Mass transfer without chemical reaction

These parameters can be determined and predicted, and the theoretical expressions may thus assist in interpretation of mass-transfer data and in prediction of equipment performance. The case of mass transfer without chemical reaction is reported elsewhere (G5). 

This model is proposed for steady-state mass transfer without chemical reaction from swarms of moving bubbles with clean interfaces and without interaction between adjacent bubbles. 

Two extreme cases of equation 9.2-22 or -22a or -22b arise, corresponding to gas-film control and liquid-film control, similar to those for mass transfer without chemical reaction (Section 9.2.2). The former has implications for the location of the reaction plane (at distance 8 from the interface in Figure 9.6) and the corresponding value of CB. These points are developed further in the following two examples. 

Table 1. Dimensionless mass flux for mass transfer without chemical reaction. [The results obtained from eqs (21), (23) and (24) are compared with the results obtained from the numerical model]...

Fig. 3. Computed fraction profiles of components A and B in the liquid film corresponding to (a) run 1 and (b) run 6 from Table 1 for mass transfer without chemical reaction.

APPENDIX A MASS TRANSFER WITHOUT CHEMICAL REACTION... 

The liquid side coefficients are for straight mass transfer without chemical reaction and are therefore based on flow through the whole film of thickness Xq. 

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. 

If there is mass transfer without chemical reaction, Eq. (2.17) gives the equation of continuity for substance A... 

As a result, we are much better off to use existing experimental correlations for mass transfer without reaction and to calculate a correction factor for the chemical reaction. Calculating this correction turns out to be easy for a first-order system. Moreover, we make good use of the 50 years of empirical correlations carefully obtained for industrial equipment. We next detail how this is achieved. 

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. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

I. Residence-Time Model for Total Mass Transfer with and without Chemical Reaction... 

Solutions for diffusion with and without chemical reaction in continuous systems have been reported elsewhere (G2, G6). In general, all the parameters in this model can be determined or estimated, and the theoretical expressions may assist in the interpretation of mass-transfer data and the prediction of equipment performance. 

Gal-Or and Hoelscher (G5) have recently proposed a mathematical model that takes into account interaction between bubbles (or drops) in a swarm as well as the effect of bubble-size distribution. The analysis is presented for unsteady-state mass transfer with and without chemical reaction, and for steady-state diffusion to a family of moving bubbles. 

In this chapter, consideration will be given to the basic principles underlying mass transfer both with and without chemical reaction, and to the models which have been proposed to enable the rates of transfer to be calculated. The applications of mass transfer to the design and operation of separation processes are discussed in Volume 2, and ihe design of reactors is dealt with in Volume 3. 

The Hatta criterion compares the rates of the mass transfer (diffusion) process and that of the chemical reaction. In gas-liquid reactions, a further complication arises because the chemical reaction can lead to an increase of the rate of mass transfer. Intuition provides an explanation for this. Some of the reaction will proceed within the liquid boundary layer, and consequently some hydrogen will be consumed already within the boundary layer. As a result, the molar transfer rate JH with reaction will be higher than that without reaction. One can now feel the impact of the rate of reaction not only on the transfer rate but also, as a second-order effect, on the enhancement of the transfer rate. In the case of a slow reaction (see case 2 in Fig. 45.2), the enhancement is negligible. For a faster reaction, however, a large part of the conversion occurs in the boundary layer, and this results in an overall increase of mass transfer (cases 3 and 4 in Fig. 45.2). 

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)... 

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