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Compact shielding design for 740 GBq 241Am-Be neutron source transport container
Radiation Physics and Chemistry 170 (2020) 108670
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Compact shielding design for 740 GBq container
241
Am-Be neutron source transport
T
Pew Basua,b,∗, R. Sarangapania, B. Venkatramana,b a b
Safety, Quality & Resource Management Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamilnadu, 603102, India Homi Bhabha National Institute, Kalpakkam, Tamilnadu, 603102, India
ARTICLE INFO
ABSTRACT
Keywords: 241 Am-Be source Composite polymer Factorial design analysis Gamma spectrometry Monte Carlo technique Shielding design
For transport and storage of neutron sources, shielding materials like polymers and multi layer shields are used. A compact shielding design for 740 GBq portable 241Am-Be neutron source transport container using Monte Carlo technique is presented. In the design, a polymer host material with lead and natural boron (NB) as fillers is chosen as the shielding medium. Monte Carlo simulation (MCS) is performed for optimizing the quantity of fillers in the polymer. The total dose rate (TDR) on the surface of the container due to neutrons and gamma rays emanating from source as well as polymer shield, is considered as the optimization criterion. MCS studies indicate that a polymer material with 5% of lead and 1% of NB as fillers is observed to give optimized composition of polymer (OCP). Statistical factorial design analysis (FDA) technique is employed for the first time in the shielding design to investigate the impact of fillers in the polymer. FDA studies reveal that the quantity of lead has more significant impact compared to NB in the polymer. MCS results are validated by carrying out shielding experiments with high density polyethylene (HDPE) and composite polymer (CP) based containers. The computed and experimental dose rates are observed to be within ± 12%. A shielding container made of OCP for the transport of 740 GBq 241Am-Be source provides 25% reduction in the volume as compared to HDPE and CP. The mass of the OCP container is lower by 18% and 26% compared to the containers made of HDPE and CP respectively. The surface dose rate of the OCP container adheres to the IAEA transport regulations.
1. Introduction 241
Am-Be neutron source is used for a wide variety of applications such as neutron calibration of monitoring instruments and detectors (Venkataraman et al., 1970; Gomaa et al., 1993; Tousi et al., 2014), irradiation of samples (Franco, 2014), neutron imaging (Jafari and Feghhi, 2012), analysis of fission products (Celenk, 2001), prompt gamma neutron activation analysis (Naqvi and Nagadi, 2004), light element analysis via neutron reflection (Jonah et al., 1999), and on-line measurement of neutron poison related to fast neutron scattering (Hussein et al., 1987). The source is fabricated in the form of metallic alloy of americium (alpha particle emitter) and beryllium (target). By double sealing, the alloyed mixture is encapsulated to guard against the leakage of 241Am. Emission of neutrons from the source is accompanied by gamma rays from the excited carbon nuclei (Gomma et al., 1993) and both these radiations cause exposure to human and environment. Neutron shielding is generally achieved by reducing the energy of the fast neutrons by inelastic/elastic scattering and finally absorbing the slow neutrons. The absorption of slow neutrons in polyethylene,
∗
paraffin, or polymer which contains significant quantity of hydrogen produces high energy gamma rays due to capture reaction (Moadab and Saadi, 2019). Therefore, it is desirable to make a neutron source transport container with a blend of elements that can effectively handle both neutrons and gamma rays. Hayashi et al. (2006) showed that the use of Mg(BH4)2, TiH2, and ZrH2 instead of the conventional materials can reduce the thickness of the shield by 23%, 20%, and 19% respectively. Fantidis (2015) showed that use of the advanced shielding material can reduce the thickness, mass, and volume of the shield by 41.3%, 44%, and 78.4% respectively. Zhang et al., (2017) observed that to maintain a dose rate criterion of 0.025 mSv/h outside a paraffin shielded container for a portable 666 GBq 241Am–Be source, volume and weight of the container becomes 1.36 m3 and 1060 kg respectively. By providing double layer shielding with tungsten as moderator, the mass of the container is reduced by 54%. Moadab and Saadi (2019) showed that a lighter shield design with polyethylene (78.5%)–bismuth (11.5%) alloy results in a reduction of volume and mass of the shield by 49% and 67% respectively. A polymer with neutron absorber (boron, cadmium, gadolinium, and indium) and high density gamma attenuator
Corresponding author. Safety, Quality & Resource Management Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamilnadu, 603102, India. E-mail address: [email protected] (P. Basu).
https://doi.org/10.1016/j.radphyschem.2019.108670 Received 12 September 2019; Received in revised form 9 December 2019; Accepted 27 December 2019 Available online 29 December 2019 0969-806X/ © 2019 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 170 (2020) 108670
P. Basu, et al.
(lead, bismuth, tungsten, and stainless steel) is likely to give optimized elemental composition for neutron shielding. The surface dose rate on the shielding container must adhere to the dose rates specified in IAEA transport regulations (IAEA Safety Standards Series No.SSR-6, 2018). In the present work, a compact shielding design of a container made of optimized composite polymer (OCP) for transporting 740 GBq 241 Am-Be neutron source is proposed. The elemental composition of OCP is obtained from Monte Carlo simulations (MCSs) by optimizing the quantity of lead and natural boron (NB) fillers in a polymer made of hydrogen, carbon, and oxygen. Factorial design analysis (FDA) technique is performed to analyze the impact of fillers in the polymer. FDA is generally used to examine the effect of two or more independent factors, each with discrete possible levels upon a single dependent response (Anderson and McLean, 1974; Montgomery, 1997). The effect of a factor is obtained as the change in the response produced by varying the levels of the factor (Wu and Hamada, 2009). MCS results are validated by carrying out experiments with high density polyethylene (HDPE) and composite polymer (CP) containers. Studies on the shielding effectiveness of OCP vis-à-vis HDPE and CP containers and advantages of shielding design with OCP are presented.
to the (n, γ) reaction with the hydrogen present in the shielding material is included in the MCS by choosing the photon production option from the neutron collision event. 2.2. Details of shielding materials HDPE is a polymer of density 920 kg/m3 produced from the ethylene monomer. The elemental composition of CP is hydrogen, carbon, and oxygen with lead and NB as fillers and the density of CP is 1010 kg/m3. The weight fraction of the elements in CP is given in Table 1. The inclusion of NB as a filler is considered for the thermal neutron absorption (Korkut and Karabulut, 2010). The hydrogen present in the polymer acts as a very good moderator and thereby making easy absorption of the slow neutrons by 10B (20% in NB). Lead acts as a good in-situ attenuator for the gamma rays emitted from the source and the shield. 2.3. Monte Carlo simulation (MCS) Computation of neutron dose rates (NDRs) and gamma dose rates (GDRs) is carried out using MCNP code (Briesmeister, 1997). The fluence rate φ(r, E) on the surface of the shield at position ‘r’ and of radiation energy ‘E’ is obtained using the ring detector tally. To get the computed dose rate D(r) at position ‘r’, φ(r, E) is multiplied with the flux to dose rate conversion factor R(E) for energy ‘E’. R(E) values are obtained from NCRP-38, 1971 and ANSI/ANS-6.1.1, 1977 for neutrons and gamma rays respectively. Finally, the dose rate obtained for each energy interval is summed to get NDRs and GDRs. In MCS, the number of particles tracked is varied from 1.0E+06 to 1.0E+07. The computed dose rates passed all the mandatory statistical tests outlined in the manual with a maximum relative error of 2%. In modelling the shield, geometry splitting technique (GST) is used. The shield thickness is sliced into a number of smaller sections based on the estimated half value layer (HVL) of the material. Incorporation of GST increases the population of particles in the favourable regions with appropriate normalization of weights to provide better sampling and thereby reducing the variance.
