- Email: [email protected]
The application of UWB1 nuclear fuel depletion code on a CANDU fuel bundle
Progress in Nuclear Energy 90 (2016) 127e139
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
The application of UWB1 nuclear fuel depletion code on a CANDU fuel bundle a, b M. Lovecký a, *, R. Skoda , M.S. Hussein c, J.J. Song c, P.K. Chan c , Czech Republic Regional Innovation Centre for Electrical Engineering, University of West Bohemia, Univerzitní 8, 306 14 Plzen 4, 160 07 Prague 6, Czech Republic Czech Technical University, Faculty of Mechanical Engineering, Technicka c Royal Military College of Canada, Department of Chemistry and Chemical Engineering, PO Box 17000, Station Forces, K7K 7B4 Kingston, Ontario, Canada a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 July 2015 Received in revised form 21 January 2016 Accepted 12 March 2016 Available online 24 March 2016
A computer code (UWB1) that is applicable for both light and heavy water reactor fuel types is being developed at the University of West Bohemia. CANDU fuel geometry was investigated in this paper. Fuel depletion with UWB1 code was performed and compared to other depletion codes. A feasibility study on the use of burnable absorbers in CANDU to improve operating margins was recently published [1]. The use of slight enriched fuel (SEU) with various burnable absorbers in CANDU has also been considered for future fuel designs. UWB1 is a fast-calculating depletion code. It is being tested and compared extensively to other six different calculation codes, which include both deterministic and probabilistic types. Although the work focuses primarily on the progress of the multiplication factor during fuel depletion, fuel inventory details were also considered. Effective cross sections as the derivation of reaction rates that directly influence Bateman burnup equations were also compared. Further improvement on the UWB1 code is ongoing. The results showed that UWB1 nuclear fuel depletion code is capable to calculate fuel depletion of CANDU fuel bundle with and without burnable absorbers. As expected, the accuracy of the UWB1 code is lower than the other codes. This paper recommends that UWB1 code be considered as a tool for supporting fuel design assessment, since discrepancies are comparable and the code is one to two orders of magnitude faster than other depletion codes. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Fuel depletion CANDU Monte Carlo Nuclear fuel Burnable absorber
1. Introduction Nuclear fuel depletion is the process of extracting recoverable energy by nuclear fission that leads to the changes in the fuel composition. Currently operating thermal CANDU reactors use fresh natural uranium fuel in the form of uranium dioxide. Each nuclide interact with neutron by a number of nuclear reactions, however, the two main reactions are fission and neutron capture. For fissile materials such as uranium-235, the highest probability of reaction is by fission that produces fission products. During in-core irradiation, as the burnup of a fuel increases, its fissile material content decreases and the fission products content increases. This results in a slow decrease in the multiplication factor or the reactivity of the nuclear fuel, to the point where the fuel eventually needs to be discharged and replaced by a fresh one or a less
* Corresponding author. E-mail address: [email protected] (M. Lovecký). http://dx.doi.org/10.1016/j.pnucene.2016.03.010 0149-1970/© 2016 Elsevier Ltd. All rights reserved.
depleted one via the process of refueling. The time of refueling could be delayed due to the creation of fissile materials from the fertile materials in the fuel. Fertile materials such as uranium-238 are most likely to interact with neutron by neutron capture. Mainly plutonium-239 is generated this way from uranium-238 in thermal reactors, other less important actinides are also formed. Between the first hours up to days of in-core irradiation, the concentration of major neutron-absorbing fission products in a CANDU fuel rapidly increase until they reach an equilibrium concentration. This process is called an initial fueling transient and it is demonstrated by a relatively large drop in multiplication factor in the first 2e3 full power days of operating a fresh fuel. Burnable absorbers (BA) have been used in LWR since the mid 1970s and their research is still ongoing as higher fuel enrichments are considered for fuel designs. Consequently, the frequency of recurrence of burnable absorbers in literature from ScienceDirect database is steadily increasing, as it can be seen in Fig. 1. Burnable absorbers are currently not used in CANDU fuel. However, by introducing burnable absorbers inside a CANDU fuel bundle, it is
128
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 1. Journal papers that reference the use of burnable absorbers. This is obtained from ScienceDirect database.
possible to remove the initial fueling transient (Chan et al., 2013). Moreover, void reactivity coefficient can be set to negative values (Talebi et al., 2006). It was shown that burnable absorbers (Chan et al., 2013) could also suppress the plutonium peak. The use of burnable absorber with SEU for a 43-elements fuel design in CANDU was proposed in technical document (R-700 Technical Descrip, 2004) and later studied in (Talebi et al., 2006). The proposed design placed dysprosium integrally into central natural uranium pin, while surrounding 42 fuel pins in 3 fuel rings are slightly enriched to 2.1 wt%. In this paper, the use of UWB1 code for CANDU fuel bundle depletion and its comparison with other codes is demonstrated. The study includes six different calculation codes; both deterministic and statistical codes are considered. Although the work focuses primarily on the multiplication factor progress during fuel depletion, fuel inventory details are also considered. Moreover, effective cross sections as the derivation of reaction rates that directly influence the Bateman burnup equations are also compared. The objective of the study is to determine the extent of decrease in the accuracy of the UWB1 code, and to determine its advantage in terms of lowering the computation time. Two cases are studied, one without burnable absorber and one with the discrete burnable absorber placed in the fuel. 2. UWB1 code and others calculation codes Results of UWB1 fast depletion code (Lovecký et al., 2014) are investigated and compared to other codes. The comparison study includes five other calculation codes, both deterministic and probabilistic. WIMS deterministic code is used as the main reference code since it is used in CANDU industry as a standard tool (Jonkmans, 2006). WIMS deterministic code uses method of characteristics to solve the transport equation. WIMS has been benchmarked via comparisons to power reactor measurements and is known to yield reasonable results. Widely recognized MCNP6 general Monte Carlo code and newly developed and popular Finnish code SERPENT are also included. Two codes from SCALE code package, Monte Carlo code KENOeVI and discrete ordinates code NEWT that both works inside TRITON code sequence are also considered in the study. First version of the newly developed UWB1 fast nuclear fuel
depletion code (Lovecký et al., 2014) was introduced in order to significantly reduce calculation time by omitting the solution step for the Boltzmann transport equation. However, estimation of multiplication factor during depletion was not sufficiently calculated (Prehradný et al., 2014). Moreover, 1-group effective cross sections for models containing strong absorbers such as gadolinium showed disagreement between the UWB1 tested code and the SERPENT reference code. Monte Carlo transport solver for UWB1 code was introduced (Lovecký et al., 2015) in order to improve code accuracy, remove pre-calculated case-dependent data libraries and eliminate constant effective cross section assumption. Two dimensional, fuel pin model with arbitrary number of concentric cylinder regions, ray-tracing algorithm and ENDF/B-VII.1 data are the main components of the solver. The solver uses 4308-group cross section data library. Speed of the UWB1 Monte Carlo solver is the product of development focused on the minimization of CPU usage at the expense of RAM demands. Due to uniform energy grid used for cross section data and relatively small number of energy groups (4308 groups) compared to continuous energy approach (cca 20,000 groups for U-238), the Monte Carlo solver is about 10 times faster than MCNP6 reference code. A simple depletion scheme was originally incorporated into UWB1 code shortly after the introduction of the Monte Carlo solver. This depletion scheme is a standard coupling of burnup and transport solver. Effective cross sections are calculated by transport solver and used by burnup solver to determine fuel and cladding composition of the next depletion time step. Two-step predictor-corrector method (2sPC) developed for UWB1 code is the second feature of the code that makes it faster than other Monte Carlo depletion codes (Dufek et al., 2013; Kotlyar and Shwageraus, 2013). Similarly to Monte Carlo solver, 2sPC method is able to speed-up the calculation approximately 10 times, therefore, fuel depletion with UWB1 code is expected to be around 100 times faster than with MCNP6 reference code. The idea of 2sPC method is to change the coupling of transport and burnup solvers by omitting a major fraction of the transport solver callings, because the transport solver is orders of magnitude slower than the burnup solver. Both transport and burnup variables are calculated for predicted states and corrected with more precise values as the two parts of the fuel depletion are coupled. Only three transport solver solutions are used, the initial fuel state and predicted and corrected states for final burnup state. Effective cross sections are evaluated during fuel depletion by assuming nuclide-based nonlinear dependency. Multiplication factors in the depletion steps other than the first and the last one are estimated by neutron production to absorption ratio that is calculated without the need to call the transport solver. UWB1 execution is performed in 5 stages - initial, predictor, corrector, depletor and estimator. The main code flowchart is depicted in Fig. 2. The initial stage uses Monte Carlo transport solver to analyze the initial state fuel composition state of the calculated fuel model. Total macroscopic cross sections are calculated before MC simulation in order to speed-up neutron random walk. Transport solver then calculates multiplication factor and neutron flux in all geometry regions in 4308 energy groups. Support calculations for burnup solver, evaluation of fuel basis and relative region powers, are made. Estimation formula describes ratio of neutron production to absorption in the fuel model. Predictor stage uses initial state variables, mainly effective cross sections, to estimate fuel model state at the end of fuel depletion without calling the transport solver in the inner depletion steps. Burnup solver is called in two loops, which are the inner depletion step loop and the outer geometry regions loop. The order of the loops was changed to increase the speed of calculation. This is particularly significant in the case of multiple depleted regions
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
129
Fig. 2. Two-step predictor-corrector UWB1 depletion scheme flowchart.
