ML20069B003

Nonproprietary Methods of Record - LWR Fuel Assembly Burnup Code

ML20069B003
Person / Time
Site:	Brunswick
Issue date:	02/28/1983
From:	Naess H, Skardhamar T, Wennemo S CAROLINA POWER & LIGHT CO.
To:
Shared Package
ML19344B748	List: ML20069A999 ML20069B003 ML20069B012
References
NF-1583.02, NUDOCS 8303160418
Download: ML20069B003 (169)

Text

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NF-1583.02 NONPROPRIETARY VERSION i

METHODS OF RECORD AN LWR FUEL ASSEMBLY BURNUP CODE TOPICAL REPORT FEBRUARY 1983

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Cp&L Carolina Power & Light Company I

0303160418 830310 j hDRADOCK 05000324 PDR

REC 0RD AN LWR FUEL ASSEMBLY BURNUP CODE H.K. Nass T. Skardhamar*

• Institute for Energy Technology, Kjeller, Norway NONPROPRIETARY VERSION TOPICAL REPORT

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Prepared by SCANDPOWER INC 4853 Cordell Avenue Bethesda, Maryland 20814

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20 aianuary 1333 Revie::cd by : '

ADD ""~ by :

N' S. E. :,'ennemo

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DISCLAIMER OF RESPONSIBILITY l This document was prepared by SCANDPOWER Incorporated on behalf of Carolina Power & Light Company. 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 Carolina Power & Light Company, SCANDPOWER Incorporated, and/or the appropriate subdivisions within the Nuclear Regulatory Commission only.

With regard to any unauthorized use whatsoever, Carolina Power & Light Company, SCANDPOWER Incorporated,'and their officers, directors, agents, and employees assume no liability nor make any warranty or representation with regard to the contents of this document or its accuracy or completeness.

Proprietary information of SCANDPOWER Incorporated is indicated by " bars"

, drawn in the margin of the text of this report.

1

ABSTRACT This report describes the methods of the RECORD computer code, the basis for fundamental models selected, and a review of code qualification against measured data. RECORD is a detailed reactor physics code for performing efficient LWR fuel assembly calculations, taking into account most of the features found in BWR and PWR fuel designs. The code calculates neutron spectrum, reaction rates and reactivity as a function of fuel burnup, and generates the few group data required by full scale core simulators.

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i VOLUME 1 METHODS OF RECORD AN LWR FUEL ASSEMBLY BURNUP CODE  !

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C0NTENTS Page ABSTRACT

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

2.

SUMMARY

DESCRIPTION AND MAIN FEATURES OF RECORD .... 2-1 2.1 Nature of Physical Problem Solved ..... .. . 2-1 2.2 Method of Solution . . . . .. .... ...... 2-2 2.3 Nuclear Data Library . . . . ... ... .... . 2-6 2.4 flain Features of Code .............. 2-8 2.5 Data Generation Unit of FMS .... . ..... . 2-12 2.6 Computer Requirements ... .. ..... ... . 2-15

3. THERMAL SPECTRUM AND FEW-GROUP DATA ......... . 3-1 3.1 Fundamental Equations .... ..... .... . 3-2 3.2 Flux Disadvantage Factor Calculation . .. .... 3-4 3.3 Spectrum Calculation . . . . .. .... .... . 3-7 3.4 Scattering Models .. .... . .... .... . 3-9 3.5 Point Energy Approach ............ . . 3-10 3.6 Macrogroup Data .......... . .... .. 3-13 1

ii Page

4. EPITHERMAL SPECTRUM AND FEW-GROUP DATA . . . . . . . . . 4-1 4.1 Fundamental Equations . . . . . . . . . . . . . . 4-1 4.2 Treatment of Resonance Absorption and Fission . . 4-6 4.3 Fast Advantage Factor . . . . . . . . . . . . . . 4-15 4.4 Macrogroup Data ................. 4-17

5. TREATMENT OF BURNABLE POISON . . . . . . . . . . . . . . 5-1 5.1 The THERMOS - GADPOL Method . . . . . . . . . . . 5-1 5.2 Gadolinium Treatment . . . . . . . . . . . . . . . 5-2 5.3 Shim Rod (Boron glass) Treatment . . . . . . . . . 5-4

6. CONTROL ABSORBES . . . . . . . . . . . . . . . . . . . . 6-1 6.1 Control Blades - BWR Option . . . . . . . . . . . 6-1 6.2 Rod Cluster Control - PWR Option . . . . . . . . . 6-6

7. TWO-DIMENSIONAL FLUX.AND POWER DISTRIBUTION . . . . . . 7-1 7.1 Multigroup Diffusion Equation . . . . . . . . . . 7-1 7.2 Geometry and Mesh Descriptions . . . . . . . . . . 7-2 7.3 Difference Equations . . . . . . . . . . . . . . . 7-3 7.4 Method of Solution . . . . . . . . . . . . . . . . 7-4

8. BURNUP CALCULATIONS .................. 8-1 8.1 Fuel Burnup Chains . . . . . . . . . . . . . . . . 8-1 8.2 Fission Product Representation . . . . . . . . . . 8-2 8.3 Solution of Burnup Equations . . . . . . . . . . . 8-3

9. OTHER FEATURES OF RECORD . ............... 9-1 9.1 TIP Insturmentation Factors . . . . . . . . . . . 9-1 9.2 Delayed Neutron Parameters . . . . . . . . . . . . 9-2

iii Page

10. CODE QUALIFICATION . .................. 10-1 10.1 Analysis of Clean Critical UO and UO /Pu0 2 2 2 Lattices . . . . . . . . . . . . . . . . . . . . . 10-2 10.2 Fuel Depletion Isotopic Analysis Comparisons . . . 10-5 10.3 Gamma Scan Comparisons of BWR Assembly Pin-Power Distributions .................. 10-5 10.4 Historical Review of LWR Analyses with RECORD -

PRESTO . . . . . . . . . . . . . . . . . . . . . . 10-8 ,

11. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . 11-1 APPENDICES :

A Breit-Wigner Formula for Cross-Section Calculations B Output Options in the Record Code C Excerpts from RECORD Output

1-1

1. INTRODUCTION In the design and operation of a Light Water Reactor (LWR), there exists a need for performing, in a routine way, the complicated reactor physics calculations necessary for the accurate analysis of LWR fuel assemblies, and to generate directly the few group data required for use in reactor simula-tion and fuel management calculations. Answers to reactor operation or design problems should be obtained quickly and efficiently from basic geo-metric and material specification of fuel assembly and control system, together with operating conditions and burnuo requirements, and with a minimum of time consuming work in data preparation and data transfer between different codes.

The code RECORD has been developed to meet the requirements of performing efficient LWR calculations, taking into account most of the complex features which arise in BWR and PWR fuel designs, and treating these with sufficient detail to ensure necessary accuracy. RECORD calculates neutron spectra, group data and reactivity as function of fuel burnup in LWR fuel assemblies.

Reaction rates, power and burnup distributions in two dimensions are calculated with individual treatment of each fuel pin, and taking into account effects of control absorbers, burnable poison rods, soluble poison, voids, and other heterogeneities which may be present. Of importance also are flexible restart options which enable straight-forward calculations to be performed at low-power conditions, and of differential effects dur-ing burnup. More over, RECORD is a User-oriented code, with an easily applied input, and provides clear and precise output listings in accordance with flexible output options.

The development of the RECORD code is intimately connected with the l development of Scandpower's Fuel Management System (FMS), an integrated code system for fuel management and core performance calculations in Light Water Reactors (Ref. 1). The basic units of this system are shown in i

1-2 RECORD represents the data generation unit supplying, through l Figure 1.0.1.

a data bank, the necessary reactor physics data to the macroscopic codes of FMS. In particular, RECORD generates the few group data and coefficients to the PRESTO Code (Refs. 2, 3), which is the 3-dimensional reactor simulator of FMS.

The RECORD Code and FMS have been under development since about 1969, with first commercial applications in 1972. The code has been in routine use since then. Through the years, RECORD has been subject to continuous revisions and extensions, with the introduction of model improvements to increase code accuracy and effectiveness, and incorporation of new options and features as needs have arisen. Users of RECORD have been Utilities and consultants in Europe and USA. Of particular importance in the development of RECORD and FMS, has been the active cooperation of reactor operators in providing feedback of information from actual raactor operating data from many different LWRs. The exchange of results and experiences between code developers and code Users has been of utmost importance.in bringing the RECORD code to its present high level of accuracy and performance.

The basic assumptions and theoretical models on which the code is based have been validated through extensive applications of. the code by many Users through the years in evaluation calculations, in project calculations, and data bank generation for PRESTO and other FMS codes. Reference 4 gives a review of some of the experiences accumulated through these years, using RECORD and PRESTO in the simulation of LWR cores.

Experiences in using RECORD-generated cross-section data base in BWR transient analysis with the In such analyses, RAMONA codes are discussed in some detail in Reference 5.

it is of particular importance to be able to model correctly during burnup, the coolant density (void) dependence of cross-sections, as well as effects t

due to fuel and moderator temperature variations.

This report provides a description of the main features of RECORD, and the physical assumptions on which the code is based. The basic physical models can be regarded as being well established and a.e not expected to be changed radically within the present concept of the code. In any large code system like RECORD, however, there will always be room for further refinements and

1-3 improvements, or introduction of new desirable features, as needs become defined through the accumulated experience of past and future applications of the code. Unless stated otherwise, the description of RECORD in this report applies to the 1981 production version of the code. A detailed program description, including description of input and output of the code, is otherwise given in the FMS Documentation System (Ref. 6), available to Users, and in various internal reports (e.g., Refs. 7 and 8).

After a summary description of the code and its main features, the report describes in detail the distinct models for the thermal and epithermal neutron spectra and group data calculation. A satisfactory model for the treatment of buenable poison is very essential for present LWR designs, and a chapter is devoted to the description of the THERMOS-GADPOL model used in RECORD. The treatment of control absorbers, and calculation of flux / power distributions and fuel burnup are described in subsequent chapters. Also described are the methods of RECORD in calculating TIP instrumentation factors, and delayed neutron parameters for application in neutron kinetic codes. A review of some of the analyses on which the code qualification is based is given in Chapter 10.

I i

1-4 l

l FALC FUEL CYCLE

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4L A FCS_n 1-0 T SURVEY CALC.

A II RECORD PRESTO NUCLEAR 3-D DATA i REACTOR SIMULATION CENERATION B 4L FDCA-POSHO A FUEL PERFORMANCE I ANAL'YSES E

K a^=ou^ i. n ni TRANSIENT ANALYSES FMS ScP'S FUEL MANAGEMENT SYSTEM l

FIGURE 1.0.1 The FMS Code System for Light Wat(c Reactor Calculations l

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2-1

2.

SUMMARY

DESCRIPTION AND MAIN FEATURES OF RECORD RECORD performs reactor physics calculations on BWR and PWR fuel assemblies, and generates data banks containing required few-group data, isotopic den-sities and other nuclear data for use by core simulators, such as PRESTO and other codes of the Fuel Management System, FMS. It is a production code, implying that these calculations can be performed directly and efficiently, and where system efficiency is viewed both in terms of computer resources as well as manpower needed to prepare input data and to digest the output.

This chapter summarizes the basic physical principles and features of the RECORD code. The physical models are described in more detail in the ensuing chapters of the report.

2.1 Nature of Physical Problem Solved RECORD determines reactivity, reaction rates, power and burnup distributions in two dimensions across an LWR fuel assembly. Typical BWR and PWR config-urations are indicated in excerpts of code printouts, as shown in Figures 2.1.1 and 2.1.2. The code can also treat internal water-cross fuel with geometry as indicated in Figure 2.1.3. The solution area on which calcula-tions are performed is the fuel assembly, together with the associated sur-rounding water gaps. The fuel is composed of cylindrical rods in a square regular array embedded in the water moderator. In BWRs, the lattice cells are surrounded by a flow box region, where the code always treats the whole assembly geometry. In PWRs, 1/4-assembly symmetry option must be assumed in most real cases.

l Each lattice position defines, in general, a fuel pin cell composed of one fuel rod and its surrounding moderator. Some positions may be empty (water holes) or, in PWRs, may be occupied by rod cluster control rod fingers or burnable poison shim rods. RECORD thus takes into account perturbations due to control absorbers within the assembly, as well as those which may be inserted in the surrounding water gaps. The code is specifically designed to handle directly the heterogeneities which arise in LWR designs, such as variable fuel enrichments and dimensions, burnable poison (gadolinium) pins, I

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2-2 burnable absorber (boron) shim rods, water holes, and soluble poison and voids in the moderator.

An example of a typical BWR configuration treated directly by RECORD is given in Figure 2.1.4. The Figure shows the solution area on which calcu-Lations are performed, and typical region divisions within that area.

2.2 Method of Solution In development of RECORD, the aim has been, at all times, to achieve as far as possible a balanced system with respect to the detail adopted in des-cribing the physical processes occurring in an LWR fuel assembly. The degree of sophistication adopted for the different models depends on the importance of physical events occurring, and their sensitivity to the accuracy aimed at in the final results. The modelling, in turn, has to be balanced against computer costs (running times, core storage, etc.), to be within limits acceptable for an efficient production code for extensive use in a wide range of calculations.

This section outlines the method of solution made in the RECORD code for solving the physical problems of determining group data and other char-acteristics of LWR fuel assemblies as function of fuel burnup. The model-Ling has been critically appraised in relation to the usage of the code, and required accuracies. Systematic validation of methods against experimental data from lattice experiments, from reactor operating data, and from com-parisons with more detailed codes, form the basis of confidence in the physical models adepted in RECORD. The descriptions given here are brief summaries only, and the different models are described in more detail in the following chapters.

2.2.1 Neutron Spectrum Calculation The thermal energy range in RECORD is taken to extend up to 1.84 eV (thus 239 240 including the large resonances in Pu and Pu ), where neutron thermal-ization is treated by a transport theory approach with point energy repre-sentation (Refs. 9, 10), and where the Nelkin scattering model is applied

2-3 (Ref. 11). The thermal spectrum for fuel, clad and moderator regions are determined for each fuel pin cett in the assembly Lattice, and are recalcu-Lated after given burnuo intervals, being functions of the isotopic concen-trations reached at any given time in each fuel pin. These spectra are obtained from energy-dependent flux disadvantage factors calculated for each pin cell, using a modified Amouyal-Ber.oist method (Ref.12), together with a homogeneous pin cell spectrum, calculated for an average pin cell represen-tative of the spectrum region where the given pin cell is situated. The fuel pins are grouped into a number of thermal spectrum regions, depending on their spectral environment.

In the epithermal energy region, the neutron spectrum is calculated, using a multigroup B-1 or P-1 approximation with extended Greuting-Goertzel slowing down (Ref. 13). The epithermal spectrum is calculated for an average pin cett representative of the whole assembly cell, and is assumed to be space-independent over the fuel assembly. This spectrum is generally recalculated during burnup at the same states at which the thermal spectrum calculation is performed. Resonance absorbers are treated by means of Lattice resonance integrals, calculated from total single-pin resonance integrals and modified by resonance distribution functions for each energy group, and by shielding factors taking into account the influence of the lattice on the resonance absorption in each fuel pin.

, 2.2.2 Burnable Poison Highly absorbing cells, such as burnable poison (gadolinium) fuel pins or burnable absorber (boron) shim rods, require more detailed transport theory calculations for correct predictions of reaction rates. Such cells are treated by the THERMOS - GADPOL System, two auxiliary codes to RECORD, which include a burnup version of the THERMOS code (Refs. 14, 15). These generate required effective thermal group data, which are read into RECORD as func-tion of void (or boron concentration), plutonium content and time integrated thermal flux (Ref.16). The data transfer between THERMOS, GADPOL and RECORD is automated via disc files.

2-4 2.2.3 Cell Homogenization i

j The code identifies as distinct diffus~lon subregions, each fuel pin cell in l

)

the assembly, each water hole or shim rpd cell, and water gaps and flow box '

j regions. The lattice cell (unit cell) dreas are defined by the lattice pitch, being equal to the square of the pitch for most cells of a given fuel l assembly. The flow area within the flow box not included in this way in the

{ Lattice cell areas in a SWR assembly (i.e., eventual inner water gap), is generally added to the moderator area associated with the edge lattice j celts. Similarly, the area of the very narrow water gap, usually present in PWR geometry, is generally included in the edge lattice cell moderator areas. The other region divisions in the assembly cell depend on the con-figuration geometry (e.g., Fig. 2.1.4). In usual applications of RECORD, the code lays out the mesh spacings and region divisions automatically, depending on the case data.

i Macroscopic five group data (two thermal and three epithermal groups) are calculated for each region from the isotopic concentrations, and by effec-tively integrating the isotopic cross-sections over the spectrum calculated for each region. These data are then used in the diffusion calculation over l the fuel assembly, and in the subsequent assembly homogenization calcula-i tions. Pinwise microscopic five-group cross-sections for all fuel isotopes used in the calculations of fuel burnup are also determined for the lattice  !

cells.

2.2.4 control Rods j

Cruciform control rods, either solid blade or rodded blade design, or clus-l ter control rods (RCC), are treated as nondiffusion subregions and are defined by boundary conditions applied at the absorber surfaces. These l boundary conditions are current-to-flux ratios, calculated from transport theory reflection and transmission probabilities of isotropic and Linearly l

anisotropic flux components (Ref. 17), together with special treatment of high resonance isotopes (Ref.18). Both boron based and Ag-In-Cd based control elements can be treated directly by the code.

1 i

2-5 2.2.5 Spatial calculations The flux distribution across fuel assembly and adjacent water gaps, and eigenvalue or k f

of the system, are obtained by solving the five-group, two-dimensional diffusion equations in x y geometry, using a fast overre-laxation iterative procedure, combined with a periodic use of coarse-mesh-group rebalancing (Ref. 19). A modified Wielandt technique is used to give fast convergence. Five-group diffusion theory with two thermal and three epithermal groups, and with up-scattering in the lowest thermal group, is found to be a minimum for adequate spatial representation of a fuel assemb-bly.

The mesh grid, imposed on the solution area, defines the mesh points at which the macrogroup diffusion fluxes are determined. The diffusion calcu-Lations utilize the regionwise group data from the neutron spectrum and cell homogenization calculations, and the boundary conditions from the control

• rod calculations. From the mesh point fluxes are derived normalized average group fluxes for att regions used in the subsequent assembly homogenization calculations, and in the calculation of power distributions and fuel burnup.

2.2.6 Assembly Homogenization Assembly averaged five- and two-group data are obtained by further averaging the regionwise group data over volume and group fluxes from the spatial calculation. This gives assembly-averaged, few group fission and removal cross-sections, as weLL as diffusion coefficients. The assembly-averaged absorption cross-sections are subsequently obtained from the neutron balance

> equations and the eigenvalue of the diffusion calculation. Here the assembly unit is considered as the fuel assembly, together with the associated sur-rounding water gap.

2.2.7 Burnup Model The fuel burnup chains assumed in RECORD are the chains starting at U and 0

0 , and where the main trans-plutonium isotopes americium and curium are explicitly represented. These chains are shown in Figure 8.1.1. The fission l

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2-6 products are treated by a scheme consisting of 12 fission products in six chains, and four pseudo fission products (Ref. 20), as shown in Figure 8.2.1. Calculation of fuel burnup is based on an analytical solution of the burnup difterential equations for each fuel pin in an assembly. After each burnup interval, new spectrum calculation, cell-homogenization, spatial calculation, and assembly homogenization are made.

2.2.8 Assembly Environment Problems, Four-Assembly Calculations The solution area in a RECORD calculation is a two-dimensional representa-tion of an LWR fuel assembly and surrounding water gap. Effect of assembly environment is obtained by defining appropriate boundary conditions at the outer edges of the solution area. When control absorbers are present in the water gap, the required boundary conditions are usually determined directly by the code. Zero current boundaries are otherwise generally assumed, but for some calculations, different sets of five group current-to-flux ratios at each outer edge may be defined. Axial leakage is represented by an input buckling parameter.

RECORD may be coupled to a large, two-dimensional diffusion code, MD2 (Ref.19), such that five-group,, four-assembly calculations, with explicit representation of all lattice cells at any burnup state for each assembly, can be performed when required and with a minimum of manual data prepara-tion.

2.3 Nuclear Data Library The Nuclear Data Library contains the microscopic cross-sections and reso-nance integral data for nuclides which may be needed in the spectrum and group data calculation by RECORD. These data have been processed mainly from the basic ENDF/B-III data files. Other data contained in the library include neutron production parameters for the fissile nuclides, normalized fission spectrum, inelastic scattering matrix data, and delayed neutron data. The library consists of two parts: a library for the thermal data, and one for the epithermal data, respectively.

2-7 2.3.1 Thermal Cross-sections In RECORD, the thermal energy range extends up to 1.84 eV, and the thermal absorption and fission cross-sections for non-1/v nuclides are represented in the library at 180 energy points (equidistant in velocity units). The cross-sections at these points for nuclides showing non-1/v behavior are obtained either by linear interpolation of the energy-dependent cross-sections, or calculated directly from the resonance parameters in ENDF/

B-III, applying the single-level Breit-Wigner formula. Details of the methods used in these calculations are given in Reference 20 and in Appendix.

A. For nuclides with a 1/v-dependent cross-section, only the 2200 m/s value is required in the RECORD library. These values were obtained from ENDF/

B-III whenever possible; otherwise, for some fission products, from Refer-ence 21. The elastic scattering cross-sections are generally assumed to be constant in the thermal energy region but may, where resonance parameters are given in the ENDF/B-III file, also be calculated from the single-level Breit-Wigner formula, and are tabulated in the library at 60 equidistant velocity (energy) points.

The point energy model in RECORD uses 15 fixed energy points (Table 3.5.1),

and the required cross-section data for each needed nuclide are interpolated by the code from the data on the library file.

2.3.2 Epithermal Cross-Sections l

[

In RECORD, 35 energy groups are used to describe the epithermal region, which is defined in the energy range 10 MeV to 1.84 eV. The absorption, fission and scattering cross-sections for these groups, are primarily evaluated from resonance parameters and/or smooth cross-sections given in ENDF/O-III, using single or multi-level Breit-Wigner formalism, applying the Finnish processing code ETOF (Ref. 22). The ETOF code, which is based on l

ETOM-1 (Ref. 23), but with several modifications, derives point cross-sections for absorption, fission and scattering, and the group-averaged cross-sections are then calculated assuming a 1/E spectrum in the epithermal energy region. Also calculated for each energy group, are the averaged anisotropic elastic scattering cross-section, the slowing down cross-l l

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2-8 section, and inelastic scattering cross-section for each nuclide. Where fission product data are not available in ENDF/B, the group cross-sections are obtained from Reference 21 by linear interpolation.

The epithermal group structure in RECORD is fixed (Table 4.1.1), and the 35-group data are tabulated for each nuclide for direct application by RECORD, depending on the nuclides present in any given case.

2.3.3 Resonance Integral Data The Nuclear Data Library also contains data for use in thc treatment of resonance capture in uranium and plutonium isotopes. This comprises data for evaluating the single-pin total resonance absorption and fission integrals, as well as resonance distribution functions, giving the fraction of the resonance integral which is contained in the different epithermal groups.

The distribution functions take into account the variation in resonance absorption and fission distribution for different lattices, and have been precalculated as function of pin-cell geometry, isotopic' composition and fuel temperature, depending on the different isotopes. In running a case, RECORD will select from the library those functions which are most appro-priate for a given lattice.

2.4 Main Features of Code Some of the more important, general features of RECORD, as distinct from solution methods, are outlined in this section.

2.4.1 Integrated Code System RECORD is an integrated code system, consisting of component codes which operate efficiently together via a processing and steering system, and which reads and generates data files and calls upon and transfers data between the different units of the code, depending upon the case under consideration. The processing and steering system is automatic and depends only upon case input data. Efficiency and accuracy in using the code is

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ensured through a minimum of manual data transfer and computer time. A simplified schematic outline of RECORD is given in Figure 2.4.1.

2.4.2 User-Oriented Features Considerable effort has gone into making RECORD a User-oriented code, with respect to input specification and output listings. This is of importance, not only for ease in using the code, but also in connection with Quality Assurance in performing the necessary reactor physics calculaticns.

High standard in input description and other code documentation, and clear, readable output listings greatly facilitate avoidance, as well as detection, of invalid calculations due to input errors. Erroneous runs not only increase calculation costs, but may have potentially large economic consequences if faulty results form the basis for decision making in reactor operation andn fuel reload strategies. If errors enter design calculations, safety implications may also be involved. The input and output of a production code used for these calculations must be clearly auditable and verifiable.

2.4.3 Input Specification The input data to RECORD is designed such that the User, as far as possible, f need only specify his problem in usual engineering terms, as regards geo-metry, material composition, operation data, etc., together with a number of

option parameters determining the extent of calculations and output 1

required. The subsequent processing of this information into a form whereby the reactor physics calculations can be performed is done automatically by the code, together with reading of necessary cross-sections and other data from the data libraries.

The input data is supplied to the code on cards and/or card images read from a file. Each card is identified by an identification number in the first columns of the card, which define the input variables given in the remaining columns (specified in free format). The input card images can thus, in principle, be read into the code in any order. The identification number on

i 2-10 each card also enables easy specification of sub-cases. Several cases can be run in succession, where one need only to specify those cards which differ from that of the previous case.

The card images of all data cards are listed by the code at the beginning of the printed output. In addition, the code supplies what may be called an interpreted listing of the input data set. All quantities, dimensions and options, either defined in the input data or implied, are printed with clear, explanatory texts, and with units given for all numerical values printed.

The code also performs tests for elementary errors in the input data, or if some input data exceed given limitations in the code. If some errors are found, error messages will be printed and the calculation stopped. A " Check Input" option helps the User in checking that his input data are correct, and to detect errors at an early stage before much computing time is used.

A detailed description of input and output of RECORD is given in the FMS Documentation (Ref. 6).

2.4.4 Output of RECORD The output of the RECORD code consists essentially of two parts:

a) the output listing obtained from the line printer, and b) the data files (disc files) generated by the code.

The output listing of RECORD is designed to give, in a precise form, the input to the code and the essential results of calculations. The data in the j output are grouped together in a number of parts and, wherever possible, each part is listed on the same page with all quantities defined with a f

l clear text. The listing pages are of A4 format for easy copying or other l

handling by User. All output pages are numbered sequentially and, at each

2-11 page top, the Code Version Number, Case Number, and the Case Identification Card text is printed.

A one page output is always obtained at each calculation state, giving the main results of calculations. These include k, and k values, homogen-ized few group data for the assembly cell, average fuel composition, power peaking factors, etc. Flexibla output options otherwise enable the User to obtain additional and more detailed calculation results to be listed at any particular burnup state. Typical outputs often requested are power maps and pinwise burnup distributions in a fuel assembly. Detailed fuel inventory (weight per cent of the main uranium and plutonium isotopes, and/or isotopic concentrations of all fuel isotopes present) in each fuel pin can be listed as function of fuel burnup. Another useful output group that may be requested is the neutron balance, showing, in a two group scheme, the rela-tive contributions to the neutron reaction rates from the most important isotopes and regions of an LWR fuel assembly. The output option groups presently available in RECORD are given in Appendix B. Excerpts from RECORD output listings are shown in Appendix C.

Discussion of the data files is deferred to Section 2.5 of this report.

2.4.5 Restart Options In performing reactor physics calculations on reactor fuel, the need often arises to be able to initiate calculations on a fuel which has been depleted j to a given burnup state. Restart options are available in RECORD, enabling such calculations to be performed for depleted LWR fuel assemblies by making use of a fuel burnup file, or so-called BFILE, generated in a previous RECORD calculation. Application of restart options enable, e.g., burnup

calculations to be continued after given burnup states, either with same or j new operating conditions, and makes possible the generation of " cold" data banks as function of burnup. Depleted fuel pins may also be replaced by pins with fresh fuel or new densities. Restart calculations with RECORD can be performed all in one run, or at some later time, by using files generated and saved in a previous run.

2-12 2.4.6 Limitations of RECORD Some of the limitations of RECORD should be noted. These limitations or restrictions relate to the physical problems which can be handled, the geo-metries which can be treated, the solution methods adopted, and limitations due to computer requirements.

The RECORD code has been designed to handle light water lattices only, as represented by the LWR fuel assemblies described in Section 2.1. The fuel must be UO or Pu0 , but specific enrichment and dimensions can be 2

specified for each fuel pin. The moderator is H20, but may also contain soluble poison and other isotopes. Uniform or non-uniform void distributions can also be defined for the moderator regions. Burnable poison and control absorber types usual to present commercial LWR fuel assembly designs, can be treated directly by the code.

The main limitations of RECORD are summarized in Tables 2.4.1 and 2.4.2.

2.5 Data Generation Unit of FMS RECORD is the data generation unit of FMS. The results of the reactor physics calculations over an LWR fuel assembly and associated, surrounding water gaps, are condensed in a systematic manner to supply the few-group data required by the macroscopic codes of FMS. The code generates a number of files (Fig. 2.4.1), containing the required few-group data, isotopic concentrations, and other data, which are later activated by PRESTO and other codes of FMS or by RECORD, itself, in later runs. These files essen-l tially constitute the Data Bank, being the basis for subsequent fuel man-agement and transient calculations on Light Water Reactors with FMS (Fig.

I 1.0.1).

Most of the data written on the files can also be listed in the RECORD output listing, from which is additionally obtained certain coefficients and other data also needed by the macroscopic codes. The contents of the main files generated will now be described.

l 2-13 2.5.1 RECFILE This is the main data bank file generated by RECORD, and contains assembly cell-averaged, two-group data, assembly-averaged fuel isotopic concentra-tions, and k -values, for use by PRESTO and the other FMS codes. Optionally, the file may also contain normalized pin-powers for given fuel assembly.