2. Materials and methods 2.1. Sources of radiation 241
Am-Be source emits neutrons of energy in the range of 1–11 MeV as a continuous spectrum due to (α, n) reaction with an average energy of 4.4 MeV. The normalized neutron spectrum of 241Am-Be source is shown in Fig. 1 (Zhang et al., 2017; Nasrabadi and Baghban, 2013). The total neutron yield from a 740 GBq 241Am-Be source is 4.4E+07 n/s. The gamma rays of 4.43 MeV are emitted during the de-excitation of the 12C* nucleus as a result of (α, 9Be) reaction and the γ/n ratio vary from 0.38 to 0.75 (Moadab and Saadi; Venkataraman et al., 1970; Liu et al., 2007; Murata et al., 2014). As a conservative approximation, γ/n ratio of 0.75 is assumed in the present work which corresponds to source strength of 3.3E+07 γ/s for 4.43 MeV gamma ray. The gamma rays emitted from the source due to the decay of 241Am is quantified by gamma spectrometry using a portable HPGe detector connected to ORION@ make MCA and Inter-winner@ spectrum acquisition software. The schematic of the experimental set up is shown in Fig. 2. The sides of the detector are shielded by lead rings of annular thickness 5 cm. A lead collimator of thickness 5 cm with an orifice of 0.5 cm is placed in front of the detector. The detector is calibrated with 241Am and 152Eu standard sources. The capture gamma rays of energy 2.2 MeV emitted due
2.4. Optimization of concentration of lead and natural boron fillers in polymer MCS is performed for optimizing the quantity of lead and NB fillers in polymer. A 740 GBq 241Am-Be source is assumed at the centre of the air cavity in a shielding container of thickness 20 cm. The cavity of the container has diameter of 7 cm and length of 14 cm. The shielding thickness of the container is sliced into five equal sections and GST is applied. All the components of radiations emanating from the source and the polymer are considered. The TDRs are computed on the surface of the container along the mid plane by varying the quantity of lead and NB each from 1% to 6% in steps of 1%. The weight percent of host elements is suitably adjusted to keep the density of the shield at 1010 kg/m3. The computed TDR is used as the criterion during the optimization of elemental composition. The schematic of the sourceshield model considered for the optimization of elemental composition is shown in Fig. 3. 2.5. Factorial design analysis (FDA) technique
Fig. 1.
In the present work, lead weight percent (L) and NB weight percent (B) in the polymer are considered as two independent factors in the FDA technique. By varying the quantity of lead and NB from 1% to 6% in steps of 1%, six discrete levels of each factor is proposed and the response based on the computed TDR for 36 compositions is analysed. A 6 × 6 FDA input matrix is constructed from the data to investigate the effect of lead, NB, and their interaction using analysis of variance (ANOVA).
241
Am-Be neutron energy spectrum. 2
Radiation Physics and Chemistry 170 (2020) 108670
P. Basu, et al.
Fig. 2. Schematic of the gamma spectrometry experimental set up. Table 1 Elemental composition of CP. Elements in CP
Weight fraction (%)
Hydrogen Carbon Oxygen Lead NB Total
10.9 75.6 5.7 2.0 5.8 100.0
Fig. 4. Schematic of the HDPE container.
Fig. 3. Schematic of the shielding container for optimization of fillers in polymer.
The mathematical model that represents the overall response yijk is given below.
yijk = µ + riL i + rjBj + rijL i Bj +
ijk
(1)
where i (1, 2, ...6) and j (1, 2, ...6) determines the possible levels of lead and NB, and k (1, 2) is the simulation replication times. µ is the mean value of TDR of the 36 observations, Li and Bj represents the main effects due to the change in concentration of lead and NB, LiBj represents the interaction effect of lead and NB, ri and rj are the linear coefficients for Li and Bj respectively, rij is the interaction coefficient for the combined effect due to Li and Bj, and ijk is a random error term. The mean values due to the change in the levels of lead and NB are computed using the expressions (2), (3), (4), and (5) wherein yi..denote
Fig. 5. Schematic of the CP container.
the total of all the observations under the ith level of the factor L, y.j. denote the total of all the observations under the jth level of the factor B, yij. denote the total of all the observations of the ijth elements, y… 3
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Fig. 6. Gamma spectrum of Table 2 Major gamma lines and intensity of 37 GBq
241
Am-Be source obtained with HPGe detector. Table 3 Elemental composition of OCP.
241
Am-Be source.
Gamma energy (keV)
Photon emission rate (γ/s)
Relative intensity
Elements in OCP
Weight fraction (%)
59.54 98.97 102.98 125.30 146.55 208.01 511.00 662.40 Total
1.71E+09 1.74E+07 1.68E+07 4.18E+06 5.77E+05 1.41E+06 3.96E+06 8.34E+05 1.76E+09
0.9740 0.0099 0.0096 0.0024 0.0004 0.0008 0.0023 0.0005 1.0000
Hydrogen Carbon Oxygen Lead NB Total
11.2 76.9 5.9 5.0 1.0 100.0
yi.. =
yi.. bn
where yi.. =
y.j. =
n y k= 1 ijk ,
a i= 1
n y k= 1 ijk
i =1, 2, ……., a
y.j.
(3)
an
where y.j. =
yij. =
(2) b j= 1
, j =1, 2, ……., b
y...
(4)
n
where yij. =
n y , k= 1 ijk
i =1, 2, ……., a and j = 1, 2, ……., b
y y… = ... abn
(5) a i= 1
b j= 1
n y k= 1 ijk
where y… = Using the above expressions, we get
yi.. =
y.j. = Fig. 7. Computed TDR on shielding container for varying quantity of lead and NB in the polymer.
yij. =
denote the grand total of all the observations, a is the number of levels of factor L (a = 6), b is the number of levels of factor B (b = 6), n is the number of times each simulation is replicated (n = 2).
y… =
yi.. 12
y.j. 12 y... 2 y... 72
The total sum of squares is 4
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Table 4 ANOVA results based on computed TDRs. a C
Source of variation
SS
DOF
MS
F0,
L B Interaction (LB) Total (T) Error (E)
SSL = 2.81E+07 SSB = 9.92E+04 SSLB = 3.31E+04 SST = 2.82E+07 SSE = 3.00E+04
5 5 25 71 36
MSL = 5.62E+06 MSB = 1.98E+04 MSLB = 1.33E+03 MST = 3.98E+05 MSE = 8.32E+02
6.75E+03 2.38E+01 1.59E+00 NAc NA
a b c
Distance between source and detector (cm)
NDR (mSv/h)
25 50 75 100 150
1.80 0.49 0.25 0.14 0.06
a
b
n
Am-Be source.
MCS (C) ± ± ± ± ±
C/E Experiment (E)
1.08E-02a 5.88E-03 1.50E-03 8.40E-04 3.70E-04
1.66 0.48 0.27 0.14 0.07
± ± ± ± ±
0.33 0.10 0.05 0.03 0.01
1.08 1.02 0.92 1.00 0.86
y …2
y 2ijk
72
i= 1 j= 1 k= 1
(6)
The sum of squares (SS) for the main effects is
SSL =
SSB =
1 12 1 12
SSST =
1 2
a
y …2
y 2i..
i= 1 b
C
/ F0,
T
2.72E+03 9.60E+00 8.74E-01
a
b
MCSs are carried out to study the shielding effectiveness of HDPE, CP, and OCP. It is assumed that a 740 GBq 241Am-Be source is placed inside an air cavity of a cylindrical container of shielding thickness 20 cm. The cavity of the container has diameter of 7 cm and length of 14 cm. HDPE, CP, and OCP are chosen as the shielding media of the container. The shielding efficacy is evaluated based on the computed TDR on the surface of the containers. IAEA transport regulations stipulates that the maximum permissible surface dose rate on consignment is 2 mSv/h. MCSs are carried out to estimate the shielding thickness required for HDPE, CP, and OCP to restrict the TDR within the permissible level.
y …2
2 y .j.
