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Journal of Environmental Management 81 (2006) 118

Review

Modelling anaerobic biofilm reactorsA review

V. Saravanan, T.R. Sreekrishnan

Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology Delhi, New Delhi-110 016, India

Received 7 October 2004; received in revised form 4 October 2005; accepted 5 October 2005

Available online 6 March 2006

Abstract

Anaerobic treatment has become a technically as well as economically feasible option for treatment of liquid effluents after the

development of reactors such as the upflow anaerobic sludge blanket (UASB) reactor, expanded granular sludge bed (EGSB) reactor,anaerobic biofilter and anaerobic fluidized bed reactor (AFBR). Considerable effort has gone into developing mathematical models for

these reactors in order to optimize their design, design the process control systems used in their operation and enhance their operational

efficiency. This article presents a critical review of the different mathematical models available for these reactors. The unified anaerobic

digestion model (ADM1) and its application to anaerobic biofilm reactors are also outlined.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Mathematical model; UASB; AFBR; EGSB; Biofilter; Biofilm; Anaerobic

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Models for UASB reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.1. Flow model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2. Reactor model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3. Proposed models for the structure of the biofilm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.1. Multi-layer model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2. Syntrophic microcolony model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.3. Non-layered structure model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.4. Granule cluster structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4. Models for AFBR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.1. Bed fluidization model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.1.1. Terminal settling velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.1.2. Fluidization mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.1.3. Effect of gas production on hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4.1.4. Bed stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.2. Kinetic and reactor sub-models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2.1. Stratified biofilm models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

5. The EGSB reactor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6. The anaerobic biofilter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

7. The unified model for anaerobic digestion (ADM1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

7.1. The extension of ADM1 to biofilm reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8. Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

ARTICLE IN PRESS

www.elsevier.com/locate/jenvman

0301-4797/$ - see front matterr 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jenvman.2005.10.002

Corresponding author. Tel.: +91 11 26591014; fax: +91 11 26582282.

E-mail address: [email protected] (T.R. Sreekrishnan).
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1. Introduction

The term biofilm reactor refers to that class of

bioreactors where the biocatalyst exists in an anchored

form, either on the surface of an inert carrier or attached

to one another. The carrier could be the wall of the reactor,

baffles provided for this purpose or particles of some inertmaterial. Biocatalysts such as microorganisms could also

grow attached to one another, giving rise to a biogra-

nule. The carrier or the biogranule could be stationary as

in a packed-bed or expanded bed system or mobile as in the

case of a fluidized bed system. Typically, in such reactors,

the rate of substrate conversion is limited by the rate of

transport of substrate into the biofilm. In an anaerobic

biofilm reactor, the biocatalyst will include all the different

bacterial species responsible for the break down of complex

organic molecules to a final end product consisting of

methane and carbon dioxide. The anaerobic treatment, as

the main biological step in wastewater treatment systems,

was scarce until the development of the upflow anaerobic

sludge blanket (UASB) reactor in the early 1970s (Lettinga

et al., 1980). UASB processes are based on the develop-

ment of dense granules (14 mm) formed by the natural

self-immobilization of the anaerobic bacteria. This kind of

immobilization does not employ any support material such

as Raschig rings or clay in the reactor (Nicolella et al.,

2000). A schematic of a typical UASB reactor is shown in

Fig. 1. Wastewater enters the bottom of the reactor

through the inlet liquid distribution system and passes

upward through the dense anaerobic sludge bed. Because

of the high biomass concentration, it was demonstrated

that volumetric organic loading rates as high as 50 kgchemical oxygen demand (COD) per m3 per day could be

employed (Hulshoff Pol, 1989). The liquid velocity inside

the reactor is usually in the range of 0.51.0 m/h. This

reactor consists of a sludge bed, a sludge blanket and a

clarifier zone supplemented with a physical device called

the gassolid separator.

In anaerobic fluidized bed reactor (AFBR), the liquid to

be treated is pumped through a bed of inert particles

(typically sand with a particle size range of 0.20.8 mm) at

a velocity sufficient enough (1020 m/h) to cause fluidiza-

tion (Nicolella et al., 2000). In the fluidized state, the media

provides a large surface for attached biological growth and

allows biomass concentrations to develop in the range of

1040 kg/m3 (Cooper and Sutton, 1983). A typical flow

diagram of an AFBR is shown in Fig. 2. Compared to

other high rate anaerobic reactors such as UASB, the

fluidized bed system is claimed to have the following

advantages: higher purification capacity, no clogging of

the reactor (as in filters), no problem of sludge washout

(as in UASB systems if granular sludge is not obtained),

and small volume and land area requirements (Heijnen

et al., 1989).

To study the sensitivity of the process to various

operating parameters and to optimize the design of these

reactors, it is necessary to have mathematical models which

are simple in concept and close to the physical situation

existing in these reactors. During the past few decades there

have been a number of studies on modelling of UASB and

AFBR reactors. An effort is made in this article to present

the gist of different approaches used in developing

mathematical models for these reactors. This article also

reviews different proposals available for modelling the

structure of the biological granules and biofilm-covered

particles in these reactors.

2. Models for UASB reactors

The formation of anaerobic granular sludge is consid-

ered to be a necessary condition for the successful

operation of a UASB reactor. The efficiency of the reactor

depends mainly on active biomass concentration and the

influent flow rate. As the reactor reaches steady state, a

dense bed composed of granulated sludge develops at the

bottom. Immediately above the sludge bed, a zone

consisting of finely suspended particles called the sludge

blanket forms. A clear zone over this sludge blanket

constitutes the settling zone. To keep the sludge granules in

suspended condition inside the reactor, the inlet flow rate

ARTICLE IN PRESS

Biogas

Effluent

Influent

Baffles

Weir

Settler

Sludge Bed

Sludge Blanket

Sludge granules

Fig. 1. Schematic diagram of UASB reactor.

Wastewater feed

Carrier

Biofilm

Recycle line

Treated water

Biogas

Fig. 2. Anaerobic fluidized bed reactor (AFBR).

V. Saravanan, T.R. Sreekrishnan / Journal of Environmental Management 81 (2006) 1182


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should be below a threshold limit (normally below 1 m/h).

This low influent flow rate causes channelling problems in

the sludge bed zone, resulting in lowered efficiency of the

reactor. Hence to develop mathematical models for this

reactor, it is important to analyse the flow pattern inside

the reactor and reaction kinetics within the biological

granules. In general, models for UASB reactors consist oftwo parts:

1. fluid flow model;

2. reactor model.

2.1. Flow model

Fluid flow models for UASB reactors differ considerably

in their approach. The different zones of a UASB reactor

are modelled as continuos stirred tank reactors (CSTR) or

plug flow reactors (PFR) having dead volume with bypass

flow between the zones (Bolle et al., 1986; Van der Meer,1979;Wu and Hickey, 1997). The flow behaviour within a

zone mainly depends on the concentration and character-

istics of the biomass (Ojha and Singh, 2002).

Wu and Hickey (1997) have developed a flow model to

describe the flow pattern in a UASB reactor. They modelled

the sludge bed and blanket as a non-ideal CSTR by using a

combination of an ideal CSTR along with a dead zone and

a bypass flow. This CSTR is in series with a dispersed plug

flow reactor (PFR) (non-ideal PFR) that represents the

clarification zone above the sludge blanket (Fig. 3).

The equation of the flow model is given by

VbdCdt

VbEt QfCt, (2.1)

Et MfVbTin

if 0ptpTin;

0 ifTinp0; (2.2)

whereC(t) is the tracer concentration within the CSTR, Vbthe CSTR working volume, E(t) the input function for

tracer impulse, Qfthe low fraction that enters the working

volume, Mf the fraction of mass input that go through

reactors working volume, andTinthe tracer injection time.

