Membrane distillation (MD) is considered as a relatively high-energy requirement. To overcome this drawback, it is recommended to couple the MD process with solar energy as the renewable energy source in order to provide heat energy required to optimize its performance to produce permeate flux. In the present work, an original solar energy driven direct contact membrane distillation (DCMD) pilot plant was built and tested under actual weather conditions at Jeddah, KSA, in order to model and optimize permeate flux. The dependency of permeate flux on various operating parameters such as feed temperature (46.6–63.4°C), permeate temperature (6.6–23.4°C), feed flow rate (199–451L/h) and permeate flow rate (199–451L/h) was studied by response surface methodology based on central composite design approach. The analysis of variance (ANOVA) confirmed that all independent variables had significant influence on the model (where *P*-value <0.05). The high coefficient of determination (*R*^{2} = 0.9644 and *R*_{adj}^{2} = 0.9261) obtained by ANOVA demonstrated good correlation between experimental and predicted values of the response. The optimized conditions, determined using desirability function, were T_{f} = 63.4°C, T_{p} = 6.6°C, Q_{f} = 451L/h and Q_{p} = 451L/h. Under these conditions, the maximum permeate flux of 6.122kg/m^{2}.h was achieved, which was close to the predicted value of 6.398kg/m^{2}.h.

## INTRODUCTION

During the last decade, membrane distillation (MD) has gained widespread interest in academic research and becomes an alternative to conventional separation processes such as multistage flash, multiple effect distillation, reverse osmosis and electrodialysis (Al-Obaidani *et al.* 2008). The driving force of the MD process is different from other separation processes, in which a vapour pressure difference between the two sides of a membrane is generated by a temperature gradient. As the process is non-isothermal, only vapour molecules are transported through the membrane pores from the high vapour pressure side (interface feed/solution membrane) to the low vapour pressure side (interface membrane/permeate solution) (Qtaishat *et al.* 2009). The membrane used in MD must be porous and hydrophobic. The hydrophobic nature of the membrane prevents the penetration of the liquid solution into the pores (Dao *et al.* 2013). The lower vapour pressure generated at the permeate side can be set up in various ways, including vacuum membrane distillation (VMD), sweeping gas membrane distillation (SGMD), air gap membrane distillation (AGMD) and direct contact membrane distillation (DCMD). Among various types of MD, DCMD is considered to be the simplest configuration and requires the least equipment to operate. DCMD does not require a vacuum pump as in VMD, a condenser as in SGMD or a cooling surface as in AGMD. Thus, DCMD is the most widely studied configuration. However, the lower permeate production of DCMD compared with other membrane processes, such as reverse osmosis, has presented serious drawbacks to its commercialization in the industry until now. In this way, much research has been investigated to enhance the permeate production of DCMD. Most DCMD studies were performed to investigate the effects of operating conditions (Bahmanyar *et al.* 2012; Kamrani *et al.* 2014), and other research groups have investigated the effects of membrane parameters on DCMD permeate flux (Phattaranawik *et al.* 2003; Ali *et al.* 2012).

*et al.*2014a). These drawbacks of the conventional methods can be discarded by studying the effect of all parameters using a statistical optimization method. Response surface methodology (RSM) is a combined mathematical and statistical tool for designing experiments, building models, evaluating the interactive effects of independent factors, and obtaining the optimum conditions for responses with a limited number of planned experiments (Nair

*et al.*2014). The RSM procedure can be summarized as shown in Figure 1.

