Selectivity pore diffusion

Pore diffusion encountered in gas-solid reaction systems is generally rather more complex, because the solid structure may change in the course of the reaction. Moreover, the actual nature of the porous matrix may also be less well defined. In selecting pore diffusion models for the description of gas-solid reaction systems care should be taken that the sophistication of the model is consistent with the accuracy of the information available on the behavior of the system. 

The work of Thiele (1939) and Zeldovich (1939) called attention to the fact that reaction rates can be influenced by diffusion in the pores of particulate catalysts. For industrial, high-performance catalysts, where reaction rates are high, the pore diffusion limitation can reduce both productivity and selectivity. The latter problem emerges because 80% of the processes for the production of basic intermediates are oxidations and hydrogenations. In these processes the reactive intermediates are the valuable products, but because of their reactivity are subject to secondary degradations. In addition both oxidations and hydrogenation are exothermic processes and inside temperature gradients further complicate secondary processes inside the pores. 

Inert gas pressure, temperature, and conversion were selected as these are the critical variables that disclose the nature of the basic rate controlling process. The effect of temperature gives an estimate for the energy of activation. For a catalytic process, this is expected to be about 90 to 100 kJ/mol or 20-25 kcal/mol. It is higher for higher temperature processes, so a better estimate is that of the Arrhenius number, y = E/RT which is about 20. If it is more, a homogeneous reaction can interfere. If it is significantly less, pore diffusion can interact. 

For testing and optimizing catalysts, the temperature region just below that where pore diffusion starts to limit the intrinsic kinetics provides a desirable working point (unless equilibrium or selectivity considerations demand working at lower temperatures). In principle, we would like the rate to be as high as possible while also using the entire catalyst efficiently. For fast reactions such as oxidation we may have to accept that only the outside of the particles is used. Consequently, we may decide to use a nonporous or monolithic catalyst, or particles with the catalytic material only on the outside. 

The most difficult problem to solve in the design of a Fischer-Tropsch reactor is its very high exothermicity combined with a high sensitivity of product selectivity to temperature. On an industrial scale, multitubular and bubble column reactors have been widely accepted for this highly exothermic reaction.6 In case of a fixed bed reactor, it is desirable that the catalyst particles are in the millimeter size range to avoid excessive pressure drops. During Fischer-Tropsch synthesis the catalyst pores are filled with liquid FT products (mainly waxes) that may result in a fundamental decrease of the reaction rate caused by pore diffusion processes. Post et al. showed that for catalyst particle diameters in excess of only about 1 mm, the catalyst activity is seriously limited by intraparticle diffusion in both iron and cobalt catalysts.1... 

Modeling of pore diffusion phenomena can be a helpful tool mainly in terms of catalyst design considerations but also in terms of understanding the effects caused by diffusional restrictions. For example, a modeling study by Wang et al.7 demonstrated a negative impact on selectivity by particle diffusion limitations. 

Three types of membrane transporter are found channels, carriers and pumps (Fignre 6.10). Channels are transmembrane proteins that function as selective pores throngh which ions or uncharged molecules can diffuse passively. Their selectivity for solutes depends on the size of the pore and the density of surface charges lining it. These are altered in response to external and internal stimuli in the plant, so regnlating the transport. 

When type X is utQized, in any of its ion exchange forms, for dehydration or possibly for sweetening (sulfur removal), there is little likelihood that the intracrystalline diffusion will be the dominant resistance to mass transfer. Large aromatic sulfurs would of course be an exception. When type X is used for adsorption of hydrocarbons or aromatics then it is possible that the micro-pore diffusion might dominate. When type A is used there is always a distinct possibility that intra-crystalline diffusion will be slow and may dominate the mass transfer, even for relatively small molecules. This is especially true when the chosen structure is a K A or type 3A. Selection of other small pore structures, for separations or purification applications can also create situations where the dominant resistance is found in the crystaUites. 

The optimum performance of a reactor will occur when the rate is as high as possible. We can always increase k" by increasing the temperature, assuming there is only one reaction so that selectivity is not important. However, we will find that at some temperature the mass transfer and/or pore diffusion processes wiU begin to limit the rate. 

Another important catalyst characteristic is porosity. Particularly when heavy feeds are processed, high pore volumes and pore diameters are required to reduce pore diffusion limitations. These limitations occur when the intrinsic rate of reaction is high compared with the rate of diffusion of the reactants through the catalyst particle to the active surface. The catalyst is then not used effectively, and reaction rates and selectivity become functions of particle size. If the kinetics of the reaction are known, it is possible to estimate from theory the reaction rate or threshold above which a catalyst of known size will begin to exhibit diffusion limitations. 

Besides influencing over-all reaction rates, pore diffusion can cause changes in selectivity. An extreme example of this was observed (26) when a high molecular weight California solvent-deasphalted oil was hydrocracked over a small pore size palladium zeolite catalyst at high temperatures. The feedstock gravity was 16.4° API, and 70% boiled above 966°F. The resulting product distribution is compared with that... 

Although the effect of pore diffusion on catalyst activity is usually undesirable, its effect on selectivity can sometimes be used to advantage, as reported by Weisz and others at the Mobil Research Laboratories (27). 

