+modelling the sorption of zn ions onto luffa cylindricaarticle.aascit.org/file/pdf/9021047.pdf ·...

American Journal of Science and Technology

2018; 5(1): 1-13

http://www.aascit.org/journal/ajst

ISSN: 2375-3846

+Modelling the Sorption of Zn2+ Ions onto Luffa cylindrica

Oboh Innocent O.1, Aluyor Emmanuel O.

2

1Department of Chemical and Petroleum Engineering, University of Uyo, Uyo, Nigeria 2Department of Chemical Engineering, University of Benin, Benin City, Nigeria

Email address [email protected] (Oboh I. O.)

Citation Oboh Innocent O., Aluyor Emmanuel O. +Modelling the Sorption of Zn2+ Ions onto Luffa cylindrical. American Journal of Science and

Technology. Vol. 5, No. 1, 2018, pp. 1-13.

Received: April 30, 2017; Accepted: January 8, 2018; Published: February 27, 2018

Abstract: Biosorption experiment for Zn (II) was investigated in this study using the plant material Luffa cylindrica. The

applicability of some selected kinetic models was tested. Characterization like the surface area, chemical bonds, bulk density,

Pore size distribution, microstructures, composition, morphology and elemental composition were determined. The coefficient

of determination (R2) of all the models studied were mostly greater than 0.9. In most cases these coefficients were found to be

close to one. This indicates that all the kinetic models adequately describe the experimental data of the biosorption of Zn (II)

ions. Kinectic models were developed mathematically, and also, Artificial Neural Network (ANN) was applied to develop a

Multiple Input Single Output (MISO) back propagation neural network model which was validated. The RMSE value was

found to be 0.5912 and 1.6267 for MISO Zn-1 and MISO Zn-2 respectively. Artificial neural network was able to predict the

sorption capacity quite reasonably for the model.

Keywords: Artificial Neural Network, Kinectic Model, Luffa cylindrica, Biosorption, Waste Water

1. Introduction

Environmental pollution due to the discharge of heavy

metals from various industries, including metal plating,

mining, painting and agricultural sources such as fertilizers

and fungicidal sprays are causing significant concern because

of their toxicity and threat to human life, especially when

tolerance levels are exceeded [1].

Water contaminated with metal ions can cause several

health problems. Heavy metal ions such as cadmium, zinc,

nickel, chromium, copper and lead can bio-accumulate to be

toxic comounds through the food chain [2].

Zinc is often found in effluents discharged from industries

involved in acid mine drainage, galvanizing plants, natural

ores and municipal waste water treatment plants and is not

biodegradable and travels through the food chain via

bioaccumulation. Therefore, there is significant interest

regarding zinc removal from waste waters since its toxicity

for humans is 100-500 mg/day. World health organization

(WHO) recommended the maximum acceptable

concentration of zinc in drinking water as 5 mg/L [3].

Activated carbon is the most employed adsorbent for

heavy metal removal from aqueous solution and have been

well documented in the literature [4-5]. However, the

extensive use of activated carbon for metal removal from

industrial effluents is expensive [6], limiting its large

application for wastewater treatment. Therefore, there is a

growing interest in finding new alternative low-cost

adsorbents for metal removal from aqueous solution, such as:

the residuals of agricultural products [7-8].

Biosorption is an attractive technology which involves

sorption of dissolved substances by a biomaterial [9].

Very low cost and environmentally friendly plant materials

are now used as biosorbents for the removal of divalent

cations from aqueous solutions as the cellulose,

hemicelluloses, pectin and lignin present in the cell wall are

the most important sorption sites [10]. The structure of Luffa

cylindrica for example, is cellulose based [11-12], and the

surface of cellulose in contact with water is negatively

charged. Metal compounds used in this study will dissolve to

give the cationic metal and this will undergo attraction on

approaching the anionic Luffa cylindrica structure [13].

However, few researchers have addressed the

mathematical modelling of the sorption of metal ions onto

2 Oboh Innocent O. and Aluyor Emmanuel O.: +Modelling the Sorption of Zn2+ Ions onto Luffa cylindrical

these biosorbents. Earlier reported mathematical models for

the sorption of heavy metal ions included: surface-

complexation, cation-exchange and triple-layer models [1].