In recent years, RSM has become a popular tool to improve various scientific and technical fields such as applied chemistry and physics, biochemistry and biology, chemical engineering, environmental protection, membrane science and technology (Preetha & Viruthagiri 2007; Bezerra *et al.* 2008; Moghaddam *et al.* 2009; Khayet *et al.* 2010). However, few recent publications have shown the effectiveness of RSM modelling for laboratory plate and frame module direct contact MD (Khayet *et al.* 2007; Boubakri *et al.* 2014b). The selected operating variables and their ranges, which had an effect on the obtained results, are different from those chosen in previous works. The optimization of DCMD process with prediction of permeate flux when using NaCl salt aqueous solution was carried out (Khayet *et al.* 2007). RSM was applied in this case to optimize three operating parameters including feed temperature, stirring velocity and salt concentration. The optimum feed temperature, stirring velocity and salt concentration were found to be 52.21°C, 777.4 rpm and 0.036 M, respectively, when using M12 membrane. DCMD permeate flux of 4.193 10^{−6} m/s was obtained and found to be close to the predicted RSM results. The effect of various operating parameters on DCMD permeate flux was also studied using the RSM method (Boubakri *et al.* 2014b). The optimum operating parameters were found to be 0.355 × 10^{5} Pa of vapour pressure difference, feed flow rate of 73.6 L/h, permeate flow rate of 17.1 L/h and feed ionic strength of 309 mM. Under these conditions, the permeate flux was 4.191 L/m^{−2}.h^{−1}, which confirms the validity of the model for the DCMD process.

In the present study, central composite design (CCD) using RSM has been applied to model and optimize a solar energy driven DCMD process. The main and interaction effects of the operating parameters, including feed temperature, permeate temperature, feed flow rate and permeate flow rate, on permeate flux were investigated. An empirical quadratic model for the DCMD permeate flux as a function of the most significant variables and their interaction has been developed and validated based on analysis of variance (ANOVA) tests. Furthermore, an optimization of the DCMD process was carried out using the desirability function to maximize the permeate flux applying the adequate optimum operating conditions.

## MATERIALS AND METHODS

### DCMD pilot plant

#### Solar collectors system

The thermal solar loop consists of eight flat-plate collectors with an effective area of 20 m^{2}. The collectors are arranged in a series: parallel (4:2) configuration. The DCMD loop and the solar collector loop are connected via a heat exchanger (16 kW_{th}), placed in a 300 L thermally stabilizing storage tank. This stores the surplus thermal energy produced by the collectors during the peak solar radiation intensity. The stored sensible heat surplus is used during the period of low solar radiation intensity.

#### Photovoltaic panels

The photovoltaic (PV) loop consists of three main components, including the eight PV panels, the electric batteries, and the direct current/alternating current (DC/AC) inverter. The eight PV panels are assembled in parallel with a peak generating capacity of 1,480 kW_{peak}. This is used solely to drive the electrical equipment of the pilot plant. Two electric storage batteries (24 V, 100 Ah) are used to stabilize and regulate the power from the PV panels. The DC from the storage batteries is converted to AC by a DC/AC electric inverter located upstream of the pilot plant.

#### Membrane module

Material . | Polypropylene . |
---|---|

Effective fibre length | 0.198 m |

Outer fibre area | 1.4 m² |

Inner fibre area | 1.13 m² |

Nominal inner diameter of the fibres | 240 10^{−6} m |

Nominal outer diameter of the fibres | 300 10^{−6} m |

Effective pore size | 0.04 10^{−6} m |

Membrane thickness | 30 10^{−6} m |

Nominal porosity | 40% |

Membrane tortuosity | 2.6 m |

Module diameter | 0.067 m |

Module length | 0.256 m |

Material . | Polypropylene . |
---|---|

Effective fibre length | 0.198 m |

Outer fibre area | 1.4 m² |

Inner fibre area | 1.13 m² |

Nominal inner diameter of the fibres | 240 10^{−6} m |

Nominal outer diameter of the fibres | 300 10^{−6} m |

Effective pore size | 0.04 10^{−6} m |

Membrane thickness | 30 10^{−6} m |

Nominal porosity | 40% |

Membrane tortuosity | 2.6 m |

Module diameter | 0.067 m |

Module length | 0.256 m |

### Permeate flux equation

^{2}.h) was calculated using the following equation: where

*W*is the weight of permeated liquid after 1 h (kg),

*S*is the effective membrane area (m

^{2}) and Δ

*T*is the sampling time (h).

