Response surface modeling and optimization of direct

Desalination 394 (2016) 108–122

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Desalination journal homepage: www.elsevier.com/locate/desal

Response surface modeling and optimization of direct contact membrane distillation for water desalination Dongjian Cheng a, Wei Gong a, Na Li a,b,⁎ a b

Department of Chemical Engineering, School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an 710049, China Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Regression models were established by response surface methodology in DCMD process. • The models were proved to be able to predict the responses accurately. • Interaction effects of operational and module-configural factors were investigated. • Optimal conditions for multi-objectives were determined and confirmed.

a r t i c l e

i n f o

Article history: Received 9 January 2016 Received in revised form 18 April 2016 Accepted 29 April 2016 Available online 19 May 2016 Keywords: Direct contact membrane distillation Desalination Response surface methodology Operating parameters Module configuration parameters

a b s t r a c t Response surface methodology was applied for modeling and optimization of direct contact membrane distillation (DCMD) for water desalination with PVDF hollow fiber membrane. The optimization objectives included average permeate flux, water productivity per unit volume of module, water production per unit energy consumption, and a comprehensive index to find out a balance among high water flux, high production, and low energy consumption. Effects of both operating parameters and configuration parameters of membrane module, including inlet temperatures of feed and permeate, flow velocity of feed solution, module packing density, and length-diameter ratio of module, on the objectives were investigated. The models for predicting the objectives were developed and statistically validated by analysis of variance. The binary interaction effects of the variables on the objectives were illustrated and discussed. All of the objectives were significantly influenced by the interaction effects of the variables. Under the optimum conditions, 67.1 kg/(m2·h) average permeate flux, 4.9825 × 104 kg/(m3·h) water productivity per unit volume of module, 2.1839 × 10−4 kg/kJ water production per unit energy consumption, and comprehensive index of 0.7587 were obtained within investigated experimental range. The experimental and predicted results are in good agreement confirming the validity of the models. © 2016 Elsevier B.V. All rights reserved.

⁎ Corresponding author at: Department of Chemical Engineering, School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an 710049, China. E-mail address: [email protected] (N. Li).

http://dx.doi.org/10.1016/j.desal.2016.04.029 0011-9164/© 2016 Elsevier B.V. All rights reserved.

D. Cheng et al. / Desalination 394 (2016) 108–122

1. Introduction Membrane distillation (MD) is a thermally-driven process in which vapor molecules evaporate from feed solution and transport through microporous hydrophobic membrane as distillate product. Its driving force is based on the vapor pressure difference generated by temperature gradient between the feed side and the permeate side of membrane [1]. MD process is conducted at lower operating temperatures (30–80 °C) than conventional distillation (N 100 °C) and under lower operating pressures (b100 kPa) than conventional pressure-driven membrane processes such as reverse osmosis (RO) (N 10 bar). The rejection to non-volatile solute in MD is theoretically 100%. MD system is generally performed in four configurations, including direct contact membrane distillation (DCMD), sweeping gas membrane distillation (SGMD), air gap membrane distillation (AGMD), and vacuum membrane distillation (VMD) [2,3]. DCMD is the most commonly used MD configuration due to its simple operation without the need of external condensers like in SGMD and VMD configurations [3,4], which has been widely applied for fresh water production [5–7], wastewater treatment and reuse [8,9], and food processing [10,11]. Factors affecting the performance of DCMD have been studied extensively, including operating conditions [12–17], module configuration parameters [12–14,18], and membrane properties [12,16,19]. The operating conditions investigated are generally the temperature of the feed and permeate, the flow rate (flow velocity) of feed and permeate, and the feed concentration. Feed temperature has a significant influence on permeate flux. In most cases, increasing feed temperature leads to an exponential increase of permeate flux since water vapor pressure driving force increases exponentially with the increase in temperature according to Antoine equation [12–15,20]. The increase in flow rate of feed and permeate is beneficial for reducing temperature polarization and concentration polarization on membrane surface leading to the increase in permeate flux and thermal efficiency [14]. High feed concentration will cause the decrease in water vapor pressure and the increase in concentration polarization, and lead to a negative effect on permeate flux [13]. However, the influence of feed concentration (activity) on the driving force of MD may not be significant compared to that of temperature difference across the membrane. For instance, Khayet et al. [21] reported that the most significant individual effect upon the permeate flux was attributed to the feed temperature while the feed solute concentration had the lowest individual effect upon the DCMD permeate flux in comparison to the feed temperature and stirring rate. Elzahaby et al. [22] also reported that pure water productivity decreased by only 2.7% with the increase in NaCl concentration from 3 to 50 g/L in DCMD process. As to the module configuration parameters, increasing hollow fiber length will decrease permeate flux due to the reduction of average transmembrane temperature difference [13,14], and will also make the membrane prone to be wet due to the increased hydrodynamic pressure at the same flow rate [3]. The large packing density of membrane in a module is favorable to increase the unit volume productivity, but the increasing channeling and dead zones will reduce mass transfer [18]. The increased packing density of membrane module decreased the ratio of permeate flux to the overall driving force dramatically, due to the uneven flow distribution in the lumen side of the module and the channeling effect [20]. As to membrane properties, the studies on the relationship of DCMD performance with membrane thickness, porosity, tortuosity, pore size, and thermal conductivity have been widely reported [23–24]. The permeate flux increases by increasing membrane pore size and porosity and by decreasing membrane thickness and pore tortuosity [25]. Since the factors influencing MD process are very complicated, conventionally MD research varies one parameter and keeps the others constant. This research method is expensive, laborious and ignores the interaction effects between the independent parameters [21,26–28]. Therefore, a design of experiment allows the simultaneously varying of input parameters, which can reveal their significance and complex

