determination of reactor parameters for different

Marinell B. Palangao1,2*, Alvie Asuncion-Astronomo1, Jeffrey D. Tare1,2, Ronald Daryll E. Gatchalian1, and Ryan U. Olivares1

1Nuclear Reactor Operations Section Philippine Nuclear Research Institute

Department of Science and Technology Quezon City 1101 Philippines

2Science Education Institute Department of Science and Technology Bicutan, Taguig City 1631 Philippines

Determination of Reactor Parameters for Different Subcritical Configurations of the Philippine

Research Reactor-1 TRIGA Nuclear Fuel

Keywords: Monte Carlo simulation, research reactor, subcritical assembly, TRIGA fuel

The Philippine Research Reactor-1 (PRR-1) will be revived as a subcritical assembly for training, education, and research (SATER) in the field of nuclear science and technology. SATER will utilize the existing slightly irradiated nuclear fuel rods that have been maintained in the PRR-1 facility for more than 30 years. A subcritical arrangement for the fuel rods was chosen considering the inherent safety of this configuration. In this paper, we calculate relevant reactor parameters that characterize different annular and hexagonal subcritical configurations of 44 PRR-1 fuel rods. These parameters include the neutron multiplication factor ( ), the effective delayed neutron fraction ( ), and the mean neutron generation time ( ), which are essential quantities to describe reactor behavior. Calculations were performed using the well-validated Monte Carlo radiation transport code MCNP5 v.1.6 together with the ENDF/B-VII.1 evaluated nuclear data library. The maximum value is at 4.0 cm pitch for the chosen annular arrangement, while the maximum value is at 4.3 cm pitch for the chosen hexagonal arrangement. For these configurations, the reactor kinetic parameters were and for the annular arrangement, while

and for the hexagonal arrangement. Results demonstrate that with 44 fuel rods, different fuel arrangements remain subcritical with a subcriticality margin that is at least or maximum of 0.97. The key reactor performance characteristics determined in this study can aid in the analysis of transient behavior and safety assessment of subcritical core configurations with TRIGA fuel rods. Our results provide support in expanding the utilization options for irradiated TRIGA fuel rods, even for other TRIGA facilities.

*Corresponding Author: [email protected]

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Philippine Journal of Science150 (2): 453-460, April 2021ISSN 0031 - 7683Date Received: 06 Aug 2020

INTRODUCTIONResearch reactors (RRs) are science and technology infrastructures that offer a diverse range of applications – including training, education, and research in different fields. Compared to nuclear power reactors, RRs generally operate at lower temperatures and power levels. Power plants are used to produce electricity, while RRs are mainly used to provide neutrons for various purposes such as radioisotope production, material characterization, silicon doping, material testing, analytical techniques, and neutron physics applications, among others (Xoubi 2013; Vega-Carillo et al. 2015). In the Philippines, the only nuclear facility that was successfully operated is the PRR-1. PRR-1, which first became critical in August 1963, was provided to the Philippine government under the United States Atoms for Peace Program. Throughout its operation from 1963–1984, PRR-1 was used for radioisotope production, neutron activation analysis, and reactor physics research. It also served as an avenue for applied science research as well as a training facility to increase nuclear manpower development (AspireTech Corp. 2015). From 1984–1988, PRR-1 was converted into a TRIGA (training, research, isotopes, general atomics) reactor. The conversion was initially found to be successful until several technical problems were identified, which led to the extended shutdown of the facility since 1988. The long-term shutdown of the facility resulted in the loss of expertise in the field of nuclear science and engineering in the country (AspireTech Corp. 2015).

The PRR-1 SATERWhile the PRR-1 is in extended shutdown, the TRIGA nuclear fuel rods that were acquired as part of the conversion were carefully maintained as an untapped resource in the facility. These fuel rods were only slightly irradiated during the conversion testing in 1988. To utilize this resource and rebuild capacity in nuclear science and technology, the Philippine Nuclear Research Institute (PNRI) is currently implementing a project to use the TRIGA fuel in a SATER. A subcritical configuration is chosen for SATER due to its inherent safety. SATER is envisioned to meet the following objectives: 1) support capacity building for reactor operators, regulators, and users; 2) be a demonstration facility for reactor operation and utilization; 3) demonstrate the implementation of the nuclear 3S: Safety, Security, and Safeguards; 4) build stakeholder engagement and further clarify stakeholder needs; and 5) maximize existing fuel and structures in a cost-effective way. The planned facility is designed to be safe and accessible to make it suitable as a training and research facility in nuclear science and technology for academic and research institutions.

