3.4. Effect of leaching parameters on cobalt/molybdenum Recovery
The effect of leaching parameters such as solid-liquid ratio, leaching duration, and temperature on cobalt and molybdenum leaching efficiency was investigated.
3.4.1. Solid-liquid ratio
The effects of the solid-liquid ratio on cobalt/molybdenum dissolution are depicted in Fig. 4 (a). The response time and temperature were set at 48 hours and 100°C, respectively. The value of cobalt/molybdenum extraction declined as the solid-liquid ratio grew, and all samples demonstrated a similar trend. A larger solid-liquid ratio also resulted in a high metal content in the DESs, resulting in increased viscosity, which hampered the practical process. At solid-liquid ratios of 50 to 100 g/L, there was no notable decline in cobalt/molybdenum dissolution. The best solid-liquid ratio was found to be 20 g/L, which resulted in the most cobalt/molybdenum dissolution for all samples.
3.4.2. Time
The effects of leaching time on cobalt/molybdenum dissolution are shown in Fig. 4 (b). At the start of the reaction, the cobalt/molybdenum dissolution increased with time in the case of DES-1. After 8 hours, the dissolution of cobalt/molybdenum increased with a linear slope in the second phase, then increased with a slight slope in the third step to the end of the reaction. Although DES-2 was compared to DES-1, cobalt/molybdenum dissolution increased with a slight slope. Although extremely high cobalt/molybdenum recovery rates were obtained with a shorter reaction duration in DES-1, 48-hour reaction durations for both DES may be appropriate.
3.4.3. Temperature
The effect of leaching temperature on cobalt/molybdenum extraction is examined by varying the temperatures from 50 to 100°C while maintaining a constant S/L ratio of 20 g/L and a leaching period of 48 hours. cobalt/molybdenum dissolving increases as the leaching temperature rises. The findings are displayed in Fig. 4. (c). This phenomenon might arise for two reasons: First, the viscosity of DESs lowers with increasing temperature, and reduced viscosity improves ion mobility and mass transfer in the leaching system. falls and reduced viscosity improves ion mobility and mass transfer in the leaching system (Tang et al. 2022). As a result, the chance of a solid fraction colliding with DES components increased, enhancing the cobalt/molybdenum dissolving rate. Furthermore, increasing the leaching temperature enhanced the dissolution rates of the cobalt/molybdenum, allowing it to achieve dissolution equilibrium more quickly. The leaching temperature of 100°C was chosen as the best leaching temperature based on the study's findings.
3.6. Kinetic modeling of cobalt and molybdenum leaching
Typically, heterogeneous reactions occur in several steps, only with the slowest controlling the total reaction rate. The following stages are commonly involved in the dissolution of cobalt/molybdenum spent catalyst in DES as a solid-liquid heterogeneous reaction. The reactant diffuses from the liquid phase's bulk to the interface between the liquid and solid phases. Inert or insoluble substrates, such as alumina, are present in the catalyst samples, forming a product layer around the reacting core. To reach the unreacted core, the reactants must diffuse across this product layer. The porosity and thickness of the inert layer, as well as the diffusion coefficients of the ions created during the reaction, are the key parameters influencing diffusion through the product layer. The reactant then diffuses from the interface to the cobalt and molybdenum major bodies. Furthermore, chemical interactions occur between the reactants and the elements on the surface of the reacting core. Finally, at the interface of inert material, the products diffuse into the bulk of the liquid phase. The reaction can then proceed topochemical, with the inner core of the sample progressively transforming into the unreacted particle (alumina) (Oza R and Patel S 2011).
Based on the results in Tables S2-S5, it was observed that spherical geometry models give a more appropriate approximation for kinetic processes than all other models studied. Diffusion control (Eq. 2), chemical reaction control (Eq. 3), and mixed control models (surface reaction control; and diffusion via product layer) (Eq. 4) are commonly proposed as methods for managing the rate of leaching reactions by reducing core models (Meshram et al. 2015).
kt\(= 1-{3(1-\text{X})}^{2/3}+ 2(1-X)\) (Eq. 2)
\(\text{k}\text{t}= 1-{(1-\text{X})}^{1/3}\) (Eq. 3)
\(\text{k}\text{t} =-\text{l}\text{n}(1-\text{X})\) (Eq. 4)
Where X is the cobalt/molybdenum leaching efficiency (%), k is the apparent rate constant (hˉ¹); and t is the leaching time (h). The rate-controlling step is thought to be the mechanism with high correlation coefficients (R²), and its model shows the best matches with experimental data.
Figure S1 and S2 show the well-fitted graphs for (DES-1). According to the correlation coefficients shown in Table S2 (DES-1, Cobalt), the diffusion through the product layer was well-matched with the experimental data. A perfect linear relationship \(1-{3\left(1-\text{X}\right)}^{\frac{2}{3}}+ 2\left(1-X\right)\)and t was observed in the case of (DES-1), indicating that the leaching kinetic mechanism for DES-1 was diffusion control through the product layer. Based on correlation coefficients presented in Table S3 and Fig. S2-S3, the mixed control model well matched (DES-2) during the reaction (about 12 hrs).
The apparent activation energy (Ea) of cobalt/molybdenum leaching reaction in different DESs, was determined by the Arrhenius equation using the apparent reaction rate constants k obtained from the slopes of the kinetics models at various temperatures:
\(ln k=-\frac{Ea}{RT}+\text{ln}A\) (Eq. 5)
Where k is the apparent reaction rate constant; t is the leaching time, h; Ea is the apparent activation energy, kJ/mol; R is the universal gas constant, 8.314 J/K.mol; T is the temperature, K; and A is the pre-exponential factor.
The activation energy provides important insights into the kinetics and thermodynamics of chemical processes. The greater the activation energy, the greater the influence of temperature on the rate. Activation energies can also be used to assess the kinetics control step. Mass transit plays a significant role in the overall rate of many responses. Diffusion is one example of a low-activation-energy mass transport method. The activation energy of surface chemical reactions is substantially larger than that of diffusion control (Levenspiel 1998; Fogler 2016). As a result, the temperature has less effect on diffusion-controlled processes than it does on chemical-controlled processes. The activation energy is often used to estimate mass transport and response control in processes (L. Free 2022).
The plot of ln k against 1/T for all samples presented in Fig. 6 shows a straight line with an intercept of ln k and a slope of Ea/R. According to(Anand et al. 1988), A diffusion-controlled process has an activation energy that varies between 3 and 6 kcal/mol (12.55–25.08 kJ/mol). The activation energy of a chemically regulated process is often greater than 10 kcal/mol (41.84 kJ/mol) (Habashi 2017). A mixed control has an activation energy in the range of 20.92–33.44 kJ/mol or 5–8 kcal/mol (Habashi 1999). According to Fig. 6 (a,b), the calculated activation energies were 22.56, and 29.34kJ/mol for Co and Mo in the (DES-1), respectively. Therefore, it is evident that the (DES-1) leaching controlling step was the diffusion through the product layer. Based on Fig. 6 (c,d), the calculated activation energies were 38.09, and 31.48 kJ/mol for Co and Mo in the (DES-2), respectively. Therefore, the mixed control reaction may control the kinetic mechanism of the spent catalyst in (DES-2).