Application of RSM for modeling and optimization of MD desalination process

Journal of Industrial and Engineering Chemistry xxx (2014) xxx–xxx

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JIEC-1722; No. of Pages 7

Application of response surface methodology for modeling andoptimization of membrane distillation desalination process

Ali Boubakri a,*, Amor Hafiane a, Salah Al Tahar Bouguecha b

a Laboratory of Wastewater Treatment, Center of Researches and Water Technologies, P.B. 273, Soliman 8020, Tunisiab Department of Mechanical Engineering, Faculty of Engineer, King Abdul-Aziz University, P.B. 80204, Jeddah 21589, Saudi Arabia

A R T I C L E I N F O

Article history:

Received 9 August 2013

Accepted 28 November 2013

Available online xxx

Keywords:

Response surface methodology

Direct contact membrane distillation

Desalination

Permeate flux

Polypropylene membrane

A B S T R A C T

In this work, response surface methodology (RSM) was applied for modeling and optimization of

operating parameters for water desalination by direct contact membrane distillation (DCMD) process

using polypropylene membrane (PP) with low pore size. Operating parameters including vapor pressure

difference, feed flow rate, permeate flow rate and feed ionic strength were selected and the optimum

parameters were determined for DCMD permeate flux. The developed model for permeate flux response

was statistically validated by analysis of variance (ANOVA) which showed a high value coefficient of

determination value (R2 = 0.989). The obtained optimum operating parameters were found to be

0.355 � 105 Pa of vapor pressure difference, feed flow rate of 73.6 L/h, and 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/(m2 h).

Compared to a predicted value, the deviation was 3.9%, which confirms the validity of the model for the

DCMD process desalination optimization. In terms of product water quality, the DCMD process using

hydrophobic PP membrane can produce high quality of water with low electrical conductivity for all

experimental runs.

� 2013 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights

reserved.

Contents lists available at ScienceDirect

Journal of Industrial and Engineering Chemistry

jou r n al h o mep ag e: w ww .e lsev ier . co m / loc ate / j iec

1. Introduction

Membrane distillation (MD) is an emerging non-isothermalmembrane separation process. It is a thermally driven process thatinvolves transport of water vapor through microporous hydro-phobic membrane [1]. The driving force of MD is supplied by thevapor pressure difference generated by temperature gradientimposed between the liquid/vapor interfaces [2]. Since the 1980s,the membrane distillation process has gained renewed attentionworldwide due to the rapid development of advanced membranepreparation techniques and low energy consumption of separation[3]. The main advantage of MD is the ability to operate at lowerhydrostatic pressure than conventional pressure-driven mem-brane processes and a lower operating feed temperature,considerably below its boiling point, than conventional distillation.Theoretically, MD is able to perform a rejection of non-volatilesolute of 100% and their performance is not limited by highosmotic pressure or concentration polarization. There are differentways to maintain the transmembrane vapor pressure difference todrive the flux, such as direct contact membrane distillation

* Corresponding author. Tel.: +216 99 155 999.

E-mail addresses: [email protected], [email protected]

(A. Boubakri).

Please cite this article in press as: A. Boubakri, et al., J. Ind. Eng. Ch

1226-086X/$ – see front matter � 2013 The Korean Society of Industrial and Engineer

http://dx.doi.org/10.1016/j.jiec.2013.11.060

(DCMD), air gap membrane distillation (AGMD), sweeping gasmembrane distillation (SGMD), and vacuum membrane distilla-tion (VMD) [4].

DCMD is the most studied configuration because the conden-sation step is carried out inside the membrane module leading to asimple operation mode without the need of external condenserslike in SGMD and VMD configurations. In DCMD configuration, thehot feed solution is in direct contact with the inlet membrane sidesurface. Therefore, evaporation takes place at the feed membranesurface. Vapor is moved by the pressure difference across themembrane to the permeate side and condenses inside membranemodule. Because of the hydrophobic nature of the membrane, theliquid feed cannot penetrate inside dried membrane pores [5]. Upto the present, DCMD has been applied, in major part, for theproduction of fresh water [3,6–10], in wastewater treatment andreuse [11–15] and in the food industry [16–19].

