Analytical expressions for predicting permeability of bimodal fibrous porous media

Pressure drop is one of the most important characteristics of a fibrous media. While numerous analytical, numerical, and experimental published works are available for predicting the permeability of media made up of fibers with a unimodal fiber diameter distribution (referred to as unimodal media here), there are almost no easy-to-use expressions available for media with a bimodal fiber diameter distribution (referred to as bimodal media). In the present work, the permeability of bimodal media is calculated by solving the Stokes flow governing equations in a series of 3-D virtual geometries that mimic the microstructure of fibrous materials. These simulations are designed to establish a unimodal equivalent diameter for the bimodal media thereby taking advantage of the existing expressions of unimodal materials for permeability prediction. We evaluated eight different methods of defining an equivalent diameter for bimodal media and concluded that the area-weighted average diameter of Brown and Thorpe [2001. Glass-fiber filters with bimodal fiber size distributions. Powder Technology 118, 3-9], volume-weighted resistivity model of Clague and Phillips [1997. A numerical calculation of the hydraulic permeability of three dimensional disordered fibrous media. Physics of Fluids 9 (6), 1562-1572], and the cube root relation of the current paper offer the best predictions for the entire range of mass (number) fractions, 0?n_c?1, with fiber diameter ratios, 1?R_cf?5, and solidities, 5?α?15.     

A realistic approach for modeling permeability of fibrous media: 3-D imaging coupled with CFD simulation

Determining permeability of fibrous media is of great importance to many industries. While there are several 2-D and 3-D analytical models developed for predicting the permeability of fibrous disordered media, there are not many numerical works that compare the predictions of these models with that of real media. In this work, we present a series of numerical simulations performed on the microstructure of a real fibrous media. An efficient procedure is presented for reconstructing 3-D images from the 2-D images of the real fibrous media and processing them for the purpose of performing fluid flow simulation. Digital volumetric imaging (DVI) of a typical hydroentangled fibrous fabric is obtained, as an example, and its permeability is computed. These results are compared with those obtained from the analytical equations given in the literature. In particular, it was found that permeability of a typical hydroentangled material can be closely predicted by the layered anisotropic models.     

Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds

Computational fluid dynamics as a simulation tool allows obtaining a more detailed view of the fluid flow and heat transfer mechanisms in fixed-bed reactors, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. In this way, this tool permits obtaining of mean and fluctuating flow and temperature values in any point of the bed. An important problem when modeling a turbulent flow fixed-bed reactor is to decide which turbulence model is the most accurate for this situation. To gain insight into this subject, this study presents a comparison between the performance in flow and heat transfer estimation of five different RANS turbulence models in a fixed bed composed of 44 homogeneous stacked spheres in a maximum space-occupying arrangement in a cylindrical container by solving the 3D Navier-Stokes and energy equations by means of a commercial finite volume code, Fluent 6.0^®. Air is chosen as flowing fluid. Numerical pressure drop, velocity and thermal fields within the bed are obtained. In order to judge the capabilities of these turbulence models, heat transfer parameters (Nu_w, k_r/k_f) are estimated from numerical data and together with the pressure drop are compared to commonly used correlations for parameter estimations in fixed-bed reactors.     

Effect of fabric structure on the permeability and regeneration ability of porous SiCf/SiC composite prepared by CVI

In this paper, porous SiC_f/SiC composites are prepared by chemical vapor infiltration of SiC matrix on stitched fibrous preforms with different fabrics laminate structure. The microstructure of the fibrous preforms before and after infiltration of SiC matrix and the permeability and the regeneration efficiency of the porous SiC_f/SiC composites with different laminate structure have been determined. Experimental results show that the porous SiC_f/SiC composites with twill fabrics laminate structure exhibits a higher permeability with a higher volume porosity and mean pore diameter. In comparing the regeneration ability of two types laminate structure filter medium, as expected, the twill fabrics laminate structure exhibits a better regeneration efficiency than the plain fabrics laminate structure due to its higher air permeability.     

