STARBUCS: A Scale Control Module for Automated Criticality Safety Analyses Using Burnup Credit

G. Radulescu and I. C. Gauld

STARBUCS is an analysis sequence in SCALE for automating criticality safety and burnup loading curve analyses of spent fuel systems employing burnup credit. STARBUCS requires only the fresh fuel composition, an irradiation history, and the KENO model for a spent fuel configuration to be provided in an input file. It automatically performs all necessary calculations to determine spent fuel compositions, self-shielded cross sections, and the keff of the spent fuel configuration. In addition, for burnup loading curve analyses, STARBUCS performs iterative calculations to search for initial fuel enrichments that result in an upper subcritical limit. STARBUCS allows the user to simulate axial- and horizontal-burnup gradients in a spent fuel assembly, select the specific actinides and/or fission products that are to be included in the criticality analysis, and apply isotopic correction factors to the predicted spent fuel nuclide inventory to account for calculational bias and uncertainties. A depletion analysis calculation for each of the burnup-dependent regions of a spent fuel assembly, or any other system containing spent nuclear fuel, is performed using the ORIGEN-ARP sequence of SCALE. For criticality safety calculations employing multigroup cross section data, the spent fuel compositions are used to generate resonance self-shielded cross sections for each region of the problem. The region dependent nuclide concentrations and cross sections are applied in a three-dimensional criticality safety calculation using the KENO code. Both KENO V.a and KENO-VI criticality codes are supported for single criticality safety calculations using burnup credit, but only KENO V.a can be used in criticality calculations for burnup loading curve analyses. Although STARBUCS was developed specifically to address the burnup-credit analysis needs for spent fuel transport and storage applications, it provides sufficient flexibility to allow criticality safety assessments involving many different potential configurations of UO2 spent nuclear fuel.

Introduction

The U.S. Nuclear Regulatory Commission (NRC) issued Revision 3 of the Interim Staff Guidance 8 (ISG-8) ([Com12]) on burnup credit in September, 2012. ISG-8 provides guidance on the application of burnup-credit in criticality safety analyses for pressurized-water reactor (PWR) spent fuel in transportation and storage casks. Burnup credit is the concept of taking credit for the reduction in reactivity in spent fuel due to burnup. The reduction in reactivity that occurs with fuel burnup is due to the change in concentration (net reduction) of fissile nuclides and the production of actinide and fission-product neutron absorbers. In contrast to criticality safety analyses that employ a fresh-fuel assumption (i.e., conservatively assuming unirradiated fuel compositions), credit for burnup requires the prediction of both fissile material and absorber nuclide concentrations in spent nuclear fuel (SNF) and consideration of many burnup-related phenomena, in addition to the criticality issues.

Consideration of the depletion aspects in the criticality assessment of SNF places an increasing reliance on computational tools and methods, and significantly increases the overall complexity of the criticality safety analysis. The use of spent fuel nuclide concentrations in the criticality evaluation also necessitates consideration of many additional sources of uncertainty associated with fuel depletion. ISG-8 highlights, for example, the need for applicants employing burnup credit in criticality safety assessments to address the axial and horizontal variation of the burnup within a spent fuel assembly, uncertainties and bias in the nuclide predictions, and the additional reactivity margin available from fission products and actinides not credited in the licensing basis.

To assist in performing and reviewing criticality safety assessments of transport and storage casks that apply burnup credit, a new control sequence called STARBUCS (Standardized Analysis of Reactivity for Burnup Credit using SCALE) was developed in SCALE 5. STARBUCS automates the generation of spatially-varying nuclide compositions in a spent fuel assembly, and applies the assembly compositions in a three-dimensional (3-D) Monte Carlo analysis of the system. STARBUCS automatically prepares input files for each of the modules in the sequence, executes the modules through the SCALE driver, and performs all flow control, module interface, and data management functions. The STARBUCS sequence uses well-established code modules currently available in SCALE. STARBUCS also performs iterations over a range of initial fuel enrichments to determine the initial enrichments below which UO2 commercial spent fuel may be loaded in a transport/storage cask for specified burnup values. With this capability, STARBUCS assists in generating burnup loading curves for criticality safety analyses of spent fuel in transport and storage casks.

The STARBUCS sequence automates the depletion calculations using the ORIGEN-ARP methodology to perform a series of cross section preparation and depletion calculations to generate a comprehensive set of spent fuel isotopic inventories for each spatially-varying burnup region of an assembly. The spent fuel nuclide concentrations are subsequently input to either CSAS5 or CSAS6 to and perform a criticality calculation of the system using the KENO V.a or KENO-VI code, respectively, to determine the neutron multiplication factor (keff) for the system. Only minimal input is required by the user to perform a typical burnup-credit analysis. The user can specify the assembly-average irradiation history, the axial density variation of the reactor moderator, the axial- and horizontal-burnup profile, and the nuclides that are to be applied in the criticality safety analysis. Nuclide correction factors may also be applied to the predicted concentrations to account for known bias and/or uncertainty in the predicted SNF compositions.

Methodology

The STARBUCS control module is a burnup-credit sequence designed to perform 3-D Monte Carlo criticality safety calculations that include the effects of spatially-varying burnup in SNF configurations. STARBUCS offers two options: either perform a single criticality safety calculation with burnup credit or perform iterative calculations for burnup loading curve analyses of commercial UO2 spent fuels. The sequence contains a set of instructions designed to automatically process input data, execute code modules currently available in SCALE for depletion, resonance cross section, and criticality calculations. In addition, for burnup loading curve analyses, STARBUCS checks whether keff converges to a user-provided upper subcritical limit, adjusts the initial fuel enrichment using the least squares method, and repeats the sequence until either convergence is achieved or determine that no solution can be found. The overall program structures and flow for a single criticality calculation and for burnup loading curve calculations are illustrated in Fig. 17 and Fig. 18, respectively.

The sequence uses well-established code modules currently available in the SCALE code system. These modules include ARP and ORIGEN to perform the depletion analysis phase of the calculations. ORIGEN-ARP is a sequence within the SCALE system that serves as a faster alternative to the TRITON depletion sequence of SCALE to perform point-irradiation calculations with the ORIGEN code using problem-dependent cross sections. ARP uses an algorithm that enables the generation of cross section libraries for the ORIGEN code by interpolation over pregenerated cross section libraries. The ORIGEN code performs isotopic generation and depletion calculations to obtain the spent fuel nuclide compositions. For criticality safety calculations using multigroup cross section data, problem dependent cross sections are processed with the resonance self-shielding capabilities of XSProc using the region-dependent compositions from the depletion analyses. Finally, the region dependent nuclide concentrations and cross sections are applied in a 3-D criticality calculation for the system using either KENO V.a or KENO-VI to calculate the keff value.

The ORIGEN-ARP depletion analysis methodology represents a significant increase in computational speed as compared to equivalent calculations performed using the SCALE depletion analysis sequences that use two-dimensional transport methods, with virtually no sacrifice in accuracy. ARP uses an algorithm that enables the generation of cross sections for the ORIGEN code by interpolating on cross sections available in pre-generated data libraries. For uranium-based fuels the interpolation parameters available are initial fuel enrichment, burnup and, optionally, moderator density. STARBUCS creates input files for ARP and ORIGEN for each burnup-dependent region of an assembly and calculates the spent fuel nuclide concentrations for the region using a user-specified assembly irradiation history, cooling time, and burnup profiles. The ORIGEN libraries must be available in advance of a STARBUCS burnup-credit calculation. These libraries may be created using TRITON. The libraries include the effects of assembly design and operating conditions on the neutron cross sections used in the burnup analysis. Several ORIGEN libraries are distributed in the SCALE code system and can be applied in a STARBUCS analysis. Alternatively, a user may create a specific ORIGEN library for other assembly types or operating conditions not available in the default libraries. The generation of ORIGEN reactor libraries is discussed in the ORIGEN Reactor Libraries chapter.

The depletion phase of the analysis is performed using ARP and ORIGEN to calculate the compositions of each discrete fuel region (axial or horizontal). After a single ORIGEN-ARP depletion calculation is completed, control is passed back to the STARBUCS module which reads the spent fuel nuclide inventories generated by ORIGEN, saves them, prepares the ARP and ORIGEN input files for the next burnup region, and executes the codes in sequence. This cycle continues until the fuel compositions for all axial and horizontal regions have been calculated and saved, completing the depletion phase of the analysis. The depletion calculations for each axial and radial zone are performed using an initial fuel basis of 1 MTHM (10:sup:6 g heavy metal).

After all depletion calculations are completed, STARBUCS reads the spent fuel nuclide inventories for all regions and prepares input for the criticality calculation. The concentrations of all nuclides in the ORIGEN depletion analysis are converted from gram-atom units (per MTU) to units of atoms/b-cm applied in the criticality calculation. The criticality calculation is performed using the capabilities in the CSAS5 or CSAS6 control module of SCALE. Specifically, STARBUCS prepares input for the CSAS5 module when criticality calculations are to be performed using KENO V.a, and for the CSAS6 sequence when using KENO-VI. Note that only the criticality safety sequence CSAS5 of SCALE can be used for burnup loading curve calculations.

For burnup loading curve iterative calculations, STARBUCS employs the search algorithm described in CSAS5 section on Optimum (Minimum/Maximum) Search to determine initial fuel enrichments that satisfy a convergence criterion for the keff of the spent fuel configuration. If convergence is not achieved in a search pass, the initial fuel enrichment is automatically adjusted. This sequence repeats until either keff converges to an upper subcritical limit or until the algorithm determines that a solution is not possible. The procedure is repeated for each requested burnup value. The maximum allowable iterations, upper subcritical limit, tolerance for convergence, and a range of initial fuel enrichments can be set by the user. The lower and upper enrichment bounds as well as the burnup values for spent fuel regions must be contained within the range of enrichment and burnup values used to generate the applicable ORIGEN library. The control module prepares a STARBUCS input file for each search pass requesting a single criticality calculation using the calculated spent fuel compositions. In this input file, the burnup history data block and/or the fuel mixture compositions are updated based on the outcome of the search sequence. The pre-burnup compositions for the two minor uranium isotopes, 234U and 236U, are updated in the STARBUCS input file for a new pass only if they were included in the initial input file prepared by the user. Their updated weight percentages are based on the assumption that the mass ratios 234U/235U and 236U/235U do not change with fuel enrichment.

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Fig. 17 Modules and flow of STARBUCS sequence for criticality calculations.

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Fig. 18 Modules and flow of STARBUCS sequence for burnup loading curve calculations.

Capabilities and Limitations

STARBUCS is designed to facilitate criticality safety analyses employing burnup credit by automating and linking the depletion and criticality calculations. The STARBUCS sequence has been designed to readily allow analysts and reviewers to assess the subcritical margins associated with many of the important phenomena that need to be evaluated in the context of the current regulatory guidance on burnup credit. However, STARBUCS is sufficiently general to allow virtually any configuration involving irradiated nuclear material to be analyzed. Limitations and some of the key capabilities of the STARBUCS sequence are described below.