Ojha and Singh (2002) analysed the flow distribution in

different zones of the reactor in order to simulate the

UASB reactor performance. They used the flow resistance

approach to represent flow distribution. It was found that

with an increase in flow resistance in the UASB reactor

system, the magnitude of short-circuiting flows at the

reactor bed increased. The flow distribution at the blanket

and clarifier was found to have an influence on the flow

resistance. But no generalized model could be obtained.

Bolle et al. (1986) divided the reactor into three

compartments (Fig. 4): sludge bed, sludge blanket and

settler. The liquid flow in the sludge bed and the sludge

blanket were described by completely stirred tank reactor

systems. Liquid flow in the internal settler was described by

a plug flow model.

Narnoli and Indu (1997) developed a model for the

sludge blanket of a UASB reactor. According to them, the

maximum organic load which a reactor can assimilate

depends on proportioning of the reactor height into the bed

and the blanket sections. A condition of force equilibrium

was considered between the rising gas bubbles from the

sludge bed and the adjacent water mass. The negative

pressure behind the bubble attracts the water mass and

leads to the formation of a wake. Using diffusion concepts,

solid particles moving along the wake due to the

concentration gradient were equated to those settling down

under the influence of gravity at steady state. The solid

concentration along the blanket height was computed and

found to match the experimental observations. This model

could be used to optimize the reactor dimensions and the

desludging schedule.

Singhal et al. (1998) reported that a simple two-zone

axial dispersion model adequately describes the fluid flow

characteristics of UASB reactors. They found that the fluid

flow behaviour is very sensitive to the volume of zones and

degree of bypassing between them but less sensitive to the

dead volume. The model assumed that some of the liquid

bypasses the first zone and enters directly into the second

zone. The schematic representation is shown inFig. 5.

ARTICLE IN PRESS

Dead volume

CSTR Dispersed

plug flow

By-pass flow

Fig. 3. Representation of hydraulic model (Wu and Hickey, 1997).

Effluent

Settler

Sludge blanket

Short circuit

Dead space Sludge bed

Influent

Fig. 4. Block diagram of fluid flow pattern (Bolle et al., 1986).

V. Saravanan, T.R. Sreekrishnan / Journal of Environmental Management 81 (2006) 118 3


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They had verified the model efficacy through tracer

studies. The step response of an axially dispersed tubular

flow reactor for an inert tracer is described by the following

partial differential equation:

1

Pe

q2C

qZ2

qC

qZ

qC

qy, (2.3)

where C is the dimensionless concentration of the tracer

(c/c0), Pe is the Peclet number (uL/D), Z is the dimension-

less distance (z/L),y is the dimensionless time (t/t), u is the

linear average velocity of the liquid in the reactor, L is the

length of the reactor, and D is the axial dispersion

coefficient. The simulation and experimental results gave

a very good fit validating this flow model.

All the above multi-compartment models were capable

of fitting laboratory scale experimental data well. In the

case of full-scale reactors, the feed distribution is very

different from that in the laboratory scale reactor. Distinct

zones of sludge bed, sludge blanket and clarifier may not be

observed due to the large volume of the reactor and uneven

flow distribution. This will make the task of quantifying theextent of non-ideality in the flow patterns difficult. It may

not be correct to predict the fluid flow pattern based on lab

scale studies alone. Hence, further investigations are

required to test the models for full-scale reactors.

2.2. Reactor model

Substrate degradation in the bioreactor is dependant on

the observed reaction rate. In a biofilm type of reactor set-

up, the observed reaction rate is normally less than the rate

predicted by the reaction kinetics. The reason for this is

that the substrate concentration actually available to the

microorganisms is less than the substrate concentration

present in the bulk liquid. This is due to the control exerted

by the mechanism of molecular diffusion on the penetra-

tion of substrate into the biofilm. It is, therefore, important

to analyse the rate-determining step while developing

models. Hence, the reactor model consists of 3 parts:

substrate utilization within the biofilm (granules), mass

transfer and transport in the granule bed and blanket, and

mass transport within the clarifier.

Kinetic models are based on the relationship between

limiting substrate concentration and growth rate as

proposed byMonod (1950).James (1961)pointed out that

in biological processes a wide variety of substances might

act as limiting substrates.Stewart (1956)and Agardy et al.

(1963) have used COD as the limiting substrate in the

development of their models for the anaerobic digestion

process.Lawrence and McCarty (1967) used volatile acids

concentration as the limiting substrate, since it is generally

believed that the rate-limiting step in the anaerobic

decomposition of complex organics is the conversion ofvolatile acids to methane. Andrews (1969)has presented a

dynamic model for the anaerobic digestion process, which

considers only the methanogenesis step. It is commonly

observed in the field that a high volatile acids concentration

and low pH value leads to digester failure. To represent this

phenomenon in a quantifiable way an inhibition function

(Haldane type) was used in the model. The un-ionized form

of volatile acids was considered as the rate limiting

substrate since it is a function of both pH and the total

volatile acids concentration.

Rittman and co-workers have presented a biofilm model

describing the biofilm growth and substrate flux under

steady-state conditions (Rittmann, 1982; Rittmann and

McCarty, 1980a). UASB reactor models using methano-

genic biofilm models have focused on mass transfer

limitations and single as well as multiple limiting substrates

(Alphenaar et al., 1993; Atkinson and Davies, 1974;

Atkinson and How, 1974; Buffiere and Steyer, 1995; de

Beer et al., 1992; Lens et al., 1993;Lin, 1991).

Thick biofilms may give rise to mass-transfer limitations

for the substrate within the biofilm, resulting in an overall

reduction in the substrate conversions achieved. Under this

condition, the transport of substrate into the biofilm or

transport of products out of the biofilm could become the

rate-determining step. Contradictory results have beenreported on the impact of internal (within the biofilm) and

external (in the bulk liquid phase) mass transport. While

some reports indicate that both internal and external

diffusion limitations influence the rate of substrate utiliza-

tion (Dolfing, 1985; Wu et al., 1995), others indicate that

mass transport limitations are not observed in anaerobic

biofilms (de Beer et al., 1992; Schmidt and Ahring, 1991)

even at film thicknesses as high as 2.6 mm (Droste and

Kennedy, 1986). In addition, it has been reported that pH

profiles inside anaerobic granules may affect the conversion

rate more than mass transport limitations (de Beer et al.,

1992).

Gonzalez-Gil et al. (2001a) studied the influence of

external and internal mass transport in anaerobic granular

sludge. For this, kinetic properties of acetate degrading

methanogenic sludge granules of different mean diameters

were assessed at different up-flow velocities. It was

experimentally found that external mass transport resis-

tance can be neglected and that biogas formation does not

influence the diffusion rates. The substrate uptake could be

explained by biofilm (internal) diffusion.

The general approach to the modelling problem starts

with development of the biofilm model. These are then

used to find the substrate flux at the surface of each

granule. The biofilm model is then tailored with the flow

ARTICLE IN PRESS

Zone-1 Zone-2

Sludge

Blanket

Clarifier

Fig. 5. Schematic of the two-compartment axial dispersion model

(Singhal et al., 1998).



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model to predict the overall performance of the reactor. In

general, the following assumptions were made in develop-

ing anaerobic biofilm models:

1. Granules are spherical.

2. Substrate utilization is described by the Monod model.

3. External mass transport is negligible.4. Density of the biofilm is constant throughout the

granule.

5. The relative concentrations of the acidogenic and

methanogenic bacteria are constant throughout an

anaerobic granule. This remains true irrespective of

the location in the reactor from where the granule was

taken.

Many of the reported studies deal with steady-state

conditions. Unsteady state is the most critical situation for

modelling, associated with real-time control strategies.Wu

and Hickey (1997)developed a dynamic model to describeUASB reactors with methanogenic anaerobic granules.

