Mass transfer coefficients with chemical reaction

Mass-Transfer Coefficients with Chemical Reaction. Chemical reaction can occur ia any of the five regions shown ia Figure 3, ie, the bulk of each phase, the film ia each phase adjacent to the iaterface, and at the iaterface itself. Irreversible homogeneous reaction between the consolute component C and a reactant D ia phase B can be described as... 

Example 6.5 asymptotic Sh and mass transfer coefficient (with chemical reaction)... 

Liquid-phase mass transfer coefficient with chemical reaction, m s ... 

The quantity in the square brackets corresponds to the mass transfer coefficient with chemical reaction. Remembering that the mass transfer coefficient without reaction equals Dijl, we have... 

Chemical reaction rates, 14 607. See also Kinetic measurements Chemical reactions. See also Chemical processes Reaction entries with absorption, 2 47-48, 71-76 activated carbon for control of, 4 755 on adsorbents, 2 629-630, 650-651 atomic level of, 16 736 contexts of, 22 336 engine knock and, 22 390—391 heterogeneous, 22 331-332, 339 homogeneous, 22 339 independent and dependent, 22 336—337 mass-transfer coefficients with, 20 753-755... 

From the above it can be concluded that only the reaction with component B may enhance mass transfer of ozone substantially. And only if the Hatta number HaB is much higher than 1. Therefore it can be expected that whenever we have to deal with an enhancement of mass transfer due to chemical reactions, this influences the selectivity of the oxidation process in a negative way. The factor which has to be considered in this respect is the Hatta number for the reaction of ozone with component B (equation 29). HaB increases with increasing value of kB and CBb and with decreasing value of the mass transfer coefficient for ozone, kHq,... 

This model was applied to the same data for batch and flowthrough systems with and without acid addition as for the previous two models, and some of the xylan conversion predictions calculated from the data and concentration predictions via Eq. 8 are summarized in Figs. 5 and 6 for batch and flowthrough systems, respectively. Tables 4 and 2 present the parameters and the SSE values for the branched pore model, respectively. Overall, although some data are better matched than others, hemicellulose hydrolysis models based on mass transfer alone can predict performance in batch and flow systems as well as, if not better than, reaction-only models. In addition, the changes in mass transfer coefficient with flow are consistent with expectations for a mass transfer model but not for strictly a chemical reaction. 

The technique involving simultaneous absorption with chemical reaction and physical desorption was employed to determine mass transfer coefficients with and without chemical reaction under identical hydrodynamic conditions. The gas phase consisted of CO2 and N2, and the liquid phase consisted of 0.2M NaOH solution containing dissolved oxygen. 3mm and 4mm glass beads were used as the solid phase. 

In fact, the mass transfer coefficient is often an ambiguous concept, reflecting nuances of its basic definition. To begin our discussion of these nuances, we first compare the mass transfer coefficient with the other rate constants given in Table 8.2-1. The mass transfer coefficient seems a curious contrast, a combination of diffusion and dispersion. Because it involves a concentration difference, it has different dimensions than the diffusion and dispersion coefficients. It is a rate constant for an interfacial physical reaction, most similar to the rate constant of an interfacial chemical reaction. 

With a reactive solvent, the mass-transfer coefficient may be enhanced by a factor E so that, for instance. Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally. There are no generalized correlations. Some calculations have been made for idealized situations, such as complete reaction in the liquid film. Tables 23-6 and 23-7 show a few spot data. On that basis, a tower for absorption of SO9 with NaOH is smaller than that with pure water by a factor of roughly 0.317/7.0 = 0.045. Table 23-8 lists the main factors that are needed for mathematical representation of KgO in a typical case of the absorption of CO9 by aqueous mouethauolamiue. Figure 23-27 shows some of the complex behaviors of equilibria and mass-transfer coefficients for the absorption of CO9 in solutions of potassium carbonate. Other than Henry s law, p = HC, which holds for some fairly dilute solutions, there is no general form of equilibrium relation. A typically complex equation is that for CO9 in contact with sodium carbonate solutions (Harte, Baker, and Purcell, Ind. Eng. Chem., 25, 528 [1933]), which is... 

Two complementai y reviews of this subject are by Shah et al. AIChE Journal, 28, 353-379 [1982]) and Deckwer (in de Lasa, ed.. Chemical Reactor Design andTechnology, Martinus Nijhoff, 1985, pp. 411-461). Useful comments are made by Doraiswamy and Sharma (Heterogeneous Reactions, Wiley, 1984). Charpentier (in Gianetto and Silveston, eds.. Multiphase Chemical Reactors, Hemisphere, 1986, pp. 104—151) emphasizes parameters of trickle bed and stirred tank reactors. Recommendations based on the literature are made for several design parameters namely, bubble diameter and velocity of rise, gas holdup, interfacial area, mass-transfer coefficients k a and /cl but not /cg, axial liquid-phase dispersion coefficient, and heat-transfer coefficient to the wall. The effect of vessel diameter on these parameters is insignificant when D > 0.15 m (0.49 ft), except for the dispersion coefficient. Application of these correlations is to (1) chlorination of toluene in the presence of FeCl,3 catalyst, (2) absorption of SO9 in aqueous potassium carbonate with arsenite catalyst, and (3) reaction of butene with sulfuric acid to butanol. 

