ML19353A422
| ML19353A422 | |
| Person / Time | |
|---|---|
| Site: | Vermont Yankee File:NorthStar Vermont Yankee icon.png |
| Issue date: | 12/31/1980 |
| From: | Cacciapouti R, Pilat E, Turnage J YANKEE ATOMIC ELECTRIC CO. |
| To: | |
| Shared Package | |
| ML19353A418 | List: |
| References | |
| YAEC-1232, NUDOCS 8101080443 | |
| Download: ML19353A422 (108) | |
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!!ETHODS FOR THE ANALYSIS OF I BOILING WATER REACTORS l
LATTICE PIIYSICS I
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Prepared By //o m / '
' .Ys 3[, I Dr. Edward E. Pilat"
!!anager, Applied Methods Development (Da t'e)
Reviewed 3y /L f/ [O
/ R. y Cacciapouti '( Da't e )
Manager, Reactor Physics Approved By W C. h 11 31 80 l Q Dr. J. p Turnage (Date) Director, Nuclear Engineering Department l Yankee Atomic Electric Company li Nuclear Services Division 1671 Worcester Road Framingham, Massachusetts 01701 l l . 8101080 hQ
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I DISCLAIMER OF RESPONSIBILITY This document was prepared by Yankee Atomic Electric Company on behalf of Vermont Yankee Nuclear Power Corporation. This document is believed to be completely true and accurate to the best of our knowledge and information. It is authorized for use specifically by Yankee Atomic
# Electric Company, Vermont Yankee Nuclear Power Corporation and/or the appropriate subdivisions within the Nuclear Regulatory Commission only.
With regard to any unauthorized use whatsoever, Yankee Atomic Electric Company, Vermont Yankee Nuclear Power Corporation and their
'g of ficers, directors, agents and employees assume no liability nor make any
.N w rranty r represent tion with respect to the contents of this document or to its accuracy or completeness. 'l l lI I E 15 5 l I I i 11 I
I ABSTRACT Volume I of this report describes the physics of the CASMO computer program used by YAEC for B'4R lattice calculations and the bases for confidence provided by comparisons with measured data and higher order me tho d s . l I I I I L 'l 11 lI I y 111 I 1E
I I TABLE OF CONTENTS I Page DISCLAIMER................................................ 11 ABSTRACT.................................................. iii TABLE OF C0NTENTS......................................... iv LIST OF FIGURES........................................... v I LIST OF TABLES............................................ ix ACKN0WLEDGEMENTS.......................................... x l.0 D E SC RI PT IO N O F CA SM0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 I 1.1 1.2 1.3 Introduction.............................................. The Nuclear Data Library.................................. Calculations on Unit Cells................................ I 5 6 1.4 I Strong Absorbers.......................................... 8 1.5 The Two-Dimensional Calculation........................... 11 1.6 T h e Bu r nu p Ca l cul a t io n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 Input and 0utput.......................................... 14 2.0 B A S I S FO R CO NF I DE NC E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.1 Yankee Calculations....................................... 31 l 2.1.1 Compa risons With Unifo rm Pin Cell Lattice Criticals. . . . . . . 31 2.1.2 Comparisons With Measured Yankee Rowe Iso topics. . . . . . . . . . . 33 l5h l 2.1.3 Comparisons With Criticals Containing Strong Absorbers. . . . 34 2.1.4 Compa riso ns Wi th Mo nte Ca rlo Calcula tions . . . . . . . . . . . . . . . . . 35 2.2 Swedish Calculations...................................... 37 l l 2.2.1 Hot and Cold Criticals in KRITZ........................... 37 2.2.2 Co ld Cr i t ic als o n Un i fo rm La t t ic e s . . . . . . . . . . . . . . . . . . . . . . . . 40 l 2.2.3 Saxton Isotopics.......................................... 40 2.2.4 Gd Depletion in Oskarshamn................................ 41 2.2.5 C ASMO Powe r Reacto r Benchma rking in Sweden. . . . . . . . . . . . . . . . 42 1 2.3 Summary of CASMO Benchmarking............................. 44 R E F E R E NC E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 1 . I - -
I I LIST OF FIGURES 1 Page i 'E 1.1 Flow Chart o f C A SM 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 li 1.2 Flow Chart of Resonance Calculation...................... 21 1.3 Flow Chart of Pin Cell Calculation....................... 22 t l.4 Flow Chart of MICBURN.................................... 23 !l l5 1.Sa Actual Control Rod Configuration......................... 24 1 1.5b Representation of Control Rod Wing in CASM0.............. 24 1.6 Typical BWR Assembly Geometry in 2-D Calculation......... 25 1.7 Typical PWR Assembly Geometries in 2-D Calculation....... 26 1.8 Heavy Nuc lide Chains in CASM0. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 I 1.9 Fission Product Chains in CASM0.......................... 28 2.1 K-Effective Versus Enrichment............................ 57 2.2 K-Effective Versus Critical Buckling..................... 58 2.3 K-Effective Versus Lattice Pitch......................... 59 2.4 K-Ef fective Versus Boron Concentration. . . . . . . . . . . . . . . . . . . 60 2.5 K-Effective Versus Water to Metal Ratio.................. 61 I 2.6 2.7 CASMO Ve rsus MIC BURN K-In f ini tie s . . . . . . . . . . . . . . . . . . . . . . . . U-235 Atom Percent Versus Burnup for Yankee Core I 62 Spent Fue1............................................... 63 2.8 U-236 Atom Percent Versus Burnup for Yankee Core I Spent Fue1............................................... 64
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2.9 U-238 Atom Percent Versus Burnup for Yankee Core I Spent Fuel............................................... 65 2.10 Pu-239 Atom Percent Versus Burnup for Yankee Core I Spent Fuel............................................... 66 I g v I
I LIST OF FICURES (continued) Page 2.11 Pu-240 Atom Percent Versus Burnup for Yankee Core I Spent Fue1............................................... 67 2.12 Pu-241 Aton Percent Versus Burnup for Yankee Core I Spe nt Fue1............................................... 68 2.13 Pu-242 Atom Percent Versus Burnup for Yankee Core I Spe nt Fue1............................................... 69 2.14 Pu-239 to U-238 Atom Ratio Versus Burnup for Yankee Core I Spent Fuel........................................ 70 2.15 Calculated Eigenvalues for Heterogeneous 1y Poisoned Critica1s................................................ 71 l 2.16 Comparison of CASSf0 and KENO Local Power Distributions - VY219 Bundle - No Gd 023-
- g 0 voia - No Rods......................................... 72 2.17 Comparison of CASMO and KENO Local Power Distributions - VY219 Bundle - No Gd 033-40 Void - No Rods........................................ 73 l
l lg 2.18 Comparison of CASMO and KENO Local Power lg l ~ Distributions - VY219 Bundle - No Gd,,03-70 Void - No Rods...................'.................... 74 2.19 Comparison of CAS!!0 and KENO Local Power Distributions - VY219 Bundle With Cd 033-0 Void - No Rods......................................... 75 2.20 Comparison of CASS10 and KENO Local Power l Distributions - VY219 Bundle With Cd,,0 - 40 Void - No Rods...................I.3................... 76 l 2.21 Comparison of CASMO and KENO Local Power l Distributions - VV219 Bundle With Gd,30 3 - l 70 Void - No Rods...................'..................... 77 2.22 Comparison of CASMO and KENO Local Power 'l Distributions - VY274 Bundle With Gd 033-P. 40 Void - No Rods........................................ 78
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I LIST OF FIGURES (continued) Page 2.23 Comparison of CASMO and KENO Local Power i Distributions - VY219 Bundle - Rodded - 0 Void - With Gd23 0 ...................................... 79 2.24 Comparison of CAS!!O and KENO Local Power Distributions - VY219 Bundle - Rodded - 40 Void - With Gd23 0 ..................................... 80 2.25 Comparison of CASMO and KENO Local Power Distributions - VY219 Bundle - Rodded - 70 Void - With Gd 33 0 ..................................... 81 2.26 Comparison of CASMO and KENO Local Power Di stributions - VY274 Bundle - Rodded - 40 Void - With Gd 33 0 .................... ................ 82 2.27 Comparison of CAS:10 and KENO Local Power I 2.28 Distributions - VY274 Bundle With Gd 033-40 Vo id - No Rods - Nomi nal Tempe ra tur es . . . . . . . . . . . . . . . . . BWR Lattices in KRITZ.................................... 83 84 2.29 P WR La t t i c e s i n KR I TZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.30 Deviation in Percent Between Calculated and Measured I, Fission Rates in an 8 x 8 UO,, Assembly With 3 Gd Poisoned Rods..........I............................ 86 2.31 Deviation in Percent Between Calculated and Measured i Fission Rates in an 8 x 8 UO,, Assembly Without l Ga d o l i n i u m . . . . . . . . . . . . . . . . . 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 11 l 2.32 Deviation in Percent Between Calculated and Measured Fission Rates in an 8 x 8 UO 3 Assembly With 5 Gd Poisoned Rods....................................... 88 ,I I 2.33 Deviation in Percent Between Calculated and Measured Fission Rates in an 8 x 8 Assembly of the Pu-Island lE 89 l3 l Type..................................................... l 2.34 Deviation in Percent Between Calculated and Measured Fission Rates in a 15 x 15 PWR M0 2 Assembly I Wi t h Wa t e r IIo le s a nd Abso r be r Rod s . . . . . . . . . . . . . . . . . . . . . . . 90 vii I .
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W LIST OF FIGURES (continued) Page 2.35 Deviation in Percent Between Calculated and Measured Fission Rates in a 14 x 14 PWR M0 2 Assembly 1 With Water Holes......................................... 91 2.36 K-Ef fective Predicted by CASMO Versus Experimental -lll 4 a Material Buckling........................................ 92 2.37 Deviation in Percent Between Calculated and 'feasured I Burnup in an 8 x 8 As sembly Wi t h 3 Gd Rods . . . . . . . . . . . . . . . 93 l i I I I I I I I 3 .m I
I I LIST OF TABLES l.1 Nuclides in the CASMO Libraries.......................... 16 1.2 Energy Group S t ruc tures in the CASMO Libraries. . . . . . . . . . . 19 2.1 B a s e s fo r Co n f id e n c e in CASM0. . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 l i 2.2 Critical Experiments with Strong Absorbers............... 48 l 2.3 Assemblies Analyzed for KENO-CASMO Comparisons. . . . . . . . . . . 49 6 2.4 Compa rison of K Infinities f rom KENO and CASM0. . . . . . . . . . . 50 2.5 Compariso n of Local Peaking f rom KENO and CASM0. . . . . . . . . . 51 2.6 CASMO Results for the KRITZ Critical Lattices............ 52 2.7 C A SMO Re s ul t s fo r TRX C r i t i c a l s . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.8 CASMO Re sult s fo r ESADA C ri ticals . . . . . . . . . . . . . . . . . . . . . . . . 54 2.9 Isotopic Composition in SAXT0N........................... 55 2.10 Comparison Be tween Calculated and Measured Fraction in the Ir rad i ated Gd -Po isoned Pins . . . . . . . . . . . . . . . . . . . . . . . 56 2.11 Comparison Between Measured and Calculated Number Densities of Gadolinium Isotopes......................... 56 lI il I I I I ix I
3 I ACKNOWLEDGEMENTS W The author of this report has merely compiled work performed by others. Dr. Malte Edenius of Studsvik of America has helped in the implementation I and intelligent use of CASMO at Yankee, as well as in reporting benche nk wo rk performed at Studsvik Energiteknik and elsewhere in Sweden. The Yankee work reported here would not have been possible without tne computer expertise and intellectual assistance of David M. VerPla.tek of Yankee. I The Yankee analyses were performed by members of the Aprlied Methods Development and Reactor Physics Groups: Mark Hebert, .% chelle Kmetz, Darvin Kapitz and Claudia Heumer. Special thanks are due Ricnard J. Cacciapouti, Manager of Reactor Physics, and Professors Don R. Harris of Rensselaer Polytechnic Institute and John Mayer of Worcester Polytechnic Institute. lI l l 3 l 1 I I I
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1.0 DESCRIPTION
OF CASMO I 1.1 Introduction CASM0(1.2) is a two-dimensional, multigroup transport code for the calculation of eigenvalue, spatial reaction rate distributions, and depletion of pin cells and of BWR and PWR fuel assemblies. The code can handle cruciform control rods containing cylindrical absorber elements, cluster control rods, water gaps, boron curtains, burnable absorber rods and burnable absorbers within the fuel rods. The nuclear data library is based on ENDF/B-III. The data are collected in a library containing cross sections in 69 or 25 energy groups. CASMO is, to a great extent, identical to the CPM (3) program. The most important differences are input / output and the two-dimensional transport theory routines. CPM is an accurate benchmark code which requires much lI computer time while CASMO is an extremely user oriented code designed for large numbers of production calculations. The simplified input and output of CASMO makes the QA easy and the change from the slow, two-dimensional l j collision probability routine in CPM to a fast transmission probability l l routine in CASMO has been done almost without losing anything in accuracy. 1 Both the collision and transmission probability routines are based on integral transport theory and the results are nearly identical for typical applications. I The program has a flexible output and for use in global reactor calculations produces few group parameters for the whole assembly or any subregion. Further, the neutron balance, power distribution, reaction rates 1 1
I in fuel rods and in detectors, delayed neutron yields and number densities versus burnup are printed if asked for. The Five Functional Parts of CASMO Figure 1.1 shows the relationship between the five functionally significant parts of CASMO: Nuclear data library
- Calculations on unit cells (spatial transport and energy spectrum of neutrons in individual pin cells)
I - Calculation of strong al erbers (control rods, gadolinia in fuel pins, B4C burnable poison) Calculation of the 2-D space energy distribution of flux within I the bundle and of the local power distribution and bundle reactivity Depletion calculation. In terms of these five functional parts, the program operates as l follows: 'I - For each group in the microscopic library group structure, macroscopic 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 2 I -- -
I resonance theory, using pin dependent Dancof f factors. For each typical pin cell, a four region, cylindrical, collision probability solution to the transport equation in the library group structure provides space-depende.nt micro-group spectra and disadvantage factors. I - Gadolinia strong absorber is treated by an auxiliary calculation which is analogous to, but more detailed than the pin cell treatment within the bundle calculation. It produces effective gad cross sections which can then be used just like any other pin microscopic cross section in the ordinary library. Control rods and ordinary burnable poison pins are homogenized, as part of the CASMO calculation itself, in such a way as to preserve their blackness. I - The resulting infinite medium cross sect.)ns, homogenized over unit cells, are corrected for the influence of the rest of the assembly using factors derived from cylindrical macro-group ll l l u calculations of the whole bundle including water gaps, channel, 1 control rod, curtains, etc. They are then collapsed to the l 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 rates from which k infinities and local power distributions are de t e rmined . I - The local reaction rates are used to calculate the build'p and 3 I
I depletion of 14 heavy nuclides and 24 fission products over selected time intervals, via a predictor-corrector technique. These individual pin cell number densities may then be used to repeat the entire process for subsequent time steps. I Energy Group Structures Three sets of energy group structures are used in CASMO calculations I and two in editing: I - The micro group or library group structure contains either 69 or 25 groups, as shown in Table 1.2. As implied by the name, the library of nuclear data that accompanies CASMO exists and is used in this structure. Pin cell calculations are performed in this group structure. I - The macro group structure contains up to 25 groups. It is used in cylindrical calculations of the whole bundle.
