ORIGINAL CONTRIBUTION

Dynamic Simulation of Batch Photocatalytic Reactor (BPR)for Wastewater Treatment

Suman Dutta

Received: 6 March 2012 / Accepted: 21 September 2012 / Published online: 8 December 2012

� The Institution of Engineers (India) 2012

Abstract Reactive dyes discharged from dyehouse causes

a serious environmental problem. UV/TiO2 photocatalysis

has been employed effectively for these organic dyes

removal from dye-house effluent. This process produces less

amount of non-toxic final product. In this paper a photocat-

alytic reactor has been designed for Reactive red 198

(RR198) removal from aqueous solution. The reactor is

operating in batch mode. After each batch, TiO2 catalyst has

been separated and recycled in the next batch. Mathematical

model equation of this batch photocatalytic reactor (BPR)

has been developed considering Langmuir–Hinshelwood

kinetics. Simulation of BPR has been carried out using fourth

order Runge–Kutta (RK) method and fifth order RK method

(Butcher method). This simulation results can be used to

develop an automatic photocatlytic reactor for industrial

wastewater treatment. Catalyst activity decay and its effect

on each batch have been incorporated in this model.

Keywords Reactive red 198 �Batch photocatalytic reactor � Catalyst deactivation �Dynamic simulation � Fifth order R–K method

List of Symbols

a Catalyst activity (-)

a0 Initial catalyst activity (-)

b Langmuir isotherm constant (Lm g-1)

cA; ½Dye� Dye concentration in the reactor (mg L-1)

cA0 Initial dye concentration in reactor (mg L-1)

Cper Permissible limit of dye concentration (mg L-1)

½Dye�ads Dye concentration in the solid (adsorbent)

phase (mg g-1)

h Time step during simulation (min)

k0

Reaction rate constant with fixed TiO2

concentration (g L-1 min-1)

kad Catalyst deactivation kinetic constant (min-1)

KL Langmuir isotherm constant (L g-1)

kr Apparent kinetic constant (L mg-1 g-1)

rdecol Rate of dye decolorization in the reactor

(mg g-1 min-1)

t Time (min)

½TiO2� TiO2 concentration in the reactor (g L-1)

t0 Initial/starting time (min)

tn Time after nth step (min)

V Reactor volume (L)

W Catalyst weight (g)

Introduction

Textile industry is one of the highest water consuming

sectors. Water pollution due to organic dyes is a major

problem for textile industries. After dying, more than 15 %

of the dyes are lost in wastewater streams [1]. These dyes

impart color to water and thus lower its aesthetic value [2].

Dyes are difficult to remove since many of them are bio-

logically non-degradable. Conventional methods for color

removal, using a primary and a secondary treatment are

unsuitable. A tertiary treatment is often needed to remove

color for discharge into a municipal sewer or into a natural

stream [3]. Unless properly treated, the dyestuffs present in

wastewaters can significantly affect photosynthesis activity

due to reduced light penetration and may also be toxic

to certain forms of aquatic life due to the presence of

substituent metals and chlorine [4].

S. Dutta (&)

Department of Chemical and Polymer Engineering,

Birla Institute of Technology Mesra, Ranchi, India

e-mail: ss.dutta@hotmail.com

123

J. Inst. Eng. India Ser. E (March–August 2012) 93(1):25–30

DOI 10.1007/s40034-012-0003-4

Azo dyes are widely used by the textile industry, and

due to their complex structure and synthetic origin, are

difficult to decolorize by conventional processes. So, the

wastewater generated is considered as the most polluting

among all industrial sectors [5]. Azo dyes are defined as

compounds that have one –N=N– bond or more in their

structure. These bonds are known as dye chromophore

structure and can provide color through radiant energy

absorption [6]. Reduction of the polluted water coloration

is observed by the –C:C– and –N=N– bond breakage or

by the breakage of the aromatic and heterocyclic rings [7].

