Resistance, macropore

Diffusion in the macro-pores of a formed parhcle is generally speaking a very important mechanism. If we speak in terms of resistances to mass transfer macropore resistance is often the largest of the resistances to mass transfer. For transport in the macro-pores we must introduce two parameters that influence the transport. 

In the experimental systems considered here, the controlling resistance was in each case zeolitic diffusion, but systems in which macropore resistance is dominant are equally common. As examples one may cite the sorption of light hydrocarbons in the Davison 5A molecular sieves which contain much smaller zeolite crystals and correspondingly smaller macropores than the equivalent Linde products (18). 

Incidentally, these features cannot be accounted for by assuming different values of macropore radius or tortosity factor in the predictive equations. Even with the assumptions of negligible Knudsen resistance (rpore- ) and no tortuosity (rw = D, the predicted macropore resistances (excluding surface effects) would be lowered by only forty percent, which is still insufficient to account for the low LUB values, at least in the 5A and 13X systems. There appears, therefore, to be a fairly strong case for the presence of a surface diffusion effect in these systems, with the possibility of such an effect in the CO2/ air/4A system as well. 

In the application of the chromatographic method to the measurement of intracrystalline diffusivity it is preferable to pack the column directly with unaggregated crystals rather than with composite (pelleted) material since this eliminates the possible intrusion of macropore resistance. The small crystal size of commercial zeolite samples presents a significant practical problem. Early attempts to utilize a column packed directly with such crys-... 

A composite pellet offers two distinct diffusional resistances to mass transfer the micropore diffusional resistance of the individual zeolite crystals and the macropore diffusional resistance of the extracrystalline pores. A low resistance to mass transfer is normally desirable and this requires a small crystal size to minimize intracrystalline diffusional resistance. However, the diameter of the intercrystalline macropores is also determined by the crystal size and if the crystals are too small the macropore diffusivity may be reduced to an unacceptable level. The macropore resistance may of course be reduced by reducing the gross particle size but the extent to which this is possible is limited by pressure drop considerations. The optimal choice of crystal size and particle size thus depends on the ratio of inter- and intracrystalline diffusivities which varies widely from system to system. 

The relative importance of microporc and macropore resistances depends on the ratio of the diffusiona time constants which varies widely depending on the system and conditions. The time constant depends on the square of the particle radhis variation of the particle size therefore provides a simple and straightforward experimental itest to confirm the nature of the controlling resistance. 

It is evident that in this regime both the external mass transfer and macropore resistances are directly proportional to the square of Ihe particle radius. The contribution of these terms may therefore be reduced to an insignificant level by using sufficiently small particles. Furthermore, in he low Reynolds number regime, the axial dispersion coefficient becomes independent of particle size so variation of the particle size provides a convenient experimental test for the significance of external film and macropore diffusion resistances. 

The analytical solution given by Ruckenstein et al. (1971) expresses the dimensionless uptake of adsorbate mt/m as a function of time. The solution is complex and Involves two parameters defined by c = DJrc)t DpIR ) and = 3a (1 - gp) qo/epCo- When the resistance to diffusion is controlled by diffusion in the micropores (j3 -> 0), the system is described by equations (4.17) to (4.21) inclusive, the uptake of adsorbate being represented by equation (4.22). When, on the other hand, macropore resistance dominates the diffusion process (/ -v oo), then equations (4.27) to (4.30) inclusive apply and the condition (4.18) is redundant because the concentration throughout the crystal is uniform. The solution is then identical to equation (4.22) with rp and Dp replacing rc and Dc, respectively. 

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. 

As illustrated ia Figure 6, a porous adsorbent ia contact with a fluid phase offers at least two and often three distinct resistances to mass transfer external film resistance and iatraparticle diffusional resistance. When the pore size distribution has a well-defined bimodal form, the latter may be divided iato macropore and micropore diffusional resistances. Depending on the particular system and the conditions, any one of these resistances maybe dominant or the overall rate of mass transfer may be determined by the combiaed effects of more than one 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...

Important physical properties of catalysts include the particle size and shape, surface area, pore volume, pore size distribution, and strength to resist cmshing and abrasion. Measurements of catalyst physical properties (43) are routine and often automated. Pores with diameters <2.0 nm are called micropores those with diameters between 2.0 and 5.0 nm are called mesopores and those with diameters >5.0 nm are called macropores. Pore volumes and pore size distributions are measured by mercury penetration and by N2 adsorption. Mercury is forced into the pores under pressure entry into a pore is opposed by surface tension. For example, a pressure of about 71 MPa (700 atm) is required to fill a pore with a diameter of 10 nm. The amount of uptake as a function of pressure determines the pore size distribution of the larger pores (44). In complementary experiments, the sizes of the smallest pores (those 1 to 20 nm in diameter) are deterrnined by measurements characterizing desorption of N2 from the catalyst. The basis for the measurement is the capillary condensation that occurs in small pores at pressures less than the vapor pressure of the adsorbed nitrogen. The smaller the diameter of the pore, the greater the lowering of the vapor pressure of the Hquid in it. 