  1. STARBUCS limitations include the use of a single UO2 fuel type and, for analyses employing multigroup cross section data, the use of geometry configurations consisting of spent fuel rod arrays. However, the type of spent fuel configurations that can be analyzed is entirely general. STARBUCS can be used to perform criticality safety assessments of individual fuel assemblies, a spent fuel cask, a spent fuel storage pool, or any nuclear system containing UO2 irradiated nuclear fuel.

  2. Only the criticality safety sequence CSAS5 of SCALE can be used for burnup loading curve calculations; therefore KENO V.a geometry description must be available in a STARBUCS input file for burnup loading curve calculations.

  3. Burnup calculations can incorporate any desired operating history. The user may enter the specific power, cycle lengths, cycle down time, post-irradiation cooling time, etc. The axial-water-moderator density variation may also be specified in the depletion analysis, provided the ORIGEN cross section library contains such data.

  4. The effects of assembly design, soluble boron concentrations, burnable poison exposure, reactor operating conditions, etc., are accounted for in the ORIGEN cross section libraries used in the ORIGEN depletion calculations. Libraries for several fuel assembly designs are distributed with SCALE. These libraries can also be readily created for any reactor and fuel assembly design that can be represented in the depletion analysis sequences of the SCALE system.

  5. The user can select the specific actinide and/or fission product nuclides to be included in the criticality safety analysis. The user also has the option to perform a criticality calculation employing all nuclides for which cross section data exist.

  6. Isotopic correction factors may be input to adjust the calculated nuclide inventories to account for known bias and/or uncertainties associated with the depletion calculations.

Minimal user input is required to perform many types of analyses. Default values are supplied for many of the input parameter keywords. The user may select from built-in burnup-dependent 18-axial-zone profiles taken from [LFKR98], or the user may input an arbitrary user-defined burnup distribution with up to 100-axial zones and up to 7-horizontal zones. The depletion analysis calculations for each zone are performed for all nuclides (the ORIGEN data libraries contain cross section and decay data for more than 1000 unique actinides, fission products, and structural activation products). The specific nuclides to be considered in the keff analysis may be input by the user. If no nuclide set is explicitly selected, then all nuclides that have cross section data in the ORIGEN library are automatically applied in the criticality analysis, resulting in a “full” burnup-credit criticality assessment. A capability to adjust the calculated isotopic inventories using correction factors that can account for biases and/or uncertainties in the calculated isotopic concentrations is also provided.

An appropriate ORIGEN cross section library for UO2 fuel must be available for the depletion analysis using STARBUCS. The user may use the libraries distributed with SCALE (e.g., ge7×7-0, ge8×8-4, ce14×14, w15×15, w17×17_ofa) or the user may generate their own problem-specific libraries using the TRITON depletion analysis sequence available in SCALE. A complete list of ORIGEN libraries distributed with SCALE and methods for generating ORIGEN libraries are both described in the ORIGEN Reactor Libraries chapter. The range of initial fuel enrichment and requested burnup values to be used in the STARBUCS calculations must be contained within the range of the enrichments and burnups used to generate the applicable ORIGEN library.

The user is required to provide a complete KENO V.a model of the spent fuel configuration for burnup loading curve calculations and a complete KENO V.a or KENO-VI model of the spent fuel configuration for single criticality calculations using burnup credit. The initial material composition information is defined in a standard composition data block. The fuel material is automatically depleted in the sequence for each of the burnup-dependent regions or zones in the problem. The nuclide concentrations after irradiation and decay are automatically applied to the KENO criticality analysis. The mixture numbers for each of the fuel regions are identified by unique mixture numbers assigned automatically by STARBUCS based on the axial and horizontal regions in the problem (see Fig. 19). The user is required to specify the geometry/extent of the axial and horizontal zones in the KENO model and apply the appropriate mixture numbers for the desired configuration based on the mixture identifying scheme. STARBUCS performs no checking of the criticality model to verify that all mixtures in the problem have been used or that the order of the mixture numbers in the KENO model corresponds to the corresponding order of the input burnup profile. This provides the user a great deal of flexibility in setting up problems. However, it also requires that the user accurately prepare the input files to ensure that the spent fuel zone mixtures are assigned to the correct KENO V.a or KENO-VI geometry regions. For instance, the user could (intentionally) reverse the order of the axial-material identifiers in the KENO model to simulate inverted fuel, or zone mixtures could be omitted to simulate a problem using only a subset of the available fuel zones that were simulated in the depletion analysis.

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Fig. 19 Fuel and material mixture numbering convention used in STARBUCS.

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Fig. 20 Example of mixture numbering scheme used in STARBUCS.

There are several conventions that must be followed when using STARBUCS. In general, these relate to the specification of materials and mixture numbering of the cross section mixing table.

  1. The maximum number of horizontal zones is restricted to seven if there is no gap or second moderator mixture, six if a gap or second moderator mixture is defined, and five if both a gap and a second moderator are defined. The number of axial-fuel zones is limited such that the product of horizontal zones ∗ axial zones is less than or equal to 100. These limits constrain the maximum mixture number used for burned fuel in the KENO criticality calculation to less than 1000 and assign unique mixture numbers to clad, moderator, and gap mixtures for lattice cell descriptions. The convention used to number the depleted fuel zones is to start at mixture 101 and increment by 1 for each axial-burnup region. Thus, for a case with 10 axial-burnup regions, the fuel mixtures used in the criticality analysis would range from 101 to 110. For a similar case having two horizontal zones in addition to the axial zones, the mixture numbers would also include mixtures 201 to 210.

  2. Mixture numbers for the clad, gap (if applicable), and moderator may also be used directly in the KENO model. Additional unique mixture numbers are required by the code for the lattice cell descriptions for each separate fuel zone (except for mixture 0 for void). These additional mixtures are assigned automatically by the code and are shown in Fig. 19 for a lattice cell consisting of fuel, gap, clad, and moderator. The additional mixture numbers may also be used directly in the KENO model. Mixture number allocation is illustrated in Fig. 20 for an example case where the number of different horizontal zones is four and the maximum number of axial zones is limited to 25.

  3. All structural materials in the problem must have mixture numbers different from the numbers automatically generated by the code (see Fig. 20 for an example of available mixture numbers). For the example shown in Fig. 20, mixtures 5–100, 126–200, 226–300, 326–400, 501, 601, 701, 426–500, and 801–2147 are not allocated by STARBUCS and may be defined by the user in the composition data block and used in the geometry model. If the constraints in paragraph 1 are followed, mixture numbers less than 100 that were not used for fuel, gap, clad, moderator and mixture numbers from 1001 to 2147 are always available for structural materials. Note that STARBUCS does not provide a warning or stop program execution if a mixture number assigned to a structural material has also been generated internally by the computer code. The mixture numbers for structural materials are not changed and are thus applied in the KENO model in a one-to-one correspondence with the standard composition mixture as done for typical CSAS calculations. Therefore, the use of a mixture number for structural materials that is identical to one of the mixture numbers automatically generated by the code results in the combination of both materials in the composition for the mixture number.

  4. Not all SCALE standard composition alphanumeric names (see the Standard Composition Library chapter) are currently recognized by STARBUCS. The use of special materials (e.g., C-GRAPHITE, NIINCONEL, H-POLY), particularly as fuel materials, that have nuclide identifiers that are not readily translated to ORIGEN ZA numbers should be avoided since these materials cannot be depleted.

  5. A single STARBUCS calculation is limited to a single initial fuel type (composition, enrichment, assembly design, etc.). Configurations involving multiple fuel types may be solved by running a separate STARBUCS case for each type, saving the corresponding CSAS cases generated by STARBUCS that contain the irradiated fuel nuclide compositions, and manually merging the cases in such a way that all required fuel types are represented in the final case.

Input Description

STARBUCS input is divided into different data blocks containing related types of information. The standard composition data block used to define initial (fresh) fuel composition and all other materials in the criticality analysis problem, is read and processed by the material and cross section processing module of SCALE (XSProc) and conforms to the standard input conventions (see Chapter 7 (SECTIONREFERENCE) In addition to the standard composition data, three more input data blocks are required by STARBUCS. The data blocks are entered in the form

READ XXXX    input data   END XXXX

where XXXX is the data block keyword for the type of data being entered. The types of data blocks that are entered include general control parameter information, irradiation history and decay data or search parameter data, and the KENO V.a or KENO-VI input specifications. The valid block keywords for a single criticality safety calculation using burnup credit and for burnup loading curve calculations are listed in Table 9 and Table 10, respectively. A minimum of four characters is required for most keywords. The exception is the criticality model input data block READ KENOVA or READ KENOVI in which case the code must check additional character positions to determine the CSAS control sequence to be executed. The keywords can be up to twelve characters long, the first four of which must be input exactly as listed in the table. Entering the words READ XXXX followed by one or more blanks activates the data block input. All input data pertinent to block XXXX are then entered. Entering END XXXX followed by two or more blanks terminates data block XXXX.

Table 9 Valid data block keywords for a single criticality safety calculation using burnup credit

Data block type

Block keyword

Control parameters

CONTROL

Burnup history

HISTORY or BURNDATA

KENO V.a input

KENOVA or KENO5

KENO-VI input

KENOVI or KENO6

Table 10 Valid data block keywords for burnup loading curve calculations.

Data block type

Block keyword

Control parameters

CONTROL

Search parameters

SEARCH

KENO V.a input

KENOVA or KENO5

All input within a data block is entered using keywords and is free format. Keyword entries may be of variable or array type. Variable keyword entries include the keyword plus the “=”, followed by the value. Array keywords are usually followed by a series of entries, each separated by a blank or comma, and must always be terminated with an END that does not begin in column one. In some instances a single value may be input as an array entry; however, the word END is still always required. Within a given input data block the keyword entries may be in any order.

A single data entry may be entered anywhere on a line but cannot be divided between two lines; however, array data entries may be divided over many lines. The code identifies data keywords using only the first four (maximum) characters in the keyword name. Beyond the first four characters, the user may enter any alphanumeric or special character acceptable in FORTRAN, including single blanks, before the “=” character. Floating-point data may be entered in various forms; for example, the value 12340.0 may be entered as: 12340, 12340.0, 1.234+4, 1.234E+4, 1.234E4, or 1.234E+04. Also, the value 0.012 may be entered as 12E−3, 12−3, 1.2−2, etc. Numeric data must be followed immediately by one or more blanks or a comma.

Overview of input structure

An overview of the input to the STARBUCS sequence is given in Table 11. This table provides an outline of the input data block structure. The input data in positions 1 to 5 (see Table 11) are read and processed by the material and cross section processing module of SCALE (XSProc). These are the first data read by the code and must be in the order indicated. Data positions 6, 7 or 8, and 9 are read directly by STARBUCS and may be entered in any order.

