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.

  • 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.

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)

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.

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.

The integrated O3 and BAC (O3–BAC) system is particularly effective in removing micropollutants from pre-treated wastewater and has recently received much research attention as an alternative to RO. The principle of combining O3 and BAC processes is further discussed in Section 5.1. The O3–BAC treatment system has already been implemented in various WRPs' treatment plants across the globe (Swartz et al. 2022). One of the notable examples of the application of O3–BAC in WRPs is the full-scale New Goreangab Water Reclamation Plant (NGWRP), located in Windhoek, Namibia, which has been in operation for over 20 years with a capacity of 21 ML/d, whose treatment train is illustrated in Figure 1. Inspired by the success of NGWRP, the O3–BAC system has also been included in the design of other WRPs in Southern Africa, such as Cape Flats WRP, which is currently under construction (Smuts 2021). The remainder of this paper will focus on O3 and BAC operation units of tertiary treatment systems.
Figure 1

A process configuration of the NGWRP (adapted from Wallmann et al. (2021)).

Figure 1

A process configuration of the NGWRP (adapted from Wallmann et al. (2021)).

Close modal

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).

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.

Table 1

Selected comprehensive ozonation models and their underlying processes

No.ReferenceOzone decompositionDisinfectionAOC formationHydraulic characteristicsCalibration/test data descriptionPrediction performance and shortcoming
Rapid phaseSlow phaseNOM impactOH·exposureOxidation
Zhang et al. (2007)  IOD Equation (1– – Equation (4Equation (8– CFD Natural water; full-scale Good prediction accuracy for flow dynamics. Accuracy of O3 decay and disinfection not satisfactory 
Van Der Helm et al. (2007, 2008Equation (1Equation (1Equation (3– Equation (5Equation (8Regression 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. 
Audenaert et al. (2010)  Equation (1Equation (1Equation (3– Equation (5Equation (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 
Gerrity et al. (2012, 2014IOD Equation (2Empirical (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. 
Audenaert et al. (2019), Muoio et al. (2023)  Includedb Includedb UVA-basedb RCT – concept Equation (7Figure 1   CSTR-PFRa WWTP effluent; Bench-scale batch reactor Good prediction for O3 decay, bromate formation and a wide range of micropollutant groups, 
No.ReferenceOzone decompositionDisinfectionAOC formationHydraulic characteristicsCalibration/test data descriptionPrediction performance and shortcoming
Rapid phaseSlow phaseNOM impactOH·exposureOxidation
Zhang et al. (2007)  IOD Equation (1– – Equation (4Equation (8– CFD Natural water; full-scale Good prediction accuracy for flow dynamics. Accuracy of O3 decay and disinfection not satisfactory 
Van Der Helm et al. (2007, 2008Equation (1Equation (1Equation (3– Equation (5Equation (8Regression 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. 
Audenaert et al. (2010)  Equation (1Equation (1Equation (3– Equation (5Equation (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 
Gerrity et al. (2012, 2014IOD Equation (2Empirical (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. 
Audenaert et al. (2019), Muoio et al. (2023)  Includedb Includedb UVA-basedb RCT – concept Equation (7Figure 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.

Most comprehensive models use empirical or semi-mechanistic models for describing ozone decomposition. An instantaneous ozone demand (IOD), a zero-parameter parameter, is sometimes used to depict the rapid ozone decomposition phase (Buffle et al. 2006; Gerrity et al. 2014), whereas some models adopt semi-mechanistic models to describe rapid and slow-phase ozone decomposition and the impact of organic matter on ozone decomposition (Van Der Helm et al. 2008) shown in Equations (1)–(3). UVA oxidation is often used as a surrogate for organic matter. The first and second parts of Equation (1) represents the rapid (initial) and slow (second) phases of ozone decomposition, respectively. Equation (2) describes ozone decomposition in the second phase only. The comprehensive ozonation models reviewed in this study highlight a prevalent use of semi-empirical models to describe the ozone self-decomposition and the ozone reaction with organic matter, as summarised in Table 1 (Van Der Helm et al. 2007, 2008; Gerrity et al. 2014):
(1)
(2)
(3)

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 (residual O3 concentration × contact time) approach assumes direct ozone disinfection only, which can be modelled using various existing semi-empirical equations, such as Equations (4) and (5) (Von Gunten 2003a, b; Van Der Helm et al. 2008; Audenaert et al. 2010):
(4)
(5)

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.

