<%BANNER%>

Analysis of Light Water Reactors including 3-D Deterministic Burnup of a Boiling Water Reactor Fuel Assembly

Permanent Link: http://ufdc.ufl.edu/UFE0024696/00001

Material Information

Title: Analysis of Light Water Reactors including 3-D Deterministic Burnup of a Boiling Water Reactor Fuel Assembly
Physical Description: 1 online resource (100 p.)
Language: english
Creator: Rowe, Mireille
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: adjoint, burnup, bwr, detector, transport
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ANALYSIS OF LIGHT WATER REACTORS INCLUDING 3-D DETERMINISTIC BURNUP OF A BOILING WATER REACTOR FUEL ASSEMBLY By Mireille Anjaline Rowe August 2009 Chair: Glenn Sjoden Major: Nuclear Engineering Sciences Accurate transport analysis of reactor systems is important in the Nuclear Engineering field since it provides essential information in power monitoring, criticality safety and fuel reload optimization. Monte Carlo methods have primarily been used to analyze these reactor systems, yet drawbacks include difficulty converging the source in an eigenvalue problem when dealing with high dominance ratio systems (Brown, et. al., 2003). Deterministic 3-D Sn transport computations have been utilized in limited ways due to the large memory requirements of these methods. For this reason, 1-D or 2-D geometry set-ups are usually implemented, and important information regarding the system may be lost as is the case with boiling water reactors (BWRs). In order to evaluate a 3-D model of a system with a deterministic transport code, one that runs in parallel can provide unique advantages. This thesis presents a method to generate a multigroup cross section data set and transport models for analysis of reactors. Next an analysis of a light water reactor system using the 3-D parallel code PENTRAN (Parallel Environment Neutral particle Transport) to perform adjoint transport calculations and provide information on effective detector ranges in PWRs is discussed. In addition, a detailed fuel burnup analysis of a BWR using the PENTRAN/PENBURN (Parallel Environment Burnup) suite is presented.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Mireille Rowe.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Sjoden, Glenn E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024696:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024696/00001

Material Information

Title: Analysis of Light Water Reactors including 3-D Deterministic Burnup of a Boiling Water Reactor Fuel Assembly
Physical Description: 1 online resource (100 p.)
Language: english
Creator: Rowe, Mireille
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: adjoint, burnup, bwr, detector, transport
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ANALYSIS OF LIGHT WATER REACTORS INCLUDING 3-D DETERMINISTIC BURNUP OF A BOILING WATER REACTOR FUEL ASSEMBLY By Mireille Anjaline Rowe August 2009 Chair: Glenn Sjoden Major: Nuclear Engineering Sciences Accurate transport analysis of reactor systems is important in the Nuclear Engineering field since it provides essential information in power monitoring, criticality safety and fuel reload optimization. Monte Carlo methods have primarily been used to analyze these reactor systems, yet drawbacks include difficulty converging the source in an eigenvalue problem when dealing with high dominance ratio systems (Brown, et. al., 2003). Deterministic 3-D Sn transport computations have been utilized in limited ways due to the large memory requirements of these methods. For this reason, 1-D or 2-D geometry set-ups are usually implemented, and important information regarding the system may be lost as is the case with boiling water reactors (BWRs). In order to evaluate a 3-D model of a system with a deterministic transport code, one that runs in parallel can provide unique advantages. This thesis presents a method to generate a multigroup cross section data set and transport models for analysis of reactors. Next an analysis of a light water reactor system using the 3-D parallel code PENTRAN (Parallel Environment Neutral particle Transport) to perform adjoint transport calculations and provide information on effective detector ranges in PWRs is discussed. In addition, a detailed fuel burnup analysis of a BWR using the PENTRAN/PENBURN (Parallel Environment Burnup) suite is presented.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Mireille Rowe.
Thesis: Thesis (M.S.)--University of Florida, 2009.
Local: Adviser: Sjoden, Glenn E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024696:00001


This item has the following downloads:


Full Text

PAGE 1

1 ANALYSIS OF LIGHT WATER REACTORS INCLUDING 3 D DETERMINISTIC BURNUP OF A BOILING WATER REACTOR FUEL ASSEMBLY By MIREILLE ANJALINE ROWE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2009

PAGE 2

2 2009 Mireille Anjaline Rowe

PAGE 3

3 To Ricardo A. Cortes Jr. and my parents Mireya and Franklin Sotillo and Tomas Rowe

PAGE 4

4 ACKNOWLEDGMENTS I would like to thank my advisor Dr. Glenn Sjoden for providing technical guidance throughout my research and for always being available for help and advice. I also wish to acknowledge Kevin Manalo, Travis Mock and Thomas Plower for their contribution in the PENTRAN/PENBURN suite and helping with adapting the code package for use in analyzing BWRs And I would also like to thank my thesis committee members Dr. Edward Dugan and Dr. Robert Smith.

PAGE 5

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES ...........................................................................................................................7 LIST OF FIGURES .........................................................................................................................9 LIST OF ABBREVIATI ONS ........................................................................................................11 ABSTRACT ...................................................................................................................................12 CHAPTER 1 INTRODUCTION ..................................................................................................................13 1.1 Introduction ..................................................................................................................13 1.2 Transport Theory .........................................................................................................13 1.3 Diffusion Theory ..........................................................................................................14 1.4 Monte Ca rlo Method ....................................................................................................15 1.5 Deterministic Code: PENTRAN/PENBURN Suite .....................................................16 1.6 Previous Work .............................................................................................................17 1.6.1 SCALE S AS2H BWR Burnup Analysis ............................................................17 1.6.2 Void Fraction Uncertainties ...............................................................................18 2 MULTIGROUP CROSS SECTION GENERATION ............................................................19 2.1 Cross Section Generation with SCALE 5.1 Package using DEV XS Procedure ........19 2.1.1 SCALE 5.1 TNEWT Control Sequence ............................................................19 2.1.2 Post Processing Utilities ....................................................................................20 2.1.3 GMIX Code .......................................................................................................20 2.2 BWR 2.2 wt% Fuel Pin Cross Section Generation ......................................................21 2.3 XSMERGE Code .........................................................................................................22 3 AN APPLICATION OF FORWARD AND ADJOINT TRANSPORT ................................28 3.1 Silicon Carbide Detector Design .................................................................................28 3.2 Multigroup Cross Section Generation ........................................................................29 3.3 Forward versus Adjoint Detector Response ................................................................30 3.4 PENTRAN Criticality Calculation ..............................................................................32 3.5 FSPREP Code ..............................................................................................................33 3.6 PENTRAN Adjoint Calculation ..................................................................................33 3.7 Results and Findings ....................................................................................................33 4 PENTRAN/PENBURN ANALYSIS OF A SINGLE BWR FUEL ROD ..............................41

PAGE 6

6 4.1 Steady State Two Phase Flow in a Heated Channel ....................................................41 4.2 Axial Distribution of Vapor Quality in a BWR Assembly ..........................................43 4.3 Single Pin Burnup Comparison with SFCOMPO ........................................................43 4.4 BWR Fuel Rod Axial Zone Optimization ...................................................................44 5 GUNDREMMINGEN ASSEMBLY ANALYSIS .................................................................52 5.1 BWR Assembly Specifications ....................................................................................52 5.1.1 Fuel Pin Homogenization ..................................................................................52 5.1.2 PENTRAN Geometry ........................................................................................53 5.2 MCNP Criticality Calculation ......................................................................................53 5.3 BWR Assembly Burnup Results ..................................................................................55 5.4 Burnup Dependent Cross Section Generation .............................................................56 5.5 Accounting for Power Shift .........................................................................................57 6 CONCLUSIONS AND FUTURE WORK .............................................................................79 APPENDIX A SCALE 5.1 SAMPLE INPUT FILE .......................................................................................82 B FSPREP SAMPLE INPUT .....................................................................................................85 C FSPREP SAMPLE OUTPUT .................................................................................................86 D ALPO INP UT MODIFICATION FOR XSMCNP .................................................................87 E MCNP INPUT FILE ...............................................................................................................88 F SCALE 5.1 T DEPL INPUT ..................................................................................................92 G ALPO INPUT FOR COLLAPSED CROSS SECTION FILE ...............................................95 H BURNSET INPUT FILE ........................................................................................................96 LIST OF REFERENCES ...............................................................................................................98 BIOGRAPHICAL SKETCH .......................................................................................................100

PAGE 7

7 LIST OF TABLES Table page 21 BWR/6 fuel assembly specifications .................................................................................24 22 BWR/6 2.2 wt% fuel pin composition ...............................................................................24 23 Eigenvalue comparisons for PENTRAN unit cell meshing schemes ................................25 24 XSMERGE example problem material numbers assigned. ...............................................25 31 Nuclide composition of 3 wt% enriched UO2 fuel ............................................................36 32 Integral System Balance from Criticality Run ...................................................................36 33 Integral System Balance from Fixed Source Run ..............................................................36 41 A1 fuel element at 44 cm 0.74153 g/cc percent differences between SFCOMPO values and PENBURN burnup results (22.6 GWD/MTU) ................................................49 42 B3 fuel pellet at 268 cm 0.33973 g/cc percent differences between SFCOMPO values and PENBURN burnup results (22.6 GWD/MTU) ................................................50 43 B3 fuel pellet at 268 cm 0.74153 g/cc percent differences between SFCOMPO values and PENBURN burnup results (22.6 GWD/MTU) ................................................51 51 Gundremmingen BWR assembly specifications ...............................................................59 52 Fuel composition of homogenized fuel ..............................................................................59 53 Homogenized fuel PENTRAN and SCALE comparison ..................................................59 54 SCALE 5.1 keff values by water density region ................................................................60 55 Nubar data by fuel region ..................................................................................................60 56 MCNP particle histories .....................................................................................................60 57 Gundremmingen B23 assembly operation history .............................................................61 58 Burnup steps with keff results ............................................................................................62 59 PENTRAN material numbers corresponding to SFCOMPO analyzed fuel ......................62 510 A1 fuel element at 44 cm percent difference between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 25.7 GWD/MTU) ..................................63

PAGE 8

8 511 A1 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results(SFCOMPO reports 27.4 GWD/MTU) ...................................64 512 B3 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 21.2 GWD/MTU) ..................................65 513 B4 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 22.3 GWD/MTU) ..................................66 514 C5 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 23.0 GWD/MTU) ..................................67 515 E3 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 23.5 GWD/MTU) ..................................68 516 E5 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results(SFCOMPO reports 25.2 GWD/ MTU) ...................................69

PAGE 9

9 LIST OF FIGURES Figure page 21 Flow path of cross section development. ...........................................................................26 22 Flow path of cross section development for BWR. ...........................................................26 23 XSMERGE example problem model with corresponding material numbers. ...................27 31 PWR quarter assembly view with SiC detector (top right mesh). .....................................37 32 Flow path with FSPREP to generate fixed source. ............................................................38 33 Normalized adjoint results for the thermal group (E<0.625 eV). ......................................39 34 Normalized adjoint results for the epithermal group (0.625eV < E < 1.01 MeV). ............39 35 No rmalized adjoint results for the fast group (E > 20 MeV). ............................................40 41 Coordinate system reference for axial void solver where z=0 represents midpoint of core. ....................................................................................................................................45 42 Void fraction distribution in a typical BWR/6 assembly. ..................................................46 43 Initial flux at centerline of BWR/6 pin for case with six different moderator densities around fuel assembly. ........................................................................................................47 44 Optimum axial zone distribution in a typical BWR/6 assembly. .......................................48 51 Gundremmingen void fraction distribution. ......................................................................70 52 Gundremmingen axial quality. ...........................................................................................70 53 Gundremmingen water density. .........................................................................................71 54 Gundremmingen BWR axial zone partitioning. ................................................................71 55 Gundremmingen B23 assembly location in core. ..............................................................72 56 Gundremmingen B23 assembly enrichments and sampling positions. .............................73 57 Gundremmingen B23 assembly relative fluxes (0.00 GWD/MTU) for (a) group 1 (b) group 2 (c) group 3 [PENTRAN code run, 16 processors (4 in angle, 1 in energy, 4 in space),cross section s with a P1 Legendre order, S8 quadrature, specular reflective boundary conditions in xy direction, vacuum boundaries in z directions ]. ...................74

PAGE 10

10 58 Gundremmingen B23 assembly relative group fluxes (0.00 GWD/MTU) [PENTRAN code run, 16 processors (4 in angle, 1 in energy, 4 in space),cross sections with a P1 Legendre order, S8 quadrature, specular reflective boundary c onditions in xy direction, vacuum boundaries in z directions ]. ...............................................................75 59 Gundremmingen B23 assembly relative group fluxes (0.00 G WD/MTU). .......................76 510 Gundremmingen B23 assembly relative group fluxes (0.06 GWD/MTU). .......................76 511 Gundremmingen B23 assembly relative group fluxes (3.74 GWD/MTU). .......................77 512 Gundremmingen B23 assembly relative group fluxes (5.83 GWD/MTU). .......................77 513 Gundremmi ngen B23 assembly relative group fluxes (7.73 GWD/MTU). .......................78 514 Gundremmingen B23 assembly relative group fluxes (19.12 GWD/MTU). .....................78

PAGE 11

11 LIST OF ABBREVIATIONS ALPO ANISN library production option BONAMI Bondarenko AMPX interpolator BWR Boiling Water Reactor CENTRM Continuous energy transport module GMIX Generalized cross section mixer MCNP Monte Carlo neutral particle transport code NEWT New extended step characteristicbased transport code PENBURN Parallel environment burnup PENTRAN Parallel environment n eutral particle transport PMC Produce multigroup cross sections SCALE Standardized computer analysis for licensing evaluation SFCOMPO Spent fuel isotopic composition database TRITON Transport rigor implemented with quasi static time dependent operation for neutronic depletion

PAGE 12

12 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ANALYSIS OF LIGHT WATER REACTORS INCLUDING 3 D DETERM INISTIC BURNUP OF A BOILING WATER REACTOR FUEL ASSEMBLY By Mireille Anjaline Rowe August 2009 Chair: Glenn Sjoden Major: Nuclear Engineering Sciences A ccurate transport analysis of reactor systems is important in the Nuclear Engineering field since it provides essential information in power monitoring, criticality safety and fuel reload optimization. Monte Carlo methods have primarily been used to analyze these reactor systems yet drawbacks include difficulty converging the source in an eigenvalue pr oblem when dealing with high dominance ratio systems (Brown, et. al., 2003) Deterministic 3 D Sn transport c omputations have been utilized in limited ways due to the large memory requirements of thes e methods. For this reason, 1D or 2 D geometry set ups are usually implemented and important information regarding the system may be lost as is the case with boiling water reactors (BWR s ) In order to evaluate a 3 D model of a system with a deterministic transport code, one that runs in parallel can provide unique advantages. This thesis presents a method to generate a multigroup cross section data set and transport models for analysis of reactors Next an analysis of a l ight water reactor system using the 3 D parallel code PENT RAN (Parallel Environment Neutral particle Transport) to perform adjoint transport calculations and provide information on effective detector ranges in PWRs is discussed In addition, a detailed fuel burnup analysis of a BWR using the PENTRAN/PENBURN (Pa rallel Environ ment Burnup) suite is presented.

