1. Introduction

Anantharaman et al. (2008) investigated the utilization of thorium in nuclear reactors. The results indicate on this fact that the large-scale utilization of thorium requires the adoption of a closed fuel cycle. However, the stable nature of thorium and the radiological issues associated with it poses challenges in the adoption of a closed fuel cycle ^[1]. Sahin et al. (2004) investigated power flattening in the fuel bundle of a CANDU reactor using SCALE code. The results showed an elegant method of power flattening has been achieved in the bundle by decreasing the LWR spent fuel fraction and creasing the ThO₂ fraction in the mixed fuel in radial direction, by keeping the fuel rod dimensions unchanged ^[2]. Sahin et al (2006) evaluated CANDU reactor as a thorium burner. Two different fuel compositions have been selected for investigations: (1) 96% thoria (ThO₂) + 4% PuO₂ and (2) 91% ThO₂ + 5%UO₂ + 4% PuO₂. As the computational data shows, the reactor criticality kinf remains nearly constant between the 4th year and the 7th year of plant operation, and then, a slight increase is observed thereafter, along with a continuous depletion of the thorium fuel; this behavior is approximately identical for both investigated fuels. After the 2nd year, the CANDU reactor begins to operate practically as a thorium burner. The reactor criticality would be sufficient until a great fraction of the thorium fuel is burned up, provided that the fuel rods could be fabricated to withstand such high burn-up levels. Fuel fabrication costs and nuclear waste mass for final disposal per unit energy could be reduced drastically ^[3]. Vu and Kitada (2015) investigated multi-cycle seed and blanket ADS core for higher thorium utilization and TRU waste transmutation. They concluded that instead of wasting thorium fuel and its breeding 233U, by removing the Th assemblies after each cycle, thorium fuel assemblies are remained inside the core and utilized to produce energy by employing multiple cycles. In addition, they reported in the equilibrium state, the thorium fuel contribution to total core power is improved (35.7%) compared to the startup cycle. It also has the benefit of reducing the axial power peaking at BOC from 2.50 at startup cycle to 1.42 at equilibrium state. Compared to the startup cycle, the TRU transmutation rate of the equilibrium cycle reduces about 15 kg per ton of spent HM ^[4]. Other work carried out by them investigates conceptual designs of accelerator driven systems (ADS) that utilize thorium fuel as blanket and reprocessed fuel as seed. Their results showed with increasing MA content, the TRU transmutation rate is increased while void reactivity of the system becomes less negative and increasing the core size by introducing more thorium and reprocessed fuel assemblies into the system reduces the TRU transmutation rate and reactivity swing due to burnup of the system. In this work, higher MA content is suggested to match the efficient transmutation purpose and safety features during operation ^[5].

Ding and Kloosterman (2014) studied a concept of seed-and-blanket (S&B) fuel block in a long-life block-type HTR with a thermal power of 20 MWth in order to assess of thorium utilization in high temperature gas-cooled reactors (HTRs). The data showed the comparative analysis of the S&B fuel block with the Th/U MOX fuel block shows that the former has a longer lifetime and a lower reactivity swing ^[6].

Different compositions of thorium-contained nuclear fuels were investigated to evaluate their neutronic behavior in the modeled CANDU 6 reactor such as ThC+PuC and ThO₂+UO₂ ^[7-9].

In addition, many works were carried out to compare and investigate the UO₂ and ThO₂ fuel physical properties such as thermal conductivity in a range of different temperatures, oxygen self-diffusion over a range of temperatures which is important in UO₂ and ThO₂ nuclear fuel applications, the fuel compound stability and so on ^[10-12]. These appreciated works verify the ThO₂ has admirable physical behavior as UO₂ fuel properties or even more appropriate when it must be used as nuclear fuel.

