# OSCAR-4 CODE SYSTEM COMPARISON AND ANALYSIS WITH A FIRST-ORDER SEMI-EMPIRICAL METHOD FOR CORE-FOLLOW DEPLETION CALCULATION IN MNR

## Abstract

*Knowledge of the isotopic composition of a nuclear reactor core is important for accurate core-follow and reload analysis. In the McMaster Nuclear Reactor, fuel depletion estimates are based upon a semi-empirical calculation using flux-wire measurements. These estimates are used to plan and guide fuelling operations. To further support operations, an OSCAR-4 model is being developed. To evaluate the performance of the OSCAR-4 code for this application, 2 points of comparison, considering the period between 2007 and 2010, are presented: (i) the multiplication factor k*

_{eff}and (ii) U-235 fuel inventory. The latter is compared with a simple first-order semi-empirical calculation. The calculation of k_{eff}for the last operational 3 months yields 0.997 ± 0.002 (vs. 1.000 for an operating reactor), and differences in both core-average inventory and the maximum standard fuel assembly inventories estimates are found to be 5.7% and 7.5%, respectively.## Résumé

*La connaissance de la composition isotopique du cœur d’un réacteur nucléaire est importante pour la réalisation d’une analyse exacte du suivi et du rechargement du cœur. Dans le réacteur nucléaire McMaster, les estimations de l’épuisement du combustible sont fondées sur un calcul semi-empirique qui fait appel à des mesures du fil de flux. Ces estimations sont utilisées pour planifier et guider les opérations de chargement. Pour faciliter les opérations, un modèle OSCAR-4 est en cours d’élaboration. Pour évaluer le rendement du code OSCAR-4 pour cette application, deux points de comparaison sont présentés pour la période de 2007 à 2010 : (i) le facteur de multiplication k*

_{eff}et (ii) l’inventaire du combustible U-235. Ce dernier facteur est comparé à un simple calcul semi-empirique du premier ordre. Le calcul de k_{eff}pour les trois derniers mois opérationnels donne 0,997 ± 0,002 (contre 1,000 pour un réacteur en exploitation), et les différences dans les estimations de l’inventaire moyen du cœur et des inventaires maximaux des assemblages combustibles standards se révèlent être de 5,7 % et 7,5 %, respectivement.## 1. Introduction

*i*) testing the OSCAR-4 code model, this is done by seeing how the code predicts

*k*

_{eff}= 1 as this is an actual value to compare against the reactor operation, using the critical rods positions, and (

*ii*) examining the fuel composition with depletion including a comparison against a first-order semi-empirical approach.

## 2. The MNR

^{13}n/cm

^{2}s [1]. It is licensed to operate at a power up to 5 MW

_{th}. The nominal power is 3 MW

_{th}. Reactivity within the MNR core is controlled by 5 silver–indium–cadmium (Ag–In–Cd) shim-safety rods and 1 stainless steel regulating rod. The core is comprised of MTR-type fuel assemblies arranged in a 9 × 6 grid plate [1]. Cooling of the core is achieved at low power via natural circulation and at high power via forced down-flow driven by the hydrostatic head of the pool and returned by a pump. An MNR SFA contains 18 curved plates, the inner 16 of which contain fuel while the 2 outer (dummy) plates are aluminium. The MNR control fuel assembly (CFA) contains 9 fuelled plates, leaving space for an absorber rod in the center. The SFA and CFA share the same outer assembly dimensions, differing only in material specifications and number of plates. Lattice spacing on the MNR grid is 8.100 cm × 7.709 cm radially. The core has an active height of 60 cm. A row of graphite assemblies acts as a reflector on 1 side of the core, while the other sides are flanked by a lead block and 6 radial beam tubes [1]. Table 1 presents the general core specifications of the MNR.

## 3. Calculational Tool

### 3.1. The OSCAR-4 code system

*k*

_{eff}predictions. Figure 3 presents the first core configuration of the first cycle.

## 4. Methodology

### 4.1. The first-order semi-empirical method (FOSEM)

^{56}Mn is counted using an NaI detector system. Each wire is measured twice and the background is subtracted. The measured activity is then converted into a relative flux distribution across the reactor core. With that, given that the cycle length and reactor power are known from reactor operation data, the fuel depletion at the end of cycle (EOC) for each fuel assembly can be estimated. A simplistic approach to a fuel consumption estimate assumes all fission power coming from U-235 thermal fission and leads to the following equation.