because the calling transition matrix preparation subroutine is minimized. At the end of predictor stage, transport solver is called for the second time in the calculation, predicting final state variables. The corrector stage works in identical way that the predictor stage works. The only difference is that the initial state's effective cross sections are taken from the predicted final state effective cross sections. By using this method, the averaged values of the predictor and the corrector are used to calculate the final state composition with approximately averaged effective cross sections (i.e. mid-burnup effective cross sections). Corrector stage employs the third and final transport solver execution. Averages of predictor and corrector values (effective cross sections, relative region powers, multiplication factor estimates, transport multiplication values) are used as final state values for the second step of 2sPC method. Depletor stage is used to calculate fuel composition and multiplication factor estimate during burnup. Similarly to predictor stage, depletor stage uses two loops over depletion steps and geometry regions. On the other hand, third loop over the second predictor-corrector step is added. In this innermost loop, both effective cross sections and fuel composition at the end of depletion step are predicted, corrected and averaged. No transport solver is called during depletor stage. Estimator stage is used to compare initial and final state multiplication factors calculated by transport solver with multiplication factor estimates. It is assumed that estimator formula has a difference that is linearly dependent on burnup. Multiplication factor estimates are corrected for the expected differences and used in final output. Widely recognized MCNP6.1 general Monte Carlo code (Pelowitz, 2013) cannot be dismissed in any neutron transport comparison study. MCNP6 is a general purpose neutron transport code that was created by merging capabilities of previous two parallel developed MCNP versions, MCNP5 and MCNPX. Newly developed and popular Finnish code SERPENT 1.1.19 €nen, 2007) (Leppa €nen, 2013), was used as a representative of (Leppa new Monte Carlo codes developed primary for reactor physics calculations that run faster than the MCNP6 code. Monte Carlo technique is accelerated with Woodcock delta-tracking method, however, it is expected that the method's efficiency decreases when strong absorbers (e.g. burnable absorber) are present in the model. Two codes from the SCALE 6.1.3 code package (Scale, 2011), the Monte Carlo code KENOeVI and the discrete ordinates code NEWT, which both work inside the TRITON code sequence, are the last codes considered in the study. KENOeVI is a statistical code similar to MCNP6, but use multigroup nuclear data. NEWT code represents a standard discrete ordinates code that use spatial discretization approach called Extended Step Characteristic.
3. CANDU fuel bundle model The CANDU 37-element fuel bundle was modeled by the depletion codes described in section 2. Two dimensional model of fuel bundle is depicted in Fig. 3. Since the UWB1 code does not allow for such a complicated geometry, the exact geometry as shown in Fig. 3 was not used for the model. CANDU fuel bundle have lattice that cannot be simplified like PWR fuel assembly, therefore, homogenization was chosen as the best approach to simplify the geometry. For this purpose, the UWB1 code was extended to be able to model arbitrary number of concentric cylinders. The resulting geometry is shown in Fig. 4. SERPENT fuel depletion was performed for both investigated cases where case01 is natural uranium fuel without burnable absorbers and case02 is with burnable absorbers placed in the CANLUB layer between fuel and its sheath. Burnable absorber content of 150 mg Gd2O3 and 300 mg Eu2O3 per fuel bundle was chosen as one of the promising designs (Chan et al., 2013). The effect of fuel pins homogenization in the rings on multiplication factor is shown to be less than 0.002, which is negligible as indicated in Fig. 5. The burnable absorbers of interest in the fuel bundle consist of both gadolinium and europium oxides. Present nuclear fuels use mainly gadolinium, europium and erbium oxides. Gadolinium oxide is burned faster than europium oxide and because of the very high absorption cross section of Gd-157 nuclide; the initial reactivity compensation for gadolinium is higher than for europium. For this reason, gadolinium is used mainly for the removal of the initial transient peak while europium is used to suppress the plutonium peak. Gadolinium nuclides of interest include Gd-155 and Gd-157 which are available at natural abundances of 14.80% and 15.65%,
Fig. 3. CANDU 37-element fuel bundle geometry layout.
130
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
outer fuel pins are homogenized into a final outer ring. Dimensions are summarized in Table 1. The fuel was depleted with constant power assumption at the typical power level of 1.27578E-02 MW/cm (3.29080E þ 01 MW/ MTU) for 42 depletion time steps up to final burnup slightly over 20,000 MW d/MTU. This exceeds the typical CANDU burnup of 7500 MW d/MTU. Depletion time steps varied from 0.2 days at the beginning of the depletion up to 20 days at the end of fuel depletion. Fuel rings are surrounded with a zirconium alloy sheath, heavy water coolant fills the remaining space inside the pressure tube. The area between inner pressure tube and outer calandria tube is filled with CO2 gap. The calandria tube is the part of reactor core and it is enclosed by moderator region. Model materials are summarized in Table 2. Periodic boundary condition was applied when possible; otherwise, mirror or white boundary conditions were used. Nonetheless, differences between the boundary options are negligible since the moderator area is very large compared to fuel bundle dimensions. In order to evaluate the speed of the codes, all codes except quick WIMS calculation were run on the same computer. The computer operates under RedHat OS with Intel Xeon E5-4650 processor with frequency 2700 MHz, the server is slightly faster than common desktop or laptop processors.
Fig. 4. Homogenized CANDU fuel bundle geometry layout.
4. Results The work focuses primarily on the multiplication factor progress during fuel depletion, fuel inventory details were not overlooked. Moreover, the effective cross sections as the derivation of reaction rates that directly influence the Bateman burnup equations were compared. Two cases were investigated. Case01 with natural uranium without burnable absorber, and case02 with 150 mg Gd2O3 þ 300 mg Eu2O3 burnable absorbers placed in the sheath. Calculation times in both cases were compared. 4.1. Multiplication factor Fig. 5. Effect of CANDU fuel bundle homogenization on multiplication factor.
respectively. Europium isotopes are available at natural abundances of 47.81% Eu-151 and 52.19% Eu-153. Both europium nuclides behave as good absorbers of neutrons, as they both possess high neutron capture cross sections with end-product nuclide characterized by low capture cross section. The fuel pellets were assumed to consist of natural uranium oxide. The central fuel pin represents the first fuel ring, the 6 fuel pins in the inner ring are homogenized into a secondary fuel ring, the 12 fuel pins are homogenized into a tertiary ring, and the last 18
Table 1 CANDU fuel bundle model dimensions. Region ()
Parameter ()
Value (cm)
Fuel CANLUB layer Sheath Inner fuel ring Intermediate fuel ring Outer fuel ring Coolant Pressure tube Gap Calandria Moderator
Outer radius Outer radius Outer radius Pitch circle radius Pitch circle radius Pitch circle radius Outer radius Outer radius Outer radius Outer radius Half pitch
0.609 0.6096 0.65046 1.4885 2.8755 4.3303 5.15 5.59308 6.4478 6.5875 14.2875
Basic comparison of multiplication factor during depletion is shown in Fig. 6 (case01) and Fig. 9 (case02). The initial transient peak is removed when burnable absorbers are added. The magnitude of the plutonium peak is reduced and delayed to higher burnups. As the burnable absorbers are consumed, their effect on the reactivity of the fuel decreases and the multiplication factor of case02 converges to that of case01. The reactivity curves produced by all codes behave similarly and for the major part of fuel depletion they are bounded by that of WIMS and UWB1. During the first part of the fuel depletion, in which plutonium accumulates within the fuel, the UWB1 code generally yields the highest multiplication factor value while WIMS provides the lowest boundary. However, the results from the codes SCALE package, KENOeVI and NEWT, result in values higher than UWB1 for case02, in the first part of fuel depletion. In the second part of fuel depletion (after the plutonium
Table 2 CANDU fuel bundle model materials. Region ()
Material ()
Density (g/cm3)
Temperature (K)
Fuel Sheath Coolant Pressure tube Gap Calandria tube Moderator
UO2 Zircaloy-4 Heavy water 99.11 wt% Zr2.5Nb CO2 Zircaloy-2 Heavy water 99.97 wt%
10.5057 6.3918 0.8179 6.5041 0.001195 6.4003 1.08699
1011 561 561 561 450 339 339
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
131
Fig. 6. Case01 (no BA) e multiplication factor during depletion.
Fig. 8. Case01 (no BA) e multiplication factor comparison.
Fig. 7. Case01 (no BA) e multiplication factor near plutonium peak.
Fig. 9. Case02 (Gd þ Eu BA) e multiplication factor during depletion.
peak to a burnup slightly over 10000 MW d/MTU), the UWB1 code yields the lowest values of reactivity, while WIMS provides the highest values. A plot of the evolution of reactivity during the plutonium peak, for each code, is shown in Fig. 7 (case01) and Fig. 10 (case02). The horizontal axis is changed from burnup to irradiation days. Statistical uncertainty is provided when applicable, showing that statistical uncertainty is not the cause of the differences between the codes. Number of simulated neutrons was chosen to be the lowest possible value that still imparts negligible impact on the value of the multiplication factors. A total of two million active neutrons were tracked in 200 cycles, each having 10000 neutrons each. Five inactive cycles were also added. Errors are not shown for the deterministic codes, WIMS and NEWT, because they have no defined uncertainty associated with them. Initial multiplication factor values are slightly higher for SCALE codes KENOeVI and
NEWT (Table 3). The difference between the highest and lowest values is 0.007. The differences between WIMS reference and UWB1 investigated codes are around 0.002. Plutonium peak occurs at 42 days for WIMS and 22 days for UWB1, the rest of the codes calculate the peak to evolve around 30 days for case01. When burnable absorbers are added (case02), the plutonium peak is delayed by around 10 days. It is important that all codes predict the same delay, i.e. the differences between the case01 and case02 are calculated to be the same by all the codes. A relative comparison of the multiplication factors for each of the codes was conducted and its results are displayed in Fig. 8 (case01) and Fig. 11 (case02). The relative values were calculated as a ratio in comparison to the WIMS code that was chosen as the reference, because the WIMS code is the standard toolset used to model the CANDU lattice. Statistical uncertainty is shown as error bars for the probabilistic codes. As described earlier, the fuel
132
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
typically around 0.02, but reach up to 0.03. The closest match to the WIMS reference code is achieved by KENOeVI and NEWT codes from SCALE code package; their differences are at an order of magnitude lower than of the other codes. For all the codes it is possible to find a depletion interval at which the code gives the extreme multiplication factor value when compared to that of other codes. However, for most of the depletion time, the highest range of values are predicted by either WIMS or UWB1 code. The evolution of fuel reactivity past the refueling transients are not significantly different between case01 and case02, and the trends are very similar. In assessment of the performance of the UWB1 code, it can be concluded that the multiplication factor of the modeled fuel lattice is predicted in the same manner as the other codes. All the codes exhibit some level of difference to the WIMS code. Amongst the compared codes, the UWB1 code has been shown to yield the greatest difference to the WIMS code and also the greatest magnitudes of unwanted oscillations in the multiplication factor. 4.2. Nuclear density Fig. 10. Case02 (Gd þ Eu BA) e multiplication factor near plutonium peak.
