A simulation benchmark to evaluate the performance of advanced control techniques in biological wastewater treatment plants

A SIMULATION BENCHMARK TO EVALUATE THE PERFORMANCE OF ADVANCED CONTROL TECHNIQUES IN BIOLOGICAL WASTEWATER TREATMENT PLANTS

O.A.Z.Sotomayor1^*, S.W. Park¹ and C.Garcia2

1Laboratory of Simulation and Process Control, Department of Chemical Engineering,

²Laboratory of Automation and Control, Department of Telecommunications and Control

Engineering, Polytechnic School of the University of São Paulo, Av. Prof. Luciano Gualberto,

travessa 3, n° 380, Fax: [phone], São Paulo - SP, Brazil.

E-mail: [e-mail]

(Received: January 10, 2000 ; Accepted:January 11, 2001)

Abstract - Wastewater treatment plants (WWTP) are complex systems that incorporate a large number of biological, physicochemical and biochemical processes. They are large and nonlinear systems subject to great disturbances in incoming loads. The primary goal of a WWTP is to reduce pollutants and the second goal is disturbance rejection, in order to obtain good effluent quality. Modeling and computer simulations are key tools in the achievement of these two goals. They are essential to describe, predict and control the complicated interactions of the processes. Numerous control techniques (algorithms) and control strategies (structures) have been suggested to regulate WWTP; however, it is difficult to make a discerning performance evaluation due to the nonuniformity of the simulated plants used. The main objective of this paper is to present a benchmark of an entire biological wastewater treatment plant in order to evaluate, through simulations, different control techniques. This benchmark plays the role of an activated sludge process used for removal of organic matter and nitrogen from domestic effluents. The development of this simulator is based on models widely accepted by the international community and is implemented in Matlab/Simulink (The MathWorks, Inc.) platform. The benchmark considers plant layout and the effects of influent characteristics. It also includes a test protocol for analyzing the open and closed-loop responses of the plant. Examples of control applications in the benchmark are implemented employing conventional PI controllers. The following common control strategies are tested: dissolved oxygen (DO) concentration-based control, respirometry-based control and nitrate concentration-based control.

Keywords: simulation benchmark, activated sludge processes, wastewater treatment plants, organic matter removal, nitrogen removal, DO concentration-based control, nitrate concentration-based control, respirometry-based control, process control.

INTRODUCTION

Activated sludge is the most widespread process for biological wastewater treatment. In this process, wastewater is mixed with a concentrated biomass suspension responsible for the degradation of pollutants. When microbial degradation processes have come to an end, the sludge flocs are separated from the treated water by sedimentation in a clarifier (or secondary settler). Treated water is discharged into surface waters while concentrated sludge suspension is continuously withdrawn at the bottom of the secondary settler. Most of the concentrated sludge suspension is recycled and mixed again with wastewater entering the treatment plant. The excess sludge produced due to bacterial growth during degradation processes is normally discarded as a fraction of the concentrated sludge flow withdrawn at the bottom of the secondary settler and treated separately in the sludge treatment facilities of the activated sludge plant. The activated sludge process (ASP) has undergone successive modifications since its original application, which have improved its efficiency and expanded its use from the elimination of carbonaceous organic matter to the simultaneous removal of nutrients, especially nitrogen (as nitrate and ammonium).

Biological nitrogen removal occurs in two stages: (1) nitrification, where ammonium is converted to nitrate by autotrophic bacteria under aerobic conditions; and (2) denitrification, where nitrate is converted to nitrogen gas by heterotrophic bacteria under anoxic conditions with the use of organic compounds as reducing agent. Anoxic zones can be placed either in the beginning of the bioreactor (pre-denitrification) or in the end of the bioreactor (post-denitrification). In a pre-denitrifying system, an internal recirculation flow is usually introduced to transport the nitrate rich water back to the anoxic zone.

Biological nutrients removal (BNR) processes inherently offer little operational flexibility. These processes are characterized by stiff dynamics (a wide range of time constants, from a few minutes to several days), nonlinearities, uncertainties, time-variant parameters and multivariability with many cross couplings and variable influent conditions, such as wide variations in the inflow and the composition of the incoming wastewater. From their input/output behavior, these processes can appear to be highly stable until something fails. On the one hand, apparently significant input disturbances do not excite any significant output response, while, on the other hand, a very significant response can occur in the absence of any obvious motivating input disturbance (Beck, 1986). Thus, the process will rarely operate at steady state under manual control and may even require advanced control techniques for satisfactory performance.

