Monte Carlo Simulation and Experimental Validation for Radiation Protection with Multiple Complex Source Terms and Deep Penetration for a Radioactive Liquid Waste Cementation Facility

A new radioactive liquid waste cementation facility was under commissioning recently in the Institute of Nuclear and New Energy Technology of Tsinghua University, which is designed to simultaneously process multiple intermediate-level radioactive waste drums. +erefore, the multiple volume sources and the scattering effect becomes a key issue in its radiation protection. For this purpose, the Monte Carlo program FLUKA code and experimental measurement were both adopted. In the FLUKA simulation, five different scenarios were considered, i.e., one drum, two drums, four drums, six drums, and eight drums. For the multiple volume sources, the source subroutine code of FLUKA was rewritten to realize the sampling.+e complex shielding also leads to a deep penetration problem; hence, the optimization algorithm and variance reduction techniques were adopted. During the measurement, two scenarios, outdoor and indoor, were carried out separately representing the dose field when only one drum is considered and when the scattering effect is considered. A comparison between the experiments and calculations shows very good agreement. From both of the Monte Carlo simulation and the experimental measurement, it can be drawn that, in the horizontal direction, with the increase of the drum number, the dose rate increases very little, while in the vertical direction, the increase of the dose rate is very obvious with the increase of the drum number. +e complicated source term sampling methods, the optimization algorithm and variance reduction techniques, and the experimental verification can provide valuable references for the similar scattering problem in radiation protection and shielding design.


Introduction
For a room with walls, roof, and other structures, when considering the dose from a gamma radiation source to the point of interest, if the scattering effect is ignored, the dose may be underestimated. In addition, when several radioactive sources exist, the total dose contribution of these radioactive sources to the point of interest should be considered. However, it will be extremely difficult to accurately predict the dose distribution when each gamma source is covered with multiple shielding layers so that the dose outside the shielding is very low.
In this work, the radiation protection of a radioactive liquid waste cementation facility is investigated, which meets the above scenario. is facility is located at the Institute of Nuclear and New Energy Technology (INET) [1] of Tsinghua University, China. e facility is a room for processing radioactive waste storage drums, with a sliding track and an iron shielding, as shown in Figure 1. In actual operation, there may be multiple intermediate-level radioactive waste (ILW) drums in the room. Every drum contains about 2E10 Bq of Cs-137, and the surface dose rate for one drum may exceed 3 mSv/h [2]. ese drums will be placed on the sliding track. Although there is an iron shielding of 12 cm thickness which can be remotely controlled to move up and down, from Figure 1(a), it can be seen that when multiple drums exist behind the shielding, the photons reflected by the roof to the front of the shielding may greatly increase the dose in the operation area. For the safety of the staff, an accurate assessment of the dose field from the multiple complex source term will be very necessary.
However, each ILW drums contains multiple shielding layers, as shown in Figure 1(c), which is to ensure the dose rate on the drum surface meets the requirements of national regulations [3][4][5][6]. However, this kind of design also brings a deep penetration problem in the Monte Carlo simulation [7][8][9], that is, when the shielding layers are too thick or the shielding structures are very complicated, if the number of simulated particles is low, the statistical result will be zero or obviously lower than the true value. Only when the number of simulated particles is large enough, the accurate result can be obtained. So, when multiple ILW drums coexist, this deep penetration problem will be very apparent. e purpose of this work is to research the accurate calculation method of the dose field distribution under this kind of multiple source term and deep penetration condition. Traditional theoretical formula prediction methods, such as the QAD program [10][11][12][13] which is based on pointkernel integration technology [14][15][16], can quickly perform the shielding calculation, but usually, the calculation results are too conservative. Currently, there are many Monte Carlo programs widely used, such as MCNP [17][18][19], FLUKA (http://www.fluka.org/fluka.php) [20], and GEANT4 [21,22], which have been verified, can provide very accurate simulation results [23].
For the multiple-source term problem, whether adopting the empirical formula method or the Monte Carlo method, the dose field distribution corresponding to each source can be calculated one by one then summed. However, this method is time consuming for successive data processing.
is work attempts to adopt the FLUKA program and rewrite the source subroutine code to realize the sampling of multiple volume sources in one calculation routine and give the total dose field results, which greatly reduces the workload for the data processing.
For the deep penetration problem, different variance reduction techniques can be adopted. Based on the previous work [2], this work comprehensively considers the room walls, roof, internal structures, and all drums. en, the optimization algorithm and variance reduction techniques proposed in [2] were adopted to complete the simulation calculation.
Furthermore, to verify the accuracy of the above method, an experiment was carried out and the measurement results were compared with the calculation result. e experiment was carried out under two scenarios: one is the outdoor measurement, which represents the dose field when only one drum is considered; another is the indoor measurement, which represents the dose field when the scattering effect is considered. In this way, the accuracy of the Monte Carlo calculation is verified by the actual measurement. e complicated source term sampling methods, the optimization algorithm and variance reduction techniques, and the experimental verification can provide valuable references for similar problems in radiation protection and shielding design.