2. Material and method

In this work, MCNPX 2.6.0 has been used as a powerful particle transport code with ability of calculation of steady-state reaction rates, normalization parameters, neutronic parameters as well as fuel burn up using CINDER90 to calculate the time-dependent parameters ^[7,8]. A square-lattice 380-assembly CANDU 6 core has been modeled using the code. Heavy water has been considered as coolant and moderator. A 3D neutronic model was set up using MCNPX 2.6.0 code in cold zero power situations by means of ENDF/B-VI continuous-energy cross section. The cross sections of S(α, β) have been used for heavy water. KCODE capability has been used for neutronic parameter calculations. In any fuel assembly, 31 concentric UO₂ fuel rods and 6 ThO₂ rods have been considered with CANDU 6 ^[9] assembly characteristics. Weight fraction of ²³⁵U was 1.2% in any fuel rod. Neutronic parameters of the modeled CANDU core have been calculated. The cross sectional view of the modeled CANDU core in MCNPX, has been depicted in Fig. 1.

Fig 1.Full-screen View

Cross sectional view of a) Fuel assembly b) the modeled CANDU core.

To investigate impacts of ThO₂ rod insertion in UO₂ fuel assemblies on neutronic performances of the modeled core, the following neutronic parameters have been calculated. Radial and axial deposited power distributions have been calculated using a mesh tally card for the hottest fuel assembly. Average fission per absorption ratio has been calculated using F4 tally. Reactivity coefficients of fuel, coolant and moderator have been calculated using TMP card and temperature-related cross section libraries of .70c, and.71c from endf70 in MCNPX. Void reactivity variations of the coolant have been calculated for the different fuel loads in the modeled CANDU core. Delayed neutron fraction and effective delayed neutron fraction have been calculated for the core fueled the different. Burn-up calculation has been performed by the power of 2600 MW for 1 year using BURN card.

2.1. Results and discussion

Therefore, obviously the hottest fuel assembly is the central one. Power distribution in the hottest fuel assembly has been calculated using a mesh tally card. The calculations showed in the hottest fuel assembly, the external ring contained fuel rods experiences the most power deposition in comparison with the inner rings (Fig.2).

Fig 2.Full-screen View

Power distribution in a) the hottest fuel assembly b) total core.

Hence, power density has been calculated for the hottest fuel rod. Radial power peaking factor of the hottest fuel assembly was 1.15. The radial and axial power peaking factors of the modeled core were 1.66 and 1.54. Neutron spectra have been calculated for the CANDU 6 core fueled with ThO₂ and UO₂ fuel rods. The calculations showed about 68% of neutron spectra available in whole CANDU core is thermal while about 35.6% of neutrons in Calandria are thermal The obtained results in Table 1 showed neutron generation time of the modeled core was 633 μs. Delayed and effective delayed neutron fractions were 755 pcm and 692 pcm respectively. The carried out calculations showed the UO₂ fuel rods experiences noticeably higher fuel temperature reactivity coefficient than the ThO₂ fuel rods with 81% relative discrepancy; both temperature reactivity coefficients are negative. Computational data showed moderator and coolant reactivity coefficients are negative as well. The computational data showed the hottest fuel rod receives higher power density (407 W/cm3) than the other fuel rods. In addition, the hottest ThO₂ rod experiences considerably less power deposition than the hottest UO₂ at 2600 MW power ($0.69\ll 23.9 kW$).

Table 1.Full-screen View

Comparison of different neutronic parameters of the modeled CANDU core fed different fuel matrixes.

Neutronic parameters	Values
Neutron Generation time (μs)	633
Delayed neutron fraction (pcm)	755±17
Effective delayed neutron fraction (pcm)	692±15
Fission per non-fission absorption ratio in UO2	0.64
UO2 temperature reactivity (mk/K)	-0.0142
ThO2 temperature reactivity (mk/K)	-0.0026
Coolant temperature reactivity (mk/K)	-0.0104
Moderator temperature reactivity (mk/K)	-0.0439
Deposited power in the hottest UO2 rod (kW)	23.9
Deposited power in the hottest ThO2 rod (kW)	0.69
The hottest UO3 rod power density (W/cm3)	407
Radial power peaking factor	1.66
Axial power peaking factor	1.54
Radial power peaking factor of the hottest assembly	1.15
Fraction of neutrons with En<1 eV in total core (%)	68.60
Fraction of neutrons with 1eV< En <1 keV in total core (%)	13.20
Fraction of neutrons with En>1 keV in total core (%)	18.30
Statistical errors (%)	<0.2

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* The variation has been calculated during transit from 293 K to 599 K

Burn-up calculations showed after burn-up beginning, the effective multiplication has a growth with a fast slope so that after 45-days burn-up process a positive reactivity about 5993 pcm is occurred. As it is seen in Fig. 5, the effective multiplication factor starts to decrease up EOC (1 year) so that there is about -9928 pcm reactivity variation comparing the BOC reactivity (Fig.3).

