Iraqi Journal of Chemical and Petroleum Engineering 

 Vol.15 No.3 (September 2014) 37-50 

ISSN: 1997-4884 

 
 
 
 

Study the Feasibility of Alumina for the Adsorption of Metal Ions 

from Water 
 

Jenan A. Alnajar
*
, Asawer A. Kwaeri

**
, Ramzi H. Sayhood

**
 and Abbas H. Slaymon

***
 

*
Chemical Engineering Department, University of Technology, Baghdad, 

**
Petroleum Technology Department, University of Technology, Baghdad, 

***
Chemical Engineering Department, College of Engineering, University of Baghdad, 

Baghdad 

 
Abstract 

The present work describes the adsorption of Ba
2+

 and Mg
2+

ions from aqueous 

solutions by activated alumina in single and binary system using batch adsorption. 

The effect of different parameters such as amount of alumina, concentration of metal 

ions, pH of solution, contact time and agitation speed on the adsorption process was 

studied. The optimum adsorbent dosage was found to be 0.5 g and 1.5 g for removal 

of Ba
2+ 

and Mg
2+

,
 
respectively. The optimum pH, contact time and agitation speed,  

were found to be pH 6, 2h and 300 rpm, respectively, for removal of both metal ions.  

The equilibrium data were analyzed by Langmuir and Freundlich isotherm models 

and the data fitted well to both isotherm modes as indicated by higher correlation of 

determination R
2
> 0.87 in both single and binary systems. Pore diffusion model for 

batch adsorption was used to predict the concentration decay curve for adsorption of 

Ba
2+

 and Mg
2+

 onto activated alumina. There was a good agreement between the 

experimental data and the predicted decay curves using pore diffusion model. 

 

Keywords: Adsorption, magnesium, barium, diffusion model 

 
Introduction 

The presence of heavy metals in the 

environment is of major concern 

because of their toxicity, bio-

accumulating tendency and threat to 

human life and the environment [1, 2]. 

These metal ions are presented in 

wastewater from industrial activities 

such as mining, metal processing, 

pharmaceuticals, pesticides, organic 

chemicals, rubber and plastics, etc [3, 

4]. 

The removal of metals in wastewater 

has been an important issue for many 

years due to environmental harm [5]. 

Many methods are used for the 

removal of heavy metal ions from 

wastewater including: precipitation, 

electrolytic process, ultra-filtration, 

reverse osmoses, ion exchange, solvent 

extraction, adsorption and biological 

system [6, 7, 8]. 

Adsorption is an important, highly 

effective, cheap and easy method 

among the physicochemical treatment 

process [9, 10]. A number of materials 

have been used to remove heavy 

metals from wastewater such as 

activated carbon, charcoal, lignite, 

titanium dioxide, calcium carbon, 

alumina and clay [11]. Alumina can be 

used as an alternative for activated 

Iraqi Journal of Chemical and 
Petroleum Engineering 

 

University of Baghdad 
College of Engineering 



Study the Feasibility of Alumina for the Adsorption of Metal Ions from Water 
 

38                               IJCPE Vol.15 No.3 (September 2014)              -Available online at: www.iasj.net 
 

carbon [12]. Alumina is a fine weight 

material similar in appearance to 

common salt and it is highly porous 

and exhibits tremendous surface area, 

resulting in superior adsorbent 

capabilities. It is more preferable than 

activated carbon especially for 

removing inorganic compounds [13, 

14]. 

Barium and magnesium can end up in 

water and soil due to a number of 

activities. These activities include the 

discharge and disposal of drilling 

wastes, copper smelting, motor vehicle 

parts, plastic and accessories 

manufacturing. The presence of these 

metals in drinking water may cause 

stomach irritation, muscle weakness, 

increased blood pressure, or 

cardiovascular disease. They can be 

removed by several ways like: reverse 

somosis, filtration, adding softeners 

and coagulation. 