72
j= 1
y 2ij.
i= 1 j= 1
SSLB = SSST
(8)
y …2 72
(9)
SSL
(10)
SSB
The SS for the error is
SSE = SS T
SSL
SSB
(11)
SSLB
The mean sum of squares (MS) viz., MSL , MSB , MSLB , and MSE are obtained by dividing the respective SS given in equations (7), (8), (10) and (11) with the degrees of freedom (DOF). The F0 values are obtained by dividing each of the mean sum of squares (MSL , MSB , and MSLB ) with the mean sum of square error MSE .
3. Results and discussions 3.1. Gamma spectrometry analysis The gamma spectrum of a 37 GBq 241Am-Be source obtained with HPGe detector is shown in Fig. 6. The energy range of the gamma spectrum is 40 keV–3201 keV. The energy and abundance of the L X-ray emitted by 241Am is 59.54 keV and 35.9% respectively. The other gamma lines such as 98.97 keV, 102.98 keV, 125.30 keV, 146.55 keV,
2.6. Validation experiments Three validation experiments with neutron source and shields are Table 6 Computed and measured NDRs and GDRs on HDPE and CP containers with Shielding medium
HDPEa CPb
c
2.48E+00 2.48E+00 1.82E+00 NA NA
F0,
2.7. Shielding efficacy of HDPE, CP, and OCP and design of transport container
(7)
72
The SS for the interaction effect between lead and NB is
b
b
performed. NDR is measured using Wedholm make Digipig neutron monitor (222A) and GDR is measured using Automess make universal radiation meter (6150AD). In the first experiment, NDR in air is measured at various distances for a 185 GBq 241Am-Be source. In the second experiment, a 37 GBq 241Am-Be source is housed in a HDPE container of height 47 cm and thickness 15 cm. The cavity of the container has diameter of 5 cm, length of 7 cm, and it is lined with 0.5 cm thick mild steel. The outer surface of the container is lined with 3 cm of mild steel. The schematic of the HDPE container is shown in Fig. 4. In the third experiment, a 185 GBq 241Am-Be source is housed in a CP container of height 79.5 cm and thickness 24 cm. The cavity of the container has diameter of 6 cm and length of 13 cm. The cavity as well as the outer surface of the container is lined with 0.5 cm mild steel. The schematic of the CP container is shown in Fig. 5. MCS is performed by simulating the experimental arrangement and the dose rates are computed at the locations for which measured values are available.
241
At 2σ confidence level.
SS T =
a
T
From calculation. From F distribution table for α (significance level) = 0.05. NA – Not applicable.
Table 5 Computed and measured NDRs in air for 185 GBq
a
F0,
241
Am-Be source.
NDR (μSv/h)
Ratio
GDR (μSv/h)
Ratio
MCS (C)
Experiment (E)
C/E
MCS (C)
Experiment (E)
C/E
21.06 ± 0.10c 97.50 ± 0.20
20.00 ± 4.00 99.10 ± 19.82
1.05 0.98
7.00 ± 0.01 41.80 ± 0.10
8.00 ± 1.20 40.20 ± 6.03
0.88 1.04
37 GBq 185 GBq At 2σ confidence level. 5
Radiation Physics and Chemistry 170 (2020) 108670
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Fig. 9. Ratio of NDRs and GDRs for OCP relative to HDPE and CP.
on the surface of the shielding container. Similarly, with 1% of NB, the increase of quantity of lead from 1% to 5% increases the NDR by 10% but the GDR decreases by 83%. When the quantity of lead is increased from 5% to 6%, a marginal reduction in the TDR of about 2% is observed. Hence, the optimization study reveals that the quantity of lead above 5% is not very effective in reducing the TDR. Hence, a polymer with quantity of lead of 5% and NB of 1% is observed to give the optimized composition. The elemental composition of OCP is given in Table 3. 3.3. Factorial design analysis (FDA) The 6 × 6 FDA data matrix analyzed with ANOVA at 95% confidence level for the significance of the main effects due to the change in the quantity of lead and quantity of NB and their combined effect is shown in Table 4. The estimated value of F0.05, 5, 36 for lead and NB is higher than the table value by a factor of 2720 and 9.6 respectively. The variation in the concentration of lead is observed to be more significant. The estimated value of F0.05, 25, 36 for the combined effect of lead and NB is lower than the table value by 13.6%, which indicates that the interaction effect is statistically insignificant at 95% confidence level. The validity of choosing Eq. (1) for the present FDA is checked by computing the coefficient of determination (R2 ). The coefficient enables us to examine the correlation between the simulation and the predicted responses. The R2 value is always between 0 and 1 and the estimates of the models are acceptable if R2 is closer to 1 (Elhalil et al., 2016). In the present work, the R2 value obtained is 0.9989 which represents that about 99.89% of the variability of the response can be described by the chosen expression.
Fig. 8. Computed (A) NDRs and (B) GDRs at various thicknesses of HDPE, CP, and OCP.
208.01 keV, 511.0 keV, and 662.40 keV have abundance in the range from 3.65E-04% to 2.03E-02%. The spectral details deduced from the measurements are given in Table 2. The major gamma line is observed to be the 59.54 keV with relative intensity of 97.4%.
3.4. Validation experiments
3.2. Optimization of concentration of lead and natural boron fillers in polymer
The computed (C) and experimental measurements (E) of NDRs at several distances from a 185 GBq 241Am-Be source in air is given in Table 5. The C/E ratios observe to vary between 0.86 and 1.08. The computed dose rates are in good agreement with the measured values and the variations are found to be within the fluctuations associated with the measurements. The computed and experimental measurements of NDRs and GDRs on the surface of HDPE and CP containers are given in Table 6. For HDPE container, the C/E ratio is 1.05 and 0.88 for NDR and GDR respectively. Similarly, for CP container, the C/E ratio is 0.98 and 1.04 for NDR and GDR respectively. It is observed that the computed dose rates are in good agreement with the measured values.
Fig. 7 shows the computed TDRs for different quantity of lead and NB. As the concentration of lead and NB increases in the polymer, the concentration of other elements such as hydrogen, carbon, and oxygen are proportionally decreased to maintain the shield density at 1010 kg/ m3. Therefore, the change in the concentration of hydrogen in the polymer results in the reduced moderation of the fast neutrons. Irrespective of the quantity of lead, increase in the quantity of NB from 1% to 6% results in the increase of NDR by 7%. However, the GDR remains the same. Therefore, NB concentration of 1% gives the minimum TDR 6
Radiation Physics and Chemistry 170 (2020) 108670
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Table 7 Computed radiation level on the surface of the shielding containers of thickness 20 cm for 740 GBq Source of radiation
Neutron 12 C* de excitation gamma 241 Am gamma Capture gamma Total gamma Total (neutron + gamma) a
241
Am-Be source.
Dose rate (μSv/h)
Ratio
Shielding materials
(1)/(2)
(1)/(3)
1.01 0.97 0.11 0.99 0.22 0.63
1.29 1.12 0.10 0.28 0.20 0.67
OCP (1)
CP (2)
HDPE (3)
1881.5 ± 10.2a 167.2 ± 2.2 171.6 ± 6.4 39.5 ± 0.1 378.3 ± 6.8 2259.8 ± 12.2
1864.6 ± 10.0 173.2 ± 2.2 1511.0 ± 55.9 40.1 ± 0.2 1724.3 ± 55.9 3588.9 ± 56.8
1455.0 ± 9.0 149.1 ± 1.9 1637.0 ± 60.7 139.6 ± 0.4 1925.7 ± 60.7 3380.7 ± 61.4
At 2σ confidence level.
Table 8 Computed radiation level on the surface of the shielding containers with 740 GBq Source of radiation
241
Am-Be source.
