Use of Genetic Algorithm Optimization Technique in the Adsorption of

Mehmet Fatih Dilekoglu

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Use of Genetic Algorithm Optimization Technique in the Adsorption of Phenol on Banana and Grapefruit Peels Mehmet Fatih Dilekoglu* Department of Environmental Engineering, Harran University, Sanlıurfa, Turkey. [email protected]* (Received on 9th May 2016, accepted in revised form 1ST November 2016) Summary: Adsorption studies for phenol removal from aqueous solutions on banana and grapefruit peels were carried out under varying experimental conditions of contact time, phenol concentration and pH. The maximum adsorption capacities for 100 ppm initial phenol concentration were determined as 33.66 mg.g-1 and 23.50 mg.g-1 for banana and grapefruit peel at the pH values of 7, respectively. Two-three and four parameter isotherm equations were used to determine the equilibrium adsorption capacities of banana and grapefruit peel for phenol removal. Among the two and three parameter equation, Redlich-Peterson equation gives the satisfactory fit over all ranges of concentration whereas, Langmuir and Freundlich did not give adequate result, with respect to standard deviation. The parameters of Jeager-Erdoes contained four unknown constants (A, B, K and D) were solved by Genetic Algorithm (GA) method under no assumption. Among the equations considered, the four parameter equation of Jeager-Erdoes represents the best approximation with experimental data.

Keywords: Genetic algorithm, Adsorption isotherm, Adsorption of phenol, Adsorption kinetics. Introduction Aromatic compounds such as phenols vastly occur in wastewater, being generated in petroleum refining, petrochemical, plastics, coal conversion industries and steel industries [1]. Such aromatic hydroxy compounds are regarded as hazardous material, since they are harmful to organisms and human healthy at low concentrations. According to US Environmental Protection Agency (EPA), the concentration of phenol in wastewater must be less than 1 mg/l. [2] EPA also designated phenol compounds as principal pollutant constituents among 126 chemicals [3]. The removal methods of phenolic materials from aqueous solutions include chemical oxidation, coagulation, solvent extraction, membrane separation and adsorption into porous solids. The choice of systems depends on phenol concentration, economy and other factors. In water treatment, the most widely used method for removing phenolic compounds is to adsorb onto activated carbon with moderate and low concentrations. Activated carbon both in granular and powdered form exhibits high adsorption capacity for phenolic compounds [3-9]. Although activated carbon has been used widely and effectively for this purpose, the higher the adsorption capacity, the greater the cost. Both chemical and thermal regeneration of carbon is expensive, impractical on large scale and produces additional effluents and results in considerable loss of the adsorbent. Due to all these disadvantages, the researchers search new low cost natural adsorbents such as clay minerals (bentonite, montmorillonite *

To whom all correspondence should be addressed.

etc.), coal, agricultural waster (bagasse pith, orange peel, coconut shell, rice husk, etc.) and cotton waster for the removal of toxic metals and some organics pollutants from aqueous solutions [1, 10-15]. In this paper, the influence of various factors including aqueous phenol concentration, contact time and pH of solution on the adsorption capacities of banana and grapefruit peels have been investigated. Although many isotherms have been given in literature [16-21] to optimize the adsorption equilibria, to our knowledge, among these equations, there are no studies on the most general four parameter isotherm equation and the “n th” order adsorption rate equation [22]. In general, adsorption isotherms are important to decide how adsorbates will interact with adsorbent and are critical in optimizing the use of adsorbent. In this regard, the correlation of adsorption data using either a theoretical or an empirical equation is essential to practical adsorption operation. Thus, the main aim of this study is to determine the constant of most general four parameter isotherm equation proposed by Jeager and Erdoes and the “n th” order rate equation of adsorption under no assumption by genetic algorithm (GA) method. A comparison was made on the applicability of various two-three and four parameter

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isotherm equation which correlated the equilibrium data most satisfactorily.

assumptions. However, they are all simplifications of Eq. 1[23].

