References mass transfer Chapter

Transfer units are also used extensively in the calculation of mass transfer rates in countercurrent columns and reference should be made to Chapter 10. 

In the processing of materials it is often necessary either to increase the amount of vapour present in a gas stream, an operation known as humidification or to reduce the vapour present, a process referred to as dehumidification. In humidification, the vapour content may be increased by passing the gas over a liquid which then evaporates into the gas stream. This transfer into the main stream takes place by diffusion, and at the interface simultaneous heat and mass transfer take place according to the relations considered in previous chapters. In the reverse operation, that is dehumidification, partial condensation must be effected and the condensed vapour removed. 

The present book is devoted to both the experimentally tested micro reactors and micro reaction systems described in current scientific literature as well as the corresponding processes. It will become apparent that many micro reactors at first sight simply consist of a multitude of parallel channels. However, a closer look reveals that the details of fluid dynamics or heat and mass transfer often determine their performance. For this reason, besides the description of the equipment and processes referred to above, this book contains a separate chapter on modeling and simulation of transport phenomena in micro reactors. 

An overview of this kind is, of necessity, limited in detail. Readers interested in a more thorough development of mass transfer principles are encouraged to consult the references listed at the end of the chapter. In particular, Cussler s excellent textbook on diffusion is an accessible introduction to the subject geared toward the physical scientist [11], Those with a more biological orientation may prefer Friedman s text on biological mass transfer [12], which is also exceptional. A classic reference in the field is Crank s Mathematics of Diffusion [13], which contains solutions to many important diffusion problems. 

The design of two-phase contactors with heat transfer requires a firm understanding of two-phase hydrodynamics in order to model effectively the heat- and mass-transfer processes. In this chapter we have pointed out areas where further theoretical and experimental research is critically needed. It is hoped that design engineers will be motivated to test the procedures presented, in combination with their use of the details from the original references, in the solution of pragmatic problems. 

In Volume 1, the behaviour of fluids, both liquids and gases is considered, with particular reference to their flow properties and their heat and mass transfer characteristics. Once the composition, temperature and pressure of a fluid have been specified, then its relevant physical properties, such as density, viscosity, thermal conductivity and molecular diffu-sivity, are defined. In the early chapters of this volume consideration is given to the properties and behaviour of systems containing solid particles. Such systems are generally more complicated, not only because of the complex geometrical arrangements which are possible, but also because of the basic problem of defining completely the physical state of the material. 

Many of the results and correlations in heat and mass transfer are expressed in terms of dimensionless groups such as the Nusselt, Reynolds and Prandtl numbers. The definitions of those dimensionless groups referred to in this chapter are given in Appendix 2. 

Another type of mass transfer equipment, shown in Figure 6.2d, is normally referred to as the packed- (fixed-) bed. Unlike the packed column for gas-liquid mass transfer, the packed-bed column is used for mass transfer between the surface of packed solid particles (e.g., catalyst particles or immobilized enzyme particles) and a single-phase liquid or gas. This type of equipment, which is widely used as reactors, adsorption columns, chromatography columns, and so on, is discussed in greater detail in Chapters 7 and 11. 

The film model referred to in Chapters 2 and 5 provides, in fact, an oversimplified picture of what happens in the vicinity of interface. On the basis of the film model proposed by Nernst in 1904, Whitman [2] proposed in 1923 the two-film theory of gas absorption. Although this is a very useful concept, it is impossible to predict the individual (film) coefficient of mass transfer, unless the thickness of the laminar sublayer is known. According to this theory, the mass transfer rate should be proportional to the diffusivity, and inversely proportional to the thickness of the laminar film. However, as we usually do not know the thickness of the laminar film, a convenient concept of the effective film thickness has been assumed (as... 

The influences of the liquid and gas flow rates, the diameter of the absorption chamber, the distance between nozzles, and the flow configuration on absorption rate were studied by the researchers mentioned above. These will not be discussed in detail here because of the length limitation of the chapter for the details, the reader may refer to the original references as cited in the text above. It should be noted, however, that in all the investigations above, the data for mass transfer coefficients are always correlated with the gas and/or liquid flow rates, but not with the impinging velocity, m0, although the latter is the operation parameter extremely important in every impinging stream device. 

