It can be seen from Eqs. 1 and 2 that there is an imbalance between the stoichiometric requirements of Na+, OH−, RE3+, and SO42− ions. In each process cycle, according to Eq. 1, 1 mol of Na was required to produce 1 mol of double salt. Subsequently, additional 3 mol of Na per 1 mol of REE were added into the system during hydroxide conversion stage, resulting in 4 mol of Na per 1 mol of REE ratio in the process. However, it is commonly known that REE double salts are slightly soluble in sulfuric acid [7], and their precipitation efficiency can be improved via common ion effect by having an excess of sodium sulfate in the solution. It has been reported that to achieve > 95% double salt precipitation efficiency, a stoichiometric ratio (Na/REE) of 1–3 is required when operating at metal concentrations typical to NiMH battery recycling [20]. It is therefore advantageous for the process that ratio of 4 mol Na per 1 mol of REE is maintained in the process circulation system.
Initially, fresh Na2SO4 is injected in the double salt precipitation tank to start the process. Based on Eqs. 1 and 2, Na/REE molar ratio of 1:4 can be achieved in one complete circulation cycle of the process. After the initial batch of DS is produced, the sodium sulfate originating from the added NaOH in the double salt conversion to hydroxide is enough to fulfil the requirement for the double salt precipitation because of presence of the excess stoichiometry of Na with respect to REE (4:1 Na/REE ratio). However, this will come at a cost of dilution of the main PLS. This is undesirable, as it will reduce the concentrations of valuable metals in the leach solution and ultimately, push the downstream processes to handle larger volumes. Furthermore, La loss will also increase in more diluted PLS due to its relatively high solubility in water and sulfuric acid, as shown by Lokshin et al. (2.32 g/L in H2O at 20 °C) [7]. However, in this process flowsheet model, only stoichiometric ratio of Na and REE was taken into consideration in DS precipitation efficiency, not REE solubility, and same precipitation efficiency was assumed regardless of the REE concentration in the solution. By adjusting the L/S ratio (liters of NaOH solution per kg of double salt) used in the double salt conversion to hydroxide, the magnitude of dilution factor can be affected. This trade-off of optimal L/S ratio will be investigated in this flowsheet simulation, and a regression model was built in order to find an optimal bleed fraction for different situations.
Flowsheet Metamodeling Results
The flowsheet model presented here has been simplified with several assumptions. (1) La is selected to represent all REEs as a group. (2) Ni is representing other metals that are soluble and will not be recovered in double salt precipitation stage. Ni concentration will act as an indicator of dilution due to recirculation. (3) Due to lack of electrolyte density data in the literature, the effect that the dissolved La will have on the density of the electrolyte will be estimated by using the value of Al2(SO4)3 [21]. (4) Energy balance will not be considered in the model since the thermodynamic formation values for lanthanum double salt (LaNa(SO4)2·H2O) were not found in the literature. It needs to be noted that the fitted regression model equations are not based on chemistry confirmed by the experimental work, but the literature.
The parameters given in Table 2 were used in Minitab to generate a DOE composed of CCD. The experimental matrix was entered into HSC SIM, and the resulting data originated from HSC simulation using process flowsheet shown in Fig. 1 was again entered back to Minitab. As a result, several models were created, each corresponding to a response. These were fully quadratic models that could be used to predict the responses in the whole precipitation system. Responses that are critical to the precipitation process itself and to the subsequent downstream unit processes were chosen such as Na2SO4 feed conc., dilution ratio, Ni and Na content in the PLS, produced REE precipitate, resulting Na/REE ratio, and La loss in the process. The responses listed in Table 4 have a varying degree of importance to the process design. Response R1 is the descriptor for how much fresh sodium sulfate is required in order to achieve the set Na/REE ratio (parameter P1). Negative number would indicate that there is an excess and the ratio has not been achieved, and a positive number would indicate that there is a need for fresh Na2SO4. Negative number would be an indication that the amount of Na in the system could be reduced by removing part of it by, e.g., bleeding it out (parameter P7) or by adjusting other process parameters, such as parameter P6. Response R2 is the descriptor for how much volume percentage of the recirculated Na2SO4 solution was bled out of the process. Response R3 is the Ni concentration in the raffinate after REE double salt precipitation. Observing Ni concentration is vital to the subsequent downstream extraction processes, as its dilution would indicate increased volumes. This may affect further solution purification, e.g., Ni precipitation or solvent extraction of other elements at later stages. Response R4 is the Na concentration in raffinate, and it is followed in the case of event of overly saturated solution conditions. R5 is the yield of double salt (D.S.) in (kg/h) that will enter the conversion unit process. This will be maximized. R6 is the actual achieved Na/REE ratio in the double salt precipitation process. There are situations where the combination of used parameters will not yield the desired Na/REE ratio. Modeling this response helps in finding those constraints. R7 is the lost La%, i.e., the La that is not precipitated as double salt and will go downstream along with Ni.
