INTRODUCTION
Separation and purification processes using membrane technology are gaining popularity in many chemical and food processing as well as in wastewater treating industries. The technology offers several advantages over and above the traditional techniques, including low energy requirement and low temperature operation (Sulaiman et al., 2001). The membrane separation and filtration processes, comprises a continuum of processes designed to separate particles or solute of different sizes by utilization of membranes containing appropriately sized pores (Ohya, 1976). The processes are Microfiltration (MF), Ultrafiltration (UF), Nanofiltration (NF) and Reverse Osmosis (RO) in order of decreasing pore size. A membrane has the ability to transport one component more readily than the other because of differences in physical and/or chemical properties between the membrane and the solute. Transport through the membrane occurs as a result of a driving force (pressure) and the permeation rate (flux), which is proportional to the force.
Meanwhile, this study focuses on UF and its applications in the treatment of water for irrigation purposes using deadend mode because of its relative low energy consumption compared to the crossflow mode (Kennedy et al., 1998; Katsikaris et al., 2005). UF has a pore size of about 0.010.1 μm and thus prevents particles, colloids, microorganisms and dissolved solids that are larger in dimension than the pores in the membrane surface from passing.
Ultrafiltration processes have been widely applied to a variety of fields. More specifically, in the area of industrial wastewater treatment, UF has been applied to tannery wastewaters in order to recycle trivalent chromium (Fabiani et al., 1996; Shaalan et al., 2001) or to remove colour from tannery wastewaters (Alves and De Pinho, 2000) in textile industry as a pretreatment step prior to NF or RO for recycling and reuse of textile wastewaters (Marcucci et al., 2001) in olivemill waster waters in combination with centrifugation for the reduction of organic polluting compounds (Turano et al., 2002) and even in the artificial kidney mechanisms (Serra et al., 1998). Therefore, the great extent of the UF in industrial operations generates the need of a useful tool for determination of membrane performance and indeed the minimization of the operating costs.
Membrane fouling and scaling, a major problem in membrane technologybased
processes, affects the performance of the process and eventually damage the
membranes. This hampers the economic viability for the development and spreading
of the process (Reith and Birkenhead, 1998; Alonso et al., 2001). In
clarification/filtration operations, deposits from fouling create an additional
resistance to mass transfer (Serra et al., 1998). Fouling decrease would
increase permeate flux and so proportionally reduce plant size and/or operating
costs. However, fouling decrease depends on the method of removal such as backwashing,
backflushing and so on. Therefore, there is a need to better understand UF process
in term of the fouling mechanism and backwash effectiveness as it is presented
in this paper. Accurate backwash modelling and optimization is very paramount
to achieving greater backwash effectiveness. Thus reducing fouling.
Backwashing can either be Hydraulic Backwashing (HB) or Chemically Enhanced
Backwashing (CEB) (Cheryan, 1998). During backwash, permeate flows back through
the membrane, lifts off the cake and flushes it out of the module in deadend
mode. Each operating cycle is thus made up of a filtration phase followed by
a backwash phase that allows the membrane to recover its initial properties.
Meanwhile, this method of reversing the membrane properties (hydraulic backwash)
does not lead to 100% recovery due to availability of some particles embedded
within the membrane pores and fibres. To remove this, another form of backwash
called Chemically Enhanced Backwash (CEB) is needed. Therefore, the effectiveness
of cleaning procedures (HB and CEB) plays an important role in the performance
of membranes (Heijman et al., 2007). However, these procedures require
a break in the production process, use of chemicals and consumption of part
of the permeate produced, thus reducing the productivity of the process and
increasing the total operating costs with additional chemical costs, energy
costs and waste water disposal costs.
Therefore to maximize productivity and minimize operating costs in UF, it is necessary to optimize the backwash process. However, optimizing this process depends on availability of accurate models that will adequately explain the interrelationships/interactions among the influencing factors. However, some models have been developed for membrane filtration explaining the mechanisms of fouling especially ultrafiltration (Jaffin et al., 1997; Gaurdix et al., 2004; Heijman et al., 2007). Even Roling (2005) came up with a model which tries to measure the efficiency of CEB considering coagulant concentration dosing, filtration flux and the filtration time in a chemically enhance backwash. Meanwhile, the model is very cumbersome and will require a lot of time for model update as this is necessary since water quality changes periodically.
Nevertheless, studies by Kennedy et al. (1998), Kennedy (2006) and Roling (2005) resulted into identifying coagulant concentration dosing, CEB frequency, filtration time, filtration flux, soak time and backwash flux as factors influencing both hydraulic backwashing and chemically enhanced backwashing. Using physical modeling approach, a good starting point in studying the dynamic and thus optimizing a UF, to formulate an accurate backwash model has a disadvantage of many unknowns which invariably make such models complex. Consequently, the objective of this paper is to provide a methodology to find appropriate backwash models for further insight and optimization of the process. The methodology described in this paper employed empirical modeling approach (Box and Draper, 1987) which makes use of the experimental data with the accommodation of process data in the model if available and the need be.
EXPERIMENTAL DESIGN
This study employed (fractional) factorial designs for the experiments. These designs were adopted because of their relative goodness, as explained by Box and Hunter (Box and Hunter, 1961). A twolevel factorial design was used for HB while this was extended to a star twolevel fractional factorial design for (CEB). The use of the more advanced design for CEB was to reduce the number of experimental runs while still keeping a good coverage of the region around the nominal settings.
MATERIALS AND METHODS
The experiments were performed using SMARTXIGA pilot plant provided by Norit
Membrane Technology, Enscede, The Netherlands (Fig. 1 for
the process flow diagram of the plant and Fig. 4 for the photograph
of the experimental setup) containing an 8inch polyether sulfone (PES) UF
membrane module. The PES is a capillary hollow fibre type with an effective
length of 25 cm and membrane area 0.0754 m^{2} with a total of 120 fibres.
The membrane, which is capable of insideout filtration, was operated in deadend
mode. Chemicals used for CEB were NaOH solution of pH = 12.3 and HCl of pH =
2.3. The coagulant was an acidified solution of FeCl_{3} prepared from
a concentrated solution of FeCl_{3} containing 14 wt% of Fe^{3+}.
The coagulation pump (WATSON MARLOW 323) was calibrated experimentally to accommodate
the desired flow for the inline coagulation according to the experimental design
for the CEB.
For hydraulic backwash, nine experimental runs were performed and the change
in TMP (ΔTMP) in bar was estimated from:

Fig. 1: 
The process flow diagram of the smart XIGA UF pilot plant.
AV = Automatic valve, FT = Flow transmitter, TT = Temperature transmitter,
P1001 = Feed pump, P2001 = Backwash pump, P4001 = Coagulation pump,
CEB1 = Tank containing diluted hydrochloric acid and CEB2 = Tank containing
NaOH solution 

(1) 
Where:
TMP_{f} 
= 
Final transmembrane pressure at the end of filtration, i.e.,
at T_{f} = 20 min, 
TMP_{0} 
= 
Transmembrane pressure of the membrane at the commencement of the filtration. 
Furthermore, the following holds:

(2) 
Where:
t_{f} 
= 
Filtration cycle time (min), 
T_{f} 
= 
Total time for the filtration with time for hydraulic backwash inclusive, 
B_{f} 
= 
Backwash frequency, 
t_{b} 
= 
Backwash time (min). 
The experimental range and coded factors used in the experimentation is presented
in Table 1.
Reversibility of the fouling layer during CEB was estimated according to Roorda
(2004) using:
Table 1: 
Experimental range and coded levels of the three independent
variables for HB 


(3) 
However, R_{h,n} was not easily determined from the experiments because
the CEB rapidly starts immediately after the completion of the specified nth
filtration. Therefore, based on the area observed, 100% effectiveness of the
hydraulic backwash was assumed. The gradient of each filtration cycle (β_{n})
was calculated and averaged. The average value was used in the prediction of
R_{h,n} using the following relationship:

(4) 
Where:
β_{av} 
= 
Average gradient (bar min^{1}) over n1 cycles. 
The raw water used in the experimentation was the same as in the fullscale
plant. Under the given experimental conditions the resistance measured was very
small to the extent that it was difficult to use the values in the model formulation.
However, according to Cheryan (1998), resistance at a constant flux and viscosity
can be expressed as:

(5) 
Where:
R 
= 
Resistance during filtration (m^{1}), 
J 
= 
Filtration flux (l m^{2} h^{1}), 
μ 
= 
Viscosity (Ns m^{2}). 
If μ and J are constant and setting TMP_{hCEB} = TMP_{h,n}
for n = 10, substitution of Eq. 5 in 3 gives:

(6) 
Where:
TMP_{hCEB} 
= 
Transmembrane pressure after the hydraulic backwash before
CEB commences (bar), 
TMP_{CEB} 
= 
Transmembrane pressure after the CEB and TMP_{CEB} the transmembrane
pressure before the start of filtration (bar). Hence from (6) and given
the TMP profile, R_{x} can be calculated. Table 2
gives the experimental range and coded factors used in CEB experimentation. 
Statistical analysis and modelling: For HB the proposed mathematical
relationship between the independent variables and the response is given by:

(7) 
Where:
ΔTMP 
= 
Predicted response, 
ΔTMP_{o} 
= 
Intercept. 
Furthermore, α_{1},... α_{9} denote the regression
coefficients related to linear, quadratic and interaction terms.
For the CEB modelling, we propose the following secondorder polynomial equation:

(8) 
Table 2: 
Experimental range and coded levels of the three independent
variables for CEB 

Where:
R_{x} 
= 
Predicted response, 
R_{xo} 
= 
Intercept, 
α1, ...., α_{10} 
= 
Regression coefficients. 
Validation of the models: In order to determine the accuracy of the
models, additional experimental runs were designed and performed at constant
operating conditions. Crossvalidation and ANOVA analysis (Daniel, 1977) were
then carried out to further establish the validity of the models.
RESULTS
Modelling: The results obtained from the experiments were analysed and the regression coefficients calculated using ordinary leastsquares estimation. As a result of this the following regression equations (with standard deviations of the estimated coefficients) are obtained
HB:

(9) 
CEB:

(10) 
Equation 9 reveals that backwash flux (J_{b}) has
no effect at all on ΔTMP and thus allowing a significant model reduction
when compared with Eq. 7. Furthermore, taking into account
the standard deviation of the estimation errors, only B_{f} has a pronounced
effect on ΔTMP. However, this may be different when the same experimental
design is performed under different process conditions. Also, Eq.
10 excludes some terms, in particular the term with the squared filtration
time and the interaction of the three influencing factors considered as suggested
in Eq. 8.

Fig. 2: 
Response surface (plus data points) and contour plot for HB 
Table 3: 
Measured and predicted ΔTMP from the HB experiments using
a 2^{3} factorial design 

*: see Table 1 for coded levels 
Notice furthermore from Eq. 10 that the effect of t_{f}
is questionable anyway. The HB regression model has a Mean Square Error (MSE)
of 2.475x10^{5}, while for the CEB regression model this was estimated
to be 3.812. These values are the lowest among a large set of possible model
candidates, which are obtained by setting one or more α’s in Eq.
8 to zero. The measured responses and the model output responses obtained
for HB and CEB are presented in Table 3 and 4,
respectively.

Fig. 3: 
Response surface (plus data points) and contour plot for CEB
at t_{f} = 62.5 min 
Table 4: 
Measured and predicted R_{x} from the CEB experiments
using a fractional factorial 2^{3} + star design 

Graphical interpretation: Figure 2 show the response
surface and contour plot for the HB model Eq. 9 and Fig.
3 shows it for the CEB model Eq. 10. However, to understand
the relationship among the influencing factors in CEB and given that t_{f}
has very little effect, the model was evaluated at a fixed value of t_{f}.
To allow a response surface analysis of the full model with three factors, which
cannot be done graphically, Eq. 10 is written in vectormatrix
notation,

(11) 
Where:
Substituting the estimated coefficients of Eq. 10 and performing
eigenvalue decomposition, i.e., h = VDV^{T} with V^{T}V = VV^{T}
= I (identity matrix) and D a diagonal matrix gives:
These matrices indicate the shape and orientation of ellipsoidal contours (Abusam
et al., 2001) for further explanation of ellipsoidal analysis). As a
result of this, dominant directions on the response surface can be found. For
instance, the first eigenvector (first column of V) with large corresponding
eigenvalue D_{11} indicate a clear valley, more or less aligned with
the axis of J_{f}. This is also confirmed by considering the third eigenvector
and eigenvalue. Notice that, after equal scaling of the axis, this valley is
also clearly visible in Fig. 3. The second eigenvector and
eigenvalue indicate that t_{f} does not induce a curvature in the response
surface.
In addition to this response surface analysis in higher dimensions, it is also
possible to estimate extrema of the response surface, indicating optimal process
conditions. For the CEB the optimum is given by:

(12) 
Clearly, these steady state values are unrealistic and out of the applicability
region. However, from Fig. 3 one can readily observe that
approximately all linear combinations of J_{f }and C_{c} on
the 100%contour give an appropriate result in terms of R_{x}.

