New absorption liquids for the removal of CO2 from dilute gas streams using membrane contactors

A new absorption liquid based on amino acid salts has been studied for CO₂ removal in membrane gas-liquid contactors. Unlike conventional gas treating solvents like aqueous alkanolamines solutions, the new absorption liquid does not wet polyolefin microporous membranes. The wetting characteristics of aqueous alkanolamines and amino acid salt solutions for a hydrophobic membrane was studied by measuring the surface tension of the liquid and the breakthrough pressure of the liquid into the pores of the membrane. The dependence of the breakthrough pressure on surface tension follows the Laplace-Young equation. The performance of the new absorption liquid in the removal of CO₂ was studied in a single fiber membrane contactor over a wide range of partial pressures of CO₂ in the gas phase and amino acid salt concentrations in the liquid. A numerical model to describe the mass transfer accompanied by multiple chemical reactions occurring during the absorption of CO₂ in the liquid flowing through the hollow fiber was developed. The numerical model gives a good prediction of the CO₂ absorption flux across the membrane for the absorption of CO₂ in the aqueous amino acid salt solutions flowing through the hollow fiber.     

Hollow fiber membrane contactor transient experiments for the characterization of gas/liquid thermodynamics and mass transfer properties

We present results from experiments and numerical simulations of contact between a non-reactive gas (N₂O and CO₂) and a physical solvent (H₂O) occurring in a polypropylene (PP) hollow fiber membrane contactor. The closed-loop liquid flow within the experimental setup provides transient curves representing the progressive saturation of the solvent by the gas. We develop an in-house numerical model to fully characterize the gas/liquid mass transfer both in the non-wetted and in the wetted modes, i.e., when the liquid starts partially wetting the pores of the membrane. Using experiments and numerical simulations, we show that the Henry constant (H) and the molecular diffusion coefficient of a non-reactive gas absorbing into a liquid solvent can be extracted by parameter estimation. Both parameters are obtained within a single experiment at a constant temperature and the comparison with temperature-dependant correlations yields excellent agreement over the whole range of temperature studied in this work. Simulations show a partial wetting of the membrane pore by the liquid meniscus during a contact between CO₂ and H₂O, possibly due to the plasticizer effect of CO₂ inside the membrane contactor fibers.     

Thin-layer drying of porous materials: Selection of the appropriate mathematical model and relationships between thin-layer models parameters

Experimental investigation of the drying kinetics of various types of materials was carried out in laboratory-scale dryers under different conditions of temperature, microwave heating power and pressure. Leather samples (mechanically and vacuum-dewatered bull napa and wet blue cutting), paperboards (grafopack, testliner), wood (alder, birch, willow) and two pharmaceutical powders (chlorpropamide and hydrochlorotiazide) were dried in a microwave dryer. Thin clay slabs, Al–Ni catalyst and chlorpropamide were dried in a convection dryer, while chlorpropamide and ketoprofen were dried in a vacuum dryer. In order to compare drying kinetics, experimentally obtained data, X = f(t), were correlated with the Lewis “thin-layer” equation, the modified Page equation and Fick's second law. The drying constant, effective diffusion coefficient, mass transfer coefficient and modified Page model parameters were estimated by fitting the selected mathematical models to experimental data. High levels of correlation between measured and calculated data were obtained for all materials and dryers using modified Page model. The application of the Lewis and Fick's equation is justified only for drying of clay, catalyst and leather. Mass transfer coefficient depends linearly on the drying constant. The relation between the modified Page model parameter and the drying constant can be represented by a unique power function.     

Modeling of particle deposition in a vertical turbulent pipe flow at a reduced probability of particle sticking to the wall

Particle deposition on the wall in a dilute turbulent vertical pipe flow is modeled. The different mechanisms of particle transport to the wall are considered, i.e., Brownian motion, turbulent diffusion and turbophoresis. The Saffman lift force, the electrostatic force, the virtual mass effect and wall surface roughness are taken into account in the model developed. A boundary condition that accounts for the probability of particle sticking to the wall is suggested. An analytical solution for deposition of small Brownian particles is obtained. A particle relaxation time range, where the model developed is reliably applicable, is evaluated. Computational results obtained at different particle-wall sticking probabilities in the wide particle relaxation time range are presented and discussed.     

