### 1. Introduction

*Giardia*cysts and

*Cryptosporidium*oocysts. Moreover, continuous advances in membrane technologies have lowered the costs for membrane filtration, which is now economically competitive with conventional sand filtration [4].

### 2. Materials and Methods

### 2.1. Feed Water

### 2.2. Coagulation Conditions

_{2}O

_{3}) was added into the feed water for the pretreatment of MF process. A jar-tester (YUYU Scientific M.F.G, Korea) was used for coagulation treatment. The working volume of each feed tank was 2 L. Details in the experimental conditions are provided in Table 2.

### 2.3. Membrane Filtration

^{2}-h.

### 2.4. Water Quality Measurement

### 2.5 Theoretical Fundamentals

*J*is the flux of the permeate; Δ

*P*is the transmembrane pressure;

*η*is the water viscosity;

*R*

*is the intrinsic hydraulic resistance; and*

_{m}*R*

*is the hydraulic resistance for the cake layer formed on the membrane surface. The*

_{c}*R*

*is proportional to the ratio of cake mass (*

_{c}*m*

*) to membrane area (*

_{c}*A*

*).*

_{m}*α*is the specific resistance of the cake layer. Then, the following equation can be derived:

*t*is the time for membrane filtration and

*c*

*is the effective concentration of the foulants. It should be mentioned here that*

_{f}*c*

*and*

_{f}*c*

*(the bulk concentration of foulants) are different due to the existence of critical flux. Finally, Δ*

_{b}*P*can be expressed as:

*θ*is the fouling rate, which can be experimentally obtained from the slope of the graph for

*t*and Δ

*P*.

*θ*is linearly proportional to

*J*

^{2}. Accordingly,

*θ*increases with an increase in J even if cf and α are constant. In other words, θ is affected not only by the feed water characteristics (

*ηαc*

*) but also the operation condition of the membrane (*

_{f}*J*). Thus, the normalized fouling rate,

*θ*/

*J*

^{2}, was used to quantify the fouling potential of the feed water instead of

*θ*.

### 2.6. Response Surface Method

#### 2.6.1. Experimental design

_{1}) and pH (X

_{2}) were selected as the independent variables. The normalized fouling rate (Y

_{1}), turbidity (Y

_{2}), and UV-254 (Y

_{3}) were selected as the responses. Each represents the fouling potential, particle concentration, and humic-like organic concentration for the pretreated water, respectively. The measurement for the turbidity and UV-254 was triplicated. Table 4 summarizes our design of experiment.

#### 2.6.2. Statistical analysis and regression analysis

^{®}16.2.0 (Minitab, USA). The general form of the equations is given by:

##### (5)

$${Y}_{k}={\beta}_{k0}+\sum _{i=1}^{2}{\beta}_{ki}{X}_{i}+\sum _{i=1}^{1}\sum _{j=i+1}^{2}{\beta}_{kij}{X}_{i}{X}_{j}+\sum _{i=1}^{2}{\beta}_{kii}{X}_{i}^{2}$$*Y*

*is the responses of the independent variable;*

_{k}*β*

_{k}_{0},

*β*

*,*

_{ki}*β*

*and*

_{kii}*β*

*are the coefficients; and*

_{kij}*X*

*is the independent variables. The suitability of the equations is examined based on*

_{i}*R*

^{2}value and the lack-of-fit (LOF).

### 3. Results and Discussion

### 3.1. Analysis of Membrane Fouling Based on the Response Surface Method

_{1}), turbidity (Y

_{2}), and UV-254 (Y

_{3}). The terms that are not statistically significant (

*p*> 0.05) were omitted from the regression equation. The final forms are given by:

_{1}(fouling rate) and Y

_{3}(UV-254 nm) are dependent on X

_{1}(coagulant concentration) and X

_{2}(pH). However, Y

_{2}(turbidity) seems to depend only on X

_{2}(pH). This is probably because the turbidity was not sensitive to the operation conditions under the coagulation conditions considered in these experiments. In Eq. (6) and Eq. (8), the quadratic terms of X

_{1}and X

_{2}are significant. On the other hand, in Eq. (7), the quadratic term of X

_{2}is significant. In Eq. (8), the quadratic term of X

_{2}is significant. All the interaction terms were not included due to low significance.

*R*

^{2}for the three equations were 90.21, 68.63 and 98.10, respectively. This suggests that the regression is statistically significant. The lack-of-fit results also indicate that the regression is reasonable. It is evident from these results that the model equations represents the dependence of responses on the independent variable.

### 3.2. Influence and Interaction of Independent Variables

^{−10}to 1.1×10

^{−9}in fouling rate; from 0.35 to 0.55 NTU in turbidity; from 0.018 to 0.022 ABS/cm in UV-254 nm. The results indicate that the modeling results match the experimental data well. Based on the results of RSM analysis, the desired operation conditions can be obtained using the response optimizer. Fig shows the optimum conditions for fouling rate, turbidity, and UV-254 nm. According to this result, the optimum coagulant dose and pH are 3 and 7.5, respectively. Under this condition, fouling rate, turbidity and UV-254 nm are 7.7×10−10, 0.5 NTU and 0.02 ABS/cm respectively.

### 4. Conclusions

Using a simple model, the normalized fouling rates were experimentally obtained depending on the coagulation conditions. The model was useful to analyze the experimental results from a laboratory-scale MF equipment.

RSM was introduced to examine coagulation efficiency as a function of coagulant does and pH. This technique was found to be useful to examine the interactions between the independent and dependent variables.

Compared with the RSM models for coagulant dose and pH, the model equation for turbidity was less reliable. This was attributed to the wider error range of the turbidity measurement data.

Using the RSM equations, the optimum coagulation condition was estimated: The coagulant dose ranges from 3 mg/L to 5 mg/L and the pH ranges from 7 to 8. It is expected that this approach has potential for process control of pilot or full-scale membrane plant.