Monitoring biofilm thickness using the membrane aerated biofilm reactor (MABR) fingerprint soft sensor to optimize nitrogen removal

The ongoing commercialization and installation of full‐scale membrane aerated biofilm reactors (MABRs) stimulate the increasing need to monitor biofilm development. Biofilm thickness in MABRs can be assessed indirectly by plotting the exhaust oxygen purity versus bulk ammonia concentration, defined here as the MABR fingerprint soft sensor. Dynamic simulations with diurnal flow variations of an MABR unit model were implemented over a broad range of biofilm thicknesses and influent conditions consisting of variable C/N ratios and applied ammonia fluxes to assess the utility of the MABR fingerprint. Results show that the continuously decreasing trend of the MABR fingerprint plot slopes can be employed as a useful signal for biofilm thickness control in nitrogen removal processes. This technique is useful in a wide range of influent conditions and is helpful for MABR operators and designers to arrange biofilm thickness control events efficiently and determine where in an overall treatment process the technique can be applied to control biofilm thickness and optimize process performance.


Practitioner points
• The linear relationship between exhaust oxygen purity and bulk ammonia concentration is defined as the MABR fingerprint plot.
• MABR fingerprint plots are generated for a given biofilm thickness with diurnal flow or short-term loading variations implemented.
• Continuously decreasing trends of the MABR fingerprint plot slopes are useful signals for biofilm control in nitrogen removal.
• The MABR fingerprint is useful over a wide range of influent conditions regarding C/N ratios and applied ammonia fluxes.
• MABR practitioners can use the fingerprint plots to determine when biofilm control measures should be taken.
Yi Cao is a member of the Water Environment Federation (WEF).

INTRODUCTION
Monitoring and management of biofilm thickness are important for optimal reactor performance and have received increasing attention from membrane biofilm reactor (MBfRs) designers and operators (Lu et al., 2021;Martin & Nerenberg, 2012).Gaseous substrates in MBfRs are supplied from the inside of a gas-permeable membrane lumen to the biofilm growing on the outside of the lumen.Liquid substrates diffuse oppositely from the bulk liquid into the biofilm, resulting in a counter-diffusional biofilm (Nerenberg, 2016).Substrate removal performance is limited when the biofilm thickness is low due to insufficient functional biomass, while active biomass, as well as the mass transfer resistance for substrate delivery to the active biomass, will increase along with biofilm growth.Mass transfer resistance restricts transport and removal of substrates and reduces substrate removal performance when the biofilm is overly thick (He et al., 2021;Pérez-Calleja et al., 2022).Identifying the optimal biofilm thickness and determining the appropriate frequency for biofilm thickness control activities (e.g., air scouring (Ravishankar et al., 2022)) are critical to the effective design and operation of biofilm reactors.
Measurement and assessment of biofilm morphology and thickness are recognized as useful and informative approaches to biofilm monitoring.Several technologies have been employed in laboratory settings, including X-ray tomography (Carrel et al., 2018), nuclear magnetic resonance (Renslow et al., 2014), confocal laser scanning microscopy (CLSM) (Wang et al., 2022), and optical coherence tomography (OCT) (Li et al., 2016).Lu et al. (2022) used CLSM and OCT for in situ characterization of development of the counter-diffusion biofilm in an MBfR applied for aerobic methane oxidation coupled with denitrification and revealed that manipulating oxygen partial pressure could help manage biofilm thickness and stratification.Li et al. (2023) applied OCT and a dissolved oxygen (DO) microsensor, as well as CLSM, to observe and evaluate the biofilm thickness and density of a membraneaerated biofilm (MAB) in a flow cell.These technologies can provide useful information for researchers and engineers to understand biofilm development and optimize biofilm thickness and composition.Equipment is needed to make these measurements, however, and these techniques may not be easily applied for operating facilities.
The membrane aerated biofilm reactor (MABR) is a subset of MBfRs where air or pure oxygen is supplied to the inside of the gas-permeable membrane lumen (He et al., 2021).The activities of oxygen-consuming microorganisms create a DO concentration gradient in the counter-diffusional biofilm, forming the driving force for oxygen transfer through the membrane to the biofilm.The remaining gas will be vented from the lumen, either to the atmosphere or collected in the off-gas line as is done in commercial MABR units such as Zeelung and OxyMem (He et al., 2021).The direct capture of off-gas facilitates measurement of exhaust oxygen purity and data to determine the oxygen transfer rate and efficiency for reactor performance assessment.These data also quantify microbial activity and can indicate biofilm development.This approach has been applied in lab/fullscale MABR studies (Castrillo et al., 2019;Peeters et al., 2017;Uri-Carreño et al., 2021).Most of the nitrification in an MABR, which oxidizes ammonia to nitrate, occurs in the inner layer of the biofilms where DO concentrations are higher (Cole et al., 2004;Kuypers et al., 2018;Lu et al., 2022).Therefore, MABR nitrification performance, as well as nitrifying biofilm development, can be evaluated by monitoring oxygen transfer, based on monitoring exhaust gas oxygen purity and effluent ammonia concentration.
A previous study from our group illustrated a method to monitor nitrification performance and biofilm development in MABRs using a soft sensor called the MABR fingerprint, which is a plot of exhaust oxygen purity in the gas phase versus the bulk liquid ammonia concentration (Yang et al., 2022).The results presented there indicated that biofilm thickness can be evaluated indirectly by analyzing the slope of the inclined linear segment of this plot, referred to as representing ammonia-limited conditions in the MABR biofilm.This soft sensor assessment only requires regular monitoring sensors for gas-phase oxygen and liquid-phase ammonia, unlike the aforementioned methodologies, which require extra instruments.It can also be employed in full-scale MABR systems while in operation as the data are collected during normal operation and do not require interruption of operation.Uri-Carreño et al. (2021) have demonstrated that such a fingerprint plot can characterize nitrifying biofilm growth during MABR start-up.However, an instructive methodology to incorporate the fingerprint soft sensor into on-going MABR operation and monitoring has not yet been documented.
This paper applies diurnal flow dynamic model simulations to mimic actual influent fluctuations to (1) identify useful signals from MABR fingerprint plots for biofilm thickness indication; (2) test the usefulness of the fingerprint technique for assessing nitrogen removal in a sensitivity analysis of variable C/N ratios and MABR applied ammonia fluxes; and (3) propose biofilm control event planning strategies for MABR designers and operators using the fingerprint technique.

