Burnup at U)

CR removal

(GWd/MTU) 3.0 4.0 5.0

5 0.0045 0.0028 0.0018

15 0.0213 0.0121 0.0082

30 0.0553 0.0339 0.0203

45 0.0866 0.0619 0.0411

3.2.6 B&W Gray Axial Power Shaping Rods

In addition to the Ag-In-Cd CRs analyzed in Section 3.2.3, B&W has developed gray part-length APSRs made

out of Inconel with stainless steel cladding (the balance of the length is filled with water). Note that B&W has

also developed black part-length APSRs made out of Ag-In-Cd with stainless steel cladding. However, the black

APSRs are not being analyzed in this report due to their similarity with the Ag-In-Cd CRs (Section 3.2.3).

Calculations were performed using a B&W 15 × 15 assembly in order to investigate the reactivity effect of the

gray APSRs. Dimensional specifications for the fuel assembly and APSRs are given in Table 8 (Ref. 11). The

B&W 15 × 15 assembly design considered is shown in Figure 16.

As in the previous CR studies, various rod exposures were considered in order to better understand the effect

these power shaping rods have on reactivity as a function of burnup. In reality, the APSRs are shorter than the

active fuel length. However, this analysis is done in 2-D and consequently the APSRs and the active fuel are both

infinite lengthwise. The kinf values, as a function of burnup from the calculations with and without APSR

exposure are compared in Figure 17. The ∆k values between these two conditions demonstrate the effect of

APSRs on reactivity.

Calculations were performed with initial enrichments of 3, 4, and 5 wt % 235U and APSRs exposures of 5, 15, 30,

and 45 GWd/MTU (full exposure). Three cycles of 15 GWd/MTU per cycle were assumed for the analysis. The

results (∆k as a function of burnup) are shown in Figure 18 for initial enrichments of 3, 4, and 5 wt % 235U. The

maximum positive ∆k values for the various APSR cases considered are summarized in Table 9. For the cases

considered here the highest ∆k is approximately 2.7 % ∆k (the case when APSRs are present during the entire

depletion at 3 wt % 235U fuel enrichment), which is significantly less than the 7–10% ∆k observed for the other

CR designs. Consistent with the results shown in previous sections for other CR designs, the reactivity effect of

the APSRs increases with increasing exposure and decreasing fuel enrichment. Note, however, that the APSRs

have a significantly smaller reactivity effect compared to the other CR designs considered in this report; this is

because the APSRs do not contain strong thermal neutron absorbing materials such as boron or cadmium.
Reactivity Effects of Control Rods Section 3

30

Figure 19 compares the ∆k for various initial fuel enrichment cases in which the APSRs have been inserted for

30 GWd/MTU (representing 2 cycles). As noted previously, the reactivity effect of the APSRs increases with

decreasing initial enrichment.

Based on a limited survey of operational data, it is difficult to characterize “typical” APSR operational practices.

However, it is often the case that they are present during the majority of an assembly’s second burnup cycle,

being withdrawn gradually late in the cycle.11 Therefore, calculations were performed for scenarios in which the

APSRs were inserted during the first (0–15 GWd/MTU), second (15–30 GWd/MTU), and third

(30–45 GWd/MTU) cycle of burnup to quantify the reactivity effect. The results (∆k as a function of burnup) are

shown in Figure 20 for an initial enrichment of 4.0 wt % 235U and demonstrate that, consistent with the results

shown previously for CRs, the APSR exposure has a larger effect on discharge reactivity when it occurs later in

the assembly burnup.

Table 8 B&W 15 × 15 fuel assembly and APSR specifications

Parameter

Dimension

(cm)

Fuel assembly specifications

Rod pitch 1.44272

Assembly pitch 21.81

Cladding outside diameter 1.09220

Cladding inside diameter 0.95758

Pellet outside diameter 0.940

Guide/instrument tube outside diameter 1.34620

Guide/instrument tube inside diameter 1.26492

Array size 15 × 15

Number of fuel rods 208

Number of guide/instrument tubes 17

APSR specifications

Rod material Inconel

Inconel outer diameter 0.95250

Inconel axial height 160.02

Cladding (304 SS) outside diameter 1.11760

Cladding (304 SS) inside diameter 0.98044
Section 3 Reactivity Effects of Control Rods

31

Fuel Rod Guide tube/APSR location

Instrument Tube

Figure 16 B&W 15 × 15 assembly lattice representing the APSR locations
Reactivity Effects of Control Rods Section 3

32

Figure 17 Comparison of kinf values (out-of-reactor conditions) as a function of burnup with and without

APSR exposure. The results correspond to 4 wt % 235U enriched B&W 15 × 15 fuel and gray APSRs.

0.80

0.90

1.00

1.10

1.20

1.30

1.40

0 5 10 15 20 25 30 35 40 45

Burnup[GWd/MTU]

kinf

noaxial power shapingrods

axial power shaping rods inserted
Section 3 Reactivity Effects of Control Rods

33

Figure 18 Comparison of ∆k values as a function for various APSR exposures with initial fuel

enrichments of 3, 4, and 5 wt % 235U. The results correspond to B&W 15 × 15 fuel and gray APSRs.

