Unisense A/S N₂O Dissolved Sensing-Based Emission Calculation

Purpose

This page documents how dissolved N₂O measurements can be converted into N₂O emission rates and emission factors using the same mass-transfer logic applied in the digital twin. The aim is to ensure that measurement-based and simulation-based N₂O emissions are quantified consistently.

Overview

Dissolved N₂O was monitored in the biological reactors using liquid-phase sensors installed at representative locations in aerated and non-aerated zones. The sensor signal is interpreted as dissolved N₂O-N in the liquid phase. This is useful because it captures:

accumulation during low-stripping periods,
rapid release during aeration transitions,
peak-driven behavior that is often more relevant than daily averages alone.

A key principle of the workflow is that the same gas-liquid transfer logic is used to:

convert measured dissolved N₂O into emitted N₂O, and
compute emissions from simulated dissolved N₂O.

This is important because full-scale N₂O emissions often reflect stripping of previously accumulated dissolved N₂O, not only instantaneous biological production. The formulation below follows the project note you provided for Unisense-based sensing and emission quantification.

Dissolved N₂O sensing

The Unisense Environment A/S liquid sensor reports dissolved N₂O as mg N₂O-N L⁻¹. Numerically, this is equivalent to:

\[1 \; \mathrm{mg \; N_2O\text{-}N \; L^{-1}} = 1 \; \mathrm{g \; N_2O\text{-}N \; m^{-3}}\]

The sensor head used in the project note is described as Standard Range (SR): 0–1.5 mg N₂O-N L⁻¹. fileciteturn25file0

For documentation and implementation, it is therefore convenient to work internally with:

\[S_{N_2O} \quad [\mathrm{g \; N_2O\text{-}N \; m^{-3}}]\]

Unit conventions

The following unit conventions are recommended throughout this section:

Quantity	Symbol	Recommended unit
Dissolved N₂O concentration	\(S_{N_2O}\)	\(\mathrm{g \; N \; m^{-3}}\)
Airflow from plant signals	\(Q_A\)	\(\mathrm{m^3 \; h^{-1}}\)
Airflow in emission equations	\(Q_{A,d}\)	\(\mathrm{m^3 \; d^{-1}}\)
Aeration field area	\(A_{aer}\)	\(\mathrm{m^2}\)
Reactor volume	\(V_R\)	\(\mathrm{m^3}\)
Diffuser submergence	\(D_R\)	\(\mathrm{m}\)
Laboratory reference depth	\(D_L\)	\(\mathrm{m}\)
Process temperature	\(T_{proc}\)	\(^\circ\mathrm{C}\)
N₂O mass transfer coefficient	\(kLa_{N_2O}\)	\(\mathrm{d^{-1}}\)
Dimensionless Henry constant	\(H_{N_2O}\)	\([-]\)
Emission rate per reactor volume	\(r_{N_2O}\)	\(\mathrm{g \; N \; m^{-3} \; d^{-1}}\)
Daily emitted mass	\(E_{N_2O}\)	\(\mathrm{kg \; N \; d^{-1}}\)

When airflow is measured as \(\mathrm{m^3 \; h^{-1}}\), convert it to daily flow before using the emission-rate equations:

\[Q_{A,d} = 24 \, Q_A\]

Rationale for the emission formulation

The dissolved-N₂O signal alone is not an emission rate. A physically consistent emission estimate requires a gas-liquid transfer formulation.

For full-scale benchmarking and control evaluation, the same mass-transfer logic should be applied to both:

measured dissolved N₂O, and
simulated dissolved N₂O.

This makes measurement and simulation directly comparable within the same boundary and with the same stripping assumptions.

Mass transfer coefficient from aeration field size and airflow

Superficial gas velocity

Let the total aeration field be the reactor surface area above active diffusers where bubble release is observed:

\[A_{aer} \quad [\mathrm{m^2}]\]

The superficial gas velocity is then:

\[\nu_g = \frac{Q_A}{A_{aer}} \qquad [\mathrm{m^3 \; m^{-2} \; s^{-1}}]\]

where \(Q_A\) here is expressed in \(\mathrm{m^3 \; s^{-1}}\).