A two-scale second-order moment particle turbulence model and simulation of dense gas-particle flows in a riser

A two-scale second-order moment particle turbulence model is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. It is then used to simulate dense gas-particle flows in a riser. The predicted results are in reasonable agreement with the experimental results and show the core-annulus flow structure observed in experiments. It is seen that the two-scale model is somewhat better than k_f-ε_f-k_p-ε_p-θ two-phase turbulence model and the single-scale second-order moment two-phase turbulence model (USM-θ model).     

Oxygen transport at porous flow-by air electrodes: theoretical approach

The theory of oxygen transport at porous flow-by air electrodes is treated mathematically. The three transport mechanisms of diffusion and convection in the gas channel, pore diffusion, and diffusion in the electrolyte are considered, and combined in the derivation of an asymptotic solution to electrode performance when U_avef²/L → ∞ ¹. Together with a further asymptote for the condition of oxygen exhaustion, ieU_avef/L → 0, this effectively defines the limit of real operation of an air electrode.     

External mass transfer in silica monolithic stationary phases

A detailed analysis of a procedure of measurement of the external mass transfer coefficients (k_f) in RPLC systems is provided. Application is described for a system consisting of a C₁₈-silica monolithic column and a methanol/water eluent (70/30, v/v). The k_f values of butylbenzene at 298 K were derived from peak profiles recorded in pulse response experiments by subtracting the contributions of the kinetic processes, i.e., axial molecular diffusion, eddy diffusion, pore and surface diffusion, from the band variance. This approach provided the Sherwood number (Sh) for a range of Reynolds number (Re) between 0.002 and 0.005 and a Schmidt number (Sc) equal to 2.7×10³. The experimental values of k_f were compared with those estimated from literature correlations, giving a relative error of ca. 11% when Pfeffer equation was used for estimating k_f. The exponents obtained for Re and Sc in Sh were 0.43 and 0.39, values comparable with those found in literature correlations, i.e., 0.33. The k_f values estimated using the reference correlations are of the same order of magnitude as the experimental k_f values. The acquisition of more experimental data is needed for deriving an improved correlation affording more accurate estimates of k_f in stationary phases of cylindrical shape, like silica monoliths.     

Surface diffusion of strongly adsorbing vapors in activated carbon by a differential permeation method

Conventional methods to determine surface diffusion of adsorbed molecules are proven to be inadequate for strongly adsorbing vapors on activated carbon. Knudsen diffusion permeability (B_k) for strongly adsorbing vapors cannot be directly estimated from that of inert gases such as helium. In this paper three models are considered to elucidate the mechanism of surface diffusion in activated carbon. The transport mechanism in all three models is a combination of Knudsen diffusion, viscous flow and surface diffusion. The collision reflection factor f (which is the fraction of molecules undergoing collision to the solid surface over reflection from the surface) of the Knudsen diffusivity is assumed to be a function of loading. It was found to be 1.79 in the limit of zero loading, and decreases as loading increases. The surface diffusion permeability increases sharply at very low pressures and then starts to decrease after it has reached a maximum (B_μm) at a threshold pressure. The initial rapid increase in the total permeability is mainly attributed to surface diffusion. Interestingly the B_μms for all adsorbates appear at the same volumetric adsorbed phase concentration, suggesting that the volume of adsorbed molecules may play an important role in the “surface” diffusion mechanism in activated carbon.     

A numerical study of capillary pressure–saturation relationship for supercritical carbon dioxide (CO2) injection in deep saline aquifer