On the other hand, models that take into account OH exposure require the ozonation system to be characterised in terms of O3 and OH concentrations. Since measuring OH in an aqueous solution is extremely difficult, OH exposure is incorporated in the models through an indirect measure that uses the so-called RCT concept (Elovitz & Von Gunten 1999), which relates the fraction of OH and O3 exposures (i.e., . is back-calculated from the degradation of the OH -probe compound, such as para-chlorobenzoic acid (pCBA) (Elovitz & Von Gunten 1999). Determining this RCT value for every sample point then makes it possible to calculate OH concentration for such points using Equation (6) (Elovitz & Von Gunten 1999):
(6)
In other studies, OH exposure has also been obtained using linear relationships between OH exposure and an operational parameter O3:TOC ratio (Gerrity et al. 2012; Lee et al. 2013). With OH concentration known, a kinetic reaction given by Equation (7) can be used for predicting micropollutant (MPx) removal by the combined effect of O3 and OH (Elovitz & Von Gunten 1999; Von Gunten 2003b). The inclusion of OH exposure in disinfection models has been included in two of the models reviewed in this study, namely, Models 4 and 5 in Table 1:
(7)

Bromate formation

Bromate formation is a product of a complex multi-reaction scheme involving direct and indirect oxidation by O3 and OH, respectively (Von Gunten 2003a, b). Various studies have developed and discussed various bromate formation mechanisms of varying complexities (Haag & Hoigne 1983; Pinkernell & von Gunten 2001; Mandel et al. 2012; Morrison et al. 2023). Figure 2 shows a bromate formation reaction scheme developed by Pinkernell & von Gunten (2001). Only one (Model No. 5) of the five reviewed models in this study used a fully mechanistic bromate formation scheme.
Figure 2

The mechanism for bromate formation during ozonation of bromide-containing waters (Pinkernell & von Gunten 2001).

Figure 2

The mechanism for bromate formation during ozonation of bromide-containing waters (Pinkernell & von Gunten 2001).

Close modal
Bromate formation is often replicated using multiple linear regression models (Sohn et al. 2004) or semi-empirical first-order kinetic equations (Equation (8)) (Audenaert et al. 2010):
(8)

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.

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.

Mathematical modelling of the BAC process generally involves the mass-balanced equations describing the following five processes within the BAC layers: (1) bulk solution transport due to advection and dispersion; (2) diffusion and biodegradation within the biofilm, (3) biofilm growth and loss, (4) surface and pore diffusion within the GAC, (5) and adsorption of compounds in the GAC. These processes are summarised in the conceptual diagram in Figure 3.
Figure 3

Conceptual definition of mechanisms of biological activated carbon system (adapted from Yuan et al. (2022)).

Figure 3

Conceptual definition of mechanisms of biological activated carbon system (adapted from Yuan et al. (2022)).

Close modal

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).

The following discussion presents a critical review of four BAC models, including the generic model and a novel BAC modelling framework by Yuan et al. (2022) and two additional models published after the review by Yuan et al. (2022). These models solve a continuity (mass-balanced) equation that describes the change in mass over time for specific components involved and can be divided into two parts, transport and conversion, in a generic form given by Equation (9). Although the exact equations used in different models may differ, this study presents general forms of the model equations to demonstrate the modelling approach and considerations:
(9)

Regarding hydraulic characteristics, BACs are typically developed based on fixed-bed reactors and are simulated as PFRs.

