Consecutive reactions diffusion limited

Figure 11. Evolution with time of the effective rate profile of the main reaction in a plug flow reactor. Consecutive coking. Diffusion limited process on a ZSM-5 type catalyst.

The selectivity in a system of parallel reactions does not depend much on the catalyst size if effective diffusivities of reactants, intermediates, and products are similar. The same applies to consecutive reactions with the product desired being the final product in the series. In contrast with this, for consecutive reactions in which the intermediate is the desired product, the selectivity much depends on the catalyst size. This was proven by Edvinsson and Cybulski (1994, 1995) for. selective hydrogenations and also by Colen et al. (1988) for the hydrogenation of unsaturated fats. Diffusion limitations can also affect catalyst deactivation. Poisoning by deposition of impurities in the feed is usually slower for larger particles. However, if carbonaceous depositions are formed on the catalyst internal surface, ageing might not depend very much on the catalyst size. 

The shape selectivity in products is evidenced mainly by the mdCB/pdCB ratio at a given conversion (Table 4). The behaviour of HPILC cannot be taken into account since the majority of products are formed by radical mechanism. On the protonic zeolites the isomerisation of dichlorobenzenes follows a consecutive reaction scheme for the main part, and the mdCB/pdCB ratio depends on the odCB conversion. However, this ratio can be modified when limitation to diffusion occurs, and the final product pdCB will be then favoured. 

Studies on cyclohexane oxidation at Monash University were started in the year 1965 (see Wild, 4). Initial reaction studies indicated that the reaction rate was high. Wild (4) presented a theoretical analysis of the reaction by idealizing it as a consecutive reaction. It was found that diffusion limitation reduces selectivity towards the intermediate product. Selectivity could be enhanced by minimizing the contact time between the gas and the liquid, and also decreasing the partial pressure of the reactive gas. For systems not under diffusion control, these two factors will not have any effect on the reaction course. 

High selectivity produces high yields of a desired product while suppressing undesirable competitive and consecutive reactions. This means that the texture of the catalyst (in particular pore volume and pore distribution) should be improved toward reducing limitations by internal diffusion, which in the case of consecutive reactions rapidly reduces selectivity. 

The conditions are substantially more favorable for the microporous catalytic membrane reactor concept. In this case the membrane wall consists of catalyti-cally active, microporous material. If a simple reaction A -> B takes place and no permeate is withdrawn, the concentration profiles are identical to those in a catalyst slab (Fig. 29a). By purging the permeate side with an inert gas or by applying a small total pressure difference, a permeate with a composition similar to that in the center of the catalyst pellet can be obtained (Fig. 29b). In this case almost 100% conversion over a reaction length of only a few millimeters is possible. The advantages are even more pronounced, if a selectivity-limited reaction is considered. This is shown with the simple consecutive reaction A- B- C where B is the desired product. Pore diffusion reduces the yield of B since in a catalyst slab B has to diffuse backwards from the place where it was formed, thereby being partly converted to C (Fig. 29c). This is the reason why in practice rapid consecutive reactions like partial oxidations are often run in pellets composed of a thin shell of active catalyst on an inert support [30],... 

A final application that can be envisaged for permselective IMRs concerns the enhancement of reaction selectivity toward intermediate products of consecutive reaction pathways. Such a goal could be attained by developing a membrane capable of separating the intermediate product from the reaction mixture [39,40]. The most critical point in this regard is that intermediate product molecules (e.g., partially oxidized hydrocarbons) are often larger in size than the complete reaction products (e.g., CO2) or the reactants themselves (e.g., O2). This seriously complicates the separation process, limiting the number of selective transport mechanisms that can be utilized for the purpose of capillary condensation, surface diffusion, or multilayer diffusion (described later in this chapter). 

This competitive adsorption drives the platinum deeper into the extrudates, and when sufficient HCl is added, the PtCl / adsorption reaction is moderated to such an extent that a reasonably homogeneous distribution is obtained. One can also add acids that adsorb even more strongly than chloroplatinic acid, e.g. oxalic or citric acid, with which Pt profiles such as shown in Fig. 10.6 can be prepared. Profile (b) can be useful when a strongly adsorbing poison is present in the stream to be treated, e.g. Pb in automobile exhaust gas, while profiles (c) and (d) could be advantageous e.g. in diffusion-limited consecutive reactions. 

