1. Introduction

2. Results and Discussion

2.1. Continuous FBR Performance

2.1.1. Fluoride Removal

The fluoride removal profile in FBR during its continuous operation is depicted in Figure 1a. The influent fluoride concentration to the FBR was 300 mg/L. The initial fluoride removal efficiency was low at 32% on the first day, from which it grew to reach nearly 70% during the first 10 days of reactor operation. The respective effluent fluoride concentration varied between 81-204 mg/L (Figure 1a). During this initial operation the Ca²⁺ to F^- ratio was 0.55 which was based on the optimum ratio obtained during earlier experiment. However, as desired low effluent fluoride concentration could not be achieved at this ratio and the calcium utilization was very high, the inlet calcium concentration was increased to make the Ca²⁺ to F^- ratio as 0.6 from 11th day onwards. With this increase in influent Ca²⁺ concentration a positive impact on the fluoride removal could be observed. A consistent fluoride removal efficiency of 80.7 ± 1.8% could be achieved during next 17 days of continuous reactor operation (Figure 1a). Consequently, the fluoride concentration in the reactor effluent lowered to 60 ± 6 mg/L during this time period. This positive impact of inlet Ca²⁺ ion increase on fluoride removal is consistent with previous studies where a high inlet calcium value correlated with better fluoride removal performance [24]. Following this period, the reactor performance showed further improvement with fluoride removal reaching 90.2 ± 1.7% during the following 22 days of FBR operation. The resulting fluoride concentration was 30 ± 8 mg/L during this period (28-50th day). From 51th day onwards the effluent the fluoride concentration gradually increased as its removal efficiency depleted. This lowering of fluoride removal can be distinguished in two stages, for the first 10 days the removal efficiency was 80.9 ± 1.4% along with an effluent F- concentration of 57.2 ± 4.2 mg/L and for the remaining 10 days these values were 73.9 ± 2.9% and 78 ± 8.9 mg/L, respectively (Figure 1a). The continuous reactor experiment showed that the FBR can successfully remove fluoride as calcium fluoride crystals, however, over a prolong period of time without replacing the seeds, the performance declined.

2.1.2. Calcium and Sulfate Profile during FBR Operation

The calcium and sulfate profile during the continuous FBR operation is shown in Figure 1b. The calcium profile showed an increasing profile during the continuous operation. Initially, the calcium utilization was very high and the effluent calcium concentration was 12-60 mg/L. Following the increase in influent calcium concentration to meet the demand of crystallization, the effluent calcium concentration also increased beyond 100 mg/L. There was a lot of fluctuations in the effluent Ca concentration during the later period of FBR operation with periodic rise in Ca concentration to as high as 150 mg/L or even 200 mg/L. The mean effluent calcium value during 11-50th day period was 96.3 mg/L with a high standard deviation (44.3). During the later period when fluoride removal performance declined a corresponding increase in the effluent calcium concentration can also be observed. The calcium concentration in the effluent stream remained above 200 mg/L and later above 300 mg/L from 55th day and 64th onwards, respectively. This increase in the Ca concentration during later period of the FBR operation could be due to accumulation of excess Ca from recycle stream as well as from the continuous CaCl₂ input to the reactor. However, it needs to be mentioned here that effluent Ca values ≈300 mg/L is common in industrial processes treating fluoride containing wastewater including calcium-based fluoride precipitation methods. Hence, from the treatment point of view this isn’t unusual, but recovery and utilization of this calcium ions from effluent should be explored to further improve the process economics.

The sulfate concentration was also measured to understand its impact on fluoride removal through the calcium fluoride crystallization. Sulfate is present as co-pollutant in semiconductor industry wastewater, and can interfere with CaF₂ synthesis by forming calcium sulfate. However, in this study no such interference was observed. The sulfate concentration in the FBR effluent remained almost same (401.8 ± 8.2 mg/L) throughout the reactor operation (Figure 1b). This indicate that sulfate was not removed during FBR operation and did not interfere in the CaF₂ crystallization process in any way. This is important as in many cases formation of undesired CaSO₄ can decrease the fluoride removal efficiency by reacting with Ca ions present inside the reactor and if precipitated along with CaF₂, can reduce its purity as well.

