Optimizing Electrodialytic Recovery of Mineral Ions from Bittern Wastewater Using D-Optimality Design

Electrodialysis has been proven effective due to its high selectivity for separating monovalent and divalent ions. This study statistically evaluated the simultaneous electrodialytic recovery of mineral ions from bittern wastewa - ter. The objective was to investigate the effect of cell number, anode materials, and applied voltage to optimize mineral ion recovery. A D-optimality design response surface methodology was performed to estimate the model parameter and identify the factors contributing to mineral ions recovery. The effects of independent variables and their interactions on the responses were investigated using ANOVA. All developed models were highly significant, with a p -value of <0.0001. The applied voltage was considered very important for the recovery process of all mineral ions as it affects the driving force of ion migration through the ion-exchange membrane. The optimiza - tion analysis (desirability value of 0.967) revealed 12% Cl – , 14% SO 4 2– , 0.7% Mg 2+ , and 21% Ca 2+ recovery at the combination of 5-cells configuration, graphite electrode, and 9 V.

Bittern contains a high concentration of minerals, such as chloride, magnesium, sodium, calcium, potassium, and sulfate (Dave and Ghosh 2005; Kartika and Bagastyo 2022) that can be recovered to increase their potential added value. The extraction of minerals from rejected brine or bittern wastewater has gained much interest in the past few decades. The recovery of minerals is typically carried out by nanofiltration, electrolysis, electrodialysis, precipitation, solvent extraction, ion exchange, or thermal operation (Bagastyo et al. 2021b). Those technologies can be used as a sole recovery treatment or combined to enhance recovery efficiencies.
In this study, electrodialysis was used to recover mineral ions from bittern wastewater. This technology employs the driving force of ionic exchange membranes to separate ions from the Optimizing Electrodialytic Recovery of Mineral Ions from Bittern Wastewater Using D-Optimality Design solution (Strathmann 1986). Electrodialysis has advantages such as higher ion selectivity, low energy consumption, and a wide range of operational pH. It also has low waste by-products since fewer/no chemicals are required (Bagastyo et al. 2021a). Previous studies have proven that electrodialysis can be used to recover metals, minerals, or nutrients from various wastewater (Barakwan et al. 2019;Hikmawati et al. 2019; Mohammadi et al. 2021). Several parameters that may affect the performance of the electrodialysis process include temperature, flow rate, feed pH, salinity, current density, applied voltage, the concentration of coexisting ions, and the type of membrane (Nie et al. 2017;Ye et al. 2018;Zhang et al. 2020).
Apart from those parameters, the number of cells in the reactor configuration may also affect the efficacy process since it affects the membrane surface area and involves the recirculation process of feed water. To the author's knowledge, the effect of cell number and applied voltage on the process performance has rarely been statistically discussed. For this reason, this study aims to investigate the effect of cell number, anode materials, and applied voltage to optimize the recovery of mineral ions (e.g., Cl -, SO 4 2-, Mg 2+ , and Ca 2+ ). The experiments were performed using D-optimality design response surface methodology (RSM). The application of RSM could simplify the number of experimental runs, evaluate multiple parameters and their interaction with the response, and optimize the process (Wang et al. 2010). Moreover, the Doptimality design would search the candidates for the best design point and estimate the effects of the factors. Applying this method can identify the active factor that mostly drives the recovery process using a minimum number of experiments. In addition, specific energy consumption for each recovered mineral ion was also calculated for economic consideration.

Bittern characteristics
Bittern wastewater was taken from a salt processing industry located in Surabaya, Indonesia. This wastewater is a residual stream of the salt washing process that uses brine (20)(21)(22)(23)(24)(25) as the washing water. The bittern characteristics are described in Table 1.

The electrochemical process design
The experiments were carried out using acrylic reactors that consisted of 3-cell compartments (external dimension of 14 x 5 x 24 cm) and 5-cell compartments (external dimension of 14 x 8 x 24 cm), as seen in Figure 1. Each compartment was separated by ion exchange membranes, i.e., AMI-7001 or CEM-7000 (Membrane International Inc., USA), with a dimension of 14 x 24 cm (active surface area of 336 cm 2 ). Each experiment was conducted for 5 hours. Before experiments, the membranes were immersed in a 5% NaCl solution for 12 h for the pre-conditioning process. The anode comprises of platinum (Pt) and graphite plates, while the cathode is stainless steel (SS). The electrodes have an active surface area of 24 cm 2 (3 x 8 cm) each. The distance of electrodes was arranged at 2 cm for the 3-cell compartments and 6 cm for the 5-cell compartments. The experiment was performed galvanostatically using a 60 V/30 A DC power supply (Volomax KXN-6030D, China).

