International Conference Nuclear Energy for New Europe 2004Nuclear Energy for New Europe 2004Nuclear Energy for New Europe 2004Nuclear Energy for New Europe 2004

Portoro Slovenia September 6-9

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+386 1 588 5247, fax +386 1 561 2276 PORT2004, Nuclear Society of Slovenia, Jamova 39, SI-1000 Ljubljana, Slovenia

211.1

Evaluation of Uranium-Plutonium Criticality Benchmark Experiment

Milan Tomazin, Igor Lengar, Matja Ravnik

Joef Stefan Institute Jamova 39, SI-1000 Ljubljana, Slovenia

Milan.Tomazin@ijs.si, Igor.Lengar@ijs.si, Matjaz.Ravnik@ijs.si

ABSTRACT

Preliminary results are presented for a series of criticality safety benchmark experiments, consisting of MOX fuel rods inserted in homogeneous nitric acid solution of uranium and plutonium oxide containing also gadolinium and boron. Criticality is achieved by adding the solution and measuring the critical level. The benchmark experiment was performed at Battelle Pacific NW Labs using several combinations of fuel rods and solutions in 1976. A Monte-Carlo calcualtional model with the use of MCNP/4B is developed. Effects of various uncertainties on the multiplication factor are studied. The sensitivity studies include parametric variations of material composition and geometry. The calculated multiplication factors agree within 0.01 with the experimental value. Systematic underprediction of calculated keff with respect to the measurement is observed, which can be explained by the deficiency of the nuclear data library (ENDFB/VI.0).

1 INTRODUCTION

The chemical process of uranium and plutonium separation of NPP spent fuel begins by dissolving the fragments of fuel rods in the nitric acid. Homogeneous solution of uranium and plutonium salts is formed containing also undissolved parts of fuel rods. Strong neutron absorbers are added to the solution to prevent criticality. The multiplication factor of such systems is difficult to calculate and for the evaluation of the calculation models of such systems, a series of benchmark experiments has been performed.

In the present work preliminary criticality analysis of such a uranium-plutonium system is presented. The benchmark experiments were performed at Battelle Pacific North-West Laboratories in 1976. They are reviewed and analyzed within the scope of the International Criticality Safety Benchmark Evaluation Project (ICSBEP) organized by OECD Nuclear Energy Agency [1]. Due to incompleteness of original documentation some of the experimental conditions and the geometry of the set-up are not accurately known.

One of the key features of any benchmark problem is exact estimation of the error and uncertainty of the calculation including geometry and composition of the materials [2]. In the

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Proceedings of the International Conference Nuclear Energy for New Europe, Portoro, Slovenia, Sept. 6-9, 2004

present paper the sensitivity analysis is presented to enable reasonable estimation of how much the uncertainties in input data reflect in the final result.

The study is divided into two parts. In the first part fuel composition uncertainties and uncertainties in other material compositions with emphasis on the concentration of soluble poisons, which exhibit the highest experimental inaccuracy, are examined. In the second part the geometry of the set-up is studied. Additionally a study of the influence of the cross-section library used for Monte-Carlo calculations is performed.

2 EXPERIMENTAL SET-UP

The fuel assembly is composed of a triangular lattice of 301 fuel pins inserted in a 55.5 cm diameter stainless steel vessel. The vessel was, in turn, contained within a larger cylindrical vessel providing for water reflection. The set-up is shown in Figure 1 with a schematical view of a fuel pin. The U+Pu nitrate solution, containing about 80 g Pu/l and varying amounts of gadolinium and boron, was added to the loaded lattice assembly to obtain criticality through variation of solution height. The Pu contained 6.3% 240Pu and the U 0.66% 235U. The Pu made up about 30% of the total U+Pu by weight. The solution contained a combination of B and Gd in the ratio approximately 3 to 1 by weight.

(a) (b)

Figure 1: (a) Vertical cross-section of reactor vessel containing 301 fuel pins and U+Pu nitrate

solution with varying amounts of gadolinium and boron, (b) view of a fuel pin.

