Research Article 
Corresponding author: Aleksey V. Lavronenko ( lavronenkoaleksey@gmail.com ) Academic editor: Yury Korovin
© 2022 Aleksey V. Lavronenko, Vyacheslav G. Savankov, Ruslan A. Vnukov, Elena A. Chistozvonova.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Lavronenko AV, Savankov VG, Vnukov RA, Chistozvonova EA (2022) Comparison of methods for calculating the neutronic characteristics of a VVER1200 fuel assembly. Nuclear Energy and Technology 8(3): 161165. https://doi.org/10.3897/nucet.8.93894

This article presents the results of neutronic calculations of a VVER1200 fuel assembly carried out using the multipurpose threedimensional continuousenergy Monte Carlo particle transport code Serpent 2. The study compares neutronic characteristics during the fuel burnup process (1) with and (2) without fuel cooling. In the first option, the FA fuel campaign was simulated with 30day cooling periods between reactor campaigns. The second option assumed simulating the FA fuel campaign without fuel cooling. In the course of the study, the authors determined the infinite neutron multiplication factors as well as the fuel burnup dependence of the concentrations of xenon, samarium and gadolinium nuclides. In addition, it should be noted that no differences were found in the change in the concentration of gadolinium isotopes, the discrepancy in the values of the multiplication factor, and the accumulation of samarium isotopes during the campaign.
Fuel assembly (FA), neutronic characteristics, Serpent, fuel cooling and simulated refueling, Samarium, Xenon, fuel burnup, infinite multiplication factor, deflection, absorption crosssection
The question of setting the task is fundamental in the framework of justifying the operation of a particular nuclear power facility. Neutronic calculations can be carried out using different approaches: some researchers believe that there is no need to simulate fuel cooling when studying material burnup (
Therefore, the equivalence of the proposed calculation methods seems to be quite a topical issue. If the results differ by values significantly exceeding the statistical error, it is necessary then to choose the most reliable method from the available ones for calculating the campaign, that is, the one that corresponds to real operating conditions. Under such conditions, fuel cooling is carried out to reduce the concentration of neutron absorbers (^{135}Xe, ^{135}I).
The research objectives include as follows: (1) to determine infinite multiplication factors for VVER1200 fuel assemblies with simulated 30day fuel cooling periods after every 340 effective days of operation and continuous fuel burnup; (2) to monitor the concentrations of the most important nuclides (in terms of neutron absorption) in fuel elements and fuel rods (^{135}Xe, ^{149}Sm, ^{155}Gd (
The calculations were carried out using the Serpent 2 software package. The results of calculating the burnup of fuel assemblies with gadolinium for VVER440 and VVER1000 reactors are also presented in (
The selected model was calculated using the multipurpose threedimensional continuousenergy Monte Carlo particle transport code Serpent 2. Each cycle contained a packet of 10,000 neutrons, 50 inactive and 750 active cycles. The following burnup steps per day were set: 1, 5, 10, 15, 40 and further up to 340 effective days in increments of 30 days. The frequency of the initial dividing is due to the need to track changes in the concentrations of xenon, plutonium and other important isotopes. In the study, the concentrations of the mentioned elements were also monitored to substantiate the processes occurring in the fuel and their influence on the multiplication factor. An infinite lattice of fuel assemblies, which is analogous to real BelNPP lattices, was chosen as the computational geometry (VVER1200 reactor core,
A hexagonal FA of the Z49A2 type was considered, containing 300 fuel rods with a ^{235}U concentration of 4.95% and 12 fuel rods with a ^{235}U concentration of 3.6%. In the fifth ring (from the center) there is a measuring channel, in the fourth and sixth rings there are six and twelve guide channels. Fuel rods in the tenth and eleventh rings were selected to track the flux nonuniformity. A geometry infinite in height and radius (set bc 2) (Status Report,
Fig.
The significant deviations in the K_{inf} values between the models are explained by transient processes: when the calculation is started at the initial burnup steps, the xenon concentration is nonstationary. It can be seen from the graph that Model 1 gives results lower than Model 2 by 12, 24, 36 MW∙day/kg.
The deviations were determined by analogy with (
$\frac{{K}_{inf2}{K}_{inf1}}{{K}_{inf1}}*100\%$
where K_{inf1} is the value close to real operating conditions (Model 1); and K_{inf2} is the value compared with the “optimal” value (Model 2).
