3.3. Kinetic Analysis
In this study, lepidolite concentrate particles could be considered as non-porous spherical particles. The reaction proceeds on the surface of the particles at the beginning, and a solid product layer is formed on the surface of the particles by the generated aluminum sulfate and orthosilicate. Sulfuric acid then needs to pass through the product layer before continuing to react at the interface between the unreacted solid phase and the solid product layer [
28]. The reaction process is shown in
Figure 11.
The reaction of lepidolite and sulfuric acid can be interpreted by the shrinking core model (SCM) with constant particle size of the non-catalytic liquid-solid reaction [
29], the dynamic equation as shown in Equation (6).
where
t is the reaction time;
b is the molar ratio of reactants;
ρ is the density of solid particles;
x is the Li yield;
M is the relative molar mass of lepidolite concentrate powder;
c is the concentration of sulfuric acid;
rL is the initial radius of the lepidolite particles;
k0 is the Arrhenius constant;
Dc is the is the diffusion coefficient in porous product layer. The parameters
rL,
Dc,
ρ, etc., which are not easy to measure, can be expressed by the equation relationship with the reaction rate constant
k (
kC,
kD) which is easier to be measured by the experiment.
Assuming
Dc >>
k0, it can be considered that the reaction process is only controlled by the chemical reaction, then the reaction kinetic function of the reaction control process can be simplified and expressed by
YC as follows.
On the contrary, if the reaction is controlled by the diffusion process in the solid product layer, i.e.,
k0 >>
Dc, then the reaction kinetic function of diffusion control process can be simplified and expressed by
YD as follows. [
30]:
In order to obtain the controlling step and conduct kinetic analysis in this work, the Li yield at different temperatures and different leaching times were studied. A series of experiments with temperatures of 413 K, 423 K and 433 K were carried out under the conditions of fixed sulfuric acid mass fraction of 60 wt%, acid ore mass ratio of 2.5:1, agitation rate of 120 r min−1.
The lithium yield at different leaching times of 413 K, 423 K and 433 K were substituted into Equations (7) and (8), respectively, to calculate the values of
YC and
YD. Then, use
YC;
YD as the Y-axis, and leaching time
t as the X-axis to get
YC-t; YD-t, as shown in
Figure 12. The linear equation is fitted by linear regression using the least squares method, the slope of the straight line is the reaction rate constant
k at different temperatures.
kc, kd and the correlation coefficient
R2 at different temperatures are shown in
Table 7, the experimental results are shown in
Figure 12.
The experimental results show that both YC and YD have a linear relationship with the leaching time t. Although the correlation coefficient (R2) between Yc and t is greater than 0.979, the correlation coefficient between YD and t is also greater than 0.970. This result is hard to judge whether the reaction control step of lepidolite and sulfuric acid is product layer diffusion or chemical reaction.
Therefore, the apparent activation energy (
Ea) of the reaction needs to be further studied to draw the rate-determining steps. Activation energy is a cogent evidence to find the rate-determining step of a reaction. If the apparent activation energy is less than 13 kJ mol
−1, the rate-determining step is diffusion of the solid product layer, while the rate-determining step is the chemical reaction control when the apparent activation energy is greater than 40 kJ mol
−1 [
31]. The Arrhenius equation shows that the apparent reaction rate constant
k is a function of temperature, and the equation between the
k, T, and
Ea is shown in Equation (6) [
32]:
where
A refers to pre-exponential factors;
Ea is the reaction activation energy;
T is the reaction temperature;
R is the molar gas constant.
Figure 13 was obtained by plotting ln
kC and ln
kD vs.
T−1, with a slope of −
Ea/
R and an intercept of ln
A, The
Ea of the chemical reaction controlling step can be calculated from the slope of the line as
Ea(C) = 34.14 kJ mol
−1, and the
Ea of the product layer diffusion controlling step is
Ea(D) = 31.39 kJ mol
−1.
The good linear relationship between
YC (
R2 > 0.979) and
YD (
R2 > 0.970) vs. leaching time
t, as well as the value of
Ea between 13 and 40 kJ mol
−1, all indicated that reaction between lepidolite and sulphuric acid was controlled by the hybrid behavior of diffusion through the insoluble layer and chemical reaction. This is different from the conclusion of single step control in previous literature [
33,
34]. The better correlation coefficients of
YC (
R2 > 0.979) and
kC (
R2 = 0.969) indicate that the chemical reaction step plays a major role in determining the leaching process, and the activation energy of this leaching reaction can be approximated as 34.14 kJ mol
−1 which is equal to
Ea(C). The value of
k0 calculated from the straight line in
Figure 13a is 1389.209.
