Modelling of a membrane bioreactor system for municipal wastewater treatment

Journal of Membrane Science 216 (2003) 55–65

Modelling of a membrane bioreactor system formunicipal wastewater treatment

T. Wintgensa,∗, J. Rosena, T. Melina, C. Brepolsb, K. Drenslab, N. Engelhardtba Department of Chemical Engineering, Institut für Verfahrenstechnik, Rheinisch-Westfälische Technische

Hochschule Aachen, Turmstrasse 46, 52056 Aachen, Germanyb Erftverband, Bergheim, Germany

Received 3 May 2002; received in revised form 14 January 2003; accepted 16 January 2003

Abstract

Within the presented study a model to describe the filtration performance of submerged capillary hollow fibre modules inmembrane bioreactor applications for wastewater treatment was developed. The model was implemented in a software platformfor simulation and calibrated using operating data of the full-scale municipal wastewater treatment plant Rödingen, which isoperated by the Erft River Association (Erftverband) and equipped with activated sludge treatment and microfiltration unitsfor biomass retention. Mathematical expressions for filtration resistances like cake layer forming and fouling are presented andcombined with an activated sludge model (ASM) to describe the biological treatment processes. The model proved successfulin simulating the long-term decrease in permeability of the membranes and the final effluent quality in terms of standardparameters.© 2003 Elsevier Science B.V. All rights reserved.

Keywords:Membrane bioreactor; Wastewater treatment; Fouling model; Microfiltration; Simulation

1. Introduction

Membrane bioreactor systems are increasinglyapplied for municipal wastewater treatment, withsubmerged membrane units featuring rather lowtrans-membrane pressure (TMP) differences andfeed-sided air pulsing predominantly being employed.The combination of activated sludge units and mem-brane filtration for biomass retention generally resultsin high effluent qualities and compact plant configu-rations. While investment costs are already lower thanfor conventional wastewater treatment plants withsecondary clarification, operating costs are still higher

∗ Corresponding author. Tel.:+49-241-80-96-233;fax: +49-241-80-92-252.E-mail address:[email protected] (T. Wintgens).

due to membrane replacement costs and high-energydemand for aeration[1].

Fouling phenomena on the membrane surface andwithin the pores reduce the long-term stability of fluxperformance. Permeate back flushing and chemicalcleaning are standard procedures applied to minimisethese effects and stabilise overall permeability of themembrane systems, but result in losses of net filtra-tion efficiency and possible damage the membrane bycleaning agents. Neither the evolution of membranepermeability under certain operating conditions northe effect of cleaning measures can nowadays be pre-dicted. These uncertainties cause considerable diffi-culties in plant layout, design and operation.

For many industrial processes as well as for conven-tional wastewater treatment models are used to sim-ulate process performance and to derive optimisation

0376-7388/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0376-7388(03)00046-2

56 T. Wintgens et al. / Journal of Membrane Science 216 (2003) 55–65

Nomenclature

cb bulk concentration (g/m3)cM concentration on membrane

surface (g/m3)COD chemical oxygen demand (g/m3)dC characteristic diameter (m)F trans-membrane flux (l/m2 h)∫

F dt temporal flux integral (m3/m2)H0, HP geometric heights (m)kC model parameter cake layer (m2/kg)kF model parameter fouling (1/m)kP mass transfer coefficient (m3/m2s)phydro hydrostatic pressure (Pa)ppump suction pressure (Pa)�pax axial pressure losses (Pa)�pTM trans-membrane pressure difference

(Pa)RC cake layer resistance (1/m)RF fouling resistance (1/m)RM membrane resistance (pure water flux)

(1/m)SF model parameter fouling saturation

(1/m)SI inert dissolved organic matter

(g/m3)SNH ammonia–nitrogen

(NH4+–N + NH3–N) (g/m3)

SNOx nitrate–nitrogen and nitrite–nitrogen(NO3

−–N + NO2–N) (g/m3)SO2 dissolved oxygen, O2 (g/m3)SS biodegradable dissolved organic

matter (g/m3)T temperature (◦C)XA autotrophic organisms (g/m3)XH heterotrophic organisms (g/m3)XI inert particulate organic matter

(g/m3)XS biodegradable particulate organic

matter (g/m3)XSTO storage products (g/m3)

Greek letters� shear rate (1/s)η viscosity (Ns/m2)τW wall shear stress (N/m3)

approaches based on the output of simulation studies.No comprehensive models for membrane bioreactorsystems exist so far, which integrate interdependen-cies between biological processes and filtration per-formance as well as mathematically describe the mainflux-determining phenomena, occurring in submergedmembrane units for municipal wastewater treatment.