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(APSR) - k(no_APSR)]

5.0 wt% U-235

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(APSR) - k(no_APSR)]

4.0 wt% U-235

-0.010

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

k [k(APSR) - k(no_APSR)]

APSRs removed at 5 GWd/MTU

APSRs removed at 15 GWd/MTU

APSRs removed at 30 GWd/MTU

APSRs present during entire depletion

3.0 wt% U-235
Reactivity Effects of Control Rods Section 3

34

Table 9 Summary of maximum positive ∆k values observed for B&W

APSR cases considered (discharge burnup of 45 GWd/MTU)

Enrichment (wt % 235 Burnup at U)

CR removal

(GWd/MTU) 3.0 4.0 5.0

5 0.0008 0.0004 0.0002

15 0.0059 0.0026 0.0017

30 0.0164 0.0098 0.0057

45 0.0268 0.0187 0.0121

Figure 19 Comparison of ∆k values as a function of burnup with APSR exposure during the first

30 GWd/MTU (2 cycles) for various initial fuel enrichments. The results correspond to B&W 15 × 15 fuel and

gray APSRs.

-0.005

0.000

0.005

0.010

0.015

0.020

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

∆k [k(APSR) - k(no_APSR)]

3 wt % U-235

4 wt % U-235

5 wt % U-235
Section 3 Reactivity Effects of Control Rods

35

Figure 20 Comparison of ∆k values as a function of burnup for 15 GWd/MTU APSR exposures at

various times during the burnup with initial fuel enrichment of 4 wt % 235U. The results correspond to B&W

15 × 15 fuel and gray APSRs.

3.2.7 Cooling Time

To study the effects of cooling time, a few calculations were performed at cooling times other than zero. The

Westinghouse 17 × 17 fuel assembly and the Ag-In-Cd/B4C CRs were employed for the study. Infinite assembly

array calculations were performed for cooling times of 5, 20, and 40 years with initial fuel enrichment of 4 wt %

235U and CR exposure of 45 GWd/MTU (full exposure). The results (∆k as a function of burnup) are shown in

Figure 21. It can be seen that cooling time has little impact on the ∆k values, and thus, the results at zero cooling

time are expected to be representative within the time frame relevant to cask storage and transport.

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

∆k [k(APSR) - k(no_APSR)]

APSRs inserted between 0 - 15 GWd/MTU

APSRs inserted between 15 - 30 GWd/MTU

APSRs inserted between 30 - 45 GWd/MTU
Reactivity Effects of Control Rods Section 3

36

Figure 21 Comparison of ∆k values as a function of burnup for various cooling times for 45 GWd/MTU

CR exposures with initial fuel enrichment of 4 wt % 235U. The results correspond to Westinghouse 17 × 17 fuel

and the B4C segment of the Ag-In-Cd/B4C CRs.

3.2.8 Summary of Two-Dimensional Analyses

It can be concluded from the analyses in this subsection that the reactivity effect of CR insertion increases with

increasing exposure and decreasing fuel enrichment. The gray APSRs showed similar trends to CRs, although the

reactivity effects were not as pronounced for the APSRs. For a discharge burnup of 45 GWd/MTU, the CRs

showed maximum (worst-case) ∆k values between 7–10%, while the APSRs had maximum ∆k values around

2–3%. When considering these quoted “maximum ∆k values,” the reader should be mindful that they are based

on calculational assumptions selected to bound the reactivity effect (i.e., full axial CR insertion during the entire

burnup), and not realism of operations. A summary and comparison of ∆k values for the various CR designs and

burnup exposures considered are shown in Figure 22. To gain an understanding of the reactivity effect of CRs on

SNF loaded in a burnup credit cask and the reactivity effect of partially inserted CRs, 3-D cask calculations are

presented in the following section

Regarding the effect of the various CR designs considered, it is noted that there exists a direct relationship

between the initial reactivity worth of a CR design and its effect on the discharge reactivity – higher reactivity

worth CR designs result in larger effects on discharge reactivity. To examine this relationship, the effect of CR

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 5 10 15 20 25 30 35 40 45

Burnup [GWd/MTU]

∆k[k(CRs) - k(no_CRs)]

0 year cooling time

5 year cooling time

20 year cooling time

40 year cooling time
Section 3 Reactivity Effects of Control Rods

37

exposure on discharge reactivity (in terms of ∆k) was plotted against the CR initial reactivity worth (in terms of

∆k/k) for each of the CR and APSR designs considered. The relationship is plotted in Figure 23 for cases

involving fuel with 45 GWd/MTU burnup and 4.0 wt % 235U initial enrichment that have experienced different

CR exposure durations. The results in Figure 23 show that the positive reactivity effect of CRs on discharged

SNF increases in a linear manner with increasing negative CR reactivity worth. Note that the CR reactivity worth

was determined based on criticality calculations with and without the CRs/APSRs present for in-reactor

conditions and zero burnup, while the reactivity effect on the discharged SNF is based on criticality calculations

in out-of-reactor conditions (without CRs/APSRs present) with isotopic compositions from depletion cases with

and without CRs/APSRs present.

Besides establishing a relationship between the initial CR reactivity worth and the reactivity effect on discharged

SNF, Figure 23 could be used as a guide for estimating the reactivity effect of other CR and APSR designs that

are not included in this report. For example, calculations were performed for Westinghouse Hf CRs and

Westinghouse Ag-In-Cd-CRs with 4 wt % 235U enriched Westinghouse 17 × 17 fuel and 5 and 45 GWd/MTU CR

exposures. The results are included on Figure 23 to demonstrate that the calculated reactivity effect of these

additional CRs is consistent with that predicted by the 5 and 45 GWd/MTU lines displayed in Figure 23.

