Blind Pores Research Articles

Diffusion of methane through coal

Both methane and helium flow through solid coal by Knudsen diffusion, even at relatively high pressures. Knudsen permeabilities were determined for samples of Pittsburgh, Pocahontas No.3, and Oklahoma Hartshorne coals. The average permeability for dry methane was 1.3 × 10 −6 cm 2/s for Pittsburgh coal, 20 × 10 −6 for Pocahontas No.3 coal, and 13.8 × 10 −6 for Oklahoma Hartshorne coal. A molecular-sieve effect exists for methane in all three coals examined and it is very strong in Pittsburgh coal. If the methane is saturated with water vapour the permeability decreases by a factor of 3 to 25, depending on the coal. The Knudsen permeability of solid coal discs seems to bear no relation to coalbed permeability. Lag-time measurements indicate systems of both larger and finer pores and the presence of blind pores. This effect is again more pronounced in the Pittsburgh coal.

Isothermal and thermo-osmotic transport of sorbable gases in microporous carbon membranes

With the use of helium and a series of gases adsorbed to give dilute films, measurements have been made of thermo-osmotic steady-state pressure ratios established across microporous carbon membranes through which linear temperature gradients were maintained. Two contrasting adsorbents were employed: Carbolac I, a carbon black having an energetically heterogeneous high area surface and Graphon, a graphitized carbon black of one-tenth the surface area of Carbolac but energetically homogeneous. Complementary studies of isothermal transport of the gases through the membranes and determination of equilibrium adsorption isotherms at all temperatures employed for the flow experiments were required in order to analyse the non-isothermal experimental results. Part I is concerned with the equilibrium properties of the adsorbed films. Henry’s law constants, k, energies of adsorption, A E'and isosteric heats of adsorption, for the Gibbs excess adsorption were derived from the experimental isotherms. Taking the thickness of the adsorbed layer as one molecular diameter, the corresponding energies, A E,and heats qBt for absolute adsorption have been calculated. For the very dilute films the ratios AE'jAE and q'BtlqBt can differ appreciably from unity. Also in the Henry law range, values of the thermodynamic equilibrium constants and standard energies, AE&, and entropies, A for absolute adsorption have been evaluated. A linear relation between AS& and AE&, was observed. — A was considerably larger on Carbolac than on Graphon surfaces. This has been interpreted in terms of greater mobility of the adsorbed molecules on the more homogeneous Graphon surface. Good correlations have been found between K or A Eand properties, such as polarizability, a, related to the condensability of the sorbates. Part II is concerned with isothermal transport of the gases through the membranes. For the majority of systems studied the permeability, K and time-lag, L, were independent of pressure. For helium in both membranes the ratio K/^T was independent of temperature and pressure, indicating transport only in the gas phase and the absence of a viscous flow component. For an adsorbed gas the extra flux generated by the mobile adsorbed films per unit area of surface, JJA, were considerably greater for the more homogeneous Graphon membrane. Diffusion coefficients associated with the extra fluxes also indicated greater mobility of adsorbed molecules on the more homogeneous surface. Good correlations between K{MT)^ and ke have been demonstrated and, at constant temperature, a linear relation was observed between KM$ and the product, aTb, of polarizability and boiling-point TB. Gas-phase structure factors obtained by the procedure of Barrer & Gabor (1959) were considerably less than unity, indicating a dominant influence in each membrane of tortuosity and bottlenecks. For each membrane a linear relation has been demonstrated between the products KL and kB from which parameters associated with blind pore character have been obtained. Part III is concerned with the thermo-osmotic transport of the gases in the membranes. The nonisothermal flow is formulated in terms of the thermodynamics of irreversible processes and relations derived between the straight phenomenological coefficients of this treatment and the permeabilities and diffusion coefficients of part II. Equations are also presented relating the overall heat of transport, Q0, at temperature T0 to component heats of transport for the gas-phase flow (Qg, Q*) and extra flow (QB, Q*). In none of the systems studied did Q0 = — %RT0, the ideal value expected for a gas transported by molecular streaming (Knudsen flow). For He, H 2 and Ne in the Carbolac membranes, — ifiRT0 where /?, for a particular gas, is a constant < 1. With increasing sorbability of the flowing gas the temperature dependence of Q0 was progressively modified until, in the presence of substantial extra flow, — Q0 decreased strongly with increasing T0. Calculations of Qs and Q* are presented for the two limiting cases Q e— and Qg = 0. It is shown that Qs must always be negative and positive. A procedure for calculating isobaric permeabilities, utilizing a combination of thermo-osmotic steady-state and isothermal steady-state measurements, has been developed. For various pairs of gases, the ratios of isobaric permeabilities differed greatly from the corresponding ratios of isothermal permeabilities. Enhanced separations of sorbable mixtures by isobaric flow appear to be possible especially for the Graphon membrane.