Geometry Models and Material
(1) e ILW Drum. e detailed description of the geometry structure and materials compositions for one ILW drum can be found in previous work [2]. From outside to inside, one ILW drum consists of the following four parts: (1) the standard 200L steel drum, (2) the cement inner shielding layer, (3) the auxiliary support structure, and (4) the cement solidified radioactive waste. e standard 200L steel drum is 56 cm in diameter and 85 cm in height. e cement inner shielding layer is 6 cm of thickness. e auxiliary support structure is specially designed with stainless steel of 1.0 mm thickness. e radioactive waste in the solidified cement form was filled in the inside. Figure 2 shows the geometry model of one ILW storage drum.
(2) Room and Shielding Structure. In the real operating environment, multiple ILW storage drums will be placed in the room. Figure 3 shows the geometry model of the room and shielding structures. e room is 11 m of length, 2.6 m of width, and 3.5 m of height. Walls are made of ordinary concrete with 50 cm of thickness. e drums will be transported on an iron sliding track with 8 m of length, 0.8 m of width, and 17 cm of thickness. An iron shielding with 12 cm of thickness and 1.5 m of height is set to separate the high dose area and the operating area. In the calculation model, it was assumed that the center axis distance of two adjacent drums is 82 cm. e sliding track can hold up to eight ILW storage drums.

Source Term.
e radioactive source is homogeneously distributed in the solidified cement (i.e., part 4 in Figure 2). As described in the previous work [2], the radioactive waste is from the spent nuclear fuel reprocessing process, and dominant includes Cs-137 and Sr-90 (>95% of the total activity). In the simulation calculation, only Cs-137 was taken into account. And only the gamma ray of the highest energy (661.6 keV with a branching ratio of 85.1%) was considered, while the gamma rays of lower energies were ignored.
Different from previous work [2], the actual total activity of Cs-137 was detected in this work. e measured gamma intensity was 2.05E10 c/s, which is 0.87-fold of the designed highest total activity. Based on the above, the source shape should be a cylinder that exists inside each ILW drum. When multiple drums exist simultaneously, there are multiple volume sources. In this work, the "source.f" source file in the FLUKA program was rewritten to achieve the Monte Carlo sampling of multiple volume sources. e detailed method is as follows.
First, sample the drum that the volume source should belong to. Assuming there are m numbers of drums. Figure 4 shows the flowchart to sample which drum the source particle comes from, where rand n represents the nth random number.
en, sample the source particle position (x, y, z) by Eqs. (1)-(4): x � r × sin rand 4 + d m , where R is the radius of the cylinder; d m is the horizontal distance from the central axis of the drum to the origin of the x-axis; and h 1 and h 2 are the height coordinates of the bottom and top surfaces of the cylinder respectively. Eqs.
(1)-(4) realize homogeneous sampling in a cylinder. ird, sample the emission direction (u, v, w) of the source particles by equations (5)- (9): φ � rand 7 × 2π, Eqs. (5)-(9) realize isotropic sampling. Finally, it should be noted that the calculated result should be multiplied by a normalization factor that takes the number of drums into account to obtain the final dose matrix.

