# Ion Exchange Dialysis for Aluminium Transport through a Face-Centred Central Composite Design Approach

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}and standard deviation of the model are 0.9548 and 0.2932, respectively. Depending on the time zone of reference (24 h or 32 h), the highest enrichment of >1.50 was achieved. The designed variables were numerically optimized by applying the desirability function to achieve the maximum Al transport. The optimised condition values were found to be a feed concentration of 1600 ppm, feed flowrate of 61.76%, sweep flowrate of 37.50% and sweep concentration of 0.75 N for the 80% target response at 32 h. Overall, the model can be used to effectively predict Al recovery using the designed system.

## 1. Introduction

_{3}

^{−}, PO

_{3}H

^{−}, –COO

^{−}, PO

_{3}

^{2−}and C

_{6}H

_{4}O

^{−}, and that of AEMs are NH

_{3}

^{+}, NRH

^{2+}, NR

_{2}H

^{+}, NR

_{3}

^{+}and PR

_{3}

^{+}[11,12,13].

^{+}, Na

^{+}and Cs

^{+}) and divalent (Ca

^{2+}and Mg

^{2+}) transport [32,33,34,35]. Further records on the application of IED using Nafion 117 for Al

^{3+}have shown a high recovery of >70% [16]. Despite the high Al recovery, there is limited information on the effect of process variables on Al transport through Nafion 117 CEMs. A comparative study on the effect of sweep concentration and different membranes (homogeneous Nafion 117 and heterogeneous Ionac 3470) on the recovery was performed using a one-factor-at-a-time (OFAT) approach [36].

_{o}is a constant coefficient; $\beta $

_{i}is a linear coefficient; $\beta $

_{ii}is the quadratic coefficient; $\beta $

_{ijk}is the interaction coefficient; $\epsilon $ is the random error; and k is the number of variables studied.

## 2. Materials and Methods

#### 2.1. Materials and Chemicals

_{2}(SO

_{4})

_{3}·18H

_{2}O (≥97%) and HCl (32% w/w) was supplied by Lichro Chemicals, South Africa. Demineralized water (17.5 MΩ/cm, Purite-HP+BOOST 030773) was used. These reagents were used without further purification. The Nafion 117 with an equivalent weight of 1100 g, thickness of 177.8 µm and ion exchange capacity of 0.94 meq/g (as provided by the manufacturers) was used for this experiment. Generally, Nafion (C

_{7}HF

_{13}O

_{5}S·C

_{2}F

_{4}) is a long side chain thermoplastic resin made by the copolymerization of hydrophobic tetrafluorothylene and perfluorovinyl ether which is terminated at the end with a sulfonyl fluoride (SO

_{2}F). Preceding acid treatment (3 wt% HCl, 90 °C, 1 h), the CEM was soaked in demineralized water for 15 min, heated at 60 °C in 3 wt% H

_{2}O

_{2}, and rinsed with demineralized water. Further treatment steps included pre and post rinsing with demineralized water after another acid conditioning (1 wt% HCl, 25 °C, 180 min) for 15 min.

#### 2.2. Experimental Design and Statistical Analysis

_{1}), feed flowrate (%; X

_{2}), sweep flowrate (%; X

_{3}) and sweep concentration (HCl; X

_{4}). The Al

^{3+}transport (Y

_{1}) was considered as the dependent factor (response). Performance of the counter flow IED system was evaluated by analysing the Al in the feed and sweep chambers.

_{i}is the dimensionless coded value of the i-th independent variable; X

_{i}is the un-coded value of the i-th independent variable; X

_{i}is the real value of the independent variable; X

_{0}is the value of X

_{i}at the centre point; and $\Delta $X is the step change value of the variable i.

^{k}factorial portion augmented by 2k axial points and accentor runs (cp), where k is the number of variables. Information about the response system and evaluation of the significance of the factors is mostly achieved at the first order design [42]. According to the FC-CCD matrix, Table 1, a total of 30 (=2

^{k}+ 2k + cp) runs comprising of 16 factorial points, 8 axial points and 6 centre points is required. The remaining five are centre point replications to get a good estimation of the experimental error via the sum of squares. Furthermore, the proposed matrix by the software was randomized in order to prevent systematic error.

