3. Results and discussion

#### 3.1. Kinetic modeling

Kinetic simulation of banana floret biosorption was carried out using four models: Lagergren pseudo-first order (PFO) model; pseudo-second order (PSO) model; Weber and Morris intraparticle diffusion (ID) model; and the diffusion-chemisorption (DC) model.

In 1898, Lagergren developed a first-order rate equation which was subsequently described as pseudo-first order [17]. The linear and nonlinear forms are:

$$q\_t = q\_e \left(1 - \exp^{-K\_{\rm PO}t} \right) \tag{8}$$

and

$$
\log\left(q\_{\varepsilon} - q\_{t}\right) = \log q\_{\varepsilon} - \frac{K\_{\text{PFO}}}{2.303}t \tag{9}
$$

The PSO equation is represented by Eqs. (10) and (11) [18]. The model is based on PSO chemical reaction kinetics [19].

$$\eta\_t = \frac{K\_{PSO} q\_e^2 t}{1 + K\_{PSO} q\_e t} \tag{10}$$

and

$$\frac{t}{q\_t} = \frac{1}{K\_{PSO}q\_\varepsilon^2} + \frac{t}{q\_\varepsilon} \tag{11}$$

Weber and Morris [20] proposed that the rate of ID varies proportionally with the half power of time and is expressed as Eq. (12). If the rate-limiting step is ID, a plot of solute adsorbed against the square root of time should yield a straight line passing through the origin [20].

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based… http://dx.doi.org/10.5772/intechopen.74398 389

$$q\_t = K\_{\rm id} \left( t^{1/2} \right) + c \tag{12}$$

The DC kinetic model was developed to simulate sorption of heavy metals onto heterogeneous media [21]. It is based on the assumption that both diffusion and chemisorption control the biosorption process. Linear and nonlinear forms are as follows:

$$q\_t = \frac{1}{\frac{1}{q\_\epsilon} + \frac{t^{0.5-1}}{K\_{DC}}} \tag{13}$$

and

maximum sorption capacity was attained) in a shaking water bath (Julabo SW23) at temperatures varying from 300 � 2 to 328 � 2 K. The concentration of metal ions on the biosorbent was

qe <sup>¼</sup> ð Þ Co � Ce

The goodness of fit by the various models to the experimental data was evaluated using the

error function (HYBRID), mean square error (MSE) and relative percent error (RPE) and is

Kinetic simulation of banana floret biosorption was carried out using four models: Lagergren pseudo-first order (PFO) model; pseudo-second order (PSO) model; Weber and Morris

In 1898, Lagergren developed a first-order rate equation which was subsequently described as

<sup>¼</sup> log qe � KPFO

The PSO equation is represented by Eqs. (10) and (11) [18]. The model is based on PSO

qt <sup>¼</sup> KPSOq<sup>2</sup>

<sup>¼</sup> <sup>1</sup> KPSOq<sup>2</sup> e þ t qe

Weber and Morris [20] proposed that the rate of ID varies proportionally with the half power of time and is expressed as Eq. (12). If the rate-limiting step is ID, a plot of solute adsorbed against the square root of time should yield a straight line passing through the origin [20].

e t

intraparticle diffusion (ID) model; and the diffusion-chemisorption (DC) model.

log qe � qt

t qt

pseudo-first order [17]. The linear and nonlinear forms are:

<sup>M</sup> � <sup>V</sup> (2)

, the Marquardt's percent standard deviation (MPSD), hybrid

qt <sup>¼</sup> qe <sup>1</sup> � exp �KPFOt (8)

<sup>2</sup>:<sup>303</sup> <sup>t</sup> (9)

(11)

<sup>1</sup> <sup>þ</sup> KPSOqet (10)

determined using the following mass balance equation:

2.6. Error analysis

388 Desalination and Water Treatment

presented in Table 1.

3.1. Kinetic modeling

and

and

coefficient of determination, R2

3. Results and discussion

chemical reaction kinetics [19].

$$\frac{t^{0.5}}{q\_t} = \frac{1}{q\_e} \ast t^{0.5} + \frac{1}{K\_{DC}}\tag{14}$$

Assuming, a linear region as t !0, the initial rate is given as:

$$k\_i = K\_{\rm DC}^2 / q\_e \tag{15}$$

#### 3.1.1. Linear regression

Table 2 shows the results of the linear regression analysis. The goodness of fit was assessed using error functions presented in Table 1. First, the experimental data were modeled using each of the kinetic models through linear regression. The highest coefficient of determination (R<sup>2</sup> = 0.9981) was produced by the PSO model. This was followed by the DC model (R<sup>2</sup> = 0.9972), PFO model (R2 = 0.9831) and finally the ID model (R<sup>2</sup> = 0.9435). The equation parameters obtained from linear regression were subsequently used to construct the theoretical


Table 2. Results of linear and nonlinear regression analysis.

nonlinear curves, i.e. the form of the curve used for system design. These nonlinear plots were then compared to the primary experimental data using the error functions (RPE, MPSD, HYBRID, and R<sup>2</sup> ). The nonlinear R<sup>2</sup> values in Table 2 show the correlation of the PSO model fell off significantly (R2 = 0.9743) while that of the DC model and ID model improved. The other error functions also support this trend. This type of occurrence has been reported by Motulsky and Christopoulos [22], where the authors explicated that the transformation of experimental data to linear forms causes some assumptions of linear regression to be violated (e.g. distortion of the experimental error) and consequently the derived slope and intercept of the regression line are not the most accurate determinations of the parameters of a model.

superior simulation. What is most significant is the high precision of the DC model curves which demonstrates minimal violation as the data was transformed from linear to nonlinear forms.

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The DC model was used to assess the kinetic effect of mixing speed on the biosorption of Cu(II) onto banana floret and is presented in Table 3. The overall rate of biosorption increased with increasing agitation. This was expected as agitation promotes good contact between media and liquid and maintains a high-ion concentration gradient between the inner and outer regions of the particle. Further, the solvent film thickness, which surrounds the particle, reduces, and by extension, the resistance to film diffusion. This is supported by the significant increase in initial

To elucidate the impact of changing pH on biosorption, the pH was varied as presented in Figure 2. Maximum removal was observed at pH 5.3, followed by a significant decrease. Figure 3 shows the results of the point of zero charge (pHPZC) of the banana floret, which was found to be 6.2. At pH values far below the pHPZC, functional groups on the surface of the biosorbent become highly protonated, which can result in reduced efficiency. At pH 6.0, there exist three species, Cu2+ in very small quantity and Cu(OH)+ and Cu(OH)2 in large quantities [23]. The reduction in sorption observed at pH 5.6 may indicate a preference by floret for the Cu2+ ions over that of the other species. The maximum biosorption at pH 5.3 (below pHPZC) may in part be due to the greater preference of the higher valency Cu2+ ions over H+ ions.