These data are stored as function of average fuel burnup, and either exposure-weighted void (BWR) or ppm boron (PWR). The file is built up on the basis of a previcusly generated RECFILE, such that the file produced will contain the new data generated, added to that contained in the previous RECFILE.

2.5.2 E-file This file conteins detailed specification of mesh point divisions, region boundaries, composition identification, and macroscopic five group data for all material compositions in the different regions of a given fuel assembly cell. The group data are generated and stored on the file as function of average fuel burnup. The original purpose of this file was to transfer data to the larger, two-dimensional diffusion code, MD2, for eventual detailed four-assembly calculations (Section 2.2.8). The file is now more often used to couple the GADPOL code to RECORD when performing burnable poison calcu-Lations. As will be explained in Chapter 5, the GADPOL code is a link bet-ween the THERMOS code and RECORD, making adjustments to the THERMOS-calculate ~d cross-sections, so as to preserve the burnable poison lattice cell reaction rates in going from the cylindrical geometry of THERMOS to the x y dif fusion calculation in RECORD. By introducing the E-file from RECORD, the GADPOL code will extract from the file the required mesh point distribution for a given burnable poison cell configuration.

l

l 2-14 2.5.3 Restart File (BFILE)

This file is generated for use in subsequent restart calculations (see also Section 2.4.5). The file contains all required data for the fuel, enabling restart calculations to be initiated on a fuel assembly at some given burnup state. Specifically, the file contains case parameters, isotope identifica-tion, densities and enrichments of initial fuel, and pinwise burnups and fuel isotopic concentrations, as function of average fuel burnup. The file also contains, as function of burnup, necessary gadolinium data, isotopic concentrations in eventual shim rods, and concentration of boron absorber in eventual curtains. In particular, the file is much applied when generating

" cold" data banks for describing low power conditions during burnup.

2.5.4 FILEED_ File Also of some importance when performing project calculations involving a large number of calculations, is the construction of an input data bank, providing a systematic way of storing case input data, together with logical assignment of identification. numbers to each data set. This enables easy retrieval of particular case data, and the construction of new input data sets. A subroutine, FILEED, is included in RECORD as an input pre-processor to the code, and performs the following main functions:

Generates a file (FILEED file), containing the case data sets for a given run, and which are added to the input case data bank contained in an existing FILEED file

- Builds new data sets on the basis of data from an existing file, and adds this new data set to that file 4

Assigns identification numbers to each new case data set given to or generated by the FILEED routine Lists prescribed parts of the input data file.

. . _ - _ _ _ . ~ .__. . ._ . ~-

2-15 i

In general, the FILEED file is generated whenever the FILEED input pre-processor is used in specifying case input data to RECORD. The FILEED  ;

function may also be bypassed if unwanted, in which case the User must always present complete input case specification for main case of run, and also where the User must provide his own case identification numbers.

2.6 Computer Requirements The RECORD code has been developed using the CDC CYBER-74 computer at Kjeller, Norway, and is operative also on other CDC machines. The code is programmed in FORTRAN IV (CDC Extended). With a few exceptions, the state-ment types conform to ANSI Standards. The code has one main program, and is then structured into seven overlays which are called by the main program.

l Some of the ovarlays are further divided into segments. In order to keep the central memory requirements' at a reasonable level, the code makes use of a number of disc files to store and transfer data between the overlays. The data transfer between the central memory and these disc. files is generally made via BUFFER IN/0UT statements. These are the main non-ANSI statements of the code, but make possible a very efficient data transfer on CDC computers.

I For the library files and the data bank files generated by the code, the data transfer is made via READ / WRITE statements.

The memory requirements and computing times are machine-dependent. For the CDC CYBER-74 computer, the code's central memory requirement is, at present, 45000 (or 130000 octal) CDC words, and typical computing time for an 8 x 8 BWR assembly (using 20 x 20 mesh points) is about 30 CPU seconds for an initial calculation, including all the initial processing. Each subsequent burnup interval, with new spectrum and diffusion calculation and where use is made of previous flux, wiLL require about 20 CPU seconds. In the standard data bank generation procedure with RECORD, a complete burnup calculation to 35000 MWD /TU for one fuel assembly at a given void, will require about 300 CPU seconds. The main computer requirements for RECORD are summarized in Table 2.6.1.

(

_ - . , _ . , - ____.,_m_. . _ _ . . _ _ . _ _ . _ _ , _ . - _ . _ . , . . , _..%_,,

a 2-16 TABLE 2.4.1 Main Limitations to Physical Problems Treated by RECORD GEOMETRY General  : 2-Dimensional x y geometry l

Fuel Assembly Type  : BWR, PWR, or single pin cell Lattice Positions  : Square array, max. no. 9 x 9 FUEL No. of Fuel Rods  : Maximum 81 Composition  : UO 2 -Pu02, initial enrichment specified in input for all rods Geometry  : Cylindrical rods, dimensions may be specified individually for all rods Fuel Rod Types  : Max. 81 (i.e., of different composi-tions and dimensions)

BURNABLE Composition  : Gadolinium (Gd20 3) + UO2/Pu02 POISON Type and Number  : Max. 10 rods, max. four types Thermal Group Data  : From THERMOS-GADPOL, or f rom Gadolinium Lib ra ry CLAD Composition  : Specified in input (max, five isotopes)

Geometry  : Cylindrical, dimensions may be speci-fied individually' for all rods MODERATOR Composition  : H 2 O + soluble poison and eventual other

($5) isotopes Voids  : Uniform, or specific void f ractions can be specified for each lattice cell FLOW BOX Composition  : Specified in input (max. fiv8 isotopes)

Geometry  : Rectangular regions of given thickness surrounding lattice area of BWR assem-bly CONTROL Geometry  : Solid blade, rodded blade, or rod ABSORBERS cluster l Absorber  : BgC, boron steel, boral or Ag-In-Cd l

l Clad  : Zircaloy, stainless steel or aluminium l

l Other Types  : Boundary conditions calculated extern-l ally and specified in input SHIM RODS Geometry  : Cylindrical, max.10 rods, max. four l

types t

l Absorber  : Specified in input (max. 10 isotopes);

of these, max. five burnable isotopes) l Clad  : Specified in input (max. five isotopes)

Thermal Group Data  : From THERMOS-GADPOL l

r--,, ,

e

2-17 TABLE 2.4.2 Main Limitations in Solution Methods and Other Details in RECORD NEUTRON Thermal Spectrum -

15 energy points GROUPS 35 energy groups Eptithermal Spectrum .

Diffusion Calculations  : 5 macrogroups (3 epithermal & 2 thermal)

Output Data Bank  : 2 macrogroups (1 thermal & 1 fast)

Thermal Cutoff  : 1.84 eV MESH Mesh Points in ,

Max. 30 x 30 (mesh point numbers and Diffusion Calculation spacings generally determined by code itself)

REGIONS Lattice Region  : Maximum 81 Total No. of Regions  : Max. 100 (i.e., Lattice + water gaps and other regions)

ISOTOPES No. of Isotopes in ,

Max. 40 (heavy isotopes and fission Fuel products accounted for in each fuel pin)

No. of Isotopes in ,

Max. 48 (fuel, clad and moderator Lattice regions)

BURNUP No. of Burnup States  : Max. 50, in general; (at which spectrum Max. 20, when generating RECFILE (main recalculation and data bank file) output generation occurs) i l

! I l

l l

l 1

)

l

2-18 TABLE 2.6.1 Main Computer Requirements for RECORD COMPUTER TYPE  : CDC CYBER-74, -75, -76 CDC-6500, -6600 CDC CYBER-170 PROGRAMMING LANGUAGE  : FORTRAN, CDC Extended (ANSI Standards mostly)

CORE STORAGE  : 130 K (octal) words PERIPHERAL DEVICES NEEDED  : Disc storage device CODE STRUCTURE  : Overlay NO. OF SOURCE CARDS  : Approximately 28,000 TYPICAL RUNNING TIME  : On CYBER-74, about 30 CPU sec.

initially, and about 20 CPU sec.

per subsequent burnup step for l

typical BWR assembly configuration i

, ,, m _ - . , _ -

2-19

1. Ca5E IDENT. AE.5A 1 0 BmR SAMPLE #ECBLEM.

8uR SYMPETRY SPECIFIED

2. rsEL ASSEMdLY GE0MEikY

......................... .................................................g i I 1

I ///////////////////////////////////////////

I / / I 1 / 1 2 3 4 5 6 7 8 / I I / / I I / / I I / 9 to 11 12 13 14 15 16 / I I / / 1 I / / AK 1 / 17 18 19 20 21 22 23 24 / AA I / / AK I / / AA I / 25 26 27 *** 29 30 31 32 / AA I / / AA I / / AA I / 33 34 35 36 37 38 39 40 / AA I / / AA I / / AA 1 / 41 42 43 44 45 66 47 48 / AA I / / AA I / .

/ AA I / 49 50 51 52 53 54 55 56 / AA 1 / / AA I / / AA I / 57 58 59 60 61 62 63 64 / AA I / / AA 1 /////////////////////////////////////////// AA AA I

I AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA I. ..-........AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

////// e Flow 80Ae OUTER DIMEN$10NS e 13.8120 CM hum 4ER OF LATTICE P351f10h5 a 64 WALL THICANE$$ a .2030 CM PITCn a 1 6256 CM OUTER O!MEh$10NS OF ASSEM8LY CELL e 15.2400 CM RAAAAA a CONTROL PLATE, EFF. MALF SPAN s 12.2950 CM

= .4750 CM AAAKKA MALF THICANESS = 3960 CM wlDTM of NARR0s WATER GAP CENTRE PIECE HALF $ PAN s 1.9840 CM

. t ul0TH Or v!DE WATER GAP = .9530 CM I RUCALING a .6842E *0 4 CM**.2 l

FIGURE 2.1.1 Example of BWR Configuration in RECORD l

i I

1 i

l L.

i l

t

2-20

3. CASL IDENT. SL-$A 4 0 Pea SAM *LE PHOOLEM.

Pe h les AssEu3LY Sirw[isY SPECIFIED 2 FUCL A55tanLY GCCMt'IRY I

E I  !

! ............................................g i I I I I I 2 3 4 5 6 7 6 e I t I

!  ! I I I to  !! 17 13 14 15 16 17 in

!  ! I I  ! 3.

I 1 19 20 21 72 23 *** 2% 26 ***

l i 1 1 1 I 1 1 28 29 30 *** 32 33 34 3b 36 1 1 I I I I I I 37 38 39 40 41 42 43 44 45 t ! I I I I I I 46 47 *** 49 50 *** 52 53 ***

I I I

.1  ! I I I 55 56 57 56 59 60 61 62 63 I I I I 1 I I t 6* 65 66 67 60 69 70 71 72 I I I I ~!

---.--.1 . 74--***=. 76. 77..***. 79.. so..***-.

I I

No. OF LafflCF POSITIums IN 1/4 AShEMhLY a 81 tin!5 INCLUDES in05E ON SYMMETRY AAlg) piirn a 1.2600 Cm Outra DIMthSIONS OF 1/4 AS$[M9LY CELL =a 10.7A00 CM HUCMLING s .6A44E.04 CM**-2 etDrn or EATER GAP .0500 CM FIGURE 2.1.2 Example of PWR Configuration in RECORD

,i l

2-21 i

1. Ca5C ICLNT. RC.5v i 0 SVCA INTCANAL WATER Ce055 ruCe, trST CASE.

2. FuCL ASSEMBLY GCC=CTRY 8wA svCA INTERNAL .4TCA 08054 FUCL ttP"CTAY 9PCClflCS

......................................................g I I L s/////////////////////////////////////////////// 1 I s //// / 1 I s 1 2 3 4 //// 5 4 7 m / I I r //// / 1 i e / / / l I e 9 to 11 12 / / 13 16 15 16 / I I o / / / 1 1 # / / / vn I i 17 18 19 20 / / 21 27 23 26 / ex 1 # / / / va i s / / / vs 1 # 25 26 27 28 / / 29 35 31 37 / va

! t / / / su

! /////////////////////// /////////////////////// ex I t//// ///// sx 1 t////////////////////// /////////////////////// ss 1 o / / / sa I ) 31 34 35 36 / / 37 3e 39 en / s 1/ / / / vs I o / / / rx 1 ) 41' 42 43 64 / / 65 64 67 64 / vs i / / / / va i s / / / Tx I } 49 50 51 52 / / 53 56 55 54 / rz I o / / / sx 1 / //// / sn

I e 57 58 59 60 //// 61 67 63 66 / vs 1 # //// / fx I #/////////////////////////////////////////////// sy I sz I xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxrxxxExts t- ..----.-.-..xxxxxxxxxxxxxxxxxxxxxxixxxxxxxxxxxxxvas FIGURE 2.1.3 Example of Internal Water Cross Fuel in RECORD t

1 i

l l

1 2-22 g 15.24 >j i

13.812 L 12.295 y 1 d 1.984 l

\g t V/////$ h4 Y////////////////////////// *I92 ~

~~T 1 906

/ K _

@l@ @ @ @'8'@'8. + -

203 CONTROL ROD ,

j ,

CENTRE PIECE < --- FLOWBOX

_O!O.8!@'8 @ @ @

O OO'88 8 @;8 " "

"'";,'y#- ~oOOLOd 8WGi O;O OO O O 8l8 ---  ;;; ,A, O!O O O O 0 1,5 0 0 0 0 0 0,,8 6 0@ --

755 , 8.95 - l h WIDE / I 3 GADOLINIUM WATER ROD WATE R GAP

[

OUTER BOUNDARY OF SOLUTION AREA

( HEAVY LINE )

All dimensicns are in cm.

l Fuel U0 2 , radius 0.54 cm, initial enrichment as above in

! wt% U 23s to total U. 4 pins containing gadolinium with given wt% Gd 20 3.

Clad Zircatoy-2.

Inner / outer radius = 0.54/0.626 cm.

Floxbox Zircaloy-2.

j Control Rod Rodded blade type, BgC absorber.

Absorber radius 0.175 cm, clad thickness 0.0635 cm, pitch of pins 0.4884 cm. Clad and centerpiece are of stainless steel, SS-304.

FZGURE 2.1.4 Example of Typical BWR Configuration Treated by RECORD, Showing Region Division and Solution Area

l 2-23 TN.

INPUT INPUT D ATA M FILEE0 W PROCESSOR GAD.

FILE

OFILE

^

TNERMAL 15 ENERGV PotNTS

, SPECTRUM q, 1.84 ev CUTOFF b

IM.

ir #

35 GROUPS

, , EPliMERMAL , ,,,,,

S.E APPROI.

SPECIRUM if G.G SLOWING DowN s

E PITH.

ir W r CONTROL RCD TRANSPORT

~ ~~~

TH. d. VALUES THEORY E ,,

s

'{" C. goc A55EW6LT FLUE _,,,,,

2 0 DIFFUSION

(

& PQwtR DISTR. 5 M4CRO.GNOUPS Kett u 9 OUTPUT OUTPUT TM. Psi PROCESSOR LISTING

<, +,

s y 8LE *'

u ,

.. +aggnag NO MAX.

~,k* FM5 CODES PINW13E ,

SURNUP CALC. guRNUP rnt _ _> M D:

j TES GAN

eFnE ,,

l AANALVTic END 5OLUTION FOR Fuf L 150f 0Pic CONC.

i l

[ FIGURE 2.4.1 Schematic Flow Diagram for RECORD Code, with l Indication of Main Data Files Used and Generated 1

3-1

3. THERMAL SPECTRUM AND FEW-GROUP DATA This chapter describes the method used in RECORD for determining the neutron spectrum in the thermal energy range and derivation of macrogroup parameters for use in subsequent diffusion and burnup calculations over a fuel assemb-bly.

The thermal energy range in RECORD extends to 1.84 eV and, in this interval, the neutron spectrum is determined by solving the transport equation applied to the basic Wigner-Seitz unit cell of the fuel assembly lattice, i.e., the circular cell of the same area as the square cross-section of the unit lattice cell. The transport equation is solved using a development (Ref. 9) of the point energy approach (Ref.10). The Nelkin scattering model (Ref.

11) is applied for hydrogen' bound in water, and the Brown-St. John model (Ref. 24) is applied for oxygen.

The philosophy in RECORD is to calculate the neutron spectrum in the thermal energy range for a so-called " average pin cell", using three space regions (fuel, clad and moderator). This average pin cell is representative of specific spectrum regions, and it is defined as that cell having the amount of each isotope as found from averaging over all pin cells in the spectrum region. The pin cells of a fuel assembly are grouped into a number of thermal spectrum regions, depending on their spectral environment, (an example of thermal spectrum regicq division is shown in Fig. 3.0.1).

Having obtained the homogeneous pin cell spectrum, the procedure is then to calculate the Energy-dependent flux ratios for each pin cell, using a mod-ified Amouyal-Benoist method (Refs.12, 25). These are the ratios between the flux in a certain region (fuel, clad or moderator) to the homogeneous pin cell flux. Assuming that the homogeneous pin cell spectrum is constant and equal for all fuel pin cells in a given spectrum region, and using this spectrumfromtheaveragepinc3tl calculation, regionwise neutron spectra  !

is obtained for each pin cell in the fuel assembly.  !

)

I

I 3-2 From these regionwise microgroup neutron spectra for each pin cell, thermal macrogroup cross-sections and constants are determined for all isotopes present in all pin cells in the fuel assembly. Summation over all isotopes present in a certain pin cell gives effective macrogroup cross-sections and constants for use in the two-dimensional diffusion calculation over the fuel assembly. The procedure for calculating the spectrum and group constants in the thermal energy range is repeated at specified burnup intervals given in the input.

The following sections contain some of the basic equations and discussions of some essential points involved in the treatment of the thermal energy range in RECORD. For more details in the derivation of these equations and discussion of the assumptions, the reader is referred to the References.

3.1 Fundamental Equations The thermal neutron flux spectrum, over which the above mentioned averaging must be done, is the solution of the time-independent Boltzmann integral neutron transport equation. With the assumption of isotropic scattering and no up-scattering above thermal cut-off E , this equation can be written in usual notation.

E*

Eg ($,E)4($,E) = [ dE'T($'+3,E)(S($;E) + [ dE'E,($;E'4)4($;E')) (3.1.1) v o In RECORD, Equation (3.1.1) is solved by starting with an integration over the cell volume V, which yields E,

l I(E)S(E)=[dE' b,(E'+E)$(E')+S(E) (3.1.2) t o

where y(E) and S(E) are the volume-averaged cell spectrum and source, res-pectively, while the E's are volume and flux weighted cross-sections. Here the property has been used that, irrespective of the energy, the transport kernel T(r' + r,E) integrates to unity

[d7T($'+r,E)=1

3-3 and where:

$(E) =

[ d$ ((r,E) = { F;(E) $(E) (3.1.3a) 1 s(E) =

fds(i,c)={pc(E) 1 g 0.1.3b) b(E)=yfg)[dEE g t * }*( * }" i t,i

}

• 1 f,(E'+E) = y [$E,($,E'+E)$(3,E)=[fF(E')E,g(E'+E) g (3.1.3d) with F (E) being the ratio of the neutron flux in region,,i at energy E, to that of the whole cell.

7 (g) ,$i(E) i = 1,2,3 (3.1.4) i $(E) where i = 1,2,3 refers to the three regions:

fuel, clad and moderator.

The solution of the problem then proceeds in two steps. First, spatial calculations using the modified Amouyal-Benoist method is performed, generating the flux ratios F,(E) in the different thermal microgroups. Next, 1

l these flux ratios are used to weight cross-sections, Equation (3.1.3), that enter the homogeneous medium spectrum, Equation (3.1.2). This equation is solved by a multigroup method (Refs. 12, 14).

From the cell spectrum $(E), obtained in this way, and the flux ratios for

[

l each energy group F (E), the average thermal neutron spectrum for region i is obtained.

$g(E) = Fg (E)

• 4(E) (3.1.5)

3-4 3.2 Flux Disadvantage-Factor Calculations The Amouyal-Benoist method is employed in RECORD to calculate the flux disadvantage-factors (3.2.D 6.(E) 1

= U$W ( i = 1.2,3 1

which are the ratios between flux in region i to the flux in the fuel region.

As seen in the previous section, we need the ratio between the flux in region i to that of the whole cell. But it is easily seen that this ratio is given by:

6i(E) (3.2.2)

F.(E) = **i l)={V.6.(E)/V g 1 1 The specific method used for calculation of flux disadvantage-factors in RECORD is by Z.J. Weiss. For details in the derivation of the equations and on discussions of principles and assumptions on which the theory is based, see Reference 12.

l If one defines the probabilities To and Ti as the probability that a neutron l entering the cladding from the moderator will be absorbed in the fuel or I

cladding, respectively, the disadvantage-factor can be written as:

l 6 =

al 1 (3.2.3) a2 2,o 2R E (3.2.4) l a1 ( y)2 1 T1-T2 , [1, 3T)(g ,o F(R3/Rd1-\B lR Y += 3(x))

l 6 =

3 2 ,

To o 2 3 j l \

! l l

3-5 where

+

F(Z)=f" 2Z2 (3.2.5) and x = EtsR2 and where E

g3

=

the total cross-section in the moderator, R2 = the outer radius of cladding material, and A ,(x) = effective linear extrapolation length for a black cylinder embedded into a nonabsorbing, infinite medium.

0 316 x + 0 7675 05xs1 A,( x) = 4 (3.2.6)

O. b+x+07104 x>1 g

The problem has then been reduced to the evaluation of the probabilities To and P2 . They can be expressed in terms of first collision probabilities, as follows :

r,= (1 - c y)o "

(3.2.7b) r1 = (1 - c 2}S

3-6 where P3 (1 - c Pg yg) + c gPgPgy

. . c)

• (1 - c Py 3 )(1 - c P2 22) ~ "1"2 P12Pg1 P2 (1 ~ "1 Py3) + c 2P2Pyy (3.2.7d)

" (1 - c Py g)(1 - c P2 22) ~ #1# 2P 12P g

• r 42 /I W2 (3.2.7e) e 2

P and P are the first collision probabilities in fuel and cladding due to an isotropic incident flux on the cladding. The remaining four probabil-ities are defined as: P is the probability that a neutron, born uniformly and isotropically in region il i, will suffer its first collision in region J.

These collision probabilities can be expressed by third order Bickley func-tions, and Bessel functions of the first and second kind.

The calculation of Bickley and Bessel functions are relatively time con-suming. In RECORD, these disadvantage-factors are calculated for each microgroup and for each fuel pin in the fuel assembly. In order to reduce computer cost, some further approximations are introduced. These are by Van der Kamp (Ref. 25), and based on considerations of Nordheim and Sauer.

This leads to much simpler expressions for the actual collision probabil-ities, avoids the time consuming Bickley and Bessel functions, and reduces

/

3-7 the computer time by a factor of ca. 40. This original method has been tested on numerous occasions against exact, one group transport calculations (Ref. 26). Errors of more than 1% were observed only very rarely. The new,

, fast version of the method not involving the Bickley and'Bessel functions has been tested against the original one. Results showed (Ref. 25) that the discrepancy was always less than 1% in the one group case, while the dif-ference in the disadvantage factors in the multigroup case is negligible.

t 3.3 Spectrum Calculations ,,

The homogeneous medium spectrum equation (3.1.2)

. E* . .

E(E)$(E)=fdE'I,(E'+E)$(E')+S(E) g (3.3.1) will be reduced to a set of N algebraic equations by dividing the thermal energy range from 0 to E into a number of intervals. These equations are solved by an over-relaxed, normalized, Gauss-Seidel,(Liebmann) technique, as described in Reference 15. The over-relaxation factor is taken as 1.2, and normalization is achieved by requiring from each iterant that it sat-isfies the condition of neutron conservation fb,(E)S(E)dr=fS(E)dE (3.3.2) where S(E) is the slowing down source per unit energy.

Before the numerical solution of Equation (3.3.1) is sought, the energy variable will be replaced by the velocity, because the scattering kernel is a smoother function of velocity than of energy. The following relation exists :

E = 0.0253 v (3.L3) with the velocity (v) in units of 2200 m/s and the energy in eV.

3-8 With $(E)dE = Q(v)dy, Q(v) = vN(v) and E3 (E' + E)dE = E3 (v' + v)dv Equation (3.3.1) will be expressed as v

kg (v) N(v) = f dv' 2 3(v'+ v)v' N(v')/v + h(v)/v (3.3.4 )

o This equation may be written as k.N.=

tJ J [ P..

1J N.

1

+ 5.

J (3.3. 5) i where P..=k(v.+v.)v.av./v.

la s 1 a 1 1 a (3.3.6)

This is the set of algebraic equations which is solved in the code. The subscripts j and i denote j'th and i'th velocity group. The scattering kernel will be mentioned in the next section.

The source is calculated assuming a spatially flat 1/v epithermal flux, no upward scattering in the epithermal range, and by use of the free gas scattering model (Ref. 12). With the velocity (v) as the independent vari-able, the source of thermal neutrons slowed down from the epithermal inter-val can be expressed as

• 2 2 2 2 S(v)/v = E(1/v -a /v )/(1 -a )

S with a = (M - 1)/(M + 1),

i.e., the maximum fractional velocity loss possible 4

upon collision between a neutron and a moderating atom with free atomic mass M.

3-9 3.4 Scattering Models The calculation of the scattering kernel P above, is given in detail 11 in Reference (12). Consequently, only some comments will be given here.

A derivation of the scattering kernel in the thermal range must take into account the Maxwellian motion of the moderator atoms and the variation of the scattering cross-section with the relative velocity between neutron and scattering nucleus.

In RECORD, two scattering models are used. The first one is the free gas model by Brown-St. John (Refs. 24, 12), and the second one is the molecular model for water, proposed by Nelkin (Refs. 11, 12).

The main assumption of the Brown-St. John (BSJ) model considers the mod-erator to be composed of free particles with a Maxwellian velocity distri-bution. For neutron energies below 1 eV, this picture is not quite correct, as the neutrons do not collide with individual atoms but rather with the molecule (H 0) as a whole. However, the chemical binding can be accounted for by replacing the actual proton mass by an effective rotational mass. The oxygen atoms can still be treated as free gas particles with their own mass.

The effective mass of proton is calculated on the assumption that the neu-tron energy.is small compared with the quanta of molecular vibration, but large compared to the energy differences between the rotational levels of the molecules, so that rotations can be treated as classical ~.

A further refinement of the scattering model considers the entire molecule, rather than the individual scattering atom, as the basic dynamical unit.

Translation of the molecule as a whole, as well as rotations and vibrations of its nuclei about their equilibrium positions, have to be considered. The molecular model for water proposed by Nelkin (Refs. 11, 12) was chosen for use in RECORD. Its basic assumptions are :

1) The translation of the molecule is free and described by the center of mass motion with weight A = 1/m , where o

m is the mass of the molecule.

I o l

i 1

l 3-10 )

2) The rotation of the molecule is hindered by neighboring water molecules and the hindered rotation has been replaced by a single oscillation with energy w = 0.06 eV and r

weight A =1/m . Here m is the effective r r r rotational mass.

3) The three degrees of freedom of the OH bond have been described by isotropic vibrational modes of energies w = 0.205 eV, W = W = 0.481 eV with equal weights A1 =A 2 = A . Here 3 3

A. = 1/mi where m 1

i is the vibrational mass of the i'th mode. Their values have been obtained from the condition that, for large energy transfer, the free-gas scattering kernel obtains A1

= A 2 A = 0.1712.

3 In the Nelkin model for H 0, the contribution from oxygen was calculated by treating it in the free gas (BSJ) approximation.

Detailed formulae and a discussion of the numerical methods used to eval-uate these kernels may also be found in an IAEA Report (Ref. 27).

3.5 Point Energy Approach The production of plutonium isotopes during burnup of uranium fuel requires some changes, either in a theoretical view of our problem or in a numerical treatment of the transport equation. These changes are necessary because of 239 240 the large thermal resonances in Pu and Pu at 0.297 eV and 1.055 eV, respectively.

The reactor core design may also contain other elements with resonances inside or closely above the pure thermal energy range. It may be in burnable poisons, such as europium, dysprosium, and samarium, or in control rods of silver, indium and cadmium.

One possibility for eliminating the problems introduced by these resonances i

is to increase the number of thermal microgroups. In RECORD, however, l

3-11 I

i microgroup calculations of the flux disadvantage-factors are performed for each fuel pin cell. An increase in number of microgroups will greatly increase computer costs.

These considerations led to the adoption of the point energy method (Ref. 10), where the necessary number of energy points treated is about one half of the number of groups which otherwise had been necessary.

The method generally comprises an improvement of all numerical integrations that occur during the solution of the problem, e.g., energy transfer integral, reaction rates, etc.

Fredin (Ref. 10) showed that a numerical integration scheme based on the Gaussian type quadrature formula, being developed for an accurate evaluation of the thermal reaction rates in U/Pu systems, can be successfully used even in a solution to the problem of thermal neutron spectra.

The whole thermal energy range (0 to 1.84 eV) is divided into N subinter-vals. Before the Gaussian quadrature formula is used in each interval, appropriate variable transformations, E = Tk(z), are applied, which cluster the integration points towards the range of the resonance influence.

E' N z, dt (z) fr(r)+(E)dr= { f x,2 r (r (z g)) + ('k *I O az d*

o k=1 z k,1 (3.5.1) k

=,[ vg I(Ei)$(E;)

1=1 where E. = the energy points, 1

w ,

= corresponding weights, and 1

k = total number of the points.

Other symbols have their usual meaning.

3-12 A similar scheme (Ref. 9) is used in WECORD for calculation of thermal neutron data for light water moderated lattices during burnup.

Having chosen a suitable, numerical integration scheme for evaluation of the reaction rates, a new problem arises in determining the value of the neutron spectrum in the given set of velocity points. Going back to the homogeneous medium spectrum equations, (3.3.6), we have

. k .