The aim of the present work is to 

examine environment friendly material 

like alumina as an adsorbent for 

removal of Magnesium and Barium 

ions from aqueous solution, the effect 

of different experimental parameters 

such as adsorbent dosage, 

concentration of the adsorbate, contact 

time and pH of the solution under 

study single and binary systems were 

investigated, as well as to study the 

isotherms model and pore model ions 

to predict the concentration decay 

curve for the adsorption of Ba and Mg 

onto activated alumina. 

 

Adsorption Isotherm 

Adsorption isotherm is defined as the 

ratio between the amount of material 

adsorbed per unit weight of adsorbent 

(qe) and the material concentration in 

the solution (Ce) at equilibrium 

constant temperature [15]. Adsorption 

isotherm models are used to describe 

the adsorption isotherm data. Several 

models have been published in the 

literature to describe experimental data 

of adsorption isotherm. The Langmuir 

and Frundlich models are the most 

frequently employed models. 

 

Langmuir Isotherm  
Langmuir isotherm was derived in 

1916 by Irving Langmuir [16, 17]. It is 
one of the most known models which 

are frequently employed for the 

determination of adsorption parameter 

[18]. The Langmuir equation is 

represented by: 
 

e

e
e

bC

abC
q




1
                                  …(1) 

 

And the equation may be linearized as: 
 

ab
C

aq

C
e

e

e
11

                              …(2) 

 

Freundlich Isotherm  
The Freundlich isotherm is the earliest 

known relation presented by Herbert 

Freundlich in 1906 [19]. The 

Freundlich equation is represented by: 
 

n

efe
CKq

/1
                                   ...(3) 

 

The linear form of the equation 

obtained by taking the logarithm as 

follows 
 

efe
C

n
Kq log

1
loglog              …(4)

 
 

Materials and Experimental Work 

1. Materials 
 

1.1. Adsorbent 

The adsorbent used was aluminum 

oxide 90 standardized for column 

chromatography adsorption analysis, 

supplied by MERCK chemical 

company; the properties of the alumina 

are listed in Table 1: 

 
 

 

 

 



Jenan A. Alnajar, Asawer A. Kwaeri, Ramzi H. Sayhood and Abbas H. Slaymon 

 

-Available online at: www.iasj.net                   IJCPE Vol.15 No.3 (September 2014)                          39 
 

Table 1: Properties of alumina 

Product name ,Aluminum oxide 90 

standardized 

Formula Al2O3 

 Particle size 

range 

60-200 µm (70% in 

this range) 

Specific surface 

area 

Approx. 120-160 m
2
/g 

Specific pore 

volume 

Approx. 0.7-0.3 ml/g 

Mean pore size 6 – 15 nm 

pH (10% aq. 

Suspension) 

8.5 – 10.5 

Bulk density Approx. 83.6 g/100 ml 

Ref. MERCK Chemical Company 

 

1.2. Adsorbate 

Metal ions used in the present work 

were barium nitrate Ba(NO3)2 and 

magnesium nitrate Mg(NO3)2. 1000 

mg/l standard stock solutions of Ba
2+

 

and Mg
2+

 were prepared by dissolving 

1.902 g and 10.540 g, respectively, in 

one liter of distilled water. 

 

2. Experimental Work 
Experiments of single and binary 

system were carried out in batch 

model. In general, the adsorption 

experiments were achieved by 

agitation of 20 ml of metal ion solution 

(single or binary system solution) of a 

given mass of adsorbent. The agitation 

speed was 300 rpm for 30 min. the 

contact time was 24 h at 20 ˚C. After 

that the alumina was separated from 

the liquid phase by filtration through 

membrane filter 0.45 μm. The filtrate 

was analyzed to find the remaining 

metal ion concentration by Atomic 

Absorption Spectrometer (AAS). The 

pH of the initial solution was adjusted 

using diluted solution of either 0.1 M 

HCl or NaOH. The following 

parameters were studied. 

 

2.1. Adsorbent Dose 

The effect of adsorbent weight on the 

adsorption was studied by agitating 20 

ml of 50 mg/l of metal ion (Ba
2+

,  Mg
2+

 

or mixture of them) with different 

adsorbent weight (0.1 – 2 g) at 

equilibrium time. These experiments 

were conducted for single and binary 

system. 

