Correlation of isothermal and non-isothermal flow of dilute adsorbable gases in porous media

The general correlation has been established between isothermal and non-isothermal transport of a Knudsen gas through a porous medium where the resultant flux comprises several components. On this basis it is possible to decide between existing conflicting treatments [4, 6, 10] of non-isothermal flow of dilute adsorbable gases in porous media. With the aid of our recent treatment [1] for isothermal dilute gas flow, the basic predictions of the calibration gas approach for non-isothermal flow of moderately to strongly adsorbed gases have been confirmed, and a realistic interpretation of the behaviour of moderately to weakly adsorbed gases has been found.     

Heat of transport of dilute adsorbable gases in single pores and model porous media as a function of pore structure

A previous theoretical study of the heat of transport of a dilute adsorbable gas in a model pore, based on a new, more rigorous approach, is here extended to confirm and amplify the general features of the behavior predicted by the new approach in contradistinction to conventional theory. A simple analytical semiquantitative treatment is developed for moderate to high heats of transport and the effects of the form of the adsorption potential and of pore shape are elucidated. Some important aspects of pore structure in real porous media are then simulated by means of suitable simple capillary models. The results obtained permit a significant advance in the interpretation of experimental results.     

Separation of mixed gases through porous polymeric membranes

The separation of a gas from a two component gas system was studied both theoretically and experimentally. Helium and argon as an inorganic gas pair, ethylene and butane as an organic gas pair, and air were used. The theory based on the free molecular flow could not be applied to all the combinations of the gases experimentally studied. Experiments showed that the permeability coefficient of each component in the mixture was very close to that of each single component, when the pressure in the low pressure side became zero, but those of the mixture approached one another rapidly as the pressure increased. In the case of the separation of one inorganic gas from another, there exists most suitable pressures both in the high and low pressure sides for the most efficient separation, as considered from the selectivity and permeability. In the cases of the mixed organic gases and the organic-inorganic gas combination, a rather high separation efficiency is expected for a very high pressure on the high pressure side.     

An approach to the mathematical description of the permeation of hydrocarbons through liquid membranes

A mathematical model describing transport of hydrocarbons through liquid membranes is proposed. This model describes both the diffusion of hydrocarbons through the surfactant layer and through the aqueous core of the membrane, and also takes into account the equilibria in the oilwater-micelle system. Diffusion of hydrocarbons through surface layers is described with the help of Eyring's theory. The equilibria in the system studied were calculated on the basis of the Scatchard-Hildebrand theory of solubility using the available values of the solubility parameters. Diffusion through the aqueous layer, treated as facilitated transport, was described with the help of Cussler's model of solubilization. The model was verified by comparison of calculated and experimental data (obtained by the author or available in the literature). The verification was positive and the proposed model allows one to predict the course of the process as a function of feed composition, type of surfactant used and membrane thickness.     

A theoretical analysis of micelle-mediated transport through porous membranes

A novel method is proposed for the purpose of controlled release of a sparingly water soluble compound. The solubility of a sparingly water soluble compound can be increased by addition of a sufficient amount of surfactant to form micelles. The flux of the compound across a porous membrane can be enhanced if the membrane has pores larger than the micelle size so that the compound-loaded micelles can diffuse simultaneously, and micelle-mediated transport occurs. The membrane permeability of the micelle is a monotonically decreasing function of the ratio of the size of the micelle to the membrane pore size (R_m/R_p). However, the solubilizing capacity of the micelle increases with increasing size of the micelle. These opposing effects influence the transport and may result in an optimum flux of the solubilizate at a particular size of the micelle. In the determination of the optimum surfactant molecule, the concept of the hydrophilic-lipophilic balance (HLB) is employed in order to have stable aqueous solutions of the surfactants. For a family of nonionic surfactants solubilizing the hydrophobic and hydrocarbon substance n-heptane, it is shown that there exists a maximum flux of the solubilizate at a value of R_m/R_p within the limitation of the HLB. The release rates over a long period of time are nearly constant for micelles close to the optimum size for a given pore size.     

