Mass diffusion process description

This simplified description of molecular transfer of hydrogen from the gas phase into the bulk of the liquid phase will be used extensively to describe the coupling of mass transfer with the catalytic reaction. Beside the Henry coefficient (which will be described in Section 45.2.2.2 and is a thermodynamic constant independent of the reactor used), the key parameters governing the mass transfer process are the mass transfer coefficient kL and the specific contact area a. Correlations used for the estimation of these parameters or their product (i.e., the volumetric mass transfer coefficient kLo) will be presented in Section 45.3 on industrial reactors and scale-up issues. Note that the reciprocal of the latter coefficient has a dimension of time and is the characteristic time for the diffusion mass transfer process tdifl-GL=l/kLa (s). 

The following, well-acceptable assumptions are applied in the presented models of automobile exhaust gas converters Ideal gas behavior and constant pressure are considered (system open to ambient atmosphere, very low pressure drop). Relatively low concentration of key reactants enables to approximate diffusion processes by the Fick s law and to assume negligible change in the number of moles caused by the reactions. Axial dispersion and heat conduction effects in the flowing gas can be neglected due to short residence times ( 0.1 s). The description of heat and mass transfer between bulk of flowing gas and catalytic washcoat is approximated by distributed transfer coefficients, calculated from suitable correlations (cf. Section III.C). All physical properties of gas (cp, p, p, X, Z>k) and solid phase heat capacity are evaluated in dependence on temperature. Effective heat conductivity, density and heat capacity are used for the entire solid phase, which consists of catalytic washcoat layer and monolith substrate (wall). 

The above description is of a thermally propagating steady-state wave. It must be emphasized, however, that the basic feature of a thermal mechanism is not altered by the superposition of molecular diffusion onto the diffusional transport of heat. This applies not only to interdiffusion of reactants and products but also to the diffusion of chain carriers participating in the chemical reaction, provided that the chains are unbranched. The reason for this is that in a wave driven by a diffusion process, the source strength of an entering mass element must continue to grow despite the drain by the adjacent sink region. This growth can occur only if the reaction rate is increased by a product of the reaction, which may be temperature as well as a material product. 

For k>kf the adspecies mass transfer process is described by the diffusion Eq. (63). If the species migration in the subsurface region and the exchange with the gaseous phase occur fast, then k — l, therefore the boundary condition comprises the 3rd kind condition. Otherwise, it would be necessary to take into account the temporal evolution of the species in subsurface layers k , and the kinetic equations for these layers can contain the time derivatives. Most works devoted to mass transfer problems and also to the surface segregation of the alloy components [155,173]. The boundary conditions in the non-ideal systems are discussed in Ref. [174]. They require the use of equations for the pair functions of the type d(6,Jkq)/dx — 0. When describing the interphase boundary motion, the 3rd kind boundary conditions are also possible, although the 1st and the 2nd kind conditions are used more often. The latter are mainly applied to the description of many problems with species redistribution in the closed volume [175],... 

Mass transport processes - diffusion, migration, and - convection are the three possible mass transport processes accompanying an - electrode reaction. Diffusion should always be considered because, as the reagent is consumed or the product is formed at the electrode, concentration gradients between the vicinity of the electrode and the bulk solution arise, which will induce diffusion processes. Reactant species move in the direction of the electrode surface and product molecules leave the interfacial region (- interface, -> interphase) [i-v]. The - Nernst-Planck equation provides a general description of the mass transport processes. Mass transport is frequently called mass transfer however, it is better to reserve that term for the case that mass is transferred from one phase to another phase. 

The diffusion-layer imaging technique which was developed by McCreery is another method for studying intermediates in the diffusion layer [71-75]. A laser beam is directed in a parallel direction through the diffusion layer of the electrode and the light is then magnified and focused on a diode-array detector. With this method, spatial resolution of the diffusion layer of 1.25 pm is achieved, and concentration profiles in the diffusion layer are mapped. A detailed description of mass transport processes as well as the kinetics and spectra of intermediates can be obtained. Diffusion coefficients and extinction coefficients for, for example, the benzophenone radical anion were measured with this technique [74, 75]. 

In the description of the interphase mass transfer process, a variety of measures for constituent concentrations, mixture reference velocities, and diffusion fluxes (with respect to the arbitrarily defined mixture velocity) are used. Table 1.1 summarizes the most commonly used concentration measures together with a number of other quantities that will be needed from time to time. 

The result obtained from the film theory is that the mass transfer coefficient is directly proportional to the diffusion coefficient. However, the experimental mass transfer data available in the literature [6], for gas-liquid interfaces, indicate that the mass transfer coefficient should rather be proportional with the square root of the diffusion coefficient. Therefore, in many situations the film theory doesn t give a sufficient picture of the mass transfer processes at the interfaces. Furthermore, the mass transfer coefficient dependencies upon variables like fluid viscosity and velocity are not well understood. These dependencies are thus often lumped into the correlations for the film thickness, 1. The film theory is inaccurate for most physical systems, but it is still a simple and useful method that is widely used calculating the interfacial mass transfer fluxes. It is also very useful for analysis of mass transfer with chemical reaction, as the physical mechanisms involved are very complex and the more sophisticated theories do not provide significantly better estimates of the fluxes. Even for the description of many multicomponent systems, the simplicity of the model can be an important advantage. 

