At wastewater treatment plants (WWTPs) aeration is the largest energy consumer. This high energy consumption requires an accurate assessment in view of plant optimization. Despite the ever increasing detail in process models, models for energy production still lack detail to enable a global optimization of WWTPs. A new dynamic model for a more accurate prediction of aeration energy costs in activated sludge systems, equipped with submerged air distributing diffusers (producing coarse or fine bubbles) connected via piping to blowers, has been developed and demonstrated. This paper addresses the model structure, its calibration and application to the WWTP of Mekolalde (Spain). The new model proved to give an accurate prediction of the real energy consumption by the blowers and captures the trends better than the constant average power consumption models currently being used. This enhanced prediction of energy peak demand, which dominates the price setting of energy, illustrates that the dynamic model is preferably used in multi-criteria optimization exercises for minimizing the energy consumption.

## GLOSSARY

*A,B,C*Parameters of the generic blower curve based on

*N*(–)*A*_{PL},B_{PL},C_{PL}Parameters of the power law (–)

*A*_{QL},B_{QL},C_{QL}Parameters of the quadratic law (–)

*BC*Blower curve

*BC*_{VFD}Blower curve when controlled by a variable-frequency drive

*d*Air line inside diameter (mm)

*ƒ*_{IGV}Guide vane opening fraction (–)

- ƒ
_{Diff}Linear pressure loss factor (m H

_{2}O/(Nm^{3}/(h·m^{2}))) *f*_{fouling}Fouling factor (–)

*f*_{fouling,max}Maximum fouling factor (–)

*FP*Fraction of the power consumption at full load (–)

*FPL*Friction power loss at actual operating conditions (kW)

*g*Gravitational acceleration (m/s²)

*H*_{0}Cut-off head (m H

_{2}O)*H*_{w}Height of water above the diffusers (m)

*k*Experimental scaling factor (–)

*K*_{v}Valve-specific flow factor (Nm³/h)

*L*Air line length (m)

*L*_{equiv}Equivalent pipe length (m)

*L*_{fittings}Equivalent pipe length for fittings (m)

*L*_{pipe}Real pipe length (m)

*N*Relative blower speed (–)

*n*Dimensionless constant for air (0.285) (–)

*N*_{desired}Desired relative blower speed (–)

*OP*Operating point

*OP*_{throttling}Operating point when controlled with outlet throttling

*OP*_{VFD}Operating point when controlled by a variable-frequency drive

*p*_{blower}Blower outlet pressure (kPa)

*p*_{in}Inlet pressure (kPa)

*p*_{m}Mean system pressure (kPa)

*p*_{out}Pressure at the blower outlet (kPa)

*p*_{out,IGV}Pressure at the blower outlet in the case of inlet guide vane control (kPa)

*p*_{std}Atmospheric pressure at sea level (kPa)

*P*Power draw (kW)

*P*_{actual}Actual power draw (kW)

*PV*_{a}Saturated vapour pressure of water (kPa)

*Q*_{1},*Δp*_{1}Flow rate – pressure combination on the blower curve (Nm³/h, kPa)

*Q*_{2},*Δp*_{2}Flow rate – pressure combination on the blower curve (Nm³/h, kPa)

*Q*_{3},*Δp*_{3}Flow rate – pressure combination on the blower curve (Nm³/h, kPa)

*Q*_{Air}Airflow rate (Nm³/h)

*Q*_{Air,actual}Actual airflow rate (Nm³/h)

*Q*_{Air,desired}Desired airflow rate (Nm³/h)

*Q*_{Air},_{in}Incoming air flow rate (Nm³/h)

*Q*_{Air},_{in,N}Normalized volumetric air flow rate (Nm³/h)

*Q*_{BEP}Airflow rate at which the best efficiency is reached (Nm³/h)

*Q*_{design}Design airflow rate (Nm³/h)

*Q*_{max}Maximum airflow rate (Nm³/h)

*Q*_{0}Blower's theoretical airflow rate at full speed and

*p*=_{out}*p*(Nm³/s)_{in}*R*Universal gas constant (J/(K.mol))

*RH*Relative humidity (–)

*SC*System curve

*SC*_{throttling}System curve when controlled with outlet throttling

*t*Time (d)

