Modeling carbonate/bicarbonate and nitrate disturbance during secondary effluent disinfection by UV/H₂O₂ and UV/ozone

The presence of pathogenic microorganisms in waters is of particular concern for human health, and the discharge of wastewater into receiving waters is an important source of microbial pathogens (Zhang et al. 2019; Shi et al. 2021a). Therefore, in a wastewater treatment system, the disinfection stage is extremely important to reduce the prevalence of waterborne diseases such as diarrhea, cholera, dysentery, polio, and typhoid, ensuring the health of humans and environmental hygiene (Zhang et al. 2019; Di Cesare et al. 2020; Lei et al. 2021).

Conventional chlorination is still the most used disinfection method due to its easy applicability and its relative cost-efficiency (Radcliffe & Page 2020; Shi et al. 2021a). The ability of ozone to inactivate a wide range of microorganisms, especially when chlorination processes fail, has made the oxidizer widely studied for application in disinfection processes (Nasuhoglu et al. 2018). The main disadvantage of chlorination or ozonation is the likely generation of disinfection by-products (DBPs), resulting from the reaction of oxidants with natural organic matter. The DBPs are known to contribute to the overall toxicity of reclaimed water, as in the case of secondary effluents, which have a considerable amount of dissolved organic matter (Park et al. 2016; Du et al. 2017; Cui et al. 2020).

As the formation of these toxic DBPs depends, among other factors, on the dose of oxidant (Park et al. 2016; Kozari et al. 2020; Laflamme et al. 2020; Moreno-Andrés et al. 2020), a viable alternative to reduce the dose of oxidants and improve disinfection processes is the combination of a single treatment process, such as ozonation, with physical methods such as ultraviolet radiation (UV) and/or other oxidants such as H₂O₂, resulting in the well-known Advanced Oxidation Processes (AOPs) (Moreno-Andrés et al. 2020). Thereby, the generation of mainly hydroxyl radicals (HO^•) can improve the process of inactivating biological agents (Moreno-Andrés et al. 2020). In fact, studies have shown that the O₃/UV process significantly increases the disinfection processes in wastewater (Chin & Bérubé 2005; Meunier et al. 2006; Cheema et al. 2017).

The search for alternative disinfection methods also includes the ultraviolet-activated hydrogen peroxide (UV/H₂O₂) process (Lei et al. 2021). This oxidation process is considered interesting for disinfection applications because it prevents or reduces the formation of DBPs such as chlorite, bromate, trihalomethane and haloacetic acid (Jo et al. 2011; Ding et al. 2019; Pai & Wang 2022).

An important factor that affects the performance of AOPs is the concentration of inorganic anions in the water matrices. Calcium carbonate is a common element found in many environmental compartments such as sea, rivers, effluents and soil (Torres et al. 2013). It is known that its presence in effluents is inevitable due to its large application in diverse activities such as civil construction (Saulat et al. 2020), steel industries (Mo et al. 2016), toothpaste (Hall et al. 2017), fertilizers (Javied et al. 2011) and in various industrial applications.

It is evident that the presence of CO₃²⁻/HCO₃⁻ and NO₃⁻ may disturb the efficiency of the process of disinfection by AOPs, causing the need of more oxidant and/or UV light to perform the treatment (Malvestiti & Dantas 2018). Since their concentration in effluents can vary depending on the regions, the oxidant doses can be insufficient. Thus, the removal kinetics of microorganisms in the presence of inorganic anions need to be understood, which in turn makes it possible to relate the applied oxidant dose with the disinfection efficiency (Vélez-Colmenares et al. 2011). Therefore, the establishment of a mathematical relationship between the nitrate and carbonate concentration and the needed oxidant dose will make possible the adjustment of the treatment for a specific effluent.

In the literature, kinetic models are widely developed to predict the micropollutant oxidation during disinfection processes and to explore the effect of the water matrix on the micropollutant degradation mechanism.

Concerning UV/H₂O₂, several studies have shown that a kinetic approach can be successfully applied to predict the efficiency of microcontaminant removal and disinfection (Timchak & Gitis 2012; Rubio et al. 2013; Rodríguez-Chueca et al. 2015; Yin et al. 2018; Shi et al. 2021b). In the case of O₃/UV, some kinetic models have been proposed (Jung et al. 2008; Chen et al. 2016; Xu et al. 2018). However, a systematic evaluation of these models to predict the effect of inorganic anions on the disinfection of wastewater has not been comprehensively studied.

