Improved Computational Model (AQUIFAS)for Activated Sludge, Integrated Fixed-FilmActivated Sludge, and Moving-Bed BiofilmReactor Systems, Part I: Semi-Empirical

Model Development

Dipankar Sen1*, Clifford W. Randall2

ABSTRACT: Research was undertaken to develop a model for activated

sludge, integrated fixed-film activated sludge (IFAS), and moving-bed

biofilm reactor (MBBR) systems. The model can operate with up to 12 cells

(reactors) in series, with biofilm media incorporated to one or more cells,

except the anaerobic cells. The process configuration can be any combination

of anaerobic, anoxic, aerobic, post-anoxic with or without supplemental

carbon, and reaeration; it can also include any combination of step feed and

recycles, including recycles for mixed liquor, return activated sludge, nitrates,

and membrane bioreactors.

This paper presents the structure of the model. The model embeds a biofilm

model into a multicell activated sludge model. The biofilm flux rates for

organics, nutrients, and biomass can be computed by two methods—a semi-

empirical model of the biofilm that is relatively simpler, or a diffusional model

that is computationally intensive. The values of the kinetic parameters for

the model were measured using pilot-scale activated sludge, IFAS, and MBBR

systems. For the semiempirical version, a series of Monod equations were

developed for chemical oxygen demand, ammonium-nitrogen, and oxidized-

nitrogen fluxes to the biofilm. Within the equations, a second Monod ex-

pression is used to simulate the effect of changes in biofilm thickness and

fraction nitrifiers in the biofilm. The biofilm flux model is then linked to the

activated sludge model. The diffusional model and the verification of the

models are presented in subsequent papers (Sen and Randall, 2008a, 2008b).

The model can be used to quantify the amount of media and surface area

required to achieve nitrification, identify the best locations for the media, and

optimize the dissolved oxygen levels and nitrate recycle rates. Some of the

advanced features include the ability to apply different media types and fill

fractions in cells; quantify nitrification, denitrification, and biomass produc-

tion in the biofilm and mixed liquor suspended solids; and perform dynamic

simulations. Water Environ. Res., 80, 439 (2008).

KEYWORDS: modeling, biofilm, integrated fixed-film activated sludge,

and moving-bed biofilm reactor, activated sludge, AQUIFAS, dynamic

simulation, model development.

doi:10.2175/106143008X268452

IntroductionIn the past 20 years, there has been considerable interest in

finding alternatives to increase nitrification and denitrification in

activated sludge tanks that were originally designed for biochemical

oxygen demand (BOD) removal. Further, with the increase in the

value of land and the need to increase plant capacity to meet

population growth, there is a need to reduce the footprint of plants

per unit of flow treated. More recently, following the implementa-

tion of stringent total nitrogen permits and total-maximum-daily-

load-based strategies that require reduction to 3 mg/L total nitrogen,

there has been an interest in increasing nitrification and de-

nitrification rates in aerobic zones and in the pre- and post-anoxic

zones of nitrogen removal systems that were being operated to

satisfy an 8-mg/L total nitrogen level.

One of the alternatives being considered is the addition of biofilm

carrier particles (media) in existing or new activated sludge tanks.

If the plant continues to operate with return sludge (RAS) following

the addition of media to the activated sludge system, it gets con-

verted from an activated sludge to an integrated fixed-film activated

sludge (IFAS) system. Figure 1 shows how this can be done with

fixed-bed media or moving-bed media to increase the rates of chem-

ical oxygen demand (COD) removal and nitrification. In some in-

stances, a plant may be designed without RAS (Figure 1d). In this

case, the configuration is called a moving-bed bioreactor (MBBR)

system. A retrofit can also be made, with media addition, to sepa-

rate stage nitrification systems, to increase nitrification; or to the

anoxic zones of single-stage or separate-stage systems, to increase

denitrification.

One of the hurdles in existing models is the lack of full- or pilot-

scale verification against operating systems, principally because of

the scarcity of IFAS systems with continuous-flow data. Another

hurdle is the lack of good data on biofilm surface areas that can be

achieved with various types of media and the variation in surface area

based on aeration patterns and the location of media along an

activated sludge tank. This paper presents the process kinetics and

methodology for model design. The model can be operated for

steady-state and dynamic simulations. The dynamic simulation

provides information on the variation in effluent quality, based on

hourly, daily, weekly, or monthly changes in the influent loadings and

recycle rates, including changes in loadings from solids dewatering.

Literature ReviewThe modeling of biofilm reactors is more complex than activated

sludge modeling. This is principally because of the introduction of

diffusion. Further, the modeling of IFAS is more complex than

1 Santa Clara Valley Water District, San Jose, California.

2 Department of Civil Engineering, Virginia Tech, Blacksburg, Virginia.

* 1290 Bryant Avenue, Mountain View, CA 94040; dsen@valleywater.org.

May 2008 439

‘‘pure’’ biofilm systems, such as MBBRs, where it can be assumed

that, for low-strength wastewaters, the mixed liquor volatile sus-

pended solids (MLVSS) concentration is so low that there is very

little removal of COD, nitrification, and denitrification by the sus-

pended solids (Figure 1). Within the realm of biofilm modeling,

there are different levels of complexity. The simpler models use a

set of equations that can be solved analytically (Wanner et al.,

2006). The analytical approach simplifies the set of differential

equations, but requires more assumptions, such as knowledge of the

rate-limiting substrate in each cell within a reactor. Also, it assumes

knowledge of the limiting substrate in the layers within the bio-

film (Harremoes, 1978; Rittmann and McCarty, 1981). Bae and

Rittmann (1996) presented examples where this could be extended

to multiple limiting substrates. The numerical 1-dimensional model

relaxes these assumptions further (Reichart, 1998a, 1998b; Wanner

and Reichart, 1996 [AQUASIM 2.0]). The 1-dimensional model

can be extended to multiple dimensions. Some researchers treat the

length of a reactor or a multicell reactor as the second dimension

(also referred to as a pseudo 2 d). Others treat the spatial diversity

within the biofilm as a second dimension, wherein the biofilm is

allowed to grow and cover more of the media surface (Picioreanu,

1999). There is recognition that incorporation of the concepts of

2-dimensional modeling is important in IFAS and MBBR media

systems, where the thickness of the biofilm can lead to loss in

specific surface area on the inside surface of plastic cylinders, but

may be partially compensated for by the increase in the biofilm that

develops on the outer surface (Sen, Randall, Copithorn, Huhtamaki,

Farren, and Flournoy, 2007).

Several pilot studies of activated sludge, IFAS, and MBBR

systems were undertaken between 1992 and 1995 (Mitta, 1994; Sen,

1995). The purposes were to understand the conditions under which

COD removal, nitrification, denitrification, and biological excess

phosphorus removal were affected by the introduction of biofilm

support media in activated sludge systems and by the reduction in

mixed liquor suspended solids (MLSS) mean cell residence time

(MCRT) and to develop a simple version of the IFAS model.

Several process kinetic parameters were identified, and their values

were measured. Some of the parameters for the biofilm were sub-

sequently published as flux rates of COD removal and nitrification

(Sen and Randall, 1996, 2005; Sen et al., 2000).

Earlier versions of the IFAS model were published by Sen and

Randall (1996, 2005) and by Sriwiriyarat et al. (2005). Several full-

scale IFAS and MBBR facilities were evaluated using the model,

and the results were published in 2006 (Sen et al., 2006). The facili-

ties included Broomfield, Colorado (Rutt et al., 2006); Annapolis,

Maryland (Copithorn et al., 2006); Geisselbullach, Germany

(Lessel, 1994); Mamaroneck, New York (Psaltakis et al., 2003);

and Providence, Rhode Island (Masterson et al., 2004). The IFAS

model was able to predict the improvement in nitrification at all nine

of the nine full-scale IFAS and MBBR facilities for which data was

available. What is more important is that it was able to accurately

simulate the loss of nitrification/limited nitrification in winter at two

of the facilities.

Model DevelopmentThe biofilm can be modeled using a semiempirical methodology

and a mechanistic method. The semiempirical method is based on

modeling the biofilm flux rates based on a set of equations for

biofilm flux. These equations were developed from measurements

of biofilm flux in pilot studies (Sen, 1995). They include a second

Monod expression to simulate the effect of changes in biofilm

thickness and fraction nitrifiers in the biofilm, with changes in the

external substrate concentrations. In the mechanistic model (Sen and

Randall, 2008a), the biofilm is modeled as 12 layers and a stagnant

liquid layer (biofilm 1-and 2-dimensional diffusional model).

The basic premise of the model is to add equations for uptake,

oxidation, and reduction of COD, ammonium-nitrogen, and oxidized

nitrogen, and for sludge production in biofilms, in a format that is

compatible with the International Association on Water Quality

(London, United Kingdom) (IAWQ) activated sludge model. The

IAWQ model is available in several user-friendly forms, the most

common of which is the Biowin (Envirosim Associates Ltd., 2006).

