Two-Stage Batch Adsorber Design Using Pseudo-Second-Order
Kinetic Model for the Adsorption of Acid Blue 25 Dye onto Peat
Pei-Yu Lin1#, Ming-Huang Wang1, Yu-Ting Feng1, I-Hsin Lin1 and Yuh-Shan Ho2*
1School of Public Health, Taipei Medical University
2Bibliometric Centre, Taipei Medical University - Wan-Fang Hospital
Introduction
Batch adsorber design has mainly concentrated on reducing adsorbent costs, which is particularly relevant when expensive sorbent
materials such as active carbon, silica, zeolites and resins are used. But for cheaper adsorbents minimizing the contact time for a fixed
percentage of pollution removal using a fixed mass of adsorbent will result in being able to process more batches of polluted wastewater per
day, thus enabling the required treatment plant items to be reduced in size, with a decrease in the plant capital cost. This paper studies the
adsorption of Acid Blue 25 dye onto peat and develops a two-stage batch adsorber design model.
Methods
A 0.5 g sample of peat (500-710 m) was added to each 50 ml volume of Acid Blue 25 (AB25) dye solution. The initial concentrations of
AB25 dye solution tested were 20, 50, 100 and 200 mg/dm3. Samples were withdrawn at suitable time intervals, filtered through a filter paper
and then analysed AB25 concentration using UV.
Results
Pseudo-second-order kinetic model
Cn  Cn1 
t
1
1

 t
qt kqe2 qe
100 St n kqn2
Rn 


LC0 n1 1  kqn t
n1
n
k  12.3C 01.86

n



0.157C  t
0.157C t 


0.839 2
0
0.839
0
100St n 12.3C01.86 0.157C

LC0 n1 1  12.3C01.86 0.157C

0.839 2
0
0.839
0
1.86
0
1.86
0
 
n
t
350
80% Removal
Stage 1
Time (min)
250
300
250
200
89% Removal
86% Removal
83% Removal
80% Removal
150
100
50
0
0
2
4
6
8 10 12 14 16 18 20 22 24
Adsorption system number
Figure 1: Comparison of 80% AB25 removal time of each stage
in two-stage AB25/peat process
300
450
400
100Cn1  Cn  100S 12.3C

C0
LC0 1  12.3C
R
n 1
LC0  Cn1   S qn  q0 
350
Skqn2t
L1  kqn t 
q e  0.157C 00.839
Rn 
Figure 2. Minimum contact time for various percentage
AB25 removal in a two-stage AB25/peat process
Time (min)
t
1
t

2
kqe qe
qt 
Mass balance equation
Stage 2
Table 1. Parameters for effect of initial concentration on
the AB25/peat system
C0
mg/dm3
qe
mg/g
k
g/mg min
h
mg/g min
r2
20
1.85
0.0442
0.152
0.999
50
4.40
0.0110
0.213
0.999
100
7.76
0.00156
0.0941
0.994
200
12.7
0.000747
0.121
0.924
Conclusions
200
 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.
150
100
 The method proposed in this study enables the contact
time in a two-stage batch adsorber to be minimized to
achieve a fixed percentage of Acid Blue 25 removal
using a fixed mass peat.
50
0
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Adsorption system number
 An optimised operating condition, the minimum contact
time is 191 min, with reaction times of 100 min for stage
1 and 91 min for stage 2.