1 Introduction

The radioactive isotope ⁶⁰Co is widely used in fields as diverse as food irradiation, materials science, commercialization of Chinese herbs, and environmental management ^[1-3]. Due to the broad range of applications of ⁶⁰Co and their high economic benefit, methods of producing a large quantity of high specific activity ⁶⁰Co have become an important issue in many countries. The nuclear reaction ⁵⁹Co (n, γ) ⁶⁰Co ^[4] is often used to produce ⁶⁰Co ^[5]; a high specific activity is obtained by placing a ⁵⁹Co-containing target in a high-flux reactor for neutron irradiation ^[6].

Currently, there are only seven commercial nuclear power operations in the world that are producing the radioactive isotope ⁶⁰Co: the Russian MAYAK facility, the Leningrad nuclear power plant (graphite reactor), the Bruce Power and Ontario Power Generation CANDU reactors (Canada), the Embalse CANDU reactors (Argentina), the Qinshan CANDU reactors (China), the Clinton boiling water reactor (BWR) power plant (USA), and the Hope Creek (BWR) reactors (USA). Table 1 estimates the amount of ⁶⁰Co supplied by these commercial nuclear power plants. Although thermal reactors, experimental fast reactors, and subcritical reactors can be used to produce ⁶⁰Co, the CANDU reactor is the most widely used for this; no country has made full use of PWRs to produce ⁶⁰Co ^[7]. In recent years, the demand for ⁶⁰Co has grown significantly; the market size for ⁶⁰Co from 2006 to 2011 is shown in Fig. 1. Considering the availability of cobalt metal as an irradiation target for ⁶⁰Co production, the consulting firm Roskill predicts that the industrial demand for cobalt will maintain a growth rate of over 6% per year, based on recent years ^[6]. The expected global demand for cobalt will be more than 100,000 metric tons in 2020; since the annual production of cobalt is limited, the world supply will be insufficient to meet the demand ^[1]. To compensate for this mismatch, an effective method to produce the required ⁶⁰Co in PWRs is needed, as most of the commercial reactors in operation are PWRs (Table 2) ^[8-10]. Pressurized water reactors are found in a large majority of the world’s nuclear power plants, with the number of PWRs being much larger than BWRs and supercritical water reactors (SCWRs).

Fig. 1.Full-screen View

The analysis of market size for ⁶⁰Co from 2006 to 2011 (billion yuan)

PWRs have a secondary neutron source, whose main function is to improve the neutron flux level of the reactor during the loading and unloading processes, so the source count rate will be in a suitable range and provide a reliable basis for safe reactor startup. Some (αa, n) neutron sources and spontaneous fission neutron sources in the spent fuel assemblies in Daya Bay Nuclear Power Plant (NPP) produce a large number of neutrons; if spent fuel assemblies were substituted for the secondary neutron sources, the measurement accuracy of the instruments would be increased and the replacement of the secondary neutron sources during the lifetime of the reactor could be avoided. Beginning in October 2010, Daya Bay NPP discontinued the use of secondary neutron source assemblies and introduced some spent fuel assemblies with a known burnup value as the secondary neutron sources.

Because of its neutron absorption properties, a ⁵⁹Co rod can be put in the original position of the secondary neutron source and ⁶⁰Co will be produced. Preliminary analysis shows that this method is feasible. Success in finding an optimal location for a ⁵⁹Co target in a specific reactor would provide a starting point to investigate ⁶⁰Co production in that reactor. In this article, the effects on PWR operations of adding ⁵⁹Co in rod form are studied.

In order to study the characteristics of ⁶⁰Co production in a PWR, we combine the design principles of thermal neutron reactors with the method of producing ⁶⁰Co in other reactors. The core design is optimized to reach k_eff after adding ⁵⁹Co rods to the PWR. The parameters of the PWR are then adjusted to find the solution which has the smallest impact on the core ^[11].

2 The design of a PWR core

The Monte Carlo N-Particle Transport Code (MCNP) ^[12] is internationally recognized for analyzing the transport of neutrons, photons, and electrons, and can be used to simulate a PWR. MCNP is widely used in the analysis of fuel assemblies as well as core design. It can be used for calculations of the multiplication factor, reaction rates, neutron flux and spectrum, power peaking factors, reaction rate distribution, and radiation shielding ^[13]. Monte Carlo methods do not solve an explicit equation deterministically ^[14], but simulate the motion of individual particles statistically to obtain a solution. In addition, the code can work with a 3D geometry and can even include time as a fourth dimension; an example would be an ellipsoidal surface with an arbitrary three-dimensional perturbation ^[15]. MCNP uses statistical methods to solve complex problems that cannot be modeled directly by computer algorithms. The neutron energy range with the MCNP program is: 10^-11 to 20 MeV; the photon energy range is: 1 keV to 1000 MeV ^[16].

