Towards a modelling framework for nature-based solutions in wastewater treatment Open Access

There is growing interest in nature-based solutions (NBS) as ‘green’ alternatives to conventional ‘grey’ approaches to wastewater treatment. ‘Grey’ refers to a reliance on concrete basins and mechanical equipment, whereas ‘green’ means infrastructure that is more natural in appearance (Cross et al. 2021), possibly utilizing existing natural features (Sowińska & García 2022) (natural ponds or wetlands) or else human-built structures that are engineered to mimic nature-like constructed ponds, wetlands (Haddis et al. 2020), swales, green roofs, and stormwater basins (Kuller et al. 2017). NBS are promoted for their sustainability and cost-effectiveness (Dorst et al. 2019) in providing a wide range of benefits, including pollutant removal (Pascual et al. 2021), flood prevention (Steis et al. 2020; Mubeen et al. 2021), water retention, and many co-benefits (Dagenais et al. 2017) such as heat dissipation, habitat creation for wildlife, and biodiversity enhancement (Cohen-Shacham et al. 2016; Sowińska & García 2022; Bousquet et al. 2023).

A useful classification system that distinguishes NBS as water-based or substrate-based systems as well as the types of influent wastewater that can be treated was presented by Cross et al. (2021). The classification system is applied to 21 distinct NBS types and achievable treatment efficiencies and co-benefits are identified. Whether NBS can meet expectations in practice, however, is not always evident. As stated in a recent publication from the UN, ‘there are also still too many cases where NBS are deployed based on uncertain science (Istenič et al. 2023) and then do not deliver on their stated impacts (Sowińska & García 2022)’ (WWAP 2018). Modelling tools could go a long way to bridging the knowledge gap or ‘uncertain science’ referred to in this statement. Mathematical models are how engineers typically codify knowledge and experience, but there is limited availability of NBS modelling tools in the literature. The authors propose the following reasons for the limited availability of modelling tools:

• 1. Limitations in understanding of first principles and mechanisms of how a particular NBS operates. In this respect, NBS would be viewed by engineers somewhat as a black box. The NBS provides a benefit but the exact causes of this benefit (and therefore how to optimize it, or under what conditions the benefit may be lost) are unknown or poorly understood. For example, consider the benefit of pathogen removal by waste stabilization ponds (Nelson et al. 2004). A practitioner might be an expert in the behaviour of the NBS but may not understand the underlying mechanisms of pathogen removal.

• 2. Underlying first principles and mechanisms are known but have not been consolidated into a comprehensive model that is broadly available to the community of NBS practitioners. There are a few mathematical models available, such as River Water Quality Model No. 1 (RWQM1) (Shanahan et al. 2001) for streams or SURFWET, a biokinetic model for surface-flow constructed wetlands (Aragones et al. 2020) but they are specific to only certain NBS categories. This is very common in engineering disciplines where specialized knowledge exists in a small group of specialists who have not seen the value in codifying and sharing a model.

• 3. The mechanisms are known but of a complexity such that it is not practical to try to solve them mathematically in a computer model. Flow networks that require advanced computational fluid dynamics (CFD) to solve may fall into this category for most practical engineering applications (Rajabzadeh et al. 2015).

• 4. The required inputs to the model are not quantifiable. For example, plant roots are known to provide surface area for bacterial nitrification in constructed wetlands and the nitrifying capacity of wetlands is directly proportional to this surface area (Morgan et al. 2008). Quantifying the surface area of all root structures (and how they change seasonally and under different loading conditions) may be seen as an impossible task.

Certain sub-model details, however, may need to be rethought concerning parameterization and level of detail. For example, the settling properties of humic substances found in wetlands may be markedly different from what is assumed in a sedimentation model developed for (or borrowed from) clarifier technologies. Since humic substances in wetlands accelerate particle settling through bridging and sweep flocculation methods, they also significantly increase the hydraulic resistance of accumulated solids (Liu et al. 2019). Moreover, modelling flow through constructed wetland root structures using CFD may be computationally onerous and otherwise impossible given the lack of information on the nature and abundance of the roots themselves. These sorts of challenges are very common.