 

2.2. pH of the Solution 

The effect of pH was studied by 

adjusting the pH of metal ion solutions 

(Ba
2+

 and Mg
2+

) from 3 to 10 by using 

dilute 0.1 M of HCl and NaOH 

solutions. The experiments were 

conducted for the single system. 

 

2.3. The Concentration of Metal Ion 

and Adsorption Isotherm 

The effect of metal ion concentration 

was studied for both single and binary 

systems. This was carried out by 

agitating 20 ml of metal ion 

concentration (50-200 ppm) with 0.5 g 

alumina for Ba
2+

 and 1.5 g alumina for 

Mg
2+

. The amounts of metal ion 

adsorbed by alumina were calculated 

experimentally using the following 

equation: 

 

)(
eoe

CC
W

V
q                           …(5) 

 

The percentage of adsorption of metal 

ion was calculated using the following 

equation: 

 

100*Re% 








 


o

eo

C

CC
moval          …(6) 

 

Result and Discussion 

1. Single System 
 

1.1. Effect of Adsorbent Dosage 

The effect of alumina dosage for 

adsorption of Ba
2+

 and Mg
2+

 was 

examined. Alumina dosage was varied 

from 0.1 g to 2 g. This experiment was 

carried out using fixed volume of metal 

ion solution of 20 ml and constant 

metal ion concentration of 50 mg/l, pH 

of 6, contact time 24 h, 300 rpm 

agitation speed and at room 



Study the Feasibility of Alumina for the Adsorption of Metal Ions from Water 
 

40                               IJCPE Vol.15 No.3 (September 2014)              -Available online at: www.iasj.net 
 

temperature of 25 ˚C. The results are 

presented in Fig. 1 for both metal ions. 

 

 
Fig. 1: The effect of alumina dose on the 

adsorption of Ba
2+ 

and Mg
2+

 in single system, 

T=20 ˚C, pH= 6, CO= 50 mg/l, V= 20 ml 

solution 

 

Fig. 1 indicates that metal ion removal 

increases with increasing weight of 

alumina. Increasing weight of alumina 

leads to an increase in the number of 

active sites available for adsorption 

[20]. Also, this figure shows the 

difference between the adsorption of 

alumina for both Ba
2+

 and Mg
2+

 used. 

Fig. 1 shows the removal of Ba
2+ 

and 

Mg
2+

 attained maximum removal at 

adsorbent dosage of 1 g and 2 g, 

respectively, with 100% removal. 

Hence 0.5 g and 1.5 g was chosen as 

the optimum adsorbent dosage for 

removal of Ba
2+ 

and Mg
2+

,
 

respectively. 
 

1.2. Effect of pH 

The pH of aqueous solution is an 

important controlling parameter in the 

adsorption process [21]. The influence 

of pH on the adsorption ofBa
2+

 and 

Mg
2+

 onto alumina at 30 
o
C and metal 

ion concentration of 50 mg/l was 

studied and it is shown in Figs. 2 and 

3, respectively. The pH range used was 

(3-10). These figures show that the 

percentage removal of Ba
2+

 and 

Mg
2+

increased with increasing pH of 

the solution.  Similar behavior has 

been reported by [22]. The most 

effective pH was found to be 6 for both 

metal ions.  

 
Fig. 2: The effect of pH on the adsorption of 

Ba
2+

 in single system, T= 20 ˚C, Co= 50 mg/l, 

W= 0.5 g alumina, V= 20 ml solution 
 

 
Fig. 3: The effect of pH on the adsorption of 

Mg
2+

 in single system, T= 20 ˚C, , Co= 50 

mg/l, W= 0.5 g alumina, V= 20 ml solution 
 

At low pH values, there is high 

concentration of H
+
 in the solution; a 

competition exists between the 

positively charged hydrogen ions and 

metal ions for available adsorption 

sites. The high percentage removal at 

high pH values is due to the metal 

precipitation as hydroxides and 

therefore the removal takes place by 

adsorption as well asprecipitation. This 

can be explained by the fact that as pH 

of solution increases, the OH
-
 ions in 

the solution increase and form some 

complexes with metal ions and 

precipitate as metal hydroxide [23, 24]. 

