2011 International Nuclear Atlantic Conference - INAC 2011 Belo Horizonte,MG, Brazil, October 24-28, 2011 ASSOCIAÇÃO BRASILEIRA DE ENERGIA NUCLEAR - ABEN ISBN: 978-85-99141-04-5

MEASURED AND CALCULATED EFFECTIVE DELAYED NEUTRON FRACTION OF THE IPR-R1 TRIGA REACTOR

Rose Mary G. P. Souza, Hugo M. Dalle, Daniel A. M. Campolina

Centro de Desenvolvimento da Tecnologia Nuclear (CDTN) Comissão Nacional de Energia Nuclear (CNEN) Campus da UFMG - Pampulha – Caixa Postal 941 30123-970, Belo Horizonte, MG, Brazil. [email protected], [email protected]; [email protected]

ABSTRACT

The effective delayed neutron fraction, βeff , one of the most important parameter in reactor kinetics, was measured for the 100 kW IPR-R1 TRIGA Mark I research reactor, located at the Nuclear Technology Development Center - CDTN, Belo Horizonte, Brazil. The current reactor core has 63 fuel elements, containing about 8.5% and 8% by weight of uranium enriched to 20% in U235. The core has cylindrical configuration with an annular graphite reflector. Since the first criticality of the reactor in November 1960, the core configuration and the number of fuel elements have been changed several times. At that time, the reactor power was 30 kW, there were 56 fuel elements in the core, and the βeff value for the reactor recommended by General Atomic (manufacturer of TRIGA) was 790 pcm. The current βeff parameter was determined from experimental methods based on inhour equation and on the control rod drops. The estimated values obtained were (774 ± 38) pcm and (744 ± 20) pcm, respectively. The βeff was calculated by Monte Carlo transport code MCNP5 and it was obtained 747 pcm. The calculated and measured values are in good agreement, and the relative percentage error is -3.6% for the first case, and 0.4% for the second one.

1. INTRODUCTION

The nominal thermal power of the IPR-R1 TRIGA reactor, at the Nuclear Technology Development Center - CDTN, Belo Horizonte, Brazil, is 100 kW. The work presented in this paper shows the effective fraction of delayed neutrons (βeff) calculated by Monte Carlo transport code MCNP5, and estimated experimentally by two methodologies: the inhour equation and the rod drop.

One of the most important aspects of the fission process from the point of view of controlling the reactor is the presence of delayed neutrons. In general, delayed neutrons are more effective to control the reactor than prompt neutrons because they are born at lower energy compared to prompt (fission) neutrons. Thus, they have a better chance to survive leakage and resonance absorption. A delayed neutron is a neutron emitted by an excited fission product nucleus during beta disintegration some appreciable time after the fission. There are six decay chains which are of significance in the emission of delayed neutrons. Correspondingly, delayed neutrons are commonly discussed as being in six groups. Each of these groups, (i), are characterized by a fractional yield βi and a decay constant λi. The amount βi is defined as the fraction of the total number of fission neutrons that are emitted by the decay of fission products in the group i.

The effective total delayed neutron fraction is designated βeff. The value of this parameter for a given fuel will vary over the lifetime of the reactor core, and also with the average energy of the neutrons producing fission. βeff depends on the core size and presents higher values for smaller cores. The effective fraction of delayed neutrons recommended by the General Atomic Technologies inc. (manufacturer of TRIGA) is 790 pcm [1, 2].

2. BRIEF DESCRIPTION OF THE IPR-R1 REACTOR

The IPR-R1 TRIGA reactor is a 100 kW facility. The reactor reached its first criticality on November 1960, and since then its core configuration and the number of fuel elements have been changed several times. As calculated in [3] about 4% of the U-235 in the core was burned during its 50 years. The fuel is a homogeneous mixture of uranium-zirconium hydride containing about 8.5% and 8% by weight of uranium, for stainless-steel and aluminum clad elements, respectively, enriched to 20% in 235U [1, 2]. The reactor core has 91 positions of which 63 are filled with fuel elements (59 Al-clad and 4 SS-clad elements) arranged in five concentric rings, inside a water tank. In the F ring there are 23 graphite dummy elements. The power level of the reactor is controlled by three control rods: Regulating, Shim, and Safety. The reactor is equipped with three irradiation facilities: rotary specimen rack, pneumatic transfer tube, and central thimble. A complete description of the IPR-R1 reactor can be found in [4]. Figure 1 shows the current core configuration which was used in the experiments.