Fortunately, engineers are adept at making creative simplifications and approximations to manage complexity and still develop insightful design models with predictive power. Initially, simple rules of thumb and regression equations were used, along with the first-order k-C model – one of the earliest and most well-known models, which relate the rate of degradation of contaminants to their concentration in the water (Rousseau et al. 2004; Ho et al. 2017). However, after the 1990s, due to the rapid advancement of computer technology and a growing understanding of underlying NBS mechanisms, more dynamic and compartmental models were developed to better represent the behaviour of these systems (Rousseau et al. 2005; Houweling et al. 2008; Patry 2020). These models incorporate more detailed information about the physical, chemical, and biological processes that occur in NBS systems and are often used to predict their long-term performance (Meyer et al. 2015; Ho & Goethals 2020). Data-driven models, employing machine learning techniques to identify model structures for both linear and non-linear processes (Dunn 2020), CFD modelling and compartment-based modelling have also been applied to model NBS systems with greater accuracy (Wood et al. 1995; Alvarado et al. 2012).

Parameter sensitivity analyses are standard procedures for applying NBS models in cases of ‘data scarcity’ where there is insufficient data to meet the ‘gold standard’ of model calibration and validation. Sensitivity analysis can then be combined with methods such as Monte Carlo Analysis to propagate parameter uncertainty into scenario simulation results (Sin et al. 2009; Ho et al. 2018; Borzooei et al. 2019). Sensitivity analysis also provides ancillary benefits to the NBS model user in revealing which parameters have the greatest influence and can be considered ‘governing parameters’, the latter being good candidates for further investigation through laboratory or field measurements. Identifying ‘which are the governing parameters’ is equivalent to identifying ‘which are the governing mechanisms’, an important insight that NBS models can provide.

The sheer number of use cases and categories of technologies are also challenges in developing a framework for modelling NBS. For instance, Cross et al. (2021) categorize NBS as either water-based (e.g., ponds and in-stream restoration) or substrate-based (e.g., soil infiltration, subsurface flow treatment wetlands), and there are numerous other possible categorizations and sub-categorizations, such as reactive vs. non-reactive and photosynthetic vs. mechanically aerated. Furthermore, difficulties arise in capturing transient phenomena that can impact system performance, such as storm events in wetlands, integrating and adapting the activated sludge model (ASM) kinetics for NBS systems with long solids retention time (SRT) (Friedrich et al. 2017).

A modelling framework for NBS should be both broad and flexible. To this end, this article adopts an approach inspired by a series of case studies with different objectives and challenges. These serve as the foundation for developing a multidimensional framework that accounts for the NBS type, use case, and required sub-models. It is then extended to cover a more inclusive list of NBS categories identified by Cross et al. (2021). It is the authors' hope that this framework may guide future development efforts, and in so doing, address the central question of this opinion article: ‘How can good modelling practices inspired by guidelines for activated sludge models be applied to bridge the knowledge gap in modelling NBS?’

Four case studies presented below are drawn from the academic research and consulting practice of the co-authors and participants of a workshop at the 8th IWA Water Resource Recovery Modelling Seminar (WRRmod2022 +) in January 2023. While they do not cover the full spectrum of existing NBS types and use cases, they do present sufficient variety in objectives and sub-models to form the foundation of the multidimensional framework proposed in this article. This article does not fully cover the modelling results of the case studies. Instead, it seeks to summarize the findings to demonstrate the accuracy of the models and highlight what is essential for supporting the proposed NBS modelling framework. The case studies include:

• Municipal aerated lagoons (ALs) where the modelling objective is predicting BOD₅ removal.

• A biofilm-enhanced AL arrangement treating municipal effluent with the objective of modelling nitrification and the relationship between methane generation in the sediment layer and effluent TSS.

• A stormwater basin with the objective of predicting pathogen removal.

• A constructed wetland treating contaminated groundwater with the objective of validating use of supplemental oxygen supply to enhance nitrification capacity.

Each lagoon is equipped with subsurface aeration diffusers to meet the oxygen requirements at an aeration intensity equivalent to 2.18 m³ air/m³ treatment volume/d (or 1.94 W/m³) in the first lagoon. Information related to HRT, aeration intensity, and sediment accumulation is presented in Table 1.

