Intraparticle convection

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... 

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... 

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. 

However, creating an optimum balance of surface reaction and intraparticle convection requires the pore structure to be appropriately designed and fabricated. This has so far not been achieved, although the basic requirements to do this are clear. 

To evaluate the impact of intraparticle convection it is necessary to impose a pressure gradient across the network. Such pressure gradients arise naturally in fixed-bed operation, though the pressure difference across a particle is usually only about I cm H O. By solving the Hagen-Poisenille equation across every pore in the network, the overall flow through the particle (network) is known. 

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). 

Let us now deal with "large-pore" catalysts (e.g., a-alumina supports) in which intraparticle convection is a mass transport mechanism which cannot be ignored. 

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. 

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. 

Although the other plate height contributions, /i isp and hint, niay also be affected by intraparticle convection, it is assumed that they are not and that they... 

Considering the effects of the radial and the angular components of the velocity vector of intraparticle convective flow in the pores of the spherical particles. 

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

In both cases the enhancement of conversion due to intraparticle convection is higher for some intermedite value of Thiele modulus. The reactor performance is worse in the case of shell-progressive deactivated catalysts for cc=0-1 however, the enhancement due to convection is higher in this case. 

The importance of intraparticle convection in the area of catalytic reaction engineering was addressed a long time ago by Wheeler [3], who claims that convection will only be important for large pores (10000 A) or high-pressure (100 atm) gas-... 

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). 

However, to be able to use the extended Van Deemter equation the intraparticle convective velocity Vq must be estimated for calculation of the parameter A. The simplest way is to write the equahty of pressure drop across the particle and along the bed, i.e. Ap/d = AP/L. By using Darcy s law for the flow in the column and in the pores [13] we get ... 

A very detailed model of the effect of intraparticle convection inside large-pore catalyts (e.g. selective oxidation catalyts) on the transient behavior of fixed-bed catalytic reactors was published by Quinta Ferreira [75]. Analysis of the transient response data fix>m fixed-bed reactors is in general more complicated than other reactor types as one has to account for the spatial and temporal dependence of the species concentrations and temperature. Catalytic reaction and chromatographic column can be combined in a gas chromatogrqihic pulse reactor. 

A. 1. Liapis, Y. Xu, O. K. Grosser, and A. Tongta, Perfusion Chromatography". The effects of intraparticle convective velocity and microsphere size on column performance.. / Chromatogr. A.. 702 45-57 (1995). 

In this paper we will first review some basic concepts and apply them to the design of isothermal reactors working in the diffusional regime.Then we will concentrate our attention on the problem of intraparticle convection in large pore catalysts.Several aspects of this question will be dealt with - effectiveness factors for iso -thermal and nonisothermal catalysts, measurement of effective diffu-sivities and the implication of intraparticle convection effects on the design and operation of fixed bed catalytic reactors. 

Implication in reactor design of neglecting intraparticle convection. 

In the above equations c is the outlet tracer concentration in the fluid phase, E is the particle porosity, e is the reactor porosity, 0=t/T (with T Sefined as the ratio between the reactor volume and the flowrate) and X=v S./D is the intraparticle Peclet number (v is the intraparticle convective velocity). °... 

In the absence of intraparticle convection, A=0 and we have f(A)=l.It follows that if convection were neglected we really get ... 

Again the same conclusion can be drawn,that is,the apparent effective diffusivity (obtained from a model which did not include intraparticle convection) increases when the flowrate increases,as shown from Equation (22). 

However,experiments can be carried out in such a way that intraparticle convective transport is not important.This is the case in the dynamic Wicke-Kallenbach apparatus used by different authors (Dogu and Smith [12],Furusawa et al.[l3]) and shown in Figure 2. 

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