As the process is very complex, a large number of specifications are necessary in order to achieve the required performance of the wastewater treatment. One way to improve process efficiency might be by damping disturbances by increasing process inertia (using largesized equipment), which is normally expensive and often unfeasible. Another way is to introduce advanced control techniques, which may provide a reduction in the required residence time, improvement in the quality of the treated effluent and a decrease in the consumption of chemicals and utilities. As a consequence, it is possible to save energy and reduce operational costs, and to obtain a sufficiently low concentration of biodegradable organic matter and low concentrations of nutrient in the outflow along with minimal sludge production.

Automatic control of the ASP is rare for reasons such as a lack of control over the effluent quality, nonexistence of economic incentives for treating the wastewater, lack of reliable sensors and difficulties in applying process control due to a poor understanding of the process behavior. On the other hand most wastewater treatment design engineers and operating personnel are not familiar with process control. Currently there are some relevant facts that are intensifying efforts to actually implement automatic control in the ASP (Lee et al., 1999). Such facts are:

(a) the growing importance of conserving natural sources of freshwater, confirmed by the recent environmental conservation standards, which specify limits for the composition of effluent discharge, in particular with regard to nutrient removal; and

(b) due to the restrictions quoted in the former item and to the increasing volumes of wastewater to be treated, there is an increase in the size and complexity of wastewater treatment plants.

Those efforts to implement automatic control in the wastewater treatment plants are stimulated and made easier by the rapid development of new sensors, the availability of powerful computers and an extensive knowledge of process dynamics in the form of mathematical models.

Many control techniques have been proposed in the literature ranging from classical control, including cascade control, model-based control such as LQG and MPC, adaptive control to rule-based control, including knowledge-based control, neural network control and fuzzy control (Weijers and Preisig, 2000). However, the literature does not provide a clear basis for comparison of these techniques, because of the multifaceted nature of the process under study (i.e different mathematical models, different plant configurations, a variety of influent wastewater characteristic, etc). It is consequently often impossible to determine whether the presented results are primarily due to local factors or if the control technique is generally applicable. From a practical viewpoint, it is not reasonable to experimentally test and verify the effectiveness of all proposed control techniques. Alternatively, given a standardized procedure as a simulation benchmark, it is possible to efficiently evaluate numerous control techniques through realistic/dynamic computer simulations. Simulations provide a cost-effective means for control technique performance evaluation (Coop, 2000).

In this work, a simulation benchmark that represents a continuous flow ASP, in a configuration with pre-denitrification, including the processes of organic matter removal, nitrification and denitrification of domestic effluents, is developed for the unbiased performance evaluation of advanced control techniques in wastewater treatment plants. Validation of the computer simulations is difficult without supporting experimental or full-scale data, but the value of this work is enhanced by the use of models widely accepted by the international community, namely the Activated Sludge Model No.1 from IAWQ (International Association on Water Quality) (Henze et al., 1987) and the double exponential settling velocity model proposed by Takács et al. (1991), which are implemented on Matlab/Simulink v.5.3 (MathWorks, 1999) platform.

The proposed simulation benchmark is a comprehensive description of a standardized simulation protocol including plant layout, simulation models and model parameters, wastewater characteristics and disturbances, performance evaluation and a test procedure for analyzing the open and closed-loop response of the plant.

As application examples of the benchmark, single-loop PI controllers are used in the following control strategies: dissolved oxygen (DO) concentration-based control, respirometry-based control and nitrate concentration-based control.

In order to avoid confusing it with other benchmarks found in the literature, the one herein presented is named ASWWTP-USP Benchmark (Sotomayor et al., 1999a).

