Study on Precipitation Kinetics of Calcium Pyro-Vanadate and Thermodynamics of Vanadium Water System

: Selective catalytic reduction (SCR) is a technology widely used in large coal-fired units to remove nitrogen oxides from flue gas, but it also generates a large number of waste catalysts every year. At present, the recovery of V from discarded SCR catalysts has good application prospects and environmental significance. In this paper, the kinetics and thermodynamics of vanadium precipitation process are described with the vanadium-containing liquid of waste denitration catalyst recovered by alkali leaching as raw material and CaCl 2 as precipitant in order to further explore the mechanism of vanadium precipitation. The kinetics study showed that the crystallization process of calcium pyrovanadate can be well-described by Avrami kinetic model when the precipitation time is 95–130 min, and the vanadium precipitation temperature is 60–80 °C. After that, the Arrhenius equation was used to analyze the fitted kinetic data, and the apparent activation energy Ea of vanadium precipitation reaction was calculated to be 98.196 kJ/mol, and the pre exponential factor A = 8.59 × 10 39 min −1 . Thermodynamic study showed that when the pH of the vanadium water system is low, the +5 valence vanadium in the solution mainly exists in the form of VO 2+ cation. When the pH is between 0–1, the solubility of vanadium reaches the minimum and then increases the solution pH again, and various polymerized anions are formed in the vanadium water system. When the temperature is 25 °C, the activity of vanadium in vanadium-containing solution is 10 −1 , the pH of solu-tion is 8–12, and the existence form of +5 valence vanadium in solution is mainly HV 2 O 73− . By analyzing the existing forms of V with different activities in a vanadium water system at 25 °C, it can be seen that with the decrease of V activity in liquid, the dominant region of polymerized vanadium-containing species in the potential pH diagram will disappear, indicating that vanadium mainly exists in the form of mononuclear ions in low-concentration vanadium-containing solutions, which is not conducive to precipitation. Therefore, in the process of precipitation of vanadium in solution, the concentration of V should be increased as much as possible.


Introduction
Vanadium metal has the characteristics of good ductility, corrosion resistance, a high melting point and easy deformation processing. The steel industry is the largest consumption area of vanadium metal. The demand for vanadium in the global steel industry accounts for 84.5% of the total global supply [1][2][3]. Vanadium has good ductility and corrosion resistance. Adding it to steel to make alloy can strengthen the properties of steel. In addition, vanadium, as a deoxidizer in steelmaking, is a very important additive in the steel industry. It can be seen that vanadium plays an important role in metal refining and alloy preparation [4][5][6][7].
At present, the recovery of V from discarded SCR catalysts has good application prospects and environmental significance. Generally, the catalyst is recovered by wet process in industry. In order to separate impurity ions such as Na + and Cl − from the vanadium-containing solution and the target element vanadium, appropriate precipitants are required. According to different precipitators, vanadium precipitation processes can be divided into calcium salt vanadium precipitation process, iron salt vanadium precipitation process, ammonium salt vanadium precipitation process, and hydrolysis vanadium precipitation process [8][9][10]. Among them, the calcium salt vanadium precipitation method has the advantages of a short process and high vanadium precipitation rate. In this paper, the kinetics of the vanadium precipitation process are described, with the vanadium-containing liquid of waste denitration catalyst recovered by alkali leaching as raw material and CaCl2 as precipitator, in order to further explore the mechanism of vanadium precipitation. In the thermodynamic part, the Nernst equation is used to plot the potential pH diagram of a vanadium water system at different activities in combination with the standard Gibbs free energy of related substances, and the conversion process of vanadium ions in the system is analyzed to provide a theoretical basis for vanadium precipitation experiments.

Characteristics
The name, specification, and model of the instrument used in the experiment and characterization are recorded in Table 1. In the experiment, XRF, XRD, SEM, XPS, and other methods were used to characterize the experimental raw materials and products, which can analyze the composition, element content, element valence, and microstructure of the product. Table 1. Instruments used in the experiment.