Table 11 Outline of input data for the STARBUCS sequence

Data

position

Type of data

Data entry

Comments

Sequence name

=STARBUCS

Start in column one

1

TITLE

Enter a title

80 characters

2

Standard SCALE pointwise or multigroup cross section library name or

the name of a user-supplied multigroup cross section library

Library name

The currently available standard SCALE cross section libraries are listed in the SCALE Cross Section Libraries chapter, table Standard SCALE Cross-Section Libraries.

STARBUCS allows a non-standard SCALE multigroup cross section library to be used in a criticality calculation.

3

Standard Composition specification data

Enter the appropriate data

Begins this data block with READ COMP and terminate with END COMP. See Standard Composition section for details.

4

Type of calculation

LATTICECELL

Begins this data block with READ CELL and terminates with END CELL. Only regular unit cells may be used. See XSProc section for details.

5

Unit cell geometry specificationa

Enter the appropriate data

Each dimension may be entered as a diameter. See XSProc section for LATTICECELL.

6

Control parameter data

Enter the desired data

Begins this data block with READ CONT and terminate with END CONT. See Conntrol parameter data sec

7b

Burnup history specification

Enter the desired data for each cycle

Begins this data block with READ HISTORY (or BURNDATA) and terminate with END HISTORY (or BURNDATA). See Burnup hist/ ory data sec.

8b

Search parameter data

Enter the desired data

Begins this data block with READ SEARCH and terminate with END SEARCH. See Search para/ meter data sec.

9

KENO data

Enter KENO criticality model

Begins this data block with READ KENOVA (or KENO5) and terminate with END KENOVA (or KENO5).

For KENO-VI use block keyword KENOVI (or KENO6) in place of KENOVA (or KENO5). See Keno Input Data.

Terminate input

END

Must begin in column 1.

a Input data required only for criticality calculations employing multigroup cross section libraries. Only one unit cell may be defined in the cell data block for STARBUCS.

b Either burnup history specification or search parameter data may be defined in a STARBUCS input.

Sequence specification card

The STARBUCS analytical sequence is initiated with “=STARBUCS” beginning in column 1 of the input. This instructs the SCALE driver module to execute the STARBUCS sequence. The input data are then entered in free-format. The input is terminated with the word “END” starting in column 1. An “END” is a special data item, which may be used to delimit an input data block, end an array of input items, and terminate the input for the case. In the context of input data blocks, the “END” has a name or label associated with it. An “END” used to terminate an array of entries must not begin in column 1 as this instructs the SCALE driver to terminate input to the sequence.

Optional sequence parameters

To check the input data, run STARBUCS and specify PARM=CHECK or PARM=CHK after the analytical sequence specification as shown below.

=STARBUCS PARM=CHK

Other optional input for the PARM field to control multigroup resonance self-shielding calculations are described in the XSProc section of this manual.

XSProc

The XSProc is used to read and process the standard composition specification data that define the initial compositions of the fuel and all structural materials in the problem, into mixing tables and unit cell geometry information that are used by STARBUCS. All composition data required for the problem are entered as standard composition entries. A detailed description of this portion of the input can be found in the section on XSProc (Chapter 7 (SECTIONREFERENCE)). Only one UO2 fuel type is permitted in STARBUCS. Therefore, a single fuel mixture defining the fresh fuel composition and, for criticality safety calculations employing multigroup cross sections, the geometry description of a single fuel lattice cell are required in a STARBUCS input file. Only the regular unit cells SQUAREPITCH, TRIANGPITCH, SPHSQUAREP, SPHTRIANGP, and SYMMSLACELL may be specified for the LATTICECELL entry. Outside diameters of the fuel, gap, and clad mixtures (i.e., not the radii) are required.

Control parameter data

The control parameter data block allows the user to specify control parameters and array data related to many of the burnup-credit analysis parameters to be used in the problem. All input is by keyword entry. All keywords are three-character identifiers that must be followed immediately by an equals sign (“=”). The keywords may be in any order within a data block. Input to the parameter data block is initiated with the data block keywords READ CONTROL (only first four characters of block name are required). The data block is terminated by the keywords END CONTROL.

The types of control parameter data that may be input are summarized in Table 2.3.4. The individual keyword entries are described below.

  1. ARP= NAME OF THE ORIGEN LIBRARY TO BE USED. A character string with the name of the ORIGEN library to be used in the depletion calculation. This is a required entry. The library must be defined in the SCALE text file ARPDATA.TXT that contains the cross section library names and interpolation data used by ARP. A description of an ARP input and the location of the ORIGEN cross section libraries are provided in ARP Input Description located in the ORIGEN ARP Module chapter. STARBUCS calculations are limited to UO2 spent fuels.

  2. NAX= NUMBER OF AXIAL ZONES. This is the number of axial-burnup subdivisions. For a user-input profile the value of NAX is determined automatically by the code, and the NAX keyword is optional, provided the AXP= array has been entered. The maximum value of NAX must be chosen such that due product of NAX * NHZ is less than or equal to 100 (i.e., NAX:sub:max is 100, 50, 33, 25, 20, 16, or 14 when the number of horizontal zones is 1, 2, 3, 4, 5, 6, or 7, respectively). By default, the profile is automatically normalized to unity by the code unless NPR=no. Built-in burnup-dependent 18‑axial-zone profiles may be selected with an entry of –18. These built-in profiles and the burnup range over which they are applied, are listed in Table 13. These profiles have been proposed elsewhere (Ref. 2) as bounding axial profiles and are included as options for convenience only. The default value of NAX is –18 (use built-in profiles).

  3. NHZ= NUMBER OF HORIZONTAL ZONES. This is the number of horizontal-burnup subdivisions in the assembly. An optional entry if no horizontal profile is requested. The maximum value is seven zones. The exact limit is determined by the number of mixtures defined in the lattice cell description. If a gap and second moderator type are used the number of horizontal zones is limited to five.

  4. NUC= BURNUP-CREDIT NUCLIDES used in the criticality calculation. A list of actinides and/or fission products that are to be included in the KENO criticality safety calculation. This is an array entry keyword and is delimited by the keyword END. The nuclides are entered using their standard composition alphanumeric names, as listed in the Standard Composition Library chapter of the SCALE manual. Isotopic correction factors may be entered, optionally, immediately following the nuclide name. The isotopic correction factors will be multiplied times the spent fuel nuclide concentrations to account for isotopic composition bias. The concentration of any nuclide that does not have a correction factor is not adjusted. To select all available actinide and fission product nuclides (with cross section data and atom densities greater than 1.0E−29) for the criticality calculation, the user may select NUC= ALL, without an END terminator. This is the only situation where an array entry does not require an END. Note that the set of nuclides tracked by ORIGEN in any decay or irradiation calculation, documented in the ORIGEN Reaction Resource Contents chapter, is much larger than the set of nuclides with available cross sections for neutron transport calculations, documented in the SCALE Cross Section Libraries chapter. Only nuclides with available cross sections for neutron transport calculations are included in the irradiated fuel compositions for criticality calculations.

  5. FLE= FUEL LIGHT ELEMENT NUCLIDES. A user-provided list of light element nuclides that are to be included in the irradiated fuel compositions for a CSAS5 or a CSAS6 calculation. This is an array entry keyword and is delimited by the keyword END. The nuclides are entered using their standard composition alphanumeric names, as listed in Standard Composition Library chapter of the SCALE manual. To select all available light element nuclides (with cross section data and atom densities greater than 1.0E−29) for the criticality calculation, the user may specify FLE= ALL, without an END terminator. This is the only situation where an array entry does not require an END. The use of the keyword FLE is not required if only o-16 is to be included in the composition of irradiated uranium oxide fuel pellets. For these material mixtures, o-16 will be automatically included in irradiated fuel compositions due to its significant concentration. Isotopic correction factors are not allowed for light element nuclides. Note that the set of nuclides tracked by ORIGEN in any decay or irradiation calculation, documented in the ORIGEN Reaction Resource Contents chapter, is much larger than the set of nuclides with available cross sections for neutron transport calculations, documented in the SCALE Cross Section Libraries chapter. Only nuclides with available cross sections for neutron transport calculations are included in the irradiated fuel compositions for criticality calculations.

  6. AXP= AXIAL-BURNUP PROFILE. The user-supplied axial-burnup profile of the assembly to be used in the analysis. This entry is required unless use of the built-in burnup-dependent axial profiles shown in Table 13 is requested (NAX= −18). If NAX is set to anything other than −18, the AXP array must contain NAX entries. Otherwise, the value of NAX is determined automatically by the code. By default (NPR=yes), the profile is automatically normalized by the code; this may be disabled by setting NPR=no. If the burnup profile is normalized, it is implicitly assumed that the height/volume of each axial region is uniform when determining the average fuel burnup (i.e., the burnup of each axial region is equally weighted). The user is cautioned that if fuel region subdivisions of unequal volume are used, normalization should not be applied and the user must ensure a correct correspondence between the axial-profile input and the axial regions specified in the criticality calculation. AXP is an array entry and must be delimited by an END that must not start in the first column.

  7. HZP= HORIZONTAL-BURNUP PROFILE. An optional array entry used to specify a burnup gradient across assemblies. The elements of the array are the ratios of the burnups of horizontal subdivisions in the assembly to average assembly burnup (entry for the POWER= keyword described in Burnup history data). If NHZ is input, the HZP array must contain NHZ entries delimited by an END that must not start in the first column. Otherwise, the value of NHZ is determined automatically by the code. The profile will be normalized if NPR=yes (default). Sample problem 5 illustrates use of this option.

  8. FIX= FIXED ASSEMBLY POWER OPTION. Option to select a constant specific power level for the depletion analysis for all axial and horizontal zones of the assembly. For FIX=yes, the depletion analysis for all zones is performed using the specific power input in the power history data block for the POWER= keyword. The irradiation time is adjusted to achieve the desired burnup. The default of FIX=no applies a variable power for all zones and a constant irradiation time as defined by the BURN= keyword.

  9. NPR= NORMALIZE PROFILE. Option to control whether the user input axial- and horizontal-burnup profiles will be normalized. The input profiles are automatically normalized using NPR=yes (default). If fuel region subdivisions of unequal volume are used, NPR=NO should be specified.

  10. MOD= AXIAL MODERATOR DENSITY. This is an array entry keyword and is delimited by the keyword END. The array dimension is equal to the number of axial zones (NAX entry) and the array values are provided in the same order as the AXP array elements. This input array is required only if the applicable ORIGEN library contains variable moderator density cross sections.

  11. BUG= DEBUG PRINT OPTION. BUG=yes will print program debugging variables and arrays in STARBUCS. The default is BUG=no.

Table 12 Table of control parameter data.

Keyword

name

Data

type

Default

value

Comments

READ CONTROL

Initiate reading the control parameter block of data

ARP=

Character

None

Name of the ORIGEN library to be used. Required. Library must be defined in SCALE text file ARPDATA.TXT.

NAX=

Integer

−18

Number of axial-burnup subdivisions in fuel assembly. The value of NAX is determined automatically if an axial profile is input using AXP= entries. The maximum value of NAX is 100. Default value (−18) applies a built-in 18‑axial-region -burnup profile.