Fig. 4: 
Picture of the SMARTXIGA pilot plant used for experimentation 
Table 5: 
Results of model validation for HB using again the
2^{3} factorial design 

*: see Table 1 for coded levels 
Table 6: 
Result of model validation for CEB using the complementary
fractional factorial 2^{3} design 

Validation of models: Table 5 and 6
present the results of crossvalidation of the models. Table 5
shows that the predicted ΔTMP_{p} agrees fairly with the estimated
R_{x} from the experimental data (MSE 0.18) and thus confirming the
validity of the model. Also, Table 6 shows that the predicted
reversibility R_{xp} and the estimated R_{x} are in fair agreement,
with MSE 5.802.
In addition the ANOVA analysis of the two models presented in Table
7 and 8 shows F_{0.995 }= 18.63 for HB model and
F_{0.995} = 16.24 for CEB while their variance ratios (VR) are 0.001856
and 0.003278, respectively. According to Daniel (1977), since the VR values
for both models are much more less that their respective F values, then this
indicates that the models are reliable to explain the relationships investigated
with the properly designed experiments.
Table 7: 
ANOVA analysis for HB model 

Table 8: 
ANOVA analysis for CEB model 

Hence, there is a clear indication that the models are valid in the region
of our nominal working points.
DISCUSSION
Small data sets: Depending on the process conditions, an individual
experimental run can take several hours to more than one day. Hence, effective
experimental designs must be chosen and thus usually small data sets are obtained.
In our application on the influencing factors related to HB, 9 experimental
runs (Table 1) were performed, while the number of regression
coefficients is 5 (Eq. 9). Consequently, the error characteristics
and especially the autocorrelation of the residuals, are difficult to evaluate
and thus the standard deviations presented in Eq. 9 are only
rough indications. As an alternative to the stochastic approach and most appropriate
to small data sets, in the past a socalled setmembership or boundederror
approach has been proposed. In this approach it is assumed that the measurement
error is bounded, so that effectively at each sample instant only intervals
are considered instead of single points. For a full treatment of this approach
we refer to e.g., (Walter, 2002; Norton, 2002; Keesman, 2002). In particular,
for the linear estimation case exact solutions can be found. These exact solutions
can be tightly bounded by boxes, which can be found by solving a couple of LP
problems. Assuming an error bound on ΔTMP of 0.005; the following bounded
(interval) estimates of the coefficients in Eq. 9 are found
and presented in the second row of Table 9.
If the error bound is chosen too small no feasible solution will be found.
Hence, there exists a minimum error bound for which the interval estimates reduce
to a single point. This point estimate is called the minmax estimate. For our
application, the minmax estimate of the coefficients is presented in the third
row of Table 9. Notice that these minmax estimates are not
too far from the leastsquares estimates. The essence of this boundederror
approach is that now reliable uncertainty regions around the estimates are found.
Similar results have been found for the CEB case, but not presented here. Just
notice that for the CEB model only 11 experimental runs, using a fractional
factorial + star design, were performed while potentially for the secondorder
regression model Eq. 8, 10 coefficients
were estimated.
Table 9: 
Boundederror estimation results for HB 

Consequently, 11 experimental runs are about the minimum, resulting in relatively
high estimation errors. Nevertheless, the four crossvalidation experiments
(Table 6) indicate that the resulting CEB model (10)
is reliable.
Prior physical knowledge: Notice from the contour plot of Fig.
2 that the model predicts a small decrease of ΔTMP when B_{f}
is smaller than 2.5. This is a rather unlikely phenomenon. If there is sufficient
evidence that the maximum should be at B_{f} = 2, then this information
can be easily incorporate into the empirical modelling approach.
where the derivative can be easily found from Eq. 9, leads
to the following constraint between α_{2} and α_{3}:
α_{2} + 2α_{3} B_{f} = 0, so that α_{2}
= 4α_{3}. Hence, after substitution of this relationship, the
model structure of Eq. 9 becomes:

(13) 
in which the coefficients have to be reestimated.
Hydraulic backwashing modelling: In Fig. 2 as the
t_{b} increases, the ΔTMP linearly decreases. It can be explained
that the longer the time for backwashing, the lower the change in the TMP. This
shows a good removal of the fouled layer. Meanwhile, it is expected that for
t_{b} →0, ΔTMP will become very high, indicating a hyperbolic
relationship. Notice, however, that the experimental data (Table
3, 5) only support a linear relationship. Therefore, most
likely the relationship between ΔTMP and t_{b} is inverse proportionality.
However, this can only be verified through additional experimental runs to get
more data points beyond the region considered in this study. Nevertheless, this
is in agreement with the findings of earlier research (Roling, 2005; Kennedy
et al., 1998; Kennedy, 2006; Delgado et al., 2004).
Figure 2 also shows that as the backwash frequency B_{f}
increases from 2 to 4, ΔTMP decreases quadratically with increase of B_{f}.
It can be explained that at low frequencies, there is more formation of cake
layer than can be removed with backwash. But as the frequency increases, the
cake layer is washed off the membrane. Thus restoring the original property
of the membrane. Therefore, the model shows that the higher the number of frequency
of hydraulic backwash, the lower the ΔTMP. Thus the higher the rate of
recovery of the flux.
Chemical enhanced backwashing modelling: First of all, it is good to
notice that 0 ≥ R_{x} ≥ 100. Figure 3 describes
that the reversibility decreases nonlinearly with an increase in the coagulant
concentration dosing but increases nonlinearly (almost linear) with an increase
in the filtration flux. The decrease with respect to increased coagulant concentration
dosing can be attributed to the more deposited particles as a result of coagulation
action on the membrane. Thus providing more particles for possible blockage
of the pores which is in tune with explanation of fouling mechanism in the studies
of previous researchers Jaffin et al. (1997) and Gaurdix et al.
(2004). In addition to this, the increase of R_{x} as a result
of an increase in the filtration flux can be attributed to the fewer blockages
of the membrane pores by the cake/coagulated particles as a result of high filtration
flux. Thus making CEB more effective.
CONCLUSIONS
In this study, models for hydraulic backwashing and chemically enhanced backwashing have been developed and cross validated using an empirical modelling approach, in particular the Response Surface Methodology (RSM) (Box and Draper, 1987). The modelling was based on experimental data from the SMARTXIGA pilot plant, using modified factorial designs to limit the number of experimental runs, with the aim to study the full behaviour and the possibilities for optimization of UF plants. Crossvalidation and ANOVA analysis led to the conclusion that the models are reliable under the given experimental conditions. The models showed that HB is largely influenced by backwash time and backwash frequency with backwash flux having no effect. The CEB depends largely on the coagulant concentration dosing and the filtration flux and not so much on the filtration time. For further implementation in practice, due to changes in e.g., the feed water quality, a regular update of the models is necessary and can be easily obtained using the methodology presented in this study.
ACKNOWLEDGMENTS
We want to acknowledge WMD/WLN and NORIT Membrane Technology situated in The
Netherlands for the opportunity given and support in cash and kind in carrying
out this study successfully.
NOMENCLATURE
B_{f} 
= 
Backwash frequency. 
C_{c} 
= 
Coagulant concentration closing (ppm). 
CEB 
= 
Chemically enhanced backwash. 
HB 
= 
Hydraulic backwash. 
J_{b} 
= 
Backward flux (l m^{2} h^{1}). 
J_{f} 
= 
Filtration flux (l m^{2} h^{1}). 
MSE 
= 
Mean square error. 
n 
= 
No. of filtration cycle before CEB. 
R_{CEB} 
= 
Resistance of the membrane after CEB (m^{1}). 
R_{h,n} 
= 
Resistance after hydraulic backwash at the end of n filtration cycle (m^{1}). 
R_{o} 
= 
Initial resistance of the membrane before filtration (m^{1}). 
ΔR_{fo} 
= 
Resistance of fouling layer after UF of feed water without cleaning (m^{1}). 
R_{x} 
= 
Reversibility of the fouling layer as a function of the cleaning procedure
(%). 
t_{b} 
= 
Backwash time (min). 
t_{f} 
= 
Filtration time (min). 
TMp_{f} 
= 
Transmembrane pressure at the end of the n filtration cycle (bar). 
TMP_{hCEB} 
= 
Transmembrane pressure after the hydraulic backwash before CEB commences
(bar). 
TMP_{o} 
= 
Initial TMP before UF (bar). 
ΔTMP 
= 
Change in transmembrane pressure (bar). 
α_{i} 
= 
Coefficient in secondorder regression model 
β_{av} 
= 
Average gradient (bar min^{1}). 
μ 
= 
Dynamic viscosity (Nsm^{2}). 
SSTR 
= 
Treatment sum of squares. 
VR 
= 
Variance ratio. 
MSTR 
= 
Treatment mean squares. 
SST 
= 
Total sum of squares. 
SSE 
= 
Error sum of squares. 
SS 
= 
Sum of squares. 
MS 
= 
Mean squares. 
d_{f} 
= 
Degree of freedom. 