I P.. N. + S. (3.5.2) ta. Na . =g,[ la a a The main trouble with a direct application of the numerical integration scheme in the calculation of neutron spectrum is due to the undesirable behavior of the scattering kernet. To improve the accuracy of Equation (3.5.2), the behavior of the scattering kernet, as well as that of the neutron spectrum in the vicinity of the point, have been taken into account.

The construction of the scattering matrix is based on a method (Ref. 28) utilizing straight-forward interpolation of the spectrum between two integration points by the Lagrange formula, taking into account the spectrum values in two additional nearest points. A procedure for the construction of the scattering matrix based on this idea has'been used in RECORD.

One may suppose that the main contribution to the value of the integral in Equation (3.3.4) or the discretization in Equation (3.5.2) is due to the interval containing the diagonal _ element of the scattering matrix. Since the scattering kernet has a sharp maximum there, a great deal of attention was paid to that interval. The rest of the scattering matrix was left almost uncorrected.

It has been shown (Ref. 9) that the described version of the multipoint method, which is used in RECORD, gives approximately the same accuracy as the multigroup approach, with about one-half of the number of velocity intervals. The number of energy points in RECORD are fixed at 15, and are listed in Table 3.5.1.

3-13 j l

3.6 Macrogroup Data The macrogrcup data for all lettice cells are calculated from the thermal microgroup neutron spectrum.

An effective macroscopic cross-section for the thermal energy interval may be expressed as:

k V[ d$ f dE 4(E,E) o (E) N ($)

I = (3.6.1) eff ,

vfdr/dE4(,r,E) o l

where the index k denotes element (or isotope) k, and v the volume of the fuel pin cell.

We consider homogeneous composition in the individual regions and with k

N, denoting the number density of element k in region no. i we get 1

I ff

= N.k ,k(2200)

• gk.P (3.6.2) where i;k , 7 3 k1 1y, jy 7, 1

g g

={NfV g g F g / ({ Nf Vg F) i (3.6.3) 1 1 h = {1 N'gVg F g / ([1 Nf Vg) J

l l >

3-14 and where I=f g $g(E) , $g(E) = h j d$ $($,E)

)

v.

F g=ig/$ , $=[Vg $g / V 1

E* E k

s{=$/o*(2200). %=fdEo(E)+1(E)/fdE$g(E))

o o In RECORD, as described in Section 3.1, the regionwise neutron spectrum

$$ (E) is calculated, where'i = 1,2,3 denotes the three regions: fuel, clad and moderator, respectively. With this neutron flux $ (E) $

known, the absorption, scattering and fission cross-section are calculated according to the formulae above. A summation over all isotopes k present in a given fuel pin cell give effective data for this pin cell. This procedure is repeated for all pin cells in the fuel assembly.

Two thermal macrogroups are always used in standard usage of RECORD.

Optionally, it may be specified in the input to the code that only one thermal macrogroup is to be used. In the two group case, RECORD calculates thescatteringremovalcross/se\tionfrom:

dv' $(v')k,(v'+v)dvE I RGleG2 1

I J .

[ Av g g II; [ I,(v g-*v v

) Av

• • 1 3"1 I

RI,J = I (3.6.6)

[ AV i Vi Ng 1=1

i 3-15 where N, = neutron density at velocity v = v,.

1 1 From Equation (3.3.6), we have the following relation for the scattering kernel P..=k(v.+v.)v.

1J s 1 0 1 Av.1

/ v.J (3.6.7)

With Equation (3.6.7) into Equation (3.6.6), we get I J I I

rl,J = [ N.

1 [

j,1 P..

la v.a Av.a / (i=1[ Av.

1 v.1 N.)1 (3.6.8) which is the expression used in RECORD for calculating the scattering removal cross-section.

The calculation of this scattering removal cross-section is performed with the neutron density N, = N(v ) from the " average pin cell" calculation 1 i representative for a specific spectrum region. Afterward, this removal cross-section is assumed to be constant and equal for all the fuel pin cells in this spectrum region.

The thermal diffusion coefficient for a region R is calculated from the following expression I

R S D =

(3.6.9) k in R 3(I g +I g )(I A +E t

)

with g go gk(2200) F*k R k *k E

g

=N R k jk gk o(2200)h I

g

= > (3.6.10) a t,= q, 4 (22 ) 7 ,

3-16 where the summation is made over all isotopes k present in the region R. ES'EA and E tr is the scattering, absorption and transport cross-section, respectively.

The transport cross-section is calculated in the following way. For all materials (isotopes), except hydrogen, we use o (v) = (1 - 2/3M) og(v) (3.6.11) where M is atomic mass of the material. For hydrogen in water Radkowsky's (Refs. 29, 12) prescription is used.

o (v) = (1 - U (v)) o g(v) N.m where o

5(v) 3 3

,o = 20.4 barn (3.6.13) og (v)

This procedure for calculation of transport cross-sections and diffusion coefficients is made for all regions in the fuel assembly.

Effective thermal macrogroup microscopic absorption and fission cross-sections for all isotopes k are also calculated for each fuel pin cell in the lattice. These cross-sections are needed in the burnup routine, and are obtained f rom Equation (3.6.2).

k k(2200) g pk o

eff (3.6.14)

The thermal water gap spectrum is obtained from a single pin calculation on a water hole cell, using a fission spectrum as source. The group data for l

the water gap are calculated using that water cell spectrum and the formu-Las in Equations (3.6.2) - (3.6.4) .

1

3-17 The group data describing the flowbox wall are calculated using the water cell spectrum. Optionally, other group data describing water gap and flow-box may be introduced into RECORD through special input data.

I

/

t I

i e

I i

3-18 _

TABLE 3.5.1 Thermal Energy Point (Group) Structure in RECORD VELOCITY POINT I ENERGY UPPER BOUNDARY OF ENERGY (in units of POINT I ENERGY " GROUP" I POINT I 2200 m/s) (in eV) (in eV) i 1 .1607 .0006556 .004181 2 .7906 .01587 .03814 3 1.7131 .07448 .1229 4 2.6358 .1763 .2315 5 3.2655 .2706 .2979 6 3.4936 .3098 .3299 7 3.8069 .3678 .4333 8 4.5374 .5225 .6270 9 5.4723 .7600 .8909 10 6.1798 .9693 1.0033 11 6.3067 1.0095 1.0337 12 6.4384 1.0521 1.0645 13 6.5425 1.0864 1.1148 14 6.7428 1.1539 1.2608 15 7.7425 1.5214 1.8400

I 3-19

• *e t C0x 0 S t *" It.dJ T Rd.HA 1 1 . ni. T C ri FT 2 7082 34.=G 0 0 35GdD/ T. 8u RN. HOT .4 0%VoIQ THERMAL ;PECf Wurt C GIJNs IN LtrTICE CELL PJOI T ! 0r43 i JEFAULT VALUES I

............................................g I I I ////////////////////////////////////// I I / / I I / 5 5 3 3 3 5 6 / I I / / I I / / I I / 5 1 1 1 GAD 1 5 / I I / / I I / / Xt I / 3 1 GAD 2 2 1 4 / Ex

! / / Xr I / / XX I / J 1 2 2 2 1 4 / rr I / / XX

! / / rr

! / 1 GAa 2 2 GAD 5 4- / x*

I / / XX I / / KK I / 5 1 1 1 5 5 6 / rr I / / Xr

,I / / XX I / 6 5 4  % 4 6 6 / tr I / / Xr i ////////////////////////////////////// KE I rr I 4rx xx xg re rr rr uzrxxxrg r xx grr r rx I-.........-.. 4 4 4 x x x g r z g g rix x xx g rrg u r g a r r g x x 1 fo 6 DJ10TC ru!L PIra CELL REGIONS GAD Jer.QTES GA00LINId1 CO eT AIN!r4G FUE6 PIN CELLS FIGURE 3.0.1 Example of Thermal Spectrum Region Division in BWR Fuel Assembly, as Applied in RECORD t

L 4-1 4 EPITHERMAL SPECTRUM AND FEW-GROUP DATA This chapter describes the theoretical basis used in RECORD in determining the spectrum and few group data in the epithermal energy region. The des-cription includes the main assumptions and equations involved in treating the neutron slowing down, and those for treating resonance absorption and fission. For detailed derivations of equations and discussion of assump-tions, the reader is referred to the reports listed in References, Chapter 11.

While the energy spectrum and group data calculation in the thermal energy range is based on rather detailed pinwise treatment of the thermal spectrum over a fuel assembly, a more approximate treatment, based on an average spectrum, can be applied for the epithermal energy range. The, mean free path of epithermal neutrons is large, compared to Lattice cell dimensions, and the spatial variation of the epithermal spectrum across typical LWR assemblies is small. This allows, with acceptable accuracy, the use of an average cell spectrum concept in determining the epithermal few-group data.

4.1 Fundamental Equations The neutron spectrum and group constants in the epithermal region is cal-culated using the method of the BIGG-II code (Ref.13). This is a multigroup i Fourier transform neutron spectrum code, whose fundamental equations are 1

1 derived by applying a Greuling-Goertzel slowing-down model to a B-1 or P-1 approximation of the one-dimensional Boltzmann equation.

The following set of equations are solved (for formal derivation, see Ref. 13) : s f

T (I(u)-G)&(u)+B(u)J(u)+[ f=o

+ = S(u) (4.1.1)

- f B(u) 4(u) + (h(u)E (u) - G (u)) J(u) +f=o =0 (4.1.2)

4-2 dl dq G (u)(1 - 'f)4(u)+q(u)+Ag,7(u) p du f =0 (4.1.3) qF (") " I I.,(u) 4(u)

F (4.1.4)

F dA dp G

f(u) (1- 'I)J(u)+p(u)+A f f

=0 (4.1.5) where u = lethargy variable

$(u) = neutron flux J (u) = neutron current f = no. of light elements treated by the o

Greuling-Goertzel slowing down model Q (u) = slowing down density from the f'th light element a (u) = total slowing down density from heavy F

(or " Fermi age") elements 4

P (u) = anisotropic slowing down density from the f'th light element S(u) = neutron fission source I(u) = source from inelastic scattering

4-3 E (u) = total macroscopic cross-section

[pI (u) = average slowing down density for F'th heavy element B(u) = buckling 1 B t an -1[B/I (u))

h(u) = -

3 gT (u)

- ^

1-t an -1(B/I (u))

Gf,(u)

= - ^"

A.1r f(u) 1

.,r(u)

G.

G = coef ficients in Greuling-Goertzel f(u) expansion (as defined in Ref. 30).

The P-1 approximation is obtained by entering h(u) = 1.

In the numerical solution of the above equation set, the 3 + 2f equations 0

are approximated by a finite difference scheme, in which the epithermal region is divided into a number of energy groups, in accordance with a lethargy mesh chosen as suitable. The equations are integrated over the lethargy interval du = uj - uj_1 where uj is the upper Lethargy boundary of microgroup j, and in these intervals cross-sections and slowing down constants are replaced by average values of the type

[Au.E(u)&(u)du I.= ~

(4.1.6)

J 0 3

where $, is the total flux in group j, given by J

t j * [Au.t(u)du (4.1.7)

J i __ _ ._. _ _ - -

4-4 Inelastic slowing down in the system is treated using an inelastic slowing down matrix a il, which gives the probability that a neutron inelastically scattered in microgroup j shall be transferred to group i. The prob-ability that a neutron inelastically scattered in microgroup j shall be transported out of that group will then be given by d in A. (4 1 8)

J = [

a. .

i,j+y 1.J in denotes the " inelastic cutoft".

where j We then have for the inelastic removal term I (4.1.9)

J 7 (u) 4(u)du = A.I 4 JJJ Au.

J and source term j-1 7

I ={ , a3 g E g $g (4.1.10) 1=1 whereIfisthetotalinelasticscatteringcross-sectionand$ $

is the group flux in microgroup i.

RECORD is designed for uranium fueled systems, where most of the inelastic 238 scattering takes place in the U isotopes. The apprcximation is therefore presently made by using only one inelastic matrix, that of U , in the L inelastic slowing down calculations.

i The above fundamental equations are valid for a homogeneous one-dimensional system. Before these equations can be applied to a heterogeneous lattice, such as a light water fuel assembly, the real system must first be homogen-ized to an equivalent fictitious, homogeneous system. In RECORD, the proce-dure is to calculate the epithermal spectrum for an average pin cell having

I 4-5 )

geometric dimensions at.d material properties, defined from averaging over all lattice cetts containing fuel and moderator, also including the modera-tor in the associated water gap surrounding the fuel assembly. This averase pin cell, consisting of fuel, clad and moderator is, in turn, homogenized to tne required equivalent homogeneous system. During this latter homogeni-zation procedure, proper account has to be taken of resonance absorption in the fuel.

The epithermal group structure in RECORD is fixed at 35 energy groups, defined in the range 10 MeV to 1.84 eV, and is listed in Table 4.1.1. The solution of the equations then determine the 35 group neutron spectrum for the so-called average pin cell. The philosophy in RECORD is now to assume this spectrum to be space-independent over the fuel assembly and, to apply the spectrum to all individual lattice cells to calculate effective average absorption, fission and removal cross-sections in each cell at any given time. This spectrum is used also in calculating the effective epithermal group data in the water gap.

In RECORD, the number of epithermal few-groups are fixed at 3 (a fast fis-sion, an interm'ediate, and a resonance group) having the following energy division:

Macrogroup 1 10 - 0.821 MeV (microgroups 1- 8)

Macrogroup 2 821 - 5.560 key (microgroups 9 - 17)

Macrogroup 3 5560 - 1.840 eV (microgroups 18 - 35)

The effective few-group data for all lattice cells, as well as assembly-averaged data, are recalculated during burnup, being functions of the fuel isotopic concentrations at any given time. Even though the epithermal spectrum will not change as markedly during burnup as the thermal spectrum, it will also be influenced by the change in uranium, plutonium and fission product concentrations, and is therefore generally recalculated at the same burnup states at which the thermal spectrum calculation is performed. (An option in the code allows one, if desired, to keep the epithermal spectrum constant at that calculated for the initial state.)

l

4-6 4.2 Treatment of Resonance Absorption and Fission The method in RECORD for treating resonance absorption reactions is based on calculation of resonance integrals and the determination of resonance distribution functions for the fuel resonance isotopes. The resonance reactions are dependent on isotopic compositions of resonance isotopes in a fuel and will therefore, in general, show both spatial and burnup dependence over an LWR fuel assembly. Resonance integrals and distribution functions are determined in RECORD for all fuel pin cells of an assembly, and are modified by Dancoff factors, which take into account the different resonance shielding effects for fuel pins at different positions in the fuel assembly lattice.

4.2.1 Resonance Absorption Under the assumption of spatially flat source in the moderator, and where the rescnsuce absorption at a given lethargy can be. considered normalized to the moderator source (Ref.13), the total resonance absorption in a micro-group j can by expressed by R , = (1 p )q (4,2,1)

) J j-1 where T

Ej-1 ~{o + (4.2.2) f=0 5- '~

4-U t A

l p. = exp [o N AR , (4.2.3)

J ,

Rj-1 t=0 'U d

4-7 and where

$! = asymptotic flux at lower lethargy J

boundary of microgroup j E = no. of resonance absorption isotopes Ng = homogenized number density of resonance isotope t

= resonance absorption integral for AR^Er J.

isotope t in microgroup j q and q are slowing down densities p

(defined in Section 4.1.)

The lattice resonance integral is evaluated from A A AR

=afRgp g 4g (4.2.4) where A

R ~ = total single pin resonance absorption gg,g integral of isotopes t A

$ te]. = resonance distribution function, giving fraction of resonance absorption integral which is contained in microgroup j A

ag = mutual shielding factor The calculation of Lattice resonance integral for microgroup j is therefore based on a total single pin resonance integral, which is modified by (a) the mutual shielding factor taking into account the influence of the lattice on

i 4-8 the resonance absorption in a given pin, and (b) the resonance distribution functions. See Sections 4.2.4 and 4.2.5 below.

For resonance absorption isotope 1, the resonance absorption in micro-group j is then calculated as g

AR^ .

'J R.

(Res. abs) lo J!=N g J (4,2,5)

[ N AR g g,J i=1 The resonance absorption isotopes considered by RECORD are the fuel isotopes 235 238 239 240 241 0 ,U , Pu , Pu and Pu . For calculation of total resonance integrals, see Section 4.2.3.

4.2.2 Resonance Fission For the resonance fission isotopes m, we assume that the ratio between fis-sion and absorption in the microgroup is not influenced by energy variation of the moderator source or the shielding effect due to the presence of resonances in other isotopes. The resonance fission is then given by N" AR F I

m AR m ,

"'A R. (4.2.6)

(Res.fis) J . =AR M'A (Res. abs.)J.=t

, g J m,J fo UgAR 1=1 g*)

F where LR m,). is the fraction of resonance fission integral contained in micro-group J. This lattice resonance fission integral is evaluated simular to the resonance absorption integral:

F AR .=a F pF F (4.2.7) m SP,m 9m,J m,J

4-9 where R = total single pin resonance p

fission integral of isotope m F =

$ m,) , fraction of resonance fission integral contained in microgroup j F

a, = mutual shielding factor.

4.2.3 Resonance Integrals The procedure in RECORD for determining resonance reaction rates is based on representing the resolved resonance integrals as functions of composition and geometry of the fuel lattice. Together with energy distribution func-tions extracted from the code library, this enables very fast computation of resonance absorption and fission within required degree of accuracy. The method thus depends on using single-pin resonance integrals which have been determined for a wide range of Lattices, and representing these in a suit-able way in RECORD. The resonance integrals are based either on experiments, or have been calculated from more basic data.

The temperature-dependent, single pin resonance integral for U is calcu-Lated from an empirical expression (Ref. 31), normalized to the well-known Hellstrand's formula (Ref. 32) for U0 fuel:

2 i

i RIU23e = RI 0 expla(/T-vT)l+C 9

(4.2.8) where l

l RI = 30/ EM+ 0.077 (4.2.9) o l

a = 0.0696 - 0.000262

• ES (4.2.10) l

- -r--- - ,-- - - ----w y-- -' -

4-10 o

T = effective fuel temperature ( K) o '

T = 300 o

S/M = effective surface-to-mass ratio 2

for fuel rod (cm /gm), and C = the normalization factor to the Hellstrand formula at T = T :

o S

C= 4.15 + 26.6 / g

• W - RI o

(4,2,11)

In this expression W = 0.97. Extensive evaluation calculations with RECORD on different lattices and using the present' cross-section libraries, have shown the need for a reduction of the basic resonance integral by about 3%

to obtain good agreement between calculated and measured reactivities.

Experimental values for lumped fission or absorption resonance integrals for other isotopes are not readily available, but can be calculated from resonance parameters using multi-level Breit-Wigner formalism. For the isotopes U235, Pu239, Pu240, and Pu241; the single pin resonance integrals in the resolved resonance energy region are represented in RECORD by the fol-Lowing function :

al a2 RI

=a + (4.2.12)

SP,E o

/RoE c

+Rc g where R = fuel rod radius (cm) o cg = isotopic enrichment (wt %) of isotope l

4-11 and a , a and a are fitted constants for isotope E and reaction x (absorp-o 1 2 tion or fission). These constants have been determined from resonance inte-grals calculated for a broad range of isotopic enrichments and fuel pin radii, and fi ting the data to the function (Eq. 4.2.12), using a least square procedure. An example of such a fitting is given in Figure 4.2.1. The error due to the fitting is of the order 1 - 2%, depending on the isotope and reaction type for a broad interval of R e g, which is substan-tially less than the errors in the resonance integrals themselves being of the order of 5%. The contribution to the total resonance integral from the unresolved resonance energy region is obtained by adding the appropriate parts of the infinite dilution resonance integral to Equation 4.2.12. It should also be noted that the function (Eq. 4.2.12) is valid only for enrichments higher than some limiting value for Eg. If the isotopic enrich-ments are below this limiting value, then the resonance integrals are rec'efined by linear interpolation in the range from icwer limiting value to infinite dilution value.

As is seen from the above, with the exception of U , the temperature depend-ence of the resonance integrals is neglected, being small compared to other effects. The reader is reminded that the resonance integrals apply for energies above 1.84 eV. The by far dominant resonance absorption in plut-onium nuclides, are in the large resonances at 0.296 and 1.056 eV of Pu and Pu , respectively, and these are treated with the point energy approach in the thermal energy region. The temperature-dependent Doppler broadening is important for these resonances, and is taken into account using the Doppler functions of the single-level formalism in the calculation of capture and fission thermal cross-sections for these nuclides.

L In the pinwise treatment of resonance reactions, RECORD calculates the single pin resonance integrals using Equations (4.2.8) and (4.2.12), or

, using linear interpolation for low eg , for each fuel pin in a given fuel assembly, as well as for the " average pin cell" in the epithermal spectrum calculation. In addition, for each fuel pin cell the code may also read the epithermal library and extract, if necessary, new distribution functions I

appropriate for given fuel rod radius and isotopic enrichments. Furthermore, as the isotopic compositions change during burnup, the code recalculates the

4-12 pinwise lattice resonance integrals, and new distribution functions are read from the library when necessary.

4.2.4 Mutual Shielding Factor The expressions for resonance integrals given in the previous section apply for an isolated rod, and the calculation of resonance reactions must include a correction term, the so-called mutual shielding factor, which takes into account that the fuel rods in a lattice are not isolated from each other.

For U RECORD uses the method of Levine (Ref. 29), who has shown that the total lattice resonance integral for UO rods, with dimensions of practical 2

interest, can be expressed by the following equation :

R = 2.619 /1.102 0 +2R ' 1 + 0 1(1-0) + 0.89 (4.2.13) o where o = 3.7 is the approximate constant epithermal scattering cross-section for oxygen 238 N = number density of the U absorber R = fuel rod radius, and o

D = the usual Dancoff Factor, expressing the probability that a neutron entering the moderator isotropically, will suffer a

! moderator collision before reaching another fuel rod.

The derivation of Equation (4.2.13) includes straight-line fits to Monte Carlo results of calculated resolved and unresolved resonance integrals. For further discussion of Equation (4.2.13) see Reference 12.

4-13 238 U*38 The single pin resonance integral for U ,R is obtained from Equa-SP tion (4.2.13) by putting D = 1, and the mutual shielding factor is then given by a=R /R (4.2.14)

L SP For U and plutonium isotopes, another procedure is used. The resonance nance integral for a pin in a lattice, RI ,g ,is calculated using Equa-tion (4.2.12), but with an effective fuel pin radius given by R = R /D (4.2.15) eff o where R is the fuel rod radius and D is the Dancoff factor for the lattice.

o The effective mutual shielding factor for isotope E and reaction x is then calculated by a[=RI g / RI p,g (4.2.16)

The mutual shielding factor is thus a function of the Dancoff factor for a given pin. RECORD performs very fast calculation of this factor, by making use of the method of Sauer (Ref. 33), assuming a homogeneous eixture of clad and water as effective " moderator" outside the fuel pin:

D=1- (4.2.17) 1 + (1- )Emm I where 4V

• I, =

3

= average chord leng.th in " moderator" f

= total epithermal cross-section in E,

" moderator"

4-14 V = volume of " moderator" (including a

clad volume)

S = surface area of fuel rod T = a " geometric index" which is given by T = T/t - 0.08 = (P - 2R )/t -C (4.2.18) m o m where T = shortest chord length in " moderator" P = lattice pitch R = fuel rod radius o

'O.08, square lattice C = < 0.12, hexagonal lattice, (single pin s case only in RECORD)

Equation (4.2.17) assumes a fuel pin embedded in a uniform lattice. This will not.be the case for the corner and edge pins in a fuel assembly, nor those pins adjacent to empty positions in a lattice, and the Dancoff factor has to be modified accordingly. In the square lattice geometry assumed in RECORD, the screening factors 1-D for the corner and edge pins are at present approximated by multiplying by 3/8 and 5/8, respectively, together with a semi-empirical correction due to shielding effects from neighboring

) fuel assemblies, which will be dependent on the water gap thickness.

Corresponding corrections to 1-D are made also for those pins in the vicinity of water holes within the lattice.

4-15 4.2.5 Resonance Distribution Functions A

Normalized distribution p functions for resonance absorption, vg,J , and for resonance fission, $g,3 , are used in the lattice resonance integral calcu-Lations for a resonance isotope 1, to determine the fraction of the reso-nance integral which is contained in a microgroup j. The normalization condition is

@2,j Lu. = 1 (4.2.19) 3 3 where the summation is taken over all microgroups and Au is the j

lethargy width of group j.

$ ,J1 is equal to zero outside the defined region, so that the normalization condition corresponds to normalization in the resonance region. The defined resonance region will vary from element to element.

The $-functions will depend on lattice geometry, and. composition or fuel temperature. The method in RECORD is to use precalculated $-values which have been obtained for a broad range of Lattices covering the variations in typical lattices to be expected when applying RECORD to LWR analysis. The

$-functions are stored in the code epithermal library as functions of rod 235 radius and isotopic enrichments for U and the plutonium isotopes.

For U .the $-functions have been calculated and stored in the library as function of rod radius and fuel temperature.

For a given case, RECORD will select from the library those $-functions most appropriate to the lattice to be treated. As has been mentioned in Section 4.2.3, the code selects $-functions for each fuel pin in the lattice j depending on enrichment, dimensions or temperature, and will redefine these during burnup, if necessary, as the isotopic concentrations change- .

4.3 Fast Advantage Factor l At high energies, due to the fission source in fuel, the average flux in the fuel will be higher than the average flux in clad and moderator. In the

4-16 epithermal calculations, the spectrum calculated is a space-average of the real flux in the moderator and clad regions of the average pin cell, and a correction must be introduced to obtain correct calculation of the reaction rates at the high energies. This is accounted for by the introduction of a

" fast advantage factor", defined as the ratio of the average flux in fuel to the average flux in clad and moderator. From the balance equations for the fuel and moderator at lethargies where we have only slowing-down of neu-neutrons, we obtain the general expression for the fast advantage factor:

V l-P

( =

(f(u)

= (1-S)

E

. +B (4.3.1) 4mb") f f o where P* = escape probability from fuel to moderator o

S = normalized scattering source in moderator V = volume of moderator a

V = volume of fuel

= total epithermal cross-section in I,

moderator E = total epithermal cross-section in fuel f

h Basically, the fast advantage factor is a function of neutron energy. How-ever, the absorption, fission and scattering cross-sections for the main fuel isotopes show only small variations in the high energy range (lethargy range 0 < u < 2.4), and it can be shown that, to a first approximation, an energy-independent fast advantage factor may be applied for the high energy range under consideration. The main fuel isotopic cross-sections are there-l fore multiplied by a constant fast advantage factor in the specified energy

4-17 range, to give approximate correct absorption, fission and scattering rates in the fuel.

More detailed discussion of the assumptions involved, and expressions for evaluating the terms in Equation (4.3.1), are given in Referrence 12.

For those energy groups below the range where the fast advantage factor is applied, the flux is assumed to be the same in the moderator, cladding and fuel. The flux in the fictitious homogeneous system for which the epithermal equations are solved, will then be equal to the assumed flux in the heterogeneous system.

4.4 Macrogroup Data When the epithermal neutron energy spectrum has been calculated using the theory described in the previous sections, the next stage in the calcula-tions is tFe determination of effective epithermat few group data for aLL Lattice cells and other regions of the fuel assembly cell. As has been explained in Section 4.1, the number of epithermal few groups in RECORD is fixed at three, and the effective cross-sections for these macrogroups are obtained in principle by integrating the microgroup cross-sections over the neutron spectrum, and where proper account is taken also of the resonance absorption and fission in the relevant isotopes.

4.4.1 Macrogroup Absorption and Fission Cross-Sections For a given neutron energy spectrum &(u), an effective microscopic cross-section for reaction x is defined by

[0x(u) 4(u)du f4(u)du Integrating over a macrogroup M, and replacing the integration by summation, the effective cross-section of isotope i in that macrogroup is given by i 1 i (4.4.2) o*'M { M o*'I4j

• M j in

4-18 where

$g

=

[$ is the group flux in macrogroup M, and j in M j o is the effective microgroup cross-section for isotope i, reaction x, in microgroup j For a resonance absorption isotope , the absorption in macrogroup M can be expressed as L L t

kd.),=n,.a ,3 g + (Res..ws.), u.n where Ng is the homogenized number density of isotope t .

The resonunce absorption is calculated from 1

(Res. abs.)M 1 . . ^1.j (4*4*4}

J in M

.where A

AR

(4.4.5)

A R.

Ad=

n to A U

1. 1 1,3 1=1

= total resonance absorption in microgroup j h

R)

(Eq. 4.2.1)

AR = lattice resonance absorption integral (Eq. 4.2.4) t = no. of resonance absorption isotopes

4-19 The total absorption in macrogroup M is then given by T ko t o t (es.)x =,1 n1 3,,x xe +t=1I (nes..ds.)M (4.4.6) 1=1 where k = total no. of isotopes in system.

o The last term reduces to j

j in M The average macroscopic absorption cross-section for group M is defined from the total absorption according to T

I,,g(M"(AD8*) M (4'4'7}

giving ko ,

1 E

a.M

=

{NicaM+b g,y 9 M

f j in M R.

J (4.4.8)

From the total fissions in macrogroup M is derived, in a similar way, the macroscopic fission cross-section

= N1 3 f,M+b 9 I fsM g,y 9 M m=1 N

• j[nM F*'O i

. (4.4.9) where AR,,3 R

j (4.4.10)

F,3=[g o N g AR .

g'O t=1

4-20 AR lattice resonance fission integral mil =

(Eq. 4.2.7)

N = homogenized number density of resonance m

fission isotope m s = no. of resonance fission isotopes o

4.4.2 Macroscopic Removal Cross-Section In the calculation of the removal cross-section in a macrogroup M, con-sidered separately, is the removal of neutrons due to elastic scattering in light "Greuting-Goertzel" isotopes, and that due to scattering in the more heavy " Fermi age" isotopes. In addition comes the contribution from inelastic scattering.

