Enhancement of the Mass Transfer Rates

Sub-millimeter inter-electrode gaps (in the case of plate and charmel reactors) or electrode widths (in the case of coplanar interdigitated band electrodes) lead to thin concentration boundary layers with any flow rate [14,23] resulting in enhanced mass transfer rates and thus increasing the attainable space-time-yield [Equation (17.17)]. 

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The enhancement of the mass transfer rate in the first part of the reactor, resulting from the developing concentration profile, is negligible. It was stated in Section III that for relative pitches larger than 1.1 this assumption is valid, and that even for smaller relative pitches the effect of the enhanced mass transfer rate is small, except when film layer mass transfer is the limiting factor in the reactor performance. 

The enhanced rate expressions for regimes 3 and 4 have been presented (48) and can be appHed (49,50) when one phase consists of a pure reactant, for example in the saponification of an ester. However, it should be noted that in the more general case where component C in equation 19 is transferred from one inert solvent (A) to another (B), an enhancement of the mass-transfer coefficient in the B-rich phase has the effect of moving the controlling mass-transfer resistance to the A-rich phase, in accordance with equation 17. Resistance in both Hquid phases is taken into account in a detailed model (51) which is apphcable to the reversible reactions involved in metal extraction. This model, which can accommodate the case of interfacial reaction, has been successfully compared with rate data from the Hterature (51). 

For a more general and quantitative description of the mass transfer rate and in the absence of mass transfer limitations on the gas side, the enhancement factor E> 1 is defined as ... 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

Equation 10.30 is known as Stefan s Law(3). Thus the bulk flow enhances the mass transfer rate by a factor Cj/Cjj, known as the drift factor. The fluxes of the components are given in Table 10.1. 

The Hatta criterion compares the rates of the mass transfer (diffusion) process and that of the chemical reaction. In gas-liquid reactions, a further complication arises because the chemical reaction can lead to an increase of the rate of mass transfer. Intuition provides an explanation for this. Some of the reaction will proceed within the liquid boundary layer, and consequently some hydrogen will be consumed already within the boundary layer. As a result, the molar transfer rate JH with reaction will be higher than that without reaction. One can now feel the impact of the rate of reaction not only on the transfer rate but also, as a second-order effect, on the enhancement of the transfer rate. In the case of a slow reaction (see case 2 in Fig. 45.2), the enhancement is negligible. For a faster reaction, however, a large part of the conversion occurs in the boundary layer, and this results in an overall increase of mass transfer (cases 3 and 4 in Fig. 45.2). 

For the rhodium-catalyzed hydroformylation of propylene in an aqueous biphasic system. Cents et al. have shown that the accurate knowledge of the mass transfer parameters in the gas-liquid-liquid system is necessary to predict and optimize the production rate [180]. Choudhari et al. enhanced the reaction rate by a factor of 10-50 by using promoter Ugands for the hydroformylation of 1-octene in a biphasic aqueous system [175]. 

By placing the impeller within a draft tube within the reactor, the fluids are forced to pass through the impeller, where the bubbles are redispersed by impacting on the impeller surfaces. The draft tube is placed in the center of the reactor so the fluids recirculate repeatedly (a recycle reactor) to allow bubbles to be repeatedly redispersed in the draft tube. The overall reactor becomes well mixed and is therefore described by the CSTR equations. The rapid flow of this reactor enhances the mass transfer rate and thus increases the overall reaction rate if it is limited by mass transfer of a reactant from the liquid phase into the bubbles. 

In addition to importance of the catalyst composition and temperature, we have shown that methane partial oxidation selectivity is strongly affected by the mass transfer rate. Our experiments show that increasing the linear velocity of the gases or choosing a catalyst geometry that gives thinner boundary layers enhances the selectivity of formation of H2 and CO. Since H2 and CO are essentially intermediate... 

A convention used in most literature on ozone mass transfer and in the rest of this book is to define the mass transfer coefficient as the one that describes the mass transfer rate without reaction, and to use the enhancement factor E to describe the increase due to the chemical reaction. Furthermore, the simplification that the major resistance lies in the liquid phase is used throughout the rest of the book. This is also based on the assumption that the mass transfer rate describes physical absorption of ozone or oxygen, since the presence of a chemical reaction can change this. This means that KLa - kLa and the concentration gradient can be described by the difference between the concentration in equilibrium with the bulk gas phase cL and the bulk liquid concentration cL. So the mass transfer rate is defined as ... 

Furthermore, it is almost impossible to use ozone for fc, -measurements when organic substances are present that are (easily) oxidized by molecular ozone. Mass transfer enhancement will occur during such measurements, so that the mass transfer coefficient based on only the physical process cannot be determined. In this case, the oxygen mass transfer coefficient kLa 02) should be determined to assess the mass transfer rate without reaction. The enhanced mass transfer due to reaction should be considered separately, because it is not only dependent on the parameters listed above in equation 3-10, but also dependent on the concentration of the reactants. 

When chemical reactions occur in an extraction process, the effective mass transfer coefficient may be higher or lower than that expected from purely physical considerations, e.g., Eqs. (10) and (11). For example, the slow interfacial reaction of Eq. (5) will tend to reduce the mass transfer rate. On the other hand, a rapid irreversible reaction can enhance the mass transfer rate. 

The acceleration of mass transfer due to chemical reactions in the interfacial region is often accounted for via the so-called enhancement factors [19, 26, 27]. These parameters are defined as a relationship between the mass transfer rate with reaction and mass transfer rate without reaction, assuming the same mass transfer driving force. 

If the catalyst particles have a diameter much smaller than the thickness of the mass transfer film, and if sufficient particles are available in the film, then enhancement of gas adsorption due to chemical reaction may occur provided that the specific chemical conversion rate is high enough. For enhancement in a slurry re-... 

One effect of pore flow is that it enhances the mass transfer rate between the pore and interstitial volumes. Instead of by molecular diffusion only, which is by nature slow in solution, mass exchange occurs also by perfusive EOF. This effect can be treated as a form of stimulated diffusion. Following the original treatment for pressure-driven LC according to Rodrigues et al. [31], the plate height contribution from stationary-phase mass transfer resistance HCs in the presence of pore flow can be written as... 

The mass-transfer rate is slow in CIEC. By increasing temperature this parameter is sizably enhanced and the rate of ion exchange becomes more rapid. The increase in temperature, however, may cause the evolution of gas bubbles from the solution and result in their entry into column systems. The gases are formed in chemical reactions and are due to the air dissolved in the solutions employed. They can influence the stability of fluid flow, distort the bandshape, and even promote the formation of cavities in the exchange bed, thereby disturbing the separation process. Because the bubbles rise while the fluid flow is down in a column, it is difficult to remove these bubbles in CIEC. 

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