109

interaction under real operation conditions. The response surface methodology (RSM), a collection of mathematical and statistical technique, is one of the most relevant multivariate methods [26]. In RSM, the predicted response is plotted in 3D as a function of two inputs allowing to visualize their contribution and interaction influence [4,28]. RSM method has been applied successfully in MD process in modeling, optimization, and investigation of interactions between several parameters in recent years [21,28–33]. Both single objective [21,28–30] and multi-objective [31–33], such as permeate flux and thermal efficiency, have been investigated with RSM method. The most studied variables for the optimization were operating parameters such as temperatures and flow rates of the feed and permeate, and feed concentration. Khayet et al. employed a central compositional design (CCD) for modeling and optimization of DCMD process [21] and SGMD process [28]. In DCMD, the interaction effect between feed temperature and stirring velocity increased the permeate flux while the interaction effects between stirring velocity and feed concentration and between feed temperature and feed concentration decreased the permeate flux. In SGMD, the significant interactions were observed between the variables such as gas temperature and gas flow rate, feed temperature and gas flow rate, and feed flow rate and gas flow rate. Chang et al. [29] developed quadratic response surface models to predict the performance of DCMD and AGMD in terms of separation efficiency (water production per unit hot fluid flow rate) and heat requirements. The studied factors were flow rates of hot and cold fluids, hot fluid temperature, and membrane thickness in DCMD, and hot fluid flow rate and hot fluid temperature in AGMD. Under the optimal conditions, separation efficiency of 8.2% and 5.8% were obtained for DCMD system and AGMD system, respectively, close to the obtained efficiency of reverse osmosis technology. Boubakri et al. [30] studied the effects of vapor pressure difference, feed flow rate, permeate flow rate, and initial ionic strength on DCMD permeate flux and found the significant interaction between feed flow rate and initial ionic strength. C. Cojocaru and M. Khayet [31] developed RS-models to predict permeate flux and sucrose concentration rate in SGMD as functions of feed inlet temperature, air circulation velocity, and initial sucrose concentration. The interaction effect between air circulation velocity and initial sucrose concentration was more significant than that between feed inlet temperature and initial sucrose concentration, whereas the interaction between feed inlet temperature and air circulation velocity was negligible. He et al. [32] observed the highest positive effect of hot feed inlet temperature on both distillate flux and gained output ratio and a trade-off between distillate flux and gained output ratio by varying cold feed inlet temperature and feed flow rate when keeping hot feed inlet temperature as constant. Zaherzadeh et al. [33] reported the optimization of membrane structural characteristics (pore size, porosity, and contact angle) for increasing permeate fluxes with the influencing factors of membrane synthesis process (temperature, pressure, and polymer concentration). It has been reported that both operating conditions and membrane module configuration parameters play significant roles in MD performance based on experiments or simulations [12–14,20, 34–36]. However, the study on the optimization of DCMD process considering operating conditions and module configuration parameters simultaneously is few. Cheng et al. [14] applied the genetic algorithm to a two-objective (water productivity and thermal efficiency) optimization of DCMD under different operating conditions and fiber dimensions. They found that thermal efficiency decreased as water production increased and vice versa with the designed variables including inlet cold flow rate, fiber length, and module packing density. In addition, Yu et al. [36] suggested that the simulations of DCMD process could provide qualitative predictions on the effects of operating conditions and module configuration parameters on MD performance, which could guide future study on the hollow fiber module design, module scale-up, and process optimization to facilitate MD commercialization.

110


In this study, a quadratic rotation-orthogonal composite design (QRCD) and RSM were applied to model and optimize DCMD process and to investigate the interaction effects among operating and module configuration parameters on DCMD performance. The QRCD method, a special form of the central composite design (CCD) with orthogonality and rotatability, is a comprehensive and accurate statistical tool for multiple linear regression analysis. It not only provides specific information from all treatments but also presents inherent interaction effects with the least experimental trials [37]. Four optimization objectives were involved including average permeate flux (J), water productivity per unit volume of module (Pv), water production per unit energy consumption (Pe), and a comprehensive index (CI). CI was introduced to take the other three objectives into account by a weight grade method, with attempt for a balance between high permeate flux (production) and low thermal energy consumption. The investigated independent variables were feed inlet temperature, permeate inlet temperature, flow velocity of feed solution, module packing density, and length–diameter ratio of module. The regression models for the objectives were developed and the predicted results were presented in representative threedimensional (3D) response surface plots to identify the contributions of the variables and their binary interactions on the responses. The predicted responses were compared with the experimental results to confirm the validity of the models. 2. Materials and methods 2.1. Materials, DCMD apparatus and experimental parameters Polyvinylidene fluoride (PVDF) hollow fiber membrane obtained from Tianjin polytechnic university, China, was employed for DCMD modeling and optimization. The principal membrane parameters are membrane thickness of 150 μm, average pore size of 0.16 μm, hollow fiber inner diameter of 800 μm, porosity of 85%, and liquid entry pressure of water of above 200 kPa, according to the provider and our measurement. The PVDF hollow fiber bundle was assembled into a plexiglass tube and both ends of the bundle were sealed with solidified epoxy resin. The laboratory-made membrane modules have outer diameter of 22 mm and inner diameter of 15 mm with different length– diameter ratio of module (Rld) as shown in Fig. 1. Fig. 2 is the schematic diagram of DCMD experimental set-up. 3.5 wt% NaCl feed solution was applied in the optimization of DCMD process. The hot feed solution was circulated through the lumen side of the hollow fibers and the cold fluid was circulated through the shell side of the module by peristaltic pumps. Feed and permeate flow rates were monitored by rotor flow meters. The temperature of the feed was controlled by a heater. The temperature of

Fig. 2. Schematic diagram of DCMD setup: (1) feed tank; (2) peristaltic pumps; (3) rotameters; (4) heater; (5) thermocouples; (6) hollow fiber membrane module; (7) chiller; (8) permeate tank; (9) analytical balance; and (10) computer.

cold fluid on the permeate side of membrane was adjusted by a chiller. The feed and permeate temperatures at the inlet and outlet of the membrane module were measured by digital thermocouples with ± 0.1 °C accuracy. All of containers and pipes were insulted to reduce the heat loss of the system. In this case, a small temperature difference (b2 °C) existed between the heater temperature (Th) and feed temperature at the inlet of membrane module (Twf,in) and between feed tank temperature (T f ) and feed temperature at the outlet of membrane module (T wf,out ). The relative standard deviations between Th and Twf,in and between Tf and Twf,out were b 5%. In all of the experimental runs, the volume and concentration of feed solution were controlled within 0.05 wt% fluctuation by adding fresh water to the feed tank. The weight gain of the distillate was measured by a digital balance. The salt rejection was determined based on the conductivity measurement of feed and permeate solutions with a conductivity meter. The data was recorded when the PVDF hollow fiber membrane performance is stable, and the permeate flux was the average value for 30 min running. The standard deviation of water flux during each experimental run ranged within 0.35–1.37 and the relative standard deviation was b 4.2%. NaCl rejection was above 99.9% for all of the experimental runs.

2.2. Optimization variables and objectives for DCMD experiments 2.2.1. Variables Five influencing factors including both operating parameters and module configuration parameters were taken into consideration as optimization variables. The operating conditions are feed inlet temperature (Twf,in, °C), permeate inlet temperature (Twp,in, °C), and flow velocity of feed solution (Vf, m/min). The module configuration parameters are module packing density (D) and length–diameter ratio of module (Rld). Vf is the linear flow velocity of feed solution in hollow fiber membranes, calculated by Eq. (1). D is the ratio of the total crosssectional area of the hollow fiber bundle to the inner cross-sectional area of membrane module, as shown in Eq. (2). Rld is the ratio of effective length of membrane module to inner diameter of membrane module, calculated by Eq. (3).

Vf ¼

D¼ Fig. 1. Photo of membrane modules with different length–diameter ratio of module.

