Intraparticle mass transfer, effect

One often finds that either external or intraparticle mass transfer effects are significant in reactors of this type. Although the treatments... 

Schematic representation of shift in activation energy when intraparticle mass transfer effects become significant.

The usual experimental criterion for diffusion control involves an evaluation of the rate of reaction as a function of particle size. At a sufficiently small particle size, the measured rate of reaction will become independent of particle size. The reaction rate can then be safely assumed to be independent of intraparticle mass transfer effects. At the other extreme, if the observed rate is inversely proportional to particle size, the reaction is strongly influenced by intraparticle diffusion. For a reaction whose rate is inhibited by the presence of products, there is an attendant danger of misinterpreting experimental results obtained for different particle sizes when a differential reactor is used, because, under these conditions, the effectiveness factor is sensitive to changes in the partial pressure of product. 

Here, issues in relation to the trickle flow regime—isothermal operation and plug flow for the gas phase—will be dealt with. Also, it is assumed that the flowing liquid completely covers the outer surface particles (/w = 1 or aLS = au) so that the reaction can take place solely by the mass transfer of the reactant through the liquid-particle interface. Generally, the assumption of isothermal conditions and complete liquid coverage in trickle-bed processes is fully justified with the exception of very low liquid rates. Capillary forces normally draw the liquid into the pores of the particles. Therefore, the use of liquid-phase diffusivities is adequate in the evaluation of intraparticle mass transfer effects (effectiveness factors) (Smith, 1981). 

Table 3.2 summarises the effect which intraparticle mass transfer effects have on parameters involved explicitly or implicitly in the expression for the overall rate of reaction. 

In assessing whether a reactor is influenced by intraparticle mass transfer effects WeiSZ and Prater 24 developed a criterion for isothermal reactions based upon the observation that the effectiveness factor approaches unity when the generalised Thiele modulus is of the order of unity. It has been showneffectiveness factor for all catalyst geometries and reaction orders (except zero order) tends to unity when the generalised Thiele modulus falls below a value of one. Since tj is about unity when 0 < ll for zero-order reactions, a quite general criterion for diffusion control of simple isothermal reactions not affected by product inhibition is < 1. Since the Thiele modulus (see equation 3.19) contains the specific rate constant for chemical reaction, which is often unknown, a more useful criterion is obtained by substituting l v/CAm (for a first-order reaction) for k to give ... 

The initial rate data were also analysed to check the significance of gas-liquid, liquid-solid and intraparticle mass transfer effects under the conditions used in this work. For this purpose the criteria described by Ramchandran and Chaudhari were used. In these criteria, factors a, 02 and < ) are calculated which are defined as the ratios of the observed rates to the maximum rates of gas-liquid, liquid-solid and intraparticle mass transfer respectively. The calculations of these factors are described in the following sections. 

One often finds that either external or intraparticle mass transfer effects are significant in trickle bed reactors. Although the treatments of these topics outlined in Sections 12.3 and 12.4 are in general applicable to trickle bed reactors, analyses specific to such reactors have been reviewed by Gianetto and Specchia (3). 

Figure 4.8. Schematic representation of shift in activation energy when intraparticle mass transfer effects become significant. (Reprinted from ref. 1, copyright 1977. This material is used by permission of John Wiley Sons, Inc.)...

A detailed literature review on esterification of carboxylic acids with different alcohols has been made. The type of catalysts used, their activity, selectivity, kinetic modeling and reaction engineering aspects have been discussed. A general review of the esterification of carboxylic acid with alcohol in presence of mineral acid or heterogeneous acid catalyst have been presented. Critical analyses of reaction engineering aspects such as external and intraparticle mass transfer effects and reactor performance models have been presented and scope and objective of the present thesis outlined. 

Trickle-bed reactors, wherein gas and liquid reactants are contacted in a co-current down flow mode in the presence of heterogeneous catalysts, are used in a large number of industrial chemical processes. Being a multiphase catalytic reactor with complex hydrodynamics and mass transfer characteristics, the development of a generalized model for predicting the performance of such reactors is still a difficult task. However, due to its direct relevance to industrial-scale processes, several important aspects with respect to the influence of external and intraparticle mass transfer effects, partial wetting of catalyst particles and heat effects have been studied previously (Satterfield and Way (1972) Hanika et. al., (1975,1977,1981) Herskowitz and Mosseri (1983)). The previous work has mainly addressed the question of catalyst effectiveness under isothermal conditions and for simple kinetics. It is well known that most of the industrially important reactions represent complex reaction kinetics and very often multistep reactions. Very few attempts have been made on experimental verification of trickle-bed reactor models for multistep catalytic reactions in the previous work. 

Rijnaarts HHM, A Bachmann, JC Jumelet, AJB Zehnder (1990) Effect of desorption and intraparticle mass transfer on the aerobic biomineralization of alpha-hexachlorocyclohexane in a contaminated calcareous soil. Environ Sci Technol 24 1349-1354. 