In developing the model described herein, the equations for the

biofilm were structured in a manner that is compatible with the

activated sludge model. The COD, ammonium-nitrogen, and

oxidized nitrogen uptake and removals are computed as the sum

total of removals by the MLSS and the biofilm. The percentage of

removal in the biofilm increases as the amount of biofilm surface

area is increased and the MLSS MCRT (and MLVSS) is decreased.

The equations to compute the COD removal, ammonium-nitrogen

removal (biomass uptake for synthesis and nitrification), and deni-

trification were developed based on Monod process kinetics. The

removals in suspended solids are computed as per the IAWQ/Inter-

national Water Association activated sludge model and are dependent

on the concentrations of suspended solids, biodegradable soluble

COD, ammonium-nitrogen, and dissolved oxygen. Additional

removal resulting from the biofilm in IFAS and MBBR configurations

is computed based on removal rates per unit of surface area of biofilm,

multiplied by the surface area of biofilm in each reactor (cell).

The model is set up to operate with up to 12 cells (reactors) in

series. Influent and recycles can be fed to and removed from any cell.

Figure 1—Plant configurations.

Sen and Randall

440 Water Environment Research, Volume 80, Number 5

Biofilm support media can be installed in one or more cells. Each cell

can be operated with or without aeration, as part of an anaerobic, pre-

or post-anoxic, aerobic, or reaeration zone. For the unaerated cells,

the model computes the dissolved oxygen and oxidized nitrogen

(NOxN). This is compared with user-specified thresholds for aerobic,

anoxic, and anaerobic conditions, to determine whether aerobic,

anoxic, or anaerobic decay rates should be used for each cell.

The removals in the biofilm can be computed by two different

methods. The semiempirical version of the biofilm model incorpo-

rates Monodlike equations for the biofilm for substrate uptake and

removal under aerobic and anoxic conditions. These equations are

based on experimental measurements of biofilm flux rates observed

in pilot studies. The maximum nitrification rate per unit surface area

of biofilm (qm,NH4N2Nitr,bf) and the maximum COD utilization

rate per unit surface area of biofilm under aerobic and anoxic condi-

tions (qmH,COD,bf,aer and qmH,COD,bf,anx) were quantified. The half-

saturation constants for substrate and dissolved oxygen for the

biofilm (KN,bf and KDO,bf) were determined through a separate model

calibration and from the literature. The methodology for quantifying

rates was published in Sen (1995) and is summarized below.

The modeling of the aeration system for IFAS and MBBR

systems are based on the equations for aeration modeling in the

Aeration Manual of Practice FD-13 (WPCF, 1988). Research is

being undertaken by various manufacturers on the aeration and

oxygen transfer efficiencies in IFAS tanks. This supplements the

work done with diffusers in activated sludge systems, in which the

oxygen transfer efficiency was measured for various roll config-

urations and diffuser placements types on the floor of the activated

sludge tank (Rooney and Huibregtse, 1980; Schmit et al., 1978).

This paper presents the structure of the semiempirical version. The

semiempirical model requires a shorter run time compared with the

biofilm 1-dimensional model presented in Sen and Randall (2008a).Ammonium-Nitrogen Uptake Rate. Equations 1 to 17 show

how ammonium-nitrogen is incorporated to the semiempirical

version of the IFAS and MBBR models. The default values of the

various kinetics parameters mentioned in the discussion below are

based on literature values for activated sludge systems and observa-

tions from biofilms.

Ammonium-Nitrogen Uptake Rate by Nitrifiers in Biofilm. Eq-

uation 1 shows the ammonium-nitrogen uptake rate in the biofilm

(kilograms per day). The ammonium-nitrogen (NH4N) uptake rate

is the sum total of the ammonium-nitrogen uptake by nitrifiers for

synthesis and nitrification. For cell n, the NH4N uptake by the

nitrifiers (NH4Nu,bf,n 5 BN,,n) is computed as follows:

NH4Nu;bf;n BN;n ¼ qm;NH4N�Nitr;bf

3SO2n

KDO;nitr;bf þ SO2n

SNn

KN;nitr;bf þ SNn

Vn Mnð1Þ

Where

qm,NH4N2Nitr,bf 5 flux rate for ammonium-nitrogen uptake by the

nitrifiers (expressed as kg/1000 m2 of biofilm

surface/d or mg/cm2/d).

The value of qm,NH4N2Nitr,bf for the biofilm is adjusted for mixed

liquor temperature. This is done using the Arrhenius equation, with

a temperature adjustment coefficient, h, as follows:

qm;NH4N�Nitr;bf;T ¼ qm;NH4N�Nitr;bf;25ðhÞðT�25Þ ð2ÞThe literature on nitrification in activated sludge systems shows

a range of values of the coefficient to adjust nitrification rates for

temperature. These vary from 1.03 to greater than 1.07 (Marais and

Ekama, 1976; Randall et al., 1992; Wentzel et al., 1991). Research

conducted by Weiss et al. (2005) using an MBBR showed a

temperature coefficient of 1.047. A value of 1.05 1/2 0.02 is

recommended for the model.

For eq 1,

SN n and SO2 n 5 ammonium-nitrogen and dissolved oxygen

concentrations (mg/L), respectively, measured

in the liquid outside the biofilm in cell n (i.e.,

as measured in activated sludge systems);

Vn 5 volume of cell n (m3);

Mn 5 m2 of biofilm surface area per m3 of cell

volume in cell n; and

KN,nitr,bf 5 half-saturation constants for NH4N for nitrifier

growth in the biofilm (mg/L).

The default value of KN,nitr,bf 5 2 mg/L; this is based on data

presented by Hem et al. (1994) and Odegaard et al. (1994), which

show that nitrification rates in biofilms at 11 to 158C, when mea-

sured at high dissolved oxygen and low soluble COD levels, vary

almost linearly, from 0 to 4 mg/L NH4N (the relationship is first-

order over this range) and are fairly constant (zero-order) above

that. This relationship can also be represented using a Monod

expression with a half-saturation constant for NH4N of 2 mg/L.

For eq 1,

KDO,nitr,bf 5 half-saturation constant for dissolved oxygen for

nitrifier growth in the biofilm (mg/L).

The default value of KDO,nitr,bf 5 4 mg/L. Within the model, the

user may also select a first-order kinetics equation to simulate the

variation in nitrification rates with dissolved oxygen, as follows:

NH4Nu;bf;n BN;n ¼ qm;NH4N�Nitr;bf

3SO2n

KDO1;nitr;bf

SNn

KN;nitr;bf þ SNn

Vn Mn ð3Þ

Where

KDO1,nitr,bf 5 4.5 mg/L.

Both forms of the equation (eqs 1 and 3) replicate the variation in

nitrification rates with dissolved oxygen and are consistent with the

data presented by Huhtamaki and Sen (2007), Odegaard (2005b),

and Weiss et al. (2005). In the data presented by Odegaard (2005b),

the maximum nitrification rate in biofilms, measured at 11 to 158C

and operating at NH4N levels above 3 mg/L and low soluble COD

levels, varies linearly with dissolved oxygen from 3 to 6 mg/L.

The rates increased from 0.75 kg/d/1000 m2 at 3 mg/L to 1.5 kg/d/

1000 m2 at 6 mg/L dissolved oxygen, which shows a first-order

relationship. The rate began to deviate gradually from first-order to

half-order at dissolved oxygen levels above 6 mg/L. At a dissolved

oxygen concentration of 9 mg/L, the rate was 2 kg/d/1000 m2. In the

equation presented by Weiss et al. (2005), the nitrification rate in

an MBBR varied linearly with dissolved oxygen over a range of 1 to

7 mg/L when the NH4N levels were above 3 mg/L, as follows:

qm;NH4N�nit;bf ¼ 0:214ðSO2 � 1:15Þð1:047ÞðT�20Þ

Biofilm Nitrification Rates from Pilot Studies. Bench-scale pilot

systems were operated to determine rate coefficients. The activated

Sen and Randall

May 2008 441

sludge, IFAS, and MBBR systems were operated under identical

wastewater loads, tank sizes and configurations, and nitrate recycle

configurations, except for the biofilm support media in the aerobic

zones of the IFAS and MBBR systems. The flowrate was 208 L/d,

and the nominal hydraulic retention time (HRT) was 12 hours. Of

this, 17% of the volume was anaerobic, 17% was anoxic, and

the remaining 66% was aerobic (aerobic HRT of 8 hours). The

operating temperature of 128C was low enough to stress the

nitrifiers in the MLSS as the mixed liquor MCRT was lowered.