NHZ=

Integer

1

Number of horizontal-burn up subdivisions. Maximum value of 5–7 zones (see Sect. 2.3.4.5). No entry is required if horizontal profile is not used.

NUC=

Character and real mixed arraya

None

List of burnup-credit nuclides, and optionally the corresponding isotopic correction factors, to be included in the criticality calculation.b Array entry generally delimited by END, unless ALL is selected. Nuclides are input using their standard composition alphanumeric identifiers.

FLE=

Character arraya

o-16

List of light element nuclides to be included in the criticality calculation.b Array entry generally delimited by END, unless ALL is selected. Nuclides are input using their standard composition alphanumeric identifiers.

AXP=

Real arraya

See NAX

Axial-burnup-pr ofile array. Required if NAX > 0. NAX entries that define the axial-burnup shape. The profile is automatically normalized if NPR=YES (default). Delimited by END.

HZP=

Real arraya

None

Horizontal-burn up-profile array. Required if NHZ > 1. Array containin g NHZ entries that define the horizontal, or radial, burnup profile for the analysis. Array is automatically normalized by the code. Delimited by END.

MOD=

Real arraya

None

Axial-moderator density, applied in the fuel depletion analysis. Note that MOD= is required only if the ORIGEN library contains variable moderator density cross sections. NAX entries ordered as AXP= array. Delimited by END. Moderator density default values are not available in STARBUCS for variable moderator density cross sections.

FIX=

Character

No

Option to select a constant specific power level for all axial and horizontal zones of the assembly using FIX=yes.

NPR=

Character

Yes

Option to normalize user-input axial- and horizontal-burn up profiles. Default is to automatically normalize profiles.

BUG=

Character

No

Optional debug printout with BUG=yes.

END CONTROL

End of the control parameter block of data

a Termina

te array data entries with end. Do not place this end in column 1.

b Note th

at the set of nuclides tracked by ORIGEN in any decay or irradiation calculation, documented in the ORIGEN Reaction Resource Contents chapter, is much larger than the set of nuclides with available cross sections for neutron transport calculations, documented in the SCALE Cross Section Libraries chapter. Only nuclides with available cross sections for neutron transport calculations are included in the irradiated fuel compositions for criticality calculations.

Table 13 Built-in burnup-dependent axial profiles, NAX= 18 from [LFKR98])

Axial

zone no.

Fraction of

core height

Burnup < 18 GWd/MT U

18 ≤ Burnup < 30 GWd/MT U

Burnup ≥ 30 GWd/MT U

1

2

3

1

0.0278

0.649

0.668

0.652

2

0.0833

1.044

1.034

0.967

3

0.1389

1.208

1.150

1.074

4

0.1944

1.215

1.094

1.103

5

0.2500

1.214

1.053

1.108

6

0.3056

1.208

1.048

1.106

7

0.3611

1.197

1.064

1.102

8

0.4167

1.189

1.095

1.097

9

0.4722

1.188

1.121

1.094

10

0.5278

1.192

1.135

1.094

11

0.5833

1.195

1.140

1.095

12

0.6389

1.190

1.138

1.096

13

0.6944

1.156

1.130

1.095

14

0.7500

1.022

1.106

1.086

15

0.8056

0.756

1.049

1.059

16

0.8611

0.614

0.933

0.971

17

0.9167

0.481

0.669

0.738

18

0.9722

0.284

0.373

0.462

Burnup history data

The burnup history data block defines the irradiation history for the assembly. These data are entered by keyword. The keywords are summarized in Table 14. Only the first four characters of the keywords are required (i.e., any characters after the first four characters are optional). A minimum of two entries are required for each cycle, (1) the average assembly power (POWER=) and (2) the irradiation time (BURN=). The decay time (DOWN=), if any, at the end of the cycle, and the number of cross section libraries (NLIB=) are optional. The word END is required to delimit the entries for each cycle. The entries within a given cycle may be in any order.

The burnup history data block reading is initiated with the keywords READ HISTORY (or BURNDATA) and terminated by END HISTORY (or BURNDATA).

POWER= The average specific power of the assembly for this cycle. The units of the specific power are in MW/MTU (W/g) of initial uranium. The axial and horizontal profiles are multiplied by the specific power to achieve the desired spatially-dependent burnup profiles for the assembly when FIX=NO (default). If FIX=YES, the specific power input using this keyword is assumed to be uniform over all fuel regions (axial and horizontal) and the code will adjust the irradiation time to obtain the desired burnup for each region.

BURN= THE IRRADIATION TIME FOR THIS CYCLE. The cycle irradiation time in days.

DOWN= CYCLE DOWN TIME. An optional entry to specify the down time, in days, at the end of an irradiation cycle. The down time is simulated as an irradiation time step of effectively zero power after the irradiation cycle. The down time for the last cycle is simulated as a separate ORIGEN decay case with nine equally-spaced time steps. If a negative down time is input, the time steps are spaced logarithmically.

NLIB= LIBRARIES PER CYCLE. An optional entry to request multiple cross section libraries during a depletion cycle. If requested, the code automatically subdivides the cycle in NLIB segments of uniform duration and generates a separate library for the depletion analysis for each segment using ARP. Generating multiple libraries provides a more accurate representation of the time-dependent cross section variation during the burnup analysis. Each segment of the cycle is assumed to have the same specific power, and no down time is assumed between each segment of the cycle.

END The word END is required to terminate the input for each cycle.

Repeat the above entries for each cycle to define the complete assembly power history.

Table 14 Table of power history data.

Keyword

name

Data

type

Default

value

Comments

READ HISTORY (or BURNDATA)a

Start of burnup history data block

POWER=

Real variable

None

Average assembly power for this cycle (MW/MTU)

BURN=

Real variable

None

Cycle irradiation time (days)

DOWN=

Real variable

0

End-of-cycle decay time (days). Optional. A negative down time may be used to select logarithmic decay time intervals for the last decay case.

NLIB/CYCLE=

Integer variable

1

Number of libraries to be applied in this cycle. Optional. If multiple libraries are requested for this cycle, the cycle is subdivided into equal time segments, and an updated library is generated for each segment. No down time is simulated between segments.

END

Required. Defines the end of the data for the current cycle. Repeat the above entries for each cycle in the irradiation history. An END, not to begin in column 1, must terminate each cycle definition.

END HISTORY (or BURNDATA)a

End block

a Only the first four characters are required, i.e., HIST (or BURN).

Search parameter data

The search parameter data block defines input data for burnup loading curve analyses for commercial UO2 spent fuels. Burnup history input data are not allowed in an input file that supplies search parameters. A burnup history data block is generated in STARBUCS for subsequent iterative calculations using the initial user-supplied search parameter data. STARBUCS sample problem starbucs1.input contains a search data block to request burnup loading curve analyses for spent fuel at various burnups. The search data block reading is initiated with the keywords READ SEARCH and terminated by END SEARCH. The keywords are summarized in Table 15. These keywords may be in any order.

USL= THE UPPER SUBCRITICAL LIMIT FOR BURNUP LOADING.

EPS= TOLERANCE ON CONVERGENCE. The convergence criterion used in the search for initial fuel enrichment so that user-specified keff value is within USL ± EPS. The tolerance value must be greater that the standard deviation of the calculated keff for the solution to converge.

ITMAX= MAXIMUM ITERATIONS ALLOWED FOR EACH ENRICHMENT SEARCH. The search for initial fuel enrichment stops when the number of iterations exceeds this parameter and a warning message is provided to the user.

ECL= LOWER ENRICHMENT CONSTRAINT. The unit for this parameter is wt% 235U. The lower enrichment constraint must be within the enrichment interval used in the ORIGEN library specified in READ CONTROL data block.

ECH= UPPER ENRICHMENT CONSTRAINT. The unit for this parameter is wt% 235U. The upper enrichment constraint must be within the enrichment interval used in the ORIGEN library specified in READ CONTROL data block.

BU= ARRAY OF REQUESTED BURNUP VALUES (GWd/MTU). The word END is required to terminate this array. The user inputs a series of discharge burnup values for which the initial fuel enrichments that result in a desired keff value (USL ± EPS) are to be determined.

AVGBU= AVERAGE BURNUP PER CYCLE (GWd/MTU). An optional entry used to determine the number of irradiation cycles as the ratio of a burnup value in the BU array to AVGBU.

POWER= The average specific power of the assembly. The units of the specific power are in MW/MTU (W/g) of initial uranium. This entry has the same function as the entry for POWER= keyword in the HISTORY data block (see Burnup history data). It is also used to determine cycle irradiation time as the ratio of a burnup value in the BU array to average assembly power.

FDT= FRACTIONAL DOWNTIME. An optional entry used to determine down time between irradiation cycles (the entry for DOWN= keyword in the HISTORY data block) if fuel irradiation requires two or more cycles. For example, for a cycle with 365 days of irradiation followed by a 30-day downtime, FDT = 30 / 395 = 0.07595. STARBUCS uses the user-provided FDT to compute cycle downtime as the irradiation time per cycle multiplied by FDT and divided by (1-FDT).

DEC= DECAY TIME AFTER IRRADIATION. An optional entry to specify the decay time, in days, after fuel discharge. A negative value may be used to select logarithmic decay time intervals.

NLIB= NUMBER OF LIBRARIES PER CYCLE. An optional entry to request multiple cross section libraries during a depletion cycle. Generating multiple libraries provides a more accurate representation of the time-dependent cross section variation during the burnup analysis. Each segment of the cycle is assumed to have the same specific power.

FFE= FRESH FUEL ENRICHMENT. The purpose of this option is to help in reducing the total number of iterations needed to achieve convergence. There are two options implemented in STARBUCS for the fresh fuel enrichment value to be used in the first inner iterations over fuel enrichment, FFE=SEARCH (default) and FFE=INPUT. With the default option (FFE=SEARCH), the lower enrichment bound and the starting fresh fuel enrichment at the beginning of a search are adjusted based on the results of the previous outer iteration over burnup. The procedure includes the following steps. First, the user requested burnup values are sorted in ascending order so that STARBUCS outer iterations over burnup proceed from the lowest to the highest burnup value. Then, the initial fresh fuel for the lowest burnup is changed to the mid-value of the enrichment interval, (ECL+ECU)/2, and the search for the fresh fuel enrichment corresponding to the lowest burnup is initiated and completed. Suppose that a solution for this burnup step exists. This solution becomes the lower enrichment constraint (ECL) in the search passes for the next burnup value and the initial fresh fuel enrichment is chosen as the middle point of the enrichment interval. The procedure is applied for the entire set of the requested burnups. The average number of iterations for each burnup step with this option is approximately 4. The alternate option (FFE=INPUT) starts a search for fuel enrichment with the user supplied fresh fuel enrichment.

Table 15 Table of search data.

Keyword

Name

Data

type

Default

value

Comments

READ SEARCHa

Initiate reading the search block of data.