Biokinetic model
The MABR unit model was built in SUMO 21 (Dynamita) based on a fixed-thickness, one-dimensional biofilm model described in the studies of Wanner andReichert (1996) andTak acs et al. (2007).The biokinetic model used is Sumo1 with one-step nitrification/denitrification, which is framed based on the prevalent activated sludge models in Henze et al. (2006).
The oxygen concentration at the base of the biofilm is calculated by combining oxygen partial pressure, volumetric air supply, and the rate of the gas diffusion into the biofilm using Fick's law and Henry's law, along with the microbial activities in the biofilm.The exhaust oxygen purity can be obtained from these calculations.The key assumptions for oxygen transfer simulation include that (1) transport of oxygen between the membrane lumen and the base of the biofilm is governed by Fick's law (Tak acs et al., 2007;Wanner & Reichert, 1996) and, therefore, the oxygen concentration gradient is calculated; (2) the saturation oxygen concentration at the base of biofilm, which is required for computing the oxygen concentration gradient, is calculated from the oxygen partial pressure by Henry's law; and (3) the oxygen partial pressure in the membrane is assumed to be linear along the depth of the membrane lumen, and the average of inlet and outlet oxygen partial pressure is used in Fick's law.
The biofilm is stratified as three layers in the model (Carlson et al., 2021;He & Daigger, 2023), with biofilm activities in each layer simulated as a continuous stirred tank reactor and each layer connected by simulating diffusion.Three layers are selected for simplicity after running some preliminary models with different layers (data not shown).The amount of biomass in the biofilm is governed by a parameter called the biofilm specific mass (g TSS/m 2 ).To simulate biomass truly increasing with biofilm thickness growing, biofilm specific mass increases along with biofilm thickness increasing proportionally to make sure that new increasing thickness portion has the same biofilm density (100 kg TSS/m 3 ) as the existing thickness portion.

MABR process model setup
The configuration of the MABR process model consisted of a single MABR unit, a state-variable-based influent unit, and a standard effluent unit (Figure 1).The MABR unit volume was set at 16 m 3 with tank depth of 3.5 m and membrane area of 1,920 m 2 to reflect the size of a typical commercial cassette (Zeelung 2.0).The MABR media wall thickness was 160 μm, the median of the tested range in the previous study from our group (Yang et al., 2022).The biofilm thickness was varied from 20 to 1,000 μm (50 thicknesses), and the biofilm specific mass was varied from 2 to 100 g TSS/m 2 correspondingly.
The influent total chemical oxygen demand (COD) concentration was set at 200 g COD/m 3 consisting of 50 g COD/m 3 readily biodegradable COD and 150 g COD/m 3 slowly biodegradable COD.Influent COD concentrations are set to reflect the primary effluent fed to the MABR system.The unbiodegradable COD was zero for all simulations.Ammonia, varying from 5 to 50 g N/m 3 , was the only nitrogen in the influent.The objective of keeping constant influent COD concentration and varying influent ammonia concentration is to test different C/N ratios in the influent with modeling simplicity.Some preliminary modeling has been done to determine how to adjust influent C/N ratios (data not shown).The influent concentration of orthophosphate was 10 g P/m 3 to eliminate the effect of insufficient orthophosphate on microbial growth (half-saturation constant of orthophosphate for biomass growth is 0.002 g P/m 3 in Sumo1), along with zero concentrations for polyphosphate and organic phosphorous for model simplicity.The detailed influent composition is listed in Table S1.Influent parameters not mentioned above or in Table S1 were left at default values.The operational settings for the MABR unit also followed the defaults, which are the recommended values in the Zeelung 2.0 manual.A single unit of MABR cassette without external aeration in a biological reactor was

