Computational Fluid Dynamics Simulation to Investigate Diffuser Outlet Factors in Anaerobic Membrane Bioreactors Treating Wastewater

Abstract

Anaerobic membrane bioreactors (AnMBRs) require biogas recycling to stir the mixed liquid and flush particles away from the membrane surfaces for stable operation. With the fixed gas cycling rate, gas diffuser configuration is an important factor that affects stirring and flushing performance. This study investigated the effect of different outlet diameters on biogas diffusers in AnMBR by using computational fluid dynamics (CFD) to analyze gas–liquid flow in a numerical model constructed based on an experimental AnMBR. According to the CFD results, as the outlet diameter increased from 2.5 to 5.0 mm, the average velocity increased from 0.15 to 0.31 m/s and the average wall shear stress (WSS) increased from 0.21 to 1.10 Pa on the membrane surface. The increase in gas velocity enhances the stirring effect, and the increase in WSS improves the flushing performance. However, when it was further increased to 10.0 mm, the average velocity and average WSS was 0.27 m/s and 0.22 Pa, respectively, indicating that too large an outlet diameter leads to a concentrated gas distribution, which reduces the performance of stirring and flushing. Furthermore, these results provide a basis for optimizing diffuser configuration, which is significant for promoting the practical application of AnMBR in wastewater treatment.

1. Introduction

Sustainable development is a key issue today, and water pollution is a priority concern for all sectors of society. In a way, whenever water is used, regardless of the activity, whether for domestic use or agro-industrial use, it results in pollution to the eco-system and water bodies [1,2]. Therefore, treating wastewater before it is discharged into natural water bodies is significant for the protection of ecology and environment [3,4,5]. Over the past decades, a variety of technical solutions, including physical methods, chemical methods, and biological approaches, have been developed and used for the treatment of wastewaters [6,7,8,9]. However, the conventional treatment process, usually a combination process of physical, chemical, and biological approaches [10], generally requires a large amount of energy while discharging the greenhouse gases and resulting in some secondary pollution or environment risks (for example, the large amount of waste sludge) [11,12]. Policies related to the promotion of wastewater treatment are being developed and implemented in countries around the world. For example, the Ministry of Land, Infrastructure, Transport and Tourism (MLIT), the Japanese government’s policy agency in charge of environment-related policies, has been implementing a program since 2011 called the Breakthrough by Dynamic Approach in Sewage High Technology Project (B-DASH) [13]. In terms of international cooperation and policies, international organizations such as the United Nations and the OECD have been promoting integrated water resources management (IWRM) as an approach to address water resource challenges [14].

The anaerobic membrane bioreactor (AnMBR) combines membrane separation and anaerobic digestion, providing many advantages such as energy recovery potential, low excess sludge production, and good performance in sludge-water separation [15]. Therefore, it is highly expected to be applied in the real process of wastewater treatment. According to a previous report, AnMBR can not only reduce energy by more than 50% and sludge production by 75%, but can also effectively reduce greenhouse gas emissions compared to the traditional activated sludge method [15].

Beside the advantages that can be obtained from the AnMBR treating wastewater, it also has some disadvantages, among them, major concerns are the membrane fouling and the energy increasing along with the filtration [16]. Thus, membrane cleaning is required during the process to prevent membrane fouling proceeding [17]. In particular, the regular online cleaning strategy provides a good anti-fouling method with timesaving, low-cost, and convenient operation [18]. However, either the membrane cleaning (off-line) or the online cleaning strategy generally require stopping of the treatment process, for hours or even days [19].

In aerobic treatment processes, aeration not only provides the oxygen needed for the reaction process, but also provides a scouring feature on the surfaces of the membrane [20]. This scouring feature makes the pollutants and microorganisms in the wastewater relatively less likely to adhere to the membrane surface, achieving the effect of slowing down the membrane fouling [21]. Although AnMBR treatments do not need aeration due to the anaerobic digestion bioreaction, the installation of a gas diffuser and biogas circulation to scour the membrane surface can prevent fouling occurring during the filtration process, and further, can ensure the operation flux during the AnMBR treatment [22]. In addition, the gas blowing provides sufficient agitation of the mixture in the bioreactor, allowing the biochemical reaction process to proceed smoothly [23].