UV/TiO2 advanced oxidation process is a promising

technology for removing reactive dyes. TiO2 mediated

photocatalysis have been widely used to destroy organic

pollutants including pharmaceutical compounds and pesti-

cides [8, 9]. Heterogeneous photocatalysis takes advantage

of semiconducting metal oxides that can be used on photo-

assisted reactions either suspended in the water effluent to

be treated, or immobilized on various types of supports.

TiO2-based photocatalysis appears as the most emerging

destructive technology. The key advantage of this method

is that it can be carried out under ambient conditions and

may lead to complete mineralization of organic carbon into

CO2. Moreover, TiO2 photocatalyst is largely available,

inexpensive, non-toxic and shows relatively high chemical

stability. Finally, the TiO2 photocatalytic process, is

receiving increasing attention because of its low cost when

using sunlight as the source of irradiation [10].

Reactor modeling is essential for the application of

heterogeneous photocatalysis on an industrial scale [11].

Modeling and simulation of photocatalytic process is

essential to develop an automated wastewater treatment

plant. In this present study a mathematical model of pho-

tocatalytic reactor have been developed considering L–H

reaction kinetics. The reactor is operating in batch mode;

after each batch TiO2 catalyst was separated and recycled.

Simulation of this BPR was also carried using fourth order

Runge–Kutta and Butcher method (fifth order Runge–Kutta).

Algorithms of these methods are given and C programming

language was used for simulation purpose.

Experimental Methods

The substances that are adsorbed strongly degrade faster

[12], so adsorption was studied to ensure the dye degradation

by photocatalytic reaction on TiO2 surface. Experiments

were conducted with different pH to find the optimum pH for

adsorption. Dark adsorption test of dye on TiO2 surface was

carried out in the Jar Tester manufactured by Phipps and

Bird, Virginia, USA. All of these experiments were con-

ducted in presence of infrared light to prevent any degrada-

tion of dyes by photocatalytic reaction. This test was

conducted at three different pH values (3, 5.5, and 7) with an

initial dye concentration 350 mg L-1. The pH of the solution

(mixture of dye solution and TiO2 adsorbent) was controlled

using 10 M HCl and 10 M NaOH solution. After starting the

experimental run, samples were collected from the Jar Tester

at several times. Then the collected samples were filtered

using 0.45 lm polyethersulfone microfiltration membranes

(Pall, Gelman Laboratory, Michigan) to separate the TiO2

particles. After filtration, the concentration of dye was

measured using a spectrophotometer (Jenway 6505 UV/Vis

spectrophotometer; Dunmow, Essex, UK) at a wavelength

kmax = 516 nm. After completing adsorption test, decolor-

ization test of dyes was carried out in presence of UV ray

illumination. A UV light illuminating bulb (100 W) was

used for this purpose. The experiment was carried out in

batch mode, the schematic of experimental set up is shown in

Figure 1. Samples were collected and filtered as earlier and

concentrations of dyes were measured using an UV–Vis

spectrophotometer. A five cycles experiment was performed

with 350 mg L-1 catalyst concentration and 5 g L-1 initial

dye concentration. Viability of TiO2 recycling was tested

after both adsorption and decolorization test. TiO2 was fil-

tered by 0.45 lm microfiltration membrane after each cycle

and reused to the next cycle.

Results and Discussion

This present study shows that the adsorption and photo-

catalysis depend on many factors viz. pH, TiO2 concen-

tration and time. The details of the effects of all these

parameters are described below.

Fig. 1 Schematic of experimental setup

26 S. Dutta

123

Effect of pH on Adsorption

Experimental results show that the dye adsorption strongly

depends on pH. Adsorption is a surface phenomenon and it

depends on adsorbent surface properties. The point of zero

charge of TiO2 (pHpzc) is 6.8; so TiO2 surface becomes

positively charged at pH lower than 6.8 and negatively

charged at pH higher than 6.8 [13]. The reactive dye

RR198 (Figure 2) contains negatively charged sulfonate

groups thus at acidic condition interaction between posi-

tively charged catalyst surface and negatively charged dyes

favour the adsorption. At pH 7 (higher than pHpzc), the

adsorption capacity is very low whereas adsorption

capacity is high at pHs (3 and 5.5) lower than pHpzc; as

shown in Figure 3. This result corroborates that pH 3 is

suitable for industrial application.

