# Micellar-Enhanced Ultrafiltration to Remove Nickel Ions: A Response Surface Method and Artificial Neural Network Optimization

^{*}

## Abstract

**:**

_{SDS}= 10.05 mM, and MWCO = 10 kDa, resulting in a rejection rate of 98.16% and a flux of 119.20 L/h∙m

^{2}. Experimental verification indicates that the RSM model could adequately describe the performance indicators within the examined ranges of the process variables. An artificial neural network (ANN) modelling followed to predict the MEUF performance and validate the RSM results. The obtained ANN models showed good fitness to the experimental data.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

_{2}O) was purchased from Sigma-Aldrich, Canada. Its properties are listed in Table 2. Nickel sulfate hexahydrate (NiSO

_{4}∙6H

_{2}O, J.T. Baker) were used as sources of metal ions. The pH of feed solutions was adjusted to 8 ± 0.1. Nickel reference standard solutions (1000 ppm ± 1%/certified) for Flame Atomic Absorption (FAA) tests were purchased from Fisher Scientific and diluted as needed. Distilled water was used in all experimental procedures. Permeate samples were collected and stored using sorption-free materials.

#### 2.2. Dead-End Ultrafiltration Experiments

^{2}). An initial 250-mL feed solution was filled and continuously stirred (at a constant rate to get effective agitation and prevent membrane fouling) in each experimental run. All experiments were conducted at room temperature (23 ± 1 °C). The applied transmembrane pressure was controlled by pressurized nitrogen gas.

#### 2.3. Sample and Data Analysis

_{P}) were measured using a Varian Model 55B SpectrAA FAA Spectrophotometer at 232.0 nm. The mean values of triplicate measurements for each permeate sample were calculated (%RSD ≤ 1.3%). FAA calibration curves were made before each set of measurement (R

^{2}> 0.999).

_{p}and C

_{r}denote the nickel concentration in the permeate and retentate, respectively. C

_{r}was calculated using material balance.

#### 2.4. Response Surface Modeling

#### 2.4.1. Design of Experiments

#### 2.4.2. RSM Modeling

_{0}the constant coefficient, b

_{i}the linear coefficients, b

_{ii}the quadratic coefficients, b

_{ij}the interaction coefficients; n the number of design variables, and X

_{i}, X

_{j}the coded levels of design variables.

^{2}), the adjusted R-squared (R

^{2}-adj), and the predicted R-squared (R

^{2}-pre). The R

^{2}value increases with the number of model terms, even when non-significant terms are added to the model. Therefore, the R

^{2}value of a refined model is usually smaller than that of the full model. The R

^{2}-adjusted coefficient is used to adjust to the number of model terms, where the addition of non-significant terms usually decreases the R

^{2}-adjusted value. The predicted R-squared shows how well a model predicts responses for new observations. Based on the obtained response surface models, optimal conditions were determined by maximizing the nickel rejection and the permeate flux.

#### 2.5. Artificial Neural Network (ANN) Modeling

^{2}for the ANN model. For comparison purposes, an inverse range scaling was performed on all modeling outputs to transfer them from (0, 1) to their original scales.

## 3. Results and Discussion

#### 3.1. Ultrafiltration Experimental Results

^{2}) in run 17, with a transmembrane pressure of 30 psi, nickel concentration of 1.25 mM, SDS concentration of 16.6 mM, and MWCO of 3 kDa. The maximum flux 178.28 L/h∙m

^{2}(R = 91.83%) was found in run 26 with 50 psi pressure, 1.25 mM nickel, and 16.6 mM SDS using membrane MWCO of 10 kDa. It can be seen that higher rejection (or flux) tends to compromise on lower flux (or rejection), yet in practice high values of both rejection (indicates MEUF effectiveness) and flux (indicates efficiency) are desired. As such, an operating condition generating high rejection and flux is needed.

#### 3.2. RSM Models

^{2}(0.8486) and adjusted R

^{2}(0.7813) was reasonably close to 1, showing good fitness of the regressed model. The difference between predicted R

^{2}and the adjusted R

^{2}is over 0.02. This may be due to the close values of the response (which can be sensitive to experimental and measurement errors).

