NFCSS Reactor Model (CAIN)

A reactor model (fuel depletion or burnup model) is the most important part of the nuclear fuel cycle simulation system since it calculates the inventory of spent nuclear fuel after irradiation. A number of existing codes have been investigated and it has been decided that there is a need for a new code which will be an optimum combination of simplicity, accuracy and speed. So CAIN ( CA lculation of IN ventory of spent fuel) was developed by the IAEA for the needs of NFCSS simulation system.

It solves Bateman's Equations for a point assembly like in ORIGEN code which is similar but commonly used tool with more details. CAIN code uses one group neutron cross sections. The cross sections could be selected from any standard library like ORIGEN library, or could be generated by using more complex lattice codes. Accuracy in the cross section library affects actually the accuracy of the NFCSS results. Hence, in a high accuracy need, a more complex lattice code might be used with a complex assembly model to generate average one group cross sections for the assembly. Then this cross section set might be used in CAIN.

Currently there are 7 different reactor types in CAIN library. These are PWR, BWR, PHWR, RBMK, AGR, GCR, WWER. AGR, GCR, RBMK, PHWR has cross sections for only for uranium fuel type (UOX) whereas PWR, BWR and WWER has two different cross section sets for uranium and mixed oxide fuels (MOX).

The accuracy, simplicity and speed requirements bring a set of assumptions. Main assumptions are listed below. In the light of below assumptions, the CAIN currently has 28 reaction and decay chains during irradiation and 14 decay chains during cooling/storage.

• The selection of the nuclides have been performed for the importance of the nuclides in radiotoxicity of the spent fuel and their nuclear characteristics.

• Although natural uranium includes ²³⁴U (<0.01%), this nuclide is ignored, because the transmutation from ²³⁴U to ²³⁵U is too small.

• Nuclides with short half lives (half life < 8days) are ignored. That is, ²³⁷U (7days), ²³⁸Np (2days), ²⁴³Pu (5hrs), ²⁴²Am (16hrs), ²⁴⁴Am (10hrs) and ^244mAm (26min) are assumed to decay and go to next nuclide simultaneously.

• Long half life nuclides (half life > 400years) are assumed as stable for the irradiation period. For example, ²⁴¹Am (432yr) is treated as stable during irradiation. For decay (cooling) period after discharge, all nuclides are treated by their actual decay scheme.

• In the chain shown in below figure, transmutation is terminated for certain nuclides (shown as mark "x"). For example, ²³⁸Pu decreases by neutron capture, but the decrease of ²³⁸Pu is not added to ²³⁹Pu. This treatment is imposed in order to stop endless calculation of Bateman's equation. This assumption is reasonable, because the contribution due to this transmutation is very small.

• The 28 reaction chains and 14 decay chains are selected to be suitable for fresh fuels containing any of the 14 nuclides of the CAIN library. Some reaction chains are neglected due to their contribution to the composition of the spent fuel, such as chains starting from decay of ²⁴¹Am (432 years).

• Among 14 nuclides, decays of ²³⁸Pu (87.7yr), ²⁴¹Pu (14.4yr), ²⁴²Cm (0.447yr) and ²⁴⁴Cm (18.1yr) are considered during irradiation. Below figure shows the transmutation chain after simplification for the CAIN code.

The nuclides included in the calculations are:

Uranium	235U	236U	238U
Neptunium	237Np
Plutonium	238Pu	239Pu	240Pu,	241Pu	242Pu
Americium	241Am	242mAm	243Am
Curium	242Cm	244Cm

CAIN is capable of handling variable neutron flux and cross sections throughout the irradiation. In order to do this, the flux and cross sections must be entered as different values for different burnup steps. Otherwise, both cross sections and neutron flux are assumed to be constant throughout the burnup period. Also, only the discharge point is important for the evaluation of the inventory of spent fuels.

For further needs such as modeling thorium fuel cycle, new nuclides could be added to the cross section library. In that case, the reaction and decay chains have also to be expanded.