Sensitivity analysis and dynamic simulations
The MABR model was run under different combinations of influent wastewater C/N ratios and applied ammonia fluxes to evaluate the utility of the MABR fingerprint over a wide range of operating conditions, as shown in the map of Figure 2a.The C/N ratio ranged from 4 to 40 g COD/g N by adjusting influent ammonia from 50 to 5 g N/m 3 , with 5 g N/m 3 steps accordingly (horizontal axis of the map in Figure 2a).The applied ammonia flux ranged from 0.1 to 10 g N/m 2 /day, including nine different ammonia fluxes (vertical axis of the map in Figure 2a).The average influent flow rate was calculated to achieve the specified ammonia flux under the same influent ammonia concentration (and C/N ratio) conditions by reversing the following expression: where J NH X is the applied ammonia flux (g N/m 2 /day), S NH X , in is the influent ammonia concentration (g N/m 3 ), Q is the influent flow rate (m 3 /day), and A is the membrane area (m 2 ).The average influent flow rate for each combination of C/N ratio and applied ammonia flux is listed in Table S2.Under each influent combination (the combination of C/N ratio at 8 g COD/g N and applied ammonia flux at 3 g N/m 2 /day circled as an example in Figure 2a), a range of biofilm thicknesses from 20 to 1,000 μm (right-hand side in Figure 2a), increasing 20 μm per step, was tested to acquire the appropriate biofilm thicknesses, which could achieve optimal nitrification and denitrification performance for the specific influent conditions.The dynamic simulation mode was applied for each simulation for a given biofilm thickness, where diurnal flow coefficients of a small plant in Sumo1 influent tool were multiplied by the average influent flow rate to form a diurnal flow pattern for each day in all dynamic simulations (right-hand side in Figure 2a).A simulation period of 100 days was determined to allow the MABR system to reach a dynamically steady state at the end of the simulation.The data collection interval was 1 h.An MABR fingerprint plot for a given biofilm was generated by plotting the 24 data points on the last day of each simulation (right-hand side in Figure 2a).In total, there were 90 combinations of C/N ratios and applied ammonia fluxes and 50 biofilm thicknesses for each influent combination.A total number of 4,500 dynamic simulations were implemented in SUMO using a SUMO-Python interface tool.The next step (Figure 2b) in the sensitivity analysis was to analyze the slope of the MABR fingerprint plot for each thickness by plotting the slopes versus last-day average effluent concentrations, including effluent ammonia (example in Figure 2b), nitrate, and total COD.A final map (Figure 2c), identifying under which influent combinations the MABR fingerprint is useful to indicate biofilm development, was produced.The usefulness of the MABR fingerprint technique was evaluated by the shape of plots of fingerprint slopes versus average effluent ammonia generated in the second step.Generation and use of the plots and map will be discussed in detail in the following sections.

MABR fingerprint
The MABR fingerprint is defined as the plot of exhaust oxygen purity and bulk ammonia concentration.The correlation between these two variables is strong (R 2 > 0.9), which has the following benefits for monitoring biofilms: (1) the variable on each axis is independent, and variable interdependence is not needed to consider in the correlation; (2) the gas-phase oxygen sensor is more reliable and less susceptible to drift or calibration errors than sensors used in the liquid phase; and (3) these two variables represent the activities of electron donor and acceptor in nitrification respectively, and nitrifiers have a higher oxygen utilization to growth ratio compared to heterotrophs (19:1 and 0.5:1) (Houweling & Daigger, 2019).Therefore, the correlation between exhaust oxygen purity and bulk ammonia concentration could indicate the nitrogen removal performance of MABRs, similar to an individual's unique fingerprint.
A case study at the Yorkville-Bristol Sanitary District reported in Houweling and Daigger (2019) demonstrates that a diurnal flow pattern fed to an MABR unit can produce a daily MABR fingerprint plot with the anticipated linear shape.In this paper, the 24 data points collected on the last day of each dynamic simulation after running with the specified diurnal flow pattern for 100 days were used to draw the fingerprint plot for a given biofilm thickness under the specified influent combination of C/N ratio and applied ammonia flux.The analysis of 4,500 fingerprint plots was performed using linear regression in R software to calculate the slope, y-intercept, and the coefficient of determination (R 2 ).The slopes mentioned in the following analysis were calculated by multiplying a minus sign to the original slopes.Most slopes would be positive in this way.

MABR fingerprint plots
The shape, scale, location, and inclination of the fingerprint plots for a given C/N ratio (e.g., 10 g COD/g N) display distinct features when applied ammonia flux or biofilm thickness is different.Figure 3 presents the MABR fingerprint plots for the selected biofilm thicknesses when the C/N ratio is 10 g COD/g N (influent ammonia concentration as 20 g N/m 3 ) and the applied ammonia flux is 0.1, 2, and 10 g N/m 2 /day, respectively.

Effects of ammonia loading flux
Different applied ammonia fluxes result in different locations of the fingerprint plots along the x axis, that is, bulk ammonia concentrations, reflecting the effluent quality achieved for each of these loading and operating conditions.As the membrane supply gas pressure and flow rate were fixed in all simulations, oxygen consumption is inversely proportional to the exhaust oxygen purity.Therefore, different locations of the fingerprint plots along the y axis, that is, exhaust oxygen purity, result from differences in the oxygen consumed for the given loading and operating condition.
The fingerprint plots for the applied ammonia flux of 0.1 g N/m 2 /day (Figure 3a) form an ellipse, ranging from around 0.2 to 0.6 g N/m 3 for bulk ammonia and around 19.9% to 20.2% for exhaust oxygen purity.While a fitted linear line encircled by the ellipse can easily be envisioned, the resulting fingerprint plots overlap with each other, and the slopes are quite similar, even though the biofilm thickness varies substantially.In this low ammonia loading condition, the MABR system is underloaded, and ammonia is nearly fully consumed over the diurnal cycle, and the oxygen demand is quite small.The result is that effluent ammonia performance is not noticeably affected by biofilm thickness, making biofilm control unnecessary.
The fingerprint plots expand more broadly for the 2 g N/m 2 /day case (Figure 3b), with most fingerprint plots locating at bulking ammonia concentrations less than 10 g N/m 3 with lower exhaust oxygen purity, meaning more oxygen consumption.The ellipse shape of each fingerprint plot also narrows into a linear line shape.Biofilm thickness has obvious impacts on the location and slope on the fingerprint plots for this ammonia loading rate.The exception is the fingerprint plot for a biofilm thickness of 20 μm, which is located at average bulk ammonia of 17.9 g N/m 3 and average exhaust oxygen purity of 19.6%, indicating little nitrification has occurred due to insufficient nitrifying biomass (Casey et al., 2000;Wang et al., 2016).
The bulk ammonia concentrations for most biofilm thicknesses for the highest ammonia flux considered (10 g N/m 2 /day) varied from 10 to 17.5 g N/m 3 (Figure 3c), higher than for the other two applied ammonia flux values considered.The fingerprint plot for biofilm thicknesses of 60, 80, 100, or 200 μm is essentially a flat line with slopes close to zero.The flat lines represent the oxygen limitation condition where increasing the bulk ammonia concentration will not lower the exhaust oxygen purity (Yang et al., 2022).In such high ammonia loading condition, the MABR system is overloaded, and oxygen demand is higher than the fixed oxygen supply typically used in practice.