Previous studies have found that a larger gas circulation rate can lead to a better surface scouring performance [24]. However, in actual operation, it was also found to be related to sludge concentration, filtration rate, and gas diffuser configuration. In particular, the size and position of the pores (outlet diameters of the diffuser) have a significant impact on the distribution of the cross-flow velocity (CFV) and the flushing effect on the membrane surface, where a concentrated or uniform distribution of scouring force is concerned [25,26]. These factors greatly affect the longevity and stability of the membrane filtration performance. Therefore, a more balanced gas distribution on the membrane surface by optimizing the distribution and size of the aeration ports is an important requirement for the stable operation of AnMBR systems.

Computational fluid dynamics (CFD) is a numerical simulation method that has gained widespread use in studying fluid systems where experimental measurements are either challenging or prohibitively expensive. This technique facilitates the acquisition of flow parameters and phenomena that are not easily accessible or available through experimental means [27,28]. For example, wall shear stress (WSS) is an important parameter of the interaction at the intersection and is often used to describe the mechanical properties of a material or structural surface [29]. However, it is usually difficult to obtain or measure WSS directly experimentally, and the experimental procedure can be complex and costly. Therefore, in research and engineering applications, CFD methods can be used in computers to calculate approximate values of WSS by establishing suitable models and boundary conditions. Obtaining important hydrodynamic parameters through the CFD approach has been widely used in previous research [30]. In particular, the simulation approach allows one to obtain data at any position in the entire fluid field, which is almost impossible to achieve in the experiments. Applying the CFD simulation method to bioreactors for wastewater treatment not only allows for reliable data, but also significantly reduces the high costs of time and economic required for experiments. Some studies have reported the use of CFD simulation to resolve the fluid state in bioreactors including AnMBRs, in order to achieve energy savings or sufficient mixing during the wastewater treatment process [26,31]. However, further progress is needed for the analysis of gas diffuser configuration, especially in terms of exploration into the impact of gas scouring on membrane surface and optimization of the gas diffuser device and CFV condition. Some previous studies reported the relationship between the angle formed between the gas diffuser outlet and the membrane surface using CFD simulation and found that the angle formed between the gas diffuser and the membrane is conducive to controlling membrane contamination [32].

The purpose of this study is to investigate the effect of different outlet diameters of gas diffusers on the scouring effect of membrane surfaces in AnMBR. By simulating the mixed-phase flow fluid in the bioreactor, the flow regime is analyzed, and the gas diffuser layout can be optimized to obtain better anti-fouling performance in membranes to improve the efficiency of the bioreactor and reduce the energy consumption in the suction filtration process simultaneously. There is a lack of research on the relationship between gas diffuser outlet diameter and membrane efficiency. The distribution characteristics and hydrodynamic parameters of the fluid on the membrane surface have not been effectively studied. In this study, CFD simulation is used to reveal the hydrodynamic characteristics of the membrane surface at different outlet diameters and explain the relationship between the outlet diameter and membrane efficiency from the hydrodynamic point of view.

2. Materials and Methods

2.1. Geometry of the Model

The 3D model constructed in this study is shown in Figure 1. Figure 1a represents the perspective structure of the bioreactor, including the gas diffuser, the membrane module, and the gas inlet pipe connected to the gas diffuser. The models used in this study were constructed based on real experimental setups. The size and shape of the model is basically the same as the real experimental setup.

The structure of the gas diffuser and membrane module is represented in Figure 1b. The upper and lower ports of the membrane module allow free passage of liquid and gas. The use of membrane module in the experiment is for the purpose of fixing the membranes. The structure and dimensions of the membrane are shown in Figure 1c. Three groups with a total of six membranes were used in the bioreactor. Of these, plane a, plane b, and plane middle were selected for a better analysis in this study.

According to the objectives of this study, a total of three gas diffuser models with different outlet diameters were built, as shown in Figure 2 (front and top views). The three diameters are 2.5 mm, 5.0 mm, and 10.0 mm, and the corresponding number of inlets for controlling the total area of the gas outlet (1256 mm²) are 256, 64, and 16. Among those, the outlet diameter of 5.0 mm is constructed by referring to the model in a real experiment. For all these models, the height of the outlet was 1 mm.

