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

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

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

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Acknowledgement

It has been a long course since the beginning of this thesis, which was 4 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

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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 bio-shield filling materials on the dose rate estimation

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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 1 The Training Reactor of Budapest University of Technology and Economics 1

1.1 General overview 1

1.2 Reactor core geometry and configuration 3

Chapter 2 Neutron flux and flux density in the reactor core 7

2.1 Diffusion equation in a Finite multiplying system 7

2.2 One - group reaction equation 8

2.3 The BME - Reactor (Parallelepiped Reactor) 10

Chapter 3 Reactor parameter determinations using Monte-Carlo 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

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Chapter 4 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

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List of Figures

Figure 1: Side and upper view of the BME - Reactor 2

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 3

Figure 3: Configuration of the BME - Reactor core 4

Figure 4: Cross sectional diagram of a) Automatic and b) Manual control rod 5

Figure 5: 3d view model of the BME - Reactor 5

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) Cross-section 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

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List of Tables

Table 1: The detailed components and information about materials [2] 6Table 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

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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

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Chapter 1 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, 5 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]

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The reactor is used, among others, in the following fields:

• Activation analysis for radiochemistry and archeological research

• Analysis of environmental samples

• Determination of uranium content of rock samples

• Biomedical applications

• Nuclear instrument development and testing

• Experiments in reactor physics and thermohydraulics development and testing of Neutron tomographic methods for safeguards purposes

• Development of noise diagnostic methods, isotope production and investigation of radiation damage to instrument/equipment

Figure 1: Side and upper view of the BME - Reactor [1]

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1.2 Reactor core geometry and configuration

The BME - Reactor core geometry can be described as having a two-level

hierarchy of lattices; the first level of the hierarchy corresponds to fuel assemblies,

formed as a lattice of cylindrical fuel pins - these pins has an external diameter of 1 cm

and a total length of 60 cm, contain fuel meat of which diameter and height are

respectively 0.7 cm and 50 cm, absorbing material for controlling the nuclear chain

reaction and one layer of aluminum cladding While in the second level, nine type of

EK-10 fuel assemblies (Figure 2) are arranged in a lattice to form the reactor core, six of

them are cut corner due to the insertion of four control rods and two particularly types

have a cavity for the irradiation channel

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 [1]

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As mentioned above, the layout strategy used in the placement of fuel pin and in the placement of fuel assemblies of the BME - Reactor is a hexahedrical lattice of fuel, graphite reflecting block and several irradiation channels; which form a rectangular prism with the dimensions of 58 by 65 by 60 centimeters The surrounding materials like water is either coolant or a neutron energy moderator and the aluminum grid simply is function as a supporting structure (Figure 3) With this lattice layout, there are four formed square located in the center of a group of 2 by 2 fuel assemblies that are designed for one manual, one automatic, and two safety control rods For specific, the manual control rod has its inner part made from boron carbide (1.8 cm of diameter) while the outer part is iron with 0.1 cm of thickness The automatic one includes an hollow iron tube (1.8 cm of inner diameter, 2.0 cm of outer diameter) covered by cadmium with 0.001cm of thickness (Figure 4) The full length of these control rods is 64 cm and the length of cover materials is 60 cm [2]

Figure 3: Configuration of the BME - Reactor core

a - Automatic control rod

c - Fast pneumatic rabbit system

d - Thermal pneumatic rabbit system

e - Vertical irradiation channels in water

f - Fuel assemblies

g - Graphite reflectors

h - Vertical irradiation channels in graphite

i - Vertical irradiation channels in fuel assembly

j - Neutron-source

k - Manual control rod

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Figure 4: Cross sectional diagram of a) Automatic and b) Manual control rod

Figure 5: 3d view model of the BME - Reactor

The active core is enclosed by water in a cylindrical aluminum (2 cm) - air (3 cm) - iron (1 cm) tank Shielding concretes are arranged at the outer of the reactor core for radiation protection, which is the combination of heavy and normal concrete in case of the Training Reactor The accommodation of two concrete block outside the core

is shown in Figure 5

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Chapter 2 Neutron flux and flux density in the reactor core

To design a nuclear reactor properly, it is necessary to predict how the neutrons will be distributed throughout the system Unfortunately, determining the neutron distribution is a difficult problem in general The neutrons in a reactor move about in

of these collisions is that the neutrons undergo a kind of diffusion in the reactor medium, much like the diffusion of one gas in another The approximate value of the neutron distribution can then be found by solving the diffusion equation This procedure, which

is sometimes called the diffusion approximation, was used for the design of most of the early reactors