The optimum conditions for both metal 

ions were found to be at pH 6. 
 

1.3. Effect of Initial Metal Ion 

Concentration 
The effect of initial concentration of 

Ba
2+

 and Mg
2+

 on adsorption was 

studied and is shown in Figs. 4 and 5, 

respectively.  



Jenan A. Alnajar, Asawer A. Kwaeri, Ramzi H. Sayhood and Abbas H. Slaymon 

 

-Available online at: www.iasj.net                   IJCPE Vol.15 No.3 (September 2014)                          41 
 

 
Fig. 4: The effect of initial concentration of 

Ba
2+

 on the adsorption of Ba
2+

 in single 

system, onto alumina T=20 
o
C, pH= 6, M= 0.5 

g alumina, V= 20 ml solution 

 

 
Fig. 5: The effect of initial concentration of 

Mg
2+

 on the adsorption of Mg
2+ 

in single 

system, onto alumina T=20 
o
C, pH= 6, M= 1.5 

g alumina, V= 20 ml solution 

 

It is clear from these figures that the 

percentage removal of Ba
2+

 and Mg
2+

 

decreased as the initial concentration 

of the metal ions increased from 25-

200 mg/l; this was due to the saturation 

of the active adsorption sites of the 

adsorbent with the initial metal ions 

concentration. In other words, the 

lower concentration of metal ion 

solution was fully adsorbed at the 

active sites present in the alumina and 

then as the concentration increased the 

number of active site decreased and 

later no free sites were available to 

adsorb. 

 

1.4. Equilibrium Isotherm Studies 

Equilibrium isotherm studies were 

performed to obtain equilibrium 

isotherm curves. The adsorption 

isotherm curves were obtained by 

plotting the amount of solute (Ba
2+ 

and 

Mg
2+

) adsorbed per unit weight 

adsorbent (qe) against the equilibrium 

concentration of the solute (Ce) in the 

solution. The values of qe for each 

metal ion were calculated using 

Equation 5. 

Figs. 6 and 7 show the experimental 

and theoretical adsorption isotherm 

curve for Ba
2+

 and Mg
2+

 at 20 
o
C. The 

theoretical data for both metal ions 

were obtained by using Langmuir and 

Freundlich models. 

 

 
Fig. 6: Adsorption isotherm for adsorption of 

Ba
2+

 onto alumina in single system, T=20 
o
C, 

pH= 6, M= 0.5 g alumina, V= 20 ml solution 

 

 
Fig. 7: Adsorption isotherm for adsorption of 

M
2+

 onto alumina in single system, T=20 
o
C, 

pH= 6, M= 1.5 g alumina, V= 20 ml solution 

 

Figs. 6 and 7 show that the 

experimental data fitted the Langmuir 

model better than Freundlich model 

with Ba
2+

 and Mg
2+

. The 

corresponding Langmuir and 

Freundlich parameters along with the 

correlation coefficients are given in 

Table 2.  

As shown in Table 2, the correlation 

coefficient R
2
 for Langmuir model for 

both metal ions is slightly greater than 

that for Freundlich model. This 



Study the Feasibility of Alumina for the Adsorption of Metal Ions from Water 
 

42                               IJCPE Vol.15 No.3 (September 2014)              -Available online at: www.iasj.net 
 

indicates that the experimental data 

gives best fitting with the Langmuir 

model than the Freundlich model for 

both metal ions. 

The values of Langmuir parameter (a) 

are the monolayer adsorption capacity 

and (b) are constant related to the free 

energy of adsorption and that of 

Freundlich parameter (Kf) are constant 

indicative ofthe relative adsorption 

capacity of the adsorbent and (b) 

and(1/n) are constant indicative of the 

intensity of adsorption. As given in 

Table 2, these parameters vary in the 

following order: 

 

Ba
2+ 

> Mg
2+

      for a and Kf 

Ba
2+

> Mg
2+

     for b and 1/n 

 

The values of the models parameters 

indicate that the capacity of alumina 

for these metals followed the order 

Ba
2+

> Mg
2+

. 

