1 © IWA Publishing 2014 Water Science & Technology | in press | 2014

Uncorrected Proof

Deposit membrane fouling: influence of specific cake

layer resistance and tangential shear stresses

A. Charfi, J. Harmand, N. Ben Amar, A. Grasmick and M. Heran

ABSTRACT

Cake fouling is the leading cause of membrane permeability decrease when filtering mixed liquor

suspension containing high suspended solid concentrations. A simple model is proposed to simulate

the cake resistance evolution with time by considering a macro-scale fouling only linked to the

accumulation of particles on the membrane surface. This accumulation appears as the difference

between the flux of deposited particles due to the filtration and the flux of particles detached from

the membrane surface due to the tangential shear stresses caused by, recirculation flow in

sidestream membrane bioreactor (MBR) or gas sparging close to the membrane surface for

submerged MBR configuration. Two determining parameters were then highlighted: the specific cake

resistance and the ‘shear parameter’. Based on these parameters it is possible to predict model

outputs as cake resistance and permeate flux evolution for short-time filtration periods.

doi: 10.2166/wst.2014.186

A. Charfi (corresponding author)A. GrasmickM. HeranInstitut Européen des Membranes (IEM),Université Montpellier 2, place Eugene Bataillon,

CC05, 34095 Montpellier, FranceE-mail: amine.charfi@ymail.com

A. CharfiN. Ben AmarLaboratoire de Modélisation Mathématique et

Numérique dans les Sciencesde l’Ingénieur, ENIT, B. P 37 Le Belvédère 1002

Tunis, TunisiaandInstitut National des Sciences Appliquées et de

Technologie,B. P. 676, 1080 Tunis Cedex, Tunisia

J. HarmandLaboratoire de Biotechnologie de l’Environnement,

INRA, UR0050, Avenue des étangs,11100 Narbonne, FranceandMODEMIC Research Group,INRIA, Laboratoire de Mathématiques,Informatique et Statistique pour l’Environnement

et l’Agronomie-INRA,2 Place Viala, 34060 Montpellier, France

Key words | cake formation, membrane fouling modelling, specific cake resistance, tangential shear

stresses

NOMENCLATURE INTRODUCTION

macc

Specific mass of accumulated cake (g/m2)

macc,lim

Maximum specific mass of accumulated cake

(g/m2)

min

Specific mass of particles approaching the mem-

brane surface (g/m2)

mout

Specific mass of particles removed from the mem-

brane by shear forces (g/m2)

X

Total suspended solids concentration (gTSS/L)

Jp

Permeate flux (Lm�2 h�1)

TMP

Trans-membrane pressure (Pa)

μ

Dynamic viscosity (Pa s)

R0

Clean membrane resistance (m�1)

Rc

Cake resistance (m�1)

J0

Initial permeate flux (Lm�2 h�1)

β

Shear parameter (kg�1)

α

Specific cake resistance (mk g�1)

Rc,max

Resistance at steady state (m�1)

Jp,end

Permeate flux at steady state (Lm�2 h�1)

Many studies have tried to model fouling in membrane pro-cesses. Many are based on the four basic foulingmechanisms introduced by Hermia () namely cake foul-ing, pore constriction, complete blocking, and intermediate

blocking. Despite being established for dead-end filtrationat constant pressure, these models have been also used forcross-flow filtration (Ho & Sung ; Charfi et al. ) orhave been adapted to cross-flow filtration (Field et al. )by taking into account the role of shear forces to eliminateparticle deposition on the membrane surface (De Bruijn

et al. ). More realistic models are also presented whenconsidering simultaneous fouling mechanisms; whileBolton et al. () combined Hermia’s models, Wu et al.() established a model considering simultaneouslythree fouling mechanisms namely pore constriction, poreblockage, and cake filtration associated to soluble, colloidaland suspended activated sludge components, respectively.

Abdelrasoul et al. () considered the probability of par-ticle deposition on the membrane surface or on another

Q1

2 A. Charfi et al. | Deposit membrane fouling Water Science & Technology | in press | 2014

Uncorrected Proof

particle to predict the mass of particles accumulated on

membrane surface, on membrane pores and inside pores.Other authors considered the resistance in series model

based on Darcy’s law in which the resistance term is the

sum of resistances associated to the membrane, the internalclogging and the cake deposit (Song ; Ho & Zydney; Kuberkar&Davis ; Katsoufidou et al. ). A con-centration polarization resistance term was also proposed

(Choi et al. ). An adsorption resistance term could bealso insertedwhen affinity is important between effluent com-ponents and membrane material (Bhattacharjee &

Bhattacharya ; Vela et al. ). Li & Wang (), con-sidered the uneven shear stress on membrane surfaceleading to uneven cake deposit and modelled fouling based

on biomass attachment and detachment. Many studies arebased onto the critical flux approach proposed by Fieldet al. () who assume that avoiding membrane foulingwould be possible if working under a so-called critical flux

for which no trans-membrane pressure (TMP) increase isdetected. However, even in sub-critical flux operation, atwo-step TMP increase would be observed. Ognier et al.() proposed a model describing TMP increase assumingthat a progressive pore blocking would lead to a local fluxincrease and consequently to membrane fouling increase.

