ABSTRACT
Despite water being a significant output of water and resource recovery facilities (WRRFs), tertiary wastewater treatment processes are often underrepresented in integrated WRRF models. This study critically reviews the approaches used in comprehensive models for ozone (O3) and biological activated carbon (BAC) operation units for wastewater tertiary treatment systems. The current models are characterised by limitations in the mechanisms that describe O3 disinfection and disinfection by-product formation, and BAC adsorption in multi-component solutes. Drawing from the insights from the current O3, BAC, and WRRF modelling approaches, we propose an integrated O3–BAC model suitable for simulating dissolved organic carbon (DOC) and micropollutants removal in the O3–BAC systems. We recommend a hybrid modelling approach in which data-driven models can be integrated to compensate for structural limitations in mechanistic models. The model is developed within the activated sludge model (ASM) framework for flexibility in coupling with other WRRF models and hence facilitates developing system-wide WRRF models for wastewater reclamation and reuse systems.
HIGHLIGHTS
Advanced wastewater treatment processes are underrepresented in current WRRF models.
Integrated O3–BAC is a viable and sustainable advanced treatment alternative for tertiary treatment systems.
Current O3 and BAC models have limitations in simulating disinfection by-product formation and multi-component adsorption, respectively.
An integrated O3–BAC model based on hybrid mechanistic and data-driven approach is proposed.
NOMENCLATURE
GAC particle porosity
GAC particle density
rate expression
maximum growth rate of heterotrophic biomass
biofilm surface area
- Amacro
specific macropore surface area
- Amicro
specific micropore surface area
biofilm surface area
maximum decay rate of heterotrophic biomass
diffusivity in the bulk phase
diffusivity in the biofilm
diffusivity in the GAC
fraction of available internal surface area for GAC adsorption
ozone-to-total organic carbon ratio
- i
single component of a multi-component solution
mass transfer coefficient
second-order kinetic rates for bromate formation reactions)
first-order kinetic adsorption rate of component i
first-order kinetic desorption rate of component i
Langmuir adsorption constant of adsorbate
Freundlich isotherm capacity constant
saturation constant for substrate
first-order ozone decomposition rate
UVA254 decay rate
kinetics of oxidation of specific micropollutants with ozone
kinetics of oxidation of specific micropollutants with OH•
first-order bromate formation rate constant
biofilm thickness
- LBL
boundary layer thickness
equilibrium solute phase loading with respect to initial DOC concentration
adsorbed DOC concentration
maximum adsorbent-phase concentration of adsorbate when surface sites are saturated with adsorbate
total concentration of adsorbed components
adsorbed fraction of MP i
- RCT
OH• to O3 exposures ratio
GAC grain/particle radius
DOC concentration in the BAC biofilm phase
DOC concentration in the BAC bulk phase
DOC concentration in the BAC biofilm phase
DOC model component
- S
DOC concentration
DOC concentration in the GAC phase
IAST-based equilibrium adsorbed DOC concentration of adsorbate i
current equilibrium adsorbed DOC concentration of adsorbate i
- t
time
stoichiometry constant variable
stoichiometric parameter for biodegradation
flow velocity in the y direction (vertical interstiti
boundary layer thickness
heterotrophic biomass concentration
XOHO concentration set point
mass fraction in the adsorbed phase of adsorbate i regarding the total adsorbed phase (obtained from IAST equilibrium calculations)
INTRODUCTION
The water and sanitation sector is currently grappling with urbanisation, population growth, industrialisation, and the impact of climate change. To address these challenges, wastewater treatment plants (WWTPs) are being transformed into water and resource recovery facilities (WRRFs), aligning them with the circular economy framework. Effectively managing wastewater is the key to achieving a circular water economy, as this resource contains valuable materials that can be reclaimed and reused through proper treatment (Voulvoulis 2018). Given the global water crisis, adopting alternative water sources, such as wastewater reclamation and reuse, is critical. Successful full-scale projects worldwide have demonstrated the effectiveness of water reuse as a viable and sustainable alternative water supply (Lazarova & Asano 2013; Swartz et al. 2022). With the increasing importance of water reuse, wastewater treatment is becoming a crucial component of the water supply system, prompting an integrated system-wide management approach to achieve sustainable water security for future climate-resilient water systems. This requires significant support in terms of engineering tools for decision-support for design, operation and management to ensure that the required water quality and quantity is produced efficiently and sustainably.
Mathematical models are widely used in the wastewater sector for research, system design, process simulation, and operator training (Gernaey et al. 2004). The International Water Association (IWA)’s activated sludge models (ASMs), which were developed in the 1980 and 1990s, have remained relevant until today in wastewater bioprocess modelling. The application of ASMs has also been extended to modelling unconventional treatment technologies such as novel nutrient removal technologies (Santos et al. 2020), biological activated carbon (BAC) (Alonso et al. 2021), and membrane bioreactors (MBRs) (Fenu et al. 2010). Along with the evolution of WWTPs to WRRFs, modellers have moved their focus towards developing integrated WRRF models instead of modelling WWTPs as stand-alone operation units (Ekama 2009; Regmi et al. 2019; Ikumi 2023). This has resulted in two modelling paradigms: Plant-wide modelling (within the fence of WWTP) and system-wide modelling (beyond the fence of WWTPs). Plant-wide models (PWMs) are well established and have already found applications in various full-scale projects (Maere et al. 2011; Flores-Alsina et al. 2021; Nqayi et al. 2023). System-wide models, on the other hand, remain an emerging concept. However, system-wide models can potentially become powerful tools in promoting a circular water economy, climate resilience, and efficient resource use in the water sector (Montwedi et al. 2021; Ikumi 2023).
Since water is an essential output of WRRFs, it is vital to ensure that reusable water is generated efficiently and sustainably while meeting the required standards. Hence, having reliable engineering tools to evaluate the fate of various pollutants throughout the entire WRRF is crucial in guiding decision-making processes. Although wastewater PWMs are well established, there is still a shortage of good predictive modelling tools for advanced treatment processes of water reclamation facilities to facilitate the development of integrated system-wide models for wastewater reclamation and reuse.
This review aims to provide an ensemble perspective on the state of advancement in modelling approaches for tertiary wastewater treatment processes within the context of WRRF modelling. Focusing on ozone (O3) and BAC models, the review highlights limitations in existing modelling approaches and proposes possible improvements, particularly to the WRRF modelling community interested in wastewater reclamation and reuse. To the authors' knowledge, this study is the first attempt to combine mechanisms for ozone decomposition, disinfection and bromate formation and control with BAC biodegradation and adsorption mechanisms into an integrated O3–BAC model within the WRRF modelling framework.