4q nπdm;in

nπ

π

dm;out 2

2

2 di 2

ð1Þ

2

2 dm;out 100% ¼ n 100% di

ð2Þ


Rld ¼

l : di

ð3Þ

Here q (m3/min) is the feed flow rate, dm,in (m) is the inner diameter of hollow fiber membrane, dm,out (m) is the outer diameter of hollow fiber membrane, n is the number of the fibers in membrane module, di (m) is the inner diameter of the membrane module, and l (m) is the effective length of the membrane module. 2.2.2. Objectives (1) Average permeate flux (J, kg/(m2·h)). J is calculated according to the following equation: J¼

ΔW At

Here ΔW (kg) is the mass variation on the permeate side over a given period t (h), A (m2) is the total surface area of membrane in the lumen side. In general, J will reduce as increasing the membrane area under certain operating conditions [38]. (2) Water productivity per unit volume of module (Pv, kg/(m3·h)). Pv is used to evaluate the overall water production capacity of membrane module, and can be calculated by Eq. (5). Pv ¼

4ΔW 2

πdi lt

:

ð5Þ

Here di (m) is the inner diameter of the membrane module, and l (m) is the effective length of membrane module. Pv value is a key factor in assessing DCMD performance, since it reflects the water productivity based on the equipment investment. (3) Water production per unit energy consumption (Pe, kg/kJ). Pe is the permeate production consuming per kilojoule energy, defined in Eq. (6) as the mass variation on the permeate side of membrane over a given time frame divided by the corresponding energy consumption of the system and is calculated as [39] ΔW Pe ¼ : Q Et

In MD process, permeate flux, water production per unit volume and thermal energy consumption are all important, due to both cost and footprint consideration in commercial application. Thus, multiobjective optimization is necessary. CI is introduced for a multiobjective optimization taking J, Pv, and Pe into account via a weight grade method to find out an optimum condition to achieve both high water production (permeate flux) and low energy consumption. In this method, each objective variable is converted to a normalized value in a range of 0–1. The following equation is used to normalize the objectives [41,42]: xi ¼

ð4Þ

ð6Þ

111

zi −zi; min ; i¼ J;P v ; and P e : zi; max −zi; min

ð10Þ

Here xi is the normalized objective i; zi, zi,min, and zi,max are the actual, minimum, and maximum values of the optimization objective i. Then CI is calculated as: CI ¼ w J x J þ wPv xPv þ wPe xPe :

ð11Þ

Here wJ, wPv, and wPe are the weight coefficients of J, Pv, and Pe, respectively, which can be various depending on the requirement of users. The larger the weight coefficient value given, the greater the dominance of the corresponding single objective is. In case of equal importance of the three single objectives, the values of wJ, wPv, and wPe should be the same. In general, the weight coefficients can be determined by means of Delphi method (expert consultation method), order relation analysis method (G1-method), and statistical method [43,44]. In this study, the statistical method was employed to determine the weight coefficients based on the calculated results of average relation error (ARE) and Marquradt's percent standard deviation (MPSD) between the experimental CI values and predicted CI values. For practical using, the cost and user's requirement become important and thus comprehensive evaluation should be considered in selecting suitable weight coefficients to have a desired MD performance. 2.3. Experimental design and statistical analysis

Q h ¼ cp;h mh T h −T f

ð7Þ

A quadratic rotation-orthogonal composite design (QRCD) is applied for modeling and optimization. In this method, all of the test points (N) are divided into three distinct portions. The three kinds of test points, rotation design points (Mc), star points (Mr), and center points (M0), distribute on the spherical surfaces with spherical radius of M1/2, M1/4 c , and zero, respectively, in which M is the factor number. Based on QRCD, a quadratic model widely used for developing a response surface method with experimental data is built to describe the response as follows [21,27–33]:

Q c ¼ cp;c mc ðT 0 −T c Þ

ð8Þ

Y ¼ b0 þ

The total energy consumption QE (kJ/h) throughout the system includes the energy input on the hot feed side (Qh, defined in Eq. (7)) and the permeate side (Qc, defined in Eq. (8)) to maintain the temperatures, and the electrical energy consumption for circulating feed water and permeate water by two peristaltic pumps (Qp, defined in Eq. (9). Thus, QE was obtained as follows:

X i

Q E ¼ Q h þ Q c þ Q p:

ð9Þ

Here cp,h (kJ/(kg·°C)) and cp,c (kJ/(kg·°C)) are the specific heat capacity of feed water and permeate water, respectively; mh (kg/h) and mc (kg/h) are the mass flow rate of feed water and permeate water, respectively; Th (°C) is the feed temperature in the heater and Tf (°C) is the feed temperature in the feed tank, T0 (°C) is the temperature of the environment and Tc (°C) is the permeate temperature in the chiller. Qp is determined by the rated power of the peristaltic pump. When the permeate temperature is higher than the environment temperature, the feed water at ambient temperature can be circulated through a heat-exchanging coil to cool the permeate [40]. Therefore, the cooling energy was excluded when calculating the process thermal consumption in case Tc N T0. (4) Comprehensive index (CI).

bi X i þ

X

bii X i 2 þ

X

i

bij X ij :

ð12Þ

ij

Here Y is the response, bi is the linear coefficients, bii is the quadratic coefficients, bij is the binary interaction coefficients, and Xi and Xj are the coded values of the variables. The subscripts i and j are the integer variables. In this study, a second order polynomial equation can be obtained using the coded independent variables as below:

Y ¼ b0 þ b1 X 1 þ b2 X 2 þ b3 X 3 þ b4 X 4 þ b5 X 5 þ b11 X 1 2 þ b22 X 2 2 þb33 X 3 2 þ b44 X 4 2 þ b55 X 5 2

þ b12 X 1 X 2 þ b13 X 1 X 3 þ b14 X 1 X 4

þb15 X 1 X 5 þ b23 X 2 X 3 þ b24 X 2 X 4 þ b25 X 2 X 5 þ b34 X 3 X 4 þb35 X 3 X 5 þ b45 X 4 X 5 : ð13Þ

112


The QRCD for response surface modeling of DCMD process is employed to analyze the effect of the variables on the studied objectives. The levels of the considered variables fall in the general ranges reported in literature and their actual values are given in Table 1. According to QRCD, a total number of 36 experiments (1/2 design, Mc = 16, Mr = 10, M0 = 10) were carried out to optimize the DCMD process. The QRCD experimental matrix and responses are reported in Table 2. The experimental design and data analysis were performed with statistical and graphical analysis software Statistical Product and Service Solutions (SPSS).

in the equations indicate the positive or negative effect of the parameters on the corresponding objectives. It is noteworthy that the regression equation of CI was dependent on various combinations of weight coefficients. The average relation error (ARE) and Marquradt's percent standard deviation (MPSD) between the experimental CI value and predicted CI value with different combinations of the weight coefficients were calculated according to following equations [45]:

ARE ¼

3. Results and discussion

k Y exp −Y calc 100 X n i¼1 Y exp

ð14Þ

i

3.1. Application of response surface methodology 3.1.1. Range analysis and main effects plot The range analysis method was used to primarily assess the dominance degrees of the five variables as well as their optimum conditions. In general, the larger the range analysis value is, the greater the effect of variables on experiment objective will be. By comparing the range analysis value, the dominance degree and optimum value of each factor can be distinguished. The range analysis results are listed in Table 3. It is indicated that Twf,in and Rld are the two key factors for both J and Pe. This can be explained that Twf,in plays a significant role in driving force and thermal consumption of DCMD. The factor Rld affects the driving force and thermal efficiency of DCMD process by changing the average temperatures on both sides of the membrane [13–14]. D and Twf,in are the two important factors for Pv since high feed inlet temperature and large effective membrane area tend to achieve high overall water production. The result is consistent with the observations by Cheng et al. [14]. It is understandable that Twf,in is the most significant factor for CI, which is in agreement with the results for the other three objectives. Furthermore, the influences of the five variable parameters on J, Pv, Pe, and CI are illustrated in Fig. 3. As it is observed, higher Twf,in is beneficial for achieving greater values of J, Pv, Pe, and CI. Maintaining a low Twp,in value can increase J and Pv. The high value of D is favorite for increase of Pv, Pe, and CI. For the influence of Rld on all of the four objectives, the analogous trend is shown as follows: for Rld b 10, the lower the length–diameter ratio of module is, the better the DCMD performance will be, and for Rld N 10, the reverse trend is obtained. However, the above results could not demonstrate the interaction effect among the variables but just represented some general rules about DCMD process. Therefore, the optimum conditions cannot be derived comprehensively. Thus, the regression equations were developed and the response surface plots were depicted in the next section. 3.1.2. Regression model equations Regression models of J, Pv, Pe, and CI were constructed in terms of actual variables as shown in Table 4. A total number of 20 variables including 5 single factors, 10 interaction factors, and 5 quadratic factors were involved in the equations. The RS-models are statistically valid based on the high value of the fitting coefficients. The regression equations were simplified by stepwise regression analysis. The simplified equations (all the insignificant items were ignored) and the fitting coefficients are shown in Table 5. The positive or negative coefficients of the variables

2vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 u k 6u 1 X Y exp −Y calc 7 MPSD ¼ 1004t 5: k−d i¼1 Y exp

ð15Þ

i

Here Yexp refers to the experimental objective value, Ycalc denotes the calculated objective value by regression equation, k is the number of data points and d is the number of the regression coefficients. The results are shown in Table 6. As can be seen, when the weight coefficients of J, Pv, and Pe were 0.3, 0.3, and 0.4 respectively, ARE and MPSD showed the smallest values. Thus, the CI results shown in Table 2 and the prediction model of CI shown in Tables 4 and 5 were obtained with wJ of 0.3, wPv of 0.3, and wPe of 0.4. This is an efficient and convenient method to select the weight coefficient for the calculation of the overall comprehensive index. However, for practice using, weight coefficients should be adjusted according to the requirements of the users. 3.1.3. Analysis of variance The simplified regression equations were tested for statistical validation using analysis of variance (ANOVA). The statistical estimators such as P-value, F-value, R2, adjusted R2 are used to measure the effectiveness of model [26,30]. Their values are presented in Table 7. As can be seen, the F-values are high, and the P-values are smaller than 0.0001. Furthermore, the R2 values of the regression models are in good agreement with the adjusted R2adj value for each objective model. Therefore, the results indicate that the RS-models are statistically valid and can be used for good prediction of the DCMD objectives. The responses of the objectives in Table 2 were predicted by the regression equations. The predicted data and the experimental results were compared in Fig. 4. It can be seen that the results from RSmodels show reasonably good agreements with the experimental results. The average relation errors for J, Pv, Pe, and CI are 7.8%, 7.7%, 12.6%, and 12.5%, respectively. Good agreements between the predicted data and experimental results indicate the statistical validity of the RSmodels. RS-model is generally analyzed by means of Student ‘t’-test to determine the significance of the regression coefficients of influencing factors [27,28]. The determined dominance degrees of the variables are shown in Table 8. It can be seen that the most significant interaction effects are between Twf,in and Rld on J and CI, between Twf,in and D on Pv, and between Twf,in and Twp,in on Pe.

Table 1 Independent variables, their coded levels, and actual values in DCMD experimental design. Variables

Feed inlet temperature (Twf,in), °C Permeate inlet temperature (Twp,in), °C Flow velocity of feed solution (Vf), m/min Module packing density (D), % Length-diameter ratio of module (Rld)

Symbol

X1 X2 X3 X4 X5

Separation distance

10 5 12 10 3.3

Actual values of coded levels (α = 2) −α

−1

0

1

+α

40 15 6 5 3.3

50 20 18 15 6.7

60 25 30 25 10

70 30 42 35 13.3

80 35 54 45 16.7


113

Table 2 Quadratic rotation-orthogonal composite design and DCMD experimental results. Run

Twf,in, °C

Twp,in, °C

Vf, m/min

D, %

Rld

J, kg/(m2·h)

Pv, kg/(m3·h)

Pe, kg/kJ

CIa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

70 70 70 70 70 70 70 70 50 50 50 50 50 50 50 50 80 40 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60

30 30 30 30 20 20 20 20 30 30 30 30 20 20 20 20 25 25 35 15 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25

42 18 18 42 18 42 42 18 18 42 42 18 42 18 18 42 30 30 30 30 30 30 30 30 54 6 30 30 30 30 30 30 30 30 30 30

35 15 35 15 35 15 35 15 35 15 35 15 35 15 35 15 25 25 25 25 25 25 45 5 25 25 25 25 25 25 25 25 25 25 25 25

13.3 13.3 6.7 6.7 13.3 13.3 6.7 6.7 13.3 13.3 6.7 6.7 13.3 13.3 6.7 6.7 10 10 10 10 16.7 3.3 10 10 10 10 10 10 10 10 10 10 10 10 10 10

18.89 11.92 23.23 30.47 12.18 12.24 31.55 26.20 7.80 15.22 9.65 8.88 13.29 9.48 11.04 12.05 20.50 1.01 6.77 12.23 16.76 24.87 15.29 20.34 13.75 7.88 14.84 14.56 13.20 12.20 10.82 12.13 12.16 11.95 14.78 14.10

17,459.080 4745.054 21,475.073 12,134.656 11,255.315 4873.443 29,165.764 10,434.779 7124.072 6061.864 8923.535 3537.886 12,282.653 3774.475 10,207.983 4788.513 13,705.119 671.857 4521.821 8175.513 11,205.897 16,625.305 18,268.460 2892.984 9190.092 5269.167 9919.321 9730.597 9467.983 8152.866 7231.935 8167.964 8130.219 7986.789 9881.576 9425.619

0.00011288 0.00010321 0.00015803 0.00011863 0.00009658 0.00005191 0.00009283 0.00007433 0.00013192 0.00016617 0.00007954 0.00006549 0.00008530 0.00005973 0.00006845 0.00003869 0.00009257 0.00001320 0.00006402 0.00006708 0.00014876 0.00008781 0.00011495 0.00007140 0.00008472 0.00008928 0.00011158 0.00008560 0.00007637 0.00007234 0.00006441 0.00007188 0.00007198 0.00007063 0.00008606 0.00008242

0.48597 0.35458 0.65860 0.59904 0.35906 0.22399 0.59259 0.43623 0.39631 0.55560 0.28283 0.22260 0.34353 0.21407 0.54302 0.18734 0.43765 0 0.20086 0.27337 0.54043 0.47674 0.45848 0.34867 0.33740 0.28010 0.42051 0.34924 0.31102 0.28671 0.24971 0.28489 0.28538 0.27930 0.35310 0.33554

a

CI values obtained with 0.3, 0.3, and 0.4 weight coefficient of J, Pv, and Pe.

3.2. Response surface plots The response surfaces of objectives J, Pv, Pe, and CI were plotted using Matlab software. The significant effects of binary variables on the objectives are presented in Figs. 5, 6, 7, and 8 while other variables are set to be constant at their center points that have been shown on top of each plot. The interaction effects of the variables were examined and the optimum level of each variable for maximum response was determined accordingly. Crossing line of the plots means the interaction of two considered variables [46].

