The study's framework is presented in Figure 1. It illustrates the methodology for analysing the behaviour of AgNPs in WWTPs through the simulations of the ASM-AgNP within the BSM1 (BSM1-AgNP), Bardenpho 4-stage model (Bardenpho-AgNP), and the anoxic/oxic model (A/O-AgNP). Furthermore, the removal efficiency of AgNPs is evaluated in the WWTP layouts and compared to the baseline BSM1 without AgNPs. The ASM-AgNP model was developed by Vilela et al. [26], based on the conditions established by the International Water Association (IWA) [18]. The variables and process rates used in this model are presented in Figure 2.

Figure 1.

Figure 2.

Suitable coefficients and process rates for the removal mechanisms were determined and calculated in [26], where the authors performed a system analysis and validated the model's response to varying nanomaterial influent concentrations. The model also includes chemical precipitation to enhance AgNP removal efficiency and NaOH precipitation to facilitate easy solid-liquid separation [27], enabling comparisons with previous work.

This study used GPS-X version 8.0.1 software for technical and qualitative analyses of the baseline model BSM1 without AgNPs and three WWTP configurations mentioned in the preceding section.

The model development follows the tool of the model developer from the software. The stoichiometry and kinetics of the ASM-AgNP model were implemented and generated using the model developer tool. Furthermore, the operational parameters and characteristics are summarised in Table 1 following the standard BSM1 framework to ensure comparability. The influent characteristics, flowrate, sludge retention time, aeration, and sludge were maintained. The primary differences among the studied configurations are the physical configuration and the internal recycle flowrate, with BSM1 as the baseline. These variations in hydraulic and process design are critical factors influencing nutrient removal and organic matter degradation.

The key dimensions of the suggested approach are as follows: First, the ASM1-AgNP model is configured in GPS-X; second, the BSM1-AgNP, Bardenpho-AgNP and A/O-AgNP models are developed; third, the influent/sludge characteristics and operating parameters of the biological model are calibrated to the base model; fourth, the validity of the steady and dynamic simulations is evaluated on every model. The different configurations developed in GPS-X are presented in Figure 3.

Figure 3.

The dynamic simulations were performed according to the standard BSM1 dynamic conditions described by Alex et al. [18]. The simulation time is 14 days, and the results are analysed at the end of the simulation period. The initial phase of the simulation describes the system's stabilisation; thus, the performance evaluation focuses on the end of the simulation period.

Furthermore, the influent concentrations were primarily adopted from the BSM1 report [18], and the AgNP concentrations utilised in the WWTP models were 14.92 mg/L for AgNPs and 72.24 mg/L for Ag ion, adopted from the study of Cervantes-Avilés et al. [28]. The same value of 14.92 mg/L was used in all configurations, enabling a direct comparison of the calculated removal efficiencies. The influent AgNP concentration represents a worst-case scenario, with high nanomaterial levels used to evaluate system robustness rather than typical environmental conditions. Although typical environmental concentrations of AgNPs are generally reported at lower levels, higher concentrations were used to evaluate the robustness and sensitivity of the treatment configurations. This approach allows assessment of system behaviour, potential inhibitory effects, and removal performance. Given the scarcity of research and the difficulty of conducting large-scale experiments, these data have been fully adopted from published works. Hence, to partially overcome this limitation, comparisons with BSM1 without AgNPs, the baseline model, are made to analyse the validity of the results from the models. The stoichiometric processes that the model implemented for AgNP, adapted from [21] and [22], come from the mass balances presented in equations (1) to (4).

Adsorption of AgNP to biomass:

Desorption of adsorbed AgNP:

Dissolution of AgNP to Ag ion:

Chemical precipitation of Ag ion:

where S_ag is the AgNP [mg/L], X_BH + X_BA represents the biomass [mg COD/L], and X_ag is the adsorbed AgNP [mg/L]. The remaining symbols denote concentrations [mg/L] of: AgNP₀ – silver, Ag⁺ – silver ion, O₂ – oxygen, H⁺ – hydrogen, H₂O – water, Na⁺ – sodium, and NaOH – sodium hydroxide.

