Transport processes types

Specific reactor characteristics depend on the particular use of the reactor as a laboratory, pilot plant, or industrial unit. AH reactors have in common selected characteristics of four basic reactor types the weH-stirred batch reactor, the semibatch reactor, the continuous-flow stirred-tank reactor, and the tubular reactor (Fig. 1). A reactor may be represented by or modeled after one or a combination of these. SuitabHity of a model depends on the extent to which the impacts of the reactions, and thermal and transport processes, are predicted for conditions outside of the database used in developing the model (1-4). 

FIG. 23-24 Reactors with moving catalysts, a) Transport fluidized type for the Sasol Fischer-Tropsch process, nonregenerating, (h) Esso type of stable fluidized bed reactor/regeuerator for cracldug petroleum oils, (c) UOP reformer with moving bed of platinum catalyst and continuous regeneration of a controlled quantity of catalyst, (d) Flow distribution in a fluidized bed the catalyst rains through the bubbles. 

All criteria proposed here are constructed such that if absolutely no gradient of a particular type exists, then the value of the corresponding criterion is zero. For fast catalytic processes this is not reasonable to expect and therefore a value judgment must be made for how much deviation from zero can be ignored. For the dimensionless expressions the Damkdhler numbers are used as these are applied to each particular condition. The approach is that the Damkdhler numbers can be calculated from known system values, which are related to the unknown driving forces for the transport processes. 

From a thermodynamic and kinetic perspective, there are only three types of membrane transport processes passive diffusion, faeilitated diffusion, and active transport. To be thoroughly appreciated, membrane transport phenomena must be considered in terms of thermodynamics. Some of the important kinetic considerations also will be discussed. 

It seems probable that a fruitful approach to a simplified, general description of gas-liquid-particle operation can be based upon the film (or boundary-resistance) theory of transport processes in combination with theories of backmixing or axial diffusion. Most previously described models of gas-liquid-particle operation are of this type, and practically all experimental data reported in the literature are correlated in terms of such conventional chemical engineering concepts. In view of the so far rather limited success of more advanced concepts (such as those based on turbulence theory) for even the description of single-phase and two-phase chemical engineering systems, it appears unlikely that they should, in the near future, become of great practical importance in the description of the considerably more complex three-phase systems that are the subject of the present review. 

This chapter focuses on types of models used to describe the functioning of biogeochemical cycles, i.e., reservoir or box models. Certain fundamental concepts are introduced and some examples are given of applications to biogeochemical cycles. Further examples can be found in the chapters devoted to the various cycles. The chapter also contains a brief discussion of the nature and mathematical description of exchange and transport processes that occur in the oceans and in the atmosphere. This chapter assumes familiarity with the definitions and basic concepts listed in Section 1.5 of the introduction such as reservoir, flux, cycle, etc. 

The advent of fast computers and the availability of detailed data on the occurrence of certain chemical species have made it possible to construct meaningful cycle models with a much smaller and faster spatial and temporal resolution. These spatial and time scales correspond to those in weather forecast models, i.e. down to 100 km and 1 h. Transport processes (e.g., for CO2 and sulfur compounds) in the oceans and atmosphere can be explicitly described in such models. These are often referred to as "tracer transport models." This type of model will also be discussed briefly in this chapter. 

The selection of reactor type in the traditionally continuous bulk chemicals industry has always been dominated by considering the number and type of phases present, the relative importance of transport processes (both heat and mass transfer) and reaction kinetics plus the reaction network relating to required and undesired reactions and any aspects of catalyst deactivation. The opportunity for economic... 

Transport processes of this type are called nonfaradaic transport. The nonfaradaic transport considered here is a steady-state process, in contrast to nonfaradaic currents mentioned previously that were due, for example, to charging of the electric double layer. Electrokinetic processes are of great practical significance, as discussed in Section 31.3. 

As a rotating disk is a very useful device for many types of electrochemical research, convective diffusion to a rotating disk, treated theoretically by V. G. Levich, will be used here as an example of this type of transport process. Consider a disk in the xz plane, rotating around the y axis with radial velocity a) (see Fig. 2.22). If the radius of the disk is sufficiently larger... 

A number of transport mediators are transport proteins in the absence of an external energy supply, thermal motion leads to their conformational change or rotation so that the transported substance, bound at one side of the membrane, is transferred to the other side of the membrane. This type of mediator has a limited number of sites for binding the transported substance, so that an increase in the concentration of the latter leads to saturation. Here, the transport process is characterized by specificity for a given substance and inhibition by other transportable substances competing for binding sites and also by various inhibitors. When the concentrations of the transported substance are identical on both sides of the membrane,... 

An alternative to the stirred tank system is a column-type device which provides for constant fluid flow through a powder bed. The mass transport process was shown to be primarily determined by the length and cross-sectional area of the cylinder and the fluid flow rate [36],... 

Bulk or forced flow of the Hagan-Poiseuille type does not in general contribute significantly to the mass transport process in porous catalysts. For fast reactions where there is a change in the number of moles on reaction, significant pressure differentials can arise between the interior and the exterior of the catalyst pellets. This phenomenon occurs because there is insufficient driving force for effective mass transfer by forced flow. Molecular diffusion occurs much more rapidly than forced flow in most porous catalysts. 

There are three types of mass transport processes within a microfluidic system convection, diffusion, and immigration. Much more common are mixtures of three types of mass transport. It is essential to design a well-controlled transport scheme for the microsystem. Convection can be generated by different forces, such as capillary effect, thermal difference, gravity, a pressurized air bladder, the centripetal forces in a spinning disk, mechanical and electroosmotic pumps, in the microsystem. The mechanical and electroosmotic pumps are often used for transport in a microfluidic system due to their convenience, and will be further discussed in section 11.5.2. The migration is a direct transport of molecules in response to an electric field. In most cases, the moving... 

The types of systems we deal with are primarily gas-solid (Section 9.1) and gas-liquid (Section 9.2). In these cases, we assume first- or second-order kinetics for the intrinsic reaction rate. This enables analytical expressions to be developed in some situations for the overall rate with transport processes taken into account. Such reaction models are incorporated in reactor models in Chapters 22 and 24. 

In biological systems, one often observes membrane structures with nonzero spontaneous curvatures, e.g. in mitochondria. This type of bilayer structure is also essential in various transport related processes such as endo- and exocy-tosis (see Chapter 8 of this volume). These curved membrane systems may be stabilised by protein aggregation in the bilayer, or may be the result of the fact that biological membranes are constantly kept off-equilibrium by lipid transport and/or by (active) transport processes across the bilayer. These interesting... 

Let us consider the transport of one component i in a liquid solution. Any disequilibration in the solution is assumed to be due to macroscopic motion of the liquid (i.e. flow) and to gradients in the concentration c,. Temperature gradients are assumed to be negligible. The transport of the solute i is then governed by two different modes of transport, namely, molecular diffusion through the solvent medium, and drag by the moving liquid. The combination of these two types of transport processes is usually denoted as the convective diffusion of the solute in the liquid [25] or diffusion-advection mass transport [48,49], The relative contribution of advection to total transport is characterised by the nondimensional Peclet number [32,48,49], while the relative increase in transport over pure diffusion due to advection is Sh - 1, where Sh is the nondimensional Sherwood number [28,32,33,49,50]. 

The data of figure 2 demonstrate, that at the present choice (3=0,25 in reesterification reaction course only antipersistent (subdiffusive) transport processes are possible (a=l is achieved for low-molecular substances with Df= 0 only), i.e., active time is always smaller than real time. This indicates on the important role of Levy flights in strange diffusion type definition. 

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