One can observe the following trend: throughout the entire fuel assembly campaign (excluding the beginning of the 2^{nd}, 3^{rd} and 4^{th} reactor campaigns), the deviation grows evenly. An apparent difference in the values between the models can be seen in Fig.
The difference between the values accumulates, and in the third and fourth years it exceeds the statistical error. This is presumably due to the fact that the concentration of the strong absorber in the stationary areas for Model 1 deviates more and more from the corresponding values of Model 2 after the burnup year, and, by the end of the fourth year, this difference becomes maximum. Therefore, the value of K_{inf} for the model without fuel cooling turns out to be greater than for the model with fuel cooling. To test the hypothesis, the concentrations of such strong absorbers as ^{135}Xe, ^{149}Sm and ^{155}Gd were compared. It is clear that ^{157}Gd is a stronger absorber than Gd155, and since the concentration of gadolinium oxide in the fuel assemblies is low, it almost completely burns up by the end of the first microcampaign. Thus, it cannot affect the K_{inf} change in the final microcampaigns.
Fig.
The difference in the ^{35}Xe concentration values between the models appears only in the fuel cooling periods. This is due to the fuel decay. In the process of stationary burnup, the concentrations are identical. This means, that this nuclide does not contribute to the difference in the K_{inf} values between the models.
Fig.
Before the simulation of the first fuel cooling, the calculations are identical; therefore, the dependences on the graph reflect the process after 10 MW∙day/kg. The significant deviations (up to 17% at 12, 24, 36 MW∙day/kg) are explained by the accumulation of samarium in the model with fuel cooling: in the absence of power, the neutron flux decreases significantly but the concentration of ^{149}Sm increases. During the simulation of the next reactor campaign, the concentration of ^{149}Sm first drops sharply, then rises until equilibrium is established. This behavior affects the K_{inf} values. Since the process of establishing the equilibrium concentration takes a considerable time, the process of fuel burnup occurs differently for the two considered models due to the specifics of the calculation method using the Serpent software package (
The figure does not show the burnup steps after 25 MW∙day/kg, since after 16 MW∙day/kg (after the first microcampaign) the absorber burns up almost completely. At the same time, it is not an accumulated isotope in the process of fuel burnup; therefore, it does not have jumps like ^{149}Sm. Since the difference in the K_{inf} values in the models occurs after the second cooling, when there is no more gadolinium left in the FA (Fig.
The absence of the ^{149}Sm contribution to the change in the ^{135}Xe concentrations can be explained by the low equilibrium concentration of the isotope in the system and its insignificant contribution to the campaign (excluding transients). In contrast to the ^{155}Gd concentration, the nonequilibrium ^{149}Sm concentration makes no contribution either, since, after the first microcampaign, there is practically no burnable absorber left, and it has practically no effect on the criticality of the model. The same effect is achieved in the works of other researchers (
The authors have calculated the burnup of the Z49A2 FA model for a VVER1200 reactor with a fouryear fuel campaign. As part of the study, options were modeled: (1) with fuel cooling between microcampaigns lasting 340 effective days and without fuel cooling. The K_{inf} showed discrepancies between the models starting from 24 MW∙day/kg. The discrepancies increase as the burnup progresses.
The evaluated concentrations of the poisoners (^{135}Xe, ^{149}Sm) and the burnable absorber (Gd155) showed the ^{149}Sm contribution to the K_{inf} deviation between the models.
Significant jumps in the K_{inf} deviation between the models by 12, 24, 36 MW∙day/kg are explained by the ^{135}Xe decay in the model with fuel cooling. The equilibrium ^{135}Xe concentration is reached faster as compared to ^{149}Sm. The difference between the models in the poisoner concentration over a long period of time introduces significant changes in the fuel burnup process and the model criticality calculation. For this reason, when calculating burnup, one should use the model that provides the closest approximation to the real conditions of the phenomenon under study. In this case, the model with fuel cooling is the most correct. Of course, it is important to take into account the differences in simulations and under real operating conditions and fuel reloading, since this comparison leaves out the features of the neutron spectrum during fuel burnup or the cooling procedure at a particular nuclear power plant, regulated by the relevant acts and regulatory documents. In this regard, further studies should be directed to the consideration of the effects, taking into account the existing differences, and the comparison of indicators using different characteristics of the core.
The work was supported by the NRNU MEPhI Competitiveness Improvement Program.