MonteCarlo Calculations Of The Training Reactor Of Budabest University Of Technology and Economics using MCNP code

The training reactor of BME is a swimming pool type reactor located at the university campus.The reactor was designed and build between 1969 and 1971,by Hungarian nuclear and technical experts.It first went critical on May 20,1971.The maximum power was originally 10 kW.After upgrading ,which involved modifications of the control system and insertion of one more fuel assembly into the core , the power was increased to 100 kW in 1980.

VIETNAM NATIONAL UNIVERSITY, HANOI VNU UNIVERSITY OF SCIENCE FACULTY OF PHYSICS Nguyễn Hoàng Dũng Monte – Carlo calculations of the Training Reactor of Budapest University of Technology and Economics using MCNP code Submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Nuclear Technology (Advanced Program) Hanoi - 2017 VIETNAM NATIONAL UNIVERSITY, HANOI VNU UNIVERSITY OF SCIENCE FACULTY OF PHYSICS Nguyễn Hoàng Dũng Monte – Carlo calculations of the Training Reactor of Budapest University of Technology and Economics using MCNP code Submitted in partial fulfillment of the requirements for the degree of Bachelor of Science in Nuclear Technology (Advanced Program) Supervisor: Dr Nguyễn Tiến Cường Hanoi - 2017 Acknowledgement It has been a long course since the beginning of this thesis, which was months ago (Feb 2017) Without the help from my supervisor, my friends, my family, I could not have made such progress nor have the motivation to finish this thesis Therefore, I spend the very first page to send my deepest gratitude toward: First of all, my supervisor Dr Nguyen Tien Cuong, Faculty of Physics, VNU University of Science, who has given me the initial idea of what has to be done His invaluable comments throughout this thesis has enlightened, guided me to the very last word Secondly, all of my classmates, thank you for your continuously inspiring and support Finally, I would like to thank my family for their support and for believing in me Student, Nguyen Hoang Dung i Abstract The applicability of the Monte Carlo N-Particle code (MCNP) to evaluate reactor physics parameters, shielding applications on the Training Reactor of Budapest University of Technology and Economics (BME) Some of reactor physical calculations were carried out for simulating the reactor critical state: multiplication factor and its dependence on the water level, vertical and horizontal neutron flux distributions Criticality is the condition where the neutron chain reaction is self-sustaining and the neutron population is neither increasing nor decreasing This study also deals with the analysis of variance reduction methods, specifically, variance reduction methods applied in MCNP on the determination of dose rates for neutrons and photons Calculations for the outer wall contains two different types of concrete compositions were performed to investigate the impact of the bioshield filling materials on the dose rate estimation ii Table of Contents Acknowledgement i Abstract ii Table of Contents iii List of Figures .v List of Tables vi List of Abbreviations vi Introduction vii Chapter The Training Reactor of Budapest University of Technology and Economics 1.1 General overview 1.2 Reactor core geometry and configuration Chapter Neutron flux and flux density in the reactor core .7 2.1 Diffusion equation in a Finite multiplying system 2.2 One - group reaction equation 2.3 The BME - Reactor (Parallelepiped Reactor) 10 Chapter Reactor parameter determinations using MonteCarlo Method 12 3.1 Introduction 12 3.2 Monte-Carlo and Particle Transport 13 3.3 MCNP Code 14 3.4 MCNP model of the BME - Reactor 15 3.5 Neutron flux calculations 16 3.6 Dose rate determinations 17 3.6.1 “Weight” of a particle 17 3.6.2 Geometry Splitting with Russian Roulette 18 iii Chapter Results and Discussions 20 4.1 Reactor-physical calculations 20 4.1.1 The dependence of 𝑘𝑒𝑓𝑓 on water levels 20 4.1.2 Neutron Flux distribution in reactor core 21 4.2 Dose rate calculations in concrete structures 24 4.3 Conclusions 28 References 29 iv List of Figures Figure 1: Side and upper view of the BME - Reactor Figure 2: Schematic drawing (not to scale) of