NUREG/IA-0414 

International 

Agreement Report

Comparison of the U.S. NRC PARCS Core Neutronics 

Simulator Against In-Core Detector Measurements for 

LWR Applications

 

Prepared by:

C. Demaziére, M. Stálek, P. Vinal

 

 Division of Nuclear Engineering

Chalmers University of Technology 

SE-41296 Gothenburg

Sweden

 

A. Calvo, NRC Project Manager

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: February 2011

Date Published: April 2012

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission
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NUREG/IA-0414 

International 

Agreement Report

Comparison of the U.S. NRC PARCS Core Neutronics 

Simulator Against In-Core Detector Measurements for 

LWR Applications

 

Prepared by:

C. Demaziére, M. Stálek, P. Vinal

 

 Division of Nuclear Engineering

Chalmers University of Technology 

SE-41296 Gothenburg

Sweden

 

A. Calvo, NRC Project Manager

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Manuscript Completed: February 2011

Date Published: April 2012

Prepared as part of 

The Agreement on Research Participation and Technical Exchange

Under the Thermal-Hydraulic Code Applications and Maintenance Program (CAMP)

Published by

U.S. Nuclear Regulatory Commission

v 

TABLE OF CONTENTS 

Page

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

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

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

ACKNOWLEDGMENT ................................................................................................................... xi

ABBREVIATIONS ......................................................................................................................... xiii

EXECUTIVE SUMMARY .............................................................................................................. xv

1. INTRODUCTION.................................................................................................................. 1-1

2. PARCS MODELLING .......................................................................................................... 2-1

2.1 Description of the card name based input files .............................................................. 2-1

2.1.1 Ringhals-3 reactor model ................................................................................... 2-1

2.1.2 Forsmark-2 reactor model .................................................................................. 2-1

2.2 Cross-sections preparation and PMAXS files ................................................................ 2-2

2.2.1 Description of the Chalmers cross-section interface .......................................... 2-2

2.2.2 Preparation of PARCS cross-sections for the Ringhals-3 PWR unit ................ 2-12

2.2.3 Preparation of PARCS cross-sections for the Forsmark-2 BWR unit ............... 2-13

2.2.4 Verification of the Chalmers cross-section interface ........................................ 2-14

2.3 3-D distribution of the history and instantaneous variables .......................................... 2-16

3. RESULTS OF THE STATIC CALCULATION AND COMPARISONS WITH 

MEASUREMENT DATA ...................................................................................................... 3-1

3.1 PWR case ...................................................................................................................... 3-2

3.2 BWR case .................................................................................................................... 3-11

4. SUMMARY AND CONCLUSIONS ...................................................................................... 4-1

5. REFERENCES..................................................................................................................... 5-1

 

vii 

LIST OF FIGURES 

Page

Figure 2-1 Construction of the macroscopic and microscopic two-group cross-sections, 

discontinuity factors, fission product data, and detector data in the CASMO4/SIMULATE-3 code package ................................................................................................... 2-4

Figure 2-2 ”Tree-leave” formalism in PARCS for PWR cases (the subscript 0 denotes 

the base case, the subscript 1 the perturbed value). The last ramification about the 

burnup dependency is not explicitly displayed for reason of clarity of the chart ...................... 2-10

Figure 2-3 PWR case, variation of k∞ as a function of burnup, instantaneous and history 

variables. The infinite multiplication factor calculated from the original data is 

represented by lines, whereas the infinite multiplication factor calculated from the 

reconstructed data is represented by crosses ......................................................................... 2-15

Figure 3-1 Ringhals-3 PWR unit, fuel cycle 19, exposure 0.3694 GWd/tHM: axial power 

profile calculated with PARCS version 3.0 and version 2.71. .................................................... 3-3

Figure 3-2 Ringhals-3 PWR unit, fuel cycle 19, exposure 0.3694 GWd/tHM: differences 

between the assemblywise radial power fraction calculated with PARCS version 3.0 

and version 2.71 ........................................................................................................................ 3-4

Figure 3-3 Ringhals-3 PWR unit, fuel cycle 19, exposure 0.3694 GWd/tHM: axial power 

profile ......................................................................................................................................... 3-5

Figure 3-4 Ringhals-3 PWR unit, fuel cycle 19, exposure 4.5983 GWd/tHM: axial power 

profile ......................................................................................................................................... 3-6

Figure 3-5 Ringhals-3 PWR unit, fuel cycle 19, exposure 9.830 GWd/tHM: axial power 

profile ......................................................................................................................................... 3-7

Figure 3-6 Ringhals-3 PWR unit, fuel cycle 19, exposure 0.3694 GWd/tHM: radial RPF 

relative differences (%) .............................................................................................................. 3-8

Figure 3-7 Ringhals-3 PWR unit, fuel cycle 19, exposure 4.5983 GWd/tHM: radial RPF 

relative differences (%) .............................................................................................................. 3-9

Figure 3-8 Ringhals-3 PWR unit, fuel cycle 19, exposure 9.830 GWd/tHM: radial RPF 

relative differences (%) ............................................................................................................ 3-10

Figure 3-9 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: axial power 

profile calculated with PARCS version 3.0 and version 2.71 ................................................... 3-12

Figure 3-10 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: 

differences between the assemblywise radial power fraction calculated with PARCS 

version 3.0 and version 2.71 .................................................................................................... 3-13

Figure 3-11 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: control 

rods that are inserted and their positions in steps withdrawn (‘100’ is the value for a 

control rod that is completely withdrawn) ................................................................................. 3-14

Figure 3-12 Forsmark-2 BWR unit, fuel cycle 21, exposure 2.311 GWd/tHM: control 

rods that are inserted and their positions in steps withdrawn (‘100’ is the value for a 

control rod that is completely withdrawn) ................................................................................. 3-15
viii 

Figure 3-13 Forsmark-2 BWR unit, fuel cycle 21, exposure 5.191 GWd/tHM: control 

rods that are inserted and their positions in steps withdrawn (‘100’ is the value for a 

control rod that is completely withdrawn) ................................................................................. 3-16

Figure 3-14 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: axial 

power profile ............................................................................................................................ 3-17

Figure 3-15 Forsmark-2 BWR unit, fuel cycle 21, exposure 5.191 GWd/tHM: axial 

power profile ............................................................................................................................ 3-18

Figure 3-16 Forsmark-2 BWR unit, fuel cycle 21, exposure 5.191 GWd/tHM: axial 

power profile ............................................................................................................................ 3-19

Figure 3-17 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: radial RPF 

relative differences (%) ............................................................................................................ 3-20

Figure 3-18 Forsmark-2 BWR unit, fuel cycle 21, exposure 2.311 GWd/tHM: radial RPF 

relative differences (%) ............................................................................................................ 3-21

Figure 3-19 Forsmark-2 BWR unit, fuel cycle 21, exposure 5.191 GWd/tHM: radial RPF 

relative differences (%) ............................................................................................................ 3-22
ix 

LIST OF TABLES 

Page

Table 2-1 CASMO-4/SIMULATE-3 data functionalization for PWR cases. ............................... 2-5

Table 2-2 CASMO-4/SIMULATE-3 data functionalization for BWR cases. ............................... 2-6

Table 3-1 Ringhals-3 PWR unit, Operating conditions of the measurement sets. ..................... 3-2

Table 3-2 Ringhals-3 PWR unit, Summary of the assembly-wise deviations in power 

density. ..................................................................................................................................... 3-11

Table 3-3 Forsmark-2 BWR unit, Operating conditions of the measurements sets. ................ 3-11

Table 3-4 Forsmark-2 BWR unit, Summary of the assembly-wise deviations in power 

density. ..................................................................................................................................... 3-23

xi 

ACKNOWLEDGMENT 

The authors wish to thank Prof. Tom Downar, Dr. Yunlin Xu, and Dr. Tomasz Kozlowski for their 

help with the PARCS code and the PMAXS files, as well as their feedback about this work. 

