Absorption without reaction, mass transfer

Figures 7(a)-(c) show a comparison between the numerically computed absorption flux and the absorption flux obtained from expression (31), using eqs (24), (30) and (34)-(37). From these figures it can be concluded that for both equal and different binary mass transfer coefficients absorption without reaction can be described well with eq. (24), whereas absorption with instantaneous reaction can be described well with eq. (30). If the Maxwell-Stefan theory is used to describe the mass transfer process, the enhancement factor obeys the same expression as the one obtained on the basis of Fick s law [eq. (35)]. Finally, from Figs 7(b) and 7(c) it appears that the use of an effective mass transfer coefficient m the Hatta number again produces satisfactory results.

The square of this number represents the ratio between the maximum reaction rate of ozone near the water interface (film thickness) and the maximum physical absorption rate (i.e., the absorption without reaction). In Eq. (9), kD and kL are parameters representing the chemical reaction and physical diffusion rate constants, that is, the rate constant of the ozone-compound reaction and water phase mass transfer coefficient, respectively. Their values are indicative of the importance of both the physical and chemical steps in terms of their rates. However, two additional parameters, as shown in Eq. (9), are also needed the concentration of the compound, CM, and the diffusivity of ozone in water, Z)0i. The ozone diffusivity in water can be calculated from empirical equations such as those of Wilke and Chang [55], Matrozov et al. [56], and Johnson and Davies [57] from these equations, at 20°C, D0 is found to be 1.62xl0 9, 1.25xl0-9, and 1.76xl0 9 m2 s 1, respectively. 

Multiphase Reactors Reactions between gas-liquid, liquid-liquid, and gas-liquid-solid phases are often tested in CSTRs. Other laboratory types are suggested by the commercial units depicted in appropriate sketches in Sec. 19 and in Fig. 7-17 [Charpentier, Mass Transfer Rates in Gas-Liquid Absorbers and Reactors, in Drew et al. (eds.), Advances in Chemical Engineering, vol. 11, Academic Press, 1981]. Liquids can be reacted with gases of low solubilities in stirred vessels, with the liquid charged first and the gas fed continuously at the rate of reaction or dissolution. Some of these reactors are designed to have known interfacial areas. Most equipment for gas absorption without reaction is adaptable to absorption with reaction. The many types of equipment for liquid-liquid extraction also are adaptable to reactions of immiscible liquid phases. 

Mass Transfer in Absorption without Reaction. We measured k in the stirred cell with an 0 - H2O system (figure 2). Forced convection k in the reaction mixtures was calculated from this result according to ]... 

Discussion of the concepts and procedures involved in designing packed gas absorption systems shall first be confined to simple gas absorption processes without compHcations isothermal absorption of a solute from a mixture containing an inert gas into a nonvolatile solvent without chemical reaction. Gas and Hquid are assumed to move through the packing in a plug-flow fashion. Deviations such as nonisotherma1 operation, multicomponent mass transfer effects, and departure from plug flow are treated in later sections. 

Membrane diffusion illustrates the uses of Fick s first and second laws. We discussed steady diffusion across a film, a membrane with and without aqueous diffusion layers, and the skin. We also discussed the unsteady diffusion across a membrane with and without reaction. The solutions to these diffusion problems should be useful in practical situations encountered in pharmaceutical sciences, such as the development of membrane-based controlled-release dosage forms, selection of packaging materials, and experimental evaluation of absorption potential of new compounds. Diffusion in a cylinder and dissolution of a sphere show the solutions of the differential equations describing diffusion in cylindrical and spherical systems. Convection was discussed in the section on intrinsic dissolution. Thus, this chapter covered fundamental mass transfer equations and their applications in practical situations. 

The J value denotes the absorption rate without the dispersed phase where the mass transfer rate can be accompanied by zero- or first-order chemical reactions in the continuous phase. These are well-known equations J = k° (O -i- - Ol)... 