The effluent quality assessment is performed in accordance with the BSM1 report, firstly, given that the ASM-AgNP was derived from it. The conditions for the evaluation were: total nitrogen (TN) should be less than 18 mg/L, total chemical oxygen demand (COD_t) less than 100 mg/L, nitrogen ammonia less than 4 mg/L, and BOD_t less than 10 mg/L [18]. In addition, the effluent quality index (EQI) has been used to assess the quality of removal achieved by each WWTP configuration. Equation (5) shows the EQI calculation and the variables considered for this analysis [18].

where b_i are the weighting factors assigned to each variable, and the concentrations of the variables are taken in [g/m³]. All the b_i values have been adopted from the BSM1 report, namely b_ss = 2, b_COD = 1, b_NKj = 30, b_NO = 10, b_BOD5 = 2 [18]. Furthermore, each of the variables expressed by equations (6) to (9) represents the sum of the different variables in the model at the effluent:

where the subscript eff signifies the values representing concentration in the effluent. S_Nkj,eff is the Kjeldahl nitrogen in the effluent concentration, which is the sum of the soluble and particulate nitrogen in the model; SS_eff is the suspended solids of the effluent concentration; BOD_5,eff is the BOD concentration at the effluent; and COD_eff is the effluent concentration of COD.

Furthermore, removal efficiencies were calculated following standard procedures. Constant influent concentrations from the BSM1 were used for steady-state conditions. For dynamic state conditions, removal efficiencies were calculated based on the average influent concentrations over the evaluation period. For AgNPs, removal efficiency is defined based on total AgNP concentration, including both soluble and particulate fractions considered in the model. Two removal approaches are considered: first, overall removal, which accounts for total mass removal and sedimentation; second, removal calculated from the effluent AgNP concentration, estimated with the influent and effluent in the liquid phase. Eq. (10) is used to estimate the removal efficiency.

where C_in and C_eff represent the influent and effluent concentrations [mg/L].

Figure 4 shows the results obtained at the effluent from the models' simulations with base influent conditions (BSM1) for steady-state operation.

Figure 4.

The concentrations of total nitrogen (TN), nitrate/nitrite nitrogen (NO₃/NO₂), total biochemical oxygen demand (BOD_t), and total chemical oxygen demand (COD_t) are shown. Figure 4a corresponds to a TN value of 4.57 mg/L, NO₃/NO₂ value of 0.034 mg/L, BOD_t value of 7.53 mg/L, and COD_t value of 46.11 mg/L, from the BSM1-AgNP model. These values fall within the range of the simulation results for the BSM1 model. The total COD shows a slightly higher value than that from the base BSM1; however, this might be related to differences in the estimation method used in the simulation software GPS-X [29]. It is known that the software can produce some differences in decimal places when calculations are shortened in some instances [30].It should be noted that the values presented in the figures are approximate graphical representations. In contrast, the numerical values reported in the text correspond to the exact simulation outputs obtained from GPS-X.

Compared to the baseline BSM1 without AgNPs (Figure 4d), the model yielded results similar to those, with final effluent concentrations around the same values, differing by a few decimal places; for instance, COD_t was 39.1 mg/L, and TN was 5.33 mg/L in the BSM1. The major highlight is that the TN concentration in the BSM1-AgNP is slightly lower than in the BSM1, indicating similar removal for both. Moreover, for AgNPs, a high removal was observed, obtaining an average effluent concentration of 2.7 mg/L for all the WWTP configurations, as shown in Figure 5 (next page), and it did not interfere with the removal of the rest of the components considered in this analysis, such as TN, COD, and BOD.

Figure 5.

Following the analysis, Figure 4b shows TN at 2.22 mg/L, NO₃/NO₂ reaching zero, BOD_t value at 12.85 mg/L, and COD_t value at 52.79 mg/L from the Bardenpho-AgNP model.