*et al.*2011): where

*B*is the membrane coefficient and

_{m}*P*and

_{mf}*P*are the vapour pressures at the feed and permeate vapour/liquid interface, respectively.

_{mp}*P*and

_{mf}*P*at the temperature T

_{mp}_{mf}and

*T*, respectively, are related to the activity of the solution by: where

_{mp}*a*is the water activity and

_{wi}*P*

_{mi}

^{0}is pure water vapour, which can be evaluated by using the Antoine equation (Bouguecha

*et al.*2002):

*P*

_{mi}

^{0}in Pascal and

*T*in Kelvin.

_{mi}### Experimental design and statistical analysis

In RSM, several design methods have been applied for any process optimization: the most popular are the CCD, Box-Behnken design, Plackett and Burman design and Dohlert matrix (Witek-Krowiak *et al.* 2014). In this study, the CCD design, which is a widely used form of RSM, was selected to evaluate the performance of our DCMD setup. This method is suitable for fitting a quadratic surface, and it helps to optimize the effective parameters with minimum.

*Y*refers to the response,

*b*

_{0}the constant coefficient,

*b*the linear coefficients,

_{i}*b*the quadratic coefficients,

_{ii}*b*the interaction coefficients and

_{ij}*X*

_{i},

*X*the coded values of the variables.

_{j}*et al.*2014b). The quality of the fitted polynomial model was also expressed by the coefficient of determination

*R*

^{2}. The significant terms in the model equation were determined with the help of

*P*-value and

*F*-value.

*k*is the number of independent variables and

*n*

_{0}is the number of experiments at the centre point. The first term shows the number of corner points, which correspond to full factorial design. The second terms present the number of axial points required to perform an RSM analysis (Vining & Kowalski 2010). In this study, four factors including feed temperature (T

_{f}), permeate temperature (T

_{p}) feed flow rate (Q

_{f}) and permeate flow rate (Q

_{p}) with five levels were employed for response surface modelling and optimization of the DCMD process. A design of 28 experiments was formulated according to CCD design, with 16 orthogonal design points, eight star points to form a CCD with α = ±1.682, and four centre points, which are usually repeated to get a good estimation of experimental error.

The experimental domains and the levels of the variables are given in Table 2. The levels of the factors were selected according to the literature and our preliminary experience. The CCD experimental matrix and response (*J _{p}*) are reported in Table 3. The experimental design and analysis of data were performed with statistical and graphical analysis software MINITAB

^{®}release 16 developed by Minitab Inc., USA.

. | . | Actual value of coded levels . | ||||
---|---|---|---|---|---|---|

Factors . | Symbol . | − α . | − 1 . | 0 . | + 1 . | + α . |

Feed temperature (°C) | X_{1} | 46.6 | 50 | 55 | 60 | 63.4 |

Permeate temperature (°C) | X_{2} | 6.6 | 10 | 15 | 20 | 23.4 |

Feed flow rate (L/h) | X_{3} | 199 | 250 | 325 | 400 | 451 |

Permeate flow rate (L/h) | X_{4} | 199 | 250 | 325 | 400 | 451 |

. | . | Actual value of coded levels . | ||||
---|---|---|---|---|---|---|

Factors . | Symbol . | − α . | − 1 . | 0 . | + 1 . | + α . |

Feed temperature (°C) | X_{1} | 46.6 | 50 | 55 | 60 | 63.4 |

Permeate temperature (°C) | X_{2} | 6.6 | 10 | 15 | 20 | 23.4 |

Feed flow rate (L/h) | X_{3} | 199 | 250 | 325 | 400 | 451 |

Permeate flow rate (L/h) | X_{4} | 199 | 250 | 325 | 400 | 451 |

. | Factors (controllable input variables) . | J_{p} (kg/m^{2}h). | ||||
---|---|---|---|---|---|---|