Feed-sided air pulsing was described to be a mainflux-determining mechanism in submerged hollowfibre applications[2]. The shear forces created by aslug flow along the fibres were correlated to the masstransfer coefficients at the membrane surface[3]. Themass transfer coefficient controls the concentrationpolarisation occurring in front of the membrane inall separation applications, as rejected componentsaccumulate at the membrane. In case of membranebioreactors, micro- or ultrafiltration processes areused to retain biomass in the system. Macromolecularand particulate components of the activated sludgeaccumulate at the membrane leading to significantlosses of driving force due to the resulting cake layerformation and colloidal fouling. Apart from these phe-nomena on the membrane surface, pore-blocking mayoccur and contribute significantly to the long-termdecrease in permeability of the membrane[4].

The mentioned phenomena, determining filtrationperformance in membrane bioreactors, will be math-ematically described within this paper and an inte-grated model will be presented. The model was usedto describe the evolution of membrane permeability ata full-scale membrane bioreactor plant for municipalwastewater treatment. Simulation results with respectto biological parameters and flux performance will bepresented in comparison to the operational data.

2. Model description

The integrated membrane bioreactor model de-veloped consists of a compartment describing theactivated sludge processes to account for the biologi-cal treatment performance and an element to describethe permeability of the filtration unit. Both elementswere coupled within an integrated simulation envi-ronment to account for interdependencies, mainlythe membrane-initiated accumulation of biomass inthe system with consequences both for the metabolicstate of the micro-organisms and filtration resistance.

T. Wintgens et al. / Journal of Membrane Science 216 (2003) 55–65 57

2.1. Activated sludge model

The activated sludge model 3 (ASM3) was fre-quently used as a basis for the description of pro-cesses in the biological stage. Like the first versionof the activated sludge model (ASM1), the ASM3 hasbeen designed as a tool for description and simulationof aerobic and anoxic stages in municipal wastewatertreatment[5].

Unlike in ASM1, the endogenous respiration con-cept is used, introducing storage substances as majorcomponents. They were used in ASM2 for the firsttime and are specifically important for cell metabolismin conditions of low organic loads, which are typicallyencountered in the operation of membrane bioreactorsfor municipal wastewater treatment in order to min-imise excess sludge production. Extra-cellular poly-meric substances (EPS), produced by micro-organismsin biological wastewater treatment systems, exert acritical influence on the flux-rate achieved in mem-brane filtration of activated sludge suspensions andare not yet included in the description of biotransfor-mation processes. Their generation is supposed to bestrongly dependent on the metabolic stage, which cor-relates with the organic loading rate of the biologicaltreatment system[6].

The ASM3 in its basic version considers 12 micro-bial transformation processes with 13 dissolved and

Fig. 1. Metabolic pathways according to activated sludge model 3[1].

particular components involved in the decompositionof carbon and nitrogen compounds in wastewater. Thebiochemical processes undergone by the ASM3 com-ponents are visualized inFig. 1. While autotrophic or-ganisms use inorganic substances as the main energysource, heterotrophic organisms utilise reduced carbonsources for growth and endogenous respiration.

The reactions described by ASM3 represent asystem of coupled ordinary differential equations,which can be numerically solved for a given setof initial concentrations in the bioreactor. Hence, adynamic calculation of the time-dependent concen-tration schemes for the individual components can beaccomplished.

2.2. Modelling of the filtration process inmembrane bioreactors

In membrane bioreactor configurations for mu-nicipal wastewater treatment micro- or ultrafiltrationmembranes are used to retain the biomass in the sys-tem, leading to a considerably high total suspendedsolid concentration in the bioreactors. The filtrationperformance, namely, the permeability and its evo-lution of long periods of time, is the main focusof interest due to its crucial importance for systemreliability and economic feasibility[1]. The under-standing and quantitative description of performance


Fig. 2. Phenomena limiting flux performance in membrane filtration.

determining phenomena is supposed to be a presup-position for further process optimisation.

