

ORIGINAL ARTICLE 

Year : 2019  Volume
: 42
 Issue : 4  Page : 144149 


Mathematical simulations for studying the effectiveness of HTO removal mechanism from spent fuel storage bay and estimating the environmental releases
Lokesh Kumar^{1}, Rajendrakumar B Oza^{2}, Ranjit Sharma^{1}, Rayroath K Gopalakrishnan^{1}
^{1} Health Physics Division, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India ^{2} Radiation Safety System Division, Bhabha Atomic Research Centre, Mumbai, Maharashtra, India
Date of Submission  29Aug2019 
Date of Acceptance  09Oct2019 
Date of Web Publication  27Jan2020 
Correspondence Address: Mr. Lokesh Kumar Health Physics Division, Bhabha Atomic Research Centre, Mumbai  400 085, Maharashtra India
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/rpe.RPE_28_19
The diffusion of tritiated water (HTO) vapor from the spent fuel storage bay to the spent fuel storage building (SFSB) may lead to internal exposure to occupational workers. In order to reduce this internal exposure, air curtains are provided over the spent fuel storage bay to effectively remove HTO diffusing from spent fuel storage bay to SFSB. The radiation doses to the occupational workers are controlled well below the permissible level by monitoring the air concentration of HTO in the SFSB area. In the present study, it is brought out that few additional monitoring of air concentration of HTO above the spent fuel storage bay can give useful information about the effectiveness of air curtains in the removal of HTO and the estimation of environmental releases of HTO. A threedimensional advectiondiffusionbased model is developed to demonstrate the effectiveness of air curtains in the removal of HTO and for the estimation of environmental releases of HTO, utilizing these additional measurements. The study showed that air curtains are an effective mechanism to reduce the air concentration of HTO in SFSB and remove almost 50% of HTO activity using only around 24% of the ventilation air supplied to the SFSB. The environmental release rate of HTO estimated in this study was in good agreement with the measured release rate. The methodology developed here can also be utilized to carry out parametric studies to see the impact of changes in the parameters related with air curtains in the removal of HTO, thus for better designing of air curtains.
Keywords: Advectiondiffusion, air curtains, modeling, spent fuel storage bay, tritiated water
How to cite this article: Kumar L, Oza RB, Sharma R, Gopalakrishnan RK. Mathematical simulations for studying the effectiveness of HTO removal mechanism from spent fuel storage bay and estimating the environmental releases. Radiat Prot Environ 2019;42:1449 
How to cite this URL: Kumar L, Oza RB, Sharma R, Gopalakrishnan RK. Mathematical simulations for studying the effectiveness of HTO removal mechanism from spent fuel storage bay and estimating the environmental releases. Radiat Prot Environ [serial online] 2019 [cited 2020 Feb 29];42:1449. Available from: http://www.rpe.org.in/text.asp?2019/42/4/144/276920 
Introduction   
The main source of tritium in heavy water moderated and cooled nuclear reactor is the neutron capture by the deuterium. Tritium is also produced in fuel as the product of ternary fission. It rapidly converts into tritiated water (HTO) when it comes to the environment.^{[1]} Since HTO vapor is easily absorbed by the human body through skin and inhalation, it results in internal radiation exposure.
The tritium concentration starts increasing in the primary coolant and moderator system, where heavy water is exposed to neutrons during reactor operation for a long period. The spent fuel contains traces of heavy water, which results in tritium contamination of the spent fuel storage bay water. The HTO vapor from the spent fuel storage bay has the potential for the internal radiation dose to occupational workers in the building. In order to reduce the tritium exposure to the occupational workers, air curtains are provided above the spent fuel storage bay to remove the HTO diffusing from the spent fuel storage bay to spent fuel storage building (SFSB). The regular monitoring of HTO concentration in SFSB helps in controlling the radiation dose to the occupational workers well below the permissible level. Additional measurements of HTO concentration above the spent fuel storage bay, and by simulations, one can provide useful information about the effectiveness of the air curtains as well as the estimation of the environmental release rate of HTO. For this, few additional measurements over the spent fuel storage bay were carried out, and a threedimensional advectiondiffusionbased model was developed using the finitedifference method. The results of this study are summarized in this paper.
Materials and Methods   
Spent fuel storage building
[Figure 1] shows the position of different water bays in SFSB. The irradiated fuel assemblies are transferred from the nuclear reactor to Bay1 for short time storage through underwater fuel transfer trench. These are transferred to Bay2 for long time storage. The main source of tritium in the bay water is the contamination of tritiated heavy water on fuel assemblies transferred from the reactor core.