N₂O mass transfer coefficient at 20 °C

The N₂O mass transfer coefficient at \(20^\circ\mathrm{C}\) is obtained from an empirical relation using superficial gas velocity and depth scaling:

\[kLa_{N_2O,20} = 34500 \left( D_R \, D_L^{-0.49} \right) \nu_g^{0.86} \qquad [\mathrm{d^{-1}}]\]

where:

\(D_R\) is the water depth above the diffuser in the full-scale reactor,
\(D_L\) is the laboratory reference depth.

This form Unisense Environment A/S N₂O Calculation documents.

Temperature correction

The mass transfer coefficient is corrected from \(20^\circ\mathrm{C}\) to the process temperature using an Arrhenius-type factor:

\[kLa_{N_2O,T} = kLa_{N_2O,20} \; 1.024^{(T_{proc}-20)}\]

This correction is needed because gas-transfer rates depend on temperature under full-scale operation.

Henry’s law constant

Temperature-dependent Henry coefficient

The Henry coefficient is calculated from a reference value at \(T_\theta = 25^\circ\mathrm{C}\):

\[kH(T) = kH_\theta \exp\left[ \left(\frac{-\Delta solnH}{R}\right) \left( \frac{1}{T_K} - \frac{1}{T_{\theta,K}} \right) \right]\]

with:

\[T_K = T_{proc} + 273.15\]

\[T_{\theta,K} = T_\theta + 273.15\]

and the constants:

\[kH_\theta = 0.0247 \quad [\mathrm{mol \; L^{-1} \; bar^{-1}}]\]

\[\frac{-\Delta solnH}{R} = 2675 \quad [\mathrm{K}]\]

\[R = 8.314 \times 10^{-5} \quad [\mathrm{m^3 \; bar \; mol^{-1} \; K^{-1}}]\]

Dimensionless Henry constant

The dimensionless Henry constant is then:

\[H_{N_2O,T} = \frac{R \, T_K \, 10^3}{kH(T)}\]

This is the gas-liquid equilibrium coefficient used in the emission-rate equations. The factor \(10^3\) converts from liters to cubic meters.

Aerated-zone emission rate

For an aerated reactor region of volume \(V_R\), the finite-gas-residence stripping rate per reactor volume is:

\[r_{N_2O,aer} = H_{N_2O,T} \, S_{N_2O} \left[ 1 - \exp\left( - kLa_{N_2O,T} \, H_{N_2O,T} \, \frac{V_R}{Q_{A,d}} \right) \right] \frac{Q_{A,d}}{V_R}\]

where:

\(S_{N_2O}\) is dissolved N₂O concentration,
\(Q_{A,d}\) is airflow in \(\mathrm{m^3 \; d^{-1}}\),
\(V_R\) is the aerated reactor volume.

The corresponding daily emitted mass is:

\[E_{N_2O,aer} = \frac{r_{N_2O,aer} \, V_R}{1000}\]

with \(E_{N_2O,aer}\) in \(\mathrm{kg \; N \; d^{-1}}\).

Non-aerated-zone emission rate

For a non-aerated zone, gas transfer is approximated as a low-kLa surface exchange process:

\[r_{N_2O,non} = kLa_{N_2O,non} \left( S_{N_2O} - \frac{C_{N_2O,air}}{H_{N_2O,T}} \right)\]

where:

\[kLa_{N_2O,non} \approx 2.0 \quad [\mathrm{d^{-1}}]\]

and:

\[C_{N_2O,air} = 3 \times 10^{-4} \quad [\mathrm{g \; N \; m^{-3}}]\]

The corresponding daily emitted mass from a non-aerated region of volume \(V_R\) is:

\[E_{N_2O,non} = \frac{r_{N_2O,non} \, V_R}{1000}\]

Total emission over multiple zones

If the reactor or plant is split into multiple aerated and non-aerated measurement zones, then total emitted mass over a day is:

\[E_{N_2O,tot} = \sum_j E_{N_2O,aer,j} + \sum_k E_{N_2O,non,k}\]