INTRODUCTION
Waste water originated from petrochemical plants contains high COD, BOD and toxic pollutants. Almost all wastewater contains several pollutants, some of which are more difficult to degrade compared to others. A local petrochemical industry making primarily polyethylene terephthalate (PET) resins generates raw effluent containing ethylene glycol and 1,4 dioxane apart from other pollutants. The estimated contribution of COD by these two components (ethylene glycol and 1,4dioxane) is about 75% of the total COD. While ethylene glycol is easily biodegraded and is relatively safe, 1,4 dioxane a group 2B carcinogen with high solubility in water and low vapor pressure is resistant to both aerobic and anaerobic biological degradation. This effluent is currently treated using a different treatment scheme and meets the pollution control standards.
Fenton’s oxidation, an Advanced Oxidation Process (AOP), has been proven
promising, in terms of cost effectiveness and ease of operation in the treatment
of various waste waters (Perez et al., 2002; Guzzella
et al., 2002; Alaton et al., 2002; Benitez
et al., 2001; Andreozzi et al., 2000).
Fenton Process has also been employed for decolorization of dyes (Rezaee
et al., 2008; SaifUrRehman et al., 2008).
Fenton’s reaction has a short reaction time among AOPs and is used when
a high COD removal is required (Sarria et al., 2001).
This AOP process has been well studied for its prospective applications in unmanageable
wastewater treatment (Prousek, 1996). High efficiency
of this process is traditionally thought to be due to the generation of hydroxyl
radical (HO_), which has high oxidation potential (E^{0} = 2.80V) and
can oxidize the organic compounds completely to water and carbon dioxide (Huston
and Pignatello, 1999; Murugandham and Swaminathan, 2007;
Lucas and Peres, 2006; Gogate and
Pandit, 2004; Legrini et al., 1993). In acidic
medium, this radical mechanism can be described by the following equations:
While, hydroxyl radicals can oxidize most organic pollutants directly, the
refractory ones can only be degraded through complex pathways. It can be safely
assumed that almost all industrial effluents contain more than one component
and often some of those are more refractory.
The mechanism of Fenton’s oxidation of organic compounds is very complicated
even for singlecomponent solutions. Typically, the oxidation undergoes a complex
reaction scheme and leads to the formation of many different intermediates,
such as recalcitrant shortchain organic acids (Pintar
et al., 2004). In the case of industrial wastewaters, many compounds
are present in the waste stream. The oxidation of such a mixture is much more
complex than the oxidation of a singlecompound solution.
The concentration of organic materials must be expressed by means of a lumped parameter such as Total Organic Carbon (TOC), which accounts for all organic species present in a wastewater, or Chemical Oxygen Demand (COD), which also takes into account oxidizable inorganics. Therefore, the kinetic models that solely predict the disappearance rate of pure compounds are not sufficient: a lumped kinetic model capable of predicting complete conversion of all organic species present in wastewater is needed.
The organic pollutant (COD) degradation kinetics can be expressed by pseudo
first order kinetics according to the following rate equation (Kim
et al., 1997): r = kC●_{OH} C = k_{exp}C in
which r is the rate of degradation, C is the concentration of the organic substances
in terms of COD, C_{OH} is concentration of ^{●}OH radical,
k is the second order rate constant and k_{exp} is pseudofirst order
rate constant when C__{OH} is supposed to be constant. The pseudo first
order of this reaction is based on the assumption that the ^{●}OH
radical attains a steady concentration within a short time.
Experiments in connection with an investigation on treatability of the effluent
by Fenton’s process were conducted to determine optimum process conditions
with respect to COD reduction. The present study attempts to develop a kinetic
model based on data of COD reduction in the presence of Fenton’s reagent
with a lumped kinetic description of Chemical Oxygen Demand (COD). This approach
is useful when dealing with the kinetics of the reactions with complex mixtures
such as wastewaters (Li et al., 1996). The generalized
lumped kinetic model proposed by Li et al. (1991)
has been applied extensively for the different types of wastewaters (Rivas
et al., 2001; Lin et al., 1996; Luck,
1996). Apart from the data generated by the authors, the results of fitting
the lumped models to data reported in literatures are required to illustrate
the generality and applicability of this approach.
MATERIALS AND METHODS
The study reported here was carried out for 3 months from March 15, 2010 to Jun 15, 2010 in the research laboratory in the Department of Chemical Engineering, Indian Institute of Technology Kharagpur, India.
Chemicals or reagents: Characteristics of the raw (untreated) wastewater collected from the petrochemical plant are shown in Table 1.
Hydrogen peroxide solution (50%, w/v), Ferrous sulfate heptahydrate (FeSO_{4}.7H_{2}O), Monoethylene glycol (MEG), 1,4Dioxane, NaOH, H_{2}SO_{4} were all analytical grades. Distilled water was used throughout this study.
Experimental procedure: Fenton’s oxidation was carried out in batch mode in beakers of 250 mL capacity with 150 mL of wastewater. Appropriate amount of FeSO_{4} was dissolved using part of the liquid in the beaker and then transferring back to beaker. Initial pH of the reaction solution was adjusted by using 1 M H_{2}SO_{4} solution and the beaker was kept in a temperature controlled bath and allowed to attain the preset experimental temperature. Appropriate amount of H_{2}O_{2} were added into the beaker to start the reaction. Small volume of samples were withdrawn after 20, 40, 60 and 80 min using a pipette and filtered through Whatman No. 42 filter paper. The filtrate was analyzed for COD. The optimum process conditions were: initial pH 3, H_{2}O_{2} concentration 3 M, Fe^{2+} concentration 0.06 M. At these conditions, maximum COD reduction (97.5%) was achieved. These experiments were with undiluted as well as diluted effluent. Reproduciblity of the results was established to be within 5% by repeating specific experiments several times.
Analytical methods and instruments: The pH was recorded using a digital
pH meter (Model: CL 46, Toshniwal Instruments, India). Conductivity was measured
by a digital conductivity meter (Model: 611E, from M/s EI Products, India).
COD of the reaction medium were measured by Open reflux method (Clesceri
et al., 1998). BOD_{5} and total solids were measured according
to standard methods (Trivedy and Goel, 1984). Ethylene
glycol and Dioxane concentrations were determined using a gas chromatograph
(Chemito India Ltd. GC 8610 with a Chemito 10% OV17 column, 6x 0.125) with 25
mL min^{1} nitrogen as carrier gas and 0.5 μL sample volume being
injected.
Table 1: 
Characteristics of the waste water used 