- 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 structural regions.
I - The " Edit A" group structure is the two group structure in which assembly average cross sections are edited for ultimate use in SIMUL \TE core calculations. This group structure is not used in any calculations internal to CASMO. I 4 I
I The " Edit B" group structure is an arbitrary arrangement of up to 10 groups, used only for editing. I The impo rtan t features of the various parts of the program are described in the following sections. 1.2 The Nuclear Data Library The source of the basic nuclear data is ENDF/B, version III, from which libraries have been produced with microscopic cross sections in 69 and 25 energy groups. Except for some small changes in gadolinium cross sections and a small correction to the natural boron data, the 69 group I library is identical to the CPMLIB3 distributed by EPRI(4) with CPM. The EPRI documentation includes a summary of the 2200 m/s cross sections and resonance integrals for each nuclide. The twenty-five group library was produced by Studsvik by collapsing the 69 group library. Table 1.1 shows the nuclides in the library and the temperatures at which cross sections and scattering matrices are available. Data for other temperatures are obtained by interpolation. The scattering matrices for hydrogen are based I I on the Haywood model. lI The group boundaries are distributed in the manner shown in Table 1.2. The group structure is based on the assumption that 4 eV is the highest energy at which thermal motion of the moderator is of any importance.
- I Ef fective resonance integrals for 235U , 236 U, 238U and 239Pu have been provided by the Intermediate Resonance (IR) approximation originally developed by Goldstein(5). They are used as two-dimensional tables tabulated lI as functions of the ef fective potential scattering cross section and the 5
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I temperature. As explained in the EPRI documentation (4), the well-known anomaly in ENDF/B-III U-238 resonance capture has been eliminated by adjusting its parameters to reduce the infinite dilution resonance integral f rom the ENDF/B-III value of 273.6 barns to 271.2 barns. Details of the adjustment are given in the EPRI reference. I 1.3 Calculations on Unit Cells I The Resonance Treatment l The resonance energy region is defined ta lie between 4 eV and 9 kev. Resonance absorption above 9 kev is regarded as being unshielded. The 1.0 eV resonance in 240Pu and the 0.3 eV resonance in 239Pu are adequately covered by the concentration of thermal groups around these resonances and are consequently excluded from the special resonance l t rea tme n t . In the present version, four nuclides - 235U, 236U, 238U and 239P u - are treated as resonance absorbers. Figure 1.2 shows a flow chart of the subroutine for resonance cross lI section calculations. It can be interpreted in the following way. 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 from a sum of two rational functions which determine two ef fective potential cross sections. Reaction l 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 dif ferent nuclides is obtained by a correction l 6 I
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. 1 ,E The Micro-Group Calculations Each micro-group pin cell calculation provides a solution to the t space-energy transport equation for isotropic scattering by means of
= collision probability calculations in 69 or 25 energy groups and in a 1
simplified, cylindrical geometry consisting of three or four regions. The regions represent fuel, cladding, coolant and, for pin cells in assemblies, a fourth 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. 1 1 The micro group calculation provides 69 or 25 group spectra which 1 1 j are used for energy condensation and spatial homogenization of the elementary l pin cells. Thus, broad group cross sections are determined for smeared l pin cells. The micro-group calculation is fast and is repeated for each di f fe rent 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. 'I 7 I
I 1.4 Strong Absorbers Cadolinia in Fuel When gadolinium is used as burnable absorber in fuel rods, the gadolinium which is initially homogeneously distributed is burnt in a complicated way. The microscopic burnup of gadolinium in fuel rods is calculated outside CASMO by the code MICBURN(19), which provides effective i!E cross sections, homogenized over the fuel rod, for the gadolinium as a function of burnup. The ef fective cross sections are used as input to CASMO and the flux in a rod containing gadolinium is then alculated in the same way as for absorber rods. An advantage of performing the detailed burnable absorber burnup outside CASMO is that this calculation does not have to be repeated when i the same burnable absorber pin is used in several CASMO calculations. CASMO ,g can read either individual MICBURN files generated for each type of Gd-rod ig i in the assembly or a permanent Cd-library. The permanent Gd-library was generated by a series of MICBURN runs for dif ferent Gd-concentrations. CASMO makes interpolations in this library. I The MICBURN calculations are carried out in the library group s t ruc tur e , i.e. , in 69 or 25 energy groups. The nuclear data library is the same one used in CASMO. The gad-rod is first divided into equidistant 1E IW radial micro regions. Up to 100 regions may be used, but 20 is a typical number. Each micro region defines a burnup region. The transport equation is solved using collision probabilities for a number of macro regions, each consisting of one or more micro regions. The boundaries (and the number) l of the micro regions are the same at all burnup steps. The number of :racro l 8 l0
I regions is also kept constant but the boundaries are changed automatically at each burnup step so that the macro regions 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, except that more regions are used. I To generate a realistic spectrum for the burnup calculation, it is assumed that the gad-rod is surrounded by a uniform pin cell lattice. Before the main transport calculation in MICBURN can be carried out, this j buffer zone is homogenized, using fluxes obtained from a special transport calculation in the three regions, fuel, clad and moderator, which define the uniform lattice of the buffer zone. Again, the formalism for the buf fer homogenization is identical to that used for the pin cell calculations in CASMO. The main transport calculation in MICBURN is then made in an annular geometry where the gad-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 (see Figures 1.8 and 1.9). The buf fer zone is also burnt. At each burnup step ef fective cross sections for the gadolinia are homogenized over the fuel rod, parameterized as a function of gad depletion, and saved for use in the main CASMO calculation. A flow chart of MICBURN is shown in Figure 1.4. I Cruciform Control Rods I Crucifo rm control rods, such as those in a BWR are treated as I 9 I
I homogeneous slab regions in the two-dir:nsional calculation. The two-dimensional calculation dif ferentiates 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 1.5a. For use in the two-dimensional calculation, the wings are homogenized in such a way as to maintain their blackness. The homogenization is performed on the assumption that the wing consists of two regions - the cylindrical absorber material and a homogeneous mixture made up of the absorber tube walls, the surrounding metal sheet, and any water between the two . The relative flux in the two regions shown in Figure 1.5b is obtained for each 2-D energy group by a collision probability calculation which includes the ef fect of an anisotropic surface current. Cluster Control and Burnable Absorber Rods Cluster control rods and burnable absorber rods which do not contain fuel are both homogenized using micro-group pin cell solutions to the traasport equation (analogous to those for unit cells containing fuel rods), followed by an " empirical blackness theory" treatment (6). In contrast to the fuel pin case, however, a four region annular geometry is used, 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 f rom the previous micro-group calculation on an assembly average fuel pin cell. Correction factors for use 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 10 I
I water using flux weighted cross sections from the four region calculation) and buf fer zone. The correction factor for each microgroup is defined as the ratio of 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. 1.5 The Two-Dimensional Calculation A two-dimensional calculation is required to determine the flux, local power distribution, and bundle reactivity in a BWR or PWR assembly. This calculation is generally carried out in 5-12 energy groups in xy-geometry using the transmission probasility routine, COXY(7). Typical geometries of BWR and PWR assemblies treated by the two-dimensional routines are shown in Figures 1.6 and 1.7. The condensation of the 69 or 25 group spectra to the number of groups used for the 2-D assembly calculations is either made in one step (PWR geometry) or for BWR geometry via cylindrical macro group calculations in a maximum of 25 groups. Separate cylindrical calculations are performed for the BWR assembly approximated as a cylinder with the wide gap and with the narrow one. When a control rod is present, it is treated as the ou te rmo s t ring of the wide gap calculation only. During the condensation f rom the library micro-group structure to the 2-D group structure, the micro-group spectrum for each pin is adjusted (via the macro group spectrum) to reflect the pin's actual location in the bundle relative to its neighbors, the water gaps and the control rod. I 11 I
I I The actual 2-D calculation is performed by COXY, which solves the integral transport equation by use of escape and transmission probabilities I to determine the interf ace currents between mesh blocks. Up to 12 energy groups may be used. Within each mesh block, the neutron flux is .ssumed to be linearly dependent on the x- y-coordinates. The angular dependence is given by a P .t approximation. At the mesh surfaces, cne asymmetric flux distribution relative to the surface normal is considered. The escape and transmission probabilities include coupling between different 2ngular modes. COXY is much 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 fundamental buckling mode is used for modifying the infinite lattice results obtained from the transport calculation to include the ef fects of leakage. This calculation may be carried out either in diffusion theory or by use of the B -leakage 1 method. P l -scattering matrices are available in the CASMO library for the principal moderators and the P t . scattering terms are explicitly represented in the B 1-equations. 1.6 The Burnup Calculati.on I The basic burnup chains, with the isotopes linked through absorntion 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 nuclidas as shown in Figure 1.8. Twenty-two individual and two pseudo-fission products are included in fourteen linear fission product chains shown in Figure 1.9. 12 I
I The individually treated fission products account for about 90% of the total fission product absorption. Boron in boron steel curtains or in burnable poison rods is also burnt, 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 I equilibrium value at all times. The flux level is determined by the average power density given in the input. The fluxes used to determine reaction rates are constant during a burnup step. The length and the number of burnup steps are set in the program, but they can also be chosen by the user. Depletion and buildup of gadolinium isotopes is not calculated explicitly I in CASMO. Rather, it is accounted for through the definition of an energy dependent, effective microscopic gad 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 in MICBURN, as described in Section 1.4. The depletion calculation for each burnup step is carried out in two partial steps. Going f rom the time ne -1 to tn, first a " predictor" step is made using the fluxes obtained from the spectrum calculation at t n -1 The predictor step provides predicted number densities at t where, n af ter the cross sections are updated, a new spectrum celculation gives fluxes to be used in a " corrector" step. The final number densities at t n are then given by the average value cf the results from the predictor and corrector steps. This method is very ef ficient and makes it possible to take much longer burnup steps than is usually the case in cell burnup codea. I I 13 I
I i 1.7 Input and Output The input to CAS'!0 is arranged to make the use of the code as easy as possible, and consequently, also minimizes the risk of input errors. Input data are blocked together, and most of the blocks consist of one card only. Separate blocks specify for example, materials composition, dimensions and arrangement 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 I for later use. CASMO 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,, is obtained from the two dimensional transport calculation, and the fundamental mode calculation gives keff fo r a given geometric buckling. B$ corresponding to kef f 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, if requested, also for nuclides not normally occurring in the reactor, e.g., for detector materials. From I the calculated reaction rates, the power distribution within the fuel assembly, conversion ratios and other cell parameters are obtained. In burnup runs, intermediate and end results can be stored on file. The data saved are nuclide concentrations and fluses. Starting from these 14
I stored data it is possible to make branch calculations at, for example, dif fe rent values of coolant void or moderator boron content. l I I l I i !I l I i l l l I I lI lI l I i 15 1 1 l --- . - --, ,---. -_. ........ ...- - - _ _ ,. -- __ --,_ _ ..,. ,,..-., - _ ,- .-_--,., _ ,...,-.-...- ,,. . . - - - - - . --
j 1 TABLE 1.1 Nuclides in the CAS10 Libraries l I gg Nuc}jsg Iseg;ijig3; igg UIE6 Igggg;333;gs_f:51 nu 52I 1 H 1001 0 296,350,000,450,500,600 2 D 1002 0 296 3 3 5000 0 300 4 3-10 5010 0 293.6 5 C 6000 0 300 ( 6 0 3000 0 296 . 400, E CO
/
7 0 (in UO,) 3001 0 296,500,300,1200 3 Al 13000 0 300 9 Si 14000 0 300 10 Cr 24000 0 300 11 Mn 25000 1 300 l 12 Fe 26000 0 300 13 Ni 28000 0 300 14 Cu-63 29063 1 300 15 Ag 47000 0 300 I 16 Cd 48000 0 300 17 In 49000 0 300 13 Gd-154 64154 1 300 19 Gd-155 64155 1 293.6 20 Gd-156 64156 1 300 21 Gd-157 64157 1 293.6 22 Gd-138 64158 1 300 23 Dy-164 66164 1 293.6 24 Lu-176 71176 1 293.6 25 Kr-83 36083 1 29 3.6 26 Rh-103 15103 1 293.6 27 Rh-105 45105 1 293.6 28 Ag-109 47109 1 293.6 29 Xe-131 54131 1 293.6 30 Xe-135 54135 1 293.6
TABLE 1.1 (Cont'd) Nuclides in the CASMO Libraries No Nuclide n
!dentification NINA") Tecceraturas ('O
n_um__b _e _r 31 Cs-133 55133 1 293.6 32 Cs-134 55134 1 293.6 33 Cs-135 55135 1 293.6 I 34 35 Nd-143 Nd-145 60143 60145 1 1 293.6 293.6 36 ?=-147 61147 1 293.6 37 ?=-148 61148 1 293.6 38 ?=-148= 61248 1 293.6 1 39 S=-147 62147 1 293.6 40 Sc-149 62149 1 293.6 41 Sc-150 62'50 1 293.6 42 Sc-151 62151 1 293.6 l 43 S=-152 62152 1 293.6 l 44 Eu-153 63153 1 293.6 l I 45 Eu-154 63154 1 293.6 46 Eu-135 63155 1 293.6 47 NSFP ) 401 1 293.6 48 SSFP } 402 1 293.6 49 U-234 92234 0 300 50 U-235 92235 0 300 (300,900 in res. tab.) lI 51 U-236 92236 0 300 (300,900 in res. ab.) I 52 53 U-238 Np-237 92238 0 300 (300,600,900,1500 in res. tab.) l 93237 0 300 54 Pu-238 94238 0 300 55 Pu-239 94239 0 300 (300,600,900,1500 in res. tab.) 17
I
, TABLE 1.1 (Cont'd)
Nuclides in the CAS!!0 Libraries E9 22S15$$ Is!BEiliS3EicB EIES ISEESE25's E!_151 _n u_._c _e _r 56 Pu-240 94240 0 300,600,1200 57 Pu-24l 94241 0 300 58 Pu-242 94242 0 300 59 A=-24l 95241 0 300 l 60 A=-242 95242 0 300 l 61 A=-243 95243 0 300 62 C=-242 96242 1 300 63 C =- 2 41. 96244 1 300 6- i/v abs 1 1 293.6 63 2irkalloy-2 302 0 300,600,1200 n6 Ag/In/Cd4 ) 303 0 300 ( 67 Inconel-750 750 0 300 1 1 68 Inconel-718 718 0 300 n9 Stainless steel 347 0 300 70 Co-59 27059 0 300 lI l l L) NINA = 1 for nuclides where only absorption or activation cross sec-tions are tabulated, otherwise NINA = 0.