The influence of particle size was studied and is also presented in Table 3. It is observed that as particle size decreased, both the overall rate and the initial rate increased. The reduction in

Operational conditions Values Overall rate, KDC (mg/g-t0.5) Initial rate ki (mg/g-t)

4.1 7.6858 4.1949 5.3 13.3577 6.3379 5.6 13.1258 9.7131

350 13.3577 6.3379 400 16.7028 9.8186

0.35 11.2768 4.5407 0.6 8.6429 3.0784

pH 3.2 6.4836 4.8743

Agitation (RPM) 250 12.0172 5.0386

Particle, GMS (mm) 0.17 13.3873 6.3447

Table 3. DC model rate parameters for different operational conditions.

3.2. Effect of mixing speed on biosorption

rate as agitation is increased.

3.3. Effect of pH on biosorption

3.4. Effect of particle size on biosorption

#### 3.1.2. Nonlinear regression

A more robust simulation was performed using nonlinear regression by the Levenberg-Marquardt algorithm. The results of this analysis were assessed using error functions which revealed that the DC model produced the highest R2 and the lowest RPE, MPSD, and HYBRID values. Figure 1a–d shows the comparison of the experimental data to the nonlinear plots generated by both linear regression and nonlinear regression parameters. The accuracy of the DC model is confirmed by the

Figure 1. Comparison of experimental data to nonlinear kinetic curves by (a) PFO model, (b) ID model, (c) PSO model and (d) DC model.

superior simulation. What is most significant is the high precision of the DC model curves which demonstrates minimal violation as the data was transformed from linear to nonlinear forms.

#### 3.2. Effect of mixing speed on biosorption

nonlinear curves, i.e. the form of the curve used for system design. These nonlinear plots were then compared to the primary experimental data using the error functions (RPE, MPSD,

fell off significantly (R2 = 0.9743) while that of the DC model and ID model improved. The other error functions also support this trend. This type of occurrence has been reported by Motulsky and Christopoulos [22], where the authors explicated that the transformation of experimental data to linear forms causes some assumptions of linear regression to be violated (e.g. distortion of the experimental error) and consequently the derived slope and intercept of the regression line are not the most accurate determinations of the parameters of a model.

A more robust simulation was performed using nonlinear regression by the Levenberg-Marquardt algorithm. The results of this analysis were assessed using error functions which revealed that the DC model produced the highest R2 and the lowest RPE, MPSD, and HYBRID values. Figure 1a–d shows the comparison of the experimental data to the nonlinear plots generated by both linear regression and nonlinear regression parameters. The accuracy of the DC model is confirmed by the

Figure 1. Comparison of experimental data to nonlinear kinetic curves by (a) PFO model, (b) ID model, (c) PSO model

). The nonlinear R<sup>2</sup> values in Table 2 show the correlation of the PSO model

HYBRID, and R<sup>2</sup>

390 Desalination and Water Treatment

3.1.2. Nonlinear regression

and (d) DC model.

The DC model was used to assess the kinetic effect of mixing speed on the biosorption of Cu(II) onto banana floret and is presented in Table 3. The overall rate of biosorption increased with increasing agitation. This was expected as agitation promotes good contact between media and liquid and maintains a high-ion concentration gradient between the inner and outer regions of the particle. Further, the solvent film thickness, which surrounds the particle, reduces, and by extension, the resistance to film diffusion. This is supported by the significant increase in initial rate as agitation is increased.

#### 3.3. Effect of pH on biosorption

To elucidate the impact of changing pH on biosorption, the pH was varied as presented in Figure 2. Maximum removal was observed at pH 5.3, followed by a significant decrease. Figure 3 shows the results of the point of zero charge (pHPZC) of the banana floret, which was found to be 6.2. At pH values far below the pHPZC, functional groups on the surface of the biosorbent become highly protonated, which can result in reduced efficiency. At pH 6.0, there exist three species, Cu2+ in very small quantity and Cu(OH)+ and Cu(OH)2 in large quantities [23]. The reduction in sorption observed at pH 5.6 may indicate a preference by floret for the Cu2+ ions over that of the other species. The maximum biosorption at pH 5.3 (below pHPZC) may in part be due to the greater preference of the higher valency Cu2+ ions over H+ ions.

#### 3.4. Effect of particle size on biosorption


The influence of particle size was studied and is also presented in Table 3. It is observed that as particle size decreased, both the overall rate and the initial rate increased. The reduction in

Table 3. DC model rate parameters for different operational conditions.

The Langmuir model (Eq. (16)) is a theoretical equilibrium isotherm originally developed to

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based…

qe <sup>¼</sup> qLKLCe 1 þ KLCe

Firth as cited in [25], explained that the equation of the form x = kc1/n was first applied to adsorption of gases by De Saussure in 1814. Its application was further extended to solutions by Boedecker in 1859 [25]. In 1906, Freundlich described the adsorption isotherm mathematically as a special case for nonideal and reversible adsorption [26]. This equation is presented as:

The Redlich-Peterson isotherm (Eq. (23)) is a hybrid isotherm that incorporates the features of

qe <sup>¼</sup> KRPCe <sup>1</sup> <sup>þ</sup> <sup>α</sup>RPCgRP e

The Sips isotherm (Eq. (19)) is also a combined form of the Langmuir and Freundlich isotherms

qe <sup>¼</sup> qSð Þ <sup>α</sup>SCe nS

Table 4 shows that among the two-parameter models, the Langmuir isotherm best represented the equilibrium data. Approximately 34% increase in sorption capacity occurred as temperature was increased from 300 to 328 K. Hall et al. [30] postulated that the constant separation factor, RL, may be used to further describe the nature of the adsorption process and to assess

RL <sup>¼</sup> <sup>1</sup>

ð Þ 1 þ KLCo

The authors went on to explain that equilibrium conditions have an interesting effect on the shape of column breakthrough curves whereby for 0 < RL < 1 (favorable equilibrium) the curve of the mass transfer zone tends to attain a constant pattern and thus become relatively selfsharpening as it advances through the column. Figure 4 presents a plot of RL vs. Co for varying reaction temperatures. In all cases, the value of RL was between 0 and 1 indicating a favorable equilibrium and by extension confirms the applicability of banana floret for column application. Equilibrium data are also useful for batch design whereby attainable levels of treatment can be explained. Therefore, the importance of challenging the experimental data against various models and obtaining an accurate simulation cannot be overemphasized. Table 4 shows the results of the nonlinear regression of the Redlich-Peterson and the Sips model. The Sips model produced the highest R<sup>2</sup> among all tested equilibrium models (R<sup>2</sup> 0.9947–0.9982). According to

[28]. The model was developed for predicting heterogeneous adsorption systems [29].

qe <sup>¼</sup> KFð Þ Ce <sup>1</sup>=nF (17)

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<sup>1</sup> <sup>þ</sup> ð Þ <sup>α</sup>SCe nS (19)

(16)

393

(18)

(20)

relate the amount of gas adsorbed on a surface to the pressure of the gas [24].

the Langmuir and Freundlich isotherms [27]:

the suitability of the biosorbent for column applications.

