Measuring the Efficiency and Ranking of Photocatalytic Degradation of Azo dye AR 206 and COD Using Data Envelopment Analysis
محورهای موضوعی : Applied Mathematics
1 - Department of Statistics, Arak-Branch, Islamic Azad University, Arak, Iran
کلید واژه: Photocatalytic Degradation, Acid Red 206, Chemical Oxigen Demand, Data envelopment analysis, Super-efficiency,
چکیده مقاله :
In this study a new photocatalyst was prepared and identified using XRD pattern and SEM image. This catalyst is used to decomposition of azo dye Acid Red 206(AR 206) in aqueous solution. In the previous study optimum conditions has been obtained by using experimental design which is parametric method and is not proposed method for converting the inefficient experiments to efficient. Data Envelopment Analysis (DEA) involves an alternative principle for extracting information about a population of observations called Decision Making Units (DMUs) with similar quantitative characteristics. This is reflected by the assumption that each DMU uses the same set of inputs to produce the same set of outputs, but the inputs are consumed and outputs are produced in varying amounts. In this paper the input oriented CCR model and its super-efficiency model are proposed for measuring the efficiency and ranking of photocatalytic degradation of Azo dye AR 206 and Chemical Oxigen Demand (COD) photocatalytic degradation experiments . We consider these experiments as DMUs. Finally inefficient experiments by using of the projection points were converted to the efficient experiments.
Measuring the efficiency and ranking of photocatalytic degradation of AZO dye AR 206 and COD by using data envelopment analysis
Abstract
In this study a new photocatalyst was prepared and identified using XRD pattern and SEM image.
This catalyst is used to decomposition of azo dye Acid Red 206(AR 206) in aqueous solution.
In the previous study optimum conditions has been obtained by using experimental design which is parametric method and is not proposed method for converting the inefficient experiments to efficient. Data Envelopment Analysis (DEA) involves an alternative principle for extracting information about a population of observations called Decision Making Units (DMUs) with similar quantitative characteristics. This is reflected by the assumption that each DMU uses the same set of inputs to produce the same set of outputs, but the inputs are consumed and outputs are produced in varying amounts. In this paper the input oriented CCR model and its super-efficiency model are proposed for measuring the efficiency and ranking of photocatalytic degradation of Azo dye AR 206 and Chemical Oxigen Demand (COD) photocatalytic degradation experiments . We consider these experiments as DMUs. Finally inefficient experiments by using of the projection points were converted to the efficient experiments.
Kywords: Data Envelopment Analysis; CCR Model; Chemical Oxigen Demand; Photocatalytic degradation; Acid Red 206; Super-efficiency.
Organic dyes including azo dyes are one of the largest groups of pollutants in industrial effluents produced from textile and other industrial processes. The potential toxicity of dyes such as azo dyes has long been known. Therefore, it is necessary to find an effective method of wastewater treatment in order to remove dye from industrial wastewater. A number of physical and chemical techniques have been reported for the removal of dye and organic compounds such as adsorption on absorber such as activated carbon, biodegradation, ozonation, and advanced oxidation processes[1]. In recent years, advanced oxidation processes (AOP) have been proposed as an effective method for the treatment of contaminated effluents containing non-biodegradable and toxic organic dye pollutants. One of the most important AOPs methods in effluent treatment is the heterogeneous photo-catalytic process. Because of its unique advantages of complete mineralization of organic pollutants and relatively easy separation of the heterogeneous catalyst from the treated wastewater, many studies have been in this field [1–6].
Data envelopment analysis (DEA), was first proposed by Charnes et al. [7] and was developed by Banker et al. [8]. The DEA has grown into a powerful quantitative, analytical tool for measuring and evaluating the performance. The DEA has been successfully applied to a host of many different types of entities engaged in a wide variety of activities in many contexts worldwide. The DEA is a approach for evaluating the performance of a set of peer entities called Decision Making Units (DMUs), which convert multiple inputs into multiple outputs. The definition of a DMU is generic and flexible. Recent years have seen a great variety of applications of DEA for use in evaluating the performances of many different kinds of entities engaged in many different activities in many different contexts in many different countries. These DEA applications have used DMUs of various forms to evaluate the performance of entities, such as hospitals, US Air Force wings, universities, cities, courts, business firms, and others, including the performance of countries, regions, etc. Because it requires very few assumptions, DEA has also opened up possibilities for use in cases that have been resistant to other approaches because of the complex (often unknown) nature of the relations between the multiple inputs and multiple outputs involved in DMUs. In their originating article, Charnes et al. [7] described DEA as a “mathematical programming model applied to observational data [that] provides a new way of obtaining empirical estimates of relations-such as the production functions and/or efficient production possibility surfaces-that are cornerstones of modern economics.” Formally, DEA is a methodology directed to frontiers rather than central tendencies. Instead of trying to fit a regression plane through the center of the data as in statistical regressions, for example, one “floats” a piecewise linear surface to rest on top of the observations. Because of this perspective, DEA proves particularly adept at uncovering relationships that would remain hidden from other methodologies. For instance, consider what one wants to mean by “efficiency,” or more generally, what one wants to mean by saying that one DMU is more efficient than another DMU. This is accomplished in a straightforward manner by DEA without requiring explicitly formulated assumptions and variations that are required with various types of models such as linear and nonlinear regression models.