At the high fluxes encountered when using porousmembranes as in ultra- and microfiltration concentra-tion polarisation on the feed side has a strong effect.A cake layer of the retained components is formedon the membrane surface causing filtration resistance,which is a critical factor for the overall performanceachieved in membrane filtration of activated sludgesuspensions. Components held back by the membranecan cause scaling or colloidal fouling, defined as anyperformance-limiting interaction between feed com-ponents and the membrane material, on the membranesurface and within the pores (Fig. 2). It has been shownthat the presence of extra-cellular storage componentsincreases the fouling potential of the feed suspensiondramatically[7–10].

The formation of the concentration profile and thusthe influence of the cake layer upon total filtrationresistance can be positively influenced by a suitableflow-regime along the membrane. One measure to en-hance mass transfer at the membrane is air pulsing onthe feed side, which results in a multiphase flow in-ducing enhanced shear forces to the membrane[3].

2.3. Semi-empirical modelling of a capillaryhollow fibre module

Due to their low specific energy consumption andthe economic advantages arising from that fact, low-pressure processes are predominantly applied in mem-brane filtration of activated sludge. In these processes,

permeate is withdrawn through submerged membranemodules using a suction pressure on the permeate-sideto increase the driving force. Hollow fibre moduleswith a high specific membrane surface in outside–infiltration mode are frequently used in this configura-tion [11].

The hollow fibres with a nominal pore-diameter inthe range of 0.1�m are submerged in upright positionand exposed to a flow of relatively coarse air bubblesfrom an aeration device situated under the module inorder to minimize cake formation and clogging.

In contrast to the flow-regime in a tubular module,which can be described rather precisely, cross-flow fil-tration in a submerged capillary hollow fibre moduleis characterized by a rather complex flow-regime con-sisting of the two-phase air and activated sludge sus-pension in a barely describable cross-section betweenand around the fibres.

2.4. Modelling approach for the time-dependentbehaviour of total filtration resistance

The two-phase flow between capillary hollow fi-bres consisting of air and a suspension was describedas a slug flow-regime by Chang et al.[12]. For theirexperiments, conducted with a couple of hollow fibremembranes, they introduced a system of equationsconsisting of mass-balances and empirical correla-tions which can be coherently solved in an ideal case(gas-content of the liquid-slug is zero) and for knownboundary conditions (air flow-rate, geometry). Previ-ous modelling approaches have explained the effect


of enhanced mass transfer induced by slug flow basedon computational fluid dynamics. The highly turbu-lent wake region of the gas slug is supposed to createa peak in wall shear stress[13].

In contrast, the approach introduced here accountsfor average hydrodynamic shear effects upon masstransfer and consequently concentration polarisation,while an accurate description of the geometric con-straints is not possible in case of submerged capil-lary hollow fibre systems without fixed flow channelsbetween the membranes. As the diffusivity of parti-cles and macromolecules encountered in membranefiltration of activated sludge is low, back-transport ofspecies accumulated on the membrane surface to thebulk flow can only be shear-induced.

Formally, the model is based on the resistance-in-series model, describing the area specific permeateflux F as the ratio of driving force�pTM and a sum ofresistances, comprising the hydraulic resistance of theclean membraneRM, a cake layer resistanceRC, and afouling resistanceRF, multiplied by the temperature-dependent dynamic viscosity of the permeateηP:

F = �pTM

(RM + RC + RF)ηP

The pressure gradient along the fibre is deter-mined by the depthH (m) to which the module is

Fig. 3. Submerged capillary hollow fibre modules and idealised trans-membrane pressure[15].

submerged, the suction pressurep (Pa) applied bythe permeate suction pump, and the pressure lossescaused by the permeate flow through the hollowfibres.

