Kinetics of extracting valuable components from Ti-bearing blast furnace slag by acidolysis with sulphuric acid

Ti-bearing blast furnace slag is a kind of solid waste produced by Pangang Group Company through the blast furnace smelting method. A variety of valuable components can be extracted from the Ti-bearing blast furnace slag after acidolysis with concentrated sulphuric acid. In order to study the kinetics of acidolysis, this paper investigated the effects of the acidolysis temperature, acid-slag ratio and raw material particle size on the overall extraction rate of Ti4+, Mg2+ and Al3+ components at different reaction times, and simulated the acidolysis process by using the unreacted shrinking core model. The results showed that the acidolysis process was controlled by internal diffusion with an apparent activation energy of 19.05 kJ mol–1 and the semi-empirical kinetic equation of the acidolysis process was obtained.

other additives to prepare corresponding chemical products (Zhou et al., 1999;Zhou et al., 2013).Among the various extraction processes, sulphuric acidolysis has rapidly become a research hotspot because of its mature process technology, stable and easy-to-control reaction, simple operation and the ability to extract a variety of valuable components simultaneously.In the process of using sulfuric acid to hydrolyze TBFS, whether dilute or concentrated sulfuric acid as a reaction agent, or use one stage leaching (Jiang et al., 2010), or two stage leaching (Nie et al., 2023a), or roasting (He and Wang, 2023), or hydrothermal as reaction method, the extraction rate for titanium is high using this method (Valighazvini et al., 2013;Zhang et al., 2022;Li et al., 2024a).The acidolysis of TBFS using sulfuric acid can convert solid phase Ti, Mg, and Al into soluble Ti 4+ , Mg 2+ and Al 3+ , which are then sequentially separated by boiling hydrolysis and stepwise precipitation (Hongjuan et al., 2015).Therefore, optimizing the acidolysis conditions, improving the extraction rate, and efficiently extracting the valuable components in TBFS are of great significance to achieve the dual purposes of waste treatment and resource utilisation.At present, domestic and international studies on sulfuric acid hydrolysis of TBFS mainly focus on reaction processes and mechanisms (Ju et al., 2022), while there are fewer studies on the kinetic process of sulfuric acid hydrolysis.The following problems have arisen in actual process research: the acidolysis rate of each component in TBFS did not reach the equilibrium point of acidolysis kinetics, resulting in a high content of metal components in the remaining mud after acidolysis (Wang et al., 2022a).At the same time, the amount of mud increases and the component recovery decreases.This type of problem occurs not only in sulfuric acid hydrolysis of TBFS, but also in many sulfuric acid hydrometallurgy processes.Kinetic analysis can provide insight into the characteristics and mechanisms of sulphuric acid acidolysis of TBFS and predict the reaction rate, so as to effectively regulate the reaction conditions and improve the process efficiency.In order to provide a theoretical basis for the sulfuric acid acidolysis of TBFS, this study investigated the relationship between the total extraction rate of each component (i.e., all of Ti, Mg and Al) and the acidolysis time at different acidolysis temperatures, acid-slag ratios and raw material particle sizes.A kinetic model of the acidolysis process was fitted and the activation energy was calculated.The TBFS samples were dried at 106 °C for 24 h and some TBFS samples were ground to a particle size of less than 0.074 mm for XRD and XRF testing.The XRD results in Figure 1 show that the main mineral phase is perovskite with some amorphous phase (Zhu et al., 2023;Li et al., 2024b).Table 1 shows the XRF analysis results of TBFS.The main chemical components are CaO, SiO2, TiO2, Al2O3 and MgO, with low contents of SO3, Fe2O3, K2O, MnO and Na2O, and the lowest contents of F, BaO, SrO and ZrO2.
Figure 2 shows the SEM and EDS results of TBFS.From Figure 2A, it can be seen that the morphology of TBFS particles is an irregular structure with edges, smooth and dense surface, and uneven particle size.The EDS analysis was conducted on Ti, Mg, and Al elements in the A1 region.The distribution of each element is shown in Figures 2B-D.Ti, Mg, and Al elements are present on all visible particles and the enrichment zone boundary is not obvious, so the correlation between the three elements is well.