PAGE 13

13 CHAPTER 1 INTRODUCTION 1.1 Introduction Radiation analysis of large power reactors is rarely performed using 3 D deterministic transport techniques. Reaction rates and flux calculations for burnup analysis are usually evaluated using 3D nodal diffusion theory and 2D transport theory approximations This leaves an unsatisfied technical need for burnup validation in a 3D environment sim ulation. PENTRAN has proved to be a time efficient algorithm for solving the Linear Boltzmann Transport equation in a heterogeneous 3D environment. PENBURN was developed in order to process 3 D neutron flux distributions from PENTRAN and calculate reaction rates for 3 D burnup analysis. The body of this work contains the method of multigroup cross section generation, calculation of detector response, analysis of a 6x6 BWR assembly full 3D reactor flux, and burnup distributions in comparison with post irradiation experiments from SFCOMPO 1.2 Transport Theory The distribution of neutrons in a given nuclear reactor system can be characterized by linear Boltzmann equation (LBE) similar to the equation governing the kinetic theory of gases. The integrodifferential form of the neutron transport equation is given in the following equation: 1 ( ) + + ( ) = 0 4 , + ( ) 4 0 ( ) ( ) 4 + (1 1) Where v = neutron speed = neutron location in space

PAGE 14

14 E = neutron energy = direction of unit vector t = time = differential scattering cross section = fission cross section = external neutron source The left hand side of this equation includes the losses in the s ystem due to leakage and collision while the right hand sign includes the production in the system from scatter, fission and any independent external sources. In all there are seven independent variables in the neutron transport equation, along with a s trong cross section dependence on energy which results in a complex and difficult equation to solve, even with the use of computers. For this reason, diffusion theory is sometimes used instead of the neutron transport equation (Lewis and Miller, 1993) 1.3 Diffusion Theory The diffusion approximation considers the neutron flux as a function of space, energy and time. In order to obtain this the neutron transport equation is integrated ter m by term over all directions resulting in the zero e th angular mo ment balance equation The first angular moment is then introduced to provide two equations with two unknowns: flux and current. Assuming the angular flux depends weakly on angle the set of P1 1 ( ) + ( ) + ( ) ( ) = ( ) ( ) + ( ) ( ) + ( ) (1 2) equations are derived as shown in equations 12 and 13. 1 ( ) +1 3 ( ) + ( ) ( ) = 1( ) ( ) + 1( ) (1 3)

PAGE 15

15 Additional approximations include considering only isotropic source s, and that th e time derivative in current can be neglected in comparison with the other terms in the equations. An approximation for the current is subsequently obtained, as shown in Equation 14, and the diffusion constant is determined as noted in E quation 15. ( ) = 1 3 ( 1 ) ( ) (1 4) = 1 3 ( 1 ) (1 5) The P1 1 ( ) D 2 ( r t ) + ( r E ) ( r t ) = s( r ) ( r t ) + f( r ) ( r t ) (1 6) equations can then be simplified by substituting the diffusion constant into equation 12 to obtain the one speed diffusion equation as shown below. Recalling the different assumptions that were made in order to arrive at the diffusion equation, it is evident that there are significant limitations that should be considered when using the diffusion approximation. In stances when the diffusion approximation is not valid include when the angular flux is highly dependent on angle. Certain cases where this approximation is not valid include regions where the neutron flux varies drastically over short distances compared t o the neutron mean free path, interfaces between dense material s, and a vacuum, close to external neutron sources, materials with high absorption cross sections such as control rods, or materials that have a strong anisotropic scattering cross section (Dud erstadt and Hamilton, 1976) 1.4 M onte Carlo M ethod The Monte Carlo method uses a series of random events to simulate a physical process This statistical method uses random numbers generated from a computer to determine an average value for a physical process by means of random sampling of probability distribution functions (Kalos and Whitlock, 1986) In nuclear engineering this technique has been used for reactor

PAGE 16

16 shielding and criticality and dose calculations. Although it has been widely used for particle transport simulation s it does contain drawbacks including the large computational time required to sample sufficiently from a certain region s to obtain reliable results as well as experiencing false source convergence when dealing with eigenvalue problems (Haghighat and Wagner, 2003) 1.5 Deterministic C ode : PENTRAN/PENBURN S uite The PENTRAN/PENBURN Suite was used primaril y for this work. PENTRAN is a 3 D transport solver that can be run in parallel with angle, group and spatial decomposition (Sjoden and Haghighat, 2008) It solves the 3D multigroup steady sta te form of the LBE as shown in Equation 17 by averaging over the energy groups from high to low energies. ) ( ) () ( r r rg g g ) ( ) ( ) ( ) ( ) ( 1 4 1 4 r q r r d k r r dg ind G g g g f o g g g g g g s (1 7) PENBURN is a coupled fuel depletion solver that when provided with reaction rates computes the time dependent isotope concentrations using the direct Bateman solution for a set of about 150 actinides and fission products (Manalo, 2008). The path matrix keeps track of the linear chain that the actinides and fission products undergo, and the Bateman batch equation in Equation 18 provides the solution for the nuclide concentrations. t i t je N e N t No i i l i j i j k l k j k i l l o l i 1 1 11 1... ) ( ( 18) Where Nl = number of atoms of precursor nuclide l at time t=0 l = the chain linking precursor rate constant i = the effective decay constant for nuclide I, accounting for = 1

PAGE 17

17 Ni 0= the number of atoms of nuclide I at time t=0 (t)= the number of atoms of nuclide i at time t A useful feature is the availability to modify the path matrix to add additional actinides of interest if the user would like to track more nuclides 1.6 Previous Work Significant work on burnup in BWR systems has been performed in 2D; by comparison, less research has been published with regard to computing full 3 D burnup analysis of boiling water reactor fuel assemblies (DeHart and Hermann, 1998. Limitations have inc luded computational time and memory requirements. Burnup code developers have however used SFCOMPO post irradiation examination data from fuel removed from reactors as a way to validate their code results. The SFCOMPO database provides the isotopic composition of spent fuel from light water reactors and operating paramet ers including initial fuel enrichment, burnup, and axial location of the fuel pellet sample analyzed There is a lack of information however regarding c ontrol rod positioning and moderator density at different core heights which experience has shown greatly affects fuel discharge isotopics and fission product content. The SFCOMPO database also con tains fuel assembly designs that are different from more recent BWRs including the uniform enrichment of the fuel axially, and the lack of water holes in the assembly. 1.6.1 SCALE SAS2H BWR Burnup A nalysis The SAS2H sequence in SCALE uses transport methods along with depletion and decay from ORIGEN S to determine the isotopic composition of fuel after a set burnup level It had previously been used to compare with SFCOMPO data available for BWR assemblies. T he transport code XSDRNPM used in SCALE is 1D and therefore simplifications were necessary to model the BWR. A set of rings with the fuel, clad and moderator was modeled while still

PAGE 18

18 preserving material mass. Although multiple fuel pin data was available for different axial heights in the assembly an average of the final fuel composition was computed before comparing to the burnup results from SCALE. The report indicated agreement with SFCOMPO for a majority of the actinide results to within 32% Since all of the fuel was essentially lumped together it was not a direct comparison with SFCOMPO data which provides spe cific pin isot opic compositions (DeHart and Hermann, 1998). 1.6.2 Void Fraction U ncertainties Studies have been conducted to determine the effect that void uncertainties have even initially during startup due to absorber blade insertions, utilizing different cross section data libraries and water films created within bundles. The study was performed when analyzing a 10 x 10 BWR Westinghouse fuel assembly and utilizing different data libraries resulted in a 40% differences between void predictions. Accounting for water films within channels accounted for a 4% difference in pin powers and insertion of control blades contributed to a change of 10% in pin power values (Jatuff, F., et. al., 2005).

PAGE 19

19 CHAPTER 2 MULTIGROUP CROSS SEC TION GENERATION Developing accurate cross section data sets is important in order to model the physics correctly for any reactor system. The deterministic code used in these analyses requires the user to provide multigroup cross section data for the reactor systems being analyzed. This section will describe the procedure used to acquire the multigroup cross section data from the SCALE 5.1 package in addition to demonstrating how to generate multiple cross section data for the same nuclide as it applies to different void fractions for the BWR problem 2.1 Cross Section G eneration with SCALE 5.1 Package using DEV XS P rocedure SCALE is a modular code system which uses automated sequences that can provide information on cross section processing, reactor physics, criticality safety, radiation shielding, and spent fuel and high level waste characterization. For reactor physics applications the TRITON control module is utilized in addition to the functional module NEWT. TRITON is a SCALE control sequence that calls NEWT to perform the transport physics analysis for a specified 2 D configuration. The SCALE 5.1 package was primarily used to generate the multigroup cross section data for the reacto r systems analyzed following the DEV XS procedure, a cross section development primer for the PENTRAN/PENBURN suite Figure 21 displays the flow path for the cross section development used when following the DEV XS procedure (P lower 2008) 2.1.1 SCALE 5.1 TNEWT Control Sequence The t newt driver for the transport calculation was used, which executes NEWT transport calculations using cross sections prepared within the sequence. The sequence includes the self shielding modules: BONAMI, WORKER, CENTRM and PMC.

PAGE 20

20 The BONAMI module is the unresolved resonance self shielding processor which use s the Bondarenko method (Greene, 2006) CENTR M creates the space dependent (1 D), point wise continuous energy flux file (Asgari et al, 2006) PMC creates a problem dependent master library from t he CENTR M flux spectrum (Hollenbach and Williams, 2006) Finally, t he WORKER module creates working libraries from the master libraries (Hollenbach and Petrie, 2006) A sample SCALE 5.1 input file is found in Appendix A. 2.1.2 Post Processing Utilities In addition to using the TNEWT control sequence, three utilities are used to create inputs needed for GMIX, which creates the macroscopic data set used by PENTRAN. The SCALFORM utility converts cross section file generated us ing the SCALE5.1 ALPO module into a standard ASCII format file used by PENTRAN. The user indicates the name of the cross section input file, number of energy groups, number of columns of data, the column position for tThe Perl script GMIXFORM uses the initial SCALE 5.1 input file to create a GMIX input file that contains the material composition information and cross section formatting data. The Perl script COLLAPSEFORM uses the initial SCALE 5.1 input file to create the file with neutron energy group structure and primary neutron fission tem perature. and the column position number in which all scattering cross section values are nonzero. The output file created by SCALFORM contains all of the microscopic cross section data. 2.1.3 GMIX Code The previous section discussed how to generate the three input files required by GMIX: .xsc, .gmx, and .grp files. Once these files are generated, the user modifies the .gmx input file to include the microscopic cross section input filename, the data path location, the output filename, the number of energy groups, column information and the Pn order. The GMIX code blends the

PAGE 21

21 cross section data into macroscopic material cross section data used by PENTRAN (.xs file) and also outputs the .chi file containing the normalized fission spectrum data. 2.2 BWR 2.2 wt% Fuel Pin Cross Section G eneration Some preliminary analysis on a unit pin cell was performed in order to gain useful information for the full 3 D reactor model. The pin sele cted for this study is a UO2, 2.2% enriched BWR 6 fuel element. The composition of the fuel pin clad was chosen as natural zirconium with a density of 6.508 g/cm3 and a temperature of 577 K, while the fill gas was helium with a density of 0.07518 g/cm3SCALE 5.1 was used to generate group flux weighted multigroup cross sections for a 2D unit cell. The cross sections were used to validate eigenvalue calculations between SCALE5.1 and PENTRAN. Ma terial balance approximations for the Cartesian hexahedral geometry in PENTRAN were also considered. The core had a specified operating pressure of 7.17 MPa. P1As a result of usin g a Cartesian geometry in PENTRAN, it was important to validate material balance on eigenvalue results. The amount of excess fissile material was particularly of concern for ei genvalue comparisons. Table 23 displays the eigenvalue comparisons between SC ALE 5.1 and meshing associated with excess fissile material values. After examining the results it was apparent that a 19 x 19 meshing scheme for each pin cell provides the most physically accurate results, while still reasonably representing the amount o f fissile material. cross sections were developed using SCALE 5.1 and the DEV XS process developed for blending group flux weighted cross sections in the specified material s for use in PENTRAN. The 238 group ENDF/B VI library was collapsed to 3 groups with upper MeV bounds of 20.0 MeV, 1.0 MeV, and 0.625 eV respectively to match the energy group structure in the ORIGEN S depletion module from SCALE 5.1.

