Effects of Transport Phenomena

In the sections below a brief overview of static solvent influences is given in A3.6.2, while in A3.6.3 the focus is on the effect of transport phenomena on reaction rates, i.e. diflfiision control and the influence of friction on intramolecular motion. In A3.6.4 some special topics are addressed that involve the superposition of static and transport contributions as well as some aspects of dynamic solvent effects that seem relevant to understanding the solvent influence on reaction rate coefficients observed in homologous solvent series and compressed solution. More comprehensive accounts of dynamics of condensed-phase reactions can be found in chapter A3.8. chapter A3.13. chapter B3.3. chapter C3.1. chapter C3.2 and chapter C3.5. 

Minimize the effects of transport phenomena If we are interested in the intrinsic kinetic performance of the catalyst it is important to eliminate transport limitations, as these will lead to erroneous data. We will discuss later in this chapter how diffusion limitations in the pores of the catalyst influence the overall activation energy. Determining the turnover frequency for different gas flow velocities and several catalyst particle sizes is a way to establish whether transport limitations are present. A good starting point for testing catalysts is therefore ... 

The effect of transport phenomena on the overall electrode process can also be expressed in terms of the concentration or transport overpotential. The original concentration of the oxidized form cQx decreases during the cathodic process through depletion in the vicinity of the electrode to the value (c0x)x=o and, similarly, the concentration of the reduced form cRed increases to the value (cRed)A.=0. It follows from Eqs (5.4.18), (5.4.19) and (5.4.20) that... 

In the final, hydrodynamic stage, the system is described by the density, the average velocity, and the local temperature and evolves towards equilibrium by means of the effect of transport phenomena (conductivity, diffusion, viscosity,. . . ). This takes place in times of the order of the hydrodynamic time rh,... 

Finally, this study provides an extensive set of data on thick wood pyrolysis which can be better interpreted and generalized by the use of mathematical models taking into account the effects of transport phenomena and chemical reactions. Models including such features are already available in the literature (for instance, see References 23,24) and have proven to give quantitative predictions of temperature dynamics, but product yield predictions are still unacceptable, mainly because of unreliable kinetic constants. Therefore, this issue deserves further investigation before extensive computer simulation and/or development of more advanced physical models of thick wood pyrolysis are proposed. 

Chemical interactions at the solid phase may comprise (i) formation or rupture of a bond between sorbate and surface (ii) further reaction between adsorbed species and, (iii) rearrangements of the solid structure and formation and disappearance of solid species. It is often incorrect to apply simple kinetic models such as first- or second-order rate equations to such interactions because reacting solid surfaces are rarely homogeneous and because effects of transport phenomena and chemical reactions are often experimentally inseparable (Sparks, 1989). 

The effects of transport phenomena on the global reaction rate are prevalent in... 

The rate expressions derived above describe the dependence of die reaction rate expressions on kinetic parameters related to the chemical reactions. These rate expressions are commonly called the intrinsic rate expressions of the chemical reactions. However, as discussed in Chapter 1, in many instances, the local species concentrations depend also on the rate that the species are transported in the reaction medium. Hence, the actual reaction rates are affected by the transport rates of reactants and products. This is manifested in two general cases (i) gas-solid heterogeneous reactions, where species diffusion through the pore plays an important role, and (ii) gas-hquid reactions, where interfacial species mass-transfer rate as wen as solubility and diffusion play an important role. Considering the effect of transport phenomena on the global rates of the chemical reactions represents a very difficult task in the design of many chemical reactors. These topics are beyond the scope of this text, but the reader should remember to take them into consideration. 

Environmental problem solving creates major conflict areas with the politicians in developing countries. For example. Environmental Impact Assessment Studies is a good Eulerian approach to predict the effects of transport phenomena and a very convenient planning tool for future activities. However, in its application local politicians may block the scientific opinions from reaching the public. Thus new technologies such as pollution prevention measures are sometimes refused. Thus they cause local people to lose an economic benefit, although it ensures the future of politicians near election time. 

In studying the ideal reactors, which are limiting cases, no significant influence of other phenomena caused by the flow, the mass, and heat transfer. Therefore, the parameters studied so far were determined in kinetic regime and without considering the effects of transport phenomena. When this happens the actual rate is less than the intrinsic rate constant. 

In Chapter 7 the effects of transport phenomena on the scale of the reactor are considered. We call these macro flow effects. These can be described in terms of macro-mixing. For continuous reactors macro>mixing causes residence time distribution. Combined with micro-mixing this will lead to backmixing. When two or more phases are present in the reactor, the way these are each introduced into and removed from the reactor are quite essential for the performance of the reactor. These various effects are considered in this chapter in order to arrive at an integral reactor model. As in Chapter 3, only isothermal reactor models are considered so far. 

In recent times, considerable progress has been made in describing complicated flow patterns in vessels, with flow simulations. These are combined with measurements of local flow velocities. This leads to much more accurate predictions of the effects of transport phenomena. It is expected that in the future computational fluid dynamics" will be applied generally to chemical reactors (Trambouze, 1993). Until now, practical applications for reactors are still quite limited. 

In Chapter 3 we considered chemical reactors with ideal macro flow patterns where the reactor behaviour was independent of scale. In Chapters 4, 5 and 6 an overview was given of various physical phenomena on the intermediate scale, some of which interact with chemical reactions. Several of these phenomena are scale dependent. To arrive at integral reactor models, we have to consider macro-flow effects, i.e. the effects of transport phenomena on the scale of the reactor dimensions. These are as a rule strongly scale dependent. 