the EK-10 fuel assembly (dimensions are given in mm unit) and its various types used in the BME - Reactor Figure 3: Configuration of the BME - Reactor core Figure 4: Cross sectional diagram of a) Automatic and b) Manual control rod Figure 5: 3d view model of the BME - Reactor Figure 6: Lifecycle of a Neutron in Monte-Carlo simulation 13 Figure 7: Cross-section top view of MCNP model of BME - Reactor core 15 Figure 8: MCNP geometric model of the BME - Reactor: a) Side view, b) Cross-section top view (dimensions are given in cm unit) 16 Figure 9: The Splitting Process 18 Figure 10: The Russian Roulette Process 19 Figure 11: The dependence of 𝑘𝑒𝑓𝑓 on water level 20 Figure 12: Vertical flux distribution in fuel rod 21 Figure 13: Vertical flux distribution in fuel cladding 21 Figure 14: Thermal vertical flux distribution in Dy-Al wire, experimental and simulated result 22 Figure 15: Horizontal flux distribution in fuel rod 23 Figure 16: Horizontal flux distribution in fuel cladding 23 Figure 17: Schematic of split model for calculating dose rate: a) Side view, b) Crosssection top view 24 Figure 18: Neutron dose rate as a function of distance from the core vessel at different water level (60 to 80 cm) 25 Figure 19: Photon dose rate as a function of distance from the core vessel at different water level (60 to 80 cm) 26 v List of Tables Table 1: The detailed components and information about materials [2] Table 2: Relative errors (Err.) in the split sub-layers of concretes of the MCNP dose rate calculations for neutrons and photons 27 List of Abbreviations MCNP Monte Carlo N-Particle BME Budapest University of Technology and Economics vi Introduction The Monte Carlo N-Particle (MCNP) code, version 5.19 (MCNP5) and a set of neutron cross-section data were used to develop an accurate three-dimensional computational model of the Training Reactor of BME with the geometry of the reactor core was modelled as closely as possible The following reactor core physics parameters were calculated for the low enriched uranium core: multiplication factor, horizontal and vertical neutron flux distributions Shielding analysis also forms a crucial part of reactor design The precise calculation of dose rates of neutrons and photons is highly desired to perform neutron activation analysis, production of radioisotopes, determination of safety in standard operation circumstance or even in accident situations, criticality calculation or evaluation of many other processes Especially, during the planning and the operation of the reactor, it is a crucial task to make a safety analysis The public, operating personnel and reactor components must be protected against sources of radiation Thermal and biological shields positioned in front of intense radiation sources are highly absorbent materials to photons and neutrons Thermal shields prevent the embitterment of the reactor components, whereas biological shields protect people from neutrons and gammas Typical shielding calculations performed in the industry are the transport of neutrons and gammas through large regions of shielding material The behavior of radiation particles is a stochastic process based on a series of probabilistic events These probabilistic events are characterized by random variables such as location, energy, the particle direction of flight, mean free path of the medium and type of interaction The transport phenomena can be solved with the Monte-Carlo method because radiation particles have a stochastic behavior However, the disadvantage associated with this method is that they require long calculation times to obtain well converged results, especially when dealing with complex systems vii Chapter The Training Reactor of Budapest University of Technology and Economics 1.1 General overview The Training Reactor of BME is a swimming pool type reactor located at the university campus The reactor was designed and built between 1969 and 1971, by Hungarian nuclear and technical experts It first went critical on May 20, 1971 The maximum power was originally 10 kW After upgrading, which involved modifications of the control system and insertion of one more fuel assembly into the core, the power