Table 3 CANDU fuel bundle initial multiplication factor values (2-D). Code
Case01
Case02
WIMS UWB1 MCNP6 SERPENT KENOeVI NEWT
1.12629 1.12866 1.12574 1.12712 1.13209 1.13296
1.06748 1.06948 1.06930 1.06890 1.07422 1.07463
During fuel depletion, the nuclear density of two set of nuclides are stored. The first set includes nuclides for which the cross section data is available. Only nuclear data libraries supplied with the codes were used, which are the ENDF/B-VII.0 from 2006 (SERPENT, KENOeVI, WIMS) and the ENDF/B-VII.1 from 2011 (UWB1, MCNP6). There are only minor differences between the two libraries, as major improvements in the library are introduced only for new versions (e.g. VI vs VII). The newer library predicts neutron multiplication factor values lower by 0.0006e0.0018 for investigated CANDU cases. The number of nuclides in neutron data library increased from 393 to 423, however, not all nuclides are easily harvested from the output files and a total number of 281 nuclides were compared. The main reason for the comparison of fuel inventory is that the UWB1 code estimates the fuel lattice multiplication factor during depletion from the inventory and transport values at the beginning and the end of fuel irradiation. In addition, the fuel inventory directly influences the decay heat, activity, radiation sources and other parameters that are needed in the overall evaluation of fuel performance.
Fig. 11. Case02 (Gd þ Eu BA) e multiplication factor comparison.
depletion is divided into three parts. In the first and third part, the compared codes predict higher values than that of the reference WIMS code. In the second part of fuel depletion, the WIMS code gives the highest values. The typical difference between each of the codes to the WIMS code is around 0.01. The highest differences are
Fig. 12. Comparison of fuel inventory depending on nuclide density, ratio relative to WIMS code.
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fuel inventory is compared in Fig. 12 and Fig. 13. As burnable absorbers are placed in the sheath, the fuel inventory is not significantly influenced. The third of four fuel rings was chosen to the comparison, the results for other rings are very similar. Ratios of nuclear density (atoms/b-cm) between the investigated code and WIMS reference code were evaluated for 7500 MW d/MTU. On independent axis, both WIMS nuclide density and nuclide ZAID number was used. ZAID number is related to the mass of the nuclide (ZAID ¼ 10000*Z þ 10*A þ m). Generally, nuclear density is over-predicted by all the codes when compared to WIMS results. The over-prediction is seen for both fission products and actinides. Differences at the level of tens per cents are typically observed. As expected, the largest differences are visible for UWB1 calculation. The best agreement with WIMS results were predicted by MCNP6 code that also under-predicted nuclear densities for a large number of nuclides. Fuel inventory comparison of selected nuclides was divided into two groups: fission products and actinides. Uranium-235 concentrations are compared in Fig. 14 for all fuel rings. The closer the ring is to the moderator area, the faster the fission is and the U-235 concentration is lower. The decrease of U-235 concentration was over-calculated by all the codes, however, the UWB1 results are the least precise and the rate of consumption is so high that the concentration in the outermost ring calculated by UWB1 code is less than the value in the innermost ring predicted by all the other codes. The differences between the codes in ring 3 for 7500 MW d/ MTU are up to 12% excluding UWB1. For UWB1, the difference is approximately 50%. Plutonium and minor actinides are generated by successive neutron capture of uranium-238. Given the fact that the actinide generation processes is similar between codes, the evolution of actinides predicted by each code are similar. The UWB1 code overpredicts the concentration when compared to other codes (see Fig. 15 a Fig. 16). The most important of these nuclides, Pu-239, is over-predicted by 21% for the UWB1 code in ring 3 for 7500 MW d/ MTU. All the codes over-predicts the concentration of Pu-239 and under-predicts the concentration of U-235 against WIMS results, these two opposing observations are likely the cause of the division of fuel depletion into three intervals when looking after the multiplication factor differences. U-235 fission dominates in the
133
Fig. 14. Comparison of U-235 nuclear density in fuel rings during depletion.
Fig. 15. Comparison of Pu-239 nuclear density in fuel rings during depletion.
Fig. 13. Comparison of fuel inventory depending on nuclide mass, ratio relative to WIMS code.
first part of fuel depletion so the under-prediction of U-235 concentration results in lower U-235 fission rates and lower multiplication factor values. Evolution of fission products are shown to be similar between the codes. The major part of fission products increase the nuclear density of the fuel as the burnup is increased. The curve shown in Fig. 17 is a typical depiction of the accumulation of Ag-109, which is a fission product with large impact on criticality and is one of the nuclides considered in burnup evaluation. Most of the investigated fission products exhibit the same trends in the accumulation process, but the nuclear density calculated by UWB1 is higher than that of the rest of the codes. The lowest concentration is usually predicted by the WIMS reference code. The agreement between WIMS and other industry codes such as MCNP6 is great; however, the concentration of I-129 was strongly under-predicted by WIMS (see Fig. 18). Iodine-129 is an important nuclide from the safety perspective. Deep geological repository inventory consider I-129 one of the most important nuclides due to its long half-life. At the
134
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 16. Comparison of Pu-242 nuclear density in fuel rings during depletion.
Fig. 18. Comparison of I-129 nuclear density in fuel rings during depletion.
151 concentration is under-predicted. WIMS results are slightly different from other codes and its final predicted concentration is the lowest of all the codes. 4.3. Effective cross sections
Fig. 17. Comparison of Ag-109 nuclear density in fuel rings during depletion.
discharge burnup of 7500 MW d/MTU, MCNP6 and other codes predicted 11-times higher I-129 concentration than the WIMS code. Nuclear densities of the most important burnable absorber nuclides, Eu-151 and Gd-157, were compared (see Fig. 19 and Fig. 20). The densities of the absorbers were spatially averaged over all CANLUB layers. Gd-157 with the high absorption cross section is consumed the most quickly and removes the initial transient peak. After a few days of irradiation, double neutron capture by Gd-155 generates and slowly increases the concentration of Gd-157 until an equilibrium concentration is reached. The UWB1 code predicts the concentration of Gd-157 closely similar to that of the WIMS code. The other codes did not match the prediction of the WIMS code as well as the UWB1 code did (note MCNP6 over-predicted). The Eu-151 nuclide affects the plutonium peak generation during the fuel depletion. The concentration of the Eu-151 absorber constantly decreases until it reaches almost equilibrium state when almost all Eu-151 nuclides are consumed. The rate of Eu-151 consumption is over-predicted by the UWB1 so the evolution of the Eu-
The UWB1 code estimates the lattice multiplication factor during depletion as a neutron production to absorption ratio. Therefore, a good prediction of effective cross sections is desirable. The effective cross section is an energy-averaged cross section with neutron flux serving as a weighting function. Comparison of neutron flux in the fuel at the beginning of the fuel depletion is indicated in Fig. 21. This figure shows that the differences in the flux are negligible compared to the energy scale. The effective cross section describes the rate at which a nuclear reaction occurs. Fission and neutron capture were investigated mainly in fuel ring 3, but behaviors in the other rings showed similar trends. MCNP6 calculates reaction rates instead of the effective cross sections. The conversion between the two parameters takes into account nuclear density of the nuclide as well as total neutron flux. At first look, the effective cross sections produced by MCNP6 are calculated differently at the beginning of fuel depletion for nuclides with small nuclear densities. The effective cross sections could be calculated by energy weighting at the end of transport calculation, when neutron flux is known. This is the standard for Monte Carlo codes (UWB1, SERPENT and KENOeVI) and all deterministic codes. The MCNP6 code, on the other hand, does not keep track of the flux, but instead directly evaluates reaction rates. As a result of this difference in methodology, there is an apparent discrepancy between the effective crosssections calculated by the MCNP6 code and the other codes. This is, however, not an issue of the precision of the codes, but a consequence of the difference in the methodologies used. Fission cross section is compared in Fig. 22 for U-235 and in Fig. 23 for Pu-239. Fuel ring 3 was selected as the representative fuel region. Results for case01 are depicted since case02 gives similar curve shapes. Effective cross section comparison is compatible with the conclusions made from nuclide density changes. The UWB1 code calculated the highest fission cross section for U-235, which resulted in the lowest prediction of U-235 concentration. Despite the overall high values, the shape of the curve is similar to other codes. The 2sPC depletion scheme of the UWB1 code has therefore effectively captured the decrease in effective cross
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 19. Comparison of Eu-151 nuclear density averaged over all CANLUB layers.
135
Fig. 21. Negligible differences in fuel flux compared to the energy scale for Monte Carlo codes.
Fig. 20. Comparison of Gd-157 nuclear density averaged over all CANLUB layers. Fig. 22. Comparison of U-235 effective fission cross section in 3rd fuel ring.
section although the transport equation is solved only at the beginning and at the end of fuel irradiation. In contrast to other codes, the WIMS reference code unexpectedly predicted that U-235 effective cross section is not a monotonically decreasing function. Pu-239 effective cross section showed remarkable agreement between the codes for the beginning of the fuel depletion (MCNP6 values are the result of the way the data were harvested). For Pu239 also, the WIMS reference code again predicted that the effective fission cross section is not a monotonically decreasing function, which is not in agreement with the other codes. The effective cross section for neutron capture of U-238 (Fig. 24) is important because it is the precursor to the production of Pu-239. Initial effective cross section is over-estimated by UWB1 by 5% that is significantly higher than the differences between the other codes. WIMS reference code agrees with other codes for burnups up to about 5000 MW d/MTU, then the slowly decreasing function is replaced by slowly increasing function (only by WIMS code). The higher capture cross section predicted by the UWB1 code leads to higher Pu-239 concentration. The slightly lower fission cross
section of Pu-239 (Fig. 25) predicted by the UWB1 code supports the trend of higher Pu-239 concentration. During the last part of fuel depletion, the UWB1 cross section remains constant. This is not the result of the 2sPC depletion scheme approximation; however, it is linked to the use of 2sPC method. As the cross section is calculated based on the initial and final burnup values, a protection against getting off this interval to either too low or too high cross section was programmed into UWB1 code. This is applied to all cross sections including both for capture and fission. As a result, when the Depletor stage reaches the nuclide density equal to that of the Corrector stage as illustrated in Fig. 2, the effective cross section is prevented from changing. Consequently, non-physical values are not reached. Capture cross section of fission products is depicted for Ag-109 (Fig. 26) and I-129 (Fig. 27). Both nuclides have similar progress of effective capture cross section during fuel depletion, as do the major part of the rest of the fission products. Effective cross sections
136
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 23. Comparison of U-235 effective fission cross section in 3rd fuel ring.
