Mainstream short-cut N removal modelling: current status and perspectives

Conventional nitrogen (N) removal by nitrification/denitrification is an energy and resource-intensive process: nitrification requires oxygen and alkalinity, and denitrification requires carbon as either influent carbon or supplemental carbon. Compared to nitrification-denitrification, the application of short-cut N removal processes in mainstream wastewater treatment has significant potential to save energy (oxygen demand), resources (carbon demand), and to pursue energy independence for water resource recovery facilities (WRRF). For that reason, short-cut N removal (deammonification and nitrite shunt) has received considerable attention over the last decade from both academia and practice.

Deammonification short-cuts the conventional N removal pathway by directly converting ammonium (NH₄⁺-N) to nitrogen gas (N₂) via nitrite (NO₂⁻-N). The process relies on preventing the oxidation of nitrite to nitrate (NO₃⁻-N) and making nitrite available for anammox (Zhang et al. 2019). The availability of nitrite can be achieved through two pathways: partial nitritation-anammox (PNA) or partial denitrification-anammox (PdNA) (Figure 1). In practice, PNA and PdNA can be combined in full-scale applications for desired N removal performance.

The efficiency of deammonification has been proven for ammonium-rich wastewater such as treatment of side-streams resulting from dewatering of digested sludge, leachate, or industrial wastewaters (van Dongen et al. 2001; Wyffels et al. 2004; Volcke et al. 2005; Wett 2007; Ganigué et al. 2009; Lackner et al. 2014). Short-cut N removal can also be combined with a pretreatment process for carbon diversion in mainstream applications such as high-rate activated sludge (HRAS), chemically enhanced primary treatment and energy recovery in the side-stream, or even direct anaerobic sewage treatment (Kartal et al. 2010; Leal et al. 2016). This provides WRRFs with an excellent opportunity to move to energy-neutral or energy-positive operations (Jetten et al. 1997; Siegrist et al. 2008). However, full-scale applications are currently limited to side-stream treatment and only a few successful mainstream applications are reported so far (O'Shaughnessy 2016; Cao et al. 2017; Klaus et al. 2020).

PNA is a fully autotrophic process that consists of partial oxidation of NH₄⁺-N to NO₂⁻-N (nitritation) and the anammox process in which NH₄⁺-N is oxidized using NO₂⁻-N as an electron acceptor under anaerobic conditions without the need for carbon (Kartal et al. 2010) (Figure 1). Thus, the process requires the cooperation of ammonia-oxidizing bacteria (AOB) and anammox bacteria (AnAOB), and out-selection of nitrite-oxidizing bacteria (NOB). The successful application can reduce the required oxygen input by 60%, eliminate the carbon source demand and reduce the sludge production by 90% in comparison to conventional N-removal (Morales et al. 2015; Miao et al. 2016).

Partial nitritation-denitritation (nitrite-shunt) relies on partial nitritation of NH₄⁺-N into NO₂⁻-N as the first step, then denitritation of NO₂⁻-N into N₂ as the second step by heterotrophic bacteria (HB). Thus, it consumes 25% less oxygen than complete nitrification and reduces the organic carbon demand by 40% compared to the full denitrification (Daigger 2014). The process requires both out-selection of NOB and also carbon availability for denitritation. The nitrite-shunt process has been successfully implemented in side-stream treatment (e.g. SHARON process (Mulder et al. 2001)) and there is an interest to implement it in mainstream treatment in a single reactor (Jimenez et al. 2020). However, it is not commonly applied due to the lack of complete understanding of the underlying mechanisms for NOB out-selection and carbon availability for denitritation under these conditions.

During PdNA a portion of the influent NH₄⁺-N is aerobically oxidized to NO₃⁻-N. The NO₃⁻-N is subsequently reduced to NO₂⁻-N via heterotrophic denitratation and the resulting mix of residual NH₄⁺-N and NO₂⁻-N serves as substrate for the anammox process (Le et al. 2019a; Lu et al. 2021b) (Figure 1). This process does not require NOB out-selection and needs a carbon donor to achieve partial denitrification (Zhang et al. 2019). The PdNA process consumes slightly more resources (energy for aeration and carbon) than the PNA route; however, the nitrite generating pathway is understood compared to the NOB out-selection pathway (B. Ma et al. 2017; Lu et al. 2021a). Theoretically, 50% of aeration needs and 80% of carbon demand can be saved and sludge production can be reduced by 60% compared to conventional N removal (Z. Zhang et al. 2020). To overcome the external carbon need, recent research efforts aim to take advantage of the slowly biodegradable organics in wastewater or to produce soluble microbial products through fermentation (Ji et al. 2020; Liu et al. 2022). Also, simultaneous nitrogen and phosphorus removal with lower carbon and oxygen demand can be accomplished by combining endogenous partial denitrification with denitrifying phosphorus removal (X. Wang et al. 2019).

Current mainstream deammonification implementations include a variety of processes in laboratory and pilot scales including suspended, attached growth, or hybrid systems in single-stage or 2-stage reactors (e.g. Hoekstra et al. 2018; Klaus 2019; Le et al. 2019a; Huang et al. 2020). Due to the slow growth rate of anammox bacteria (Valverde Pérez et al. 2016; Lotti et al. 2015), an anammox retention mechanism is required to allow for adequate solids retention time (SRT). In a single-stage process, all biokinetic reactions occur in one basin which decreases both the investment and the operational costs (Pérez et al. 2014). Biofilm processes (Lotti et al. 2015; Gustavsson et al. 2020) or hybrid systems that combine suspended sludge with the biofilm systems such as integrated fixed-film activated sludge system (IFAS) (Cao et al. 2017) are used in these single-stage systems (W.-J. Ma et al. 2020) to retain AnAOB. In 2-stage systems, partial nitritation or full-nitrification (aerobic environment) and the deammonification processes (anoxic environment) occur in separate basins. Suspended or biofilm processes can be used in the aerated basin and biofilm-based processes may be used in the anammox basin (Regmi et al. 2014; Pérez et al. 2015).

Despite all the efforts, the mainstream application is still facing challenges due to NOB out-selection, wastewater characteristics, temperature and meeting the strict effluent criteria under dynamic loads (Cao et al. 2017). The competition for substrates and growth space between the different functional species is another major application challenge. High influent C/N ratios in the raw wastewater promote the growth of HB in the system, thus hampering deammonification under limiting oxygen concentrations (Gao & Xiang 2021). Also, lower ammonium concentrations and temperature variations make the stable out-selection of NOB very difficult in the PNA systems and lead to competition over oxygen by AOB, NOB and HB (M. Zhang et al. 2020).

