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Received for review September 8, 1983 Revised manuscript received December 17, 1984 Accepted March 19,1985
Part of this work was presented in the Third International Conference on Fluid Properties and Phase Equilibria for Chemical Process Design, Callaway Gardens, GA, April 10-15,1983 ( R o c . Conf., Fluid Phase Equilib. 1983,13, 143).
Modeling of the Impregnation Step To Prepare Supported Pt/A1,03 Catalysts Osvaldo A. Scelza, Albert0 A. Castro, D a h R. Ardlles, and Josd M. Parera' Institufo de Investig8ciones en Cat6lisis y Petroqdmica, INCAPE, Santiago del fstero 2654, 3000 a n t a Fe, Argentina
This paper reports a mathematical model that describes the process of impregnating porous particles with a solution that contains two or more adsorbable components. The parameters of the model (adsorption rate constants and diffusivities of the different solution species) can be estimated from the variation of the concentration of different adsorbable specles wlth the impregnation time. With these parameters, the profiles of deposited species into the particles are predicted and compared with those experimentally obtained. The model was applied to alumina impregnation with H,RCI, and HCI.
Introduction One of the most commonly used methods to prepare supported catalysts is the impregnation of particles of a porous support with solutions that contain species which are adsorbed on the support. Sometimes all the adsorbed species are catalytically active, but in other cases some of them only modify the distribution of the other species on the support surface. 0196-4313/86/1025-0084$01.50/0
The behavior of supported catalysts usually depends on the spatial distribution profiles of the species deposited on the internal surface of the support. Hence, the factors which define the distribution profiles must be known in order to design supported catalysts. The Maatman and Prater (1957) paper raised interest in the study of the impregnation step. Since then, much research has been done on this subject. Several mathe0 1986 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 25, No. 1, 1986
matical models with different degrees of complexity and rigorousness have been reported. For instance, Vincent and Merrill (1974) developed a model applied to the deposition process of one adsorbable species in a single pore. Komiyama et al. (1980) and Kulkarni et al. (1981) extended this model to spherical particles and two adsorbable components. Hegedus et al. (1979) and Melo et al. (1980) proposed more general models that take into account multicomponent impregnation for different working conditions. When applying these last models to specific cases, some of the authors used parameters which were determined from impregnation experiments conducted separately with each component. A mathematical model based on a diffusion-adsorption process is presented in this paper. The model describes the multicomponent impregnation of a porous support using limited quantities of each species. Competitive adsorption for some kind of adsorption sites with reversible kinetics is considered. A method to estimate the parameters in the model is proposed using experimental data on the variation of the concentration of adsorbable species in the solution phase during impregnation. From these parameter values the distribution profiles can be predicted. The model was applied to co-impregnation of alumina pellets with H2PtC16and HC1 in order to estimate the parameters from the experimental data. With these parameters, H2PtC16and HC1 radial profiles in cylindrical tablets were calculated and compared with the experimental results. Mathematical Model The deposition of one or more solutes on the internal surface of a porous solid, preflooded with pure water, involves a diffusion-adsorption process. Mass balances for species i in the solution into the pores and in the adsorbed state are respectively given by the following equations
ac,
E-
at
= DiV2Ci - ui
a4 - - hi _ at
ppcsvi
for i = 1,2, ...,I. Considering competitive adsorption of I species on the same kind of surface sites Ai + Xi(s) s Ai(ads) (3) with Langmuir type rate expressions.
=0
The mathematical model formulated by eq 5 and 6 with conditions 7 and 8 can be solved by using an implicit method of finite differences (Crank-Nicolson, 1947). See Appendix A. In order to compute the concentration radial profiles for a particular case, a previous knowledge of the parameter values is required. As there is little possibility to get the required values from the literature or by application of empirical correlations, it is necessary to estimate the values from the experimental data. Hence, the parameters are estimated through the minimization of an objective function that computes the difference between the observed and predicted values of some variable. The concentrations of species remaining in solution at different impregnation times are chosen as the variables in the objective function. Defining C f ( t )- Ci(R,t) ei(t)= (9) CiO
the objective function becomes
Minimization of the objective function was accomplished by applying the method of steepest descent (Seinfeld, 1969) as described in Appendix B. Application of the Model The mathematical model was applied to alumina impregnation with H2PtC&and HCl in order to interpret the competitive effect of HC1 on the adsorption of H2PtC1, on y-Al203. When alumina pellets are impregnated with H2PtC1, by using amounts smaller than the adsorption capacity of the support, the metallic compound is deposited primarily in the outer shells of the particles. However, the radial profile of the deposited metal can be modified by co-impregnating the support with some substances, like HC1, able to compete for the adsorption site. The HC1 competitive effect on the H2PtC1,adsorption on y-A1203can be represented chemically as (Santacesaria et al., 1977; Sivasanker et al., 1979; Le Page, 1978; Castro et al., 1983)
pH +
I
Vi
= kici(i -
Ce,)- ,yei
i=l
AI
(4)
Applying eq 1 and 2 to long cylindrical particles with negligible mass transfer in the axial direction, we obtain the following equations.
The initial and boundary conditions for the above equations are Ci(R,O)= Ci0 (74 Ci(r,O) = 0 0
