Sötemann, S.W. et al - eWISA

INTEGRATED BIOLOGICAL, CHEMICAL AND PHYSICAL
PROCESSES KINETIC MODELLING PART 1: ANOXIC AND
AEROBIC PROCESSES OF CARBON AND NITROGEN
REMOVAL IN THE ACTIVATED SLUDGE SYSTEM
S.W. Sötemann*, E.V. Musvoto, M.C. Wentzel and G.A. Ekama
Water Research Group, Department of Civil Engineering, University of Cape Town, Rondebosch, 7701,
Cape Town, South Africa. *E-mail: ssotema@eng.uct.ac.za
ABSTRACT
The biological kinetic Activated Sludge Model No. 1 (ASM#1, Henze et al., 1987; Dold et al., 1991)
for carbon (C) and nitrogen (N) removal is integrated with the mixed weak acid/base model of
Musvoto et al. (1997, 2000a,b,c) to extend application of ASM#1 to situations where an estimate for
pH is important. Because chemical precipitation is generally not significant when treating municipal
wastewaters, only gas and liquid phase processes were considered for this integrated model. The
biological processes in ASM#1 were modified to take into account the effect of the interaction of the
weak acid/base species of the ammonia, carbonate, phosphate and short chain fatty acid systems
and pH on heterotrophic and autotrophic organism behaviour, which includes generation and
utilization CO2 in metabolism, use of specific weak acid/base species for organism growth and
generation and utilization of H + . With these modifications, simulations with the model were compared
with those of ASM#1 (Dold et al., 1991) and experimental data in the literature; a good correlation
was obtained. However, these comparisons are only a preliminary validation, because, despite their
inclusion, the weak acid/bases and pH do not have a significant effect on the biological processes in
the cases considered (i.e. well buffered wastewater). The performance of a ND activated sludge
system with low influent alkalinity is evaluated.
INTRODUCTION
A number of mathematical models describing the biological processes of carbon (C), nitrogen (N)
and phosphorus (P) removal by the activated sludge system have been developed, e.g. the C and
N removal models of van Haandel et al. (1981) and Activated Sludge Model No.1 (ASM#1, Henze
et al., 1987), and the C, N and P removal models of Wentzel et al. (1992), and ASM#2 (Henze et al.,
1995). These models are commonly used in research, design, operation and system development
and can be coded into computer shell packages such as ASIM (Gujer, 1998) and Aquasim (Reichert,
1998) and various versions of them are commercially available such as Biowin (Envirosim and
Associates,1998) and GPX (Hydromantis).
In all these models, it is assumed that the biological processes operate in a liquid phase of constant
pH, i.e. that there is sufficient buffer capacity in the liquid phase to absorb or supply the protons (H + )
and CO2 required or generated by the biological processes without a change in pH. For most
applications with municipal wastewater, where the concentrations of C, N and P are low, this is a
reasonable assumption. In fact, in some models, the parameter Alkalinity is included to check that
this condition remains true (e.g. ASM#1, Henze et al., 1987; UCTOLD and IAWPRC, Dold et al.,
1991). However, in the treatment of a number of wastewaters this assumption is not valid, e.g. in the
nitrification of wastewaters with low buffer capacity and/or high nitrogen (N) concentrations, or in the
treatment of wastewaters where the generation or utilisation of short-chain fatty acids (SCFA) is
significant.
In this paper, the biological processes of C and N removal are integrated into the three phase mixed
weak acid/base physical-chemical kinetic model developed by Musvoto et al. (1997, 2000a,b,c). This
chemical-physical model includes kinetic descriptions for (i) the ionic equilibrium reactions of the
Proceedings of the 2004 Water Institute of Southern Africa (WISA) Biennial Conference 2 –6 May 2004
ISBN: 1-920-01728-3 Cape Town, South Africa
Produced by: Document Transformation Technologies Organised by Event Dynamics

important weak acid/base systems that govern pH in wastewater treatment systems, i.e. the
ammonia, carbonate (inorganic carbon), short chain fatty acid (SCFA) and phosphate systems, (ii)
CO2 and NH3 gas exchange between liquid and gas, (iii) ion pairing and (iv) precipitation of common
minerals associated with Calcium (Ca), Magnesium (Mg), carbonate and phosphate system species.
Because in the activated sludge system, mineral precipitation is usually not significant, only parts (i)
to (ii) of the model, i.e. the liquid and gas phase processes, will be considered. Furthermore,
because of the complex interaction between pH and biological excess P removal (BEPR), only the
biological processes of C and N removal are included into the integrated model at this stage. In
subsequent papers, the biological processes of anaerobic digestion will be included into the model,
and because in this system mineral precipitation is important, all four parts of the physical-chemical
model will be considered (Sötemann et al., In Prep.).
MODEL DEVELOPMENT
Central to the mixed weak acid base chemical model of Musvoto et al. (1997, 2000a,b,c) is that the
hydrogen ion (H + ) is included explicitly as a compound. Integrating the biological processes of C and
N removal of ASM#1 into this chemical model will require a number of interactions between the
chemical and biological processes to be defined, e.g. (i) the influence of the biological processes on
the weak acid/base systems species and H + concentrations, such as production and/or utilization of
H + , CO2, N2, ammonia and phosphate in the growth and death (endogenous respiration) processes,
and (ii) the effect of pH on the biological process rates where these are expected to be significant
such as the autotrophic nitrifier organism (ANO) maximum specific growth rates.
The mixed weak acid base kinetic model of Musvoto et al. (1997) comprises (their Table 1):
• The liquid phase forward and reverse dissociation chemical processes of the ammonia,
carbonate, phosphate and SCFA system species, i.e. processes 1-6 and 9-18 involving
compounds 1-5 and 7-14.
• The gas and solid phase physical processes of the carbonate system, i.e. CO2 gas exchange
(dissolution and expulsion) and CaCO3 precipitation, i.e. processes 7, 8 and 19 respectively.
• Keeping the same numbering of processes and compounds, Musvoto et al. (2000a) extended
this model to include (their Tables 1b and 3):
• Ion pairing of Ca and Mg with hydroxide and the species of the carbonate and phosphate
systems; this added 22 processes, i.e. the liquid phase forward and reverse dissociation
chemical processes of the 11 ion pairs (processes 20-41) and 12 compounds, i.e. Mg and 11 ion
pair species (compounds 16-27) respectively (their Table 1b.)
The gas and solid phase processes of ammonia, carbonate and phosphate systems, i.e. ammonia
gas stripping and mineral precipitation of four additional minerals associated with Ca and Mg and
species of the ammonia, carbonate and phosphate systems, i.e. struvite (MgNH4PO4), newberyite
(MgHPO4), amorphous calcium phosphate [ACP, Ca3(PO4)2] and MgCO3; this added 5 additional
processes i.e. 42 to 46 but no new compounds (see their Table 3).
Before incorporating the biological processes of ASM#1 into the weak acid/base chemical physical
(CP) model of Musvoto et al. (1997,2000a), all the processes and compounds were categorised into
chemical, physical and biological groups and subgroups. This was done for ease of discussion of the
assembly of a particular integrated chemical – physical – biological (CPB) processes model, be it
aerobic or anaerobic. For easy cross reference to the source chemical physical and biological
models, the numbers of the processes and compounds were not changed from those in the source
models.
The following general groups and subgroups of processes and compounds were adopted:
• The chemical processes, which comprise those of equilibrium (forward and reverse dissociation)
and ion pairing. These are processes 1-41 in the Musvoto et al. (2000a) CP source model, but
exclude the physical processes 7, 8 and 19. These processes have the same numbers as in the
source model, but the prefix C is added, i.e. C1-C41. The 27 compounds associated with these
chemical processes are also numbered identically as in the source model but have the prefix C
added, i.e. compounds C1-C5 and C7-C14 involved in the equilibrium (CE) processes and

