External diffusion effects

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

Acrivos, A., On the combined effect of longitudinal diffusion and external mass transfer resistance in fixed bed operations. Chem. Eng. Sci. 13, 1 (1960). 

The mass flux vector is also the sum of four components j (l), the mass flux due to a concentration gradient (ordinary diffusion) jYp), the mass flux associated with a gradient in the pressure (pressure diffusion) ji(F), the mass flux associated with differences in external forces (forced diffusion) and j,-(r), the mass flux due to a temperature gradient (the thermal diffusion effect or the Soret effect). The mass flux contributions may then be summarized ... 

When the internal diffusion effects are considered explicitly, concentration variations in the catalytic washcoat layer are modeled both in the axial (z) and the transverse (radial, r) directions. Simple slab geometry is chosen for the washcoat layer, since the ratio of the washcoat thickness to the channel diameter is low. The layer is characterized by its external surface density a and the mean thickness <5. It can be assumed that there are no temperature gradients in the transverse direction within the washcoat layer and in the wall of the channel because of the sufficiently high heat conductivity, cf., e.g. Wanker et al. 

Ma et al. [104] attributed a decrease in diffusivity with an increase in initial concentration to pore diffusion effects. Because zeolites are bi-dispersed sorbents, both surface and pore diffusions may dominate different regions. In micropores, surface diffusion may be dominant, while pore diffusion may be dominant in macropores. This, therefore, supports the use of a lumped parameter (De). To explore further the relative importance of external mass transfer vis-a-vis internal diffusion, Biot number (NBl — kf r0/De) was considered. Table 9 summarizes the NBi values for the four initial concentrations. The NBi values are significantly larger than 100 indicating that film diffusion resistance was negligible. 

The overall process can be affected by pore diffusion and external mass transfer. Molecular diffusion coefficients DPB may be calculated by Aspen Plus. Effective pore diffusion may be estimated by the relation DP = Dpb( j,/tp) = 0.1 DPE, in which ep is the particle porosity and rp the tortuosity. Furthermore, the Thiele modulus and internal effectiveness can be calculated as ... 

This problem arises even at low conversion, because although the product concentration may then be negligible at the external pellet surface, in general this is not the case inside the pellet, unless diffusion effects upon the effective reaction rate are absent. Therefore, a difference normally exists between the effectiveness factor of irreversible and reversible reactions which becomes increasingly important as the equilibrium constant A cq of the reaction is shifted to smaller values. 

The problem of the optimal particle shape and size is crucial for packed bed reactor design. Generally, the larger the particle diameter, the cheaper the catalyst. This is not usually a significant factor in process design - more important are the internal and external diffusion effects, the pressure drop, the heat transfer to the reactor walls and a uniform fluid flow. 

External Diffusion Effects on Heterogeneous Reactions Chap. 11... 

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. 

For gas space diffusion conditions, the criteria are clearly contained in formulas (12) and (14), in that diffusion effects will be absent or negligible if the measured reaction rate dn/dt obtained from the geometric (external) surfaces of catalyst solid is such that from equation (12)... 

Intraparticle Diffusion and External Mass-Transfer Resistance For typical industrial conditions, external mass transfer is important only if there is substantial intraparticle diffusion resistance. This subject has been discussed by Luss, Diffusion-Reaction Interactions in Catalyst Pellets, in Carberry and Varma (eds.), Chemical Reaction and Reactor Engineering, Dekker, 1987. This, however, may not be the case for laboratory conditions, and care must be exerted in including the proper data interpretation. For instance, for a spherical particle with both external and internal mass-transfer limitations and first-order reaction, an overall effectiveness factor r, can be derived, indicating the series-of-resistances nature of external mass transfer followed by intraparticle diffusion-reaction ... 

An experimental test to verify the absence of significant concentration gradients inside the catalyst particle is based on the inverse proportional relation between the effectiveness factor and the particle diameter for strong internal diffusion limitations. Hence, a measured rate that is independent of the particle size indicates that internal diffusion limitations can be neglected. Care should be taken to avoid artefacts. External heat transfer effects also depend on particle size and for exothermic reactions might balance the internal diffusion effects. Furthermore, if the catalyst particle consists of a support with a non-uniformly distributed active phase, crushing and sieving to obtain smaller particles is hazardous. 

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