MCNP Based Calculation of Reactivity Loss due to Fuel Circulation in

121MCNP Based Calculation of Reactivity Loss due to Fuel Circulation inMolten Salt ReactorsJozsef KOPHAZI 1 , Mate SZIEBERTH 1*, , Sandor FEHER 1 , Szabolcs CZIFRUS 1 and Piet F. A. de LEEGE 21 Institute of Nuclear Techniques, Budapest University of Technology and Economics,1111 Budapest, Muegyetem rkp. 9., Hungary2 Interfaculty Reactor Institute, Delft University of Technology,2629 JB Delft, Mekelweg 15, The NetherlandsIn molten salt reactors, the delayed neutron precursors continuously change their positionin the reactor and primary loop due to the circulation of the fuel. Therefore, the influence ofthe delayed neutrons on the reactivity differs from that of solid fuel reactors. The paperdescribes a method, which is developed in order to modify the program MCNP so that it cantake into account the transport of the delayed neutron precursors, and therefore it is capable tocalculate the reactivity loss of reactors with circulating fuel. With the aid of the modifiedversion of MCNP, calculations were performed on a simple homogeneous reactor withcylindrical core. The method was also applied to perform calculations on the reactivity loss ofthe MSRE (Molten-Salt Reactor Experiment, Oak Ridge National Laboratories, 1960s). Theresults obtained are in good agreement with the theoretical predictions and the measuredreactivity loss values.KEYWORDS: molten salt, fluid fuel, fuel circulation, delayed neutrons, Monte Carlomethod, criticality calculation, reactivity loss1. IntroductionThe molten salt reactor (MSR) concept seems to beone of the most promising systems for the realization oftransmutation and one of the proposed Generation IVreactor types 1) . In molten salt reactors (or subcriticalsystems), the fuel circulates dissolved in some moltensalt. The main advantage of this reactor type is thepotential for continuous feed and on-line reprocessing.Due to the motion of the fuel, the precursor nucleichange their position between the fission and neutronemission events and decay may even occur outside thecore. Therefore, the reactivity and effective delayedneutron fraction of these reactors are lower than thoseof solid fuel systems. The extent of the reactivity loss isprimarily influenced by the velocity field of the fueland the length of fuel recirculation cycle.Since all of the presently operating power reactorsutilize solid fuel, until recently little attention had beenpaid to the calculation of the reactivity loss caused bythe circulation of the fuel. In the 1960s, measurementswere performed on the Molten-Salt ReactorExperiment (MSRE) at the Oak Ridge NationalLaboratory and a theory was developed to determinethe above mentioned reactivity loss 2) . When the interesttoward such type of reactors started to grow a few yearsago, research in this field gained a great impetus again.Efforts have been made to determine the reactivity lossby deterministic methods, such as the point kineticstheory and the one dimensional diffusion modelpresented in 3-5) . Though the deterministic theories arecapable of describing the phenomena in full detail, theyusually contain simplifications.The problem can be efficiently studied with the aidof the Monte Carlo method since the motion of delayedneutron precursor nuclei can easily be accounted for byshifting the place of birth of the delayed neutrons. Afurther advantage of the Monte Carlo method is thattasks involving complex geometries and a largenumber of different materials can also be computed inan uncompromising manner. This is why it isreasonable to develop a method which enables certaingeneral Monte Carlo neutron transport codes toperform criticality calculations on circulating fuelsystems without any approximation.This paper present such a method and itsimplementation to the MCNP4C 6) code. First, theapplicability of the method is illustrated on a simplehomogeneous reactor with cylindrical core. As asecond step, some capabilities of the method incomputing three-dimensional effects are presented inconnection with the modeling of the already mentionedMSRE. Finally, the results of an MSRE calculationalbenchmark are presented, pointing out the effects anddifferences caused by the use of different data libraries.2. Method of calculationThe method developed is based on the determinationof the shift of the precursors from the velocity of the* Corresponding author, Tel. +36-1-463-1633, Fax. +36-1-463-1954, E-mail: szieberth@reak.bme.hu