compounds C4, C5, C8, C10-c12 and C15-C27 involved in the ion pairing processes. The only
compound that does not belong to this group is the CO2 gas (C6). CO2 is included with the
compounds associated with the physical processes and so is also labelled P1.
• The physical processes, which comprise those of mineral precipitation (PMP) and gas exchange
(PGE). The five mineral precipitation processes 19 and 42 to 45 in the Musvoto et al. (2000a) CP
source model are renumbered processes P1 to P5. These processes involve only existing
compounds in the model (viz. C1, C5, C11, C12, C15 and C16) and so add no new compounds.
The CO2 exchange and ammonia stripping are processes 7, 8 and 46 respectively and these are
numbered P6-P8. Gaseous ammonia is omitted because the gas phase is accepted to contain
zero ammonia (infinite sink). Added to the PGE processes of the source model to form the
integrated CPB model are the gas exchange processes (dissolution and expulsion) of oxygen
and nitrogen gasses required for the ND activated sludge system and these were numbered
P9-P12. The compounds associated with these additional PGE processes are dissolved and
gaseous compounds of ammonia, oxygen and nitrogen. Dissolved oxygen is a compound of the
biological processes part of the model (see below, B8) so only three compounds need to be
added for the CBP AS model, i.e. gaseous oxygen (P1) and dissolved and gaseous nitrogen (P2
and P3).
• The biological processes, which comprise the biological C and N removal process of ASM#1.
Also for these biological processes and compounds the same numbering of ASM#1 was retained,
except the prefix B was added to each, i.e. processes B1 to B8 and compounds B1 to B13.
However, two biological processes are added, viz. aerobic and anoxic growth of heterotrophs
(OHOs) with nitrate as N source and these were numbered B1b and B2b. Of the 13 compounds
in ASM#1, two become redundant in an integrated CPB model – (i) the free and saline ammonia
(FSA, B10) because NH3 and NH4 + are in the chemical compounds group and (ii) the Alkalinity
(B13), which is now obsolete. Apart from the ammonium (C1), three other compounds in the
source CP model are also involved with the biological processes, i.e. H2CO3* (C3) through CO2
generation or uptake, H + (C7) through ammonification, nitrification and denitrification and HPO4 2-
through uptake for OHO growth.
Following the grouping and numbering system above, the integrated two phase (liquid/gas) CPB AS
model was assembled as follows:
• The CE processes (C1-C6 and C9-C18) with associated compounds C1-C5 and C7-C14 (Table
1 of Musvoto et al., 1997, not repeated here).
• The biological processes of C and N removal (B1 to B8) including aerobic and anoxic OHO
growth on ammonium (processes B1a and B2a) and nitrate (processes B1b and B2b) with their
associated compounds NH4 + (C1), H2CO3* (C3), H + (C7), HPO4 2- (C11) and the remaining 11
biological system compounds (B1-B9, B11-B12).
• The PGE processes of carbon dioxide (P6/C7and P7/C8), oxygen (P9 and P10) and nitrogen
(P11 and P12) and ammonia stripping (C46/P8) with associated compounds dissolved and
gaseous carbon dioxide (C3 and C6), oxygen (B8 and P1) and nitrogen (P2 and P3) and
dissolved ammonia (C2). A gaseous ammonia compound is not included because in the pH
range 5-8.5 little ammonia is stripped into the gas phase.
Not included in integrated chemical-physical-biological activated sludge system model are (i) the
chemical ion pairing processes (C20-C41) because this was not considered important for activated
sludge systems treating municipal wastewater (TDS < 1000 mg/l) and (ii) the physical mineral
precipitation processes (C19, C42-C45 or P1-P5) because only the gas and liquid phases are
considered in this first integrated AS model.
For brevity, only the biological and PGE processes parts of the integrated CBP AS model with their
associative compounds are shown in Tables 1 and 2. Because the chemical and physical parts of the
model have units mol/l, these were changed to reflect the usual units in biological models, viz. gC/m 3 ,
gN/m 3 and gP/m 3 . Hence, when the H + interacts with the C, N or P species, it was divided by the
molar mass of C, N and P respectively. Also, the kinetic rate equations for the biological processes
were modified to take into account the effect of H + where this effect is significant. This was done in
two ways: (i) Where there is a direct influence of pH on the biological process rate, pH was included
in the kinetic rate formulation, and (ii) the kinetic rates of the biological processes were reformulated

