Response surface methodology to investigate the effects of operational parameters on membrane bioreactor Open Access

Stringent effluent standards imposed by regulatory authorities highlight the need to develop a sustainable and environment-friendly treatment process (Shakir et al. 2017). The quality of urban wastewater varies with time and along the sewage network (Thomas & Thomas 2022). As a result of the increase in the volume and wastewater pollution level, treatment costs also increase (Pajares et al. 2019). Biological methods have been widely adopted in wastewater treatment with the advantages of being more cost-efficient, having more footprint requirements and higher specific biomass activities (Gukelberger et al. 2020). One of the alternative technologies for wastewater treatment is the use of membrane biological reactors. It is a combination of biological processes with membrane filtration that is called membrane bioreactor (MBR) (Krzeminski et al. 2017). Biological wastewater treatment combining membrane filtration has been the focus of research worldwide (Ji et al. 2023; Khan et al. 2024). In this case, the degradation of biomass occurs inside the bioreactor tank, while the separation of treated wastewater from microorganisms is completed in a membrane module (Rahman et al. 2023). As more stringent effluent standards are expected, and the costs of membrane and membrane process continue to fall, the full-scale applications of MBR in domestic and industrial wastewater treatment become increasingly widespread (Praveen et al. 2019; Du et al. 2020; Global Membrane Bioreactor (MBR) Market 2021). The global MBR market has experienced significant growth in recent years and is projected to continue expanding (Al-Asheh et al. 2021). It was reported that 8.4% of the compound annual growth rate (CAGR) was expected for the MBR market. Recent reports showed that the market size of MBR was valued at approximately 4.2 billion USD in 2024 and is expected to reach 8.9 billion USD by 2033. Table 1 presents a regional breakdown of the MBR market (Jijingi et al. 2024; IMARC Group 2033).

However, membrane biofouling is a significant concern of membrane technology and should be seriously considered (Sahaa et al. 2023). Biofouling reduces the membrane's flow and affects the quality of permeate while using more energy and shortening the life of the membrane (Wu et al. 2020). Operational parameter optimization can reduce membrane fouling, improve membrane properties, and tweak hydrodynamics near the membrane surface (Irfan et al. 2022). Optimization of operational parameters has an essential role in biological wastewater treatment (Waqas et al. 2023) and can help increase the bioreactor's performance efficiency (Díaz et al. 2023). Experimental limitations in optimizing membrane performance can be overcome by applying the statistical method which is well known as response surface methodology (RSM) (Kumari & Gupta 2019).

RSM uses statistics and mathematics to model the behavior of the response variable (related to the properties of the studied product) in the function of two or more extraction variables (Thomareis & Dimitreli 2022). The response is in effect modeled by factorial techniques and ANOVA, but these are extended for more detailed modeling of the effects. It combines the design of experiments, regression analysis, and optimization methods in a general-purpose strategy to optimize the expected value of a stochastic response (Kacem et al. 2024). The method has been applied successfully in various fields. Yan et al. (2023) worked on a novel heliostat-based combined cooling, heating, and power (CCHP) system based on heliostats, which uses 3E analysis (energy, exergy, and economic analysis) and multi-criteria optimization with RSM to improve performance and sustainability. In the geotechnical engineering field, Erzin & Tuskan (2019) studied an advanced predictive model, neural networks have been utilized to forecast the factor of safety against soil liquefaction and predict standard penetration test (SPT) values, as demonstrated in studies conducted by Erzin & Tuskan (2017). Similarly, many studies integrated methodologies such as AHP-VIKOR (Tuskan & Basari 2023) and Monte Carlo simulations (Tuskan & Erzi̇n 2024) have been applied to improve slope stability. Manimaran et al. (2022) reported that RSM coupled with genetic algorithms (GAs) proved to be a modern and highly efficient approach for optimizing biodiesel production from okra.