In front of the difficulty to model so complex interactionbetween suspension components and membrane structureand its associated dynamic layers formed by accumulation

of compounds closed to the membrane surface, it wasdecided to propose a simple model of membrane foulingby defining parameters in link with tangential shear stresses.Such a simple model is proposed in this work. Considering

mainly the case of filtration of activated sludge suspensions,the main fouling mechanism in this model is supposed to becake formation due to compound accumulation onto the

membrane surface during filtration (Charfi et al. ). Thiskind of model is typically intended to complete those devel-oped for bioprocess control design such as the AM2b

proposed by Benyahia et al. () for AnMBRs. Such amodel is proposed hereafter.

MATERIAL AND METHODS

A cross flow filtration set up (Membralox) was used. Mem-

branes used were mono-tubular ceramic membranes withan area of 55 cm2 and pore sizes of 0.8, 0.05, and 0.02 μm.Temperature was maintained at 37 WC by thermostatic bath.

Experiments of 80 min were conducted under a constantTMP of 0.5 bar and with a recirculation velocity of 1.7 m/s.

No cleaning operations have been applied during exper-

iments. Nevertheless membranes were cleaned chemicallyafter each experiment. The influents were digestate effluentsextracted from two different anaerobic digesters treating

both agricultural wastes. It was either directly filtrated (rawdigestate) or pre-treated by centrifugation (Dig A and Dig B)for 15 min under a relative centrifugation force of 2,500 g.

THE CAKE MODEL

Model development

In this section, the assumed hypotheses are presented and

mass balances are established to develop the basic relationsof the model.

Hypothesis

The size of particles present in the suspension is supposedlarger than the membrane pores. Given that particles are

totally retained by the membrane barrier, it is then assumedthat membrane fouling is only due to particular accumu-lation on membrane surface. The only fouling mechanismconsidered is cake formation. Considering a constant TMP

conditions, the membrane fouling would be described bypermeate flux decrease according to the hydraulic resistanceincrease with time (Darcy’s law).

Mass balance

The establishment of mass balance on the membrane surface(Equation (1)) should allow the determination of the accumu-lated cake massmacc per membrane surface unit at time t andits corresponding influence on permeate flux decline. During

a short period of filtration dt, the specific mass dmacc of par-ticles accumulated can be estimated as the differencebetween the specific mass dmin of particles carried on to

the membrane surface by permeation forces during filtrationand the mass dmout of particles dragged away from the mem-brane surface by shear forces due to tangential flow:

dmacc=dt ¼ dmin=dt� dmout=dt (1)

At time t, the specific mass brought by filtration is con-sidered as proportional to the concentration X of

suspended solid (supposed as a constant value) and to theflux of permeation, as shown in (Equation (2)) where Jp is

3 A. Charfi et al. | Deposit membrane fouling Water Science & Technology | in press | 2014

Uncorrected Proof

the specific permeate flux at time t:

dmin

dt¼ X:Jp (2)

The detached specific mass of particle within a shortperiod of time due to parietal shear stresses is assumed to be

proportional to (i) the specific mass macc of particle accumu-lated at time t (supposed proportional to the instantaneouscake thickness), and (ii) the specific flux of particles broughtto membrane surface by permeation dmin/dt (Equation (3)).

This relation is based on the following assumptions, (i) whenmacc is low, the detachment is weak, and (ii) when macc hasreached its maximal value (corresponding to the laminar

boundary layer thickness), the detachedflux is equal to the par-ticle flux coming onto the membrane surface due to filtration.In this relation, β appears as a coefficient representing the

capacity of parietal shear stresses to detachdeposited particles:

dmout

dt¼ dmin

dt:

macc

macc, lim¼ β

dmin

dt:macc (3)

In relation 3, macc,lim is supposed an inverse function of localshear stresses, expressed through the criterion β (with β¼ 1/macc,lim). The variation of the accumulated particle mass per

membrane surface unit is then expressed by Equation (4).

dmacc

dt¼ XJp 1� βmaccð Þ (4)

To describe the permeate flux Jp, a resistance in series modelbased on Darcy’s law is used (Equation (5))

Jp ¼ TMPμ R0 þ Rcð Þ (5)

with TMP is the trans-membrane pressure, μ is the dynamic vis-cosity of permeate, R0 is the clean membrane resistance, andRc is the cake resistance.Rc andR0 are expressed in Equations

(6) and (7), respectively.