Experimental procedure
a. Grind TBFS to the specific particle size shown in Table 2.
Weigh the ground sample (10 g) in a 100 mL ceramic crucible with a lid and add concentrated sulfuric acid at the specific acid-slag mass ratio shown in Table 2. b.After the acid and TBFS have been thoroughly mixed, the crucible is placed in a tubular program high-temperature furnace and the acidolysis reaction is carried out for a certain time at the specific temperature shown in Table 2.At the end of the reaction, the acidolysed slag was finely ground and 10 g of the slag is placed in a 150 mL conical flask, mixed with 60 mL of deionised water and placed in a water bath at 60 °C with magnetic stirring at 20 rpm for 60 min.c.After the water leaching, the leached slurry is vacuum filtered at 0.09 MPa to separate the liquid from the solid and separated into leach residue and leachate.The content of Ti, Mg and Al in the leachate is determined by chemical titration and the percentages of components extracted (R) were calculated according to Eq. 1 (Shangguan et al., 2022a;Ma et al., 2023): Here, m 1 and m 2 are the total masses of Ti, Al, and Mg components in the TBFS and leachate, respectively.

Results and discussion
It can be seen from Figure 1 that the main phase of TBFS is an amorphous structure, and the analysis in Figure 2 shows the high correlation between occurrence of Ti, Mg, and Al.Therefore, Ti, Mg, and Al are considered as a whole to calculate the total extraction rate of the components in the dynamic simulation (Nie et al., 2020;Nie et al., 2023b).The correlation calculation is carried out by investigating the relationship between the total extraction rate and the acidolysis time at different reaction temperatures, acidslag ratio, and raw material particle sizes.The acidolysis reaction of concentrated sulphuric acid with TBFS is a typical liquid-solid reaction.Since the surface of the TBFS particles is relatively dense, it can be considered a non-porous structure.The particles containing Ti, Mg and Al gradually shrank during the reaction, so the most suitable model for the reaction kinetic is the unreacted shrinking core model (Alkan and Doğan, 2004;Zhang and Nicol, 2010;Liang et al., 2023a).The reaction started at the contact surface of concentrated H2SO4 and TBFS particles.The generated products (e.g., titanium sulphate) are wrapped around the surface of The relationship between 1 + 2(1r) -3(1r) 2/3 and t under different conditions: (A) acidolysis temperature, (B) acid-slag ratio and (C) TBFS particle size.
unreacted particles, and the H2SO4 diffused through the product layer to reach the unreacted interface to continue the acidolysis reaction.Thus, the overall rate of the reaction is affected by two steps: the internal diffusion step and the chemical reaction step (Sohn and Wadsworth, 2013;Wang et al., 2022b), the slower of which is the rate-controlling step during the acidolysis reaction process.Table 3 shows the relationship between the extraction rate r and time t for the two control steps of the unreacted shrinking core model.
Figure 4 shows the relationship between time and extraction rate at different acidolysis temperatures, acid-slag ratios and TBFS particle sizes.When the extraction rate tends to be stable, the acidolysis reaction is basically end, so only extraction rate before the end of acidolysis reaction can be used for calculation in the fitting calculation of the kinetic model.Therefore, the data before the reaction stabilizes in Figure 4 are fitted by substituting the equation in Table 3 and the fitting results are shown in Figures 5, 6.The kinetic fitting model is considered to be well fitted when the correlation coefficient (R 2 ) is greater than 0.85 (Wang et al., 2020;Li et al., 2023a), which shows that the R 2 between the internal diffusion Equation (1) + 2(1r) -3(1r) 2/3 and time t is greater than 0.85 for different acid-slag ratios, acidolysis temperatures and TBFS particle sizes.It can be assumed that the acidolysis reaction rate is mainly controlled by the internal diffusion of H 2 SO 4 in the product layer (Zhang et al., 2023).The related fitting equation and reaction rate constant k r are shown in Table 4.
The apparent rate constant kr is influenced by the acidolysis temperature, the concentration of acidolysis solution in the reaction system and the feedstock radius, as shown in empirical Eq. 2 (Wang et al., 2013).Combined with the acidolysis conditions in this paper, this is translated into Eq. 3 to include the acid-slag ratio and TBFS particle size (Li et al., 2023b;Liang et al., 2023b).
Frontiers in Chemistry frontiersin.org Here, kr is the apparent rate constant, x is the acid-slag ratio, k is the temperature-dependent reaction rate constant, C2 is the concentration of concentrated sulphuric acid in the reaction system (the ratio of the molar concentration of sulphuric acid), M1 is the molar mass of TBFS,ρ2 is the density of the concentrated sulphuric acid, r1 is the radius of TBFS particles (mm); M2 is the molar mass of the concentrated sulphuric acid andρ1 is the density of TBFS.
The relationship between kr and the acidolysis temperature follows the Arrhenius Eq. 4. The logarithm of both sides of the equation is taken to obtain Eq. 5 (Shangguan et al., 2022b;Wang et al., 2022c).
Here, kr is the apparent rate constant, A is the frequency factor, Ea is the apparent activation energy (J•mol-1), R is the molar gas constant (8.314J mol-1) and T is the acidolysis temperature.
According to the data inTable 4, the relationship between lnkr and 1/T is plotted.As shown in Figure 6A, the apparent activation energy of the acidolysis reaction is estimated to be 19.05kJ mol-1 based on the slope of the straight line in Eqss 4, and A was estimated as 8.23 based on the intercept.It is generally accepted that higher activation energies (>40 kJ mol -1 ) indicate chemical control, while activation energies of <20 kJ mol -1 indicate diffusion-controlled processes (Habashi, 1980;Santos et al., 2010).Thus, these results further indicated that the acidolysis process is consistent with internal diffusion control.The relationship between k r and the acidolysis temperature T could be expressed as Eq. 6.
When r1M2 kM1 is replaced by constant A1, Eq. 3 is transformed into an equation relating kr to the acid-slag ratio x by taking the reciprocal and then the logarithm of both sides, as shown in Eq. 7 .
The relationship between lnk r and ln( ) is shown in Figure 6B.The slope of the fitted line is 9.80201, so the relationship between k r and x can be expressed as Eq. 8.
is replaced by the constant A 2 , Eq. 3 can be converted into Eq.9.
Figure 7C shows the relationship between lnk r and lnr 1 .The slope of the fitted line is −0.40437, so the relationship between k r and r 1 can be expressed as Eq. 10.

