Liquid film enhancement factors with

Figure 1 compares calculated and measured values of the liquid-film enhancement factor with five buffers. The calculated values are within 10% of the measured values. In order to fit the measured data, the diffusivity of sulfopropionic acid was reduced by an additional 50% from the value estimated by Chang and Rochelle (16). 

Figure 1. Comparison of measured and calculated liquid-film enhancement factors with 0 to 40 mM buffer and 1000 ppm SOai at pH 5.5 and 25°C. Key O, sulfosuccinic in 0.3 M NaCl , sulfosuccinic in 0.1 M CaCls A, hydroxypropionic in 0.1 M CaCh , sulfopropionic in 0.3 M NaCl sulfopropionic in 0.1 M CaCls V, acetic in 0.3 M NaCl , acetic in 0.1 M CaCla +, adipic in 0.1 M CaCli 0, adipic in 0.3 M NaCl (pH 4.2) and , adipic in 0.1 M CaCls. (pH 4.2).

Figure 2 shows the calculated liquid-film enhancement factor for five buffers as a function of buffer concentration in 0.1 M CaCl2 at pH 5.5 with 1000 ppm SO2 at the gas/liquid interface. 

Figure 3 illustrates the effect of adipic acid on the overall enhancement of SO2 absorption. It gives the ratio of the overall mass transfer coefficient, Kg, to the gas-film coefficient, kg, as a function of a dimensionless parameters including adipic acid concentration. The overall coefficient includes an effect of k and the liquid-film enhancement factor which increases with adipic acid concentration. The ratio, Kg/kg, represents the fraction resistance of the gas film and cannot exceed 1.0. 

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... 

The parameter p (= 7(5 ) in gas-liquid sy.stems plays the same role as V/Aex in catalytic reactions. This parameter amounts to 10-40 for a gas and liquid in film contact, and increases to lO -lO" for gas bubbles dispersed in a liquid. If the Hatta number (see section 5.4.3) is low (below I) this indicates a slow reaction, and high values of p (e.g. bubble columns) should be chosen. For instantaneous reactions Ha > 100, enhancement factor E = 10-50) a low p should be selected with a high degree of gas-phase turbulence. The sulphonation of aromatics with gaseous SO3 is an instantaneous reaction and is controlled by gas-phase mass transfer. In commercial thin-film sulphonators, the liquid reactant flows down as a thin film (low p) in contact with a highly turbulent gas stream (high ka). A thin-film reactor was chosen instead of a liquid droplet system due to the desire to remove heat generated in the liquid phase as a result of the exothermic reaction. Similar considerations are valid for liquid-liquid systems. Sometimes, practical considerations prevail over the decisions dictated from a transport-reaction analysis. Corrosive liquids should always be in the dispersed phase to reduce contact with the reactor walls. Hazardous liquids are usually dispensed to reduce their hold-up, i.e. their inventory inside the reactor. 

The main factor determining the stability of such foams is the rate and extent of drainage from the thin liquid film. In general, this type of foam is relatively unstable. The stability may be enhanced by increasing the viscosity of the liquid by increasing the dry matter content or adding certain hydrocolloids. The foam stability may also be enhanced with hydrocolloids, in particular microcrystalline cellulose. 

As discussed in Sec. 7, the factor E represents an enhancement of the rate of transfer of A caused by the reaction compared with physical absorption, i.e., Kq is replaced by EKq. The theoretical variation of E with Hatta number for a first- and second-order reaction in a liquid film is shown in Fig. 19-25. The uppermost line on the upper right represents the pseudo first-order reaction, for which E = Ha coth (Ha). Three regions are identified with different requirements of liquid holdup 8 and interfacial area a, and for which particular kinds of contacting equipment may be best ... 

We studied these phenomena experimentally in a wetted wall column and two stirred cell reactors and evaluated the results with both a penetration and a film model description of simultaneous mass transfer accompanied by complex liquid-phase reactions [5,6], The experimental results agree well with the calculations and the existence of the third regime with its desorption against overall driving force is demonstrated in practice (forced desorption or negative enhancement factor). 

Other mole fractions in Eq. (11.33) refer to the absorbing gas, as with previous notation. The term in parentheses on the right of Eq. (11.33) is the enhancement factor for chemical reaction in the liquid film. As V/j increases, x and y decrease until they become effectively zero. 

A generalized theoretical model based on the film theory was also developed for the calculation of the enhancement factor for the simultaneous absorption of two gases coupled with a complex reaction mechanism in liquid phase, in which the rate is negative-order with respect to one of the gases and first order with the other [40], This phenomenon is typically observed in hydroformylation reactions, where the reaction rate is first order with respect to hydrogen partial pressure and negative order with respect to CO. Practical implications of this analysis have been illustrated with the hydroformylation of 1-hexene. Thereby, an expression for the enhancement factor Eco has been derived, which is applicable irrespective of the regime of absorption. 