#### 2.3. Ion Exchange Dialysis Set-Up

^{2}. The process involved recirculation of the feed and sweep with a pump of maximum flowrate of 2.6 mLs

^{−1}. Pump calibration was performed using a randomized complete block design in order to reduce residual error and controlling nuisance factors. The volume ratio of the feed to the sweep was 2:1. The feed and sweep electrolyte solutions were prepared as provided in Table 1 and homogeneity was ensured during the experiment with the aid of magnetic stirrers. Previous work done by the authors expounds on the choice of the ranges for the variables of concern [41]. All experiments were performed in an air-thermostated room between 22 and 25 °C. The data obtained was evaluated in terms of Al transport (%) from the feed solution as follows:

_{feed}

_{(0)}and [Al]

_{feed}

_{(t)}denote, respectively, the aluminium concentrations at time t = 0 and at an elapsed time, t, in the feed compartment.

#### 2.4. Analytical

_{3}to volume. The total loss of the feed and sweep solution due to sampling was between 3% and 4% of the total volume [41].

## 3. Results

## 4. Discussion

#### 4.1. Regression Models and Statistical Testing

^{2}) [45].

^{2}recorded for the cubic model (0.27 and 0.99, respectively), the quadratic model showed a better correlation than the cubic, linear and 2FI models. The efficiency of variability in the actual response values can be expounded on by the experimental value and their interactions as given by the act-R

^{2}. However, the acceptable difference between the act-R

^{2}and the adj-R

^{2}should be less than 0.2 [40]. Statistically, a high adj-R

^{2}(>0.75) is acceptable [46].

_{2}, X

_{4}and X

_{1}X

_{4}) while the negative signs (X

_{1}, X

_{1}X

_{2}$,{X}_{1}^{2},{X}_{2}^{2}$ and ${X}_{4}^{2}$) indicates the antagonistic effect. The actual values of the model terms in their specified units can be fitted into Equation (5) to predict the Al

^{3+}transport at 32 h.

#### 4.1.1. Analysis of Variance (ANOVA)

^{2}indicates the percentage of the variation in the response that is attributed to the input variables [47]. In Table 5, the indicated act-R

^{2}of 0.9548 was close to 1. This represented 95.48% variability of the predicted response value (Al

^{3+}transport), which is a function of the four process variables. The adj-R

^{2}(0.9358) also represents 0.0642 of the variations in the response that cannot be attributed to the significant independent terms. The clear exemption of statistically insignificant terms in the model was through the forward screening method under the condition (p-value ≤ α = 0.05).

_{1}, X

_{2}, X

_{4}), two way interaction (X

_{1}X

_{2}and X

_{1}X

_{4}) and pure quadratic effect (${X}_{1}^{2},{X}_{2}^{2}$ and ${X}_{4}^{2}$) were highly significant for Al

^{3+}transport. More so, the F-value of 50.18 implied the model term was statistically significant and there was only a 0.01% chance that the large F-value could be due to noise. F-values of the independent variables X

_{1}, X

_{2}and X

_{3}were 148.28, 28.95 and 107.66, respectively. Considering the F-values, the effect of the independent variables on Al

^{3+}mobility was therefore high for variables with a high F-value. The calculated CV of 3.48% further assented to the reliability of the model. A measure of the relative dispersion with respect to the mean provides information on the reproducibility, repeatability and precision of the model, where CV < 10% [48,49]. The adequate relationship between the signal–to-noise ratio must also exist to inform that the model can be used to navigate the design space. The signal-to-noise ratio, given by the adequacy precision, was 22.839, which is >4. Therefore, the noise level did not compete with useful information from the model.

#### 4.1.2. Diagnostic Plots

^{2}and adj-R

^{2}within 20% was found to be significantly acceptable. Meloun and Militky [50] suggested that a model could be used after a residual analysis has been performed, whereby the residual analysis is used to investigate outliers and detect influential observations. In Figure 3a, the diagnostic plot of the model with the pred-R

^{2}of 0.8736 showed that data points were close to the diagonal line. Likewise, in Figure 3b, the data points of the residuals followed a normal distribution as maximum plots are interlocked with the straight line. Furthering the residual analysis, Figure 3c showed a conformance to a random non-linear scattering trend along the run number and the absence of outliers. As such, there was no time-related variable lurking in the background. While the negative residual implies an over prediction, a positive residual indicates a low prediction. A plot close to the estimated regression line at zero (0) expounded on the exactness of prediction.

#### 4.2. Combined Effects of Operating Parameters on the Response

_{1}X

_{2}), as well as feed concentration and sweep concentration (X

_{1}X

_{4}). The three-dimensional plots (3D-plots) of the regression model were used for the graphical explanation of the interactions. Corresponding response surface plots (RSM) obtained from Equation (5) are presented in Figure 4a–c and Figure 5a–c. The degree of curvature on the 3D-plots depicts the levels of uncertainties attributed to the parametric interactions. Decision making using the RSM must take into account the variable effects on the response and the economic implications. For any good decision, there must be a balance between the considerations. Comparative Al transport at 24 h (Figure 4c and Figure 5c) and 32 h was undertaken using contour plot studies. Random flagged points (Prd) are shown on figures to illustrate the prediction points.