Let u and u be the Lethargy boundaries for a macrogroup M, and let u

< u' < u (a) "Greuling-Goertzel" Isotope :

Total number of neutrons scattered out of macrogroup M due to a " Light" isotope f is given by W

Q M"1 f Z a' "M-1 f (" ) # {" ) (* ~ "f) du (4.4.11)

! 4-21

Assuming " flat" flux over microgroup j, we get

For u -u < - ln G M M-1 f

~

' 2

4.c 1 .f a.:.nI M 4 ,3 9 . e"3-" % ^"3) - d (4.4.12) a where

-Ln af = maximum Lethargy gain per collision 1

af = (A -1)2/(A +1)2 (A is atomic mass) l

= flux in microgroup j

$3 Au = lethargy width of microgroup j j

= elastic scattering cross-section of " Light"

{#'I isotope f in microgroup j For u -u > - ln a f

Q = q (u ) (4.4.13) fM f M i

where 4 (u ) is the slowing down density at u from f M M isotope f.

1 l

4-22 (b) " Fermi Age" Isotopes :

Since aluminium is the lightest of the isotopes treated by Fermi age theory in RECORD, we will always have ug

- u g_) 1 - in aAl - 0.16 The elastic scattering out of the macrogroup because of the " heavy" isotopes is then given by

= q (u )

QR F,M F M (4.4.14) where 9 (u ) is the total slowing down density at u F M M from the " heavy" isotopes.

(c) Inelastic Removal :

The removal of neutrons due to inelastic scattering is given by M".h J in M 1>J 3

• i j J *j ##5in

• 5M (4.4.15)

R '

I g =0 for fin Ab M -

where L

a = element in the inelastic scattering matrix Ef = total inelastic scattering cross-section 3

in microgroup j j, = inelastic " cut-off" in

4-23 The total removal of neutrons from macrogroup M, due to both elastic and inelastic slowing down, is thus f

G = TQ g

+

F,M The removal cross-section in macrogroup M is then defined as Q

=

E r,g (4.4.17) 4.4.3 Diffusion Coefficient From the solution of the fundamental one-dimensional B-1 equations, is derived the general expression for the lethargy-dependent diffusion coefficient L (u)

D(u) = "*'* '

8o$ o(u) where L (u) is the net Leakage in the middle of the reactor, o

corresponding to the flux $ (u), and B2 is the buckling.  :

The effective diffusion coefficient for macrogroup M is calculated as

{ L.

" (4.4.19)

D" = .5.1 No #j j in M where j l

L =B J, is the microgroup leakage  !

j o j '

J = microgroup current

1

! 4-24 TABLE 4.1.1 Energy and Lethargy Structure in the 35-Group Epithermal Cross-Section Library of RECORD LOWER ENERGY UPPER LETHARGY GROUP BOUNDARY (eV) BOUNDARY 1 7.189 10' O.3300 2 5.169 - "

0.6599 3 3.716 - 0.9899 4 2.671 1.3201 5 1.920 1.6503 6 1.381 1.9798 5

7 9.926 10 2.3100 8 8.210 - 2.5000 9 5.130 - 2.9701 10 3.688 3.3001 11 2.652 - 3.6299 12 1.906 3.9602 13 1.370 4.2904 14 '5.572 10" 5.1900 15 2.265 - 6.0902 16 9.210 10 8 6.9901 17 5.560 7.5000 18 1.522 8.7903 19 6.190 10 2 9.6900 20 2.517 10.5899 21 1.900 10.8711 22 1.350 11.2128 23 1.100 - 11.4176 24 82.000 11.7114 25 63.000 11.9750 26 45.000 12.3114 27 32.000 12.6524 28 26.000 12.8600 29 20.000 13.1224 30 15.000 13.4100 31 11.000 13.7202 32 8.000 14.0387 33 5.400 14.4317 34 3.150 14.9707 35 1.840 15.5083

4-25 i

a i '

i Rieff Rl"s140b

( barns ) A r, s.54 cm I 8 o 2*/. PuO ( 8*/.Pu ) ; r, f (0.4,.75 cm) 130 - A x 2 */. PuO ( 16*/. Pu2 ) ; -

~

Y a 4*/. PuO ( 8*/.Pu ) ; r, ([O.4,1. cm )

8 V V Burnup Case ; 2OOOOMWD/TU; r ((0.4. 75cm]

+ Lettice Integrals ; r a r, / 0 17 X - RI 'N # : 61 + @70 ,

foe YO

~

12 0 -

X o

Y

+

o t

o 110 - ~

a

+o 100 - _

0 l t I 90

1. 2. 3. r, E *

( */. cm) +

t FIGURE 4.2.1 Effective Single-Pin Capture Resonance Integral for Pu 239 as a Function of Pin Radius and Isotopic Enrichment (1.84-110 eV)

5-1

5. TREATMENT OF BURNABLE POISON Modern LWR fuel assemblies contain highly absorbing cells, such as burnable poison (gadolinium) fuel pins or burnable absorber (boron) shim rods. The presence of such highly absorbing pins requires detailed calculations of neutron distributions in space and energy within these pins as function of burnup for correct prediction of reaction rates and reactivity. In BWR fuel assemblies, the reaction rates in burnable poison pins are sensitive to the void in the surrounding moderator, and the accuracy of the burnable poison model is of importance also for void coefficient calculations.

In the FMS-system, two associated codes, THERMOS and GADPOL, are used in treating burnable poison cells. The results of calculations with these codes are subsequently fed into the RECORD code in the form of effective cross-sections for gadolinium containing pin cells or boron shim rods.

Optionally, a precalculated GADOLINIUM LIBRARY is available for gadolinium-containing fuel pins in 8 x 8 assemblies for a certain range of uranium and gadolinium enrichments.

5.1 The THERMOS - GADPOL Method The method uses a burnup version of the transport theory code, K7-THERMOS (Ref. 15), to treat the burnable poison cell configuration and the deple-tion of the burnable absorber, while the GADPOL code modifies the THERMOS results to be suited for the later diffusion theory calculations in RECORD.

In THERMOS, a local part of the fuel assembly is described in cylindrical geometry (Fig. 5.1.1). It consists of the burnable poison cell, described explicitly, and its eight closest lattice cells, given as a homogeneous mixture of fuel and moderator. Additional hydrogen is introduced in an outer region to simulate the spectrum softening effect of the water gap sur-rounding the assembly. Use of fine mesh and several regions inside the poison cell, ensures a detailed description of the thermal flux dip. The maximum number of mesh points is 24, and 17 energy points can be used in the thermal energy range up to 1.84 eV. The point energy approach (Refs. 9, 10)

5-2 is applied in THERMOS where 17 energy points is equivalent to about 30 - 35 energy groups.

The THERMOS-calculated cross-sections are normalized to the surface flux of the poisoned pin cell. To ensure the conservation of the reaction rates in this highly absorbing pin cell when using RECORD, the GADPOL Code is applied to modify the THERMOS cross-sections before these are given as input to RECORD. In GADPOL, two-dimensional diffusion calculations in x y geometry are performed. The calculation extends over the same region of the assembly as defined in THERMOS, while the mesh point distribution is equal to the RECORD distribution in that part of the assembly. Any mesh in RECORD may then be freely chosen, also with mesh points inside the poison cell, and still get the correct reaction rates and burnup distribution.

Thus effective shielded thermal cross-sections, representing the highly absorbing pin cell, are provided to RECORD. These cross-sections are func-tions of time-integrated thermal surface flux for the pi.n cell, and they are given in tabular form for use in RECORD.

All data transfer between THERMOS / GADPOL / RECORD is automated on disc files.

The description given assumes, in principle, a single burnable poison cell surrounded by lattice cells which do not contain any burnable poison. A modification of the THERMOS /GADPOL model, however, also enables treatment of the problem of two gadolinium-containing fuel pins in adjacent lattice positions, arising in certain BWR fuel assembly designs.

5.2 Gadolinium Treatment 152 161 In natural gadolinium, all isotopes from Gd to Gd occur (Table 5.2.1).

In the FMS modelling of gadolinium burnup, using the THERMOS /GADPOL system, the following Gd-isotopes are included:

152 154 155 156 157 158 Gd , Gd , Gd , Gd , Gd , Gd

5-3 The main absorption in gadolinium isotopes occurs in the thermal energy range. The initial epithermal contributions to the total absorption rates are about 10 - 12 % for Gd155 and less for the other isotopes.

The effect of epithermal resonance capture on the burnup of Gd-isotopes is included by introducticn of an " epithermal group" in the thermal spectrum code THERMOS. This is done by using externally calculated effective reso-nance integrals. These are calculated by taking into account self-shielding and shielding from other important resonance absorbers (U235, U238 , Pu and gadciinium isotopes), and a spatially flat and 1/E-dependent epithermal spectrum.

Results from THERMOS consist of microscopic fission and absorption cross-sections for the U and Pu isotopes present, together with macroscopic absorption cross sections for the poison, and scattering removal cross-sections and diffusion coefficient for the whole pin cell. The cross-sections are given for the two thermal macro energy groups used in RECORD, and at different burnup steps, until the absorption.in gadolinium is negli-gible.

As the highly absorbing isotopes Gd155 and Gd157 deplete, the total absorp-tion in gadolinium goes into an equilibrium situation, and we have a so-called residual gadolinium effect. It was found that this residual poison is practically constant after a given flux-time, which is chosen as the

" switch-over point".

Before this point in time, the cross-sections applied in RECORD for fuel pin cells containing gadolinium, come from the THERMOS /GADPOL codes. After this l

1 point, hcwever, RECORD generated cross-sections are used, and the effect of

(

residual gadolinium is accounted for through the macroscopic rest absorption of the cell, as calculated from THERMOS /GADPOL at this burnup.

5-4 5.3 Shim Rod (Boron Glass) Treatment The FMS modelling of burnup in the PWR burnable absorber shim rods (both the annular, pyrex glass type, and the solid boral type absorber) is performed using the THERMOS /GADPOL system.

The effect of epithermal absorption in B10 on boron burnup is taken into account by introduction of an " epithermal group" in THERMOS. This epithermal absorption is calculated based on the assumption of a spatially constant and 1/E-dependent epithermal neutron spectrum. It is also assumed that this epithermal absorption does not influence the thermal spectrum.

Because of this arti#icial epithermal treatment in THERMOS, the depletion of 8 10 is recalculated in RECORD, using the effective thermal microscopic 8 0 cross-sections from THERMOS'and the epithermal ones from the RECORD calcu-Lation.

The effective quantities calculated by THERMOS /GADPOL and transferred to RECORD are : the effective thermal microscopic cross-sections mentioned above, the shim rod cell diffusion coefficientL, macroscopic scattering removal, and rest absorption cross-sections (810 poison excluded).

The THERMOS.results are modified by GADPOL, similar to the description given in Section 5.1, and the quantities are given as function of time-integrated thermal surface flux of the shim rod cell.

i l

5-5 TABLE 5.2.1 Average Neutron Cross-Sections for the Gd-Isotopes Cross-Sections (c) / Resonance Integrals (RI)

(barns)

ISOTOPE THERMAL EPITHERMAL o

ny o nn RI"y R yI'"

Gd152 0.2 1100 100 6.813 ) 3000 300 2000 2

Gd 153 ) Unstable (S+) 97 -

~100 Gd15 2.2 85 12 6.863 ) 215 20 180 Gd155 14,9 61100 500 63.5 1550 50 1110 Gd156 20.6 1.5 1.2 8.243 ) 95 5 90 Gdl57 15.7 254300 2000 1010 730 20 493 Gd158 24.7 2.5 0.5 5.313 ) 61 6 -

2)

Gd159 S-unstable I t =18.56 hrs ~ ~

Gd160 21.7 0.77 0.02 5.03 } 7.0 1.0 -

2)

Gd161 8-unstable 31000 12000 -

I t\~=3.7 min Ref. : BNEr-325, 3. Edition

1) ENDF/B-III

2) Nuklidkarte, 4. AufZage 1974

3) Calculated uith RESU-II, based on resonance parameters from BNL-325.

5-6 i

h i

WAT ER

, H OMOG E NIZ E D REGION '

J WAT E RN CL A DDING N

_[UEL FIGURE 5.1.1 Geometry in THERMOS for Gadolinium Fuel Calculations I

i 6-1 6 CONTROL ABSORBERS Control rod absorbers are treated in RECORD as non-diffusion subregions, defined by boundary conditions applied at the absorber surfaces. The boundary conditions are current-to-flux ratios calculated from transport theory approximations. Both BWR control blades and PWR rod cluster control elements ar* treated directly by the code.

6,1 Control Blades - BWR Option Two types of boron-based BWR control absorbers are modelled in RECORD:

Solid-blade cruciform absorbers Rodded-blade cruciform absorbers The effect of an inserted control blade is accounted for by treating the blade as the boundary for the neutron diffusion region ('ee s Chapter 7).

Effective 5-group boundary conditions are obtained, as below described, based on transport theory approximations accounting for detailed, geometri-cal effects and for the presence of neutron scattering materials in addi-tion to the absorbing material.

6.1.1 Solid Blade Absorbers The mono-energetic, diffusion theory, current-to-flux ratio, a, is obtained by :

1 - T. - R.

a=1. 2 1+T 1

+R 1

(6.1.1) an an where T, = slab transmission probability, 1

isotropic angular distribution

l 6-2 R = slab reflection probability, isotropic angular distribution T = slab transmission probability, linearly an ansisotropic angular distribution R = slab reflection probability, linearly an anisotropic angular distribution The transmission and reflection probabilities are functions of the slab optical thickness and the ratio of scattering-to-total cross-section. A semi-empirical formulation (Ref. 34), yielding very good agreement with tabulated transport theory results (Ref. 35), is used to calculate T , R ,

T and R .

an an The diffusion theory current-to-flux ratio is normalized to the transport corrected current-to-flux ratio for a black boundary :

- 05 + 0.4692 (6.1.2)

,ff where

= effective, diffusion theory current-to-flux a,ff ratio a = Equation (6.1.1)

(a gff = 0.4692 for a black slab)

Effective boundary conditions are obtained for each microgroup, and are subsequently collapsed into the macrogroup (5-group) structure used in RECORD. The lattice flux spectrum, modified with slab flux depression fac-tors, 1/(1 + vTa), (Ref. 36), is used as weight factors in calculating the macrogroup average a values.

6-3 Optionally, the macrogroup values are further modified to account for the infuence of an outer stainless steel clad on the absorber blade.

6.1.2 Rodded-Blade Absorbers The blade of a rodded control absorber typically consists of an array of B C-filled, stainless steel tubes contained within a stainless steel sheath. Water is allowed to flow inside the shecth.

Diffusion theory current-to-flux ratios are calculated for the outer sur-face of the blade sheath or clad. The mono-energetic current-to-flux ratio is obtained by Equation 6.1.1, replacing the slab transmission and reflect-tion coefficients by the corresponding values for cylindrical absorbers.

These coefficients are calculated by a formulation (Ref. 37) making use of the corresponding slab values, and applying empirical correction factors to account for the cylindrical geometry. Blackness coefficients as calculated by the method used in RECORD, in comparison with tabulated transport theory results (Ref. 38), are shown in Figure 6.1.1. The blackness coefficient, B, is related to the current-to-flux ratio,a, by :

4a 8 = 1 + 2a (6.1.3)

The following formula, as derived in Reference 37, is used to account for the stainless steel tube, regarded as a clad to the B C absorber :

4 1 - 2I AC1 T

- F 3) - -

8=B o 1 - 2E sAF1o S 1~ A T) F 2 + 2Es AF)- (6.1.4)

I where l

S = albedo (= 1-B), unclad absorber 8 = albedo at clad outer surface

6-4 ET'Es = clad total and scattering macroscopic cross-sections a = clad thickness F = probability that neutrons originating from a uniform, isotropic source in the clad will enter the absorber F robability that neutrons with a P 2

angular distribution at the clad outer surface wiLL be directed toward the absorber The following approximations are used :

3 2 R, + A F

3=4 R where R

o

= absorber outer radius R =' clad outer radius R

o F

2,i

• R F

2,an *

• 1 where subscripts i and an denote the isotropic and linearly anisotropic components of F .

For cylindrical absorbers, transformation to a,ff is obtained as follows (Ref. 17) :

• 6.1.9 "eff 3A ff

6-5 with

• * 'I0 '

4 tr A

eff 3

1-B*I 8

tr R + 0.4052 0.7104 (6.1.6) where E = transport cross-section of exterior medium tr (lattice region) -

The single cylinder a,ff (Eq. 6.1.5) is calculated for each macrogroup (five groups) after collapsing the microgroup values, as described above, for slab absorbers.

The ef fective current-to-flux ratio, a ,s n a plane surface tangential to an array of absorbing cylinders is given by

=

7

+ -

(6.1.7)

LE, where P = cylinder pitch R = cylinder radius L = exterior medium diffusion length E, = exterior medium macroscopic absorption cross-section a = single cylinder a,ff (from Eq. 6.1.5) c G = expression containing modified Bessel functions I

6-6 This formula, derived in Reference 37, is based on an expression for the diffusion theory current into an absorbing cylinder, being a member of an infinite, linear array of equal cylinders given in Reference 39 Comparisons of a,f f-values, calculated with the method described above with reference transport calculations (numerical integration, Ref. 40), are shown in Figure 6.1.2. Results are shown both for typical cold and hot voided exterior medium (Eq. 6.1.7) and for R/P = 0.5 and 0.3. A further discus-sion of these results is given in Reference 37.

The final step in calculating the rodded-blade current-to-flux ratio is to account for the stainless steel blade sheath. Reflection and transmission coefficients for the sheath, regarded as an absorbing and scattering stab, are obtained by the method described above under Section 6.1.1. These coefficients are used to account for the influence of the blade sheath on the final, macrogroup current-to-flux ratios, as described in Reference 41.

6.2 Rod Cluster Control - PWR Option Rod cluster control elements, based on either boron or Ag-In-Cd as the absorber material, may be represented in RECORD. The elements are regarded as absorbing cylinders with an optional stainless steel or zircaloy clad.

Effective current-to-flux ratios are calculated as described above (Eq. 6.1.5), based on transport theory approximations for the neutron transmission and reflection coefficients. An exception is made for the resolved resonance region (10 eV to 350 eV) for Ag-In-cd absorbers. Here, the neutron slowing-down process is described by a modified NRIM approxi-mation. An analytic expression for the resonance integral is obtained, t

including the Doppler effect on resonance absorption. The method ic based on work described in Reference 42, and described in detail in Reference 18.

The cylindrical absorber elements are represented as equivalent square

[

l regions in the rectangular mesh of the diffusion routine in RECORD. Trans-l l

6-7 formation of the effective current-to-flux ratios from cylindrical to rect-angular geometry is performed following a method described in Reference 17 :

e,_, = v . 21l e ,< <e.a.,>

The transformation factor y is unity for the epithermal region and for the highest thermal group. For the lowest thermal group, Y is reprer.ented by the following polynomial :

Y = a, + a) ecyl + a2 " yl (6.2.2)

The coefficients a , a g and a are found by least square fitting to data 0 2 reported in Reference 17.

l 4

il

?*

5

_ ~ _ - - - - - - 2

)

8 3

f e s R u

- (

_ i d

D y a R r R O o C e 0 l E h a

_=

, 1

+ R T 2 i

c f t t o r p o O d p o s .

h n s t a v e r M T s r

e b

r

• 5 o

, i s 1 b A

l

) a T c

( i r

S d 1

• 3 6- U I

n 0, O* o, 5 0 0, D i

l y

g A c C c C C R C 0 L f

, i A o 1 C I t T n P e O i c

i f

f e

o C

s s

5 e

, 1 n

0 k T c E a l

B E 3pT R

= = 1

- C T 1 6

E

- - _ - - - - - - R U

0 9 0 G 8 7 6 4 3 2 1 I

. s. F 1

l

- H t8om0EEd t i i

n. . ..

i i I i 1 0.5 -

COLD EXTERIOR MEDIUM

- " - - - R/P = 0.5

1. r-0.4 -

',s- -

HOT VOIDED t -

O COL D 0.3 N

/ _ _ _ _ _ R/P = 0.3 7 __

/ HOT VOIDED I

e

/

0.2 -

/ -

/ /

/ s'

/ /

/

0.1 -

METHOD OF RECORD

-o-- TRAf1 SPORT THEORY (Ref.40)

R CvuNDER RADIUS P PITCH OF CYLifl0ERS I I l 1 i 0.5 1.0 1.5 Ia .R+ 2.0 2.5 FIGURE 6.1.2 Effective Current-to-Flux Ratios for Array of Cylindrical Absorbers as Calculated with Method used in RECORD, in Comparison with Transport Theory Reference Results

1 7-1 7 TWO-DIMENSIONAL FLUX AND POWER DISTRIBUTION I

The multigroup flux calculations across a fuel assembly and adjacent water gaps, and the eigenvalue (keff) of the system, are determined from two-dimensional five group diffusion theory, using the methods of the MD-2 code (Ref. 19).

7.1 Multiaroup Diffusion Equations The two-dimensional diffusion equation for group g (g = 1,2...,G) in Cartesian coordinates is written:

-fg-D(x,y)j-$(x,y)__,3(x,y)

E 6 8 , ,5( x ,y )

(7.1.1)

+ oE (x,y) 96 (x,y) ,38(x,y) where G

c8=DE BE+IE+ E*8, (7.1.2)

• [ I g'=1 Y E'/5 g'

s E= I 8 8 4 + *

("Zf)E (7.1.3) r g'=1 g'=1 i 8'/8 9

with D9 = diffusion coefficient, group g 9 = macroscopic absorption cross-section,

';a group g

7-2 9 'G' = macroscopic removal cross-section from E

r group g to g' X9 = fraction of fission yield in group g (VE )9 = v times macroscopic fission cross-section, f

group g B9 = transverse buckling, group g

=

l A eigenvalue (k,ff)

$9 = neutron flux, group g The boundary conditions are:

D9 (x,y) g- $9 (x,y) +09(x,y) $9 (x,y) =0 (7.1.4) g = 1,2, . . . . . . G where 3

g- = the normal derivative operator, and a = the current-to-flux ratio 7.2 Geometry and Mesh Description The solution is approximated over a rectangular area that is composed of subregions separated by interfaces parallel to the outer boundaries of the rectangular area.

i Two types of subregions exist, the diffusion subregions in which all the coefficients for group g in Equation (7.1.1) are constants, and the non-diffusion subregion where the neutron flux is not defined.

7-3 Across an interface between two diffusion subregions, the flux and the current are continuous. On the outer boundaries and the interfaces between diffusion and non-diffusion subregions, the bou.ndary conditions (Eq. 7.1.4) must be satisfied. I A nonuniform grid of mesh lines is imposed on the rectangular area. Each line must be parallel to a boundary line and must extend from one boundary to the opposite boundary. The mesh lines must be chosen such that the sub-region interfaces coincide exactly with the mesh lines.

7.3 Difference Equations Equation (7.1.1) is approximated by five point difference equations at the mesh points (1,j), i = 1,2,....,1, j= 1,2....,J. The usual box-integrated method is used (Ref. 43).

The equation for mesh point (1,j) and group g is of the form:

og 3 .j~"g 4

-1.j ~ " g 3 0 +1.j ~ g

• ,j-1 (7.3.1)

-a 8 = yE Bf'. (@'.

i,j

$.l'J.+ g'=1 (f'.

10 + A 8 1.J 1J i,j g'=1 8'/8 where

". *2h i-1 (Df_y,3 k 3+Df_y,3_1 k_y) (7.3.2) 3 1,a g

as ,o (7.3.3) i,j i+1,j h,y+Df3_y h) (7.3.4) i,j

• 2 k.a-1 -1.j-1 g g

7-4

.)

i i

"g " a h.1,3 "3 1,J+1

. (7.3.5) h "o.

1,a E

t=1 "!..+F 1,a g,3 % + ah; < .

1,;

(7.3.6) e Y

=F;,3({,E'+8) (7.3.7)

=F g,3 ((vr )SJ- j7.3.8)

Bf,3 f The functional Fij(n) denotes the integration of n around mesh point (1,j),

and i,j U " D i-1,j N

j*Ui-1,j-1 hj-1 i-1 (7.3.9)

+ U i,j-1 j_y k + ng ) k)) hg A$,j,j is the contribution to a$,j,j from the integration of a9 (x,y) along a mesh line at the boundary of a diffusion - nondiffusion interface, hj and k j denote the mesh length in x and y direction.

7.4 Method of Solution W

A one-line overrelaxation iterative procedure, combined with a periodic use of coarse-mesh group rebalancing is used to obtain the solution of the difference equations.

7-5  !

One-Line Overrelaxation Procedure The one-line overrelaxation procedure is written:

N Af,if(m+1)=A E E

if_y(m+1)+A , if,y(m) 1 1-1 1 8-1 G i

+[g'=1 Cf 8 f ,(m+1) + {

g'=g+1 Cf,^8if(m) g g-1 G '

) (7.4.1)

+ " "

(n) g,=1 g,=g i, 8

if(m+1)=w if(m+1)-if(m) +if(m);

i = 1,2,....I  ; g = 1,2,.... G

/

where g

-a 8 o

i,1 i,1 g

-a 8 O

-a i,2 i,j

' \

N (7.4.2) g

• N A \ \

o.

1 N N 8

b"*

N -ag

\ i,J-1 s

a8 i,J Af, = diag {c8 ,,

) (7.4.3) 1 1.a Bf = ding {B } (7.4.4)

7-6  ;

i l

C 8 = ding {y! ) (7.4.5)

• (* 1 * ,2

$ ,J (7.4.6) l The relaxation parameters u9 ;g= 1,2,....,G are calculated by estimating the spectral radius of the Jacobian iterative matrix for each group, and making use of the matrix possessing the Young's property A (Ref. 44). The iteration index for the overrelaxation is denoted by m, and n has been used to denote the number of rebalancing performed. The eigenvalue is calculated in each rebalancing calculation and is kept constant during the overrelaxa-tion iterations. For each m, g and i, the Equation (7.4.1) is solved by factorization techniques (Ref. 44). Convergence of Equation (7.4.1) is assumed when:

f.

(l'J(m+1) - $@1 J(m)$g max (7.4.7) 1 i,j,g

$f (m) and 1(n+1) - A(n) <

A(n) *2 (7.4.8)

Coarse-Mesh-Group Rebalancing The equations (Eq. 7.3.1) are written in the following way:

+ 1 -+

A4=7 P& (7.4.9) where the matrices and the vector are of order I

• J

• G.

7-7 On the fine-mesh group system, a number of coarse-mesh group blocks are imposed. Each block is identified by the set ( 5, j ,g') where

~ ~ ~ ~ ~ ~

1 < i < I; 1 1 j i J; 1 1 g 1 G.

The upper i-line, j-line and g-line in coarse cell (i,j,'g), is denoted by i~ , j~ and g, 1 J 9 Let$a bethelastiteratedfluxvector.Acorrectedflux$ with the elements e

~

i. +15i5i.

i-1 i i,j i,j *i j 3,1 } (7.4.10)

g. +15g5g.

, 8-1 g may be found by solving the following equation for the largest in modulus eigenvalue (which is the same as k,ff) (Ref. 45):

k2=fP2 (7.4.11) where the matrices are of order I

• J

• G with the elements:

Im.m, = < 1, A ia' > (7.4.12) m F ,

=

< 1, P i, > (7.4.13)

Here $a m' den tes a vector of order I

• J

• G with nonzero elements & j only if (i,j,g) is belonging to the coarse cell numbered by m'.

7-8 The solution of (7.4.11) is obtained by Wielandt iterations and the inhomo-geneous equation is solved by factorization technique (Ref. 44).

a t

l 8-1

8. BURNUP CALCULATIONS Fuel burnup is determined from the isotopic concentrations in the fuel, their effective cross-sections, and integrated flux-time for a given fuel assembly. The description which follows emphasizes the main assumptions )

regarding fuel and fission product chains, and the principle of the solution method.

8.1 Fuel Burnup Chains For enriched fuel where burnup proceeds to high levels, it is important that all nuclides are represented in the burnup chain which contribute signifi-cantly to the neutron production and absorption. The fuel burnup chains assumed in RECORD are the chains starting at U 235 and U238, ,,

shown in Figure 8.1.1.

The U 235 chain is assumed to terminate with the neutron capture in U 236 without leading to formation of other nuclides. In reality, absorption in U 236 Leads to formation of U237, which decays rapidly to Np237 The (n,2n) reaction in U235, which is not included in the chain either, also leads to the formation of Np 237 . Although at present neglected, the absorp-tion in Np237 in LWR fuels may become more important at high burnups if, for instance, irradiated U235 and associated U236 is used in recycled fuel.

The U238 chain also includes the trans plutonium nuclides Am241, A,242, Am243 and Cm244. The neutron absorption in some of these nuclides are of significance at high burnups and has to be taken into account. The absorp-tion in Am241 leads to Am242, with some fraction being the fissile Am242m, This fraction is spectrum-dependent, and a value of 16% is often used as being representative for thermal reactor systems. The curium isotopes, Cm242 and Cm244, have no significance on the neutron absorption from a reactivity point-of-view, but have their importance in their G-decay and spontaneous fissions, which cause problems in the transport of irradiated fuel.

l I

8-2 i l

8.2 Fission Product Representation The fission product model incorporated in RECORD is a result of a general study of the individual nuclide contribution to the total poisoning in a typical BWR reactor. The model consists of a scheme with explicit treatment 135 of 11 fission products in four chains, together with the chains for Xe 149 and Se generated by direct fission. The remaining fission products are condensed inte four pseudo fission products, in accordance with their satur-ation characteristics. The nuclide chains assumed, are shown in Figure 8.2.1.

