ML20151H958
| ML20151H958 | |
| Person / Time | |
|---|---|
| Site: | Vermont Yankee, Yankee Rowe, Maine Yankee, 05000000 |
| Issue date: | 04/30/1988 |
| From: | Digiovine A, Napolitano D, Pappas J, Spinney K YANKEE ATOMIC ELECTRIC CO. |
| To: | |
| Shared Package | |
| ML20151H952 | List: |
| References | |
| YAEC-1363, NUDOCS 8804210012 | |
| Download: ML20151H958 (99) | |
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CASMO-3G VA1.IDATION
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April 1988 By A. S. DiGiovine K. B. Spinney D. G. Napolitano J. Pappas I
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Prepared By:
w eJC 4.T.'DiGiobine.' Senior Engineer
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S Nuclear Engineering Department N3 h rrA.
Prepared By:
K.'B. Spinney,1Nuc16rEngineer (Date)
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Nuclear Engineering % partment Prepared By:
MA v2,
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F. G. Napolitat{p', Nu'elear Engineer
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Nuclear Engineering Department
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MfM (Date) f.Pappas. Engineer Nuclear Engineering Department Approved By:
dd/d 84 [8 R[/.Caccia"uti, Manager
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Vactor Phy cs Group Nuclear Engineering Department N
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B. C. Slifer, Dire to f (bate)
Nuclear Engineerin partment
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Ysnkee Atomic Electric Company
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Nuclear Services Division 1671 Worcester Road Framinghan, Massachusetts 01701 2090R/2.20 8804210012 880411 PDR ADOCK 0"AOOO29 j
plSCLAIMER t,
This document was prepared by Yankee Atomic Electric Company for its The use of information contained in this document by anyone other own use.
than Yankee Atomic Electric Company is not authorized, and in regard to unauthorized use neither Yankee Atomic Electric Company or any of its officers, directors, agents or employees assumes any obligation, responsibility or liability, or makes any warranty or representation, with respect to the contents of this document, or its accuracy or completeness.
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c 2090R/2.20
J ABSTRACT l
L This report presents the validation and verification of the CASMO-3G code as a lattice physics code. The intended use of the code is as a r
generator of lattice physics parametera necessary for global reactor physics cnalysis codes and isotopic inventory accounting. The validation and verification consists of examining the functional calculations performed within the code. This includes repeating calculations previously documented for earlier versions of the CASMO code (CASMO and CASMO-2) ss well as adding several new benchmarks.
The report is broken up into four sections. The iirst section presents the theoretical description of the code and each of the A3jor calculational subroutines within the code. The second section presents results of benchmarking cases conducted within Yankee as well as by the code vendor.
Section 3.0 presents the conclusion of Yankee Atomic's benchmarking efforts with CASMO-3G and Section 4.0 presents the pertinent references associated with this work.
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TABLE OF CONTENTS 1
L Page 11 DISCLAIMER........................................................
iii ABSTRACT..........................................................
iv TABLE OF CONTENTS.................................................
v LIST OF TABLES....................................................
vi LIST OF FIGURES...................................................
viii ACKNOWLEDGMENTS...............................................,..
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1.0 DESCRIPTION
OF CASMO-3G...........................................
1 1.1 Code Description 0verview...................................
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5 1.2 Nuclear Data Library........................................
7 1.3 Calculations on Unit Ce11s..................................
9 1.4 Strong Absorbers............................................
11 1.5 The Two-Dimensional Calculation............................
13 1.6 The Depletion Calculation...................................
14 1.7 The Diffusion Theory Calculation - DIXY.....................
15 1.8 Gansna Trans po r t Cal culations................................
15 1.9 Kinetics....................................................
1.10 Discontinuity Factors and Baffle / Reflector Data.............
16 17 1.11 Input and 0utput............................................
40 2.0 VALIDATION CALCULATIONS...........................................
41 2.1 Comparisons With Uniform Pin Cell Lattice Criticals.........
42 2.2 Comparisons With Measured Yankee Isotop1cs..................
43 2.3 Comparisons With Measured Zion Isotopics....................
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2.4 Quad Citie s Gansna Scan Compari s ons..........................
2.5 Comparison with DIXY-Generated Diffusion Theory Cross Sections (CASMO-3 versus PDQ).........................
46 47 2.6 Other Validation Cases......................................
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82 3.0 SinMARY AND C ONC LU S ION............................................
O 4.0 R E F E R EN C E S........................... * * * *. * * * * *. ' * * * * * * * * * * * * * * * *
- A-1 APPENDIX A - BNL TUEL ASSEMBLY STANDARD PR0BLEM.........................
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LIST OF TABLES I
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Number Title Pan 1.1 Energy Group Structures in the CASMO-3G Neutron Libraries 18 1.2 Nuclides in the CASMO-3G Neutron Libraries 21 1.3 Energy Group Structures for the 10 and 18 Group CASMO-3G
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Gaauna Libraries 26 1.4 Nuclides in the CASMO-3G Gansna Library 27
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2.1 The Pin Cell Critical Statistics 51
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8.2 Zion Isotopics - CASMO-3G Calculated vs. Measured 52 2.3 DIXY K-Effective Comparisons for CE Assemblies 53 2.4 DIXY G-Factors for CE Assemblies 54 2.5 Data for the KRITZ Series of Critical Cores 55 8.6 Description of KRITZ Critical Cores 56 8.7 Calculated K-Effectives for KRITZ Cores 57 2.8 Summary of BW Cores 58 89 Sunenary of Data for the T6, B20, and ESADA Cores 59 2.10 CASMO-3G Fundamental Mode K-Effectives for Different
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Pin Cell criticals 60 8.11 K-Effective Statistics for CASMO-3G 61
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LIST OF FIGURES Number Title h
28 1.1 Flow Diagram of CASMO-3G 1.2 Flow Chart of Resonance Calculation 29 1.3 Flow Chart of Microgroup Calculation 30
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1.4 Example of Geometry in Macrogroup Calculation 31 32 1.5 Heavy Nuclide Chains in CASMO-3G 1.6 Fission Product Chains in CASMO-3G 33 1.7 Flow Chart of MICBURN-3 34 1.8a Actuel Control Rod Configuratic,n 35
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l.8b Representation of Control Rod Wing in CASMO-3G 35 1.9 Example of BWR Cell Georeetry in the 2-D Calculation 36 1.10 Examples of PWR Cell Geometry in the 2-D Calculation 37 1.11 Flow Diagram for 2-D Calculations 38 1.12 Calculation of G-Factors with DIXY 39 2.1 Pin Cell Critical Comparison of CASMO-3G Libraries 62 2.2 Pin Cell Critical K-Effectives vs. Lattice Pitch 62 2.3 Pin Cell Critical K-Effectives vs. Enrichment 63 2.4 Pin Cell Critical K-Effectives vs. Nater to Metal Ratio 63 2.5 Pin Cell Critical K-Effectives vs. Soluble Boron 64
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2.6 Pin Cell Critical K-Effectives vs. Critical Buckling 64 2.7 KRITZ Criticals - K-Effective vs. Moderator Tamperature 65 2.8 U-235 Atom Percent vs. Burnup for Yankee Core I 66 2.9 U-236 Atom Percent vs. Burnup for Yankee Core I 66 2.10 U-238 Atom Percent vs. Burnup for Yankee Core I 67
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2.11 Pu-239/U-238 Atom Ratio vs. Burnup for Yankee Core I 67
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L 2.12 Pu-239 Atom Percent vs. Barnup for Yankee Core I 68 i
2.13 Pu-240 Atom Percent vs. Burnup for Yankee Core I 68
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2.14 Pu-241 Atom Percent vs. Burnup for Yankee Core 1 69 2.15 Pu-242 Atom Percent vs. Burnup for Yankee Core I 69
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70 8.16 Quad Cities LA-140 Comparisons at the 15" Level 71 3 17 Quad Cities LA-140 Comparisons at the 56" Level 2.18 Quad Cities LA-140 Comparisons at the 93" Level 72 73 2.19 Quad Cities LA-140 Comparisons at the 129" Level 74
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2.20 Assembly Layout for CE Assemblies Used in DIXY L
Validation 75 2.21 Pin layout of KRITZ-3, U-kT1 Core 76 2.22 Pin Layout of KRITZ-3. U-kH2 Core 77 2.23 Assembly Layout of the KRITZ-4 Cores 2.24 Calculated to Measured Fission Rate Ratios for KRITZ Cores 78
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i ACKNOWLEDCMENTS e
The authors wish to acknowledge those who hava assisted in this cndeavor. Particularly, thanks to Malte Edenius of Studsvik for his consultations on the use of the CASM0-30 code and to liike Tremblay for his assistance in the analysis of CASM0-30 benchmark results. We would also like to thank the people in the Word Processing Department for typing this report.
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1.0 DESCRIPTION
OF CASMO-1G 1.1 Code Description Overview "ASM0-3GII) is a two-dimensional, multigroup transport theory code for the calculation of eigenvalue, spatial reaction rate distributions.
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nuclide depletion of pin cells, and depletion of BWR and PWR fuel lattices.
The code is an improved version of the CASMO and CASMO-2 codes (2'
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can model cruciform control rods containing cylindrical absorber elements, cluster control rods, water gaps, incore instrumentation channels, boron curtains, burnable absorber rods, burnable absorbers within the fuel rods, and fuel rods loaded with gadolinium. CASMO-3G can generate transport theory corrected cross sections suited for fine mesh diffusion theory core calculations (like PDQ) and has the capability to handle full nonsymetric 19 x 19 PWR bundles, four BWR bundle color set geometries, and PDQ color set geometries. Gamma detector responses can also be calculated using a new gama transport capability in CASMO-30. Other new features of CASMO-3G include a sophisticated baffle / reflector cross-section generation model, and the ability to generate flux discontinuity factors for use in an advanced nodal neutronics code such as SIMULATE-3 The nuclear data library is based on ENDF/B-IV with some fission spectra data taken from ENDF/B-V. The data are collected in a library containing cross sections in 40 or 70 energy groups, for neutron energies f rom
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0 to 10 Mev.
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The program has a flexible output, produces few-group parameters for the whole assembly or any subregion, and can be used for global reactor calculations. Further, the neutron balance, power distribution, reaction rates in fuel rods and in detectors, de: layed neutron yields and number densities versus burnup are printed if requested.
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L The Seven Functional Parts of CASMO-3G P
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Figure 1.1 shows the relationship between the seven functionally significant parts of CASMO-3G which are:
Nuclear data library and resonance calculation, Calculations on unit cells (spatial transport and energy spectrt.m
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of neutrons in individual pin cells).
Calculation of strs.z absorbers (control rods, Gadolinia in fuel pins, B C burnable poison).
4 Calculation of the 2-D space energy distribution of flux within the bundle and of the local power distribution and bundle _ reactivity.
Depletion calculation (isotopics),
DIXY calculation for the generation of few-group diffusion theory constants, and Gama transport module.
In terms of these seven functional parts, the program operates as follows:
For each group in the microscopic library group structure, macroacopic cross sections for each material in the bundle are constructed from number densities and the microscopic, temperature-dependent cross sections in the library.
Before any pin cell calculations are performed, resonance group cross sections for each pin type are calculated by intermediate resonance theory, using pin-dependent Dancoff factors. For each 2090R/2.20 I
v typical pin cell, a four region, cylindrical, collision probability J
solution to the transport equation in the library group structure provides space-dependent, microgroup spectra and disadvantage r-factors.
L Gadolinium is treated by an auxiliary calculation, MIC8 URN-3 which is analogous to, but more detailed than, the pin cell e-eatment within the bundle calculation.
It produces effective gadolinium croes sections which can then be used like any other pin microscopic cross section in the ordinary library. Control rods and boron burnable poison pins are homogenized, as part of the CASM0-3G calculation itself, in auch a way as to preserve their blackness.
The resulting infinite medium cross sections, homogenized over unit cells, are corrected for the influence of the rest of the assembly using factors derived from cylindrical macrogroup calculations of the whole bundle including water gaps, channel, control rod, boron curtains, etc. They are then collapsed to the two-dimensional group structure and used in a two-dimensional, transmission probability solution to the bundle transport equation. The resulting bundle average spectrum is adjusted for leakage and used to compute space-dependent reaction rotes from which K-infinities and local power distributions are determined.
The local reaction rates are used to calculate the buildup and depletion of 17 heavy nuclides and 24 separate and two pseudo fission products over selected time intervals, via a predictor-corrector technique. For each burnup step the depletion is calculated twice, first using the spectra at the start of the step and then, after a new spectrum calculation, using the spectra at the end of the step. Average number densities from these two calculations are used for the next burnup step. These individual pin cell number densities may then be used to repeat the entire process for subsequent time steps. 2090R/2.20 b
s If the user requests, diffusion theory cross sections are available
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from CASM0-3G by using the DIXY module. DIXY solves the same diffusion equations as PDQ, and by comparison with COXY (transport theory solution), corrections (G-factors) are produced which will b
give close agreement with transport theory. Material dependent cross sections and G-factors can be produced for any region of the
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assembly. Thus, by using DIXY one can develop PDQ cross sections for assembly or global reactor models.
Gamma sources may be calculated and a gamma transport calculation performed using COXY, in 10 or 18 energy groups over an energy range from 0 to 10 McV. The sources are determined from prompt sources due to neutron capture, fission, and inelastic scattering and from delayed neutron precursors, assuming steady state. The gamma transport solution is then used in conjunction with a user input detector sensitivity function to determine a detector response for the prompt, delayed, and total gamma fluxes.
Energy Group Structures Three sets of neutron energy group structures are used in CASMO-3G calculations and three in editing:
The microgroup or library group structure contains either 40 or 70
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groups, as shown in Table 1.1.