Carbon capture and sequestration (CCS) is expected to play a major role in reducing greenhouse gas in the atmosphere. It is applied using different methods including geological, oceanic and mineral sequestration. Geological sequestration refers to storing of CO₂ in underground geological formations including deep saline aquifers (DSAs). This process induces multiphase fluid flow and solute transport behaviour besides some geochemical reactions between the fluids and minerals in the geological formation. In this work, a series of numerical simulations are carried out to investigate the injection and transport behaviour of supercritical CO₂ in DSAs as a two-phase flow in porous media in addition to studying the influence of different parameters such as time scale, temperature, pressure, permeability and geochemical condition on the supercritical CO₂ injection in underground domains. In contrast to most works which are focussed on determining mass fraction of CO₂, this paper focuses on determining CO₂ gas saturation (i.e., volume fraction) at various time scales, temperatures and pressure conditions taking into consideration the effects of porosity/permeability, heterogeneity and capillarity for CO₂–water system. A series of numerical simulations is carried out to illustrate how the saturation, capillary pressure and the amount of dissolved CO₂ change with the change of injection process, hydrostatic pressure and geothermal gradient. For example, the obtained results are used to correlate how increase in the mean permeability of the geological formation allows greater injectivity and mobility of CO₂ which should lead to increase in CO₂ dissolution into the resident brine in the subsurface.     

Branched-pore model applied to the adsorption of basic dyes on carbon

The branched-pore adsorption model, expressed by an external mass transfer coefficient k_f, a solid diffusivity D_s, a lumped micropore diffusion rate parameter k_b, and the fraction of macropores f, describes kinetic data from initial contact of adsorbent-adsorbate to the long-term ( > 24 hours) adsorption stages with reasonable accuracy.In this work the model is applied for three basic dye systems, namely Basic Red 22, Basic Yellow 21 and Basic Blue 69, all on carbon. A single value of each parameter describes each dye system. The k_f values are 0.18 × 10⁻²±28%, 0.3 × 10⁻²±17% and 0.2 × 10⁻² ± 20% cm s⁻¹, the D_s values are 0.33 × 10⁻⁹ 21%, 0.72 × 10⁻⁹ ± 9% and 0.72 × 10⁻⁹ ± 9% cm² s⁻¹, the k_b values are 0.65 × 10⁻⁶ ± 7.7%, 1.8 × 10⁻⁶ 0.2 × 10⁻⁶ 1% s⁻¹, while the f values are 0.55 ± 9%, 0.60 ± 10 % and 0.18 ± 11%, each for Basic Red 22, Basic Yellow 21 and Basic Blue 69 respectively.The model is based on the internal structure of the carbon particle being divided into a macropore and a micropore region. The latter has an upper-bound capacity of 241, 245 and 656 mg g⁻¹ for Basic Red 22, Basic Yellow 21 and Basic Blue 69 respectively. A sensitivity analysis for each parameter has been carried out.     

Models Proposed to Explain the Electrical Conductivity of Polymer‐Derived Silicon Carbide Fibers

Two types of silicon carbide fibers (SiC_f) were prepared employing different pyrolysis techniques. The relationship between the microstructure and the electrical resistivity of the fibers was investigated. The results indicated that the carbon layer present on the fiber surface acted as the main conductive phase in the SiC_f obtained by direct pyrolysis, whereas a free carbon phase determined the conductivity of the SiC_f prepared by the preheated pyrolysis method. A core‐shell model and a general effective media (GEM) theory were proposed to explain the conductivity of different types of SiC_f. Quantitative analysis based on these models indicated an electrical resistivity of ~10^?2 Ω·cm for the carbon layer on the surface of SiC_f obtained by direct pyrolysis. The electrical resistivity and the percolation threshold of the free carbon in SiC_f prepared by the preheated pyrolysis method were 10^?1 Ω·cm and 11.3% respectively.     

Kinetic study of the free‐radical polymerization of vinyl acetate in the presence of deuterated chloroform by 1H‐NMR spectroscopy