Mathematical Model for Equilibrium Adsorption and Adsorption Rate

Up to now, the all constants of Eq. 1 can not be found without assumptions. But in this study, Eq.1 contained four unknown constants (A, B, K and D) were solved by Genetic Algorithm (GA) method under no assumption. In order to apply the GA method to Eq.1, it can be rewritten in the following form:

The preliminary requirements for an adsorbent design which is based on empirical equations are; 



The rate of adsorption, i.e., the time elapsed before a given amount of solute is removed from the solution. This is provided by studies of the kinetics data given in terms of effluent concentration as a function of time. The capacity of the adsorbent for the solute and hence the dosage of adsorbent required to remove a unit mass of solute from solution. This is provided by equilibrium studies that yield information on the process static, adsorbent weight. In order to provide the above information theoretically by mathematical modeling, a detailed knowledge of the adsorption mechanism is required [23].

Once the adsorption process starts, it continues until equilibrium approached between the sorbate concentration on the solid phase and in solution. Many efforts have been made over the years to develop isotherm model [16-21] for data correlation and design predictions for both single component and multicomponent adsorption. Unfortunately, no single model is accurate over broad ranges of adsorbent and adsorbent types, pressure and temperatures. This is probably due to deficiencies in the model in adequately describing both the heterogeneities of the surface and the effect of the adsorbate on the properties of the adsorbent itself. Most model assume the adsorbate is inert, ie, not changed by the presence of the adsorbate molecules. However, each of the more popular isotherm models has been found useful for modeling adsorption behavior on particular circumstances. But, a general model containing four meaningful parameters proposed by Jeager and Erdoes [16] is:

qe 

K .C e A  B .C e

D

(1)

where, qe(mg.g-1) and Ce(mg.dm-3) are the solid phase and liquid phase solute equilibrium concentration, respectively. K, A, B and D are the isotherm constants. Over the years, several researchers have proposed several isotherms based on different

K .C e D  A  B.C e qe

(2)

The equilibrium adsorption data were used for the application of the GA method through Eq. 2. Despite the fact that interest in GA has increased rapidly during the last decade, the overall GA theory still reveals plenty of gaps and a large variety of strategies exits. Therefore, users who intend to solve problems GA still have to look for their own solution strategy by empirical optimization of the GA structure. However, as shown in previous studies [24, 25], the increasing number of unknown constants results in a low efficiency for searches by the GA method. Thus, the value of K in Eq. 2 were calculated for each constant value of A, B and D obtained randomly in GA program by least square method as follows: i N

K 



i 1

( A  B .Ce i N



i 1

D i

)

(3)

C ( ei ) q ei

In order to compare the applicability of various isotherm equations more definitely, the value of standard deviation can be calculated as follows: in

 



i 1

( q e ,i

exp .

 q e ,i

N 1

cal .

)2 (4)

where the superscripts “cal.” and “exp.” are the calculated and experimental values, respectively. N is the number of measurements. Langmuir Equation The most widely used two parameter equation is the Langmuir Equation [17] which is

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developed for homogeneous adsorption. The Langmuir equation is obtained by setting A=D=1 in Eq. 1.

a 1 1   L qe K L .C e KL

(5)

where KL (dm3.g-1) and aL (dm3.mg-1) are Langmuir constants. Their values are related to the energy of adsorption. (Kl/aL) is defined as the monolayer adsorbent capacity. Plotting 1 vs 1 , KL and aL qe Ce can be obtained from the slope and the intercept, respectively. Freundlich Equation The Freundlich equation [18] is an empirical one described by equilibrium on heterogeneous surface. Mathematically, it is expressed by

ln( q e )  ln( K F ) 

1 ln(C e ) n

(6)

where KF(dm3.g-1) and (1/n) are the Freundlich constants. KF expresses the adsorbent capacity; the larger its value, the higher the capacity. (1/n) is the heterogeneity factor. A plot of ln(qe ) vs ln(Ce ) would give n and KF from slope and intercept, respectively. Redlich Peterson Equation This is a more general formula which contains three parameters. It is obtained by setting A=1 in Eq. 1 [22].