To illustrate the masking effects that arise from intraparticle and external mass transfer effects, consider a surface reaction whose intrinsic kinetics are second-order in species A. For this rate expression, equation 12.4.20 can be written as... 

Intraparticle Mass Transfer. One way biofilm growth alters bioreactor performance is by changing the effectiveness factor, defined as the actual substrate conversion divided by the maximum possible conversion in the volume occupied by the particle without mass transfer limitation. An optimal biofilm thickness exists for a given particle, above or below which the particle effectiveness factor and reactor productivity decrease. As the particle size increases, the maximum effectiveness factor possible decreases (Andrews and Przezdziecki, 1986). If sufficient kinetic and physical data are available, the optimal biofilm thickness for optimal effectiveness can be determined through various models for a given particle size (Andrews, 1988 Ruggeri et al., 1994), and biofilm erosion can be controlled to maintain this thickness. The determination of the effectiveness factor for various sized particles with changing biofilm thickness is well-described in the literature (Fan, 1989 Andrews, 1988)... 

Finally, intraparticle diffusion appears to be an important factor in adsorption kinetics for many types of systems. In the past it has been customary to define such mass transfer quantitatively in terms of an effective diffusivity. However, even in gas-solid systems more than one process can be involved for porous particles. Thus, two-dimensional migration on the pore surface, surface diffusion, is a potential contribution. Liquid systems appear to be more complex, and, with electrolytes, it has been shown that the electric potential induced by counter-diffusing ions should be taken into account. A realistic description of intraparticle mass transfer in such cases requires more than a single rate coefficient for a binary system. 

The effectiveness factor is very low, indicating that intraparticle mass transfer resistance is very significant. The gas-liquid mass transfer resistance is also important, as expected. On the other hand, the liquid-solid mass transfer resistance is negligible. As a result, the rate of reaction in the slurry reactor is about 50 times higher than that in the trickle-bed. Therefore, in cases of such high rates of reaction, the slurry reactor is a better choice, although the gas-liquid mass transfer and the filtration of the catalyst may be a problem. 

Even better yields of C result if components X and Y are incorporated in the same catalyst particle, rather than if they exist as separate particles. In effect, the intermediate product B no longer has to be desorbed from particles of the X type catalyst, transported through the gas phase and thence readsorbed on Y type particles prior to reaction. Resistance to intraparticle mass transfer is therefore reduced or eliminated by bringing X type catalyst sites into close proximity to Y type catalyst sites. Curve 4 in Fig. 3.10 illustrates this point and shows that for such a composite catalyst, containing both X and Y in the same particle, the yield of C for reaction 3 is higher than it would have been had discrete particles of X and Y been used (curve 3). 

If enzymes are immobilized by copolymerization or microencapsulation, the intraparticle mass-transfer resistance can affect the rate of enzyme reaction. In order to derive an equation that shows how the mass-transfer resistance affects the effectiveness of an immobilized enzyme, let s make a series of assumptions as follows ... 

The analysis of intraparticle mass-transfer resistance requires the knowledge of the effective diffusivity Ds of a substrate in an immobilized matrix, such as agarose, agar, or gelatin. Gels are porous... 

Figure 11. Effectiveness factor ij as a function of the observable variable t/Dau- Combined influence of intraparticle mass transfer and interphase heat and mass transfer on the effective reaction rate (first order, irreversible reaction in a sphere, Biot number Biw = 100, Arrhenius number y = 30, modified Prater number / as a parameter).

Table 2 lists most of the available experimental criteria for intraparticle heat and mass transfer. These criteria apply to single reactions only, where it is additionally supposed that the kinetics may be described by a simple nth order power rate law. The most general of the criteria, 5 and 8 in Table 2, ensure the absence of any net effects (combined) of intraparticle temperature and concentration gradients on the observable reaction rate. However, these criteria do not guarantee that this may not be due to a compensation of heat and mass transfer effects (this point has been discussed in the previous section). In fact, this happens when y/J n [12]. 

Heat or mass transfer effects, caused by intrareactor, interphase, or intraparticle gradients (see Figure 5), can disguise the results and lead to misinterpretations. Before accurate and intrinsic catalyst kinetic data can be established, these disguises must be eliminated by adjusting the experimental conditions. 

The use of nonporous supports for protein immobilization will eliminate the problems associated with the intraparticle diffusion limitations. With columns regularly packed with small spherical particles of limited size distribution, the mass transfer effects associated with a nonuniform flow distribution will be minimized. Extra column effects due to diffusion in the stagnant liquid pockets will be reduced by using short and properly designed connecting lines to the injector and the detector. 

The mass transfer effects due to the diffusion into the intraparticle medium will be eliminated with nonporous supports 49.501. One can also use pellicular supports by immobilizing the protein on the external surface. This approach is possible (21-25] with silica adsorbents of small pore size (< 6 nm) because the large biomolecules of antibodies cannot penetrate into the pores of the support, and the immobilization takes place on the external surface of the particles. 

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