Pin cell calculations are performed in either of these group structures. However, the 40-group library
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is generally the one used due to its quicker execution time and accurate reproduction of 70 group results.
The macrogroup structure contains up to 25 groups.
It is used in an intermediate step for BWR assemblies, and on option for pin cell geometries, with a 1-D cylindrical geometry. The macrogroup structure may be selected by the user or default to a 23-group structure. 2090R/2.20 r
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The two-dimensional (2-D) group structure contains up to 12 groups.
It is used in the 2-D bundle calculation in which a transmission probability solution to the transport equation determines the flux distribution in homogenized pin cells and in L
structural regions. The 2D-group structure may be selected by the user or default to a seven-group structure.
The "Edit A" group structure is the two-group structure in which assembly average cross sections and discontinuity factors are edited for use in SIMULATE-3 core calculations. This group structure is not used in any calculations internal to CASM0-3G.
The "Edit B" group structure is an arbitrary arrangement of up to 10 groups, used only for editing.
The "PDQ" group structure is an arbitrary arrangement of up to 10 groups, usually 2 or 4 for use in diffusion theory calculations like PDQ.
The important features of the various parts of the program are described in the following sections.
1.2 The Nuclear Data Library Neutron Cross-Section Data
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The CASMO-3G neutron library (8) is based upon ENDF/B-IV with some data taken from ENDF/B-V. U-238 resonance integrals and the strongly shielded silver and indium resonances for control rods were adjusted to provide better agreement with measured data The neutron data library consists of 70 energy groups and a 40-group production library which was collapsed from the 70-group library. The two energy group structures are shown in Table 1.1.
The 70-group structure was used to provide 14 fast groups above 9,118 eV for accurate mideling of fast leakage and fast fission, 13 resonance groups to
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provide a uniform distribution of resonances in each group and to provide the correct flux level in each group, and 43 thermal groups below 4 eV to make the thermal cross sections independent of the weighting spectra used for their j
generation.
L The 70-group and 40-group ENDF/B-IV, V libraries used in CASM0-3
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provide improvements over the 69-and 25-group ENDF/B-III libraries used with CASMO and CASM0-2(10)Specifically, the following have been improved upon:
Moderator temperature coefficients were predicted slightly too negative.
Neutron leakage was underpredicted.
Fission rates in fuel rods containing gadolinium were slightly
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underpredicted.
Ag-In-Cd control rod worths were underpredicted.
Also, a trend towards increasing eigenvalues with depletion was observed.
The improvements are due to modifications of the cross-section library. The modifications include improved data for heavy metal nuclides,
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fission product data, and for isotopes of silver, cadmium, and indium.
Additionally the resonance self-shielding factor for U-238, silver and indium
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have been adjusted to agree more closely with experimental results. Several new nuclides previously not in the library have also been introduced, All materials contained in the new library are listed in Table 1.2.
This table also contains'the temperatures for which the data are provided.
Data for other temperatures are obtained by interpolation.
Gamma Cross-Section Data Data for the gaarna library were obtained from the CLOSEUP code ( },
which is based on ENDF/B-IV. The library contains data for 18 and 10 gamma energy groups. These energy structures are shown in Table 1.3.
The nuclides 2090R/2.20 I
contained in the gamma library are shown in Table 1.4.
This library contains frequency functions for prompt and delayed gammas, and cross sections for cbsorption, transport, P -scattering, and energy deposition.
O 1.3 Calculations on Unit cells The Resonance Treatment The neutron resonance energy region is defined to lie between 4 eV and 9,118 eV.
Resonance absorption above 9,118 eV is regarded as being unshielded. The 1.0 eV resonance in Pu-240 and the 0.3 eV resonance in Pu-239 are adequately covered by the concentration of thermal groups around these resonances and are consequently excluded from the special resonence treatment.
In the present version, four nuclides (U-235, U-236, U-238 and Pu-239) are treated as resonance absorbers. Figure 1.2 shows a flow chart of the subroutine for resonance cross section calculations.
Resonance cross sections are calculated using a generalized equivalence relation which considers the scattering in cladding and coolant. The fuel-to-fuel collision probability is obtained fram a sum of two rational functions which determine two effective potential cross sections. Reaction cross sections are then obtained by interpolation from the tables of effective resonance integrals in the library, with background (effective potential) cross sections and temperature as parameters. The interaction effect between resonances in different nuclides is obtained by a correction to the background cross section. The spatial dependence of the resonance cross sections within the assembly is taken care of by Dancoff factors, which are calculated separately for each fuel pin.
The Microgrou'p Calculations Each microgroup pin cell calculation provides a solution to the space-energy transport equation for isotropic scattering by means of collision probability calculations in 40 or 70 energy groups and in a simplified, 2090R/2.20 I
cylindrical geometry consisting of three or four regions. The regions represent fuel, cladding, coolant and, for pin cells in assemblies, a fourth I
L region for the rest of the cell, e.g., the water gap and the channel in a BWR cell. A flow chart is shown in Figure 1.3.
The microgroup calculation provides 40 or 70 group spectra which are used for energy condensation and spatial homogenization of the elementary pin cells. The cross sections prepared in the resonance calculation are used.
Thus, broad group cross sections are determined for smeared pin cells. The microgroup calculation is fast and is repeated for each different type of pin in the assembly, so that individual spectra are obtained for pins containing fuel of different initial enrichment. During depletion, pins which were originally identical will develop slightly different nuclide inventories. A single average spectrum based on the average nuclide inventory will be calculated for this group of pins, but the macroscopic cross sections used for each pin in the two-dimensional calculation will reflect its own nuclide inventory.
Macrogroup Calculations Prior to performing the two-dimensional calculation an intermediate calculation is done. This intermediate step is different for a PWR and BWR assembly.
In a PWR assembly the microgroup spectra are directly used to obtain broad energy group cross sections for smeared pin cells for succeeding two-dimensional calculations.
In a BWR one-dimensional assembly, calculations on a cylindricized assembly are performed using the discrete integral transport method These calculations are referred to as macrogroup calculations and are made in up to'a maximum of 25 energy groups. The solution from these calculations provides new neutron fluxes to be used for the energy condensation of cross sections for the two-dimensional calculation. They also allow for BWR assemblies some consideration to be taken for the effect of different water gap thicknesses on opposite sides of the assembly.
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Figure 1.4 is an example of geometry representation for the macrogroup
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calculation.
L 1.4 Strong' Absorbers Gadolinium in Fuel
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When gadolinium is used as burnable absorber in fuel rods, the gadolinium, which is initially homogeneously distributed, depletes in a complicated manner. The microscopic depletion of gadolinium in fuel rods is calculated outside CASMO-3G by the code MICBURN-3(7}, which provides effective cross sections, homogenized over the fuel rod, for the gadolinium as a function of burn".p.
The effective cross sections are used as input to CASM0-3G. The flux in a rod containing gadolinium is then calculated in the same way as for absorber rods.
An advantage of performing the detailed burnable absorber depletion outside CASM0-3G is that this calculation does not have to be repeated when the same burnable absorber pin is used in succeeding CASM0-3G calculations.
MICBURN-3 is an updated version of MICBURN The neutronics module in MICBURN-3 is identical to earlier versions of MICBURN, and results are comparable between different versions. The major modification to the code is its compatibility with the new CASMO-3G 40 and 70 group cross-section libraries.
Earlier versions of MICBURN will not work with the new libraries.
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Using MICBURN-3, therefore, allows one to take advantage of the improvements offered by the new libraries, which were previously discussed in this report.
The gadolinium bearing pin is first divided into equidistant radial
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microregions. Up to 100 regions may be used, but 20 is a typical number.
Each microregion defines a burnup region. The transport equation is solved using collision probabilities for a number of macroregions, each consisting of one or more microregions. The boundaries (and the number) of the microregions are the same at all burnup steps. The number of macroregions is also kept
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constant but the boundaries are changed automatically at each burnup step so
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that the macroregions are distributed in an efficient way for the transport calculation. The formalism for the transport calculation is identical to that used in the pin cell calculations in CASMO-3G, except that more regions are nied.
To generate a realistic spectrum for the burnup calculation, it is s.ssumed that the gadolinium bearing rod is surrounded by a uniform pin cell lattice. Before the main transport calculation in MICBURN-3 can be carried out, this buffer zone is homogenized using fluxes obtained from a special transport calculation in the fuel, clad, and moderator regions, which define the uniform lattice of the buffer zone. Again, the formalism for the buffer homogenization is identical to that used for the pin cell calculations in CASMO-3G. The main transport calculation in MICBURN-3 is then made in an annular geometry where the gadolinium baaring rod is surrounded by clad, moderator, and buffer zone.
In the burnup calculation, the whole gadolinium chain from Gd-154 to Gd-158 is taken into account.
In addition, the burnup of heavy nuclides and buildup of fission products is also calculated, just as in CASMO-3G (see Figures 1.5 and 1.6).
The buffer zone is also depleted. At each depletion step effective cross sections for the gadolinium are 1.omogenized over the fuel rod, parameterized as a function if Gadolinium depletion, and saved for use in the main CASMO-3G calculation. A flow chart of MICBURN-3 is shown in Figure 1.7.
Cruciform Control Rods
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Cruciform control rods, such as those in a BWR, are treated as
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homogeneous slab regions in the two-dimensional calculation. The two-dimensional calculation differentiates between the hub (which is actually homogeneous) and the wings of the blade, which consist of tubes of absorber material enclosed within a perforated metal sheet, as shown in Figure 1.8a.
For use in the two-dimensional calculation, the wings are homogenized by CASMO-3G in such a way as to maintain their blackness. The homogenization
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is performed on the assumption that the wing consists of two regions; the cylindrical absorber material and a homogeneous mixture made up of the 2090R/2.20
Ebsorber tube walls, the surrounding metal sheet, and any water between the two.
The relative flux in the two regions shown in Figure 1.8b is obtained for each 2-D energy group by a collision probability calculation which includes the effect of an anisotropic surface current.
Cluster Control and Burnable Absorber Rod 3 Cluster control rods and burnable absorber rods are homogenized using nicrogroup pin cell solutions from a four-region annular geometry, in which the innermost three regions represent absorber, absorber cladding, and water, and the fourth region consists of homogenized fuel.
In this calculation, cross sections for the fourth region are determined from the previous microgroup calculation on an assembly average fuel pin cell.
Correction factors used to account for the approximation caused by the pin cell homogenization used in the two-dimensional bundle calculation are then derived on a microgroup basis by repeating the calculation with only two regions; homogenized absorber cell (absorber plus cladding plus water using flux-weighted cross sections from the four region calculation) and buffer The correction factor for each microgroup is defined as the ratio of zone.
the integrated flux in the absorber cell from the heterogeneous four-region calculation to that from the homogeneous two-region calculation. The correction factors are then collapsed to the group structure used for the two-dimensional calculation. The correction factors are analogous to
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blackness tneory used in other calculational models.
1.5 The Two-Dimensional Calculation
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A two-dimensional calculation is required to determine the flux, power distribution 'and eigenvalue in a BWR or PWR lattice. This calculation is carried out in x-y geometry containing a maximum of 19 x 19 pin cells plus water using the transmission probability routine, C0XY generally in 6 to 12 energy groups. Typical geometries of BWR and PWR lattices treated by the two-dimensional routines are shown in Figures 1.9 and 1.10. 2090R/2.20 b
L The condensation of the 40 or 70 group spectra to the number of groups used for the 2-D lattice calculations is either made in one step (PWR W
geometry) or for BWR geometry via cylindrical macrogroup calculations in a maximum of 25 groups. Separate cylindrical calculations which are performed for the BWR lattice are approximated as a cylinder with the wide gap and with the narrow one. When a control rod is present, it is treated as the outermost ring of the wide gap calculation only. During the condensation from the library microgroup structure to the 2-D group structure, the microgroup spectrum for each pin is adjusted (via the macrogroup spectrum) to reflect the pin's actual location in the bundle relative to its neighbors, the water gaps and the control rod.
The actual 2-D ->.lculation is performed by C0XY, which solves the integral transport equation by use of escape and transmission probabilities to determine the interface currents between mesh blocks. Up to 12 energy groups may be used.
Within each mesh block, the neutron flux is assumed to be linearly dependent on the x-y coordinates.
The angular dependence is given by aP approximation. At the mesh surf aces, the asymetric flux distribution y
relative to the surface normal is considered. The escape and transmission probabilities include coupling between different angular modes. COXY is auch faster than conventional collision probability routines because a mesh area is only coupled to its nearest neighbors. Further, the linearly varying flux approximation within each mesh allows a larger mesh size than the flat flux approximation. A flow chart of the 2-D calculation is found in Figure 1.11.
A fundamental buckling modo is used for modifying the infinite lattice results obtained from the transport calculation to include the effects of leakage. This calculation may be carried out either in diffusion theory or by use of the B leakage method. P scattering matrices are available in the 1
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scattering terms CASMO-3G library for the principal moderators and the Pg are explicitly represented in tha B equations.
In previous versions of y
approximation. However, CASMO, the accepted methodology ma to use the By this has been found to be inadequate for certain situations because the leakage term is sensitive to the buckling.
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L 1.6 The Depletion Calculation
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1 The basic burnup chains, with the isotopes linked through absorption and decay, are linearized and the differential burnup equations are solved by a fast analytical treatment.
Five standard linear chains are treated for the heavy nuclides as shown in Figure 1.5.
Twenty-four individual and two pseudo-fission products are included in fourteen linear fission product chains shown in Figure 1.6.
The individually treated fission products account for cbout 90 percent of the total fission product absorption. Baron in boron steel curtains or in burnable poison rods is also depleted, as is gadolinium in burnable absorber rods.
The depletion equations are solved separately for each fuel pin and each burnable absorber pin.