In evaluating their results they assumed the film theory, and, because the oxygen is sparingly soluble and the chemical reaction rate high, they also assumed that the liquid film is the controlling resistance. The results were calculated as a volumetric mass-transfer coefficient based, however, on the gas film. They found that the volumetric mass-transfer coefficient increased with power input and superficial gas velocity. Their results can be expressed as follows ... 

With a reactive solvent, the mass transfer coefficient may be enhanced by a factor E so that, for instance Kg is replaced by EKg. Like specific rates of ordinary chemical reactions, such enhancements must be found experimentally, although some theoretical relations for idealized situations have been found. Tables 8.1 and 8.2 show a few spot data. A particular... 

The variation of efficiencies is due to interaction phenomena caused by the simultaneous diffusional transport of several components. From a fundamental point of view one should therefore take these interaction phenomena explicitly into account in the description of the elementary processes (i.e. mass and heat transfer with chemical reaction). In literature this approach has been used within the non-equilibrium stage model (Sivasubramanian and Boston, 1990). Sawistowski (1983) and Sawistowski and Pilavakis (1979) have developed a model describing reactive distillation in a packed column. Their model incorporates a simple representation of the prevailing mass and heat transfer processes supplemented with a rate equation for chemical reaction, allowing chemical enhancement of mass transfer. They assumed elementary reaction kinetics, equal binary diffusion coefficients and equal molar latent heat of evaporation for each component. 

For simplicity, this section discusses only the mass transfer of one component in a liquid-liquid system with negligible miscibility of both liquids and with one transitional component. On the other hand, calculations must consider mass transfer rates of several components and more or less strong variation in the mass flows along the column, where both complicate the equation considerably [21-23]. Chemical reactions may cause further complications. Their kinetics can enhance the mass transfer coefficients and, therefore, the reaction equations have to be part of the mathematical model of the extractor [24,25]. 

In what follows, the preceding evaluation procedure is employed in a somewhat different mode, the main objective now being to obtain expressions for the heat or mass transfer coefficient in complex situations on the basis of information available for some simpler asymptotic cases. The order-of-magnitude procedure replaces the convective diffusion equation by an algebraic equation whose coefficients are determined from exact solutions available in simpler limiting cases [13,14]. Various cases involving free convection, forced convection, mixed convection, diffusion with reaction, convective diffusion with reaction, turbulent mass transfer with chemical reaction, and unsteady heat transfer are examined to demonstrate the usefulness of this simple approach. There are, of course, cases, such as the one treated earlier, in which the constants cannot be obtained because exact solutions are not available even for simpler limiting cases. In such cases, the procedure is still useful to correlate experimental data if the constants are determined on the basis of those data. 

The chemical method used to estimate the interfacial area is based on the theory of the enhancement factor for gas absorption accompanied with a chemical reaction. It is clear from Equations 6.22-6.24 that, in the range where y > 5, the gas absorption rate per unit area of gas-liquid interface becomes independent of the liquid phase mass transfer coefficient /cp, and is given by Equation 6.24. Such criteria can be met in the case of absorption with... 

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 ... 

Which experimental method should be used depends on the type of reactor and how it will be operated, and if clean or process water is to be used for the measurement. Nonsteady state methods are generally simpler and faster to perform if kLa is to be determined in clean water without reaction. For processes that are operated at steady state with a reaction, determination of kLa using steady state methods are preferred, since continuous-flow processes need not be interrupted and operating conditions similar to the normal process conditions can be used. This is especially important for systems with reactions because the reaction rate is usually dependent on the concentration of the reactants present. They are thus often applied for investigations of the mass transfer coefficient under real process conditions with chemical reactions kLa(02) or biological activity kLa(02), e. g. in waste water treatment systems. 

The driving force for the mass transfer of the solute in the three-phase system can be determined with the solvent/water partition coefficient, just as the partition coefficient for gas/liquid phases, the Henry s Law constant, is used to determine the driving force for the mass transfer of ozone. A solute tends to diffuse from phase to phase until equilibrium is reached between all three phases. This tendency of a solute to partition between water and solvent can be estimated by the hydrophobicity of the solute. The octanol/water partition coefficient Kow is a commonly measured parameter and can be used if the hydrophobicity of the solvent is comparable to that of octanol. How fast the diffusion or transfer will occur depends not only on the mass transfer coefficient in addition to the driving force but also on the rate of the chemical reaction as well. 

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