Reaction with Pore Diffusion

Here, as in Section 8.5.4, we treat the isothermal case for ijo, and relate tj0 to 17. may then be interpreted as the ratio of the (observed) rate of reaction with pore diffusion and external mass transfer resistance to the rate with neither of these present. 

Surface reaction with pore diffusion dp, w, [ ], [5](, temperature Pore structure Type of impeller and stirring speed (mechanically agitated contactor), gas velocity (sparged contactor)... 

Surface reaction with pore diffusion dp, [,4], [ ](, temperature, replacement of active by inactive catalyst particles Superficial liquid velocity (above certain minimum) Superficial gas velocity ... 

Zeolite crystal size can be a critical performance parameter in case of reactions with intracrystalline diffusion limitations. Minimizing diffusion limitations is possible through use of nano-zeolites. However, it should be noted that, due to the high ratio of external to internal surface area nano-zeolites may enhance reactions that are catalyzed in the pore mouths relative to reactions for which the transition states are within the zeolite channels. A 1.0 (xm spherical zeolite crystal has an external surface area of approximately 3 m /g, no more than about 1% of the BET surface area typically measured for zeolites. However, if the crystal diameter were to be reduced to 0.1 (xm, then the external surface area becomes closer to about 10% of the BET surface area [41]. For example, the increased 1,2-DMCP 1,3-DMCP ratio observed with decreased crystallite size over bifunctional SAPO-11 catalyst during methylcyclohexane ring contraction was attributed to the increased role of the external surface in promoting non-shape selective reactions [65]. 

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... 

A branched pore leaching model as applied to release of water-soluble carbon from soil incorporates reaction to soluble compounds coupled with pore diffusion within the solids and leaching into the bulk solution. Application of such a model appears to describe hemicellulose hydrolysis reasonably well but not significantly better than chemical reaction only or simple leaching models. 

Isothermal reaction with the diffusion resistance in the pore Solving the differential equation for the mass balance at steady-state (output - input + disappearance by reaction = 0), see e.g. [119], in a volume element of the pore delivers an equation which describes the change of concentration in the pore as a function of its length, L ... 

Non-isothermal reaction with the diffusion resistance in the pore In an exothermal reaction, temperature gradients will arise within the pellet and, consequently, the temperature of pellet will be elevated compared with its surroundings. As a result, the reaction will be faster than the isothermal counterpart. AT in the film as well in the pellet can be theoretically predicted and, consequently, the maximum AT between the outer surface (Ts) and the inside of the catalyst (T n) calculated, when there c = 0 ... 

Therefore, it is necessary to determine the influence of mass transfer to or from the above-mentioned interfaces on the conversion, which leads to expressions for the flux of a reactant across the interface and for the overall reaction rate. After balancing the disappearance of the components Ai and A2, e. g., at the gas/liquid interface, by analogy with the treatment of the rate of chemical reaction and pore diffusion in heterogeneous catalysis, the overall reaction rate is given by eq. (1) [2] ... 

The effectiveness factor, rj, is defined as the ratio of the reaction rate with pore diffusion resistance to the reaction rate without pore diffusion resistance (i.e., all of the active catalytic sites are restricted to the external surface of the particle). In mathematical terms... 

Shell-and-tube exchanger with reactants and catalyst inside the tubes, 250 to 400 m /m. Tube diameter <50 mm. Gas with fixed bed of catalyst use high mass gas velocity to improve heat transfer kg/s m > 1.35. To ensure good gas distribution and negligible backmixing, Pe > 2 height/catalyst particle diameter H/D > 100 and D/D < 0.10. Gas velocity 3 to 10 m/s residence time 0.6 to 2 s. Heat transfer coefficient U = 0.05 kW/m K. For fast reactions, catalyst pore diffusion mass transfer may control if catalyst diameter is >1.5 mm. Liquids with fixed bed of catalyst to minimize backmixing, Pe> use UD > 200 and D/D <0.10. Liquid velocity 1 to 2 m/s residence time 2 to 6 s. Heat transfer coefficient U = 0.5 kW/m -K. 

The selectivity ratio with pore diffusion limitations is foutul by solving the diffusion-reaction equation ... 

For adiabatic operation with exothermic reactions, limit the height of the bed to keep temperature increase < 50 °C. Tube diameter < 50 mm to minimize extremes in radial temperature gradient. For fast reactions, catalyst pore diffusion mass transfer may control if the catalyst diameter >1.5 mm. 

In the design of a fixed bed reactor, it is necessary to know the rate of reaction encompassing mass and diffusion effects. These effects on the reaction rate can be represented by the effectiveness factor r), with pore diffusion, besides the effects of mass. This will be represented by an overall rate r" (mol mass h ) or r (mol/area h ). 

Mass transfer resistances may also change the selectivity of parallel and consecutive reactions. For parallel reactions and equal reaction orders, pore diffusion and external mass transport have no influence on selectivity. For different orders, the reaction with the lower order is favored. For a series reaction, the influence of external and internal mass transfer leads to a lower yield and selectivity of the intermediate product. 

Chemical reaction without pore diffusion resistance in the remaining core (0 < r < r<-) with a constant density of the solid reactant B, p ... 

To conclude, an overall summary of calculations based on the above results indicates that the usual order of events is to have first chemical reaction control throughout the pellet. Next, with higher intrinsic rates of reaction, internal pore diffusion begins to have an effect, followed by external heat transfer resistance. Finally, for extremely rapid reactions there is the possibility of external mass transfer resistance and temperature gradients of some significance. Only for unrealistic situations is it likely that particle instabilities might occur, and even then only for narrow ranges of temperature. 

In recent years considerable advances have been made in our understanding of gas-solid reaction systems. These advances are due in part to the development of more sophisticated mathematical models in which account is taken of such structural effects as pore size, grain size, and pore diffusion. Another important contributory factor has been the use of more sophisticated experimental techniques such as electron microscopy. X-ray diffraction, and porosimetry, which together with pore diffusion measurements provide information on the key structural parameters and make possible the critical assessment of this new generation of models. 

Fig. 9. Catalyst pore and reaction. The CO diffuses into a precious metal site D reacts with O2 and leaves as CO2.

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