The effective trans-membrane pressure difference�pTM (TMP) for a membrane element is composedof three pressure components as follows (Fig. 3):

�pTM = phydro + ppump− �pax

Cake resistanceRC is assumed to be dependent ona cake layer forming component at the membrane sur-face, wherecM represents the corresponding concen-tration at the membrane surface:

RC = kC cM

The concentrationcM at the membrane surface de-pends on the concentration profile at the membraneand is expressed in another relation, accounting forconcentration polarisation effects:

F = kP ln

(cM

cb

)

This expression describes the deviation betweenthe bulk concentrationcb and the concentration at themembrane surface of cake layer forming components,which depends on the local mass transfer coefficient


kP and the permeate flux:

kP = τWdC

ηF

where τW characterizes the mean wall shear stressexerted by the two-phased medium of activated sludgeand air upon the membrane surface,ηF the viscosity ofthe activated sludge anddC a characteristic diameter,which is dependent on the particle size distribution inthe system and on the lower end determined by size ofparticles rejected by the applied membrane. In orderto estimate the local mass the shear rate was assumedto beγ = 1/40 [14] and characteristic diameter dC =1�m, respectively[15].

The fouling resistanceRF is assumed to be depen-dent on the total permeate volume produced in a fil-tration interval under consideration, e.g. between twochemical cleanings:

RF = SF

(1 − e−kF

∫ t0 F(t) dt

)

The coefficientskC andkF have to be fitted to theshort-term and long-term characteristics of total mem-brane resistance, respectively.

The model parameterkF in particular is assumedto be strongly dependent on the concentration of po-tentially pore-blocking and membrane-adhesive com-ponents in the feed suspension. The amount of EPSmight have a crucial contribution here, which couldnot be quantified in this particular study so far due tothe lack of appropriate data.

Another parameterSF is a membrane constantand, quite similar to adsorption processes, repre-senting a factor for the specific surface area of themembrane material, which ultimately can be coveredby fouling products. Thus,SF is also an indicatorfor the maximum increase of fouling resistance tobe expected. Dependency upon the properties ofthe membrane material like pore-size distribution,hydrophobicity, and porosity can also be assumedhere.

In its final form, an implicit expression for the per-meate flux can be written as:

F(t) = �pTM(RM+kC cbeF(t)/kP+SF

(1−e−kF

∫ t0 F(t) dt

))ηP

3. Operational data from a full-scalewastewater treatment plant with membranebioreactor configuration

The wastewater treatment plant Rödingen is oper-ated by the Erft River Association in the western partof Germany and was the first full-scale municipalwastewater treatment plant with a membrane biore-actor configuration when it went into operation 1998[16]. The plant is equipped with a 3 mm screening unitand a grit chamber for mechanical pre-treatment. Thetwo bioreactors can perform alternating denitrificationand nitrification phases (Fig. 4). An additional 0.5 mmdrum screen removes filamentous material from theprocess, which otherwise may lead to a clogging ofthe membrane filtration units. The biomass is retainedin the system by submerged Zee-Weed® microfil-tration units[14], with a nominal pore-size 0.1�m.There are two filtration units to handle peak hydraulicloads.

Both filtration units were monitored in terms ofmembrane permeability according to a standardizedmeasuring procedure. During those tests the mem-brane unit was operated in a 40 s filtration intervalwith a constant “norm-flux” of 27 l/m2 h and thetrans-membrane pressure was measured. The fluxto pressure ratio gives an indication of the currentpermeability of the membrane filtration unit for thegiven set of operation parameters (e.g. temperatureand total suspended solids content).

A long-term decrease of system permeability couldbe observed on a time scale of several months. Thepermeability decrease was partly reversible by intensechemical cleaning but re-appeared in a similar wayduring the subsequent months (Fig. 5).

Based on the analysis of the operating data, per-meability cycles were defined as the period of timebetween two major chemical cleaning procedures.The characteristic decrease of permeability in anasymptotic curve, approaching a nearly stable mini-mum value, was attributed to fouling phenomena onthe membrane surface and within the pores. Periodicincreases of the permeability could be explained bycorresponding increases in water temperature, alteringthe feed and permeate viscosity.

System permeability data, the corresponding tem-peratures and total suspended solid contents in thefiltration units as well as the total throughput of


Fig. 4. Flow sheet of the wastewater treatment plant Rödingen.

Fig. 5. Permeability and hydraulic loads.


permeate within a filtration cycle along with extensiveinformation on the general system set-up were usedto calibrate the model presented in Chapter 2.

4. Model implementation simulation results

The model comprising the biological and filtrationpart were implemented using a Matlab/Simulink® pro-gramming package and a flow-sheet simulation inter-face was developed (Fig. 6).