2.2. Details of CFD Simulation

CFD calculates the state of a fluid by solving the Navier–Stokes equation, which is given in Equation (1). Specific parameters are solved by solving the three governing equations: the continuity equation, the momentum equation, and the energy equation. This study is concerned with the specific motion of both gas and liquid flows, so the CFX solver Eulerian Multiphase Mode of ANSYS is used for the solution and the fluids are assumed to be incompressible Newtonian fluids. The liquid is set as a continuous phase and the gas as a discrete phase. The surface tension of the fluid was set to 0.44. The mesh generator was subdivided using the ANSYS mesh and different regions are subdivided in different ways. The geometrically simple areas such as membranes were meshed with hexahedral mesh and the geometrically complex areas were meshed with tetrahedral mesh. The specific results of the mesh refinement are shown in

Table 1. The details of meshing for all models.

Diameter of Outlet (mm)	2.5	5.0	10.0
Nodes	1,095,788	1,485,935	906,832
Elements	3,950,165	4,314,573	3,357,353

. The flow rate of the inlet biogas was set to 24 L/min according to the experimental value, and the outlet was set as a free pressure outlet boundary condition with a relative pressure of one atmosphere. In this study, the effect of gravity is not negligible and the acceleration of gravity in the vertical direction was set to 9.8 m/s². The total simulation time was 2 s with a time step of 0.001 s and the convergence residual was set to 0.001. The K turbulence model is used to simulate multiphase flow and the convergence residual for k was set to 0.01.

$$\frac{\partial v}{\partial t}+v·\nabla v=-\frac{\nabla P}{\rho }+\mu {\nabla }^{2}v$$

(1)

where $v$ is the fluid velocity vector, $P$ is the fluid pressure, $\rho$ is the fluid density, $\mu$ is the viscosity, and ${\nabla }^2$ is the Laplacian operator.

2.3. Flowchart of Methodology

The process of this study is shown in Figure 3. The flow chart shows the steps of this study and the important aspects of each step.

3. Results and Discussion

3.1. Superficial Velocity Distribution on the Membrane Surfaces

Figure 4 shows the simulation results of superficial velocity streamline of gas and liquid on the surface of membranes. According to the results of gas superficial velocity streamline, the average superficial velocity increases with the increase in the outlet diameter of gas diffuser with the constant of the inlet gas cycling rate. However, the distribution of gas superficial velocity streamline on the membrane surfaces is greatly influenced by the outlet diameter of gas diffuser. For example, when the outlet diameter is 2.5 mm, the main flow region of the gas is concentrated in the middle of the bioreactor, i.e., the gas superficial velocity on plane a and plane b is much slower than that on plane middle. In addition, the distribution result of gas on plane middle is concentrated in the central area. The average gas superficial velocity on plane middle is four times or more than that of on plane a and plane b. When the gas diffuser outlet diameter reaches or exceeds 5.0 mm, the distribution of gas superficial velocity streamlines changes significantly and is relatively more dispersed.

On plane a, in the case of outlet diameter 2.5 mm of the gas diffuser, the vortex distribution is at the bottom of membrane which is in the area that near to the outlets of the gas diffuser, and it affects about only 25% of the membrane surface. When the outlet diameter of gas diffuser increased to 5 and 10 mm, multiple vortex nuclei can be observed on the membrane surface, which means that the vortex could affect more than 50% of the membrane surface. In addition, an increase in the velocity of gas enhances the force of the gas on the membrane surface. The gas streamlines results on plane b and plane middle are similar to those obtained on plane a. It has been shown that strong vortices are more effective in scouring the membrane surface, which is helpful in maintaining the efficiency of the membranes [33]. A quite small gas diffuser outlet diameter will concentrate the gas entering the interior of the reactor too much to interact with the membrane over a larger area, which could reduce the velocity of the gas as well as the strength of the resulting vortex. These factors may weaken the interaction at the membrane surface to the point where membrane efficiency cannot be maintained.

The superficial velocity streamline distribution of liquid on the membrane surface is similar to that of gas. The result that outlet diameter of gas diffuser effects the velocity is also in accordance with that obtained of gas superficial velocity, although the superficial velocity of liquid is much higher than that of gas. Due to the influence of liquid environment and gas motion, liquid on the membrane surfaces has higher intensity vortex even at a gas diffuser outlet diameter of 2.5 mm.