3.2.1. Interaction analysis for the average permeate flux The effect of feed inlet temperature (Twf,in) and permeate inlet temperature (Twp,in) on the average permeate flux (J) is presented in Fig. 5 (a). The response surface plot indicates that J increases exponentially with Twf,in, which is consistent with the observations in other studies [1,3,12–15,21]. This is mainly due to an exponential increase of the vapor pressure of feed solution with the increase in Twf,in. In contrast, Table 3 The dominance degree of variables and their optimum values. Objectives

J, kg/(m2·h) Pv, kg/(m3·h) Pe, kg/kJ CI

Effect sequence of the variables

Twf,in N Rld N Vf N Twp,in N D D N Twf,in N Twp,in N Rld N Vf Twf,in N Rld N Twp,in N D N Vf Twf,in N Twp,in N Rld N D N Vf

Optimum values Twf,in, °C

Twp,in, °C

Vf , m/min

D, %

Rld

70 50 70 70

20 20 30 30

42 18 18 42

5 35 45 45

3.3 6.7 16.7 16.7

Twp,in shows slight effect on J within the tested range. Therefore, the interaction effect between Twf,in and Twp,in is insignificant. It can be observed in Fig 5 (b), there is a significant interaction effect between feed inlet temperature (Twf,in) and length–diameter ratio of module (Rld) on the average permeate flux (J). When Rld value is low, an increase of Twf,in leads to a dramatic increase of J, and a maximum flux of 66.8 kg/(m2·h) is obtained at the maximum Twf,in of 80 °C and lowest Rld of 1. It is known that there is a temperature drop of feed solution along membrane fibers due to water evaporation and heat conduction loss across membrane wall. Thus, increasing the length of fibers leads to the reduction of average temperature difference across the membrane, so as to decrease the water flux [13–14,36]. The result indicates that a significant enhancement of permeate flux can be acquired by adjusting the operating condition and the membrane module parameter simultaneously. In addition, another increase trend of J is found at low Twf,in and high Rld. This is because that at the low Twf,in the average temperature difference across the membrane will not change greatly. This means that a noticeable improvement of J can be expected by increasing Rld even at low feed inlet temperature. Fig. 5 (c) shows the response of permeate flux (J) as a function of feed inlet temperature (Twf,in) and flow velocity of feed solution (Vf). It can be seen, J increases with the increase of Twf,in and Vf and the coupling effect between the two operating variables can be found. The positive effect of Twf,in is more intense on flux at high Vf than that at low Vf. Similarly, at high Twf,in, the Vf has greater influence on flux than that at low Twf,in. Therefore, to achieve a significant enhancement of permeate flux, the combination of high Twf,in and high Vf is required. Similar finding was also reported by Duong et al. [47] in AGMD due to the decrease in temperature polarization on membrane surface by increasing Vf. At high Twf,in, the temperature polarization across the membrane is worse

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Fig. 3. Main effects plot of variables for permeate flux (a), water productivity per unit volume of module (b), water production per unit energy consumption (c), and comprehensive index (d).

than that at low temperature. Therefore, the high velocity has more influence on alleviating temperature polarization effect (boundary effect) at high Twf,in than that at low Twf,in, besides average temperature difference (driving force) increase at high flow velocity [21,48–49]. The permeate flux is plotted in Fig. 5 (d) as a function of permeate inlet temperature (Twp,in) and the flow velocity of feed solution (Vf). It can be seen that J increases linearly by increasing Vf and decreasing Twp,in and there is negligible interaction between them. Although changing Twp,in in the range of 15–40 °C does not have much influence on J, increasing Vf plays a significant role in the enhancement of J. Obviously, increasing Vf is an efficient and preferable way in increasing permeate flux, and is beneficial to reduce the energy consumption required for the cooling of the permeate to a very low temperature. However, this result might also depend on the level of module packing density, as shown in Fig. 5 (e) that illustrates the effect of permeate inlet temperature (Twp,in) and module packing density (D) on permeate flux. It can be observed that the permeate flux increases by decreasing D and Twp,in. When D is greater than about 25%, the Twp,in should correspondingly decrease to a very low temperature even below room temperature to obtain a considerable high permeate flux. However, it should be noted that the result is obtained at a relative low value of Vf (about 30 m/min). According to Fig. 5 (d), a high permeate flux can be expected by increasing Vf with a moderate value of Twp,in. This can be confirmed by the results in Fig. 5 (f), which shows the variation of permeate flux (J) as a function of flow velocity of feed solution (Vf) and module packing density (D). It is indicated that Vf plays a more significant role in J than D. Even at a high D, a high J can be achieved by increasing Vf when the permeate inlet temperature is close to a room temperature 25 °C. 3.2.2. Interaction analysis for water productivity per unit volume of module The effect of feed inlet temperature (Twf,in) and module packing density (D) on water productivity per unit volume of module (Pv) is

presented in Fig. 6 (a). It can be seen, the increase of one factor results in an enhancement of Pv when another factor is at high level. The maximum value of Pv is obtained at the highest Twf,in and the highest D, due to the largest vapor pressure of the feed solution and membrane surface area. The surface plot presents a crossing behavior of the effect of the variables on the objective, indicating the significant interaction effect between the two variables. Fig. 6 (b) shows the effects of module packing density (D) and length–diameter ratio of module (Rld ) on water productivity per unit volume of module (P v ). Because the high D means that large membrane area is loaded in the membrane module, the water productivity per unit volume can be increased by increasing D. However, it is found that the influence of D on Pv is interacted significantly by the Rld. If Rld is low, increasing D will lead to a significant enhancement of Pv. However, when Rld is high, increasing D does not result in a significant increase of Pv. Low Rld is generally beneficial to obtain high value of permeate flux as discussed in Section 3.2.1. Cheng et al. [14] and Kim et al. [50] found that the total water production (kg/h) of a given module will increase by increasing both Rld and D. However, enhancing total production rate by increasing Rld will also increase the fabrication cost and the footprint of the module. Therefore, water productivity per unit volume of module (kg/(m3·h)) seems more reasonable to show the module performance than that of the total production rate of the module. Fig. 6 (c) presents the response surface plot of water productivity per unit volume of module (Pv) as a function of permeate inlet temperature (Twp,in) and module packing density (D). It is observed that the effect of D on Pv is more significant than Twp,in. As expected, an increase of D leads to an increase of Pv. Moreover, the decrease of Twp,in obviously improves Pv at high D, but the improvement is negligible when D is low. Thus, to improve the water productivity of a low D module, it is not necessary to use low temperature on the permeate side.

D. Cheng et al. / Desalination 394 (2016) 108–122 Table 4 Regression equations of average permeate flux, water productivity per unit volume of module, water production per unit energy consumption, and comprehensive index in terms of actual variables and fitting coefficients in DCMD. Objectives Regression equations J

=1.0968Twf,in − 0.6167Twp,in − 0.5451Vf − 1.0109D

0.993

0.0068Twf,inD − 0.1097Twf,inRld + 0.0145Twp,inVf − 0.0166Twp,inD + 0.0657Twp,inRld + 0.0034VfD + 0.0078VfRld + 0.0122DRld − 2 0.0013Twf,in –0.0196T2wp,in–0.0017V2f + 0.0151D2 +

0.2018R2ld =292.9633Twf,in − 3.8296Twp,in − 192.1564Vf −

Table 6 Error results with various weight coefficient values for determination of CI according to Eq. (11). No.

