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Monte Carlo simulation of moderator and reflector in coal analyzer based on a D -T neutron generator
Author’s Accepted Manuscript Monte Carlo simulation of moderator and reflector in coal analyzer based on a D-T neutron generator Shan. Qing, Chu Shengnan, Jia Wenbao
www.elsevier.com/locate/apradiso
PII: DOI: Reference:
S0969-8043(15)30171-8 http://dx.doi.org/10.1016/j.apradiso.2015.08.029 ARI7118
To appear in: Applied Radiation and Isotopes Received date: 3 June 2015 Revised date: 12 August 2015 Accepted date: 19 August 2015 Cite this article as: Shan. Qing, Chu Shengnan and Jia Wenbao, Monte Carlo simulation of moderator and reflector in coal analyzer based on a D-T neutron g e n e r a t o r , Applied Radiation and Isotopes, http://dx.doi.org/10.1016/j.apradiso.2015.08.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Monte Carlo simulation of moderator and reflector in coal analyzer based on a D-T neutron generator Shan Qing1,2, Chu Shengnan1, Jia Wenbao1,2 1
Department of Nuclear Science and Engineering, College of Materials Science and Engineering,
Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People’s Republic of China 2
Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education
Institutions, Suzhou 215000, People’s Republic of China
Corresponding author: Shan Qing Department of Nuclear Science and Engineering College of Materials Science and Engineering Nanjing University of Aeronautics and Astronautics Nanjing 211106 People’s Republic of China E-mail: [email protected]
Highlights
Moderator and neutron reflector have been designed in a PGNAA-based coal analyzer. Monte Carlo simulation is used to optimize the neutron source term for the optimal objective. Heavy metal front moderators and reflectors were modeled and that the Pb(n,2n) reaction was used to augment the thermal neutron flux. The ratio of thermal to fast neutron is 1:1, and the total neutron flux in the coal sample increases about 102% after optimization.
Abstract Coal is one of the most popular fuels in the world. The use of coal not only produces carbon dioxide, but
1
also contributes to the environmental pollution by heavy metals. In prompt gamma-ray neutron activation analysis (PGNAA)-based coal analyzer, the characteristic gamma rays of C and O are mainly induced by fast neutrons, whereas thermal neutrons can be used to induce the characteristic gamma rays of H, Si, and heavy metals. Therefore, appropriate thermal and fast neutrons are beneficial in improving the measurement accuracy of heavy metals, and ensure that the measurement accuracy of main elements meets the requirements of the industry. Once the required yield of the deuterium–tritium (D-T) neutron generator is determined, appropriate thermal and fast neutrons can be obtained by optimizing the neutron source term. In this article, the Monte Carlo N-Particle (MCNP) Transport Code and Evaluated Nuclear Data File (ENDF) database are used to optimize the neutron source term in PGNAA-based coal analyzer, including the material and shape of the moderator and neutron reflector. The optimized targets include two points: (1) the ratio of the thermal to fast neutron is 1:1 and (2) the total neutron flux from the optimized neutron source in the sample increases at least 100% when compared with the initial one. The simulation results show that, the total neutron flux in the sample increases 102%, 102%, 85%, 72%, and 62% with Pb, Bi, Nb, W, and Be reflectors, respectively. Maximum optimization of the targets is achieved when the moderator is a 3-cm-thick lead layer coupled with a 3-cm-thick high-density polyethylene (HDPE) layer, and the neutron reflector is a 27-cm-thick hemispherical lead layer. Keywords: PGNAA, coal, ratio of the thermal neutron to fast neutron, moderator, neutron reflector
1. Introduction Prompt gamma-ray neutron activation analysis (PGNAA) technology is based on the detection of the prompt gamma rays emitted through thermal neutron capture or neutron inelastic scattering reactions, which have characteristic energies. The qualitative and quantitative analyses of the elements can be performed by measuring the energy and intensity of the prompt gamma rays (Chen Xiaowen, 2006). The PGNAA technology has the features of in situ and on-line measurements, and nondestructive, accurate, and entire element component examination. It has been widely used in industrial production, environmental measuring, explosive detection, and other fields, especially in the coal industry (Khelifi R, 2007; Idiri Z, 2007; Naqvi A A, 2004; Naqvi A A, 2003; Zhang Jinzhao, 2013). At present, the neutron sources used in PGNAA coal on-line measurement system mainly include americium–beryllium (Am-Be) and deuterium–tritium (D-T). Compared with Am-Be, the D-T neutron source has more advantages such as high yield, good stability, good monochromaticity, and ease of protection setup, storage, and transportation. 2
