SOME OTHER MASS TRANSFER CONSIDERATIONS

The absorption of ozone by cyanide solutions in stirred reactors is complicated by mass transfer considerations. The presence of ozone gas in the exhaust from such a reactor does not indicate that equilibrium has been obtained between ozone gas bubbles and ozone in solution, but rather that the mass transfer through the individual bubbles is not complete, because of the resistance on the gas side. In other words, mass transfer controls the reaction, as the ozone will react almost instantaneously with the cyanide ion in solution. The presence of some metals, particularly copper, appears to speed up the absorption by acting as oxygen carriers. A solution of ozone in dilute acid decomposes somewhat more quickly when a trace of cupric ion is added. The presence of these metal catalysts, if this be their function, does not appear to be a necessary condition to ozone oxidation. What is important is that adequate mass transfer time and surface be available, as would be found in a countercurrent packed tower. 

The mathematical basis for calculating the potential and current distribution was established by the pioneering contributions of Kasper, Wagner, and others [1-6]. Here, we briefly address these principles and some applications related to chlor-alkali operations. The current distribution in electrochemical systems is governed by cell geometry, electrode kinetics, and mass transfer considerations. These individual contributions to current distribution are called primary, secondary and tertiary current distributions. 

Earlier studies of intracrystalline diffusion in zeolites were carried out almost exclusively by direct measurement of sorption rates but the limitations imposed by the intrusion of heat transfer and extra-crystalline mass transfer resistances were not always fully recognized. As a result the reported diffu-sivities showed many obvious inconsistencies such as differences in diffusivity between adsorption and desorption measurements(l-3), diffusivities which vary with fractional uptake (4) and large discrepancies between the values measured in different laboratories for apparently similar systems. More recently other experimental techniques have been applied, including chromatography and NMR methods. The latter have proved especially useful and have allowed the microdynamic behaviour of a number of important systems to be elucidated in considerable detail. In this paper the advantages and limitations of some of the common experimental techniques are considered and the results of studies of diffusion in A, X and Y zeolites, which have been the subject of several detailed investigations, are briefly reviewed. 

The foregoing considerations refer to an isomerization reaction but may be generalized and applied to sequences of steps involving other substances as reactants, products, or catalysts. These considerations also hold when some steps are homogeneous reactions, other steps are phase boundary reactions, and some steps are diffusion or mass transfer processes (17). 

Two aspects of velocity that need to be kept in mind in a consideration of the effects of velocity in connection with chemical reaction fouling are the effects on mass transfer and heat transfer. The transfer of mass and heat will be increased with increased turbulence. If the fouling deposition is solely controlled by the reaction rate then enhanced mass transfer to the surface will not change the situation. On the other hand if some of the products of reaction or intermediates even, remain in the reaction zone then the rate of production of deposits could be reduced. Increased turbulence (i.e. increased flow rate for a given geometry) will assist not only the rate of arrival of reactants but also the removal of products of reaction from the reaction zone. It is possible that in part, this may account for some of the contradictions apparent in the literature in respect of flow rate. 

In general, nonuniform structures, in both time and space, is widespread in bubbling, turbulent, and fast fluidization regimes. On the one hand, such nonuniformity can enhance the mass and heat transfer of a bed. On the other hand, it decreases the contact efficiency of gas and solids and makes the scale-up rather difficult. Internals are usually introduced not to eliminate the nonuniform flow structure completely but to control its effect on chemical reactions. The function of internals varies in different fluidization regimes, as do the types and parameters of internals. Taking these purposes into consideration, internals may be successfully applied to catalytic reactors with high conversion and selectivity, and some other physical processes. 

In many situations the concentrations of solute in the bulk fluid, and even at the fluid interface, may vaiy in the direction of flow. Further, the mass-transfer coefficients depend upon fluid properties and rate of flow, and if these vary in the direction of flow, the coefficients will also. The flux of Eqs. (3.1) and (3.3) to (3.6) is therefore a local flux and will generally vary with distance in the direction of flow. This problem was dealt with, in part, in the development leading to Illustration 3.1. In solving problems where something other than the local flux is required, allowance must be made for these variations, ITiis normally requires some considerations of material balances, but there is no standard procedure. An example is offered below, but it must be emphasized that generally some sort of improvisation for the circumstances at hand will be required. 

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