Run . | T_{f} (X_{1})
. | T_{p} (X_{2})
. | Q_{f} (X_{3})
. | Q_{p} (X_{4})
. | Experimental . | Predicted . |

1 | − 1 | − 1 | − 1 | − 1 | 1.398 | 1.585 |

2 | + 1 | − 1 | − 1 | − 1 | 1.982 | 2.127 |

3 | − 1 | + 1 | − 1 | − 1 | 0.912 | 0.923 |

4 | + 1 | + 1 | − 1 | − 1 | 1.195 | 1.202 |

5 | − 1 | − 1 | + 1 | − 1 | 2.319 | 2.273 |

6 | + 1 | − 1 | + 1 | − 1 | 3.000 | 3.175 |

7 | − 1 | + 1 | + 1 | − 1 | 1.496 | 1.387 |

8 | + 1 | + 1 | + 1 | − 1 | 2.027 | 2.026 |

9 | − 1 | − 1 | − 1 | + 1 | 1.965 | 1.987 |

10 | + 1 | − 1 | − 1 | + 1 | 2.726 | 2.938 |

11 | − 1 | + 1 | − 1 | + 1 | 1.310 | 1.239 |

12 | + 1 | + 1 | − 1 | + 1 | 1.858 | 1.927 |

13 | − 1 | − 1 | + 1 | + 1 | 2.929 | 3.027 |

14 | + 1 | − 1 | + 1 | + 1 | 4.327 | 4.338 |

15 | − 1 | + 1 | + 1 | + 1 | 2.177 | 2.055 |

16 | + 1 | + 1 | + 1 | + 1 | 3.186 | 3.104 |

17 | − α | 0 | 0 | 0 | 1.469 | 1.547 |

18 | + α | 0 | 0 | 0 | 3.142 | 2.884 |

19 | 0 | − α | 0 | 0 | 3.665 | 3.248 |

20 | 0 | + α | 0 | 0 | 1.416 | 1.653 |

21 | 0 | 0 | − α | 0 | 1.602 | 1.316 |

22 | 0 | 0 | + α | 0 | 2.779 | 2.884 |

23 | 0 | 0 | 0 | − α | 1.522 | 1.363 |

24 | 0 | 0 | 0 | + α | 2.628 | 2.608 |

25 | 0 | 0 | 0 | 0 | 2.097 | 2.142 |

26 | 0 | 0 | 0 | 0 | 2.087 | 2.142 |

27 | 0 | 0 | 0 | 0 | 2.094 | 2.142 |

28 | 0 | 0 | 0 | 0 | 2.077 | 2.142 |

. | Factors (controllable input variables) . | J_{p} (kg/m^{2}h). | ||||
---|---|---|---|---|---|---|

Run . | T_{f} (X_{1})
. | T_{p} (X_{2})
. | Q_{f} (X_{3})
. | Q_{p} (X_{4})
. | Experimental . | Predicted . |

