In this paper, neutronic calculations and the core analysis of the VVER-1000 reactor were performed using MCNP6 code together with both ENDF/B-VII.1 and ENDF/B-VIII libraries. The effect of thorium introduction on the neutronic parameters of the VVER-1000 reactor was discussed. The reference core was initially filled with enriched uranium oxide fuel and then fueled with uranium-thorium fuel. The calculations determine the delayed neutron fraction βeff, the temperature reactivity coefficients, the fuel consumption, and the production of the transuranic elements during reactor operation. βeff and the Doppler coefficient (DC) are found to be in agreement with the design values. It is found that the core loaded with uranium and thorium has lower delayed neutron fraction than the uranium oxide core. The moderator temperature coefficients of the uranium-thorium core are found to be higher than those of the uranium core. Results indicated that thorium has lower production of minor actinides (MAs) and transuranic elements (mainly plutonium isotopes) compared with the relatively large amounts produced from the uranium-based fuel UO2.

1. Introduction

Countries are building nuclear power plants to meet their energy needs; the site of nuclear power plant in Egypt is El Dabaa. The VVER-1200 is the predecessor of the VVER-1000 reactor. The VVER-1000 is a 3000 MW thermal power nuclear power plant which is cooled and moderated by light water. The core is filled with 163 enriched uranium (UO2) fuel assemblies (FAs). The reactor includes international safety standards with evolutionary design improvement in the areas of fuel technology, modularized construction, safety systems, and standardized designs [1, 2].

In fact, thorium is three times more abundant than uranium, and the feasibility of loading the core with thorium uranium fuel was carried out. Thorium is made up mainly of “fertile” isotope (232Th). Experiments have been made on power reactors that were successfully operated using ThO2-UO2 fuel in light water reactors (LWRs). 233U and 232Th are the best “fissile” and “fertile” materials, respectively, for thermal neutron reactors [3].

The neutronic parameter effects due to loading thorium as a part of VVER-1200 fuel under normal operation were studied by Dwiddar et al. [4]. The investigation used two different configurations, mixed uranium fuel with thorium and seed-blanket fuel. The amount of thorium inserted and the location of the thorium assemblies in the core of the reactor presented the master factor in determining the value of keff and the core cycle length. The results concluded that the safest position of thorium is in the periphery of the core, and it is recommended to provide a blanket of mixed thorium uranium fuel for the entire core as the peripheral layer with the highest value of uranium enrichment. Mixing thorium with plutonium instead of uranium for the uranium enrichment, limited to 5%, was suggested.

Minimizing the fission products (FPs) using thorium as a fuel in place of the traditional UO2 fuel has been studied by Galahom [5]. This paper discussed the VVER-1200 neutronic features for one assembly. The assembly fuel is a mix of thorium (fertile) with uranium (fissile). The neutronic features were calculated and compared with the traditional UO2 fuel by using MCNPX code. The purpose of this study is to minimize the production of long-lived actinides and improve the fuel cycle length. The moderator temperature coefficient and the percentage of fissile inventory have been measured at different burn steps. The results showed that thorium fuels were better than UO2, and by replacing 238U with 232Th, we need much 235U as a fissile material to sustain the same burnup level. For 232Th+235U fuel, the Doppler coefficient (DC) was more negative [5]. Production of long-lived actinides using thorium, fertile material, was reduced.

The possible advantages of the seed-blanket (SB) assembly used in the VVER-1200 core instead of the homogeneous assembly were investigated using MCNPX 2.7 code and the ENDF/B-VII library [6]. The blanket region fertile material was 232Th, while in the seed region, four different fissile materials have been investigated. The work concluded that in the homogeneous assembly, the power distribution is flatter than that of the heterogeneous assembly. The suggested fuels achieved a longer fuel cycle and a higher conversion ratio in the SB assembly than the homogeneous assembly. Moreover, using 232Th instead of 238U resulted in reducing the plutonium and the production of transuranic atoms.

Heterogeneous and homogeneous seed-blanket concepts were used to study the thermal hydraulics feasibility and the neutronics to change the AP1000 PWR reactor from UO2 to (U-Th)O2 [7]. The burnable poison geometry and materials in the core were not varied and only the fuel pin material was varied keeping the low enriched uranium (LEU) for 235U. The study used three different fuel types, the first being 68% ThO2-32% UO2; the second being 76% ThO2-24% UO2; and the third being 80% ThO2-20% UO2. The work goals were to increase 233U and minimize production of plutonium. The results showed that the homogeneous concept with three distinct types of fuel meets the optimization requirements. The results revealed that (U-Th)O2 hase many benefits, including a lower power density, retaining the same 18 months cycle, and a lower concentration of B-10 in the soluble poison and the elimination of B-10 in the coated integral boron poison [7].