Analytical methods
All chemicals used in this process were analytical grade. The parameter analyses were duplicated and carried out according to the standard method (American Public Health Association 2005). A total of 100 mL samples were collected from each experiment and immediately filtered using a 0.45 μm syringe filter (ANPEL Technology, Shanghai, Inc.). The pH and TDS measurements were conducted using a handheld pH/TDS meter (YK-2005 WA, Lutron, Taiwan). The Cland SO 4 2ions were analyzed using argentometric Mohr and turbidimetric methods, respectively.
Additionally, the measurement of Mg 2+ and Ca 2+ ions was performed using the titrimetric method. The concentration of COD was determined by the closed reflux and colorimetric method (Merck and Spectroquant NOVA), whereas the BOD 5 measurement was carried out by the titrimetric method and Winkler analysis. A scanning electron microscope-SEM (EVO MA10, Carl Zeiss) equipped with an energy dispersive x-ray (EDX) system was used to observe the morphology and characteristic of the recovered precipitates in the experiment.

Experimental design
The experiments and statistical analysis were conducted using Design Expert (version 11.1.2.0, Stat-Ease, Inc., USA). The individual factors of the model comprise of applied voltage (e.g., 3, 5, 7, 9 V), cell number (e.g., 3-cell and 5-cell), and electrode types (e.g., Pt and graphite). In this model, the applied voltage was set as a 4-level discrete numeric type, while the cell number and electrode type were sequentially set as 2-level ordinal and nominal categoric types. The ordinal scale was meant for a categorical variable with ordered categories, whereas the nominal scale is for a categorical variable without natural order (Agresti 2002). By default, the D-optimality required a minimum of 5 lack of fit points. However, the experimental design was set to 4 fit points and replicated to minimize the number of runs. Thus, a total of 20 runs were carried out in this study (i.e., 12 model points, four lack of points, and four replicate points). Statistical analysis was conducted using analysis of variance (ANOVA). The quality and significance of the developed models were determined using coefficient R 2 , adjusted R 2 , and the Fischer F-test. The p-value < 0.05 indicates that the term is significant.

Data analysis
The recovery efficiency of minerals was calculated as follows: where: η (%) is the recovery efficiency of mineral ions; C 0 (mg L -1 ) is the initial concentration of a mineral ion in the feed solution; C t (mg L -1 ) is the concentration of a mineral ion in the concentrated compartment; C rt (mg L -1 ) is the concentration of a recovered mineral ion in the recovered tank; V ct (L) is the volume of the concentrate solution at time t. a) b)

Recovery of mineral ions
Based on Figure 2, the overall recovery percentages can be ranked as follows: Ca 2+ > SO 4 2-> Cl -> Mg 2+ . The recovery efficiency was substantially enhanced with the increased applied voltage and cell number. These results were in accordance with Honarparvar and Reible (2020), who revealed that increasing cell number could improve ion transport across the membrane by amplifying the residence time involved in salt fluxes and osmotic transport. These results also showed that graphite electrodes provide better ionic mobility than Pt due to their higher conductivity. Nonetheless, only 0.25-21.48% of targeted ions can be recovered from bittern wastewater, which was very low considering the removal of ions can be up to 93%, 61%, 86%, and 85% for Cl -, SO 4 2-, Mg 2+ , and Ca 2+ , respectively. The lower recovery percentages of ions were likely because the recovery calculation only considered the dissolved ions and disregarded the readily formed precipitates in the electrode and membrane.