*M*

_{235}and are the U-235 amounts in gram at the EOC and beginning of cycle, respectively;

*C*is the consumption value in g/MWh; and

*X*is the total energy released up to the EOC in MWh. This semi-empirical method was used at MNR for high enriched uranium (HEU) fuel cycle calculations, with a value of

*C*= 0.05417 g/MWh of U-235. It is herein investigated in comparison with the OSCAR-4 simulation approach in light of the current LEU fuel cycle.

*i*) the flux wires are consistently positioned in the central coolant channel of each SFA, (

*ii*) the assembly average fission rate is proportional to Mn activation in the central coolant channel, (

*iii*) the activation distribution is representative of an average flux distribution over the operating cycle, and (

*iv*) burnup occurs only by U-235 fission.

### 4.2. Modelling MNR in OSCAR-4

## 5. Start-up Critical Rod Positions

*i*) reactor power, (

*ii*) control rod extraction in 30 minute periods during the operation, and (

*iii*) the total time of the reactor operation. Table 2 illustrates an example of the first few days from the operational data that was used for this investigation.

*k*

_{eff}values for each day to the actual value. In contrast, a daily average control rod extraction was used for the depletion calculation. More detailed Operations data that records rod positions every 30 minutes, were used to calculate the daily average positions.

## 6. Results and Analysis

### 6.1. OSCAR4 *k*_{eff} calculation

*k*

_{eff}at the critical rod positions for the daily operational data covering the entire period of study. Owing to the long-documented data for this study, about 1050 days of information including shutdown days, Figure 8 presents solely the operational days.

*k*

_{eff}values and the control rod positions extracted from the operational data (Table 2). The tracked data contain 31 cycles with a total of 738 operational days of the core-follow calculation. The total core burnup between the beginning and the end of this calculation is 33.1 MWD/kg, and about 1279 MWD energy was released. A number of trends are evident in Figure 8. Firstly, there appears to be a day-to-day variation in the critical

*k*

_{eff}estimates related to the specific day of the week. All the

*k*

_{eff}peaks, or control rod valleys, can only be found on Mondays. Secondly, the cycle trend of the

*k*

_{eff}, which varies from 7 to 80 days per cycle, is decreasing, i.e., the calculated critical

*k*

_{eff}decreases per cycle. These 2 observations can be explained by inconsistencies between rod worth and xenon worth in the model. In contrast to Mondays, the xenon concentration is considerably high during the start-up for all operating days. This will lead to extraction of the control rods to compensate for the negative reactivity in the core, contrary to Mondays, when xenon concentration is significantly low after 40–50 hours of shutdown. Thirdly, the overall trend of the

*k*

_{eff}is improving, i.e., getting closer to unity. Unlike FOSEM, the core inventory tracking is considering all the major isotopes inventory that are neutronically important. Table 3 presents 8 values of

*k*

_{eff}, each is averaging 92 operational days along with its standard deviation to the total average.

### 6.2. Tracking comparison of U-235 contents in MNR core and a fuel assembly

*k*

_{eff}estimates described previously. Table 4 shows each date of the data available in MNR for each EOC. These data are plotted in Figure 9 along with the OSCAR-4 calculation.

*C*= 0.05417 g/MWh for HEU to LEU is not straightforward.

*C*is the fuel consumption value of the FOSEM approximation and

*C*is the average value of the fuel consumption from Figure 11:

*E*is the energy release, and

*C*(

*E*) is the consumption value at a specific energy

*E*. The difference for MNR-329, at 63.65 MWD in January 2010, was found to be 7.58%. In other words, 2.62% of the difference is due to the other factors that are not related to the fuel inventory such as power distribution.

## 7. Conclusion

*k*

_{eff}is improving, i.e., getting closer to unity, as core inventory is being tracked. This was due to the consumption rate of the U-235 when LEU fuel is being used. Additionally, noticeable peaks were seen when criticality calculation occurred on Mondays. This perhaps due to the CRs worth differences between the actual value to the model value. Further investigation is left as future work.

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*CNL Nuclear Review*.

**9**(1): 73-82. https://doi.org/10.12943/CNR.2019.00011

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