^{2}(0.9972) and adjusted R

^{2}(0.9968) show good fitness of the regressed model. High predicted R

^{2}(0.9958) indicates that the model can well predict response for new observations.

_{Ni}+ 1.26 C

_{SDS}+ 2.60 MWCO − 0.05 (Pressure)(MWCO) + 0.32 C

_{Ni}C

_{SDS}− 0.06 (C

_{SDS})(MWCO) − 0.03 (C

_{SDS})²

_{Ni}≤ 2 mM, 8.3 ≤ C

_{SDS}≤ 24.9 mM, 3 ≤ MWCO ≤ 10 kDa. Equations (4) and (5) can be used to predict the nickel rejection for given levels of each factor.

_{SDS}− 0.09 MWCO + 0.024 (MWCO)²

_{Ni}≤ 2 mM, 8.3 ≤ C

_{SDS}≤ 24.9 mM, 3 ≤ MWCO ≤ 10 kDa.

_{SDS.}

#### 3.3. Effect of Factors on Rejection Rate and Permeate Flux

#### 3.3.1. Effect of Factors on Rejection

#### 3.3.2. Effect of Factors on Flux

#### 3.4. RSM Optimization

_{SDS}) to treat large volumes of water (maximize flux rate), as well as obtaining a high efficiency in removing nickel ions (maximize rejection).

_{Ni}=1 mM, minimum C

_{SDS}, and 3 ≤ MWCO ≤ 10 kDa. The predicted maximum rejection rate (major response) and flux (secondary response) are 98.16% and 119.20 L/h∙m

^{2}, respectively, where pressure = 30 psi, C

_{Ni}= 1.0 mM, C

_{SDS}= 10.05 mM, and MWCO = 10 kDa.

#### 3.5. ANN Modeling

^{2}were all higher than 0.99 (except for the testing values for rejection model, R

^{2}= 0.719), indicating a close match between the experimental and modeling results. Therefore, the trained ANN model was able to accurately simulate the rejection rate and permeate flux for nickel removal process.

## 4. Conclusions

^{2}) are: pressure = 30 psi, C

_{SDS}= 10.05 mM, and MWCO = 10 kDa. Verification experiments showed that the quadratic models could adequately predict the MEUF performance. Furthermore, ANN modeling showed good model fitness to the experimental data. This study shows that RSM and ANN models could be used and provide information for the MEUF treatment of nickel-contaminated water. In future works, a cross-flow MEUF system will be used to better reflect the industrial practice. Furthermore, the recycle and reuse of SDS will be attempted to further reduce the capital cost.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**A Schematic diagram of (

**a**) SDS monomer, (

**b**) SDS micelle (when SDS concentration > CMC) (

**c**) micellar-enhance ultrafiltration (MEUF) setup, and (

**d**) mechanism of MEUF removal of metal ions.

**Figure 2.**Response surface (

**a**) and contour (

**b**) showing the effect of pressure and MWCO on rejection rate. C

_{Ni}= 1.25mM, C

_{SDS}= 16.6mM.

**Figure 3.**Response surface (

**a**) and contour (

**b**) showing the effect of nickel and SDS concentrations on rejection rate. Pressure = 40 psi, MWCO = 5 kDa.

**Figure 4.**Response surface (

**a**) and contour (

**b**) showing the effect of SDS concentration and MWCO on rejection rate. Pressure = 40 psi, C

_{Ni}= 1.25 mM.