In the case of MBRs, numerous studies have focused on optimizing the operating conditions of membrane processes. These studies have employed RSM to examine the effects of process conditions on filtration membrane removal efficiency and to optimize hydrodynamics for cake layer biofouling control (Yang et al. 2017; Askari et al. 2018). RSM involves simultaneous variations of many operational parameters over a set of experimental runs and enables the elucidation of the operational conditions which are optimized by evaluating their relative significance even in the presence of complex interactions (How et al. 2023). These operational parameters can alter microorganism properties and optimize system performance parameters such as hydraulic retention time (HRT), sludge retention time (SRT), and transmembrane pressure (TMP), which influence microbial activity and membrane biofouling potential (Hee-deung et al. 2015). Recent studies have depicted that HRT and SRT significantly affect biodegradation and micropollutant removal in membrane systems (Kitanou et al. 2019). Statistically designed experimental plans allow for the optimization of operational parameters by analyzing the results obtained from bench-scale tests (Tibi et al. 2021).

In this study, RSM based on a Box–Behnken design (BBD) was applied to investigate the effects of operational parameters such as HRT, aeration rate (AR), and TMP on membrane permeability. Experiments under variable operational parameters were conducted and evaluated by comparing the system performances observed experimentally with those predicted by the quadratic model obtained.

The laboratory-scale MBR was fed with domestic wastewater. Wastewater composition and characteristics, listed in Table 2, are within the standard limits of the World Health Organization (WHO) and US EPA (WHO 2006). Total suspended solids (TSS) (397–457 mg/L), biological oxygen demand (BOD₅) (275–470 mg/L), and chemical oxygen demand (COD) (527–647 mg/L) are considerably deviated from their prescribed limits, indicating the high level of contamination.

Pollution loads are assumed to be all of domestic origin. As shown, the wastewater characteristics can represent the medium–strength urban wastewater seen in Morocco and in most cities around the world (Bruursema 2011; MDCE Ministère Délégué Chargé de l'Eau 2014). Furthermore, these values exceed the specific limit values of Moroccan domestic discharge and the reuse standards, hence the necessity for wastewater treatment (Kitanou et al. 2018, 2021a).

The ultrafiltration membrane employed in the study is ceramic tubular (Membralox^®) allowing the separation of the treated effluent and the purifying biomass, it is placed outside the bioreactor. The membrane characteristics are listed in Table 3. Ceramic ultrafiltration (UF) membranes are by far widely used through the physical removal of particles from liquid in the size range of 0.01–10 μm, because of their potential advantages including chemical and thermal stability, physical strength, and a longer operational life (Mancha et al. 2014). The membrane was cleaned following the manufacturer's recommendation. Before starting the membrane's chemical cleaning, the biological section was isolated from the membrane filtration section. Membrane cleaning was done altering a solution of NaOH and a solution of citric acid. The solutions were prepared and put in the cleaning tank, each solution was recirculated through the membrane for about 20 min and was preceded and followed by a water rinse. The pressure is measured using pressure sensors and gauges installed at the outlet of the recirculation pump, just before the inlet of the membrane module, at the outlet of the membrane module, and within the permeate collection circuit.

The bioreactor was inoculated with 15 L of secondary aerobic sludge (15–25 °C) from the wastewater treatment plant (WWTP), without previous acclimatization to psychrophilic conditions. The initial concentration of sludge in the bioreactor was around 10 g/L of TSS. Then, the reactor was fed with wastewater from the same WWTP.

The seed sludge was obtained from an activated sludge taken from a WWTP situated in the National Office of Electricity and Drinking Water (ONEE) in Rabat, Morocco. During the start-up period, the bioreactor was operated for 37 days and the RSM tests were carried out on the experimental data over this period.

The bioreactor was operated continuously to assess the long-term treatment efficiency of the MBR at psychrophilic (15–25 °C) temperature (Kitanou et al. 2017). Because, in addition to the heat of biological reaction, pumping operations in MBRs can provide additional benefit in raising the reactor temperature to both increase biotreatment efficacy and reduce liquid viscosity and the energy input of crossflow ultrafiltration could also raise temperatures in MBRs to the optimum.

The influent, mixed liquor, and permeate samples were collected and analyzed periodically in accordance with the standard methods. Quality parameters such as COD (Hach DR2800 Spectrophotometer) and TSS were determined following sample filtration through 0.45 μm. Total nitrogen (TN) and total phosphorous (TP) were measured with reagent kits (HACH DR4000, USA) (APHA (American Public Health Association), AWWA (American Water Works Association) & WEF (Water Environment Federation) 2005; WHO 2006; Rodier et al. 2009).