was increased to 100 kW in 1980 [1] The main purpose of the reactor is to support education in nuclear engineering and physics; however, extensive research work is carried out as well Neutron irradiation can be performed using 20 vertical irradiation channels, horizontal beam tubes, two pneumatic rabbit systems and a large irradiation tunnel The reactor core is made of 24 EK-10 type fuel assemblies, which altogether contain 369 fuel rods The fuel is 10%-enriched uranium dioxide in magnesium matrix The pellets are filled into aluminum cladding at a length of 50 cm The total mass of uranium in the core is approximately 29.5 kg The reactivity is controlled by four control rods, two of them are safety rods with one automatic and one manual rod To minimize neutron leakage and thereby conserve neutron economy, the horizontal reflector is made of graphite and water, while in vertical direction water plays the role of reflector The highest thermal neutron flux is 2×1012 𝑛/𝑐𝑚2 /𝑠, measured in one of the vertical channels [1] Seven measuring chains are applied for reactivity control and power regulation The detectors are ex-core ionization chambers, two of which operate in pulse mode in the startup range, four operate in current mode and one is a wide range detector In all power ranges, doubling time and level signals can invoke automatic scram operations The reactor is operated when required for a student laboratory exercise or a research experiment Accordingly, operation at 100 kW power for many hours is quite rare; on the average, it occurs once a week As a fortunate consequence, burn-up is very low: only 0.56% of the 235U has been used up and 3.4 g 239Pu and 12.3 g fission products have accumulated Therefore, there has been no need to replace any of the fuel assemblies since 1971 [1] Besides the tally information, the output file contains tables of standard summary information to summerize how the problem ran This information can give insight into the physics of the problem and the adequacy of the Monte Carlo simulation If errors occur during the running of a problem, detailed diagnostic prints for debugging are given Printed with each tally is also its statistical relative error corresponding to one standard deviation Following the tally is a detailed analysis to aid in determining confidence in the results 3.4 MCNP model of the BME - Reactor Based on the real structure of the BME - Reactor, a simplified MCNP geometry model was created in a three-dimensional, Cartesian coordinate system The center of the graphite reflector cell in position B7 was taken as the origin (0 0) in the x- and y plane and the core’s bottom in the z- plane In the criticality benchmark of the reactor, simplification of the geometry is done by neglecting some details of the surroundings of the core to an extent that does not affect the critical condition significantly Although the omitted structures not have a significant effect, they affect neutron flux distribution Therefore the benchmark model serves only as the basis speculation Figure 7: Cross-section top view of MCNP model of BME - Reactor core 15 Figure 8: MCNP geometric model of the BME - Reactor: a) Side view, b) Cross-section top view (dimensions are given in cm unit) 3.5 Neutron flux calculations In MCNP, the most common way to calculate neutron flux in a reactor core is through the use of KCODE option Flux and dose rate have been calculated using a cell flux tally (tally F4) along with DE, DF cards of MCNP Dose function DF and dose energy DE cards are used for energy to dose conversion using ANSI/ ANS - 6.1.1 - 1977 data Since MCNP results are normalized to one source particle, the result has to be properly scaled to compare with the measured quantities such as flux and dose rate The following formula has been used to scale the calculated results 𝑛𝑒𝑢𝑡𝑟𝑜𝑛 [ ] [ ] 𝑃 𝑊 𝜈̅ 𝑛𝑒𝑢𝑡𝑟𝑜𝑛 1 𝑓𝑖𝑠𝑠𝑖𝑜𝑛 ]= 𝜙[ × ×𝜙𝐹4 [ ] (15) 𝐽 𝑀𝑒𝑉 𝑐𝑚 𝑠 𝑘 𝑐𝑚 −13 𝑒𝑓𝑓 (1.6022×10 )𝐸 [ ] 𝑀𝑒𝑉 𝑅 𝑓𝑖𝑠𝑠𝑖𝑜𝑛 16 It is important to note that all the standard MCNP tallies can be made during a criticality calculation So, the MCNP model of the reactor was used to estimate these parameters: • Multiplication factor was calculated with different