MODELING OF THE WASTEWATER TREATMENT PLANT BENCHMARK

Plant Description

The process configuration shown in Figure(1), is a predenitrifying ASP formed by a bioreactor (composed of an anoxic zone and two aerobic zones) and a secondary settler. Each of the compartments of the bioreactor is assumed to have a constant volume (13 m³, 18 m³ and 20 m³, respectively) and to be ideally mixed, whereas the secondary settler (volume=20 m³) is modeled as a series of 10 layers (a one-dimensional model). In nominal operation, the average influent flow, , is 4.17 m³/h, with an average concentration of biodegradable COD of 224 mg/l and a hydraulic retention time of 17.0 h (based on total volume, i.e., bioreactor + secondary settler). The internal recycle flow rate is , the external recycle flow rate is and the wastage flow rate is The airflow rates are and for the first aerobic zone and second aerobic zone, respectively. In the anoxic zone, no airflow rate is assumed.

Bioreactor Model

The model for each bioreactor zone is based on the IAWQ Activated Sludge Model No. 1 (Henze et al., 1987), abbreviated as ASM1. The ASM1 is a mechanistic dynamical model with the capacity of modeling the biological processes of carbonaceous energy removal, nitrification and denitrification, but it does not include processes that describe behaviors under anaerobic conditions (Petersen et al., 2001). In spite of the continuous model updating with the version ASM2 (Gujer et al., 1995; Henze et al., 1997), ASM2d (Henze et al., 1999) and ASM3 (Gujer et al., 1999), the ASM1 is probably the most used in the world for describing the processes that occur in biological treatment of domestic wastewater (Jeppsson, 1996; Weijers et al., 1997; Coen et al., 1998). Due to its great impact in the wastewater treatment community, the ASM1 deserves special attention and can be considered to be state of the art whenever the enhanced biological phosphorous removal process is not considered.

Next the set of equations that is part of the ASM1 is presented, which corresponds to the reaction rates of the process. According to Jeppsson (1996), each equation is explicitly written aiming to demonstrate the complexity of the process, contrary to the original matrix form presented by Henze et al. (1987). The parameters are explained in Table 1.

Heterotrophic biomass :

Autotrophic biomass :

Biodegradable particulate substrate :

Particulate organic nitrogen :

Inert particulate products :

Inert particulate organic matter :

Dissolved oxygen concentration :

Soluble ammonium (and ammonia) nitrogen :



Soluble organic nitrogen :



Soluble nitrate (and nitrite) nitrogen :



Readily biodegradable substrate :



Soluble inert organic matter :

Alkalinity :



In order to obtain the complete set of differential equations for the different states, the reaction rates previously presented have to be complemented by the terms for mass balance. Assuming a system such as that shown in Figure 1, with a bioreactor divided into N zones or compartments (each of the compartments is assumed to have a constant volume and to be ideally mixed), the general mass balance formula for each of the concentrations is given by the following equations:

for k = 1 (first compartment in the input of the influent flow):



for k = 2 to N

where is the volume of the compartment.

for the special case of dissolved oxygen concentration :



where

is the oxygen transfer function,

is the air flow (that comes from the aeration blowers), and

is the oxygen saturation concentration.

Each zone of the bioreactor is implemented using the ASM1, taking into account the following assumptions and modifications:

(a) is assumed that the system operate at constant temperature (15°C);

(b) the concentration is not implemented because it is not important in this study;

(c) the and concentrations are combined into one variable, , as their fractions are not of great interest in this study. Therefore,



(d) to describe the oxygen transfer from gaseous air to dissolved oxygen in the reactor as a function of the air flow rate from the compressors to the aerators, the following model for the oxygen transfer function is used (Olsson et al., 1999):



(e) the saturated dissolved oxygen concentration = 8.65 mg/l;

(f) an equation for the measurement of the bacterial respiration rate was implemented, aiming to evaluate control techniques based on respirometry, according to Bastin and Dochain (1990):



where is the reaction rate for the dissolved oxygen concentration.

The values of kinetic and stoichiometric parameters are the default values for a temperature of 15°C (see Cost 624), as shown in Table 1. These values are typical for neutral pH and domestic wastewater. For more details, see Sotomayor et al. (1999b).

Secondary Settler Model

The secondary settler response is frequently reported as the system bottleneck. It is an important element in determining the overall process dynamics because of the close coupling between reactor and settler. Despite the importance of this step, only rare studies have explicitly mentioned it in the complete modeling of the plant.