PAGE 22

22 2.3 XSMERGE Code Certain problem s et ups use multiple regions of the same material while utilizing varied microscopic cross sections as is the case with the BWR In order to generate the cross sections necessary for PENTRAN, the DEV XS procedure is followed for each configuration which results in multiple microscopic cross section files. Each of the microscopic cross section files has to be combined into one file and sorted by nuclide in order for GMIX to process it. The X S MERGE code was developed to combine and sort multiple microscopic cross section files generated by the user The X S MERGE code combines each microscopic cross section file generated by the user, groups them according to nuclide, and sorts the nuclide lists in ascendin g order based on the SCALE 5.1 material number previously assigned The output file generated by X S MERGE is now in a usable format that GMIX can process to create the macroscopic cross sections that PENTRAN directly utilizes. This ensures the correct cro ss sections are used in each of the regions of the problem. In order to run X S MERGE the user specifies the input file name that will contain the number of files to sort, the microscopic cross section file names and the output file name. The flow path for the cross section development utilizing XSMERGE is displayed in Figure 2 2. A sample problem to display the use of the XSMERGE code was developed and deals with a single BWR pin containing two different water densities as shown in Figure 23. The DEV XS procedure was followed twice for each pin, the first with a moderator density of 0.75574 g/cm3 corresponding to the core height within the nonboiling length of 154 cm and the second with a moderator density of 0.72055 g/cm3corresponding to a core height of 157 cm. Table 2 4 demonstrates the material numbers used in the SCALE 5.1 input and Figure 2 1 displays the BWR pin model with the appropriate SCALE 5.1 material numbers used. The microscopic cross

PAGE 23

23 section files (water1.xsc and water2.xsc) generated aft er running the first and second SCALE 5.1 inputs are merged together using the X S MERGE program and results in the combined and sorted microscopic cross section file (bwrpin.xsc). The following displays the sample input needed to run XSMERGE: Below is an example of the sample input file: X S MERGE SCALFORM Cross Section file (.xsc) sorter G. Sjoden, K. Manalo, T. Plower, M. Rowe Enter input file name xmerge.inp /No of files to process 2 /xsc file names water1.xsc water2.xsc /output file name bwrpin.xsc

PAGE 24

24 Table 2 1. BWR/6 fuel assembly specifications Thermal Output 3579 MW(t) Active Height 375.92 cm Number of Fuel Assemblies 732 Fuel Element Array 8 x 8 Assembly Dimensions 14.02 cm x 14.02 cm Assembly Pitch 15.24 cm Number of Fuel Rods/Assembly 62 Total Number of Fuel Rods 45,384 Fuel Rod O.D. 1.25222 cm Fuel Rod Pitch 1.6256 cm Pitch/Diameter 1.3 Clad Thickness 0.08636 cm Fuel Pellet Diameter 1.05664 cm Pellet Clad Gap 0.01143 cm Fuel Enrichment 2.2 2.7% System Pressure 7.17 MPa Average Exit Quality 14.6% Core Average Void Fraction 42.6% Maximum Exit Void Fraction 76% Core Inlet Temperature 532 F Outlet Temperature 547 F Table 2 2. BWR/6 2.2 wt% fuel pin composition Nuclide Wt% O 16 11. 8502 U 234 0.0224 U 235 1.9393 U 236 0.0122 U 238 86.17424 Total 100

PAGE 25

25 Table 2 3. Eigenvalue comparisons for PENTRAN unit cell meshing schemes Eigenvalue (PENTRAN) % difference from SCALE 5.1 (1.185) % excess fissile material Meshing 1.191 0.506 2.8 15 x 17 1.182 0.253 1 19 x 19 1.200 1.266 0.8 23 x 23 Table 2 4. XSMERGE example problem material numbers assigned. Material #'s in SCALE5.1 Input Scale Input 1 2 Density (g/cc) 0.75574 0.72055 Fuel 11 12 Gap 21 22 Clad 31 32 H 2 O 41 42

PAGE 26

26 Figure 2 1. Flow path of cross section development. Figure 2 2. Flow path of cross section development for BWR.

PAGE 27

27 Figure 2 3. XSMERGE example problem model with corresponding material numbers.

PAGE 28

28 CHAPTER 3 AN APPLICATION OF FORWARD AND ADJOINT TR ANSPORT Evaluation of silicon carbide (SiC) semiconductor detectors for use in power monitoring is of interest because of their distinct advantages, incl uding small size, small mass, and their inactivity both chemically and neutronically The main focus of this section is in evaluating the predicted response of a SiC detector when placed in a 17x17 Westinghouse PWR assembly. Transport computations were pe rformed using the PENTRAN (Parallel Environment Neutralparticle Transport) code system for the 3 D deterministic ad joint transport computations Adjoint transport results enable one to assess the relative spectral contributions of a source in causing a s ignal in a detector, and can therefore be used to evaluate the effective detector range. Subsequent sections in this chapter will include a description of the detector model, multigroup cross sections, description of the forward and adjoint transport res ponse calculations, and results. Included is a discussion of the relative influence (as determined by the adjoint results) of fuel pins to the SiC neutron detector response based on pin radial proximity to the detector. 3.1 Silicon Carbide Detector Design Silicon carbide detectors have been proposed primarily by Westinghouse for power monitoring purposes in PWRs. The silicon carbide detector design considered in this paper is u, 8 (Khorsandi, et. al. 2006) The neutron response in the detector is produced by the neutrons penetrating the SiC; fast and epithermal neutrons interact directly with the SiC to form energetic reaction products capable of producing ionization events in the detector (Dulloo et. al, 2003) Also, after penetrating the SiC, neutrons can interact with the thin lithium layer to produce alpha and triton reaction products. The aluminum layer is placed in between the LiF and Au la yers in order to minimize radiation damage effects from the alpha particles. The

PAGE 29

29 triton particles pass through the aluminum foil and are deposited in the inactive SiC substrate layer. Previous analysis shows that SiC detectors withstand a fast neutron irr adiation fluence of 3.4 x 1017 cm2 and are designed to work at high temperatures (Ruddy, et. al., 2006) For the purposes of this study, the SiC detector was modeled as a homogenized material of LiF, Al, Au and primarily SiC with a density of 3.2 g/cm33.2 Multi group Cross Section G eneration Three group cross sections (E3 < 0.625 eV; 0.625 eV < E2 < 1.01 MeV; E1 > 20 MeV) were developed using SCALE 5.1s T NEWT control sequence by collapsing the 238 group ENDF B VI AMPX library as discussed in the previ ous chapter A lattice cell calculation was performed for a homogenized 3 wt% enriched PWR fuel pin, and the SiC detector was modeled as a homogenized, density scaled mesh cell comprised of LiF, Al, Au and SiC. The nuclide composition of the 3 wt% enrich ed UO2 fuel is shown in Table 1. The density of the water was 0.6612 g/cm3, based on an operating pressure of 15.2 MPa and an operating temperature of the homogenized PWR fuel pin. For the SCALE 5.1 NEWT flux calculations (S8), a convergence value of 5x105 was chosen for the spatial and eigenvalue iterations. Mirror reflection albedo conditions were chosen for the external boundaries of the unit cell. The keff results for the homogenized PWR pin (fuel and cladding) compared to that of the homogenized PWR with the SiC detector placed nearby it displayed a difference of 0.3% k, indicating the impact the presence of the SiC detector has neutronically to the lattice.

PAGE 30

30 3.3 Forward versus Adjoint Detector Response The steady state multigroup form of the transport equation operating on the forward group angular flux g is [5]: ) ( ) ( ) ( r g r g r g G g r g q r g r g g s d 1 ) ( ) ( ) ( 4 ( 31) Principally, scattering comes from all other groups g into group g. is dominated by downscattering from higher energies to lower energies. The adjoint transport operator H+ can be derived using the adjoint identity for real valued functions, and the for ward multigroup transport operator, where represents integration over all independent variables: g H g g H g ( 32) Using Equation 31, it can be seen that the forward operator is G g r g g s d r g H 1 ) ( 4 ) ( ( 33) The angular adjoint (importance) function is g Applying the adjoint boundary condition that particles leaving a bounded system have an importance of zero in all groups (converse of the forward vacuum boundary condition) with the above equations, and requiring a continuous importance function mathematically leads to the multigroup adjoint transport operator: G g r g g s d r g H 1 ) ( 4 ) ( ( 34) Note the minus sign on the streaming term indicates that adjoint particles travel along a reverse d direction, where adjoint scattering progresses from group g back to other groups g

PAGE 31

31 (those groups formerly contributing to group g in the forward equation). The forward neutron detector fixed source response can be solved by satisfying the transport eq uation g q g H ( 35) and the adjoint transport equation can be satisfied using an adjoint source that is aliased to the group detector response cross section dg g d g H : ( 36) Applying Equations 32, 35, and 36, and integrating over all variables results in the useful expression for detector response R : g q g d g R g ( 37) From Equation 37, it is clear that, detector response can be obtained by complete integration of the source distribution with the adjoint functionfor any arbitrary source distribution. Therefore, R can be computed directly from the results of either of several forward transport computations for each neutron source distributions, or one single adjoint transport computation with coupling to each source density distribution. Therefore, the silicon carbide detector response can be calculated by summing the product of the neutron flux, detector cross section, and cell volume for all groups and all meshes that contain t he detector, as indicated in Equation 38 (Sjoden, 2002) = 1 ( 38) Similarly, the adjoint transport response is determined by summing the product of the adjoint function, neutron source, and cell volume for all groups and all meshes as displayed in Equation 39.

PAGE 32

32 + = 1 ( 39) 3.4 PENTRAN Criticality Calculation A quarter model of a 17x17 Westinghouse OFA assembly with the SiC detector placed in the center location of the assembly and a transport calculation was performed with PE NTRAN as illustrated in Figure 3 1. The dimensions of the quarter assembly were 0.0 cm to 10.75 cm in the x and y axes, and an axial height of 17 cm, with a geometry consisting of 48 coarse meshes. The SiC detector location resided in coarse mesh 32 (top right corner) with its center at a z level of 8.5 cm, occupying a total of 3 fine meshes. The density of the SiC detector material was decreased to 0.022864 g/cm3 accordingly to preserve mass. The multi group cr oss sections developed from the homogenized fuel and homogenized SiC unit cell model were used for the quarter assembly. The angular quadrature was set to S8 with an inner flux tolerance of 1x104 and outer criticality tolerance of 1x105. Reflective bou ndary conditions were set for all outer boundaries of the model. The keff value was 1.31525, with a tolerance of 2.72 x 106. Based on a criticality calculation, a fixed source calculation was performed with PENTRAN. The fixed source calculation was s caled according to the relative number of particles from the criticality run. A post processing code, FSPREP, was developed to render the fixed fission source distribution based on the criticality calculation output; this was used to set up the source in the fuel for a fixed source calculation. The total source from both runs is in good agreement, as shown in Tables 2 and 3. The balance shown in these tables is an absolute particle balance.

PAGE 33

33 3.5 FSPREP Code The FSPREP code extracts the fission source resul ts from an initial criticality run and outputs the fine mesh spatial distribution for the coarse mesh source. The input file required by FSPREP contains the number of energy groups in the model, the source file names for each energy group, the number of c oarse meshes that contain the source, and the reference location of the sources in order of source number by coarse mesh number. A sample input file is shown in Appendix B. The source files for each energy group should use the format of: coarse number, m esh number, material number, x location, y location, z location and source value. The resulting output file contains the spacpf variable for Block 5 of the PENTRAN input deck. This variable indicates the source number, group number, number of sequentiall y numbered meshes, and corresponding mesh spatial probabilities only for the sources that require a nonuniform spatial probability distribution. Figure 3 2 displays the flow path taken when utilizing the FSPREP code. Appendix C contains a n excerpt of a s ample output file generated by FSPREP. 3.6 PENTRAN Adjoint Calculation The PENTRAN forward transport solver can be utilized to solve for the adjoint function with the detector cross section as the adjoint source. This is performed by transposing (reversin g) group cross sections, sources and the scattering matrix. The forward cross sections are automatically reversed internally by the code, while sources are reversed by the user in the energy group probability distribution card. Group G is reported as Gro up 1, and subsequently Group 1 is reported as Group G for PENTRAN adjoint results. The tolerances set for the adjoint run were 1x1043.7 Results and F indings for the inner convergence criteria. The adjoint function results by energy group are displayed i n the following figures at a z level of 9 cm. Each of the adjoint values represents the local neutron importance relative to the

PAGE 34

34 response in the SiC detector. The maximum relative adjoint values for the thermal, epithermal and fast energy groups are 1, 0.507, and 0.308 respectively. The thermal group adjoint function values decrease rapidly as the radial distance from the semiconductor location increases. The importance relative to a thermal neutron causing a reaction in SiC drops by three orders of mag nitude in moving more than 2 fuel pins away from the detector. Alternatively, in the epithermal and fast energy groups, the adjoint importance drops by three orders of magnitude after a radial distance of five fuel pins from the detector location. The res ponse of the detector is calculated from the forward transport compu tations with Equation 38 by summing the product of the neutron flux, the absorption cross section of the detector, and the cell volume of the meshes containing SiC over all the energy groups. The total cell volume of the SiC detector was 0.008 cm3, and the forward neutron source was 4880 n/cm3s. The response of the detector is alternatively calculated from a single adjoint transport computation using Equation 39 and summing the product of the local adjoint function, cell fission source density, and cell volume over all energy groups. The total predicted neutron response from the forward calculation was 1.724x104 per second, and from the adjoint calculation the detector response was 1. 654x104 neutrons (counts) per second. The differences between the two values can be attributed to the relative convergence and to some truncation error causing differences between the forward and the adjoint. The fuel pins within the inner circle shown in Figure 3 3 (at a radial distance of 6.08 cm) contribute to 75.33% of the neutron response from the thermal group. Similarly, 35.85% of the neutron response from the epithermal group comes from fuel in this radius, as does 21.58% from fast group contributions to neutron response. The relative fractions of the thermal, epithermal, and fast group to the overall neutron response were 72%, 27% and 1% respectively.

PAGE 35

35 This work demonstrates the application of adjoint transport methods to determine the predicted response of a SiC detector when placed in a 17x17 Westinghouse PWR assembly. A single adjoint transport computation can be used to calculate the response of the detector, and can be utilized for different source terms, as opposed to performing several forward transport computations when dealing with varied sources. The adjoint results display the relative neutron importance by energy group, with the thermal group reporting the highest adjoint value for the SiC detector. For neutrons, the effective monit oring range of the SiC detectors is on the order of five PWR fuel pins away from the detector; pins outside this range in the fuel lattice are minimally seen by the SiC detector. Similar calculations can be performed for different detector designs to ev aluate the use of SiC detectors in different systems.

