The aim of this work is to compare the capability of two recently proposed two-pathway models for predicting nitrous oxide (N2O) production by ammonia-oxidizing bacteria (AOB) for varying ranges of dissolved oxygen (DO) and nitrite. The first model includes the electron carriers whereas the second model is based on direct coupling of electron donors and acceptors. Simulations are confronted to extensive sets of experiments (43 batches) from different studies with three different microbial systems. Despite their different mathematical structures, both models could well and similarly describe the combined effect of DO and nitrite on N2O production rate and emission factor. The model-predicted contributions for nitrifier denitrification pathway and hydroxylamine pathway also matched well with the available isotopic measurements. Based on sensitivity analysis, calibration procedures are described and discussed for facilitating the future use of those models.

INTRODUCTION

Mathematical modeling of nitrous oxide (N2O) emitted from biological wastewater treatment is one of the major challenges for minimizing greenhouse gas emissions (Ni et al. 2011, 2013a; Pan et al. 2013; Harper et al. 2015). Several studies were dedicated to the development of new models describing N2O emission during nitrification and denitrification, with the mechanisms being still under review (Ni et al. 2011, 2013b, 2014, 2015; Law et al. 2012; Harper et al. 2015; Pocquet et al. 2016). N2O production associated to nitrification by autotrophic ammonia-oxidizing bacteria (AOB) was proven to contribute significantly to overall emissions (Kampschreur et al. 2011; Wunderlin et al. 2013; Wang et al. 2014; Harper et al. 2015), and mainly through two pathways: (i) the nitrifier denitrification (ND) pathway (N2O as the terminal product of nitrite reduction) (Law et al. 2012; Wunderlin et al. 2012; Ni et al. 2013b); (ii) the incomplete hydroxylamine oxidation (NN) pathway (N2O as the side-product of NH2OH oxidation) (Wunderlin et al. 2012; Ni et al. 2013b; Pocquet et al. 2016). Previous work showed that single-pathway models, either based on ND or NN pathway, cannot reproduce all the N2O production data including both short-term and long-term process monitoring (Ni et al. 2013b; Spérandio et al. 2014; Peng et al. 2015a). Those conclusions indicated that both pathways are involved and a unified model was urgently required to incorporate both pathways in order to increase the genericity of the N2O production model (Ni et al. 2013b; Ni & Yuan 2015; Mannina et al. 2016; Pocquet et al. 2016).

The first innovative two-pathway model (marked Model I) was proposed by Ni et al. (2014) linking all biochemical oxidation and reduction processes through introducing a pool of electron carriers as new model components. This model has been able to describe the individual effect of dissolved oxygen (DO) on N2O productions, and the simulated contribution of each pathway was consistent with the isotope measurements (Peng et al. 2014). In addition, considering higher NO2 levels (from 3 to 50 mg N/L), the model was also calibrated to experiments with the combined effect of DO and nitrite (NO2), and was capable of reproducing the batch experiment results (Peng et al. 2015b). However, further calibration and validation of this two-pathway model based on more varied experimental data and long-term monitoring are now necessary.

In parallel with a different model structure, another two-pathway model (marked Model II) including five successive enzymatic reactions was developed by Pocquet et al. (2016). Unlike Model I, all the consumptions of electron donor and acceptor are connected without considering electron carriers. This model was calibrated and was shown to well describe not only the data from batch experiments with various accumulated levels of nitrite, especially the trends observed for the NO/N2O ratio as well as N2O emission factors (N2OEF), but also the long-term N2O emission data from an SBR process with variations of nitrite, pH and DO (Pocquet et al. 2016). However, intrinsic assumptions due to the case study contained in this model should be further extended and more calibration and validation efforts from varying experimental observations are also required (Mannina et al. 2016).