Moreover, Am-Be sources are not easily available, as only fewer facilities are producing 241Am in quantity. Therefore, in recent years, the D-T neutron generator is generally used as the neutron source in PGNAA-based coal analyzers. In order to protect the environment and reduce the emission of heavy metals from coal-fired enterprises, the on-line measurement accuracy of heavy metals should be improved. By the use of the more accurate data, these enterprises can reduce the emission of heavy metals by taking corresponding measures. In the PGNAA technology, the measurement of the carbon and oxygen is mainly based on the fast-neutron inelastic scattering reaction, whereas that of other elements is dependent on the thermal neutron capture reaction. When the fast neutrons outnumber the thermal neutrons, gamma rays induced by the former will hamper the estimation of the thermal peak heights. Therefore, appropriate number of thermal and fast neutrons is required to improve the measurement accuracy of mercury, lead, and other heavy metals, and at the same time ensuring that the observed measurement accuracy of main elements (such as carbon and oxygen) meets the requirement of the industry. In this article, the Monte Carlo N-Particle (MCNP) Transport Code and Evaluated Nuclear Data File (ENDF) databases are used to optimize the neutron source term in PGNAA-based coal analyzer, including the material and shape of the moderator and neutron reflector. The optimized targets include two points: (1) the ratio of the thermal to fast neutron is 1:1 and (2) the total neutron flux in the sample increases at least 100% when compared with the initial one. 2. PGNAA-based coal analyzer The schematic of a PGNAA-based coal analyzer is shown in Figure 1. A rubber belt, passing through the middle of the system, is used as coal conveyor. A D-T neutron generator, located below the belt, is used as the neutron source. In order to examine the entire element components of coal, a moderator is placed between the belt and the D-T neutron generator for moderating the emitted 14-MeV neutrons. The moderator is made of high-density polyethylene (HDPE). A 5 × 5 inch (diameter × height) bismuth germanium oxide (BGO) detector is installed above the level of coal for detecting the prompt gamma rays. In order to prevent the thermal neutrons entering the BGO detector, a boron carbide layer and a lead layer are used as shielders. The prompt gamma rays of structural materials and scattering gamma rays enter the BGO detector and produce interference. The outer HDPE shielding is used for protection against radiation. The thicknesses of the coal, belt, and the original moderator are 20, 1.2, and 5 cm, respectively. The elemental compositions of the coal are listed in Table 1.
3
Figure 1 Schematic of the PGNAA-based coal analyzer (two-dimensional profile) Table 1 Elemental compositions of the simulated coal Element
C
O
H
Si
S
Al
Na
Ca
Wt%
70.9
11.2
2.8
4.2
3.0
3.5
2.0
0.1
Hg
Pb
Cd
Cr
As
4
0.5
1
1
2
*10-5
*10-6
*10-6
*10-5
*10-5
Others
2.3
Type of NIS*
NIS
TNC*
TNC
TNC
TNC
TNC
TNC
TNC
TNC
TNC
TNC
TNC
---
0.42
0.31
0.33
0.12
0.35
0.08
0.24
0.35
251
0.14
1860
1.38
1
----
4.44
6.13
2.22
3.54
0.84
0.03
0.09
1.94
0.37
7.37
0.56
0.83
0.17
-----
reaction Cross sections (barn) Eγ (MeV)
*TNC: thermal neutron capture *NIS: neutron inelastic scattering. The value of neutron inelastic scattering cross section is obtained when the neutron energy is 14 MeV. The 14-MeV neutrons, generated from D-T neutron generator, are moderated by the moderator and rubber belt. The moderated neutrons then enter the coal and interact with its elements. The prompt gamma rays, produced by fast-neutron inelastic scattering and thermal neutron capture reaction, are emitted from the coal and detected by the BGO detector. Using the 14-MeV neutrons as incident particles, MCNP (J.F. Briesmeister, 1997) is applied to simulate the whole process of neutron transport. The properties of the D-T neutron generator are shown in Table 2. 4
Table 2 Properties of D-T neutron generator D-T gas mixture Voltage (kV)
Target material
Average neutron energy (MeV)
Neutron yield (n/s)
65–90
Ti
14.0
5 × 108
(%) 50/50 3. Simulation Neutrons of the following three energy ranges, 0–0.0001, 6.0–14.0, and 0–14.0 MeV, are selected for the simulation process. The neutrons of 6.0–14.0, 0–0.0001, and 0–14.0 MeV are important for the production of characteristic gamma rays of carbon and oxygen, characteristic gamma rays of other elements such as hydrogen, silicon, and heavy metals, and the investigation of the variation of the total neutron flux in the sample, respectively. Two physical quantities p and k are defined for the comparison of the increment of neutron before and after optimization and the ratio of the thermal to fast neutron, respectively, as follows:
p
C C0 100% C0
k
CT CF ,
(1)
(2)
where C0 and C denote the neutron numbers in a certain energy range before and after optimization, and CT and CF represent the neutron numbers in the 0–0.0001 and 6.0–14.0 MeV energy ranges after moderation, respectively. The values of p0–0.0001 MeV, p6–14 MeV, and p0–14 MeV are also calculated. 3.1. Optimization of the moderator A k value of 9.50 × 10−2 can be obtained by the simulation of the initial moderator. This indicates that the number of neutrons in the energy range of 0–0.0001 MeV is very less than that in the 6.0–14.0 MeV energy range. In order to obtain k = 1, the neutron flux needs to be further moderated. Some elements, such as lead, can be obtained (n, 2n) in reaction with the 14-MeV neutrons (Jarman SE, 2007). This process may help increase the neutron yields in the 0–0.0001 and 0–14 MeV energy ranges. In this study, lead-208 and HDPE are chosen as the moderating material, and a 5-cm-thick initial moderator is used. The lead layer is placed between the D-T neutron source and the HDPE. Then, the influences of different thickness combinations of lead and HDPE on the moderating neutrons are studied, and the results are depicted in Figure 2. 5
Figure 2 Values of p (left) and k (right) versus different thicknesses of lead Figure 2 illustrates the change in the values of p and k with the thickness of the lead. With an increase in the thickness of the lead layer, p0–0.0001 MeV increases initially and then decreases, and is optimum when the thickness of the lead reaches about 2 cm. Simultaneously, p0–14 MeV continuously increases whereas p6–14 MeV
continuously decreases. The (n, 2n) reaction between the lead and 14-MeV neutrons is attributed to
these results. It is evident from the figure on the right-hand side that k reaches its maximum value when the thickness of the lead is about 2–3 cm. In order to improve the ratio of thermal to fast neutron and the total neutron flux simultaneously, the thicknesses of the lead and HDPE are chosen to be 3 and 2 cm, respectively. As a consequence, the number of neutrons in the 0–0.0001 and 0–14 MeV energy ranges increases about 37% and 7%, respectively, whereas that in the 6–14 MeV energy range decreases about 17%. 3.2. Neutron reflector After the preliminary optimization of the moderator, the total neutron flux increases about 7%, and the value of k is 0.15. However, this does not satisfy the optimized targets. As depicted in Figure 1, there is a considerable space below the D-T neutron source at the bottom of the PGNAA-based coal analyzer. A layer of neutron reflector is added in that space to improve the ratio of thermal to fast neutron and the total neutron flux. The commonly used neutron reflector materials are Pb, Bi, W, Be, Nb, V, and graphite (Uhlá00 R, 2014; Durisi E, 2007; Gohar Y, 2000; Rahmani F, 2011). Because of the space constraints in the system, the maximum thickness of the reflector is 30 cm. The reflectors with different materials are simulated from 5 to 30 cm using the MCNP code. During simulation, the initial shape of the neutron reflector is set to a hemisphere.
6
Figure 3 The p0–14 MeV (left) and k (right) versus different thicknesses of the reflector Figure 3 shows the relationship between p0–14MeV and k and the thickness of the reflector. It is evident from the figure that, for all reflector materials, the values of p0–14 MeV and k increase with an increase in their thickness. The maximum value of the total neutron flux is obtained when Be is used as the reflector material, and k~1 is obtained when the thickness of Be is about 15 cm. However, beryllium is not suitable for industrial application as it is a highly toxic, very expensive, and chemically active metal. For other reflector materials (e.g., tungsten, k = 0.95), although the thickness reaches its maximum value, they cannot meet the requirement of k = 1. This illustrates that further moderation is still needed. 3.3. Further optimization of the moderator The moderator is further optimized to make the ratio of thermal to fast neutron equal 1. Two optimization schemes are considered in the simulation process: (1) an extra 1-cm-thick HDPE layer is added above the initial moderator for improving the moderating power of the moderator, thereby changing the thickness of the moderator to 6 cm and (2) other moderating materials, which have lesser macroscopic neutron absorption cross section than HDPE, such as graphite, heavy water, and paraffin wax, are used to partially replace the HDPE. In this case, the order of the moderating materials from bottom to top is lead, HDPE, and other materials. The properties of moderating materials are listed in Table 3. Two schemes are simulated and the results are shown in Figure 4. The neutron reflector used in this simulation is a 30-cm-thick tungsten layer, because of its largest value of k.
