Format And Type Fonts


 

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 39, 2014 

A publication of 

 
The Italian Association 

of Chemical Engineering 

www.aidic.it/cet 
Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong  

Copyright © 2014, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI: 10.3303/CET1439126 

 

Please cite this article as: Vafajoo L., Mohammadpour A., Khorasheh F., 2014, A theoretical and experimental investigation 

of wastewater treatment for a polyethylene terephthalate production unit, Chemical Engineering Transactions, 39, 751-756  

DOI:10.3303/CET1439126 

751 

A Theoretical and Experimental Investigation of Wastewater 

Treatment for a Polyethylene Terephthalate Production Unit 

Leila Vafajoo*
a
, Abdolah Mohammadpour

a
, Farhad Khorasheh

b
 

a
Chemical Engineering Group, Islamic Azad University, South Tehran Branch, Tehran, Iran 

b
Chemical and Petroleum Engineering Dept., Sharif University of Technology, Azadi Ave., Tehran, Iran 

*vafajoo@azad.ac.ir 

In this research, mathematical modelling of an anaerobic hybrid bioreactor for effluent treatment of a Poly-

Ethylene Terephthalate (PET) unit in a petrochemical complex was performed. The developed model 

included a combination of a biofilm model for describing the substrate kinetics; a fluidized bed model for 

determination of species profiles along the reactor length and a bioreactor model for particle distribution 

inside the reactor.  

The reactions performed in the bioreactor included; i) the polymers hydrolysis; ii) fermentation of the 

resulting monomers; iii) the volatile fatty acids fermentation to Acetate and Hydrogen and iv) the Methane 

formation as the final product. The reactor was divided into n-segments each being fully mixed and the 

changes of granule densities at each one caused by granules growth were neglected.  

On the other hand, the experimental data obtained from an industrial unit in which, the pH was controlled 

by adding NaHCO3 and NaOH while; a mixture of Urea, di-ammonium phosphate and molasses were 

utilized as substrates. The total flow rate inside the 2,200 m
3
 bioreactor was set 180 m

3
/h with 0.7 m/h up-

flow velocity. 

The theoretical data determined from the developed model for the volatile fatty acids’ (VFAs) production 

while the corresponding experimental data obtained from the industrial unit. Moreover, the comparison 

between the bioreactor effluent’s COD determined through both the theoretical and experimental studies 

were presented. The current model reproduced the experimental data with mean error of 14 % which 

considering the complexity of the undertaken system was rather satisfying. 

1. Introduction 

The particle structure in a hybrid anaerobic reactor had been studied (Saravanan et al., 2008). On the 

other hand, the flow inside an aerobic fluidized bed reactor had been studied using axial dispersion model 

by several researchers (Palatsi et al., 2010). 

In this research, an up flow anaerobic contact filter (UACF) was utilized for effluent treatment of an actual 

Petrochemical Refinery stream containing polyethylene terephthalate (PET). The lower part of the 

aforementioned biofilter was empty above which suspended growth took place while the upper section of it 

was filled with random packing upon which occurred the attached growth of particulates.  

Moreover, a mathematical model of a hybrid anaerobic reactor was developed. This was validated by data 

of a petrochemical effluent treatment reactor. In addition, the volatile fatty acid concentration gradient was 

compared with that of an actual plant data. 

2. Mathematical modeling 

The developed theoretical picture included combination of the following three models; i) a biofilm model for 

describing the substrate reaction kinetics; ii) a fluidized bed model for determination of particle distribution 

inside the bioreactor and iii) a bioreactor model for connecting the two aforementioned models illustrating 

substrate concentration profile inside the bioreactor. (Steyer et al., 1999) 



 

 

752 

 
These three models were coupled and solved utilizing the following assumptions; 1) the granules were 

spherical with 1 mm diameter and fully fluidized, 2) the mass transfer resistance in the liquid phase was 

neglected (Yu et al. 2013)., 3) the substrate transfer within biofilm and granule particles was described by 

Fick’s first law, 4) the reactions inside biofilm were expressed by Monod’s kinetics and 5) the steady state 

conditions existed throughout.  