The different types of kinetic disinfection models suggested in the literature to fit experimental data and explain the process of microorganism inactivation range from a simple first-order model of Chick to quite multiplex models, such as Collins–Selleck and multikinetic models (Vélez-Colmenares et al. 2011). In most of the cases, the microorganism inactivation results can be described satisfactorily with the first-order disinfection kinetic model, resulting in a straight line in the representation of microorganism inactivation as a function of time (Vélez-Colmenares et al. 2011; Rodríguez-Chueca et al. 2015).

Several changes to the Chick model have been introduced to improve the applicability of mathematical descriptions in order to explain the different characteristics of the process (Labas et al. 2005). However, in some situations, linear kinetic models have several limitations and are unable to describe certain deviations observed in the inactivation of microorganisms (Rodríguez-Chueca et al. 2015). Many researchers try to increase their accuracy; however, it is common for this improvement to result in a great increase of new variables, causing the empirical data to be reformulated for a range of use that is rarely the same as the previous one (Lambert & Johnston 2000). As a result, the reformulated model becomes tedious and difficult to apply in practice.

Here we report a simple disinfection model, based on an advance from the Chick model, substituting in the mathematical terms a simple average for a weighted average. This was developed in order to improve first-order inactivation kinetics to model linear inactivation curves. Thus, a straight line is obtained in the representation of bacterial inactivation as a function of time, which allows the use of this model in several processes of disinfection technologies. Therefore, we hope with this work to demonstrate the applicability of a kinetic model that can be used for scaling purposes in some disinfection processes, without complex mathematical steps such as those found in multi kinetic models. With this approach, the main objective of this work was focused on evaluating a new modified Chick model to predict the inactivation kinetics of total coliforms and Escherichia coli in secondary effluent treated by combinations of ozone or H₂O₂ and UV radiation. The proposed model was applied to predict disinfection disturbance in the presence of dissolved CO₃²⁻/HCO₃⁻ and NO₃⁻ ions. The performance of the proposed model was evaluated by comparison with the established Chick model. Finally, the validity of the proposed model was investigated using the Spearman and Pearson correlation coefficients.

The secondary effluent samples were collected from a pilot wastewater treatment plant located on the campus of the School of Technology of the University of Campinas (Limeira SP, Brazil, 23°26′17″S 48°34′35″W). The pilot plant is composed of an Upflow Anaerobic Sludge Blanket Reactor (UASB) with the capacity to treat 1 m³ day⁻¹ and receives effluents generated throughout the campus, such as bathrooms, laboratories and kitchens. Samples were collected in the outlet of the plant and stored at 4 °C in 20-L bottles until experimentation. The analysis of the physicochemical parameters of the effluent sample was performed according to the procedures described in the Standard Methods for the Examination of Water and Wastewater (Greenberg et al. 2005). The main physicochemical characteristics of the effluent were: pH = 7.4; total suspended solids, TSS = 18.2 mg L⁻¹; turbidity = 55.1 nephelometric turbidity units (NTU); alkalinity = 302.2 ± 30.4 mg CaCO₃ L⁻¹; Nitrate = 1.28 ± 0.14 mg L⁻¹; chemical oxygen demand, COD = 104.2 ± 3.4 mg O₂ L⁻¹; biochemical oxygen demand, BOD₅ = 37.9 ± 4.4 mg O₂ L⁻¹.

Disinfection experiments were conducted to investigate the inactivation of total coliforms and E. coli by the UV/H₂O₂ and UV/O₃ treatments and, consequently, to obtain experimental data for the development of kinetic modeling.

The UV/O₃ experiments were carried out in the same experimental apparatus used in the UV/H₂O₂ system, with a coupled ozone generator (Ozonar GT 8000, Brazil), as can be seen in the scheme shown in Figure 1(b). The O₃ was produced by the generator from ambient air at a flow rate of 4 L min⁻¹ and fed into the reservoir tank containing 1 L of effluent through an inert porous gas diffuser. The concentration of O₃ in the effluent sample inside the reservoir tank was determined by the iodometry method (Tjahjanto et al. 2012). To carry out this determination, gaseous ozone was bubbled into a 0.012 mol L⁻¹ potassium iodide solution and afterwards titrated with a previously standardized solution of 0.025 mol L⁻¹ potassium thiosulfate. The O₃ dose determined was 11 mg O₃ L⁻¹, previously established according to studies in the same operating system (Malvestiti & Dantas 2018).