to utilize specific species of the weak acid/base systems - stoichiometric coefficients were added and
existing ones modified to take this into account.
The modifications set out above were developed for the two organism groups included in ASM#1, i.e.
ordinary heterotrophic (OHOs) and autotrophic nitrifier (ANOs) organisms. For both groups,
information in the literature on their behaviour was used for the modifications and these are reviewed
briefly below. A review of bioenergetics and activated sludge model development is not given since
these topics are already covered in the literature (e.g. McCarty, 1964, 1972; Dold et al., 1981; van
Haandel et al., 1981; Henze et al., 1987; Cloete and Muyima, 1995, Ohron et al., 1996, Sperandio
et al., 1999). Only aspects relevant to the integration are discussed to clarify the additions and
changes to the stoichiometric coefficients and kinetic rates listed in Tables 1 and 2.
MODIFICATIONS TO THE IWA ACTIVATED SLUDGE MODEL NO. 1 (ASM#1)
Ordinary Heterotrophic Organisms (OHOs)
The processes that involve the OHOs in ASM#1 (Table 1) are growth (B1 and B2), death (B4),
hydrolysis of enmeshed particulate biodegradable organics (B7) and associated particulate
biodegradable organic nitrogen (B8) and ammonification of soluble biodegradable organic nitrogen
(B6). The growth of OHOs is described by four processes, two under aerobic conditions using either
ammonia or nitrate as N source, and two under anoxic conditions, also using either ammonia or
nitrate as N source. These processes were modified to include (i) production of CO2 in metabolism,
(ii) uptake or release of specific weak acid/base N and P species for growth and death and (iii)
utilization or production of H+.
OHO Metabolism
The bioenergetics of OHO growth is quantified in terms of the lumped electron donating capacity
parameter COD because in wastewater treatment, the different kinds organics involved in the growth
processes are not known. This is possible because the free energy released per electron (e - )
transferred in the breakdown of different types of organics varies in the narrow range 105 to 121 kJ/e -
eq. The integrated model requires a carbon balance to be made over the activated sludge system.
Hence the mass of CO2 generated in the growth process needs to be known, which requires
COD/TOC ratio of the wastewater organics to be known. For the range of different organics listed in
Table 2, the COD/TOC ratio was calculated and varies between 2.67 and 4.0. Because most of the
organics wastewater are of carbohydrate type with a relatively small proportion of organics with high
COD/TOC ratios, an average COD/TOC ratio would seem to be around 3.0. Because CO2 is
generated only in catabolism, the CO2 generation is proportional to the oxygen utilized, i.e.
where
YZH
O2 utilised in producing 1 gCOD/m 3 OHO = (1-YZH)/YZH [1a]
= yield coefficient (mg COD/mg COD)
Hence the CO2 generated in producing 1 gOHOCOD/m 3
= O2 utilised/(COD/TOC ratio) = (1-YZH)/(3.0 YZH) [1b]

Table 1. Matrix representation of the biological processes of ASM#1, including anoxic and aerobic growth of OHOs on nitrate (processes B1b and B2b), combined with
the mixed weak acid base chemical-physical model of Musvoto et al. (2000a) to yield the two phase (liquid-gas) integrated chemical-physical-biological (CPB) model for
C and N removal in the activated sludge system (see Table 2 for physical processes).
No
B1a
B1b
B2a
B2b
B3
No
Compound→
Process↓
Aerobic growth of ZBH
with NH4 +
Aerobic growth of ZBH
with NO3 -
Anoxic growth of ZBH
with NH4 +
Anoxic growth of ZBH
with NO3 -
Aerobic growth of ZBA
B1
SI
B2
Sbs
-1/YZH
-1/YZH
-1/YZH
-1/YZH
B3
XI
B4
Senm
B5
ZBH
1
1
1
1
B6
ZBA
1
B7
ZE
B8
O
dissolved
-(1-YZH)
/YZH
-(1-YZH)
/YZH
B9
NO3 -
-fZB,N
C1/B10
NH4 +
-fZB,N
-(1-YZH)
/(2.86YZH) -fZB,N
B*
-(4.57-YZA
)
/YZA 1/YZA
-(1/YZA)
-fZB,N
B11
Nobs
B12
Nobp
B13
SALK
C3
H2CO3 *
(1-YZH)
/(3YZH)
(1-YZH)
/(3YZH)
(1-YZH)
/(3YZH)
(1-YZH)
/(3YZH)
-3/8
C7
H +
fZB,N/14-2f
ZB,P/31
C11
HPO4 2-
-fZB,P
-fZB,N/14-2f
ZB,P/31 -fZB,P
A*
C*
fZB,N /14+
1/(7YZA)
-fZB,P
-fZB,P
P2
N2
dissolved
D*
D*
Rate
⎡H
Air⎤
+
⎡ Sbs
⎤ ⎡NH4
µ
⎢ ⎥
H ⎢
⎢
KSH
+
⎥
⎣ S
⎢ ⎥
bs⎦
limit
⎢ On ⎥
⎣
⎣ ⎦
⎡H
Air⎤
⎡ Sbs
⎤ ⎡1-
NH
µ
⎢ ⎥
H ⎢
⎢
KSH
+
⎥
⎣ S
⎢ ⎥
bs⎦
lim
⎢ On ⎥
⎣
⎣ ⎦
µ
µ
µ
H
H
A
⎡H
Air⎤
+
⎡ Sbs
⎤ ⎢ ⎥ ⎡NH4
⎢
⎢
KSH
+
⎥
⎣ S
⎢ ⎥
bs⎦
limit
⎢ Off ⎥
⎣
⎣ ⎦
⎡H
Air⎤
⎡ Sbs
⎤ ⎢ ⎥ ⎡1-
NH
⎢
⎢
KSH
+
⎥
⎣ S
⎢ ⎥
bs⎦
lim
⎢ Off ⎥
⎣
⎣ ⎦
⎡A
Air⎤
+ ⎡ NH4
⎤ ⎢ ⎥
⎢
+ Z
KSA
+
⎥
⎣ NH
⎢ ⎥
4 ⎦
⎢⎣
On ⎥⎦
BA