Ringhals AB, Forsmark Kraftgrupp AB and Vattenfall Nuclear Fuel AB are acknowledged for 

providing the plant data. In particular, the authors wish to thank Urban Sandberg, Mattias 

Carlsson and Gustav Andhill from Ringhals AB; Dr. Jyrki Peltonen and Dr. Gustav Dominicus 

from Forsmark Kraftgrupp AB; Dr. Hongwu Cheng from Vattenfall Nuclear Fuel AB. 

The Swedish Radiation Safety Authority (SSM) is acknowledged for the financial support. 

xiii 

ABBREVIATIONS

ANM Analytic nodal method 

BWR Boiling water reactor 

LWR Light water reactor 

MIC Movable in-core 

NEM Nodal expansion method 

NPP Nuclear power plant 

PARCS Purdue Advanced Reactor Core Simulator 

PMAXS Purdue macroscopic cross-section 

PWR Pressurized water reactor 

RPF Relative power fraction 

Sm-149 Samarium-149 

SSM The Swedish Radiation Safety Authority 

TIP Traversing incore prove 

U.S. NRC The United States Nuclear Regulatory Commission 

Xe-135 Xenon-135 

xv 

EXECUTIVE SUMMARY 

The safety analysis of a Nuclear Power Plant (NPP) is based on the application of complex 

computer codes that are able to simulate the physical behaviour of the system under normal 

operations and abnormal conditions. Therefore, such codes must be extensively and 

continuously verified and validated in order to demonstrate their reliability. 

In this context, the current report presents an assessment study for the U.S. NRC 3-D neutronic 

core simulator PARCS, and it includes an evaluation of the performances of the code for LWRs 

applications. For this purpose, the cores of the Swedish Ringhals-3 Pressurized Water Reactor 

(PWR) unit and the Forsmark-2 Boiling Water Reactor (BWR) unit were modeled with PARCS. 

As regards the cross-sections needed for this kind of calculations, they were prepared by 

following a special procedure developed by the present authors since core material data were 

only available in the format of library and restart files created by the SIMULATE-3 neutronic core 

simulator. Correspondingly, a new cross-section interface was developed and verified by the 

Division of Nuclear Engineering, Chalmers University of Technology, in order to convert the 

SIMULATE-3 data into data suitable for PARCS. Thereafter, the PARCS models developed for 

Ringhals-3 and Forsmark-2 were used for neutronic core analyses, at different operating 

conditions, along several fuel cycles. The results achieved from these simulations were then 

compared against the axial power and the radial power distribution estimated from the 

measurements that were provided by the owners of the plants. 

In the PWR case, the PARCS simulations predict satisfactorily both the core axial power profile 

and the core radial power distribution, although, in some cases, the deviations between 

calculated and measured data exhibit trends that need further investigations. For instance, the 

PARCS simulation at the beginning of a fuel cycle seems to overestimate the power in the 

center of the core and to underestimate the power at the periphery, whereas, at the end of a fuel 

cycle, the situation is opposite. 

In the BWR case, the core axial profile was predicted in a reasonable manner, but quite 

significant discrepancies for the radial power distribution was found. The current work suggests 

that such a disagreement might be due to the inability of PARCS to properly model multiple 

composition control rods. In fact the largest deviations in the computed power from the 

measurements were observed for those fuel assemblies placed in the neighborhood of control 

rods. 

1-1 

1. INTRODUCTION 

The safety analysis of a Nuclear Power Plant (NPP) is based on the application of complex 

computer codes that are able to simulate the physical behaviour of the system under normal 

operations and abnormal conditions. Therefore, an extensive verification and validation work of 

these computational tools is crucial, so that safety analyses based on such tools can be 

considered as reliable. 

The division of Nuclear Engineering at Chalmers University of Technology has been active in 

the development of coupled thermal-hydraulic / neutronic models for the analysis of transients 

that are relevant in the safety analysis of the Swedish NPPs, and, in this framework, efforts in 

validating the U.S. NRC 3-D core neutronics simulator PARCS [1, 2, 3] were initiated. More 

specifically, PARCS models were developed for the Ringhals NPP - Unit 3 (a PWR core type) 

and for the Forsmark NPP - Unit 2 (a BWR core type). Then static calculations at different 

operating conditions were performed by making use of these two models, and the results were 

compared to the radial power distributions and the axial power profiles reconstructed from the 

in-core measurements provided by the owners of the plants. 

The present document is organized as follows. In section 2, the two PARCS models are 

described. In section 3, the results from the assessment work are presented and discussed. 

Finally, in section 4, conclusions are drawn. 

2-1 

2. PARCS MODELLING 

For the PARCS simulation of the neutronic behavior of a reactor core, one needs to prepare: 

• a card name based input deck in which the calculation options and the core 

geometry and nodalization are specified; 

• the PMAXS files that contains the data from which the neutron cross-sections and 

kinetic parameters can be obtained; and 

• a file that contains the 3-dimensional spatial distribution of the history variables 

(burnup inclusive) and, in the present case, the instantaneous variables that 

identify the reactor core conditions at which the neutron cross-sections and kinetic 

parameters must be estimated. 

2.1 Description of the card name based input files

Following the guidelines provided by the PARCS User’s Manual [3], two input decks were 

developed for describing the Ringhals-3 and the Forsmark-2 cores, respectively. 

2.1.1 Ringhals-3 reactor model 

The Ringhals-3 core consists of 157 fuel assemblies, and each of them is modeled with 26 axial 

levels, and, divided radially into 2 x 2 nodes. The first and the last axial levels are used for the 

bottom and top reflectors, respectively. As regards the radial reflector, 64 reflector ‘assemblies’ 

are employed and they surround radially the active core. These 64 reflector assemblies are of 

two types: the ones that only take the baffle in account, and the ones that include both the baffle 

and the core barrel. 

Although control rods have no effect during normal operations (i.e., the control rods are 

completely withdrawn), they are also included since the present model is meant at investigating 

transient scenarios as well [4]. In the Ringhals-3 unit, all the control rods belong to the same 

type, and the different banks are defined on the basis of the different movements that groups of 

control rods can do. 

Among those options that are used for the solution of the neutronic problem in PARCS, the 

boundary conditions for the neutron field are settled by assuming to zero incoming current. In 

addition, the PARCS hybrid neutronic solver based on a combination between an Analytic Nodal 

Method (ANM) and a Nodal Expansion Method (NEM) is selected. 

2.1.2 Forsmark-2 reactor model 

The nodalization used for the Forsmark-2 core is such that each of the 676 fuel assemblies is 

modeled radially with one node and axially with 27 equidistant nodes. Again, the first and the 

last axial levels are employed for the bottom and top reflectors, respectively. The other axial 

levels are such that the several different segments in which one fuel assembly is divided can be 

taken in account with little approximations. Besides, similarly to the PWR case, the radial 

reflector is reproduced by making use of dummy assemblies that surrounds the active core and 

that are associated to the proper radial reflector materials and conditions. 
2-2 

Then, since control rods in BWR play a role in normal operation, their modeling is also important 

for static predictions. In the Forsmark-2 core, there are 161 cruciform control rods, and they are 

of 5 different types. Since PARCS cannot model explicitly cruciform control rods, each control 

rod is defined as a bunch of 4 control rods placed in those fuel assemblies that are near the 

specific cruciform control rod. The 5 different types of control rods are modeled with the card 

‘CRB_DEF’, the several banks of control rods and their location in the core are specified with 

the card ‘BANK_CONF’, the control rods positions are given in the card ‘BANK_POS’, and the 

type of control rods in each of the banks is provided in the card ‘CRB_TYPE’. 