Ce 1 bR    .C e qe a R a R

(7)

where ß shows heterogeneity factor that lies between 0 and 1. This equation gave a good representation for phenol adsorption from dilute aqueous solution on XAD-8 and XAD7 resins [26] and on activated carbon [5]. For both adsorbent used in the experiments, the three parameters were obtained using a least square fitting procedure to minimize the deviation between the calculated and experimental values. Jossens et al. Equation

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Jossens et al. [23] suggest the following isotherm equation;

qe P exp( K J .q e ) H

Ce 

(8)

where H corresponds to the Henry’s law constant, P is characteristic of the adsorbent only, irrespective of both temperature and the nature of adsorbents. A good representation of equilibrium data using this equation was reported for adsorption of phenolic compounds from aqueous solution onto activated carbon [7], and on Amberlite XAD-4 and XAD-7 macroreticular resins [26]. Rearranging Eq.8,

ln(

Ce P )   ln(H )  K J .q e qe

(9)

If P is known in Eq.9, the values of H and KJ can be obtained either from the plot of ln( C e ) against qe

qe or using a least square fitting procedure. Adsorption Rates: “n th order Lagergren equation” In order to examine the controlling mechanism of adsorption such as mass transfer and chemical reaction, several kinetic models are used to the test the experimental data. The simple one is the Lagergren model [22]. This model can be written in the following general form:

dqt  k.(qe  qt ) r dt

(10)

where qt is the amount of adsorption at time t and k is the rate constant of “r” order adsorption. Eq. 13 can be integrated under the conditions r≠1 and qt=0 at t=0. After integration, the general expression for the adsorption rate becomes

1 1 1 (  )  k.t (r  1) (qe  qt ) r 1 (qe ) r 1

(11)

by substituting

Y1 

1 1 1 (  ) r 1 (1  r ) (q e  qt ) (q e ) r 1

Y2=kt

(12) (13)

Mehmet Fatih Dilekoglu

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In the literature, Eq. 13 was used by assuming a reaction order of r =1 and r =2 [27-28]. But in this study the kinetic parameters (r and k) in Eq.11 was determined by using the genetic algorithm (GA) operation without assuming any constant n values. The values of standard deviation for the rth order Lagergren equation is as follows: i N

 

 (Y 1 i 1

i

 Y 2i )2

N 1

(14)

Experimental Experimental Design Evaluation by natural selection which is one of the most compelling themes of modern science, has led to revolutionary way of thinking about the biological system. This is a form of evolution referred to as the genetic algorithm (GA) developed theoretically by Holland [29] and Goldberg [30]. The GA method has been successfully applied to several kinds of problems, including thermal analysis kinetics [31], optimal profile in feed-batch reactor [32], crystallization process [33], in determination of ground state energy of impurity [34], in material desig and processing [35] and in irradiation and sunshine duration data [36]. In order to solve a problem by using GA method the following steps should be followed [37]:      

Definition of solution space and the initial distribution of the individuals. An evaluation function that plays the role of environment, rating solutions in terms of their “fitness”. Selection of individuals surviving according to a survival rate. A mode of crossover Mutation of individuals in the determined population through a mutation limit Best individual replaced the current population depending on the value of the objective function.

The initial population of individuals is usually generated randomly as applied in this study. Each individual is run in the current environment to determine its effectiveness which is assigned a numerical evaluation of its merit by a fitness function. The fitness function determines how each

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gene (bit) of an individual will be interpreted. All the individuals in the population are evaluated and their fitnesses are used as the basis for selection which is determined by standard deviation. The selection probabilities are then computed for each structure based on its utility, with proportionally higher probabilities assigned to higher utility structure. The selection is performed with the classical Goldberg based roulette wheel [30]. Genetic operation such as mutation, crossover and inversion are applied probabilistically to the selected individuals to produce a new population (or generation) of individuals. Crossover takes two selected current generation structures, splits and string at the same randomly determined point and then creates the new generation structures by swapping the tail portion of the string. One example of uniform crossover between two parent individuals can be given as follow: 1 1 0 1 0 1 1 1 1 0 1 0  uniform crossover 1 1 1 1 0 0 1 1 0 0 1 1

1  107 (parent string 1) 1  117 (parent string 2) 1  121 (child string 1) 1  103 (child string 2)

Mutation on the other hand, randomly changes a bit in a structure thereby introducing a new individual. The setup of mutation parameters in this work can be shown by a example as follows: 1 0 0 1 1 0  102  mutation 1 0 0 0 1 1 1  71 1

