Interfacial area correlation , 615

Most often, at atmospheric pressure the interfacial area correlations use pressure drop as a variable because of their similarities. For example, Midoux et al. [56] proposed the following correlation for the cocurrent downflow in TBR ... 

There are no effective interfacial area correlations in the literature for the specific cases discussed here. The correlation that conies closest to that required for trickle bed operation is that of Puranik and Vogelpohl [29], which is for a continuous gas phase and a dispersed liquid phase, but in a countercurrent packed column, well below the loading point. They derived the following correlation (for piLfQ, = 1.5 kg/m s) ... 

Lujuid-Pha.se Transfer. It is difficult to measure transfer coefficients separately from the effective interfacial area thus data is usually correlated in a lumped form, eg, as k a or as These parameters are measured for the Hquid film by absorption or desorption of sparingly soluble gases such as O2 or CO2 in water. The Hquid film resistance is completely controlling in such cases, and kjji may be estimated as since x (Fig. 4). This... 

Other correlations based partially on theoretical considerations but made to fit existing data also exist (71—75). A number of researchers have also attempted to separate from a by measuring the latter, sometimes in terms of the wetted area (76—78). Finally, a number of correlations for the mass transfer coefficient itself exist. These ate based on a mote fundamental theory of mass transfer in packed columns (79—82). Although certain predictions were verified by experimental evidence, these models often cannot serve as design basis because the equations contain the interfacial area as an independent variable. 

Model Reactions. Independent measurements of interfacial areas are difficult to obtain in Hquid—gas, Hquid—Hquid, and Hquid—soHd—gas systems. Correlations developed from studies of nonreacting systems maybe satisfactory. Comparisons of reaction rates in reactors of known small interfacial areas, such as falling-film reactors, with the reaction rates in reactors of large but undefined areas can provide an effective measure of such surface areas. Another method is substitution of a model reaction whose kinetics are well estabUshed and where the physical and chemical properties of reactants are similar and limiting mechanisms are comparable. The main advantage of employing a model reaction is the use of easily processed reactants, less severe operating conditions, and simpler equipment. 

The important point to note here is that the gas-phase mass-transfer coefficient fcc depends principally upon the transport properties of the fluid (Nsc) 3nd the hydrodynamics of the particular system involved (Nrc). It also is important to recognize that specific mass-transfer correlations can be derived only in conjunction with the investigator s particular assumptions concerning the numerical values of the effective interfacial area a of the packing. 

With complicated geometries, the product of the interfacial area per volume and the mass-transfer coefficient is required. Correlations of kop or of HTU are more accurate than individual correlations of k and since the measurements are simpler to determine the produc t kop or HTU. 

To determine the mass-transfer rate, one needs the interfacial area in addition to the mass-transfer coefficient. For the simpler geometries, determining the interfacial area is straightforward. For packed beds of particles a, the interfacial area per volume can be estimated as shown in Table 5-27-A. For packed beds in distillation, absorption, and so on in Table 5-28, the interfacial area per volume is included with the mass-transfer coefficient in the correlations for HTU. For agitated liquid-liquid systems, the interfacial area can be estimated... 

In developing correlations for the mass-transfer coefficients Icq and /cl, the various authors have assumed different but internally compatible correlations for the effective interfacial area a. It therefore would be inappropriate to mix the correlations of different authors unless it has been demonstrated that there is a valid area of overlap between them. 

Experimental values of Hqg -nd Hql for a number of distillation systems of commercial interest are also readily available. Extrapolation of the data or the correlations to conditions that differ significantly from those used for the original experiments is risky. For example, pressure has a major effect on vapor density and thus can affect the hydrodynamics significantly. Changes in flow patterns affeci both mass-transfer coefficients and interfacial area. 

Flow Reactors Fast reactions and those in the gas phase are generally done in tubular flow reaclors, just as they are often done on the commercial scale. Some heterogeneous reactors are shown in Fig. 23-29 the item in Fig. 23-29g is suited to liquid/liquid as well as gas/liquid. Stirred tanks, bubble and packed towers, and other commercial types are also used. The operadon of such units can sometimes be predicted from independent data of chemical and mass transfer rates, correlations of interfacial areas, droplet sizes, and other data. 

Interfacial Area This consideration in agitated vessels has been reviewed and summarized by Tatterson (op. cit.). Predictive methods for interfacial area are not presented here because correlations are given for the overall volumetric mass transfer coefficient liquid phase controlhng mass transfer. 

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. 

Gas/Liquid Interfacial Area This has been evaluated by measuring absorption rates like those of CO9 in NaOH. A correlation by Charpentier (Chem. Eng. Journal, 11, 161 [1976]) is... 

The effective interfacial area is used in mass transfer studies as an undivided part of individual and overall coefficients when it is difficult to separate and determine the effective area. The work of Shulman et.al.,65 presents a well organized evaluation of other work in addition to their own. One of the difficulties in correlating tower packing performance lies in obtaining the correct values for the effective interfacial areas of the packing on which the actual absorption, desorption, chemical reaction, etc. are completed. Figures 9-47 A, B, C, D, E, F, G present a correlation for Avater flow based on the ammonia-water data of Fellinger [27] and are valid for absorption work. 