The SFSB is kept at slightly negative pressure than atmospheric pressure with the oncethrough ventilation to minimize the airborne radioactivity in the ambient air. Fresh air is supplied at different elevations in the SFSB at a rate of around 12 m^{3}/s, as documented. Air curtains are provided above all the three bays, i.e., Bay1, Bay2, and Bay3 to reduce the diffusion of tritiated water vapors (HTO) from water surface to ambient air of the building. Fresh air is supplied at a flow rate of 3.75 m^{3}/s to all the air curtains. There are 10 air curtains in Bay2 and 13 in Bay1 and Bay3. The supply air provided in the occupancy zone of SFSB is exhausted through the air curtain exhaust system.
Simulation for HTO concentration profile in air above Bay2
The behavior of tritiated water vapor (HTO) concentration in the air above the bay water surface is governed by the following advectiondiffusion equation.
Where, C = HTO concentration in air (units/m^{3})
t = Time (s)
V = Velocity vector of air flow (m/s)
D = Diffusion coefficient for HTO in air (m^{2}/s).
The position of air curtains over water surface in Bay2 is shown in [Figure 2]. The water level in the bay depends on the evaporation and feed and bleed of water in it. At the time of experiment, the water level was approximately 1.30 m below the working floor.
Assumptions
The HTO concentration in the air above bay water and its release rate from the air curtain exhaust system has been estimated under the following two assumptions:
 The airflow is only in the region of air curtain at constant velocity u along positive Xdirection toward the air exhaust system
 The effective diffusion coefficient D is constant throughout the volume of air above the bay water.
Under these assumptions, Equation 1 can be simplified to
Here, u is the Xcomponent of velocity vector V. In order to solve Equation 2 using the explicit scheme of the finitedifference method, it is discretized using Taylor's series expansion.^{[2]} After rearranging terms, it becomes
Where, n represents discretization in time and, i, j and k represent discretization in space along X, Y, and Z axis, respectively.
As illustrated in [Figure 2], the width of Bay2 along the Xaxis is 3.15 m, the length along the Yaxis is 15.20 m, and the elevation of the working floor from the bay water along the Zaxis is 1.30 m. The domain of interest is discretized with Δx = 0.05 m along the Xaxis, Δy = 0.04 m along the Yaxis, and Δz = 0.02 m along the Zaxis. Fresh air is supplied to all the 10 air curtains, each of width 1.00 m along the Yaxis with separation of 0.53 m in between and a height of 0.08 m along the Zaxis. All the airflow velocities in SFSB areSTgoverned by the main exhaust fan speed, which was operating at 0.7 times the documented flow speed on the day of the experiment. Therefore, the air supplied to all the 23 air curtains in Bay1, Bay2, and Bay3 are considered as . The velocity of airflow, u in the air curtain, is then calculated by dividing the air supplied to air curtains by the crosssectional area of all the air curtains; therefore, The time step (Δt)for simulation is selected based on the Courant–Friedrichs–Lewy criteria, which are the necessary conditions for the stability of the numerical solution to solve partial differential equations using explicit scheme of finitedifference method.
Boundary conditions
The HTO concentration profile above the bay water can be estimated by solving Equation 3 using the following boundary conditions.
 C (x, y, 0); Experimentally measured HTO concentration just above the water surface
 C (x, y, 1.30 m); Experimentally measured HTO concentration at z = 1.30 m elevation above the water surface
 At four walls of the bay except at inlets and outlets of air curtains, the normal component of the flux is zero, i.e.,
 Fresh air is supplied to the curtains; therefore, the HTO concentration at inlets of air curtains is zero
 At the exhaust of air curtains, the value of HTO concentration is estimated in each simulation time step using the concentration value at the previous grid point and neglecting diffusion in comparison with advection.
The measurement of HTO concentration at various positions above bay water
The HTO concentration in the air above the bay water surface was measured by sampling air from a specific location in cold trap with the help of pipe attached to a rigid support, as shown in [Figure 3].  Figure 3: Setup for the measurement of HTO concentration in air at different elevations above the bay water surface using cold trap method
Click here to view 
There is a gap of 0.53 m between consecutive air curtains along the Yaxis; therefore, the measurements have been carried out for two different locations along the Yaxis, one at the position of air curtains and the other in between the air curtains. HTO concentrations have been measured at three positions along the Xaxis, at x = 0.52 m, x = 1.62 m, and x = 2.62 m for a fixed Ycoordinate; moreover, for a given X and Y coordinates, the measurements have been carried out at three different elevations from water surface, z = 0.01 m, z = 0.90 m and at z = 1.30 m. The measurements carried out at elevation z = 0.01 m and z = 1.30 m are used for boundary conditions of the problem, and those at elevation 0.90 m are used for the estimation of effective diffusion coefficient, as explained in the next section.
