DETERMINATION OF THE EQUILIBRIUM COMPOSITION OF CORES WITH CONTINUOUS FUEL FEED AND REMOVAL USING MOCUP

Supercomputing in Nuclear Applications (M&C + SNA 2007) Monterey, California, April 15-19, 2007, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2007) DETERMINATION OF THE EQUILIBRIUM COMPOSITION OF CORES WITH CONTINUOUS FUEL FEED AND REMOVAL USING MOCUP Massimiliano Fratoni and Ehud Greenspan University of California at Berkeley Nuclear Engineering Department Berkeley CA 94720-1730 maxfratoni@nuc.berkeley.edu, gehud@nuc.berkeley.edu ABSTRACT Algorithms and scripts were developed for determining, using MOCUP, the equilibrium fuel composition in cores operating with continuous fuel feeding and removal. Two types of Generation-IV systems are considered: Molten Salt Reactors and Pebble Bed Reactors. The methodology developed for the Molten Salt Reactor required limited modifications to the MOCUP functions and was widely applied and tested. A novel methodology is proposed for the Pebble Bed Reactor to determine the pebble composition as a function of its residence time and the resulting core average composition. This methodology uses a detailed full core model to properly account for the fuel double heterogeneity. Key Words: MOCUP, MCNP, ORIGEN, depletion, molten salt, pebble 1 INTRODUCTION This paper describes algorithms and scripts developed for determining, using MOCUP [1], the equilibrium fuel composition in cores operating with continuous fuel feeding and removal. Two types of Generation-IV systems are considered: Molten Salt Reactors (MSR) and Pebble Bed Reactors (PBR). MOCUP couples MCNP [2] for cross sections calculations and ORIGEN2 [3] for depletion calculations. Here and in the rest of the paper, MCNP and ORIGEN2 imply, respectively, MCNP5 Version 1.40 and ORIGEN2.2. The use of MCNP allows to accurately model the systems under investigation and in particular allows to account for fuel double heterogeneity in the PBR. An introductory description of MOCUP features and adopted upgrades is given in the next section, before describing the new methodologies developed. For each of the two systems a brief features description is given and the applied scheme to search for the equilibrium composition is illustrated. Computational times are discussed as well. 2 MOCUP FEATURES MOCUP [1] is a known utility program for performing depletion analysis based on Monte Carlo particle transport. It consists of a sequence of processing functions that operate on and communicate with MCNP [2] and ORIGEN2 [3] input/output files. A special set of flux and

Massimiliano Fratoni and Ehud Greenspan reaction rates tallies are applied to MCNP input for those cells that must be treated as timedependent. The flux and reaction rates obtained from MCNP are read by one of the MOCUP functions (mcnppro) that also calculates the effective one-group cross sections for all the nuclides tallied in MCNP. The number of nuclides with time dependent concentration, for which cross sections are generated by MCNP, is limited. Preliminary calculations need to be done for chosing the most relevant nuclides to include in the MCNP analysis. The cross sections calculated are used by a second MOCUP function (origenpro) to complete the ORIGEN2 input provided by the user. One of the ORIGEN2 default cross sections libraries is selected to be used for all those nuclides for which cross sections are not generated by MCNP. At this point ORIGEN2 performs the depletion analysis according to the power or flux level and time step input by the user. For each nuclide ORIGEN2 solves the following balance equation: dn i dt = ( f j i tot j + j i j )N j ( tot i + i )N i + F i RN i (1) j Where N is the nuclide concentration in the core, f j i probability that a neutron reaction with nuclide j will yield nuclide i, tot effective one-group total cross section, average neutron flux in the core, j i branching ratio for decay of nuclide j into nuclide i, decay constant, F i feed rate of nuclide i per unit volume of salt in the reactor, and R removal rate. Equation 1 is solved by the exponential matrix technique [4]. The updated material composition after depletion is extracted from the ORIGEN2 output by the last MOCUP function (comppro) and transferred into a new MCNP input to start the second depletion step and the entire process is repeated. The current MOCUP version in use at the University of California at Berkeley features many improvements that have been implemented during the years, to enhance the code capabilities [5]. Some of the advanced features are described here. (a) The spectrum dependent branching ratio for 242g Am and 242m Am production from capture reactions on 241 Am can be accounted for; same treatment can also be applied to the branching ratio of other reactions. (b) MOCUP is capable of treating multi-zone depletion problems but the operating power of each zone must be known and specified in the input. A processing function has been developed that by applying additional special tallies in the MCNP input can calculate the zone-wise power distribution and automatically assign the correct power to each zone in the corresponding ORIGEN2 input. (c) The decay library, that includes data like decay constant, branching ratio, decay heat and maximum permissible concentration in air and in water, has been updated to include the data in use for the ORIGEN-S code of the SCALE 5.1 package [6]. The following paragraphs describe how the MOCUP processing functions are adapted to systems that feature on line fuel feeding and removal. The two models considered are the MSR in which the fuel is continuously fed and removed from the core mixed with the salt and the PBR in which the fuel elements (pebbles) are re-circulated in the core until they reach a target burnup level. In both cases the core average composition is assumed to reach an equilibrium state after an initial transient. The described methodologies focus on the seeking of the equilibrium composition regardless of the initial transient but, with proper modifications, they could also be applied for the transient period. Although at a first glance the two models considered look similar, there is a 2/12