In this paper, the neutronic performance and core analysis of the VVER-1000 one-six core were performed from the beginning of life (BOL) at cold zero power state (CZP) to the end of life (EOL) at hot full power state (HFP). The VVER-1000 reference core was initially filled with enriched uranium oxide fuel and then fueled with uranium-thorium fuel. Since thorium-based fuel is more favorable from the safeguard viewpoint, it is investigated in the present work as a fuel option to increase the fuel cycle length and reduce the plutonium amount produced. The neutronics calculations were made by MCNP6 code with two cross section libraries ENDF/B-VII.1 and ENDF/B-VIII.

2. The VVER-1000 Reactor Core Description

The VVER-1000 reactor type is a four-loop Russian version of the pressurized water reactor (PWR) producing about 1000 MW electric power. Figure 1 shows the core loading pattern for the first cycle of operation at the beginning of life (BOL) [8]. The reactor fresh core consists of FAs, which differ from one another by the enrichment of the fuel. The brief details of the core FAs were illustrated by Aghaie et al. [9]. The reactor core, FA, and fuel rod characteristics are shown in Table 1 [10].

In order to provide lower center temperatures and a free volume to allow any released fission gas to expand and thus decrease internal pressure, the fuel contains a central void hole in its fuel pellet [11]. The form of FAs, numbers, and average enrichment loaded for the first cycle of operation are shown in Table 2 [12].

The core configuration for the mixed thorium-uranium fuel used in this simulation is shown in Figure 2, where the 3rd fuel batch with 4.95% enrichment is composed of 50% UO2 and 50% ThO2.

3. Methods of Calculation and Validation

MCNP6 is the result of merging MCNP5 and MCNPX codes with new available options capabilities and features. MCNP6 includes more capabilities such as Shannon entropy, more options for tally treatments and tagging, variance reduction control methods, and more options for geometry and particles. This code is high fidelity due to its accuracy in simulating geometries and materials with continuous energy processing of nuclear parameters [13].

The largest update to the ENDF library is represented in ENDF/B-VIII. These neutron sublibraries have been expanded by 32% to include 557 evaluations. ENDF/B-VIII and ENDF/B-VII.1 were the libraries used in this study [14, 15].

In this study, the VVER-1000 one-six core shown in Figure 3 was simulated. It was fueled firstly with UO2 and then fueled with ThO2+UO2. The neutronic parameters are presented for the two fuels. The simulation performed used 100000 neutron per cycle, 150 skipped cycles, and 250 active cycles.

ENDF/B-VIII library has the maximum neutron reactions changes on nuclides including actinides which affect nuclear criticality simulations. Two of the most important re-evaluated isotopes are uranium-235 and uranium-238. The re-evaluated parameters include the following.(i)The capture and fission cross section values: the cross sections for capture reaction have been reduced as compared with ENDF/B-VII.1 in the 0.5–2 keV region, but increased in energies up to 80 keV. The fission cross section evaluation agrees with the ENDF/B-VII.1 uncertainties around 0.4% higher for incident energies less than 15 MeV [14, 16].(ii)The neutron multiplicity: the neutron multiplicity ν was re-evaluated and expanded below 30 eV to include fluctuations. Unlike ENDF/B-VII.1 in which ν is constant over a wide range of incident neutron energy, there is no constant ν in ENDF/B-VIII, but its value varied as the incident neutron energy varied [14, 16].(iii)The thermal neutron constants (TNCs): TNC new evaluations for uranium-235 show a neutron multiplicity reduction and a fission cross section increment as compared with ENDF/B-VII.1 evaluations at thermal energy. The comparison between the evaluated thermal neutron constants for ENDF/B-VII.1, ENDF/B-VIII, and the standard 2017 values [14, 16] is illustrated in Table 3.(iv)(n,f) Prompt fission neutron spectrum (PFNS): the ENDF/B-VIII evaluation for the PFNS mean energy is clearly softer than that of ENDF/B-VII.1, but it fits well with experimental data. The new average released neutron energy becomes 2.00 ± 0.01 MeV; on the other hand, it was 2.03 MeV in thermal range [16].(v)Cross sections of (n, n’) and (n, xn): the ENDF/B-VIII evaluation for the total inelastic scattering cross section (n, n’) is slightly decreased than the last ENDF/B-VII.1 evaluation. ENDF/B-VIII valuation for the (n, xn) secondary neutron was not changed but showed a difference above 14 MeV.(vi)Nubar: evaluators used the parameter nubar to study criticality problems since criticality is highly sensitive to nubar. Several simulations have shown that the use of the new PFNS and TNCs of ENDF/B-VIII produces marginally higher keff values than those of ENDF/B-VII.1 [17, 18].

