External Mass Transfer Effect

To illustrate the masking effects that arise from intraparticle and external mass transfer effects, consider a surface reaction whose intrinsic kinetics are second-order in species A. For this rate expression, equation 12.4.20 can be written as... 

When a biocatalyst is immobilized on or within a solid matrix, mass transfer effects may exist because the substrate must diffuse from the bulk solution to the immobilized biocatalyst. If the biocatalyst is attached to non-porous supports there are only external mass transfer effects on the catalytically active outer surface in the reaction solution, the supports are surrounded by a stagnant film and substrate and product are transported across this Nemst layer by diffusion. The driving force for this diffusion is the concentration difference between the surface and the bulk concentration of substrate and product. 

The external mass-transfer effects on the activity of an itmnobilized biocatalyst can be expressed quantitatively by the external effectiveness factor defined as the ratio of... 

When a biocatalyst is immobihzed within a porons snpport, in addition to possible external mass-transfer effects there conld also exist resistance to internal diffusion of snbstrate, as this mnst dififnse throngh the pores in order to reach the biocatalyst. Conseqnently a snbstrate concentration gradient is established within the pores, resnlting in a concentration decreasing with increased distance (in depth) from the surface of immobihzed biocatalyst preparation. Similarly, a corresponding product concentration gradient is obtained in the opposite direction. 

Fig. 7.19. Experimental tests to diagnose external mass transfer effects.

MODELS WHICH INCLUDE EXTERNAL MASS-TRANSFER EFFECTS... 

To study the kinetics of immobilized enzymes a recirculation reactor may be used. This reactor allows one to perform kinetic measurements with defined external mass transfer effects, reached by establishing a high flow rate near the catalyst, minimizing mass transfer resistance. The reactor behaves as a differential gradientless reactor allowing initial-rate kinetic measurements to be made. 

When the reaction rates in the monolith channels are sufficiently high, a significant gradient will develop between the concentration at the channel center and that at the catalyst surfaces. This external mass transfer effect must be considered in addition to internal diffusion effects. The rate of external mass transfer at a given value of z is equal to the reaction rate inside the catalyst at steady state ... 

Exercise 7.16 External mass-transfer effects on a second-order reaction... 

Notice that O2 is in excess and both CO and C3H6 reach very low values within the pellet. The log scale in Figure 7.23 shows that the concentrations of these reactants change by seven orders of magnitude. Obviously the consumption rate is large compared to the diffusion rate for these species. The external mass-transfer effect is noticeable, but not dramatic. 

Although the external mass transfer controlled polymer dissolution approach [51] may be intuitive, experiments have indicated that external mass transfer effects are insignificant. Papanu et al. [40] showed that for dissolution of PMMA in MIBK, vigorous agitation of the solvent increased the dissolution rate by only 15% relative to that for a stagnant solvent. Also, since the chain disentanglement mechanism was not considered, these models fail to explain the swelling time needed before dissolution. 

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]. 

Note that fem,e F or rra,eS re the effective (measured) values of the rate constant and rate, respectively, which includes all internal and external mass transfer effects. 

In a fixed-bed PFR, the flow rate is varied at constant space time and if the rate remains constant, external mass transfer effects are assumed to be unimportant however, this test can become insensitive at low Reynolds number [61]. 

To illustrate the influence of the various parameters investigated, Rj. was defined as the "kinetic" conversion rate Rk calculated at the average concentration in the bed, neglecting external mass transfer effects and assuming total catalyst utilization ... 

We note that in region II, where the diffusional resistance is high, the gasification of a porous solid may be described by an expression that is formally equivalent to a relationship developed for nonporous solids. Let us recall that in Chapter 3 we developed the following expression for the gasification of a nonporous solid in the absence of external mass transfer effects ... 

FIG. 6.10. The minimization of external mass transfer effects by operation at high gas... 

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