Characterization of Denitration Catalyst before and after Deactivation
The catalyst used in this experiment is a deactivated SCR denitration catalyst from a power plant in Shanghai, which belongs to honeycomb titanium oxide based catalyst. Due to the high temperature and high dust environment over a long time, the denitration catalyst is blocked by fly ash, sintered, and other phenomena, resulting in its own activity decline or even complete deactivation [10][11][12][13]. Therefore, it is pretreated by soot blowing, crushing, grinding, etc. Then, we screened out the deactivated catalyst raw materials of less than 60 meshes with a sieve and dried them in a 105 °C drying oven for 3 h as the raw materials for the alkali-leaching experiment. Before the alkali-leaching experiment, the experimental raw materials were characterized and analyzed by X-ray fluorescence spectroscopy (XRF), X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), etc.
The catalyst before and after deactivation was analyzed by XRF, and the composition is shown in Table 2. Table 2 shows that the main component of vanadium titanium-based catalyst is TiO2, and the active components are V2O5, WO3, etc. After comparing the components of the catalyst before and after deactivation, it was found that the content of TiO2, the carrier material in the catalyst, and V2O5 and WO3, the active materials, decreased [14][15][16]. This may be due to the mechanical wear of the carrier material and active components in the catalyst during use, but the content of oxides did not change significantly, indicating that the deactivated denitration catalyst has high recovery value. At the same time, the content of silicon dioxide, calcium oxide, and aluminum oxide in the deactivated catalyst increased, which may be because the particles and dust in the flue gas gather on the surface and pores of the catalyst during the flue gas denitration process, reducing the activity of the denitration catalyst, which is a factor causing catalyst deactivation. XRD characterization analysis was carried out on the SCR catalyst before and after deactivation, and the characterization results are shown in Figure 1. It can be seen from Figure 1 that there are obvious TiO2 diffraction peaks in the XRD detection results of both fresh and deactivated catalysts, which are anatase TiO2 diffraction peaks. It can be seen from the analysis that, in the process of flue gas denitrification, although the SCR catalyst was in a high-dust and high-temperature environment for a long time, the crystal morphology of TiO2 as the carrier did not change, and it is still anatase [16][17][18]. At the same time, it can be judged from the area of each peak of XRD that the relative content of TiO2 in the denitration catalyst is the highest. At the same time, there is no obvious characteristic peak of V2O5 and WO3 on the XRD spectrum, which indicates that V2O5 and WO3 are still highly dispersed in the deactivated denitration catalyst, and no obvious chemical change or agglomeration occurs. The deactivated denitration catalyst can be treated by the subsequent alkali-leaching recovery process, and the recovery value is high.   Figure 2 shows the XPS full spectrum of SCR catalyst before and after deactivation. As shown in Figure 2, the main elements in SCR catalyst are Ti, W, and Si, which is consistent with the XRF characterization analysis results of waste catalyst. The binding energy of V is between 507 eV and 535 eV, and the peak position is not obvious due to low content. Through the analysis of XPS full spectrum of SCR catalyst before and after deactivation, it can be concluded that the peak position and peak type of XPS spectrum of fresh and deactivated SCR catalyst are basically the same, which indicates that the valence state of main elements in SCR catalyst has not changed during use, and the deactivated SCR catalyst has good recovery value.  As shown in Figure 3, XPS characterization and analysis were carried out on the V element in the fresh denitration catalyst, and the V 2p spectrogram was fitted to divide the peaks. Referring to the XPS binding energy comparison table, it can be seen that the V 2p spectrogram of the fresh catalyst contains three peaks, and the corresponding binding energies are 514.72 eV, 515.37 eV, and 516.91 eV, which belong to the characteristic peaks of V 3+ , V 4+ , and V 5+ , respectively. The percentage contents of V 3+ , V 4+ , and V 5+ atoms are 4.01%, 75.88%, and 20.11%, respectively.  Figure 4 shows the V 2p spectrum of the deactivated denitration catalyst. According to the peak fitting and the XPS binding energy comparison table, there are three peaks in the V 2p spectrum of the deactivated catalyst, and the corresponding binding energies are 514.37 eV, 515.78 eV, and 517.11 eV respectively. The peak values may shift slightly due to the errors of equipment and detection methods, but it can be seen that the valence state of V element did not change before and after the deactivation of the denitration catalyst, However, the binding energy content corresponding to different valence states of V changed. After deactivation, the percentages of V 3+ , V 4+ , and V 5+ atoms in the denitration catalyst were 28.37%, 58.65%, and 12.98%, respectively.  The content of different valence V elements in the denitration catalyst before and after deactivation was compared and analyzed [19]. As shown in Table 3, the content of V 3+ in the catalyst before and after deactivation increased from 4.01% to 28.37%. Because the trivalent V does not have catalytic activity, it can be speculated that the increase of V 3+ content in the denitration catalyst during use is a factor leading to the decline of its catalytic efficiency. The content of V 5+ in the catalyst before and after deactivation decreased from 20.11% to 12.98%, indicating that the content of active components containing V 5+ in the catalyst decreased. As an important active substance in the denitration catalyst, the reduction of V2O5 content will inevitably lead to the decline of denitration catalyst performance or even deactivation.