7
Figure 4 p0–14 MeV and k versus the composition of moderator Table 3 Properties of moderating materials Material
HDPE
Graphite
D2O
Paraffin wax
Lead
Molecular formula
C2H4
C
D2O
C30H62
Pb
Density(g∙cm−3)
0.95
2.25
1.11
0.9
11.34
Σa (cm−1)
0.0271
0.000295
4.06E-05
0.0264
0.0243
ΣS (cm−1)
0.107
0.14
0.0852
0.102
0.0923
Σa, macroscopic absorption cross section; ΣS, macroscopic scattering cross section. The value of Σa is obtained when neutron energy is 14 MeV. It is evident from Figure 4 that every structure of moderator can meet the second optimized target, but the value of k can only be >1 when an extra 1-cm-thick HDPE is added to the initial moderator. Therefore, the composition of the moderator is changed to a 3-cm-thick lead layer and a 3-cm-thick HDPE layer. In this case, the total neutron flux in the sample increases by 87%, and the value of k is about 1.16. 3.4. Further optimization of the neutron reflector In order to obtain k = 1, further optimization of the neutron reflector is performed. The simulation results are shown in Figure 5, which depicts the relationship between the values of k and p and the thickness of the neutron reflector. It is evident from the figure that the first optimized target can be satisfied when the material of the neutron reflector is Pb, Bi, Nb, W, or Be, with the corresponding thicknesses of 27, 30, 30, 18, or 14 cm. The corresponding values of p0–14 MeV are listed in Table 4, from which, lead, with a thickness of 27 cm, is selected as the neutron reflector.
8
Figure 5 Relationship between the values of k and p and the thickness of the neutron reflector Table 4 Values of p0–14 MeV versus thicknesses of different materials Thickness (cm)
p0–14 MeV (%)
Pb
27
102
Bi
30
102
Nb
30
85
W
18
72
Be
14
62
The effect of the shape of neutron reflector on the neutron yield is also simulated. Shapes such as hemisphere, cube, and rectangular pyramid are discussed during the simulation, as listed in Table 5. It is evident from the table that the best result is obtained when the shape of the neutron reflector is hemisphere. As a consequence, the number of neutrons in the 0–0.0001 and 0–14.0 MeV energy ranges increases by 704% and 102%, respectively, and that in the 6.0–14.0 MeV energy range decreases by 23.7%. Table 5 Effect of the shape of neutron reflector on neutron yield Shape
k
p0–14 MeV
Hemisphere
1.00
102%
Cube
1.00
101%
Rectangular pyramid
0.95
98%
4. Conclusion In order to protect the environment and reduce the emission of heavy metals, the neutron source term is optimized to improve the measurement accuracy of heavy metals in the PGNAA-based coal analyzer. The neutron source term, including the moderator and the neutron reflector, is simulated using the Monte Carlo method. The simulation results show that the optimized targets can be satisfied when the moderator is 9
a 3-cm-thick lead layer combined with a 3-cm-thick HDPE layer, and the neutron reflector is a 27-cm-thick hemispherical lead layer. In this case, the ratio of thermal to fast neutron is 1:1, and the total neutron flux in the sample increases by 102%. In our future work, the characteristic gamma rays and the noise from background gamma rays will be considered during simulation, and a validation test will also be conducted to verify the obtained results using the foil activation technique. Acknowledgment This research was supported by the Fundamental Research Funds for the Central Universities (NS2014056).