Kinetic description of bimolecular reactions with low energy cross sections in dilute gases

The rate ν of bimolecular chemical reaction A+A=B+C is analyzed for simple models of reactive cross sections. Collisions of particles colliding with energy E larger than a relatively low characteristic energy E _Lare either non-reactive (reversed Prigogine-Xhrouet model = rPX) or the ability to react is decreasing for E>E _L(reversed line-of-centres model = rLC). After solution of the Boltzmann equation analytical expressions for the distribution function f and the rate coefficient k have been derived. It is shown that the Arrhenius activation energy E _Ais small and even negative for sufficiently small E _L. The non-equilibrium corrections to ν are small.     

Coarse-grained nonequilibrium approach to the molecular modeling of permeation through microporous membranes

We present a modeling technique that combines a statistical-mechanical coarse-graining scheme with a nonequilibrium molecular simulation algorithm to provide an efficient simulation of steady-state permeation across a microporous material. The coarse-graining scheme is based on the mapping of an atomistic model to a lattice using multidimensional free-energy and transition-state calculations. The nonequilibrium simulation algorithm is a stochastic, lattice version of the recently developed atomistic dual-control-volume grand canonical molecular dynamics. We demonstrate the approach on a model of methane permeating through a bulk portion of siliceous zeolite ZK4 at 300 K under imposed fugacity differences. We predict the coarse-grained (cage-level) density profiles and observe the development of nonlinearities as the magnitude of the fugacity difference is increased. From the net flux of methane we also predict a mean permeability coefficient under the various conditions. The simulation results are obtained over time scales on the order of microseconds and length scales on the order of dozens of nanometers.     

Studies on permeation of hydrocarbons through liquid membranes in a continuous contactor

This paper reports experimental studies, in a continuous cocurrent packed column, on the removal of aromatics from hydrocarbon streams by making use of selective transfer through aqueous surfactant membranes. Two types of feed mixtures were used: (i) benzene—heptane and (ii) straight run naphtha from Bombay High crude oil. The receiving phase in both cases was kerosene. The height of a mass transfer unit (HTU) was determined and found to largely lie in the range 2-2.5 m, irrespective of feed composition and solvent/feed ratio. The experimental study confirms the feasibility of a liquid membrane process for dearomatization and provides HTU data for further feasibility and scale-up studies.     

Studies on the electrochemical and permeation characteristics of asymmetric charged porous membranes

Asymmetric charged porous membranes were prepared by imbedding 10% (W/W) ion-exchange resin in cellulose acetate binder. Membrane potential and conductance measurements have been carried out in sodium chloride solutions at different concentrations to investigate the relationship between concentration of fixed charges and electrochemical properties of developed nonselective cation- and anion-exchange membranes. Counterion transport number and permselectivity of these membranes were found to vary due to the presence of ion-exchange resin. The hydrodynamic and electroosmotic permeability of sodium chloride solutions has been studied in order to compute equivalent pore radius. For cation- and anion-exchange membranes good agreement was observed between pore radius values estimated from hydrodynamic and electroosmotic permeability coefficient separately, while for nonselective membranes no correlation was found. Membrane conductance data, along with values of concentration of fixed charges, were used for the estimation of the tortuosity factor, salt permeability coefficient, and frictional coefficient between solute and membrane matrix employing an interpretation by nonequilibrium thermodynamic principles based on frictional forces. Moreover, surface morphological studies of these membranes also have been carried out and the membranes were found to be reasonably homogeneous.     

Experimental and theoretical studies of asymmetry of transport properties of modified ultrafiltration membranes

Ultrafiltration membranes based on polyamide and polysulfone modified by polyelectrolytes are produced. The effect of the nature of a polymer matrix and modifier on the rejection ability and diffusion permeability of membranes is studied. The effect of the asymmetry of transport properties, which is manifested at different orientations of membrane with respect to the flow of electrolyte, is quantitatively evaluated. It was demonstrated that the asymmetry of substance transport is more pronounced in the ultrafiltration regime than in the diffusion of sodium chloride solutions. A mathematical model that describes the filtration of binary electrolyte solutions on partially charged two-layer membranes is proposed and the corresponding boundary-value problem is solved analytically. The qualitative correspondence between theoretical calculations and experimental data on the asymmetry effect of the rejection ability of two-layer system is revealed.     