No
No
Compound→
Process↓
B1
SI
B2
Sbs
B3
XI
B4
Senm
B5
ZBH
B6
ZBA
B7
ZE
B8
O
dissolved
B4 Death of ZBH 1-fE -1 fE fZB,N-fEfZE,N 2(fZB,P-fEfZ
E,P)/31
B5
B6
B7
B8
Death of ZBA
Ammpnification of Nobs
Hydrolysis of Senm
Hydrolysis of Nobp
Units
1
1-fE
-1
gCOD/
m 3
gCOD
/m 3
gCOD/
m 3
gCOD
/m 3
gCOD
/m 3
gCOD
/m 3
gCOD
/m 3
gCOD
/m 3
-1
fE
B9
NO3 -
gN/m 3
C1/B10
NH4 +
1
gN/m 3
B11
Nobs
-1
1
B12
Nobp
fZB,N-fEfZE,N
-1
gN/m 3
gN/m 3
B13
SALK
C3
H2CO3 *
* 1-
YZH
f ZB, N f ZB, P
A = -
+ -2*
14*
2.86Y
ZH 14 31
* 1-
YZH
B = - + f ZB, N
2.86Y
ZH
* 1-
YZH
f ZB,
C = -
-
14*
2.86Y
ZH 14
⎛ ⎡H
Air⎤
⎞
* 1-
=
YZH
H Air
* ⎡ ( Senm
/ ZBH)
⎤ ⎜
NO
D
=
⎢ ⎥ ⎡ ⎤ ⎡ 3⎤
⎟
E KH
+ S
ZBH
2.86
⎢
⎜
⎟
YZH
KX
+ ( Senm
/ ZBH)
⎥ ⎢ ⎥
η ⎢
⎜
Off
⎥ ⎢
limit
⎥
⎣
⎦
On
⎣ ⎦ ⎣ ⎦⎟
⎝
⎢⎣
⎥⎦
⎠
gC/m 3
C7
H +
-1/14
g/m 3
N
C11
HPO4 2-
fZB,P-fEfZE,P
gP/m 3
f
-2*
ZB, P
31
P2
N2
dissolved
gN/m 3
Rate
bH ZBH
bA ZBA
KR Nobs
ZBH
E *
. S
( N
/ S
*
E enm obp enm
Notes: (1) Compound B1-B13 numbered identically to ASM#1, except NH 4 + , which is C1 in Musvoto et al. (1997) and B10 in ASM#1. NH4 + in ASM#1 is actually the free (NH3) and saline
(NH 4 + ) ammonia (FSA), where here it is only the saline. Alkalinity (compound 13) is no longer required. Ammonium (C1), dissolved CO2 (C3) and nitrogen (P2), H + (C7) and
mono-hydrogen phosphate (C11) are included here because they are involved with the biological processes.
)

Table 2. Matrix representation of the physical gas exchange (PGE) processes incorporated in the integrated two-phase chemical-physical-biological (CPB) model for
C and N removal in the activated sludge system (see Table 1 for biological processes).
No
No
Compound→
Process↓
C7/P6 Dissolution of CO2
C8/P7 Expulsion CO2
P8
P9
P10
P11
Gas stripping of
CO2
Gas stripping of
NH3
Gas stripping of N2
Aeration -
dissolution of O2
Units
C2
C3
NH3
dissolved H2CO3*
-1
mol/l
+1
-1
-1
mol/l
C6 /P1
CO2
gas
-1
+1
+1
mol/l
B8
P2
O2 O2
dissolved gas
+1
mgO/l
-1
mol/l
P3
P4
N2 N2
dissolved gas
-1
mol/l
+1
mol/l
P5
NH3
gas
+1
mol/l
Rate
K’fCO2 [CO2gas]
K’rCO2 [H2CO3 * ]
( [ H2
CO3*]
- p 2 K
KLa-CO2 CO H-CO
( [ ] )
NH
KLa- NH3
3diss
( [ ] - p 2 )
KLa- N2
N2diss
KH-N
2
( [ ] - [ ] )
O
O
KLa- O2
2sat
2diss
N

The CO2 released during metabolism is in the dissolved form and therefore adds to the H2CO3 *
concentration (C3) in the bulk liquid. Hence the stoichiometric coefficient (1-YZH)/(3YZH) is added to
the compound H2CO3 * in the integrated CPB model matrix (see Table 3 below).
Table 3. COD/TOC ratio of some organic compounds.
Organic compound Formula COD/TOC Ratio
Carbohydrates
Sugars
1 Carboxylic acids
(SCFA and LCFA)
Primary amines
Amino acids
Alkanes
Alcohols
Cn(H2O)n
Cn(H2O)n-2
CH3(CH2)nCOOH
CH3 (CH2)n NH2
H(CH2)nC2H4O2N
H(CH2)nH
H(CH2)nOH
2.67
2.67
4(3n+2)/[3(n+1)]
= 3.33 for n=1;= 3.94 for n=20
4
4(n+1)/(n+2) < 4
4(3n+1)/3n ~ 4
4
1 Unsaturated fats have slightly lower COD/TOC ratio because for every double C bond (C=C), there are 2 Hs fewer.
The COD/TOC ratio accepted will not influence the mixed liquor pH. This is because in the
breakdown of the organics listed in Table 3, no net release of H + takes place. The CO2 generated
therefore is stripped from the bulk liquid (higher partial pressure than in the atmosphere) without a
pH change. In contrast, the proteins release their N content as NH3, which at pH between 6.5 and 8.0
will take up a H + to form NH4 + , a process called ammonification (B6). This increases the alkalinity of
the bulk liquid and at constant CO2 partial pressure (pCO2) will produce a pH increase. Therefore, it
is not the breakdown of organics the affects the pH, but the uptake of a H + by the NH3 released from
the breakdown of organic N (proteins). Hence, to predict the pH correctly, the COD/TOC ratio does
not need to be known accurately, but the organic N content of the wastewater does need to be known
accurately.
Under anoxic conditions, nitrate (NO3 - ) serves as terminal electron acceptor and the specific yield
coefficient (YZHanx) is decreased to ~80% of the aerobic value (YZHaer = 0.67). With nitrate as electron
acceptor approximately the same quantity of free energy from the organics is available to the
organism as when oxygen is the electron acceptor, but only 2 ATP moles are formed per pair of
electrons transferred to the nitrate (Payne, 1981) compared with 3 ATP moles per pair of electrons
with oxygen. Measurements by Orhon et al. (1996), Sperandio et al. (1999) and Muller et al. (2003)
confirm this reduction in yield experimentally with artificial and real domestic wastewaters. This
reduction in yield under anoxic conditions is not recognised in early activated sludge models like
UCTOLD (Dold et al., 1991), ASM#1 (Henze et al., 1987), UCTPHO (Wentzel et al., 1992) and ASM2
(Henze et al., 1995) but is accepted in later models like ASM2d, ASM3 (Henze et al., 1999, 2002)
and Biowin (Barker and Dold, 1997). This reduction also has been accepted in the model developed
here (i.e. YZHanx = 0.67*0.80 = 0.54), so that under anoxic conditions, 20% less CO2 is generated than
under aerobic conditions. The processes that influence the H2CO3 * concentration are listed in Table
4.
Use of Specific Weak Acid/Base Species For OHO Growth
The nitrogen required for OHO growth is obtained from either ammonia (Processes 1a and 2a) or, in
the absence of ammonia, nitrate (Processes 1b and 2b). Phosphorus is also incorporated in OHO
mass. The concentrations of N and P required for synthesis is quantified in biological models as fZB,N
= 0.068 mgN/mgOHOCOD and fZB,P = 0.020 mgP/mgOHOCOD, but it is not specified which of the
ammonia and phosphate weak acid/base system species are taken up for synthesis.
From the literature on bioenergetics, it is accepted that the non-ionic ammonia and phosphate
system species are taken up for synthesis, i.e. NH3 and H3PO4. Because the operating pH range for
the activated sludge system is generally 6.8 - 8.5, it has been accepted in the model that the most
abundant species of the systems in this pH range, i.e. NH4 + and HPO4 2- , are taken up, releasing one
proton and taking up two protons respectively during cell synthesis. In this operating pH range, the
concentrations of NH3 and H3PO4 are extremely low and their use in the model for synthesis leads to
numerical instability.