The study leading to the choice of fission product model, and the methods of generating cross-sections and effective yield data for the fission products, is described in References 20 and 46, and only the essence of that study will be discussed here. The work involved the study of different reduced representations of fission products and comparing these against a more exact scheme, where all fission products in explicit chains are followed during burnuo.

A general fission product code, FISSION (Ref. 46), was first developed, where all known fission products of significance are incorporated, and where a complete analytic method similar to that of CINDER (Ref. 47) is used to solve the linear burnup differential equations. The general nuclide decay chains are split into linear sub-chains and, after discarding negligible components, the detailed fission product representation consisted of 69 sub-chains containing 370 components of 179 different nuclides. A study of the individual nuclide contribution to the total poisoning for a typical BWR

fuel, showed that about 20 fission products were responsible for 135 approximately 85 - 90% of the total poison, excluding that due to Xe and 149

. Sm .

A number of different fission product aggregates were now constructed and tested against the complete analytical method. From six to 26 fission pro-ducts were treated explicitly in these models, together with one to four pseudo fission products. Concentrations and thermal and epithermal absorp-t

8-3 tion cross-sections for all nuclides, including the pseudo fission products, were calculated and compared for a variety of reactor states as function of burnup (or time). An example of such a comparison is shown in Figure 8.2.2.

The choice of fission product model is made on a judgement of (a) accuracy, in comparison with exact method and computer limitations; (b) respect to detail that can be handled in the pinwise treatment of fuel burnup in RECORD; and (c) the implication on computing time in solving the burnup differential equations in each of a large number of fuel pins in a general fuel assembly calculation. The model finally incorporated in RECORD, altogether consisting of 12 fission products in six chains, and four pseudo fission products, showed good agreement with exact representation for burnups up to about 30 000 MWD /TU.

The fission products not given explicit treatment are combined into the four pseudo fission products, depending on their saturation properties which, in turn, are mainly dependent on their effective absorption, cross-sections. The nuclides in the pseudo fission products are grouped according to their resonance integrals, being in the range 0 - 100,100 - 500, 500 - 1200, and 1200 - 3400 barns for the four pseudo elements, respectively.

8.3 Solution of Burnup Equations The general system of differential equations describing fuel depletion and fission product buildup as function of neutron irradiation, is given by dN.(t) 1 -

=Y$ + Yg_3 Ng ,3(t) - A 4g N (t) CO*S*l) where l

N. (t) = concentration of isotope i at time t i 1 A =

fa(E)&(E)dE+A g A = decay constant q

G-4 I

l

either (a) decay constant, Yi -1 or (b) capture rate,f"oce- (E)$ (E)dE of precursor isotope c (E) = absorption (fission + capture) cross-section cci(E) = capture cross-section 4(E) = flux E = energy and where the yield term is given by t

Y; = [ Yf f N k(t) f o (E) f $ (E) dE dt (8.3.2) k o o where k =

Y. fractional yield for fission product i 1

per fission in fissile isotope k The summation is taken over all the fissile isotopes k.

Assuming constant flux and cross-sections during a time interval t, and assuming the isotope chains to be resolved into single path or linear chains with no branching, Equation (8.3.1) can be solved analytically to give:

-A t i i i Nk (0) [ ?j +

N.

1 (t) = [bi k=1 T ""g y" (8.3.3) 1 jrk .,

• ' s ag-A.)

0 Luk lb

8-5

-A t '

,Y 1

i *j ,

(8.3.3) k , 2.

{ * ' (Cont'd)

A j=k tbk ^j f b 1 ^j)

1. 3 where N (o) = initial concentration of isotope k (i.e. at beginning of time interval), and

, Y = time-averaged direct yield rate to nuclide k from all fissile nuclides in the time interval For small values of t, rounding errors may occur in the summations within the main brackets of Equation (8.3.3). The exponential terms cannot be evaluated to more than N significant digits in double precision on the computer and, hence, the summations cannot be correctly calculated if they

-N are smaller than ~lX;l* 10 , where lX l is the largest term of the summa-I tion. Accordingly, following the metho of England (Ref. 47), the following l test is incorporated into.the code:

i lXl*10-">

3

,[X j (8.3.4)

,) = k where X are the terms of the summation. If Equation (8.3.4) is true, all j

terms with j $ k are neglected, being insignificant contributions from far-

away isotopes in the chain on the isotope i.

Using recurrance relations between the different terms in the expansion of Equation (8.3.3) and England's method of discarding insignificant terms, the concentrations of isotopes in the linear burnup chains can be calculated accurately on the computer with very short computing times.

8-6 The poisoning due to Xenon-135 formation is treated at all burnup states with' the assumption of equilibrium xenon concentration. This equilibrium concentration is given by (in the same notation as before):

E k Xe "k E9 g Y ,g NXe (8.3.5) axe + I o** a,g ig 9

where k

Y = effective yield for Xe per fission Xe in fissile isotope k.

The energy generated in each burnup ir'.erval is calculated from the fission rate in each fissile nuclide. If E k is the energy release (in MeV) per fission of nuclide k, the total energy (MeV/cm 8) generated in time step t sec, is given by t =

P=[ckk

[ Nk (t) o[ o o

(E)4 (E) dE dt (8.3.6) where the summation is taken over all fissile nuclides k.

Using average group cross-sectior.s and fluxes, and a conversion factor to convert the power density to the usual units, Megawatt-days per initial tonne heavy metal, the above expression, applied to all fuel pins of a fuel assembly, determines the burnup distribution at any given time.

In RECORD, the isotopic concentrations of each nuclide (uranium, plutonium, trans plutonium and fission product nuclides) in each fuel pin of a fuel assembly, are followed as function of burnup, using Equation (8.3.3) where the fluxes and effective cross-sections in each fuel pin will be functions of the isotopic concentration reached a*. any given burnup. Within each burnup interval, the burnup equations are solved for each fuel pin; during which, the spectrum, fluxes and cross-sections in each pin cell are held

8-7 constant at the values evaluated at the beginning of the burnup interval. i The code iterates to precise burnup values by iterating the burnup calcu-Lations (seldom using more than two or three steps) over the assembly unit until the average burnup of the fuel is within 1/2 MWD /TU of the required, specified average fuel burnup at the end of a given burnup interval as given in the code input.

{

8-8 U  ;

U ~ --+ PATHS CALCULATED

---* PATHS NOT CALCULATED X* NUCLIDES INCLUDEr IN THE U --* (U 9) BURNUP CALCULAT'ONS 23 min (Y") NUCLIDES NOT i.4CLUDED y

Np 239 -... ( Np2O) 1 56h ' 7m.1h U T Pu239 Pu 240  ; Pu 241 Pu242 [py243) 14y Sh 9 Am 242m y l - - - - - - - -- ] Am241 Am243 ,,__, ( Am244)

!g  !

' A ( Am242g),,#

' / o 4- l e e

I e16h 10h e

k y 244 L__________

, (Cm242) __.. ,(Cm243} .... ,Cm _,p J' d' d' FIGURE 8.1.1 Fuel Burnup Chains in RECORD i

h

l

8-9 Ndl43 --* Nd147--*

Pm147

• Pm148m  : Sm 149 y v

\ Pm'47  : Pm448

• Sm14 9  :

y ir NSmISI N  : Sm152 --* Eu153 --* \Eu  : Eu 15 5 %

. y u

~ ~

f; ~ ~IELD ~]

113 5 ) Pml49) g I (n,y) l

" l  ; I Xe135  : \" l49 Sm ----'* I l 1 4'" I I l

" i KEY I L _ _ _ _ _ _J NPFP N NPFP NPFP 3

--* PFP2 --> 3 4 --*

(PF P e P5tuDO FISSION PRODUCis i FIGURE 8.2.1 Fission Product Chains in RECORD

8-10 Thermat (2200 m/s):

110 1: Emact Method II : 26 nuclides + 1 pseudo fission prod.

{, III : 11 "

+4 " " "

IV : 6 +4 V: 6 +3 J.

- .; s 8 93 Ng

_ __ A. FI E

rII E

'.% / 111 o

70 N %w ~ _

/CI.V N -

N D NA w x 50 N o 15 tc3a: hrs) #

EoithermaL 30 f  % ~

/ "~

%i hm g

[g 7  %  % ~

N  %

~

E 20 -g ( g- %

_d Il g II' f f 10 0 D t(108 hrs)

FIGURE 8.2.2 Effective Macroscopic Fission Product Absorption Cross-Sections for a Typical BWR (40% void)

9-1

9. OTHER FEATURES OF RECORD 9.1 TIP Instrumentation Factors The relative power levels in different regions of a BWR core is often determined from measurements from a travelling-in-core detector, inserted in i the narrow-narrow water gap corner region outside the fuel assemblies. For proper interpretation of the power levels, it is necessary to relate the detector readings to the average power level of the surrounding fuel assem-blies.

In the calculation of the reaction rate in the narrow-narrow water gap region, the so-called TIP-region, the influence from the spectrum variations in the surrounding fuel assemblies must be taken into account. Of particu-lar importance in this respect, is the influence on the TIP-region spectrum due to void variations in the moderator within the adjacent fuel assemblies.

In modelling the TIP-region reaction rate, RECORD assumes the TIP-detector to be a fission chamber where the detector signal R is proportional to the 235 fission rate in U  :

Raf c2o sfs ( E) $(E) dE (9.1.1) where 235 ojs s (E) = fission cross-section for U at energy E , and

$(E) = flux spectrum in the detector region The detector region is assumed to be the quadratic region in the narrow-narrow water gap corner outside the assembly flow box (see Fig. 2.1.4). It is assuraed that the amount of U235 present in the detector is sufficiently small so as not to influence the spectrum or flux level in that region.

l

9-2 A detailed study has been made on typical BWR assembly cells to determine the void dependence of the TIP-region reaction rates, where the void is the average void in the surrounding fuel assemblies. From this work, it has been pDssible to establish a correlation that relates the effective two-group U 235 thermal fission cross-sections to the average void within the assembly flow box. This correlation is incorporated in RECORD and, in standard BWR applications, is used in calculating the TIP-region fission rate according to Equation (9.1.1). In non-standard applications of RECORD, or in cases where the User so wishes, the calculation of detector fission rate from the established correlations is replaced by applying group data and effective detector fission cross-sections for the TIP-region, as defined in the code input.

The application of instrumentation factors in PRESTO is described in Ref-ence 3. The instrumentation factors derived from the standard calculation method in RECORD, is routinely used in PRESTO reactor simulation studies, and extensive verification of PRESTO-calculated axial TIP-traces in com-parison with measured data (Refs. 3, 4) testifies to the soundness of the established calculation procedures.

9.2 Delayed Neutron Parameters Kinetic parameters, represented by effective delayed neutron fractions and associated decay constants, are calculated for applications in neutron kinetics codes.

The fraction of neutrons being delayed (B) varies considerably between the fissionable isotopes. The value of S will vary f rom pin-to pin in the lat-tice and is a relatively strong function of irradiation. The delayed neutron fission spectrum differs from that of the prompt neutrons, and is reflected in the calculation of the effective delayed neutron fraction, O

eff" Due to the specific fission spectrum of the delayed neutrons, a detailed calculation of Beff would be complicated and time-consuming. To avoid this, the following approximations are introduced in RECORD to calculate the

9-3 delayed neutron parameters : Neutron spectra and reaction rates from the conventional prompt neutron calculation is used, but the neutron events at energies above the delayed neutron fission spectrum are excluded in the calculation of 8,ff. However, the effects on the neutron spectrum at lower energies, caused by the fast neutron events, are neglected.

Delayed neutrons are grouped together into the conventional six groups.

The following expression (for nomenclature, see end of section) is used in thecalculationoftheeffectivedelayedneutronfraction,Sfff,g,for isotope 1 in delayed neutron group i (cf. Ref. 13) :

J i k D

[0 1i j =1 PRODg O

eff, *E **'

((PRODg EJ with the multiplication factor, k, from J

• PROD k= (9.2.2) e c (ABS E,J. + LEAK E,J.)

L L E j=1 and the " delayed" multiplication factor, k , from J

{[

1 j=J PROD g.

D k" (9* * }

D J

[{

1 j =J (ABS

'J

. + LEAK E,J

.)

D where the energy group index j runs from 1 (highest group) to J (total no.

of energy groups) in the calculation of k, but from J D , the highest group containing delayed fission neutrons, to J in the calculation of k D*

Thebasic,isotopicdelayedneutronfractions,Sf,arecalculatedfromdata onyields,y,andgroupfractions,a{:

g i Yg

• ag Sg= __ (9.2.4)

"1

9-4 Average delayed neutron fractions are calculated by summation over the fis-site isotopes  :

6 = B (9.2.5) ff ff,g The total delayed neutron fraction is given by S[=,fBfff 1=1 (9.2.6) and average data for each isotope expressed as 6 -

O eff,1 ff,E The average group decay constants are given by a

i

• eff,L t TOT Y=f,O (9.2.8) ef1,L yi gg g TOT E eff Fundamental data on group yields and decay constants are those recommended in Reference 48 and given in Table 9.2.1.

All calculations of kinetics. parameters in RECORD are performed in the five group scheme, i.e., J=5, and with the delayed fission neutrons intro-duced in Group 2, i.e., J D =2. The accuracy of the approximative expres-sion (Eq. 9.2.3) for the delayed neutron multiplication factor, k , under these assumptions, has been investigated by comparing it with the exact value of k calculated with a detailed delayed neutron fission spect-rum. For a typical BWR fuel design, the approximation was found to intro-duce an error in S gf of only 0.2%.

9-5 The following nomenclature is used in this section :

i = delayed neutron group index j = energy group index 1 = isotopic index  ;

J = total no. of energy groups (=5)

J = highest energy group with delayed fission neutrons (=2)

D PROD = production rate of isotope t in group j gj ABS = absorption rate of isotope E in group j g,)

LEAK = leakage rate of isotope E in group j gj

= absolute delayed neutron yield Yg a

i = fractional delayed neutron yield A

i = decay constant U = average no. neutrons per fission e

9-6 l l

TABLE 9.2.1 Delayed Neutron Data (Ref. 48) '

FRACTIONAL ABSOLUTE DELAYED GROUP GROUP YIELD DECAY CONSTA 14T ISOTOPE NEUTRON YIELD i ag Ag (sec-1)

U2 ss 0.01697 1 0.038 0.004 0.0127 0.0003 0.00020 2 0.213 0.007 0.0317 0.0012 1.2% 3 0.118 0.024 0.115 0.004 4 0.407 0.010 0.311 0.012 5 0.128 0.012 1.40 0.12 6 0.026 0.004 3.87 0.55 U388 0.04508 1 0.013 0.001 0.0132 0.0004 0.00060 2 0.137 0.003 0.0321 0.0009 1.3% 3 0.162 0.030 0.139 0.007 4 0.388 0.018 0.358 0.021 5 0.225 0.019 1.41 0.10 6 0.075 0.007 4.02 0.32 Pu 2s' O.00655 1 0.038 0.004 0.0129 0.0003 0.00012 2 0.280 0.006 0.0311 0.0007 1.8% 3 0.216 0.027 0.134 0.004 4 0.328 1 0.015 0.331 0.018 5 0.103 0.013 1.26 0.17 6 0.035 0.007 3.21 0.38 2

Pu %o 0.0096 1 0.028 0.004 0.0129 0.0006 0.0011 2 0.273 0.006 0.0313 0.0007 11.5% 3 0.192 0.078 0.135 0.016 4 0.350 0.030 0.333 0.046 5 0.128 0.027 1.36 0.30 6 0.029 0.009 4.04 1.16 Pu 2S1 0.0160 1 0.010 0.003 0.0128 0.0002 0.0016 2 0.229 0.006 0.0299 0.0006 10.0% 3 0.173 0.025 0.124 0.013 4 0.390 0.050 0.352 0.018

)

5 0.182 0.019 1.61 0.15 6 0.016 0.005 3.47 1.7 Pu 242* 0.0228 1 0.004 0.001 0.0128 0.0003 0.0025 2 0.195 0.032 0.0314 0.0013 11.0% 3 0.161 0.048 0.128 0.009 4 0.412 0.153 0.325 0.020 5 0.218 0.087 1.35 0.09 6 0.010 1 0.003 3.70 0.44

• Same data used for the other fissionable trans-plutonium isotopes not included in the Table.

c ^ _ _ _ ___

10-1

10. CODE QUALIFICATION The REC 0dD code is founded on the accumulated experiences from the reactor physics development work at the Institute for Atomic Energy (Institute for Energy Technology since 1980), Kjeller, Norway, during the 1960's and early 1970's. Some of the component modules of RECORD are based on codes developed during this period, and initially tested during the experimental activity also taking place at this time; in particular, in conjunction with the international NORA Project. Initial confidence in some of the basic reactor physic.s methods later incorporated in RECORD, was therefore established during this time. This reactor physics development work at the Institute is well summarized in IAEA reports (Refs. 27, 49 and 50).

The reactor physics models in RECORD have undergone extensive modifications and improvements, during the years of ccde development. New features have been incorporated and new computational techniques in the solution methods have been introduced. The code qualification work described in this chapter pertains, unless otherwise stated, to that performed with the latest (1981) version of RECORD and associated codes.

This chapter first recapitulates the RECORD analyses of altogether 55 cold, clean critical uranium and plutonium lattice configurations, as measured at different laboratories. These analyses constitute the basic integral verification of the fundamental reactor physics methods of RECORD and the adequacy of basic cross-sections used. The further integral verification of basic methods at hot operating conditions, and of the code's Nuclear Data Library, is provided by the analyses of the uranium and plutonium isotopics as function of fuel burnup, as measured during the Yanke:>9 owe Core Evalua-tion Program.

The ability of RECORD to predict local power distributions within a fuel assembly has been investigated in some detail, and a discussion is given of ,

the results of comparisons with gamma scan measurements on different assemblies f rom Quad Cities-1. Of particular importance in this and other analyses is the ability to demonstrate that the power in gadolinium-

10-2 contained fuel rods is predicted with an accuracy consistent with that of other rods.

A code's qualification can finally be stated to depend on how the code is to be applied. From the Utility's or reactor operator's point-of-view, the main qualification of a reactor code can be said to be its proven performance in actual reactor fuel and core calculations. The RECORD code has its main applications in the generation of data banks containing few-group cross-sections, and other data, such as differential effects due to control rod absorbers, Xenon, Doppler, voids, etc., which are relevant for describing LWR fuel as function of fuel exposure. These data form the basic data sets used by the reactor simulator, PRESTO. The main integral qualification of RECORD, therefore, can be considered to be the very posi-tive experiences accumulated through many years in the application of RECORD - PRESTO in the accurate analyses of a large number of BWR and PWR operating cycles. _This. experience is reviewed in the final section of this chapter.

10.1 Analysis of Clean Critical UO and UOg /Pu0 Lattices 7 2 A set of clean critical UO and 2

UO /2pug 2Lattices have been used to qualify the basic reactivity predictions of RECORD at room temperatures (in the region of 20 oC). The measurements have been made at different labora-tories, and the lattice and experimental data are well documented.

The lattices have been analyzed using RECORD in single pin option, in generating the standard RECORD five group data for lattice regions and surrounding reflector. The leakage calculations were performed by repre-senting the cylindrical core geometry of the critical configurations in a I

radial one-dimensional diffusion calculation with the code MD-1 (Ref. 51),

using the RECORD calculated five group data for each region. This analysis I assumed a two-region, radial model of the reactor; i.e., a homogeneous core and a nomogeneous reflector, and where the axial leakage was represented by the axial buckling.

~

, _- -_w

10-3 10.1.1 Critical UO * **

2 The UO 2

Lattices analyzed are from Westinghouse (Refs. 52, 53, 54 and 55),

Babcock & Wilcox (Refs. 56, 57), and NORA Project (Ref. 50). The enrichment in these lattices varied from approximately 1.3 to 4.0 weight per cent U235, Lattice pitches varied from 1.03 to 2.69 cm, and the water-to-fuel volume ratios varied f rom approximately 1 to 5. The configurations included both

! square and hexagonal lattices. The clad material is either aluminium or stainless steel. Tables 10.1.1 and 10.1.2 show the main characteristics of these critical lattices, together with the RECORD / MD-1 calculated keff-values. Figure 10.1.1 also shows the keff-values plotted as function of water-to-fuel volume ratio.

The mean keff-values and standard deviations obtained for Lattices from the different Laboratories are as follows :

Westinghouse  : Mean k,ff = 0.9997 0.0040 Babcock & Wilcox : Mean keff = 0.9990 0.0038 NORA  : Mean k,ff = 1.0046 0.0041 The mean k,ff-value for the 25 UO 2 Lattices analyzed is 1.0001 0.0042.

10.1.2 Critical UO 2/P.y0qLattices

~

The plutonium lattice experimental data from Battelle Pacific Northwest Laboratories (Ref. 58) have been analyzed with RECORD / MD-1 in the same manner as the UO 2 Lattices. The critical lattice measurements were made on

+

different UO2/Pu02 rods, ranging in Pu02 enrichments from 1.5 to 4.0 weight per cent, and Pu zu content varying from 8 to 24%. The lattice measurements i

were made over a broad range of water-to-fuel volume ratios, varying from approximately 1.1 to 11.6. Details of the 30 lattices analyzed are given in Tables 10.1.3 and 10.1.4, together with the resulting k,f f values f rom l

l l

1 l 10-4 RECORD / MD-1. The results are also shown in Figure 10.1.2, where k,f f is plotted against water-to-fuel volume ratio.

The mean kgf -values and standard deviations obtained for the different UO2

/Pu0 lattices are given in Table 10.1.5. The mean value for all 30 Lat-2 tices analyzed is 1.0071 0.0046.

Also shown in Figure 10.1.2 are the results of BNWL's own, detailed analysis of the critical lattices (Ref. 59). As can be observed, there is a consis-tent bias in the RECORD / MD-1 results in comparison with the BNWL calcula-ted k gf -values. For a broad range of Lattices, a parallel displacement of the results, can be observed, reflecting that variations in the experimen-tal conditions are similarly reproduced in the different calculation models.

The results agree best for the more open lattices with larger critical core radii. There are many uncertainties involved in the theoretical predi:-

tions, and the BNWL Paper (Ref. 59) discusses the detailed analyses of some of these uncertainties related to calculation models, energy detail, lattice hardware, and reactivity effects due to particulate fuel and other hetero-genities.

It is not the intention here to further discuss at length the adequacy of the different models. Notice should be taken, however, of the small size of' the critical assemblies, and the difficulty in calculating leakage accur-ately. It is most questionable if ene-dimensional, five group diffusion theory (four group in the BNWL analysis) is adequate for such systems and, as stated in Reference 59, higher order calculations are necessary to ensure proper calculation of leakage for these assemblies. Analysis of these same assemblies with the WIMS and MURLI codes (Ref. 60) used 27 group, one-dimensional calculations for representing the critical systems in suffi-cient energy detail. There, four group leakage calculations gave a bias of up to +1% in k,ff in comparison with the 27 group calculations, the differ-ence being highest for the lower critical core radii and tighter lattices.

The direct results of the analysis indicates that RECORD / MD-1 tend to overpredict the reactivity of plutonium lattices, in the order of 700 pcm, compared with clean UO2 Lattices. Including corrections for reactivity

l 10-5 effects of lattice grid plates, Pu02 particle size and more detailed leak-age calculations wiLL reduce the apparent o'verprediction considerably.

10.2 Fuel Depletion Isotopic Analysis Comparisons RECORD calculated uranium and plutonium isotopics as function of fuel burnup have been compared to the isotopic measurements made during different phases of the Yankee-Rowe Core Evaluation Program (Refs. 61, 62). The experimental data represent detailed isotopics of fuel rods in perturbed, intermediate and asymptotic reactor neutron spectra, measured over a broad range of fuel burnups up to approximately 31 000 MWD /TU.

The analysis of the data was made with RECORD for a single pin in an asymp-totic spectrum. The calculated plutonium-to-uranium mass ratio, and isoto-pic concentrations for U235, U236, U238, Pu239, Pu240, Pu241, and Pu242, in comparison with the experimental data, are shown in Figures 10.2.1 through 10.2.8.

The agreement between RECORD-calculated isotopic concentrations and meas-0 sured data is generally quite good, except for Pu which tends to be underestimated at higher burnups. There is also a tendency for overpredic-tion of Pu 29 isotopics at burnups greater than about 25 000 MWD /TU.

The general good agreements constitute an integral verification of the basic l

unit cell model in RECORD under hot operating conditions. In addition, the results verify the adequacy of the Nuclear Data Library and the treatment for temperature-dependence of cross-st;tions and resonance integrals, as well as verifying the burnup calculation method.

10.3 Gamma-Scan Comparisons of BWR Assembly Pin-Power Distributions l

! The local power distribution within the fuel assembly, as generated by RECORD, was compared with the experimental data from the 1976 Quad Cities-1 gamma scan measurements (Ref. 63). In those experiments, five fuel assemb-Lies were removed from the reactor at the end of Cycle 2, disassembled and 140 pinwise gamma-scanned for the La isotope intensity. Before the shutdown,

10-6 the reactor had been operated with all control rods out for a period of 1-1/2 months, and with a total core power-level change of only 12% during I the same period (Ref. 64). The measured isotope distribution is therefore proportional to the power distribution over the assembly at noncontrolled, rated conditions. Since the gamma scans were taken at several axial eleva-tions, a wide range of exposure and void levels were covered. The quoted accuracy in the reported rod-to-rod La140 intensities is approximately 3%.

Out of the five measured assemblies, two were of the mixed oxide (MO ) type 2

and three of standard UO2design. The three UO 2-bundles were selected for the RECORD benchmark analysis and have the characteristics given in Table 10.3.1. (The M02 -bundles were excluded f rom this analysis due to lack of data on isotopic content.) A detailed description of the fuel design is found in Reference 64. Each fuel bundle was measured at eight axial eleva-tions (15, 21, 51, 56, 87, 93,123 and 129 inches above the bottom of the active fuel). Data at the pair-wise close positions were merged together in order to reduce the experimental uncertainty, and the RECORD data analysis was therefore done at four axial levels. The nodat distributions of exposure and exposure-weighted void of Quad Cities-2 had been generated in a core-follow analysis, using the 3-D BWR simulator CORE, and were obtained from Reference 65.

The RECORD data were generated in depletion calculations performed at three different void levels: 0, 40 and 70% void. The actual, local power distri-butions used in the benchmarking, were derived by interpolation between the void levels, as weLL as the discrete burnup points in the depletion calcu-Lation.

Figures 10.3.1 through 10.3.6 compare the calculated and measured local power distributions. The main results, represented by the root-mean-square (RMS) power differences, are listed in Table 10.3.2. The total RMS differ-ence of 540 pins is 3.1%, which is in the same order of magnitude as the measurement uncertainty.

1

10-7 The RECORD calculations were performed with reflective boundary conditions, and assuming diagonal symmetry within the assembly, and will therefore not account for possible flux tilts over the fuel bundle. In an attempt to reduce this'inconsistence between measurements and calculations, the experimental data we:re also reflected and averaged with respect to the symmetry line (the diagonal). This resulted in a reduced, total RMS power difference of 2.9%.

The local pin power peaking factor is, in RECORD, overpredicted by an aver-age of 2.4 % + 2.3 %, relative to the gamma scan. All the analyzed cases show conservatism (overprediction) in the calculated peaking factor.

RECORD systematically overpredicts the power somewhat on the boundary along the narrow water gap. It is, however, difficult to draw any definite con-clusions as to the modelling in RECORD based on this observation, because of both the uncertainty in the measurements ( 3%) and the limitations of the

" cell" approach of the RECORD calculations. The cell calculations will neglect effects like:

influence of neighboring assemblies macroscopic flux tilts control rod history nonuniform void distribution within the assembly void variations during burnup influence of detector tubes and sources.

These effects wiLL mostly influence the peripheral row of pins; e.g., the presence of a detector tube will reduce the power in the narrow-narrow corner pin by approximately 2%. (Of the analyzed fuel bundles, CX-214 is located next to a detector string and GEH-002 next to a source.)

The power in the gadolinia-bearing fuel rods is predicted with an c.ccuracy consistent with the other rods.

l

10-8 10.4 Historical Review of LWR Analysis with RECORD - PRESTO e

Th,e core simulator PRESTO, with nuclear data from RECORD, has been applied in core-follow calculations and other applications for LWRs, yhere a sys-tematic comparison with operating data has been possible. Feedback from these applications has played an important role in the evaluation and tur-ther' development of RECORD over the past ten years. Substantial parts of the basic methodology employed in RECORD was evaluated in a core-follow study for the Dodewaard BWR in 1971.(Ref. 66). Following the completion of the I

first version of RECORD in 1972 (Ref.1), ScP has systematically tested the RECORD,- PRESTO system in the analysis of more than 20 BWR and PWR operating cycles-. A summary of this experience is reported _in Reference 4. Core-follow analyses with RECORD . PRESTO on M0hleberg (BWR), Quad Cities (BWR), and

'ne Yankee (PWR). reactors, are described in References 67 and 68.

1 Table 10.4.1.gives.an overview of the reactors and operating cycles which i have'provided the. main' basis for evaluations of RECORD - PRESTO by ScP's own staff.-The average kef t ano its standard deviation at critical states through each cycle, are also given. In addition, the Users of FMS have independently conducted their own qualification of the programs (Refs. 69 and70$.

The procedures used for the aralyses of gadolinium poisoned fuel were first tested against critical measurements in Dodewaard (Ref. 16) and, later, against gamma scan results from MUhleberg. Figure 10.4.1 shows the results of the analysis on the Dodewaard gadolinium-contain5rg assembly at the cold, initial state. Results from comparisori with proprietry data on low burnup gadolinium fuel is shown in Figure 10.4.2.