(The xenon concentration is set to the equilibrium value determined by the power density at all times.) The flux level is de emine.d by the average power density. The fluxes used to determine reaction rates are constant during a depletion step. The length and the number of depletion steps are set in the program as default values, but they can also be chosen by the user. Depletion and buildup of gadolinium isotopes is not calculated explicitly in CASMO-3G. Rather, it is accounted for through the definition of an energy-dependent, effective microscopic gadolinium cross section as a function of the concentration of Gd-155 plus Gd-157. However, the effective cross sections are obtained from explicit calculations performed externally by MICBURN-3, as described in Section 1.4.
The depletion calculation for each depletion step is carried out in two n-1 n, first a "predictor" step partial steps. Going from the time t is made using the fluxes obtained from the spectrum calculation at tn-1*
The predictor step provides predicted number densities at t where, after n
the cross sections are updated, a new spectrum calculation gives fluxes to be
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used in a "corrector" step. The final number densities at t are then given by the average value of the results from the predictor and corrector steps.
This method is very efficient and makes it possible to take much longer depletion steps than is typically employed by other lattice depletion codes.
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k I
L 1.7 The Diffusion Theory Calculation - DIXY Once the 2-D bundle calculation has been completed, the user may request' diffusion theory cross sections homogenized over specified regions within an assembly. These cross sections may be used directly in fine mesh diffusion theory codes such as PDQ.
The diffusion theory cross sections are available from the CASMO-3G code by using the DIXY module within the code. DIXY solves the same diffusion theory equations as PDQ and using the same input it can be shown that both codes give identical results. The availability of DIXY thus allowc the comparison of diffusion theory results to transport theory results within the CASMO-3G code.
The DIXY module uses only macroscopic cross sections which the user may specify to be conventional or MND. Therefore, no depletion is conducted within the DIXY subroutine.
DIXY is followed by a fundamental mode calculation. This is necessary in order for the DIXY results to be consistent with the transport theory solution within CASMO-3G. The transport theory solution is done with the COXY subroutine followed by a fundamental mode calculation.
This consistency between DIXY and COXY allows for direct comparison of the results from each of the subroutines.
If requested, the code can adjust the diffusion theory cross sections so that the DIXY reaction rates match the COXY reaction rates. The main weakness of diffusion theory is its tendency to underestimate large flux gradients. Such gradicnts typically occur in the
{
presence of water holes (i.e., guide tubes) and strong absorbers (i.e.,
burnable shim's).
CASMO-3G will adjust the diffusion theory cross sections by applying material-dependent multipliers, called G-factors, to each cross section type.
CASMO-3G generates user requested G-factors by comparing the DIXY solution to the COXY solution.
If the comparison shows a discrepancy, the diffusion 2090R/2.20 r
7 v
theory cross sections are adjusted and the DIXY calculation repeated. This j
[
process is repeated until agreement between DIXY and COXY is obtained.
Figure 1.12 presents a flow chart of this process.
1.8 Gama Transport Calculations The gama transport calculation consists of determination of the gamma source, then using this source in the COXY transport module to calculate the space and energy distribution of the gamma flux in the model. Detector response functions are then evaluated as the ratio of the assembly power to calculated flux at the assembly detector location.
The gamma source is evaluated after the neutron flux solution has been determined.
Prompt gama f requency functions for each nuclide are evaluated from the 25 neutron energy group data contained in the CASMO-3G library which were derived from the CLOSEUP data. The delayed gamma frequency functions are obtained from the data library for each Uranium and Plutonium isotope. The library also has absorption, transport, and energy deposition and scattering cross sections for fuel, moderator, and structural material.
The prompt gama source is calculated by suming over energy groups and nuclides the product of the flux, neutron absorption cross section, and prompt frequency function. The delayed gama source is the sum over nuclides of the product of the delayed frequency function and the fission reaction rate for each nuclide. The gamma sources and cross sections are then averaged over each region for use in the COXY gamma module, which calculates the space and energy dependence of the gama flux in assembly. This may be done for the total gamma source, or for the prompt and delayed gamma sources separately, as
(
requested by the user.
{
1.9 Kinetics The CASMO-3G code also calculates the effective delayed neutron fraction,6,gg as well as inverse neutron velocity. These constants are based upon spectra 11y-weighted, delayed neutron fraction yields for the
[
nuclides of interest.
( 2090R/2.20 I
1.10 Discontinuity Factors and Baffle / Reflector Data J
L The CASMO-3G code generates discontinuity factors for advanced nodal code applicati m and cross sections for baffle / reflector regions. The discontinuity factors, or flux discentinuity factors. are calculated in two explicit energy groups for each side of an assembly. These discontinuity factors are defined as ratios of the surface flux to the assembly average flux, using zero flux boundary conditfons. The factors are required by the advanced nodal code, SIMULATE-3. They are necessary so that the net currents on an interface calculated by multigroup transport theory (CASMO-3G) are preserved within SIMUI. ATE-3.
The preservation is conducted so that the net current calculated by SIMULATE-3 for the homogenized region matches the net current from the heterogeneous calculation performed at the CASMO-3G 1evel.
The discontinuity factors are also applicable to most finite difference codes that employ homogenized regions and, more specifically, are applicable to generat.ing baffle / reflector data for codes such as SIMULATE-3 and PDQ.
These codes can model the baffle / reflector geometry as homogenized regions at the radial core periphery and the reflector regions located axially at top and bottom of the reactor core.
CASMO-3G will generate two-group cross sections and discontinuity factors for pure water reflectors or for steel and water mixtures. The calculation of this data is analogous to the calculation performed for fuel storage rack geomett2es. The C0XY calculation is performed in either two dimensions for a full bundle or in one dimension for only one row of pins
{
along the side of an assembly.
The baffle / reflector two-group cross sections are divided by the appropriate dlscontinuity factors for direct application to finite difference codes such as PDQ, which do not use flux discontinuity factors. SIMULATE-3, however, does use these factors. Therefore, the discontinuity factors are available for input into SIMULATE-3 along with the two-group cross sections.
( 2090R/2.20
1.11 Input and Output The input to CASM0-3G is arranged to make the use of the code as easy as possible, and consequently minimizes the risk of input errors.
Input data are blocked togett.er, and most of the blocks consist of one card only.
Separate blocks specify, for example, materials composition, dimensions and errangement in the box, energy group condensation, burnup, output edit, etc.
In successive runs, only those blocks that contain changes need be repeated.
Special options are available for saving the results of runs for later use.
CASM0-3G produces few-group homogenized macroscopic cross sections for use in overall reactor calculations. Optionally, cross sections for portions of the fuel assembly are available.
The infinite multiplication constant, K-infinity, is obtained from the two-dimensional transport calculation, and the fundamental mode calculation gives K-effective for a given geometric buckling. The material buckling corresponding to a K-effective equal to unity is also provided by the fundamental mode calculation.
The fluxes obtained from the two-dimensional transport calculation are used to calculate reaction rates for any specified nuclide in the library.
Reaction rates are calculated for nuclides not normally occurring in the
- reactor, e.g.,
for detector materials. From the calculated reaction rates, the power distribution within the fuel assembly, conversion ratios and other cell parameters are obtained.
[
In depletion calculations, intermediate and end results can be stored on a restart file. The data saved are nuclide concentrations.
Starting from these restart' files it is possible to conduct branch calculations at, for example, different values of coole.nf void or moderator boron content.
[
r L 2090R/2.20
[
[
4 TABLE 1.1 Energy Group Structures in the CASMO-3G Neutron Libraries
/
L 40-70-Upper energy Energy Lethargy group group boundary width width MeV 1
1 10.0 3.9345 0.49997 2
2 6.0655 2.3865 0.49998 3
3 3.679 1.448 0.50019 4
4 2.231 0.878 0.50013 5
5 1.353 0.532 0.49956 6
0.821 0.321 0.49592 7
0.500 0.1975 0.50253 7
8 0.3025 0.1195 0.50260 9
0.183 0.072 0.49996 10 0.1110 0.04366 0.49978 11 0.06734 0.02649 0.49985 8
12 0.04085 0.01607 0.49987 13 0.02478 0.00975 0.49999 14 0.01503 0.005912 0.49980 9
15 9118.0 3588.0 0.50006 16 5530.0 2010.9 0.45198 17 3519.1 1279.65 0.45198 10 18 2239.45 814.35 0.45199 19 1425.1 518.202 0.45197
(
20 906.898 539.636 0.90395 21 367.262 218.534 0.90396
{
22 148.728 73.2266 0.67797 23 75.5014 27.4494 0.45187 33 12 24 48.052 20.352 0.55085 13 25 27.700 11.732 0.55085 14 26 15.968 6.091 0.48038
(
15 27 9.877 5.877 0.90391 r
s ki TABLE 1.1 Energy Group Structures in the CASMO-3G Neutron Libraries (Continued) b 40-70-Upper energy Energy Lethargy
(.
group group boundary width width
- 1 16 28 4.00 0.700 0.19237
{
17 29 3.30 0.700 0.23841 10 30 2.60 0.500 0.21357 19 31 2.10 0.245 0.12405 20 32 1.855 0.355 0.21242 21 33 1.50 0.2,00 0.14310 22 34 1.30 0.150 0.12260 35 1.15 0.027 0.02376
[
23 36 1.123 0.026 0.02342 37 1.097 0.026 0.02399 24 38 1.071 0.026 0.02458 39 1.045 0.025 0.02421 0
1.020 0.024 0.02381 25 41 0.996 0.024 0.02439 20 42 0.972 0.022 0.02289
{
43 0.950 0.040 0.04302 27 44 0.910 0.060 0.06821 45 0.850 0.070 0.08594 28 46 0.780 0.155 0.22154 47 0.625 0.125 0.22314 29 48 0.500 0.100 0.22314 49 0.400 0.050 0.13353
[
50 0.350 0.030 0.08961 30 51 0.320 0.020 0.06454 52 0.300 0.070 0.06899 53 0.280 0.030 0.11333
(
31
(
54 0.250 0.030 0.12783 32 55 0.220 0.040 0.20067 33 56 0.180 0.040 0.25131
(
[ f
L f.
L TABLE 1.1 f
Energy Group Structures in the CASMO-3G Neutron Libraries (Continued) 40-70-Upper energy Energy Lethargy group group _
boundary width width SE 34 57 0.140 0.040 0.33647 35 58 0.100 0.020 0.22314
(
5, 0.080 0.013 0.17733 60 0.067 0.009 0.14425
(
61 0.058 0.008 0.14842 37 62 0.050 0.008 0.17435 63 0.042 0.007 0.18232 38 64 0.035 0.005 0.15415 65 0.030 0.005 0.18232 39 66 0.025 0.005 0.22314 67 0.020 0.005 0.28768
(.
68 0.015 0.005 0.40547 40 69 0.010 0.005 0.69315 70 0.005 0.005 t
[
l
[
[
[ - - -
. ~
4 TABLE 1.2 Nuclides in the CASMO-3G Neutron Libraries s
Nuclide ID No.
Temperatures, K Comments
[
H 1001 300, 350, 400, 450, 1
500, 600 D
1002 300 2
D 1102 300, 450, 600 1,2
[
Be 4000 300 B
5000 300 3
(
B-10 5010 300 3
B-11 5011 300 3
C 6000 300 O
8000 300, 450, 600 1
{
Al 13000 300 Si 14000 300 V
23000 300 Cr 24000 300 Mn 25000 300 4
Fe 26000 300
(
Co-59 27059 300 Ni 28000 300
(
Cu-63 29063 300 4
Gd-154 64154 300 4
Gd-155 64155 300 4
Gd-156 64156 300 4
{
Gd-157 64157 300 4
Gd-158 64158 300 4
(
Dy-164 66164 300 4
Lu-176 71176 300 4
Hf 72000 300 4
Pt-195 78195 300 4
Pb 82000 300
(
Structure materials Zr-2 302 300, 600, 1200 1
SS 347 300 5
[
Inc-718 718 300 5
Inc-750 750 300 5
(
A_rtificial nuclides 1/v-absorber 1
300 4,6 Unit absorber 2
300 4,6
(
Unit scatter 3
300 6
( f
TABLE 1.2 Nuclides in the CASMO-3G Neutron Libraries (Continued)
L Nuclide ID No.
Temperatures, K Comments f
L Shielded nuclides Rh-103 (det.)
45001 300 4,7 b
Ag (17x17) 47400 600 7
Ag-107 (15x15) 47307 600 4,7
[
Ag-107 (17x17) 47407 600 4,7 L
Ag-109 (15x15) 47309 600 4,7 s
Ag-109 (17x17 ) 47409 600 4,7
(
Cd (17x17) 48A00 600 7
Cd-113 (15x15) 48313 600 4,7 Cd-113 (17x17 ) 48413 600 4,7
(
In (17x17) 49400 600 7
In-115 (15x15) 49315 600 4,7 In-115 (17x17) 49415 600 4,7
(
Hf (17x17) 72400 300, 600 7
Hf (BWR) 72500 300, 600 7
Hf-174 (17x17) 72474 300, 600 4,7
(
Hf-176 (17x17) 72476 300, 600 4,7 Hf-177 (17x17) 72477 300, 600 4,7 Nf-178 (17x17) 72478 300, 600 4,7 Hf-179 (17x17) 72479 300, 600 4,7 Hf-180 (17x17 ) 72480 300, 600 4,7 Heavy nuclides U-234 92234 300 4
(
U-235 92235 300, 900 1
U-236 92236 300, 900 1
U-238 92238 300, 600, 900, 1500 1
Np-237 93237 300 Pu-238 94238 300 Pu-239 94239 300, 600, 900, 1500 1
Pu-240 94240 300, 600, 1200 1
Pu-241 94241 300 Pu-242 94242 300 Am-241 95241 300 Am-242 95242 310 Am-243 95243 300
(
Cm-242 96242 300 Cm-244 96244 300 4 r
l TABLE 1.2 Nuclides in the CASMO-3G Neutron Libraries (Continued) r L
Nuclide ID No.
