Diffusion macropore-micropore

FIGURE 4 Schematic diagram of a biporous adsorbent pellet showing the three resistances to mass transfer (external fluid film, macropore diffusion, and micropore diffusion). R9 pellet radius rc crystal radius. 

A high level of macropores (diameter more than 0.1J m) facilitates the intraparticular diffusion, as micropores (diameter less than 20 nm) are necessary to develop a high surface area. This double feature is know as bimodality, illustrated in fig. 4. 

This type of diffusion takes place when the pore diameter is large compared to the mean free path of the gas molecules. In this case collisions between the molecules represent the main barrier to diffusion. In contrast to micropore diffusion, macropore diffusion, which is largely determined by this mechanism, is not an activated process. The order of magnitude of the diffusion coefficient for a gas A can be estimated by means of the simple kinetic gas theory (Equation 2.1-22)... 

Macropore-Micropore diffusion This is the case often called the bimodal diffusion model in the literature. In this case the two diffusion processes both control the uptake. This is expected when the particle size is intermediate. 

The value in the numerator is the time scale of diffusion in macropore while that in the denominator is the time scale of diffusion in micropore. A value of 50 for y suggests that the system overall kinetics is controlled by the macropore diffusion as the time scale it takes to diffuse along the macropore is 50 times longer than that in the micropore. 

For the case of comparable rates between macropore diffusion and micropore diffusion (y = 0(1)), the solution for the fractional uptake is ... 

Macropore—Micropore Diffusion with External Film Resistance... 

Diffusion path in microparticles is far smaller than that in macroparticles Hence, unless diffusion rate in microparticles is far slower compared with the rate in macropores, it may not be necessary to take into consideration the contribution of the diffusion in micropores to the second moments since the time constant of diffusion is proportional to the square of the particle size. Then the diffusion in microparticles is considered to be solid diffusion or activated diffusion. This becomes the case for most adsorbates in zeolites or molecular sieve carbon. 

Macropore-micropore diffusion with external film resistance Kawazoe and Takeuchi (1974) Cen and Yang (1986) Rasmuson (1982)... 

Mass transfer through the external fluid film, and macropore, micropore and surface diffusion may all need to be accounted for within the particles in order to represent the mechanisms by which components arrive at and leave adsorption sites. In many cases identification of the rate controlling mechanism(s) allows for simplification of the model. To complicate matters, however, the external film coefficient and the intraparticle diffusivities may each depend on composition, temperature and pressure. In addition the external film coefficient is dependent on the local fluid velocity which may change with position and time in the adsorption bed. 

It arises solely because we continue Co describe micropore diffusion in terms of smooch macropore concentration fields and their gradients, even under reactive conditions where these no longer adequately describe Che actual concentration gradients in the micropores. 

The first thing to notice about these results is that the influence of the micropores reduces the effective diffusion coefficient below the value of the bulk diffusion coefficient for the macropore system. This is also clear in general from the forms of equations (10.44) and (10.48). As increases from zero, corresponding to the introduction of micropores, the variance of the response pulse Increases, and this corresponds to a reduction in the effective diffusion coefficient. The second important point is that the influence of the micropores on the results is quite small-Indeed it seems unlikely that measurements of this type will be able to realize their promise to provide information about diffusion in dead-end pores. 

The mesopores make some contribution to the adsorptive capacity, but thek main role is as conduits to provide access to the smaller micropores. Diffusion ia the mesopores may occur by several different mechanisms, as discussed below. The macropores make very Htde contribution to the adsorptive capacity, but they commonly provide a major contribution to the kinetics. Thek role is thus analogous to that of a super highway, aHowkig the adsorbate molecules to diffuse far kito a particle with a minimum of diffusional resistance. 

Fig. 6. Concentration profiles through an idealized biporous adsorbent particle showing some of the possible regimes. (1) + (a) rapid mass transfer, equihbrium throughout particle (1) + (b) micropore diffusion control with no significant macropore or external resistance (1) + (c) controlling resistance at the surface of the microparticles (2) + (a) macropore diffusion control with some external resistance and no resistance within the microparticle (2) + (b) all three resistances (micropore, macropore, and film) significant (2) + (c) diffusional resistance within the macroparticle and resistance at the surface of the...

For a macroporous sorbent the situation is slightly more complex. A differential balance on a shell element, assuming diffusivity transport through the macropores with rapid adsorption at the surface (or in the micropores), yields... 

Activated carbons for use in Hquid-phase appHcations differ from gas-phase carbons primarily in pore size distribution. Liquid-phase carbons have significantly more pore volume in the macropore range, which permits Hquids to diffuse more rapidly into the mesopores and micropores (69). The larger pores also promote greater adsorption of large molecules, either impurities or products, in many Hquid-phase appHcations. Specific-grade choice is based on the isotherm (70,71) and, in some cases, bench or pilot scale evaluations of candidate carbons. 

Fig. 10. Catalyst macropores showing D noble metal sites and (a) narrowed micropores after exposure to high temperatures where H represents thermally damaged noble metal sites and (b) pore mouth plugging from poisons where A, if aUowed, diffuses in to be converted to B.

The absorption property exhibited by active carbon certainly depends on the large specific surface area of the material, though an interpretation that it is based solely on this is incomplete. This is borne out by the fact that equal amounts of two activated carbon specimens, prepared from different raw materials or by different processes and having the same total surface area, may behave differently with regard to adsorption. Such differences can be partly explained in terms of the respective surface properties of the carbon samples and partly in terms of their relative pore structure and pore distribution. Every activated carbon particle is associated with at least two types of pores of distinctly different sizes. They are the macropores and the micropores. The macropores completely permeate each particle and act as wide pathways for the diffusion of material in and out of carbon, but they contribute very little to the total surface area. The micropores are more important since they... 

Table 16-4 shows the IUPAC classification of pores by size. Micropores are small enough that a molecule is attracted to both of the opposing walls forming the pore. The potential energy functions for these walls superimpose to create a deep well, and strong adsorption results. Hysteresis is generally not observed. (However, water vapor adsorbed in the micropores of activated carbon shows a large hysteresis loop, and the desorption branch is sometimes used with the Kelvin equation to determine the pore size distribution.) Capillary condensation occurs in mesopores and a hysteresis loop is typically found. Macropores form important paths for molecules to diffuse into a par-... 

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