Effects of biofilm thickness
Figure 3d shows the change of the slopes of the fingerprint curves as biofilm thickness increases over the range F I G U R E 3 MABR fingerprint plots of the selected biofilm thicknesses (20, 40, 60, 80, 100, 200, 400, 600, and  of the selected biofilm thicknesses.The complete plots of slopes versus biofilm thickness for all influent conditions are provided in Figures S31 to S40.The results presented in Figure 3b for the applied ammonia flux of 2 g N/m 2 / day suggest that the fingerprint plot slope would provide a quite useful indication of biofilm thickness.This expectation is confirmed when the fingerprint plot slope is plotted versus biofilm thickness in Figure 3d (green curve).The slope of the fingerprint plot increases from 0.44 to 0.64 as biofilm thickness increases from 20 to 60 μm.This thin biofilm corresponds with biomass limited conditions, along with decreasing bulk ammonia concentration with increasing biofilm thickness (Figure 3b) and increasing slope.The slope then decreases between biofilm thicknesses of 60 and 200 μm and reaches a relative constant value of about 0.2 as the biofilm thickness increases further.Ammonia limitation occurs during the slope-decreasing segment for biofilm thicknesses between 60 and 200 μm, and the lowest bulk ammonia concentrations representing this biofilm range with the best effluent quality.There is little change in the slope for biofilm thickness greater than 200 μm, averaging 0.21 with variation less than 10% of the mean.Both ammonia and oxygen are limited (dual-substrate limitation) when the biofilm is thicker than 200 μm as higher mass transfer resistance builds, which has negative impacts on diffusion of ammonia from the bulk liquid and the resulting bulk ammonia concentration (Casey et al., 2000;Pérez-Calleja et al., 2022;Yang et al., 2022).
Nitrification is complete for the applied ammonia flux of 0.1 g N/m 2 /day (light blue curve) since both of ammonia and carbon fluxes are so low.Thus, no variation in nitrification performance is observed, and a distinct fingerprint is not produced for any given biofilm thickness.In contrast, when the applied ammonia flux is 10 g N/m 2 /day, the MABR system is overloaded, and oxygen could be the limited factor.As shown by the dark blue curve in Figure 3d, the slope increases back to 0.22 as biofilm thickness increases up to 200 μm after reaching oxygen-limited condition at 60-μm biofilm.In this condition, oxygen limitation still occurs within the biofilm for high ammonia loading and oxygen demand.Similar to the pattern for 2 g N/m 2 /day, the slopes change little for biofilm thickness above 200 μm, averaging 0.22 and varying within 10% of the mean.With higher mass transfer resistance, the diffusion of ammonia from the bulk to the biofilm is increasingly limited.