Temperatures, K Comments Fission products Kr-83 36083 300 4
(
Rh-103 45103 300 4
Rh-105 45105 300 4
Ag-109 47109 300 4
Xo-131 54131 300 4
{
Xe-135 54135 300 4
Cs-133 55133 300 4
[
Cs-134 55134 300 4
Cs-135 55135 300 4
Nd-143 60143 300 4
Nd-145 60145 300 4
Pm-147 61147 300 4
Pm-148 61148 300 4
Pm-148m 61248 300 4
Sm-147 62147 300 4
Sm-149 62149 300 4
Sm-150 62150 300 4
Sm-151 62151 300 4
Sm-152 62152 300 4
Eu-153 63153 300 4
Eu-154 63154 300 4
Eu-155 63155 300 4
LFP1 401 300 4,8 LFP2 402 300 4,8
[
[
[
(
-n-r
L TABLE 1.2 Nuclides in the CASMO-3G Neutron Libraries (Continued) r L
Comments to the list of nuclide identifications 1
CASMO interpolates in temperatures if cross sections are
[
tabulated for more than one temperature. These nuclides are marked in the table. Most other nuclides were tabulated for room temperature, marked by 300 K in the
[
table. The temperature dependence of nuclides with only one temperature value in the CASMO library is negligible for LWR analysis.
2 The two tabulations for deuterium differ as follows:
ID=1002 is tabulated os.ly for room temperature. Cross
(
sections are from ENDF/B-3.
l ID=1102 is tabulated for three temperatures. Data are from UKNDL with the Effective Width model for thermal scattering.
3 ID=5000 represents natural boron and must be used when boron should not be depleted, e.g. as soluable boron in water. It can also be used in control rods.
ID=5010 represents B-10 and must be used when boron is depleted, e.g. in burnable poison rods.
4 Nuclides marked with 4 in the comment column have only absorption cross sections tabulated, i.e. scattering is neglected for these nuclides.
{
5 The compositions of stainless steel (ID=347), Inconel-718 (ID= 718 ) and Inconel-750 (ID=750) are in weight
(
percentage.
Nuclide 347 718 750
(
Al (13000) 0 0
0.98 Si (14000) 0.51 0.35 0
Cr (24000) 17.40 18.96 20.14
(
Mn (25000) 1.99 0.87 0.99 Fe (26000) 68.35 27.93 8.88 Ni (28000) 11.70 51.19 69.02 6
The 1/v absorber (ID=1) is normalized to 1 barn at 2200 m/sec.
The unit absorber (ID=2) has a constant 1 barn absorption r
L cross section.
The unit scatterer (ID=3) has a constant 1 barn in-group scattering cross section and zero absorption.
[
The atomic weight for nuclides 1, 2 and 3 is also unity.
( - _
\\
3.
s TABLE 1.2 Nuclides in the CASMO-3G Neutron Libraries (Continued) r L
7 Shielded cross sections for special geometric configurations are tabulated for Rh, Ag, Cd, In and Hf.
c
[
The following convention is used for the ID numbers:
Third digit = 3 corresponds to RCC in 15x15 PWR
=5 BWR control blade The shielded Ag-In-Cd cross sections for 15x15 and 17x17 bundles differ so little that 47400, 48400 and 49400 can be used for both lattices.
ID=45001 marks Rh cross sections for a Rh detector.
{
8 Fission products which are not separately treated are lumped together into two pseudo nuclides; one r
(
non-saturating (ID=401) and one slowly saturating (ID=402) lumped fission product.
(
l
[
[
[
[
(
{
{
{
2s.
f
0 8
?
Table 1.3 c'
Energy Group Structures for the 10 and 18 Group CASMO-3G L
Ganuna Libraries I
(
Upper Energy Energy 10-18-Boundary Width Group Group (MeV)
(MeV) 1 1
10.00 2.00 2
8.00 1.50 3
6.50 1.50
(
4 5.00 1.00 2
5 4.00 1.00
[
6 3.00 0.50 7
2.50 0.50 3
8 2.00 0.33 9
1.67 0.33 10 1.33 0.33 4
11 1.00 0.20 5
12 0.80 0.20 6
13 0.60 0.20 7
14 0.40 0.10 8
15 0.30 0.10
(
9 16 0.20 0.10 10 17 0.10 0.05 18 0.05 0.05
{
[
[
l l 2090R/2.20
(
s F-Table i.4 Nuclides in the CASMO-3G Gamma Library Nuclide-ID No.
Nyclide ID No.-
H 1001 U-235
'92235 B
5000 U-236 92236
(
B-10 5010 U-238 92238 0
8000 Pu-239 94239 Cr 24000 Pu-240 94240 Mn 25000 Pu-241 94241
(.'
Fe 26000 Pu-242 94242 Ni 28000 LFP 401 Zr-2 302 HFP 402 r
[
Gd 64000 Notes:
-1.
Data for 64000 are used for ID No. <300-7899, i.e., for Gd-203.
2.
LFP and HFP are light and heavy fission product data and are used for all fission products.
l l
(
(
(
l
{
l 2090R/2.20
(
{
s e
FIGURE 1.1 Flow Diagram of CASMO-3G r
L 1
r Restart file i
i InW1 r
Tape 61 g
[
}
___y Resonance calculation
~
I Data library g
Ta 10 _g I
Gd library Macroscopic cross section depe11/ Tape 13j 4
Micro group calculatbn r.
PWR Condense tc rnacro groups
[
Homogenizu to macro regions l
o Macro [roup calculation in annutar geometry f
o Condense to max 12 groups Calc. cross section for 2D regions
=
ir g
.5 Control rod calc.
(
CROCOP d
Two dimensional transport f
cateutstion. COXY l
Fundamental mode cate.
[
--- - a f Punch file Two dimensional F ew group constants
-g Tap 11
(
diffusion theory Reion retn DlXY o
Burnup corrector Zero burnup o
Numoer densities i
B urnup predictor I
Eno f
I FIGURE 1.2 Flow Chart of Resonance Calculation f
FLURES Collision probabilities
[
i f
[
RESPAR Parameters for the equivalens theorem P,in loop 3r RESABS Effective cross sections for uniform pin cell lattice P,n cell i
U DANSO Dancoff factors
[
l
?
Assembly
[
U DANCOR Position dependent I
effective cross section U
[
STOP t
{ l f
FIGURE 1.3 Flow Chart of Microgroup Calculation Define average f uel pin cell Fuel pin cells i f Coolant Collision probabilities for cylindricalized pin cell Can Fuel x
y 3
Correction of CP for the Homogenized gap c
[
L 3
influence of water gap Coolant I
00 o
OOO o
0000
-Qn
(
OO h
Solve the neutron balance eq in 4 COOO puei regions and micro energy groups ooo 00
(
R i t Detemine various types of pin cells Absorber rods and water holes
' f Calculate crou sections for buffer zones Homogenized butfer zone j
Coolant C-"
Collision probabilities for cylindricalized Can absorber pin cell ( or water hole )
+
y surrounded by buffer zone Absorber
,g b
h
[
I Solve neutron balance eq in up to "
y7 5 regions and micro energy groups
<a
{
i f Homogenization of pin cells and condensat',- n to macro groups
. f
FIGURE 1.4 Example of Geometry in Macrogroup Calculation
(
1 O 0 0 0 0 0 0 0
[
O O O O O O OlC o w
0 W,- pin O O @ @ @ @ O
(
O O @ 8 @ @ O O e rug-pin O O @ @ @ @ O O O O @ @ @ @ O O 0 0 0 0 0 0 0 0 O O O O O O O O messesenesursemeni
/
\\
Narrow water gap Wide water gap
(
0 I
h l
j I
J 4
I outer water /
horregeruted g
pg, control rod y
9,p box homogenized fuel WI layers ber fue ho*0 9'n't e outer water inner water gap inner watet gap
[
[...
(
FIGURE'1.5 r
Heavy Nuclide Chains in CASHO-3G J
1.
U234 + U235 + U236
- Np237 + Pu238
(
U238 + U239 + Np239
- Pu239 + Pu240 + Pu241 + Pu242
- Am243 + Cm244 2.
(25 %)
Am242m
- Am243
- Cm244 3.
U238 + U239
- NP239
- Pu239 + Pu240 + Pu241 + Am241 (75 %)
cm242
- Pu238 4.
U238 + U239 + Np239
- Pu233 + Pu240 + Pu241 + Am241
+
{
(n,2n)
Np237 + Pu238 5.
U238
(
[
(
[ r
s s
FIGURE 1.6 Pission Product Chains in CASMO-3G 1.
Kr83 5
2.
Rh103 3.
Rh105 4.
Ag109 5.
Xe131 6.
Cs133
- Cs134 7.
1135
- Xe135
- Cs135 8.
Nd143 9.
Nd145 (52.77 %)
Pm148
- Pm149
- Sm149
- Sm150
- Sm151
- Sm152
- Eu153 *
- 10. Pm147
- Eu154
- Eu155 (47.23 %).
Pm148m
- Pm149
- Sm149
- Sm150
- Sm151
- Sm152 *
- 11. Pm147
- Eu153
- Eu154
- Eu155
- 12. Pm147
- Sm147
(
- 13. NSFP (non saturating F.P.)
- 14. SSFP (slowly saturating F.P.)
A
{
[
( f
FIGURE 1.7 Flow Chart of MICBURN s
1 Input k
ir Resonante Data Ubrary Calculation Tape
't WatfoSCopic Cfots $9ClionS it Pin Cell Calc.
SVff er Ione
<r Homog enitation of buff e r 2cne i,
Define
[
macro tegions
' r
(
Transport Calculation
't Flux distribution in mitto regions C
-r Burnup Calculation END 1
[
.u.
(
r
FIGURE 1.8c Actual Control Rod Configuration s
iT}
h Stainless Steel y
central Structure se j
Stainless Steel Stainless Steel Sheet Clad y_ \\_ /
OSGO N'////////c GGr/////
BC 3
3 h
[
c
[
FIGURE 1.8b
(
Representation of Control Rod Wing in CASMO-2 steel or
(
(
steel and water absorber (B;CJ
./
V
\\
i.i:j:-
N. I.;.
0..l.i.
ib.Ei.
[
[ r
M l
FIGURE 1.9 Example of BWR Cell Geometry in the 2-D Calculation l
Steel Cc. trol,od
) < Wide water gap
! x x
Fuel pin cell y
x N
(
i e., mi.,,8, s
l
, BOX Wall M
p t
s
[ g f
s F
L FIGURE 1.10 p
Examples of Ph'R Cell Geometry in the 2-D Calculation An octant of a PWR assembly containing 15 :15 pin cell positions.
Center of the assembly N
Water hole a
-< Fuel pin cell B A-tod N
Water gap
<x
(
An octant of a PWR assembly containing 14x14 pin cell
{
positions and large water holes
(
Center of the assembly Sh Fuel pin cell d
Water hole
\\
(
yWa,e, ga, s
c
( --
s w
FIGURE 1.11 Flow Diagram for 2-D Calculations h
[-
Control and input routines 1/
Calculations of escape and transmiss. probabilities a
f Flux guess consistent with calculated fission source Outer and inner iterations for epi-thermal groups. Test of convergence.
v Calculation thermal Fundamental mode calculation and
?
normalia. for thermal groups sources ss -
1/
Fundamental mode Outer and inner itera-(
calculation and tions for thermal groups-normalia. for Repeat 2 or 3 times.
Repeat for thermal groups 1 st outer iteration
(
( -
s FIGURE 1.12 Calculation of G-Factors with DIXY L
Is DIXY 2-D diff.th, e
'k,h-4 Homogenize 4
'x,h *
- cell
. cell h
u E
v w
k, Fund. Mode g
with B
=B from CASMO k,,ff eff x
U y
, cell,FM f
h
[
g M
A
, cell,TM
{
FM h
e,h
, cell
,k,h k
h Absorption rates a
DIXY-COXY NO G-factors Comparison Agree?
,Yes Output
(
( __-
7 s
2.0 VALIDATION CALCULATIONS
(
L This section presents the results of the validation benchmark cases r'
that were conducted. The major reasons for this validation project were:
L To verify the code and associated libraries were working correctly.
To test important features by independent paths.
To benchmark the code against existing measured data, To benchmark the code against existing methods, and To become familiar with input, options and defaults.
(
The major areas of testing encompassed by validation calculations ares
(
The nuclear data libraries.
5 Isotopics,
{
Treatment of neutron transport and spectrum in pin cells.
(
Treatment of strong absorbers,
[
The 2-D bundle transport calculation - COXY, Depletion Calculation.
Diffusion Calculation DIXY, and Gansna transport.
The discontinuity factors and baffle reflector calculations of CASMO-3G are not addressed in this document. These options will be covered in a later
(
document, which will be a report on SIMULATE-3 using CASMO-3G data. 2090R/2.20 f
~'
'2.1 Coniparisons With Uniform Pin Cell Lattice Criticals i
N The eigenvalues from the CASMO-3G analyses of 74 uniform rod criticals cre shown in Figures 2.1 through 2.7.
These comparisons constitute an integral verification of the following:
The nuclear data library (particularly uranium, oxygen and water cross sections)
Treatment of neutron transport and spectrum in pin cells including:
o Resonance integral calculations o
Slowing-down treatment Spatial transport within the pin cell o
(
The following pin cell criticals were performed:
39 NSLE( 6) criticals with variations in pitch, enrichment, and soluble boron.
24 KRIT2 0) criticals with variations in moderator temperature and soluble boron, and
[
11 ESADA(1 ) criticals with variations in plutonium isotopics, pitch and soluble boron.
The data compared are the multiplication factors (K-effective) as a function of enrichment', lattice pitch, critical buckling, soluble boron and water-to-metal ratio. The comparisons presented are for light water, uranium dioxide criticals in both aluminum and stainless steel clad. The enrichment varied from approximately 1.30 to 4.90 atom percent U-235.
