Transactions Template


 

  

JOURNAL OF ENGINEERING RESEARCH AND TECHNOLOGY, VOLUME 4, ISSUE 2, JUNE, 2017 

 

  

61  

Modelica-Based Model for Activated Sludge System  

Khalil T. Matar
1
, Fahid K.J. Rabah

2
, Mohamed M. Abdelati

3
 

Abstract—Activated sludge system is the most important stage in municipal wastewater treatment process. It is a biological 

operation used for treating sewage by means of microorganism. One type of activated sludge systems is the oxidation ditch. 

In this work, models  derived  through  object-oriented programming  will  be  used  to  build  a simulation model  for a  

typical  oxidation ditch.  The  derived model  was constructed  and  programmed  using  Modelica  language.  The simulation 

model will help better understand the system behavior. Thereby, the model will be provided as an assessment or evaluation 

tool for the performance of control schemes. The tool gave the expected results, in terms of reducing the concentration of 

organic matter in wastewater coming out from oxidation ditches. 

Key words— oxidation ditch, modeling, Modelica, activated sludge, wastewater treatment plant 

I INTRODUCTION

Wastewater is water containing solids, whether sus-

pended or dissolved. Therefore, wastewater treatment is 

defined as the process of separating solids from water to get 

cleaner water that can be reused or safely disposed into the 

environment. There are many methods used for  separating  

solids from water such as physical, chemical, and biological 

methods [1].In this paper a biological method for wastewater 

treatment was focused on and modeled. The principal bio-

logical processes used for wastewater treatment are divided 

into two main categories; the first category is the suspended 

growth processes while the second one is the attached 

growth processes[2]. For the suspended growth processes, 

microorganisms are maintained in suspension while convert-

ing organic matter or other constituents in the wastewater to 

gases and cell tissue. Examples for these processes are con-

ventional activated sludge system, oxidation ditches(OD), 

sequencing batch reactors (SBR), aerated lagoons and up 

flow sludge blanket reactors.  On the other hand, the at-

tached growth processes are characterized by microorgan-

isms responsible for conversion of organic matter  or  other  

constituents  in  wastewater to gases and cell tissue are  at-

tached  to  some  inert material  such  as:  rocks,  sand,  ce-

ramic, or  plastic materials.  

This research contributes to the rehabilitation of the 

wastewater treatment plant of the European Hospital located 

in the southern of Gaza Strip. This plant receives a daily 

average amount of 141 m  of untreated wastewater coming 
out of the European hospital. The average concentration of 

organic matter)BOD) entering the plant is 317 mg /L [3], so 

this   wastewater needs to be treated before it is injected into 

the aquifer or prior to use in irrigation, to prevent the pollu-

tion of the groundwater. The plant utilizes an oxidation ditch 

for the biological treatment process. The main objective of 

this research is to create a simulation model for the organic 

matter removal process from wastewater in the OD using the 

component-oriented language Modelica in order to better 

understand the process dynamics and investigate the effi-

ciency of possible control schemes. In [4,5] wastewater 

pumping stations are modeled using Modelica. In [6] The 

Modelica application library Wastewater containing three 

Activated Sludge Models of different complexity with the 

essential components of municipal wastewater treatment 

plants is presented. In [7] the dynamic optimization method 

was applied to a wastewater treatment plant (WWTP) mod-

el. With the help of the library Wastewater an ASM No. 2d 

model of the WWTP Jena was examined and evaluated. 

This  research  deals  with  mathematical  modeling  and  

process  control  of  OD    wastewater treatment  in  Europe-

an  hospital  in  KhanYounis as a case study.  The  increased  

importance  of  biological purification processes has also 

resulted in increasing interest in their mathematical model-

ing, for understanding as well as for predictive and control 

purposes. 

The plant under study consists of 15 parts, as illustrated 

in the process flow diagram depicted inFigure1.Part  I: IN-

LET PUMPING STATION consists of a tank for wastewater 

collection entering the wastewater to plant, in addition to the 

two screw pumps capacity of each is 10 L/S. Part II: 

MUNCHER which is used to remove solids. Part III: OXI-

DATION DITCH, which is the most important part of the 

plant because the biological treatment process occurs within 

this part. Part IV: SEDIMENTATAION TANK, which is 

used to separate and  remove Settleable suspended solids. 