 
Table 2: Model isotherm parameters for single metal ion adsorption system 

Metal 

ion 

Langmuir Model Freundlich Model 

a b R
2
 Kf 1/n R

2
 

Ba
2+

 3.665 0.210 0.998 0.889 0.331 0.877 

Mg
2+

 1.098 0.069 0.981 0.244 0.292 0.946 

 

2. Binary System 
2.1. Effect of Adsorbent Dose 

The effect of alumina dose on the 

adsorption of both Mg
2+

 and Ba
2+

 in 

binary system is shown in Fig. 8. 

 

 
Fig. 8: The effects of alumina dose on the 

adsorption of both Mg
2+ 

and Ba
2+

in binary 

system. Initial concentration of both ions Co= 

50mg/l, pH=6, V= 20ml solution 

 

A similar behavior was obtained for 

the effect of alumina dose on the 

percentage removal for the single and 

binary system; i.e. the percentage 

removal of both metal ion increases 

gradually with the amount of absorbent 

up to a certain value. Also, the 

percentage removal of Ba
2+

 is greater 

than that for Mg
2+

 at the same amount 

of alumina. This indicates that alumina 

is more efficient for adsorption of Ba
2+

 

than Mg
2+

.
 

 

 
Fig. 9: The effect of alumina dose on the 

adsorption of Ba
2+

 in single and binary system. 

Initial concentration of Ba
2+

and Mg
2+ 

 in single 

and binary system i Co= 50 mg/l, pH= 6, V= 

20 ml solution 
 

 
Fig. 10: The effect of alumina dose on the 

adsorption of both Mg
3+

 in single and binary 

system. Initial concentration of both ions Co= 

50 mg/l, pH= 6, V= 20 ml solution 

 



Jenan A. Alnajar, Asawer A. Kwaeri, Ramzi H. Sayhood and Abbas H. Slaymon 

 

-Available online at: www.iasj.net                   IJCPE Vol.15 No.3 (September 2014)                          43 
 

A comparison between the percentage 

removal for both Ba
2+

 and Mg
2+

 in 

single and binary system is shown in 

Figs. 9 and 10. It can be observed from 

these figures that the percentage 

removal in single phase is higher than 

that in multi-phase; this behavior may 

be attributed to the competition 

between these two components to 

sorption; hence, the chance for getting 

for both of them will be lowered in 

multi component system. 

 

2.2. Effect of Initial Metal Ion 

Concentration 

The effect of initial concentration of 

Ba
2+

 and Mg
2+

in binary system was 

studied and the results are shown in 

Figs. 11a, 11b, 12a and 12b. 

 
(a) 

 

 
(b) 

 
Fig. 11: The effect of initial ion concentration 

of (a) Ba
2+

 and (b) Mg
2+

 and dose of alumina 

on the percentage removal of Ba
2+

 and Mg(II) 

in binary system 

 

These Figures show that the percentage 

removal of Ba
2+

 and Mg
2+ 

decreases 

with increasing the initial 

concentration and increases with the 

increasing of mass of adsorbent. This 

is similar to the results obtained by 

single component system. These 

figures also show that the percentage 

removal of Ba
2+

 is greater than that for 

Mg
2+

. This is because in the case of 

binary system when the Ba
2+

 and Mg
2+

 

ions exist in the same solution, 

competition occurs between them for 

the active adsorption sites on the 

adsorbent surface and one of them will 

occupy the larger number of active 

sites. In this work, Ba
2+

 will occupy 

the greater amount of active sites than 

Mg
2+

 and therefore the percentages 

removal of Ba
2+

 are greater than Mg
2+.

 

As explained in the single system, the 

alumina is more efficient for the 

removal of Ba
2+

 than Mg
2+

.
 
Figs. 13 

and 14 illustrate the comparison 

between the adsorption rate of metal 

ions in single and binary system.  
 