The correction factor ‘CF’ accounts for release of BOD₅C from anaerobic decomposition in the lagoon sediment layer (CF = 1.05 in winter and 1.20 in summer). It is applied only to the first and second ponds for a series of three or more ponds. The removal coefficient at 20 °C (K_e@20°C) is 0.37 d⁻¹ and the temperature coefficient (θ) is 1.07. The HRT in this model is varied based on the volume occupied by the accumulation of sludge at the bottom of the lagoons as well as for the formation of ice cover on the surface in winter (5%) for lagoons 2–4 (MELCC 2010).

The authors believe that many relevant mechanisms are improperly accounted for or simply out of scope. For example, the Eckenfelder model did not consider the interaction of water and sediment layer and temperature stratification in lagoons, especially during the fall. Additionally, it oversimplifies the decay kinetics assumption, failing to capture microbes' dormancy in cold weather, thus impacting BOD₅ removal. It overlooks the influence of algae growth in the summer, potentially leading to increases in effluent TSS and BOD₅. To enhance prediction accuracy in ALs, a more robust model was suggested to address these limitations. A model that includes two specific sub-models, one concerning biokinetics and another regarding the compartmentalization of the water column and sediment layer, is expected to improve the accuracy of the simulation. This model could also include a photosynthesis sub-model to capture the algal growth impact on AL performance, such as provided in the pond model included in the SUMO simulation software (Dynamita, Sigale, France).

All biochemical reactions were assumed to occur in the biofilm reactors and digesters, hence the use of the ‘non-reactive CSTR’ to represent the lagoon water column. This simplification of the model combines the activity of the biofilm with the potentially present activity of the suspended biomass in the real system. The connection from the settler model to the digester model, representing the sedimentation flux, has a minimal liquid flow through the digester block (0.001 m³/d), and it was confirmed that this flow has no discernible impact on the overall lagoon hydraulics. Additionally, there is a return link from the digester to the non-reactive CSTR describing the bulk liquid volume above the sediment layer, enabling the modelling of biogas-induced sediment resuspension (ebullition) and the release of soluble compounds from the sediments.

The results of this case study suggest that the selected sub-models and the strategy of dividing autotrophic bacteria into two groups have the potential to improve the modelling of enhanced-biofilm AL.

The model of this stormwater basin was built in the WEST modelling software (DHI, Hørsholm, Denmark) (Vanhooren et al. 2003). The model discussed in the case study extends the stormwater sedimentation model of Vallet et al. (2016) and focuses on Escherichia coli removal mechanisms, primarily through sedimentation of particles to which E. coli is attached. This model utilizes a layered approach and a mass balance to describe spatial heterogeneity, simulating particle concentration gradients and pollutant behaviour.

The model defines a population of particle classes with different sedimentation velocities and associated suspended solids masses. The ViCAs protocol (Chebbo & Grommaire 2009) is employed for experimental determination of particle class fractions. The population balance model, incorporating sorption/desorption processes, simulates pathogen dynamics in stormwater basins. Inactivation of E. coli is described through natural decay, predation, and solar disinfection, with these processes applied to both particulate and free E. coli populations. The overall sorption/desorption process rate, base decay, and solar disinfection are detailed in the model, offering a comprehensive understanding of E. coli dynamics in stormwater systems (Vergeynst et al. 2012).

The proposed stormwater basin model consists of three sub-models, including a one-dimensional, vertical flux hydraulic model, an influent fractionation model to distinguish between soluble and particulate components and to classify particulate components according to their sedimentation velocities and a sedimentation model.

The removal of free E. coli (Figure 10(b)) increases as particulate concentration decreases, leading to enhanced disinfection. In the absence of radiation at night, the removal of free pathogens is solely due to base decay. The rise in solar disinfection takes longer in deeper layers and for slower-settling particles, resulting in lower light intensities and noticeable wave-shaped concentration profiles. Solar disinfection's importance is evident in the decrease of free bacteria in deeper layers (Figure 10), particularly when higher light intensity reaches subsurface layers during the second day. The model successfully replicates various stormwater basin phenomena, including decay, adsorption/desorption to particles, settling, and solar disinfection (Vergeynst et al. 2012).

The robustness of this model still requires validation through longer datasets or by including other NBS categories. Nevertheless, this case study illustrates how these three sub-models were developed for a specific use case, pathogen removal.