The secondary settler separates the sludge flocks from the treated water (clarification) and compacts the sludge to be returned to the bioreactor (thickening). But the third and most important feature is that it acts as mass storage for the activated sludge mass operating in the system. This role is important for process control (Marsili-Libelli, 1993). The simulated dynamic response deteriorates significantly when the secondary settler is underloaded because the buffering action of the sludge blanket is lost and bioreactor disturbances are positively reinforced by the recycle loop. This suggests that the primary goal of the control system should be to maintain the sludge level in the secondary settler. Sludge blanket control can lead to swings in bioreactor solids concentrations, what is undesirable. Conversely, a control system designed to regulate only the bioreactor can cause the settler to become underloaded or overloaded. (Attir and Denn, 1978).

Grijspeerdt et al. (1995) conducted a comparative study of several settler models available in the literature and concluded that the double exponential settling velocity model proposed by Takács et al. (1991) most realistically represents the sedimentation/clarification process. The settler is modeled as a tank with several horizontal layers, as shown in Figure 2, where it is assumed that no biological reaction occurs.




The solids mass balance in each layer is given by the following equations (Lindberg, 1997):

where

is the sludge concentration or suspended solids (SS) concentration,

h is the height of each layer,

A is the area of the transversal settler section,

n is the number of layers,

m is the feed layer,

is the solids flow, corresponding to the gravity settling,

is the solids flow, corresponding to the bulk upward movement,

is the solids flow, corresponding to the bulk downward movement,

is the threshold of suspended solids concentration, and

is the double exponential settling velocity function given by Takács et al. (1991):



The settler is implemented, considering the following assumptions and modifications:

(a) effects such as hydrodynamics, biological activity (as denitrification) and compression in the secondary settler are not taken into account;

(b) the soluble concentrations are implemented in the following manner:



These concentrations are considered homogeneous for all the settler layers so that. For the special case of dissolved oxygen concentration, it is assumed that it is consumed within the settler and, consequently, the oxygen concentration in the water leaving the settler is set to zero, which is a realistic assumption (Diehl and Jeppsson, 1998). Therefore,



(c) the total sludge concentration in the settler input is given by (Jeppsson, 1996):



(d) the particulate concentrations in the treated effluent are calculated as follows, for example for :



where is the SS concentration in the first layer. Similarly, the equations for and are obtained.

(e) the particulate concentrations in the recycled sludge and the sludge excess are calculated as follows, for example for :



where is the SS concentration in the last layer.

Similarly, the equations for and are obtained.

The parameter values for the settler are given in Table 2. The operational parameters were obtained from data collected at a full-scale WWTP, in Vanderhasselt (1999). These values were used along with the parameters for medium loading reported in Takács et al. (1991). For more details, see Vanhooren and Nguyen, (1996).




Wastewater Characteristics (Average values)

The following influent wastewater concentrations are proposed, as shown in Table 3. Some of these concentrations were taken from Wikström (1994).




Initial Conditions and Numerical Algorithm

The complete plant model includes approximately 52 large, complex and coupled nonlinear differential equations. Steady-state values are used as initial conditions for the state variables (bioreactor and secondary settler). To simulate the plant model, the Matlab ode15s numerical integrator (Matlab version 5.x) is employed. This algorithm is based on the principle of variable time steps and is especially designed to solve stiff systems, i.e., models where the different processes have very different time constants.

Control Performance Evaluation

The performance evaluation occurs on two levels: the first level is concerned with the local control loops and the second provides a measure of the effect of the proposed control technique on plant response.

Controller Efficiency

Local control loops are evaluated using the integrated squared error (ISE) criterion as the performance index. The ISE is defined as