In this study, by comparing the surface velocities of gas and liquid on the membrane surface, it was found that the interaction of liquid and membrane surface is much stronger than the interaction of gas and membrane surface. The properties of liquid and gas, and the way in which liquid and gas interact with membranes, is considered to be the main reason for this phenomenon. The liquid phase is a continuous phase, so the area acting on the membrane surface is larger. However, the gas phase is a dispersed phase, which results in a smaller area acting on the membrane surface. In addition, the gas cannot be uniformly stabilized in a liquid environment for long periods of time, which further reduces the gas–membrane interaction. The streamline provides direct evidence of this difference, and it becomes more pronounced as the gas diffuser outlet diameter increases. In other words, this suggests that the liquid-membrane interaction remains the dominant interaction even with a continuous influx of gas. As mentioned above, the flushing effect enhances the scouring performance on the membrane surfaces to guarantee the filtration process, since maintaining the permeability is of great importance to ensure stable operation of the AnMBR. According to previous research, it has been shown that the scouring effect of fluid motion on the membrane surface is positive and the more pronounced the scouring effect is, the more it contributes to maintaining the permeability and filtration efficiency [34]. The results of surface velocity show that the gas outlet diameter is positively correlated with fluid perturbation. The rate of change in the average velocity obtained exceeds 50% when the outlet diameter increases from 2.5 mm to 10.0 mm, which indicated that larger gas outlet diameter is more favorable for the membrane in maintaining the filtration efficiency.

3.2. Membrane Surface Pressure

The pressure distribution on the membrane surface is shown in Figure 5, corresponding to the gas outlet diameter of 2.5 mm, 5.0 mm, and 10.0 mm and the three different locations are marked in Figure 1c. As described in the Methods section, the pressure boundary condition used in this study is a relative pressure condition for atmospheric pressure, and this boundary is a simplified constrained condition. The use of a particular, simplified relative pressure boundary condition may make the resulting absolute values of pressure not practically meaningful. However, the effect of this boundary condition on the distribution of the pressure is relatively small. This approach has been used in various earlier studies and the experimental results have confirmed its practical applicability [35].

The main driving force of membrane filtration is the pressure difference between its two sides; therefore, the pressure distribution on the membrane surface is an important factor affecting the membrane’s performance. At the gas outlet diameter of 2.5 mm, the pressure distribution in the plane middle was clearly stepped, with relatively high pressure in the lower area of the membrane and relatively low pressure in the upper area. At outlet diameter conditions of 5 and 10.0 mm, there is a three-step pressure distribution at all three locations, i.e., the pressure is stepped down in the gravitational direction. As the outlet diameter increases from 2.5 mm to 5.0 mm, the pressure increases in some areas of the membrane, for example, in the areas near the liquid line of the bioreactor. When the outlet diameter of gas diffuser is further increased from 5.0 mm to 10.0 mm, the pressure distribution over the entire membrane surface does not change in the same way, but the average pressure and the area of relatively high pressure are reduced. The reason for this phenomenon is considered to be the separation of the liquid from the membrane by the gas flushing, which leads to a reduction in the influence of the liquid on the membrane surface and thus a reduction in the pressure that is reflected on the surface of the membrane.

As previously mentioned, the difference in the pressure between the inside and outside of the membrane is an important factor that affects membrane filtration performance [36]; therefore, a high transmembrane pressure difference is very beneficial for the membrane filtration process [37]. If the pressure inside the membrane is kept constant, it is beneficial to increase the pressure on the membrane surface. Therefore, if the pressure inside the membrane is assumed to be constant in this study, the gas outlet diameter of 5.0 mm is considered to be the best solution. It is also important to note that the pressure difference at the membrane surface is at most less than 1 kPa, and the true effect of this pressure difference on the membrane needs to be further investigated. In addition, the assumption that the internal membrane forces remain constant is an important support for the above conclusions. The validity of this condition also needs further investigation.