They assumed that substrate diffuses into the granules

outer layer upto a thickness of 100 mm. At the inner edge of

this layer, the substrate gradient reaches zero. Growth of

acetate utilizing methanogens is neglected due to their low

growth rate.

By applying an acetate mass balance on anaerobic

granules, the granular bed and the clarifier, respectively,

the dynamic model equations are obtained.

For anaerobic granules:

qs

qt D

q2s

qx2

2

Rx

@s

@x

kmxms

ks s . (2.4)

Boundary conditions:

1. Dqs

qxklsb klsb; x 0,

2. qs

qx 0; x d,

where R is the granule radius; km the specific substrate

utilization rate;ksthe half velocity constant; D the effective

diffusion coefficient;kl the mass transfer coefficient;xmthe

active acetate utilizer biomass within the outer layer d;sthe

acetate concentration within the biofilm.

A mass balance on a granule bed involves three terms:

substrate entering the reactor, substrate leaving the reactor,

and substrate being taken up by the granules and

subsequently being utilized:

Vbds

dt VbEt Qfst klArsb s0; t. (2.5)

Initial condition: sb(0) sb0

Et MfVbTin

if 0ptpTinfor impulse;

0 ifTinp0;

(2.6)

whereAris the total granule surface area; Tinthe substrate

injection time for the acetate impulse; klArsb s0; tdescribes the substrate transferring from the bulk solution

through the liquid boundary layer into the granules. Data

from an acetate impulse experiment was simulated using

these hydraulic- reactiondiffusion models with a good fit.

The results indicated that diffusion inside the granules,reaction kinetics and hydraulic behaviour play important

roles in the performance of a UASB reactor.

Bolle et al. (1986) developed an integrated dynamic

model for the UASB reactor. Their flow model has been

described in Section 2.1. Substrate and biomass balance

were done over the sludge bed and sludge blanket. Thus the

model was developed by integrating the fluid flow pattern

in the reactor, the bacterial growth and substrate utiliza-

tion kinetics, and the mass transport between different

compartments and different phases. This model was able to

predict the sludge bed height, the biomass concentration in

the sludge blanket, the short-circuiting flows over the bed

and the blanket, and the effluent COD concentrations as a

function of the hydrodynamic load, COD load, pH and

settler efficiency.

Skiadas and Ahring (2002) proposed a model for

UASB reactors based on the cellular automata (CA) concept.

A cellular automation is a simulation, which is discrete in

time, space and state. A CA model usually consists of an

array of compartments similar to the spaces in a game of

naughts and crosses. The CA theory has been applied to

predict the layer structure of the granules, which is high

acidogen and low methanogen concentrations at the outer

granule layers and the reverse at the inner granule layers. It

has also predicted the granule diameter and granulemicrobial compositions as functions of the operational

parameters. The other models do not consider the effect of

operational parameters on granule size and composition.

Details on automation models can be found in the excellent

review paper byWimpenny and Colasanti (1997).

Even though different authors have presented good

experimental fit for their models, a unified approach is

lacking. The above kinetic models, in general, assume

external mass transfer to be negligible. Some of the

assumptions may lead to poor predictions. For example,

the assumption of Monod kinetics, spherical shape and

uniform density of the granules may not be true in actual

reactors. The lack of versatile models in the literature

shows that a lot of improvements can be made in future

models. Some of them could be

1. Incorporation of the variation of density within the

biofilm/granule.

2. Kinetic expressions, which include inhibition terms.

3. Kinetic expressions, which include the non-uniform pH

profile inside the biofilm.

4. Diversity in the bacterial population distribution

inside the granule in terms of the predominant species/

groups.

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3. Proposed models for the structure of the biofilm

In an anaerobic reactor, under favourable conditions,

bacterial cells can attach to each other and grow as a

granule. This granule has a 3-D structure. When some inert

carrier particles or surfaces are introduced in the system,

cells grow on the carrier particles/surfaces forming abiofilm. Depending upon the structure of the carrier

material the resulting biofilm will have a 2-D or 3-D

structure. Microbial composition and their distribution

inside the granules play an important role in substrate

conversion. Conversion could be limited by the process of

diffusion of the substrate within the biofilm as well as the

concentration of biomass bringing about the conversion.

This information is very essential to develop the biofilm

model. Many authors have reported that the structure of

the granule/biofilm is mainly determined by the substrate

degradation kinetics rather than the geometry with which it

is formed (Batstone et al., 2004;Fang et al., 1995;Guiot et

al., 1992). Batstone et al. (2004) have developed a biofilm

structure model which predicts the structure of a 2-D

biofilm. This model has been formulated based on

substrate degradation and diffusion kinetics. They exam-

ined four different types of granules obtained from UASB

reactors treating wastewaters from a cannery, a slaughter-

house, and two breweries. The microbial structures of these

granules were assessed by fluorescence in situ hybridization

probing with 16S rRNA-directed oligonucleotide probes,

scanning electron microscope and transmission electron

microscope. The biofilm model could exactly predict the

structures of different types of granules observed through

the experiments when the model was simulated for thesame operating conditions. This proves that the structure

of the biofilm is influenced by the substrate kinetics and not

by the geometry of the biofilm. Van Loosdrecht et al.

(2002)has shown that a 2-D model is sufficient to represent

a 3-D structure.Picioreanu et al. (2001)also has supported

the same. Hence, the different models proposed for the

biofilm structure in this section are applicable to both

granules and 2-D biofilms.

3.1. Multi-layer model

MacLeod et al. (1990)andGuiot et al. (1992)proposed a

three-layered structure for the bacterial aggregates treating

carbohydrates in a UASB reactor. According to this

model, the microbiological composition of granules is

different in each layer. The inner layer mainly consists of

methanogens that may act as nucleation centres necessary

for the initiation of granule development. H2-producing

and H2-utilizing bacteria are dominant species in the

middle layer, and a mixed species including rods, cocci and

filamentous bacteria takes the predominant position in the

outermost layer (Fig. 6).

To convert a target organic compound to methane, the

spatial organization of methanogens and other microbial

species in the granules (such as those in a UASB reactor) is

essential. The layered structure of UASB granules is

supported by the works ofArching et al. (1993) andLens

et al. (1995) with immunological and histological methods.

The dynamic model proposed by Arcand et al. (1994) also

supports this structure. Similar support for the layered

structure is found in reports fromSantegoeds et al. (1999)

using microelectrodes. Sekiguchi et al. (1998, 1999) and

Tagawa et al. (2000) also confirmed this structure by

fluorescence in situ hybridization using 16S rRNA targeted

oligonucleotides. A distinct layered structure was also

found in the methanogenicsulfidogenic aggregates, with

sulfate-reducing bacteria in the outer 50100mm and

methanogens in the inner part (Sekiguchi et al., 1998).

Unlike the initial multi-layer model proposed byMacLeod

et al. (1990) recent research showed that UASB granules

have large, dark, non-staining centres, in which neither

archaeal nor bacterial signals could be found (Rocheleau

et al., 1999). In fact, the non-staining centre in the UASB

granules might be the result of the accumulation of

metabolically inactive, decaying biomass and inorganic

materials (Sekiguchi et al., 1998).The importance of ECP in anaerobic granulation has

been observed by Schmidt and Ahring (1994, 1996). They

conclude that ECP may play an important role in building

spatial structure and maintaining the stability of UASB

granules, but are unsure of its contribution to the initiation

of anaerobic granulation. A large quantity of ECP is

unnecessary for making up active granules since it

decreases the porosity and thereby increases the diffusional

resistance for substrate to penetrate the granule. Too much

ECP could even cause deterioration of floc formation

(Schmidt and Ahring, 1996).

