A mini-review of modeling studies on membrane bioreactor … · 2012-08-17 · A.N.L. Ng, A.S. Kim / Desalination 212 (2007) 261–281 263 that are also practical for real applications

Desalination 212 (2007) 261–281

0011-9164/07/$– See front matter © 2007 Elsevier B.V. All rights reserved

*Corresponding author.

A mini-review of modeling studies on membrane bioreactor(MBR) treatment for municipal wastewaters

Aileen N.L. Ng, Albert S. Kim*Civil and Environmental Engineering, University of Hawaii at Manoa,

2540 Dole Street Holmes 383, Honolulu, HI 96822, USATel. +1 (808) 956-3718; Fax +1 (808) 956-5014; email: [email protected]

Received 3 July 2006; accepted 19 October 2006

Abstract

Membrane bioreactor (MBR) technology is a promising method for water and wastewater treatment because ofits ability to produce high-quality effluent that meets water quality regulations. Due to the intrinsic complexity anduncertainty of MBR processes, basic models that can provide a holistic understanding of the technology at afundamental level are of great necessity. Compared to experimental research and development, followed bycommercialization of the technology, modeling studies for system design analysis and performance prediction areat a relatively rudimentary state. In this light, this review was conducted to provide an assessment of present effortsin modeling MBR systems, specifically for municipal wastewater treatment. Models considered in this review areclassified into three categories: biomass kinetic models, membrane fouling models, and integrated models with(light) couplings to describe the complete MBR process. The specific features, unique advantages, and capturingcapability of experimental observations of each model are discussed and assessed. Crucial components in MBRmodeling studies are carefully selected and assessed, based on the importance of their roles in characterizing MBRperformance, and future MBR modeling directions are suggested.

Keywords: Membrane bioreactor (MBR); Wastewater treatment; Activated sludge models; Membrane fouling

1. Introduction

The membrane bioreactor (MBR) is a systemthat combines biological treatment with mem-brane filtration into a single process. The first re-ported application of MBR technology was in

1969, when an ultrafiltration membrane was usedto separate activated sludge from the final efflu-ent of a biological wastewater treatment systemand the sludge was recycled back into the aera-tion tank [1]. Since then, the MBR system hasevolved, and research on MBR technology hasincreased significantly, particularly in the last 5years [2].

262 A.N.L. Ng, A.S. Kim / Desalination 212 (2007) 261–281

Two basic MBR configurations are shown inFig. 1 (modified from [3]). The first is a recircu-lated configuration with an external membraneunit (Fig. 1a). Mixed liquor is circulated outsideof the reactor to the membrane module, wherepressure drives the separation of water from thesludge. The concentrated sludge is then recylcedback into the reactor. The second is a submergedconfiguration with the membrane module im-mersed in the activated sludge (Fig. 1b). A suc-tion force is applied to draw the water throughthe membrane, while the sludge is retained on themembrane surface. A manifold at the base of thereactor diffuses compressed air within the reac-tor, providing oxygen to maintain aerobic condi-tions. The air bubbles also function to scour themembrane surface and clean the exterior of themembrane as they rise in the reactor. The sub-merged configuration is more commonly usedthan the recirculated configuration because it isless energy-intensive and provides a cleaningmechanism to reduce membrane fouling. Thus,more fouling models focus on the submerged con-figuration than on the external configuration.

There are many applications for the MBR sys-tem. In general, the applications can be groupedinto three categories of processes involving wa-ter filtration membranes, gas diffusion mem-branes, and extractive membranes (including ionexchange). In the last 15 years, research on MBR

Influent

(b)

Air

Effluent

Bioreactor

Membrane module

Air

Influent

Effluent

Bioreactor

Membrane module

(a)

Fig. 1. Schematic diagrams of basic membrane bioreactor configurations [3]: (a) MBR with external membrane moduleand (b) MBR with immersed membrane module.

applications for water and wastewater treatmenthas been predominant, while research on MBRapplications for the other two areas has receivedless attention [2].

The advantages of the MBR system over con-ventional biological treatment processes spur thegrowing interest in MBR technology for waterand wastewater treatment. MBR treatment ofmunicipal wastewater yields high-quality waterwith reported removal percentages of 95%, 98%,and 99% (or greater) for chemical oxygen demand(COD), biochemical oxygen demand (BOD), andsuspended solids (SS), respectively [4]. This isimportant as water quality regulations have be-come increasingly stringent. A MBR has greater(independent) control over the suspended solidsretention time (SRT) and hydraulic retention time(HRT) because membrane filtration rather thangravitational settling is used to separate the bio-mass from the effluent. This allows for operationat a longer SRT and at higher loading rates, whichresults in less sludge production and shortens thenecessary HRT. The use of membranes to sepa-rate the biomass from the effluent also eliminatesthe need for large clarifying basins to settle outthe biomass, thus enabling the system to be morecompact.

Models that can accurately describe the MBRprocess are valuable for the design, prediction,and control of MBR systems. Complex models

A.N.L. Ng, A.S. Kim / Desalination 212 (2007) 261–281 263

that are also practical for real applications cangreatly assist in capitalizing on the benefits ofMBR technology. This review of published workson MBR process modeling for treatment of mu-nicipal wastewaters is classified into biomass ki-netics models, membrane fouling models, andintegrated models (that combine biomass kinet-ics and membrane fouling models to describe thecomplete MBR system).

2. MBR model description and assessment

2.1. Biomass kinetic models

2.1.1. The activated sludge model (ASM)family

In 1983, the International Association on Wa-ter Pollution Research and Control, later knownas the International Association on Water Qualityand now the International Water Association(IWA), formed a task group to develop a practi-cal model for the design and operation of the bio-logical wastewater treatment process. The prod-uct of the group’s efforts is activated sludge modelno. 1 [5], introduced in 1987. Versions that ex-panded and improved upon the first model wereintroduced by the association in later years. Theyinclude activated sludge model no. 2 [6], whichincorporates phosphorus removal from wastewa-ters; activated sludge model no. 2d [7], whichaccounts for the ability of phosphorus-accumu-lating organisms to use cell internal substrates fordenitrification; and activated sludge model no. 3[8], which does not include phosphorus removalbut addresses problems found in the first model.

Although the ASMs were developed to de-scribe the conventional activated sludge process,it has been suggested that the models can also beused to simulate biomass kinetics in an MBR sys-tem [9–11]. The MBR process is the activatedsludge process with the secondary clarificationstep replaced by membrane filtration; therefore,it is reasonable to use ASMs to characterize thebiomass dynamics in an MBR system. Presented

here is a brief overview of the four ASMs. TheIWA task group publication [12] should be re-ferred to for further details on the models’ com-ponents, processes, calibration methods, applica-tions, and limitations.

2.1.1.1. Activated sludge model no. 1 (ASM1)

Activated sludge model no. 1 was developedto model biological treatment for organic carbonremoval, nitrification, and denitrification. Themodel can be used to predict oxygen demand andsludge production in an activated sludge system.Two main concepts have been incorporated intothe model. The first concept is that biodegradableCOD in wastewater is composed of readily bio-degradable COD (RDCOD) and slowly biode-gradable COD (SBCOD). RBCOD can immedi-ately be used by organisms for synthesis, whereasSBCOD must be broken down before it can passthrough the organisms’ cell wall to be metabo-lized. Total COD in the model is comprised ofbiodegradable COD, non-biodegradable COD(i.e., inert material), and the active biomass. Thesecond concept in this model is death-regenera-tion. When the biomass decays, a portion of thedecayed cell material is non-biodegradable andremains inert. The rest of the decayed material isslowly biodegradable and can be broken down tobe used by active organisms for growth.