Utilisation and Generation of H + in OHO Growth And Death (Endogenous Respiration)
When NH4 + and HPO4 2- are taken up for growth, a proton is released and two protons taken up
respectively to convert these species to their unionised forms NH3 and H3PO4. This changes the H +
concentration which has to be taken into account, viz.
Concentration NH4 + taken up for synthesis = fZB,N (gN/gOHOCOD) [2a]
Concentration HPO4 2- taken up for synthesis = fZB,P (gP/gOHOCOD) [2b]
Hence the change H + concentration during synthesis = fZB,N /14 -2 fZB,P /31. [2c]
In organism death (or endogenous respiration), NH3 and H3PO4 are released to the bulk liquid. These
take up one and release two protons respectively to form the ionised forms NH4 + and HPO4 2-
originally taken up. This changes the H + concentration which has to be taken into account, viz.
Concentration NH4 + released in OHO death = fZB,N (1-fE) (gN/gOHOCOD) [3a]
Concentration HPO4 2- released in OHO death = fZB,P (1-fE) (gP/gOHOCOD) [3b]
Associated change H + concentration = -fZB,N (1-fE) /14 +2 fZB,P (1-fE)/31 [3c]
When ammonia is depleted, NO3 - is taken up by the OHOs as the N source for growth. However, the
NO3 - is first reduced to NH4 + by accepting 8H + and 8e - , which are supplied by the biodegradable
organics. Two additional H + , which are taken up from the bulk liquid, are also involved, viz.
- + + -
+
NO + 2H
+ (8H
+ 8e
) NH4
+ 3H
2 O
3 → [4a]
As before, one H + is released to the bulk liquid when the NH4 + taken up for growth. Hence,
Change in H + concentration with NO3 - as N source for OHO growth = -fZB,N /14 - 2fZB,P /31 [4b]
The biodegradable organics that supply the 8H + and 8e - for this reaction (Eq 4a) are lost from the
system, which is shown graphically in Fig 1. Even though Eq 4a is thermodynamically an energy
generating reaction, bioenergetically, the OHOs do not get any energy from this reaction. It is
therefore not correct to change the yield coefficient to account for this additional H + and
e - consumption. The yield coefficients under anoxic and aerobic conditions therefore remain YZH,Aer
= 0.67 and YZH,Anx = 0.54 mgOHOCOD formed/mgCOD organics utilized. To keep account of the
COD that is lost this way, the compound Slost is added to the model so that (i) the magnitude of this
lost COD is determined and (ii) COD balances can still be used to verify the model.
For completely mixed aerobic systems, the ammonia is unlikely to be depleted sufficiently for NO3 - to
be utilized as the N source 1 . This situation is more likely to occur in plug flow type systems.
1 In nitrifying aerobic digestion of waste activated sludge, nitrate utilization for OHO growth can occur even when there is
sufficient ammonia available. This happens because the rate of nitrification is faster than the rate of OHO growth, which is
limited by the supply rate of SBCOD from the OHO death process. This leads to uptake of nitrate for OHO growth but the
release of ammonia in OHO death. This released ammonia is then nitrified with an associated OUR for nitrification. The
consequence is an incorrectly high nitrification OUR from the continual supply of ammonia nitrogen from the death process,
nitrogen that was taken up by the OHOs as nitrate. This problem can be eliminated in the model by reducing the switching
function K value which controls the switch from ammonia to nitrate uptake for OHO growth to a very low value (0.0001). This
stops the OHO growth process from slowing down when the ammonia concentration gets low, allowing it to successfully
“compete” for ammonia against the nitrification process. In aerobic digestion of waste activated sludge, there is always
sufficient ammonia for growth because the ammonia released in OHO death is always greater than that taken up for OHO
growth on the SBCOD released in OHO death. The same problem can happen with aerobic digestion of primary sludge,
even when sufficient ammonia is dosed for sludge production from the primary sludge particulate biodegradable organics.
This problem therefore has nothing to do with ammonia deficiency but everything to do with the relative rates of processes
competing for the same compounds, in this case ammonium (NH 4 + ). K values of switching functions on processes
competing for the same compounds therefore need very careful scrutiny.