2.1.3. Crystallization Efficiency

The fluoride speciation and CaF₂ crystallization efficiency are shown in Figure 1c. The crystallization efficiency was initially low (53.9-88.1%) for first 7 days, following which the value consistently stayed above 95% during next 41 days of continuous FBR operation. From 50th day onwards along with reduction in fluoride removal efficiency, the crystallization efficiency started to decline in a gradual manner. During this phase, except for the last 5 days of FBR operation, the crystallization efficiency was >80%. The maximum crystallization efficiency value obtained in the reactor was 98.6% on 38th day of continuous reactor operation. The fluoride speciation during the reactor operation corresponds well with the crystallization efficiency results. The portion of fluoride removed as calcium fluoride fines during the initial days of FBR operation was high (25-82 mg/L) compared with the next 42 days of FBR operation during which the amount of calcium fluoride fines remained <20 mg/L or even <10 mg/L. During the initial time period (1-7 d), the amount of fluoride removed as CaF₂ crystals were low (96-186 mg/L) indicating that although calcium fluoride formation was initiated in the reactor, the particles could not be retained onto the silica seed materials and they escaped the reactor along with effluent. During the best performing operating period (8-50th days) of the FBR, the concentration of CaF₂ fines were much lower (<18 mg/L) than the initial phase and majority (204-284 mg/L) of the fluoride removed in the reactor went towards CaF₂ crystallization (Figure 2c). However, as the FBR performance declined during the last phase of FBR operation in terms of fluoride removal, the amount of fluoride removed as crystals also reduced (≈210 mg/L). Consequently, the amount of CaF₂ fines increased to >60 mg/L during this last phase of FBR operation.

This increase in CaF₂ fines is the later period of continuous reactor operation is not uncommon and can be explained in two ways. The calcium concentration increases along with operating time as can be seen from the calcium profile. This increase in calcium concentration causes it to thicken and form scaling on the inner wall of the reactor. Some of the fluoride ions get captured in this calcium scaling which does not precipitate onto the silica seed rather comes out of the reactor as calcium fluoride fines. Other reason is breakdown of CaF₂ scales from the deposited crystals formed over silica seeds due to shearing and tearing by upflow fluidization during continuous reactor operation over extended time period. Therefore, proper care must be taken regarding operating time of the FBR so that an optimum fluoride removal along with ideal crystal recovery could be achieved.

The seed bed height was also monitored during 70 days of continuous reactor operation and is shown in Figure 1d. As can be seen from the figure, the seed bed height grew consistently throughout the reactor operation indicating formation and growth of CaF₂ crystals inside FBR. The growth rate of the seeds was at its maximum during 15 to 50 days of reactor operation which correlate well with the time period during which the other reactor performance indicators, namely fluoride removal and crystallization efficiency were at their best as well. The increase in the particle size of the seeds also showed similar pattern with 75%, 90%, 107.7% and 150.7% growth over 10-, 20-, 40- and 70-days reaction period, respectively (Figure 1d).

2.1.4. Characterization of Calcium Fluoride Crystals

Figure 2a,b depicts the SEM images of silica seed and CaF₂ crystal after 70 days of continuous reactor operation. The crystal size increased by more than double from 402.7 µm in diameter of the initial silica seed to 1003 µm diameter on 70th day. The outer appearance of the crystal was smooth and the shape seems to be irregular but nearly spheroid. Similar shape of CaF₂ crystal formed during fluidized bed crystallization has been previously reported [12,13]. The corresponding elemental compositions of the crystal surface is provided by EDX spectra of the initial silica seed and calcium fluoride crystals (Figure 2c,d). The initial seed contained Si, O and C, which when exposed to fluorine and calcium inside the FBR showed peaks for the presence of other elements including F, Ca, Na, Al, Cl, and S in addition to the original elements Si, C and O. The F and Ca composition in the 70 day old CaF₂ crystals was 44.8 and 44.4%, respectively. This indicates the extent of deposition of CaF₂ onto the silica seed. Furthermore, presence of Si was not detected in the 70th day sample which could be due to the fact that entire seed surface is covered with deposited CaF₂ by such prolong reactor operation.