ARE/%

MPSD/%

Fitting coefficient/R2

− 0.4994Rld + 0.0135Twf,inTwp,in + 0.0045Twf,inVf +

Pv

115

0.994

1 2 3 4 5 6 7 8 9

21.3 25 18.2 12.5 29.9 23.2 13.8 14 24.5

43.9 48.3 38.3 25.6 58.3 45 25.7 27.4 49.5

Weight coefficients wJ

wPv

wPe

0.2 0.2 0.3 0.3 0.3 0.4 0.4 0.5 0.6

0.3 0.4 0.2 0.3 0.4 0.2 0.3 0.2 0.2

0.5 0.4 0.5 0.4 0.3 0.4 0.3 0.3 0.2

699.0327D − 248.2193Rld + 9.3916Twf,inTwp,in + 4.9254Twf,inVf + 17.3488Twf,inD − 67.1832Twf,inRld − 7.2402Twp,inVf − 11.9600Twp,inD + 48.8144Twp,inRld + 6.6419VfD + 7.6708VfRld − 18.1568DRld − 2 0.8536Twf,in − 12.8707T2wp,in − 0.9759V2f + 6.9724D2

Pe

+ 136.4845R2ld =485.9259 × 10−8Twf,in − 741.5999 × 10−8Twp,in −

0.975

145.6467 × 10−8Vf − 154.2742 × 10−8D − 619.6335 × 10−8Rld + 8.0942 × 10−8Twf,inTwp,in − 43.1616 × 10−8Twf,inVf + 7.2764 × 10−8Twf,inD − 2.1523 × 10−8Twf,inRld + 8.5076 × 10−8Twp,inVf − 7.1102 × 10−8Twp,inD + 42.7912 × 10−8Twp,inRld − 7.3283 × 10−8VfD + 12.8290 × 10−8VfRld − 6.8581 × 10−8DRld − 2.0591 × 10−8T2wf,in + 0.8253 × 10−8T2wp,in + 2.8007 × 10−8V2f + 5.5766 × 10−8D2 + 107.4969 × CI

10−8R2ld =0.0252Twf,in − 0.0323Twp,in − 0.0215Vf + 0.0197D

0.983

− 0.0577Rld + 0.0005Twf,inTwp,in + 0.0001Twf,inVf +

The effect of feed inlet temperature (Twf,in) and length–diameter ratio of module (Rld) on water productivity per unit volume of module (Pv) is shown in Fig. 6 (e). It is observed that Pv increases with increasing Twf,in and decreasing Rld. The reason has been discussed above. The surface plot of Pv presents a parallel behavior indicating no interaction of the two variables. Water productivity per unit volume of module (Pv) is plotted as a function of feed inlet temperature (Twf,in) and flow velocity of feed solution (Vf) in Fig. 6 (f). The increase of both factors results in an enhancement of Pv. However, when one factor is low, the other factor shows slightly stronger influence on Pv than that of the one is high. For instance, the increase of Twf,in from 40 to 80 °C causes an increase of Pv to 3.6-fold when Vf is 10 m/min, and increases to 1.2-fold when Vf increases to 60 m/min. It means that there is a weak interaction effect between the two factors.

0.0001Twf,inD − 0.0021Twf,inRld + 0.0005Twp,inVf − 0.0008Twp,inD + 0.0026Twp,inRld − 0.0003VfD + 2 0.0008VfRld − 0.0007DRld − 0.0001Twf,in –0.0003T2wp,in

+ 0.0001V2f + 0.0003D2 + 0.0035R2ld

The combined effect of flow velocity of feed solution (Vf) and module packing density (D) on water productivity per unit volume of module (Pv) is shown in Fig. 6 (d). It can be seen, Vf only has more influence on Pv at high D than that of low D. It means that D and Vf have coupling effect on Pv. A high D means a larger membrane surface area in a module, leading to a higher water production but also a greater temperature and concentration polarization effect. In this case, a higher Vf can increase the heat and mass transfer coefficient and decrease the thermal and concentration boundary layer, resulting in the reduction of the temperature and concentration polarization effects. A higher Vf also means a shorter residence time of hot feed in the membrane module, leading to a higher average temperature difference across the membrane and thus higher water production of MD.

Table 5 Simplified regression equations of average permeate flux, water productivity per unit volume of module, water production per unit energy consumption, and comprehensive index in terms of actual variables and fitting coefficients in DCMD. Objectives Regression equations

Fitting coefficient/R2

J

=0.0106T2wf,in − 0.0855Twf,inRld + 0.2150R2ld +

0.970

Pv

0.0028Twf,inVf − 0.0018Twp,inD =11.9837Twf,inD − 24.4545DRld − 8.0296Twp,inD +

0.946

Pe

3.8707VfD =4.2328 × 10−8Twf,inTwp,in + 6.8649 × 10−8DRld +

0.930

CI

8.3341 × 10−8R2ld − 0.3038 × 10−8VfD = − 0.0025Twf,inRld + 0.0214Twf,in − 0.0529Twp,in +

0.983

0.0047R2ld + 0.0003D2 + 0.0004Twf,inTwp,in + 0.0004Twp,inVf − 0.0004VfD + 0.0019Twp,inRld

3.2.3. Interaction analysis for water production per unit energy consumption The surface plot of water production per unit energy consumption (Pe) as a function of feed inlet temperature (Twf,in) and permeate inlet temperature (Twp,in) is presented in Fig. 7 (a). It can be observed, Pe increases by increasing Twf,in and Twp,in and there exists an interaction effect between them. Increasing Twp,in means the reduction of the energy consumption for cooling on the permeate side, which leads to an enhancement of Pe. As for the effect of increasing Twf,in, both thermal energy consumption and transmembrane driving force are increased leading to a significant increase in permeate flux and water production. The phenomena that Pe increases with increasing Twf,in indicates that the degree of increment in water production is higher than that in thermal consumption, especially at high level of Twp,in, due to the exponential relationship of driving force and linear relationship of heat conduction loss to the feed temperature. Al-Obaidani et al. [1] simulated the effect of feed temperature on the thermal efficiency of DCMD process and found that the thermal efficiency could be significantly enhanced by increasing feed temperatures. Besides, Duong et al. [40] observed that increasing feed temperature from 45 to 50 °C led to 30% increase in gain output ratio (GOR) and concluded that increasing feed temperature was beneficial for improving GOR. Fig. 7 (b) shows the responses of water production per unit energy consumption (Pe) by varying module packing density (D) and length– diameter ratio of module (Rld). The surface plot shows that the coupling effect between D and Rld is significant since a high value of Twp,in must be combined with a high level of D in order to achieve a significant improvement of Pe. Increasing module packing density and fiber length are common ways to increase membrane area. Water production increases with the increase in membrane area and Pe is thus enhanced. It is noteworthy that the two variables showing significant interaction are module configuration parameters. The combined effect of flow velocity of feed solution (Vf) and module packing density (D) on water production per unit energy consumption (Pe) is shown in Fig. 7 (c). It is observed that Pe reaches to a high value

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Table 7 ANOVA results of the simplified quadratic models of average permeate flux, water productivity per unit volume of module, water production per unit energy consumption, and comprehensive index in terms of actual variables. Objectives

Different items

DF

Sum of squares

Mean square

F-value

P-value

R2adj

J

Model Residual Total Model Residual Total Model Residual Total Model Residual Total