As for the PWR model, zero incoming current is assumed as boundary condition for the neutron 

field, and a hybrid neutronic solver is used. 

2.2 Cross-sections preparation and PMAXS files

In order to perform core calculations, material constants and kinetic parameters representative 

of the actual local conditions, of the exposure, and of the history effects for a specific core are 

needed. Such properties are provided to PARCS via proper files, so-called PMAXS files. These 

files can be generated from the 2-D transport calculations performed at fuel-assembly level with 

the HELIOS code [5] or the CASMO-4 code [6]. For this purpose, the separate core module 

GenPMAXS [7] was developed. 

 

In the context of the work presented in this report, an alternative interface for building the 

PMAXS files was developed by the Division of Nuclear Engineering, Chalmers University of 

Technology, because data from HELIOS or CASMO-4 could not be released by the utilities. 

This novel approach is based on the capability of the Studsvik Scandpower 3-dimensional core 

simulator SIMULATE-3 [8] to retrieve, from binary library and restart files, all the material 

constants and kinetic parameters of all the fuel assemblies loaded in a specific core. Most 

importantly, the SIMULATE-3 code can then be used to edit any material/kinetic data for any 

fuel/reflector segment loaded in the considered core at any specified set of instantaneous and 

history variables. In such a way, the complete dependence of the material/kinetic data on 

instantaneous and history variables can be obtained. Therefore, no additional transport 

calculation is required, and the PMAXS files can be constructed relatively fast. Nevertheless, 

the procedure needs to take in account the fact that the CASMO-4/SIMULATE-3 formalism is 

different than the PARCS one, i.e., the data functionalization is different in the two cases. 

In the following subsections, the Chalmers cross-section interface is described, the preparation 

of the cross-sections for the Ringhals-3 and Forsmark-2 cases is discussed, and the correct 

implementation of such a procedure is verified. More details on this topic (for the PWR case) 

can be found in reference [9]. 

2.2.1 Description of the Chalmers cross-section interface 

As mentioned above, the CASMO-4/SIMUALTE-3 and the PARCS functionalizations of the 

cross-sections and of the neutron kinetic parameters with respect to the reactor core conditions 

differ from each other. Therefore, first, the two formalisms are introduced, and, then, the crosssection interface that was developed for the generation of the PMAXS files from the SIMULATE3 library and restart files is described. 
2-3 

2.2.1.1 CASMO-4/SIMULATE-3 formalism 

According to the CASMO-4/SIMULATE-3 model [10], the macroscopic and microscopic twogroup cross-sections, discontinuity factors, fission product data and detector data can be 

expressed in a generic form as 

(ܥ ,ܤ ,ܣ)஼ܲ∆ + (ܤ ,ܣ)஻ܲ∆ + (ܣ)஺ܲ∆ + (଴ܥ ,଴ܤ ,଴ܣ)ܲ = (ܥ ,ܤ ,ܣ)ܲ

eq. 2-1 

where ܲ(ܣ଴, ܤ଴, ܥ (଴is the base value, and 

߲ න) = ܣ)஺ܲ∆

′ܣ݀(଴ܥ ,଴ܤ ′,ܣ)ܲ ′ܣ߲

஺

஺బ

eq. 2-2 

߲ න) = ܤ ,ܣ)஻ܲ∆

ᇱܤ݀(଴ܥ ′,ܤ ,ܣ)ܲ ᇱܤ߲

஻

஻బ

eq. 2-3 

߲ න) = ܥ ,ܤ ,ܣ)஼ܲ∆

′ܥ݀(′ܥ ,ܤ ,ܣ)ܲ ′ܥ߲

஼

஼బ

eq. 2-4 

The approach for the generation of this specific type of parameters via eqs. 2-1 to 2-4 is 

displayed in a more intuitive manner in Fig. 2-1. 

In brief, the data needed in eq. 2-1 are obtained from CASMO-4 lattice calculations and 

organized into additive series of tables containing the partial functions. For those points of the 

tables in which data are not available, second-order Lagrangian interpolation is applied. 

Moreover, one can notice that, according to this scheme, parameters can only depend on a 

limited number of variables, i.e., no more than three variables are allowed. Tables 2-1 and 2-2 

summarize the possible CASMO-4/SIMULATE-3 data functionalization in PWR cases and in 

BWR cases [11, 12], respectively. 
Figure 2-1 Construction of the macroscopic and microscopic two-group crosssections, discontinuity factors, fission product data, and detector data in 

the CASMO-4/SIMULATE-3 code package 

 

2-4 
2-5 

Table 2-1 CASMO-4/SIMULATE-3 data functionalization for PWR cases 

Parameter P Fuel segment 

Reflector segment 

Radial and 

bottom Top 

 ଶܦ ,ଵܦ

Σଵ→ଶ

Σ௔,ଵ, Σ௔,ଶ

ߥΣ୤,ଵ, ߥΣ୤,ଶ

ߥ/ߢ

ଵ,௔ߪ

஻భబ

ଶ,௔ߪ ,

஻భబ

(௕ܥܪ ܾ,)್஼ுܲ ∆+௠) ܶܪ ܾ,)ܲ

(௠ܶ ܾ,)೘்ܲ∆ + (௕ܥ ܾ,)್஼ܲ∆ +

+ ∆்ܲ೑൫ܾ, ܶ௙൯ + ∆ܲఈ಴ೃ(ܾ, ߙ஼ோ)

+ ∆்ܲ೎೚೚೗೔೙೒൫ܾ, ܶ௖௢ ௚ ௢௟௜௡ ൯

[(௉஻ܾ ܾ,)ಳು௕ܲ∆+ ,ݕ݈݈݊ܽ݋݅ݐ݌݋]

(௠ܶ ,௕ܥ)ܲ (௕ܥ)ܲ

ߥ

ߛூభయఱ, ߛ భయఱ, ߛ భరవ, ߛௌ௠భరవ ௑௘ ௉௠

ଶ,௔ߪ

௑௘భయఱ

ଶ,௔ߪ ,

ௌ௠భరవ

Gd fraction remaining 

- - 

discontinuity factors 

(௠ܶ ܾ,)೘்ܲ∆ + (௕ܥ ܾ,)್஼ܲ∆

+ ∆்ܲ೑൫ܾ, ܶ௙൯ + ∆ܲఈ಴ೃ(ܾ, ߙ஼ோ)

+ ∆்ܲ೎೚೚೗೔೙೒൫ܾ, ܶ௖௢ ௚ ௢௟௜௡ ൯

[(௉஻ܾ ܾ,)ಳು௕ܲ∆+ ,ݕ݈݈݊ܽ݋݅ݐ݌݋]

(௠ܶ ,௕ܥ)ܲ (௕ܥ)ܲ

 
2-6 

Table 2-2 CASMO-4/SIMULATE-3 data functionalization for BWR cases 

Parameter P Fuel segment 

Reflector segment 

Radial and 

bottom Top 

ଶܦ ,ଵܦ

 

Σଵ→ଶ

Σ௔,ଵ, Σ௔,ଶ

ߥΣ୤,ଵ, ߥΣ୤,ଶ

 ߥ/ߢ

ଵ,௔ߪ

஻భబ

ଶ,௔ߪ ,

஻భబ

(ߙ ,ߙܪ ܾ,)ఈܲ ∆+) ߙܪ ܾ,)ܲ

+ ∆்ܲ೑൫ܾோாௌ, ܶ௙൯

+ ∆ܲఈ಴ೃ(ܾோாௌ, ߙ஼ோ)

+ ∆ܲுఈ಴ೃ(ܾ, ߙ஼ோ, ߙܪ஼ோ)