**Figure 5.**The scatter plots of ANN model predicted values (rejection rate of nickel ions) versus experimental values for (

**a**) training, (

**b**) validation, (

**c**) testing, and (

**d**) all data sets.

**Figure 6.**The scatter plots of ANN model predicted values (permeate flux) versus experimental values for (

**a**) training, (

**b**) validation, (

**c**) testing, and (

**d**) all data sets.

Solute | UF System (Surfactant and Flow) | RSM Design | Independent Variables | Optimization Model | References |
---|---|---|---|---|---|

Pb^{2+} | SDS, cross-flow | BBD (3 factors and 3 levels, 17 runs) | C_{SDS} (2–6 mM), S/M (5–15), pH (2–12) | ANN and ANFIS | [25] |

Zn^{2+} | SDS and Brij-35, cross-flow | FFD (7 factors, 22 runs) | Pressure, pH, C_{SDS}, S/M, L/M, C_{NaCl}, Brij35/SDS ratio | ANN, R^{2} > 0.91 | [26] |

Pb^{2+} | SDS, cross-flow | BBD (3 factors, 3 levels) | C_{SDS} (2–6 mM), S/M (5–15), pH (2–12) | Fuzzy logic models, R > 0.91 | [27] |

Pb^{2+} | CTAB, cross-flow | BBD (3 factors, 3 levels) | C_{SDS} (1.61–6.43 mM), S/M (5.64–13.8), pH (2.34–12.1) | Interval type-2 fuzzy logic | [28] |

Properties | Specifications |
---|---|

Name | Sodium dodecyl sulfate (SDS) |

Chemical structure | |

Ionic type | Anionic |

Molecular weight | 288.38 g/mol |

Critical micellar concentration (CMC) | 8.2-8.3 mM |

Factors | Levels | ||
---|---|---|---|

Minimum (−1) | Center (0) | Maximum (+1) | |

(A) Pressure (psi) | 30 | 40 | 50 |

(B) Ni concentration (mM) | 0.5 | 1.25 | 2 |

(C) SDS concentration (mM) | 8.3 | 16.6 | 24.9 |

(D) Molecular weight cut-off, or MWCO (kDa) | 3 | 5^{*} | 10 |

Std. | Run | Factor Input Variables | Response Variable | ||||
---|---|---|---|---|---|---|---|

Factor A Pressure (psi) | Factor B Ni conc. (Mm) | Factor C SDS conc. (Mm) | Factor D MWCO (kDa) | Rejection ^{a} (%) | Flux ^{a} (L/h∙m ^{2}) | ||

