Monte Carlo Burnup Research Articles

Numerical stability of the predictor–corrector method in Monte Carlo burnup calculations of critical reactors

Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor–corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems.

Development of burnup methods and capabilities in Monte Carlo code RMC

The Monte Carlo burnup calculation has always been a challenging problem because of its large time consumption when applied to full-scale assembly or core calculations, and thus its application in routine analysis is limited. Most existing MC burnup codes are usually external wrappers between a MC code, e.g. MCNP, and a depletion code, e.g. ORIGEN. The code RMC is a newly developed MC code with an embedded depletion module aimed at performing burnup calculations of large-scale problems with high efficiency. Several measures have been taken to strengthen the burnup capabilities of RMC. Firstly, an accurate and efficient depletion module called DEPTH has been developed and built in, which employs the rational approximation and polynomial approximation methods. Secondly, the Energy-Bin method and the Cell-Mapping method are implemented to speed up the transport calculations with large numbers of nuclides and tally cells. Thirdly, the batch tally method and the parallelized depletion module have been utilized to better handle cases with massive amounts of burnup regions in parallel calculations. Burnup cases including a PWR pin and a 5×5 assembly group are calculated, thereby demonstrating the burnup capabilities of the RMC code. In addition, the computational time and memory requirements of RMC are compared with other MC burnup codes.

Startup of “CANDLE” burnup in a Gas-cooled Fast Reactor using Monte Carlo method

During the past decade, the CANDLE burnup strategy has been proposed as an innovative fuel cycle and reactor design for complete utilization of uranium resources. In this strategy the shapes of neutron flux, nuclide densities and power density distribution remain constant but the burning region moves in axial direction. The feasibility of this strategy has been demonstrated widely by using the diffusion technique in conjunction with nuclide transmutation equations. On the other hand since the Monte Carlo method provides the exact solution to the neutron transport, the Monte Carlo technique is becoming more widely used in routine burnup calculations. The main objective of this work is startup of CANDLE burnup in a Gas cooled Fast Reactor using a Monte Carlo burnup scheme. In this case only natural or depleted uranium is required for fresh fuel region. However, the construction of the first CANDLE core is faced with a big problem. In equilibrium state the burning region contains a spectrum of fission products as well as higher actinides. These isotopes are not easily available for constructing the initial CANDLE core. The solution is startup of a special reactor using the enriched uranium in starter zone. At the end of core life the fuel for the next core is produced with the composition close to the equilibrium state. An originally MCNP–ORIGEN linkage program named MOBC has been used for criticality and isotopic evaluation of the core. The results of analysis showed that the use of burnable absorber rods for positive reactivity swing offset is necessary. In this regard the multiplication factor changes are limited in acceptable margin where the maximum reactivity swing is 655pcm during a transient and 180pcm during equilibrium state. On the other hand, although the power shape changes drastically in the earlier stage of core operation, it remains constant during the equilibrium state. In summary, by using the enriched uranium as a starter fuel the achievement of an equilibrium state is possible.

Analysis of measured isotopic compositions of high-burnup PWR MOX and UO2 fuels in the MALIBU program

The measured isotopic compositions of fuel samples taken from high-burnup spent PWR MOX and UO2 assemblies in the MALIBU program has been analyzed by lattice physics codes. The measured isotopes were U, Np, Pu, Am, and Cm isotopes and about 30 major fission product nuclides. The codes used in the present study were a continuous-energy Monte Carlo burnup calculation code (MVP-BURN) and a deterministic burnup calculation code (SRAC) based on the collision probability method. A two-dimensional multi-assembly geometrical model (2 × 2 model) was mainly adopted in the analysis in order to include the fuel assemblies adjoining the relevant fuel assembly, from which the samples were taken. For the MOX sample, the 2 × 2 model significantly reduces the deviations of the calculated results from the measurements compared with a single assembly model. The calculation results of MVP-BURN in the 2 × 2 model reproduce the measurements of U, Np, and Pu isotopes within 5% for the MOX sample of 67 GWd/t. The deviations of their calculated results of U, Np, and Pu isotopes from the measurements are less than 7% for the UO2 sample of 72 GWd/t.

Accuracy assessment of a new Monte Carlo based burnup computer code

This study aims to test for the suitability and accuracy of a new home-made Monte Carlo burnup code, called BUCAL1, by investigating and predicting the neutronic behavior of a “VVER-1000 LEU Assembly Computational Benchmark”, at lattice level. BUCAL1 uses MCNP tally information directly in the computation; this approach allows performing straightforward and accurate calculation without having to use the calculated group fluxes to perform transmutation analysis in a separate code. ENDF/B-VII evaluated nuclear data library was used in these calculations. Processing of the data library is performed using recent updates of NJOY99 system. Code to code comparisons with the reported Nuclear OECD/NEA results are presented and analyzed.