Figure 1. IPR-R1 TRIGA reactor core.

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3. MONTE CARLO CALCULATION METHOD AND MODEL

The general purpose, continuous energy, generalized-geometry Monte Carlo transport code MCNP5 was used in the calculations. In MCNP it is possible to model the reactor in 3-D geometry in details. A very detailed description of the MCNP reactor core model can be found in [3]. In this model the fuel burnup since the first criticality of the IPR-R1 was simulated taking into account the power history as recorded in the reactor log books. ENDF/B-VII pointwise cross sections data libraries were used in the simulations. When such data were not available then ENDF/B-VI data was used, instead.

Three core configurations were simulated. The first two are the Beginning Of Life (BOL) core, as it was in 1960, considering one configuration with graphite elements filling the positions into the F ring and the other with water filling the positions in F ring. The third core is the current core, as shown in Fig. 1.

The effective delayed neutron fraction, βeff, was calculated using the following equation [5, 6]:

kP β eff = 1 − (1) keff where kp is the effective neutron multiplication factor only for prompt neutrons and keff is the effective neutron multiplication factor for both, prompt and delayed neutrons.

The MCNP calculations were run with 4.0x105 histories per cycle and 2500 active cycles of neutrons, leading to a standard deviation within 0.00008 (8 pcm).

The results of calculated βeff for all the three core configurations are presented in the Table 1. One can notice that the calculation result of the BOL core without any dummy elements surrounding the core agrees very well with the nominal value of 0,00790 for βeff informed by the reactor manufacturer, GA. This may be an indirect indication in favor of the adopted calculation model. Furthermore, it can be observed that when graphite dummy elements are filled into the F ring, then the βeff value reduces, as expected because the graphite elements work as a reflector, diminishing the leakage of the high energy prompt neutrons and thus improving the contribution of these neutrons in the balance. The current core is larger than the BOL, thus, the additional reduction in the βeff is also expected as the effective delayed neutron fraction depends on the core size and presents higher values for smaller cores. Such results agree with other authors [5, 6] as the delayed neutrons are born with lower energies and are more effective in inducing fission in system with larger leakage.

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Table 1. Reactor core configurations and calculated βeff

Number of Date of the Element in Error β Fuel Factor Mean eff Configuration the F Ring (pcm) (pcm) Elements

keff 0.99576 8 06/11/1960 56 H2O 789 kp 0.98790 8

keff 1.02254 8 06/11/1960 56 Graphite 750 kp 1.01487 8

keff 1.02183 8 06/11/2004 63 Graphite 747 kp 1.01420 8

4. EXPERIMENTAL DETERMINATION OF DELAYED NEUTRON FRACTION

A brief discussion of the methodologies that were adopted to obtain βeff and the results of the experiments performed for such purposes are given in the following items.

4.1. Measurement Results Based on Inhour Equation

Theoretically, the reactivity of a control rod can be given approximately by [7, 8]:

 Z 1  2π Z  ρ (Z ) = ρ (H )  − sen   (2)  H 2π  H  where ρ (Z) and ρ (H) refer to the control rod reactivity worth inserted the distance Z and fully inserted, respectively. Knowing the control rod worth ρ (H), the value of the reactivity at different Z positions can be calculated. The integral curve of the Regulating control rod is shown in Fig. 2, and of the Shim and Safety rods in Fig. 3. These curves were obtained by the Eq. (2). The total reactivity worth of the Regulating, Safety and Shim rods are 379 pcm, 2244 pcm and 2536 pcm, respectively [9].

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400 350 300 250 200 150

Reactivity (pcm) 100 50 0 0 200 400 600 800 1000 Regulating Rod Position

Figure 2. Integral curve of the Regulating control rod.

3000

2500

2000 Safety 1500 Shim 1000 Reactivity (pcm) 500

0 0 200 400 600 800 1000 Rod Position

Figure 3. Integral curves of the Shim and Safety control rods.

