NF Separation of NaCl and MgCl2

NEURAL NETWORKS SIMULATION OF THEFILTRATION OF SODIUM CHLORIDE ANDMAGNESIUM CHLORIDE SOLUTIONS USINGNANOFILTRATION MEMBRANES

N. A. Darwish1�, N. Hilal2, H. Al-Zoubi2 and A. W. Mohammad3

1Department of Chemical Engineering, The Petroleum Institute, Abu Dhabi, United Arab Emirates.2Centre for Clean Water Technologies, School of Chemical, Environmental and Mining Engineering,

The University of Nottingham, UK.3Department of Chemical and Process Engineering, Universiti Kebangsaan Malaysia, Selangor Darul

Ehsan, Malaysia.

Abstract: Artificial neural network (ANN) simulation is used to predict the rejection of two salts(NaCl and MgCl2) at typical seawater concentrations in a cross-flow nanofiltration membraneprocess. Rejections are predicted as a function of feed pressure and permeate flux with thesalt concentration as a parameter. ANN predictions of the two salts’ rejections are comparedwith experimental results obtained using three different nanofiltration membranes (NF90,NF270 and N30F) in a cross flow filtration set-up. The experimental program spans a concen-tration range of 5000 to 25 000 ppm for NaCl solution and of 5000 to 20 000 ppm for MgCl2 sol-ution at pressures covering the range of 2–9 bars. The effects of the training algorithm, neuralnetwork architectures and transfer function on the ANN performance, as reflected by the percen-tage average absolute deviation are discussed. A network with one hidden layer comprising fourneurones is found to be adequate for mapping input–output relationships and providing a goodinterpolative tool. Algorithms based on the conjugate gradient, regularization and quasi-Newtonprinciples were found to outperform those based on the gradient descent and variable momen-tum gradient descent. The former algorithms gave an average absolute percentage deviation upto 5% whereas deviations up to 20% are obtained from the latter algorithms. For most of thecases considered, the ANN proved to be an adequate interpolation tool, where an excellent pre-diction was obtained for some concentration levels not represented in the training data set. Forvery limited cases, the ANN predictive performance was poor. However, the network’s perform-ance in these extreme cases didn’t improve even with increasing the data points in the trainingdata set.

Keywords: nanofiltration; membranes; artificial neuron networks; rejection; permeate flux.

INTRODUCTION

Nanofiltration (NF) membranes are a type ofpressure driven membranes that have proper-ties in between those of ultrafiltration (UF) andreverse osmosis (RO) membranes. NF mem-branes have the advantages of providing ahigh water flux at low operating pressureand maintaining a high salt and organicmatter rejection (Raman et al., 1994). TheNF process benefits from ease of operation,reliability and comparatively low energy con-sumption as well as high efficiency of pollutantremoval (Eriksson, 1988). In addition, NFmembranes have recently been employed inpre-treatment facilities in both reverse osmo-sis and thermal processes (Hassan et al.,1998; Al-Sofi et al., 1998). This will enhance

the production of desalted water, reduces itsproduction cost, and lowers the energy con-sumption of the desalination processes.Moreover, nanofiltration is an environmentallyfriendly process. Therefore, NF membraneshave boosted worldwide interest. A recentcomprzehensive review on the use of NFmembranes in water treatment has been pre-sented elsewhere (Hilal et al., 2004).The performance of NF membrane separ-

ations is important for the design and optimiz-ation of filtration processes. This will reducethe number of experiments and subsequentlysave time and money. Since most commercialNF membranes are electrically charged, theirperformance depends heavily on the sieving(steric-hindrance) effect and Donnan (electro-static) effect. Therefore, the removal of neutral

417 Vol 85 (A4) 417–430

�Correspondence to:Dr N. Darwish, Department ofChemical Engineering,The Petroleum Institute,Abu Dhabi, UAE.E-mail: [email protected]

