Intraparticle convection, diffusion and

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... 

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. 

INTRAPARTICLE CONVECTION,DIFFUSION AND REACTION IN NONISOTHERMAL CATALYSTS. 

Rodrigues,A.,0rfao,J. and A.Zoulalian.Intraparticle Convection, Diffusion and Zero Order Reaction in Porous Catalysts.Chem. 

Model parameters are the Thiele modulus 0 and the intraparticle Feclet number X=v0t/De relating the intraparticle convective flow and the diffusive flow. 

Nir,A. and L.Pismen.Simultaneous Intraparticle Forced Convection,Diffusion and Reaction in a Porous Catalyst.Chem.Eng. 

Intraparticle convection can also occur in packed beds when the adsorbent particles have very large and well-connected pores. Although, in general, bulk flow through the pores of the adsorbent particles is only a small frac tion of the total flow, intraparticle convection can affec t the transport of veiy slowly diffusing species such as macromolecules. The driving force for convec tion, in this case, is the... 

Available reaction-transport models describe the second regime (reactant transport), which only requires material balances for CO and H2. Recently, we reported preliminary results on a transport-reaction model of hydrocarbon synthesis selectivity that describes intraparticle (diffusion) and interparticle (convection) transport processes (4, 5). The model clearly demonstrates how diffusive and convective restrictions dramatically affect the rate of primary and secondary reactions during Fischer-Tropsch synthesis. Here, we use an extended version of this model to illustrate its use in the design of catalyst pellets for the synthesis of various desired products and for the tailoring of product functionality and molecular weight distribution. 

Reactions that are strongly diffusion influenced benefit from intraparticle convection. This is because the supply of primary reagents can now be driven by bulk diffusion. Furthermore, reversible reactions of the type A + B 5= C + D will show an additional benefit because the reaction products will be swept from the pzulicle interior by convection, when otherwise their greater accumulation would reverse (and therefore hinder) the local rate of reaction. 

In these materials, mass transport inside particles occurs not only by diffusion but also by convecdon. Nir and Pismen (ref. 1) showed that the effectiveness factor of a catalyst (slab geometry) for 1 order isothermal reacdon, working in the intermediate regime increases due to intraparticle convective flow. The enhancement of catalyst effectiveness can be quantified by E= doAl(], shown in Fig. 1. This pioneering work was later extended to other kinetic laws (refs. 2-4). 

Model parameters an the Thiele modulus and the intraparticle Peclet number X=Vot/De relating the intrapordcle convective flow and the diffusive flow. 

Meyers, J.J., Liapis, A.I. Network modeling of the intraparticle convection and diffusion of molecules in porous particles packed in a chromatographic column, J. Chromatogr. A, 1998, 827, 197-213. 

Liapis and McCoy [63] have assumed that the bimodal pore structure of per-fusive adsorbent particles is made of a macroporous region, in which mass transfer takes place through intraparticle convection and pore diffusion, and a microp-orous region made of spherical microparticles in which mass transfer takes place through pure diffusion. Frey et al. [61] developed a model for the analysis of mass transfer in spherical particles having a bimodal pore distribution and derived the following expression for h nt in perfusion chromatography. 

At low velocities /(A) <= 1 and both equations lead to similar results. However, at high superficial velocities, /(A) <= 3/A and so the last term in Rodrigues equation becomes a constant since the intraparticle convective velocity Vq is proportional to the superficial velocity u. The HETP reaches a plateau that does not depend on the value of the solute diffusivity but only on the particle permeability and pressure gradient (convection-controlled limit). 

Coming back to the effect of intraparticle convection on the measured value of the effective diffusivity let us mention two experimental examples.The first one deals with a dynamic chromatographic method in a SPSR.The characteristics of the catalyst and reactor are listed below [9J. 

We see on Fig.5 that the apparent effective dif fusivity for hydrogen is higher than for argon and helium.However the ratio of apparent diffusivities for two tracer gases is lower than the ratio of the corresponding diffusion coefficients.This may be due to the influence of intraparticle convective velocity.In fact,let us take a... 

One should be careful when using a measured value of the effective diffusivity by a dynamic chromatographic method for reactor design.As said before we get at a given Reynolds number an apparent effective diffusivity D (as a result of a model which does not include convective transport inside the pellet).How will the reactor design be affected by using this value for 5 instead of that of the true effective diffusivity and the intraparticle Peclet number for convection In order to answer this question let us define a quantity... 

Moreover a detailed account of the importance of intraparticle forced convection when measuring effective diffusivities and designing reactors has been presented.This includes the analysis of non-isothermal catalysts and simulation and operation of a fixed bed catalytic reactor. 

In this equation the entire exterior surface of the catalyst is assumed to be uniformly accessible. Because equimolar counterdiffusion takes place for stoichiometry of the form of equation 12.4.18, there is no net molar transport normal to the surface. Hence there is no convective transport contribution to equation 12.4.21. Let us now consider two limiting conditions for steady-state operation. First, suppose that the intrinsic reaction as modified by intraparticle diffusion effects is extremely rapid. In this case PA ES will approach zero, and equation 12.4.21 indicates that the observed rate per unit mass of catalyst becomes... 

The desorptive process may be analyzed before boiling. The key assumption is that the vapor and adsorbed phases are in equilibrium in the bulk of the bed. This assumption eliminates intraparticle resistances from further consideration and is reasonable for rotary kiln applications. The two remaining resistances are associated with hydrocarbon diffusion out of the bed and with convection from the bed surface to the bulk gases. The flux of species Al from the desorbing bed becomes... 

Considering the intraparticle, the convective and the diffusive mass transport mechanisms in the pores of the particles as separate mass transport mechanisms, each one characterized by its own individual and proper driving force, rather than as a convective flux augmented of a diffusive flux in the pores of the particles... 

The classic Thiele-Damkohler theory accounts for these effects, but is restricted to isothermal behavior and intraparticle mass transfer only by diffusion. If the reaction is highly exothermic and the particle is a poor heat conductor, the temperature in the particle center may rise above that in the contacting fluid and cause the overall rate to be higher than in the absence of heat- and mass-transfer limitations. Moreover, gas-phase reactions with change in mole number cause forced inward or outward convection that assists or counteracts reactant penetration into the particle and so enhances or depresses the rate. 

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