Figure 22 Comparison of ∆k values for an infinite assembly array (45 GWd/MTU, 0-year cooling time)

with various CR exposures. The results correspond to fuel with 4.0 wt % 235U initial enrichment.

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

5 15 30 45

CRBurnupExposure[GWd/MTU]

k [k(CR) - k(no_CR)]

Westinghouse CRs; B4C B&WCRs; Ag-In-Cd

CE CRs; B4C B&WAPSR; Inconel

Total Burnup = 45 GWd/MTU for all cases

∆k [k(CR) –k(no_CR)]

CR Burnup Exposure [GWd/MTU]
Reactivity Effects of Control Rods Section 3

38

Figure 23 Relationship between the effect of CR exposure on discharge reactivity (in terms of ∆k) and CR

initial reactivity worth (in terms of ∆k/k) for each of the CR and APSR designs considered. The results

correspond to fuel with 45 GWd/MTU burnup and 4.0 wt % 235U initial enrichment that have experienced

different CR exposure durations. CR exposure durations are continuous, beginning at zero burnup and continuing

until the specified burnup exposure (e.g., 5 GWd/MTU exposure occurs from 0–5 GWd/MTU.)

3.3 THREE-DIMENSIONAL ANALYSES

Although the 2-D analyses presented in the previous section correspond to full axial CR insertion, CRs are not

fully inserted during power operations. As stated earlier, the goal of the 2-D analysis was to establish trends and

upper bounds; the results overestimate the reactivity effect of CR exposure on actual discharged SNF. The

majority of the time, CRs are completely withdrawn from the active fuel region. At other times, the CRs may be

inserted into a small upper portion of the active fuel. Any realistic modeling of CR exposure should represent the

partial axial insertion, which requires 3-D calculations. Therefore, 3-D calculations are performed and presented

in this section to achieve a more accurate and realistic assessment of the effect of CR exposure on the reactivity of

discharged SNF.

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 0.02 0.04 0.06 0.08

Reactivity Effect on Discharged SNF

(∆ k [k(CR) - k(no_CR)] out-of-reactor conditions)

Control Rod Reactivity Worth

(ρ [∆ k/k] in-reactor conditions at zero burnup)

B&W APSR; Inconel

B&W CRs; Ag-In-Cd

CE CRs; B4C

Westinghouse CRs; B4C

Westinghouse CRs; Hf

Westinghouse CRs; Ag-In-Cd

45 GWd/MTU

30 GWd/MTU

15

GWd/MTU

5

GWd/MTU

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0 0.02 0.04 0.06 0.08

Reactivity Effect on Discharged SNF

(∆ k [k(CR) - k(no_CR)] out-of-reactor conditions)

Control Rod Reactivity Worth

(ρ [∆ k/k] in-reactor conditions at zero burnup)

B&W APSR; Inconel

B&W CRs; Ag-In-Cd

CE CRs; B4C

Westinghouse CRs; B4C

Westinghouse CRs; Hf

Westinghouse CRs; Ag-In-Cd

45 GWd/MTU

30 GWd/MTU

15

GWd/MTU

5

GWd/MTU
Section 3 Reactivity Effects of Control Rods

39

3.3.1 Code Description

The criticality calculations presented in the following subsections were performed using the KENO V.a module of

the SCALE system.18 KENO V.a is a multigroup Monte Carlo criticality program employed to calculate the

neutron multiplication factor, keff, of a 3-D system. The KENO V.a criticality calculations used the

SCALE 238-group cross sections based on ENDF/B-V data. The spent fuel isotopics used in the KENO V.a

calculations were calculated using the HELIOS-1.6 code package.17

3.3.2 Reactivity Behavior with CRs Present for a Rail-Type Cask

The results in Section 3.2 provide understanding of the general behavior of reactivity as a function of burnup

when assemblies are exposed to fully-inserted CRs and establish an upper-bound for their impact on the reactivity

of discharged SNF. In this section, the effect of CR exposure on SNF loaded in a high-capacity rail-type cask is

briefly examined and quantified. First, calculations one performed for conditions in which the CRs are assumed

to be fully-inserted during depletion. These results may be compared to the 2-D infinite assembly array results in

the previous section to assess the impact of the cask environment on the calculated ∆k values. Then, to better

approximate realistic CR insertion conditions, calculations are presented for variations in CR exposure in terms of

axial insertion and burnup duration.

For this analysis, the generic 32 PWR-assembly Burnup Credit (GBC-32) cask was used. A physical description

of the cask is provided in Ref. 19 and a cross-sectional view of the computer model, as prepared by KENO V.a, is

shown in Figure 24. The GBC-32 design was developed to provide a reference cask configuration that is

representative of typical high-capacity rail casks being considered by industry. The boron loading in the Boral

panels in the GBC-32 cask is 0.0225 g 10B/cm2

.