+ ∆்ܲ೎೚೚೗೔೙೒൫ܾ, ܶ௖௢௢௟௜௡௚൯

(ߙ)ܲ (௠ܶ)ܲ

ߥ

ߛூభయఱ, ߛ భయఱ, ߛ భరవ, ߛௌ௠భరవ ௑௘ ௉௠

ଶ,௔ߪ

௑௘భయఱ

ଶ,௔ߪ ,

ௌ௠భరవ

Gd fraction remaining 

- - 

discontinuity factors 

(ߙ ,ோாௌܾ(ఈܲ ∆+) ߙܪ ܾ,)ܲ

+ ∆்ܲ೑൫ܾோாௌ, ܶ௙൯

+ ∆ܲఈ಴ೃ(ܾோாௌ, ߙ, ߙ஼ோ)

+ ∆்ܲ೎೚೚೗೔೙೒൫ܾ, ܶ௖௢௢௟௜௡௚൯

(ߙ)ܲ (௠ܶ)ܲ

Fission rate of U-235 in 

detector position 

Peaking factor 

(ߙ ,ோாௌܾ(ఈܲ ∆+) ߙܪ ܾ,)ܲ

+ ∆்ܲ೑൫ܾோாௌ, ܶ௙൯

+ ∆ܲఈ಴ೃ(ܾோாௌ, ߙ, ߙ஼ோ)

- - 

 
2-7 

In addition, for those quantities for which the principal variation is due to burnup, like, 

• pin-by-pin power distribution, 

• corner flux ratios, 

• detector flux, 

• peaking factors, 

• detector microscopic cross-sections, 

• two-group neutron velocities, 

• effective neutron precursor yields, and 

• precursor decay constants, 

one-dimensional table sets in exposure are given. The additional dependencies are modeled 

with one-dimensional tables of the derivatives of the data as function of the exposure. Thus, the 

model applied in this case is as follows [10], 

(ܾ)௓ܲ∆ + ⋯ + (ܾ)஼ܲ∆ + (ܾ)஻ܲ∆ + (଴,ܼ...,଴ܥ ,଴ܤ ܾ,)ܲ = (ܼ , ... ,ܥ ,ܤ ܾ,)ܲ

eq. 2-5 

where ܾ is the exposure (burnup), and 

∆ܲ஻(ܾ) = න ߲

′ܤ݀(଴,ܼ...,଴ܥ ′,ܤ ܾ,)ܲ ′ܤ߲

஻

஻బ

eq. 2-6 

∆ܲ஼(ܾ) = න ߲

ᇱܥ݀(଴ܼ , ... ′,ܥ ,଴ܤ ܾ,)ܲ ′ܥ߲

஼

஼బ

eq. 2-7 

∆ܲ௓(ܾ) = න ߲

ܼ݀′(ܼ′ , ... ,଴ܥ ,଴ܤ ܾ,)ܲ ߲ܼ′

௓

௓బ

eq. 2-8 
2-8 

down decay time. 

.2.1.2 PARCS formalism 

ion, an assem ly discontinuity factor, a kinetic parameter, etc.) 

an be

The variables ܣ, ܤ, ܥ, ... , ܼ that appear in eq. 2-5 depend on the case that is studied and they 

can be, besides burnup ܾ, 

• fuel temperature ܶ௙; 

• history-averaged fuel te erature mp ܪܶ ;௙

• moderator temperature ܶ௠; 

• history-averaged moderator temperature ܪܶ ;௠

• void fraction ߙ ;

• history-averaged void fraction ߙܪ ;

• boron concentration ܥ ;௕

• history-averaged boron concentration ܥܪ ;௕

஼ோ

story-averaged co ol rod rtion ߙܪ஼ோ; 

• control rod insertion ߙ ; 

• hi ntr

• bur

inse

nable absorber exposure ܾ஻௉; and

• ܶ௖௢௢௟௜௡௚ for the shut

2

In the case of PARCS, any generic parameter ܲ (that could represent a macroscopic crosssection, a m c icroscopi cross-sect b

 written as [2, 7], 

൯௠ܶ ,௙ܶ ,௕ܥ ,௠ܦ ,ோ஼ߙ ,ܪ ܾ,൫ܲ

߲ܲ + ൯଴,௠ܶ ,଴,௙ܶ ,଴,௕ܥ ,଴,௠ܦ ,଴,ோ஼ߙ ,ܪ ܾ,൫ܲ= 

ோ஼ߙ߲

c

ฬ

൫௕,ு,ఈ಴ೃ,ೝ೐೑൯

൫ߙ஼ோ − ߙ஼ோ,଴൯

+

߲ܲ

௠ܦ߲

ฬ

൫௕,ு,ఈ಴ೃ,஽೘,ೝ೐೑൯

߲ܲ + ൯଴,௠ܦ − ௠ܦ൫

௕ܥ߲

ฬ

൫௕,ு,ఈ಴ೃ,஽೘,஼್,ೝ೐೑൯

൯଴,௕ܥ − ௕ܥ൫

+

߲ܲ

߲ඥܶ௙

ቤ

൫௕,ு,ఈ಴ೃ,஽೘,஼್,்೑,ೝ೐೑൯

൬ටܶ௙ − ටܶ௙,଴൰																																			

+

߲ܲ

߲ܶ௠

ฬ

൫௕,ு,ఈ಴ೃ,஽೘,஼್,்೑,்೘,ೝ೐೑൯

(ܶ௠ − ܶ௠,଴)

eq. 2-9 
2-9 

he

ector of two history variables; 

ction; 

; and 

nce point that is defined 

ross-section interface was 

he partial derivatives that appear in e

w re 

• ܾ is the burnup; 

• ܪ is either one history variable or a v

• ߙ஼ோ is the effective rodded fra

• ܦ ௠is the moderator density; 

• ܥ ௕is the boron concentration; 

• ܶ௙ is the effective fuel temperature

• ܶ௠ is the moderator temperature. 

The subscript 0 denotes the base case, and the subscript ref the refere

as the midpoint between the instantaneous value and the base value. 

It must be borne in mind that PARCS, at the time when the c

developed, could not handle m e than 2 h r or istory va iables. 

q. 2-9 can be estimated as, 

߲ܲ

ݒ߲

T

ฬ

൫௨,௩ೝ೐೑൯

(଴ݓ ,଴ݒ ,ݑ)ܲ − (଴ݓ ,ݒ ,ݑ)ܲ =

଴ݒ−ݒ

eq. 2-10 

he

alues; and 

s 

e 

he tree-leave formalism, and used through eqs. 2-9 and 2-10. 

w re 

• ݑ represents all the variables having their instantaneous v

• ݓ ଴represents all the variables having their base values. 

In addition, according to the PARCS formalism, the data related to each of the parameters are 

stored into a three levels structure, each level having a ‘tree-leave’ structure (an example for a 

PWR case is shown in Fig. 2-2). The highest level represents the history cases. The second 

level in the PARCS structure is related to the different possible instantaneous states of variable

as the control rod insertion, moderator density, boron concentration, fuel temperature, etc., for 

each history case. In the third level the burn-up dependency of the data can be reproduced. 

Therefore, when any parameter is needed by PARCS at a given set of operating conditions, th

data are retrieved from t
Figure 2-2 ”Tree-leave” formalism in PARCS for PWR cases (the subscript 0 

denotes the base case, the subscript 1 the perturbed value). The last 

ramification about the burnup dependency is not explicitly displayed for 

reason of clarity of the chart 

 

2-10 
2-11 

2.2.1.3 Description of the Chalmers cross-section interface 

The Chalmers cross-section interface developed to build-up the PMAXS files consists of 3 

steps. 