*t*_{last cleaning}Last cleaning time (d)

*T*_{in}Air temperature at the blower inlet (K)

*Z*Altitude above sea level (m)

*α, β*Experimental scaling factors (–)

*η*_{m}Mechanical efficiency (–)

*η*_{max}Maximum efficiency (–)

*η*_{min}Minimum efficiency (–)

*η*_{e}Electrical efficiency (–)

*η*_{p}Pneumatic efficiency (–)

*η*_{v}Volumetric efficiency (–)

*η*_{VFD}Variable frequency drive efficiency (–)

*η*_{t}‘Wire-to-air’ efficiency or total efficiency (–)

*η*_{throttling}Efficiency for outlet throttling control (–)

*ρ*_{air}Relative specific gravity of air (kg/m

^{3})*ρ*_{w}Density of the water (kg/m

^{3})*Δ*_{η}Difference between the maximum and minimum efficiency (–)

*Δp*_{design}Design pressure difference (kPa)

*Δp*_{DWP}Diffuser dynamic wet pressure (kPa)

*Δp*_{line}Pressure losses in the air line (kPa)

*Δp*_{max}Maximum pressure (kPa)

*Δp*_{system}Total pressure loss in the system (kPa)

*Δp*_{w}Water head above the diffuser (kPa)

*Δt*_{cleaning}Periods in between consecutive cleaning (kPa)

## INTRODUCTION

One of the main challenges for the optimization of wastewater treatment plants (WWTPs), today, is the proper evaluation of all important performance indicators such as effluent quality (including priority pollutants), energy consumption and greenhouse gas emissions. At WWTPs aeration is the largest energy consumer (Tchobanoglous *et al.* 2004; Devisscher *et al.* 2006; Ast *et al.* 2008; Fenu *et al.* 2010; Zahreddine *et al.* 2010) and as such aeration energy consumption and related costs are an essential factor to be considered in the optimization of WWTPs.

Key factors that influence WWTP aeration cost are the type of aeration blower employed, the aeration system configuration (e.g. diffuser types, water head and piping characteristics) and the control strategy implemented on the aeration system. In addition it is important to consider the application of different energy pricing structures (e.g. time-of-use rates) and charges (e.g. energy usage, peak power demand charges) in the different billing terms (Aymerich *et al.* 2015). In order to appropriately consider the different energy pricing structures one needs a time varying or dynamic prediction of the energy consumption.

The blowers employed in fine bubble diffuser aeration systems are compressors operating at low relative pressures and can be classified into two broader classes, i.e. centrifugal and positive displacement (PD) types (Henze 2008). To date, three main control strategies are implemented to enable ‘turn-up’ or ‘turn-down’ capacity of these aeration blowers, namely variable inlet guide vane (IGV) control, outlet throttling (OT) control and variable frequency drive (VFD) control.

Despite the increasing level of detail in wastewater treatment process models, oversimplified energy consumption models (i.e. constant ‘average’ power consumption), without any mechanistic knowledge, are still being used in design and optimization exercises (Copp 2002; Rosso & Stenstrom 2005; Gernaey *et al.* 2006; Martín de la Vega *et al.* 2013; Wambecq *et al.* 2013). Only a few publications mention the idea of including more rigour in modelling the aeration supply side but they fail to give a clear description of the details and implementation (Alex *et al.* 2002; Beltrán *et al.* 2011; Arnell & Jeppsson 2015). As these wastewater treatment process models have the interesting potential to be used in multi-criteria optimization exercises (e.g. optimizing effluent quality, greenhouse gas emissions and operational costs simultaneously (Flores-Alsina *et al.* 2014), they may lead to poor predictions and their use in optimization could lead to suboptimal operation. There is a clear hiatus in knowledge specifically with regard to rigorous mechanistic models for energy or cost optimisation of these systems. As described above, such models have not yet been reported.