This equation expresses the fact that in a process with the various flow rates /, work is continuously dissipated to overcome the barriers, the resistance, or the friction that all the processing such as heat and mass transfer and chemical conversion introduce. In Chapter 5, we refer to this as the result of the "magic triangle." There is no clearer way to illustrate the origin of the process s energy bill, nor a better way to calculate it. This relation also defines the challenge that in order to keep the energy bill as low as possible one should find, as Bejan calls it, "the path of least resistance" [6]. 

This chapter describes the fundamental principles of heat and mass transfer in gas-solid flows. For most gas-solid flow situations, the temperature inside the solid particle can be approximated to be uniform. The theoretical basis and relevant restrictions of this approximation are briefly presented. The conductive heat transfer due to an elastic collision is introduced. A simple convective heat transfer model, based on the pseudocontinuum assumption for the gas-solid mixture, as well as the limitations of the model applications are discussed. The chapter also describes heat transfer due to radiation of the particulate phase. Specifically, thermal radiation from a single particle, radiation from a particle cloud with multiple scattering effects, and the basic governing equation for general multiparticle radiations are discussed. The discussion of gas phase radiation is, however, excluded because of its complexity, as it is affected by the type of gas components, concentrations, and gas temperatures. Interested readers may refer to Ozisik (1973) for the absorption (or emission) of radiation by gases. The last part of this chapter presents the fundamental principles of mass transfer in gas-solid flows. 

This chapter is concerned with the mathematical modeling of coupled chemical reaction and heat and mass transfer processes occurring in porous catalysts. It focuses primarily on steady state catalyst operation which is the preferred industrial practice. Stationary operation may be important for the startup and shutdown of an industrial reactor, or with respect to dynamic process control. However, these effects are not discussed here in great detail because of the limited space available. Instead, the interested reader is referred to the various related monographs and articles available in the literature [6, 31, 46-49]. 

Then die solution of a mass ditfusion problem can be obtained directly from the analytical or graphical solution of the corresponding heat conduction problem given in Chapter 4. The analogous quantities between heat and mass transfer are summarized in Table 14-11 for easy reference. Tor the case of a seiiii-Lnfinite medium with constant surface concentration, for example, the solution can be expressed in an analogous manner to Eq. 1-45 as... 

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. 

For multiphase reactive systems of types (a) and (b), at least one of the reactants has to reach the reaction zone from a different phase. In such systems, generally mass transfer between these two different phases (and its interaction with chemical reactions) is of primary importance and turbulent mixing is often of secondary importance. For such systems, modeling multiphase flows as discussed in Chapter 4 is directly applicable. The only additional complexity is the possibility of interaction between mass transfer and chemical reactions. The typical interphase mass transfer source for component k between phases p and q can be written (for the complete species conservation equation, refer to Chapter 4) ... 

If the flows are unsteady, the terms containing apo can be added on both sides of Eq. (7.10) (refer to Section 6.4). It must be noted that for multiphase flows, the inflow and outflow terms require considerations of interpolations of phase volume fractions in addition to the usual interpolations of velocity and the coefficient of diffusive transport. The source term linearization practices discussed in the previous chapter are also applicable to multiphase flows. It is useful to recognize that special sources for multiphase flows, for example, an interphase mass transfer, is often constituted of terms having similar significance to the a and b terms. Such discretized equations can be formulated for each variable at each computational cell. The issues related to the phase continuity equation, momentum equations and the pressure correction equation are discussed below. 

Real chromatograms (Fig. 2.6-3) take into account the thermodynamic influences as well as the kinetics of mass transfer and fluid distribution. A rectangular concentration profile of the solute at the entrance of the column soon changes into a bell-shape Gaussian distribution, if the isotherm is linear. Figure 2.7a shows this distribution and some characteristic values, which will be referred to in subsequent chapters. With mass transfer resistance or nonlinear isotherms the peaks become asym-... 