The XRD spectra of the calcium fluoride crystals formed inside the FBR was shown in Figure 3a. The original silica seed showed peaks at 2θ = 20.39º, 26.07º and 49.02º which are typical to the SiO₂ [14]. The sample obtained after 5 h of FBR operation was more or less similar to the SiO₂ as the peaks present in the diffractogram matched more with SiO₂ (Figure 3a). The amount of CaF₂ deposited onto the seed materials after 5 h is proportionally much smaller than silica which is reason behind detecting SiO₂ in this sample. However, peak intensity for SiO₂ in this sample reduced compared with original seed sample indicating that CaF₂ crystallization process has started and there is other elements too in the sample along with SiO₂. The characteristic peaks corresponding to the CaF₂ was observed in the crystal samples obtained after 40 d reactor operation. The peaks corresponding to CaF₂ that are present in this sample were at 2θ = 28º, 46.6º, 55.7º, 68.7º, 75.8º and 87.4º (JCPDS no. 87-0971) [15,16]. Formation of CaF₂ with the FBR was confirmed with this XRD analysis. The XRD characterization of the CaF₂ crystals also revealed the absence of calcium carbonate (CaCO₃), calcium sulfate (CaSO₄) or fluorapatite (Ca₅(PO₄)₃F) in the resulting crystals. These compounds are known to precipitate during fluorine removal through fluidized bed crystallization and even some cases are the main product instead of CaF₂ [14,17]. The possibility of any of these compounds’ formation in this study is completely eliminated through this XRD analysis which also in turn highlight the high purity of CaF₂ formed.

The FTIR spectra obtained for silica seed material and calcium fluoride crystals obtained from different time interval is shown in Figure 3b. The broad peak at 3450 cm⁻¹ and 1620 cm⁻¹ represents stretching and bending vibrations of hydroxyl (–OH) group [18]. A range of small peaks at 1875 cm⁻¹ and 2000 cm⁻¹ could be due to the presence of C=O and C=C stretching vibrations, respectively [19]. The sharp peak at 1080 cm⁻¹ indicates the presence of asymmetric stretching vibrations of Si−O−Si bond [20]. The C=C bending vibration is also can be seen by the peak at 830 cm⁻¹ [21]. Other peaks at 750 cm⁻¹ and 460 cm⁻¹ can be attributed to the presence of sulfate and phosphate groups [18]. However, Si–O stretching vibration can also be indicated by the presence of a peak at 460 cm⁻¹ [22]. Although, it is difficult to confirm the presence of CaF₂ with FTIR spectra alone as it can only indicate presence of functional groups, some of the previous studies [18,21] have suggested that peak near 750 cm⁻¹ is due to CaF₂ presence which can be observed even in this current study too. The change in certain peak intensity following exposure to fluoride indicate role of this active group in the interaction with this fluoride. For example, peaks at 460, 830, 1080, 1875 and 2000 cm⁻¹ showed reduced intensities for calcium fluoride crystals than silica seed, indicating role related functional groups such as Si–O, Si−O−Si, C=O and C=C have role to play in interaction of fluoride ions with silica seeds. The increase in peak intensities of OH group at 3450 cm⁻¹ for CaF₂ sample is due to presence of water in the crystals due prolong exposure to experimental conditions inside FBR.

Compositional analysis of the silica seed and CaF₂ crystals obtained at the end of reactor operation was carried out using ICP-OES and the results is shown in Table 1. For this analysis, the samples are first acid digested and only the acid soluble parts are analyzed. It can be overserved from the result that the calcium and fluoride composition increased significantly from 0.34 and 1.53% in the seed material to 33.69 and 57.37% after 40 days of FBR operation. This increase in Ca and F composition in the samples directly corresponds to the reduction in silica composition from (94.81% to 2.05%) and confirms the calcium fluoride crystal formation onto the silica seed. Other elements such as sulfur, aluminum, iron, potassium, magnesium, sodium and phosphate are also present in the samples in minute quantities which may have been contributed by either the silica seed material or by the simulated wastewater used in the study. The purity of the CaF₂ crystals was also calculated using this study by converting the elemental percentages to molar fraction and subtracting the impurities from CaF₂ crystals (details shown in supplementary material). By this method the purity of the CaF₂ crystals obtained after 70 days of FBR operation is 91.12% which is relatively high compared to many other previous studies.

Table 1. Elemental analysis of the silica seed and calcium fluoride crystals using ICP-OES.

Table 1. Elemental analysis of the silica seed and calcium fluoride crystals using ICP-OES.

Element	Silica seed (%)	CaF2 - 70 day (%)
Sulfate (S)	0.14	0.18
Aluminium (Al)	0.34	0.27
Calcium (Ca)	0.34	53.2
Fluoride (F)	1.53	44.4
Copper (Cu)	0.01	0.00
Iron (Fe)	0.70	0.56
Potassium (K)	0.27	0.36
Magnesium (Mg)	0.12	0.05
Sodium (Na)	0.38	0.47
Phosphate (P)	0.13	0.00
Silica (Si)	94.81	0.51
Zinc (Zn)	0.04	0.00

