Desalination 249 (2009) 210–221

Development of a statistical and mathematical hybrid model to predict membrane

fouling and performance

Tae-Mun Hwanga,b,*, Hyunje Oha, Yong-Jun Choib, Sook-Hyun Namb, Sangho Leeb, Youn-Kyoo Chounga

aDepartment of Civil and Environmental Engineering, Yonsei University, Sinchondong 134, Sudaemungu, Seoul 120-749, Republic of Korea

b Department of Advanced Environmental Engineering, Korea Institute of Construction Technology, 2311 Daehwa-dong, Ilsan-gu,

Goyang-si, Gyeonggi-Do, 411-712, Republic of KoreaTel. +82-3-9100741; Fax: +82-3-9100291; email: taemun@kict.re.kr.

Received 13 November 2008; revised 17 December 2008; accepted 24 December 2008

Abstract

In this study, we explored the potential of a hybrid model combining mathematical and statistical mod-els. Mathematical models are capable of simulating microscopic phenomena but fail to explain the com-plicated situations in practical cases. On the other hand, statistical models are suitable to predict complex and non-linear behaviors. Thus, a hybrid model can have advantages in both mathematical and statistical models. This paper focusses on the techniques to combine mathematical models with statistical models. As a mathematical model, we have applied the Hagen–Poiseuille equation and fi ltration models modifi ed with the critical fl ux concept to predict the performance of hollow fi ber membranes. Statistical model such as ANN (artifi cial neural networks) was used to correlate operating conditions with membrane fouling. Experimental data were collected from a pilot plant using hollow fi ber microfi ltration membranes for surface water treat-ment. Diff erent methods to hybridize mathematical and statistical models were compared to develop a feed-forward guidance simulator. Comparison of model calculations with experimental results revealed that the hybrid model was useful to evaluate membrane fouling characteristics. An algorithm for process controller based on the hybrid model was also suggested as an initial step toward an “intelligent” membrane system.

Keywords: Microfi ltration; Cake formation; Filtration model; ANN

*Corresponding author.

Presented at the 2nd joint workshop between the Center for Seawater Desalination Plant and the European Desalination Society, Gwangju Institute of Science and Technology, Korea, October 8–9, 2008.

0011-9164/09/$– See front matter © 2009 Elsevier B.V. All rights reserved.doi: 10.1016/j.desal.0000.00.000

T.-M. Hwang et al. / Desalination 249 (2009) 210–221 211

1. Introduction

Although membrane fi ltration has drawn attention as an aff ordable technology for pota-ble water treatment, membrane fouling is still a critical problem. Membrane fouling cannot be avoided in most cases and causes a signifi cant loss in permeability. Nevertheless, no single model can successfully predict membrane foul-ing, which involves various fouling mechanisms and physical/chemical interactions. In pilot- or full-scale plants, variations of feed water qual-ity as well as changes in membrane characteris-tics contribute to the complexity in membrane fouling. Fouling is an unavoidable deleterious phenomenon in the membrane process that causes serious permeate fl ux decline followed by deterioration of product water quality.

Many studies on permeate fl ux decline and fouling index increase describe that particle accumulation during cross-fl ow membrane fi ltration is aff ected by physical and chemical characteristics of feed water as well as hydrody-namic operating conditions. Membrane fouling is responsible for the non-steady-state nature of membrane process, as it causes permeate fl ux decline to occur with passage of time. For this reason, steady-state fl ux decline models are not capable of describing membrane performance accurately in membrane process and therefore it is necessary to use non-steady state model.