The major part of the reported researches on membranedistillation was carried out using conventional method ofexperimentation, changing one of the independent parameterswhile maintaining the others at fixed levels. Conventional methodinvolves an elevated number of experimental runs, which are time-consuming, expensive and ignore the interaction effects betweenthe dominant parameters affecting the performance of themembrane distillation process. A possible solution is to applystatistical tools such as Design of Experiments (DoE) and Response

em. (2014), http://dx.doi.org/10.1016/j.jiec.2013.11.060

ing Chemistry. Published by Elsevier B.V. All rights reserved.


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Table 1Characteristics of PP membrane.

Material Polypropylene

Nominal pore size 0.064 mm

Thickness 25 mm

Porosity 55%

Manufacturer Hoechst-Celanese, USA

Contact angle 1208Liquid entry pressure 200 kPa

Effective membrane area 4.2 � 10�3 m2

A. Boubakri et al. / Journal of Industrial and Engineering Chemistry xxx (2014) xxx–xxx2

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Surface Methodology (RSM), in which all significant parametersvary at the same time over a set of experimental runs. RSM wasdeveloped by Box and Wilson in 1951 [20], and it is a collection ofmathematical and statistical techniques that are useful for themodeling and analysis of problems in which a response of interestis influenced by several variables and the objective is to optimizethis response [21]. This model can be used to predict the values ofthe responses at different variable settings.

RSM has been applied successfully in scientific and researchareas such as chemistry, physics, biochemistry, biology, environ-ment, etc. In the field of membrane distillation, few studies havebeen carried out using RSM [22–25].

Khayet et al. [22] used the RSM for the optimization of DCMDprocess together with prediction of permeate fluxes when usingNaCl salt aqueous solution. The considered factors were thestirring velocity, the feed temperature and the NaCl concentration.It was found that the DCMD parameters affect the permeate flux inthe same way as observed from the classical method ofexperimental flux. There is a good agreement between theexperimental and the predicted permeate fluxes by RSM.

Cojocaru and Khayet [23] reported on the applicability of RSMand desirability function approach to modeling and multi-responseoptimization of SGMD used for concentration of sucrose aqueoussolution with three variables: feed temperature, air circulationvelocity and concentration of sucrose. Second-order polynomialmodels as function of the considered factors were developed topredict the permeate flux and the sucrose concentration rate. Toinvestigate the mutual effects of factors on the AGMD performancetaking into account energy consumption and to determine theoptimal operating conditions of the experimental performance ofused process, Khayet and Cojocaru [24] have applied the statisticalexperimental design and RSM in AGMD. The obtained experimentalspecific performance index was also found to have the highest value.In all cases, the experimental results are in good agreement with thepredicted ones by the developed models.

Khayet et al. [25] employed experimental design and RSM formodeling and optimization of SGMD process. It was found that theliquid temperature, gas temperature, liquid flow rate and gas flowrate were the chosen factors which control the permeate flux. Theoptimum operating conditions have been determined by MonteCarlo method. Under optimal conditions the measured waterdistillate flux was smaller than the predicted distillate flux by only2%, which confirmed the developed model.

The objective of this study was to model and optimize thedesalination of NaCl aqueous solution by using DCMD process. Forthis purpose, the response surface methodology is used:

- To develop a mathematical correlation between the vaporpressure difference, feed flow rate, permeate flow rate and feedionic strength for DCMD permeate flux.

- To confirm the validity of the model, the predicted values werecompared to the experimental results. The predicted valuesobtained from the regression models were also presented in 3Dresponse surface plots to identify the contributions of operatingvariables and their interaction effect on permeate flux. Inaddition, the DCMD performance was verified by consideringall optimized factors.

2. Materials and methods

2.1. Materials and DCMD apparatus

Experiments were carried out using a flat sheet microporousmembrane made of polypropylene (PP) polymer. The principalmembrane characteristics are presented in Table 1.