This paper aims at developing an original and novel dynamic model for more accurate prediction of aeration energy costs in activated sludge systems, equipped with submerged air distributing diffusers (producing coarse or fine bubbles) connected via piping to blowers. This is needed to overcome the imbalance in the coupled sub-models (Amaral *et al.* 2016). The objective of the proposed model is to allow for dynamically and accurately simulating the power consumed by an aeration system as a function of (a) the physical characteristics of the aeration system (i.e. blowers, piping, diffusers), (b) the water height in the aerated tanks and (c) the volumetric air flow rate imposed by a control system. The remainder of the paper will illustrate the dynamic model, its calibration and application to the WWTP of Mekolalde (Spain). Finally, a comparison is made with the currently frequently used average power consumption models, and the preferable use of the newly proposed model in optimisation efforts for energy cost minimisation is explained.

## MATERIALS AND METHODS

### Centrifugal and PD blowers

Similar to pumps, aeration blowers are classified into two main categories: (i) centrifugal blowers and (ii) PD blowers. Centrifugal blowers, sometimes referred to as dynamic type blowers, have the air intake along the axis of rotation at the impeller centre and continuously discharge air radially. This rotational action increases the kinetic energy within the air stream, thereby increasing the pressure over the system (Henze 2008).

PD blowers utilise a different approach compared to that of centrifugal blowers by virtually moving ‘batches' of air from the blower inlet to the oulet (Henze 2008). The result is that PD blowers have the capacity to operate against higher ouput pressures than centrifugal blowers for the same air flow rates (Henze 2008). However, the efficiencies of PD blowers are lower than those of centrifugal blowers, specifically at high air flow rates. In addition, there is a significant difference between the characteristic blower curves of centrifugal and PD blowers and this needs to be accounted for in the models.

The energy consumption for blowers, similar to that of pumps, is a function of air flow rate, ambient conditions of the inlet air, efficiencies and discharge pressure. However, the compressibility of air needs to be considered for blowers and this introduces significant differences between the characteristics of aeration systems compared to the characteristics influencing the water and sludge pumps (WEF 2009). The aeration blower process can be described as an adiabatic compression process (Tchobanoglous *et al.* 2004; WEF 2009), which can be defined as a thermodynamic process where no heat is lost or added to the process. Technically this is valid for aeration systems where heat loss to the environment is negligible, e.g. well-insulated systems, where temperature changes in the system are the net result of a change in pressure.

*Q*), decreasing as function of the pressure. This relation is described by the blower characteristic curve (Figure 1), which is as well as the blower efficiency usually provided by the manufacturer. The total pressure or head delivered by the blower shows a monotonic decreasing trend with increasing flow rate, whereas the blower efficiency (Figure 1) shows an optimum with varying flow rate. This optimum is more explicit for centrifugal blowers than for PD blowers. This optimum of the blower efficiency curve is called the best efficiency point (BEP), although the term usually refers to the flow rate at which the best efficiency is reached (

_{Air}*Q*).

_{BEP}While in operation, a blower experiences a certain pressure, which is both of static and dynamic nature, caused by the system. This varying pressure caused by the system is expressed by the system curve (Figure 1). The most important factors influencing the system curve are (i) the pressure losses in the air line due to friction caused by the piping and in-line equipment, (ii) the diffuser dynamic wet pressure (DWP) and (iii) the water head above the diffuser.

The system curve and the blower curve intersect in one point only, i.e. the duty point or operating point (OP), expressing the only possible flow rate and pressure in that particular system with that particular blower configuration and blower settings (e.g. speed) (Figure 1). The OP also coincides with a certain efficiency and power consumption. For a well-designed system this OP should be as close as possible to the BEP.

The efficiency of centrifugal aeration blowers can have a significant impact on the energy requirement for these units during operation and is dependent on the blower type, design, air conditions and control strategies (Bureau of Energy Efficiency 2006). Blower efficiency is the ratio of the output kinetic energy contained in the airflow stream over the electrical energy input at the wire supply point. The overall energy efficiency of a centrifugal aeration blower (*η*_{t}) considers the pneumatic efficiency (*η _{p}*), the volumetric efficiency (

*η*) (air tightness of the airline), the electrical efficiency (

_{v}*η*) (including losses incurred from the controller and transformers) and the mechanical efficiency (

_{e}*η*) (including losses incurred from the motor, bearings and shaft).