3.3. Gas Volume Fraction Distribution on the Membrane Surfaces

Figure 6 shows the gas volume fraction distribution on the membrane surface at three different locations corresponding to gas diffuser outlet diameters of 2.5 mm, 5.0 mm, and 10.0 mm, respectively. The results show that when the outlet diameter is 2.5 mm, the gas is largely concentrated in the middle part of the bioreactor, i.e., plane middle, and there is essentially no gas distribution on the membrane surface in planes of a and b. The gas distribution on the membrane surface in the plane middle position is not uniform, and the gas is concentrated in the middle part of the horizontal direction. This suggests that an outlet diameter of 2.5 mm would concentrate the gas too much to have an effective effect on the other parts. The reason for this result could be that the small diameter limits the volume of biogas entering the bioreactor. When the gas diffuser outlet diameters are 5.0 and 10.0 mm, the gas distribution on the membrane surface at the plane middle location is higher than that of 2.5 mm. More importantly, the gas distribution in planes a and b is greatly improved, except for plane middle. This means that the non-uniform gas distribution is effectively improved. The gas distribution on the membrane surface is slightly increased for the 10.0 mm gas diffuser outlet compared to the 5.0 mm one. However, the increase is much less than the change in the gas diffuser outlet from 2.5 mm to 5.0 mm.

In conclusion, the outlet diameter of gas diffuser affects the biogas entering the reactor and thus the effect of gas distribution on the membrane and mixed liquid. Inside the gas diffuser near the two-side part, the gas velocity is lower while the center part of the velocity is faster. When the gas diffuser outlet diameter is too small (such as 2.5 mm), the volume and velocity of the bubbles that are generated on the side part of the inner of gas diffuser are small and low. It is difficult for those bubbles to resist the liquid pressure, which are produced by the gravity, and enter the reactor. The bubbles’ volume increase, and the speed becomes faster if the outlet diameter of gas diffuser is increased. Increasing the outlet diameter of gas diffuser helps improve the distribution of gas over the membrane surface, which is an important way to increase membrane life and filtration efficiency. However, increasing the outlet diameter from 5.0 mm to 10.0 mm results in only a slight improvement in the distribution of gas over the membrane surface.

3.4. Gas Volume Fraction Distribution on the Gas Outlet Cross Surfaces

Figure 7 shows the gas volume fraction distributions for the front center section, the side center section, the section above the gas diffuser outlet (plane over the gas outlet holes), and the section below the gas diffuser outlet (plane under the gas hole) for different outlet diameters of the gas diffuser. The results of the gas distribution in the frontal center section show the effect of the outlet diameter on the gas distribution near the gas diffuser outlet device and inside the bioreactor. It can be observed from the figure that the larger the diameter of the gas diffuser outlet, the larger the area of increased gas volume distribution in the middle and upper part of the cross section. This indicates that the larger the diameter of the gas diffuser outlet, the larger the total amount of gas entering the bioreactor interior and the more pronounced the stirring effect is on the liquid inside the bioreactor. In the area from the gas diffuser outlet to the bottom of the membrane, a gas diffuser outlet diameter of 5.0 mm is the ideal distribution that meets the expectations, in which the gas is relatively large and uniformly distributed. In this region, when the outlet diameter of gas diffuser is 2.5 mm, the gas is concentrated only in the most central position, and there is almost no gas distribution on both sides’ regions. This means that the gas distribution area is very limited, and interaction with a larger area of the membrane surface is not possible. The gas diffuser outlet diameter of 10.0 mm significantly improves the gas distribution compared to the 2.5 mm diameter. However, the dispersion of the gas distribution is not sufficient compared to that of the 5.0 mm diameter, which means that the possible area of gas action on the membrane surface is smaller than that of the 5.0 mm diameter. Comparing the above results, the gas diffuser outlet diameter of 5.0 mm is a relatively better choice.