Subcritical AssemblySubcritical assemblies (SCAs) are well known to be safe due to its neutron multiplication factor (k𝑒𝑓𝑓) that is less than 1. This means that an SCA cannot sustain a fission chain reaction and will require an external neutron source to be operated. Therefore, SCAs typically have a lower neutron fluence rate and result in lower radiation exposure compared to critical reactors, which have k𝑒𝑓𝑓 =1 (Xoubi 2016). Although SCAs cannot offer all utilization capabilities that are available for other RRs, the facility can be optimized for training, education, and reactor physics research. Most SCAs also have additional advantages such as low operating costs, negligible fuel burnup or usage, and simpler operation and maintenance procedures. These characteristics make an SCA an ideal facility for PNRI considering its current context (Asuncion-Astronomo et al. 2019).

A detailed model of the PRR-1 TRIGA fuel was previously developed to design and characterize an SCA in a square configuration (Asuncion-Astronomo et al. 2019). This configuration was used as the basis of the core design of the SCA that is under construction at PNRI. The core design consists of 44 TRIGA fuel rods arranged in a 7 × 7 square lattice at 4 cm pitch with light water moderator. In this configuration, the effective multiplication factor k𝑒𝑓𝑓 was computed to be 0.95001 ± 0.00009 with effective delayed neutron fraction and mean neutron generation time (Asuncion-Astronomo et al. 2019). The reactor physics characteristics of a subcritical core of TRIGA fuel rods with a non-rectangular lattice have not been determined.

In this work, alternative subcritical configurations of 44 PRR-1 TRIGA fuel rods in hexagonal and annular arrangements are investigated. Reactor physics and kinetic parameters of the fuel configurations were determined, which include the effective neutron multiplication factor (k𝑒𝑓𝑓), the effective delayed neutron fraction (�𝑒𝑓𝑓), and the mean neutron generation time (Λ). This study aims to demonstrate that, under normal operating conditions, 44 PRR-1 TRIGA fuel rods under different arrangements will remain subcritical, hence in criticality safe condition. Moreover, the result of this study can provide a reference for other TRIGA reactor operators who may opt to optimize the use of irradiated TRIGA fuel before proceeding to disposal or decommissioning.

METHODOLOGY

The PRR-1 TRIGA FuelThe PNRI has been maintaining 130 TRIGA fuel rods in the PRR-1 facility for more than three decades; 115

Palangao et al.: Reactor Parameters for Subcritical Configurations of PRR-1 TRIGA Fuel

Philippine Journal of ScienceVol. 150 No. 2, April 2021

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of these rods were slightly irradiated when the PRR-1 conversion into a TRIGA-type reactor was tested in 1988. The PRR-1 TRIGA fuel rod is 75.2 cm long and contains four fuel elements (FEs) composed of a solid homogenous mixture of U, Er, and a ZrH moderator. Each FE consists of ~ 20 wt.% uranium with 19.7% 235U enrichment. Erbium (a burnable poison) is uniformly mixed with U-ZrH. The active section of the fuel-moderator rod has an overall length of 50.8 cm and an outside diameter of 2.97 cm. It has a cylindrical body, with Incoloy cladding, and has a large prompt negative temperature coefficient, very low fission product release, and high-temperature capability (GA Technologies 1987). The detailed specifications and modeling of the fuel are reported in a previous paper (Asuncion-Astronomo et al. 2019).

An MCNP model of the PRR-1 TRIGA fuel rod with detailed specifications of geometry and material compositions was used to simulate the fuel in various hexagonal and annular arrangements. The pitch, i.e. the distance between the centers of adjacent fuel rods of adjacent rings (for annular configuration) or simply the distance between centers of adjacent fuel rods (for hexagonal configuration), that will result in a maximum k𝑒𝑓𝑓 for each chosen arrangement is determined. For the case of the hexagonal configuration, a lattice that contains 44 fuel rods is modeled using MCNP5, with the pitch ranging from 3.5–5.5 cm at 0.2-cm interval to obtain a k𝑒𝑓𝑓 vs. pitch plot. For the annular configuration, 44 fuel rods arranged in a circular concentric ring are modeled with the pitch ranging from 3.6–4.4 cm at 0.2-cm interval.

Monte Carlo/ MCNP CalculationsCalculations were performed using the Monte Carlo N-Particle Transport Code (MCNP) 5 v.1.6 (X-5 Monte Carlo Team 2003) with the ENDF/B-VII.1 nuclear data library (Chadwick et al. 2011) to obtain k𝑒𝑓𝑓. The parameter k𝑒𝑓𝑓 is defined as the ratio of the neutrons generated in one generation to the number of neutrons lost in the preceding generation (Duderstadt and Hamilton 1976; Lamarsh and Baratta 2001).