^{3+}transport at a decreasing feed concentration. At higher flowrates >55%, the Al-transport ranged between 80% and >90% for a feed range of 100 ≤ X

_{1}≤ 1070 ppm at 32 h. An estimated 55–62% transport (Figure 4c) was also observed for decreasing feed concentration from 2000 ppm to about 1740 ppm at 24 h. As such, a higher feed flowrate does not translate into high mass transport at a high feed concentration. Recirculation of feed for a longer time increased the transport as long as the potential difference across the feed and sweep ends existed. A low transport of <60% was therefore reported between 1930 and 2000 ppm for a >75% flowrate at 32 h (Figure 4b). Under low to mid flow schemes (35–55%), one should expect an estimated 65% to >78.5% Al

^{3+}transport from the feed phase with an operating feed concentration of 17,450–1340 ppm in 32 h.

^{3+}increased with increasing sweep concentration. However, the negative impact of the increasing feed concentration was observed again in Figure 5a as the steepest point towards 2000 ppm. The mid to lowest Al-transport occurred at a lower sweep strength for sweep concentration of 0.25–0.38 N HCl. At that sweep concentration range, a transport of 42%–54% was observed for feed regions of 1800 to >1950 ppm. While attribution of the low Al transport to the drawing potential of the acid is valid, the bulk distribution at the membrane boundary at a high feed concentration could also be a great contributor to the reduced stoichiometric ion exchange. Above 0.48 N HCl, a feed range of 100–1550 ppm resulted in 70% to >90% target ion mobility (Figure 5b). An increasing operating concentration above 1N to maximize transport is not advisable. This can result in osmotic dehydration of membrane structure, loss of solute across sweep phase and osmotic transport [52]. The peak point on the curvature of Figure 5a, which reflected as the oval shape in Figure 4b, expounds on the high transport (93–94.1%) being in the region of 0.7–0.81 N HCl for a feed concentration ≤500 ppm. Observing Figure 5c at 24 h, an Al mobility of 60–68% is obtained for a 0.72–0.84 N and 1750–1980 ppm acid and acidic salt solution concentration, respectively. The high points (83–86%) for transport at 24 h occurred for a sweep concentration of 0.7–0.84 N and a feed concentration of 120–640 ppm. Therefore, any model generated for 24 h would predict within the range of responses observed in Figure 4c and Figure 5c (max = 90%). Interactions with sweep flowrate, which singularly has a linear-horizontal effect, and others such as X

_{1}X

_{3}was excluded due to p > 0.05.

#### 4.3. Enrichment Effect

^{3+}highs at 0.25, 0.625 and 1 N were 0.63, 0.90 and 1.19 for 24 h and 0.70, 1.01 and 1.33 for 32 h, respectively.

#### 4.4. Desirability

_{i}) are transmuted into individual scale-free desirability values with a range of 0 ≤ d

_{i}≤ 1. A dimensionless desirability value of 0 indicates the response is outside of an acceptable region and the quality of the response is therefore undesirable. Having the response at its goal or target signifies that d

_{i}= 1. In the Design Expert 11.0 worksheet, the goals of the desirability functions of the response are structured into minimum or maximum, within range or target and none. The goals of the factors only are set to exact values. The design variables are then chosen to maximize the overall desirability [53]:

_{l}and L

_{u}), optimal value (red dotted for process variables and blue dotted for response) and desirability of the process variables and response. Out of a total of 51 solutions, the optimal parameters to achieve Al transport for feed concentration, feed flowrate, sweep flowrate and sweep concentration was 1600 ppm, 61.74%, 43.83% and 0.75 N, respectively, for the 32 h Al-transport model. The optimum results for maximum Al-transport is desirable with a combined desirability of 0.964, which is close to 1. To validate the results and performance of the counter flow IED system, five experimental runs at three-day intervals were conducted with optimal values of the process variables. An Al transport of 77.13% ± 4.19% was observed as compared to the set target of 80% and 78.81% predicted by the model. Setting an Al-permeation target at 70% for a 24 h experimental period, a difference of 1.23 was observed between the target and validation value at a desirability of 1 [41]. Although different targets were set for the two study zones, the closeness of the desirability to 1, the mechanism of the ion transport and the difference between the predicted and actual coefficient of variation plays an important role in the validation of optimum conditions.