As a result, the limited ability of unit processes to create a viable niche for themselves within chemical engineering must ultimately be understood in terms which also involve unit operations. Although the historical resilience of unit processes turned out to be less than that of unit operations, it was no different in its essential elements. Studying the uneasy and ultimately unsuccessful career of unit processes can therefore be easily justified as a way to shed light on the far more successful career of unit operations. In particular, the career of unit processes raises a hypothesis about the evolution of unit operations. The staying power of unit operations was not so much because of the structural coherence of its conceptual elements as its essential links with social and, more specifically, professional groups. As a theoretical entity, unit operations appears far less stable and, in fact, appears quickly threatened by notions which rest on fewer and more fundamental scientific concepts. Ultimately, this threat came to be realized with the advent of transport phenomena, but this is another story. In effect, unit processes can be interpreted as both the attempt to extend the reach of unit operations and a symptom of their conceptual fragility. 

For the light molecules He and H2 at low temperatures (below about 50°C.) the classical theory of transport phenomena cannot be applied because of the importance of quantum effects. The Chapman-Enskog theory has been extended to take into account quantum effects independently by Uehling and Uhlenbeck (Ul, U2) and by Massey and Mohr (M7). The theory for mixtures was developed by Hellund and Uehling (H3). It is possible to distinguish between two kinds of quantum effects— diffraction effects and statistics effects the latter are not important until one reaches temperatures below about 1°K. Recently Cohen, Offerhaus, and de Boer (C4) made calculations of the self-diffusion, binary-diffusion, and thermal-diffusion coefficients of the isotopes of helium. As yet no experimental measurements of these properties are available. 

Equation (56) states that the effect of a thermal gradient on the material transport bears a reciprocal relationship to the effect of a composition gradient upon the thermal transport. Examples of Land L are the coefficient of thermal diffusion (S19) and the coefficient of the Dufour effect (D6). The Onsager reciprocity relationships (Dl, 01, 02) are based upon certain linear approximations that have a firm physical foundation only when close to equilibrium. For this reason it is possible that under circumstances in which unusually high potential gradients are encountered the coupling between mutually related effects may be somewhat more complicated than that indicated by Eq. (56). Hirschfelder (BIO, HI) discussed many aspects of these cross linkings of transport phenomena. 

The physical properties of most acids (esters) and alcohols allow the reaction to be carried out either in the liquid or in the vapour phase. In the liquid phase, the effects of solvents and of transport phenomena may play a more important role than in the vapour phase. On the other hand, the side reactions (mainly the ether and/or olefin formation from the alco- TABLE 20 Reactants and inorganic catalysts used in kinetic studies of esterification (transesterification) ... 

Effect of Critical Phenomena on Transport Properties in the Supercritical Region... 

The more active a catalyst is, the more difficult it is to obtain benefits, due to an increased influence of transport phenomena on the conversion rate for fast chemical reactions. For some types of chemical reactions, such as consecutive reactions with the intermediate as the desired product, an increase of catalytic activity may lead to undesired effects if transport phenomena inside and outside the catalyst pellet play a role. 

This chapter concerns the structures and propagation velocities of the deflagration waves defined in Chapter 2. Deflagrations, or laminar flames, constitute the central problem of combustion theory in at least two respects. First, the earliest combustion problem to require the simultaneous consideration of transport phenomena and of chemical kinetics was the deflagration problem. Second, knowledge of the concepts developed and results obtained in laminar-flame theory is essential for many other studies in combustion. Attention here is restricted to the steadily propagating, planar laminar flame. Time-dependent and multidimensional effects are considered in Chapter 9. 

Bizzi, M., Basini, L., Saracco, G., and Specchia, V. Short contact time catalytic partial oxidation of methane Analysis of transport phenomena effects. Chemical Engineering Journal, 2002, 90, 97. 

It must be stressed that although the trend observed in the coastal zone of the Ross Sea was not so marked and regular as the results of Saager et al., the effect of local phenomena can be assumed. In fact, glacier transport and the ice pack formation/dissolution cycle can play a fundamental role in the composition of surface coastal sea water. However, more detailed information about the local sources (eolian dust composition and deposition rate, glacier composition and dissolution rate, effect of pack ice dissolution and formation) are necessary to establish the origin of the surface water enrichment. 

Fig. 5). Although the reasons for this effect were not perfectly clear, they concluded that small amounts of impurities do have a significant effect on transport phenomena in ionic liquids. 

A fundamental shortcoming of the Chilton-Colburn approach for multicomponent mass transfer calculations is that the assumed dependence of [/ ] on [Sc] takes no account of the variations in the level of turbulence, embodied by r turb/, with variations in the flow conditions. The reduced distance y is a function of the Reynolds number y = (y/R )(//8) / Re consequently. Re affects the reduced mixing length defined by Eq. 10.2.21. An increase in the turbulence intensity should be reflected in a relative decrease in the influence of the molecular transport processes. So, for a given multicomponent mixture the increase in the Reynolds number should have the direct effect of reducing the effect of the phenomena of molecular diffusional coupling. That is, the ratios of mass transfer coefficients 21/ 22 should decrease as Re increases. 

Some authors (7, ) have used measured parameters of solute and solvent transport for calculation of membrane pore size distributions. Difficulties associated with this approach are of both experimental and theoretical nature. The experiments need to be carried out under conditions that minimize or eliminate effects of boundary phenomena (polarization) and of solute adsorption (fouling) on the measured coefficients. This is rarely done. An even more serious obstacle in this approach is the absence of quantitative and valid relations between measured transport parameters and the size parameters of a "representative pore."... 

---