Product, diffusional resistance

Decompositions may be exothermic or endothermic. Solids that decompose without melting upon heating are mostly such that can give rise to gaseous products. When a gas is made, the rate can be affected by the diffusional resistance of the product zone. Particle size is a factor. Aging of a solid can result in crystallization of the surface that has been found to affect the rate of reaction. Annealing reduces strains and slows any decomposition rates. The decompositions of some fine powders follow a first-order law. In other cases, the decomposed fraction x is in accordance with the Avrami-Erofeyev equation (cited by Galwey, Chemistry of Solids, Chapman Hall, 1967)... 

When the product layer is porous the reaction will continue but at decreasing rate as the diffusional resistance increases with increasing conversion. Then,... 

A simple rectifying column consists of a tube arranged vertically and supplied at the bottom with a mixture of benzene and toluene as vapour. At the top a condenser returns some of the product as a reflux which flows in a thin film down the inner wall of the tube. The tube is insulated and heat losses can be neglected. At one point in the column the vapour contains 70 mol% benzene and the adjacent liquid reflux contains 59 moi% benzene. The temperature at this point is 365 K. Assuming the diffusional resistance to vaponr transfer to be equivalent to the diffusional resistance of a stagnant vapour layer 0.2 mm thick, calculate the rate of interchange of benzene and toluene between vapour and liquid. The molar latent heats of the two materials can be taken as equal. The vapour pressure of toluene at 365 K is 54.0 kN/nt2 and the diffusivity of the vapours is 0.051 cm2/s... 

Let us now assume that isomerization of xylenes is a simple series reaction. Starting with pure o-xylene feed, and in the absence of any diffusional resistance, most molecules of o-xylene which enter the zeolite crystallites leave after, at most, one reaction step (to m-xylene), yielding primarily a single-step product. When substantial diffusion-resistance exists, most molecules remain in the crystallite long enough for several reaction steps to occur (to m-xylene and p-xylene), and the products are mostly multistep products. Wei (4) has shown that in such a case the apparent kinetics—i.e., those determined from the respective reactant product concentrations in the bulk phase—change from that of a simple series reaction... 

The high values of CH4/total hydrocarbons ratio observed for C-155 and SC-155, suggest that when CO and H2 reach the catalyst active sites and the reactions proceed CH4 is kinetically the first product obtained, and it can leave immediately the catalyst due to the big dimensions of the catalyst pores, denoting a low diffusional resistance for this process. 

The internal structure, comprising pores and surface area, is important for making the active catalytic sites accessible to the reactant molecules. The location of the active species is important for minimizing diffusional resistance since reactants must diffuse within the particle to the active sites and products must diffuse away. Finally, high catalytic surface area and high dispersion of active species are advantageous for maximum reaction rate and utilization of the catalytic components. 

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. 

A major disadvantage of the gel entrapment route to immobilization is the potential for physical loss of the enzyme as time elapses. To circumvent this problem, cross-linking agents, such as A,A -methylene-bis-acrylamide or glutaraldehyde, may be used to more firmly immobilize the enzyme or to provide mechanical stability. However, the more rigid the matrix the greater is the possibility that diffusional resistance to transport of reactants (substrates) to the site of the enzyme and of products out of the gel will limit the reaction rate. 

Various types of solid adsorbents have been used to concentrate different biochemical products from fermentation broths. The size of the solid adsorbent particle is important because large macroscopic beads can easily be separated and recovered from fermentation broths. However, large porous beads exhibit internal diffusional resistance and depending on processing time, all the binding sites of the adsorbent may not be utilized, resulting in a lower adsorption capacity. Also, for some adsorbents cell debris and proteinaceous materials may tend to adhere to the surface of the solid adsorbent and would contaminate the product in the subsequent elution process (7) ... 

A novel approach to increase the overall extraction yield of a microbial product has been developed. The primary isolation steps of fermentation derived microbial products generally involve procedures including solid removal, wash and volume reduction using either solvent extraction or ion-exchange. These steps can be further simplified by the use of whole broth extraction. In the case of using solid phase adsorbents, extraction performance can be drastically affected by the size and the nature of the adsorbent used. If the adsorbent size is large, it exhibits internal diffusional resistance (pore diffusion) and the resultant mass transfer resistance reduces the overall rate of adsorption... 