Tha transport mechanisms of molecular diffusion and mass carried by eddy motion are again assumed edditive although the contribution of the molecular diffusivity term is quite small except in the region nenr a wall where eddy motion is limited. The eddy diffusivity is directly applicable to problems snch as the dispersion of particles or species (pollutants) from a souree into a homogeneously turbulent air stream in which there is little shear stress. The theories developed by Taylor.36 which have been confirmed by a number of experimental investigations, can describe these phenomena. Of more interest in chemical engineering applications is mass transfer from a turbolent fluid to a surface or an interface. In this instance, turbulent motion may he damped oni as the interface is approached aed the contributions of both molecolar and eddy diffusion processes must he considered. To accomplish this. 9ome description of the velocity profile as the interface is approached must be available. 

In the description of mass transfer processes another fluid layer is frequently postulated, viz. the stagnant film (see Figure 6.8) or, as it is sometimes called, the effective film for mass transfer , 8. This hypothetical film is not the same thing as the more fundamental diffusion boundary layer 6n, but it may be considered to be of the same order of magnitude. 

This order of magnitude of 100 suggests that the viscous flow is so significant in this capillary of 1 micron, and hence any disturbance in the total pressure will be dissipated very quickly by the action of the viscous flow before any diffusive processes occur. For smaller pores, say r = 0.2 micron, the viscous parameter O is equal to 1, suggesting that the viscous flow is very comparable to the diffusion flow and it can not be neglected in the description of flow into the particle. What this means is that the total pressure variation will persist in the system while the mass transfers of all diffusing species are occurring. 

AH mass transport processes, which can be defined as the technology for moving one species in a mixture relative to another, depend ultimately upon diffusion as the basis for the desired selective motion. Diffusion takes many forms, and a general description is provided in Table 115.7 of Chapter 115 of previous edition. However, a great deal of information can often be obtained by carefully written statements of simple constraints, and that of conservation of mass is the most useful for our purposes. We shall begin with examples where this suffices and show how one can determine the vaUdity of such a simple approach. We then proceed to situations where more detailed analysis is needed. 

In the film theory description of the mass-transfer process occurring between two fluid phases or between a solid and a fluid phase, the complex mass-transfer phenomenon is substituted by the notion of simple molecular diffusion of the species through a stagnant fluid fUm of thickness <5. The actual concentration profiles of species A being transferred from phase 2 to phase 1 are shown in Figures 3.1.6 (a) and (b) in one phase only for a solid-liquid and a gas-iiquid system, respectively. The concentration of A in the liquid phase at the solid-liquid or the gas-Uquid interface is C. Far away from the interface it is reduced to a low value in the liquid phase. In turbulent flow, the curved profile of species A shown would correspond to the time-averaged value (Bird et al, 1960, 2002). According to the... 

Oscillatory behavior observed as periodic potential transients at constant current or periodic current transients at constant potential is found frequently when more than two parallel electrode reactions are coupled. Usually, an upper and a lower current-potential curve limit the oscillation region. These two curves represent stable states [139] according to the theory of stability of electrode states [140]. Oscillatory phenomena occurring during the oxidation of certain fuels on solid electrodes are discussed in this section. The discussion is not extended to porous electrodes because the theory of the diffusion electrode has not been developed to the point to allow an adequate description of the complex coupling of parallel electrode reactions and mass transport processes in the liquid and gaseous phase. 

In fact the piston flow model, as well as the diffusion model, gives too ideal picture of the structure of the flows. They take into account neither the diffusion boundary layer nor the real movement of the phases. These models are especially far from the real situation in flie apparatus in respect to the liquid phase which moves not like a piston flow but in the form of film, drops and jets which are not only separate in space but have also different and continuously changing velocities. Nevertheless, not only the diffusion model but in some cases also its simpler variant, the piston flow model, gives oflxm very good description of the mass transfer processes in industrial apparatuses. This can be explained with the comparatively weak influence of the real structure of the flows on the mass transfer. On the other side using in the model such experimentally obtained values as mass transfer coefficient, effective surface, and Peclet number, it is possible to take into account the important for the mass transfer rate characteristics of the flows structures. In Chaptra 8 the cases when it is possible to use the simpler piston flow model, and when it is necessary to use the diffusion model are considered and specified. 

The reactions are still most often carried out in batch and semi-batch reactors, which implies that time-dependent, dynamic models are required to obtain a realistic description of the process. Diffusion and reaction in porous catalyst layers play a central role. The ultimate goal of the modehng based on the principles of chemical reaction engineering is the intensification of the process by maximizing the yields and selectivities of the desired products and optimizing the conditions for mass transfer. 

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