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Publication: CNL Nuclear Review
16 June 2020


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 keff and (ii) U-235 fuel inventory. The latter is compared with a simple first-order semi-empirical calculation. The calculation of keff 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.


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 keff 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 keff 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

The McMaster Nuclear Reactor (MNR) is a light-water moderated material testing reactor (MTR) used for, among other things, the production of the medical radio-isotope I-125, neutron radiography, reactor physics experiments, and education and training purposes [1]. The standard operating schedule at MNR is two 8-hour shifts per day, Monday to Friday, with an extra shift on some Saturdays.
The in-core fuel management in MNR is an important task for keeping the reactor operation optimal for isotope production and for running experiments. This includes fuel reload and fuel shuffling, which can be carried out with the goal of satisfying certain criteria, such as boosting the neutron flux in the irradiation positions and beam tubes and meeting safety constraints and economic parameters. In MNR, prior to fuel reload or shuffling, the fuel inventory of U-235 for each standard fuel assembly (SFA) is estimated from a flux-wire measurement and the preceding operation cycle energy output.
As part of the overall system for calculation of reactors (OSCAR-4) code validation, the fuel composition must be estimated adequately. The purpose of this study is two-fold: (i) testing the OSCAR-4 code model, this is done by seeing how the code predicts keff = 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

MNR is a light-water cooled and moderated plate-fuel reactor with a U-235 enrichment of 19.75% and a maximum neutron flux of 5.8 × 1013 n/cm2 s [1]. It is licensed to operate at a power up to 5 MWth. The nominal power is 3 MWth. 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.
Table 1.
Table 1. A general description of the MNR facility and core specifications [3].
For the nonproliferation of nuclear materials, MNR started to convert the fuel to low enriched uranium (LEU) in 1998 on a burnup basis and was totally converted to LEU in 2007.

3. Calculational Tool

3.1. The OSCAR-4 code system

The OSCAR-4 was developed and is supported by the Radiation and Reactor Theory section of Necsa (South Africa Nuclear Energy Corporation) [2, 3]. The code is comprised of 3 main modules: CROGEN, CROLIN and CORANA.
The CROGEN module includes the 2-D lattice code HEADE that uses the collision probability method to solve the neutron transport equation to generate multi-group cell cross-sections and nodal parameters based on a WIMS-E 172-group cross-section library. The MNR model adopts a 6 group structure that is used by Necsa for the SAFARI-1 reactor. Cell data are then passed to the CROLIN module, which uses the POLX and LINX codes to paramatrize (POLX code) the multi-group cell data and link it (LINX code) into a runtime library used by the core solver. The core analysis module, CORANA, uses the nodal diffusion theory solver MGRAC (multi-group reactor analysis code). MGRAC compiles all the geometry (CONFIG), fuel load (LOAD), axial levels (BASE), and history (HIST) of the assemblies and produces a 3-D core solution. A schematic of the subset of the OSCAR calculation path used in this study is shown in Figure 1.
Figure 1.
Figure 1. OSCAR-4 reactor calculational path for MNR.
MGRAC can perform both snapshot flux and reactivity solutions, as well as cycle depletion analysis. Depletion is conducted in a quasi-static fashion, using alternating flux and burnup calculations. A predictor–corrector scheme is used to capture the nonlinear impact of changing number densities on flux, and step sizes are limited by the rate of change of plant data (rod positions, power levels, etc.). This process is largely automated using the OASYS (OCSAR analysis system) as illustrated in Figure 2.
Figure 2.
Figure 2. OASYS database structure.
One of the inputs to OASYS is the reactor operation history (plant data), such as reactor power, operation time, control rod positions, shutdown times, number of time steps per burn step, Xenon tracking/equilibrium, and critical rod searching. In this study, the plant data for MNR operation are captured in 1 log entry per day (12–14 hours burn step). Each entry includes the reactor power and start-up critical rod positions (1 position for the low-worth regulating rod and 1 for the gang-operated shim-safety rods). Because of the xenon transient in each day, MNR absorber rods are repositioned several times each day. In this study a single core-follow timestep was used per operational day with daily average extraction rod positions to account for the rod movement. This is adopted to improve tracking the axial profile of each fuel assembly compared with using the start-up rod positions for the entire burnup timestep. In contrast, the critical rod positions, which is the position at the reactor start-up, were used for the keff predictions. Figure 3 presents the first core configuration of the first cycle.
Figure 3.
Figure 3. MNR core grid configuration, cycle 54A.