Strategies are being developed to accelerate successful deammonification process implementation. Microorganisms involved in the short-cut N-removal processes are sensitive to operational and environmental conditions such as pH, dissolved oxygen (DO) level, temperature, SRT and the presence of inhibitors. Several control strategies have been adopted such as low or high DO operation, aerobic SRT, real-time aeration or oxidation-reduction potential control to take advantage of the growth characteristics and the kinetics difference between the microorganisms (Liu et al. 2020; Gao & Xiang 2021). However, the shift and adaptation of microbial communities’ growth characteristics to mainstream conditions remain a challenge (Agrawal et al. 2018; Gao & Xiang 2021). In addition, due to high nitrite accumulation and ammonia conversion rates, the short-cut processes inevitably generate nitrous oxide (N₂O) as a by-product which is one of the most significant greenhouse gases (Castro-Barros et al. 2016; Li et al. 2020) (Figure 1). Further research is needed under mainstream conditions to achieve long-term process stability (e.g. varying loads or temperatures) and to understand the role of influent characteristics, varying substrates, intrinsic kinetics of the microorganisms involved and competition between them.

Mathematical models and model-based control strategies are under development to overcome implementation challenges and to deal with the complexity of mainstream deammonification (Agrawal et al. 2018). Through modelling, it is possible to identify the proper conditions for microbial competition under different operational and environmental conditions and to optimize the processes and implement deammonification successfully (Pérez et al. 2014; Liu et al. 2017; Shourjeh et al. 2021). However, the mechanistic models that are currently being used for the modelling are not sufficiently accurate to model short-cut N removal processes and require specific attention. For example, while the models include the key microbial groups, they do not consider the individual species which are crucial to reflect the competition among them and predict a community shift (e.g. NOB community shift (Liu & Wang 2013)). Also, different process configurations such as biofilm systems require specific sub-models such as the mass transport between the bulk liquid and the microorganisms inside the biofilm (Arnaldos et al. 2015; Baeten et al. 2019). Thus, the pilot and full-scale applications reported provide invaluable information for models development and to overcome bottlenecks while modelling efforts accelerate the success of practical applications.

The main focus of this paper is pointing out future needs and perspectives to facilitate the technology transfer between the model applications in research studies and accelerate the successful application of mainstream deammonification. The objectives of the presented review article are: (i) to illustrate the current practice in modelling of short-cut N removal processes, (ii) to reveal the challenges in modelling applications with examples, and (iii) to determine the immediate needs and the potential of more advanced modelling approaches and perspectives in the near future.

Modelling plays an essential role in improving process understanding and determining the optimal operating conditions and control strategies for applying short-cut nitrogen removal processes. There has been a concerted effort by academics and practitioners to model mainstream short-cut nitrogen removal recently, but these efforts have not yet resulted in consensus on process models and model parameter values that are transferable to practice. The activated sludge models (ASMs) developed by the IWA task group (Henze et al. 2006) are generally being used as default mathematical models for carbon and nutrient removal in wastewater treatment and are available in commercial software packages. For modelling short-cut nitrogen removal processes, ASMs have been used as well with extensions and modifications such as 2-step nitrification, 4-step denitrification, N₂O emission pathways and inhibition mechanisms. Despite its limitations, modelling can serve as a useful tool to improve process knowledge, screen technologies, and develop preliminary designs in a short-cut process. In this section, the required model selection mechanisms and current modelling perspectives for mainstream short-cut N removal processes are given.

Out-selection of NOB is crucial, especially for PNA or nitrite-shunt systems, and is widely recognized as one of the major challenges to mainstream application. The out-selection of NOB has been proven to be quite effective in warm nitrogen-rich wastewater streams (Lackner et al. 2014); due to the effect of elevated temperatures on growth rates for AOB and NOB (Hellinga et al. 1999), and also the high free ammonia (FA) and free nitrous acid (FNA) concentrations in side-stream liquors which inhibits the growth of NOB (Lackner & Agrawal 2015). However, FA inhibition is not possible in mainstream treatment due to the lower influent ammonium concentration (Cao et al. 2017). There are also reports of NOB out-selection achieved through side-stream generated FNA exposure (D. Wang et al. 2016) and alternating the sludge treatment strategy between FA and FNA can result in a stable nitrite-shunt with nitrite accumulation above 95% in the mainstream (Duan et al. 2019a).

The operating conditions to favour AOB and wash out NOB are thoroughly investigated in literature based on DO, pH, temperature and inhibitors. The intrinsic kinetics of these two groups of microorganisms including maximum growth rate and substrate half-saturations are crucial (Liu et al. 2020). DO affects the diversity and kinetics significantly, thus DO control to manipulate the competition for oxygen between AOB and NOB is one of the main strategies in mainstream conditions (Pérez et al. 2014; Jimenez et al. 2020). The oxygen half-saturation constant for AOB is generally accepted to be lower than for NOB which creates a disadvantage for NOB to compete for oxygen at low concentrations (Sin et al. 2008; Cao et al. 2017). On the other hand, the predominance of Nitrobacter or Nitrospira, which are the two main genera of NOB, affect the performance of NOB out-selection through DO control. The systems enriched with Nitrospira rather than Nitrobacter have a higher oxygen affinity, thus have lower oxygen half-saturation than AOBs and can be well adapted to low DO conditions (Regmi et al. 2014; Al-Omari et al. 2015). The use of transient anoxia is another approach by providing a lag-time for NOB to transition from anoxic to aerobic condition or nitrite limitation (Zekker et al. 2012; Gilbert et al. 2014). By consuming nitrite in anoxic conditions, heterotrophs restrict substrate availability for NOB in the aerobic phase (Regmi et al. 2014). Moreover, in mainstream treatment under limited DO, the AOB growth rate is higher than the NOB's at high temperatures (above 20°C) (Regmi et al. 2014; Yang et al. 2016). This allows operating the system at the SRT that is suitable for the growth of AOB and wash out the NOB (Blackburne et al. 2008). In addition, there are lab-scale works that support that NOB out-selection can be achieved at lower temperatures depending on the dominant NOB species in the system and the reactor configuration (De Clippeleir et al. 2013; Gilbert et al. 2015; Cao et al. 2017).

For modelling the short-cut processes, nitrite should be considered as an intermediary step in nitrification and denitrification. Modelling the two-step nitrification process is well established where NOB out-selection can be modelled through distinctly defined growth kinetics, substrate affinities, temperature and pH effect on AOB and NOB (Sin et al. 2008; Shourjeh et al. 2021). However, most simulation studies so far deal with side-stream conditions associated with high-strength nitrogenous wastewater where NOB out-selection can be achieved much more easily with direct pH and temperature effect on the NOB (Volcke et al. 2006, 2012; Van Hulle et al. 2007; Wett et al. 2010; Hubaux et al. 2015). For mainstream processes, community shifts and the changes in biokinetics become important which are not implemented in the ASM-based models yet. Favourable conditions to support the existence of AOB and facilitate NOB out-selection through different control systems could be demonstrated in the limited number of existing modelling works for mainstream treatment (Table 1). NOB out-selection is achievable in the models but there are still limitations to these models such as the calibrated half-saturation constants that can be a function of the environmental conditions, process configuration and operating conditions; thus, posing an issue of not being transferable to other systems.