Side-by-side comparison of N2O modeling by AOB is an effective method to examine both the capability and the applicability of models (Ni et al. 2013b; Spérandio et al. 2014; Peng et al. 2015a; Pocquet et al. 2016). Up to now, several studies were focused on the N2O production model comparison work (Guo & Vanrolleghem 2013; Mampaey et al. 2013; Peng et al. 2015a; Mannina et al. 2016; Pocquet et al. 2016). Ni et al. (2013b) compared the abilities of four different single-pathway models to predict N2O dynamics in three case studies, and results showed that each case, but not all, could be described by one single-pathway model. Spérandio et al. (2016) compared five activated sludge models describing N2O production by AOB with four different long-term process data sets and the satisfactory calibration was obtained but none of the models was able to describe all the N2O data obtained in the different systems with a similar parameter set. Peng et al. (2015a) compared two single-pathway models with Model I and identified the practical application conditions for each model in terms of DO and NO2. Furthermore, the comparison between Model II with other existing models was recently studied by Pocquet et al. (2016) which showed that NN pathway model was capable of describing the NO emissions but did not match the N2O emission. However, the comparison between the two newly developed two-pathway models has not been done until now.

The first purpose of this study was to test and then compare the capabilities of the recently developed two-pathway models in describing the combined effect of DO and nitrite on the N2O production by AOB from three different case studies (Peng et al. 2014, 2015b; Pocquet et al. 2016). The second is to provide insights into the applicability and the future calibration of these two-pathway models of N2O production by AOB.

MATERIALS AND METHODS

Experimental data

As shown in Table 1, N2O measurements (43 data sets in total) from three series of kinetic experiments with different types of microbial culture containing AOB were used for model evaluation. Conditions were chosen for testing the predictive abilities of two models respecting the combined effect of DO and NO2. Different influent feeding modes were used: continuous step-feeding for Cases 1 and 2 and batch feeding for Case 3 (Peng et al. 2014, 2015b; Pocquet et al. 2016).

Table 1

Summary of the experimental data and operating conditions for three study cases

  Case 1: Batch DO and NO2 effect Case 2: Batch DO effect Case 3: Batch NO2 effect 
Data 30 (N2ORsp7 (N2ORsp) and SP measurements 6 (N2OEF
DO (mg O2/L) Five levels: from 0.35 to 3.5 Seven levels: from 0.2 to 3.0 Similar level, dynamic Average at 4.5 
NO2 (mg N/L) Six levels: from 3.0 to 50 Low levels: from 1 to 1.5 Six levels: from 20 to123 
Feeding mode Continuous feeding Continuous feeding Batch feeding 
NH4+(mg N/L) Around 20 Around 18 Initial of 10.5 
pH 7.5 7.5 8.5 ± 0.1 
Temperature (°C) 22 22 28 
Biomass Ia: Enriched AOB + NOB Ia: Enriched AOB + NOB Ib: Enriched AOB 
II: Another enriched NOB IIc:OHO 
  Case 1: Batch DO and NO2 effect Case 2: Batch DO effect Case 3: Batch NO2 effect 
Data 30 (N2ORsp7 (N2ORsp) and SP measurements 6 (N2OEF
DO (mg O2/L) Five levels: from 0.35 to 3.5 Seven levels: from 0.2 to 3.0 Similar level, dynamic Average at 4.5 
NO2 (mg N/L) Six levels: from 3.0 to 50 Low levels: from 1 to 1.5 Six levels: from 20 to123 
Feeding mode Continuous feeding Continuous feeding Batch feeding 
NH4+(mg N/L) Around 20 Around 18 Initial of 10.5 
pH 7.5 7.5 8.5 ± 0.1 
Temperature (°C) 22 22 28 
Biomass Ia: Enriched AOB + NOB Ia: Enriched AOB + NOB Ib: Enriched AOB 
II: Another enriched NOB IIc:OHO 

aWith NOB activity.

bWithout NOB activity.

cOrdinary heterotrophic organism.

