External mass transfer criterion

According to their analysis, if is zero (practically much lower than 1), then the liquid-film diffusion controls the process rate, while if tfis infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the so-called mechanical parameter represents the ratio of the diffusion resistances (solid and liquid film). The authors did not refer to any assumption concerning the type of isotherm for the derivation of the above-mentioned criterion it is sufficient to be favorable (not only rectangular). They noted that for >1.6, the particle diffusion is more significant, whereas if < 0.14, the external mass transfer controls the adsorption rate. 

Criteria are usually derived so that deviations from the ideal situation are not larger than 5%. In order for external mass transfer limitations to be negligible, for an isothermal, n order irreversible reaction in a spherical particle, a criterion for the Carberry number can be derived, which assures that the observed rate does not deviate more than 5% from the ideal rate ... 

Mears Criterion for External Mass Transfer Effects In a number of cases, it may be necessary to rapidly estimate whether transport limitations are present or not, and Mears criterion is... 

The Weisz-Prater criterion makes use of observable quantities like -Ra)p, the measured global rate (kmol/kg-s) dp, the particle diameter (m) pp, the particle density (kg/m ) Dg, the effective mass diffusivity (m /s) and the surface concentration of reactant (kmol/m ). The intrinsic reaction rate constant ky need not be known in order to use the Weisz-Prater criterion. If external mass transfer effects are eliminated, CAb can be used, and the effective diffusivity can be estimated using catalyst and fluid physical properties. The criterion can be extended to other reaction orders and multiple reactions by using the generalized Thiele modulus, and various functional forms are quoted in the literature [17, 26, 28]. 

The Mears criterion is used to check for external mass transfer limitation in microchaimels ... 

The term CA.g is the concentration in the gas phase but all equations derived here also apply for liquids. The criterion for a negligible influence of external mass transfer (i.e., a deviation of the mean rate from zero-gradient rate within 5%) equals the condition that the concentration gradient in the boundary layer should be less than 5% relative to the maximum gradient ... 

For Da < 0.1, external mass transfer can be neglected. Before this criterion can be used, the reaction rate must be known. To circumvent this issue, Berger and Kapteijn [48] proposed an easier to use criterion based on the conversion to check the absence of external diffusion limitations ... 

This relation states that external mAss transfer is not the limiting step. A similar criterion was suggested by Satterfield [68]. 

Koros [44] obtained a criterion for neglecting external mass transfer by comparing the Weisz-Prater criterion for the absence of a diffusional limitation within the catalyst as given by Froment and Bishoff [14] ... 

The criterion of external mass trasnport is also due to Mears (I ml Eng. Chem. Process Des. Develop. 10 (1971) 541) who considered the mass transfer rate equal to the observed rate... 

In fluid-solid systems, the reaction takes place on the catalyst surface. Prior to this, the reactant molecules have first to reach the catalyst surface and, therefore, the rate of mass transfer is an important operational parameter (Figure 15.3). Two types of mass transfer need to be considered in fluid-solid reactions external and internal mass transfer. In particular, internal mass transfer limitations should be avoided, since they more often limit the performance of the reactor and more strongly influence the product selectivity. The internal mass transfer is characterized by an effectiveness factor, q, defined as the ratio of the observed reaction rate to that at constant concentration throughout the catalyst layer. To ensure an effectiveness factor of q > 0.95 in an isothermal catalyst layer, the following criterion must be fulfilled [16] ... 

The Biot number was originally established as a criterion for gauging relative resistances for fhe analogous heat transfer case. Here the span of Biot numbers extends into both regions of controlling resistances. This is in large part due to the wide range of thermal conductivities of solids seen in practice. Thus, heat transfer from a turbulent stream of air to a sheet of copper k = 390 W/mK) would have external (air) resistance control, while in heat transfer fo a sheef of asbestos k = 0.15 W/mK) under the same conditions the principal resistance would reside in the solid. The reach of the Biot number in mass transfer is more limited but still of some importance. 

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