k r
A 2 r 0.40437 1 (10) Combining Eqs 6, 8, 10, the semi-empirical kinetic equations related to the acid-slag ratio, acidolysis temperature, TBFS particle radius and k r are established as follows.
1 Here, x is the acid-slag ratio, d 1 is the TBFS particle size (m), R is the molar gas constant (R = 8.314 J mol -1 ) and T is the acidolysis temperature (K).
The data in Figure 4 are substituted into the left-hand side of Eq. 11 and the corresponding values of the relevant process parameters are substituted into the right-hand side of Eq. 11 for comparative analysis.Figure 8 shows the results of the comparison between experimental and fitted values, which are in good correlation with each other.This indicates that the derived kinetic equations are valuable in reflecting the actual situation.
Under the conditions of average particle size of 150 μm, acid/ solid ratio of 1.4, acidolysis temperature of 300 °C, and acidolysisi time of 40 min, the extraction rates of Ti, Mg, and Al reached 82.85%, 93.16%, and 96.96%, respectively.The chemical analysis and XRD of the leached residue are shown in Table 5 and Figure 9.After acidolysis with sulfuric acid and leaching with deionized water, the main elements in residual are S, Si, and Ca, with Ca mainly present in the form of gypsum.Frontiers in Chemistry frontiersin.org08 Wang et al. 10.3389/fchem.2024.1369937a.The chemical composition of TBFS is complex, with the main chemical componets are CaO, SiO 2 , TiO 2 , Al 2 O 3 , and MgO.There is a certain correlation and close connection between different elements in TBFS, and the main mineral phase of TBFS is perovskite, and there are also some amorphous structures.b.The acidolysis temperature, acid-slag ratio and TBFS particle size are positively correlated with the extraction rate of TBFS, with the higher the value of these three variables, the higher the extraction rate.c.The acidolysis process is consistent with the 'unreacted shrinking core model' and the reaction rate is controlled by internal diffusion through the solid product layer.d.The apparent activation energy of the acidolysis reaction is calculated by the Arrhenius equation as 19.05 kJ mol -1 and the kinetic equation is:

FIGURE 3
FIGURE 3 Occurrence state of Ti, Mg and Al in TBFS (A) Ti; (B) Mg; (C) Al.

FIGURE 4
FIGURE 4Variation in total extraction rate of components with acidolysis time under different process conditions: (A) acidolysis temperature; (B) acid-slag ratio; (C) TBFS particle size.

TABLE 1
Chemical composition of TBFS.

TABLE 3
Integrated rate equation for unreacted shrinking core model.

TABLE 4
Fitting parameters of internal diffusion kinetic equations under different acidolysis conditions.