John H. Petropoulos

Influence of adsorption forces on the flow of dilute gases through porous media

Abstract An approximate theoretical treatment is presented for combined gaseous Knudsen and surface flow. The novel features of this treatment include the method of calculating the gas phase component of the flux and the use of a narrow slit as a pore model. These features allow study of the gas permeability of a porous medium as a function of temperature and pore size with greater precision and detail than was previously possible. As a result, a semiquantitative interpretation of recent data on the temperature dependence of gas permeability of porous solids over a wide temperature range is offered. A different earlier interpretation is shown to be unsatisfactory, and discrepancies in the data of two groups of workers are seen to be a natural consequence of a difference in mean pore size of the membranes used.

Calculation of the “surface flow” of a dilute gas in model pores from first principles: II. Molecular gas flow in model pores as a function of gas-solid interaction and pore shape

Abstract The dependence of the free molecule flux through slits and cylinders, on U 0 (adsorption energy parameter/ kT ) is investigated using the molecular path tracing method validated in Part I and a “continuum solid” model for the adsorbent substrate. For both types of geometry and for the wide range of diameters and channel lengths studied, the flux has a minimum with respect to U 0 and falls initially below the classical gas-phase ( U 0 = 0) flux. The diameter dependence of the shape of the minimum region is shown to account for apparently conflicting experimental data. The validity of the “calibration gas” approach to investigations of the flow of adsorbable gases in porous media is discussed in the light of these results, and the relationship between the usual “surface flow” interpretation of experimental data in the higher U 0 region and the present treatment is established. Temperature and channel diameter dependence of the “surface flux” in this region is found to be functionally similar to, but stronger than, that predicted by earlier theories.

Calculation of the “surface flow” of a dilute gas in model pores from first principles

An earlier theoretical investigation of the transport of a dilute (collisionless) adsorbable gas through narrow model pores has been extended to include model porous media, and to a more detailed examination of the strong adsorption region. Certain characteristics of the pore structure of real porous media have also been modeled in a simple manner. The strength of the gas-solid interaction is characterized by the parameter U0, normalized with respect to temperature. At high U0 the behavior of δ (= flux at a given U0/flux at U0 = 0) was similar to that predicted by conventional surface flow theory, with the important difference that the dependence of δ on the radius of the model pore was stronger and varied with pore geometry, but not with the form of the adsorption potential function. Porous media were modeled by considering simple examples of the extreme cases of a previously investigated network model, namely parallel or serial arrays of pores of varying radius. In all the cases examined the minimum in the θ vs U0 plot, previously found for single pores was retained, thus confirming that the main conclusions from our earlier investigations of single pores are relevant to the flow behavior of real porous media.

Calculation of the “surface flow” of a dilute gas in model pores from first principles. I. Calculation of free molecule flow in an adsorbent force field by two methods

Abstract An ab initio calculation of the flow of a dilute (i.e., collisionless) gas, through a channel in which a force field due to the walls acts on the flowing molecules, can be carried out either by a molecular path tracing (MPT) method or by a Monte Carlo (MC) method. The latter yields diffusion coefficients both from transmission probabilities and also by a direct application of random walk theory. The two methods are described here as applied to a two-dimensional slit in which the adsorbate-adsorbent potential is represented by a triangular well. Although highly simplified, this model retains the essential features of a more realistic system. It is shown that discrepancies between the MPT method as usually applied and the MC method can be attributed to “end-effects” and a previously described procedure which corrects for these in MPT calculations is verified here by the MC results. The significance of end-effects in the wider context of model porous materials is briefly discussed.

Realistic modeling of the interaction of vapors with densely packed spherical particles: Part II: Relative permeability

Abstract A two-dimensional network, composed of convergent—divergent flow channels has been employed for the simulation of the relative permeability behavior of a dense random pack of equal spheres as a function of amount of vapor sorbed. The sizes of the flow channels are determined on the basis of the structural characteristics of the pack which have been considered in detail in Part I. Results are given for the conditions of vapor sorption studied in Part I, including hypothetical cases of pure adsorption and condensation, and are compared with results obtained from a model consisting of identical cavities formed from particles of the same size and at the same porosity. Particular attention is paid to the form of the functional dependence of the relative permeability on the amount sorbed in relation to the model parameters and to observed behavior. Another important aim is to study the effect of “structural” and of “physical” absorption—desorption hysteresis on the relative permeability.

Realistic modeling of the interaction of vapors with densely packed spherical particles: Part I: Vapor absorption—desorption isotherms

Abstract A two-dimensional network model is described, based on the structural characteristics of a dense random packing of equal spheres. The model is used to compute absorption—desorption isotherms with multilayer adsorption and capillary condensation. Two types of calculation have been employed based on different approximate methods of formulating the criteria for filling and emptying of cavities according to their size and the size of their “windows.” Results are given for different pore sizes and different cases of separate and simultaneous adsorption and condensation. The different sources of hysteresis are considered. Finally, a comparison is made with the behavior of a model consisting of identical cavities formed from particles of the same size and at the same porosity.

Capillary models for porous media. V. Flow properties of random networks with various radius distributions

For pt.IV see abstr. A67969 of 1973. Gas-phase fluxes, with and without additional surface flow, have been calculated for random, isotropic, two-dimensional and three-dimensional networks comprising a wide range of connectivities. A set of distribution functions which have previously been studied by the authors in parallel (P) and serial (S) models was used. Evidence for the importance of connectivity is augmented by these results. The intermediate status of the network model between the P and S models is confirmed. However when surface flow is present the surface-flow structure factor ks, but not the total flux, can be anomalous in this respect.

Permeation time-lag analysis of “anomalous” diffusion. Part 2.—Helium and nitrogen in graphite powder compacts

The results of the first experimental application of the method of time-lag analysis previously developed for the identification and study of different types of anomalous diffusion behaviour are reported. The permeation of He and N2 in a graphite compact prepared by (uniaxial) compression of successive increments of powder was found to exhibit time-lag anomalies, which were broadly similar to those observed in extensive studies of gaseous permeation through other powder compacts constructed by the same procedure. The analysis covered different temperatures and was extended by varying the method of construction of the plug and by considering transient permeation curves also. The results indicate considerable macroscopic nonhomogeneity of the compact in the axial direction; thus throwing doubt on the view that, in diffusion barriers constructed as above, non-homogeneity on the macroscopic scale cannot be the main cause of the relevant observed time-lag anomalies.

Gas relative permeability in the capillary-network model

A theory for the permeability to a gaseous phase of a network of capillaries containing a second adsorbate phase is derived in terms of equations previously developed for the flow of gas in regular capillary networks with radii randomly selected from a distribution. The role of blind, as well as through, pores is considered. Numerical calculations, using a matrix-inversion method, are used to evaluate the theory. Excellent agreement is found at low volume fractions Vs of the adsorbate, but divergence becomes marked as Vs→ 1. This can be attributed to the inability of the theory to account for the non-regular nature of a random network in which some capillaries are filled by condensed adsorbate.

Study of gas relative permeability in a mesoporous alumina pellet

The helium relative permeability of an alumina mesoporous pellet partially blocked by sorbed CCl4 has been studied on both sorption and desorption branches of the sorption isotherm. The plot of relative permeability (PR) against the amount of CCl4 sorbed (vs) is concave upwards; this is in contrast to the initially convex upwards curve reported previously for microporous Carbolac carbon containing paraffin sorbates, but in agreement with some preliminary computations based on a capillary-network model. Differences between the PR against vs plots for the sorption and desorption branches of the isotherm are not significant in relation to the repeatability of the results.