Intraparticle Resistances

The Biot number Bim for mass transport. This can be interpreted as the ratio of internal to external transport resistance (intraparticle diffusion versus interphase diffusion) ... 

The Biot number Bib for heat transport. Analogous to Bim, this is defined as the ration of the internal to external heat transfer resistance (intraparticle heat conduction versus interphase heat transfer). 

On the basis of extensive computations which were performed with a three-phase dispersion model for bubble column slurry reactors accounting for all relevant jiie-nomena, i.e., dispersion in all phases, catalyst settling, nonlinear reaction kinetics, gas-liquid and liquid-solid mass transfer resistances, intraparticle diffusion and variable gas flow rate, the following conclusions can be stated ... 

Physical Properties. Physical properties of importance include particle size, density, volume fraction of intraparticle and extraparticle voids when packed into adsorbent beds, strength, attrition resistance, and dustiness. These properties can be varied intentionally to tailor adsorbents to specific apphcations (See Adsorption liquid separation Aluminum compounds, aluminum oxide (alumna) Carbon, activated carbon Ion exchange Molecular sieves and Silicon compounds, synthetic inorganic silicates). 

Intraparticle mass transport resistance can lead to disguises in selectivity. If a series reaction A — B — C takes place in a porous catalyst particle with a small effectiveness factor, the observed conversion to the intermediate B is less than what would be observed in the absence of a significant mass transport influence. This happens because as the resistance to transport of B in the pores increases, B is more likely to be converted to C rather than to be transported from the catalyst interior to the external surface. This result has important consequences in processes such as selective oxidations, in which the desired product is an intermediate and not the total oxidation product CO2. 

Combined Intraparticle Resistances When solid diffusion and pore diffusion operate in parallel, the effec tive rate is the sum of these two rates. When solid diffusion predominates, mass transfer can be represented approximately in terms of the LDF approximation, replacing/c in column 2 of Table 16-12 with... 

Overall Resistance With a linear isotherm (R = 1), the overall mass transfer resistance is the sum of intraparticle and extraparticle resistances. Thus, the overall LDF coefficient for use with a particle-side driving force (column 2 in Table 16-12) is ... 

Solutions are provided for external mass-transfer control, intraparticle diffusion control, and mixed resistances for the case of constant Vj and F, out = 0- The results are in terms of the fractional... 

The ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

Polymer-supported catalysts often have lower activities than the soluble catalysts because of the intraparticle diffusion resistance. In this case the immobilization of the complexes on colloidal polymers can increase the catalytic activity. Catalysts bound to polymer latexes were used in oxidation reactions, such as the Cu-catalyzed oxidation of ascorbic acid,12 the Co-catalyzed oxidation of tetralin,13 and the CoPc-catalyzed oxidation of butylphenol14 and thiols.1516 Mn(III)-porphyrin bound to colloidal anion exchange resin was... 

Solutions are provided for external mass-transfer control, intraparticle diffusion control, and mixed resistances for the case of constant Vf and F0 in = FVi out = 0. The results are in terms of the fractional approach to equilibrium F = (ht — hf)/(nT — nf), where hf and are the initial and ultimate solute concentrations in the adsorbent. The solution concentration is related to the amount adsorbed by the material balance - (hi - nf )M,Ay. 

Chen et al. [54] have reported a model for the assessment of the combined effects of the intrinsic reaction kinetics and dye diffusion into phosphorylated polyvinyl alcohol (PVA) gel beads. The analysis of the experimental data in terms of biofilm effectiveness factor highlighted the relevance of intraparticle diffusion to the effective azo-dye conversion rate. On the basis of these results, they have identified the optimal conditions for the gel bead diameter and PVA composition to limit diffusion resistance. 

To evaluate the effect of intraparticle resistance on the overall reaction rate, an approach based on the introduction of effectiveness factor q is usually proposed ... 

Research with pilot scale units has shown that the major resistances to mass transfer of reactant to catalyst are within the liquid film surrounding the wetted catalyst particles and also intraparticle diffusion. A description of these resistances is afforded by Fig. 14. Equating the rate of mass transfer across the liquid film to the reaction rate, first order in hydrogen concentration... 

Recently, Pacheco et al developed and validated a pseudo-homogeneous mathematical model for ATR of i-Cg and the subsequent WGS reaction, based on the reaction kinetics and intraparticle mass transfer resistance. They regressed kinetic expressions from the literature for POX and SR to determine the kinetic parameters from their i-Cg ATR experimental data using Pt on ceria. 

The employment of small particles results in effectiveness factors near unity. In other words, the intraparticle diffusion resistance is low. 

Adsorption According to Fernandez and Carta (1996), who studied mass transfer in agitated reactors, the relative importance of external and intraparticle mass transfer resistances is strongly dependent on the solution composition. They used the following dimensionless number ... 

Cooney defined qmgx as the solid concentration in equilibrium with C0. This number is dimensionless, and thus the concentration units are the same for the liquid and solid phase (e.g. mg/g). Cooney pointed out that for Bi < 0.5, complete dominance of the liquid-film resistance exists, while for Bi > 30, reasonably complete dominance of intraparticle resistance exists. The only restriction is that the isotherm be favorable. 

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