Lattice pitch varied from approximately 0.6 to 2.5 cm; the critical buckling varied from 17
-2 to 100 m The soluble boron varied from 0 to 3400 ppe and the water to
. 2090R/2.20 r
metal ratio from approximately 1.0 to 4.0.
The CASMO-3G recults are from unit F
cell calculations using the measured critical bucklings. Figures 2.1 through 2.7 show the multiplication factor versus the selected parameters mentioned cbove. The pin cell critical statistics are shown in Table 2.1.
The average multiplication factor for all 74 criticals is 0.9954 1
.0088 for the 40 group and 0.9959 2 0080 for the 70 group library. This shows that there is no significant difference between the 40 group and 70 group libraries. The greatest variance comes from the NS&E criticals and is probably because these cases had the greatest variation in measurement uncertainties. The ESADA mixed oxide criticals require a macrogroup calculation in addition to the microgroup calculation in order to produce K-effective near unity. The macrogroup calculation is necessary for mixed oxide fuel and for lattices with large pitches (greater than 2 cm). No significant trends with pitch, enrichment, soluble boron, water to metal ratio, buckling are indicated in Figures 2.1 to 2.7.
{
2.2 Comparisons With Measured Yankee Isotopics The comparison of calculated uranium and plutonium isotopics as a function of burnup with the values measured during the Yankee Core Evaluation Pregram(
} constitutes ir.tegral verification of all the parts of the CASMO-3G method discussed in the section on unifora, pin cell criticals, as well as the following:
[
o Additional parts of the nuclear data libraryt Temperature dependence of resonance integrals
- Temperature dependence of other cross sections Plutonium cross sections
(
o Two-dimensional transport theory calculation (COXY) o Depletion calculation 2090R/2.20
The data presented here represent measurements of fuel rods in perturbed, intermediate and asymptotic reactor neutron spectra. The perturbed i
neutron spectrum occurs in the vicinity of the water slots which surround the cruciform control rod positions and near the core reflector. The asymptotic neutron spectrum is found in those regions of the core which are well away from and unaffected by the perturbations mentioned above. The intermediate spectrum is in those fuel regions between the perturbed and asymptotic regions. The isotopics were measured over a broad range of burnup from approximately 1,200 to 31,000 mwd /Mtu.
The CASM0-3G calculation modeled an entire Yankee Rowe Core I assembly and rirealoy follower region. This allowed for the explicit representation of all three neutron spectra regions previously mentioned.
Isotopics produced from the CASMO-3G depletion were then compared to measured data.
The comparisons for U-235 U-236 and U-238 are presented in Figures 2.8 through 2.10.
The remaining comparisons for Pu-239/U-238 Pu-239, Pu-240,
(
Pu-241 and Pu-242 are found in Figures 2.11 through 2.15.
The calculated results compare well to the measured results in the various reactor neutron
{
spectra. The major task attempted in this study was the modeling of the perturbed region. As the isotopic results demonstrate, this was accomplished.
2.3 Comparisons With Measured Zion Isotopics The comparison of calculated uranium, plutonium, and transuranic isotopics at selected burnups to those measured values from the Zion Hot Cell Examination Study (19,20) provides additional integral verification of all parts of the CASMO-3G method discussed in Section 2.2.
The Zion benchmark also provides a verification for a contemporary Westinghouse PWR 15 x 15 assembly and for extended burnup ranges.
The data presented here represent uranium and plutonium atom percents, and americium and Curium isotopic ratios to Pu-239 for five different pin locations. These pin locations were in two different assemblies and represent locations in an assembly removed from a water hole (Rod 624), adjacent to a 2090R/2.20 i
s li water hole (Rods (42, 616, and 614), and diagonally adjacent to a water hole p
(Rod 699). Burnups range from 23,471 mwd /Mtu for Rod 616 to 51.754 mwd /Mtu for Rod 614 and represent insertion in the core from one to four cycles, i
The calculated versus measured results are provided in Table 2.2.
They show excellent agreement for the uranium and plutonium isotopes. The RMS difference for all the uranium atom ratios is less then 0.04 percent, and for the plutonium ratios less than 0.5 percent. The transuranics compare less well, but still well within the measurement uncertainty considering the difficulty in measuring such small concentrations.
2.4 Quad Cities Gansna Sean Comparisons The Quad Cities benchmark consisted of reproducing gamma scan results(
using CASMO-30.
This test problem demonstrates the accuracy and validity of the
{
following parts of the codet o
The nuclear data library (neutron cross section and depletion chain data).
o Treatment of neutron transport and spectrum in pin cells.
Calculation of strong absorbers (Gadolinium depletion using o
MICBURN-3).
I o
The 2-D bundle transport calculation - COXY.
Depletion calculation and isotopics.
o
[ 2090R/2.20 7
m k
The fuel bundle of interest is an 8 x 8 bundle of Type 4 as described
(
in Reference 22.
This bundle was chosen for its relatively flat radial power profile which makes it ideal as a lattice benchmark.
It also contains gadolinium bearing rods which require the use of MICBURN-3 for generation of
{
gadolinium cross sections and, hence, also serves as an indirect validation of MICBURN-3.
The,gama scan data involved measuring relative La-140 activity on a pin-by-pin basis within the bundle. La-140 is a daughter of Ba-140, which itself is a fission product. The Ba-140 distribution (and, therefore, the proportional La-140 distribution) is directly proportional to the power distribution within a month or so before the scans were done. All measured values were adjusted backwards to the date of the shutdown of Cycle 2 removing decay effects of the La-140 concentrations. The gama scans were compared at four axial locations in the bundle. These locations are 15, 56, 93, and 129 inches.
The benchmark consisted of depleting the fuel bundle with CASMO-3G at three void history conditions: O percent, M percent, and 70 percent.
(
Fission reaction rates from these CASMO-3G runs were used to determine the relative La-140 concentrations for a given axial level.
The procedure used for calculating the La-140 concentrations at a given level was to obtain the fission reaction rates from the CASMO-3G cases which bound both the void history and the exposure values for the level. The reaction rates were obtained for all pins and for the nuclides U-235. U-238,
(
Pu-239, and Pu-241. These reaction rates were used to calculate the absolute La-140 concentrations at the two bounding void history statepoints and at the
(
two bounding exposure statepoints using the formula La-140=nhy Y(n) x FRR(n) where Y(n) = the La-140 yield for nuclide n.
{
FRR(n) = the fission reaction rate for nuclide n.
n = the nuclides U-235, U-238, Pu-239, and Pu-241. 2090R/2.20 I
o e
s-The absolute La-140 concentrations for each exposure and void history
[
trere then converted to relative concentrations by normalizing to the average.
h Finally, the relative La-140 concentrations at each axial location were determined for the specific exposure and void history by linear interpolation. Figures 2.16 through 2.19 provide a comparisor. of the CASMO-3G/MICBURN-3 results versus the measured results. Note good agreement at all levels with the highest RMS difference of 2.070 at the 56 inch level.
2.5 Comparisons with DIXY Generated Diffusion Theory Cross Sections The examination of the performance of the DIXY subroutine provides integral verification of the following features of the CASMO-3G codet o
Diffusion theory calculation (DIXY),
(
Calculation of macroscopic ab erption cross-section G-factors, and o
PDQ diffusion theory cross section edit.
(
o Thir, benchmark is being conducted to verify DIXY because PDQ will be used as a benchmark for the SIMULATE-3 code in a future report.
In order to validate the DIXY subroutine of the CASMO-3G code, two Combustion Engineering design assemblies were examined. This design was
(
aelected due to the large water holes which exacerbate the G-factor application.
A 3.0 w/o U-235 assembly and a 3.0 w/o U-235 with eight burnable shims assembly were examined. They are designated CE-0 and CE-8, respectively.
Figure 2.20 illustrates the assembly layout for these assemblies. Cross sections used in the DIXY routine were also used in a PDQ model.
Two applications of the DIXY routine were examined. They weret 1.
DIXY results versus PDQ results without G-factors applied, and 2.
DIXY results versus PDQ with G-factor applied. [
2090R/2.20
s L
A comparison was made of K-infinity (or K-effective, since there is I
sero buckling). Table 2.3 contains the K-infinity results for DIXY versus PDQ with and without G-factors. The C0XY results are considered the truth calculation. The results demonstrate that the DIXY calculation matches PDQ with excellent agreement. Additionally, the effect of the G-factors applied is significant in achieving transport theory (C0XY) results. By applying these G-factors, the difference in K-infinity between DIXY and PDQ, or DIXY cnd COXY can be reduced by orders of magaitude versus the no G-factor case.
Table 2.4 is presented to further illustrate the effect of the G-factors in matching diffusion theory to transport theory.
In the analysis, CASMO-3G was instructed to calculate G-factors for the guide tube areas for the CE-0 fuel and guide tube and burnable shim areas for CE-8 fuel. As Table 2.4 illustrates, the initial relative error in the DIXY absorption rate (no G-factors applied) is reduced an order of msgnitude when G-factors are cpplied.
(
For the CE-0 fuel, the G-factors in Table 2.4 indicate that thermal cbsorption calculated by diffusion theory in the guide tube is too small, hence, the K-infinity from the DIXY calculation in Table 2.3 is higher than the COXY result. By increasing the thermal absorption by 18 percent, the DIXY K-infinity effectively matches COXY K-infinity.
The CE-8 case involves the use of G-factors applied to two regions, the shim and the guide tube. The guide tube behavior is similar to that witnessed for the CE-0 fuel. However, shim G-factors indicate that diffusion theory
(
(DIXY) is overpredicting thermal absorption. Since the fast and thermal shim absorption rates are roughly three times larger than the guide tube absorption
(
rate, the shim effect is overriding. Therefore, the DIXY K-infinity is low when compared to COXY. By decreasing the shim therm 1 absorption by 24 percent, however, the DIXY K-infinity is raised to match COXY.
2.6 Other Validation Cases Other validation cases have been performed by Studsvik Energitenik using the 70-group library. These cases are: 2090R/2.20
1 F
L o
KRITZ critical experiments. These consist of KRITZ-1 and KRITZ-2 cores, which are pin cell cores, KRITZ-3 cores which contain PWR assemblies, and KRITZ-4 cores which contain BWR assemblies with two percent Gd 0 burnable poison in selected fuel rod 23 locations. Data for these cores are presented in Tables 2.5 and 2.6.
The KRITZ-3 and KRIT2-4 core laydowns are shown in Figures 2.21, 2.22, and 2.23.
K-effectives provided in Table 2.7 and calculated to measured fission rate ratios for selected cores are provided in Figure 2.24.
o Five B&W critical experiments performed at room temperature. The first core is a pin cell lattice, and the other four consist of 3 x 3 PWR assemblies, each with 14 x 14 pins. All five cores have a U-235 enrichment of 2.46 percent. The K-effectives from these experimenta are presented in Table 2.8.
o Four pin cell cases, consisting of a BAPL-UO T6 pin cell core 2
16 cm in radius with 1.45 w/o enrichment, a B&W B20 pin cell core 31 cm in radius with 2.46 w/o enrichment, an ESADA A-1 pin cell core 22 cm in radius containing natural uranium and two percent Pu0, and an ESADA C-18 two region pin cell core with radii 15 cm 2
and 26 cm.
Both regions in the ESADA core have natural uranium and l
two percent Pu0. The Pu-239/Pu-240 enrichments are 92 2
percent /8 percent and 72 percent /24 percent for Regions 1 and 2, respectively. These cores and their calculated K-effectives are sumarized in Table 2.9.
o Twenty-one pin cell fundamental mode experiments consisting of eight BAPL-UO cases, tw TRX cases, and thirteen ESADA cases.
2 Th'e U-235 enrichments ranged from 0.7 percent to 1.3 percent.
Tt e ESADA cases consisted of 0.7 w/o U-235 with 1.8 w/o enriched Pu-239. The pin radii varied from 0.49 cm to 0.76 cm, the pitch ranged from 1.5 cm to 3.5 cm, ano the boron concentrations were between 0 and 330 ppm. These experiments are sumarized with their calculated K-effectives in Table 2.10. 2090R/2.20 f.
s I
These cases covered a wide range of core designs, including cold pin cell lattices, hot and cold Bh1 and PWR lattices, mixed oxides, and Gadolinia rl burnable absorbers. The results show no trend in calculated K-effective versus any parameters such as pin radius and pitch, enrichment, temperature, boron concentration, and buckling. The calculated K-effective all compared closely to unity within the range of experimental uncertainty for each case as seen in Table 2.11.
In addition, two Ph1 and six Bh1 fission rate distributions were analyzed from the KRITZ cases, and the deviations from the measured values were also within the experimental uncertainty.
These validation cases provide a vt,rification of the nuclear data library, calculations on unit cells including the fundamental mode calculation, calculation of strong absorbers, and 2-D COXY calculation.
A series of gamma transport calculations were carried out by
(
Brockhaven(20 and Studsvik(2H to test the gamma methodology used in CASMO-3G. These cases aret
(
A gansna transport calculation benchmarked against SAM-CE Monte o
Carlo calculations conducted by BNL. This benchmark tested the gamma flux calculation performed by CASM0-3G for a typical Bh1 lattice and detector design. The results demonstrated the gamma module in CASMO-3G to be accurate to a lo error of 5 to 10 percent with e. total uncertainty of the total response (energy group integrated) of approximately 3 percent.