Preparation and Characterization of Vanadium-Containing Solution
Because the deactivated denitration catalysts used in the experiment are all from a power plant in Shanghai, the catalyst volume is large, and in the process of use, there will be sintering, plugging, metal poisoning, and other phenomena [20]. Therefore, in order to reduce the influence of external conditions on the experiment as much as possible, it is necessary to pretreat the waste denitration catalyst before recycling the V element in the waste denitration catalyst. Firstly, the waste denitration catalyst is divided into cuboids of basically the same size, and a blower is used to blow away the dust on its surface and in its pores; after that, a hammer is used to break the catalyst after soot blowing into sheets of different sizes, which is conducive to the next grinding operation; finally, the crushed catalyst is put into the pulverizer and ground into particles smaller than 60 meshes. Then, NaOH solution is used to leach the waste catalyst powder, and then, the waste catalyst is treated after alkali leaching to separate other elements (Si, Al, W, etc.) and prepare the vanadium-containing solution. The preparation method is shown in Figure 5.

Alkali-Leaching Experiment
In this experiment, the method of direct alkali leaching is used to recycle the waste SCR catalyst. Taking a single alkali-leaching recovery as an example, 100 g of the pretreated catalyst is weighed each time and added into a Teflon beaker. Then, 500 mL of 40% sodium hydroxide solution is weighed and added into the beaker to mix with the catalyst evenly. Then, it is put into a constant temperature magnetic stirrer, and the reaction temperature is set at 150 °C The reaction time is 4.5 h, and the stirring speed is 200 r/min to produce the leaching reaction. The oxides of tungsten, vanadium, and silicon in the spent SCR denitration catalyst are converted into soluble salts, while TiO2 does not react with sodium hydroxide solution and exists in the slag. The following reactions mainly occur: After alkali leaching, the liquid is cooled to room temperature, a filter press is used for solid-liquid separation, the liquid is poured into the reactor of the filter press, a filter membrane with a fixed filter diameter is added for pressure filtration, and then, deionized water is added into the reactor to repeat the pressure filtration operation several times to avoid the loss of precious metals and other elements in the catalyst residues in the filter residue.
Next, we wash, dry, and weigh the filtered filter residue (TiO2 crude product) and use the filtrate as the raw material for subsequent experiments. The leaching rate of tungsten and vanadium and the recovery rate of titanium in waste SCR catalyst can be measured by titration, XRD, and other methods on the filtered residue.