Bidispersed Particles For particles of radius Cp comprising adsorptive subparticles of radius r, that define a macropore network, conservation equations are needed to describe transport both within the macropores and within the subparticles and are given in Table 16-11, item D. Detailed equations and solutions for a hnear isotherm are given in Ruthven (gen. refs., p. 183) and Ruckenstein et al. [Chem. Eng. Sci., 26, 1306 (1971)]. The solution for a linear isotherm with no external resistance and an infinite fluid volume is ... 

Size exclusion chromatography (SEC, also known as GPC and GFC) has become a very well accepted separation method since its introduction in the late-1950s by works of Porath and Flodin (1) and Moore (2). Polymers Standards Service (PSS) packings for SEC/SEC columns share this long-standing tradition as universal and stable sorbents for all types of polymer applications. In general, PSS SEC columns are filled with spherical, macroporous cross-linked, pressure-stable, and pH-resistant polymeric gels. 

Since the natural passivity of aluminium is due to the thin film of oxide formed by the action of the atmosphere, it is not unexpected that the thicker films formed by anodic oxidation afford considerable protection against corrosive influences, provided the oxide layer is continuous, and free from macropores. The protective action of the film is considerably enhanced by effective sealing, which plugs the mouths of the micropores formed in the normal course of anodising with hydrated oxide, and still further improvement may be afforded by the incorporation of corrosion inhibitors, such as dichromates, in the sealing solution. Chromic acid films, in spite of their thinness, show good corrosion resistance. 

Macroporous resin beads, due to their mode of preparation, consist of a macroporous internal structure and highly cross-linked areas (>5%). The latter impart the resin with rigidity, whereas the porous areas provide a large internal surface for functionalization, even in the dry state. These macroporous polystyrene-based resins are subsequently modified in various manners, which render them compatible with numerous organic solvents. Furthermore, they show high resistance toward osmotic shock, but can be brittle when not manipulated carefully. 

The chiral recognition ability of the insoluble (+)-l was estimated by HPLC using a column packed with small particles of l.25 However, this column showed a poor efficiency because of a low theoretical plate number. This defect was overcome by coating soluble poly(TrMA) with a DP of 50 on macroporous silica gel.26 The 1-coated silica gel had higher resistance against compression and longer lifetime than the CSP of insoluble 1. Moreover, the two 1-based CSPs show quite different chiral recognition for several race-mates, which may be attributed to the different orientation of 1 in bulk and on the surface of the silica gel.27... 

Inorganic membranes employed in reaction/transport studies were either in tubular form (a single membrane tube incorporating an inner tube side and an outer shell side in double pipe configuration or as multichannel monolith) or plate-shaped disks as shown in Figure 7.1 (Shinji et al. 1982, Zaspalis et al. 1990, Cussler 1988). For increased mechanical resistance the thin porous (usually mesoporous) membrane layers are usually supported on top of macroporous supports (pores 1-lS /im), very often via an intermediate porous layer, with pore size 100-1500 nm, (Keizer and Burggraaf 1988). 

Porous ceramic membrane layers are formed on top of macroporous supports, for enhanced mechanical resistance. The flow through the support may consist of contributions due to both Knudsen-diffusion and convective nonseparative flow. Supports with large pores are preferred due to their low resistance to the flow. Supports with high resistance to the flow decrease the effective pressure drop over the membrane separation layer, thus diminishing the separation efficiency of the membrane (van Vuren et al. 1987). For this reason in a membrane reactor it is more effective to place the reaction (catalytic) zone at the top layer side of the membrane while purging at the support side of the membrane. 

Reid, Sherwood and Prausnitz [11] provide a wide variety of models for calculation of molecular diffusion. Dr is the Knudsen diffusion coefficient. It has been given in several articles as 9700r(T/MW). Once we have both diffusion coefficients we can obtain an expression for the macro-pore diffusion coefficient 1/D = 1/Dk -i-1/Dm- We next obtain the pore diffusivity by inclusion of the tortuosity Dp = D/t, and finally the local molar flux J in the macro-pores is described by the famiUar relationship J = —e D dcjdz. Thus flux in the macro-pores of the adsorbent product is related to the term CpD/r. This last quantity may be thought of as the effective macro-pore diffusivity. The resistance to mass transfer that develops due to macropore diffusion has a length dependence of R]. 

It may not be obvious but driving selectivity to a high value is best done by driving N2 adsorption to some acceptably high value and then driving O2 to a minimum. This dramatically changes the volume of gas that must pass in and out of the macro-pore structure of the adsorbent In aU PSA separations it is the macropore diffusion that is the dominant resistance to mass transfer. 

Micropore mass transfer resistance of zeoUte crystals is quantified in units of time by r /Dc, where is the crystal radius and Dc is the intracrystalline diffusivity. In addition to micropore resistance, zeolitic catalysts may offer another type of resistance to mass transfer, that is resistance related to transport through the surface barrier at the outer layer of the zeoHte crystal. Finally, there is at least one additional resistance due to mass transfer, this time in mesopores and macropores Rp/Dp. Here Rp is the radius of the catalyst pellet and Dp is the effective mesopore and macropore diffusivity in the catalyst pellet [18]. 

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