1 | − 1 | − 1 | − 1 | − 1 | 1.398 | 1.585 |

2 | + 1 | − 1 | − 1 | − 1 | 1.982 | 2.127 |

3 | − 1 | + 1 | − 1 | − 1 | 0.912 | 0.923 |

4 | + 1 | + 1 | − 1 | − 1 | 1.195 | 1.202 |

5 | − 1 | − 1 | + 1 | − 1 | 2.319 | 2.273 |

6 | + 1 | − 1 | + 1 | − 1 | 3.000 | 3.175 |

7 | − 1 | + 1 | + 1 | − 1 | 1.496 | 1.387 |

8 | + 1 | + 1 | + 1 | − 1 | 2.027 | 2.026 |

9 | − 1 | − 1 | − 1 | + 1 | 1.965 | 1.987 |

10 | + 1 | − 1 | − 1 | + 1 | 2.726 | 2.938 |

11 | − 1 | + 1 | − 1 | + 1 | 1.310 | 1.239 |

12 | + 1 | + 1 | − 1 | + 1 | 1.858 | 1.927 |

13 | − 1 | − 1 | + 1 | + 1 | 2.929 | 3.027 |

14 | + 1 | − 1 | + 1 | + 1 | 4.327 | 4.338 |

15 | − 1 | + 1 | + 1 | + 1 | 2.177 | 2.055 |

16 | + 1 | + 1 | + 1 | + 1 | 3.186 | 3.104 |

17 | − α | 0 | 0 | 0 | 1.469 | 1.547 |

18 | + α | 0 | 0 | 0 | 3.142 | 2.884 |

19 | 0 | − α | 0 | 0 | 3.665 | 3.248 |

20 | 0 | + α | 0 | 0 | 1.416 | 1.653 |

21 | 0 | 0 | − α | 0 | 1.602 | 1.316 |

22 | 0 | 0 | + α | 0 | 2.779 | 2.884 |

23 | 0 | 0 | 0 | − α | 1.522 | 1.363 |

24 | 0 | 0 | 0 | + α | 2.628 | 2.608 |

25 | 0 | 0 | 0 | 0 | 2.097 | 2.142 |

26 | 0 | 0 | 0 | 0 | 2.087 | 2.142 |

27 | 0 | 0 | 0 | 0 | 2.094 | 2.142 |

28 | 0 | 0 | 0 | 0 | 2.077 | 2.142 |

## RESULTS AND DISCUSSION

### Modeling of the DCMD process

*X*) and the response (

_{i}*Y*). The experimental results of DCMD permeate flux obtained from CCD experiments are shown in Table 3. Using the designed experimental data presented in Table 3, the polynomial proposed model, in terms of coded values, for predicting the permeate flux response was: where

*Y*is the permeate flux, and

*X*

_{1},

*X*

_{2},

*X*

_{3}and

*X*

_{4}are the coded variables for feed temperature, permeate temperature, feed flow rate and permeate flow rate, respectively. In Equation (8), the plus sign in front of the coefficients indicates that the corresponding operating parameter increases the permeate flux response. However, the minus sign indicates that the operating parameter reduces the response.

### ANOVA and validation of model

In order to ensure the statistical significance of the quadratic model employed for explaining the experimental data at a 95% confidence level, the model was tested by ANOVA results. The overall efficiency of a model is generally explained by coefficient of determination (*R*^{2}), which should be close to 1. In ANOVA, *F*-value is used to check the statistical significance of a quadratic model equation. The *P*-values are used as a tool to check the significance of each coefficient, which in turn may indicate the pattern of the interactions between the independent variables (Hou & Chen 2008). In other words, the larger the magnitude of *F*-value and correspondingly the smaller the *P*-value, the bigger the significance of the corresponding model and individual coefficients. If the *P*-value is below 0.05, then the model is significant at the 95% confidence interval (Nair *et al.* 2014).

*R*

^{2}is equal to 0.9643, which indicated that the model was adequate for prediction and only 3.57% of the total variation could not be explained by the model within the range of experimental variables. Furthermore, the value of adjusted coefficient of determination , close to

*R*

^{2}, was also high, indicating that the obtained model was significant. To clarify the goodness of the proposed model, Figure 4 presents the plot of observed data as a function of those obtained from the model equation (Equation (8)). From this figure, it was found that the points marked by open circles are concentrated near the diagonal line, which confirms that there is a very good agreement between the experimental data and the model prediction. In addition, a very high

*F*-value of 25.16, greater than unity, and a very low

*P*-value of 0.000, lower than 0.05, were obtained, which indicated that the model was highly significant.