For the analyses in the previous section, the depletion and criticality calculation were both performed with the

HELIOS-1.6 code package and the criticality calculations included all of the nuclides available in the HELIOS1.6 data library. For the criticality calculations in the following 3-D analyses, the isotopic compositions are

calculated by HELIOS, and subsequently extracted for use in KENO V.a input. Therefore, it is necessary to

identify the isotopes considered. The use of a subset of possible actinides in burnup credit calculations is referred

to as “actinide-only” burnup credit. The nuclides used here for actinide-only calculations are consistent with

those specified in a DOE Topical Report on Burnup Credit,5 with the exception that 236U and 237Np are also

included. While not commonly defined, the use of a subset of possible actinides and fission products will be

referred to herein as “actinide + fission product” burnup credit. The nuclides used here for actinide + fission

product calculations are consistent with those identified in Table 2 of Ref. 20 as being the most important for

burnup credit criticality calculations. Table 10 lists the nuclides included for the two classifications of burnup

credit. These “classes” of burnup credit and the nuclides included within each are defined here for the purposes of

discussion; other terminology and specific sets of nuclides have been defined and used by others studying burnup

credit phenomena.
Reactivity Effects of Control Rods Section 3

40

Figure 24 Cross-sectional view of one quarter of the KENO V.a calculational model of the GBC-32 cask

loaded with Westinghouse 17 × 17 assemblies
Section 3 Reactivity Effects of Control Rods

41

Table 10 Nuclides associated with the various classifications of burnup credit

Actinide-Only Burnup Credit Nuclides (12 total)

234U 235U 236U 238U 238Pu 239Pu 240Pu 241Pu 242Pu 237Np

241Am O

Actinide + Fission Product Burnup Credit Nuclides (29 total)

234U 235U 236U 238U 238Pu 239Pu 240Pu 241Pu 242Pu 241Am

243Am 237Np 95Mo 99Tc 101Ru 103Rh 109Ag 133Cs 147Sm 149Sm

150Sm 151Sm 152Sm 143Nd 145Nd 151Eu 153Eu 155Gd O

† Oxygen is neither an actinide nor a fission product, but is included in this list

because it is included in the calculations.

3.3.2.1 Full-Axial Insertion Analyses

The keff values for actinide-only and actinide + fission product burnup credit in the GBC-32 cask loaded with

Westinghouse 17 × 17 OFA assemblies, assuming uniform axial burnup, for various CR exposures are listed in

Tables 11 and 12, respectively. The results correspond to fuel with 4 wt % 235U initial enrichment that has been

exposed to fully-inserted Westinghouse hybrid B4C CRs while accumulating a burnup of 45 GWd/MTU. The ∆k

values based on actinides only are essentially the same as those calculated based on actinides + fission products.

Note that the ∆k values in the cask environment are shown to be somewhat larger than those predicted by the

infinite assembly array calculations presented in the previous section, and the amount by which they are larger

increases with increasing CR exposure. These differences were also observed with HELIOS criticality

calculations simulating an infinite array of cask storage cells and are attributed to the fact that the neutron

absorber in the cask environment (10B in the Boral panels) competes for neutrons with the absorbers in the SNF

composition, which influences their reactivity worth. The results in Tables 11 and 12 correspond to calculations

in which the CRs are assumed to contain B4C over the full axial length. In contrast, Tables 13 and 14 present

results for calculations in which the actual axial variation in absorber material (B4C/Ag-In-Cd) was included.

Note that since we are interested in the impact of CR exposure on the reactivity of SNF, these results consider

CRs present during depletion only (i.e., CRs are not included in the KENO V.a model).

The keff values for actinide-only and actinide + fission product burnup credit in the GBC-32 cask loaded with

B&W 15 × 15 fuel assemblies, assuming uniform axial burnup, for various CR exposures are listed in Tables 15

and 16, respectively. The results correspond to fuel with 4 wt % 235U initial enrichment that has been exposed to

fully-inserted B&W Ag-In-Cd CRs while accumulating a burnup of 45 GWd/MTU. Consistent with the results

shown for the Westinghouse CRs, the ∆k values with and without fission products are essentially the same and are

somewhat larger than those predicted by the 2-D assembly array calculations.
Reactivity Effects of Control Rods Section 3

42

Table 11 Value of keff for various CR exposures for actinide-only burnup credit in the GBC-32 cask.

Results correspond to Westinghouse 17 × 17 fuel with 4 wt % 235U enrichment, 45 GWd/MTU

burnup, zero year cooling, and B4C CRs fully inserted for various burnup durations

CR exposure

(GWd/MTU)

KENO V.a

keff Standard deviation

∆k

(kCRs -knoCRs)

0 0.9110 0.0005 N/A

5 0.9194 0.0005 0.0084

15 0.9315 0.0006 0.0205

30 0.9592 0.0005 0.0482

45 1.0051 0.0006 0.0941

Table 12 Value of keff for various CR exposures for actinide + fission product burnup credit in the GBC-32

cask. Results correspond to Westinghouse 17 × 17 fuel with 4 wt % 235U enrichment, 45 GWd/MTU

burnup, zero year cooling, and B4C CRs fully inserted for various burnup durations

CR exposure

(GWd/MTU)

KENO V.a

keff Standard deviation

∆k

(kCRs -knoCRs)

0 0.8345 0.0005 N/A

5 0.8422 0.0005 0.0077

15 0.8557 0.0006 0.0212

30 0.8832 0.0006 0.0487

45 0.9237 0.0005 0.0892
Section 3 Reactivity Effects of Control Rods

43

Table 13 Value of keff for various CR exposures for actinide-only burnup credit in the GBC-32 cask.