13 | 1 | 40 | 0.5 | 8.3 | 5 | 94.86 | 37.93 |

18 | 2 | 50 | 1.25 | 8.3 | 5 | 92.98 | 45.15 |

25 | 3 | 40 | 1.25 | 16.6 | 5 | 98.13 | 36.83 |

7 | 4 | 40 | 1.25 | 8.3 | 10 | 94.30 | 158.67 |

29 | 5 | 40 | 1.25 | 16.6 | 5 | 97.09 | 37.43 |

20 | 6 | 50 | 1.25 | 24.9 | 5 | 98.13 | 43.31 |

6 | 7 | 40 | 1.25 | 24.9 | 3 | 97.15 | 29.96 |

19 | 8 | 30 | 1.25 | 24.9 | 5 | 98.17 | 28.74 |

22 | 9 | 40 | 2 | 16.6 | 3 | 97.98 | 31.03 |

23 | 10 | 40 | 0.5 | 16.6 | 10 | 97.76 | 148.64 |

14 | 11 | 40 | 2 | 8.3 | 5 | 88.06 | 37.41 |

10 | 12 | 50 | 1.25 | 16.6 | 3 | 98.67 | 38.25 |

3 | 13 | 30 | 2 | 16.6 | 5 | 96.15 | 29.27 |

28 | 14 | 40 | 1.25 | 16.6 | 5 | 96.59 | 39.51 |

11 | 15 | 30 | 1.25 | 16.6 | 10 | 97.84 | 115.56 |

27 | 16 | 40 | 1.25 | 16.6 | 5 | 96.32 | 37.78 |

9 | 17 | 30 | 1.25 | 16.6 | 3 | 98.70 | 23.03 |

26 | 18 | 40 | 1.25 | 16.6 | 5 | 96.47 | 36.45 |

8 | 19 | 40 | 1.25 | 24.9 | 10 | 80.53 ^{b} | 149.23 |

4 | 20 | 50 | 2 | 16.6 | 5 | 95.70 | 45.36 |

2 | 21 | 50 | 0.5 | 16.6 | 5 | 95.08 | 46.16 |

17 | 22 | 30 | 1.25 | 8.3 | 5 | 91.31 | 28.78 |

16 | 23 | 40 | 2 | 24.9 | 5 | 98.20 | 35.00 |

21 | 24 | 40 | 0.5 | 16.6 | 3 | 98.40 | 29.10 |

1 | 25 | 30 | 0.5 | 16.6 | 5 | 90.43 ^{b} | 30.19 |

12 | 26 | 50 | 1.25 | 16.6 | 10 | 91.83 | 178.28 |

15 | 27 | 40 | 0.5 | 24.9 | 5 | 96.94 | 35.67 |

24 | 28 | 40 | 2 | 16.6 | 10 | 93.53 | 138.17 |

5 | 29 | 40 | 1.25 | 8.3 | 3 | 92.61 | 28.96 |

^{a}Rejection/flux values of an ultrafiltration run are the mean values of rejection/flux of all permeate samples (n=5) in that run.

^{b}Observed outliers; eliminated from analysis.

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 158.79 | 8 | 19.85 | 12.61 | <0.0001 | significant |

A-Pressure | 12.24 | 1 | 12.24 | 7.78 | 0.0121 | |

B-C-Ni | 10.51 | 1 | 10.51 | 6.68 | 0.0187 | |

C-C-SDS | 17.18 | 1 | 17.18 | 10.92 | 0.0039 | |

D-MWCO | 13.18 | 1 | 13.18 | 8.37 | 0.0097 | |

AD | 12.10 | 1 | 12.10 | 7.69 | 0.0125 | |

BC | 16.26 | 1 | 16.26 | 10.33 | 0.0048 | |

CD | 7.33 | 1 | 7.33 | 4.66 | 0.0447 | |

C² | 27.39 | 1 | 27.39 | 17.40 | 0.0006 | |

Residual | 28.33 | 18 | 1.57 | |||

Lack of Fit | 26.16 | 14 | 1.87 | 3.46 | 0.1200 | not significant |

Pure Error | 2.16 | 4 | 0.5409 | |||

Cor Total | 187.12 | 26 |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 10.68 | 4 | 2.67 | 2173.32 | <0.0001 | significant |

A-Pressure | 0.5914 | 1 | 0.5914 | 481.41 | <0.0001 | |

C-C-SDS | 0.0033 | 1 | 0.0033 | 2.67 | 0.1151 | |

D-MWCO | 7.65 | 1 | 7.65 | 6229.95 | <0.0001 | |

D² | 0.3832 | 1 | 0.3832 | 311.97 | <0.0001 | |

Residual | 0.0295 | 24 | 0.0012 | |||

Lack of Fit | 0.0256 | 20 | 0.0013 | 1.31 | 0.4387 | not significant |

Pure Error | 0.0039 | 4 | 0.0010 | |||

Cor Total | 10.71 | 28 |

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## Share and Cite

**MDPI and ACS Style**

Lin, W.; Jing, L.; Zhang, B.
Micellar-Enhanced Ultrafiltration to Remove Nickel Ions: A Response Surface Method and Artificial Neural Network Optimization. *Water* **2020**, *12*, 1269.
https://doi.org/10.3390/w12051269

**AMA Style**

Lin W, Jing L, Zhang B.
Micellar-Enhanced Ultrafiltration to Remove Nickel Ions: A Response Surface Method and Artificial Neural Network Optimization. *Water*. 2020; 12(5):1269.
https://doi.org/10.3390/w12051269

**Chicago/Turabian Style**

Lin, Weiyun, Liang Jing, and Baiyu Zhang.
2020. "Micellar-Enhanced Ultrafiltration to Remove Nickel Ions: A Response Surface Method and Artificial Neural Network Optimization" *Water* 12, no. 5: 1269.
https://doi.org/10.3390/w12051269