Diffusion effects outside catalyst particle

The characteristic times on which catalytic events occur vary more or less in parallel with the different length scales discussed above. The activation and breaking of a chemical bond inside a molecule occurs in the picosecond regime, completion of an entire reaction cycle from complexation between catalyst and reactants through separation from the product may take anywhere between microseconds for the fastest enzymatic reactions to minutes for complicated reactions on surfaces. On the mesoscopic level, diffusion in and outside pores, and through shaped catalyst particles may take between seconds and minutes, and the residence times of molecules inside entire reactors may be from seconds to, effectively, infinity if the reactants end up in unwanted byproducts such as coke, which stay on the catalyst. 

First, let us examine the criteria applicable to diffusion effects in the gas phase, i.e., the spaces and channels over or between catalyst particles. When the catalyst solids are not porous but have all their active surfaces located in their geometric contours, diffusion in the outside gas space will be the only existing diffusion problem. However, even when the catalyst particles are subject to internal diffusion effects, the external gas space conditions need still be examined separately. The criteria will be examined assuming the reaction to be of first order, keeping in mind that deviation from exact first-order kinetics does not alter the diffusion picture by considerable magnitudes, as was seen above. 

The methods used for modeling-supported PTC systems are all based on the standard equations developed for porous catalysts in heterogeneous catalysis (Chapter 6). These are expressed in terms of an overall effectiveness factor that accounts both for the mass transfer resistances outside the supported catalyst particles (film diffusion resistance, expressed as a Biot number) and within them (intraparticle diffusional resistance, expressed in terms of a Thiele modnlns). Then, for any given solid shape, the catalytic effectiveness factor can be derived as a function of the Thiele modulus A. Thus, for a spherical support solid, we have... 

If the first two inequalities hold /8,9/, it can be expected that heat and mass transport outside the catalyst particle is not limiting and therefore there is no need for a heterogeneous model a pseudo-homogeneous model may be sufficient, in which the whole catalyst particle is regarded as a sink and/or source for heat and mass in the fluid phase. This results in a drastic reduction of the number of model equations, and the transfer terms in the fluid phase equations are lumped into effective reaction rate terms. If the second inequality holds /9/, pore diffusion is not limiting. The third inequality is valid if axial dispersion can be neclected /lO/ and the fourth if radial dispersion is of no importance /lO/. 

Two effects cause the low production capacity of large-grained catalyst. First, large grain size retards transport of the ammonia formed inside the catalyst into the bulk gas stream. This is because the ammonia transport proceeds by slow diffusion through the pore system. The second effect is a consequence of the fact that a single catalyst grain in the oxide state reduces from the outside to the interior of the particle. The water vapor produced inside the catalyst by reduction comes into contact with already reduced catalyst on its way to the outer surface of the catalyst. This induces a severe recrystallization. As an example, if the particle size increases from about 1 to 8 mm, the inner surface decreases from 11 to 16 m2/g to 3 to 8 m2/g74. Therefore the choice of catalyst requires the optimization of 1) catalyst size versus catalyst activity, 2) catalyst size versus pressure drop across the converter and 3) the impact of 1 and 2 on... 

Many catalyst layer models have appeared in the literature during the last few years [15, 16, 17, 18, 19,20, 21]. This observation partly explains the complications associated with this topic. Still, much work remains to be completed since many effects have not yet been included, such as proton surface diffusion (outside the ionomer, [22,23]) and ionomer density (water content effect), which effectively and respectively increases/modifies the reactive surface area. The surface-sensitive nature of Pt catalysts on the oxygen reduction reaction rate [24] and electrochemical promotion (a catalytic effect, [25]) represent other examples which can also affect the reaction rate and surface area. All these effects are further compounded by the potential presence of hquid water which effectively modifies the reaction front, access to speeifie eatalyst particles and surface properties. 

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