Fig 5.Full-screen View

Dependence ¹³⁵Xe buildup to burn-up time.

Fig 3.Full-screen View

Dependence of effective multiplication and integrated neutron flux of whole the modeled core to burn-up time.

As the Fig.4 shows, after 1 year the ThO₂ burn-up was 38.2 MW/MTU and the value was 140 MW/MTU in case of UO₂ fuel rods.

Fig 4.Full-screen View

Dependence of burn-up of the modeled core to time.

As it is seen in Figs 5-6, ¹³⁵Xe and ¹⁴⁹Sm buildups are noticeably higher in UO₂ fuel rods comparing ThO₂ fuel rods. As the figures show there is a peak in concentration of the neutron poisons around the 15th day while after that ¹³⁵Xe and ¹⁴⁹Sm concentration is decreasing up EOC.

Fig 6.Full-screen View

Dependence ¹⁴⁹Sm buildup to burn-up time.

²³³Th and ²³³Pa will decay to ²³³U during a proposed cooling time of the spent fuel. ²³²Pa produced low concentration (~1.16 g) decays to ²³²U during the cooling time of the spent fuel as well. Concentrations of the uranium isotopes will be about 50.01 kg of ²³³U, 1.168 g of ²³²U, 29.44 kg of ²³⁴U, 6.262 kg of ²³⁵U and 12.09 kg of ²³⁶U. Consequently, ²³³U and ²³⁴U devote respectively 27.8% and 44.5% of weight fractions of the uranium isotopes of the spent fuel (Table 2).

Table 2.Full-screen View

Investigation of the different produced actinides in ThO₂ burnt fuel rods at 2600 MW power.

Isotope	Mass (g)	Decay chain
231Th	1.151E+00	${}_{90}{}^{231}Th\stackrel{25.52 h, {\beta }^{-}}{\to }{}_{91}{}^{231}Pa\stackrel{32760 y, \alpha }{\to }{}_{89}{}^{227}Ac\dots$
233Th	2.631E+01	${}_{90}{}^{233}Th\stackrel{22.3 m, {\beta }^{-}}{\to }{}_{91}{}^{233}Pa\stackrel{26.697 d, {\beta }^{-}}{\to }{}_{92}{}^{233}U\dots$
232Pa	1.168E+00	${}_{91}{}^{232}Pa\stackrel{1.31 d, {\beta }^{-}}{\to }{}_{92}{}^{232}U\stackrel{68.9 y, \alpha }{\to }{}_{90}{}^{228}Th\dots$
233Pa	3.165E+04	${}_{91}{}^{233}Pa\stackrel{26.697 d, {\beta }^{-}}{\to }{}_{92}{}^{233}U\dots$
233U	1.838E+04	${}_{92}{}^{232}U\stackrel{1.592E+5 y, \alpha }{\to }{}_{90}{}^{229}Th\stackrel{7340 y, \alpha }{\to }{}_{88}{}^{225}Ra\dots$
234U	2.944E+04	${}_{92}{}^{234}U\stackrel{2.455E+5 y, \alpha }{\to }{}_{90}{}^{230}Th\stackrel{7.538E+4 y, \alpha }{\to }{}_{88}{}^{226}Ra\dots$
235U	6.262E+03	${}_{92}{}^{235}U\stackrel{7.038E+8 y, \alpha }{\to }{}_{90}{}^{231}Th\stackrel{25.52 h, {\beta }^{-}}{\to }{}_{91}{}^{231}Pa\dots$
236U	1.209E+04	${}_{92}{}^{236}U\stackrel{2.342E+7 y, \alpha }{\to }{}_{90}{}^{232}Th\stackrel{1.405E+10 y, \alpha }{\to }{}_{88}{}^{228}Ra\dots$

