At wastewater treatment plants (WWTPs), the aerobic conversion processes in the bioreactor are driven by the presence of dissolved oxygen (DO). Within these conversion processes, the oxygen transfer is a rate limiting step as well as being the largest energy consumer. Despite this high importance, WWTP models often lack detail on the aeration part. An extensive measurement campaign with off-gas tests was performed at the WWTP of Eindhoven to provide more information on the performance and behaviour of the aeration system. A high spatial and temporal variability in the oxygen transfer efficiency was observed. Applying this gathered system knowledge in the aeration model resulted in an improved prediction of the DO concentrations. Moreover, an important consequence of this was that ammonium predictions could be improved by resetting the ammonium half-saturation index for autotrophs to its default value. This again proves the importance of balancing sub-models with respect to the need for model calibration as well as model predictive power.

INTRODUCTION

At wastewater treatment plants (WWTPs), the conversion processes in the bioreactor are driven by the presence of an electron acceptor, i.e. dissolved oxygen (DO) in the case of aerobic processes (e.g. aerobic heterotrophic growth and nitrification). Within these conversion processes, the gas–liquid oxygen transfer has been reported as a rate limiting step (Ardern & Lockett 1914; Garcia-Ochoa & Gomez 2009). In addition, aeration is the largest energy consumer at WWTPs (Reardon 1995; Tchobanoglous et al. 2004; Devisscher et al. 2006; Zahreddine et al. 2010). Hence, a sound description of this process is vital in the cost-effective optimization of the aerobic biokinetic processes.

From a modelling perspective, a good description of the gas–liquid and liquid–gas transfer is crucial. Benedetti et al. (2008) performed a global sensitivity analysis on biochemical, design and operational parameters with the benchmark simulation model no. 2 (Jeppsson et al. 2007; Nopens et al. 2010) illustrating that the oxygen transfer coefficient is the second most sensitive parameter in the model. In a modelling study comparing different model choices on a full scale WWTP, Maere et al. (2008) and Cierkens et al. (2012) show that a good estimation of the aeration flow rate (and hence of the oxygen input), leads to excellent prediction of oxygen consumption and concentrations in the activated sludge process. Further modelling work on improving the aeration model has led to even better prediction of the oxygen consumption and concentrations, consequently, improving the prediction of ammonium (NH4) removal, which omits the need for unnecessary calibration of the biokinetic model (personal communication, Cierkens).

The most used concept for aeration in WWTP modelling is the two-film theory (Whitman 1923, 1962), which is based on the assumption that when two phases contact, a thin stagnant layer exists on each side of the phase boundary. Due to the rather low solubility, oxygen diffuses very slowly through the liquid film but quickly through the gas film. As a consequence, the liquid at the interface is rapidly saturated and the gas film resistance can be omitted. The total change in concentration over time due to aeration can be described by Equation (1) considering the liquid phase in equilibrium with the gas phase and that kLa, which is typically used in WWTP modelling to quantify the amount of aeration, is defined by Equation (3). 
formula
1
where cs* (Equation (2)) is the saturation concentration in the liquid [mol/L] and kLa (Equation (3)) is the oxygen gas transfer coefficient [1/s]. The first factor in Equation (1) defines the rate at which the transfer occurs. The second factor, on the other hand, defines the driving force for the transfer. 
formula
2
where kH is the Henry coefficient for oxygen [mol/(l.atm)] and pG is the oxygen pressure in the gas phase [atm]. 
formula
3
where kL is the resistance to mass transfer in the liquid film [m/s], A is the surface of the gas–liquid interface [m2] and V is the volume of the liquid phase [m3].

In order to estimate the oxygen transfer, correlations exist that link the kLa to the airflow rate (Gillot & Héduit 2000) or the gas flow velocity (Dold & Fairlamb 2001; Gillot et al. 2005; Rosso et al. 2005; Gillot & Héduit 2008).

In addition, the consideration that environmental factors or contamination (salt concentrations, surfactants) have an impact on the gas–liquid transfer is considered. The environmental factors may influence the driving force (i.e. caused by changes in the saturation concentration), the resistance factors or the interfacial area A. The corrections to apply for the calculation of the actual transfer rates can be described by Equation (4) as proposed by the US EPA (1989). 
formula
4
where AOTR is the actual oxygen transfer rate [g/(d.m3)], kLaCW,20 is the oxygen transfer coefficient in clean water at 20 °C and 1 atm with a DO concentration of 0 mg/L [1/d], α is the ratio of process water kLa over clean water kLa [−], F is a fouling factor defined as the ratio of the aeration system performance after use to new aeration system performance [−], β is the ratio of process water oxygen saturation concentration to clean water oxygen saturation concentration [−], τ is the ratio of oxygen saturation concentration at actual temperature to oxygen saturation concentration at 20 °C [−], Ω is the oxygen saturation concentration pressure correction factor [−], is the oxygen saturation concentration at 20 °C and 1 atm [g/m3], C is the actual mixed liquor DO concentration [g/m3], θ is the temperature correction coefficient and T is the mixed liquor temperature [°C].