- 2) Te=peratures for which data are given. The program interpolates and extrapolates to other temperatures.
- 3) Not separately treated fission products are represented by two pseudo fission product one non-saturating (NSFP) and one slowly saturating (SSFP).
- 4) The Ag-In-Cd =ixture was prepared for a special application with ho=ogenized cell data and should not be used.
I 13 ,
TABLE 1.2 Enerzy Group Structures in the CASMO Libraries I c uo C ouo "*#37 cr m it. o
"' 37 Mev ev 1 1 10.0 -6.0655 12 36 1.097-1.071 1 2 6.0655 -3.679 12 37 1.071-1.045 3.679 -2.231 12 38 1.045-1.020 I
2 3 2 4 2.231 -1.353 13 39 1.020-0.996 3 5 1.353 -0.821 13 40 0.996-0.972 l 3 6 0.821 -0.500 13 41 0.972-0.950 l " 4 7 0.500 -0.3025 14 42 0.950-0.910 . 4 S 0.3025 -0.183 14 43 0.910-0.850 4 9 0.813 -0.1110 14 44 0.850-0.780 4 10 0.1110 -0.06734 14 45 0.780-0.625 0.06734-0.04085 0.625-0.500 I 4 11 15 46 4 12 0.04085-0.02478 15 47 0.500-0.400 4 13 0.02478-0.01503 15 48 0.400-0.350 4 14 0.01503-0.009118 16 49 0.350-0.320 e7 16 50 0.320-0.300 5 15 9118.0 -5530.0 16 51 0.300-0.280 5 16 5530.0 -3519.1 17 52 0.280-0.250 5 17 3519.1 -2239.45 17 53 0.250-0.000 t I 5 5 5 18 19 20 2239.45 -1425.1 14:5.1 - 906.898 906.898 - 367.262 17 la 19 54 55 56 0.220-0.180 0.180-0.140 0.140-0.100 5 21 367. 52 - 148.728 20 57 0.100-0.080 6 22 148.723 - 75.5014 21 58 0.080-0.067 6 23 75.5014- 48.052 21 59 0.067-0.058 i j 7 24 48.05 - 27.700 22 60 0.058-0.050 25 27.700 - 15.968 22 61 0.050-0.042 ( 7 l 8 26 15.968 - 9.877 23 62 0.042-0.035 l= 9 27 9.877 - 4.00 23 63 0.035-0.030 , 10 28 4.00 - 3.30 24 64 0.030-0.025 l 10 3.30 - 2.60 24 65 0.025-0.020 l 29 10 ^ 30 2.60 - 2.10 24 66 0.020-0.015 10 31 2.10 - 1.50 25 67 0.015-0.010 'I 1 10 32 1.50 - 1.30 1.15 25 25 68 69 0.010-0.005 0.005-0 11 33 1.30 - .- 11 34 1.15 - 1.123 l 11 35 1.123 - 1.097 I 19 i
I I I t ?!GURE 1.1 FLOW CHART OF CASMO LIBRARY 69 Group Or 25 Group I
?IN CELL CALCULATIONS 69 or 25 groups)
Dancoff Resonance I
< STRONG ABSORBER Space-Energy Spectrum CALCULATIONS Control Reds I '
( 2-D CALCULATIONS Gadolinia Burrable Poison Cylindrical Macro Groups (6 25) Collapse cf 2D Groups (f 12) 4 2D Reaction Rates 1 (7-12 groups) B-1 Leakage l lI V i i DEPLETION Predict or-Correcto r Heavy Nuclides I Fission Procucts l Il } I 20 l
I I . Figure 1.2 FLCW CHART CF RESCNANCE CALCULATION R Octlision precaciuties I FLURES V 22rameters for the RESPAR ecuivaience tneerem ( l E8fective cfCSs Sections RESAES f:r unrferm pin ced tattice c. I b [ pin ced assemety 9 DANSQ Cancet? ' actors t :
',f P0sition decendent effective OANCCR c 333 3,etien I sm, II I
l 1 l 21 l - 1.....__..__..._._._._.___.___.______,_,_,_ . , , _ , , ,_ . _ , _ _ _ _
I l Figure 1.3 Flew chart of Din Cali calculation. h g C etine average fuel pin ceil 7, , fuel cln cells I ,, Collision procacilities for ccotant i e cylincncalized ein cell
'~ac h' fuel l <r Correction of CF f or the
{g influence of water gac j coolant i T / , e Solve the neutron manance - etae 3 eq in /. regicns and , i 1 e ' j
- 59 er 25 energy groups /
2e. E ,,
' nemogent:ec Cetermine varicus.:ypes assemely
~
cf pin cells sypass region s 1 I I lt I 'I 18 l OS
~~
l
I I m _ m _ =., . 1..
., m e m inout RIIOOIOEI l Cala UDraG t
=. _, o n ,-
7, , ,a . t h ...,:,_ t 1 =,.
,et,on,,
Fin cett case, l 3 Suffer :ene g
<r Homogenizaten of buffer zene t -
Define macro region. Transcort I calculation l Rux o stnbution in micro regions
'r l B urnuo calculation I el i
I 23 I
I I
" 1-
-> Stainless Steel Central Straccure Stainless Steel Stainless Steel Sheet Clad l
!g ( -----
\-- - - - - -
AT g/ \ -
\ *-
; l\ .r.;'a /
~
/ : 'L.' / 4.'
< Y: l /
'l N ///////// r 3c 3
- I \ \
V
... S Figure 1.5a. Actual Control Rod Configuration I;
I steel or steel and water absorber (3 4C,) i ** V/ .- 1, .* ,
. i'.- l :. ;,. . .'.
I I Figure 1.5b. Representation of Control Rod Wing in CASMO 24
1 Figure 1.6 Exampie Of EWR dstemb/v ge cm e!P'f ni 20 03ICUI3ficn i ,I COntrCl rCC Wide water gaC 3ox *all I- ' '
/[ Fuel regon
"# / / inner water gao I '
'. N -// NarrCw water gao
- l l l l h YS j
- urtain 1 I I I I Vi fi / oron steet ll s
- s i l l i l' II !! - ,
!I t ll l l l l l l li j s a i i i i I, E i i a:
! I Il l l l l l5
! i l l l I i i l!
l e ' f I I I l l I I 25
I i Figure 1.7 Ex0m0les cf WR ce!! gecFetry in 20 ciculction A quarter :t a PWR assemcly c. ntaining is xis sin cett positions. Water Mete Centmt rec pi -l gyg -l 7 ij I l l l l l Fuet psn cett l l l l y l ! l l Water gao .l - E l l l l l l I N I i llI l I g i lI A quarter of a FWR cssembly centaining 1/. x 1/.
- pin cell positions and large water holes F"*0'"**'
i l i l li I i Water hote g; j ,g ; j l H water sao i l l I I II I i l II I I I I .---__--___-_- . _ _ _
il
; Figure 1.8 Ee s'. nucilie :hains in CAS?C I
I-1,
,,e
---g
_ - q _ 3 syp _ - - - p.;
.,=
_ $ _ O M M
- 3. : 2 e, _ : ,,., -
_ : . e c ,., _ m ., _ mm_mm_mm_:. g 1 se,_:se,.,_ m,.,_ m , _ mm_mm _ : e,., (n,2n) l 3. 03eu _ 3 sp _ :38,u I I . E I I I E I E
/
E
I Figure 1.9 I Fission product chains
- 1. KrS3
- 2. Rh103 3 Rh105 4 Ag109 5 Xe131
- 6. Cs133 - Csl34
- 7. Xe135 + Cal 35 I 8. Nd143
- 9. Nc145 (52.77 %)
- 10. Pal 47 -
Pm148 - Sal 49 + Sm150 - Sm151 + Sm152 + Eu153 +
- Eul54 - Eul55 \
1 (47.23 ")
- 11. Pal 47 -
Pm148m
- Sml49 - Sm150 - Sm151 - Sm152 + Eul53 -
1 - Eul54 - Eul55
- 12. Pal 47 - Sml47
- 13. .NSFP (non saturating F.P.)
- 14. SSFP (slowly saturating F.P.-)
I I I II _. . . .
I 2.0 BASIS FOR CONFIDENCE The bases for confidence in the CASMO code are of four kinds. First, the program is based conceptually on known methods and data. For example, the treatment of spatial and energy transport in a pin-cell by radial collision probability methods is common practice in LWR neutronics (THERMOS (8), GE(9), TVA(10)) and is based here on the well-known methods developed by Carlvik(ll) . Similarly, the two-dimensional flux calculation is based on a publicly available method described in Nuclear Science and Engineering (7). The library is based on ENDF/B-III data, with only a few minor changes, chiefly to eliminate the well-known discrepancy in U-238 resonance integrals (12), Second, the authors of the code, both corporately and personally are well-known and have made significant contributions to LWR modeling. Third, a version cf the program which is only slightly different has been applied to LWR's in Sweden for some years. The CASMO bundle physics I code was developed and has seen its most extensive use there, having been employed for over five years in the design or follow of more than 20 BWR l cycles and 3 PWR cycles. In the United States, it is distributed by EPRI to member utilities (on a proprietary basis). EPRI has additionally suppo rted CASMO benchmarking and the development of interface programs to 'I link CASMO with nodal programs. The CASMO programs used in Sweden and in the United States are similar except for the cross-section libraries and certain editing capabilities. The Swedes typically use a library based on British data, whereas the United States uses a library based on ENDF/B-
~ - - sectt .