Figure 1. Graphical representation of the additional COD substrate-use term.
Ammonification of Soluble Organic Nitrogen
Ammonification is the process mediated by OHOs (B6) whereby biodegradable soluble organic
nitrogen (Nobs), which is in the unionized NH3 form, is converted to saline ammonia (NH4 + ).
Associated with ammonification is therefore a decrease in the H + concentration of the bulk liquid due
to uptake of a H + by the NH3 to form NH4 + . The concentration of H + taken up in ammonification is
1/14gH + /gN Organic N ammonified.
In ASM#2, the ammonification process is omitted. Instead, the conversion of soluble biodegradable
organic N (Nobs) is linked to the utilization of readily biodegradable organics (RB COD) of which it is
part. So if a wastewater has an influent soluble organic N to RBCOD ratio, (Nobsi/Sbsi) of say 0.03
(iNSF in ASM#2), the rate of ammonia (NH3) release is 0.03 times the rate of RBCOD utilization. The
release of ammonia from the particulate biodegradable organic N is modelled in the identical way in
ASM#1 and ASM#2. Two models were developed and compared, one conforming strictly to ASM#1
including the ammonification process and the other linking the release of ammonia from the soluble
organic N to the utilization of RBCOD. No important difference between the two approaches was
found for the cases considered.
A Note on the Utilisation of SCFA in OHO Growth
The SCFA weak acid/base system in the model arises from the earlier application of the CP source
model to aeration treatment of anaerobic digester liquor (ADL) (Musvoto, 2000a,c), where it is
required to establish the correct pH. Practically, the SCFA is not required in this integrated model to
include ASM#1 because the SCFAs are included in the RBCOD. If the SCFAs are modelled
separately as a subfraction of the RBCOD, which may be necessary with activated sludge treatment
of ADL, then four processes need to be added to the model, viz. processes 1c and 1d - aerobic
growth of OHOs on acetate with ammonia (1c) and nitrate (1d) as N source, and processes 2c and
2d, the anoxic equivalents. These processes have identical stoichiometry as growth on RBCOD, but
the substrate utilization is deducted from the HAc species of the SCFA system. Also, the SCFA
concentration would need to be deducted from the RBCOD to correctly reflect the RBCOD as the
remaining fermentable RBCOD, as is done in UCTPHO (Wentzel et al., 1992) or ASM#2 (Henze et
al., 1995), where SCFA is modelled separately from the fermentable RBCOD for biological P
removal.

Autotrophic Nitrifier Organisms (ANOs)
Autotrophic Metabolism
Although mediated by a number of different ammonia oxidizing and nitrite oxidizing organisms in two
sequential steps from ammonia to nitrite and nitrite to nitrate, in ASM#1 nitrification is modelled as
a single step from ammonia to nitrate by a generic group of autotrophic nitrifier organisms (ANOs).
The nitrification rate is defined by the slower organism group of the sequence, which under most
circumstances are the ammonia oxidizers. Stoichiometrically, nitrification of saline ammonia requires
2 mol (32gO) oxygen and produces 1mol nitrate and 2 mol protons, i.e.
NH
+ 2O
-
+
NO3
+ H2
O + 2H
+
4 2 → [5]
The ANOs obtain their anabolic carbon requirements from dissolved CO2 (H2CO3*) and their
catabolic energy (e - ) requirements from oxidizing ammonia to nitrate. Accepting that C5H7O2N
represents the C, H, O and N content of the ANOs and has a COD content of 160g/mol, then five mol
CO2 are required to synthesize one mol ANOs, viz.
+
+ -
5 CO + NH4
+ (20H
+ 20e
)
+
C5
H7
O2
N + 8 H2
O + H
2 → [6]
which includes also the ammonia requirement for cell synthesis.
The catabolic ammonia (e - and H + ) requirement is determined from the ANO yield coefficient, i.e.
YZA
= 0.15 (gANOCOD/gNH4 + -N nitrified)
= 0.15*14/160 (mol ANOs/mol NH4 + -N nitrified)
From Eq 6 the mol CO2 required is 5 times the mol of ANOs formed
So mol CO2 required = 5YZA*14/160 (mol CO2/mol NH4 + -N nitrified)
= 5YZA*12/160 (gCO2-C/gNH4 + -N nitrified)
But 1 gANOCOD synthesized requires nitrification of 1/YZA gNH4 + -N nitrified, so
CO2 required = (5YZA*12/160)*1/YZA = 3/8 (gCO2-C/gANOCOD synthesized) [7]
This stoichiometric ratio for CO2 utilised by the ANOs is added to the model, accepting that the CO2
taken up is in the dissolved form and represented as H2CO3 * (Table 1). The processes that influence
the H2CO3 * concentration are listed in Table 4.
The ANOs are conventionally considered to use the NH4 + species because this is the most abundant
species in the optimum pH range for nitrification, i.e. 7.2-8.5 (Casey et al., 1994). However, Suzuki
(1974), in studies on Nitrosomonas europae concluded that the NH3 species is used in the oxidation
process. Also, Drozd (1976) argued that Nitrosomonas use the NH3 form, because a rapid decrease
in pH was noticed in the medium in growing cultures suggesting that a proton remains on the exterior
of the cell wall in the medium. In this integrated model, it has been accepted that the unionized NH3
species is used in oxidation, but that NH4 + species is taken up from solution with the release of H + .
This is done because NH4 + is the most abundant species at optimum pH for nitrification. In this
operating pH range, the NH3 concentration is extremely low and its use in model leads to numerical
instability.
Production/Utilisation of H + ANO Growth
The change in H + during nitrification (NH4 + oxidation and uptake for ANO growth) is derived from Eqs
5 and 6 and the yield coefficient of ANOs as follows,
Concentration of NH4 + -N oxidised to produce 1 gANOCOD/m 3 = 1/YZA

From Eq 5, 14 g of NH4 + -N produce 2g H +
So 1/YZA g NH4 + oxidized produces 1/(7YZA) gH +
Also, from Eq (5), the NH4 + incorporated into ANO biomass during synthesis releases a H + . The
concentration of N incorporated into ANO mass is defined by the N content of the ANOs, which is
accepted to be equal to that of the OHOs, i.e. fZB,N = 0.068 mgN/mgANOCOD. So from Eq 6,
14 g NH4 + -N is incorporated into ANOs releases 1 g H +
∴ fZB,N g NH4 + -N incorporated into ANOs releases fZB,N /14 g H +
Thus in total, during nitrification 1/(7YZA) + fZB,P/14 gH + are released per gANOCOD generated.
Because the ANO mass constitutes such a small part of the measured reactor COD (or VSS)
concentration and the endogenous respiration rate is so low, endogenous residue accumulation (XE)
and release of N from ANO endogenous respiration (death) is ignored.
Effect of pH on Maximum Specific Growth Rate of ANOs
The maximum specific growth rate of nitrifiers µnm is very sensitive to pH, with nitrification rates
declining sharply outside the optimum pH range of 7.0-8.5. In the activated sludge system treating
reasonably well buffered wastewaters, quantitative modelling of the effect of pH on nitrification is not
critical because pH reduction can be limited or completely obviated by including anoxic zones
thereby ensuring alkalinity recovery via denitrification (WRC, 1984). However, because the
interaction between the biological processes, pH and nitrification is the single most important one for
the N removal activated sludge system, it is essential to include the effect of pH on the nitrification
rate in the integrated model to simulate this important interaction.
Quantitative modelling of the effect of pH on the maximum specific growth rate of nitrifiers has been
hampered by a lack of information and the general expected trends have been formulated based on
empirical assumptions. Many studies have shown that the maximum specific growth rate of nitrifiers
µnm can be expressed as a percentage of the highest value at optimum pH. Accepting this approach
and that µnm is highest and remains approximately constant in the pH range for 7.2

