Prediction model to analyze the performance of VMD desalination process

Prediction model to analyze the performance of VMD desalination process

Computers and Chemical Engineering 132 (2020) 106619 Contents lists available at ScienceDirect Computers and Chemical Engineering journal homepage: ...

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Computers and Chemical Engineering 132 (2020) 106619

Contents lists available at ScienceDirect

Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng

Prediction model to analyze the performance of VMD desalination process Chaohuan Yang a,c,d,1, Xin Peng b,1, Yajing Zhao a,c, Xin Wang a,c, Jingxia Fu a,c, Kai Liu a,c, Yingdong Li a,c, Pingli Li a,c,∗ a

Chemical Engineering Research Center, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300350, PR China School of Life Sciences, Tianjin University, Tianjin 300350, PR China Tianjin State Key Lab of Membrane Science and Desalination technology, Tianjin 300350, PR China d Qingdao Conson Oceantec Valley Development Co., Ltd., Qingdao, 266000, PR China b c

a r t i c l e

i n f o

Article history: Received 26 July 2019 Revised 15 October 2019 Accepted 19 October 2019 Available online 21 October 2019 Keywords: Vacuum membrane distillation Desalination Artificial neural network Machine learning

a b s t r a c t The performance of vacuum membrane distillation process (VMD) including permeate flux and specific heat energy consumption (SHEC) under different feed inlet temperature, feed flow rate and membrane length was modeled by Artificial Neural Network (ANN) based on 36 different experimental VMD tests. It was found that the ANN model could obtain reliable data to forecast the behavior of the hollow membrane module for the whole range of input variables. The binary interaction impacts of the variables on the performance index were discussed and the objective was significantly affected by the interaction impacts of the variables. In this study, ANN model showed the potential to evaluate VMD performance successfully.

1. Introduction Membrane distillation (MD), a thermally driven process, utilizes the micro-porous membrane with hydrophobicity to separate water from saline aqueous solution. The trans-membrane temperature difference generates a water vapor pressure gradient and yields to purified water production (Kim et al., 2018). MD have some advantages compared with other conventional separation technologies such as large evaporation area integrated in a membrane module (Geng et al., 2014), a lower operating pressure compared with pressure-driven membrane processes (Kim et al., 2013), the ability to use low-grade heat energy and reduce energy consumption (Tian et al., 2014) and a high rejection rate of dissolved and non-volatile species to produce permeate water (Kim et al., 2018). Therefore, MD process is a promising approach to separate water from aqueous solution. Direct contact membrane distillation (DCMD), air gap membrane distillation (AGMD), sweeping gas membrane distillation (SGMD) and vacuum membrane distillation have been well developed for water treatment and desalination (Khayet, 2011). For VMD configuration, it can be obtained higher permeate water flux with a slight conductive heat loss across



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Corresponding author. E-mail address: [email protected] (P. Li). These two authors contributed equally to this work.

https://doi.org/10.1016/j.compchemeng.2019.106619 0098-1354/© 2019 Elsevier Ltd. All rights reserved.

© 2019 Elsevier Ltd. All rights reserved.

membrane (Zhang et al., 2016). Therefore, VMD has got wide attention in water treatment. Recently some research efforts mainly focused on interaction effects under real operation conditions (Cheng et al., 2016). An outstanding merit of ANN compared with other multivariable regression methods like Response Surface Methodology (RSM) is that ANN method does not need to use special experimental design scheme for the data prediction (Khayet et al., 2011), so different experimental designs can be employed in the model. ANN modeling was employed regularly in many different technological research fields because of the ability to deal with complex multiple regression problems (Abbas and Al-Bastaki, 2005). It is able to map non-linear relationships between the inputs and outputs of a system, which has extended the applications of ANN model. Many researchers used ANN model in various engineering or scientific research fields to predict unseen data based on experimental results. Rall et al. (2019) built an ANN model with high predictive accuracy which could predict membrane properties such as ion retention and water flux according to membrane fabrication conditions for the first time. Lee et al. (2009) employed ANN model to forecast the performance of a seawater reverse osmosis desalination plant, and the trained ANN model was able to produce good agreement between the observed and simulated data. A radial basis function (RBF) artificial neural network (Zhao et al., 2019) was applied to predict the interfacial interactions with randomly rough