As a result, GA operators generate a new set of individuals that has a better average chance of being good, by transforming the previous set of good individuals into a new one. Each combination of genetic operators, representation and problem has its own characters. The advantage of the GA method is that it requires only the information concerning the quality of the solution procedure by each parameter set. In this respect, it differs from many optimization methods which need linearization, assumption and information on derivatives. Thus, GA does not require special information and can be applied directly and is flexible and easy to optimize any function. Additionally, the GA method searches the best function result considering many points in the search space simultaneously and therefore have a

Mehmet Fatih Dilekoglu

reduce change of converging to local optima [38]. From the above discussion, it can be seen that the GA differs substantially from more traditional search and optimization methods. The four most significant differences are: • GAs search a population of points in parallel, not a single point. • GAs do not require derivative information or other auxiliary knowledge; only the objective function and corresponding fitness levels influence the directions of search. • GAs use probabilistic transition rules, not deterministic ones. • GAs work on an encoding of the parameter set rather than the parameter set itself (except in where real-valued individuals are used). In this study, a general adsorption equilibrium equation having four constant suggested by Jeager and Erdoes [16] and the “r th” order Lagergren Equation [22] were solved by the GA method under the following boundaries: 0< A, B, D and n < 3 Size of population: 100 Number of iteration steps: 150 (max) Type of crossover: uniform crossover Total mutation probability for each constant: 50% Length of chromosome: 18 The detailed procedure related to GA can be found in Refs.[32; 37]. Adsorption Studies Banana and grapefruit peels were obtained from a local fruit stall at Sanlıurfa- TURKEY. The peels of both fruits were crushed and washed with twice distilled water to remove surface impurities. In order to avoid leaching of colors 15 g banana and grapefruit peels were boiled in 250 ml of water for 2 h separately. This operation was repeated until a colorless solution was obtained. The peels of both materials were removed from solution and dried in an air oven maintained at 100 oC for 24 h. The dried material was ground and particles having an average diameter of 400 m (-300+500 m ) were taken for the further studies. Adsorption experiments were carried out by adding 250 mg of the dried adsorbent in 100 ml aqueous solutions of known initial concentration of phenol and whole adsorption setups were maintained at 30 oC in a shaker water bath having 150 rpm. For each sample, the suspension was filtered, centrifuged

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for 45 min. at 10.000 rpm. A stock solution was obtained by dissolving 1 g of phenol of analytical reagent grade obtained from Merck, in 1 dm3 of double distillated water. The pH of the solution was adjusted by diluted hydrochloric acid and sodium hydroxide. The concentration of phenol was determined by applying the method of Gales and Booth [39] which is based on spectrophotometer analysis of the developed color resulting from the reaction of phenol with 4-aminoantipridiyne. The amount of phenol adsorbed onto the banana and grapefruit peels were calculated by a mass balance relationship (Eq.15).

q  ( CO  C )

V m

(15)

where Co and C are the initial and any time liquidphase concentration of phenol (mg.dm-3), respectively. V is the volume of solution (dm-3), m is the amount of dry peels (g). In the case of equilibrium Eq.15 takes the form below:

q e  ( Co  Ce )

V m

(16)

Results and Discussion Effect of Solution pH on Adsorption Capacity Fig.1 represents the effect of different initial pH values on equilibrium adsorption capacities of phenol determined by using graph method for banana and grapefruit peels. It can be seen from Fig. 1 that adsorption of phenol by banana peels increases with pH, maximum sorption being reached between pH 4 and pH 9 and the removal efficiency decreases for pH values higher than 9. The electrostatic attraction/repulsion theory can not be completely explained the changes of phenol adsorption with pH by banana peel. There might be another mechanism effect the adsorption such as ion exchange. The adsorption of direct red by banana peel and the adsorption of phenol by activated palm seed coat and XAD resin show similar behavior [40, 6, 41]. But it differs for adsorption of some other dyes by banana peels [42]. In the case of grape fruit peel, the removal of phenol is greatest in the pH value of 7 and then decreases for the values higher and lower than 7. The adsorption behavior of phenol by banana and grapefruit are attributed to the ionization of phenol which depends on the pH values. The ionic

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fraction of phenolate ion(ion) can be calculated by the following equation.

 io n 

1 1  1 0 ( pK a  pH )

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behavior of phenol can be explained by comlexing groups on the banana and grapefruit peels.