3.2. Syntrophic microcolony model

According to the syntrophic microcolony model, a close

synergistic relationship among different microbial groups is

essential for efficiently breaking down the complex organic

compounds. In fact, the syntrophic microcolonies provide

the kinetic and thermodynamic requirements for inter-

mediate transference and therefore efficient substrate

conversion (Schink and Thauer, 1988). They state that

the synergistic requirements would drive bacteria to form

granules, in which different species function in a synergistic

way and can easily survive.

ARTICLE IN PRESS

Acidogens

Methanothrix

H2producing Acetogens and

H2consuming organisms

Fig. 6. Three-layered structure of the bacterial aggregates (MacLeod

et al., 1990).



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3.3. Non-layered structure model

Contrary to the multi-layer model, anaerobic granules

with non-layered structure have also been reported (Fang et

al., 1995; Grotenhuis et al., 1991; Wu et al., 2001).

There is evidence that a layered structure of the UASB

granules would be developed with carbohydrates and a non-layered one using substrates having a rate-limiting hydrolytic

or fermentative step (e.g. proteins) (Fang, 2000;Fang et al.,

1995). This is probably due to different initial steps in the

degradation of carbohydrate as compared

to that of proteins. Degradation of carbohydrates to

small molecules is faster than the subsequent degradation

of the intermediates, whereas the initial step in protein

degradation is a rate-limiting step. That is, the protein

degradation step is slower than the steps which follow it.

Results from fluorescence in situ hybridization com-

bined with confocal scanning laser microscopy clearly

showed that protein-fed granules possess non-layered

structure with a random distribution ofMethanosaeta concilii

(Rocheleau et al., 1999). However, granules, which differ in

their composition in terms of the predominant microbial

species, can still be formed from the same substrate

(Daffonchio et al., 1995;Schmidt and Ahring, 1996).

Based on microscopic examination of the UASB

granules, recentlyFang (2000)proposed that the microbial

distribution of the UASB granules strongly depends on the

degradation thermodynamics and kinetics of individual

substrate. Therefore, it appears that different dominating

catabolic pathways may give rise to granules, which are

different in their structure. Spontaneous and sudden

washout of the established granular sludge bed, as a resultof a change in wastewater composition, is a common

problem encountered in the operation of UASB systems.

So far, none of the individual models for the granule

structure can explain this phenomenon. If a factor that is

independent of the wastewater composition can initiate the

formation of UASB granules, a change in the wastewater

composition should not lead to the washout of the entire

granular sludge bed. Thus, it is a reasonable speculation

that there should be a substrate composition-associated

factor that highly contributes to the formation of UASB

granules, but is not yet included in the present models of

granule structure (Liu et al., 2003).

Liu et al. (2003)proposed a general model for anaerobic

granulation in UASB reactors. This model consists of four

steps for granulation.

1. Physical movement to initiate bacterium-to-bacterium

contact or bacterial attachment onto nuclei.

2. Initial attractive forces to keep stable multi-cellular

contacts, e.g. physical, chemical and biochemical forces.

3. Microbial forces to make cell aggregation mature, e.g.

production of ECP.

4. Hydrodynamic shear force shaping 3-D structure of

microbial aggregates.

3.4. Granule cluster structure

Recently the structure of anaerobic granules of an

expanded granular sludge bed (EGSB) reactor was studied

byGonzalez-Gil et al. (2001b). They found black spherical

granules having numerous whitish spots on their surfaces.

Cross-sectioning these aggregates revealed that the whitishspots appeared to be white clusters embedded in a black

matrix (Fig. 7). High magnification electron microscopy

showed that the white clusters mainly consisted of acetate

utilizing methanogens (Mathanosaeta spp.) and the black

matrix consisted of syntrophic species and hydrogenotrophic

methanogens (Methanobacterium like and Methaospirillum

like organisms). Fluorescent in situ hybridization using 16 s

rRNA probes of crushed granules showed that 70% of the

cells belonged to the archaebacterial domain and 30% to

eubacterial domain. The authors have provided a very logical

explanation as to why a cluster structure, as observed, is

advantageous over a layered structure. Acetate produced in

the black zone is transported by random diffusion in all

directions and thus penetrates the Methanosaeta clusters from

all sides. Hence, substrate depleted zones are circumvented,

which allows the growth of more active biomass per unit area

of aggregate.

Batstone et al. (2004) studied the influence of substrate

degradation kinetics on the microbial community structure

in granular anaerobic biomass. The granules, which were

grown in the effluent containing soluble as well as

particulate protein, had homogeneous structure. The

primary cause of this structure was assessed through

biofilm modelling. They postulate that the particulate

nature of the wastewater and the slow rate of particulatehydrolysis, rather than the presence of proteins in the

wastewater, was responsible for the homogeneous structure

of the granules. Because solids hydrolysis was rate limiting,

soluble substrate concentrations were very low (below

Monod half-saturation concentration), which caused low

growth rates.

From the above information it can be concluded that

there are two key factors which determine the structure of a

granule (i.e. the organization of the microbial community

within a granule). They are

1. The nature of organic compounds present in the

wastewater.

2. The kinetics of substrate degradation.

ARTICLE IN PRESS

Methanosaetaclusters

Zone with syntrophic

eubacteria and

hydrogenotrophic

methanogens

Seed aggregate

Fig. 7. Schematic representation of the architecture of anaerobic

aggregates (Gonzalez-Gil et al., 2001b).



8/18

The relative concentrations of different microbial species

within a granule is another important factor required in

developing a biofilm model. This seems to depend on the

concentration of the substrate. Since there could be

concentration gradients with respect to substrate concen-

tration within the same reactor, the composition of the

granule in terms of the microbial species may vary fromgranule to granule obtained from different parts of the

same reactor. Hence a robust model, capable of incorpor-

ating the structure as well as composition of the granules in

terms of the different microbial communities present, is

required. Such a model for the biofilm/granule can be used

in developing reactor models which are more versatile as

well as reproducible with a higher level of accuracy.

4. Models for AFBR

The AFBR uses inert carrier particles to provide

mechanical support for growth of the biofilm. These

biogranules are maintained in a fluidized state by using

the energy of the influent liquid. Such a fluidized bed

system is free from the channelling problems encountered

in other biofilm reactors. A serious operational problem

associated with the AFBR is that when the biofilm grows

on the carrier surface, the composite density of the film-

covered particle decreases, ultimately resulting in the carry

over of the film-covered particles out of the reactor. Full-

scale application of AFBRs is not common due to lack of

sound design principles. Many attempts have been made to

study the process kinetics and the factors affecting process

performance.

In general, models for AFBRs include the followingelements:

1. A bed fluidization model which describes the size and

number of bioparticles per unit fluidized bed volume.

2. A biofilm model which describes the rate of substrate

conversion per individual granule.

3. A reactor flow model, which links the biofilm and bed

fluidization models to yield substrate concentration as a

function of axial position within the AFBR.

4.1. Bed fluidization model

Hydrodynamic behaviour of carrier supported biogra-

nules plays an important role in designing AFBRs. When

the granules grow, their size, shape and composite density

change. This has an impact on the hydrodynamic

behaviour of the granules. Information on settling and

fluidization characteristics, such as fluidized bed-height, as

a function of liquid velocity is required for the designing of

AFBRs. Information on fluidized-bed height is important

because it establishes the solids residence time and the

specific biofilm surface area in the biologically active zone.

The relationships valid for fluidization of rigid particles,

readily available in the chemical engineering literature (e.g.

Di Felice, 1995), have to be modified to take into account

the effect of the biofilm layer on the rigid particles

(Nicolella et al., 2000).