water levels • Vertical neutron flux distribution at E6 position; thermal neutron flux density in a Dy-Al wire which was inserted to the top left water pin of E6 was calculated simultaneously because in this position, measured data are also available Horizontal flux distribution was also calculated in the mid-plane of the core through the “E” column All processes is covered by the flux averaged over a cell (tally F4) with segmentation cards 3.6 Dose rate determinations The application of the analog model to shielding problems can be very inefficient In cases of dose rate calculations of neutron and photon at the top and outer of a nuclear reactor, the obtained results had low precision (high variance) This is because most of the calculation time is spent on particle histories that not contribute significantly to the result The numbers of escaped particles from core to outer shielding concrete are not large enough to satisfy statistical tests In this case Monte Carlo fails because only a few particles are detected, leading to unacceptable uncertainties in the results There are variance reduction techniques that can be used to improve the efficiency of the Monte Carlo calculations such as implicit capture, geometry splitting and Russian roulette, weight windows, weight cut - off, etc Among them, geometry splitting and Russian roulette with suitable particle importance are simple but effective techniques 3.6.1 “Weight” of a particle At the fundamental level, “weight” is a tally multiplier represented by a particle emitted from a source That is, the tally contribution for a weight 𝑤 is the unit weight multiplied by 𝑤 The 𝑤 physical particles all would have different random walks, but the one MCNP particle representing these 𝑤 physical particles will only have one random walk Clearly this is not an exact simulation; however, the true number of physical particles is preserved in MCNP in the sense of statistical averages and therefore in the limit of a large number of MCNP source particles Each MCNP particle result is multiplied by the weight so that the full results of the 𝑤 physical particles represented by each MCNP particle are exhibited in the final results (tallies) [5] 17 This procedure opens a way to normalize the calculations to whatever desired source strength in a particular region The default normalization is to weight one per MCNP particle A second normalization to the number of Monte Carlo histories is made in the results so that the expected means will be independent of the number of source particles actually initiated in the MCNP calculation, which may become handy in the determination of dose rate 3.6.2 Geometry Splitting with Russian Roulette In order to apply this technique, a distribution of importances must be provided for the cells/regions involved in the geometry modelled for an MCNP calculation When particles move to a more important region, the number of particles is increased to provide better sampling and the weight of the particle is split If the particles move to a less important region, they are killed in an unbiased way to prevent wasting time on them Splitting increases the calculation time and decreases the history variance, whereas Russian roulette does the complete opposite The assigned cell importance can have any value, they are not limited to integers However, adjacent cells with greatly different importances place a greater burden on reliable sampling Once a sample track population has deteriorated and lost some of its information, large splitting ratios (like 20 to 1) can build the population back up, but nothing can regain the lost information It is generally better to keep the ratio of adjacent importances small (for a factor of a few) and have cells with optical thicknesses in the penetration direction less than about two mean free paths [6] Figure illustrates how geometry splitting is applied when a particle is transported from one cell with a lower importance to another cell with higher importance Figure 9: The Splitting Process [6] 18 It can be seen from Figure that the total weight of the particles is preserved in the splitting process Figure 10 presents a particle with weight 𝑤 