The total gansna detector response was benchmarked by Studsvik
{
o against measured data from an operating BWR, Hatch 1(
Gansna TIP responses were compared to measured data using detector response functions calculated by CASMO input into a three-dimensional nodal model of the Hatch core. These detector functions are basically the ratio of detector response (i.e.,
current) to the relative assembly power of the four assemblies
(
surrounding the detector. A total of 11 TIPS which were surrounded by bundles that were later ganem-scanned were analyzed. These
(
1,undits ranged in void fraction from 0 to 70 percent and in (
2090R/2.20 f
s I
L exposure from 5 to 20 mwd /ks, and some also included the presence f
of control rods. The RMS error, in predicting relative assembly power, for all bundles was 2.6 percent, which is within the le uncertainty for the measured power. No trend with void fraction, exposure, or control rods was noted. These calculations were performed using the gamma transport method along witit CASMO-1G.
This data is proprietary to EPRI and has not been released.
Therefore, to verify the CASMO-3G gamna transport calculation.
Yankee Atomic perfcrmed a series of gansna transport calculations using CASMO-30. These calculations were compared to Studsvik
(
results for CASMO-1G applied to the Hatch 1 assembly. The total samma responses versus exposure and void matched to within 1%.
Therefore Yankee concludes the CASMO-3G gama transport is verifled by the previously mentioned CASMO-1 benchmarks.
These benchmarks verify the validity of using the gama transpo *t calculation capabilities within CASMO-3G to calculate samma detector responses.
(
[
[
[
(
(
(
( 2090R/2.20 f
s.
~
Table 2.1 The Pin Cell Critical Statistics h
K (40 Group)t K
(70 Group)t criticals off eff NS&E_
0.9939 :.0119-0.9945;g.0120 KKITZ 0.9955 1 0023' O.9963 3 0023 ESADA*
1.0007 !'.0033 0.9997 !.0052 All Cases 0.9954 1 0088 0.9959
.0000
(
- Mixed oxide fuel.
{
t mean and standard deviation.
(
(
(
(
(
I L
L I
' 2090R/2.20 l
f
n m
m m
m.
m m_
r--
m r--
m_
m m
g3 m
1
- 7____,
i TABLE 2.2 SION ISOTOFICS - CASMO-3G CALCULATED TS. MEASURED BURNUF CASMO U-234 U-235 U-236 U-238 FU-239/U-238 (E 10-3) 200 (MWD /MT)
FIN O CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF 616 23471.
22
.018
. 018
.000 1.307 1.386
.079
.375
.370
.005 98.299 98.226
.073 4.881 4.917
.036 642 37295.
22
.014
.016
.002
.451
.721
.870
.470
.464
.006 98.865 98.799
.066 S.104 5.081
.023 699 42915.
23
.013
.014
.001
.510
.536
.026
.487
.490
.003 98.991 98.960
.031 5.183 5.074
.109 624 49879.
26
.011
.013
.002
.383
.370
.013
.499
.503
.004 99.106 99.114
.008 5.211 5.149
.062 614 51754.
22
.011
.014
.003
.260
.308
.048
.504
.507
.003 99.226 99.171
.055 4.974 4.883
.091 RMS DIFFERENCE
.002
.054
.004
.053
.072 l
l SURNUF CASMO FU-238 FU-239 PU-240 FU-241 FU-242 l
ROD (MWD /MT)
FIN O CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF 1
l 616 23471.
22
.861
.840
.021 62.823 63.450
.627 21.752 21.348
.404 11.703 11.563
.140 2.861 2.800
.061 l
642 37295.
22 1.990 1.982
.008 51.367 51.849
.482 25.663 25.655
.008 14.303 13.894
.409 6.677 6.620
.057
[
699 42915.
23 2.462 2.600
.138 48.758 48.316
.442 25.261 26.622
.361 14.565 14.190
.375 7.953 8.272
.319 l
e 624 49879.
28 3.062 3.491
.429 46.326 44.986 1.340 26.567 27.430
.863 14.734 13.944
.790 9.312 10.149
.837 l
614 51754.
22 3.396 3.539
.143 43.815 43.854
.039 27.262 27.333
.071 14.555 13.961
.594 10.973 11.313
.340 l
e RMS DIFFEREWCE
.212 724
.457
.511
.430 l
l l
BURNUF CASMO AM-241/FU-239 AM-243/PU-239 CM242/PU-239 CF244/PU-239 RCD (MWD /MT)
FIN 8 CASMO NEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF CASMO MEAS DIFF 616 23471.
22 3.67E-03 4.75E-03 -1.08E-03 5.90E-03 3.33E-03 2.65E-03 1.10E-03 9.75E-04 1.27E-04 1.06E-03 9.29E-04 1.31E-04 642 37295.
22 7.10E-03 7.80E-03 -7.04E-04 2.88E-02 1.90E-02 9.83E-03 3.50E-03 3.32E-03 1.75E-04 9.48"J-03 7.59E-03 1.89E-03 699 42915.
23 8.06r-03 9.59E-03 -1.53E-03 4.14E-02 2.39E-02 1.75E-02 4.44E-03 4.32E-03 1.17E-04 1.62E-02 1.45E-02 1.70E-03 624 49879.
28 9.0*E-03 1.51E-02 -6.05E-03 5.81E-02 4.41E-02 1.40E-02 5.49E-03 6.22E-03 -7.33E-04 2.71E-02 2.62E-02 8.56E-04 RMS DIFFERENCE 3.19E-03 1.23E-02 3.87E-04 1.34E-03
-s i
e l"
Table 2.3 I
DIXY K-Effective Comparisons For CE Assemblies L
Mp*
CASMO-3 CASMO-3 Difference Case COXY DIXY pg From COXY CASMO-3 PDQ l
CE-0 No G-Factors 1.23287 1.23720 1.23720 0.284 0.285 CE-0 W/G-Factors 1.23287 1.23317 1.23318 0.020
-0.020 CE-8 No G-Factors 1.11624 1.09715 1.09719-
-1.559
-1.559 CE-8 W/G-Factors 1.11624 1.11699 1.11698 0.060
-0.059 0 Mp = (1/K - 1/K )
- 100 g
2
{
l
(
(
(
(
(
( 2090R/2.20 f
L Table 2:4 DIXY G-Factors for CE Assemblies L
(
Initiale Final Relative G-Factor G-Factor Relative Case Difference Grou.n 1 Group 2 Difference _
CE-0 Guide Tube
.17097
.966228 1.18189
.00455 CE-0 Water cap
.17097
.996330 1.02988
.00455 CE-8 Guide Tube
.20402-
.969943 1.19376
.00464 CE-8 Shim
.20402
.980833
.75787
.00464
(
CE-8 Water Gap
.20402
.997647 1.03172
.00464
(-
- Absorption Rate Difference COXY vs. DIXY
(
N
(
(
(
(
(
( 2090R/2.20
(
f
Table 2.5
(
Data for the KRITZ Series of Critical Cores r
L Enrichment Pitch Pin Radii Series (1)
_(em)
(em)
(
K1 1.35 1.80 0.62 K2 1.86 1.48 and 1.63*
0.53 K3 3.00 1.40 0.50
{
K4 2.60 1.69 0.50
(
(
CFor K2 2:1 and 2:13, respectively.
(
(
(
(
(
(
(
( 2090K/2.20 f
k 4
Table 2.6 peseription of KRITZ Critical Cores Core
{
K3 U-W1 Sixtein 1 x 1 water holes, including guide tubes in the central assembly.
K3 U-CR1 Same as U-W1 but with Ag-In-Cd control rods inserted in the guide tubes.
K3 U-W2 Five 2 x 2 water holes in the central assembly and three in the peripheral ones.
(
K3 U-CR2 Same as U-W2 but with boron-carbide control rods inserted in the central water holes.
K4 2:1 All assemblies unpoisoned.
K4 2:2 Same as 2:1. but with a control rod cross in the central water gap.
(
K4 215 Same as 2:1. but with seven Gd rods in each of the four central assemblies.
(
K4 3:1 All assemblies unpoisoned.
K4 3:2 Same as 3 1. but with five Gd rods in each of the four central assemblies.
K4 3:5 Same as 3:1. but with three Gd rods In each of the four central assemblies.
K4 4:1 Same as 3:1. but with !ive Gd rods in every second of the assemblies, in checker board configuration.
K4 4:1 Same as 3:1. but with three Gd rods in every second of the assemblies, in check board configuration.
(
K4 5:1 Same as 3:1 but with three Gd rods in each assembly.
(
(
( 2090R/2.20 f
L Table 2.7
(
Calculated K-Effectives for KRIT2 Cores Boron e
L Temperature Concentration K-Effective Core (K)
(ppm)
(CASMO)
(
K1 200 180 0.99869 480 180 0.99878 K2 2:1 290 220 1.00000
(
520 30 1.00072 K2 2:13 290 450 0.99887
[
520 280 0.99895 K3 U-WH1 300 1100 0.998SO 500 1000 0.99926
(
E3 U-CRI 300 700 1.00027 500 500 0.99876
[
K3 U-VH2 300 1100 1.00031 500 1000 1.00024 K3 U-CR2 300 700 0.99970 500 500 0.99953 K4 2:1 300 300 1.00064 K4 2:2 300 100 1.00018 K4 2 5 300 50 1.00014 K4 3:1 300 300 1.00104 500 350 1.00155 K4 3:2 300 100 1.00164 500 50 1.00147
[
K4 3:5 300 200 1.00180 1
500 200 1.00152 K4 4: 1 300 100 1.00067
(
500 50 1.00036 K4 4:2 300 200 1.00127 K4 5:1 300 50 1.00034 500 0
0.99932 2090R/2.20 f
+
Table 2.8 Swnmary of B&W Cores L
Boron p
Concentration K-Effective L
C_o re_
(ppm)
(CASMO) o I
O 1.00026
(
II 1040 1.00145 III 760 1.00291 IX 0
1.00037 X
140 1.00240
(
[
[
[
[
{
(
[ 2090R/2.20
(
Table 2.9
- Sumnary of Data of the T6. B20, and ESADA Cores Boron Pin Radii Pitch Concentration Core (cm)
(cm)
(ppm)
K-Effective
-BAPL-UO T6 0.49 1.45 0
1.00132-l B&W B20 0.52' 1.51' 1670 1.00082 ESADA A-1 0.64 1.75 0
0.99937 f
ESADA C-18 0.64 1.75 0
1.00080 t
l f-h s 2090R/2.20 f
s
~
Table 2.10 CASMO-3G Fundamental Mode K-Effectives for Different F-
[
Pin Cell Criticals Pin Boron 2
Radii Pitch Enr Concentration
'B Pin Cell (cm)
(cm)
(7.)
(ppm)
(m- )
K-Effectlye BAPL-UO2 T1 0.76 2.1 1.3 0
28 0.99424 BAPL-UO2 T2 0.76 2.2 1.3 0
30 0.99608 BAPL-UO2 T3 0.76 2.3 1.3 0
29 0.99528 BAPL-UO2 T4 0.49 1.4 1.3 0
25 0.99591 BAPL-UO2 T5 0.49 1.5 1.3 0
25 0.99565 BAPL-UO2 T6 0.49 1.4 1.3 0
33 0.99888 BAPL-UO2 T7 0.49 1.5 1.3 0
35 0.99736 f
BAPL-UO2 T8 0.49 1.7 1.3 0
34 0.99705 TRX 1 0.49 1.7 1.3 0
57 0.99228
(
TRX 2 0.49 2.0 1.3 0
55 0.99137 ESADAl A-1 0.64 1.8 0.7 0
69 0.98827
(
ESADAl A-3 0.64 1.9 0.7 0
90 0.98295 ESADAl A-4 0.64 2.5 0.7 0
105 0.99873 ESADAl A-6 0.64 2.7 0.7 0
98 1.00044 ESADAl A-7 0.64 3.5 0.7 0
50 0.99707 ESADA1 A-8 0.64 1.8 0.7 260 63 0.99651 ESADAl A-9 0.64 2.5 0.7 260 84 0.99490 ESADAl A-10 0.64 1.8 0.7 530 58 0.99517
{-
ESADAl A-11 0.64 2.5 0.7 530 63 0.99571 ESADA1 A-12 0.64 2.5 0.7 0
80 0.99737 ESADAl A-13 0.64 2.7 0.7 0
73 0.99763
[
[
1 nrichment is 0.7 w/o U-235, 1.8 w/o Pu-239 for tne ESADA criticals.
E
[
[ 2090R/2.20 r
i 9
Table 2.11 I
-K-Effective Statistics For CASMO-3G L
K-Effective
. Case Description
[.
L 1.0018.00102t Cold pin. cells (9 cases) 0.99948.00107 Hot pin cells (3 cases) 1.00001!.00103 All pin cells (12 cases) 0.99977.00070 Cold PWR cores (4 cases) b-Hot PWR cores (4 cases) 0.999451 00062 All PWR cores (8 cases) 0.999611 00064 1.00086.00062
-Cold BWR cores (9 cases) 1.00084.00099 f
Hot BWR cores (5 cases) 1.00085.00073 All BWR cores (14 cases)
Cold B&W cores (5 cases) 1.001482 00118 1.00056.00105 All cold cores (25 cases)
Cold : ores which were also measured hot.(12 cases) 1.00018i.00104 1.00004.00108 1
All hot cores (12 cases) 1.00039.00107 All cores (37 cases)
(
i mean and standard deviation, k
(
{ 2090R/2.20
(
C--
FIGURE 2.1
~
CRSMO-3G PIN CELL CRIT!CRLS 40 GROUP LIBRRRY VS 70 GROUP LIBRARY K-EFFECTIVES
?
L 1.02 r
L 1.c1 -
W b
P O
o La.