The volume distribution of gas in the horizontal section above the gas diffuser outlet (the plane above the gas outlet hole, shown by the black dashed line) and below the gas diffuser outlet (the plane under the gas hole, shown by the red dashed line) shows more visually the effect of the gas diffuser outlet diameter on the gas distribution. In the plane under the gas hole cross section, the liquid is excluded, and the gas occupies the area. When the gas diffuser outlet diameter is different, the gas volume fraction distribution shows similar characteristics. However, when the gas diffuser outlet diameter is 2.5 mm and 10.0 mm, a distinct liquid region is formed in a part of the area, which may be the result of the relatively concentrated distribution of gas at this time. For the plane over the gas hole, the gas distribution is significantly different for the gas diffuser outlet diameter. For a gas diffuser outlet diameter of 5.0 mm, the gas has the expected distribution throughout the cross section, is relatively well dispersed, and is able to act over a wide area. In contrast, when the gas diffuser outlet diameter is 2.5 mm, the gas in this cross-section is concentrated in the central area and cannot effectively affect the surrounding edge areas. Similar to the 2.5 mm diameter case, when the gas diffuser outlet diameter is 10.0 mm, the gas at this cross section shows a relatively concentrated distribution, but unlike the 2.5 mm case, the concentrated distribution forms four regions distributed along the longitudinal direction at the outlet. Although the area of gas influence at this point is improved compared to the 2.5 mm diameter, it is still less than that of the 5.0 mm diameter. It has been shown in previous studies that the gas is dispersed into a series of bubbles after passing through the gas diffuser, and the size of this bubble is an important factor affecting the efficiency of the system [38,39]. In this study, the 2.5 mm gas diffuser outlet diameter limited the volume of gas bubbles entering the liquid column because it was too small, resulting in a concentrated distribution of gas in the central region. The 10.0 mm gas diffuser outlet diameter, on the other hand, was too large to allow the volume of gas bubbles entering the liquid column, resulting in a concentrated distribution of gas in the region. The use of gas diffusers is expected to disperse the gas and interact with the liquid and a wider range of membrane surfaces to improve efficiency. Simulation results with a 5.0 mm gas diffuser outlet diameter can meet these expectations. Other gas diffuser outlet diameters may cause the membrane to fail to maintain its efficiency, contrary to the original intent of using a gas diffuser. The efficiency of the membrane is also affected by other factors such as temperature, pH, flux, and wastewater composition. However, these parameters are not the focus of this study and therefore will not be specifically analyzed.

The side view of the gas volume fraction in the intermediate section visualizes the gas distribution inside the bioreactor, inside the membrane module, and between the membranes. With a gas diffuser outlet diameter of 2.5 mm, it can be seen that the gas height is mainly concentrated in the area between the left and middle membranes. In this study, three groups of six membranes in total were set, which means that only two membranes were exposed to relatively high gas interaction, while the other four membranes were not exposed to gas interaction. When the outlet diameter of the gas diffuser was increased to 5.0 mm, the gas distribution within the membrane box became more dispersed, with more gas distributed at different locations rather than being confined to localized areas. In this case, the gas can agitate the liquid to the maximum extent and participate in the interaction with the membrane surface. This gas distribution meets our expected requirements. When the outlet diameter of the gas diffuser is further increased to 10.0 mm, the gas distribution inside the membrane box is similar to that with a 5.0 mm diameter. The gas distribution and effective area are better than the gas distribution at a 2.5 mm diameter, but slightly less than at a 5.0 mm diameter. The gas distribution near the left membrane is significantly less, with a reduced gas–membrane interaction area compared to the middle and right membranes. This distribution characteristic is consistent with the gas distribution near the outlet of the gas diffuser described above.

The bubble properties of membrane surfaces have been studied experimentally by B.G. Fulton et al. [40]. It was found that the number of bubbles between membranes was essentially independent of gas velocity. The manner of fluid motion inferred from the characteristics of the measured bubbles is similar to the results of the gas volume fraction in this study. The number of rising bubbles between the membrane assemblies is constant. A large amount of fluid in the region with a relatively high number of bubbles flows upward, while for the region with a low number of bubbles a large amount of fluid flows downward. This also explains why the gas distribution in this study for 2.5 mm and 10 mm gas diffuser outlet diameters is relatively inferior to that of 5 mm outlet diameter. İlker Parlar et al. have shown that larger outlet diameters of gas diffuser are not better [41]. This is consistent with the conclusions of the present study.

In general, under the conditions of this study, increasing the gas diffuser outlet diameter is beneficial to maintaining and improving membrane efficiency. This approach results in a more distributed gas distribution and an extended operating range. However, if the gas diffuser outlet diameter is too large, problems of concentrated gas distribution similar to those experienced with small diameter gas diffuser outlets may occur, which may prevent the membrane from operating stably. Therefore, choosing a gas diffuser outlet diameter of 5.0 mm between 2.5 mm and 10.0 mm is a suitable choice. The relatively uniform and moderate range of gas distribution at this diameter allows for optimal liquid agitation and full participation in the interaction with the membrane surface. In summary, an appropriate increase in gas diffuser outlet diameter can help improve membrane efficiency, but too large a diameter can create new problems. A gas diffuser outlet diameter of 5.0 mm is a reasonable choice to achieve the best working results under the conditions of this study.