Determination of the Equilbrium Composition of Cores with Continous Fuel Feed and Removal Using MOCUP fundamental difference between them: in the MSR the fuel is in the liquid form and is mixed in the salt so that the composition of the fuel is uniform throughout the core and the fuel composition in the removal stream is the same as that in the core. In the PBR the fuel is confined to the pebbles and each pebble is a finite entity. The core equilibrium composition is the average of the composition of all the pebbles in the core, while each pebble has a different composition. The problem is complicated by the fact that pebbles are not randomly removed from the core; they are tested at the exit from the core and only if above the target burnup level they are removed from the reactor. The core equilibrium composition can be determined only by knowing the composition of the pebbles at discharge. This requires to calculate the pebble composition as a function of depletion time. 3 EQUILIBRIUM COMPOSITION FOR MOLTEN SALT REACTORS The MSR has been selected as one of the candidates for the IV Generation of nuclear reactors. Its unique design features molten actinides dissolved in a liquid salt. Different design solutions have been proposed: critical or subcritical, fueled with enriched uranium or thorium or minor actinides, single or multi flow, once-through or with multi-recycling. The reference model considered for this study assumes a single flow and once-through model. The fuel feed composition is that of the trans-uranium isotopes (TRU) extracted from the spent fuel from Light Water Reactors (LWRs). The salt, carrying the fuel, flows in and out of the core. When inside the core, the mixture is critical and generates power that is transferred to a heat exchanger when the salt is outside the core. Actinides are continuously fed into the core and at the same time a fraction of the salt is removed so as to keep the total salt volume in the core constant. A small fraction of the salt is continuously circulated into a make-up stream where the salt is processed to remove fission products. After an initial transient the actinides and fission products concentration reach an equilibrium composition. When at this state the concentration of each nuclide i must satisfy: dn i = 0 (2) dt In principle, ORIGEN2 is capable of accounting for the continuous feeding and removal terms of Equation 1. But when it is interfaced with MCNP, the MOCUP functions are not compatible with the feed/removal subroutine of ORIGEN2. The search for the equilibrium composition is implemented in the MOCUP utility using a simple script that was created for use in between the origenpro function and ORIGEN2. This script modifies the ORIGEN2 input created by the origenpro function so as to add the required feed and removal input data. To fit MOCUP to the MSR model, one more adjustment is necessary: when the salt is circulating in the reactor only part of the time is in the core and exposed to a neutron flux; for the rest of the time it would be outside of the core, with zero neutron flux and the changes in the composition are due only to radioactive decay. For this reason Equation 1 is corrected as follows: dn i dt = ( f j i tot j + j i j )N j ( tot i + i )N i + F i RN i (3) j 3/12

