Mass transfer dispersed flow

To simulate the effects of reaction kinetics, mass transfer, and flow pattern on homogeneously catalyzed gas-liquid reactions, a bubble column model is described [29, 30], Numerical solutions for the description of mass transfer accompanied by single or parallel reversible chemical reactions are known [31]. Engineering aspects of dispersion, mass transfer, and chemical reaction in multiphase contactors [32], and detailed analyses of the reaction kinetics of some new homogeneously catalyzed reactions have been recently presented, for instance, for polybutadiene functionalization by hydroformylation in the liquid phase [33], car-bonylation of 1,4-butanediol diacetate [34] and hydrogenation of cw-1,4-polybutadiene and acrylonitrile-butadiene copolymers, respectively [10], which can be used to develop design equations for different reactors. 

We have attempted to present here, in a rather condensed form, a vievc of the present status of the fxmdamentals of preparative and nonlinear chromatography. The fundamental problems and the various models used to model chromatography are discussed first (Chapter 2). As the thermodynamics of phase equilibrium is central to the separation process, whatever model is used, we devote two chapters to the discussion of equilibrium isotherms, for single components (Chapter 3) and mixtures (Chapter 4). A chapter on the problems of dispersion, mass transfer and flow rate in chromatography (Chapter 5) completes the fundamental bases needed for the thorough discussion of preparative chromatography. 

As in ideal reactors, the kinetics and reaction conditions are similar. However, the distribution of products is quite different and to correlate them with the experiments, it requires a more detailed study of the conditions of nonideality, for example, interfacial and surface phenomena, heat and mass transfer, and flows types. These phenomena characterize the axial and radial dispersion, caused by diffusion and convection. 

It is very important to understand key elements of the hydrodynamic behavior of gas-fluidized beds before planning new applications or undertaking design, since the flow characteristics affect gas-soUd contacting, heat and mass transfer, dispersion of the gas as it passes through the bed, entrainment, attrition, wear, and so on, all of which are related to overall process and reactor performance. 

Fig. 17. Effect of axial dispersion in both phases on solute distribution through countercurrent mass transfer equipment. A, piston or plug flow B, axial...

Convection heat transfer is dependent largely on the relative velocity between the warm gas and the drying surface. Interest in pulse combustion heat sources anticipates that high frequency reversals of gas flow direction relative to wet material in dispersed-particle dryers can maintain higher gas velocities around the particles for longer periods than possible ia simple cocurrent dryers. This technique is thus expected to enhance heat- and mass-transfer performance. This is apart from the concept that mechanical stresses iaduced ia material by rapid directional reversals of gas flow promote particle deagglomeration, dispersion, and Hquid stream breakup iato fine droplets. Commercial appHcations are needed to confirm the economic value of pulse combustion for drying. 

Commonly, the most important feature of a nozzle is the size of droplet it produces. Since the heat or mass transfer that a given dispersion can produce is often proportional to (1/D ) , fine drops are usually favored. On the other extreme, drops that are too fine will not settle, and a concern is the amount of liquid that will be entrained from a given spray operation. For example, if sprays are used to contact atmospheric air flowing at 1.5 m/s, drops smaller than 350 [Lm [terminal velocity = 1.5 m/s (4.92 ft/s)] will be entrained. Even for the relative coarse spray of the hoUow-cone nozzle shown in Fig. 14-88, 7.5 percent of the total hquid mass will be entrained. 

Neglecting flow nonuniformities, the contributions of molecular diffusion and turbulent mixing arising from stream sphtting and recombination around the sorbent particles can be considered additive [Langer et al., Int. ]. Heat and Mass Transfer, 21, 751 (1978)] thus, the axial dispersion coefficient is given by ... 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

Countereurrent bubble flow with liquid-supported solids, whieh ean be affeeted by downward liquid fluidization of partieles having a density lower than that of the liquid, has been referred to as inverse three-phase fluidization. The mass transfer potential of sueh a eountercurrent operation is worthy of study, especially for cases in whieh dispersion of the gas rather than the liquid is ealled for and the required gas-liquid ratio and throughput ean be effected without flooding. In contrast, the eorresponding eoeurrent mode has reeeived more attention than all other eases and eonstitutes the majority of the literature on three-phase fluidization. 

The main relationships between the agitation intensity of the dispersion and the total mass-transfer rate are summarized qualitatively for constant gas flow rate by Fig. 1 (G9) wherein interaction effects among the bubbles are indicated by dashed lines. Intermediate phenomena not shown, such as the direct and feedback effects between coalescence and mass transfer (G5, G9), should also be considered. 

In Section I, a qualitative schematic description of the main connection between increased agitation intensity and increased total mass-transfer rate was given. It can readily be seen from this description that further research in gas and liquid flow patterns and in the area of relative bubble velocities in dispersions will contribute to the basic knowledge necessary for understand ing the real mechanisms occurring in these systems. 

Certain hydrodynamical problems, as well as mass-transfer problems in the presence of surface-active agents, have been investigated theoretically under steady-state conditions (L3, L4, L10, R9). However, if we take into account the fact that in gas-liquid dispersions, the nonstationary term must appear in the equation of mass- or heat-transfer, it becomes apparent that an exact analysis is possible if a mixing-contacting mechanism is adopted instead of a theoretical streamline flow around a single bubble sphere. 

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