Diffusivities zeolites

Prediction of the breakthrough performance of molecular sieve adsorption columns requires solution of the appropriate mass-transfer rate equation with boundary conditions imposed by the differential fluid phase mass balance. For systems which obey a Langmuir isotherm and for which the controlling resistance to mass transfer is macropore or zeolitic diffusion, the set of nonlinear equations must be solved numerically. Solutions have been obtained for saturation and regeneration of molecular sieve adsorption columns. Predicted breakthrough curves are compared with experimental data for sorption of ethane and ethylene on type A zeolite, and the model satisfactorily describes column performance. Under comparable conditions, column regeneration is slower than saturation. This is a consequence of non-linearities of the system and does not imply any difference in intrinsic rate constants. 

There are three distinct mass-transfer resistances (1) the external resistance of the fluid film surrounding the pellet, (2) the diffusional resistance of the macropores of the pellet, and (3) the diffusional resistance of the zeolite crystals. The external mass-transfer resistance may be estimated from well-established correlations (4, 5) and is generally negligible for molecular sieve adsorbers so that, under practical operating conditions, the rate of mass transfer is controlled by either macropore diffusion or zeolitic diffusion. In the present analysis we consider only systems in which one or other of these resistances is dominant. If both resistances are of comparable importance the analysis becomes more difficult. 

The appropriate form of the diffusion equation, when zeolitic diffusion is the controlling resistance, is thus... 

The solution of Equations 2-4 and 7-11 gives the theoretical breakthrough curve for the case of zeolitic diffusion control. 

If zeolitic diffusion is sufficiently rapid so that the sorbate concentration through any particular crystal is essentially constant and in equilibrium with the macropore fluid just outside the crystal, the rate of mass transfer will be controlled by transport through the macropores of the pellet. Transport through the macropores may be assumed to occur by a diffusional process characterized by a constant pore diffusion coefficient Z)p. The relevant form of the diffusion equation, neglecting accumulation in the fluid phase within the macropores which is generally small in comparison with accumulation within the zeolite crystals, is... 

Figure 1. Theoretical breakthrough curves for zeolitic diffusion control at X = 1.0 saturation (-------------------------), regeneration (------)...

Figure S. Comparison of asymptotic constant pattern saturation breakthrough curves for X = 0.1 5 (1) zeolitic diffusion control with Dz independent of concentration, (2) zeolitic diffusion control, (8) macropore diffusion control...

Curves calculated in this way for macropore control and zeolitic diffusion control are compared in Figure 3 for one particular value of X. Also shown in this figure is the theoretical curve for zeolitic diffusion control with a constant diffusivity. Differences between the shapes of these curves are not large although the case of zeolitic diffusion control with a constant diffusivity leads to substantially greater tailing. 

Also shown in Table I are the estimated values of the time constant for macropore diffusion based on estimated macropore diffusivities. From the ratio of the time constants for macropore diffusion and zeolitic diffusion, it is clear that the assumption of zeolitic diffusion control is a valid approximation for these systems. 

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). 

D limiting zeolitic diffusivity at zero sorbate concentration Dp macropore diffusivity (based on pore sectional area) rrt ratio of bed void space to zeolite crystal volume = e/(l — e ) q local sorbate concentration in a zeolite crystal... 

Although the systems investigated here exhibited predominantly macropore control (at least those with pellet diameters exceeding 1/8" or 0.32 cm), there is no reason to believe that surface diffusion effects would not be exhibited in systems in which micropore (intracrystalline) resistances are important as well. In fact, this apparent surface diffusion effect may be responsible for the differences in zeolitic diffusion coefficients obtained by different methods of analysis (13). However, due to the complex interaction of various factors in the anlaysis of mass transport in zeolitic media, including instabilities due to heat effects, the presence of multimodal pore size distribution in pelleted media, and the uncertainties involved in the measurement of diffusion coefficients in multi-component systems, further research is necessary to effect a resolution of these discrepancies. 

Ruthven, D.M. (2006) The window effect in zeolitic diffusion. Micropor. Mesopor. Mater., 96, 262. 

Single Crystals. Naturally-occurring zeolites are sometimes found as large single crystals. Tiselius (34, 35) used this feature to study diffusion in zeolites. Diffusion of water in heulandite crystals was followed by an... 

There are several models to describe intracrystalline diffusion (step 3) in microporous media. Diffusion in zeolites is extensively described in Ref. 30. For the modeling of permeation through zeolitic membranes, such a model should take the concentration dependence of zeolitic diffusion into account. Moreover, it should be easy applicable to multicomponent systems. In Section III.C, several models will be discussed. 