Cutoff Energy and Variance Reduction Technique.
e cutoff energy is under the assumption that if the transported particle cannot go out from the current layer with enough energy, its contribution to the final statistical result is negligible. So, if the particle energy is lower than the cutoff energy, the particle will be killed. e variance reduction technique adopted in this work is based on the Russian Splitting skill: if a transported particle goes into the region with splitting number N, the particle will split into N particles and every split particle will weight 1/N. In the previous work [2], it has been verified that proper cutoff energy and variance reduction technique settings can improve the calculation efficiency more than 20 times, while the deviation of the calculation results is ignorable.  Science and Technology of Nuclear Installations erefore, in the Monte Carlo simulation of this work, the cutoff energy setting and variance reduction technique similarly as in previous work [2] were also adopted. For the new geometry structures, including the surrounding walls, the roof, the sliding track, and the iron shielding, to reduce the influence on the accuracy of the calculation result, the cutoff energies were set very low and no variance reduction technique was set. e cutoff energy and variance reduction technique settings are summarized in Table 1.

Dose and Error.
In the FLUKA simulation, the ambient dose equivalent, H * (10), were scored for five scenarios: one drum, two drums, four drums, six drums, and eight drums. e conversion coefficients are taken from the ICRP Publication 74 [24,25]. e FLUKA program provides the three-dimensional dose matrix. e software SimpleGEO (http://www.fluka.org/fluka.php) can read and process the dose matrix and give a 3D display. ree interesting lines are drawn out in Figures 3(b) and 3(c). Line 1 and line 2 are along the X-axis and Y-axis, respectively, representing the distance to the side surface of the first drum. Line 3 is along the Z-axis, representing the distance to the top of the first drum. Dose comparisons along these three lines were made to evaluate the scattering effects and dose distribution in the operating area.
Corresponding with the three-dimensional dose matrix results in the FLUKA calculation, an error matrix will be given. By increasing the number of simulated particles, the statistical errors can be reduced. Also, it can be seen from the 3D dose display figure that smoother the color transition, the smaller the error. In this work, the error is controlled less than 3% by adopting enough transported particle number and parallel calculation. e total numbers of transport particles were more than 2e9.
However, the use of the variance reduction method may bring other errors. In this regard, the experimental measurement method was adopted for comparison, which shows that the simulation calculation results are in good agreement with the measurement results (see Section 3.3). So, it can be believed that the error caused by the variance reduction method is negligible.

Measurement Equipment.
e measurement equipment is the ambient dose rate meter (9DP), as shown in Figure 5. In addition, the measurement props also include a lead apron, two rulers, and a telemeter rod.

Measurement Scenarios.
During measurement, two scenarios, outdoor and indoor, were adopted, representing the cases without and with scattering considered, respectively. The source particle is from the 1st drum

True
The source particle is from the 2nd drum The source particle is from the (m-1)th drum The source particle is from the (m)th drum e outdoor measurement can reflect the dose field distributions with no affection by scattering.
Before measurement, a ruler was fixed vertically to the outside of the drum, and another ruler was placed horizontally on the ground along the symmetry axis of the drum, as shown in Figure 6(a). en, the surveyor held a telemeter rod and the monitor and measured along the horizontal ruler, as shown in Figure 6(b). e horizontal measured positions include 1/2/3/4/5 meters to the outside of the drum. e vertical measurement only includes a height of 50 cm above the ground.
(2) Scenario 2 (indoor). e indoor measurement can reflect the dose field distributions under the scattering effect. During measurement, eight drums were all put on the sliding track, in which, seven drums were behind the iron shielding, and one was out of the shielding. Figure 7 was taken during the measurement. e horizontal measured positions include 10 cm/50 cm/1 m/2 m to the outside of the drum. e vertically measured position was at the halfheight of the drum.