For both treatments, the UV-C dose (mW·s·cm⁻²) supplied was calculated as a product of the average UV intensity rate into the reactor (mW·s·cm⁻²) and the irradiation time (s). Irradiation was performed at room temperature, between 22 and 25 °C. Bacteria were exposed to a UV-C dose of 20 mW·s·cm⁻².

We evaluated the effects of the interference of CO₃²⁻/HCO₃⁻ and NO₃⁻ ion concentration on the proposed disinfection treatments and on kinetic modeling of the inactivation results. In a first sequence of experiments, samples of secondary effluents were treated by O₃/UV and UV/H₂O₂ without addition of interfering ions in order to quantify total coliforms and E. coli inactivation. Then, the secondary effluent samples were enriched with ion salts, individually and simultaneously.

The experiments were carried out with the following concentrations and combinations of ions: (i) carbonate = 250 and 750 mg L⁻¹; (ii) nitrate = 20 and 60 mg L⁻¹; (iii) mixed = 250 mg L⁻¹ of carbonate with 20 mg L⁻¹ of nitrate; and 750 mg L⁻¹ of carbonate with 60 mg L⁻¹ of nitrate. The concentrations of 250 mg L⁻¹ of carbonate and 20 mg L⁻¹ of nitrate were chosen based on studies in the literature that evaluated the interference of these ions in the disinfection processes of secondary effluents (Malvestiti & Dantas 2018, 2022; Adak et al. 2019). To verify the influence of these ions in the proposed modeling, experiments were carried out with three times the concentrations initially proposed.

The disinfection of the samples was assessed by the bacterial inactivation, measured by the Colilert^® test, which quantifies both E. coli and total coliforms' presence in the effluent with a chromogenic reagent (IDEXX Laboratories 2022). To perform the test, the sample to be analyzed was properly diluted to 100 mL with dilution water prepared from 1 g of peptone bacteriological reagent in 1,000 mL of distilled water. After this step, the commercial Colilert reagent was mixed with the diluted sample and then poured and sealed into a 97-well Quanti-Tray. The sealed Quanti-Tray^® was incubated for 24 h at 35 ± 0.5 °C. Yellow color changes indicate the presence of total coliforms, and yellow/fluorescence checked by 365-nm UV indicates the presence of E. coli. After incubation, the total yellow wells (small and large) in the Colilert tray were counted and the most probable number (MPN) values were determined by looking at the respective values in the manufacturer's MPN tables (IDEXX Laboratories 2022). The MPN values counted by the yellow and yellow/fluorescent wells were multiplied by the applied dilution factor and the concentrations of E. coli and total coliforms were determined. Colilert can simultaneously detect these bacteria at 1 MPN unit of total coliforms and E. coli per 100 mL sample volume.

The Colilert^® test used in this work is commonly applied for disinfection tests and is a validated test. In the literature, studies using this test for disinfection are commonly found (Bailey et al. 2018; Malvestiti & Dantas 2018; Kolosov & Yargeau 2019; Ahile et al. 2021; da Silva et al. 2021). It is a test approved by the U.S. EPA and has been included in Standard Methods for Examination of Water and Wastewater.

The disinfection efficiency in terms of total coliforms and E. coli inactivation was evaluated graphically by the log (N_t/N₀) over the reaction time (t), where N_t is the concentration of pathogenic bacteria [MPN/100 mL] for a certain time (t) of disinfection and N₀ is the concentration of microorganisms [MPN/100 mL] in effluent samples prior to disinfection.

The disinfection prediction was based on the calculations of inactivation kinetics of microorganisms obtained from experimental results of inactivation for total coliforms and E. coli by UV/H₂O₂ and UV/O₃ processes.

Consequently, applying the Chick's equation (Equation (4)), a value of k, named in this work as k₁, was obtained for each sample collected at a predetermined time. Then, an arithmetic mean was performed for each calculated k₁ value, thus finding the average value of k involving all the reaction times, denominated in this work as k_1M, which in this case was of first order.

