Porous Structure and Observed Reaction Rate

The effects of mass transfer within a porous structure on observed reaction characteristics were apparently first recognized and mathematically analyzed by Thiele (1939) in the United States. The work has been extended and developed by Wheeler (1995) and many other researchers. The important result of these analyses is the quantitative description of the factors which determine the effectiveness of a porous catalyst. The effectiveness factor, here symboHzed by t], is defined as the ratio of the actual reaction rate to that which would occur if all of the surface throughout the inside of the catalyst particle were exposed to reactant of the same concentration and temperature as the existing at the outside surface of the particle. 

Hydrodemetallation reactions require the diffusion of multiringed aromatic molecules into the pore structure of the catalyst prior to initiation of the sequential conversion mechanism. The observed diffusion rate may be influenced by adsorption interactions with the surface and a contribution from surface diffusion. Experiments with nickel and vanadyl porphyrins at typical hydroprocessing conditions have shown that the reaction rates are independent of particle diameter only for catalysts on the order of 100 /im and smaller (R < 50/im). Thus the kinetic-controlled regime, that is, where the diffusion rate DeU/R2 is larger than the intrinsic reaction rate k, is limited to small particles. This necessitates an understanding of the molecular diffusion process in porous material to interpret the diffusion-disguised kinetics observed with full-size (i -in.) commercial catalysts. 

The reactivity of manganese(II) oxalate is significantly influenced by the conditions during dehydration. Rate coefficients for decomposition of reactant previously held (2 h) at 460 K in a maintained vacuum were about 2.5 times greater than those found for a similarly treated sample heated at 460 K in air. This difference was apparent in both decomposition and oxidation reactions. These data, together with electron microscopic observations, showed that nucleation in the vacuum dehydrated porous salt occurred at internal surfaces, while in the air dehydrated salt some reorganization of the crystal structure was possible and there was more pronounced product formation at the external surfaces. 

The CVD technique is based on the diffusion of a carbonbearing gas into a porous substrate and the diffusion-controlled reaction of the gas on the hot substrate into carbon and gaseous by-products. A variety of parameters (such as temperature, pressure, flow rate, substrate density, and surface area) affect the quality and structure of the deposited carbon and the deposition presents a difficult and complex problem. The present deposition conditions are based on empirical observations. Various CVD techniques have been developed for the infiltration of porous substrates. The most extensively utilized are the isothermal and the temperature gradient processes. The isothermal process technique is illustrated schematically in Fig. 4a. The substrate is heated by an induction-heated susceptor (graphite). If the hydrocarbon gas comes in contact with the hot substrate, carbon is deposited and gaseous by-products (mainly H2) are released. The disadvantage of this technique is the overcrusting of the outer... 

The general theoretical approach is to develop the mathematical equations for simultaneous mass transfer and chemical reaction, as the reactants and products difHise into and out of the porous catalyst. When reaction occurs simultaneously with mass transfer within a porous structure, a concentration gradient is established. Since interior surfaces are thus exposed to lower reactant concentrations than surfaces near the exterior, the overall reaction rate throughout the catalyst particle under isothermal conditions is less than it would be if there were no mass transfer limitations. As will be shown, the apparent activation energy, the catalyst selectivity, and other important observed characteristics of a reaction are also dependent upon the structure of the catalyst and the effective diffusivity of reactants and products (Charles and Thomas, 1963). 

Bruemmer et al. (55) studied Ni, Zn, and Cd sorption on goethite, a porous iron oxide known to have defects within the structure in which metals can be incorporated to satisfy charge imbalances. At pH 6, as reaction time increased from 2 hours to 42 days (at 293K), sorbed Ni increased from 12 to 70% of Ni removed from solution, and total increases in Zn and Cd sorption over this period increased 33 and 21%, respectively. The kinetics of Cd, Zn, and Ni were described well with a solution to Pick s second law (a linear relation with the square root of time). Bruemmer et al. (55) proposed that the uptake of the metal follows three-steps (i) adsorption of metals on external surfaces (ii) solid-state diffusion of metals from external to internal sites and (iii) metal binding and fixation at positions inside the goethite particle. They suggest that the second step is the rate-limiting step. However, they did not conduct microscopic level experiments to confirm the proposed mechanism. In view of more recent studies, it is likely that the formation of metal-nucleation products could have caused the slow metal sorption reactions observed by Bruemmer et al. (55). 

---