Uncertainty Estimation of Measurement.
e statistical uncertainties (Type A) and the systematic uncertainties (Type B) were considered for the experimental error. e statistical uncertainty can be calculated by where U A is the statistical uncertainty of the samples, X is the mean value of the replicate measurement, and N is the number of the replicate measurements, which is in the range of 5 to 10. e systematic uncertainty can be calculated by where U B is the systematic uncertainty, Δ i is the instrument error, Δ e is the estimation error which comes from the measurement object, environment, and human factors, etc., and E and V are the relative inherent error and the measurement standard deviation, respectively. According to the equipment verification certificate, E � 11.4% and V � 2.3%.  Science and Technology of Nuclear Installations en, the combined uncertainty of measurement (U) can be calculated by

FLUKA Simulation Results.
In the previous work [2], only the dose distribution within 15 cm from the drum surface was calculated. is work mainly focuses on the real dose field distribution when there are several drums in the room, and the scattering effect from other structures such as the walls should also be concerned. e size of the dose field considered is 11 m of length, 2.6 m of width, and 3.5 m of height. Figure 8 gives the results of three-dimensional dose distribution for the five scenarios: one drum, two drums, four drums, six drums, and eight drums. For each scenario, the 3D view shows the three plans intersect at the center point of the first drum. en, the front view and the top view, respectively, correspond to the section position in the 3D view.

3D Dose Rate Distribution.
For the scenario of one drum, the FLUKA simulated results indicate that the dose rates on the other side of the iron shielding are rather low, generally lower than 10 μSv/h. As the number of drums increases, the dose rates also increased significantly on the other side of the iron shielding. And the dose rates directly above the drums are usually higher. When there are eight drums on the sliding track, the dose rates on the inside (right side in the front view) of the iron shielding generally range from 76 μSv/h to 5 mSv/h, and this area will be forbidden entrance during operation.

Dose Rate Distribution along the ree Lines of Interest.
It was observed that, with the increase of the drum number, the dose rates outside iron shielding would also increase. Since the iron shielding is designed to be liftable and the area above iron shielding is unshielded, the gamma rays may enter the work area by scattering of the walls and roofs. is kind of physical mechanism was not considered in the previous design for one drum. To compare the effect of scattering on the dose rate in the working area, the dose rates on the three lines of interest shown in Figures 3(b) and 3(c) were extracted from the three-dimensional dose matrix and plotted in Figure 9.
It can be seen from Figures 9(a) and 9(b) that, in the horizontal direction (Line 1 and Line 2), with the increase of the drum number, the dose rate increases very little. In line1, at a position of 2.5 m from the first drum surface was quite near the wall, the dose rate is 79 ± 2 μSv/h for one drum scenario, while the dose rate is 84 ± 3 μSv/h for eight drums scenario. Similarly, in line 2, at a position of 1.1 m from the first drum surface, the corresponding dose rates are 269 ± 8 and 274 ± 8 μSv/h for one drum and eight drums' scenario, respectively.
It can be seen from Figure 9(c) that, in the vertical direction (Line 3), the increase of the dose rate is very obvious with the increase of the drum number. In the case of one drum and eight drums, at 1 m from the top surface of the first drum, the corresponding dose rates are 112 ± 3 and 195 ± 6 μSv/h, respectively. And at 1.5 m, the two values were 62 ± 2 and 177 ± 5 μSv/h, which increased by nearly three times. At 2.5 m, the two values were 31 ± 1 and 140 ± 4 μSv/h, which increased more than four times.
In summary, in the horizontal direction corresponding to the middle of the drum, the increase of the dose rate is not obvious, while in the vertical direction, the dose rate increase by scattering is significant and unneglectable.

Front view
Top view 3D view 9.7e -05 3.7e -04 1.4e -03 5.3e -03 2.0e -02 7.6e -02 2.9e -01 1.1e + 00 4.2e + 00 1.6e + 01 6.0e + 01 5.0e -05 1.9e -04 7.2e -04 2.7e -03 1.0e -02 3.9e -02 1.5e -01 5.6e -01 2.1e + 00 8.1e + 00 3.1e + 01 mSv/h Color bar    Figure 8: e front views, the top views, and the 3D views for the five scenarios: one drum, two drums, four drums, six drums, and eight drums. Science and Technology of Nuclear Installations Table 2 lists the outdoor measured ambient dose equivalent results which can reflect the dose field distributions with no affection by scattering. e horizontal measured positions include 1/2/ 3/4/5 meters to the outside of the drum. e vertical measurement was at a height of 50 cm above the ground. e corresponding FLUKA simulation results are also listed in Table 2. From the ratio of the FLUKA calculated and measured H * (10) (F/M value), which ranges from 1.4 to 1.5, it can be seen that the differences between the measurement and the FLUKA simulation are within two times. Table 3 lists the indoor measured ambient dose equivalent results which can reflect the dose field distributions affected by scattering. In this scenario, seven drums were behind the iron shielding on the sliding track, and one was out of the shielding. e horizontal measured positions include   Table 3. From the F/M value, it can be seen that the FLUKA simulation results are about 1.8 to 2.6 times higher than the measurement results.