The schematic diagram of the laboratory scale flat sheet DCMDprocess designed, built and tested for this study is shown in Fig. 1.The installation consisted of two thermostatic cycles (feed andpermeate) that were connected to a membrane module which wasmade by Plexiglas. The feed compartment, which connected to aheating system, is maintained at a hot temperature and thepermeate compartment, which connected to a cooling system, ismaintained at a cold temperature. The hydrophobic membranewas placed between the two compartments with spacer material.The effective membrane area is 0.0042 m2. The bulk feed andpermeate temperatures were measured inside each compartmentby a digital thermocouple with an accuracy of �0.1 8C. Twoperistaltic pumps are used to circulate the hot feed and the coldpermeate in batch mode operation. The electrical conductivity of feedand permeate solution was measured using a conductivity-meter.

2.2. Permeate flux equation

During experimental runs, the permeated liquid was collectedin a graduated cylinder and the volume was measured at regulartime interval. The permeate flux (L/(m2 h)) was calculated by thefollowing equation:

J ¼ DV

SDt(1)

where DV is the volume of permeate (L), S is the effectivemembrane area (m2) and Dt is the sampling time (h).

The permeate flux (J) of water vapor diffusing through the dryporous membrane is proportional to the vapor pressure differenceacross the membrane, and can be expressed by Darcy’s law [26]:

J ¼ BmðP f � P pÞ (2)

where Bm is the membrane coefficient, Pf and Pp are the vaporpressures at the feed and permeate vapor/liquid interface,respectively. Pf and Pp at the temperature Tf and Tp, respectively,are related to the activity of the solution by

Pi ¼ awiP0i ; i ¼ f ; p (3)

where awi is the water activity and P0i is pure water vapor and can

be evaluated by using Antoine equation:

P0i ¼ exp 23:238 � 3841

Ti � 45

� �(4)

P0i is measured in Pascal and Ti in Kelvin.

The vapor pressure composition can be estimated using theRaoult’s law, which can be written in case of dilute solutions as

Pi ¼ ð1 � xiÞP0i ; (5)

where xi is the mole fraction of the solute at the membraneinterface.



Fig. 1. Schematic diagram of DCMD setup: (1) Permeate tank; (2) cooling element;

(3) peristaltic pumps; (4) thermocouples; (5) conductivity-meter; (6) flat sheet

module; (7) feed tank; (8) heating element.

A. Boubakri et al. / Journal of Industrial and Engineering Chemistry xxx (2014) xxx–xxx 3

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2.3. Experimental design and statistical analysis

In this study, the Central Composite Design (CCD), which is thewidely used form of RSM, was selected for the optimization ofDCMD process used for desalination of salt aqueous solution. Thismethod is suitable for fitting a quadratic surface and it helps tooptimize the effective parameters with minimum number ofexperiments, as well as to analyze the interaction betweenparameters. Each curve represents the evolution of permeate fluxby varying one variable in the extreme of the CCD model, with itspair variable equal to upper value (+1) and equal to low value (�1)[27] parallel lines mean there is no interaction between the studyvariables, crossing lines indicate the contrary. The level ofinteraction of one variable on the other is represented betweenthese two situations.

A mathematical function is assumed for the response in termsof the significant independent variables. A quadratic modelcorresponding to the following second order equation was builtto describe the response:

Y ¼ b0 þX

i

biXi þX

i

biiX2i þ

Xi j

bi jXiX j (6)

where Y is the response, b0 the constant coefficient, bi the linearcoefficients, bii the quadratic coefficients, bij the interactioncoefficients and Xi, Xj the coded values of the variables.

