Role of convection and diffusion in a single pore with adsorptive walls

The importance of intraparticle convection during and after the pressurization step of a pressure swing adsorption process is assessed by considering a single, cylindrical, closed-end pore with adsorptive walls exposed to a binary mixture of an adsorbable component and an inert gas. Gas-phase mass transfer is comprised of pore diffusion and convection, and surface diffusion occurs in the adsorbed phase. Concentration, velocity, and flux profiles are obtained inside the pore both during and after pressurization. Solutions are obtained analytically for the limiting cases of no adsorption, no diffusion, and no inert gas. Complete solutions of the material balance equations are obtained by orthogonal collocation. The pressurization rate, the adsorptive capacity of the pore wall, and the gas-phase mole fraction are varied over a wide range to study the relative importance of convection and diffusion under different conditions. Results show that convection makes a large contribution to transport in the pore except when the adsorbable component has a small mole fraction.     

Preparation and Characterization of Adsorption-Selective Carbon Membranes for Gas Separation

The preparation and characterisation of adsorption-selective carbon membranes (ASCMs) is described. ASCMs can separate the components of a gas mixture depending on their adsorption strength. These membranes allow the separation of non-adsorbable or weakly adsorbable components (e.g. N₂, H₂, O₂, etc) from the more strongly adsorbable components (e.g. hydrocarbons) in a gas mixture. They are prepared from the deposition of a thin film of a phenolic resin on the inner face of an alumina tube. Air oxidative treatment at temperatures in the range of 300–400°C, prior to carbonisation (pre-oxidation) or after carbonisation (under vacuum at 700°C) (post-oxidation) gives rise to an adsorption-selective carbon membrane. This membrane shows a high permeability and selectivity towards the separation of gas mixtures formed by hydrocarbons and N₂. Taking into account the permeation and separation properties of the membranes, post-oxidation treatment is shown to be more effective than pre-oxidation. The separation characteristics of the carbon membranes are dependent on the composition of the gas mixture (i.e. proportion of more strongly adsorbable components) and temperature.     

Gas separation mechanisms in microporous modified γ-al2o3 membranes

The transport of pure gases and of binary gas mixtures through a microporous composite membrane is discussed. The membrane consists of an alumina support with a mean pore diameter of 160 nm and an alumina top (separation) layer with pores of 2-4 nm. The theory of Knudsen diffusion, laminar flow and surface diffusion is used to describe the transport mechanisms. It appears for the composite membrane that Knudsen diffusion occurs in the toplayer and combined Knudsen diffusion/laminar flow in the support at pressure levels lower than 200 kPa. For the inert gas mixture H₂/N₂ separation factors near 3 could be achieved which is 80% of the theoretical Knudsen separation factor. This value is shown to be the product of the separation factor of the support (1.9) and of the top layer (1.5). The value for the top layer is rather low due to the relatively small pressure drop across this layer. This situation can be improved by using composite membranes consisting of three or more layers resulting in a larger pressure drop across the separation layer.CO₂ surface diffusion occurs on the internal surface of the investigated alumina membranes. At 250-300 K and a pressure of 100 kPa the contribution of surface diffusion flow measured by counterdiffusion is of the same order of magnitude as that resulting from gas diffusion. The adsorption energy amounts —25 kJ/mol and the surface coverage is 20% of a monolayer at 293 K and 100 kPa. The calculated surface diffusion coefficient is estimated to be 2-5 x 10^-9 m²/sec.Modification of the internal pore surface with MgO increases the amount of adsorbed CO₂ by 50-100%.Modifications with finely dispersed silver are performed to achieve O₂ surface diffusion.     

Modelling the effect of operating conditions on hydrodynamics and mass transfer in a Pd–Ag membrane module for H2 purification

In this work a novel modelling approach based on Computational Fluid Dynamics (CFD) for the prediction of the gas separation process in a Pd–Ag membrane module for H₂ purification is presented. With this approach, the pressure and velocity flow fields of the gas mixture and the species concentration distribution in the selected three-dimensional domain are simultaneously and numerically computed by solving the continuity, momentum and species transport equations, including a gas-through-gas diffusion term derived from the Stefan–Maxwell formulation. As a result, the H₂ permeation calculations depend on the local determination of the mass transfer resistances offered by the gas phase and by the membrane, which is modelled as a permeable surface of known characteristics. The applicability of the model to properly predict the separation process under a wide range of pressure, feed flow rate, temperature and gas mixtures composition is assessed through a strict comparison with experimental data. The influence of inhibitor species on the module performance, that is obtained by implementing in the CFD model a suitable literature correlation, is also discussed.     

