Towards advanced aeration modelling: from blower to bubbles to bulk

This paper discusses why more detailed aeration system submodels are required and why the imbalance between the levels of detail in the various submodels is a critical problem. To model the entire aeration system in more detail, various processes have to be described. An overview of critical aeration system submodels is provided, including examples for successful modelling approaches, leading edge research, and gaps in the understanding of aeration processes. Aeration processes discussed include air compression using blowers, air distribution using pipes and control valves, introduction of air bubbles into the aeration tank via diffusers, and oxygen transfer from the bubbles to the bulk liquid. Whereas the air generation and distribution models establish the paradigm shift to an equipment modelling level, the oxygen transfer is impacted by several critical factors which currently can only be described in an empirical way. With this contribution, the authors will highlight on-going efforts that aim to improve the modelling of the aeration system with the emphasis on the complex interactions within the aeration system and the biological processes. In addition, a discussion of opportunities for future developments is initiated.

Diffused aeration systems supply compressed air using blowers that force air through supply pipes that feed diffusers submerged in the aeration tanks (Figure 1). The load to and the temperature in WRRF vary throughout a day, week, or season leading to varying oxygen demands. In addition, aeration tanks built as plug-flow tanks lead to an uneven load distribution within the system. However, aeration tanks built as completely stirred tank reactors never actually behave as such and show discrepant air distribution, especially considering the distribution pattern of the aeration system and the potential operation as sequenced aeration. The result is a highly variable DO demand in terms of both time and space. To maintain sufficient DO levels throughout the facility and over time, the aeration system has to be equipped with sensors, actuators, and advanced aeration control systems for both air pressure generation and air distribution.

Recently, modelling of air distribution networks has received increased attention and led to the development of very detailed submodels on a physical equipment level rather than describing the overall performance of aeration systems (Beltrán et al. 2011; Schraa et al. 2015, 2016). Other research focused on developing better submodels to predict energy consumption of the aeration systems (Amerlinck et al. 2016b). In fact, the increasing application of energy demand side tariffs (Aymerich et al. 2015) requires the inclusion of more accurate and fully dynamic energy predictions for realistic cost calculations.

Blowers, aeration networks and diffusers are described separately below, but it should be kept in mind that the entire aeration system is highly interactive. For example, a change of a valve position can have a significant impact on the efficiency of the blowers.

Two main types of blowers are typically used in wastewater treatment: (i) positive displacement (PD) blowers and (ii) centrifugal blowers. PD blowers are very robust and are not susceptible to surge, but are less energy efficient than centrifugal blowers and designed for lower flow rates. Centrifugal blowers and especially two-point controlled blowers are highly efficient but have to be protected against surge and choking.

Secondly, controlling blowers is the part of the aeration control system which defines the energy consumption but currently only a demand-side modelling approach is typically applied. This means whatever air is required in the different sections of the aeration tanks, the aeration system is assumed to be able to deliver. For trouble-shooting aeration system control or aligning the aeration control system to the available equipment, more detailed models are required.

Thirdly, the detailed submodels also allow a more detailed design, where the air demand of the biological processes can be predicted against the ability of the aeration system to match the air requirements. This reduces the uncertainty in the design process, and perhaps even more importantly, helps to overcome or minimise the challenges encountered when commissioning WRRF.

Amerlinck et al. (2016b) showed that their developed dynamic blower model yields a more accurate prediction of the real energy consumption by the blowers and captures the trends (in particular the peak energy demand) better than constant average power consumption models (e.g. Gernaey et al. 2014) currently being used. The model comprises a detailed description of both the blower characteristics and the aeration system characteristics and was calibrated in two cases.

Since the blower models are based on manufacturer supplied testing data to a large extent, only limited calibration is required. The bottleneck is the availability of blower curves including all required information such as efficiency or brake power.

The air distribution starts at the blower outlets and is designed to deliver sufficient air to the diffuser grids in the aeration tanks. To match the oxygen demand in the different parts of the aeration tanks and also over time, the aeration system has to be designed so that pressure drops in the different parts, e.g. caused by control valves, control the air distribution. The pressure drops are caused by pipe friction, losses due to fittings, bends, and fixed installations like flow meters and finally the diffusers, which have the largest contribution to the pressure drop.