To get the normalized value of average HTO concentration at 0.01 m elevation, all the concentration values have been normalized with respect to the average concentration at 0.01 m elevation. The normalized values of measured tritium concentration (units/m^{3}) above the bay water surface are shown in [Table 1].  Table 1: The normalized values of measured HTO concentration (units/m^{3}) in air above bay water at three elevations from water surface and at three positions along the direction of airflow in air curtain
Click here to view 
[Table 1] provides average normalized concentrations C (x, y, 0) =1.0 unit/m^{3} at an elevation of 0.01 m and C (x, y, 1.30 m) = 0.22251 unit/m^{3} at an elevation of 1.30 m from the water surface, which are used as the boundary conditions for the problem. The average value of normalized HTO concentration at elevation of 0.90 m from the bay water is 0.28220 unit/m^{3}.
Estimation of effective diffusion coefficient
The concentration of HTO in the air above the bay water surface is estimated by solving Equation 3 using the explicit scheme of finitedifference method. The solution of Equation 3 requires the specification of the diffusion coefficient. The reported values of diffusion coefficient for indoor industrial environments vary from 8.3 × 10^{4} m^{2}/s (3 m^{2}/h) to 0.192 m^{2}/s (690 m^{2}/h) with 2.78 × 10^{3} m^{2}/s (10 m^{2}/h) being a typical value.^{[3]} In order to get the effective value of diffusion coefficient for a given problem, HTO concentration values were estimated by the model at an elevation of 0.90 m from the water surface using different values of diffusion coefficients in the range 7.0 × 10^{3} m^{2}/s to 2.0 × 10^{2 } m^{2}/s and boundary conditions specified earlier. The simulation results were compared with the experimentally measured HTO concentration at 0.90 m above the water surface. The diffusion coefficient, which gave better matching with the measurement, was selected as the effective diffusion coefficient for our study. Simulated values of HTO concentration at 0.90 m elevation from the bay water using different values of diffusion coefficient are shown in [Table 2].  Table 2: Normalized values of HTO concentration at elevation 0.90 m above the bay water estimated by the model using different values of diffusion coefficient
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The average value of normalized HTO concentration at elevation of 0.90 m from the bay water, estimated by the numerical model using time step size Δt of 0.008 s and diffusion coefficient D of 1.35 × 10^{2 } m^{2}/s is 0.28238 units/m^{3}, which is in good agreement with the average of experimentally measured value of 0.28220 units/m^{3}. Therefore, the parameters used for the simulation are as following:
Δx = 0.05 m, Δy = 0.04 m, Δz = 0.02 m, u = 1.40 m/s, C (x, y, 0) = 1.0 unit/m^{3}, C (x, y, 1.30 m) = 0.22251 unit/m^{3}, Δt = 0.008 s and D = 1.35 × 10^{2} m^{2}/s.
Results and Discussion   
[Figure 4] shows the isocontour plot of HTO concentration in XZcross section for Y coordinate of 2.26 m which passes through the middle of one of the air curtains in the absence of airflow in the air curtains. [Figure 5] gives the same in the presence of air curtains. As shown in [Figure 4], the HTO concentration monotonically decreases with height in the absence of airflow through air curtains. However, in the presence of flowthrough air curtains (as shown in [Figure 5] using arrows), the concentration distribution changes significantly. Fresh air supplied to the air curtains has lowest HTO concentration, which is represented by the blue color in [Figure 5]. The airflow in the curtain carries evaporated HTO vapors from the bay water into the exhaust resulting in increasing HTO concentration from the inlet toward the exhaust, as shown in [Figure 5].  Figure 4: Isocontour plot for normalized HTO concentration profile in units/m^{3} of XZcross section at y = 2.26 m in air above water surface in the absence of air curtains. The normalized color scale is shown in the right
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 Figure 5: Isocontour plot for normalized HTO concentration profile in units/m^{3} of XZcross section at y = 2.26 m in air above water surface in the presence of air curtains. The normalized color scale is shown in the right
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The contour plots show that the HTO concentration decreases more rapidly with elevation from bay water in the presence of air curtains as compared to that in the absence of air curtains.