Results correspond to Westinghouse 17 × 17 fuel with 4 wt % 235U enrichment, 45 GWd/MTU

burnup, zero year cooling, and B4C (top part, approximately 160 cm)/ Ag-In-Cd (lower part,

approximately 102 cm) CRs fully inserted for various burnup durations

CR Exposure

(GWd/MTU)

KENO V.a

keff Standard deviation

∆k

(kCRs -knoCRs)

0 0.9110 0.0005 N/A

5 0.9189 0.0005 0.0079

15 0.9332 0.0005 0.0222

30 0.9609 0.0005 0.0499

45 1.0039 0.0006 0.0929

Table 14 Value of keff for various CR exposures for actinide + fission product burnup credit in the GBC-32

cask. Results correspond to Westinghouse 17 × 17 fuel with 4 wt % 235U enrichment, 45 GWd/MTU

burnup, zero year cooling, and B4C (top part, approximately 160 cm)/ Ag-In-Cd (lower part,

approximately 102 cm) CRs fully inserted for various burnup durations

CR Exposure

(GWd/MTU)

KENO V.a

keff Standard deviation

∆k

(kCRs -knoCRs)

0 0.8345 0.0005 N/A

5 0.8419 0.0004 0.0074

15 0.8553 0.0004 0.0208

30 0.8828 0.0005 0.0483

45 0.9232 0.0006 0.0887
Reactivity Effects of Control Rods Section 3

44

Table 15 Value of keff for various CR exposures for actinide-only burnup credit in the GBC-32 cask.

Results correspond to B&W 15 × 15 fuel with 4 wt % 235U enrichment, 45 GWd/MTU burnup,

zero year cooling, and Ag-In-Cd CRs fully inserted for various burnup durations

CR Exposure

(GWd/MTU)

KENO V.a

keff Standard deviation

∆k

(kCRs -knoCRs)

0 0.9371 0.0006 N/A

5 0.9393 0.0005 0.0022

15 0.9497 0.0005 0.0126

30 0.9680 0.0006 0.0309

45 1.0021 0.0005 0.0650

Table 16 Value of keff for various CR exposures for actinide + fission product burnup credit in the GBC-32

cask. Results correspond to B&W 15 × 15 fuel with 4 wt % 235U enrichment, 45 GWd/MTU burnup,

zero year cooling, and Ag-In-Cd CRs fully inserted for various burnup durations

CR Exposure

(GWd/MTU)

KENO V.a

keff Standard deviation

∆k

(kCRs -knoCRs)

0 0.8566 0.0006 N/A

5 0.8602 0.0005 0.0036

15 0.8691 0.0006 0.0125

30 0.8880 0.0005 0.0314

45 0.9185 0.0004 0.0619

The keff values for actinide-only and actinide + fission product burnup credit in the GBC-32 cask loaded with

CE 14 × 14 fuel assemblies, assuming uniform axial burnup, for various CR exposures are listed in Tables 17

and 18, respectively. The results correspond to fuel with 4 wt % 235U initial enrichment that has been exposed to

fully-inserted CE B4C CRs while accumulating a burnup of 45 GWd/MTU. Upon comparing the ∆k values of

actinide-only versus the ∆k values of actinide + fission products it can be seen that the reactivity behavior is

essentially the same. When comparing the results of these calculations in the GBC-32 cask to those shown in

previous sections for an infinite assembly arrays, it is apparent that the CR effect is marginally larger in the cask

configuration.
Section 3 Reactivity Effects of Control Rods

45

Table 17 Value of keff for various CR exposures for actinide-only burnup credit in the GBC-32 cask.

Results correspond to CE 14 × 14 fuel with 4 wt % 235U enrichment, 45 GWd/MTU burnup,

zero year cooling, and B4C CRs fully inserted for various burnup durations

CR Exposure

(GWd/MTU)

KENO V.a

keff Standard deviation

∆k

(kCRs -knoCRs)

0 0.8809 0.0005 N/A

5 0.8826 0.0005 0.0017

15 0.8936 0.0005 0.0127

30 0.9145 0.0005 0.0336

45 0.9491 0.0006 0.0682

Table 18 Value of keff for various CR exposures for actinide + fission product burnup credit in the GBC-32

cask. Results correspond to CE 14 × 14 fuel with 4 wt % 235U enrichment, 45 GWd/MTU burnup,

zero year cooling, and B4C CRs fully inserted for various burnup durations

CR Exposure

(GWd/MTU)

KENO V.a

keff Standard deviation

∆k

(kCRs -knoCRs)

0 0.8053 0.0005 N/A

5 0.8090 0.0004 0.0037

15 0.8191 0.0005 0.0138

30 0.8390 0.0005 0.0337

45 0.8736 0.0005 0.0683
Reactivity Effects of Control Rods Section 3

46

3.3.2.2 Partial-Axial Insertion Analyses

In this section, 3-D calculations are performed with the GBC-32 cask to establish the reactivity effect of CR

exposure as a function of axial insertion. For each CR design considered, a series of calculations were performed

to determine the effect of various axial depths of CR insertion. The criticality models included isotopics from

depletion calculations with CRs present (in the axial region representing the CR insertion) and isotopics from

depletion calculations without CRs present (in the remaining axial region). Figure 25 provides an illustration of

the partial CR insertion and the criticality model.