Effluent Quality

The constraints related to effluent quality are defined so that the average effluent concentration must fall within specific limits. The constraints for the effluent are defined as follows (Singman, 1999):



where



Open-loop Dynamic Response

The open-loop dynamic behavior of the process is presented in order to validate the simulator. The disturbances in the incoming flow are introduced as step functions since the purpose is to test the models rather than to describe a true situation. Moreover, step changes produce a more rapid model response, making model discrepancies easier to detect than they would be if more realistic smooth variations were used. The simulations are initiated under steady-state conditions. At time , 3 and 4 h, , the total influent biodegradable substrate concentration and the total influent biodegradable organic nitrogen are increased by 50%, respectively. At time 5 and 6 h, they are returned to their original condition. The responses are shown in Figures 3 to 5 and they are coherent. For example, in Figure 3 an increase in the inflow rate and in the total influent biodegradable substrate concentration makes the concentration in the bioreactor to increase, mainly in the anoxic zone, making easier the denitrification process, with the consequent decrease in the concentration. This causes a reverse effect in the concentration, which together with the increase in , forces an increase in the consumption of dissolved oxygen. In Figure 4 are presented the responses for some of the main particulate concentrations and in Figure 5 the secondary settler response. For a better observation of the effects generated by the disturbances, the concentrations in the upper layers of the secondary settler are presented in logarithmic scale. A global view of the effects of these disturbances may be seen in the tridimensional graph located in the lower part of Figure 5.

CONTROL STRATEGIES USING THE ASWWTP-USP BENCHMARK

The relevant literature in activated sludge wastewater treatment processes reflect a number of different control problems, covering all aspects from dissolved oxygen and respiration rate control to more comprehensive strategies involving sludge recycle and secondary settler management. Significant benefits may be obtained by employing advanced model-based control techniques (Olsson and Newell, 1999; Vanrolleghem, 2000). In this respect, two questions are addressed (Steffens and Lant, 1999):

1) What is the best control strategy for biological nutrients removal (BNR) wastewater treatment processes?

2)What are the most appropriate control techniques?

In this section, some control strategies applied to ASP are presented as illustrative examples in the use of the benchmark. Classic single-loop PI controllers are employed. The main objective is to provide a way to compare the performance of the advanced control techniques with that of the PI controller. Tuning the PI controllers is not easy, so heuristic methods (trial and error) are applied. In all cases, the dynamics of sensors and final control elements are neglected. The values of the controller parameters are omitted. The idea is to study whether a control technique is successful in controlling such a complex process as ASP. A state of the art review of control techniques applied to ASP can be found in Weijers (2000).

DO Concentration-Based Control

DO concentration control of ASP has been recognized as efficient, both from an economic and a biological point of view. DO concentration in the aerobic zone of an ASP must be sufficiently high to supply enough oxygen to the microorganisms in such a way that the organic matter is degraded and the ammonium is converted to nitrate. On the other hand, a very high DO concentration, which requires a high air flow, generates high energy consumption and may also cause a deterioration in the quality of the sludge. Furthermore, a high DO concentration in the internal recycle flow causes the denitrification to be less efficient.

The objective of this strategy is to maintain the dissolved oxygen concentration in zone 2 and zone 3 at a predetermined set point (2.0 mg O₂/l) by manipulation of the air flow injection (m³/h).

The system is submitted to several disturbances as shown in Figure 6(a), in normalized form. The PI controllers were adequate to control the process, as can be seen in Figure 6(b). Nevertheless, the effects of those disturbances may be more easily observed in the responses of the manipulated variables and in the concentration levels of BOD and COD in Figures 6(c) and 6(d), respectively. The calculated performance index is J₁=0.9481 for the PI controller in zone 2 and J₂=0.4714 for the PI controller in zone 3.

Respirometry-Based Control

Respirometry is the measurement and interpretation of the bacterial respiration rate (or oxygen uptake rate, OUR). The respiration rate is the amount of oxygen per unit volume and unit time that is consumed by the microorganisms. The OUR is directly related to two important biochemical processes that must be controlled in a wastewater treatment plant: biomass growth and substrate consumption (Spanjers et al., 1998a). Furthermore, a rapid decrement of OUR may implicate that some form of toxic material has entered the plant.

A control strategy based on respirometry is presented here. This control strategy aims to keep the respiration rate in zone 3 at a predetermined set point (23.64 mg O₂/l.h) and implicitly control the concentration of active biomass, (deduced or inferential variable), by manipulation of the external recycle flow . In this case the wastage flow rate varies . For this particular control strategy, it is assumed that the true endogenous respiration rate has been measured, i.e., no substrate is present (Spanjers et al., 1996, 1998b). Since DO control is essential in ASP (Dochain et al., 1995), PI controllers of DO are assumed to be part of the plant layout.

