Catalytic Weisz modulus

Figure 6.13 Effectiveness factor versus Weisz modulus for different Biot numbers. (Adapted from Carberry, J.J., Chemical and Catalytic Reaction Engineering, McGraw-Hill, New York, 1976.)...

Fig. 10.8 Effectiveness factor t] as a function of the Weisz modulus j/ for an isothermal, first-order irreversible reaction in a porous slab. (From A. Renken, L. Kiwi-Minsker, in eds. M. Seller, A. Renken, R.A. V. Santen (Eds.), Catalytic Engineering Principles. Catalysis From Molecular to Reactor Design, 2012. Copyright 2012 Wiley).

Paul Weisz suggested in a lucid note published in 1973 that cells, and indeed even entire organisms, have evolved in a way that maintains unity effectiveness factor [24]. That is, the size of the catalytic assembly is increased in nature as the overall rate at which that assembly operates decreases, and the relationship between characteristic dimension and activity can be well approximated by the observable modulus criterion for reaction limitation. It is possible that Weisz s arguments may fail under process conditions, and internal gradients within a compartment or cell may be important. However, at present it appears that the most important transport limitations and activities in cells are those that operate across cellular membranes. Therefore, to understand and to manipulate key transport activities in cells, it is essential that biochemical engineers understand these membrane transport processes and the factors influencing their operation. A brief outline of some of the important systems and their implications in cell function and biotechnology follows. 

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-... 

Another criteria due to Satterfield [65] is one that is based on work by Petersen [56], as developed further by Froment and Bischoff [16], which has as a starting point the observation that the film mass transfer coefficient in a catalytic system cannot limit unless pore diffusion is also limiting. Hence, a mass transfer limitation on the outside of the porous catalyst pellet can only be important, for example, if "the Weisz and Prater modulus is greater than about 3 to 10 which corresponds to an effectiveness factor, n, of 0.3 to about 0.7. Thus, the criteria suggests that if the effectiveness factor of the catalyst in question in a reactor is close to unity mass transfer limitations cannot be important. 

On the other hand, the Weisz-Prater modulus ( P) provides an estimate of the extent of the catalytic layer diffusion limitations (Equation (4.7)). This is defined as follows is the observed reaction rate) ... 

---