4 32 36 2 34 36 2 34 36 9 27 36

8.809 × 103 2.777 × 102 9.087 × 103 4.129 × 109 3.060 × 108 4.435 × 109 2.845 × 10−7 2.192 × 10−8 3.064 × 10−7 5.169 0.163 5.332

2.022 × 103 8.677

253.817

b0.0001

0.966

2.065 × 109 8.999 × 106

229.439

b0.0001

0.927

1.423 × 10−7 6.447 × 10−10

253.817

b0.0001

0.924

0.547 0.006

94.931

b0.0001

0.959

Pv

Pe

CI

by increasing D and decreasing Vf simultaneously. The effect of Vf on Pe is negligible at low D, but becomes more significant at higher D. The positive effect of increasing D on improving Pe is enhanced by decreasing Vf. This indicates the interaction influence of the two variables on the energy consumption of DCMD. The decreasing of Vf has the same function as increasing Rld in prolonging the retention time of hot feed in the membrane fibers, which leads to a higher water production. In addition, the increase in the turbulence of the feed due to high feed flow rate increases the heat loss inside the module, which decreases the energy efficiency [40,51]. Water production per unit energy consumption (Pe) is plotted as a function of permeate inlet temperature (Twp,in) and module packing density (D) in Fig. 7 (d). As can be seen, the interaction effect between these two factors is negligible. The increase in both Twp,in and D results in an improvement of Pe. The reason is that the increase in Twp,in leads

to a reduction of thermal energy consumption and the higher levels of D are beneficial for higher water production. 3.2.4. Interaction analysis for comprehensive index CI is a comprehensive objective which takes into account J, Pv, and Pe simultaneously. High values of water permeate flux and production are generally accompanied with high thermal consumption and large membrane area (large equipment cost). Therefore, the coupling and interaction effect of actual factors on the comprehensive index should be more significant and complicated. The evaluation of CI is necessary to search for a balance among high water production, low cost of equipment investment, and low thermal consumption. Fig. 8 (a) shows the response of comprehensive index (CI) as a function of feed inlet temperature (Twf,in) and permeate inlet temperature (Twp,in). It is indicated that increasing Twf,in is beneficial to achieve a

Fig. 4. Comparison between experimental and predicted DCMD permeate flux J (a), water productivity per unit volume of module Pv (b), water production per unit energy consumption Pe (c), comprehensive index CI (d).

D. Cheng et al. / Desalination 394 (2016) 108–122 Table 8 Dominance degree of the variables and their interactions for average permeate flux, water productivity per unit volume of module, water production per unit energy consumption, and comprehensive index in the simplified regression equations. Objectives

Effects of the interact variables

J Pv Pe CI

T2wf,in N Twf,inRld N R2ld N Twf,inVf N Twp,inD Twf,inD N DRld N Twp,inD N VfD Twf,inTwp,in N DRld N R2ld N VfD Twf,inRld N Twf,in N Twp,in N R2ld N D2 N Twf,inTwp,in N Twp,inVf N VfD N Twp,inRld

high value of CI which means a high level of water production at a considerable low cost of equipment investment and thermal energy. This is because of the positive effect of increasing Twf,in on J, Pv, and Pe as illustrated in Figs. 5, 6, and 7. The effect of Twp,in on CI is complicated, since an increase of Twp,in will remarkably increase Pe but will decrease of both J and Pv. As shown in Fig. 8 (a), in case of low Twf,in, decreasing

117

Twp,in is a strategy to increase CI, but the most favorite condition for a high CI is the combination of a high Twf,in with a moderate Twp,in. The influence of both feed inlet temperature (Twf,in) and length– diameter ratio of module (Rld) on comprehensive index (CI) is presented in Fig. 8 (b). It can be observed, the interaction effect between Twf,in and Rld is very significant. By increasing Twf,in, CI increases at low Rld whereas decreases at high Rld. Similarly, increasing of Rld is beneficial to increase CI at low Twf,in. The highest value of CI is obtained by increasing Twf,in while keeping low Rld as much as possible. This result is related to the complicated effect of the two variables on the J, Pv, and Pe. On the one hand, the surface plot shape of CI in Fig. 8 (b) is similar to that in Fig. 5 (b) with two extreme values of the objectives. On the other hand, the simultaneous increase of Twf,in and Rld leads to increase of Pv and Pe. It can be concluded that although the CI can be improved by either increase of energy consumption or increase of the cost of membrane module, the former way is more efficient in achieving higher value of CI.

Fig. 5. 3D response surface plots of DCMD permeate flux as a function of (a) feed inlet temperature and permeate inlet temperature; (b) feed inlet temperature and length–diameter ratio of module; (c) feed inlet temperature and flow velocity of feed solution; (d) permeate inlet temperature and flow velocity of feed solution; (e) permeate inlet temperature and module packing density; and (f) flow velocity of feed solution and module packing density.

118


Fig. 6. 3D response surface plots of water productivity per unit volume of module as a function of (a) feed inlet temperature and permeate inlet temperature; (b) module packing density and length–diameter ratio of module; (c) permeate inlet temperature and module packing density; (d) flow velocity of feed solution and module packing density; (e) feed inlet temperature and length-diameter ratio of module; and (f) feed inlet temperature and flow velocity of feed solution.

The combined effect of permeate inlet temperature (Twp,in) and flow velocity of feed solution (Vf) on comprehensive index (CI) is shown in Fig. 8 (c). It can be seen, by increasing Vf, CI decreases at low Twp,in value while increases at high Twp,in. The variation of CI by increasing Twp,in is similarly dependent on the level of Vf. This phenomenon is because that, as discussed before, the increase in Vf leads to an increase in J and Pv but a decrease in Pe. Similarly, low level of Twp,in is beneficial to increase J and Pv, but causes a decrease of Pe. Finally, at high Twp,in and Vf, the increment of J, Pv, and Pe is significant, which leads to the increase in CI. Both of the two variables are operating parameters and the interaction effect is significant on CI. Comprehensive index (CI) is plotted as a function of flow velocity of feed solution (Vf) and module packing density (D) in Fig. 8 (d). It is observed that the interaction effect between Vf and D is significant. The highest value of CI is obtained under the condition of a high Vf and a low D. This is due to the fact that high Vf is beneficial for J and P v , and the high D is favorable for P v and P e . There is a trade-off

among J, Pv, and Pe as Vf and D increase. This can also explain the phenomenon that CI increases with an increase of D at low Vf and decreases with an increase of D at high Vf. The results also suggest that a high CI can be obtained by increasing the cost of the membrane module or increasing the energy consumption, which is similar to the conclusion from Fig. 8 (b). 3.3. Optimization of DCMD process According to the common range of variables in literature and the feasibility for actual experiment, the investigated region of the variables for optimization of DCMD process is within 40–80 °C for Twf,in, 15–40 °C for Twp,in, 4–60 m/min for Vf, 4–50% for D, and 1–20 for Rld, which is slightly wider than the experimental range of the variables in Table 1. The optimum conditions were determined using Matlab function and presented in Table 9. It can be seen that, the optimum value of T wf,in is the highest value in the above designated range


119

Fig. 7. 3D response surface plots of water production per unit energy consumption as a function of (a) feed inlet temperature and length–diameter ratio of module; (b) module packing density and length–diameter ratio of module; (c) flow velocity of feed solution and module packing density; and (d) permeate inlet temperature and module packing density.