In this work a second order polynomial equation was obtainedusing the uncoded independent variables as below:

Y ¼ b0 þ b1X1 þ b2X2 þ b3X3 þ b4X4 þ b11X211 þ b22X2

22

þ b33X233 þ b44X2

44 þ b12X1X2 þ b13X1X3 þ b14X1X4

þ b23X2X3 þ b24X2X4 þ b34X3X4 (7)

The statistical significance of the models was justified throughanalysis of variance (ANOVA) for polynomial model with 95%confidence level, and residual plots were used to examine thegoodness of models fit. The quality of the fit polynomial model wasalso expressed by the coefficient of determination R2. Finally,

Table 2Designed variables and their coded and actual values used for experimental design.

Factors Symbol Actual value o

�a

Vapor pressure difference (105 Pa) X1 0.035

Feed flow rate (L/h) X2 6.4

Permeate flow rate (L/h) X3 5.2

Initial ionic strength (mM) X4 21.4


optimum values of factors were obtained by determining a targetin dedicated RSM program (response optimizer).

In this study, four factors including vapor pressure difference(DP), feed flow rate (Qf), permeate flow rate (Qp), and feed ionicstrength (IS) with five levels were employed for response surfacemodeling and optimization of DCMD process. According to CCD, atotal number of 28 experiments have been performed with 16orthogonal design points (24 full factorial design), 8 star points toform a CCD with a = �1.682 and 4 replicate points to estimate theexperimental error.

The experimental domains and the levels of the variables aregiven in Table 2. The levels of the factors were selected accordingto the literature and our preliminary experience. The CCDexperimental matrix and response (J) are reported in Table 3.The experimental design and analysis of data were performed withstatistical and graphical analysis software MINITAB1 release 16developed by Minitab Inc., USA.

3. Results and discussion

3.1. Behavior of DCMD permeate flux as function of running time

DCMD experiments were carried out to determine the steadystate of permeate flux. Fig. 2 presents the behaviors of DCDMpermeate flux as function of operating time using PP membraneunder the following conditions: DP = 0.29 � 10�5 Pa, Qf = 60 L/h,Qp = 20 L/h and IS = 85.6 mM. It can be seen that the permeate fluxafter 8 h of DCMD operating is almost stable. In other words, thevalue of the permeate flux measured during 8 h of DCMD process isthe same and ranged between 3.083 and 3.357 L/(m2 h).

In terms of water quality, the product permeate conductivityslightly increased from 0.4 to 1.8 mS/cm during 8 h of experiment.The high quality of DCMD product water indicates that thedesalination of saline aqueous solution, in the range of 21.4–338 mM as ionic strength, does not affect the hydrophobicity of thepolypropylene membrane during the running time. These obtainedresults demonstrate that the PP hydrophobic membrane had astable permeability and low permeate conductivity value during8 h of DCMD operation. Therefore, the permeate flux of allexperiments will be carried out for 90 min, which the flux have is atsteady state.

3.2. Application of response surface methodology

3.2.1. Regression model equation

Table 3 shows the results of CCD experiments for the studiedeffect of four independent variables that affect the DCMDperformance with the mean of predicted and observed permeateflux (J). The obtained regression equation in terms of codedvariables can be written as follows:

J ¼ 2:350 þ 0:824X1 þ 0:24X2 þ 0:095X3 � 0:013X4

� 0:074X21 þ 0:108X2

2 � 0:177X23 � 0:04X2

4 � 0:044X1X2

þ 0:018X1X3 � 0:069X1X4 � 0:028X2X3 þ 0:143X2X4

� 0:047X3X4 (8)

f coded levels

�1 0 +1 +a

0.1 0.195 0.29 0.355

20 40 60 73.6

10 17 24 28.8

85.6 179.7 273.8 338



Table 3CCD of experiments and output DCMD responses.