4. Methodology

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

As part of fuel management activities at MNR, a set of short-length Mn–Cu flux wires are inserted into the coolant channels, as shown in Figure 4, of each SFA and activated at low power [4]. This activation profile is used to estimate the power profile of the core which in turn is available for use in fuel consumption estimates. The wire holder design is such that a collar stops the holder at the top of the fuel plates and consistently positions the flux wire near the axial centerline of the active height of the core. The flux wires are then irradiated at low power, typically 200 W, for about 10 minutes. The activation reaction induced in the wires is described by the following equation:
Figure 4.
Figure 4. Wire holder (top), xy and x–z views of a fuel assembly.
After the radial wires are irradiated, they are removed. The activity induced in the 56Mn 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.
where M235 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.
The assumptions made in the flux-wire estimate of the fuel depletion are: (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

The work described here considers MNR operational data from 2007 until 2010, starting with Core 54A (February 2007). This core configuration contained only 1 HEU SFA and 36 LEU FAs (30 SFAs and 6 CFAs) at different degrees of fuel burnup.
The MNR OSCAR-4 model is based on the one developed by NECSA for a 2008–2011 IAEA Coordinated Research Project [5], used for calculation of Core 54A characteristics. This model has been only slightly modified and is applied to core-follow cases for multiple reactor cycles in the work herein.
The MNR core model is defined as a 12 × 11 rectangular node grid. Each in-core node is associated with a grid position in the MNR grid plate, housing a single type of core component (e.g., fuel, reflector, irradiation position). The ex-core nodes are of the same dimension and extend the model 3 nodes (roughly 24 cm) beyond the grid plate. Ex-core nodes include those for beam tubes and the gamma shield lead block.
The active height of the core is divided into 7 axial layers of 8.57 cm each, see Figure 5, allowing for the capture of the axial variation in fuel consumption. The axial reflector (i.e., above and below the active core) is modelled by 2 additional layers, a homogeneous light water and aluminum blend (6 cm), and light water (9 cm). The MNR model here is 15 × 12 assemblies, adding up to 1260 calculational nodes, and with 31 standard fuel assemblies and 6 control fuel assemblies, adding up to 259 fuel calculation nodes. Initial number densities for each element over the 7 layers were taken from the in-house empirical approach.
Figure 5.
Figure 5. Axial fuel nodes or burnup zones used for core-follow calculations (all in cm).
The MNR 18-plate SFA was modelled as an infinite lattice on a 2-D Cartesian mesh. All 18 plates, as well as the side plates and side water, were captured explicitly. Apart from ignoring the curvature of the fuel plates, the fuel assembly was modelled as per nominal dimensions. The span or width of the fuel plates was dictated by the distance maintained between the 2 side plates. Similarly, the nominal thickness of the fuel plate, including that of the clad and fuel meat, is maintained. Side plate dimensions were also conserved, requiring a thin row of cells beyond the 2 dummy plates to capture the small amount of water that exists beyond the ends of the side plates. Each fuel plate was divided into 8 sub-cells (meshes), the middle 6 containing fuel meat (around 1.038 cm each) and the outer 2 composed of only the extension of the clad between the fuel meat and the side plates.
For the reflector assemblies and ex-core structures some approximations were made for the complexity of the model geometry, necessitated by the restrictions of using a 2-D cartesian geometry code. In all cases material volume was conserved. The graphite and beryllium reflector model geometries are shown in Figures 6 and 7. The model for the central irradiation position is identical to that for the graphite reflector assembly with only the graphite material replaced by light water. The ex-core regions, i.e., beyond the MNR Grid Plate, which include structure such as the beam tubes and lead block, were modelled by conserving the volume of the different materials.
Figure 6.
Figure 6. Actual and modelled graphite assembly. The left diagram was obtained from reactor drawings and presented also in Day [1].
Figure 7.
Figure 7. Actual and modelled Be assembly. The left diagram was obtained from reactor drawings and presented also in Day [1].
The HEADE code was used to produce a set of homogenized microscopic cross-sections. HEADE uses 38 isotopes that are important isotopic fission and actinide chains in the reactor calculation. Additionally, HEADE considers all the other isotopes lumped into a single structural macroscopic material. The energy group structure used was the 6-neutron energy group structure (HEADE uses nuclear data from the WIMS-E 172-group library, which were then collapsed into 6 groups for this study) [6].