Comparison and Discussion.
is work mainly focuses on the effect of scattering when there are several ILW drums in the operation room. From the above data and analysis, it can be seen that the calculated and measured results are in good agreement. erefore, although the experimental data is relatively limited, it can be believed that the FLUKA simulation calculation can give very accurate results.
From the measurement results, at a distance of 1 meter from the drum, the H * (10) for outdoor and indoor are 170 ± 10 μSv/h and 180 ± 10 μSv/h, respectively. And at a distance of 2 meters, outdoor and indoor results are 60 ± 4 μSv/h and 58 ± 4 μSv/h, respectively. ese results show that, in the horizontal direction corresponding to the middle of the drum, the effect of scattering is not obvious, which is also consistent with the FLUKA calculated results.
From the FLUKA simulation results, which is also discussed in detail in Section 3.1, it is pointed out that, at a distance of more than 1 m from the top surface of the drum, as the height increases, the dose rate increases by scattering is significant.

Conclusions
In this work, the Monte Carlo program FLUKA was adopted to calculate the dose field distribution in a radioactive liquid waste cementation facility. e main emphasis was put on the effect of scattering when several ILW drums exist in the room. And measurement was made to verify the accuracy of the simulation calculation.
In the FLUKA simulation, by rewriting the source file, complex source sampling is realized when several ILW drums coexist. And the optimization algorithm and variance reduction techniques are adopted to improve the calculation efficiency. e above method can greatly reduce the time cost of calculation and results processing. e simulation was performed for the five scenarios: one drum, two drums, four drums, six drums, and eight drums exist. For each scenario, the three-dimensional dose field distribution was calculated and the corresponding 3D view, front view, and top view were given. e dose rate distributions along the three lines of interest were also analyzed.
e FLUKA simulation shows that, in the horizontal direction, with the increase of the drum number, the dose rate increases very little. Typically, at a position of 2.5 m away from the outside drum, the dose rate is 79 ± 2 μSv/h for one drum scenario and 84 ± 3 μSv/h for eight drums' scenario. While in the vertical direction, the increase of the dose rate is very obvious with the increase of the drum number. Typically, at 1.5 m from the top surface of the outside drum, the dose rates are 62 ± 2 and 177 ± 5 μSv/h for one drum's and eight drums' scenario, which increased by nearly three times. At 2.5 m, the two values were 31 ± 1 and 140 ± 4 μSv/h, which increased more than four times. e measurement was performed for the two scenarios, outdoor and indoor, representing the cases without and with scattering considered, respectively. From the measurement results, at a distance of 1 meter from the drum, the H * (10) for outdoor and indoor are 170 ± 10 μSv/h and 180 ± 10 μSv/h, respectively. A comparison between the experiments and calculations shows very good agreement. For the outdoor scenarios, the differences between the measurement and the FLUKA simulation are within two times. And for the indoor scenarios, the FLUKA simulation results are about 1.8 to 2.6 times higher than the measurement results. erefore, although the experimental data is limited, the FLUKA calculation results for the whole dose field are accurate enough. e complicated source term sampling methods, the optimization algorithm and variance reduction techniques, and the experimental verification can provide valuable references for the scattering problem in radiation protection and shielding design.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.

Authors' Contributions
Data curation, formal analysis, software calculation, and writing of the original draft were carried out by Wenqian Li. Experiment supervision, data analysis, and funding acquisition were carried out by Xuegang Liu. Conceptualization, methodology, supervision, writing-review and editing-and funding acquisition were carried out by Sheng Fang. Experiment execution was carried out by Xueliang FU and Kaiqiang GUO.