1.00-o4
[
~
Ee
[
J 0.99 -
%8
[
O c
0.9s -
o - NS&E o - KRITZ s - ESRDR 0,g7 0.se 0.99 1.00 1.01 1.02 U'8
(
70 GROUP LIBRARY K-EFFECTIVE
[
FIGURE 2.2 CASMO-3G PIN CELL CRITICALS WITH 70 GR]UP LIBRARY K-EFFECTIVE VS LATTICE SPACING o - NS&E
!.De -
o - KRITZ
{
A - ESRDA 1.07 -
1.06 -
1.05 -
3.04 -
1.03 -
g 1.02-C 2 01 -
oo a 3
3
^
^
0 1.00 "o
'g a j$
oo*
g ol 0.99 -
3 g
D D
U b
0.98 -
o a
o o
0.97 -
0.96-0.95 -
0.94 -
0.93 -
C.92 -
0.91 -
0.90 1
2 3
4 LATTICE SPACING (CM) [
FfGURE 2.3 CRSMO-33 Piti CELL CRI'IICRLS WITH 70 GROUP L?BRRRY K-EFFECTIVE VS ENRICHMEtJT 3.10 3 - NSLE
- 3.09 -
o - KRITZ 1.08 -
1.07 -
[.
i.c6 -
2.05 -
1.04-(
1.c3-y 1.02 -
g 2.c2 -
y 2.00,
b C.99-l S
0.99 -
[
o.97 -
c.9s -
0.95 -
0.94-(
0.93 -
0.92 -
C.92 -
C.90 2
s 1
5 1
Et;RICHMEt;T (W%)
(
FIGURE 2.4
[
CRSMO-3G PIN CELL CRITICALS WITH 70 GROUP LIBRRRY K-EFFECTIVE VS H20/U RATIO
{
o - NSLE o - KRITZ f
a - ESRDA 1.C2 4 e
A O
]
J g y^
l w 2P b
O E
o i:
4 a
[
0 a
0.99 -
g c.9e-(
c.94 2
3 4
5 6
7 8
9 10 11 H20/U RATIO
FIGURE 2.S LRSMO-33 PIN CELL CRITICALS WITH 70 GROUP L!BRARY K-EFFECTIVE VS BCRON 1.04.
o - NSEE o - KRITZ c - ESROR j
L 1.C2 i N
'E I
a a
1*
l 2
Y oc a w
D c
E r
=
C. 98.
g
[
[
- 5~.'500 M
M 35 %
0 500 1000 1500 M
l BCRON [ PPM)
FIGURE 2.6 CRSMO-33 PIN CELL CRITICRLS WITH 70 GROUP LIBRRRY f
K-EFFECTIVES VS BUCKLIN3 1.10 1 CS ~
a - NS&E
[
1.Ce -
o - KRITZ
- r. - ESROR 3,7 _
1.06 -
1.05 -
1.04 -
1.03-g 1.c:-
p 1.01 -
a a
a 3 6
a c
o n
6 o O O
I*N
'~
.irP' -gg R
e o
o s
b 0.93 -
a o
U E
0.98 -
O a
0O 0.97 -
0.96 -
0.95 -
O 94 -
0.93-C 92 -
C.91 -
0.90 4
5 6
7 8
9 10 1
2 3
BUCKLIN3 (=10-3 1/CM21
(
7 r
L' I
L
[
FIGURE 2.7 CRSMD-3G KRITZ CRITICALS HITH 70 GROUP LIBRRRY K-EFFECTIVE VS MODERATOR TEMPERATURE 1.02 o
.8 PPM o - 46.3 PPM s - 175.0 PPM 1.01 -
w p
[
o N
I 0.99 -
[.
[-
- 0..
400 500 600 200 300 MODERRTOR TEMPERRTURE tDEGREES K)
(
[
[
[, -
W FIGURE 2.8 U-23S ATOM PERCENT VS. BURN'JP FOR YRNKEE CORE I SPENT FUEL (W/236) r 3-d 6
y 2-e p
?o o - ASYMPTOTIC SPECTRUM
~
1-x - PERTURSED SPECTRUM a - INTERMEDIATE SPECTRUM CASMO-3G ASYMPTOTIC
CASMO-3G PERTURSED 0
0 10000 20000 30000 40000 BURNUP (MWJ/MTU)
FIG'JRE 2.9 U-236 ATOM PERCENT VS, BURNUP FOR YANvEE CORE I SPENT FU"L (W/236) 0.5
..,.<9 4
O.4 -
a y
d 50.3-
- p. '
o-
,x 5
S c
E
[
to 0.2 -
N
^
o - ASYMPTOTIC SPECTRUM x - PERTURSED SPECTRUM 03' 6-INTERMEDIATE SPECTRUM o
CASMO-3G ASYMPTOTIC r
CASMD-3G PERIURSED 0.0 z
0 10000 20000 30000 40000 BURNUP (MWD /MTU) _ - _ _ - - - -- - -
FIGURE 2.10 U-238 RTOM PERCENT VS. BURNUP
~
FOR YRNKEE CORE I SPENT FUEL (W/236) 100 w
l 99 -
. * ~. -
w b
g se-0 a
g 97 -
?
D o - RSYMPTOTIC SPECTRUM x - PERTURBED SPECTRUM A-INTERMEDIRTE SPECTRUM 96 -
CASMO-3G RSYM?TOTIC
CRSMO-3G PERTURBED 95
[
O IM 22 30000 40000 BURNUP 1 MWD /MTU)
FIG'JRE 2.11 PU-239/U-238 RTOM RAT 0 VS. BURNUP FOR YANKEE CORE I SPENT FUEL (W/236) 10i-9-
~~~~~~
o s
^4 x
5 7:
x xX H
5 C
m 4.
o - RSYMPTOTIC SPECTRUM N
x 7
x - PERTURBED SPECTRUM 6
s-'
a - INTERMEDI ATE SPECTRUM A
CRSMC-33 RSYMPTOTIC N
2-'
a
/
CRSMO-3G PERTURBED 6
A T
g.
~
0 O
ICOOO 20000 30000 40000 i
BURNUP IMWD/MTU)
. [
FIGURE 2.12 PU-239 RTOM PERCENT VS. BURNUP FOR YRNKEE CORE I SPENT FUEL (W/236) i
,g gg.
h 90 -
[
Y g es-5 c-m.
5 o
252
^
E N
n:
2 o - RSYM?TOTIC SPECTRUM x - PERTURBED SPECTRUM 65 -
a - INTERMEDI ATE SPECTRUM k p '
CRSMO-3G RSYMPTOTIC CASMD-3G PERTURSED so.
ss 0
10000 20bO3 30 BOO 40000 B"JRNUS (MWJ/MTU)
FIGURE 2.13 PU-240 RTOM PERCENT VS. BURNUP FOR YRNMEE CORE I SPENT FUEL (W/2361 25 h
x xx_,,,,....-
20 -
x Q
s
{ 15 -
$ s' E
wa xV g
g 10-N o
h o - RSYMPTOTIC SPECTRUM x - PERTURSED SPECTRUM A-INTERMEDIATE SPECTRUM
'~
~
CRSMO-3G ASYMPTOTIC CASMD-3G PERTURSED 0
0 1:c00 20000 30C00 40000 BURNUP (MWD /MTU) -
k FIGURE 2.14 PU-241 RTOM PERCENT VS. BURNUP I
FOR 1RNKEE CORE I SPENT FUEL I4/236) h g
e
^**,..x a *,,_......
15 -
y 4
8 r
'.e g 10-
,s o - RSYMPTOTIC SPECTRUM
^
2 x - PERTURSED SPECTRUM s-4-
INTERMEDIATE SPECTRUM CRSMO-3G RSYM?TOTIC
^
CRSMO-3G PERTURSED 0
20000 30000
_a0000 0
10000 8'JRNUP (MWD /MTU)
[
FIGURE 2.15 PU-242 RTOM PERCEN! VS. BURNUP FOR YRN<EE CORE I SPENT FUEL (W/236) s-o - RSYM?TOTIC SPECTRUM x - PERTURSED SPECTRUM a - INTERMEDIRTE SPECTRUM g
zd*~
CRSMO-3G RSYMPTOT!C CRSMO-3G PERTURSED Ei a.
h3
[
y A
,A q
-'f,.
~
m S~
,- y
.E 1.
0 30000 40000 0
10000 20000 BURNUP (MWD /MTU) - - - - - - - - - - - - - - - - -
6 FIGURE 2.16 Quad Cities LA-140 Comparison at the 15" Level LEVEL =
15 INCHES 1.008.....HEASURED
.980.....CASMO-3
-2.778.....%
DELTA 1.013
.990 1.027
.978 1.382 -1.212 1.098
.985 NMA 1.078
.979
-1.821
.609 1.045 1.042
.947
.921 1.022 1.032
.940
.914
-2.201
.960
.739
.760 1.038 1.032
.940
.941 1.015 1.022
.930
.931
-2.216
.969 -1.064 -1.063
[
1.038 956
.921
.927
.926 NMA 1.040 948
.920
.934
.920
.193
.837 109
.755
.648 s
1.050 1.091 1.002
.956
.927
.940 1.000 1.062 1.094 999
.959
.944
.952
.983 1.143
.275
.299
.314 1.834 1.277 -1.700 1.043 1.002 1.044 1.004 1.088
.964
^
1.049 1.017 NMA 1.077 1.000 NMA 1.089
.963
.575 1.497 3.161 5.578
.092
.104
(
5.578 MAXIMUM %-DELTA
=
RMS OF THE %-DELTAS -
1.653 NMA - No Measurement ?.vaileble. _ - - _ _ - _ _ _ _.
h W
FIGURE 2.17 1
Quad Cities La-140 Comparison at the 56" Level LEVEL =
56 INCHES 1.067.... MEASURED 1.049.....CASMO-3
[
-1.687.....%
DELTA i
1.074 1.012 1.081 1.012
.652
.000 1.085 1.005 NMA 1.100
.983 1.382 -2.189 1.055 1.042
.943
.912 1.054 1.044
.936
.897 095
.192
.742 -1.645 1.044 1.007
.904
.932 1.042 1.027
.920
.905
.192 1.986 1.770 -2.897 1.038
.931
.882
.903
.898 1.044
.936
.894
.900
.886 NMA
.578
.537 1.361
.332 -1.336
{
1.091 1.083
.967
.917
.895
.910
.940 1.094 1.100
.985
.936
.915
.921
.950
.275 1.570 1.861 2.072 2.235 1.209 1.064 1.079
.990 1.020
.996 1.040 1.000 1.092 1.035 NMA 1.063 1.039 NHA 1.070
.961
, 1.205 4.545 1.216 4.317 2.885 -3.900 4.545 MAXIMUM %-DELTA
=
RMS OF THE %-DELTAS =
2.072 [
a F
b FIGURE 2.18 Quad Cities La-140 Comparison at the 93" Level
[
LEVEL =
93 INCIIES
(
1.085..... MEASURED 1.096.....cASMO-3 1.014.....% DELTA 1.101 1.014 1.114 1.032 1.181 1.775 1.105 1.015 NMA 1.114
.989
.814 -2.562 1.079 1.060
.945
.915 1.073 1.052
.939
.894
.556
.755
.635 -2.295 1.063 1.009
.913
.902 1.058 1.031
.918
.895
(
.470 2.180
.548
.776 1.040
.924
.897
.913
.876 r
(
NMA 1.046
.931
.881
.880
.865
.577
.758 -1.784 -3.614 -1.256 1.092 1.075
.969
.898
.889
.895
.913 1.111 1.100
.975
.922
.896
.899
.924 1.740 2.326
.619 2.673
.787
.447 1.205 1.090 1.000 1.015 1.002 1.035
.954 1.116 1.044 NMA 1.051 1.022 NMA 1.052
.956 2.385 4.400 3.547 1.996 1.643
.210 4.400 MAXIMUM %-DELTA
=
RMS OF THE %-DELTAS =
1.854 I
k r-L b~
L FIGURE 2.19 w
Quad Cities La-140 Comparison at the 129" Level
[
[-
LEVEL = 129 INCHES 1.107..... MEASURED 1.129.....CASMo-3 1.987.....% DELTA 1.131 1.043 1.145 1.050
[
1.238
.671 1.131
.994 NMA 1.133
.990
.177
.402 1.083 1.066
.939
.898 1.088 1.062
.937
.886
.462
.375
.213 -1.336 1.057 1.018
.916
.890
[
1.068 1.037
.913
.884 1.041 1.866
.328
.674 1.055
.926
.870
.882
.858 NMA 1.052
.924
.869
.864
.847
.284
.21'
.115 -2.041 -1.282 1.117 1.100
.968
.916
.885
.872
.918 1.128 1.110
.965
.910
.880
.882
.901
.985
.909
.310
.655
.565 1.147 -1.852 1.128 1.027 1.047 1.014 1.027
.965
(;
1.136 1.048 NMA 1.044 1.011 NMA 1.040
.938
.709 2.045
.287
.296 1.266 -2.798 2.045 MAXIMUM %-DELTA
=
RMS OF THE %-DELTAS =
1.151 r
r a
FIGURE 2.20 Assembly Layout for CE Assemblies Used in DIXY Validation I
X X
X X
X X
X X
0 SHIM ASSEMBLY 8 SHIM ASSEMBLY X - DENOTE SHIM
[
[
1
s
.dt FIGURE 2.21 Pin Layout of'KRITZ-3, U-WH1 Core l
5 center
!y IIIII IIIII i
l I
i l
Q I
I I
l l
l
_l' NOTE: Shaded Areas are Water Holes f
v' w
Pin Layout of I Z-3, U-WH2 Core 1
[
W i
i llI III I
I ll lll lll l
l li
___d l:
!!Y!