3.5. Membrane WSS

Figure 8 shows the distribution of the WSS on the membrane surface at three different locations for different gas diffuser outlet diameters. The results show that the WSS in plane middle (mean value of 1.10 Pa) is much higher than that in plane a (mean value of 0.12 Pa) and plane b (mean value of 0.22 Pa) by an order of magnitude at the gas diffuser outlet diameter of 2.5 mm. The high WSS region in the plane middle is mainly concentrated in the middle position and close to the reactor outlet. This indicates that a relatively uniform and high WSS distribution cannot be achieved at all positions of the membrane at 2.5 mm diameter conditions. Previous studies have pointed out that proper WSS is an important condition for maintaining stable membrane operation and that lower WSS affects the long-term stability and efficiency of the membrane [42]. At a 2.5 mm diameter, even in the plane middle where the WSS is relatively high, the WSS distribution is too concentrated, which may lead to local performance degradation and thus reduce the efficiency. When the gas diffuser outlet diameter was increased to 5.0 mm, the average value of WSS in plane a was 0.62 Pa, in plane b was 1.22 Pa, and in plane middle was 0.82 Pa. Compared to the 2.5 mm diameter, the average WSS of the membrane surfaces in plane a, plane b, and plane middle are significantly higher. At this point, the WSS at these locations is much closer and there is no significant difference as in the case of the 2.5 mm diameter. According to the previous study, high WSS can effectively reduce membrane fouling. Therefore, increasing the WSS on the membrane surface is helpful in stabilizing membrane efficiency [43]. When the gas diffuser outlet diameter was further increased to 10.0 mm, the average WSS of the membrane surfaces in plane a, plane b, and plane middle did not increase, but rather decreased. The average WSS decreased to 0.52 Pa for plane a, 0.26 Pa for plane b, and 0.30 Pa for plane middle. The WSS results at this point are close to those at 2.5 mm diameter, except that the specific distribution differs. The forces on the membrane surface under the conditions in this study are composed of two parts, the interaction force of liquid–membrane surface and the interaction force of gas–membrane surface. As mentioned previously, the interaction force between liquid and membrane surface is the main force on membrane surfaces. An excessively large outlet diameter of gas diffuser can result in an over-concentration of gas entering the bioreactor, creating a large gas cavity, which can force the liquid to separate from the membrane, thereby reducing the membrane surface interaction. This is believed to be the main reason for the decrease in WSS at the membrane surface. As mentioned earlier, the reduced WSS may not provide the conditions for the membrane to maintain stable efficiency over time, which is contrary to expectations.

In summary, increasing the outlet diameter of the gas diffuser helps to improve the concentrated distribution characteristics of the WSS on the membrane surface. However, the gas diffuser outlet diameter is not positively correlated with the WSS size, and an excessively large diameter may instead reduce the WSS on the membrane surface and lead to a decrease in the membrane efficiency. Therefore, a gas diffuser outlet diameter of 5.0 mm was chosen as a better choice under the conditions of this study.

4. Conclusions

This study investigates the effect of different outlet diameters of gas diffuser on the efficiency of AnMBR membranes, with a fixed total gas diffuser outlet area, by using CFD simulations. Detailed analysis was performed on fluid velocity and WSS on the membrane surface. The results indicate that an appropriate outlet diameter is critical for maintaining stable operation and high efficiency in AnMBR systems, rather than a larger diameter. The simulation results show that fluid velocity and WSS at the membrane surface increases when the outlet diameter of gas diffuser increased from 2.5 mm to 5.0 mm, while it then decreases as the outlet diameter further increases to 10.0 mm. The results show that an outlet diameter of 10.0 mm leads to too much gas concentration and reduces the interaction of the membrane surface, decreasing efficiency. Conversely, an outlet diameter of 5.0 mm is optimal among the three different outlet diameters. At this outlet diameter, the average velocity and WSS of the membrane surface reach the highest value, which improves filtration efficiency and reduces energy consumption in the AnMBR system.