In cases for which several DMUs have the same efficiency score of “1”, a standard DEA approach is not able to discriminate amongst this DMUs. The related literature provide several approaches to rank efficient DMUs in DEA. Adler et al.[9] , for example, classify and present these approaches into six streams: 1) cross-efficiency ranking methods; 2) benchmark ranking method; 3) ranking with multivariate statistics in the DEA context; 4) ranking inefficient DMUs; 5) DEA and multi-criteria decision-making (MCDM) methods and 6) super-efficiency ranking techniques. The sixth stream is super-efficiency ranking techniques proposed by Anderson and Petersen[10]. They rank efficiency DMUs by measuring the distance from an efficiency DMU to a frontier, based on a set of observations, excluding the efficiency DMU in question. Therefore, the most efficient DMU is the one that can proportionally reduce outputs relative to the most efficient one without becoming inefficient.
Almost, all of the previous works in photocatalytic degradation have been used the parametric approach. As far as we know DEA models have not already been used in analysis of photocatalytic degradation experiments.
In this study a new catalyst was prepared and identified using XRD and SEM. Then the efficiency and ranking by useing DEA and super efficiency has been done. The best conditions for a photocatalytic experiments were determined. Finally inefficient experiments by using of the projection points were converted to the efficient experiments.
2. Experimental
2. 1. Materials
The raw material was an Iranian commercial Clinoptilolite (CP) (Afrand Tuska Company, Iran) from deposits in the region of Semnan. According to the supplier specification, it contains about 90 wt.% CP (based on XRD internal standard quantitative analysis), the Si/Al molar ratio is 5.78 concentration of Fe2O3, TiO2, MnO and P2O5 impurities have been reported to be 1.30, 0.30, 0.04 and 0.01 wt. %.
The xanthene dye, Acid Red 206 (AR206), was obtained from Rang Azar Company (Iran) and used without further purification. The molecular structure of AR52 is shown in Fig.1. Other materials prepared from Merck Company.
Fig. 1. Molecular Structure of Acid Red 206
2.2. Preparation of Fe2O3 - Supported CP Catalysts
Fe2O3 were prepared by precipitation of the nitrate salts (Merk) with an aqueous solution of NH4OH (50 v/v) at 50 o C and a constant pH of 8. The solids were filtered and carefully washed with demineralized water, dried at 110 o C overnight in a vacuum oven and then calcined in static air at 300 o C for 2 h.
The solid state dispersion (SSD) method was used for preparing the Zeolite-based photocatalyst. In this method, Fe2O3 was mixed with zeolite using ethanol using agate pestle and mortar; ethanol was then removed by evaporation. Samples prepared by this method were dried at 110 o C and calcined in air at 300 o C for 2 h to obtain Fe2O3-supported zeolite catalysts.
2.3. Apparatus
For the UV/photocatalyst process, irradiation was performed in a Circulating Fluidized Bed Photo Reactor(CFBPR) as show in Fig.2.Volume of reactor is 1 liter with a mercury lamp Philips 32W (UV-C). UV/VIS Spectrophotometer, Perkin Elmar (Lambada25) was employed for absorbance measurements using silica cells of path length 1 cm. XRD analysis of the samples was done using a D-500 diffractometer (Siemens). The morphology of the resultant pure and loaded Fe2O3 was obtained with a scanning electron microscope (5800- JSM JEOL). BET surface areas of CP and Fe2O3/CP were measured in an all-glass high vacuum system by N2 adsorption at 77 K.