Removal of Silicon and Aluminum Impurities and Desalination
Next, the filtrate filtered by alkali leaching is put into a beaker, and it is concentrated in an oil bath at 120 °C. Since the filtrate after alkali leaching contains more silicon and aluminum impurities that affect the subsequent precipitation of elements such as tungsten and vanadium, the silicon and aluminum in the filtrate should be removed first. According to the different solubility of silicon and aluminum impurities under different pH conditions, silicon and aluminum in the solution can be converted into insoluble precipitates by adjusting the pH of the solution, and elements such as tungsten and vanadium in the solution will not precipitate. Therefore, hydrochloric acid is dropped into the filtrate cooled to room temperature to adjust the pH of the filtrate, and a pH meter is used to measure the pH value of the solution while dropping. When the pH drops to 12, white precipitates begin to appear in the solution. With the continued dripping of hydrochloric acid, when the pH drops to about 10, the color of the solution changes to light yellow, and precipitates begin to appear in large quantities. When the pH value of the solution is controlled between 9.2 and 9.5, the silicon and aluminum in the solution will be converted into Al(OH)3 and H2SiO3 precipitation. The main reactions are: Next, we settle the solution after adding hydrochloric acid, cool it to room temperature, filter it, dry the filter residue, weigh and detect the components, and then calculate the removal rate of silicon and aluminum in the solution and the purity of silicon acid.

Tungsten Deposition Experiment
Then, we add 6 mL oxidant to the concentrated precipitated silicon aluminum liquid. The purpose of this step is to ensure that the W containing ions in the solution are oxidized to WO4 2− , and the vanadium in the vanadium-containing ions is oxidized to 5 valence. A glass rod is used to mix the oxidant and tungsten precipitation solution evenly, and then we let them stand for reaction for 20 min. Then, we use the inverted dropping method to add tungsten precipitation solution drops into concentrated hydrochloric acid (AR) with a dropper and mix them with a glass rod while dropping. The main chemical reactions that occur are as follows: Before the vanadium precipitation experiment, the liquid before vanadium precipitation was characterized and analyzed by ICP-AES method, as shown in Table 4. It can be seen from Table 4 that in the tungsten precipitation experiment, the precipitation effect of W was obvious, the precipitation rate was 85.86%, and the V in the solution was almost not removed. After calculation, the mass of V in the tungsten precipitation filtrate was 85.59% of the total V in the deactivated catalyst, and the liquid still had good recovery value.

Dynamic Model Establishment
During the vanadium precipitation experiment, we control the pH of the solution to be 10.0-10.5, add CaCl2 with a molar ratio of 15:1 calcium to vanadium, control the rotating speed of the magnetic stirrer to be 200 r/min, control the vanadium precipitation time to be 95-130 min under different reaction temperatures, conduct vanadium precipitation experiments, and record the vanadium precipitation rate. Next, we select four groups of data at 60, 80, 100, and 120 °C to obtain Figure 6. Because of the high stirring rate in the reactor and the small diffusion resistance of the solution body during the vanadium precipitation reaction, it can be inferred that the crystallization process of calcium pyrovanadate is mainly a surface reaction. Therefore, the relationship between the time and the degree of crystallization in the calcium pyrovanadate crystallization process can be established.
Avrami dynamics model describes that in an ideal state, each crystal nucleus in the substance generated by crystallization forms a crystal, and the crystal nucleus is irregularly distributed during the crystallization process. The equation of this model is shown in Equation (8): In the equation, φ is the percentage of the crystalline part in the total mass of the sample at time t; k is the crystallization rate constant; n is the Avrami index, which is related to the way of crystal nucleus formation, and the value is generally 1~4.
Considering the specific conditions of the precipitation process, the relationship between the non-crystalline part and the crystallization time in the crystallization process can be expressed by the following formula: 1 -X(t) = exp(-kt n ) (9) In the equation, X(t) is the degree of crystallization at t time; K is the kinetic rate constant; n is the Avrami index. We next take the logarithm of the left and right sides of formula (9) to obtain the following: lg[-ln(1 -X(t))] = nlgt + lgk (10) Then, we use lg [−ln (1 − X (t))] on the left side of the equation to plot lgt and fit a straight line. The slope of the line is the Avrami kinetic index n, and the intercept of the line is a function of the crystallization rate constant k lgk.
We then substitute the vanadium precipitation rate and reaction time in Figure 6 into Formula 10 to obtain the kinetic parameters lg [−ln (1 − X (t))] and lgt at different temperatures, as shown in Table 5.  Figure 7 is obtained by fitting the Avrami kinetic data in Table 5. As shown in Figure  6, when the precipitation time is in the range of 95-130 min, and the vanadium precipitation temperature is 60-80 °C, the crystallization and growth process of calcium pyrovanadate can be well-described by Avrami kinetic model.  The kinetic parameters at different temperatures are arranged as shown in Table 6. It can be seen that the crystallization rate constant k of vanadium precipitation reaction in-creases with the increase of reaction temperature, which is consistent with the experimental results. When the precipitation temperature is 100 °C and 120 °C, the Avrami index of the reaction is 0.5872 and 0.4277, respectively, indicating that with the increase of temperature, the Brownian motion of the grains in the solution becomes more intense, the probability of collision between grains also increases, the growth rate of calcium pyrovanadate is accelerated, and the crystallization process is gradually complicated.  Figure 8 shows the SEM images of vanadium precipitation experiments at different temperatures. It can be seen that the microstructure of calcium pyrovanadate is spherical. With the increase of temperature, the precipitates gradually changed from small grains to large grains.