DOI: 10.1205/cherd06037

0263–8762/07/$30.00+0.00

Chemical EngineeringResearch and Design

Trans IChemE,Part A, April 2007

# 2007 Institutionof Chemical Engineers

components (such as organics) results from size exclusion(solute and pore size), or differences in diffusion rates in anon-porous structure, which depends also on molecularsize (Van der Bruggen and Vandecasteele, 2003; Chellamand Taylor, 2001). The polarity and the charge of organicsmight influence the separation processes (Van der Bruggenet al., 1999), especially in large-pore membranes. In additionto the sieving effect, rejection of ionic components (saltsolutions) in NF membranes occurs as a result of chargeinteraction between the membrane surface and the ions(Donnan exclusion), as well as differences of diffusivity andsolubility of the ionic components or a combination of these(Peeters et al., 1998). These interactions depend, in additionto temperature and pressure of the filtration processes, onthe characteristics of the electrolyte solution (such as theconcentration, pH level and the composition for the electro-lyte solution) and the membrane itself (e.g., surface charge,pore size and the roughness of the membrane). These fac-tors will affect the efficiency and cost of membrane proces-sing which is dependent on the flux and rejection ofpermeates. Therefore, permeation flux and solute rejectiondata are necessary for the design, operation and optimizationof new membrane separation processes. Towards this objec-tive, many mathematical models have been used to predictthe rejection of ionic solutes, as well as other variablessuch as permeate flux, feed concentration and pressure.One of these models is Spiegler–Kedem model (Spieglerand Kedem, 1966; Jitsuhara and Kimura, 1983; Perry andLinder, 1989; Schirg and widmer, 1992; Levenstein et al.,1996; Pontalier et al., 1999; Diawara et al., 2003; Hilalet al., 2005; Xu and Spencer, 1997). This model treats amembrane as a black box and characterises it in terms oftwo parameters; salt permeability, Ps and reflection coeffi-cient, s. These two parameters are obtained from theexperimental data of rejection versus permeate flux by abest-fit method. Donnan steric-pore model (DSPM) (Vander Bruggen and Vandecasteele, 2003; Bowen et al., 1997;Schaep et al., 2001) is another model that is based on theextended Nernst–Planck equation. This model describesthe transport of ions in terms of an effective membrane thick-ness, porosity ratio and an effective membrane chargedensity. This model has undergone several modifications bytaking into account the hindrance effect of the ions throughthe pores in the membranes (Bowen and Mukhtar, 1996),concentration polarization (Bowen and Mohammad, 1998),and dielectric constant (Bandini and Vezzani, 2003). Further-more, Straatsma et al. (2002) developed a NF membrane

model based on the Maxwell–Stefan transport equations.This model is claimed to predict permeate flux and rejectionsof multi-component liquid feeds as a function of membraneproperties (mean pore size, porosity, thickness, surfacecharge characteristic) and feed pressure.The above mathematical models were derived from phys-

ical descriptions and understanding of the NF process.These models are mathematically complex, computationallyexpensive and they ideally require a very detailed knowledgeof filtration process as well as characterization of the mem-branes (Bowen et al., 2000). Therefore, there is a need tofind an alternative means for predicting process performanceby exploiting available process data and extending it to una-vailable data. Linear and nonlinear regression methods areexamples of what are known as black box models. However,this is a significant problem in this approach since numeroustypes of non-linearity get scrambled together with no clue asto which of these nonlinearities is predominant.Artificial neural networks (ANNs) are another type of black

box models. ANNs, however, are capable of modelling highlycomplex and non-linear systems with large numbers of inputsand outputs. Therefore, ANNs offer a more attractive alterna-tive to conventional black box models in dealing with complexphenomena (Bowen et al., 2000).From the early 1990s, ANNs have been widely applied in

many research areas such as modelling (Trichard et al.,1995), prediction, fault detection and process control (Dirionet al., 1996; Fakhr-Eddine et al., 1996). In the field of mem-brane separation processes ANNs have successfully beenapplied to different types of the membranes; microfiltration(Dornier et al., 1995; Piron et al., 1997; Hamachi et al.,1999), ultrafiltration (Bowen et al., 1998a, b; Delgrangeet al., 1998a, b; Teodosiu et al., 2000), nanofiltration(Bowen et al., 2000). Dornier et al. (1995) used ANNs to pre-dict the evolution of membrane fouling during crossflowmicrofiltration of cane sugar and gum streams. Their resultsshowed a good prediction of time evolution of the resistance.Recurrent ANNs and a hybrid model (combining a physicalmodel with an ANN) were used to predict the performanceof the dynamics of baker’s yeast crossflow microfiltration(Piron et al., 1997). Results obtained from the hybrid modelwere found to be more accurate than those coming frompure ANN modelling. The hybrid model, however, is limitedand its assumptions need to be verified for other applications.Hamachi et al. (1999) used the recurrent ANNs to predict fluxand deposition thickness in bentonite suspension microfiltra-tion. In another study, Bowen et al. (1998a, b) applied ANNs

