# 5.1.6. ARP Module

The ARP module performs multidimensional interpolation on a set of specially prepared ORIGEN libraries using interpolation methods discussed in Sect. 5.1.3.1.5, with available interpolators listed in Table 5.1.7. The ORIGEN reactor libraries distributed with this version of SCALE are described in the ORIGEN Reactor Libraries chapter, as well as details on how users can generate their own libraries. The ARP module has been validated extensively for light water reactor (LWR) spent fuel . Benchmarking studies for MOX fuel were also conducted .

Table 5.1.7 Interpolation options in ARP

Type

Interpolation keyword

Nearest value

nearest

Searches for closest value to the desired value

Linear interpolation

linear

Uses nearest two values bounding the desired value

Lagrangian interpolation

lagrange(N)

with order N from 1 to 4

Uses N points near desired value and creates a polynomial of order N-1 using Eq. (5.1.54)

lagrange

same as lagrange(4)

The specification of lagrange(1) is equivalent to nearest and lagrange(2) to linear.

Standard cubic spline

stdspline

Standard, natural cubic spline (without monotonicity fix-up).

Monotonic cubic spline

spline

Natural cubic spline with a monotonicity fix-up designed to prevent nonphysical oscillations that in some cases may result in negative interpolated cross sections.

Parametrizations for three types of problems have been developed: uranium-based fuel, mixed-oxide (MOX) fuel, and general activation.

• The parametrization for uranium-based fuel (e.g., UO:sub:2), as would be found in most LWRs, can interpolate on

• fuel enrichment,

• moderator density, and

• burnup.

• The parametrization for MOX fuel contains a mixture of plutonium and uranium oxide and can interpolate on

• total plutonium content in the heavy metal,

• plutonium isotopic vector (Pu vector) that defines the relative concentrations of the Pu isotopes,

• moderator density, and

• burnup.

• The parametrization for general activation problems has only one-dimensional interpolation on fluence.

Variation of the absorption cross sections was observed to be near linear as a function of Pu content. Interpolation on the Pu vector is more complex than the uranium enrichment for UO2 fuel since the vector is composed of five different isotopes: 238Pu, 239Pu, 240Pu, 241Pu, and 242Pu. Furthermore, the elements in the vector depend on one another and can therefore not be evaluated independently of one another since the entire vector must sum to 100%. The scheme developed for the Pu vector was based on an evaluation of a large database of plutonium compositions from actual MOX fuel assemblies of European origin. It might be expect edthat the parametrization would need to include all Pu isotopes. However, an evaluation of the MOX fuel database indicated that there is a strong correlation between 239Pu and the other isotopes in the vector that permits cross sections for the MOX fuel to be determined to sufficient accuracy using only the 239Pu concentration.

## 5.1.6.1. Input Description

ARP has a simple input scheme, a different line-by-line input expected for each of the three problem types—uranium, MOX, or activation—with the input required for each type shown in Table 5.1.8, Table 5.1.9, and Table 5.1.10. Available input depends on what is available in the relevant arpdata.txt file and the arplibs directory.

Table 5.1.8 Input description for uranium fuels

Entry

#

Data type

Entry

requirements

Comment

1

Data set name

Line 1 always required

Enter a uranium CONFIGNAM from the active arpdata.txt

(see Table 5.1.11).

2

Enrichment

New line always

Enter the wt % 235U in toal U

3

Number of cycles

Always

Enter the number of irradiation cycles $$N$$.

4

Always

Enter the irradiation time for each cycle in days $$\Delta T_{i}$$, for $$i = 1,\ 2,\ldots,N$$.

5

Average power

Always

Enter the specific fission power (MW/MTHM) for each cycle $$P_{i}$$, for $$i = 1,\ 2,\ldots,N$$.

6

Data interpolations per cycle

Always

Enter the nummber of cross section sets to interpolate during each cycle $$m_{i}$$, for $$i = 1,\ 2,\ldots,N$$.

7

Moderator density

Always

Enter the moderator density (g/cm3).

Enter only one value

8

New library name

New line

always

Enter the filename of the new ORIGEN library created from interpolation.

9

Interpolation keyword

Optional

Enter the interpolation algorithm which will be used from Table 5.1.7

(DEFAULT: spline)

Table 5.1.9 Input description for MOX fuels

Entry

#

Data type

Entry

requirements

Comment

1

Data set name

(starts with MOX)

Line 1

Always required

Enter a MOX CONFIGNAM from the active arpdata.txt

(see Table 5.1.12)

2

Plutonium content

New line

always

Enter the Pu content as wt % Pu in total heavy metal.