Recently, several studies were conducted to predict membrane performance using artifi -cial neural networks (ANNs). Artifi cial neural network is an eff ective predictive method for modeling the behavior of non-linear dynamic systems. Shetty and Chellam developed an ANN model to predict membrane fouling dur-ing municipal drinking water nanofi ltration. In their study, ANN model accurately simu-lated the total resistance to water permeation across NF membranes during bench-scale experiments with fl at membrane sheets, tests with single spiral-wound elements, as well as pilot-and full-scale test with multiple spiral-

wound elements arranged in two stages [1]. Curcio et al., demonstrated an innovative met-hod for the control of permeate fl ux decay in cross-fl ow membrane processes [2]. Chen and Kim developed radial basis function neural network (RBFNN) to predict long-term per-meate fl ux decline in cross-fl ow membrane fi l-tration [3]. Sahoo and Ray illustrated that GA (genetic algorithm)-optimized ANN predicts the permeate fl ux decline more accurately than a network in which the ANN calibration was applied using a trial-and-error approach in cross-fl ow membranes [4]. As mentioned, with the recent developments in computing system, artifi cial neural networks have been used and showed promising results in treat-ment modeling, control, and optimization. The primary advantage of ANN over theoreti-cal approaches is that, as a black box model, it does not require any governing equation with forceful assumptions specifi cally describing the underlying engineering phenomena. The ANN approach focuses on fi nding repeated, recognizable, and predictable patterns between the process inputs and outputs. ANN models learn from past operational data records, and bypass the modeling of actual micro-scale interactions. The ANN modeling approach does not require a description of how the processes occur in either micro or macro envi-ronments, but requires only some key factors that govern the entire process. The objective of this research is to combine mathematical and statistical models for the prediction of mem-brane fouling. The hybrid model was evalu-ated through fouling indices and specifi c fl ux.

2. Theory

2.1. Filtration model

The membrane fouling steps can be described as pore adsorption, pore blocking, and cake for-mation. Pore adsorption and blocking are inter-nal membrane fouling mechanisms, while cake

T.-M. Hwang et al. / Desalination 249 (2009) 210–221212

formation occurs on the surface of membrane and is defi ned as external fouling. Based on blocking fi ltration theory, permeate fl ux decline can be predicted by these three mechanisms. The pore adsorption model assumes that per-meate fl ux decline is attributed to the decrease in membrane pore diameter that results from particle deposition within membrane pores, while the pore blockage model describes the decrease in permeate fl ux as the reduction of the overall number of pores caused by complete pore blockage by particles. While the cause of pore volume reduction diff ers from each model, both processes cause a reduction in membrane permeability. Unlikely, permeate fl ux decline is induced by cake formation, with formation of a particle cake layer on the membrane sur-face [5].

To establish a mathematical and statistical hybrid model, we applied the Hagen–Poiseuille equation and fi ltration models modifi ed with the critical fl ux concept and ANN models. Especially, a mathematical model was formu-lated by a cake formation model among the fi ltration models. Particles deposited on the membrane surface form cake layer that causes an additional hydraulic resistance. Thus, Rt(x,t) is given by Darcy’s law as

R x t R R x tR K m x t

t m c

m f d

( , ) ( , )( ( , ))

= += +1

where Rc(x,t) is the local cake resistance and Kf is the cake permeability constant, which is expressed as 180(1-ε)/(ε 3ρρd

2pRm) based on

the Carman-Kozeny equation. For the cake formed on the outside surface of hollow fi ber membranes, the cake resistance can be described as [6]. Rt is described as a function of the amount of foulant deposition (md)

J x tp x t

R x tp p x tR R x t

R x t

t

o

m c

cc

( , ) ( , )( , )

( , )( , )

( , )

= =−( )+( )

=

Δη η

α ρcc c o o c

o

D D x tD

φ δ2

2ln

( , )+⎛⎝⎜

⎞⎠⎟

where δc(x,t) is the thickness of the cake layer and φc is the volume fraction of the cake layer, which is assumed to be 0.67 for incompress-ible and polydispersed particles [7].

δc can be obtained by solving an equation based on a mass balance on the surface of a growing cake layer [6].

d x tdt

DD x t

J x t J

c b

c b

o

o cc

δ φφ φ

δ

( , )

( , )( ( , ) )

=−

+−

2

Details about cake fi ltration model are described in [8]. Figure 1 illustrates the fl ow

v(x,t) v(x,t) + dvp(x,t) p(x,t) + dp

L

x dx

p0

Q0 = πDoLJavg

LLp

x = 0 x = L x = L+Lp

DiDo

J(x,t)v(0,t)=0

p(L, t) p(L + Lp,t)

v(L,t) v(L+Lp,t)=v(L,t)

Fig.1. Permeation fl ow through the hollow fi ber membrane.