1I
I Fourth, the ultimate basis for confidence in CASMO consists of integral comparisons of CASMO-calculated results with measured data and with the results of higher order calculations or those done by different methods. I For the purposes of these integral comparisons, the functionally significant aspects of CASMO are considered to be: I - Nuclear data library Treatment of neutron transport and spectrum in pin cells Tr ea tment of strong absorbers (control rods and gadolinia) I - The two-dimensional calculation of the whole fuel bundle Treatment of depletion The integral and higher order results available for comparison are shown I in Table 2.1, and the CASMO functions which they test are indicated. The first four integral comparisons were performed by Yankee using the United States library (ENDF/B-III). These United States results alone are fl i l5 sufficient to provide tests of all five functional parts of CASMO and are l lE "d*'*d**""*'"**"'"*""*"'" ' '"* ^S" *"'^ * "" """** l3 of operating cycles of Vermont Yankee and Quad Cities, to provide sufficient l basis for confidence in the use of CASMO on Vermont Yankee. Nevertheless, because the Swedish results are so extensive, they are included here for l background information and as further proof of the program's general i ! applicability. l ll l 3 I -
I 2.1 Yankee Calculations 2.1.1 Comparisons With Uniform Pin Cell Lattice Criticals The eigenvalues from the CASMO analyses of 59 uniform rod criticals are shown in Figures 2.1 through 2.5. These comparisons constitute an integral verification of the following: The nuclear data library (particularly uranium, oxygen and water cross sections) I - Treatment of neutron transport and spectrum in pin cells including: o Resonance integral calculations o Slowing down treatment i o Spatial transport within the pin cell I t j - Fundamental mode calculation (also used in the 2-D bundle l calculation) Data for criticals came from two sources (References 13 and 14]. The data l compared are the multiplication factors (keff) as a function of enrichment, lattice pitch, critical buckling, soluble boron and water-to-metal ratio. l The comparisons presented are for light water, uranium dioxide criticals in both aluminum and stainless steel clad. The enrichment varied from ,g 3 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 f rom 17 to 100 m-2 The soluble boron varied from 0 to 3400 ppm and the water to metal ratio 31 I
I from approximately 1.0 to 4.0. The CASMO results are from unit cell calculations using the measured critical bucklings. Figures 2.1 through 2.5 show the multiplication factor versus the selected para:neters mentioned above. As can be seen, the CASMO results agree with the dat.a over the wide range of critical experiments presented here, and without any significant trends. The average of all 59 values of k effective is 0.9993+0.0103 for the 69 group library and 0.9992 1 0.0102 for the 25 group library. Figure 2.3 shows that a large part of the variance arises from the set of five experiments with 2.07 w/o fuel, whose k effectives range from 0.9 to 1.05. I If one excludes this set of data on the grounds that these :neasurements 'I_ or their descriptions are somehow faulty, the results average 0.9988 1 0.0067 for the 69 group library and 0.9987 1 0.0066 for the twenty-five group lib ra ry . l l When viewed as a function of the nuclear library used (25 or 69 group), these results show the excellent agreement between the two. Although l the fif ty-nine critical experiments include various degrees of leakage, thermalization, and resonance capture, the average k effectives from the two libraries are within 0.0001, and the maxi:num dif ference for any single l expe riment was 0.0015. In addition, Figure 2.6 compares the values of pin cell k infinity for the same lattices, as calculated by CASMO and MICBURN. The agreement between the results from the two codes is an operational verification that , the pin cell calculations in the two are identical. 32 I
I 2.1.2 Comparisons With Measured Yankee Rowe Isotopics The comparison of calculated uranium and plutonium isotopics as a function of burnup with .he values measured during the Yankee Core Evaluation Program (16) constitutes integral verification P all the parts of the CASMO method discussed in the section on uniform rod criticals, as well as the following: I - Additional parts of the nuclear data library; I o Temperature dependence of resonance integrals o Temperature dependence of other cross sections o Plutonium cross sections Unit cell slowing down and transport calculation under hot conditions; .I - Depletion calculation. I The data presented here represent measurements of fuel rods in perturbed, intermediate and asymptotic reactor neutron spectra. The perturbed 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 I are well away from and unaf fected 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 /!!TU. I 33
I The CASMO calculation modeled a unit fuel pin cell corresponding to the asymptotic region in the measured data. The pin cell model included the fuel pin itself, clad plus gap, pin cell water, and a fourth region consisting of instrument thimble, Zircaloy control rod follower and associated wa ter. I The comparisons for U-235, 236 and 238 are presented in Figures 2.7 through 2.9 and the comparisons for Pu-239, 240, 241 and 242 are presented in Figures 2.10 through 2.14. The calculated isotopics agree well with the measured data for the three types of spectra. 2.1.3 Comparisons k'ith Criticals Containing Strong Absorbers The correctness of the CASMO control rod calculation has been demonstrated by comparison of the reactivity worth of heterogeneous strong absorbers measured in critical experiments performed by B&W(15). Figure 2.15 shows that the values of k effversusapproximateabsorberworth(%g) are approximately constant independent of absorber worth. The average k effective of the 11 cases poisoned heteror,eneously with absorbers was 1.005 compared to an average of 1.009 for the five cases without heterogeneous po iso ns . Furthermore, the two higit poison worth cases yielded n average k of 1.006, substantially identical to all the other cases. (The k effectives are somewhat above unity here because the critical facility was a small, high-leakage unit. Except for Case 1, however, the size and therefore the leakage was essentially constant.) As shown in Table 2.2, up to 12% reactivity worth was held down by the strong absorbers. The experiments were performed by measuring the critical water height and soluble boron concentration in a critical facility containing a 3x3 34 I
I assembly mockup with various borated absorber sheets located between the assemblies. The calculations utilized a radial, two-dimensional, four group, PDQ model with macroscopic cross sections f rom CASMO for the various regions. The radial PDQ model was needed because radial flux distributions and leakage were an important feature of these experiments. Axial leakage was small and approximately constant in these experiments and was represented as a buckling. Unit assembly PDQ calculations, with the same mesh spacing as in the core calculation, were used to adjust the diffusion theory cross sections for the strong absorbers so that they held down the same reactivity as they did in the unit assembly CASMO. I 2.1.4 Comparisons With Monte Carlo Calculations KENO-IV Monte Carlo calculations have been performed (17) as a general check on the transport and spectrum treatment in CASMO. These constitute an integral verification of the following aspects of the CASMO method: I - Calculation of strong absorbers o Treatment of gadolinia bearing fuel pins o Treatment, including homogenization, of the control rods Treatment of slowing down and spatial transport in unit fuel cells; I - Treatment of spatial transport and slowing down in the 2-D bundle calculation. I 35 I
I Considerable care was taken to assure that corresponding CASMO and KENO calculations were consistent: I - Identical geometries were used; I - Identical cross section libraries were used at identical temperatures; Identical nuclide densities were used. In some cases, consistency required that the CASMO model be slightly modified f rom that of an actual fuel bundle to assure that it was identical to the KENO model. This has no ef fect on the comparison of neutron transport in KENO versus CASMO and in any case the deviations from reality, listed below, are small. These were: The corners of the channel were squared off rather than rounded; The temperatures of water, clad and fuel were slightly dif ferent than expected at. normal operation, so that the CASMO scattering ,g W cross sections could be accessed at library temperatures to avoid interpolation; lW l The pitch of the B4C tubes in the control rod was made commensurable with the fuel pin pitch (3 control rod tubes per fuel pin pitch) and the hub of the cruciform was squared of f. l l Except for the above factors, the KENO model was an explicit 2-D, detailed representation of the fuel assembly. Each square pin cell and ig the cy11ndrica1 fue1 gin and c1edaing within it were representea exp11 cit 1 7. I 3e I
I The assemblies analyzed are listed in Table 2.3. The results of these analyses are shown in Tables 2.4 and 2.5 and Figures 2.16 through 2.27. Table 2.4 shows the excellent agreement in eigenvalue obtained for I the two codes. The standard deviation of the dif ferences between the CASMO and I KENO local power distributions is 3.01% for all pins. For only the peak pin in each bundle, the standard deviation is 2.33%. These values are consistent with the typical neutron flux uncertainties resulting directly from the Monte Carlo statistics. 2.2 Swedish Calculations Swedish work consists of comparisons with critical experiments (on both UO2 and mixed oxide fuel) performed in the KRITZ f acility at temperatures ranging from 200C to 2450C, analyses of the TRX and ESADA criticals, comparisons of measured and calculated values of SAXTON isotopics, and comparisons of measured and calculated gadolinia concentrations in burned fuel rods. As stated before, most of the Swedish analysis using CASMO is based on a British cross section library. However, the behavior of the British library is similar to that of the ENDF/B library, and the Swedish results are provided here both as background information and as further evidence of the program's general applicability and consistency. I 2.2.1 Hot and Cold Criticals in KRITZ Unique experiments used for benchmarking CASMO are the high temperature critical measurements in the Studsvik KRITZ facility (18) . BUR I and PWR systems as well as uniform pin-cell lattices, using enriched UO2 37 I
I (1.2 w/o to 3 w/o) or mixed oxide fuel (1.5 w/o to 6 w/o Fu) have been studied at various temperatures up to 2450C. The comparisons with calculated values include fission rate distributions, reactivity, void effects, etc. These comparisons provide a basis for confidence in the CASMO treatment of: I - Pin cells
- Strong absorbers
- Two-dimensional bundle.
I The reactivity ef fect of gadolinium poisoning has further been studied in KRITZ using fuel bundles with up to 7 Gd203 poisoned rods per assembly. Geometries with cluster control rods containing B4C as Ag-In-Cd and cruciform control rods with B4C have also been studied. The facility is large enough to allow experiments to be performed with full length power reactor fuel assemblies and for many of the experiments such fuel has been used prior to its insertion in a power reactor. Each of the three BWR cases (shown in Figure 2.28) consists of a l 4x4 array of BWR type assemblies containing an 8x8 lattice of fuel rods. For BWR-1, three fuel rods in each assembly contained two w/o gadolinia. l For BWR-2, half the assemblies contained no gadolinia, and the other half lI each contained five fuel rods with gadolinia. For BWR-3, half the assemblies contained islands of mixed-oxide fuel rods. The PWR cases are shown in Figure 2.29. PWR-1 includes two mixed-oxide assemblies with water holes and absorber rods, surrounded by a uniform UO2 lattice. PWR-2 includes one mixed-oxide assembly surrounded by UO2 assemblies. The same uniform pin cell lattice of 1.35 w/o U-235 in UO2 rods was measured at 20 C and 2450C. I 3e I
I For further details of experiments and ca?culations, see Reference 19. The predicted reactivities for the critical systems studied are given in Table 2.6. The calculated values are all close to unity, in fact the agreement with the experimental value is, in many cases, better than could be expected from the uncertainty in the macroscopic calculation and in the experiments themselves. The fact that there is no special trend among all calculated values for these very different lattices is worth pointing out. I Values of keff are given for two temperatures for the uniform lattice. The high temperature value is slightly lower than the value for the cold lattice, a tendency that has been observed, also, in many other lattice physics codes, and which has been extensively studied by CASMO analyses of KRITZ experiments (20), I Measured and calculated fission rate distributions are compared in Figures 2.30-2.35. The figures show the deviation in percent between theory and experiment for all measured pins in a given assembly. In the experiments, considerable effort was devoted to eliminating systematic errors and to correcting for differences in source distribution inside the fuel pins (important especially for the Gd poisoned rods). The resulting uncertainty assigned to the fission rate in a given fuel pin depended on the number of measured rods of dif ferent enrichments, how the normaliza tion was made, etc. For the comparisons discussed here, average value s can be used, i .e. , a value of 11% for non poisoned UO2 rods and 11.2% for Gd poisoned rods (excluding contributions trom possible geometrical uncertainties). 39 I
I I Additional analvses have been made of KRITZ lattices with varying amount of Gd poison in the core. oombining the results from cores with dif ferent Cd content the experimental and calculated reactivity worth of gadolinium could be compared. In total about 20 critical systems with Gd were analyzed. The agreement between the Gd reactivity worth calculated by CASMO and the experimental value was very good. For typical values of (Ak )Gd/k = 0.2 the uncertainty in the CASMO predicted value of that quantity was within 1%, i.e. , within + 0.002. I 2.2.2 Cold Criticals On Uniform Lattices I CASMO has been benchmarked against TRX and ESADA (cold critical pin cell lattices). Results are listed in Tables 2.7 and 2.8 and in Figure 2.36, which show the calculated k effective as a function of the measured critical buckling. These provide a basis for confidence in the pin cell treatment used by CASMO. 2.2.3 Saxton Isotopics I Calculated and measured isotopic compositions for Saxton are compared in Table 2.9. These provide a basis for confidence in:
- Pin cell treatment
- Depletion calculations.
I The agreement is good for the most important uranium and plutonium isotopes as well as for americium and curium. The concentrations of Np237, 'u238 and Pu242 appear to be underestimated. 40 I - -
I 2.2.4 Gd Depletion in Oskarshamn One 8x8 assembly containing gadolinia poisoned fuel pins was removed f rom the Oskarshamn I BWR af ter a short irradiation to undergo non-destructive and destructive testing to determine the depletion of the gadolinium isotopes (21) . The initial Gd203 content was 1% for two of the I Gd rods and 2% for the third one. The results provide confidence in the CASMO treatment of:
- Pin cells
- Strong absorbers
- Depletion.