Using the calculated k₂ values of each stipulated sampling time, the average k value was calculated and called k_2M. Then, using the values of k_2M in Equation (5), the theoretical values of the total coliforms and E. coli concentration decay were calculated as a function of time for each simulated experiment.

To perform the disinfection evaluation, the effluents were subjected to treatment, and samples were collected and placed in a Colilert^® tray and incubated for 24 hours. After that, the results of E. coli and total coliform concentrations were measured as presented in Table S1 of the supplementary material.

Disinfection conducted by HO^• radicals includes two main mechanisms: (i) destruction of the cell wall and cell membrane and (ii) diffusion of the oxidant into the cell, causing enzyme inactivation, damage to intracellular genetic materials, etc. (Mamane et al. 2007; Chen et al. 2021). In addition to the amount of HO^• radical generation from the employed AOP, the inactivation efficiency also depends on the type of process involved. When AOP are based on UV radiation, the inactivation of microorganisms might be due to the germicidal effect of UV-C photons, which are known to produce modifications of DNA pyrimidine bases, leading to protein damage and consequently resulting in cell death (Moussavi et al. 2019).

Ozone alone can lead to disinfection due to the attack to cell membranes, resulting from the reaction of O₃ with unsaturated bonds in phospholipids and lipopolysaccharides (Chen et al. 2021). It can also destroy the metabolic and reproductive capacity of bacteria due to the ability to oxidize bacterial enzymes and nucleic acid and to damage macromolecular polymers of polysaccharides, including DNA, RNA, proteins and fatty acids (Zheng et al. 2017).

The combination of ozone and UV radiation strongly enhances the disinfection process (Oh et al. 2007; Fang et al. 2014). Figure 2(c) and 2(d) shows the inactivation of total coliforms and E. coli, respectively, during the ozonation combined with UV radiation. In the absence of added radical scavengers, rapid inactivation of microorganisms was observed, due to the increase in the production of HO^• radicals by UV photolysis of ozone (Equations (10)–(12)) (Chen et al. 2016; Rekhate & Srivastava 2020).

Figure 2 also shows the effect of different concentrations of CO₃²⁻/HCO₃⁻, NO₃⁻ and the mixture of both species in the disinfection processes. The disinfection efficiency was reduced in the presence of CO₃²⁻/HCO₃⁻ ions for both microorganisms, regardless of the type of applied AOP. This behavior can be explained by the fact that in the presence of CO₃²⁻/HCO₃⁻ ions, HO^• radicals are consumed, generating the CO₃^•− radical, as shown by Equations (1) and (2). Since CO₃^•− radical has a lower reduction potential, the efficiency of the process has been greatly reduced. It is important to remark that the pH of the solution can directly affect the carbonate and bicarbonate ion forms present in solution. In this study, the effluent samples had a pH around 7.4; thus, in terms of the proportion of CO₃²⁻/HCO₃⁻ species, more than 80% were in the form of HCO₃⁻ ions (Wang & Wang 2020). Therefore, HCO₃⁻ were the main species contributing to the generation of CO₃^•− radicals.

Regarding the carbonate inhibition in the disinfection process, it was dependent on the concentration. In the presence of 250 mg L⁻¹ of carbonate, the disinfection by UV/H₂O₂ process (Figure 2(a) and 2(b)) was less affected than in the presence of 750 mg L⁻¹. This is in accordance with expectations, since during the UV/H₂O₂ treatment the main disinfection mechanism is caused by HO^• radicals.

To perform the modeling of the disinfection experiments, the values of inactivation rate constant ‘k’ were calculated according to the Chick model (Equation (4)), in which the concentration of total coliforms and E. coli was taken into relation to the treatment time. This calculation was executed for each sample collected at the pre-defined time during the disinfection process; thus, different reaction rates ‘k’ were obtained for the different times. If the reaction were equivalent to first order, all ‘k’ would be the same; however, the reaction that occurs in a disinfection process tends to be monotonic and with an asymptote profile, making the ‘k’ value different for each time. Therefore, as described by Chick (1908), it is necessary to perform the arithmetic mean calculation to obtain only a value referring to ‘k’ in order to determine the disinfection rate for the experiment.