MCNP determines k𝑒𝑓𝑓 by simulating neutron transport and interactions in consecutive cycles that correspond to successive generations of neutrons. Each fission process is regarded as an initial event that separates generations of neutrons. To run the criticality problem, i.e. to calculate k𝑒𝑓𝑓, we used the KCODE card. On the other hand, the effective delayed neutron fraction �𝑒𝑓𝑓 and mean neutron generation lifetime Λ were computed using the command “KOPTS” and likewise gave the output in one run, combined with the criticality calculation output.

Reactor Physics and Kinetics Parameter CalculationsThe effective delayed neutron fraction �𝑒𝑓𝑓 is an important parameter in reactor kinetics because it describes the behavior of delayed neutrons, which is necessary for reactor control (Duderstadt and Hamilton 1976). Thus, this parameter normally arises in problems involving reactor transient and safety analysis. All neutrons are categorized as either “prompt” or “delayed” at birth, and then transport of neutrons is tracked in the reactor until they are eliminated by fission, capture, or leakage out of the reactor. The effective delayed neutron fraction out of the total number of neutrons in the system is obtained using:

(1)

where kp is the prompt neutron multiplication factor. �𝑒𝑓𝑓is unique for each reactor configuration as it depends both on the geometry and material composition of the reactor. The mean neutron generation time Λ, on the other hand, characterizes the time behavior of the neutron population. It is defined as the average time between the birth of a neutron and the birth of a single neutron in the next generation and is given by:

(2)

where 𝑙 is the prompt neutron lifetime (Snoj et al. 2010). In MCNP, both �𝑒𝑓𝑓 and Λ can be obtained using the built-in KOPTS card, which calculates the adjoint weighted kinetic parameters �𝑒𝑓𝑓 and Λ in a single run (Kiedrowski et al. 2010).

RESULTS AND DISCUSSION

Annular ConfigurationFour arrangements for the annular configuration . Figure 1 shows the four selected annular configurations with a total of 44 fuel rods. All configurations have a central hole, three rings with all their positions filled with fuel rods, and a fourth (outermost) ring only partially filled with eight fuel rods in different arrangements.

Figure 1a displays an annular configuration with eight fuel rods positioned in the topmost part. Figure 1b displays the outer fuel rods on both sides arranged symmetrically. Figure 1c displays the outer fuel rods in an alternate position distributed symmetrically. Figure 1d displays the outer fuel rods with two empty slots apart and distributed evenly. The multiplication factors for these assemblies are all less than 1.0, signifying subcriticality.



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Among these, arrangement d was chosen because of its symmetry, which will result in a symmetrical neutron distribution. This is advantageous in the utilization aspect where the empty slots in symmetric locations will have relatively similar neutron spectra, which is useful for irradiation applications. Figure 2 shows the MCNP5 model of the selected arrangement d as projected in the x-z and x-y planes.

Calculation of k𝑒𝑓𝑓 vs . pitch in the annular configuration . Calculations were performed to determine the k𝑒𝑓𝑓 for different fuel pitches of the chosen arrangement d. In all calculations, 5.0 × 105 neutrons per cycle were considered, with an initial guess of 1.0 for the k𝑒𝑓𝑓 value. There were a total of 2100 cycles ran, from which 100 cycles were skipped before accumulating the data. The maximum k𝑒𝑓𝑓 value was achieved at 4.0-cm pitch, which is similar to the case of square lattice configuration reported earlier (Asuncion-Astronomo et al. 2019). The resulting k𝑒𝑓𝑓 at 4.0 cm pitch is 0.96735 with a standard

deviation of 0.00003. At this pitch, the average neutron energy causing fission is 3.0933 × 10⁻2 meV, and the average number of neutrons produced per fission (ν) is 2.440. The percentages of fissions caused by neutrons in the thermal (< 0.625 eV), intermediate (0.625–100 keV), and fast (> 100 keV) neutron ranges are 91.29%, 7.35%, and 1.35%, respectively. Figure 3 shows the plot of k𝑒𝑓𝑓 at different fuel pitch values for arrangement d. The standard deviations of the calculated k𝑒𝑓𝑓 for these fuel pitch values range from 2–3 pcm.

The effective delayed neutron fraction is �𝑒𝑓𝑓 = 756 ± 4 pcm and the mean neutron generation time is Λ = 41 μs.

Hexagonal ConfigurationFour arrangements for the hexagonal configuration . Figures 4 illustrates different arrangements of 44 fuel rods in a hexagonal lattice with an empty slot in the middle. As shown in these figures, the multiplication factors k𝑒𝑓𝑓 are all less than 1.0, indicating subcriticality in these assemblies.

Figure 1. The four selected arrangements for the annular configuration. Cells with yellow cross marks correspond to locations of the TRIGA fuel rods.