that moves from a region with higher importance (𝑖𝑚𝑝𝑅 ) to a region with lower importance (𝑖𝑚𝑝𝐿 ) and shows the Russian roulette process Figure 10: The Russian Roulette Process [6] When the Russian roulette process is applied to a particle, the particle will survive with weight 𝑤′ = 𝑤 𝑖𝑚𝑝𝑅 𝑖𝑚𝑝𝐿 , with a probability 𝑝 = 𝑖𝑚𝑝𝐿 𝑖𝑚𝑝𝑅 and the particle is killed with probability − 𝑝 This method is also an unbiased method since the expected outcome of the weight is equal to 𝑝𝑤′ = 𝑤 Therefore, the variance of any tally is reduced when the possible contributors all have the same weight [6] 19 Chapter Results and Discussions 4.1 Reactor-physical calculations 4.1.1 The dependence of 𝐤 𝒆𝒇𝒇 on water levels A previous study has shown the BME - Reactor would reach critical state when automatic and manual control rods were both in positions of 42cm [7], which is agreed with the simulated result of the total effective multiplication factor: k 𝑒𝑓𝑓 = 1.00276 ± 0.00029 This critical state is regarded as a standard state for other calculations in the thesis The dependence of k 𝑒𝑓𝑓 on water levels was calculated The results are shown in Figure 11 The reactor reached criticality (by applying critical rod positions) when the water level was above 60 cm (from the bottom of fuel rod) Besides, if the water level is higher than 80 cm, the values of k 𝑒𝑓𝑓 will saturate These results are in good agreement with the expectations Because, after a distance of some diffusion length, the presence of water does not affect to the multiplication factor 1.2 keff 0.8 0.6 0.4 0.2 0 20 40 60 80 100 120 140 160 180 Water level Figure 11: The dependence of 𝑘𝑒𝑓𝑓 on water level The KCODE card was used in the calculations, 20000 particles was generated per iteration in the total of 1500 cycles The 10 statistical checks for each tally was satisfied with the relative error less than 1% 20 4.1.2 Neutron Flux distribution in reactor core The vertical neutron flux distribution was calculated at E6 position Calculated data are obtained in fuel material, in cladding and in a Dy-Al wire which was inserted to the top left water pin of E6 In case of the vertical flux, the fuel rod and the wire is divided equally in length to 29 and 80 segments (Figure 12, 13 and 14 respectively) Besides, the horizontal flux distribution is calculated in the mid-plane of the reactor core at the second fuel pin from the left through the “E” column (Figure 15 and 16) Thermal Fast Total Neutron flux (n/cm2/s) 7.00E+11 6.00E+11 5.00E+11 4.00E+11 3.00E+11 2.00E+11 1.00E+11 0.00E+00 -25 -15 -5 15 25 Distance from core center (cm) Figure 12: Vertical flux distribution in fuel rod Thermal Fast Total Neutron flux (n/cm2/s) 7.00E+11 6.00E+11 5.00E+11 4.00E+11 3.00E+11 2.00E+11 1.00E+11 0.00E+00 -30 -20 -10 10 20 Distance from core center(cm) Figure 13: Vertical flux distribution in fuel cladding 21 30 MCNP Experiment Neutron flux (normalize to 1) 1.20E+00 1.00E+00 8.00E-01 6.00E-01 4.00E-01 2.00E-01 0.00E+00 -40 -30 -20 -10 10 20 30 40 Distance from core center (cm) Figure 14: Thermal vertical flux distribution in Dy-Al wire, experimental and simulated result We can see that the vertical neutron flux distribution in the fuel pin and in the cladding (Figure 12 and 13) have the shape of a cosine, which is in a good agreement with the reactor physical expectations according to Eq (14) The peaks of the thermal neutron flux are called reflector peaks These peaks can be clearly seen in the bottom and the top of the reactor (Figure 14) The reflector peaks appear in both ends of the Dy-Al wire due to the thermalization and reflection of the escaping fast neutrons from the core By reducing neutron leakage, the reflector increases k 𝑒𝑓𝑓 and reduces the amount of fuel necessary to make the reactor critical It can be seen that these peaks are not the same which can be explained by the presence of the fast pneumatic system (two air holes located in the top half of the core) in the vicinity of the Dy-Al core The KCODE card was used in both of the vertical and horizontal calculations, 20000 particles was generated per iteration in the total of 1500 cycles The 10 statistical checks for each tally was satisfied with the relative