Fig. 2 shows the main processes included inASM1, i.e., the hydrolysis of slowly biodegrad-able material and the growth and decay of the or-ganisms in the biomass. Two groups of organismsconsidered in the model are autotrophs (XB,A) andheterotrophs (XB,H). Autotrophs perform the nitri-fying activities. Their growth occurs through theoxidation of ammonia (SNH) to nitrate (SNO), whichtranspires only under aerobic conditions. Thisprocess is modeled using saturation-type (Monod)kinetics. Heterotrophs perform the carbon removaland denitrifying activities. They consume solublesubstrate (SS), which includes readily biodegrad-able decayed cell material, and ammonia for


growth under both aerobic and anoxic conditions.Under aerobic conditions, oxygen is utilized inthe growth process. Under anoxic conditions,when oxygen is absent, nitrate is used as the elec-tron acceptor and is reduced to dinitrogen. Theheterotrophic growth process is likewise modeledusing saturation-type kinetics. The decay pro-cesses for both types of organisms are describedby the death-regeneration concept with first-or-der kinetics. However, only heterotrophs can re-use the biodegradable decay material for growth,and the autotrophic decay rate is relatively slower.

The basic structure of ASM1 is a mass bal-ance equation to describe the accumulation rateof a particular component within the system:

Accumulation = Input – Output + Reaction

The model supplies reaction rate expressionsfor the various model components, so that theycan be applied to many different process configu-rations. A matrix format is used to allow easy iden-tification of the rate processes that affect the fateof each component. A partial section of the ASM1matrix is shown in Table 1. The reaction rate r ofa component, i, can be read from the matrix by

Anoxic

SS

XB,A

XS

XP

XB,H

Growth

Growth Decay

Hydrolysis

Heterotrophs

Autotrophs

SNO

XND SND Hydrolysis

Ammonification

SNH

SO

Decay

or

Aerobic

Fig. 2. Diagram of model processes and substrate flow in ASM1.

traversing down column i and adding the prod-ucts of the coefficient νij and the correspondingprocess rate ρj, i.e.,

i ij jj

r = ν ρ∑ (1)

If no coefficient is listed in the table, the coef-ficient is assumed to be zero. To demonstrate, thereaction rate for autotrophic biomass, XB,A, is

( )

B,A

NH OA B,A

NH NH O,A O

A B,A

ˆ1

1

XS Sr X

K S K S

b X

⎛ ⎞⎛ ⎞= ⋅µ ⎜ ⎟⎜ ⎟⎜ ⎟+ +⎝ ⎠⎝ ⎠+ − ⋅ (2)

and the reaction rate for particulates arising frombiomass decay, XP, is

P H B,H A B,AX p pr f b X f b X= ⋅ + ⋅ (3)

In the model, µ? denotes a maximum growthrate, K? is a saturation coefficient, and b? is a rateconstant. Thirteen components are incorporated


Table 1A partial section of the matrix of process kinetics and stoichiometry from ASM1

Component i j Process

6 XB,A

7 XP

8 SO

Process rate, ρj [M/L3/T]

1 Aerobic growth of heterotrophs

1 H

H

Y

Y

−−

,

,

ˆ S OH B H

S S O H O

S SX

K S K S+ +

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠µ

3 Aerobic growth of autotrophs

1 4.57 A

A

Y

Y

−−

,

,

ˆ NH OA B A

NH NH O A O

S SX

K S K S+ +

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠µ

4 Decay of heterotrophs fP ,H B Hb X

5 Decay of autotrophs –1 fP ,A B Ab X

in the model, and a mass balance equation can bederived for each of these components from theeight rate processes listed in Table 2. The inertmaterials, XI and SI, are incorporated in the modeldespite having a zero reaction rate. Particulateinert material, XI, becomes enmeshed in the acti-vated sludge and is removed from the systemthrough sludge waste. Soluble inert material, SI,leaves the system at the same concentration withwhich it enters. All organic material and biomasscomponents are expressed in terms of COD be-cause it can be used to link organic substrates,biomass, and consumed oxygen by electron equi-valents. Likewise, oxygen is expressed as nega-tive oxygen demand.

A number of simple assumptions made in themodel impose limitations on its application. Oneassumption is that the system operates at a con-stant temperature. However, the thermal sensitiv-ity of the model parameters can be incorporatedin the rate expressions by applying the Arrheniusequation. Another assumption is that the systemoperates at a constant pH near neutral. Althoughit is known that pH can influence some modelparameters, few expressions exist to capture this

influence. Therefore, alkalinity has been includedin the model to allow detection of problems withpH control. The model parameters in the rate ex-pression are assumed to be constant. Conse-quently, the model does not handle changes inwastewater characteristics. The effects of lownutrient concentrations (e.g., phosphorous, nitro-gen, and other inorganic nutrients) on the removalof organic substrate and cell growth are not spe-cifically considered. It is presumed that sufficientquantities of nutrients are present to allow forbalanced growth of organisms. Although the bio-mass may change in species diversity over time,the kinetic parameters remain fixed in the modelas it would be too complicated to capture such aneffect on the kinetic parameters. Other assump-tions made in the model include a constant valuefor nitrification-related parameters, which are pre-sumed to incorporate inhibitory effects of wasteconstituents, instantaneous entrapment of particu-late organics by the biomass, coupled and simul-taneous occurrence of the hydrolysis of organicmatter and organic nitrogen at equal rates, andindifference of the electron acceptor type on bio-mass decay.


Table 2Components and rate processes in ASM1, ASM2, and ASM3

Components Processes

ASM

1

Soluble inert organic matter (SI) Readily biodegradable substrate (SS) Particulate (suspended) inert organic matter (XI) Slowly biodegradable substrate (XS) Active heterotrophic biomass (XB,H) Active autotrophic biomass (XB,A) Particulates arising from biomass decay (XP) Oxygen (negative COD) (SO) Nitrate and nitrite nitrogen (SNO) Ammonia and ammonium nitrogen (SNH) Soluble biodegradable organic nitrogen (SND) Particulate biodegradable organic nitrogen (XND) Alkalinity (SALK)

Aerobic growth of XB,H Anoxic growth of XB,H Aerobic growth of XB,A Decay of XB,H Decay of XB,A Ammonification of SND Hydrolysis of entrapped organics Hydrolysis of entrapped organic nitrogen

ASM

2

Dissolved oxygen (SO2) Fermentable (readily biodegradable substrate (SF) Fermentation products (SA) Ammonium and ammonia nitrogen (SNH4) Nitrate and nitrite nitrogen (SNO3) Inorganic soluble phosphorus (SPO4) Inert soluble organic material (SI) Alkalinity (SALK) Dinitrogen (SN2) Inert particulate organics (XI) Slowly biodegradable substrates (XS) Heterotrophic organisms (XH) Phosphate accumulating organisms (XPAO) Polyphosphates (XPP) Cell internal storage products of PAO (XPHA) Nitrifing organisms (XAUT) Total suspended solids (XTSS) Metal hydroxides (XMeOH) Metalphosphate (XMeP)

Aerbobic hydrolysis Anoxic hydrolysis Anaerobic hydrolysis Aerobic growth of XH on SF Aerobic growth of XH on SA Anoxic growth of XH on SF Anoxic growth of XH on SA Fermentation Lysis of XH Storage of XPHA Storage of XPP Aerobic growth of XPAO on XPHA Lysis of XPAO Lysis of XPP Lysis of XPHA Aerobic growth of XAUT Lysis of XAUT Precipitation of SPO4 Redissolution of SPO4

ASM

3

Dissolved oxygen (negative COD) (SO) Inert soluble organic matter (SI) Readily biodegradable organic substrate (SS) Ammonium plus ammonia nitrogen (SNH4) Dinitrogen (SN2) Nitrate and nitrite nitrogen (SNOX) Alkalinity (SALK) Inert particulate (suspended) organic matter (XI) Slowly biodegradable substrate (XS) Active heterotrophic organisms (XH) Cell internal storage product of heterotrophic organisms (XSTO) Nitrifying organisms (XA) Suspended solids (XSS)

Hydrolysis Aerobic storage of SS Anoxic storage of SS Aerobic growth of XH Anoxic growth of XH Aerobic endogenous respiration of XH Anoxic endogenous respiration of XH Aerobic endogenous respiration of XSTO Aerobic endogenous respiration of XSTO Aerobic growth of XA Aerobic endogenous respiration of XA Anoxic endogenous respiration of XA