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membrane surface related with membrane fouling in membrane bioreactors, and the samples showed high calculation accuracy. The application of accurate models to predict MD system performances plays a more important role in the design of industrial projects. Gil et al. (2018) used RSM and ANN to simulate the permeate flux and SHEC of a commercial-scale permeate gap membrane distillation system, and the results proved that the ANN model was able to predict the system behavior in a more accurate way. A feed-forward ANN was developed by Khayet and Cojocaru (2013) for the forecast of SGMD performance on a set of 53 different experiments and the agreement between the experimental data and ANN predicted results was acceptable. Shirazian and Alibabaei (2016) employed a particle swarm optimization based controlled neural network to explore the impact of input operational parameters on AGMD using experimental data collected in other literature, and they found that the models had satisfying precision. As can be seen, a few research works on employing ANN to simulate VMD process and investigate thermal efficiency were performed (Cao et al., 2016; Gil et al., 2018; Shirazian and Alibabaei, 2016; Tavakolmoghadam and Safavi, 2012), and many studies passed over the impact of module parameter on MD performance. The main objective was to design an ANN model for the prediction of the VMD performance under different operation conditions and module parameters including feed inlet temperature, feed flow rate and membrane length. Compared to previous studies in the literatures, both permeate flux J∗ and specific heat energy consumption SHEC∗ were selected as predicted performance parameters simultaneously in this work. 2. Theory ANN, simulating the behavior of biological neural networks, is a mathematical model used to obtain results in response to external inputs (Gil et al., 2018). An artificial neuron is a single computational processor which has two operators: summing junction and transfer function (Khayet and Cojocaru, 2012). The connections include weights and biases, and the summing junction operator of a single neuron that summarizes the weights and bias into a net input λ is as follows:

λ=

n 

xi · w i + b

(1)

i=1

where wi (i = 1, n) are the connection weights, xi is the input variable, n is the number of input variables, i is the integer index and b is called bias. In the transfer function block of this investigation, the linear (Purelin) and the tangent sigmoid transfer functions (Tansig) are used. So the outputs of neurons could be calculated as (Hagan and Demuth, 2002; Beale et al., 2017; Zhao et al., 2007):

Purelin(λ ) = λ Tansig(λ ) =

1 − exp (−λ ) 1 + exp (−λ )

Table 1 Characteristics of the modules. Parameters

Value

Number of hollow fiber membranes per module Effective length of module (m) Effective membrane area (m2 ) Outer diameter (mm) Inner diameter (mm) Porosity (%) Average pore size (μm)

200 0.1/0.2/0.3 0.0276/0.0552/0.0828 0.64 0.44 68 0.2

may be defined as:

1 (Y − Y ∗ )2 N N

MSE =

where N is the number of data points and j is the integer index. Y and Y∗ are the actual experimental data and predicted responses respectively. Generally, a single iteration of BP algorithm using gradient descent method is as follows:

W(new) = W(old ) − η · grad(MSE )

(5)

where W is a vector containing weights and biases, grad(MSE) is the gradient of performance function and η is the learning rate. 3. Experimental section A VMD experiment was conducted in previous study. Appendix A provided all used experimental data (Yang et al., 2019). The membrane modules were employed in this study with polypropylene (PP) hollow fiber membranes provided by Tianjin Chemical Separation Technologies Co. Ltd, China, and the basic properties of membrane modules were listed in Table 1. The fabrication method of a VMD hollow fiber membrane module was as follows: (i) the membranes were put in a plastic tube, (ii) epoxy resin were poured to the ends of tube in order to seal the space between the membranes and wall of tube, (iii) the hollow fiber membranes were cut open at both ends to accommodate lumenside feed channel when the epoxy resin solidified completely. Fig. 1 depicted the schematic diagram of VMD experimental apparatus. CuSO4 aqueous solution (10 g/L) was heated up to a preset temperature in the feed tank, then it was pumped into the lumen side of hollow fiber membrane module, and the retentate was turned back to the feed tank. The feed inlet temperature, feed flow rate, and vacuum degree were monitored in real time, all experiments were conducted under vacuum degree was 0.095 MPa.

(2) (3)

The neurons are divided into hidden layers and output layer. The most frequently used network topology is the multi-layer feed-forward topology (Shahsavand and Chenar, 2007). Once the architecture of the network is chosen, the weights and biases are adjusted by means of a training algorithm. The most commonly employed training algorithm is the back propagation (BP) algorithm (Hagan et al., 1996; Yi et al., 2007) which is based on gradient descent method. The network training by BP algorithm includes an iterative optimization process where the weights and biases are updated while minimizing a performance function such as mean squared error MSE (Khayet and Cojocaru, 2012). The MSE

(4)

j=1

Fig. 1. Schematic diagram of VMD experimental apparatus.

