Marine Algae Biomass for Removal of Heavy Metal Ions 25.6 Modeling of Biosorption in Dynamic Conditions 637
Part D | 25.6
ions, or at external intralayer surface. Hence, the experimental data suggest a limited contribution of mass
transfer and boundary layer diffusion in the biosorption process of heavy metal ions, onto marine algae
biomass, and that the intraparticle diffusion influenced
the biosorption process up to a certain degree.
25.6 Modeling of Biosorption Process
in Dynamic Continuous-Flow Conditions
The large-scale utilization of biosorption processes for
the removal of heavy metal ions from aqueous environments requires the use of continuous systems, where the
biosorbent (marine algae biomass) can be used in multiple biosorption–desorption cycles [25.64]. In addition,
the heavy metal ions biosorption is more effective if
it is carried out in a dynamic continuous-flow column, and these systems allow the treatment of very
large volumes of wastewater and have lower operating cost [25.146]. The recording of the variation of
heavy metal ions concentration of the effluent solution,
as a function of the operating time of the column, or
the volume of treated aqueous solution, gives usually
a typical S-shaped breakthrough curve whose shape and
slope is a result of the equilibrium biosorption isotherm
relationship, the mass transfer to and throughout the
biosorbent in the column, and operation macroscopic
flow parameters.
Any optimized column system is based on the accurate prediction of the characteristic of the breakthrough
curve under given specific operating conditions. When
the heavy metal ions concentration in the effluent solution reaches a predefined level, the column operation is
terminated. At this point, the regeneration process may
begin before activation for the next cycle of operation.
Therefore, successful design of a column biosorption
process required prediction of breakthrough curves for
the effluent, and for this purpose various mathematical
models can be used [25.65, 153, 154].
The Bohart–Adams, Thomas, and Yoon–Nelson
models have been frequently used for modeling of the
metal ions biosorption process on various types of materials in continuous systems. These models are able to
describe the breakthrough curves with accuracy in most
of the cases, and at the same time, they provide important system parameters that can be used to predict
the useful time of the column for the scale-up of the
experiments.
The Bohart–Adams model is mainly used when the
effluent concentration is lower than 0:35 c 0 [25.155],
so to describe the initial part of the breakthrough curve.
This model assumed that the biosorption rate is proportional to the residual capacity of the solid and the
concentration of the sorbent substances [25.156]. The
mathematical expression of this model is as follows,
ln
c t
c 0
D k BA c 0 t k BA N 0
H
v
(25.6)
where c 0 is the initial heavy metal ions concentration, c t
is the effluent heavy metal ions concentration at time t,
k BA is the kinetic constant of the Bohart–Adams model,
N 0 is the saturation concentration of column, H is the
bed height of column, and v is the linear velocity calculated by dividing the flow rate by the column section
area.
The parameters k BA and N 0 of the Bohart–Adams
model can be estimated from the slope and intercept of
lnc t =c 0 versus t dependence.
The Thomas model is one of the most general
and widely used to describe the biosorption process
in a packed-bed column [25.65, 156]. This model assumes that biosorption is not limited by the chemical
interactions, but by the mass transfer at the interface [25.66, 69]. The linear expression of the Thomas
model is
ln
 c 0
c t
1
Ã
D
k T q 0 m
F
k T c 0
F
V eff
(25.7)
where k T is the Thomas rate constant, m is the biomass
packed in the column, F is the solution flow rate
through the column, q 0 is the maximum concentration
of solute in the solid phase, and V eff is the effluent
volume.
Most commonly, the Thomas model is applied
to analyze the obtained data between breakthrough
and saturation points of the experimental breakthrough
curves, and the characteristic parameters (k T and q 0 )
were determined from the slope and intercept of the linear plot ln.c 0 =c t 1/ versus V eff .
The Yoon–Nelson model is based on the assumption
that the rate of decrease in the probability of adsorption for each adsorbate molecule is proportional to the
Part D | 25.6
ions, or at external intralayer surface. Hence, the experimental data suggest a limited contribution of mass
transfer and boundary layer diffusion in the biosorption process of heavy metal ions, onto marine algae
biomass, and that the intraparticle diffusion influenced
the biosorption process up to a certain degree.
25.6 Modeling of Biosorption Process
in Dynamic Continuous-Flow Conditions
The large-scale utilization of biosorption processes for
the removal of heavy metal ions from aqueous environments requires the use of continuous systems, where the
biosorbent (marine algae biomass) can be used in multiple biosorption–desorption cycles [25.64]. In addition,
the heavy metal ions biosorption is more effective if
it is carried out in a dynamic continuous-flow column, and these systems allow the treatment of very
large volumes of wastewater and have lower operating cost [25.146]. The recording of the variation of
heavy metal ions concentration of the effluent solution,
as a function of the operating time of the column, or
the volume of treated aqueous solution, gives usually
a typical S-shaped breakthrough curve whose shape and
slope is a result of the equilibrium biosorption isotherm
relationship, the mass transfer to and throughout the
biosorbent in the column, and operation macroscopic
flow parameters.
Any optimized column system is based on the accurate prediction of the characteristic of the breakthrough
curve under given specific operating conditions. When
the heavy metal ions concentration in the effluent solution reaches a predefined level, the column operation is
terminated. At this point, the regeneration process may
begin before activation for the next cycle of operation.
Therefore, successful design of a column biosorption
process required prediction of breakthrough curves for
the effluent, and for this purpose various mathematical
models can be used [25.65, 153, 154].
The Bohart–Adams, Thomas, and Yoon–Nelson
models have been frequently used for modeling of the
metal ions biosorption process on various types of materials in continuous systems. These models are able to
describe the breakthrough curves with accuracy in most
of the cases, and at the same time, they provide important system parameters that can be used to predict
the useful time of the column for the scale-up of the
experiments.
The Bohart–Adams model is mainly used when the
effluent concentration is lower than 0:35 c 0 [25.155],
so to describe the initial part of the breakthrough curve.
This model assumed that the biosorption rate is proportional to the residual capacity of the solid and the
concentration of the sorbent substances [25.156]. The
mathematical expression of this model is as follows,
ln
c t
c 0
D k BA c 0 t k BA N 0
H
v
(25.6)
where c 0 is the initial heavy metal ions concentration, c t
is the effluent heavy metal ions concentration at time t,
k BA is the kinetic constant of the Bohart–Adams model,
N 0 is the saturation concentration of column, H is the
bed height of column, and v is the linear velocity calculated by dividing the flow rate by the column section
area.
The parameters k BA and N 0 of the Bohart–Adams
model can be estimated from the slope and intercept of
lnc t =c 0 versus t dependence.
The Thomas model is one of the most general
and widely used to describe the biosorption process
in a packed-bed column [25.65, 156]. This model assumes that biosorption is not limited by the chemical
interactions, but by the mass transfer at the interface [25.66, 69]. The linear expression of the Thomas
model is
ln
 c 0
c t
1
Ã
D
k T q 0 m
F
k T c 0
F
V eff
(25.7)
where k T is the Thomas rate constant, m is the biomass
packed in the column, F is the solution flow rate
through the column, q 0 is the maximum concentration
of solute in the solid phase, and V eff is the effluent
volume.
Most commonly, the Thomas model is applied
to analyze the obtained data between breakthrough
and saturation points of the experimental breakthrough
curves, and the characteristic parameters (k T and q 0 )
were determined from the slope and intercept of the linear plot ln.c 0 =c t 1/ versus V eff .
The Yoon–Nelson model is based on the assumption
that the rate of decrease in the probability of adsorption for each adsorbate molecule is proportional to the