USL=

Real

1.0

Upper subcritical limit.

EPS=

Real

0.005

Tolerance on convergence.

ITMAX=

Integer

10

Iteration limit.

ECL=

Real

1.5

Lower initial fuel enrichment constraint (U-235 wt%).

ECH=

Real

5.0

Upper initial fuel enrichment constraint (U-235 wt%).

BU

Realb

None

Array entry of requested burnup values (GWd/MTU).c

AVGBU=

Real

20.0

Average burnup per cycle.

POWER=

Real

25.0

Average specific power (W/g).

FDT=

Real

0.2

Fractional downtime.

DEC=

Real

1825.0

Decay time (days).

NLIB=

Integer

2

Libraries per cycle.

FFE=

Character

SEARCH

Fresh fuel option. FFE=INPUT starts the outer iterations over the burnup values with user supplied fresh fuel composition. FFE=SEARCH helps in reducing the number of search passes (approximately 4 in average).

END SEARCH

End of the search data

a Only the first four characters are required.

b Terminate array data entries with end. Do not place this end in column 1.

c There are no restraints on the maximum number of the burnup values requested in burnup loading curve calculations. A user may consider computer time and resources in assessing the maximum number of burnup values in this array.

KENO input data

The KENO input for the problem is specified in the KENO data block. Input to the data block is initiated with the data block keywords READ KENO or READ KENOVA and is terminated by the keywords END KENO or END KENOVA for criticality calculations using KENO V.a. Input to the data block is initiated with the data block keywords READ KENOVI or READ KENO6 and is terminated by the keywords END KENOVI or END KENO6 for criticality calculations using KENO VI. STARBUCS performs no error checking of the KENO input. The data within the data block delimiters is copied, without change, to the CSAS input file and executed. The user is therefore advised to ensure that the KENO input is free of errors by first running the case within CSAS5 or CSAS6 before applying the input in STARBUCS.

The input requirements for KENO V.a and KENO-VI are not described in this section, but are described in detail in the KENO chapter of this manual. This section describes only the input requirements as related to the execution of KENO within STARBUCS and the conventions used for module compatibility.

The mixture numbers for each of the non-fuel materials applied to the material regions of the KENO model are defined as the mixture numbers (MX) specified in the standard composition input. STARBUCS automatically defines the MIXTURE ID for each of the fuel regions according to the axial and/or horizontal zones defined by the NAX and NHZ entries in the burnup-profile arrays. The first axial-zone mixture is assigned MX=101, and is incremented by one for each additional axial zone. Therefore, in a problem that defines 18 axial zones, spent fuel mixtures will be generated with identifiers that range from 101 to 118. The correspondence of these mixtures to the assembly locations is determined by the ordering of the AXP= input array that defines the axial-burnup profile for the assembly. If the AXP= array orders the burnup profile from the bottom of the assembly to the top of the assembly, the resulting MX=101 will correspond to the bottom axial-zone segment, and MX=118 would correspond to the top axial zone. If multiple horizontal zones are defined, then the numbering sequence of the second horizontal zone will start at MX=201 and, in the example given here, would range up to MX=218. Refer to Capabilities and Limitations for limitations in the mixture-numbering scheme. The mixture-numbering scheme is illustrated in Fig. 19.

Sample problems

A series of example problems are presented to illustrate the application of STARBUCS to burnup-credit criticality safety and burnup loading curve analyses. Sample problem 1 is a simple pin-cell problem for burnup loading curve iterative calculations. The fuel pin contains a single axial-burnup zone (i.e., uniform-axial burnup). It is useful to illustrate the main features of the system and demonstrate functionality of the system modules within SCALE. Problem 2 illustrates the same problem with 18-axial burnup-dependent zones. Problem 3 extends the pin-cell model to an array of spent fuel assemblies residing in a water-filled pool. The models apply 18-axial-burnup-dependent zones. Problem 4 is a generic cask model, and this problem exercises more of the burnup credit options available in STARBUCS. Problem 5 illustrates the use of the horizontal-burnup option for a simple 4 × 4 array of spent fuel assemblies residing in water. Sample problem 6 uses KENO-VI to model a hexagonal VVER‑440 fuel assembly.

Sample problem 1

Sample problem 1, listed in Listing 1, defines a simple infinite UO2 pin-cell model with uniform-axial burnup for burnup loading curve calculations. The initial fuel enrichment is 2.0 wt %. The control parameter data block specifies that the standard Westinghouse (W) 17 × 17 ORIGEN library is to be used for the depletion analysis. The burnup-credit criticality calculation uses a subset of the major actinides as defined in the NUC= array. The sample problem contains a “read search” data block, which provides an upper limit for subcriticality, usl, a tolerance value for the search algorithm, eps, the lower and upper enrichment bounds, ecl and ech, respectively, the maximum number of iterations for each burnup value requested, imaxl, average specific power in W/g, power, decay time after irradiation in days, dec, number of libraries per cycle, nlib, average burnup per cycle in GWd/MTU, avgbu, fractional downtime, fdt, and a set of burnup values, bu array.

Sample problem 2

Sample problem 2, listed in Listing 2, illustrates a simple pin-cell model using 18-axial-burnup-dependent zones. In this example, the built-in axial profiles for three burnup ranges are applied using the NAX= −18 option (see profiles in Table 13). STARBUCS determines the average assembly burnup from the power history data input, and automatically selects the appropriate profile based on the discharge assembly burnup. The axial-profile data were developed for a predefined axial-zoning structure (i.e., fraction of the assembly height). It is important that the KENO V.a geometry model therefore also reflect this axial-zone structure. That is, the height of each axial zone in the criticality model must conform to the axial zones for the profile applied in the analysis. In this example, the total pin height is 365.7 cm (144 in.), which is subdivided into 18 equal-height segments of 20.32 cm each.

The burnup-dependent cross sections generated for the criticality analysis have material identifiers ranging from 101 (bottom) to 118 (top). There is no constraint on how the fuel materials can be applied in the KENO V.a model. For example, the order of the material numbers could easily be reversed, which would effectively invert the profile and could be used to simulate an assembly loaded upside down. It is also not necessary to use all of the materials in the problem. For instance, all fuel regions in the KENO V.a model could be assigned the same fuel mixture number to represent a flat axial profile having a burnup value equal to that of the particular mixture used. The average assembly burnup would also be equal to that of the particular mixture used, and not that defined by the power history data block.

Listing 1 STARBUCS input listing for sample problem 1
    =starbucs
   PWR 17x17 Fuel Assembly - uniform axial burnup rods
  v7-238
  read comp
  ' UO2 Fuel 2.0 wt% u-235
   uo2    1 den=10.96 0.95 293.0 92235 2.0 92238 98.0 end
  'Zircalloy
   zirc4  2  1  end
  'Water
   h2o    3  1  end
  'Gap
   n 4 den=0.00125 1 end
  end comp
  read celldata
   latticecell squarepitch  pitch=1.259 3 fueld=0.805 1 cladd=0.95 2 gapd=0.822 4 end
  end celldata
  ' Enter burnup credit control parameters
  read control
   arp=w17x17
   axp= 1 end
   nuc= u-234 u-235 u-236 u-238 pu-238 pu-239 pu-240
        pu-241 pu-242 am-241 am-242m am-243 np-237 end
   fle=all
  end control
  read search
    usl=0.96
    eps=0.002
    ecl=1.51
    ech=4.99
    itmax=10
    power=60.0
    dec=1826.25
    nlib=2
    avgbu=20
    fdt=0.2
    ffe=input
    bu= 10 50 70  end
  end search
  read kenova
  ' infinite pin cell lattice
  '
  '**************************************
  '* materials
  '* 101 = uo2, uniform axial region
  '* 2 = Zircaloy
  '* 3 = Water
  '* 4 = Gap
  '**************************************
  read param tme=10000 gen=510 nsk=10 npg=1000 end param
  read geom
  '           Fuel Pin
  global unit 1
   cylinder   101  1   0.4025  50.0  -50.0
   cylinder   4    1   0.4110  50.0  -50.0
   cylinder   2    1   0.4750  50.0  -50.0
   cuboid     3    1 4p0.6295  50.0  -50.0
  '
  end geom
  read bounds  all=reflect  end bounds
  end data
  end kenova
  end
Listing 2 STARBUCS input listing for sample problem 2
=starbucs
 PWR 17x17 Fuel Assembly - 18-zone axial burnup profile
v7-238
read comp
' UO2 Fuel 2.0 wt% u-235
 uo2    1 den=10.96 0.95 293.0 92235 2.0 92238 98.0 end
'Zircalloy
 zirc4  2  1  end
'Water
 h2o    3  1  end
'Gap
 n 4 den=0.00125 1 end
end comp
read celldata
 latticecell squarepitch  pitch=1.259 3 fueld=0.805 1 cladd=0.95 2 gapd=0.822 4 end
end celldata
' Enter burnup credit control parameters
read control
arp=w17x17  nax=-18
nuc= u-234 u-235 u-236 u-238 pu-238 pu-240
    pu-241 pu-242 am-241 am-242m am-243 np-237 end
fle=o-16 h-1 end
end control
read hist
  power=35.001 burn=100 nlib=1 end
  power=28.5   burn=230 down=100 nlib=2 end
  power=24.001 burn=300 nlib=2 down=1826 end
end hist
read kenova
'**************************************
'* materials
'* 101-118 = uo2, 18-axial zone model
'* 2 = Zircaloy
'* 3 = Water
'* 4 = Gap
'**************************************
read param  tme=10000 gen=510 nsk=10 npg=1000 end param
read geom
'           Fuel Pin
global unit 1
 cylinder   101  1  0.4025 -162.53  -182.85
 cylinder   102  1  0.4025 -142.22  -182.85
 cylinder   103  1  0.4025 -121.90  -182.85
 cylinder   104  1  0.4025 -101.58  -182.85
 cylinder   105  1  0.4025  -81.27  -182.85
 cylinder   106  1  0.4025  -60.95  -182.85
 cylinder   107  1  0.4025  -40.63  -182.85
 cylinder   108  1  0.4025  -20.32  -182.85
 cylinder   109  1  0.4025    0.00  -182.85
 cylinder   110  1  0.4025   20.32  -182.85
 cylinder   111  1  0.4025   40.63  -182.85
 cylinder   112  1  0.4025   60.95  -182.85
 cylinder   113  1  0.4025   81.27  -182.85
 cylinder   114  1  0.4025  101.58  -182.85
 cylinder   115  1  0.4025  121.90  -182.85
 cylinder   116  1  0.4025  142.22  -182.85
 cylinder   117  1  0.4025  162.53  -182.85
 cylinder   118  1  0.4025  182.85  -182.85
 cylinder   4    1  0.4110  182.85  -182.85
 cylinder   2    1  0.4750  182.85  -182.85
 cuboid     3    1 4p0.6295 182.85  -182.85
'
end geom
read bounds  all=reflect  end bounds
end data
end kenova
end

Sample problem 3

Sample problem 3, listed in Listing 3, performs a burnup-credit criticality safety calculation using the SCALE 238-group ENDF/B-VII cross section library (V7-238) for an array of Combustion Engineering (CE) 14 × 14 spent fuel assemblies in water. A subset of burnup-credit actinides and fission products are included in the criticality calculation. A user-supplied 18-axial-region-burnup profile of the assemblies is input. This profile was obtained from the axial-burnup-profile database [Cac00] for Maine Yankee assembly N863. Note that the axial profile will be normalized automatically by the code using NPR=yes (default). The normalization is performed such that the average value of the profile values is unity (i.e., the sum of the profile values is equal to the number of axial zones). The 3.3 wt % enriched UO2 fuel is assumed to achieve a discharge burnup of 37,626 MWd/MTU in three cycles of approximately 12.5 GWd/MTU per cycle and a downtime per cycle of 80 days, followed by a cooling time of 5 years after discharge (1826 days). An average assembly power level of 32 MW/MTU is used for the depletion calculation. Two libraries per cycle are requested during the depletion. Note that by increasing the number of libraries generated per cycle, the cross sections used in the burnup analysis are updated more frequently to reflect the changes that occur with burnup. The nominal CE 14 × 14 assembly design specifications were obtained from [DH96]. The assembly pitch in the criticality calculations is 22.78 cm. A cross section view of the assembly geometry, a 2 × 8 array of water reflected assemblies, is illustrated in Fig. 21.