The study employed a narrative review approach, using multiple search strategies, keywords, and databases to identify relevant literature. This was followed by manual skimming and scanning screening to select papers describing representative comprehensive models for O3, BAC, or O3–BAC. This approach was adopted because it allows for a comprehensive examination of a broader range of literature on the subject matter without the constraints of rigid inclusion and exclusion criteria of the systematic review approach.
TERTIARY TREATMENT PROCESS AND MODELLING
While most WWTPs are designed and operated to meet environmental discharge regulations, their tertiary treatment capabilities are usually insufficient for water reuse, especially for potable reuse (Tchobanoglous et al. 2003). Consequently, a dedicated wastewater reclamation plant (WRP), which receives WWTP effluent, is established and often operated independently to guarantee safe potable water production. This approach is commonly practised in potable reuse projects in Namibia and South Africa, which are regarded as pioneers in wastewater reclamation and reuse (Schutte 2007; Swartz et al. 2022). Although the tertiary treatment process is technically part of the wastewater treatment system, this study addresses tertiary treatment as part of a WRP rather than a WWTP. Therefore, in this study, coupling WWTP and WRP models is referred to as a system-wide wastewater reclamation and reuse model.
The WRP treatment trains typically combine conventional water treatment units of operations (e.g., flocculation and coagulation, filtration, etc.) with advanced water treatment processes (e.g., membrane processes, advanced oxidation processes (AOPs), etc.) to achieve partial or complete removal of multiple contaminants. Most modern trains employ either membrane (e.g., microfiltration (MF), reverse osmosis (RO), etc.) or AOPs (i.e., ozone and UV-based AOPs) or a combination of both to remove persistent pollutants (Leverenz et al. 2011; Tchobanoglous et al. 2015). Although RO effectively removes contaminants, it is energy-intensive and produces difficult-to-manage brine from an environmental perspective (Leverenz et al. 2011; Gerrity et al. 2014). Therefore, alternative treatment approaches such as AOPs and biologically activated carbon (BAC) filtration processes are preferred due to their proven success, low operation and maintenance costs, and energy efficiency.
A process configuration of the NGWRP (adapted from Wallmann et al. (2021)).
The increasing need for wastewater reclamation and reuse underscores the necessity for model-based tools for planning, designing and operating tertiary treatment technologies and water reuse processes. In the water reuse modelling workshop held at the eighth IWA Water Resource Recovery Modelling Seminar (WRRmod2022+) (2023), experts highlighted the lack of reliable models for tertiary wastewater treatment processes compared to their primary and secondary treatment counterparts. Furthermore, while there is general agreement on the importance of including physicochemical models (PCMs) in current WRRF models, processes based on aquatic chemistry, such as chemical oxidation (e.g., O3) and adsorption (e.g., BAC), are still not adequately represented in these models (Batstone & Flores-Alsina 2022). These pose a significant challenge in developing system-wide mathematical models for wastewater reclamation and reuse within the WRRF context. Integrated system-wide models are essential decision-support tools for advancing a circular water economy and holistically addressing water and sanitation challenges. For instance, system-wide models can be applied to evaluate the viability of decentralised or centralised options and provide valuable insights for strategic planning to promote water reuse, enhance climate change resilience, and maximise the use of renewable energy resources (Ikumi 2023).
OZONATION SYSTEM AND PROCESS MODELLING
Overview of the Ozonation technology
In water and wastewater treatment, ozone (O3) is a highly effective natural oxidant, second only to hydroxyl radical (OH•) (Audenaert et al. 2010). When O3 reacts with water, it has the unique ability to generate OH• via a side reaction with electron-rich compounds. These two compounds, O3 and OH•, play crucial roles in removing pollutants from water by directly oxidising inorganic and organic compounds and disinfecting microbiological contaminants and micropollutants (Von Gunten 2003a, b). However, this disinfection process can lead to the formation of excessive disinfection by-products, particularly bromate. Once formed, bromate is challenging to remove from water and is also known to be a potential human carcinogen (Von Gunten 2003b; Lim et al. 2022). This presents a paradox, as the legal criteria for excess bromate limit the amount of O3 that can be used, thereby reducing the efficacy of the disinfection process (Van Der Helm et al. 2007).
The reaction mechanisms of ozone in water and wastewater have been extensively studied by researchers such as Staehelin & Hoigne (1985) and Bezbarua & Reckhow (2004). However, the kinetics of these reactions remain complex due to the high reaction rate kinetics of ozone and the challenges in characterising dissolved organic matter (DOM) in ozone systems. Despite efforts to simplify reaction models, these models still lack the robustness to deal with variations in influent composition and operational conditions, and hence, their prediction accuracy is still limited (Mandel et al. 2012; Audenaert et al. 2013). Therefore, empirical and semi-empirical modelling techniques are often used in full-scale ozone processes (Van Der Helm et al. 2008; Morrison et al. 2023).
Lessons from existing models
To facilitate the discussion of the ozone models in this paper, we define a comprehensive ozonation model as a system of models describing an ozonation process. This includes ozone decay or decomposition, disinfection and bromate formation, which are the most commonly modelled processes of the ozonation system. Some models also include the formation of assimilable organic carbon (AOC), an important by-product of bulk organic matter oxidation, particularly in the context of O3–BAC treatment, as discussed later in Section 5. Hence, modelling AOC is also discussed in this section.
The O3 system is usually described using sets of non-linear ordinary differential equations (ODEs) derived from reactor mass balance. These ODEs are often characterised by a mix of fast processes, making the model stiff, and hence, they cannot be practically solved using analytical methods. Instead, numerical methods are employed to rapidly solve these stiff systems of ODEs. Examples of numerical methods used in ozone systems include the Runge-Kutta method used for simulating ozone decomposition (Lovato et al. 2009) and the finite-difference method (FDM) for simulating bromate formation (Olsinska 2019). Batstone & Flores-Alsina (2022) provide a detailed discussion on a general approach for implementing and finding solutions to ODEs using numerical methods. For water and wastewater treatment applications, various simulation software, such as Stimela (Delft University of Technology, Netherlands), and WEST (DHI 2023, Hørsholm, Denmark), has built-in numerical simulation codes. Models employing computational fluid dynamics (CFD) techniques, which combine hydraulic and reaction phenomena, have also emerged (Zhang et al. 2007; Mandel et al. 2012).
