MONTE CARLO CALCULATION OF RADIAL BURNUP DISTRIBUTION OF VVER-1000 FUEL PELLET WITH TEMPERATURE EFFECT Fatemeh Roosta, Ahmad Pirouzmand ∗ Department of Nuclear Engineering, School of Mechanical Engineering, Shiraz University, Shiraz, Iran. Abstract Safe and economic nuclear power generation requires a fundamental knowledge of fuel behavior in different situations. Due to the importance of a fuel rod behavior in high burnup from safety and economic viewpoints, in this paper, radial burnup, fission products, and actinide atom density distributions and their variation by increasing burnup, and other factors such as temperature, enrichment and power density are studied in a fuel pellet of VVER-1000 reactor in an operational cycle using MCNPX 2.7 code. A benchmark including a Uranium-Gadolinium (UGD) fuel assembly is used for verification of the results. For calculating radial temperature profiles and analyzing the effect of temperature on burnup and vice versa, HEATING 7.2, which is a general-purpose conduction heat transfer program, and MCNPX code are used together. The results show the accuracy and capability of our model in MCNPX and HEATING codes for radial burnup calculations. Considering the accuracy of MCNPX Monte Carlo code in complex geometry modeling and updated continuous energy neutron cross sections data libraries, the results of this study could be incorporated in a simple new radial burnup model for using in computer codes which calculate the thermo-mechanical response of light water reactors fuel rod during long-term burnup. Keywords: Radial burnup distribution, MCNPX code, VVER-1000 reactor, HEATING code.
1. Introduction In recent decades there has been an increasing interest in performing burnup-dependent core analysis including prediction of the nuclides concentration in a fuel rod [1]. The prediction of fuel rod behavior in a Light Water Reactor (LWR) at high burnup is difficult because the thermal and mechanical analyses depend strongly on composition of fuel pellet that varies with burnup [2]. At high burnup, material concentrations in fuel pellet vary with burnup especially by generation 239Pu in rim region. This process increases with burnup and must be taken into account in the thermal analyses. Recently, great effort has been done to generate complete and accurate model for predicting radial burnup and nuclides concentration distribution in a fuel pellet as a part of nuclear codes for the prediction of fuel rod behavior. The first developed program to model the buildup of 239Pu near the pellet edge for the analysis of fuel performance was RADAR [3]. RADAR considers only 239Pu, and other plutonium isotopes such as 240Pu, 241Pu and 242Pu, are not considered. After that TUBRNP model was developed. This model can be considered as an extension of the RADAR model. This new model predicts the radial power density distribution as a function of burnup (and hence the radial bumup profile as a function of time) together with the radial profiles of 235U, 238U, 239Pu, 240Pu, 241Pu, and 242Pu. The model was included in the TRSURANUS code [2]. Finally, RAPID model, which can calculate the radial variations of local power and burnup by following the changes of the fissionable nuclides with the burnup and radial position, was developed by Lee et al. This model is considered all fissionable nuclides [3]. All mentioned models are used as a part of fuel rods performance analysis codes. Due to the accuracy of Monte Carlo codes in neutronic calculations, in this paper we attempt to calculate the radial burnup and isotopes atom density distributions using MCNPX 2.7 code, by consideration the effect of radial temperature profile in the pellet. MCNPX is well suited to solve complicated three-dimensional and time-dependent problems [4] and uses point-wise and continuous energy neutron cross section libraries which increase the accuracy of results. Since most fuel properties and phenomena are temperature dependent, therefore an accurate description of the temperature distribution in a fuel rod is required before other effect can be quantitatively defined [5]. Thermal conductivity of fuel pellets is one of the most important thermal properties for calculating the fuel temperature during irradiation. The thermal conductivity of fuel pellets is expected to degrade with burnup due to the accumulation of fission products and irradiation-induced defects [6]. Thus to implement effect of these events in burnup calculations, and obtained accurate radial temperature profiles, HEATING 7.2 code, which is a code for calculating heat conduction is applied [7].