HTO release rate from the air curtains exhaust
[Figure 6] shows isocontour plot of HTO concentration profile in YZcross section for X coordinate of 3.15 m which is the surface of the wall containing exhaust grills of the air curtains. The variations in HTO concentration along the Yaxis are due to the presence of air curtains with the gaps in between. This simulated HTO concentration profile at the exhaust of air curtains may be used to calculate the HTO release rate from the air curtains.  Figure 6: Isocontour plot for normalized HTO concentration profile in units/m^{3} of YZcross section at x = 3.15 m, i.e. at exhaust of air curtains. The normalized color scale is shown in the right
Click here to view 
The HTO concentration at each grid of the exhaust of curtain multiplied by the velocity of airflow and crosssectional area of the grid provides the HTO release rate from that grid. For example, HTO release rate from the first air curtain will be . Here grid indices j and k are grid numbers in Y and Zdirections respectively. X index 63 denotes grid situated at the boundary in Xdirection. The summation of release rates from all the grids in the 10 air curtains provides the total HTO release rate from the Bay2 which is 4.150 × 10^{4} units/d.
There are 13 more air curtains present in the adjacent Bay1 and Bay3. The HTO contamination in the waterfilled in these bays is the same as in Bay2. Therefore, if the HTO release rate from each air curtain exhaust in Bay1 and Bay3 is assumed the same as the average HTO release from each air curtain in Bay2, then total HTO released from all the 23 curtains will be 9.545 × 10^{4} units/d, although the simulation has not been carried out for these additional air curtains.
HTO release rate from the main building ventilation
Some amount of airborne HTO from the bay water is swiped out by the air curtains, which is estimated as given in the previous section. The remaining HTO diffuses to the SFSB ambient air. In order to remove HTO from SFSB ambient air, fresh air is supplied at different elevations in the building, which carry away the airborne HTO through the exhaust. The air supplied in the occupancy zone of SFSB is exhausted through the air curtain exhaust, which assists the curtains. All airflow rates in building were 0.7 times the documented flow rates at the time of measurements because of the reduced speed of the main exhaust fan. The normalized value of average HTO concentration in the SFSB ambient air measured by the cold finger method^{[4]} was 0.12829 unit/m^{3}. Therefore, HTO release rate from the building ventilation is evaluated to be 9.358 × 10^{4} units/d by multiplying rate of air exhaust from the building and HTO concentration in the ambient air.
The HTO release rate from all the 23 air curtains present in Bay1, Bay2, and Bay3 estimated by the model is 9.545 × 10^{4} units/d and that from main building ventilation is 9.358 × 10^{4} units/d. Therefore, the total HTO release rate from SFSB is the sum of the two values, i.e., 1.890 × 10^{5} units/d. The routinely measured HTO release rate from the SFSB exhaust varies from 2.3 × 10^{5} units/d to 4.7 × 10^{5} units/d. As can be seen, the theoretically estimated HTO release rate is in reasonable agreement with the measured value. The difference between estimated and measured release rate values could be attributed to the assumption that the airflow is only in the region of air curtains. However, actually, the exhaust of SFSB ambient air is also through the air curtain exhaust, which introduces the airflow from ambient air to the outlet of air curtains. However, the methodology presented here provides a reasonable estimate of the environmental source term for HTO. As discussed, the airflow supplied to air curtains is 2.625 m^{3}/sec which carries away 9.545 × 10^{4} units/d of HTO vapors, whereas the airflow supplied to building ventilation is 8.443 m^{3}/s, and it carries away 9.358 × 10^{4} units/d of HTO. The total air supply in the SFSB includes air supply to air curtains and main building ventilation, i.e., 11.068 m^{3}/sec. Therefore, the airflow in the air curtains is only 24% of the total airflow supplied to SFSB; however, it effectively carries nearly 50% of the total HTO vapors from the SFSB.
Conclusions   
The study shows that the air curtains provided over the spent fuel storage bays are effective removal mechanism for the HTO diffusing from these bays to the SFSB. These air curtains effectively remove almost 50% of the airborne radioactivity using only 24% of the ventilation air supplied to the SFSB. The estimated environmental release rate of HTO is also found to be in good agreement with the measured values. Thus, few additional measurements of HTO concentration over the spent fuel storage bay provided useful information on the effectiveness of air curtains in the removal of HTO and estimation of the environmental release rate of HTO. Moreover, the methodology suggested here can also be utilized for parametric studies and improved design of air curtains over the spent fuel storage bays.
Acknowledgment
The authors are extremely thankful to Dr. M. S. Kulkarni, Head, HPD and Shri Kunal Chakrabarty, ROD for the valuable guidance. The valuable suggestions during the work from Shri Yesuraja V, Shri Krishnamohnan T, Shri Sajin Prasad, Shri Saurav, Shri Lalit K. Vajpyee and Shri K. S. Babu are gratefully acknowledged.
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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4.  Traub RJ, Jensen GA. Tritium Radioluminescent Devices, Health and Safety Manual. United States 1995. 
[Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6]
[Table 1], [Table 2]