Adsorption Isotherm Study

Adsorption isotherms were formed from dark adsorption

experiment data at pH 3. Figure 4 shows that the RR198

adsorption follows Langmuir isotherm (R2 = 0.988)

better than Freundlich isotherm (R2 = 0.957). Values of

Langmuir and Freundlich isotherm constants have been

calculated from the Figure 4.

BPR Model Development

Modeling of a reactor allows obtaining mathematical

expressions for studying the different effects that take place

in it [14]. This paper elucidates a batch reactor within

which a photocatalytic reaction takes place. Experimental

results show that the dye concentration decreases with

time. In a previous paper the authors developed the kinetic

model equation for both photocatalytic reaction and cata-

lyst activity decay. In presence of constant light intensity

the rate of dye decolourization by photocatalytic reaction is

given by [13].

rdecol ¼ k½TiO2�n½Dye�ads ð1Þ

Catalyst activity decreases with increasing time, con-

sidering catalyst activity decay

rdecol ¼ ka½TiO2�n½Dye�ads ð2Þ

Equation (1) is similar to an empirical equation given by

Galindo, et al. [15] and at constant TiO2 concentration:

rdecol ¼ k0a½Dye�ads ð3Þ

It is observed from the isotherm data (Figure 4) that the

Langmuir isotherm fits better than the Freundlich one, and

hence we get:

rdecol ¼ ak0KL½Dye�

1þ b½Dye� ð4Þ

Equation (4) represents the Langmuir–Hinshelwood (L–H)

model equation combined with catalyst activity (a). When

equilibrium dye concentration in liquid phase reaches

almost zero (½Dye� ! 0) then it is assumed that

1 � b[Dye] and Equation (4) becomes:

rdecol ¼ ak0KL½Dye� ð5Þ

The previous study shows that the catalyst decay follows

1st order kinetic.

a ¼ a0e�kadt ð6Þ

Fig. 2 Molecular structure of

RR198

Fig. 3 Dye adsorption at different pH

Dynamic Simulation of BPR for Wastewater Treatment 27

123

Fresh catalyst was used for the study, so the initial

catalyst activity a0 = 1.0. Catalyst deactivation co-efficient

kad was determined from experimental data [13].

Material balance over the batch reactor gives the

following equation:

Rate of accumulation of dye = rate of loss of

dye due to reaction ð7Þ

dcA

dt¼ �W

VkrcAa0e�kadt ð8Þ

Developed final problem is an initial value problem

which can be solved by fourth and fifth order Runge–Kutta

method.

Simulation of BPR

Equation (8) represents the mathematical model of the

BPR. Many parameters are required for simulation pur-

pose. Values of those parameters are given in Table 1. The

apparent kinetic constants are taken from the previous

study [13] where catalyst concentration in the BPR was

5 g L-1. The apparent kinetic constant has a dependence

on catalyst concentration which is described by an

adsorption model [16]. C programming language was used

for computer simulation.