Fig. 25. Comparison of Pu-242 effective capture cross section in 3rd fuel ring.
Fig. 24. Comparison of U-238 effective capture cross section in 3rd fuel ring.
Fig. 26. Comparison of Ag-109 effective capture cross section in 3rd fuel ring.
influence neutron multiplication factor values by integration of all nuclides in the fuel, the most important nuclides (around 20 fission products) are part of burnup credit nuclide's set in criticality safety analyses. Even though I-129 is calculated at an order of magnitude differently by the WIMS code, its effective cross sections are predicted similar to the rest of the codes. Therefore, the probable cause behind the I-129 concentration differences is either the fission product yield of I-129 or the yield of fission products that quickly decay into I-129. Higher effective cross sections for the UWB1 code were again observed. The UWB1 code uses 4308 energy groups that provide a good agreement with the other codes for the lattice multiplication factor, but the self-shielding effect is not fully accounted for. To resolve this difference, an increased number of energy groups could be implemented, but this will greatly increase the calculation time of the code (see Figs. 28 and 29). The capture cross sections of the most important burnable absorber nuclides in the sheath, Eu-151 and Gd-157, were
compared for case02 (see Figs. 19 and 20). Cross sections were spatially averaged over all CANLUB layers. For both nuclides, similar conclusions could be made. The UWB1 code estimates capture cross sections below the NEWT and WIMS codes and above that of the other codes. The capture cross section calculated by the UWB1 code reaches constant values faster than the other codes which calculate the initial decrease period to last for longer times. The WIMS code alone allows the cross section to increase during the second half of the depletion. Conversion from reaction rates to effective cross sections gives correct MCNP6 values only for the end of the depletion. The effective cross section was spatially averaged over all CANLUB layers. The UWB1 code was primary tested on PWR fuel. Both transport and burnup equations and the 2sPC depletion scheme are as good for CANDU fuel as for PWR (see Fig. 30 and Fig. 31). The main idea behind 2sPC is the relative change in the effective cross sections. Even though the effective cross sections for natural uranium fuel in
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
137
Fig. 29. Comparison of Gd-157 effective capture cross section in the sheath. Fig. 27. Comparison of I-129 effective capture cross section in 3rd fuel ring.
Fig. 30. Absolute comparison of PWR and CANDU effective cross sections. Fig. 28. Comparison of Eu-151 effective capture cross section in the sheath.
CANDU fuel bundle is an order of magnitude higher than for 5.0 wt % enriched uranium fuel in PWR fuel assembly (Fig. 30), when plotted on a relative scale against burnup (Fig. 31), the effective fission cross sections of U-235 and Pu-239 between the two fuels exhibit almost the same decreasing trend. The effective capture cross sections of Eu-151 and Gd-157, however, exhibit different behaviors. This difference is likely due to the locations within the fuel to which the burnable absorbers are inserted (the proposed CANDU fuel includes absorbers discretely in the CANLUB coating whereas the PWR fuel includes them integral in the fuel). 4.4. Total flux The CANDU fuel bundle depletion was executed under the assumption of constant power level. The relation between power and total flux is described by an equation in which nuclear densities and recoverable energies of the nuclides appear. Total flux is used in
the Bateman equation to calculate changes in the inventory. Reaction rates are calculated as a product of the total flux and the effective cross section. Therefore, the total flux is an important normalization function in fuel depletion. Comparison of the total flux in a fuel bundle is depicted in Fig. 32. The total flux predicted by the WIMS code is 15%e17% higher than that of the MCNP6 code. Differences between other codes are lower than WIMS and MCNP6 comparison. The ratio of the maximum to minimum differences between the codes for the total flux is between 4% and 7%. The explanation of higher WIMS differences was not found in the analysis of previous sections. The difference could be caused by a normalization issue, because the shape of the flux is the same as for the rest of the codes. Also, higher burnup leads to higher concentrations of fission products that absorb large amounts of neutrons, thereby causing the total flux to increase. 4.5. Calculation time The slightly decrease in the accuracy of using UWB1 comes
138
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 33. CANDU fuel depletion calculation time comparison. Fig. 31. Relative comparison of PWR and CANDU effective cross sections.
slower than the WIMS code. The results showed that between Monte Carlo codes, the UWB1 code is significantly faster. Deterministic codes WIMS and NEWT are executed in different time framework. The NEWT code is as fast as a typical Monte Carlo code with 2 million active neutrons per depletion step, but WIMS is significantly faster. The reason behind this difference is caused by the different implemented method used by the two codes. The NEWT code uses discrete ordinates method whereas the WIMS code uses the faster method of characteristics. The development of the SCALE package and its NEWT code is focused on implementing the method of characteristics so further decreases in calculation time can be expected in near future. 5. Conclusions
Fig. 32. Comparison of total neutron flux used in burnup solver during depletion.
inherently with the methodology and assumptions used in the code. This is expected as the code development focused significantly on the speed of calculation. The lower accuracy is outweighed by the speed-up factor between one and two orders of magnitude, as it can be seen from Fig. 33. All codes except MCNP6 were run in serial mode. The MCNP6 time was converted to serial execution. WIMS fuel depletion takes around 5 min and it is the fastest code. UWB1 fuel depletion takes around 1.5 h, assuming that 2 million neutrons are used in the Monte Carlo simulation. The SERPENT code was able to finish fuel depletion in around 17 h. The SCALE codes KENOeVI and NEWT were slower than SERPENT. The NEWT deterministic code needed around 29 h, while KENOeVI Monte Carlo code finished the calculation in 40 h. The slowest execution was observed for MCNP6 code as it took around 670 h (28 days) to finish fuel bundle depletion. The UWB1 code is around 10 times faster than most of other codes, more than 100 times faster than MCNP6, but almost 20 times
The UWB1 nuclear fuel depletion code was used to simulate CANDU fuel bundle depletion and the results were compared to WIMS, MCNP6, SERPENT, KENOeVI and NEWT codes. Results show that the UWB1 nuclear fuel depletion code is capable to calculate fuel depletion of CANDU fuel bundle with and without burnable absorbers. The behaviors of all investigated parameters were captured by the code. A slight decrease in the accuracy comes inherently with the methodology and assumptions used in the code. This is expected as the code development focused significantly on the speed of calculation. The lower accuracy is outweighed by the speed-up factor between one to two orders of magnitude, as it can be seen from Fig. 33. The development of UWB1 code is ongoing. Acknowledgments R&D has been funded by TE01020455 Centre for Advanced Nuclear Technologies (CANUT) project. References ACR-700 Technical Description. AECL, 10810-01371-TED-001 Revision 1, 2004. Chan, P.K., Paquette, S., Bonin, H.W., French, C., Pant, A., July 29eAugust 2, 2013. Neutron absorbers in CANDU natural uranium fuel bundles to improve operating margins. In: Proceedings of the 2013 21st International Conference on Nuclear Engineering (Chengdu, China). Dufek, J., Kotlyar, D., Shwageraus, E., Lepp€ anen, J., 2013. Numerical stability of the predictorecorrector method in Monte Carlo burnup calculations of critical reactors. Ann. Nucl. Energy 56, 34e38.
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139 Jonkmans, G., 2006. WIMS-AECL Version 3.1 User's Manual. ISTP-05e5115/WP51504, 153-119190-UM-001, FFC-RRP-667, Revision 1. Atomic Energy of Canada Limited. Kotlyar, D., Shwageraus, E., 2013. On the use of predictorecorrector method for coupled Monte Carlo burnup codes. Ann. Nucl. Energy 58, 228e237. €nen, J., 2007. Development of a New Monte Carlo Reactor Physics Code. D.Sc. Leppa Thesis. Thesis. Helsinki University of Technology. VTT Publications 640. €nen, J., March 6, 2013. Serpent e a Continuous-energy Monte Carlo Reactor Leppa Physics Burnup Calculation Code. VTT Technical Research Centre of Finland. Lovecký, M., Piterka, L., Prehradný, J., Skoda, R., 2014. UWB1 e fast nuclear fuel depletion code. Ann. Nucl. Energy 71, 333e339. Lovecký, M., Jiri ckov a, J., Skoda, R., 2015. Monte Carlo solver for UWB1 nuclear fuel depletion code. Ann. Nucl. Energy 85, 778e787.
139
Pelowitz, D.B., May 2013. MCNP6 User's Manual, Version 1. Los Alamos National Laboratory. Report LA-CP-13e00634, Revision 0. Prehradný, J., Lovecký, M., Skoda, R., July 7e11, 2014. Burnable absorber comparison between VVER, PWR and SFR with UWB1 and SERPENT codes. In: Proceedings of the 2014 22nd International Conference on Nuclear Engineering (Prague, Czech Republic). Scale: a Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, ORNL/TM-2005/39, Version 6.1, June 2011. Radiation Safety Information Computational Center at Oak Ridge National Laboratory as CCC-785. Available from: Talebi, F., Marleau, G., Koclas, J., 2006. A model for coolant void reactivity evaluation in assemblies of CANDU cells. Ann. Nucl. Energy 33, 975e983.