Table 4 The selected responses and the stream or unit process from where the value of the response was recorded Firstly, quadratic regression models for each response (R1–R7) were created. CCD provides a quadratic model of following form:
$$ \mathrm{Y}={\upbeta}_0+\sum \limits_{i=1}^{k=7}{\beta}_i\cdot {\mathrm{P}}_i+\sum \limits_{i=1}^{k=7}{\beta}_{ii}\cdot {P}_i^2+\sum \limits_{1\le i\le j}^{k=21}{\beta}_{ij}\cdot {P}_i{P}_j+\epsilon $$
(4)
where βi are the regression coefficients for the parameters Pi [15]. The first term is the constant coefficient β0, the second term represents the linear effects (7 in total), third term represents the polynomial effects (7 in total), and fourth term represents the second-order interactions (21 in total). In total, 35 terms consisting of linear, binomial, and second-order interactions must be considered. This is exemplified by the uncoded regression equation for raffinate Ni concentration, shown in Eq.5:
Due to the large amount of terms in the equations, the models for the other responses (R1–R2 and R4–R7), are not presented, instead, only results statistical analysis are shown.
In Table 5, the results are summarized for the created models for each investigated response. S is the standard error of regression and R2 (pred) is the predicted value. R2 (pred) is obtained by the software removing observed data points, after which the model is refitted and the removed data point is compared to the refitted model. It can be seen that the regression and predictive power is relatively high (≥ 95%) for each response except for responses R1 (fresh Na2SO4 needed), R2 (dilution factor), R3 (Ni concentration in raffinate), and R5 (D.S. produced). This may be due to the fact that a quadratic model is not sufficient to predict La% losses due to many factors having simultaneous effect on the amount of La% being lost. This is an inherent weakness in DOE-only approach to process simulation optimization [22]. The use of only cube and axial points will cause smoothing of the data due to small number of levels (3) each parameter has. It is also possible that there are higher than second-degree interactions, causing flawed regression fitting. The face-centered CCD employed in this study has issues in detecting quadratic effects. Further improvements may be achieved by using other designs than CCD [23].
Table 5 Regression coefficients of the each response surface Once fitted, the models can be analyzed. As shown in Table 4, there are several responses that need to be optimized in the flowsheet model. Optimization of these parameters may be difficult manually due to many interdependencies of the different feed parameters. This will be especially true in more complex flowsheets. Minitab allows multi-parameter optimization, however as a result, there may be a large set of optimal parameters corresponding to the goals. It is up to the human operator to choose the criteria and weights for the multi-parameter optimization and its results. The goal (G1-G8) of the optimization in this study is summarized in Table 6. Certain responses are preferred to be minimized (raffinate volume, Na concentration in raffinate) or maximized (double salt yield, raffinate Ni concentration) or not optimized at all, based on the user preference. The optimization runs G1–G7 were single response optimizations which predict at what parameters values, it is possible to optimize one response at time. In optimization run G8, a multi-parameter optimization was performed. Simultaneously, two conflicting parameters were optimized: Ni concentration in raffinate and the yield of double salt, both were maximized. These two goals are in conflict: in order to maximize the double salt yield, more Na is required. However, the use of recirculated solution as a source of Na will produce more dilute Ni-containing raffinate. In this optimization run, the need for fresh Na2SO4 balance was also set to target a value of 0 t/h. Negative value would indicate an excess of Na originating from the recirculation, and a positive value would indicate the needed quantity of fresh Na2SO4.
Table 6 Response optimization targets. Not opt. = not optimized. Max. = maximized. Min. = minimized These data originated in experiments G1–G8 was then input in Minitab in order to find optimal solutions for desired responses, as shown in Tables 7 and 8. The results based on modeling are shown in Fig. 3. This optimization mainly explains that 74% of the solution must be bled out in order to satisfy the responses involving G8. The reason for model to predict that the optimal PLS acid concentration is high (4 M), is that the acid concentration would slightly affect the density of the solution, and hence, the Ni concentration present in equal volumes. D is the desirability (0–1), and shows how well the set goals were achieved in terms of response optimization. Since G1–G7 were single response optimizations, the desired result was always achieved. In Fig. 3, the optimization scenario (exp. G8) is described as seen in Minitab. The results clearly indicate that significant bleeding (47.6%) of the recirculated solution will be required in order to limit excessive dilution of the raffinate, while simultaneously maintaining high enough Na (Na/REE = 2.0) content by only using the recirculated solution (fresh Na = − 0.294 kg/h) to cause satisfactory recovery of REEs as double salts (12.44 kg/h). It can also be seen that increase in REE concentration of PLS will cause decrease in raffinate Ni concentration. The [Na2SO4] has mostly no effect on anything as the source of Na is the recirculated solution (fresh Na2SO4 needed = 0).