Model fitting and statistical analysis of mineral recovery
The experimental results ( Table 2) revealed slight differences in chloride, sulfate, magnesium, and calcium recovery percentages throughout each variable combination. According to the data, the anions recovery varied from 3.4-14.78% and 4.21-14.91% for Cland 2-, respectively. Meanwhile, the cations recovery ranged from 0.25-0.72% for Mg 2+ and 8.63-21.48% for Ca 2+ . The highest percentage recoveries of Cl -(14.78%), SO 4 2-(14.19%), Mg 2+ (0.72%), and Ca 2+ (21.48%) were achieved at a 5-cell reactor using a graphite electrode and 9 V of voltage. While the minimum percentages of recovery were mainly obtained at a 3-cell reactor using a Pt electrode and 3 V of voltage.
A D-optimal design was then used to determine the independent factor's effects and interactions. The obtained results were then evaluated using the sequential model sum of squares test and model summary statistics. By focusing on the maximum adjusted R 2 (adj. R 2 ) and predicted R 2 (pred. R 2 ), it was found that each response may fit a different model ( Table 3). As observed, the quartic model of all responses was found to be aliased; thereby, it cannot accurately fit the design. For this reason, this study uses the suggested models (i.e., linear, linear, 2FI, and cubic) to describe the effects of cell number, applied voltage, and electrode type on the simultaneous removal of Cl -, SO 4 2-, Mg 2+ , and Ca 2+ . The coded mathematical equations of those polynomial models can be expressed using the following equations: where: Y is the predicted response; k is the number of design factors; β 0 is the constant coefficient; β i is the linear term; β ij , β iij , β ijj , β ijk are the coefficient interaction, β ii , β iii are the quadratic and cubic terms, respectively; X i and X j are an independent factor; X i 2 and X i 3 are the quadratic and cubic terms of the factors; ε is the error term.
Subsequently, regression analysis and ANOVA were performed according to the suggested models. The Cl -, SO 4 2-, Mg 2+ , and Ca 2+ model terms were all highly significant (confirmed by a p-value of < 0.0001 and F-value of 22.67, 254.98, 40.68, and 86.07, respectively). In contrast, the lack of fit of the developed models was not significant, showed by the pvalue of 0.3140 (Cl -), 0.4933 (SO 4 2-), 0.2032 (Mg 2+ ), and 0.1591 (Ca 2+ ). This non-significant lack of fit is crucial for the model to smoothly fit. Furthermore, the coefficient of determination (R 2 ) assesses the proportion of variation explained by the model relative to the mean of the response (Anderson and Whitcomb, 2017). A value of R 2 over 0.9 is said to be highly correlated. However, this value may exhibit a statistical bias, particularly when the model is built based on a relatively small sample size (Anderson and Whitcomb, 2017). As an alternative, the adj. R 2 could provide a more accurate fit measure than R 2 since it reflects the number of factors involved in the model. Based on the statistical fitting (Table 4), the adjusted R 2 of all responses was between 77-98%, indicating a strong significance of the model to fit the experimental data and predict the response value. The predicted R 2 values of all models agreed with adj R 2 (indicated by the difference value < 0.2). Adequate precision is measured by dividing the maximum and the minimum predicted response by the mean standard deviation of predicted responses (Montgomery, 2013). In our study, the adequate precision of all models exceeded 4, which is desirable and indicates an adequate signal-to-noise ratio.
The effects of the independent factors on the responses are described in Table 5. The significant value of the coefficient indicates a substantial contribution to the recovery of targeted minerals. As observed, the p-value of linear coefficients (applied voltage, cell number, and electrode type) was significant to the recovery of all targeted mineral ions. The linear coefficient of cell number and electrode type was found insignificant except for magnesium and calcium recovery.
Meanwhile, the coefficient of interaction between x 1 x 2 (applied voltage and cell number) and x 1 x 3 (applied voltage and electrode   type) indicated a highly significant effect on magnesium recovery. Likewise, the interaction coefficient between x 1 x 3 (applied voltage and electrode type), the quadratic coefficient of applied voltage, the interaction between x 1 2 x 3 (the quadratic coefficient of applied current and the linear coefficient of electrode type), and the cubic coefficient of applied voltage showed significant model terms to the calcium recovery. The polynomial regression equation for mineral ions recovery in terms of actual factors can be written in Table 6.

Model adequacy
In addition, an adequacy check was performed to validate the developed model. Model validation is required to prevent poor or misleading results from the analysis (Box et al., 1978). Figure 3 illustrates the plot of residuals versus the predicted responses, the graph of predicted responses versus the actual responses, and the box-cox plot for power transform. It can be seen that a random scatter was found in all the plots of residuals versus the predicted responses. A constant range of residuals was distributed across the graph and around the zero line up to a value of 3.62-4.59, suggesting a good linear relationship between residual and predicted response. An outlier was found in the residual plot of magnesium recovery. However, it does not deviate significantly from the normal pattern of the entire data set. The graph of predicted responses versus the actual responses aims to identify a group of responses that are not easily predicted by the model. It can be seen that all points are close to the fitted line and have a narrow confidence band, which is considered a good fit for the model. Meanwhile, it can also be observed that some models (i.e., chloride and sulfate recovery) went through a box-cox plot transformation to improve their statistical analysis and diagnostic plots. As illustrated, chloride and sulfate recovery models (Fig. 3 a-b) were transformed into inverse and square root transformations, respectively, which are the closest to the best lambda (λ) value and within the confidence interval (CI).
In contrast, the magnesium and calcium recovery model (Fig. 3 c-d) did not require any transformation since the lambda (λ) optimal values already lie between two pink limit lines, i.e., 3.806 to -3.806 for Mg 2+ recovery, and 4.594 to -4.594 for Ca 2+ recovery.

Optimization of responses
The optimization process searches for a combination of factors that can meet each factor's desired criteria and responses. Numerical optimization was applied to search the factor space for the best trade-offs to achieve multiple goals. All individual factors were set "as in range" with the same weight and importance level. Meanwhile, the responses were set as "maximize" to optimize the mineral ion recovery. The ideal desirability function is 1 (Montgomery 2013). According to the result, optimal recovery can be achieved using 5-cell compartments and 9 V voltage with a graphite electrode. As seen in Figure 4, the highest desirability value of Cl -, SO 4 2-, Mg 2+ , and Ca 2+ recovery was 0.967. An additional experiment was performed based on the optimal scenario to verify the predicted result (Table 7).

CONCLUSION
This study evaluated the simultaneous recovery of mineral ions from bittern wastewater with the electrodialysis process. These results showed that the percentage of recovered minerals was quite small due to unaccounted precipitates that may be deposited in the electrodes or ion exchange membranes. The statistical analyses of mineral recovery were determined using the D-optimality design approach. The minerals recovery was correspondingly fit into linear (for Cl -), linear (for SO 4 2-), 2FI (for Mg 2+ ), and cubic polynomial models (for Ca 2+ ) with adjusted R 2 between 77-98% and p-value < 0.001. The results illustrated that the linear coefficient of the applied voltage was highly significant to the responses. The linear coefficient of cell number and electrode type was also significant to the responses, except for magnesium and calcium.