(17)

It is obvious that ion, increases in parallel with the pH values. At low pH values the adsorption of phenol decreases because of the H+ ions which suppress the ionization of phenol and thus its uptake on polar adsorbent is reduced. In the higher pH range phenol forms salts which easily ionize leaving negative charge on the phenolic group. And the presence of OH- ions on the adsorbent also prevents the adsorption of phenol ion [5, 6]. Hence, subsequent experiments were performed at the initial pH of 7.

Fig. 2: Equilibrium adsorption of phenol on banana and grapefruit peel (Co=different initial phenol con.; T=30 oC; dosage =0,25 g; V= 100 ml solution) Effect of Contact Time

Fig. 1: Effect of initial pH values of solution on the equilibrium adsorption of phenol using banana and grapefruit peel (Co=50 ppm phenol; T=30 oC; dosage =0,25 g; V= 100 ml solution) Effect of peels dose The relations between the amount of phenol adsorbed per unit mass of banana and grapefruit peels (qe) and their remaining concentration in the aqueous solutions (Ce) at equilibrium conditions determined by graph method were illustrated in Figure 2. As shown in Fig.2 as more sites on the adsorbent are occupied, it becomes increasingly less probable for a phenol ion to bind a vacant site. However, a maximum sorbed concentration is reached, indicating that the adsorbent is saturated. The maximum adsorbent capacities of banana and grapefruit peels were determined as 43 and 23 mg.dm-3 for the initial concentration of 150 mg.dm-3 and 100 mg.dm-3 phenol, respectively. Therefore the affinity is based on a weight uptake by banana having higher values than grapefruit. The difference in the adsorption

Removal of phenol by banana and grapefruit peels as a function of time at various initial concentrations is shown in Figures 3 and 4. The adsorption of phenol on banana and grape fruit peels increases with increasing initial phenol concentration. It can be seen from Figures 3 and 4 that banana and grapefruit peels have approximately the same adsorption capacity except that at the initial concentration of 100 mg/l phenol. At an initial concentration of 100 mg/l phenol, banana and grapefruit peels have the adsorption capacities of 33.66 mg.g-1 and 23.5 mg.g-1, respectively. Figs. 3 and 4 shows that the amount of phenol adsorption increases with time and it remains constant after a contact time of about 75 min. and 150 min.

Fig. 3: Effect of contact time on the removal of phenol for various initial concentration (pH=7; banana peels = 0.25 g ; T=30 oC; V=100 ml solution).

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At the beginning of a GA program run, the data for both banana and grapefruit peels given in Figure 2 were taken to observe the behavior of the GA program, and then the GA program was studied using these data until the number of iteration steps reached 25. During this operation, the behavior of A, B, D and K were observed for both adsorbent through the minimum standard deviation. Figures 5 and 6 show the changes of adsorption parameters (A, B, D, and K) of Jeager and Erdoes with the iteration number for banana and grapefruit peel, respectively. As seen in both figures, the GA program reached the desired value at the end of 15 iteration steps. Therefore the number of iteration step for each run was limited to 15. Fig. 4: Effect of contact time on the removal of phenol for various initial phenol concentration( pH=7; grapefruit peels = 0.25 g; T=30 oC; V=100 ml solution). Genetic Algorithm Application Jeager-Erdoes Equation In this study, the parameters of Freundlich, Langmuir, Redlich Peterson and Jossens et al. adsorption isotherm were estimated by non-linear regression and by fitting transformer data to linearized form of the model(Eqs.5-7,9) which are tabulated in Table 1 with standard deviations. The genetic algorithm was not applied the above isotherm since their parameters can be easily found by least square fitting procedure. Whereas the constants of Jeager-Erdoes equation contained four unknown parameters can not be found by least square method. Thus, the constants of Jeager-Erdoes equation were determined by the GA method using the equilibrium data given in Fig. 2. The implementation of the computer program and the elimination of the data can be summarized as follows: 



150 values of A, B and D were generated randomly using boundary conditions. Then each A, B and D values were used in Eq.3 to calculate a K value utilizing all of the qe and Ce data. These 150 values of A, B, D and K values were used in Eq.1 to calculate 150 values of standard deviation represented by Eq.4. The fitness of data was evaluated according to the standard deviation and then the other GAs operation (selection, crossover, mutation and inversion) were performed. At the end of these operations, one iteration step has been completed.