The first series of calculations was performed with the Westinghouse 17 × 17 OFA assembly and the hybrid

B4C/Ag-In-Cd CRs. The ∆k values for actinide-only and actinide + fission product burnup credit in the GBC-32

cask as a function of axial CR insertion depth are shown in Figure 26. In accordance with the actual design, the

axial variation in CR absorber material [B4C absorber in the top part of the CR (approximately 260 cm) and

Ag-In-Cd absorber in the bottom part (approximately 102 cm)] was modeled. The results correspond to fuel with

4 wt % 235U initial enrichment that has been exposed to Westinghouse hybrid B4C/Ag-In-Cd rods for the first 5,

15, and 45 GWd/MTU while accumulating a total burnup of 45 GWd/MTU. The KENO V.a models include the

axial variation in the depletion isotopics due to CR exposure, but assume uniform axial burnup. The results show

that even for significant burnup exposures, minor axial CR insertions (e.g., <20 cm) result in an insignificant

effect on the keff of the cask. Note also that for the cases with CRs, all assemblies in the 32-assembly GBC-32

cask are assumed to have the same CR exposure, which is conservative considering the number of assemblies per

core that are positioned under CR clusters.

The calculations were repeated for the B&W 15 × 15 fuel assemblies employing Ag-In-Cd CRs. The ∆k values

for actinide-only and actinide + fission product burnup credit in the GBC-32 cask as a function of axial CR

insertion depth are shown in Figure 27. The results correspond to spent fuel with 4 wt % 235U initial enrichment

that has been exposed to B&W Ag-In-Cd CRs for the first 5, 15, and 45 GWd/MTU while accumulating a total

burnup of 45 GWd/MTU. Consistent with the results for the Westinghouse hybrid CRs, the effect of minor axial

CR insertions is shown to be very small. Further, the effect is shown to be even smaller for the B&W Ag-In-Cd

CRs than what is seen for the Westinghouse hybrid CRs.

Finally, the calculations were repeated for the CE 14 × 14 fuel assemblies employing B4C/Ag-In-Cd CRs.

Consistent with the actual design, the axial variation in the CR absorber material [B4C absorber in the top part of

the CR (approximately 315 cm) and Ag-In-Cd absorber in the bottom part (approximately 20 cm)] was modeled.

The ∆k values for actinide-only and actinide + fission product burnup credit in the GBC-32 cask as a function of

axial CR insertion depth are shown in Figure 28. The results correspond to spent fuel with 4 wt % 235U initial

enrichment that has been exposed to CE B4C CRs for the first 5, 15, and 45 GWd/MTU while accumulating a

total burnup of 45 GWd/MTU. Consistent with the results for the Westinghouse hybrid CRs, the effect of minor

axial CR insertions is shown to be insignificant.
Section 3 Reactivity Effects of Control Rods

47

Figure 25 Illustration of (a) partially inserted control rods and (b) a cross section of the criticality model

Depletion isotopics

based on portion of

B4C CRs present

during depletion

Depletion isotopics

based on Ag-In-Cd

portion of CRs

present during

depletion

Depletion isotopics

without any CRs

present during

depletion

B4CAg-In-Cd

Active fuel region

Active

fuel

height

Axial

depth

of CR

insertion

a) Partial CR insertion b) Criticality model
Reactivity Effects of Control Rods Section 3

48

Figure 26 ∆k as a function of axial depth of CR insertion for the GBC-32 cask. Results correspond to

4 wt % 235U enriched Westinghouse 17 × 17 fuel and B4C/Ag-In-Cd CRs.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 50 100 150 200 250 300 350 400

Axial depth of CR insertion (distance from top of active fuel, cm)

∆k[k(CRs) - k(no_CRs)]

actinide only

actinide and fission products

Series4

CRs for 45 GWd/MTU

CRs for 15 GWd/MTU

CRs for 5 GWd/MTU
Section 3 Reactivity Effects of Control Rods

49

Figure 27 ∆k as a function of axial depth of CR insertion for the GBC-32 cask. Results correspond to

4 wt % 235U enriched B&W 15 × 15 fuel and Ag-In-Cd CRs.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 50 100 150 200 250 300 350 400

Axial depth of CR insertion (distance from top of active fuel, cm)

∆k[k(CRs) - k(no_CRs)]

actinide only

actinide and fission products

Series4

CRs for 45 GWd/MTU

CRs for 15 GWd/MTU

CRs for 5 GWd/MTU
Reactivity Effects of Control Rods Section 3

50

Figure 28 ∆k as a function of axial depth of CR insertion for the GBC-32. Results correspond to 4 wt %

235U enriched CE 14 × 14 fuel and B4C CRs.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 50 100 150 200 250 300 350 400

Axial depth of CR insertion (distance from top of active fuel, cm)

∆k[k(CRs) - k(no_CRs)]

actinide only

actinide and fission products

Series4

CRs for 45 GWd/MTU

CRs for 15 GWd/MTU

CRs for 5 GWd/MTU
Section 4 Discussion and Implications

51

4 DISCUSSION AND IMPLICATIONS

Because of spectral hardening, an assembly exposed to CRs can have a higher reactivity for a given burnup than

an assembly that has not been exposed to CRs. While it is known that CRs are typically fully withdrawn from the

active fuel region during operation, exceptions to this practice exist. Consequently, a wide range of CR exposure

conditions and initial fuel enrichments were studied in order to establish a better understanding of their effect.