Dose rate (μSv/h) Thickness (cm), volume (m3), and mass (kg) of the shielding materials
Neutron C* de excitation gamma 241 Am gamma Capture gamma Total gamma Total (neutron + gamma) 12
a
OCP (20.5, 0.09, and 93.8)
CP (23, 0.12, and 126)
HDPE (23, 0.12, and 115)
1648.9 ± 26.4a 158.9 ± 2.1 143.6 ± 4.5 35.4 ± 0.4 337.9 ± 5.0 1986.9 ± 26.9
1066.6 ± 18.2 130.1 ± 1.7 714.3 ± 26.4 29.7 ± 0.3 874.1 ± 26.4 1940.7 ± 32.1
809.9 ± 16.2 108.9 ± 1.4 783.9 ± 29.0 111.0 ± 0.9 1003.8 ± 29.0 1813.7 ± 33.2
At 2σ confidence level.
3.5. Shielding efficacy of HDPE, CP, and OCP and design of transport container
to be 45%, 55%, and 83% respectively. Similarly, the ratio of GDR to TDR for HDPE, CP, and OCP containers is observed to be 55%, 45%, and 17% respectively. The volume of OCP container is lower than both HDPE and CP containers by 25%. The mass of the OCP container is lower than HDPE and CP containers by 18% and 26% respectively.
The computed NDRs and GDRs for different shielding thicknesses of HDPE, CP, and OCP are shown in Fig. 8. The computed NDRs for all the three shielding media are nearly the same for thickness up to 7.5 cm. Thereafter, the computed NDRs for HDPE is lower compared to CP and OCP and the difference increases with increase in the thickness of the shield. The computed GDRs remains same for all the shield media up to 2.5 cm and thereafter, the computed GDRs for OCP is lower compared to HDPE and CP. The ratios of NDRs and GDRs for OCP/HDPE as well as OCP/CP are shown in Fig. 9. The ratio of NDR for OCP/HDPE for thickness of 20 cm is 1.26 and the similar value for OCP/CP is 1.02. It is observed that HDPE provides better neutron shielding compared to OCP. The neutron shielding effectiveness of OCP and CP is observed to be nearly the same. Similarly, the ratio of GDR for OCP/HDPE and OCP/CP for shielding thickness of 20 cm is 0.65 and 0.63 respectively. Hence, OCP provides better gamma shielding compared to both HDPE and CP. The computed NDRs and the GDRs on the surface of the container of shielding thickness 20 cm from various sources of radiation for 740 GBq 241Am-Be source is given in Table 7. NDR on the surface of the HDPE container is lower by a factor of 1.3 compared to OCP container and the GDR of the HDPE container is higher by a factor of 5.1 compared to OCP container. The NDR of CP and OCP containers is observed to be nearly the same. However, the GDR of CP container is higher by a factor 4.6 compared to OCP container. The computed TDR for OCP container is lower by a factor of 1.5 and 1.6 compared to HDPE and CP containers respectively. The shielding thickness required for the three materials to restrict the surface TDR of the container within 2 mSv/h for 740 GBq 241Am-Be source is given in Table 8. For the thickness of 23 cm of HDPE and CP, the computed TDR on the surface of the containers is about 1814 μSv/h and 1941 μSv/h respectively. However, in case of OCP, the required shielding thickness is 20.5 cm and the computed TDR is 1987 μSv/h. The ratio of NDR to TDR for HDPE, CP, and OCP containers is observed
4. Summary and conclusions Compact shielding design of a transport container for a 740 GBq portable 241Am-Be neutron source with OCP is carried out using MCS. OCP is obtained by optimizing the concentration of lead and NB fillers in the host polymer. The computed TDR on the surface of the shielding container is considered as the criterion for optimization. All the neutron and gamma radiations due to source and shield are considered in the computation. The optimization study shows that 5% of lead and 1% of NB serves as the best concentration of the fillers in the host polymer. FDA technique is performed to examine the effect of lead and NB fillers in the polymer. Thirty six simulation runs are performed by changing the quantity of lead and NB from 1% to 6% in steps of 1% and each simulation run is replicated for two times to investigate the factorial effects. FDA indicate that the presence of lead in the polymer has more significant impact than NB and the interaction effect between the fillers is found to be statistically insignificant at 95% confidence level. MCS results are validated by experimental measurements with HDPE and CP containers. The C/E values of dose rate for neutron and gamma radiations vary by a factor of 0.86–1.08 and 0.88–1.04 respectively. The computed TDR on the surface of the shielding container of thickness 20 cm made of HDPE, CP, and OCP with 740 GBq 241Am-Be source is 3381 μSv/h, 3589 μSv/h, and 2260 μSv/h respectively. Although, HDPE is found to be most suitable in attenuating neutrons but OCP is observed to be a better shield for both neutrons as well as gammas. Using OCP, a compact shielding container is designed with 25% reduction in the volume and a minimum of 18% reduction in the mass compared to the shielding containers made of HDPE and CP. 7
Radiation Physics and Chemistry 170 (2020) 108670
P. Basu, et al.
CRediT authorship contribution statement
SAND 2014-16188. Gomaa, M.A., Henaish, B.A., Ali, E.M., 1993. Calculated neutron and gamma dose rates around a moderated Am-Be neutron source. Appl. Radiat. Isot. 44 (3), 638–640. Hayashi, T., Tobita, K., Nishio, S., 2006. Neutronics assessment of advanced shield materials using metal hydride and borohydride for fusion reactors. Fusion Eng. Des. 81, 1285–1290. Hussein, E.M.A., O'Connor, D.R., Mosher, M.E., 1987. A non-intrusive neutron method for poison concentration monitoring in CANDU reactors. Nucl. J. Canada 1 (1), 46–52. IAEA Safety Standards Series No SSR-6, 2018. Regulations for the Safe Transport of Radioactive Material. Specific Safety Requirements. International Atomic Energy Agency, Vienna. Jafari, H., Feghhi, S.A.H., 2012. Design and simulation of neutron radiography system based on 241Am–Be source. Radiat. Phys. Chem. 81, 506–511. Jonah, S.A., Zakari, I.I., Elegba, S.B., 1999. Determination of the hydrogen content of oil samples from Nigeria using an Am-Be neutron source. Appl. Radiat. Isot. 50, 981–983. Korkut, T., Karabulut, A., 2010. Investigation of fast neutron shielding characteristics depending on boron percentages of MgB2, NaBH4 and KBH4. J. Radioanal. Nucl. Chem. 286 (1), 61–65. Liu, Z., Chen, J., Zhu, P., Li, Y., Zhang, G., 2007. The 4.438 MeV gamma to neutron ratio for the Am–Be neutron source. Appl. Radiat. Isot. 65, 1318–1321. Moadab, N.H., Saadi, M.K., 2019. Optimization of an Am-Be neutron source shield design by advanced materials using MCNP code. Radiat. Phys. Chem. 158, 109–114. Montgomery, D.C., 1997. Design and Analysis of Experiments, fourth ed. John Wiley & Sons. Murata, I., Tsuda, I., Nakamura, R., Shoko, N., Masao, M., Hiroyuki, M., 2014. Neutron and gamma-ray source-term characterization of AmBe sources in Osaka University. Prog. Nucl. Sci. Technol. 4, 345–348. Naqvi, A.A., Nagadi, M.M., 2004. Performance comparison of a 241Am-Be neutron sourcebased PGNAA setup with the KFUPM PGNAA setup. J. Radioanal. Nucl. Chem. 260, 641–646. Nasrabadi, M.N., Baghban, G., 2013. Neutron shielding design for 241Am–Be neutron source considering different sites to achieve maximum thermal and fast neutron flux using MCNPX code. Ann. Nucl. Energy 59, 47–52. NCRP-38, 1971. NCRP Scientific Committee 4 on Heavy Particles, H. H. Rossi. Protection against Neutron Radiation. National Council on Radiation Protection and Measurements. Tousi, E.T., Kardani, H., Firuzabadi, M.M., Jaafar, M.S., Aljarrah, A.M., Ghasemi, L., Khaniabadi, P.M., Amin, Y.A., 2014. Shielding design for an Am-Be neutron source using MCNP4C code and real dosimetry. Casp. J. Appl. Sci. Res. 3 (4), 13–22. Venkataraman, G., Dayashankar, Jayakar, J.S., 1970. The gamma to neutron ratios for PuBe and Am-Be neutron sources. Nucl. Instrum. Methods 82, 49–50. Wu, C.F.J., Hamada, M., 2009. Experiments: Planning, Analysis and Parameter Design Optimization, second ed. Wiley, New York. Zhang, F., Wu, H., Xinguang, W., Guoli, W., Wenbao, J., Yongzhou, T., 2017. Compact shielding design of a portable 241Am–Be source. Appl. Radiat. Isot. 128, 49–54.