In the first instance, air distribution is a highly dynamic and interactive process and the aeration system response can only be accurately estimated if the entire piping network is modelled.

In the second instance, most WRRFs suffer from under- or over-aeration in certain parts of the aeration tanks. However, limited information is typically available on the DO profile, as the DO concentration is only available from the DO sensor locations. A detailed air distribution model provides more insights into the facility status and enables optimisation of the process performance and efficiency.

A comprehensive aeration model was developed by Schraa et al. (2015) that includes the following features:

• The air distribution system including air piping, fittings, valves, and diffusers is modelled in detail. The pipe segments are modelled using the Darcy–Weisbach equation with the friction factor calculated using the Swamee & Jain (1976) equation. Pressure drops across valves and diffusers are calculated using polynomial functions that are a function of air flow rate and are calibrated to manufacturer-supplied data or experimental data when available.

• Dynamic terms have been incorporated into all the modelling equations to account for dynamic variations in pressure throughout the system.

Whereas the aeration system itself is now modelled in detail, the resolution at the end point in the aeration tanks limits a more detailed description. The current tanks-in-series (TIS) does not allow a sufficiently accurate description of species heterogeneities that prevail. Hence, this TIS approach should, in the cases where this is crucial, be replaced by conceptual compartment models (CM) (see further for more detailed discussion).

The models are currently used in full-scale studies and the results show minimal calibration requirements. However, it is suggested that sensitivity analyses be conducted to gain a better understanding of potential simplifications, such as not modelling the impact of heat loss throughout the piping system. Temperature has a significant impact on air volume and could be high enough to melt plastic pipes in higher pressure applications.

The modelling of valve positioning in terms of speed, accuracy and control execution is currently under study and first models are tested against experimental data. This adds an additional layer of complexity but will help trouble-shooting and better design of aeration control systems. It will also allow an objective comparison of different valve types (e.g. butterfly vs. novel jet valves).

Diffusers cause the largest pressure drop in the aeration system, excluding control valves. The diffuser distribution and density therefore defines the air distribution in the system and the reason for the typically higher diffuser density in the high-loaded upstream aeration zones of aeration tanks. The diffusers also define the bubble size and therefore have a major influence on the oxygen transfer efficiency. Being the link between air distribution and oxygen transfer, diffusers have to be modelled for both these processes.

First, the focus of diffuser models was purely on predicting the oxygen transfer efficiency. However, the impact of the diffuser density on the air distribution may even be more significant for the accuracy of the model predictions if a portion of the aeration tank is operated below a DO concentration of 1 g DO/m³ due to imbalanced air distribution.

Second, diffusers define the resulting bubble size distribution (BSD) and therefore have a significant impact on the oxygen transfer efficiency. Each diffuser type has its own unique performance characteristics that vary with airflow and diffuser density. Therefore, it is important to model how diffuser performance varies with operational conditions.

Aeration concepts like ammonia-based aeration control (Rieger et al. 2012, 2014) require wider operational ranges in terms of air flow rate per diffuser. More detailed models help to better understand the impact of different operation conditions on overall performance and support the design engineer in selecting the correct diffuser type along with an appropriate diffuser distribution.

Two models are required to model the impact of diffusers on air distribution and oxygen transfer efficiency:

• The recent work by Schraa et al. (2015) calculates the oxygen transfer to the bulk liquid using the equations given in the ASCE/EWRI Standard 2-06 (ASCE 2007). A model has been developed to calculate the standard oxygen transfer efficiency for different diffuser types as a function of diffuser depth, air flow rate per diffuser, and diffuser density using data from the literature (US EPA 1989; Mueller et al. 2002) and manufacturer data. Further discussion on other factors affecting the oxygen transfer efficiency is provided in the next section.

• The pressure drop across the diffusers is calculated using polynomial functions that are a function of air flow rate and are calibrated to manufacturer-supplied data.

The impact of operating diffusers outside the manufacturer-specified air flow rate per diffuser ranges may lead to increased fouling problems or a drop in oxygen transfer efficiency. Modelling the impact of diffuser aging on both pressure drop and oxygen transfer efficiency may be required (Kaliman et al. 2008).