In the first step, the fuel/reflector assemblies loaded in the core are retrieved from the 

SIMULATE-3 restart file, and the operating points (i.e. instantaneous and history conditions, 

burnup inclusive) at which the material/kinetic data are available are also extracted from the 

SIMULATE-3 library file. More specifically, the following data are gathered into a summary file: 

• the segment number, its name, the type of segment (i.e., fuel or reflector), the 

number of rods, the number of heated rods, the average enrichment; 

• the burnup points; 

• the instantaneous values and the histories for the fuel temperature, moderator 

density/temperature, boron concentration, and control rod position, as well as 

which points are referred to as base condition or branch; and 

• the shutdown cooling times, and whether these points are referred to as base 

conditions or branches. 

In the second step, the data contained in the summary file are edited according to the PARCS 

‘tree-leave’ formalism discussed in subsection 2.2.2, and stored in a SIMULATE-3 output file. As 

mentioned above, this ‘tree-leave’ structure does not correspond to the way the data are 

functionalized in CASMO-4/SIMULATE-3 (see subsection 2.2.1). Nevertheless, the SIMULATE3 interpolation procedure can be used with confidence for following each branch of the PARCS 

‘tree-leave’ structure and then editing the corresponding data. 

In the third and last step, the PMAXS files are built for each of the fuel/reflector segments. This 

is done by successively stacking the results of different sets of values for the history variables. 

For each set of values for the history variables, the results corresponding to the ‘base’ branch 

are first stored for each burnup point. The partial derivatives associated to each instantaneous 

variable are then computed for each branch associated to a change of the considered 

instantaneous variable according to eq. 2-10 and for each burnup point. When constructing the 

PMAXS files, care has to be taken about the transport cross-sections and the macroscopic 

thermal absorption cross-sections. The transport cross-sections, which it is not directly given by 

SIMULATE-3, is derived from the diffusion coeff ie ts ܦ ௜ic n as follows, 

Σ௧௥,௜ = 1

௜ܦ3

eq. 2-11 

As regards the thermal absorption cross-section Σ௔,ଶ, the effect of the Xe-135 and Sm-149 

poisons might be included. This is the case when the SIMULATE-3 libray file is created with 

equilibrium fission products [13]. However, in a PARCS calculation (and, especially, when the 

concentration of the poisons is different from the equilibrium one), PARCS itself will provide the 

concentration of the poisons explicitly. Thus, the effect of the poisons in the thermal absorption 
2-12 

ross-section ret

eq. 2-12 

he current interface has also some limitations, i.e. some data cannot be retrieved, such as 

ts, fractions of delayed neutrons, inverse 

mblies; 

actors; 

•

.2.2 Preparation of PARCS cross-sections for the Ringhals-3 PWR unit 

 PARCS data functionalization of any parameter o any 

el segment is 

Th

c rieved from SIMULATE-3 has to be removed, i.e. 

Σ௔,ଶ

௪௜௧௛௢௨௧	௣௢௜௦௢௡௦ = Σ௔,ଶ௪௜௧௛	௣௢௜௦௢௡௦ − ቀܰ௑௘భయఱߪ௔,ଶ

௑௘భయఱ + ܰௌ௠భరవߪ௔,ଶௌ௠భరవቁ

T

• the kinetic data (precursor decay constan

velocities) for individual fuel asse

• the corner discontinuity f

the power form factors. 

2

For the Ringhals-3 core, e th ܲ related t

fu based on: 

• the burnup ܾ, 

• the history of the moderator density ܦܪ௠, 

• the history of the boron concentration ܥܪ௕, 

• the instantaneous boron concentratio ܥ௕, 

, 

n

• the instantaneous effective fuel temperature ܶ௙

• the instantaneous moderator density ܦ௠, and 

• the eff ctiv rodded fraction ߙ஼ோ. 

erefore eq. 2-9 becomes, 

൯௙ܶ ,௕ܥ ,௠ܦ ,ோ஼ߙ ,௕ܥܪ ,௠ܦܪ ܾ,൫ܲ

൯଴,௠ܶ ,଴,௙ܶ ,଴,௕ܥ ,଴,௠ܦ ,଴,ோ஼ߙ ,଴,௕ܥܪ ,଴,௠ܦܪ ܾ,൫ܲ= 

+

߲ܲ

ோ஼ߙ߲

e e

ฬ

൫௕,ு஽೘,ு஼್,ఈ಴ೃ,ೝ೐೑൯

൫ߙ஼ோ − ߙ஼ோ,଴൯ + ߲ܲ

௠ܦ߲

ฬ

൫௕,ு஽ ,ு஼ ,ఈ ,஽ ൯

൯଴,௠ܦ − ௠ܦ൫

+

߲ܲ

௕ܥ߲

೘ ್ ಴ೃ ೘,ೝ೐೑

ฬ

൫௕,ு஽೘,ு஼್,ఈ಴ೃ,஽೘,஼್,ೝ೐೑൯

൯଴,௕ܥ − ௕ܥ൫

+

߲ܲ

߲ඥܶ௙

ቤ

൫௕,ு஽೘,ு஼ ,ఈ ,஽ ,஼ ,் ൯

൬ටܶ௙

್ ಴ೃ ೘ ್ ೑,ೝ೐೑

− ටܶ௙,଴൰

eq. 2-13 
2-13 

onal d

stantaneous value of the b , 

For the reflector segments, the parameters ܲ is ncti fu ize only with respect to the 

oron concentration, i.e.

߲ܲ + ൯଴,௕ܥ൫ܲ௕) = ܥ)ܲ

௕ܥ߲

in

ฬ

൫஼್,ೝ೐೑൯

൯଴,௕ܥ − ௕ܥ൫

eq. 2-14 

uch 

LATE-3 

ummary file that is used for PARCS static calculations (see subsection 2.3) [14]. 

.2.3 Preparation of PARCS cross-sections for the Forsmark-2 BWR unit 

aneous effective rodded fraction. For this 

pe n then be reduced to: 

Although the cross-section interface discussed in subsection 2.2.3 allows retrieving the 

dependency of the reflector material data on the instantaneous moderator density as well, s

dependency is not used because the necessary data are not available in the SIMU

s

2

In the case of the Forsmark-2 model, history of void fraction ߙܪ and history of control rod 

insertion ߙܪ஼ோ are chosen to be the two history variables in the PARCS functionalization of the 

parameters ܲ for the fuel segments, together with the instantaneous effective fuel temperature,

the n us o a ensity, and the instant instanta eo m der tor d

cific application, eq. 2-9 ca

൯௙ܶ ,௠ܦ ,ோ஼ߙ ,ோ஼ߙܪ ,ߙܪ ܾ,൫ܲ

߲ܲ + ൯଴,௙,,ܶ଴,௠ܦ ,଴,ோ஼ߙ ,଴,௕ܥܪ ,଴,௠ܦܪ ܾ,൫ܲ= 

ோ஼ߙ߲

s

ฬ

൫௕,ு஽೘,ு஼್,ఈ಴ೃ,ೝ೐೑൯

൫ߙ஼ோ − ߙ஼ோ,଴൯

+

߲ܲ

௠ܦ߲

ฬ

൫௕,ு஽೘,ு஼್,ఈ಴ೃ,஽೘,ೝ೐೑൯

൯଴,௠ܦ − ௠ܦ൫

+

߲ܲ

߲ඥܶ௙

ቤ

൫௕,ு஽೘,ு஼್,ఈ಴ೃ,஽೘,஼್,்೑,ೝ೐೑൯

൬ටܶ௙ − ටܶ௙,଴൰

eq. 2-15 

ey are computed by 

nly taking in account the

As regards the parameters ܲ that characterize the reflector segments, th

o instantaneous moderator density, as follows,

߲ܲ + ൯଴,௠ܦ൫ܲ௠) = ܦ)ܲ

௠ܦ߲

ฬ

൫஽೘,ೝ೐೑൯

൯଴,௠ܦ − ௠ܦ൫

eq. 2-16 
2-14 

 For 

ucted from the PMAXS files, according to eq. 2-9, for each 

f the calculations, were compared with the data that were built from the SIMULATE-3 library 

ther 

rresponding values of burnup, instantaneous variables, and history variables, for a single 

ith the 

e PMAXS files generated with the new interface), one can find an excellent agreement 

ly. 

s regards BWR applications, only a random check was performed for verifying that PARCS 

ry 

ontrol rod branches, a 

ure branches; and 

gain, the data reconstructed by PARCS matched the original data, and the correct 

plementation of the interface could thus be demonstrated for BWR applications as well. 