The highlight of this study was to propose to change the arithmetic mean described in the Chick model (Chick 1908) by a weighted average. Weighting is used as an additional factor in the calculation expressed in Equation (6), considering the time interval factors of each sample in relation to the total disinfection time. The final mean values of ‘k’ calculated by the Chick method (referred to in this study as k_1M) and the values obtained from the modification of the Chick model (called k_2M) are shown in Table 1. Figure S1, provided in the supplementary material, presents a comparison between the k values calculated by the Chick model (k_1M) and by the modeling proposed in this work (k_2M) for all investigated treatment systems, taking into account the inactivation of total coliforms and E. coli.

Figure 3 shows the comparison between the experimental and theoretical concentrations of total coliforms and E. coli during disinfection by the UV/H₂O₂ and UV/O₃ processes without the addition of interferents. For both analyzed pathogens, a greater proximity between the disinfection experimental results and the simulation was obtained by the proposed method. These observations clearly show that the inactivation calculations using the kinetic constant k_2M predict the measured data in a more satisfactory way compared to k_1M.

Carbonate/bicarbonate ions are anions commonly found in effluents, and these species have a negative effect on the performance of disinfection processes, due to their known reactivity against HO^• radicals (Maniakova et al. 2021). The characteristics of secondary effluents, in particular the concentration of carbonates/bicarbonates, depend mainly on the characteristics of their geological origin (Maniakova et al. 2021). Consequently, choosing the best treatment option depends on the influence of carbonate/bicarbonate in the reaction medium. In this sense, modeling studies are extremely important to assess the influence of these species on disinfection processes.

Figure 4 shows UV/H₂O₂ and UV/O₃ disinfection in the presence of 250 and 750 mg L⁻¹ of CO₃²⁻/HCO₃⁻. As previously discussed, the inactivation of total coliforms and E. coli was reduced considerably in the presence of CO₃²⁻/HCO₃⁻ ions. For example, the value of k_2M (results shown in Table 1 and Figure S1) for the inactivation of total coliforms by UV/H₂O₂ disinfection decreases by about 89% in the presence of 750 mg L⁻¹ of CO₃²⁻/HCO₃⁻ ions. Therefore, the increase in CO₃²⁻/HCO₃⁻ ions had a negative effect on disinfection during the UV/H₂O₂ process. A similar finding was also observed by Malvestiti & Dantas (2018) in the UV/H₂O₂ disinfection.

Figure 4 demonstrated that the presence of CO₃²⁻/HCO₃⁻ ions, in addition to causing disinfection inhibition, also caused an oscillation in the linearity of microorganism inactivation during the treatment time. It is possible that apart from inhibiting the disinfection process itself, the presence of carbonate/bicarbonate may disturb the bacteria identification. In the presence of high concentrations of HCO₃⁻ ions, there was a change in the pH of the effluent (pH was around 8–9). Therefore, the change in pH combined with the consumption of HO^• radicals, as shown in Equations (1) and (2), can lead to contrasting effects on the disinfection process and produce non-linear phenomena (Rommozzi et al. 2020). In addition, HCO₃⁻ ions absorb irradiation, hindering its penetration in the effluent, thus protecting the microorganisms (Rubio et al. 2013).

The presence of 750 mg L⁻¹ of carbonate/bicarbonate caused a high inhibition of the disinfection by UV/H₂O₂ process (Figure 4(c) and 4(d)), and the difference between the modeling using the Chick model and that proposed in this work (modified Chick model) is exceptionally low. However, when 250 mg L⁻¹ of carbonate/bicarbonate was added to the system (Figure 4(a) and 4(b)), the data for disinfection were better predicted by applying the modified Chick model.

Analyzing the prediction of disinfection data for the UV/O₃ process (Figure 4(e)–4 (h)), it is also evident that the model proposed using k_2M was the best to simulate the experimental data of the inactivation concentration for both total coliforms (Figure 4 (g)) and E. coli (Figure 4(f)).

