Intraparticle composites

In such studies one may also eliminate intraparticle gradients of temperature and composition by using very fine catalyst particles or by confining the catalytic species to the exterior surface of a nonporous or impervious pellet. Unfortunately, the conditions that are optimum for the elucidation of the intrinsic chemical kinetics are often inappropriate for use in... 

At steady state, the rates of each of the individual steps will be the same, and this equality is used to develop an expression for the global reaction rate in terms of bulk-fluid properties. Actually, we have already employed a relation of this sort in the development of equation 12.4.28 where we examined the influence of external mass transfer limitations on observed reaction rates. Generally, we must worry not only about concentration differences between the bulk fluid and the external surface of the catalyst, but also about temperature differences between these points and intraparticle gradients in temperature and composition. 

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. 

Characteristics of a catalyst particle include its chemical composition, which primarily determines its catalytic activity, and its physical properties, such as size, shape, density, and porosity or voidage, which determine its diffusion characteristics. We do not consider in this book the design of catalyst particles as such, but we need to know these characteristics to establish rate of reaction at the surface and particle levels (corresponding to levels (1) and (2) in Section 1.3). This is treated in Section 8.5 for catalyst particles. Equations 8.5-1 to -3 relate particle density pp and intraparticle voidage or porosity p. 

The long-term goal in the science of thermochemical conversion of a solid fuel is to develop comprehensive computer codes, herein referred to as a bed model or CFSD (computational fluid-solid dynamics). Firstly, this CFSD code must be able to simulate basic conversion concepts, with respect to the mode, movement, composition and configuration of the fuel bed. The conversion concept has a great effect on the behaviour of the thermochemical conversion process variables, such as the molecular composition and mass flow of conversion gas. Secondly, the bed model must also consider the fuel-bed structure on both micro- and macro-scale. This classification refers to three structures, namely interstitial gas phase, intraparticle gas phase, and intraparticle solid phase. Commonly, a packed bed is referred to as a two-phase system. 

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 ... 

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... 

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). 

The properties of wood(7,14) were used to analyze time scales of physical and chemical processes during wood pyrolysis as done in Russel, et al (15) for coal. Even at combustion level heat fluxes, intraparticle heat transfer is one to two orders of magnitude slower than mass transfer (volatiles outflow) or chemical reaction. A mathematical model reflecting these facts is briefly presented here and detailed elsewhere(16). It predicts volatiles release rate and composition as a function of particle physical properties, and simulates the experiments described herein in order to determine adequate kinetic models for individual product formation rates. 

The foregoing discussion refers solely to intraparticle diffusivity (micropore diffusion) as distinct from interparticle effects (macropore diffusion). Since a practical zeolite catalyst will consist of composite particles, each containing a large number of individual zeolite crystals, it is important to make a clear distinction between these two types of diffusion. In some cases macropore diffusion may be important in determining the overall reaction kinetics but will obviously not introduce or affect shape selectivity in any way. 

The evaluation of catalyst effectiveness requires a knowledge of the intrinsic chemical reaction rates at various reaction conditions and compositions. These data have to be used for catalyst improvement and for the design and operation of many reactors. The determination of the real reaction rates presents many problems because of the speed, complexity and high exo- or endothermicity of the reactions involved. The measured conversion rate may not represent the true reaction kinetics due to interface and intraparticle heat and mass transfer resistances and nonuniformities in the temperature and concentration profiles in the fluid and catalyst phases in the experimental reactor. Therefore, for the interpretation of experimental data the experiments should preferably be done under reaction conditions, where transport effects can be either eliminated or easily taken into account. In particular, the concentration and temperature distributions in the experimental reactor should preferably be described by plug flow or ideal mixing models. 

Using the dusty gas model [5] analytical solutions are derived to describe the internal pressure gradients and the dependence of the effective diffusion coefficient on the gas composition. Use of the binary flow model (BFM, Chapter 3) would also have yielded almost similar results to those discussed below. After discussion of the dusty gas model, results are then implemented in the Aris numbers. Finally, negligibility criteria are derived, this time for intraparticle pressure gradients. Calculations are given in appendices here we focus on the results. 