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 CO2 gas is absorbed into an aqueous solution of Na2CO3, the following reaction takes place in the liquid phase. 

A convention used in most literature on ozone mass transfer and in the rest of this book is to define the mass transfer coefficient as the one that describes the mass transfer rate without reaction, and to use the enhancement factor E to describe the increase due to the chemical reaction. Furthermore, the simplification that the major resistance lies in the liquid phase is used throughout the rest of the book. This is also based on the assumption that the mass transfer rate describes physical absorption of ozone or oxygen, since the presence of a chemical reaction can change this. This means that KLa - kLa and the concentration gradient can be described by the difference between the concentration in equilibrium with the bulk gas phase cL and the bulk liquid concentration cL. So the mass transfer rate is defined as ... 

It is obvious that re-atomization yields decrease the mean diameter of the liquid droplets and thus an increased interface area at the same time, it results in reduced average transfer coefficients, because heat and mass transfer coefficients between gas flow and particle or droplet are in positive correlation with the diameter of the particle or droplet, while coalescence of droplets yields influences opposite to those described above. In their investigation on the absorption of C02 into NaOH solution, Herskowits et al. [59, 60] determined theoretically the total interface areas and the mass transfer coefficients by comparing the absorption rates with and without reaction in liquid, employing the expression for the enhancement factor due to chemical reaction of second-order kinetics presented by Danckwerts [70],... 

Two books deal almost exclusively with the subject of mass transfer with chemical reaction, the admirably clear expositions of Astarita (A6) and Danckwerts (D2). Since then a flood of theoretical and experimental work has been reported on gas absorption and related separations. The principal object of this chapter is to present techniques, results, and opinions published mainly during the last 6 or 7 years on mass-transfer coefficients and interfacial areas in most types of absorbers and reactors. This necessitates some review of mass transfer with and without chemical reaction in the first section, and comments about the simulation of industrial reactors by laboratory-scale apparatus in the concluding section. Although many gas-liquid reactions are accompanied by a rise in temperature that may be great enough to affect the rate of gas absorption, our attention here is confined to cases where the rise in temperature does not affect the absorption rate. This latter topic (treated by references B20, TIO, S3, T3, V5) could justify another complete chapter. 

The technique involving simultaneous absorption with chemical reaction and physical desorption was employed to determine mass transfer coefficients with and without chemical reaction under identical hydrodynamic conditions. The gas phase consisted of CO2 and N2, and the liquid phase consisted of 0.2M NaOH solution containing dissolved oxygen. 3mm and 4mm glass beads were used as the solid phase. 

One can also frequently choose between a purely mass-transfer operation and a chemical reaction or a combination of both. Water can be removed from an ethanol-water solution either by causing it to react with unslaked lime or by special methods of distillation, for example. Hydrogen sulfide can be separated from other gases either by absorption in a liquid solvent with or without simultaneous chemical reaction or by chemical reaction with ferric oxide. Chemical methods ordinarily destroy the substance removed, while mass-transfer methods usually permit its eventual recoveiy in unaltered form without great difficulty. 

This necessitates some theoretical presentation of mass transfer with and without chmical reaction that will be strictly focused in the first part of this review to the case of desorption or vdien a rise in tanperature is acccmpanying and is great enough to affect the rate of gas absorption. Indeed many general papers and also many papers confined to specific reaction schane (simultane-... 

Mass transfer with and without chanical reaction and exothermic absorption... 

Propose a model for this system in the form of a BVP, specifying both the set of PDEs and the appropriate boundary conditions. Assiune a film of thickness b = I mm, length L = 50 cm, inclined at 0 = 80°. Use effective binary diffusivities in the film of Dj = 10 cm /s, j = A, B, AB. Compute the steady-state concentration profile of each species within the film and the average absorption rate per unit area. Then, decrease the rate constant to zero to see what the mass transfer rate would be without reaction. 

---