Fig. 2. Schematic diagram of CFBR with recycle current: (1) Air pump, (2) Water pump, (3) Thermo-Bath, (4) Water Current, (5) Dye Solution Current, (6) Valve, (7) Heat Exchanger, (8) Reactor, (9) UV-C Lamp, (10) Recycle Current, (11) Tank, (12) Magnetic Stirrer
2.4. Procedures
For the photodegradation of AR52, a solution containing known concentration of dye and photocatalyst was prepared. The suspension pH values were adjusted at desired level using dilute NaOH and H2SO4 (the pH values were measured with Horiba M12 pH meter) and were allowed to equilibrate for 30 min in the darkness. Subsequently 4 liter of the prepared suspension was transferred to a tank. The photodegradation reaction took place under the radiation of Mercury lamp while agitation (in tank) was maintained to keep the suspension homogeneous. The concentration of the samples was determined using a spectrophotometer (UV/VIS Spectrophotometer, Perkin-Elmar (Lambda25)) at 
nm. The degree of photodegradation (X) as a function of time is given by:
(2.1)
Where 
and C are the concentration of dye at t = 0 and t, respectively.
We assume that there are n 
to be evaluated. where each 
(j=1,...,n) uses m different inputs, 
, to produce s different outputs, 
.We assume that 
and 
and further assume that each DMU has at least one positive input and one positive output value.
3.1 . Input-Oriented CCR Model
One of the basic DEA model for evaluating DMUs is the input-oriented CCR model introduced by Charnes et al. [7]. The CCR-efficiency is obtained by solving the following model:
(3.1)
Definition 3.1 (CCR-efficient) 
is said to be CCR-efficient if and only if the following two conditions are both satisfied:
i. All slack variables are zero in the alternative optimal solution.
One of the basic models for ranking DMUs is the “super-efficiency” model where introduced by Anderson and Peterson [10]. The efficiency scores from these models are obtained by eliminating the data on the to be evaluated from the solution set. For the input model this can result in values which are regarded as according the status of being “super-efficient". These values are used to rank the DMUs and thereby eliminate some (but not all) of the ties that occur for efficient DMUs. Now, by using model (3.1) we propose the super-efficiency for DEA model (3.1) is as follows :
(3.2)
Super-efficiency model (3.2) computes the score of the DMU under evaluation with removing it from constraints.
4.1. Effect of photocatalyst
This is due to the fact that when Fe2O3 is illuminated with the light of 
nm, electrons are promoted from the valence band to the conduction band of the semi conducting oxide to give electron–hole pairs. The valence band (
) potential is positive enough to generate hydroxyl radicals at the surface and the conduction band (
) potential is negative enough to reduce molecular oxygen. The hydroxyl radical is a powerful oxidizing agent and attacks organic pollutants present at or near the surface of Fe2O3. It causes photooxidation of dye according to the following reactions [11-13]:
Fe2O3 + hν → Fe2O3 (e
+ h
)
(2)
h + H2O
→ H+ + •OH (3)
h+ OH
→ •OH (4)
e + O
O
(5)
•OH + dye → degradation of the dye (6)
h + dye dye
oxidation of the dye (7)
4.2. Effect of the Composition of the Supported Photocatalyst
The effect of the ratio of Fe2O3 / CP on the AR52 removal is shown in Fig.5. The effective decomposition of AR52 after 120 min irradiation time was observed when photocatalyst contained 15% Fe2O3 and 85% CP prepared by using solid state dispersion (SSD) method.
Fig. 5. Effect of composition of photocatalyst (wt. % Fe2O3 in mixture of Fe2O3 and CP) on photocatalytic degradation of AR206 after 150 min. [AR206]0 = 25 ppm, concentration of photocatalyst = 125 ppm, T = 298 K, pH =9.
For comment of this result, we propose that the OH (hydroxyl radical), on the surface of Fe2O3 are easily transferred onto the surface of zeolite. That means the organic pollutants, which have already been adsorbed on the non-photoactive zeolite, have chances to be degraded due to the appearance of OH, resulting in the enhancement of photodegradation performance of Fe2O3–zeolite. Experimental results show that about 15 wt. % of Fe2O3 with respect to zeolite is the best condition to achieve the synergism between Fe2O3 and CP. This synergic effect may be due to the fact that the presences of zeolite maintaining the molecules of dye near the photocatalyst (local concentration effect). As depicted in fig 4, the enhanced photocatalytic activity over the composite Fe2O3+CP reflects the beneficial adsorption properties of CP. If the Fe2O3 decreases in composition of photocatalyst (less than15 wt. %), rate of OH production would not be enough. Under these conditions a few of molecules of dye that absorbed onto the surface of zeolite can react with OH. If Fe2O3 increased in composition of photocatalyst (more than15 wt %) the rate of dye absorption would not be enough. Under these conditions some of the OH can react with molecules of dye [14].