From the foregoing dicussion it is apparent that residuum hydroconversion processes can be influenced adversely by pore diffusion limitations. Increasing the catalyst porosity can alleviate the problem although increased porosity is usually accompanied by a decrease in total catalytic surface area. Decreasing the catalyst particle size would ultimately eliminate the problem. However, a different type of reaction system would be required since the conventional fixed bed would experience excessive pressure drops if very fine particles were used. A fluidized system using small particles does not suffer from this limitation. However, staging of the fluidized reaction system is required to minimize the harmful effects that backmixing can have on reaction efficiency and selectivity. 

The literature indicates that selectivity often can be improved, particularly with Ni and Pd catalysts by the use of promoters such as amines (ref. 34). Presumably, the amine competes for reactive sites with the alkenes and is effective if its adsorption constant lies between the constants of the competing alkenes. The effectiveness of the promoter is not diminished with the depletion of the more reactive alkene and is most useful with a supported catalyst where the concentration of molecules near a reactive site may be limited by pore diffusion. Selectivity would also improve if the promoter increases the rate of desorption of the alkenes (ref. 35). 

This fact indicates that selectivity will be lowered due to pore diffusion limitation. This is illustrated in table 2, where apparant rate constants and initial selectivity are given for IRA 401 gel type and IRA 904 macroporous type ion-exchanger in normal size, - 0.5 mm, and ground,... 

If the reactions were not influenced by in-pore diffusion effects, the intrinsic kinetic selectivity would be kjk2(= S). When mass transfer is important, the rate of reaction of both A and X must be calculated with this in mind. From equation 3.9, the rate of reaction for the slab model is ... 

The results show that crystallites in the range 0.1-0.3 pm have the highest activity and selectivity. The authors demonstrated that the higher activity of the small particles is a consequence of reducing pore-diffusion limitations. 

Good quality RO membranes can reject >95-99% of the NaCl from aqueous feed streams (Baker, Cussler, Eykamp et al., 1991 Scott, 1981). The morphologies of these membranes are typically asymmetric with a thin highly selective polymer layer on top of an open support structure. Two rather different approaches have been used to describe the transport processes in such membranes the solution-diffusion (Merten, 1966) and surface force capillary flow model (Matsuura and Sourirajan, 1981). In the solution-diffusion model, the solute moves within the essentially homogeneously solvent swollen polymer matrix. The solute has a mobility that is dependent upon the free volume of the solvent, solute, and polymer. In the capillary pore diffusion model, it is assumed that separation occurs due to surface and fluid transport phenomena within an actual nanopore. The pore surface is seen as promoting preferential sorption of the solvent and repulsion of the solutes. The model envisions a more or less pure solvent layer on the pore walls that is forced through the membrane capillary pores under pressure. 

Relative rate constants for a-olefin readsorption decrease as follows kr c0>kr Ru> r Fe (7)- Although kr on Fe catalysts is smaller than on Ru or Co, the other parameters in Eq. (2), such as the low diffusivity of large hydrocarbon and the high site density on unsupported Fe catalysts, ultimately increase the probability of a-olefin readsorption therefore, pore diffusion effects also play a crucial role in Fe-catalyzed FT synthesis (Figures 3 and 4). Fe catalysts, however, give lower C20+ selectivity because of lower intrinsic values of kr- even though asymptotic chain termination probabilites are lower on Fe. 

In macro- and mesoporous membrane layers the nature of the flow is determined by the relative magnitude of the mean free path X of the molecules and the pore size dp. When the mean free path of the gas molecules is much larger than the pore size, i.e. X dp, collisions of molecules with the pore walls are predominant and the mass transport takes place by the well-known selective Knudsen diffusion process. If the pore radius is much larger than the mean free path of the molecules and a pressure difference over the membrane exists the mass transport takes place by non-selective viscous flow. 

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],... 

Homogeneous catalysts are structurally well-defined complexes and because they are soluble in the reaction mix are not subject to pore diffusion limitations as are heterogeneous catalytic materials. They are almost always highly selective towards desired products. The main consideration is that the complex be stable and reactor conditions chosen such that all the gaseous reactants are adequately dissolved and mixed in the liquid phase. Homogeneous catalysts are easily characterized by standard instrumental methods for compound identification such as XRD or spectroscopy. Deactivation is associated with attack by traces of carboxylic acidic byproducts and impurities in the feed such as 02 and chlorides that attack the ligand groups. 

Sophisticated mathematical models based on the numerical simulation of the chromatographic process consider different kinetic and thermodynamic mechanisms [19], The theoretical approaches describe the biospecific adsorption of monovalent and multivalent adsorbates. They also account for the film mass transfer and pore diffusion contributions to the adsorption process and can be applied to analyze various complex experimental situations. Thus, ideally, the appropriate model will have to be selected to describe the actual chromatographic system. 

Trocha and Koros [1994] applied a diffusion-controlled caulking procedure with colloidal silica to plug large pores or defects in ceramic membranes. An important feature of this proc ure is the proper selection of the colloid particle size to eliminate or reduce large, less selective pores while minimizing deposition in the small desirable pores. The technique has b n successfully proven with anodic alumina membranes (having the majority of the pores about 2(X) nm in diameter) using 10-20 nm silica colloids. 

Selective surface diffusion is governed by a selective adsorption of the larger (nonideal) components on the pore surface. The critical temperature, 7), of a gas will thus indicate which component in a mixmre is more easily condensable. The gas with the highest T will most likely be the fastest permeating component where a selective surface flow can take place. Eor a mixed gas an additional increase in selectivity may be achieved if the adsorbed layer now covering the internal pore walls restricts the free pore entrance so that the smaller nonadsorbed molecules cannot pass through. 

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