A comparison between the experimental data and the results from calculations using MICBURN-CASMO was performed. The depletion of Gd 'in MICBURN-CASMO is given by the fraction f defined as: f . (N155+N157) irradiated (N155+N157) initial where N155 and N157 are the number densities of Gd155 and Gd157. The gadolinium absorber was depleted to f-values of the order of 0.3 and 0.5 1 in the 1 and 27. rods, respectively. Calculated and measured values are (I compared in Table 2.10. l 'E MICBURN yields the depletion of all five gadolinium isotopes. In Table 2.11 the ratios of calculated to measured isotopic concentrations are given. I All calculated results in the present comparison agree with the 41 I
I experiments within the experimental uncertainties. In the same assembly, the burnup was measured in 16 of the 64 pins. Figure 2.37 shows the deviation between calculated and measured burnup of the individual pins. The average burnup of the assembly was about 650 mwd /t. 2.2.5 CASMO Power Reactor Benchmarking in Sweden The longest experience in the use of CASMO for power reactor calculations is in Sweden. A total of more than 20 cycles in 5 BWRs and 3 cycles in a PWR have been followed using few group cross sections generated by CASMO. The three-dimensional core calculations were carried out with the Swedish core simulator, POLCA. The experience in Sweden shows that CASMO is capable of generating data which result in an essentially constant kef f throughout each cycle and about the same kef f for each cycle in a reactor. Calculated k eff values are the same for highly poisoncd gadolinia cores and cores without gadolinia. Of special interest is the benchmarking of CASMO against cycle 4 i in the Oskarshamn 1 BWR which contained a substantial amount of gadolinium. A total of 90 fresh assemblies with an average enrichment of 2.5% 1 and containing 6 rods poisoned with 3% Gd203 were loaded at the refueling in 1976. The gadolinium assemblies consisted of 3 different axial zones, each with dif ferent gadolinium contents but with the same U-235 enrichment. In addition, 28 fresh assemblies with 2.2% enrichment and 21 earlier irradiated assemblies were inserted. The remaining 309 assemblies were l of 7 different types with initial average enrichments from 1.7 to 2.6%. lI l The burnup rate of the gadolinium loading was designed to compensate 42
- I
I for the reactivity loss from the depletion of U235 during about 80% of the cycle. During the remaining period, compensation could have been achieved by increasing the main recirculation flow. For other reasons the total cycle length was shortened somewhat and control by the recirculation flow was not necessary. The re fo re , the core contained only four deeply inserted control rods which were moved only slightly during the cycle. In addition, eight shallow rods were occasionally inserted in the bottom of the core to minimize the peak power. The benchmarking of reactor physics codes against Oskarshamn I, cycle 4, constitutes a thorough test of the methodology because: The large amount of gadolinium in the core requires the use of highly sophisticated and accurate programs to predict the gadolinium depletion correctly. The small and constant amount of control rods in the core facilitates I the calculations and reduces the risk that compensating errors would conceal errors in the gadolinium calculations. The good operating statistics for the cycle, especially during the first part when the reactor was operated at full power during 122 consecutive days made the simulation of the operating history simple. The data library used with CASMO in the Oskarshamn analysis was the standard 25 group library used by Swedish utilities. It is based on the Uni Kingdom Nuclear Data Library (UKNDL). The reactivity level is about ( 4 higher with the UKNDL library than with ENDF/B-III data but all types of I reactivity coefficients differ very little. The reactivity worth of I 43 I
gadolinium was about 57. at BOC and 0.257. at EOC. Control rod movements we re small. I Since the analysis of Oskarshamn 1, cycle 4, in 1977 several heavy Gd loadings have been operated in all the other Swedish BWRs (Oskarshamn 2, Barsebeck 1 and 2 and Ringhals 1). The analyses of more than 10 dif ferent cores with various Cd designs using CASMO generated few group cross sections all give consistent results. Thus, the results for Oskarshamn 1 are typical for core following in the Swedish BWRs. I It is also worth noting that cycles 5 and 6 in Oskarshamn 1 contained no or very little gadolinium. The analyses with CASMO data gave the same calculated k eff level and the same agreement with TIPS as the analyses of Gd cores. 2.3 Summary of CASMO Benchmarking CASMO has been extensively benchmarked against U.S. and Swedish critical experiments, power reactor measurements and power reactor operating data, and higher order calculations. Many different and independent series of information have been used for the verification: I - Measured criticals for a wide range of UO2 or M02 enrichments. Fuel i radius, pin pitch, temperature, boron concentration, core size and 1 i I other parameters were varied in the experiments. Typical BWR and PWR geometries with or without absorber rods were included in the benchmarking. The hot critical measurements in KRITZ give unique experimental information which has been used for verifying CASMO. l Measured data include criticalities and fission rate distributions. I
I I - Measurements of the gadolinium isotopic compositions in irradiated fuel. I Measured isotopics in Yankee Rowe and Saxton irradiated fuel. Operating data for BURS. I - Criticals containing strong absorber sheets. Monte Carlo calculations. l l The results from the different types of benchmarking are consistent. We conclude that: Most calculated k eff values for critical experiments lie close to unity with a standard deviation of + 0.007. No or very weak treads versus leakage, boron concentration, enrichment and pitch are observed. This is consistent with the eigenvalues from Monte Carlo calculations, which show good agreemenc with the CASMO values. I - The reactivity worth of gadolinium was predicted within + 1% (i.e., kGd = 10.002 for kGd = 0.2) for hot and cold criticals in KRITZ. The standard deviation between calculated and measured internal power distributions is less than 2% in assemblies with or without absorber rods. This is again consistent with Monte Carlo results which show standard deviations of 2-3% between CASMO and Monte Carlo local power I distributions. The Gd depletion was predicted within experimental uncertainties. I 45 I - -- . -- - -- -- .
l I Core follow in Sweden of more than 20 cycles in BWRs and a PWR using CASMO few group cross sections generated a flat value of keff versus II l exposure. The agreement between calculated and ceasured TIP-curves ! is satisfying. The analyses cover cores with heavy 8adolinium loadings and cores without gadolinfun. I I tI I I 'I 'I I I I I I 46
m e e e e m M M M W W E M r 4 i TAlilE 2. I l !!ASES FOR Cor1FIDEllCE Ill CASHO i YAt1KEE VERIFICATIOt1 __ SWEDISit VERIFICATIOli il6W Strong KENO ESADA/ OSKARSilAMil OSKARSilAMil j PARTS OF Pin Celi Howe Absorber Monte KRITZ ' THX SAXTOil Cad llepletion Ciitical CASMO Cr i tic als Isotopics Criticals Carlo Criticals Criticals Isotopics Measurements Eigenvalue Cr oss Section I.ibrary X X X (X) (X) (X) (X) (X) i Pin Cell Cal cul a t ions X X X X X X X X X , Strong Absorber i Treatment X X X X Two- D i me ns i ona l CaleutaLions X X X 1 X X j 1)e p l e t i on Calculations X l X X X f t j ( ) Swedish calculations used the IIKNDL based Ilbrary i I
1 I l TABLE 2.2 Critical Experiments with Strong Absorbers Soluble Gap Boron Between Core * (ppm) Assemblies ** Abso rbe r+ I O 0 - II 1037 0 - III 764 1 - IX 0 4 - X 143 3 - XI 514 1 SS304 lI XII XIII XIV 217 15 92 2 1 1 1.614AL 1.257AL SS304 XV 395 1 . 401AL XVI 121 2 . 401AL XVII 487 1 . 242AL XVIII 197 2 . 242AL I XIX XX XXI 634 320 72 2 3 1 . 100AL
. 100AL
. 100AL lI
- Core designations from Reference 15.
l ** In pin pitches.
+ Number in front of aluminum sheet designations is approximate weight pe r ce nt natural boron.
I I I l 48
--.--.,,.m--- -
,,y-.m- , , , . ----------.,_.y..,,--,.--,---.,-,,---.y.,-,,e,--,-s-
,-=.s-----.,,~...-.-----.w- ,.---w--- .,,-.w+- . - - -- - - - - * - . - , - - - - * - - - - -- - - + , - --
I TABLE 2.3 i Assemblies Analyzed for KENO-CAS!!O Comnarison Avg. No. of Void Control Assembly Designation
- Enrich (w/o) Rods With Gad (%) Rods?
21931 2.19 0 0 No I 219M 219M 219M 2.19 2.19 2.19 0 0 3 40 70 0 No tio Jo 219M 2.19 3 40 No 219M 2.19 3 70 No 219M 2.19 3 0 Yes 219M 2.19 3 40 Yes 219M 2.19 3 70 Yes l 274M 2.74 5 40 :o 274M 2.74 5 40 Yes 274 2.74 5 40 No .I
- Bundles designated "M" are compared (both KENO and CASMO) at non-nominal co ndi t io ns . See Section 2.1.4 for details.
l I l n i 1 1 I 49 !I
TABLE 2.4 Comparison of K Infinities From KE!!O & CASMO i l Bundle Avg. No. of Void Control K Infinity Desienation Enrich (w/o) Rods w. Gad (%) Rods? CASMO KE!!O* 219M 2.19 0 0 No 1.249 1.250 219tt 2.19 0 40 No 1.242 1.240 219M 2.19 0 70 No 1.219 1.224 21951 2.19 3 0 No 1.125 1.120 219M 2.19 3 40 No 1.110 1.104 21931 2.19 3 70 No 1.082 1.078 219M 2.19 3 0 Yes 0.898 0.901 219M 2.19 3 40 Yes 0.827 0.834 I 219M 274M 274M 2.19 2.74 2.74 3 5 5 70 40 40 Yes No Yes 0.751 1.099 0.835 0.755 1.094 0.841 274 2.74 5 40 !:o 1.046 1.039 I
- KE!!O values of K infinity have standard deviations of 0.002 to 0.003.
I i l I 1 I l I l 50 l
I TABLE 2.5 Comparison of Local Peaking From KENO and CASF10 Peak Rod to Assembly Average Ratio Avg. No. of Bundle Enrich Rods Void Control Designation (w/o) w. Cad (%) Rods? CAS310 KE N0* Percent Dif. 21931 2.19 0 0 No 1.169 1.164 -0.4 219M 2.19 0 40 No 1.159 1.140 -1.7 219M 2.19 0 70 No 1.171 1.165 -0.5 219:t 2.19 3 0 No 1.310 1.241 -5.4 219M 2.19 3 40 No 1.238 1.201 -3.0 219M 2.19 3 70 No 1.206 1.222 +1.3 219M 2.19 3 0 Yes 1.813 1.735 -4.4 219M 2.19 3 40 Yes 1.766 1.711 -3.2 219M 2.19 3 70 Yes 1.704 1.641 -3.8 274M 2.74 5 40 No 1.269 1.301 +2.5 274M 2.74 5 40 Yes 1.706 1.660 -2.7 274 2.74 5 40 No 1.254 1.263 +0.7
- KENO values have standard deviations of 0.02 to 0.03.
1 l l l 1 51 l
I TABLE 2.6 l CASMO Results For The KRITZ Critical Lattices I Case Temp, "C CASMO k eff BWR 1 245 1.001 BWR 2 245 1.000 BUR 3 245 0.999 PWR 1 245 0.998 PUR 2 245 0.995 Pin Cell 20 0.997 Lattice 210 0.993 I I I I 'I I 52 l
I I TABLE 2.7 CAS'!O Results for TRX Criticals i No. !!exagonal Pellet B2 (exp) k eff Iattice diameter l pitch (in) (in) (m-2) 1 .868 .601 28.4 .997 I, 2 .929 .601 30.2 .999 3 .989 .601 29.1 .998 4 .613 .388 25.3 .998 5 .650 .388 25.2 .997 I 7 .650 .383 35.5 1.000 8 .711 .383 34.2 1.000 E I E I I I I 53 I . - - _-_ ___ -. _ - _ _ - . -_ __
I TABLE 2.8 CASMO Resul t s for ESADA Cri tical s Exp Fuel Type Lattice Boron B2 (exp) k eff pitch cone (in) (ppm) (m-2) 1,2 8 % Pu240 .69 0 69.1 .999 3 .75 90.0 1.000 4,5 .9758 105.9 1.008 6 1.0607 98.4 1.010 7 1.3e0 3e.3 .ee7 y 8 .69 261 62.6 1.004 9 .9758 83.7 1.002 10 .69 526 58.3 1.002 11 .9758 63.1 .999 'g 12 24 x eu2 e .975e 0 7e.5 1.004 13 1.0607 73.3 1.002 1 I I I D
=
54 I - - _
I I TABLE 2.9 Isotopic Composition in Saxton Comparison Between CAS!!O and Experiment
!!uclide Experiment Experimental CAS$10-exp . 100 uncertainty exp Atom *
, U234 .00465 28.7 +15.9 U235 .574 0.9 - 0.3 U236 .0355 5.6 + 2.8 U238 99.386 0 0 Pu238 .109 2.2 -11.4 Pu239 73.77 0 - 0.3 Pu240 19.25 0.2 + 1.6 I Pu241 6.29 0.3 + 0.4 Pu242 .579 0.9 I
-16.0 Atom Ratios
!!p237/U238 1.14 10-4 15 -26.4 Pu239/U238 .04383 0.7 + 0.2 Pu238/Pu239 1.75 10-3 0.4 - 9.8 An241/Pu239 .0123 15 -10.6
< Ca242/Pu239 1.05 10-4 10 0 Ca244/Pu239 1.09 10~0 20 0 I I 55
I I TABLE 2.10 Comparison Between Calculated and !!easured Fraction f in the Irradiated Gd-Poisoned Pins I Initial Gd-cone 1-f eale 1-f (7, ) meas 1 1.00 2 1.03 I I TABLE 2.11 _ Comparison Between !!easured and Calculated Number Densities of Gadolinium Isotopes I
- Initial Gd-cgne Nealc/ N aeas I, (og Gd23 0 /cm )
154 155 156 157 158 100 - 1.01 1.00 1.00 1.00 200 1.01 1.02 1.00 0.99 I
*) N
- II irr-Ninitial I **)N154 too small to allow a comparison I
I I l 56 I _ . .. . - .. _ -
- M M M M M M M M M M M M M M M M M M Figure 2.1 COSMO-25 GROUP LIBRARY K-EFFECTIVE VERSUS CRITICRL BUCKLING i.Os .........i....... ui.........i......... ......... ................... .........n........i.........
I I l l 8 I I I I , 1.052 ._ 1.042 - 1.03 _
~
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1 M M M M M M M M M W M M M M M M M M M I i t f i )'ll!'t! 2.2 CASH 0-25 GROUP LIBRARY K-EFFECTIVE VERSUS LATTICE PITCH 1.06 - i . . . . . . iii ... I i'. . - - i i i i i . . . . - i . . l i I . 1.05__ . I 4 1.04 _ j i ! 1 03:_ -- l _ 1 - 1 022. , to 1 01 _
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- . . . . . = = .
.ji=.=i 3 .4-4
- LRTTICE PITCH (CH)
m W W m M W W W m M M M M M M M M m m i Figure 2.3 CASNO-25 GROUP LIBRARY K-EFFECTIVE VERSUS ENRICHNENT 1.06 . . . . . . . . j - . . . ....i ......
.g........ .
i 1.05 _
~
1.04 _ 1.03 _
~
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........j......... . . . . . . . . . . . . . . . . .