Several attempts have been made to predict the α-factor, assigning its observed variation to either surfactant concentrations (Rosso & Stenstrom 2006), mixed liquor suspended solids (MLSS) concentration (Germain et al. 2007; Racault et al. 2011), sludge age (Rosso et al. 2005; Gillot & Héduit 2008; Henkel et al. 2011) and viscosity (Fabiyi & Novak 2008). Most of the observed correlations have in common that the studied factors affect the shape of the bubbles and the gas flow at the interface. Also, the physical properties of the liquid, together with its flowing regime, can influence the kLa as coalescence or breakage can vary the bubble size distribution and, thus, the available area for gas transfer, i.e. the a part of the oxygen transfer coefficient (Fayolle et al. 2010). Viscosity, in particular, was observed to affect the shape of a bubble plume and, thus, increasing the probability that a bubble will collide with a neighbouring one (Ratkovich et al. 2013).

The β-factor is the correction for the process water oxygen saturation concentration. This factor is governed by the same corrections (e.g. temperature and salt concentration) as the Henry coefficient, by which the saturation concentration is determined in combination with the mole fraction of oxygen in the gas phase.

The θ-factor, also known as geometric temperature correction coefficient, is used to relate mass transfer coefficients to a standard temperature (Equation (4)). Because of lack of a proper appraisement, a value of 1.024 should be used unless differently specified and strongly supported by consultants and manufacturers. Moreover, it is recommended to limit the temperature correction for deviations smaller than 10 °C, although it is well known that corrections over a wider range are often needed (Stenstrom & Gilbert 1981).

Ω is the oxygen saturation concentration pressure correction factor, which depends on the height of the water column. In submerged aeration, oxygen transfer occurs throughout the tank volume and saturation concentration varies with depth (Equation (5)) caused by the progressive decreases in both hydrostatic pressure and the oxygen mole fraction as the bubbles move upward (Stenstrom et al. 2006). 
formula
5
where z is the actual depth [m], zd is the aerator submergence depth, assumed to be equal to liquid height above the aerator h [m], pa is the atmospheric pressure [Pa], Y is the mole fraction of oxygen in gas phase [0.2095, −], ρ is the density of water [kg/m3] and g is the gravitational acceleration [9.81 m/s2].
Although a variation in oxygen mole fraction in the bubble occurs over depth, it is not easily calculated. Actually, in order to calculate the dependence over the depth, one would need to calculate the depletion in the bubbles for which the oxygen saturation concentration itself is needed. So, for the moment, in anticipation of a better approach, a constant factor is deemed to be the best possible approach. As such, for submerged aerators placed at the bottom of the tank Equation (6) is derived for the pressure correction factor. 
formula
6
where pa is the atmospheric pressure at the surface [Pa].

To date, WWTP models consist of highly detailed biokinetic models (Barker & Dold 1997; Henze et al. 2000) but often lack detail of other critical processes, such as aeration. This paper is addressing (1) the need for higher detail in modelling of the aeration process, hereby using off-gas measurements for more detailed insight in the process and (2) the impact on the calibration of the model. Based on an extensive measurement campaign, the applied aeration model, which is a combination of several models available in literature, is calibrated. The effect of this improved calibration on the overall model calibration is shown.

MATERIALS AND METHODS

Aeration system at the WWTP of Eindhoven

With a treatment capacity of 750,000 population equivalents (PE), the WWTP Eindhoven (The Netherlands) is the largest treatment plant of Waterboard De Dommel and the third largest in The Netherlands. The incoming wastewater is treated in three parallel lanes with a total plant maximum hydraulic load of 26,250 m3/h. Each lane consists of a primary settler, a biological tank and four secondary clarifiers. An extra 8,750 m3/h can be treated mechanically and passes a pre-settling tank before it is discharged in the river Dommel or treated in the biological tanks when the hydraulic load again drops below 26,250 m3/h. The biological tanks (Figure 1) comprise a modified UCT configuration (Tchobanoglous et al. 2004).
Figure 1

The circular modified UCT configuration of the activated sludge tanks at the WWTP of Eindhoven.

