Internal/intraparticle transport

As pointed out earlier, the major external resistance is that of mass transfer, and therefore, the effect of external heat transfer can be neglected. Furthermore, internal (intraparticle) transport effects can be neglected in slurry reactors except under some unusual reaction conditions since the size of the catalyst particles is of the order of 100 microns. In trickle-beds, however, both the internal heat and mass transport effects can be important. 

The intraparticle transport effects, both isothermal and nonisothermal, have been analyzed for a multitude of kinetic rate equations and particle geometries. It has been shown that the concentration gradients within the porous particle are usually much more serious than the temperature gradients. Hudgins [17] points out that intraparticle heat effects may not always be negligible in hydrogen-rich reaction systems. The classical experimental test to check for internal resistances in a porous particle is to measure the dependence of the reaction rate on the particle size. Intraparticle effects are absent if no dependence exists. In most cases a porous particle can be considered isothermal, but the absence of internal concentration gradients has to be proven experimentally or by calculation (Chapter 6). 

Diffusion of reactants from the exterior surface to the active interior surface of the porous particle (internal or intraparticle transport)... 

The first set of preliminary experiments in a kinetic study carried out in laboratory PBRs should establish the flow conditions at which external transport effects are negligible. The second set of diagnostic experiments conducted should verify the particle size requirements under which intraparticle transport effects are eliminated. A study of intrinsic kinetics must make use of the flow rates and particle sizes that exclude both external and internal transport limitations, respectively. 

In Chapter 4, two different transport regimes were identified transport inside the particles and transport between the bulk fluid and the surface of the catalyst particles. Transport inside the catalyst particles is known as internal or intraparticle transport, or as pore diffusion. Transport between the bulk fluid stream and the external surface of the catalyst particles is known as external or interparticle transport. The mechanisms of transport are different fiar these two regimes, and the rates of transport are influenced by different variables. Internal transport will be treated first, followed by extmial tranqiort. These discussions will be preceded by a brief overview iff the physical nature of heterogeneous catalysts. 

In general, as an adsorbate is transported in the internal matrix of adsorbent, there is tendency of adsorbate-adsorbate interaction in the pores and hopping, from site to site, of adsorbed species along the wall of the adsorbent. These phenomena give rise to pore and surface diffusion resistances to intraparticle... 

The Biot number Bim for mass transport. This can be interpreted as the ratio of internal to external transport resistance (intraparticle diffusion versus interphase diffusion) ... 

The Biot number Bib for heat transport. Analogous to Bim, this is defined as the ration of the internal to external heat transfer resistance (intraparticle heat conduction versus interphase heat transfer). 

Figure 7. Diagnostic tests for intraparticle (internal) transport disguises.

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... 

In addition, it is important to recognize that catalysis by solids involves diffusion of reactants from fluid bulk to the catalyst surface, as well as diffusion within the solid matrix. The latter invariably occurs simultaneously with the reaction, and the former is usually (but not necessarily rigorously) treated as an independent precursor to it. Thus any analysis of catalysis by solids is based on understanding its action under the physical influence of the microenvironment in which it functions. Catalysis by solids actually occurs on the catalyst surface and constitutes the surface field problem, which is the core of its action. Diffusion of reactant within its matrix is an internal or intraparticle field problem, and its transport from bulk to surface is an external or interphase field problem. 

---