_{m}### Control strategies

Control strategies can be designed to ensure process stability or for the optimization of the overall plant including energy cost. However, changing or controlling the OP, in order to meet operational requirements, can only be established by modifying either the system curve (e.g. by using valves) or the blower curve (e.g. by changing its speed). However, in doing so, the energy requirement of a specific aeration system is changed and should be accounted for in the overall evaluation.

Three control strategies are commonly implemented for aeration blowers: (a) VFD control, (b) variable IGV control and (c) OT (with either an in-line valve or a blow-off valve). The selection of the control strategy is based on the blower type. VFD control can be applied to both centrifugal and PD blowers. Actually, VFD control is the only realistic control strategy to be implemented for PD blowers. With regard to OT both the blow-off valve and the in-line throttling valve are commonly used as a control strategy under operating conditions. A blow-off valve or vane is mostly used (i) at the start-up of large centrifugal blowers in order to reach steady state conditions and (ii) as a security measure to prevent damage due to too high pressures in the aeration system.

Variable IGV control is commonly applied as a control strategy to centrifugal blowers. The design of IGV control is based on rotatable guide vanes fitted at the inlet section, before the impeller, of a centrifugal blower. These guide vanes are commonly straight-blades with low aerodynamic resistance that can adjust within a 90° angle as they are fitted in the inlet air flow path (Xiao *et al.* 2007). In practice, the capacity of most IGV-controlled blowers can only be turned down to about 60% to 80% of the maximum capacity. On adjustment of the guide vanes angle, the OP of the aeration system is shifted due to a change in the blower curve (Boyce 2002).

Single stage, lower speed centrifugal blowers can be controlled with OT using an in-line valve similar to throttling on centrifugal pumps. The characteristic of the system curve is based on a control valve being fully open (in system design); thus any change in the setting of the control valve will result in an increase in pressure and a change in the system curve, similar to the case of centrifugal pumps. OT is less commonly used as control strategy for aeration systems and will not be addressed in the remainder of the paper.

### Mathematical model

In this section, the generic dynamic models that were developed for both uncontrolled and controlled aeration systems are explained. In contrast to textbook knowledge and blower manufacturer data (that are often intended for selecting a blower for a certain application), these models can be used to dynamically calculate the energy consumption of a certain motor-blower combination, thereby accounting for the required flow rate as well as the control actions. The basic assumption is always that the dynamic blower model input is the desired flow rate (*Q _{Air,desired}*), as demanded by the controller, and that the dynamic model outputs are the actual flow rate (

*Q*) and actual power draw (

_{Air,actual}*P*), given certain blower and system characteristics, which need to be specified by the user. These system characteristics can be parameters that are fixed during the simulation (e.g. the blower curve at full speed, piping layout) or dynamic model inputs that vary in time (e.g. the water level in the aerated tank, air temperature). Note that most equations for variable speed blowers can also be written in terms of the relative blower speed (

_{actual}*N*) as the independent variable. This allows transforming the model in a way that desired speed is the input signal (

*N*) rather than

_{desired}*Q*. This approach links better to reality, where the WWTP's automatic control system instructs the actuators to run at a certain percentage of their maximum capacity. However, in an integrated water quality modelling context, it is common to use the blower flow rate as the controlled variable.

_{Air,desired}Key issues to be considered when modelling the energy consumption of aeration systems are: (1) energy requirement for compression, (2) inlet conditions of the air, (3) system characteristic curve, (4) blower characteristic curve, (5) blower efficiency and (6) the type of process control strategy employed.

#### The mathematical model for the energy requirement for compression

The blower energy consumption, in the case of centrifugal blowers for both fine and coarse bubble diffuser aeration systems, can be estimated using the expression for power requirement *P* [kW] for adiabatic compression (Tchobanoglous *et al.* 2004). However, considering the significant impact of the dynamics in the inlet air on the energy requirements, a modified form proposed by WEF (2009) is used (Equation (1)).

*Q*is the normalized volumetric air flow rate [Nm

_{Air},_{in,N}^{3}/h] and

*n*is a dimensionless constant for air (0.285) [–]. The number 9.816 × 10

^{−4}lumps constants related to air characteristics (amongst others, the universal gas constant

*R*and the number of moles per volume of air) and those related to the use of

*Q*instead of the air mass flow rate.