Finally, Figure 4c shows that, according to the A/O-AgNP model, the TN value was 2.85 mg/L, NO₃/NO₂ reached 0, BOD_t was 15.65 mg/L, and COD_t was 56.56 mg/L. For these two model configurations, the results show higher COD concentrations, which are related to the physical conditions of fewer reactors and lower or absent internal recycle flowrates. This provides insight into the influence of the recycle flowrate on COD removal efficiency in wastewater treatment plants. Moreover, the BSM1 model without AgNP concentration yielded final values of COD_t 39.1 mg/L and TN 5.33 mg/L, as shown in Figure 4d, indicating that TN removal was higher and COD removal was lower compared to the Bardenpho-AgNP model. Similarly, comparing the Bardenpho-AgNP model, the TN was lower, and the COD_t was slightly higher within the same range, both showing good removal in this configuration. Meanwhile, for the A/O-AgNP model, TN also had a low value and a smaller increase in COD_t than in the BSM1 results. Hence, both configurations show good removal results. In general, both configurations showed similar behaviour for steady-state conditions.

Table 2 summarises the steady-state performance of the WWTP configurations, integrating effluent concentrations, removal efficiencies, and EQI values.

It is noted that removal efficiencies were calculated based on influent and effluent concentrations, in agreement with the values presented in the figures and tables. For AgNPs, the reported percentages correspond to effluent-based removal, consistent with the observed concentration reduction, accounting for combined soluble and particulate AgNPs in the model. The results indicate that all configurations achieved high treatment efficiencies, particularly for BOD removal, exceeding 90%, especially in the BSM1-AgNP configuration. Nitrogen removal efficiencies were also consistently high, whereas COD removal was lower in the Bardenpho-AgNP and A/O-AgNP configurations. The EQI results further confirmed that the BSM1-AgNP configuration provides the best overall effluent quality. Higher EQI values represent a relation to increased residual organic matter in the effluent.

Overall, as shown in Figure 6, steady-state removal efficiencies were estimated relative to the standard BSM1 baseline. BOD removal exceeded 90% in all configurations, with the highest value in the BSM1-AgNP configuration at approximately 96%. This removal may indicate strong biodegradation under stable conditions. Nitrogen removal efficiencies were 85% in BSM1-AgNP and over 92% in the Bardenpho-AgNP configuration, suggesting enhanced denitrification processes. Furthermore, COD removal was slightly lower, 81% and 85%, in the Bardenpho and A/O configurations, respectively. This result might be related to the low internal recirculation flowrate and the number of reactors per configuration. The steady-state results show that all configurations provide robust treatment performance, especially BSM1-AgNP, with a more stable removal efficiency across all parameters.

Figure 6.

The results for AgNP concentrations under dynamic conditions (AgNP and particulate AgNP) are shown in Figure 7, which shows similar behaviour and an average value of 2.2 mg/L. Moreover, Figure 8 shows the results from the models' dynamic simulations. Figure 8a corresponds to a TN value at 14 days of 11.34 mg/L, NO3/NO2 value at 14 days of 0.68 mg/L, BODt value at 14 days of 6.03 mg/L, and CODt value at 14 days of 43.04 mg/L, from the BSM1-AgNP. The TN and BOD values are slightly different, being lower and higher than those reported in the BSM1 report, respectively. This result might be related to the stoichiometric and physical conditions of the model. Furthermore, Figure 8b corresponds to a TN value at 14 days of 26.68 mg/L, NO3/NO2 value at 14 days of 0.053 mg/L, BODt value at 14 days of 11.18 mg/L and CODt value at 14 days of 49.83 mg/L, from the Bardenpho-AgNP. The values of TN, BOD, and COD are higher than those described in the BSM1 report and the BSM1-AgNP. However, this did not affect the model's performance simulation. Furthermore, the BSM1 model without the AgNPs final effluent concentration values, for dynamic conditions, of CODt 35.07 mg/L and TN 5.81 mg/L, as presented in Figure 8d, which compared to the BSM1-AgNP model, represents a lower value, indicating that the removal of nitrogen and COD was not as good in the BSM1-AgNP. Compared to the Bardenpho-AgNP, the results are consistent with previous observations; TN and COD were less removed, with a small difference. Finally, Figure 8c corresponds to a TN value at 14 days of 32.2 mg/L, NO₃/NO₂ value at 14 days of 0.022 mg/L, BOD_t value at 14 days of 14.69 mg/L, and COD_t value at 14 days of 54.74 mg/L, from the A/O-AgNP model.