Sorption and surface flow in graphitized carbon membranes - II. Time-lag and blind pore character

A general expression has been obtained for the time-lag in transport through membranes, based only on the conservation of mass condition and independent of any assumed equation of flow. When considered in relation to Fick’s equation the time-lag expression covers all situations in which diffusion coefficients, D , are functions of concentration, distance or time, or combinations of these variables. When D is a function only of concentration, C , two new ways have been given for exact treatments of the time-lag. These avoid difficulties which arise in using the formula originally given by Frisch (1957) and previously used in time-lag studies. Differences can arise between time-lags where D is a function only of C and the time lag L given by the general equation. These differences serve for the study of non-Fickian diffusions in which D is a function also of distance or time. This treatment, applied to a number of microporous membranes, leads to the conclusion that in these membranes non-Fickian components sometimes arise which are mostly dominated by time-dependence in the overall diffusion coefficient. It is shown how this behaviour can result from the partial blind-pore character of the channels in the membranes. In this and other ways the time-lag has been shown to give information about micropore systems which is not readily found from other measurements.

Sorption and diffusion of simple paraffins in silica-alumina cracking catalyst

Sorption and diffusion measurements have been made of methane, ethane and propane in the silica-alumina cracking catalyst previously employed in similar measurements for permanent gases (Barrer & Gabor 1959). The sorption data show no evidence of molecular sieve behaviour in the micropore structure of the catalyst, for the species studied. The ratio of surface to volume flow increases with increasing molecular weight of hydrocarbons and with decreasing porosity. On the other hand, in or near the Henry’s law region of sorption, this ratio decreases as the temperature rises. In a micropore system there are many points where surface flow may be interrupted by roughnesses, blind pores or crevices. A treatment has been given which permits the influence of such pore properties upon surface diffusion to be considered. The procedure developed has been applied to the data obtained in this research, and estimates have been made of some properties of the surface diffusion coefficients which could be expected upon uninterrupted surfaces of the catalyst. Owing to differences in the roles of pores in steady and transient states of flow, transient state (time-lag) diffusion coefficients could depend on time. Some consequences of this have also been examined.

A comparative structural study of cracking catalyst, porous glass, and carbon plugs by surface and volume flow of gases

Transient and steady states of volume and surface flow of gases and vapours in microporous media require for their description four different diffusion coefficients, namely, a surface and a gas-phase coefficient for transient and a surface and gas-phase coefficient for steady flow. The distinction between steady and transient flow arises in part because of the role of blind pores. Similarly, two different porosities ∊ and ∊ 8 and two different surface areas A and A 8 govern transient and steady-state flow respectively. By comparing the two gas-phase and the two surface diffusion coefficients with gas-phase and surface diffusion coefficients in a smooth cylindrical capillary having ∊/ A equal to that for the porous medium, four structure factors can be defined, in terms of which the pore properties of microporous media can be discussed. Data are presented for sorption, transient flow (time lag) and steady flow of He, Ne, A and N 2 in compressed alumina-silica catalyst plugs. These, and previously obtained data for Vycor porous glass (Barrer & Barrie 1952) and Carbolac carbon plugs (Barrer & Strachan 1955) have been analyzed according to the above procedure, and pore properties compared. In this way it was possible to obtain information regarding pore structure which could not have been derived by other methods.

The measurement of surface area of finely divided solids by the flow of gases through them

An account is given of the theory and application of several procedures which have been used for determining the surface areas of finely divided solids, and which depend upon either the steady or the transient state of flow. Characteristic differences can arise between pore properties of microporous media determined by steady and by transient state methods which have at least in part received an explanation in terms of the heterogeneity of pore sizes and in the presence of some blind pores. Attention has been directed to several additional possible procedures for measuring surface areas. These refer to flow systems in which a saturated immobile monolayer is formed at all points reached by the flowing gas. One of the latter methods covers the case where a mobile, dilute second layer forms on the immobile saturated first layer and where transport of sorbate may occur by combinations of one or more of Poiseuille, Knudsen and surface flow.