Radial heat transport limitations

Note that criterion 7.186 requires a knowledge of the apparent activation energy for the reaction. Criterion 7.186 holds whether internal diffusion limitations exist or not. When the criterion concerning external heat transfer is compared to criterion 7.167 concerning radial heat transport limitations through the bed, it can been seen that the latter are more critical unless ... 

Radial temperature gradients are more critical than axial gradients. In order to limit the effects of heat transport limitations on the observed rates to 5% it is sufficient that for a single reaction with the following kinetics ... 

We can compare this with the rate of radial heat transport in the bed, by dividing the effective conductivity by the radius of the bed, which gives 208 W/m K. Apparently, the heat transfer coefficient at the wall is rate determining. Still, the influence of the limited rate of radial heat transport on the reaction rate can be considerable. 

The TAP reactor is very well suited for kinetic studies. At low pressure, all transport of gas-phase species is by (Knudsen) diffusion, thus ruling out any external mass transfer limitations. The diffusion as a random movement also eliminates all radial concentration gradients. Very low amounts of reactants are pulsed into the reactor, which are on the order of a few nanomoles. Thus, the amount of heat generated is very small even in the case of strongly exo- or endothermic reactions. Therefore, the reactor is operated isothermally and no heat transfer limitations occur. Concentration profiles inside the pores for transient experiments might arise even in the absence of chemical reaction. If significant diffusion of reactants and products inside the catalyst pores occurs, it will be revealed by the transient response and then needs to be addressed correctly by a modeling approach. This is often the case for microporous materials [26,27,72]. 

Electroosmotic flow has emerged as a viable alternative transport mechanism to pressure-driven flow in column chromatography. Benefits include a plug-flow profile (reduced transaxial contributions to zone broadening) and a mobile phase velocity that is independent of the column length and particle size. The electroosmotic-driven flow is governed by the dielectric constant of the mobile phase, the zeta potential at the stationary phase/mobile phase interface, and the applied electric field. The efficiency obtainable is limited by double layer overlap or radial dispersion induced by inefficient heat dissipation. 

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/. 

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