Contents lists available at ScienceDirect
Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
The application of UWB1 nuclear fuel depletion code on a CANDU fuel bundle a, b M. Lovecký a, *, R. Skoda , M.S. Hussein c, J.J. Song c, P.K. Chan c , Czech Republic Regional Innovation Centre for Electrical Engineering, University of West Bohemia, Univerzitní 8, 306 14 Plzen 4, 160 07 Prague 6, Czech Republic Czech Technical University, Faculty of Mechanical Engineering, Technicka c Royal Military College of Canada, Department of Chemistry and Chemical Engineering, PO Box 17000, Station Forces, K7K 7B4 Kingston, Ontario, Canada a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 21 July 2015 Received in revised form 21 January 2016 Accepted 12 March 2016 Available online 24 March 2016
A computer code (UWB1) that is applicable for both light and heavy water reactor fuel types is being developed at the University of West Bohemia. CANDU fuel geometry was investigated in this paper. Fuel depletion with UWB1 code was performed and compared to other depletion codes. A feasibility study on the use of burnable absorbers in CANDU to improve operating margins was recently published [1]. The use of slight enriched fuel (SEU) with various burnable absorbers in CANDU has also been considered for future fuel designs. UWB1 is a fast-calculating depletion code. It is being tested and compared extensively to other six different calculation codes, which include both deterministic and probabilistic types. Although the work focuses primarily on the progress of the multiplication factor during fuel depletion, fuel inventory details were also considered. Effective cross sections as the derivation of reaction rates that directly influence Bateman burnup equations were also compared. Further improvement on the UWB1 code is ongoing. The results showed that UWB1 nuclear fuel depletion code is capable to calculate fuel depletion of CANDU fuel bundle with and without burnable absorbers. As expected, the accuracy of the UWB1 code is lower than the other codes. This paper recommends that UWB1 code be considered as a tool for supporting fuel design assessment, since discrepancies are comparable and the code is one to two orders of magnitude faster than other depletion codes. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Fuel depletion CANDU Monte Carlo Nuclear fuel Burnable absorber
1. Introduction Nuclear fuel depletion is the process of extracting recoverable energy by nuclear fission that leads to the changes in the fuel composition. Currently operating thermal CANDU reactors use fresh natural uranium fuel in the form of uranium dioxide. Each nuclide interact with neutron by a number of nuclear reactions, however, the two main reactions are fission and neutron capture. For fissile materials such as uranium-235, the highest probability of reaction is by fission that produces fission products. During in-core irradiation, as the burnup of a fuel increases, its fissile material content decreases and the fission products content increases. This results in a slow decrease in the multiplication factor or the reactivity of the nuclear fuel, to the point where the fuel eventually needs to be discharged and replaced by a fresh one or a less
* Corresponding author. E-mail address: [email protected] (M. Lovecký). http://dx.doi.org/10.1016/j.pnucene.2016.03.010 0149-1970/© 2016 Elsevier Ltd. All rights reserved.
depleted one via the process of refueling. The time of refueling could be delayed due to the creation of fissile materials from the fertile materials in the fuel. Fertile materials such as uranium-238 are most likely to interact with neutron by neutron capture. Mainly plutonium-239 is generated this way from uranium-238 in thermal reactors, other less important actinides are also formed. Between the first hours up to days of in-core irradiation, the concentration of major neutron-absorbing fission products in a CANDU fuel rapidly increase until they reach an equilibrium concentration. This process is called an initial fueling transient and it is demonstrated by a relatively large drop in multiplication factor in the first 2e3 full power days of operating a fresh fuel. Burnable absorbers (BA) have been used in LWR since the mid 1970s and their research is still ongoing as higher fuel enrichments are considered for fuel designs. Consequently, the frequency of recurrence of burnable absorbers in literature from ScienceDirect database is steadily increasing, as it can be seen in Fig. 1. Burnable absorbers are currently not used in CANDU fuel. However, by introducing burnable absorbers inside a CANDU fuel bundle, it is
128
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 1. Journal papers that reference the use of burnable absorbers. This is obtained from ScienceDirect database.
possible to remove the initial fueling transient (Chan et al., 2013). Moreover, void reactivity coefficient can be set to negative values (Talebi et al., 2006). It was shown that burnable absorbers (Chan et al., 2013) could also suppress the plutonium peak. The use of burnable absorber with SEU for a 43-elements fuel design in CANDU was proposed in technical document (R-700 Technical Descrip, 2004) and later studied in (Talebi et al., 2006). The proposed design placed dysprosium integrally into central natural uranium pin, while surrounding 42 fuel pins in 3 fuel rings are slightly enriched to 2.1 wt%. In this paper, the use of UWB1 code for CANDU fuel bundle depletion and its comparison with other codes is demonstrated. The study includes six different calculation codes; both deterministic and statistical codes are considered. Although the work focuses primarily on the multiplication factor progress during fuel depletion, fuel inventory details are also considered. Moreover, effective cross sections as the derivation of reaction rates that directly influence the Bateman burnup equations are also compared. The objective of the study is to determine the extent of decrease in the accuracy of the UWB1 code, and to determine its advantage in terms of lowering the computation time. Two cases are studied, one without burnable absorber and one with the discrete burnable absorber placed in the fuel. 2. UWB1 code and others calculation codes Results of UWB1 fast depletion code (Lovecký et al., 2014) are investigated and compared to other codes. The comparison study includes five other calculation codes, both deterministic and probabilistic. WIMS deterministic code is used as the main reference code since it is used in CANDU industry as a standard tool (Jonkmans, 2006). WIMS deterministic code uses method of characteristics to solve the transport equation. WIMS has been benchmarked via comparisons to power reactor measurements and is known to yield reasonable results. Widely recognized MCNP6 general Monte Carlo code and newly developed and popular Finnish code SERPENT are also included. Two codes from SCALE code package, Monte Carlo code KENOeVI and discrete ordinates code NEWT that both works inside TRITON code sequence are also considered in the study. First version of the newly developed UWB1 fast nuclear fuel
depletion code (Lovecký et al., 2014) was introduced in order to significantly reduce calculation time by omitting the solution step for the Boltzmann transport equation. However, estimation of multiplication factor during depletion was not sufficiently calculated (Prehradný et al., 2014). Moreover, 1-group effective cross sections for models containing strong absorbers such as gadolinium showed disagreement between the UWB1 tested code and the SERPENT reference code. Monte Carlo transport solver for UWB1 code was introduced (Lovecký et al., 2015) in order to improve code accuracy, remove pre-calculated case-dependent data libraries and eliminate constant effective cross section assumption. Two dimensional, fuel pin model with arbitrary number of concentric cylinder regions, ray-tracing algorithm and ENDF/B-VII.1 data are the main components of the solver. The solver uses 4308-group cross section data library. Speed of the UWB1 Monte Carlo solver is the product of development focused on the minimization of CPU usage at the expense of RAM demands. Due to uniform energy grid used for cross section data and relatively small number of energy groups (4308 groups) compared to continuous energy approach (cca 20,000 groups for U-238), the Monte Carlo solver is about 10 times faster than MCNP6 reference code. A simple depletion scheme was originally incorporated into UWB1 code shortly after the introduction of the Monte Carlo solver. This depletion scheme is a standard coupling of burnup and transport solver. Effective cross sections are calculated by transport solver and used by burnup solver to determine fuel and cladding composition of the next depletion time step. Two-step predictor-corrector method (2sPC) developed for UWB1 code is the second feature of the code that makes it faster than other Monte Carlo depletion codes (Dufek et al., 2013; Kotlyar and Shwageraus, 2013). Similarly to Monte Carlo solver, 2sPC method is able to speed-up the calculation approximately 10 times, therefore, fuel depletion with UWB1 code is expected to be around 100 times faster than with MCNP6 reference code. The idea of 2sPC method is to change the coupling of transport and burnup solvers by omitting a major fraction of the transport solver callings, because the transport solver is orders of magnitude slower than the burnup solver. Both transport and burnup variables are calculated for predicted states and corrected with more precise values as the two parts of the fuel depletion are coupled. Only three transport solver solutions are used, the initial fuel state and predicted and corrected states for final burnup state. Effective cross sections are evaluated during fuel depletion by assuming nuclide-based nonlinear dependency. Multiplication factors in the depletion steps other than the first and the last one are estimated by neutron production to absorption ratio that is calculated without the need to call the transport solver. UWB1 execution is performed in 5 stages - initial, predictor, corrector, depletor and estimator. The main code flowchart is depicted in Fig. 2. The initial stage uses Monte Carlo transport solver to analyze the initial state fuel composition state of the calculated fuel model. Total macroscopic cross sections are calculated before MC simulation in order to speed-up neutron random walk. Transport solver then calculates multiplication factor and neutron flux in all geometry regions in 4308 energy groups. Support calculations for burnup solver, evaluation of fuel basis and relative region powers, are made. Estimation formula describes ratio of neutron production to absorption in the fuel model. Predictor stage uses initial state variables, mainly effective cross sections, to estimate fuel model state at the end of fuel depletion without calling the transport solver in the inner depletion steps. Burnup solver is called in two loops, which are the inner depletion step loop and the outer geometry regions loop. The order of the loops was changed to increase the speed of calculation. This is particularly significant in the case of multiple depleted regions
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
129
Fig. 2. Two-step predictor-corrector UWB1 depletion scheme flowchart.