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UO₂ burn-up calculations at 949 GWd showed ²³⁴U concentration at the EOC is less than 1 g while 4.471 kg of ²³⁶U was produced in the spent fuel. In addition, the produced mass of ²³⁷U and ²³⁹U isotopes was low at the EOC of the modeled core (100.1 and 169.6 g respectively). Three neptunium isotopes were produced at the EOC consisted of ²³⁷Np, ²³⁸Np and ²³⁹Np with concentrations of 0.354, 0.015 and 23.46 kg respectively that after the cooling time the only remained isotope is ²³⁷Np. The produced plutonium isotopes are ²³⁸Pu, ²³⁹Pu, ²⁴⁰Pu, ²⁴¹Pu and ²⁴²Pu which only ²³⁸Pu concentration is less than 0.07 kg. Total produced mass of plutonium isotopes is about 94.339 kg. It should be noted after a proposed cooling time the ²³⁹Pu concentration will increase to 55.3 kg (Table 3). According to the presented data in Table 4, 99.99% of the initial loaded ²³⁵U was consumed after 1-year burn-up while about 74.49% of ²³⁸U initial load was depleted after the burn-up time. In case of ThO₂ fuel, 36.94% of the ²³²Th initial load was depleted after the burn-up time.

Table 3.Full-screen View

Investigation of the different produced actinides in UO₂ burnt fuel rods at 2600 MW power.

Isotope	Mass (g)	Decay chain
234U	8.242E-02	${}_{92}{}^{234}U\stackrel{2.455E+5 y, \alpha }{\to }{}_{90}{}^{230}Th\stackrel{7.538E+4 y, \alpha }{\to }{}_{88}{}^{226}Ra\dots$
236U	4.471E+03	${}_{92}{}^{236}U\stackrel{2.342E+7 y, \alpha }{\to }{}_{90}{}^{232}Th\stackrel{1.405E+10 y, \alpha }{\to }{}_{88}{}^{228}Ra\dots$
237U	1.001E+02	${}_{92}{}^{237}U\stackrel{6.75 d, {\beta }^{-}}{\to }{}_{93}{}^{237}Np\stackrel{2.14E+6 y, \alpha }{\to }{}_{91}{}^{233}Pa\dots$
239U	1.696E+02	${}_{92}{}^{239}U\stackrel{23.45 m, {\beta }^{-}}{\to }{}_{93}{}^{239}Np\stackrel{2.3565 d, {\beta }^{-}}{\to }{}_{94}{}^{239}Pu\dots$
237Np	3.546E+02	${}_{93}{}^{237}Np\stackrel{2.14E+6 y, \alpha }{\to }{}_{91}{}^{233}Pa\dots$
238Np	1.547E+01	${}_{93}{}^{238}Np\stackrel{2.117 d, {\beta }^{-}}{\to }{}_{94}{}^{238}Pu\stackrel{87.7 y, \alpha }{\to }{}_{92}{}^{234}U\dots$
239Np	2.346E+04	${}_{93}{}^{239}Np\stackrel{2.3565 d, {\beta }^{-}}{\to }{}_{94}{}^{239}Pu\dots$
238Pu	6.999E+01	${}_{94}{}^{238}Pu\stackrel{87.7 y, \alpha }{\to }{}_{92}{}^{234}U\dots$
239Pu	3.184E+04	${}_{94}{}^{239}Pu\stackrel{244110 y, \alpha }{\to }{}_{92}{}^{235}U\dots$
240Pu	1.616E+04	${}_{94}{}^{240}Pu\stackrel{6563 y, \alpha }{\to }{}_{92}{}^{236}U\dots$
241Pu	1.043E+04	${}_{94}{}^{241}Pu\stackrel{14.35 y, {\beta }^{-}}{\to }{}_{95}{}^{241}Am\stackrel{432.2 y, \alpha }{\to }{}_{93}{}^{237}Np\dots$
242Pu	3.590E+04	${}_{94}{}^{242}Pu\stackrel{3.733E+5 y, \alpha }{\to }{}_{92}{}^{238}U\dots$

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Table 4.Full-screen View

Investigation of variations of the most important neutronic parameters, fissile and fertile consumption and fissile inventory after 1-year burn-up process at 2600 MW power.