Ozone decomposition
To realistically describe the ozone decomposition process, the process must include initial ozone decomposition (rapid phase), second (slow) phase ozone decomposition and the reaction of O3 and natural organic matter (NOM) (Buffle 2005; Van Der Helm et al. 2007). Mechanistic kinetic models have been developed, but because of their high complexity, calibrating them is impractical (Bezbarua & Reckhow 2004; Audenaert et al. 2013) or rather need specific calibration frameworks that are not readily available in published material due to intellectual properties (IPs) (Audenaert et al. 2019), and therefore, they are often not preferred. For example, the ozone decomposition reaction scheme described in Audenaert et al. (2013) comprises 29 kinetic reactions describing ozone decomposition and ozone reaction with NOM. None of the models reviewed in this study (listed in Table 1) used these kinetic reaction schemes for ozone decomposition.
Selected comprehensive ozonation models and their underlying processes
No. . | Reference . | Ozone decomposition . | Disinfection . | ![]() | AOC formation . | Hydraulic characteristics . | Calibration/test data description . | Prediction performance and shortcoming . | |||
---|---|---|---|---|---|---|---|---|---|---|---|
Rapid phase . | Slow phase . | NOM impact . | OH·exposure . | Oxidation . | |||||||
1 | Zhang et al. (2007) | IOD | Equation (1) | – | – | Equation (4) | Equation (8) | – | CFD | Natural water; full-scale | Good prediction accuracy for flow dynamics. Accuracy of O3 decay and disinfection not satisfactory |
2 | Van Der Helm et al. (2007, 2008) | Equation (1) | Equation (1) | Equation (3) | – | Equation (5) | Equation (8) | Regression | CSTR-PFRa | Natural water; bench (batch) & pilot (continuous flow) scale | Good prediction for O3 decay in the rapid phase, E. coli disinfection, and AOC formation. Slow-phase O3 decay and bromate formation models had limitations in applicability to certain dosages and contact times. |
3 | Audenaert et al. (2010) | Equation (1) | Equation (1) | Equation (3) | – | Equation (5) | Equation (8) | – | CSTR | Natural water; full-scale | Good predictive capabilities for O3 decay and bacteria removal, while bromate predictions required additional data for more robust validation |
4 | Gerrity et al. (2012, 2014) | IOD | Equation (2) | Empirical (O3:TOC based) | Regression | Equation (7) | – | Regression | CSTR | WWTP effluent; Bench-scale batch reactor | No formal verification of prediction accuracy was conducted. The study contextualises its results by citing previous research findings. |
5 | Audenaert et al. (2019), Muoio et al. (2023) | Includedb | Includedb | UVA-basedb | RCT – concept | Equation (7) | Figure 1 | CSTR-PFRa | WWTP effluent; Bench-scale batch reactor | Good prediction for O3 decay, bromate formation and a wide range of micropollutant groups, |
No. . | Reference . | Ozone decomposition . | Disinfection . | ![]() | AOC formation . | Hydraulic characteristics . | Calibration/test data description . | Prediction performance and shortcoming . | |||
---|---|---|---|---|---|---|---|---|---|---|---|
Rapid phase . | Slow phase . | NOM impact . | OH·exposure . | Oxidation . | |||||||
1 | Zhang et al. (2007) | IOD | Equation (1) | – | – | Equation (4) | Equation (8) | – | CFD | Natural water; full-scale | Good prediction accuracy for flow dynamics. Accuracy of O3 decay and disinfection not satisfactory |
2 | Van Der Helm et al. (2007, 2008) | Equation (1) | Equation (1) | Equation (3) | – | Equation (5) | Equation (8) | Regression | CSTR-PFRa | Natural water; bench (batch) & pilot (continuous flow) scale | Good prediction for O3 decay in the rapid phase, E. coli disinfection, and AOC formation. Slow-phase O3 decay and bromate formation models had limitations in applicability to certain dosages and contact times. |
3 | Audenaert et al. (2010) | Equation (1) | Equation (1) | Equation (3) | – | Equation (5) | Equation (8) | – | CSTR | Natural water; full-scale | Good predictive capabilities for O3 decay and bacteria removal, while bromate predictions required additional data for more robust validation |
4 | Gerrity et al. (2012, 2014) | IOD | Equation (2) | Empirical (O3:TOC based) | Regression | Equation (7) | – | Regression | CSTR | WWTP effluent; Bench-scale batch reactor | No formal verification of prediction accuracy was conducted. The study contextualises its results by citing previous research findings. |
5 | Audenaert et al. (2019), Muoio et al. (2023) | Includedb | Includedb | UVA-basedb | RCT – concept | Equation (7) | Figure 1 | CSTR-PFRa | WWTP effluent; Bench-scale batch reactor | Good prediction for O3 decay, bromate formation and a wide range of micropollutant groups, |
aA combination of CSTR and PFR is modelled as ‘tanks-in-series,’ whereby a series of CSTRs replicate PFR-like behaviours.
bThe study mentioned that the components have been accounted for in the model but did not specify the equations used.
Disinfection
The main difference in approaches for modelling ozone disinfection is the assumption of whether direct ozonation is the only disinfectant or whether ozone and OH• play a role in disinfection (Von Gunten 2003b). While this has been an ongoing debate, there is evidence that OH• plays an important role in disinfection, particularly compounds that react slowly with ozone (i.e., < 104 m−1s−1) (Buffle et al. 2006). Hence, the main difference between the two modelling approaches is whether OH• disinfection is taken into account.
The O3–CT approach is easy and straightforward to use but does not capture the significant disinfection and bromate formation that occurs during the initial phase of O3 decomposition due to OH• exposure (Von Gunten 2003a, b; Buffle et al. 2006). Models based on this oversimplification are overly conservative with regard to disinfection potential, which can lead to O3 overdosing during operation and correspondingly high bromate formation (Buffle et al. 2006; Zhang et al. 2007). Nonetheless, as can be seen from Table 1, this approach has remained popular due to its simplicity and proven success in predicting disinfection efficacy at various scales and operating conditions (Van Der Helm et al. 2008; Audenaert et al. 2010). The O3–CT approach also remains the standard way of designing ozone reactors.


Bromate formation
The mechanism for bromate formation during ozonation of bromide-containing waters (Pinkernell & von Gunten 2001).
The mechanism for bromate formation during ozonation of bromide-containing waters (Pinkernell & von Gunten 2001).