Characterization of microporous membranes for use in membrane contactors

Methods of selecting applicable membranes for use in membrane contactors for flue gas desulfurization are proposed in this paper. The mass transfer mechanism for SO₂ diffusion through gas filled pores is explored by simple measurements in order to identify suitable membrane structures for use in contactors for flue gas cleaning. It is attempted to correlate the experimentally determined membrane mass transfer coefficient to intrinsic physical properties of the membrane by applying theoretical and empirical correlations for the porosity-tortuosity relationship of the porous structure. Thereby limiting fluxes can be predicted with good accuracy from data quoted in the manufactures catalogue.     

Study of experimental and theoretical procedures when using thermogravimetric analysis to determine kinetic parameters of carbon black oxidation

Combustion of carbon black (CB) in the crucible of a thermobalance is controlled by both carbon reactivity and oxygen transport from the oxidizing flux to the surface of the bed and within the porous bed. The kinetic constant of combustion has been determined using a fixed-bed reactor in which CB combustion is mainly under kinetic control. Then, modelling of oxygen transport in the thermobalance allowed determining the oxygen diffusivity within the CB pile. Fickian diffusion is a good approximate value of the diffusion coefficient for modelling of internal oxygen transport. The effects of the initial sample mass and of the sample containment on the initial combustion rate have been investigated. The effectiveness factor of the bed was calculated for different experimental conditions. Advices to correctly extract a kinetic constant from thermogravimetric experiments are given. According to the required precision, an experimental procedure is proposed. Limitations to oxygen transport within the bed may be ignored. They can be minimized by the use of an inert material to remove the stagnant atmosphere between the surface of the bed and the mouth of the crucible. It appears mandatory to account for oxygen transport limitations within the CB pile. It can be assumed that the sample temperature (not known) during reaction is the regulation temperature. Thermal effects are also minimized by use of the inert material. A 30–50 mg sample mass seems to be optimal for determination of the kinetic parameters.     

Liquid-supported membranes in chromium(VI) optical sensing: transport modelling

Flat sheet liquid-supported membranes (FSLSM) containing Aliquat 336 as a carrier have been evaluated as sample interface in an optical sensor for Cr(VI) monitoring. A model describing the transport mechanism of Cr(VI) through the membrane is reported. The model considers a diffusion process through a feed aqueous diffusion layer, a fast interfacial chemical reaction and a diffusion of ALQHCrO₄ and (ALQ)₂CrO₄ species through the membrane (Aliquat 336, ALQ). The mathematical equations describing the transport rate are derived and they correlate the membrane permeability coefficient to diffusional and equilibrium parameters as well as to the chemical composition of the system, i.e. extractant concentration in the membrane phase and acidity in the feed phase. The experimental data are explained by the derived equations and the diffusion resistances to mass transfer are evaluated. The influence of other experimental parameters, such as stirring speed in the feed phase and nature of the diluent and stripping agent on the transport is also discussed. Experiments with optical detection demonstrate the suitability of liquid-supported membranes (LSM) containing ALQ as interfaces for optical sensing.     

Influence of Water Vapor on Silica Membrane: Adsorption Properties and Percolation Effect

The influence of water vapor on silica membrane with pore size of 4 ? has been investigated in terms of adsorption properties and percolation effect at 50 and 90 oC. Two methods are employed: spectroscopic ellipsometry for water vapor adsorption and gas permeation of binary mixture of helium and H₂O. The adsorption behaviors on the silica membrane comply with the first-order Langmuir isotherm. The investigation demonstrates that helium flux through the silica membrane decreases dramatically in presence of H₂O molecules. The transport of gas molecules through such small pores is believed not to be continuous any more, whereas it is reasonably assumed that the gas molecules hop from one occupied site to another unoccupied one under the potential gradient. When the coverage of H₂O molecules on the silica surface increases, the dramatic decrease of helium flux could be related to percolation effect, where the adsorbed H₂O molecules on the silica surface block the hopping of helium molecules.     