Part V: FLOWMETER &CHLORINATION, which is used 

to control the sterilization process and to add chlorine. Part 

VI: SLUDGE PUMPING STATION, which is a tank to col-

lect the sludge for distribution either to oxidation ditch or to 

be sent for sludge treatment. Part VII: SLUDGE CONSOL-

IDATION TANK, which is a tank that mixes the sludge to 

become homogeneous, so it  is   transferred  for drying. Part 

VIII: DISTRIBUTION CHAMBER, which is the place 

where the treated water is being  distributed to downstream 

units. Part IX:  FINAL COLLECTION TANKS, which are 

used to collect water that has been treated. Part X: OUTLET 

PUMPING STATION, which is used to transfer the water 

that has been treated to Finishing Ponds and Soakaway Ar-

ea. Part XI: SOAKAWAY AREA, are ponds to inject  treated 

water    into groundwater. Part XII: CHLRINATION UNIT, 

which is used for the disinfection of treated water using 

chlorine. Part XIII: SLUDGE DRYING BEDS, is the place,  



Khalil T. Matar, Fahid K.J. Rabah, and Mohamed M. Abdelati/ Modelica-Based Model for Activated Sludge System (2017)  

 

  

62  

 

 
Figure 1:  European hospital Gaza-sewage treatment plant 

 

where the sludge is  being dried  for disposal or some 

industrial use. 

The rest of this paper is organized as follows: Section 2 

describes the biological treatment stage, Section 3 describes 

modeling, and Section 4 presents simulation results. Finally, 

Section 5 provides a conclusion and an outlook on future 

work. 

II PROCESS DESCRIPTION  
Activated sludge is a process for treat-

ing wastewater  using microorganisms in the presence or 

absence of oxygen. The activated sludge process is a biolog-

ical process that can be used to convert dissolved and partic-

ulate organic biodegradable compounds into acceptable end 

products and remove nutrients, such as nitrogen and phos-

phorus. In this paper, it is focused on organic matter as the 

major contaminant material. There are a variety of types of 

activated sludge plants. Such as, conventional activated 

sludge system, oxidation ditches, sequencing batch reactor 

(SBR), aerated lagoons, and up flow anaerobic sludge blan-

ket (UASB). 

The plant under study utilizes an oxidation ditch which 

is a suspended growth system as shown in Figure 2.  

It is a modified version of the conventional activated 

sludge system. Oxidation ditches may be considered as a 

traditional completely-mixed systems characterized by long 

detention hydraulic time and sludge age. Oxidation ditch 

consists of one or multiple channels forming a loop, oval or  

 

 

horseshoe. Wastewater is recycled in the oxidation ditch 

by using a rotating brush. The brush has another function 

which is dissolving some atmospheric oxygen in the liquor 

which is necessary for microorganisms growth. 

 
Figure 2: The oxidation ditch under study. 

The flow velocity in the oxidation ditch is maintained in 

the range of 25-30 cm/s to keep the microorganisms sus-

pended. In general the process consists of anoxic zone fol-

lowed by aerobic one as illustrated in Figure 3.  

At the influent to the oxidation ditch, there are organic 

matter and nitrates  (NO 
 ) coming from the aerobic zone 

along with a low level of dissolved oxygen (O2) (which is 

usually less than 0.5 mg O2 /L).  This  is  called  anoxic  

condition  where denitrification occurs. At the end of the 

anoxic zone and the beginning of the aerobic zone at the 

brush, the pollutants that exist are: the remaining organic 

matter that was not used for denitrification in addition to O2 

introduced by the aerator and ammonium  (NH 
 ) that comes 

http://en.wikipedia.org/wiki/Sewage


Khalil T. Matar, Fahid K.J. Rabah, and Mohamed M. Abdelati/ Modelica-Based Model for Activated Sludge System (2017)  

 

  

63  

with influent and passes through the anoxic zone without 

any reduction in its concentration. In these conditions both 

BOD5 (organic matter measurement unit) removal and nitri-

fication occurs ( conversion of NH 
  to NO 

 ) under aerobic 

conditions. At the end of the aerobic zone the dissolved oxy-

gen is reduced again to around zero due to the consumption 

by the microorganism. Oxidation ditches differ from con-

ventional activated sludge system in terms of the ability to 

achieve the removal targets with high-performance and low 

operation and maintenance costs. In addition,  OD produces 

less sludge compared to  other activated sludge biological 

treatment processes[8,9,10]. 

 
Figure 3: The process flow in oxidation ditches. 

 

III MODEL DERIVATION  
For the modeling of oxidation ditch process, component 

models are not found in the standard simulation tool librar-

ies. In this work, it is not intended to build a sophisticated 

model for detailed investigations rather to conclude with a 

manageable working model. The objective is to design a 

simulation tool that simulates oxidation ditch operations, 

particularly the reduction of organic matter (i.e. reduction of 

BOD concentration. To this end, the modeling and simula-

tion environment “Dymola” which is based on the compo-

nent-oriented language Modelica was used [2]. 