While there is proof of successful prediction of bromate formation using empirical and semi-empirical correlations (Van Der Helm et al. 2008; Audenaert et al. 2010), it is also worth noting that these models generally do not generate much process knowledge and tend to be only valid within specific operational boundaries (i.e., highly dependent on the water matrix) (Audenaert et al. 2019; Morrison et al. 2023). With the improved techniques for measuring ozone concentration in the initial rapid phase (and the subsequent determination of RCT and OH• concentration) (Buffle et al. 2006; Audenaert et al. 2019), it is encouraging to use mechanistic-based models to predict bromate formation.
AOC formation
The formation of AOC has not been widely modelled; in fact, its underlying mechanisms have not been established yet. The major limitation for developing these mechanisms is largely due to the complex nature of the reaction between O3 and organic matter (Von Gunten 2003b). Two models reviewed in this study (Table 1) included the prediction of AOC using linear regression models based on UVA as a surrogate parameter (Van Der Helm et al. 2008; Gerrity et al. 2014). Considering that the analytical methods for determining AOC concentration are labour-intensive, surrogate-based correlation models have been useful as soft sensors for online monitoring of AOC formation during ozonation (Ross 2019).
Integration of hydraulic characteristics
Various hydraulic modelling frameworks have been used in modelling ozone reactors, ranging from the simplest axial dispersion models (ADMs), systematic networks (assuming ideal reactor patterns), and stochastic models to the more detailed CFD models (Mandel et al. 2012). The models reviewed in this study are dominated by systematic hydraulics models, in which ozone reactors are modelled as continuously stirred tank reactors (CSTRs), plug-flow reactors (PFRs), or a combination. These models are advantageous due to their simple structure, which makes them easy to solve and are mostly paired with semi-empirical models.
Summary of ozone models
The models reviewed in this study show a trend where semi-mechanistic models are predominantly used in modelling ozone decomposition, where UVA is commonly used as a surrogate variable for bulk organic transformation. Earlier models did not take into account OH• exposure when modelling disinfection. However, recent disinfection models account for OH• exposure in disinfection models by using data-driven approaches or RCT concept to determine OH• concentration. Bromate formation is commonly modelled using first-order kinetic models with respect to O3 exposure. Several studies also attempted to model AOC formation using linear regression models. In all cases, the models assumed ideal reactor hydraulic conditions. The underlying structures and characteristics of the ozone representative models reviewed in this study are summarised in Table 1. Although exact equations may vary among different models, this study presents the general form to demonstrate the modelling approach.
Most models were reported to have some limitations in predicting parameters such as disinfection and bromate formation, demonstrating room for further refining and validation of these models. Future models should not only focus on predicting bromate formation but also include strategies for controlling bromate, such as dosing ammonia or hydrogen peroxide (H2O2), whose mechanisms already exist in the literature (Pinkernell & von Gunten 2001; Morrison et al. 2023). There has been significant recent research on using ozone for disinfecting micropollutants; hence, it is becoming more possible to integrate micropollutant removal phenomena into future models, which is important for water reuse. Model 5 reported good overall prediction accuracy for various micropollutant removal processes and bromate formation. However, it is important to note that this model is a commercial product with limited information in the peer-reviewed literature. Hence, there is a need to continue refining the existing models to improve their performance. Without resorting to complex mechanisms of ozone reactions with their associated complex calibration procedures, data science and artificial intelligence (AI) could potentially be applied to harness the predictive power and reliability of the existing simplified models.
BAC SYSTEM AND MODELLING
Overview of the BAC filtration technologies
In modern water treatment works, granular activated carbon (GAC) filters, which typically operate on the principle of adsorption, are converted into biologically GAC or simply BAC filters by introducing an oxidation step before the GAC filter media (Zhang et al. 2017). The GAC filter media typically has an irregular, porous particle shape that allows it to absorb specific organic contaminants (Simpson 2008). As the media slowly gets saturated with organic matter, a layer of biofilm grows into the surfaces of the filter media (Takeuchi et al. 1997; Levine et al. 1999; Alonso et al. 2021). This naturally occurring active biofilm enhances biological activity and hence facilitates the removal of a significant fraction of nutrients, NOMs, and microorganisms from water by biodegradation. Within the O3–BAC treatment system context, this active biofilm layer is particularly important as it helps remove assimilable organic compounds (AOCs) produced during ozonation and reserves the GAC adsorption capacity for non-degradable contaminants.
Conceptual definition of mechanisms of biological activated carbon system (adapted from Yuan et al. (2022)).
Conceptual definition of mechanisms of biological activated carbon system (adapted from Yuan et al. (2022)).
The interaction between the three BAC layers and the processes within are intricate, which makes modelling, especially multi-solute systems such as wastewater, challenging (Alonso et al. 2021). One significant limitation of existing models is their tendency to be oversimplified through assumptions that are not realistic for multi-component solute systems. For instance, most models focus on single-component adsorption, hence neglecting competitive adsorption between different wastewater components such as DOC and trace organic compounds (TrOCs), and sometimes, the description of boundaries interface conditions are not incorporated in the mass transport equations (Yuan et al. 2022).
Lessons from existing models
In this study, we define a comprehensive BAC model as one that describes the compound mass transport in bulk liquid, biofilm, and GAC phases and considers both the biofilm biodegradation and GAC adsorption processes. Yuan et al. (2022) previously conducted a similar review and concluded that most comprehensive models developed at that stage generally have a similar structure. These models generally describe compound diffusion in all three phases using Fick's law, biofilm biodegradation using Monod kinetics, and adsorption using Freundlich or Langmuir isotherms (Yuan et al. 2022). Based on this, they formulated a generic model representing all the reviewed comprehensive models and further proposed a novel model incorporating the shortcomings of the previously developed models. However, based on our examination of the model previously reviewed by Yuan et al. (2022), we found that the model by Alonso et al. (2021), which was also part of their generic model, differs significantly from the other models in the context of this study. This is because the model of Alonso et al. (2021) includes additional mechanisms not considered in the other models, particularly competitive adsorption phenomena and desorption. Therefore, in this study, the model by Alonso et al. (2021) is discussed as a separate model from the generic model formulated by Yuan et al. (2022).
Regarding hydraulic characteristics, BACs are typically developed based on fixed-bed reactors and are simulated as PFRs.