Figure 1. Architecture of feed-forward neural network with a single hidden layer of S neurons.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A4): 417–430

418 DARWISH et al.

with single hidden layer for proteins and colloids crossflow fil-tration using UF membrane. It was found that the carefulselection of input variables and training points helps in opti-mizing the ANN training process and in achieving very accu-rate predictions of the experimental results. For the samemembrane, ANNs have been applied to predict trans-mem-brane pressure in a drinking water process and time evolutionof membrane fouling (Degrange et al., 1998a, b). Differentnetwork structures have been checked and some of themallowed prediction of pressure with very good accuracy. Inanother study employing ANN approach, a model was devel-oped to predict the flux during ultrafiltration of wastewater(Teodosiu et al., 2000). The trained networks were able toaccurately capture the non-linear dynamics for initial fluxes.On the other hand, ANNs have been used successfully tosimulate reverse osmosis of ethanol and acetic acid andultrafiltration of bleach plant effluent (Niemi et al., 1995). Ithas therefore been possible to estimate the permeate fluxand the rejection rate from the process variables. The studyof Bowen et al. (2000) is among very few studies in theopen literature about utilizing ANN in modelling nanofiltrationprocesses; Toward this end, ANN has been used to predictthe rejections of single salts (NaCl, Na2SO4, MgCl2 and

MgSO4) and mixtures of these salts at a nanofiltration mem-brane. The predictions have been compared to pilot plantrejection data obtained with a spiral-wound membrane. Theoverall agreement between ANN predictions and experimen-tal data was very good for both single salts and mixtures.In this study, ANN analysis will be applied to provide a

means of modelling NF process performance. In particular,the rejections as a function of pressure and permeate fluxof single salts (NaCl and MgCl2) at three nanofiltration mem-branes will be predicted using ANN model. In addition, theaffect of the input training dataset, the training algorithmand network architecture on the efficiency of ANN predic-tions, as reflected by percentage average absolute deviation,will be investigated.

ARTIFICIAL NEURAL NETWORKS APPROACH

ANNs may be described as a group of simple processingelements called neurons arranged in parallel layers that arefully interconnected by weighted connections. There are sev-eral types of ANNs mentioned in the literature (Hagan et al.,1996) such as feed-forward networks (or perceptron

Figure 2. The average absolute percentage deviation for differenttraining algorithms for the 4,1 net using log-sigmoid transfer function(algorithms acronyms as per Matlab 6.5).

Figure 3. Reproducibility of ANN prediction from 10 different runsusing the same training data set (a) trainbr: at each pressure the10 predicted R% coincide with each other (b) traingdx: at eachpressure the predicted R% differ from one trial to another (data set:5000 ppm NaCl).

Table 1. Percentage average absolute deviations for different net-work architectures operated with two different training algorithmsand two different transfer functions.

Network architecture

Percentage average absolute deviation

Trainbr Traincgp

logsig tansig logsig tansig

2:1 2.8 6.6 2.9 3.13:1 2.8 2.7 2.8 2.94:1 2.5 2.5 2.6 2.55:1 2.5 2.5 2.5 2.83:3:1 8.9 11.5 3.1 4.42:2:1 11.3 11.4 3.3 2.9

(Input: system pressure, P and salt concentration, C; output: rejectionpercentage, R%; data set: NaCl).


NEURAL NETWORKS SIMULATION OF THE FILTRATION OF NACL AND MGCL2 SOLUTIONS 419

network), competitive networks (Hamming network) and recur-rent networks (Hopfield network). Most recently, stackedneural networks have been applied to solve complex problems(Shuang-Quang et al., 2006; Wolpert, 1992). The most famoustype of ANN in use is the feed-forward networks, particularly,the multi-layer perceptron network. In this type of ANNs, infor-mation flows in the forward direction only. ANNs interface inde-pendent variables through the neurons of an input layer andtransmit output of dependent variables through the neuronsof an output layer. The number of independent and dependentvariables, therefore, dictates number of neurons in the inputand the output layers, respectively. In between the input andthe output layers there is at least one hidden layer that canhave any number of neurons. According to the universalapproximation theory (Tambe et al., 1996), an ANN with asingle hidden layer with enough number of hidden neuronscan map any input to any output to any degree of accuracy.Additionally, bias is an extra input added to neurons, whichalways has a value of 1 and treated like other weights. The