4.3. Characterization of catalyst
To reveal the interactions between the Fe2O3 and zeolite, the crystal structures of the raw zeolite and the Fe2O3–zeolite calcined at 300o C after 2 h were measured, as shown in Fig. 6 It is clear that the XRD patterns of Fe2O3–zeolite are consistent with the raw zeolite calcined at 300o C for 2h, and no diffraction peaks corresponding to typical Fe2O3.It implies that the frame structure of zeolite after Fe2O3 loading has not been destroyed. Partial sizes of Fe2O3 are between 50-85 nm that determined from the half width of the diffraction peak using Sherrer equation [15].
Fig. 6. XRD pattern of Fe2O3, raw CP after calcined in air at 300o C for 5 h and 15Wt.% Fe2O3 and 85Wt.% CP zeolite prepared by the (SSD) method after calcined in air at 300o C for 2 h
As known, the pore size of Clinoptilolite is 0.4–0.7 nm [16]. Fig. 7 shows the SEM images of pure Fe2O3 nanoparticles and Fe2O3 particles have loaded on the surface of CP. As seen, the particle size of pure Fe2O3 is 50-80 nm, which is much larger than that of the loaded ones. Thus, Fe2O3 particles are not able to enter into the pores. Therefore, we suggest that the protrusions are Fe2O3 and nearly all of the Fe2O3 particles have been loaded on the surface of zeolite, instead of into the pores and cavities. It means that the photocatalytic degradation of Acid Red52 mostly takes place at the zeolite surface, but not in the pores. In addition, as shown in Fig. 7, the small Fe2O3 particles does not distribute compactly but reserves lacunas on the zeolite surface, which enable the support to show its adsorption ability.
Fig. 7. SEM images of A) pure Fe2O3 nanoparticles and B) Fe2O3 particles have loaded on the CP
The surface area of the CP (
) decreased in general on supporting Fe2O3 (BET surface area of Fe2O3 / CP with different Fe2O3 wt% is between 264-372
. The surface area of the Fe2O3 supported zeolite may be taken as an index of the available porosity. Considering the particle sizes of Fe2O3 and the sizes of CP zeolite medium pores (<1 nm) we conclude that there is no possibility of Fe2O3 particles entering the zeolite pores in SSD method of preparation.
In this section, an example of photocatalytic degradation is presented to demonstrate the modeling idea and the effectiveness of the proposed method. We apply the DEA methodology and super-efficiency for measuring the efficiency and ranking 16 photocatalytic degradation experiments. We consider these experiments as DMUs, and denote them by 
. Thus, by solving models(3.1) and (3.2) can be obtain the efficiency of experiments and its rank. The labels of inputs and outputs are shown in Table 1.
Table 1: The labels of inputs and outputs.
Input1 | pH (i.e. initial acidity of dye solution) |
Input2 | Dye (i.e. initial concentration of Azo dye AR 206) |
Input3 | C (i.e. Photocatalyst amount) |
Input4 | T (i.e. temperature of photocatalytic reaction solution) |
Output1 | PPR (i.e. percent photocatalytic removal) |
Output2 |
|
The data set for this example is shown in Table 2.
Table 2: The data set of practical example.
| Input 1 | Input 2 | Input 3 | Input 4 | Output 1 | Output 2 |
Experiment1 | 6 | 50 | 6 | 15 | 82.198 | 0.01404 |
Experiment2 | 6 | 100 | 8 | 20 | 84.034 | 0.01366 |
Experiment3 | 6 | 150 | 10 | 25 | 83.866 | 0.01386 |
Experiment4 | 6 | 200 | 12 | 30 | 84.683 | 0.01354 |
Experiment5 | 7 | 50 | 8 | 25 | 80.523 | 0.01441 |
Experiment6 | 7 | 100 | 6 | 30 | 79.333 | 0.01458 |
Experiment7 | 7 | 150 | 12 | 15 | 86.891 | 0.01326 |
Experiment8 | 7 | 200 | 10 | 20 | 84.696 | 0.01353 |
Experiment9 | 8 | 50 | 10 | 30 | 77.992 | 0.01504 |
Experiment10 | 8 | 100 | 12 | 25 | 80.98 | 0.01431 |
Experiment11 | 8 | 150 | 6 | 20 | 83.556 | 0.01377 |
Experiment12 | 8 | 200 | 8 | 15 | 82.743 | 0.01388 |
Experiment13 | 9 | 50 | 12 | 20 | 83.365 | 0.01387 |
Experiment14 | 9 | 100 | 10 | 15 | 81.037 | 0.01425 |
Experiment15 | 9 | 150 | 8 | 30 | 80.012 | 0.01448 |
Experiment16 | 9 | 200 | 6 | 25 | 81.811 | 0.01406 |
We run models (1) and (2) by means of GAMS software and the results are shown in Table 3.