_{Air,in,N}*N*the relative rotational speed [–],

*Q*the blower's theoretical flow rate at full speed, and

_{0}*p*=

_{out}*p*[Nm

_{in}^{3}/s] and

*FPL*is the friction power loss at actual operating conditions [kW]. The latter is to be received from the manufacturer, but is typically around 5% of the power consumption at full load (maximum pressure

*Δp*[kPa]) at that speed

_{max}*N*. This means that if

*FPL*would not be available, an acceptable default value could be calculated as in Equations (3) and (4):

with *FP* the fraction of the power consumption at full load (0.05 corresponds to 5%).

*Q*) need to be transformed into a normalized desired air flow rate

_{in}*Q*(Equation (5)). The definition of standard conditions varies a lot, depending on the application, the country, etc., but 101,325 kPa, 293 K and 50% relative humidity (

_{Air,in,N}*RH*) are common in Europe (International Organization for Standardization 2002). where

*RH*is the relative humidity [–],

*PV*is the saturated vapour pressure of water at the actual temperature [kPa],

_{a}*T*is the air temperature at the blower inlet [K],

_{in}*p*is the inlet pressure [kPa], which can be approximated to consider altitude using Equation (6) (The Engineering Toolbox 2005). where

_{in}*p*is 101,325 kPa and

_{std}*Z*is the altitude above sea level [m].

#### The mathematical model for the system curve

*Δp*), (ii) the diffuser dynamic wet pressure (

_{line}*Δp*) and (iii) the water head above the diffuser (

_{DWP}*Δp*). The total pressure loss in the system (

_{w}*Δp*) is calculated as the sum of the three pressure losses (Equation (7)).

_{system}*et al.*(2004) quantify the pressure losses based on a modified form of the Darcy–Weisbach equation. Alternatively, WEF (2009) describes the pressure loss in the air line using an empirical formula for air flow in clean steel pipes (Equation (8)). where

*T*is the air temperature [K],

_{in}*L*is the air line length [m],

*d*is the air line inside diameter [mm],

*Q*is the normalized air flow rate [Nm

_{Air,in,N}^{3}/h],

*K*is the valve-specific flow factor [Nm

_{v}^{3}/h],

*ρ*is the relative specific gravity of air [–],

_{air}*p*is the pressure at the blower outlet (= the pipe inlet) [kPa] and

_{out}*p*is the mean system pressure [kPa]. The value of

_{m}*p*can be calculated iteratively according to Equation (9). Friction losses due to fittings are included in this equation via the equivalent pipe length method (Equation (10)). with

_{m}*L*the equivalent pipe length [m] of a fitting (Table 1).

_{equiv}Fitting | Equivalent pipe length [m] |
---|---|

90° elbow | 30 d |

45° elbow | 16 d |

T straight through | 20 d |

T through side | 60 d |

Transition | 20 d |

Open butterfly valve | 20 d |

Fitting | Equivalent pipe length [m] |
---|---|

90° elbow | 30 d |

45° elbow | 16 d |

T straight through | 20 d |

T through side | 60 d |

Transition | 20 d |

Open butterfly valve | 20 d |

Second, the diffuser dynamic wet pressure loss (*Δp _{DWP}*) is the pressure loss over the fine bubble diffuser membrane, disk or plate during operation under submerged conditions (US EPA Risk Reduction Engineering Laboratory 1989). The variation of DWP with air flow rate is product-specific. Most manufacturers provide this variation in tabulated form (usually two points only). Considering the limited amount of information available a linear approach is adopted (first term in Equation (11)).

The increase of the pressure drop over the diffuser due to membrane fouling is another factor affecting the DWP (Rosso *et al.* 2008). After cleaning, the pressure drop, and consequently the power consumption, returns to approximately its original level.

*Δp*) is calculated according to Equation (11), derived from Rosso

_{DWP}*et al.*(2008). where

*Q*[Nm

_{Air,in,N}^{3}/h] is the normalized air flow rate,

*ƒ*is the linear pressure loss factor [m H

_{Diff}_{2}O/(Nm

^{3}/(h·m

^{2}))],

*H*

_{0}is the cut-off head [m H

_{2}O],

*ρ*is the density of the water [kg/m

_{w}^{3}] and

*f*is a fouling factor [–]. The latter is a function of time (Equation (12)) and increases linearly from 1 to

_{fouling}*f*[–] over a period of

_{fouling,max}*Δt*[d] (the cleaning interval): with

_{cleaning}*t*the current time [d] and

*t*the last cleaning time [d].