The modeling of oxidation ditch is addressed in the lit-

erature as completely mixed reactor [8,9]. The  OD  process 

is illustrated in the simplified schematic drawing as shown 

in Figure 4. The following variable notation will be used in 

the model development: 

Q wastewater flow rate, (m3/d). 
𝜃 hydraulic detention time of the reac-

tor, (day). 

𝜃  the mean cell-residence time, (day). 
S concentration of the limiting sub-

strate in solution, (mg/L). 

Y maximum yield coefficient measured 
during any finite period of logarith-

mic growth, defined as the ratio of 

the mass of cells formed to the mass 

of substrate consumed, (mg biomass 

/ mg substrate). 

𝑘  endogenous decay coefficient, 

(1/day) 

𝑉 reactor volume, (m
3
). 

 

𝑋  concentration of microorganisms in 
the influent, (mg/L). 

 

𝑋 concentration of microorganisms in 
the reactor, (mg/L). 

𝑄  sludge waste flow rate, (m
3
/d). 

𝑋  concentration of biomass in the re-
turn line, (mg/L). 

𝑄  effluent flow rate, (m
3
/d). 

𝑋  concentration of biomass in the ef-
fluent, (mg/L). 

 

 
Figure 4: Oxidation ditch system: Completely mixed reactor 

with solids recycles 

The biomass concentration in the influent (X0) of this reactor 

is negligible compared to the biomass concentration in the 

reactor (X). 

 The hydraulic detention time in the OD is related to the 

reactor's volume and the flow rate as follows: 

𝜃 =
𝑉

𝑄
 (1) 

 The net production of sludge during wastewater treat-

ment Px, measured in KgVss/d, is given by the following 
equation: 

𝑃𝑥 =
𝑌

1 + 𝑘 𝜃 
𝑄(𝑆1 − 𝑆2) (2) 

Where S1 and S2 are the concentration of organic matter in 

the influent an effluent , respectively. 

The concentration of oxygen (R  ) kg O2/d affects the 
reduction of organic matter as well as the net production of 

sludge. In [1,2] it has been shown that these quantities are 

related as follows: 

𝑅  = 𝑄 (𝑆 − 𝑆 ) − 1.42𝑃  (3) 

Solving Equations 2 and 3 results in the following equa-

tion; 

𝑆 = 𝑆 − 𝐾
𝑅  
𝑄 

 (4) 

Where K  is a coefficient that depends on Y,k and   θ .  



Khalil T. Matar, Fahid K.J. Rabah, and Mohamed M. Abdelati/ Modelica-Based Model for Activated Sludge System (2017)  

 

  

64  

After describing the mathematical equations of the oxi-

dation ditch system, the following is a description of the 

wastewater treatment control system. The main strategy fol-

lowed is to control the treatment efficiency by controlling 

the oxygen concentration in the oxidation ditch. 

 

In the Oxidation ditches the amount of dissolved oxy-

gen is controlled through adjusting the speed of the rotating 

brush. Manufacturers of aerators provide an empirical quad-

ratic equation that relates R  and the rotational speed of the 
brush (r). The parameters of such an equation depend on the 
physical characteristics of the aerator. The one used in this 

study has the following characteristic equation: 

𝑅  =
 

    
𝑟2 -  

   

  
𝑟 +

  

 
 (5) 

 

The feedback in the controller is the concentration of 

organic matter at the effluent (S ). An oxygen    sensor is 
used to estimate this quantity assuming a quadratic relation-

ship between r and oxygen level (O).Depending on the char-
acteristics of the brush aerator installed in the OD under 

study , the relation of  (O) to( r ) is as follows: 

𝑂 = 0.0116[
1250

(𝑟 − 500)
+

𝑟 

8(𝑟 − 500)

−
65𝑟

(𝑟 − 500)
] 

(6) 

Now, the control problem is to adjust the aerator speed to 

keep the organic matter of the effluent at a specific level. In 

order to carry simulations, an estimate for the daily variation of 

influent is required. An estimate is depicted in Figure 5. 

 

 
 

Figure 5: Daily flow pattern of wastewater in the hospital  

IV IMPLEMENTATION PROCEDURE 

This subsection describes briefly how modeling is im-

plemented in Modelica using the Dymola tool. The first step 

is defining  the wastewater  connector (W). Its icon is repre-

sented by a small blue square and it is defined as follows: 

connector W  

         Real S(min=0.0); 

         Real X(min=0.0); 

         flow Real Q; 

end W; 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6: Modelica code of  the oxidation ditch. 