Numerical simulation of mass transport in a filter press type electrochemical reactor FM01-LC: Comparison of predicted and experimental mass transfer coefficient

This paper studies flow characteristics and their effect on local mass transfer rate to a flat plate electrode in a FM01-LC electrochemical reactor. 3D reactor simulations under limiting current and turbulent flow conditions were performed using potassium ferro-ferricyanide electrochemical system with sodium sulfate as supporting electrolyte. The model consists of mass-transport equations coupled to hydrodynamic solution obtained from Reynolds-averaged Navier–Stokes equations using standard k–? turbulence model, where the average velocity field, the turbulence level given by the eddy kinetic energy and the turbulent viscosity of the hydrodynamic calculation were used to evaluate the convection, turbulent diffusion and the concentration wall function. The turbulent mass diffusivity was evaluated by Kays–Crawford equation using heat and mass transfer analogies, while wall functions, for mass transport, were adapted from Launder–Spalding equations. Simulation results describe main flow properties, concentration profiles throughout the entire volume of the reactor and local diffusion flux over the electrode. Overall mass transfer coefficients estimated by simulation, without fitting parameters, agree closely with experimental coefficients determined from limiting current measurements (1.85% average error) for Re between 187 and 1407.     

A general rate model approach for the optimization of the core radius fraction for multicomponent isocratic elution in preparative nonlinear liquid chromatography using cored beads

Cored beads (also known as pellicular, superficially porous, and fused-cored beads or particles) offer advantages over fully porous beads in reduced diffusional mass transfer resistances in particle macropores and separation times in liquid chromatography (LC). They are also used to regulate bead densities. The core of a bead has a relatively small volume and yet presents a large linear distance for diffusional mass transfer inside particle macropores. Using a non-porous inert core, intraparticle diffusional mass transfer resistance can be reduced with a relatively small loss in binding capacities. In multicompnent isocratic elution chromatography, cored beads are a compromise between fully porous beads and non-porous beads. Non-porous beads completely eliminate intraparticle diffusion, providing sharp elution peaks with the shortest retention times. However, they do not provide a sufficient retention time range for peaks to separate in preparative LC because of their limited binding capacities. At the other end, fully porous beads offer the largest retention time differences, but suffering from excessive band broadening. For a particular multicomponent elution system, core radius fraction can be optimized to take the advantages of both fully porous beads and non-porous beads. This work presented a general rate model for cored beads and its numerical solution strategy. The model considered axial dispersion, interfacial mass transfer, intraparticle diffusion, and multicomponent Langmuir isotherm. Computer simulation was used to study the effects of core radius fraction on breakthrough curves and elution peaks. The model was used to optimize the core radius fraction for a preparative ternary elution system as an example case.     

Development of a comprehensive free radical photopolymerization model incorporating heat and mass transfer effects in thick films

A comprehensive kinetic model describing photopolymerization is developed which allows variation of temperature, species concentrations, and light intensity through the thickness of a photopolymerized film. Heat and mass transfer effects are included, as is the generation of heat by both reaction and light absorption. In addition to initiation, propagation, and termination mechanisms, both primary radical termination and inhibition are incorporated into the model. The possible presence and diffusion of an inert solvent are also accounted for. Thus, the model is useful for examining complex polymerization kinetics and behavior in industrially and commercially important thick film photopolymerizations, such as the curing of contact lenses, dental restorative materials, photolithographic resists, and optoelectronic coatings. The comprehensive model is used to predict polymerization rate, temperature, and conversion profiles in a variety of systems. The effects of heat generation and the thermal boundary conditions are explored, with the result that heat generation in thick samples leads to greatly increased conversions approaching 100 percent. Increased temperature in these samples also may lead to the appearance of two rate maxima, with the first due to the temperature increase and the second caused by the autoacceleration process. The magnitude of the temperature increase, along with the resultant effects, is more pronounced in insulated systems.     