2.2.4 Verification of the Chalmers cross-section interface 

Before using the cross-section interface for practical applications, it was verified that PARCS

can correctly reconstruct the data from the PMAXS files generated with such an interface.

that purpose, all the possible combinations of values of instantaneous and history variables 

appearing in the PMAXS files were employed as sets of operating conditions for PARCS 

calculations. Thus, the data reconstr

o

file, according to eq. 2-1. 

The procedure for the verification process can be summarized as follows. First, data are 

retrieved from the SIMULATE-3 library file, for all the possible combinations of values of the 

instantaneous variables, of the history variables, and of burnup. Thereafter, the PARCS input 

files for each set of variables are built-up. In particular, each of the PARCS input files models 

only one assembly through a pseudo-assembly, where segments covering the whole range of 

exposure were axially stacked, so that the whole dependency of the material data on burnup 

can be handled in one single calculation and computational effort can be saved. On the o

hand, the moderator density, fuel temperature, boron concentration, etc. are kept constant in

each input file. Finally, from each of the PARCS runs, the material data are edited at the 

co

segment, and compared to the original data directly coming from the SIMULATE-3 binary file. 

 

In the case of PWR applications, the verification procedure was applied fully, and, for the sake 

of simplicity, the results achieved for only a few combinations of instantaneous and history 

variables are shown in Fig. 2-3. By comparing the infinite multiplication factor calculated w

SIMULATE-3 cross-sections and with the PARCS cross-sections (i.e. the cross-sections from 

th

between the two cases, and conclude that the Chalmers cross-section interface works correct

A

retrieves the correct data from SIMULATE-3: 

• detector flux, for the base history, one history of moderator density, and one histo

of the control rod position; 

• on each of the histories, for the reference branch, a few c

few moderator density branches, and a few fuel temperat

• on each of the branches, for two random burnup points. 

A

im
2-15 

Figure 2-3 

history variables. The infinite multiplication factor calculated from the 

original data is represented by lines, whereas the infinite multiplication 

factor calculated from the reconstructed data is represented by crosses 

PWR case, variation of k∞ as a function of burnup, instantaneous and 
2-16 

2.3 3-D distribution of the history and instantaneous variables

In order to run a static core calculation with PARCS, 3-D distribution of the history and 

instantaneous variables must be available, so that cross-sections and neutron kinetic 

parameters can be evaluated at the proper local conditions. Former SIMULATE-3 calculations 

were performed for the same reactor core conditions of interest as in the current work. 

Thereafter, the SIMULATE summary files from these simulations were properly modified and 

directly used as spatial distributions of both history and instantaneous variables fed to PARCS 

ee the description of the PARCS card ‘INP_HST’ in [3]). However, it must be mentioned that 

d 

On the contrary, the concentration of the poisons was recalculated by PARCS, based on the 

corresponding microscopic cross-sections and fission yields stored in the PMAXS files, by 

activating the PARCS card ‘XE_SM’. 

(s

PARCS has also the capability to calculate the spatial distribution of the moderator density an

of the fuel temperature over the core. Such a capability was not used in the present work. 
3-1 

3. RESULTS OF THE STATIC CALCULATION AND COMPARISONS 

WITH MEASUREMENT DATA 

Several sets of measured data at different core exposures and for different fuel cycles were 

available for the Swedish Ringhals-3 PWR unit and the Forsmark-2 BWR unit. In the Ringhals 

unit 3, the neutron flux measurements were carried out by making use of Movable In-Core (MIC) 

detectors, which are fission chambers. These detectors can only be positioned in the central 

instrumentation tube of a limited number of assemblies. In the Forsmark unit 2, neutron flux 

measurements are given by Traversing Incore Prove (TIP) detectors that are located in a certain 

number of inter-assembly instrumentation tubes. For both cases detector signals can be used in 

SIMULATE-3 to reconstruct the Relative Power Fraction (RPF) for each of the nodes in which 

the reactor core has been discretized for the solution of the neutronic equations. 

In order to evaluate the accuracy of the static calculations, the values of the RPF estimated with 

SIMULATE-3 from the detector signals are thus compared against the values predicted by 

PARCS, node by node, in terms of rel diffe as follows: ative rences,

∆=

ܴܲܨ஺௉ோ஼ௌ − ܴܲܨ௔௘௠௦௨௥௘ௗ

ܴܲܨ௔௘௠௦௨௥௘ௗ

eq. 3-1 

where 

• ܴܲܨ஺௉ோ஼ௌ is th

• ܴܲܨ௔௘௠௦௨௥௘ௗ is the RPF estimated by SIMULATE-3 from the detector signals, for 

one core node. 

e RPF calculated with PARCS, for one core node; and 

 
3-2 

3.1 PWR case

The cases studied for Ringhals-3 are summarized in Table 3-1. The sets of measurements 

correspond to three different fuel cycles, and, for each cycle, they referred to operating 

conditions at about the beginning, the middle and the end of the cycle (except for cycle 22 for 

which measured data at the end of the cycle were not available). 

Table 3-1 Ringhals-3 PWR unit, Operating conditions of the measurement sets 

Fuel 

Cycle 

Exposure

[GWd/tHM]

Relative 

Power 

[%] 

Coreaveraged 

Coolant 

Temperature

[°C] 

Critical Boron 

Concentration

[ppm] 

10 0.2208 99.8 303.3 965 

10 4.8136 99.8 303.0 524 

10 9.5929 99.8 303.2 79 

19 0.3694 100.0 301.4 915 

19 4.5983 100.0 301.4 519 

19 9.830 100.1 301.2 25 

22 0.1442 99.1 301.2 1270 

22 4.6668 100.1 301.3 828 

The results are reported in details only for the fuel cycle 19, since similar trends can be 

observed for the others. The simulations shown in the following are computed with PARCS 

version 2.71. Nevertheless, the discussion is still valid for PARCS version 3.0, since almost 

identical predictions can be obtained (see Figs. 3-1 and 3-2). 
Figure 3-1 Ringhals-3 PWR unit, fuel cycle 19, exposure 0.3694 GWd/tHM: axial 

power profile calculated with PARCS version 3.0 and version 2.71 

3-3 
Figure 3-2 Ringhals-3 PWR unit, fuel cycle 19, exposure 0.3694 GWd/tHM: 

differences between the assemblywise radial power fraction calculated 

with PARCS version 3.0 and version 2.71 

 

3-4 
Figures 3-3 to 3-5 show the comparison between the axial power calculated with PARCS and 

the profile estimated from the measured data. A systematic deviation of the PARCS predictions 

from the measurements can be seen. As mentioned in subsection 2.2.3, the variation of the 

cross-sections and neutron kinetic parameters in the reflector region due to the instantaneous 

moderator density is not included. This approximation might not be valid and can lead to a poor 

estimation of the axial leakage of neutrons through the top and bottom reflectors. Therefore, this 

fact could explain the larger discrepancy observed close to the top and the bottom of the active 

core. Nevertheless, the overall axial power profile is correctly reproduced by the PARCS 

simulations. 