All calculations were performed with MCNP 4B program package [3] using ENDF B-VI.0 cross-section data libraries. Multiplication factor is calculated for experimental critical conditions. The results for the multiplication factor were obtained for seven different values of the concentration of soluble poisons, and correspondingly for seven different heights of the

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Proceedings of the International Conference Nuclear Energy for New Europe, Portoro, Slovenia, Sept. 6-9, 2004

Pu+U+Gd+B solution. The specification of the solutions and critical heights are presented in Table 1.

Table 1: Concentrations of Pu, U, Gd and B for the seven critical experiments and the

corresponding critical heights.

test case critical height [cm] Pu concentration

[g/l] U concentration

[g/l] Gd [g/l] B [g/l]

1 21.20 84.5 182.1 0.13 0.27

2 25.37 84. 183.2 0.235 0.6

3 30.49 82.7 180.6 0.309 0.9

4 43.86 81.2 180.0 0.424 1.35

5 51.97 81.0 180.4 0.519 1.5

6 55.18 81.0 180.3 0.537 1.548

7 65.42 80.5 180.5 0.541 1.662

The calculated multiplication factors for the seven experiments are presented in Table 2.

Table 2: Calculated multiplication factors for seven critical configurations specified in

Table 1.

test case critical height [cm] calculated multiplication factor

1 21.20 0.99302 +/- 0.00023

2 25.37 0.99158 +/- 0.00023

3 30.49 0.99541 +/- 0.00022

4 43.86 1.00019 +/- 0.00021

5 51.97 0.99608 +/- 0.00021

6 55.18 0.99575 +/- 0.00020

7 65.42 1.00033 +/- 0.00020

average: 0.99605 +/- 0.00056

The calculated multiplication factors are in average 400 pcm below the experimental value (1.00000 +/- 0.00010). Maximum difference is observed in first two cases with low absorber concentration but high leakage due to small critical height. All results are within [-850 pcm, + 50 pcm] interval relative to the measured values indicating a systematic error of approximately 400 pcm. As presented later, it can be attributed to nuclear data library.

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Proceedings of the International Conference Nuclear Energy for New Europe, Portoro, Slovenia, Sept. 6-9, 2004

3 MATERIAL COMPOSITION SENSITIVITY STUDIES

The data for the boron concentration in the fissile solution in the experimental report and logbooks are in some cases given with poor accuracy. In some cases, they are also in contradiction with other experiments. The determination of their effect on the critical value of k is therefore crucial to evaluate whether the experiments could be developed into criticality safety benchmarks or not. The results for the sensitivity of the system to changes in the concentration of the soluble poisons boron and gadolinium are presented in Table 3. For their determination the MCNP perturbation option was used.

Table 3: Dependence of k on changes in the concentrations of B and Gd in the fissile

solution for all experimental cases.

test case Bck / [pcm/(g/l)] (Boron concentration sensitivity)

Gdck / [pcm/(g/l)] (Gadolinium concentration sensitivity)

1 8519 21875

2 7667 20000

3 7444 18447

4 7037 16745

5 6733 15607

6 6654 15456

7 6679 15342 For the consistency of the results the sensitivity to the amount of the fissile material

should be tested as well. The results are presented in Table 4. Table 4: Sensitivity of k to the amount of uranium and plutonium in the fuel rods and in

the fissile solution.

test case U weight in fuel rods variation

[pcm/%]

U weight in solution variation

[pcm/%]

Pu weight in fuel rods variation

[pcm/%]

Pu weight in solution variation

[pcm/%]

1 1 -28 22 86

2 0 -27 23 126

3 -1 -26 23 156

4 -1 -25 23 197

5 -2 -25 24 216

6 -2 -24 24 220

7 -2 -24 24 227

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Proceedings of the International Conference Nuclear Energy for New Europe, Portoro, Slovenia, Sept. 6-9, 2004

4 GEOMETRY SENSITIVITY STUDIES

The geometry of the set-up is in the experimental report [4] described in a simplified manner and rather inaccurate way. Sensitivity studies have to be performed to evaluate the influence of poor geometrical data on the multiplication factor [5]. A source of inaccuracy also stems from the fact, that the original dimensions were given in the Imperial unit system, but in the report [4] they were transformed into the metric system, introducing round-off and truncation errors.