Artificial Neural Network (ANN) modelling is a non-

linear statistical technique used to solve problems that

conventional statistical methods cannot solve. Apart from

that, application of ANN in modelling is about 20 times

faster than numerical integration of a differential equations

system [14]. Therefore the application of ANN in various

branches of science and process technology by researchers is

becoming popular and hence its usage in this study.

The purpose of this work is to develop empirical models for the

effect of Luffa cylindrica dosage and the initial ion concentration

on the uptake of Zinc (II) ions from aqueous solution.

2. Materials and Methods

2.1. Preparation of Luffa cylindrica

The seeds and sponges of L. cylindrica were gathered into

a clean plastic bag. They were dried in the oven at 105°C for

24 hours and afterwards ground with a grinding mill. The

ground seeds and sponges were sieved and were of particle

size 0.3 to 0.6mm. This was to allow for shorter diffusion

path, resulting in a higher rate of biosorption [15]. The

ground seed and sponge were mixed at a ratio of 1:1.

2.2. Preparation of Aqueous Solutions

Stock solution of Zinc was prepared with distilled water and

Zinc (II) tetraoxosulphate (VI). All working solutions were

obtained by diluting the stock solutions with distilled water.

The pH of the solutions was adjusted to their respective

optimum pH. The concentration of metal ions in solutions was

analyzed by Atomic Absorption Spectrophotometer. A

duplicate was analyzed for every sample to track experimental

error and show capability of reproducing results [16].

2.3. Determination of Optimum pH

A gramme of L. cylindrica seeds and sponge mixture were

put into 250ml conical flasks containing 50 ml of the aqueous

solutions each adjusted to pH 2, 3, 4, 5, 6, 7, 7, 8, 9 and 10

for each metal ions studied. They were agitated for 2h at

25°C. The biosorbents were removed from the aqueous

solutions after biosorption using the centrifuge at 2400 rate

per minute (rpm) for 10 minutes. The final concentrations of

the metal ions remaining were determined using Atomic

Absorption Spectrophotometer (AAS).

2.4. Biosorption Experiment

The biosorption studies for evaluation of the Luffa

cylindrica mixture for removal of Zinc (II) ions from

aqueous solutions was carried-out in triplicate using the batch

biosorption procedure [7-8].

The method of least squares was used to predict the kinetic

model by linear regression method. A trial and error was

used for nonlinear regression to minimize or maximize the

objective function using the solver add-in function, Microsoft

Excel, Microsoft Corporation.

2.5. Determination of Surface Area

The Autosorb-1c was used for the determination of the

surface area of the ground Luffa cylindrica mixture under study.

2.6. Determination of Pore Size Distribution

The PoreMaster PM-60 was used to test the ground Luffa

cylindrica mixture sample. The instrument determines both

Pore volume and Pore diameter of a solid or powder by

forced intrusion of a non-wetting liquid (mercury) [17].

2.7. Determination of the Microstructures,

Composition, Morphology and Elemental

Composition of the Luffa cylindrica

Mixture

The microstructures, composition, and morphology of the

Luffa cylindrica mixture were analysed by means of scanning

electron microscopy (SEM). A Philips scanning electron

microscope (ESEM XL30) equipped with energy dispersive

X-ray spectrometer (EDX) was used to analyse the various

elemental composition found in the Luffa cylindrica mixture.

2.8. Determination of Chemical Bonds in

Luffa cylindrica Mixture

Fourier transform infrared spectroscopy (FTIR) of the

adsorbent was done by using an FTIR spectrometer (Model

FTIR 2000, Shimadzu, Kyoto, Japan) [18].

2.9. Determination of Bulk Density of Luffa cylindrica Mixture

The method of Okaka and Potter [19] was used in

determining the bulk density.

3. Results and Discussion

Table 1. Physical properties of the Luffa cylindrica biosorbent.

Specific surface area - BET (m²/g) 0.28

Total Surface area (m²/g) 1.1895

Pore Diameter Range (µm) 1051.309204 to 0.003577

Bulk density (g/cm3) 0.34

Table 1 show the bulk density, surface area and pore diameter

range for the biosorbent used for this study. The Specific surface

area using the BET method was 0.28m²/g and the Pore diameter

range was between 1051.309204 to 0.003577µm. The bulk

density was 0.34g/cm3. As observed, the surface area for the

seed and sponge mixture of L. cylindrica is relatively low, with

pore diameter values in agreement with those found for typical

mesoporous materials [20].

American Journal of Science and Technology 2018; 5(1): 1-13 3

Figure 1. SEM Scan and plot showing elemental composition of Luffa cylindrica.