PAGE 36

36 Table 3 1. Nuclide composition of 3 wt% enriched UO2 Nuclide fuel Wt% O 16 11.8532 U 234 0.0224 U 235 2.6444 U 236 0.0122 U 238 85.4678 Total 100 Table 3 2. Integral System Balance from Criticality Run Group Leakage Collisions ScatterSrc FissionSrc Vol&BdySrc Balance 1 9.69E 03 1.00E+04 6.67E+03 3.38E+03 0.00E+00 9.36E 02 2 7.44E 02 9.07E+04 8.92E+04 1.49E+03 0.00E+00 8.97E 01 3 4.80E 03 5.43E+04 5.43E+04 1.04E 06 0.00E+00 2.65E 02 Total 8.89E 02 1.55E+05 1.50E+05 4.88E+03 0.00E+00 7.77E 01 Table 3 3. Integral System Balance from Fixed Source Run Group Leakage Collisions ScatterSrc FissionSrc Vol&BdySrc Balance 1 4.56E 03 1.00E+04 6.66E+03 0.00E+00 3.38E+03 3.04E 02 2 1.57E 03 9.06E+04 8.91E+04 0.00E+00 1.49E+03 2.24E 02 3 7.82E 03 5.43E+04 5.43E+04 0.00E+00 1.04E 06 2.74E 02 Total 4.83E 03 1.55E+05 1.50E+05 0.00E+00 4.88E+03 8.02E 02

PAGE 37

37 Figure 3 1. PWR quarter assembly view with SiC detector (top right mesh)

PAGE 38

38 Figure 3 2. Flow path with FSPREP to generate fixed source

PAGE 39

39 Figure 3 3. Normalized a djoint results for the thermal group (E<0.625 eV). Figure 3 4. Normalized a djoint results for the epithermal group (0.625eV < E < 1.01 MeV).

PAGE 40

40 Figure 3 5. Normalized a djoint results for the fast group (E > 20 MeV).

PAGE 41

41 CHAPTER 4 PENTRAN/PENBURN ANAL YSIS OF A SINGLE BWR FUEL ROD Efforts to accurately represent the fissile material quantities can quickly increase memory requirements for 3 D deterministic calculations. For a full core model deterministic analysis, parallel computing is a needed feature for even 2 D geometries. In order to accurately represent burnup distributions axially in a BWR, it imperative that we model in 3 D, particularly because of the changing void fraction along the axial dimension. 4.1 Steady State Two Phase Flow in a Heated Channel To account for the twophase flow that the water undergoes in a BWR a solver was created that determines the axial void dis tribution for any BWR model given the thermal output of the reactor, operating pressure, inlet and outlet coolant temperature, fuel height and the exit quality. To further simplify the equations any pressure drop was neglected and sinusoidal heat generatio n was considered (Kazimi and Todreas, 1990) The specific heat with constant pressure, saturation temperature, saturated liquid enthalpy and saturated vapor enthalpy are determined with the given input parameters from available data given the oper ating pa rameters. Equations 41 to 414 indicate the equations used in the solver to determine the axial void distribution. These equations were developed assuming a sinusoidal behavior for the initial power profile and neglect ed control rod effects due to insuf ficient rod positioning data. Figure 4 1 displays a coordinate system reference for the solver where z=0 represents the midline of the core. = (4 1) = ( ) (4 2) = + (4 3)

PAGE 42

42 = + 2 sin + 1 (4 4) = + 2 + 1 (4 5) = (4 6) = 2 ( ) + 1 (4 7) = sin 1 1 + 2 (4 8) = 2 (4 9) = (4 10) = 2 sin + 1 (4 11) = sin 1 1 +2 (4 12) = + 2 sin + 1 (4 13) =1 1 + 1 (4 14) Where q = Thermal output (kW) P = System Pressure (Pa) Tin = Inlet Temperature (C) Tout = Outlet Temperature (C) L = Fuel Height (m) Xout = Exit quality of the core Cp = Specific Heat Constant Pressure (kJ/kgK) Tsat = Saturation Temperature (C) hf = Saturated liquid enthalpy (kJ/kg) hg = Saturated vapor enthalpy (kJ/kg) hfg = Saturated enthalpy (kJ/kg) hin = Inlet enthalpy (kJ/kg) hout = Outlet enthalpy (kJ/kg) Xin = Inlet quality of the core m = mass flow rate (kg /s) zout = Top of core (m)

PAGE 43

43 zb = Non boiling length (m) Xz = Quality of the core along axial direction z z = Axial location (m) z = Axial void fraction along axial direction z v = Saturated vapor density l = Saturated liquid density 4.2 Axial Distribution of Vapor Quality in a BWR Assembly Using the thermalhydraulics characteristics of a typical BWR/6 assembly of 3579 MWth, 7.17 MPa, an inlet coolant temperature of 277 C, an outlet coolant temperature of 286 C, fuel length of 3.7592 m, a nd an exit quality of 0.146, the axial void distribution was determined. Figure 4 2 displays the axial distribution of the void fraction determined from the solver. The figure expresses that the void fraction is zero (the coolant is 100% liquid) from the bottom of the core to around 1.1 meters where the coolant begins to transition to steam. 4.3 Single Pin Burnup C omparison with SFCOMPO Utilizing the burnup history from the SFCOMPO data set a preliminary effective 2 D single fuel pellet analysis was ana lyzed with PENBURN with a moderator density at 0.74153 g/cm3 at an axial height of 44 cm and the other with a moderator density at 0.33973 g/cm3 and an axial height of 268 cm. A comparison between using initial cross sections versus burnup dependent cross sections was also investigated, and results for these are shown in Table 4 1 and Table 4 2, respectively Although the burnup dependent cross sections decreased the percent differences of the PENBURN single pin burnup results relative to the SFCOMPO results at that pin location, with a significant decrease in the Pu 241 percent difference, there were still large differences noted between a single fuel pellet and the SFCOMPO r esults. It is evident that moving to a full 3D model would be necessary to represent the flux at the multiple locations. When comparing a fuel pellet burnup with a water density of 0.74153 g/cm3 at the 268 cm height the burnup results agreed within 30% of the SFCOMPO data as displayed in Table 43.

PAGE 44

44 4.4 BWR Fuel Rod Axial Zone Optimization Once the axial distribution of the vapor quality was determined the model was partitioned to contain a different water density in each region. After performing a tran sport calculation it was apparent from the flux shown in Figure 43 that consideration should be taken when choosing the number of varying water regions to use for the problem. The initial number of water densities used displayed step decreases at locatio ns where the water density was lower and would not represent what occurs in a typical BWR fuel assembly. Multiple transport calculations were performed to determine the minimum number of water densities required for an accurate initial model for the BWR f uel rod. Results indicated that a minimum of seven different water regions from 0.7 g/cm3 to 0.2 g/cm3 was necessary with no more than a 0.1 g/cm3 decrease from region to region. The results from this partitioning are shown in Figure 44.

PAGE 45

45 Figure 4 1. Coordinate system reference for axial void solver where z=0 represents mi dpoint of core.

PAGE 46

46 Figure 4 2. Void fraction distribution in a typical BWR/6 assembly. 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9core height (m)void fraction

PAGE 47

47 Figure 4 3. Initial f lux at centerline of BWR/6 pin for case with six different moderator densities around fuel assembly 0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 0 50 100 150 200 250 300 350 400Flux (1/cm2s2)Axial Height (cm) Group 1 Group 2 Group 3

PAGE 48

48 Figure 4 4. Optimum axial zone distribution in a typical BWR/6 assembly. 0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 0 50 100 150 200 250 300 350 400 450Flux (1/cm2s2)Axial Height (cm) Group 1 Group 2 Group 3

PAGE 49

49 Table 4 1. A1 fuel element at 44 cm 0.74153 g/cc percent differences between SFCOMPO values and PENBURN burnup results ( 22.6 GWD/MTU) Data Type SFCOMPO Values Percent Difference initial xs burnup xs Pu 239/Total Pu(RateOfWeight) 5.56E 01 43.56% 40.73% Pu 239/U 238 3.89E 03 275.73% 258.53% Pu 240/Pu 239 4.88E 01 87.86% 78.32% Pu 240/Total Pu(RateOfWeight) 2.69E 01 82.42 69.23% Pu 241/Pu 239 1.87E 01 7.83% 19.57% Pu 241/Total Pu(RateOfWeight) 1.17E 01 17.58% 0.58% Pu 242/Pu 239 9.01E 02 76.41% 75.80% Pu 242/Total Pu(RateOfWeight) 4.85E 02 65.02% 64.82% Total Pu/Total U 6.93E 03 160.10% 153.17% U 235/Total U(RateOfWeight) 6.61E 03 91.63% 88.73% U 235/U 238 6.76E 03 90.36% 87.48% U 236/Total U(RateOfWeight) 3.41E 03 12.29% 6.93% U 236/U 238 3.46E 03 12.18% 6.81% U 238/Total U(RateOfWeight) 9.90E 01 0.57% 0.57%

PAGE 50

50 Table 4 2. B3 fuel pellet at 268 cm 0.33973 g/cc percent differences between SFCOMPO values and PENBURN burnup results ( 22.6 GWD/MTU) Data Type SFCOMPO Values Laboratory Percent Difference Initial xs burnup xs Pu 239/Total Pu(RateOfWeight) 0.638 Karlsruhe 25.11% 22.65% Pu 239/Total Pu(RateOfWeight) 0.641 Ispra 24.52% 22.07% Pu 239/U 238 0.0057 Karlsruhe 158.69% 146.85% Pu 239/U 238 0.0055 Ispra 163.83% 151.75% Pu 240/Pu 239 0.345 Karlsruhe 82.83% 69.34% Pu 240/Pu 239 0.345 Ispra 82.83% 69.34% Pu 240/Total Pu(RateOfWeight) 0.221 Karlsruhe 78.61% 62.55% Pu 240/Total Pu(RateOfWeight) 0.219 Ispra 78.41% 62.21% Pu 241/Pu 239 0.143 Karlsruhe 20.53% 5.17% Pu 241/Pu 239 0.147 Ispra 17.25% 2.31% Pu 241/Total Pu(RateOfWeight) 0.104 Karlsruhe 32.28% 13.16% Pu 241/Total Pu(RateOfWeight) 0.104 Ispra 32.28% 13.16% Pu 242/Pu 239 0.0414 Karlsruhe 48.67% 47.33% Pu 242/Pu239 0.0418 Ispra 49.16% 47.83% Pu 242/Total Pu(RateOfWeight) 0.0264 Karlsruhe 35.75% 35.37% Pu 242/Total Pu(RateOfWeight) 0.0261 Ispra 35.01% 34.63% Total Pu/Total U 0.0088 Karlsruhe 106.00% 100.51% Total Pu/Total U 0.0085 Ispra 111.81% 106.17% U 235/Total U(RateOfWeight) 0.0104 Karlsruhe 21.80% 19.95% U 235/Total U(RateOfWeight) 0.0102 Ispra 24.19% 22.31% U 235/U 238 0.0105 Karlsruhe 22.56% 20.70% U 235/U 238 0.0103 Ispra 24.94% 23.04% U 236/Total U(RateOfWeight) 0.0031 Karlsruhe 2.89% 3.05% U 236/Total U(RateOfWeight) 0.0031 Ispra 2.26% 3.72% U 236/U 238 0.0031 Karlsruhe 2.61% 3.34% U 236/U 238 0.0031 Ispra 2.30% 3.67% U 238/Total U(RateOfWeight) 0.987 Karlsruhe 0.27% 0.27% U 238/Total U(RateOfWeight) 0.987 Ispra 0.27% 0.27%

PAGE 51

51 Table 4 3. B3 fuel pellet at 268 cm 0.74153 g/cc percent differences between SFCOMPO values and PENBURN burnup results ( 22.6 GWD/MTU) Data Type SFCOMPO Values Measurement Laboratory Percent Difference Initialxs Burnupxs Pu 239/Total Pu(RateOfWeight) 6.38E 01 Karlsruhe 4.84% 6.22% Pu 239/Total Pu(RateOfWeight) 6.41E 01 Ispra 4.35% 5.72% Pu 239/U 238 5.65E 03 Karlsruhe 10.16% 25.76% Pu 239/U 238 5.54E 03 Ispra 12.34% 28.26% Pu 240/Pu 239 3.45E 01 Karlsruhe 46.52% 23.70% Pu 240/Pu 239 3.45E 01 Ispra 46.52% 23.70% Pu 240/Total Pu(RateOfWeight) 2.21E 01 Karlsruhe 44.16% 19.28% Pu 240/Total Pu(RateOfWeight) 2.19E 01 Ispra 43.65% 18.54% Pu 241/Pu 239 1.43E 01 Karlsruhe 77.16% 20.94% Pu 241/Pu 239 1.47E 01 Ispra 72.34% 17.64% Pu 241/Total Pu(RateOfWeight) 1.04E 01 Karlsruhe 62.94% 12.69% Pu 241/Total Pu(RateOfWeight) 1.04E 01 Ispra 62.94% 12.69% Pu 242/Pu 239 4.14E 02 Karlsruhe 38.15% 4.82% Pu 242/Pu 239 4.18E 02 Ispra 36.83% 5.73% Pu 242/Total Pu(RateOfWeight) 2.64E 02 Karlsruhe 44.91% 1.15% Pu 242/Total Pu(RateOfWeight) 2.61E 02 Ispra 46.57% 2.32% Total Pu/Total U 8.75E 03 Karlsruhe 4.94% 18.25% Total Pu/Total U 8.51E 03 Ispra 7.90% 21.58% U 235/Total U(RateOfWeight) 1.04E 02 Karlsruhe 0.91% 2.35% U 235/Total U(RateOfWeight) 1.02E 02 Ispra 1.03% 0.43% U 235/U 238 1.05E 02 Karlsruhe 0.54% 1.99% U 235/U 238 1.03E 02 Ispra 1.39% 0.08% U 236/Total U(RateOfWeight) 3.08E 03 Karlsruhe 5.74% 2.66% U 236/Total U(RateOfWeight) 3.06E 03 Ispra 5.13% 2.02% U 236/U 238 3.12E 03 Karlsruhe 5.71% 2.63% U 236/U 238 3.11E 03 Ispra 5.40% 2.31% U 238/Total U(RateOfWeight) 9.87E 01 Karlsruhe 0.02% 0.02% U 238/Total U(RateOfWeight) 9.87E 01 Ispra 0.02% 0.02%