Massimiliano Fratoni and Ehud Greenspan where is the ratio between the time the salt is exposed to the neutron flux and the total residence time of the salt in the reactor. Typical value of is 50%. In the ORIGEN2 input this correction is expressed assuming a core power equal to the actual power times, so that the resulting flux will be as in Equation 3. Once core power, feed composition, feed and removal rate are established, the search for the equilibrium composition proceeds using MOCUP with the modifications described above. Convergence to equilibrium is established when the multiplication factor and main nuclides concentration remain unchanged for at least two consecutive iterations. As the final solution is time independent, the ORIGEN2 solution is not sensitive to the depletion time step specified. Convergence to the equilibrium composition can be accelerated by minimizing the MCNP runs that are the most time consuming operations. After each MCNP step the ORIGEN2 depletion calculation is performed repeatedly, keeping cross sections constant but adjusting the flux amplitude until the fuel composition is unchanged. Only after convergence the process moves to the next MCNP calculation (Figure 1). Guessed Composition MNCP Are k eff and main nuclide concentration unchanged? Yes Equilibrium Composition New Core Composition No ORIGEN2.2 Updated Composition Yes Is ORIGEN2.2 composition unchanged? No Figure 1 MOCUP scheme applied to search for molten salt reactors equilibrium fuel composition Figure 2 shows the multiplication factor evolution with the number of MCNP iterations using different number of neutron histories per MCNP run. The comparison was done applying a constant number of total and active cycles and changing only the number of histories per cycle. The number of cycles to be skipped (i.e., the difference between the total and active number of cycles) was fixed to guarantee the convergence of the fission source distribution even for the less accurate calculations. Convergence to an almost constant k value is achieved in few iterations and the converged value is insensitive to the total number of histories per iteration. When at 4/12

Determination of the Equilbrium Composition of Cores with Continous Fuel Feed and Removal Using MOCUP equilibrium k oscillates around an average value; as expected, the oscillations width decreases when increasing the number of histories. It is estimated that at least 10 5 histories are required to reduce the uncertainty of the equilibrium state multiplication factor below 0.5% (Table 1). The number of iterations required to reach the equilibrium composition only depends on the accuracy of the MCNP results since feed/removal rate and power only influence the number of ORIGEN2 runs required within each iteration. Figure 2 Evolution of the multiplication factor with iterations for different total number of histories applied in MCNP Table 1 Average value and relative statistical error for multiplication factor, selected nuclides concentration and Pu cross sections after reaching equilibrium composition Histories 10 4 10 5 10 6 10 7 Multiplication factor 1.0571 1.0540 1.0548 1.0550 ±0.6454% ±0.1101% ±0.0388% ±0.0275% 235 U 4.727 10-8 4.708 10-8 4.707 10-8 4.708 10-8 ±1.7666% ±0.5428% ±0.1390% ±0.0584% Concentration 239 Pu 4.372 10-3 4.359 10-3 4.362 10-3 4.362 10-3 ± 0.4440% ±0.2012% ±0.0803% ±0.0272% Cm 1.965 10-3 1.952 10-3 1.950 10-3 1.951 10-3 ±0.7608% ±0.5915% ±0.2048% ±0.0764% 137 Cs 1.628 10-3 1.628 10-3 1.627 10-3 1.627 10-3 ±0.0338% ±0.0074% ±0.0032% ±0.0011% Fission 11.253 11.253 11.244 11.245 ±0.5760% ±0.1458% ±0.0683% ±0.0192% 7.994 8.015 8.018 8.015 Capture Pu ±0.7199% ±0.1565% ±0.0625% ±0.0222% Cross Section 4.682 10-2 4.498 10-2 4.426 10-2 4.451 10-2 n,2n ±7.3957% ±3.4814% ±0.7872% ±0.1528% n,3n 2.018 10-7 6.796 10-7 7.516 10-7 7.604 10-7 ±110% ±73% ±15% ±5.3% 5/12