The maximum ammonium-nitrogen uptake rates by nitrifiers in

the biofilm (qm,NH4N2Nitr,bf) were measured for biofilm removed

from the pilot systems. To measure the maximum rates of

ammonium uptake, 2 L of the biofilm carrier particles and mixed

liquor were removed from each of three aerobic cells of the IFAS

and MBBR continuous-flow system. These were placed in flasks

and spiked with ammonium chloride and bicarbonate, and aerated.

The ammonium-nitrogen uptake rate was measured over time. The

tests were conducted at ammonium-nitrogen concentrations of 10 to

50 mg/L. The rates were determined for the mixed liquor alone and

for the mixed liquor with biofilm carrier particles. The tests were

conducted when the systems were operated at 3.1-, 2.4-, 1.7-, 1.0-,

and 0.3-day MLSS MCRTs. The combination of 5 MLSS MCRTs

and three aerobic cells allowed one to measure rates for uptake of

ammonium-nitrogen by biofilm that developed under various

soluble biodegradable COD and ammonium-nitrogen conditions.

The method has been described by Sen (1995). The batch tests for

ammonium-nitrogen uptake were operated at very low soluble

biodegradable COD concentrations. This limited the ammonium-

nitrogen uptake by the heterotrophs in the biofilm. The systems

were operated for a minimum of 3 MLSS MCRTs or 8 weeks,

whichever was longer, and monitored to ensure that steady-state

was achieved following each change in MLSS MCRT. This was to

ensure that the biofilm reached a reasonable degree of equilibrium

with the new soluble biodegradable COD profile.

The qm,NH4N2Nitr,bf data for the biofilm were graphed against

biodegradable soluble COD levels (SCODbio) for those conditions

where the soluble biodegradable COD in the aerobic reactor was

above 10 mg/L (Figure 2a). Note that the concentration referenced

is the concentration measured in the continuous-flow reactor under-

steady state operation at the various MLSS MCRTs. Above 10 mg/L,

Figure 2—Nitrification rates for biofilm in IFAS and MBBR systems (DO 5 dissolved oxygen).

Sen and Randall

442 Water Environment Research, Volume 80, Number 5

the studies showed that the nitrifiers in the biofilm were inhibited by

the concentration of soluble biodegradable COD and not influenced

by the concentration of NH4N in the reactor. An empirical relation-

ship (equation for the line) was developed from the data (points on

the graph) using SYSTAT (a statistical software package by Systat

Software Inc., San Jose, California) to relate qm,NH4N2Nitr,,bf to

soluble biodegradable COD (Figure 2a), as follows:

qm;NH4N�Nitr;bf ¼AN KS;bfg;Nitr

KS;bfg;Nitr þ SCODbio � 10ð4Þ

Where

AN 5 1.8 kg/1000 m2 of biofilm surface/d;

KS,bfg,Nitr 5 half-saturation constant for nitrifier growth in biofilm

(5 9.4 mg/L SCODbio); and

SCODbio 5 biodegradable soluble COD in the mixed liquor.

For SCODbio,10 mg/L, it was determined that the COD concentra-

tion did not inhibit the development of nitrifiers in the biofilm. The

qm,NH4N2Nitr,,bf that could be sustained by the biofilm increased

linearly with NH4N in the continuous-flow reactors (Figure 2b), as

follows:

qm;NH4N�Nitr;bf ¼ ðDÞSN ð5Þ

Where

D 5 0.47 kg-L/mg/m2 of biofilm surface/d, and

SN 5 ammonium-nitrogen concentration in the mixed liquor

(mg/L).

An alternate form of eq 5 was used to simulate the conditions

observed at SCODbio,10 mg/L, as follows:

qm;NH4N�Nitr;bf ¼AN SN

KN;bfg�Nitr þ SN

ð6Þ

Where

KN,bfg,Nitr 5 half-saturation constant term in the equation to derive

qm,NH4N2Nitr,bf (maximum flux rate for ammonium-

nitrogen uptake by the nitrifiers) from AN.

The value of KN,bfg,Nitr 5 2.1 mg/L NH4N. Note that this is not the

same as KN,bf in eq 1.

The value of AN over the range observed is in general agreement

with the value of 2 to 2.5 kg/1000 m2/d observed by Odegaard

(2005) and Odegaard et al. (1994) for Kaldnes Miljøteknologi

(KMT) carriers at 10 to 158C, low soluble BOD concentrations, and

without oxygen limitation. The default value recommended for

modeling 5 2 kg/1000 m2/d.

Ammonium-Nitrogen Uptake Rate by Nitrifiers in Mixed LiquorVolatile Suspended Solids. Equation 7 represents the ammonium-

nitrogen uptake by nitrifiers in the suspended solids (SS) in

cell n. The units for MLVSS are kilograms per cubic meter. The

BVFn is the fraction of liquid volume in cell n that is displaced by

biofilm and its support media. It is characteristic of the type of

media and media fill volume fraction (mf) in the cell. The mf is

the fraction of empty tank volume that is filled with bare media.

For example, if 50% of the empty tank volume is filled with bare

media (media without biofilm on its surface), the mf 5 0.5. The fnitr

is the fraction of nitrifiers in the MLVSS.

The NH4N uptake by nitrifiers in cell n, AN,n, is computed as

follows:

AN;n ¼ qm;NH4N�Nitr;SS

SO2n

KDO;nitr;SS þ SO2n

SNn

KN;nitr;SS þ SNn

3 Vnð1� BVFnÞ fNitrXn ð7Þ

Where

qm,NH4N2Nitr,SS 5 maximum ammonium-nitrogen up-

take rate for nitrifiers in the MLVSS

at temperature T (mg NH4N/mg

nitrifier VSS/d);

KDO,nitr,SS and KN,nitr,SS 5 half-saturation constants for nitrifiers

in the MLVSS at temperature T;

fNitr 5 fraction of nitrifiers in the MLVSS; and

Xn 5 MLVSS concentration in cell n (kg

VSS/m3).

The value of qm,NH4N2Nitr,SS measured by calibration of the

model to the performance of the activated sludge system in the pilot

studies was 8.51 mg NH4N uptake by nitrifiers/mg nitrifier VSS � dat 128C (Table 1). This is in agreement with the value for

qm,NH4N2Nitr,SS of 12.5 mg NH4N at 258C uptake/mg nitrifier

VSS � d and a temperature adjustment coefficient of 1.03 (Randall

et al., 1992; Wentzel et al., 1991).

The default value of KDO,nitr,SS 5 1 mg/L dissolved oxygen at

258C. Its temperature adjustment coefficient, h 5 1.00. The default

value of KN,nitr,SS 5 1 mg/L of NH4N at 258C. Its temperature ad-

justment coefficient, h 5 1.06. This results in a value of 0.46 mg/L

at 128C. These values of the coefficients are based on the work

on nitrification and denitrification in activated sludge systems by

Marais and Ekama (1976) and Wentzel et al. (1991).

For the purposes of design, the model allows the user to inhibit

the value of qm,NH4N2Nitr,SS (8.51 day21) by a certain percentage,

to account for nitrifier inhibition experienced at a full-scale facility.

A typical percentage for the inhibition recommended for design is

25%. The inhibition is because of the presence of certain chemicals

in the wastewater, such as in a system that receives a combination of

wastewater and septage. Certain facilities have significantly higher

inhibition, such as inhibition by cyanide recirculated from multiple

hearth incinerators burning sludge. This has been observed at the

Western Branch Wastewater Treatment Plant, Washington Sub-

urban Sanitary Commission, Maryland, and the Virginia Initiative

Plant, Hampton Roads Sanitation District (Norfolk, Virginia) plants

when operated with recycle flow from multiple hearth furnace

exhaust gas scrubbers. The inhibition was as high as 50% (Solley,

2000). At other facilities, such as in Broomfield, Colorado (Sen,

Phillips, Murthy, Pattarkine, Copithorn, Randall, Schwinn, and

Banerjee, 2007), continuous simulation against extended periods of

plant data showed no significant inhibition.

Mass Balance for Ammonium-Nitrogen in Each Reactor. The

ammonium-nitrogen concentration (mg/L) in cell n is calculated

using a mass balance approach, as follows:

IN;n þ Ndecay;n þ Norg�N;hydr;n

¼ AN;n þ BN;n þ CN;n þ DN;n þ EN;n ð8Þ

Where

IN,n 5 quantity of unassimilated ammonium-nitrogen

entering aerobic cell n (kg/d);

Sen and Randall

May 2008 443

Table 1—Values of coefficients measured in pilot studies and default values for the semiempirical model.a Refer to notesb and c at the bottom of the table for sources of the values.