These gamma scan results from KKM were particularly important, as they con-firmed the ability of the model to properly predict the burnup of the gado-linium pins. This assembly was located close to'the core boun'dary, such that there was considerable flux-tilting across the assembly. This does not measurably affect the comparison of peaking factors in the. gadolinium pins relative to its neighbors, b'o wever.

I l

TABLE 10.1.1 WESTINGHOUSE UO2 Critical Lattices LAME WH CATALOG U 235 HO/2 BUCKLING (m-2) CORE .

RADIUS k'

ENRICHMENT SQUARE OR NO. HEXAGONAL TOTAL AXIAL (cm) RECORD & MD-1 (wt%)

W1 2.70 1.029 SQ. 1.049 40.7 1 0.4 5.4 32.01 0.9966 W2 1.062 "

1.200 47.1 1 0.3 12.4 32.79 0.9990 W3 1.105 "

1.405 53.2 0.7 5.4 26.82 0.9974 W4 1.194 "

1.853 63.3 0.4 5.4 24.27 0.9974 W5 1.252 "

2.164 68.8 i 0.5 10.96 25.12 0.9995 W6 1.455 .

3.369 65.64 2 0.6 5.53 23.60 0.9949 W7 1.562 "

4.077 60.07 0.8 5.48 24.77 0.9931 W8 1.689 "

4.983 52.92 1 0.5 5.41 27.17 0.9905 W9 1.311 1.558 HEX. 1.430 32.59 0.15 5.24 38.13 1.0045 W10 1.652 "

1.762 35.47 0.18 5.29 36.34 1.0039 o W11 1.806 "

2.402 34.22 0.13 5.30 37.63 1.0025 W12 2.205 "

1.073 28.37 0.06 5.05 41.24 1.0040 W13 2.359 "

1.405 30.17 0.06 5.13 39.69 1.0037 W14 2.512 "

1.758 29.06 0.07 5.20 41.44 1.0021 W15 1.558 "

1.393 25.28 1 0.10 5.11 45.14 1.0016 W16 1.652 "

1.735 25.21 1 0.10 5.24 45.77 1.0008 W17 3.70 1.062 SQ 1.225 68.30 0.3 18.6 26.36 1.0027 W18 1.252 "

2.210 95.10 0.7 8.86 19.01 0.9997 1

4 1

TABLE 10.1.2 B&W and NORA UO2 Critical Lattices U 235 LATTICE BUCKLING (m-*) CORE CATALOG ENRICHMENT PITCH H20/ FUEL RADIUS eff

, NO. (wt%) SQ. (cm) TOTAL AXIAL (cm) RECORD & MD-1 i

! BW5 4.02 1.511 1.136 88.0 3.60 18.75 0.9977 BW13 4.02 1.450 0.955 79.0 3.95 20.18 0.9953 BW16 2.46 1.511 1.370 70.1 4.07 20.82 1.0042 BW27 4.02 1.511 1.139 87.1 -14.58 16.36 0.9988 g, o

NH18 3.41 2.687 4.505 86.4 1.0 22.12 23.49 0.9999 ,

NH19 2.314 3.032 98.8 1.2 21.22 20.56 1.0072 ,

4 '

NH2O 1.900 1.655 91.8 i 1.7 20.08 21.01 1.0068 1

i ScP Form B;i-:!6a

TABLE 10.1.3 BNWL UO 2 -2 wt% Pu02 Critical Lattices CATALOG NO. PU ENRICHMENT

"

• k LT E H20/ FUEL R US g 2 s. o BNWL- wt% Pu02  % Pu PITCH (cm) TOTAL AXIAL (cm) RECORD & MD-1 2.1 2.0 8 2.032 1.515 93.7 8.86 19.08 1.0084 2.2 2.362 2.489 103.3 8.70 17.20 1.0141 2.3 2.667 3.515 101.3 8.65 17.27 1.0090 2.4 2.903 4.397 97.0 8.84 18.51 1.0126 2.5 3.353 6.282 75.6 8.89 22.48 1.0079 2.6 "

3.520 7.054 68.9 9.10 24.76 1.0028 2.7 2.0 16 2.362 2.489 86.3 8.60 19.44 1.0135 2.8 2.667 3.515 85.4 8.58 19.52 1.0096 2.9 "

2.903 4.397 81.5 8.77 20.87 1.0092 y 2.10 3.353 6.282 61.6 8.89 26.17 1.0045 0 2.11 3.520 7.054 55.6 9.28 29.49 0.9987 2.12 2.0 24 2.032 1.515 63.1 8.48 24.32 1.0007 2.13 " "

2.362 2.488 79.4 8.67 20.98 1.0053 2.14 2.667 3.515 77.6 8.71 21.38 1.0060 2.15 "

2.903 4.397 72.2 8.88 23.22 1.0075 2.16 "

3.353 6.282 53.7 9.30 30.30 1.0014 2.17 " "

3.520 7.054 44.3 9.43 35.33 0.9979

TABLE 10.1.4 BNWL UO 2 -4 & 1.5 wt% Pu02 Critical Lattices CATALOG NO. PU ENRICHMENT

" "

• k L E H20/ FUEL R US ef, 28.o BNWL- wt% Pu02  % Pu PITCH (cm) TOTAL AXIAL (cm) RECORD & MD-1 4.1 4.0 18 2.159 1.929 94.7 8.59 18.02 1.0019 4.2 "

2.362 2.563 107.9 8.70 16.59 1.0029 4.3 "

2.667 3.622 108.7 8.70 16.50 1.0139 4.4 2.903 4.531 107.9 8.78 16.86 1.0130 4.5 3.520 7.268 88.4 9.06 20.55 1.0135 4.6 4.064 10.115 59.5 9.48 28.70 1.0066 4.7 "

4.318 11.585 41.1 9.46 37.38 1.0019 1.1 1.5 8 1.397 1.099 48.0 5.04 28.28 1.0112 1.2 "

1.524 1.557 65.1 5.10 23.04 1.0006 1.3 1.803 2.705 78.5 5.20 20.83 1.0102 h

1.4 2.032 3.788 74.9 5.26 21.86 1.0072 U 1.5 2.286 5.143 60.9 5.28 25.52 1.0063 1.6 2.362 5.580 55.2 5.30 27.40 1.0070 l

l

10-13 TABLE 10.1.5 RECORD /MD-1 Calculated k,ff-Values for UO2/Pu02 Lattices I  % Pu02  % Pu 24o LA TI S eff l

l 2 8 6 1.0091 0.0040 16 5 1.0071 0.0057 24 6 1.0031 0.0037 l 4 18 7 1.0077 0.0057 1.5 8 6 1.0086 0.0020 Mean k,ff for 30 lattices : 1.0071 1 0.0046 i

s

10-14 TABLE 10.3.1 Characteristics of the Gamma Scanned Fuel Bundles in Quad Cities-1 CORE AVERAGE IDENTIFICATION LOCATION FUEL DESIGN EXPOSURE GEH-002 13 - 36 8 x 8 Reload , 2.50% 8 933 MWD /TU CX-672 15 - 36 7 x 7 Initial, 2.12% 17 150 MWD /TU CX-214 33 - 34 7 x 7 Initial, 2.12% 17 328 MWD /TU GADOLINIUM LOADING IDENTIFICATION NO. INITIAL Gd230 LATTICE POSITIONS GEH-002 4 1.5 % C3, G3, C7, G7 CX-672 2 3.0 % F4, D6 CX-214 2 3.0 % F4, 06 1 0.5 % C3 i

TABLE 10.3.2 Summary of Comparison Between RECORD and Fuel Bundle Gamma Scan Data in Quad Cities-1 AXIAL GEH-002 CX-672 CX-214 ELEVATION (Inches EXP.W. RMS EXP.W. RMS EXP.W. RMS from EXPOSURE VOID DIFF. EXPOSURE VOID DIFF. EXPOSURE VOID DIFF.

Bottom) (MWD /TU) (%) (%) (MWD /TU) (%) (%) (MWD /TU) (%) (%)

i 18 10.948 11.1 1.8 16.885 4.4 4.2 17.207 6.1 3.1 53.5 10.231 45.2 2.1 20.592 34.5 3.9 20.636 36.0 2.9 90 9.548 61.6 2.6 19.530 54~.0 3.8 19.753 54.5 3.1 1

126 6.798 69.9 2.2 14.584 ,

63.5 3.4 14.203 63.8 2.9 1

TOTAL 2.2 3.8 3.0 i$

i 10-16 TABLE 10.4.1 Overview of the Main Reactor Cycles Used for Evaluat;on of RECORD - PRESTO by ScP REACTOR CYCLE TYPE AN Y S ^ ^

eff REFERENCE MOHLEBERG (KKM) 1 BWR 1974 1.0097 1 0.0025 (67) 2 1975 1.0011

• 0.024 "

3 1977 1.0062 0.0014 -

QUAD CITIES "

1 1976 0.9947 0.0034 (68) 2 1976 0.9901 1 0.0020 "

SANTA MARIA de GARONA "

(NUCLENOR) 7 1978 1.0015 1 0.0010 -

BPUNSBOTTEL (KKB) 1A 1979 0.9992 0.0033 -

1B 1982 1.0035 i .0012 HATCH 1 1982 0.9972 0.0025 (3)

MAINE YANKEE 1 PWR 1976 .9848 .0029 (68) 1A 1976 .9919 .0015 "

BEAVER VALLEY "

1 1980 0.9951 t 0.0020 -

Mcff An lysis of critical UO, lattices with RECORD (Version 81-4 ) and MD1 codes Mean K,gg value for 25 tattices: 1.0001 2 0.0042 0 Westinghouse tottices 1.010 -

A B & W tuttices a o o NORA lattices 1.005 -

O ao 0 o

U O

, o o

7.000 -

go a y A0 4 A o o o

A o

.995 -

o

. . I . . . . . . . i . . . I . , , . C

'99 i i i i 2.0 2.0 3.0 4.0 5.0 H OIFUEL FIGURE 10.1.1 Calculated k gf -values for Critical UO2 Lattices at 20 OC

10-18 1.02 2 wt % Puo2, 8% Pu240 Analysis of ENWL crgtical UO 2-Puo2

, lattices at 22 - 25 C.

/ /

~

g' s -+- Restalts fa RECORD (Version 81-4) 9 s and MD1 codes.

-C--- Result frcm IBM. analysis (1972):

H2O/ FUEL Codes HIC 3, BRT-I and HEN.

I 2 3 p 4, f 5 ~ ~ ~ ~6% 12 7 Mean k df value for 30 lattices:

./ \ s RECCRD + MDl: 1.0071 0.0046 g' 's / ENHL analysis: 0.9985 0.0036 0.9e -

(No h actions fer reactivity effect of particulate fuel, or lattice grid plates) 1.02 -

2 wt % PuO2 .16 % Pu240 2 wt % PuO2, 24 % Pu 240 1.01 -

5, 1.01 -

N .o A s Y1

/

's s I

2 H20/ FUEL 3

4 ,7 T -' W

. \.s ,,,,

1

/

2 2

d . H 0/ FUEL.n 3 4 T

-J g N% ,

, u e I

y' N

/* 99 -

0.99 -

1.02 1.02 -

4 wt % PuO2 ,18 % Pu240 1.5wt% PuO ,18% Pu240 Kn e K et p .o_ _ _ - --g

/ 's IA 1.01 = / 's 1.01 t-I s

/ Y J$

/

P.,C

• • • ,,,*,4 __ ~~ .. Q Q

(f f H20/ FUEL g H20/ FUEL too y' ' s' s' a' s' ' 1.00 '

2 4 7 to 11 12 1 62 43, 4 s' p s' cg ,I ~**A

~~g 0.99 -

0.99 -

l FIGURE 10.1.2 Calculated K,ff-values for Critical UO2 - Pu02 Lattices

10-19 t5 9

o O

t 10 - C

?

9 _

9

<t x

<r I _

o w

o a- 0.5 -

Measured e Phase 1 a Phase 2 > asymptotic o Phase 3 spectrum RECORD unit cell calculation r 0.0 e i i i i i 30000 O 10000 20000 BURNUP (MWD /TU) i l

FIGURE 10.2.1 Plutonium-to-Uranium Mass Ratio vs. Burnup, Maine Yankee, Core 1 I

l

4 o Measured, phase 1, 2 & 3 Asymptotic spectrum 9

Q 3 - O RECORD unit cell calculation x

9 2 O O

4 2

"3 a 2  ?

5 2 - E

~_

b s

R "3

O j l l l l l l I O 10000 20000 30000 BURNUP (MWD /TU)

FIGUkE 10.2.2 U 23s ccncentrations vs. Burnup, Maine Yankee, Core 1

6 a

o 5 --

9 co y o8 2 4 -

9 s o '

O E 3 -

5 o J  ?

< o O N p

~

2 -

o Z-o y o Measured, phase 1, 2 & 3 O o g

1 -

Asymptotic spectrum o

RECORD unit cell calculation 0 I ' I ' ' I I O 10000 20000 30000 BURNUP (MWD /TU)

FIGURE 10.2.3 U 23s concentrations vs. Burnup, Maine Yankee, Core 1

10-22 LOO i

l O 0.99 -

E a:

52 2

O

= 0.98 -

~

U O

.J t- o Measured, phase 1,2 & 3 z

Asymptotic spectrum 2 0.97 -

RECORD unit cell calculation 0 l I I I I I I O 10000 20000 30000 BURNUP (MWDITU)

FIGURE 10.2.4 U23e Concentrations vs. Burnup, Maine Yankee, Core 1 w

10-23 9 -

8 -

7 o O O e

7 -

b E

0: 6 -

9 I

o q 5 -

0 "o 4 -

o Phase 1 measured h

a Phase 2p asymptotic 3 -

3 0 o Phase 3 spectrum

2 o

RECORD unit cell calculation n.

I -

0 I ' ' ' ' ' '

O 10000 20000 30000 BURNUP (MWD!TU)

FIGURE 10.2.5 Pu 239 Concentrations vs. Burnup, Maine Yankee, Core 1

10-24 10 -2 _

_ wxf o

10-8 G< _-

a: _

~

U 5

O -

y _ a O

a

.a S

t-z-- jo-' _

a "a -

4, 6 Phase 1 measured o.

o Phase 2> osymptotic 0 Phase 3 spectrum RECORD unit cell calculation gg-5 l l l l l l l 0 10000 20000 30000 e

BURNUP (MWD /TU) 240 FIGURE 10.2.6 Pu Concentrations vs. Burnup, Maine Yankee, Core 1

10-25

-2 10 o

9 r

168 -

0: -

o_

1 -

S -

A E

D _

_a 5

~_

[- 10' ' -

"o 1

- k a Phase l' measured

_ o Phase 2y asymptotic

- I o Phase 3 spectrum

> RECORD unit cell calculation 5

16 l I I i l i I 0 10000 20000 30000 l

BURNUP (MWD /TU)

FIGURE 10.2.7 Pu 2

.1 Concentrations vs. Burnup, Maine Yankee, Core 1

10-26 10 _

i

)

10~' =

O_ _

w x

o_

2 O

Q 10 --

2 -

c -

.a 2 -

t- -

z_

[ g a Phase l' measured

~

o 10-' - a Phase 2 > osymptotic 1 =A O spectrum Phase 3

- 6 .

t RECORD unit cell calculation

]

l 10-7 I I i i i i i j 0 10000 20000 30000 BURNUP (MWD /TU) 242 Concentrations vs. Burnup, Maine Yankee, Core 1 FIGURE 10.2.8 Pu l

l

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3 seas.3 asse. Laist gattnggyy 3 3,ggg 3 g,g;3 g ,ggg 3 ,ggs 3 ,g;g g ,g;g 3 ,957 g g,gey 3 3 64ff.8 s tatt. etal. I 1.C36 1 8.634 1 967 1 516 I 93s I 537 1 .945 2 1.061 3 4 3 3 1 1 1 1 1 1 3 1 .LLL 1 ..C11 1 .C*6 1 .CLL E .C11 1 0L1 3 .CCi 8 .CCL i abiaa61 of 55 aces . 1.C .........................-............ ...-......................

6pt #6.sh $3fftsantt : 1.4 1 1 1.LLt 1 1.L12 1 .531 1 .521 I b 6 h ! .53C 1 947 1 S.C54 3 1 1.031 1 1.L36 1 .537 1 .545 1

• h a 3 .934 1 .946 3 1.C53 3 51 2 3 1 1 3 1 1 1 1 .L24 1 ..G24 1 .CCe i .. Lie 3 h h 6 1 .CC4 3 .C03 8 .CC3 1 1 aab 1 1.s29 1 .541 1 .526 1 .930 1 .934 1 9ea 3 saa1 3asa1 1.L43 1 .55F 3 92* I .529 1 .922 1 .9551 a a a 1 e1 1 1 1 2 3 1 1 2 3 a a a 1 .C14 1 .CC9 1 .CCL I .CC1 1 .C12 3 .CC9 3aaa3 1 1.052 1 1.078 1 557 3 .557 1 547 1 .964 3 1.C12 1 1.114 3 1 1.051 1 1.G 4 5 1 557 3 .955 1 .529 3 .94C 2 .989 1 1.C95 1 71 1 2 3 1 2 3 3 3 3 .CCC 1 .CCF 1 .CCC 3 .CC2 3 . tit 3 .C24 3 C23 1 .C23 3 3 1.047 1 1.C12 1 a a a 1 1.067 1 1.C56 1 a a a 1 1.114 1 1.031 3 2 1.035 I .996 3 33 I I 1.C35 1 1.004 1aa3 1 1.080 3 .962 1 8 I 1 1 1 1 1 3 1 I 1 .C12 1 .014 1 aaa1 .C28 1 . Cat I aaa3 .038 1 .C69 3 a 6 C e E f G h tune (31315 1 ECC; aggt --........---------... .....-..----.-----....---.- .. ------

6tatsmaat 6aara Stah biet 1 1.CF3 3 1.Ct3 3 a a 3 3 1.C47 1 1.C35 3 a a a 3 1.C&3 3 1.C93 3 Ear 3 1.041 3 1.066 I E 3 a 3 1.C5 5 1 1.C57 1 3 a a 1 1.C10 3 1.094 1 sitG36 at &WL15 (thf aae t 61th 1 3 1 8 3 3 3 2 3 3 Kaastatatais 3 012 3 .017 3 3 I a 3 .CC8 I .C22 1 aaa! .CO3 1 .001 3 a6 tall Stalat numhts Eth-CO2 3 1.C13 1 1.015 1 1. Cal 2 1.C29 1 1.012 1 1.02 8 1 1.079 3 1.C30 I ama af act PLahas La14C 3151alsut1th 1 1.CFL I 1.C10 3 8.1C2 3 1.C44 3 1.029 3 1.06C 3 1.C89 1 1.008 I 53.5 Intut1 Atent 6CT10m Cf tbtL 23 1 1 1 1 3 I I 1 3 .013 I .0C5 1 .[21 1 .C15 1 .017 3 .C32 1 .010 3 .022 1 3 a a a 3 1.081 1 .557 1 .932 1 916 I .932 I .997 3 a a 3 3 at6ther 1aaaI 1.035 1 1.01C 3 .966 1 .921 1 .942 3 989 1 a a 3 1 31 3 3 3 1 2 3 3 1 1 x* a a 1 .CC4 1 .C13 1 .034 3 .C05 3 .010 3 .CCa 3 a a a 1 3 tatt.1 hCap. PCete tatt 61 atteaD 1 mial.! I hCam. La140 Ibith53TT I 1.047 1 1.L29 3 .532 3 .9C2 I .898 I .9C3 I 931 1 1.052 1 3 altf.1 : CALC. - Pla5.

I 1.C52 3 1.035 1 .542 1 .917 1 .933 1 .911 3 933 1 1.C13 3 4 1 2 3 3 3 1 1 1 I 1 .CCS 1 .CC6 1 .C1c 1 .C15 3 .C35 3 .CCr 1 .CC2 3 .C31 1 atteast of 55 acal . 1.0 - - - . . . . . - - - . . . . . - . . . . . . . . . . - . -----------.---.-- - ----

an1 Po.te 33ffisahti 2.1 1 1.025 1 1.012 1 .916 1 .458 3 b b b 3 .699 1 915 3 1.035 2 1 1.C37 1 1.012 1 .516 1 .534 1 h h h 1 931 1 920 1 1.C52 1 53 1 1 1 2 3 1 3 1 3 .CC2 3 .CCO 1 .CCC 1 .C34 3 6 == 1 .C32 .0C5. 1 .017 3 33aaI 1.024 1 .532 3 .9C3 3 .595 1 .9C3 3 935 3 a a 31 1 3 a a 1 1.030 3 .535 3 .a 94 2 .912 I .654 3 .930 8 a a a 1 e1 3 1 I I 3 3 1 1 1 a a 3 1

.CC2 1 .CC7 I .CC7 3 .C13 I .CCS I .001 3saaI 1 1.C83 1 1.079 I .557 2 931 3 915 3 .931 1 .997 I 1.099 3 1 1.072 3 1.079 1 572 3 933 I 9L4 3 .915 3 .949 1 1.098 1 73 3 3 3 3 3 3 3 3 3 .611 1 CCD 1 .C25 3 .002 3 .009 3 .014 1 .044 1 '.C01 1 1 1.054 1 1.C30 3 a a a 3 1.C52 3 1.035 1 a a a 1 1.099 1 1.C36 1 1 1.075 3 .983 1 3 a I 31.0271 .999 3 3E R 3 1.051 1 .946 2 5 1 1 1 2 3 3 3 1 3 3 .019 1 .047 1 : : : 3 .025 3 .03s 3 a a a 3 .04: I .C50 1 FIGURE 10.3.1 RECORD Results Compared with Quad Cities Gamma Scan, Fuel Bundle GEH-002

l 10-28 l l

6 6 1 e t 0 & D 4.as (19861 1 ttti e8tt .............................. .................................

6aat** ass taena Stan .364 I t.117 3 1.115 3 aa3 3 1.t t e 3 1.C6% 3 aa3 1 1.cet 3 1.116 3 6aP 3 t. Lie 3 9.100 1 a a a I 1.t t t 3 1.C46 3 aaa3 1.1C7 I 1.11C 3 6 sites et1LL1h (Safangs esta 13 3 3 3 3 3 3 3 3 Paabatt*tath 3 .b43 3 015 8 aB a 3 .C24 3 .C11 1 a a s 3 .C09 3 .CC9 1 bumett Sla3at hun ts ste.CC2 1 1.115 3 1.033 I t.C91 3 1.C 33 1 1.C11 3 S.C2P 3 1.CF9 3 S.C37 4 e66 67 aos Ptamaa tat 4C elsteleUf 30h 8 1.C57 8 1.021 3 1.12b 1 1.C68 8 1.C41 3 1.053 3 1.C86 I t.C2e !

SC.0 2ntats a60Wt tettom Of fust 21 3 8 3 3 3 3 3 3 3 . CSS 8 .012 3 .C29 3 .035 5 .C34 3 .026 8 .007 1 .011 I Ia3 a1 1.099 8 1.Cl4 1 92F I .9CS I .922 3 1.C03 3 a a a 3 at6thet I a a a 3 1.1CC I 5.Ctc ! 9ec 1 .934 3 937 5 .986 3aaa1 38 1 1 3 I 3 3 3 I 1 a a a 3 .CC9 3 .CC4 3 .C33 3 .C25 3 .C15 8 .C17 I a a a 3 8 Catt.1 3 bC6P. PCete CALC 31 etCC66 ..--...........-......... .......- .---......- ---.=......... .

3 ma a t.1 hisp. La140 thith13ft i 1.064 8 1.033 3 927 I . tic I .247 3 .451 3 916 8 t.C4C 1 3 elff.I : te6t. - plan. I 1.CF4 1 t.C58 3 .545 1 543 1 .917 3 .984 8 .934 8 1.Cet 3 4 1 2 3 3 8 I 1 1 3 5 ..Ctc I .021 3 .Cle 3 .017 3 .C3C 3 .C23 3 .022 8 .C21 I avseast cf 55 eCas e s.C --................-........................-...................-.

tes P6.tesafftsants s 2.6 1 1 1.04% ! 1.012 3 .SC9 3 .487 8 b b = I .413 8 .497 1 1.C2C 3 1 S.C49 I t.CCF I .916 3 .941 1 b bb 3 .9CS 3 914 I S.C16 3 53 1 2 3 3 3 3 1 3 3 .CCC 5 .DC5 1 .CC5 1 .C24 3 mb w 3 .C22 1 .01F 1 .CC4 3

.-......= == =-

3 a a a 3 1.C28 3 .922 3 .elt t .843 3 .447 3 919 3 a a a 3 Aaaa3 1.047 3 .537 3 .909 3 .912 3 .475 1 .910 3 a a a A e1 2 3 3 3 3 3 3 3 3 a a a 3 .019 3. .C15 3 .010 3 .029 & .C12 1 .001 3aaa3 1 1.C96 1 1.C79 3 1.CC3 3 .914 3 .99F 1 .941 3 .992 3 1.C84 3 3 1.052 3 1.C78 1 .9 64 3 .9CS 1 . 864 3 .s99 I 922 3 1.041 3 73 3 3 1 2 3 3 3 3 3 .004 3 .004 3 .C3F 3 .011 3 .C13 I .C12 3 _

.070 8 .043 3 3 1.119 3 1.037 3 a a a 3 1.C40 3 1.C20 3 a a a 3 1.084 1 1.C34 3 3 1.091 1 1.001 3 I a a 3 1.029 3 1.001 3 a a a 3 1.034 3 .954 3 83 1 1 2 3 3 3 3 3 3 .028 3 .036 3aaa3 .011 3 .019 3 aaa1 .047 3 .078 I a e C 8 C t G M

& bat CIT 3ES-1 80C2 mist - -.. . - - - - - - . - - - - - - - . - - - . - - -------. ==------

stat > mass 6Appa Stah wist 1 1.137 3 1.lJ9 3 a a a 3 1.CF3 3 1.054 3 a a a 3 1.109 8 1.132 3 ser 1 1.104 3 1.120 3 a a a 1 1. Cat I 1.054 1 a a a 3 1.121 3 1.103 3 etCose etSUL18 CCmPAsta htta 13 8 1 1 2 3 1 2 3 atAttatatuts 3 .033 3 .019 3 a a a 3 .CIS 3 .CC4 1 a a a 1 .012 3 .C28 I 6LheLE Statat husets ssp.CC2 31.13911.0483 1.1C5 3 1.C39 1 1.C15 3 1.C3C 3 1.086 3 1.037 3 act by see rtahes LAS4C Distalauf geh 3 1.133 3 1.045 3 1.125 3 1.054 3 1.C37 3 1.C37 3 1.116 1 1.022 3 lie.C thtut$ Abett SCTICR CF Fb1L 23 3 3 3 3 1 3 3 1 3 .CCe 3 .0C2 3 .C20 3 .019 1 .C22 1 .CC7 3 .030 1 .C15 3 3 a a a 3 1.1Ce 3 1.036 3 .922 3 .901 1 914 3 1.Ctf 3 a a a 1 LLCthes 3 a a a 3 1.122 3 .999 3 .943 1 .9C6 1 922 3 .980 3 a a a 3 33 1 2 3 3 3 3 3 3 1 a a a 3 .017 3 .C37 1 .021 2 .007 3 .008 3 .037 3 a a a 3 8 CALC.3 3 hCeP. PCWER CALC Of SECCe8 ---.. -----==

1 alas.! 4 acer. Lat40 3mTEh5I17 3 1.C73 3 1.039 3 .922 3 .888 1 .276 3 840 3 9 04 3 1.C33 3 3 8188.3 : Catt. - ptA1. 1 1.C43 3 1.053 1 .941 3 .9C3 1 .t98 3 .stC 1 924 3 1.044 3

---

**-* 4 3 3 3 1 3 1 2 3 3 I .CIC 8 a.C14 1 .C19 3 .015 3 .C22 1 .C1C 3 .021 1 .C11 1 AttaAGE 08 55 eCBS = 1.0 .. ---------. ----.-------.- - -

6al Posta elf fissett 2.2 & 3 1.C54 3 1.015 3 9C1 3 .874 I b 6 b 3 .549 3 .882 3 1.CC9 3 3 1.C58 3 1.C21 1 .Sta 1 .896 3b bk 1 .sto 3 . ass 1 1.CCA 1 53 3 1 3 3 3 3 1 1 2 .004 1 .0C6 I .CC7 1 .r?C 3 h bb I .017 3 .CC4 3 .001 3

.--.. =-...-.. =...-..=== ==

1 a a a 1 1.030 3* .914 3 88C 1 .669 3 .472 3 .895 1 aa3 3 a a a 4 1.052 3 .929 3 .683 3 . 294 3 .454 3 .095 3 a a a 3 4 3 3 3 3 3 3 4 3 3 3 a a a 3 .022 3 . CSS I .CC3 3 .G25 1 .016 1 .000 3 a a a 3 1 1.1C9 1 1.08e 3 1.Cl? 3 .9C4 3 .682 3 .455 3 996 3 1.074 I I 1.1C9 1 1.098 3 949 3 912 3 . 8 64 I .845 3 .927 3 1.C44 3 73 1 3 1 2 3 3 3 3 3 .0LC 5 a.C12 3 '.048 1 .CC4 3 .002 3 .01C 1 .069 3 .C30 3 3 1.132 3 1.C38 3 a a a 3 1.C33 3 1.009 3 a a 3 1 1.074 3 1.C231 3 1.123 3 1.023 3 a a a I 1.C64 1 1.010 3 3 a a 3 1.039 1 .9FF 3

&1 2 3 3 3 3 3 3 1 3 .C09 : .014 3 m a s : .Cis 3 .00 Iaaa3 .039 3 .046 2 Figure 10.3.2 RECORD Results Compared with Quad Cities Gamma Scan, Fuel Bundle GEH-002