reason for adding the bias term is that it allows a represen-tation of phenomena having thresholds (Delgrange et al.,1998b). Neurons in the hidden and the output layers calculatetheir inputs by performing a weighted sum of the outputs theyreceive from the previous layer. Their outputs, on the otherhand, are calculated by transforming their inputs using anon-linear transfer function. The most widely used transferfunctions are the S-shaped log-sigmoid (logsig) transfer func-tions, the S-shaped tan-sigmoid (tansig) transfer functions,and the pure linear transfer function (purlin). The ‘logsig’ trans-fer function produces outputs in the range of 0 to 1. The tansigfunction, on the other hand, produces output in the range of21 toþ1. Outputs in the range of21 toþ1 can be producedfrom the linear transfer function (Niemi et al., 1995; Delgrangeet al., 1998b).The architecture of the feed-forward ANN with a single

hidden layer of S neurons is shown in Figure 1. In thisfigure, the input vector P is represented by the solid verticalbar at the left. The dimension of P is displayed below the vari-able as R � 1 indicating that the input is a single vector of Relements. These inputs go to the S � R weights matrix W1 in

Figure 4. Performance of ANN in correlating the rejection-pressuredata of NaCl nanofiltration using NF90 membrane: (a) trainingusing 12 data points, (b) training using 16 data points, solid symbols:training data set, open symbols: validation data set, solid lines: ANNprediction.



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the hidden layer. A constant 1 enters the neurons as an inputand is multiplied by a bias b i and represented as b vector.This vector is summed with the weighted inputs (W1) toform the net input n 1 vector with S dimension as seen inequation (3):

n1 ¼ W1Pþ b1 (1)

The neurons output vector a1 with S dimension is thenobtained by operating the transfer function on n1. Thesame procedure is repeated in the output layer. The netinputs of the output layer are shown in equation (4), whilea3 represents the overall output of the network. This outputcould be a scalar or a vector, depending on the case understudy.

n2 ¼ W2a1 þ b2 (2)

There are usually four steps involved in ANN modelling: (1)assembling the training data of input (independent variables)

and output (dependent variables), (2) deciding the networkarchitecture, (3) training the network, and (4) simulating thenetwork response to new inputs. The training process issimply an optimization process which aims at finding theset of weights and biases associated with each layer thatwill minimize the error objective function related to the devi-ations of the ANN predictions from the target values. Theerror objective function is usually the sum of squared errorsbetween the targets and ANN outputs. ANN weights andbiases in this process are updated in a systemic way bymeans of minimizing an error function using any of the well-known optimization techniques. The most widely used isthe back propagation algorithm (Rumelhart et al., 1986),which is based on the steepest-descent principle. Thereare several input variables to this algorithm, such as thelearning rate (h), the momentum coefficient (a), number ofhidden layers (L) and the number of hidden neurons (H)that have an effect on the ANN training. The predictions,also, can be judged by a combination of some parameterssuch as absolute errors and number of training cycles orepochs (C).


Figure 7. Performance of ANN in correlating the rejection-pressuredata of MgCl2 nanofiltration using NF90 membrane: (a) trainingusing eight data points, (b) training using 12 data points, solid sym-bols: training data set, open symbols: validation data set, solidlines: ANN prediction.



The algorithms used here fall in four categories:

(1) Training algorithms based on the batch steepest descent(traingd): The weights and biases here are updated in thedirection of the negative gradient of the performancefunction in which the learning rate is held constantthroughout training. Based on the same algorithm butwith variable learning rate, another training algorithm(traingdx), which is another example of high performancebatch steepest descent training algorithms, is used. Thisalgorithm is known to converge from 10 to 100 timesfaster than the previous traingd.

(2) Training algorithms based on the quasi-Newton (secant)method, which, in minimizing the error objective function,track the steepest descent direction but do not requirecalculations of the Hessian matrix. The one-step-secantalgorithm (trainoss) have been utilized as an exampleof this algorithm.

(3) Training algorithms based on the conjugate gradient prin-ciple, which follow a path in the direction of conjugate

gradient in their search for the minimum. The Polak–Ribiere algorithm (traincgp) has been as a representativefor this family of algorithms.