Correlations to evaluate permeation of vapor and liquid hydrocarbons through polymer membranes

It has been shown in this investigation that the permeation of propane and propylene through polyethylene membranes exhibit a generalized behavior in the vicinity of the condensation point of the penetrant. Correlations to evaluate the permeation flux are presented.     

Experimental contribution to the understanding of transport through polydimethylsiloxanenanofiltration membranes: Influence of swelling,compaction and solvent on permeation properties

This study aims to better understand the permeation properties of polydimethylsiloxane (PDMS) membranes. The compressibility and nanofiltration fluxes were measured for swollen PDMS films using several solvents at applied pressures ranging from 5 to 50 bar. The degree of swelling varied according to the solvent and the pressure applied. To show the correlation between the behaviour of the swollen PDMS under pressure and its permeation performance, the thickness reduction of the membrane was mimicked using uniaxial compression tests. The evolution of the nanofiltration flux as a function of the transmembrane pressure proved to be non-linear. Linearization was achieved by taking into account both the swelling and the thickness reduction previously measured, confirming that these phenomena may have occurred during the nanofiltration experiments. Moreover, the solvents' viscosity and affinity for the polymer were confirmed to have a great influence on their ability to permeate the membrane. Finally, employing the most commonly used models, a study of transport through the membrane led to the conclusion that the experimental results were in agreement with the hydraulic theory of transport.     

Studies on the permeation of aromatic hydrocarbons through liquid surfactant membranes

The effect of operating parameters on the batch scale permeation of hydrocarbons from benzene—heptane mixtures and a straight run naphtha through liquid membrane is reported. The thirteen operating parameters studied include: mixing intensity, surfactant concentration, treat ratios, contact times, temperature and additives. The variations observed in the two key properties of selectivity and aromatic recoveries as well as in product compositions with change in operating parameter is discussed. Surfactant concentration contact time during permeation, type and concentration of additive used appear to exert a marked effect on the enrichment obtained. The careful optimization of operating parameters give selectivities as high as 50 and aromatic recoveries of 75% in one stage at 30°C. Comparison of data with batch liquid—liquid extraction data from extraction of similar feed mixtures with the most widely used solvent, sulpholane, under typical industrial conditions, has shown that selectivities and aromatic recoveries in liquid membrane permeation (LMP) are much higher. Batch scale LMP experiments with straight run naphtha as feed show that under optimum conditions of membrane stability and operating parameters the dearomatization of naphtha from an initial aromatic level of 22 vol.% to 10.5 vol.% is possible in one stage at 30°C with a raffinate yield of 63%. The results obtained on benzene—heptane model mixture compare fairly well with those obtained on naphtha feed.     

Pore size control and gas permeation kinetics of silica membranes by pyrolysis of phenyl-substituted ethoxysilanes with cross-flow through a porous support wall

A silica membrane was produced by chemical vapor deposition using tetraethoxysilane (TEOS), phenyltriethoxysilane (PTES) or diphenyldiethoxysilane (DPDES) as the Si source. Amorphous silica was deposited in the mesopores of a γ-alumina film coated on a porous -alumina tube, by evacuating the reactant through the porous wall. Hydrogen permeance at a permeation temperature of 600°C was of the order of 10⁻⁷ mol m⁻² s⁻¹ Pa⁻¹, and was not greatly dependent on the Si sources. The silica membrane produced using TEOS contained micropores permeable to both helium and hydrogen, but CO₂ and larger molecules were only slightly permeated through those mesopores which were left unplugged. The silica membrane produced from DPDES showed a single-component CO₂ permeance equivalent to that of single-component He, and CO₂/N₂ selectivity was approximately 9 at a permeation temperature of 30°C. When a mixture of CO₂ and N₂ was fed, however, CO₂ permeance decreased to the level of N₂ permeance. The H₂/N₂ selectivity, determined from single-component permeances to H₂ and N₂, was approximately 100, and these permeances remained unchanged when an equimolar mixture of H₂ and N₂ was fed. Thus, the DPDES-derived membrane possessed two types of micropores, abundant pores through which helium and hydrogen permeated and a small number of pores in which molecules of CO₂ and N₂ were permeable but not able to pass one another. Neither meso or macropores remained in the DPDES membrane.     