The determination of the reaction order n requires further study of the relationship between Li yield and sulfuric acid concentration. 20 g lepidolite powder was weighed and mixed with sulfuric acid of 40, 50, 60 wt%. All experiments were conducted at a series of different leaching times of 1, 2, 3, 4 and 5 h, and the liquid-solid mass ratio and the agitation rate were fixed at 2.5:1, 120 r min−1, respectively.
The leaching kinetic equation of lepidolite can be approximated by the chemical reaction process kinetic equation
YC, according to the research of this experiment:
where
k0 is Arrhenius constant,
n is the reaction order of sulfuric acid concentration.
A similar fitting plot of
YC and
t was obtained at initial different sulphuric acid mass fractions
c and shown in
Figure 14a,
k and the
R2 (correlation coefficient) are shown in
Table 8. The apparent rate constant (
k) and a plot of ln
k with ln
c were calculated from the slopes of the straight lines shown in
Figure 14b, and the apparent reaction order
n = 1.711 relative to the sulfuric acid concentration is determined by the slope.
Through the above analysis, the obtained Arrhenius constant
k0 = 1389.209 and the apparent reaction order
n = 1.711 were substituted into the chemical reaction control kinetics equation, and the kinetic equation for the leaching of lepidolite by sulfuric acid is as follows:
3.4. Nanofiltration Separation Process of Actual Leaching Solution
The pH of lepidolite leaching solution (1 L dilution) was measured to be 0.5 under the optimal leaching conditions. The Ca(OH)
2 solution (pH = 12.5) was used to adjust the pH of the lepidolite leaching solution to 1.4 and 2.2 respectively, and CaCl
2 was added to the mother-liquid to ensure that the molar ratio of the raw material solution was SO
42−:Cl
− = 0.6:0.4. The pH, total salinity, and the concentration of ions in the nanofiltration feed solution are shown in
Table 9.
Nanofiltration separation experiments of the actual lepidolite leaching solution were carried out at a fixed operating pressure of 3.4 MPa and a temperature of 293.15 K ± 0.5 K. The results about retention of ions, separation factor of Al/Li and flux of the DK membrane are shown in
Figure 15. The retention rate of ions in descending order were: R(Al
3+) > R(Ca
2+) > R(K
+) > R(Na
+) > R(Li
+), which was consistent with the ions retention of the simulated leaching solution in our previous study [
26]. The retention rate of DK membrane for Al
3+ was stable above 96%, and the retention rate for Li
+ was stable between 42–52%, which has shown an excellent separation performance for Al
3+/Li
+. In addition, DK membrane also shown a high retention of over 94% for Ca
2+.
As shown in
Figure 15, the pH of feed solution has little effect on the retention of multivalent ions, which was because the larger hydration radius and higher valence of Al
3+ and Ca
2+ have determined the steric and dielectric exclusion resistance that enter into the permeate through the membrane were relatively large. However, the pH has a greater impact on the retention of K
+, Na
+, and Li
+, and their retention all decreased to varying degrees as the pH increases. The corresponding reason was that the increase of pH will reduce the content of H
+ in the solution, and there were more negative charges on the membrane surface accordingly, therefore, more cations were attracted by electrostatic action, resulting in a decrease in the monovalent cations retention. This change in separation performance of ions caused by the pH variance would lead to the change in the separation efficiency of Al
3+/Li
+ correspondingly, and the lower the pH of the feed solution, the better the separation performance of Al
3+/Li
+ of the DK membrane. The change of pH has a small impact on the ion retention, but has a greater impact on the membrane flux and separation factor. As the pH of the feed solution increases, the membrane flux gradually decreases. When the pH is 0.5, the salinity and the membrane flux of the solution were the highest. The reason was that the excessive unreacted sulfuric acid and large amount of H
+ in the solution has changed the micro-structure of the membrane and resulted in the increase on the membrane flux.
The experimental results of nanofiltration separation have revealed that DK membrane has excellent retention of Al3+ and Ca2+ and also can effectively permeate Li+, which means it is completely feasible to apply DK membrane to the separation of Al3+/Li+ in the lepidolite leaching solution.