The free‐radical polymerization of vinyl acetate was performed in the presence of deuterated chloroform (CDCl₃) as a chain‐transfer agent (telogen) and 2,2′‐azobisisobutyronitrile as an initiator. The effects of the initiator and solvent concentrations (or equivalent monomer concentration) and the reaction temperature on the reaction kinetics were studied by real‐time ¹H‐NMR spectroscopy. Data obtained from analysis of the ¹H‐NMR spectra were used to calculate some kinetic parameters, such as the initiator decomposition rate constant (k_d), k_p(f/k_t)^1/2 ratio (where k_p is the average rate constant for propagation, f is the initiator efficiency, and k_t is the average rate constant for termination), and transfer constant to CDCl₃ (C). The results show that k_d and k_p(f/k_t)^1/2 changed significantly with the solvent concentration and reaction temperature, whereas they remained almost constant with the initiator concentration. C changed only with the reaction temperature. Attempts were made to explain the dependence of k_p(f/k_t)^1/2 on the solvent concentration. We concluded from the solvent‐independent C values that the solvent did not have any significant effect on the k_p values. As a result, changes in the k_p(f/k_t)^1/2 values with solvent concentration were attributed to the solvent effect on the f and/or k_t values. Individual values of f and k_t were estimated, and we observed that both the f and k_t values were dependent on the solvent (or equivalent monomer) concentration. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Fibrous MnO2 electrode electrodeposited on carbon fiber for a fuel cell/battery system

A novel fibrous MnO₂ electrode for a fuel cell/battery system is fabricated on carbon fiber by the electrodeposition method. The characteristics of the fibrous MnO₂ electrode are examined by electrochemical impedance spectra, galvanostatic performance and cyclic voltammetry. The experimental results indicate that the fibrous MnO₂ electrodes are superior to pasted electrodes because of the following: (i) better contact between MnO₂ and the electrical conducting material; (ii) high charge-transfer rate because of a smaller diameter than conventional electrodeposited MnO₂ particles (thus it is expected that the specific surface area would be higher); and (iii) a low overpotential. The morphology and the crystal structure of the fibrous MnO₂ electrode are investigated by scanning electron microscopy and X-ray diffraction, respectively. The entire surface of the carbon fiber is found to be coated with γ-MnO₂ after 2 h of electrodeposition at 0.01 A dm⁻² current density.     

Selective enantioseparation of levocetirizine via a hollow fiber supported liquid membrane and mass transfer prediction

The enantioselective separation of levocetirizine via a hollow fiber supported liquid membrane was examined. O,O′-dibenzoyl-(2R,3R)-tartaric acid ((?)-DBTA) diluted in 1-decanol was used as a chiral selector extractant. The influence of concentrations of feed and stripping phases, and extractant concentration in the membrane phase, was also investigated. A mathematical model focusing on the extraction side of the liquid membrane system was presented to predict the concentration of levocetirizine at different times. The extraction and recovery of levocetirizine from feed phase were 75.00% and 72.00%, respectively. The mass transfer coefficients at aqueous feed boundary layer (k _f ) and the organic liquid membrane phase (k _m ) were calculated as 2.41×10² and 1.89×10² cm/s, respectively. The validity of the developed model was evaluated through a comparison with experimental data, and good agreement was obtained.     

Mathematical modeling of extraction of egg yolk oil with supercritical CO2

Extraction of egg yolk oil (EYO) from egg yolk powder (EYP) with supercritical CO₂ was performed on a laboratory apparatus. Solubility of EYO in supercritical CO₂ was measured. The external diffusion and the equilibrium between solid and fluid phases were experimentally found to be the controlling steps during the extraction process. Based on this mechanism, a mathematical model for this extraction process was developed. The model parameters, adsorption equilibrium constant (k_p), EYO concentration in solid controlling the transition in the equilibrium (x_k) and the overall volumetric mass transfer coefficient (K_fa_p), were obtained by simulation. The simulation results indicated that x_k is 0.56, K_fa_p is directly proportional to CO₂ flow rate with an exponent of 0.548, and the adsorption heat of EYO is 6–9 kJ mol⁻¹. The model was verified by concentration profiles of solid. The extraction process of EYO with supercritical CO₂ was conducted on a pilot plant and the developed model could predict satisfactorily the process.     