DO in Cases 1 and 2 was controlled at a desired level by a gas mixture of N2 and air with a constant total flow rate (Peng et al. 2014, 2015b). Comparatively, for Case 3, air flow rate was constant and DO showed a dynamic profile similar for all the tests (Figure S1, available with the online version of this paper). Average DO (4.5 mg O2/L) is reported but the real dynamic DO data were used as the input for simulation. The NO2 concentrations remained constant for Case 1 and Case 2, but accumulated gradually during the batch test for Case 3. All the details of the experimental data and operating conditions could be found in the corresponding articles (Peng et al. 2014, 2015b; Pocquet et al. 2016). For Cases 1 and 2, the total gas flow rate was controlled constantly at 0.5 L/min. For each change in altering DO concentration, the change in the air flow rate was compensated for by an equivalent opposite change in the N2 flow rate. Consequently, the effect of the change in DO on N2O emission was only due to a biological effect rather than a modification of the N2O stripping.

Biomass specific ammonia oxidation rate (AORsp), biomass specific N2O production rate (N2ORsp) and the ratio between N2O nitrogen emitted and the ammonium nitrogen converted (N2O emission factor or N2OEF) were determined for each test. N2O emission rate (N2OR) was calculated by multiplying the measured gas phase N2O concentration and the known gas flow rate. For Cases 1 and 2, as continuous feeding was maintained during several hours, the emission rate stabilized and it was considered that the emission rate was equal to the formation rate. The average rate over each testing period (with constant conditions applied) was calculated by averaging the measured N2OR over the period (relatively constant in all cases). N2ORsp (mgN2O-N/hr/g VSS) and AORsp (mgNH4+-N/hr/g VSS) were calculated by normalizing the N2OR and AOR data with the MLVSS concentration (VSS: volatile suspended solids; MLVSS: mixed liquor volatile suspended solids). The N2O emission factor was calculated based on the ratio between the total N2O emitted (mg N2O-N) and the total NH4+ converted (mg NH4+-N) during each test. Comparatively, for Case 3, as batch feeding was performed, a dynamic emission of N2O was obtained. The N2O emission rate was then integrated in order to estimate the total N2O emitted (mg N2O-N) and calculate the N2O emission factor.

Mathematical models

The kinetic and stoichiometric matrices for the two two-pathway models describing the N2O productions are provided in the appendix (Tables S1 and S2, available with the online version of this paper) and detailed in published articles (Ni et al. 2014; Pocquet et al. 2016).

Both Model I and Model II considered the incorporation of NN and ND pathways and the simplification of ND by reducing the two-step nitrite reduction into onestep for avoiding the NO loop (Table 2). The main differences between those two models are the introduction of the electron carrier and the oxygen reduction as a separate process in Model I, while Model II does not. A recent study (Guo & Vanrolleghem 2013) showed that the role of DO is still a controversial aspect regarding to N2O modelling. For this consideration, in Model II inhibition of ND by oxygen was introduced into the ND pathway with a modified Haldane term which decreases that process under high DO level, but also limits it at a very low level. pH influence was included in Model II but not in Model I.

Table 2

Major differences between Model I and Model II

  Model I Model II 
One-step simplification for ND pathway Yes Yes 
Intracellular electron carrier (reduced and oxidized form) Yes No 
True substrate for NH4+ oxidation NH4+ NH3 
True substrate for NO2 reduction NO2 HNO2 
pH dependency No Yes 
AOB growth No Yes 
Effect of DO on the ND pathway Electron competition Inhibition 
  Model I Model II 
One-step simplification for ND pathway Yes Yes 
Intracellular electron carrier (reduced and oxidized form) Yes No 
True substrate for NH4+ oxidation NH4+ NH3 
True substrate for NO2 reduction NO2 HNO2 
pH dependency No Yes 
AOB growth No Yes 
Effect of DO on the ND pathway Electron competition Inhibition 