PAGE 52

52 CHAPTER 5 GUNDREMMINGEN ASSEMB LY ANALYSIS After developing methods for determining the multigroup cross sections for a BWR and achieving the optimum axial zone p artitionin g the Gundremmingen BWR was chosen as the candidate design for performing the burnup calculations to compare to SFCOMPO Again, the major purpose here was to characterize the general effects of fuel burnup on the BWR case. The impact of slight changes to moderator density on spent fuel isotopics was investigated and improvements to the model discussed. 5.1 BWR Assembly S pecifications Based on the operating parameters in Table 5 1 the inlet water density was calculated as 0.74153 g/cm3 and the outlet water density as 0.289 g/cm35.1.1 Fuel Pin H omogenization using the solver discussed in Chapter 4. The axial void fraction, quality and density distributions are displayed in Figures 51, 5 2, and 53 respectively. The PENTRAN model was partitioned with 7 different water densities as discussed previously and the different regions can be seen in Figure 5 4. Assembly B23 was chosen to compare PENBURN burnup results with the re sults from the SFCOMPO database. This assembly primarily remained in the lower right hand side of the core for all 4 cycles as presented in Figure 5 5. The Gundremmingen BWR assembly consists of a 6x6 array of fuel rods with enrichments of either 1.87 or 2.53 percent as demonstrated from the Tecplot generated image shown in Figure 5 6. Due to a lack of information, the use of control rods was not taken into account in this analysis. Analysis was performed to determine the optimum meshing scheme for homogenizing the fuel, gap and clad into one material. This was performed in order to save on memory requirements when moving from a single full length fuel r od to the entire BWR assembly. Table

PAGE 53

53 52 contains the homogenized fuel composition data. The resulting meshing went from 19x19 to 11x11 and still maintained a reasonable mass balance in addition to agreeable eigenvalue results between PENTRAN and SCALE a s shown in Table 5 3. The multigroup cross sections were generated for each of the water densities from the same procedure discussed in Chapter 2 and the SCALE 5.1 keff results for each region are in Table 54. 5.1.2 PENTRAN G eometry The 6x6 Gundremminge n BWR assembly was partitioned into 10 axial z coarse meshes with a top and bottom water region. The middle 8 regions contained the fuel pins and the material numbers were assigned based on water density. Therefore fuel pins 1 through 36 were surrounded by the denser water and fuel pins 217 to 252 were the pins surrounded by the water region with the largest void fraction. The 3 D relative flux profile by energy group at 0.00 GWD/MTU is illustrated in Figure 5 7 and exhibits the skewed flux as a result of the initial voi d fraction distribution. Figure 58 contains the 3D relative flux profiles at around a meter above the bottom of the core with the water material locations blanked out and displays how the epithermal group experienced the highest flux values. Recalling the fuel pins on the left corner of the image are initially of lower enrichment it is evident the 3 D flux profile contains information that would be lost in a 2D representation of the assembly. 5.2 MCNP Criticality C alculation In ord er to compare the PENTRAN criticality run with the MCNP criticality calculation the XSMCNP code was utilized to convert the macroscopic cross sections from the PENTRAN format into the MCNP multigroup format. The code asks the user for the PENTRAN cross se ction file name, the Pn order of the cross section file, and the Pn order desired in the MCNP input deck. The only required input file is the PENTRAN macroscopic cross section file.

PAGE 54

54 Optional input files include: 1. grp_erg.bnd : indicates energy group str ucture by specifying upper energy bound in each group (MeV) NOTE: group 1 is entered first 2. grp_mat.chi: contains the normalized fission spectrum data for each material and energy group 3. Out put files: A. mgxs: MCNP multigroup cross section data file B. xsdir: MCNP cross section isotope index file C. mcnp.inp: A sample MCNP input file with generated material cards when using multigroup cross sections. The ALPO module settings used previously were f, af t for each energy group. A sample input file for the ALPO input required to generate the additional info rmation is in Appendix D. data can be found in Table 5 5. The fission spectrum was determined by using GMIX for all seven fuel regions. Appendix E contains a sample MCNP input deck containing the BWR assembly g eometry. Using the resulting multigroup cross section file along with the MCNP input resul ted in a k eff value of 1.13323 a percent difference of 3.4% with the PENTRAN k eff value. A total of 50,000 particles per cycle were used with 200 skipped cycles a nd a total of 1000 cycles. Different runs were performed as shown in Table 5 6 yet not all of the flux tally bins passed the ten statistical tests and some calculations reported large relative errors. This difference can be attributed to the fact that PEN TRAN uses a Cartesian geometry to represent the problem setup and as a result the fissile mass in both models are different. In addition to this Monte Carlo experiences difficulty converging since the source is not known initially. There may have been a false source convergence which resulted in underestimating the k eff value (Haghighat and Wagner 2003). Other factors contributing in differences include the method of

PAGE 55

55 multigroup cross section generation when using a homogenized (fuel+gap+clad) fuel mater ial surrounded by water. Comparing an MCNP model using the continuous energy cross section library with an MCNP model using the multigroup cross sections is useful to verify the collapsed library group structure. 5.3 BWR Assembly Burnup R esults The burnup steps chosen in Table 57 were modeled after the data provided form SFCOMPO. The fuel assembly remained in the reactor for 4 cycles with cooling times in between for a total of 22.3 GWD/MTU Table 5 8 contains the keff result at the beginning of each burnup step. It is interesting to note that the keff value increases slightly and then starts decreasi ng again during two instances in the burnup steps; once during the second burnup step and another time during burnup step 21. This is most likely due to the shifting power profile that is a result of the changing void fraction in a BWR assembly. Initially the flux is extremely skewed with the peak flux towards the bottom of the assembly and as a result the fuel at the bottom experiences more burnup. A s this continues the peak power begins to shift upwards towards the center of the assembly. This shifting power is seen assuming there were no control rods inserted next to the fuel assembly during the cycle length since there is no data available regardi ng control rod use for this reactor. The output from PENBURN was compared to SFCOMPO post irradiation results for the fuel material numbers of in terest as indicated in Table 5 9. Differences between the two are s hown in the subsequent tables. One thing to note however was that the burnup reported for the fuel element sometimes differed from the average burnup calculated from the amount of time the fuel assembly was in the reactor. For instance, for fuel element A1 the lab reported a burnup of 25.7 GWD/ MTU, a value si gnificantly larger than the 22.6 GWD/MTU used in the burnup simulation. The U 238 results consistently agreed with t he SFCOMPO data, while there were

PAGE 56

56 significant differences overall with the other data values. These differences can be attr ibuted to insufficient data regarding control rod movements in the BWR in addition to not using burnup dependent cross sections for the burnup steps in this comparison. Since the control rod data is unavailable, one step to take to more accurately represent physics of the problem was to generate the burnup dependent cross sections. 5.4 Burnup Dependent Cross Section G eneration The DEV XS procedure outlined previously was utilized to generate the burnup dependent cross sections. This time however the t dep l control sequence was used to extract burnup dependent cross sections a t specific burnup points. The minimum number of burnup points to consider had been determined from a previous study (Plower, 2008). A library was generated at 0, 0.0459, 17.85, 26.35 GWD/MTU burnup points and at fuel temperatures of 900 and 1000 K. Modifications to the previous SCALE input were necessary in order to save the collapsed cross sections at each burnup step. Initi ally the user should include savlib in the parm input and indicate parm=(savlib,addnux=3). The user should not include a space between the savlib and addnux keywords otherwise SCALE 5.1 fails to recognize the addnux keyword and no additional nuclides wil l be added to the cross section database. A burnup data block was set to generate the collapsed cross section s at the desired burnup points. SCALE uses a predictor corrector approach when running the burnup sequence and therefore outputs data at the midpoint of each burnup length. SCALE also does not allow the user to exceed 8.647 GWD/MTU between burnup steps. For this reason, the number of days for each burnup step was chosen as 40, 300, 300, 272, 200 and 68 days with 23 W/g. If the user exceeds the 8.647 GWD/MTU between burnup steps SCALE automatically increases the number of burnup ste ps and the user may confuse which collapsed cross section file corresponds to a specific burnup point. It is important to note that the collapsed cross sections saved at each burnup point are obtained when using

PAGE 57

57 modified versions of TRITO N and PMC obtained from ORNL. A sample SCALE 5.1 input file to generate burnup dependent cross sections is in Appendix F, while Appendix G contains the APLO input required to format the multiple cross section files at the different burnup points. 5.5 Accounting for Power Shift The initial relative flux as a function of energy group at the centerline of the fuel rod located in position A1 is displayed in Figure 59. As burnup progresses however there is a power shift as the peak progresses upward along the assembly due to the burnout of U 235. The power shift continues to occur until the peak flux is seen at outer edges with a dip in the middle of the fuel rod after 5.83 GWD/MTU. Then at 7.73 GWD/MTU the peak flux in group 2 is no longer at a core height of 100 cm but has shifted to a peak flux location a t the core height of 200 cm. Figures 5 10 through 514 contain the relative flux profile by energy group at the centerline of fuel p in A1 at different burnup points. Due to this power shift the water density at each axial zone should be repositioned beginning after 3.74 GWD/MTU of burnup. This can be accomplished by implementing a coupled thermal hydraulic and transport step during the PENTRAN/PENBURN burnup sequence. A new void fraction distribution solver should be created which takes into account the new power profile as opposed to a sinusoidal shape. Therefore one could obtain a new axial enthalpy equation based on the power shape the enthalpy as a function of axial height takes the form of Equation 51. And the quality at any axial position would be determined from Equation 52. ( ) = + 2 [ ( ) ] (5 1) ( ) = + 2 [ ( ) ] (5 2) Where, h( z )= enthalp y as a function of axial height z(kJ/kg) z= axial height location (m) hin q= thermal output (kW) = enthalpy at the inlet (kJ/kg)

PAGE 58

58 m= mass flow rate (kg/s) f(z)=normalized flux from transport calculation as a function of axial height z x(z)= quali ty as a function of axial height z xin h = quality at inlet fg = saturated enthalpy (kJ/kg) After a transport calculation is completed the resulting power profile can be utilized with these equations to determine the void distribution once the power profile changes. Since the flux profile changes as a function of burnup, the most effective way to perform this new calculation is by imple menting a coupled thermal hydraulic and transport solver method at every burn step. An efficient way to perform this calculation is by creating a driver to apply this new step to the calculations.

PAGE 59

59 Table 5 1. Gundremmingen BWR assembly specifications Power 250 MWe Water density at bottom (g/cm 3 ) 0.74153 Average density of fuel 10.50 Fuel enrichment 1.87/2.53 Homogenized fuel pellet diameter (cm) 1.4280 Fuel rod pitch (cm) 1.7800 Clad material Zr 2 Length of fuel rods (cm) 3.30E+02 Rod array 6x6 Number of rods 36 Side of square fuel section (cm) 11.3520 Assembly fuel channel thickness (cm) 0.3350 Number of assemblies 368 Inlet temperature (C) 266 Outlet temperature (C) 286 Table 5 2. Fuel composition of homogenized fuel Enrichment 2.53 1.87 Nuclide Wt% Wt% O 16 9.8977 9.8969 U 234 0.0169 0.0169 U235 1.8622 1.3764 U 236 0.0088 0.0088 U 238 71.7204 72.2070 He 4 0.0256 0.0256 Nat. zirc 16.4681 16.4681 Total 100 100 Table 5 3. Homogenized fuel PENTRAN and SCALE comparison Eigenvalue (PENTRAN) % difference from SCALE (1.23210) % excess fissile material 1.230234 0.15% 0.27%

PAGE 60

60 Table 5 4. SCALE 5.1 keff values by water density region density (g/cm 3 ) keff 0.74153 1.23210 0.72039 1.22614 0.64761 1.20311 0.54668 1.16336 0.44533 1.11133 0.33973 1.03885 0.28956 0.99551 Table 5 5. Nubar data by fuel region Group fuel zone fast epithermal thermal 1 2.78402 2.43631 2.43663 2 2.78358 2.43620 2.43666 3 2.78216 2.43625 2.43656 4 2.78016 2.43629 2.43682 5 2.77762 2.43636 2.43674 6 2.77451 2.43650 2.43667 7 2.77263 2.43662 2.43669 Table 5 6. MCNP particle histories # particles/hist # ksrc pts. Cycles S kipped T otal Cycles keff E rror Stat. Test Not P assed Large Rel. E rror 10000 1764 100 300 4 3 100000 1764 200 500 7 3 5000 2340 200 500 6 4 100000 2484 200 600 1.13319 0.00017 2 0 50000 2484 200 1000 1.13274 0.00017 1 0 50000 3024 200 1000 1.13292 0.00016 3 1 50000 7452 200 1000 1.13323 0.00016 1 0

PAGE 61

61 Table 5 7. Gundremmingen B23 assembly operation history Cycle of Operation Periods Days Core Burnup (MWD/MTU) Second 8/25/1969 279 5839 5/30/1970 Shutdown 5/31/1970 56 7/24/1970 Third 7/25/1970 323 6131 6/12/1970 Shutdown 6/13/1971 33 7/15/1971 Fourth 7/16/1971 290 5483 4/30/1972 Shutdown 5/1/1972 61 6/30/1972 Fifth 7/1/1972 309 5174 5/5/1973