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NuRER – 4. International Conference on Nuclear and Renewable Energy Resources, Antalya, TURKEY, 26-29 Oct. 2014
2. MCNPX model descriptions To verify the results of this work, an LEU fuel assembly model in MCNPX code is used [8]. The LEU fuel assembly is hexagonal in shape and consists of total 331 cell locations. These locations are occupied by four main types of cells: 300 fuel pin cells with 3.7 wt% 235U, 12 Uranium-Gadolinium (UGD) pin cells with 3.6 wt% 235U and 4 wt% Gd 2 O 3 , one central water filled instrumentation tube and 18 water filled tubes for control insertion. Fuel rods are supposed in 1027 K and other elements of fuel assemblies are in 575 K. In this model moderator includes ordinary water with density of 0.7235 g/cc and soluble boron with concentration of 600 ppm in 575K. Other parameters are reported in the benchmark [8]. Fig. 1 (a) shows the schematic of this fuel assembly. For analyzing the other objects of this study such as the effects of enrichment, temperature, and power density on burnup distribution, a 36 fuel type assembly (Fig. 1(b)) of Bushehr nuclear power plant (BNPP), which is a VVER-1000 type reactor, is modeled in MCNPX code [9]. Parallel computing is used for speeding up Monte Carlo neutron transport and nuclide transmutation calculations. MCNPX allows running multiple processes for the same task using an MPI protocol.
3. Results 3.1. Verification For verification of MCNPX calculation, The LEU fuel assembly model that was descripted in the previous section is used. Herein, burnup and criticality calculations are performed for the fuel assembly with reflective boundary condition. Also, radial burnup and isotope distributions are calculated in cell 24 as shown in Fig. 1(a). To calculate the radial isotope distributions and consider the neutron flux radial variation, this fuel rod is subdivided into radial nodes with finer nodalization near the pellet edge to increase accuracy of calculations in the rim region. Small time steps in MCNPX burn card are needed to increase the accuracy of results. In this case, the assembly is depleted for 1014 days at a specified mean power density of 108 MW/m3 (40MWd/kgHM). The first time steps are chosen shorter to consider the effect of Gadolinium absorption, accurately. All neutron cross-sections are generated by makxsf utility in 1027K. The makxsf is a utility program for manipulating cross-section library files for the MCNP5 Monte Carlo code. Routines from the NJOY and DOPPLER codes were incorporated into makxsf to provide for Doppler broadening of resolved data to any higher temperature [10]. Fig.2 shows the k inf values versus burnup compared with the benchmark’s mean values. As shown for the LEU assembly as burnup increases the reactivity increases initially till Gd burn out and then monotonically decreases [8]. The maximum relative error is %2. Fig. 3 illustrates the variation of radial fissile atomic density distributions (239Pu and 235U) at the burnup of 40 MWd/kgHM in comparison with benchmark’s mean values. This figure also shows that the generated 239PU in the fuel pellet is distributed non-uniformly and accumulation of this isotope in the rim region of fuel pellet is almost two times of central region. The maximum relative errors occur in the fuel pellet periphery region which are less than 11% and 4% for 239Pu and 235U distributions, respectively. Due to the importance effect of burnup on fission gas release, 135Xe concentration in radial direction as a main gaseous fission product in fuel is shown in Fig. 4 (a) at 40MWd/kgHM. As expected, accumulation of this gas in peripheral region is much more than central region owing to more fission rate in the rim region. 239PU radial distribution in different burnup values also is shown in Fig. 4 (b). The radial variation of 239Pu is mainly due to higher fission rate at the peripheral region of fuel pin. Fig. 4 (b) also presents that neutron epithermal absorption is more effective in the higher burnup values. Fig. 5 shows calculated radial burnup distributions in different mean fuel assembly burnup values. The local burn up in the rim regions increases by a factor of 2-3 as burnup increases.