The same adsorption parameters of Jeager and Erdoes may not be obtained at the end of each run of GA program, since GA is a stochastic method. In order to see this feature of GA method 10 runs with each of them having 15 iteration steps were realized for both banana and grapefruit peels. Table-1: Parameters and standard deviation in the selected isotherms. Isotherm Langmuir Equation Freundlich Equation Redlich-Peterson Equation Jossens et al. Equation Jeager- Erdoes Equation Calculated GAs

Constant KL aL standard dev. KF n Standard dev. ar br ß Standard dev. H p KJ Standard dev. K A B D Standard dev.

Banana peel 3.701 0.063 1.782 3.577 0.757 7.543 3.789 0.064 0.991 1.4928 3.3919 1.975 0.0006 3.826 2.692 0.735 0.04 1.025 1.482

Grapefruit peel 1.577 0.034 1.755 1.787 0.739 2.138 1.632 0.039 1.05 0.807 1.656 1.180 0.0236 1.420 0.897 1.432 0.035 1.025 0.564

Adsorption parameters of Jeager and Erdoes equation obtained at the end of each run are given in Table 2. As seen in Table 2, the adsorption parameters of Jeager and Erdoes found for grapefruit peels represent the experimental data better than banana peels with respect to standard deviation. The adsorption parameters (A, B, D and K) values marked (in bold) in Table 2 were also used to calculate the qe values from Eq.1 for both banana and grapefruit peels. These calculated qe and the other isotherm values were compared with the experimental values as shown in Figures 7 and 8. As can be seen in Figures 7 and 8, the qe values obtained from Jeager and Erdoes isotherm represents the best approximation with experimental data. The

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parameters of all used isotherms and their standard deviation are given in Table 1 for both banana and grapefruit peels. Table 1 shows that with respect to standard deviation, Redlich-Peterson Equation gives a good representation for phenol adsorption on the both adsorbents but the best parameters representing the phenol adsorption are obtained for Jeager-Erdoes equation by the GA method. Table-2: Changes in the adsorption parameters and standard deviation in the Jeager and Erdoes equation. with run number for banana and grapefruit peels Adsorbent

Banana peel

Grapefruit Peel

run no. 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

A

K

B

D

0.466 0.975 1.013 1.023 0.655 0.653 1.018 1.016 0.735 0.830 1.013 0.885 0.885 0.740 1.021 0.920 0.946 0.752 0.897 0.962

1.913 3.551 3.697 3.5667 2.408 2.404 3.744 3.739 2.692 3.058 1.749 1.436 1.4187 1.213 1.642 1.472 1.512 1.218 1.432 1.554

0.051 0.053 0.055 0.053 0.036 0.036 0.056 0.056 0.04 0.046 0.069 0.036 0.036 0.036 0.042 0.037 0.037 0.032 0.035 0.042

0.877 1.019 1.021 1.023 1.023 1.023 1.023 1.023 1.025 1.022 0.907 1.023 1.013 0.974 1.012 1.015 1.023 1.007 1.025 0.997

Standard deviation 1.972 1.507 1.496 1.485 1.483 1.483 1.483 1.483 1.482 1.483 0.665 0.577 0.570 0.597 0.570 0.569 0.564 0.575 0.564 0.580

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The results in Table 3 illustrate that the reaction order “r” take the values of about 1.500 and 1.0 at the condition of different initial concentration of phenol adsorption on banana and grapefruit peels, respectively. But, the reaction order depends on the initial pH values of phenol solution for both adsorbents. As seen in Table 3, the n value of each pH is different, since the mechanism of phenol adsorption changes in the presence of different pH values. The “r ” values given in Table 3, show that the adsorption of phenol on banana peels made progress with two different reaction mechanism depending on pH values : the first mechanism realizes at the pH values of 2 and 12 while the other realizes at the out of these pH values. In case of phenol adsorption on the grapefruit peel, the reaction rate mechanism consist of three different steps depends on different initial pH values.