PAGE 62

62 Table 5 8. Burnup steps with keff results Step W/g days Burnup ( G WD/MTHM) keff error 1 20.928 1 0.020928 1.17451 8.89E 05 2 20.928 1 0.041857 1.17636 7.98E 05 3 20.928 1 0.062785 1.17578 7.66E 05 4 20.928 1 0.083713 1.17507 7.96E 05 5 20.928 3 0.146498 1.17448 7.30E 05 6 20.928 12 0.418566 1.17313 8.58E 05 7 20.928 40 1.255698 1.16756 8.46E 05 8 20.928 40 2.09283 1.14725 9.55E 05 9 20.928 80 3.746166 1.12539 7.85E 05 10 20.928 100 5.838996 1.01876 8.39E 05 11 0 56 5.838996 12 18.981 100 7.737136 1.01876 8.39E 05 13 18.981 100 9.635276 0.9742 7.79E 05 14 18.981 123 11.969988 0.95017 7.15E 05 15 0 33 11.969988 16 18.907 90 13.671609 0.93533 2.02E 05 17 18.907 100 15.562299 0.92192 5.73E 05 18 18.907 100 17.452989 0.91524 7.95E 05 19 0 61 17.452989 20 16.744 100 19.127419 0.90964 6.73E 05 21 16.744 100 20.801849 0.91091 6.27E 05 22 16.744 109 22.626978 0.91094 1.72E 05 Table 5 9. PENTRAN material numbers corresponding to SFCOMPO analyzed fuel Location (cm) density (g/cm3) A1 B3 B4 C5 E3 E5 44 0.74153 31 20 14 9 23 11 268 0.33973 211 200 194 189 203 191

PAGE 63

63 Table 5 10. A1 fuel element at 44 cm percent difference between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 25.7 GWD/MTU) Data Type SFCOMPO Values Percent Difference initialxs burnupxs Cs 137/U 238 2.12E 03 87.72% 81.83% Nd 148/U 238 4.88E 04 84.13% 77.97% Pu 239/Total Pu(RateOfWeight) 5.56E 01 10.30% 0.63% Pu 239/U 238 3.89E 03 16.98% 1.52% Pu 240/Pu 239 4.88E 01 67.97% 39.67% Pu 240/Total Pu(RateOfWeight) 2.69E 01 41.89% 9.44% Pu 241/Pu 239 1.87E 01 52.08% 8.48% Pu 241/Total Pu(RateOfWeight) 1.17E 01 49.07% 4.20% Pu 242/Pu 239 9.01E 02 1.31% 17.60% Pu 242/Total Pu(RateOfWeight) 4.85E 02 15.43% 15.42% Total Pu/Total U 6.93E 03 6.35% 0.63% U 235/Total U(RateOfWeight) 6.61E 03 52.24% 52.95% U 235/U 238 6.76E 03 52.98% 53.68% U 236/Total U(RateOfWeight) 3.41E 03 5.61% 8.33% U 236/U 238 3.46E 03 4.79% 7.49% U 238/Total U(RateOfWeight) 9.90E 01 0.33% 0.32%

PAGE 64

64 Table 5 11. A1 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 27.4 GWD/MTU) Data Type SFCOMPO Values Percent Difference initialxs burnupxs burnupxs burnupxs .33 g/cc .33 g/cc .445 g/cc .546 g/cc Cs 137/U 238 1.67E 03 85.72% 87.81% 76.99% 81.60% Nd 148/U 238 5.22E 04 86.43% 88.43% 79.88% 83.75% Pu 239/Total Pu(RateOfWeight) 5.55E 01 46.78% 50.73% 38.54% 38.74% Pu 239/U 238 4.99E 03 29.60% 36.38% 25.97% 13.94% Pu 240/Pu 239 4.41E 01 81.87% 74.65% 60.86% 61.11% Pu 240/Total Pu(RateOfWeight) 2.50E 01 73.95% 62.60% 46.92% 47.17% Pu 241/Pu239 1.97E 01 32.52% 61.33% 43.71% 44.13% Pu 241/Total Pu(RateOfWeight) 1.31E 01 17.34% 51.35% 34.92% 35.31% Pu 242/Pu 239 8.64E 02 83.04% 91.37% 80.24% 80.19% Pu 242/Total Pu(RateOfWeight) 5.13E 02 76.73% 87.84% 74.41% 74.31% Total Pu/Total U 8.95E 03 12.73% 10.60% 9.72% 18.45% U 235/Total U(RateOfWeight) 7.09E 03 89.36% 94.28% 14.47% 14.48% U 235/U 238 7.27E 03 87.69% 92.65% 12.95% 12.95% U 236/Total U(RateOfWeight) 3.42E 03 22.32% 20.37% 1.91% 1.91% U 236/U 238 3.49E 03 22.63% 20.66% 1.04% 1.04% U 238/Total U(RateOfWeight) 9.89E 01 0.51% 0.56% 0.06% 0.06%

PAGE 65

65 Table 5 12. B3 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 21.2 GWD/MTU) Data Type Measurement Laboratory Percent Difference initial xs burnupxs burnupxs .339 g/cc .339 g/cc .445 g/cc Cs 137/U 238 Karlsruhe 84.61% 77.17% 75.20% Cs 137/U 238 Ispra 84.31% 76.72% 74.71% Nd 148/U 238 Karlsruhe 82.41% 75.87% 73.91% Pu 239/Total Pu(RateOfWeight) Karlsruhe 27.70% 31.25% 20.41% Pu 239/Total Pu(RateOfWeight) Ispra 27.10% 30.64% 19.85% Pu 239/U 238 Karlsruhe 14.43% 19.91% 11.07% Pu 239/U 238 Ispra 16.71% 22.29% 13.28% Pu 240/Pu 239 Karlsruhe 76.82% 67.74% 49.77% Pu 240/Pu239 Ispra 76.82% 67.74% 49.77% Pu 240/Total Pu(RateOfWeight) Karlsruhe 70.52% 57.83% 39.76% Pu 240/Total Pu(RateOfWeight) Ispra 70.25% 57.44% 39.21% Pu 241/Pu 239 Karlsruhe 7.12% 47.20% 22.24% Pu 241/Pu239 Ispra 9.65% 48.63% 24.36% Pu 241/Total Pu(RateOfWeight) Karlsruhe 461.53% 273.93% 254.42% Pu 241/Total Pu(RateOfWeight) Ispra 461.53% 273.93% 254.42% Pu 242/Pu 239 Karlsruhe 64.66% 82.22% 58.48% Pu 242/Pu239 Ispra 64.99% 82.39% 58.87% Pu 242/Total Pu(RateOfWeight) Karlsruhe 143.70% 43.61% 115.85% Pu 242/Total Pu(RateOfWeight) Ispra 54.32% 76.38% 49.40% Total Pu/Total U Karlsruhe 10.76% 9.08% 7.72% Total Pu/Total U Ispra 8.25% 6.52% 5.12% U 235/Total U(RateOfWeight) Karlsruhe 29.20% 34.17% 22.12% U 235/Total U(RateOfWeight) Ispra 31.73% 36.80% 20.59% U 235/U 238 Karlsruhe 30.06% 35.15% 21.95% U 235/U 238 Ispra 32.59% 37.78% 20.44% U 236/Total U(RateOfWeight) Karlsruhe 13.86% 10.95% 13.12% U 236/Total U(RateOfWeight) Ispra 13.30% 10.37% 13.86% U 236/U 238 Karlsruhe 13.58% 10.60% 12.98% U 236/U 238 Ispra 13.30% 10.31% 13.35% U 238/Total U(RateOfWeight) Karlsruhe 0.31% 0.37% 0.14% U 238/Total U(RateOfWeight) Ispra 0.31% 0.37% 0.14%

PAGE 66

66 Table 5 13. B4 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 22.3 GWD/MTU) Data Type SFCOMPO Values Percent Differences initialxs burnupxs burnupxs .339 g/cc .339 g/cc .445 g/cc Cs 137/U 238 1.57E 03 84.81% 77.45% 75.52% Nd 148/U 238 4.22E 04 83.21% 76.95% 75.08% Pu 239/Total Pu(RateOfWeight) 6.24E 01 30.49% 34.14% 23.03% Pu 239/U 238 5.24E 03 23.30% 29.21% 19.65% Pu 240/Pu 239 3.68E 01 78.21% 69.68% 52.78% Pu 240/Total Pu(RateOfWeight) 2.29E 01 71.49% 59.21% 41.75% Pu 241/Pu239 1.46E 01 8.78% 48.14% 23.63% Pu 241/Total Pu(RateOfWeight) 1.07E 01 1.35% 40.77% 20.00% Pu 242/Pu 239 4.66E 02 68.42% 84.11% 62.89% Pu 242/Total Pu(RateOfWeight) 2.89E 02 58.54% 78.56% 54.06% Total Pu/Total U 8.30E 03 5.94% 4.17% 2.74% U 235/Total U(RateOfWeight) 9.35E 03 43.46% 49.00% 13.69% U 235/U 238 9.60E 03 42.01% 47.58% 14.95% U 236/Total U(RateOfWeight) 3.12E 03 14.91% 12.04% 11.72% U 236/U 238 3.19E 03 15.42% 12.51% 10.55% U 238/Total U(RateOfWeight) 9.88E 01 0.41% 0.47% 0.04%

PAGE 67

67 Table 5 14. C5 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 23.0 GWD/MTU) Data Type SFCOMPO Values Percent Difference initialxs burnupxs burnupxs .339 g/cc .339 g/cc .445 g/cc Cs 137/U 238 1.78E 03 86.60% 80.10% 78.40% Kr 84/Kr 83 2.49E+00 97.71% 97.83% 97.07% Nd 148/U 238 4.36E 04 83.75% 77.69% 75.88% Pu 239/Total Pu(RateOfWeight) 6.07E 01 33.97% 37.74% 26.27% Pu 239/U 238 5.12E 03 25.96% 32.03% 22.17% Pu 240/Pu 239 3.97E 01 79.67% 71.71% 55.94% Pu 240/Total Pu(RateOfWeight) 2.41E 01 72.77% 61.04% 44.37% Pu 241/Pu 239 1.56E 01 14.05% 51.13% 28.05% Pu 241/Total Pu(RateOfWeight) 1.09E 01 0.03% 41.52% 21.08% Pu 242/Pu 239 5.36E 02 72.15% 86.00% 67.26% Pu 242/Total Pu(RateOfWeight) 3.25E 02 62.65% 80.70% 58.62% Total Pu/Total U 8.37E 03 6.77% 5.01% 3.62% U 235/Total U(RateOfWeight) 8.96E 03 49.08% 54.93% 10.73% U 235/U 238 9.05E 03 50.00% 55.98% 10.59% U 236/Total U(RateOfWeight) 3.29E 03 19.16% 16.46% 6.03% U 236/U 238 3.32E 03 18.58% 15.81% 6.30% U 238/Total U(RateOfWeight) 9.88E 01 0.41% 0.47% 0.05%

PAGE 68

68 Table 5 15. E3 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 23.5 GWD/MTU) Data Type SFCOMPO Values Percent Difference initialxs burnupxs burnupxs .339 g/cc .339 g/cc .445 g/cc Cs 137/U 238 1.59E 03 84.99% 77.73% 75.82% Nd 148/U 238 4.58E 04 84.53% 78.77% 77.04% Pu 239/Total Pu(RateOfWeight) 6.15E 01 32.23% 35.95% 24.63% Pu 239/U 238 5.02E 03 28.47% 34.66% 24.61% Pu 240/Pu 239 3.82E 01 78.87% 70.60% 54.21% Pu 240/Total Pu(RateOfWeight) 2.35E 01 72.07% 60.05% 42.95% Pu 241/Pu239 1.50E 01 10.62% 49.17% 25.18% Pu 241/Total Pu(RateOfWeight) 1.08E 01 440.44% 260.10% 241.07% Pu 242/Pu 239 5.05E 02 70.45% 85.14% 65.26% Pu 242/Total Pu(RateOfWeight) 3.10E 02 60.85% 79.76% 56.62% Total Pu/Total U 8.07E 03 3.30% 1.48% 0.03% U 235/Total U(RateOfWeight) 9.03E 03 47.93% 53.70% 11.43% U 235/U 238 9.14E 03 48.53% 54.42% 11.48% U 236/Total U(RateOfWeight) 3.27E 03 18.66% 15.94% 6.68% U 236/U 238 3.31E 03 18.33% 15.55% 6.62% U 238/Total U(RateOfWeight) 9.88E 01 0.41% 0.47% 0.05%

PAGE 69

69 Table 5 16. E5 fuel element at 268 cm percent differences between SFCOMPO values and PENBURN burnup results (SFCOMPO reports 25.2 GWD/MTU) Percent Difference Data Type Measurement Laboratory initial xs burnupxs burnupxs .339 g/cc .339 g/cc .445 g/cc Cs 134/Cs 137 (Ratio of Activity) Ispra 93.19% 93.17% 93.18% Cs 137/U 238 Karlsruhe 87.23% 81.04% 79.44% Cs 137/U 238 Ispra 86.58% 80.08% 78.40% Eu 154/Cs 137 (Ratio of Activity) Ispra 99.61% 99.59% 99.64% Nd 148/U 238 Karlsruhe 85.59% 80.23% 78.63% Pu 239/Total Pu(RateOfWeight) Karlsruhe 42.94% 47.06% 34.68% Pu 239/Total Pu(RateOfWeight) Ispra 42.19% 46.28% 33.97% Pu 239/U 238 Karlsruhe 38.08% 44.83% 33.84% Pu 239/U 238 Ispra 35.75% 42.38% 31.58% Pu 240/Pu 239 Karlsruhe 82.44% 75.58% 61.99% Pu 240/Pu239 Ispra 82.44% 75.58% 61.99% Pu 240/Total Pu(RateOfWeight) Karlsruhe 74.92% 64.12% 48.85% Pu 240/Total Pu(RateOfWeight) Ispra 74.72% 63.85% 48.46% Pu 241/Pu 239 Karlsruhe 22.09% 55.71% 34.91% Pu 241/Pu239 Ispra 23.84% 56.70% 36.36% Pu 241/Total Pu(RateOfWeight) Karlsruhe 3.07% 43.30% 23.70% Pu 241/Total Pu(RateOfWeight) Ispra 2.21% 42.80% 23.02% Pu 242/Pu 239 Karlsruhe 79.35% 89.64% 75.79% Pu 242/Pu239 Ispra 79.55% 89.74% 76.02% Pu 242/Total Pu(RateOfWeight) Karlsruhe 70.44% 84.74% 67.35% Pu 242/Total Pu(RateOfWeight) Ispra 69.94% 84.49% 66.80% Total Pu/Total U Karlsruhe 4.34% 2.53% 1.13% Total Pu/Total U Ispra 5.27% 3.48% 2.09% U 235/Total U(RateOfWeight) Karlsruhe 84.11% 91.52% 8.99% U 235/Total U(RateOfWeight) Ispra 88.85% 96.45% 11.79% U 235/U 238 Karlsruhe 85.28% 92.86% 9.17% U 235/U 238 Ispra 90.00% 97.77% 11.95% U 236/Total U(RateOfWeight) Karlsruhe 23.40% 20.91% 0.18% U 236/Total U(RateOfWeight) Ispra 21.38% 18.82% 2.84% U 236/U 238 Karlsruhe 22.83% 20.27% 0.47% U 236/U 238 Ispra 21.03% 18.41% 2.81% U 238/Total U(RateOfWeight) Karlsruhe 0.50% 0.56% 0.03% U 238/Total U(RateOfWeight) Ispra 0.60% 0.66% 0.13%

