Petr Schneider

Multicomponent isothermal diffusion and forced flow of gases in capillaries

Abstract Isothermal transport is described of a multicomponent gas mixture in a capillary. The governing equation (eqn 24) derived in the paper accounts for sim and pressure. The equation applies to the transition region between the Knudsen diffusion and the region of continuum and provides also for the slip on equations for the H 2 ue5f8C 2 H 2 , H 2 ue5f8C 2 H 2 ue5f8C 2 H 4 and H 2 ue5f8N 2 ue5f8NH 3 mixtures indicates give rise to a pressure gradient representing the driving force for additional transport. Notions of a critical component and diffusion-stoichiometric

Dynamics of non-isobaric diffusion in porous catalysts

Abstract A measuring cell was constructed for determining the time development of total pressure changes inside porous pellets, caused by composition step-change of the gas flowing along one flat face of pellets. Using this cell and swopping of gases in binary systems H2-N2, H2-Ar, He-N2, He-Ar, experimental pressure response curves were obtained for porous α-alumina pellets with mono- and bidisperse pore structures. Utilizing description of the combined gas transport according to the mean transport-pore model and dusty gas model the pressure responses were simulated numerically. Transport parameters of pellets obtained by fitting experimental responses were compared with parameters determined independently by steady-state methods.

Direct transport parameters measurement versus their estimation from mercury penetration in porous solids

Abstract It has become widespread practice to rely on mercury penetration data for the determination of pore-size distribution when calculating transport processes occurring in the porous structure of catalysts and adsorbents. The authors, working in independent laboratories, summarize recent results which show that mercury penetration analysis is not reliable. A mean transport-pore model (MTPM) is proposed which requires permeation, steady-state diffusion or pulse chromatographic measurements with several gases or gas pairs and/or at different pressures and temperatures. This method provides basic parameters for calculating the transport processes in catalysis or adsorption, making no direct use of mercury penetration and other textural data.

A novel cell for gas-counterdiffusion measurements in porous pellets

Abstract A new type of isobaric diffusion cell for measuring the countercurrent gas diffusion in porous catalyst pellets at atmospheric pressure is proposed. To determine the diffusion fluxes, the rate of change of gas volume in one part of the cell is measured, which follows from Grahams law; this change corresponds to the rise of a soap bubble film in a calibrated burette. To obtain the information needed for evaluating the parameters of equations describing diffusion transport in a porous medium the use of several pairs of gases is proposed. The method of evaluating transport parameters from diffusion measurements of this type is demonstrated for the mean transport-pore model.

Liquid expulsion permporometry for characterization of porous membranes

The processes in a liquid pre-wettted porous membrane are described for the situation when a gradually increasing pressure difference of an inert gas is imposed across the membrane (liquid expulsion permporometry). The description takes into account the compressible nature of the gas and the distribution of the pore sizes. By comparing the experimentally obtained dependence of the gas flowrate through the membrane versus the imposed pressure difference (wet curve) it is possible to evaluate the distribution of the fractional membrane porosity (pore-volume distribution) with the pore size. At the same time the ratio of porosity and tortuosity of transport pores (geometric membrane parameter, ψ) is determined. This parameter can be used together with the mean integral pore radius and the mean integral squate of pore radii (determined by analysis of the gas flowrate dependence versus Δp for a dry membrane - dry curve) for the prediction of diffusion and/or viscous flow for any gas or gas mixture under any temperature and pressure condition. The stimulated pore-size distributions are compared with the results of the traditional method; it appears that the traditional approach leads to systematic deviations in the obtained pore-size distribution.

Effect of internal diffusion on catalytic reactions

Abstract The effectiveness factors η have been calculated for a reversible, isothermal, catalytic reaction proceeding without a change in the number of moles, for the case when the reaction rate is expressed by means of rate Eq. (3). The effectiveness factor depends on the dimensionless modulus M L [Eq. (20)] and dimensionless parameter B . If equilibrium composition is attained at the centre plane of the slab of catalyst, the effectiveness factor η can also be calculated analytically from Eqs. (32) and (33). A comparison with the analogous irreversible reaction reveals that the retardation effect of internal diffusion is always stronger for a reversible reaction.

Transport characteristics of bidisperse porous α-aluminas

A series of porous α-alumina samples with intentionally varied pore size distributions was used for verification of the appropriateness of the mean transport pore model (MTPM) for bidisperse porous structures. Model parameters r- and ψ were determined by combining experimental results for permeation of four simple gases and counter-current diffusion of four simple gas pairs. MTPM correlates the experimental data quite satisfactorily. The mean transport pore radius, r-, runs in parallel with the mean radius of macropores, indicating the predominant role of these pores in mass transport. Large anisotropy of pellet surfaces was demonstrated by comparing parameters ψ, corresponding to pellet flat circular faces and cylindrical surfaces.

Peak moments for gas chroatographic columns with a pressure drop

Abstract Relationships have been derived for the first absolute and the second and third central moments of the chromatographic curv from a non-isobaric column for the Kubin and Kucera model (axial dispersion, external diffusion, internal diffusion, rate of adsorption). The dependence of the axial dispersion coefficient, mass transfer coefficient and effective diffusion coefficient on the pressure of carrier gas velocity is taken into account. In expressing the internal diffusion, the transition region between Knudsen and bulk diffusion is considered. By using the relationships for th moments, the dependence of the plate height on the carrier gas velocity is expressed (a modified Van Deemter equation for the non-isobaric case). If the rate of adsorption is not significant and internal diffusion takes place into the bulk region, it is possible to use the isobaric form of the Van Deemter equation with a corrected plate height.

Stationary catalytic kinetics via surface concentrations from transient data: Methanol dehydration

Abstract A novel approach to the analysis of the transient data from CSTR is illustrated on the catalytic dehydration of methanol. The method allows to determine adsorbed amounts of reaction components under reaction conditions and it is applicable in cases where at least one reaction component is not (or slighty) adsorbed. Because new types of data can be obtained in this way a deeper discrimination between rival kinetic models is possible. The method permits also determination of total concentration of active sites on the catalyst surface. Comparison of transient data analysis with the steady-state results is presented.

Transport parameters of porous catalysts via chromatography with a single-pellet-string column

Abstract A method was developed for chromatographic determination of effective diffusion coefficients in porous solids which is suitable for cylindrical pellets. Pellets are stacked coaxially along the axis of the measuring column in the form of a pseudo-infinite cylinder. The advantage of this arrangment is that (i) fewer pellets are required for column packing than for conventional columns, (ii) axial dispersion in the annular space between coaxial cylinders can be expressed theoretically and (iii) high carrier gas linear velocities are easily achieved. The method was verified on ten samples of bidisperse α-alumina with changing volume and size of meso and macro pores. A mean transport pore model (MTPM) was used to extract parameters independent of measuring conditions from effective diffusion coefficients obtained chromatographically.