Run Factors (controllable input variables) J (L/(m2 h))

DP (X1) Qf (X2) Qp (X3) I (X4) Experimental Predicted

1 �1 �1 �1 �1 0.984 0.996

2 +1 �1 �1 �1 2.855 2.835

3 �1 +1 �1 �1 1.326 1.335

4 +1 +1 �1 �1 3.024 2.997

5 �1 �1 +1 �1 1.268 1.295

6 +1 �1 +1 �1 3.224 3.206

7 �1 +1 +1 �1 1.524 1.522

8 +1 +1 +1 �1 3.266 3.258

9 �1 �1 �1 +1 0.84 0.917

10 +1 �1 �1 +1 2.426 2.480

11 �1 +1 �1 +1 1.755 1.826

12 +1 +1 �1 +1 3.172 3.213

13 �1 �1 +1 +1 0.946 1.026

14 +1 �1 +1 +1 2.602 2.662

15 �1 +1 +1 +1 1.736 1.825

16 +1 +1 +1 +1 3.244 3.285

17 �a 0 0 0 0.912 0.754

18 +a 0 0 0 3.542 3.528

19 0 �a 0 0 2.356 2.253

20 0 +a 0 0 3.13 3.061

21 0 0 �a 0 1.764 1.693

22 0 0 +a 0 2.106 2.005

23 0 0 0 �a 2.184 2.259

24 0 0 0 +a 2.462 2.215

25 0 0 0 0 2.348 2.350

26 0 0 0 0 2.346 2.350

27 0 0 0 0 2.284 2.350

28 0 0 0 0 2.222 2.350


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where X1, X2, X3 and X4 are the coded values of the independentvariables.

In terms of actual variables the empirical model may be writtenas follow:

J ¼ ð�1260:55 þ 13722:5 DP � 15:4216 Q f þ 15:6882 QP

þ 1:1765 IS � 8200:83 DP2 þ 0:271 Q2f � 3:617 Q2

p

� 0:0045 IS2 � 23:158 DPQ f þ 27:256 DPQP � 7:691 DPIS

� 0:1973 Q f Q p þ 0:0758 Q f IS � 0:07 QPISÞ10�3 (9)

where 0.035 � 105 Pa � DP � 0.355 � 105 Pa; 6.4 L/h � Qf �73.6 L/h; 5.2 L/h � Qp � 28.8 L/h and 21.4 mM � IS � 338 mM.

As can be seen from Eq. (8), the vapor pressure difference had asignificantly greater influence on permeate flux than feed flow ratefollowed by permeate flow rate. All these variables have a positiveeffect on permeate flux, but feed ionic strength had a slightnegative effect on the range of variation of each variable selected inthis work. These results were in concordance with that of large

Fig. 2. Permeate flux as function of DCMD running time.


studies on desalination using DCMD process [3,28,29]. As seen also,a wide variation in permeate flux ranging from 0.754 to 3.528 L/(m2 h) occurred for the predicted response. This indicates that thepermeate flux response is strongly related to the selected variablesin this work.

3.2.2. Analysis of variance study

The regression model developed for the prediction of permeateflux was tested for statistical significance using analysis of variance(ANOVA). The statistical validation of the model was performed bymeans of ANOVA which is presented in Table 4. There are certainstatistical estimators that can help in measuring the effectivenessof the model, such as p-value, F-value, R2, adjusted R2 [30]. It is wellknown that a corresponding variable is more significant if its p-value is smaller than 0.05. The results of ANOVA showed a lowprobability or p-value (0.000) and high F-value (89.36). This meansthat the obtained permeate flux model is highly significant and theregression model gives a good prediction of the experimental data.The coefficient of determination (R2), which is the proportion ofvariation in the response attributed for the regression model,should be close to 1. The R2 of the regression model is 0.988,meaning that more than 98.8% of the data deviation can beexplained by the empirical model, which indicates that theregression model is statistically significant. Moreover, it ispreferred to use the adjusted R2

Adj values to evaluate the modeladequacy since it is adjusted for the number of terms in the model[31]. The R2

Adj value is 97.9%, indicating a high degree ofcorrelation between the experimental and predicted responses.

The comparison between the permeate flux response, calculat-ed from the empirical model, and observed experimental data ispresented in Fig. 3. It can be seen that the response model shows agood fit to experimental data. The statistical indexes and graphicalrepresentation reveal that regression model developed for theprediction and optimization of the DCMD process using PPmembrane is statistically validated over the range of consideredexperimentation for the permeate flux response.



