Intraparticle pore diffusion

In many processes of interest to the hydrocarbon processing industry the size and shape of the catalyst has been chosen as a compromise between catalyst effectiveness and pressure drop. Hence, with effectiveness factors for the main reaction somewhat below 1, intraparticle pore diffusion is generally a factor to be reckoned with. Its effect is not easily quantified since the processing of a practical feedstock involves the conversion of a large variety of molecules with widely different reaction rates and therefore the translation of catalyst performance data obtained with crushed particles to that of the actual catalyst may be difficult and of questionable validity. 

When the length-over-diameter ratio of the catalyst beads is not much larger than 0.5 (and the particles are not very tightly packed on the strings), the LC model is obviously expected to underestimate the reactant conversion in the BSR if the performance is limited by intraparticle pore diffusion. 

The intraparticle (pore) diffusion coefficient defined in Section 6.2.2.4 may estimated by the Mackie-Meares correlation (Mackie and Meares, 1955) ... 

Although this solution was derived for plug flow (Da = 0), it can be generalized by using an apparent mass transfer coefficient to account for axial dispersion, a coefficient that is related to axial dispersion, the external film mass transfer coefficient and intraparticle pore diffusion through the following equation [16] ... 

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... 

External Mass Transfer and Intraparticle Diffusion Control With a linear isotherm, the solution for combined external mass transfer and pore diffusion control with an infinite fluid volume is (Crank, Mathematics of Diffusion, 2d ed., Clarendon Press, 1975) ... 

A breakthrough curve with the nonretained compound was carried out to estimate the axial dispersion in the SMB column. A Peclet number of Pe = 000 was found by comparing experimental and simulated results from a model which includes axial dispersion in the interparticle fluid phase, accumulation in both interparticle and intraparticle fluid phases, and assuming that the average pore concentration is equal to the bulk fluid concentration this assumption is justified by the fact that the ratio of time constant for pore diffusion and space time in the column is of the order of 10. ... 

Intraparticle Transport Mechanisms Intraparticle transport may be limited by pore diffusion, solid diffusion, reaction kinetics at phase boundaries, or two or more of these mechanisms together. 

The most difficult problem to solve in the design of a Fischer-Tropsch reactor is its very high exothermicity combined with a high sensitivity of product selectivity to temperature. On an industrial scale, multitubular and bubble column reactors have been widely accepted for this highly exothermic reaction.6 In case of a fixed bed reactor, it is desirable that the catalyst particles are in the millimeter size range to avoid excessive pressure drops. During Fischer-Tropsch synthesis the catalyst pores are filled with liquid FT products (mainly waxes) that may result in a fundamental decrease of the reaction rate caused by pore diffusion processes. Post et al. showed that for catalyst particle diameters in excess of only about 1 mm, the catalyst activity is seriously limited by intraparticle diffusion in both iron and cobalt catalysts.1... 

Pore diffusion or intraparticle diffusion Transport of the azo dyes from the surface to within the pores of the particle... 

Intraparticle diffusivity (DJ can be related to pore diffusivity (Dp) and surface diffusivity by... 

Note that in the case of a solid diffusion control, X- is replaced by X in the analytical solutions. The presented analytical solutions were developed primarily for solid diffusion control, also termed surface diffusion kinetics. However, the same equations can be used as approximations for pore diffusion as the controlling intraparticle diffusion step, if ksau is set equal to 15D (1 — e)/yi. ... 

In this study the ratio of the particle sizes was set to two based on the average value for the two samples. As a result, if the diffusion is entirely controlled by secondary pore structure (interparticle diffusion) the ratio of the effective diffusion time constants (Defl/R2) will be four. In contrast, if the mass transport process is entirely controlled by intraparticle (platelet) diffusion, the ratio will become equal to unity (diffusion independent of the composite particle size). For transient situations (in which both resistances are important) the values of the ratio will be in the one to four range. Diffusional time constants for different sorbates in the Si-MCM-41 sample were obtained from experimental ZLC response curves according to the analysis discussed in the experimental section. Experiments using different purge flow rates, as well as different purge gases... 

Diffusion of the reactants through the porous interior of the catalyst to the point at which the chemical transformation occurs (pore diffusion or intraparticle diffusion)... 

A Rodrigues, R Quinta Ferreira, Effect of intraparticle convection, diffusion and reaction in a large-pore catalyst particle , AlChE Symp Ser, 1988, 84, 80-87... 

The diffusion coefficient of S02 through the product layer has also been measured, the value of which is about 10 12 m2/s. Figure 9 shows comparison of intraparticle gas diffusivity between the sulfurated sorbent and its calcined sample, indicating calcination can enhance gas diffusivity. The inert matter in the sorbent, however, is beneficial for improving gas diffusion. Measurements (Zhang, 1992) indicated that pores greater than 700 A in diameter for different limestones possess the same distribution function /i(r), as can be expressed by the following correlation ... 

Arve and Liapis [34] suggest estimating the parameters characterizing the intraparticle diffusion and the adsorption-desorption step mechanisms of affinity chromatography from the experimental data obtained in a batch system. The numerical simulations of the chromatographic process will use the values of the parameters of the adsorption isotherm and those of the effective pore diffusion as determined from stirred tank experiments together with the film mass transfer coefficients calculated from chemical engineering expressions found in the literature. 

An intraparticle diffusion model including svurface and pore diffusion has been presented by other researchers [2,3,4,6]. The mathematical equation for parallel diffusion model is expressed as... 

Deactivation of large-pore slab catalysts where intraparticle convection, diffusion and first order reaction are competing mechanisms was analyzed by uniform and shelLprogressive models. For each situation, analytical solutions for concentration profiles, effectiveness factor and enhancement factor due to convection were developed thus providing a sound basis for steady-state reactor design. 

Generally, the overall kinetics is primarily governed by the external and internal diffusion (also called the two-step mass transport mechanism Steps 2 and 3 above). The intraparticle diffusion model described below can therefore be used for calculation of ion uptake by IX resins. When the mass transfer is due only to the diffusion of adsorbate molecules through the pore liquid, a pore diffusion model is often used. On the other hand, in the case where the intraparticle mass transfer is contributed by the diffusion... 

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