Reactant transport

If the reaction is diffusion controlled, i.e. the charge transfer is fast compared to reactant transport, the value of A i/2 is equal to k. ... 

The behavior of metal electrodes with an oxidized surface depends on the properties of the oxide layers. Even a relatively small amount of chemisorbed oxygen will drastically alter the EDL structure and influence the adsorption of other snb-stances. During current flow, porous layers will screen a significant fraction of the surface and interfere with reactant transport to and product transport away from the surface. Moreover, the ohmic voltage drop increases, owing to the higher current density in pores. All these factors interfere with the electrochemical reactions, particularly with further increase in layer thickness. 

The platinum concentrations in the platinized carbon blacks are reported to be between 10 and 40% (by mass), sometimes even higher. At low concentrations the specific surface area of the platinum on carbon is as high as lOOm /g, whereas unsupported disperse platinum has surface areas not higher than 10 to 15m /g. However, at low platinum concentrations, thicker catalyst layers must be applied, which makes reactant transport to reaction sites more difficult. The degree of dispersion and catalytic activity of the platinum depend not only on its concentration on the carrier but also on the chemical or electrochemical method used to deposit it. 

The second variant is designed for solid state reactants to the exclusion of liquid or gas. This powder variant of Thermostar is described by the Fig. 1.19 (right). The microwave applicator is the same as for the device for liquids heating but the reactant transport is ensured by a metallic screw set within the dielectric pipe. This specific traveling metallic screw crosses all the microwave applicators. The coexistence of this metallic screw with the electric field is ensured by the fact that the major electric field direction is parallel to the major direction and perpendicular to the local curving of the screw. A typical industrial unit for solid or liquid reactants is powered with microwave generators units of 2 or 6 kW for a total microwave power close to 20 or 60 kW. 

These models describe simple vessels and shapes only. If the vessel structures become more complicated or if reactant transport determines the reaction rate, as is often the case with oxidation by air, more complex numerical models must be used [138]. 

The convolution treatment of the linear and semi-infinite diffusion reactant transport (Section 1.3.2) leads to the following relationship between the concentrations at the electrode surface and the current ... 

High current density performance of PEFCs is known to be limited by transport of reactants and products. In addition, at high current densities, excess water is generated and condenses, filling the pores of electrodes with liquid water and hence limiting the reactant transport to catalyst sites. This phenomenon known as flooding is an important limiting factor of PEFC performance. A fundamental... 

A model of such structures has been proposed that captures transport phenomena of both substrates and redox cosubstrate species within a composite biocatalytic electrode.The model is based on macrohomo-geneous and thin-film theories for porous electrodes and accounts for Michaelis—Menton enzyme kinetics and one-dimensional diffusion of multiple species through a porous structure defined as a mesh of tubular fibers. In addition to the solid and aqueous phases, the model also allows for the presence of a gas phase (of uniformly contiguous morphology), as shown in Figure 11, allowing the treatment of high-rate gas-phase reactant transport into the electrode. 

Spacer chain catalysts 3, 4, and 19 have been investigated under carefully controlled conditions in which mass transfer is unimportant (Table 5)80). Activity increased as chain length increased. Fig. 7 shows that catalysts 3 and 4 were more active with 17-19% RS than with 7-9% RS for cyanide reaction with 1-bromooctane (Eq. (3)) but not for the slower cyanide reaction with 1-chlorooctane (Eq. (1)). The unusual behavior in the 1-bromooctane reactions must have been due to intraparticle diffusional effects, not to intrinsic reactivity effects. The aliphatic spacer chains made the catalyst more lipophilic, and caused ion transport to become a limiting factor in the case of the 7-9 % RS catalysts. At > 30 % RS organic reactant transport was a rate limiting factor in the 1-bromooctane reations80), In contrast, the rate constants for the 1 -chlorooctane reactions were so small that they were likely limited only by intrinsic reactivity. (The rate constants were even smaller than those for the analogous reactions of 1-bromooctane and of benzyl chloride catalyzed by polystyrene-bound benzyl-... 