Model calibration

Models were calibrated with three data series (Table 1) obtained from three different cultures (Ni et al. 2014; Pocquet et al. 2016). Model was initialized by inputting all the parameter values obtained originally from one specific data series (Ni et al. 2014; Pocquet et al. 2016). Simulation results were obtained or calculated, sensitivity analysis was then performed (based on an absolute/absolute deviation function) followed by a systematic analysis of the differences between the simulations and calibration targets (based on the root mean square deviation). Subsequently, a limited number of key parameters were chosen according to the sensitivity analysis and expert human knowledge in order to find the best-fitted values by continuing multiple calibration steps. Before prediction of N2O emissions, the ammonium uptake rate and the profile of NH4+, DO and nitrite should be properly captured. Hence, the calibration was performed in two steps: first some parameters were calibrated to predict accurately the ammonium uptake rate and oxygen uptake rate (as for conventional nitrification models): , and for Model I; and , , for Model II. Then, regarding the N2O prediction specifically, the most important parameters to be adapted were those related to the maximum production rate of each pathway: , for Model I, and , for Model II. Additionally, the affinity constant for nitrite or free nitrous acid (Model I or II), the oxygen inhibition constant (Model II), the affinity constants for Mred,3 and Mred,4 and for Mox (Model I) were adapted, if necessary.

Parameter values were estimated by minimizing the root mean square deviation between measured data and model predictions for all three cases. All simulations were performed with AQUASIM software.

RESULTS

Case 1: combined DO and NO2 effect on culture 1

Figures 13 show all the simulation results of Case 1 with Model I and Model II including the N2Osp (specific N2O production rate) and the contributions of ND and NN pathways.
Figure 1

Experimental and simulated N2Osp in function of DO and NO2 concentrations in Case 1 (Peng et al. 2015b): the value of mark from the left figures represent the values for DO, for the right figures NO2.

Figure 1

Experimental and simulated N2Osp in function of DO and NO2 concentrations in Case 1 (Peng et al. 2015b): the value of mark from the left figures represent the values for DO, for the right figures NO2.

Figure 2

Comparison of simulated N2Osp between Model I and Model II against the experimental data in Case 1.

Figure 2

Comparison of simulated N2Osp between Model I and Model II against the experimental data in Case 1.

Figure 3

Model-predicted contributions of ND and NN pathways with Model I and Model II under various DO and NO2 concentrations in Case 1.

Figure 3

Model-predicted contributions of ND and NN pathways with Model I and Model II under various DO and NO2 concentrations in Case 1.

Prediction of the N2Osp

As shown in Figures 1 and 2, both Model I and Model II are able to describe the tendency of experimental N2Osp concerning the effect of NO2 and DO as well as the values. Simulation results showed that under each investigated DO level, N2Osp increased as the NO2 increased from 3 to 50 mg N/L, while for each NO2 level, the maximum N2Osp occurred at DO of 0.85 mg O2/L (Figure 1). Even with a small difference, the simulated N2Osp of two models matched the experimental data very well (Figure 2).

Prediction of the relative contributions

The model-predicted relative (Figure 3) contributions of ND and NN pathways by Model I and Model II were also compared in terms of NO2 and DO, respectively.

On the one hand, regarding the effect of NO2, both models predict similarly that the contribution of the ND pathway increases with nitrite (3 to 10 mg N/L) under all the DO levels and remained almost constant after further increase of nitrite, accompanied by the corresponding decrease or constancy for the NN pathway. On the other hand, as DO increases, the same decreasing trend of the predicted ND contribution with two models was observed. This decrease was mostly when DO was higher than 0.85 mg O2/L for Model II, while under the entire DO levels (0.35 to 3.5 mg O2/L) for Model I.

As to the predictions of the ND pathway by two models, the result from Model I was slightly lower than that in Model II, which is even stronger at higher DO levels. Simulations with Model II showed that the ND pathway dominated over NN during the whole DO and nitrite levels, which is not the case for Model I where the contribution of NN pathway was higher than 50% under the DO of 3.5 mg O2/L and NO2 of 3 and 5 mg N/L.

In order to see whether the NN pathway could be the dominant pathway over ND with the further decrease of the NO2 concentration by Model II, additional simulations were performed under three even lower NO2 levels (0.1, 0.5 and 1.5 mg N/L) and the highest DO of 3.5 mg O2/L. The simulation results (Figure 3) showed that, with the continued decreasing of NO2 concentration, the contribution of the ND pathway decreased and reached almost half at NO2 of 0.5 mg N/L and declined to no more than one fifth, accompanied with the NN pathway becoming the major contributor.