The system is submitted to several disturbances as shown in Figure 7(a), in normalized form. The results show a slow response of OUR, with a similar reaction in the response of the concentration. The increase in the total influent biodegradable organic matter causes the OUR to rise in the third zone, canceling the controller action, as can be seen in Figures 7(b) and 7(c). The effects of these disturbances in the treated effluent quality is shown in Figure 7(d). The choice of the OUR set point was based on calculations in steady-state conditions. The calculated controller performance index is J=2.1839.

Nitrate Concentration-Based Control

The wide variation in influent flow and composition, which is typical of WWTP, generates a demand for on-line control of the denitrification process in order to guarantee a sufficiently low effluent nitrate concentration. Two variables can be manipulated to achieve this objective: the addition of an external carbon source (Yuan et al., 1997; Lindberg, 1997; Barros and Carlsson, 1998, Marsili-Libelli and Manzini, 2000; Samuelson and Carlsson, 2000), to guarantee complete removal of recirculated nitrate in the anoxic zone, and the nitrate recirculation flow rate (Londong, 1992; Andersson et al., 1995; Sotomayor et al., 2000), to control the amount of nitrate that is recirculated. The best solution might take into account a multivariable control system including both the manipulated variables (Yuan et al., 1997). In order to make possible this solution, a variation is included in the simulator that assumes the addition of an external carbon source (treated as a soluble substrate with a concentration equal to 80,000 mg COD/l). However, in this work, only the second control strategy is presented.

In this strategy the objective is to keep the nitrate concentration in zone 1 at a predetermined set point by manipulation of the internal recycle flow rate , which is rich in nitrate, from the last aerobic zone to the anoxic zone. According to Yuan et al. (1997), a good choice of set point for in the anoxic zone is , which yields N/l, but a process of trial and error has shown that the set point 2.0 mg N/l is almost as good for the outcome, reducing the need for an external carbon source (Singman, 1999). Assuming complete denitrification, the final choice of a set point of 1.0 mg N/l is derived from the fact that the fluctuations in in zone 1, when is high, are lower for a low set point. The PI controllers of DO are assumed to be part of the plant layout.

The disturbances are shown in Figure 8(a), in normalized form. An increase in the influent readily biodegradable substrate provokes an increase in the denitrification rate and, therefore, a decrease in the concentration, as can be seen in Figure 8(b). The amplitude of these disturbances causes saturation in the controller response, as shown in Figure 8(c). The fluctuations in the nitrogen concentration in the effluent are shown in Figure 8(d). The calculated controller performance index is J=2.2406.

CONCLUSIONS

In this paper, a simulation benchmark of a biological WWTP has been developed based on widely accepted process models, namely the ASM1 and the multi-layers double exponential settling model of Takács et al. (1991). These models present several limitations, nevertheless their universal appeals and practical verifications overshadow these limitations.

The benchmark represents a pre-denitrifying ASP, and a bioreactor and a secondary settler form it, being designed to operate at 15 °C. The influent is fed to the anoxic zone of the bioreactor. This configuration was chosen because it is commonly used in practice for organic matter and nitrogen removal from municipal wastewater (predominately domestic).

The earliest applications of control theory to ASP showed little concern about the practical constraints to which these processes are exposed. In many cases the performance of a determined control technique has been demonstrated, either by means of simulation or by real experiments in pilot and full-scale plant. However, a discerning control performance evaluation is difficult due to the nonstandardization plant used. Thus, is often impossible to determine if the control technique is really successful and generally applicable.

The simulation benchmark provides to the water quality community, either academic or practical, a useful tool for development, evaluation and comparison of advanced control techniques, including optimization and identification algorithms. Every new proposed technique can be objectively and unbiasedly compared to other technique and the general applicability of a technique can be determined. This benchmark also can be used for knowledge of the process and training of operators and to test new control strategies (structures) in ASP.

The open-loop dynamic simulations showed coherent responses. In closed-loop, PI controllers were implemented and they can be taken as base to compare the performance of advanced control techniques. The control performance evaluation is based on the controller efficiency (ISE index) and effluent quality. The PI controllers comply with basic control requirements (regulatory control), however they were not successful in providing treated water of the expected quality, violating the majority of the constraints.