fuel and the sampled lifetime of the nuclide. Thedelayed neutron is born in this new position.The above method is realized in MCNP4C.Although this is a highly flexible code and can handlethe delayed neutrons in every detail, it cannot accountfor the motion of delayed neutron emitters. Therefore,modifications were introduced in to the code. With theaid of the modified version the multiplication factorcan be determined at different fuel velocities anddifferent circulation cycle lengths.The method can obviously be implemented for agiven geometry, thus newer and newer versions of theprogram should be created when calculating reactorswith different geometries. This is due to the fact thatthe motion of the neutron birth places should bedescribed according to the geometry in question.Concerning the simulation of the precursor nuclei,the simplest geometry is offered by a cylindricalhomogeneous core. The delayed neutron emitter isborn at the place of fission, where a correspondingdecay time is sampled. By use of the velocity the lengthof time is determined in which the emitter nucleuswould reach the upper plane of the cylindrical core. Ifthis time is longer than that sampled for the emitter todecay, the distance traveled until the decay iscalculated and the point of neutron creation is shiftedwith this distance parallel with the axis of the core. Ifthe sampled decay time is longer than that needed forthe emitter to reach the cover plane, the simulationtakes the emitter off the core and it enters the primary(external) loop. In the next step it is determinedwhether the emitter can re-enter the core before itdecays. If the sampled decay time is shorter than thetime the emitter needs to reach the lower plane and thento re-enter the core, the neutron that would begenerated by the delayed neutron emitter is not tracked.In the opposite case the emitter re-enters the core. Theentrance position along the base surface is sampleduniformly. From now on, the emitter moves upwardparallel with the axis of the core and the decay positioncan be modeled according to the algorithm describedabove. The above steps are repeated as long as thedecay position of the emitter is not determined.In the case of a more complex geometry the detailsof the algorithm are more complicated as well,however, the basic principle is the same as thatdescribed in the previous paragraph.Two subroutines of the MCNP source code weremodified: COLIDK (which generates the fissionneutrons for the next cycle of the simulation) andSOURCK (which starts the required number of fissionneutrons for the next cycle).In order to theoretically estimate what results can beexpected, a simple formula was derived in a onedimensional model. During the operation of the reactor,a precursor nucleus born at height z in the core starts tomove parallel to the axis of the core. The probabilitythat it exits from the core is:λ( z−H)vPz ( ) = e(1)where λ is the decay constant of the precursor, v is thefuel velocity in the core, and H is the height of thecore. Assuming that the spatial distribution of theprecursors is uniform along the z axis (i.e. there is nochange in the flux), we can easily obtain the followingformula by integrating (1) over the entire core:61 ∆ ρ = 1 −β∑i=1⎡ ⎛ −λ⎞⎤β ⎢1v Hi− ⎜ ⎟−vi1 e⎥, (2)⎢⎣λiH ⎝ ⎠⎥⎦where ∆ρ is the reactivity loss in $, β is the delayedneutron fraction, β i are the delayed neutron fractions,and λ i are the decay constants of the individual delayedneutron groups.3. CalculationsFirst, calculations were performed for a simplehomogeneous cylindrical reactor, in which 100%enriched 235 UF 3 is dissolved in 32 mol% BeF2 + 68mol% 7 LiF molten salt with a concentration of 4.8mol%. The diameter and height of the reactor are 80 cmand 100 cm, respectively. The change in reactivity wasinvestigated for cases of different velocities andrecirculation times. The velocity was in the intervalbetween 0 and 100 cm/s, while the recirculation timewas changed between 2 s and infinity (which was infact modeled as 100000 s). The results are shown inFigures 1 and 2.Reactivity Loss [$]1.000.900.800.700.600.500.400.300.200.100.000 20 40 60 80 100Fuel Velocity [cm/s]MCNPTheoreticalFig. 1 Reactivity loss vs. fuel velocity, in the case ofinfinitely long (100000 s) recirculation timeThe results obtained using the modified MCNP meetthe expectations based on theoretical considerations.As it can be seen in Figure 1, the trends of the results