Central tube cell
Central tube cell
Guide tube cell
Guide tube cell
Fuel cell with 3.7 wt% 235U
Fuel cell with 3.7 wt% 235U
Fuel cell with 3.6 wt% 235 U & 4wt% Gd2O3
Fuel cell with 3.3 wt% 235U
Cell Number 24
(a)
(b)
Figure 1.Schematic of fuel assemblies (a) LEU fuel assembly [8], (b) BNPP fuel assembly [9].
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NuRER – 4. International Conference on Nuclear and Renewable Energy Resources, Antalya, TURKEY, 26-29 Oct. 2014
Figure 2. k inf values versus burnup for LEU fuel assembly
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(b)
Figure 3. Variation of radial fssile atomic density distributions at the burnup of 40 MWd/kgHM, (a)239Pu and (b) 235U
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Figure 4. (a)Radial 135Xe concentration at 40MWd/kgHM, (b) Radial 239Pu distribution in different burnup values.
3.2. Temperature effect For calculating radial temperature profiles and analyzing the effect of temperature on burnup and vice versa, HEATING and MCNPX codes are used together. To obtain an accurate temperature profile, first, burnup calculation is done for mean temperature fuel of 1027 K till 40 MWd/kgHM. Then the calculated radial power density profile in cell 24 is used as heat generation data in HEATING code. Pellet radial conduction coefficient is determined using Eq. (1) given in FRAPCON3 code user manual [11]. Fig. 6 presents computed radial power density and thermal conductivity profiles needed for temperature effect simulation. Higher burnup causes more porosity in fuel pellet due to uniformly distributed fission gas bubbles between subgrains. The accumulated gases decrease thermal conductivity with increasing burnup (Fig. 6 (b)).
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NuRER – 4. International Conference on Nuclear and Renewable Energy Resources, Antalya, TURKEY, 26-29 Oct. 2014
(a)
(b)
(c)
(d)
Figure 5. Radial burnup distributions at different burnup values in mean pellet temperature of 1027 K.
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(b)
Figure 6. (a) Radial power density distribution and (b) Radial thermal conductivity coefficient at different burnup values. This figure also shows the effect of the porosity on the thermal conductivity coefficient as well. To investigate the effect of temperature on burnup and vice versa, an iterative procedure is applied. Calculated radial temperature profile in HEATING is applied to generate new neutron cross- sections in pellet radial direction using makxsf which then is used in MCNPX material card for burnup calculation and generation of a new radial power profile. This profile is applied to produce new radial heat conduction coefficients in next step of burnup for using in HEATING code and finally generating a new radial temperature profile. This process is repeated till the last step of burnup calculation (40 MWd/kgHM). Fig. 7 shows calculated radial temperature profiles at different burnup values. Temperature profiles have variation with increasing burnup. These profiles indicate that in the high burnup values due to sudden growth in the gap conduction coefficient, which has the dominant effect, the fuel pellet temperature decrease with increasing the burnup. However, in the low burnup values (e.g. 5 and 10 MWd/kgHM), the reduction of fuel pellet conduction coefficient with increasing burnup has an effective role in the central regions and hence increases the pellet temperature profile magnitude.
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NuRER – 4. International Conference on Nuclear and Renewable Energy Resources, Antalya, TURKEY, 26-29 Oct. 2014
(1)
1 E exp(− F / T ) + A + a.gad + BT + f ( Bu ) + (1 − 0.9 exp(−0.04 Bu )) g ( Bu )h(T ) T 2
k=
where: k T Bu f(Bu) g(Bu)
= thermal conductivity, W/m-K = temperature, K = burnup, GWd/MTU = effect of fission products in crystal matrix (solution)= 0.00187Bu = effect of irradiation defects, = 0.038Bu0.28,
h(T)
= temperature dependence of annealing on irradiation defects=
Q A B E F a gad
= temperature dependence parameter (“Q/R”) = 6380 K = 0.0452 m-K/W = 2.46E-4 m-K/W/K = 3.5E9 W-K/m = 16361 = constant = 1.1599 = weight fraction of gadolinia.