10-29 a g E g g f &

.we6 tatatt.) Ltt; oggt . . . . . . . . . . - - . . . . . . . . . . . . . . . . . . . - . . . . . . . . . . . . . . - - - . . . . . -

temerassa 6ames Stat bitt 1 1.LC1 1 .939 3 3 3 8 1 547 3 a a a 3 1.LC4 3 9th 8 I haf 1 1.L31 1 .942 1 a a a 1 S.CC3 3 3 aa3 1.Get 8 933 3 tate 6h al5Wtib (CafAtts b11m II I 1 8 1 2 3 3 '

eaAss.aaahts 3 .C31 .643 a a a s ..ste 3 a a a 3 . set a .032 1  !

h666LL 41 stat hussia Ca.672 1 .935 1 944 3 .9C4 3 1.C32 3 1.C3a 1 1.063 3 943 1 6te at &&D PLehaa ta14C sistaloufach  ! .963 3 .993 3 .9C5 8 1.C75 8 1.ct3 3 1.043 3 999 8 14.U 1Dlatl A40bt 6011GR &f SWEL 23 1 1 3 3 8 3 1 3 .044 1 .C50 3 .CC3 3 a.C43 1 .C27 3 .CIL 1 .CC6 I 33 aa8 .9C4 1 .597 3 .57i 8 .$76 1 1.ble 1 aaaI (8Gan6s 13 3 a1 543 3 1.C44 1 .546 3 963 3 1.023 3 aa3 3

!!  ! 3 3 1 1 3 1 1 a a a 1 ..C35 3 .44% 3 .C17 1 .CC5 1 .0C9 3 A aa3 2 tatt.1 acto. Pcet6 talc tv attsas - - . . . - . . - - - - - - . . . . - . . . . . - . . . . . - . . . . . . . . . . . . - - . . . . . . . -

3 pas..I hete. L814C Intt h& liv 3 5&7 1 1.C32 8 .572 3 aaaI 955 1 1.C11 1 1.075 8 1 63ff.8 tatt. - *(45. I 1.be9 1 1.064 8 545 1sB B 1 972 1 1.L13 I .900 1 41 8 3 1 2 3 1 1 8 .661 3 ..Lia 4 .C17 8 a a a 3 .C17 1 .C12 3 .C35 1 At(.a61 sf og stan a 1.C = = = . - - - . . . . . . . . - - - - . . - . . . - - - . . - . - - - - - - - . . . - - - - - . - . -

sa& tweta s3fftaahts 3 4.151 1 1 a a a 1 1.G36 3 .57e I .935 3 96C 3 .956 4aI a8 1aaa1 1.C9) 1 944 1 .5a4 1 .919 1 1.012 1 a a a 3 51 3 3 1 1 1 3 1 3 a a a 1 .057 1 .(16 3 .Ct3 3 .041 1 .Cta 3 a a a 1 1 1.C10 3 1.Gs3 8 1.Cth 1 1.C11 8 .967 3 1. Cia 1 1.104 8 3 1.C33 1 1.072 1 1.C27 3 .954 I 976 3 1.GC5 3 1.045 3 43 3 3 3 3 1 3 3 1 .C21 3 .CC9 3 .C13 1 .015 3 .C2a 3 .021 3 .059 1 3 565 3 .943 3 a a a 1 1.C75 3 a a a 1 1.1C4 3 1.090 3 1 .911 3 .915 3 a a a 31.089 3 a a a 3 1.015 1 920 3 71 1 1 2 3 1 3 1 3 .054 3 .Ch4 3 a a a 3 . Cat 1 a a a 3 .049 1 .090 3 A 6 't D C E &

tuat (3181S*1 teC2 L3st -- - . ----- ---........-. -----.---4--- --

6 t h C haa tE 6 Apha Scat hast 1 1.C7L 3 .994 3 a a a 3 1.0121 a a a 1 1.0321 1.021 3 6AP 1 1.015 3 .951 3*aa3 .977 3 m a a 3 .994 4 .958 3 otteGe at1WL18 (CasaeE6 mIth 11 2 3 3 3 3 3 3 h&A&betatmTS 3 .055 3 .043'I a a a 3 .C35 3 a a a 3 .034 3 .063 I buhtLE SteIAL hun 6te Ca-672 1 .994 3 .967 3 .926 1 1. Cit 3 1.C21 1 1.046 1 1.001 1 000 ht see Ptahan 6414L 8151816d13Ch 3 .934 1 .958 3 .919 3 1.069 3 1.03t 1 1.040 1 .942 3 53.5 1htMtl Atovt 80Tien et futL 21 3 1 1 3 1 3 1 3 .06G 3 .0C9 3 .CCF 3 .C51 1 .C17 3 .CC6 3' .059 3 3aaa3 .926 1 934 3 .957 3 .961 3 .955 3 h a a 1 Lt&thGs 1aaa3 .917 3 3.C35 3 j.Cjg 3 .999 3 1.C33 3 a a a 1 31 1 1 3 3 1 3 1 3aaa3 .009 3 .C51 3 .053 3 .C34 1 .043 3 a a a 3 3 CALC.1 aean. PChIa (ALC 8Y a&CCEt ... - - - - - - . . . . . - - - . - - - - . - . - - - - -

3 msA&.3 s hCam. LA140 Ihtth1111 3 1.012 1 1.Lt& 1 .957 1 a a a 1 .933 I .925 I 1.056 I 1 4888.1 : (ALC. - mL&5. 3 1.C15 3 1.075 1 .952 1 a a a 3 .577 3 1.C21 1 1.014 1

---

41 1 3 3 3 3 3 I 1 .0L3 I .037 3 .C35 3 a a a 3 .C641 .C36 3 .038 1 Avtea61 Of 40 SCD5 m 1.0 - .. .--..-------.-.---------.-------.. ---

Sh1 Poeta tifftsahtt 3.563 1 3aaa1 1.021 1 961 1 .933 3 936 3 .973 3 a a a 3 3A a a 1 1.037 1 .974 1 .942 3 .923 1 .95C 3 3 a a 3 53 1 1 3 3 1 1 1 1 a a a 1 .044 3 .Ct3 3 .045 1 .004 3 .0t$ 3 a a a 3 3 1.C32 8 1.046 3 .955 3 .985 3 971 3 .959 1 1.C41 2 3 1.004 1 1.084 1 S.C32 3 .954 1 917 3 1.Cl3 3 1.056 3 s1 3 1 2 3 3 8 1 I .G28 I .038 4 .C37 a .C11 1 .C14 3 .C14 1 .025 3 3 1.C21 1 1.GC1 3 a a a 8 1.C5e 3 a a a 3 1.Ct1 3 1.027 1 1 1.004 1 967 3 3 m a 1 1.C131 a a a 3 1.C16 3 1.001 1 73 3 1 3 3 1 3 3 I .C13 3 .034 3 aaa3 .0431 a a a 1 .065 3 .026 I FIGURE 10.3.3 RECORD Results Compared with Quad Cities Gamma Scan, Fuel Bundle CX-672

10-30 a t t 4 4 9 6

.6a8 4413tl.1 ICtt eILL . - - - - - - . . - - . . . . - - - - - - - - - . . . - - - - . . - - - . . . . . . - - - - - - - . . . . . . .

al6.****a Ge**a stam east 1 1.115 3 1.C3L 8 aaa 3 1.t 3 7 3 aaa3 1.C5a 2 1.C54 8 bar 3 1.bts 3 .See 1 aaa3 544 1 aaa3 1.Let 1 996 1 6a466 ettLatn (Catasis talm 13 1 3 3 1 2 3 3 tea &b6tatatt 3 .Cai 3 .C42 8 aaaI . Col 3 saa! .017 8 .058 3 6666&t titlet h6 pets ts-672 3 1.C3L 8 .981 1 936 1 1.C15 1 1.C24 1 1.048 1 1.016 3

&&e 61 606 Ptabas Latet pista8&u11&m 3 1.bC% I 944 3 .917 3 1.Ce7 3 1.057 1 1.017 1 992 3 6C.s lhtet1 abget 601904 Of fu8t 23 1 1 3 8 3 1 1 3 .G21 1 .LC4 3 .C19 8 .04E 1 .037 1 .C21 1 .024 1 2 aaa1 .93e 3 .576 1 942 3 943 3 9 41 1 a a a 3 L&&&hs Ia aa! 936 3 1.C24 1 578 1 977 1 1.C2C 3 & aa1 33 1 8 3 1 1 2 3 3 a a a 1 .000 3 ..CSC 3 .Cil 1 .C34 1 .C35 3 aaa3 1 Catt.1 : mtsp. Ptets tatt at att0s6 - - - - - - . . . . . . . . . . - - - . . . - - - - - . - - - - - . - . . - - . . . . . - - - - - - - .

A plat.8 : ac e s. La14C ghtlh1119 3 1.037 3 1.L19 1 .542 1aaaf 9C$ j .$34 3 1.047 3

, 3 siff.1 : Catt. - plas. I 1.Lis 3 1.052 1 .$73 1 a a a 1 954 1 .944 1 1. Col 1 el 1 2 3 1 1 3 1 aetna&t of et acts e 1.0 a>$ 76 68 eststeamC6 3 3.752 1 1 aaa1 1.02C 1 .543 1 .9CS 1 .9C6 3 5451 a a a 3 3 aaa1 1.Le9 1 .54L 1 .544 1 .45i 3 1.LC1 3 aaa1 51 1 1 3 I I 1 1 1 a a a 3 .049 3 .CC3 3 .041 1 .014 1 .C54 1aaa3 3 1.L5% 1 1.ue9 1 941 1 934 1 945 3 .974 1 1.075 3 1 1. Chi 3 1.C3R 1 .957 2 .974 3 .957 3 954 1 1.076 8 el 1 1 3 8 3 1 2 3 .037 1 .011 3 .Cte 2 .04C 1 .C12 3 .C2C 1 .001 3 1 1.05s 3 1.016 1 a a a 1 1.C47 3 a a a 3 1.075 1 1.038 1 2 .9&e 3 .951 3 a a a a 1.C22 1 a a a 2 1.017 3 1.022 1 23 3 3 1 2 3 3 1 1 .CTC 1 .065 3 m a a 3 .C25 1 a a a 2 .058 1 .016 8

=== -

a a C D 1 f G tune (313ts-1 ECC2 bist -.=--

6thtumasa tappa Sta6 6141 2 1.144 1 1.037 3 a a a 1 1.C1C 1 aaa3 1.075 3 1.058 1 6ar 3 1.053 3 1.013 3 a a a 1 1.CC4 1 a . a 1 1.048 1 1.015 3 etteet atSUL15 (Caraats WITN 11 3 1 3 1 3 1 I phankeththil 3 .L54 3 .024 3 a a a 1 .044 3 a a a 3 .027 3 .043 1 6stett statal 60m6te Ca-672 3 1.C34 5 1.CC2 1 .932 1 1.029 3 1.C27 2 1.044 3 1.019 2 eGe at set Ptamaa ta140 D117altu110h I .973 1 .985 1 .a9 7 1 1.073 1 1.04 6 1 1.044 3 1.009 2 lie.C thCall a6 Cut 801 Tom of futL 23 1 2 3 1 I 3 1 3 .064 3 .016 1 .C35 1 .044 3 .C19 1 .0C2 3 .010 1 _

3aaa! .932 1 .578 3 930 3 929 1 974 3 a a a I LE&thes Iaaa2 .943 3 1.C18 1 .96C 3 944 1 1.016 3 a a a 1 31 1 1 2 3 3 3 1 I a a a 3 .011 1 .C40 1 .C3C 1 .C19 1 .04 4 3 xaa1 3 Catt.1 a hCBP. P0mth CALC Of AICCat ~ ~ - .---.... --. . . . . . - - - . - - - - - - - - . . - - - - - -