The above 6 factors explain the marginal increment of ENDF/B-VIII than ENDF/B-VII.1 in the criticality calculations as will be shown in results.

4. Results and Discussion

The neutronic calculations of the VVER-1000 reactor are presented starting from the beginning of life (BOL) to the end of life (EOL). At BOL, the reactivity coefficients were estimated. The reactivity coefficients together with the delayed neutron fraction βeff are the key parameters in the reactor dynamics response. The reactivity coefficients include the moderator temperature coefficient (MTC) and Doppler coefficient (DC). The end of life calculations include the burnup results (fuel consumptions and actinide productions). The neutronic parameters were calculated by MCNP6 with ENDF/B-VII.1 and ENDF/B-VIII and compared with the reactor design parameters [19] and published results [9, 20]. It is necessary for any reactor core to have delayed neutrons since they can control the increase in the reactor power [21]. βeff is calculated by using the following equation:

where kprompt is the effective multiplication factor using only prompt neutrons, while keff is the effective multiplication factor using both prompt and delayed neutrons. The fuel temperature coefficient of reactivity (DC) can be calculated by using the following equation:

K1 is calculated in case moderator and fuel are at 300 K and k2 is calculated in case moderator is at 300 K while fuel is at 600 K [22]. MTC was determined by the following equation:

K3 is calculated in case fuel and moderator are at 600 K.

4.1. The Beginning of Life (BOL) Results

The comparison between the calculated parameters with the published results is shown in Table 4. This comparison allows assessing the validity of the current VVER-1000 simulation. A general overall good agreement can be observed. In case of fueling the core with UO2, βeff values were 0.0078 and 0.00688 with ENDF/B-VII.1 and ENDF/B-VIII, respectively, while the expected value from the 235U fission is 0.00650 according to Lamarsh and Baratta [23], so it was realistic to see the core has a delayed neutron fraction that is greater than this expected value. According to RFANE [19], the delayed neutron fraction is 0.00740 and 0.007110 according to Gholamzadeh et al. [20] which is in agreement with the obtained results. The fraction of the delayed neutrons differs from fuel material to another. βeff was 0.0031 and 0.0069 for 233U and 235U materials, respectively, according to IAEA [3] which means that the ThO2+UO2 core is expected to have a low delayed neutron fraction and this is clear in Table 4. βeff values are 0.00628 and 0.00545 with ENDF/B-VII.1 and ENDF/B-VIII falling in the expected range for ThO2+UO2 core.

4.2. Temperature Coefficients of Reactivity

This section discusses the reactor operation safety parameters which are the variation of the reactivity with temperatures (the temperature coefficients of reactivity). Table 4 presents the main operating safety parameters (DC and MTC). As the temperature of the moderator increases, its density decreases and lower fraction of neutrons is slowed down, resulting in negative change of reactivity. On the other hand, the neutron spectrum hardens due to the decrease of moderator fraction, which will decrease the core reactivity. The above two factors compete with each other and might lead to a negative MTC.

The DC is the most important safety parameter because it measures the reactor operation stability. The higher temperature of fuel permits the fertile material to absorb many neutrons away from the fission. 232Th absorbs larger neutrons than 238U in higher fuel temperatures. Therefore, thorium-based fuel has more negative DC than the uranium fuels; this is clearly shown in Table 4. The MTC is the change in reactivity by changing the moderator temperature. The reactor is designed to have negative MTC value to provide negative reactivity feedback, which indicates that the more the temperature increases, the more the reactivity decreases. The UO2 MTC is more negative than ThO2+UO2; this is because of the larger fast fission cross section of U-238 than that of Th-232, and this agrees with the results in Table 3. The higher temperature of fuel permits the fertile material to absorb many neutrons away from the fission. Th-232 absorbs larger neutrons than U-238 in higher fuel temperatures [5].

4.3. The Middle of Life (MOL) Results

The behavior of keff over time for the VVER-1000 core can be seen in Figure 4. The calculations were performed along with 5 burnup steps of 100 days. The standard deviations for keff values ranged from 0.00036 to 0.0004 for UO2 fuel and from 0.00036 to 0.00041 for ThO2+UO2 fuel. keff values were 1.19911 and 1.23126 for UO2 and ThO2+UO2, respectively, at BOL. It then decreased with the depletion of the fuel. ThO2+UO2 core can keep criticality for more than 500 effective full power days while the UO2 core can keep criticality nearly up to 450 effective full power days. In the following figures, UO2-7 represents current results for UO2 core by ENDF/B-VII.1; UO2-8 represents current results for UO2 core by ENDF/B-VIII; UTh-7 represents current results for ThO2+UO2 core by ENDF/B-VII.1; UTh-8 represents current results for ThO2+UO2 core by ENDF/B-VIII.

