Intraparticle diffusion limitations

Mass transfer considerations are critical in any bioprocess. In typical, aerobic, suspended cell fermentations, the major concern is the oxygen transfer rate, determined by the overall mass transfer coefficient, kft, and the driving force. In three-phase biofluidization, in which the cells are immobilized as a biofilm or within carrier particles, the situation is further complicated by possible intraparticle diffusion limitations. Numerous recent studies have addressed these issues. 

Intraparticle diffusion limits rates in triphase catalysis whenever the reaction is fast enough to prevent attaiment of an equilibrium distribution of reactant throughout the gel catalyst. Numerous experimental parameters affect intraparticle diffusion. If mass transfer is not rate-limiting, particle size effects on observed rates can be attributed entirely to intraparticle diffusion. Polymer % cross-linking (% CL), % ring substitution (% RS), swelling solvent, and the size of reactant molecule all can affect both intrinsic reactivity and intraparticle diffusion. Typical particle size effects on the... 

Solid particles are in the range of 0.01 to 1.0 mm (0.0020 to 0.039 in), the minimum size limited by filterability. Small diameters are used to provide as large an interface as possible to minimize the liquid-solid mass-transfer resistance and intraparticle diffusion limitations. Solids concentrations up to 30 percent by volume may be handled however, lower concentrations may be used as well. For example, in hydrogenation of oils with Ni catalyst, the solids content is about 0.5 percent. In the manufacture of hydroxylamine phosphate with Pd-C, the solids content is 0.05 percent. 

We can now summarize where slurry reactors are an attractive option in heterogeneous catalytic processes. For any application where a liquid is present and which benefits from small catalyst particles below 200 pm, for example because intraparticle diffusion limitation has to be avoided (see below), the slurry reactor is attractive, provided pressure drops in the order of one to several bars are acceptable. 

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. 

When the effectiveness factor of such practical catalysts is 1, i.e., there is no intraparticle diffusion limitation at all, crushing or grinding the catalyst to obtain smaller particles can be a way to assess catalyst performance in small-scale laboratory... 

Intraparticle diffusion limitation (step 6) is a well-documented phenomenon in catalysis in general, and its effect on catalyst utilization is given by the Thiele modulus (f), defined by... 

The catalyst particle sizes used in RD are usually of 1-3 mm range to avoid intraparticle diffusion limitations. To overcome the flooding limitations, the catalyst particles are contained within wire gauze envelopes. Most commonly, the catalyst envelopes are packed inside the column. Various shapes of catalyst envelopes have been patented. Some of these structures include ... 

SOLID ACID CATALYSED ACYLATION OF 2-METHOXY-NAPHTHALENE ROLE OF INTRAPARTICLE DIFFUSION LIMITATION... 

The effects of particle size and temperature clearly demonstrated that the reaction was controlled by intraparticle diffusion resistance. Thus, the initial rates were plotted against dp (inverse of particle diameter) to find that a straight line passing through origin was obtained (Fig.7). This confirms that the reaction was intraparticle diffusion limited". 

Mordenite etc. Dodecatungstophosphoric acid (DTPA) and the ion exchange resin catalysts showed maximum activities. Clay based catalysts and sulphated zirconia showed a moderate activity. Zeolites did not demonstrate any activity to the reaction due to pore size restriction. A 100% selectivity towards the ortho product (l-acetyl-2-methoxy naphthalene) was observed for almost all the reactions for all the catalysts. The para product (2-methoxy-6-acetyl naphthalene) was formed when the aluminium chloride was used as a homogeneous catalyst with nitrobenzene as the solvent. The reaction product was isolated and conformed by the melting point, FT-IR, H-NMR, etc. The reaction is intraparticle diffusion limited. A different catalyst would be required to get p-product selectively. 

The TPD data of Cat 1 and Cat 2 (Figure 1) were analysed kinetically to obtain more information on the adsorption behaviour. The kinetic analysis was based on the following assumptions 1) intraparticle diffusion limitations were negligible in the... 

EXTERNAL MASS TRANSFER AND INTRAPARTICLE DIFFUSION LIMITATIONS... 

In a catalytic reactor, the fluid flows through the catalyst particles and may face a resistance caused by the concentration gradient between the bulk fluid and the external particle surface. This resistance (interparticle or external mass transfer limitation) must be added to intraparticle diffusion limitation. 

Curve n shows a lower concentration gradient outside the particle, compared to curve 1, but followed by a concentration gradient inside the pore due to the intraparticle diffusion limitation. On the other hand, curve III does not have influence of external limitations, representing the reaction rate in the presence of pore-diffusion resistance as shown in the following equation ... 

Defining a new factor that comprises both external mass transfer and intraparticle diffusion limitations (Fogler, 2000) ... 

Bukhavtsova and Ostrovskii [9] have studied the effect of capillary condensation on the reaction rate of p-xylene hydrogenation in transitions by variations of the feedstock flow and temperature. In order to avoid the intraparticle diffusion limitation, the crushed catalyst particles were used (0.25-0.5 mm). 

Table 4.3 lists some typical gas-liquid hydrogenation reactions investigated in order to explore the features of three-phase catalytic membrane reactors. An example of the application of three-phase catalytic membrane reactors to the hydrogenation of sunflower seed oil can be found in Veldsmk (2001), where it was shown that for this hydrogenation running under kinet-ically controlled conditions the interfacial transport resistances and intraparticle diffusion limitations did not have any effect. Unfortunately the catalyst underwent a serious deactivation process. 

The Weisz modulus [11] allows for the estimation of intraparticle diffusion limitations in packed bed microchannel reactors ... 

Griteria for the importance of intraparticle Diffusion Limitations Example 3.9.A Application of the Extended Weisz-Prater Griterion... 

A more refined theory taking intraparticle diffusion limitation into account has been developed by Sada et al. [l42] while Pal et al. [l30] consider the bimolecular reaction A(G) -> A(L)... 

Fixed- and Ebulliating-Bed Processes Intraparticle Diffusion Limitations in FT Catalysts. In a fixed-bed mode of operation, pressure drop considerations will dictate a minimum particle size, which in general is of the order of one or a few millimetres. Heat removal and minimization of temperature gradients in the bed rely on the effective heat conductivity in the bed, which is favoured by high fluid velocities and large particles. In an ebulliating bed, too, catalyst particles should not be too small lest they be entrained by the fluid as in a slurry reactor. 

It can be envisaged that, in particles a few millimetres in size, intraparticle diffusion limitations will prevail, and this constitutes a constraint on the use of large-sized particles, which are desirable from the viewpoints of pressure drop and heat conductivity in a fixed bed. 

The study of the possible effects of particle size and pore diameter on intraparticle diffusion limitations was invariably carried out with synthesis gas having a H2/CO feed ratio of 2 mol/mol. As the H2/CO usage ratios observed were also very close to 2 mol/mol in this... 

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