Listing 3 STARBUCS input listing for sample problem
  =starbucs
CE 14x14 assembly 2 x 8 array
V7-238
read comp
' UO2 Fuel 3.3 wt% u235
uo2  1 den=10.045 1 273 92234 0.0294 92235 3.3 92236 0.0152 92238 96.6554 end
'Zircalloy
 zirc4 2  1  end
'Water
 h2o    3  1  end
end comp
read celldata
 latticecell squarepitch  pitch=1.473 3 fueld=0.968 1
                          cladd=1.118 2  gapd=0.985 0  end
end celldata
read control
arp=ce14x14 nax=18
axp=
  0.67053 0.93322 1.02433 1.05329 1.06026 1.06185
  1.06215 1.06249 1.06312 1.06408 1.06541 1.06702
  1.06836 1.06760 1.05918 1.02515 0.92262 0.66935 end
nuc=
  u-234  u-235  u-236  u-238  pu-238 pu-239 pu-240
  pu-241 pu-242 am-241 np-237
  mo-95  tc-99  ru-101 rh-103 ag-109 cs-133 nd-143
  nd-145 sm-147 sm-149 sm-150 sm-151 eu-151 sm-152
  eu-153 gd-155 end
end control
read hist
  power=32.00  burn=391.937 nlib=2 down=80  end
  power=32.00  burn=391.937 nlib=2 down=80  end
  power=32.00  burn=391.937 nlib=2 down=1826 end
end hist
read keno
'
'******************************************
'* materials
'* 101 = uo2, lower axial region (0.67053)
'* 118 = uo2, upper axial region (0.66935)
'* 2 = Zircaloy
'* 3 = Water
'******************************************
read param
 tme=10000 gen=510 nsk=10 npg=1000
end param
read geom
'  Fuel Pin
unit           1
 cylinder   101  1  0.484 -162.53  -182.85
 cylinder   102  1  0.484 -142.22  -182.85
 cylinder   103  1  0.484 -121.90  -182.85
 cylinder   104  1  0.484 -101.58  -182.85
 cylinder   105  1  0.484  -81.27  -182.85
 cylinder   106  1  0.484  -60.95  -182.85
 cylinder   107  1  0.484  -40.63  -182.85
 cylinder   108  1  0.484  -20.32  -182.85
 cylinder   109  1  0.484    0.00  -182.85
 cylinder   110  1  0.484   20.32  -182.85
 cylinder   111  1  0.484   40.63  -182.85
 cylinder   112  1  0.484   60.95  -182.85
 cylinder   113  1  0.484   81.27  -182.85
 cylinder   114  1  0.484  101.58  -182.85
 cylinder   115  1  0.484  121.90  -182.85
 cylinder   116  1  0.484  142.22  -182.85
 cylinder   117  1  0.484  162.53  -182.85
 cylinder   118  1  0.484  182.85  -182.85
 cylinder   0    1  0.4925 182.85  -182.85
 cylinder   2    1  0.559  182.85  -182.85
 cuboid     3    1 4p0.7365 182.85  -182.85
'
'  2 x 2 Array of Fuel Pins
unit           2
 array 1 3*0
'
'  Large Water Hole
unit           3
 cylinder   3    1  1.3140  182.85  -182.85
 cylinder   2    1  1.4160  182.85  -182.85
 cuboid     3    1 4p1.473  182.85  -182.85
'
'  Assembly Unit
unit           4
 array      2 -10.311 -10.3124 -182.85
 cuboid     3    1 4p11.390  182.85  -182.85
'
'  Assembly Array (2x8)
global
unit           5
 array      3  3*0
 reflector  3  1 6r30.0  1
end geom
read array
ara=1  nux=2  nuy=2  nuz=1 fill
  1 1
  1 1  end fill
ara=2  nux=7  nuy=7  nuz=1 fill
  2 2 2 2 2 2 2
  2 3 2 2 2 3 2
  2 2 2 2 2 2 2
  2 2 2 3 2 2 2
  2 2 2 2 2 2 2
  2 3 2 2 2 3 2
  2 2 2 2 2 2 2  end fill
ara=3  nux=2  nuy=8  nuz=1 fill
  16r4  end fill
end array
read bounds  all=void  end bounds
end data
end keno
end
_images/fig514.png

Fig. 21 Plot of the CE 14 × 14 assembly array geometry in sample problem 3.

Sample problem 4

Sample problem 4, listed in Listing 4, illustrates the application of STARBUCS for a criticality safety analysis of a burnup-credit cask. The cask geometry in this example is based on a 32-assembly generic burnup-credit cask model and is illustrated in Fig. 22.

The assemblies are assumed to be W 17 × 17 OFA assemblies with an initial enrichment of 4.98 wt %. The standard composition description for this problem includes the fuel assembly and all cask structural material definitions. The analysis applies built-in 18-axial-zone profiles, and actinide-only burnup credit (i.e., only a subset of actinides and no fission products). The assembly is irradiated to an average burnup of about 50 GWd/MTU. The axial-burnup profile is automatically selected by the code based on the average assembly burnup. Isotopic correction factors are applied to the calculated actinide inventories. The correction factors were obtained from Ref. 4. An axial-moderator density is also applied. Note that actual entries in the MOD= array are not realistic for a PWR and are only intended to illustrate the use of this feature. Since the ORIGEN library applied in this calculation does not have variable moderator density, the values in the MOD= array have no effect on the calculation. The criticality evaluation of the cask is performed following a cooling time of 1826 days (5 years).

_images/fig610.png

Fig. 22 Cutaway view of the generic 32-assembly burnup-credit cask showing the cask bottom half with a quarter of the model removed.

Listing 4 STARBUCS input listing for sample problem 4
=starbucs
 PWR 18-axial zone W17x17 assembly, GBC-32 assembly cask model
v7-238
read comp
' UO2 Fuel Rod 4.98 wt % u235
 uo2    1 den=10.96 0.95 293.0 92235 4.98 92238 95.02 end
'Zircalloy
 zirc2  2  1  end
'Water
 h2o    3  1  end
'Stainless Steel
 ss304  4  1  end
' BORAL Center - B-10 loading of 0.0225 g/cm3
 b-10   5  0  6.5795E-03   293.0  end
 b-11   5  0  2.7260E-02   293.0  end
 c      5  0  8.4547E-03   293.0  end
 al     5  0  4.1795E-02   293.0  end
'Stainless Steel
 ss304  6  1  end
' aluminum
 al     7  0  0.0602       293.0  end
end comp
read celldata
 latticecell squarepitch  pitch=1.2598 3 fueld=0.7844 1 cladd=0.9144 2 gapd=0.8001 0 end
end celldata
read control
 arp=w17x17_ofa nax=-18
 nuc= u-234 0.635
      u-235 1.085
      u-236 0.910
      u-238 0.992
     pu-238 0.856
     pu-239 1.076
     pu-240 0.945
     pu-241 1.087
     pu-242 0.848
     am-241 0.609
     am-243 0.804
     np-237 0.697 end
mod= 0.720 0.709 0.699 0.688 0.678 0.667 0.657
     0.646 0.635 0.625 0.614 0.604 0.593 0.583
     0.572 0.562 0.551 0.540 end
end control
read hist
 power=32.89 burn=100 end
 power=32.89 burn=200 end
 power=32.89 burn=900 nlib=3 end
 power=32.89 burn=320 down=-1826 end
end hist

read kenova
'**************************************
'* Assembly Type: Westinghouse 17x17 OFA/V5
'* Materials
'* 101 - 118 = uo2, axial regions 1 through 18
'* 2 = Zircaloy
'* 3 = Water
'* 4 = Stainless Steel
'* 5 = Boral
'* 6 = Stainless Steel
'* 7 = Al

'**************************************
read param tme=10000 gen=510 nsk=10 npg=1000 end param

read geom
unit 1
com='Fuel Pin'
 cylinder   101  1  0.3922 -162.53  -182.85
 cylinder   102  1  0.3922 -142.22  -182.85
 cylinder   103  1  0.3922 -121.90  -182.85
 cylinder   104  1  0.3922 -101.58  -182.85
 cylinder   105  1  0.3922  -81.27  -182.85
 cylinder   106  1  0.3922  -60.95  -182.85
 cylinder   107  1  0.3922  -40.63  -182.85
 cylinder   108  1  0.3922  -20.32  -182.85
 cylinder   109  1  0.3922    0.00  -182.85
 cylinder   110  1  0.3922   20.32  -182.85
 cylinder   111  1  0.3922   40.63  -182.85
 cylinder   112  1  0.3922   60.95  -182.85
 cylinder   113  1  0.3922   81.27  -182.85
 cylinder   114  1  0.3922  101.58  -182.85
 cylinder   115  1  0.3922  121.90  -182.85
 cylinder   116  1  0.3922  142.22  -182.85
 cylinder   117  1  0.3922  162.53  -182.85
 cylinder   118  1  0.3922  182.85  -182.85
 cylinder   0    1  0.40005  182.85  -182.85
 cylinder   2    1  0.4572  182.85  -182.85
 cuboid     3    1  2p0.6299  2p0.6299  182.88  -182.88

unit 2
com='Guide Thimble/Instrument Tube'
 cylinder 3 1 0.56135  365.76  0
 cylinder 2 1 0.602    365.76  0
 cuboid   3 1  0.6299  -0.6299  0.6299  -0.6299  365.76  0