Partial nitritation-denitritation is an efficient biological pathway for N removal, but it has been challenged by the aforementioned difficulties (Section 2.1). The process can be applied as the first step of a 2-stage PNA process where nitrite-shunt is facilitated with controlled aerobic SRT. To improve effluent quality, the anammox process can be applied as a polishing step (Regmi et al. 2015a, 2015b; W. Zhang et al. 2020). Application of nitrite-shunt in mainstream treatment is desired through simultaneous nitrification denitrification because of the opportunity to enhance the utilization of the organic matter in the influent for denitrification. Note that the goal here is to maximize the use of the influent carbon through denitrification and not oxidation; hence, improving N removal while reducing energy consumption. However, it is not easy because the denitritation relies on utilizing the influent COD solely and thus the efficiency of the carbon pretreatment process. In addition, the mechanisms for achieving controllable simultaneous nitrification denitrification are not well understood yet (Klaus 2019; Jimenez et al. 2020) and it is out of the scope of this paper.

Operational strategies for stable nitrite-shunt performance have not been demonstrated yet in large-scale systems (Xu et al. 2017; H. Wang et al. 2019). Modelling of nitrite-shunt requires a holistic approach by simultaneously monitoring the influent dynamics and using the data for controlling the operational conditions and considering their effect on competition for the different substrates. Recent research efforts mostly deal with the application of deammonification in full-scale mainstream as opposed to nitrite-shunt (Table 1).

For application of PNA processes for mainstream treatment, a further concern is the competition between HB and anammox bacteria for nitrite. Few modelling studies under mainstream conditions have dealt with the interaction between AnAOB, AOB, NOB and ordinary heterotrophs (e.g., Al-Omari et al. 2015). As for side-stream applications, simulations showed that the availability of some influent COD can lower the effluent nitrate concentration (produced by anammox) by heterotrophic denitrification and thus increase the total nitrogen removal efficiency of anammox reactors (Hao & van Loosdrecht 2004; Mozumder et al. 2014). In many anammox studies, the presence of HB was ignored, and the COD in the reactor was neither measured nor considered in mass balances (Schielke-Jenni et al. 2015). Nevertheless, heterotrophic denitrifiers have been widely found in anammox reactors and can account for up to 23% of the biomass in biofilm reactors even without organic matter in the influent because HB could grow both on soluble microbial products and decay released substrate (Ni et al. 2012).

When modelling the anammox stoichiometry, one should be careful because the experimentally determined yield for the overall metabolic reaction (⁠=0.172 g COD/g NH₄⁺-N, Strous et al. (1998)) mistakenly has been used in many simulation studies (Hao et al. 2002; Volcke et al. 2010; Ni et al. 2012). Ammonium in the anammox process in ASMs is consumed in both catabolic and anabolic reactions, while the yield coefficient only accounts for the ammonium taken up in the catabolic path. Therefore, the experimentally determined yield cannot be directly implemented. To remedy this, Jia et al. (2018) proposed an alternative stoichiometric equation based on the biomass yield per amount of ammonium consumed in the overall metabolic reaction or recalculating the widely model yield (Y^mod) from the measured as follows; where i_NXB represents the nitrogen content of anammox bacteria (g N g COD⁻¹).

Modelling outputs of the mainstream PNA process also tend to be strongly affected by the oxygen inhibition coefficient of anammox bacteria, as demonstrated by Pérez et al. (2020) for MBBR and IFAS systems. The external mass transfer resistance plays a significant role in this case, as the biofilm can be exposed to lower DO concentrations under thicker boundary layers. Although low oxygen levels benefit anammox bacteria, AOB activity could be hampered too. In this case, ammonia-oxidizing archaea (AOA) could be better coupled to anammox bacteria, as the latter can thrive at lower DO levels compared to AOB (You et al. 2009). Nevertheless, few models consider the contribution of AOA to nitrogen conversions (Pan et al. 2016).

Steady-state simulations have been used to assess PNA systems (Bozileva et al. 2017), and only a few studies address dynamic simulations (Table 1). Under varying influent conditions, a higher sensitivity to temperature oscillation was found compared to steady-state simulations (Jia et al. 2020). Therefore, dynamic simulations are recommended to assess process feasibility and long-term stability.

An early indication of PdNA process in the literature was in a 2-stage pilot-scale PNA system (Regmi et al. 2015b). Eliminating the challenge of NOB out-selection has led to significant research interest in the PdNA process (Du et al. 2017; Cao et al. 2019; Du et al. 2019; X. Wang et al. 2019; B. Ma et al. 2020; You et al. 2020; Chen et al. 2021) and multiple successful pilot-scale and full-scale implementations (McCullough et al. 2021). As complete nitrification is already well established in process models, the primary challenge of modelling PdNA is understanding the reduction of nitrate to nitrite under various process configurations, substrate concentrations, redox conditions, and with/without the presence of anammox.

PdNA is typically implemented as a 2-stage system which can be an integrated process (Le et al. 2019a; Li et al. 2019) or a post-polishing (Campolong et al. 2018). Controlling and maximizing denitratation over denitritation is key to PdNA start-up and performance because full denitrification results in a loss of carbon efficiency and no ammonia removal. Multiple carbon sources have been demonstrated to be effective for partial denitrification such as acetate, glycerol, or methanol (Campolong et al. 2018; Le et al. 2019b; McCullough et al. 2021), ethanol (Du et al. 2017), fermentation products (Cao et al. 2013; Ali et al. 2020) and endogenously stored carbon (Ji et al. 2017; X. Wang et al. 2019). Beyond carbon source selection, numerous factors can affect the partial denitrification efficiency including influent C/N ratio, pH, sludge retention time and microbial population. Recent literature suggests that under mainstream conditions, the dominant factor impacting partial denitrification efficiency is in fact the nitrate concentration in the reactor (nitrate residual) (Le et al. 2019a). Nitrate residual has been demonstrated to be an effective method for controlling PdNA and partial denitrification efficiency during start-up (Schoepflin et al. Manuscript in preparation), pilot-scale (Le et al. 2019a), and full-scale (McCullough et al. 2021). Since it can be well correlated with partial denitrification efficiency and was used successfully for process control, the nitrate residual is found to be a key parameter in modelling PdNA as well (Al-Omari et al. 2021).

