Intraparticle Diffusion Limitations Research Articles

Spontaneous combustion in beds of coal particles

This paper describes a simple experimental technique to determine the ignition temperature of various cylinder-shaped beds (diameter 17–160 mm, height 10–80 mm) of a South African coal and it reports the application of thermal ignition models in interpreting and extrapolating the small scale results. Measurements of the rate heat generation in isothermal conditions are also reported and compared with the results of ignition tests. The coal used in this work was found to undergo spontaneous ignition in small scale tests at temperature from 120 to 220°C. The thermal ignition model provides a good correlation for critical ignition temperature of bodies of different sizes. The correlation has proved to be relatively insensitive to complications in reaction (oxygen interparticle diffusion) and to physical changes in the material (reactant consumption), but it depends on the boundary conditions (Biot number). An effect of coal particle sizes indicates the existence of intraparticle diffusion limitations. Comparison between ignition and thermal data yields a satisfactory agreement in prediction of critical dimension by menas of the thermal ignition model. Small scale tests have been extrapolated and examples of prediction of critical dimensions at different temperatures are also reported.

Kinetics and equilibria of the hydration of linear butenes over a strong acid ion-exchange resin as catalyst

The hydration of 1-butene (B), cis-2-butene (C) and trans-2-butene (T) to 2-butanol (A) catalysed by a strong acid ion-exchange resin (XE-307) was studied in the temperature range of 75–150°C. Kinetic experiments were performed by passing aqueous solutions of these butenes or 2-butanol through a resin bed (particle size 0.6–0.7 mm) of known capacity at a constant flow rate. Besides hydration, isomerization of the three butenes takes place. The experimental results can be explained by assuming that all reactions proceed via the sec-butyl carbenium ion as reactive intermediate. The reactions involved are equilibrium reactions. Numerical values of the rate constants of the various reactions and the equilibrium constants have been determined. The overall equilibrium constant of the hydration reaction of the butenes in the liquid phase is considerably less favourable than in the corresponding hydration of propene. The rate constants for butene hydration are of a similar order of magnitude to those for propene hydration. When resin particles of 0.65 mm diameter are used, the rate of reaction is found to be affected by intraparticle diffusion limitations at temperatures above 115°C.

Intraparticle diffusion and char combustion

A diffusion and reaction model describing the combustion of porous char particles is developed and used to study the effects of intraparticle diffusional limitations on their pseudo-steady state and dynamic behaviour. The model allows for intraparticle temperature gradients and shrinkage of the reacting particles. Extensive computations over a wide range of ambient temperature and particle size reveal a strong dependence of the ignition and extinction phenomena observed in the combustion of porous particles, and hence of the predicted burning times, on the initial mass transport resistances and on their evolution with the extent of reaction.

Mathematical modelling of gas-solid reactions with solid product

Random pore structural models, that can be used with any type of pore size distribution, are developed for the study of gas-solid reactions with solid product under reaction conditions controlled by kinetics and diffusion in the product layer. An intraparticle diffusion and reaction model is also developed and used, along with the structural models, to study the transient behaviour of solid particles reacting under significant intraparticle diffusional limitations. Simulation results for the limestone-SO 2 system show that the transient behaviour of the reacting particles is strongly influenced by the type of the pore size distribution. Various pore structures characterized by the same values of internal surface area and porosity can lead to completely different reaction trajectories. The predictions of the mathematical models compare well with experimental data from the literature.

Phase‐transfer reactions catalyzed by phosphonium salts attached to polystyrene resins by spacer chains

AbstractThe rate of reaction of 1‐halooctanes with aqueous sodium cyanide catalyzed by phosphonium salts attached to insoluble polystyrene resins by tetramethylene or heptamethylene spacers was studied as a function of catalyst particle size, degree of polymer crosslinking, percentage of ring substitution, and temperature. Rates of reaction of 1‐bromooctane with 17–38% ring‐substituted catalysts increased as spacer‐chain length increased. Rates of reaction of 1‐bromooctane decreased, whether the percentage of ring substitution increased or decreased from 17–19%. Rates of reaction of 1‐chlorooctane increased with increasing spacer‐chain length and decreasing percentage of ring substitution. Apparent activation energy for the reaction of 1‐bromooctane with 9% ring‐substituted, spacer‐modified catalysts was 9–10 kcal/mol and 13 kcal/mol with 17–19% ring‐substituted catalysts. The hydrophilicity of catalysts decreased with increasing spacer‐chain length and decreasing percentage of ring substitution. The mechanisms of reaction were discussed in terms of intrinsic reactivity and intraparticle diffusion limitations on the reaction rates.