Figures S2–S4 (available with the online version of this paper) show other simulation results in terms of N2OEF and an example of the dynamic for the batch test with Model II.

In summary, for the investigated DO (from 0.35 to 3.5 mg O2/L) and NO2 (from 3 to 50 mg N/L), both Model I and Model II could well describe all the experimental N2Osp. Similar tendency of the predicted contributions for the ND and NN pathways was obtained by two models but contributions of ND predicted with Model I are lower than that obtained with Model II. By decreasing NO2 level, further predictions by Model II showed the contribution of the NN pathway will gradually increase and exceed the ND pathway.

Case 2: DO effect at low nitrite level with culture 2

Figures 46 show all the simulation results of Case 2 with Model I and Model II in terms of N2Osp, contributions of ND and NN pathway and N2OEF.
Figure 4

Comparison of experimental and simulated N2Osp with Model I and Model II in Case 2 (Peng et al. 2014).

Figure 4

Comparison of experimental and simulated N2Osp with Model I and Model II in Case 2 (Peng et al. 2014).

Figure 5

Comparison of the model-predicted contributions between Model I and Model II in Case 2. SP: site-specific measurements.

Figure 5

Comparison of the model-predicted contributions between Model I and Model II in Case 2. SP: site-specific measurements.

Figure 6

Comparison of simulated and experimental data for AOR and N2OEF between Model I and Model II in Case 2.

Figure 6

Comparison of simulated and experimental data for AOR and N2OEF between Model I and Model II in Case 2.

Prediction of the N2Osp

As shown in Figure 4, both models enable to capture the tendency and value of experimentally observed N2Osp very well during the investigated DO range from 0 to 3 mg O2/L. Specifically, both model predictions showed that N2Osp increased as the DO increased from 0 to 1 mg O2/L and remained almost constant for further increase.

Meanwhile, the predicted contributions for the ND and NN pathways by two models are also in agreement with that obtained by the isotopic measurements (Figure 5), both of which showed that the contribution of ND pathway decreases when DO increases from 0.2 to 3 mg O2/L, and that for NN increases accordingly.

Prediction of the relative contributions

Prediction of the AOR and N2OEF

For further analysis, both simulated AOR and calculated N2OEF (emission factor estimated by averaging simulated N2Osp with simulated AOR) against the experimental data are displayed in Figure 6.

In terms of AOR, the simulation results of the AORs matched well with the experimentally observed AOR, except for lower rates at DO equal or lower than 0.5 mg O2/L. Regarding the N2OEF, both models showed similar predictions and described the decrease tendency of the N2OEF during the whole DO levels from 0.2 to 3 mg O2/L, except for the lowest DO level (0.2 mg O2/L), both model simulations were under-estimated over the experimental data. But this was related to the difficulty for predicting low DO effect on AOR, the N2O production rate being correctly predicted.

To summarize, both Model I and Model II could well describe the experimentally observed N2Osp during this investigated range for DO (from 0.2 to 3 mg O2/L) and nitrite (lower than 2 mg N/L). Both model predictions and SP measurements showed the similar contributions for both ND and the NN pathways. The simulated AOR and N2OEF matched quite well with the experimental data, but N2OEF was underestimated when DO was lower than 0.5 mg O2/L.

Case 3: nitrite effect in culture 3

Figure 7 shows the simulation results of N2OEF in Case 3 with Model I and Model II in terms of nitrite and HNO2.
Figure 7

Comparison of experimental and simulated N2OEF with Model I and Model II in function of NO2 and HNO2, respectively, in Case 3.

Figure 7

Comparison of experimental and simulated N2OEF with Model I and Model II in function of NO2 and HNO2, respectively, in Case 3.

