### 1. Introduction

^{2+}ions [17–19]. Using the factorial design method, the subsets of key factors identified and interactions that impacted the flux recovery and cleaning efficiency were sequentially used in the CCD to model the response variables with curvature, and a response surface designed experiment was then used to determine the optimal setting for each factor during RO membrane cleaning. The objective of this study was to suggest a methodology for selecting an optimal combination of cleaning agents and chemical/physical conditions for efficient cleaning, using DOE as a statistical design tool. Overall, four key chemical/physical factors impacting the RO membrane cleaning efficiency, as reported in Ang et al. [20] and Garcia-Fayos et al. [11], were selected for use in evaluating multiple factors set at various levels: cleaning agent type, chemical concentration, cleaning time, flowrate, and cleaning temperature.

### 2. Experimental Methods

### 2.1. RO Membrane

^{2}·h (LMH) and stabilized salt rejection was 99.6% under the following standard manufacturer-recommended test conditions: NaCl solution of 1,500 mg/L, pressure of 150 psi (10.34 bar) and temperature of 25°C. BWRO membranes were stored in deionized (DI) water at 4°C prior to each experiment.

### 2.2. Organic Fouling Matter

_{2}·2H

_{2}O (OCI Company Ltd., Korea) as divalent cations to aggressively form an organic fouling layer on the RO membranes. Sodium alginate was stirred for over 24 h to completely dissolve the foulant.

### 2.3. Cleaning Chemical Agents

### 2.4. Dead-end RO System and Operating Conditions

*J*

*; LMH) was measured using a digital balance (GF-6100, A&D, USA) and was automatically recorded on a computer. The operating conditions of the dead-end filtration are summarized in Table 1.*

_{w}### 2.5. Cross-flow RO System and Operating Conditions

### 2.6. Experimental Design Using FFD

### 2.7. Experimental Design Using CCD

*α*) are added to the FFD. Experimental conditions in the CCD analysis are summarized in Table 5. Eq. (1) of the quadratic polynomial model was obtained using Minitab 17 (Minitab Inc., USA) [21]:

##### (1)

$${Y}_{u}={\beta}_{0}+{\beta}_{1}{x}_{1u}+{\beta}_{2}{x}_{2u}+{\beta}_{11}{x}_{1{u}^{2}}{\beta}_{22}{x}_{2{u}^{2}}+{\beta}_{12}{x}_{1u}{x}_{2u}+{e}_{u}$$*Y*

*is the predicted response,*

_{u}*β*

_{0}is the constant coefficient,

*x*

_{1}

*and*

_{u}*x*

_{2}

*are the linear effect coefficients,*

_{u}*x*

_{1}

_{u}_{2}and

*x*

_{2}

_{u}_{2}are the quadratic effect coefficients,

*x*

_{1}

_{u}*x*

_{2}

*is the interaction effect coefficient, and*

_{u}*e*

*is an unobserved random error.*

_{u}### 2.8. Organic Fouling and Cleaning Experiments

#### 2.8.1. RO dead-end filtration and static cleaning tests

_{2}, then, it can gain the 80 mL of permeate water; 4) perform static cleaning with each chemical agent at 30°C for 1 h; 5) measure the water flux after static cleaning for 15 min, and 6) calculate the cleaning efficiency using Eq. (2).

##### (2)

$$Flux\hspace{0.17em}recovery\hspace{0.17em}ratio\hspace{0.17em}(FRR,\hspace{0.17em}\%)=\left(\frac{{J}_{wc}}{{J}_{wi}}\right)\times 100$$*J*

*is the initial water flux, and*

_{wi}*J*

*is the water flux after membrane cleaning.*

_{wc}#### 2.8.2. RO cross-flow filtration and dynamic cleaning test

_{2}, then, it can gain the 75 mL of permeate water, 4) perform cross-flow cleaning with EDTA solution using DOE experimental conditions, 5) measure the water flux after cleaning for 15 min, and 6) calculate the cleaning efficiency using Eq. (2).

### 3. Results and Discussion

### 3.1. Static Cleaning Test; Normalized Water Flux (J_{w}/J_{0}) and Flux Recovery Ratio (FRR)

^{2+}when Ca

^{2+}exists in the organic fouling layer. By the same token, EDTA, a metal chelating agent, can be combined with divalent cations such as Ca

^{2+}, to break down the bonds between alginate and Ca

^{2+}[12]. Therefore, EDTA was chosen as chemical agent to clean the fouled-RO membrane, and DOE was then used to optimize the cleaning parameters in this study.

### 3.2. FFD in RO Cross-flow Filtration System

*p*-value of more than 0.1 was treated as the error-term, and a stepwise method was used. Overall, eight factors including combinations of concentration, cleaning time, temperature, and flowrate affecting the flux recovery are summarized in Table 6. From the table, the equation model created by factorial design is deemed unsuitable for determining the optimum chemical cleaning conditions. Furthermore, the center points of all factors are much higher than the linear line between the low and high levels. Since a curvature effect was detected in the FFD, CCD was subsequently performed to model a response variable having curvature.

### 3.3. CCD in RO Crossflow Filtration System

#### 3.3.1. Regression model equation and analysis by CCD

##### (3)

$${Y}_{FRR}=85.48+0.57A+0.0410B-0.348C+0.0331D-2.72{A}^{2}-0.000036{D}^{2}+0.1561AC-0.000188BD$$*Y*

*, as a dependent variable, is the predicted FRR by chemical cleaning, and independent variables are the concentration of EDTA (A), cleaning time (B), temperature (C), and flowrate (D). To evaluate the suitability of the regression equation of FRR, Eq. (3) was verified using a coefficient of determination (R*

_{FRR}^{2}), a value representing whether a regression model fits the experimental data. In addition, an adjusted coefficient of determination (adj-R

^{2}) was used to verify the suitability of the model, since the value of R

^{2}tends to increase when independent variables are added to the model. The values of R

^{2}and adj-R

^{2}at a 90% confidence level were 83.95% and 76.82%, respectively. Therefore, the values predicted using the equation present a relatively high correlation with the experimental data.

#### 3.3.2. Residual analysis of CCD regression model equation

#### 3.3.3. Contour plot and response surface plot of CCD

#### 3.3.4. Optimization condition for chemical cleaning of organic fouling

### 3.4. Verification of Modeling

### 4. Conclusions and Summary

^{2}= 83.9 at a 90% confidence level) Based on this regression model, the optimal conditions for the chemical cleaning of RO membrane are: EDTA concentration of 0.68 wt%, cleaning time of 20 min, temperature of 20°C, and flowrate of 409 mL/min; the flux recovery is then estimated to be ~86.6%.