2.1.1.2. Activated sludge model no. 2 (ASM2)

Activated sludge model no. 2, presented in1995, expands upon ASM1 by including biologi-cal phosphorous removal. The model incorporatesa new group of organisms to the biomass, whichoriginally consisted of heterotrophs and auto-trophs. The new group, called phosphorus-accu-mulating organisms (PAOs), encompasses the dif-ferent types of microorganisms capable of accu-mulating phosphorous and storing them in theform of cell internal polyphosphates (XPP) andpoly-hydroxyalkanoates (XPHA). PAOs are as-sumed to be incapable of denitrifying activity andcan only grow on stored cell internal organic ma-terial XPHA. Fig. 3 shows the storage and growthprocesses of PAOs in ASM2. PAOs store externalfermentation products (SA) in the form of internalcell storage material XPHA. This process occurs pri-marily under anaerobic conditions, although it hasbeen reported to occur under aerobic and anoxicconditions as well. For this reason, the kinetic ex-pression for the storage of XPHA does not includeinhibition terms for dissolved oxygen and nitrateplus nitrite nitrogen. Energy for the process comesfrom the hydrolysis of XPP, which leads to the re-lease of soluble phosphates (SPO4

). PAOs also storephosphates in the form of XPP with the energy sup-plied from the respiration of XPHA. XPP is regener-ated because PAOs require SA stored in the formof XPHA for growth, and the storage of SA requiresthe energy from the hydrolysis of XPP. According

XPP

SO

XPHA Growth

SPO4

XPAO XPHA SA

SPO4

Storage

XPP

Fig. 3. Storage and growth processes involving PAO in ASM2 (modified from [2]).

to the model, growth of PAOs occurs only underaerobic conditions at the expense of XPHA and in-volves the consumption of SPO4

and lysis of XPP.Separate process rates are provided in the modelfor the lyses of PAOs and each of the two storageproducts to capture all losses of biomass due torespiration and maintenance or death.

In ASM2, the growth of heterotrophic organ-isms occurs under both aerobic and anoxic con-ditions from the consumption of both fermentablesubstrates (SF) and fermentation products (SA),thus involving four separate growth processes.The growth rates (µm) and yield coefficients (YH)are assumed to be identical regardless of the or-ganic substrate (SF or SA) consumed. Under aero-bic conditions, heterotrophic growth processesconsume oxygen (SO2

) and nutrients (SNH4 and SPO4

),and possibly alkalinity (SALK) to produce sus-pended solids (XTSS). The anoxic growth processesutilize nitrate (SNO3

) instead of oxygen, and thenitrate is reduced to dinitrogen (SN2

). Denitrifica-tion, which releases alkalinity, is assumed to beinhibited by the presence of SO2

, and the maxi-mum growth rate is reduced to a fraction of thatunder aerobic conditions. The slower growth rateaccounts for the fact that not all heterotrophs arecapable of performing denitrification reactions.Under anaerobic conditions, when both oxygenand nitrate are not available, fermentation is as-sumed to occur. In this process, SF is directly trans-formed by heterotrophs to SA, and alkalinity isrequired due to the release of negatively charged


SA. Aside from rate limitations imposed by phos-phate concentrations that are incorporated into therate expression for autotrophic growth, processesinvolving autotrophic organisms are the same asin ASM1.

Two additional rate processes (precipitationand redissolution of phosphates) and two compo-nents (metalhydroxides and metal phosphates)were included in ASM2 to capture effects of theprecipitation and redissolution of phosphates.Metals are naturally present in wastewater and canprecipitate with soluble ortho-phosphates if bothconstituents exist in high enough concentrations.Also, it is common practice to add iron or alumsalts to aid in phosphorous removal throughchemical precipitation in conventional treatmentprocesses. Table 2 lists the 19 components and19 rate processes in the ASM2 model. The samemodel limitations of ASM1 apply to ASM2. Fur-ther assumptions and restrictions of ASM2 includethe following. The heterotrophic and phosphate-accumulating biomasses are spatially homogenousand time-invariant. The internal structure of eachindividual cell is not distinguished, and only anaverage composition is considered despite the useof nonlinear kinetic expressions. A pragmatic de-cision was made to accept the problems associ-ated with the use of average biomass composi-tions, as the introduction of population modelswould pose additional problems. The hydrolysisof organic matter, organic nitrogen, and organicphosphates is assumed to occur simultaneouslyin a coupled manner, and XS comprises a constantfraction of nitrogen and phosphorous. This is asimplified assumption to avoid the addition of sixmore hydrolysis processes and two particulatecomponents. Denitrification reactions of PAOs arenot included in the model, although it is knownthat some PAOs can denitrify. Therefore, themodel should be used only to simulate processeswith low nitrate input into anaerobic tanks. Themodel assumes sufficient concentrations of phos-phate, ammonia, potassium, and magnesium. Thedetailed mechanisms of growth limitations from

low nutrient concentrations are not known andmay not be accurately modeled. The effects oflow potassium and magnesium concentrations onbiological phosphorus removal are not considered.Finally, although nitrate and nitrogen monoxidehave been observed to inhibit biological phospho-rus removal, such effects are not incorporated inthe model. In this review only critical assump-tions that greatly affect model performance arehighlighted. Other assumptions made in ASM2are detailed in the IWA publication [12].

2.1.1.3. Activated sludge model no. 2d(ASM2d)

Activated sludge model no. 2d incorporates theobservation that PAOs can use internal cell or-ganic storage products for denitrification and thusgrow under anoxic conditions. This observationled to the addition of two rate processes: the stor-age of polyphosphates and growth of PAOs un-der anoxic conditions. All other details of ASM2carry over to ASM2d.

2.1.1.4. Activated sludge model no.3 (ASM3)

In 1999, the IWA task group revised ASM1 toproduce a more accurate and updated model,ASM3. One of the major changes is the inclusionof internal cell storage compounds in heterotro-phs, shifting the focus from hydrolysis to the stor-age of organic substrates. All readily biodegrad-able substrates are taken up by the heterotrophicbiomass and stored as internal cell componentsprior to growth. Thus, heterotrophic growth is notfully dependent upon external compounds. Theinclusion of internal cell storage structures alsoleads to the distinction between the decay of bio-mass and storage products under both aerobic andanoxic conditions. Another significant differenceis the replacement of the death-regeneration con-cept by the growth-endogenous respiration model.In ASM1, the decay of organisms occurs at a cer-tain rate, and a portion of the decayed cell mate-rial returns to the heterotrophic growth process.


In ASM3, endogenous respiration is used to cap-ture all forms of biomass loss and energy require-ments and is not associated with growth. Thegrowth and decay of the two groups of organismsare clearly distinguished, as shown in Fig. 4, andidentical models are used to describe the decayprocesses. These changes better reflect observedphenomena.

Components in ASM1 not included in ASM3,are particulates from biomass decay as well assoluble and particulate biodegradable organic ni-trogen. Components added in ASM3 aredinitrogen, internal cell storage product of het-erotrophic organisms, and suspended solids. The13 components and 12 rate processes describedin ASM3 are listed in Table 2. Limitations of themodel are as follows. The model was developedfor domestic wastewater and, therefore, should notbe used to model industrial water treatment. It isapplicable within the temperature range of 8–23ºCand a pH range of 6.5–7.5, excluding anaerobicconditions. The model is designed for systemsonly with low loads and high SRT (> 1 d) and islimited to low concentrations of nitrite.

2.1.1.5. Assessment of activated sludge models

ASM1 was tested extensively against experi-mental and operational data for activated sludgesystems. Main problems found with ASM1 were

SO

SNH XA

XI

Growth Endogenous Respiration

Nitrifiers

SO

Growth Hydrolysis

Heterotrophs

XS XH XSTO Storage

SNO

SS Endogenous Respiration

Fig. 4. Diagram of substrate in ASM3(modified from [8]).

addressed in the development of ASM3. ASM2,ASM2d, and ASM3 were also validated againstexperimental data for conventional activatedsludge systems, although less extensively. It hasbeen suggested that ASMs may be suitable forcharacterizing biomass kinetics in an MBR sys-tem. However, few studies have demonstrated thevalidity (or invalidity) of ASMs for modelingMBR systems.

