1
Appendix: Modelling microbial competition in nitrifying biofilm reactors
2
T.P.W. Vannecke and E.I.P. Volcke*
3
Department of Biosystems Engineering, Ghent University, Coupure links 653 9000 Ghent,
4
BE
5
*
6
E-mail address: Eveline.Volcke@UGent.be
Corresponding author Tel: +32 (0)9 264 61 29; fax: +32 (0)9 264 62 35
7
Appendix
8
In the appendix, the equations used for conversion of microbial parameters of AOB and NOB
9
to values valid for a temperature of 30°C and a pH of 7.5 is given (A1). Next, the
10
stoichiometric matrix of the developed 1-dimensional biofilm model together with the
11
corresponding kinetics and parameter values are given (A2). Finally, the results of the
12
literature review on the microbial characteristics of AOB and NOB are summarized (A3).
13
A1.
14
Published maximum growth rates of AOB and NOB were converted to a rate at 30°C using
15
Equation (A1) and Equation (A2) with EAOB
= 68 kJ.(mol.K)-1; ENOB
= 44 kJ.(mol.K)-1 and R
a
a
16
= 8.31 J. (mol.K)-1.
Conversion of microbial characteristics to 30°C and pH = 7.5
17
EaAOB ∙ (T − Tref )
AOB (T )
(T)
µAOB
=
µ
∙
exp
(
)
max
max ref
R ∙ T ∙ Tref
18
µNOB
max (T)
=
µNOB
max (Tref )
EaNOB ∙ (T − Tref )
∙ exp (
)
R ∙ T ∙ Tref
19
All affinity constants for ammonium (AOB) and the affinity constants for nitrite (NOB) were
20
converted to g TNH-N.m-3 and g TNO2-N.m-3, respectively, unless the published affinity
21
constant was expressed as g N.m-3. Affinity constants for nitrogen expressed as NH3-N.m-3 or
22
NH4+-N.m-3 (AOB) and as HNO2-N.m-3 or NO2--N.m-3 (NOB) were converted to g TNH-N.m-
23
3
24
Yield coefficients expressed in g organic dry matter.(g N)-1 or g odm.(gN)-1were converted to
25
yield coefficients expressed as g COD.(g N)-1 by using the conversion factor of 1.3659 g
26
COD.g odm-1, based on the typical biomass composition CH1.8O0.5N0.2.
and g TNO2-N.m-3, respectively (Table A1).
27
Table A1 Equations to express affinity constants for ammonium (AOB) and nitrite (NOB) in units of TNH-N.m-3 and TNO2-N.m-3, respectively,
28
with pKa(NH4 ) = −log(e(−273.15+T) ) and pKa(HNO2 ) = − log (e(−273.15+T) ) calculated for T = 30 °C and pH = 7.5 following Anthonisen et al.
29
(1976).
2300
6344
Input:
𝐴𝑂𝐵
𝐾𝑁𝐻
expressed as →
Output:
𝐴𝑂𝐵
𝐾𝑁𝐻
expressed as
(TNH-N.m-3)
Input:
𝑁𝑂𝐵
𝐾𝑁𝑂2
expressed as →
Output:
𝑁𝑂𝐵
𝐾𝑁𝑂2
expressed as
(TNO2-N.m-3)
Units
-3
g NH3.m
[NH3 ]∙
14
∙(1+10(pKa(NH4) - pH) )
17
-3
g NH4+.m-3
g NH3-N.m
[NH3 ]∙(1+10(pKa(NH4) − pH) )
[NH4+ ]∙
14
∙(1+10(pH - pKa(NH4 )) )
18
g NH4+-N.m-3
[NH+4 ]∙(1+10(pH − pKa(NH4 )) )
Units
g NO2-.m-3
[NO-2 ]∙
14
∙(1+10(pKa(HNO2 ) − pH) )
46
g NO2--N.m-3
[NO-2 ]∙(1+10(pKa(HNO2) − pH) )
g HNO2.m-3
[HNO2 ] ∙
14
∙ (1 + 10(pH − pKa(HNO2 )) )
47
g HNO2-N.m-3
[HNO2 ]∙(1+10(pH − pKa(HNO2)) )
30
A2.
Two-step nitrification 1-dimensional multispecies biofilm model
31
Table A2 gives the stoichiometric matrix of the two-step nitrification 1-dimensional
32
multispecies biofilm model used in this study. The corresponding process rates and
33
stoichiometric and kinetic parameters are given in Table A3 and Table A4, respectively.
4
34
Table A2 Stoichiometric matrix describing the growth and decay of 60 ammonium-oxidizing species (AOBi) and 60 nitrite-oxidizing species
35
(NOBi), i = 1 – 60.