The electrode has a central function in cell operation. In its catalyzed layer, it provides a large number of sites where gases and electrolyte can react By virtue of a porous couliguration. last reactant transport and removal of inerts and products moisture is possible. The electrode also provides a path for current lo flow to the terminals and serves to contain the electrolyte. The latter not only provides ionic conduction, but also assures separation of the reactants. 

Available reaction-transport models describe the second regime (reactant transport), which only requires material balances for CO and H2. Recently, we reported preliminary results on a transport-reaction model of hydrocarbon synthesis selectivity that describes intraparticle (diffusion) and interparticle (convection) transport processes (4, 5). The model clearly demonstrates how diffusive and convective restrictions dramatically affect the rate of primary and secondary reactions during Fischer-Tropsch synthesis. Here, we use an extended version of this model to illustrate its use in the design of catalyst pellets for the synthesis of various desired products and for the tailoring of product functionality and molecular weight distribution. 

Surprisingly, the synthesis rate is not influenced strongly by pellet diameter, in a size range where marked selectivity changes occur (Table V). This reflects reaction kinetics that are negative order in the diffusion-limited reactant (CO). These types of kinetics delay the inevitable decrease in catalyst productivity that ultimately accompanies reactant transport limitations and that occurs on Co catalysts only for larger and more active pellets. 

The probability of readsorption increases as the intrinsic readsorption reactivity of a-olefins (k,) increases and as their effective residence time within catalyst pores and bed interstices increases. The Thiele modulus [Eq. (15)] contains a parameter that contains only structural properties of the support material ( <>, pellet radius Fp, pore radius 4>, porosity) and the density of Ru or Co sites (0m) on the support surface. A similar dimensional analysis of Eqs. (l9)-(24), which describe reactant transport during FT synthesis, shows that a similar structural parameter governs intrapellet concentration gradients of CO and H2 [Eq. (25)]. In this case, the first term in the Thiele modulus (i/>co) reflects the reactive and diffusive properties of CO and H2 and the second term ( ) accounts for the effect of catalyst structure on reactant transport limitations. Not surprisingly, this second term is... 

The initial increase in C5+ selectivity as x increases arises from diffusion-enhanced readsorption of a-olefins. At higher values of CO transport restrictions lead to a decrease in C5+ selectivity. Because CO diffuses much faster than C3+ a-olefins through liquid hydrocarbons, the onset of reactant transport limitations occurs at larger and more reactive pellets (higher Ro, 0m) than for a-olefin readsorption reactions. CO transport limitations lead to low local CO concentrations and to high H2/CO ratios at catalytic sites. These conditions favor an increase in the chain termination probability (jSr, /Sh) and in the rate of secondary hydrogenation of a-olefins (j8s) and lead to lighter and more paraffinic products. 

The olefin readsorption model does not predict the observed decrease in C5+ selectivity (Figs. 20 and 21) that occurs at higher values of x because this model was derived assuming that such pellets maintain intrapellet H2 and CO concentrations in equilibrium with the interpellet gas phase. Such assumptions are relaxed in the reactant transport model described in Section III,C, which predicts that intrapellet CO concentration gradients begin to develop in pellets with x values greater than about 5 x 10 m. ... 

Reactant transport restrictions that occur at high values of x also lead to a decrease in the FT synthesis activation energy from 125 kJ mol to values of 65-75 kJ mor (Fig. 23). This behavior reflects primary reactions that become limited by reactant transport. The overall pressure order increases as X approaches values where CO transport limits overall reaction rates (Fig. 23). This reflects the increased severity of transport restrictions as CO pressures decrease, because transport rates decrease linearly with total pressure but kinetic pellet requirements decrease much less rapidly (cf. Table I). 

Fig. 20 toward higher values of without a significant change in the shape of the curve. Therefore, the net effect of supercritical operation will depend on whether catalysts at normal operating conditions reside on the olefin readsorption or reactant transport parts of the C5+ selectivity curve (Fig. 20). 

The route from reactant to product molecule in a monolith reactor comprises reactant transport from the bulk gas flow in a channel toward the channel wall, simultaneous diffusion and reaction inside the porous washcoat on the channel wall, and product transport from the wall back to the bulk flow of the gas phase. 

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