Comments on the HDS, HDM and HDN activities of commercial catalysts in the hydrotreating of heavy crude oils

The influence of pretreatment conditions on the hydrodesulfurization (HDS), hydrodemetallization (HDM) and hydrodenitrogenation (HDN) activities of heavy crude oils was studied under industrial conditions. Sulfidation enhances both the HDS and HDM activities. The initial deactivation of sulfided catalysts is best interpreted in terms of sulfiding degree adjustment of the catalyst surface rather than by carbon or metal poisoning. Catalyst subject to different chemical pretreatments exhibits a similar evolution of HDS and HDM activities. A correlation between HDS, HDM and HDN is observed when commercial catalysts are tested under similar conditions. This correlation is not explained by intraparticle diffusion limitations or by degradation of asphaltene-type molecules. Results are interpreted assuming that HDM is a catalytic reaction for which the active phase is also involved in HDS and HDN.

EFFECT OF SLOW INTRAPARTICLE DIFFUSION ON pH-STABILITY PROFILES OF IMMOBILIZED ENZYME

Stabilities of immobilized enzymes at varying pH under different levels of intraparticle diffusion limitation have been analyzed theoretically and numerically. Unlike pH-activity profiles, which are broadened at high levels of diffusion limitation, pH-stability profiles are narrowest at intermediate levels of limitation. When diffusion limitation is cither absent or very severe, pH-stability profiles are identical in shape, those under severe limitation having half-lives exactly double those free of limitation at all pHs.

Analysis of immobilised multi‐enzyme reaction systems with Michaelis‐Menten kinetics

AbstractThe consecutive sequence of reactions S → P1 → P2 taking place inside a permeable spherical particle is analysed for the case in which the enzyme‐catalysed steps in the reaction follow Michaelis‐Menten type kinetics. The case in which each step in the reaction is inhibited by its product is also considered. The theoretical analysis takes into account both interparticle and intraparticle diffusional limitations and utilises an orthogonal collocation technique to obtain the effectiveness factor and selectivity of the reaction sequence. The orthogonal collocation method is found to be both convenient and simple and the analysis should prove useful in the design of immobilised multi‐enzyme reactors.

Analysis of immobilised multi‐enzyme reaction systems with michaelis‐menten kinetics

AbstractThe consecutive sequence of reactions S → P1 → P2 taking place inside a permeable spherical particle is analysed for the case in which the enzyme‐catalysed steps in the reaction follow Michaelis‐Menten type kinetics. The case in which each step in the reaction is inhibited by its product is also considered. The theoretical analysis takes into account both interparticle and intraparticle diffusional limitations and utilises an orthogonal collocation technique to obtain the effectiveness factor and selectivity of the reaction sequence. The orthogonal collocation method is found to be both convenient and simple and the analysis should prove useful in the design of immobilised multi‐enzyme reactors.

Optimum catalyst formulation for the aromatization of methylcyclopentane

AbstractThe formation of benzene from methylcyclopentane over platinum impregnated silica‐alumina represents a typical reforming reaction occurring in the presence of a bifunctional catalyst.A detailed experimental investigation enabled a previously established kinetic model of the system to be extended and parameters to be evaluated. By application of the maximum principle the catalyst composition could be formulated so as to maximize the yield of benzene, simultaneously suppressing the formation of undesirable products. For an isothermal reactor operating in a temperature region where chemical reaction is rate controlling, it was found that a constant catalyst composition along the reactor length represents a sub‐optimal policy which, nevertheless, closely approximates the optimal solution. The effect of intraparticle diffusion limitation on the optimum profile is also investigated.The model developed is limited to low conversions for the reaction model under dehydrogenative conditions.