Rc ¼ αmacc (6)

R0 ¼ TMPμJ0

(7)

with α and J0 are the specific resistance of the cake deposit andthe initial permeate flux obtained with the clean membrane,respectively.

Equations (4) and (8) show the basic relation of the cake

model finally obtained. Two parameters are then identifiedas α and β. Their knowledge allow the simulation of the evol-ution of the specific cake mass in the studied system, the

value of the cake resistance and the evolution of the perme-ate flux with time.

dmacc

dt¼ XJp 1� βmaccð Þ

Jp(t) ¼ TMPTMPJ0

þ αmacc(t)� �

8>>>><>>>>:

(8)

Numerical simulation

Parameter values were determined using the experimentaldata by the least square method programmed with matlabR2008b.

Qualitative behaviour

A preliminary study of the qualitative model behaviour was

conducted. Numerical simulations (Figure 1) confirm a cakemass increasing evolution with time till reaching a stationaryvalue corresponding to an equilibrium between accumulation

of particles due to filtration and their detachment due to parie-tal shear stresses, this phenomenon induces a permeate fluxdecreasing with time till reaching a stationary value.

α increasing induces a decrease of permeate flux and an

increase of cake resistance. β increasing induces an increaseof permeate flux which reaches more quickly its stationaryvalue and a decrease of the deposit mass and cake

resistance.

Model predictions of the stationary conditions

Figure 2 gives an illustration of the influence of α and β par-ameters on two practical keys variables Rc,max and Jp,endwhich represent the stationary values obtained at the equili-

brium between deposition and detachment of particles onthe membrane surface.

Figure 2 clearly points out the following points: (i) whenα is low (<1013 m/kg), the cake resistance appears low and

it is not necessary to develop high shear stresses to maintaina high level of permeate flux, and (ii) in opposite when α ishigh (>1014m/kg), the influence of β is evident but its effi-

ciency could be rapidly limited for very high α valuesexcept by combining parietal shear stresses and other ways

Figure 2 | Obtained cake resistance and permeate flux when varying the parameters α and β.

Figure 1 | Model simulations of macc and Jp evolutions with time (α1¼ 1013, α2¼ 1014mkg�1, and β1¼ 10, β2¼ 400 kg�1).

4 A. Charfi et al. | Deposit membrane fouling Water Science & Technology | in press | 2014

Uncorrected Proof

of surface cleaning (relaxation period or back-flushing forexample).

To study their effect on the model out-put, a sensitivity

study of the parameters: the specific cake resistance α

(mkg�1) and the shear parameter β (kg�1), is conducted.The variations of parameters α and β leads to a consider-

able variation of the cake resistance and the permeate flux atstationary phase noted Rc,max and Jp,end. These outputs aresensitive to parameters α and β which should be well opti-

mized to control the system.

Parameters identification and model validation

Parameters identification

The two model parameters, specific cake resistance α

(mkg�1) and shear parameter β (kg�1), are hard to be accu-rately determined experimentally.

Two approaches have been developed. The former hasconsidered the experimental measurement of α by a specificdead-end mode filtration and β was obtained by adjustment

of simulated stationary Jp value with experimental data. Thesecond has considered a global simulation, the optimal par-ameter values were obtained by least squares method when

comparing experimental data and simulation of Jp evolutionversus time (Equation (8)).

Figure 3(a), represents the Jp evolutions obtained (i)

experimentally when filtering an effluent from an anaerobicdigester with a MF membrane (0.8 μm), (ii) by simulation(S1) carried out by using α measured by dead-end filtration,and (iii) by simulation (S2) when α and β were directly cal-

culated by global simulation.It is clearly obvious that the simulation taking into

account the experimental value of α measured in dead-end

filtration (1015m/kg) did not allow the representation ofthe evolution of Jp even when choosing very high value of

Figure 3 | Simulation and experimental data: (a) centrifuged digestate (Dig A) filtered using membrane (0.8 μm), and (b, c and d) raw digestate filtered with membrane pore sizes: 0.05,

0.02, and 0.8 μm, respectively.