Map of where the MABR fingerprint is useful
Results such as those illustrated in the "MABR fingerprint plots" section provided the basis for analyzing each combination of C/N ratio and ammonia flux to identify those combinations where a useful relationship between biofilm thickness and the slope of the linear portion of the fingerprint was identified.The result is the map shown in Figure 4.The blue colored region represents those combinations of influent wastewater C/N ratio and applied ammonia flux where the MABR fingerprint was found to be useful to indicate where biofilm thickness The map of the sensitivity analysis indicating where the MABR fingerprint is and is not useful.The map is divided into three subregions, labeled 1-3.Region 1 is where the MABR fingerprint is useful (all of the blue grids).Region 2 represents the scope of the applied ammonia flux at 0.1 g N/m 2 /day for all C/N ratios, and the MABR fingerprint might not be useful in this region.Region 3 is the upper-left region ranging from 4 to 13 g COD/g N of C/N ratio and from 3 to 10 g N/m 2 /day of applied ammonia flux.The MABR fingerprint might not be useful in Region 3.
affected ammonia removal performance.This is referred to as Region 1 in Figure 4.The gray colored regions represent those combinations of influent wastewater C/N ratio and applied ammonia flux where the MABR fingerprint might not be useful to indicate biofilm thickness and its impact on the ammonia removal process.This "useless" region is referred to as Region 2 (applied ammonia flux of 0.1 g N/m 2 /day and all of C/N ratios) and 3 (the upper left gray part).The usefulness of the MABR fingerprint in the ammonia removal process was determined by plotting the slopes of the MABR fingerprint plots versus the last-day average bulk ammonia concentrations for every biofilm thickness simulated under each combination of C/N ratio and applied ammonia flux.The process for identifying these regions is illustrated in the following sections, with example plots for select conditions.The plots of the slopes versus last-day average bulk ammonia concentrations for all conditions are presented in Figures S1 to S10.
Region 1 where the MABR fingerprint is useful Taking an applied ammonia flux of 2 g N/m 2 /day as an example, the MABR fingerprint technique was found to be useful under all C/N ratios evaluated.C/N ratios of 5, 10, and 20 g COD/g N were selected as example conditions (Figure 5) to illustrate the analysis performed.
For this applied ammonia flux, the slope of the linear portion of the fingerprint plot generally increases in all cases when the biofilm thickness increases from 20 to 60 μm (first three points after starting point).In this condition, ammonia and DO fully penetrated the biofilm, and, consequently, microbial activity is more affected by the nitrifier mass, a condition typically referred to as biomass limitation.The bulk ammonia concentration decreases as biofilm thickness increases, reflecting increased nitrifying organism mass in the biofilm and the resulting increased nitrification.This situation typically exists during start-up of the MABR or times when the MABR is recovering from severe loss of biofilm for one reason or another.
The slope of the MABR fingerprint starts to decrease consistently (the vertical segment of any of three curves) as the biofilm thickness increases beyond 60 μm until the biofilm thickness reaches 200 μm for a C/N ratio of 5 g COD/g N, 260 μm for a C/N ratio of 10 g COD/g N, and 220 μm for a C/N ratio of 20 g COD/g N. For biofilm thicknesses within the "slope-decreasing segment" range, the biofilm is fully penetrated by DO, and ammonia becomes the limited substrate.The average bulk ammonia concentrations for the three slope-decreasing segments are 6.48 ± 0.24, 5.59 ± 0.18, and 4.28 ± 0.05 g N/ m 3 for C/N ratio of 5, 10, and 20 g COD/g N, respectively.As indicated in Figure 5, the slope-decreasing segment (nearly vertical lines on the left) represents the best ammonia removal performance (lowest bulk ammonia concentrations and highest ammonia removal flux), with little discernible difference in performance over this range for each C/N ratio.The ammonia removal efficiency is 83.8%, 72.1%, and 57.2% for this biofilm thickness range for C/N ratios of 5, 10, and 20 g COD/g N, respectively.Higher C/N ratios correspond with lower ammonia removal efficiency because, relatively, more F I G U R E 5 Plot of the slope of the MABR fingerprint plot versus last-day average bulk ammonia concentration for each biofilm thickness when the applied ammonia flux is 2 g N/m 2 /day, and C/N ratios are 5 (light blue), 10 (green), and 20 (dark blue) g COD/g N. Each curve has 50 data points representing 50 biofilm thicknesses simulated under each C/N ratio.The curve connects the slopes successively from 20 to 1,000 μm.The data point of 20 μm on each curve is (11.6, 0.06) for 5 g COD/g N; (19.6, 0.44) for 10 g COD/g N; and (8.59, 0.54) for 20 g COD/g N. carbon leads to more competition for oxygen between heterotrophs and nitrifying organisms (Ravishankar et al., 2022).Relevant slope-decreasing segments can still be obtained for higher C/N ratios (e.g., 20 and 40 g COD/g N) for higher ammonia fluxes (Figure 4), indicating that ammonia limitation conditions can still exist in higher ammonia loading conditions for higher C/N ratio wastewater.The MABR fingerprint is only valid in ammonia limited conditions.
The slopes of the MABR fingerprint plots have no regular trends when the biofilm is thicker than the upper thickness threshold of the slope-decreasing segment.Dual-substrate limiting conditions exist with these thicker biofilms, meaning neither DO nor ammonia fully penetrates the biofilm.The bulk ammonia concentrations for thicker biofilms are higher than those values for the biofilm thickness within the slope-decreasing segment, indicating that these thicker biofilms are undesirable from a performance perspective (lower ammonia removal flux).
These results demonstrate that the slope-decreasing segment can be used as a signal for biofilm thickness control in an MABR system operating within this range of conditions by observing the change in the fingerprint slope.Best performance is observed when the slope of the fingerprint plot is maintained within the identified range of slopes, and deviations outside of this range can indicate when biofilm control measures should be taken, either biofilm sloughing measures such as aeration (if the slope is below the selected range) or reduced turbulence to allow the biofilm thickness to increase (if the slope is above the selected range).
Regions 2 and 3 where the MABR fingerprint might not be useful Regions 2 and 3 are the combinations of influent wastewater C/N ratio and ammonia loading where the MABR fingerprint technique might not be useful to indicate changes in biofilm thickness (gray region in Figure 4).These represent influent wastewater and ammonia loading conditions where a regular slope-decreasing segment was not formed in the plots of fingerprint plot slopes versus last-day average bulk ammonia concentrations.Example influent conditions within these regions are presented in Figure 6 to illustrate the shape of plots of slopes versus last-day average bulk ammonia concentrations: applied ammonia flux of 0.1 g N/m 2 /day and C/N ratio at 5, 10, and 20 g COD/g N in Figure 6a and applied ammonia flux of 8 g N/m 2 /day and C/N ratio at 4.4, 6.7, and 13 g COD/g N in Figure 6b.
When the applied ammonia flux is 0.1 g N/m 2 /day and C/N ratio is 5 g COD/g N, the fingerprint plot slope decreases consistently as biofilm thickness increases from 20 to 1,000 μm.Under the same ammonia flux but C/N ratio of 10 g COD/g N, the slope increases from 0.58 to 0.64 as biofilm grows up to 40 μm, after which the slope also continuously declines.The fingerprint plot slope decreases consistently for a C/N ratio of 20 g COD/g N after rising from 0.37 to 0.68 along with biofilm thickness up to 100 μm.As shown on the x axis of Figure 6a, all of the bulk ammonia concentrations are within the range of 0.34 to 0.42 g N/m 3 .Nitrification should occur completely since the ammonia and carbon loadings are low but concentrations are sufficient for nitrification to occur.Connected back to Figure 3a, the fingerprint curves are not defined sufficiently under such low ammonia flux.It is concluded that the MABR fingerprint might not be useful when the ammonia flux is just 0.1 g N/m 2 / day (Region 2 in Figure 4).
Region 3 in Figure 4, generally ranging from a C/N ratio of 4 to 13 g COD/g N and from an applied ammonia flux of 3 to 10 g N/m 2 /day, is another influent range where the MABR fingerprint might not be useful.This is illustrated in Figure 6b for an applied ammonia flux of 8 g N/m 2 /day.Consider the results for the C/N ratio of 4.4 and 6.7 g COD/g N in Figure 6b.When the biofilm thickness is 20 μm, the slopes are much greater than other points in the same curve and with higher bulk ammonia concentration, indicating that little ammonia removal is achieved with this thin biofilm due to biomass limitation.With increased biofilm thickness, the biofilm becomes oxygen limited where ammonia can fully penetrate the biofilm, but DO could not because the high ammonia flux creates a far higher oxygen demand than can be met with the oxygen supply.Biomass limitation occurs for biofilm thicknesses of 20 and 40 μm at the 13 g COD/g N C/N ratio.Oxygen limitation occurs with biofilm thickness of 60 μm or more.For thicker biofilms with higher mass transfer resistance, although ammonia can fully penetrate the biofilm, the concentration at the base of the biofilm is low, and DO is obviously deficient.Dual-substrate limited conditions have possibilities to occur as the biofilm grows much thicker.Although good ammonia removal performance is achieved when the fingerprint slope is lowest, there is no regular shape of the plots of the fingerprint slopes versus last-day average bulk ammonia concentrations, so the lowest fingerprint slope is a less useful signal for biofilm thickness control.