[
[
NOTE:
Shaded Areas are '
j jlj j
water anes II III I
II III I
II III I
II III L
m F
FIGURE 2.23 Assembly Layout of the KRITZ-4 Cores i
L i
7s 7s 7s 7s j
i 2:1 2:2 2:5
$a la 3x 3a
$a 5x 3a 3x A
A A
3:1 3:2 3:5 I
Sa 1:
3x 3x 3x 3x la 3x 1
la 3x la 2x Ju 3x 3x la 1x Ja 3x 3x la 3a 3a A
L A
la Sa 32 37 3x 3a 3x 3a t
4:1 4:2 5:1 NOTE: 1) Fission Rate Comi.arisons are presented in Figure 2.36 for assemblics marked by a triangle,
- 2) See Table 2.5 for explanatson of these cores. f
~
u FIGURE 2.24 c'
Calculated to Measured Fission Rate Ratios for KRITZ Cores e
l s
not measured positions M water holes l
l BA pin a) K3 U-WH1, SE quarter of the central assembly e.ater 1.004 0.994 0.993 0.996 EBEEE
[
1.005 1.006
(
RMS = 0.006
[
b) K3 U-WH2, SE quarter of the central assembly enter
(
0.973 1.004 0.989 1.005
[
1.011 0.996 1.006 0.995 1.008 1.014 1.002 RMS = 0.010
FIGURE 2.24 Cmiculatad to Meatured Fiasion Rate Ratios for KRITZ Cores (Continued) c) R4 3:1, SE central assembly
{-
1.006 1.005 1.006 1.032 1.001 1.008 1.006 0.991 1.015 0.999 1.005 0.989 1.007 1.001 0.980 0.994 0.989 0.995
(
0.989 0.992 1.007 1.000 RMS = 0.009 d)
X4 3:2, SE Central assembly n*n 1.024 1.003 1.010 1.016 0.994 0.999 0.973 1.021 1.000 0.997
{
0.999 l 0.989 1.008
'(
0.989 0.978 0.986 1.002 0.980 1.002 0.998 1.014 1.017 RMS = 0.014 L
FIGURE 2.24 Calculated to Mtamured Fission Rate Ratios for KRITZ Cores l
-(Continued) u rl e ) R4 3 : 5, SE central assembly B*4 1,013 1.006 1.006 l
1.002 1
3.009 0.992 0.999 1.028 1.001 0.995 0.985 0.989 Ft.oi4 I 0.985 11.001 l 0.985
(
0.987 0.987 0.992 1.010 1.014 1.009 wow RMS = 0.012
{
f) K4 4:1, SW central assembly non 1.001 0.993 1.008 1.013 1.003 1.004 0.998 1.015
{
1.000 0.997 0.998
(
1.001 0.989 0.997 0.997 0.994 0.999 1.004 0.999 0.992 0.006 RMS
= f
FIGURE 2.24 Calculated to Meast. red Fission Rate Ratios for KRITZ Cores (Continued) t g) K4 4:1, SE central assembly B*B 0.997 1.011 1
l 1.003 l 1.007 l0.984 0.993 1.000 0.983 0.997 l l
1.012 1.005 l 1.008 l 1.006 0.991 0.993 l o.992 l 1.006 0.999 1.009 1.007 RMS = 0.009
(
h) K4 5:1, SE central assembly h*h 1.018 1.007 1.024 1.007 0.999 1.002 1.018 1.000 0.996
[
0.992 0.986 1.002 0.981 0.997 0.993 0.991 0.989 0.999 0.995 1.003
(
RMS = 0.011 (
L-
SUMMARY
AND CONCLUSION 3.0 I
This report demonstrates the validity of the CASMO-3G code as a lattice physics computer code to be used for the 3eneration of few-group constants for
[-
cpplication to global core analysis codes, as well as the generation of isotopic data.
The validation conducted snd reported here demonstrates the validity of the code through verification of the integral calculations performed by the code.
In particular:
o The associated nuclear data libraries.
Neutron transport and spectrum for pin cells.
o o
Treatment of strong absorbers.
The 2-D transport calculation (COXY) o The diffusion thcory calculation (DIXY) o
//
Depletion calculation and isotopics.
o
{
o Gansna transport.
In addition, the majority of these verifications were conducted
(
internally by Yankee Atomic and, thut demonstrate the proficiency of Yankee Atomic in the use and application of CASMO-3G, independent of the code vendor.
(
(
{
{ 2090R/2.20 f
F'
4.0 REFERENCES
1.
- Edenius, M., A. Ahlin, and H. Haggblom, "CASMO-3. A Fuel Assembly Burnup Program," Studsvik/NFA-86/7, November 1986. Studsvik Energitenik, 1981.
2.
Ahlin, A., M. Edenius, "CASMO - A Fast Transport Theory Assembly
.f Depletion Code for LWR Analysis," Trans. ANS, 26, 1977, 604.
3.
- Ahlin, A., M. Edenius, H. Haggblom, "CASMO - A Fuel hssembly Burnup Program," AE-RF-76-4158, Proprietary Studsvik Report.
4.
- Edenius, M., A. Ahlin, and H. Haggblom, "CASMO-2, A Fuel Assembly Burnup Program " Studsvik Energitenik, 1981.
5.
Cadwell, W.
R., "PDQ-7 Reference Manual," WAPD-IM-678, Westinghouse Bettis Atomic Power Laboratory, 1967.
6.
VerPlanck, D., and K. Smith, "SIMULATE-3 Manual," to be published.
7.
- Ahlin, A., M. Edenius, Gragg, C., "MICBURN Microscopic Burnup in Burnable Absorber Rods," Studsvik/NFA-86/26, November 1986.
8.
- Haggblom, H., "The CASMO-3 Nuclear Data Library," Studsvik/NFA-86/12, 1986.
9.
- Edenius, M., K. Smith, et al., "New Data and Methods for CASMO and SIMULATE," Studsvik of America, September 17, 1986.
10.
- Persson, R., E. Blomsjo, and M. Edenius, "Critical Experiments up to
(
24500 with H O Moderated UO -Rod Lattices in KRITZ," Studsvik 2
2 RF-71-267, 1971.
11.
- Carivik, I., "Integral Transport Theory in 1-0 Geometry," Nukleonik,
(
Volume 10. Page 104 (1967).
12.
"Advanced Recycle Methodology Program Computer Code Manuals " EPRI, CCM-3, Part 11.3, Part 2. Chapter 7 "MICBURN " September 1977.
13.
Radkowsky, A., Editor, Naval Reactors Physics Handbook, Volume I, pp. 612, 613 TID-7030, 1964.
See also, Rampolla, D.
S., "Adjusting Absorption Cross Sections in Transport Calculations to Achieve Specified Region Capture Integrals," NSE 31, 396, 1968.
[
14.
- Haggblom, H., A. Ahlin, T. Nakamura, "Transmission Probability hethod of Integral Neutron Transport Calculation for Two-Dimensional Rectangular Cells," NSE 56, 411, 1975.
- 15. Ahlin A., "DIXY - A Two-Dimensional Diffusion Theory Code." Studsvik Proprietary Code.
16.
Strawbridge, L.
E., and R. Barry, "Criticality Calculations for Uniform Water-Moderated Lattices," NSt.E, 23, 58-73, 1965. 2090R/2.20
(
1 I
Fueled Critical Experimentr.," WCAP-3..j-1, R. D. Learner, 17.
"Pu0 -UO2 2
W. L. Orr, R. L. Stover, E. C. Taylor, J. P. Tokin, and A. Vukmir,
(
July 1967.
- 18. Nodvik, R.
J., "Supplementary Report on Evaluation of Mass Spectrometric and Radiochemical Analysis of Yankee Core I," WCAP-6086 August 1969.
19.
Final Report EP80-16, "Hot Cell Examination of Zion Fuel Cycles 1 Through 4," M. G. Balfour, et al., WCAP-10473, April 1985.
20.
"Reactor Core Physics Design and Operating Data for Cycles 1 and 2 of the Zion Unit 2 PWR' Power Plants," EPRI NP-1232, December 1979.
21.
Cutrone, M. B., Valby, G. F., "Canna Scan Measurements at Quad Cities Nuclear Power Station Unit 1, Following Cycle 2 " EPRI NP-214. July 1976.
22.
Larsen, N.
H., et al., "Core Design and Operating Data for Cycles 1 and 2 of Quad Cities," EPRI NP-240, November 1976.
23.
- Jernberg, P., "CASMO-3 Benchmark Against Critical Experiments,"
(
Studsvik/NFA-86/11, August 1986.
[
24.
- Ahlin, A., et al., "Integral Transport Computation of In-Core Gamma t
Effects with CASM0/ CPM," Trans. Am. Nucl. Soc., Volume 47. Page 434 Washington, D.C., November 1984.
f 25.
- Edenius, M., et al., "Benchmarking of the Gamma-TIP Calculation in CASMO Against the Hatch BWR " Trans. Am. Nucl. Soc., Volume 49, Page 432, Boston, Massachusetts, June 1985.
26.
"Gansna Scan Measurements at Edwin L. Hatch Nuclear Plant Unit 1 Following Cycle 1," EPRI NP-511, August 1978.
{
l l
l
{ 2090R/2.20
(
(
\\
N f
L
[
Appendix A s,
BNL Fuel Assembly Standard Problem f
As part of the CASHO-3G validation and verification, the BNL Fuel Assembly Stctdard Problem was evaluated using CASH 0-3G.
The problem consists of two fuel
(
cssembly lattices that are to be evaluated at several statepoint conditions and co: pared to the BNL solution.
The lattices consist of a 17 by 17 array of fuel rods, similar to designs currently used in operating PVR's.
The two lattices differ in that one contains 16
(
burnable absorber pins and the other does not contain any burnable poison.
[
The problem stipulates that the following calculations be performed with the lettice codel as a function of exposure at Hot Full Power conditions provide the following; Relative pin power distribution f
Infinite multiplication factor Delayed neutron fraction
(
Assembly averago isotopics At BOL and EOL provide the f ollowing reactivity defects Fuel temperature Moderator temperature f
Boron concentration Xenon concentration f-Control rod vorth (unpoisoned lattice) l A-1 I
l The analysis of this Standard provides integral verification of the following L
-calculations performed by CASMO-3; The nuclear data library (neutron cross-sections
[
o and depletion chain data),
b Spatial calculation of pin cells (spatial o
transport and energy spectrum in individual pin cells),
calculation of strong absorbers (control rods and o
burnable poisons),
Calculation of the 2-D space energy distribution o
of the flux vithin the assembly (COXY),
Depletion calculation and isotopics, and o
o Kinetics parameters.
(
Tables A.1 through A.4 summarize the results of these calculations compared to the BNL solutions. The evaluation was conducted by BNL. Their conclusion vas that the agreement between YAEC and BNL calculations was very good and within the f
uncertainty of the reference solutions.
l I
A-2 L
^
L TABLE A.1 I.
DIFFERENCE BETVEEN YAEC AND BNL CALClfLATED FUEL ASSEMBLY NEUTRONICS CHARACTERISTICS
(
PVR 17x17 FUEL ASSEMBLY STANDARD PROBLEM YAEC/BNL Exposure Dependence Quantity
% Difference of Difference
{
Power Distribution e i 1.5*
Decreasing Peak Pin Power I.5' Decreasing i 1.5 K,
6 I3 K,- Assembly multiplication factor S - Delayed neutron fraction I
- e - Standard Deviation between the YAEC and BNL pin povers.
+
Difference between the YAEC and BNL assembly peak pin povers.
A-3
TABLE A.2 DIFFERENCES BETVEEN YAEC AND BNL CALCULATED FUEL ASSEMBLY NUMBER DENSITIES
(:
PVR 17X17 FUEL ASSEMBLY
(
STANDARD PROBLEM YAEC/BNL Exposure Dependence
(
Isotope
% Difference Trend of Difference U-235
&3 U-238 i1 Pu-239 i3 Underprediction Decreasing Pu-240 i5 Underprediction Decreasing
(
Pu-241 I3 Underprediction Decreasing f
Pu-242 23 l
l A-4
TABLE A.3.
r DIFFEREHCES BETVEEN YAEC AND BNL CALCULATED FUEL ASSEMBLY GROUP CONSTANTS PVR 17x17 FUEL ASSEMBLY STANDARD PROBLEM YAEC/BNL Exposure Dependence
[
Group Constant
% Difference Trend of Difference D
25 1
D 25 Overprediction 2
Ia1 I3
{
Ea2 I3 f
Erl i5 Underprediction vtf1 75 vEf2 i5 If1 i5 Decreasing Ef2 i5
(
l 3 (D ) Fast (Thermal) diffusion coefficient D
2 Ea1(TE2) Fast (Thermal)diffusioncrosssection Ir1 Fast removal cross section NEf1 (vEf2) Fast (Thermal) neutron production cross sections If1 (If2) Fast (Thermal) fission cross section A-5
TABLE A.4 DIFFERENCES BETVEEN YAEC AND BNL CALCULATEDJ ACTIVITY DEFECTS r
PVR 17X17 FUEL AFSEMBLY STANDARD PROELEM Reactivity Defect
% Difference Trend
(
i 10 Overprediction 1.
FuelTempgrature (Tp = 560 K)+
2.
Moderator Temperature i 25+
Overprediction (Tg = 535 K) f 3.
Moderator & Fuel Temperature i 20' (T =Tg = 68 F) p 4.
Moderator & Fue). Temperature i 15
[
(Tp-Tg = 300*F) 5.
Boron Concentration i 10 f
(NB = 0 ppm) 6.
Xenon Concentration i 5 Overprediction l-(N, = 0) x 7.
Control Rod i 10 Overprediction *
(Rodded) f Perturbed value indicated in parentheses.
The moderator temperature defect (item-2) and the moderator and fuel
+
temperature defect (item-3) in the unshimmed case are <.5%&/k, and these relatively large percent dif ferences correspond to <.1%&/k differences in the unshimmed reactivity defect.
The control rod defect is negative and the indicated result is for the magnitude of the defect.
4 A-6
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