Figure 3-3 Ringhals-3 PWR unit, fuel cycle 19, exposure 0.3694 GWd/tHM: axial 

power profile 

3-5 
Figure 3-4 Ringhals-3 PWR unit, fuel cycle 19, exposure 4.5983 GWd/tHM: axial 

power profile 

3-6 
Figure 3-5 Ringhals-3 PWR unit, fuel cycle 19, exposure 9.830 GWd/tHM: axial 

power profile

 

3-7 
As regards the radial power distribution, a trend can be identified by looking at the relative 

differences computed with eq. 3-1. At beginning of cycle conditions, the PARCS simulations 

overestimate the power in the center of the core and underestimate the power at the periphery 

(see Fig. 3-6). At middle of cycle conditions, the deviation of the PARCS results from the 

measured data does not exhibit any systematic behavior (see Fig. 3-7). At end of cycle, the 

calculations show an underestimation in the center of the core and an overestimation at the 

periphery (see Fig. 3-8). 

Figure 3-6 Ringhals-3 PWR unit, fuel cycle 19, exposure 0.3694 GWd/tHM: radial 

RPF relative differences (%) 

3-8 
Figure 3-7 Ringhals-3 PWR unit, fuel cycle 19, exposure 4.5983 GWd/tHM: radial 

RPF relative differences (%) 

3-9 
Figure 3-8 Ringhals-3 PWR unit, fuel cycle 19, exposure 9.830 GWd/tHM: radial RPF 

relative differences (%) 

3-10 
3-11 

A summary of the relative differences between calculations and measurements for the several 

cases analyzed is reported in Table 3-2. It can be seen that the largest discrepancies are at the 

beginning and at the end of cycle, while the best performances can be found at the middle of 

cycle. Moreover, the effective multiplication factor keff shows a similar behavior, with a deviation 

from the expected criticality within typically 200 pcm. 

Table 3-2 Ringhals-3 PWR unit, Summary of the assembly-wise deviations in power 

density 

Fuel 

Cycle 

Exposure 

[GWd/tHM]

Calculated 

keff

Relative difference between PARCS 

and measured relative power 

fraction (%) 

Average Minimum Maximum 

10 0.2208 0.99865 -0.91 -10.22 8.95 

10 4.8136 1.00116 -0.21 -4.81 5.07 

10 9.5929 1.00189 0.11 -5.14 7.01 

19 0.3694 0.99986 -0.68 -6.72 5.25 

19 4.5983 1.00052 0.02 -4.27 3.70 

19 9.8300 1.00120 0.22 -5.67 5.56 

22 0.1442 0.99764 -0.4 -5.10 5.79 

22 4.6668 1.00017 0.17 -3.54 4.47 

3.2 BWR case

The PARCS model of the Forsmark-2 BWR unit was compared against TIP measurements 

provided by Forsmark Kraftgrupp AB / Vattenfall Nuclear Fuel AB to Chalmers. The core 

operating conditions corresponding to these measurements are summarized in Table 3-3. This 

database includes the measurements performed in three different fuel cycles (21, 24, and 25), 

at about the beginning, the middle and the end of each cycle. 

Table 3-3 Forsmark-2 BWR unit, Operating conditions of the measurements sets 

Fuel 

Cycle 

Exposure

[GWd/tHM]

Relative 

Power

[%] 

Coreaveraged 

Coolant 

Temperature

[°C] 

21 0.341 108 283.82 

21 2.311 108.1 283.75 

21 5.191 107.9 283.67 

24 0.485 108.1 284.48 

24 4.622 108.1 284.18 

24 7.394 108 283.42 

25 0.135 107.9 284.65 

25 3.050 107.7 284.46 

25 5.731 107.8 283.97 
In the following discussion, only the results for the fuel cycle 21 are shown in details, since 

similar conclusions can be drawn for all the other cases. Besides, the calculations were 

performed with PARCS version 3.0. Nevertheless, as shown in Figs. 3-9 and 3-10, PARCS 

version 3.0 and version 2.71 produce simulations with negligible differences. 

Figure 3-9 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: axial 

power profile calculated with PARCS version 3.0 and version 2.71 

3-12 
Figure 3-10 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: 

differences between the assemblywise radial power fraction calculated 

with PARCS version 3.0 and version 2.71 

 

3-13 
Figures 3-11 to 3-13 display the positions of the control rods for the three operating conditions in 

cycle 21. Such control rods are moved through the fuel cycle, in order to compensate for the 

loss of reactivity that the core experiences during the life of one fuel load, and to keep the radial 

power distribution as flat as possible. 

Figure 3-11 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: control 

rods that are inserted and their positions in steps withdrawn (‘100’ is 

the value for a control rod that is completely withdrawn) 

3-14 
Figure 3-12 Forsmark-2 BWR unit, fuel cycle 21, exposure 2.311 GWd/tHM: control 

rods that are inserted and their positions in steps withdrawn (‘100’ is 

the value for a control rod that is completely withdrawn) 

3-15 
Figure 3-13 Forsmark-2 BWR unit, fuel cycle 21, exposure 5.191 GWd/tHM: control 

rods that are inserted and their positions in steps withdrawn (‘100’ is 

the value for a control rod that is completely withdrawn) 

 

3-16 
Figures 3-14 to 3-16 show the comparison between the calculated axial power profile and the 

profile estimated from the detector signals via SIMULATE-3, for the beginning, the middle and 

the end of the cycle, respectively. From these plots, the prediction of the axial power profile is 

quite satisfactory, throughout the entire fuel cycle. However, it can be noticed that larger 

discrepancies occur in the lowest axial half of the core (and, indeed, BWR control rods are 

inserted from the bottom of the core). Since control rods are inserted from the bottom of the 

core in BWRs, this suggests that the model for the control rods implemented in PARCS might 

be somehow inaccurate. 

Figure 3-14 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: axial 

power profile 

3-17 
Figure 3-15 Forsmark-2 BWR unit, fuel cycle 21, exposure 5.191 GWd/tHM: axial 

power profile 

3-18 
Figure 3-16 Forsmark-2 BWR unit, fuel cycle 21, exposure 5.191 GWd/tHM: axial 

power profile 

 

3-19 
Figures 3-17 to 3-18 provide the relative differences (see eq. 3-1), for each fuel assembly, 

between the calculated RPFs and the RPFs that are derived from the detector signals via

SIMULATE-3, again, at the beginning, middle, and end of the cycle, respectively. When the 

radial power distribution is investigated, one can find that the discrepancies are quite significant 

for those fuel assemblies close to the control rods and less pronounced in the region less 

affected by the control rods (e.g., see Fig. 3-11 together with Fig. 3-17). Moreover, near the 

control rods, the RPFs for the majority of the fuel assemblies are underestimated, whereas a 

relatively strong RPF overestimation is achieved for a few fuel assemblies. This fact seems to 

point out that a problem in the modeling of control rods exists in. As a matter of fact, an issue 

with the modeling of multiple composition control rods is known by the PARCS developers, who 

are currently working on resolving such an issue [15]. Since all control rods in the present 

Forsmark-2 model are multiple composition control rods, the discrepancies noticed in Figs. 3-17 

to 3-19 may thus be attributed to such a pending issue of the PARCS code. 