unit 4
com='Top Half Horizontal Boral Panel'
cuboid          7  1  9.5250   -9.5250     0.02540   0.0       365.76   0.
cuboid          5  1  9.5250   -9.5250     0.12827   0.0       365.76   0.
cuboid          3  1  11.75   -11.75       0.12827   0         365.76   0

unit 5
com='Right-Hand Side Half Vertical Boral Panel'
cuboid          7  1  0.02540   0.0       9.5250   -9.5250     365.76   0.
cuboid          5  1  0.128270  0.0       9.5250   -9.5250     365.76   0.
cuboid          3  1  0.12827    0       11.75    -11.75       365.76   0

unit 6
com='Bottom Half Horizontal Boral Panel'
cuboid          7  1  9.5250   -9.5250     0.0     -0.0254      365.76   0.
cuboid          5  1  9.5250   -9.5250     0.0     -0.12827     365.76   0.
cuboid          3  1  11.75   -11.75       0.0     -0.12827     365.76   0

unit 7
com='Left-Hand Side Half Vertical Boral Panel'
cuboid          7  1   0.0     -0.0254     9.5250   -9.5250     365.76   0.
cuboid          5  1   0.0     -0.12827    9.5250   -9.5250     365.76   0.
cuboid          3  1   0.0     -0.12827   11.75    -11.75       365.76   0

unit 8
com='Empty Corner (Water)'
cuboid          3  1   0.12827   0       0.12827      0         365.76  0

unit 10
com='Top Boral/Basket Plate with water added to fit array dimensions'
cuboid          5  1   9.525    -9.525     -0.7754  -0.87827    365.76  0
cuboid          7  1   9.525    -9.525     -0.75    -0.87827    365.76  0
cuboid          3  1  11.7500  -11.75      -0.75    -0.87827    365.76  0.
cuboid          4  1  11.7500  -11.75       0.0     -0.87827    365.76  0.
cuboid          3  1  11.87827 -11.87827    0.12827 -0.87827    365.76  0

unit 11
com='Bottom Boral/Basket Plate with water added to fit array dimensions'
cuboid          5  1   9.525    -9.525     0.87827   0.7754     365.76  0
cuboid          7  1   9.525    -9.525     0.87827   0.75       365.76  0
cuboid          3  1  11.7500  -11.75      0.87827   0.75       365.76  0.
cuboid          4  1  11.7500  -11.75      0.87827   0.0        365.76  0.
cuboid          3  1  11.87827 -11.87827   0.87827  -0.12827    365.76  0

unit 12
com='Left-Hand Side Boral/Basket Plate with water added to fit array dimensions'
cuboid          5  1   0.87827   0.7754     9.525    -9.525     365.76  0
cuboid          7  1   0.87827   0.75       9.525    -9.525     365.76  0
cuboid          3  1   0.87827   0.75      11.75    -11.75      365.76  0.
cuboid          4  1   0.87827   0.0       11.75    -11.75      365.76  0.
cuboid          3  1   0.87827  -0.12827   11.87827 -11.87827   365.76  0.

unit 13
com='Right-Hand Side Boral/Basket Plate with water added to fit array dimensions'
cuboid          5  1  -0.7754   -0.87827     9.525    -9.525    365.76  0
cuboid          7  1  -0.75     -0.87827     9.525    -9.525    365.76  0
cuboid          3  1  -0.75     -0.87827    11.75    -11.75     365.76  0.
cuboid          4  1   0.0      -0.87827    11.75    -11.75     365.76  0.
cuboid          3  1   0.12827  -0.87827    11.87827 -11.87827  365.76  0

unit 20
com='Top Boral/Basket Plate'
cuboid          5  1   9.525    -9.525     -0.7754  -0.87827    365.76  0
cuboid          7  1   9.525    -9.525     -0.75    -0.87827    365.76  0
cuboid          3  1  11.7500  -11.75      -0.75    -0.87827    365.76  0.
cuboid          4  1  11.7500  -11.75       0.0     -0.87827    365.76  0.

unit 21
com='Bottom Boral/Basket Plate'
cuboid          5  1   9.525    -9.525     0.87827   0.7754     365.76  0
cuboid          7  1   9.525    -9.525     0.87827   0.75       365.76  0
cuboid          3  1  11.7500  -11.75      0.87827   0.75       365.76  0.
cuboid          4  1  11.7500  -11.75      0.87827   0.0        365.76  0.

unit 22
com='Left-Hand Side Boral/Basket Plate'
cuboid          5  1   0.87827   0.7754     9.525    -9.525     365.76  0
cuboid          7  1   0.87827   0.75       9.525    -9.525     365.76  0
cuboid          3  1   0.87827   0.75      10.9999  -10.9999    365.76  0.
cuboid          4  1   0.87827   0.0       10.9999  -10.9999    365.76  0.

unit 23
com='Right-Hand Side Boral/Basket Plate'
cuboid          5  1  -0.7754   -0.87827     9.525    -9.525    365.76  0
cuboid          7  1  -0.75     -0.87827     9.525    -9.525    365.76  0
cuboid          3  1  -0.75     -0.87827    10.9999  -10.9999   365.76  0.
cuboid          4  1   0.0      -0.87827    10.9999  -10.9999   365.76  0.


unit 100
com='17x17 Fuel Assembly in Basket'
 array 1 -10.7083  -10.7083  0
 cuboid 3 1  11  -11  11  -11  365.76  0
 cuboid 0 1  11  -11  11  -11  365.76  0
 cuboid 4 1  11.75  -11.75  11.75  -11.75  365.76  0

unit 101
com='17x17 Fuel Assembly in Basket with Half Boral Panels'
  array 2 0  0  0

unit 112
com='Top Row of Fuel Assemblies'
  array 12  -47.51308  -12.38154   0
unit 113
com='Left Row of Fuel Assemblies'
  array 13  -12.38154   -47.51308  0

unit 114
com='Bottom Row of Fuel Assemblies'
  array 14  -47.51308  -12.38154   0

unit 115
com='Right Row of Fuel Assemblies'
  array 15  -12.38154  -47.51308   0

global unit 200
com='Cask with 32 Fuel Assemblies'
  array 3  -47.51308   -47.51308   0
  cylinder 3 1 87.5  395.76  -30
  hole 112   0       59.89463  0
  hole 114   0      -59.89463  0
  hole 113 -59.89463  0        0
  hole 115  59.89463  0        0
  hole  20  59.39136   48.39136 0
  hole  20 -59.39136   48.39136 0
  hole  21  59.39136  -48.39136 0
  hole  21 -59.39136  -48.39136 0
  hole  22 -48.39136   59.39136 0
  hole  22 -48.39136  -59.39136 0
  hole  23  48.39136   59.39136 0
  hole  23  48.39136  -59.39136 0
  cylinder 6 1 107.5  425.76  -60
  cuboid 0 1  108  -108  108  -108  425.76  -60
end geom

read array
ara=1 nux=17 nuy=17 nuz=1
fill 39*1 2 2*1 2 2*1 2 8*1 2 9*1 2 22*1 2 2*1 2 2*1 2 2*1 2 2*1 2 38*1 2 2*1 2
 2*1 2 2*1 2 2*1 2 38*1 2 2*1 2 2*1 2 2*1 2 2*1 2 22*1 2 9*1 2 8*1 2 2*1 2 2*1
 2 39*1
end fill
ara=2 nux=3 nuy=3 nuz=1
fill 8  4  8
     5 100 7
     8  6  8
end fill
ara=3 nux=4 nuy=4 nuz=1
fill f101 end fill
ara=12 nux=4 nuy=2 nuz=1
fill 101 101 101 101
      10  10  10  10
end fill
ara=13 nux=2 nuy=4 nuz=1
fill 12 101
     12 101
     12 101
     12 101
end fill
ara=14 nux=4 nuy=2 nuz=1
fill  11  11  11  11
     101 101 101 101
end fill
ara=15 nux=2 nuy=4 nuz=1
fill 101 13
     101 13
     101 13
     101 13
end fill
end array
read plot
 ttl='2-d cross section of gbc-32 cask'
 xul=-90  yul=90  zul=100
 xlr=90  ylr=-90  zlr=100
 nax=800
 uax=1 vdn=-1 end
end plot
read bounds  xyf=mirror   end bounds
end data
end kenova
end

Sample problem 5

Sample problem 5, listed in Listing 5, uses the CE 14 × 14 assembly design from problem 3, and performs a burnup-credit calculation using the horizontal burnup-profile option. The assembly configuration is taken to be a simple 2 × 2 assembly array with water reflection. This problem is only designed to illustrate the basic features of the horizontal profile option. In this example, it is assumed that there is a burnup gradient across the assemblies, such that half the fuel pins have a burnup exceeding the average assembly burnup by 10% and half the pins have a burnup of 10% less than the average, with the two burnup regions separated by the assembly diagonal. The input card required to simulate the two horizontal burnup regions in an assembly is

hzp= 0.9 1.1 end

STARBUCS applies these factors to calculate compositions for each of the horizontally-varying burnup regions in each zone of the problem. It is important to note that the option inherently assumes that there is an equal volume/mass of fuel in each of the horizontal (or axial) zones since the code weights all regions equally when determining the average assembly burnup. To illustrate this, consider modeling an assembly with only one quadrant having a burnup that is 10% higher than the other three quadrants. The user would enter data for each of the four horizontal assembly quadrants or zones, e.g.,

hzp= 0.9766 0.9766 0.9766 1.0700 end

such that the average of the HZP array entries is unity. This ensures that the average assembly burnup will be that specified in the power history data block. Note that this array is automatically normalized if NPR=yes (default). However, the user could substantially reduce the computational time involved by specifying only two fuel regions, e.g.,

hzp= 0.9766 1.0700 end

and turning off the normalization option (e.g., NPR=no). The normalization option must be turned off to prevent the profile from being altered (since the sum is not equal to 2). This allows the user to account for the fact that, in this scenario, there are three quadrants having a lower burnup (and consequently three times the mass) and just one quadrant having an elevated burnup compared to the average. However, it is the responsibility of the user to ensure that the profiles and the KENO V.a problem description produce the desired average burnup.

In this sample problem the four assemblies are aligned so the lower burnup regions of the assemblies are adjacent to one another to maximize the system reactivity. The assembly geometry showing the different burnup regions of the assemblies is illustrated in Fig. 23. The criticality calculation is performed using the SCALE ENDF/B-VII continuous cross section library (CE_V7).

Following the STARBUCS calculation, the KENO V.a geometry model could be readily altered to simulate other assembly configurations (e.g., shuffle the fuel assembly locations). The CSAS5 case could subsequently be executed as a standalone case since all of the material compositions have already been created during the initial STARBUCS run. This facilitates the rapid evaluation of different fuel configurations without the need to regenerate the material compositions using STARBUCS.