Figure 2. Effect of solution pH on Cu(II) uptake.

Figure 3. Point of zero charge of banana floret.

particle size is accompanied by an increase in surface area which can account for the increase in initial rate. Also, if the characteristics of the active sites on the surface of the biosorbent are the same as those within the pores, then this increase in overall rate with decreased particle size is expected.

#### 3.5. Equilibrium modeling

The equilibrium capacity of banana floret for Cu(II) was assessed by nonlinear regression using two- and three-parameter equilibrium models, namely, the Langmuir isotherm, the Freundlich isotherm, the Redlich-Peterson isotherm and the Sips isotherm.

The Langmuir model (Eq. (16)) is a theoretical equilibrium isotherm originally developed to relate the amount of gas adsorbed on a surface to the pressure of the gas [24].

$$\eta\_{\epsilon} = \frac{q\_L K\_L \mathbf{C}\_{\epsilon}}{1 + K\_L \mathbf{C}\_{\epsilon}} \tag{16}$$

Firth as cited in [25], explained that the equation of the form x = kc1/n was first applied to adsorption of gases by De Saussure in 1814. Its application was further extended to solutions by Boedecker in 1859 [25]. In 1906, Freundlich described the adsorption isotherm mathematically as a special case for nonideal and reversible adsorption [26]. This equation is presented as:

$$\eta\_{\varepsilon} = \mathbb{K}\_{F}(\mathbb{C}\_{\varepsilon})^{1/n\_{F}} \tag{17}$$

The Redlich-Peterson isotherm (Eq. (23)) is a hybrid isotherm that incorporates the features of the Langmuir and Freundlich isotherms [27]:

$$\eta\_{\varepsilon} = \frac{K\_{RP} \mathbb{C}\_{\varepsilon}}{1 + \alpha\_{RP} \mathbb{C}\_{\varepsilon}^{\otimes p}} \tag{18}$$

The Sips isotherm (Eq. (19)) is also a combined form of the Langmuir and Freundlich isotherms [28]. The model was developed for predicting heterogeneous adsorption systems [29].

$$q\_{\epsilon} = \frac{q\_{\mathcal{S}}(\alpha\_{\mathcal{S}} \mathbb{C}\_{\epsilon})^{\text{tr}}}{1 + (\alpha\_{\mathcal{S}} \mathbb{C}\_{\epsilon})^{\text{tr}}} \tag{19}$$

Table 4 shows that among the two-parameter models, the Langmuir isotherm best represented the equilibrium data. Approximately 34% increase in sorption capacity occurred as temperature was increased from 300 to 328 K. Hall et al. [30] postulated that the constant separation factor, RL, may be used to further describe the nature of the adsorption process and to assess the suitability of the biosorbent for column applications.

$$R\_L = \frac{1}{(1 + K\_L C\_o)}\tag{20}$$

The authors went on to explain that equilibrium conditions have an interesting effect on the shape of column breakthrough curves whereby for 0 < RL < 1 (favorable equilibrium) the curve of the mass transfer zone tends to attain a constant pattern and thus become relatively selfsharpening as it advances through the column. Figure 4 presents a plot of RL vs. Co for varying reaction temperatures. In all cases, the value of RL was between 0 and 1 indicating a favorable equilibrium and by extension confirms the applicability of banana floret for column application.

particle size is accompanied by an increase in surface area which can account for the increase in initial rate. Also, if the characteristics of the active sites on the surface of the biosorbent are the same as those within the pores, then this increase in overall rate with decreased particle

The equilibrium capacity of banana floret for Cu(II) was assessed by nonlinear regression using two- and three-parameter equilibrium models, namely, the Langmuir isotherm, the

Freundlich isotherm, the Redlich-Peterson isotherm and the Sips isotherm.

size is expected.

3.5. Equilibrium modeling

Figure 3. Point of zero charge of banana floret.

Figure 2. Effect of solution pH on Cu(II) uptake.

392 Desalination and Water Treatment

Equilibrium data are also useful for batch design whereby attainable levels of treatment can be explained. Therefore, the importance of challenging the experimental data against various models and obtaining an accurate simulation cannot be overemphasized. Table 4 shows the results of the nonlinear regression of the Redlich-Peterson and the Sips model. The Sips model produced the highest R<sup>2</sup> among all tested equilibrium models (R<sup>2</sup> 0.9947–0.9982). According to


the Sips isotherm, banana floret exhibited a maximum adsorption capacity of 28.06 mg/g. This compared well with other biosorbents reported in the literature including peanut shells [31], Irish peat moss [32] and the fungal biomass Cladosporium cladosporioides [33] and banana stem

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based…

Thermodynamic effects were assessed at four different temperatures (300, 308, 318, and 328 K). Parameters such as standard Gibb's free energy change (ΔG�), enthalpy change (ΔH�) and

The following form of the van't Hoff equation was applied whereby Kd is the distribution

ΔS<sup>0</sup> <sup>T</sup> � <sup>Δ</sup>H<sup>0</sup>

Table 5 presents the results of the thermodynamic analysis. The ΔG� values for the range of temperature and concentration were negative, indicating a spontaneous feasible reaction and varied from �12.39 to �7.75 kJ/mol. Values of ΔG� lower than �20 kJ/mol signify the involvement of physisorption in the biosorption process [35]. Oepen et al. as cited in [34], highlighted that the association of energy (ΔH�) are as follows: van der Waals interactions (4–8 kJ/mol); hydrophobic bonding (4 kJ/mol); hydrogen bonding (2–40 kJ/mol); charge transfer, ligandexchange and ion bonding (40 kJ/mol); direct and induced ion-dipole and dipole-dipole interactions (2–29 kJ/mol). In this study, ΔH� ranged from 1.5 to 9.38 kJ/mol, and consequently, the

The negative values of ΔH� are indicative of an exothermic sorption process. The positive ΔS� reveals increasing randomness at the solid/liquid interface during sorption or structural changes among the active sites of the biosorbent. The values of activation energy, Ea, varied according to initial concentration and ranged from 3000 to 94,000 kJ/mol. As initial concentration increases, Ea

Co (mg/L) △H� (kJ/mol) △S� (kJ/mol/K) △G� Ea (kJ/mol) S\*

 �5.1147 0.0529 �10.84 �11.19 �11.45 �12.39 93.6905 0.2073 �1.5114 0.0399 �10.51 �10.78 �11.06 �11.66 52.0972 0.1863 �3.6217 0.0459 �10.13 �10.54 �11.02 �11.42 26.0112 0.1867 �8.7953 0.0597 �9.16 �9.54 �10.15 �10.82 15.5156 0.2086 �8.6914 0.0565 �8.38 �8.66 �9.19 �9.96 10.2670 0.2364 �9.3850 0.0569 �7.75 �8.07 �8.75 �9.30 3.3152 0.1975

300 K 308 K 318 K 328 K

¼ �RTln Kd (21)

RT (22)

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395

[11], which exhibit capacities of 25.39, 17.6, 19.5 and 19.7 mg/g, respectively.