Aij
i component
j process
↓
Growth
1. growth of XAOBi
2. growth of XNOBi
Decay
1. decay of XAOBi
2. decay of XNOBi
gCOD/unit comp
gN/unit comp
→
SS
[gCOD.m-3]
SNH
[gN.m-3]
SNO2
[gN.m-3]
SNO3
[gN.m-3]
SO2
[gO2.m-3]
XAOBi
[gCOD. m-3]
-1/YAOBi -iNXB
-iNXB
1/YAOBi
-1/YNOBi
1-3.43/YAOBi
1-1.14/YNOBi
1
1/YNOBi
1-fI
1-fI
iNXB - fI iNXI – (1-fI) iNSS
iNXB - fI iNXI – (1-fI) iNSS
1
0
1
iNSS
XNOBi
[gCOD. m-3]
1
-1
Composition matrix
-3.43
-4.57
1
1
36
5
-1
0
XI
[gCOD. m-3]
1
iNXB
-1
fI
fI
1
iNXB
1
iNXI
37
Table A3 Reaction kinetics for growth and decay corresponding to the processes from Table
38
A2 with AOBi the ammonium-oxidizing species, NOBi the nitrite-oxidizing species and i= 1
39
– 60.
j process
↓
S
1. growth of XAOBi
G,AOBi =  AOBi
max 
2. growth of XNOBi
G,NOBi =
3. decay of XAOBi
𝜌𝐷,𝐴𝑂𝐵𝑖 = 𝑏𝐴𝑂𝐵𝑖 ∙ 𝑋𝐴𝑂𝐵𝑖 
4. decay of XNOBi
𝜌𝐷,𝑁𝑂𝐵𝑖 = 𝑏𝑁𝑂𝐵𝑖 ∙ 𝑋𝑁𝑂𝐵𝑖 
NOBi
 max

K
O2
AOBi
O2
 SO 2

S NH
 X AOBi
K
 S NH
AOBi
NH
SO 2
S NO 2
S NH


.X NOBi
NOBi
NOBi
NOBi
KO

S
K

S
K
O2
NO 2
NH  S NH
2
NO 2
40
6
41
Table A4 Stoichiometric, kinetic and mass transfer parameter values of the multispecies
42
biofilm model with AOBi the ammonium-oxidizing species, NOBi the nitrite-oxidizing
43
species and i= 1 – 60.
Parameter
Description
Value
Unit
Reference
Stoichiometric parameters
iNXB
Nitrogen fraction in biomass
0.07
g N.(g COD)-1
Mozumder et al. (2013)
iNXI
Nitrogen fraction in inerts
0.07
g N.(g COD)-1
Mozumder et al. (2013)
iNSS
Nitrogen fraction in soluble organic substrate
0.03
g N.(g COD)-1
ASM3 (Henze et al. 2000)
fXI
Fraction of inert COD generated in
biomass decay
0.08
g COD.(g COD) -1
ASM2 (Henze et al. 2000)
YAOBi
Yield coefficient of AOBi
0.09 – 0.41
g COD.(g N)-1
Literature study (Table S1)
YNOBi
Yield coefficient of NOBi
0.02 – 0.20
g COD.(g N)-1
Literature study (Table S2)
Endogenous respiration rate of AOBi
0.017 – 0.17
d-1
Endogenous respiration rate of NOBi
0.012 – 0.18
d-1
AOBi
K NH
Affinity of AOBi for ammonium
0.07 – 51.30
g TNH-N.m-3
Literature study (cfr. Table A5)
AOBi
K O2
Affinity of AOBi for oxygen
0.07 – 3.00
g O2.m-3
Literature study (cfr. Table A5)
NOBi
K NO 2
Affinity of NOBi for nitrite
0.05 – 38.69
g TNO2-N.m-3
Literature study (cfr. Table A6)
NOBi
K O2
Affinity of NOBi for oxygen
0.04 – 4.01
g O2.m-3
Literature study (cfr. Table A6)
K NO 3
Affinity for nitrate of endogenous respiration
1
g N.m-3
de Kreuk et al. (2007)
K NO 2
Affinity for nitrite of endogenous respiration
1
g N.m-3
Assumed equal to K NO 3
Maximum growth rate AOBi
0.33 – 3.40
d-1
Literature study (cfr. Table A5)
Maximum growth rate NOBi
0.24 – 3.54
d-1
Literature study (cfr. Table A6)
Kinetic parameters (pH 7.5 and T=30 °C)
b
b
AOBi
NOBi
AOBi
 max
NOBi
 max
AOBi
Set to 0.05  max
NOBi
Set to 0.05  max
Mass transfer parameters
D NH 4
Diffusion coefficient NH4
1.6e-4
m2.d-1
Picioreanu et al. (1997)
D NO 2
Diffusion coefficient NO2
1.5e-4
m2.d-1
Picioreanu et al. (1997)
D NO 3
Diffusion coefficient NO3
1.5e-4
m2.d-1
Picioreanu et al. (1997)
DO 2
Diffusion coefficient O2
1.7e-4
m2.d-1
Picioreanu et al. (1997)
D SS
Diffusion coefficient SS
1.0e-4
m2.d-1
Hao and van Loosdrecht (2004)
7
44
A3.