Bulk liquid phase

The bulk liquid phase is typically modelled with a diffusive transport of a compound from a bulk liquid into the biofilm layer (according to Fick's law) and an axial dispersion term. It is assumed that no reaction occurs in the bulk liquid phase. The mass balance equation for the bulk liquid phase is described by Equation (10). In some models (i.e., Model 3 by Yuan et al. (2022) in Table 2), this mass balance equation is modified with an empirical term accounting for biofilm diffusion coefficient (kf) (Liang et al. 2007; Alonso et al. 2021):
(10)
Table 2

Summary of the structure of representative BAC models

No.ReferenceMass balance
Biofilm thicknessReaction equations characteristics
Calibration/test data descriptionPrediction performance and shortcoming
Bulk liquidBiofilmGAC phaseBiodegradationAdsorptionDesorptionEffect of adsorbed oxygen
Alonso et al. (2021)  Equation (10Equation (11Equation (18Equation (12Monod 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 
Yuan et al. (2022) and references cited therein (the generic model) Equation (10Equation (11Equation (14Equation (13Monod 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 
Yuan et al. (2022)  Equation (10Equation (11Equation (17Equation (13Monod EBC approach + Freundlich   Not calibrated or validated Generic model presented. No simulation performed 
Kaiser et al. (2023)  Equation (10Equation (11Equation (19Equation (12Monod IAST + Freundlich + fictive GAC surface adsorption First-order kinetics w.r.t dissolved concentration at equilibrium (Si,eBased 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.ReferenceMass balance
Biofilm thicknessReaction equations characteristics
Calibration/test data descriptionPrediction performance and shortcoming
Bulk liquidBiofilmGAC phaseBiodegradationAdsorptionDesorptionEffect of adsorbed oxygen
Alonso et al. (2021)  Equation (10Equation (11Equation (18Equation (12Monod 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 
Yuan et al. (2022) and references cited therein (the generic model) Equation (10Equation (11Equation (14Equation (13Monod 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 
Yuan et al. (2022)  Equation (10Equation (11Equation (17Equation (13Monod EBC approach + Freundlich   Not calibrated or validated Generic model presented. No simulation performed 
Kaiser et al. (2023)  Equation (10Equation (11Equation (19Equation (12Monod IAST + Freundlich + fictive GAC surface adsorption First-order kinetics w.r.t dissolved concentration at equilibrium (Si,eBased 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

The biofilm phase is modelled by coupling the diffusive transport (Fick's law) of a compound within the biofilm layer and the biodegradation reaction mechanism (using Monod kinetics) represented by Equation (11) (Alonso et al. 2021; Yuan et al. 2022):
(11)
where is the stoichiometric parameter.
There are two modelling approaches concerning the biofilm thickness (Lf): Those that assume a constant biofilm thickness throughout the operation based on biomass growth and detachment concept (Alonso et al. 2021) and those that implement a dynamic biofilm thickness (Liang et al. 2007; Yuan et al. 2022), described by Equations (12) and (13) (Liang et al. 2007; Alonso et al. 2021; Yuan et al. 2022; Kaiser et al. 2023):
(12)
where
(13)

GAC phase

The GAC adsorption is the major source of differences in the BAC modelling. Most earlier BAC models described the mass balance in the GAC phase by integrating surface diffusion (Fick's law) and adsorption using either Freundlich or Langmuir equilibrium isotherms (Yuan et al. 2022) described by Equations (14)–(16). Due to their oversimplification, these models were more suitable for simulating adsorption in single-component solutions and virgin GAC operations (Liang et al. 2007; Yuan et al. 2022):
(14)
(15)
(16)
To overcome the shortcomings of non-realistic assumptions in the previous GAC adsorption models, the models developed over the past five years are focused on integrating the impact of pore diffusion on adsorption, desorption after GAC saturation, competitive adsorption in multi-solute systems, and the effect of dissolved oxygen on adsorption. The mass balance equations of these models are given by Equations (17)–(19) (Alonso et al. 2021; Yuan et al. 2022; Kaiser et al. 2023):
(17)
where
(18)
where γad and γdes represent the adsorption and desorption rates and reaction νad and νdes are their respective stochiometric parameters:
(19)
where is the dissolved oxygen adsorption rate, and is its respective stoichiometric parameters

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).