(4) Training algorithms based on modifying the performancefunction by adding a term to the sum of squares of the net-work errors. This term consists of the mean sum of squaresof the networkweights and biases. Automated regularization(trainbr) is an example of this training algorithm, which isbased on Baysian principles (Hagan et al., 1996). Here,the weights and biases of the network are assumed to berandom variables with specified distributions. The regulariz-ation parameters are related to unknown variables associ-ated with these distributions. These parameters, then, areestimated using statistical techniques.

EXPERIMENTAL

Filtration Experiments

The experimental set-up used in this study for the crossflow filtration experiments has been described in a previous




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published paper (Hilal et al., 2005) on the filtration of sodiumchloride salt solution using three NF membranes, i.e., NF90,NF270 and N30F. The same set-up with the same kind of NFmembranes are employed for the filtration of magnesiumchloride (MgCl2) at the same pressure levels previouslyencountered but with different salt concentrations. The set-up, which was designed to carry out the experiments in a lab-oratory scale, consisted of a circular disc membrane with aneffective filtration area of 12.6 cm2 and a stainless steel gearpump. The pump was used to circulate the feed solution ofMgCl2 at ambient temperature in a total re-circulation mode,i.e., both the concentrate and the permeate streams are re-circulated into the feed tank, so that the feed concentrationis kept approximately constant. The pressure was variedbetween 2 and 9 bars while the concentrations varied from5000 to 20 000 ppm. These concentrations cover the salinityrange of MgCl2 in seawater where NF membranes haverecently been used in the pretreatment operations in desali-nation processes. The MgCl2 salt was obtained from Fisherscientific-UK with purity better than 99.5%. The permeateflux and rejection were determined by varying the appliedfeed pressure at different feed concentrations. In order todetermine the concentration of salt in the feed and the perme-ate solutions, the conductivity of these solutions were

measured at 258C by a conductivity meter (Hand-HeldMeter, LF 330/340, WTW-Germany). Three commercial NFmembranes were used in this study, two of which were sup-plied by FILMTEC and manufactured by DOW chemical com-pany (USA). These two membranes are NF90 and NF270,which are made from polyamide. The third membrane wasNADIR N30F, obtained from MICRODYN-NADIR Gmbh(Germany), which is made of polyethersulfone. Furtherdetails to the filtration experiments can be found elsewhere(Hilal et al., 2005).

Application of Neural Network

The feed-forward ANN (perceptron network) has beenused in this work with single hidden layer and using purelinear transfer function for the output layer. Different networkarchitectures and two sigmoidal transfer functions (logsig andtansig) for the hidden layers have been studied in seeking thebest network in describing the experimental data. The net-work architectures investigated are 2 : 1, (i.e., one hiddenlayer with two neurones and one output layer) 3 : 1, 4 : 1,5 : 1, 3 : 3 : 1 and 2 : 2 : 1. Towards the same objective, differ-ent back propagation training algorithms have been explored.

Figure 10. Performance of ANN in correlating the rejection-flux data of NaCl nanofiltration using NF90 membrane; solid symbols: training dataset, open symbols: validation data set, solid lines: ANN prediction.



In this work, ANN algorithms as programmed in the neuralnetwork toolbox of Matlab 6.5 have been used to predictrejections versus pressure and rejections versus permeatefluxes for NaCl and MgCl2 solutions using three differentnanofiltration membranes (that is NF90, NF270 and N30F).The network prediction is compared with the data obtainedfrom a carefully conducted experimental program using theaforementioned three membranes in a cross flow membraneset-up. The experimental study covers pressures in the rangeof 2–9 bar and concentrations in the range of 5000–25000 ppm. The network was trained using two differentinput training sets of data. In both cases, the input data tothe ANN are feed pressure, permeate flux and the concen-tration of the salts while the output is rejection. The computerprogram used in this paper was written using Matlab pro-gramming language and executed on a PC.

RESULTS AND DISCUSSION

Salt filtration using membranes is a highly complicated andnon-linear phenomenon due to the complex ion–membraneand ion–ion interactions that occur near and through themembrane. In the following sections, we present our results

of applying ANN in the modelling of NF membranes usingtwo training algorithms as programmed in Matlab.

