Modeling mass transfer effects

One goal of catalyst designers is to constmct bench-scale reactors that allow determination of performance data truly indicative of performance in a full-scale commercial reactor. This has been accompHshed in a number of areas, but in general, larger pilot-scale reactors are preferred because they can be more fully instmmented and can provide better engineering data for ultimate scale-up. In reactor selection thought must be given to parameters such as space velocity, linear velocity, and the number of catalyst bodies per reactor diameter in order to properly model heat- and mass-transfer effects. 

An examination of the catalyst-layer models reveals the fact that there are many more cathode models than anode ones. In fact, basically every electrode-only model is for the cathode. This arises because the cathode has the slower reaction it is where water is produced, and hence, mass-transfer effects are much more significant and it represents the principal inefficiency of the fuel cell. In other words, while the cathode model can be separate from the anode model, the converse is not true due to the... 

A factor closely related to the catalyst loading is the efficiency or utilization of the electrode. This tells how much of the electrode is actually being used for electrochemical reaction and can also be seen as a kind of penetration depth. To examine ohmic and mass-transfer effects, sometimes an effectiveness factor, E, is used. This is defined as the actual rate of reaction divided by the rate of reaction without any transport (ionic or reactant) losses. With this introduction of the parameters and equations, the various modeling approaches can be discussed. 

The integral reactor is useful for modeling the operations of larger packed bed units with all their heat and mass transfer effects, particularly for systems where the feed and product consist of a variety of materials. 

The model provides a good approach for the biotransformation system and highlights the main parameters involved. However, prediction of mass transfer effects on the outcome of the process, through evaluation of changes in the mass transfer coefficients, is rather difficult. A similar mass transfer reaction model, but based on the two-film model for mass transfer for a transformation occurring in the bulk aqueous phase as shown in Figure 8.3, could prove quite useful. Each of the films presents a resistance to mass transfer, but concentrations in the two fluids are in equilibrium at the interface, an assumption that holds provided surfactants do not accumulate at the interface and mass transfer rates are extremely high [36]. 

The role of hydrate intrinsic kinetics has been more recently suggested to play a smaller role in hydrate growth in real systems than heat and mass transfer effects. In view of this, the discussion on the kinetics models is only briefly presented here. For a more thorough treatment, the reader is referred to the original references (Englezos et al., 1987a,b Malegaonkar et al., 1997). 

These results could suggest that what has been traditionally been described as "biphasic" behavior may reflect a combination of chemical reaction and mass transfer effects, with each limiting xylan reaction and removal at different stages or modes of operation. This effect might be better described by a model that incorporates reaction of solids to form soluble species as a function of temperature and acid concentration coupled with a second mass transfer step that is affected by flow. On this basis, we plan to investigate whether the pore leaching model could be simplified and adapted in this way to better describe hemicellulose hydrolysis. 

Many working groups have modeled the performance of diesel particulate traps during the past few decades. Concentrated parameter models (CSTR assumption) have been applied for the evaluation of formal kinetic models and model parameters. The formal kinetic parameters lump the heat and mass transfer effects with the reaction kinetics of the complicated reaction network of diesel soot combustion. Those models and model parameters were used for the characterization of the performance of different filter geometries and filter materials, as well as of the performance of a variety of catalytically active coatings and fuel additives [58],... 

Another enzyme that was studied extensively in microreactors to determine kinetic parameters is the model enzyme alkaline phosphatase. Many reports have appeared that differ mainly on the types of enzyme immobilization, such as on glass [413], PDMS [393], beads [414] and in hydrogels [415]. Kerby et al. [414], for example, evaluated the difference between mass-transfer effects and reduced effidendes of the immobilized enzyme in a packed bead glass microreactor. In the absence of mass-transfer resistance, the Michaelis-Menten kinetic parameters were shown to be flow-independent and could be appropriately predicted using low substrate conversion data. 

While the intrinsic activity and selectivity of a catalyst establish its performance in the absence of mass transfer effects, it is well known that the placement of the active components and access to these components by reactants can play a major role in the performance of practical catalysts. One of the challenges for reaction engineers is to develop models for predicting the distribution of active components in a catalyst and the effects of this distribution, together with the pore size distribution and particle size and shape, on the performance of a catalyst. 