4.1.1. Terminal settling velocity

The terminal settling velocity of a single spherical

particle in an infinite expanse of fluid is

ut 4grs rl

3CDrl

0:5. (4.1)

Depending on the biofilm thickness and on the carrier

type, values for the equivalent density of biofilm particles

(rs) range typically from 1100 to 1500 kg/m3. The drag

coefficient CD is a function of the particle Reynolds

number defined as

Ret rldsut

ml. (4.2)

Biofilm particles are in the intermediate flow regime(1oReto100) for the vast majority of cases, obtained

when sand (0.51 mm) or carrier materials with densities in

the same range are used as the inert support. In the

intermediate flow regime, the drag coefficient for a smooth,

rigid sphere is (Perry and Green, 1997)

CD 18:5Re0:6t . (4.3)

This correlation cannot be used for carrier-supported

granules, since they are neither smooth nor rigid. For this

reason, empirical correlations have been suggested for the

estimation ofCD for biofilm particles:

CD 17:1Re0:47t ; 50oReto100 (4.4)

Hermanovicz and Ganczarczyk (1983),

CD 36:66Re0:67t ; 40oReto90 (4.5)

Mulcahy and Shieh (1987),

CD 24

Ret21:55Re0:518t ; 15oReto87 (4.6)

Ro and Neethling (1990),

CD 24

Ret14:55Re0:48t ; 40oReto90 (4.7)

Yu and Rittmann (1997),

CD 29:6Re0:6t ; 7oReto90 (4.8)

Nicolella et al. (1999).

The drag coefficient of the biofilm covered carrier

particle is generally found to be more than that of smooth,

rigid spheres. Surface roughness has generally been

considered as the reason for the increase in the drag

coefficient of biofilm covered carrier particles (Hermano-

vicz and Ganczarczyk, 1983;Mulcahy and Shieh, 1987).

The above correlations are all empirical since they were

obtained by fitting experimental data generated by

different groups, who employed fluidized bed systems,

which differed from one another in one or more aspects.

ARTICLE IN PRESS



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The deformable nature and surface roughness of the

biofilms and the type of carrier particle used play a major

role in determining the hydrodynamic nature of the biofilm

covered particle. Hence, bed fluidization models should be

able to incorporate those parameters which have an

influence on the hydrodynamic behaviour of the biofilm

covered particles. It may not be feasible to have ananalytical expression for this purpose, given the complexity

and variability inherent to the system. While an empirical

relationship is acceptable, it should be able to cater to a

wider range of operational parameters normally encoun-

tered rather than a narrow set of operating conditions.

4.1.2. Fluidization mechanics

In a fluidized bed anaerobic reactor, the film-covered

particles are kept in a fluidized state by the incoming liquid.

The bed porosity and biomass concentration in the bed are

determined by the mechanics of fluidization. Hence, a

realistic mathematical expression for the bed fluidization is

necessary.

For a bed of uniform spherical particles, the following

relation was proposed (Richardson and Zaki, 1954):

us uien, (4.9)

where us is the superficial liquid velocity, e porosity and

ui ut10d=D, (4.10)

where ut is the terminal settling velocity of particle, d the

particle diameter and D the diameter of bed, n is a constant

given by

n 4:6520d=DReto0:2, (4.11)

n 4:418d=DRet0:03 0:2oReto1, (4.12)

n 4:418d=DRet0:1 1oReto200, (4.13)

n 4:4Ret0:1 200oReto500, (4.14)

n 2:4500oRet. (4.15)

Whether this equation can be applied directly and in its

entirety to a biological fluidized bed is a controversial

subject. Richardson and Zaki have derived the equation for

a bed of uniform spherical particles, which are hard and

have a smooth surface. But the biological film coveredparticles seldom have these characteristics.

Andrews and Tien (1979) related the bed height to the

amount of biomass in the bed. The fluidized bed tends to

stratify vertically based on the settling velocity of the

bioparticles. If no stratification is assumed, the bed height

is related to average biofilm thickness x by

H

Hc

1ec1 x

1ec1 x1=3=1A x1=n

. (4.16)

In the case of complete stratification

H

Hc 1ec Z

xmax

0

1x

1e

gx dx. (4.17)

A practical working expression was derived based on the

above two expressions by Andrews and Tien (1979) as

follows:

H

Hc1 1B x, (4.18)

where

B ecD

31ec 3x0 2D

1ec

1ec

13A2

13A

D

1 3A

3n ,

where H is the bed height, e the bed porosity, x the film

volume/clean particle volume, x the mean value of

distribution function of bacterial film gx, A the buoyant

density of bacterial film/buoyant density of clean particle, n

the exponent in the RichardsonZaki correlation. The

subscript c denotes the bed of clean particles.

This expression was found to predict the experimental

data well.

Mulcahy and La Motta (1978) have developed specific

correlations to determine ut and n for the case of

bioparticles in a fluidized bed as follows:

ut rsrlgd

1:67p

27:5r0:33l m0:67

" #0:75, (4.19)

n 10:35Re0:18t 40oReto90, (4.20)

wherersis the density of bioparticles; rl the liquid density;

m the liquid viscosity.

Ngian and Martin (1980)found that the Richardson and

Zaki correlations gave a satisfactory estimate for ui for

small support particles whereas ui was 3070% below theexperimentally determined value for larger support parti-

cles.Nicolella et al. (1999) found u i to be only 80% of the

unhindered settling velocity. They recommend that the

correlation should be used with caution while determining

the constant ui.

In general, the Richardson and Zaki correlation is found

to describe the bed expansion characteristics of a fluidized

bed. But the values of the constants n and ui seem to be a

function of the property of the biofilm covered particles.

The application of these correlations to a full-scale reactor

containing a wide size distribution of biofilm covered

particles needs to be verified.

4.1.3. Effect of gas production on hydrodynamics

The effect of gas production on hydrodynamics of

fluidized beds is an important factor to be studied for

design and scale-up of AFBRs. Many investigations on the

flow pattern in an AFBR suggested that an axially

dispersed plug flow model can be used for the flow model

(Hirata et al., 2000; Seok and Komisar, 2003). In these

studies the effect of gas production on the flow pattern was

not considered.Diez-Blanco et al. (1995) have studied the

effect of gas production on the hydrodynamic behaviour of

an AFBR. In this study, the bed contraction due to biogas

production in a fluidized bed of 6 m height was estimated to

ARTICLE IN PRESS



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be less than 6%. Based on this, the investigators considered

the effect of biogas on the hydrodynamic behaviour to be

negligible. In contrast,Buffiere et al. (1998a) reported that

the effect of biogas on bed height could be negligible. But

the biogas effervescence affects the phase hold-ups (which

affects the liquid solid contact time) and liquid mixing of

the reactor system. The experimental study ofBuffiere et al.(1998b) compared the hydrodynamic behaviour of a gas

producing fluidized bed with a classical gas injected three

phase fluidized bed reactor. The overall gas hold up was

found to be more in the case of the gas producing fluidized

bed than the gas injected one. They also observed axial

variation of phase hold-up.

4.1.4. Bed stratification

Schreyer and Coughlin (1999)reported a stratification of

biofilm coated sand particles in a fluidized bed reactor.

Stratification can be attributed to the influence of a biofilm

on a particles settling velocity. The presence of a biofilm

cover decreases a particles overall density, thereby

increasing its buoyancy. The biofilm also increases the

particles size thereby increasing the drag force exerted on

it by the liquid flowing upward. The particles in a fluidized

bed are expected to segregate according to size and mean

density (Ro and Neethling, 1994; Safferman and Bishop,

1996;Trinet et al., 1991).

Bed stratification has many negative effects on the

performance of the reactor. Thicker biofilms pose diffusion

limitation and wash out problems. Hence, to prevent

stratification and to maintain uniform particle size, efforts

have been made to remove excess biofilm from largerparticles (Ruggeri et al., 1994;Safferman and Bishop, 1996;

Shieh et al., 1981; Trinet et al., 1991). Examples of such

efforts include external sand-biomass separators (screens),

operation of an impeller at the top of the bed and internal

screen cleaning devices. Many researchers have examined

the effect of shear on biofilm and biofilm detachment rate,

mainly as a tool to control biofilm thickness (Chang and

Rittmann, 1988;Chang et al., 1991;Gjaltema et al., 1997;

Peyton and Characklis, 1992; Rittmann, 1982; Safferman

and Bishop, 1996; Stewart, 1993; Trinet et al., 1991).