error less than 1% 22 Thermal Fast Total Neutron flux (n/cm2/s) 7.00E+11 6.00E+11 5.00E+11 4.00E+11 3.00E+11 2.00E+11 1.00E+11 0.00E+00 -20 -15 -10 -5 10 15 20 Distance from core center (cm) Figure 15: Horizontal flux distribution in fuel rod Thermal Fast Total Neutron flux (n/cm2/s) 7.00E+11 6.00E+11 5.00E+11 4.00E+11 3.00E+11 2.00E+11 1.00E+11 0.00E+00 -20 -15 -10 -5 10 15 20 Distance from core center (cm) Figure 16: Horizontal flux distribution in fuel cladding The horizontal flux is determined in the middle segment of the fuel rods across the “E” column Because of arrangement of the fuel pins in the core, the distributions are skewed to the left due to the difference in materials of the two peripheral regions One is made of graphite which has much lower rate of neutron absorption compare to water Results in a flattening curve on the left side, which is the water region 23 4.2 Dose rate calculations in concrete structures In order to calculate the dose rates at the outer shielding concrete wall of the BME - Reactor, heavy concrete and normal concrete regions are split into sub-layers with a thickness of 10 cm and 14 cm, respectively as shown in the Figure 17 The dose rate is calculated at the outer surface of the concrete wall inside the annulus between 270 cm and 271 cm radius with a height of 70 cm - the “P tally” The amount of particles - the intensity distribution within the sub-layers is defined so that each of them has similar contribution to the particle flux at the tally “P” region Figure 17: Schematic of split model for calculating dose rate: a) Side view, b) Cross-section top view 24 When a parallel beam of particles goes through the material, the intensity decrease can be very roughly approximated by an exponential function Thus, particle importance is chosen as the exponential functions of the concrete sub-layers index, 𝐼 = 𝐼0 𝑒 𝜇𝑖 where 𝜇 is the coefficient of increment, 𝑖 is sub-layers index One can predict that the particle populations change slightly through both heavy and normal concrete sub-layers These sub-layers have therefore enough particles to satisfy MCNP statistical tests, which result in their low corresponding relative errors After several iterations with modification of the IMP function, which is adjusted the particle weight within each run, the variances eventually reached the satisfied value A previous study have shown that the dose rate does not increase when the water level raise above 80 cm from the core’s bottom [2], this happens can be explain by the saturation of the k 𝑒𝑓𝑓 value So, in this thesis, the dose rate of neutrons and photons as a function of distance from the inner protection concrete wall at the water levels from 60 cm to 80 cm and at the power of 100 kW were calculated 60 cm 65 cm 70 cm 75 cm 80 cm 1E-10 Dose rate (rem/h/n*cm2*s) 1E-11 1E-12 Normal concrete 1E-13 1E-14 1E-15 1E-16 1E-17 Heavy concrete 1E-18 1E-19 50 100 150 200 Radial distace (cm) Figure 18: Neutron dose rate as a function of distance from the core vessel at different water level (60 to 80 cm) 25 60 cm 65 cm 70 cm 75 cm 80 cm 1E-11 Dose rate (rem/h/n*cm2*s) 1E-12 1E-13 Normal concrete 1E-14 1E-15 1E-16 1E-17 1E-18 Heavy concrete 1E-19 1E-20 50 100 150 200 Radial distace (cm) Figure 19: Photon dose rate as a function of distance from the core vessel at different water level (60 to 80 cm) The obtained results in Figure 18 indicate that the transport of neutron does not change significantly when the particles go through the heavy and normal concrete On the other hand, two different slopes of the intensities of transported photons particles through two layers were clearly observed (Figure 19) This is due to the sensitive effect of photon to different heavy elements contained in the heavy and normal concrete walls Furthermore, as the water level dropped, the neutron dose rate at the inner region of the shield is also decrease This happened because of the absorption of neutron at different water level Contradict to the photon dose rate which seem to be unchanged due to the express of the y-axis is in the exponential order Thus, the decrease of the dose rate can hardly be seen As the photon beam penetrate