The sequence for an MCNP simulation is as follows (Fig. 2):

Fig. 2.Full-screen View

The running process of the Monte Carlo N-Particle Transport Code (MCNP)

A number of input files are used by MCNP, including XSDIR and a cross-section database file. The main file requiring user input is designated INP. Output files containing calculated results and various running information are created by MCNP ^[17].

In this paper, a PWR core model is created using the MCNP and SCALE codes. We use MCNP to calculate the neutron flux density and energy deposition, assuming different numbers of ⁵⁹Co rods loaded into a pressurized water reactor. The criticality source condition is used to calculate the effective multiplication factor (k_eff). The initial estimate of the core k_eff is set to 1, the number of cycles is 500, and 100 cycles are skipped to ensure that the normal spatial mode for fission sources is achieved. When we study the axial distribution of neutron flux, the reactor core is divided into 74 parts (on average) along the axis, and the neutron flux density in each part is counted. For the calculation of the radial energy deposition in the core, the component is taken as the research object, and the reactor core is divided into 15 modules spaced equidistantly along the diameter from (-7,0,0) to (7,0,0); each module is calculated separately. The SCALE (Standardized Computer Analyses for Licensing Evaluation) ^[18] code contains a different set of analysis and calculation modules; this paper mainly uses the Origen-S module to calculate burnup.

2.3 Core modeling of the PWR

The control rods have a great influence on reactivity and are used for dynamic regulation during normal operation; to simplify the calculations, all control rods have been replaced by a water gap cell for modelling. Based on the geometry and material composition described above, the PWR model assumed for the MCNP simulation is shown in Fig. 3a.

Fig. 3.Full-screen View

(a) Cross section of the reactor core. (b) The prototype PWR after replacement of two fuel assemblies

3 Alternate design

In order to approach the design model of the Daya Bay Nuclear Power Plant ^[21] and obtain precise calculation data, the thimble plug assemblies (namely, the spent fuel assemblies) are used to replace the secondary neutron sources and are placed at the same locations. Then we have a new reactor type, based on the original, and suitable for comparison. The assemblies requiring replacement are located at (3, H) and (13, H); the prototype reactor after the replacements is shown in Fig. 3b.

There is a big difference between light water reactors and heavy water reactors in structure, so from the perspective of nuclear materials security, the study of using a Qinshan CANDU reactor to produce ⁶⁰Co cannot provide significant reference information ^[22]. Obviously, the technology of producing ⁶⁰Co in an American BWR is worth investigating; when the General Electric Company produced ⁶⁰Co in a BWR, it inserted 4 or 5 ⁵⁹Co rods in 10 × 10 fuel assemblies. Since BWRs and PWRs are both light water reactors, there are many common features. It is reasonable to increase the number of ⁵⁹Co rods inserted in the PWR and conduct a comparative analysis. The three analysis schemes of this paper are as follows:

Scheme One: replace the secondary neutron source rods (four rods);

Scheme Two: replace the secondary neutron source rods (four rods) and two stopper rods; and

Scheme Three: replace the secondary neutron source rods (four rods) and four stopper rods.

3.1 The prototype reactor

The secondary neutron source locations are replaced in the prototype by a thimble plug component, which contains 24 stopper rods and one tube for a neutron flux detector, as shown in Fig. 4a.

Fig. 4.Full-screen View

Fuel assembly with different numbers of ⁵⁹Co rods. (a) The thimble plug component. (b) The position of the four ⁵⁹Co rod replacements within the component (Scheme One). (c) The position of the six ⁵⁹Co rod replacements (Scheme Two). (d) The position of the eight ⁵⁹Co rod replacements (Scheme Three)

4 Analysis of the simulation results

4.1 Estimation of core lifetime and ⁶⁰Co production

Loading the cobalt rods will change the core lifetime of a reactor and affect its electricity production. Therefore, in order to have a rough estimation of the cost-benefit balance, we calculate k_eff and the ⁶⁰Co content for different burnup values using the SCALE code. The results are shown in Fig. 5 and Table 5, respectively.