Even though Equations (18) and (19) show pore diffusion as the only mass transfer process, it is important to note that Equation (19) also takes into account GAC surface diffusion. However, this surface diffusion term was not mechanistically implemented but was included by modifying the adsorption equilibrium calculations with an empirical surface diffusion model (Kaiser et al. 2023), i.e.:
(20)

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.

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.

Table 3

Selected notable full-scale WRP employing O3–BAC treatment

Plant nameLocationCapacity (ML/d)StatusSystemAdded valueReference
Gwinnett County Georgia, USA 227 Operational since 1999 WRP: IPR via MAR 
  • O3–BAC train achieves similar organic micropollutants and microbial contaminants removal as the MF-RO-UV/H2O2 train

 
Snyder et al. (2014)  
New Goreangab WRP Windhoek, Namibia 21 Operational since 2002 WRP: DPR 
  • 43–45% DOC removal

  • Enhanced DOC removal without the regular high cost of regeneration of GAC

  • Complete barrier for bacteria and virus

  • Partial barrier for micropollutant

 
Theron-Beukes et al. (2008)  
South Caboolture WRP Queensland, Australia Operational since 1999 NPR 
  • + 90% micropollutant reduction

  • 30–35% DOC removal

  • 16% toxicity reduction

 
van Leeuwen et at. (2003); Reungoat et al. (2010)  
Flemish Water Supply Company Waterworks Kluizen, Belgium 60 Operational since 2003 Drinking WTP 
  • Due to improved disinfection by ozone, the first chlorination step could be omitted

 
Audenaert et al. (2010)  
Cape Flats MAR WRP Cape Town, South Africa 40 Under construction WRP: IPR via MAR 
  • To be used as the main barrier for the removal of pathogens and organic micropollutants

 
Smuts (2021)  
Plant nameLocationCapacity (ML/d)StatusSystemAdded valueReference
Gwinnett County Georgia, USA 227 Operational since 1999 WRP: IPR via MAR 
  • O3–BAC train achieves similar organic micropollutants and microbial contaminants removal as the MF-RO-UV/H2O2 train

 
Snyder et al. (2014)  
New Goreangab WRP Windhoek, Namibia 21 Operational since 2002 WRP: DPR 
  • 43–45% DOC removal

  • Enhanced DOC removal without the regular high cost of regeneration of GAC

  • Complete barrier for bacteria and virus

  • Partial barrier for micropollutant

 
Theron-Beukes et al. (2008)  
South Caboolture WRP Queensland, Australia Operational since 1999 NPR 
  • + 90% micropollutant reduction

  • 30–35% DOC removal

  • 16% toxicity reduction

 
van Leeuwen et at. (2003); Reungoat et al. (2010)  
Flemish Water Supply Company Waterworks Kluizen, Belgium 60 Operational since 2003 Drinking WTP 
  • Due to improved disinfection by ozone, the first chlorination step could be omitted

 
Audenaert et al. (2010)  
Cape Flats MAR WRP Cape Town, South Africa 40 Under construction WRP: IPR via MAR 
  • To be used as the main barrier for the removal of pathogens and organic micropollutants

 
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 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).

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.

Table 4

A summarised framework for a proposed ozone model

R#Reactions/processesReaction kineticsReference
Ozone decomposition and transport 
Initial phase decomposition  Van Der Helm et al. (2008)  
Second phase decomposition  
UVA254 oxidation  
Mass transfer  Audenaert et al. (2013)  
Micropollutant disinfection 
  Von Gunten (2003b)  
  
Bromate formation 
  Pinkernell & von Gunten (2001)  
  
  
10   
11   
12   
13   
14   
15   
16   
17   
18   
19   
20   
21   
22   
23   
R#Reactions/processesReaction kineticsReference
Ozone decomposition and transport 
Initial phase decomposition  Van Der Helm et al. (2008)  
Second phase decomposition  
UVA254 oxidation  
Mass transfer  Audenaert et al. (2013)  
Micropollutant disinfection 
  Von Gunten (2003b)  
  
Bromate formation 
  Pinkernell & von Gunten (2001)  
  
  
10   
11   
12   
13   
14   
15   
16   
17   
18   
19   
20   
21   
22   
23   

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.