because the calling transition matrix preparation subroutine is minimized. At the end of predictor stage, transport solver is called for the second time in the calculation, predicting final state variables. The corrector stage works in identical way that the predictor stage works. The only difference is that the initial state's effective cross sections are taken from the predicted final state effective cross sections. By using this method, the averaged values of the predictor and the corrector are used to calculate the final state composition with approximately averaged effective cross sections (i.e. mid-burnup effective cross sections). Corrector stage employs the third and final transport solver execution. Averages of predictor and corrector values (effective cross sections, relative region powers, multiplication factor estimates, transport multiplication values) are used as final state values for the second step of 2sPC method. Depletor stage is used to calculate fuel composition and multiplication factor estimate during burnup. Similarly to predictor stage, depletor stage uses two loops over depletion steps and geometry regions. On the other hand, third loop over the second predictor-corrector step is added. In this innermost loop, both effective cross sections and fuel composition at the end of depletion step are predicted, corrected and averaged. No transport solver is called during depletor stage. Estimator stage is used to compare initial and final state multiplication factors calculated by transport solver with multiplication factor estimates. It is assumed that estimator formula has a difference that is linearly dependent on burnup. Multiplication factor estimates are corrected for the expected differences and used in final output. Widely recognized MCNP6.1 general Monte Carlo code (Pelowitz, 2013) cannot be dismissed in any neutron transport comparison study. MCNP6 is a general purpose neutron transport code that was created by merging capabilities of previous two parallel developed MCNP versions, MCNP5 and MCNPX. Newly developed and popular Finnish code SERPENT 1.1.19 €nen, 2007) (Leppa €nen, 2013), was used as a representative of (Leppa new Monte Carlo codes developed primary for reactor physics calculations that run faster than the MCNP6 code. Monte Carlo technique is accelerated with Woodcock delta-tracking method, however, it is expected that the method's efficiency decreases when strong absorbers (e.g. burnable absorber) are present in the model. Two codes from the SCALE 6.1.3 code package (Scale, 2011), the Monte Carlo code KENOeVI and the discrete ordinates code NEWT, which both work inside the TRITON code sequence, are the last codes considered in the study. KENOeVI is a statistical code similar to MCNP6, but use multigroup nuclear data. NEWT code represents a standard discrete ordinates code that use spatial discretization approach called Extended Step Characteristic.
3. CANDU fuel bundle model The CANDU 37-element fuel bundle was modeled by the depletion codes described in section 2. Two dimensional model of fuel bundle is depicted in Fig. 3. Since the UWB1 code does not allow for such a complicated geometry, the exact geometry as shown in Fig. 3 was not used for the model. CANDU fuel bundle have lattice that cannot be simplified like PWR fuel assembly, therefore, homogenization was chosen as the best approach to simplify the geometry. For this purpose, the UWB1 code was extended to be able to model arbitrary number of concentric cylinders. The resulting geometry is shown in Fig. 4. SERPENT fuel depletion was performed for both investigated cases where case01 is natural uranium fuel without burnable absorbers and case02 is with burnable absorbers placed in the CANLUB layer between fuel and its sheath. Burnable absorber content of 150 mg Gd2O3 and 300 mg Eu2O3 per fuel bundle was chosen as one of the promising designs (Chan et al., 2013). The effect of fuel pins homogenization in the rings on multiplication factor is shown to be less than 0.002, which is negligible as indicated in Fig. 5. The burnable absorbers of interest in the fuel bundle consist of both gadolinium and europium oxides. Present nuclear fuels use mainly gadolinium, europium and erbium oxides. Gadolinium oxide is burned faster than europium oxide and because of the very high absorption cross section of Gd-157 nuclide; the initial reactivity compensation for gadolinium is higher than for europium. For this reason, gadolinium is used mainly for the removal of the initial transient peak while europium is used to suppress the plutonium peak. Gadolinium nuclides of interest include Gd-155 and Gd-157 which are available at natural abundances of 14.80% and 15.65%,
Fig. 3. CANDU 37-element fuel bundle geometry layout.
130
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
outer fuel pins are homogenized into a final outer ring. Dimensions are summarized in Table 1. The fuel was depleted with constant power assumption at the typical power level of 1.27578E-02 MW/cm (3.29080E þ 01 MW/ MTU) for 42 depletion time steps up to final burnup slightly over 20,000 MW d/MTU. This exceeds the typical CANDU burnup of 7500 MW d/MTU. Depletion time steps varied from 0.2 days at the beginning of the depletion up to 20 days at the end of fuel depletion. Fuel rings are surrounded with a zirconium alloy sheath, heavy water coolant fills the remaining space inside the pressure tube. The area between inner pressure tube and outer calandria tube is filled with CO2 gap. The calandria tube is the part of reactor core and it is enclosed by moderator region. Model materials are summarized in Table 2. Periodic boundary condition was applied when possible; otherwise, mirror or white boundary conditions were used. Nonetheless, differences between the boundary options are negligible since the moderator area is very large compared to fuel bundle dimensions. In order to evaluate the speed of the codes, all codes except quick WIMS calculation were run on the same computer. The computer operates under RedHat OS with Intel Xeon E5-4650 processor with frequency 2700 MHz, the server is slightly faster than common desktop or laptop processors.
Fig. 4. Homogenized CANDU fuel bundle geometry layout.
4. Results The work focuses primarily on the multiplication factor progress during fuel depletion, fuel inventory details were not overlooked. Moreover, the effective cross sections as the derivation of reaction rates that directly influence the Bateman burnup equations were compared. Two cases were investigated. Case01 with natural uranium without burnable absorber, and case02 with 150 mg Gd2O3 þ 300 mg Eu2O3 burnable absorbers placed in the sheath. Calculation times in both cases were compared. 4.1. Multiplication factor Fig. 5. Effect of CANDU fuel bundle homogenization on multiplication factor.
respectively. Europium isotopes are available at natural abundances of 47.81% Eu-151 and 52.19% Eu-153. Both europium nuclides behave as good absorbers of neutrons, as they both possess high neutron capture cross sections with end-product nuclide characterized by low capture cross section. The fuel pellets were assumed to consist of natural uranium oxide. The central fuel pin represents the first fuel ring, the 6 fuel pins in the inner ring are homogenized into a secondary fuel ring, the 12 fuel pins are homogenized into a tertiary ring, and the last 18
Table 1 CANDU fuel bundle model dimensions. Region ()
Parameter ()
Value (cm)
Fuel CANLUB layer Sheath Inner fuel ring Intermediate fuel ring Outer fuel ring Coolant Pressure tube Gap Calandria Moderator
Outer radius Outer radius Outer radius Pitch circle radius Pitch circle radius Pitch circle radius Outer radius Outer radius Outer radius Outer radius Half pitch
0.609 0.6096 0.65046 1.4885 2.8755 4.3303 5.15 5.59308 6.4478 6.5875 14.2875
Basic comparison of multiplication factor during depletion is shown in Fig. 6 (case01) and Fig. 9 (case02). The initial transient peak is removed when burnable absorbers are added. The magnitude of the plutonium peak is reduced and delayed to higher burnups. As the burnable absorbers are consumed, their effect on the reactivity of the fuel decreases and the multiplication factor of case02 converges to that of case01. The reactivity curves produced by all codes behave similarly and for the major part of fuel depletion they are bounded by that of WIMS and UWB1. During the first part of the fuel depletion, in which plutonium accumulates within the fuel, the UWB1 code generally yields the highest multiplication factor value while WIMS provides the lowest boundary. However, the results from the codes SCALE package, KENOeVI and NEWT, result in values higher than UWB1 for case02, in the first part of fuel depletion. In the second part of fuel depletion (after the plutonium
Table 2 CANDU fuel bundle model materials. Region ()
Material ()
Density (g/cm3)
Temperature (K)
Fuel Sheath Coolant Pressure tube Gap Calandria tube Moderator
UO2 Zircaloy-4 Heavy water 99.11 wt% Zr2.5Nb CO2 Zircaloy-2 Heavy water 99.97 wt%
10.5057 6.3918 0.8179 6.5041 0.001195 6.4003 1.08699
1011 561 561 561 450 339 339
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
131
Fig. 6. Case01 (no BA) e multiplication factor during depletion.
Fig. 8. Case01 (no BA) e multiplication factor comparison.
Fig. 7. Case01 (no BA) e multiplication factor near plutonium peak.
Fig. 9. Case02 (Gd þ Eu BA) e multiplication factor during depletion.
peak to a burnup slightly over 10000 MW d/MTU), the UWB1 code yields the lowest values of reactivity, while WIMS provides the highest values. A plot of the evolution of reactivity during the plutonium peak, for each code, is shown in Fig. 7 (case01) and Fig. 10 (case02). The horizontal axis is changed from burnup to irradiation days. Statistical uncertainty is provided when applicable, showing that statistical uncertainty is not the cause of the differences between the codes. Number of simulated neutrons was chosen to be the lowest possible value that still imparts negligible impact on the value of the multiplication factors. A total of two million active neutrons were tracked in 200 cycles, each having 10000 neutrons each. Five inactive cycles were also added. Errors are not shown for the deterministic codes, WIMS and NEWT, because they have no defined uncertainty associated with them. Initial multiplication factor values are slightly higher for SCALE codes KENOeVI and
NEWT (Table 3). The difference between the highest and lowest values is 0.007. The differences between WIMS reference and UWB1 investigated codes are around 0.002. Plutonium peak occurs at 42 days for WIMS and 22 days for UWB1, the rest of the codes calculate the peak to evolve around 30 days for case01. When burnable absorbers are added (case02), the plutonium peak is delayed by around 10 days. It is important that all codes predict the same delay, i.e. the differences between the case01 and case02 are calculated to be the same by all the codes. A relative comparison of the multiplication factors for each of the codes was conducted and its results are displayed in Fig. 8 (case01) and Fig. 11 (case02). The relative values were calculated as a ratio in comparison to the WIMS code that was chosen as the reference, because the WIMS code is the standard toolset used to model the CANDU lattice. Statistical uncertainty is shown as error bars for the probabilistic codes. As described earlier, the fuel
132
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
typically around 0.02, but reach up to 0.03. The closest match to the WIMS reference code is achieved by KENOeVI and NEWT codes from SCALE code package; their differences are at an order of magnitude lower than of the other codes. For all the codes it is possible to find a depletion interval at which the code gives the extreme multiplication factor value when compared to that of other codes. However, for most of the depletion time, the highest range of values are predicted by either WIMS or UWB1 code. The evolution of fuel reactivity past the refueling transients are not significantly different between case01 and case02, and the trends are very similar. In assessment of the performance of the UWB1 code, it can be concluded that the multiplication factor of the modeled fuel lattice is predicted in the same manner as the other codes. All the codes exhibit some level of difference to the WIMS code. Amongst the compared codes, the UWB1 code has been shown to yield the greatest difference to the WIMS code and also the greatest magnitudes of unwanted oscillations in the multiplication factor. 4.2. Nuclear density Fig. 10. Case02 (Gd þ Eu BA) e multiplication factor near plutonium peak.