Table 4Analysis of variance (ANOVA) of the quadratic model for the permeate flux.

Source DF Sum of squares Mean square F-value p-value R2 R2Adj

Model 14 17.428 1.245 89.36 0.000 0.989 0.979

Residual 13 0.181 0.014

Lack of fit 10 0.170 0.017 2.58 0.132

Pure error 3 0.011 0.004

Total 27 17.609


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3.2.3. Response surface plots

3D response surface curves were plotted to examine theinteraction of the variables and to determine the optimum level ofeach variable for maximum response [32]. For the permeate flux,the response surface is plotted using the regression modelequation (Eq. (9)). Response surfaces of the permeate flux arepresented in Fig. 4(a–f) as a function of two operating variables,while the other two were fixed constant at their respective zerolevel (center value of the testing ranges).

The influence of both vapor pressure difference (DP) and feedflow rate (Qf) on permeate flux for feed ionic strength of 179.7 mMand permeate flow rate of 17 L/h is presented in Fig. 4(a). As can beseen the increase in both factors leads to an increase in thepermeate flux up to a maximum value of 4.115 L/(m2 h) calculatedby regression model. The main effect of DP (b1 = 0.824) is greaterthan the main effect of Qf (b2 = 0.240). Therefore, a high value of DP

and Qf is preferred for achieving a higher DCMD permeate flux. Anincrease in vapor pressure difference leads to an exponentialincrease in the DCMD permeate flux; this trend can be explained bythe Raoult equation (Eq. (4)) and the Antoine equation (Eq. (5))which predict an exponential variation between the temperaturedifference at two membrane sides and vapor pressure difference asthe driving force. Likewise, an increase in feed flow rate led to anincrease in Reynolds number, that decreases the feed sidetemperature boundary layer and the DCMD flux is enhanced.From Eq. (8), it can be seen that there is no interaction effectbetween DP and Qf on DCMD permeate flux.

Fig. 4(b) shows the responses of DCMD permeate flux withvarying DP and Qp. It is observed that the effect of vapor pressuredifference on product flux is highly significant than the effect ofpermeate flow rate (b3 = 0.092); the magnitude effect of DP on fluxis about 9-fold than Qp. For the pair of variables (DP and Qp), thecurve presents a parallel behavior; it may be assumed that there isno interaction and the modification of one does not affect the otherone.

The combined effects of DP and feed ionic strength on permeateflux are shown in Fig. 4(c). As expected, the DCMD flux increasedwith increasing DP and slightly decreased with increasing ionic

Fig. 3. Comparison between experimental


strength (b4 = �0.013). The surface plot of interaction between DP

and IS presents a parallel behavior, and may indicate that there isno interaction.

The permeate flux is plotted as a function of Qf and Qp inFig. 4(d). It can be observed that increasing both factors results inan enhancement of DCMD flux, but the effect of Qf is moresignificant than Qp by about 2.6-fold.

Fig. 4(e) presents the response surface plot of DCMD permeateflux as a function of Qf and ionic strength. It is observed that at lowfeed flow rate, the permeate flux decreases with increasing feedionic strength, but at high Qf, the permeate flux increases slightlywith increasing ionic strength. As shown in Fig. 4(e), the curves ofinteraction between Qf and IS tend to cross. It may be assumed thatthe interaction between two variables is significant. This was alsoconfirmed by the value of p < 0.05 calculated by ANOVA.

The effect of Qp and ionic strength on permeate flux is given inFig. 4(f). As can be seen, both factors have a slight effect on DCMDpermeate flux. At center value of Qp and ionic strength a maximumresponse value was obtained, the permeate flux is 2.351 L/(m2 h)as calculated by regression model. It is to be mentioned that theinteraction between Qp and ionic strength on DCMD flux isnegligible.

3.3. DCMD optimization using desirability function

The last step of the RSM is to obtain the optimal conditions forthe desalination of NaCl solution in terms of product flux by DCMDprocess using polypropylene membrane.