T Value

measured

Default Units/formula Reference

Heterotrophs in MLVSS

Aerobic

um,H,aer,SS Max growth rate 12 3.57 3.57 mg VSS (mg COD d)21 Note b

qm,H,aer,SS Max substrate util rate 12 8.72 8.72 mg COD (mg VSS d)21 Note b

YH,aer Yield 12 0.41 0.41 mg VSS (mg COD)21 Note b

kd,H,aer Decay rate 12 0.042 0.042 day21 Note b

KH,S,,aerSS Half sat constant 12 48 48 mg/L SCOD Note b

KH,DO,SS Half sat constant 12 1 mg/L dissolved oxygen Note c

qm,hydr,aer,COD,SS Max hydrolysis rate (0.1)

(qm,H,aer,SS)

mg COD (mg VSS d)21 Note d

qm,hydr,aer,PorgN,SS Max conversion rate

(particulate orgN to sol orgN)

(qm,hydr,aer,COD,SS)

(influent COD/TKN)

qm,hydr,aer,PP,SS Max conversion rate

(particulate orgP to sol P, not OP)

(qm,hydr,aer,COD,SS)

(influent COD/total

phosphorus)

qm,hydr,aer,SorgN,SS Max ammonification rate

(sol orgN to NH4N)

(0.8) (qm,hydr,aer,PorgN,SS)

qm,hydr,aer,SP,SS Max ammonification rate

(sol P to OP)

(0.8) (qm,hydr,aer,PP,SS)

Anoxic

um,H,anx,SS Max growth rate 12 1.77 1.77 mg VSS (mg COD d)21 For pre-anx

qm,H,anx,SS Max substrate util rate 12 5.71 5.71 mg COD (mg VSS d)21 For pre-anx

YH,anx Yield 12 0.31 0.31 mg VSS (mg COD)21 Note b

kd,H,anx Decay rate 12 0.022 0.022 day21 Note b

KH,S,anx,SS Half sat constant 12 56 48 mg/L SCODbio Note b

KH,DO,I,SS Half inhibition constant 12 0.25 mg/L dissolved oxygen Note c

KH,NO3N,SS Half sat constant 12 1.0 mg/L NO3N Note c

Hydrolysis rate (Aerobic rate)

(qm,H,anx,SS/qm,H,aer,SS)

Note d

Anaerobic

kd,Hana Decay rate 12 0.005 0.005 day21 Note b

Hydrolysis rate (0.5)(anoxic rate)(0.5) Note d

Autotrophs in MLVSS

Nitrosomonas or ammonia-oxidizing bacteria Values from literature calibrated to pilot studies

um,NH4N-Nitr,SS Max growth rate 12 0.43 0.43 mg VSSNitr1 (mg NH4N d)21 Note e

qm,NH4N-Nitr,SS Max NH4N util rate 12 8.51 8.51 mg NH4N (mg VSSNitr1 d)21 Note b

YN1 Yield 12 0.05 0.05 mg VSSNitr1 (mg NH4N) Note c

kd,N1 Aerobic decay rate 12 0.023 0.023 day21 Note c

KDO,nitr,SS Half sat constant for nitrifiers 12 1 mg/L dissolved oxygen Note c

KN,nitr,SS Half sat constant for nitrifiers 12 1 mg/L NH4N Note c

Biofilm in semiempirical model These are concentrations in the bulk liquid, not inside biofilm

KS,H,aer,bf Half sat, aerobic, heterotrophs 12 48 48 mg/L SCODbio Note b

KS,H,anx,bf Half sat, anoxic, heterotrophs 12 56 48 mg/L SCODbio Note b

KDO,H,aer,bf Half sat, aerobic, heterotrophs 12 4.0 mg/L dissolved oxygen Note f

KDO,H,i,bf Half inhibition constant, anoxic 12 2.0 mg/L dissolved oxygen Note b

ASaer Max aer COD uptake rate, biofilm 12 21 21 kg COD/1000 m2/d Note b

ASanx Max anx COD uptake rate, biofilm 12 14 14 kg COD/1000 m2/d Note g

BSaer Half sat, for AS 12 19.3 19.3 mg/L SCODbio Note b

BSanx Half sat, for AS 12 19.3 19.3 mg/L SCODbio Note b

KDO,nitr,bf Half sat, aerobic, nitrifiers 12 4.0 mg/L dissolved oxygen Note f

KN,nitr,bf Half sat, aerobic, nitrifiers 12 2.0 mg/L NH4N Note f

AN Max NH4N uptake rate (nitr rate) 12 1.8 1.8 kg/1000 m2/d Note b

KS,bfg,nitr Half inhibition, AN for nitrif 12 9.4 9.4 mg/L SCODbio Note b

KN,bfg,nitr Half sat, AN for nitrif 12 2.1 2.1 mg/L NH4N Note b

Sen and Randall

444 Water Environment Research, Volume 80, Number 5

EN,n 5 quantity of unassimilated ammonium-nitrogen

exiting cell n (kg/d);

AN,n and BN,n 5 ammonium-nitrogen uptake by nitrifiers in

suspended solids and biofilm, computed by

eqs 7 and 1, respectively (kg/d);

CN,n and DN,n 5 ammonium-nitrogen use in cell n resulting from

heterotrophic biomass production by MLVSS

and biofilm, respectively (kg/d);

Ndecay,n 5 ammonium-nitrogen released through decay of

VSS in cell n (kg/d); and

Norg-N,hydr,n 5 hydrolysis of organic nitrogen (kg/d).

The variable CN,n 5 NH4N uptake by biomass in the MLSS using

dissolved oxygen and NOxN in cell n, as follows:

CN;nðkg=dÞ ¼ f½CODu;aer;SS;n�½YAH;aer;SS�þ ½CODu;anx;SS;n�½YAH;anxSS�g fN ð9Þ

Where

fN 5 fraction of nitrogen in the

biomass (MLVSS) synthe-

sized (default value of 0.12);

CODu,aer,SS,n and CODu,anx,SS,n 5 COD used by MLVSS under

aerobic and anoxic conditions,

respectively, in cell n (kg/d);

and

YAH,aerSS and YAH,anxSS 5 actual biomass yields for aer-

obic and anoxic uptake of

COD by the suspended solids

(mg VSS/mg COD).

The variable YAH,BF (eq 10) 5 actual biomass yield for heterotrophs

in the biofilm (mg VSS/mg COD). Heterotrophic biomass produc-

tion is discussed in the section titled Biomass Production.

The variable DN,n (kg/d) 5 NH4N uptake by heterotrophic yield

of the biofilm in cell n, as follows:

DN;n ¼ ½CODu;bf;n�½YAH;BF�g fN ð10Þ

Unlike NH4N uptake rates by MLVSS, A,n,N and D,n.N, are the

measured net decay of autotrophic and heterotrophic biomass in the

biofilms, respectively. The Ndecay,n is the nitrogen released from

biomass in MLVSS (kg/m3) as a result of decay in cell n. When the

dissolved oxygen concentration is above the threshold that repre-

sents aerobic conditions, the form of the equation is as follows:

Ndecay; nðkg=dÞ ¼ ðfNÞðkdH;aerT MLVSS VnÞð1� BVFnÞ ð11Þ

If the dissolved oxygen concentration is below the threshold for

aerobic conditions, but above the NOxN threshold for anoxic

conditions, the decay rate is reduced from the aerobic decay rate of

kdH,aerT to the anoxic decay rate of kdH,anxT (Table 1). If it is below

the NOxN threshold, the decay rate is reduced to the anaerobic

decay rate of kdH,anaT.

The Ndecay,n is not included when the value of the ammonium-

nitrogen utilization rate term for sludge production (CN,n) by the

MLVSS is the measured net of biomass decay. The corresponding

decay term for biofilm is not included, because the ammonium-

nitrogen uptake rate in eq 1 is the measured net of biofilm decay.

The Norg-N,hydr,n is the unassimilated organic nitrogen that is

hydrolyzed in cell n. It is computed as follows (in kg/d):

Norg�N;hydr;n ¼ ðIPorgN þ ISorgN � EPorgN � ESorgNÞn ð12Þ

In this model, the rate of hydrolysis is computed based on a series

of Monod equations. For the MLVSS, the maximum hydrolysis rate

for unassimilated particulate organic nitrogen (qm,hydr,EA,PorgN,SS) is

expressed in units of kg particulate organic nitrogen hydrolyzed/kg

MLVSS � d; the half-saturation constant (Khydr,EA,PorgN,SS) is ex-

pressed in mg/L particulate organic nitrogen. The subscript EA

represents aerobic, anoxic, or anaerobic conditions for the electron

acceptor (EA), based on the thresholds of dissolved oxygen and

NOxN, which represent aerobic and anoxic conditions, respectively.