The Fick [D] exhibits a complex composition dependence, reflecting as it does both frictional and thermodynamic interactions and the elements D-j cannot be interpreted simply. The elements D j are dependent on the choice of the reference velocity frame. Since [D] is a product of two positive definite matrices [//] and [G], the Fick [D] is positive definite. The Fick [D] is singular at the critical point, which imparts some interesting characteristics to the mass transfer trajectories in that region (see Chapter 5). The symmetry of [H] and [G] matrices places restrictions on the elements of [D] and only — 1) of the D j are independent. The Fick formulation is more easily introduced into the continuity equations and in this sense they are often referred to as being practical. ... 

In Chapter 10, we chose to describe the mass transfer process using mass fluxes and the mass average reference velocity frame because of the need later to solve the equations of continuity of mass in conjunction with the equations of motion. In terms of these mass fluxes the energy flux is given by... 

Chapter 1 serves to remind readers of the basic continuity relations for mass, momentum, and energy. Mass transfer fluxes and reference velocity frames are discussed here. Chapter 2 introduces the Maxwell-Stefan relations and, in many ways, is the cornerstone of the theoretical developments in this book. Chapter 2 includes (in Section 2.4) an introductory treatment of diffusion in electrolyte systems. The reader is referred to a dedicated text (e.g., Newman, 1991) for further reading. Chapter 3 introduces the familiar Fick s law for binary mixtures and generalizes it for multicomponent systems. The short section on transformations between fluxes in Section 1.2.1 is needed only to accompany the material in Section 3.2.2. Chapter 2 (The Maxwell-Stefan relations) and Chapter 3 (Fick s laws) can be presented in reverse order if this suits the tastes of the instructor. The material on irreversible thermodynamics in Section 2.3 could be omitted from a short introductory course or postponed until it is required for the treatment of diffusion in electrolyte systems (Section 2.4) and for the development of constitutive relations for simultaneous heat and mass transfer (Section 11.2). The section on irreversible thermodynamics in Chapter 3 should be studied in conjunction with the application of multicomponent diffusion theory in Section 5.6. 

Diffusion coefficients are important for mass-transfer operations (see Chapter 8, Mass Transfer ). There are several differently defined diffusion coefficients (self-diffusion coefficient, interdiffusion [or mutual diffusion] coefficient, intradiffusion [or tracer diffusion] coefficient) this can be a source of confusion. These are delineated in standard references [15, 68, 69]. 

The physical aspects of gas-liquid, liquid-liquid, solid-liquid, and gas-liquid-solid systems are discussed in the subsequent sections of this chapter. Using the guidelines given there, it is possible to get an estimate of local and average mass-transfer coefficients, interfacial areas, and contacting patterns. This section briefly considers the effect of reactions on mass transfer, a subject treated elsewhere in this handbook and in advanced texts [29, 30]. Note that while we will refer mostly to gas-liquid systems, the same treatment would more or less apply to liquid-liquid and liquid-solid systems. In the case of gas-liquid-solid systems, it may be possible to determine the controlling resistance and simplify the analysis to a two-phase system, as far as the reaction part is concerned. 

The volumetric mass-transfer coefficient, k a, increases as the stirrer speed increases. (Refer to correlations given in Section 9.7 later in this chapter.) If the process is bulk-reaction controlled, then the stirrer speed increases and the volumetric mass-transfer coefficient, kija, increases (refer to correlations given in Section 9.7). If the process is mass-transfer controlled (regimes 2, 3, 4),... 

Inverse mass balance modeling here only employs the mass balance principle thermodynamics and equilibrium are not considered. Inverse models are usually nonunique. A number of combinations of mass transfer reactions can produce the same observed concentration changes along the flow path. Mass transfer reactions here refer to the reactions that result in the mass transfer between two or more phases, such as the dissolution of solid and gas or precipitation of solids. Chapter 9 describes the details of the models and shows a few examples. 

Reactions carried out in supercritical fluids have been found to accelerate the reaction rate greatly.- By manipulating the properties of the solvent in which the reaction is taking place, interphase mass transfer limitations can be eliminated. Application of transition states theory discussed in the Professional Reference Shelf on the CD-ROM of Chapter 3 has proven useful in the analysis of these reactions,... 

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