Listing 5 STARBUCS input listing for sample problem 5
=starbucs
CE 14x14 assembly 4x4 array - horizontal burnup gradient
ce_v7
read comp
' UO2 Fuel Rod 3.038 wt %
uo2  1 den=10.045  1  273
   92234 0.027 92235 3.038 92236 0.014 92238 96.921   end
'Zircalloy
arbmzirc 6.44 4 0 0 1 40000 97.91 26000 0.5 50116 0.86 50120 0.73 2 1 620  end
'Water
 h2o    3  1  end
end comp
read celldata
 latticecell squarepitch  pitch=1.473 3 fueld=0.968 1 cladd=1.118 2  gapd=0.985 0  end
 end
end celldata
read control
arp=ce14x14
nax=18
axp=
  0.67053 0.93322 1.02433 1.05329 1.06026 1.06185
  1.06215 1.06249 1.06312 1.06408 1.06541 1.06702
  1.06836 1.06760 1.05918 1.02515 0.92262 0.66935 end
 nhz= 2
hzp= 0.9 1.1  end
nuc=
  u-234  u-235  u-236  u-238  pu-238 pu-239 pu-240
  pu-241 pu-242 am-241 am-242m am-243 np-237 end
end control
read hist
  power=28.00  burn=520.833 nlib=2 down=80  end
  power=28.00  burn=520.833 nlib=2 down=80  end
  power=28.00  burn=520.833 nlib=2 down=-1865 end
end hist
read kenova
'*************************************************************
'* materials
'* 101 = uo2, lower axial region, low burnup region
'* 118 = uo2, upper axial region, low burnup region
'* 201 = uo2, lower axial region, high burnup region
'* 218 = uo2, upper axial region, high burnup region
'* 2 = Zircaloy
'* 3 = Water
'*************************************************************
read param
tme=10000 gen=510 nsk=10 npg=1000
end parm
read geom
'  Fuel Pin, Low Burnup Region
unit           1
 cylinder   101  1  0.484 -162.53  -182.85
 cylinder   102  1  0.484 -142.22  -182.85
 cylinder   103  1  0.484 -121.90  -182.85
 cylinder   104  1  0.484 -101.58  -182.85
 cylinder   105  1  0.484  -81.27  -182.85
 cylinder   106  1  0.484  -60.95  -182.85
 cylinder   107  1  0.484  -40.63  -182.85
 cylinder   108  1  0.484  -20.32  -182.85
 cylinder   109  1  0.484    0.00  -182.85
 cylinder   110  1  0.484   20.32  -182.85
 cylinder   111  1  0.484   40.63  -182.85
 cylinder   112  1  0.484   60.95  -182.85
 cylinder   113  1  0.484   81.27  -182.85
 cylinder   114  1  0.484  101.58  -182.85
 cylinder   115  1  0.484  121.90  -182.85
 cylinder   116  1  0.484  142.22  -182.85
 cylinder   117  1  0.484  162.53  -182.85
 cylinder   118  1  0.484  182.85  -182.85
 cylinder   0    1  0.4925 182.85  -182.85
 cylinder   2    1  0.559  182.85  -182.85
 cuboid     3    1 4p0.7365 182.85  -182.85
'
'  Fuel Pin, High Burnup Region
unit           2
 cylinder   201  1  0.484 -162.53  -182.85
 cylinder   202  1  0.484 -142.22  -182.85
 cylinder   203  1  0.484 -121.90  -182.85
 cylinder   204  1  0.484 -101.58  -182.85
 cylinder   205  1  0.484  -81.27  -182.85
 cylinder   206  1  0.484  -60.95  -182.85
  cylinder   207  1  0.484  -40.63  -182.85
 cylinder   208  1  0.484  -20.32  -182.85
 cylinder   209  1  0.484    0.00  -182.85
 cylinder   210  1  0.484   20.32  -182.85
 cylinder   211  1  0.484   40.63  -182.85
 cylinder   212  1  0.484   60.95  -182.85
 cylinder   213  1  0.484   81.27  -182.85
 cylinder   214  1  0.484  101.58  -182.85
 cylinder   215  1  0.484  121.90  -182.85
 cylinder   216  1  0.484  142.22  -182.85
 cylinder   217  1  0.484  162.53  -182.85
 cylinder   218  1  0.484  182.85  -182.85
 cylinder   0    1  0.4925 182.85  -182.85
 cylinder   2    1  0.559  182.85  -182.85
 cuboid     3    1 4p0.7365 182.85  -182.85
'
'  2 x 2 Array of Lower Burnup Fuel Pins
unit           3
 array 1 3*0
'
'  2 x 2 Array of Higher Burnup Fuel Pins
unit           4
 array 2 3*0
'
'  Large Water Hole
unit           5
 cylinder   3    1  1.3140  182.85  -182.85
 cylinder   2    1  1.4160  182.85  -182.85
 cuboid     3    1 4p1.473  182.85  -182.85
'
'  Assembly 1 Unit
unit           6
 array      3 -10.311 -10.311 -182.85
 cuboid     3    1 4p11.390  182.85  -182.85
'
'  Assembly 2 Unit
unit           7
 array      4 -10.311 -10.311 -182.85
 cuboid     3    1 4p11.390  182.85  -182.85
'
'  Assembly 3 Unit
unit           8
 array      5 -10.311 -10.311 -182.85
 cuboid     3    1 4p11.390  182.85  -182.85
'
'  Assembly 4 Unit
unit           9
 array      6 -10.311 -10.311 -182.85
 cuboid     3    1 4p11.390  182.85  -182.85
'
'  Assembly Array (2 x 2)
global
unit           10
 array      7  3*0
 reflector  3  1 6r30.0  1
end geom
read array
ara=1  nux=2  nuy=2  nuz=1 fill
  1 1
  1 1  end fill
ara=2  nux=2  nuy=2  nuz=1 fill
  2 2
  2 2  end fill
ara=3  nux=7  nuy=7  nuz=1 fill
  3 3 3 3 3 3 3
  3 5 3 3 3 5 4
  3 3 3 3 4 4 4
  3 3 3 5 4 4 4
  3 3 3 4 4 4 4
  3 5 4 4 4 5 4
  4 4 4 4 4 4 4  end fill
ara=4  nux=7  nuy=7  nuz=1 fill
  3 3 3 3 3 3 3
  4 5 3 3 3 5 3
  4 4 4 3 3 3 3
  4 4 4 5 3 3 3
  4 4 4 4 3 3 3
  4 5 4 4 4 5 3
  4 4 4 4 4 4 4  end fill
ara=5  nux=7  nuy=7  nuz=1 fill
  4 4 4 4 4 4 3
  4 5 4 4 4 5 3
  4 4 4 4 4 3 3
  4 4 4 5 3 3 3
  4 4 3 3 3 3 3
  4 5 3 3 3 5 3
  4 3 3 3 3 3 3  end fill
ara=6  nux=7  nuy=7  nuz=1 fill
  3 4 4 4 4 4 4
  3 5 4 4 4 5 4
  3 3 4 4 4 4 4
  3 3 3 5 4 4 4
  3 3 3 3 3 4 4
  3 5 3 3 3 5 4
  3 3 3 3 3 3 4  end   fill
'
ara=7  nux=2  nuy=2  nuz=1 fill
  8 9
  7 6  end fill
end array
read bounds  all=void  end bounds
end data
end kenova
end
_images/fig78.png

Fig. 23 Plot of the 2 x 2 array of CE 14 14 assemblies with burnup gradient.

Sample problem 6

The last sample problem uses KENO-VI to model a hexagonal VVER-440 fuel assembly. In this example the axial burnup profile is simulated using five axial regions of non-uniform volume (height). In this case the profile input in the AXP= array is not normalized by the code (i.e., NPR=NO). The criticality calculation is performed using actinide credit only. The input file is listed in Listing 6 and is the geometry is illustrated in Fig. 24.

Listing 6 STARBUCS input listing for sample problem 6
=starbucs
VVER assembly array
V7-238
read comp
'UO2 Fuel
 uo2     1 den=8.7922 1.0 293 92235 3.3  92238 96.7 end
'Cladding
  zr  2 den=6.4073 1.0  293  end
'Moderator
 h2o   3 den=0.71533 0.9994 293 end
 boron   3 den=0.71533 0.0006 293 end
end comp
'
read celldata
 latticecell triangpitch pitch=1.22 3 fueld=0.772 1 cladd=0.91 2 end
end celldata
'
read control
 arp=vver440(3.6)  npr=no
 axp= 0.652 0.967 1.084 0.738 0.462 end
 nuc= u-234 u-235 u-236 u-238 pu-238 pu-239 pu-240
      pu-241 pu-242 am-241 am-243 np-237 end
end control
read hist
  power=35.00  burn=1428.6 down=1826 nlib=4 end
end hist
read keno6
read param gen=110 npg=1000 nsk=10 end param
read geom
unit  2
com='Vacant(water filled) hex'
 hexprism 10 0.610 257.0 0.0
 media 3 1 10
 boundary 10
unit   4
com='UO2 Fuel Rod'
 cylinder 11 0.386  14.28 0.0
 cylinder 12 0.386  28.56 0.0
 cylinder 13 0.386 228.44 0.0
 cylinder 14 0.386 242.72 0.0
 cylinder 15 0.386 257.00 0.0
 cylinder 20 0.455 257.00  0.0
 hexprism 30 0.610  257.00  0.0
 media 101 1 11
 media 102 1 12 -11
 media 103 1 13 -12
 media 104 1 14 -13
 media 105 1 15 -14
 media 2   1 20 -15
 media 3   1 30 -20
 boundary 30
unit  5
com='UO2 Fuel assembly'
 hexprism 10 11.800 257.0 0.0  rotate a1=-30
 array 1 10 place 12 12 1 3*0.0
 boundary 10
global unit 1
com='UO2 assembly'
 cuboid 10  4p15.0  257.0 0.0
hole 5 rotate a1=30
 media 3  1 10
 boundary 10
end geom
read array
 com='Assembly hexagonal rod array'
 ara=1 typ=hexagonal nux=23 nuy=23 nuz=1
fill
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 2
2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 2
2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2
2 4 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2
2 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2
2 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
end fill
end array
read bounds  xyf=reflect zfc=water end bounds
end data
end keno6
end
_images/fig86.png

Fig. 24 Cutaway 3-D view of the hexagonal VVER assembly model with water hidden.

Cac00

R. J. Cacciapouti. Axial Burnup Profile Database for Pressurized Water Reactors. Technical Report, Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States), 2000.

DH96

M. D. DeHart and Otto W. Hermann. An extension of the validation of SCALE (SAS2H) isotopic predictions for PWR spent fuel. Technical Report, Oak Ridge National Lab., 1996.

LFKR98(1,2)

D. B. Lancaster, E. Fuentes, C. Kang, and M. Rahimi. Actinide-only burnup credit methodology for PWR spent nuclear fuel. Technical Report, TRW Environmental Safety Systems, Inc., 1998.

Com12

US Nuclear Regulatory Commission. Burnup Credit in the Criticality Safety Analyses of PWR Spent Fuel in Transportation and Storage Casks, Interim Staff Guidance—8, Rev. 3. Technical Report, US Nuclear Regulatory Commision, September 2012.