Pew Basu: Formal analysis. R. Sarangapani: Writing - review & editing. B. Venkatraman: Supervision, Writing - review & editing. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors thank Shri S. Viswanathan, RESD, IGCAR, Dr. T. K. Srinivasan, and Shri K. Bajeer Sultan, HISD, IGCAR for their valuable support during experiments. Authors are thankful to Dr. D. Datta, Head, RPAD, BARC for his valuable suggestions in carrying out the work. Authors are thankful to Dr. R. Venkatesan, Head, RESD, IGCAR and Dr. V. Subramanian, Head, RAMS, RESD, IGCAR for their support in carrying out the work. References Anderson, L.V., McLean, A.R., 1974. Design of Experiments: A Realistic Approach, vol. 5 Marcel Dekker Inc. ANSI/ANS-6.1.1, 1977. ANS-6.1.1 Working Group, M. E. Battat. American National Standard Neutron and Gamma Ray Flux to Dose Rate Factors. American Nuclear Society, La Grange Park, Illinois. Briesmeister, J.F., 1997. A General Monte Carlo N-Particle Transport Code, Version 4A. ORNL RSICC-CCC-200. Celenk, I., 2001. Determination of cumulative yields of fission products from 238U by 5.0 MeV neutrons. Radiochim. Acta 89 (8), 481–484. Elhalil, A., Tounsadi, H., Elmoubarki, R., Mahjoubi, F.Z., Farnane, M., Sadiqa, M., Abdennouri, M., Qourzal, S., Barka, N., 2016. Factorial experimental design for the optimization of catalytic degradation of malachite green dye in aqueous solution by Fenton process. Water Resour. Ind. 15, 41–48. Fantidis, J.G., 2015. The comparison between simple and advanced shielding materials for the shield of portable neutron sources. Int. J. Radiat. Res. 13 (4), 287. Franco Jr., M., 2014. Characterization of the Neutron Irradiation System for Use in the Low-Dose-Rate Irradiation Facility at Sandia National Laboratories. Sandia Report.
8
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Compact shielding design for 740 GBq container
241
Am-Be neutron source transport
T
Pew Basua,b,∗, R. Sarangapania, B. Venkatramana,b a b
Safety, Quality & Resource Management Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamilnadu, 603102, India Homi Bhabha National Institute, Kalpakkam, Tamilnadu, 603102, India
ARTICLE INFO
ABSTRACT
Keywords: 241 Am-Be source Composite polymer Factorial design analysis Gamma spectrometry Monte Carlo technique Shielding design
For transport and storage of neutron sources, shielding materials like polymers and multi layer shields are used. A compact shielding design for 740 GBq portable 241Am-Be neutron source transport container using Monte Carlo technique is presented. In the design, a polymer host material with lead and natural boron (NB) as fillers is chosen as the shielding medium. Monte Carlo simulation (MCS) is performed for optimizing the quantity of fillers in the polymer. The total dose rate (TDR) on the surface of the container due to neutrons and gamma rays emanating from source as well as polymer shield, is considered as the optimization criterion. MCS studies indicate that a polymer material with 5% of lead and 1% of NB as fillers is observed to give optimized composition of polymer (OCP). Statistical factorial design analysis (FDA) technique is employed for the first time in the shielding design to investigate the impact of fillers in the polymer. FDA studies reveal that the quantity of lead has more significant impact compared to NB in the polymer. MCS results are validated by carrying out shielding experiments with high density polyethylene (HDPE) and composite polymer (CP) based containers. The computed and experimental dose rates are observed to be within ± 12%. A shielding container made of OCP for the transport of 740 GBq 241Am-Be source provides 25% reduction in the volume as compared to HDPE and CP. The mass of the OCP container is lower by 18% and 26% compared to the containers made of HDPE and CP respectively. The surface dose rate of the OCP container adheres to the IAEA transport regulations.
1. Introduction 241
Am-Be neutron source is used for a wide variety of applications such as neutron calibration of monitoring instruments and detectors (Venkataraman et al., 1970; Gomaa et al., 1993; Tousi et al., 2014), irradiation of samples (Franco, 2014), neutron imaging (Jafari and Feghhi, 2012), analysis of fission products (Celenk, 2001), prompt gamma neutron activation analysis (Naqvi and Nagadi, 2004), light element analysis via neutron reflection (Jonah et al., 1999), and on-line measurement of neutron poison related to fast neutron scattering (Hussein et al., 1987). The source is fabricated in the form of metallic alloy of americium (alpha particle emitter) and beryllium (target). By double sealing, the alloyed mixture is encapsulated to guard against the leakage of 241Am. Emission of neutrons from the source is accompanied by gamma rays from the excited carbon nuclei (Gomma et al., 1993) and both these radiations cause exposure to human and environment. Neutron shielding is generally achieved by reducing the energy of the fast neutrons by inelastic/elastic scattering and finally absorbing the slow neutrons. The absorption of slow neutrons in polyethylene,
∗
paraffin, or polymer which contains significant quantity of hydrogen produces high energy gamma rays due to capture reaction (Moadab and Saadi, 2019). Therefore, it is desirable to make a neutron source transport container with a blend of elements that can effectively handle both neutrons and gamma rays. Hayashi et al. (2006) showed that the use of Mg(BH4)2, TiH2, and ZrH2 instead of the conventional materials can reduce the thickness of the shield by 23%, 20%, and 19% respectively. Fantidis (2015) showed that use of the advanced shielding material can reduce the thickness, mass, and volume of the shield by 41.3%, 44%, and 78.4% respectively. Zhang et al., (2017) observed that to maintain a dose rate criterion of 0.025 mSv/h outside a paraffin shielded container for a portable 666 GBq 241Am–Be source, volume and weight of the container becomes 1.36 m3 and 1060 kg respectively. By providing double layer shielding with tungsten as moderator, the mass of the container is reduced by 54%. Moadab and Saadi (2019) showed that a lighter shield design with polyethylene (78.5%)–bismuth (11.5%) alloy results in a reduction of volume and mass of the shield by 49% and 67% respectively. A polymer with neutron absorber (boron, cadmium, gadolinium, and indium) and high density gamma attenuator
Corresponding author. Safety, Quality & Resource Management Group, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamilnadu, 603102, India. E-mail address: [email protected] (P. Basu).