The perturbations due to changes in geometry were always calculated using the values of k in two separate runs, which differed form each other by changing only one geometrical property. A linear dependence was assumed and the result for the sensitivity of a particular study was the difference in the values of k of the corresponding runs with the belonging statistical uncertainty, associated with Monte-Carlo calculations:

2

22

121 += kkk . The study included variation of the thickness of the fuel pin cladding and lower support

plate, the variation of the solution height and the pitch dimension. The variations were performed for a critical height of 21.20 cm and an additional variation of the solution height was performed at a height of 25.37 cm. The results of the study are presented in Table 5.

Table 5: Effect of geometry parameter variations on multiplication factor

perturbed quantity k / relative variation of perturbed quantity [pcm / %]

thickness of lower support plate

0.9 +/- 0.8

fuel pin cladding thickness 2.3 +/- 3.4

pitch dimension 2 +/- 7

Solution level height (at 21.2 cm critical height)

275 +/- 80

Solution level height (at 25.37 cm critical height)

305 +/-92

As can be observed, the sensitivity on solution level height significantly prevails among

effects of geometry sensitivity. As the critical solution level height was measured with 1/16 inch accuracy [4], total uncertainty due to geometry can be estimated to be 200 pcm.

5 INFLUENCE OF DIFFERENT NUCLEAR DATA LIBRARIES

The choice of the nuclear cross-section data library to be used in Monte-Carlo calculations is an important factor that influences the value of k [1]. This effect was studied on a set-up that slightly differed from the one described earlier, since the evaluated results with the use of the earlier version of the ENDF B/V cross-section data library were attainable. The geometrical and material properties were equal to the ones of the benchmark studied with one difference - the only soluble poison in the solution was Gd (B was absent). Due to the similarity of both

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Proceedings of the International Conference Nuclear Energy for New Europe, Portoro, Slovenia, Sept. 6-9, 2004

systems the influence of the cross section library change was anticipated to be similar in both cases. Results of both runs are shown in Table 6.

Table 6: Comparison of data k for two different cross-section data libraries.

ENDF B / VI ENDF B / V

k = 0.99034 +/- 0.00043 k = 0.99884 +/- 0.00020 The difference in the calculated multiplication factor is considerable and amounts to

850 pcm. This difference is much bigger than uncertainities, connected with geometry or material composition, as anticipated. It has to be given special attention.

6 CONCLUSIONS

A calcualtional model for a uranium-plutonium benchmark, which was carried out at Battelle Pacific NW Labs in 1976, was developed. The focus of the study is set on the sensitivity analysis of geometrical and material characteristics of the experimental system. Emphasis was given to variation of the data, not precisely represented in the experimental documentation soluble poison concentration in fissile solution, amount of fissile material, size of fuel elements. The uncertainties in geometry and material data seem to be smaller than the calculational error due to the choice of the nuclear data library.

REFERENCES

[1] B. B. Briggs (ed.), International handbook of evaluated criticality safety Benchmark experiments, NEA Nuclear Science Committee, Paris, 2003.

[2] Anno J. (ed.), International handbook of evaluated criticality safety Benchmark experiments: ICSBEP guide to the expression of uncertainties, NEA Nuclear Science Committee, Enghien, 2001.

[3] ORLN, RSICC computer code collection MCNP, Los Alamos National Laboratory, Los Alamos, (2000)

[4] R. C. Lloyd, E. D. Clayton, Summary of Criticality Data Obtained at Battelle Pacific Northwest Laboratories on Fixed and Soluble Poisons in U+Pu Nitrate Solutions, in BNWL-B-482, UC-46, 1976, pp. 13-24.

[5] R. Jeraj, A. Peri, T. agar, M. Ravnik, Sensitivity Studies of the TRIGA Benchmark Critical Experiment, Proc. Int. Conf. Nuclear Energy in Central Europe '99, Portoro, Slovenia, September 6-9, Nuclear Society of Slovenia, 1999, pp. 629-635.

INTRODUCTIONEXPERIMENTAL SET-UPMATERIAL COMPOSITION SENSITIVITY STUDIESGEOMETRY SENSITIVITY STUDIESINFLUENCE OF DIFFERENT NUCLEAR DATA LIBRARIESCONCLUSIONS