Biofilm detachment rate appears to depend on turbulence

and particle concentration; an increase in either increases

detachment rate. Biofilm has been observed to be relatively

smoother and more homogeneous under conditions of high

shear (i.e., high liquid velocity) than under low shear

conditions (Lau, 1995;Zhang and Bishop, 1994). The study

by Schreyer and Coughlin (1999) showed that the

introduction of a thinner to increase the shear resulted in

a non-stratified bed.

Bed stratification could occur due to differences in the

biofilm thickness or differences in the carrier particle size or

both. But bed stratification is most common when carrier

particles are not of uniform size. A completely mixed bed

(i.e. no stratification) was observed by Andrews and Tien

(1979)when uniform carrier particles were used.

4.2. Kinetic and reactor sub-models

Substrate removal within a biological film of uniform

thickness attached to a spherical particle is described by

D

r2d

dr r2

ds

dr Rt, (4.21)where D is the effective diffusion coefficient of substrate

within the biological film; r the radial coordinate measured

from the centre of the support particle; s the substrate

concentration within the biofilm and Rtthe intrinsic rate of

substrate consumption per unit volume of biological film.

It is generally accepted by many authors that substrate

removal kinetics can be modelled using the microbial

growth model proposed by Monod. Many researchers

(Grady, 1982; Henze and Harremoes, 1983; Iwai and

Kitao, 1994) have suggested that depending on the values

of the model constants, reaction rate can be represented by

first- or zero-order kinetics. For AFBRs, many authors

demonstrated that zero-order kinetics provide an adequate

description of substrate consumption (i.e. considering the

acidogenesis and methanogenesis phases together) (La

Motta and Patricio, 1996; Mulcahy and La Motta, 1978;

Mulcahy et al., 1980;Shieh et al., 1982).

For zero-order reaction, the reaction rate term is

Rt rk0. (4.22)

The solution of Eq. (4.21) for complete substrate

penetration inside the biofilm and for the partial penetra-

tion has been presented by Mulcahy et al. (1980).

For fully penetrated biofilm:

Observed rate 43prk0r3p r

3m. (4.23)

For partial substrate penetration:

Observed rate 1:76rk01:45r3p r

3m

1:9s0:45br3pr

3m

1:9

r1:8p D0:45

.

(4.24)

rm is the radius of support particle; rp the radius of

biological particle; sb the concentration of substrate in the

bulk of the liquid within the fluidized bed.

A simple plug flow model was used to describe dissolved

substrate transport in the axial direction in a fluidized bedreactor (Mulcahy and La Motta, 1978):

Udsb

dz Rv 0. (4.25)

With the boundary condition

z 0; sb s0

where U is the average liquid velocity in the longitudinal

direction; sb the substrate concentration in the bulk of the

liquid; s0 the influent substrate concentration; Rv the rate

of reaction.

For fully substrate penetrated biofilm, the concen-

tration profile along the reactor was given by Mulcahy

ARTICLE IN PRESS



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et al. (1980)as

se s0rk0Vm

Q

rp

rm

3 1

" #, (4.26)

where se is the concentration of substrate in the effluent

stream.La Motta and Patricio (1996)tested this model by

conducting experiments. This test showed a reasonable

agreement between the zero-order kinetic model with

complete substrate penetration and the experimental data.

Hirata et al. (2000)used a different approach to evaluate

the kinetic parameters of the biochemical reactions taking

place in a three phase fluidized bed reactor. Using the

substrate balance at steady state and assuming Monod

kinetics, an equation relating the substrate consumption

rate to substrate concentration (expressed as Biochemical

Oxygen Demand, BOD5) and total biofilm surface area was

established. The following assumptions were made in

formulating the model:

1. Reactor system is completely mixed.

2. Total organic carbon (TOC), which is expressed in terms

of BOD5, is the only rate-limiting substrate. Other

substrates are in excess.

3. The reaction follows Monod kinetics and substrate

inhibition is negligible.

4. Reaction occurs at constant volume.

Performing a substrate balance at steady state yielded

Fsin sss 1

Yx=srxV, (4.27)

where F is the inlet flow rate, Vthe reactor volume, rxthe

biofilm growth rate, Yx/s the yield coefficient mass of

biomass formed/mass of substrate consumed, Sss the

steady-state value of the rate limiting substrate concentra-

tion inside the reactor, Sinthe inlet substrate concentration.

If the reaction followed Monod kinetics, then the proposed

rate equation was

rx mx mmaxsss

km sss

x, (4.28)

where m is the specific growth rate, mmax is the maximum

specific growth rate and km the Monod constant.

Substituting rx into the substrate balance equation

Fsin sss 1

Yx=s

mmax sss

km sss

Vx Rt, (4.29)

Vx rbdsb, (4.30)

where rb is the biomass dry density, d the effective biofilm

thickness and sb the total biofilm surface area. The total

surface area was computed as follows:

sb pDave2N, (4.31)

where N is the total number of particles inside the reactor

and Dave is the average particle diameter. Modifying

Eq. (4.29) gave

Rt K sbsss

kmsss

, (4.32)

where K rbdmmax=Yx=s:Transforming the above equation using Lineweaver

Burke linearization,

sb

Rt

km

K

1

sss

1

K. (4.33)

Plotting sb/Rt versus 1/sss gave a straight line with slope

km/K and intercept 1/K. Using the above plot for the

known value of inlet substrate concentration, the steady-

state substrate concentration could be found.

Buffiere et al. (1998c) studied the biofilm activity along

the reactor height. They developed a biofilm model

assuming

1. Homogeneous biofilm of uniform thickness.

2. Spherical support media of uniform size.

3. Internal mass transfer described by Ficks law.

4. Liquid phase perfectly mixed with homogeneous con-

centration.

5. No external mass transfer limitation.

The mass balance for a substrate s in the biofilm is

expressed by

D

r2d

dr r2

ds

dr

Xi

Vsi. (4.34)

The boundary conditions are

r rp; s s0,

r rc; ds

dr 0,

Vs xs

Yx=s

mmaxs

kss

. (4.35)

The right-hand side of (4.34) is the sum of all substrate

uptake rates minus the sum of all substrate production

rates.

In the liquid phase, the mass balance for one substrate s

is given by

VLds

dt Qsins DAp

ds

dr

rrp

!, (4.36)

where s is the concentration of component s; sin the inlet

concentration ofs;Q the input flow rate; rp the bioparticle

radius; r the radial distance measured from bioparticle

centre;D the diffusivity of component s in the biofilm;mmaxthe maximum specific growth rate for s-utilizing bacteria;

Vsi the reaction rate of s through reaction I; Ap the

exchange area of the bioparticles; VL the liquid phase

volume; xs the s-utilizing bacteria concentration; Yx=s the

biomass yield factor for s-utilizing bacteria.

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The substrate gradient at the surface of a bioparticle in

Eq (4.36) is taken from the biofilm model. The biomass

composition used in this simulation was averaged from

several studies such as the modelling work ofMosey (1983)

and the experimental investigation ofSanchez et al. (1994)

(Table 1).

A set of batch experiments was conducted using

bioparticles taken from different heights. Glucose, acetate

and propionate were used as substrates. Substrate con-

sumption with time was monitored. Simulation results were

found to give reasonable fit for experimentally observed

values. The biomass composition (i.e. the relative concen-

tration of acidogens and methanogens) within the biofilm

was manipulated to fit the experimental results. This

indicated the crucial role of biomass composition in

substrate kinetics. The specific activity of the biofilm was

also measured. The following were the findings:

1. Thicker film bioparticles were found on the top of the

reactor and thinner in the bottom.