The simulation benchmark is being continuously updated and the next version will include adequate functions for on-line real-time optimization of the process. The current version is made available to interested users, who agree to report and document problems with the ASWWTP-USP benchmark. These users should request a copy of the simulator to the corresponding author.

ACKNOWLEDGEMENTS

The authors acknowledge the financial support from the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), under grant N° 98/12375-7.

NOMENCLATURE

Bioreactor Model

Soluble ammonium nitrogen (mg N/l) Soluble nitrate-nitrite nitrogen (mg N/l) Dissolved oxygen concentration DOC (mg COD/l) Soluble organic nitrogen (mg N/l) Soluble biodegradable substrate (mg COD/l) Soluble inert organic matter (mg COD/l) Alkalinity (m mol/l) Autotrophic biomass (mg/l) Heterotrophic biomass (mg/l) Particulate substrate biodegradable (mg COD/l) Particulate organic nitrogen (mg N/l) Inert particulate products (mg COD/l) Particulate inert organic matter (mg COD/l) Heterotrophic yield (g cell COD formed (g COD oxidized)^-1) Autotrophic yield (g cell COD formed (g N oxidized)^-1) Fraction of biomass yielding particulate products (dimensionless) Mass N/mass COD in biomass (g N (g COD)^-1 in biomass) Mass N/mass COD in products from biomass (g N (g COD)^-1 in endogenous mass) Autotrophic maximum specific growth rate (h^-1) Heterotrophic maximum specific growth rate (h^-1) Heterotrophic decay rate (h^-1) Autotrophic decay rate (h^-1) Ammonium half-saturation coefficient (hsc) for autotrophs (g NH₃-N m^-3) Oxygen hsc for autotrophs (g O₂ m^-3) Oxygen hsc for heterotrophs (g O₂ m^-3) Nitrate hsc for denitrifying heterotrophs (g NO₃-N m^-3) Hsc for heterotrophs (g COD m^-3) Correction factor for anoxic growth of heterotrophs (dimensionless) Correction factor for anoxic hydrolysis (dimensionless) Ammonification rate (m³ (g COD h)^-1) Maximum specific hydrolysis rate (g slowly biodegradable COD (g cell COD h)^-1) Hsc for hydrolysis of slowly biodegradable substrate (g slowly biodegradable COD (g cell COD)^-1) Saturated oxygen concentration (mg O₂/l) Oxygen transfer function (h^-1) Flow rate (m³/h) Volume (m³) Concentration (mg/l) S Soluble element (mg/l) X XParticulate element (mg/l) r r Reaction rate (mg/l.h) OUR OUROxygen uptake rate (mg O₂/l.h) COD CODChemical oxygen demand (mg/l) BOD BODBiochemical oxygen demand (mg/l)

Settler Model

Suspended solids concentration or TSS (mg SS/l) h Height of layers (m) A Settler transversal section (m²) Volume of the settler (m³) n Number of layers (dimensionless) m Feed layer (dimensionless) Solids flow corresponding to gravity settling (mg SS (l.h)^-1) Solids flow corresponding to the bulk upward movement (mg SS (l.h)^-1) Solids flow corresponding to the bulk downward movement (mg SS (l.h)^-1) Double-exponential settling velocity function (m/h) Maximum theoretical settling velocity (m/h) Maximum practical settling velocity (m/h) Settling parameter associated with the hindered settling component of settling velocity equation (l/mg) Settling parameter associated with the low concentration and slowly settling component of the suspension (l/mg) Nonsettleable fraction of the influent suspended solids (dimensionless) Minimum attainable suspended solids concentration in the effluent (mg/l) Threshold suspended solids concentration (mg/l) Conversion factors of SS to COD

Controllers

Performance index Error Control signal

Subscript

Wastewater influent Internal recycle Sludge recycle Feed layer of settler Flow upwards Wastage flow Flow downwards Air injection Set point 1 Zone 1 2 Zone 2 3 Zone 3

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*

To whom correspondence should be addressed

Publication Dates

• Publication in this collection
  25 May 2001
• Date of issue
  Mar 2001

History

• Accepted
  11 Jan 2001
• Received
  10 Jan 2000