ΔG�

coefficient under equilibrium conditions calculated from the relationship (qe/Ce).

ln ð Þ¼ Kd

involvement of one or all of these mechanisms of attachment cannot be discounted.

entropy change (ΔS�) were calculated using Eqs. (21) and (22) [34]:

3.6. Thermodynamic studies

Table 5. Thermodynamic parameters.

Table 4. Biosorption isotherm constants for various temperatures.

Figure 4. Variation in separation factor.

the Sips isotherm, banana floret exhibited a maximum adsorption capacity of 28.06 mg/g. This compared well with other biosorbents reported in the literature including peanut shells [31], Irish peat moss [32] and the fungal biomass Cladosporium cladosporioides [33] and banana stem [11], which exhibit capacities of 25.39, 17.6, 19.5 and 19.7 mg/g, respectively.

#### 3.6. Thermodynamic studies

Models Solution temperature (K)

Table 4. Biosorption isotherm constants for various temperatures.

Figure 4. Variation in separation factor.

Langmuir

394 Desalination and Water Treatment

Freundlich

Redlich-Peterson

Sips

300.15 308.15 318.15 328.15

qL 33.37 34.42 39.98 44.86 KL 0.0526 0.0521 0.0425 0.0402 R2 0.9913 0.9900 0.9883 0.9929

KF 4.2153 4.3226 3.9603 4.1283 nF 2.2753 2.2691 2.0508 1.9877 R<sup>2</sup> 0.9575 0.9572 0.9607 0.9679

KRP 1.3514 1.3783 1.2902 1.3398 aRP 0.0110 0.0106 0.0052 0.0037 gRP 1.2948 1.3024 1.4153 1.4750 R<sup>2</sup> 0.9962 0.9949 0.9937 0.9981

qs 28.06 28.86 32.12 37.43 as 0.0756 0.0749 0.0663 0.0585 ns 1.4127 1.4226 1.4622 1.3098 R<sup>2</sup> 0.9974 0.9962 0.9949 0.9982 Thermodynamic effects were assessed at four different temperatures (300, 308, 318, and 328 K). Parameters such as standard Gibb's free energy change (ΔG�), enthalpy change (ΔH�) and entropy change (ΔS�) were calculated using Eqs. (21) and (22) [34]:

$$
\Delta G^{\circ} = -RT\ln K\_d \tag{21}
$$

The following form of the van't Hoff equation was applied whereby Kd is the distribution coefficient under equilibrium conditions calculated from the relationship (qe/Ce).

$$\ln\left(K\_d\right) = \frac{\Delta S^0}{T} - \frac{\Delta H^0}{RT} \tag{22}$$

Table 5 presents the results of the thermodynamic analysis. The ΔG� values for the range of temperature and concentration were negative, indicating a spontaneous feasible reaction and varied from �12.39 to �7.75 kJ/mol. Values of ΔG� lower than �20 kJ/mol signify the involvement of physisorption in the biosorption process [35]. Oepen et al. as cited in [34], highlighted that the association of energy (ΔH�) are as follows: van der Waals interactions (4–8 kJ/mol); hydrophobic bonding (4 kJ/mol); hydrogen bonding (2–40 kJ/mol); charge transfer, ligandexchange and ion bonding (40 kJ/mol); direct and induced ion-dipole and dipole-dipole interactions (2–29 kJ/mol). In this study, ΔH� ranged from 1.5 to 9.38 kJ/mol, and consequently, the involvement of one or all of these mechanisms of attachment cannot be discounted.

The negative values of ΔH� are indicative of an exothermic sorption process. The positive ΔS� reveals increasing randomness at the solid/liquid interface during sorption or structural changes among the active sites of the biosorbent. The values of activation energy, Ea, varied according to initial concentration and ranged from 3000 to 94,000 kJ/mol. As initial concentration increases, Ea


Table 5. Thermodynamic parameters.

decreases resulting in an increase in the number collision as well as an increase in reaction rate. Activation energy values between 5 and 20 kJ/mol infer physisorption is the predominant adsorption mechanism. Values greater than 20 kJ/mol and up to 40 kJ/mol generally indicate a diffusion-controlled process, and a higher value represents a reaction controlled by chemical process [36]. It can, therefore, be surmised that the mechanisms of biosorption of Cu(II) onto banana floret were significantly influenced by the initial Cu(II) concentration. The values of the sticking probability (S\* < 1) reveal that the process was favorable.

#### 3.7. Development of a predictive model

#### 3.7.1. Artificial neural network

In this study, a multilayer feed-forward backpropagation ANN model [37, 38] was developed for predicting the biosorption of copper onto banana floret. A total of 60 experimental data points was used to train and test the performance of the ANN. Each set contained four input variables comprising pH (3.2–5.6), particle size (GMS 0.17–0.06 mm), mixing speed (250–400 RPM), contact time (0–60 min), and one output variable, namely, the adsorbed concentration (4.06–23.28 mg/g). The dataset was divided into three parts, 70% for training the network, 15% for validation and 15% for testing the accuracy of the neural network model and its prediction.

The optimum architecture of the ANN was developed by first assessing the impact of 13 training backpropagation algorithms whereby the Levenberg-Marquardt algorithm produced the lowest MSE of 0.4030 and highest R2 of 0.9938. The lowest MSE and highest R<sup>2</sup> within two training runs revealed the Tansig transfer function at the hidden layer and the Tansig transfer function at the outer layer were most optimal. A schematic representation of the architecture is shown in Figure 5. In this protocol, the number of neurons was varied from 2 to 20, and its

impact on performance assessed using the MSE as shown in Figure 6. The lowest MSE (0.0025) was obtained using 20 neurons. The figure also reveals fluctuations in MSE as the number of neurons increased. This may have resulted from the network being trapped into the local minima [39]. Figure 7 shows a comparison of the ANN predicted data and the experimental data, which reveals a significantly high correlation (R<sup>2</sup> = 0.9972) and underscores the accuracy

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based…

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Figure 6. Effect of the number of neurons and training on ANN performance.

Figure 7. Comparison of experimental and ANN model prediction.

of the ANN prediction.

Figure 5. Optimized ANN-GA architecture.

