Transfer, mass, limiting drop conversion

In the following, the concepts of drop conversion rate and over-all conversion rate are used. In the same way as the chemical reaction rate is used to indicate the change in concentration of a reactant with time in a very small volume of a single phase in which the concentration may be considered to be uniform, the concept of drop conversion rate is used for the change in average concentration of a reactant with time where this average is taken over the whole volume of a single drop. Because of mass transfer limitation, this drop conversion rate may be lower than the pure chemical reaction rate (see Section II,B,1). 

Because of mass transfer limitation, the order of drop conversion may also be reduced, as will be shown in Section II,B,1. 

As selectivity is a factor of importance in commercial production, we will deal here only with reaction schemes which are of practical interest. This means that when a product C is made on a commercial scale according to the reaction A — C, where a second reaction C — W may destroy the product C, this second reaction generally will be of a lower rate than the main reaction. Otherwise this reaction scheme would have no commercial value. This means that we may restrict ourselves to those cases for which the second reaction C — W is of an order (order of drop conversion) higher than or the same as that of the first reaction A — C, since this first reaction is more likely to be limited by mass transfer than the slower second reaction. 

In this section the effect of mass transfer limitation on the drop conversion rate and the order of drop conversion will be treated, and it will be shown that a process for which the real chemical reaction is of first order in the reactant A (which is dissolved in the dispersed phase) can still be influenced by the effect of segregation when the chemical conversion rate is limited by mass transfer of the reactants. 

With the help of qualitative reasoning, however, it can be shown that when mass transfer is really limiting the conversion rate, the order of drop conversion in the component A is lower than 1 and, occasionally, when the mass transfer outside the drop becomes limiting, may even become zero. 

As shown in Section II,B,1, zero-order drop conversion will occur when the drop conversion rate is limited by a relatively low outside mass transfer coefficient. It was derived that then... 

Provided that the catalyst is active enough, there will be sufficient conversion of the pollutant gases through the pellet bed and the screen bed. The Sherwood number of CO is almost equal to the Nusselt number, and 2.6% of the inlet CO will not be converted in the monolith. The diffusion coefficient of benzene is somewhat smaller, and 10% of the inlet benzene is not converted in the monolith, no matter how active is the catalyst. This mass transfer limitation can be easily avoided by forcing the streams to change flow direction at the cost of some increased pressure drop. These calculations are comparable with the data in Fig. 22, taken from Carlson 112). 

Interfacial mass transfer of trace gases into aqueous pnase is investigated in a UV absorption-stop flow apparatus. For the first time, the mass accommodation coefficients are determined for O3 (5.3x10" ) and for SO2 (>2x10 2) The results are incorporated into a simple model considering the coupled interfacial mass transfer and aqueous chemistry in cloud drops. It is shown that dissolution of O3 into a drop is fast compared with its subsequent oxidation of dissolved S02 In addition, the conversion rate of S(IV) to S(VI) in aqueous drops by ozone reactions is not limited by interfacial resistance. 

The mass transfer coefficient km for gas-phase plus interfacial mass transport has units s 1. The rate / aq in (12.1 IS) is in equivalent gas-phase concentration units, but the conversion to aqueous-phase units is straightforward multiplying by H h. The mass transfer coefficient as a function of the accommodation coefficient cc and the droplet radius is shown in Figure 12.13. For values of a > 0.1 the mass transfer rate is not sensitive to the exact value of a. However, for a < 0.01, surface accommodation starts limiting the mass transfer rate to the drop, and km, decreases with decreasing a for all droplet sizes. 

When the reaction takes place over PdAlO or PdLlO, we observed a plateau around 90% conversion due to mass transfer limitations. When the temperature rises further to reach 800 °C, a drop in catalytic activity can be noticed. This phenomenon has been widely reported in several papers [7, 8, 18] and is attributed to the reduction of palladium oxide into metallic palladium. The intensity of this drop in activity is more pronounced when the metallic particles are supported on modified alumina supports. The interaction of La and Ba with PdO species increases the reduction rate of the palladium oxide species. 

The reactor is assumed to be adiabatic with plug flow. Axial dispersion can be ignored. Any effect of limitations of mass or heat transfer inside the catalyst pellet is lumped into the rate constants given in Table 1. The catalyst activity is assumed to be constant. Use the conversion of ethylbenzene or water in the set of continuity equations. Use the Ergun equation to describe the pressure drop. 

A good experimental approach to check the presence/absence of internal mass transfer resistance is to carry out experiments with various particle sizes. By gradually minimizing the particle size, the conversions, yields, and selectivities should approach a limiting value corresponding to the intrinsic kinetics. Sometimes this approach can, however, lead to a cul-de-saq the pressure drop increases, as the particle size is diminished and the kinetic conditions are not attained. Another type of test reactor should then be considered, for instance, a fluidized bed (for gas-phase reactions) or a slurry reactor (for liquid-phase reactions). 

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