3

239Pu isotopic vector

Always

Enter the 239Pu isotopic concentration as wt % 239Pu in total Pu.

4

Reserved parameter (not used)

Always

Enter a dummy value (e.g., 1.0)

5

Number of cycles

Always

Enter the number of irradiation cycles $$N$$.

6

Fuel irradiation period (days)

Always

Enter the irradiation time for each cycle days $$\Delta T_{i}$$, for $$i = 1,\ 2,\ldots,N$$.

7

Average power (MW/MTHM)

Always

Enter the specific fission power (MW/MTHM) for each cycle, $$P_{i}$$, for $$i = 1,\ 2,\ldots,N$$.

8

Data interpolations per cycle

Always

Enter the number of cross section sets to interpolate during each cycle, $$m_{i}$$ for $$i = 1,\ 2,\ldots,N$$.

9

Moderator density

Always

Enter the water moderator density (g/cm3).

Enter only one value.

10

New library name

New line always

Enter the name of the new interpolated library created by ARP.

11

Interpolation keyword

Optional

Enter the interpolation algorithm which will be used from Table 5.1.7

(DEFAULT: spline)

Table 5.1.10 Input description for activaiton problems

Entry no.

Data type

Entry requirements

Comment

1

Data set name

(starts with ACT)

Line 1 always required

Enter an activation CONFIGNAM from the active arpdata.txt

see Table 5.1.13

2

Dummy parameter

Always

Enter 1.

3

Number of cycles

Always

Enter the number of irradiation cycles $$N$$.

4

Always

Enter the irradiation time for each cyce time in days $$\Delta T_{i}$$, $$i = 1,\ 2,\ldots,N$$.

5

Average neutron flux

Always

Enter the average flux level (n/cm2-s) for each cycle, $$\Phi_{i}$$, for $$i = 1,\ 2,\ldots,N$$.

6

Data interpolations per cycle

Always

Enter the number of cross section sets to interpolate during each cycle, $$m_{i}$$, for $$i = 1,\ 2,\ldots,N$$.

7

Flux type (flag)

Always

Enter 1.

8

New library name

New line always

Enter the name of the new interpolated library created by ARP.

9

Interpolation keyword

Optional

Enter the interpolation algorithm which will be used from Table 5.1.7

(DEFAULT: spline)

## 5.1.6.2. ARPDATA.TXT listing file

In addition to the user input file, ARP also reads a file named arpdata.txt when it runs. This file describes the parametrization of the ORIGEN libraries. The file is required because the cross section libraries contain no imbedded information on the reactor type, fuel type, or irradiation conditions. Both the file arpdata.txt and the directory of ORIGEN libraries named arplibs is searched for, first in the working directory so that a user can override the default libraries, and then to the SCALE data directory. An example arpdata.txt file is shown in Example 5.1.20

Example 5.1.20 Examples of arpdata.txt entries.
 !ce14x14
6 1 11
1.5 2.0 3.0 4.0 5.0 6.0
0.7332
'ce14_e15.f33' 'ce14_e20.f33' 'ce14_e30.f33'
'ce14_e40.f33' 'ce14_e50.f33' 'ce14_e60.f33'
0. 1500. 4500. 7500. 10500. 13500.
16500. 31500. 46500. 58500. 70500.

!mox_bw15x15
3 5 1 1 10
4.0000 7.0000 10.0000
50.0000 55.0000 60.0000 65.0000 70.0000
1.0
0.7135
'mox_bw15_e40v50.f33' 'mox_bw15_e70v50.f33' 'mox_bw15_e10v50.f33'
'mox_bw15_e40v55.f33' 'mox_bw15_e70v55.f33' 'mox_bw15_e10v55.f33'
'mox_bw15_e40v60.f33' 'mox_bw15_e70v60.f33' 'mox_bw15_e10v60.f33'
'mox_bw15_e40v65.f33' 'mox_bw15_e70v65.f33' 'mox_bw15_e10v65.f33'
'mox_bw15_e40v70.f33' 'mox_bw15_e70v70.f33' 'mox_bw15_e10v70.f33'
0.00 1040.00 3000.00 5000.00 7500.00

!w17x17
6 1 11
1.5 2.0 3.0 4.0 5.0 6.0
0.723
'w17_e15.f33' 'w17_e20.f33' 'w17_e30.f33'
'w17_e40.f33' 'w17_e50.f33' 'w17_e60.f33'
0. 1500. 4500. 7500. 10500. 13500.
16500. 31500. 46500. 58500. 70500.