Figure 1

The circular modified UCT configuration of the activated sludge tanks at the WWTP of Eindhoven.

Within the 7 m deep biological tanks, aeration is provided in the outer ring by plate aerators divided in two sections: a continuously active summer package and a winter package (used as additional capacity under extreme conditions and when T is low leading to a reduced nitrification rate). The summer package comprises 504 plate aerators, totalling a surface of 1,063 m2, whereas the winter package comprises 84 plate aerators totalling a surface of 177 m2.

The airflow of the summer package is continuously controlled by an NH4-DO cascade feedback controller. On the other hand, the winter package is only switched on in case the capacity of the summer package proves not to be sufficient (mainly during storm events) and is running on full capacity when active.

Modelling of aeration

The WWTP was modelled using WEST (mikebyDHI 2014) and is based on a modified version of ASM2d (Amerlinck 2015). Cierkens et al. (2012) implemented a new model for the calculation of the oxygen transfer based on the work of Rosso et al. (2005), which proved to give an excellent description of the dynamics in DO concentration. Within this model, the α-factor and standard oxygen transfer efficiency (SOTE) are calculated based on a correlation with the sludge retention time (SRT) and the airflow rate (Equations (7)–(10)). 
formula
7
 
formula
8
 
formula
9
 
formula
10
where Qair is the airflow rate [m3/s], aspec is the diffuser specific area [m2], Nd is the total number of diffusers [−], Z is the diffuser submergence depth [m] and QN,air is the resulting normalized airflow rate [s−1].

Because the aeration model is not able to capture all the variability observed in the measurement campaign, the model is also evaluated using the measured αSOTE as input to the whole plant model.

Off-gas measurements

In order to evaluate the parameters of this correlation, off-gas measurements were performed according to the official protocol for process water testing described by the Oxygen Transfer Standards Subcommittee from the American Society of Civil Engineers (1997). In the month of August 2012, three locations at the outer ring of the aeration tank of lane II (Figure 2), namely the beginning, the middle and the end of the summer package, were monitored during an extensive measurement campaign.
Figure 2

Picture of the aeration hood placed at the beginning of the summer package of the aeration tank of line II (left) and schematic view of the three hood locations (right).

Figure 2

Picture of the aeration hood placed at the beginning of the summer package of the aeration tank of line II (left) and schematic view of the three hood locations (right).

The off-gas equipment was composed of a reinforced polyethylene hood floating on the wastewater surface (1.5 × 1.5 × 0.3 m, L × W × H). The hood was connected to an off-gas analyser through a flexible hose of 40 mm in diameter. In the off-gas analyser (Figure 3), a vacuum pump diverges a small fraction of the off-gas from the main hose to a desiccator unit in order to remove water vapour. The spilled airflow is then circulated inside a zirconium oxide fuel cell (AMI Model 65, Advanced Micro Instruments, USA) to measure oxygen partial pressure. Ambient air was sampled by means of a three-way valve at the start and end of each experiment as reference for the efficiency evaluation.
Figure 3

A schematic overview of the off-gas analyser.

Figure 3

A schematic overview of the off-gas analyser.

When the humidity is stripped out of the gas stream, only the knowledge of the CO2 content is necessary in order to calculate the actual mass fraction of oxygen (Redmon et al. 1983). With this purpose, the CO2 content of both the ambient air and the off-gas stream was measured with a photo-acoustic infrared gas analyser (X-Stream, Emerson). Knowing the CO2 content of the gas stream, the partial pressure of oxygen and its ratio with inerts were calculated using Equations (11) and (12). 
formula
11
 
formula
12
where and represent the molar ratio of oxygen to inerts (mainly nitrogen gas) in the inlet (or reference) and off-gas, respectively [−]. [−] and [−] are the mole fractions of oxygen in the inlet and off-gas, while [−] and [−] are the mole fractions of CO2. Finally, oxygen transfer efficiency (OTE) can be calculated with Equation (13) considering the dynamic CO2 content in the off-gas. 
formula
13
Typically, for clean water applications, results are reported as SOTE (%), referring to zero DO, zero salinity, 20 °C and 1 atm. In order to correct for process water conditions, the α-factor is used and results are normally shown as αSOTE (Equation (14)). 
formula
14
where C is the actual oxygen concentration [mg/L] and T the actual temperature [°C]. This method allows standardisation of results of OTE calculating the oxygen saturation concentration in clean water at 20 °C () and the saturation concentration for clean water at effective saturation depth in process temperature conditions ().