Figure 1 gave the elemental composition of Luffa cylindrica that was analysed by means of scanning electron microscopy

(SEM). The Luffa cylindrica showed it contained a very high percentage of carbon at 79.33% followed by oxygen, potassium,

calcium, chlorine, phosphorus and sulphur with weight % values of 12.25, 3.86, 1.58, 1.29, 0.95 and 0.75 respectively.

Figure 2. Scanning electron microscopy of Luffa cylindrica biosorbent: A transversal view of the mixture of seed and sponge 1000×.

Scanning electron microscopy (SEM) of the Luffa

cylindrica biosorbent was taken in order to verify the

presence of macropores in the structure of the fiber. In the

micrographs presented, Figure 2 when observed show the

fibrous structure of Luffa cylindrica, with some fissures and

holes, which indicate the presence macroporous structure.

These, should contribute a little bit to the diffusion of the Zn

(II) ions to the Luffa cylindrica biosorbent surface [21-24].

The small number of macroporous structure is confirmed by

the low specific surface area of the biosorbent (see Table 1).

As the biosorbent material presents few numbers of

macroporous structure, it adsorbed low amount of nitrogen,

which led to a low BET surface area [21-24]. Therefore the

major contribution of the Zn (II) ions uptake can be attributed

to micro- and mesoporous structures (see Figure 2).


Figure 3a. FTIR spectrum of the mixture of seed and sponge of L. cylindrica biosorbent before biosorption.

Figure 3b. FTIR spectrum of the mixture of seed and sponge of L. cylindrica biosorbent after biosorption of Zn2+ ions.


Figures 3 a - b show the FTIR spectral. The functional

groups on the binding sites were identified by FTIR spectral

comparison of the free biomass with a view to understanding

the surface binding mechanisms. The significant bands

obtained are shown in Figure 3 a - b. Functional groups

found in the structure include carboxylic, alkynes or nitriles

and amine groups [25].

The stretching vibrations of C-H stretch of -CHO group

shifted from 2847.05 to 2922.20, 2852.58, 2852.46 and

2852.43 cm-1

after Zn2+

ions biosorption. The assigned

bands of the carboxylic, amine groups and alkynes or

nitriles vibrations also shifted on biosorption. The shift in

the frequency showed that there was biosorption of Zn2+

ions on the L. cylindrica biosorbent and the carboxylic and

amine groups were involved in the sorption of the Zn2+

ions

[10].

Figure 4. A plot showing the pore size distribution of the biosorbent - L. cylindrical.

The pore size distribution of the Luffa cylindrica sample

was obtained by Mercury intrusion method, and it is shown

in Figure 4. The distribution of average pore diameter curve

presents a maximum with an average pore diameter of about

30 µm. The amount of pores seen in the Luffa cylindrica

biosorbent; decreases for average pore diameters ranging

from 30 to 1000 µm. On the other hand, the amount of

average pores ranging from 3.0 x 10-03

to 30 µm is

predominant. Therefore, this biosorbent can be considered

mixtures of micro- and mesoporous materials [21-24].

Table 2a. Kinetic models and parameters of initial ion concentration for Zn

(II) ions using L. cylindrica as biosorbent.

Kinetic parameters Concentration (mol/dm3)

Pseudo-first order 25.0 50.0 100.0 200.0

qe (mg/g) 1.1161 2.3641 4.8582 9.8589

kf (min-1) 0.8952 1.0225 1.2995 1.4007

R2 0.9981 0.9997 0.9999 0.9999

Pseudo-Second order

qe (mg/g) 1.1217 2.3698 4.8609 9.8615

ks(g/mg/min) 7.6376 7.4646 15.285 15.296

R2 0.9985 0.9998 0.9999 0.9999

Kinetic parameters Concentration (mol/dm3)

Elovich

α(mg/g/min) 2x1020 3x1015 1x1020 1x1020

β(g/mg) 48.539 17.772 10.687 5.2271

R2 0.9980 0.9957 0.9963 0.9961

Intra-particle diffusion

Ki(mg/g min-0.5) 0.0041 0.0037 0.0018 0.0018

C 1.0900 2.3400 4.8500 9.8500

R2 0.9992 0.9999 0.9999 0.9999

Avrami

qe (mg/g) 1.1147 2.3626 4.8572 9.8589

Ka(min-1) 1.6156 1.6156 1.2502 1.2965

na 1.9387 1.9387 1.0419 1.0804

R2 0.9980 0.9998 0.9999 0.9999

Table 2b. Kinetic models and parameters of Dosage for Zn (II) ions using L.

cylindrica as biosorbent.