_{last cleaning}Both *ƒ _{Diff}* and

*H*

_{0}can be determined from measuring and plotting the DWP at different airflow rates.

*Δp*is the pressure loss due to the water head [kPa] and

_{w}*H*is the (variable) water height above the diffuser [m].

_{w}#### The mathematical model for the blower curve

*et al.*2014). where the coefficients

*A*,

_{PL}*B*and

_{PL}*C*(Equations (15)–(17)) can be determined as a function of three given (

_{PL}*Q*,

_{Air}*p*) combinations (Figure 3, left).

Note that *p _{out}*,

*p*,

_{in}*p*

_{1},

*p*

_{2}and

*p*

_{3}are used here as absolute pressures, whereas in most manufacturer data sheets only the differential pressure over the blower (

*Δp*,

_{out}*Δp*

_{1},

*Δp*

_{2}and

*Δp*

_{3}) is considered.

Following the pragmatic approach for pumps described in Walski *et al.* (2004), this method constructs a blower curve expressing the pressure (*p*) as a continuous function of the flow rate (*Q _{Air,in,N}*). Point 1 (0,

*p*

_{1}) should be the cut-off pressure at zero flow, point 2 (

*Q*

_{2},

*p*

_{2}) is to be selected in the real operating window of the blower (probably around the BEP), and point 3 (

*Q*

_{3},

*p*

_{3}) is to be selected at a larger air flow rate. In a situation where no blower curve is available, a default blower curve can be constructed (Figure 3, right) based on the selection of a single desired OP (

*Q*

_{2},

*p*

_{2}), near a design OP or BEP. The curve is then completed based on the following two assumptions. First, the projected maximum pressure at zero air flow (

*Δp*

_{1}) is 1.45 times

*Δp*

_{2}and, second, the projected maximum blower flow, at zero pressure loss (i.e.

*p*

_{3}=

*p*or

_{in}*Δp*

_{3=}0), is 1.5 times

*Q*

_{2}.

*A*,

_{QL}*B*and

_{QL}*C*(Equations (19)–(21)) can be determined as a function of three given (

_{QL}*Q*,

_{Air}*p*) combinations (Figure 5, left). Equation (18) actually describes a parabolic shape, so two solutions are possible: one

*p*corresponds to two different values for

_{out}*Q*. Obviously a boundary check is necessary and only the left half of the parabolic function should be used, i.e. for

_{Air}*Q*≤

_{Air}*Q*. The latter can be found from the first derivative (Equation (23)) of Equation (22).

_{max}*Q*,

_{design}*Δp*) can be used as (

_{design}*Q*

_{1},

*Δp*

_{1}), assuming

*Δp*to be the maximum pressure to operate against at full speed. The remaining two points are then calculated with Equations (24)–(27).

_{design}#### The mathematical model for the blower efficiency (*η*_{t})

*η*the maximum and minimum efficiency [–] respectively,

_{min}*Δ*the difference between the maximum

_{η}*η*[–] and minimum efficiency,

_{max}*Q*the BEP flow rate and

_{BEP}*Q*the normalized flow rate.

_{Air,in,N}The efficiency of PD blowers differs from that of centrifugal blowers because they operate in a completely different manner. In the calculation of the power consumption for PD blowers (Equation (2)) the term *FPL*, i.e. the friction power loss at actual operating conditions, was introduced to quantify the efficiency loss induced by the rotary parts causing shear on the inside casing of the blower. This shear depends on the rotational speed and the blower characteristics (Equations (3) and (4)).

The blower efficiency of centrifugal blowers normally transcends that of PD blowers (Henze 2008). For PD blowers, efficiency ranges from 50 to 60% are observed and from 72 to 80% for single stage centrifugal blowers with IGV control.

#### Mathematical modelling of control for aeration blowers

Since the exponent 2−*C*, in Equation (30), is not an integer, an iterative or interpolation method is needed to solve for N. By filling in the desired *Q _{air,in,N}* and several values for

*N*in Equation (30), the corresponding pressures can be calculated. Next, a linear interpolation yields the

*N*that allows for obtaining the

*p*that corresponds to

_{out}*Q*via the system curve.