Insights into total nitrogen removal
As discussed in the "Region 1 where the MABR fingerprint is useful" section, the MABR fingerprint is useful in the blue-colored region in Figure 4 to control biofilm thickness and optimize the MABR ammonia removal.The slope-decreasing segment provides the lowest bulk ammonia concentration and highest ammonia removal flux and has ammonia-limited condition within the biofilm.Figure 7 portrays how last-day average bulk concentrations of total inorganic nitrogen (TIN, sum of ammonia and nitrate) vary with changes of the fingerprint plot slope.The example applied ammonia flux (2 g N/m 2 /day) and C/N ratio conditions were selected to illustrate the useful signals that could be obtained from the MABR fingerprint technique for TIN removal (the curve segment declined to left).The completed sets of plots of slopes versus bulk TIN concentrations are presented in Figures S11 to S20.
As discussed above, the decreasing slope segment of the MABR fingerprint is a useful indicator for biofilm control when the applied ammonia flux is 2 g N/m 2 /day, with the decreasing slope segment corresponding to biofilm thicknesses of 60-200, 60-260, and 60-220 μm for C/N ratios of 5, 10, and 20 g COD/g N, respectively.For any curve within this biofilm thickness range (the curve segment declined to left) in Figure 7, the thicker the biofilm, the lower the bulk TIN concentration.Dualsubstrate limitation conditions develop when the biofilm F I G U R E 6 Plots of the slope of the MABR fingerprint plot verses last-day average bulk ammonia concentration for each biofilm thickness when the influent conditions are (a) applied ammonia flux of 0.1 g N/m 2 /day and C/N ratios at 5 (light blue), 10 (green), and 20 (dark blue) g COD/g N; (b) applied ammonia flux of 8 g N/m 2 / day and C/N ratios at 4.4 (light blue), 6.7 (green), and 13 (dark blue) g COD/g N. Each curve has 50 data points representing 50 biofilm thicknesses simulated under each combination of applied ammonia flux and C/N ratio.The curve connects the slopes successively from 20 to 1,000 μm.The data point of 20 μm on each curve is (a) (0.355, 0.64) for 5 g COD/g N, (0.371, 0.58) for 10 g COD/g N, (0.393, 0.37) for 20 g COD/g N; (b) (43.5, 0.52) for 4.4 g COD/g N, (28.8, 0.58) for 6.7 g COD/g N, and (14.3, 0.67) for 13 g COD/g N.
thickness is beyond this range.While even lower bulk nitrate concentrations can be achieved, higher bulk average ammonia concentrations will be produced due to increased mass transfer resistance.Importantly, the slope of the fingerprint plot becomes relatively insensitive to biofilm thickness so the opportunity to use the fingerprint plot slope for biofilm thickness control is lost.
The MABR fingerprint might not be useful to determine the optimal thickness for TIN removal in Regions 2 and 3 identified in Figure 4. Biomass limitation in Region 2 results in insufficient denitrifiers growing for nitrate reduction.Although lower nitrate concentrations can be achieved in Region 3 by thicker biofilms, oxygen limitation conditions restrain how much ammonia can be oxidized.Operating within both Regions 2 and 3 identified in Figure 4 is not favorable for TIN removal.
The results presented in Figure 7 generally indicate that the lowest bulk average effluent TIN concentrations correspond to lower values of the fingerprint plot slope, especially for the 10 and 20 g COD/g N C/N ratios.The curves for all three C/N ratios show a significant drop in fingerprint plot slope corresponding with a decrease in bulk average effluent TIN concentration.Although not expressly indicated in Figure 7, this decreasing slope region (the curve segment declined to left) corresponds to the biofilm thickness region (Figures 3b and 5) of 60-200, 60-260, and 60-220 μm for C/N ratios of 5, 10, and 20 g COD/g N, respectively, where the fingerprint plot slope is useful for biofilm control relative to best bulk effluent ammonia performance.As discussed above, this represents the range of biofilm thicknesses where MABR performance is ammonia limited.Within this region, increasing biofilm thickness allows increased denitrification in the outer portion of the biofilm without adversely impacting bulk average effluent ammonia concentrations, resulting in reduced bulk average effluent TIN concentrations.Thus, practicing biofilm control to maintain the fingerprint plot slope at the lower end of this range can result in lowest bulk average effluent TIN concentrations without adversely impacting bulk average effluent ammonia concentrations.
The results above are consistent with experimental observations.Denitrifying organisms in MABRs mainly accumulate in the outer layer of the biofilm, which is exposed to more carbon resources and less DO concentrations (Syron & Casey, 2008).Thicker biofilms provide more available spaces for heterotrophs, like denitrifiers, to grow, but higher mass transfer resistance occurs with thicker biofilms, which will adversely affect diffusion of ammonia from the bulk liquid (Martin & Nerenberg, 2012).This conflict for biofilm thickness in nitrogen removal has also been demonstrated in previous studies.Brindle et al. (1998) reported that a biofilm thickness of around 213 μm in an MABR achieved 98% nitrogen removal and 83% nitrification at a nitrogen loading rate of 1.2 kg NH 4 -N/m 3 /day.In contrast, a recent study by Sanchez-Huerta et al. (2022) showed that 82% ammonium removal and trace-level nitrate in the effluent were already achieved by an MABR with biofilm thickness of 330 μm during the start-up period.Ammonium removal efficiency increased as operation progressed to over 95% with trace levels of nitrate in the effluent when the biofilm thickness increased to 870 μm.Similar to this study, different carbon and nitrogen loadings will lead to F I G U R E 7 Plot of the slope of the MABR fingerprint plot versus last-day average bulk total inorganic nitrogen (ammonia + nitrate) concentration for each biofilm thickness when the applied ammonia flux is 2 g N/m 2 /day, and C/N ratios are 5 (light blue), 10 (green), and 20 (dark blue) g COD/g N. Each curve has 50 data points representing 50 biofilm thicknesses simulated under each C/N ratio.The curve connects the slopes successively from 20 to 1,000 μm.The data point of 20 μm on each curve is (36.5, 0.06) for 5 g COD/g N; (17.9, 0.44) for 10 g COD/g N; and (8.6, 0.54) for 20 g COD/g N.
different biofilm thicknesses for optimal nitrogen removal performance.Experience with the specific system is needed to determine the optimum biofilm thickness.
The vast majority of bulk TIN is ammonia under the applied ammonia flux of 2 g N/m 2 /day.Optimal bulk TIN concentration and the biofilm thickness providing lowest bulk TIN concentration decrease as C/N ratio increases.Higher C/N ratio wastewater, however, achieves lower TIN removal efficiency.The mass transfer resistance for ammonia from bulk to the biofilm influences TIN removal performance.When the C/N ratio is extremely high, the growth of nitrifying organisms could be inhibited even though oxygen supply is adequate (LaPara et al., 2006).Ravishankar et al. (2022) identified soluble biodegradable COD (sbCOD) to total nitrogen (TN) ratio as an important factor influencing simultaneous nitrification and denitrification in a pure standalone MABR system.In addition, COD/TN ratio higher than 10 has been reported to be needed for good nitrogen removal and COD/TN ratio less than 5 is disadvantageous for total nitrogen removal (Lin et al., 2016), which is supportive of the results in this study.