Table 7 Optimized parameters for investigated G1–G8 Table 8 Results: the optimized responses, obtained by using parameters, Table 7 The results showed that combination of DOE and process flowsheet modeling can be a powerful tool to quickly identify possible bottlenecks in process design. However, response surface methodology in itself is not enough to create a robust regression model of the entire flowsheet. The future work on this model should involve extension and addition of downstream processes for the raffinate and the mixed rare earth hydroxide. Furthermore, the double salt conversion to hydroxide and other parts of the simulation can be further refined with experimental data on equilibration and kinetics to complete the full process design. Additionally, more appropriate designs should be considered in creating models that better conform to the higher order responses.
Experimental Verification of the Process Flowsheet
Experimental work was conducted in order to verify that the chemistry suggested by Eqs. 1 and 2 and flowsheet is valid and technically feasible. Before circulation experiments, 20 mL of 355 g/L Na2SO4 was added to 80 mL of PLS. The obtained precipitate was the baseline mass (4.11 g) for the REE recovery. It was discovered with ICP-OES that the La yield was 99.1%. Recirculation experiments were performed in two rounds. In the first round, the recyclant obtained from the initial conversion was used. The results clearly indicate that the circulation experiments can be performed with no carryover of impurities to recyclant as shown in Table 9 and Fig. 4. However, the wash waters of rare earth double sulfate both contained large quantities of base metals and rare earths. It is clear that vacuum was not sufficient in removing the remaining PLS from the double sulfate precipitate. Another key issue in the washing of the rare earth double sulfates is that they are slightly soluble in water [11]. It may be necessary to consider this by utilizing washing reagent where the solubility is minimized, e.g., hot water or hot sodium sulfate solution. It would also be beneficial to recycle the wash waters back to precipitation stage; however, this would amount to dilution of the PLS which might be undesirable. 60 °C wash water was utilized in this study; however, some losses still occurred. The contents of La in the wash water is higher in relation to other metals than in the leach residue wash water (0.17 vs. 0.47 La/Ni)—an indication that some of the double salts may have dissolved, regardless of the 60 °C wash water. Unsurprisingly, NaOH solutions were devoid of metals as the measured pH of these solutions was 13 after the conversion. No dissolved aluminum was found either. The sulfur content found in these solutions mirrors the dissociation of the REE double salt and its subsequent hydrolytic precipitation. By calculating the mole quantity of S in round 1 recyclant (14 mmol), one can find that the amount of S mirrors the amount of double sulfate (2.74 g of feed D.S. vs. 2.66 g D.S. based on sulfur content) that was fed to the experiments. The yield of lanthanum changed between round 1 and round 2 (96.9% and 92.8% respectively). This can be attributed to Eqs. (1) and (2): the amount of double sulfate obtained was less, and since rigid 3NaOH/REE = 1.6 ratio was used, the Na concentration in NaOH solution was less as it was subsequently too in the recyclant between the two experiments, decreasing the saturation degree in precipitation. This shows that the principle chemistry of flowsheet using the Na and SO4 containing solution originating from the double salt conversion as a precipitation agent is valid. Utilization of this method will have potential to drastically reduce the consumption of Na in the processing of NiMH battery waste.
Table 9 Experimental input and output concentrations of elements in precipitation reactor (300-RC-001) and alkaline conversion reactor (300-RC-002) when circulating the solution internally (round 1, round 2). n.a. = not analyzed Observed, Modeled, and Metamodeled
The results showed that combination of DOE and process flowsheet modeling can be a tool to quickly identify possible bottlenecks in process design. However, response surface methodology in itself is not enough to create a robust regression model of the flowsheet. This can be used for early evaluation of the process optimization, to be further verified by experimental work in the desired conditions. Experimental work conducted verified that the modeled chemistry works in the laboratory scale and that recirculation of the process solution can result in internal usage of Na as precipitation agent for REE. To illustrate this, Fig. 5 shows the comparison of data from flowsheet model (Fig. 5a) and metamodel (Fig. 5b) at process held process condition. In this investigation, the effect of L/S ratio and bleed fraction (%) on raffinate Ni concentration is investigated. The experiments conducted at shown hold conditions show that it is in good agreement with the model however with slight variation. The experiments were performed at L/S = ~ 28, and Ni in raffinate was 35 g/L after precipitation experiments as shown in Table 9.
The future work on this model should involve extension and addition of downstream processes for the raffinate and the mixed rare earth hydroxide. Furthermore, the double salt conversion to hydroxide and other parts of the simulation can be further refined with experimental data on equilibration and kinetics to complete the full process design. Additionally, more appropriate designs should be considered in creating models that better conform to the higher order responses. Furthermore, the optimization work can be improved by iteratively looking at ever smaller parameter space.