Adsorption dynamique en phase liquide sur charbon actif : comparaison et simplification de différents modèles

L'adsorption en phase liquide sur charbon actif est un sujet très travaillé sur le plan expérimental et de plus en plus dans le domaine de la modélisation. Les tentatives de description des courbes de percée ou de fuite des filtres montrant la saturation du matériau adsorbant remontent aux travaux de BOHART et ADAMS en 1920. D'autres équations avec d'autres approximations ont été proposées par la suite (THOMAS 1944 ; DOLE et KLOLZ 1946), HUTCHINS (1973) ; plus récemment, WOLBORSKA (1989) ou CLARK (1987) ont proposé d'autres modèles. Nous avons essayé de faire le point sur ces différents modèles, de montrer leurs origines communes, souvent à partir des équations de BOHART et ADAMS, les approximations apportées limitant leur domaine d'application, les grandeurs qu'ils permettent de déterminer : capacité maximum d'adsorption, constante cinétique d'adsorption, vitesse de déplacement du front d'adsorption. De tous ces modèles, un seul (CLARK 1987) permet une bonne représentation des courbes de percée. Nous en avons proposé une linéarisaüon qui facilite la détermination des paramètres nécessaires au calcul des courbes de fuite. Tous ces modèles ont été testés sur les résultats expérimentaux obtenus pour l'adsorption d'un tensioactif anionique : le décylsulfonate de sodium et ceci sur cinq petites colonnes de hauteurs différentes de charbon actif. Le modèle de CLARK a également été appliqué à des résultats obtenus au laboratoire (El HANI, 1987) sur l'adsorption et la dégradation biologique des acides humiques sur un filtre de charbon de 1m de haut, sur une période beaucoup plus longue (1 mois) et avec des lavages du filtre. Ce modèle permet de calculer la part qui n'est pas simplement de l'adsorption rapide (dégradation biologique et adsorption lente).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). Some investigators 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 rate (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 relationship 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 the y-intercept.Recently, 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 is similar to equation (4) obtained tram the BOHART-ADAMS hypothesis. The mass transfer coefficient, ßa, the maximum adsorption capacity and the migration velocity v (eq.9) of the concentration fronts can be calculated from the constants 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 existence of 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 different models. 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 section. The Freundlich 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 to 2.38.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 (fig. 5 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 of 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 slow 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 electon microscopy 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 case of successive muld adsorbates fixation (REYDEMANEUF et al. to be published) can be studied and compared to the only adsorption phenomena.In conclusion, nome of the tested models lead to different parameters by using low break-through curve concentrations or others with the whole range of experimental points, but only one (CLARK) gives a good description of the break-through curves in our actual knowledge