For the biofilm, the maximum hydrolysis rate for particulate organic

nitrogen (qm,hydr,EA,PorgN,bf) is expressed in units of kilograms of

particulate organic nitrogen hydrolyzed per day per 1000 m2 of

biofilm surface. The half-saturation constant (Khydr,EA,PorgN,bf) is

expressed in milligrams per liter of particulate organic nitrogen. The

Table 1—(Continued)

T Value measured Default Units/formula Reference

Aerobic COD hydrolysis rates by biofilm 20% of qmaer,COD,bf kg COD/1000 m2/d Note h

fN Nitrogen in biomass 0.12 mg-N/mg VSS Note b

fCOD COD in biomass 1.42 mg COD/mg VSS Note b

a Model is structured such that the modeler can use observed values instead of the default values for kinetic coefficients and � when

observed values are available.b Unless mentioned, these values were determined from continuous-flow bench-scale pilot studies operated in activated sludge, IFAS, and

MBBR modes (Sen, 1995).c Literature referenced: Barker and Dold (1997); Marais and Ekama (1976); Randall et al. (1992); Wentzel et al. (1991).d Maximum hydrolysis rate should be refined by calibrating model results to operating data.e The value of 0.43 day21 was determined by calibrating the model to the performance of the bench-scale activated sludge system operated

at different MLSS MCRTs.f Hem et al. (1994); Huhtamaki and Sen (2007); Odegaard (2005b); Weiss et al. (2005).g Based on ratio of maximum substrate utilization rates under preanoxic and aerobic conditions. The value must be corrected for post-anoxic

cells.h For aerobic hydrolysis by biofilm, substitute qmaer,COD,bf for qm,H,aer,SS in the equation for MLVSS; all other hydrolysis equations for the biofilm

are related to this equation based on a form similar to the equations for hydrolysis with MLVSS.

Sen and Randall

May 2008 445

effluent particulate organic nitrogen (EPorgN) is computed from the

influent particulate organic nitrogen (IPorgN) and the hydrolysis of

particulate organic nitrogen by the MLVSS and biofilm. This is

simulated using eqs 13 to 16, as follows:

IPorgN;n ¼ EPorgN;n þ Porg Nhydr;SS;n þ Porg Nhydr;bf;n ð13Þ

Porg Nhydr;SS;n ¼ qm;hydr;EA;PorgN;SS

3ECPorgN;n

Khydr;EA;PorgN;SS þ ECPorgN;n

3 Vnð1� BVFnÞ MLVSSn ð14Þ

Porg Nhydr;bf;n ¼ qm;hydr;EA;PorgN;bf

3ECPorgN;n

Khydr;EA;PorgN;bf þ ECPorgN;nVn Mn ð15Þ

EPorgN ¼ ðECPorgNÞðQeff;nÞ=1000 ð16Þ

Where

ECPorgN 5 concentration of particulate organic nitrogen in the

effluent from cell n (mg/L), and

Qeff,n 5 effluent flow from cell n (m3/d).

The particulate organic nitrogen gets hydrolyzed to soluble organic

nitrogen. The soluble organic nitrogen is then converted (deammi-

nated) to ammonium-nitrogen. The effluent soluble organic nitrogen

(ESorgN) is computed as follows:

ISorgN þ Porg Nhydr;SS;n þ Porg Nhydr;bf;n

¼ ESorgN þ Sorg Nhydr;SS;n þ Sorg Nhydr;bf;n ð17Þ

The equations to determine soluble organic nitrogen hydrolyzed

by the biofilm and suspended solids (Sorg Nhydr,SS,n 1 Sorg

Nhydr,bf,n) are structured in a format similar to eqs 13 to 16. The

subscript SorgN is substituted for PorgN. The values of maximum

hydrolysis rate for soluble organic nitrogen for MLVSS and biofilm

(qm,hydr,SorgN,SS and qm,hydr,SorgN,bf) and the corresponding half-

saturation constants for soluble organic nitrogen are used in eqs 14

and 15.

A set of values of coefficients have been developed for use in the

model (Table 1). These values are derived by calibrating the model

to the data from the continuous-flow pilot studies (Sriwiryarat et al.,

2005) and calibration of the model to several full-scale MBBRs and

IFAS plants (Sen et al., 2006). In eqs 14 and 15, the half-saturation

constants Khydr,EA,PorgN,SS and Khydr,EA,PorgN,SS are 1 mg/L for all

electron acceptor (EA) conditions.

It should be noted that the value of the hydrolysis rate selected

has a greater affect in winter compared with summer and in an

MBBR compared with an IFAS. This is because of a slower

hydrolysis rate in winter and the relatively low MLVSS in the

MBBR, which requires most of the hydrolysis to be in the biofilm.

The values computed from the pilot studies were revised based on

comparison with MBBRs running in winter. Particular care should

be taken in running models for MBBRs at low temperatures (2 to

128C). The results should be checked against actual plants and the

values of the coefficients adjusted if necessary.

The equations for nitrification, denitrification, and COD removal

are summarized in a matrix format for substrate uptake in the

MLVSS (Table 2) and by the biofilm (Table 3) in each cell of a

multicell reactor.Chemical Oxygen Demand Removal. The COD removal

rates are computed by a set of equations similar to those for

nitrification.

The COD can be removed aerobically and anoxically by the

biofilm and the MLVSS in each cell. Equation 18 shows the aerobic

COD uptake (CODu,aer,bf 5 Bn,1,S) by the biofilm, as follows:

CODuaer;bf B1;S;n ¼ qm;aer;COD;bf

SO2n

KDO;H;aer;bf þ SO2n

3SCODbio;n

KS;H;aer;bf þ SCODbio;nVn Mn ð18Þ

Maximum COD removal rates (qm,COD,bf) also increased with

the soluble biodegradable COD concentration (SCODbio). Based

on batch tests to measure rates by biofilm removed from the

Table 2—Matrix showing equations for heterotrophs and the interrelationship of kinetic coefficients for the mixed liquorin each cell of reactor (X 5 MLVSS).

XH

(X [12fnitr])

XN

(X fnitr)

SS

(SCODbio)

SN

(NH4N)

SO2

(dissolved

oxygen)

SNO3N

(NO3N) Kinetic expression for cell n (n 5 cell number in multicell reactor)

Heterotrophs

using

dissolved

oxygen

1 21YHaer

2fN2ð12fCODYHaerÞ

YHaerYHaer[qm,H,aer,SS

SO2n

KH;DO;SS1SO2n

SCODbio;n

KH;S;aer;SS1SCODbio;nVn(12BVFn) (12fNitr) Xn]

Heterotrophs

using NO3N

1 21YHanx

2fN2ð12fCODYHanxÞ

2:86 YHanxYHanx[qm,H,anx,SS

SNOxNn

KH;NOxN;SS1SNOxNn

SCODbio;n

KH;S;anx;SS1SCODbio;n

KH;DO;i;SS

KH;DO;i;SS1SO2n

Vn(12BVFn) (12fNitr)Xn]

AOB (N1) using

dissolved

oxygen

1 21YN1

23:43ð12fNYN1ÞYN1

YN1[qm,NH4N2Nitr,SSSO2n

KDO;nitr;SS1SO2n

SNn

KN;nitr;SS1SNnVn(12BVFn) fNitrXn]

NOB (N2) using

dissolved

oxygen

1 2fN21:14

YN2

21YN2

AOB 1 NOB

(if YN1 5 YN2

and eff

NO2N 5 0)

2 21YN1

2 fN24:57ð12fNYN1Þ

YN1

21YN1

2 YN1[qm,NH4N2Nitr,SSSO2n

KDO;nitr;SS1SO2n

SNn

KN;nitr;SS1SNnVn(12BVFn) fNitrXn]

Sen and Randall

446 Water Environment Research, Volume 80, Number 5

continuous-flow reactor cells, an empirical relationship was devel-

oped to relate qm,COD,bf to SCODbio (Figure 3), as follows:

qm;aer;COD;bf ¼AS;aer SCODbio

BS;aer þ SCODbio

ð19Þ

Where

AS,aer 5 21 kg/1000 m2 of biofilm surface/d, and

BS,aer 5 19.3 mg/L SCODbio.

Equation 18 shows that the rate changes with biodegradable

soluble COD (SCODbio,n) and dissolved oxygen (SO2,n) in cell n. The

default value of the half-saturation constant for COD, KS,H,aer,bf 5 48

mg/L COD at 128C; this is equal to the value of KSHaer,SS measured

for biomass in MLSS in the pilot studies (Table 1).

The default value of the half-saturation constant for dissolved

oxygen, KDO,H,aer,bf, at 258C 5 4 mg/L dissolved oxygen. It is set at

the same level as used for nitrification in the biofilm.

