Elsevier

Catalysis Today

Volume 118, Issues 1–2, 30 October 2006, Pages 113-120
Catalysis Today

Competitive diffusion and adsorption in Vycor glass membranes—A lumped parameter approach

https://doi.org/10.1016/j.cattod.2005.11.094Get rights and content

Abstract

The interaction of simultaneous diffusion and adsorption of pure gases and gas mixtures in a Vycor glass membrane has been studied under transient conditions in a modified Wicke–Kallenbach cell. A lumped two parameter approach was developed in order to analyse all the observed pressure responses in a unified manner. This approach was found to be capable to fit well almost all the observations made for different types of gases and at different temperatures with sufficient or excellent accuracy.

Introduction

In order to use membranes successfully in separation processes and in membrane reactors, the rate of transport should be known [1], [2]. This study is devoted to quantify the transport rate in a porous glass possessing interesting properties. Vycor glass applied for measurements was already used in the previous studies [3], [4], [5], [6]. It consists of 96% silica with the remainder to be mainly B2O3.

The average pore diameter of Vycor glass is approximately 4 nm. The pore size distribution is relatively narrow. The glass strongly adsorbs many organic and inorganic gases. Vycor glass membranes can be used for gas separation and dosing processes with and without simultaneous reactions. The understanding of mass transfer through the membranes is essential for successful applications.

The modified dynamical Wicke–Kallenbach diffusion cell [7] is an effective approach to investigate the mass transfer in a porous medium such as in solid adsorbents and catalysts and membranes. Do et al. [8] simulated the transient pressure response at the downside reservoir to quantify mass transfer of hydrocarbons as single component system in activated carbons by taking into account gas phase diffusion and adsorption. Dogan and Dogu [9] analysed the dynamics of flow and diffusion of adsorbing tracers in Al2O3 and Pd–Al2O3 pellets using a pulse-response technique. In previous works, the generalized Maxwell–Stefan theory [10] was applied to study gas phase diffusion and surface diffusion in Vycor glass [4], [5]. A relatively good description of coupled gas phase and surface diffusion was achieved for experiments with single components or with binary mixtures of inert gases. Less effort was devoted to study the behaviour of mixtures of adsorbable gases.

In this work the interplay between simultaneous diffusion and adsorption of pure gases and gas mixtures has been studied using a modified Wicke–Kallenbach cell, which consists out of two chambers and which was operated under transient conditions. In the pore size range of Vycor glass for light gases, such as He, N2, CO2, and small hydrocarbons, like C3H8 and C4H10, the mean free path length at atmospheric pressure and temperature is much larger than the pore width (λ/dpore > 10) [11]. Thus, contributions of bulk molecular diffusion and viscous flow to overall mass transfer are small and can be ignored. If two gases cross the membrane counter-currently with different velocities the pressure within one chamber changes as a function of time. Several pressure responses were measured with different gases and at various temperatures.

In contrast to the relatively complicated Stefan–Maxwell equations mentioned above, a simple two parameter equation – which applies rigorously in case of pure Knudsen type diffusion – is suggested to describe the observations made using binary mixtures of non-adsorbable and adsorbable gases. The relation between the parameters determined and conventional transport coefficients is elucidated.

Section snippets

Experimental

The glass membrane provided by CORNING Inc. (USA) is originally opalescent and gradually turns brown during its exposition to the atmosphere. It was cleaned by heating in a solution of 30% hydrogen peroxide at 60 °C over night until the contaminating color disappears. Before measurements, the glass membrane was activated firstly by drying in nitrogen flowing over night at room temperature and then by heating at 180 °C for 2 h. The activation treatment removes absorbed water from the pore surface,

Prediction of transients

A lumped parameter approach is suggested for the prediction of the pressure difference between both chambers of the diffusion cell ΔP(t). The notation is introduced in Fig. 2. The following assumptions are made:

  • 1.

    c = Pex/RT = constant.

  • 2.

    Large sweep gas flow G, i.e. y1,ex = constant.

  • 3.

    Permeabilities β1 and β2 are constant.

  • 4.

    The fluxes N1 and N2 are independent of each other and are driven by linear concentration differences.

  • 5.

    At t = 0: P(t) = Pex.

  • 6.

    Initial mol-fraction in the closed chamber: yi,0.

  • 7.

    Binary mixtures are

Results and discussions

Below the results of several experiments will be reported in comparison with the theoretical model leading to Eq. (12).

Conclusion

The suggested lumped two parameter approach, Eq. (12), is found simple and capable of fitting a large amount of experimental data regarding mass transfer in a porous Vycor glass membrane studied in a transient diffusion experiment with sufficient or excellent accuracy.

For inert gases like He/N2 the fitted relaxation times t.1 and t.2 are in perfect agreement with the predicted ones based on the assumption of pure Knudsen diffusion.

For the adsorbable gases, like CO2 and C3H8, the relaxation

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