Severe diffusion limitations

Concentrated sulfuric acid and hydrogen fluoride are still mainly used in commercial isoalkane-alkene alkylation processes.353 Because of the difficulties associated with these liquid acid catalysts (see Section 5.1.1), considerable research efforts are still devoted to find suitable solid acid catalysts for replacement.354-356 Various large-pore zeolites, mainly X and Y, and more recently zeolite Beta were studied in this reaction. Considering the reaction scheme [(Eqs (5.3)—(5.5) and Scheme 5.1)] it is obvious that the large-pore zeolitic structure is a prerequisite, since many of the reaction steps involve bimolecular bulky intermediates. In addition, the fast and easy desorption of highly branched bulky products, such as trimethylpentanes, also requires sufficient and adequate pore size. Experiments showed that even with large-pore zeolite Y, alkylation is severely diffusion limited under liquid-phase conditions.357... 

As expected, the fluid bed system looks most attractive when the reaction is severely diffusion limited. Here the required reactor volume is only 20-30% of that required by a fixed bed of 1/8-inch particles. However, reducing the particle size in a fixed bed from 1/8 to 1/16 inch would accomplish a similar reduction. As a result, we can conclude that from a reaction kinetics viewpoint a reaction must be limited severely by pore diffusion before the extra reactor volume required for small particles in fluidized beds is offset by their increased activity. Few residuum reactions are presently hindered to this extent. 

This relationship is plotted in Figure 6.3.9. The effectiveness factor for a severely diffusion-limited reaction in a catalyst particle is approximated by the inverse of the Thiele modulus. 

When macromolecular substrates are involved in the transformation under study, concentration polarization phenomena affect the EMR performance more severely. Diffusion limitations of macromolecular substrates hamper the use of immobilized enzymes in the hydrolysis of high-molecu-lar-weight substrates. By selecting membranes with an appropriate molecular weight cut-off, both enzyme and substrate are retained in an EMR in touch with each other, and hydrolysis products and/or inhibitors are continuously removed from the system. Soluble enzymes can then act directly on substrate macromolecules without diffusion limitations and steric hindrance imposed by enzyme fixation to a solid support. The stirring features of CST EMRs moreover assures that substrates and/or inhibitors within the reactor vessel are maintained at the lowest possible concentration level. Such reactor configuration is then extremely useful when substrate inhibited reaction patterns are involved, or when inhibiting species are assumed to exist in the feed stream. 

Suppose that you have made activation energy measurements on a reaction-catalyst system that you suspect to be severely diffusion-limited, and obtained a value of = 10.5 kcal/mol. What would be the difference in the rate constants projected from 100 °C to 125 °C for the diffusion-limited and the diffusion-free reaction ... 

Construction of Support around the Catalyst Early work employing this approach focused mainly on siHca-based supports. Sol-gel methods were used to polymerize the support around the organometallic complex. A key problem of this approach is the difficulty in controlling the pore size and overall strac-ture of the support material, leading to a substantial variation in the available space around the complex. Severe diffusion limitations are introduced, but the effect on ee can be either positive or negative relative to the homogeneous systems [7]. 

Therefore, in spite of the uncertainty in the value of D, one can be confident that the reaction is severely diffusion-limited, and write... 

Although the tested catalyst shows a good intrinsic selectivity for butadiene hydrogenation, the results evidenced the presence of severe diffusion limitations in spite of the thin active shell (230 im). The experimental data were modeled by Langmuir-Hinshelwood kinetic expressions derived from an elementary mechanism. Nine kinetic parameters were reliably estimated by means of a regression analysis and it is concluded that the proposed kinetic model provides a good fitting of the experimental observations. 

As severe diffusion limitations were expected, mass conservation equations inside the catalytic layer should be solved to relate the observable reaction rates to the bulk liquid composition. Details about the formulation and the numerical solution are given in [5]. 

This behaviour indicates that the catalyst is intrinsically selective, but severe diffusion limitations becomes evident as IBE starts to react when the diffusion capacity of Ha exceeds that of BD. 

The effectiveness factor is a global multiplier of the intrinsic reaction rate that accounts for the severe diffusion limitations encountered in industrial reformers. Effectiveness factors of industrial Ni-based catalysts for the methane-steam and shift reactions are of the order of 0.02 this means that the actual reaction rate experienced by the bulk fluid in the reformer is typically only about few percents of the reaction rate measured in the laboratory under the same conditions but writh very small catalyst particle sizes. 

Severe diffusion limitation at large values of q>i (for q>i > 3), where tanh surface reaction is fast (large fcv)> and/or the diffusion is slow (small Dcomb)... 

A tacit assumption used in the foregoing development is that the system is kinetically controlled. When a single species undergoes an th-order reaction, the effect of a severe diffusion limitation is to shift the order from nto n + l)/2. The order remains intact when n = 1. Then there remains the question, Would the overall order of many first-order reactions remain intact if all the constituent reactions become severely diffusion limited ... 

The solution of the pellet-side conservation equation (Eq. 9.33) is a two-point boundary value problem but is not difficult to solve numerically so long as the intrinsic kinetics are simple and the reaction is moderately diffusion-limited. The problem becomes difficult to solve because of numerical sensitivity when the reaction is severely diffusion-limited and the accuracy of the result is not assured. However, an analytical expression can be obtained in this case for arbitrary intrinsic kinetics as shown in Chapter 4. 

The basic approximations made in arriving at the reactor point effectiveness are (1) isothermal pellet, (2) negligible external mass transfer resistance, and (3) estimation of the pellet center concentration by a simple relationship when the reaction is not severely diffusion-limited. The first two approximations are quite adequate in view of the fact that the mass Biot number is of the order of hundreds under realistic reaction conditions. Both theoretical and experimental justifications for these approximations have been given in Chapter 4. The first approximation will be relaxed when reactions affected by pore-mouth poisoning are considered since a definite temperature gradient then exists within the pellet. An additional approximation is the representation of the difference between the Arrhenius exponentials evaluated at the pellet surface and the bulk-fluid temperatures by a linear rela-... 

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