Stefano Brandani

Analysis of ZLC desorption curves for liquid systems

Abstract An improved mathematical model to represent the desorption curve obtained in a ZLC (zero length column) experiment is derived and used to reinterpret previously published experimental data for benzene-hexane in NaX zeolite crystals. The resulting diffusivity data agree well with earlier liquid chromatographic data for the same experimental system (and also with vapour phase ZLC data measured at much lower concentrations). The parameters derived from the new model thus appear to be more reliable than those obtained from the original approximate analysis and the new model should therefore be adopted in future applications of the ZLC method to liquid systems.

Analysis of ZLC desorption curves for gaseous systems

The theoretical model and underlying assumptions used in the analysis of ZLC (zero length column) desorption curves are examined in detail. It is shown that the long time analysis generally yields reliable diffusivity values although, if the initial equilibrium condition is not properly established there will be significant error in the apparent equilibrium constant. The short time analysis is much more sensitive to such errors and a modified way of data analysis is suggested to overcome this problem. Varying the initial equilibration time provides an alternative ZLC experiment that can be used to establish the nature of the rate controlling mass transfer resistance. The utility of this approach is illustrated experimentally for the system C3H8-13X zeolite.

Self-diffusion of propane and propylene in 5A and 13X zeolite crystals studied by the tracer ZLC method

Abstract A new variant of the zero length column method (tracer ZLC) has been developed and used to study the self-diffusion of propane and propylene in 5A and 13X zeolite crystals at 358 K. Diffusivities of propane and propylene in both zeolites are similar; the diffusivities in 13X are about an order of magnitude greater than for 5A. For propane-5A the tracer diffusivities are consistent with the corrected diffusivities from gravimetric measurements with large zeolite crystals and with the limiting diffusivity at zero concentration derived from traditional ZLC measurements. The trend with loading is similar to that observed for the p.f.g. n.m.r. self-diffusivities, although the actual values are somewhat smaller. By contrast, in 13X the tracer diffusivities are much smaller than the n.m.r. values (for propane), and they show the opposite trend with concentration. Partial loading experiments show that the desorption process is controlled by intracrystalline diffusion so that the discrepancy cannot be ascribed to the intrusion of surface resistance. Similarly, there can be no significant thermal effect in a tracer exchange experiment, so the discrepancy cannot be attributed to heat effects.

Diffusion, self-diffusion and counter-diffusion of benzene and p-xylene in silicalite☆

Abstract This paper reports the results of a detailed experimental study of transport diffusion and tracer diffusion of benzene and p -xylene in large crystals of silicalite. The measurements were carried out by the zero length column (ZLC) method. Benzene behaves as a textbook example of an idealized system in which the self-diffusivity is essentially independent of loading and coincides, in the low loading limit, with the limiting transport diffusivity. The behavior of p -xylene is more complex. The self-diffusivity is smaller than the (corrected) transport diffusivity by a factor of about 2.5–3.0, and this difference persists even as the zero loading limit is approached, implying a difference in mechanism between the self-diffusion and transport diffusion processes. A tentative explanation for the difference in behavior between benzene and p -xylene is suggested on the basis of the difference in the length of the molecule.

Concentration dependence of self-diffusivity of methanol in NaX zeolite crystals

The self-diffusivity of methanol in NaX zeolite has been measured, at 100°C, over a wide range of concentration, by the newly developed tracer ZLC (zero length column) technique. The diffusivity values agree well with the values measured by p.f.g. n.m.r., and the unusual maximum in the trend of self-diffusivity with loading, shown by the n.m.r. data, is confirmed.

Liquid phase sorption and diffusion of branched and cyclic hydrocarbons in silicalite

Abstract Sorption and diffusion of several singly branched, doubly branched and cyclic C 6 and C 7 hydrocarbons (2-methylpentane, 3-methylpentane, 3,3 dimethylbutane, 2,2-dimethylbutane, 2,4-dimethylpentane, cyclohexane, cyclohexene, n -hexane and 2 methyl-1-hexene) in large silicalite crystals, with n -hexane as the carrier, have been studied by liquid chromatography and by liquid ZLC measurements. The equilibrium data show mildly endothermic exchange energies and rather low equilibrium constants. Both the absolute values of the equilibrium constants and the exchange energies are consistent with vapor phase data. The kinetic data are more surprising, yielding exchange diffusivities which are larger by several orders of magnitude relative to the values derived from (single component) vapor phase measurements at low sorbate loading. The diffusivity values derived from the chromatographic and ZLC measurements are self-consistent. A tentative explanation involving expansion of the silicalite lattice under saturation conditions, is suggested, to explain these observations.

Transport diffusion and self-diffusion of benzene in NaX and CaX zeolite crystals studied by ZLC and tracer ZLC methods

Abstract Transport and self-diffusion of benzene in NaX and CaX zeolite crystals has been studied by zero length column (ZLC) and tracer ZLC methods. In order to investigate the possible intrusion of extracrystalline mass transfer limitations a series of experiments was performed in which the sample quantity, crystal size, sorbate partial pressure and the nature of the purge gas (He or N 2 ) were changed. At higher sorbate pressures and with larger samples the intrusion of external effects becomes evident but, under properly selected conditions, with sufficiently large crystals, desorption rates are clearly controlled by intracrystalline diffusion. Under these conditions there is good agreement between the limiting transport and tracer exchange diffusivities, confirming the absence of any heat transfer limitation. Diffusivities for benzene-NaX are consistent with earlier reported ZLC values but are substantially smaller than the values obtained from PFG NMR self-diffusion measurements. Diffusivities for benzene-CaX are somewhat smaller than for the NaX system but the trends with concentration are similar. In the presence of water vapour the diffusivity is increased slightly but the effect is not dramatic.

ZLC Measurements under non-linear conditions

Abstract Experimental zero length column (ZLC) response curves are presented for benzene and p -xylene in silicalite over a range of conditions under which the isotherm varies from nearly linear to highly favorable. It is shown that the analytic approximation suggested by Brandani (Chemical Engineering Science, 53, 1998, 2791–2798) provides a good representation of the experimental curves and that this model allows the extraction of reliable values for the diffusional time constant even under non-linear conditions. The conditions under which it is possible to use the simplified linear analysis without introducing major errors are also examined.

Evaluation of the main diffusion path in zeolites from ZLC desorption curves

A simple method of distinguishing between one-dimensional and three-dimensional diffusion in zeolite crystals is suggested based on the difference in the expressions obtained for the zerolength column (ZLC) desorption curve for “slab” and “spherical” diffusion models. The application of this approach is illustrated by experimental data for diffusion in erionite (threedimensional channel system) and offretite (one-dimensional channels).

Measurement of Intracrystalline Diffusion by Zero Length Column Tracer Exchange

The zero length column (ZLC) technique has been adapted to the measurement of tracer self-diffusivities in zeolite crystals. In this new variant the method is applicable over the entire range of sorbate loadings and the resulting diffusivity values should be directly comparable with PFG NMR self-diffusivities. The application of the technique is illustrated by a detailed study of the C 3 H 8 -5A system.