https://doi.org/10.1016/j.radphyschem.2019.108670 Received 12 September 2019; Received in revised form 9 December 2019; Accepted 27 December 2019 Available online 29 December 2019 0969-806X/ © 2019 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 170 (2020) 108670
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(lead, bismuth, tungsten, and stainless steel) is likely to give optimized elemental composition for neutron shielding. The surface dose rate on the shielding container must adhere to the dose rates specified in IAEA transport regulations (IAEA Safety Standards Series No.SSR-6, 2018). In the present work, a compact shielding design of a container made of optimized composite polymer (OCP) for transporting 740 GBq 241 Am-Be neutron source is proposed. The elemental composition of OCP is obtained from Monte Carlo simulations (MCSs) by optimizing the quantity of lead and natural boron (NB) fillers in a polymer made of hydrogen, carbon, and oxygen. Factorial design analysis (FDA) technique is performed to analyze the impact of fillers in the polymer. FDA is generally used to examine the effect of two or more independent factors, each with discrete possible levels upon a single dependent response (Anderson and McLean, 1974; Montgomery, 1997). The effect of a factor is obtained as the change in the response produced by varying the levels of the factor (Wu and Hamada, 2009). MCS results are validated by carrying out experiments with high density polyethylene (HDPE) and composite polymer (CP) containers. Studies on the shielding effectiveness of OCP vis-à-vis HDPE and CP containers and advantages of shielding design with OCP are presented.
to the (n, γ) reaction with the hydrogen present in the shielding material is included in the MCS by choosing the photon production option from the neutron collision event. 2.2. Details of shielding materials HDPE is a polymer of density 920 kg/m3 produced from the ethylene monomer. The elemental composition of CP is hydrogen, carbon, and oxygen with lead and NB as fillers and the density of CP is 1010 kg/m3. The weight fraction of the elements in CP is given in Table 1. The inclusion of NB as a filler is considered for the thermal neutron absorption (Korkut and Karabulut, 2010). The hydrogen present in the polymer acts as a very good moderator and thereby making easy absorption of the slow neutrons by 10B (20% in NB). Lead acts as a good in-situ attenuator for the gamma rays emitted from the source and the shield. 2.3. Monte Carlo simulation (MCS) Computation of neutron dose rates (NDRs) and gamma dose rates (GDRs) is carried out using MCNP code (Briesmeister, 1997). The fluence rate φ(r, E) on the surface of the shield at position ‘r’ and of radiation energy ‘E’ is obtained using the ring detector tally. To get the computed dose rate D(r) at position ‘r’, φ(r, E) is multiplied with the flux to dose rate conversion factor R(E) for energy ‘E’. R(E) values are obtained from NCRP-38, 1971 and ANSI/ANS-6.1.1, 1977 for neutrons and gamma rays respectively. Finally, the dose rate obtained for each energy interval is summed to get NDRs and GDRs. In MCS, the number of particles tracked is varied from 1.0E+06 to 1.0E+07. The computed dose rates passed all the mandatory statistical tests outlined in the manual with a maximum relative error of 2%. In modelling the shield, geometry splitting technique (GST) is used. The shield thickness is sliced into a number of smaller sections based on the estimated half value layer (HVL) of the material. Incorporation of GST increases the population of particles in the favourable regions with appropriate normalization of weights to provide better sampling and thereby reducing the variance.
2. Materials and methods 2.1. Sources of radiation 241
Am-Be source emits neutrons of energy in the range of 1–11 MeV as a continuous spectrum due to (α, n) reaction with an average energy of 4.4 MeV. The normalized neutron spectrum of 241Am-Be source is shown in Fig. 1 (Zhang et al., 2017; Nasrabadi and Baghban, 2013). The total neutron yield from a 740 GBq 241Am-Be source is 4.4E+07 n/s. The gamma rays of 4.43 MeV are emitted during the de-excitation of the 12C* nucleus as a result of (α, 9Be) reaction and the γ/n ratio vary from 0.38 to 0.75 (Moadab and Saadi; Venkataraman et al., 1970; Liu et al., 2007; Murata et al., 2014). As a conservative approximation, γ/n ratio of 0.75 is assumed in the present work which corresponds to source strength of 3.3E+07 γ/s for 4.43 MeV gamma ray. The gamma rays emitted from the source due to the decay of 241Am is quantified by gamma spectrometry using a portable HPGe detector connected to ORION@ make MCA and Inter-winner@ spectrum acquisition software. The schematic of the experimental set up is shown in Fig. 2. The sides of the detector are shielded by lead rings of annular thickness 5 cm. A lead collimator of thickness 5 cm with an orifice of 0.5 cm is placed in front of the detector. The detector is calibrated with 241Am and 152Eu standard sources. The capture gamma rays of energy 2.2 MeV emitted due
2.4. Optimization of concentration of lead and natural boron fillers in polymer MCS is performed for optimizing the quantity of lead and NB fillers in polymer. A 740 GBq 241Am-Be source is assumed at the centre of the air cavity in a shielding container of thickness 20 cm. The cavity of the container has diameter of 7 cm and length of 14 cm. The shielding thickness of the container is sliced into five equal sections and GST is applied. All the components of radiations emanating from the source and the polymer are considered. The TDRs are computed on the surface of the container along the mid plane by varying the quantity of lead and NB each from 1% to 6% in steps of 1%. The weight percent of host elements is suitably adjusted to keep the density of the shield at 1010 kg/m3. The computed TDR is used as the criterion during the optimization of elemental composition. The schematic of the sourceshield model considered for the optimization of elemental composition is shown in Fig. 3. 2.5. Factorial design analysis (FDA) technique
Fig. 1.
In the present work, lead weight percent (L) and NB weight percent (B) in the polymer are considered as two independent factors in the FDA technique. By varying the quantity of lead and NB from 1% to 6% in steps of 1%, six discrete levels of each factor is proposed and the response based on the computed TDR for 36 compositions is analysed. A 6 × 6 FDA input matrix is constructed from the data to investigate the effect of lead, NB, and their interaction using analysis of variance (ANOVA).
241
Am-Be neutron energy spectrum. 2
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Fig. 2. Schematic of the gamma spectrometry experimental set up. Table 1 Elemental composition of CP. Elements in CP
Weight fraction (%)
Hydrogen Carbon Oxygen Lead NB Total
10.9 75.6 5.7 2.0 5.8 100.0
Fig. 4. Schematic of the HDPE container.
Fig. 3. Schematic of the shielding container for optimization of fillers in polymer.
The mathematical model that represents the overall response yijk is given below.
yijk = µ + riL i + rjBj + rijL i Bj +
ijk
(1)
where i (1, 2, ...6) and j (1, 2, ...6) determines the possible levels of lead and NB, and k (1, 2) is the simulation replication times. µ is the mean value of TDR of the 36 observations, Li and Bj represents the main effects due to the change in concentration of lead and NB, LiBj represents the interaction effect of lead and NB, ri and rj are the linear coefficients for Li and Bj respectively, rij is the interaction coefficient for the combined effect due to Li and Bj, and ijk is a random error term. The mean values due to the change in the levels of lead and NB are computed using the expressions (2), (3), (4), and (5) wherein yi..denote
Fig. 5. Schematic of the CP container.
the total of all the observations under the ith level of the factor L, y.j. denote the total of all the observations under the jth level of the factor B, yij. denote the total of all the observations of the ijth elements, y… 3
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Fig. 6. Gamma spectrum of Table 2 Major gamma lines and intensity of 37 GBq
241
Am-Be source obtained with HPGe detector. Table 3 Elemental composition of OCP.
241
Am-Be source.
Gamma energy (keV)
Photon emission rate (γ/s)
Relative intensity
Elements in OCP
Weight fraction (%)
59.54 98.97 102.98 125.30 146.55 208.01 511.00 662.40 Total
1.71E+09 1.74E+07 1.68E+07 4.18E+06 5.77E+05 1.41E+06 3.96E+06 8.34E+05 1.76E+09
0.9740 0.0099 0.0096 0.0024 0.0004 0.0008 0.0023 0.0005 1.0000
Hydrogen Carbon Oxygen Lead NB Total
11.2 76.9 5.9 5.0 1.0 100.0
yi.. =
yi.. bn
where yi.. =
y.j. =
n y k= 1 ijk ,
a i= 1
n y k= 1 ijk
i =1, 2, ……., a
y.j.