DISCUSSION
The unique advantages of counter-current diffusion occurring within MABR biofilms result in increased interest in various MABR configurations for nitrogen removal, for example, the hybrid mode with suspended microbial growth (Carlson et al., 2021;Downing & Nerenberg, 2008;Landes et al., 2011); MABRs combined with other downstream biological processes (Ahmar Siddiqui et al., 2022;Wu et al., 2017); and MABRs designed for multiple bioprocesses within the biofilm (Lu et al., 2022;Siriweera et al., 2023).Installation of commercialized MABR cassettes into existing activated sludge bioreactors to extend process capacity for wastewater treatment plants (WWTPs) around the globe to deal with more stringent discharge restrictions represents one such emerging application (Heffernan et al., 2017;Uri-Carreño et al., 2023).Consequently, expedient and punctual biofilm monitoring and control are of increasing concern and necessity to maintain stable and optimal MABR performance.
While effective equipment and technologies for biofilm thickness measurements are available (see discussions in the introduction), most accurate and adequate direct measurements are conducted in lab-scale reactors.Some indirect assessments of biofilm thickness have been invented and implemented for full-scale MABR processes.OxyMem developed an indirect biofilm thickness measurement method where the membrane lumen is charged with an inert gas and closed to create an original elevated pressure, and biofilm thickness is reflected by measuring the rate of change of pressure within the lumen (Casey et al., 2014).MABR cassettes can also be weighed for indirect biofilm thickness measurement (Liao & Liss, 2007).
Nitrification generally occurs in the inner layer of the biofilm of municipal WWTP MABR applications when additional ammonia is available to be nitrified.In this study, the MABR fingerprint plot slope is used as an indirect measure of biofilm thickness.This technique is useful for an existing MABR facility where the membrane area is already known and fixed.Under a specific set of influent and operating condition, each biofilm thickness should have a unique MABR fingerprint plot slope.As long as a diurnal flow pattern or sufficiently varied loading is applied onto the MABR system over a short period, an MABR fingerprint plot can be obtained corresponding to a given thickness, as the biofilm thickness will change little during this time period.These data can be collected and analyzed in near real-time, and as the process is operating, by simply conducting linear regression analysis of the available data.Fingerprint plot slopes collected and recorded consistently can be used to assess changes in biofilm thickness over time and take corrective actions (biofilm control measures such as air scouring).Under specific ammonia loadings, optimized biofilm thicknesses assessed by the change of the fingerprint slopes will provide highest ammonia removal flux and lowest effluent ammonia concentration.Moreover, no additional equipment is required besides the regular oxygen gas sensor and ammonia liquid sensor.All that is needed is regular automated programming to analyze the collected data by linear regression analysis.
Comparable application of MABR fingerprint analysis has been implemented by Uri-Carreño et al. (2021).They ran a full-scale MABR at the Ejby Mølle Water Resource Recovery Facility with ammonia loading of 1.1-4.88g N/ m 2 /day.Their results showed that the curve of exhaust oxygen purity versus bulk ammonia started to depart from a horizontal position at the third week, indicating the presence of nitrifying organisms in the biofilm.As shown in Figures 3b and 5, when the applied ammonia flux is 2 g N/m 2 /day, increasing slope at the beginning manifests the growth of the nitrifiers driving more oxygen consumption in the biofilm and resulting in lower exhaust oxygen purity.Initial use of the MABR fingerprint can be extended significantly to monitor and control biofilm thickness to achieve optimum performance.As for MABR designers, the MABR fingerprint technique is useful in the blue region in Figure 4 and covers a broad range of C/N ratios, which is important because the C/N ratio depends largely on the nature of the raw wastewater (Muttamara, 1996).The applied ammonia flux, however, is selected based on treatment objectives.Our results indicate that the MABR fingerprint can be useful for biofilm monitoring for MABR ammonia loadings where nitrification is occurring, but the loading is not so low that nitrification is complete under all conditions.Biofilm control can be less important under these underloaded conditions.This guidance can help MABR designers to understand the circumstances under which biofilm control is important to affect process performance as, under these conditions, the MABR fingerprint can be useful to monitor changes in biofilm thickness that can affect process performance.
The MABR unit process simulated in this work represents currently available commercial hollow fiber MABR units implemented in a single step and completely mixed configuration.The analysis methodology developed can be applied to other applications, such as simultaneous nitrification and denitrification and shortcut nitrogen removal.The first MABR for MABRs in series (e.g., Ravishankar et al., 2022) will usually face higher carbon loading where nitrification could be limited, thereby limiting application of the fingerprint plot technique there.The MABR fingerprint can subsequently be applied to downstream stages where nitrification can occur and biofilm control may be more important for overall process performance.Chen and Zhou (2022) operated two lab-scale MABRs in series with high COD removal achieved in the first one and high total nitrogen removal achieved in the second one.Upstream MABR(s) can buffer treatment capacity to influent loading variations (Veleva et al., 2022), leading to efficient nitrification and nitrogen removal in downstream units.Investigations in practical full-scale MABR systems with variable operating conditions are needed.