The floating hood was equipped with an LDO probe (Hach-Lange) and DO data were acquired in order to correct for variable DO gradients during the oxygen transfer process and relate the efficiency results to standard conditions with Equation (4). Data of DO and oxygen content in the off-gas were acquired with a data acquisition card (DAQ-card USB-6341, National Instruments, USA) using a graphical user interface developed in LabView (National Instruments, USA). Adjustments for CO2 content in the off-gas were performed in a post-processing step when both the data from the off-gas analyser and the X-Stream were available.

RESULTS

The main findings of the campaign were the observation of a high variation in the αSOTE (Figure 4), a significant increase in αSOTE from the beginning towards the end of the summer package (following the flow direction) and the relatively high efficiency of this system as compared to other similar applications (10–20% deduced from Gillot & Héduit (2008)). The aeration at the beginning of the summer package shows, on average, although the variation is rather large, about 2% and 6% less efficiency than the middle and end locations, respectively. This increase in αSOTE over the locations, assuming that the entire aeration package distributes the airflow homogeneously, may be attributed to the gradual contaminant oxidation occurring (Rosso & Stenstrom 2006). The high variation in αSOTE looks inversely correlated with the airflow rate, when the airflow rate is gradually changing. Fast changes in airflow rate, however, seem to make αSOTE follow the trend of the airflow rate. This effect, i.e. increasing airflow rate combined with increasing αSOTE, makes the change made by the controller more pronounced than what the controller expects and, as such, creates oscillations when the controller tries to correct for the too-strong manipulation. Further investigation is needed to disclose the mechanisms related to this behaviour.
Figure 4

The high variation in αSOTE (grey line), DO (dashed line), NH4 (dash-dotted line) dynamics and airflow rate (black line) measured continuously at the end of the summer package during the last 2 days of the measurement campaign.

Figure 4

The high variation in αSOTE (grey line), DO (dashed line), NH4 (dash-dotted line) dynamics and airflow rate (black line) measured continuously at the end of the summer package during the last 2 days of the measurement campaign.

The manner of calculating the saturation concentration may influence the results of αSOTE. In particular, the pressure correction and the applied effective saturation depth vary depending on the source, either 50% (Tchobanoglous et al. 2004), 22–44% (US EPA 1989) or 33% (Gillot et al. 2005) of the total submergence depth. The application of 33% of the total submergence depth would result in slightly higher αSOTE values and, as such, lead to the same conclusion as the applied 44%.

The aeration model (Rosso et al. 2005) was not able to describe the variation observed in αSOTE during the measurement with one unique set of parameter values. Some of the variations could be captured very well (Figure 5, left) but with different parameter sets for each day. During other days, the variation could not be characterized at all with the model (Figure 5, left).
Figure 5

The best fit for the aeration model of Rosso et al. (2005) (black line) on the measurement data of αSOTE during 2 days of the measurement campaign (dots).

Figure 5

The best fit for the aeration model of Rosso et al. (2005) (black line) on the measurement data of αSOTE during 2 days of the measurement campaign (dots).

The data collected during the off-gas measurements were compared with the modelling results in order to evaluate the prediction performances of the aeration model (Figure 6). The modelling results for DO are 4 to 6% lower than the ones measured in the middle of the summer package (which previously was assumed to be representative for the entire aeration package). When applying the measured αSOTE directly as model input instead of the correlation described above, DO predictions improve (dashed line versus full line) compared to the DO values from the supervisory control and data acquisition (SCADA) logs (dots) and DO measurements at the hood location (triangles) (Figure 6, left). This improvement reveals the need to update the correlation specific for the WWTP of Eindhoven.
Figure 6

Left – the improved DO predictions for the model using αSOTE directly as model input (new DO prediction – full line) versus the model using the correlation with SRT and airflow rate (old DO prediction – dashed line) compared to the DO values from the SCADA logs (dots) and DO measurements at the hood location (triangles). Right – the model using αSOTE directly as model input shows improved NH4 predictions for the model where the half-saturation constant for NH4 was reset to the default value (new NH4 prediction – full line) versus the model using the adapted value (old NH4 prediction – dashed line) compared to the NH4 values from the SCADA logs (dots).

Figure 6

Left – the improved DO predictions for the model using αSOTE directly as model input (new DO prediction – full line) versus the model using the correlation with SRT and airflow rate (old DO prediction – dashed line) compared to the DO values from the SCADA logs (dots) and DO measurements at the hood location (triangles). Right – the model using αSOTE directly as model input shows improved NH4 predictions for the model where the half-saturation constant for NH4 was reset to the default value (new NH4 prediction – full line) versus the model using the adapted value (old NH4 prediction – dashed line) compared to the NH4 values from the SCADA logs (dots).