A model for the corrosion of steel subjected to synthetic produced water containing sulfate, chloride and hydrogen sulfide

A model was developed for the prediction of corrosion rates associated with steel subjected to synthetic produced water. The corrosive species included in the model, identified through water analysis conducted in the field, are sulfate, chloride and hydrogen sulfide. The effect on corrosion of these species was examined through polarization experimentation using a three electrode glass corrosion cell and potentiostat. Samples of carbon steel, used in sub-sea pipeline systems, were used at the working electrode and the experiments were carried out at similar physicochemical conditions observed in pipeline systems in the field. The model was based on heterogeneous reactions at the metal surface, with electrochemical parameters determined through experimentation employed in the model to describe the anodic and cathodic processes involved in the corrosion of steel. The model consists of a system of equations with Butler–Volmer kinetics describing the charge transfer and the Nernst diffusion model the mass transfer processes occurring in the corrosion system. The solution is based on a charge balance between the reduction and the oxidation processes which occur at the steel surface. Current density convergence criteria were used in the model to solve the system of equations for corrosion potential, surface species concentration and component current densities. The corrosion rate is determined as the rate of oxidation of iron at the surface and model results have been validated using experimental data. The model demonstrates a reasonable qualitative match with corrosion data collected in the potential region close to the corrosion potential in general, with good qualitative match in the anodic region near the corrosion potential. Some deviation occurs between model and experimental values where overpotentials become large but the model is shown to respond well to changes in input parameter values and predicts the corrosion potential and corrosion rate for each system within experimental variability and the accepted standards of accuracy.     

Evaluation of density-based models for the solubility of solids in supercritical carbon dioxide and formulation of a new model

Many models have been developed to calculate supercritical solubility behavior and most can be either a semi-empirical relationship or based on an equation of state. In this work, density-based, semi-empirical models were evaluated in terms of their ability to accurately correlate solid solubility in supercritical carbon dioxide. The models considered were the methods of Chrastil, del Valle and Aguilera, Adachi and Lu, Méndez-Santiago and Teja, and Bartle. Six binary systems (solid + supercritical carbon dioxide), each with three isotherms, were selected for this evaluation. The average error was calculated for all 18 isotherms with each of the models evaluated. The solid compounds used in this study were naphthalene, anthracene, fluorene, hydroquinone, 1,5-naphthalenediamine, and cholesterol. The solubility data were obtained from literature. Of the previously mentioned models, the Adachi-Lu and del Valle-Aguilera equations provided, in general, lower average error than the other models. Since the Adachi-Lu equation and the del Valle-Aguilera equation correct for different effects, a new model is proposed in this work as a combination of the previous two methods. The proposed equation provided the least overall average error compared to all other models considered in this study. The new model is particularly useful when the reduced density of the solvent is below 1 where previous models tend to fail. This work also emphasizes on the advantages of expressing density-based models in dimensionless form to avoid dimensional inconsistencies in Chrastil-type models. One of the benefits, for example, is that parameters obtained by different authors can be readily compared, regardless of the units used.     

Formulation of a new generic density-based model for modeling solubility of polyphenols in supercritical carbon dioxide and ethanol

The aim of this work is to present a first approach in formulating a generic model for polyphenols solubility in ternary mixtures (polyphenol + ethanol + sc-CO₂). Solubility data of six polyphenols were collected from the literature, and six different groups of parameters were proposed for the new generic model in order to evaluate their effects and find the best set for each polyphenol. Likewise, four dimensional groups of factors were proposed to evaluate the effect of dimensions on solubility data calculation. The results show that the originally formulated model and its modifications are particularly useful in calculating polyphenols solubility data; for instance, when resveratrol solubility data was fitted, the AARD decreased from a value of 38.52 to 14.03, upon changing from a simple to a complex model. Additionally, this generic model with a specific modification can estimate solubility maxima occurring in the ternary resveratrol + ethanol + sc-CO₂ system.     

Analytical study of effects of finger-growth velocity on reaction characteristics of reactive miscible viscous fingering by using a convection-diffusion-reaction model

Reactive miscible viscous fingering occurs when a reactive and miscible less-viscous liquid displaces a more-viscous liquid. Effects of bulk finger-growth velocity on reaction characteristics of miscible viscous fingering with a chemical reaction were studied analytically by using a convection-diffusion-reaction model. The model assumes the existence of a distinct interface between both liquids, assumes the existence of a two-dimensional, steady, stagnated flow field in the less-viscous liquid, and assumes an infinite chemical reaction rate. The model was then used to determine the reaction characteristics, such as the location of the reaction surface and the profile of the product, as functions of the velocity and initial reactant concentrations. The results reveal that the effects of the velocity on the reaction characteristics can be divided into low-, intermediate-, and high-velocity regions. In the low-velocity region, the reaction characteristics strongly depend on the reactant concentrations. In the intermediate-velocity region, the dependence of the reaction characteristics on the reactant concentrations decreases with increasing velocity. In the high-velocity region, the reaction characteristics are nearly independent of the reactant concentrations. Experiments confirm the existence of these three velocity regions predicted by the model.     