In Chapter 7 we discussed the basics of the theory concerned with the influence of diffusion on gas-liquid reactions via the Hatta theory for flrst-order irreversible reactions, the case for rapid second-order reactions, and the generalization of the second-order theory by Van Krevelen and Hofitjzer. Those results were presented in terms of classical two-film theory, employing an enhancement factor to account for reaction effects on diffusion via a simple multiple of the mass-transfer coefficient in the absence of reaction. By and large this approach will be continued here however, alternative and more descriptive mass transfer theories such as the penetration model of Higbie and the surface-renewal theory of Danckwerts merit some attention as was done in Chapter 7. 

Huang and Kuo also solved two equations for a rapid first-order reversible reaction (i.e., equilibrium in the bulk liquid). The solutions are extremely lengthy and will not be given here. From a comparison of the film, surface renewal, and intermediate film-penetration theories it was found that for irreversible and reversible reactions with equal diffusivities of reactant and product, the enhancement factor was insensitive to the mass transfer model. For reversible reactions with product diffusivity smaller than that of the reactant, the enhancement factor can differ by a factor of two between the extremes of film and surface renewal theory. To conclude, it would seem that the choice of the model matters little for design calculations the predicted differences are negligible with respect to the uncertainties of prediction of some of the model or operation parameters. 

The film theory has an important drawback. Although, the value of 6 is not known, one should regard it as uniquely dete mined by the hydrodynamics of the liquid phase. On the basis, Eq.l2 would predict k to be proportional to the diffusivity D. Empiri cal mass transfer coefficient correlations available in the lit rature for a liquid in contact with a gas consistently indicate that in fact k is proportional to the square root of D. Therefore, analyses based on the film theory model are not expected to predict correctly the influence of diffusivity values on the enhancement factor I. Therefore, one is lead to a more complex model of the fluid mechanics involved, the penetration theory model. This model leads, in its several variations, to the correct prediction of the... 

An analysis of chemical desorption has recently been published (Chem.Eng.Sci., 21 0980)), which is based on a number of simplifying assumptions the film theory model is assumed, the diffusivities of all species are taken to be equal to each other, and in the solution of the differential equations an approximation which is second order with respect to distance from the gas-liquid interface is used this approximation was introduced as early as 1948 by Van Krevelen and Hoftizer. However, the assumptions listed above are not at all drastic, and two crucial elements are kept in the analysis reversibility of the chemical reactions and arbitrary chemical mechanisms and stoichiometry.The result is a methodology for developing, for any given chemical mechanism, a highly nonlinear, implicit, but algebraic equation for the calculation of the rate enhancement factor as a function of temperature, bulk-liquid composition, interface gas partial pressure and physical mass transfer coefficient The method of solution is easily gene ralized to the case of unequal diffusivities and corrections for differences between the film theory and the penetration theory models can be calculated. 

Since the earlier treatments of this problem by Ramachandran and Sharma(4) and Uchida et.al.(7).several experimental studies and verifications of predictions of enhancement factors have been reported(7,15,16) several detailed models based on film concept have also been proposed(7-12).Recently a penetration model for an instantaneous irreversible chemical reaction has also been presented.which however differs numerically only negligibly than the film model(13).The most important modification of Ramachandran and Sharma s treatment is due to Uchida et. al.(7-9) who consider that the rate of solid dissolution may be accelerated by the absorption of gas as discussed above.They have also considered the case where the concentration of solid component in the bulk liquid phase may not be maintained at the saturation solubility(that is,"finite" slurry) which occurs of course when the rate of solid dissolution is relatively slow compared with gas absorption rate(8).The case where the solid dissolution is finite was further considered by Sada et.al.(12) both theoretically and experimentally.Uchida et.al.(8) could also explain the data of Takeda et.al.(14) by their modified model.Analytical solutions presented above are for instantaneous reactions ... 

Film Theory and Gas-Liquid and Liquid-Liquid Mass Transfer. The history and literature surrounding interfacial mass transfer is enormous. In the present context, it suffices to say that the film model, which postulates the existence of a thin fluid layer in each fluid phase at the interface, is generally accepted (60). In the context of coupled mass transfer and reaction, two common treatments involve 1) the Hatta number and (2) enhancement factors. Both descriptions normally require a detailed model of the kinetics as well as the mass transfer. The Hatta number is perhaps more intuitive, since the numbers span the limiting cases of infinitely slow reaction with respect to mass transfer to infinitely fast reaction with respect to mass transfer. In the former case all reaction occurs in the bulk phase, and in the latter reaction occurs exclusively at the interface with no bulk reaction occurring. Enhancement factors are usually categorized in terms of reaction order (61). In the context of nonreactive systems, a characteristic time scale (eg, half-life) for attaining vapor-liquid equilibrium and liquid-liquid equilibrium, 6>eq, in typical laboratory settings is of the order of minutes. 

Referring to Equation 11.9, the reaction in the film (that occurs simultaneously with diffusion in this regime) can be written in terms of pure mass transfer in the liquid film multiplied by the enhancement factor ... 

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