Nitrate is an inorganic ion commonly present in effluents; however, few studies have evaluated the influence of inorganic ions on disinfection behavior. In this context, it is extremely important to promote studies aimed at modeling as a way to predict the influence of nitrate in the disinfection process. Figure 5 summarizes the experimental and modeling results of the inactivation tests of total coliforms and E. coli carried out upon addition of nitrate. During experiments to disinfect the effluent with the addition of nitrate it was also possible to observe an oscillation in the linearity of microorganism inactivation. This oscillation is more evident for the disinfection performed by the UV/H₂O₂ process (Figure 5(a)–5(d)). With the presence of 60 mg L⁻¹ of nitrate in the UV/H₂O₂ process (Figure 5(c) and 5(d)), both the established Chick modeling and the proposal in this study were not accurate to predict nitrate disturbance in the disinfection system within 30 min of reaction. In contrast, with the addition of 20 mg L⁻¹ of nitrate (Figure 5(a) and 5(b)), applying the modeling proposed in this work, it is possible to observe a better prediction of disinfection compared to the Chick model.

Comparing the experimental values of inactivation of total coliforms and E. coli for disinfection by the UV/O₃ process with both models in Figure 5(e)–5 (h), it is possible to observe a good agreement between the experimental and theoretical results. The efficiency of microorganism inactivation during the UV/H₂O₂ process increased in the presence of 60 mg L⁻¹ of NO₃⁻ ions compared to the addition of 20 mg L⁻¹ of NO₃⁻, due to the additional generation of HO^• radicals as shown by Equations (13)–(16). However, with a UV/O₃ process occurring in a well-mixed reactor, the effluent quickly becomes saturated with O₃; thus, the NO₂⁻ ions generated by the photolysis of the NO₃⁻ ions (Equation (14)) would be oxidized rapidly by O₃ (Xu et al. 2018). It will suppress the availability of O^•− and the additional generation of HO^• radicals (Equation (16)). Thus, it reduces the non-linear phenomena of the disinfection process, as observed by the greater linearity of the inactivation of both microorganisms as a function of time for the UV/O₃ process in the presence of NO₃⁻ ions (Figure 5(e)–5(h)). This may be a reason that contributed to a better prediction of the calculated concentrations of microorganism inactivation.

Figure 6 illustrates the experimental and modeling results of the time-based inactivation of total coliforms and E. coli by UV/H₂O₂ and UV/O₃ with the simultaneous addition of CO₃²⁻/HCO₃⁻ and NO₃⁻. With the addition of both HO^• scavengers, the disinfection reaction becomes even slower in the UV/H₂O₂ process (see k values in Table 1 and Figure S1a and S1b); however, it does not change the profile of bacterial inactivation, since the inactivation behavior of both microorganisms is the same observed for the study of scavengers separately.

Concerning the UV/H₂O₂ disinfection (Figure 6(c) and 6(d)), the increase in the addition of CO₃²⁻/HCO₃⁻ and NO₃⁻ ions limited the effectiveness of the modeling. This behavior was also observed to predict the concentrations of microorganisms in the highest concentrations of carbonate/bicarbonate and nitrate ions added alone (Figures 4(c), 4(d) and 5(c), 5(d)). When both scavengers were added in the lowest concentrations (Figure 6(a) and 6(b)), the influence of these species was better predicted by modeling using k_2M (Modified Chick Model).

During UV/O₃ disinfection (Figure 6(e)–6 (h)), the increase in the concentration of radical scavengers (Figure 6(g) and 6 (h)) does not interfere in the prediction of the inactivation concentrations of the microorganisms. It is also evident that the best prediction was achieved by using k_2M, especially for calculations of E. coli inactivation. The simultaneous addition of both scavengers did not significantly change the inactivation behavior and the prediction of microorganism concentrations.

Pearson method validation shows that both the Chick model and the proposed methodology in this work using k_2M (Modified Chick Model) were similar to predict total coliform inactivation by UV/H₂O₂ process as well as in the presence of carbonate/bicarbonate and nitrate disturbance (Figure 7(a)). Evaluating the validation by Pearson's correlation for E. coli inactivation in the absence of radical scavengers, the best prediction was obtained by modeling with k_2M (R = 0.969), while using the k_1M the R-value was 0.897 (Table S3). In contrast, in the presence of the scavengers, the predictions were similar for both applied models, with R values ranging from 0.964 to 0.808 for modeling performed with k_1M and 0.948 to 0.823 for modeling performed with k_2M.