Source . | Degrees of freedom . | Sum of square . | Mean of square . | F-value
. | P-value
. |
---|---|---|---|---|---|

Model | 14 | 16.7584 | 1.19703 | 25.16 | 0.000 |

Square | 4 | 0.2057 | 0.06267 | 1.32 | 0.315 |

Interaction | 6 | 0.548 | 0.09133 | 1.92 | 0.153 |

Residual error | 13 | 0.6186 | 0.04759 | ||

Lack-of -fit | 10 | 0.6184 | 0.06184 | 807.5 | 0.000 |

Pure error | 3 | 0.0002 | 0.00008 | ||

Total | 17 | 17.337 |

Source . | Degrees of freedom . | Sum of square . | Mean of square . | F-value
. | P-value
. |
---|---|---|---|---|---|

Model | 14 | 16.7584 | 1.19703 | 25.16 | 0.000 |

Square | 4 | 0.2057 | 0.06267 | 1.32 | 0.315 |

Interaction | 6 | 0.548 | 0.09133 | 1.92 | 0.153 |

Residual error | 13 | 0.6186 | 0.04759 | ||

Lack-of -fit | 10 | 0.6184 | 0.06184 | 807.5 | 0.000 |

Pure error | 3 | 0.0002 | 0.00008 | ||

Total | 17 | 17.337 |

*R*^{2} = 0.9644, *R*^{2}_{adj} = 0.9261.

### Analysis of response surface and contour plots

*et al.*2015). In this study, the results of permeate flux affected by feed temperature, permeate temperature, feed flow rate and permeate flow rate are presented in Figures 5–10.

Figure 5 shows the effect of feed temperature and permeate temperature and their interaction on DCMD permeate flux while keeping feed flow rate and permeate flow rate at their central point (325 L/h). It is observed that the permeate flux increased with increasing feed temperature to obtain a maximum at 62°C and decreased with increasing permeate temperature to obtain a minimum at about 22°C. Therefore, a suitable T_{f} more than 62°C and T_{p} less than 22°C are preferable for achieving a higher permeate flux. In the DCMD process, the permeate flux increased with increasing temperature difference between feed and permeate sides to create a vapour pressure difference, which can be estimated by the Antoine equation (Equation (8)) (Boubakri *et al.* 2014c). It is evident from this equation that water vapour pressure will be increased exponentially as a function of temperature, and then the driving force will be enhanced. Consequently, to obtain a high permeate flux, it is recommended that temperature be increased. In addition, at feed side, when increasing feed temperature, the temperature polarization and feed viscosity declined, which was favourable to enhance the permeate flux (Boubakri *et al.* 2014d).

The combined effect of feed temperature and feed flow rate, when keeping constant permeate temperature at 15°C and feed flow rate at 325 L/h, on permeate flux is shown in Figure 6. It can be seen that the permeate flux increased with both increasing feed temperature and increasing feed flow rate. At higher feed temperature and higher feed flow rate, the permeate flux reached a maximum value of 3.380 kg/m^{2}.h, which is calculated by the regression model. This trend can be explained increasing feed flow rate leading to an increased Reynolds number, which induced a local turbulence at the feed side. Therefore, the benefit of working at high flow rate was to increase the Reynolds number, which in turn enhances the heat transfer coefficient and thus reduces the effect of both temperature and concentration polarization phenomenon. This causes a larger driving force for mass transfer through the micro-porous membrane and consequently enhances the permeate flux.

The 3D response surface and 2D contour plot of permeate flux as a function of feed temperature and permeate flow rate are shown in Figure 7. When fixed permeate temperature and feed flow rate were at their central point, the permeate flux increased with both increasing feed temperature and increasing feed flow rate. A maximum value of permeate flux of 3.638 kg/m^{2}·h was obtained at higher feed temperature and higher permeate flow rate. In DCMD, increasing permeate flow rate can lead to enhanced mixing in the permeate compartment, which decreases the thickness of temperature boundary layer. Therefore, the temperature at the membrane surface, permeate side, decreased, which reduced the temperature polarization, and then the permeate flux was increased (Pal & Manna 2010).

