N₂O Pathways and Gas Transfer
Purpose
This page documents how the current asm2d_n2o represents N₂O
formation, conversion, and stripping. It is intended as a scientific
reference page that connects the conceptual pathways to the actual
process-rate terms implemented in the compiled reactor code.
Scope
The current ASM2d-N₂O reactor extends ASM2d with three biological N₂O
production pathways:
NN pathway: nitrifier nitrification,
ND pathway: nitrifier denitrification,
DEN pathway: heterotrophic denitrification.
Pathway map
The implemented biological route can be read as follows:
DEN pathway
\[NO_3^- \rightarrow NO_2^- \rightarrow NO \rightarrow N_2O \rightarrow N_2\]
This route is carried by heterotrophic organisms and is split in the code
into separate rates for growth on fermentable substrate and on acetate.
NN pathway
\[NH_2OH \rightarrow NO_2^- \quad \text{coupled with} \quad NO \rightarrow N_2O\]
This is the nitrifier-nitrification route.
ND pathway
\[HNO_2 \rightarrow N_2O
\quad \text{coupled with} \quad
NH_2OH \rightarrow NO_2^-\]
This is the nitrifier-denitrification route.
DEN pathway equations
The heterotrophic denitrification chain is implemented separately for:
SF-based growth,
SA-based growth.
SF-based branch
NO₂ to NO:
\[r_{H,SF}^{NO2 \rightarrow NO}
=
\mu_H \, hH_{NO2}
\frac{KH3_{O2}}{KH3_{O2}+S_{O2}}
\frac{S_F}{K_{F3}+S_F}
\frac{S_F}{S_F+S_A}
\frac{S_{NO2}}{KH_{NO2}+S_{NO2}}
\, Monod_{NH4} \, X_H\]
NO to N₂O:
\[r_{H,SF}^{NO \rightarrow N2O}
=
\mu_H \, hH_{NO}
\frac{KH4_{O2}}{KH4_{O2}+S_{O2}}
\frac{S_F}{K_{F4}+S_F}
\frac{S_F}{S_F+S_A}
\frac{S_{NO}}{KH_{NO}+S_{NO}+S_{NO}^2/KI_{NO}}
\, Monod_{NH4} \, X_H\]
N₂O to N2:
\[r_{H,SF}^{N2O \rightarrow N2}
=
\mu_H \, hH_{N2O}
\frac{KH5_{O2}}{KH5_{O2}+S_{O2}}
\frac{S_F}{K_{F5}+S_F}
\frac{S_F}{S_F+S_A}
\frac{S_{N2O}}{KH_{N2O}+S_{N2O}}
\, Monod_{NH4} \, X_H\]
SA-based branch
NO₂ to NO:
\[r_{H,SA}^{NO2 \rightarrow NO}
=
\mu_H \, hH_{NO2}
\frac{KH3_{O2}}{KH3_{O2}+S_{O2}}
\frac{S_A}{KH_{A3}+S_A}
\frac{S_A}{S_F+S_A}
\frac{S_{NO2}}{KH_{NO2}+S_{NO2}}
\, Monod_{NH4} \, X_H\]
NO to N₂O:
\[r_{H,SA}^{NO \rightarrow N2O}
=
\mu_H \, hH_{NO}
\frac{KH4_{O2}}{KH4_{O2}+S_{O2}}
\frac{S_A}{KH_{A4}+S_A}
\frac{S_A}{S_F+S_A}
\frac{S_{NO}}{KH_{NO}+S_{NO}+S_{NO}^2/KI_{NO}}
\, Monod_{NH4} \, X_H\]
N₂O to N₂:
\[r_{H,SA}^{N2O \rightarrow N2}
=
\mu_H \, hH_{N2O}
\frac{KH5_{O2}}{KH5_{O2}+S_{O2}}
\frac{S_A}{KH_{A5}+S_A}
\frac{S_A}{S_F+S_A}
\frac{S_{N2O}}{KH_{N2O}+S_{N2O}}
\, Monod_{NH4} \, X_H\]
NN pathway equation
The nitrifier-nitrification N₂O production term is written as:
\[r_{NN,N2O}
=
q_{AOB,N2O,NN}
\frac{S_{NH2OH}}{K_{AOB,NH2OH}+S_{NH2OH}}
\frac{S_{NO}}{K_{AOB,NN,NO}+S_{NO}}
X_{AOB}\]
ND pathway equation
The nitrifier-denitrification term is written as:
\[r_{ND,N2O}
=
q_{AOB,N2O,ND}
\frac{S_{NH2OH}}{K_{AOB,NH2OH}+S_{NH2OH}}
\frac{S_{FNA}^{\,n_{KAOB,HNO2}}}
{S_{FNA}^{\,n_{KAOB,HNO2}} + K_{AOB,HNO2}^{\,n_{KAOB,HNO2}}}
f_{SO2}
X_{AOB}\]
where the oxygen dependence is:
\[f_{SO2}
=
\frac{S_{O2}}
{K_{AOB,ND,O2}
+ \left(1-2\sqrt{\frac{K_{AOB,ND,O2}}{K_{AOB,I,O2}}}\right)S_{O2}
+ \frac{S_{O2}^2}{K_{AOB,I,O2}}}\]
Gas transfer and stripping
The measured and simulated N₂O signal is shaped strongly by stripping.
General gas-liquid transfer logic
Anoxic transfer
\[\frac{dM_{i,gas}}{dt}
=
KLa_i
\left(C_{i,liq} - K_{H,i} C_{i,gas}\right)
V_{liq}\]
with a default anoxic transfer coefficient of about 2 d^-1 for the
non-aerated period.
Aerated transfer
\[\frac{dM_{i,gas}}{dt}
=
\frac{C_{i,liq}}{H_i}
\left(
1 -
\exp\left(
- \sqrt{\frac{D_i}{D_{O2}}}
\, KLa_{O2} \, H_i \, \frac{V_{liq}}{Q_{gas}}
\right)
\right)
Q_{gas}\]
References
Henze et al. (2000).
Hiatt and Grady (2008).
Pocquet et al. (2016).
Massara et al. (2018).
Lei et al. (2025).