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Table 2 Input model variables. Variable

Nomenclature

Range

Feed inlet temperature (°C) Feed flow rate (L/h) Membrane length (m)

T F L

60–70–80 15–18–21–24 0.1–0.2–0.3

After the desalination system run stably, the condensed permeate water in the collector was weighted. The permeate water was collected and poured back to the feed tank each time after each experiment finished, so the VMD was run at almost constant feed salinity with a small concentration variation (10–10.1 g/L) as the experiment went on. The permeate water flux, J is calculated as follow:

J=

m t ×A

(6)

where water production m means the amount of permeate water per hour (kg/h), A is the effective membrane area (m2 ). Specific heat energy consumption SHEC represents the heat energy (kWh/m3 ) required to produce 1 m3 of permeate water and can be expressed as follows (Gao et al., 2017):

SHEC =

F ρCp (Tin − Tout ) 3600 × 1000 × m

Fig. 2. Optimal architecture of the ANN model for prediction of the VMD performance.

(7)

where F is feed flow rate, ρ is the feed density, Cp is the specific heat capacity of the feed. Tin and Tout are the inlet temperature and outlet temperature of membrane module. The concentration of feed and permeate were measured via conductivity meter (DDSJ-308A, Shanghai Leici Instrument Factory, Shanghai, China). The rejection rate R can be determined by:

R=

c f − cd × 100% cf

(8)

where cf and cd are the CuSO4 concentration in the feed and the permeate water. 4. Results and discussion 4.1 ANN model In this paper, feed inlet temperature, feed flow rate and membrane length were chosen as input variables, permeate flux and SHEC were set as outputs. A 3 × 4 × 3 full factor design was used to determine the effect of the main parameters for the membrane distillation performance. All input variables were well distributed along the operating range of each input variable as shown in Table 2, thus 36 experiments were conducted to develop the ANN model using neural network toolbox (MATLAB R2014a), 70% of the total experimental data was utilized for training, 10% for validation and 20% for testing of the ANN model. The rejection rate exceeded 99.9% in all these experiments. In order to avoid overfitting, both input variables and response results were normalized in the range [−1, 1] before training process according to the following equation:

y=

(ymax − ymin ) × (x − xmin ) + ymin (xmax − xmin )

(9)

where y is the normalized sample, x is the actual sample, xmax and xmin are the maximum and minimum values of the variable, and ymax and ymin are the upper and lower bounds considered to define the output network range (ymax = 1, ymin = −1). In order to optimize the neural network architecture, calculation procedure started to run by using one neuron in the hidden layer in the first, and the model was selected according to the minimization of performance function. The optimal architecture of the ANN model contained three inputs, one hidden layer with 7

Fig. 3. Mean squared error for training, validation and test data subsets computed by LMA.

neurons and one output layer with a single neuron was shown in Fig. 2. All neurons from the hidden layer had tan-sigmoid transfer function and the single neuron from the output layer had linear transfer function. To figure out the optimal values of weights and biases, the network ANN (3:7:1) has been trained using back-propagation method based on Levenberg-Marquardt algorithm (LMA). In this case, the training quit after 17 epochs. Fig. 3 depicted the evolution of mean squared error during training phase, which showed that the ANN model was performed effectively. Table 3 showed the optimal values of weights and biases. The ANN model can be expressed as:







Y ∗ n(x ) = f(2) LW(2,1) f(1) IW(1,1) x + b(1) + b(2) f(k)



(10)

where is the transfer function vector consistent with layer k (k = 1, 2). For k = 1, the transfer function is Tansig, for k = 2, the transfer function is Purelin. It was show in Fig. 4 that experimental data and the ANN predicted results had good linear relationships. Table 4 displayed the analysis of variance (ANOVA) of the VMD performance index. As can be observed, the correlation coefficient (close to 1) showed the good fit obtained by ANN model in permeate flux and SHEC. Therefore, ANN model had the power to predict the experimental data for VMD process well.

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Fig. 4. Experimental data and the ANN predicted results for all subsets.

4.2 Response surface The effect of feed inlet temperature T and feed flow rate F on performance index J∗ and SHEC∗ under membrane length L was 0.2 m were shown in Fig. 5. For example, improving both T and F resulted in an enhancement of J∗ . The permeate flux of VMD process is proportional to mass transfer coefficient and trans-

membrane pressure difference as follows (Guan et al., 2015):

J = Cm (Phm − Ppm )

(11)

where Cm is mass transfer coefficient, Phm is the hot feed water vapor pressure, Ppm is the absolute permeate pressure. The partial vapor pressure of pure water can be calculated as follows (Lawson and Lloyd, 1997):



P ∗ (T ) = Exp 23.1964 −

3816.44 T − 46.13



(12)