RESULTS AND DISCUSSION
The COD reduction kinetics considering single lump of pollutants oxidized in a single step Considering 1st order kinetics for COD reduction by Fenton’s reaction in a single step for a single lump of pollutant lead to the exponential decay equation:
Where:
COD (t) 
= 
COD after time t min 
COD(0) 
= 
Initial COD 
k 
= 
1^{st} order kinetic constant for COD reduction, min^{1} 
Experimental data of COD vs time (20, 40, 60, 80 min) for same process conditions were fitted to Eq. 1 by minimizing the sum of square of deviations in % error with respect to the experimental data. The minimization program written in MATLAB software used LSQNONLIN routine with LevenbergMarquardt nonlinear optimization algorithm. The bestfit k is 0.04149 min^{1}. Predicted vales of COD plotted against experimental COD values for different experiments with initial COD of 11500, 9200, 5950 and 3100 mg L^{1} are shown in Fig. 1. with a diagonal (45°) line and 10% deviation limit lines. Several predictions can be seen to deviate beyond the 10% limit lines and the average of the sum of the square of deviations % is 2591.1.
COD reduction kinetics considering two lumps of pollutants oxidized simultaneously
in single step: Generalized chemical formulae for the two hydrocarbon pollutant
lumps are considered to be C_{m}H_{n} and C_{p}H_{q}.
These lumps are assumed to be individually oxidized completely during Fenton’s
oxidation in single step following 1st order kinetics at different rates. Based
on the stoichiometry of complete oxidation in a single step, the COD contribution
(α_{1 }and α_{2}) from 1 g mol L^{1} concentration
of C_{p}H_{q} and C_{p}H_{q} can be written
as:

Fig. 1: 
Predicted COD from model considering a single lump of pollutants
oxidized in a single step vs actual COD 
COD of the sample having [C_{m}H_{n}] and [C_{p}H_{q}]
g mol L^{1} of pollutant can be written as (α_{1 }x [C_{m}H_{n}]
+ α_{2} x [C_{p}H_{q}]) mg L^{1}; where
the two constituent terms are COD contributions from the individual lumps. Considering
two degradation reactions are independent and are both of 1^{st} order,
the COD contribution from each lump will have exponential decay but at different
rates. Therefore, the COD of the sample as a function of time can be written
as:
Where:
COD (t) 
= 
COD of sample after t min 
f 
= 
Mole fraction of lump 1 in the sample initially 
k_{1}, k_{2} 
= 
1st order kinetic constant for COD reduction for lump 1 and lump 2, min^{1} 
During COD reduction by Fenton’s reaction at optimum process conditions,
the terms f, COD(0), k_{1} and k_{2} remain constant with time
for Eq. 2. Values of these terms are found by fitting COD
of sample vs time to Eq. 2 by minimizing the sum of square
of deviations in % error with respect to the experimental data. Previously mentioned
MATLAB routines and algorithms are used in this case. The best fit values are:
k_{1 }= 0.0177; k_{2 }= 1.6753; f
= 0.3575 
Predicted vales of COD plotted against experimental COD values are shown in Fig. 2. with a diagonal (45^{o}) line and 10% deviation limit lines. Fewer predictions can be seen to deviate beyond the 10% limit lines and the average of the sum of the square of deviations % is 334.8.