 
(a) 

 

 
(b) 

 
Fig. 12: The effect of initial ion concentration 

of Ba
2+

 and Mg
2+

 on the percentage removal of 

Ba(II) and Mg(II) in binary system using (a) 

0.5 g alumina and (b) 1.5 g alumina 



Study the Feasibility of Alumina for the Adsorption of Metal Ions from Water 
 

44                               IJCPE Vol.15 No.3 (September 2014)              -Available online at: www.iasj.net 
 

 
Fig. 13: The effect of initial ion concentration 

of Ba
2+

on the percentage removal of Ba
2+

 in 

single and binary system 

 

 
Fig. 14: The effect of initial ion concentration 

of Mg
2+

 on the percentage removal of Mg
2+

 in 

single and binary system 

 

It can be seen from these figures that 

the adsorption rate in single component 

system is greater than that in binary 

system due to the competition effect in 

the binary system on the adsorption 

process as explained above. 

 

2.3. Equilibrium Isotherm Studies 

The Langmuir and Freundlich isotherm 

models were used to describe the 

adsorption equilibrium data for Ba
2+

 

and Mg
2+

 onto alumina for binary 

system as shown in Figs. 15 and 16 for 

Ba
2+

 and Mg
2+

, respectively. 

It is clear from these figures that the 

experimental isotherm data for Ba
2+

 

gives good fitting with both Langmuir 

and Freundlich isotherm models and 

the experimental isotherm data for 

Mg
2+

 gives better fitting with 

Langmuir model than that with the 

Freundlich model. 

 

 
(a) 

 

 
(b) 

 

Fig. 15: The adsorption isotherm of Ba
2+

 in 

binary system of Ba
2
using (a) 0.5g alumina,    

(b) 1.5g alumina 
 

(a) 
 

(b) 
 

Fig. 16: The adsorption isotherm of Mg
2+

 in 

binary system of Mg
2+

 using (a) 0.5g alumina,    

(b) 1.5g alumina 



Jenan A. Alnajar, Asawer A. Kwaeri, Ramzi H. Sayhood and Abbas H. Slaymon 

 

-Available online at: www.iasj.net                   IJCPE Vol.15 No.3 (September 2014)                          45 
 

Table 3 shows the adsorption isotherm 

parameters. It can be seen from Table 2 

that the value of adsorption capacity a 

and Kf for Langmuir model and 

Freundlich model respectively and the 

correlation coefficient R
2 

varies in the 

following order: 

 

Ba
2+

> Mg
2+

      for a, Kf and R
2 

 

Table 3: Model isotherm parameters for binary metal ion adsorption system 

Mass 

alumina g 

Metal 

ion 

Langmuir Model Freundlich Model 

a b R
2
 Kf 1/n R

2
 

0.5 
Ba

2+
 1.840 0.027 0.995 0.155 0.475 0.992 

Mg
2+

 0.553 0.039 0.997 0.054 0.446 0.873 

1.5 
Ba

2+
 2.932 0.196 0.997 0.485 0.656 0.989 

Mg
2+

 0.516 0.516 0.999 0.281 0.141 0.907 

 

Figs. 17 and 18 show the adsorption 

isotherm for Ba
2+

 and Mg
2+

 in single 

and binary system. It can be seen from 

these figures that the adsorption 

capacity of alumina for adsorption of 

both metals in single system is greater 

than that in binary system. This is due 

to the competition among the metals 

for activation sites in case of binary 

system which lowered the adsorption 

capacity for both metals. It can be 

noticed from the values of a and Kf 

which take the following order: 

Single>Binary for a and Kf 
 

 
Fig. 17: The adsorption isotherm of Ba

2+
 in 

single and binary system, M= 0.5 g alumina 
 

 
Fig. 18: The adsorption isotherm of Mg

2+
 in 

single and binary system 

Mathematical Model for Batch 

Adsorption 

Pore diffusion model was used in the 

present work to describe the adsorption 

of metal ion in batch system through 

predicting the concentration decay 

curve. The mathematical model using 

pore diffusion model [25] is: 
 External mass transfer can be 

obtained by mass balance in the 

bulk fluid outside the particle: 