T.-M. Hwang et al. / Desalination 249 (2009) 210–221 213

and geometry of a single fi ber in a hollow fi ber membrane module. The model is used to fi nd the system parameters including αc and Jc by fi tting the model with experimental data. Upon knowing these parameters, the model equations can be used to simulate the TMP profi les under various operating conditions

2.2. Artifi cial neural networks (ANN)

Artifi cial neural networks can be con-sidered as simplifi ed mathematical models for computationally complex systems like a human brain, working as parallel distributed computing systems. A key advantage of neu-ral network system is in its fl exibility: the sim-ple, yet powerful learning procedures can be defi ned, allowing the systems to adapt to the environments. The essential characteristic of such networks is that they map similar input patterns to similar output patterns. One of the popular neural networks for pattern rec-ognition application is the multilayer percep-tron (MLP) network. Multilayer perceptron (MLP) used in this study is feed-forward neu-ral networks trained with the standard back propagation algorithm. They are supervised networks so they require a desired response to be trained. They learn how to transform input data into a desired response, so they are widely used for pattern classifi cation and prediction. A typical multilayer feed forward neural network architecture is shown in Fig. 2. A multilayer perceptron consists of three lay-ers: input layer, hidden layer and output layer. Each layer is fully connected to the next one. The strength of each connection, referred to its connection weight, can then be adjusted. The connection weight from node i to node j is denoted by wij. Input data are presented to the network through the input layer, the values of which are denoted by xi. Data are passed from the input layer to the hidden layer. Each node in the hidden layer receives the weighted outputs (wij xi) of the nodes in the preceding

layer. These outputs are then summed and added to a threshold value (θj) to produce the node input (Ij) as shown in the equation below. The node input (Ij) is then passed through an activation function (f(Ij)) to produce the node output, yj. This node output is then used to compute the inputs for nodes in the following layer, until the fi nal output is calculated [9].

I w xj ij i ji

= +∑ θ

Neural network predictions were quantita-tively evaluated using the root mean squared error (RMSE).

RMSEP O

ni i=−∑ ( )2

where, Pi is the ith predicted value of the normalized resistance, Oi the correspond-ing observed value, and n is the number of observation.

3. Materials and methods

3.1. Pilot-scale membrane system

A pilot-scale pressurized membrane fi ltra-tion system was composed of rapid m ixing/

Input layer Output layer

y1

y2

yn

Hidden layer

Fig. 2. Schematic diagram of a multilayer feed for-ward neural netwok.

T.-M. Hwang et al. / Desalination 249 (2009) 210–221214

coagulation/sedimentation process and fi ltra-tion using PVDF membranes (Asahi Kasei, Japan) (Fig. 3). Raw water used in this study was collected from the Han River, Guui intake (the water supply source for Seoul, Korea). Poly aluminum chloride (17%) was used as coagulant in the study, and optimal coagulant dosage was determined by jar-test and streaming current detector (SCD). The specifi cations of membrane are summarized in Table 1. Operating conditions are as fol-lows: 40-minute fi ltration; 30-second back-wash with permeate; and 1-minute backwash with pressurized air.

3.2. Analytical methodsThe analytical methods from standard

methods were adapted to the measurements of

total organic carbon (TOC), UV absorbance and algae [10]. TOC was measured by TOC analyzer (Yena Multi N/C 3000, Germany). Turbidity was measured by online turbidity meter (Hach, USA). The algae were examined naturally or concentrated by centrifuge or nat-ural sedimentation method according to their concentration, and then counted through the observation by phase microscope and Sedwig–Rafter counting chamber method. Turbidity, total organic carbon, algae and temperature of the feed water were 1.13–94.95 NTU, TOC 1.54–3.18 mg/L, algae 280–14,080 No./mL and 14.8–24.6, respectively. Table 2 summa-rizes the details of water quality parameters. It lists the results of a statistical analysis on input parameters in model development. As can be seen, there is large variation in water quality throughout the experimental period.