5 A. Charfi et al. | Deposit membrane fouling Water Science & Technology | in press | 2014

Uncorrected Proof

β (more than 104 kg�1). This point confirms the fact that the

deposit obtained in tangential mode has not the samecharacteristics notably in term of specific hydraulic resist-ance (Gasmi ). Despite the fact that shear forces is

supposed dragging out the biggest particles and formingdenser cake deposit, the specific cake resistance of suchdeposit obtained in tangential mode appears lower than

when working in dead-end mode that quickly generates animportant accumulation of matter presenting a very highspecific hydraulic resistance.

In opposite, the global approach of simulation madepossible the determination of α and β values with a qualitat-ively good fitting to the experimental data.

Evaluation of the model

To evaluate the model, three sets of experimental data have

been considered, these data were obtained while filteringunder the same operating conditions (same shear stress

conditions) the same anaerobic digestate (raw digestate) by

means of three different membrane pore sizes (0.8, 0.05and 0.02 μm).

When filtering, an important decrease of permeate flux

was observed (Figures 3(a)–3(d)), due to a quick build-up ofdeposit on the membrane surface in accordance with thehigh concentration of suspended solids (≈40 g/L) in the

suspension, as indicated by Ho & Sung (). Accordingto the filtering conditions (same shear stress, and same sus-pension) the formed cake could have similar characteristics

(even if the smallest cut-off should retain smallest com-pounds). When fitting the model with data obtained usingthe 0.05 μm membrane (Figure 3(b)), the parametersvalues found were α¼ 5.84 × 1013mkg�1 and β¼ 237 kg�1.

Using these values for the two other experiments(0.02 μm in Figure 3(c) and 0.8 μm in Figure 3(d)), theobtained simulated curves give a qualitatively good rep-

resentation of Jp evolutions versus time, however, a spacebetween model and experimental data can be observed at

Table 1 | Cake model parameters optimized values

Effluent Membrane pore size (μm) gTSS/L α β Least squares R2

Dig A 0.8 4 0.13 × 1014 258.25 4.88 × 10�10 0.97

Dig A 0.02 4 1.83 × 1014 263.42 5.06 × 10�10 0.85

Dig B 0.8 4 0.88 × 1014 265.44 6.05 × 10�10 0.87

Dig B 0.02 4 3.37 × 1014 281.12 2.49 × 10�10 0.87

6 A. Charfi et al. | Deposit membrane fouling Water Science & Technology | in press | 2014

Uncorrected Proof

the end of experiment (coefficient of determination R2 ofalmost 80%). Nevertheless, as this model should allow

the development of a tool optimizing the washing pro-cedure of membrane during operation, including notablybackwashing, it is considered that the model is able to

give a good illustration of the cake formation and a suffi-cient accuracy of its specific resistance during the first10–20 min of each filtration cycle.

Table 1 gives other examples of values of α and β

obtained with the same two liquid phases after centrifu-gation (Dig A and Dig B), the new obtained liquid phasescontained lower suspended solids concentration (4 g/L

instead of 40 g/L).Because the filtrations were carried out in the same shear

stresses conditions, β values obtained by simulation are very

close for the four experiments. The new specific cake resist-ances appeared only slightly higher proving the determiningrole of the smallest particles remained in the centrifuged sus-

pension on cake resistance. Moreover α obtained for the UFmembrane (0.02 μm) appears notably higher than the valueobtained with MF membrane (0.8 μm). In fact, the digestatecentrifugation kept only small particles in liquid phase, then

the membrane cut-off played an important role for small par-ticles selectivity, deposit structuring, and dominantmembrane fouling mechanisms.

It can be noticed that the values obtained for α, aresatisfying regarding to the values mentioned in literature(Lin et al. ). Nevertheless, as shown in Figure 3 and

described in literature, the hydraulic resistance due tocompounds accumulation onto the membrane surfacecontinuously increases with time due to fouling deterio-

ration including biofilm development, pore blocking andadsorption which should be incorporated to completethis model.

CONCLUSION

A simple model is proposed to describe tangential filtrationof anaerobic digestate suspension where cake layer deposit

is the dominant fouling mechanism. The development ofthe proposed model equations let appear two determining

parameters, one is represented by the specific resistance α

of the cake deposit, while the second one, β represents theinfluence of parietal shear stresses on the limitation of the

cake development on the membrane surface. Model simu-lations confirm the determining role of α and β.Comparisons between experimental data and simulations

confirm the interest of such a simple model to determinethe specific cake resistance in a cross flow filtration modefor which it is hard to quantify experimentally α and β dueto the difficulty to observe in line the cake layer structuring

and quantify the shear stress intensity close to the mem-brane surface.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the financialsupport of the French National Research Agency(ANR–Fisscarden), notably the TREASURE Euromedresearch network and the competitiveness cluster TRIMA-

TEC, as well as the PHC UTIQUE project No. 13G1120.