Kinetic parameters Dosage (g)

Pseudo-first order 0.2 0.4 0.6 0.8 1.0

qe(mg/g) 24.32 12.29 8.105 6.083 4.867

kf(min-1) 1.230 1.016 1.199 1.303 0.973

R2 0.999 0.999 0.999 0.999 0.999

Pseudo-Second order


Kinetic parameters Dosage (g)

qe(mg/g) 24.34 12.31 8.112 6.086 4.877

ks(g/mg/min) 1.982 1.684 5.700 12.90 3.789

R2 0.999 0.999 0.999 0.999 0.999

Elovich

α(mg/g/min) 2x1021 2x1041 2x1061 3x1061 4x1061

β(g/mg) 2.201 8.210 18.22 24.39 30.61

R2 0.997 0.999 0.999 0.999 0.999

Intra-particle diffusion

Ki(mg/g min-0.5) 0.014 0.011 0.004 0.002 0.004

C 24.22 12.21 8.076 6.069 4.835

R2 0.999 0.999 0.999 0.999 0.999

Avrami

qe(mg/g) 24.32 12.29 8.105 6.082 4.867

Ka(min-1) 1.109 1.008 1.095 1.141 0.987

na 1.109 1.008 1.095 1.141 0.987

R2 0.999 0.999 0.999 0.999 0.999

A selected set of kinetic reaction models [26-30] were

used to fit the experimental data and the correlation

coefficients were as high as the rate law for a pseudo-second

order (Table 2a and 2b). The sorption of metal ion onto Luffa

cylindrica could be a pseudo-second order process.

These results reinforce the need of using a statistical error

function to better evaluate the adsorption models, as

previously reported [24], [31].

Additionally, it was verified that the qe values found in the

pseudo-second-order for both Table 2a and 2b were in good

agreement with the experimental qe values. These results

indicate that the pseudo-second- order kinetic model should

be taken into account for explaining the biosorption process

of Zn (II) removal by the L. cylindrica biosorbent.

When analyzing the values of the kinetic parameters

depicted on Tables 2a and 2b, it should be mentioned that the

ks values strongly depend on the initial concentration, since

its units is gmg−1

min−1

. Table 2a show that the kinetic results

fitted very well to all the kinetic models studied. Table 2b

show that the kinetic results fitted very well to all the kinetic

models studied with R2 values of 0.999 except for 0.2g Luffa

cylindrica dose which had 0.997 for the Elovich kinetic

model.

3.1. Derivation of Empirical Model for Zn2+

Ions Sorbed by Luffa cylindrica

Luffa cylindrica contains polar functional groups such as

aldehydes, ketones, and acids. These groups can be involved

in chemical bonding and are responsible for the cation

exchange capacity of the Luffa cylindrica [32]. It appears

reasonable that in many cases ion exchange rather than

sorption to free sites is the relevant overall-mechanism for

the binding of metal ions in biosorption. Since the overall

charge of the biomass particle has to be neutral, any binding

of one cation must be accompanied by either a stoichiometric

release of other cations or by the binding of anions [33]. Thus,

the Luffa cylindrica-metal reaction may be represented in two

ways:

2L- + Zn2+ → ZnL2 (1a)

and

2HL + Zn2+ → ZnL2 + 2H+ (1b)

where L and HL are polar sites on the Luffa cylindrica

surface.

In developing the mathematical description of this sorption

process, certain assumptions were made:

a. The process may be pseudo-second order and the rate

limiting step may be chemical sorption or

chemisorption;

b. there is a monolayer of metal ion on the surface of Luffa

cylindrica;

c. the energy of sorption for each ion is the same and

independent of surface coverage;

d. the sorption occurs only on localised sites and involves

no interactions between sorbed ions;

e. the rate of sorption is almost negligible in comparison

with the initial rate of sorption.

The rate of pseudo-second order reaction may be

dependent on the amount of divalent metal ion on the surface

of Luffa cylindrica and the amount of divalent metal ion

sorbed at equilibrium. The sorption equilibrium, qe, is a

function of, for example, the initial metal ion concentration,

the Luffa cylindrica dose and the nature of solute-sorbent

interaction [32].