Modelling PdNA requires accurate description of partial denitrification in the model and the ability to address microbial competition over electron donors and acceptors. While denitrification is included in ASM 1, ASM 2-2d and ASM3 models as a single-step (Henze et al. 2006), at least two-step denitrification must be modelled for PdNA. Monod functions were used to model two-step denitrification by Hellinga et al. (1999), in ASM3 by Ni & Yu (2008) and for granular sludge by De Kreuk et al. (2007). Many multi-step denitrification models included terms to inhibit denitratation in favour of denitritation (referred to here as ‘nitrite preference’) based on experimental observations where nitrite accumulation was not observed or was impeded. Wett & Rauch (2003) proposed a model using the ASM structure in which the rate of denitritation is elevated and the rate of denitratation is hampered by an inhibition factor based on the ratio of nitrate to nitrite. Similar practices appeared to be common practice, as Hiatt & Grady (2008) state that denitrification models from Gujer and colleagues included a nitrite inhibition term for each step of nitrogen reduction, e.g. Wild et al. (1995). Their four-step activated sludge model for nitrogen (ASMN) includes a nitric oxide inhibition factor for denitrification as well as separate anoxic reduction factors for each denitrification rate. More advanced three-step or four-step denitrification models introduce additional complexity and parameters, but do not appear to be necessary to successfully model PdNA. These models are discussed in more detail in Section 4.4.

The nitrite preference applied to all electron donor sources used for denitrification hindered the ability to induce partial denitrification in existing models. Al-Omari et al. (2021) introduced a partial denitrification switch based on bench-scale and pilot-scale observations where partial denitrification was observed in batch tests and was controlled in continuously fed systems by maintaining nitrate residual. This was observed when using specific carbon sources such as acetate and glycerol but not methanol. The ‘nitrite preference’ was eliminated in this case for the nitrate reduction reactions using the volatile fatty acids (VFA) substrate state variable.

N₂O is produced mainly from three microbial pathways: the NH₂OH oxidation and nitrifier denitrification pathways carried out by AOB, and the heterotrophic denitrification pathway carried out by HB (Duan et al. 2017) (Figure 1). N₂O is a potent greenhouse gas with a large global warming potential of 265 times that of CO₂, as well as the single most significant ozone-depleting substance (Edenhofer et al. 2014). Accurate assessment, modelling, and mitigation of N₂O emissions is critical due to the large contribution of N₂O to the WRRF carbon footprint (Vasilaki et al. 2019). Peng et al. (2020) analysed the carbon footprint of the mainstream PNA process, including electricity consumption, N₂O emissions, and reduction in carbon emissions through energy recovery. Based on this study, the N₂O emission factor for mainstream PNA should not exceed 0.78% to achieve a carbon-neutral operation. However, the N₂O emissions from the PNA process could be staggeringly high, with up to 10% of the nitrogen removed emitted as N₂O (Domingo-Félez et al. 2014; Staunton & Aitken 2015).

The capability to simulate N₂O emissions by mathematical models allows the consideration of N₂O emissions in the design and operation of short-cut nitrogen removal processes. N₂O models have evolved from simple one-pathway models (from AOB or from 3rd or 4th steps of heterotrophic denitrification) (Hiatt & Grady 2008; Mampaey et al. 2013; Pan et al. 2013) to two-pathway AOB models (Ni et al. 2014; Pocquet et al. 2016) that involve both N₂O production pathways from AOB. Thereafter, integrated pathway models were developed that consider both AOB and heterotrophic N₂O generations (Guo & Vanrolleghem 2014; Domingo-Félez & Smets 2016; Spérandio et al. 2016), and indicating that N₂O can also be further removed but only by HB (Guo & Vanrolleghem 2014). These integrated pathway models have been applied in conventional systems as a powerful tool to evaluate N₂O mitigation strategies (Chen et al. 2019; Duan et al. 2020, 2021).

With essentially the same principles of N₂O generation, models developed in nitrification and denitrification systems can be directly applied to the short-cut nitrogen removal processes. For example, Wan et al. (2019) integrated the two pathway N₂O model by Pocquet et al. (2016), with the heterotrophic N₂O production model by Hiatt & Grady (2008) to describe N₂O emissions in a single-stage PNA reactor. The established N₂O model was used to evaluate the effects of operational conditions on N₂O emissions from the PNA system and identified the potential operational conditions to reduce emissions.

Challenges and uncertainties are present in the modelling of N₂O emissions in mainstream short-cut nitrogen removal systems. The largest uncertainty results from the lack of datasets. N₂O emission data from full-scale mainstream short-cut nitrogen removal systems are limited. On the other hand, the data obtained from lab-scale applications show high emission ratios (5.2±4.5% of total inorganic N removed) (Roots et al. 2020). In addition, many short-cut nitrogen removal evaluations lack N₂O data. Therefore, adequate nitrogen species profiling data becomes crucial to establish nitrogen mass balances. Another challenge is that N₂O process models tend to overparameterize the description of biological pathways and this impacts the N₂O model calibration (Domingo-Félez & Smets 2020).

In the mainstream application of short-cut N removal processes, mathematical models are being mostly used to simulate the behaviour of biological processes under different operating scenarios and cost-effectiveness (Shourjeh et al. 2021). Although currently experimental work in laboratory and pilot-scale systems prevails over mechanistic model analysis for short-cut processes (M. Zhang et al. 2019; Z. Zhang et al. 2020), modelling efforts can help to accelerate mainstream full-scale applications. In this section, several modelling goals and potential benefits are presented from a modeller perspective to reveal how modelling could be useful to achieve successful applications (Figure 2).

As presented in Section 2, models are mainly being used to facilitate the process understanding and improve process efficiency through improved operation and process control. Existing models can improve mainstream NOB out-selection applications for PNA processes since it allows assessment of the impacts of stable and dynamic influent conditions, biofilm characteristics and aeration control strategies (Al-Omari et al. 2015; Rosenthal et al. 2018). With the ability to simulate varying influent conditions such as low or high COD/N ratios, modellers can examine the hydrolysis of biodegradable substrates and impacts on processes (Tao & Hamouda 2019). In addition, models permit the exploration of how different biofilm systems (MBBR, granular sludge, IFAS and filters) would work for mainstream applications (Boltz et al. 2011; Rosenthal et al. 2018).

Similar to NOB out-selection, existing models can be used to improve the efficiency and nitrogen removal contribution via PdNA pathway by evaluating the impact of feedstock carbon characteristics, biofilm characteristics, process configuration, aeration controls and operational conditions.

Pilot and full-scale applications of different control algorithms are increasing rapidly to provide the operational and environmental conditions to sustain short-cut N removal in mainstream treatment. Modelling can be used to design control strategies to improve the operation of existing plants and serves as a time and cost-saving tool for the evaluation of different control algorithms (Salem et al. 2002; Gernaey et al. 2004). To fulfil the effluent quality standards, reduce carbon footprint and keep the operational costs at a low level, it is imperative to use control strategies to optimize resource consumption (Ostace et al. 2011; Revollar et al. 2020).