Bulk liquid phase
Summary of the structure of representative BAC models
No. . | Reference . | Mass balance . | Biofilm thickness . | Reaction equations characteristics . | Calibration/test data description . | Prediction performance and shortcoming . | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
Bulk liquid . | Biofilm . | GAC phase . | Biodegradation . | Adsorption . | Desorption . | Effect of adsorbed oxygen . | |||||
1 | Alonso et al. (2021) | Equation (10) | Equation (11) | Equation (18) | Equation (12) | Monod | IAST + Freundlich | First-order kinetic w.r.t dissolved concentration at equilibrium (Si,e) | WWTP effluent; pilot-scale | Good prediction accuracy for DOC removal by biodegradation but an anomaly in adsorptive removal modelling | |
2 | Yuan et al. (2022) and references cited therein (the generic model) | Equation (10) | Equation (11) | Equation (14) | Equation (13) | Monod | Freundlich/Langmuir isotherms | Various, mostly synthetic solutions | Generally good agreement between simulated and experimental data. Discrepancy in some models relating to biofilm loss coefficient, biofilm density, and adsorption kinetic parameters | ||
3 | Yuan et al. (2022) | Equation (10) | Equation (11) | Equation (17) | Equation (13) | Monod | EBC approach + Freundlich | Not calibrated or validated | Generic model presented. No simulation performed | ||
4 | Kaiser et al. (2023) | Equation (10) | Equation (11) | Equation (19) | Equation (12) | Monod | IAST + Freundlich + fictive GAC surface adsorption | First-order kinetics w.r.t dissolved concentration at equilibrium (Si,e) | Based on the calculation of adsorbed oxygen equilibrium concentration | WWTP effluent; pilot-scale | Overall good predictive capabilities for DOC removal in both biofilm and GAC phase. Minor systematic anomalies were observed in the biofilm model. |
No. . | Reference . | Mass balance . | Biofilm thickness . | Reaction equations characteristics . | Calibration/test data description . | Prediction performance and shortcoming . | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
Bulk liquid . | Biofilm . | GAC phase . | Biodegradation . | Adsorption . | Desorption . | Effect of adsorbed oxygen . | |||||
1 | Alonso et al. (2021) | Equation (10) | Equation (11) | Equation (18) | Equation (12) | Monod | IAST + Freundlich | First-order kinetic w.r.t dissolved concentration at equilibrium (Si,e) | WWTP effluent; pilot-scale | Good prediction accuracy for DOC removal by biodegradation but an anomaly in adsorptive removal modelling | |
2 | Yuan et al. (2022) and references cited therein (the generic model) | Equation (10) | Equation (11) | Equation (14) | Equation (13) | Monod | Freundlich/Langmuir isotherms | Various, mostly synthetic solutions | Generally good agreement between simulated and experimental data. Discrepancy in some models relating to biofilm loss coefficient, biofilm density, and adsorption kinetic parameters | ||
3 | Yuan et al. (2022) | Equation (10) | Equation (11) | Equation (17) | Equation (13) | Monod | EBC approach + Freundlich | Not calibrated or validated | Generic model presented. No simulation performed | ||
4 | Kaiser et al. (2023) | Equation (10) | Equation (11) | Equation (19) | Equation (12) | Monod | IAST + Freundlich + fictive GAC surface adsorption | First-order kinetics w.r.t dissolved concentration at equilibrium (Si,e) | Based on the calculation of adsorbed oxygen equilibrium concentration | WWTP effluent; pilot-scale | Overall good predictive capabilities for DOC removal in both biofilm and GAC phase. Minor systematic anomalies were observed in the biofilm model. |
Biofilm phase


GAC phase


Equation (18) is an extension of surface diffusion (Equation (14) with a pore diffusion phase to describe component mass transport in the GAC phase. Yuan et al. (2022) used this equation integrated with the equivalent background compound (EBC) approach to describe competitive adsorption between NOM and TrOC. An EBC is a fictive component representing the entire background of the competitive adsorbates competing for adsorption sites with the target compound (Graham 2000).
Equations (18) and (19) take into account both adsorption and desorption mechanisms integrated with pore diffusion transport. However, unlike in all previously discussed models, adsorption and desorption in Equations (18) and (19) are discussed as reaction processes, although they are largely considered mass transfer processes (Kaiser et al. 2023). The adsorption reaction consisted of pseudo-first-order kinetics (PFO) coupled with Freundlich equilibrium isotherms, which were integrated with the ideal adsorbed solution theory (IAST) to describe a multi-component adsorption system. The IAST is used for predicting multi-component adsorption based on a single-solute isotherm parameter (Alonso et al. 2021). More literature on the application of IAST in multi-component adsorption systems can be found in studies by Atallah Al-Asad et al. (2022), Nowotny et al. (2007), and Worch (2010).
Obtaining fq requires dividing the GAC adsorption capacity into a macropore domain where pore diffusion takes place and a fictive micropore domain that represents an empirical surface diffusion model as presented in the model of Kaiser et al. (2023). Consequently, fq is a function of dissolved concentration in the GAC phase (Si,GAC), the ratio between specific macropore and micropore areas (Amacro and Amicro), GAC grain radius (Rp), GAC surface diffusion coefficient (Di,GAC_S), and filter operation time. More details on the derivation of fq and its integration with equilibrium isotherms can be found in the study by Kaiser et al. (2023). Therefore, as a result of this modification, the γad term, and consequently γdes of Equations (18) and (19) are significantly different. Computation of γad and γdes terms involves a series of steps not included in this study but can be found in the studies by Alonso et al. (2021) and Kaiser et al. (2023).
Desorption reaction, which takes place after saturation of the GAC, in both Equations (18) and (19) was implemented by reversing the adsorption rate and expressed as a first-order kinetic rate with respect to dissolved concentration at equilibrium (Si,e). Finally, Equation (19) also takes into account the impact of oxygen adsorbed in GAC on biofilm growth. However, a sensitivity analysis in the study by Kaiser et al. (2023) indicates that adsorbed oxygen has little effect on biofilm growth.
Summary of BAC models
The underlying structures of the representative BAC models reviewed in this study are summarised in Table 2.
All models typically use the same equations to describe the mass balances in the bulk and biofilm phases. Adsorption mass balance equations and biofilm thickness dynamics are, in most cases, what differentiate different BAC modelling approaches. The major advancement in Models 1, 3, and 4, which represent the latest developed models, is the inclusion of multi-component adsorption and desorption mechanisms. Previous models (i.e., represented by Model 2) neglected the competitive nature of adsorption in multi-solute mixtures, such as secondary effluents.