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based… http://dx.doi.org/10.5772/intechopen.74398 397

Figure 6. Effect of the number of neurons and training on ANN performance.

decreases resulting in an increase in the number collision as well as an increase in reaction rate. Activation energy values between 5 and 20 kJ/mol infer physisorption is the predominant adsorption mechanism. Values greater than 20 kJ/mol and up to 40 kJ/mol generally indicate a diffusion-controlled process, and a higher value represents a reaction controlled by chemical process [36]. It can, therefore, be surmised that the mechanisms of biosorption of Cu(II) onto banana floret were significantly influenced by the initial Cu(II) concentration. The values of the

In this study, a multilayer feed-forward backpropagation ANN model [37, 38] was developed for predicting the biosorption of copper onto banana floret. A total of 60 experimental data points was used to train and test the performance of the ANN. Each set contained four input variables comprising pH (3.2–5.6), particle size (GMS 0.17–0.06 mm), mixing speed (250–400 RPM), contact time (0–60 min), and one output variable, namely, the adsorbed concentration (4.06–23.28 mg/g). The dataset was divided into three parts, 70% for training the network, 15% for validation and 15% for testing the accuracy of the neural network model and its prediction. The optimum architecture of the ANN was developed by first assessing the impact of 13 training backpropagation algorithms whereby the Levenberg-Marquardt algorithm produced the lowest MSE of 0.4030 and highest R2 of 0.9938. The lowest MSE and highest R<sup>2</sup> within two training runs revealed the Tansig transfer function at the hidden layer and the Tansig transfer function at the outer layer were most optimal. A schematic representation of the architecture is shown in Figure 5. In this protocol, the number of neurons was varied from 2 to 20, and its

sticking probability (S\* < 1) reveal that the process was favorable.

3.7. Development of a predictive model

3.7.1. Artificial neural network

396 Desalination and Water Treatment

Figure 5. Optimized ANN-GA architecture.

impact on performance assessed using the MSE as shown in Figure 6. The lowest MSE (0.0025) was obtained using 20 neurons. The figure also reveals fluctuations in MSE as the number of neurons increased. This may have resulted from the network being trapped into the local minima [39]. Figure 7 shows a comparison of the ANN predicted data and the experimental data, which reveals a significantly high correlation (R<sup>2</sup> = 0.9972) and underscores the accuracy of the ANN prediction.

Figure 7. Comparison of experimental and ANN model prediction.

#### 3.7.2. Formulation of empirical equation

The weights of the optimized ANN and the fitness function were used to develop an empirical expression for predicting biosorption kinetics without the ANN software using Eqs. (23), (24) and (25) [39].

$$Fi = \frac{2}{\left[1 + \exp\left(-2^\*Ei\right)\right]} - 1\tag{23}$$

where Fi is the Tansig transfer function used at the hidden layer. The input data are normalized in the range �1 to 1 using Eq. (24):

$$X\_{norm} = 2\left[\frac{X\_i - X\_{\min}}{X\_{\max} - X\_{\min}}\right] - 1\tag{24}$$

(pH, particle size, agitation and time) necessary for maximizing biosorption. The equation

where IW and b1 are the weight and bias of the hidden layer, and LW and b2 are the weight and

The optimized structure was achieved by a double vector population type, and the population size, population generation, crossover fraction and mutation rate were set to be 200, 100, 0.7 and 0.01, respectively. The selection, crossover and mutation operators were chosen as stochastic uniform, scattered and uniform, respectively. The fitness values versus generation are presented in Figure 8. The value of fitness reached to a minimum after approximately 30 generations. The ANN-GA optimization revealed that maximum removal could be obtained using pH 5.2, particle size 0.211 mm, agitation 388 rpm, and contact time 55 min. The model prediction of relative sorption capacity under these conditions was 23.25 mg/g. Laboratory experiments were subsequently conducted to validate these findings. The tests produced a

Objective function ¼ tansig LWð Þ ∗tansig IWð ∗½x 1ð Þ; x 2ð Þ; x 3ð Þ; x 4ð Þ� þ b1Þ þ b2 (27)

obtained from the ANN model was used as the objective function as follows [41]:

Table 6. Performance evaluation of combinations of ANN input variables.

No. Combination MSE R2

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399

 p1 11.6000 0.3264 p2 14.4100 0.1692 p3 34.9900 0.0052 p4 10.2250 0.4445

 p1 + p2 8.3300 0.5329 p1 + p3 23.2000 0.2916 p1 + p4 0.1900 0.9052 p2 + p3 9.4400 0.1600 p2 + p4 7.6580 0.5476 p3 + p4 5.3254 0.5806

 p1 + p2 + p3 74.2140 0.0062 p1 + p2 + p4 0.2770 0.8879 p1 + p3 + p4 1.0400 0.5184 p2 + p3 + p4 9.9110 0.5685

15 p1 + p2 + p3 + p4 0.0025 0.997202

bias of output layer.

Group of one variable

Group of two variables

Group of three variables

Group of four variables

where Xi is the input or output variable X, and Xmin and Xmax are the minimum and maximum value of variable X. Ei is the weighted sum of the normalized input calculated whereby Wi represents the weights and bi is the biases and is defined as follows:

$$E\_i = W\_{i1} \ast t + W\_{i2} \ast RPM + W\_{i3} \ast d\_p + W\_{i4} \ast pH + bi \tag{25}$$

The predicted adsorbed concentration is therefore given by the following equation:

qt predicted ð Þ <sup>¼</sup> <sup>2</sup> ð�2<sup>∗</sup>ð�1:6177F<sup>1</sup> � <sup>0</sup>:5105F<sup>2</sup> � <sup>0</sup>:4558F<sup>3</sup> <sup>þ</sup> <sup>2</sup>:5298F<sup>4</sup> <sup>þ</sup> <sup>1</sup>:1608F<sup>5</sup> <sup>þ</sup> <sup>0</sup>:6342F<sup>6</sup> � <sup>0</sup>:7647F<sup>7</sup> <sup>þ</sup> <sup>1</sup>:0149F<sup>8</sup> � <sup>0</sup>:8711F<sup>9</sup> þ0:7553F10 � 0:2475F11 � 0:4772F12 � 0:6349F13 � 0:3057F14 þ 2:2585F15 � 0:0421F16 þ 1:219F17 þ 1:7408F18 þ0:1456F19 þ 0:2931F20 � 1:0660Þ 1 þ e 2 6 6 6 4 3 7 7 7 5 � 1 (26)

#### 3.7.3. Sensitivity analysis

A sensitivity analysis was carried out to determine the effect of each variable on the performance of the ANN model. Using the MSE and R2 , an evaluation of the performance of various possible combinations of variables was investigated [40]. The variables were combined to form four groups as presented in Table 6. The input variables are defined as follows: p1 is time, p2 is agitation, p3 is particle size and p4 is solution pH. The table shows p4 (pH) to be the most influential parameter in the group of one variable, while p1 (time) and p4 (pH) were the most influential in the group of two variables, which produced the most significant improvement in the network. The greatest performance occurred with the inclusion of all four variables, which produced the lowest MSE (0.0025) and highest R2 (0.9972). Consequently, it is resolved that pH and time have the greatest influence on the ANN structure.

#### 3.8. Genetic algorithm (GA) optimization

Following the development of the ANN model, the GA technique was applied using the optimization toolbox of Matlab 2012a to determine the value of the operational parameters Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based… http://dx.doi.org/10.5772/intechopen.74398 399


Table 6. Performance evaluation of combinations of ANN input variables.