Prediction of the N2OEF

As shown in Figure 7, the two two-pathway models were both able to reproduce the experimental N2OEF in this case study. For the relation with NO2, the total N2OEF increased with the increase of average NO2 concentration almost linearly and the models could generally describe the experimental data. From the perspective of HNO2, which considers the effect of pH, the simulation results are even closer to the experimental data compared with that obtained by the nitrite with a slight advantage of Model II, which takes into account the pH effect by considering free ammonia (FA) and free nitrous acid (FNA) as substrates in kinetics. However, only the small pH difference (≤0.2) was observed among those experiments.

To summarize, both Model I and Model II could well describe the experimentally observed N2OEF in this case during the investigated NO2 concentration (20–123 mg N/L). A better simulation could be obtained in consideration of the HNO2 instead of NO2 with Model II.

DISCUSSION

In this work, we selected three different cases including 43 kinetic experiments considering a large range for both DO and nitrite concentrations (Table 1), and the two models were compared for the first time based on their capabilities to predict the observed N2O data including both N2Osp and N2OEF (Ni et al. 2014; Peng et al. 2014, 2015b; Pocquet et al. 2016). Overall, the two different two-pathway models with different mathematical structures could be calibrated to describe similarly the experimental N2O emissions collected in the different experimental systems.

Peng et al. (2015b) investigated the combined effect of DO (0.35 to 3.5 mg O2/L) and NO2 (3 to 50 mg N/L) on N2O production by AOB as well as the corresponding mechanisms and the experimental data were well captured with Model I at all conditions (Case 1). For Model II, by adjusting only three parameters (, , ) compared with the original model (Pocquet et al. 2016) (Tables S2 and S4, available with the online version of this paper), the model was also able to well describe the data. As to the individual effect of DO and nitrite on N2O emissions for Case 2 (Peng et al. 2014) and Case 3 (Pocquet et al. 2016), both models also showed a good prediction of the N2Osp (Case 2: Figure 4) and N2OEF (Case 3: Figure 7) as well as the predicted contributions of the ND and NN pathways (Case 2, Figure 5) which were in accordance with the isotopic measurements. For the effect of DO on the N2O emission factor, both the two different model structures allowed the prediction of the observed tendencies. It should be noticed that both models can describe a contradictory effect of oxygen depending on the preponderant pathway. At low nitrite, the N2O emission can increase with DO due to the importance of the NN pathway, whereas at high nitrite level, the N2O emission decreases with DO due to the preponderance of the ND pathway (Figure 1). In both models, the DO increase limits the ND pathway due to either electron acceptor competition (Model I) or inhibition (Model II), while it favors the NN pathway contribution. This is in accordance with the studies based on isotopes signature measurements (Peng et al. 2014).

Concerning the predicted contribution of each pathway, the same variations and tendencies were obtained but quantitative contribution of each pathway can slightly differ. For the contributions of each pathway, considering the effect of NO2- at higher levels (Case 1: from 3 to 50 mg N/L) and lower levels (Case 2: lower than 2 mg N/L), predictions by both models showed the same stimulating effect of NO2 on the contribution of the ND pathway (NN: inhibiting) but with slightly different values (Case 1: Figure 3 and Case 2: Figure 5). The same result was also obtained by a further simulation with Model II considering even lower NO2 (0.1, 0.5 and 1.5 mg N/L) which showed that the NN pathway could become the dominant pathway with enough lower NO2 level (Figure 3 and Table 3). This positive correlation between the ND contribution and NO2 concentration is also consistent with the simulation results obtained by Peng et al. (2015a). It should be noted that the similar observation found by Wunderlin et al. (2013) showed the same contribution of the ND pathway around 75% to 100%, which is closer to the results obtained by Model II than in Model I. Therefore, the difference between the simulated contributions of two pathways by two models should be further confirmed with diverse situations and new isotopic measurements.