As shown in Example 5.1.20, the arpdata.txt is simply a list of entries, each beginning with a !CONFIGNAM, where CONFIGNAM is the name to be used to reference the entire data set. Whether the entry is for a uranium, MOX, or activation problem is dictated by the actual CONFIGNAM. If it begins with MOX, it is a MOX entry, and if it begins with ACT, it is an activation entry. Otherwise it is uranium. The ORIGEN libraries listed must reside next to arpdata.txt:, in a directory called arplibs. Each type of entry is described fully in Table 5.1.11, Table 5.1.12, and Table 5.1.13 for uranium, MOX, and activation, respectively.

Table 5.1.11 ARPDATA.TXT uranium-type entry

Line no.

Data name

Description

1

CONFIGNAM

Data set name

Must begin with “!” in column one, followed by the alphanumeric name this data will be referenced by.

(40-character maximum)

May not begin with ACT or MOX

2

N1

Number of enrichments

Entries pertain to the number of parameterized cross section data points for each variable type.

N2

Number of water densities

N3

Number of burnup steps

3

ENR

Enrichment values (wt % 235U); values at which ARP libraries were generated

N1 entries defining the discrete enrichment values for each library

4

DENS

Water density values (g/cm3)

N2 entries defining the discrete moderator density values for each library

5

FILES

Filenames of ORIGEN libraries for this fuel assembly type

N1 $$\times$$ N2 entries

(Enclose each filename in single quotes with at least one space between each name.)

Filenames are ordered first by density values, then by enrichment values.

6

BURN

Burnups (MWd/MTU) corresponding to each position on the ORIGEN library

N3 entries

Each set of burnup-dependent cross sections is stored within a single ORIGEN binary library file (the first burnup is usually zero).

NOTE: Repeat all of the above entries for each fuel assembly configuration type

Table 5.1.12 ARPDATA.TXT MOX-type entry

Line no

Data name

Description

1

CONFIGNAM

Data set name

Must begin with “!” in column one, followed by the alphanumeric name by which this data set will be referenced.

(40-character maximum)

Must begin with MOX (e.g., !mox_bw15x15).

2

N1

Number of Pu content values

Entries pertain to the number of separate cross section sets generated for each parameter.

N2

Number of 239Pu values

N3

Not used (enter 1)

N4

Number of water densities

N5

Number of burnup steps

3

PU

Pu content values (wt % Pu in heavy metal)

N1 entries

4

VECT

239Pu | N2 entries vector values | (wt % 239Pu/Pu) |

5

RESRV

Not used (enter 1)

N3 entries; dummy entry required.

6

DENS

Water density | N4 entries values | (g/cm3) |

7

FILE

Filenames of ORIGEN libraries for this fuel assembly type. Enclose each filename in single quotes with at least one space between each name.

N1 × N2 × N3 × N4 entries

Increment FILE names in the order of N1, then N2, then N3, and then N4 values

8

BURN

Burnups (MWd/MTU) corresponding to each position on the ORIGEN library

N5 entries

(first burnup is usually zero)

NOTE: Repeat all of the above entries for each fuel assembly configuration type

Table 5.1.13 ARPDATA.TXT activation-type entry

Line no.

Data name

Description

1

CONFIGNAM

Data set name

Must begin in colummn one followed by the alphanumeric name by which this data set will referenced.

(40-character maximum)

Must begin with ACT (e.g., !actcntlrod).

2

N1

Reserved (enter 1)

The first two entries pertain to the number of separate cross section sets generated for each variable parameter.

N2

Not used (enter 1)

N3

Number of fluence values

These are usually set to 1.

The variable N3 corresponds to the number of fluence-dependent cross section sets available in the library.

3

RESRV

Not used (enter 1)

Enter 1.

4

FTYPE

Neutron flux type (flag)

Enter 1.

5

FILES

Filenames of ORIGEN library. Enclose filename in single quotes.

Generally only one one library name is required.

6

FLUENCE

Neutron fluence values (n/cm:sup2) at each of the ORIGEN libraries

N3 entries

The fluence values are reduced by the factor $$10^{-24}$$ to avoid numerical problems during the interpolation

(First value is usually zero.)

NOTE: Repeat all of the above entries for each fuel assembly configuration type