During the design of a water resource recovery facility, it is becoming industry practice to use simulation software to assist with process design. Aeration is one of the key components of the activated sludge process, and is one of the most important aspects of modelling wastewater treatment systems. However, aeration systems are typically not modelled in detail in most wastewater treatment process modelling studies. A comprehensive dynamic aeration system model has been developed that captures both air supply and demand. The model includes sub-models for blowers, pipes, fittings, and valves. An extended diffuser model predicts both oxygen transfer efficiency within an aeration basin and pressure drop across the diffusers. The aeration system model allows engineers to analyse aeration systems as a whole to determine biological air requirements, blower performance, air distribution, control valve impacts, controller design and tuning, and energy costs. This enables engineers to trouble-shoot the entire aeration system including process, equipment and controls. It also allows much more realistic design of these highly complex systems.

## BACKGROUND

Aeration is one of the key components of the activated sludge process, and is one of the most important aspects of modelling water resource recovery facilities (WRRFs). It is essential for WRRF models to accurately predict the mass transfer of oxygen into the bulk liquid for given wastewater and aeration equipment characteristics. There are three aspects to be modelled when considering aeration systems:

*Air supply system*: the supply of compressed air to diffusers installed in bioreactors.*Oxygen transfer*: the release of air bubbles into the wastewater within the bioreactors and the transfer of oxygen from the bubbles to the wastewater.*Oxygen demand*: the consumption of oxygen by the microorganisms and the oxygen required to maintain a residual dissolved oxygen (DO) concentration in the bioreactors.

WRRF simulators typically focus on modelling oxygen transfer and assume that the required air can be supplied. As part of the presented work, an integrated dynamic model has been developed, which integrates both the air supply system and the oxygen transfer to the bulk liquid and combines it with a state-of-the-art biokinetic process model.

## MODEL DEVELOPMENT AND CALIBRATION

The developed comprehensive aeration model includes the features listed below. A detailed description can be found in Schraa *et al.* (2015).

**Blowers:**Models for both centrifugal and positive displacement blowers have been developed. The centrifugal blower model is based on the pump model of Rossman (2000) with modifications to allow air flowrate regulation through changes in inlet guide or outlet variable diffuser vanes or through changes in motor speed. In a positive displacement blower, the air flowrate is proportional to the motor speed with some slippage losses (Aerzen 2011).**Pipes and fittings:**The Darcy-Weisbach equation for fluid flow can be used to calculate the pressure drop through pipe sections. The Colebrook-White equation is used to calculate the friction factor in the Darcy-Weisbach equation. Simplified empirical correlations, such as the Swamee-Jain equation (Swamee & Jain 1976), are available to approximate the Colebrook-White equation. Air is assumed to be incompressible at the typical pressures in aeration equipment, although factors for gas expansion can be included if high pressure drops are encountered. Pressure drops through fittings are calculated as the losses through equivalent lengths of pipe using tabulated resistance coefficients for specific fittings. Temperature changes throughout the piping network can be substantial and are modelled using Newton's law of cooling.**Control valves:**The modelling of the flowrate and pressure drop through valves can be done using the Darcy-Weisbach equation. The resistance coefficient is defined as a function of a valve coefficient,*K*in SI units or_{v}*C*in U.S. units, which expresses the flow through the valve under certain conditions. The valve coefficient is a function of valve stem position, and each type of valve has its own characteristic valve coefficient curve. Example valve coefficient curves are given by Stephanopoulos (1984) and Schraa_{v}*et al.*(2015).**Diffusers:**The pressure drop through diffusers is often a linear or quadratic function of air flowrate. These curves are derived from experimental data. The oxygen transfer to the bulk liquid is calculated 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 (SOTE) for different diffuser types as a function of diffuser depth, airflow per diffuser, and diffuser density using data from the literature (USEPA 1989; Mueller*et al.*2002) and from diffuser suppliers. The SOTE model, which is shown below in Equation (1), was developed using the SOTE correlations of USEPA (1989) and Sproull*et al.*(2002) as a basis: where:Air flowrate (Nm

^{3}/h)Number of diffusers

Diffuser density (diffuser area/tank area, m

^{2}/m^{2})Default diffuser density used in calibration dataset

Diffuser submergence (m)

Model parameters.

