Sahel, M. and O. Ferrandon--Dusart (1993). Dynamic adsorption
on activated carbon in the liquid phase comparison and simplification of
different models. Rev. Sci.
Eau, 6 (1) : 63-80. [article in
Original title : Adsorption dynamique
en phase liquide sur charbon actif : comparaison et simplification de différents
Low concentrations of organic contaminants are not easily
removed by conventional treatment methods, but activated carbon bas a good
affinity for various organics and is used in batch or column reactors.
Much has been written concerning the prediction of the performance of powdered
activated carbon (PAC) ; adsorptive capacity and equilibrium isotherms determined
in « batch » reactor are proposed to simulate the performance of
PAC for single or bisolute systems (DUSART et al. 1990, SMITH 1991).
have attempted to simulate column performance with mathematical models and
the aim of this work is to present the principal models and verify how the
different models are applied to break-through curves ; parameters which can
be evaluated by the different equations will also be compared.
As early as 1920 BOHART and ADAMS presented differential equations which govern
the dynamics of the adsorption of vapours and gases on fixed beds and the
final result, applied to the liquid-solid phase, yields the kinetic adsorption
(k) and the maximum adsorption capacity (No) (eq. 3). By transposition to the
liquid phase, we have calculated the concentration distribution in the bed
(eq. 5) by using the kinetic constant k and the maximum adsorption capacity
No obtained by equation 4; it was noted that only the low concentration range
of the break-through curve can be used. Some approximations from DOLE and
KLOTZ (1946) lead to the « Bed Depth/Service-Time (BDST) equation 7
proposed by HUTCHINS (1973) ; the service time of a column tb has a linear
with the bed depth Z (fig.3). The activated carbon efficiency No can
be estimated and the adsorption rate constant calculated from the slope and
WOLBORSKA (1989) proposed a rectilinear equation InC/Co = At + B (eq.
10) for the initial segment of the break-through curve. The form of this equation
similar to equation (4) obtained tram the BOHART-ADAMS hypothesis.
The mass transfer coefficient, ßa, the maximum adsorption capacity and
velocity v (eq.9) of the concentration fronts can be calculated from the
A and B.
The model developed by CLARK (1987) is based on the use of e mass-transfer
concept in combination with the Freundlich isotherm (fig.4). The
originality of this modal, in comparison to the others, consists in the
the equilibrium concentration Ce and the driving force equilibrium « C-Ce ».
The general equation is equation (14). Two parameters A and r are determined
by regression equations ; we proposed a simple method to calculate A and
r by a linearization of the preceding equation (eq. 14). This is equation
(16) In [(Co/C)n-1 -1] = In A -rt.
Sodium decanesulfonate at a concentration of 20 mg ·l-1 was
used as influent and activated powdered carton (200 ø 315 µm)
as the fixed bed adsorbent layer to illustrate the comparison between the
The linear flow rates were 3.0 m . h-1 and the five columns
tested were 3.1 ; 4.0 ; 7.5 ; 10.2 ; 12.5 cm high with a 1.45 cm2 cross
isotherm equation (fig. 4) obtained in a batch system for an
equilibrium time (t = 24 h for this activated carbon) gives a « n
value » equal
Figure 2 presents the experimental break-through curves obtained for
the different bed heights ; by using equations (4 or 10) in the system
(In C/Co, t) they
are represented on the same figure by the dotted line. The agreement is
only for the low values of C in the break-through curves.
The coefficients A and B (table 1) are determined from the straight
lines obtained with the low break-curve concentrations (fig. 1).
The kinetic coefficient Sa,
and the maximum capacity adsorption No are shown in table 1. The No value
is similar to those obtained from the other equations. The migration velocity
of the concentration fronts (r = 0,133 cm · h-1) is in
good agreement with the experimental value (0,128 cm · h-1).
The linearized Clark equation (16) gives a good representation of experimental
results (fig. 6) alter the determination of A and r parameters
and table 2). With the use of the two parameters, the break-through
curves have been
recalculated (fig.6) and compared to experimental results. Their
is good agreement. The A parameter is related to the depth Z of the adsorbant
A = Bez ·. B value
can be determined with the different columns (fig.7).
The Clark model can be applied to filers which have a biological activity
; the results obtained in the laboratory by EL HANI (1987) for the adsorption
humic acids (10 mg · l-1) on a 1m granular activated
carton bed were analyzed by the Clark equation (fig. 8). The initial
concentrations of humic acids
are never obtained in the effluent because of biological degradation and/or
adsorption in mesopores. From the difference in the area of the two curves,
it is possible to calculate the supplementary biological degradation.
For 95 cm of activated carbon in the column and after 800 h, the biological
degradation represents 55 % of the total elimination. The percentage is
constant alter 35 cm depth of the activated carton in agreement with the
study that showed that the flora was only present in the 10 first centimeters.
The use of this model is facilitated by our linearization and the case
of particular phenomena : biological degradation or desorption. in the
muld adsorbates fixation (REYDEMANEUF et al. to be published)
can be studied and compared to the only adsorption phenomena.
the tested models lead to different parameters by using low break-through
curve concentrations or others with the whole range of experimental points,
one (CLARK) gives a good description of the break-through curves in our
Mode, dynamic adsorption, activated carton, kinetic parameters,
anionic surfactant, humic acids.
Sahel, M., Université de Limoges, laboratoire de Génie
chimique -Traitement des eaux, Faculté des Sciences, 123, avenue Albert-Thomas,
87060 Limoges cedex (France)