Equation 20 shows the anoxic COD uptake (CODu,anx,bf 5 B2,S,n)

by the biofilm, as follows:

CODu;anx;bf B2;S;n ¼ qm;anx;COD;bf

KH;DO;i;bf

KH;DO;i;bf þ SO2n

3SCODbio;n

KS;H;anx;bf þ SCODbio;n

SNOxNn

KNOxN;bf þ SNOxNn

Vn Mn ð20Þ

qm;anx;COD;bf ¼AS;anx SCODbio

BS;anx þ SCODbio

ð21Þ

Where the default values of A and B are as follows:

AS,anx 5 13.8 kg/1000 m2 of biofilm surface/d, if the media is in

the preanoxic zone; and

BS,anx 5 19.3 mg/L SCODbio.

Equation 20 can be split into two separate equations, based on

COD uptake with NO2N and NO3N as the two separate forms of

Table 3—Matrix showing equations for heterotrophs and biofilm flux associated with the biofilm in each cell in thesemiempirical biofilm model.*

XH

(X [12fnitr])

XN

(X fnitr)

SS

(SCODbio)

SN

(NH4N)

SO2

(dissolved

oxygen)

SNO3N

(NO3N)

Kinetic expression for cell n

(n 5 cell number in multicell reactor)

Heterotrophs using

dissolved oxygen

1 21YHaer

2fN2ð12fCODYHaerÞ

YHaerYHaer[qm,aer,COD,bf

SO2n

KDO;H;aer;bf1SO2n

SCODbio;n

KS;H;aer;bf1SCODbio;nVn Mn]

Heterotrophs

using NO3N

1 21YHanx

2fN2ð12fCODYHanxÞ

2:86 YHanxYHanx[qm,anx,COD,bf

KH;DO;i;bf

KH;DO;i;bf1SO2n

SCODbio;n

KS;H;anx;bf1SCODbio;n

SNOxNn

KNOxN;bf1SNOxNn

Vn Mn]

AOB (N1) using

dissolved oxygen

1 21YN1

23:43ð12fNYN1ÞYN1

YN1[qm,NH4N2Nitr,bfSO2n

KDO;nitr;bf1SO2n

SNn

KN;nitr;bf1SNnVn Mn]

NOB (N2) using

dissolved oxygen

1 2fN21:14

YN2

21YN2

AOB 1 NOB (if

YN1 5 YN2 and

eff NO2N 5 0)

2 21YN1

2 fN24:57ð12fNYN1Þ

YN1

21YN1

2 YN1[qm,NH4N2Nitr,bfSO2n

KDO;nitr;bf1SO2n

SNn

KN;nitr;bf1SNnVn Mn]

* The value of qm,aer,COD,bf and qm,anx,COD,bf are computed using eqs 19 and 21, respectively.

The value of qm,NH4N2Nitr,bf is computed using eq 4 or 6.

Equations 4, 6, 19, and 21 are similar to Monod equations. The Monod expression takes into account the change in biofilm flux for SCODbio and

NH4N as a result of external substrate concentrations and the associated changes in the biofilm thickness and fraction of nitrifiers.

Figure 3—COD uptake rates for biofilm in IFAS and MBBR systems (DO 5 dissolved oxygen).

Sen and Randall

May 2008 447

NOxN. The current version treats all of the NOxN as NO3N and

nitrification kinetics as the kinetics of ammonia-oxidizing bacteria.

The code is structured to allow for future separation of the two forms.

The value for AS,anx is based on the ratio of maximum substrate

utilization rates for heterotrophs in the MLVSS under preanoxic and

aerobic conditions (qmHanx SS/qmHaer SS). The default value recom-

mended for the half-saturation constant for dissolved oxygen inhibi-

tion, KH,DO,i,bf, at 128C 5 2 mg/L dissolved oxygen (Table 1).

The default value of COD, KS,H,bf,anx, at 128C 5 48 mg/L COD,

which is the same recommended for aerobic conditions. Measure-

ments in the pilot units indicated that the actual value may be

slightly higher (Table 1, 56 mg/L). The default value half-saturation

constant of NOxN, KNOxN,bf, at 258C 5 1 mg/L NOxN.

As with the biofilm, the COD can be taken up anoxically and

aerobically by the suspended solids. The model allows for simul-

taneous aerobic and anoxic uptake of COD in a reactor. The user

has the option to modify the code and switch one form of uptake off

in each reactor.

Equations 22 and 23 calculate the aerobic (A1,S,n) and anoxic

(A2,S,n) uptake of COD by the suspended solids in reactor n, as

follows:

CODu;aer;ss A1;S;n ¼ qm;H;aer;SS

SO2n

KH;DO;SS þ SO2n

3SCODbio;n

KH;S;aer;SS þ SCODbio;n

3 Vnð1� BVFnÞð1� fNitrÞ Xn ð22Þ

CODuanx;ss A2;S;n ¼ qm;H;anx;SS

SNOxNn

KH;NOxN;SS þ SNOxNn

3SCODbio;n

KH;S;anx;SS þ SCODbio;n

KH;DO;i;SS

KH;DO;i;SS þ SO2n

3 Vnð1� BVFnÞð1� fNitrÞXn ð23Þ

Where

qm,H,aer,SS and qm,H,anx,SS 5 maximum COD uptake rates for

heterotrophs in the MLVSS at tem-

perature T (mg COD/mg VSS/d);

KH,DO,SS and KH,S,aer,SS 5 half-saturation constants for dis-

solved oxygen and COD for the

heterotrophs in the MLVSS during

aerobic uptake of COD at temper-

ature T;

KH,NOxN,SS and KH,S,anx,SS 5 half-saturation constants for NOxN

and COD for the heterotrophs in

the MLVSS during anoxic uptake

of COD at temperature T; and

KH,DO,i,SS 5 half-inhibition constant for denitri-

fication, expressed as mg/L dis-

solved oxygen.

The value for qm,H,aer,SS measured at 128C was 8.72 mg COD taken

up per milligram heterotrophic VSS per day (Table 1). This is in

agreement with the value 12.8 per day at 258C and a temperature

adjustment coefficient of 1.03 (Barker and Dold, 1997; Randall

et al., 1992; Wentzel et al., 1991). The values of h for heterotrophs

in the literature vary from less than 1.03 to 1.07 (Marais and Ekama,

1976; Wentzel et al., 1991).

The value of KH,S,aer,SS measured in pilot studies was 48 mg/L

(Table 1). This agrees with the KH,S,aer,SS value of 70 mg/L COD at

258C observed by McClintock et al. (1988) and a temperature

adjustment coefficient of 1.03. The default value of KH,DO,SS 5 1

mg/L dissolved oxygen at 258C.

The value for qm,H,anx,SS measured at 128C was 5.71 mg COD

taken up per milligram heterotrophic VSS (Table 1). This is for

biomass that grows using a primary effluent with 25 to 33% of the

COD available as soluble biodegradable COD. A separate value of

qm,H,anx,SS should be determined for post-anoxic cells with supple-

mental carbon. This value may be lower when using methanol as a

substrate (Dold et al., 2007).

The value of KH,S,anx,SS measured under anoxic conditions at

128C was 56 mg/L (Table 1). This is slightly higher than the value

of 48 mg/L under aerobic conditions. As a default, one may use the

same value for modeling anoxic and aerobic zones.

The default values of KH,NO3N,SS and KH,DO,i,SS are from the

literature (Table 1). The value of KH,NO3N,SS 5 1 mg/L NO3N, and

the value of KH,DO,i,SS 5 0.25 mg/L dissolved oxygen.

The soluble biodegradable COD (SCODbio) concentration (mg/L)

in each aerobic cell n is calculated using a mass balance approach

similar to eq 8. The units of the terms in eq 24 are in kg/d.

In;S þ Sdecay;n þ Shydr;n

¼ A1;S;n þ A2;S;n þ B1;S;n þ B2;S;n þ En;S ð24Þ

Where

In,S and En,s 5 influent and effluent kg/d of SCODbio for cell n,

and

Sdecay,n 5 COD released through the decay of MLVSS (kg/d).

A corresponding term for COD release through decay of the biofilm

was not included, because the COD flux in eqs 19 and 21 are net of

decay. The COD flux in the biofilm diffusional model (Sen and

Randall, 2008a) is also net of decay.

Sdecay;nðkg=dÞ ¼ ðfCODÞ ðkdH;aerT MLVSS VnÞ ð1� BVFnÞ ð25Þ

Where

fCOD 5 COD content of biomass (with a default value of 1.42 mg

COD/mg VSS), and

Shydr,n 5 amount of unassimilated particulate COD converted to

SCODbio in cell n (kg/d).

The structure of the equations for hydrolysis is similar to eqs 13

to 16.

The half-saturation constant (KS,EA,hydr,SS and KS,EA,hydr,SS) is

10 mg/L of particulate COD for EA 5 aerobic, anoxic, or anaerobic

conditions.