Massimiliano Fratoni and Ehud Greenspan Figure 3 shows convergence of the concentration of selected isotopes. It is found that 5 to 6 iterations are sufficient to reach the equilibrium concentration of prominent isotopes such as 239 Pu and 244 Cm, as well as of isotopes with negligible concentration such as 235 U and as well as fission products like 137 Cs. The evolution, with iterations, of the effective one-group cross sections of 239 Pu is displayed in Figure 4. Convergence is usually achieved in few iterations, independent of the total number of histories used for the MCNP calculations, but once again, oscillations are large when using smaller number of histories. Uncertainty of the fission and capture cross sections at equilibrium is of the same order as that of the multiplication factor (Table 1). Cross sections for (n,2n) and (n,3n) reactions require larger number of histories to get comparable uncertainty. The large uncertainty in (n,3n) cross section is acceptable due to its negligible contribution to the neutron balance. 235 U 239 Pu 244 Cm 137 Cs Figure 3 Evolution of concentration of selected isotopes with iteration for different total number of histories applied in MCNP The equilibrium composition only depends on the feed composition, feed/removal rate and power level; it does not depend on the initial composition assumed. Table 2 shows the multiplication factor and concentration of selected nuclides at equilibrium when assuming three different initial fuel compositions: (a) 20% enriched uranium; (b) plutonium extracted from LWR spent fuel discharged at 50 GWd/tHM and cooled for 10 years; (c) all TRU from the LWR spent fuel discharged at 50 GWd/tHM burnup and cooled for 10 years. In all cases the initial fission products concentration is assumed to be zero. 6/12

Determination of the Equilbrium Composition of Cores with Continous Fuel Feed and Removal Using MOCUP Table 2 Selected characteristics of the equilibrium composition obtained starting with different initial fuel compositions: 20% enriched uranium, plutonium from LWR spent fuel and all TRU from LWR spent fuel Parameter at equilibrium U Pu TRU k 1.05538 ± 0.00170 1.05466 ± 0.00160 1.05486 ± 0.00166 239 Pu [atoms/b-cm] 4.352 10-5 4.361 10-5 4.374 10-5 240 Pu [atoms/b-cm] 6.297 10-5 6.309 10-5 6.291 10-5 241 Pu [atoms/b-cm] 3.084 10-5 3.085 10-5 3.099 10-5 241 Am [atoms/b-cm] 1.569 10-6 1.575 10-6 1.578 10-6 242m Am [atoms/b-cm] 9.375 10-8 9.396 10-8 9.445 10-8 244 Cm [atoms/b-cm] 1.950 10-5 1.963 10-5 1.941 10-5 246 Cm [atoms/b-cm] 9.138 10-6 9.068 10-6 9.155 10-6 Tot actinides [atoms/b-cm] 2.487 10-4 2.488 10-4 2.487 10-4 Tot fission products [atoms/b-cm] 1.065 10-4 1.065 10-4 1.065 10-4 Fission Capture (n,2n) (n,3n) Figure 4 Evolution of 239 Pu effective one-group cross sections with iteration for different total number of histories applied in MCNP 7/12