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Table 3 Optimal values of weights and biases for the ANN model. Input weight matrix, IW

IW {1,1} =

{Destination: hidden layer Source: inputs}

0.4639 −0.6322 −0.1904 2.7389 −0.285 1.5892 2.142

2.4219 1.8043 1.7831 −0.2148 −0.0763 0.7071 −1.5027

−1.0156 0.7415 0.2326 −0.1711 1.9372 1.5155 −0.4464

b {1} =

Bias vector, b

−2.8629 2.0258 −0.7063 −0.4907 −2.3287 1.3014 2.8294

{Destination: hidden layer}

Layer weight vector, LW

LW {2,1}T = −0.1348 0.1215 0.2329 −0.1182 −0.0036 0.0096 −0.5645

{Destination: output layer Source: hidden layer}

Bias scalar, b

0.3300 −0.5409 −0.3306 −0.0317 −0.7288 0.0575 0.0827

b {2} = −0.1502 −0.2459

{Destination: output layer}

Table 4 Analysis of variance (ANOVA) of the VMD performance index.

J∗ SHEC∗

P-value

R2

R2 adj

0.000 0.000

0.9938 0.9655

0.9936 0.9645

For non-ideal binary mixtures the water vapor pressure can be determined from:

P (T, x ) = α (1 − x )P ∗ (T )

(13)

where T is hot feed temperature, α is water activity coefficient, and x is salt mole fraction of feed respectively. As illustrated in Eqs. (12)–(13), increasing T enhanced hot feed water vapor pressure, which meant that trans-membrane pressure difference for mass transfer in VMD process grew exponentially. Although the impact of temperature and concentration polarization both increased with the build-up of J∗ , this degradation effect was slight comparing with the increasing temperature difference (Duong et al., 2015). Thus J∗ showed increased trend as T grew due to the increase of driving force. Meanwhile, J∗ increased as function of F. When F grew, the hot feed was mixed more evenly caused by improved shear force, which reduced the thickness of heat and mass transfer boundary layers adjacent to inner membrane surface. The alleviation of temperature and concentration polarization caused the increase of water activity and water vapor pressure of hot feed, hence the trans-membrane pressure difference was also enhanced (Liu et al., 2018). Meanwhile, the increasing feed flow rate enhanced the module average feed temperature because of declined aqueous solution retention time in the module, which also boosted J∗ . It could be found that the impact of one factor on objective is more significant when the other factor is at higher level due to the synergetic effect of T and F. For example, increasing F from 9 to 30 L/h at 50 °C of T led to 25.9% increase of J∗ , but 45.7% increase of J∗ at 85 °C of T. Therefore, high T combined with high F could obtain larger J∗ . The highest J∗ was 13.61 kg/m2 -h when T was 85 °C and F was 30 L/h.

Fig. 5. Effects of T and F on J∗ and SHEC∗ in response surface plots (L = 0.2 m).

As shown in Fig. 5(b), SHEC∗ decreased with the increase of T, it could be inferred that the external input heat energy was more fully utilized. The decrease of T form 85 °C to 45 °C under L was 0.2 m and F was 30 L/h yielded to 10.9% increase of SHEC∗ , which was similar as results in other literatures that specific heat energy consumption improved with reduction of feed temperature. The reduction of F would cause lower average feed inlet temperature of membrane module, and the water production m decreased simultaneously, so decreasing F resulted in the improvement of SHEC∗ (Ali et al., 2016). However, the electrical energy consumption of pump and wetting risk of the MD system both grew as function of F, which should be considered when choosing appropriate operating conditions to reduce heat energy consumption. Fig. 6(a) depicted the influence of hot feed temperature T and membrane length L on the performance index J∗ while maintaining feed flow rate F at 21 L/h. There was an intensive interacion effect between the two input parameters T and L. The decrease

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Fig. 7. Effects of F and L on J∗ and SHEC∗ in response surface plots (T =70 °C).

Fig. 6. Effects of T and L on J∗ and SHEC∗ in response surface plots (F = 21 L/h).