1 1 + 396e −Q / T
3.3. Fuel enrichment effect The effect of fuel enrichment on radial burnup distribution is investigated by considering three fuel rods with various enrichment values (e.g. 1.6, 2.4 and 3.3 %wt) in the BNPP fuel assembly (Fig. 1 (b)).The calculation is performed in the same average power density and the results are presented in Fig. 8 (a). As shown, the radial burnup distribution rises due to increase in the fission rate.
(a)
(b)
Figure 7. Radial temperature profiles at different burnup values.
(a)
(b)
Figure 8. Radial burnup distribution in fuel rods with different (a) enrichment and (b) power density at 40Mwd/kgU.
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NuRER – 4. International Conference on Nuclear and Renewable Energy Resources, Antalya, TURKEY, 26-29 Oct. 2014
3.4. Power density effect To analyze the effect of pellet average power density on the radial burnup distribution, the burnup calculations in three fuel rods with the same enrichment values but different position in BNPP fuel assembly are done. Fig. 8 (b) shows radial burnup distribution variation with power density. This figure shows that increasing power density increase burnup as expected due to the more fission rate.
4. Conclusion In this study, a standard model was chosen to investigate the capability of MCNPX 2.7 code in the prediction of radial burnup, fission products, and actinide atom density distributions. The variation of these quantities by increasing burnup, and other factors such as temperature, enrichment and power density were studied in a fuel pellet of VVER-1000 reactor in an operational cycle as well. The results verified the accuracy and capability of our model in MCNPX and HEATING codes for radial burnup calculations. Bearing in mind the accuracy of MCNPX Monte Carlo code in complex geometry modeling and utilizing continuous energy neutron cross sections data libraries, the results of this study is under further examination to be incorporated in a simple new radial burnup model for using in computer codes which analyze the thermo-mechanical response of VVER-1000 reactor fuel rod during long-term burnup.
References [1] Siraj-ul-Islam, A. and Nasir, A., “Burnup-dependent core neutronics analysis and calculation of actinide and fission product inventories in discharged fuel of a material test research reactor”, Nuclear Energy, 599-616 (2006). [2] Lassmann, K., O’Carroll, C., van de Laar, J., and Walker, C.T., “The radial distribution of plutonium in high burnup UO2 fuels”, Journal of Nuclear Materials, 252, 71-78 (1994). [3] Lee, C.B., Kim, D. H., Song, J.S., Bang, J.G., and Jun, Y.H., “RAPID model to predict radial burnup distribution in LWR UO2 fuel”, Jornal of Nuclear Materials, 282, 196-204 (2000). [4] Plukiene, R., Plukis, A., Puzas, A. Remeikis,V., Duškesas, G. and Germanas, D., “Modelling of Impurity Activation in the RBMK Reactor Graphite Using MCNPX”, Nuclear Science and Technology, 2, 421-426 (2011). [5] Wiesenack, W., “Review of Halden reactor project high burnup fuel data that can be used in safety analyses”, Nuclear Engineering and Design, 83-92 (1997). [6] IAEA-TECDOC., “ Nuclear fuel behaviour modelling at high burnup and its experimental support”, International Atomic Energy Agency, Austria, (2000). [7] Childs, K.W., “HEATING 7.2 USER'S MANUAL”, U.S. Nuclear Regulatory Commission, Washington DC, (2000). [8] NEA, OECD., “ A VVER-1000 LEU and MOX Assembly Computational Benchmark”,Nuclear Science, (2002). [9] Atomic Energy Organization of Iran, “Final Safety Analysis Report (FSAR) for BNPP”, Moscow, (2007). [10] Brown, F.B., “The makxsf Code with Doppler Broadening”, Los Alamos national laboratory, (2000). [11] Lanning, D.D., Beyer, C.E., and Geelhood, K.J., “FRAPCON-3 Updates, Including Mixed-Oxide Fuel Properties”, U.S. Nuclear Regulatory Commission, Washington DC. (2010).
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