Transfer with Reaction

There are a number of environmentally significant compounds that undergo a reaction while moving through the water-side, concentration boundary layer, such that the flux rate is altered. If the flux rate is altered, then the apparent rate coefficient is also affected. Typical examples would be the compounds that react with 

EXAMPLE 8.7 Absorption rate of carbon dioxide by the oceans 

Carbon dioxide is one of the maj or global warming gases. The ocean acts as a reservoir for carbon dioxide and therefore will slow the effects of this gas on global warming. How is this air-water transfer rate dependent on the rate of reaction of carbon dioxide with liquid water to form H2CO3  

the diffusion equation within the water concentration boundary layer 

From equation (E8.7.4), we can see that an equivalent, bulk, liquid-film coefficient, Ke, would be 

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The quantity (RA) can be further elaborated if interface mass and heat transfer coefficients are known, and with the theory of mass transfer with reaction inside porous catalysts as treated in Chapters 6 and 7 ... 

Fig. 7. Interface concentration profiles for the eight distinct kinetic regimes for mass transfer with reaction.

Mathematical Models for Mass Transfer with Reaction... 

Many operations in chemical engineering require the contact of two liquid phases between which mass and heat transfer with reaction occurs. Examples are hydrometallurgical solvent extraction, nitrations and halogenations of hydrocarbons, hydrodesulfurization of crude stocks, emulsion polymerizations, hydrocarbon fermentations for single-cell proteins, glycerolysis of fats, and phase-transfer catalytic reactions. A most common method of bringing about the contact of the two phases is to disperse droplets of one within the other by mechanical agitation. 

Conceptually, the framework of the theory permits description of interphase heat and mass transfer with reaction occurring in either or both phases. In theory one can use this approach to study the affects of partial mixing of the dispersed phase on extent of reaction for non-first-order reactions which occur in the droplets. Analyses can be made for mass-transfer-controlled reactions and selectivity for complex reactions. Difficulties in the solution of the resulting integro-diflferential equations have restricted applications at present to partial solutions. For example, the effects of partial droplet mixing on extent of reaction were studied for uniform drops. Mass transfer from nonuniform drops for various reactor geometries was studied for dispersions with drop breakage only or drop coalescence only. 

The work discussed in this section clearly delineates the role of droplet size distribution and coalescence and breakage phenomena in mass transfer with reaction. The population balance equations are shown to be applicable to these problems. However, as the models attempt to be more inclusive, meaningful solutions through these formulations become more elusive. For example, no work exists employing the population balance equations which accounts for the simultaneous affects of coalescence and breakage and size distribution on solute depletion in the dispersed phase when mass transfer accompanied by second-order reaction occurs in a continuous-flow vessel. Nevertheless, the population balance equation approach provides a rational framework to permit analysis of the importance of these individual phenomena. 

The deterministic population balance equations governing the description of mass transfer with reaction in liquid-liquid dispersions present a framework for analysis. However, signiflcant difficulties exist in obtaining solutions for realistic problems. No analytical solutions are available for even the simplest cases of interest. Extension of the solution to multiple reactants for uniform drops is possible using a method of moments but the solution is limited to rate equations which are polynomials (E3). Solutions to the population balance equations for spatially nonhomogeneous dispersions were only treated for nonreacting dispersions (P4), and only a simple case was solved for a spray column (B19). Treatment of unmixed feeds presents a problem. 

DP E F f f. Ha He AG Degree of polymerization Activation energy, enhancement factor for gas-liquid mass transfer with reaction, electrochemical cell potential Faraday constant, F statistic Efficiency of initiation in polymerization Ca/CaQ or na/nao, fraction of A remaining unconverted Hatta number Henry constant for absorption of gas in liquid Free energy change kj/kgmol Btu/lb-mol... 

Dk DP E Knudsen diffusivity Degree of polymerization Activation energy, enhancement factor for gas-liquid mass transfer with reaction. mVs ft"/s... 

Exercise 7,12 Mass transfer with reaction for reversible kinetics... 

Mass transfer involves establishing a transfer between the elementary regions of the reactor and between individual phases (interfacial mass transfer coefficients gas phase mass transfer, liquid phase mass transfer, mass transfer with reaction, liquid-solid mass transfer), as well as other elementary phenomena and processes connected with mass transfer gas phase phenomena and processes (gas hold-up, bubble size, interfacial area and bubble coalescence/redispersion), volumetric mass transfer and power consumption during mass transfer (2). 

The immobilized-catalysts are confined to a region in space defined by the dimensions of the polymer particle. Reactant(s) must diffuse ftom the external surface to the catalytic sites within the particle before any chemical reaction can occur. This sequential process, mass transfer with reaction, has been treated extensively for catalytic reactions in porous solids (13,14,15). A limited number of studies have shown that the mathematical formalism which is applied to heterogeneously-catalyzed reactions can be used to interpret mass transfer with reaction in immobilized catalysts which employ polymers as supports (11,16,17). 

Mass transfer with reaction in a slurry containing sparingly soluble particles... 

Distillation with reaction, where the normal process is coupled with a liquid phase reaction, is also interesting and esterifications of certain alcohols with acids are typical industrial applications. These include, among others the homogeneously catalyzed butyl acetate process and the production of the plasticizer di-octyl-phthalate from phthalic anhydride and 2-ethyl-hexanol. However, the subject which involves both product formation and separation aspects has not usually been treated in the literature relating specifically to "mass transfer with reaction". 

Gas absorption and any associated chemical reaction is always accompanied by the simultaneous release of heat of solution and heat of reaction. The micro-scale phenomena taking place close to the interface therefore involve the generation and diffusion of heat as well as the diffusion and reaction of material species. In developing a fundamental appreciation of simultaneous mass and heat transfer in gas-liquid reactions it is important for the heat effects to be incorporated into the analysis of diffusion and reaction because the rates and pathways of chemical reactions are usually enormously sensitive to temperature. In particular, for the case of gas-liquid reactor performance, if the heat effects are such that the mass transfer with reaction zone adjacent to the interface is at a temperature significantly different from the bulk, the yield and the selectivity performance will be erroneously interpreted if reaction is assumed to take place at the bulk liquid temperature. In consequence, the basic conceptual design of a commercial gas-liquid reactor could incorporate fallacious reasoning leading to inefficient operation at sub-optimal yield. 

The interaction of the processes of dissolution, mass transfer with reaction and the overall input and output flows of gas and liquid can be set out as follows. If G. is the molar feed rate of gas containing a dissolving and reacting component at a mol fraction y, then the rate of absorption at the... 

II. MATHEMATICAL MODELS FOR MASS TRANSFER WITH REACTION IN LIQUID-LIQUID DISPERSIONS... 

As previously mentioned, this arises from the consideration that the residence time of a surface element at the interface is very short, so that it is likely that A has never penetrated to the inner edge of the element before it is replaced. Models that limit the depth of the surface element have also been proposed and applied to purely physical mass transfer first — such as the surface rejuvenation model of Danckwerts [1955] and the film penetration model of Toor and Marchello [1958], These were later extended to mass transfer with reaction. Harriott [1962] and Bullin and Dukler [1972] extended these models by assuming that eddies arriving at random times come to within random distances from the interface. This leads to a stochastic formulation of the surface renewal. 

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