 

),(
3

Rprpcbc
pRp

fWk

dt

bdC
V 


                 …(7)  

 

 Interpartical diffusion can be 
obtained from the mass balance of 

metal ion inside the porous 

adsorbent particle: 

 

































r

pc
r

rr
pDp

t

pc
p

dt

q
p

2
2

2

1
               …(8)   

 

The initial and boundary conditions 

are: 

I.C.: 

 

ob
cc 

,
0

p
c

,
0q

, 0t    …(9) 
 

BC:  
0

0





r

p

t

c

 ,
0

0





r

r

q

0r ,  
…(10) 

 

),( RprpCbCfkRr
r

pC

pDp p 





 pRr    

…(11) 



Study the Feasibility of Alumina for the Adsorption of Metal Ions from Water 
 

46                               IJCPE Vol.15 No.3 (September 2014)              -Available online at: www.iasj.net 
 

Where b
c

and p
c

are the solute 

concentration in the bulk liquid and 

particle phase, respectively. 

 

Local equilibrium was assumed 

between the solute in the pore and the 

solute adsorbed in the pore surface. 

This local equilibrium was represented 

by the Langmuir: 

 

p

pe

bC

bCq
q




1
                                …(12) 

 

The external mass transfer coefficient 

can be correlated in term of 

dimensionless correlation. The 

following correlation was developed 

based on the experimental data [26]:  

 

461.

019,0
/

011.0173.0283.0
Re046.0

o
Sc

pd

T
UGamSh 















  

…(13) 

 
Equation (11) is valid for: 104 < Rem 

< 3×104; 1.1×105 < Ga < 106; 300 

<sc<2000 and 27 < U < 2900, where U 

is a group characterizing the solid 

concentration. This correlation has a 

deviation between experimental and 

calculated value of 2.5%.  

The external mass transfer coefficient 

can be obtained by the analytical 

solution for Equation 6 and where at t 

= 0, CP,r=Rp = 0 and Cb = Co , hence: 

 
















oC

tC

Wt

VppR

fk ln
3

                             ...(14) 

 

The set of partial differential Equations 

7-12 were first solved by reduction to a 

set of ordinary differential equation, 

ODE, using the Finite element, FE, and 

Orthogonal collocation, OC, methods, 

respectively. The resulting ODE 

system was solved using an existing 

ODE solver provided by MATLAB v-

7. The mathematical model was 

developed to obtain the theoretical 

concentration decay curve. The 

experimental concentration decay 

curves for each metal ion (Ba
+2

 and 

Mg
+2

) were obtained by plotting Ce/Co 

versus time, at different agitation 

speeds.  

Figs. 19 and 20 show the experimental 

concentration decay curve at different 

agitation rates and that is predicted by 

the mathematical model for Ba
2+

 and 

Mg
2+

, respectively, at different 

agitation rates. The mathematical 

model used was the pore diffusion 

model. These figures show a good 

fitting between the experimental and 

predicted results. The results for 

adsorption for both metals slightly 

change with agitation speed. 

 

 
Fig. 19: The experimental concentration decay 

curve and that predicted by pore diffusion 

model for adsorption Ba
2+

 in single component 

system at different agitation speed 

 

 
Fig. 20: The experimental concentration decay 

curve and that predicted by pore diffusion 

model for adsorption Mg
2+

 in single 

component system at different agitation speed 

 

 



Jenan A. Alnajar, Asawer A. Kwaeri, Ramzi H. Sayhood and Abbas H. Slaymon 

 

-Available online at: www.iasj.net                   IJCPE Vol.15 No.3 (September 2014)                          47 
 

1. The External Mass Transfer 
Coefficient kf and the Pore 

Diffusion Coefficient Dp 

The principal parameters required for 

using the program were the external 

mass transfer coefficient kf and the 

pore diffusion coefficient Dp. By 

minimizing the differences between the 

theoretical and experimental decay 

curves for the batch adsorption, it was 

possible to obtain the individual Dp 

and kf for each metal ion using the 

Langmuir isotherm equation [27] as 

presented in the Table 4.  