Uncertainty Propagation Analysis for PWR Burnup Pin-Cell Benchmark by Monte Carlo Code McCARD

In the Monte Carlo (MC) burnup analyses, the uncertainty of a tally estimate at a burnup step may be induced from four sources: the statistical uncertainty caused by a finite number of simulations, the nuclear covariance data, uncertainties of number densities, and cross-correlations between the nuclear data and the number densities. In this paper, the uncertainties ofkinf, reaction rates, and number densities for a PWR pin-cell benchmark problem are quantified by an uncertainty propagation formulation in the MC burnup calculations. The required sensitivities of tallied parameters to the microscopic cross-sections and the number densities are estimated by the MC differential operator sampling method accompanied by the fission source perturbation. The uncertainty propagation analyses are conducted with two nuclear covariance data—ENDF/B-VII.1 and SCALE6.1/COVA libraries—and the numerical results are compared with each other.

Systematic Uncertainty Due to Statistics in Monte Carlo Burnup Codes: Application to a Simple Benchmark with TRIPOLI-4-D

Systematic Uncertainty Due to Statistics in Monte Carlo Burnup Codes: Application to a Simple Benchmark with TRIPOLI-4-D

Neutronics and material attractiveness for PWR thorium systems using monte carlo techniques

Thorium (Th) oxide fuel offers a significant advantage over traditional low-enriched uranium and mixed uranium/plutonium oxide (MOX) fuel irradiated in a Light Water Reactor. The benefits of using thorium include the following: 1) unlike depleted uranium, thorium does not produce plutonium, 2) thorium is a more stable fuel material chemically than LEU and may withstand higher burnups, 3) the materials attractiveness of plutonium in Th/Pu fuel at high burnups is lower than in MOX at currently achievable burnups, and 4) thorium is three to four times more abundant than uranium. This paper quantifies the irradiation of thorium fuel in existing Light Water Reactors in terms of: 1) the percentage of plutonium destroyed, 2) reactivity safety parameters, and 3) material attractiveness of the final uranium and plutonium products. The Monte Carlo codes MCNP/X and the linkage code Monteburns were used for the calculations in this document, which is one of the first applications of full core Monte Carlo burnup calculations. Results of reactivity safety parameters are compared to deterministic solutions that are more traditionally used for full core computations. Thorium is fertile and leads to production of the fissile isotope 233U, but it must be mixed with enriched uranium or reactor-/weapons-grade plutonium initially to provide power until enough 233U builds in. One proposed fuel type, a thorium-plutonium mixture, is advantageous because it would destroy a significant fraction of existing plutonium while avoiding the creation of new plutonium. 233U has a lower delayed neutron fraction than 235U and acts kinetically similar to 239Pu built in from 238U. However, as with MOX fuel, some design changes may be required for our current LWR fleet to burn more than one-third a core of Th/Pu fuel and satisfy reactivity safety limits. The calculations performed in this research show that thorium/plutonium fuel can destroy up to 70% of the original plutonium per pass at 47 GWd/MTU, whereas only about 30% can be destroyed using MOX. Additionally, the materials attractiveness of the final plutonium product of irradiated plutonium/thorium fuel is significantly reduced if high burnups (∼94 GWD/MTU) of the fuel can be attained.

Analysis of Measured Isotopic Compositions of High-Burnup BWR MOX Fuel

Analysis of measured isotopic compositions of four high-burnup BWR MOX fuel samples was performed by using a general-purpose neutronic calculation code SRAC and a continuous-energy Monte Carlo burnup code MVP-BURN. The initial Pu fissile content of the samples was 5.52 wt%, and the burnups ranged from 50 to 80 GWd/t. It is confirmed that a geometrical model including the effect of UO2 assemblies adjacent to the MOX assembly is necessary in the burnup calculations to obtain accurate calculated isotopic compositions. The calculated results of MVP-BURN with JENDL-3.3 taking such effect into account show more accurate results for major actinides (U, Pu, and Am isotopes) and most fission products than those of infinite assembly calculations. The paper also shows the results calculated using SRAC with JENDL-3.3, ENDF/B-VII, and JEFF-3.1.