ENRICHMENT (HEIGHT PERCENT) e
M M M M M M M M M M M M M M M M M m M ligure 2.4 CASH 0-25 GROUP LIBRRRY d-EFFECTIVE VERSUS BORON CONCENTRATION 1.Os . . . . 1 05 - 1 4 1.04 _ 1 . 0 3.~ _i-4 1.02i_ _ m _; W g 1 01_._
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-5 30 C .Sd0 1030. . . .1530 2030 2r30 3030 .
. . 35b0 BORCN CONCENTRATION (PPN)
. M M M M M M M M M M M M M M M M M M M '
Fi tpire 2. 5 CASMO-25 GROUP LIBRARY K-EFFt.CTIVE VERSUS HATER TO NETAL RATIC 1.06 . i1 i
.I i i i i . ii.. t . ii ie i i ii.. .
i e i i i i , s 1.05 _1 1.04__ i - 1.03:.- __~. 1.02 _
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W W M M M M M M M M M M M M M M M M M l'igure 2.7 U-235 ATON PERCENT VS. BURNUP FOR YANKEE CORE I SPENT FUEL 4 i i - - i - - - - i - - - - - - - - l 1 i - - - - - - - - i i i > - - - - i = I i
- 3. -
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~
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7. ga . U - M " td ~ g - c 2:- O -I g _ g - a to m _~ he ~ N ~ l - D l[_ cl AGYnPTOTIC 6PECTRun nEASURED X PERTURSED SPECTRun nERSURED _ M INTERnEDIATE SPECTRun HERSURED _ - CASno AsyneToTIC SPECTRUN _ i cn O' I' 0 010 0 ' ' ' ' ' ' ' ' 02 C 0 0 ' ' ' ' ' ' 3 0 O d * ' ' ' ' ' ' l0 0 0 0 BURNUPfIIND/MTU1
M M M M W W W W W W W M M M M M M m i l Figure 2.8 l i U-236 ATON PERCENT VS. BURNUP FOR YANKEE CORE I SPENT FUEL
. 5 0. > i i i i i i . i i i i i > > > > i i i i i i i i i i e i i i i i i > > >
I I I I x ~. x x . i \ 40:. *
^
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'4 :
- p .-. -
4 2 - 4< w x o 3 0_- _ M - E x w j a. n - g, E _ x
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l to .20 _. e a asyneratic sercraun nEnsuRED M E _ _ , N . gg
\
1 1' 3 X PEnruRBED SPECrRun MEAGURED e x _
. 5 N INTERMEDIRTE 6PECfMun MEHSURED _
m _ i - casna asyneratic seECrRun i 10_ _ i : e -
) .
4 i i 0.00- ' g.........I . . . . . . . i 20d0d ' ' ' ' ' ' ' 30d0d ' ' ' ' ' ' ' 4'0000 BJRNUP(MH0/MTU) a
)
d
m M M M M M M M M M M M M M M M M m m I Figure 2.9 l U-238 ATOM PERCENT VS. BURNUP FOR YANKEE CORE I SPElli FUEL 100- . . . . . . . . .i I
.......i . . > > > . . . *
. I I
, 99-l : :
.g I Z -
I Ej 9 8_~ x . A. E c O
.M :
i V~ . E . m (O
- 97. _
m A3Yn.*TOTIC SPtCTRun nERSutED . ~-
- X PERTURSED SPECTRUM HEAGURED
', 3 . M INTERnEDIATE SPECIMun MEASURED l - CASno ASYnPTOIIC SPECTRUn 1 46 q _ e v.
, 95' i . . . . . . . ' ' ' ' '
' 30[0d ' ' ' ' ' ' ' 4'OL00 l 0(10 d ' ' ' ' ' ' ' d 0r(10 d BURNUP(NHD/MTU) 1
M M M M M M M M M M M M M M M M m m i i, Figure 2.10 , PU-239 HTOM PERCENT VC. BURNUP FOR YANKEE CORE I SPENT FUEL 100 - - - - - - - - - i i - - - - i = . - i - - - - - - - - - i - - - - - - - - -
~
1 ~
, 1
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.- xga m 702
_ ci AsynProtic sPEcrRun stEqsusEo W. _ i i - X PERTIRBE0 SPE"TRun nEASIRED a - l _ 1 _ M ItiTE1MEDIHTE S*ECTRUn nERSURED l l _ ** n \
- o. .
M
<n _
- CASMO ASYnPTOTIC SPECTRUM 2 60_ , . . . . . . . .
t0005 ' ' ' ' ' BURNUP(MW0/MTU)
' ' 200Cd ' ' ' ' ' ' ' 30C100 ' ' ' ' ' ' ' 40000
M M M M M M M M M M M M M M M M M Figure 2.I1 i PU-240 ATON PERCENT VS. BURNUP FOR YANKEE CORE I SPENT FUEL 25_ i iiiiiiiiii iiiI - - i - - i - i i _ t_ i i i . . . . . I I i g 2 0_._ * **
.. = _.1 i _
t
=
n r"q= 2 w : na : j g 15_^ _
=
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=,
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[ j MNM , o, 10_- dM N - a_ _ 2 O ASYMPTOTIC SPECTRun nEHSURED l 8 X PERTLRSE0 6PECTRun nEASURED b.: . M INTERNEDIATE SPECTRun MEASURED
- a
- casno asynPfoTIC .:PECrRun :
i1 - of .........
. . . . . . . $0d0d ' ' ' ' ' .
BdRNUP(NWD/NTU)
' $0C10d ' ' ' ' ' ' ' 40C00
- l i
I I j Figure 2.12 i PU-241 HTON PERCENT VS. BURNUP FOR YANKEE CORE I SPENT FUEL
- 16 . . . . . . . . i i . . . . . . ...i...... ..i...... . .
j i I i t y K _ m x _ 12_ . m . . l t n e ttJ _ U M N - f -~ , c g_ g . l-- PI RSYnPT9 TIC SPECTRUn itEASURED _ , e M un
! ta _
X Peti'IRBt0 S*ECTRUM MERSURED _
; I Q_
M INTERr1EDIATE SPE?TRUn itEASURED . a m
- 4__ - C9SnD RSYr1PTDTIC 6PECTRun _ .
i e x
~
.l ~ t _ E - O_
,.gcgg . . . . . . . jocgg . . . . . . 3gcgg . . . . . . . j, gg BURNUP!MHD/NTU1 i
M M M M M M ' M M M M M M M M M M ! Figure 2.13 PU-242 RTON PERCENT VS. BURNUP FOR YANKEE CORE I SPENT FUEL i
, G_ i . . . . e i i i i i i i . . . . . . I e i i i , i i , i i i i e i i e i i a 1 I i 1 J : -
- si .
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, n. - I _ ! ! N E[ I G RGYMPTOTIC JPECTRun MERSUMED l 1 X PERTtRSED OPECTNUn HERSURED _ ~_
- , M INTERnEDIHTE SPECTMun MERSURED ..
- - JASMO ROYnPTOTIC SPECTRUn
~
g . e _a-
- O , _ g ;- , i C. IOC'00 20d00 3CdOC 40000 BURNUP(PNG/MTil)
i Figure 2.14 PU-239/U-238 ATOMS /ATON VS. BURNJP
- 10_ . .. i FOR YANKEE CORE I SPENT FUEL
> >> .> ii 1 - iiii ' -
1 I i l 9_ _ i 5
~5 i :
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to - G ASYMPTOTIC SPECTRun MEAS RLD ' g :- xx -
' a :
x n : 89 X PERTURSED SPECTRun HERSudED : l m 3. _ I" g M INTs.RMEDIATE JPECTdun MEASURED _ j. i N a
- CRSnD RSYrPT0ile *PECTRun 5
- n. 2.I - e
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med :
. 1_b _
8 = "" _5 2 i O i _ 0- 3 10C0$ ' ' ' ' 'BURNUP(NWD/MTUi ' ' 20L0d ' ' ' ' ' ' ' 30 cod ' ' ' ' ' ' ' 4'OCOU l
m m M M M m M M m m i l Figure 2.15 1 j CALCULATED EIGENVALUES FOR HETEROGENE00 SLY POISONED CRITICALS
! 1.05 i i i i i i i i i 1 8 I I I 1 l ! I I I I ! I I
1 1 i e
, u g _
l > x x
- x x x
! >- x i y 1.00 x x 1;
- u. x u.
- w r .
t i - i l - ! u l 95 i i ! I i i i e i 6 l' d i L d d i d d 13 15 th 13 POISON h0RTH IPERCENTAg) l 80/12/12<
Figure 2.16
--------.,----.--------7------
I i .
.913 I ' '
I i l
.916 3 l l
.997 I I s l -'l
----r---- ----- - -
xsNo rissIcN dis?. -- I
.?93 .990 1 I
c.g s,v0 r!SSION DIST. l g
.990 .994 I l '
I 1.013 .396 I l I l i i RAT:o ( NO R.S.AI.:
- E D TO
- 1 * )
I t
.377 .906 1.000 l 1
.902 f i
.897 .979 I
, j g
.372 1.021 1.021 I g i I I
' I I I
I L_----._--- y I I 1.025 1.096 .950 l 1
.914 a g i g
1.056 1.046 .923 . 901 : ;
, g
.371 1.048 1.029 1.014 I i i ! '
, i I i i ,
7 1.054 1.027 .921 .906 --- i I f 1.013 1.029 .916 .932 0.00 1 1 g 1.011 .998 1.005 .372 --- i 1 , 1 I-- - L_----' I i 1.082 1.085 .940 .397 .933 .926 I i 1.069 1.056 .937 .916 .950 .939 1 g 1.010 1.027 1.003 .979 .982 .366 1 g i I.- . _
.926 1.127 1.011 .958 .931 .930 1.071 I
.923 1.141 1.014 .967 .965 992 1.077 a 1.003 .969 .997 .991 .965 .938 .994 i i
1.045 1.092 .967 1.128 1.147 1.164 1.020 .927 I 1.125 1.020 1.159 1.022
.956 1.012 1.140
.3e9 1.129 1.017 1.169
.996 1.009 1.011
.9?6
.990 VY 219 B['NOI.E NO Od;O3 - 0% VOID - NO RCDS 72
I Figure 2.17 I
.992 I i i l I I
.976 I ; ,
I i 1.016 ' l i I ( i I
)
1 i l l I ,
* - ~ '" -T* ~ ~ ~ ~
. KENO FISSION OI3T. !~~~
1.065 1.089 I c333g 7 33;cg 3737, I 1.035 1.043 1 1 1.029 1.039 l l 1 I I I i RA7:0 3 1---- J l
- - -t i i .N0 a.-A:.::ED TO - 1 3 ,
.334 .909 1.02 l 1 3
.939 .924 -1.006 : I
' l
.995 . 984 1.016 ,
I i l I i
'._ _L --+ --_
I l I i I 1.370 1.100 .947 .896 , g i 1.088 1.077 .933 .890 : g I '
.983 1.021 1.015 1.007 I I I s I i i i i g
g --t , i 1.067 1.049 . 323 .886 --- i l 3 1.066 1.050 .?16 .904 0.00 I l ; 1.001 .999 1.00d .960 --- I g _ _ . _ _ _ L - - _. _ _ l I 1.097 1.093 .935 .921 .904 .915 I i 1.090 1.075 .934 .891 .909 401 I g 1.006 1.017 1.001 1.034 .994 1.016 g I I t______q
.950 1.140 1.023 .909 .896 .333 1.029 I 941 1.15) 1.003 .945 .o33 .M8 1.04: ,
1.010 .984 1.014 .962 .960 . 374 .388 l i I 1.094 1.079 .953 1.080 1.066 1.097 .96: .882 1.043 1.065 .943 1.103 1.097 1.1:4 .971 .901 1.049 1.013 1.016 .975 .981 .376 .991 . 979
'/Y 219 BUND!.E NO Gd 02 3 - 40% VOID - NO RCDS II l
l l 73 1 L
I Figure 2.18 i l
- 1 s l ,
i i 1.035 I l i i 1.019 : I i i , I 1.016 i e ! I i l I 6
-____p--__1 -___I _ -;
I Kn;0 7:ss:0N 0:st. i i--- I 8 1.074 1.099 I j CASMC T!53!CN 0:57 '
' I 1.077 1.096 I I ! ' ' '
.9:7 1.003 >
) I i .A..U
-" -- i I '_---- ---- -
(NO .u l::IO To ala) ' - - - 1.012 .376 1.040 1 I a
, .367 g .?62 1.044 I I i
. 1.047 6 1.015 .396 '
3 , I l l I I ______L_____+__________y I I ; 1.118 1.135 .959 .867 l l l 1 l' 1.110 1.110 .957 .a98 i g I l, 1.007 1.021 1.002 .965 I i
, , (
} , i i i 1
1 I l 1.107 1.060 .936 .379 --
' ' I 1.090 1.076 .930 .a97 0.00 1.025 .385 1.006 .360 ---
I i I l i ! I j 1 1 1.111 l.105 .928 .899 .SS7 .872 1 ' l.101 1.095 .941 .980 .882 .873 3 l 1.009 1.009 .986 1.020 1.006 .999 3 [ t f I
=
, ,--____)
.965 1.165 .993 .916 .384 .918 1.016 I
.949 1.171 1.003 .929 .?C6 525 1.001 i 1.017 .9v5 .?d5 .996 .376 .992 1.015 I i
i I ! 1.037 1.063 .917 1.067 1.023 1.050 .336 .827 1.047 1. ?A l . 32 9 1.074 1.044 1.073 .925 .955 l 1 .990 1.000 .988 .393 .960 .379 1.010 .979 i i e l l 1 J J
.c 219 acuC:.s NO Od;03 - 70% VOID - NO RCDS 1
1 i 1 74
I I Figure 2.19
---_7.___
1.039 8 1 i 8 1 I I I l.023 g , . 1.016 3 i i , , l 1 I i i I
---r-----*
g
. I KE:o risS:cN DIST.