Quasi-1D and 3D TPOX porous media diffuser reformer model

This paper focuses on the numerical simulations of methane thermal partial oxidation reforming process within inert porous media and their comparison with experiments. In order to produce hydrogen rich mixtures and for the sake of reaction stability, the reformer consists on a diffuser filled with porous media. The validity of using a quasi-1D approach to model this system is explored based on 3D simulations of the isothermal fluid flow through the porous solid structure. Several fluid flow cases were taken into account as well as two different porous materials, Al₂O₃ fiber lamellae and SiSiC foam. The detailed fluid flow information obtained from the 3D study was used to provide the realistic cross-sectional area variation of the quasi-1D model. The quasi-1D 12-steps reduced chemistry model predictions are in very satisfactory agreement with the temperature and concentration fields measured within the diffuser porous reformer.     

Gasification of carbon by CO2: A transient kinetics experiment

A transient kinetic technique was used to measure the intrinsic rate constant k₂ of the reaction C(O) → CO + C_f, where C_f is an available site and C(O) is an occupied site. It was found that k₂ = 10^{11.6 ± 2.3} exp[ −(225 000 ± 39000)/RT]min⁻¹. Two systems were studied, one using an uncatalysed carbon, the other a Ca-catalysed carbon. The gasification rates for these two systems differed by a factor of 100, yet they yielded the same k₂. This strongly supports the contention that Ca catalyses the system by increasing the number of active sites.     

MgO as a non-pyrolyzable pore former in porous membrane supports

The gas permeability of Y_0.03Zr_0.97O₂ (3Y-TZP) porous supports from thermoplastic feedstocks has been improved by adding MgO as a non-pyrolyzable pore former. Common pyrolyzable pore formers such as graphite often produce tortuous and narrow pore channels with low gas permeability, limiting the performance of oxygen transport membranes or other membranes relying on gas transport to the active membrane surface. Thermoplastic feedstocks for extrusion of tubular 3Y-TZP supports were prepared with four different amounts of pyrolyzable pore formers and/or MgO as non-pyrolyzable pore former. The MgO was removed after sintering by leaching in acetic acid. With this technique we obtained porosities above 70 vol% and gas permeabilities above 3?10^?14?m². Compared to samples with only pyrolyzable pore formers, the non-pyrolyzable pore former increases the gas permeability and reduces the tortuosity.     

Ablation behavior and mechanism of Cf/SiBCN composites in plasma ablation flame

In this work, C_f/SiBCN composites are fabricated by an improved precursor infiltration and pyrolysis (PIP) approach. Ablation behavior of the C_f/SiBCN composites is investigated in plasma ablation flame at a heat flux of 4.02 MW m⁻², which provides a quasi-real hypersonic service environment at a temperature up to 2200°C. After ablation, the ablated surface is covered with oxidation products in the form of oxide layer, fibrous residues, or bubbles, which effectively isolates the sample surface from the plasma flame and inhibits the scouring of high-speed flame to the composites. As a result, the C_f/SiBCN composites present an excellent ablation-resistant property, with linear and mass recession rates as low as 0.0030 mm s⁻¹ and 0.0539 mg mm⁻² s⁻¹, respectively. It is also revealed that the material at ablation center undergoes crystallization and oxidation processes during ablation, while the ablation behavior at transition area and ablation fringe only contains oxidation process due to the local temperature difference. Si₃N₄ and SiC grains are precipitated from amorphous SiBCN matrix during the crystallization process, and the oxidation process mainly involves the oxidation of carbon fiber and SiBCN matrix, etc.     

Non-steady-state kinetic analysis of coupled transport of thiocyanate ions through binary liquid membranes

The coupled transport of thiocyanate (SCN⁻) ions through binary liquid membranes of various compositions was investigated using trichloromethane and dichloromethane as membrane components in non-steady-state kinetics. The influence of the membrane composition on the kinetic parameters (k_1d, k_2m, k_2a, R^max_m, t_max) were calculated. The present work shows the importance of the nature of binary liquid membranes in establishing transport efficiency, which is increased by varying membrane composition. Striking variations of the kinetic parameters with the membrane composition were observed. It is shown that transport kinetics obeys the competitive preferential solvation theory in the whole concentration range.