With reference to the models presented in Table 2, the models developed by Alonso et al. (2021) (Model 1) and Kaiser et al. (2023) (Model 4) made significant advancements towards the realistic simulation of the BAC processes. Of particular interest is the inclusion of multi-component adsorption BAC models, which enables modelling competitive adsorption. Additionally, adding the desorption mechanisms in Models 1 and 4 is an important improvement for modelling preloaded GAC. This is a more realistic feature for simulating the continuous and long-term operation of BAC systems. One of the shortcomings in Model 1 was the overprediction of DOC removal, which was attributed to the implemented adsorption kinetics.
Model 4 was specifically developed for adsorption mechanisms in Model 1 by modifying the adsorption kinetics to incorporate both pore and surface diffusion. This modification is important as it improves the overall model prediction accuracy at various stages of GAC operation. Surface diffusion is dominant at an early stage of GAC operation (virgin GAC) (Liang et al. 2007), whereas pore diffusion is dominant for pre-loaded GAC (Carter & Weber 1994). This model has already been implemented into the ASM framework, making it suitable for integrating with most existing WRRF wastewater PWMs towards developing system-wide models for wastewater reclamation and reuse systems. More importantly, this model has undergone rigorous validation, including calibration, sensitivity analysis and validation, and showed a good agreement between simulated and experiment results, demonstrating the model's applicability and transferability (Kaiser et al. 2023).
The multi-component adsorption mechanisms in the reviewed models have only been applied to simulate the removal of different DOC fractions. It remains to be seen if this model could be extended to simulate competitive adsorption between DOC and micropollutants.
OZONE AND BIOLOGICAL ACTIVATED SYSTEM AND MODELLING
Principles of ozone and BAC combination
Tertiary wastewater treatment involves disinfection and filtration processes. Disinfection removes persistent microorganisms, while filtration removes particulate matter. During ozonation, ozone only inactivates TrOCs without chemically transforming them, making ozone effluents less suitable for reuse or safe for disposal (Tchobanoglous et al. 2003; Wu et al. 2018). The principle of combining ozone with the downstream biofiltration process is one of the alternatives that improve ozone-treated effluent quality. In this regard, ozone followed by BAC is the most promising alternative due to their high organic micropollutant removal rate, economic feasibility, familiarity, and flexibility in their configuration (Reungoat et al. 2012; Gerrity et al. 2014; Wu et al. 2018).
In the O3–BAC system, O3 is highly effective in inactivating pathogens and transforming complex bulk organic matter into smaller biodegradable fragments such as AOC, while BAC further removes O3 by-products through biological and adsorption activities. In a recent pilot-scale study by van der Hoek et al. (2024), it was observed that denitrifying BAC filters in the ozone–BAC system mitigates bromate formation. This is a promising prospect because, in practice, the risk of bromate formation during the ozonation process limits O3 dine and, consequently, the extent of MP disinfection. Combining the oxidation properties of O3 and the biodegradation and adsorption properties of BAC has been proven globally as an effective process for removing bulk organic compounds and micropollutants. Table 3 summarises some examples of full-scale applications of O3–BAC in tertiary treatment trains.
Selected notable full-scale WRP employing O3–BAC treatment
Plant name . | Location . | Capacity (ML/d) . | Status . | System . | Added value . | Reference . |
---|---|---|---|---|---|---|
Gwinnett County | Georgia, USA | 227 | Operational since 1999 | WRP: IPR via MAR |
| Snyder et al. (2014) |
New Goreangab WRP | Windhoek, Namibia | 21 | Operational since 2002 | WRP: DPR |
| Theron-Beukes et al. (2008) |
South Caboolture WRP | Queensland, Australia | 8 | Operational since 1999 | NPR |
| van Leeuwen et at. (2003); Reungoat et al. (2010) |
Flemish Water Supply Company Waterworks | Kluizen, Belgium | 60 | Operational since 2003 | Drinking WTP |
| Audenaert et al. (2010) |
Cape Flats MAR WRP | Cape Town, South Africa | 40 | Under construction | WRP: IPR via MAR |
| Smuts (2021) |
Plant name . | Location . | Capacity (ML/d) . | Status . | System . | Added value . | Reference . |
---|---|---|---|---|---|---|
Gwinnett County | Georgia, USA | 227 | Operational since 1999 | WRP: IPR via MAR |
| Snyder et al. (2014) |
New Goreangab WRP | Windhoek, Namibia | 21 | Operational since 2002 | WRP: DPR |
| Theron-Beukes et al. (2008) |
South Caboolture WRP | Queensland, Australia | 8 | Operational since 1999 | NPR |
| van Leeuwen et at. (2003); Reungoat et al. (2010) |
Flemish Water Supply Company Waterworks | Kluizen, Belgium | 60 | Operational since 2003 | Drinking WTP |
| Audenaert et al. (2010) |
Cape Flats MAR WRP | Cape Town, South Africa | 40 | Under construction | WRP: IPR via MAR |
| Smuts (2021) |
WRP, water reclamation plant; MAR, managed aquifer recharge; WTP, water treatment plant; IPR, indirect potable reuse; DPR, direct potable reuse; MF, microfiltration; RO, reverse osmosis; UV/H2O2, ultraviolet–hydrogen peroxide.
Lessons from existing models
A comprehensive O3–BAC model should typically integrate the major O3 and BAC processes discussed above. However, despite the advancement in mathematical modelling of O3 and BAC as stand-alone operation units, a literature search shows that no significant progress has been made in integrating the two processes. Smuts (2021) developed a framework for the O3–BAC system that attempts to balance O3 dose, organic micropollutant oxidation, pathogen disinfection, DOC removal via BAC, and the system's capital and operating costs. They used surrogate correlation models incorporating factors such as ozone dosage, contact time, water quality parameters and specific characteristics of the contaminants to predict the removal of DOC and micropollutants from an O3–BAC water treatment system.
Although this framework is useful in predicting useful parameters for the design and operation of O3–BAC systems, the prediction accuracy was not conducted. Moreover, the reliance of this framework on empirical relationships means the model cannot be generalised for different operating scales and conditions. Therefore, owing to the complementing nature of O3 and BAC operation units and the state of advancement in modelling O3 and BAC as stand-alone models, it is encouraging to develop integrated O3–BAC models based on mechanistic aspects that can be used for the design, operation and optimising of O3–BAC systems.