5. Start-up Critical Rod Positions

The operational data of MNR are recorded on a daily basis. The information provides (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.
Table 2.
Table 2. MNR operational data for the first week of the cycle 54A, 2007.
Table 2 presents sample data of the first week of this calculation from the control room data sheet. These data show the start-up extraction position. The data used for this study are extending until January 2010. The calculation in this study evaluates all the available data, which is extending up to January 2010. These data were used to test and compare the keff 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 keff calculation

The first comparison made with the MNR operational data is the effective multiplication factor at the critical control rod positions (start-up). MNR experiences xenon poisoning in the early hour during the weekdays. Therefore, the control rod positions in the start-up, after the night-shift shutdown, are usually extracted higher than the rest of the day to achieve the criticality. In this model, MGRAC treats the xenon concentration explicitly. Figure 8 shows the keff 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.
Figure 8.
Figure 8. keff and critical rod position (% extraction) vs. operating days.
Figure 8 shows the calculated keff 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 keff estimates related to the specific day of the week. All the keff peaks, or control rod valleys, can only be found on Mondays. Secondly, the cycle trend of the keff, which varies from 7 to 80 days per cycle, is decreasing, i.e., the calculated critical keff 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 keff 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 keff, each is averaging 92 operational days along with its standard deviation to the total average.
Table 3.
Table 3. Multiplication factor and its standard deviation for 8 points average.