(3)
an
where y.j. =
yij. =
(2) b j= 1
, j =1, 2, ……., b
y...
(4)
n
where yij. =
n y , k= 1 ijk
i =1, 2, ……., a and j = 1, 2, ……., b
y y… = ... abn
(5) a i= 1
b j= 1
n y k= 1 ijk
where y… = Using the above expressions, we get
yi.. =
y.j. = Fig. 7. Computed TDR on shielding container for varying quantity of lead and NB in the polymer.
yij. =
denote the grand total of all the observations, a is the number of levels of factor L (a = 6), b is the number of levels of factor B (b = 6), n is the number of times each simulation is replicated (n = 2).
y… =
yi.. 12
y.j. 12 y... 2 y... 72
The total sum of squares is 4
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Table 4 ANOVA results based on computed TDRs. a C
Source of variation
SS
DOF
MS
F0,
L B Interaction (LB) Total (T) Error (E)
SSL = 2.81E+07 SSB = 9.92E+04 SSLB = 3.31E+04 SST = 2.82E+07 SSE = 3.00E+04
5 5 25 71 36
MSL = 5.62E+06 MSB = 1.98E+04 MSLB = 1.33E+03 MST = 3.98E+05 MSE = 8.32E+02
6.75E+03 2.38E+01 1.59E+00 NAc NA
a b c
Distance between source and detector (cm)
NDR (mSv/h)
25 50 75 100 150
1.80 0.49 0.25 0.14 0.06
a
b
n
Am-Be source.
MCS (C) ± ± ± ± ±
C/E Experiment (E)
1.08E-02a 5.88E-03 1.50E-03 8.40E-04 3.70E-04
1.66 0.48 0.27 0.14 0.07
± ± ± ± ±
0.33 0.10 0.05 0.03 0.01
1.08 1.02 0.92 1.00 0.86
y …2
y 2ijk
72
i= 1 j= 1 k= 1
(6)
The sum of squares (SS) for the main effects is
SSL =
SSB =
1 12 1 12
SSST =
1 2
a
y …2
y 2i..
i= 1 b
C
/ F0,
T
2.72E+03 9.60E+00 8.74E-01
a
b
MCSs are carried out to study the shielding effectiveness of HDPE, CP, and OCP. It is assumed that a 740 GBq 241Am-Be source is placed inside an air cavity of a cylindrical container of shielding thickness 20 cm. The cavity of the container has diameter of 7 cm and length of 14 cm. HDPE, CP, and OCP are chosen as the shielding media of the container. The shielding efficacy is evaluated based on the computed TDR on the surface of the containers. IAEA transport regulations stipulates that the maximum permissible surface dose rate on consignment is 2 mSv/h. MCSs are carried out to estimate the shielding thickness required for HDPE, CP, and OCP to restrict the TDR within the permissible level.
y …2
2 y .j.
72
j= 1
y 2ij.
i= 1 j= 1
SSLB = SSST
(8)
y …2 72
(9)
SSL
(10)
SSB
The SS for the error is
SSE = SS T
SSL
SSB
(11)
SSLB
The mean sum of squares (MS) viz., MSL , MSB , MSLB , and MSE are obtained by dividing the respective SS given in equations (7), (8), (10) and (11) with the degrees of freedom (DOF). The F0 values are obtained by dividing each of the mean sum of squares (MSL , MSB , and MSLB ) with the mean sum of square error MSE .
3. Results and discussions 3.1. Gamma spectrometry analysis The gamma spectrum of a 37 GBq 241Am-Be source obtained with HPGe detector is shown in Fig. 6. The energy range of the gamma spectrum is 40 keV–3201 keV. The energy and abundance of the L X-ray emitted by 241Am is 59.54 keV and 35.9% respectively. The other gamma lines such as 98.97 keV, 102.98 keV, 125.30 keV, 146.55 keV,
2.6. Validation experiments Three validation experiments with neutron source and shields are Table 6 Computed and measured NDRs and GDRs on HDPE and CP containers with Shielding medium
HDPEa CPb
c
2.48E+00 2.48E+00 1.82E+00 NA NA
F0,
2.7. Shielding efficacy of HDPE, CP, and OCP and design of transport container
(7)
72
The SS for the interaction effect between lead and NB is
b
b
performed. NDR is measured using Wedholm make Digipig neutron monitor (222A) and GDR is measured using Automess make universal radiation meter (6150AD). In the first experiment, NDR in air is measured at various distances for a 185 GBq 241Am-Be source. In the second experiment, a 37 GBq 241Am-Be source is housed in a HDPE container of height 47 cm and thickness 15 cm. The cavity of the container has diameter of 5 cm, length of 7 cm, and it is lined with 0.5 cm thick mild steel. The outer surface of the container is lined with 3 cm of mild steel. The schematic of the HDPE container is shown in Fig. 4. In the third experiment, a 185 GBq 241Am-Be source is housed in a CP container of height 79.5 cm and thickness 24 cm. The cavity of the container has diameter of 6 cm and length of 13 cm. The cavity as well as the outer surface of the container is lined with 0.5 cm mild steel. The schematic of the CP container is shown in Fig. 5. MCS is performed by simulating the experimental arrangement and the dose rates are computed at the locations for which measured values are available.
241
At 2σ confidence level.
SS T =
a
T
From calculation. From F distribution table for α (significance level) = 0.05. NA – Not applicable.
Table 5 Computed and measured NDRs in air for 185 GBq
a
F0,
241
Am-Be source.
NDR (μSv/h)
Ratio
GDR (μSv/h)
Ratio
MCS (C)
Experiment (E)
C/E
MCS (C)
Experiment (E)
C/E
21.06 ± 0.10c 97.50 ± 0.20
20.00 ± 4.00 99.10 ± 19.82
1.05 0.98
7.00 ± 0.01 41.80 ± 0.10
8.00 ± 1.20 40.20 ± 6.03
0.88 1.04
37 GBq 185 GBq At 2σ confidence level. 5
Radiation Physics and Chemistry 170 (2020) 108670
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Fig. 9. Ratio of NDRs and GDRs for OCP relative to HDPE and CP.
on the surface of the shielding container. Similarly, with 1% of NB, the increase of quantity of lead from 1% to 5% increases the NDR by 10% but the GDR decreases by 83%. When the quantity of lead is increased from 5% to 6%, a marginal reduction in the TDR of about 2% is observed. Hence, the optimization study reveals that the quantity of lead above 5% is not very effective in reducing the TDR. Hence, a polymer with quantity of lead of 5% and NB of 1% is observed to give the optimized composition. The elemental composition of OCP is given in Table 3. 3.3. Factorial design analysis (FDA) The 6 × 6 FDA data matrix analyzed with ANOVA at 95% confidence level for the significance of the main effects due to the change in the quantity of lead and quantity of NB and their combined effect is shown in Table 4. The estimated value of F0.05, 5, 36 for lead and NB is higher than the table value by a factor of 2720 and 9.6 respectively. The variation in the concentration of lead is observed to be more significant. The estimated value of F0.05, 25, 36 for the combined effect of lead and NB is lower than the table value by 13.6%, which indicates that the interaction effect is statistically insignificant at 95% confidence level. The validity of choosing Eq. (1) for the present FDA is checked by computing the coefficient of determination (R2 ). The coefficient enables us to examine the correlation between the simulation and the predicted responses. The R2 value is always between 0 and 1 and the estimates of the models are acceptable if R2 is closer to 1 (Elhalil et al., 2016). In the present work, the R2 value obtained is 0.9989 which represents that about 99.89% of the variability of the response can be described by the chosen expression.
Fig. 8. Computed (A) NDRs and (B) GDRs at various thicknesses of HDPE, CP, and OCP.