The predictive accuracy using Spearman correlation coefficients demonstrates that for both tested bacteria and for all the added scavenging concentration, the proposed methodology using k_2M was better to predict disinfection by UV/H₂O₂ process (Figure 7(b) and 7(d)). As shown in Table S3, for modeling performed in the absence of scavengers and using the Chick model, the Spearman coefficient values were 0.550 and 0.437 for the inactivation of total coliforms and E. coli, respectively. In contrast, performing the same prediction using the k_2M, the values of Spearman's coefficients were 0.983 and 0.926 for the inactivation of total coliforms and E. coli, respectively.

Concerning the microorganism concentration modeling from UV/O₃ disinfection, a similar behavior to that previously discussed for the UV/H₂O₂ process was obtained. The results (Figure 7(e) and 7 (g)) demonstrate that both models have high values of Pearson correlation coefficients to predict the concentrations of total coliforms and E. coli as a function of the disinfection time. However, the results in Figure 7(f) and 7 (h) show that by Spearman's correlation analysis, the best predictions were obtained applying the modeling proposed in this study, which uses k_2M. It obtained excellent values of correlation coefficient for all verified situations (R values greater than 0.91, see Table S3). In summary, the validation demonstrates that the modeling proposed in this study significantly improved the accuracy of the prediction of the concentrations of total coliforms and E. coli during disinfection by UV/H₂O₂ and UV/O₃ processes.

This study explored the effect of CO₃²⁻/HCO₃⁻ and NO₃⁻ ions on the efficiency of total coliform and E. coli inactivation during disinfection by UV/H₂O₂ and UV/O₃ processes. The efficiency of disinfection was clearly reduced in the presence of CO₃²⁻/HCO₃⁻ and/or NO₃⁻ ions for both studied disinfection processes, except for disinfection by UV/H₂O₂ process performed in the presence of the highest concentration of NO₃⁻ ions. In this case, an increase in disinfection was observed in comparison to lower concentrations of NO₃⁻ due to the additional generation of HO^• radicals induced by the photolysis of NO₃⁻ ions.

The prediction of effluent disinfection is an overly complex process that is affected by the presence and concentration of inorganic ions. The development of models to predict the disinfection of secondary effluents by AOPs is one of the extremely important issues to contribute to the scaling-up studies for application in wastewater treatment. The Chick model has some limitations, and it has been modified over time to better represent the disinfection in a complex water matrix. This study contributed to improving the Chick model not only to predict the disinfection of wastewater by AOPs, but also to assess its accuracy in predicting the inactivation of microorganisms in the presence of radical scavengers.

The proposed model proved to be more efficient than the Chick model for calculating the theoretical concentrations of microorganisms during the studied disinfection processes. The greater accuracy of the prediction using the modeling proposed in this study was confirmed by the validation using the Pearson and Spearman correlation coefficients. In addition, and most importantly, the modeling proposed in this study was more accurate to predict the disturbance caused by the presence of carbonate/bicarbonate and nitrate, which are inorganic anions commonly present in secondary effluents.

The prediction model proposed using the k_2M allows us to determine the ideal disinfection time by the UV/H₂O₂ and UV/O₃ processes depending on the concentration of carbonate/bicarbonate and nitrate present in the effluent to be treated. This shows that in an application, modeling helps to reduce process costs and treatment time. In this context, this modeling can be very useful for wastewater treatment management.

The authors thank the financial support of the São Paulo Research Foundation (FAPESP) [grant numbers #2022/00454-0; #2022/04015-1; #2019/26210-8; #2018/03248-7; #2014/17774-1], project CAPES/COFECUB [grant number 88881.191742/2018-00], and National Council for Scientific and Technological Development (CNPq) [grant number 311674/2021-6].

The authors report there are no competing interests to declare.

All authors contributed to the design of this study, as follows: Rodrigo Pereira Cavalcante: Data curation, Formal analysis, Methodology, Writing – original draft. Jacqueline Aparecida Malvestiti: Experimentation, Formal analysis, Writing. José Paulo Diogo Júnior: Experimentation, Formal analysis. Renato Falcao Dantas: Conceptualization, Funding acquisition, Methodology, Project administration, Supervision, Writing – review and editing. All authors commented on previous versions of the manuscript and read and approved the final manuscript.

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

The authors declare there is no conflict.