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

The next stage of the analysis involved comparison of depletion estimates derived from the FOSEM estimates with those from the OSCAR-4 model. In this calculation we use the control rod average insertion during the reactor operation. This is thought to be an improvement on the approach used for the keff 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.
Table 4.
Table 4. EOC first-order semi-empirical method date.
Figure 9.
Figure 9. Total SFAs U-235 inventory.
The EOC core inventory estimate from the FOSEM approximation shows a noticeably lower U-235 inventory than that from the OSCAR-4 model. The data show an initial burnin period as both calculations start from the same fuel composition estimates. To further examine these differences a detailed tracking of SFA (MNR-333) was selected to present its U-235 depletion over the period of this calculation. The MNR-333 SFA was introduced to the core in the fresh (unirradiated) state in Core Cycle 54A, the first cycle of this calculation. Figure 10 illustrates the U-235 against burnup.
Figure 10.
Figure 10. MNR-333 U235 content vs. burnup.
The OSCAR-4 fuel depletion calculation shows a divergence from the FOSEM estimate during the fuel irradiation calculation. A notable discrepancy can already be seen after a number of cycles. This is due to the assumption that all the energy comes from U-235 fission in the FOSEM approximation. This assumption is more accurate for HEU case. Thus, using the same value of C = 0.05417 g/MWh for HEU to LEU is not straightforward.
Figures 11 and 12 show the fuel consumption (in g/MWh) variation throughout the fuel irradiation and the Pu-239 buildup, respectively. In LEU fuel, unlike HEU fuel, the U-238 concentration is considerable. This results in a buildup of the Pu-239 and a subsequent contribution to the total fission rate and energy release from Pu-239 fission. As a result, for the same energy generation the U-235 consumption is significantly reduced compared with the estimates from the FOSEM. To further illustrate this effect, Figure 13 shows the U-235 consumption in g/MWh with burnup. At 90 MWD (typical SFA exit burnup in MNR), the consumption of U-235 in LEU is only about half of that in HEU. This calculation was done with HEADE for both HEU and LEU.
Figure 11.
Figure 11. HEU and LEU fuel consumption using HEADE cell calculation.
Figure 12.
Figure 12. HEU and LEU Pu-239 buildup using HEADE cell calculation.
Figure 13.
Figure 13. U-235 inventory using OSCAR-4 and first-order approximation method.
The buildup of Pu-239 shows the opposite effect, as shown in Figure 14; compared with LEU, there is almost no buildup of Pu-239 in HEU.
The fuel inventory estimates from FOSEM approximation are lower than the OSCAR-4 code. Table 5 summarizes the maximum difference, which is found in MNR-329, among all SFAs, and the average difference of all SFAs.
Table 5.
Table 5. Atom density differences.
The maximum difference that was found in MNR-329 SFA with 10.2% does not solely represent the atom density difference. In fact, this difference includes other uncertainties in both methods as indicated in the methodology, which are out of scope for this study. To explain this difference, MNR-329 was primarily located at high power level between 2 control rods in 5E position (see section 3) until March 2009. Then, MNR-329 was moved to the peripheral region in 2F for the next 2 months. In May 2009, it was moved again to 1C for 5 months before it was lastly moved, in October 2009, to 6D for the rest of the period.
To present the maximum difference that was found in MNR-329 due to the atom density concentration, Equations (3) and (4) are used.
where C is the fuel consumption value of the FOSEM approximation and C is the average value of the fuel consumption from Figure 11:
where 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

Core-follow calculations for MNR were performed using the OSCAR-4 code system. Results of the operational period of 3 years, comprised of 31 cycles, were used to predict the multiplication factor of each start-up critical condition, for a total of 738 days. In addition, a simple FOSEM of U-235 estimates was utilized to compare with OSCAR-4 simulation model to investigate fuel consumption.
It was found that the keff 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.
The OSCAR-4 model U-235 depletion estimates showed notable differences compared with those using the FOSEM, which was found to significantly overestimate U-235 consumption. This overestimation of the fuel depletion in the FOSEM was found due to the lack of consideration of Pu-239 to the energy production. Differences in U-235 inventory in the individual SFAs increase with fuel exposure, to an average of 5.7% and to a maximum of 10.2% for a single SFA.
The findings suggest that OSCAR-4 represents an improvement over the FOSEM for core follow calculations. The OSCAR-4 code for MNR core-follow purposes can better estimate the fuel inventory since all fissile isotopes that contribute to the energy production are considered.


The authors would like to thank Chris Heysel, Director of the McMaster Nuclear Reactor, for the support of the MNR Reactor Group in terms of the provision of data, consultation, and guidance, and Drs. Rian Prinsloo and Francois van Heerden from Necsa for their support in the use of the OSCAR-4 code and for providing helpful suggestions.


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Published In

cover image CNL Nuclear Review
CNL Nuclear Review
Volume 9Number 1December 2020
Pages: 73 - 82


Received: 10 May 2019
Accepted: 30 October 2019
Version of record online: 16 June 2020


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Key Words

  1. keff
  2. depletion calculation
  3. flux-wire estimate
  4. OSCAR-4


  1. keff
  2. estimation du fil de flux
  3. OSCAR-4



Mohammed Alqahtani
McMaster University, Hamilton, ON L8S 4L8, Canada
Nuclear Science Research Institute (NSRI), KACST, Riyadh, Saudi Arabia
Simon Day
McMaster University, Hamilton, ON L8S 4L8, Canada
Adriaan Buijs
McMaster University, Hamilton, ON L8S 4L8, Canada

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