208.01 keV, 511.0 keV, and 662.40 keV have abundance in the range from 3.65E-04% to 2.03E-02%. The spectral details deduced from the measurements are given in Table 2. The major gamma line is observed to be the 59.54 keV with relative intensity of 97.4%.
3.4. Validation experiments
3.2. Optimization of concentration of lead and natural boron fillers in polymer
The computed (C) and experimental measurements (E) of NDRs at several distances from a 185 GBq 241Am-Be source in air is given in Table 5. The C/E ratios observe to vary between 0.86 and 1.08. The computed dose rates are in good agreement with the measured values and the variations are found to be within the fluctuations associated with the measurements. The computed and experimental measurements of NDRs and GDRs on the surface of HDPE and CP containers are given in Table 6. For HDPE container, the C/E ratio is 1.05 and 0.88 for NDR and GDR respectively. Similarly, for CP container, the C/E ratio is 0.98 and 1.04 for NDR and GDR respectively. It is observed that the computed dose rates are in good agreement with the measured values.
Fig. 7 shows the computed TDRs for different quantity of lead and NB. As the concentration of lead and NB increases in the polymer, the concentration of other elements such as hydrogen, carbon, and oxygen are proportionally decreased to maintain the shield density at 1010 kg/ m3. Therefore, the change in the concentration of hydrogen in the polymer results in the reduced moderation of the fast neutrons. Irrespective of the quantity of lead, increase in the quantity of NB from 1% to 6% results in the increase of NDR by 7%. However, the GDR remains the same. Therefore, NB concentration of 1% gives the minimum TDR 6
Radiation Physics and Chemistry 170 (2020) 108670
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Table 7 Computed radiation level on the surface of the shielding containers of thickness 20 cm for 740 GBq Source of radiation
Neutron 12 C* de excitation gamma 241 Am gamma Capture gamma Total gamma Total (neutron + gamma) a
241
Am-Be source.
Dose rate (μSv/h)
Ratio
Shielding materials
(1)/(2)
(1)/(3)
1.01 0.97 0.11 0.99 0.22 0.63
1.29 1.12 0.10 0.28 0.20 0.67
OCP (1)
CP (2)
HDPE (3)
1881.5 ± 10.2a 167.2 ± 2.2 171.6 ± 6.4 39.5 ± 0.1 378.3 ± 6.8 2259.8 ± 12.2
1864.6 ± 10.0 173.2 ± 2.2 1511.0 ± 55.9 40.1 ± 0.2 1724.3 ± 55.9 3588.9 ± 56.8
1455.0 ± 9.0 149.1 ± 1.9 1637.0 ± 60.7 139.6 ± 0.4 1925.7 ± 60.7 3380.7 ± 61.4
At 2σ confidence level.
Table 8 Computed radiation level on the surface of the shielding containers with 740 GBq Source of radiation
241
Am-Be source.
Dose rate (μSv/h) Thickness (cm), volume (m3), and mass (kg) of the shielding materials
Neutron C* de excitation gamma 241 Am gamma Capture gamma Total gamma Total (neutron + gamma) 12
a
OCP (20.5, 0.09, and 93.8)
CP (23, 0.12, and 126)
HDPE (23, 0.12, and 115)
1648.9 ± 26.4a 158.9 ± 2.1 143.6 ± 4.5 35.4 ± 0.4 337.9 ± 5.0 1986.9 ± 26.9
1066.6 ± 18.2 130.1 ± 1.7 714.3 ± 26.4 29.7 ± 0.3 874.1 ± 26.4 1940.7 ± 32.1
809.9 ± 16.2 108.9 ± 1.4 783.9 ± 29.0 111.0 ± 0.9 1003.8 ± 29.0 1813.7 ± 33.2
At 2σ confidence level.
3.5. Shielding efficacy of HDPE, CP, and OCP and design of transport container
to be 45%, 55%, and 83% respectively. Similarly, the ratio of GDR to TDR for HDPE, CP, and OCP containers is observed to be 55%, 45%, and 17% respectively. The volume of OCP container is lower than both HDPE and CP containers by 25%. The mass of the OCP container is lower than HDPE and CP containers by 18% and 26% respectively.
The computed NDRs and GDRs for different shielding thicknesses of HDPE, CP, and OCP are shown in Fig. 8. The computed NDRs for all the three shielding media are nearly the same for thickness up to 7.5 cm. Thereafter, the computed NDRs for HDPE is lower compared to CP and OCP and the difference increases with increase in the thickness of the shield. The computed GDRs remains same for all the shield media up to 2.5 cm and thereafter, the computed GDRs for OCP is lower compared to HDPE and CP. The ratios of NDRs and GDRs for OCP/HDPE as well as OCP/CP are shown in Fig. 9. The ratio of NDR for OCP/HDPE for thickness of 20 cm is 1.26 and the similar value for OCP/CP is 1.02. It is observed that HDPE provides better neutron shielding compared to OCP. The neutron shielding effectiveness of OCP and CP is observed to be nearly the same. Similarly, the ratio of GDR for OCP/HDPE and OCP/CP for shielding thickness of 20 cm is 0.65 and 0.63 respectively. Hence, OCP provides better gamma shielding compared to both HDPE and CP. The computed NDRs and the GDRs on the surface of the container of shielding thickness 20 cm from various sources of radiation for 740 GBq 241Am-Be source is given in Table 7. NDR on the surface of the HDPE container is lower by a factor of 1.3 compared to OCP container and the GDR of the HDPE container is higher by a factor of 5.1 compared to OCP container. The NDR of CP and OCP containers is observed to be nearly the same. However, the GDR of CP container is higher by a factor 4.6 compared to OCP container. The computed TDR for OCP container is lower by a factor of 1.5 and 1.6 compared to HDPE and CP containers respectively. The shielding thickness required for the three materials to restrict the surface TDR of the container within 2 mSv/h for 740 GBq 241Am-Be source is given in Table 8. For the thickness of 23 cm of HDPE and CP, the computed TDR on the surface of the containers is about 1814 μSv/h and 1941 μSv/h respectively. However, in case of OCP, the required shielding thickness is 20.5 cm and the computed TDR is 1987 μSv/h. The ratio of NDR to TDR for HDPE, CP, and OCP containers is observed
4. Summary and conclusions Compact shielding design of a transport container for a 740 GBq portable 241Am-Be neutron source with OCP is carried out using MCS. OCP is obtained by optimizing the concentration of lead and NB fillers in the host polymer. The computed TDR on the surface of the shielding container is considered as the criterion for optimization. All the neutron and gamma radiations due to source and shield are considered in the computation. The optimization study shows that 5% of lead and 1% of NB serves as the best concentration of the fillers in the host polymer. FDA technique is performed to examine the effect of lead and NB fillers in the polymer. Thirty six simulation runs are performed by changing the quantity of lead and NB from 1% to 6% in steps of 1% and each simulation run is replicated for two times to investigate the factorial effects. FDA indicate that the presence of lead in the polymer has more significant impact than NB and the interaction effect between the fillers is found to be statistically insignificant at 95% confidence level. MCS results are validated by experimental measurements with HDPE and CP containers. The C/E values of dose rate for neutron and gamma radiations vary by a factor of 0.86–1.08 and 0.88–1.04 respectively. The computed TDR on the surface of the shielding container of thickness 20 cm made of HDPE, CP, and OCP with 740 GBq 241Am-Be source is 3381 μSv/h, 3589 μSv/h, and 2260 μSv/h respectively. Although, HDPE is found to be most suitable in attenuating neutrons but OCP is observed to be a better shield for both neutrons as well as gammas. Using OCP, a compact shielding container is designed with 25% reduction in the volume and a minimum of 18% reduction in the mass compared to the shielding containers made of HDPE and CP. 7
Radiation Physics and Chemistry 170 (2020) 108670
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CRediT authorship contribution statement
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