CONCLUSIONS
MABR fingerprint plots are generated for a given biofilm thickness using dynamic steady state data with diurnal flow patterns or short-term loading variations implemented.Useful signals for biofilm thickness control can be derived by analyzing the slopes of the fingerprint plots against average bulk ammonia concentrations.When the MABR fingerprint is used for an ongoing MABR facility, if a trend of continuously decreasing slopes is detected, the biofilm is in ammonia limited conditions, and its thickness is optimized to achieve highest ammonia removal flux and lowest ammonia effluent concentrations.Increasing biofilm thickness within the range of slope-decreasing segment can promote denitrification without adversely impacts on ammonia removal.There are trade-offs applying this technique for biofilm thickness control relative to TIN removal performance.The MABR fingerprint is useful over a broad range of C/N ratios when the applied ammonia flux results in nitrification but not significantly underloaded conditions where biofilm control is less necessary.Fingerprints plots can be generated continuously with system operation ongoing to indirectly indicate biofilm development for operators to arrange biofilm control events efficiently.Guidance is provided to MABR designers concerning the operating conditions where the MABR fingerprint technique can be best used to monitor biofilm thickness to optimize performance.

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I G U R E 1 The configuration of MABR process in SUMO simulated.The kinetic parameters were kept at the Sumo1 default values.
Flowchart of the sensitivity analysis.(a) The map of the scope of C/N ratios and applied ammonia fluxes to be tested in the sensitivity analysis.The point of C/N ratio at 8 g COD/g N and applied ammonia flux at 3 g N/m 2 /day is used as an example.The right-hand side plots show that, under this influent condition, 50 biofilm thicknesses are simulated dynamically with diurnal flow repeated for 100 days and an MABR fingerprint plot is generated using the last-day data for each thickness.(b) The second step in the sensitivity analysis: plotting and analyzing the slope of the fingerprint plot with the average effluent concentrations on the last day for each thickness (average effluent ammonia as example).(c) The completed map to show the portion where the MABR fingerprint can be useful to indicate biofilm growth based on the results from Step 2 in (b) 800 μm) under C/N ratio of 10 g COD/g N with different applied ammonia fluxes: (a) 0.1 g N/m 2 /day; (b) 2 g N/m 2 /day; and (c) 10 g N/m 2 /day.(d) The change of slopes as biofilm thickness increases in the range of the selected thicknesses under C/N ratio of 10 g COD/g N and applied ammonia flux of 0.1, 2, and 10 g N/m 2 /day.Note that x and y axis scales are different in (a)-(c).