Fig. 2: 
Prediction from model considering two lumps of pollutants
oxidized simultaneously in single step 
COD reduction kinetics considering pollutants oxidized in two steps:
It is assumed that the general formula of the pollutant lump originally present
is D_{m}H_{n}. This gets oxidized by Fenton’s reaction
to another product C_{mp}H_{nq} along with production of CO_{2}
and H_{2}O. C_{mp}H_{nq} gets oxidized independently
in a single step. In a previous work a lumped kinetic model based on adsorption/electrocatalysis/oxidation
mechanism for COD reduction was proposed by Zhou et al.
(2004). These reactions are also assumed to be pseudo 1st order reactions
with rate constants k_{1} and k_{2} and are shown below:
In the line of treatment presented in previous for single lump of pollutants
oxidized in single step, the COD of the sample having [C_{m}H_{n}]
and [C_{p}H_{q}] g mol L^{1} of pollutant can be written
as:
where, COD due to 1 g mol L^{1} concentrations of C_{m}H_{n}
and C_{mp}H_{nq} are:
Based on pseudofirst order decay kinetics of C_{m}H_{n}, the
following expressions can be written as:
or
Decay of C_{mp}H_{nq} follows pseudofirst order, but there is a generation term. Therefore the transient balance of the species is written as:
Generalized form of equation Eq. 4 is:
and this equation has analytical solution: x (t) = (b/(ac)) x {exp (ct)exp(at)}
Therefore,
and
Equation 5 represents the expression for COD of the sample with time involving constants β_{1}, β_{2}, k_{1} and K_{2}.
Similar to the procedure followed considering two lump of pollutants oxidized simultaneously in single step, values of these constant terms are found by fitting COD of sample vs. time to Eq. 5 by minimizing the sum of square of deviations in % error with respect to the experimental data. The earlier mentioned MATLAB routines and algorithms are used in this case.
The best fit values are: β_{1}= 0.01640, β_{2}=0.00536, k_{1} = 0.28068 and k_{2} = 0.01835. Predicted vales of COD plotted against experimental COD values are shown in Fig. 3. with a diagonal (45°) line and 10% deviation limit lines. Most predictions can be seen to below the 10% limit lines and the average of the sum of the square of deviations % is 247.9.
Validating the models using data reported in literature: In order to
check the generality of the model, these models need to be fitted to data from
literature. This is done with COD values with time during treatment by Fenton’s
oxidation of leachate streams.

Fig. 3: 
Prediction from model considering two lumps of pollutants
oxidized in two steps 

Fig. 4: 
Prediction from model considering a single lump of pollutants
oxidized in a single step for literature data 

Fig. 5: 
Prediction from model considering two lumps of pollutants
oxidation in parallel for literature data 
The data sets B and D are from the same literature (Zhang
et al., 2006), data set F (Zhang et al.,
2005) is from the same group of investigators and the data set H, J and
L are from a different source (Gotvajn et al., 2009).
The above data set from literature are present in the respective publications
without relating the same to any mathematical model. Therefore both single and
the proposed multilump models are fitted to the data.
Figure 4 shows the fit for model considering a single lump of pollutants oxidized in a single step. The average absolute errors in prediction for the data sets (B, D, F, H, J and L) are 26.48, 44.34, 34.84, 59.75, 33.65 and 47.48, respectively.
Figure 5 shows the fit for the model considering two lumps
of pollutants oxidized simultaneously in single step. In this case, the average
absolute errors in prediction for the data sets (B, D, F, H, J and L) are 2.57,
16.49, 1.07, 1.45, 1.05 and 0.65 respectively.

Fig. 6: 
Fitting of data from literature for considering pollutants
oxidized in two steps for literature data 
Table 2: 
Mean square (%) error in prediction for the three models
on the literature data 

These errors are markedly lower than the case of fit for model considering
a single lump of pollutants oxidized in a single step.
The quality of fit for the model considering pollutants oxidized in two steps is shown in Fig. 6. In this case, the average absolute errors in prediction for the data sets (B, D, F, H, J and L) are 2.63, 16.49, 1.02, 1.66, 1.05 and 0.87, respectively.
Table 2 shows the mean square (%) error in prediction for the three models on the literature data. In all cases the mean square (%) error is practically one order higher in case of the single lump model.
CONCLUSIONS
Although, the chemistry of the Fenton’s reaction system involves a complex mechanism of oxidizing hydrocarbons to CO_{2} and H_{2}O, approximations by 1st order kinetic models in various forms can be used to describe the process of COD reduction. In case of the specific effluent from the local petrochemical industry, the model considering a lump of pollutants oxidized in two steps with intermediate product formation fits better than the model considering simultaneous degradation of two lumps of pollutants. It also has an extra constant that allows a degree of freedom more than the other model. Both the said models fit the practical observations markedly better than the classical simplistic model considering single step 1^{st} order kinetics of complete mineralization of a single lump of pollutants present.
Results from fitting these models on literature reported data also suggest that considering the oxidizables as a single lump is clearly an over simplification. Models involving either two lumps being oxidized simultaneously or the process occurring in two steps represent the Fenton’s process much more closely, observed as COD reduction with time.
In actual practice the degradation of the complex pollutants involves intermediate formation and degradation of these intermediates. The model considering a lump of pollutants oxidized in two steps with intermediate product formation is more realistic.
ACKNOWLEDGMENTS
The authors wish to express their gratitude to M/s South Asian Petrochemicals Limited, Haldia Unit, West Bengal, India for providing the effluent sample. Formulation of models and the experimental work was done by the first author. The coauthors contributed to solution of the multilump models.