DATA-DRIVEN APPROACHES
Data-driven models (DDMs) are designed to learn from patterns identified in measured data and metadata without relying on specific domain knowledge. It is essential to distinguish DDMs from empirically derived phenomenological models, which derive their parametric values from domain knowledge (Schneider et al. 2022). Over the past two decades, data-driven approaches to modelling water and wastewater treatment processes have gained popularity due to advancements in data collection through sensor-based technologies and cloud-based data storage (Therrien et al. 2020). DDMs have the capability to handle extensive datasets and predict various operational conditions, making them well-suited for real-time applications (Schneider et al. 2022). Modern DDMs commonly employ machine learning (ML) algorithms to extract information and knowledge from large datasets.
The application of DDMs in operational units for tertiary treatment has been widely discussed in several systematic review papers, notably in the work by Aliashrafi et al. (2021) and Li et al. (2021). These reviews consistently illustrate the predominant use of DDMs for predicting difficult-to-measure variables and modelling processes that involve complex mechanisms. For instance, DDMs have been employed to model bromate formation (Civelekoglu et al. 2007; Gregov et al. 2023), determine ozone dosage requirement and residual ozone concentration (Kwon et al. 2022), and predict hydroxyl radical (HO·) exposure (Lee et al. 2013; Cha et al. 2024). This trend highlights the potential for broader application of DDM in ozonation systems, which can be used to predict other disinfection by-products, such as AOC. Furthermore, DDMs have been used to model the adsorption process of various adsorbates, as Lowe et al. (2022) demonstrated. While DDMs often yield acceptable prediction accuracy, they have been criticised for their lack of interpretability, raising questions about their acceptability. Within the WRRF modelling community, it is widely acknowledged that the strong prediction capability of DDMs should not come at the expense of interpretability (Therrien et al. 2020; Schneider et al. 2022). Nevertheless, DDMs remain valuable in mechanistic–DDM hybrid models, where they can compensate for missing or incomplete mechanisms in mechanistic models (Schneider et al. 2022).
TOWARDS INTEGRATED O3–BAC MODELLING
Based on the above critical review of previous (O3) and BAC models and the general state of advancement in WRRF modelling, we propose an integrated modelling approach that can be used to predict the fate of DOC and micropollutants in the O3–BAC system. The proposed model was not limited to using only the knowledge from the comprehensive O3 and BAC models discussed in Sections 3 and 4. We also explored alternative mechanisms from other sources, with the potential to modify the existing comprehensive models. The aim was to propose a model with the following features: (i) balanced in terms of mechanistic complexity to ensure reliability and practicality; (ii) A flexible and adaptable model that can be integrated with other WRRF models (e.g. WWTP plant-wide or other advanced wastewater treatment unit models). While all the components and mechanisms used to recommend modifications to the current O3 and BAC discussed in the sections below are derived from literature, integrating these mechanisms into an integrated model could lead to a novel O3–BAC modelling approach with significant practical applications.
Having practical and reliable models are particularly important as the WRRF models transition into integrated models. Additionally, noting the dominance of IWA's activated sludge modelling framework in WRRF models, it is important that future models are developed within the ASM framework to ensure they are compatible with coupling with other WRRF unit models.
Ozone treatment objective
The ozone model comprises ozone decomposition, disinfection and bromate (disinfection by-product) formation.
Ozone decomposition
The ozone decomposition model describes the rapid and slow phases of ozone decay by using UVA254 as a surrogate variable for the transformation of bulk organic matter (Van Der Helm et al. 2007, 2008). This model, based on a semi-mechanistic approach, was preferred over the kinetic reaction models (von Gunten 2003a; Audenaert et al. 2013) because of its robustness, and it has been validated with various pilot-scale and full-scale data (Van Der Helm et al. 2008, 2009; Audenaert et al. 2010). The relevant model equations are Equations (1) and (3) discussed in Section 3. On the other hand, highly mechanistic kinetic multi-reaction models are not suitable for wastewater application due to their high level of complexity, particularly due to challenges with characterising DOM in the ozone system (von Gunten 2003a), which may prove difficult with model calibration if used. To account for the gaseous ozone inflow in the ozone reactor, a gas–liquid mass transfer equation needs to be included (Audenaert et al. 2013).
Disinfection and bromate formation
Modelling disinfection and the corresponding disinfection by-product (bromate) formation is quite complicated and needs to be approached carefully in order to improve the models' prediction accuracy. To realistically predict disinfection efficacy, the model will consider both direct O3 and OH• oxidation pathways. This requires characterising the ozonation system in terms of O3 and OH• concentrations, which could be achieved through the RCT concept (Equation (6)). Following this, micropollutant disinfection can be modelled with Equation (7).
Likewise, the bromate formation mechanism must consider both direct and indirect bromate formation pathways. The simplified bromate formation and minimisation scheme for ozonation of bromide-containing waters developed by Pinkernell & von Gunten (2001) (Figure 1) is selected for implementation in the proposed ozone model. In addition to bromate formation, this model also includes reactions with ammonia, which is important because ammonia is one of the popular chemicals used (or dosed) to suppress bromate formation (Pinkernell & von Gunten 2001; Morrison et al. 2023). Hence, the model can also be used as an operational tool to evaluate bromate minimisation strategies via ammonium-based approaches. Table 4 shows a summarised structure of the proposed ozone model discussed above.
A summarised framework for a proposed ozone model
R# . | Reactions/processes . | Reaction kinetics . | Reference . |
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Ozone decomposition and transport | |||
1 | Initial phase decomposition | ![]() | Van Der Helm et al. (2008) |
2 | Second phase decomposition | ![]() | |
3 | UVA254 oxidation | ![]() | |
4 | Mass transfer | ![]() | Audenaert et al. (2013) |
Micropollutant disinfection | |||
5 | ![]() | ![]() | Von Gunten (2003b) |
6 | ![]() | ![]() | |
Bromate formation | |||
7 | ![]() | ![]() | Pinkernell & von Gunten (2001) |
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R# . | Reactions/processes . | Reaction kinetics . | Reference . |
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Ozone decomposition and transport | |||
1 | Initial phase decomposition | ![]() | Van Der Helm et al. (2008) |
2 | Second phase decomposition | ![]() | |
3 | UVA254 oxidation | ![]() | |
4 | Mass transfer | ![]() | Audenaert et al. (2013) |
Micropollutant disinfection | |||
5 | ![]() | ![]() | Von Gunten (2003b) |
6 | ![]() | ![]() | |
Bromate formation | |||
7 | ![]() | ![]() | Pinkernell & von Gunten (2001) |
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BAC treatment objective
The proposed BAC model is intended to be applicable for predicting the removal of DOC and micropollutants during tertiary water treatment systems. It is developed by making the following modifications to the model developed by Kaiser et al. (2023): (i) replacing ASM1 with an ASM3 biotransformation mechanism and (ii) extending it to include micropollutant adsorption and desorption processes. The ASM1 model (Henze et al. 1986) is commonly used to simulate bioprocesses for unconventional nutrient removal technologies such as biofiltration (Bernier et al. 2014), MBRs (Fenu et al. 2010) and more recently, BACs (Alonso et al. 2021; Kaiser et al. 2023). However, to keep up with advancements in WRRF modelling, it would be beneficial to incorporate ASM3-based mechanisms (Gujer et al. 2000). In this study, we propose implementing ASM3P, which includes enhanced biological phosphorus removal (Rieger et al. 2001) as the biotransformation mechanism for the BAC model. Although tertiary effluents are typically characterised by low phosphorus concentrations, including the fate of phosphorus removal in the BAC model allows the model to be adapted for biofiltration wastewater treatment applications.