In catalytic applications, monoliths can provide better control of the contact time of reactants and products with the catalyst. This leads to a potential increase in selectivity. Together with the advantages over conventional trickle-bed reactors (pressure-drop surface area, short diffusion lengths), this makes the monohth reactor very suitable for use in consecutive reaction schemes, such as selective oxidation or hydrogenation. Literature dealing with carbon monolith structures is not yet extensive, however, and a limited number of applications have been reported, as shown in Table 11.2. 

Concerning the role of observable intermediates, it should be pointed out that there is an important mechanistic principle which applies to all reactions (not only enzymic ones) which is commonly overlooked it is simply that the isolation of an intermediate does not necessarily mean that the intermediate lies on the reaction pathway. Furthermore, the observation of an intermediate in a reaction which has reached a stationary state does not necessarily mean that that intermediate lies on the reaction pathway.The problem can sometimes be solved by examining the non-stationary state, where more complex kinetics are then observed, e.g. consecutive, concurrent or mixed regimes may be used to reach the stationary state or by examining the absolute magnitudes of rate constants bearing in mind such restrictions as diffusion limits or, in some cases, by using isotope effects. Studies of these latter kinds have been done on some zinc metalloenzymes but not many. 

The limitation of the diffusion of products outside the crystal lattice affects the selectivity of products. In this type of selectivity at least two products with different molecular dimensions may form from a parallel or consecutive reaction. In this case, a reaction occurs at the expense of another. As such, the concentration of less bulky molecules decreases rapidly within the pore structure for a reaction. In some instances, the selectivity is independent of the size of the crystals. The selectivity of the transition state is intrinsically of chemical effects, since a single molecule can react in a certain transition state and not in another [13]. Also, upon increasing... 

Figure 8 shows data gained from stopped-flow fluorescence experiments in which warferin s (W) fluorescence emission (excited at 330 nm and detected at 360 nm and above) is used to study its binding to human serum albumin (A). This reaction proceeds by two, consecutive reversible steps. A fast, diffusion limited bimolecular reaction by which the initial complex is formed (A.W). followed by a unimolecular conformational change in the protein following complex formation (A W). 

The kinetics of the consecutive reaction (4) could be found, however, from the resulting distribution of manganese over the silica granules. An example of such a distribution as obtained from electron microprobe analysis is shown in Fig. 6. The qualitative shape of the distribution indicates that reaction (4) is influenced by both kinetic and diffusion effects. In order to further extract quantitative information from the manganese distributions we have assumed that the kinetics of reaction (4) can be approached by a first-order dependence in manganese and a zero—order dependence for the other components. With these assumptions one can make use of the Thiele concept of diffusion-limited reactions [11]. 

However, when one gets down to detailed quantitative equations to represent real, actual reactions with several steps in consecutive sequence, the mathematics become very complex. Thus, the change in the limiting current with time introduces complications that one tries to avoid in other transient methods by working at low times (constant current or constant potential approaches) or at times sufficiently high that the current becomes entirely diffusion controlled. However, taking into account the... 

When the catalyst is immobilized within the pores of an inert membrane (Figure 25.13b), the catalytic and separation functions are engineered in a very compact fashion. In classical reactors, the reaction conversion is often limited by the diffusion of reactants into the pores of the catalyst or catalyst carrier pellets. If the catalyst is inside the pores of the membrane, the combination of the open pore path and transmembrane pressure provides easier access for the reactants to the catalyst. Two contactor configurations—forced-flow mode or opposing reactant mode—can be used with these catalytic membranes, which do not necessarily need to be permselective. It is estimated that a membrane catalyst could be 10 times more active than in the form of pellets, provided that the membrane thickness and porous texture, as well as the quantity and location of the catalyst in the membrane, are adapted to the kinetics of the reaction. For biphasic applications (gas/catalyst), the porous texture of the membrane must favor gas-wall (catalyst) interactions to ensure a maximum contact of the reactant with the catalyst surface. In the case of catalytic consecutive-parallel reaction systems, such as the selective oxidation of hydrocarbons, the gas-gas molecular interactions must be limited because they are nonselective and lead to a total oxidation of reactants and products. For these reasons, small-pore mesoporous or microporous... 

Any of the above consecutive steps may control the etching process, but it is always the slowest step that is rate limiting. Steps 1 and 7 of the transport of the reacting species and reaction products are controlled by diffusion kinetics, while surface reactions control the remaining steps. Some of the above steps may be very important in certain systems, while... 

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