The response surface and contour plot of Figure 8 represent the permeate flux as a function of permeate temperature and feed flow rate. From this figure, the permeate flux increased when decreasing permeate temperature from 23.4 to 6.6°C and increasing feed flow rate from 199 to 451 L/h. Using the regression model of permeate flux (Equation (6)), a maximum value of 4.146 kg/m^{2}.h was obtained.

The variation of permeate flux as a function of permeate temperature and permeate flow rate when keeping constant feed temperature at 55 °C and feed flow rate at 325 L/h is given in Figure 9. As expected, at higher permeate flow rate and at lower permeate temperature, the permeate flux was improved. Within the studied experimental range, the maximum permeate flux obtained was 3.773 kg/m^{2}.h as calculated using the regression model equation (Equation (6)).

In order to investigate the interaction between feed flow rate and permeate flow rate, the response surface and contour plots were exhibited in Figure 10. When feed temperature and permeate temperature were kept constant at 55 and 15°C, respectively, the highest permeate flux was obtained at maximum feed flow rate and permeate flow rate. Using the model equation (Equation (6)), the maximum permeate flux obtained was 3.597 kg/m^{2}.h.

### DCMD optimization and confirmation study

^{2}.h. The desirability function of the optimization plot for permeate flux is presented in Figure 11. It was seen that the maximum permeate flux was obtained at maximum feed temperature of 63.4°C, minimum permeate temperature of 6.6°C, maximum feed flow rate of 451 L/h and maximum permeate flow rate of 451 L/h. Under these conditions, the maximum permeate flux predicted by the model is 6.398 kg/m

^{2}·h, and the desirability value was equal to 0.899.

The final stage after the determination of the optimal conditions was the validation of the method by verifying the precision of the regression model equation. A triplicate experiment was carried out under optimized conditions, and mean values are shown in Table 5. It has been observed that the experimental permeate flux is almost similar to the predicted value, the deviation errors being equal to 4.31%. The percentage of prediction errors is much less, and hence the prediction performance of the regression model to determine the permeate flux is quite satisfactory.

. | . | . | . | J (kg/m².h) . | . | |
---|---|---|---|---|---|---|

Tf (°C) . | Tp (°C) . | Qf (L/h) . | Qp (L/h) . | Predicted . | Observed . | Errors . |

63.4 | 6.6 | 451 | 451 | 6.398 | 6.122 | 4.31% |

. | . | . | . | J (kg/m².h) . | . | |
---|---|---|---|---|---|---|

Tf (°C) . | Tp (°C) . | Qf (L/h) . | Qp (L/h) . | Predicted . | Observed . | Errors . |

63.4 | 6.6 | 451 | 451 | 6.398 | 6.122 | 4.31% |

## CONCLUSION

MD is considered to be an emerging thermal membrane technology and has been investigated as an alternative process for water and wastewater treatment. In this research, the performance of a solar energy driven DCMD process, in terms of permeate flux, has been modelled and optimized using a CCD approach according to RSM. The results showed that studied operating parameters including feed temperature, feed flow rate and permeate flow rate had a positive effect on permeate flux response, but permeate temperature had a negative effect. The predicted values, obtained by the regression model equation, were found to be in good agreement with observed values (*R*^{2} = 96.44%). The desirability function in RSM was used to optimize the DCMD process in order to obtain the maximum permeate flux. Under the obtained optimum conditions, T_{f} = 63.4°C, T_{p} = 6.6°C, Q_{p} = 451L/h and Q_{f} = 451L/h, a maximum value of 6.398kg/m^{2}·h was obtained. This study demonstrates that a CCD approach can be successfully applied to modelling and optimizing the performance of a solar energy driven DCMD process, which may save considerable time and resources to perform experiments.