Fast reactors

The three-dimensional models of the three fast reactors depicted in Figure 3.1 were created in the KENO-VI transport module of the SCALE 6.0 code. In order to decrease the computational time needed for the core calculations, a SCALE 6.0 sequence with two-step homogenization was used in the preparation of the cross-section databases (see Figure 3.3), and the core geometries were built from the homogenized fuel assemblies of the different fuel regions. In the first homogenization step the hexagonal unit cell was homogenized in 1D cylindrical geometry using white boundary conditions. The height of the core was taken into account with buckling correction in the resonance treatment for the proper consideration of axial leakage.

The fuel assemblies consisted of the homogenized unit cells, the assembly wrapper and the coolant between the assemblies, and they were also homogenized in 1D cylindrical geometry. Other core components and structural elements (axial and radial reflectors, rod followers and gas plenums) were modeled with smeared densities and treated in infinite homogeneous medium approximation. The three-dimensional core models were built from the homogenized assemblies and other core components, and the full core calculations were performed using the KENO-VI criticality code.

The actinide reaction rates and the average fluxes in the different fuel regions were recorded from the calculations, as well as thekeff for the different fuel compositions.

With the two-step homogenization the time demand of one full core calculation was about 40 minutes on one 2 GHz CPU with 1 GByte memory.

Due to the high-dimensional fitting domain, purely deterministic sampling meth-ods such as orthogonal sampling or Latin hypercube sampling would have required

an impracticable number of data points [63, 64]. The different compositions were therefore obtained by random sampling of the actinide mass fractions – although combined deterministic and Monte Carlo sampling might be a future improve-ment [34] – taking into account the following constraints:

• Pu fraction in the fuel was uniformly sampled between 10-25% of the total actinide mass.

• MA fraction varied between 0-10% of the total actinide mass.

• The rest of the actinide content was U.

• The Pu content of the different core regions were kept at constant ratio corre-sponding to the initial loading. The MA fraction was the same in all regions.

• Fission products were considered with an average fission yield vector, and their total quantity was calculated from the sampled burn-up which varied between the specified limits.

The use of an average, characteristic fission product composition was possible due to the fast neutron spectrum of the reactors. Since most fission products have high absorption mainly at thermal energies, the variation of the FP composition during burn-up has small effect on the actinide one-group cross-sections. Isotopic compositions of the actinide elements on the other hand were also randomly sam-pled between the beginning-of-life (BOL) composition and equilibrium compositions estimated by preliminary studies (see Table 3.6) [P10]. The aim of the random sam-pling was to cover a wide range of possible fuel compositions that can occur in the fuel cycle simulations, therefore unrealistic compositions were not only unnecessary in the cross-section database, but they would have decreased the accuracy of the fitted polynomials for realistic fuel compositions. To eliminate these points from the database, preliminary fits of the keff were performed based on the results of few hundred core calculations, and rejection method was used to sample compositions with estimated keff ranging from 0.90 to 1.15.

The FITXS models of the reactors calculate the evolution of the average fuel composition in the cores, therefore separate handling of the different core regions is not possible during the fuel cycle simulation. On the other hand the fitting is performed on core homogenized cross-sections which are calculated using region-wise fluxes and atomic densities. In order to preserve total reaction rates for the full cores, a homogenization correction factor was introduced (h), that can be expressed as a weighted sum of atomic density ratios and flux ratios between the different core

3.3. Preparation of the cross-section databases 33

Table 3.6: Limits for the random sampling of fast reactor actinide isotopic com-positions

Component Isotope Mass percent in component

Minimum Maximum

U

234U 0 1

235U 0 1

236U 0 1

238U 99 100

Pu

238Pu 1 10

239Pu 40 70

240Pu 20 40

241Pu 1 15

242Pu 1 15

MA

237Np 0 50

239Np^∗ 0 1.4·10⁻²

241Am 30 75

242mAm 0 10

243Am 10 45

244Cm 0 15

245Cm 0 5

∗239Np fraction was compared to the total actinide mass

regions. The total reaction rate can be calculated using the correction factors as follows:

R=N σhΦV, (3.1)

where N denotes the average atomic density of the nuclide in the core, σ denotes the core homogenized one-group microscopic cross-section, h denotes the homoge-nization factor andV is the total fuel volume. The general form forn regions is the following:

σ = Pn

k=1NkσkΦkVk

Pn

k=1NkΦkVk

(3.2)

N = Pn

k=1NkVk

V , (3.3)

Φ = Pn

k=1ΦkVk

V , (3.4)

h= Pn

k=1ckfkVk

V , (3.5)

V =

n

X

k=1

Vk, (3.6)

where ck is the atomic density of the isotope in region k compared to the average atomic density, and fk is the flux in region k compared to the average flux in the core:

ck= Nk

N , (3.7)

fk = Φk

Φ . (3.8)

Simple substitution shows that in knowledge of the atomic density ratios and flux ratios, the h correction factor allows to preserve the total reaction rates without the explicit calculation of region-wise compositions. Atomic density ratios between the different core regions were kept constant, nevertheless flux ratios varied for the different compositions. The average core composition with fixedck ratios determines the region-wise atomic densities as well, therefore the fk flux ratios were fitted as functions of the average atomic densities, with the same procedure as the keff and the one-group cross-sections.