Transcript Two-stage batch adsorber design using pseudo-second

Two-Stage Batch Adsorber Design Using Pseudo-second-order
Kinetic Model for the Adsorption of Cadmium Ions onto Tree Fern
Ming-Huang Wang1#, Pei-Yu Lin1, I-Hsin Lin1, Yu-Ting Feng1 and Yuh-Shan Ho2
1School of Public Health, Taipei Medical University
2Bibliometric Centre, Taipei Medical University - Wan-Fang Hospital
Introduction
The cost and performance of product/equipment/system or the mode of application are always of concern to control the process efficiency.
Therefore the adsorption capacity and required contact time are two of the most important parameters to understand in an adsorption
process. It is important to determine how adsorption rates depend on the concentrations of adsorbate in solution and how rates are affected
by adsorption capacity or by the character of adsorbent in terms of kinetics. From the kinetics analysis, the solute uptake rate which
determines the residence time required for completion of the adsorption reaction may be analysed and established. This approach has been
adopted and is presented in the present paper.
Materials and Methods
Figure 1. Schematic for two-stage countercurrent
batch adsorption
All contact investigations were carried out using a baffled, agitated 2 dm3 adsorber
vessel. Samples (2 ml) were withdrawn at suitable time intervals, filtered through a 0.45
m membrane filter and then analysed cadmium ion concentration. A fixed mass of tree
fern was added to each 1.7 dm3 volume of cadmium solution and a constant agitation
speed was used for all experiments.
q0 S1
C0
Batch Adsorber Design
STAGE 1
L
Pseudo-second-order kinetic model
qt 
t
1
t

kqe2 qe
t
1
1

 t
qt kqe2 qe
Skqn2t
Cn  Cn1 
L1  kqn t 
n
R
n1
n

LC0  Cn1   S qn  q0 
100 St n kqn2

LC0 n1 1  kqn t
qe 
C0
0.0543C0  3.19
k
C0
22.3C0  697
q1 S1
2
30
95% Removal
25
Stage 2
110
90
80
Time (min)
L
q2 S2
Stage 1
15
10
5
0
1 2
3
4 5 6 7 8 9 10 11 12 13 14 15 16
Adsorption system number
Table 1. Parameters for effect of initial concentration on
the Cd(II)/tree fern system
100
70
60
50
10
C2
20
0
20
STAGE 2
35
Table 1. Minimum contact time for various percentage cadmium
removal in a two-stage process
30
L
Figure 1: Comparison of 95% cadmium removal time of each
stage in two-stage process
Time (min)



C0
C0

 t
100S 
22
.
3
C

697
0
.
0543
C

3
.
19
0
0



 


C0
C0

t 
LC0 1  
22
.
3
C

697
0
.
0543
C

3
.
19
0
0


 



C0
C0



n
100St n  22.3C0  697  0.0543C0  3.19 
Rn 


LC0 n 1 


C0
C0
n 1

t
1  
22
.
3
C

697
0
.
0543
C

3
.
19
0
0



40
C1
Mass balance equation
2
100Cn 1  Cn 
Rn 

C0
q0 S2
99% Removal
98% Removal
97% Removal
96% Removal
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
Adsorption system number
C0
mg/dm3
qe
mg/g
k
g/mg min
h
mg/g min
r2
65.8
9.53
0.0824
7.48
1.000
137
13.2
0.0594
10.3
1.000
280
15.2
0.0505
11.6
1.000
Conclusions
 The design model presented is based on a pseudosecond-order kinetic model, and this has been used for
minimizing the reaction time used in a two-stage contact
system that operating cost would be reduced.
 The model has been optimized with respect to contact in
order to minimize total contact time to achieve a fixed
percentage of cadmium ions removal using a fixed mass
of tree fern.