2.1 Diffusion equation in a Finite multiplying system

Consider an arbitrary volume V within a medium containing neutrons As time goes on, the number of neutrons in V may change if there is a net flow of neutrons out

of or into V if some of the neutrons are absorbed within V or if sources are present that emit neutrons within V The equation of continuity is the mathematical statement of the

obvious fact [3] In particular, it follows:

[Rate of change in number of neutrons]

= [rate of production of neutrons] − [rate of absorption of neutrons]

− [rate of leakage of neutrons]

This equation can be written explicitly as:

𝜕𝑛

Which: 𝑛: the density of neutrons at any point and time in V

𝑠: the rate at which neutrons are emitted from sources per cm3 in V

Σ𝑎𝜙: the rate at which neutrons are lost by absorption per cm3/sec

𝑱: the neutron current density vector on the surface of V

Consider flux is generally a function of three spatial variable, apply Fick’s law:

𝑱 = −𝐷 𝑔𝑟𝑎𝑑 𝜙 = −𝐷𝛻𝜙, into Eq.(1) and assume the diffusion coefficient 𝐷 is not a function of the spatial variables gives:

𝐷𝛻2𝜙 − Σ𝑎𝜙 + 𝑠 = 𝜕𝑛

This is the diffusion equation [3]

2.2 One - group reaction equation

Consider a critical reactor, of which neutrons is supposed to be monoenergetic, containing a homogeneous mixture of fuel and coolant It is assumed that the reactor consists of only one region and has neither a blanket nor a reflector Such a system is

said to be a bare reactor [3]

This reactor is described in a one - group calculation by the one - group time dependent diffusion equation - Eq.(3)

In a reactor at a measurable power, the source neutrons are emitted in fission To determine 𝑠, let Σ𝑓 be the fission cross-section for the fuel If there are ν neutrons produced per fission, then the source is: 𝑠 = νΣ𝑓𝜙

If the fission source does not balance the leakage and absorption terms, then the right-hand side of Eq.(3) is non-zero To balance the equation, we multiply the source term by a constant 1/𝑘 where 𝑘 is an unknown constant If the source is too small, then

𝑘 is less than 1 If it is too large, then 𝑘 is greater than 1 Eq.(3) may now be written as:

Or:

−𝐷𝐵2𝜙 − Σ𝑎𝜙 +1

This important result is known as the one - group reactor equation The one -

group equation may be solved for the constant 𝑘:

𝑘 = νΣ𝑓𝜙

𝐵2𝜙 + Σ𝑎𝜙 =

νΣ𝑓

𝐵2+ Σ𝑎

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Also, the source term in the one - group equation can be written in terms of the fuel absorption cross-section - Σ𝑎𝐹 Let 𝜂 be the average number of fission neutrons emitted per neutron absorbed in the fuel The source term is given by:

The source term in Eq.(7) can be written in terms of the multiplication factor for

an infinite reactor Consider an infinite reactor having the same composition as the bare reactor under discussion With such a reactor, there can be no escape of neutrons as there

is from the surface of a bare reactor and the neutron flux must be a constant, independent

of position Thus, the absorption of Σ𝑎𝜙 neutrons in one generation leads to the absorption of 𝜂𝑓Σ𝑎𝜙 in the next Because the multiplication factor is defined as the number of fissions in one generation divided by the number in the preceding generation

So in an infinite reactor, it follows that:

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2.3 The BME - Reactor (Parallelepiped Reactor)

For a parallelepiped, the eigenvalue equation - Eq.(5): 𝛻2𝜙 = −𝐵2𝜙 becomes:

1𝑓(𝑥)

𝐵𝑥2+ 𝐵𝑦2+ 𝐵𝑧2 = 𝐵2

To solve Eq.(11), we evaluate the first part of it:

1𝑓(𝑥)

𝑑2𝑓(𝑥)

Without loss of generality, the slab is placed symmetrically about 𝑥 = 0, in the interval [−𝑎/2, 𝑎/2] Because of that, the flux must be symmetric about 𝑥 = 0 and vanishes at the extrapolated boundaries, which is called ±𝑎𝑒𝑥/2

The general solution to Eq.(12) is:

Placing the derivative of Eq.(13) equal to zero at 𝑥 = 0 gives: 𝐶 = 0

Next, introducing the boundary conditions gives:

functions 𝑐𝑜𝑠(𝐵𝑛𝑥𝑥) are called eigenfunctions It can be shown that if the reactor under consideration is not critical, the flux is the sum of all such eigenfunctions, each

multiplied by a function that depends on the time However, if the reactor is critical, all