Literature review on microbial characteristics of nitrifiers
45
The results of the literature review on the microbial characteristics of AOB and NOB are
46
summarized in Table A5 and Table A6, respectively.
8
47
𝐴𝑂𝐵
𝐴𝑂𝐵
𝐴𝑂𝐵
Table A5 Values of the maximum growth rate (µ𝑚𝑎𝑥
), affinity for ammonium (𝐾𝑁𝐻
), affinity for oxygen (𝐾𝑂2
) and yield (𝑌𝐴𝑂𝐵 ) for ammonium oxidizers
48
(AOB) at 30 °C and pH 7.5 found in literature. Growth type: S = suspended growth and A = attached growth. Publication type: E = experimental determination, C
49
= calibration of model based on experimental results and L = other literature values.
AO B
K NH
AO B
 m ax
d-1
g
TNH-N.m-3
AO B
K O2
g O2
.m-3
0.93
0.97
0.34
1.00
3.40
28.39
11.28
28.72
11.28
11.93
0.92
9.33
0.72
1.45
0.99
0.24
YAOB
g COD.(g N)-1
0.19
0.14
0.41
0.21
0.41
1.08
0.84
0.74
2.01
1.37
0.58
1.90
2.34
1.26
0.84
2.51
18.29
17.95
19.21
0.72
7.86
11.13
1.03
3.74
35.90
23.06
1.2
1.36
18.61
6.15
0.13
0.14
0.16
0.16
0.25
0.74
0.15
0.18
0.5
1
0.18
0.43
0.68
0.086
0.21
0.15
0.18
0.79
0.21
5.13
3.08
1.32
1.79
1.95
1.96
2.04
1
3
1.92
0.3
19.88
0.065
42.15
11.09
51.30
14.99
0.334
0.325
1.66
0.26
4.37
0.57
1.26
0.33
0.92
0.42
1.03
0.65
2.51
1.93
1.91
2.02
1.46
1.68
2.71
1.62
8.90
16.15
29.65
3.56
14.32
29.82
3.30
1.11
28.23
1.03
27.84
2.87
0.19
0.20
0.074
0.17
0.10
0.94
0.40
0.30
0.4
0.24
0.20
0.15
Growth
type
S
S
S
A
A
S
A
A
S
S
S
S
A
S
A
S
S
S
S
S
S
S
A
S
A
A
S
S
S
S
S
S
S
S
S
S
S
S
S
S
S
A
A
S
A
S
A
S
S
A
S
S
S
S
S
S
S
S
S
S
S
A
S
S
9
Publication
type
E
E
E/C
E/C
E
E
L
E/C
C
E
E
E
L
E
L
E
L
E
E
C
L
E
L
E
E
E
E
E
E
E
L
C
C
E/C
C
C
E
C
E
E
E
E
E
E
E
E
E
E
C
C
E
E
E
E
E
E
E
E
L
L
E/L
L
C
E
Publication
Blackburne et al. (2007a)
Brouwer (1995)
Carrera et al. (2004)
Carrera et al. (2004)
Carvallo et al. (2002)
Ciudad et al. (2006)
Downing and Nerenberg (2008)
Fang et al. (2009)
Gee et al. (1990)
Glover (1985)
Glover (1985)
Guisasola et al. (2005)
Hao et al. (2002)
Hellinga et al. (1999)
Hunik et al. (1994)
Hunik et al. (1992)
Jones et al. (2007)
Jubany et al. (2008)
Jubany (2007)
Kaelin et al. (2009)
Kampschreur et al. (2007)
Keen and Prosser (1987)
Koch et al. (2000)
Laanbroek and Gerards (1993)
Lackner et al. (2010)
Lackner et al. (2010)
Lochtman (1995)
Lopez-Fiuza et al. (2002)
Manser et al. (2005)
Manser et al. (2005)
Manser et al. (2006)
Moussa et al. (2005)
Moussa et al. (2005)
Munz et al. (2011a)
Munz et al. (2011b)
Munz et al. (2012)
Nowak et al. (1995)
Pambrun et al. (2006)
Poduska and Andrews (1975)
Rongsayamanont et al. (2010)
Rongsayamanont et al. (2010)
Rongsayamanont et al. (2010)
Rongsayamanont et al. (2010)
Sanchez et al. (2001)
Sanchez et al. (2003)
Sánchez et al. (2005)
Schramm et al. (1999)
Shaw et al. (2006)
Sheintuch et al. (1995)
Shi and Tao (2013)
Sliekers et al. (2005)
Sliekers et al. (2005)
Suzuki et al. (1974)
Terada et al. (2013)
Terada et al. (2013)
Vadivelu et al. (2006a)
Vadivelu et al. (2006b)
Van Hulle et al. (2007)
Wett and Rauch (2003)
Wiesmann (1994)
Wiesmann (1994)
Wik and Breitholtz (1996)
Wyffels et al. (2004)
Yoshioka et al. (1982)
50
𝑁𝑂𝐵
𝑁𝑂𝐵
Table A6 Values of the maximum growth rate (µ𝑁𝑂𝐵
𝑚𝑎𝑥 ), affinity for nitrite (𝐾𝑁𝑂2 ), affinity for oxygen (𝐾𝑂2 ) and yield (𝑌𝑁𝑂𝐵 ) for nitrite oxidizers (NOB) at 30
51
°C and pH 7.5 found in literature. Growth type: S = suspended growth and A = attached growth. Publication type: E = experimental determination, C = calibration
52
of model based on experimental results and L = other literature values.