The values of maximum hydrolysis rates for particulate COD by

biomass in MLVSS and biofilm are presented in Table 1. As in the

case of nitrogen, these were derived by analyzing the substrate

profiles in the pilot-scale units and refined based on the predictions

in full-scale MBBRs operated at low temperatures (less than 108C).Biomass Production. The amount of heterotrophs and nitri-

fiers generated as a result of COD removal and nitrification is

computed for the MLSS and biofilm. This computation is performed

for each cell n. The sum total for all n cells is the total biomass

production.

The user has to specify an MLSS MCRT for the computation. The

model uses information on the plant configuration, such as anaerobic,

Sen and Randall

448 Water Environment Research, Volume 80, Number 5

anoxic, aerobic, and post-anoxic volume fractions, and step-feed,

Modified Ludzack Ettinger (MLE), University of Capetown (UCT),

or anaerobic-anoxic-oxic (A2O) configuration. Each configuration

results in different amounts of MLSS in each cell or different

fractions of MLSS MCRT under aerobic, anoxic, and anaerobic

conditions. Additionally, the user specifies the biomass yield for

heterotrophs and nitrifiers in the biofilm or an equivalent biofilm

MCRT. This was discussed in the Model Development section.

Mixed Liquor Volatile Suspended Solids. The biomass yield for

heterotrophs (kg/d) in the MLVSS is computed in four steps, as

follows:

(1) The first step computes the yield in cell n, as follows:

Heterotrophic biomass yield by MLVSS in cell n is computed

in eq 26.

AXHy;n ¼ ðCODu;aer;SS;nÞ ðYHaerÞ þ ðCODu;anx;SS;nÞ ðYHanxÞ ð26Þ

The CODu,aer,SS,n and CODu,anx,SS,n are computed in eqs 22

and 23.

(2) The second step computes the decay of MLVSS biomass in

reactor cell n in kilograms per day. As discussed earlier for eq

11, the decay rate, kdH,EA,n, in cell n, is a function of dissolved

oxygen and NOxN in the cell.

Biomass decay for heterotrophs in cell n, is as follows:

An;XHd ¼ �ðkdH;EA;nÞðMLVSSÞð1� fnitrÞðVnÞð1� BVFÞ ð27Þ

The overall heterotrophic biomass production in reactor cell n is

the sum of biomass yield and decay, as computed in eqs 26 and

27. The value of fnitr is computed iteratively by running through

the entire set of equations (1 to 47). The model runs a maximum

of 100 iterations (which can be changed by the user) or until the

values converge to within 1%.

(3) The nitrifier yield is computed in the third step using an equation

that is similar to eq 26 for heterotrophs, as follows:

Nitrifier biomass yield by MLVSS in cell n;

An;XNy ¼ ðNH4Nu;SS;nÞðYN1Þ þ ðNO2Nu;SS;nÞðYN2Þ ð28Þ

The first term on the right side is for Nitrosomonas biomass

yield 5 (NH4Nu,SS,n) (YN1). The second term on the right side is

for Nitrobacter biomass yield 5 (NO2Nu,SS,n)(YN2).

(4) The nitrifier decay is computed in the fourth step by eqs 29,

30, and 31. Equations 29 and 30 are similar to eq 27 for

heterotrophs.

Biomass decay for Nitrosomonas ðN1Þ in cell n;

An;XN1d ¼ �ðkdN1;EA;nÞ ðfnitr1Þ ðMLVSSÞ3ðVnÞð1� BVFÞ ð29Þ

Biomass decay for Nitrobacter ðN2Þ in cell n;

An;XN2d ¼ �ðkdN1;EA;nÞ ðfnitr2ÞðMLVSSÞ3ðVnÞð1� BVFÞ ð30Þ

An;XNd ¼ An;XN1d þ An;XN1d ð31Þ

Biofilm. The structure of the equation for the biofilm is similar

to that for MLVSS. The heterotrophic biomass generated by biofilm

in cell n, BXH,n is computed by eq 32, as follows:

Heterotrophic biomass generated by biofilm in cell n;

BXH;n ¼ ½CODu;bf;n�½YH;bf;n� ð32Þ

This biomass is the quantity sloughed off the biofilm and released

into the MLVSS. The COD used by the biofilm in reactor cell n is

computed by eqs 18 (CODu,bf,aer) and 20 (CODu,bf,anx). For the

semiempirical model, the biofilm yield in cell n, YH,bf,n (flux of

heterotroph out of the biofilm for each unit flux of COD into the

biofilm per day) must be specified as an external input. Its value

can be determined by running the biofilm diffusional model in

conjunction with the semiempirical model. Alternatively, it may be

based on measurements made during pilot studies, from a data table

included as part of the semiempirical model or on data from the

manufacturer. The data table is a table of yields observed at different

SCODbio and NH4N concentrations. It is based on the results of

several runs made with the biofilm diffusional model (Table 4).

For nitrifiers, the computations are similar to heterotrophs.

Equation 32 is modified for nitrifiers, as follows:

Nitrifier biomass generated by biofilm in cell n;

BXN;n ¼ ½NH4Nu;bf;n�½YN1;bf;n� þ ½NO2Nu;bf;n�½YN2;bf;n� ð33Þ

Where

BXN,n 5 amount of nitrifiers sloughed off the biofilm and

released into the mixed liquor (kg/d);

NH4Nu,bf,n 5 computed by eq 1;

Table 4—Reference table of suggested yields, YH,bf and YN1,bf (generated by running the biofilm diffusional model orfrom pilot studies).

Based on runs

of the biofilm 1D

model or from

experiments

Substrate conc. range

Biofilm yield based on mode of uptake

Anaerobic Anoxic Aerobic

Lower mg/L Upper mg/L mg VSS hetertroph/mg COD uptake mg VSS autotroph/NH4N uptake

SCODbio 20 200 0.25 0.35

5 19 0.2 0.25

1 4.9 0.18 0.22

0.1 0.99 0.16 0.2

NH4N range 5 20 0.05

1 4.9 0.045

0.1 0.9 0.04

Sen and Randall

May 2008 449

YN1,bf,n 5 Nitrosomonas flux (as VSS out of biofilm) per

unit flux of NH4N into the biofilm per day; and

YN1,bf,n 5 Nitrosomonas flux (as VSS out of biofilm) per

unit flux of NH4N into the biofilm per day.

In the current release of AQUIFAS, the nitrifier biomass generated

is based on a lumped yield of all nitrifying (ammonia-oxidizing and

nitrite-oxidizing) bacteria (AOB and NOB, respectively) (Tables 2

and 3), as follows:

Nitrifier biomass generated by biofilm in reactor cell n;

BXN;n ¼ ½NH4Nu;bf;n�½YNtotal;bf;n� ð34Þ

Where

YNtotal,bf,n 5 ammonia-oxidizing bacteria flux (as VSS out of

biofilm) per unit flux of NH4N into the biofilm per

day. The YNtotal,bf,n is twice the value of YN1,bf,n in

Table 4.

Unlike heterotrophs, the effect of the nitrifier decay rate within the

biofilm is incorporated to the biofilm yields (i.e., the biofilm yields

are the net of decay).Fraction of Nitrifiers. The fraction of nitrifiers in the MLVSS

is computed in the following three steps:

(1) The model computes the quantity of nitrifiers generated in the

MLVSS and the quantity of nitrifiers sloughed off the biofilm in

each cell.

(2) It determines the sum total of nitrifiers and heterotrophs

generated and lost through decay across n cells in the system.

This is the biomass production per day.

(3) It computes the fraction of nitrifiers based on eq 35.

The fnitr (fraction of nitrifiers) can be computed as follows:

fnitr ¼Xn

1

Nitrifier Biomass Yield and Decay for

MLVSS and Biofilm

� �

4Xn

1

Heterotroph and Nitrifier Biomass Yields

and Decay for MLVSS and Biofilm

!ð35Þ

Where

n 5 number of reactor cells in operation.

The biomass yield and decay are computed as shown in eqs 26 to 34.

As mentioned earlier, the value of fnitr calculated during each

iteration is fed back into the next model run.

It is important to understand that, unlike activated sludge systems

operating below the threshold (washout) MLSS MCRT, where the

fnitr can be close to zero because of washout of nitrifiers, the IFAS

(and MBBR) system can have a significant fnitr, even when the

MLSS MCRTs are below the washout MCRT of single-cell acti-

vated sludge systems. This is because of biofilm nitrification and

nitrifiers sloughed off the biofilm. These nitrifiers become part of

the MLVSS, until it is wasted from the system or released in the

effluent.

Second, it is important to appreciate how the fnitr plays slightly

different roles in IFAS and MBBR systems. In IFAS, the nitrifier

population in the MLVSS can make a significant contribution to the

overall nitrification, even when operated well below the washout

MLSS MCRT. However, in the MBBR, which has a very low

MLVSS and the MLSS MCRT 5 nominal HRT of the liquid,

the MLVSS does not maintain a significant population of nitrifiers.

