Diffusional limitation, external internal

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 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. 

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. 

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. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

The extent of external and internal mass transfer limitation can be estimated by the methods introduced by Carberry and by Wheeler-Weisz [12]. A Carberry number (Ca) smaller than 0.05 means that diffusional retardation by external mass transport may be neglected. A Wheeler-Weisz group (WW) smaller than 0.1 means that pore diffusion limitation is negligible [13,14]. 

Ishikawa H, Tanaka T, Kuro K et al. (1987) Evaluation of tme kinetic parameters for reversible immobihzed enzyme reactions. Biotechnol Bioeng 29 924-933 Jeison D, Ruiz G, Acevedo F et al. (2003) Simulation of the effect of intrinsic reaction kinetics and particle size on the behavior of immobihzed enzymes under internal diffusional restrictions and steady state operation. Proc Biochem 39(3) 393-399 Katchalski-Katzir E, Kraemer DM (2000) Eupergit C, a carrier for immobDization of enzymes of industrial potential. J Mol Catal B Enzym 10 157-176 Kheirolomoom A, Khorasheh F, Fazehnia H (2002) Influence of external mass transfer limitation on apparent kinetic parameters of peniciUin G acylase immobihzed on nonporous ultrafine silica particles. J Biosci Bioeng 93 125-129... 

Mass transfer limitations can be relevant in heterogeneous biocatalysis. If the enzyme is immobilized in the surface or inside a solid matrix, external (EDR) or internal (IDR) diffusional restrictions may be significant and have to be considered for proper bioreactor design. As shown in Fig. 3.1, this effect can be conveniently incorporated into the model that describes enzyme reactor operation in terms of the effectiveness factor, defined as the ratio between the effective (or observed) and inherent (in the absence of diffusional restrictions) reaction rates. Expressions for the effectiveness factor (rj), in the case of EDR, and the global effectiveness factor (t ) for different particle geometries, in the case of IDR, were developed in sections 4.4.1 and 4.4.2 (see Eqs. 4.39-4.42,4.53,4.54,4.71 and 4.72). Such functions can be generically written as ... 

The influence of the internal effectiveness factor, t, on global rate thus has similarities to that of the external effectiveness factor, fj, in that a) the higher the reaction order, the greater the diffusional effect b) t unity for small values of the Thiele modulus, (/>, and similarly, fj unity for small values of the Damkohler number, Dao and c) at large values of these two moduli, T = l/(/)(for 0 > 3) and fj = 1/Dao. Assuming that external mass transfer limitations have been removed (Cg = Co), the effect of internal (pore) diffusion on the observed kinetics can be determined i.e., for cf) > 3, i] = l/4> and... 

The importance of internal diffusion can also be appreciated from a different point of view the fact that the internal diffusion plays a pivotal role in internal and external transport processes. For negligible concentration gradient in the pellet, Eq. 4.57 still holds. However, the value of r Da will be larger than that for diffusion-limited case for the same intrinsic rate since 17 is larger and therefore the pellet will be more isothermal as Figure 4.7 reveals. Further, a relativdy large Biot number for mass under realistic conditions still ensures negligible external mass transfer resistance. It is seen then that in the absence of diffusional resistance, the pellet tends to be more isothermal and the only major resistance is likely to be external heat transfer. 

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