In a study that introduces an integrated MBRmodel, Wintgens et al. [11] compare simulationresults from ASM3 under steady-state conditionswith mean measured values for COD, ammonium,and nitrate plus nitrite from a full-scale operationalMBR plant. The simulation results correspondedwell with the measured data. Although the studyimplies that ASM3 is a good modeling methodfor MBR systems, further in-depth studies arenecessary to consider its accuracy for capturingother components and modeling transient states.

The applicability of ASMs for modeling MBRsystems needs to be verified to further understandthe effects of higher SRTs and mixed liquor sus-pended solids (MLSS) concentrations on bio-mass. Additionally, studies comparing the conven-tional activated sludge process with the MBR pro-cess can aid in understanding the effects of filtra-tion versus clarification and estimating the poten-tial capability of ASMs to capture such effects[13]. An advantage of using the ASMs is the clear


presentation in a matrix format. The matrix aidsthe understanding of the biological treatment pro-cess and the devising of efficient experimentaldesign. Another advantage is that many simula-tion programs include ASMs or models based onASMs, providing easy access of the models forvarious applications. Also, biological phosphorousremoval, which is a key feature in biological treat-ment, is already incorporated into ASM2 andASM2d.

2.1.2. Soluble microbial products (SMP) model

While there are nuances among researchers asto what comprises soluble microbial products(SMP), SMP are generally defined as the organicmaterials arising from substrate metabolisms(usually with biomass growth) and biomass de-cay and being present in the effluent of biologicalsystems but absent from the influent [14]. Studieshave shown that SMPs comprise a considerableportion of soluble organic matter in the effluentof biological treatment processes, and the pres-ence of SMPs in the permeate is detrimental tothe MBR process as well as to post-treatment pro-cesses [14]. While it is still unclear whether theaccumulation of SMPs in the activated sludge in-hibits metabolic activity, as contradicting resultshave been reported [15,16], studies agree thatbuildup of SMPs can cause reduction in mem-brane permeability [15–19]. Additionally, SMPsin the permeate stream can lead to formation oftrihalomethanes and other disinfection by-prod-ucts and cause bacterial growth in distributionsystems [20]. Therefore, it is crucial to includeSMPs in the modeling of biological water treat-ment processes.

In 1992, Furumai and Rittmann [20] presenteda model that describes the interaction between het-erotrophic and nitrifying bacteria in biologicaltreatment processes. The model accounts for theformation and exchange of SMPs between het-erotrophs and nitrifiers, which are known to com-

pete with each other for dissolved oxygen. Ni-trifiers can also supply potential energy for het-erotrophs. They chemically reduce inorganic car-bon to organic carbon in the form of cell massand SMPs and make organic substrates availablefor growth of heterotrophs.

In the model, SMPs are divided into two groups:utilization-associated products (UAPs), which areproduced by biomass growth, and biomass-asso-ciated products (BAPs), which arise from bio-mass decay. The two types of SMP are groupedtogether in the model, but their formation is ac-counted for separately. The formation rate ofUAPs is proportional to the substrate utilizationrate, whereas the formation rate of BAPs is pro-portional to the amount of active biomass. Bothorganisms produce SMPs, but only heterotrophsdegrade them for cell synthesis. A mass balanceequation of the system is provided for each of themodel components (i.e., organic COD, ammonium,nitrite, dissolved oxygen, nitrate, originally formedSMP, actual SMP, heterotrophs, ammonium oxi-dizers, nitrite oxidizers, and inert biomass).

This model was modified in 1998 to includefeatures specific to the MBR process [21,22].Mainly, the output of biomass in the effluent waseliminated because the membranes retain the bio-mass in the system. The retention of a BAP frac-tion was considered in the same way because frac-tions of larger macromolecules are maintained inthe reactor by membranes. Additionally, denitri-fication reactions were integrated into the model,and the biodegradation rates of the two types ofSMP were modified according to recent findings,which suggested separate consumption rates forUAP and BAP using Monod-type kinetics. Themodel includes 10 transient mass balance equa-tions to characterize each constituent consideredin the model: heterotrophs, nitrifiers, inert bio-mass, soluble COD, ammonia, nitrate, nitrogengas, oxygen, BAP, and UAP. As in ASMs, the mul-tiplicative Monod equations were used to capturerate limitations stemming from the deficiency ofnecessary substrates.


The SMP model demonstrated good corres-pondence between simulation results and mea-sured data. In a study conducted by Urbain et al.[21], a comparison was made between data froman MBR pilot plant and model predictions foroxygen demand, nutrient removal, sludge produc-tion, and biomass distribution under both steadyand transient states at three different sludge ages.The model was not calibrated specifically for thepilot plant. Despite the use of default parametervalues from published works, good correspond-ence was found between model predictions andexperimental values for volatile suspended solids(VSS) concentration, effluent COD, and nitrogenspecies. The model demonstrated the capabilityof producing accurate predictions under bothsteady-state and transient-state cases. However,the SMP model could not handle technical prob-lems during operation and sudden changes in thewastewater characteristics.

Another study that likewise involved a pilot-scale MBR was conducted by de Silva et al. [22].Conditions were maintained at steady state, al-though the aerated and anoxic periods in the sys-tem were alternated every 2 h (i.e., 2-h aeratedperiod and 2-h anoxic period). The pilot-scaleMBR was operated at an HRT of 17 h and an SRTof 20 d. Again, most of the parameter values forthe model were taken from published works orcomputed stoichiometrically. Comparison be-tween the performance data and model simula-tion showed that the model was able to accuratelypredict the concentrations of sludge and nitrogenspecies and also to capture general trends for thesoluble COD in the effluent.

One advantage of the SMP model over ASMsis its capability to accurately model biomass inMBRs without the need for calibration using ex-perimental data. Also, it involves less componentsand equations while still capturing key quantities.On the other hand, there is less ease in model ap-plication compared to the ASM family, which ispresented in matrix format, and the model doesnot incorporate biological phosphorous removal.

2.1.3. ASM1-SMP hybrid model

Another model that incorporates the formationand degradation of SMP is the ASM1-SMP hy-brid model developed by Lu et al. [9]. In thismodified version of ASM1, the same definitionfor SMP is used as in the SMP model describedabove. The main concepts of ASM1 are preservedin the hybrid model, but a few changes were madeto include the fate of SMP. A schematic of themodel that depicts these changes is provided inFig. 5. UAPs are released in the metabolic pro-cesses of autotrophs and heterotrophs, and het-erotrophs can reutilize UAPs for their growth. Inaddition to inert material and soluble substrates,the decay processes of the organisms produceBAPs, which can also be reused for heterotrophicgrowth. These changes were incorporated as fol-lows. The component XP, which denotes particu-late products arising from biomass decay, wasreplaced with BAPs and UAPs. Process rates foraerobic and anoxic growths of heterotrophs bySMP consumption were added. Additionally, thedecay rates of the two organisms were separatedinto two processes, i.e., one resulting in particu-late formation and another resulting in BAP for-mation. The stoichiometric coefficients were ad-justed accordingly with the inclusion of these rateprocesses. The model comprises 12 transient massbalance equations without alkalinity.

Experiments were carried out with a singlecompletely mixed bioreactor that treated syntheticwastewater to test the validity of the AMS1-SMPhybrid model. The MBR was operated with aero-bic and anoxic cycling of 60 min (30 min withaeration, 30 min without aeration) and 120 min(60 min with aeration, 60 min without aeration).Most original parameters of ASM1 were used, butthe denitrification correction factor was enhancedto account for higher sludge concentrations in thesystem. Parameter values arising from the modi-fication to include SMPs were determined by trialand error or obtained from references. The modelsimulation results showed good correspondence


Wastage

SO or SNO

SS Growth

Hydrolysis XS

XI

SI

SBAP

SO Growth

Hydrolysis

SNH

SNH

SNH

XXD

SND

SND Ammonification

Ammonification

SUAP

XS

SS

SNO

SUAP

SO or SNO

SO or SNO

Hydrolysis

SO or SNO

decay

XBH

XBA

for soluble COD and soluble nitrogen concentra-tions under steady-state conditions. However,MLSS concentrations were significantly under-estimated for both cycling conditions. This ASM1-SMP hybrid model is a first attempt at modifyingthe ASMs to model MBRs. Progress was madebased on research that suggests the importance ofthe inclusion of SMP components for activatedsludge with high SRTs. The incorporation of theSMP model into ASM1 takes advantage of somebenefits of both models, although more work isneeded to fine-tune the hybrid model.