The first part of Section 3 (2-D analyses) provides understanding of the general behavior of reactivity as a

function of burnup when assemblies are exposed to CRs and presents some worst-case CR exposure scenarios.

The reactivity effect of CRs was shown to increase with increasing burnup and decreasing initial fuel enrichment.

Control rod exposure is shown to have a larger effect on discharge reactivity when it occurs later in the assembly

burnup. For variations in CR design, there exists a direct relationship between the reactivity worth of the CRs and

their effect on discharge reactivity – higher reactivity worth CRs result in larger effect on discharge reactivity.

For the various CR designs considered, maximum reactivity effects are shown to be between 3 and 10% ∆k,

depending on initial fuel enrichment, when maximum worst-case CR exposure was assumed for a discharge

burnup of 45 GWd/MTU.

Unlike the other CR designs, APSRs are commonly utilized in the core for longer periods of time during

operation. The reactivity effect of gray APSRs was found to be much less than that of the other CR designs (for a

given burnup exposure). The maximum reactivity increases of the gray APSR cases considered are shown to be

between 1 and 3% ∆k, depending on initial enrichment, when maximum worst-case exposure was assumed for a

discharge burnup of 45 GWd/MTU. These 2-D calculations simulated worst-case, unrealistic conditions

(i.e., full-axial CR insertion for long periods of burnup), but were effective for gaining a better understanding of

the impact of CR and APSR exposure and establishing an upper bound on the reactivity effect.

The second part of Section 3 (3-D analyses) presents the effect of CRs within a high-capacity rail-type cask.

KENO V.a calculations were performed to establish the reactivity effect of CR exposure as a function of axial

insertion. For each CR design considered, a series of calculations were performed to determine the effect of

partially inserted CRs for various burnup exposures. The results show that even for significant burnup

exposures, minor axial CR insertions (e.g., < 20 cm) result in an insignificant effect on the keff of the cask. This

conclusion is considered to be important and relevant to current U.S. PWR operations. In addition, the analyses

quantify the reactivity effect of intermediate and significant CR insertions, which have relevance to early domestic

PWR operations and operations in French PWRs.

Although it is assumed that U.S. PWRs do not currently use CRs to a significant extent (i.e., CRs are not inserted

deeper than the top ~20 cm of the active fuel and CRs are not inserted for extended periods of time), this

assumption has not been rigorously confirmed. Finally, it is worth noting that operating conditions for French

PWRs involve long periods of CR insertion for reactor control, low-power operations and load-following.7

Consequently, proposed approaches for burnup credit in France include full CR insertion.7

Section 5 Recommendations

53

5 RECOMMENDATIONS

The analyses presented in this report provide a technical understanding of the effect of CR exposure on the

reactivity of discharged SNF. The analyses demonstrate that the effect increases with increasing CR exposure

and decreasing fuel enrichment. Much of the report involves establishing the reactivity effect of CRs with burnup

exposure, fuel enrichment, and absorber material to increase understanding. However, and more importantly in

terms of practical considerations, 3-D analyses are also described in which the reactivity effect of CRs is assessed

as a function of axial CR insertion. These more realistic calculations show that even for significant burnup

exposures, minor axial CR insertions (e.g., <20 cm) result in a very small effect on the keff of a burnup credit

cask. Consequently, it is concluded that, based on the assumption that U.S. PWRs do not use CRs to a significant

extent (i.e., CRs are not inserted deeper than the top ~20 cm of the active fuel and CRs are not inserted for

extended burnups), the effect of CRs on discharge reactivity is relatively small (less than 0.2% ∆k). Note that the

effect of CR insertion on the axial burnup distribution is not addressed here because it is considered in the

selection of the bounding axial profile(s). Unfortunately, the conclusion is dependent on CR operating conditions,

which are not comprehensively known to the authors of this report. Therefore, it is recommended that future

efforts focus on achieving a greater understanding of CR usage in U.S. PWRs. A detailed understanding of CR

usage, coupled with the results presented in this report, will enable the development of a sound technical basis for

addressing CR exposure in PWR burnup credit criticality safety evaluations.

Section 6 References

55

6 REFERENCES

1. Spent Fuel Project Office Interim Staff Guidance – 8, Rev. 1 – Limited Burnup Credit, U.S. Nuclear

Regulatory Commission, July 30, 1999.

2. D. E. Carlson, C. J. Withee and C. V. Parks, “Spent Fuel Burnup Credit in Casks: An NRC

Perspective,” U.S. Nuclear Regulatory Commission, Proceedings of the Twenty-Seventh Water Reactor

Safety Information Meeting, October 25–27, 1999, Bethesda, Maryland, NUREG/CP-0169, pp. 419–

436 (March 2000).

3. J. C. Wagner and C.V. Parks, “Impact of Burnable Poison Rods on PWR Burnup Credit Criticality

Safety Analyses,” Trans. Am. Nucl. Soc., 83, 130–134 (Nov. 2000).

4. C. E. Sanders and J. C. Wagner, Study of the Effect of Integral Burnable Absorbers for PWR Burnup

Credit, ORNL/TM-2000/321, Oak Ridge National Laboratory (2002).