References Chen Xiaowen. 2006, Study on the method of on-line measuring coal components by PGNAA [D]. Lanzhou University, Khelifi R, et al., 2007, Detection limits of pollutants in water for PGNAA using Am–Be source[J]. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 262(2): 329-332. Idiri Z, et al., 2007, Monte Carlo optimization of sample dimensions of an 241Am–Be source-based PGNAA setup for water rejects analysis [J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 578(1): 279-288. Naqvi A A, et al., 2004, Validity test of design calculations of a PGNAA setup [J]. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 215(1): 283-291. Naqvi A A. 2003, A Monte Carlo comparison of PGNAA system performance using 252Cf neutrons, 2.8-MeV neutrons and 14-MeV neutrons [J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 511(3): 400-407. Zhang Jinzhao, Tuo Xianguo. 2014, A Monte Carlo simulation and setup optimization of output efficiency to PGNAA thermal neutron using 252Cf neutrons [J]. Chinese Physics C, 38(7): 078201-1-5 J.F. Briesmeister (Ed.), 1997, MCNP – A General Monte Carlo N-Particle Transport Code, Version 4B, LA-12625-M, Los Alamos National Laboratory, Los Alamos, New Mexico
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Jarman SE, Pinchin J, Brushwood JM, McCarthy T, Bray M, Beeley PA, 2007, Design and construction of a facility for neutron activation analysis using the 14 MeV neutron generator at HMS Sultan. J Radioanal Nucl Chem, 271:47–53 Uhlá00 R, Kadulová M, Alexa P, et al. 2014, A new reflector structure for facility thermalizing D-T neutrons[J]. Journal of Radioanalytical & Nuclear Chemistry, 300(2):809-818. Durisi E, Zaninni A, Manfredotti C, Palamara F, Sarotto M, Visca L, Nastasi U (2007) Design of an epithermal column for BNCT based on D–D fusion neutron facility. Nucl Instrum Methods A, 574:363–369 Gohar Y, Smith DL (2000) Multiplier, moderator, and reflector materials for advanced lithium–vanadium fusion blankets. J Nucl Mater, 283–284:1370–1374 Rahmani F, Shahriari M (2011) Beam shaping assembly optimization of Linac based BNCT and in-phantom depth dose distribution analysis of brain tumors for verification of a beam model. Ann Nucl Energy 38:404–409
11
www.elsevier.com/locate/apradiso
PII: DOI: Reference:
S0969-8043(15)30171-8 http://dx.doi.org/10.1016/j.apradiso.2015.08.029 ARI7118
To appear in: Applied Radiation and Isotopes Received date: 3 June 2015 Revised date: 12 August 2015 Accepted date: 19 August 2015 Cite this article as: Shan. Qing, Chu Shengnan and Jia Wenbao, Monte Carlo simulation of moderator and reflector in coal analyzer based on a D-T neutron g e n e r a t o r , Applied Radiation and Isotopes, http://dx.doi.org/10.1016/j.apradiso.2015.08.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Monte Carlo simulation of moderator and reflector in coal analyzer based on a D-T neutron generator Shan Qing1,2, Chu Shengnan1, Jia Wenbao1,2 1
Department of Nuclear Science and Engineering, College of Materials Science and Engineering,
Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People’s Republic of China 2
Collaborative Innovation Center of Radiation Medicine of Jiangsu Higher Education
Institutions, Suzhou 215000, People’s Republic of China
Corresponding author: Shan Qing Department of Nuclear Science and Engineering College of Materials Science and Engineering Nanjing University of Aeronautics and Astronautics Nanjing 211106 People’s Republic of China E-mail: [email protected]
Highlights
Moderator and neutron reflector have been designed in a PGNAA-based coal analyzer. Monte Carlo simulation is used to optimize the neutron source term for the optimal objective. Heavy metal front moderators and reflectors were modeled and that the Pb(n,2n) reaction was used to augment the thermal neutron flux. The ratio of thermal to fast neutron is 1:1, and the total neutron flux in the coal sample increases about 102% after optimization.
Abstract Coal is one of the most popular fuels in the world. The use of coal not only produces carbon dioxide, but
1
also contributes to the environmental pollution by heavy metals. In prompt gamma-ray neutron activation analysis (PGNAA)-based coal analyzer, the characteristic gamma rays of C and O are mainly induced by fast neutrons, whereas thermal neutrons can be used to induce the characteristic gamma rays of H, Si, and heavy metals. Therefore, appropriate thermal and fast neutrons are beneficial in improving the measurement accuracy of heavy metals, and ensure that the measurement accuracy of main elements meets the requirements of the industry. Once the required yield of the deuterium–tritium (D-T) neutron generator is determined, appropriate thermal and fast neutrons can be obtained by optimizing the neutron source term. In this article, the Monte Carlo N-Particle (MCNP) Transport Code and Evaluated Nuclear Data File (ENDF) database are used to optimize the neutron source term in PGNAA-based coal analyzer, including the material and shape of the moderator and neutron reflector. The optimized targets include two points: (1) the ratio of the thermal to fast neutron is 1:1 and (2) the total neutron flux from the optimized neutron source in the sample increases at least 100% when compared with the initial one. The simulation results show that, the total neutron flux in the sample increases 102%, 102%, 85%, 72%, and 62% with Pb, Bi, Nb, W, and Be reflectors, respectively. Maximum optimization of the targets is achieved when the moderator is a 3-cm-thick lead layer coupled with a 3-cm-thick high-density polyethylene (HDPE) layer, and the neutron reflector is a 27-cm-thick hemispherical lead layer. Keywords: PGNAA, coal, ratio of the thermal neutron to fast neutron, moderator, neutron reflector
1. Introduction Prompt gamma-ray neutron activation analysis (PGNAA) technology is based on the detection of the prompt gamma rays emitted through thermal neutron capture or neutron inelastic scattering reactions, which have characteristic energies. The qualitative and quantitative analyses of the elements can be performed by measuring the energy and intensity of the prompt gamma rays (Chen Xiaowen, 2006). The PGNAA technology has the features of in situ and on-line measurements, and nondestructive, accurate, and entire element component examination. It has been widely used in industrial production, environmental measuring, explosive detection, and other fields, especially in the coal industry (Khelifi R, 2007; Idiri Z, 2007; Naqvi A A, 2004; Naqvi A A, 2003; Zhang Jinzhao, 2013). At present, the neutron sources used in PGNAA coal on-line measurement system mainly include americium–beryllium (Am-Be) and deuterium–tritium (D-T). Compared with Am-Be, the D-T neutron source has more advantages such as high yield, good stability, good monochromaticity, and ease of protection setup, storage, and transportation. 2
Moreover, Am-Be sources are not easily available, as only fewer facilities are producing 241Am in quantity. Therefore, in recent years, the D-T neutron generator is generally used as the neutron source in PGNAA-based coal analyzers. In order to protect the environment and reduce the emission of heavy metals from coal-fired enterprises, the on-line measurement accuracy of heavy metals should be improved. By the use of the more accurate data, these enterprises can reduce the emission of heavy metals by taking corresponding measures. In the PGNAA technology, the measurement of the carbon and oxygen is mainly based on the fast-neutron inelastic scattering reaction, whereas that of other elements is dependent on the thermal neutron capture reaction. When the fast neutrons outnumber the thermal neutrons, gamma rays induced by the former will hamper the estimation of the thermal peak heights. Therefore, appropriate number of thermal and fast neutrons is required to improve the measurement accuracy of mercury, lead, and other heavy metals, and at the same time ensuring that the observed measurement accuracy of main elements (such as carbon and oxygen) meets the requirement of the industry. In this article, the Monte Carlo N-Particle (MCNP) Transport Code and Evaluated Nuclear Data File (ENDF) databases are used to optimize the neutron source term in PGNAA-based coal analyzer, including the material and shape of the moderator and neutron reflector. The optimized targets include two points: (1) the ratio of the thermal to fast neutron is 1:1 and (2) the total neutron flux in the sample increases at least 100% when compared with the initial one. 2. PGNAA-based coal analyzer The schematic of a PGNAA-based coal analyzer is shown in Figure 1. A rubber belt, passing through the middle of the system, is used as coal conveyor. A D-T neutron generator, located below the belt, is used as the neutron source. In order to examine the entire element components of coal, a moderator is placed between the belt and the D-T neutron generator for moderating the emitted 14-MeV neutrons. The moderator is made of high-density polyethylene (HDPE). A 5 × 5 inch (diameter × height) bismuth germanium oxide (BGO) detector is installed above the level of coal for detecting the prompt gamma rays. In order to prevent the thermal neutrons entering the BGO detector, a boron carbide layer and a lead layer are used as shielders. The prompt gamma rays of structural materials and scattering gamma rays enter the BGO detector and produce interference. The outer HDPE shielding is used for protection against radiation. The thicknesses of the coal, belt, and the original moderator are 20, 1.2, and 5 cm, respectively. The elemental compositions of the coal are listed in Table 1.