An extensive study was conducted of the transfer efficiency characteristics of different diffusers and representative model parameters were calibrated for each main type of diffuser (e.g. membrane or ceramic discs). See Gillot

*et al.*(2005) for a model of oxygen transfer efficiency that is developed using dimensional analysis.

**Physical properties of air:**Properties of air as a function of temperature, pressure, and relative humidity are calculated using the ideal gas law. Correlations are used to calculate the solubility of oxygen in water as a function of temperature and the viscosity of air as a function of temperature.**Dynamic variability:**Dynamic terms have been incorporated into all the modelling equations to account for dynamic variations in pressure throughout the system.

The resulting dynamic aeration system model was implemented in the simulation platform SIMBA#, and can be connected to WRRF process and detailed controller models, allowing for interactive simulations of the entire system and consequently more accurate prediction of the process and control system performance.

Configuration or setup of the comprehensive aeration model involves entering the physical characteristics of the system (i.e. blower type, pipe layout and dimensions, diffuser densities, valve types, etc.) and entering blower, valve, and diffuser curves if the equipment is not already available in the equipment library. The need for model calibration and validation after the model setup is minimised through the use of representative default model parameter values and a library of data for commonly used blowers, valves, and diffusers. Most sub-model parameters are calibrated automatically using the performance data found in the equipment database. For example, pressure drop data are available for commonly used valves and diffusers, and the simulator uses either least squares estimation or analytical methods to estimate the pressure drop model parameters from the dataset. The user can also supply their own data, which are used to estimate the model parameters. Fine-tuning of the model parameters can be done by comparing model predictions of air flowrate, pressure drop, and temperature with data from the aeration system in question. Parameters that may require adjustment during calibration of the air supply system model are the pipe roughness coefficient, the resistance coefficients for pipe fittings (such as bends, tees, entrances, and exits), and the valve flow coefficient. For design applications, default model parameters were defined, which enable realistic predictions for typical equipment ranges.

## RESULTS AND DISCUSSION

^{3}/d, and 5-day biochemical oxygen demand (BOD

_{5}) and total Kjeldahl nitrogen (TKN) concentrations of 205 and 35 mg/L respectively. The primary effluent is fed to an activated sludge system with an SRT of 12.5 days that contains four parallel plug-flow aeration basins and two secondary clarifiers. Each basin has three equally-sized zones in series and each zone has a different fine-pore diffuser density (13, 8, and 4%). The wastewater temperature is 15 °C and the plant elevation is 300 m. The aeration alpha factor (i.e. ratio of the oxygen mass transfer coefficient in process water to clean water) was assumed to vary between 0.5 in the 1st zone, 0.6 in the 2nd zone, and 0.7 in the 3rd zone. The simulations results are sensitive to the alpha factor, but all scenarios studied below used the same alpha factors and the relative comparisons should still apply to other alpha factor values. The plant layout as represented in SIMBA# is shown in Figure 2.

The following scenarios were simulated for 7 days using a diurnal influent loading pattern:

Base case: according to the original setup from the USEPA Design Manual for Fine-Pore Aeration Systems (USEPA 1989).

Scenario 1: increased diffuser density in the last zone and a most-open valve (MOV) controller to manipulate the header pressure set point.

Scenario 2: an ammonia controller manipulates the set points of the DO controllers to maintain an ammonia set point in the last zone of 1.5 mg/L. Lower and upper bounds of 0.5 and 3 mg/L respectively are imposed on the DO set point calculated by the ammonia controller to ensure adequate mixing and prevent excessive aeration.