Adsorption plays an important role in permeation through microporous media. The selectivity of a zeolitic membrane at low temperatures is largely determined by differences in adsorption between species, as was shown in Section II. Moreover, the surface concentration, which is related to the partial pressure by the adsorption isotherm, plays an important role in the models for zeolitic diffusion. Finally, the thermodynamic factor from Eq. (17) is related to the adsorption isotherm. 

Table 2 Single- and Multicomponent Diffusivities of Ethane and Ethene, Calculated Using the Maxwell-Stefan Model for Zeolitic Diffusion...

The third step, migration inside the micropore, is also denoted as intracrystalline zeolite diffusion or configurational diffusion. 

Comparison between zeolitic diffusion and self diffusion is a most actual topic of zeolite research (3,4,23-25), and it is still far from being conclusively treated, Kmr self-diffusion studies on the very adsorbate - adsorbent system of the uptake device are most likely to help to clarify this problem, since in this case one in fact has to do with the identical system in both experiments... 

Spectroscopic characterization of the zeolites. Diffuse reflectance spectroscopy reaches the spectral range comprised between 4000 and 40000 cm-1. Two types of transitions are of interest. In the first place, 4000-10000 cm-1 region contains vibrations associated with the OH groups combination bands near 4500-5000 cm-1 and the first overtone 2v0h near 72 00 cm-1. Secondly, the d-d transitions of the nickel ions show up between 4000 and 30000 cm-. ... 

Real systems can be expected to correspond to some intermediate case between the extremes. The rate laws that must be expected, either for the migration of a pure sorbate or for the exchange of one sorbate against another one, can best be derived from a more detailed consideration of the model of sorption on interstitial single sites. The intermediate case between a lattice of single sites and a macroporus sorbent will be covered as we consider how the rate laws will be modified if several types of sites exist in the solid, a situation that has been shown to prevail in zeolites. Diffusion in the solid will be considered first, subsequently how it couples with the rate of transfer at the phase boundary. 

In the frequency response method, first applied to the study of zeolitic diffusion by Yasuda [29] and further developed by Rees and coworkers [2,30-33], the volume of a system containing a widely dispersed sample of adsorbent, under a known pressure of sorbate, is subjected to a periodic (usually sinusoidal) perturbation. If there is no mass transfer or if mass transfer is infinitely rapid so that gas-solid mass-transfer equilibrium is always maintained, the pressure in the system should follow the volume perturbation with no phase difference. The effect of a finite resistance to mass transfer is to cause a phase shift so that the pressure response lags behind the volume perturbation. Measuring the in-phase and out-of-phase responses over a range of frequencies yields the characteristic frequency response spectrum, which may be matched to the spectrum derived from the theoretical model in order to determine the time constant of the mass-transfer process. As with other methods the response may be influenced by heat-transfer resistance, so to obtain reliable results, it is essential to carry out sufficient experimental checks to eliminate such effects or to allow for them in the theoretical model. The form of the frequency response spectrum depends on the nature of the dominant mass-transfer resistance and can therefore be helpful in distinguishing between diffusion-controlled and surface-resistance-controlled processes. 

A plot of the relative intensity of the broad constituent versus the observation time (i.e. the separation between the two field gradient pulses) contains information which is analogous to that of a tracer exchange experiment between a particular crystallite containing e.g. labelled molecules and the unlabelled surroundings. Therefore, this way of analysis of PFG NMR data of zeolitic diffusion has been termed the NMR tracer desorption technique [60]. The first statistical moment ( time constant ) of the NMR tracer desorption curve represents the intracrystalline mean lifetime Tintra of the molecules under study. 

It should be mentioned that—if zeolites are technically applied as formed pellets—transport limitation may be due to both intracrystalline zeolitic diffusion and long-range diffusion as just considered. Denoting the mean radii of the crystallites and of the pellets by rc and rp, respectively, the respec-... 

Deviations from normal diffusion, i.e. from molecular propagation within a quasi-homogeneous, essentially infinitely extended medium, may be taken into account by introducing an effective diffusivity Dgff. It is defined in the same way as the self-diffusivity, i.e. via Eqs. 6 and 7, however, without the requirement of the validity of Pick s laws 1 and 2. Therefore, Dgff may become a function of the (observation) time. In the considered case of zeolitic diffusion and for intracrystalline diffusion paths being sufficiently small in comparison with the crystallite radii, the effective diffusivity may be shown to be represented by a power series [106-108], leading to... 

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