The first objective of the study was to determine the adequacy of existing modelling tools for simulating a surface flow wetland. The second objective was to use the model to fill in data gaps, notably concerning the relative contributions of the deep and shallow zones to overall treatment performance, and based on this, evaluate the validity of the original design assumptions. The two distinct zones and the mass balance on nitrogen were modelled using two existing unit processes from the SUMO™ (Dynamita, Sigale, France) model library: a moving-bed biofilm reactor (MBBR) unit to simulate the root (shallow) zone and a Pond unit to simulate the open water (deep zone). Each unit process included several sub-models such as a gas–liquid transfer model for relevant gases including oxygen (MBBR and pond unit), an influent wastewater fractionation model to distinguish between soluble and particulate biodegradable and non-biodegradable components (MBBR and pond unit), a biokinetic model (MBBR and pond unit), a one-dimensional biofilm model (MBBR unit), a two-compartment water column/sediment layer model (pond model), and a sedimentation model (pond model).

The MBBR units represent shallow zones where flow through root structure biofilms is the dominant process. The pond units represent flow through deep zones where water supersaturated in oxygen is injected. The three first ponds have two inflows: recirculated aerated water and water from the previous zone.

It is assumed in the calibration protocol that most of the biological treatment occurs in the shallow zone, except for algae growth. Because the shallow zone is mostly composed of plants, which means that direct sunlight does not reach the water, algae growth should occur in the deep zone, which is modelled as a pond. Existing pond models were used to model the deep zone, and algae concentrations were simply fitted by slightly increasing the sun radiation data within their range of uncertainty. The shallow zone is modelled as an MBBR model, and the parameters in the MBBR model were calibrated to fit carbon and nitrogen water quality data. The soluble effluent pollutant concentrations were fitted by calibrating the biomass surface in the MBBR model through a reduction in media fill (from 50 to 20%) and specific surface (from 500 to 250 m²/m³). Arrhenius constants were also reduced (to 1.12 and 1.06) because the model simulated too much nitrification during the winter (below 5 °C).

Figure 13 demonstrates that the SUMO model can simulate the breakthrough in effluent ammonia concentrations from the surface flow wetland during cold months (below 5 °C). The first objective (modelling the surface flow wetland) can therefore be met, despite the lack of a dedicated constructed wetland unit process, through a combination of MBBR and pond modelling units.

The model developed has not yet been validated on independent datasets and it is unknown at this point if the model is ready to access the design assumptions (second modelling objective) of the surface flow wetland design. Nevertheless, this case study provided a valuable example of how NBS models can be developed in practice: (1) identify the modelling purpose, (2) identify the mass balances of interest, (3) identify the relevant sub-models required, and (4) combine unit processes that include the required sub-models.

The four case studies presented a modelling approach for different NBS systems, each with different objectives. In the authors' opinion, this approach could be extrapolated into a reference framework to assist in creating useful models for various NBS systems. In case study 4, for example, this concept is effectively demonstrated. By identifying the necessary sub-models and combining two process units – a pond and a media biofilm (MBBR) – the authors developed a model for a constructed wetland with the objective of modelling nitrification. Table 3 presents the initial proposed framework for modelling NBS according to their ‘category’ and the required ‘sub-models’. Here, the ‘category’ in this table refers to the case studies discussed.

Most of the sub-models listed in Table 3 are available, in some form, within commercial simulation software packages similar to those used in case studies 1–4. Descriptions of most of these sub-models can be found in the literature, such as influent sub-model (Rieger et al. 2012), layered sedimentation sub-model model (Takács et al. 1991; Torfs et al. 2016), sub-model to segregate water column and sediment (Houweling et al. 2008; Hoque et al. 2014; Ho et al. 2018), biofilm sub-model (Wanner & Gujer 1986; Takács et al. 2007), biokinetic sub-model (Henze et al. 2000), algal growth sub-model (Wágner et al. 2016; Casagli et al. 2021), pH sub-model (Fairlamb et al. 2003; Batstone & Flores-Alsina 2022), and aeration sub-models (Bencsik et al. 2022).