Adsorption kinetics The data shown in Figures 3 and 4 were used to evaluate Lagergren equation with “r th ” reaction order (Eq.11) by the GA method. The application procedure of GA and calculation of standard deviation to Lagergren equation is the similar to this previously study [43]. The kinetic data of Lagergren equation obtained by GA method at the end of one run having 15 iteration steps are given in Table 3.

Fig. 5: Changes of the Jeager and Erdoes isotherm parameters (a, b, D and K) with number of iteration step with respect to minimum standard deviation for banana peel.

Table-3: Test of “r th” order of Lagergren equation for banana and grapefruit peel (T=30 oC, Co=50 ppm phenol, dosage of peel=0.250 g) Adsorbent

Banana Peel

Grapefruit peel

Co (mg.dm-3) 5 10 50 50 50 50 50 100 5 10 50 50 50 50 50 100

Initial pH of solution 7 7 2 4 7 9 12 7 7 7 7 2 4 9 12 7

r 1.500 1.454 1.001 1.582 1.565 1.417 1.025 1.477 1.021 1.09 1.031 2.086 1.530 1.497 1.092 1.080

k.102 9.651 9.625 6.669 5.6832 9.604 7.154 6.794 11.370 5.398 5.160 5.114 1.631 1.870 4.199 4.336 4.817

qe 1.801 3.577 7.651 19.110 18.150 17.452 13.553 33.66 1.567 3.260 14.270 6.415 8.550 10.35 4.803 23.500

Standard deviation 0.359 0.232 0.595 0.330 0.128 0.400 0.064 0.082 0.412 0.289 0.366 0.250 0.027 0.786 0.071 0.239

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Conclusion

Fig. 6: Changes of the Jeager and Erdoes isotherm parameters (a, b, D and K) with number of iteration step with respect to minimum standard deviation for grapefruit peel.

Fig. 7: Comparison of the qe values calculated from different isotherm with that obtained experimentally for banana peel.

1- Both equilibrium and kinetic studies for the adsorption of phenol from aqueous solution onto banana and grapefruit peels have been carried out in the concentration range 5-100 ppm and in initial pH range 2-12 at 303 K. 2- It was found that the banana and grapefruit peels adsorption capacities were strongly dependent on pH of the solution. 3- The amount of adsorption were maximized at pH 4-9 with the values of 19.110 to 17.452 mg/g banana peels and at pH=7 with the values of 14.270 mg/g grapefruit peel for the initial phenol concentration of 50 ppm. 4- In the case of applied different adsorption isotherms, for three-parameter isotherms equations, the normalized perfect deviation was obtained using Jossens et al. equation (for banana peel : σ = 3.826, for grapefruit peel: σ =1.420). The equation of Redlich-Peterson gives the satisfactory fit over the range of concentrations (for banana peel: σ = 1,4928, for grapefruit peel: σ =0.807) among the threeparameter isotherm equation. 5- Four-parameter isotherm equation proposed by Jeager-Erdoes has been easily solved under no assumption of A, B and D values by using the GA method. The adsorption parameters obtained from Jeager-Erdoes equation by using the GA method gives the most satisfactory results among the other isotherms (for banana peel: σ = 1.482, for grapefruit peel: σ =0.564). 6- In addition, the adsorption reaction rate equation with “r th ” order has been solved with no assumption (r =1 or r = 2) by the GA method. Obtained results show that the reaction rate order changes between the values of 1-2 with initial pH values of solution but in the case of different initial phenol concentration there are no changes observed from reaction rate order. Symbols

Fig. 8: Comparison of the qe values calculated from different isotherms with that obtained experimentally for grapefruit peel.

qe - solid phase solute equilibrium concentration (mg.g-1) Ce - liquid phase solute equilibrium concentration (mg.dm-3) K- the isotherm constant A- the isotherm constant B - the isotherm constant D - the isotherm constant KL - Langmuir constant (dm3.g-1) aL - Langmuir constant (dm3.mg-1) KF - Freundlich constant (dm3.g-1) (1/n) - Freundlich constant ß - heterogeneity factor qt - the amount of adsorption Co - the initial liquid-phase concentration of phenol (mg.dm-3) C - any time liquid-phase concentration of phenol (mg.dm-3) V - Volume of solution (dm-3) M - Amount of dry peels (g).

Mehmet Fatih Dilekoglu

J.Chem.Soc.Pak., Vol. 38, No. 06, 2016

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