Theoretical probing of the phenomenon of the formation of the outermost surface layer of a multi-component particle, and the surface chemical composition after the rapid removal of water in spray drying

Spray drying is a primary process for the manufacture of powders, which satisfy a vast array of societal demands in the areas of nutrition, health and medicine. The functionality of a spray-dried product begins with its incorporation into water (wetting followed by dispersion) Therefore, as its surface chemical composition and structure determine its first contact with water (that is, its hydrophilic nature), these are of prime concern. Laboratory studies on this first layer, which is in the order of several nm in depth from the surface, have been extensive but there is still a lack of a fundamental quantitative explanation of it. This has hampered the development of any sort of approach, which would enable industries to predict what the product may be like before conducting costly trials. This current study is an attempt to describe the on-set of solid formation around the outermost layer of a single droplet during the drying process using an innovative ‘conventional’ continuum approach, i.e. diffusion–convection equations, with a few innovative derivations. Though some complexities such as multi-component equations deduced from irreversible thermodynamics, are avoided for simplicity, some comparisons with experimental/industrial results are made. The main feature of this work is that the multi-component effect is combined with the viscosity (at the surface) effect upon the diffusivities of individual components in the solution droplets or suspension droplets. The derivations allow some extended analytical procedures to proceed in order to help make sense of the experimental observations. Comparisons are made against the data published on dairy fluids. This work provides a good basis for a fruitful area of study that will have a positive impact for spray drying industries. In particular, to help this kind of industry to forge ahead into high performing functional particle production, which are becoming increasingly popular.     

An electrochemical method for measurement of mass transport in polymer membranes using acetaminophen as a model system

An electrochemical approach has been used to model and measure acetaminophen transport through a microporous polycarbonate membrane. The dynamic response of a membrane covered planar electrode system was investigated to derive a simplified middle point formula, the time at which amperometric current reaches half steady state value, that provided reliable solute diffusion coefficients. Experimental values may be noise-contaminated; when this noise is significant, the diffusion coefficient by this method needs to be refined. Here a direct simulation method with a bipartite mathematical expression for current transient was used, which fitted calculated current transients to experimental data. A best fit was reached by minimising the standard deviation between the simulated and experimental current profiles. Mathematically, the simulated curve was linear operated, i.e. shifted and stretched vertically, as well as shifted and stretched horizontally to coincide with the experimental curve. The single point formula, bipartite expression and simulation approach allowed extraction of accurate diffusion values from a previously reported approximated method. The computation approach is not only valid for membrane covered electrodes, but is suitable for other experimental set ups where a one-dimensional Fickian diffusion model is valid, for example, for axial diffusion through cylindrical geometries.     

Correction of the penetration theory based on mass-transfer data from bubble columns operated in the homogeneous regime under high pressure

A new correction term was developed which allows the classical penetration theory to be applied successfully to k_La data obtained from oblate ellipsoidal bubbles formed in bubble columns operated in the homogeneous regime at various pressures . The correction factor is a function of both the Eötvös number Eo and dimensionless gas density ratio. The new correlation was compared with literature k_La data in 18 pure organic liquids, 14 adjusted liquid mixtures and tap water. In some of the liquids (tetralin, xylene and ethanol) not only air but also other gases (nitrogen, helium and hydrogen) were used. In total, 263 experimental k_La points are fitted with an average relative error of 10.4%.In the theoretical approach for the k_La prediction, the gas-liquid contact time (used in the penetration theory) is defined as the ratio of bubble surface to the rate of surface formation. All further calculations are based on the geometrical characteristics (bubble length and height) of an oblate ellipsoidal bubble. It was found that the new correction factor f_c gradually reduces with the increase of both superficial gas velocity u_G and gas density ρ_G (operating pressure P).     

