1
Supplementary material: Analysing the effects of the aeration pattern and
2
residual ammonium concentration in a partial nitritation-anammox process
3
Luis Corbalá-Roblesa,*, Cristian Picioreanua, Mark C.M. van Loosdrechta, Julio
4
Péreza
5
a
6
The Netherlands
7
*
8
Engineering, Ghent University, Coupure links 653, 9000 Ghent, Belgium.
Department of Biotechnology, Delft University of Technology, Julianalaan 67, 2628BC, Delft,
Corresponding author. E-mail: Luis.CorbalaRobles@UGent.be.
1
Department of Biosystems
9
Temperature and pH effect on ionization constants
10
Eqs. (S1) and (S2), derived from acid-base equilibriums, were used for the calculation of the free
11
ammonia (FA or NH3) and the free nitrous acid (FNA or HNO2).
12
FA 
13
FNA 
14
The ratio between the ionization constant of the ammonia equilibrium (Kb) and the ionization
15
constant of water (Kw) is related to the temperature as shown in Eq. (S3) and the temperature effect
16
on the ionization constant of the nitrous acid equilibrium (Ka) is shown in Eq. (S4) .[1]
17
Kb
 6344 
 exp 

Kw
 273  T 
(S3)
18
  2300 
K a  exp 

 273  T 
(S4)
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The kinetics for each of the processes considered i.e. growth and decay of each kind of bacteria
20
are shown in Table S2-Supplementary Material. In addition, the oxygen limitations, substrate and
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non-competitive inhibitions for AOB and NOB growth processes were also considered. AOB
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inhibition by FA and NOB inhibition by FNA were described with a Haldane model while AOB
23
inhibition by FNA and NOB inhibition by FA were described with a non-competitive model.
S NH 4  10 pH 14

Kb
pH 17
 10
Kw
(S1)
S NO 2
47

pH
K a  10  1 14
(S2)
2
Table S 1. Stoichiometric matrix .[2]
component
→
SS
[gCOD.
m-3]
process ↓
growth
1. growth of XAOB
2. growth of XNOB
3. growth of
anammox
4. aerobic growth
of heterotrophs
5. anoxic (on NO2-)
growth of
heterotrophs
6. anoxic (on NO3-)
growth of
heterotrophs
decay
7. decay of XAOB
8. decay of XNOB
9. decay of XAMX
10. decay of XHET
-1/YHET
-1/
YHET,NO2
-1/
YHET,NO3
1-fI
1-fI
1-fI
1-fI
SNH4
[gN.m-3]
SNO2
[gN.m-3]
SNO3
[gN.m-3]
SN2 [gN.m-3]
SO2
[gO2.m-3]
SN2AMX
[gN.
m-3]
-1/YAOB iNXB
1/YAOB
-iNXB
-1/YNOB
1/YNOB
-1/YAMXiNXB
-iNXB+
1/YHET.
iNSS
-iNXB+
1/YHET.
iNSS
-iNXB+
1/YHET.
iNSS
-(1/YAMX ) (1/1.14)
1/1.14
SN2H
[gN m-3]
13.43/YAOB
11.14/YNOB
XAOB
[gCOD.
m-3]
XNOB
[gCOD.
m-3]
XAMX
[gCOD.
m-3]
XHET [gCOD.m-3]
XO2,HET XNO2,HET
[gCOD. [gCOD.
m-3]
m-3]
XNO3,HET
[gCOD.
m-3]
XI
[gCOD.
m-3]
1
1
2/
YAMX
1
1- 1/YHET
1
(1-YHET,NO2)/
(1.71YHET,NO2)
-(1-YHET,NO2)/
(1.71YHET,NO2)
1
1
-(1-YHET,NO3)/
(1-YHET,NO3)/
(1.14YHET,NO3)
(1.14YHET,NO3)
iNXB - fI iNXI
– (1-fI) iNSS
iNXB - fI iNXI
– (1-fI) iNSS
iNXB - fI iNXI
– (1-fI) iNSS
iNXB - fI iNXI
– (1-fI) iNSS
-1
fI
-1
fI
-1
fI
-1
3
fI
Table S2. Kinetic rate expressions.
j
1
2
3
Process rate (d-1)
SO2
max, AOB 