Biases and Statistical Errors in Monte Carlo Burnup Calculations: An Unbiased Stochastic Scheme to Solve Boltzmann/Bateman Coupled Equations

External linking scripts between Monte Carlo transport codes and burnup codes, and complete integration of burnup capability into Monte Carlo transport codes, have been or are currently being developed. Monte Carlo–linked burnup methodologies may serve as an excellent benchmark for new deterministic burnup codes used for advanced systems; however, there are some instances where deterministic methodologies break down (i.e., heavily angularly biased systems containing exotic materials without proper group structure) and Monte Carlo burnup may serve as an actual design tool. Therefore, researchers are also developing these capabilities in order to examine complex, three-dimensional exotic material systems that do not contain benchmark data.Providing a reference scheme implies being able to associate statistical errors to any neutronic value of interest like keff, reaction rates, fluxes, etc. Usually in Monte Carlo, standard deviations are associated with a particular value by performing different independent and identical simulations (also referred to as “cycles,” “batches,” or “replicas”), but this is only valid if the calculation itself is not biased. And, as will be shown in this paper, there is a bias in the methodology that consists of coupling transport and depletion codes because Bateman equations are not linear functions of the fluxes or of the reaction rates (those quantities being always measured with an uncertainty). Therefore, we have to quantify and correct this bias. This will be achieved by deriving an unbiased minimum variance estimator of a matrix exponential function of a normal mean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. Numerical tests will be performed with an ad hoc Monte Carlo code on a very simple depletion case and will be compared to the theoretical results obtained with the reference scheme. Finally, the statistical error propagation during the time-dependent depletion process will be discussed. It will be proven that the nonlinearity of Bateman equations induces a bias in the coupling. The paper provides a formula to correct it, which is verified in a simple example.

Analysis of Measured Isotopic Compositions of High-Burnup BWR MOX Fuel

Analysis of measured isotopic compositions of four high-burnup BWR MOX fuel samples was performed by using a general-purpose neutronic calculation code SRAC and a continuous-energy Monte Carlo burnup code MVP-BURN. The initial Pu fissile content of the samples was 5.52 wt%, and the burnups ranged from 50 to 80 GWd/t. It is confirmed that a geometrical model including the effect of UO2 assemblies adjacent to the MOX assembly is necessary in the burnup calculations to obtain accurate calculated isotopic compositions. The calculated results of MVP-BURN with JENDL-3.3 taking such effect into account show more accurate results for major actinides (U, Pu, and Am isotopes) and most fission products than those of infinite assembly calculations. The paper also shows the results calculated using SRAC with JENDL-3.3, ENDF/B-VII, and JEFF-3.1.

MCNPX Monte Carlo burnup simulations of the isotope correlation experiments in the NPP Obrigheim

This paper describes the simulation work of the Isotope Correlation Experiment (ICE) using the MCNPX Monte Carlo computer code package. The Monte Carlo simulation results are compared with the ICE-Experimental measurements for burnup up to 30 GWD/t. The comparison shows the good capabilities of the MCNPX computer code package for predicting the depletion of the uranium fuel and the buildup of the plutonium isotopes in a PWR thermal reactor. The Monte Carlo simulation results show also good agreements with the experimental data for calculating several long-lived and stable fission products. However, for the americium and curium actinides, it is difficult to judge the predication capabilities for these actinides due to the large uncertainties in the ICE-Experimental data. In the MCNPX numerical simulations, a pin cell model is utilized to simulate the fuel lattice of the nuclear power reactor. Temperature dependent libraries based on JEFF3.1 nuclear data files are utilized for the calculations. In addition, temperature dependent libraries based ENDF/B-VII nuclear data files are utilized and the obtained results are very close to the JEFF3.1 results, except for ∼10% differences in the prediction of the minor actinide isotopes buildup.

Lattice Physics Analysis of Measured Rod-by-Rod FP Inventory Distributions of Burnt BWR 9 × 9 UO2 Assemblies

Fuel rod gamma-ray spectrometry was performed for five-cycle irradiated BWR 9 × 9-9 and 9 × 9-7 fuel assemblies, and relative rod-by-rod FP inventory distributions of 137Cs, 134Cs, 106Ru, 95Zr and 154Eu were obtained for lower and upper axial nodes of the assemblies. The inventories of these nuclides represent burnups, burnups multiplied by a thermal neutron flux, a buildup of Pu, and a fission rate at the end of a fuel discharge cycle. The measured distributions were compared with those calculated by a general purpose neutronics code system SRAC and a continuous energy Monte Carlo burnup calculation code MVP-BURN with infinite assembly models. The calculations adopted nuclear data libraries JENDL-3.2, −3.3, and ENDF/B-VI.8. The calculated results generally well reproduce the measured distributions, and the root mean square errors (RMSs) of the calculated results against the measurements are 1 to 2% for the inventory distributions of 137Cs, 2 to 4% for 134Cs, 2 to 5% for 106Ru, 3 to 4% for 95Zr, and 4 to 5% for 154Eu, which include measurement and analysis errors. Small differences in the calculated distributions between SRAC and MVP-BURN were observed for 134Cs, 106Ru, and 154Eu for some of the corner rods, Gd2O3-UO2 rods, and other rods in the 9 × 9-7 fuel assembly.