ANN: Training Datasets

In all ANN analysis performed in this study, the outputsought was the rejection percentage (R%) of the salt andmembrane under consideration. The neural net, however,was operated on two different inputs; in one case, a columnvector of the operating pressure and a column vector of thesalt concentration were employed. In the second case, acolumn vector of the permeate fluxes and a column vectorof the salt concentration were utilized as inputs.In each case, two different partial training datasets were

used; the first training set contained only 12 training datapoints from some of the available constant-concentrationexperimental data, i.e., 5000, 15 000 and 25 000 ppm atpressures of 2, 4, 7 and 9 bar. The remaining (18) points rep-resent the validation points for the ANN. The second data setincluded training points from all studied concentration (5000–25 000 ppm) with a total number of 16 points, whichrepresents the first dataset in addition to four other pointsat concentrations of 10 000 and 20 000 ppm and pressureof 2 and 9 bar. Again, the remaining (14) points represent



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the validation points of ANN. For MgCl2 salt, the first set con-tained eight training data points at concentrations of 2000and 5000 ppm and pressures of 2, 4, 7 and 9 bar for allstudied membranes leaving 16 experimental data points forthe validation process, while the second set contains fourmore points at concentrations of 1000 ppm and 15 000 ppmand pressure 2 and 9 bar. The points remaining for validationare 12 data points.

Effect of Architectures and Training Algorithms onthe ANN Performance

Figure 2 shows the percentage average absolute deviation(PAAD) for five training algorithms used in combination with a4-1 network employing a logsigmoid transfer function. It isclear that algorithms based on the conjugate gradient, regu-larization and quasi-Newton principles (traincgp trainbr andtrainoss, respectively) outperform those based on gradientdescent and variable momentum gradient descent (traingdand traingdx) The former algorithms give an average absol-ute percentage deviation of up to 5% whereas deviationsup to 20% are obtained from the latter algorithms. The bestalgorithms are then utilized to determine the optimum

network architecture and the best transfer function. Theresults of this study are presented in Table 1. It is clear thatthe network architecture with one hidden layer such as(4,1) and (5,1) give lower PAAD than network architecturewith two hidden layers especially for trainbr algorithm.Single hidden layer network with trainbr and traincgp algor-ithms give comparable values of PAAD. However, trainbralgorithm was found to be of more stability towards differentinitial guesses in weight and biases. Traincgp algorithm onthe other side was found to be sensitive towards initialguesses in weights and biases, i.e., results differ from onerun to another depending on the random initial guesses gen-erated by Matlab. Furthermore, the runtime using trainbr isless than that using traincgp. The effect of transfer functionwas also addressed as shown in Table 1. It is clear thatlogsig give PAAD values lower than those using tansig.Another positive point for trainbr has been concludedthroughout Figures 3(a) and (b). The sensitivity of two trainingalgorithms (trainbr and traingdx) towards initial guesses inweights and biases is presented in Figure 3, which showsthe results of 10 different iterations for the case of NaCl fil-tration at a concentration of 5000 ppm and pressure in therange of 2–9 bar using NF90 membrane Reproducibility of




trainbr results is quite obvious in Figure 3(a) and the sensi-tivity of traingdx is also evident in Figure 3(b).

ANN Prediction of Salt Rejection with Pressure

Sodium chloride saltThe ANN’s prediction of salt rejection as a function of

pressure for NaCl solutions using the three investigatedmembranes will be considered in this section. The ANNprediction, as well as the experimental data, is shown inFigures 4–6. Salt concentration spans the range of 5000 to25 000 ppm, whereas pressure covers the range of 2–9bars. In all of these figures, solid symbols are used to identifyexperimental data points which are used in the training phaseof the ANN while open symbols are used for data points notincluded in the training phase, i.e., points used in the vali-dation phase. Note also that solid lines in these figures rep-resent a polynomial fit of the ANN prediction. It can beseen that the ANN successfully predicts the nonlinear beha-viour of rejection versus pressure. As shown in Figure 4(a),the ANN performs well in the training phase where a goodprediction is obtained for concentrations levels from which

some data points have been included in the training phase.The concentration levels represented in the training phaseare the 5000, 15 000 and 25 000. The ANN interpolative per-formance for the 10 000 and 20 000 ppm concentration levels(which were not represented in the training phase) is shownto be of less quality. For the 10 000 ppm concentration, ANNprediction worsens with pressure with a tendency tooverestimate the actual salt rejection. A maximum deviationof up to 10% is observed along this concentration level.However, for the other concentration level of 20 000 ppm,the ANN performance is much better with a maximumdeviation of about 5%. When these concentration levels arerepresented in the training phase by including two extremedata points from each concentration level, the ANN predic-tions do not improve much beyond the previous case asshown in Figure 4(b).Figures 5 and 6 show the experimental rejection data and

the results of ANNs predictions for NF270 and N30F mem-branes, respectively. It is evident from these figures thatthe interpolative capability of the ANN is quite impressive.With some data at three concentration levels (5000, 15 000and 25 000 ppm) used in the training phase, the ANN

Figure 13. Performance of ANN in correlating the rejection-flux data of MgCl2 nanofiltration using NF90 membrane; solid symbols: training dataset, open symbols: validation data set, solid lines: ANN prediction.