Submodels integration and component fractionation
Generally, for fully integrated models, it is essential to ensure mass continuity throughout the submodels of the entire system. Several approaches have been used to simulate PWMs and can potentially be applied to the proposed models. This includes the supermodel (Jones & Takàcs 2004), continuity-based interface model (CBIM) (Volcke et al. 2006), and transformation-based approach (Grau et al. 2007). The supermodel approach, while effective, increases model complexity as new components are added and lacks flexibility for tailoring to specific case studies (Volcke et al. 2006; Grau et al. 2007). Lizarralde et al. (2015) introduced a transformation-based methodology for integrating biochemical, chemical, and physicochemical models within a PWM framework. However, this framework does not include processes such as chemical oxidation and adsorption processes, which are particularly applicable to the O3 and BAC modelling discussed in this study. An interfacing approach, on the other hand, involves developing a model interface to account for differences in state variables, composition/fractionation, and units for the submodels to be coupled to ensure continuity (Volcke et al. 2006). This generic, flexible approach can be easily applied to integrating O3 and BAC models.
Hybridisation prospects
While mechanistic models are favoured within the WRRF community, they also come with a great challenge when it comes to parameterising, calibrating, and validating, especially for overly complex mechanistic models (Vanrolleghem et al. 2005; Schneider et al. 2022). On the other hand, DDMs are fast in computational time and have strong interpolation capabilities (Newhart et al. 2019). On that note, Schneider et al. (2022) recommend a hybrid model (HM) approach by integrating the mechanistic and DDMs. HM offers flexibility in calibration data and improves model prediction over various operational boundaries (Schneider et al. 2022; Verhaeghe et al. 2024). Model hybridisation also holds great potential for transitioning current WRRF mathematical models into intelligent engineering tools for process control and optimisation (Schneider et al. 2022). While HMs in WRRF are still in an emerging stage, there are a few successful applications, including the prediction of nitrous oxide (N2O) emission during nitrification processes (Mehrani et al. 2021; Daneshgar et al. 2022), effluent nitrate (NO3) concentration (Verhaeghe et al. 2024) and biofiltration nitrogen removal (Serrao et al. 2024). The lessons and experience from these studies, alongside the general considerations for developing HMs for WRRFs, are useful in guiding the development of O3 and BAC HMs and other WRRF operation units.
In WRRF, it is preferred that HMs be developed using integrated approaches that involve iterative processes. In this approach, a DDM component compensates for any deficiencies in mechanistic models by allowing the mechanistic model to learn from the DDM internally instead of just combining two distinct models (Schneider et al. 2022; Verhaeghe et al. 2024).
Overview of a cooperative hybrid modelling approach (adapted from Serrao et al. (2024) and Verhaeghe et al. (2024)).
Overview of a cooperative hybrid modelling approach (adapted from Serrao et al. (2024) and Verhaeghe et al. (2024)).
CONCLUSION
This article critically reviews the current state of advancement in ozone (O3) BAC models. It aims to contribute to the development of an integrated O3–BAC model that can simulate the removal of DOC and micropollutants in a tertiary wastewater treatment system. Although some relevant papers may have been excluded from the discussion due to the search strategy employed by the study, the selected studies still offer a comprehensive overview of the topic.
The review highlights that comprehensive O3 models include ozone decomposition, disinfection, and bromate formation processes. However, the major limitation in the current models is the poor prediction accuracy of disinfection and bromate formation mechanisms. The formation of AOC is an important parameter in the context of O3–BAC modelling, but it is often excluded from the current O3 models. On the other hand, comprehensive models comprise biodegradation and adsorption–desorption as the primary processes. The major limitations in the current BAC models include the inefficiency of the adsorption mechanisms to represent competitive adsorption in multi-solute systems. While there is an emerging breakthrough in modelling competitive adsorption for different DOC fractions, it remains to be seen if these multi-component adsorptions can be applied to model competitive adsorption between DOC and micropollutants.
To integrate the O3 and BAC models into a single O3–BAC model, we need to account for how organic matter fractionates in each model. This requires developing a model interface that includes component (particularly organic matter) fractionation across submodels. Additionally, it is important to address their shortcomings to ensure good prediction accuracy. Without resorting to overly complex mechanisms, we proposed a cooperative HM approach for improvement, where DDMs can compensate for structural limitations in the mechanistic models, particularly for the disinfection, bromate formation, AOC formation and adsorption mechanisms. We believe that these improvements will result in a well-balanced model in terms of complexity, ensuring reliability and practicality, and a flexible and adaptable model that could be integrated into system-wide WRRF models and paving the way for digital transition for tertiary treatment unit processes. Future studies should focus on evaluating the feasibility of the proposed new tools by implementing the proposed O3–BAC hybrid model into a WRRF simulation software and evaluating the capability of the model to perform under varying operational conditions.
ACKNOWLEDGEMENTS
This project was conducted at the University of Cape Town with the support of the Water Research Commission (WRC) of South Africa under the grant for the project ‘Towards Data-Driven Digital Twins for Integrated Wastewater Reclamation and Reuse,’ awarded to David Ikumi. Additionally, Shalongo Angula received a joint PhD scholarship from the University of Namibia and Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) GmbH.
AUTHOR CONTRIBUTIONS
S. T. A. Conceptualisation, Investigation, Writing – Original Draft. J. O. Writing – Review & Editing, Supervision. T. H. Conceptualisation, Writing – Review & Editing. G. B. Validation, Writing – Review & Editing. D. S. I. Conceptualisation, Validation, Writing – Review & Editing, Supervision.
ETHICS STATEMENT
No human or animal participants were involved in this study.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.