3
Figure 1 Schematic of the PGNAA-based coal analyzer (two-dimensional profile) Table 1 Elemental compositions of the simulated coal Element
C
O
H
Si
S
Al
Na
Ca
Wt%
70.9
11.2
2.8
4.2
3.0
3.5
2.0
0.1
Hg
Pb
Cd
Cr
As
4
0.5
1
1
2
*10-5
*10-6
*10-6
*10-5
*10-5
Others
2.3
Type of NIS*
NIS
TNC*
TNC
TNC
TNC
TNC
TNC
TNC
TNC
TNC
TNC
TNC
---
0.42
0.31
0.33
0.12
0.35
0.08
0.24
0.35
251
0.14
1860
1.38
1
----
4.44
6.13
2.22
3.54
0.84
0.03
0.09
1.94
0.37
7.37
0.56
0.83
0.17
-----
reaction Cross sections (barn) Eγ (MeV)
*TNC: thermal neutron capture *NIS: neutron inelastic scattering. The value of neutron inelastic scattering cross section is obtained when the neutron energy is 14 MeV. The 14-MeV neutrons, generated from D-T neutron generator, are moderated by the moderator and rubber belt. The moderated neutrons then enter the coal and interact with its elements. The prompt gamma rays, produced by fast-neutron inelastic scattering and thermal neutron capture reaction, are emitted from the coal and detected by the BGO detector. Using the 14-MeV neutrons as incident particles, MCNP (J.F. Briesmeister, 1997) is applied to simulate the whole process of neutron transport. The properties of the D-T neutron generator are shown in Table 2. 4
Table 2 Properties of D-T neutron generator D-T gas mixture Voltage (kV)
Target material
Average neutron energy (MeV)
Neutron yield (n/s)
65–90
Ti
14.0
5 × 108
(%) 50/50 3. Simulation Neutrons of the following three energy ranges, 0–0.0001, 6.0–14.0, and 0–14.0 MeV, are selected for the simulation process. The neutrons of 6.0–14.0, 0–0.0001, and 0–14.0 MeV are important for the production of characteristic gamma rays of carbon and oxygen, characteristic gamma rays of other elements such as hydrogen, silicon, and heavy metals, and the investigation of the variation of the total neutron flux in the sample, respectively. Two physical quantities p and k are defined for the comparison of the increment of neutron before and after optimization and the ratio of the thermal to fast neutron, respectively, as follows:
p
C C0 100% C0
k
CT CF ,
(1)
(2)
where C0 and C denote the neutron numbers in a certain energy range before and after optimization, and CT and CF represent the neutron numbers in the 0–0.0001 and 6.0–14.0 MeV energy ranges after moderation, respectively. The values of p0–0.0001 MeV, p6–14 MeV, and p0–14 MeV are also calculated. 3.1. Optimization of the moderator A k value of 9.50 × 10−2 can be obtained by the simulation of the initial moderator. This indicates that the number of neutrons in the energy range of 0–0.0001 MeV is very less than that in the 6.0–14.0 MeV energy range. In order to obtain k = 1, the neutron flux needs to be further moderated. Some elements, such as lead, can be obtained (n, 2n) in reaction with the 14-MeV neutrons (Jarman SE, 2007). This process may help increase the neutron yields in the 0–0.0001 and 0–14 MeV energy ranges. In this study, lead-208 and HDPE are chosen as the moderating material, and a 5-cm-thick initial moderator is used. The lead layer is placed between the D-T neutron source and the HDPE. Then, the influences of different thickness combinations of lead and HDPE on the moderating neutrons are studied, and the results are depicted in Figure 2. 5
Figure 2 Values of p (left) and k (right) versus different thicknesses of lead Figure 2 illustrates the change in the values of p and k with the thickness of the lead. With an increase in the thickness of the lead layer, p0–0.0001 MeV increases initially and then decreases, and is optimum when the thickness of the lead reaches about 2 cm. Simultaneously, p0–14 MeV continuously increases whereas p6–14 MeV
continuously decreases. The (n, 2n) reaction between the lead and 14-MeV neutrons is attributed to
these results. It is evident from the figure on the right-hand side that k reaches its maximum value when the thickness of the lead is about 2–3 cm. In order to improve the ratio of thermal to fast neutron and the total neutron flux simultaneously, the thicknesses of the lead and HDPE are chosen to be 3 and 2 cm, respectively. As a consequence, the number of neutrons in the 0–0.0001 and 0–14 MeV energy ranges increases about 37% and 7%, respectively, whereas that in the 6–14 MeV energy range decreases about 17%. 3.2. Neutron reflector After the preliminary optimization of the moderator, the total neutron flux increases about 7%, and the value of k is 0.15. However, this does not satisfy the optimized targets. As depicted in Figure 1, there is a considerable space below the D-T neutron source at the bottom of the PGNAA-based coal analyzer. A layer of neutron reflector is added in that space to improve the ratio of thermal to fast neutron and the total neutron flux. The commonly used neutron reflector materials are Pb, Bi, W, Be, Nb, V, and graphite (Uhlá00 R, 2014; Durisi E, 2007; Gohar Y, 2000; Rahmani F, 2011). Because of the space constraints in the system, the maximum thickness of the reflector is 30 cm. The reflectors with different materials are simulated from 5 to 30 cm using the MCNP code. During simulation, the initial shape of the neutron reflector is set to a hemisphere.