The NBS categories and sub-models are not limited to those listed in Table 3; therefore, the proposed framework should be extended in both NBS categories and sub-models. The extended framework detailed in Table 4 provides information on which sub-models should be included based on NBS categories. Except for the non-ideal hydraulic flow and the water chemistry sub-models, all sub-models included in Tables 4 and 5 were used in the four case studies. Other sub-models, such as a heat balance or a chemical precipitation sub-model, should eventually be included. These sub-models were not yet included because the main objective is to present how the framework can be generalized from case studies. The authors' opinion is that the framework could be further extended in future studies as new case studies are included.

During the brainstorming session, workshop participants found it more instructive to consider sub-model requirements through the perspective of use cases. For instance, when modelling a waste stabilization pond, the relevant sub-models may vary significantly based on the use case being considered, such as (a) reusing the effluent for irrigation or (b) estimating capacity and planning desludging events. In scenario (a), specific hydraulic sub-models may be necessary to address storage volumes, effluent pumping, and minimum drawdowns. In contrast, for scenario (b), the focus may shift more towards influent loading and fractionation. Table 5 developed an alternative perspective on the framework by using use cases instead of NBS categories.

The cells in Table 4 corresponding to NBS categories (such as surface flow wetland and lagoon) were typically populated based on a logical idea. A black dot (●) in a cell indicates that most of the study cases utilize the sub-model; a blank dot (○) indicates that at least one of the study cases uses the sub-model; and empty boxes signify that none of the study cases employ a particular sub-model. The same logic was applied to Table 5.

Each sub-model that is usually required (●) or that may be required (○) to model a specific NBS category or use case was deduced based on the authors' opinion. The authors hope that this framework may serve as a guide for NBS practitioners and software developers in the future. These frameworks overall provide a lookup tool to enable practitioners and researchers to get started pre-selecting sub-models according to the system or use case.

The recommended approach for modelling NBS systems emphasizes the importance of seeking the simplest model that adequately addresses the specific problem at hand. The decision-making process for modelling NBS systems involves several steps, each dedicated to determining specific aspects of the model.

The initial step entails establishing the project definition and collecting data for representation in NBS modelling within a specific time frame. For example, when modelling sludge accumulation in ALs, the process unfolds over many years in response to the accumulation of organic and inorganic materials. This longer-term perspective may overlook short-duration phenomena, highlighting the need for long-term data collection and representation. Conversely, phenomena like the resuspension of sediments can impact nitrification performance (as seen in case study 2) and affect water quality within hours or days. This necessitates detailed modelling and more accurate short-term data collection.

The next step is a pivotal aspect of the decision-making process, involving the identification of components and processes to include in the model and those to exclude. Through a series of case studies, this article developed a framework for identifying the sub-models required to simulate a broad range of NBS technologies. A set of tables is presented to identify necessary sub-models based on NBS categories or use cases. Most sub-models are available in simulation software process unit libraries and can be referenced in scientific literature. The demonstration illustrated how combining readily available process units in software can lead to an adequate simulation of NBS technologies that are not explicitly modelled. This is important due to the tremendous variety of NBS technologies and use cases, coupled with the relative scarcity of process models dedicated to them. An example of the utility of this article is demonstrated when setting up the sub-models' structure for a specific NBS so that it aligns with a given column in Table 4 or 5. This exemplifies the practical utility of the framework in aligning specific NBS instances with appropriate modelling components. After establishing the model variables and reactions, the final decision can be made, with a focus on determining the boundary conditions for the model.

In moving forward, it is crucial to rephrase challenges as opportunities. Models, while not necessarily filling gaps in missing data, exhibit the capacity to identify reasonable ranges and sensitivities. Rather than viewing the absence of inputs as a challenge, the focus shifts to the potential for model sensitivity analysis to reveal which input is significant. These insights present opportunities for revisiting and refining conclusions, fostering a continuous improvement cycle in NBS modelling.

The work of A.R.D.T., Y.C., and P.A.V. was supported by the FRQNT projet d’équipe ‘Étangs aérés facultatifs: modélisation de la matière organique (DBO₅, boues, algues) et de l'azote pour prédire et assurer leur performance toute l'année, et réviser le guide de conception’. The work of P.A.V. and J.-M.P. was further supported by the NSERC Discovery Grant RGPIN-2021-04347 ‘Towards digital twin-based control of water resource recovery facilities – Methods supporting the use of adaptive hybrid digital twins’.

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

The authors declare there is no conflict.