This section discusses the transfer of oxygen contained in the pressurized air delivered to the diffusers into the bulk liquid. Only diffused aeration is discussed here but the need for more detailed models is also required to model surface aeration.

values are therefore mainly determined by the air flow rate or the gas flow velocity (Dold & Fairlamb 2001; Gillot et al. 2005; Rosso & Stenstrom 2005; Gillot & Heduit 2008) and the mixing power. Their impact is modulated by two groups of factors (Gillot et al. 2005):

• Design and hydrodynamic parameters, including:

  • o water depth

  • o the number and arrangement of the diffusers

  • o tank shape

  • o mixing conditions (number, location and power of the mixers).

• Operating parameters, including:

  • o the dissolved species which are present in the interstitial liquid at different concentrations, depending on the wastewater characteristics and operating set points (above all the sludge age that determines the degree of degradation of the substances responsible for oxygen transfer depletion, mainly surfactants)

  • o the mixed liquor suspended solids concentration that impacts viscosity.

Several studies report on the impact of the dimensions of the aerated tanks on the oxygen transfer (Pittoors et al. 2014). The dimensions of the aeration tank have a considerable impact on the hydrodynamics. Various studies (Gillot & Héduit 2000; Rosso & Stenstrom 2005; Amerlinck et al. 2016a) reported considerable variation in oxygen transfer efficiency both in time and space in aeration tanks. Part of this variation can be explained by the impact of the hydrodynamics on the oxygen transfer mechanism.

Although many modelling studies assume completely mixed tanks, aeration tanks are definitely not homogenous (Rehman et al. 2014). Different flow patterns, recirculation and dead zones exist that impact the advective transport of DO as well as the trajectory (impacting gas holdup), generated size at the diffusers and the coalescence rate of bubbles. In addition, the hydrodynamic profile in aeration tanks fluctuates considerably given the variability in the airflow rate and in the influent flow rate. The latter varies significantly from minute to minute due to the influent wastewater received from the sewer system as well as due to changes in (recycle) pump operation and storm events.

Several publications try to quantify the effect of air flow rate and mixing on the oxygen transfer (e.g. Wonderly et al. 2008 and Wambecq et al. 2013). However, the applied empirical correlations consider global flow rates and mimic the hydrodynamic behaviour in a limited manner.

Today, in most of the applied models, a simple TIS approach, which is a train of virtual completely mixed zones, is used to model the effect of mixing. This approach only aims at mimicking the dispersion occurring in the direction of flow using the concept of numerical discretization (i.e. discretizing a partial differential equation in space as a series of slices).

None of these approaches is sufficiently accurate for modelling of low DO processes or detailed system control development. For the modelling of classical activated sludge systems, these approaches result in erroneous predictions in bulk species concentrations which can often lead to unwarranted parameter adjustments in the biokinetic model. Moreover, the errors and calibration efforts needed will vary with influent flow rate and the air flow rate. This results in different calibrated parameter values under different flow conditions.

Computational fluid dynamic models (CFD) are able to describe these heterogeneities in much more detail. When integrated with biokinetic models, it provides very detailed insight into the impact of local aeration tank conditions on overall process performance (Rehman et al. 2014). An important advantage, in view of aeration modelling, is that CFD allows for the local description of factors impacting oxygen transfer. The major disadvantage of CFD models is its high computational burden which makes it difficult to use in a rigorous process optimisation or controller development. Hence, there is still a need for a computationally more tractable model.

An acceptable compromise between detail and computational burden can be found in the use of CM. These models describe the aeration tank as a conceptual network of spatially localized compartments connected through convective and exchange fluxes. The latter can be derived from the steady state CFD-biokinetic model. This methodology is currently under development.

Thorough validation of CFD-biokinetic models that serve as input to the compartmentalization is vital. The approach by (Gresch et al. 2011) using a grid with multiple sensors to get insight in the spatial distribution of certain species has shown its value, but is not straightforward to implement and expensive since a multitude of probes is required. Local measurements at different locations can be an alternative.

Current CMs are static since they are based on a steady state CFD-biokinetic model. Introducing dynamics can be done by simulating various steady state cases and determining the variations in compartment volumes and exchange fluxes. Ideally, this leads to a single compartment structure with compartment volumes and exchange fluxes being dynamically dependent on flow rates.