To design large scale supercritical desorption processes is necessary to understand in which way dynamic desorption is influenced by process variables as mass transfer effects and equilibrium considerations. The governing equilibrium in all desorption processes is the adsorption equilibrium and a description of this equilibrium is essential in all desorption models and design equations [3]. 

There appear to have been few modelling efforts for hot-wall LPCVD reactors. Gieske et al. (28) and Hitchman et al. (29) present experimental data and discuss flow fields, mass transfer effects, and possible kinetics in rather general terms. A recent model by Kuiper et al. (30) cannot account for diffusion in the spaces between the wafers and the significant volume expansion commonly associated with LPCVD processes. Furthermore, it is restricted to isothermal conditions and plug flow in the main flow region in spite of the large diffusivities associated with LPCVD. 

Individual component efficiencies can vary as much as they do in this example only when the diffusion coefficients of the three binary pairs that exist in this system differ significantly For ideal or nearly ideal systems, all models lead to essentially the same results. This example demonstrates the importance of mass-transfer models for nonideal systems, especially when trace components are a concern. For further discussion of this example, see Doherty and Malone (op. cit.) and Baur et al. [AIChE J. 51,854 (2005)]. It is worth noting that there exists extensive experimental evidence for mass-transfer effects for this system, and it is known that nonequilibrium models accurately describe the behavior of this system, whereas equilibrium models (and equal-efficiency models) sometime... 

MODELS WHICH INCLUDE EXTERNAL MASS-TRANSFER EFFECTS... 

Sloot et al. [1990] presented a simplified isothermal CNMR/ORG model which assumes that the two chambers divided by the membrane are well mixed. In practical applications, the model needs to be incorporated into a more complex model which, for example, considers the effect of flow configuration (cocurrent or countercurrent mode). In their model, mass transfer in the direction perpendicular to a flat membrane (i.e., y-direction) is considered for a general instantaneous, reversible reaction... 

Many models use an apparent reaction rate [59], with an Arrhenius-type temperature dependence and, as a result, consider the diffusion and reaction on the interior surface of the catalyst only under certain restrictive assumptions. It is important to incorporate mass transfer effects within the washcoat in the model to give a realistic description of the processes in the monolith [54,60]. 

Ellison and Schmeal [19] explored a similar approach by using the corrosion of carbon steel in concentrated sulfuric acid as the mass-transpoit/corrosion probe. A model was proposed to reconcile corrosion rate data from pipe and rotating cylinder geometries based on the premise that the corrosion rate is controlled by the transport of Fe + from the interface. The data were subsequently used by Silverman [21] to construct a more precise model for correlating mass-transfer effects between pipe flow and a rotating cylinder. 

These models represent the simplest approach to model mass transfer in liquid-liquid dispersions in that an effective interfacial surface area be-... 

Mass-transfer Effects. - Zeolites possess a large internal surface area and are necessarily subject to mass-transfer effects, although there have been relatively few studies of these. Swabb and Gates observed that for H-mordenite at low temperatures (155°C), rate was independent of crystallite size for methanol dehydration, but at higher temperature rate variation was consistent with a Thiele model. 

In the case of polyester synthesis from divinyl esters, hydrolysis of the vinyl end group partly took place, resulting in the limitation of the polymer growth.201 A mathematical model showing the kinetics of the polymerization predicts the product composition. On the basis of these data, a batch-stirred reactor was designed to minimize temperature and mass-transfer effects.202 The efficient enzymatic production of polyesters was achieved using this reactor poly(l,4-butylene adipate) with Mn 2 x 104 was synthesized in 1 h at 60 °C. 

The best-known of the early developments addressing mass transfer effects on the BCF model was that of Chernov (1961), setting diffusion of solute through a boundary layer as the rate-limiting step. Other, more complex descriptions taking both surface and bulk diffusion into effect have been presented by Bennema (1969) and Gilmer et al. (1971). 

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