## 5. Conclusions

^{2}(0.955) and adj-R

^{2}(0.936) values indicates the model at 32 h has a better goodness-of-fit and can navigate through the design space. The regression model for Al transport was obtained. A strong relation between the experimental and predicted results is shown by the 0.874 pred-R

^{2}and a standard deviation of 0.29. The interactive influence of the IED variables are illustrated and assessed in 3D surface and contour plots. An increase in feed concentration has a negative effect on Al transport. Positive impacts are observed with feed flowrate and sweep concentration. The impact of the sweep flowrate is not significant. Enrichment by Nafion 117 on the 2:1 by volume of the counter-flow IED system is between 0.47 and 1.65. The optimized parameters of the IED system are obtained to achieve the target transport using the desirability approach. Comparing the validated results to the predicted values by RSM, the optimized IED produces ±4.19 and shows that the RSM and desirability approach are reliable. The outcome of this research serves as a baseline to the Al-transport study for independent and interacting variables to determine operational periods for optimum recovery at the different time zones of 24 h and 32 h. Acidification of the residue for optimum recovery is reported at different pH values and it should be of future interest to investigate the effect of varied pH and other process variables on Al permeation.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**(

**a**) Predicted versus actual values plot; (

**b**) normal probability plot; (

**c**) residual versus total run plot.

**Figure 4.**(

**a**) Response surface plot for the interactive effect of feed flow and feed concentration at 32 h; (

**b**,

**c**) contour plots of Al transport as a function of feed flow and feed concentration at 32 h and 24 h, respectively.

**Figure 5.**(

**a**) Response surface plot for the interactive effect of sweep concentration and feed concentration at 32 h; (

**b**,

**c**) contour plots of Al-transport as a function of feed flow and feed concentration at 32 h and 24 h, respectively.

**Figure 6.**(

**a**) Enrichment factor plot for 24 and 32 h. (

**b**) Enrichment plot based on feed concentration.

**Figure 7.**(

**a**) Optimal value for the feed concentration for 32 h; (

**b**) Optimal value for the feed flowrate for 32 h; (

**c**) Optimal value for the sweep flowrate for 32 h; (

**d**) Optimal value for the sweep concentration for 32 h; (

**e**) Optimum results for Al transport for 32 h.

**Table 1.**Coded and actual values of variables of the design of experiments for overall Al-transport optimization.

Symbol | Variable | Coded Levels of Variables | ||
---|---|---|---|---|

−1 | 0 | 1 | ||

X_{1} | Feed concentration (ppm) | 100 | 1050 | 2000 |

X_{2} | Feed flowrate (%) | 25 | 55 | 85 |

X_{3} | Sweep flowrate (%) | 25 | 55 | 85 |

X_{4} | Sweep concentration (N) | 0.25 | 0.625 | 1 |

Run Order | Variable Level | Response (%) | ||||
---|---|---|---|---|---|---|

X_{1} | X_{2} | X_{3} | X_{4} | 24 h | 32 h | |

1 | 1 | −1 | −1 | −1 | 28.55 | 35.95 |

2 | 1 | 1 | 1 | −1 | 33.35 | 45.65 |

3 | −1 | 1 | −1 | −1 | 75.90 | 84.10 |

4 | 1 | −1 | 1 | 1 | 61.6 | 71.85 |

5 | −1 | −1 | −1 | 1 | 70.2 | 78.25 |