To achieve mainstream deammonification, several real-time aeration control strategies have been developed and applied such as continuously low DO operation, AvN (NH₄⁺-N vs NO_x⁻-N) with intermittent aeration, ammonia-based aeration control (ABAC) (Regmi et al. 2014; Sadowski et al. 2015; Poot et al. 2016). Together with the real-time aeration control, the application of short aerobic SRT is a robust control strategy that relies on adjusting the wasting rate, aerobic volume and DO setpoints to suppress NOB in PNA systems (Regmi et al. 2014; Han et al. 2016). Nitrate-based COD dosing control is needed in PdNA systems to ensure nitrite availability for anammox (Le et al. 2019a). Finally, yet importantly, dynamic feedforward control of the AvN setpoint to respond to changes in the influent ammonia can be implemented to maximize the PdNA efficiency with savings in carbon dosage (Le et al. 2019c). By using the information and experience obtained from lab and pilot-scale studies, modelling can be used to compare features of different process control strategies, provide a proof of concept, and develop the control algorithms (e.g. feedforward control based on the influent dynamics or multi-objective control).

Depending on the short-cut nitrogen removal process efficiency and the effluent requirements, the post-treatment might be needed for the removal of nitrate, nitrite or residual ammonia. Often in the short-cut N process, nitrate may still be present in the effluent, especially when NOB out-selection efficiency is compromised (Gustavsson et al. 2020; Muñoz 2020). This requires post-treatment such as heterotrophic denitrification with external carbon dosage. Effluent ammonia can be an issue at high loading rates and a reaeration zone might be needed. Models can be used to design and test the required post-treatment alternatives coupled with control strategies, determine the reactor volume needed, air consumption or the applicable type of chemical dosage. It can be helpful to ensure the effluent limits and analyse the overall resource consumption in long-term operation.

Modifying a conventional N removal process with short-cut N removal processes can reduce overall energy and resource consumption of a WRRF. To demonstrate and quantify the gains of such modifications, models can be used for the capacity analysis of a WRRF by identifying the SRT, volume necessity, chemical consumption and stoichiometric needs for the processes (Shao et al. 2021). For example, Al-Omari et al. (2015) used a calibrated model for a hypothetical scenario and demonstrated the potential of 60% external carbon savings by converting the conventional nitrification denitrification system to mainstream deammonification with the Blue Plains WRRF case study. Moreover, such evaluations provide an assessment of the potential performance to meet the total inorganic nitrogen effluent limits and associated risk in long-term operations. Demonstration of the benefits of technology for existing plants can be achieved when transferable validated process models are available, and the model parameter values are obtained.

Furthermore, from a plant-wide modelling perspective, mainstream short-cut N removal processes are interacting with other biochemical and chemical processes in the WRRF which would be important to capture both the dynamics of the plant and the potential environmental impacts (Arnell et al. 2017). For example, through plant-wide modelling, the influence of carbon redirection process on the downstream short-cut N removal process performance and the microbial species could be predicted; including the greenhouse gas emissions, carbon and energy footprint of the WRRF (Mannina et al. 2019). Simulating the whole plant would allow determining if the side-stream processes can be used to support the mainstream processes through seeding the bacteria (AOB or Anammox, e.g. Wett et al. 2015) or providing FNA or FN exposure (e.g. D. Wang et al. 2016; Duan et al. 2019a). In addition, combined biological P and short-cut N removal potential can be investigated. Thus, adopting the plant-wide modelling approach can be useful to demonstrate the gains in terms of process performance and stability in full-scale implementations.

Despite its limitations, modelling is proven to be useful to help achieve full-scale mainstream N removal processes (Section 2&3). The applications at different scales provide invaluable information to support and improve the models while the modelling efforts can help to accelerate successful practical application and foresee challenges. Within this section, the needs and future perspectives on model applications are presented. Based on the discussion outputs of the Workshop of the 7th IWA/WEF Water Resource Recovery Modelling Seminar Mainstream Short-cut Nitrogen Removal Modelling: From research to full-scale implementation, do we have what we need?, a feasibility versus importance chart is given in Figure 3 for the future works that are urgently needed (the discussion points with less importance are not included). The main subjects are discussed in detail below.

For the modelling of short-cut processes, robust calibration methodologies and model developments are needed to find the optimal range of influential model parameters and improve process understanding and stability. Existing process models for short-cut nitrogen removal are commonly used for scenario analysis to evaluate process performance under varying operating conditions (e.g. Mozumder et al. 2014; Pérez et al. 2014). The models are mostly goal-oriented (i.e. applied for a specific purpose and case), but are seldom followed by experimental validation. For example, the degree of stratification of AOB and NOB in nitritating granules (Soler-Jofra et al. 2019), or the postulated pH-driven inhibition of NOB in a PNA system (Y. Ma et al. 2017) are later confirmed by pH microprofiles which is related to the NOB out-selection in biofilm systems (Ma et al. 2021).

Based on the analysis of the reported modelling studies in literature, it appears that the applied calibration methodologies are seldom following good modelling practice which makes the comparison between modelling studies difficult. This is probably due to the complexity and change of the microbial communities studied with lab-scale systems when they are applied to full-scale (Rieger et al. 2012). Selection of the parameters is typically based on expert knowledge following the parsimonious principle (i.e. keep the number of parameters to be estimated as small as possible), and the calibration methodology itself mostly is not well described (Al-Omari et al. 2015; Trojanowicz et al. 2019; Drewnowski et al. 2020; Roots et al. 2020). One should be aware that this type of model calibration may lead to unrealistic model outputs when the model is run without boundary conditions and is extrapolated for process optimization. Moreover, the model parameter values estimated in this way may not be transferable to other systems. Proper model validation can protect from such unrealistic extrapolation as it would indicate to what extent extrapolation is feasible.

The application of robust sensitivity analysis and the use of more rigorous calibration methodologies would make the comparison between model structures possible and the simulated model outputs would become reproducible and transferable. Importantly, it also enables the modeller to identify the main model factors to pay attention to in terms of model algorithms and the data (Mannina et al. 2010; Vangsgaard et al. 2013). This identification can reveal which data is more informative for model calibration, thus can guide the experimental efforts (e.g. the higher sensitivity of growth rates regarding performance within the biofilm vs bulk recommends in situ microprofiling data is more informative for calibration than the bulk measurements (Y. Ma et al. 2017)). This issue may be minimized if long-term consistent data sets can be obtained which is typically the weakest link in modelling of short-cut processes currently.