are similar but the calculated reactivity loss is higher,especially at higher velocities. This fact agrees to theexpectations as the simple theory considers only theneutron loss due to ex-core emissions assuming a flataxial flux distribution while the reduction in thedelayed neutron worth due to the change of the positionis neglected. However, the results show that the lattereffect is not negligible.1.000.90within the space occupied by fuel. Accordingly, themost substantial difference compared to the algorithmfor the cylindrical homogeneous reactor is that fornuclei entering the central graphite lattice from thelower plenum one fuel channel should be selected. Thisis realized by taking the emitter nucleus to the closestfuel channel, sampling an x-y position from entirecross section of the given channel uniformly. The x-yposition of a nucleus exiting a channel is sampleduniformly over the whole area of the correspondingunit cell. The emitter moves vertically in the twoplenums and inside the fuel channel.0.800.70Reactivity Loss [$]0.600.500.400.30Tc=100000sTc=5sTc=2sTc=10s0.200.100.000 20 40 60 80 100Fuel Velocity [cm/s]Fig. 2 Reactivity loss calculated by modified MCNPfor the homogeneous cylindrical reactor with differentrecirculation timesIn order to demonstrate the capabilities of themethod in more complex geometry and to comparecalculational results to measured ones it was plausibleto set up a model and perform calculations for theMSRE.The MSRE was a graphite moderated reactor, at thebeginning fuelled with medium enriched 235 U, whichwas replaced with 233 U in the later experiments. Thescheme of the reactor is shown in Figure 3 7) . The fuelwas circulating in channels formed between graphiteblocks in the central part of the core, while the volumesclosing the reactor on the bottom and top sides arehomogeneous fuel spaces, called plenums.At the application of the above mentioned methodfor the MSRE there was a point of great importance:the simulation had to ensure that during the motion ofthe delayed neutron emitter nuclei they always stayFig. 3 Scheme of the MSRE reactorBased on the incomplete and rather poor dataavailable on the experiments performed in the 60s, amodel was worked out and implemented to the MCNP,describing the MSRE more or less adequately in termsof reactor physics. This model was not expected toreflect the measurement data at high accuracy.However, it was suitable to investigate certainthree-dimensional effects.Accordingly, with the aid of this model the influenceof replacing the cylindrical plenums below and abovethe reactor core with a more realistic elliptical andspherical structure, respectively, has been examined.The vertical section of the corresponding MCNP model

is shown on Figure 4.The reactivity losses obtained with the cylindricaland rounded models were 141 ± 13 and 191 ± 22 pcm,respectively. By comparing the difference to themeasured reactivity loss, which was 212 pcm, it can beconcluded, that the shape of the regions surroundingthe core at the bottom and top sides does have asignificant impact on the calculated reactivity loss.The other calculational experiment is related to thefuel flow velocity profile. In this case, the flow rate wasdoubled in some portion of the fuel channels situatedinside the graphite block (see Figure 5) such that thetotal flow rate remained constant. The result obtainedwas that in this case the reactivity loss increased fromthe earlier 141 ± 13 to 173 ± 13 pcm. From this itfollows that the flow profile also has substantialinfluence on the phenomenon to be calculated.plenum of 17.15 cm height filled only with fuel.Double velocity areaFig. 5 Horizontal section of the MSRE model used tostudy the effect of the velocity profileThe flow velocity of the fuel in the lattice structureis 19.67 cm/s, while that in the closing plenums is5.07 cm/s.Fig. 4 Vertical section of the MSRE model used tostudy the effect of rounded plenums (spherical top,elliptical bottom)In view of the incompleteness of the data availableon the MSRE project, the participants of the MOSTproject 8) defined a model for the MSRE in the frame ofa calculational benchmark. The third application of ourmethod was the calculation of this benchmark.Based on the data gathered within the MOST project,the model has been elaborated as follows. The reactoris approximated as a cylinder of 142.4 cm diameter and166.3 cm height, which is filled with the graphitelattice structure shown in Figure 6. The lattice pitch is4.213 cm. The side lengths of the rectangular crosssection of the fuel channels formed inside the graphiteare 3.03 cm x 1.15 cm. The cylindrical system filledwith the lattice is covered on top and bottom sides by aFig. 6 A horizontal section of the MSRE calculationalbenchmark modelThe composition of the fuel has also been set upaccording to the MOST project (see Table 1). Thepower of the reactor was assumed to be zero, so thetemperature of both the fuel and graphite moderator istaken to be 918 K, which was used in the experiment.It was decided to use two different delayed neutrondata sets. Besides the recent values of JEF-2.2 9) theoriginal ORNL data (see Table 3) were used, as well, in