Neutronic parameters				Consumption			Inventory
Radial P.P.F.	Λ (µs)	β (pcm)	βeff (pcm)	UO2 load		ThO2 load	UO2 load	ThO2 load
1.66 BOC	633 BOC	755 BOC	692 BOC	235U (kg)	238U (kg)	232Th (kg)	239Pu (kg)	233U (kg)
1.67 EOC	689 EOC	337 EOC	285 EOC	87.519	4764.00	436.60	31.84	18.38

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UO2 burn-up calculations at 365 GWd showed ²³⁴U concentration at EOC is less than 1 g while 9.78 kg of ²³⁶U was produced in the spent fuel. In addition, the produced mass of ²³⁷U and ²³⁹U isotopes was low at the EOC of the modeled core (90.1 and 123 g respectively). Three neptunium isotopes were produced at the EOC consisted of ²³⁷Np, ²³⁸Np and ²³⁹Np with concentrations of 1.09, 0.022 and 17.6 kg respectively, that after the cooling time the only remained isotope is 237Np. The produced plutonium isotopes are ²³⁸Pu, ²³⁹Pu, ²⁴⁰Pu, ²⁴¹Pu and ²⁴²Pu which only ²³⁸Pu concentration is less than 0.5 kg. Total produced masses of plutonium isotopes is about 233 kg. It should be noted after a proposed cooling time the ²³⁹Pu concentration will increase to 109.5 kg (Table 4).

In addition, the ²³³U and ²³⁹Pu buildup in the fuel rods during burn-up process decreased the effective delayed neutron fraction and delayed neutron fractions at EOC while the core radial power peaking factor did not change noticeably (Table 4).

The simulation results presented in Table 5 shows a comparison between the CANDU 6 modeled core and the reported data by AECL in case of CANDU 6 and ACR-700 cores for some dynamic parameters. In Table 5 data, it is observed the modeled core meet considerably higher reactivity coefficients comparing the two reported data by AECL. In addition, the modeled core delayed neutron fraction is higher in the case of the modeled CANDU 6 core comparing the other investigated options.

Table 5Full-screen View

Comparison of some safety parameters of the CANDU core fed different fuels [16].

Safety parameter	ThO2 and UO2 rods, CANDU 6	NatUO2, CANDU 6	EnrichedUO2, ACR-700
Fuel temperature effect (mk/K)	-0.0168	Small negative	-0.0044
Coolant temperature effect (mk/K)	-0.0104	Positive	-0.0033
Moderator temperature effect (mk/K)	-0.0439	Slightly positive	-0.0072
Void effect (mk)	-2.421	+10 ̶ 15	-3.0
Delayed neutron fraction (pcm)	633	580	560
Prompt neutron life time (ms)	0.55	0.92	0.33

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Minor actinide burn-up calculation errors were less than 0.2%, except ²³⁶U, which its error was approximately 1.5%. ¹⁴⁹Sm burn-up calculation error was about 1.5% and ¹³⁵Xe error was about 5%. Burn-up calculation errors of the other non-actinides were less than 1.5%, except ¹²C with about 13% error and ⁹⁶Zr with about 11% error.

3. Conclusion

High proliferation resistance and noble neutron economy of thorium-based fuels have caused this type of fuel is experimentally and computationally be investigated for future alternatives. Moreover, the carried out researches prove this fact that the thorium-based fuels can improve accessible energy efficiency and disposal costs if be considered in closed cycles. In the present study, MCNPX 2.6.0 Monte Carlo-based statistical code has been used to simulate neutronic performances of ThO₂ fuel rods inserted in any CANDU 6 fuel assemblies. The obtained data show the ThO₂ 6-rods ring used in the 37-rods designed CANDU 6 assembly can conclude in a peaking factor of 1.15 in the hottest assembly and keeps the core peaking factor less than 2.55 (1.66 Radial P.P.K.×1.54 Axial P.P.K.). The core burn-up calculations showed 18.38 kg of ²³³U fissile material is available in the spent ThO₂ at 949 GWd burn-up. After a proposed cooling time, about 50.03 kg of ²³³U is available in the spent ThO₂. By reprocessing of the ThO₂ spent fuel, ²³²Th and the Uranium isotopes can be separated chemically for future applications. A comparison between AECL data and the present study of some dynamic parameters showed the considered assembly configuration for the CANDU 6 core meets sufficiently negative reactivity coefficients.