Figure 7.

Figure 8.

Compared to the BSM1-AgNP, the results show higher effluent concentrations for all components. BSM1 describes dynamic results of average TN 15.57 mg/L, BOD_t 2.77 mg/L, and COD_t 48.30 mg/L [18]. Compared to these values, the results obtained with the BSM1-AgNP model fell within a range, accounting for differences in the software's decimal precision. The Bardenpho-AgNP model results showed higher TN in the effluent, a more substantial increase in BOD_t, but with a COD_t value within the same range. Compared to the BSM1 model without AgNPs, the final concentration values (COD_t 35.07 mg/L and TN 5.81 mg/L) were lower, as shown in Figure 8d. The A/O-AgNP process showed lower removal for both variables.

For the A/O-AgNP model, the TN was approximately double that reported in BSM1, and the BOD_t increased by 7 times, while the COD_t remained within the range. The last two configurations thereby show that the conditions for treatment require adaptation of physical conditions and probable enhancement of stoichiometric factors. In addition, compared with the AgNP concentrations in Figure 7, a similar behaviour was observed, with high removal of soluble and particulate AgNP from water. Compared to previous studies, the Bardenpho and A/O configurations have been commonly used for large WWTPs, with good performance in removing carbon, nitrogen and phosphorus from wastewater [31]. In general, when analysing the removal portrayed by the three configurations, they achieved satisfactory results for AgNP removal, and an increase in TN and COD_t was noticed for two of the configurations, which, compared to the literature, can be related to the inhibition that AgNPs have on nitrogen removal in the activated sludge process [28].

Table 3 presents the dynamic performance of the WWTP configurations over the last 14 days of simulation. A significant reduction in nitrogen removal efficiency was observed, particularly in the Bardenpho-AgNP and A/O-AgNP configurations, so that these configurations might require improved operational control. In contrast, BOD removal remains consistently high while COD removal shows moderate stability. Furthermore, the EQI is calculated only for steady-state conditions, as under dynamic conditions, the analysis varies over the simulation period.

In treatment performance, a reduction in removal efficiency was observed compared with the previous stage and the BSM1 baseline. Figure 9 presents the BSM1-AgNP configuration with a TN removal efficiency of approximately 62%, whereas the Bardenpho-AgNP and A/O-AgNP configurations showed removal efficiencies of approximately 11%. These results might indicate sensitivity to loading conditions, suggesting a target for implementing control strategies or operational adjustments to improve the system. In contrast, BOD removal was consistently above 92% across all configurations, indicating that organic matter was degraded. COD removal efficiencies remained between 81 to 86%, indicating a lower effect on carbon removal processes than nitrogen. Thus, dynamic operation reveals limitations in nitrogen removal, particularly in configurations with a reduced internal recirculation.

Figure 9.

Overall, the results indicate that all configurations perform well under steady state conditions, but their behaviour under dynamic conditions differs. The BSM1 configuration shows greater robustness, which can be attributed to its higher internal recirculation and the number of reactors, given that this system is designed for nitrification-denitrification processes. Further, the Bardenpho and A/O configurations showed greater sensitivity under dynamic conditions, which is likely related to the reduced internal recycle and lower number of reactors. These differences are primarily associated with the configuration design; however, the inclusion of AgNPs may also contribute to additional inhibition effects on biological processes. Therefore, the performance strongly reflects the influence of system design and nanoparticle interactions, suggesting that WWTP configurations with higher recirculation and reactor settings may improve performance under variable loading conditions.

Although the model provides valuable insights into the behaviour and removal of AgNPs across different WWTPs, some uncertainty remains due to assumptions about influent conditions and kinetic parameters, as well as the limited availability of experimental data for model calibration. Future work could include a sensitivity analysis to evaluate the influence of key operational and model parameters on system performance, thereby improving robustness.