Bio Adsorption: An Eco-friendly Alternative for Industrial Effluents Treatment 47
amount of metal that is possible to retain. In this way, a successful design of a continuous adsorption
reactor requires being able to predict the characteristics of the breakthrough curve (Acheampong
et al. 2013). The development of mathematical models describing the dynamic behavior of adsorption
in fixed beds is difficult, because the adsorbate concentration, like the feed, moves through the
column and a steady state cannot be assumed.
During the application of a model that approximates the experimental parameters, several
factors should be considered, among them the adsorbate transport in fixed beds, which is described
by the solid-liquid material balance equations. This description must account for the mass balance
of the adsorbed solute, which in turn depends on the mechanism responsible for adsorption and
may be controlled by mass transfer from within the solution to the adsorbent surface or by the
chemical reaction between the adsorbent particles and the metal (Calero et al. 2009). In this sense,
determining the parameters of models of varying complexity can be difficult, considering the large
number of resources required and the complicated solution methods (Borba et al. 2008). This is
why several simplified mathematical models have been developed, which provide parameters that
qualitatively describe the effects during adsorption in the continuous reactor (Chu et al. 2007).
Among them, the most widely applied models are Thomas (1944), Bohart-Adams (1920) and Yoon
and Nelson (1984), which will be mentioned in the present investigation. Each model presents
different mathematical equations so that from each, different parameters are obtained that provide
different information about the processes under study. The assumptions and parameters of each
model are shown in Table 3.3.
For the purpose of checking the applicability of the described models, the parameters provided
by the different models (Xcal) should be compared with the experimentally obtained parameters
Table 3.3. Comparison between the used models for continuous reactors.
Model
Thomas
Bohart-Adams
Yoon-Nelson
Mathematic
expression
0
0
0
1
1
exp
(
)
TH
ef
C
C
K
. q .W
C .V
F
=
+
−
0
0
0
0
exp
AB
ef
AB
K
.C .V
K
.N .Z
C
C
F
U
=
−
0
(
)
1
(
)
ef
YN
ef
YN
V
exp K . F
C
V
C
exp K . F
τ
τ
−
=
+
−
Parameters
Graph C/Co Vs Vef
KTH is Thomas rate constant
[mL min–1 g–1],
q0 is the maximum solute
concentration in the solid phase
[mmol g–1],
Vef is the effluent volume [L],
F is the volumetric flow rate [mL
min–1],
W is the amount of sorbent inside the
reactor [g],
C is the outlet concentration
[mmol L–1].
Graph C/Co Vs Vef
KAB is the mass transfer
coefficient [cm3 mmol–1 min–1],
N0 represents the maximum
adsorption capacity [mmol cm–3],
U is the linear liquid velocity
[cm min–1],
Z is the bed height in the reactor
[cm].
Graph C/Co Vs Vef KYN
stands for the Yoon-Nelson
rate constant [min–1],
τ [min] is the time
required to retain 50% of
the C0.
Assumptions ● Adsorption behavior follows the
Langmuir isotherm
● Intraparticle diffusion and
resistance to external mass
transfer are negligible.
● Adsorption rate is proportional
to the residual capacity of
the solid and the adsorbate
concentration
● Intraparticle diffusion and
resistance to external mass
transfer are negligible.
● Adsorption
rate decreases
proportionally with the
number of molecules
adsorbed.