the attempt to narrow down the discrepancy to theexperiment. As delayed neutron spectra were notavailable from the ORNL, therefore we used theprovided β eff values 2) and assumed prompt fissionspectrum for the delayed neutrons. This approximationactually corresponds to the definition of the β eff , andshould have the same effect as if we used the real βvalues together with the proper delayed neutronspectra.Table 1 Fuel composition of MSREIsotopeAtomic ratio [%]235U 233U7 Li 2.64E-01 2.64E-019 Be 1.18E-01 1.19E-01Zr 2.03E-02 2.03E-02F 5.94E-01 5.96E-01233 U 0 4.44E-04234 U 0 4.37E-05235 U 1.04E-03 9.27E-06238 U 2.21E-03 1.86E-05239 Pu 0 8.89E-06The MCNP model of the reactor was worked outaccording to the above considerations. A horizontaland vertical section of the model is seen in Figures 6and 7, respectively.acceptable in view of the standard deviation of thecalculations and measurements and the uncertainty ofthe fuel composition. The results obtained with ORNLdelayed neutron data show that method applied in thelack of delayed neutron spectra is feasible, however,the modern data sets can be considered as superior.Table 2 The calculated and measured reactivity loss ofthe MSRE with two types of fuelFuel k eff Measurementρ loss [pcm]CalculationORNL JEF-2.2Standarddeviation235 U 1,05980 212 224 244 13233 U 1,12714 100 ± 5% 131 85 134. ConclusionIn the work presented in this paper a Monte Carlomethod based calculational procedure has beendeveloped for the determination of the reactivity loss ofreactors with circulating fuel. The calculationaltechnique has been implemented by introducingmodifications to the MCNP4C code. The applicabilityof the technique was first demonstrated on a simplegeometry homogeneous reactor, for which the resultsobtained agreed well with the expectations formtheoretical considerations.Calculations were performed for the MSRE, as well,in order to investigate more complicated,three-dimensional effects and to be able to comparewith measured values. The results confirm that theapplication of the Monte Carlo method can be veryimportant if the aim is the simulation of a real geometrywith the best approximation possible. The need for abetter approximation was demonstrated by showingthat the reactivity loss was significantly affected bychange of the fuel velocity profile and the shape of thecore containment. The values obtained for the MSREbenchmark in the framework of the MOST projectshow that a reasonable estimation of the measuredvalues is achievable.ReferencesFig. 7 A vertical section of the MSRE calculationalbenchmark modelWe have applied the modified MCNP to calculatethe reactivity loss for both fuel compositions of thereactor. The results are summarized in Table 2.It is seen that for the 235 U fuelled reactor theagreement between the calculated (JEF-2.2) andmeasured reactivity loss values is very good. In thecase of 233 U, the calculational results can be considered1) D. J. Diamond, "Research Need for GenerationIV Nuclear Energy Systems", Proc. PHYSOR2002, Seoul, South Korea, 7-10-2002 (2002).2) "Zero-Power Physics Experiments on theMolten-salt Reactor Experiment" ORNL4233,Oak Ridge National Lab., USA, (1968)3) G. Lapenta, P. Ravetto, and G. Ritter, "EffectiveDelayed Neutron Fraction for Fluid-FuelSystems", Ann. Nucl. Energy, 27, 1523.4) G. Lapenta and P. Ravetto, "Basis ReactorPhysics Problems in Fluid-Fuel RecirculatedReactors", Kerntechnik.

5) G. Lapenta, F. Mattioda, and P. Ravetto, "PointKinetic Model for Fluid Fuel Systems", Ann.Nucl. Energy, 28, 1759.6) J. F. e. al. Briesmeister, "MCNP - A GeneralMonte Carlo N-Particle Transport Code,Version 4C", Los Alamos National Laboratory,Los Alamos, USA (2000).7) "Research, Test and Experimental Reactors",Directory of Nuclear Reactors, Vol. V, IAEA,Vienna, (1964).8) M. Delpech, S. Dulla, C. Garzenne, J. Kópházi,J. Krepel, C. Lebrun, D. Lecarpentier, F.Mattioda, P. Ravetto, A. Rinelski, M. Schikorr,and M. Szieberth, "Benchmark of DynamicSimulation Tools for Molten Salt Reactors",Proc. GLOBAL 2003, New Orleans, USA,16-11-2003 (2003).9) "The JEF-2.2 Nuclear Data Library", JEFFReport 17, NEA, Paris, France, (2000)Table 3 ORNL delayed neutron dataFuel Total Group 1 Group 2 Group 3 Group 4 Group 5 Group 6235 U β static [pcm] 640.5 21.1 140.2 125.4 252.8 74.0 27233 Uβ eff static [pcm] 666.1 22.3 145.7 130.7 262.8 76.6 28decay data [s -1 ] 0.0124 0.0305 0.111 0.301 1.14 3.01β static [pcm] 271.2 22.55 80.28 67.48 76.86 14.94 9.10β eff static [pcm] 289.38 23.76 85.76 71.9 82.14 15.79 10.03decay data [s -1 ] 0.0126 0.0337 0.139 0.325 1.13 2.5