It is for this reason that IFAS systems show a lower activated sludge

tank volume requirement compared with MBBRs when designed

with the same biofilm surface area. However, IFAS systems need

sludge volume index control and, possibly, higher clarifier surface

areas.Denitrification. The NOxN denitrified by the biofilm (NOx-

Nu,anx,bf,n 5 BNOxN,u,n) and the MLVSS (NOxNu,anx,SS,n 5

ANOxN,u,n) are computed as follows:

NOxNu;anx;bf;n;BNOxN;u;n ¼CODu;anx;bf;n

DN COD Factorð36Þ

NOxNu;anx;bf;n;ANOxN;u;n ¼CODu;anx;SS;n

DN COD Factorð37Þ

The CODu,anx,bf,n (B2,S,n) and CODu,anx,SS,n (A2,S,n) are computed

as per eqs 20 and 23, respectively. As mentioned earlier,

CODu,anx,bf,n and CODu,anx,SS,n can each be split into two terms

to separately compute COD used for denitrification of NO2N and

NO3N. The denitrification COD factor (DN COD factor) is used to

determine the oxidized nitrogen uptake based on the anoxic COD

uptake. The DN COD factor is computed from the stoichiometry

of denitrification, yield, and COD content of biomass (fCOD), as

follows:

DN COD factor NO3N ¼ 2:86=ð1� Yh;anx 3 fCODÞ ð38Þ

DN COD factor NO2N ¼ 1:71=ð1� Yh;anx 3 fCODÞ ð39Þ

As mentioned earlier, the default value of fCOD 5 1.42 mg COD/mg

VSS.

In the current version of the model, it is assumed that all of the

NO2N is oxidized to NO3N. The denitrification that takes place is

denitrification of NO3N.

The NOxN generated by the nitrifiers in the biofilm and MLVSS

are computed as follows:

NOxN generated; BNOxN�Nitr;n ¼ BN;n � fN BXN;n ð40Þ

NOxN generated; ANOxN�Nitr;n ¼ AN;n � fN AXN;n ð41Þ

The variables BN,n and AN,n are the NH4N uptake rates in the biofilm

and MLVSS and are computed by eqs 1 and 7, respectively. The

nitrifier biomass yield for the biofilm (BXN,n) is computed by eq 34.

The interrelationship of the kinetic expressions for NOxN are

represented in a matrix format in Tables 2 and 3.

The effluent NOxN (ENOxN,n) load from reactor n (kg/d) is

determined based on the influent NOxN load (INOxN,n), nitrification,

and denitrification in the MLVSS and biofilm, as follows:

INOxN;n þ BNOxN�Nitr;n þ ANOxN�Nitr;n

¼ ANOxN;u;n þ BNOxN;u;n þ ENOxN;n ð42Þ

Oxygen. The equations for oxygen requirement for the biofilm

(BDO,n) and the MLVSS (ADO,n) are computed as follows:

BDO;n ¼ B1;S;n þ B2;S;n � fCOD BXH;n

þ 4:57 BNOxN�Nitr;n � 2:86 BNOxN;u;n ð43Þ

ADO;n ¼ A1;S;n þ A1;S;n � fCOD AXH;n

þ 4:57ANOxN�Nitr;n � 2:86 ANOxN;u;n ð44Þ

Sen and Randall

450 Water Environment Research, Volume 80, Number 5

A mass balance is conducted to determine the oxygen required (kg/

d) in cell n, as follows:

IDO;n þ DDO;n þ TDO;n ¼ ADO;n þ BDO;n þ EDO;n ð45Þ

Where, for cell n,

DDO,n 5 dissolved oxygen diffusing in from the

atmosphere that is not associated with an

aeration device (kg/d);

TDO,n 5 dissolved oxygen supplied (transferred) by

the aeration device, if present (kg/d); and

IDO,n and EDO,n 5 dissolved oxygen loadings in the influent and

effluent (kg/d).

The values of DDO,n are input by the user. One way to determine

DDO,n is to run the model and determine the value that results in

a computed dissolved oxygen in the unaerated cell that is equal to

the measured dissolved oxygen level.

For each unaerated cell, the model checks the mass balance in eq

45, based on an initial estimate of dissolved oxygen that is specified

by the user. If the oxygen supplied is not within a certain percentage

of the uptake (default 5 20%), the model guides the user to change

the estimated dissolved oxygen level until the supply and uptake are

within 20%. For example, if the oxygen supplied is more than 20%

higher than the uptake, the user is asked to raise the estimate of

dissolved oxygen. The model is rerun for the new estimate.

For the aerated cells, the model computes the amount of dis-

solved oxygen that needs to be transferred, Tn,DO, to achieve the

dissolved oxygen set point. The model checks the value of Tn,DO

against the capacity of the aeration system in cell n. If the value is

exceeded, the model guides the user to lower the setpoint or raise

the capacity.Storage in Reactor Cell in Dynamic Simulation Mode. For

dynamic simulation, an additional term for storage between the

current time step t and time step t21 needs to be incorporated to the

mass-balance equations. Storage is important if the duration of

the time step of dynamic simulation is less than the actual HRT of

the cell. Therefore, storage can have a significant effect in long HRT

systems, such as oxidation ditches and lagoons. On the other hand,

when the time step is greater than 3 times the actual HRT of the cell,

the time step is too long for the effect of storage to linger on. The

effluent would have reached an equilibrium with the new flow and

load well before the time step ends. The model uses an algorithm to

account for the relationship between actual HRT and duration of the

time step.

When the duration of the time step is less than one-half the actual

HRT of cell n, the effect of storage modifies the NH4N computation

in eq 8, as follows:

In þ Ndecay;n þ Norg�N;hydr;n ¼ An þ Bn þ Cn þ En þ Sn;t ð46Þ

The units of the eq 46 are kg/time step. For example, if the time step

is 1 hour, the units are kg/h. As the time step increases above the

actual HRT of cell n, the effect of storage drops gradually, to 0.

The variable Sn,t is the storage of ammonium-nitrogen that takes

place in cell n because of the change in effluent ammonium

concentration at the current time step t (En,t ) and the previous time

step t21 (En,t21). Its value, in kilograms, is calculated as follows:

Sn;t ¼ ðEn;t � En;t�1ÞðVnÞð1� BVFÞ ð47Þ

The units for concentration, En,t in eq 47 are kg/m3.

Model Analysis and VerificationSen and Randall (2008b) discuss the results from steady-state and

dynamic simulation with the model. The model was verified in

steady-state against the results observed from the pilot studies. The

model was also evaluated in a full-scale application, by running it

with several 31-day periods of daily data from the IFAS plant in

Broomfield, Colorado (Sen, Phillips, Murthy, Pattarkine, Copithorn,

Randall, Schwinn, and Banerjee, 2007). The model’s predictions of

MLVSS and MLSS in the reactor; effluent quality (SCOD, nitrogen

forms, and phosphorus); day-to-day variation in nitrogen forms;

biofilm thickness; and amount of growth on the media in the two

IFAS cells in series were similar to those observed at the plant.

Summary

(1) A computational model has been developed for IFAS and

MBBR systems. The model is structured to operate with up to

12 reactors (cells) in series. Each cell can be configured to

operate anaerobically, anoxically, aerobically, or post-anoxically

with its own amount of biofilm support media. In the absence

of media, the model operates as an activated sludge system.

(2) In the semiempirical model, the biofilm fluxes are computed by

a semiempirical method that uses equations that are based on

the performance of media, as measured in pilot studies.

(3) The structure of the semiempirical equations for the biofilm

incorporates an additional Monod expression beyond what is

used in activated sludge models. This expression simulates the

changes in biofilm flux rates, as a result of changes in the COD

and ammonium-nitrogen concentrations in the bulk liquid, and

the associated changes in biofilm thickness and fraction of

nitrifiers in the biofilm that develops along the length of

a multicell reactor.

CreditsThe authors acknowledge the contributions of the staff and

faculty of the Environmental Engineering Program of Virginia Tech

located at both Blacksburg and Northern Virginia, specifically that

of Thomas J. Grizzard; support from Greg Farren, Jim Welch, and

Mike Bonk of the Anne Arundel County, Maryland, Department of

Public Works operations staff; and assistance from Rip Copithorn of

Stearns & Wheler, LLC (Bowie, Maryland). The U.S. Environ-

mental Protection Agency Chesapeake Bay Program (Annapolis,

Maryland), Maryland Department of the Environment, and Anne

Arundel County (Maryland) funded the pilot studies, which initiated

the model development. The Water Environment Research

Foundation (Alexandria, Virginia) funded some of the collaboration

with full-scale facilities.

Submitted for publication February 6, 2007; revised manuscriptsubmitted December 18, 2007; accepted for publication January 8,2008.

The deadline to submit Discussions of this paper is August 15,2008.

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