Table 3 CANDU fuel bundle initial multiplication factor values (2-D). Code
Case01
Case02
WIMS UWB1 MCNP6 SERPENT KENOeVI NEWT
1.12629 1.12866 1.12574 1.12712 1.13209 1.13296
1.06748 1.06948 1.06930 1.06890 1.07422 1.07463
During fuel depletion, the nuclear density of two set of nuclides are stored. The first set includes nuclides for which the cross section data is available. Only nuclear data libraries supplied with the codes were used, which are the ENDF/B-VII.0 from 2006 (SERPENT, KENOeVI, WIMS) and the ENDF/B-VII.1 from 2011 (UWB1, MCNP6). There are only minor differences between the two libraries, as major improvements in the library are introduced only for new versions (e.g. VI vs VII). The newer library predicts neutron multiplication factor values lower by 0.0006e0.0018 for investigated CANDU cases. The number of nuclides in neutron data library increased from 393 to 423, however, not all nuclides are easily harvested from the output files and a total number of 281 nuclides were compared. The main reason for the comparison of fuel inventory is that the UWB1 code estimates the fuel lattice multiplication factor during depletion from the inventory and transport values at the beginning and the end of fuel irradiation. In addition, the fuel inventory directly influences the decay heat, activity, radiation sources and other parameters that are needed in the overall evaluation of fuel performance.
Fig. 11. Case02 (Gd þ Eu BA) e multiplication factor comparison.
depletion is divided into three parts. In the first and third part, the compared codes predict higher values than that of the reference WIMS code. In the second part of fuel depletion, the WIMS code gives the highest values. The typical difference between each of the codes to the WIMS code is around 0.01. The highest differences are
Fig. 12. Comparison of fuel inventory depending on nuclide density, ratio relative to WIMS code.
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fuel inventory is compared in Fig. 12 and Fig. 13. As burnable absorbers are placed in the sheath, the fuel inventory is not significantly influenced. The third of four fuel rings was chosen to the comparison, the results for other rings are very similar. Ratios of nuclear density (atoms/b-cm) between the investigated code and WIMS reference code were evaluated for 7500 MW d/MTU. On independent axis, both WIMS nuclide density and nuclide ZAID number was used. ZAID number is related to the mass of the nuclide (ZAID ¼ 10000*Z þ 10*A þ m). Generally, nuclear density is over-predicted by all the codes when compared to WIMS results. The over-prediction is seen for both fission products and actinides. Differences at the level of tens per cents are typically observed. As expected, the largest differences are visible for UWB1 calculation. The best agreement with WIMS results were predicted by MCNP6 code that also under-predicted nuclear densities for a large number of nuclides. Fuel inventory comparison of selected nuclides was divided into two groups: fission products and actinides. Uranium-235 concentrations are compared in Fig. 14 for all fuel rings. The closer the ring is to the moderator area, the faster the fission is and the U-235 concentration is lower. The decrease of U-235 concentration was over-calculated by all the codes, however, the UWB1 results are the least precise and the rate of consumption is so high that the concentration in the outermost ring calculated by UWB1 code is less than the value in the innermost ring predicted by all the other codes. The differences between the codes in ring 3 for 7500 MW d/ MTU are up to 12% excluding UWB1. For UWB1, the difference is approximately 50%. Plutonium and minor actinides are generated by successive neutron capture of uranium-238. Given the fact that the actinide generation processes is similar between codes, the evolution of actinides predicted by each code are similar. The UWB1 code overpredicts the concentration when compared to other codes (see Fig. 15 a Fig. 16). The most important of these nuclides, Pu-239, is over-predicted by 21% for the UWB1 code in ring 3 for 7500 MW d/ MTU. All the codes over-predicts the concentration of Pu-239 and under-predicts the concentration of U-235 against WIMS results, these two opposing observations are likely the cause of the division of fuel depletion into three intervals when looking after the multiplication factor differences. U-235 fission dominates in the
133
Fig. 14. Comparison of U-235 nuclear density in fuel rings during depletion.
Fig. 15. Comparison of Pu-239 nuclear density in fuel rings during depletion.
Fig. 13. Comparison of fuel inventory depending on nuclide mass, ratio relative to WIMS code.
first part of fuel depletion so the under-prediction of U-235 concentration results in lower U-235 fission rates and lower multiplication factor values. Evolution of fission products are shown to be similar between the codes. The major part of fission products increase the nuclear density of the fuel as the burnup is increased. The curve shown in Fig. 17 is a typical depiction of the accumulation of Ag-109, which is a fission product with large impact on criticality and is one of the nuclides considered in burnup evaluation. Most of the investigated fission products exhibit the same trends in the accumulation process, but the nuclear density calculated by UWB1 is higher than that of the rest of the codes. The lowest concentration is usually predicted by the WIMS reference code. The agreement between WIMS and other industry codes such as MCNP6 is great; however, the concentration of I-129 was strongly under-predicted by WIMS (see Fig. 18). Iodine-129 is an important nuclide from the safety perspective. Deep geological repository inventory consider I-129 one of the most important nuclides due to its long half-life. At the
134
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 16. Comparison of Pu-242 nuclear density in fuel rings during depletion.
Fig. 18. Comparison of I-129 nuclear density in fuel rings during depletion.
151 concentration is under-predicted. WIMS results are slightly different from other codes and its final predicted concentration is the lowest of all the codes. 4.3. Effective cross sections
Fig. 17. Comparison of Ag-109 nuclear density in fuel rings during depletion.
discharge burnup of 7500 MW d/MTU, MCNP6 and other codes predicted 11-times higher I-129 concentration than the WIMS code. Nuclear densities of the most important burnable absorber nuclides, Eu-151 and Gd-157, were compared (see Fig. 19 and Fig. 20). The densities of the absorbers were spatially averaged over all CANLUB layers. Gd-157 with the high absorption cross section is consumed the most quickly and removes the initial transient peak. After a few days of irradiation, double neutron capture by Gd-155 generates and slowly increases the concentration of Gd-157 until an equilibrium concentration is reached. The UWB1 code predicts the concentration of Gd-157 closely similar to that of the WIMS code. The other codes did not match the prediction of the WIMS code as well as the UWB1 code did (note MCNP6 over-predicted). The Eu-151 nuclide affects the plutonium peak generation during the fuel depletion. The concentration of the Eu-151 absorber constantly decreases until it reaches almost equilibrium state when almost all Eu-151 nuclides are consumed. The rate of Eu-151 consumption is over-predicted by the UWB1 so the evolution of the Eu-
The UWB1 code estimates the lattice multiplication factor during depletion as a neutron production to absorption ratio. Therefore, a good prediction of effective cross sections is desirable. The effective cross section is an energy-averaged cross section with neutron flux serving as a weighting function. Comparison of neutron flux in the fuel at the beginning of the fuel depletion is indicated in Fig. 21. This figure shows that the differences in the flux are negligible compared to the energy scale. The effective cross section describes the rate at which a nuclear reaction occurs. Fission and neutron capture were investigated mainly in fuel ring 3, but behaviors in the other rings showed similar trends. MCNP6 calculates reaction rates instead of the effective cross sections. The conversion between the two parameters takes into account nuclear density of the nuclide as well as total neutron flux. At first look, the effective cross sections produced by MCNP6 are calculated differently at the beginning of fuel depletion for nuclides with small nuclear densities. The effective cross sections could be calculated by energy weighting at the end of transport calculation, when neutron flux is known. This is the standard for Monte Carlo codes (UWB1, SERPENT and KENOeVI) and all deterministic codes. The MCNP6 code, on the other hand, does not keep track of the flux, but instead directly evaluates reaction rates. As a result of this difference in methodology, there is an apparent discrepancy between the effective crosssections calculated by the MCNP6 code and the other codes. This is, however, not an issue of the precision of the codes, but a consequence of the difference in the methodologies used. Fission cross section is compared in Fig. 22 for U-235 and in Fig. 23 for Pu-239. Fuel ring 3 was selected as the representative fuel region. Results for case01 are depicted since case02 gives similar curve shapes. Effective cross section comparison is compatible with the conclusions made from nuclide density changes. The UWB1 code calculated the highest fission cross section for U-235, which resulted in the lowest prediction of U-235 concentration. Despite the overall high values, the shape of the curve is similar to other codes. The 2sPC depletion scheme of the UWB1 code has therefore effectively captured the decrease in effective cross
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 19. Comparison of Eu-151 nuclear density averaged over all CANLUB layers.
135
Fig. 21. Negligible differences in fuel flux compared to the energy scale for Monte Carlo codes.
Fig. 20. Comparison of Gd-157 nuclear density averaged over all CANLUB layers. Fig. 22. Comparison of U-235 effective fission cross section in 3rd fuel ring.
section although the transport equation is solved only at the beginning and at the end of fuel irradiation. In contrast to other codes, the WIMS reference code unexpectedly predicted that U-235 effective cross section is not a monotonically decreasing function. Pu-239 effective cross section showed remarkable agreement between the codes for the beginning of the fuel depletion (MCNP6 values are the result of the way the data were harvested). For Pu239 also, the WIMS reference code again predicted that the effective fission cross section is not a monotonically decreasing function, which is not in agreement with the other codes. The effective cross section for neutron capture of U-238 (Fig. 24) is important because it is the precursor to the production of Pu-239. Initial effective cross section is over-estimated by UWB1 by 5% that is significantly higher than the differences between the other codes. WIMS reference code agrees with other codes for burnups up to about 5000 MW d/MTU, then the slowly decreasing function is replaced by slowly increasing function (only by WIMS code). The higher capture cross section predicted by the UWB1 code leads to higher Pu-239 concentration. The slightly lower fission cross
section of Pu-239 (Fig. 25) predicted by the UWB1 code supports the trend of higher Pu-239 concentration. During the last part of fuel depletion, the UWB1 cross section remains constant. This is not the result of the 2sPC depletion scheme approximation; however, it is linked to the use of 2sPC method. As the cross section is calculated based on the initial and final burnup values, a protection against getting off this interval to either too low or too high cross section was programmed into UWB1 code. This is applied to all cross sections including both for capture and fission. As a result, when the Depletor stage reaches the nuclide density equal to that of the Corrector stage as illustrated in Fig. 2, the effective cross section is prevented from changing. Consequently, non-physical values are not reached. Capture cross section of fission products is depicted for Ag-109 (Fig. 26) and I-129 (Fig. 27). Both nuclides have similar progress of effective capture cross section during fuel depletion, as do the major part of the rest of the fission products. Effective cross sections
136
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 23. Comparison of U-235 effective fission cross section in 3rd fuel ring.