NO B
 m ax
d-1
NO B
K NO 2
g TNO2
-N.m-3
NO B
K O2
g O2
.m-3
0.90
0.24
0.24
0.60
0.50
0.45
3.54
1
1.25
1.60
4.10
4.10
3.53
2.80
0.39
0.27
4.85
1.00
0.54
0.43
1.40
0.51
0.4
1.44
1.75
1.43
0.86
0.53
0.72
1.37
1.31
1.02
0.94
2.36
5.04
5.55
0.05
12.60
1.91
38.69
0.54
3.00
2.80
5.00
5.42
1.00
1.00
0.50
1.75
0.20
2.65
4.01
1.78
0.79
2.01
1.88
0.67
2.18
0.26
0.77
2.40
1.96
1.89
1.47
1.7
0.17
0.28
0.13
0.47
2
1
0.6
1.62
0.16
9.59
5.66
8.82
6.45
1.60
0.14
0.52
5.11
0.21
1.49
0.30
0.51
0.63
0.80
0.21
0.357
0.967
3.53
3.38
3
0.042
1.00
1.10
0.40
YNOB
Growth Publication
Publication
-1
type
type
g COD.(g N)
0.098
S
E
Blackburne et al. (2007a)
0.20
S
E
Blackburne et al. (2007b)
S
E
Blackburne et al. (2007b)
S
E/C
Carrera et al. (2004)
A
E/C
Carrera et al. (2004)
A
E
Carvallo et al. (2002)
S
E
Ciudad et al. (2006)
0.020
S
E
Copp and Murphy (1995)
0.11
A
C/L
Downing and Nerenberg (2008)
A
C
Downing and Nerenberg (2008)
0.05
A
E/C
Fang et al. (2009)
0.11
S
C
Gee et al. (1990)
S
E
Glover (1985)
S
E
Guisasola et al. (2005)
A
L
Hao et al. (2002)
0.057
A
L
Hunik et al. (1994)
S
E
Hunik et al. (1993)
0.09
S
L
Jones et al. (2007)
0.08
S
C
Jubany et al. (2005)
0.08
S
E
Jubany et al. (2008)
S
E
Jubany (2007)
S
C
Kaelin et al. (2009)
S
L
Kampschreur et al. (2007)
0.076
S
E
Keen and Prosser (1987)
0.03
A
L
Koch et al. (2000)
S
E
Laanbroek and Gerards (1993)
A
C
Lackner et al. (2010)
A
C
Lackner et al. (2010)
0.04
S
E
Lochtman (1995)
S
E
Lopez-Fiuza et al. (2002)
S
E
Manser et al. (2005)
S
E
Manser et al. (2005)
0.03
S
L
Manser et al. (2006)
S
C
Moussa et al. (2005)
S
E/C
Munz et al. (2011a)
S
E
Nowak et al. (1995)
S
C
Pambrun et al. (2006)
S
E
Poduska and Andrews (1975)
S
E
Rongsayamanont et al. (2010)
S
E
Rongsayamanont et al. (2010)
A
E
Rongsayamanont et al. (2010)
A
E
Rongsayamanont et al. (2010)
S
E
Sanchez et al. (2001)
A
E
Sanchez et al. (2003)
A
E
Schramm et al. (1999)
0.15
S
C
Sheintuch et al. (1995)
A
C
Shi and Tao (2013)
S
E
Sliekers et al. (2005)
S
E
Vadivelu et al. (2006c)
S
L
Wett and Rauch (2003)
0.057
S
E/L
Wiesmann (1994)
S
E
Wiesmann (1994)
0.04
A
L
Wik and Breitholtz (1996)
S
E
Yoshioka et al. (1982)
10
53
A4.
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