As mentioned before, this simulation uses the ThO2+UO2 core configuration where the 3rd fuel batch with 4.95% enrichment is composed of 50% UO2 and 50% ThO2. Not only the thorium amount inserted but also the thorium assemblies location in the reactor play the principal role in keff value determination and the core cycle length. The thorium location in the periphery results in higher value of keff and longer length of cycle [3].

After 500 effective full power days, the ThO2+UO2 core remains supercritical and this can be explained by the fact that since only half of the UO2 fuel is replaced with ThO2 which is located in the low neutron flux periphery assemblies. Moreover, insertion of thorium increases the first core cycle length compared with UO2 core fuel cycle, and increasing the UO2 enrichment may help this. For this reason, in order to obtain more optimum advantage of thorium, it has to be rearranged in the middle of the core. This strategy can be realized by locating ThO2 in the core periphery for the first operational cycle and then shuffling them into the core interior in the subsequent cycles.

Thorium was mixed with 235U to provide power till building enough 233U amounts. Figure 5 illustrates the change in the burnup rate over time. As time passes, the burnup rate increases till it reaches 20.13 and 21.3 GWD/MTU for the UO2 and ThO2+UO2 one-six core, respectively, at end of life (EOL). Figure 5 shows that the core burnup results of ENDF/B-VII.1library are typically the results of the ENDF/B-VIII library, and the changes appear only in the criticality calculations.

4.4. The End of Life (EOL) Results

The 235U is the core fissionable material in that it steadily decreases as it burns over the lifetime of the core, in addition to increasing the output of 239Pu and 240Pu levels towards the EOL. The fissile component 235U is depleted from the startup until EOL, and other fissile components are created when 238U is transmuted to higher actinides, especially 239Pu and 240Pu. The quantity of total fission products (FPs) in the core grows up as the burnup level increases. FPs are neutron absorbers which have a strong adverse effect on the neutron economy of the core as time passes. Figures 6 and 7 show the fuel consumption and the production of actinides that build up in the UO2 and ThO2+UO2 cores.

The UO2 core contains 235U+238U; the two isotopes were re-evaluated in the ENDF/B-VIII library which means marginal differences in results, and this appears in Figure 6(a) especially for the consumption of 235U. On the other hand, ENDF/B-VIII did not re-evaluate thorium. The thorium core contains 235U+238U+232Th, hence the slight difference in the UTh-7 and UTh-8 mainly from 235U+238U cross section difference. The principal benefit of using thorium as a fuel option is to get as much fissile isotope 233U as possible and eliminate the plutonium production, and this is clearly demonstrated in Figure 7.

Figure 8 shows the neptunium isotope masses produced during the reactor operational cycle. Figure 9 presents the consumption of thorium in the ThO2+UO2 core. There was a thorium consumption difference between ENDF/B-VII.1 and ENDF/B-VIII at 200 days, but we do not have any explanation for this difference.

5. Conclusion

From the beginning of life to the end of life, the VVER-1000 neutronic parameters were calculated using MCNP6 code. These parameters were determined for a UO2 and a mixed ThO2+UO2 fuel. The obtained results fall within an acceptable range with respect to the reactor design parameters and the published data. The delayed neutron fraction βeff values were found to be 0.0078 and 0.00688 for UO2 fuel, with ENDF/B-VII.1 and ENDF/B-VIII, respectively, which are in an agreement with the reference value of 0.00740. On the other hand, ThO2+UO2 has lower delayed neutron fraction βeff values (0.00628 and 0.00545) than UO2 fuel. For the UO2 fuel, its MTC value was −1.39 × 10−41 (°C) while for the ThO2+UO2 fuel, it was −0.339 × 10−4 (°C) with ENDF/B-VII.1. All fall in the reactor design operational limits. It has been shown that the MTC of the UO2 core is more negative than that of the ThO2+UO2 one; this is because of the larger fast fission cross section of 238U than that of 232Th. Thorium-based fuel has more negative DC than the uranium fuels. The behavior of keff over time for both cores explained the slight increment of ENDF/B-VIII than ENDF/B-VII.1 in the criticality calculations for the UO2 fuel. keff decreased with the depletion of the fuel indicating that the UO2 core has to be refueled earlier than the ThO2+UO2 core for the first cycle of operation. The plutonium isotopes produced due to the ThO2+UO2 core were lower than those of the UO2 core.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.