There was a good agreement between 

the batch experimental data and the 

predicted decay curves using pore 

diffusion model for batch operation 

and the pore diffusion coefficient for 

each metal ion were found to be: 

 
Table 4: Model isothermal parameters for 

binary material ions adsorption system 

Metal 

ion 
Dp, m2/s 

kf 

.m/s 

Ba
2+

 8.0x10
-9

 3.600x10
-5

 

Mg
2+

 4.5x10
-9

 0.573x10
-6

 

 

Conclusions 

1- The metal ion removal of Ba
2+

 and 

Mg
2+

 increased with increasing the 

alumina dosage for single and 

binary system. The optimum dosage 

of alumina was found to be 0.5 g 

and 1.5 g for removal of Ba
2+

 and 

Mg
2+

, respectively. 

2- The percentage removal of Ba
2+

 and 

Mg
2+

 decreased as the initial 

concentration of metal ion increased 

for single and binary system. 

3- In single system, the percentage 
removal of Ba

2+
 and Mg

2+
 increased 

with increasing the alkalinity of the 

solution. The optimum pH was 

found to be pH 6. 

4- The experimental adsorption data 
fitted well with both Langmuir and 

Freundlich isotherm model in single 

system. 

5- In binary system, the percentage 
removal of Ba

2+
 was greater than 

that of Mg
2+

 at the same weight of 

alumina and initial concentration of 

metal ion. 

6- The percentage removal of metal 
ion in singular system is greater 

than that in binary system. 

7- In binary system, the experimental 
data of Ba

2+
 was fitted by both 

Langmuir and Freundlich 

isothermal model while Mg
2+

 

results showed better fitting with 

Langmuir model. 

8- The experimental data were 
modeled using pore diffusion 

mathematical model with good 

agreement. 

 

Nomenclature 

a      External surface 

area per unit 

volume of the 

particle 

m
2
/m

3
 

b  Langmuir constant 

related to energy of 

adsorption 

l/mg 

C Fluid phase 

concentration                                                    

mg/l 

Cb The solute 

concentration in the 

bulk fluid.         

Mg/l 

Ce Equilibrium liquid 

phase concentration   

mg/l 

Co Initial liquid phase 

concentration 

mg/l 

Cp The solute 

concentration in the 

particle phase 

mg/l 

Dp Pore diffusion 

coefficient 

m
2
/s 

Dm Molecular 

diffusivity 

m
2 

dp Particle diameter m 

g Gravitational force 

(9.8) 

m/s
2 

Kf Concentration in 

Freundlich relating 

to adsorption 

capacity  

(mg/g) 

(l/mg)
1/n 

kf External film mass 

transfer coefficient 

m/s 



Study the Feasibility of Alumina for the Adsorption of Metal Ions from Water 
 

48                               IJCPE Vol.15 No.3 (September 2014)              -Available online at: www.iasj.net 
 

n Freundlich constant  

relating to 

adsorption intensity 

- 

qe Equilibrium solid 

phase adsorbate 

concentration 

mg/g 

r Radial coordinate m 

S Surface area m
2 

R Correlation 

coefficient  

- 

Rp Radius of particle m 

t time s 

T Temperature K 

V Volume of solution m
3 

v Superficial velocity m/s 

W mass of adsorbent  g 

   

Creek symbols 

Ɛp Porosity of adsorbent 

particle 

- 

µc Kinematics viscosity m
2
/s 

µw Water viscosity m
2
/s 

ρ Density Kg/m
3 

Ρw Density of water Kg/m
3 

   

Dimensionless group 

Sh Sherwood number 

m

pf

D

dk
 

Re Reynolds number  

w

pw
d





 

Rem Reynolds number  

3

4

c

p
Pd


 

Sc Schmidt number 

mw

w

D


 

Ga Galileo number 

2

3

c

p
gd


 

U Solid concentration 

group 
p

Sd

W


 

 

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