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Figure 3 The p0–14 MeV (left) and k (right) versus different thicknesses of the reflector Figure 3 shows the relationship between p0–14MeV and k and the thickness of the reflector. It is evident from the figure that, for all reflector materials, the values of p0–14 MeV and k increase with an increase in their thickness. The maximum value of the total neutron flux is obtained when Be is used as the reflector material, and k~1 is obtained when the thickness of Be is about 15 cm. However, beryllium is not suitable for industrial application as it is a highly toxic, very expensive, and chemically active metal. For other reflector materials (e.g., tungsten, k = 0.95), although the thickness reaches its maximum value, they cannot meet the requirement of k = 1. This illustrates that further moderation is still needed. 3.3. Further optimization of the moderator The moderator is further optimized to make the ratio of thermal to fast neutron equal 1. Two optimization schemes are considered in the simulation process: (1) an extra 1-cm-thick HDPE layer is added above the initial moderator for improving the moderating power of the moderator, thereby changing the thickness of the moderator to 6 cm and (2) other moderating materials, which have lesser macroscopic neutron absorption cross section than HDPE, such as graphite, heavy water, and paraffin wax, are used to partially replace the HDPE. In this case, the order of the moderating materials from bottom to top is lead, HDPE, and other materials. The properties of moderating materials are listed in Table 3. Two schemes are simulated and the results are shown in Figure 4. The neutron reflector used in this simulation is a 30-cm-thick tungsten layer, because of its largest value of k.
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Figure 4 p0–14 MeV and k versus the composition of moderator Table 3 Properties of moderating materials Material
HDPE
Graphite
D2O
Paraffin wax
Lead
Molecular formula
C2H4
C
D2O
C30H62
Pb
Density(g∙cm−3)
0.95
2.25
1.11
0.9
11.34
Σa (cm−1)
0.0271
0.000295
4.06E-05
0.0264
0.0243
ΣS (cm−1)
0.107
0.14
0.0852
0.102
0.0923
Σa, macroscopic absorption cross section; ΣS, macroscopic scattering cross section. The value of Σa is obtained when neutron energy is 14 MeV. It is evident from Figure 4 that every structure of moderator can meet the second optimized target, but the value of k can only be >1 when an extra 1-cm-thick HDPE is added to the initial moderator. Therefore, the composition of the moderator is changed to a 3-cm-thick lead layer and a 3-cm-thick HDPE layer. In this case, the total neutron flux in the sample increases by 87%, and the value of k is about 1.16. 3.4. Further optimization of the neutron reflector In order to obtain k = 1, further optimization of the neutron reflector is performed. The simulation results are shown in Figure 5, which depicts the relationship between the values of k and p and the thickness of the neutron reflector. It is evident from the figure that the first optimized target can be satisfied when the material of the neutron reflector is Pb, Bi, Nb, W, or Be, with the corresponding thicknesses of 27, 30, 30, 18, or 14 cm. The corresponding values of p0–14 MeV are listed in Table 4, from which, lead, with a thickness of 27 cm, is selected as the neutron reflector.
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Figure 5 Relationship between the values of k and p and the thickness of the neutron reflector Table 4 Values of p0–14 MeV versus thicknesses of different materials Thickness (cm)
p0–14 MeV (%)
Pb
27
102
Bi
30
102
Nb
30
85
W
18
72
Be
14
62
The effect of the shape of neutron reflector on the neutron yield is also simulated. Shapes such as hemisphere, cube, and rectangular pyramid are discussed during the simulation, as listed in Table 5. It is evident from the table that the best result is obtained when the shape of the neutron reflector is hemisphere. As a consequence, the number of neutrons in the 0–0.0001 and 0–14.0 MeV energy ranges increases by 704% and 102%, respectively, and that in the 6.0–14.0 MeV energy range decreases by 23.7%. Table 5 Effect of the shape of neutron reflector on neutron yield Shape
k
p0–14 MeV
Hemisphere
1.00
102%
Cube
1.00
101%
Rectangular pyramid
0.95
98%
4. Conclusion In order to protect the environment and reduce the emission of heavy metals, the neutron source term is optimized to improve the measurement accuracy of heavy metals in the PGNAA-based coal analyzer. The neutron source term, including the moderator and the neutron reflector, is simulated using the Monte Carlo method. The simulation results show that the optimized targets can be satisfied when the moderator is 9
a 3-cm-thick lead layer combined with a 3-cm-thick HDPE layer, and the neutron reflector is a 27-cm-thick hemispherical lead layer. In this case, the ratio of thermal to fast neutron is 1:1, and the total neutron flux in the sample increases by 102%. In our future work, the characteristic gamma rays and the noise from background gamma rays will be considered during simulation, and a validation test will also be conducted to verify the obtained results using the foil activation technique. Acknowledgment This research was supported by the Fundamental Research Funds for the Central Universities (NS2014056).
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