Figure 3-17 Forsmark-2 BWR unit, fuel cycle 21, exposure 0.341 GWd/tHM: radial 

RPF relative differences (%) 

3-20 
Figure 3-18 Forsmark-2 BWR unit, fuel cycle 21, exposure 2.311 GWd/tHM: radial 

RPF relative differences (%) 

3-21 
Figure 3-19 Forsmark-2 BWR unit, fuel cycle 21, exposure 5.191 GWd/tHM: radial 

RPF relative differences (%) 

 

3-22 
3-23 

The results obtained for the several sets of TIP measurements performed in Forsmark-2 are 

summarized in Table 3-4. It can be seen that the total average value of the relative differences 

between PARCS and measured relative power fraction does not exhibit any strong bias (in fact 

it is between -0.71% and 2.34%), whereas the minimum and maximum values of the relative 

differences computed over all the nodes in which the core was discretized underline that the 

PARCS calculations are not completely satisfactory. Besides, the keff is predicted relatively well, 

with a deviation from criticality within +437.1 pcm and -731.8 pcm. 

Table 3-4 Forsmark-2 BWR unit, Summary of the assembly-wise deviations in power 

density 

Fuel 

Cycle 

Exposure

[GWd/tHM] 

Calculated 

keff

Relative difference between PARCS 

and measured relative power 

fraction (%) 

Average Minimum Maximum 

21 0.341 1.004371 0.09 -34.06 61.00 

21 2.311 1.001700 1.9 -37.67 65.07 

21 5.191 1.003494 0.25 -67.24 75.15 

24 0.485 0.996145 -0.71 -39.29 51.10 

24 4.622 0.995974 0.93 -34.41 42.26 

24 7.394 0.997569 0.5 -36.38 30.54 

25 0.135 0.992682 1.69 -29.63 49.88 

25 3.050 0.993217 1.23 -35.15 52.07 

25 5.731 0.992794 2.34 -38.17 45.17 

4-1 

4. SUMMARY AND CONCLUSIONS 

A comparison study has been presented for the U.S. NRC 3-D core neutronics simulator 

PARCS. In the present report, the work includes an evaluation of the performances of the code 

for both PWR and BWR applications. 

For this purpose, the Swedish Ringhals-3 PWR and the Forsmark-2 BWR cores were modeled 

with PARCS, and analyzed at about the beginning, the middle, and the end of three different 

fuel cycles (except for the Ringhals-3 fuel cycle 22, for which the data at the end of cycle were 

not available). Then, the PARCS simulations were compared against the axial power and the 

radial power distribution estimated from proper in-core detector measurements. 

First of all, no significant difference between the simulations computed with PARCS version 

2.71 and 3.0 was observed for both the PWR and the BWR cases (see Figs. 3-1 and 3-2, and 

Figs 3-9 and 3-10). 

As regards the PWR case, the predictions achieved with PARCS reproduce the main variations 

of the radial and axial power distributions over the core, and show a good agreement in the 

range of a few percents (see, for instance, Figs. 3-3 and 3-6, and Table 3-2). However, the 

PARCS simulation at the beginning of a fuel cycle seems to overestimate the power in the 

center of the core, and to underestimate the power at the periphery, whereas, at the end of a 

fuel cycle, the situation is the opposite. 

Concerning the BWR application, it was found that the PARCS results can capture quite well the 

behavior of the axial core power, although quite significant discrepancies can be observed in the 

radial power distribution (see, for instance, Figs. 3-14 and 3-17, and Table 3-4). The reason 

behind this shortcoming seems to be due to the fact that the control rod model implemented in 

PARCS is not fully adequate for describing multiple composition control rods as is the case for 

BWRs (e.g., see Fig. 3-11 together with Fig. 3-17). In this regard, the PARCS team has 

announced that work has already started to resolve such an issue [15]. 

For the effective multiplication factor keff, calculations give reasonable values with respect to the 

critical value: within ±200 pcm for most of the PWR cases, and between +437.1 pcm and -731.8 

pcm for the BWR cases (again, see Tables 3-2 and 3-4). 

In the framework of this study, an alternative interface was also developed and verified 

successfully for both PWR and BWR applications (see Fig. 2-3), and allows creating the 

PMAXS files (that are needed for PARCS to generate the cross-sections and the neutron kinetic 

parameters with respect to the nodal reactor core conditions) directly from the SIMULATE-3 

output and library files. No CASMO-4 input file is necessary to create the PMAXS files, as is for 

instance the case with the GenPMAXS interface. The developed interface thus represents an 

alternative and complementary procedure to generate cross-sections data to PARCS, in 

comparison with GenPMAXS. 

5-1 

5. REFERENCES 

1. Downar, T.J., Barber, D.A., Miller, R.M., et al., PARCS: Purdue advanced reactor core 

simulator, in: Proceeding of the International Meeting on New Frontiers of Nuclear 

Technology: Reactor Physics, Safety and High-Performance Computing (PHYSOR 

2002), Seoul, South-Korea, October 10-13, 2002. 

2. Downar, T., Lee, D., Xu, Y, Kozlowski, T., PARCS v2.6 - U.S. NRC Core Neutronics 

Simulator – Theory Manual (Draft), School of Nuclear Engineering, Purdue University, 

W. Lafayette, IN, USA, 2004. 

3. Downar, T., Xu, Y., Seker, V., Carlson, D., 2008. PARCS v2.7, U.S. NRC Core 

Neutronics Simulator, User Manual, 2008. 

4. Stålek, M., Bánáti, J., Demazière, C., Main Steam Line Break Calculations using a 

coupled RELAP5/PARCS model for the Ringhals-3 Pressurized Water Reactor, in: 

Proceeding of ICONE 16, Orlando, Florida, USA, May 11-15, 2008. 

5. Casal, J.J., Stamm’ler, R.J.J., Villarino, E.A., et al., HELIOS: Geometric capabilities of a 

new fuel-assembly program, in: Proceedings of the International Topical Meeting in 

Advances in Mathematics, Computations and Reactor Physics, Pittsburgh, PA, USA, 

April 28 – May 2, 1991, Vol. 2, 10.21-1. 

6. Ekberg, K., Forssén, B.-H., Knott, D., Umbarger, J.A., Edenius, M., CASMO-4: A fuel 

assembly burnup program, User’s Manual, Studsvik Scandpower, Studsvik/SOA-95/10S, 

1995. 

7. Xu, Y., Downar, T., GenPMAXS Code for Generating the PARCS Cross Section 

Interface File PMAXS, Purdue University, School of Nuclear Engineering, West 

Lafayette, IN, USA, 2006. 

8. Covington, L.J., Cronin, J.T., Umbarger, J.A., SIMULATE-3: Advanced threedimensional two-group reactor analysis code, Studsvik Scandpower, Studsvik/SOA95/15 Rev 2, 1995. 

9. Stålek, M., Demazière, C., Development and validation of a cross-section interface for 

PARCS, Annals of Nuclear Energy 35, 2008. 

10. Ver Planck, D.M., Smith, K.S., Umbarger, J.A., TABLES-3 users’s manual, Studsvik 

Scandpower/SOA-95/16, 1995. 

11. Garis, N.S., PWR model with CASMO and SIMULATE, Studsvik Scandpower, 

Studsvik/SOA-95/10S, 1995. 

12. Garis, N.S., BWR model with CASMO and SIMULATE, Studsvik Scandpower, 

Studsvik/SOA-95/11S, 1995. 
5-2 

13. Vanevenhoven, S., private communication, Studsvik Scandpower, Idaho Falls, ID, USA, 

2005. 

14. Xu, Y., Private communication, Purdue University, School of Nuclear Engineering, West 

Lafayette, IN, USA, 2005. 

15. Hudson, N., Downar, T., XU, Y., PARCS Status, presentation at the: Spring CAMP 

Meeting, Bariloche, Rio Negro, Argentina, April 27-29, 2011. 





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-0414 Comparison of the U.S. NRC PARCS Core Neutronics Simulator 

Against In-Core Detector Measurements for LWR Applications