of L resulted in an enhancement of J∗ , and this effect was more significant under high T. The largest J∗ (19.99 kg/m2 -h) was obtained at 85 °C and 0.05 m. Larger L led to declined heat transfer coefficient and more serious temperature and concentration polarization phenomena, which enhanced local transfer resistance and hindered the mass and heat transfer process (Kim et al., 2013). As L increased, the hot feed residency time in the module became longer and the temperature drop along membrane fiber grew induced by larger amount of water vapor. Furthermore, the build-up of permeate water vapor in the module shell side made a negative impact on maintaining high level of vacuum, therefore the actual driving force of VMD process decreased (Sun et al., 2014). All these factors made J∗ inversely proportional to L. As shown in the surface plot figure, the combination of high T and small L was required to achieve an enhancement of J∗ . As shown in Fig. 6(b), SHEC∗ increased with enhancement of L and decrease of T under all the conditions. Temperature declined along the membrane length and longer membrane module had larger temperature difference between inlet and outlet. The impact of temperature drop was more serious than the increased water production, which yielded to increased energy demand SHEC∗ as

function of L (Ali et al., 2019). As a result, a minimum point with respect to SHEC∗ occurred under highest T and lowest L. Fig. 7 showed the performance index J∗ and SHEC∗ with different feed flow rate F and membrane length L under feed inlet temperature T was 70 °C. A significant interaction effect between these two variables was observed. It could be found that J∗ increased as F and L. At low L values, J∗ increased with the increase of F significantly, but at higher L values, the increment of F contributed to a smaller growth of J∗ . For example, when F increased from 9 to 30 L/h, 27.4% and 50.3% increase of J∗ were obtained under L was 0.4 m or 0.05 m, respectively. This was mainly due to the declined temperature and concentration polarization and increased average feed temperature caused by shorter residence time. An interaction effect on SHEC∗ was observed in Fig. 7(b) between the two input variables F and L. The increase of F resulted in a reduction of SHEC∗ and this impact is stronger for lower L values. For unchanged F values, the effect of increased L caused a relatively minor increase of SHEC∗ . As can be seen, the main effect of F variable was greater than the main effect of L variable. 5. Conclusion In this study, a BP-ANN model (3:7:1) was developed to predict unknown data of VMD process based on the actual experiment results. The ANN model predicted data showed a strong correlation relationship with actual data (correlation coefficient of 0.9936 for

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J∗ and 0.9645 for SHEC∗ under three input variables) although the amount of available experimental data used for ANN modeling was very limited (36 samples in this case). It could be observed that J∗ improved as feed inlet temperature and feed flow rate increased and decreased as membrane length grew, SHEC∗ increased as function of membrane length and decreased as feed inlet temperature and feed flow rate increased. Intensive interaction impacts of the input parameters on the VMD performance index have been discussed. In this study, ANN model could predict VMD performance effectively. Declaration of competing interests The authors declare that there is no conflict of interest. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.compchemeng.2019. 106619. Appendix A

Number

Sample

L (m)

T (°C)

F (L/h)

J (kg/ m2 -h)

J∗ (kg/ m2 -h)

SHEC (kWh/ m3 )

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

test train train test train train train train train validation test train train test test train train test train test train train train train validation train train train train train train validation validation train train train

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3

60 60 60 60 70 70 70 70 80 80 80 80 60 60 60 60 70 70 70 70 80 80 80 80 60 60 60 60 70 70 70 70 80 80 80 80

15 18 21 24 15 18 21 24 15 18 21 24 15 18 21 24 15 18 21 24 15 18 21 24 15 18 21 24 15 18 21 24 15 18 21 24

6.26 6.41 7.11 7.49 8.85 9.37 10.31 11.51 16.72 19 20.3 21.82 4.64 5.02 5.32 6.11 6.7 7.38 7.82 8.66 8.93 9.93 11.18 12.54 3.26 3.64 3.98 4.2 5.07 5.39 5.79 6.19 6.39 7.04 8.03 8.76

6.24 6.78 7.2 7.55 8.87 9.83 11.19 12.86 16.72 18.88 20.32 21.08 4.56 5.27 5.98 6.45 6.84 7.36 7.76 8.15 8.77 10.07 11.35 12.44 3.09 3.4 3.88 4.42 4.94 5.46 5.79 6.04 6.34 7.11 8.11 8.82

878.19 824.78 805.72 728.43 791.88 771.92 741.6 703.8 772.1 733.5 724.87 685.08 901.82 870.62 840.41 775.75 824.15 802.75 792.38 747.22 798.94 779.7 758.06 694.16 923.37 883.16 857.77 811.43 832.62 817.44 808.5 758.16 822.85 796.48 767.7 713.14

SHEC∗ (kWh/ m3 ) 860.81 832.54 807.95 733.34 791.69 785.37 774.76 703.28 765.93 741.23 722.43 654.83 897.52 873.77 842.86 770.68 807.53 803.29 793.77 740.12 805.13 780.27 751.77 695.56 924.47 910.92 880.91 813.48 834.24 813.26 799.24 760.12 818.99 797.72 766.23 717.27

The VMD experiment data was provided in previous study (Yang et al., 2019).

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