The relationship between a step change in reactivity (ρ) and the resulting reactor period (T) is given by the inhour equation:

w m β w ρ = l + ∑ i (3) k 1 w + λi

In which l is the prompt neutron generation time; m is the number of delayed neutron groups; w are the (m+1) solutions, or roots, of the inhour equation; and k is the effective neutron multiplication factor.

The stable period of the reactor is defined by the Eq. (4), where w1 is the first root of the inhour equation and DT is the Doubling Time (time required for the reactor power to increase by a factor of two):

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1 DT T = = (4) w1 0.693

For small reactivity, the stable period is given approximately by [7, 8, 10]:

β − ρ T ≅ (5) λ ρ

From the above equation, the fraction of delayed neutrons is given by:

β eff ≅ ρ (T λ + 1) (6)

For the TRIGA reactor the decay constant value considered is λ = 0.0077 s-1 [10].

When positive or negative reactivity is inserted into any critical reactor, for a very short time, the reactor behaves as if all of the additional neutrons were prompt. There is a sudden change in the neutron flux (or power) during a transient period followed by a steady, constant rate of change governed by the stable reactor period.

The experiments were performed according to [11]. With the reactor in critical condition at 10 W (no influence of temperature) the control rods were removed, one at a time. Then, the DT was measured for several insertions of positive reactivity. After measuring this time, the rod in use was inserted, returning to the same position of criticality. The reactor periods were obtained from Eq. (4), and the reactivities inserted for the withdrawn of each control rod were calculated from the integral curves of the calibration rods (Figs. 2 and 3). Table 2 shows the experimental average βeff1 values calculated by Eq. (6), for several control rods withdrawn, and they are compared with the calculated value.

Table 2. The average values of βeff 1, obtained from small insertions of positive reactivities. Comparison between the experimental βeff 1 values and the calculated βeff = 747 pcm

β Control Rod eff 1 | (βeff - βeff 1)/β eff | (pcm) (%) Regulating 835 11.8 Shim 782 4.7 Safety 704 5.8

βeff 1 = (774 ± 38) pcm 3.6

4.2. Measurement Results Based on Rod Drop Method

If a reactor is operating at a power level (P0) and suddenly the reactivity is reduced by a relatively large amount, there will be a large power drop (P1). For an extremely short period of time (fraction of a second) this drop follows the expression:

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βeff (1− ρ ) P1 = P0 (7) βeff − ρ

From Eq. (7), the effective delayed neutron fraction is given by

 P1  ρ    P0  β eff = (8)  P1    − 1 + ρ  P0 

After this initial prompt drop, the power will decrease much more slowly due to the delayed neutrons. Delayed neutrons, from those fissions that occurred before this decrease in reactivity, will appear for quite some time. Neutrons emitters with extremely short half-lives soon disappear so that the only neutrons still remaining are those contributed by the neutron emitter with a 55.6 s half-life [7, 8]. Under these conditions the period is -80 second, and the power any time later can be calculated from:

t − P = P e T 1 0 (9)

The experiment basically can be described as follows. The neutron source is removed from the core, and the reactor was brought to steady state operation at low power (for several minutes to obtain the saturation of the delayed neutron precursors) with the Regulating rod completely raised and the Shim rod partially raised as per the desired power level. The reactor was scrammed to allow the Regulating rod to drop suddenly, causing a step decrease (prompt drop) in the reactivity. The monitoring of the power variation with time was done through a fast register coupled to the Linear Channel of the reactor. The same procedure was done with the Shim and Safety rods. The reactor power P1, after the shutdown of the rod, was obtained by decreasing power curve extrapolating to t = 0. Table 3 presents the numerical power values of P0 and P1, and the delayed neutrons fraction calculated using Eq. (8), for each control rods scram.

Table 3. Reactor Power P0 and P1, reactivity inserted by the shut down of each control rod, the respective βeff 2, and the average value of βeff 2. Comparison with the calculated value βeff = 747 pcm

Reactivity Control P P β | (β - β )/β | Inserted 0 1 eff 2 eff eff 2 eff Rod (W) (W) (pcm) (%) (pcm) Regulating 379.2 24.1 16.3 783 4.8 Shim 2535.9 23.0 5.3 735 1.6 Safety 2243.6 23.5 5.8 714 4.4

βeff 2 = (744 ± 20) pcm 0.4

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5. CONCLUSIONS

The effective delayed neutron fraction, βeff , of 790 pcm, was the value recommended by the General Atomic Technologies inc. (manufacturer of TRIGA) [1, 2]. The Monte Carlo calculated βeff value is 789 pcm to the non reflected BOL core, which agrees perfectly with the nominal GA value.