A Stefan-Maxwell Model of Single Pore Pressurization for Langmuir Adsorption of Gas Mixtures

A model based on the application of the Maxwell-Stefan approach has been used to describe the dynamics of intraparticle transport (pore diffusion, surface diffusion and convection) in a single pore during and after a pressurization process. The model was first compared with the model proposed by Taqvi and Levan (Adsorption, 2, 299–309 (1996)) for a linear adsorption isotherm. The effect of several parameters (pressurization rate, adsorption capacity, bulk gas-phase mole fraction, adsorption affinity and pore radius) was studied, evaluating the relative importance of each mass-transport mechanism in different conditions. A binary mixture of an inert and an adsorbable component was considered first, extending the analysis of the pore radius effect to a ternary mixture. In general, surface diffusion is dominant with very low pore radius, whereas gas-phase fluxes dominate in a large pore. However, depending on the value of the bulk gas-phase mole fraction (which is related to the surface coverage level through the adsorption equilibrium isotherm), the equilibrium and rate parameters, and the surface to volume ratio, surface diffusion cannot be always neglected for large pores. More generally, system non-linearity can switch the dominant mechanism and create fronts.     

Thermal Diffusion with Chemical Reaction: A Carrier System

The heat of transport of oxygen across a membrane mediated by hemoglobin (Hb) as a carrier is iuvestigated by the method of irreversible thermodynamics. It is assumed that oxygen combines with hemoglobin molecules to form oxyhemoglobin according to the reaction nO₂ + Hb=HbO_zn. The oxyhemoglobin molecule HbO_zn then migrates to a new position and is reconverted to Hb by releasing oxygen. It is shown that the heat of transport of oxygen consists of two contributions; one due to the reaction and the other from thermal diffusion of individual species present. Total oxygen flux across the membrane is also calculated in terms of temperature and the chemical potential difference of oxygen across the membrane. The use of the heat of transport as a measure of the efficiency of the heat pump for the carrier-mediated transport process is investigated.     

Asymmetric effects in catalytic membranes

A catalytic membrane hybrid system based on a cermet membrane with a channel size 〈d〉 of ～0.12 μm has been produced using sol-gel processing. A layer of a superfine methanol conversion catalyst with the composition Cr₂O₃ · Al₂O₃ · ZnO has been formed on the inner surface of the channels, and a thin oxide coating of composition P_0.03Ti_0.97O_{2 ± δ} with a homogeneous porous structure and 〈d〉 ～ 2 nm has been formed on the geometric membrane surface. The methanol conversion rate and the gas permeability of the membrane depend considerably on the methanol vapor and gas (H₂, He, CO₂, Ar, CH₄) flow directions. When methanol vapor diffuses toward the mesoporous layer, the catalytic activity is one order of magnitude higher and the gas permeability coefficients are 3–8 times lower than in the case of the reverse flow of the gaseous molecules. The temperature dependence of the gas permeability taking into account the possible types of mass transfer in porous solids suggests that, when the gases move toward the mesoporous coating consisting of phosphorus-modified titanium oxide, surface flow and activated diffusion dominate, whereas the reverse gas motion is dominated by free molecular flow.     

Pore Modification in Porous Ceramic Membranes With Sol-Gel Process and Determination of Gas Permeability and Selectivity

Summary: The aim of the study was to investigate the variation in total surface area, porosity, pore size, Knudsen and surface diffusion coefficients, gas permeability and selectivity before and after the application of sol-gel process to porous ceramic membrane in order to determine the effect of pore modification. In this study, three different sol-gel process were applied to the ceramic support separately; one was the silica sol-gel process which was applied to increase porosity, others were silica-sol dip coating and silica-sol processing methods which were applied to decrease pore size. As a result of this, total surface area, pore size and porosity of ceramic support and membranes were determined by using BET instrument. In addition to this, Knudsen and surface diffusion coefficients were also calculated. After then, ceramic support and membranes were exposed to gas permeation experiments by using the CO₂ gas with different flow rates. Gas permeability and selectivity of those membranes were measured according to the data obtained. Thus, pore surface area, porosity, pore size and Knudsen diffusion coefficient of membrane treated with silica sol-gel process increased while total surface area was decreasing. Therefore, permeability of ceramic support and membrane treated with silica sol-gel process increased, and selectivity decreased with increasing the gas flow rate. Also, surface area, porosity, pore size, permeability, selectivity, Knudsen and surface diffusion coefficients of membranes treated with silica-sol dip coating and silica-sol processing methods were determined. As a result of this, porosity, pore size, Knudsen and surface diffusion coefficients decreased, total surface area increased in both methods. However, viscous flow and Knudsen flow permeability were detected as a consequence of gas permeability test and Knudsen flow was found to be a dominant transport mechanism in addition to surface diffusive flow owing to the small pore diameter in both methods. It was observed that silica-sol processing method had lower pore diameter and higher surface diffusion coefficient than silica-sol dip coating method.     