Fig. 3. Schematic diagram of the pilot system (capacity: 500 m3/day).

T.-M. Hwang et al. / Desalination 249 (2009) 210–221 215

With raw water turbidity varying between 1.13 to 94.95 NTU and algae varying between 280 to 14,080 No./mL, it is clear that the qual-ity of water input has very high variation.

3.3. ANN model establishment

There are two models of ANN applied to this study. One is to establish the ANN model which can predict TMP according to fi ltra-tion time by αc (specifi c cake resistance), and Jc (critical fl ux) is calculated by mathematical model as well as fi ltration time, viscosity and the time period of membrane use. The structure of the ANN used in this study with six input and 14 hidden nodes is shown in Fig. 4(a). The other is to predict the capability of fi ltration as well as membrane fouling speed based on the water quality and other operating condi-tions. The structure of ANN used in this study with six input and eight hidden nodes is shown in Fig. 4(b). MLPs have been adapted to the

simulation of specifi c fl ux and fouling index in a pilot-scale membrane system. We used Kc as a membrane fouling index, which means the cake-resistance when unit volume of raw water was fi ltered by unit area of fi lter [11].

KP A V

c = ( )/( ) ( )/( 0× × × × ×t P A Qμ μ− )

/V A

P, transmembrane pressure (Pa); A, mem-brane area (m2); μ, viscosity (Pa·s); t, fi ltration time (sec); V, volume of permeate (m3); Kc,, cake resistance coeffi cient (m−2); Q0, initial per-meate fl ow (m3/sec).

A total of 3,635 data samples were divided into 2,000 training samples and 1,635 test sam-ples. The training data set is used to build the aggregate model in the recognition stage while the testing data set was applied to checking the performance of the network.

4. Results and discussion

4.1. Critical fl ux tests

The deposition of particles on the membr-ane surface, which are observed in the solution during the fi ltration by membrane separation, is contingent upon the precipitation velocity by driving force from the surface and back trans-port. Theoretically, if back transport is faster than precipitation velocity, the particles are not deposited on the membrane, which leads to no more membrane pollution, and the sta-ble fl ux can be obtained. Critical fl ux means

Table 1Specifi cation of the hollow fi ber membrane

Item Content

Membrane material PVDFModule type Hollow fi berPore size 0.1 μmOperation mode Pressurized typeFiltration mode Constant fl ow rateSurface area 50 m2

Interval of physical cleaning 40 min

Table 2Characteristics of water quality in this study

Items Average Std. Dev. CV Min. Max. Distribution

Turbidity (NTU) 12.01 11.68 97.17 1.13 94.95 GammaTemperature (°C) 20.12 2.56 12.71 14.80 24.60 LogisticTOC (mg/L) 2.21 0.34 15.52 1.54 2.42 LognormalAlgae (No./mL) 3360 2954.6 87.91 280 14080 Weibull

T.-M. Hwang et al. / Desalination 249 (2009) 210–221216

an equilibrium state between forces dragging the particles to the membrane and the forces driving the particles off the membrane. In the equilibrium state, the maximum fl ux can be maintained without membrane pollution. With the back transport and critical fl ux concept in membrane separation process, the membrane fi ltration is explained as follows: if fi ltration fl ux is higher than critical fl ux, the particles will