Table 5.Full-screen View

⁶⁰Co Content at Different Burnup Values

Burnup（MWd/MTU）	Scheme One 60Co /U	Scheme Two 60Co /U	Scheme Three 60Co /U
0	0	0	0
4,000	1.44E-06	1.98E-06	2.47E-06
8,000	2.65E-06	3.76E-06	4.76E-06
12,000	3.86E-06	5.46E-06	6.77E-06
16,000	5.05E-06	7.17E-06	8.94E-06
20,000	6.22E-06	8.88E-06	1.11E-05
26,000	7.99E-06	1.13E-05	1.42E-05
32,000	9.7E-06	1.37E-05	1.74E-05
38,000	1.14E-05	1.61E-05	2.03E-05
44,000	1.3E-05	1.84E-05	2.31E-05
50,000	1.45E-05	2.06E-05	2.58E-05

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Fig. 5.Full-screen View

Variation of core k_eff with burnup under different loading schemes

In the analysis and calculation, the ⁶⁰Co content in the results are not presented in absolute terms, but as the ratio of ⁶⁰Co content to the U content in the initial UO₂ fuel loading, for convenience in comparing the three schemes. When the relative content is calculated, the amount of U loaded per component at the initial time is set to 1 ton.

The activity of ⁶⁰Co at different burnup values can be estimated from the ⁶⁰Co half-life. The specific calculation is as follows:

$A=\lambda \left(\text{t}\right)\text{=}\lambda N_{\text{A}}m\left(t\right)/M,$ (1)

where the decay constant $\lambda$ is given in terms of the half-life T_1/2 by $\lambda \text{=}\ln 2/T_{1/2}$, $N_{\text{A}}$ is the Avogadro constant, $m\left(t\right)$ is the mass of the substance in the component, and $M$ is the molar mass of the substance.

From Fig. 5(inset) we can see that for four, six, or eight ⁵⁹Co rods in the assemblies, the corresponding k_eff values are smaller than for the prototype reactor. Moreover, k_eff decreases with increasing number of ⁵⁹Co rods, indicating greater absorption of neutrons by the ⁵⁹Co rod than by the reinforcing rod. It is obvious from Fig. 5 that after loading the ⁵⁹Co rods into the reactor core, the core lifetime has decreased. The calculation shows that the core lifetimes for the prototype reactor and Schemes One, Two, and Three are 188.5, 188.5, 188.8, and 190 d, respectively, indicating that loading four to eight cobalt rods into the core will shorten the core lifetime by one to two effective full-power days.

Based on the simulation results in Table 5, for a burnup of 20,000 MWd/MTU the specific activity of ⁶⁰Co for Schemes One, Two, and Three is 44.82, 43.73, and 43.25 Ci/g, respectively. When the burnup reaches 50,000 MWd/MTU, the specific activity is 104.77, 101.42, and 100.89 Ci/g, respectively, which is suitable for industrial irradiation sources.

4.2 Neutron flux in the axial direction

In this program, each rod bundle has a complete length of 365.8 cm and is divided into 73 segments of length about 5 cm; each bundle thus has 74 cross sections. The axial neutron flux distribution for all cross sections is of interest, but for simplicity of presentation, we have chosen to display only every fourth section to focus on trends in these simulations. The comparison between the three schemes and the prototype reactor is shown in Fig. 6a.

Fig. 6.Full-screen View

Neutron flux. (a) axial distribution (b) radial distribution.

It is shown from Fig. 6a that the axial neutron flux distributions of the three schemes are consistent with that of the prototype, and the deviations from the prototype are indeed small. The mean squared deviation can reflect the degree of deviation between the two groups. The smaller the value, the smaller the difference between the two groups. Table 6 (upper row) shows that the mean squared deviation of the third scheme is the smallest and its value is 8.9345e-15. The first scheme has the largest mean squared deviation, with the second scheme roughly midway between. This indicates that as more ⁵⁹Co rods are loaded in the assemblies, the less influence they exert on the axial neutron distribution.

