Marine Algae Biomass for Removal of Heavy Metal Ions 25.5 Modeling of Biosorption in Batch Conditions 635
Part D | 25.5
Table 25.10 The mathematical expressions of the pseudo-first order Lagregen and pseudo-second order Ho kinetic models (after [25.16, 18, 112, 145])
Kinetic model
Differential equation Integral equation
Significance of terms
Pseudo-first
order Lagregen
model
dqt
dt D k 1 .q e q t /
ln.q e q t / D ln q e k 1 t q e , q t are the amounts of heavy metals retained on weight
unit of biosorbent at equilibrium and at time t, (mg=g);
k 1 is the rate constant of the pseudo-first order kinetics
equation .min 1 /
Pseudo-second
order Ho model
dqt
dt D k 2 .q e q t / 2
t
qt D
1
k2q 2
e
C
t
qe
q e , q t are the amounts of heavy metals retained on weight
unit of biosorbent at equilibrium and at time t, .mg=g/;
k 2 is the rate constant of pseudo-second order kinetics
equation .g=mg min/
Table 25.11 Kinetic data for the use of some marine algae and marine algae waste biomass for the removal of heavy
metal ions
Heavy metal c 0
Biosorbent
Best kinetic model
Kinetic parameters
Reference
ion
.mg=l/
R
2
q e .mg=g/ k 2 .g=mg min/
Cd(II)
75
Laminaria hyperborea
Pseudo-second order
0.997
31.3
0.024
[25.53]
75
Sargassum muticum
Pseudo-second order
0.997
38.4
0.004
[25.53]
225
Lobophora variegata
Pseudo-second order
0.995
94.2
0.006
[25.133]
225
Cystoseira baccata
Pseudo-second order
0.999
56.2
0.007
[25.94]
100
Fucus vesiculosus
Pseudo-second order
0.999
52.8
0.051
[25.93]
50
Ceramium virgatum
Pseudo-second order
0.999
116.9
0.003
[25.95]
67.4
Algae waste biomass a
Pseudo-second order
0.999
5.83
0.056
[25.41]
45.5
Algae waste biomass b
Pseudo-second order
0.999
7.60
9.200
[25.96]
Cr(VI)
50
Ulva lactuca sp.
Pseudo-second order
0.999
12.9
0.010
[25.61]
10
Ulva fasciata
Pseudo-second order
0.999
9.7
0.013
[25.33]
Cu(II)
Sargassum sp.
Pseudo-second order
0.999
9.6
0.010
100
Fucus vesiculosus
Pseudo-second order
0.999
41.9
0.002
[25.93]
225.4
Cladophora fascicularis Pseudo-second order
0.999
144.9
0.004
[25.36]
100
Laminaria hyperborea
Pseudo-second order
0.996
50.3
0.020
[25.53]
100
Sargassum muticum
Pseudo-second order
0.997
38.2
0.017
[25.53]
200
Spirogyra sp.
Pseudo-second order
0.998
111.1
0.032
[25.102]
200
Oedogonium sp.
Pseudo-second order
0.996
117.6
0.064
[25.141]
Pb(II)
200
Nostoc sp.
Pseudo-second order
0.992
89.3
0.038
[25.141]
414
Lobophora variegata
Pseudo-second order
0.967
229.5
0.010
[25.133]
414
Cystoseira baccata
Pseudo-second order
0.999
142.9
0.001
[25.94]
100
Fucus vesiculosus
Pseudo-second order
0.999
102.2
0.009
[25.93]
133
Algae waste biomass
a
Pseudo-second order
0.999
18.1
0.022
[25.41]
–
Algae waste biomass b
Pseudo-second order
0.915
41.4
–
[25.103]
Zn(II)
75
Laminaria hyperborea
Pseudo-second order
0.991
19.2
0.075
[25.53]
75
Sargassum muticum
Pseudo-second order
0.995
34.1
0.012
[25.53]
100
Ulva fasciata
Pseudo-second order
0.976
3.2
0.168
[25.21]
c 0 is the initial concentration of heavy metal ions; a marine green algae (Ulva lactuca sp.) waste biomass obtained after extraction of
oils; b waste algae biomass obtained from agar extraction industry.
Ho model [25.145], Weber–Morrison kinetic model,
Adam–Bohart–Thomas kinetic model [25.148], firstorder reversible kinetic model [25.149], external mass
transfer model [25.32], etc. The first-order Lagregen
model and the pseudo-second order Ho model are
the most frequently used kinetic models to study the