.' - - -t 1.156 1.096 I l I I CASMO 'IS3 ION DIST. I 1.396 1.094 I I 1.064 1.011 l I
~ ~ ~ ~ ~ ~
l l
~ ~ - ' "
a
~~
SATIO (NC Fy.A* ~ 2 EO TO " 1") j'-~ I f 1.019 .955 .385 l i l ,
.987 .944 .971 i e ,
1.031 1.012 1.014 : i , I I I I I I I L--___,_..- I ; I i 1.161 1.086 .824 .205 3 , i 1.141 1.378 .317 .205 I i 1.018 1.007 1.009 1.000 I 1 l l l 1.064 1.000 .764 783 --- l l g 1 l I 7 l I I 1.112 1.319 768 768 0.00 I i i
.957 .381 .395 1.020 --- I g ,
l l
-- -- L---I I
I i l l 1.119 1.038 .227 .795 .962 '. 047 , , j 1.136 .993 .210 .804 .958 .946 , ,
.385 1.045 1.081 .989 1.004 1.051 ' l I
.983 1.195 .93- .949 .989 1.078 1.192 ;
.991 1.169 .355 .375 1.028 1.042 1.209 1.022 .977 I
.392 .973 .962 .987 .986 l
1.151 1.130 1.042 1.182 1.223 1.241 1.144 1.049 1.115 1.137 1.017 1.227 1.241 1.310 1.145 1.069 1.032 .994 1.025 .963 .985 .347 .999 .981 I I W 219 BCJDLE WIT!! Od 02 3 - On VOID - NO RODS I I I g u
I i l I l I Figure 2.20 I , , 3 ' ' 1.146 1 8 i 1.091 ' I e l.050 I I i I i 5 l ' I 1 , I f
------------: xtso r:ss:0s CIs- '--"
I 1.157 1.174 f I c333g 7 33 eg 3 37, I 1.147 1.142 I I . 1.009 1.028 i I I I
----'f--
i I .u;:0 (scar.u.::ca 0 13
-J i
t l l.057 .989 .973 l 1 , 1.027 .oA3 1.005 I l l l 3 1.029 1.006 .968 1 1 y 1 l 1 1 l t I l
----- L----_.---__ -- -
l l 1.176 1.162 .875 .257 ; i 1.173 1.111 .844 .251 s
, t 1.003 1.046 l 1.037 1.024 3 I ! ! l 1.148 1.041 .796 .009 --- 1 I I 1.136 1.047 787 .754 I Ij 0.00 1 l 1.011 .994 1.011 1.073 --- I [ ,
i
! I
- - _ - - L__-_I I
! 1 1.137 1.050 l .266 .778 .359 .920 ; i 1.157 1.029 ! .258 .786 .904 . 340 g
.983 1.020 1.031 .990 .950 .979 ,
i 1.041 1.195 .964 .936 .986 .991 1.126 l 1.010 1.190 .961 .945 .378 1.336 1.149 , I 1.031 1.004 1.003 .990 1.006 .957 .981 , l l l 1.144 1.154 1.0C0 1.139 1.135 1.201 1.033 .967 1.132 1.139 .996 1.179 1.17 1.239 1.0s4 1.013 f i i 1.011 1. 313 1.004 .967 .964 .970 .953 .955 1 l I W 219 BC;NDI.E WITH Od;O3 - 40% */0ID - NO RODS \ 9 l l
r I I Figure 2.21
, .7.----
1.1s2 8 i i l l.133 i e l.043 l I I I
' l s l I i
t ,
~
l ~~-~P . KENO ?!55: N :5- --" 1.222 1.216 3 I cx33c y;33;;y 7;37, f ' I 1.196 1.188 I i i 1.030 1.024 I I f i I ' I I I M*:0 i e~ '~ - ~ ~ j e
' ' ~ ~
( l l lNCFv.sl. :ID 0 al") lI
' I 1.051 1.047 1.062 l 3 g
1.153 1.321 1.050 1 1 l l .996 1.025 1.011 i ! g i t i I ' i 1 I
--- L-- -- _-_--
! l I '
I ; 1.143 1.103 .931 .325 s l 8 g 1.102 1.148 .888 .309 e g g
.359 .961 1.048 1.052 I I ,
1.160 1.052 I i I i l
~'t I
i I
.833 .793 --- t I I 1.143 1.000 .a23 .765 0.00 I i i .I 1.010 .974 1.012 1.037 --- 1 l
I I I
---- L-_--I I I
1.156 1.083 .327 .794 .854 .889 E 1.166 LOM .316 784 .870 .897 g g y
. S!l 1.016 1.035 1.013 .982 .991 i l .998 1.189 .988 .917 .957 .974 1.122 (
j 1.016 1.206 .971 .?25 .937 .983 1.084 , t .382 .966 .018 .991 1.021 .991 1.035 , l I i l I
- 1.142 1.127 .970 1.096 1.090 1.152 .984 .940 t
1.131 1.129 .971 1.129 1.112 1.162 1.015 .947 1.310 .998 .397 .971 .980 .991 .969 .993 I t I VY 219 BUND:.E I WIT:{ Od 03 3 - 704 VOID - NO RCDS I I n
I I Figure 2.22 7 ---- ,- , -r----7 I 1.159 1.132
.377 I
4 l l I i I 6 l I 8 l i I l l 1 l i
-____g. ___ _____ _ _
ggge p:337eg 3g37, :__ l 1.243 1.105 g I CAsMo riss:CN DIST. 1.223 1.0as I I i 1.01o 1.017 I I 8 I i I PATIO I
'---- d--- '
(scPs:.::ro To 1 1 -J l I g 1.231 1.114 .912 1 1 I 1.222 1.007 1.103 1.005
.939
.371 I
I I i i i - I l i l _L____. ____ q 1.102 .368 .832 .878 l 1.097 .354 .834 .872 I I 1.005 l 1.040 .398 1.007 , , [ l
'______'_.____h____
g i l 1.121 .995 .993 .871 -- 1 I l 1.124 .995 .850 .909 0.00
.997 1.C00 1.015 .958 -- I I
__ ___ L _ _ - ._ _ i j i 1.156 - 1.098 .875 .866 .949 .887 I I 1.177 1.089 .862 .473 . 9 2 ') .885 I i
.952 1.039 1.015 .992 1.032 1.002 I l
l i t______q I 1.261 1.269 1.155 1.154 1.001
.368
.352 1.045
.897
.932 1.017
.942
.933
.887
.987
.358
.355 I
8
.394 1.010 1.000 I i
1.008 l.301 1.137 1.155 1.103 1.105 1.103 1.170 1.104 1.245 1.123 1.131 1.136 1.134 1.139 1.180 1.119 1.045 1.012 .373 .371 .374 .368 1.056 .987 i VY 274 3U 01.E WI""H OJ 03 - 40 i VCID - NO PCDS I I I I _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ - - _ --- 78
I I Figure 2.23 g_-_-_ I
' ' I I g l I
.384 I l i __
I - I
.354 ' I ;
i
; , 1 1.085 I I I I I
I , I
~~~~~F~~~~** i KE' 0 FISSICN DIST. ~~"
.454 .629 I I I
.453 .606 I I l CASMO FISSION DIST. g 1.003 1.038 I l I !
' I I I RATIO I up '_____I___ ' l- _ J l 1 i WC??>:.!:53 TO " 1"I g i 495 .634 .785 g i l
, g I
468 .623 .779 g i j g 1.05d 1.018 1.007 i i I ! g i i l I
' _ _ _ _ _ _L_.____ ____
l l I .606
.591 1.026 790 795
.994
.761 744 1.023
.249
.236 1.]56 I
I l I I l I 3 g g 1 i
' _ _ _ _ _'- _ _ _ h _. _ _
.625 .323 .818 .941 -- i i I
.633 .820 .773 .979 0.00 t i g I .388 1.004 1.059 1.03' l I
g I l I I
.733 .891 .271 1.006 1.233 1.302 1 8
.730 .869 .249 1.001 1.248 1.336 1 3 1.004 1.025 1.087 1.005 .988 .974 I g t
I I .817 777 1.192 1.155 1.085 1.114 1.214 1.23) 1.360 1.370 1.436 1.496 1.637 1.692 i _ _ _ _ _3 l a 1.052 1.032 .974 .379 .393 360 .367 1.222 1.217 1.242 1.537 1.603 1.735 1.609 1.5C8 , 1. M 6 1.227 1.216 1.580 1.671 1.813 1.616 1.529 i 1.063 .39 1.021 .373 .959 .957 . 9 9th .966 1 l lE vy 219 BL7CLE RCCOED - Os VOID - WITH Gd;03 i lI I I 79
I l I l l Figure 2,24 ____y .___-- I I
.434 I I I
' I I
.391 g i i i I l l '
1.111 l I I i I 1 I I I e , I
----r------ ,
l
, xt::o r:ss:cs 0: 2..
I I '
.47: .665 I I
, g cagye p:33;cy 3:37
.476 .603 I I
.992 1.104 I I I
I I I I i u;:o i I
.1 '
(NCF?.A*,,
-~J l l Z3 TO *l*)
.500 .62: .754 { l
- i
.484 .612 757 i I, ,
l 1.032 1.016 .996 i 1 I i g i i 1 s I
; I I
-_--_ _L_ . + ____I__ q I
l I I g
.614 .306 .733 .335 a ; 1 g
.610 790 735 .303 e t
1.006 1.034 .397 1.107 I I g i 1 I .677
.659
.829
.a19
.806
.77:
.888
.sss 0.00 i 1 1
1 : I I I I I i I i 1.J27 1.013 1.044 1.000 -- 1 l i l L _ _ _ _ _' i g I j .788 .?;l .336 1.019 1.162 1.293 g : 768 .894 .319 .999 1.201 1.291 I. g 1.026 1.030 1.055 1.030 .968 1.0G1 g i g i i J, I \ i I l i
.853
.920 1.166 1.135 1.145 1.120 1.176 1.221 1.286 1.334 1.411 1.459 1.657 1.633 l..___q I
1.C40 I
.9d4 1.014 .963 .964 .967 1.000 I
I 1.127 1.269 1.187 1.529 1.593 1.711 1.575 1.441 I , f 1.116 1.013 1.250 1.J15 1.209
.962 1.548
.988 1.627
.979 1.74
.969 1.591
.996 1.493
. !61 I. W 219 StR;01.0 ROOCED - 401 VoIO - WIT!! Gd23 0
- I 1I l
80
I I Figure 2.25 3-_ _ .- I 1 1 e 8
.465 l I I
i I
.430 1 I I !
1.081 I
] I I
. -- ---- ----- -. ~
KENO FISSION OIST. l I I
.532 .571 I
, l cASMc FISSICN 2:ST. ) g
.501 .602 I I
+
I I I 1.061 .949 i l t PATIO 1 i 3 ' ~~J g 3 (NCPliALI2ED TO "1")
.522 .633 I
756 l 3 i
.503 .605 740 1 I i
1.037 1.047 1.021 I 1 l t i I i i
'__--- _L____.-._.-_ I I 700
.631 1.109
.900 772 1.036
.792
.732 1.031
.412
. 3%
1.06a I 1 8 i j g I i 4 i g g I f f I I I l i 757 .841 .817 .904 -- 1 I I I
.649 .825 779 .879 0.00 8 1 1 1.100 1.013 1.049 1.323 -- 3 I ;
l l -- --- L__
! I l e
.812 .976 1.007 1.153 1.207 I. .aca .925
.440
.408 ?93 1.163 1.251 I
I 1.005 1.055 1.077 1.024 .992 .965 , i
.383 1.131 1.152 1.196 1.271 1.327 1.536 1.212 1.144 1.202 1.2?A '
864 1.416 1.613 I I 1.;21 .974 1.007 .367 .981 .937 .952 I I 1.149 1.255 1.196 1.412 1.531 1.641 1.474 1.371 1.166 1.260 1.192 1.502 1.570 1 704 1.534 1.457
! .M5 .s96 1.]Q4 .940 .975 .963 .961 .941 l
a VY 213 EU'!OLZ RCODED - 70. VOID - WITH Gd 023 I I i g e1
I 1 I I ' Figuie 2.26 y_---- , I .446
.427 1.045 8
I I I I l I I l l I l l I I I , ! I
----r---- ----- --
KENC F:ss:cN OIST. --M
.523 .629 : [ g C.tSMO F:53:0N OIST. ,
.514 '
.592 g l.017 1.062 y y 1 ---- I - l NC P.*A*.
- 2 E 0 TO *1*)
g I '
.576 .744 .799 l I
.579 ' '
.742 790 I I I I
.997 1.003 1.224 l i I I I I e_____ _t I I
I I i
.623 .372 .822 .895 8 l
1 I
.576 .349 .315 .950 ' I l
1.090 1.068 1.009 .942 , , l I I.------- -.