 

To build an oxidation ditch model, two wastewater connect-

ors (w1 and w2)are needed, in addition to an output con-

nector (O) of type real and input connector (r) of type real. 
Being governed by equations 1 to 6, its Modelica code is 

shown in Figure 6. 

V SIMULATION RESULTS  
  

The goal of the simulation is to verify the derived model and to 

see the progress of operations in the oxidation ditch. The con-

trol problem is a typical feedback control scenario in which the 

concentration of organic matter at the effluent is measured in 

correlation to the oxygen sensor reading, compared to a refer-

ence value, then resultant error signal is used to derive the con-

troller which adjusts the aerator speed. Consequently, the level 

of dissolved oxygen is adapted which is the key factor of  the 

microorganisms production that affects the organic matter con-

sumption. However, excess amounts of oxygen levels are unde-

sired as it leads to growth of the filamentous bacteria which 

cause sludge bulking. It is recommended to keep the oxygen 

level below 3 mgO2/l. The top level module of such a system 

may be implemented in “Dymola” as illustrated in Figure 7. 

The proposed process controller is based on a PID controller 

with limited output, anti-windup compensation and set point 

weighting as illustrated in Figure 8. This PID controller is 

available in the Modelica standard library and it is explained 

thoroughly in[11]. The controller is tuned and its output is lim-

ited to the range from zero to 1460 rpm which is the maximum 

possible speed of our aerator. 

 



Khalil T. Matar, Fahid K.J. Rabah, and Mohamed M. Abdelati/ Modelica-Based Model for Activated Sludge System (2017)  

 

  

65  

 
Figure 7: The system model 

 
Figure 8: PID controller with limited output 

The simulated controller of this process is shown in Figure 9. 

 
Figure 9: Process controller 

The lower part of the controller has a PID module with 

limited output, anti-windup compensation and set point 

weighting. Its output specifies the required speed of the 

aerator . The upper  part has an integrator with a limited out-

put from zero to one.  

In regular cases, the error signal is positive and the inte-

grator saturates to unity value. Once the dissolve oxygen  

exceeds the specified threshold (O≈3 mg/l), the integrator 
output starts to decrease and eventually saturates to 0. This 

gives a measure for the persistence of the  dissolved oxygen 

to exceed the threshold value. The result  of this integrator is 

multiplied with the output of the Limited PID module to 

generate the recommended speed of aerator. 

The Variable Frequency Drive (VFD) is modelled by a 

first-order block with a time constant of 5 s resulting in an 

acceleration time of about half a minute to move forward or 

backward between zero speed and rated speed states. 

The wastewater flow pattern at the influent is illustrated 

in Figure 5. 
 

The concentration of organic matter at influent and ef-

fluent of the oxidation ditch are illustrated in Figure 10. The 

concentration of organic matter at the influent equals 290 

mgBOD5/L while the resultant steady state concentration of 

organic matter at the effluent is reduced to 20 mgBOD5/L.   

 
Figure 10: Concentration of organic matter at influent and 

effluent of oxidation ditch . 

The speed of aerator is shown in Figure 11,while the 

readings of the oxygen sensor are shown in Figure 12. Both 

are reasonable  compared to field measurements and are 

within the acceptable range.  

 
Figure 11: Aerator rotational speed 

 
Figure 12: Oxygen concentration in the OD. 

S2=20 

mgBOD5/L 

S1=290 

mgBOD5/L 

Oxidation ditch  

 



Khalil T. Matar, Fahid K.J. Rabah, and Mohamed M. Abdelati/ Modelica-Based Model for Activated Sludge System (2017)  

 

  

66  

VI CONCLUSION  

 

This paper targeted a small size hospital’s plant, which 

depends on oxidation ditch to  treat   wastewater. The study 

presents an easily controlled and managed model for the 

oxidation ditch of  the  wastewater  treatment  plant  of  the  

European  hospital.  The  model  provides  a  tool  for testing 

the system performance and controlling its treatment pro-

cess. It  also  helps  in  understanding  the  dynamics  of  the  

system  and  allows  designing  a  stable  and robust control-

ler unit for the system. The following conclusions were de-

rived from this work: 

1- The control system enabled the control of oxygen 

concentration from 0 to 2 mg O2/L. 

2- The system enabled the controlled reduction of or-

ganic matter concentration in the range of  290 to 

20 mg BOD5/L by controlling the brush speed and 

,consequently, the concentration of dissolved oxy-

gen in the OD.  

In Future  work, this model will be developed to include 

the simulation of ammonia and nitrate reduction in the OD 

treatment unit.  The  work  will  study  the development of 

the control system and will introduce a new effective tech-

niques in the control process.  

 

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