Mass transfer resistance micropores

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]. 

While microscopic techniques like PFG NMR and QENS measure diffusion paths that are no longer than dimensions of individual crystallites, macroscopic measurements like zero length column (ZLC) and Fourrier Transform infrared (FTIR) cover beds of zeolite crystals [18, 23]. In the case of the popular ZLC technique, desorption rate is measured from a small sample (thin layer, placed between two porous sinter discs) of previously equilibrated adsorbent subjected to a step change in the partial pressure of the sorbate. The slope of the semi-log plot of sorbate concentration versus time under an inert carrier stream then gives D/R. Provided micropore resistance dominates all other mass transfer resistances, D becomes equal to intracrystalline diffusivity while R is the crystal radius. It has been reported that the presence of other mass transfer resistances have been the most common cause of the discrepancies among intracrystaUine diffusivities measured by various techniques [18]. 

Using the computer programs discussed above, it is possible to extract from these breakthrough curves the effective local mass transfer coefficients as a function of CO2 concentration within the stable portion of the wave. These mass transfer coefficients are shown in Figure 15, along with the predicted values with and without the inclusion of the surface diffusion model. It is seen that without the surface diffusion model, very little change in the local mass transfer coefficient is predicted, whereas with surface diffusion effects included, a more than six-fold increase in diffusion rates is predicted over the concentrations measured and the predictions correspond very closely to those actually encountered in the breakthrough runs. Further, the experimentally derived results indicate that, for these runs, the assumption that micropore (intracrystalline) resistances are small relative to overall mass transfer resistance is justified, since the effective mass transfer coefficients for the two (1/8" and 1/4" pellets) runs scale approximately to the inverse of the square of the particle diameter, as would be expected when diffusive resistances in the particle macropores predominate. 

Membrane characteristics such as porosity, pore size, tortuosity, and membrane thickness dictate the resistance to mass transfer through microporous membranes used in MD [35,97-99]. Furthermore, studies [100,101] have shown that the relationship between intrinsic membrane properties and operating conditions, e.g., sweUing, compaction, and wetting, are important in deciding efficient operations. Therefore, selection of an appropriate membrane that poses the least resistance to mass transfer is crucial. Lefebvre [36] has given some criteria for the choice of membranes. 

Although the second approach can be considered a simplification of the first many systems have been satisfactorily described, and it is often preferred due to its mathematical simphcity. Studies on mass transfer through aqueous-organic interfaces immobilized at the pore mouths of a microporous membrane have shown that for a HF device, the overall mass transfer coefficient obtained can be related to the individual phase mass transfer coefficients and the membrane resistance using simple film theory. However, many authors considered that this separation controlling, overall mass transfer resistance was dominated by the resistance of the membrane. This is because the permeability of the membrane is low and because the membrane is thick [4,19,20,23,52,53]. On the other hand, other authors reported for different systems and conditions that the kinetic control of... 

Figure 9.2 shows the scanning electron microscopic (SEM) image of a cross-section of the membrane on the GE E500Amicroporous polysulfone support. It can be seen that the membrane consisted of two portions. The top portion was a dense active layer, which provided separation, and the bottom portion was a microporous polysulfone support, which provided mechanical strength. This composite structure minimizes the mass transfer resistance while maintaining sufficient mechanical strength. 

There are at least two main sources of resistance to mass transfer (Figure 5.4 [96]) external film mass transfer resistance and intrapartide diffusion that is composed of pore and surface diffusion. The latter diffusion is insignificant in numerous adsorbents but plays an important role in most adsorbents used in RPLC. For particles having micropores, there is an additional mass transfer resistance, the resistance to diffusion through micropores which is often important. This explains why considerable attention is paid in the preparation of stationary phases for FIPLC to avoid the formation of micropores. This explains also why graphi-tized carbon black, which tends to be plagued by a profusion of micropores, has not been a successful stationary phase for HPLC. 

However, a solution in the Laplace domain has been derived by Kucera [30] and Kubin [31]. The solution cannot be transformed back into the time domain, but from that solution, these authors have derived the expressions for the first five statistical moments (see Section 6.4.1). For a linear isotherm, this model has been studied extensively in the literature. The solution of an extension of this model, using a macro-micropore diffusion model with external film mass transfer resistance, has also been discussed [32]. All these studies use the Laplace domain solution and moment analysis. 

In Fig. 9 three orthogonal slices through the reconstruction of the XVUSY crystal are displayed. The x-z projection shows a cylindrical mesopore that connects the interior of the crystal with the outside world . For one and the same mesopore marked with a white arrow in all three projections it is clear that no connection to the external surface via the mesopore network exists. In other words, this mesopore is a cavity in the crystal and will hardly contribute to reduction of mass transfer resistance. From independent measurements based on physisorption and mercury intrusion [29] it has been found that 30% of the mesopore volume in this material is present in cavities that are connected to the external surface only via micropores. More recently elegant proof from thermoporometry experiments for the existence of these cavities has been published [31]. 

Note that these equations are simplified versions of the general model and based on an efifeetive diffusion eoefficient which is dependent on the slope of the adsorption isotherm. Principally speaking, the general model based on the material balance and all mass transfer resistances (concentration boundary layer around a pellet, macro and micropore diffusion, sometimes surface diffusion and laminar pore flow) has to be solved. 

In a number of adsorbents, the adsorbent particle is composed of a large number of microporous microparticles, with larger pores between them. If the dominant mass transfer resistance is within the microparticles, the adsorption process is controlled by the rate of micropore diffusion and the model is defined by the material balance on the microparticle level. For one-dimensional Fickian diffusion, it can be described by the following equation ... 

Model 1 — the micropore-macropore model. This model is obtained from the general one for negligible mass transfer resistance in the stagnant film and at the micropore mouth. 

Model 2 — the micropore-macropore-adsorption model. This model takes into consideration the finite adsorption or desorption rate at the micropore mouth, but neglects the film mass transfer resistance. 

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. 

Up to now, we have only considered the thermodynamics of adsorption. However, in technical processes - for example, in a fixed bed - adsorption is a transient process until a particle or a zone of a fixed bed has reached the equilibrium loading. The intrinsic chemical process of adsorption can be regarded as instantaneous, and the mass transfer to and into the porous adsorbent determines how fast the equilibrium is reached. Experience teaches that the mass transfer resistance by film diffusion is mostly negligible, and so the adsorption is governed by pore diffusion (Topic 3.3.4). Pore diffusion can roughly be divided into macropore and micropore diffusion, for example, zeolites have macropores as well as micropores in the small crystallites, which form a sub-structure in a partide. The... 

Often, micropores are short, that is, r/microporos = 1- Here, grains with a diameter <0.1 xm (d, i o/dp < 10 ) would be sufficiently small to suppress the mass transfer resistance of the micropores. Note that Eq. (4.5.174) indicates that the apparent activation energy is 0.25 of the intrinsic value for strong limitation by pore diffusion in micro- and macropores ... 

Extensive research both in industry and academia has resulted in the innovation of porous membranes, which are gas fiUed, with much smaller mass transfer resistance. Parallel research on microporous membranes has adjusted the pore size and membrane hydrophobicity, again yielding a much smaller mass transfer resistance. However, modules with different geometries perform differentiy. Flow outside of, but perpendicular to, the fiber bundle offers reasonably fast mass transfer. Not surprisingly, this geometry is chosen in most of the commercial membrane degasification units. 

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