A Heterogeneous Multiscale Dynamic Model for Simulation of Catalytic Reforming Reactors

The present work aims to establish a generic reforming reaction scheme to evaluate the performance of catalytic reforming systems with the aid of a one‐dimensional heterogeneous dynamic model. The novelty of the numerical model stems from the direct inclusion of interphase (fluid‐to‐particle surface), intraparticle (within particle), and intrareactor heat and mass transport resistances under transient conditions. The developed model accounts for the multicomponent gas mixture physicochemical properties and correlations for calculating mass and heat transfer coefficients. Effective macroscopic properties within the particle are calculated by incorporating diffusivities and conductivities of the porous network characteristics accounting for Knudsen and molecular transport as well as tortuosity and porosity of the overall porous path. The industrial case of a steam‐methane reforming multitubular reactor was studied as the most representative case of the generic reaction scheme, with all mass/energy resistances present under severe pressure and temperature conditions. It was shown that there are notable diffusional limitations within the particle, whereas there are also temperature and partial pressure gradients due to the heat and mass transport resistances in the particle film layer. It is further demonstrated that the proposed model can be utilized as a versatile design tool for catalytic reactor development and optimization.     

The nature of permeability anisotropy and catalytic activity

The phenomena of permeability anisotropy and an increase in the rates of catalytic reactions in porous membranes modified with highly dispersed catalytic systems were analyzed. A model of stochastic gas motions was proposed; this model is based on the hypothesis of the specific interaction of molecules with the inner surface of pores resulting in a nonisotropic distribution of molecules over traveling directions. The effects of asymmetric gas transfer in porous and gradient-porous membranes were considered to explain differences in the rates of heterogeneous catalytic reactions in a nanoporous membrane reactor under changes in the direction of supplying a reaction mixture. From the model proposed, it follows that the transversal diffusion of gas molecules is most probable in the porous medium of a ceramic membrane with a pore-size distribution gradient from large to small pores along the flow direction. This diffusion results in an increase in the frequency of molecular collisions with the wall of a microchannel and, correspondingly, in an increase in the contact time. The model proposed explains the intensification of a number of heterogeneous catalytic reactions performed in the porous media of catalytic porous membranes.     

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.     

The permeation of binary gas mixtures through support structures of composite membranes

The dusty gas model (DGM) is used to describe transport of binary gas mixtures through porous membrane supports to quantify the resistance towards permeation. The model equations account for three different transport mechanisms for the permeating components: conventional viscous pore flow, Knudsen diffusion, and binary diffusion. Experimental data obtained with the uncoated membrane supports are used to determine the morphological parameters needed in the DGM equations. Flat sheet and hollow fiber membrane supports are characterized by the permeation of a TCE/nitrogen vapor. The DGM shows an excellent fit to experimental data when the asymmetric structure of the membrane supports is taken into account, but the morphological parameters cannot necessarily be related to precise physical structure parameters such as pore size, porosity, and tortuosity. The DGM works well even when the membrane supports are modeled as a single homogenous structure. The membrane supports exhibit different resistances towards the various transport mechanisms that occur within the porous support and the resistances vary with process conditions so that support optimization is not straightforward. With the analysis presented in this paper and transport equations specific to the dense coating and module geometries, the influence of the support layer on gas or vapor separation can be quantified.     

Use of Nonlinear Frequency Response for Discriminating Adsorption Kinetics Mechanisms Resulting with Bimodal Characteristic Functions

One of the characteristic examples of the inability of the classical linear frequency response (FR) method to identify the correct kinetic mechanism is adsorption of some substances (p-xylene, 2-butane, propane or n-hexane) on silicalite-1. The linear FR resulted with bimodal FR characteristic functions, which fitted equally well to three different kinetic models: nonisothermal micropore diffusion, two independent isothermal diffusion processes, and an isothermal diffusion-rearrangement process. We show that the second order frequency response functions (FRFs), obtained from the nonlinear FR, can be used for discrimination among these three mechanisms. Starting from the nonlinear models, we derive the theoretical expressions for the first and second order FRFs corresponding to these three mechanisms and show that different shapes of the second order FRFs are obtained for each mechanism. This would enable identification of the real mechanism from nonlinear FR data.