be deposited on the membrane surface. As the actual precipitation velocity is higher than zero, it forms the cake layer on the surface, and the particle deposition works as fi ltration resistance, which leads to decrease in fl ux. Accordingly, the approaching velocity to the membrane is also decreased by fi ltration dragging force. The process is repeated until the particle-approach-ing velocity to the membrane becomes equal to back transportation, when the particle dep-osition does not occur any more. The fl ux at this point is called steady state fl ux, a kind of critical fl ux. Operation of membrane process below the critical fl ux can prevent membrane pollution, which allows no decline in the fl ux from the beginning. This is the way for effi cient energy use in membrane system operation. In this study, fl ux-step method is used to measure critical infl ux. As shown in Figure 5, with the increasing fl ux conditions, the changes in vari-able such as permeability were analyzed and fi nally found on the point of critical fl ux, where each variable is inclined mostly. The details of Flux-step method are explained in [12]. Based on the Flux step method, critical fl ux was meas-ured in summer and winter, when the summer and water input is characterized as high turbid-ity and low temperature, respectively. It was found that the fl ux was in the ranges around 92–100 LMH in high turbidity and 75–85 LMH in low temperature conditions.

With the result of critical fl ux data ana-lysis by fi ltration model, cake formation model is found most appropriate among other fi ltration models such as standard bloc-k ing, comp lete blocking, and cake formation. Figure 6 shows the comparison between the experimental data under fi ltration fl ux condi-tions and the estimated values calculated by cake formation model. Jc is about 96 LMH in high turbidity season, 85 LMH in low temper-ature season, as calculated by mathematical model based on cake formation theory, and

TMP

Operatingtime

Flowrate

Viscosity

Jc

αc

Bias

binput

binput

b1

b1

Input layer Hidden layer Output layer

Elapsed timeafter CIP

Prediction of TMP

Turbidity

Temp.

TOC

Algae

Flowrate

Operatingtime

Bias

Input layer Hidden layer Output layer

SpecificFlux

FoulingIndex

Prediction of specific flux and fouling index

(a)

(b)

.....

.....

Fig. 4. Architecture of neural networks for simu-lation of TMP, specifi c fl ux and fouling index. (a) Prediction of TMP; 6 input neurons, 12 fi rst hidden layers, 2 second hidden layers, 1 output neuron (b) Prediction of specifi c fl ux and fouling index; 6 input neurons, 8 hidden layers, 2 output neurons.

T.-M. Hwang et al. / Desalination 249 (2009) 210–221 217

α is 5.0 × 1011 kg/m in high turbidity season, 2.5 × 1013 kg/m in low temperature season.

4.2. ANN modeling

While cake fi ltration model, which was analyzed by the critical fl ux test, can provide explanation for membrane fouling mecha-nism, the particular fi ltration theory cannot explain it because membrane pollution, which would occur during membrane fi ltration process, is induced by various simultaneous mechanisms. In the long-term membrane fi l-tration practices, in fact, changes in sensitive variables such as microbial communities and algae would occur at the same time with par-ticles and the changes in operation condition like fi ltration speed. Therefore, it is impossi-ble to fi t membrane fouling characteristics in accordance with a mathematical model only. In order to improve the accuracy of models, Jc and α should be calculated mathematically by fi ltration models based on the fi ltration theory. As the time of operating membrane fi ltration, the module of use, fi ltration speed, and the velocity are set as input parameters, a hybrid model is developed in combination with statistical and mathematical models to predict TMP. With this model, apart from particle conditions, it would be possible to

predict the membrane fi ltration feature, mem-brane fi ltration speed and fi ltration capability simultaneously. Figure 7 shows the compari-son of actual TMPs with calculated TMPs by the hybrid model. With the analysis, mem-brane pollution can be predicted only with α value, which shows the features of cake lay-ered on the membrane surface.

To establish ANN model, turbidity, tem-perature, TOC, fl ow rate, algae and operation time were used as input parameters for the prediction of permeability and fouling index. Figures 8 and 9 show ANN training and pre-dicted data of specifi c fl ux and fouling index in the pilot-scale membrane system. In Figs. 8(a) and 9(a), the experimentally determined spe-cifi c fl ux and fouling index are compared with the simulated data. Figures 8(b) and 9(b) also show the comparison between observed and predicted values according to operating time. As depicted in Figs. 8 and 9, the ANN closely predicted, membrane performance in the pilot-scale study. The performances of ANN model has been evaluated by comparison with the observed results according to operating time. It appeared that the trained ANN pre-dicted fouling index and fl ux decline patterns successfully. The ANN model showed error ranges within ±10% between the simulation and experimental data