2.2. Membrane fouling models

2.2.1. Empirical hydrodynamic model

To investigate the influence of hydrodynamicconditions on the mixed liquor crossflow veloc-ity and the membrane fouling rate in an MBR, 10experiments were performed at varying suspendedsolid (SS) concentrations (X, 2–20 g/L), perme-ate fluxes (J, 4.5–27 L/m2/h), and aeration inten-sities (UGr, 10–100 m3/m2/h) in an internal-loop

Fig. 5. Schematic of the ASM1-SMP hybrid model [9].

airlift reactor [23]. The reactor is shown in Fig. 6.Air is supplied only in the riser zone of the reac-tor, which is separated from the down-comer sec-tions by baffle plates. The air hold-up in the risersection generates a difference in the bulk densityof the liquid, inducing circulation between the twozones. The crossflow velocity is an important pa-rameter to consider in the impedance of sludgebuildup on the membrane surface. Throughouteach experiment, the up-flow velocity of themixed liquor in the riser zone (Usr, m/s) and thetransmembrane pressure (∆P, Pa) were monitored.The up-flow velocity was measured as an observ-able value of the actual crossflow velocity of themixed liquor along the membrane surface. Notethat the aeration intensity, UGr, is distinct from themixed liquor crossflow velocity, Usr. The formeris a controlled parameter in the experiment, where-as the latter is a measured value that is influencedby controlled parameters. The transmembranepressure was used to calculate the membrane foul-ing rate (K, m/h), defined as the rate of increasingmembrane filtration resistance (i.e., K = dR/dt).


The following equation was used to compute fil-tration resistance (R, m–1):

93.6 10 PRJ

∆= ×η (4)

Here, η (mPa-s) is the viscosity of the permeateand is approximated as having the viscosity oftap water. The factor, 3.6×109, stems from usingthe units given in parentheses for each of the vari-ables. Membrane resistance over time was plot-ted for each experiment, and the membrane foul-ing rate was obtained from the slope of the linearregression through the plot. Correlations weredeveloped from the experimental data for themixed liquor crossflow velocity and the mem-brane fouling rate as functions of the hydrody-namic parameters.

Aeration intensity, reactor structure, and fluidviscosity were the main factors influencing themixed liquor crossflow velocity. The correlationfor the crossflow velocity was assumed to fit thefollowing power equation:

1a b

sr LrU f U= µ (5)

Membrane module

Baffle plate

Blower Flow meter

Wastewater storage tank

Feed pump Suction pump

On/Off timer Vacuum gauge

Fig. 6. Diagram of internal-loop-airlift reactor [23].

where ULr (m/s) is the crossflow velocity of tapwater, µ is the mixed liquor viscosity (mPa-s),and f1, a, and b are constants. ULr was found bymeasuring the up-flow velocity of tap water inthe reactor. The parameter was used to capturethe combined influence of aeration intensity andreactor structure. The reactor structure affects thesludge crossflow velocity but is not a directlyquantifiable parameter. Multiple regression analy-sis was used to determine the value of the threeconstants. The relationship between sludge vis-cosity and SS concentration was established fromexperimental data as

0.071.61 Xeµ = (6)

and was replaced in Eq. (5) to obtain Usr in termsof X. The following was given as the final equa-tion for the mixed liquor crossflow velocity:

1.226 0.01051.311 Xsr LrU U e−= (7)

Key factors influencing the membrane foul-ing rate were aeration intensity (again capturedby the tap water crossflow velocity to incorpo-rate the effect of the reactor structure), permeateflux, and SS concentration. The parameters werefitted to the following power equation:

2c d eLrK f U J X= (8)

where f2, c, d, and e are constants. The values ofthese constants, determined using the least squaresmethod, are as follows: f2 = 8.933×107, c = –3.047,d = 0.376, and e = 9.532. Eqs. (7) and (8) are sup-plied to quantitatively characterize membranefouling in an MBR.

The equations supplied by the hydrodynamicmodel explicitly show the correlation of varioushydrodynamic parameters to two important fac-tors: membrane fouling rate and mixed liquorcrossflow velocity. The mixed liquor crossflowvelocity is important because it gives insight intothe impact of hydraulic conditions on membrane


fouling in terms of the retardation of sludge accu-mulation on the membrane surface. While themodel is easy to use, it is too simple to capturethe complicated phenomena on the membrane sur-face and so fails to account for many other condi-tions and operational parameters. Consequently,the model was unable to accurately reproduce theexperimental results from which the model wascalibrated for the membrane fouling rate. The cal-culated mixed liquor crossflow velocities corre-sponded well with the measured values, but it mustbe tested against a different set of experimentaldata to support its validity. In general, the modelmay be useful for illustrating hydrodynamic ef-fects on membrane fouling, but it may not be suit-able for operational and design purposes.

2.2.2. Fractal permeation model

A permeation model (based on fractal theoryand Darcy’s law) was developed by Meng et al.[24] to evaluate the permeability of cake formedfrom the microfiltration of activated sludge. Themicrostructure of a cake layer is usually disor-dered and complicated and, thus, cannot be de-scribed by traditional geometry. Fractal theory canbe applied here to characterize the irregular ob-ject in terms of its average, self-similar proper-ties. The authors first introduce a model to deter-mine the pore area fractal dimension, Ds, of a cakelayer:

( )20( ) sD

cB a S A C a −≥ = − = (9)

where a is a threshold pore area, B is the totalcake layer area (Sc) minus the sum (A) of all poreareas equal to or larger than a (i.e., A = Σa), andC0 is a constant. This model stems from a fractalmodel developed by Kaye et al. and Xu et al. [25,26]. Meng et al. provide a procedure for physi-cally determining the fractal dimension of a cakelayer, which involves the use of an image ana-lyzer to evaluate each pore area. Eq. (9) can beapplied to calculate the values of B from several

defined threshold values of a. The fractal dimen-sion can then be computed from the slope of thestraight line through the plot of ln B vs. ln a.

The permeability model was derived by modi-fying the Hagen–Poiseulle equation for flow ratethrough a tortuous capillary or pore [27]. Theequation was rewritten in terms of the thresholdpore area, a, rather than the pore diameter, λ, asfollows

( ) ( )2G P aq a

g L a∆=

µ (10)

where G is the geometry factor for fluid flowthrough a pore (i.e., π/128 for circular pores), g isthe shape factor where a = gλ2, ∆P is the pressuregradient, L(a) is the tortuous length of a pore, andµ is the dynamic viscosity. Straight pores wereassumed in the cake layer, allowing the replace-ment of L(a) by a constant, L0. A unit flow ratewas obtained by dividing Eq. (10) by a, and theinfinitesimal flow rate dQ through an area dA wasexpressed as:

( )2

0

d d dq a G P aQ A A

a g L∆= − = −

µ (11)

The portion of cake area, dA, was obtained bytaking the derivative of Eq. (9) with respect to a:

( ) 10d 2 dsD

sA C D a a−= − − (12)

Substituting Eq. (12) into Eq. (11) and integrat-ing Eq. (11) over the pore area distribution range(amin to amax) gave

( )

( )

max

min

20 2

0

3 30 max min2

0

1 2 d

213

s

s s

a Ds a

D Ds

s

G PQ C D a ag L

DG P C a ag L D

−

− −

∆= −µ

−∆= −µ −

∫(13)

which was reduced to


30 max2

0

213

sDs

s

DG PQ C ag L D

−−∆=µ − (14)

by recognizing that the fractal dimension must bebetween 1 and 2, and amax is much greater thanamin (i.e., 1 < Ds < 2, so 3 – Ds > 1 and amax amin,so amax

3–Ds amin3–Ds). The expression for the flow

rate, Q, in Eq. (14) was substituted into Darcy’slaw to obtain the following equation for the per-meability of porous cake:

300 max2

213

sDs

t t s

L Q DG C aPA g A D

−µ −κ = =∆ − (15)

Cake layer permeation factor, κ′, was definedas

3max

23

sDs

s

D aD

−−′κ =− (16)

and was used to illustrate the validity of the model.A number of membrane fouling experiments wereperformed with varying activated sludge proper-ties. The specific resistance of the cake layer, rc,in each experiment was determined indirectly. Theinverse of the specific cake resistance is equal tocake permeability; therefore, the plot of the per-meation factor against 1/rc should show high lin-earity if the model is valid. A correlation coeffi-cient of 0.857 for the linear regression was ob-served. Based on this, the authors asserted thatthe model is reasonable to a certain degree and istheoretically valid.