The interaction between aeration and mixing are typically not included in standard WRRF models. However, especially for low DO technologies, it will be important to develop more detailed models for low air flow rate conditions. If not, it will not be possible to simulate these process conditions properly and one could potentially make wrong decisions. An increase in oxygen transfer efficiency may also be achieved by optimising the interaction between hydrodynamics and aeration systems. Such improvements are analysed, for example, in Fayolle et al. (2010, 2011) for looped aeration tanks equipped with fine bubble diffusers and slow speed mixers. These developments are moving in the direction of using CFD for reactor design with the objective of improving oxygen transfer efficiency.

The further application of CFD models on multiple aeration tank shapes is needed to shed light on how a specifically shaped reactor behaves in terms of flow patterns. However, given the computational cost, it is impossible to apply the CFD-route for every single facility. Hence, there is a need to develop knowledge on the link between aeration tank shape and the flow patterns that prevail in order to choose an appropriate CM without having to develop a CFD model for each specific case.

When considering a mixture of liquid and dispersed air bubbles, the transfer of oxygen is governed by the interfacial area, a, and the local gas-liquid mass transfer coefficient, (see Figure 5). The former depends on the number and size of bubbles, and can vary dynamically as bubbles grow due to pressure drop and coalesce when rising to the top of the aeration tank. Another impact is the viscosity of the mixed liquor which determines the resistance the bubble experiences when travelling. This potentially changes the bubble size during formation and the trajectory of the bubbles which can lead to increased coalescence and, hence, significant reduction of interfacial area.

On the other hand, it is well known that surfactants have a considerable impact on mass transfer (Stenstrom & Gilbert 1981; Dudley 1995; Wagner & Pöpel 1996). Obtained results differ according to the nature of the surfactants, their concentration and the observed system (bubble column, full-scale aeration tanks, etc.). Authors have agreed on the impact of surfactants on: (i) the bubble diameter, which is reduced by a decrease in the surface tension and by coalescence inhibition and (ii) a reduction in K_L, due to interface immobilisation and/or surfactant accumulation at the gas-liquid interface. More recent publications take into account the dynamic accumulation of surfactants at this interface (Capela et al. 2002; Rosso & Stenstrom 2006; Sardeing et al. 2006).

The description of the gas-liquid oxygen transfer, which is not fully understood, uses fairly simplistic base models extended with empirical relationships to introduce dependencies on environmental conditions. However, none of these models succeeds in explaining the high variability observed in α-factors in a single facility nor across different facilities. As mentioned, this can lead to erroneous predictions of bulk species concentrations and calibration of biokinetic models for the wrong reason.

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 concentration (Germain et al. 2007; Racault et al. 2011), sludge age (Rosso & Stenstrom 2005; Gillot & Heduit 2008; Henkel et al. 2009) and viscosity (Fabiyi & Novak 2008; Durán et al. 2016). 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 flow regime can influence the K_La as coalescence or breakage can vary the BSD and thus the available area for gas transfer (Fayolle et al. 2010). Viscosity in particular was observed to affect the shape of a bubble plume which increases the probability that a bubble will collide with a neighbouring one (Ratkovich et al. 2013). However, none of the studies to date has succeeded in explaining the high variability observed in α-factors in a single facility nor across different facilities.

There is currently a lack of experimental data allowing a reasonable calibration of the PBM approach. Available studies only considered clean water and an extension to the approach is required to properly account for the rheology of activated sludge. Future experiments using xanthan gum as a surrogate for activated sludge are planned. Once the PBM is finalized, the model needs to be reduced in complexity as it is too computationally expensive to be fully included. The most important phenomena need to be determined and maintained in the reduced model. One avenue could be to use integral moments of the distributions, which is a frequently used method to maintain information of the distribution without having to keep track of all the size classes.

A proper interaction with flow conditions is still needed. The shear rate in full-scale aeration tanks is not homogeneous and poses a current limitation in the approach since shear rate is the driving force of coalescence in the PBM. But prior to being able to include this interaction, the underlying mechanisms need to be better understood. CFD could be used as a tool as it is able to predict local shear rate. Such a CFD model can be directly linked to a PBM as well as the biokinetic model yielding a CFD-biokinetic-PBM model. Such a model becomes computationally expensive and validation is also a challenge. Moreover, it can only be computed under steady state conditions. Introduction of dynamics will, hence, be another challenge. However, this can be seen as an extension to the CM derivation as was discussed earlier. The CM derived there did not account for variation in oxygen transfer efficiency due to BSD dynamics as a fixed bubble size was assumed at all locations.

