Diffusional limitation, external

The activity of the Pt-exchanged catalyst for n-C f, transformation increases when the crystallites size increases, which was totally unexpected. External diffusional limitations cannot be invoked since the size of the grains of catalyst is the same. Moreover, this would lead to the opposite result. Other experiments showed that the activity of zeolite-... 

The reaction kinetics were studied at temperatures between 240°C and 400°C, propylene oxide partial pressures between. 4 10 bar and 4.0 10 J bar and oxygen partial pressures between. 02 bar and. 2 bar. At steady state external diffusional limitations as well as diffusional effects inside the porous silver film were negligible (4). The kinetics and potentiometric results can be summarized as follows (4) ... 

The insolubility of enzymes in monophasic organic systems has a controlling influence on the kinetics of enzymatic catalysis in organic media. Insolubilized enzymes are subject to intraparticle and external diffusional limitations which can mask the true, intrinsic kinetics of catalysis. These limitations are particularly severe for highly active and purified enzymes such as horseradish peroxidase. One way to overcome this problem is to increase the surface area of the enzyme in contact with the organic solvent. 

The Damkohler number indicates which characteristic first-order process is faster, external diffusion or reaction. For very large values of Da (ks the surface concentration of reactant approaches zero, whereas for very small values of Da ks the surface concentration approaches the bulk fluid concentration. An interphase effectiveness factor, Tj, is defined as the reaction rate based on surface conditions divided by the rate that would be observed in the absence of diffusional limitations ... 

Internal and external mass transfer resistances are important factors affecting the catalyst performance. These are determined mainly by the properties of the fluids in the reaction system, the gas-liquid contact area, which is very high for monolith reactors, and the diffusion lengths, which are short in monoliths. The monolith reactor is expected to provide apparent reaction rates near those of intrinsic kinetics due to its simplicity and the absence of diffusional limitations. The high mass transfer rates obtained in the monolith reactors result in higher catalyst utilization and possibly improved selectivity. 

These values allow to exclude external diffusional limitations, for which the pseudo-activation energies are in the 10-20 kJ /mol range. However, internal diffusion limitations caimot be excluded, as usual in the case of zeolites, particularly because of the high operating temperatures. So the above values should be regarded as apparent activation energies. 

The influence of diffusional limitations in gas phase reactions has been extensively treated by Wheeler and from a chemical engineering viewpoint by Hougen and Watson More recently a monograph by Satterfield and Sherwood has appeared. The problem of diffusion can be separated into two parts, the first is diffusion or mass transfer to the external surface of the catalyst and second, for those catalysts which are porous, diffusion within the catalyst pores. When diffusion is the rate limiting process, reaction rate, selectivity and activation energy are affected. 

To avoid diffusional limitations it is advisable to assay the enzyme activity under more drastic conditions. Amongst other things, this means increasing stirrer speed to exclude external diffusion, crushing the particles to reduce porous diffusion, increasing the substrate concentration to about > 100-fold of K vi-value to avoid lack of substrate at the center of the particles or adding buffer to avoid pH-shifts. If the reaction rate is increased by any of these means it is likely that diffusional control is operative and can to some extent be reduced or even eliminated. 

The catalytic behavior of enzymes in immobilized form may dramatically differ from that of soluble homogeneous enzymes. In particular, mass transport effects (the transport of a substrate to the catalyst and diffusion of reaction products away from the catalyst matrix) may result in the reduction of the overall activity. Mass transport effects are usually divided into two categories - external and internal. External effects stem from the fact that substrates must be transported from the bulk solution to the surface of an immobilized enzyme. Internal diffusional limitations occur when a substrate penetrates inside the immobilized enzyme particle, such as porous carriers, polymeric microspheres, membranes, etc. The classical treatment of mass transfer in heterogeneous catalysis has been successfully applied to immobilized enzymes I27l There are several simple experimental criteria or tests that allow one to determine whether a reaction is limited by external diffusion. For example, if a reaction is completely limited by external diffusion, the rate of the process should not depend on pH or enzyme concentration. At the same time the rate of reaction will depend on the stirring in the batch reactor or on the flow rate of a substrate in the column reactor. 

The first step in characterizing the heparinase binding rate to the catalyst particles is to establish experimental conditions where neither enzyme denaturation or external mass transfer are important. This can be accomplished by controlling the duration of immobilization, the mixing rate, and the catalyst particle size. In the absence of diffusional limitations and enzyme denaturation effects, the disappearance of enzymatic activity from the bulk phase equals the rate at which the enzyme binds to the catalyst particle. The molar conservation equation for heparinase in the bulk phase is given by... 

Step 1. Reactants enter a packed catalytic tubular reactor, and they must diffuse from the bulk fluid phase to the external surface of the solid catalyst. If external mass transfer limitations provide the dominant resistance in this sequence of diffusion, adsorption, and chemical reaction, then diffusion from the bulk fluid phase to the external surface of the catalyst is the slowest step in the overall process. Since rates of interphase mass transfer are expressed as a product of a mass transfer coefficient and a concentration driving force, the apparent rate at which reactants are converted to products follows a first-order process even though the true kinetics may not be described by a first-order rate expression. Hence, diffusion acts as an intruder and falsifies the true kinetics. The chemical kineticist seeks to minimize external and internal diffusional limitations in catalytic pellets and to extract kinetic information that is not camouflaged by rates of mass transfer. The reactor design engineer must identify the rate-limiting step that governs the reactant product conversion rate. 

The only instances in which external mass transfer processes can influence observed conversion rates are those in which the intrinsic rate of the chemical reaction is so rapid that an appreciable concentration gradient is established between the external surface of the catalyst and the bulk fluid. The rate at which mass transfer to the external catalyst surface takes place is greater than the rate of molecular diffusion for a given concentration or partial pressure driving force because turbulent mixing or eddy diffusion processes will supplement ordinary molecular diffusion. Consequently, for porous catalysts one does not encounter external mass transfer limitations except in those circumstances in which intraparticle diffusional limitations are also present. 

Koros [44] obtained a criterion for neglecting external mass transfer by comparing the Weisz-Prater criterion for the absence of a diffusional limitation within the catalyst as given by Froment and Bishoff [14] ... 

In this case the internal pore diffusional limitations are severe and thus reaction occurs only in a narrow zone (shell) close to the exterior surface. The utilization of the pellet is directly proportional to the size of this zone which in turn is directly related to the fraction of external area wetted. 

A third difference concerns Ti-MWW only. The siting of Ti in different porous environments, that is in external pockets, in internal supercages and in sinusoidal 10-MR channels, leads to active species associated with different diffusional and steric constraints [79]. Thus, the epoxidation of bulky olefins can occur exclusively in external pockets, whereas the linear ones are not subject to site limitations. Ti-MWW is also an unusual catalyst in the epoxidation of stereoisomers. At odds with TS-1 and Ti-Beta zeolites, trons-olefins are epoxidized faster than their as analogues [85]. Though the mechanism is still unclear, a better fitting of the trans configuration to the tortuous nature of 10-MR channels could be an explanation. 

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