The rate expression for the sorption described by

Eqs (1a) and (1b) is:

or

where (L)t and (HL)t are the number of active sites occupied

on the Luffa cylindrica at time t, (L)0 and (HL)0 are the

number of equilibrium sites available on the Luffa cylindrica

[32].

The kinetic rate equations can be rewritten as follows:

(2)

where k is the rate constant of sorption, (g/mg min), qe is the

amount of divalent metal ion sorbed at equilibrium, (mg/g),

qt is amount of divalent metal ion on the surface of the

sorbent at anytime, t, (mg/g).

Separating the variables in Eq. (2) gives:

integrating this for the boundary conditions t= 0 to t = t and qt

= 0 to qt = qt, gives:

(3)

( ) ( )[ ]2

0

)(t

t LLkdt

Ld−=

( ) ( )[ ]2

0

)(t

t HLHLkdt

HLd−=

( )2te

t qqkdt

dq−=

( )kdt

qq

dq

te

t =− 2

( ) ktqqq ete

+=−

11


this is the integrated rate law for a pseudo-second order

reaction.

Eq. (3) can be rearranged to obtain:

(4)

(5)

Substituting Eq. (5) into Eq. (4), gives:

(6)

Although there are many factors which will influence

sorption, contact time, pH, temperature, sorbent

concentration, nature of the solute and its concentration, a

kinetic model is concerned only with the effect of observable

parameters on the overall rate. These include initial metal ion

concentration, temperature, Luffa cylindrica dose and nature

of solute [32].

3.2. Effect of Initial Metal Ions

Concentration and Nature of Solute

The sorption capacity data obtained when Zn2+

and their

initial concentrations were varied at temperature of 25°C and

Luffa cylindrica dose of 20g/l are as shown in Figures 5a and

5b. Figure 5a shows typical data for the zinc (II) ions plotted

so that the constants initial sorption rate and equilibrium

sorption capacity in Eq. (6) can be derived. These constants

are given in Table 3. The agreement between the sets of data

reflects the extremely high correlation coefficients obtained

and shown in Table 3. Figure 5b shows typical sorption

curves for effect of initial metal ion concentrations on the

sorption kinetics of of zinc ions onto Luffa cylindrica. In

other words, the data showed good compliance with the

proposed pseudo-second order equation. It was shown in the

data that the initial metal ion concentrations influenced the

contact time necessary to reach equilibrium and that the

sorption capacity increased for the higher initial metal ion

concentrations (Table 3).

Figure 5a. The sorbed capacity against time for the effect of varied initial

ion concentration on the sorption kinetics of Zinc ion onto Luffa cylindrica

at pH= 5.0.

Figure 5b. The sorbed capacity against time for the effect of varied initial

ion concentration on the sorption kinetics of Zinc ion onto Luffa cylindrica

at pH= 5.0.

Table 3. The effect of initial ion concentration on metal ions biosorption

data.

M2+ Co (mg/l) r2 qe (mg/g) k (g/mgmin) h (mg/gmin)

Zn

25 0.999 1.1406 1.3902 1.8088

50 1.000 2.3822 2.0605 11.6935

100 1.000 4.8671 4.1497 98.3001

200 1.000 9.8649 5.3538 521.0116

The value of the initial sorption rates, h, was determined

by using the values of the intercept of the straight lines

plotted in Figure 5a. The initial sorption rate increases with

an increase in the initial metal concentrations for the zinc (II)

ions studied. While h varies from 1.8088 to 521.0116 mg/g

min, the C0 varies from 10 to 100 mg/l for zinc(II) ions, the

values of rate constant, k, was found to increase from 1.3902

to 5.3538 g/ mg min, for an increase in the initial zinc

concentration from 25 to 200 mg/l.