3. Material and Methods

3.4. CFD Guided Optimization of FBR Configuration

CFD simulation is divided into four stages, first step of which is Geometry. Geometry is the order of creating the shape to be actually analyzed or specifying conditions in flow analysis. In general, process drawings are often inserted into files or produced in the program itself. Since it is important to implement it under realistic conditions, the governing equations and numerical techniques that apply the flow conditions such as flow speed, pressure, and temperature, and the calculation conditions such as gap width, relaxation coefficient, and variable values are entered. In addition, boundary conditions must be specified to input the physical state and information of the fluid, which is the most important setting when performing simulation. First, in this study, velocity was used as the setting for the inlet condition, and pressure was used as the setting for the discharge water outlet. The reason for setting these boundary conditions is that they are applied according to the domain of the analysis target, which is common when rotation occurs in a structure due to a strong flow.

The second step is meshing, which specifies the part of the shape to be analyzed. There are significant differences in interpretation of the grid configuration of CFD depending on its shape and size. There are three types of grids, namely hexahedral, tetrahedral and pyramidal. In this study, the polyhedral shape was used. This shape was selected because it is commonly used to accurately calculate turbulence and fluid analysis. In the case of a hexahedral other than the target shape, the numerical analysis results can produce highly accurate results, but if the structure is complex or the flow changes significantly within a short period of time, many errors may occur in the connection and formation of the lattice, which can lead to large errors in actual crystals. Changes have the potential to cause large errors. In addition, in the case of tetrahedral, it is expected that the analysis time will be somewhat long as it is mainly used in structural analysis to perform accurate calculations on the boundary layer of the structure.

Typically, increased grid density correlates with improved accuracy; however, this negatively impact by increasing analysis times, necessitating the need for careful adjustments. In this study, for efficient calculations, the overall grid size was set to 5 mm, and a relatively dense grid was placed at the inlet and outlet where rapid changes in flow are expected, as well as the flow part of the crystal, to ensure efficient analysis time and detailed flow changes. The goal was to increase accuracy and reliability by enabling accurate predictions.

The third order is physics, which specifies all conditions and equations used in flow analysis. The conditions used in this study are shown in Table 1. The equation Lagrangian-mutiphase can analyze the interaction between the solid region of the crystal and the liquid region of the wastewater in the process and the flow rate and pressure of each phase. Therefore, an equation that analyzes two or more phases simultaneously was inserted.

In the case of equations, the continuity equation and momentum equation were calculated using the k-epsilon model for turbulence generated due to strong flow velocity. This model can be considered suitable for structural fluid analysis because it is an equation that provides a good compromise in terms of accuracy and stability in general-purpose simulation. The resulting equation is as follows (Eq. 2).

Equation for kinetic energy (K):

$$\frac{\alpha (\mathrm{⍴}K)}{\alpha t}+\frac{\alpha (\mathrm{⍴}{u}_{i}K)}{\alpha x_i}=\frac{\alpha }{\alpha x_i}\left[\left(\mathrm{\mu }+\frac{{\mathrm{\mu }}_t}{{\sigma }_K}\right)\frac{\alpha K}{\alpha x_i}\right]+P_K-{\mathrm{⍴}}_{\mathrm{Є}}$$

(2)

Where, ρ is the density of the fluid, t is time, u_i is the velocity component, xi is the coordinate, μ is the dynamic viscosity, μ_t is the turbulent viscosity, σ_K is the modeling constant of the turbulent viscosity, and P_K is the kinetic energy.

Equation for kinetic energy consumption rate (ε):

$$\frac{\alpha ({\mathrm{⍴}}_{\mathrm{Є}})}{\alpha t}+\frac{\alpha (\mathrm{⍴}{u}_i\mathrm{Є})}{\alpha x_i}=\frac{\alpha }{\alpha x_i}\left[\left(\mathrm{\mu }+\frac{{\mathrm{\mu }}_t}{{\sigma }_{\mathrm{Є}}}\right)\frac{\alpha K}{\alpha x_i}\right]+C_{1\mathrm{Є}}\frac{\mathrm{Є}}{K}{P}_K-C_{2\mathrm{Є}}\mathrm{⍴}\frac{{\mathrm{Є}}^2}{K}$$

(3)

Where, Є represents turbulence energy (dissipation), σ_ε represents the modeling constant of turbulence energy, and C_1ε and C_2ε represent modeling constants. Afterwards, for particle analysis, analysis was performed using the Lagrangian method as shown in the equation below, and drag force (darg force, 𝐹_𝐷), lift force (𝐹_𝐿), and gravity force were considered as the forces acting on particles. The equation is as shown below (Eq. 4-6).