Response surface design is an aggregation of mathematical and statistical approaches accommodating by examining the effectiveness of various operational parameters. This approach is used to establish second-degree mathematical models to examine a phenomenon whose responses lie on a surface. The application of RSM to design optimization reduces the cost of expensive analysis methods and their associated numerical noise. The response variable can be represented graphically (contour plots or three-dimensional space) to help visualize the response surface's shape. The RSM principle is based on two fundamental concepts: selecting the approximate model and evaluating the response. The selection of an approximate model is helpful to obtain the optimized solution at the expense of minimum experimentation. The objective of the design of experiments (DOEs) is the selection of the points where the response should be evaluated (Benalla et al. 2022).

Table 5 presents the input control factors corresponding to the process variable codes. The initial parameters were HRT (X₁), AR (X₂), and TMP (X₃). The responses examined were COD (Y₁), TSS (Y₂), and TN (Y₃). In this study, 17 series of experiments, as illustrated and described in Table 6 and generated using the BBD approach in Design-Expert 13 software, were meticulously conducted.

Table 7 summarizes the MBR performance employing the ultrafiltration membrane for domestic wastewater treatment. The domestic wastewater used as the aeration tank feed contained a high number of organics. Therefore, microorganisms undertaking the removal of the organics were expected to dominate the biofilm. The carbonaceous bacteria biodegraded the readily available substrate (organic pollutants) (Aziz et al. 2024).

The results show significantly higher removal efficiencies for the COD, TN, and TSS of 95, 99.7, and 92,7%, respectively.

This study used a single bioreactor for organics and nutrient removal. Hence, the oxidation of organic matter, nitrification, and denitrification occurred in two separate tanks (Figure 1). Denitrification can also occur in the aeration tank when the aerators are in the interruption phase, the competition between heterotrophic nitrification and aerobic denitrification for COD reduces the TN's removal efficiency (Zhang et al. 2023). The higher efficiency for COD and TN can be attributed to carbonaceous and ammonia-oxidizing bacteria (Mao et al. 2020).

The MBR achieved higher removal efficiency for TSS due to the membrane separation. The results showed that the TSS value substantially diminished from 39.3 to 4.5 mg/L in the MBR permeate attributes to 99.7% removal efficiencies (Table 7). Replacement of the secondary settling tank with the membrane separation enabled the system to achieve removal efficiency not too dependent on the sludge settling characteristics (Pelaz et al. 2018). Detached sludge from the biofilm could readily be removed from the bioreactor. Removing suspended biomass flocs resulted in higher nitrogen and phosphorous removal efficiencies (Kitanou et al. 2021b). The solid-liquid separation process ensured high effluent quality in organics and nutrients. These results indicate that the bioreactor is an excellent choice for domestic and industrial wastewater treatment due to its high microbial activity and flexible operating parameters. Furthermore, the MBR is very attractive to treat wastewater in the open-air canal of wastewater distribution networks where installation of the system is possible, and the issue of a large footprint is less important.

The three-level BBD was used to perform the analysis with 17 experimental sets, for evaluating the effects of the three main independent parameters on the efficiency of the wastewater treatment process. The three-factor BBD matrix showing the independent variable and response is presented in Table 8.

From these equations, it can be concluded that variables X₁ and X₃ positively influence the response. Furthermore, the coefficients associated with X₃ for Y₁ surpass those obtained for Y₂, closely followed by Y₃. Similarly, the coefficients associated with X₁ for Y₃ are higher than those obtained for Y₂, followed by Y₁, as the regression coefficients assigned to them are all positive. On the other hand, variable X₂ has a negative effect on all three responses, with an identical coefficient for each. Interactions (X₁X₂ and X₂X₃) appear to have non-significant effects on all three responses as their coefficients are nearly zero. X₁X₃ interaction shows a significant effect for responses Y₂ and Y₃, while its effect on Y₁ is negligible. Quadratic effects seem to have negligible repercussions. It is important to note that positive values represent a favorable effect on optimization, while negative values indicate an inverse relationship between the factor and the response (Zait et al. 2022; Addar et al. 2023).

