Catalytic internal diffusion

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

The book focuses on three main themes catalyst preparation and activation, reaction mechanism, and process-related topics. A panel of expert contributors discusses synthesis of catalysts, carbon nanomaterials, nitric oxide calcinations, the influence of carbon, catalytic performance issues, chelating agents, and Cu and alkali promoters. They also explore Co/silica catalysts, thermodynamic control, the Two Alpha model, co-feeding experiments, internal diffusion limitations. Fe-LTFT selectivity, and the effect of co-fed water. Lastly, the book examines cross-flow filtration, kinetic studies, reduction of CO emissions, syncrude, and low-temperature water-gas shift. 

The most important processes in monolith channel convection of exhaust gas, heat and mass transfer between the flowing gas and the washcoat, internal diffusion, catalytic reactions in the washcoat, heat and mass accumulation and heat conduction—are schematically depicted in Fig. 7. 

In the spatially ID model of the monolith channel, no transverse concentration gradients inside the catalytic washcoat layer are considered, i.e. the influence of internal diffusion is neglected or included in the employed reaction-kinetic parameters. It may lead to the over-prediction of the achieved conversions, particularly with the increasing thickness of the washcoat layer (cfi, e.g., Aris, 1975 Kryl et al., 2005 Tronconi and Beretta, 1999 Zygourakis and Aris, 1983). To overcome this limitation, the effectiveness-factor concept can be used in a limited extent (cf. Section III.D). Despite the drawbacks coming from the fact that internal diffusion effects are implicitly included in the reaction kinetics, the ID plug-flow model is extensively used in automotive industry, thanks to the reasonable combination of physical reliability and short computation times. 

Then the classical Thiele modulus ( ) and the effectiveness factor (t/), expressing the extent of internal diffusion limitations in the catalytic washcoat layer of thickness 8, can be calculated according to (cf. Aris, 1975 Froment and Bischoff, 1979, 1990)... 

When the internal diffusion effects are considered explicitly, concentration variations in the catalytic washcoat layer are modeled both in the axial (z) and the transverse (radial, r) directions. Simple slab geometry is chosen for the washcoat layer, since the ratio of the washcoat thickness to the channel diameter is low. The layer is characterized by its external surface density a and the mean thickness <5. It can be assumed that there are no temperature gradients in the transverse direction within the washcoat layer and in the wall of the channel because of the sufficiently high heat conductivity, cf., e.g. Wanker et al. 

This intermediate scale affords a preliminary validation of the intrinsic kinetics determined on the basis of microreactor runs. For this purpose, the rate expressions must be incorporated into a transient two-phase mathematical model of monolith reactors, such as those described in Section III. In case a 2D (1D+ ID) model is adopted, predictive account is possible in principle also for internal diffusion of the reacting species within the porous washcoat or the catalytic walls of the honeycomb matrix. 

Catalysts pre-treatment (calcination and reduction) was performed in the same testing system or in a parallel automatic activation system prior to reaction test Calcination is carried out at 600 °C under airflow for 8 h and reduction at 250 °C for 2 h under hydrogen flow. Catalytic tests were carried out at 30 bar total pressure, temperature range 200-240°C, and 2.26h-1 WHSV, H2/hydrocarbons molar ratio of 2.93. Each fixed bed microreactor contained 500 mg of catalyst (particle size 0.4—0.6 mm, for which there are no internal diffusion limitations). Reaction products distribution are analysed using a gas chromatograph (Varian 3380GC) equipped with a Plot Alumina capillary column. 

Mass transport is much more likely to be rate-controlling in the heterogeneous catalysis of solution reactions than in that of gas reactions. The reason lies in the magnitudes of the respective diffusion coefficients [48] for molecules in normal gases at 1 bar and 300 K these are 10 5 to 10 4 m2s while, for typical solutes in aqueous solution, they are 10 10 to 10 9 m2 s. The rate-determining step in many solution catalyses has indeed been found to be external diffusion of reactant(s) to the outer surface of the catalyst and/or diffusion of product(s) away from it [3, 6]. Another possibility is internal diffusion within the pores of the catalytic solid, a step that often determines the rates of catalysed gas reactions [49-51]. It is clearly an essential part of a kinetic investigation to ascertain whether any of these steps control the rate of the overall catalytic process. Five main diagnostic criteria have been employed for this purpose ... 

Testing whether the catalytic rate is proportional to the mass of solid (provided the catalysis is not controlled by internal diffusion) and whether the rate increases as expected when more solid is added during a run. 