Table 6.Full-screen View

Neutron flux, mean squared deviation from prototype PWR

Type	Scheme one	Scheme two	Scheme three
Neutron flux, axial distribution	1.8143e-14	1.2008e-14	8.9345e-15
Neutron flux, radial distribution	1.1313e-13	9.6046e-14	2.4838e-13

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4.4 The radial energy deposition(X)

The main source of heat in the reactor is the energy released in the fission chain reaction by the fissile material of the fuel pellet. MCNP provides a tally to calculate the average fission energy deposition of a cell; the tally can be used to calculate the core's power density, as energy deposition indirectly reflects the core's power level. As shown in Fig. 4, Cartesian coordinate system is established by using (8, H) components as coordinate origin, line 8 components as X axis, and column H components as Y axis. The radial distribution of energy deposition (X) for the three schemes and the prototype reactor are shown in Fig. 7a.

Fig. 7.Full-screen View

(a) The radial energy deposition (X). (b) The radial energy deposition (Y).

The difference between the various schemes cannot be seen from the Fig. 7a. However, in light of the results from Table 7, we can see that Scheme Two has a high degree of agreement with the prototype reactor, while the third scheme has a large deviation. The radial distribution of the neutron flux has an effect on the reactor power, so it follows that the second scheme has the least impact on power, while the third scheme brings about the most.

Table 7.Full-screen View

Energy deposition, compared to prototype reactor. (Mean squared deviation.)

Type	Scheme one	Scheme two	Scheme three
The radial energy deposition（X）	0.0078	0.0050	0.0158
The radial energy deposition（Y）	0.0060	0.0274	0.0374

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High local power density can lead to fuel rod melting. The local power density at the hottest part of the fuel rod is expressed by the power peaking factor, and it is therefore necessary to calculate the power peaking factor of the core before and after loading the cobalt rods. From the calculation we can see that the power peaking of the prototype reactor, Scheme One, Scheme Two, and Scheme Three is located 43 cm away from the midpoint of the reactor core in the X direction, and their power peaking factors are 1.158, 1.151, 1.156, and 1.178, respectively, showing a maximum deviation of 1.73%. This shows that the addition of the cobalt rods has little effect on the location of the power peak in the X direction.

5 Conclusion

To study the effect of loading ⁵⁹Co rods into a PWR core, we simulated the core with the ⁵⁹Co rods in three different configurations. The radial and axial distributions of neutron flux, and the radial distribution of energy deposition, were obtained from the Monte Carlo N-Particle (MCNP) program. Through comparison of the three ⁵⁹Co configurations (schemes) to a prototype PWR (without ⁵⁹Co), we can draw the following conclusions:

(1) There are differences noted between the three schemes and the prototype reactor; however, the differences are small.

(2) Because cobalt rods have a larger neutron absorption capability than the plug rods, the effective multiplication factor of these three schemes is smaller than the prototype PWR’s. Increasing the number of cobalt rods decreases the effective multiplication factor.

(3) For the axial distribution of neutron flux, the scheme with more ⁵⁹Co rods in the reactor is closest to the prototype reactor.

(4) Cobalt has a strong ability to absorb neutrons, resulting in a large change in the radial distribution of energy deposition near the location of the cobalt rods. Increasing the number of added ⁵⁹Co rods increases the deviation at those locations.

(5) The power peaking locations for the different schemes of ⁵⁹Co loading and the PWR prototype reactor are all at 43 cm from the midpoint of the core; the differences in the power peaking factor are small. Therefore, loading the ⁵⁹Co rods into the PWR has no significant effect on the radial power peaking.

In general, each scheme has its own pros and cons. Replacing the secondary neutron sources in the fuel assemblies with four ⁵⁹Co rods has only a small impact, and the parameters of the reactor remain almost unchanged. Therefore, in theory, the use of a PWR to produce ⁶⁰Co is feasible.

Producing ⁶⁰Co in the PWR is a sound way to mitigate the current shortage of the radioisotope, and an effective way to bring about extra benefits for the nuclear power plants. Yet there are still technical problems to be overcome before realizing the successful production of radioactive cobalt commercially. For instance, a prototype design of the isotope production module is needed for a specific reactor. Performance tests should be carried out on the cobalt source assemblies under the expected conditions of high temperature, high pressure, and a corrosive environment. The impact of the ⁶⁰Co radioactivity on the pressure vessel should also be tested. Moreover, it is necessary to develop the installation, disassembly, and the transportation methods for cobalt source assemblies to meet the operational requirements of the thermal chamber of the spent fuel pool.