The corresponding linear plots of the values of qe, k and h

against C0 were regressed to obtain expressions for these

values in terms of the initial metal ion concentration with

high correlation coefficients (Table 4). Therefore it is further

considered that qe, k and h can be expressed as a function of

C0 for zinc as follows:

(7)

(8)

(9)

Substituting the Eqs (7), (8) and (9) into Eq. (6), the rate

law for a pseudo-second order and the relationship of qt, C0

and t can be represented as follows:

(10)

( )ee

tqtkq

tq

//1 2 +=

2ekqh =

( )e

tqth

tq

//1 +=

qq

eBCA

Cq

+=

0

0

kk BCA

Ck

+=

0

0

hh BCA

Ch

+=

0

0

++

+

=

qqhh

t

BCA

Ct

BCA

C

tq

0

0

0

01


when Eq. (10) is rearranged it becomes

(11)

Substituting the values of the empirical parameters Ah, Bh,

Aq and Bq from Table 4 into Eq. (11), the rate law for a

pseudo-second order and the relationship of qt, C0 and t can

be represented as follows:

(12)

The Equation (12) represents the generalised predictive

model for the zinc ion sorbed at any contact time and initial

metal ion concentration within the given range. These

equations can then be used to derive the amount of metal

sorbed at any given ion concentration and the reaction time.

Table 4. Empirical parameters for predicted qe, k and h from Co.

M2+ Aq Bq r2 Ak Bk r2 Ah Bh r2

Zn -0.0041 21.089 0.9999 0.1039 15.844 0.9776 -0.008 1.915 0.9960

Figure 6. Effect of initial concentration on zinc sorption at various reaction times.

Figures 6 shows the three-dimensional plot of Equation

(12) it indicate that the Zn (II) ions sorbed at any contact time

is higher for a greater initial metal ion concentration. This is

obvious for higher C0 values, as a more efficient utilisation of

the sorptive capacities of the sorbent is expected due to a

higher concentration gradient pressure [32].

3.3. Effect of Luffa cylindrica Dose and

Nature of Solute

Table 5. The effect of dosage on metal ions biosorption data.

M2+ m (g) r2 qe (mg/g) k (g/mgmin) h (mg/gmin)

Zn

0.2 1.000 24.3924 0.4205 250.2186

0.4 0.999 12.3217 1.1412 173.2589

0.6 1.000 8.1220 2.0598 135.8782

0.8 1.000 6.0932 3.0570 113.4967

1.0 1.000 4.8765 4.2307 100.6064

Figures 7a and 7b show typical sorption curves for effect

of Luffa cylindrica dose on the sorption kinetics of zinc,

nickel, copper and lead ions onto Luffa cylindrica at

temperature of 25°C and initial ion concentration of 100 mg/l.

The plotted experimental data (Figure 7a) also gave a good

fit with the pseudo-second order equation and the regression

coefficients for the linear plots were very close to 1.00 as can

be seen in Table 5.

Figure 7b show that for all the various doses, the amount

of zinc (II) ions sorbed increases rapidly with time in the

beginning and very slowly towards the end of the reaction.

Furthermore, a large fraction of the total amount of metal

was removed within a short time that is before 20 minutes.

The plots as seen in Figure 7a also showed that sorption

capacity increased for lower Luffa cylindrica dosages at any

specific time. There were effects on the contact time required

to reach saturation due to the variation in Luffa cylindrica

doses. It was found that the equilibrium sorption of metal

ions studied was a function of Luffa cylindrica doses. The

rate constant, k, the equilibrium sorption, qe and the initial

sorption rate, h, of sorption at different Luffa cylindrica doses

were calculated from the intercept and slope of the straight

line plots of t/qt versus t. The initial sorption rate decreased

with an increase in the Luffa cylindrica dose from 0.2-1.0 g.

( )tBCABCA

tCq

qqhh

t

+++=

00

0

( )tCC

tCqt

....

0892100414091531007660 00

0

+−++−=

020

4060

80100

120

025

5075

100125

150175

2000

2

4

6

8

10

Time, t (min)

Initial ion concentration, Co (mg/l)

Sorp

tion c

apacity,

qt

(mg/g

)


The corresponding linear plots of the values of qe, k and h

against m (dosage) were regressed to obtain expressions with

exponents for these values in terms of the m parameters for

all the metal ions studied.

Figure 7a. The sorbed capacity against time for the effect of varied doses on

the sorption kinetics of Zinc ion onto Luffa cylindrica at pH= 5.0.

Figure 7b. The sorbed capacity against time for the effect of varied doses on

the sorption kinetics of Zinc ion onto Luffa cylindrica at pH= 5.0.

The expression

x = Amb (13)

Where x= qe, k or h

Table 6. Empirical parameters for predicted qe, k and h.

M2+ Aq bq r2 Ak bk r2 Ah bh r2

Zn 4.879 - 1.00 0.999 4.238 1.433 0.999 100.9 - 0.57 0.998

Table 6 shows the empirical parameters for predicted qe, k

and h and their corresponding correlation coefficients.