Effect of permeation temperature on permeation and separation of a benzene/cyclohexane mixture through liquid-crystalline polymer membranes

When a benzene/cyclohexane mixture of 10 wt % benzene was permeated through side-chain liquid-crystalline polymer (LCP) membranes by pervaporation at various temperatures, the permeation rate increased with increasing permeation temperature. The LCP membranes also exhibited a benzene permselectivity. The permselectivity for the benzene/cyclohexane mixture through the LCP membrane was different in the glassy, liquid-crystalline, and isotropic states. The LCP membrane had different apparent activation energies for permeation at each state. LCP membrane in the liquid-crystalline state had the highest apparent activation energy of the three states. Results suggest that the benzene permselectivity was influenced by changes in the LCP membrane structure, i.e., a state-transformation. It was found that a balance of the orientation of mesogenic groups and the flexibility of the siloxane chains was very important for benzene permselectivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 281–288, 1998     

Review of time lag permeation technique as a method for characterisation of porous media and membranes

The time lag permeation technique has proven to bean effective method for characterisation. Because of the simple nature of the permeation experiment, transport parameters can be directly obtained from experimental data hence avoiding the intensive mathematical treatment required by other techniques. The method has historically been applied to diffusion and adsorption in porous membranes and diffusion in polymer membranes. Since its origins in 1920, interest in the time lag method has expanded because of its value in characterising simple permeation processes and also complex systems of diffusion with simultaneous adsorption and surface diffusion. This review focuses on presenting the asymptotic solution of the mass balance diffusion equations and includes applications of time lag analysis, in order to give a critical and broad perspective of this method as a tool for characterisation. It includes much of the previously published literature in order to show that for most cases the asymptotic solution of the transport equations is simple, and for more complex cases that an analytical solution is possible hence avoiding cumbersome numerical techniques.     

Experimental and theoretical description of the isotachophoretic behavior of serum albumin

The isotachophoretic behavior of serum albumin is examined for three anionic and one cationic electrolyte systems by (i) computer simulation, (ii) capillary isotachophoresis (ITP) and (iii) continuous flow ITP. The theoretical relationship between pH of the leading electrolyte and the steady state protein plateau concentration is presented for one of the anionic systems. With leading ion concentrations of the order of 10 mM, experimental protein plateau concentrations of 1.3-2.3% w/v are obtained. The computer predictions are approximately half these values.     

Measuring the diffusion of noble gases through a porous medium using prompt gamma activation analysis

Detection of anthropogenic noble gas isotopes in the atmosphere is an important indication that a below ground nuclear-test has taken place. Diffusion plays a critical role in the transport of these gases through the geological media to the surface where they can be detected. Better techniques are need with which to study the diffusion of noble gases through porous systems. Here we demonstrate the suitability of using prompt gamma activation analysis to measure the time dependent concentration of argon as a result of its diffusion through a porous medium that is saturated with nitrogen at atmospheric pressure. The experiments were conducted in a 1 m long tube, 10 cm diameter, and packed with fine SiO₂ sand. Prompt gamma activation analysis was used to measure the concentration of argon within the experimental system as a function of time.     

Analytical theory for permeation of condensable gases in a nanopore

The permeation of a condensable gas mixture in a pressure gradient is examined within a dynamic density functional theory (DDFT). The non-equilibrium density and flux profiles of gas molecules trapped within a nanopore are calculated for each species as a function of feed gas density. Because of important fluid–fluid interaction close to condensation the flux and density gradients are not related by constant transport diffusivities with the thermodynamic correction of uniform density. For long narrow pores the relation of the selectivity to the equilibrium adsorption isotherms is validated. Improved separation is achieved by combining preferential wall interaction and advantageous attraction between gas molecules of different species and examples are discussed. Results from experiments and simulations of permeation in binary mixtures near condensation are still rare and the theory provides a simple basis to study qualitative trends using known parameters.