The fractal permeation model provides amethod for determining the permeability of cakebuildup on a membrane surface. The model in-volves only a few parameters that are fairly easyto determine and does not require intensive com-putation to solve. However, the model was onlyindirectly validated; therefore more adequate veri-fication is necessary to determine the model’sapplicability. Moreover, the model does not showhow operational parameters and conditions affect

cake resistance but primarily relies on the fractaldimension to capture different effects. Therefore,various parameters must be further correlated withthe pore area fractal dimension (or permeationfactor) to determine their effects on cake resis-tance.

2.2.3. Sectional resistance model

In a submerged MBR, coarse bubbles fromaeration provide a cleaning mechanism for theimmersed membrane modules by scouring themembrane surface. The shear force from aerationis unevenly distributed, resulting in non-uniformfouling. Li and Wang [28] applied a sectional ap-proach to account for the uneven cake formationin determining total filtration resistance. Theydivided the membrane surface into equal fractionalareas, ∆ε, and calculated separate total resistances,R, for each section, which consist of inherentmembrane resistance Rm, pore fouling resistanceRp, and resistances due to dynamic and stablesludge films, Rsf and Rsc, respectively. The totalresistance in each section is then described as

m p sf scR R R R R= + + + (17)

The pore fouling resistance, Rp, is proportionalto the amount of permeate produced and is givenby

p p fR r J= θ∑ (18)

where rp is the specific pore fouling resistance, Jis the permeate flux, and θf is the filtration periodof an operational cycle. Rsf is the product of thespecific resistance of the biomass in the dynamicfilm, rsf, and the mass of the dynamic sludge film,Msf (i.e., Rsf = rsfMsf). Likewise, Rsc, is equal to theproduct of the specific resistance of the sludgecake layer, rsc, and the mass of biomass accumu-lated on the membrane surface, Msc (i.e., Rsc =rscMsc).

The mass of the sludge in the dynamic film


can be determined from the following equationduring the filtration period:

( ) 22 12424

sf sf

d p f sf

dM GMCJdt J C d G V t M

β − α= −

+ γ + (19)

The first and second terms of Eq. (19) repre-sent the rate of attachment and detachment, re-spectively. The attachment rate was derived byconsidering the opposing forces (i.e., the dragforce that leads to attachment and a lift forcecaused by turbulence) acting on a particle as itapproaches the membrane. The probability of thedeposition of particles on the membrane surfaceis given by the attachment force divided by thesum of the two forces. Multiplying this probabil-ity by the mass flux (the sludge concentration ´the permeate flux) gives the rate of attachment.Here, C is the sludge concentration, J is the localpermeate flux in the membrane section, Cd is thecoefficient of the lifting force of a sludge particleof diameter dp, and G is the shear intensity on thesection of the membrane surface. The detachmentrate was assumed to follow a first-order kineticprocess, i.e., (dMsf/dt)d = –KdMsf. The rate coeffi-cient, Kd, was thought to vary with the mass ofthe sludge film. It increases with Msf and reachesa maximum with large values of Msf so that aMonod-type equation, Kd = κr Msf/(κs + Msf), isproposed. Expressions were assumed for the maxi-mum rate constant, κr, and half-saturation con-stant, κs. In the detachment rate expression, β isthe erosion rate coefficient of the dynamic sludge,α is the stickiness of biomass particles, γ is thecompression coefficient for dynamic sludge, Vf iswater production within the filtration period ofthe operation cycle, and t is the filtration time.During the cleaning period when no attachmentoccurs, the rate of detachment is described as

( ) 210.1

sf sf

f f sf

dM GMdt V M

β − α= −

γ θ + (20)

The factor 0.1 in the denominator arises fromthe presumption that the compression coefficientduring the cleaning period is reduced by a tenthof its original value. The remaining sludge aftercleaning, ∆Msc, adds to the stable sludge cakelayer.

For the shear intensity, G, at each section, thefollowing shear profile is assumed:

( )

0

21 9 1 sin10 20 21

i ai a

a

i a

GG

⎧ ⎡ ε − ε π⎤+ + ε < ε ⎪ ⎢ ⎥= ε⎨ ⎣ ⎦

⎪ ε ≥ ε⎩

(21)

where G0 is the apparent shear intensity of thefluid turbulence, εi is the accumulated membranearea fractions up to the ith section, and εa is thesectional area of membrane surface with reducedshear intensity (where G/G0 is less than 1).

The sectional resistance model was developedusing a partially analytic approach. The model isintended to characterize membrane fouling in sub-merged MBRs where the membranes are sub-jected to shear flow from aeration. By dividingthe membrane into sections and considering theresistance in each section, the model accounts foruneven cake formation stemming from varyingshear distribution along the membrane surface.The advantages of this transient model are that itaccounts for cleaning cycles and characterizesfouling development over time. Experiments wereconducted using a submerged MBR, which fil-tered glucose-based synthetic wastewater withvarying sludge concentrations, filtration fluxes,and aeration intensities. Comparison of the mea-sured and computer-simulated trans-membranepressure over MBR operation time revealed thatthe model is only able of capturing general trendsand may not be suitable for applications requir-ing accurate modeling of membrane fouling phe-nomena.


2.3. Integrated models

The models reviewed in this section are notfully integrated, but only lightly coupled to char-acterize both biomass transformation processesand membrane fouling. They are a first step inMBR model integration, as no truly integratedmodels have been developed yet, to the best ofour knowledge.

2.3.1. ASM1-SMP hybrid and resistance-in-series model

An integrated MBR model in which ASM1was modified to include components for SMP andadditional rate processes to describe SMP fate waspresented by Lee et al. [10]. The resistance-in-series model was adapted to account for the in-fluence of the biomass on membrane fouling.Much like the ASM1-SMP hybrid model pre-sented by Lu et al. [9], four rate process expres-sions were added to ASM1. The model stochio-metry was accordingly modified. The four pro-cesses are listed below.• Aerobic growth from SSMP:

2 4

2 2 4 4

O NHSMPSMP

O O SMP SMP NH NH

ALKH

ALK ALK

S SSK S K S K S

S XK S

µ+ + +

+

• Anoxic growth from SSMP:

32

3

2 2 3 3

4

4 4

NOOSMPSMP NO

SMP SMP O O NO NO

NH ALKH

NH NH ALK ALK

KKSK S K S K S

S S XK S K S

µ η+ + +

+ +

• Lysis of heterotrophic organisms producingSSMP: bH,SMP XH

• Lysis of autotrophic organisms producing SSMP:bA,SMP XA

This model incorporates the influence of al-kalinity and ammonia concentrations on het-erotrophic growth rate into the additional processrate expressions. Note that the previously de-scribed ASM1-SMP hybrid model does not con-sider alkalinity and removes ammonia concentra-tion limitations on the growth rates of hetero-trophs.

To model membrane fouling, the followingequation for total filtration resistance, R, was sup-plied:

mR R m= + α (22)

where

TSSpm

V Xm k

A= (23)

Here, Rm is the membrane resistance, α is the spe-cific resistance, km is a coefficient ranging from 0to 1 to reflect crossflow filtration effects (e.g.km = 1 for dead-end filtration), Vp is the permeatevolume, XTSS is the concentration of total sus-pended solids (TSS) in the biomass, and A is themembrane surface area. SMP was assumed not tocontribute to the membrane resistance since itsconcentration was thought to be negligible com-pared to the TSS concentration.

