Wicke-Kallenbach cell

Unsteady state diffusion in monodisperse porous solids using a Wicke-Kallenbach cell have shown that non-equimolal diffusion fluxes can induce total pressure gradients which require a non-isobaric model to interpret the data. The values obtained from this analysis are then suitable for use in predicting effectiveness factors. There is evidence that adsorption of the non-tracer component can have a considerable influence on the diffusional flux of the tracer and hence on the estimation of the effective diffusion coefficient. For the simple porous structures used in these tests, it is shown that a consistent definition of the effective diffusion coefficient can be obtained which applies to both the steady and unsteady state and so can be used as a basis of examining the more complex bimodal pore size distributions found in many catalysts. 

In the Wicke-Kallenbach cell, diffusion occurs in one dimension through the porous solid as a result of a concentration, Co, at one of the two faces (z=0) of the solid the other, at distance (x=L), being maintained at a value approaching zero, while keeping the total pressure at each face constant. For a two component mixture of A and B the steady state flux of A is given by ... 

Most studies have assumed equation (3) to apply, so that equation (1) takes the form of Fick s law, with the composite (effective) diffusion taking account of both bulk and Knudsen diffusion. For the stealy state operation of the Wicke-Kallenbach cell, this can often be a reasonable assumption. Smith et al (18) have also used this description of the transport processes to analyze the situation when a pulse of the trace component is applied at z=0 and the concentration is monitored at z=L. For sufficiently high flow rates of the carrier gas, the first moment of the response curve to a pulse input is ... 

Basically, the equipment is a standard Wicke-Kallenbach cell, except that provision is made for introducing a pulse of the trace component on one face of the porous sample, i.e. z=0. However the design does have to take into consideration the need to calibrate the detection unit for lags in the system.This does not seem to have been carried out in other work reported which used this technique. Failure to make this correction can lead to significant errors in the values of the diffusion coefficient which are extracted from the experimental data e.g. see Fig.l. 

For mono-disperse pore size distributions a combination of steady state diffusion and flow permeability measurements can be used to characterize the structural parameters which enable consistent values for tortuosity to be defined. These results can be used to predict the dynamic response of a Wicke-Kallenbach cell to short pulses of a tracer gas having a comparatively high diffusivity and enable a reasonable estimate of the effective diffusion coefficient to be obtained. 

Hore importantly, the response curves are noticeably affected where one or both of the components is adsorbable, even at low tracer concentrations. The interpretation of data is then much more complex and requires analysis using the non-isobaric model. Figs 7 and 8 show how adsorption of influences the fluxes observed for He (the tracer), despite the fact that it is the non-adsorbable component. The role played by the induced pressure gradient, in association with the concentration profiles, can be clearly seen. It is notable that the greatest sensitivity is exhibited for small values of the adsorption coefficient, which is often the case with many common porous solids used as catalyst supports. This suggests that routine determination of effective diffusion coefficients will require considerable checks for consistency and emphasizes the need for using the Wicke-Kallenbach cell in conjunction with permeability measurements. 

Care is needed in applying the unsteady state pulse technique to a Wicke-Kallenbach cell in order to obtain values for effective diffusion coefficients. For sufficiently small concentrations, where the trace component is of higher diffusivity than the carrier, the commonly used isobaric model is adequate for defining the transport parameters if sufficiently short pulses are used. However, where adsorption of either carrier or trace component occurs or wheipe the trace is of lower diffusivity, then the induced total pressure gradients cause the fluxes to show unusual behaviour and may require analysis by a non-isobaric model. 

A diffusion cell method was introduced by Wicke and Kallenbach [3] and therefore is called the Wicke-Kallenbach method. The experimental set up (Figure 5.1) is called the Wicke-Kallenbach cell. It is the most popular method for different diffusion measurements. 

In this study, we used the modified Wicke-Kallenbach cell which is tubular membrane cell type. Permeation measurements were performed in the 293K-373K, Oatm-Satm range for H2, N2, CO2 and CH4. Feed gas and retentate gas were controlled by MFC(Mass Flow Controller, Tylan Co.) and BPR(Back Pressure Regulator). Permeate gas flux was measured by soap bubble flow meter, MFM (Mass Flow Meter, Teledyne Co.) and wet gas meter. Especially, MFM was used to measure kinetics of membrane permeation. Separated and retentate gas composition was analyzed by on-line GC(HP 5890 II, TCD type). Helium was used as carrier gas and sweeping gas. Temperature was detected by RTD(Hanyoung. Co.) at inlet, inner cell and skin of cell. Pressures were detected by pressure transducers(Deco Co.) at inlet and permeate part. 

Permeation experiments in a Wicke-Kallenbach cell on the non-caldned layer unfortunately showed the existence of pinholes between crystals (Jable 7). Gases were measured at ambient pressure and temperature without a pressure difference over the membrane. At the permeate ade, argon was used as a sweep gas. 

In terms of catalysis, important equilibrium processes include low-temperature gas adsorption (capillary condensation) and nonwetting fluid invasion, both of which are routinely used to characterize pore size distribution. Static diffusion in a Wicke-Kallenbach cell characterizes effective diffusivity. The simultaneous rate processes of diffusion and reaction determine catalyst effectiveness, which is the single most significant measure of practical catalytic reactor performance. 

The modified Wicke - Kallenbach cell developed in our laboratory [26,27], was used for measurement of isobaric counter-current ternary diffusion. Figure 1 shows schematically the diffusion set-up including the modified Wicke-Kallenbach cell.. Gl-4 are gas sources FMC are flow-meter controllers D is the diffusion cell 01-2 are gas outlets VI-3 are valves B is a calibrated glass burette with soap film. The diffusion cell contains a metallic disc with cylindrical holes into which the porous pellets are mounted. Volumes of cell compartments are approximately 150 cm. ... 

The isobaric counter-current diffusion measurements in the modified Wicke-Kallenbach cell employ the validity of the Graham law which states that under isobaric... 

A direct measurement of y/ can be performed with a modified Wicke-Kallenbach cell. Measured values of y/ are in the order of 0.2, which is much smaller than one would expect from the Bruggemann correction or the Tomadakis-Sotirchos model. 

The second technique is based upon the Wicke-Kallenbach cell. Originally, this cell was used in the steady state mode, but presently transient... 

The modeling of the phenomena in the (adapted) Wicke-Kallenbach cell is less complicated the equation for the tracer is limited to the catalyst pellet itself. It contains only 2 parameters the effective diffusivity, DeA, and the adsorption equilibrium coefficient, Ka. 

Figure 2 - Dynamic Wicke-Kallenbach cell for measuring effective diffusivities in catalysts.

Rates of adsorption of gases and vapours by porous media 87 4.3.1 The Wicke-Kallenbach cell... 

The effective diffusivity of a porous adsorbent may be determined as the adsorption process proceeds by passing the gas for which the diffusion coefficient is being measured, diluted and carried by an inert gas, such as helium, across one face of the adsorbent pellet and the inert gas alone across the obverse face of the pellet. The fabricated adsorbent pellet is compressed into a cylindrical shape and sealed within a cell known as a Wicke-Kallenbach cell (shown in Figure 4.9) after the first publication of the method originated by Wicke and Kallenbach (1941). The measurement procedure has since been modified by Henry et al. (1961) and Suzuki and Smith (1972). The method adopted by Suzuki and Smith is to allow a pulse of the adsorbate under investigation to be injected into an inert gas stream... 

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