The combined effect of pH on µnm is therefore modelled by combining Eqs (8) and (9), giving the
maximum specific growth rate at any pH between 5.5 and 9.5 as a fraction of the maximum rate at
pH = 7.2 (Eq 10, Fig 2). It can be seen in Fig 2 that in the range pH = 7.2 to 8.3, the change in µnmpH
is small, with µnmpH /µnm7.2 > 0.9.
where
(pH-7.2)
Km
a x - pH
µ nmpH = µ nm7.2
2.
35 KI
[10]
Km
a x + KII
- pH
2.35 (pH-7.2) is set = 1 for pH > 7.2 and also and µnmpH = 0 for pH ≥ 9.5
Experimental data from the literature have also been plotted in Fig 2 to provide some quantitative
support for Eq 10. At low pH (8.5, but the few points from Antoniou
et al. (1990) show reasonable agreement with Eq 10. Accordingly, Eq 10 was accepted to calculate
µnmpH in the integrated model in the pH range 5.5 to 9.5.
Figure 2. The effect of pH on the maximum specific growth rate of Nitrosomonas µnm.
MODELING GAS-LIQUID GAS EXCHANGE
H2CO3 * (dissolved) CO2 (gas) Exchange
The ratio of CO2 to dissolved H2CO3 is fixed and equal to 99.76:0.24 at 25 o C and is independent of
pH and ionic strength. Accordingly these two species are dealt with as a combined species, H2CO3 *
= CO2 dissolved + H2CO3. The dissolved CO2 and hence the H2CO3 * tends to equilibrium with the
partial pressure of CO2 gas outside the liquid, giving rise to CO2 exchange at the liquid/gas interface
resulting in loss or gain of H2CO3 * and hence in total carbonate species concentration in solution.
In the model this is done by modeling separately the rate of the forward and reverse reactions:
rf = K’fCO2 [CO2 (g)] [11]
rr = K’rCO2 [H2CO3 * ] [12]

where:
K’fCO2 = K’rCO2 KeqCO2
K’rCO2 = 10 4
K’eqCO2 = KH,CO2 R T
KH,CO2 = 10 -pKH,CO2
pKH,CO2 = -(2025.3/Tk) - 0.0104T + 11.365
(Musvoto et al., 2000)
Note that in the Musvoto model the concentration of CO2 (g) is kept constant; CO2 (g) is included as
a compound in the model only for continuity. However, in this activated sludge / aquatic chemistry
model CO2 (g) is not kept constant. Furthermore, in this model the parameter CO2 (g) is in fact
‘dissolved’ in solution due to the fact that Aquasim does not allow for interaction between a
compound in two compartments (i.e. the reactor and the headspace) making it impossible to link the
process of CO2 dissolution / expulsion to the CO2 (g) in the headspace. Hence the CO2 (g) remains
a compound in the reactor and is effectively dissolved in the reactor contents. This intermediary
‘dissolved’ CO2 gas is however extracted to the headspace by another process which will be
described further in (iv) below.
Gas Stripping In Aerated Reactors
Models that simulate mass transfer are based on the assumption that the liquid phase resistance
controls the rate of interphase mass transfer if the solutes are sufficiently volatile (Roberts et al.,
1984). This assumption is said to be valid for values of the dimension less Henry’s coefficient Hc >
0.19 (Mackay and Leinomen., 1975) where Hc is defined as the ratio of interfacial concentration in
the gas phase to that in the liquid phase, i.e. Hc = Cg / Cl and is related to the other equilibrium
parameters as follows:
where:
Hc = 1/(KHRT) = K/(RTMW) [13]
KH = Henry’s law constant (mol/l/atm)
K = Conventional equilibrium constant of Henry’s law (atm)
MW = Molar volume of water (mol/l)
R = Universal gas constant (atm.l/mol/K)
T = Temperature (K)
The mass transfer models are also based on the principle that in general the rate constants are
proportional to one another, and this has been demonstrated for gases, organic solutes as well as
oxygen. Based on this principle, several authors (e.g. Matter-Muller et al., 1981) proposed the use
of a tracer or reference compound to predict the extent of mass transfer of organic compounds at
gas-liquid interfaces. This is convenient because only the mass transfer coefficient for the reference
compound needs to be measured, and since the geometric and hydrodynamic conditions in a given
reactor do not change, the mass transfer coefficient for the other components can be calculated from
the reference compound.
Oxygen has been found to be the most suitable reference compound because (i) it satisfies the
volatility criterion in most cases of interest (Hc = 29.9 at 20 o C which is >0.19), (ii) a lot of data is
available on oxygen transfer in wastewater treatment and (iii) oxygen transfer usually is the main
objective during aeration in wastewater treatment, making it a practical choice as a reference
compound.
Munz and Roberts (1989) found that oxygen is a suitable reference compound if the solute has a
value for the dimension less Henry’s law constant Hc >=0.55
For the compounds of interest in the activated sludge / aquatic chemistry model the dimension less
Henry’s coefficients are:
CO2 : 1.206 [>=0.55]