For micropollutant adsorption extension, three approaches could be used: coupled IAST and tracer model (TRM) (Atallah Al-Asad et al. 2022), the equivalent background compound model (EBCM) (Yuan et al. 2022) or surrogate correlation models (Zietzschmann et al. 2014). For this study, the IAST-TRM approach is selected for implementation. For simplification, because organic MPs are usually in low concentrations compared to COD or TOC measures, it is usually assumed that they do not contribute to biological growth (Ferreira 2022). Hence, only two processes are necessary to add, namely, micropollutant adsorption and desorption, which are described by Equations (21) and (22), respectively. The effect of adsorbed oxygen on biofilm dynamics can also be neglected because oxygen adsorbed has no significant effect on biodegradation activity (Atallah Al-Asad et al. 2022; Kaiser et al. 2023):
(21)
(22)

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.

The ozone and BAC models proposed in this study use UVA254 and DOC as the primary parameters for measuring organic content, respectively. On the other hand, traditional WRRF models (i.e., ASMs, ADMs, and PWMs) rely on COD as a fundamental unit for organic content. Therefore, to couple the proposed O3 and BAC models within the WRRF framework, model interfaces are needed to describe the transformation of state variables from the origin model to the destination model and accounting for state variables, as illustrated in Figure 4. Process knowledge and insight on the relationship between COD, DOC, UVA254 and other relevant parameters from previous studies can be valuable in developing the model interfaces between the three submodels. For instance, the studies by Menge et al. (2009), Phan et al. (2022), Theron-Beukes et al. (2008), and Zietzschmann et al. (2014) have found correlations between COD, DOC, and UVA254. This knowledge can potentially be used to develop algorithms that will allow for the determination of the transformation of state variables across different submodels.
Figure 4

Location of model interfaces in the proposed integrated model.

Figure 4

Location of model interfaces in the proposed integrated model.

Close modal

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 the context of O3–BAC modelling, using a hybrid approach will be particularly beneficial for enhancing the predictive power of models for processes not well-predicted by mechanistic models. This includes processes involving unestablished or overly complex mechanisms such as micropollutant oxidation, disinfection by-product formation (e.g., bromate and AOC), and multi-component adsorption. Considering the strengths and weaknesses of the O3 and BAC processes reviewed in this study, a general structure for O3 and BAC HMs was proposed and presented in Figure 5.
Figure 5

Proposed structure of O3 and BAC hybrid models.

Figure 5

Proposed structure of O3 and BAC hybrid models.

Close modal

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).

It is recommended that WRRF HMs be based on truly integrated approaches (i.e., involving iterative processes) whereby a DDM component can be used to compensate for a deficiency in mechanistic models (i.e., the mechanistic model learns from DDM) internally instead of simply combining two distinct models. Different approaches for integrating HM include serial, parallel cooperative, or parallel competitive architectures, which are discussed in detail by Schneider et al. (2022). A typical example of a fully integrated HM system is the cooperative HM approach, which was applied in the studies by Serrao et al. (2024) and Verhaeghe et al. (2024). In this approach, a DDM is trained to learn the residual error of the mechanistic model with respect to historical data. This residual error is then used to make corrections to the output of the mechanistic simulation, as illustrated in Figure 6.
Figure 6

Overview of a cooperative hybrid modelling approach (adapted from Serrao et al. (2024) and Verhaeghe et al. (2024)).

Figure 6

Overview of a cooperative hybrid modelling approach (adapted from Serrao et al. (2024) and Verhaeghe et al. (2024)).

Close modal

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.

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.

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.

No human or animal participants were involved in this study.

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

The authors declare there is no conflict.

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