3.7.2. Formulation of empirical equation

in the range �1 to 1 using Eq. (24):

and (25) [39].

398 Desalination and Water Treatment

The weights of the optimized ANN and the fitness function were used to develop an empirical expression for predicting biosorption kinetics without the ANN software using Eqs. (23), (24)

where Fi is the Tansig transfer function used at the hidden layer. The input data are normalized

where Xi is the input or output variable X, and Xmin and Xmax are the minimum and maximum value of variable X. Ei is the weighted sum of the normalized input calculated whereby Wi

Xmax � Xmin � �

ð�2<sup>∗</sup>ð�1:6177F<sup>1</sup> � <sup>0</sup>:5105F<sup>2</sup> � <sup>0</sup>:4558F<sup>3</sup> <sup>þ</sup> <sup>2</sup>:5298F<sup>4</sup> <sup>þ</sup> <sup>1</sup>:1608F<sup>5</sup> <sup>þ</sup> <sup>0</sup>:6342F<sup>6</sup> � <sup>0</sup>:7647F<sup>7</sup> <sup>þ</sup> <sup>1</sup>:0149F<sup>8</sup> � <sup>0</sup>:8711F<sup>9</sup> þ0:7553F10 � 0:2475F11 � 0:4772F12 � 0:6349F13 � 0:3057F14 þ 2:2585F15 � 0:0421F16 þ 1:219F17 þ 1:7408F18

A sensitivity analysis was carried out to determine the effect of each variable on the perfor-

possible combinations of variables was investigated [40]. The variables were combined to form four groups as presented in Table 6. The input variables are defined as follows: p1 is time, p2 is agitation, p3 is particle size and p4 is solution pH. The table shows p4 (pH) to be the most influential parameter in the group of one variable, while p1 (time) and p4 (pH) were the most influential in the group of two variables, which produced the most significant improvement in the network. The greatest performance occurred with the inclusion of all four variables, which produced the lowest MSE (0.0025) and highest R2 (0.9972). Consequently, it is resolved that pH

Following the development of the ANN model, the GA technique was applied using the optimization toolbox of Matlab 2012a to determine the value of the operational parameters

Ei ¼ Wi<sup>1</sup> � t þ Wi<sup>2</sup> � RPM þ Wi<sup>3</sup> � dp þ Wi<sup>4</sup> � pH þ bi (25)

Xnorm <sup>¼</sup> <sup>2</sup> Xi � <sup>X</sup>min

The predicted adsorbed concentration is therefore given by the following equation:

represents the weights and bi is the biases and is defined as follows:

qt predicted ð Þ <sup>¼</sup> <sup>2</sup>

þ0:1456F19 þ 0:2931F20 � 1:0660Þ

mance of the ANN model. Using the MSE and R2

and time have the greatest influence on the ANN structure.

3.8. Genetic algorithm (GA) optimization

1 þ e

3.7.3. Sensitivity analysis

<sup>1</sup> <sup>þ</sup> exp �2� ð Þ Ei � � � <sup>1</sup> (23)

� 1 (24)

, an evaluation of the performance of various

� 1

(26)

Fi <sup>¼</sup> <sup>2</sup>

(pH, particle size, agitation and time) necessary for maximizing biosorption. The equation obtained from the ANN model was used as the objective function as follows [41]:

$$\text{Objective function} = \text{tansig}(\text{LW} \ast \text{tansig}(\text{IW} \ast [\mathbf{x}(1); \mathbf{x}(2); \mathbf{x}(3); \mathbf{x}(4)] + \mathbf{b}1) + \mathbf{b}2) \tag{27}$$

where IW and b1 are the weight and bias of the hidden layer, and LW and b2 are the weight and bias of output layer.

The optimized structure was achieved by a double vector population type, and the population size, population generation, crossover fraction and mutation rate were set to be 200, 100, 0.7 and 0.01, respectively. The selection, crossover and mutation operators were chosen as stochastic uniform, scattered and uniform, respectively. The fitness values versus generation are presented in Figure 8. The value of fitness reached to a minimum after approximately 30 generations. The ANN-GA optimization revealed that maximum removal could be obtained using pH 5.2, particle size 0.211 mm, agitation 388 rpm, and contact time 55 min. The model prediction of relative sorption capacity under these conditions was 23.25 mg/g. Laboratory experiments were subsequently conducted to validate these findings. The tests produced a

Figure 8. Fitness values versus generation.

relative sorption capacity of 22.95 mg/g, which revealed a residual error of 1.3% and therefore validate the ANN-GA structure.

#### 3.9. Elucidation of mechanisms of biosorption

#### 3.9.1. Biosorbent characteristics and performance

The surface morphology of floret biomass was observed by SEM before and after biosorption of Cu(II) ions (Figure 9a and b). Prior to biosorption, a rough irregular surface with a high amount of protuberance was observed. The protuberance on the biomass surface can be attributed to potassium and other salts deposition [42]. After biosorption, there was not a significant change in biomass surface morphology. However, a reduction in protuberance was observed. The EDS analysis (Figure 10a and b) reveals that banana floret contains mainly C, O and K with trace amounts of Mg, S, Si, P and Cl. After biosorption, the K, Mg and Cl peaks were removed. Similar results were reported for the biosorption of Cr3+ and Pb2+ using Pistia stratiotes biomass [43]. The authors explained that the adsorbate ions might have replaced some of the ions initially present in the cell wall matrix and created stronger cross-linking. The removal of K during Cu(II) biosorption may be attributed to ion exchange [44]. The appearance of a Cu peak after biosorption confirms that Cu(II) was successfully sorbed onto floret.

60% of the sorbed ions. The harsh HCl wash, which is capable of destroying surface functional groups, released 87% of the sorbed ions after 60 min. Consequently, ion exchange and chemical

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Mass transfer studies were conducted using the external film diffusion model, the intraparticle

dt ¼ �kf Soð Þ <sup>C</sup> � Ci (28)

bonding are confirmed attachment mechanisms of Cu(II) binding to banana floret.

Figure 9. SEM micrograph of banana floret (a) before Cu(II) biosorption and (b) after Cu(II) biosorption.

dq

Since Ci approaches zero and C approaches Co, as t !0, Eq. (28) becomes:

3.9.3. Mass transfer studies

diffusion model and the particle diffusion model.

The external mass transfer model is expressed as [46]:

#### 3.9.2. Desorption using various eluents

The desorption performance of a material can aid in assessing its reuse applicability, metal recovery potential and provide some valuable insight related to the mechanism of biosorption. The desorbing solutions selected were distilled water, 0.1 M EDTA, 0.1 M HCl and 0.1 M CaCl2. The distilled water wash revealed only 1% of the Cu(II) was weakly bound by physical forces. The secondary ion exchange cation, Ca2+, recovered 11% of the sorbed ions after 60 min. The chelating agent, EDTA, known to form soluble complexes with metals ions [45] recovered Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based… http://dx.doi.org/10.5772/intechopen.74398 401

Figure 9. SEM micrograph of banana floret (a) before Cu(II) biosorption and (b) after Cu(II) biosorption.