_{Air,in,N}*N*into Equation (28) (Equation (34)). The incorporation of the relative blower speed

*N*[–] in the generic blower curve (Equation (18)) for PD blowers results in Equation (35). with where

*Q*

_{0}[m

^{3}/h] is the flow rate the blower would produce at full speed (

*N*= 1) when

*p*=

_{out}*p*.

_{in}##### IGV control

As variable IGV control is mainly applied as a control strategy to centrifugal blowers, only this application will be dealt with. Determining the efficiency (*η _{t}*) for IGV control is different and probably more complex than for VFD control. Unfortunately no quantitative information on IGV-controlled blowers' efficiency was found in literature. Due to the lack of a formula describing the efficiency distribution when using IGV control, a preliminary workaround was developed based on the expected curve for energy requirement.

*ƒ*[–] is the guide vane opening fraction (1 = 100% open),

_{IGV}*k*is an experimental scaling factor,

*Q*is the operating flow rate (determined using the system curve),

_{Air,in,N}*p*is the outlet pressure (determined using the system curve) and the variables

_{out,IGV}*A*,

*B*and

*C*can be determined as described for the derivation of a centrifugal blower curve using Equations (15)–(17).

## RESULTS AND DISCUSSION

The model was implemented in the WEST^{®} modelling and simulation software (mikebydhi.com) and applied for the aeration system at the Mekolalde WWTP located in Bergara (Guipúzcoa, Spain). The model is validated in two steps. In the first instance the model is compared to manufacturer data and in the second instance a measurement campaign is conducted.

The Mekolalde WWTP (originally designed to treat wastewater of 40,000 population equivalent) has two primary sedimentation tanks (3 m height and 24 m diameter) followed by three waterlines, of which at the time of the measurement campaign only one was in operation. Each waterline consists of a modified Ludzack–Ettinger process (one denitrification tank of 722 m^{3} and three nitrification tanks of 561 m^{3} each). Two secondary clarifiers (3 m height and 24 m diameter) separate the sludge from the treated water. The secondary sludge is then further thickened in a dissolved air flotation unit (2 m height and 6 m diameter) and mixed with the primary sludge coming from a thickener (3 m height and 8 m diameter). The sludge is finally further treated in an anaerobic digester (1,600 m^{3}).

### Comparison to manufacturer data

From the manufacturer's technical info sheet (Figure 6), three flow rate–pressure (*Q _{Air}*,

*p*) combinations were derived (at 2,900 rpm, assumed to correspond with

*N*= 1) and used as input to the PD blower model: (4,250 Nm

^{3}/h, 70 kPa), (4,375 Nm

^{3}/h, 40 kPa) and (4,575 Nm

^{3}/h, 10 kPa). The water height in the aerated tank was assumed to be constant at 5.7 m above the diffuser surface and the input signal (desired air flow rate during 1 day) varied between 1,615 and 4,500 Nm

^{3}/h with an average of 2,765 Nm

^{3}/h. The aeration system consisted of a 100 m pipe (diameter 0.25 m), 45 m equivalent pipe length for fittings and bends, and a diffuser surface area of 73.23 m

^{2}. The motor efficiency was put at 100% to enable comparison of simulated power consumption with the manufacturer data (the bottom graph in Figure 6 shows the power absorbed at the motor-blower coupling). Other parameters were left at their default values.

Simulations show a nearly constant system pressure, i.e. the impact of the varying flow rate (influencing *Δp _{DWP}* and

*Δp*) is small compared to the static head of the liquid

_{line}*Δp*. Moreover, the simulation results show an excellent match between the predicted air flow rates and the manufacturer data (Table 2). The simulated power consumption, on the other hand, shows a systematic underestimation compared to the manufacturer-supplied power consumption data. The presumed cause is an underestimation of the friction power loss. By adjusting the

_{w}*FP*in Equation (4) from 5 to 12%, assuming higher friction power losses for this pump type, the predictions improve significantly.