In addition to the above, the model for the catalyst bed module should include equations for the pressure drop across the bed. Although these equations are reasonably simple and their solution as a part of the model equation is a straightforward exercise, they are of crucial importance for without appreciation of the pressure drop consideration fast increases in reactor productivity can be theoretically estimated using the model with very fine particles. Obviously, this is not practically possible because of the excessive pressure drop associated with fine particles. In fact, it is the excessive pressure drop associated with small catalyst pellets that necessitates the use of relatively large catalyst particles in fixed beds. The use of these relatively large particles in turn, is the reason behind the existence of diffusional resistances and thus all the complexities associated with reliable modelling of industrial fixed bed catalytic reactors. 

Figure 1 shows a schematic diagram of an immobilized affinity adsorbent bead. Hydrogel, by virtue of its extremely high water content (>90%), offers limited diffusional resistance to the desired product. It is therefore used as an inert matrix to support... 

It was found that the decline in selectivity was least in case (c) because of a smaller overall diffusional resistance of the bead. Figure 8 shows the variation of product purity (Pu) as a function of time for these three cases. The product purity curves show the same general trend as the selectivity curves. Final product purity was also found to be highest for case (c). By virtue of their lower overall mass transfer resistance case (c) immobilized adsorbent beads not only display a higher adsorption rate but also offer a higher selectivity for the desired product. 

Often an important reason to avoid intraparticle diffusion resistances is from selectivity considerations. To maximize the intermediate product in a consecutive reaction scheme, we should avoid intraparticle diffusional resistances. For butene dehydrogenation it can be seen in Fig. 14 that... 

Given the availability of hollow fiber membranes adequately permeable to substrates and products, and the control of fluid flow all around the fibers in the bundle in order to assure uniform flow distribution and to avoid stagnation (in order to reduce mass transfer diffusional resistances), the technique offers several advantages. Enzyme proteins can be easily retained within the core of the fibers with no deactivation due to coupling agents or to shear stresses, and the enzyme solution can be easily recovered and/or recycled. 

The dynamics of substrate conversion therefore depend on enzyme kinetics as well as on mass transport conditions. Diffusion through the membrane matrix and within the flowing solution, play the most important roles in transport mechanisrris. Since the flow is laminar in most cases, substrate and product transport resistances through the dense layer are exceedingly small relative to diffusional resistances in the flowing solution. The rate-limiting step in sub-... 

Because of the small pores in zeolitic catalysts, reaction rates may be controlled by rates of diffusion of reactants and products. Beecher, Voorhies, and Eberly (4) studied hydrocracking of mixtures of n-decane and Decalin with mordenite catalysts impregnated with palladium. They found that acid leaching of the mordenite produces an aluminum-deficient structure of significantly higher catalytic activity. At least part of this improvement appears to be caused by the decrease in diffusional resistance. They observed that with this type of catalyst, the effective catalyst pore diameter appears to be smaller than calculated owing to the strong interaction or adsorption of hydrocarbon molecules on the pore walls. 

It is instructive to compare this actual pellet production rate to the rate in the absence of diffusional resistance. If the diffusion were arbitrarily fast, the concentration everywhere in the pellet would be equal to the surface concentration, corresponding to the limit - 0. The pellet rate for this limiting case is simply... 

A porous matrix is sandwiched between two membranes. The matrix supports a liquid-phase catalyst. For the reaction A -> B, membrane 1 passes A but resists B, and membrane 2 passes both freely the function of membrane 2 is to encapsulate the catalyst solution. Reactant A is fed external to membrane 1 the concentration of A drops across the catalyst as it is consumed by reaction, due to diffusional resistance. The product diffuses to the right, reactant A does not. The benefits of this reactor are the liquid phase is encapsulated, the catalyst is separated from the product stream, the product is separated from the reactant, it provides a higher gas-liquid interfacial area, and a product is removed from an equilibrium-limited reaction. The authors suggested that the system be implemented as a shell-and-tube configuration using two different hollow-fiber membranes. 

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