60% of the sorbed ions. The harsh HCl wash, which is capable of destroying surface functional groups, released 87% of the sorbed ions after 60 min. Consequently, ion exchange and chemical bonding are confirmed attachment mechanisms of Cu(II) binding to banana floret.

#### 3.9.3. Mass transfer studies

relative sorption capacity of 22.95 mg/g, which revealed a residual error of 1.3% and therefore

The surface morphology of floret biomass was observed by SEM before and after biosorption of Cu(II) ions (Figure 9a and b). Prior to biosorption, a rough irregular surface with a high amount of protuberance was observed. The protuberance on the biomass surface can be attributed to potassium and other salts deposition [42]. After biosorption, there was not a significant change in biomass surface morphology. However, a reduction in protuberance was observed. The EDS analysis (Figure 10a and b) reveals that banana floret contains mainly C, O and K with trace amounts of Mg, S, Si, P and Cl. After biosorption, the K, Mg and Cl peaks were removed. Similar results were reported for the biosorption of Cr3+ and Pb2+ using Pistia stratiotes biomass [43]. The authors explained that the adsorbate ions might have replaced some of the ions initially present in the cell wall matrix and created stronger cross-linking. The removal of K during Cu(II) biosorption may be attributed to ion exchange [44]. The appearance of a Cu peak after

The desorption performance of a material can aid in assessing its reuse applicability, metal recovery potential and provide some valuable insight related to the mechanism of biosorption. The desorbing solutions selected were distilled water, 0.1 M EDTA, 0.1 M HCl and 0.1 M CaCl2. The distilled water wash revealed only 1% of the Cu(II) was weakly bound by physical forces. The secondary ion exchange cation, Ca2+, recovered 11% of the sorbed ions after 60 min. The chelating agent, EDTA, known to form soluble complexes with metals ions [45] recovered

validate the ANN-GA structure.

Figure 8. Fitness values versus generation.

400 Desalination and Water Treatment

3.9. Elucidation of mechanisms of biosorption

biosorption confirms that Cu(II) was successfully sorbed onto floret.

3.9.1. Biosorbent characteristics and performance

3.9.2. Desorption using various eluents

Mass transfer studies were conducted using the external film diffusion model, the intraparticle diffusion model and the particle diffusion model.

The external mass transfer model is expressed as [46]:

$$\frac{dq}{dt} = -k\_f \mathbf{S}\_o (\mathbf{C} - \mathbf{C}\_i) \tag{28}$$

Since Ci approaches zero and C approaches Co, as t !0, Eq. (28) becomes:

d Cð Þ =Co dt � �

The particle diffusion is described by Boyd et al. [47]:

where X(t) is the fractional attainment at time t, given by:

Vermeulen's [48] approximation of Eq. (31) is given as:

A linear plot of ln[1/1 – X<sup>2</sup>

A plot of qt versus t

rate-limiting step [51].

The Biot number (Bi) is given by [50]:

X tðÞ¼ <sup>1</sup> � <sup>6</sup>

π2 X∞ Z¼1

where

t¼o

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based…

<sup>S</sup><sup>0</sup> <sup>¼</sup> <sup>6</sup>ms dpr 1 � ε<sup>p</sup>

1

X tðÞ¼ qt qe

X tðÞ¼ <sup>1</sup> � exp � <sup>π</sup><sup>2</sup>Det

(t)] vs. t enables De to be calculated [49]:

Bi <sup>¼</sup> kfr De

namely, GMS 0.17 and 0.6 mm is shown in Figure 11. As the particle size decreased (which accompanies an increase in surface area and a reduction in pore length), the plots move further from the origin. Such deviation from the origin infers that intraparticle transport is not the only

The plot of 0.17 mm GMS reveals two distinct slopes. The first slope, which occurs within the first 30 min of the reaction, reveals the impact of intraparticle diffusion. Some researchers have

ln <sup>1</sup> <sup>1</sup> � <sup>X</sup><sup>2</sup> ð Þt

� �

� � � � <sup>1</sup>

¼ π2

0.5 in accordance with the Weber and Morris model for two sorbent sizes,

r2

2

<sup>Z</sup><sup>2</sup> exp �Z<sup>2</sup>

π<sup>2</sup>Det r2

¼ �kf So (29)

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� � (30)

� � (31)

<sup>r</sup><sup>2</sup> Det (34)

(32)

403

(33)

(35)

Figure 10. EDS of banana floret (a) before Cu(II) biosorption and (b) after Cu(II) biosorption.

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based… http://dx.doi.org/10.5772/intechopen.74398 403

$$
\left[\frac{d(\mathbb{C}/\mathbb{C}\_o)}{dt}\right]\_{t=o} = -k\_f \mathbb{S}\_o \tag{29}
$$

where

$$S\_0 = \frac{6m\_s}{d\_p \rho \left(1 - \varepsilon\_p\right)}\tag{30}$$

The particle diffusion is described by Boyd et al. [47]:

$$X(t) = 1 - \frac{6}{\pi^2} \sum\_{Z=1}^{\nu} \frac{1}{Z^2} \exp\left[\frac{-Z^2 \pi^2 D\_\epsilon t}{r^2}\right] \tag{31}$$

where X(t) is the fractional attainment at time t, given by:

$$X(t) = \frac{\eta\_t}{\eta\_e} \tag{32}$$

Vermeulen's [48] approximation of Eq. (31) is given as:

$$X(t) = \left[1 - \exp\left[-\frac{\pi^2 D\_e t}{r^2}\right]\right]^{\frac{1}{2}} \tag{33}$$

A linear plot of ln[1/1 – X<sup>2</sup> (t)] vs. t enables De to be calculated [49]:

$$\ln\left[\frac{1}{1-X^2(t)}\right] = \frac{\pi^2}{r^2}D\_\varepsilon t\tag{34}$$

The Biot number (Bi) is given by [50]:

Figure 10. EDS of banana floret (a) before Cu(II) biosorption and (b) after Cu(II) biosorption.

402 Desalination and Water Treatment

$$Bi = \frac{k\_f r}{D\_\varepsilon} \tag{35}$$

A plot of qt versus t 0.5 in accordance with the Weber and Morris model for two sorbent sizes, namely, GMS 0.17 and 0.6 mm is shown in Figure 11. As the particle size decreased (which accompanies an increase in surface area and a reduction in pore length), the plots move further from the origin. Such deviation from the origin infers that intraparticle transport is not the only rate-limiting step [51].