Considering the measured values of the effective delayed neutrons fraction, to the current core, calculated from the positive reactivity inserted into the reactor and their respective asymptotic periods, it was observed that the largest absolute relative error between the experimental and the Monte Carlo calculated value was about 11.8% in case of the Regulating rod extractions and the lowest one was 4.7% for the extraction of the Shim rod. The average experimental value obtained by applying the technique based on inhour equation was (774 ± 38) pcm, and comparing it with the calculated value of 747 pcm, the absolute relative error was 3.6% (Table 2).

The average value of βeff determined by the rod drop technique was (744 ± 20) pcm with absolute relative error of 0.4% compared to the value calculated by Monte Carlo transport code MCNP5. The largest individual absolute relative error was 4.8%, obtained with the insertion of negative reactivity through the Regulating rod and the lowest was 1.6% by the Shim scram (Table 3).

Comparing the values of the effective delayed neutrons fraction obtained by both techniques, it was observed that the results arising from the movement of the Regulating and Shim rods differ approximately 6%, from one technique to the other, while for the Safety rod differs 1.4%. The average values of the effective fraction of delayed neutrons given in Table 2 and 3 differ from each other by 3.9%.

ACKNOWLEDGMENTS

The authors would like to thank Fausto Maretti Júnior, Dante Marco Zangirolami, Luiz Otávio Sette Câmara and Paulo Fernando Oliveira, the operation staff of the IPR-R1 TRIGA research reactor, for their cooperation during the experimental work.

REFERENCES

1 General Atomic, “Technical foundation of TRIGA”. San Diego, California (1958). (GA- 471). 2 General Atomic, “Safeguards Summary Report for the New York University TRIGA Mark I Reactor”, San Diego, California (1970). (GA-9864). 3 H.M. Dalle, “TRIGA IPR-R1 Reactor simulation using Monte Carlo transport methods”. ScD Thesis, Universidade Estadual de Campinas, São Paulo (2005) (in Portuguese). 4 CDTN/CNEN, “Safety Analysis Report of the IPR-R1 TRIGA Reactor”. (RASIN/TRIGA-IPR-R1/CDTN). CDTN, Belo Horizonte, Brazil (2007). (In Portuguese). 5 R. Klein Meulekamp, S.C. Van der Mark, “Calculating the Effective Delayed Neutron Fraction with Monte Carlo”. Nuclear Science and Engineering, v. 152, pp. 142-148 (2006).

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6 L. Snoj, A. Kavčič, G. Žerovnik, M. Ravnik, “Monte Carlo Calculation of Kinetic Parameters for the TRIGA Mark II Research Reactor”. International Conference Nuclear Energy for New Europe 2008, Slovenia (2008). 7 J.R. Lamarsh, Introduction to Nuclear Engineering, Addison-Wesley Publishing Company, Inc., New York, N.Y. (1977). 8 J.J. Duderstadt, L.J. Hamilton, Nuclear Reactor Analysis, J. Wiley & Sons New York, N.Y. (1976). 9 R.M.G.P. Souza, “Resultados da Calibração das Barras de Controle, do Excesso de Reatividade, da Margem de Desligamento e do Defeito de Potência do TRIGA IPR-R1 – Núcleo com 63 E.C.” Belo Horizonte, CDTN (2010). (NI-SERTA-03/10). (In Portuguese). 10 A.N. Santos, et alii, “Curso de Treinamento de Operadores em Reatores de Pesquisa – CTORP”. Belo Horizonte, NUCLEBRÁS, IPR, 2 v. (1975) (NB/IPR-363). (In Portuguese). 11 R.M.G.P. Souza, “Procedimentos Experimentais para Determinação da Fração Efetiva de Nêutrons Atrasados e do Tempo Médio de Geração dos Nêutrons do TRIGA IPR-R1 – Núcleo com 63 E.C.” Belo Horizonte: CDTN (2010). (NI-SERTA-02/10). (In Portuguese).

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