the concrete block, the “Buildup” factor should be taken into account, which is a increase function of the particle travelling distance Results in different slopes of the dose rate at different water level 26 When the water level dropped by cm, the dose rates drastically increased And by the time it has the same height as the reactor core, the dose rates of neutron and photon were calculated to be 185 and 234 Sv/h, respectively This might induces severe problem of significant increase of dose rate For each iteration, 40000 particles was generated and the problems was run for 500 cycles The calculated data is not quite satisfied due to the sudden increase of error in the tally of the cell located in the outer region (Table 2) For this problem, using only the geometry splitting method did not satisfy the statistical checks, the variance is exceed 10% for five tally However, the “P tally” has a relatively small variance - only 5% for every results Table 2: Relative errors (Err.) in the split sub-layers of concretes of the MCNP dose rate calculations for neutrons and photons Index Neutron Photon 60cm 70 cm 75 cm 80 cm 60 cm 70 cm 75 cm 80 cm Index Neutron Photon 60cm 70 cm 75 cm 80 cm 60 cm 70 cm 75 cm 80 cm 0.0029 0.0076 0.0110 0.0143 0.0012 0.0013 0.0014 0.0014 0.0044 0.0112 0.0158 0.0196 0.0021 0.0028 0.0029 0.0031 0.0610 0.1999 0.0567 0.0544 0.0402 0.0810 0.1661 0.0515 0.0985 0.1126 0.4064 0.0557 0.0631 0.1348 0.1781 0.0418 Heavy concrete 0.0064 0.0108 0.0213 0.0156 0.0262 0.0482 0.0215 0.0271 0.0312 0.0259 0.0309 0.0418 0.0030 0.0053 0.0109 0.0045 0.0093 0.0234 0.0047 0.0094 0.0237 0.0048 0.0087 0.0218 Normal concrete 0.1169 0.1199 0.1806 0.1451 0.1791 0.2686 0.2729 0.1944 0.1738 0.0538 0.0553 0.0580 0.0750 0.1351 0.1797 0.1264 0.1408 0.1738 0.1413 0.1495 0.1722 0.0383 0.0368 0.0359 27 10 0.0338 0.0627 0.0359 0.0398 0.0157 0.0358 0.0323 0.0313 11 0.0242 0.1257 0.0441 0.0445 0.0251 0.0509 0.0671 0.0420 0.2937 0.1928 0.1534 0.0617 0.1999 0.1798 0.5709 0.0353 Tally P 0.0356 0.0646 0.0699 0.0795 0.0224 0.0810 0.0395 0.0273 4.3 Conclusions A Monte Carlo model has been established for the BME - Reactor The calculated results for the reactor parameters like neutron distribution, multiplication factor are reasonably accurate, without using variance reduction method The ability of the Monte Carlo method to solve particle transport problems by simulating the particle behavior makes it a very useful technique in nuclear reactor physics However, the statistical nature of Monte-Carlo implies that there will always be a variance associated with the obtained value One of the main targets of research in Monte-Carlo is to decrease this variance as much as possible In the case of calculating dose rate, there is a huge contribution of the water surrounding the reactor core to the tally result, which is not executed by only split the shielding region During this process, over-split could easily happen “Informations”, once lost, cannot be regained So the purpose of one method is to conserve those important informations This thesis is not dig deep into the method of variance decreasing, but the result is rather a premise for future work in the field 28 References [1] “Training Reactor of the Budapest University of Technology and Economics”, http://www.iki.kfki.hu/radsec/irradfac/pub/Training_Reactor.pdf [2] Tran Duy Tap, Nguyen Tien Cuong, Papp Ildikó, Gábor Náfrádi, “Dosimetry calculations based on MCNP code of the Training Reactor of Budapest University of Technology and Economics”, 2016 [3] John R Lamarsh, Anthony J Baratta, “Introduction to Nuclear Engineering”, Third Edition, 2001 [4] B Rouben, Course EP 4D03/6D03, “Flux Shape in Various Reactor Geometries in One Energy Group”, 2015 [5] X-5 Monte Carlo Team, "MCNP - Version 5, Vol I: Overview and Theory", LAUR-03-1987, 2003 [6] Marisa van der Walt De Kock, “Variance reduction techniques for MCNP applied to PBMR”, Master thesis, North-West University, 2009 [7] Tran Thuy Duong, Nguyễn Khánh Hưng, Nguyễn Bá Vũ Chính, Nguyễn Quốc Hùng, Gábor Náfrádi, “Reactor-physical calculations using an MCAM based MCNP model of the Training Reactor of Budapest University of Technology and Economics”,2016 29