The resistance model given here involves fewparameters for predicting total resistance on themembrane surface. The parameter values can beeasily determined, and total resistance is simpleto calculate. However, both the biomass kineticsand resistance models have not been validated,and the applicability of the models is unknown.

2.3.2. ASM3 and resistance-in-series model

In the study by Wintgens et al. [11], a modelwas introduced to describe the filtration perfor-mance of submerged capillary hollow fiber mod-ules in an MBR. The model was combined withASM3 to include characterization of the biologi-


cal treatment process. It was acknowledged thatextra-cellular polymeric substances (EPS) pro-duced by the microorganisms can hamper mem-brane performance, but no modifications weremade to ASM3 to quantify this component.

In the model, permeate flux was given as

( )TM

P M C F

pFR R R

∆=η + + (24)

where

TM hydro pump axp p p p∆ = + − ∆ (25)

The effective transmembrane pressure differ-ence, ∆pTM, is the sum of the hydrostatic pres-sure, phydro, and the suction pressure, ppump, minusthe pressure loss from permeate flow along thehollow fibers, ∆pax. Total resistance is the sum ofmembrane resistance, RM, cake resistance, RC, andfouling resistance RF. Cake resistance is given by

C C MR k c= (26)

where kC is the cake layer model parameter andcM is the concentration at the membrane surface,which is described as

( ) / PF t kM bc c e= (27)

where cb is bulk concentration, F(t) is the trans-membrane flux, kF is the local mass transfer coef-ficient. The expression used for kP is

W CP

F

dk τ=η (28)

where τW is the mean wall shear stress, dC is char-acteristic particle diameter, and ηF is viscosity ofthe activated sludge. The fouling resistance wasgiven as

0( )

1t

Fk F t dt

F FR S e−⎛ ⎞∫= −⎜ ⎟

⎝ ⎠(29)

where SF and kF are model parameters for foulingsaturation and accumulated fouling, respectively,and

0( )d

tF t t∫ is the total permeate volume per

membrane area produced between two chemicalcleanings. The final form of the permeate flux hasan implicit expression:

0( )d( ) /

( )

1t

FP

hydro pump ax

k F t tF t kP M C b F

F tp p p

R k c e S e−

=+ + ∆

⎛ ⎞⎛ ⎞∫η + + −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(30)

This model is based on the resistance-in-se-ries model and was developed to describe the fil-tration performance of submerged capillary hol-low fiber modules in an MBR. Like the sectionalresistance model, this model accounts for clean-ing cycles and incorporates time dependency toprovide a continuous fouling profile. The modelwas tested against operational data from a full-scale MBR with two external filtration units. Datafrom the first unit were used to set model param-eters by curve-fitting using the least-square-errormethod. Simulation results from the calibratedmodel were then compared with data from thesecond filtration unit. Except for the initial pe-riod of operation, the computed permeability overtime corresponded well with measured data. Themodel was also validated with experimental datafrom a pilot MBR with submerged capillary hol-low fiber membranes [29]. The simulation resultsfor permeability evolution over time matched wellthe data from the pilot plant except for a majordeviation at the end of the considered period. Thedeviation was explained by a drop in the organicload of the influent, a factor which was not con-sidered in the simulation.

3. Concluding remarks

A mini-review of modeling studies on the ap-plication of MBR for the treatment of municipalwastewaters was conducted to assess current MBR


modeling efforts. Models describing biomass ki-netics in an MBR include the ASM model family,the SMP model, and the ASM1-SMP hybridmodel. The ASMs were developed to model theactivated sludge process, and their ability to ac-curately describe the MBR process has not beenverified by in-depth experiments.

Research suggests that SMPs are importantcomponents in describing biomass kinetics dueto high SRTs in MBR systems. Accordingly, theSMP model demonstrated the capability of char-acterizing the biomass with a reasonable to highdegree of accuracy. Also, a modified version ofASM1 that incorporates SMPs demonstratedfairly reasonable accuracy in quantifying CODand soluble nitrogen concentrations but underes-timated MLSS concentrations. Further testing isneeded to aid in model development.

Models describing membrane fouling includethe empirical hydrodynamic model, fractal per-meation model, sectional resistance model, andthe two resistance-in-series models that were pre-sented as a part of integrated models. The empiri-cal hydrodynamic model is too simple to describethe membrane fouling phenomenon, and the sec-tional resistance model lacks accuracy. Both thefractal permeation model and resistance-in-seriesmodel by Lee et al. [10] provide good scientificinsight, but specific experimental verification isnecessary for general use of the models. The re-sistance-in-series model developed by Winitgenset al. [11] shows the most promise, as it is fairlyaccurate, accounts for cleaning cycles, and canpredict permeability changes over time. Furthertests are needed to determine whether the modelrequires calibration or if the model parameters areapplicable to other MBR systems.

For any given wastewater treatment system,primary concerns are the effluent quality that thesystem is able to achieve and the investment andoperating costs required for the system. The sys-tem must be able to treat the water to meet waterquality standards as set forth by regulatory agen-cies, and it must, simultaneously, be economical.

Therefore, model development should center oncomponents for which water quality standardshave been set and on parameters which arestrongly correlated to cost. A few key model com-ponents and parameters for MBRs are given here.

Permeate flux and transmembrane pressure aredirectly related to cost. These two parameters arecorrelated by permeate viscosity and total resis-tance. The ability to quantify individual resistance(i.e., resistance from cake formation and adsorp-tive fouling) as a function of the various influ-encing parameters is important in determiningwhich parameters have the greatest influence onfouling and for designing and optimizing the sys-tem to achieve an economical balance betweenproduction and applied pressure. Parameters thataffect fouling include sludge concentration, shearrate, concentration of pore-blocking and mem-brane adsorptive materials in the feed, and mem-brane material properties.

MBRs typically operate at higher biomass con-centrations than conventional biological treatmentprocesses. The advantage that this provides is in-creased volumetric loading and less sludge pro-duction, which in turn lowers capital investmentcosts for civil works and reduces sludge disposalcosts. Conversely, higher biomass concentrationscan adversely affect membrane performance, ne-cessitating increased membrane area to maintainpermeate flow rate and, thus, increase investmentcosts. Biomass concentration also influences en-ergy costs. A reduced oxygen transfer rate is as-sociated with higher biomass concentrations, soenergy cost for aeration increases accordingly.Additionally, higher sludge viscosity, with respectto greater biomass concentration, requires a largerapplied pressure to achieve a certain permeateproduction goal. Determining the relationshipbetween biomass concentration and other param-eters can aid in identifying an optimal biomassconcentration for operation, which can lead to sig-nificant economical savings.

Aeration accounts for a significant portion ofenergy costs in the operation of MBR systems.


Thus, optimizing the oxygen supply can favor-ably affect operating costs. Determining the dis-solved oxygen requirement and the conditions tosupply the optimal amount at a high transfer ratecan reduce wasting oxygen. Some of the factorsthat influence the oxygen transfer rate include theMLSS concentration, the mechanical configura-tion of MBR, the type of bubbles used (fine orcoarse), and the specific air flow rate. The oxy-gen requirement depends on the constituents inthe wastewater, biomass concentration, and bio-mass growth rates.

It is important to include carbon and nutrient(nitrogen and phosphorous components) concen-trations in MBR models, given that the bioreactorsprocess performance is characterized by thosecomponents. COD, BOD, ammonia/ammonium,nitrate/nitrite, and orthophosphate concentrationsin the effluent should be captured by MBR mod-els. The respective concentrations of these com-ponents are affected by the concentration of thevarious types of organisms influencing the re-moval of certain components, growth rates ofthese organisms, and concentration of oxygen inthe system.

SMPs comprise a major portion of the organicmatter in effluents from biological treatment pro-cesses. It is crucial to quantify and also minimizeSMPs in the effluent because they are possibleprecursors to trihalomethane and other disinfec-tion by-products, competitively adsorb on acti-vated carbon surfaces, and potentially lead to bio-logical growth in distribution systems. Addition-ally, EPS, which is a form of SMP that surroundsthe surfaces of microorganisms, contributes tomembrane fouling, especially when the microor-ganisms form specific biofilms on the membranesurfaces. Factors that influences the formation ofSMP (and EPS) include biomass concentration,loading rates, and sludge age.