On a side note, but worthy of mention, is the difference in oxygen concentration between the SCADA system and the hood measurements. The difference amounts up to 0.5 mg/L and is due to both the distance between the plant sensor and the hood and to the heterogeneity caused by mixing patterns. It emphasizes the importance of (1) having a good location for the sensor measurements and (2) an appropriate hydraulic mixing model (Rehman et al. 2015).

As expected, the NH4 was even further depleted (dashed line) as compared to the previous simulations (not shown) and, therefore, more distant from the measured NH4 (dots) (Figure 6, right). These observations may lead to consider a re-evaluation of the model parameters linked to NH4 depletion, in particular the ammonium half-saturation index for autotrophs (KNH,ANO), which was previously fixed (0.05 mg/L) to match the SCADA measurements. Resetting the half-saturation index to its default value (1.0 mg/L) improves the model predictions for ammonium (full line) considerably (Figure 6, right). This shows again the importance of sufficient model complexity of sub-models which otherwise forces the modeller to calibrate biokinetic parameters.

DISCUSSION

The aeration model applied is certainly an improvement over state of the art aeration models applied in WWTP models and provided good simulation results for the case of Eindhoven (Cierkens et al. 2012). However, the new measurement campaign shed light on the real evolution of the α-factor in the aerated tanks and it was demonstrated that applying this more realistic α-factor improves the simulation results.

However, the model is not able to describe all the observed variations in αSOTE (Figure 5). Some of the variations in the data can be well described, whereas other days, the variations cannot be explained with the model at all. Important to note is that, for the good fit periods, the parameter values had to be changed each day. This demonstrates that the model could still be improved as, on the one hand, it obviously misses some key elements and, on the other hand, it shows some features that are doubtful. First, the fact that α-factor is linked to the sludge age (SRT) is questionable as the SRT is a global WWTP characteristic and aeration (oxygen transfer and the α-factor) is a local parameter influenced by the local physics of the tank. Actually, the US EPA (1989) mentions the change in α-factor over the length of the aeration tank.

The apparent correlation between SRT and the α-factor can be explained by the link of SRT with some of the influential factors. First, SRT is directly linked to the MLSS concentrations, which is considered as having an impact on the oxygen transfer, and also to the sludge composition and morphology. The combination of sludge concentration, composition and morphology can be related to changes in viscosity which are known to influence the gas–liquid transfer (Fabiyi & Novak 2008; Ratkovich et al. 2013). In addition, the floc volume is one of the drivers for changing α-factors mentioned by Henkel et al. (2011). The SRT is also linked to the capacity of biodegradation of, e.g. surface active agents, although that should only be really differing with very low SRTs. The surface active agents, however, are known to impact oxygen transfer (Rosso & Stenstrom 2006). Finally, the need for recalibration, in this study, suggests that the SRT is probably not the only predictor for the variations in the α-factor.

Many of the factors (surfactants, viscosity, floc volume) mentioned above, have an impact on the formation and shape of the air bubbles. With regards to this, another suggested future improvement in the modelling of the aeration process would be the evaluation of the drivers and the impact of bubble coalescence. In this evaluation, bubble column tests in combination with modelling frameworks such as population balance models (Nopens et al. 2015) will have a definite added value.

These observations prove the need for a recalibration of the aeration model. Moreover, after applying this more realistic oxygen input, ammonium predictions could be improved by resetting the ammonium half-saturation index for autotrophs to its default value. In a previous calibration exercise, this ammonium half-saturation index was lowered in order to enable the model to predict the lower ammonium concentrations measured. Apparently, the aeration model, calibrated on a single off-gas test, was not able to predict a sufficiently high oxygen input, which was then, incorrectly, corrected for by increasing the oxygen consumption for nitrification through the ammonium half-saturation index.

CONCLUSIONS

The application of the aeration model is clearly an advancement over the state of the art description of the aeration process in WWTP models. During an extensive measurement campaign with off-gas tests performed at the WWTP of Eindhoven a high variability was observed in the OTE. Applying this gathered system knowledge in the aeration model and after re-adaptation of the ammonium half-saturation index for autotrophs, the model proved, based on the airflow rates, to give good predictions for the oxygen and, consequently, ammonium concentrations at the WWTP of Eindhoven. As such, it was shown that the effect of applying the correct α-factors omits the need for calibration of the biokinetic model. This again proves the importance of balancing the complexity or detail in the different sub-models which is preferred over parameter calibration with respect to model predictive power.

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