NH3 : 0.0007171 [=0.55]
Therefore, for CO2 and N2 (this approach cannot be applied to NH3 stripping as its Hc < 0.55, see
above) the following approach is adopted (CO2 used as an example):
Rate:
KLCO2*{[H2CO3] - p_CO2*KHCO2} where [14]
KLCO2 = Overall liquid phase mass transfer rate coefficient for CO2
where
=
KL
O 2
⎛ DL
×
⎜
⎝ DL
CO 2
O 2
⎞
⎟
⎠
n
⎛
⎜
×
⎜
1 +
⎜
⎜
⎝
k
k
G
L
1
× HC
CO 2
KL = Overall liquid phase mass transfer rate coefficient for compound
DL = Liquid phase molecular diffusion coefficient for compound
kG = Gas phase individual mass transfer coefficient (m/s)
kL = Liquid phase individual mass transfer coefficient (m/s)
HC = Dimensionless Henry’s constant for compound
p_CO2 = Partial pressure of CO2 (atm)
KHCO2 = Henry’s law constant for CO2
Stoichiometry: [H2CO3] -1
[CO2 (g)] +1
Note: The CO2 (g) is the same compound ‘dissolved’ in the reactor as described in (ii) above.
Since the Hc for NH3 is

a water phase (as is the case in the activated sludge / aquatic chemistry model), the conversion
factor is the inverse of the nondimensional Henry’s coefficient of substance i:
fi=1/Hci [16]
In many cases the mass exchange coefficient, qexi, is given as the product of the surface area of the
boundary layer, A. and a mass transfer coefficient, ki
qexi = Aki [17]
which itself is often given as the ratio of the diffusion on coefficient Di of the substance in the
boundary layer and the thickness LM of the boundary layer
ki = DiLM [18]
THE COMBINED SINGLE PHASE AQUEOUS WEAK ACID/BASE BIOLOGICAL MODEL
All the changes to the processes of growth for the heterotrophs and autotrophs discussed above
were made to the ASM#1 model.The amended biological model was combined with the single phase
weak acid/base model (Musvoto et al., 1997) to give the combined single phase aqueous model
shown in matrix form in Table 1.
This model was incorporated into the AQUASIM computer programme. A number of simulations
were conducted to evaluate the model predictions. One such simulation was on the aerobic batch
test described by Dold et al. (1991). In this batch test mixed liquor drawn from a nitrifying activated
sludge system was mixed with raw municipal wastewater and aerated. For further details on the
aerobic batch test, the reader is referred to Dold et al. (1991).
Because the total species concentrations of the carbonate, ammonia, phosphate and SCFA systems
were not measured by Dold et al. (1991), values for these parameters had to be estimated for input
to the model predictions. The model predictions were identical to those from ASM#1 for the biological
processes, however the model predictions for the weak acid/base chemistry (and pH) processes
could not be compared to ASM#1 as ASM#1 does not include these processes. The model weak
acid/base (and pH) predictions can only be verified with data from an investigation that includes
measurements for the weak acid/base systems and the pH, however no such data set is currently
available.
The predictions of the two models compare very well and with the experimental data. The close
correlation between predictions with the two models is to be expected because the simulations were
done for municipal wastewater where, despite their inclusion in the combined model, the weak
acid/base systems have no significant effect on the biological processes. No suitable data on
biological treatment of wastewaters where the weak acid/base systems and pH play a significant role
could be found in the literature to adequately validate the model. Rigorous model validation was
carried out with data from experiments which were conducted later. Details of these experiments and
model validation are discussed by Musvoto et al. (1998b; In prep.).
A Note on the COD Mass Balance of The Model
Mass balances are performed over a model or experimental system to check its accuracy. Strictly
speaking, the COD balance performed on biological processes only models (see Dold et al., 1991)
is no longer possible for the combined chemical and biological processes model because inorganic
CO2 is changed to organic nitrifier VSS unless this contribution from inorganic carbon is specifically
excluded. In reality though, the contribution of the inorganic carbon is so small that it does not affect
the value of the COD mass balance very much for normal domestic wastewaters where the growth
of autotrophs is very small compared to the growth of heterotrophs. However, for wastewaters which
have a high ammonia content relative to their organic content (e.g. HNLC wastewaters) the growth
of autotrophs will be significant compared with the growth of heterotrophs and COD mass balances
much greater than 100% will be obtained if the autotrophic biomass is included in the VSS
component in the COD mass balance.

CLOSURE
In this paper, the mixed weak acid/base systems model developed by Musvoto et al. (1997) has
been integrated with the ASM#1, version IAWQ (Dold et al., 1991). This integration was greatly
facilitated by the kinetic approach developed to model mixed weak acid/base systems. In the
integration, a number of modifications had to be made to the ASM#1 as outlined above.
Specifically the following had to be modified:
• Production/utilization of CO2 in heterotrophic and autotrophic metabolism had to be included.
• Production/utilization of H + in heterotrophic and autotrophic metabolism had to be included.
• Weak acid/bases already in the ASM#1 had to be divided into individual weak acid/base species.
For example in the ASM#1 the ammonia/um weak acid/base is included as a single species with
the concentration equal to the total species concentration; the individual ammonia and
ammonium species had to be included.
• Following from the above, utilization/production of weak acid/bases in autotrophic and
heterotrophic metabolism had to be changed from total species concentration to specific weak
acid/bases. For example in the ASM#1, the autotrophs utilize the total species ammonia/um in
nitrification; this had to be changed to utilization of the ammonium weak acid/base species.
• Utilization/production of phosphorus weak acid/base had to be included; ASM#1 does not
include this.
• The effect of H + (i.e. pH) on biological processes in ASM#1 had to be included; specifically, the
effect of pH on the nitrification process. This was done by developing a relationship between the
maximum specific growth rate of the autotrophs and pH.
With the above modifications, simulations with the model were compared to those with the ASM#1
(Dold et al., 1991) and experimental data in the literature; good correlation was obtained. However,
these comparisons can serve only as a preliminary validation of the model, because, despite their
inclusion, the weak acid/bases and pH have no significant effect on the biological processes in the
cases considered. A more rigorous validation of the model was hindered by a lack of complete sets
of experimental data in the literature where weak acid/bases and pH do influence the biological
processes. Also, the combined weak acid/base chemistry and biological model as presented in this
paper has restricted application: the model only considers the aqueous phases. However, the weak
acid/bases (particularly the carbonate and ammonia and to some degree the phosphate) exist in
equilibrium with solid and/or gaseous phases. Modelling of the solid and gaseous phases has
already been discussed by Musvoto et al. (1998a). The validation of the combined three phase
systems model incorporating biological processes, chemical precipitation of minerals and gas
stripping is discussed by Musvoto et al. (1998b; In prep). The combined chemical, physical and
biological model is proving to be a useful tool in evaluating treatment schemes where these
processes are all important.
ACKNOWLEDGEMENTS
This research was supported financially by the Water Research Commission, Foundation for
Research Development and University of Cape Town and is published with their permission.
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