Sensitivity analysis is the basic method to identify the most appropriate parameter subsets to be calibrated. In short-cut process models, calibration coupled with the use of more advanced approaches has been presented but has remained limited (e.g. normalized sensitivity function (Baek & Kim 2013; Y. Ma et al. 2017)). Sensitivity analysis can be done in a simple way through local sensitivity analysis (LSA), for which the number of model simulations that need to be run is low, typically 2*N+1 runs (N: number of parameters) (De Pauw & Vanrolleghem 2006a). However, the LSA approach does not allow identifying interacting factors, thus may miss some of the influential model parameters and limit the use of the calibrated model. On the other hand, global sensitivity analysis (GSA) provides information on how the model outputs are influenced by the variation on the model inputs and parameters over a wide range of possible parameter values (Cosenza et al. 2013). Thus, GSA provides an overall view of the sensitivity and determines the important model parameters much more reliably. In addition, GSA covers interacting parameters much better (Lackner & Smets 2012). Its computational demand is higher than the one of LSA, but it can be optimized by using an appropriate sampling method, e.g. Latin Hypercube Sampling (Vanrolleghem et al. 2015).

Sensitivity analysis will further guide the identification of the most influential model inputs and allow for the design of future monitoring campaigns for full-scale applications with the aid of model-based optimal experimental designs (OED) (Ledergerber et al. 2019). OED can help design the experimental studies that are highly informative and meaningful for calibration and validation of the models and thus will make models that reliably predict the model outputs (De Pauw & Vanrolleghem 2006b). Finally, standard testing methods/protocols for the measurement of key model parameters would ensure good initial estimates of their values can be assigned since such estimates allow reducing the calibration efforts and making different case studies comparable. Examples of such standard tests are activity tests for nitrification rates and measurements of half-saturation coefficients.

While the PdNA model from Al-Omari et al. (2021) has been calibrated to a range of data from pilot-scale systems and started to be applied to full-scale processes, many questions remain that may require more advanced models (Section 2.4). The developed model can simulate partial denitrification only with methanol and VFA (glycerol or acetate) substrates but have not yet been tested for more complex carbon types. Other electron donors need to be better understood to model PdNA systems that rely on complex influent COD or fermentation products. Fermentation products have been shown to be useful for partial denitrification at pilot-scale (Ji & Chen 2010) and PdNA (Ali et al. 2020). Influent COD has also been used to drive partial denitrification, although this may require in-line fermentation (Shi et al. 2019; Ji et al. 2020; Liu et al. 2022) or pH elevation above 9.0 (Qian et al. 2019; Shi et al. 2019).

Additional work needs to be done to better understand intracellular carbon storage and its impact on PdNA. Simple carbon sources like glycerol and acetate can be stored by heterotrophs (Le et al. 2019b), and the resulting denitrification dynamics of storage versus immediate use is not well understood in these systems. Studies have shown that internally stored carbon from influent wastewater is a promising alternative for partial denitrification (Ji et al. 2017, 2018). Denitrifying glycogen-accumulating organisms present (dGAO) in enhanced biological phosphorus removal (EBPR) systems may also preferentially perform denitratation (Rubio-Rincón et al. 2017; H. Wang et al. 2019), leading to a potential synergy between next generation EBPR and PdNA systems.

Estimation of half-saturation constants: An efficient deammonification system must ensure both the activity of AOB and AnAOB while the growth of NOB is inhibited (especially in PNA systems). Also, the growth of HB should be controlled since it may shift the process from deammonification to conventional nitrification and denitrification (Cao et al. 2019; Gao & Xiang 2021). In low substrate availability conditions such as short-cut N removal processes, microbial competition for substrate becomes important for both application and modelling. The substrate competition might be between AOB and AnAOB for ammonium as electron donor; AOB, NOB and HB competition for oxygen as electron acceptor; and AOB and NOB competition for inorganic carbon (Shourjeh et al. 2021). Microorganism growth kinetics and substrate affinities provide a useful tool to understand and model the substrate competition and population shift. Expanding the previous models by accommodating for the competition between main species, we will have to revisit and further study the wide range of kinetic parameters for AOB, NOB, and AnAOB (Cao et al. 2017).

Impacts of influent load fluctuation, environmental and operational conditions on model accuracy becomes more important and perhaps more challenging for addressing competition more accurately in the model. On the other hand, strategies and operational conditions are being tested mainly in lab-scale and modelling efforts are often lacking consistent long-term experimental data (Table 1). For example, related to the successful NOB out-selection, the models are mostly applied for the data out of a short-term monitoring period and only reflects the operational conditions that favour the AOB or AnAOB activities while NOB is inhibited (Blackburne et al. 2008; Cui et al. 2017; Laureni et al. 2019; Al-Hazmi et al. 2022). Thus, not including the challenging operational conditions that promote NOB growth may lead to an inadequate calibration of NOB activity and their out-selection. Most of the models are calibrated to reflect the periods for stable operation; hence, the half-saturation values would not change drastically except the acclimation and adaptation conditions. Using long-term, where organisms are well adapted to the operational conditions, and consistent performance data for dynamic simulation with robust calibration methodologies could be useful to overcome the calibration challenges related to competing species in the short-cut process (e.g. Vangsgaard et al. 2013).

The growth kinetics of microorganisms is substrate-limited based on Monod's formulation used in the ASMs which states a fixed relation between growth rate and bulk substrate concentration (Henze et al. 2006). Thus, the substrate half-saturation constant (or affinity constant) is crucial. It represents the substrate concentration corresponding to a half-maximal rate of growth (Riet & Lans 2011). The lack of understanding and proper characterization of half-saturation constant variability between different systems leads to the need for frequent calibration of half-saturation constants. However, calibration may lump the effects of different phenomena in the system (such as mixing, advection and biofilm diffusion limitations) and that may lead to a variation on the apparent values of the half-saturation constants, thus affecting the prediction power of the calibrated model (Arnaldos et al. 2015). For example, the current practice for oxygen mass transfer modelling is to apply overly simplified models. These models require multiple assumptions that are not valid for most applications and are highly uncertain (e.g. α-factor). Thus, the calibration of DO half-saturation constants is affected especially in short-cut processes where small deviations in the simulated DO concentration have already a significant impact on the biological conversion processes (Amaral et al. 2019). In addition, transport of oxygen within the floc is driven by diffusion where temperature and DO gradient become important factors (Manser et al. 2005; Arnaldos et al. 2015). A high variation of such factors may require implementing the half-saturation constant as a model variable and calculating its value during the simulation (e.g. K_NO3 dependence on biomass growth rates, thus the temperature by Shaw et al. 2013). Furthermore, the different species of the same genera of microorganisms may have different affinities to the same substrate. For example, Nitrobacter or Nitrospira are the two main genera of NOB and their predominance in the system is affected by nitrite concentration (Nogueira & Melo 2006). For these reasons, estimation of the half-saturation constants should be handled very carefully by considering the transport phenomena and the effect of biological limitations to model the substrate competition properly. Advanced modelling tools in combination with the biokinetic models such as computational fluid dynamics and population balance models could be useful in full-scale systems (Arnaldos et al. 2015). The inclusion of different species in the same genera with their substrate affinities might be considered especially to model NOB suppression (see below: Inclusion of community shift). Also, when the kinetics are under dual limitation, both substrates should be taken into account in the model (Al-Omari et al. 2015).

