Internal diffusional effect

A first order reaction occurs in a porous slab when both external and internal diffusional resistances are present. An equation for the overall effectiveness will be devekoped. 

Internal diffusional limitations are possible any time that a porous immobilized enzymatic preparation is used. Bernard et al. (1992) studied internal diffusional limitations in the esterification of myristic acid with ethanol, catalyzed by immobilized lipase from Mucor miehei (Lipozyme). No internal mass diffusion would exist if there was no change in the initial velocity of the reaction while the enzyme particle size was changed. Bernard found this was not the case, however, and the initial velocity decreased with increasing particle size. This corresponds to an efficiency of reaction decrease from 0.6 to 0.36 for a particle size increase from 180 pm to 480 pm. Using the Thiele modulus, they also determined that for a reaction efficiency of 90% a particle size of 30 pm would be necessary. While Bernard et al. found that their system was limited by internal diffusion, Steytler et al. (1991) found that when they investigated the effect of different sizes of glass bead, 1 mm and 3 mm, no change in reaction rate was observed. 

An effectiveness factor, rj, can be defined as the ratio of the observed rate (tobs) to the rate that would be observed in the absence of internal diffusional limitations... 

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 influence of internal and interfacial diffusion on catalyst deactivation by simultaneous sintering and poisoning is examined. The study focuses on the copper catalyst used in the water gas shift reaction ( WGSR). It is found that catalyst life increases when internal and external poison diffusional resistance increases. Temperature reduces the total average activity but this effect is partially neutralized by the diffusional effects undergone by the reactants inside the pellet. 

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. 

Models for Enzyme Kinetics Under Internal Diffusional Restrictions for Different Particle Geometries Effectiveness Factor... 

Combined Effect of External and Internal Diffusional Restrictions... 

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... 

A second test addresses the potential occurrence of internal transport limitations and consists of performing experiments with catalyst pellets of varying dimensions. For larger pellet diameters, diffusional effects are more likely to affect the observed kinetics. Hence, for positive reaction orders, a decrease in the observed reaction rate is expected when internal mass transport limitations become important (see Fig. 5). Although rather unlikely at the laboratory scale. 

Transport Criteria in PBRs In laboratory catalytic reactors, basic problems are related to scaling down in order to eliminate all diffusional gradients so that the reactor performance reflects chemical phenomena only [24, 25]. Evaluation of catalyst performance, kinetic modeling, and hence reactor scale-up depend on data that show the steady-state chemical activity and selectivity correctly. The criteria to be satisfied for achieving this goal are defined both at the reactor scale (macroscale) and at the catalyst particle scale (microscale). External and internal transport effects existing around and within catalyst particles distort intrinsic chemical data, and catalyst evaluation based on such data can mislead the decision to be made on an industrial catalyst or generate irrelevant data and felse rate equations in a kinetic study. The elimination of microscale transport effects from experiments on intrinsic kinetics is discussed in detail in Sections 2.3 and 2.4 of this chapter. 

When internal diffusional limitations are present in catalysts where a reaction with power-law kinetics occurs, information on the effectiveness factor is required. For isothermal systems, the chemical and diffusional limits are included into the results of Section 3.3. According to Equation 3.68,... 

Valencia, P., S. Flores, L. Wilson, and A. Illanes. 2011. Effect of Internal Diffusional Restrictions on the Hydrolysis of Penicillin G Reactor Performance and Specific Productivity of 6-Apa with Immobilized Penicillin Acylase. Applied Biochemistry... 

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... 

Much more rigorous tests of the importance of diffusional effects can be made if the intrinsic kinetics are known on the basis of the generalized internal effectiveness factor and reactor point effectiveness. Using the rate expression of Eq. 4.2 in Eq. 4.73 for 4>c 8 =... 

For catalytic investigations, the rotating basket or fixed basket with internal recirciilation are the standard devices nowadays, usually more convenient and less expensive than equipment with external recirculation. In the fixed basket type, an internal recirculation rate of 10 to 15 or so times the feed rate effectively eliminates external diffusional resistance, and temperature gradients. A unit holding 50 cm (3.05 in ) of catalyst can operate up to 800 K (1440 R) and 50 bar (725 psi). 

The packing itself may consist of spherical, cylindrical, or randomly shaped pellets, wire screens or gauzes, crushed particles, or a variety of other physical configurations. The particles usually are 0.25 to 1.0 cm in diameter. The structure of the catalyst pellets is such that the internal surface area far exceeds the superficial (external) surface area, so that the contact area is, in principle, independent of pellet size. To make effective use of the internal surface area, one must use a pellet size that minimizes diffusional resistance within the catalyst pellet but that also gives rise to an appropriate pressure drop across the catalyst bed. Some considerations which are important in the handling and use of catalysts for fixed bed operation in industrial situations are discussed in the Catalyst Handbook (1). 

Internal surface of porous particles also has limitations. Diffusional resistances of participants may be such that only a fraction of the pore surfaces is accessed, resulting in a waste of expensive catalyst, or undersizing of equipment that is designed for full utilization of the catalytic surface. Appraising the effectiveness of internal surface is the main thesis of this chapter. 

No experiments with variation in particle size of the silica gel have been done to study intraparticle diffusion effects. In silica gel such diffusion would be only through the pores (analogous to the macropores of a polystyrene) since the active sites lie on the internal surface. The silica gel used by Tundo had a surface area of 500 m2/g and average pore diameter of 60 A.116). Phosphonium ion catalyst 28 gave rates of iodide displacements that decreased as the 1-bromoalkane chain length increased from C4 to Cg to C16, The selectivity of 28 was slightly less than that observed with soluble catalyst hexadecyltri-n-butylphosphonium bromide U8). Consequently the selectivity cannot be attributed to intraparticle diffusional limitations. 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

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