$$\overrightarrow{F_{Di}}=C_D\frac{1}{2}\mathrm{⍴}\left|u_i-u_{p,i}\right|(u_i-u_{p,i})A_p$$

(4)

$$C_D={\alpha }_1+\frac{{\alpha }_2}{R{\mathrm{Є}}_{\mathrm{⍴}}}+\frac{{\alpha }_3}{R{{\mathrm{Є}}^2}_{\mathrm{⍴}}}$$

(5)

$${R\mathrm{Є}}_{\mathrm{⍴}}=\frac{\mathrm{⍴}\left|u_i-u_{p,i}\right|d_{\mathrm{⍴}}}{\mathrm{\mu }}$$

(6)

Where, 𝑑𝑝 and 𝐴𝑝 refer to the diameter and cross-sectional area of the particle. The particle diameter was 0.5 mm, the density was 2650 kg/m³, and it was assumed to be silica sand. 𝐶𝐷 is the drag coefficient, and 𝑎₁, 𝑎₂, and 𝑎₃ are constants in the range of each constant 𝑅Є𝑝 number. 𝑅Є𝑝 refers to the Reynolds number of the particle.

$$\overrightarrow{F_{Li}}=m_{\mathrm{⍴}}\frac{2K{v}_f^{1/2}\mathrm{⍴}{S}_{ij}}{{\mathrm{⍴}}_p{d}_p{(S_{lk}{S}_{kl})}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}}(u_j-u_{p,j})$$

(7)

Where, 𝑚_𝑝 and 𝑢_𝑝 mean the mass and speed of the particle, and Li and Ahmadi’s equation, which is a generalization of the equation called Saffman’s lift, was used. The constant K is 2.594, and 𝜌_𝑝 and 𝜈_𝑓 are the density of the particle and the fluid, respectively. It means kinematic viscosity coefficient.

$$\overrightarrow{F_{gi}}=m_{\mathrm{⍴}}{g}_i$$

(8)

Where, gi means force based on the law of universal gravitation.

The fourth step is to analyze the results of the actual flow inside the reactor. In general, the process of change due to flow can be confirmed in real time and predicted by analyzing the movement of a single grid.

The reactor configuration used in this study is depicted in Figure S1 along with all the dimensions. The FBR had a total height of 2,150 mm and a width of 50 mm. The silica particles were filled upto 500 mm height. The height of the lower part of the reactor was 95 mm and the fluid inlet part was 15 mm high and 29 mm in diameter. In order to verify the validity of the CFD program developed, comparative study between the experimental and model predicted results for increase in the seed bed height at different upflow velocities were conducted. The different upflow velocities used for this experiment were as follows: 10 m/h, 20 m/h, 30 m/h, 40 m/h, 50 m/h, and 60 m/h. In this numerical analysis, particle analysis was conducted after excluding energy loss due to flow rate and the possibility of crystal shape deterioration. Once the validity of the developed CFD model was established experiment was conducted to understand the effect of FBR configuration (bottom part angle and inlet diameter) on mixing inside the reactor. For this purpose, three different configurations were chosen, i.e., first existing reactor with inlet diameter of 29 mm, second a new FBR with lower angle of 12.6 degrees and inlet diameter of 29 mm, and third another FBR with a lower angle of 19.1 degrees and inlet diameter of 20 mm (Figure S2).

Further studies were conducted to find optimal design conditions using optimized CFD-DEM model. There are three design conditions that were optimized: (i) shape of the bottom of the reactor (according to the reactor bottom angle), (ii) diameter of the reactor inlet, and (iii) ratio of width to height of the reactor. For the first experiment, the bottom angle of the reactor was increased from 0° to 5°, 10° and 12.6° by keeping the inlet diameter fixed at 29 mm. Following this study, experiment was conducted to study the effect of inlet diameter by varying it from 29 mm to 25 mm, 23 mm and 20 mm. The ratio of width to height ratio was examined for three different ratios, viz, 1:43, 1:23 and 1:15. The reactor configuration for each of these experimental conditions are shown in Figure S2.

Table 1. Conditions used for CFD flow analysis.

Table 1. Conditions used for CFD flow analysis.

Condition (unit)	Value
Liquid density (kg/m3)	997.561
Dynamic viscosity (Pa-s)	8.8871 E-4
Cp (cal/g.k)	0.998
Inlet velocity (m/s)	4.7 E-4
Temperature (°C)	25
Outlet pressure (Pa)	0
Solid density (kg/m3)	2,650
Solid diameter (mm)	0.5
Number of grains	20000
Particle count	5000

4. Conclusions

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