The plot of 0.17 mm GMS reveals two distinct slopes. The first slope, which occurs within the first 30 min of the reaction, reveals the impact of intraparticle diffusion. Some researchers have

Figure 13 presents a series of plots of the predicted values of M (g) versus V (L) for 60, 70, 80 and 90% Cu(II) ion removal at the initial concentration of 50 mg/L and 300 K. As an example, the mass of adsorbent required for 60% Cu(II) removal from aqueous solution was 10 and 15 g,

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based…

0.17 6.44E03 0.8332 5.40E5 0.9751 10.1454 0.35 1.65E02 0.8995 1.72E04 0.9609 16.8203 0.6 2.14E02 0.9241 4.35E04 0.9573 14.7441

/min) R<sup>2</sup> Bi

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Figure 12. Design of single-stage batch system for Cu(II) biosorption.

Figure 13. Biosorbent mass (M) versus volume of Cu(II) solution treated (V).

GMS (mm) kf (cm/min) R<sup>2</sup> De (cm<sup>2</sup>

Table 7. Mass transfer coefficients and Bi for the biosorption of Cu(II).

Figure 11. Kinetic plot of ID model for various particle size.

reported that the final slope corresponds to the slowing of the reaction, possibly due to a reduction in concentration gradient as the reaction approaches equilibrium [52, 53]. The plot of 0.6 mm GMS depicts the dominance of intraparticle diffusion for most of the reaction.

In order to explicate the degree of involvement of external and intraparticle diffusion, the resulting mass transfer coefficients obtained from the external and particle diffusion models were used to calculate the Bi. For Bi values <1.0, external mass transfer dominates while for Bi > 30, surface diffusion controls and for values between 1 and 30, both external and intraparticle mass transfer rates contribute [54]. The results presented in Table 7 confirm that within the range of particle sizes studied both external and intraparticle mass transfer rates contribute to the adsorption rate. Further, as particle size increased, particle diffusivity also increased while the film diffusion coefficient decreased.

#### 3.10. Design of batch biosorption system from isotherm data

Laboratory-scale equilibrium studies are used to predict batch adsorber size and performance. Figure 12 shows the schematic of a single-stage batch adsorber with a solution volume of V (L) and the initial Cu(II) concentration, Co is reduced to Ct as the reaction proceeds. The Cu(II) loading on the adsorbent in the reactor of mass M (g) changes from qo to qt with increased reaction time. The mass balance for the reactor is given by the following [55, 56]:

$$V(\mathbb{C}\_0 - \mathbb{C}\_t) = M(q\_t - q\_0) = Mq\_t \tag{36}$$

The adsorption process at 300 K was best represented by the Sips isotherm, thus the mass balance under equilibrium condition (Ct ! Ce and qt ! qe) is arranged as follows:

$$\frac{M}{V} = \frac{\mathbb{C}\_0 - \mathbb{C}\_\varepsilon}{q\_\varepsilon} = \frac{\mathbb{C}\_o - \mathbb{C}\_\varepsilon}{\frac{q\_\*(a\_\*\mathbb{C}\_\varepsilon)^{n\_\*}}{(1 + (a\_\*\mathbb{C}\_\varepsilon)^{n\_\*})}}\tag{37}$$

Figure 13 presents a series of plots of the predicted values of M (g) versus V (L) for 60, 70, 80 and 90% Cu(II) ion removal at the initial concentration of 50 mg/L and 300 K. As an example, the mass of adsorbent required for 60% Cu(II) removal from aqueous solution was 10 and 15 g,


Table 7. Mass transfer coefficients and Bi for the biosorption of Cu(II).

reported that the final slope corresponds to the slowing of the reaction, possibly due to a reduction in concentration gradient as the reaction approaches equilibrium [52, 53]. The plot of 0.6 mm GMS depicts the dominance of intraparticle diffusion for most of the reaction.

In order to explicate the degree of involvement of external and intraparticle diffusion, the resulting mass transfer coefficients obtained from the external and particle diffusion models were used to calculate the Bi. For Bi values <1.0, external mass transfer dominates while for Bi > 30, surface diffusion controls and for values between 1 and 30, both external and intraparticle mass transfer rates contribute [54]. The results presented in Table 7 confirm that within the range of particle sizes studied both external and intraparticle mass transfer rates contribute to the adsorption rate. Further, as particle size increased, particle diffusivity also

Laboratory-scale equilibrium studies are used to predict batch adsorber size and performance. Figure 12 shows the schematic of a single-stage batch adsorber with a solution volume of V (L) and the initial Cu(II) concentration, Co is reduced to Ct as the reaction proceeds. The Cu(II) loading on the adsorbent in the reactor of mass M (g) changes from qo to qt with increased

The adsorption process at 300 K was best represented by the Sips isotherm, thus the mass

<sup>¼</sup> Co � Ce qsð Þ <sup>α</sup>sCe ns <sup>1</sup>þð Þ <sup>α</sup>sCe ns ð Þ

<sup>¼</sup> Mqt (36)

(37)

reaction time. The mass balance for the reactor is given by the following [55, 56]:

balance under equilibrium condition (Ct ! Ce and qt ! qe) is arranged as follows:

<sup>V</sup> <sup>¼</sup> <sup>C</sup><sup>0</sup> � Ce qe

M

V Cð Þ¼ <sup>0</sup> � Ct M qt � q<sup>0</sup>

increased while the film diffusion coefficient decreased.

Figure 11. Kinetic plot of ID model for various particle size.

404 Desalination and Water Treatment

3.10. Design of batch biosorption system from isotherm data

Figure 12. Design of single-stage batch system for Cu(II) biosorption.

Figure 13. Biosorbent mass (M) versus volume of Cu(II) solution treated (V).

for Cu(II) solution volumes of 6 and 9 L, respectively. This evaluation becomes relevant for pilot-batch system design as well as large-scale batch applications.

KF Freundlich constant related to adsorption affinity (mg/g)

)

Artificial Neural Network-Genetic Algorithm Prediction of Heavy Metal Removal Using a Novel Plant-Based…

) (Eq. 30)

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) (Eq. 30)

) (Eq. 30)

KL Langmuir adsorption equilibrium constant (L/mg)

ms mass of biosorbent particles per unit volume (g/cm<sup>3</sup>

nF Freundlich constant related to heterogeneity

P number of parameters in the regression model

qL Langmuir monolayer sorption capacity (mg/g)

KPFO PFO rate constant (min<sup>1</sup>

M biosorbent mass (g)

t reaction time (min)

V volume (L)

Greek symbols

Author details

Trinidad and Tobago (WI)

T absolute temperature in K

αRP Redlich-Peterson constant ɛ<sup>p</sup> biosorbent porosity (Eq. 30)

r true biosorbent solid phase density (g/cm3

Clint Sutherland\*, Abeni Marcano and Beverly Chittoo

\*Address all correspondence to: clint.sutherland@utt.edu.tt

Project Management and Civil Infrastructure Systems, The University of Trinidad and Tobago,

ns Sips index of heterogeneity

N the number of experimental points

qe equilibrium adsorption capacity (mg/g)

qt adsorption capacity at any time (mg/g) R universal gas constant, 8.314 J/K-mol So surface area for mass transfer (cm<sup>1</sup>

KPSO PSO rate constant (g/mg-min)

KRP Redlich-Peterson equilibrium constant