Algorithm of RK4 Method

Simulation of the BPR by fourth order Runge–Kutta

requires the following steps:

Step 1: Define the function f t; cAð ÞStep 2: Enter the initial condition cA0; t0

Step 3: Enter the values of the parameter kr; kad; a0; V ; W

Step 4: Enter the value of tn; h

Step 5: Calculate K1; K2; K3; K4 and KRK4 according to

following formula

K1 ¼ f t0; cA0ð Þ

K2 ¼ f t0 þh

2; cA0 þ

K1

2

� �

K3 ¼ f t0 þh

2; cA0 þ

K2

2

� �

K4 ¼ f t0 þ h; cA0 þ K3ð Þ

and

KRK4 ¼ K1 þ 2K2 þ 2K3 þ K4ð Þ=6

Step 6: Calculate cA1 ¼ cA0 þ KRK4 � h

Step 7: Calculate t1 ¼ t0 þ h

Fig. 4 Adsorption isotherm at

pH 3

Table 1 Parameters used for BPR simulation

Name of the parameter Value of the parameter

Apparent kinetic constant (kr) 0.35

Catalyst deactivation co-efficient (kad) 0.1034

Initial catalyst activity (a0) 1.0

Volume of the reactor (V) 1.0

Weight of catalyst (W) 5.0

Permissible limit of dye concentration (Cper) As low as possible

28 S. Dutta

123

Step 8:cA0 ¼ cA1

t0 ¼ t1

Algorithm of RK5 (Butcher) Method

Fifth order Runge–Kutta method (Butcher method) can be

used to simulate the BPR. Required steps are same as the

RK4 method except Step 5, given below:

Step 5: Calculate K1; K2; K3; K4; K5; K6 and KRK5

according to following formula

K1 ¼ f t0; cA0ð Þ

K2 ¼ f t0 þh

4; cA0 þ h

K1

4

� �

K3 ¼ f t0 þh

4; cA0 þ h

K1

8þ h

K2

8

� �

K4 ¼ f t0 þh

2; cA0 � h

K2

2þ hK3

� �

K5 ¼ f t0 þ3h

4; cA0 þ h

3K1

16þ h

9K4

16

� �

K6 ¼ f t0 þ h; cA0 � h3K1

7þ h

2K2

7þ h

12K3

7� h

12K4

7

�

þh8K5

7

�

and

KRK5 ¼ 7K1 þ 32K3 þ 12K4 þ 32K5 þ 7K6ð Þ=90

Effect of Step Size

Step size h has an effect on real time simulation; increasing

h increases accuracy but takes more time for simulation.

For real time simulation, simulation time should be less

than process time. Sometimes stability of the solution

depends on the step size. In this present paper three

different step sizes (0.1, 0.5 and 1) were considered.

Figures 5 and 6 giving an idea about the simulated

results with different step size using RK4 and RK5 method

simultaneously. This result shows that simulation with step

size 0.5 is considerable for real time simulation, because

accuracy and simulation time both are good. Figure 7

shows a comparison between RK4 and RK5 method with

0.5 step size. It is clear from this comparison that RK5

(Butcher) method is more suitable than RK4 method.

Calculation of Batch Time

Determination of batch time is a vital job for economic

plant operation. Calculation of proper batch time optimizes

the throughput of the process. Algorithm for batch time

determination is given below:

Step 1: Define the function f t; cAð ÞStep 2: Enter the initial condition cA0; t0

Step 3: Enter the values of the parameter kr; kad; a0;

V; W

Step 4: Enter the value of permissible limit Cper and step

size h

Step 5: Calculate K by RK5 method

Step 6: Calculate cA1 ¼ cA0 þ K � h

Step 7: If cA�Cper, stop

Since RK5 method shows better results, it is used in

‘Step 5’ during batch time calculation.

Fig. 5 Experimental result versus simulation results for RK4 method

Fig. 6 Experimental result versus simulation results for RK5 method

Dynamic Simulation of BPR for Wastewater Treatment 29

123

Conclusion

The present study depicts the way of developing an auto-

mated wastewater treatment plant by advanced oxidation

process (TiO2/UV). The results show that within 30 min,

almost 100 % RR198 dye removal is possible using BPR.

This study also shows that simple RK4 and RK5 method

can be used for simulation of this BPR. Simulated results

show RK5 method follows experimental data better com-

pared to RK4. Optimum step size 0.5 gives good result and

taking less simulation time.