The software for optimization aims to scan the globalinformation of the model in terms of response surfaces, maineffects and interaction variables to obtain the best conditions forthe process [33]. Desirability function approach was employed inthis procedure.

Up and down limits used for the DCMD permeate flux were 1and 5 L/(m2 h), respectively. According to Minitab software, theoptimum conditions in terms of current variables are transmem-brane vapor pressure difference of 0.355 � 105 Pa, feed flow rate of73.6 L/h, permeate flow rate of 17.1 L/h and feed ionic strength of

and predicted DCMD permeate flux.



CurHigh

Low0,83833D

Optimal

d = 0,83833

MaximumJ (L/m²h

y = 4,1917

0,838 33Desirabili tyComposite

21,4238

337,9762

5,2260

28,7740

6,360

73,640

0,0352

0,3548Qf (L/h) Qp (L/h) IS (mM)? P (1 0 5

[0,3548] [73,6400] [17,1189] [309,198 7]

Fig. 5. Optimization plot of operating variables for permeate flux.

Fig. 4. 3D response surface plots of DCMD permeate flux as function of operating factors. (a) Permeate flux vs vapor pressure difference and feed flow rate; (b) permeate flux vs

vapor pressure difference and permeate flow rate; (c) permeate flux vs vapor pressure difference and feed ionic strength; (d) permeate flux vs feed flow rate and permeate

flow rate; (e) Permeate flux vs feed flow rate and feed ionic strength; (f) permeate flux vs permeate flow rate and feed ionic strength.


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Please cite this article in press as: A. Boubakri, et al., J. Ind. Eng. Chem. (2014), http://dx.doi.org/10.1016/j.jiec.2013.11.060


Table 5Predicted and experimental values of DCMD permeate flux at optimum conditions.

DP (105 Pa) Qf (L/h) Qp (L/h) IS (mM) J (L/(m2 h)) Errors (%)

Predicted Experimental

0.355 73.6 17.1 309 4.362 4.192 3.9


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309 mM, with a desirability value of 0.906. Fig. 5 showed theoptimization plot that was developed from optimum operatingvariables via numerical optimization.

3.4. Verification of optimized conditions and predictive model

To confirm the model adequacy and the validity of optimizationprocedure, experiments were carried out under optimized condi-tions and the results were compared with the predicted values ofresponse using the model equation. The experiments wereconducted in triplicates and mean values are reported in Table5. The optimization reveals that DCMD experimental and predictedpermeate flux are, respectively, 4.192 L/(m2 h) and 4.362 L/(m2 h).These results represent 3.9% as deviation between experimentaland predicted values. The results obtained from confirmationexperiments are within 95% of predicted values. This indicates thesuitability of the developed regression model and it may be notedthat these optimal values are valid within the specified range ofDCMD process variables.

4. Conclusion

This study investigates the modeling and optimization of lab-scale DCMD for aqueous NaCl water desalination using experimen-tal design and response surface methodology. Effects of operatingconditions, mainly vapor pressure difference, feed flow rate,permeate flow rate and feed ionic strength, were studied to optimizeDCMD permeate flux. Hydrophobic PP membrane can produce highquality of water with low electrical conductivity for all experimentalruns. The response surface model for DCMD permeate flux wasstatistically validated by ANOVA and provided good quality topredict the response, whose R2 = 0.989 and R2

Adj = 0.979. Vaporpressure difference was the most significant factor that influencedpermeate flux, followed by feed flow rate. Based on desirabilityfunction in RSM, the optimum conditions for maximum permeateflux (4.192 L/(m2 h)) were found as follows: DP = 0.355 � 10�5 Pa,Qf = 73.6 L/h, Qp = 18.8 L/h and IS = 309 mM, which was confirmedexperimentally with a percentage deviation of 3.9%.

Acknowledgments

The authors wish to thank Nesrine Hmidi for the help andconstant support during this work.


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Application of RSM for modeling and optimization of MD desalination process

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