Air flow rate [Nm^{3}/h] | Power consumption [kW] | |||
---|---|---|---|---|

Relative speed N [–] | Simulation | Manufacturer | Simulation min–max | Manufacturer |

1.00 (2,900 rpm) | 4,290 | 4,290 | 84–91.3 | 91 |

0.69 (2,000 rpm) | 2,840 | 2,800 | 57–62 | 64 |

0.51 (1,500 rpm) | 1,981 | 1,980 | 42–46 | 48 |

Air flow rate [Nm^{3}/h] | Power consumption [kW] | |||
---|---|---|---|---|

Relative speed N [–] | Simulation | Manufacturer | Simulation min–max | Manufacturer |

1.00 (2,900 rpm) | 4,290 | 4,290 | 84–91.3 | 91 |

0.69 (2,000 rpm) | 2,840 | 2,800 | 57–62 | 64 |

0.51 (1,500 rpm) | 1,981 | 1,980 | 42–46 | 48 |

### Comparison to real plant data

In the next step the model was confronted with real plant data. The diffuser area was calculated based on the number of diffusers (595) and their active surface area per diffuser (380.9 cm^{2}). Also the altitude, pipe diameter, pipe length and minor losses equivalent were derived from the system. The flow rates for the definition of the blower curve (*Q*_{1}, *Q*_{2} and *Q*_{3}) were derived from the manufacturer data.

_{2}O, motor efficiency 0.80 ± 0.03 and friction power losses = 0.36 ± 0.02) the model proved to give an accurate prediction of the real energy consumption by the blowers (Figure 7). The root of the sum of squared errors totalled 1.103 (versus 12.830 with the parameters derived in the comparison with the manufacturer data). A thorough calibration procedure, which will not be explained here as it falls outside the scope of this paper, results in a slightly better root of the sum of squared errors (1.064 versus 1.103) pointing towards an even better fit (Figure 7). In addition, the uncertainty bounds on the parameter estimates improved drastically (

*FP*= 9.64 * 10

^{−2}± 5 * 10

^{−5},

*d*= 2.8521 * 10

^{−1}± 9 * 10

^{−5}and

*Δp*

_{3}= 4377.5217 ± 6 * 10

^{−4},

*η*= 5.502 * 10

_{m}^{−1}± 3 * 10

^{−4}).

### Comparison to other models

In view of a global optimization study for WWTPs, including many different parameters such as effluent quality, energy consumption and greenhouse gas emissions, the newly developed and rigorously calibrated model adds another dimension; i.e. the model restores the balance by adding dynamics in the calculation of the energy consumption, which have a smoothening effect compared with the flow rate data. These dynamic calculations, which are worked out in a high detail as for the influent characteristics and the biokinetic model, allow now for a more accurate estimation of the peak energy demand. This peak energy demand is crucial as it determines the energy price setting.

Furthermore the study demonstrated that care has to be taken when transferring results from another study and a proper evaluation of the background should be performed; i.e. the type of blowers and the system characteristics (height of the water level, type of diffusers, etc.) greatly influence the obtained results.

## CONCLUSIONS

A new dynamic model for a more accurate prediction of aeration energy consumption in activated sludge systems, equipped with submerged air distributing diffusers (producing coarse or fine bubbles) connected via piping to blowers, has been developed and demonstrated. The new model proved to give an accurate prediction of the real energy consumption by the blowers and captures the trends better than the constant average power consumption models currently being used. In addition it is demonstrated that transferring model parameters from one installation to another introduces a large risk in incorrectly predicting the power consumption.

The results clearly illustrate, also because the cost of energy depends on peak demand values, that the dynamic model is preferably used in multi-criteria optimization exercises for minimizing the energy consumption. The newly developed model improves the balance in the model complexity between the air supply and demand side. This higher complexity is required, as the knowledge of realistic constraints on the air supply is essential for a correct prediction of the biological reactions. A future extension to improve the model could be the addition of the use of multi-stage blowers instead of single stage blowers.

## ACKNOWLEDGEMENTS

The authors would like thank the financial support received from the EU FP7-SME-2008-1 program (project ADD CONTROL 232302) as well all project partners (http://www.addcontrol-fp7.eu/). They would also like to thank the Dommel Waterboard for the data on the energy consumption of their pump.