Substituting the values of Aq, Bq, Ah and Bh from Table 6

in Eq. (13), the rate law for a pseudo-second order reaction

and the relationship between qt, m and t can be represented as:

(14)

Figure 8. Effect of L. cylindrica dose on zinc sorption at various times.

This equation can then be used to derive the sorption

amount zinc (II) ions at any given dosage and the reaction

time. The three-dimensional plot of the Equation (14) is

shown in Figure 8.

The Equation represent a generalised predictive model for

the amount of zinc (II) ions sorbed at any contact time and

involved L. cylindrica dose. It indicates that the zinc (II) ions

sorbed at any contact time is higher as the L. cylindrica dose

is decreased. This is due to the fact that increasing the L.

cylindrica dose increases the surface area for sorption and

hence the rate of metal sorption is increased when the initial

metal ion concentration is constant.

Kinetic models have been derived for the sorption of zinc

(II) ions onto L. cylindrica. The parameter which has the

greatest influence on the kinetics of the sorption reaction was

sorption equilibrium; qe is a function of initial metal ion

concentration, L. cylindrica dose and nature of solute and this

is in agreement with previous research [32].

3.4. Artificial Neural Network Model

Development

Different categories of software can be used to do

mathematical modeling [34]. Pythia is a program for the

development and design of Neural Networks. Pythia features

Backpropagation Networks and train neural networks on any

Windows machine [35].

In this study, 2 models of back-propagation feed forward

network were developed in Pythia environment. The models

are MISO Zn-1 and MISO Zn-2.

3.5. Selection of Input and Output Variables

The most important task in developing a Neural Network

model is to select the most significant variables as estimator

inputs. In this process of biosorption of Zinc (II) ions onto L.

cylindrica, there are a lot of variables that can affect the

efficiency of system.

Therefore, in order to simplify the model structure, input

variables that gave dominant impact to the process outputs

were selected while the others were neglected. The

independent experimental variables selected are Contact time,

initial metal ion concentration and biosorbent dosage. The

01570879491001

....

−− +=

mtm

tqt

0.10.2

0.30.4

0.50.6

0.70.8

0.91

020

4060

80100

1200

10

20

30

40

50

L. cylindrica dose, m (g)Time, t (min)

Sorp

tion c

apacity,

qt

(mg/g

)


output was sorption capacity.

The signal moves from the input layer towards the output

layer as shown in Figures 9a and b, and in this process each

neuron uploads all the neurons of the successive layers,

transferring a portion of the signal that has been accumulated.

The portion of signal transferred is regulated by a transfer

function [36].

A feed-forward back-propagating ANN structure as

illustrated in Figures 9a and b was used to develop yield

prediction models. Data move through the layers in one

direction, from the input through the hidden to the output

layers, without loops as opposed to feedback networks.

Figure 9a. Layers and connections of a feed-forward back propagating artificial neural network (MISO-1).

Figure 9b. Layers and connections of a feed-forward back propagating artificial neural network (MISO-2).

3.6. Developing Yield Prediction Models with

BPNN

In the present work, the input variables to the feed forward

back propagation neural network (BPNN) were as follows:

the amount of L. cylindrica (g) and initial ion concentration

of Zn (II) ions (mg/l). The sorption capacity was chosen as

the experimental response or output variable. The sigmoidal

transfer function was used as a transfer function in the hidden

and output layers. This is the most widely used transfer

function. The training function was Fermi (Min=0.00,

Max=1.00, Thld=0.00, Inc=1.00) and the learning rate was

0.500. The several data points generated were used to

develop the ANN model [37].

BPNN modelling for initial ion concentration and nature of

solute

Figure 10a. MISO Zn-1 (2,3,3,1) 7 neurons, 3 levels, 2 inputs, 1 output.

Transfer function: Fermi (Min=0.00, Max=1.00, Thld=0.00, Inc=1.00)

Learning rate 0.500.


Figure 10b. Accuracy of prediction of Sorption capacity (mg/g) of Zn (II)

ions onto L. cylindrica for MISO Zn-1 neural network model.

Figure 10c. Scatter plot of the measured sorption capacity and of the

predicted sorption capacity derived from a 7-neuron MISO Zn-1 neural

network model.

Figure 10a show the Artificial Neural Network

architecture developed for the initial ion concentration. For

MISO Zn-1 model the number of neurons was 7.