This section describes the link between all of the components of the aeration system, i.e. air compression (blower), air distribution, and oxygen transfer. The air generation and air distribution influence the oxygen transfer as they are the drivers that produce the air flow rates throughout the activated sludge process. The air flow rate is the major factor impacting the oxygen transfer (Dold & Fairlamb 2001; Gillot et al. 2005; Rosso & Stenstrom 2005; Gillot & Heduit 2008). The pressure and the type of diffusers applied determine the (initial) BSD. Blowers are known to produce heat, which alters the temperature of the delivered air and can alter the temperature of the mixed liquor and, thus, the oxygen transfer. The efficiency of the blower is influenced by a number of factors including the blower operating conditions, the characteristics of the air distribution piping network including valve stem positions, and the hydrostatic pressure due to the water column within the aeration tanks. Diffuser characteristics along with wastewater and hydrodynamic conditions will influence oxygen transfer efficiency. Aeration control systems cause an interaction between the air supply system and the oxygen transfer within the aeration tanks as the controllers will alter the air supply conditions to achieve the desired DO concentrations.

To date this interaction has been neglected in most if not all modelling studies. From the above discussions it can be deduced that modelling all the components of the aeration system (air compression, air distribution and oxygen transfer) is necessary to give a satisfactory description of an entire aeration system. This will reduce the requirement to adjust biokinetic parameters to compensate for flaws in other submodels. Only then will it be possible to more reliably use models for optimisation and control.

The improved models have currently not yet been coupled. This coupling can be done with different levels of rigour. The simplest approach is to use the output of one model as input to the other model. This does not account for interaction, though. Hence, investigations are required as to what extent this solution is satisfactory to meet current modelling objectives or whether inclusion of specific effects is required.

Overall, the level of detail incorporated in the overall aeration model will depend on the objectives set forth in the project. At some point, a guidance document will be useful to assist the modeller in making the adequate choice of aeration model complexity.

Aeration is an essential component of aerobic biological wastewater treatment but is currently modelled in a very simplistic manner when compared to the level of detail included in state-of-the-art biokinetic and settling models. Modelling the entire aeration system, considering both the dynamics of the air (or oxygen) supply side and the demand side, is essential in view of the design, optimisation and control of WRRFs, especially where aeration may be either limiting or excessive.

Key aspects to be modelled include the following:

• Blower performance curves and how they vary with inlet guide vanes, variable diffusers, and motor speed. These aspects are important in terms of predicting the delivered air flow, the discharge pressure, and the power consumption. In addition, it is important to model the operating limits of the blower to avoid regions of unstable operation such as surge where the blower cannot overcome the back-pressure and a pulsating reversal of flow occurs.

• Pressure drops in the piping network, including the pressure drop characteristics of fittings such as valves and diffusers which affect the air flow distribution. This is important as constraints such as valve stem position ranges and diffuser distribution can limit the ability to deliver the air where it is required.

• Design and hydrodynamic parameters, including: water depth, the number and arrangement of the diffusers, tank shape, and mixing conditions (number, location and power of the mixers). Physical parameters and mixing conditions are important to model as they impact the BSD and the bubble residence time within the tank and these factors impact oxygen transfer.

• Operating conditions such the concentration of surfactants present in the interstitial liquid and the mixed liquor suspended solids concentration. Surfactants impact bubble size and impede oxygen transfer at the gas-liquid interface. The viscosity of the mixed liquor imposes a resistance to the flow of the air bubbles. Both of these aspects are important to model as they effectively reduce the α-factor.

• Controllers adjust valve positions and blower operating conditions in response to changes in DO with the aeration tanks. As a result, they make the aeration system highly interactive. It is important to accurately model the controllers as they are crucial to proper aeration system performance, but must be tuned properly for stable and efficient performance.

The paper highlighted the work that is being done to develop detailed submodels of all aspects of aeration systems and how the models will be connected to provide a comprehensive picture of diffused aeration systems. The work is significant because it will facilitate improved aeration control systems, allow selection of air supply system and aeration tank hydraulic conditions that promote the most energy-efficient operation, and ease biokinetic model calibration by preventing the need to erroneously adjust biokinetic parameters and α-factors to compensate for limitations in the aeration system model.