Intraparticle diffusion limitation—pores

The presence of pores, for which the observed reaction rate is lower than the kineti-cally controlled intrinsic one, in the particles or pellets affects the reaction rate due to diffusion limitations. This intraparticle diffusion effect causes a concentration gradient within the pores. If diffusion is fast, then the concentration gradient is negligible. 

The intrinsic rate is defined by the kinetics on the pore surface or at the surface sites under the reaction conditions and r] is called the effectiveness factor. For now, let us not consider external mass and heat transfer limitations. 

Initially, we define reactant A flow per unit surface area as  

Ai = internal surface area per volume (4 rf Ar) = volume element of the layer r=pore radius. 

Under equimolar conditions, the direct flow is equal to the counter-diffusion. By Pick s law, the diffusion flow of gas A through the pore will be  

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Mordenite etc. Dodecatungstophosphoric acid (DTPA) and the ion exchange resin catalysts showed maximum activities. Clay based catalysts and sulphated zirconia showed a moderate activity. Zeolites did not demonstrate any activity to the reaction due to pore size restriction. A 100% selectivity towards the ortho product (l-acetyl-2-methoxy naphthalene) was observed for almost all the reactions for all the catalysts. The para product (2-methoxy-6-acetyl naphthalene) was formed when the aluminium chloride was used as a homogeneous catalyst with nitrobenzene as the solvent. The reaction product was isolated and conformed by the melting point, FT-IR, H-NMR, etc. The reaction is intraparticle diffusion limited. A different catalyst would be required to get p-product selectively. 

Curve n shows a lower concentration gradient outside the particle, compared to curve 1, but followed by a concentration gradient inside the pore due to the intraparticle diffusion limitation. On the other hand, curve III does not have influence of external limitations, representing the reaction rate in the presence of pore-diffusion resistance as shown in the following equation ... 

The study of the possible effects of particle size and pore diameter on intraparticle diffusion limitations was invariably carried out with synthesis gas having a H2/CO feed ratio of 2 mol/mol. As the H2/CO usage ratios observed were also very close to 2 mol/mol in this... 

If there were no limitations placed on the reaction rate by intraparticle diffusion (i.e., if the reactant concentration were C0 throughout the pore), the reaction rate would be given by... 

The most difficult problem to solve in the design of a Fischer-Tropsch reactor is its very high exothermicity combined with a high sensitivity of product selectivity to temperature. On an industrial scale, multitubular and bubble column reactors have been widely accepted for this highly exothermic reaction.6 In case of a fixed bed reactor, it is desirable that the catalyst particles are in the millimeter size range to avoid excessive pressure drops. During Fischer-Tropsch synthesis the catalyst pores are filled with liquid FT products (mainly waxes) that may result in a fundamental decrease of the reaction rate caused by pore diffusion processes. Post et al. showed that for catalyst particle diameters in excess of only about 1 mm, the catalyst activity is seriously limited by intraparticle diffusion in both iron and cobalt catalysts.1... 

Indeed, the mobility of the entrapped dopant is crucial in promoting the reactivity of the final materials. Thus, provided that the dopant molecules are at the surface and enjoy enough freedom, high porosity will certainly promote reactivity by limiting intraparticle diffusion but that will not be the case if microporous xerogels of different HLB are compared (c/. entrapped lipase and tetra-//-propy 1 am monium perruthe-nate (TPAP) where ORMOSIL with the smaller pores are more reactive). 

No experiments with variation in particle size of the silica gel have been done to study intraparticle diffusion effects. In silica gel such diffusion would be only through the pores (analogous to the macropores of a polystyrene) since the active sites lie on the internal surface. The silica gel used by Tundo had a surface area of 500 m2/g and average pore diameter of 60 A.116). Phosphonium ion catalyst 28 gave rates of iodide displacements that decreased as the 1-bromoalkane chain length increased from C4 to Cg to C16, The selectivity of 28 was slightly less than that observed with soluble catalyst hexadecyltri-n-butylphosphonium bromide U8). Consequently the selectivity cannot be attributed to intraparticle diffusional limitations. 

Spry and Sawyer (1975) developed a model using the principles of configurational diffusion to describe the rates of demetallation of a Venezuelan heavy crude for a variety of CoMo/A1203 catalysts with pores up to 1000 A. This model assumes that intraparticle diffusion is rate limiting. Catalyst performance was related through an effectiveness factor to the intrinsic activity. Asphaltene metal compound diffusivity as a function of pore size was represented by... 

If the intraparticle resistance is important, then the introduction of inert liquid will further reduce the overall effective reaction rate, because the catalyst pores filled with liquid are more likely to cause a diffusion-limitation than an all-gas-phase reaction under similar conditions. 

Intraparticle Transport Mechanisms Intraparticle transport may be limited by pore diffusion, solid diffusion, reaction kinetics at phase boundaries, or two or more of these mechanisms together. 

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