Table 3: Results of measuring the efficiency and ranking of experiments
| Efficiency | Super-Efficiency | Ranking with Andersen and Petersen method |
Experiment1 | 1 | 1.4466 | 1 |
Experiment2 | 1 | 1.0121 | 8 |
Experiment3 | 1 | 1.0051 | 10 |
Experiment4 | 1 | 1.0077 | 9 |
Experiment5 | 0.9989 | 0.9989 | 11 |
Experiment6 | 1 | 1.0380 | 3 |
Experiment7 | 1 | 1.0536 | 2 |
Experiment8 | 0.8748 | 0.8748 | 14 |
Experiment9 | 1 | 1.0347 | 4 |
Experiment10 | 0.7644 | 0.7644 | 15 |
Experiment11 | 1 | 1.0165 | 5 |
Experiment12 | 0.9974 | 0.9974 | 13 |
Experiment13 | 1 | 1.0142 | 7 |
Experiment14 | 1 | 1.0150 | 6 |
Experiment15 | 0.7589 | 0.7589 | 16 |
Experiment16 | 0.9982 | 09982 | 12 |
The projection points of practical example is shown in Table 4.
Table 4: The projection points of practical example.
| Input 1 | Input 2 | Input 3 | Input 4 | Output 1 | Output 2 |
Experiment1 | 6.00 | 50.00 | 6.00 | 15.00 | 82.20 | 0.01404 |
Experiment2 | 6.00 | 100.00 | 8.00 | 20.00 | 84.03 | 0.01366 |
Experiment3 | 6.00 | 150.00 | 10.00 | 25.00 | 83.87 | 0.01386 |
Experiment4 | 6.00 | 200.00 | 12.00 | 30.00 | 84.68 | 0.01354 |
Experiment5 | 6.99 | 49.95 | 7.99 | 21.28 | 80.52 | 0.01 |
Experiment6 | 7.00 | 100.00 | 6.00 | 30.00 | 79.33 | 0.01458 |
Experiment7 | 7.00 | 150.00 | 12.00 | 15.00 | 86.89 | 0.01326 |
Experiment8 | 6.12 | 72.90 | 7.00 | 17.50 | 84.70 | 0.01 |
Experiment9 | 8.00 | 50.00 | 10.00 | 30.00 | 77.99 | 0.01504 |
Experiment10 | 6.12 | 50.96 | 6.12 | 15.29 | 83.78 | 0.01 |
Experiment11 | 8.00 | 150.00 | 6.00 | 20.00 | 83.56 | 0.01377 |
Experiment12 | 6.75 | 80.01 | 7.98 | 14.96 | 82.74 | 0.01 |
Experiment13 | 9.00 | 50.00 | 12.00 | 20.00 | 83.37 | 0.01387 |
Experiment14 | 9.00 | 100.00 | 10.00 | 15.00 | 81.04 | 0.01425 |
Experiment15 | 6.58 | 75.89 | 6.07 | 22.77 | 81.72 | 0.01 |
Experiment16 | 6.07 | 54.09 | 5.99 | 16.23 | 81.81 | 0.01 |
Note that the inefficient experiments (number of 5, 8, 10, 12, 15, and 16 ) by using the projection points on efficiency frontier can be efficient experiments.
The results showed that a new catalyst in the photocatalytic decomposition of AR206 has been efficient. DEA is a nonparametric technique for evaluating DMUs based on the production possibility set. In this paper the DEA methodology and super-efficiency were proposed for measuring the efficiency and ranking experiments based on inputs and outputs (see Table 1). In the analysis of experiments with multiple inputs and outputs the DEA models may be better suited with respect to experimental design (which is parametric method) approaches. Therefore, we proposed a super-efficiency model for ranking of experiments and determined the optimum experiment by using input oriented CCR model. Finally, 16 photocatalytic degradation experiments was presented and it was observed that the experiment number 1 is optimum( see Table2). One of the main results of this paper is that the inefficient experiments by using the projection points on efficiency frontier can be efficient experiments (see, Table 4). In order to further studies, the approach of this research may be extended to some other DEA models and photocatalytic degradation experiments .
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* Corresponding Author's E-mail: hosseindibachi@gmail.com