Now that we have derived the intraparticle pressure gradients, we can also determine the effective diffusion coefficient as a function of the gas composition. 

Equations (16) and (18) discriminate between intraparticle and interparticle interference effects embodied in bj(q. t) and exp rq- ry(/)—r/(/) ), respectively. The amplitude function bj(q.t) contains information on the internal structure, shape, orientation, and composition of individual particles. Variations of bj(q.t) across the particle population reflect the polydispersity of particle size, shape, orientation, and composition. The phase function expjrq (ry (r) — r/(/)]( carries information on the random motion of individual particles, the collective motion of many particles, and the equilibrium arrangement of particles in the suspension medium. 

An interesting technique for the measurement of intraparticle diffusivity as well as longitudinal diffusion in the particle bed has been described by Deisler and Wilhelm (21). It deviates from all other techniques mentioned in that it is based on a dynamic flow study, analyzing the effect of the particles on the propagation of a sinusoidal variation of composition of a binary gas mixture passed through the catalyst bed. The authors have demonstrated the versatility of their general technique for determination of diffusion properties, as well as adsorption equilibria between the solids and the gas composition employed. If this general technique were modified to measure specifically the particle diffusivity, a very convenient and accurate method may result. 

For this objective the use of a composition-dependent diffusivity is perhaps warranted. Other uncertainties make this degree of detail unjustified for evaluating the effect of intraparticle transport on reaction rate. Hence we shall employ a composition-independent given by Eq. (11-4). Then Eq. (11-18) can be integrated to give... 

Region of the axial composition profile in which the composition varies from that of the feed (toward the feed end) to that of the initially present fluid (toward the product end). Despite its name, the shape of this zone can depend on mass transfer resistances, dispersion, or equilibrium effects. For uptake with a favorable isotherm, the width remains essentially constant beyond a certain axial position, leading to the term constant pattern front. In that case, the effects are exclusively due to intraparticle- and/or film-diffusion resistances. 

The Ilux can be expressed by the Fiekian type dillusion ociiialion complemented by the simplified Wilke equation (Mahfouz, 1985) for the dependence of the diffusivities on the gas mixture composition. Following some lengthy but straightforward manipulation of the equations, the following equations are obtained (Mahfouz, 1985) for the intraparticle mole fraction profiles for any component ... 

The intrinsic activity depends on the chemical and physical properties of the active component. For unsupported catalysts, the most important properties are the composition and structure of the catalyst surface and the presence, or absence, of special sites such as Br0nsted or Lewis acid centers, anion or cation defects, and sites of high coordination. For supported catalysts, the size and morphology of the dispersed phase are of additional importance. If intraparticle transport of reactants occurs with a characteristic time that is short compared to that of the reaction, then the observed and intrinsic rates of reaction will be identical. When the characteristic time for intraparticle mass transport is less than that for reaction, the observed rate of reaction per unit mass of catalyst becomes less than the intrinsic value, and the reaction kinetics are dominated by the effects of intraparticle mass transport. The factors governing intraparticle transport are the diffusivities of the reactants and products and the characteristic distance for diffusion. 

In such studies one may also eliminate intraparticle gradients of temperature and composition by using very fine catalyst particles or by confining the catalytic species... 

This equation describes the change of the solute concentration in the void space of the particle. Basically it states that the rate of change of mass hold-up in the particle (LHS of Eq. 11.164) is balanced by the rate of intraparticle diffusion (RHS). Since the mass balance equation (Eq. 11.164) is second order with respect to the spatial variable, we shall need two boundary conditions to complete the mass balance on the particle. One condition will be at the center of the particle where symmetry must be maintained. The other is at the exterior surface of the particle. If the stirred pot containing the particles is well mixed, then the fluid at the surface of particles is the same composition as the well-mked fluid. These physical requirements are written mathematically as... 

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