Liquid film enhancement factor

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... 

It has been observed that under reaction conditions mass transfer is often significantly faster than would be expected based on the film model. This is modelled by introducing an enhancement factor, E. In case the concentration in the bulk liquid, ca, is zero, the rate of mass transfer of A now becomes ... 

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. 

Enhancement factor E. For reaction occurring only in the liquid film, whether instantaneous or fast, the rate law may be put in an alternative form by means of a factor that measures the enhancement of the rate relative to the rate of physical absorption of A in the liquid without reaction. Reaction occurring only in the liquid film is characterized by cA - 0 somewhere in the liquid film, and the enhancement factor E is defined by... 

Figure 9.8 Enhancement factor, E (Ha, ,), for fast gas-liquid reaction (in liquid film) reaction A(g) + bB(9 - products (B nonvolatile)...

Note that the enhancement factor E is relevant only for reaction occurring in the liquid film. For an instantaneous reaction, the expressions may or may not involve E, except that for liquid-film control, it is convenient, and for gas-film control, its use is not practicable (see problem 9-12(a)). The Hatta number Ha, on the other hand, is not relevant for the extremes of slow reaction (occurring in bulk liquid only) and instantaneous reaction. The two quantities are both involved in rate expressions for fast reactions (occurring in the liquid film only). 

Regimes 2 and 3 - moderate reactions in the bulk (2) or in thefdm (3) and fast reactions in the bulk (3) For higher reaction rates and/or lower mass transfer rates, the ozone concentration decreases considerably inside the film. Both chemical kinetics and mass transfer are rate controlling. The reaction takes place inside and outside the film at a comparatively low rate. The ozone consumption rate within the film is lower than the ozone transfer rate due to convection and diffusion, resulting in the presence of dissolved ozone in the bulk liquid. The enhancement factor E is approximately one. This situation is so intermediate that it may occur in almost any application, except those where the concentration of M is in the micropollutant range. No methods exist to determine kLa or kD in this regime. 

Regime 4 - fast reactions in the film In region 4 ozone is entirely consumed inside the liquid film, so that no ozone can escape to the bulk liquid, i. e. cL = 0. Here, the enhancement factor is defined as ... 

Regime 5 - instantaneous reactions at an reaction plane developing inside the film For very high reaction rates and/or (very) low mass transfer rates, ozone reacts immediately at the surface of the bubbles. The reaction is no longer dependent on ozone transfer through the liquid film kL or the reaction constant kD, but rather on the specific interfacial surface area a and the gas phase concentration. Here the resistance in the gas phase may be important. For lower c(M) the reaction plane is within the liquid film and both film transfer coefficients as well as a can play a role. The enhancement factor can increase to a high value E > > 3. 

These parameters, such as the coefficient of diffusion, D, mass-transfer coefficient in the gas and liquid phase or film, kg and k], Thiele modulus, Hatta number, Ha, and enhancement factor, E, are all dependent on the pressure. 

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. 

When the reaction is completed in the diffusion film of the liquid phase, the enhancement factor in the absorption rate equals V/A Thus, the absorption rate and the reaction rate in the diffusion film are equal. The rate of absorption is given by... 

If the chemical reaction—we consider a water film—is fast compared to tlie transport time, the conditions used in defining equation 34 are no longer valid. In this case, we may assume immediate equilibrium between the species linkcxl by the fast reaction. The degree of mass transport enhancement caused by chemical reactions may be quantified by adding a chemical enhancement factor, a, to the term of liquid film resistance. 

Ho = Henry s law constant (atm/ft /mol) koi = liquid film mass transfer coefficient E = liquid film enhancement factor,... 

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. 

Figure 2. Calculated effect of buffer alternatives on the liquid-film enhancement factor, 0.1 M CaClt, 55°C, pH 5.5, 3 wM total sulfite, 1000 ppm SOti-...

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. 

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