Diffusion modulus

The effect of transport limitations can conveniently be evaluated by considering the spherical catalyst particle shown in Fig. 5.32. We will introduce a dimensionless quantity called the Thiele diffusion modulus (Og) [W. Thiele Ind. Eng. Chem. 31... 

This defines the dimensionless Thiele diffusion modulus for a spherical particle... 

Figure S.3S. Effectiveness factor e plotted as a function of the Thiele diffusion modulus Og. The effective factor is well approximated by 3/Og for Og > 10.

Thus we see again that the system can conveniently be described by the Thiele diffusion modulus Op. It is not difficult to see that two limiting cases exist. There are no diffusion limitations when D <... 

Explain the concepts behind the Thiele diffusion modulus for a spherical particle. Why is this important for the application of a catalyst ... 

Fig. 11. The change of the reaction-diffusion modulus as a function of the oxygen concentration during the fermentation (parameters are same as in Fig. 10 curve 1 Kq = 0.64 x 10 kg m curve 2 Kq = 0.016 X 10 kg m )...

The diffusion modulus diffusion effect are entirely determined by the magnitude of the modulus v>, involving size (72), diffusivity (7)en), and intrinsic activity (fc,) of the catalyst. In many practical cases of experimentation the intrinsic activity constant fc, will not be directly known, but instead it will be desirable to estimate tp from the diffusivity and size of the solid, and the actvxilly observed reaction rate dnjdt. Use is made in such cases (Wagner, 16) of the definition of the modulus p and the basic activity equation (first-order reaction being used here) ... 

Let us examine the measured catalytic behavior of an assembly of different catalyst preparations (Weisz, 12), assumed to be of identical chemical composition and thus being associated with identical real specific velocity constants A , however differing in the diffusion modulus (p, due to any or all of the above-mentioned differences in mechanical properties such as particle size, diffusivity, and specific surface area. Tracing the reaction rates which would be observed over a wide temperature range of operation on such samples leads to a series of curves A, B, C, D as shown in Figure 14, ail of a similar shape but geometrically dis-... 

The catalytic effectiveness shown in Figure 7.12a behaves in much the same manner as that for simple reactions, except in those cases where there is a difference in the thermicity of the reaction between the two steps (i.e., exothermic-endothermic or vice versa). In this event, the reaction behavior can apparently be dominated by the action of one of the reaction steps, then shift abruptly to dominance by the other step, as shown in Case F. Also, if one reaction is thermally neutral and the other is not, the region of parametric sensitivity can be shifted to ranges of the diffusion modulus not characteristic for single reactions, as shown in case D. 

Mass transfer with simultaneous chemical reaction is characterized using the reaction-diffusion modulus known as the Hatta number, defined as the ratio of the reaction in the film to the mass transfer rate through it. Thus, for a first-order reaction the Hatta number is given by... 

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