Fig. 8. 3D response surface plots of comprehensive index as a function of (a) feed inlet temperature and permeate inlet temperature; (b) feed inlet temperature and length–diameter ratio of module; (c) permeate inlet temperature and flow velocity of feed solution; and (d) flow velocity of feed solution and module packing density.

120


Table 9 Optimum DCMD parameters and corresponding average values of permeate flux, water productivity per unit volume of module, water production per unit energy consumption, and comprehensive index. Objectives 2

J, kg/(m ·h) Pv, kg/(m3·h) Pe, kg/kJ CI

Predicted

Twf,in, °C

Twp,in, °C

Vf, m/min

D, %

Rld

74.5470 5.2302 × 104 2.3683 × 10−4 1.6255

80 80 80 80

15 15 40 40

60 60 4 60

4 50 50 4

1 1 20 1

and all the other four variables are either at the highest or the lowest level in their designated range. The optimum conditions in Table 9 were derived more comprehensively resulting in different values from that in Table 3. The verification experiments were conducted to confirm the validity of optimization procedure. The comparisons between the experimental and predicted values of J, Pv, Pe, and CI are shown in Table 10. As can be seen, the experimental values of J, Pv, and Pe and the predicted ones by simplified RS-models are in good agreement. The derivations were only 2.9%, 4%, and 7.8% for J, Pv, and Pe, respectively. It should be explained that the Rld was adjusted to be 1.9 or 1.33 in verification experiment. This is because that the inner diameter of all membrane modules is 1.5 cm and it is difficult to make a membrane module with such a length when the optimum value of Rld was 1. However, the optimization results obtained from the lab scale set-up can be meaningful reference for the scale-up of membrane module and process optimization. It is noted that the predicted value of CI in Table 10 is higher than 1, however the range of CI designed is from 0 to 1 according to its definition in Eq. (11). The CI value in Table 10 reaches to a value of 0.7587 in an actual experiment under optimum conditions. By comparison, the experimental values of J, Pv, Pe, and CI measured under optimum conditions were all higher than those obtained under conditions close to the optimum conditions as shown in Table 10, and they were also higher than the QRCD experimental results in Table 2. This further confirms the validity of the developed DCMD optimization models. From Table 10, it can be seen that a slight deviation of operating conditions from their optimum values causes a remarkable drop of the maximum value of the objectives. For instance, the measured J value decreased from 67.1 kg/(m2·h) to 58.47 kg/(m 2 ·h) as T wf,in decreased from 80 °C to 75 °C when other parameters were set to be constant.

4. Conclusions The response surface methodology and experimental design were applied for modeling and optimization of lab-scale DCMD process for desalination of 3.5 wt% NaCl aqueous solution. Response surface models as functions of feed inlet temperature (Twf,in), permeate inlet temperature (Twp,in), flow velocity of feed solution (Vf), module packing density (D), and length–diameter ratio of module (Rld) were developed to predict average permeate flux (J), water productivity per unit volume of module (Pv), and water production per unit energy consumption (Pe). A multi-response optimization was performed by introducing a multiindex (CI) based on a weight grade method. The regression equations were simplified by stepwise regression analysis and statistically validated by analysis of variance. Based on the regression model equations, the three-dimensional response surface curves were plotted to check the interaction effects of the variables. The interactions between the operating parameters and the module configuration parameters are significant on all of the optimization objectives. The average permeate flux is mainly determined by feed inlet temperature and its interaction effects with length–diameter ratio of module. Water productivity per unit volume of module is dependent on the interaction effect of feed inlet temperature and module packing density, and water production per unit energy consumption is mainly determined by the feed and permeate temperature, in addition to being affected by a strong influence of the interaction effect between module packing density and length–diameter ratio of module. The interaction effect of feed inlet temperature and length–diameter ratio of module as well as the effect of the feed and permeate inlet temperatures play the most important role in the comprehensive objective. Based on the common characteristics of different MD configurations in the driving force and influencing factors, the interactions on the optimization objectives may also be applicable to the other MD processes such as VMD and AGMD. The DCMD optimal conditions for maximum J, Pv, Pe, and CI were determined using Matlab software. Under the optimum experimental conditions, the average permeate flux of 67.1 kg/(m2·h), water productivity per unit volume of module of 4.9825 × 104 kg/(m3·h), water production per unit energy consumption of 2.1839 × 10− 4 kg/kJ, and comprehensive index of 0.7587 were obtained. The permeate flux is at a leading level compared to the most reported results for MD desalination. The results indicate that MD performance on both production and energy efficiency can be remarkably improved through the optimization of both operating conditions and module parameters.

Table 10 Predicted and experimental values of average permeate flux, water productivity per unit volume of module, water production per unit energy consumption, and comprehensive index at optimum conditions. Objectives

J, kg/(m2·h)

Pv, kg/(m3·h)

Pe, kg/kJ

CI

Run

Predicted Optimum 38 39 Predicted Optimum 40 41 42 Predicted Optimum 44 45 46 Predicted Optimum 48 49 50

Objective values

65.11 67.10 58.47 55.98 5.1894 × 104 4.9825 × 104 2.5204 × 104 2.8132 × 104 3.0290 × 104 2.3683 × 10−4 2.1839 × 10−4 2.0962 × 10−4 2.0685 × 10−4 1.8548 × 10−4 1.5262 0.7587 0.6978 0.6153 0.6518

Value of the variables

Errors (%)

Twf,in, °C

Twp,in, °C

Vf, m/min

D, %

Rld

80 80 75 80 80 80 80 80 80 80 80 80 75 80 80 80 80 80 75

15 15 15 15 15 15 15 15 15 40 40 23 40 40 40 40 15 40 40

60 60 60 50 60 60 12 23 29 4 4 4 4 11 60 60 60 50 60

4 4 4 4 50 50 50 50 50 50 50 50 50 50 4 4 4 4 4

1.9 1.9 1.9 1.9 1.33 1.33 1.33 1.33 1.33 20 20 20 20 20 1.9 1.9 1.9 1.9 1.9

2.9

4

7.8

–


Nomenclature Twf.in feed inlet temperature, °C Twp.in permeate inlet temperature, °C Vf flow velocity of feed solution, m/min D module packing density, % Rld length–diameter ratio of module dm,in inner diameter of fiber membrane, m dm,out outer diameter of fiber membrane, m di inner diameter of membrane module, m q feed flux rate, m3/min l effective length of membrane module, m J average permeate flux, kg/(m2·h) Pv water productivity per unit volume of module, kg/(m3·h) Pe water production per unit energy consumption, kg/kJ CI comprehensive index ΔW mass variation, kg/h n number of the fibers A surface area of membrane, m2 t time, h c specific heat capacity, kJ/(kg·°C) T temperature, °C zi,min minimum of the parameter value zi,max maximum of the parameter value zi current parameter value xi normalized variable w weight coefficient N test points Mc rotation design points Mr star points M0 center points Y response value bi linear coefficients bii quadratic coefficients bij interaction coefficients X1, X2,…, X5 coded values of the variables Yexp experimental objective value Ycalc calculated objective value k number of data points d number of regression coefficients ARE average relation error MPSD Marquradt's percent standard deviation R2 fitting coefficient DF degree of freedom

Acknowledgements The authors acknowledge the financial support from the Fundamental Research Funds for the Central Universities of China (Grant No. xjj2013075).

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