Massimiliano Fratoni and Ehud Greenspan The computational time required to reach equilibrium by the described methodology is relatively small, mainly because the MCNP model is simple. For a unit cell with reflective boundary conditions, a run with one million histories (5,000 histories per cycle, 200 cycles, 150 active cycles for tallies) requires about 5 minutes on 20 processors (3.31 GHz CPU, 1 GB RAM). For a full core analysis, the computational time depends on the number of depletion zones. For a single depletion zone model, it is typically around 30 minutes on the same cluster of processors. MOCUP functions and ORIGEN2 computational times are on the order of few seconds but multiple ORIGEN2 runs are required between consecutive MCNP runs to speed up the convergence toward the equilibrium composition. The total time from one MCNP run to the next is between 60 and 90 seconds. Considering that 5 iterations are enough to reach equilibrium the total computational time is about 30 minutes for a single cell model and about 2 and an half hours for the full core with single depletion zone. 4 CORE AVERAGE COMPOSITION AND DISCHARGE BURNUP FOR PEBBLE BED REACTORS In the PBR the fuel is in the form of TRISO particles that are embedded in a graphite matrix at the central part of the spherical pebbles. Gas or liquid salt flowing around the pebbles removes the fission heat generated. Pebbles are continuously inserted into the core from one end and extracted, at the same rate, on the other end. The burnup level reached by each pebble is tested every time the pebble is extracted from the core. If the burnup is below the target limit the pebble is fed back to another traverse through the core. Otherwise it is discarded and a pebble containing fresh fuel is fed instead [8,9]. Although the flow of pebbles in the PBR appears quite similar to the flow of molten salt in the MSR, the methodology described above for determining the equilibrium composition of MSR is not applicable to PBR. The continuous recirculation of pebbles will bring the average core composition to an equilibrium state, but each of the pebbles will have a different fuel composition at any given time. The fuel composition in the pebbles discharged from the reactor is substantially different from the average equilibrium core composition. This is unlike the MSR where the composition of the discharged fuel is identical to the equilibrium composition. As a result, the discharge composition from the PBR is a design variable that needs to be determined. A priori, the pebble residence time in the PBR core and its discharge burnup are not known. Both must be determined for a given initial fuel composition so that the core will be just critical when at equilibrium composition. A methodology based on MOCUP was developed to search for the equilibrium composition of the PBR based on the following two main assumptions: (1) pebbles are circulated in the core many times so that the axial core composition can be approximated as uniform; (2) at each insertion pebbles are randomly distributed in the core so that the radial composition of the core can be approximated as uniform. As a results of these two assumptions the probability to find a pebble of a given burnup level in any region of the core is the same. The methodology reported here is applied for a single zone core but could be expanded to consider two or more radial core zones. The methodology scheme developed is outlined in Figure 5. 8/12

Determination of the Equilbrium Composition of Cores with Continous Fuel Feed and Removal Using MOCUP The PBR full scale core and reflectors are modeled using MCNP, representing all the TRISO fuel particles and all the pebbles so as to properly account for the double heterogeneity effects. The initial fuel composition is assumed the same all over the core. For the first iteration it is guessed. The first MCNP run provides the core average flux for a specified total core power. Then the MCNP model is modified as follows: all the pebbles are assigned a uniform composition but a small fraction of them typically less than 1%. Those are loaded with the fresh fuel composition. The fresh pebbles also are spatially distributed in the core to account for spatial neutron flux variation across the core. Effective one-group cross sections are generated only for the small fraction of fresh pebbles. The spectrum used for generating these cross sections is dictated by the uniform composition of the surrounding pebbles. Depletion is performed only for this small sample of fresh pebbles using MOCUP and assuming that the flux level, determined in the first MCNP simulation, is constant throughout the depletion. The total residence time of the fresh pebbles in the core is a guess. The time pebbles spend outside of the core during each loop is assumed negligible. At this point the fuel composition as a function of residence time is known for an average pebble. According to the assumption that pebbles are uniformly distributed in the core so that the probability to find a pebble of a given burnup level in any equal volume region of the core is the same, the core average composition is defined as the average composition over exposure time of an average pebble. This composition is fed back to the MCNP input to determine the flux and the process is repeated iteratively until the core multiplication factor, flux level and concentration for main fuel constituents is constant for at least two consecutive iterations. If k eff is not 1.0, a different pebble residence time is assumed and the search for the equilibrium composition is repeated until the desired value for the multiplication factor of the equilibrium core is obtained. Guessed Composition Guessed Residence Time MNCP Uniform Composition No Is the core composition unchanged? MOCUP Pebbles Sample Depletion Time Dependent Pebbles Composition New Core Average Composition New Residence Time Guess Yes Is k eff = 1? No Yes Equilibrium Composition Figure 5 Proposed scheme to apply MOCUP to search for the PBR average equilibrium fuel composition 9/12