REFERENCES

Abdelrasoul, A., Doan, H. & Lohi, A. A mechanistic modelfor ultrafiltration membrane fouling by latex. Journal ofMembrane Science 433, 88–99.

Benyahia, B., Sari, T., Cherki, B. & Harmand, J. Anaerobicmembrane BioReactor modeling in the presence of solublemicrobial products (SMP) – the anaerobic model AM2b.Chemical Engineering Journal 228, 2011–2022.

Bhattacharjee, S. & Bhattacharya, P. K. Flux declinebehaviour with low molecular weight solutes duringultrafiltration in an unstirred batch cell. Journal of MembraneScience 72, 149–161.

Bolton, G. R., Boesch, A. W. & Lazzara, M. J. The effects offlow rate on membrane capacity: development andapplication of adsorptive membrane fouling models. Journalof Membrane Science 279, 625–634.

7 A. Charfi et al. | Deposit membrane fouling Water Science & Technology | in press | 2014

Uncorrected Proof

Charfi, A., Ben Amar, N. & Harmand, J. Analysis of foulingmechanisms in anaerobic membrane bioreactors. WaterResearch 46, 2637–2650.

Choi, S. W., Yoon, J. Y., Haam, S., Jung, J. K., Kim, J. H. & Kim,W. S. Modeling of the permeate flux duringmicrofiltration of BSA-adsorbed microspheres in a stirredcell. Journal of Colloid and Interface Science 228, 270–278.

De Bruijn, J. P. F., Salazar, F. & Borquez, R. Membraneblocking in ultrafiltration a new approach to fouling. Foodand Bioproducts Processing 83, 211–219.

Field, R. W., Wu, D., Howell, J. A. & Gupta, B. B. Critical fluxconcept for microfiltration fouling. Journal of MembraneScience 100, 259–272.

Gasmi, A. Intérêt d’un bioréacteur à membranes immergéespour le traitement de la pollution azotée dans une uséecarencée en matière organique. PhD thesis, UniversitéMontpellier2.

Hermia, J. Constant pressure blocking filtration laws-application to power law non-Newtonian fluids. TransactionsIChemE 60, 183–187.

Ho, C. C. & Zydney, A. L. A combined pore blockage andcake filtration model for protein fouling during microfiltration.Journal of Colloid and Interface Science 232, 389–399.

Ho, J. & Sung, S. Effects of solid concentrations and cross-flow hydrodynamics on microfiltration of anaerobic sludge.Journal of Membrane Science 345, 142–147.

Katsoufidou, K., Yiantsios, S. G. & Karabelas, A. J. A study ofultrafiltration membrane fouling by humic acids and, flux

recovery by backwashing: experiments and modeling.Journal of Membrane Science 266, 40–50.

Kuberkar, V. T. & Davis, R. H. Modeling of fouling reductionby secondary membranes. Journal of Membrane Science 168,243–258.

Li, X. Y. & Wang, X. M. Modelling of membrane fouling in asubmerged membrane bioreactor. Journal of MembraneScience 278, 151–161.

Lin, H., Liao, B. Q., Chen, J., Gao, W., Wang, L., Wang, F. & Lu,X. New insights into membrane fouling in a submergedanaerobic membrane bioreactor based on characterization ofcake sludge and bulk sludge. Bioresource Technology 102,2373–2379.

Ognier, S.,Wisniewski, C.&Grasmick,A. Membranebioreactorfouling in sub-critical filtration conditions: a local critical fluxconcept. Journal of Membrane Science 229, 171–177.

Song, L. Flux decline in crossflow microfiltration andultrafiltration: mechanisms and modeling of membranefouling. Journal of Membrane Science 139, 183–200.

Vela, M. C. V., Blanco, S. A., Garcia, J. L., Gozalvez-Zafrilla, J. M.& Rodriguez, E. B. Modelling of flux decline incrossflow ultrafiltration of macromolecules: comparisonbetween predicted and experimental results. Desalination204, 328–334.

Wu, J., He, C., Jiang, X. & Zhang, M. Modeling of thesubmerged membrane bioreactor fouling by the combinedpore constriction, pore blockage and cake formationmechanisms. Desalination 279, 127–134.

First received 17 September 2013; accepted in revised form 7 April 2014. Available online 22 April 2014

Author QueriesJournal: Water Science & Technology

Manuscript: WST-EM131026R3

Q1 Please expand AM2b and AnMBRs