Fig. 25. Comparison of Pu-242 effective capture cross section in 3rd fuel ring.
Fig. 24. Comparison of U-238 effective capture cross section in 3rd fuel ring.
Fig. 26. Comparison of Ag-109 effective capture cross section in 3rd fuel ring.
influence neutron multiplication factor values by integration of all nuclides in the fuel, the most important nuclides (around 20 fission products) are part of burnup credit nuclide's set in criticality safety analyses. Even though I-129 is calculated at an order of magnitude differently by the WIMS code, its effective cross sections are predicted similar to the rest of the codes. Therefore, the probable cause behind the I-129 concentration differences is either the fission product yield of I-129 or the yield of fission products that quickly decay into I-129. Higher effective cross sections for the UWB1 code were again observed. The UWB1 code uses 4308 energy groups that provide a good agreement with the other codes for the lattice multiplication factor, but the self-shielding effect is not fully accounted for. To resolve this difference, an increased number of energy groups could be implemented, but this will greatly increase the calculation time of the code (see Figs. 28 and 29). The capture cross sections of the most important burnable absorber nuclides in the sheath, Eu-151 and Gd-157, were
compared for case02 (see Figs. 19 and 20). Cross sections were spatially averaged over all CANLUB layers. For both nuclides, similar conclusions could be made. The UWB1 code estimates capture cross sections below the NEWT and WIMS codes and above that of the other codes. The capture cross section calculated by the UWB1 code reaches constant values faster than the other codes which calculate the initial decrease period to last for longer times. The WIMS code alone allows the cross section to increase during the second half of the depletion. Conversion from reaction rates to effective cross sections gives correct MCNP6 values only for the end of the depletion. The effective cross section was spatially averaged over all CANLUB layers. The UWB1 code was primary tested on PWR fuel. Both transport and burnup equations and the 2sPC depletion scheme are as good for CANDU fuel as for PWR (see Fig. 30 and Fig. 31). The main idea behind 2sPC is the relative change in the effective cross sections. Even though the effective cross sections for natural uranium fuel in
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
137
Fig. 29. Comparison of Gd-157 effective capture cross section in the sheath. Fig. 27. Comparison of I-129 effective capture cross section in 3rd fuel ring.
Fig. 30. Absolute comparison of PWR and CANDU effective cross sections. Fig. 28. Comparison of Eu-151 effective capture cross section in the sheath.
CANDU fuel bundle is an order of magnitude higher than for 5.0 wt % enriched uranium fuel in PWR fuel assembly (Fig. 30), when plotted on a relative scale against burnup (Fig. 31), the effective fission cross sections of U-235 and Pu-239 between the two fuels exhibit almost the same decreasing trend. The effective capture cross sections of Eu-151 and Gd-157, however, exhibit different behaviors. This difference is likely due to the locations within the fuel to which the burnable absorbers are inserted (the proposed CANDU fuel includes absorbers discretely in the CANLUB coating whereas the PWR fuel includes them integral in the fuel). 4.4. Total flux The CANDU fuel bundle depletion was executed under the assumption of constant power level. The relation between power and total flux is described by an equation in which nuclear densities and recoverable energies of the nuclides appear. Total flux is used in
the Bateman equation to calculate changes in the inventory. Reaction rates are calculated as a product of the total flux and the effective cross section. Therefore, the total flux is an important normalization function in fuel depletion. Comparison of the total flux in a fuel bundle is depicted in Fig. 32. The total flux predicted by the WIMS code is 15%e17% higher than that of the MCNP6 code. Differences between other codes are lower than WIMS and MCNP6 comparison. The ratio of the maximum to minimum differences between the codes for the total flux is between 4% and 7%. The explanation of higher WIMS differences was not found in the analysis of previous sections. The difference could be caused by a normalization issue, because the shape of the flux is the same as for the rest of the codes. Also, higher burnup leads to higher concentrations of fission products that absorb large amounts of neutrons, thereby causing the total flux to increase. 4.5. Calculation time The slightly decrease in the accuracy of using UWB1 comes
138
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139
Fig. 33. CANDU fuel depletion calculation time comparison. Fig. 31. Relative comparison of PWR and CANDU effective cross sections.
slower than the WIMS code. The results showed that between Monte Carlo codes, the UWB1 code is significantly faster. Deterministic codes WIMS and NEWT are executed in different time framework. The NEWT code is as fast as a typical Monte Carlo code with 2 million active neutrons per depletion step, but WIMS is significantly faster. The reason behind this difference is caused by the different implemented method used by the two codes. The NEWT code uses discrete ordinates method whereas the WIMS code uses the faster method of characteristics. The development of the SCALE package and its NEWT code is focused on implementing the method of characteristics so further decreases in calculation time can be expected in near future. 5. Conclusions
Fig. 32. Comparison of total neutron flux used in burnup solver during depletion.
inherently with the methodology and assumptions used in the code. This is expected as the code development focused significantly on the speed of calculation. The lower accuracy is outweighed by the speed-up factor between one and two orders of magnitude, as it can be seen from Fig. 33. All codes except MCNP6 were run in serial mode. The MCNP6 time was converted to serial execution. WIMS fuel depletion takes around 5 min and it is the fastest code. UWB1 fuel depletion takes around 1.5 h, assuming that 2 million neutrons are used in the Monte Carlo simulation. The SERPENT code was able to finish fuel depletion in around 17 h. The SCALE codes KENOeVI and NEWT were slower than SERPENT. The NEWT deterministic code needed around 29 h, while KENOeVI Monte Carlo code finished the calculation in 40 h. The slowest execution was observed for MCNP6 code as it took around 670 h (28 days) to finish fuel bundle depletion. The UWB1 code is around 10 times faster than most of other codes, more than 100 times faster than MCNP6, but almost 20 times
The UWB1 nuclear fuel depletion code was used to simulate CANDU fuel bundle depletion and the results were compared to WIMS, MCNP6, SERPENT, KENOeVI and NEWT codes. Results show that the UWB1 nuclear fuel depletion code is capable to calculate fuel depletion of CANDU fuel bundle with and without burnable absorbers. The behaviors of all investigated parameters were captured by the code. A slight decrease in the accuracy comes inherently with the methodology and assumptions used in the code. This is expected as the code development focused significantly on the speed of calculation. The lower accuracy is outweighed by the speed-up factor between one to two orders of magnitude, as it can be seen from Fig. 33. The development of UWB1 code is ongoing. Acknowledgments R&D has been funded by TE01020455 Centre for Advanced Nuclear Technologies (CANUT) project. References ACR-700 Technical Description. AECL, 10810-01371-TED-001 Revision 1, 2004. Chan, P.K., Paquette, S., Bonin, H.W., French, C., Pant, A., July 29eAugust 2, 2013. Neutron absorbers in CANDU natural uranium fuel bundles to improve operating margins. In: Proceedings of the 2013 21st International Conference on Nuclear Engineering (Chengdu, China). Dufek, J., Kotlyar, D., Shwageraus, E., Lepp€ anen, J., 2013. Numerical stability of the predictorecorrector method in Monte Carlo burnup calculations of critical reactors. Ann. Nucl. Energy 56, 34e38.
M. Lovecký et al. / Progress in Nuclear Energy 90 (2016) 127e139 Jonkmans, G., 2006. WIMS-AECL Version 3.1 User's Manual. ISTP-05e5115/WP51504, 153-119190-UM-001, FFC-RRP-667, Revision 1. Atomic Energy of Canada Limited. Kotlyar, D., Shwageraus, E., 2013. On the use of predictorecorrector method for coupled Monte Carlo burnup codes. Ann. Nucl. Energy 58, 228e237. €nen, J., 2007. Development of a New Monte Carlo Reactor Physics Code. D.Sc. Leppa Thesis. Thesis. Helsinki University of Technology. VTT Publications 640. €nen, J., March 6, 2013. Serpent e a Continuous-energy Monte Carlo Reactor Leppa Physics Burnup Calculation Code. VTT Technical Research Centre of Finland. Lovecký, M., Piterka, L., Prehradný, J., Skoda, R., 2014. UWB1 e fast nuclear fuel depletion code. Ann. Nucl. Energy 71, 333e339. Lovecký, M., Jiri ckov a, J., Skoda, R., 2015. Monte Carlo solver for UWB1 nuclear fuel depletion code. Ann. Nucl. Energy 85, 778e787.
139
Pelowitz, D.B., May 2013. MCNP6 User's Manual, Version 1. Los Alamos National Laboratory. Report LA-CP-13e00634, Revision 0. Prehradný, J., Lovecký, M., Skoda, R., July 7e11, 2014. Burnable absorber comparison between VVER, PWR and SFR with UWB1 and SERPENT codes. In: Proceedings of the 2014 22nd International Conference on Nuclear Engineering (Prague, Czech Republic). Scale: a Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, ORNL/TM-2005/39, Version 6.1, June 2011. Radiation Safety Information Computational Center at Oak Ridge National Laboratory as CCC-785. Available from: Talebi, F., Marleau, G., Koclas, J., 2006. A model for coolant void reactivity evaluation in assemblies of CANDU cells. Ann. Nucl. Energy 33, 975e983.