Investigation of a compact storage pool

The criticality of a conceptual compact storage pool was also examined by the burnup distribution derived from the KOLA benchmark. The characteristics of this pool are close to a real WWER compact storage pool. Because of the large sizes of the pool, the radial leakage has minor importance in such a cases, and the pool was approximated by laterally infinite array of hexagonal units, consisting of a fuel assembly, the surrounding water and boron steel.

The schematic cross section of such a unit is shown on the next picture.

FIG. 1. The cross section of a unit of the compact storage pool.

The aim of this investigation was to get some estimation of the minimum value of the average assembly burnup required to meet the criticality safety criteria for the pool loaded by such assemblies.

This minimum required value of the average burnup could be determined from the well-known criticality safety condition:

and horizontal change of the burnup was investigated.

ks (B) + ∆ks≤ 1 - ∆kc - ∆kt - ∆kB - ∆kI - ∆km - ∆ka, where

ks is the calculated multiplication factor

∆ks is the statistical uncertainty of the calculation

∆kc is the uncertainty from nuclear data and validation

∆kt is the uncertainty from the technological data

∆km is the uncertainty of the modeling in core design calculation

∆kI is the uncertainty from the isotopic calculation

∆ka is the administrative safety margin ( usually 0.05)

∆kB is the uncertainty from using uniform burnup in the criticality analysis instead of spatially changing burnup.

In this analysis the uncertainty of the modeling in core design calculation and the uncertainty from the isotopic calculation was not considered. The influence of the axial and horizontal change of the burnup was investigated.

To examine the end effect, the multiplication factor of the pool was calculated by approximately 200 burnup distributions for 4.4 % and 3.6 % assemblies.

4.4 % enrichment

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

0 10 20 30 40 50 60

average burnup (MWd/kgU)

Keff

A+FP dist. A+FP u. NOFP dist. NOFP u.

FIG. 2. Multiplication factor calculated by the uniform burnup distributions and by the actual burnup distributions for the 3.6 % assemblies.

3.6 % enrichment

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

0 10 20 30 40 50

average burnup (MWd/kgU)

Keff

A+FP dist. A+FP u. NOFP dist. NOFP u.

FIG. 3. Multiplication factor calculated by the uniform burnup distributions and by the actual burnup distributions for the 4.4 % assemblies

The general picture that can be seen from the results can be summarized as:

• if fission products are present, the end effect negative at low burnup and positive at high burnup;

• the transition from negative to positive end effect is at about 20 MWd/kgU for 3.6 % enrichment and 28 MWd/kgU for 4.4 % enrichment;

• without fission products the end effect is essentially less.

The maximal end effect found approximately the same for 3.6 % and 4.4 % enrichment (about 3% with fission products and about 1% without fission products). This is different from the observations found in the case of PWR reactors.

Horizontal distribution:

The radial change of the burnup is essential for assemblies near core boundary. However, if such an assembly is positioned into the inner part of the core after a reloading, this change is smoothed. So we examined such assemblies, which were at the core periphery just before their removal from the core. Approximately 20 cases were investigated (all possible cases with 4.4 % or 3.6 % enrichment). The pin-by-pin burnup distribution was calculated for the 126 pins of each assembly by the SADR1 module of KARATE.

SADR1 is a fine-mesh diffusion code with coupled thermohydraulics. It is coupled to the global calculations, in a fine-mesh calculation the surrounding assemblies are taken into account. It utilizes position dependent group constants and the reflector is represented by albedo conditions.

The multiplication factor of the pool was calculated for the cases described above using the average burnup and the pin-by-pin burnup distribution. The difference was within the statistical error for all of the cases.

Minimal required average burnup:

Neglecting the modeling and isotopic uncertainties and using the most conservative axial burnup distribution, a rough estimation of the Bav which satisfy the safety criteria can be determined in a conservative way from usual criticality safety condition cited above. (The influence of the horizontal change is neglected in accordance with the previous observations.) With some rearrangement it can be written in the form

ks (Bav) (1+∆) + ∆ks≤ 1 - ∆kc - ∆kt - ∆ka = U.

From the analysis of the results calculated by the different axial distributions the value of ∆ can be determined. The resulting values are ∆=0.035 with fission products and ∆=0.015 without fission products for the 4.4 % assemblies. Using these values and the smooth keff (Bav) curve the minimal values of the average burnup required for loading to fuel assembly into the pool are given in the following Table.

Table IV. Minimum required average burnup for 4.4 % assemblies

A+FP 13 MWd/kgU

NOFP 17 MWd/kgU

REFERENCES

[1] MARKOVA, L., Preliminary Evaluation of CB4 Results (WWER-440 Burnup Credit Benchmark)(NRI 11750, 7th Meeting of AER Working Group E on Physical Problems on Spent Fuel, Radwaste and Decommissioning of Nuclear Power Plants, Rez, Czech Republic, April 16-17, 2002)

[2] PUTKIN, Y.N., et al., The Results of Physical Experiments of WWER-440 Cycles with Increased Fuel Enrichment, Atomnaya Energiya, 70, 225 (1991)

[3] PROSELKOV, V.N., SIMONOV, K.V., et al., The Results of WWER-440 Increased Enrichment Fuel 4-year Cycle, Atomnaya Energiya, 71, 209 (1991)

[4] HEGYI, G.Y., The KOLA benchmark, Proc. of the 7th Symp. on Atomic Energy Research, Hornitz near Zittau, Germany , September 23-26, 1997

[5] HEGYI, G.Y., HORDÓSY, G., KERESZTURI, A., MAKAI, M., MARÁCZI, C.S., Validation Experience with the Core Calculation Program KARATE; Proc. of the 2nd Regional Meeting on Nuclear Energy in Central Europe, Portoroz, Slovenia, September 11-14 1995

[6] MARKOVA, L., Continuation of the WWER Burnup Credit Benchmark: Evaluation of CB1 Results, Overview of CB2 Results to Date, and Specification of CB3; 8th AER Symposium on WWER Reactor Physics and Reactor Safety, Bystrice nad Pernstejnem, Czech Republic, September 21-25, 1998

[7] HORDÓSY, G., Final evaluation of the CB3+ burnup credit benchmark addition, 11th AER Symposium on WWER Reactor Physics and Reactor Safety, Csopak, Hungary, September 2001