A Feed forward back propagation Artificial Neural

Network (ANN) was trained using the training data from the

experimental results. Figure 10b show the experimental and

ANN predicted Sorption capacity for MISO Zn-1 neural

network model developed for the effect of Initial ion

concentration on the biosorption of Zn(II) ions onto Luffa

cylindrica as biosorbent.. The accuracy of the prediction of

the trained ANN was then compared with the actual

measured values. It was observed that ANN gave near

accurate prediction for Sorption capacity values.

To have a more precise investigation into the various

models, a regression analysis of outputs and desired targets

was performed as shown in Figure 10c. There was a high

correlation between the predicted values by the ANN model

and the measured values resulted from experimental data.

The correlation coefficient was 0.973 for MISO Zn-1 model,

which implied that this model succeeded in the prediction of

the sorption capacity.

3.7. BPNN Modelling for Luffa cylindrica

Dose and Nature of Solute

Figure 11a show the Artificial Neural Network

architecture developed for the Luffa cylindrica dose and Zn

(II) ions used for this study. For the MISO Zn-2 model the

maximum number of neurons was 12.

Figure 11a. MISO Zn-2 (2,3,2,4,2,1) 12 neurons, 5 levels, 2 inputs, 1 output.

Transfer function: Fermi (Min=0.00, Max=1.00, Thld=0.00, Inc=1.00)

Learning rate 0.500.

Figure 11b. Accuracy of prediction of Sorption capacity (mg/g) of Zn (II)

ions onto L. cylindrica for MISO Zn-2 neural network model.

Figure 11c. Scatter plot of the measured sorption capacity and of the

predicted sorption capacity derived from a 12-neuron MISO Zn-2 neural

network model.

A Feed forward back propagation Artificial Neural

Network (ANN) was trained using the training data from the

experimental results. Figure 11c shows the experimental and

ANN predicted Sorption capacity for MISO Zn-2 model

developed for the effect of Luffa cylindrica dose on the

biosorption of Zn(II) ions. The accuracy of the prediction of

the trained ANN was then compared with the actual

measured values. It was observed that ANN gave near


accurate prediction for Sorption capacity values.

To have a more precise investigation into the various

models, a regression analysis of outputs and desired targets

was performed as shown in Figure 11c. There was a high

correlation between the predicted values by the ANN model

and the measured values resulted from experimental data.

The correlation coefficient was 0.950 for MISO Zn-2, which

implies that the models succeeded in prediction of the

sorption capacity.

Table 7. The RMSE values for MISO neural network models.

Neural Network model RMSE

MISO Zn-1 0.5912

MISO Zn-2 1.6267

The root mean square error (RMSE) is chosen as indicator

of performance of the networks. The Root Mean Squared

error (RMSE) is calculated using the following formula [38-

39]:

(15)

Generally, the artificial neural network offers the

advantage of being fast, accurate and reliable in the

prediction or approximation affairs, especially when

numerical and mathematical methods fail. There is also a

significant simplicity in using ANN due to its power to deal

with multivariate and complicated problems [40].

The root mean square error (RMSE) of the performance of

ANN MISO model on the experimental data for predicting

Sorption capacity is 0.5912 and 1.6267 for MISO Zn-1 and

MISO Zn-2 models respectively as can be seen in Table 7.

ANN was able to predict the sorption capacity quite

reasonably for all models.

4. Conclusion

A kinetic study was carried out and the experimental data

fitted into Pseudo-first order, Pseudo-second order, Intra-

particle diffusion and Avrami models. This was done using

the nonlinear regression method to obtain the kinetic

parameters.

Kinetic models have been developed and fitted for the

sorption of the divalent metal ions onto L. cylindrica on the

effect of Luffa cylindrica dose and the initial ion

concentration. The results showed sorption for Zn (II) ions

onto L. cylindrica during agitation by suspended shaking; the

process can be described by all kinetic models but pseudo-

second order model based on the assumption that the rate

limiting step may be chemical sorption involving ion

exchange between sorbent and sorbate. The parameter which

has the influence on the kinetics of the sorption reaction was

the sorption equilibrium capacity, qe, a function of initial

metal ion concentration, Luffa cylindrica dose and the nature

of solute ion.

In this study two ANN models were developed, which

were all MISO networks. BPNN models were able to predict

the sorption capacity quite reasonably for the effect of initial

ion concentration and Luffa cylindrica dose for the

biosorption process.

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