_{x}-N) concentrations for all three scenarios presented above are shown in Figure 8. In the Base Case, with DO control and no pressure optimisation, the effluent ammonia data show peaks as high as 3 mgN/L as the aeration system cannot supply the required airflow in the necessary zones at all times. In Scenario 1, with DO control and pressure optimisation, the effluent ammonia peaks are close to 1 mgN/L because the DO control system can now supply the required airflow. In Scenario 2, with ammonia-based aeration control (ABAC), the effluent ammonia only stays at the set point of 1.5 mgN/L for short periods, due to valve position constraints and a lower limit on the DO set point that is imposed to ensure adequate mixing. The objective of ammonia-based aeration control is to keep the effluent ammonia close to a target that meets effluent guidelines, but is higher than would be achieved if a constant DO set point of 2 mg/L was maintained, so that energy savings can be realised. Scenario 2 shows that this may not be fully possible in reality due to system constraints such as valve positions and minimum airflow requirements for mixing.

The detailed aeration system model also predicts blower efficiency, and this allows accurate comparison of the energy consumed. Table 1 shows a comparison of weekly energy consumption and the energy consumption per kg of BOD_{5} treated for the three cases. The energy consumption predicted by a model that does not account for equipment limitations or constraints and assumes that the blowers have a constant efficiency (i.e. the traditional approach to aeration system modelling) is also provided in Table 1 for comparison.

Scenario | Weekly energy consumption (kWh) | Energy consumed per mass of BOD_{5} treated (kWh/kg BOD_{5}) | % Energy reduction compared to previous case |
---|---|---|---|

Base case: no pressure optimisation and default diffuser distribution | 22,500 | 0.77 | – |

Pressure optimisation and improved diffuser distribution | 19,000 | 0.65 | 16 |

Ammonia-based aeration control: pressure optimisation, improved diffuser distribution | 15,500 | 0.53 | 18 |

Classic, simplified approach ammonia-based aeration control: constraints not modelled, constant blower efficiency | 12,700 | 0.44 | 18 |

Scenario | Weekly energy consumption (kWh) | Energy consumed per mass of BOD_{5} treated (kWh/kg BOD_{5}) | % Energy reduction compared to previous case |
---|---|---|---|

Base case: no pressure optimisation and default diffuser distribution | 22,500 | 0.77 | – |

Pressure optimisation and improved diffuser distribution | 19,000 | 0.65 | 16 |

Ammonia-based aeration control: pressure optimisation, improved diffuser distribution | 15,500 | 0.53 | 18 |

Classic, simplified approach ammonia-based aeration control: constraints not modelled, constant blower efficiency | 12,700 | 0.44 | 18 |

As shown, each successive enhancement to the air supply and aeration control system results in a reduction in energy consumption. The potential energy savings with ammonia-based aeration control (i.e. 18% lower energy consumption as compared to conventional DO control with header pressure optimisation) are consistent with the full-scale savings of 16 to 20% reported by Rieger *et al.* (2012) and Amand *et al.* (2013). The savings suggested by the traditional approach to modelling aeration systems (i.e. with no constraints and a constant blower efficiency), are unreasonable given the full-scale results reported in the review paper by Amand *et al.* (2013).

This study demonstrates that detailed aeration system modelling can not only provide improved estimates of WRRF and aeration control system performance, it also allows more accurate comparison of the energy consumption and costs of different aeration control strategies as compared to the traditional simplified method of aeration system modelling.

## CONCLUSIONS AND SIGNIFICANCE

A comprehensive model of WRRF aeration systems has been developed that captures both the air supply system and the oxygen transfer to the bulk liquid. The aeration system model can be directly connected to process and controller models. This allows more realistic modelling of the overall plant performance, with the aeration system having the largest impact on treatment efficiency and being the largest energy consumer. The new integrated model can be used for improved plant designs, optimised piping layouts and diffuser distribution, and will allow development of tailored control solutions taking treatment performance and equipment constraints into account. Accurate dynamic energy optimisation studies that take into account varying blower efficiencies are also now possible. An additional benefit is accurate prediction of airflow distribution, making it possible to estimate unmeasured DO concentrations.

The integrated model connecting process, aeration system and control models enables engineers to trouble-shoot highly complex, interactive, and dynamic aeration control systems and support the design and selection of appropriate wastewater treatment equipment.