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7. M. Maillot, E. Guillou, D. Biron, and S. Janski, "Search for an Envelope Axial Burnup Profile for Use in

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References Section 6

56

17. J. J. Casal, R. J. J. Stamm'ler, E. A. Villarino, and A. A. Ferri, "HELIOS: Geometric capabilities of a

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19. J. C. Wagner, Computational Benchmark for Estimation of Reactivity Margin from Fission Products

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Commission, Oak Ridge National Laboratory, February 2000.
57

NUREG/CR-6759

ORNL/TM-2001/69

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133. J. T. Stewart, Department of Environment, Transport, and Re, RMTD, 4/18, GMH, 76

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134. T. Suto, Power Reactor and Nuclear Fuel Development Corporation, Technical Service Division,

Tokai Reprocessing Plant, Tokai Works, Tokai-Mura, Naka-gun, Ibaraki-ken, Japan

135. H. Taniuchi, Kobe Steel, Ltd., 2-3-1 Shinhama, Arai-Cho, Takasago, 676 Japan

136. D. A. Thomas, Bechtel SAIC Company, LLC, 1261 Town Center Drive, Las Vegas, NV 89134

137. P. R. Thorne, British Nuclear Fuels plc (BNFL), Nuclear and Radiological Safety,

R101 Rutherford House, Risley Warrington WA3 6AS, United Kingdom

138. J. R. Thornton, Duke Engineering & Services, 230 S. Tyron St., P.O. Box 1004, Charlotte, NC

28201-1004

139. S. E. Turner, Holtec International, 230 Normandy Circle East, Palm Harbor, FL 34683

140. A. P. Ulses, U.S. Nuclear Regulatory Commission, NRR/DSSA/SRXB, MS O10-B3,

Washington, DC 20555-0001

141. M. E. Wangler, U.S. Department of Energy, EH-33.2, Washington, DC 20585-0002

142. M. D. Waters, U.S. Nuclear Regulatory Commission, NMSS/SFPO/SLID, MS O13-D13,

Washington, DC 20555-0001
61

143. A. Wells, 2846 Peachtree Walk, Duluth, GA 30136

144. S. A. Whaley, U.S. Nuclear Regulatory Commission, NMSS/SFPO/TRD, MS O13-D13,

Washington, DC 20555-0001

145. B. H. White, U.S. Nuclear Regulatory Commission, NMSS/SFPO/TRD, MS O13-D13,

Washington, DC 20555-0001

146. R. Wilson, Rocky Flats Field Office, USDOE, 10808 Highway 93, Golden, CO 80403-8200

147. C. J. Withee, U.S. Nuclear Regulatory Commission, NMSS/SFPO/TRD, MS O13-D13,

Washington, DC 20555-0001
NRC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION

(2-89)

NRCM 1102 BIBLIOGRAPHIC DATA SHEET

3201, 3202 ( See instructions on the reverse)

1. REPORT NUMBER

(Assigned by NRC, Add Vol., Supp.,

Rev., and Addendum Numbers,

if any.)

NUREG/CR-6759

ORNL/TM-2001/69 2. TITLE AND SUBTITLE

Parametric Study of the Effect of Control Rods for PWR Burnup Credit

3. DATE REPORT PUBLISHED

MONTH

February

YEAR

2002

4. FIN OR GRANT NUMBER

W6479

5. AUTHOR(S)

C. E. Sanders and J. C. Wagner

6. TYPE OF REPORT

Technical

7. PERIOD COVERED (Inclusive Dates)

8. PERFORMING ORGANIZATION — NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address;

if contractor, provide name and mailing address.)

Oak Ridge National Laboratory

Managed by UT-Battelle, LLC

Oak Ridge, TN 37831-6370

9. SPONSORING ORGANIZATION — NAME AND ADDRESS (If NRC, type “Same as above”; if contractor, provide NRC Division, Office or Region, U.S. Regulatory

Commission, and mailing address.)

Division of Systems Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

10. SUPPLEMENTARY NOTES

R. Y. Lee, NRC Project Manager

11. ABSTRACT (200 words or less)

The Interim Staff Guidance on burnup credit for pressurized water reactor (PWR) spent nuclear fuel (SNF), issued by the

United States Nuclear Regulatory Commission’s Spent Fuel Project Office, recommends the use of analyses that

provide an “adequate representation of the physics” and notes particular concern with the “need to consider the more

reactive actinide compositions of fuels burned with fixed absorbers or with control rods fully or partly inserted.” In the

absence of readily available information on the extent of control rod (CR) usage in U.S. PWRs and the subsequent reactivity

effect of CR exposure on discharged SNF, NRC staff has indicated a need for greater understanding in these areas. In

response, this report presents a parametric study of the effect of CR exposure on the reactivity of discharged SNF for

various CR designs, including Axial Power Shaping Rods, fuel enrichments, and exposure conditions (i.e., burnup and axial

insertion).

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

criticality safety, burnup credit, transportation, dry storage, control rods, axial power

shaping rods

13. AVAILABILITY STATEMENT

unlimited

14. SECURITY CLASSIFICATION

(This Page) unclassified

(This Report) unclassified

15. NUMBER OF PAGES

16. PRICE

 NRC FORM 335 (2-89)