2.1 Biofilm model 
In this model biogranules were considered to have three layers. The mass balance for outer biofilm layer 

for different components was as follows: 

For glucose: 

       
 
  

  
 
    

        
 
  

  
 
 
   

   

    

      

     
        (1)  

By modifying the above equation, the following differential form might be obtained: 

   

   
 

 

 

  

  
  

   

      
  (2) 

 

Where kg was defined as: 

   
        

        
 (3) 

 

Boundary conditions included: 

         
  

  
                        

 

Where       was the yield coefficient, g; the substrate concentration (kg COD/m
3
),      the Monod 

saturation constant (kg COD/m
3
), De; the effective diffusion coefficient (m

2
/s),      ; the maximum 

specific growth rate(1/s)  and x was the biomass concentration (kg VSS/m
3
). 

For Acetic Acid: 

The mass balance equation of acetic acid production from glucose was: 

   

   
 

 

 

  

  
  

    

      
  (4) 

 

In which; 

    
        

        
 (5) 

 

And boundary conditions included: 

         
 
   

  
 
    

  
   

  
 
    

                      
(6) 

2.2 Fluidized bed model 
The reactor parameters utilized were provided in table 1. 

In several previous studies, the effect of gas production on bed expansion was taken to be negligible upon 

the flow pattern in an anaerobic fluidized bed reactor (Shida et al., 2012). Hence, in the present model the 

effect of gas production in the liquid up-flow velocities was neglected.  

Table 1: bioreactor parameters used in this study 

Parameters  amount unit 

Reactor height 9.5 m 

1. Reactor active height 8.65 m 

2. Suspended growth height (lower part) 4.5 m 

3. Random packing height (upper section) 4.15 m 

The relationship between the bed void fraction and liquid up-flow velocity was given (Panepinto et al., 

2013) as follows; 

      
   (7) 



 

 

753 

            (8) 

 

Terminal settling velocity (  ): 

    
          

     
 

   

 (9) 

 

And CD was determined from (Saravanan et al., 2008): 

          
    

   
   

   (10) 

 

In addition, the so called parameter n in Eq(6) was given (Saravanan et al., 2008) as follows: 

         
       (11) 

 

Ret was the terminal Reynolds number determined as: 

    
     

  
 (12) 

 

In which d was the particle diameter (m),    the liquid density (kg/m
3
), us the liquid superficial velocity 

(m/s)  the void fraction and 1 was the liquid viscosity (kg/m.s). 

To determine the bed’s void fraction, Ret was initially guessed and used in Eq (10) through which, the 

value of the CD was calculated. Next, in this iteration loop having all necessary parameters the ut was 

determined from Eq(8). Then having this, the calculated value of the Ret was obtained from Eq (12) and 

compared with the previously guessed value. This loop was continued until the toleration limit for 

convergence was satisfied. Hence, ui, n and ut were determined. Ultimately, having these as well as; the 

up-flow velocity in the reactor of 1.94x10
-4

 m/s, the bed void fraction was determined. 

2.3 Reactor modeling 

Flow within the reactor was divided into several sections shown in Figure1. Each of these was taken as a 

completely mixed reactor (CSTR).The variation of density with biogranule size (i.e.; one of the reasons for 

the bed stratification) was also found to be negligible. 

A typical value of 1 mm Sauter-mean diameter (SMD) was utilized to characterize the average biogranule 

size. Under steady state conditions, the entire column was assumed to be filled with such granules. The 

number of these biogranules was calculated as follows: 

  

 
 

         

 
 

    
 

 (13) 

 

Figure 1: reactor model scheme 

Thus, the mass balance for the i
th

 component at the steady state was taken to be: 

               
   

 
  

  
 
 

     
 

 
 

     
  (14) 

 



 

 

754 

 
The glucose concentration in the bottom-most compartment was determined through; 1) the inlet and 

recycle flow rates as well as; 2) the influent COD and 3) the initial guess for concentration of glucose in the 

recycle flow rate. Hence, according to Eq (14) the i
th
 component profile along the reactor height was 

obtained. This iteration loop was continued upon the concentration of glucose in the recycle flow compared 

with the previously guessed value until convergence was reached. 

2.4 Model parameter 
Kinetic constants: 

The kinetic parameter values and physical parameters used in the present simulation were provided in 

tables 2 and 3. (Denac et al., 1986) 

2.5 Biomass composition 
The biomass compositions used in the present simulation were taken from a previous open literature work 

(Steyer et al., 1999). These values were averages of several runs (Martin et al., 2010) in which the glucose 

degrading acidogen concentration was 65 %, acid degrading methanogens amounted to 11.5 % as well 

as; the hydrogen utility methanogens consumed was 23.5 %. (Torre et al., 2013) 

3. Experimental methodology 

Spectrometry measurements of the COD in wastewater were carried utilizing a strong oxidizer of 

potassium dichromate in concentrated sulfuric acid while the silver sulfate was used as a catalyst. 