Acknowledgments A part of this study was carried out at Centre for

Water Science (Formerly School of Water Sciences), Cranfield

University, Cranfield, Bedfordshire, MK43 OAL, UK under British

Council Higher Education Link Programme. The authors would like

to express thanks to the British Council for financial support.

References

1. H. Park, W. Choi, Visible light and Fe(III)-mediated degradation

of Acid Orange 7 in the absence of H2O2. J. Photochem. Pho-

tobiol. A159, 241–247 (2003)

2. S.A. Figueiredo, R.A. Boaventura, J.M. Loureiro, Color removal

with natural adsorbents: modeling, simulation and experimental.

Sep. Purif. Technol. 20, 129–141 (2000)

3. A. Malik, U. Taneja, Utilizing flyash for color removal of dye

effluents. Am. Dyest. Rep. 83(1), 20–27 (1994)

4. K.R. Ramakrishna, T. Viraraghavan, Use of slag for dye removal.

Waste Manag. 17(8), 483–488 (1997)

5. R.O. Cristovao, A.P.M. Tavares, A.S. Ribeiro, J.M. Loureiro,

R.A.R. Boaventura, E.A. Macedo, Kinetic modeling and simu-

lation of laccase catalyzed degradation of reactive textile dyes.

Bioresource Technol. 99, 4769–4774 (2008)

6. S. Patay, The Chemistry of the Hydrazo Azo and Azoxy Groups,vol. I (Wiley, New York, 1975)

7. C. Galindo, A. Kalt, UV/H2O2 oxidation of azo dyes in aqueous

media: evidence of a structure–degradability relationship. Dyes

Pigment. 42, 199–207 (1999)

8. C. Zwiener, F.H. Frimmel, Oxidative treatment of pharmaceuti-

cals in water. Water Res. 34, 1881–1885 (2000)

9. I.K. Konstantinou, T.A. Albanis, Photocatalytic transformation of

pesticides in aqueous titanium dioxide suspensions using artificial

and solar light: intermediates and degradation pathways. Appl.

Catal. B Environ. 42, 319–335 (2003)

10. V.A. Sakkas, Md.A. Islam, C. Stalikas, T.A. Albanis, Photocat-

alytic degradation using design of experiments: a review and

example of the Congo red degradation. J. Hazard. Mater. 175,

33–44 (2010)

11. G. Li Puma, P.L. Yue, A novel fountain photocatalytic reactor:

model development and experimental validation’’. Chem. Eng.

Sci. 56, 2733–2744 (2001)

12. B. Zielinska, J. Grzechulska, R.J. Kalenczuk, A.W. Morawski,

The pH influence on photocatalytic decomposition of organic

dyes over A11 and P25 titanium dioxide. Appl. Catal. B Environ.

45, 293–300 (2003)

13. S. Dutta, S.A. Parsons, C. Bhattacharjee, P. Jarvis, S. Datta,

S. Bandyopadhyay, Kinetic study of adsorption and photo-

decolorization of Reactive Red 198 on TiO2 surface. Chem. Eng.

J. 155, 674–679 (2009)

14. E.A. Cassano, A.C. Martın, J.R. Brandi, O.M. Alfano, Photore-

actor analysis and design: fundamentals and applications. Ind.

Eng. Chem. Res. 34, 2155–2201 (1995)

15. C. Galindo, P. Jacques, A. Kalt, Photooxidation of the pheny-

lazonaphthol AO20 on TiO2: kinetic and mechanistic investiga-

tions. Chemosphere 45, 997–1005 (2001)

16. S.L. Orozco, C.A. Arancibia-Bulnes, R. Suarez-Parra, Radiation

absorption and degradation of an azo dye in a hybrid photocat-

alytic reactor. Chem. Eng. Sci. 64, 2173–2185 (2009)

Fig. 7 Fourth Runge–Kutta against fifth order Runge–Kutta

(Butcher’s) method

30 S. Dutta

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