Several of the existing models, particularly theASMs, require validation to determine their ap-plicability for modeling the MBR process and toevaluate whether they can serve as a base for fu-

ture MBR model development. Membrane foul-ing in MBRs is affected by the biotransformationprocesses in the system, so the integration of bio-mass kinetics and membrane fouling models isessential for future modeling. Moreover, exami-nation of alternative empirical modeling ap-proaches, such as the application of artificial neu-ral networks, is worthwhile to make a rigorouslink between inputs and outputs of MBR systemsand to find phenomenological interrelationshipsamong components and parameters.

The main purpose of this review is to organizecore ideas of current MBR studies by selectingkey publications, to assess the state-of-the-artMBR modeling efforts, and to propose future di-rection for MBR simulation research in pursuitof a global optimization for design criteria, op-eration protocol, and cost evaluation. We hope thisreview contributes to reassessment of the currentpredictability of MBR processes and opens di-rections for developing fundamental mechanismsthat rigorously govern MBR performance.

Acknowledgement

This work was supported by the U.S. Geologi-cal Survey, through the Water Resources ResearchCenter, University of Hawaii at Manoa, Hono-lulu, and by Saehan Industries, Korea. This iscontributed paper CP-2006-00 of the Water Re-source Research Center.

References[1] C.W. Smith, D. Gregorio and R.M. Taleott. The use of

ultrafiltration membrane for activated sludge separa-tion, Presented at the 24th Annual Purdue IndustrialWaste Conference, 1969, pp. 1300–1310.

[2] W. Yang, N. Cicek and J. Ilg, State-of-the-art of mem-brane bioreactors: Worldwide research and commer-cial applications in North America, J. Membr. Sci., 270(2006) 201–211.

[3] G. Tchobanoglous, F.L. Burton and H.D. Stensel,Wastewater Engineering: Treatment and Reuse,McGraw-Hill, Boston, 2004, pp. 854–865.


[4] J. Manem and R. Sanderson, Membrane bioreactors,water treatment membrane processes, J. Mallevialle,P.E. Odendaal and M.R. Wiesner, eds., McGraw-Hill,New York, 1996, pp. 17.1–17.31.

[5] M. Henze, C.P.L.J. Grady, W. Gujer, G.v.R. Marais andT. Matsuo, Activated Sludge Model No. 1, in IAWPRCScientific and Technical Report No. 1, IAWPRC, Lon-don, 1987.

[6] M. Henze, W. Gujer, T. Mino, T. Matsuo, M.C. Wentzeland G.v.R. Marais, Activated Sludge Model No. 2, inIAWQ Scientific and Technical Report No. 3, IAWQ,London, 1995.

[7] M. Henze, W. Gujer, T. Mino, T. Matsuo, M.C. Wentzel,G.v.R. Marais and M.C.M. Van Loosdrecht, Activatedsludge model No.2d, ASM2d, Wat. Sci. Technol., 39(1)(1999) 165–182.

[8] W. Gujer, M. Henze, T. Mino and M. van Loosdrecht,Activated sludge model No. 3, Wat. Sci. Technol., 39(1)(1999) 183–193.

[9] S.G. Lu, T. Imai, M. Ukita, M. Sekine, T. Higuchi andM. Fukagawa, A model for membrane bioreactor pro-cess based on the concept of formation and degrada-tion of soluble microbial products, Wat. Res., 35(8)(2001) 2038–2048.

[10] Y. Lee, J. Cho, Y. Seo, J.W. Lee and K.-H. Ahn, Mod-eling of submerged membrane bioreactor process forwastewater treatment, Desalination, 146 (2002) 451–457.

[11] T. Wintgens, J. Rosen, T. Melin, C. Brepols, K. Drenslaand N. Engelhardt, Modelling of a membrane biore-actor system for municipal wastewater treatment, J.Membr. Sci., 216 (2003) 55–65.

[12] M. Henze, W. Gujer, T. Mino and M. van Loosdrecht,Activated Sludge Models: ASM1, ASM2, ASM2d, andASM3. Scientific and Technical Report Series. vol. 9,IWA Publishing, London, 2000.

[13] H.Y. Ng and S.W. Hermanowicz, Membrane bioreactoroperation at short solids retention times: performanceand biomass characteristics, Wat. Res., 39(6) (2005)981–992.

[14] D.J. Barker and D.C. Stuckey, A review of solublemicrobial products (SMP) in wastewater treatmentsystems, Wat. Res., 33(14) (1999) 3063–3082.

[15] X. Huang, R. Liu and Y. Qian, Behaviour of solublemicrobial products in a membrane bioreactor, ProcessBiochem., 36(5) (2000) 401–406.

[16] H.-S. Shin and S.-T. Kang, Characteristics and fates ofsoluble microbial products in ceramic membranebioreactor at various sludge retention times, Wat. Res.,37(1) (2003) 121–127.

[17] N. Park, B. Kwon, I.S. Kim and J. Cho, Biofoulingpotential of various NF membranes with respect tobacteria and their soluble microbial products (SMP):Characterizations, flux decline, and transport param-eters, J. Membr. Sci., 258 (2005) 43–54.

[18] S. Rosenberger, C. Laabs, B. Lesjean, R. Gnirss, G.Amy, M. Jekel and J.C. Schrotter, Impact of colloidaland soluble organic material on membrane performancein membrane bioreactors for municipal wastewatertreatment, Water Res., 40(4) (2006) 710–720.

[19] H.Y. Ng, T.W. Tan and S.L. Ong, Membrane foulingof submerged membrane bioreactors: Impact of meancell residence time and the contributing factors,Environ. Sci. Technol., 40(8) (2006) 2706–2713.

[20] H. Furumai and B.E. Rittmann, Advanced modelingof mixed populations of heterotrophs and nitrifiersconsidering the formation and exchange of solublemicrobial products, Wat. Sci. Technol., 26(3–4) (1992)493–502.

[21] V. Urbain, B. Mobarry, V. de Silva, D.A. Stahl, B.E.Rittmann and J. Manem, Integration of performance,molecular biology and modeling to describe the acti-vated sludge process, Wat. Sci. Technol., 37(4–5)(1998) 223–229.

[22] D.G.V. de Silva, V. Urbain, D.H. Abeysinghe and B.E.Rittmann, Advanced analysis of membrane-bioreactorperformance with aerobic-anoxic cycling, Wat. Sci.Technol., 38(4–5) (1998) 505–512.

[23] R. Liu, X. Huang, Y.F. Sun and Y. Qian, Hydrodynamiceffect on sludge accumulation over membrane surfacesin a submerged membrane bioreactor, Process Bio-chem., 39(2) (2003) 157–163.

[24] F. Meng, H. Zhang, Y. Li, X. Zhang and F. Yang, Ap-plication of fractal permeation model to investigatemembrane fouling in membrane bioreactor, J. Membr.Sci., 262 (2005) 107–116.

[25] B.H. Kaye, A Random Walk Through Fractal Dimen-sions, VCH, New York, 1994, chap. 6.

[26] X.Y. Xu, J.R. Xu and Y. Kang, Dynamics of air pres-sure filtration and fractal filter cake constructure, J.Chem. Ind. Eng., 46 (1995) 8–14.

[27] B.M. Yu and W. Liu, Fractal analysis of permeabilitiesfor porous media, AIChE J., 50(1) (2004) 46–57.

[28] X.-y. Li and X.-m. Wang, Modelling of membrane foul-ing in a submerged membrane bioreactor, J. Membr.Sci., (in press).

[29] S. Geissler, T. Wintgens, T. Melin, K. Vossenkaul andC. Kullmann, Modelling approaches for filtration pro-cesses with novel submerged capillary modules inmembrane bioreactors for wastewater treatment, De-salination, 178 (2005) 125–134.

Documents

A mini-review of modeling studies on membrane bioreactor … · 2012-08-17 · A.N.L. Ng, A.S. Kim / Desalination 212 (2007) 261–281 263 that are also practical for real applications