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 [ORIGEN-LHBP98]. Benchmarking studies for MOX fuel were also conducted [ORIGEN-Gau03].

Table 5.1.7 Interpolation options in ARP

Type	Interpolation keyword	Comments
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	Fuel irradiation period	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	Fuel irradiation period	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	Comments
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	Comments
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	Comments
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:sup`2`) 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