.669 I '
.850 .933 1.040 --
.662 .331 .914 1.065 0.00 ' I I 1.011 1.023 1.020 .977 -- I I
_ -__L--_.-- 1 I I l 797 1.007 .920 1.073 1.151 1.157 I I
.786 .970 .942 1.074 1.198 1.190 l l 1.014 1.038 .976 .999 .960 .973 I
[ t l I l.040 1.027 1.179 1.148
.471
.441 1.167 1.143 1.192 1.257 1.235 1.235
.525
.513 1_ _ _ _ __ 3 I
1.013 1.026 1.069 1.021 .949 1.]Q0 1.023 I i i 1.290 1.279 1.393 1.421 1.487 1.5a1 1.660 1.570 l I i
. 222 1 .043 1.224 1.045 1.411
.374 1.483
.958 1.547
. ')61 1.593
.930 1.706
.973 1.632
. 362 VY 274 BUNDLC RCODED - 401 VOID - WIT:t Cd 2C3 I
i lE 1 l I 8 ,g l
I I Figure 2.27 1.159 3 ' 3 j 1.164 l f I i l
, t l .996 l g I e I i I '
e e i 1.195 l 1.091 1 I 0 nss:cN 3:st ; l i 1.213 1.090 1 ! l cas,yo 7:33rc3 3r37 ,
. . .995 1.001 I I I
! ! I l t
' ^^T I
'_____.1___ -
' ' (NCFy.A:.!:ED TO " 1* )
1.136 1.165 .972 I I g s 1.215 1.121 .956
' i l .976 1.039 1.017 , ,
l I I l ______t_____._.___ I t ! 1.091 .361 .883 .915 8 i 1.091 .350 .849 .883 l I I 1.000 1.031 1.040 1.036 ; I I I 8 i I i i I i g . e l 1.097 1.020 .888 .906 __ i i i i 1.114 1.005 .893 .915 0.00 i I
.985 1.015 .994 .990 --
l ; I e g
'_____ 1.___.__
I I i 1.159 1.117 .883 .880 .901 .937 ' 1.165 1.096 .874 .381 .923 .891 '
' I
.9% 1.019 1.010 .999 .976 1.052 I
' i
' i i
I i
! 1.244 1.167 .358 .897 .893 - , .869 t______3
.365 ,
1 1.254 1.159 .348 .890 .938 .893 .349 l .992 1.007 1.029 1.008 .952 .973 1.046 I 1.263 1.095 l 1.193 1.109 1.110 1.088 1.191 1.145 , g 1.225 1.116 1.181 1.135 1.131 1.135 1.174 1.103 l ,' 1.031 .981 1.010 .977 .931 .959 1.014 1.038 I VT 274 31'ND12
'4ITH Gd 23 0 -40% VOID-NO RODS-NOMINAL TE'.'JERAT1 RES I /
I iI e y i
I I Figure 2.28 SWR lattices in KRIT2
/. x !. fOet assemblies 3x3 recs per assemet y.
i I i 3X 3X 3X 3Xl BWR-1 { 3X 3X 3X 3X All assemblies with three
} Gd poisoned rods.
3X 3X 3X 3X lI I SX 5 3 9.EE.:1 SX SX I Checker board tattice. SX SX Zero or five Gd poisoned rods per assemety. 5X EX i Pa U j Pu l U swr-1 U Pa Ul Pu Checker board lattice. Pu U PJ U UO2 or Pu-isIand l type of assemblies. I ul eu u . P6 I I I 84
I Figure 2.29 PWR tattices in KRITZ I I AWR 1 I U EU 15 x 15 MO2 assemoties with water holes and absorber rods, surrounded by a uniform UO2 lattice U i I I l U U U pwg 2 14 x 14 MO2 assembly and graded enrichment, l surrounded by UO2 assemblies U Pu U 'I ll U U U I I I es
I Figure 2.30 I Oeviation in oer cent bet ween calculated and measured fission rates in an 8 x $ UC2 assem0ty with 3 Gd poisoned rods. CASE SWR 1. T : 245*C (470*C) I wide gao
- 2. 9 + 2. 5 - 0. 7
-1.9 -0. 2 + 1. 8
-0. 4 -4.0 1.4 l g
-1.3 1.1 $
a 4 2 I E l - 0. 6 l
-0. 4 + 0. 6 I - 0. 5 - 2. 7 +1.2 + 0.5 I 0.0 + 1. 0 I narrow gap I Ordinary fuel pin Gd pin (2 w/o Gd 23 0 )
- I The figure shows 5; = 100 (PCASMO - PEXP )/ PCASMO for att measured positions.
I 3
I I .. Figure 2.31 I Ceviation in per cent between calculated and mea sured fission rates in an S 8 UO 2 I assemcly without gacetinium. CASE SWR 2. T = 24c'C (470* F; I wice gas
-3.7 1. g lI
- 0.3 1.1 .o. g I 0.0 + 0.1 + 0.1 lI c.
; +1.2 c.
l 1.4 3, E t a ;;
+1.0
- I
+ 0. 9 .1.2
-1.7 0.5 0.0 -1.8
-3.0 I 0.2 narrow gao
- 1.1 I
Ordinary fuel pin I The figure snows 5; = 100 (PCASMO - PEXP /PCASMO for all measured positions. I I 87
1 I ; l I Figure 2.32 I Ceviation in per :ent netween calculated and measurec fission rates in an 3 x 3 UC; I assemely with 5 Gd poisoned roc s. CASE SWR 2. I *L5'O (&~0
- F)
E wide gao I
- 2.3 2.1 -03
- 0. 7 ! - 5.1 *13
! t I . a l. -0.8 2 ; i 0.1 2.3 l -2.3 l + 3.1 g L i i i 3
I . 2 3
- 1. 0 o
I -0.5 +0.9
' i 1
. a_3 - 1.0 i :.1 '
1.2 l 1 I -0.5 narrow ,ao Orcinary fuet sin Gd sin ( 2 w/o Gd2 03 3 I 'I The figure shows 5; : 100 ( Pcy3po - Pgyp l / P;Aspo for att measured posi tions. I ,I w_,-,,w-- ___w -
1 I 1 I . 1 1 Figure 2.33 Deviation in per cent between calculated I and measured fission rates in an 3 x 8 assembly of the Pu-island type CASE SWR 3, TYP = 245 *c (470*F1 I , I ._ wide gap UO rods * "'Y 2.0 CASMO
+ 1. 8 P-- 1 1 i
- 0.1 + 0.1 i i I a -0.6 F--
l l *0.9 + 1. 6 M07 rods i I l 2
& a 4
l0 l ! 1 0 +2.9- i + 0.6 __ __ _.i : e I i I i-03 L -1.7 + 1.2 l 1 h
-0.1 +1.2 -03
-G8 [1.1 + 1. 2 i
-3.5 - 0.1 -0.9 -Q5 - -2.6 narrow gap lI The figure shows 5j 3100 -( Pj -P exD I/ i lg
!W and EP = EP,,, for all caasured positions. Operimental uncertainty ( le 1 in M02 rods
- 1. 4 '/.
.. U02 rods
- 0.5 */.
for the average I fission rate in MO2 rods relative to U02 rods: 1 1.6 */. 4 89 I
I Figure 2.34 Ceviation in per cent between calculated and measured fission rates in a 15 x 15 PWR M02 assemoly with water holes I and aesercer reds. CASE PWR 1 T = 245*C (470*F) tt l l w central water hole
/ / absorber rod
\ + < g I. C - i- .
~
- key
_j. / CASMO l
. j,4 MO2 rods I
\ ' ! ~ _ ~. _ 15 0.1 1. 2 i
=__=_
1-l
-2.7 -0.4 0.9 -C l -.-
I g< 1.2 __ = 03 0 - 1.1 I
-~~
1.7 - 0.4 -- 2.1 -10 ~ [ ~_ 19 - 14 2.0 -0.5 -19 - 2.7 0.4 1.5 - 1.S -0. S The figure shows Si : 100 ( P - P,,o } / P, and IP; : IPexo for att measured positions. Experimental uncertainty ( Ic): s 1.4 '/. (Not including geometrital uncertainties) I I e0 3
I I Figure 2.35 Ceviation in per cent between I calculated and measured fission rates in a 14 x14 PWR M02 assembly with water holes CASE PWR 2,7 = 245 'O ( 470
- F)
Center
./ . . . ! . . i . .
~
j 6
.t.7 High ennened t 0ASMO 'Y I - 0. 7
= . .
7_;
.0 "
- n/ .
I
- 1. 5 i- " 5 "*'** [
C
} .
+ 0.1 -0.2 I ,
3._ -f l 2:_-l-
-G7 7__:. >
_-L . I t
+Q1
+ 0.5
__._- 0.1 r__
-07 - 0. 3
*1.2 7* -3.5 l _
ns i Eu,W 2 rods i
,qg
*I.4 -a4
=. .: =. =*
43 5L ?U l I , . . . . . . . . . The figure shows 0; 100 - ( P; - P,,,1/ P, and I P = E P,3 g for all measured positions in the I M02 and UO2 regions separately. The average fission rate in the M02 assemblyrelative to the rate in the UO2 assemblies predicted by the core I program OlXY was 1.9 */. lower than the measured ratio. Esperimental uncertainty (la I for each typ of fuel separately : 1 0.8 '/.
" the average fission rate I in M02 rods relative to UO2 rods : t 1. 4 */.
I 91
E E E E W W g g g g Calculated keli v5 experimental a 2 m kett i l
*W 5*
l.01 O A_. ,
" !3 o o b b-
=a )
0 o o ~Ea c x g2 eg m 1.00 I g NN , -- m s x a
# # O 50 o O I o 01 A
? BO J m-2 3"# ea e o u N >
- y 0.99 __
o l e l ; 5 l t o MRliZ j l 0 ESADA
= TRF
I Figure 2.37 Oeviacion in per :en :.:veen gat uta: and measured burr.up in an 3x3 assecolv ' with 3 04 rods I wide gao I -1. 0 0.4
- 2. 2 -0.2 +1.2 I -0. 5 -1.1 I
- 1. 4 0. 4
,I 1 (5 c. 9 O 5 l . +1. 7 -0. 9 +1.1 $
.8 - ,
3 c I
+1.2 + 0. 2 +0.9
-1.0 narrow gao I
Gd-pin 1 w/o Gd 023 Ordinary fuel pin Gd-pin 2 w/o Gd 023 I 93 I . - _ _ _ __ , .- . . - -
I I REFEREFCES I 1. Ahlin, A., M. Edenius, "CASMO - A Fast Transport Theory Assembly Depletion Code for LUR Analysis", Trans. ANS, 26 (1977) 604.
- 2. Ahlin, A. , M. Edenius, H. Haggblom, "CASMO - A Fuel Assembly Burnup Program", AE-RF-7 6-415 8, Proprietary Studsvik Report.
- 3. Ahlin, A. , 'i. Edenius , "The Collision Probability Module CPM", Chapter 6, Part II of the EPRI-ARMP Documentation.
- 4. "The EPRI-CPM Data Library", Part II, Chapter 4 of the APl!P Computer Code Manuals, CCM3, Electric Power Research Institute, 11/75.
- 5. Seghal, B.R., and R. Goldstein, " Intermediate Resonance Absorption in Heterogeneous Media", NSE 25, 174 (1966).
- 6. Radkowsky, A. , Editor, Naval Reactors Physics Handbook, Vol . I, pp.
612, 613, TID-7030 (1964). See al so Rampolla , D.S . , " Adjusting l Absorption Cross Sections in Transport Calculations to Achieve Specified Region Capture Integrals", NSE 3 , 396 (1968).
- 7. Haggblom, H., A. Ahlin, T. Nakamura, " Transmission Probability Method 1I of Integral Neutron Transport Calculation for Two-Dimensional Rectangular Cells", NSE 56, 411 (1975).
- 8. Honeck, H., "THEPPOS, A Thermaliza tion Transp(.,rt Theory Code for Reactor La t tice Cal cula t ions", BNL-5826 (1961) .
- 9. "artin, C.L., " Lattice Physics Methods", NED0-20913 (July 1976).
I 94
I I 10. Darnell, B.L., T.D. Beu, G.W. Perry, " Methods for the Lattice Physics Analysis of LWR 's", TVA ~.'R78-02 ( April 1978) .
- 11. Car 1vik, I. , " Integral Neutron Transport in One-Dimensional l I Geometries", Nukleonik Q, 104 (1967).
- 12. Pearlstein, S., Editor, Seminar on U-238 Resonance Capture, BNL-NCS-50451 (1975).
- 13. Strawbridge, L.E, and R.F. Barry, " Criticality Calculations for Uniform, Wa ter-Moderated Lattices", NSE M, 58 (September 1965).
I 14. Price, G.A., " Uranium-Water Lattice Compilation, Part I - BNL , Exponential Assembliec", BNL-50035 (T449), (1966). 1 l l
- 15. Baldwin, M.N. e t al., " Critical Experiments Supporting Close Proximity Water Storage of Power Reactor Fuel", BAW-1484-7 (1979).
l l
- 16. Nodvik, R.J. , " Evaluation of Mass Spectrometric and Radiochemical Analyses of Yankee Core I Spent Fuel", WCAP-6068 (1966).
l 17. Hebert, M.J. et al., " KENO Calculations of Light Water Fuel Lattices", in A Review of the Theory and Application of Monte Carlo Methods, ORNL/RSIC-44 (August, 1980).
- 18. Persson, R., E. Blomsjo, M. Edenius, "lligh Temperature Critical Experiments with H 2O Moderated Fuel Assemblies in KRITZ", in Technical Meeting No. 2/11, NUCLEX72 (1972).
- 19. Ahlin, A., M. Edenius, "MICDURN - Microscopic Burnup in Gadolinia Fuel Pins", Chapter 7, Part II of the EPRI-ARMP Documentation.
I 95
I I I 20. Edenius, !!. , " Temperature Ef fects in Thermal Reactor Analysis", in Symposium Proceedings: !!uclear Da ta Problems for Thermal Reactor Applications, EPRI-f!P-1098 (June 1979).
- 21. Edenius, M. , K. Ekberg , V. Gustavsson, "CAS!-10 Benchmarking and ICF?!
i l Experience of the CAS>t0-POLCA Code Package", STUDSVIK/K2-78/29, l- European !!uclear Conference at Ilamburg, (?!ay 1979). I ,I I - I I . 1 I I I 96
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