Vladimír Hejtmánek

Gas transport in porous media under dynamic conditions

Abstract The dynamic version of the Wicke-Kallenbach diffusion cell with one compartment closed and equipped with a sensitive pressure gauge was used for determination of sets of Mean Transport Pore Model and Dusty Gas Model parameters for an industrial catalyst (ICI 52-1 in reduced form). The dynamic pressure responses due to gas composition step changes of inert gases (H2, He, N2, Ar) were measured and fitted to the system of partial differential equations which describe the transport (mass balances with Maxwell-Stefan constitutive equations). The optimum textural parameters were obtained by simultaneous matching of all experiments. The model parameters are material constants of the porous solid and, thus, do not depend on temperature, pressure and kind of the transported gases. Both diffusion models gave a good agreement between experiments and calculations. The parameter reliability is discussed.

Axial dispersion under liquid-chromatography conditions

Abstract Axial dispersion coefficients for three tracer-liquid—carrier-liquid systems, under conditions characteristic for liquid chromatography, were obtained by time-domain fitting of the response peak to square-wave input signals. Besides axial dispersion in the column, the fitted model accounts also for regions with ideal mixing and transport delay. The obtained Bodenstein numbers can be empirically correlated with the product of Reynolds and Schmidt numbers [eq. (13)].

Determination of effective diffusivities and transport parameters of porous solids in the Single-Pellet-String-Column

Abstract The chromatographic technique which employs SPSC and takes into account the extra-column effects of the measuring system can provide consistent transport characteristics of porous solids. These characteristics are independent of the kind of gases which are transported through pores, as well of temperature and pressure. Dispersion of the tracer band in the interparticle spaces of the SPSC increases at higher carrier gas velocities when the non-porous column packing is replaced by a porous one. This points to some additional mechanism of band spreading caused by the presence of interface gas-porous solid.

Underground coal gasification: rates of post processing gas transport

Two ex-situ and one in-situ semi-pilot plant UCG experiments in the experimental mine Barbara were performed with hard coal and lignite samples. To evaluate the influence of the UCG process on the textural properties of surrounding strata and coals, samples from various locations of the coal seam and the stratum samples before and after the UCG process were collected. Mercury porosimetry, helium pycnometry, and physical adsorption of nitrogen were used for the determination of textural properties of samples. Permeation gas transport was modelled based on the knowledge of the real structure characteristics of the stratum samples by the Mean Transport-Pore Model (MTPM). Influence of the individual texture and transport parameters on the post processing gas transport through porous strata with respect to the variability of their possible values was also evaluated.

Comparison of transport characteristics and textural properties of porous material; the role of pore sizes and their distributions

Abstract For a set of six porous materials with a range of mean pore radii from 50 to 3000 nm, and mono- or bidisperse pore structure, transport characteristics and textural properties were compared. Two standard methods (mercury porosimetry and helium pycnometry) together with liquid expulsion permporometry (that takes into account only flow-through pores) were used for determination of textural properties. Pore structure characteristics relevant to transport processes were evaluated from multicomponent gas counter-current diffusion and gas permeation. For data analysis the Mean Transport-Pore Model (MTPM) based on Maxwell-Stefan diffusion equation and a simplified form of the Weber permeation equation was used. It appears that for porous solids with monodisperse pore-size distribution the MTPM mean-pore radii and transport-pore distributions agree with the information from standard textural analysis. For porous solids with bidisperse pore-size distribution the MTPM mean-pore radii and transport-pore distributions are close to large pore sizes from standard textural analysis. Keywords: Counter-current gas diffusion, Permeation, Transport parameters, Mean Transport-Pore Model, Maxwell-Stefan equation, Weber equation

Diffusion of large molecules in porous glass

Effective diffusion coefficients for perylene and vanadyl porphyrine in acetone and six polystyrenes with molecular weight in the range 1200–19,000 g/mol in tetrahydrofuran were determined from the responses of a chromatographic column packed with porous glass (pore diameter 11 nm). The contribution of axial dispersion was evaluated from the measurements with polystyrenes which cannot penetrate the pores. To obtain the diffusion time constants a newly developed method for matching the experimental peaks in the time domain was utilized. The steric factors, S (partition coefficients), of the solutes evaluated from the first moments of the column responses were used for the determination of ratios of solute and pore sizes λ. The enhanced drag coefficient, which characterizes the interaction of the solute with the pore wall, changes with (1 − λ)1.34. Thus, the obtained tortuosity of the porous glass (2.71) is well within the expected interval. The effective diffusion coefficients are related to the bulk diffusivities of the solute—solvent pair, D, as D = e(1 − λ)3.34D/q.

Pore structure and effective permeability of metallic filters

The pore structures (microstructures) of two metallic filters were reconstructed using the stochastic reconstruction method based on simulated annealing. The following microstructural descriptors were included in the description of the real microstructures: the two-point probability function, the lineal-path functions for the void or solid phases, i.e. simulated annealing was constrained by all low-order statistical measures that were accessible through the analysis of images of polished sections. An effect of the microstructural descriptors on the course of reconstruction was controlled by modifying two parameters of the reconstruction procedure [1]. Their values resulted from repeated reconstruction of two-dimensional microstructures in such a way that the reference (experimental) and calculated two-point cluster functions deviated negligibly. It was tacitly assumed that the parameters adjusted during two-dimensional reconstruction had the same influence on the formation of the three-dimensional microstructures. Since connectivity of phases is a critical property of the stochastically reconstructed media, clusters of pore and solid voxels were determined using the Hoshen-Kopelman algorithm. It was found that the solid phase formed one large cluster in accordance with the physical feasibility. The void phase created one large cluster and a few small clusters representing the isolated porosity. The percolation properties were further characterised using the local porosity theory [2]. Effective permeability of the replicas was estimated by solving the Stokes equation for creeping flow of an incompressible liquid in pore space. Calculated permeability values matched well their experimental counterparts.