Transport effects external

For a solid-catalyzed reaction to take place, a reactant in the fluid phase must first diffuse through the stagnant boundary layer surrounding the catalyst particle. This mode of transport is described (in one spatial dimension) by the Stefan-Max well equations (see Appendix C for details)  

CHAPTER 6—EffectS.Of Transport Limitatinns nn Ratas nf Snlid-Cataly/Rfl Rsartinns 

Since there are only two components in the mixture, Xb = I and the above expression reduces to  

Equimolar counterdiffusion (iV, = —Ng) can often be assumed and further simplification is thus possible to give  

The same equation can also be derived by assuming that concentrations are so dilute that X Na + Nb) can be neglected. Equation (6.2.3) is known as Tick s First Law and can be written as  

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In the most general case, i.e. when intraparticlc and interphase transport processes have to be included in the analysis, the effectiveness factor depends on five dimensionless numbers, namely the Thiele modulus the Biot numbers for heat and mass transport Bih and Bim, the Prater number / , and the Arrhenius number y. Once external transport effects can be neglected, the number of parameters reduces to three, because the Biot numbers then approach infinity and can thus be discarded. 

When data are taken in a laboratory PER system where external transport effects are present and if this possibility is arbitrarily neglected, experimental results will lead to falsified reaction kinetics ... 

The first set of preliminary experiments in a kinetic study carried out in laboratory PBRs should establish the flow conditions at which external transport effects are negligible. The second set of diagnostic experiments conducted should verify the particle size requirements under which intraparticle transport effects are eliminated. A study of intrinsic kinetics must make use of the flow rates and particle sizes that exclude both external and internal transport limitations, respectively. 

Theron, J. N., Dry, M. E., Steen, E. V., and Fletcher, J. C. G. Internal and external transport effects during the oxidative reforming of methane on a commercial steam reforming catalyst. Studies Surface Sci. Catal. 107, 455-460, 1997. 

To eliminate external transport effects, run the reaction at a constant value of but changing the velocity. In other words, change the hydrodynamic conditions keeping the kinetic factor (MF q) constant. The conversion increases and then levels off at a velocity beyond which external mass... 

The developments so far are based on the premise that intrinsic rate expressions are available. As discussed in Chapter 3, these rate expressions are determined from the kinetic data obtained under experimental conditions that ensure negligible transport effects. Various criteria of negligible transport effects have been developed to provide guidance on the experimental conditions and these were summarized in Chapter 3 without derivation. Consider these criteria in light of the understanding gained in this chapter. In view of the fact that external transport effects usually... 

As is apparent from the y-factor correlations of Eq. 4.58, external transport effects can be minimized by a proper choice of fluid velocity. While the transfer coefficients are also affected by the pellet size, the fluid velocity is often the choice for the manipulation. As discussed earlier, the external mass transfer resistance should not pose a problem at throughputs commonly encountered in typical operation. 

Figure 9. Effects of internal and external transport resistances on the computed step-response of CO adsorption. Curve A corresponds to our experimental conditions. Key A, km = 60 cm/s, Deff = 0.0246 cm2/s B, km —r oo, Detl = 0.246 cms/s and C, km — oo, Dell oo.

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Diffusional effects were combined into apparent kinetic rate constants by using commercial-sized catalysts in kinetic experiments. The experiments were designed so that no significant external transport and axial dispersion effects occurred. 

The mass transfer effects cause, in general, a decrease of the measured reaction rate. The heat transfer effects may lead in the case of endothermic reactions also to a decrease of the equilibrium value and the resulting negative effect may be more pronounced. With exothermic reactions, an insufficient heat removal causes an increase of the reaction rate. In such a case, if both the heat and mass transfer effects are operating, they can either compensate each other or one of them prevails. In the case of internal transfer, mass transport effects are usually more important than heat transport, but in the case of external transfer the opposite prevails. Heat transport effects frequently play a more important role, especially in catalytic reactions of gases. The influence of heat and mass transfer effects should be evaluated before the determination of kinetics. These effects should preferably be completely eliminated. 

After Dekker et al. (1995), criteria for negligible transport effects in steady-state kinetics are as follows. The criterion for negligible external mass transport resistance in steady-state kinetics is... 

The external mass effects deal with mobilities with respect to the container of the salt. They are related to the internal mass effects by external transport numbers... 

Table IX contains the internal (—0.045) and external (—0.080) mass effects of Na in NaNOs at 360°C. The external transport number in this case is reported to be = 0.7 (12), Evidently these experimental data are not quite consistent.

Note that all these data concern experiments in the absence of reaction and in conditions where it can be assumed that all surfaces of the packing are wetted (dissolution of solid particles). However, when a reaction is occurring, mass transfer may be constrained to a region close to the pore openings on the outer surface of the particles and hence the effective surface area for mass transfer could be considerably less than the external surface of the catalyst, leading to lower values k a. More studies are needed on porous catalysts at conditions where external transport is important. 

Because of their tunable properties, supercritical solvents provide a useful medium for enzyme-catalyzed reactions.f The mechanism of enzyme-catalyzed reactions is similar to the mechanism described for solid-catalyzed reactions. External as well as internal transport effects may limit the reaction rate. Utilizing supercritical fluids enhances external transport rate due to increase in the diffusivity and therefore mass transfer coefficient. Internal transport rate depends on the fluid medium as well as the morphology of the enzyme. Supercritical fluids can alter both. 

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