This has been shown to correlate for a wide variety of tower packings, various operating conditions, and physical properties of the solute and inert gases. The k(j calculated must be used in conjunction with the effective interfacial areas determined by Shulman [65] Figure 9-47, to establish a reliable value for kGa. Figure 9-47 should be used with the abscissa as G/Vp/0.075 for inert gas other than air [67] ... 

Agitation of fermentation broth creates a uniform distribution of ah in the media. Once you mix a solution, you exert an energy into the system. Increasing power input reduces the bubble size and this in turn increases the interfacial area. Therefore the mass transfer coefficient would be a function of power input per unit volume of fermentation broth, which is also affected by the gas superficial velocity.2,3 The general correlation is expected to be as follows ... 

The mass transfer, KL-a for a continuous stirred tank bioreactor can be correlated by power input per unit volume, bubble size, which reflects the interfacial area and superficial gas velocity.3 6 The general form of the correlations for evaluating KL-a is defined as a polynomial equation given by (3.6.1). 

El), Oldshue (Ol), and Johnson et al. (J4)] have been concerned with the determination of the volume transfer coefficient KtAb (liter/hr), where Kx is the mass-transfer coefficient and Ab is the total gas-liquid interfacial area. The results obtained using a turbine impeller and an open pipe sparger can be correlated in terms of the nominal gas velocity wg(ft/hr) and the horsepower input to the impeller HP by an expression of the following form ... 

Later publications have been concerned with mass transfer in systems containing no suspended solids. Calderbank measured and correlated gas-liquid interfacial areas (Cl), and evaluated the gas and liquid mass-transfer coefficients for gas-liquid contacting equipment with and without mechanical agitation (C2). It was found that gas film resistance was negligible compared to liquid film resistance, and that the latter was largely independent of bubble size and bubble velocity. He concluded that the effect of mechanical agitation on absorber performance is due to an increase of interfacial gas-liquid area corresponding to a decrease of bubble size. 

Empirical Correlations of Volumetric Mass-Transfer Coefficient Ks and Specific Interfacial Area s ... 

A summary of a number of correlations proposed for volumetric mass-transfer coefficients and specific interfacial area is presented in Table II, which includes data additional to those of Westerterp et al. (W4). It is apparent that disagreement exists as to the numerical values for the exponents. This is due, in part, to the lack of geometric similarity in the equipment used. In addition, variation in operating factors such as the purity of the system (surfactants), kind of chemical system, temperature, etc., also contribute to the discrepancies. To summarize Table II ... 

Yoshida and Miura (Y3) reported empirical correlations for average bubble diameter, interfacial area, gas holdup, and mass-transfer coefficients. The bubble diameter was calculated as... 

It is seen from these examples that, in appropriate systems, it is possible to introduce product into the reactant in such a manner that an effective reaction interface is established before the reactant has been heated to the decomposition temperature. Accordingly, the induction period is removed and the acceleratory process may be less pronounced or eliminated altogether. Artificial nucleation results in changes in reaction geometry with consequent variation in the a—time curve shape and the maximum value of da/dt but does not enhance the rate of interface advance. We have found no studies in which increases in reaction rates were quantitatively correlated with the increased interfacial area and/or density of nucleation which resulted from the reactant pretreatment. 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

Although the values of kba dr in the literature are reasonable and comparable each other, the different trend mentioned above may be due to the different operating conditions. The gas-liquid interfacial area(a) and liquid side mass transfer coefHcient(ki) have been determined from the knowledge of measured values of gas holdup and kcacir [11]- The values of a and ki increase almost linearly with increasing Ug or Ul- The values of h cir and ktacir in circulating beds can be predicted by Eqs.(ll) and (12) with a correlation coefBcient of 0.92 and 0.93,... 

Dimensionless numbers (Reynolds number = udip/jj., Nusselt number = hd/K, Schmidt number = c, oA, etc.) are the measures of similarity. Many correlations between them (known also as scale-up correlations) have been established. The correlations are used for calculations of effective (mass- and heat-) transport coefficients, interfacial areas, power consumption, etc. 

Correlations for mass transfer coefficients, gas holdup volume, and interfacial area, as functions of system physical properties and agitation rate or flow velocity, etc. 

The interfacial area a was not measured, and the quantity (Ua/V) was correlated versus the total mass flow rate. From results of this type, the general parameters given in Eqs. (30) cannot be evaluated. Therefore, the only design that can be safely performed is for the Aroclor-water system in a 3-in. pipe. 

From this discussion of parameter evaluation, it can be seen that more research must be done on the prediction of the flow patterns in liquid-liquid systems and on the development of methods for calculating the resulting holdups, pressure drop, interfacial area, and drop size. Future heat-transfer studies must be based on an understanding of the fluid mechanics so that more accurate correlations can be formulated for evaluating the interfacial and wall heat-transfer coefficients and the Peclet numbers. Equations (30) should provide a basis for analyzing the heat-transfer processes in Regime IV. 

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