K O2 , AOB  SO2
Process
Growth of XAOB
Reference
S NH 4
K S , NH 4, AOB  S NH 4 
S NH 4

2
K I , NO 2, AOB
 X AOB
K I , NO 2, AOB  S NO 2
K I , NH 4, AOB
bAOB  X AOB
Decay of XAOB
max, NOB 
Growth of XNOB
[3]
[4]
SO2
KO2 , NOB  SO2
S NO 2

K S , NO 2, NOB  S NO 2 
S NO 2
2

K I , NH 4, NOB
 X NOB
K I , NH 4, NOB  S NH 4
[3]
K I , NO 2, NOB
4
Decay of XNOB
bNOB  X NOB
5
Growth of XAMX
max, AMX 
6
Decay of XAMX
bAMX  X AMX
7
Growth of XO2,HET
 max, HET 
8
Growth of XNO2,HET
max, HET  η NO 2 
S NO 2
KO 2,HET
SS
S NO 2
S NH 4



.
 X HET
KO 2,HET  SO 2 K NO 2,HET  S NO 2 K S ,HET  S S S NO 2  S NO 3 K NH 4,HET  S NH 4
[4]
9
Growth
XNO3,HET
max, HET  η NO 3 
S NO 3
KO 2,HET
SS
S NO 3
S NH 4



.
 X HET
KO 2,HET  SO 2 K NO 3,HET  S NO 3 K S ,HET  S S S NO 2  S NO 3 K NH 4,HET  S NH 4
[4]
10 Decay of XHET
of
[4]
K I ,O2 , AMX
K I ,O2 , AMX  SO2

S NH 4
S NO 2

 X AMX
K NH 4, AMX  S NH 4 K NO 2, AMX  S NO 2
[4]
[4]
S O2

SS
K O2 , HET  S O2 K S , HET  S S
.
S NH 4
 X HET
K NH 4, HET  S NH 4
bHET  X HET
[4]
[4]
4
Table S3. Stoichiometric and kinetics parameters values
parameter
value
Unit
Stoichiometric parameters
YAOB
0.20
g COD.g-1 N
[5] (1)
YNOB
[5] (1)
YAMX
YHET
YHET,NO2
YHET,NO3
iNXB
0.057
g COD.g-1 N
0.17
g COD.g-1 N
0.67
g COD.g-1 COD
[7]
0.53
g COD.g-1 COD
[8]
0.53
g COD.g-1 COD
[8]
g N.g-1 COD
[2]
0.07
[6] (2)
iNXI
0.07
g N.g-1 COD
[2]
iNSS
0.03
g N.g-1 COD
[7]
fI
0.08
g COD.g-1 COD
[7]
Kinetic parameters (at 30°C & pH 7)
max, AOB
1.36
d-1
max, NOB
0.79
d-1
max, AMX
0.052
d-1
max, HET
12
d-1
K
S , NH 4, AOB
1.1
g N.m-3
S , NO2, NOB
0.51
g N.m-3
K
[9] (3)
[9] (3)
[6] (3)
[7] (4)
[5] (5)
[5] (5)
AOB
AN
Assumed, such that ratio K NH
: K NH
K
NH 4, AMX
0.03
g N.m-3
is about the same as in [10]
5
NOB
AN
Assumed, such that ratio K NO
2 : K NO 2
K
NO2, AMX
0.005
g N.m-3
is about the same as in [10]
NO2, HET
0.3
g N.m-3
[11]
NO3, HET
0.3
g N.m-3
[11]
S , HET
20
g COD.m-3
K
O 2, AOB
0.3
g O2.m-3
[5]
K
O 2, NOB
1.1
g O2.m-3
[5]
K
0.05
g O2.m-3
[2]
K
O 2, HET
0.2
g O2.m-3
K
NH 4, HET
0.02
g N.m-3
[2]
I , NO2, AOB
828
g N.m-3
[12]
I , NH 4, AOB
9563
g N2.m-6
[12]
I , NH 4, NOB
154
g N.m-3
[12]
I , NO2, NOB
90
g N2.m-6
[13]
bAOB
0.068
d-1
AOB = bH:  H
Assumed, set such that bAOB:  max
max
bNOB
0.04
d-1
NOB
H
Assumed, set such that bNOB:  max
= bH:  max
bAMX
0.0026
d-1
AN
H
Assumed, set such that bAN:  max
= bH:  max
bHET
0.6
d-1
H
Assumed  max
/ 20 for this study
ηNO2=ηNO3
0.8
-
[7]
K
K
K
K
K
K
K
I , O 2, AMX
[7]
[7]
Mass transfer parameters
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DNH4
1.5x10-4
m2.d-1
[14]
DNO2
1.4x10-4
m2.d-1
[14]
DNO3
1.4x10-4
m2.d-1
[14]
DO2
2.2x10-4
m2.d-1
[15]
DS
1x10-4
m2.d-1
[16]
After unit conversion, using a typical biomass composition of CH1.8O0.5N0.2,
corresponding with 1.3659 g COD.g-1
(2) After unit conversion, using a anammox biomass composition of CH2O0.5N0.15,
corresponding with 36.4 g COD.mole-1 or 1.51 g COD.g-1
(3) Conversion of values given in [9] at 35°C and in [6] at 32.5°C to 30°C using the
relationship (written for XAOB, analogous for XNOB and XAMX)
(1)