Numerical Stability of Existing Monte Carlo Burnup Codes in Cycle Calculations of Critical Reactors

We show that major existing Monte Carlo burnup codes are numerically unstable in cycle calculations of critical reactors; spatial oscillations of the neutron flux can be observed even when relatively small time steps are used. This is caused by using the explicit Euler or midpoint method that appear to be numerically unstable with the step sizes common in cycle calculations. More stable methods that are common in deterministic burnup calculations, like the modified Euler method, can easily be introduced into the Monte Carlo burnup codes.

Validation of a new continuous Monte Carlo burnup code using a Mox fuel assembly

The reactivity of nuclear fuel decreases with irradiation (or burnup) due to the transformation of heavy nuclides and the formation of fission products. Burnup credit studies aim at accounting for fuel irradiation in criticality studies of the nuclear fuel cycle (transport, storage, etc…). The principal objective of this study is to evaluate the potential capabilities of a newly developed burnup code called “BUCAL1”. BUCAL1 differs in comparison with other burnup codes as it does not use the calculated neutron flux as input to other computer codes to generate the nuclide inventory for the next time step. Instead, BUCAL1 directly uses the neutron reaction tally information generated by MCNP for each nuclide of interest to determine the new nuclides inventory. This allows the full capabilities of MCNP to be incorporated into the calculation and a more accurate and robust analysis to be performed. Validation of BUCAL1 was processed by code-to-code comparisons using predictions of several codes from the NEA/OCED. Infinite multiplication factors ( k ∞) and important fission product and actinide concentrations were compared for a MOX core benchmark exercise. Results of calculations are analysed and discussed.

Lattice Physics Analysis of Measured Rod-by-Rod FP Inventory Distributions of Burnt BWR 9×9 UO2 Assemblies

Fuel rod gamma-ray spectrometry was performed for five-cycle irradiated BWR 9 × 9-9 and 9 × 9-7 fuel assemblies, and relative rod-by-rod FP inventory distributions of 137Cs, 134Cs, 106Ru, 95Zr and 154Eu were obtained for lower and upper axial nodes of the assemblies. The inventories of these nuclides represent burnups, burnups multiplied by a thermal neutron flux, a buildup of Pu, and a fission rate at the end of a fuel discharge cycle. The measured distributions were compared with those calculated by a general purpose neutronics code system SRAC and a continuous energy Monte Carlo burnup calculation code MVP-BURN with infinite assembly models. The calculations adopted nuclear data libraries JENDL-3.2, −3.3, and ENDF/B-VI.8. The calculated results generally well reproduce the measured distributions, and the root mean square errors (RMSs) of the calculated results against the measurements are 1 to 2% for the inventory distributions of 137Cs, 2 to 4% for 134Cs, 2 to 5% for 106Ru, 3 to 4% for 95Zr, and 4 to ...

Nuclear Analysis of PIE Data of Irradiated BWR 8×8-2 and 8×8-4 UO2 Fuel Assemblies

The measured pellet average inventories of actinides and fission product nuclides on the fifteen samples taken from a three-cycle irradiation BWR 8×8-2 UO2 assembly were compared with those of assembly burnup calculations using a collision probability method (SRAC) with the JENDL-3.2 nuclear data library. The present calculations overestimate the inventories of 235U, well reproduce those of 239Pu and 240Pu, yet underestimate those of 236U, 237Nd, 238Pu, 241Pu, and 242Pu. The inventories of minor actinides are underestimated by the present analysis except for 241Am. The major FP nuclides contributing to neutron absorption such as Nd, Cs, Eu, and Sm are almost well reproduced by the present calculations. The measured pellet average burnups and major actinide inventories on the twenty samples taken from four BWR 8×8-4 UO2 assemblies were also compared with those of the burnup calculations using SRAC and a continuous energy Monte Carlo burnup analysis code (MVP-BURN). Most of the calculated pellet average burnups of both codes agree with the measurements within the range of ±10%. The general trends of the measured pellet radial distributions of actinide and FP nuclides on six samples of the 8×8-4 UO2 assemblies were well reproduced by the burnup calculations of MVP-BURN.