Alternatively, hybrid models are an interesting avenue to pursue in this domain. Hybrid models combine mechanistic models with data-driven techniques and as such leverage both process knowledge and the power of data analytics. As a result, hybrid models can have good extrapolation properties while being less laborious to develop than strictly mechanistic models. Hybrid models can be used in many different configurations and with many different combinations of data-driven tools. However, they have been described to be specifically powerful in situations where the overall process model structure is quite well defined but specific knowledge on variability of subprocesses is missing (von Stosch et al. 2014). In these situations, adding a data-driven component to the well-described mechanistic model structure can specifically learn the missing dynamics and compensate for the uncertainties in the mechanistic model which can be much more efficient than going through extensive laboratory experiments to develop in-depth understanding of all the factors contributing to the variability in some subprocesses. The modelling of kinetics in short-cut N removal processes falls exactly within this definition with a lot of process knowledge and corresponding process knowledge available but a lack of mechanistic description of all factors influencing the kinetics (e.g. mixing, biofilm diffusion limitations).

Inclusion of community shift (interspecies competition): It is well-known that at low oxygen concentrations, NOBs are outcompeted because of their relatively low affinity for oxygen. Experimental evidence is available suggesting different reactor operating conditions and control strategies favour the presence of different nitrifying species, which could be different ammonium oxidizers (Bougard et al. 2006) and/or different nitrite oxidizers (Dytczak et al. 2008). Considering the oxygen concentration as the key variable governing the population shift, Volcke et al. (2008) modelled the shift in AOB species in a biofilm reactor. But also NOB could adapt to control strategies by community shifts, resulting in failed NOB control and subsequently disrupting the PNA or nitrite-shunt process. With the low DO (between 0.16 and 0.37 mg O₂/L) NOB control strategy, NOB gradually developed competitive edges over AOB for oxygen uptake by shifting the NOB community to be dominated by Nitrospira (Liu & Wang 2013). Similarly, the NOB community could adapt to inactivation from free ammonia (FA) or free nitrous acid (FNA), by shifting to Nitrobacter, or Nitrospira respectively (Duan et al. 2019a, 2019b).

The adaptation of NOB by community shift poses a challenge to the modelling of mainstream PNA or nitrite-shunt processes. The current ASMs with 2-step nitrification could predict the out-selection of NOB under low DO conditions given the commonly higher oxygen affinity constant of NOB than that of AOB. However, as the NOB community adapted to the low DO condition by shifting the dominant NOB genus from Nitrobacter to Nitrospira, NOB exhibited an increasingly higher affinity to oxygen (lower half-saturation constant). Modelling such NOB activities in the mainstream PNA or nitrite pathway is not feasible with one set of parameters. The inclusion of detailed microbial diversity (interspecies competition) in models for process design and operation may be warranted in cases where it affects the macroscopic reactor performance (e.g. nitrite accumulation). Taking the low DO control scenario as an example, if the model included kinetics parameters/processes for both Nitrospira (lower oxygen half-saturation constant) and Nitrobacter (higher oxygen half-saturation constant), the model may be able to predict the community shift, and the adaptation of the NOB community to the low DO conditions under long-term operation. The inclusion of the community shift in the model may allow predicting a more reliable NOB control performance, and thus a more stable mainstream PNA or nitrite-shunt process. Note that if the model includes the kinetics parameters/processes for competing interspecies, a complete washout of one the species can be predicted at certain conditions and it would never reappear even if the conditions later shift towards more favourable conditions. However, in reality, this might happen seldom and the two species may always coexist, only switching their predominance depending on the conditions. The reason might be the seeding of NOB from the influent wastewater. It has been reported that different NOB species may be present in raw wastewater reaching the WRRFs (Jauffur et al. 2014; Yu et al. 2016). This could potentially facilitate the development of the NOB community, which may result in unstable NOB suppression in the mainstream (Duan et al. 2019b). To reflect this situation in the model, these interspecies must be included in the input of the model.

Inorganic carbon limitation of AOB: Inorganic carbon can be a crucial factor influencing conversions, as demonstrated by Bressani-Ribeiro et al. (2021) for the treatment of anaerobic effluents. Dynamics of AOB have been reported to change significantly under inorganic carbon limitation while the NOB activity remains stable (Guisasola et al. 2007; Ma et al. 2015; Zhang et al. 2016). Biesterfeld et al. (2003) showed that nitrification rates are affected by an inorganic carbon shortage (below 45 mg CaCO₃ L⁻¹) independently of pH. Instead of inorganic carbon, alkalinity (expressed as bicarbonate) is typically introduced in models to predict possible pH changes and close charge balances (Rieger et al. 2012). The ASMs follow that approach, in which alkalinity limitation on (single-step) nitrification is described with Monod kinetics (Henze et al. 2006).

The alkalinity limitation considered in these models focuses on unfavourable pH conditions rather than inorganic carbon limitation. Nevertheless, modelling approaches considering inorganic carbon limitation effects on autotrophs have been proposed, described with Monod or sigmoidal kinetics (Wett & Rauch 2003; Guisasola et al. 2007; Al-Omari et al. 2015; Seuntjens et al. 2018). From a fundamental standpoint, NOB is likely less limited by inorganic carbon than AOB, as the latter can up-regulate its anabolism mixotrophically using traces of organic matter (Bock 1976). However, the different behaviour of AOB and NOB under inorganic carbon depleted conditions is typically neglected in models. Moreover, mainstream process models typically assume that influent inorganic carbon content is sufficiently high, meaning hardly any limitation (Sin et al. 2008). Bicarbonate as a state variable should be explicitly used to quantify inorganic carbon limitation rather than to simply indicate pH changes. In this case, sigmoidal kinetics are recommended. Furthermore, a higher inorganic carbon limitation for AOB than NOB is essential for modelling nitrogen conversions in trickling filters following direct anaerobic sewage treatment (Bressani-Ribeiro et al. 2021).

Denitrification refers to the 4-steps reduction of NO₃⁻-N to N₂ via NO₂⁻-N, NO, and N₂O. While formerly considered in denitrification models as a 1-step process, heterotrophic denitrifiers and some phosphate accumulating organisms possess a highly modular microbiome with a diverse distribution of the nar, nir, nor, and nosZ genes (Ekama & Wentzel 1999; Graf et al. 2014). External carbon sources such as acetate, ethanol or methanol are being added to enhance denitrification rates (Mokhayeri et al. 2009). The metabolic pathways to oxidize each carbon source are different: the tricarboxylic acid cycle for acetate, specific enzymes to convert ethanol to acetate, and two other pathways requiring specific enzymes for methanol degradation (Ribera-Guardia et al. 2014). Hence, the chemical composition of the electron donor pool will shape the microbial community yielding significantly different denitrification rates and yields (Hallin et al. 2006; Lu et al. 2014). In an enriched denitrifying community the individual addition of excess acetate, ethanol, and methanol showed distinctive NO₃⁻-N reduction rates, and more importantly, different accumulation of the intermediates NO₂⁻-N and N₂O (Ribera-Guardia et al. 2014). Consequently, the oxidation rate of each carbon source can be the limiting step to the overall denitrification rate even at non-limiting organic carbon concentrations (Gao et al. 2020).