Theoretical and experimental studies on the gas transport properties of mixed matrix membranes based on polyvinylidene fluoride

The effects of the impregnation of three types of inorganic fillers into polyvinylidene fluoride (PVDF) polymer membranes on the gas permeability and selectivity of these membranes were studied theoretically and experimentally. Permeabilities of He, CO₂, O₂, and N₂ through three types of mixed matrix membranes (MMMs) based on PVDF, that is, PVDF/SiO₂, PVDF/MCM‐41, and PVDF/4A MMMs, were experimentally measured and theoretically predicted using Maxwell, Higuchi, Bruggeman, and Bottcher‐Landauer models. Theoretical permeabilities of the PVDF/SiO₂ MMMs using the above four models predicted the results in the following order: Maxwell model>Bruggeman model>Bottcher model>Higuchi model. However, this sequence was reversed for PVDF/MCM‐41 MMMs. The nonporous SiO₂, mesoporous MCM‐41 and zeolite 4A inorganic fillers had effects on the permeabilities of the challenge gases for the PVDF/SiO₂, PVDF/MCM‐41, and PVDF/4A MMMs but had no effects on the selectivities of the MMMs. The experimental permeabilities of the MMMs showed that there were no significant differences among the three types of MMMs despite that the inorganic fillers, that is, SiO₂, MCM‐41, and zeolite 4A, had distinct dissimilar properties such as pore structures and particle sizes. Density measurements indicated that some voids were present in the polymer/particle interfaces. Based on the density measurement results, the void volume fractions of the resulting MMMs were calculated. An equation is derived to determine the void thickness of the MMM in terms of its physical properties and hence this proposed equation can substitute the difficult task of measuring such void thickness through any microscopy techniques. The Maxwell, Higuchi, Bruggeman, and Bottcher‐Landauer models could not predict the actual gas permeabilities of the PVDF MMMs. By taking the effects of crystallinity and immobilization factor on gas permeability into consideration, the extended modified Maxwell model showed good agreement with the experimental gas permeabilities of the resulting MMMs, indicating that the model did capture the essence of the gas transport behaviors through the MMMs. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4715–4726, 2013     

Coupling CFD and Diffusion Models for Analyzing the Convective Drying Behavior of a Single Rice Kernel

The drying behavior of a single rice kernel subjected to convective drying was analyzed numerically by solving heat and moisture transfer equations using a coupled computational fluid dynamics (CFD) and diffusion model. The transfer coefficients were computed simultaneously with the external flow field and the internal diffusive field of the grain. The model was validated using results of a thin-layer drying experiments from the literature. The effects of velocity and temperature of the drying air on the rice kernel were analyzed. It was found that the air temperature was the major variable that affected the drying rate of the rice kernel. The initial drying rates (in first 20 min) were 7, 12, and 19% per hour at inlet air temperatures of 30, 45, and 60 ^° C, respectively. Important temperature gradients within the grain existed only in the first few minutes of the drying process. The moisture content gradients reached a maximum value of 11.7% (db) mm ^?1 at approximately 45 min along the short axis in the thickness direction. The variation in the inlet air velocity showed a minor effect on the drying rate of the rice kernel. The heat and mass transfer coefficients varied from 16.57 to 203.46 W·m ^?2·K ^?1 and from 0.0160 to 0.1959 m·s ^?1, respectively. The importance of the computation of the transfer coefficients with the heat and mass transfer model is demonstrated.     

Simulation of particles and gas flow behavior in a riser using a filtered two-fluid model

Flow behavior of gas and particles is predicted by a filtered two-fluid model by taking into the effect of particle clustering on the interphase momentum-transfer account. The filtered gas–solid two-fluid model is proposed on the basis of the kinetic theory of granular flow. The subgrid closures for the solid pressure and drag coefficient (Andrews et al., 2005) and the solid viscosity (Riber et al., 2009) are used in the filtered two-fluid model. The model predicts the heterogeneous particle flow structure, and the distributions of gas and particle velocities and turbulent intensities. Simulated solids concentration and mass fluxes are in agreement with experimental data. Predicted effective solid phase viscosity and pressure increase with the increase of model constant c_g and c_s. At the low concentration of particles, simulations indicate that the anisotropy is obvious in the riser. Simulations show the subgrid closures for viscosity of gas phase and solid phase led to a qualitative change in the simulation results.