Liquid-Phase Mass Transfer with Chemical Reactions

Liquid-Phase Mass Transfer with Chemical Reactions 

So far, we have considered pure physical mass transfer without any reaction. Occasionally, however, gas absorption is accompanied by chemical or biological reactions in the liquid phase. For example, when C02 gas is absorbed into an aqueous solution of Na2C03, the following reaction takes place in the liquid phase  

In an aerobic fermentation, the oxygen absorbed into the culture medium is consumed by microorganisms in the medium. 

In general, the rates of the mass transfer increase when it is accompanied by reactions. For example, if kL indicates the liquid-phase coefficient, including the effects of the reaction, then the ratio E can be defined as  

Hatta [5] derived a series of theoretical equations for E, based on the film model. Experimental values of E agree with the Hatta theory, and also with theoretical values of E derived later by other investigators, based on the penetration model. 

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Liquid Phase Mass Transfer with Chemical Reactions I 83... 

In the case where the blood flow is turbulent, we can use the concept of enhancement factor for the case of liquid-phase mass transfer with a chemical reaction (Section 6.5). Thus,... 

Fig. 4.2. Liquid phase concentration profiles for mass transfer with chemical reaction - film theory...

Three general classes of kinetic models that may apply to systems with rate control by mass transfer in the liquid or by interdiffusion in the particle with or without chemical reaction will be briefly reviewed here (for more detail, see [Helfferich, 1962a Helfferich and Hwang, 1988]). In particular I he following models will be examined liquid-phase mass transfer with linear driving force, Nernst-Planck models for intraparticle diffusion without reac-lion, and, Nernst-Planck models for intraparticle diffusion with accompanying reaction. 

Mass transfer with chemical reaction in multiphase systems" covers, indeed, a large area. Table 1 shows a general classification of the systems encountered. From the possible two-phase systems, solid-solid reactions, liquid-solid (reactive or catalytic) and gas-solid (reactive or catalytic) reactions are not discussed here. The first one was reviewed by Tamhankar and Doraiswamy (2) and gas-solid (reactive) systems, such as, coal gasification, calcination of limestone, reduction of ores, etc. have been treated in some detail in recent reviews (3-5). The industrially important fluid-solid catalytic processes were the topic of a previous Advanced Study Institute (6) and have been also discussed authoritatively elsewhere (5,7). Concerning solid (reactive)-liquid two-phase systems, only some interesting examples are presented in Table 2 (1). 

A detailed and very fundamental analysis of mass-transfer with chemical reaction in liquid-liquid dispersions has been published recently by Tavlarides and Stamatoudis (10). These authors point out that the design and analysis problem depends on the phase in which the reaction occurs, whether multiple reactions are involved, the relative magnitudes of the rates of mass transfer and reaction, and upon macromixing processes of the dispersed and continuous phases. Hence, they first examine dispersion phenomena such as coalescence and breakage of droplets, and drop size distribution. The topics discussed by the authors (10)... 

Vasudevan,T.V. and M.M.Sharma. Some aspects of process design of liquid-liquid reactor. (Int. Sympo-siuir. on Mass Transfer with Chemical Reaction in Two-Phase Systems", ACS-Meeting, Atlanta, 1981). 

The mass transfer with chemical reaction in the liquid phase has the... 

Carbon dioxide gas diluted with nitrogen is passed continuously across the surface of an agitated aqueous lime solution. Clouds of crystals first appear just beneath the gas-liquid interface, although soon disperse into the bulk liquid phase. This indicates that crystallization occurs predominantly at the gas-liquid interface due to the localized high supersaturation produced by the mass transfer limited chemical reaction. The transient mean size of crystals obtained as a function of agitation rate is shown in Figure 8.16. 

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... 

Now that one has obtained the basic information for the molar density of reactant A within the liquid-phase mass transfer boundary layer, it is necessary to calculate the molar flux of species A normal to the gas-liquid interface at r = l bubbie, and define the mass transfer coefficient via this flux. Since convective mass transfer normal to the interface was not included in the mass transfer equation with liquid-phase chemical reaction, it is not necessary to consider the convective mechanism at this stage of the development. Pick s first law of diffusion is sufficient to calculate the flux of A in the r direction at r = /fbubbie- Hence,... 

Now, it is instructive to re-analyze the unsteady-state macroscopic mass balance on an isolated solid pellet of pure A with no chemical reaction. The rate of output due to interphase mass transfer from the solid particle to the liquid solution is expressed as the product of a liquid-phase mass transfer coefficient c, liquids a Concentration driving force (Ca, — Ca), and the surface area of one spherical pellet, 4nR. The unsteady-state mass balance on the solid yields an ordinary differential equation for the time dependence of the radius of the peUet. For example,... 

The strong interactions and coupling between the mass transfer and chemical reaction processes are the primary component in complicating the analysis of even a very simplified reactor. This can be illustrated with respect to some qualitative features of a simple single reaction in which a reagent A is decomposed irreversibly in the liquid phase to a product P, such that A — P. 

If a chemical reaction takes place between the absorbate A and absorbent B (chemisorption), the equations listed in Th-ble 3-4 to calculate the mass transfer coefficient may be applied, especially when the resistance to mass transfer is mainly in the gas phase. However, if the mass transfer is controlled by the mass transfer resistance in the liquid phase, the mass transfer coefficient of the liquid phase is increased in the case of fast chemical reactions. This increase is expressed by the enhancement factor E which is defined as the ratio of the liquid phase mass transfer coefficients, fi with and fi, without chemical reaction... 

In two-phase systems, there may be steep concentration gradients near the interfaces, particularly when rapid reactions are taking place. When mass transfer and chemical reactions can be considered as processes in series, the qualitative effects can be estimated simply (see section 5.3.5). When kinetic data are available, quantitative effects can be calculated. When diffusion and chemical reactions take place in the same zone, calculations become quite complex, but qualitative effects can yet be estimated. This may apply to situations where a reactant dissolves in a liquid and is converted widiin the diffusion layer adjacent to the interface. The dissolving reactant may be introduced as a gas, a solid or a second liquid phase (see section 5.4.2.2). It was shown that in these situations the selection of a reactor type is essential for obtaining a good selectivity (see also section 9.3). Similar effects are encountered with reactions takmg place inside porous solids (see section 5A.3.2), Therefore the structure of solid catalysts may be important in view of process selectivity. 

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