6 | 0 | 0 | 0 | 0 | 79.1 | 86.00 |

7 | 1 | 1 | −1 | 1 | 64.25 | 73.45 |

8 | −1 | −1 | 1 | −1 | 58.15 | 61.60 |

9 | −1 | 1 | 1 | 1 | 86.95 | 93.55 |

10 | 0 | 0 | 0 | 0 | 78.82 | 86.05 |

11 | −1 | 1 | −1 | 1 | 87.50 | 94.85 |

12 | 0 | 0 | 0 | 0 | 78.36 | 85.96 |

13 | 0 | 0 | 0 | 0 | 78.62 | 85.85 |

14 | 1 | 1 | 1 | 1 | 51.60 | 63.85 |

15 | −1 | 1 | 1 | −1 | 81.40 | 90.00 |

16 | −1 | −1 | 1 | 1 | 57.95 | 68.75 |

17 | 1 | 1 | −1 | −1 | 32.55 | 32.85 |

18 | 1 | −1 | −1 | 1 | 56.95 | 66.95 |

19 | −1 | −1 | −1 | −1 | 58.80 | 65.85 |

20 | 1 | −1 | 1 | −1 | 30.25 | 34.50 |

21 | 0 | 0 | 0 | 0 | 78.98 | 86.01 |

22 | 0 | −1 | 0 | 0 | 52.57 | 60.52 |

23 | −1 | 0 | 0 | 0 | 78.55 | 84.98 |

24 | 0 | 0 | 0 | 1 | 84.81 | 90.19 |

25 | 0 | 1 | 0 | 0 | 72.19 | 80.71 |

26 | 0 | 0 | 1 | 0 | 66.95 | 77.33 |

27 | 0 | 0 | 0 | 0 | 78.99 | 87.12 |

28 | 0 | 0 | −1 | 0 | 75.90 | 81.90 |

29 | 0 | 0 | 0 | −1 | 48.71 | 54.48 |

30 | 1 | 0 | 0 | 0 | 50.65 | 58.75 |

Source | Sum of Squares | Df | Mean Square | F-Value | p-Value (Prob > F) |
---|---|---|---|---|---|

Mean vs. Total | 2130.42 | 1 | 2130.42 | ||

Linear vs. Block | 24.49 | 4 | 6.12 | 12.09 | <0.0001 |

2FI vs. Linear | 4.74 | 6 | 0.7899 | 1.94 | 0.1316 |

Quadratic vs. 2FI | 5.79 | 4 | 1.45 | 16.72 | <0.0001 |

Cubic vs. Quadratic | 0.7625 | 8 | 0.0953 | 1.32 | 0.3974 |

Residual | 0.3623 | 5 | 0.0725 | ||

Total | 2166.56 | 28 |

Response | Source | Standard Deviation | Actual R^{2} | Adjusted R^{2} | Predicted R^{2} |
---|---|---|---|---|---|

Al^{3+} transport | Linear | 0.7117 | 0.6776 | 0.6216 | 0.4387 |

2FI | 0.6376 | 0.8088 | 0.6963 | 0.3961 | |

Quadratic | 0.2941 | 0.9689 | 0.9354 | 0.8034 | |

Cubic | 0.2692 | 0.9900 | 0.9459 | −3.6866 |

Source | Sum of Squares | Df | Mean Squares | F-Value | p-Value Prob > F |
---|---|---|---|---|---|

Regression model | 34.51 | 8 | 4.31 | 50.18 | <0.0001 |

X_{1}-Feed conc. | 12.74 | 1 | 12.74 | 148.28 | <0.0001 |

X_{2}-Feed flow | 2.49 | 1 | 2.49 | 28.95 | <0.0001 |

X_{4}-Sweep conc. | 9.25 | 1 | 9.25 | 107.66 | <0.0001 |

X_{1}X_{2} | 1.24 | 1 | 1.24 | 14.38 | 0.0012 |

X_{1}X_{4} | 3.01 | 1 | 3.01 | 34.97 | <0.0001 |

${X}_{1}^{2}$ | 0.4585 | 1 | 0.4585 | 5.33 | 0.0323 |

${X}_{2}^{2}$ | 0.6027 | 1 | 0.6027 | 7.01 | 0.0159 |

${X}_{4}^{2}$ | 0.4645 | 1 | 0.4645 | 5.40 | 0.0313 |

Residuals | 1.63 | 19 | 0.0859 | ||

Pure Error | 0.0018 | 3 | 0.0006 |

^{2}= 0.9548; Predicted R

^{2}= 0.8736; Adjusted R

^{2}= 0.9358; Adequate Precision = 22.8386.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Asante-Sackey, D.; Rathilal, S.; V. Pillay, L.; Kweinor Tetteh, E.
Ion Exchange Dialysis for Aluminium Transport through a Face-Centred Central Composite Design Approach. *Processes* **2020**, *8*, 160.
https://doi.org/10.3390/pr8020160

**AMA Style**

Asante-Sackey D, Rathilal S, V. Pillay L, Kweinor Tetteh E.
Ion Exchange Dialysis for Aluminium Transport through a Face-Centred Central Composite Design Approach. *Processes*. 2020; 8(2):160.
https://doi.org/10.3390/pr8020160

**Chicago/Turabian Style**

Asante-Sackey, Dennis, Sudesh Rathilal, Lingham V. Pillay, and Emmanuel Kweinor Tetteh.
2020. "Ion Exchange Dialysis for Aluminium Transport through a Face-Centred Central Composite Design Approach" *Processes* 8, no. 2: 160.
https://doi.org/10.3390/pr8020160