Effectiveness factor general definition

In general, no matter what the route, certain characteristics will predispose a material to have local effects (and, by definition, if not present, tend to limit the possibility of local effects). These factors include pH, redox potential, high molar concentration, and the low flexibility and sharp edges of certain solids. These characteristics will increase the potential for irritation by any route and, subsequent... 

For rather general kinetics the effectiveness factor definition can be approximated as... 

Figure 12 shows the effectiveness factor as a function of the Wheeler-Weisz modulus for different reaction orders, indicating that criterion (33) holds for the generalized Thiele modulus. Due to the definition of L it is fairly independent of the catalyst geometry. 

Thus, the specific surface area of synthesized adsorbents and catalysts is a quantity depending on many factors and in its explanation it should be borne in mind that none of the factors determines definitely the value of the specific surface area of adsorbents synthesized. In this connection, the structure formation of each of the hydroxides should be considered only individually and all components of this process should be analyzed. Moreover, manifestation of a particular factor is different for other hydrogels. It is most likely that only the joint effect of all the factors under required conditions determines the final structure of synthesized porous materials. Therefore, it is unnecessary to seek for some general relationships describing the structure-formation process. In this case some individual factors that make the most appreciable contributions to the behaviour of the structure can be indicated. 

Even when is low, the center and surface temperatures may differ appreciably, because catalyst pellets have low thermal conductivities (Sec. 11-5). The combined effect of mass and heat transfer on can still be represented by the general definition of the effectiveness factor, according to Eq. (11-41). Hence Eq. (11-42) may be used to find r, provided rj is the nonisothermal effectiveness factor. The nonisothermal 17 may be evaluated in the same way as the isothermal 77, except that an energy balance must be combined with the mass balance. 

The general definition of the effectiveness factor states that the factor describes the ratio between the real molar flux (A)) and the molar flux (AT) that would be obtained if the reaction proceeded in the absence of diffusion resistance. This ratio is equal to the ratio of observed rate and the rate if the diffusion resistance does not have an influence on reaction rate. 

For the single-reaction cases, we performed dimensional analysis and found a dimensionless number, the Thiele modulus, which measures the rate of production divided by the rate of diffusion of some component. A complete analysis of the first-order reaction in a sphere suggested a general approach to calculate the production rate in a pellet in terms of the rate evaluated at the pellet exterior surface conditions. This motivated the definition of the pellet effectiveness factor, which is a function of the Thiele modulus. 

The effective-to-general shale thickness ratio is a factor which determines the ability (or inability) of hydrocarbons to migrate from source rocks. In this context, of definite interest for evaluating the amount of generated hydrocarbons were also the less thick shale beds in the Ghadames, Illizi, Triassic and Reggane Basins. 

The concept of effectiveness developed separately for external or internal transport resistances can be extended to an overall effectiveness factor for treating the general diffusion-reaction problem where both external and internal concentration and temperature gradients exist The overall effectiveness factor, D, is defined for relating the actual global rate to the intrinsic rate, that is, -Ra)p to (-Ra)6- To stun up the definitions for y, 7], and D,... 

We will only focus on the effectiveness factor for CO oxidation in a stoichiometric mixture. Using the general definition of Froment and Bischoff (1979), one has... 

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