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Arrangements of a and b were both symmetric and the most compact among these arrangements. In proceeding with the calculations of k𝑒𝑓𝑓 vs. pitch and reactor parameters, arrangement b was considered. Figure 5 shows the MCNP5 model of the selected arrangement b as projected in the x-z and x-y planes.

Calculation of k 𝑒𝑓𝑓 vs . pitch in the hexagonal configuration . Results of k𝑒𝑓𝑓 for arrangement (b) were obtained from different pitches that range from 3.5–5.5 cm using MCNP5. In all calculations, 5.0 × 105 neutrons per cycle were also considered, with an initial guess of 1.0 for the k𝑒𝑓𝑓 value. There were a total of 2100 cycles ran, from which 100 cycles were skipped before accumulating the data. The maximum value was achieved at a 4.3-cm pitch. The resulting k𝑒𝑓𝑓 at 4.3 cm pitch is 0.96601 with

a standard deviation of 0.00003. At this pitch, the average neutron energy causing fission is 3.1756 × 10⁻2 meV and the average number of neutrons produced per fission (ν) is 2.440. The percentages of fissions caused by neutrons in thermal (< 0.625 eV), intermediate (0.625–100 keV), and fast (> 100 keV) neutron ranges are 90.94%, 7.67%, and 1.39%, respectively. Figure 6 shows the plot of k𝑒𝑓𝑓 at different pitch values for arrangement b. The standard deviations of the calculated k𝑒𝑓𝑓 for these pitch values range from 2–3 pcm. The maximum value was attained at 4.3-cm pitch. Compared to the square (Asuncion-Astronomo et al. 2019) and annular configurations, this is the only configuration that has a k𝑒𝑓𝑓with a maximum value at 4.3-cm pitch.

Figure 2. (a) x-z plane and (b) x-y plane cross-section views of the MCNP5 model for the annular configuration (d) at 4-cm lattice pitch.

Figure 3. ke f f vs. pitch for annular configuration (d) with TRIGA fueled rods.



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Figure 4. The four selected arrangements for the hexagonal configuration. Cells with yellow cross marks correspond to locations of the TRIGA fuel rods.

Figure 5. (a) x-z plane and (b) x-y plane cross-section views of the MCNP5 model for the hexagonal configuration (b) at 4.3 cm lattice pitch.



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Figure 6. ke f f vs. pitch for hexagonal configuration (b) with TRIGA fueled rods.

In this hexagonal configuration, the effective delayed neutron fraction is �𝑒𝑓𝑓 = 760 ± 4 pcm and the mean neutron generation time is Λ = 41 μs. A summary of effective multiplication factors and reactor parameter values for different configurations discussed is provided in Table 1.

Table 1. Calculated effective multiplication factors and reactor parameters of different configurations of 44 TRIGA rods of PRR-1

Cofiguration Pitch (cm) 𝒌e f f

𝜷e f f

(pcm)

Λ(μs)

Squarea 4.0 0.95001 ± 0.00009 748 ± 7 41

Annular 4.0 0.96735 ± 0.00003 756 ± 4 41

Hexagonal 4.3 0.96601 ± 0.00003 760 ± 4 40

Source: Asuncion-Astronomo et al (2019)

CONCLUSIONIn this paper, annular and hexagonal configurations consisting of 44 TRIGA fuel rods are presented. The reactor physics parameters of both these configurations are computed using MCNP5. The effective multiplication factors (k𝑒𝑓𝑓) of the chosen arrangements of annular and hexagonal configurations are found to be 0.96735 ± 0.00003 at 4.0-cm pitch and 0.96601 ± 0.00003 at 4.3-cm pitch, respectively. This demonstrates that the 44 PRR-1 TRIGA fuel rods under these arrangements will remain subcritical and, hence, in criticality safe condition. The kinetics parameters of the system – such as the effective delayed neutron fraction and mean neutron generation time – are calculated to be �𝑒𝑓𝑓 = 756 ± 4 pcm and Λ =

41 μs, respectively, for the annular configuration. For the hexagonal configuration, the effective delayed neutron fraction and mean neutron generation time are calculated to be �𝑒𝑓𝑓 = 760 ± 4 pcm and Λ = 40 μs, respectively. The results of this study provide a reference for other TRIGA reactor operators who may consider optimizing the use of irradiated TRIGA fuel before proceeding to disposal or decommissioning.

ACKNOWLEDGMENTSThis work is partially supported by the International Atomic Energy Agency Technical Cooperation Project No. PHI0015 and the Department of Science and Technology (DOST) – Philippine Council for Industry, Energy and Emerging Technology Research and Development Project No. 04385. M. B. Palangao and J. D. Tare are grateful for the Career Incentive Program under the DOST Science Education Institute for supporting their work at PNRI. The authors acknowledge the referees for their valuable comments and suggestions.

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