Nonuniform Activity Distributions

The benefits of nonuniform activity distributions (site density) or diffusive properties (porosity, tortuosity) within pellets on the rate of catalytic reactions were first suggested theoretically by Kasaoka and Sakata (Ml). This proposal followed the pioneering experimental work of Maatman and Prater (142). Models of nonuniform catalyst pellets were later extended to more general pellet geometries and activity profiles (143), and applied to specific catalytic reactions, such as SO2 and naphthalene oxidation (144-146). Previous experimental and theoretical studies were recently discussed in an excellent review by Lee and Aris (147). Proposed applications in Fischer-Tropsch synthesis catalysis have also been recently reported (50-55,148), but the general concepts have been widely discussed and broadly applied in automotive exhaust and selective hydrogenation catalysis (142,147,149). 

Nonisothermal effectiveness factor for gas phase reactions, 243 for multiphase reactions, 440 Nonuniform activity distribution, 126 Numerical methods... 

The factor (1 — y)/[ + active sites that are vacant, as shown in Chapter 5. This factor represents the profile of sites within the pellet that are available for both the main and deactivation reactions. If this profile is treated as the activity profile for the rate constant kp, the result obtained in Section 4-8 for the internal effectiveness factor for a pellet with a nonuniform activity distribution can be applied (Section 5-6) ... 

When a battery produces current, the sites of current production are not uniformly distributed on the electrodes (45). The nonuniform current distribution lowers the expected performance from a battery system, and causes excessive heat evolution and low utilization of active materials. Two types of current distribution, primary and secondary, can be distinguished. The primary distribution is related to the current production based on the geometric surface area of the battery constmction. Secondary current distribution is related to current production sites inside the porous electrode itself. Most practical battery constmctions have nonuniform current distribution across the surface of the electrodes. This primary current distribution is governed by geometric factors such as height (or length) of the electrodes, the distance between the electrodes, the resistance of the anode and cathode stmctures by the resistance of the electrolyte and by the polarization resistance or hinderance of the electrode reaction processes. 

One of the main reasons for a lower specific activity resides in the fact that electrodes with disperse catalysts have a porous structure. In the electrolyte filling the pores, ohmic potential gradients develop and because of slow difiusion, concentration gradients of the reachng species also develop. In the disperse catalysts, additional ohmic losses will occur at the points of contact between the individual crystallites and at their points of contact with the substrate. These effects produce a nonuniform current distribution over the inner surface area of the electrode and a lower overall reaction rate. 

An important aspect concerning catalytically active membrane reactors, is the distribution of the active phase within the membrane system. Modem modification techniques (van Praag et al. 1989, Lin, de Vries and Burggraaf 1989) allow control over the catalyst distribution and preferential deposition of the active phase at different places in the membrane (top layer/support) system. Studies on conventionally used plate-shaped and cylindrically-sha-ped catalytically active pellets (Vayenas and Pavlou 1987a, b, Dougherty and Verykios 1987) have shown that nonuniformly activated catalysts (catalysts with nonuniform distribution of active sites according to a certain profile)... 

Although the matrix may have a well-defined planar surface, there is a complex reaction surface extending throughout the volume of the porous electrode, and the effective active surface may be many times the geometric surface area. Ideally, when a battery produces current, the sites of current production extend uniformly throughout the electrode structure. A nonuniform current distribution introduces an inefficiency and lowers the expected performance from a battery system. In some cases the negative electrode is a metallic element, such as zinc or lithium metal, of sufficient conductivity to require only minimal supporting conductive structures. 

Figure 10.15. True leveling on a V-groove produced by nonuniform current distribution, ir > ip, in the presence of a leveling agent (a) nonuniform current density and deposit thickness, hs and hg, after time t = l (b) evolution of a groove profile during deposition activation control.

Deposition is nonuniform. Thus, dendrites are formed as active metal deposits emerge from the surface films. These deposits induce nonuniform current distribution that enhances the phenomenon, as illustrated in Figure 7. These dendrites react readily with solution species since they are bare active metal deposits and thus become covered with surface films. In narrow parts and bottlenecks, these surface reactions can disconnect the dendrite electronically from the bulk. This phenomenon... 

F(c/c,) denotes the dimensionless form of an arbitrary rate expression./(x) is a nonuniform, normalized catalyst activity distribution inside the pellet. A(x) is an auxiliary function, subject to the following linear differential equation ... 

With surface-active material present the convection of the liquid, from right to left in the reference frame in which the bubble is stationary, results in a nonuniform surfactant distribution on the bubble surface. The surfactant is swept toward the rear of the bubble where it accumulates. As a consequence, the surface tension varies along the bubble with its lowest value at the rear end. The surface tension gradient exerts a tractive force on the bubble and increases its resistance to motion under a driving pressure gradient pi P -... 

The objective here is to simulate duct reactor performance with nonuniform catalyst activity and identify optimal deposition strategies when reactant diffn-sion toward the active surface is hindered, particularly in the corners of the flow channel. Both types of power-function profiles, listed in Table 23-3, are evaluated for n = 1,2,4, 8. The delta-function distribution has been implemented by Varma (see Morbidelli et al., 1985) to predict optimum catalyst performance in porous pellets with exothermic chemical reaction. Nonuniform activity profiles for catalytic pellets in fixed-bed reactors, in which a single reaction occnrs, have been addressed by Sznkiewicz et al. (1995), and effectiveness factors for... 

Many commercial heterogeneous catalysts are not impregnated in a uniform fashion. For example, various precious-metal catalysts consist of an exterior active shell and an inert core in order to enhance the effectiveness factor. Several automobile-muffler catalysts have a carbon-monoxide-oxidation catalyst in one shell and an NOx-reducing catalyst in another shell. Our understanding of the reaction-diffusion interaction facilitated this rational design of the optimal profile of catalyst-activity distribution and shape. It would be of both practical importance and academic interest to develop a rational procedure for enhancing the performance of metallocenes by their nonuniform impregnation on the support. 

When the poisoning is nonuniform, there exists an activity distribution within the pellet, and the generalized effectiveness factor obtained in Chapter 4 for a nonuniform activity profile can be used to arrive at the following expression ... 

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