Two-Stage Batch Adsorber Design Using Pseudo-Second-Order
Kinetic Model for the Adsorption of Basic Blue 69 Dye onto Peat
I-Hsin Lin1#, Ming-Huang Wang1, Pei-Yu 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.
Figure 1. Pseudo-second order sorption kinetics of BB69
dye onto peat at various initial concentrations
Batch Adsorber Design
Pseudo-second-order kinetic model
qt 
t
Mass balance equation
LC0  Cn1   S qn  q0 
t
1
1

 t
qt kqe2 qe
1
t

kqe2 qe
100 St n kqn2
Rn 


LC0 n1 1  kqn t
n1
n
Skqn2t
Cn  Cn1 
L1  kqn t 


qt (mg/g)
Materials and Methods
A 0.1 g sample of peat (500±710 m) was added to each 50 ml volume
of Basic Blue 69 dye solution. The initial concentrations of BB69 dye
solution tested were 50, 100, 200, and 500 mg/dm3. Samples were
withdrawn at suitable time intervals, filtered through a filter paper and
then analysed with UV.
qe  0.70C 00.91
k  82.75C 02.03

2
n 1
n
0
n 1

150
200
250
300
70
60
50
Figure 2. Minimum contact time for various percentage BB69
dye removal in a two-stage process
180
40
30
Stage 1
Stage 2
95% Removal
20
160
10
140
Time (min)
100
Figure 3: Comparison of 95% BB69 dye removal time of
each stage in two-stage process
0.91 2
0
0.91
0
 2.03
0
 2.03
0
n
50
Time (min)
Time (min)
n
50 mg/dm3
100 mg/dm3
200 mg/dm3
500 mg/dm3
2nd order model
0
100Cn1  Cn  100S 82.75C02.03 0.70C00.91 t
Rn 

C0
LC0 1  82.75C02.03 0.70C00.91 t
 

82.75C 0.70C 
100St
 R  LC  1  82.75C 0.70C t
200
180
160
140
120
100
80
60
40
20
0
0
120
0
100
1
2
3
4
5
6
7
8
9 10 11 12 13 14
Adsorption system number
80
60
Table 1. Parameters for effect of initial concentration on
the BB69 dye/peat system
99% Removal
98% Removal
95% Removal
90% Removal
40
20
0
0
2
4
6
8
10
12
14
16
Adsorption system number
Conclusions
18
20
22
C0
mg/dm3
qe
mg/g
k
g/mg min
h
mg/g min
r2
50
23.78
0.0295
16.67
1.000
100
47.2
0.00662
14.76
1.000
200
86.4
0.001844
13.76
1.000
500
195
0.0002617
9.94
0.997
 The design model presented is based on a pseudo-second-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 Basic Blue
69 dye removal using a fixed mass of peat.
 An optimised operating condition of 95% removal, the minimum contact time is 40 min, with reaction times of 25 min for stage 1 and 15
min for stage 2.