3 pial.1 hCap. La140 I=Tths!TV 1 1.050 3 1.C29 3 .930 1 I a a 3 .242 1 .942 1 1.C46 3 1 88Fr.1 : CALC. - psal. 1 1.033 3 1.052 3 .951 2 I aa2 .904 1 .983 3 1.054 3

~~~ 41 1 2 3 1 1 1 2 1 .L17 1 .023 3 .C21 I a a a 3 .022 1 .041 3 .004 3 antaast Of 40 acts a 1.0 - - - - - - - - - - - - - - - - . - . - - - - - - - . . - - - - - - - -

ens Ponta alf risamCE : 3.410 1 3 I a a 1 1.027 3 .529 1 .882 3 481 3 .925 1 a a a 3 1aaa3 1.056 1 .54C 3 9C51 .880 1 .979 1 a a a 3 51 2 3 3 3 1 3 3 3I a a 1 .029 3 .C11 3 .C23 1 .001 1 .054 1 a a a 1 3 1.C7s 1 1.044 3 .976 1 .942 3 925 2 .943 1 1.079 3 I 1.C55 3 1.C74 3 1.C15 3 .962 3 .924 & .9aC 3 1.C91 3 41 2 2 3 1 2 8 8 3 .C20 3 .010 8 .041 3 .02C 1 .CC1 3 .017 3 .912 1 I 1.C5 2 1 1.019 3 m a a 3 1.044 2 I a a 1 1.C79 1 1.012 1 3 996 1 .958 3 a a a 3 1.034 3 m a a 3 1.051 1 1.045 I 71 .1 3 3 1  ; 3 3 1 .062 3 .041 3 m a a : .CCt I a a a 1 .02s 2 .013 3 FIGURE 10.3.4 RECORD Results Compared with Quad Cities Gamma Scan, Fuel Bundle CX-672

10-31

. . C . a e s e6as (81315-1 (C12 stat - . - - - - - - - - - - - - - - - - - - - - - - - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - -

etacosaan Esema Stan eati I t.CC4 1 942 1 aaa2 948 8 8 3 5 1 S.C1C I 968 1 6ap 3 1.e4C 3 .9f3 1 s: a 1 1.C 3 I aaa1 1.Ci3 1 933 I sacasa etsutti CCorsets esta 11 1 3 1 8 1 1 1 maa56 state 15 I .C3e 1 .Cet I a a a 3 . CSS 1 a a a 4 .C13 & .335 3

.westt stegat mus.ta Cs-214 1 942 8 949 I 9tC I 1.C31 1 1.035 8 1.C&2 4 944 1 ace et nos 76anas eatet 0351aleu180m 1 .972 I .991 8 925 8 1. C F C I 1.C56 8 1.051 1 919 1 14.C 1mCutt A6Cvt e01tca et #utt 23 1 1 1 1 3 3 3 1 .03G 1 .C42 1 .CIS I .C39 1 .C19 8 .C11 1 .064 8 3aaa3 910 8 .95e 1 .972 1 .978 3 1.C11 1 I 3s1 Lt6th6: 1saa8 912 1 1.C22 1 .9F4 3 .984 1 1.CCF 4 aaaI

!! 1 1 1 1 3 1 8 I a a a 8 .CC2 1 .C26 1 .CCI 8 .CCF 1 .CC6 8 a8 I I 1 Catt.1 : acar. Pc ta CALC et atCose - - - - - - - - - - - - - - - - - . - . . . - . - - - . . . . . . - - - - - - - . . . . . . - . - - - - - . - - -

1 psal.1 s acep. La140 thT845 tit I .988 1 1.C31 8 .572 1 aas! .954 5 1.C1C 1 1.GF4 1 8 8877.8 : CALC. - atal. I 1.CSC 3 1.C90 t .544 3 aaaI 94C 1 .91C 1 1.C64 1 41 8 1 1 1 1 1 1 1 .C22 1 .059 1 .Cte 1 I I a 1 .CC6 1 .C2C 1 .030 1 aufsatt or 4C acal

• 1.0 - - - - - - - - - - - - - - - - - - - . - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

ens aceta sarttaanCL 3.143 5 1saa1 1.035 1 .57e 1 954 1 560 1 .956 I aaa1 1aaa8 1.JF5 1 .547 1 .934 1 .968 1 .993 1 I I a1 SI 8 1 1 1 1 1 1 I E a a 1 .C40 1 .CC9 1 .C14 1 .C08 1 .CC3 3 a a x

==

1 1.01C 1 1.C42 1 1.C13 2 1.C10 I .996 3 1.C25 1 1.102 1 1 1.036 1 1.045 1 .947 11.0151 942 8 .948 I 1.059 I el 1 1 3 8 1 1 1 1 .026 3 .017 3 .C26 2 .CCS 1 .054 I .057 1 .043 8 3 944 1 .984 1 E E a I 1.0F4 1 I EI 1 1.tC2 1 1.011 3 1 .955 1 966 I a a a 1 1.048 3 I 3E 1 1.079 1 .955 1 71 . I 1 1 1 3 1 1 1 .013 1 .098 1I aa8 .C26 I ssa8 .C23 1 .056 3

. . C . , s 66a8 CIT 8L5-1 80C2 mIDE == ==

6ttChaasa samma SCah etSE 3 1.074 3 994 1 E a 3 3 1.C131 s a a 1 1.C33 2 1.023 3 6AP 1 1.G57 3 .991 1 a a a 3 1.C27 3 a a 3 3 1.026 2 984 5 811848 SE5ULTE Cearente WITA II 3 2 1 3 3 2 8 maalwetateT5 3 .017 3 .005 2 5 3 E 1 .C16 3 a a a 2 .007 1 .039 3 6uh4LL 5tatat turata 43 214 I .996 3 .t47 3 .926 2 1.017 1 1.C20 3 1.045 2 1.002 1 400' et a0D PLAhAB L A14C 915T838 2 .984 I 990 1 .932 2 1.04C 1 1.051 3 1.056 1 .948 3 53.3 1hCNES ASC91 60110R OF ,UTIOh UEL 23 3 1 2 2 3 3 1 3 .012 3 .023 2 .Cte 2 .043 I .C31 2 .011 1 .054 2 2Iaa3 .926 2 1.CCD 2 .954 3 .959 i .993 1 a I I3 Listhes 3maa3 .940 1 1.C21 1 .995 1 .979 1 1.0C71 a a a 3 31 3 3 3 3 3 2 2 233 3 3 .014 3 .C21 3 .039 I .C20 2 .014 I E E E I 3 CatC. 2 hCBa. POWla CALC Of etCOst - - - - - - - - - - ~ ~ - - - - . --- - - - - - - - - - -

2 miA1.1 3 hC5A,. LA140 2Nitk511? 21.01331.0173 .956 3 3 3 a 3 .93C 3 .941 2 1.05% 3 3 sift.1 : CALC. - REA1. 1 1.0C5 3 1.055 2 .983 2 I 3 a ! 951 3 1.CC9 1 1.022 3 41 3 3 1 I 3 1 2 2 .0C4 3 .034 I .C27 .3 a 3 3 1 .C21 1 . Cia 3 .033 I avtaart OF 40 ECD 5 = 1.0 e *----------- - ----< =

ens fC.ta 33 f fitehCE s 2.476 2 2ak51 1.020 I 559 3 .$ 31 I .933 1 .949 3 I I a 1 I a a a 1 1.031 1 140 2 .94C 1 941 1 .954 1aaa1 51 3 3 3 3 1 3 I 2 I R a 3 .011 1 .C21 1 .C5C 1 .CC8 I .D95 3 8 a I I I 1.03 1 1.045 2 .993 3 941 I 969 2 .957 8 1.080 3 8 .956 2 1.G35 2 .989 3 993 3 ,tJ1 1 1.013 8 1.074 3 41 2 3 2 'd & 2 I l 2 .054 3

.014 a .004 a .c1I 1 .011 3 .015 .coe a 1 1.024 3 1.002 3 a a a 3 1.055 3 3 a a 3 1.080 t 1.024 I I 972 1 .9461 a a E 21.057 3 a a a 1 1.V58 4 .953 I 71 2 1. 2 1 1 5 3

.e51 1 .056 2 s a a .oC2 aaa .022 .075 :

FIGURE 10.3.5 RECORD Results Compared with Quad Cities Gamma Scan, Fuel Bundle CX-214 l

l

10-32 l

4 6 ( & 4 8 6 )

6.a8 (81886-3 e sti eget -------------.-....--...-.------..-----------------------

et ht m.ana saeas stem .333 3 1.124 1 S.C31 3 s a a 1 1.C37 3 3 aa8 1. Cit 3 1. Cit ! I

&&P 3 1.124 3 1.C32 3 s a a 1 1.La) I a3 3 1 1.039 3 1.018 I sitoes alSLL11 Ctesset s bata 13 1 3 8 3 1 8 8 paan6etm**f5 3 .00L 3 .CCI 2 s 3 1 .C26 8 ssa3 . tit 3 .C40 8 6.m6Lt Stelat hupst e Cs=284 5 1.C31 3 967 3 .934 3 1.C15 8 1.019 8 1.047 3 1.Cte 3 a6D 61 a G8 P&$ hat L A14C Sllf a s tuf!Oh 3 9.033 3 .916 3 949 8 1.C33 1 1.043 8 1.027 3 959 8 90.L t ht mE 5 Abswi SOT 10m et putL 23 1 1 3 3 1 3 3 3 .004 3 .CC1 3 .C13 1 .C64 1 .C 4 3 .LiG 8 .057 8 13sa3 936 3 984 I 942 3 943 3 92033 3 s1 186566 3 aaa! 943 3 1.C12 3 .911 1 .954 3 942 1 3 3 3 1 38 1 2 1 I I 3 1

---

8 a a a 1 .CC7 8 .C24 8 .045 1 . Cit I . cit a a a a 8 3 tatt.1 mesa. Ptate Catt et attoes - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -* - - * - + - - - - - - - - - - - -

1 mist.3 mcep, tatec smith 51tf 3 1.C37 1 1.019 3 442 3 s a a 8 . c5 3 .932 3 1.046 3 5 818f.I & (ALC. - Ptal. 2 1.045 1 1.064 I 941 13 aa8 .904 I 954 3 .997 1

- - - - - - - - 43 3 3 3 3 1 1 3 3 .C23 8 .L45 1 .C19 3 s a a 1 .CC3 3 .C24 3 .049 8 aetna6L GF 4C aten . 1.0 --------------------------------------------------------

tal P&nta alertaahti s 3.C65 & 11 3 3 1 1.019 3 .943 I 9C5 3 9CS 3 .944 3 aaa1 1aa3 1 1.C54 3 930 1 52C 3 9L7 1 936 3 aaa1 53 2 1 1 1 1 1 1 33 3 a 1 .C35 1 .C07 3 .CIS 3 .CC2 3 .CC4 8 s a a 3 3 1.C55 3 1.047 3 .940 3 932 3 944 1 .977 3 1.074 8 3 1.03L 3 1.033 I .945 3 .965 3 969 3 974 8 1.034 3 41 1 2 3 3 3 1 1 3 .029 3 .014 I .t15 3 .C33 1 .C25 3 .CC3 I . 0 58 I I 1.C58 3 1.016 1 3 m a 3 1.544 1 a a a 1 1.C74 3 1.039 3 3 1.014 1 967 1 3 3 a 3 1.045 1 3 m a 3 1.044 3 .974 3 72 3 3 . I 3 3 3 3 1 .042 3 .049 1 a a 3 3 .t23 I a a a 1 .01C 3 .045 1 I

a e C e a a s tuas $33315-1 ECC2 ulet ===------- ==-- ==----------------- - -

6ththhaas Gahme $tAh W3DE I 1.143 3 1.L37 3 a a a 1 1.C50 1 a a a 1 1.074 1 1.057 3 Ger 3 1.122 3 1.04C 3 a a 3 21.03333 3 a 3 1.055 3 1.033 3 atqose etsbL15 Compaste uttu 11 2 3 3 3 3 1 3 ma a 56a t et ht1 3 .026 1 0C3 1 a a 3 3 .033 3 3 a a 3 .021 1 .024 i SumeLE Stal AL tuatt a Es-216 1 1.L37 3 1.7C2 3 '.132 & 1.030 3 1.024 3 1.065 3 1.019 &

a06 et 806 PLamaa latet tifialed1Jeb 3 1.C21 1 1.L29 3 .935 3 1.069 3 1.045 3 1.055 3 .994 1 144.L 1htat& A60vt enf10R Of FGlL 21 1 2 3 3 3 3 I 3 .C16 2 .027 1 .CC1 3 .031 3 .C21 1 .010 3 .025 2 3aaa3 .932 I 574 3 .930 1 .928 3 9733s33 1 Lt&then 1aaa1 .963 1 .599 1 .538 1 .940 3 .976 3 s a a 3 JS 3 3 1 2 2 3 3 3 a a a 3 .037 1 .C21 3 .001 1 .C12 3 .0C3 3 s a a 3 3 C ALC.! a h0am. PCeta CALE ST attest -------- - -- --- - - - - - - - - - - - -

A PLAS.! 8 hCOM. LA140 IkithstTT 3 1.C50 2 1.033 3 .130 1 a a a 3 .311 3 .944 3 1.046 3 3 sitt.1 : CALC. - ptal. I 1.C74 3 1.0&4 3 .945 3 s a a 3 .905 3 .954 3 1.046 1 43 1 2 3 3 3 3 3 3 .C24 3 .034 1 .Cte 3 a a a 3 .024 3 .01L 3 a.C00 3 avataat 57 40 aCos = 1.0 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

th5 tc.te StF8taahti s 2.944 3 3a33 3 1.C23 3 . Sin 3 .331 I .460 I 924 13aaI Iaaa1 1.043 3 943 3 .941 I .894 I .923 3 & 3 3 1 51 2 3 8 3 3 3 3 3 3 a a 1 . CSS 3 .C15 1 .C3C 1 .C15 I .001 3 s 3 3 3 3 1.L76 3 1.C63 3 .573 3 .944 3 .924 3 .962 3 1.079 1 3 1.074 1 1.C37 1 .539 3 .962 3 .525 3 943 2 1.004 3 41 2 3 3 ,3 3 1 3 2 .CC2 3 .C24 3 ,C34 3 . Cit 3 .DCS 3 .CC1 I .975 3 3 1.C57 3 1.019 I a a a 1 1.04e 3 a a a 3 1.079 3 1.C31 2 3 1.039 3 .913 4 & a a 3 1.062 3 a a a 3 1.010 1 959 3 i 33 2 3 3 . 3 3 1 3 i 3 .018 1 .036 1 a a a 3 .016 3 s a a 3 069 3 072 1 l

l

' FIGURE 10.3.6 RECORD Results Compared with Quad Cities Gamma Scan, Fuel '

Bundle CX-214 1

1 1

10-33 1.162 1.168 Thermal absorption rates in 0.5 OODEWAARD G d - o ss embly, 1.032 0.891 initial, hot, voided.

1.043 0888 Gd pin hotched.

1.1 - 0. 3 0993 0.831 0.773 1001 0.827 0.753 0.8 - 0.5 - 2.6 1004 0.819 0.730 0.730 THERMOGENE 1.006 0.804 0.71 0 0.694 i RECORO O.2 -1.8 - 2.7 - 4.9  % Dev.

1.086 0.840 2.016 0.759 0.838 1.082 0.841 , 2.006 ! O.74 3 0.840

-04 0.1

- 0.5 - 2.1 0.2  !

1.260 1.023 0.918 0.925 0.995 1.14 6 1.260 1.034 0.939 0.937 1.009 1.16 0 C. 1.1 , 2.3 1.3 1.4 1.2 1.18 6 1.17 0

-1.3 Power distribution in OODEWA ARD Gd-assembly, 1.095 0.939 cold, initial. '

1.074 0.936

- 1.9 - 0.3 1.070 0.898 0.835 1.061 0.897 0.843

- 0. 8 - 0.1 1.0 1.097 0.885 0.779 0.813 EXPERIMENT 1.084 0.877 0.795 0.794 <

RECORO

- 1. 2 -0.9 2 .1 -2.3 , % Dev.

1.221 0.903 i O241l 0.850 0.965 1.187 0.900 iO.236i O.837 0.963

.-2 8 -0.3 -2.1 - 1. 5 -0.2

, 1.425 1.180 1.050 1.103 1.191 1.310 1.447 1.172 1.079 1.102 1.194 1.402 1.5 - 0.7 2.8 -0.1 0.2 7.0 FIGURE 10.4.1 Comparisons of Power Distributions and Absorption Rates in a Dodewaard Assembly Containing Gadolinium (From Ref. 16)

10-34 M

)

FIGURE 10.4.2 Power Distribution in M0hleberg Gd-Assembly GED-01, End-of Cycle IC

y ,

E , . .

ve, .

11-1 -

?

11. REFERENCES

< .J (1) T.O. Sauar, S. Borresen, J. Haugen, E. Nitteberg, H.K. Nass, . :.

T. Skardhamar: "A Multilevel Data-Based Computer Code System for -

In-Core Management in Light Water Reactors"; Proc. 4th UN Int. ,' ,,,.; " y Conf. I AEA, A/ Conf. 49/P/293, 2, 645 (1972). ,

(2) S. Borresen: "A Simplified, Coarse Mesh, Three-Dimensional Diffu- .

sion Scheme for Calculating the Gross Power Distribution in a 1*-;

Boiling Water Reactor"; Nucl. Sci. Eng., 44, 37 (1971).

s..

(3) S. Operesen, L.Moberg, J. Rasmussen: " Methods of PRESTO, A Three- - "',-

Dimensional BWR Core Simulation Code"; Topical Report to NRC e -

(1982). -

.y (g..

s-(4) S. Berresen, T. Skardhamar, S.E. Wennemo-Hanssen: "Applica- .' \ 3 -

tions of FMS-RECORD / PRESTO for Analysis and Simulation of w.

Operating LWR Cores"; Proceedings NEACRP Specialists' 't Meeting on Calculation of 3-Dimensional Rating Distributions - : Ji[- i in Operating Reactors, Paris Nov. 1979, NEA-0 ECD publica- '

e p

tion (1980). = :; - .-

(5) L. Moberg, J. Rasmussen, T.O. Sauar, O. Oye: "RAMONA Analysis .-

of the Peach Bottom-2 Turbine Trip Transients"; EPRI-NP-1869, +'

(Research Project 1119-2), Final Report (June 1981). J. C

,, .'4 /

(6) T. Skardhamar, et at: " RECORD Program Description"; FMS Documen- ,

G g tion System, Vol. 2 (User Manual), (1972 present).

'.+ . n, .

(7) T. Skardhamar: " Summary Description and Ma'in Features of the  ;' O .-

~s RECORD Code"; IFA Internal Report, PP-363 (1977). .:' ?V, (8) T. Skardhamar: " RECORD Program Description, Its Overlays and i 4 Segments, and General Flow Charts"; IFA Internal Report (Confi- , i. E ,7 dential) (1978). .

(9) M. Hron: " Calculations of Thermal Neutron Group Constants during ).. J - .

Burnup of Light-Water-Moderated Lattices"; Nucl. Sci. Eng. 45, , [ ..g 230 (1971).

r. v*

(10) 8. Fredin, T. Bosevski, M. Matausek: " Discrete Energy Represen-tation of Thermal-Neutron Spectra in Uranium-Plutonium Lattices";

. 3 t.

q-f

(*

Nucl. Sci. Eng. 36,, 315 (1969). . .

..y (11) H. Nelkin: " Scattering of Slow Neutrons by Water"; Phys. Rev.119, .' (IT 741 (1960).

x

'. .a  :. . ;

(12) R.J.J. Stamm'ler, O.P. Tverbakk, Z. Weiss, J.M. D declein: S~ iM "DATAPREP-II. A Reactor Lattice Homogenization and BIGG-II Data f ..

Preparation Computer Code"; Kjeller Report, KR-78 (1964). =

'gG

. .t v (13) 0.P. Tverbakk, J.M. Doderlein

"BIGG-II. A Multigroup Neutron * .L pI Spectrum and Criticality Code"; Kjeller Report, KR-75 (1965). [ y .7

+ s ., .

(14) H.C. Honeck: "The Distribution of Thermal Neutrons in Space and '%'

Energy in Reactor Lattices. Part I. Theory"; Nucl. Sci. Eng., 8_, ..'"2

'3 .' -

~

193 (1960). .,... ,y z ,, -

Q ..,. ~ 6 .~

~ ' ' p. ,

,% 3

11-2 ,

(15) R.J.J. Stamm'ler: "K-7 THERMOS, Neutron Thermalization in a Heterogeneous Cylindrically Symmetric Reactor Cell"; Kjeller Report, KR-47 (1963) .

(16) K. Haugset, H.K. Nass, T. Skardhamar, P. Brand: " Analysis of BWR Fuel Assemblies Containing Gadolinium as Burnable Poison"; Trans.

Am. Nucl. Soc., ,16, 283 (1973) .

(17) S. Berresen: " Application of Effectiva Boundary Conditions to BgC Cluster Control Calculations"; Nukleonik 1_2, 2 124 (1969), and later extensions of method described in internal reports.

(18) K. Bendiksen: " Treatment of Ag-In-cd Cluster Control Rods in the Code ALFA"; IFA Work Report, PP-353 (1976).

(19) G.E. Fladmark: "MD-2 Specification. Mathematical and Numerical Techniques"; IFA Work Report, PM-151 (1970).

(20) K. Bendiksen, T. Skardhamar: " Processing Effective Fission Product Data from the ENDF/B Data File"; Seminar on Nuclear Data Proces-sing Codes, Ispra, Dec. 1973, NEA Computer Program Library, Newsletter No. 16 (1974).

(21) W.K. Bertram, et at: "A Fission Product Group Cross-Section

• Library"; AAEC/E214 (1971).

(22) E. Patrakka, R. Terasvirta: "ETOF, A Program to Process Data from ENDF/B to FORM"; Technical Research Center of Finland, Nuc. Eng.

Lab., Report 5 (1973).

(23) R. Dannels, D. Kusner: "ETOM A FORTRAN-IV Program to Process Data f rom the ENDF/B File to the MUFT Format"; WCAP-3688-1 (1968).

( (24) H.D. Brown, D.S. St. John: " Neutron Energy Spectrum in D 20"; DP-33 (1954). ,

(25) A. Tas, A.W. den Houting: "A Programme for the Calculation of '

Thermal Group Constants by Means of Converting the Energy and Space Dependent Integral Transport Equaticn into an Energy Depen-dent One"; RCN Report, RCN-95 (1968).

(26) R.J.J. Stamm'Ler: " Fast Methods for Computing Thermal Neutron Group Constants in Single-Pin Lattice Cells"; Dr. Thesis (1968).

(27) R.J.J. Stamm'ler, S.M. Takal, Z.J. Weiss: " Neutron Thermalization in Reactor Lattice Cells: An NPY-Project Report"; Tech. Report n

Series No. 68, IAEA, Vienna (1966).

(28) M. Matausek: " Calculation of Multipoint Data for Thermal Neutron Spectra Determination"; IBK-714, Boris Kidric Institute of Nuclear Sciences, Beograd-Vinca (1968).

(29) M.M. Levine: " Resonance Integral Calculations for U238 Lattices";

Nucl. Sci. Eng. 16, 271 (1963).

~

4 (30) G.A.G. de Coulon, L.D. Gates, W.R. Worley: "SSCR Basic Physics Program - Theoretical Analysis, Part II, BPG Computer Program Report". BAW-1230, Babcock & Wilcox Co. (1962).

l 11-3 1-(31) Brown Ferry Nuclear Power Station, Units 1, 2, and 3. Final Safety Analysis Report, Amendment 21; Docket-50259-38, Tennessee Valley Authority (1972).

(32) E. Hellstrand: " Measurements of the Effective Resonance Integral in Uranium Metal and Oxide in Different Geometries"; Journ. Appl.

Physics, 28, 1493 (1957).

(33) A Sauer: " Approximate Escape Probabilities"; Nucl. Sci. Eng. 16, 329 (1963).

(34) A. Mockel: " Reflection and Transmission by a Strongly Absorbing Slab"; Nucl. Sci. Eng. 22, 339 (1965).

(35) D. Schiff, S. Stein: " Escape Probability and Capture Fraction for I Gray Stabs"; WAPD-149 (1956).

(36) A.F. Henry: "A Theoretical Method for Determining the Worth of Control Rods"; WAPD-218 (1959).

(37) S. Berresen: " Cylindrical Absorbers in the Code ALFA"; IFA Work Report, PP-324 (1969) .

(38) G.W. Stuart, R.W. Woodruff: " Methods of Successive Generations";

Nucl. Sci. Eng. 3, 339'(1958).

(39) W.J. Eich, H.T. Williams, H. Aisu: "The Analytic. Representation of Rod Cluster Control Elements in Nuclear Design Calculations";

WCAP-3269-38 (1964). .

(40) B.W. Crawford, et at: " Flux Depression in a Parallel Array of Cylindrical Absorbers"; KAPL-P-3460 (1968).

(41) K. Bendiksen: " Current-to-Flux Ratios for Stab Absorbers with Clad"; IFA Work Report, PP-348 (1975).

(42) S. Stein: " Resonance Capture in a Heterogeneous System"; WAPD-139 (1955).

(43) R.S. Varga: " Matrix Iteration Analysis"; Englewood Cliffs, New Jersey, Prentice-Hall, Inc. (1962).

(44) E.L. Wachspress: " Iterative Solution of Elliptic Systems";

Englewood Clif f s, New Jersey, Prentice-Hall, Inc. (1966) .

4 (45) R. Froehlich: "A Theoretical Foundation for Coarse Mesh Varia-tional Techniques"; General Atomic Division, General Dynamics, GA-7870 (1967).

(46) K. Bendiksen: " Fission Product Poisoning in Thermal Reactors"; IFA Work Report, PP-318 (1973).

(47) T.R. England: " CINDER - A One Point Depletion and Fission Product Program"; WAPD-TM-334 (Revised), (1964).

(48) R.J. Tuttle: " Delayed-Neutron Data fcr Reactor Physics Analyses";

Nucl. Sci. Eng. 56, 37 (1975).

11-4 (49) E. Andersen, J.O. Berg, J.M. Dsderlein: " Reactor Physics Studies of H 20/D 20-moderated UO2 Cores: A NORA Project Report"; Tech.

, Report Series No. 67, IAEA, Vienna (1966).

(50) E. Andersen, et at: " Topics in Light Water Reactor physi:s: Final Report of the NORA Project"; Tech. Report Series No. 11?, IAEA, Vienna (1970).

(51) H. Finnvik, et alt " Program MD-1, a One-Dimensional Multigroup Diffusion Code"; IFA Work Report, PM-154 (1970).

(52) P.W. Davison, et at: " Yankee Critical Experiments - Measurements on Lattices of Stainless Steel Clad Slightly Enriched Uranium Dioxide Fuel Rods in Light Water"; YAEC-94 (1959).

(33) W.J. Eich, et at: " Reactivity and Neutron Flux Studies in Multi-region Loaded Cores"; WCAP-1433 (1961).

(54) V.E. Grub, et at: " Multi-Region Reactor Lattice Stud es. Results of Critical Experiments in Loose Lattices of UO 2 Rods in H20";

WCAP-1412 (1960).

(55) J.R. Brown, et at: " Kinetic and Buckling Measurements on Lattices of Slightly Enriched Uranium and UO'2 Rods in Light Water";

WAPD-176 (1958) .

(56) T.C. Engelder, et at: " Measurements and Analysis of Uniform Lat-tices of Slightly Enriched UO2 Moderated by D2 0 - H2 O Mixtures";

BAW-1273 (1963).

(57) L.G. Barrett, et at: " Exponential Experiments at Elevated Temper-atures on Lattices Moderated by D 20 - H O2 Mixtures"; BAW-1233 (1962).

(58) V.O. Uotinen, et at: " Lattices of Plutonium-Enriched Rods in Light Water - Part I: Experimental Results"; Nucl. Technol.,15, 257 (1972).

(59) R.C. Liikala, et at: " Lattices of Plutonium-Enriched Rods in Light Water - Part II: Theoretical Analysis of Plutonium-Fueled Systems";

Nucl. Technol., 15, 272 (1972).

(60) P. Mohanakrishnan, H.C. Huria: " Reactivity Prediction of Uniform Pu02 -UO 2 -Fueled Lattices and Pu(NO3 )g Solutions in Light Water";

Nucl. Sci. Eng., 68f 2 (1978).

(61) R.J. Nodvik: " Evaluation of Mass Spectrometric and Radiochemical i Analysis of Yankee Core I Spent Fuel"; WCAP-6068 (1966).

(62) R.J. Nodvik, et al: " Supplementary Report on Evaluation of Mass Spectrometric and Radiochemical Analysis of Yankee Core-I Spent Fuel, including Isotopes of Elements Thorium through Curium";

WCAP-6086 (1969).

(63) M.B. Cutrone, G.F. Valby: " Gamma Scan Measurements at Quad Cities Nuclear Power Station, Unit 1, Following Cycle 2"; EPRI NP-214 (1976).

(64) N.H. Larsen, G.R. Parkos, O. Raza: " Core Design and Operating Data

11-5 l

for Cycles 1 and 2 of Quad Cities 1", EPRI NP-240 (1976).

l l

(65) S.L. Forkner: Tennessee Valley Authority; Private Communication.

(66) J. Nitteberg, J. Haugen, J. Rasmussen, T.O. Sauar: "A Core-Follow Study of the Dodewaard Reactor with the Three-Dimensional BWR Simulator, PREST 0"; Kjeller Report, KR-145 (1971).

(67) S. Berresen, H.K. Nass, T.O. Sauar, T. Skardhamar, F. Grandchamp, J. Rognon, R. Wehrli, C. Weigel: " Core-Follow Study of the MUhleberg BWR with the Fuel Management System - FMS"; ENC, Paris (April 1975).

(68) S. Berresen, D.L. Pomeroy, E. Rolstad, T.O. Sauar: " Nuclear Fuel Performance Evaluation"; EPRI NP-409, Final Report (June 1977).

(69) H. Guyer, H. von Fellenberg, W. Wiest: " Core Simulation and Its Experimental Verification of the MGhleberg BWR"; ENC-79, Hamburg, TANSAO H , 225 (1979).

(70) W. Wiest, H. Hofer, N. Naula, C. Weigel, R. Wehrli: " Gamma-Scanning im KKM und dessen Anwendung bei der Reaktorsimulation";

presented at Reaktortagung 1978, Deutsches Atomforum e.V.,

Hannover (1978).

h

-n

APPENDIX A Breit-Wigner Formula for Cross-Section Calculations RECORD TOPICAL REPORT

A-1 APPENDIX A BREIT-WIGNER FORMULA FOR CROSS-SECTION CALCULATIONS Cross-sections in the RECORD Library are calculated, where appropriate, from resonance parameters in ENDF/8-III, applying the single-level Breit-Wigner formula:

e ny (E)

• E jy IEI' (A 1 1)

L where r 1 o (E) = I g Eo ,r (T12) - -

( A .1. 2) ny y J r r h(E' - E') /r r +1 r

without Doppler broadening, and T

o E (I) = I gJ Ic (:lL) $(C , X ) (A.1.3) ny y r

'r ' #

when Doppler broadening is included, and where o =bj..rnr (A.1.4) k r r

• =r nr(E) = P (E)r"#(lE# l} (A.1.5) nr Pg (lE l}

T r

i nr(E) + r r (*Ifr) (A.1.6)

, Sg (lE l } - S ( )

t E' =E + r "#(}E# l} (eV) (A.1.7) r r 2Pt (IEr1) _,

and P, , T are the capture and fission widths, f

assumed to be energy-independent.

A-2 The penetration factors S g and P g are given by

~

dW (+)/dr a

f)

L r=a I Sg +iP g (A.1.8)

~

~dW(-)/dr -

a ES g-iP (A.1.9)

_) t I r= a where W (~', W ( +' are the " incoming" and " outgoing" parts of the radial wavefunction; here W(g+) (kr) =gn (kr) + ijg (kr) (A.1.10)

W(~) (kr) = tn (kr) - ijg(kr)

)

-j g,n g are spherical Bessel functions of 1st and 2nd order, and

?

a is the channel radius, equal to the effective scattering radius in the calculation of phase shifts, C g, otherwise given by a = (1.23M ll' + 0.8)

• 10 ~l (cm -12)

a A-3 For positive energy channels

-1 So = 0 , S: = 1 + (ka)2 - - - -

Po = ka, Pg= 1 - -

(ka)2' e -

k =

2.19685 10-3 (M+1 00867) (barns)-l E = neutron energy (eV) in the lab. system.

M = atomic weight of the isotope in the C12=12 scale.

gj = 2J + 1 2(2I+1)

Line shape Doppler functions are defined by:

( ,. exP(-(x y )

• C /h)

Y(Er ,X r }* du 1+y h dYr (A.1.12) r J

)

! 2y x( E ,,X E

r r ***P(~I*rY) r 6 Ik) dY (A.1.13) r r ) ** /kw 2 r l + y,.

J.l

A-4 where I p2 ,g r

F2 , _

r 4lE 'jK T T = temperature (Kelvin)

K = Boltzmann's constant Xr = 2(E - E')/I r r Yp = 2(E' - E')/P p E' = the neutron energy in a system where the absorber nucleus is at rest.

For a resonince at a negative energy, E , the neutron width is specified at r

the energy lEr l. A numerical method is used to solve Equations A.1.12 and A.1.13.

In calculating cross-sections from the Breit-Wigner formalism for the RECORD Library, the 220-) m/s value for a given nuclide was compared with the recommended value given in the ENDF/B-file, and whenever an exact agreement was not obtained, a 1/v-correction compensating the difference was added.

Elastic Scattering:

If resonance parameters are given in the ENDF/B-III file, point values for scattering cross sections are calculated from the single-level Breit-Wigner formula:

L S n( E )

• I 9.n (A.1.14)

L

A-5

_ s e .

'"'# p"'#

T.

(E) = I g I o w((r,Xr ) + (o o - )I +

y J r '- r I e r e r P rr

) (A.1.15) x(c7 .x,) +o'

~

/

where the potential scattering cross-section is given by:

1 o = hw (21 + 1) sin2 i

og (A.1.16) and all other symbols have been defined before.

i I

l t

e k

I

- . . , . - - . , . , , --y- . . - - - , - -.--c-- ,y--r-----,,nrw---,-wwe, wrv--,--,,---,r-~-v------ - - = > - * - ~ ~ - ~ - - - - - - ' - - ' - " - ~ ~ - - ' - ' - ' ' " " ' ~ " ~ ~ ' '

l APPENDIX B Output Options in the RECORD Code r

{

RECORD TOPICAL REPORT

APPENDIX 8 OUTPUT OPTIONS IN THE RECORD CODE

1. Main fuel assembly data (need not be requested, is always obtained).

J

2. Burnup distribution in fuel assembly (for non-zero burnup).

3. Power map (pin-power relative to unit average power).

4. Power density distribution (for non-zero average power).

5. Thermal mesh point flux distribution.

6. Thermal absorption rates for all lattice cells.

7. Group absorption rates for all groups and regions.

8. Group production rates for all groups and lattice cells.

9. Regionwise macroscopic group constants for all groups and regions.

10. Water gap data, flow box data and alpha values for control absorber (if calculated by code).

11. Region division of fuel assembly cell, mesh point coordinates, and composition map.

12. Number densities of fuel isotopes in each fuel pin.

. 235 236 239 240 241 242 .

13. Fuel inventory (wt % U ,U , Pu , Pu , Pu and Pu , in each fuel pin.)

14. Neutron balance (two group scheme).

15. Thermal flux ratios in each burnable poison and surrounding lattice cells (for ese in THERMOS - GADPOL).

APPENDIX C Excerpts from RECORD Output RECORD TOPICAL REPORT

• • NLCUNp al-4** OUTPul AL-5A 1 O uwR SAMPLt PadbLin AWERAuk ouRNDP

• 600b. Rws/Iu la.44u m/Cn, VOID .400, f P POIS , bukh. Pul5.

Math f us L A55EMBLt DATA 4 si lih5. Ih sitt. (AtC. )

i K-INFIN!IV a 1.17325 K*EffECIIWE - 1.164&3 PDuiR PL AK!hG F ACICA = 1.0691 IIP htGIGh: f!551Ch AATE a .141241-CF MAA! MUM LINEAM LOADING a 141.956 malis /CM Al PAN hd. 41 AW. IHEAPAL ILua a .43409(*14 l MAXIMUM P0wta DEh5ITY = 20.0a5 waits /6n-u AT Pih 40. 41 Av. fASI fluA * .3045FE*15 MAnimuM outhur a 0373. nws/gu Ag FIh h0. 44 i AvtaA6L futL E6MPOSIll6N: GR/CR fu1L ASSEMLLT wt16H1 PtN LENI U235 .aF30E*01 Pu239 .9972Leb6 b235 1.9747 Phi 39 .2250 0236 .4653E*00 Pu240 .1271E*00 u236 .109a Pu240 .u2sa u23a .431FE*C1 Pue41 .33FFE-61 b436 97.6497 Pui41 .00?o y hP239 .345bE-01 PU242 .2405t-02 NP239 .uG34 Pb242 . Gov 5 --

ALCunuLATED fl551LL PLuiGNIup = .1031E*01 Gn/Cn 1

Avt A Aht MACN05COPIC GROUP D AT A AND ILunts f0A fust A5stm0Lv (ELL hkuur DIff SIGA 5164 hV*EIGF SIGf ILb4 1 .29656E*01 .53303E-01 .J'312E-02 .59204t-02 .2d945E-01 .3140?E*14 2 .139G4E*01 .52521E-01 .16144E-02 .47530E-03 .19073t-03 .41E9eE*14 4 .a4755t*00 . 5 40 2 9 E-01 .152778-01 .577360-02 .232d21-02 .31309t*14

! + .2.18315*00 .22606t*00 .3051FL-01 4GFF4E-01 .154061-01 . 6 L e 94.,t e l l 5 .44573E*00 .20693E-01 .5214FE-01 .72767E-01 .26991E-01 .2604btel4 (Asi .l?uT5E*01 .16341E-01 .613751-02 .37044t-02 .14u1FE-62 .10441E*15  %

IHtkMAL .52916t*00 6. .4730st-04 .65604L-01 .25vc2t-G1 .5ct30kel4 E'

E AvtaA6L INERMAL fLuA * .3613t*14 NEuTA/Cn**t/5EC Encerpt from RECORD Output Listing - Main Fuel Assembly Data

C-2 e e < N o e a e P N M e 4 e o 3 O O 3 o o 3 o m > > > > > > >

• = m e A e e . O  %

• N m w w e O e e o e , e , e

& M M M e a e u e O O o o 3 o 3 o

} & E E E 3 8 E R 5 J K 4 2 3 2 2 2 4 Q & & 4 L h A & b 4

e en O

L m --------------------------------

8 g

i e 4 4 a

Q e Q

0 O

% e 4  % h  % 3 0 4  % Q e se e e  %

e 0  % e e @ e e m o e  %

e e  % W N e e e a e e  %

e a

i  % 4 4 4 4 4 4 e d e  % e 0  %  %

- 4  % e O  % e E  % C 4 h 4 m e e 4  %

> 9  % U e 4 N e 4 e Q  %

e o

e  % *w en N N N e M 4  % e E

4 9

I  %

4 4 4 e a e e e  % e

@  % a t  %

%  % 3 8  % W p e e e a e M  %

E O t  % * @ m n o n m i

W 4  % 0 5  % 4

• W e e N 4 9  %

d Q a I  % @ W e e A w e 4  %

e e w 2 0  %  %

e O e - t  % e e  % e e & 8  % e p D M e W h M

& e  % 8

% 0 C w T I - 3 M e a g +  % e Q W

$  % N + e a e e -w e w a

• d 0  % 4 e e e e e W w A 0  %

4 4  % 9

&  %  % e 3 E

4

% 4 O 3 9  % 4 e e e D 3 4

W

% .e 2 e e m ~

d 0

{

%

• e e e e N *  % -

e e  % 4 e e e e e o e  %

.m E e W  % e  %

0 3 E  %  %

e c e e  % C 3 e c & @ A N  %

2 o l  % M N N Q 3 e 9 G

- E  % N M d Q  % B 3 I

M e e @ N e  % C Q w  % @ e e e e e 4 4  %

9 b

4 2 1  %  % l 3

> t - '  % O p  % 8 d g b  % P A 3 e e e d a  % 8 ai I  %

• e N e p e p 4  % i g

E l >  % e Q M @ f p e N  %

wg 4  % 4 W e e e

• O 4  %

G g 4 d l  %  %

6 C

e 3 'l et 3  %  %

0 e g p u 4 e >  % & w Q e e 4 w w e O N  % 9 e wi  % l  % 3 = M

• e e o e e e d e  % ** w e e

-l em N em N 4 rd O  % J B w 3 '

% 4 @ @ O O 4 J 4  %

9 9

Ei 3 E  % -% 4 W 1 m  %

>  % 0 w 3 3 0 ei 3 M e

n

%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0 s O t O - N I 8 o 3

Q 4 2 4

---

-- 1 Z ["

i O I 3 5 g

- W g m o e > a 4 y e 3 e & 3  %

J W e 2 - 3 M 4 E M 2 w a > e W E i

W

• O i

G 3 3 S b 3 - 3

• b e 2 2 W d w 5 -l E 2 O J b I 3 g w 4 3 1 E e 6

W W 2 - g e y E 4 E N

• e > Di 4 x e 4 J' E

• W

C-3 e

efB se Q

& 4 4

• N O ep 4 4

== N 88 ) e w en e e

M 3 O 3 O Q et > em =

3 3 3 oo e. a. e. e.

3 4 == > N A M em ch h om N og 4 4 en 3 e e e e e e e e me en ne we en e,e w w te O O Q O O O O O

1. 2 E E E E o E E E a E E E E E E E a N == me == =e == =e =a .Ee W & & & & & & & &

% e O

3 34 E

a. ==

% O E e G. ee B Gm E &

em e= es me se me me = ou =e ao me M M M as M at M as at at M as M as at M M M M as as as at O

0 MM as og at at at M at MM M at M M se at M M as M at at 4 0 as at O s G Q E M st O O W  %%%%%%%%%%%%%%%%%%%%%%%%%%%%

as as W  % et M en e W

% O e Q pm Oh art ** S  % MM

• eh A "1 W Ch 4 Q em  % as at 4 pm i  % G e9 h @ tR tr4 IA W  % 38 as em 0

• 4 e e e e e e  % at M em e 4 8  % **  % as as e em 3 t  %  %

4 O as M O  % @ Ob e seg o8t w e em  % M as as Je 4 6  % e am N 4 M em e3 M ch 3  % as M 0  % 3 Q Gb e9 P= N erg in  % MM ses g e  % e e e 0 e e e e e  % M st 5 g Ob $  % to **  % at at ta Oh 4  %  % MM s  % em 6  % Ch M en asg == , e art  % as at E 3 9  % N M Ch N 4 N 889 @  % MM tas # 4  % N em Oh Ch @ S h um  % at M d O $  % e e e e e o e e  % at M e e an e  % e= e=  % as M O + J l

%  % MM E e e  % N 4 em #m 4A em s*4 Ch  % M as G. e9 E ** e @ e W1 tF4 4 e9 Oh  % MM em ens  % 8"18

• • O O Ch e A em  % M as one we  % e e e e o eft e o e  % at og ed  % em om em se  % M ag

& 4  %  % mE M E  % Ch e tM e N erg as N  % MM 4 .J set  % en Ob 4 e Wt N W tse Q tae S  %

W  % at M 881 ** en e Q Oh 84 e  % as M eD 3 nas  % e e e e o e e o  % 34 M M N tem 2  % e" ** ** 4 em  %

3 wg O  % mE at g e e  % M at eE &  % Oh p= em trt en eB Q  % MM r, 13 em se  % N tm Q @ W Oh N *t  % MM tas  %

• N N ** tJ ch gh N  % MM b om p 49 L3  % e e e e e e e e  % MM 48 E ag  % em em om en em  % MM 3 g se m  % 1 O em Qe tas  % ee em Ch e 4 M D e * %  % 'l L em 4 3  % N Om en Gk W 881 erg A  % ll WQ eg  % en est N em om em Q e  % 0 et eJ  % e e e e e e e s  %

4 - tan **  % ** ** ** ** em e* e"  %

y trl 3 6 #e  %  % C l em W4 2  % tr% e e Ob em Ob 4 D  %

.pm ad  % E tad 3  % W N w i

N ett == h e *=  % oft a e se E i  %

• tm 4 #89 W1 N O Q  % i

• 2 hf me O  % e e e * * * * *  % i

.J E 4 .6 em  % em em em WD em em e* em  % 1 6a0  %  % l tat *'*

De e$ Gm E tal 3 O 3 3*

%%%%%%%9m%%%%%%%%%%%%%%%%%%%% i ed 3 Q se I O O

& ME i E **

t 3 O. .

wm BM l

================================t . [

o '

O4 s w

, G. E tas se a og

e et 4

e w Q e & 2 La w taJ 3 E 49 QC g E me ha om as g o.d E e 3 e O 4 & E

. < ee.

.E I E nef E G. e J J y tJ 4 5 5 e g

.e# 5 ans ese 5 8 ue R R e gp 9

e > 3 3 8 n,a e 4 m

& B 4.

O taJ

• • RtCORD 81-4e* OUIPUT RE-SA 1 1 gen 5 AMPLE P90aLER, RESTART At 600u mwd /ib AWERAGE mWRhuP a 6000. MwDtIU 16.460 m/GM, VOID .400, IP PGis , C-R&D Ihe svah. P015.

htuitch oALANCE - Two GROUP SCHEME, T H E R M AL CUT off Ai 1. d 4 E V (NO RM AL I 5E D TO TOIAL PRODUCTION

• 100000)

• AB50RPil0N RATE

• SlowlNG

• PRODUCTION RATE e REGIch / 9ATERIAL

• THERMAL EPliH. TOTAL

• DOWN RATE

• THERMAL EPIIM. 10fAL

• e e e e futL: U235 a 29320 Seat 34801 e 1

• ebu36 del 4 ed980

• U236

• 14 304 318

• 0 *

• u238

• 6344 21560 27924

• 54

• 0 6764 dios e PU239

• 106F3 794 11467

• 0

• 20138 1371 21$C9 e PU240

• 1382 116 1498 e o

• O 14 14 e P0241

• 329 43 3F2

• u

• 697 lu5 802 a PU242

• O 4 4 a 0

• 0 u o e AM*CM

• 3 1 4

• O a 1 0 1 e RE135 a 1723 0 1723 *- 0

• a SM149

• 636 2 638

• 0

• a f!55.P

• 10F0 112C 219J

• 0 * .

GAD.

• 255 15 270

• 0 * . n 016

• 1 186 18F

• 657 * . &

OTHER

• 4 C 4

• 0

• e TOTAL futt

• 51754 29646 41400

• F12

• 80EF2 1912d 100000 a

. ..... .. __ __ ... e ..... . ..... ..... . . . . . . . .

• e a (LAD:

• 345 55o 943

• 10 *

• e e e e MODERAlba ((HAhhEL) H2O

• 2617 325 2942 * ' 47253 *

• WATER N0LES

• 119 13 132

• 1965 *

• e e e e MATER EAP: e 1645 145 1790

• 21921 *

• flow box WALL: e 323 329 oS2 a 44 e a CONTROL A00: a 15071 1203F 2F1U8

• 0 * .

r e . . . .__... . ..... . ..... ..... ...... .

A55EM0Li IOTAL:

• F1916 43053 114969

• F1966 a 808F2 19128 1000u0 e

. ..... . .. ...... . ...__ e ..... .._.. ...... .

THERMAL /EPliH.tiOTAL LE AK AGE: 43 593 636 Excerpt from RECORD Output Listing - Neutron Balance

- _ _ _ _ _ _ _ _ _ - _ _