Table 3

Comparison of simulation results with Model I and Model II

  Model I Model II 
Predict the contradictory effect of DO depending on nitrite level and the preponderant pathway Yes Yes 
Predict the stimulating effect of NO2 on the ND pathway contribution Yes Yes 
Predict the stimulating effect of DO on the NN pathway contribution (validated by isotope signature) Yes Yes 
Total number of parameters 19 12 (+2 for growth) 
Number of parameters to be calibrated for the different cultures 5–10 3–8 
Predict the stimulating effect of pH decrease on ND pathway (through HNO2No Yes 
  Model I Model II 
Predict the contradictory effect of DO depending on nitrite level and the preponderant pathway Yes Yes 
Predict the stimulating effect of NO2 on the ND pathway contribution Yes Yes 
Predict the stimulating effect of DO on the NN pathway contribution (validated by isotope signature) Yes Yes 
Total number of parameters 19 12 (+2 for growth) 
Number of parameters to be calibrated for the different cultures 5–10 3–8 
Predict the stimulating effect of pH decrease on ND pathway (through HNO2No Yes 

Regarding the choice of considering HNO2 in Model II compared with NO2 in Model I, the Model II could predict a slightly better result of N2OEF than in Model I with culture 3 for which slight pH change were observed (Figure 7). One possible explanation is that Model II considers as the true substrate HNO2 instead of nitrite in Model I. As a consequence Model II predicts a stimulating effect of pH decrease on the ND pathway. Law et al. (2011) found pH can influence both the N2Osp and AOR but future work will be needed to confirm how the pH should be taken into account. This could be achieved by combining pH models with Model II and confrontation with experiments in an extended range of pH.

Regarding the calibration (see parameter values on Tables S2–S4, available with the online version of this paper) the same set of parameters was used for each culture but some parameters should be calibrated depending on the culture case. Small parameter modifications (only three parameters) were necessary with the Model II from the Case 3 (nitrite variation) to Case 1 (nitrite and DO variation), but higher effort (eight parameters) was needed for Case 2 (DO variation at low nitrite level). In comparison five parameters were modified with Model I for Case 1 and 2, but higher effort was necessary for Case 3 (10 parameters). Hence the effort was slightly higher with Model I but not that significant. On the one hand, Model I seems easier to fit to the data obtained at low nitrite with different DO, as in that condition the ND contribution was initially overestimated by Model II and the total production was practically poorly inhibited by DO. By considering the competition between nitrite and oxygen for electron career the Model I probably describe in a more realistic mechanism than inhibition. On the other hand the calibration of Model I in Case 3 with dynamic variation of ammonium and nitrite was quite complicated due to important modifications needed on affinity constant on species which are not measurable (, , ). In contrast for Model II, all parameters are related to variables which can be directly measured or calculated. Finally Table 3 gives an overview of the models comparison. Electron transport included in Model I increases the model complexity but makes it closer to the real metabolic processes, leading to a perfect model for a better understanding. This could be also useful in practice if the model would describe more accurately some observations or if the calibration effort would be reduced. However our comparison did not show a real advantage of Model I on the used data series as the Model II was also able to describe similarly the observations without needing more calibration effort. But this should not be considered as a definitive conclusion. For instance it should be remarked that suspended biomass only were simulated in this work, and a future comparison for biofilm systems would be also necessary (Sabba et al. 2015). Finally, further work should be devoted to obtain parameters with different experiments and cultures, which should be compared and synthetized, aiming to form a consistent pattern for the implementation in the improvement/simplification of the two-pathway models.

CONCLUSION

This study has validated the two different two-pathway models with extensive sets of experiments under different DO and/or nitrite conditions with different cultures. Despite their different mathematical structures, both models were able to describe accurately the synergetic effect of DO and nitrite on the N2O emissions. The results did not demonstrate a strong difference in their application ranges (e.g. higher NO2 or lower NO2). The Model I describes in detail the metabolic electron transport and is more appropriate for understanding, whereas the Model II is simpler but sufficiently accurate for capturing the combined effect of nitrite and oxygen on N2O emissions. Work is now recommended with data from full scale systems in which the medium complexity and the combination with other biochemical reactions could reveal a stronger difference between these two models.

ACKNOWLEDGEMENTS

This work was supported by the French National Research Agency (ANR) and the China Scholarship Council (CSC).

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Supplementary data