AOB1
max
(T )  
AOB1
max
 EaAOB  T  Tref  

( Tref )  exp
 R T T

ref


with E aAOB =68 kJ.mole-1 ; E aNOB =44 kJ.mole-1; EaAMX = 70 kJ.mole-1 ; R=8.31 J.mole-1.K1
.
(4) Conversion of ASM1-values given in [7], at 10°C and 20°C to 30°C using temperature
relationship proposed by these authors (ASM3).
-3
AOB
NOB
(5) Calculated value at T=30°C and pH=7 from K NH
and from K HNO
3 = 0.028 g NH3-N.m
2=
-5
-3
3.2x10 g HNO2-N.m considering the T and pH dependency of the chemical
equilibrium NH 4  NH 3  H  and HNO2  NO2  H 
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Table S4. References from the oxygen affinity values used in the study of NOB repression.R KO=KO2,AOB/KO2,NOB.
KO2,AOB
KO2,NOB
RKO
(gO2/m3)
(gO2/m3)
(KO2,AOB/KO2,NOB)
0.3 [5]
1.75 [17]
0.17
0.3 [5]
1.1 [5]
0.27
0.16 (This study)
0.16 [18]
1
0.18 [19]
0.13 [19]
1.38
1.16 [18]
0.16 [18]
7.25
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Figure S1. Comparison of the minimum ammonium concentrations for NOB repression obtained
with a CSTR (label: 20°C and 30°C) and a SBR at 30°C (label: SBR 30°C). The values were
obtained with an RKO=0.27. It was observed that the values differ in average 13% and no more
than 20%.
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Figure S2. Reduction of anammox growth rate over the granule radius due to inhibition by oxygen
in different aeration cases. The oxygen inhibition term I O2 (t , x)  K I ,O2 , AMX ( K I ,O2 , AMX  SO2 )
averaged in time over the aeration period for each aeration case (A, B and C) was related to the
one calculated for continuous aeration.
10
Figure S3. Concentrations in the bulk liquid during two cycles at steady state. The time axis
represents the cycle time, not the total time since reactor start up. The dissolved oxygen was 0.25
g/m3 for the six-hour period of simultaneous feeding and continuous aeration, and then no aeration
for the last two hours of the cycle. The temperature was 30°C, pH 7 and the granule diameter 1.1
mm.
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Figure S4. Concentrations during two cycles at steady state regarding bulk concentrations. Same
operation parameters as in the multispecies granular sludge case except for the intermittent
aeration.
12
Figure S5. Substrate concentration (ammonium, oxygen and nitrite) within the granule. Model case
(Multispecies granule).
13
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