PAGE 70

70 Figure 51. Gundremmingen void fraction distribution. Figure 5 2. Gundremmingen axial quality. 0 0.5 1 1.5 2 2.5 3 3.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7core height (m)void fraction 0 0.5 1 1.5 2 2.5 3 3.5 0 0.02 0.04 0.06 0.08 0.1core height (m)quality

PAGE 71

71 Figure 5 3. Gundremmingen water density Figure 5 4. Gundremmingen BWR axial zone partitioning. 0 0.5 1 1.5 2 2.5 3 3.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8core height (m)water density (g/cc) 0 50 100 150 200 250 300 350 400 1Axial Height (cm) 0.28956 (g/cc) top water region 0.28956 (g/cc) 0.33973 (g/cc) 0.44533 (g/cc) 0.54668 (g/cc) 0.64761 (g/cc) 0.72039 (g/cc) 0.74153 (g/cc) 0.74153 (g/cc) bottom water region

PAGE 72

72 Figure 5 5. Gundremmingen B23 assembly location in core.

PAGE 73

73 Figure 5 6. Gundremmingen B23 assembly enrichments and sampling positions.

PAGE 74

74 Figure 5 7. Gundremmingen B23 assembly relative fluxes (0.00 GWD/MTU) for (a) group 1 (b) group 2 (c) group 3 [PENTRAN code run, 16 processors (4 in angle, 1 in energy, 4 in space), cross sections with a P1 Legendre order, S8 quadrature specular reflective boundary conditions in xy direction, vacuum boundaries in z directions ]

PAGE 75

75 Figure 5 8. Gundremmingen B23 assembly relative group fluxes (0.00 GWD/MTU) [PENTRAN code run, 16 processors (4 in angle, 1 in energy, 4 in space),cross sections with a P1 Legendre order, S8 quadrature, specular reflective boundary conditions in x y direction, vacuum boundaries in z directions ]

PAGE 76

76 Figure 5 9. Gundremmingen B23 assembly relative group fluxes (0.00 GWD/MTU) Figure 5 10. Gundremmingen B23 assembly relative group fluxes (0.06 GWD/MTU) 0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 3.50E+02 0 50 100 150 200 250 300 350 400Flux (1/cm2s2)Axial Height (cm) Group 1 Group 2 Group 3 0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 3.50E+02 0 50 100 150 200 250 300 350 400Flux (1/cm2s2)Axial Height (cm) Group 1 Group 2 Group 3

PAGE 77

77 Figure 5 11. Gundremmingen B23 assembly relative group fluxes (3.74 GWD/MTU). Figure 5 12. Gundremmingen B23 assembly relative group fluxes (5.83 GWD/MTU). 0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 3.50E+02 0 50 100 150 200 250 300 350 400Flux (1/cm2s2)Axial Height (cm) Group 1 Group 2 Group 3 0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 3.50E+02 0 50 100 150 200 250 300 350 400Flux (1/cm2s2)Axial Height (cm) Group 1 Group 2 Group 3

PAGE 78

78 Figure 5 13. Gundremmingen B23 assembly relative group fluxes (7.73 GWD/MTU). Figure 5 14. Gundremmingen B23 assembly relative group fluxes (19.12 GWD/MTU). 0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 3.50E+02 0 50 100 150 200 250 300 350 400Flux (1/cm2s2)Axial Height (cm) Group 1 Group 2 Group 3 0.00E+00 5.00E+01 1.00E+02 1.50E+02 2.00E+02 2.50E+02 3.00E+02 3.50E+02 0 50 100 150 200 250 300 350 400Flux (1/cm2s)Axial Height (cm) Group 1 Group 2 Group 3

PAGE 79

79 CHAPTER 6 CONCLUSIONS AND FUTURE WORK Key findings in this study includ e the need to move from 2 D deterministic Sn transport analysis to 3 D analysis for boiling water systems, e specially when performing burnup studies in boiling water reactors to account for the impact different axial densities have on the overall isotopic result s The use of 3D deterministic transport codes is also useful when performing fixed source analyses to determine the detector range for novel detector concepts in addition to optimal positioning of the detectors Major contributions overall include modifying the multigroup cross section generation procedure to account for multiple cross sections for t he same nuclide depending on material region The XSMERGE code was developed to sort and group nuclides prior to using GMIX which converts the microscopic cross section data to macroscopic data used by PENTRAN. A void fraction distribution solver was als o created to determine the axial void distribution in a boiling water reactor assembly when provided with six operating parameters and initially assuming sinus oidal heat generation And finally the FSPREP program was developed to automatically render the fixed source for a problem set up when performing a forward transport calculation. The detector response was calculated from both the forward and adjoint transport calculations, with the adjoint transport calculation providing the detector range for the S iC semiconductor detector. The neutron response contribution from the thermal, epithermal and fast group was 72%, 27% and 1% respectively. Implementing a procedure to develop cross sections for a boiling water reactor fuel assembly and using the changing void fraction in the assembly displayed the need to use 3 D models when analyzing BWRs. The shifting flux afte r 3.74 GWD/MTU presented further advancement possibilities for the BWR model including creating a coupled thermal hydraulics

PAGE 80

80 and transport solver driver when performing burnup calculations PENBURN burnup results displayed better agreement with a water density of 0.44 g/cm3 at 268 cm as opposed to 0.366 g/cm3The multigroup cross section generation procedure using SCALE 5.1 did not allow for mor e than two lattice cell calculations within a single SCALE run due to memory allocation issues. Due to comput er requirements when generating the multigroup cross sections, a single lattice cell calculation was performed at each water density chosen and th en the microscopic cross sections were combined and sorted. Initially a minimum number of water densities w as utilized in order to decrease the amount of computations required to generate the multigroup cross section data, however, the seven different axial water density zones may not be sufficient to represent a BWR assembly when performing burnup calculations. The Pu series experienced a significant impact when dealing with different water densities around the fuel, even with a densit y delta of 0.1 g/cm 3. Moving from a water density of 0.33 g/cm3 to 0.445 g/cm3 resulted in a 15% difference for the Pu 240 amount, 16% for Pu241, and 13% for Pu242. When the water density was 0.647 g/cm3 instead of 0.546 g/cm3 there was a difference of 29% for Pu 240, 19% for Pu 241, and 33% for Pu242. These large changes in isotopic compositions with a water density change of only 0.1 g/cm3These sm all changes in water density have a large impact in burnup calculations that can be minimized if there are more water densities for the BWR model. Future BWR assembly models should include more than seven water density regions with a maximum delta between water densities of 0.025 g/cm indicates the need to include more water densities so that the change between regions is not as large. 3. C alculating the optimum number of water densities adequate for all burnup points an assembly undergoes is an area of future work. The need to significantly

PAGE 81

81 increase the number of water regions requires the development of a driver to automatically perform the DEV XS procedure especially when generating a BWR cross section library data set. Another area of improvement comes in regard to control rod positioning. Since control rod use history is not readily available for th e BWRs listed in the SFCOMPO d atabase, creating another case that implements the use of a control rod and analyzing the impact it has on the burnup results can be investigated. Modeling additional BWRs in the SFCOMPO database that include fuel rods contai ning gadolinium is future work for code validation and developing multigroup cross section data for this fuel type.

PAGE 82

82 APPENDIX A SCALE 5.1 SAMPLE INP UT FILE 'BWR Fuel Pin cross section development 1st moderator density 0.74153 'start tnewt control sequence =t newt parm=(addnux=3) 'title card BWR homogenized pin 2.53 wtp enriched 1st moderator density 0.74153 'calling the 238 fine group ENDF B6 library V6 238 'initiate composition read read comp UO2 fuel specificatio ns for 2.53 wtp BWR fuel pin from Gundremmingen 6x6 BWR WTPThomg1 11 9.23798115 16 8016 9.89770683 92234 0.01692995 92235 1.86229452 92236 0.008833017 92238 71.7204216 2004 0.025670946 40000 16.4681431 'Following nuclides are added in trace quantities in order to produce on output collapsed XS file 92237 1E 5 93238 1E 5 93239 1E 5 94236 1E 5 94244 1E 5 96245 1E 5 96246 1E 5 96247 1E 5 61601 1E 5 1 923. end WTPTh2o_1 41 0.74153 2 1001 11.189 8016 88.811 1 539. end end comp 'read celldata initiation statement read celldata 'geometry type and boundary conditions 'note that here we must define an approximation for a unit cell calculations within the cross section card latticecell squarepitch pitch 1.78 41 fueld 1.428 11 end 'end of celldata parameters' end celldata

PAGE 83

83 READ model BWR Pin READ param run=yes collapse=yes sn=8 epsilon=1e 5 echo=yes drawit=yes inners=10 prtmxsec=yes prtmxtab=yes prtxsec=yes prtbroad=yes END param READ collapse 22r1 177r2 39r3 END collapse READ materials 11 1 'homg1' end 41 1 'h2o' end END materials READ geom homogenized BWR pin 2.53 wt% global unit 1 cylinder 10 0.714 cuboid 20 4p0.89 media 11 1 10 media 41 1 20 10 boundary 20 11 11 END geom 'start reading bounds' READ bounds 'all boundaries are reflective boundary condition' x=reflective +x=reflective y=reflective +y=reflective END bounds END model 'end of tnewt sequence END =alpo textoutp notused 0$$ 7 0

PAGE 84

84 wrklibs iht ihs ihm Pnord PrtGA PrtScm NoCorr 1$$ 1 3 4 6 1 0 0 0 0 T wrklin# Accept 2$$ 30 0 T end =shell copy _pun0000 "%RTNDIR% \ water1XS"

PAGE 85

85 APPENDIX B FSPREP SAMPLE INPUT /Number of energy groups 3 /File names for the source for each energy group whasm 1.src whasm 2.src whasm 3.src /nsdef variable in block 5 of PENTRAN input deck 27 /nscmsh variable in block 5 of PENTRAN input deck 6 7 8 10 11 12 14 15 16 22 23 24 26 27 28 30 31 32 38 39 40 42 43 44 46 47 48

PAGE 86

86 APPENDIX C FSPREP SAMPLE OUTPUT 1 1 3888 75R0.00000E+00 0.58374E+01 0.57748E+01 0.57582E+01 0.57482E+01 0.57673E+01 0.58189E+01 6R0.00000E+00 0.58081E+01 0.57532E+01 0.57389E+01 0.57348E+01 0.57573E+01 0.58108E+01 6R0.00000E+00 0.58277E+01 0.57748E+01 0.57600E+01 0.57604E+01 0.57832E+01 0.58392E+01 5R0.00000E+00 0.58373E+01 0.57408E+01 0.56839E+01 0.56555E+01 0.56539E+01 0.56727E+01 0.57231E+01 0.58085E+01 4R0.00000E+00 0.58006E+01 0.57154E+01 0.56618E+01 0.56389E+01 0.56407E+01 0.56624E+01 0.57175E+01 0.58041E+01 4R0.00000E+00 0.58176E+01 0.57350E+01 0.56825E+01 0.56621E+01 0.56640E+01 0.56887E+01 0.57465E+01 0.58348E+01

PAGE 87

87 APPENDIX D ALPO INPUT MODIFICATION F OR XSMCNP =alpo textoutp notused 0$$ 7 0 wrklibs iht ihs ihm Pnord PrtGA PrtScm NoCorr 1$$ 1 5 6 8 1 0 0 0 0 T wrklin# Accept 2$$ 30 0 T end =shell copy _pun0000 "%RTNDIR% \ water1XS" end

PAGE 88

88 APPENDIX E MCNP INPUT FILE Homogenized Fuel Gundremmingen BWR Assembly c cell cards 1 8 1.0 (21 23 22 24 4 5) imp:n=1 2 1 1.0 3 u=3 imp:n=1 $fuel+gap+clad homogenized 3 8 1.0 3 u=3 imp:n=1 $moderator 0.74153 g/cc 4 0 8 7 10 9 l at=1 u=1 imp:n=1 fill=0:5 0:5 0:0 $lattice 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 5 0 7 12 9 14 5 6 imp: n=1 fill=1 6 2 1.0 3 u=4 imp:n=1 $fuel+gap+clad homogenized 7 9 1.0 3 u=4 imp:n=1 $moderator 0.72039 g/cc 8 0 8 7 10 9 lat=1 u=11 imp:n=1 fill=0:5 0:5 0:0 $lattice 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 9 0 7 12 9 14 6 15 imp:n=1 fill=11 10 3 1.0 3 u=5 imp:n=1 $fuel+gap+clad homogenized 11 10 1.0 3 u=5 imp:n=1 $moderator 0.64761 g/cc 12 0 8 7 10 9 lat=1 u=21 imp:n=1 fill=0:5 0:5 0:0 $lattice 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 13 0 7 12 9 14 15 16 imp:n=1 fill=21 14 4 1.0 3 u=6 imp:n=1 $fuel+gap+clad homogenized 15 11 1.0 3 u=6 imp:n=1 $moderator 0.54668 g/cc 16 0 8 7 10 9 lat=1 u=31 imp:n=1 fill=0:5 0:5 0:0 $lattice 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 17 0 7 12 9 14 16 17 imp:n=1 fill=31