2. Glucotrophic activity decreased from bottom to top andmethanogenic activity increased from bottom to top.

3. This indicates the change in biomass composition with

biofilm size.

Buffiere et al. (1998a) developed a model for AFBRs

based on total carbon removal kinetics. They considered

the effects of gas production in their model which were of

two kinds:

1. Gas production modified the degree of axial mixing,

which is responsible for the establishment of a concen-

tration gradient in the reactor.2. Gas production is responsible for bed contraction,

which reduces the contact between the liquid and

bioparticles.

The TOC removal kinetics were found to be in good

agreement with the Monod model. The TOC uptake rate

can be expressed by

rTOC rmaxS

ksS, (4.37)

where S is the TOC concentration in the reactor (the

reactor is assumed to be perfectly mixed). Parameters rmax

and ks were found by plotting the inverse ofrTOC and 1/S.

Bed contraction was found to reduce the liquidsolid

contact by 1025%:

es

es01 0:045U0:4g . (4.38)

Experimental results of gas hold-up in the reactor gave

the following correlation:

eg 13 1:2d0:168p U

0:7g . (4.39)

An axially dispersed plug flow model was found to

describe the liquid mixing in the reactor. The mass balance

of the reactor was given by the equation

1

Pe

d2s

dx2

ds

dxDa

s

ls (4.40)

with the following notations:

x z

H; s

s

ks; Da

rmax

ks

Hel

Ul; andPe

UlH

elEzl.

The axial dispersion co-efficient was found experimen-tally using the tracer injection method. The experimental

results were found to fit the correlation of Muroyama et al.

(fromFan, 1989) very well:

DcUl

elz 1:01U0:738l U

0:167g D

0:583c , (4.41)

where dp is the particle diameter; Dc the column diameter;

Ezl the axial dispersion coefficient; g the gravitational

acceleration; H the bed height; ks the half-saturation

concentration in Monod expression; rmax the maximal

reaction rate in Monod expression; s the substrate

concentration;Ug the gas superficial velocity; Ul the liquid

superficial velocity; Ut the terminal velocity of particles; xthe reduced bed height; es the solid hold up; es0 the solid

hold-up in the liquidsolid fluidized bed;eg the gas hold-up.

Thus by knowing hold-ups (from Eq. (4.38) and (4.39))

and Ez (from Eq. (4.41)), the performance Eq. (4.40) was

solved. The model results were found to give a more

realistic picture.

4.2.1. Stratified biofilm models

A stratified biofilm model was presented by Canovas-

Diaz and Howell (1988). The anaerobic biofilm was

modelled as two distinct layers with the inner layer

consisting of methanogens and the outer layer consistingof acidogens. The substrate is converted to acids in the

outer layers, and is subsequently converted to methane by

the bacteria in the inner layer.

The differential equations for substrate uptake in the two

layers are:

D1d2G

dz2 k1x1, (4.42)

D2d2F

dz2 ak1x1

k2x2

1F=ki, (4.43)

where D1, D2 is the diffusivities of substrate through the

acidogenic and methanogenic layer. G,Fthe concentration

ARTICLE IN PRESS

Table 1

Biomass composition of an anaerobic granule

Type of bacteria Substrates for the

bacteria

%Distribution in the

granule

Acidogens Glucose 65

Acetogens Butyrate 2.5

Propionate 2.0

Methanogens Acetate 7.0

H2 utilizing bacteria Hydrogen 23.5



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of glucose and fatty acids, k1 the zero-order kinetic

constant with respect to sugar uptake and k1 the zero-

order rate constantk2the kinetic constant for VFA uptake;

ki the inhibition constant; z the distance through biofilm;

x1, x2 the mass volume densities of acidogens and

methanogens.

The authors also explain why a stratified biofilm isadvantageous as compared to an un-stratified biofilm.

When the bulk VFA concentration is high, in the case of an

unstratified film, methanogens will face VFA inhibition. In

the case of stratified biofilm, the inhibition level is

minimized by the presence of the outer layer.

Droste and Kennedy (1986) have given a model for

sequential substrate utilization in a biofilm. This model

assumes that no interactions occur between the two groups

of microorganisms that will cause kinetic or diffusion

parameters to change from values associated with indivi-

dual cultures of each group. Unstratified biofilm and

Monod-type kinetics were assumed.

The governing differential equations are:

D1d2s1

dx2

k1x1s1

K1 s1, (4.44)

D2d2s2

dx2

k2x2s2

K2 s2

Yk1x1s1

K1 s1, (4.45)

whereD is the diffusivity;k the maximum specific reaction

velocity; K the half-velocity constant; s the substrate

concentration; x the distance; x the active microorganism

concentration; Y the acetate yield coefficient (g acetate/g

primary substrate).

From numerical analysis of the governing equation, itwas found that the production of intermediate substrate in

the biofilm increased the conversion of primary substrate to

ultimate product. The increase was not always significant.

To summarize, two ways of approaching the problem of

modelling substrate uptake kinetics are explained in this

section. In the first one, TOC is considered as the rate-

limiting substrate. In this case biomass composition,

individual reaction steps and substrate diffusion limitations

are not considered. The parameters involved in the model

are evaluated by fitting the model to the experimental

results. Even though this approach seems to be simple, it

does not have a sound theoretical explanation and remains

empirical. In the second approach, the kinetic model is

developed considering the individual substrate kinetics,

biofilm composition and diffusion limitations. This seems

to be a more realistic approach. Ultimately the validity of

these models has to be verified for large-scale reactors.

5. The EGSB reactor

The EGSB reactor comes under the family of UASB

reactors. The use of effluent recirculation in a UASB (or a

high height/diameter ratio), resulted in the EGSB reactor

(Seghezzo et al., 1998). Here also, the biomass is present in

a granular form. The higher upflow liquid velocity keeps

the granular sludge bed in an expanded condition

(Zoutberg and Frankin, 1996). Reports on models for

EGSB reactors are very scarce. But based on the knowl-

edge of UASB reactors and AFBR models, modelling of

EGSB reactor can be attempted.

1. The biofilm model is similar to the UASB reactorbiofilm model. The composition and structure of the

biofilm is expected to be influenced by the nature as well

as concentration of the substrate. However, there is no

reason to believe that this influence will be significantly

different from what has been observed for biogranules

in the UASB reactor (Section 3.4). The only significant

difference will be the reduced level of the substrate

concentration gradient along the height of the reactor

due to the effect of recirculation.

2. The liquid flow pattern could be expected to be

somewhere between completely mixed and dispersed

plug flow, the exact pattern depending on the recycle

ratio employed. However, any flow model employed will

need validation through tracer studies or any other

suitable experimental studies.

3. A fluidization model which can predict the variation of

bed height with upflow liquid velocity has to be

developed based on experimentation.

Tailoring of the above three models could result in a

complete model for an EGSB reactor.

6. The anaerobic biofilter

The anaerobic filter is an anaerobic packed-bed biofilm

reactor. Though both upflow as well as down flow

configurations are possible, the upflow mode of operation

is more common. The biomass forms a film on the surface of

the packing media. The kinetic model of such a biofilm

reactor has been studied quite extensively (Chang and

Rittmann, 1987; Hamoda and Kennedy, 1987; Meunier

and Williamson, 1981; Rittmann and McCarty, 1980a;

Rittmann and McCarty, 1980b). Fig. 8 illustrates the ideal

biofilm having uniform microbial density (Xf) and uniform

thickness (Lf). When the substrate utilization follows the

Monod relationship, the biofilm model incorporating the

external mass transfer and internal simultaneous diffusionand reaction can be derived as follows (Huang and Jih, 1997):

d2Sf

dZ2

kXfSf

DfKs Sf. (4.46)

Boundary conditions:

DfdSf

dZ

Ds

L SbSs Jat Z 0,

dSf

dZ 0 atZ Lf,

where S is the biofilm substrate concentration, Z is the

distance normal to the biofilm surface, D is the diffusivity,Ds

ARTICLE IN PRESS



14/18

is the axial dispersion coefficient, Xfis the microbial density

in the biofilm, Ks is the Monod constant, kis the maximum

specific substrate utilization rate, Jis the substrate flux.