Simulation studies were performed to reproduceparticular permeability measurement data for a char-acteristic filtration interval (27 November 2000 to25 November 2001). One set of model parameterswas used and the particular operation conditions (e.g.temperature and total suspended solids content) weretaken into account. The simulation results were com-pared with the operating data (seeFig. 7). The modelis able to reproduce the general trend of permeabilitydecrease and the fluctuations in operating condi-tions. The mean error is around 11%. Taking averagemeasurement errors and unaccounted fluctuations inoperating conditions into account, a simulation per-formance within acceptable error margins in complextechnical systems, processing heterogeneous feedmixtures, can be claimed.

Fig. 6. Simulation flow-sheet of the Rödingen plant.

Table 1Model parameters used in the simulation study

Model parameter Value

RM (1/m) 5.00× 1011

kC (m2/kg) 4.82× 1010

SF (1/m) 1.78× 1012

kF (1/m) 8.30× 10−2

The set of parameters given inTable 1was deter-mined by a least-square-error method to achieve a op-timal curve fitting.

The validity of these parameters was tested ina second simulation study in which the data fromanother filtration unit and the same period of timewas taken and a simulation was performed with theparameters determined in first study. In course ofthe simulation, an external chemical cleaning of themembrane modules in this unit was accounted for bya reset of the fouling resistanceRF. As illustrated inFig. 8 the permeability evolution is well describedwith the simulation, but difficulties exist to reproducethe huge deviations in the early stage of the filtrationinterval. The overall mean deviation for the simula-tion of the second filtration unit is 15.7% and hugelydetermined by some peak deviations, which mightbe attributed to major operational problems, whichcannot be considered in the model.


Fig. 7. Measurements and simulation of permeability in filtration unit I.

The general system behaviour in terms of biomassconcentration and effluent parameters, e.g. chemicaloxygen demand (COD), ammonia–nitrogen (NH4–N),nitrate–nitrogen and nitrite–nitrogen (NOx–N), was

Fig. 8. Measurements and simulation of permeability in filtration unit II.

simulated by the integration of membrane and ac-tivated sludge models for a steady-state case. Thesimulation was based on average feed characteris-tics and using standard ASM3 parameters with COD


Table 2Biological parameters: measurement versus simulation

Parameter Measurement(average)

Simulation(steady-state)

COD (mg/l) 23.0 23.4NH4–N (mg/l) 0.173 0.2NOx–N (mg/l) 6.2 6.6

fractionation to calibrate the model[5]. Table 2showsthe comparison of simulation results and operationaldata.

An interesting aspect is the simulation of CODturnover due to microbial growth processes in com-parison to endogenous metabolism, two processes ac-counted for in ASM3. The ratio of COD consumptiondue to growth and endogenous respiration of the het-erotrophs in the bioreactors was calculated to be closeto one, indicating a strong endogenous metabolism inthe system as expected for membrane bioreactor sys-tems with high biomass content. While the full-scaleoperational plant operates without primary clarifica-tion and with excess sludge removal, this ratio mightbe even closer to one in plants with even lower organicsludge loads.

5. Conclusion

The presented study demonstrates that the outlinedmodelling concept for membrane bioreactors couldsuccessfully be applied to describe the system be-haviour of a full-scale municipal wastewater treatmentplant, equipped with membrane filtration units. In par-ticular, the model describing filtration performance ofsubmerged capillary hollow fibre membranes couldbe applied to reproduce the characteristic decrease ofmembrane permeability.

With respect to the biological status of the system,only steady-state system behaviour was simulated sofar, but showed good results describing the tremendousimportance of endogenous respiration in membranebioreactor systems. More attention will be paid to thetransient behaviour of the activated sludge system andthe evolution of permeability on a short time-scale.Especially, the dependence of permeability on per-meate backflush-cycles and cleaning intervals will beinvestigated as a subject of further modelling and sim-

ulation activities. On a long-term, a close connectionbetween process control and simulation is envisagedto derive methods for optimised process design andoperation.

Acknowledgements

The presented ongoing research is support bythe Ministry for Environmental Affairs of NorthRhine-Westfalia (MUNLV). The corresponding au-thor acknowledges the German Research Association(DFG) for funding.

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Modelling of a membrane bioreactor system for municipal wastewater treatment