This is supported by the overall results of the analysis of variance (ANOVA), which assesses the descriptive quality of the model (Table 9). The ANOVA results demonstrate that the RSM models developed for the three responses (Y₁, Y₂, and Y₃) are statistically significant. The high F-values and very low P-values (<0.0001 for Y₁ and Y₃, <0.0002 for Y₂) indicate that the models effectively explain the variability in the responses based on the independent variables under investigation. The analysis of lack of fit (LOF) and pure error (PE) further confirms the reliability of the experimental design and replicates, as evidenced by consistent PE values. While the quadratic model fits Y₁ well, the LOF results for Y₂ and Y₃ suggest areas for potential improvement though they do not undermine the model's applicability. These results highlight the balance between model complexity and practical use, with the quadratic model providing a reasonable and interpretable representation of the system. Compared with similar studies in the field, our results show low LOF and PE values, indicating that the RSM model provides a good fit for the data and delivers reliable results. This aligns with previous research employing RSM for optimizing wastewater treatment processes (Syahira & Norhaliza 2024). These results confirm the use of RSM in optimizing operational conditions in MBRs and elucidating the complex interactions among control variables.

Moreover, RSM models are often linear or quadratic approximations that may not capture all the non-linearities or complex behaviors of the MBR system. They are generally only valid in the region where the variables are studied and extrapolations outside this region can lead to incorrect predictions (Myers et al. 2016; Ghattas & Manzon 2023). RSM results can be influenced by unaccounted variables, such as variations in ambient temperature or fluctuations in feed water quality.

TMP and HRT in the plant have significant impacts on COD. In addition, the effect of HRT in the plant is more marked than that of TMP. At the same time, the influence of the AR is more moderate, resulting in a reduction as COD increases. In addition, the interaction between HRT in the plant and the AR has a noticeable impact, especially in the upper rather than the lower limits. Other interactions have more modest effects. Under optimum conditions, COD reduction can reach up to 96%.

Both operational parameters TMP and HRT exert substantial influences on the TSS. It is particularly important to note that the predominant effect of HRT is more marked than that of TMP, with a significant interaction between these two parameters. In parallel, the influence of the AR is moderate, manifested by a decrease in TSS concentration as it increases. In addition, the other interactions show more modest effects. Under optimal conditions, a reduction in TSS concentration of up to 95% is possible.

The TMP and HRT have significant impacts on TN. Furthermore, the effect of HRT is more pronounced than that of TMP. Concurrently, the influence of the AR is more moderate, leading to a reduction as TN increases. Moreover, the interaction between HRT and TMP is highly significant. The remaining interactions exhibit more modest effects.

The concept of desirability was introduced by Harrington (1965) and subsequently developed, in particular by Derringer & Suich (1980). It is based on the transformation of all the responses obtained from different measurement scales into an identical dimensionless desirability scale (individual desirability). The values of the desirability function are between 0 and 1.

The use of RSM in MBR processing has several advantages and disadvantages. RSM optimizes operational conditions such as HRT, AR, and TMP to enhance MBR performance (Hee-deung et al. 2015; Kitanou et al. 2019; How et al. 2023). Using experimental designs like the BBD, the number of required experiments number is reduced, saving time and resources. RSM develops mathematical models that describe the relationships between independent variables and responses, allowing for the prediction of system performance (Myers et al. 2016). It also facilitates the visualization of the impact of control variables on responses through response surface plots and contour plots, enhancing the understanding of interactions between factors (Thomareis & Dimitreli 2022; Kacem et al. 2024). Additionally, RSM identifies and quantifies the interactions between independent variables, which is crucial for understanding the complex behavior of MBR systems (Mohan et al. 2022).

This study applied RSM to optimize the performance of a biological reactor coupled with external membrane ultrafiltration. The MBR was a successful biological treatment process to achieve high pollution removal efficiency, exhibiting 95% COD, 99.7% TSS, and 93% TN, removal efficiencies. The RSM results demonstrated the effects of the operating parameters and their interactive effects on pollution removal. By applying RSM, the optimum region for the bioreactor operating conditions was located. The optimum conditions reached an HRT of 15 h, an AR of 552 NL/h, and a TMP of 1.5 bar. The results demonstrated good agreement between experimental and model predictions. It is evident that RSM is an efficient statistical optimization approach that can help to distinguish between the most important operational parameters at the cost of minimum time and effort. Developing the membrane biological reactor system can significantly enhance the effluent quality to satisfy stringent regulations. It can serve as a promising alternative water in reuse irrigation to develop a sustainable environment.

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

The authors declare there is no conflict.