Here, the subscripts f and b denote biofilm and bulk

liquid, respectively.

The greatest difficulty in applying the model is to

measure the biofilm thickness (Lf).Rittmann and McCarty

(1978) and Suidan (1986) imposed another boundary

condition to the model, i.e.Sf 0 atZ LfThis model is called the deep-biofilm model. Another

reported approach for indirectly estimating the steady-state

biofilm thickness was by assuming that the biomass growthequals the biomass decay and/or shear losses in biofilm

reactors. For instance, Rittmann and McCarty (1980a)

computed the steady-state biofilm thickness using para-

meters of the substrate flux, microbial growth, biomass

decay and sloughing rate (Eq. (4.47)). The model obtained,

called the steady-state biofilm model, is given by

Lf JY

bXf, (4.47)

where Y is the biomass yield coefficient and b is the

sloughing rate.

The models mentioned above have been experimentally

verified or simulated using the results reported in the

literature (Chang and Rittmann, 1987; Liu et al., 1991;

Meunier and Williamson, 1981; Rittmann and McCarty,

1980b,Wang et al., 1987). The kinetic parameters included

in the models were either determined by independent

experiments or obtained from published papers. The liquid

flow regime was assumed to be completely mixed or plug-

flow with axial dispersion (dispersion coefficients were

calculated using empirical equations). An axial dispersion

model coupled with deep-biofilm kinetics was used by

Huang and Jih (1997). The experimental results and the

calculated values showed good agreement. The tracer study

ofHuang and Jih (1997)confirmed that the flow regime is

close to completely mixed.

7. The unified model for anaerobic digestion (ADM1)

The IWA Anaerobic Digestion Modeling Task Group

developed a generalized anaerobic digestion model (Bat-

stone et al., 2002). The biochemical as well as physico-

chemical processes were included in the model. The

biochemical steps include (i) disintegration from homo-

geneous particulates to carbohydrates, proteins and lipids,

(ii) the extracellular hydrolysis of these particulate sub-strates to sugars, amino acids, and long chain fatty acids

(LCFA), respectively, (iii) acidogenesis from sugars and

amino acids to volatile fatty acids (VFAs) and hydrogen

(iv) acetogenesis of LCFA and VFAs to acetate and (v)

separate methanogenesis steps from acetate and hydrogen/

CO2. The physico-chemical equations describe ion associa-

tion and dissociation, and gasliquid transfer. The inhibi-

tion kinetics have been incorporated in the biochemical

process.

7.1. The extension of ADM1 to biofilm reactors

The ADM1 model gives a unified approach to anaerobic

digestion. This model was successfully implemented for a

CSTR (Batstone et al., 2002). ADM1 was developed for a

suspended cell system, where there is no mass transfer

limitation for movement of the substrate from the bulk

liquid phase to the cells. On the other hand, in biofilm

reactors, the rate of transport of substrate from the bulk

liquid to the microbial population is controlled by diffusion

of substrate within the biofilm. Hence to extend the ADM1

for biofilm systems, the substrate utilization kinetics of the

single cell system must be replaced with a biofilm model.

The biofilm models for different biofilm reactor systems

have been extensively reported in the previous sections. In

ARTICLE IN PRESS

Sampling port

Inlet

Outlet

Liquid

Phase Sb

Biofilm

Carrier

materialGas phase

Ss

Lf

Fig. 8. Schematic diagram of an anaerobic filter showing the differential section.



15/18

a similar way the reactor flow system of ADM1 (i.e. CSTR

system) also has to be modified. In the case of a UASB

reactor, the reactor flow system will have a combination of

CSTRs and a plug flow system as explained in Section 2.1.

AFBR and EGSB reactors will have axially dispersed plug

flow systems as shown in Sections 4.2 and 5. A biofilter

flow system is similar to that of ADM1. The physico-chemical process system of ADM1 can be directly extended

to the biofilm reactor systems. Thus, the modification of

the biochemical processes and the reactor flow system of

ADM1 with that of the biofilm system could result in a

unified model for biofilm reactors.

8. Summary and conclusions

Development of biofilm reactors has made anaerobic

treatment an attractive option to treat wastewaters. For

optimum design and scale-up of these reactors, mathema-

tical models are required. In this paper, various parameters

affecting the performance of anaerobic biofilm reactors

were reviewed. The important parameters are:

1. the effect of hydrodynamics/flow pattern on reactor

performance;

2. the mass transfer within granules/biofilms;

3. the kinetic effects;

4. the structure and composition of biogranules.

In UASB reactors the different zones are idealized with

different flow patterns. Sludge blankets and sludge beds are

mostly described by a CSTR flow pattern with bypass. The

clarifier zone is described by the axially dispersed plug flowmodel. The application of these models for actual full-scale

reactors is yet to be studied because these models do not

consider the existence of non-ideal conditions in full-scale

reactors. These non-ideal conditions may include non-

existence of different zones, improper flow distribution and

dead zones.

Reactor models for UASB reactors consider many

questionable assumptions such as spherical granules,

steady-state operation, description of substrate degrada-

tion by simple Monod kinetics, no substrate/product

inhibition and the effect of pH. Further studies are

required to develop models which do not depend too

much on these assumptions for their development.

In developing kinetic models for both UASBs and

AFBRs, granule structure plays an important role. Studies

show that the structure of the granules and bacterial

composition depends on the type of effluent being treated.

Various theories are provided to support the layered and

un-layered structures of the granules. The variation of

granule structure within the same reactor remains un-

explained as of today. Incorporation of this variation in the

models poses a challenge for the modellers.

The hydrodynamics and bed expansion characteristics of

AFBRs have been reported in the literature. It is generally

found that the drag co-efficient of a biofilm covered

granule is more than that of a rigid particle of the same

size. The experimental evidence published so far (Andrews

and Tien, 1979; Hermanovicz and Cheng, 1990; Mulcahy

and Shieh, 1987;Ngian and Martin, 1980;Nicolella et al.,

1999) suggests that the fluidized bed expansion pattern is

observed to follow the Richardson and Zaki correlation.

The studies show that the expansion index can becalculated through the Richardson and Zaki correlation

(Nicolella et al., 1999). But the parameter u i was found to

be 3080% of the experimentally determined ut value.

All these studies were conducted with uniform biogranule

sizes.

Many authors (Ro and Neethling, 1994; Safferman and

Bishop, 1996; Schreyer and Coughlin, 1999; Trinet et al.,

1991) observed that the bed becomes stratified due to the

presence of granules with different biofilm thicknesses. In

such a context, the application of the Richardson and Zaki

correlation remains dubious. Hence models considering

expansion characteristics of stratified beds are necessary

for proper process design.

Ideal plug flow and CSTR models were used to describe

the flow pattern inside a laboratory scale AFBR. The use

of this assumption in large scale reactors has to be

investigated. Similar to UASB reactors, while developing

kinetic models for AFBRs, the influence of pH, substrate

and product inhibition, validity of Monod kinetics,

microbial composition and location and sphericity of the

granules have to be studied. In the case of anaerobic filters,

the deep-biofilm model seems to represent the laboratory

scale reactors. But, the assumption of the substrate

concentration reaching zero at the filter media has to be

verified in the large-scale reactor. A realistic modelconsidering all the above-mentioned short comings is

necessary for proper design and scale up of such reactors.

The integration of the flow model and biofilm model for

these biofilm reactors with ADM1 can result in a robust

model, which can be a tool for design purposes.

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