Flux (LMH)60 80 100 120 140

Per

mea

bilit

y (L

MH

@ 5

0kP

a, 2

0°C

)

40

60

80

100

Flux (LMH)65 70 75 80 85 90

Per

mea

bilit

y (L

MH

@ 5

0kP

a, 2

0°C

)

0

20

40

60

80

100

120

140

160(a) (b)

Fig. 5. Results of critical fl ux tests. (a) high turbidity season (b) low temperature season.

T.-M. Hwang et al. / Desalination 249 (2009) 210–221218

Fig. 6. Comparison of model predictions with experiments. The symbols represent the experimental data and the curves represent the cake formation model fi ts. (a) high turbidity season (b) low temperature season.

T.-M. Hwang et al. / Desalination 249 (2009) 210–221 219

5. Conclusions

From the study, the conclusion is acquired as follows:

(1) As a mathematical model, we have applied the Hagen–Poiseuille equation and fi ltra-tion models modifi ed with the critical fl ux concept to predict the performance of hol-low fi ber membranes. The analysis of the-

oretical fi ltration models found that cake fi ltration model is the most appropriate, in the cases where Jc and α values can be cal-culated.

(2) With the Jc and α values calculated mathematically by fi ltration model from the long-term operating membrane fi l-tration system, the TMP of membrane fi ltration can be predicted by hybrid model, combination of statistical model such as ANN with fi ltration time, vis-cosity and the time period of membrane use.

(3) Statistical models such as ANN (artifi -cial neural networks) can predict specifi c fl ux as well as membrane fouling simul-taneously according to water quality and operational conditions.

(4) Comparison of model calculations with experimental results revealed that the hybrid model was useful in the evaluation of membrane fouling characteristics. An algorithm for process controller based on the hybrid model was also suggested as an initial step toward an “intelligent” mem-brane system.

Operating time (min)

0 1000 2000 3000 4000 5000 6000 7000

TM

P (

kPa)

40

50

60

70

80

90

100

110experimental data (summer)predicted data (summer) experimental data (winter)predicted data (winter)

Fig. 7. Comparison of actual TMP and predicted TMP using ANN model.

Specific flux_observed data

Spe

cific

flux

_pre

dict

ed d

ata

20

40

60

80

100

120Train N = 2078 Test N = 2819

20 40 60 80 100 12040 60 80 100

Operation day20 40 60 80 100

Spe

cific

flux

(LM

H)

40

50

60

70

80

90

100Observed Predicted

(a) (b)

Fig. 8. ANN evaluation for specifi c fl ux in pilot-scale microfi ltration membrane system. A correlation of experi-mental observations with neural network predictions is given in (a). Panel (b) depicts comparison of observation data with neural network prediction according to operation time.

T.-M. Hwang et al. / Desalination 249 (2009) 210–221220

Acknowledgment

This work was funded by the Eco-STAR pro ject from the Korean Ministry of Environment.

Nomenclature

Di inner diameter of the fi berDo outer diameter of the fi berJc critical fl uxpo atmospheric pressureΔp (x,t) local transmembrane pressureRm membrane resistancet time for fi ltrationx longitude coordinate from the

dead-endαc specifi c cake resistanceη liquid viscosityρp particle density

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Fouling rate_observed data

Fou

ing

rate

_pre

dict

ed d

ata

0

2

4

6

8

10

12Test N = 2448 Test N = 1136

24 6 8 100 2 46 8 10 12

(a)

Operation day20 40 60 80 10

1

2

3

4

5

6

7

8Observed Predicted

F (

1012

m−

2 )

(b)

Fig. 9. ANN evaluation for fouling index in pilot-scale microfi ltration membrane system. A correlation of experi-mental observations with neural network predictions is given in (a). Panel (b) depicts comparison of observation data with neural network prediction according to operation time.

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