Massimiliano Fratoni and Ehud Greenspan The computational time strongly depends on the number of MCNP runs required. Longer time steps reduce the computational time but also reduce the accuracy of the calculations. Long time steps result in oscillations in the pebbles power density during depletion although the flux level is assumed constant. Very short time steps would be required to cancel these oscillations. To enable using larger time steps so as to save on run time a predictor/corrector scheme was introduced into MOCUP. The sequence of this scheme is shown in Figure 6: (a) a first MCNP run is performed for the fuel composition at the beginning of the time step and for this effective one-group cross sections are generated; (b) ORIGEN2 performs depletion analysis and determines the fuel composition for a certain number of sub-steps in which the total time step is subdivided in the ORIGEN2 input; (c) the fuel compositions from each sub-step are used to determine the average fuel composition during the entire depletion step; (d) this average fuel composition is transferred to MCNP to calculate the corresponding cross sections; (e) these cross sections are used as input to a new ORIGEN2 run together with the initial fuel composition and depletion is performed to the determine the fuel composition at the end of the time step. Figure 7 shows that the power oscillation is eliminated when applying this predictor/corrector scheme. Figure 6 MOCUP predictor/corrector scheme developed Figure 7 Comparison of pebbles power density during depletion with and without applying the predictor/corrector scheme 10/12

Determination of the Equilbrium Composition of Cores with Continous Fuel Feed and Removal Using MOCUP Like in the MSR methodology, convergence to the equilibrium composition for a given residence time is typically achieved in few iterations, independent of the initial composition guess. Computational times become relevant due to the complexity of the MCNP model, required to properly account the effects of the fuel double heterogeneity. About 3 hours are required per run of a full PBR core model (100,000 histories per cycle, 100 cycles, 98 active cycles; the number of cycles discarded is low because an accurate fission source distribution, from a preliminary run, is used) on 20 processors (3.31 GHz CPU, 1 GB RAM). 5 CONCLUSIONS Two methodologies to determine, using MOCUP, the equilibrium composition of continuously fueled cores were successfully developed one for molten salt reactors and the other for pebble bed reactors. The methodology for MSR is relatively easy to be implemented. It has been widely tested and applied [7]. Convergence and results accuracy is satisfactory and computational times are relatively short. The methodology for PBR is more complex due to the confinement of the fuel in the pebbles that requires to determine not only the core average equilibrium composition but also the average single pebble composition as a function of depletion time. Computational times are still acceptable but considerably longer than for the MSR and this is due not to the differences in the methodology applied but to the complexity of the MCNP model required to properly account for the double heterogeneity of the pebbles. Further work is in progress for optimizing and benchmarking this methodology. ACKNOWLEDGMENT Support from Oak Ridge National Laboratory under contract 4000045298 and support from Department of Energy under NERI grant DE-FC07-05ID14669 is gratefully acknowledged. REFERENCES 1. Moore, R.L., Schnitzler, B.G., Wemple, C.A., Babcock, R.S. and Wessel, D.E., MOCUP: MCNP-ORIGEN2 Coupled Utility Program, INEL-95/0523, September 1995 2. X-5 Monte Carlo Team, MCNP A General Monte Carlo N-Particle Transport Code, Version 5, LANL 2003 3. Croff, A.G., A User Manual for the ORIGEN2 Computer Code, ORNL/TM-7175 4. Croff, A.G., ORIGEN2: A Versatile Computer Code for Calculating the Nuclide Compositions and Characteristics of Nuclear Materials, Nuclear Technology, Vol. 62, September 1983 5. Milosevic, M., Greenspan, E. and Vujic, J., New Monte Carlo Procedures and Cross Section Libraries for Fuel Burnup in Innovative Reactor Designs, Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications, Avignon, France, September 12-15, 2005 11/12

Massimiliano Fratoni and Ehud Greenspan 6. Gauld, I.C., Murphy, B.D. and Williams M. L., ORIGEN-S Data Libraries, ORNL/TM- 2005/39 Version 5 Vol. III, Sect. M6, April 2005 7. Fratoni, M. and Ehud, G., Transmutation Capability of Molten Salt Reactors Fed with TRU from LWR, AWRIF-2005, Oak-Ridge, TN, February 16-18, 2005 8. Forsberg, C.W., Pickard, P. and Peterson P.F., Molten-Salt-Cooled Advanced High- Temperature Reactor for Production of Hydrogen and Electricity, Nuclear Technology, Vol. 144, pp. 289-302, 2003 9. de Zwaan, S.J., The Liquid Salt Pebble Bed Reactor, PNR-131-2005-008, Delft University of Technology, The Netherlands, November 2005 12/12