Moreover, the well-known invert titration method used to measure the concentration of the fatty acid (i.e.; 

using 0.1 N NaOH and 0.1 NHCl solutions). 

4. Results and discussion 

Experiments were carried out in a 2,200 m
3
 reactor with 180 m

3
/h flow rate and 0.7 m

3
/h up-flow velocity. 

(Figure 2) 

When the inlet flow rate and volatile fatty acids concentration in the entering stream were known, the acid 

profile along the reactor height was determined. To provide sampling at different heights, a 5-point reactor 

was undertaken. Thus, a comparison of the simulated results with that of the actual data obtained 

experimentally was made possible. 

5. Conclusions 

A mathematical model for a UACF was developed combining several modeling aspects including; a biofilm 

model describing the substrate kinetics, a bed fluidization model highlighting the granule distribution and a 

bio-reactor model leading to component profiles along the reactor height. To study the COD removal 

efficiency, a synthetic medium containing glucose as a carbon source was undertaken. Hence, a biofilm 

model assuming a Three-layer structure was developed. This model also revealed the profiles of the 

volatile fatty acids along the reactor. Moreover, a comparison of the model results with actual data 

obtained experimentally indicated to be rather satisfying. Ultimately, the developed model might be used 

towards optimization of the understudied production on the industrial scale. 

Table 2: kinetic parameters used in the present model 

Component  μmax (L/h) ks (kg COD/m
3
) Yx/s (kg biomass/kg COD) 

Glucose 0.05 0.140 0.036 

Acetic acid 0.01416 0.237 0.029 

Table 3: physical parameters used in the present model 

De Amount (m
2
/s) 

Deg 5.278 x 10
-11

 

Dea 7.500 x 10
-11

 

 

 

 

 



 

 

755 

 

Figure 2: Variations of the theoretical and experimental effluent COD as a function of the reactor length 

 

Figure 3: Parity plot of experimental versus theoretical VFAs concentrations inside the bioreactor 

(FLOWin=85 m
3
/h, VFAin=0.830 kgCOD/m

3
) 

References 

Denac M., Miguel A., Dunn I.J., 1986, Modeling dynamic experiments on the anaerobic degradation of 

molasses wastewater, Biotechnology and Bioengineering, 31, 1-10. 

Martin M., Rubia M., Martin A., Borja R., Montalvo S., Sanchez E., 2010, Kinetic evaluation of the 

psychrophylic anaerobic digestion of synthetic domestic sewage using an upflow filter, Bioresource 

Technology, 101, 131-137.  

Palatsi J., Illa J., Prenafeta-Boldú F.X., Laureni M., Fernandez B., Angelidaki I., Flotats X., 2010, Long-

chain fatty acids inhibition and adaptation process in anaerobic  thermophilic digestion: Batch tests, 

microbial community structure and mathematical modelling, Bioresource Technology, 101, 2243-2251. 

Panepinto D., Genon G., Borsarelli A., 2013, Improvement of Nitrogen Removal in a Large Municipal 

Wastewater Plant, Chemical Engineering Transactions, 34, 67-72 



 

 

756 

 
Saravanan V., Sreekrishnan T.R., 2008, A mathematical model for a hybrid anaerobic reactor, Journal of 

Environmental Management, 88, I. 1, 136-146. 

Shida G., Sader L., Amorim E., Kimiko I., 2012, Performance and composition of bacterial communities in 

anaerobic fluidized bed reactors for hydrogen production: Effects of organic loading rate and alkalinity, 

International Journal of Hydrogen Energy, 22, 16925-16934.  

Steyer J., Buffiere P., Rolland D., Moletta R., 1999, Advanced control of anaerobic digestion processes 

through disturbances monitoring, Water Research, V. 33, I. 9, 2059-2068. 

Torre J., Vargas M., Sanchez A., Montero M., Ruano A., 2013, Determination of alpha activity in soild 

samples by leaching or digestion, Applied Radiation and Isotopes, 81, 49-52. 

Yu L., Ma J., Frear C., Zhao Q., Dillon R., Li X., Chen Sh., 2013, Multiphase modelling of settling and 

suspension in anaerobic digester, Applied Energy, 111, 28-39.