426 DARWISH et al.

successfully predicts data at the other two intermediate con-centration levels of 10 000 and 20 000 ppm. For the NF270membrane, the ANN tends to slightly overestimate the rejec-tion versus pressure data for the 20 000 ppm with a growingdeviation with pressure up to about 5% at the highest studiedpressure. The interpolative prediction for the 10 000 ppm isalmost perfect as shown in Figures 5 and 6 for both mem-branes. By including some data from these two concentrationlevels in the training stage, the ANN makes a perfect job asevident in Figures 5(b) and 6(b). The ability of the ANN toquantitatively describe data at high salt concentrationswithout recourse to sophisticated descriptions of non-idealsolutions seems here a significant advantage. It is worthmentioning that the N30F membrane, as compared to theother two membranes, gave the lowest rejection (in therange of 3–6%) for the same NaCl concentration at 9 bar,with this rejection decreasing down to around zero at 2 bar.

Magnesium chloride saltThe experimental rejection data, as well as the ANN pre-

dictions for MgCl2 salt solutions for all studied membraneswith different pressures and concentrations are shown inFigures 7–9. Salt concentration covered the range of 5000

to 20 000 ppm with the same range of pressure used in theNaCl case, i.e., 2–9 bars. Experimentally, NF90 and NF270membranes give higher rejection of MgCl2 than of NaCl.However, rejection of MgCl2 was found almost the same asthat of NaCl for the N30F membrane.From Figures 7–9 it can be seen that the ANN has an

excellent interpolative capability. In most cases so far con-sidered, it is sufficient to train the net on a partial set ofdata belonging to the extreme concentration levels. Trainingthe net using four experimental data points from each ofthe 5000 and the 2000 ppm is seen to be sufficient for thenet to correctly predict rejection versus pressure data at theother two concentration levels of 1000 and 15 000 ppm.This is evident in Figures 7(a), 8(a) and 9(a) where includingdata points from the inner concentration levels seemsunnecessary. On the contrary, comparison of the ANN predic-tion for the 10 000 ppm concentration level in the case ofNF90 [Figures 7(a) and (b)] shows that the ANN performsbetter for less data points in the training set. This can be inter-preted in terms of the network architecture; low number ofweights and biases can lead to over-fitting problems incases of large size of training data. For the NF270 mem-brane, the ANN slightly overestimates salt rejection datawith a maximum percentage deviation of about 5% especially




at lower pressures [Figure 8(a)]. However, as shown inFigures 8(a) and (b), the performance is improved by includ-ing the inner concentration levels in the training phase of thenet. The ANN can be confidently applied in making a goodinterpolation for inner concentration levels. The experimentalrejection data and ANNs prediction for the N30F membraneare presented in Figures 9(a) and 9(b). This membranegives the lowest rejection among the studied membranesfor the same experimental conditions (range of the salt con-centration and operating pressure). The ANNs is shown tohave the capability of predicting the experimental rejectiondata for this membrane even at low values of salt rejectionand pressures. The network performance is only marginallyimproved by including data from the inner concentrationlevels and thus can be confidently applied towards interp-olation for other concentration levels not included in thetraining data sets.It is thus evident that the ANN technique, which is an easy-

to-use black box method of correlation, is able to quantitat-ively describe the rejection data of the two investigatedsalts using three different membranes without the needfor analysis in terms of effective pore radius, effective thick-ness/porosity ratio and effective membrane charge whichmay be difficult to relate to real physical parameters.