Calculation of Apparent Activation Energy
Apparent activation energy refers to the difference between the energy of molecules in a normal state and that in an activated state in chemical reaction, which is an important factor determining the rate of chemical reaction. At a certain temperature, the greater the activation energy of the chemical reaction, the slower the reaction; the smaller the activation energy, the faster the reaction. The apparent activation energy Ea can be derived from the Arrhenius equation.
According to the Arrhenius equation k = A exp [−Ea/(RT)], the logarithm is taken on both sides, and the relationship between reaction rate constant k and temperature T can be calculated as follows: In the equation, k is the reaction rate constant, A is the pre exponential factor of the reaction, Ea is the apparent activation energy of the reaction, R is the gas constant, 8.314 J/(kg·K) is taken, and T is the reaction temperature.
It can be seen from Formula 11 that since lnA and −Ea/R are constants, Formula 11 is a linear equation in the form of y = ax + b. Where y = lnk, a = −Ea/R, x = 1/T, and b = lnA. According to the above Avrami kinetic equation, the kinetic data of vanadium deposition rate at 60, 80, 100, and 120 °C can be plotted and fitted with lnk and 1/T to obtain Figure  9. It can be seen from Figure 9 that the straight line equation fitted between lnk and 1/T is y = −11811x + 91.952. From the intercept lnA and slope Ea/R of the fi ing straight line, we can calculate the apparent activation energy Ea = 98.196 kJ/mol of vanadium precipitation reaction, and the pre exponential factor A = 8.59 × 10 39 min −1 .
In the vanadium water system, the solid phase and the solid-liquid phase maintain relative equilibrium so that the entire V-H2O system is in an equilibrium state. Thermodynamic analysis and potential pH plotting of a vanadium water system can not only visually see the existence form of vanadium-containing species in water under different pH conditions but also provide data support for the vanadium precipitation experiment and analyze the optimal pH range of vanadium precipitation and the activity of the vanadium element suitable for a vanadium precipitation experiment.
The analysis of V elements with different valence states in Figure 10a shows that when the pH in the system is low, the +5 valence vanadium in the solution mainly exists in the form of VO2 + cation. This is because polyvanadate ions will be destroyed in a strong acid environment [21,22]. The pH of its isoelectric point is between 0-1. At this time, the solubility of vanadium reaches the minimum. The binding potential pH diagram also shows that the solid-phase V2O5 is formed after this point; with the increase of solution pH again, various polymerized anions will be formed in the vanadium water system. When the pH of the solution is low, the +4-valent vanadium element mainly exists in the form of vanadyl VO 2+ ; when the pH in the system is greater than 3, VO 2+ will deposit into V2O4 as solid phase; increase the pH of the solution again, and the V2O4 of the solid phase will dissolve again to form the anion HV2O5 − .
When pH in the system is less than 3, the solution containing +3-valence vanadium is blue-green in color and exists in the form of V 3+ ions. Increasing the pH of the solution will generate solid V2O3, which is because V2O3 is more stable than V(OH)3.
Comparing (a) and (b) in Figure 10, it can be seen that when the pH in the solution is less than 3, vanadium mainly exists in the form of cations; when pH > 3.5, vanadium in the system mainly exists in the form of anions. When the vanadium activities in the system are 10 −1 and 10 −5 , respectively, the dissolved phases of +2 and +3 valence V are cations+. The dissolved species of +4-valent and+5-valent vanadium exist in both anionic and cationic forms. In addition, it can also be seen that the forms of vanadium species in the vanadium water system are diverse, and their forms vary greatly according to different activities.
It can be seen from Figure 10b that when the vanadium activity in the solution drops to 10 −5 , cations such as VO + and VOH + will appear in the solution. At the same time, the dominant areas of polymerized vanadium-containing species V2O4, V2O5, V4O124−, HV2O7 3− , HV10O28 5− , and H2V10O28 4− in the potential pH diagram will disappear. It shows that in a low-concentration vanadium-containing solution, vanadium mainly exists in the form of single core, which is not conducive to precipitation and recovery. Therefore, in the process of liquid vanadium precipitation, in order to improve the vanadium precipitation efficiency and reduce the operation difficulty, the vanadium content in the liquid should be increased as much as possible.