The distinct reduction and accumulation of denitrification intermediates depending on the carbon source is crucial especially for the PdNA systems since the partial denitrification rate is the key factor for the process performance. Two-step denitrification models fit the purpose of modelling short-cut N removal processes, but the ASMN extended to 4-steps to incorporate NO and N₂O reduction based on Von Schulthess et al. (1995). The current structures based on ASMN assume that carbon oxidation supplies all the electrons necessary for the four denitrification steps, leading to include individual maximum denitrification rates, substrate affinity and inhibition constants (e.g. NO, DO). Hence, the complexity of 4-step denitrification models increases significantly while datasets for the intermediates NO and N₂O remain scarce. Thus assumptions need to be made on substrate affinity kinetics for NO and N₂O reduction (Hiatt & Grady 2008). The specific maximum reduction rates for NO₃⁻-N and NO₂⁻-N vary substantially depending on the carbon source, and are typically modified during model calibrations to fit denitrification rates (Q. Wang et al. 2016; Domingo-Félez & Smets 2020). However, the approach of additive kinetics in ASMN fails to properly describe the electron competition (Pan et al. 2015). To overcome this challenge, the ASM-ICE (indirect coupling of electrons) was introduced to explicitly calculate the concentration of internal electron carriers of a methanol-enriched denitrifying community uncoupling the denitrification and carbon oxidation processes over one branch at a cost of higher model complexity (Pan et al. 2013). Based on Almeida et al. (1997) the ASM−EC (electron competition) calculates denitrification rates and carbon oxidation as an analogy to current intensity flowing through a parallel set of resistors in electric circuits. The ASM−EC was validated with data from batch experiments with four different carbon sources including acetate, ethanol, methanol, and their ternary mixture with fewer parameters than the ASM-ICE (Domingo-Félez & Smets 2020).

N₂O models have been developed in biological nitrogen removal systems and reached maturity to facilitate process optimization of conventional N removal systems (Section 2.4). However, they have not been widely applied in modelling short-cut processes. The lack of datasets is one of the major challenges to applying N₂O models and particularly the datasets from large-scale demonstrations. For that reason, monitoring the N₂O emissions is essential in pilot and full-scale applications to improve the applicability of N₂O models in mainstream short-cut processes. Hybrid models can also be adopted for short-term laboratory or pilot-scale studies with data scarcity where mechanistic models can be used to simulate the biological process and the data generated can be used in a data-driven model that acts as input to a N₂O prediction algorithm (Mehrani et al. 2022).

N₂O modelling in mainstream short-cut N removal systems shares similar challenges as in conventional nitrification and 2-step denitrification systems. For example, since N₂O is an intermediate in the nitrogen transformation pathways, N₂O models require a laborious calibration process under varying operational conditions (Hwangbo et al. 2021). Also, microbial communities involved in N₂O production are more complex than conventional systems (e.g. NO is an intermediate of the anammox metabolism and the precursor of N₂O for AOB and heterotrophic denitrifiers). This leads to overparameterized N₂O process models for the description of biological pathways. For example, the aforementioned preferential uptake of carbon sources leads to different patterns of NO₂⁻ accumulation during denitrification (Ribera-Guardia et al. 2014; Zhao et al. 2018) and impacts N₂O model calibration (Domingo-Félez & Smets 2020). Thus, while it is important to include the N₂O models for modelling of short-cut processes, model complexity and ease-of-use should be prioritized based on the modelling goals.

A review was presented on models for short-cut N removal processes, in view of mainstream applications, considering the current practice, limitations, future needs and perspectives. Mathematical models are under development to overcome implementation challenges and to deal with the complexity of mainstream deammonification. The pilot and full-scale applications reported provide invaluable information for models development while modelling efforts can accelerate the success of practical applications.

• NOB out-selection is still a major issue for mainstream application. Its dynamics can be captured in individual models but there are still limitations such as the model parameter values that may vary depending on the process configuration and operating conditions. Thus, they may not be transferable to another system.

• Recent modelling efforts mostly deal with the application of mainstream deammonification in full-scale and there appears to be less focus on nitrite-shunt.

• To correctly model the N mass balance and anammox process performance, models should consider incorporation of heterotrophic denitrifiers and anammox bacteria and the yield for the overall anammox metabolic reaction based on ammonium take up.

• While steady-state simulations have been used to model the overall feasibility and performance of short-cut N removal systems, dynamic simulations are especially needed to address issues with capacity evaluations, control strategies for sustained performance, and assessing the risk for meeting effluent limits.

• The application of robust sensitivity analysis is urgently needed and more rigorous calibration methodologies should be adopted to allow the comparison between model structures. The simulated model outputs would become much more reproducible and transferable.

• Modelling PdNA requires accurate modelling of partial denitrification and the ability to address microbial competition among the electron acceptors for various carbon sources. The existing PdNA models were only tested thus far to simulate partial denitrification with simple carbon sources. Other electron donors need to be better characterized and evaluated using the models to simulate PdNA systems that rely on complex influent COD, fermentation products or internally stored carbon.

• Competition over different substrates and estimation of half-saturation constants should be handled carefully by considering system properties such as mixing, diffusion processes and substrate limitations such as by nitrite and inorganic carbon availability to properly model the substrate competition and out-selection. Hybrid models can be adopted by adding a data-driven component to the well-described mechanistic model structure to model substrate competition properly and compensate the lack of mechanistic description of subprocesses influencing the kinetics of short-cut processes.

• The inclusion of interspecies competition in models by implementing different genera of the same functional group (with different kinetic properties) may be warranted in cases where it affects the macroscopic reactor performance in order to predict a more reliable NOB control performance, and thus find conditions for a more successful process start-up and stable mainstream short-cut process.

• The denitrification intermediate steps are crucial especially for partial denitrification efficiency and N₂O emissions. In model development, 2-step denitrification fits the purpose of modelling short-cut process efficiency while more detailed 4-step models should be adopted if the modelling goal is to predict both process efficiency and N₂O emissions.

This work is an outcome of discussions at the ‘Mainstream Short-cut Nitrogen Removal Modelling: From research to full-scale implementation, do we have what we need?’ Workshop of the 7th IWA/WEF Water Resource Recovery Modelling Seminar. It is a collective effort by the practitioners and academics of the wastewater industry who are keen to implement the deammonification process sustainably on mainstream treatment.

The authors declare that they have no known competing financial interests or personal relationships that could influence the work reported in this paper.

All relevant data are included in the paper or its Supplementary Information.