ANN Prediction of Rejection with Permeate Flux

Sodium chloride saltThe ANN predictions of salt rejection as a function of

permeate flux for NaCl solution and the experimental datafor the three investigated membranes at different salinitylevels are shown in Figures 10-12 (each is composed offour sub-figures, a, b, c and d). Again, NaCl Salt concen-tration spans the range of 5000 to 25 000 ppm. Figure 10shows the ANN predictions for the NF90 membrane.Except for the 1000-ppm concentration level, there is anexcellent agreement between ANN prediction and the exper-imental data. At the 1000-ppm level, the ANN model over-estimates the experimental data with a deviation more than20%. Salt rejection versus flux is shown to be not heavilydependent on salt concentration in the range of 15 000–25000 ppm for NF90 membrane, as shown in Figure 10.The ANN predictions of rejection with permeate flux and

the experimental data using NF270 and N30F are shown inFigures 11 and 12, respectively. It can be seen that ANN pre-dictions for both membranes are excellent. Further improve-ments in the ANN prediction is obtained by including someexperimental data points from the inner concentrationlevels. In particular, the 3% deviation appearing in



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Figure 11(a) is shown to diminish in Figure 11(c) by includingtwo data points on that concentration level. The ANN modelperfectly describes the rejection data for the N30F membraneas shown in Figure 12. It is worthwhile mentioning that thismembrane has low rejection at high flux in comparison toNF90 membrane.

Magnesium chloride saltThe experimental rejection data, as well as the ANN

predictions for MgCl2 salt solutions for all investigatedmembranes with different concentrations are shown inFigures 13–15. Salt concentration covered the range of5000–20 000 ppm. High permeate fluxes with high rejectionof MgCl2 were obtained from all investigated membranes atlow salt concentration. However, at high concentration theflux and rejection were relatively low. It is worthwhile mention-ing that the ANN prediction using (trainbr) algorithm was notable to fit the experimental data in this case. Alternatively,(traincgp) has been used, which gave good predictions. Fur-thermore, (traincgp) algorithm gave low value of PAAD similarto the value of (trainbr), see Figure 2. The ANN prediction ofMgCl2 rejection versus permeate flux using NF90 membraneis shown in Figure 13. It can be seen from this figure that theANN prediction using a limited number of data points in thetraining phase works except for 1000 ppm concentrationlevel at pressure higher that 5 bar. The ANN prediction, inthis case, lies below the experimented results. However,this underestimation in the ANN prediction is much alleviatedby including extra data points from the inner concentrationlevels as shown in Figure 13. Figures 14 (a)–(d) show theANN prediction using NF270. Again, this membrane pro-duced relatively high flux with low rejection. It can be seenhere that the complex behaviour (non-linearity) of rejectionwith flux is well reproduced by ANN for all studied conditionsand for the two training data sets with neglected overesti-mated at concentration 10 000 ppm using the limited trainingdata set. Finally, predictions of the rejection with experimentaldata using N30F are shown in Figures 15(a)–(d). As in thecase of NaCl, N30F produced permeate with low rejectionsand fluxes. Good ANN predictions have been obtained forthis membrane with overestimation not more than 5%.

CONCLUSION

The application of artificial neural networks to the modellingof crossflow nanofiltration of NaCl and MgCl2 has been inves-tigated to predict the membrane rejection versus pressureand permeate flux at different concentrations and pressuresusing three NF membranes (NF90, NF270 and N30F). Theconcentrations levels were in the range of (5000–25000 ppm) for NaCl and (5000–25 000 ppm) for MgCl2,while the pressure spanned the range of 2–9 bar. Inadditions, the effect of the training algorithm, net work archi-tectures and transfer function on the ANN predictions hasbeen discussed. It was found that a network with onehidden layer of four neurons is sufficient for prediction pur-poses. Different training algorithms have been explored.Algorithms based on the conjugate gradient, regularizationand quasi-Newton principles were found to outperformthose based on the gradient descent and variable momentumgradient descent. The former algorithms gave an averageabsolute percentage deviation up to 5% whereas deviations

up to 20% are obtained from the latter algorithms. Rejectionversus pressure and rejection versus permeate flux, forboth salts and for all three membranes have been simulatedusing the ANN approach. ANN successfully tracked the non-linear behaviour of rejection versus pressure and rejectionversus flux. For most of the cases considered, the ANNproved to be an adequate interpolation tool, where an excel-lent prediction was obtained for some concentration levelsnot represented in the training data set. For very limitedcases, the ANN predictive performance was poor. However,the network’s performance in these extreme cases did notimprove even with increasing the data points in the trainingdata set.

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ACKNOWLEDGEMENTS

This work has been accomplished as part of a research pro-ject sponsored and funded by the Middle East DesalinationResearch Center (MEDRC).

The manuscript was received 31 March 2006 and accepted forpublication after revision 11 December 2006.


430 DARWISH et al.

NF Separation of NaCl and MgCl2

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