Conclusions
In this paper, the kinetics of vanadium precipitation process is described, with the vanadium-containing liquid of waste denitration catalyst recovered by alkali leaching as raw material and CaCl2 as precipitator, in order to further explore the mechanism of vanadium precipitation. In the thermodynamic part, the potential pH diagrams of a vanadium water system at different activities are drawn, and the conversion process of vanadium ions in the system is analyzed, which provides a theoretical basis for the vanadium precipitation experiment.
The study on the kinetics of the vanadium precipitation experiment process shows that when the precipitation time is 95-130 min, and the vanadium precipitation temperature is 60-80 °C, the crystal growth process of calcium pyrovanadate can be well-described by the Avrami dynamics model, and with the increasing of reaction temperature, the crystallization rate constant k also increases, the Brownian motion of grains in solution is more intense, the probability of collision between grains is also increased, the growth rate of calcium pyrovanadate is accelerated, and the crystallization process is gradually complicated. After that, the Arrhenius equation was used to analyze the fitted kinetic data, and the apparent activation energy Ea of vanadium precipitation reaction was calculated to be 98.196 kJ/mol, and the pre exponential factor A = 8.59 × 10 39 min −1 .
The thermodynamic study of vanadium water system shows that when the pH of the vanadium water system is low, the +5 valence vanadium in the solution mainly exists in the form of VO 2+ cation. When the pH is between 0-1, the solubility of vanadium reaches the minimum and then increases the solution pH again, and various polymerized anions will be formed in the vanadium water system. When the temperature is 25 °C, the activity of vanadium in vanadium-containing solution is 10-1, and the pH of solution is 8-12, the existence form of +5 valence vanadium in solution is mainly HV2O7 3− , which is consistent with the characterization results of vanadium products after vanadium precipitation. By analyzing the existing forms of V with different activities in a vanadium water system at 25 °C, it can be seen that with the decrease of V activity in liquid, the dominant region of polymerized vanadium-containing species in the potential pH diagram will disappear, indicating that vanadium mainly exists in the form of mononuclear ions in low-concentration vanadium-containing solutions, which is not conducive to precipitation. Therefore, in the process of precipitation of vanadium in solution, the concentration of V should be increased as much as possible.