Lattice Physics Analysis of Burnups and Isotope Inventories of U, Pu, and Nd of Irradiated BWR 9×9-9 UO2 Fuel Assemblies

As part of a validation study of burnup calculations of BWR cores, lattice physics analyses were performed on the measured burnups and the isotopic inventories of U, Pu, and Nd isotopes of eight samples taken from 9×9-9 BWR fuel assemblies of three and five cycles of irradiations. Burnup calculations in assembly geometry were carried out with a neutronics code system, SRAC, and a Monte Carlo burnup calculation method, MVP-BURN, based on a nuclear data library, JENDL-3.3. The measured burnups were determined based on the Nd-148 method, where the fission yield of 148Nd, energy release per fission, and correction factors for neutron captures by 147Nd and 148Nd were analytically obtained by averaging with burnups. The C/Es of the sample burnups are 0.96 to 1.07 for both analysis methods. By modifying the power histories to adjust the calculated burnups to the measurements of the samples, burnup calculations were performed again and the isotope inventories were compared with the measurements. The C/Es of the inventories are 1.00 to 1.09 for 235U, 0.91 to 1.04 for 239Pu, 0.96 to 1.07 for 240Pu, and 0.90 to 1.02 for 241Pu for the six samples excluding those of a corner fuel rod.

Efficient Generation of One-Group Cross Sections for Coupled Monte Carlo Depletion Calculations

Coupled Monte Carlo depletion systems provide a versatile and an accurate tool for analyzing advanced thermal and fast reactor designs for a variety of fuel compositions and geometries. The main drawback of Monte Carlo-based systems is a long calculation time imposing significant restrictions on the complexity and amount of design-oriented calculations. This paper presents an alternative approach to interfacing the Monte Carlo and depletion modules aimed at addressing this problem. The main idea is to calculate the one-group cross sections for all relevant isotopes required by the depletion module in a separate module external to Monte Carlo calculations. Thus, the Monte Carlo module will produce the criticality and neutron spectrum only, without tallying of the individual isotope reaction rates. The one-group cross section for all isotopes will be generated in a separate module by collapsing a universal multigroup (MG) cross-section library using the Monte Carlo calculated flux. Here, the term “universal” means that a single MG cross-section set will be applicable for all reactor systems and is independent of reactor characteristics such as a neutron spectrum; fuel composition; and fuel cell, assembly, and core geometries. This approach was originally proposed by Haeck et al. and implemented in the ALEPH code.Implementation of the proposed approach to Monte Carlo burnup interfacing was carried out through the BGCORE system. One-group cross sections generated by the BGCORE system were compared with those tallied directly by the MCNP code. Analysis of this comparison was carried out and led to the conclusion that in order to achieve the accuracy required for a reliable core and fuel cycle analysis, accounting for the background cross section (σ0) in the unresolved resonance energy region is essential.An extension of the one-group cross-section generation model was implemented and tested by tabulating and interpolating by a simplified σ0 model. A significant improvement of the one-group cross-section accuracy was demonstrated.

Effect of Pu-Rich Agglomerate in MOX Fuel on a Lattice Calculation

The effect of Pu-rich agglomerates in U-Pu mixed oxide (MOX) fuel on a lattice calculation has been demonstrated. The Pu-rich agglomerate parameters are defined based on the measurement data of MIMAS-MOX and the focus is on the highly enriched MOX fuel in accordance with increased burnup resulting in a higher volume fraction of the Pu-rich agglomerates. The lattice calculations with a heterogeneous fuel model and a homogeneous fuel model are performed simulating the PWR 17 × 17 fuel assembly. The heterogeneous model individually treats the Pu-rich agglomerate and U-Pu matrix, whereas the homogeneous model homogenizes the compositions within the fuel pellet. A continuous-energy Monte Carlo burnup code, MVP-BURN, is used for burnup calculations up to 70 GWd/t. A statistical geometry model is applied in modeling a large number of Pu-rich agglomerates assuming that they are distributed randomly within the MOX fuel pellet. The calculated nuclear characteristics include k-inf, Pu isotopic compositions, power density and burnup of the Pu-rich agglomerates, as well as the pellet-averaged Pu compositions as a function of burnup. It is shown that the effect of Pu-rich agglomerates on the lattice calculation is negligibly small.