PAGE 89

89 18 5 1.0 3 u=7 imp:n=1 $fuel+gap+clad homogenized 19 12 1.0 3 u=7 imp:n=1 $moderator 0.44533 g/cc 20 0 8 7 10 9 lat=1 u=41 imp:n=1 fill=0:5 0:5 0:0 $lattice 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 21 0 7 12 9 14 17 18 imp:n=1 fill=41 22 6 1.0 3 u=8 imp:n=1 $fuel+gap+clad homogenize d 23 13 1.0 3 u=8 imp:n=1 $moderator 0.33973 g/cc 24 0 8 7 10 9 lat=1 u=51 imp:n=1 fill=0:5 0:5 0:0 $lattice 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 25 0 7 12 9 14 18 19 imp:n=1 fill=51 26 7 1.0 3 u=9 imp:n=1 $fuel+gap+clad homogenized 27 14 1.0 3 u=9 imp:n=1 $moderator 0.28956 g/cc 28 0 8 7 10 9 lat=1 u=61 imp:n=1 fill=0:5 0:5 0:0 $lattice 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 29 0 7 12 9 14 19 20 imp:n=1 fill=61 30 14 1.0 (21 23 22 24 20 25) imp:n=1 31 15 1.0 (21 23 22 24 5 20) ( 7:12: 9:14) imp:n=1 77 0 4:25: 21:23: 22:24 imp:n=0 c surface cards 3 c/z 0.89 0.89 0.714 *4 pz 0.00 $ z plane fuel pin and assembly 5 pz 3 6 pz 157.9176 $ z plane fuel pin and assembly 7 px 0.00 8 px 1.78 9 py 0.00 10 py 1.78 c assembly outer volume 12 px 10.68 14 py 10.68

PAGE 90

90 c axial z 15 pz 162.1 16 pz 174.8 17 pz 192.8 18 pz 221.4 19 pz 287.6 20 pz 333.2 c zircaloy channel enclosing assembly *21 px 0.25 *22 py 0.25 *23 px 10.93 *24 py 10.93 *25 pz 345 c data cards mode n f4:n 5 f14:n 9 f24:n 13 f34:n 17 f44:n 21 f54:n 25 f64:n 29 m1 1000.22m 1.0 m2 2000.22m 1.0 m3 3000.22m 1.0 m4 4000.22m 1.0 m5 5000.22m 1.0 m6 6000.22m 1.0 m7 7000.22m 1.0 m8 8000.22m 1.0 m9 9000.22m 1.0 m10 10000.22m 1.0 m11 11000.22m 1.0 m12 12000.22m 1.0 m13 13000.22m 1.0 m14 14000.22m 1.0 m15 15000.22m 1.0 mt1 lwtr.60t mt2 lwtr.60t mt3 lwtr.60t mt4 lwtr.60t mt5 lwtr.60t mt6 lwtr.60t mt7 lwtr.60t c

PAGE 91

91 e0 6.250E 07 1.010E+00 2.000E+01 c mgopt f 3 kcode 50000 1.00 200 1000 ksrc 0.89 0.89 5 2.67 0.89 5 4.45 0.89 5 6.23 0.89 5 8.01 0.89 5 9.79 0.89 5 0.89 2.67 5 2.67 2.67 5 4.45 2.67 5

PAGE 92

92 APPENDIX F SCALE 5.1 T DEPL INPUT 'BWR Fuel Pin cross section development 1st moderator density 0.74153 'start tnewt control sequence =t depl parm=(savlib,addnux=3) 'title card BWR homogenized pin 2.53 wtp enriched 1st moderator density 0.74153 'calling the 238 fine group ENDF B6 library V6 238 'initiate composition read read comp UO2 fuel specifications for 2.53 wtp BWR fuel pin from Gundremmingen 6x6 BWR WTPThomg1 11 9.23798115 16 8016 9.89770683 92234 0.01692995 92235 1.86229452 92236 0.008833017 92238 71.7204216 2004 0.025670946 40000 16.4681431 'Following nuclides are added in trace quantities in order to produce on output c ollapsed XS file 92237 1E 5 93238 1E 5 93239 1E 5 94236 1E 5 94244 1E 5 96245 1E 5 96246 1E 5 96247 1E 5 61601 1E 5 1 900. end WTPTh2o_1 41 0.74153 2 1001 11.189 8016 88.811 1 500. end end comp 'read celldata initiation statement read celldata 'geometry type and boundary conditions 'note that here we must define an approximation for a unit cell calculations within the cross section card latticecell squarepitch pitch 1.78 41 fueld 1.428 11 end 'end of celldata parameters' end celldata

PAGE 93

93 READ burndata p=23.0 b=40.0 d=0.0 end p=23.0 b=300.0 d=0.0 end p=23.0 b=300.0 d=0.0 end p=23.0 b=272.0 d=0.0 end p=23.0 b=200.0 d=0.0 end p=23.0 b=68.0 d=0.0 end END burndata READ depletion 11 END dep letion READ model BWR Pin READ param run=yes collapse=yes sn=8 epsilon=1e 5 echo=yes drawit=yes inners=10 prtmxsec=yes prtmxtab=yes prtxsec=yes prtbroad=yes END param READ collapse 22r1 177r2 39r3 END collapse READ materials 11 1 'homg1' end 41 1 'h2o' end END materials READ geom homogenized BWR pin 2.53 wt% global unit 1 cylinder 10 0.714 cuboid 20 4p0.89 media 11 1 10 media 41 1 20 10 boundary 20 19 19 END geom 'start reading bounds'

PAGE 94

94 READ bounds 'all boundaries are reflective boundary condition' x=reflective +x=reflective y=reflective +y=reflective END bounds END model 'end of tdepl sequence END =shell copy savcol00 "%RTNDIR% \ savcol00" copy savcol01 "%RTNDIR% \ savcol01" copy savcol02 "%RTNDIR% \ savcol02" copy savcol03 "%RTNDIR% \ savcol03" copy savcol04 "%RTNDIR% \ savcol04" copy savcol05 "%RTNDIR% \ savcol05" copy savcol06 "%RTNDIR% \ savcol06" end

PAGE 95

95 APPENDIX G ALPO INPUT FOR COLLAPSED CROSS SECTION FILE =shell copy "C: \ Users\ mrowe \ Desktop \ bwr burnup xsc \ 1\ fueltemp900\ savcol00" "%TMPDIR% \ ft40f001" end =alpo textoutp notused 0$$ 7 0 wrklibs iht ihs ihm Pnord PrtGA PrtScm NoCorr 1$$ 1 3 4 6 1 0 0 0 0 T wrklin# Accept 2$$ 40 0 T end =shell copy "_pun0000" "%RTN DIR% \ water1t_3_0" end

PAGE 96

96 APPENDIX H BURNSET INPUT FILE / problem name | predictor corrector flag ( 0=no, 1=PCA Std., 2=PCA HE) | memory save option (0=inactive, 1=active) bwr 0 0 / # of processors for parallel PENTRAN run | Step 0 flux files exist (0=no, 1=yes) | Restart? ( no <0, >0 last complete step# folder) 16 0 1 / REPRO flag (1=use preconditioner flux files, 0=no preconditioner flux files) | precflx flag for initial PENTRAN run (0=no, 1=yes) 1 1 / INTERPXS flag (1=activate, 0=user supplied .xsc file for entire sequence) | INTERPXS option | Fuel Temp, Mod Temp (K) | INTERPXS optiond data 1 2 923 574 t / PENTRAN Convergence STOP flag [interrupt sequence based on PENTRAN convergence] (0=no, 1=yes) 0 / Following 3 lines dedicated to PEN POW Problem Description Gundremmingen BWR 6x6 assembly Modeled after assembly B23 in SFCOMPO 7 axial water densities / number of fuel materials 252 / range of fuel material number: eg. 1 10 1 252 / Following 3 lines dedicated to PENBURN Problem D escription Gundremmingen BWR 6x6 assembly Modeled after assembly B23 in SFCOMPO 7 axial water densities / # of irradiation/cool steps 23 / power ( () indicates Watts/g; (+) indicates Watts), time, time unit, irrad (i)/cool(c), print step, print o ption, GMIX keyword 20.9283 1 d i 1 2 s1 20.9283 1 d i 1 2 s2 20.9283 1 d i 1 2 s3 20.9283 1 d i 1 2 s4 20.9283 3 d i 1 2 s5 20.9283 12 d i 1 2 s6 20.9283 40 d i 1 2 s7 20.9283 40 d i 1 2 s8 20.9283 80 d i 1 2 s9 20.9283 100 d i 1 2 s10 0 56 d c 1 2 s11 18.9814 100 d i 1 2 s12 18.9814 100 d i 1 2 s13 18.9814 123 d i 1 2 s14 0 33 d c 1 2 s15 18.9069 90 d i 1 2 s16 18.9069 100 d i 1 2 s17 18.9069 100 d i 1 2 s18 0 61 d c 1 2 s19 16.7443 100 d i 1 2 s20 16.7443 100 d i 1 2 s21

PAGE 97

97 16.7443 109 d i 1 2 s22 0 10 d c 1 2 s23

PAGE 98

98 LIST OF REFERENCES Brown, F.B., Kornreich, D.E., Parson, D.K., and Ueki, T., 2003. Autocorrelation and Dominance Ratio in Monte Carlo Criticality Calculations, Nucl. Sci. Eng, 145, pp.279290. DeHart, M.D., Hermann, O.H. 1998. Validation of SCALE (SAS2H) Isotopic Predictions for BWR Spent Fuel. Oak Ridge National Laboratory, Oak Ridge. TN. DeHart, M. D., 2006a. NEWT: A New Transport Algorithm for TwoDimensional Discrete Ordinates Analysis in NonOrthogonal Geometries, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. DeHart, M.D., 2006b. TRITON: A TwoDimensional Transport and Depletion Module for Characterization of Spent Nuclear Fuel, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Duderstadt, J.J., Hamilton, L.J., 1976. Nuclear Reactor Analysis, John Wiley & Sons, New York. Dulloo, A.R., Ruddy, F.H., Seidel, J.G., Adams, J.M., Nico, J.S., and Gilliam, D.M., 2003. The thermal neutron response of miniature silicon carbide semiconductor detectors. Nuclear Instruments and Methods in Physics Research, Volume A 498, pp. 415423. Greene, N.M., Dunn, M.E., 2006. Users Guide for AMPX Ut ility Modules, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Haghighat, A., Wagner, J.C., 2003. Monte Carlo Variance Reduction with Deterministic Importance Functions, Progress in Nuclear Energy, Vol 42(1). Hollenbach, D.F., Petrie, L.M., 2006. WORKER: SCALE System Module for Creating and Modifying Working Format Libraries, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN. Jatuff, J., Giust, F., Krouthen, J., Helmersson, S., Chawla, R. 2005. Effects of void uncertainties on the void reactivity coefficient and pin power distributions for a 10 x 10 BWR assembly, Annals of Nuclear Energy, Vol 33, pp. 119125. Kalos, M. H., Whitlock, P. A. 1986. Monte Carlo Methods. John Wiley & Sons, Inc. Germany. Kazimi, M. S., Todreas, N. E. 1990. Nuclear Systems I: Thermal Hydraulic Fundamentals. Taylor & Francis Group, LLC, New York. Khorsandi, B., Fard, M. R., Blue, T. E., Miller, D. W.,Windl, W., 2007. Monte Carlo Modeling of Count Rates and Defects in a Silicon Carbide Detector Neutron Moni tor System Highlighting GT MHR, Nuclear Technology Volume 159, pp. 208220. Lewis, E.E., Miller, W.F., 1993. Computational Methods of Neutron Transport. American Nuclear Society Publishing, LaGrange Park, IL.

PAGE 99

99 Manalo, K.L., 2008. Development, Optimization, and Testing of a 3 D Zone Based Burnup/Depletion Solver for Deterministic Transport, Masters Thesis. University of Florida, Gainesville, FL. Mock, T., 2006. Tandem Use of Monte Carlo and Deterministic Methods for Analysis of Large Scale Heterogeneous Radiation Systems, Masters Thesis. University of Florida, Gainesville, FL Plower, T.J., 2008. Fully Automated 3D Parallel Simulation and Optimization of a Full Scale Pressurized Water Reactor Fuel Assembly with Burnup Corrected Cross Sectio ns, Masters Thesis. University of Florida, Gainesville, FL. Ruddy, F. H., Seidel, J. G., and Dulloo, A.R., 2006. Fast Neutron Dosimetry and Spectrometry using Silicon Carbide Semiconductor Detectors, Journal of ASTM International. Volume 3, No. 3. pp. 408415. Sjoden, G.E., 2002. Deterministic adjoint transport applications for He 3 neutron detector design. Annals of Nuclear Energy, Volume 29, pp. 10551071. Sjoden, G.E., Haghighat, A., 2007. The Exponential Directional Weighted (EDW) Differencing Scheme in 3D Cartesian Geometry. Proceedings of the Joint International Conference on Mathematics and Supercomputing for Nuclear Applications, Saratoga Springs, New York, Vol II, pp.12671276. Sjoden, G.E. Haghighat, A., 2008. PENTRANTMWilliams, M.L., Asgari, M., Hollenbach, D.F., 2006. CENTRM: A One Dimensional Neutron Transport Code for Computing Pointwise Energy Spectra, SCALE5.1 Manual. Oak Ridge National Laboratory Oak Ridge, TN Code System User Guide to Version 9.4X.1 Series, HSW Technologies, Gainesville, FL. Williams, M.L., Hollenbach, D.F., 2006. PMC: A Program to Produce Multigroup Cross Sections Using Pointwise Energy Spectra from CENTRM, SCALE5.1 Manual. Oak Ridge National Laboratory, Oak Ridge, TN.

PAGE 100

BIOGRAPHICAL SKETCH Mireille R owe was born in 1985 in Miami, FL and grew up in Panama and Florida. She graduated Charles W. Flanagan in 2003 and began to pursue her degree in the fall of 2003. Mireille was active in the Tau Chapter of Phi Sigma Rho and was also a member of the Americ an Nuclear Society and Alpha Nu Sigma. Mireille received a B.S. in nuclear engineering from the University of Florida in August 2007. She then remained at the University of Florida to receive her M.S. degree in nuclear engineering. Mireille has accepted a job in the nuclear industry and plans to start her career in summer 2009.