Madon and Boudart propose a simple experimental criterion for the absence of artifacts in the measurement of rates of heterogeneous catalytic reactions [R. J. Madon and M. Boudart, Ind. Eng. Chem. Fundam., 21 (1982) 438]. The experiment involves making rate measurements on catalysts in which the concentration of active material has been purposely changed. In the absence of artifacts from transport limitations, the reaction rate is directly proportional to the concentration of active material. In other words, the intrinsic turnover frequency should be independent of the concentration of active material in a catalyst. One way of varying the concentration of active material in a catalyst pellet is to mix inert particles together with active catalyst particles and then pelletize the mixture. Of course, the diffusional characteristics of the inert particles must be the same as the catalyst particles, and the initial particles in the mixture must be much smaller than the final pellet size. If the diluted catalyst pellets contain 50 percent inert powder, then the observed reaction rate should be 50 percent of the rate observed over the undiluted pellets. An intriguing aspect of this experiment is that measurement of the number of active catalytic sites is not involved with this test. However, care should be exercised when the dilution method is used with catalysts having a bimodal pore size distribution. Internal diffusion in the micropores may be important for both the diluted and undiluted catalysts. 

Exemplary results of modeling processes inside the catalytic layer are presented in Fig. 9. The solid lines show the dependency of the overall effectiveness factor on the relative distribution of the catalyst between the comers and the side regions. The two cases represent two levels of the first-order rate constants, with the faster reaction in case (b). As expected, the effectiveness factor of the first reaction drops as more catalyst is deposited in the comers. The effectiveness factor for the second reaction increases in case (a) but decreases in case (b). The latter behavior is caused by depletion of B deep inside the catalytic layer. What might be surprising is the rather modest dependency of the effectiveness factor on the washcoat distribution. The explanation is that internal diffusion is not important for slow reactions, while for fast reactions the available external surface area becomes the key quantity, and this depends only slightly on the washcoat distribution for thin layers. The dependence of the effectiveness factor on the distribution becomes more pronounced for consecutive reactions described by Langmuir-Hinshelwood-Hougen-Watson kinetics [26]. 

Although there may have been some adsorption and desorption on the pore walls during the molecule s passage into the interior of the pellet, we do not consider this the third stage until adsorption occurs at a reactive catalytic site. This, and the next two, are the steps we have been considering above, so that within the pellet the concentrations of A and which were denoted by a and b above, will be fl(r) and h(r). All that we have done above has local validity and only if the internal diffusion is very rapid, so that a(r) and 6(r) are effectively uniform, will the reaction rate expression be valid for the pellet as a whole. The rate of adsorption is given by fad, Eq. (6.2.11). 

The selectivity at a position in a fluid-solid catalytic reactor is equal to the ratio of the global rates at that point. The combined effect of both external and internal diffusion resistance can be displayed easily for a set of parallel reactions. We shall do this first and then consider how internal resistance influences the selectivity for other reaction sequences. 

Wheeler has summarized the work on internal diffusion for catalytic cracking of gas-oil. At 500°C the rate data for fixed-bed operation, with relatively large ( -in.) catalyst particles and that for fluidized-bed reactors (very small particle size) are about the same. This suggests that the effectiveness factor for the large particles is high. Confirm this by estimating rj for the -in. catalyst if the... 

At /e > 25 internal diffusion control is reached. Any substrate molecule diffusing into the enzyme layer is converted therein only part of the enzyme is acting catalytically. Diffusion controlled sensors exhibit the following characteristics ... 

The transfer of molecules from the bulk phase to the location where reaction occurs (catalytically or thermally) may significantly influence the overall reaction rate. When the transfer from the bulk fluid phase to the catalyst is limiting, this is referred to as external mass transfer limitation. If diffusion of reactants or products in the pores of the catalyst is slow, it is termed internal diffusion limitation (Fig. 3.1). Both of these effects commonly occur under relevant conditions. 

In the case of three phase heterogeneous catalytic reactions, the rate of the process and its selectivity can be determined either by intrinsic reaction kinetics or by external diffusion (on the gas-liquid and gas-solid interface) as well as by internal diffusion through the catalyst pores. Careful analysis of mass transfer is important for the elucidation of intrinsic catalytic properties, for the design of catalysts, and for the scale up of processes. 

A temperature gradient would also be expected. For an isothermal case, with rj set equal to 1, multiple steady-state solutions may be found (see Figure 10), and the concentration gradient is very significant at temperatures above 427°C (800°F). The non-isothermal catalytic effectiveness factors for positive order kinetics under external and internal diffusion effects were studied by Carberry and Kulkarni (8) they also considered negative order kinetics. 

In our laboratories extensive studies on the catalytic hydrogenation of aromatic nitrocompounds, as an example of the catalytic three-phase reactions, have been carried out in reactors of different types - e g. see [8-10]. In all cited cases the time consumed for kinetic investigations had a very significant contribution to the total experimental effort [11-13]. Particularly for the hydrogenation over palladium on alumina catalyst, the experimental investigations leading to the detection and quantitative description of internal diffusion resistances in catalyst pellets have taken a lot of time. 

In the analysis of heterogeneous solubilization, the role of the solid-phase reaction in influencing the overall reaction is different from that for the usual gas-solid catalytic reaction. The most important situation is that the film and internal diffusion effects within the solid and at the solid-liquid interface are significant. 

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