Showing papers on "Mass transfer published in 1996"

Distillation Columns Containing Structured Packings: A Comprehensive Model for Their Performance. 2. Mass-Transfer Model

Abstract: This is the second part of a two-part paper dealing with the fluid mechanics and mass transfer in structured packings for distillation column service. The first part elucidated pressure drop, flooding, and liquid holdup. The second part covers the generation of effective interfacial area and provides a general correlation for predicting the mass-transfer efficiency as a function of surface type, packing geometry, phase flow conditions, and fluid properties. The mass-transfer model has been tested against a variety of commercial structured packings, for distillation pressures ranging from 0.33 to 20.4 bar. In all cases the fit of the data is excellent, with the possible exception of the highest pressures, where additional factors of axial mixing appear to have an effect.

Transport phenomena with drops and bubbles

Abstract: 1 Fundamental Principles and Definitions.- 1.1 Introduction.- 1.2 Mathematical Description.- 1.3 Heat and Mass Transfer.- References.- 2 Shape and Size of Fluid Particles.- 2.1 Introduction.- 2.2 Shapes of Static Particles.- 2.3 Shapes of Particles in Motion.- 2.4 Drop Size Distribution.- References.- 3 Transport at Low Reynolds Numbers.- 3.1 Introduction.- 3.2 Fluid Mechanics.- 3.3 Heat and Mass Transfer.- References.- 4 Transport at Intermediate and High Reynolds Numbers.- 4.1 Introduction.- 4.2 Fluid Mechanics.- 4.3 Heat and Mass Transfer.- References.- 5 Wall Interactions.- 5.1 Fluid Mechanics.- 5.2 Dropwise Condensation.- 5.3 Dropwise Evaporation.- References.- 6 Transport with a Spectrum of Fluid Particles.- 6.1 Introduction.- 6.2 Particle Sizes and Velocity Distributions.- 6.3 Transfer without Phase Change.- 6.4 Transfer with Phase Change.- References.- 7 Formation and Breakup of Bubbles and Drops.- 7.1 Introduction.- 7.2 Formation of Bubbles and Drops.- 7.3 Breakup of Bubbles and Drops.- References.- 8 Compound Drops and Bubbles.- 8.1 Introduction.- 8.2 Fluid Mechanics.- 8.3 Heat and Mass Transfer.- References.- 9 Special Topics.- 9.1 Transport in an Electric Field.- 9.2 Transport with a Slurry Fuel Droplet.- 9.3 Thermocapillary Phenomenon and Microgravity.- References.- Nomenclature.- Author Index.

Kinetic and Heat Transfer Control in the Slow and Flash Pyrolysis of Solids

Abstract: The coupled effects of particle size and external heating conditions (reactor heating rate and final temperature) on cellulose pyrolysis are investigated by means of a computer model accounting for all main transport phenomena, variable thermophysical properties and primary, and secondary reaction processes. The dynamics of particle conversion are predicted, and final product distributions are favorably compared with experimental measurements. A map is constructed, in terms of particle size as a function of the reactor temperature, to identify the transition from a kinetically controlled conversion to a heat transfer controlled conversion (thermally thin and thermally thick regimes) and from flash to slow-conventional pyrolysis. Conditions for maximizing oil, gas, or char yields are also discussed.

Distillation Studies in a High-Gravity Contactor

Abstract: A high-gravity vapor−liquid contactor (“Higee”) was studied under distillation conditions using a semiworks scale system. The cyclohexane/n-heptane test mixture was used at operating pressures of 166 and 414 kPa and under total reflux conditions. Rotational speeds ranged from 400 to 1200 rpm. Data were collected on mass transfer efficiency, pressure drop, and hydraulic capacity. As many as six transfer units were achieved in a bed depth of 21 cm, with efficiency being directly proportional to speed of rotation. Models were developed for mass transfer and pressure drop, and the earlier packed bed flooding model of Sherwood, which includes a gravity term, was found to represent the vapor capacity of the contactor. Sufficient information is given to enable the preliminary design of a system containing a high-gravity vapor−liquid contactor. Because the test mixture has been widely used for conventional contactor studies, means for comparing high-gravity contacting with other methods are now available.

Protein Adsorption on Cation Exchangers: Comparison of Macroporous and Gel-Composite Media

Abstract: The protein uptake equilibrium and kinetics and the breakthrough behavior of recently developed commercial chromatography media are evaluated using lysozyme as a model solute. One of the adsorbents, known by the trade name POROS 50, is a macroporous matrix based on a styrene-divinylbenzene copolymer. The other adsorbent, known by the trade name HyperD, is a composite obtained by filling the pores of high-porosity polystyrene-coated silica particles with a polyacrylamide-based hydrogel. Both materials are designed for preparative and process ion-exchange chromatography of proteins at high speed and have a strong cation exchange functionality. The equilibrium and transport properties of lysozyme in each adsorbent are studied in batch experiments. The maximum equilibrium uptake capacity in a 10 mM sodium phosphate buffer at pH 6.5 is 160 ± 5 mg/cm 3 of particle volume for the macroporous adsorbent and 260 ± 10 mg/cm 3 for the gel-composite material. With the macroporous adsorbent mass transfer appears to be dominated by macropore diffusion with an effective pore diffusivity of 1.1 x 10 -7 cm 2 /s, except during the initial saturation of the outermost layer of the particle, when external film mass transfer is controlling. An idealized two-step model of this process is found to be consistent with the experimental data. With the gel-composite adsorbent, however, mass transfer appears to be dominated by homogeneous gel diffusion with an effective pseudo-homogeneous diffusivity of 7.5 x 10 -9 cm 2 /s at high protein concentrations and by the external film resistance at low protein concentrations. For both adsorbents, breakthrough profiles obtained experimentally at elevated flow rates in packed columns are in good agreement with predictions based on the batch measurements and external film coefficients predicted from literature correlations. In spite of the fact that it possesses a larger particle size, the gel-composite adsorbent appears to be superior to the macroporous medium, exhibiting a dynamic capacity at 10% breakthrough more than a factor of 2 larger at mobile phase velocities in the range 0-5000 cm/h.

Simulating equilibrium within aerosols and nonequilibrium between gases and aerosols

Abstract: A numerical method to solve chemical equilibrium equations and a method of coupling the equilibrium calculations to nonequilibrium growth and evaporation are discussed. The equilibrium program solves any number of equations for gas, aqueous, ionic, and solid equilibrium concentrations over large spatial grids and particle size grids. It also simultaneously computes electrolyte mean mixed activity coefficients and aerosol liquid water content. Mean mixed activity coefficient calculations require mean binary activity coefficient information. Temperature-dependent mean binary activity coefficient polynomials were constructed using mean binary activity coefficient data at 298 K, apparent molal enthalpy data, and apparent molal heat capacity data. The equilibrium solver is mole and charge conserving, requires iteration, but always converges. Solutions to the equilibrium equations are used for two purposes. The first is to estimate surface vapor pressures over particles containing a solution and/or a solid phase. Such vapor pressures are then applied in gas-aerosol transfer equations. The second is to estimate intraparticle composition and size immediately after gas-aerosol transfer.

Shrinking-core leaching model for supercritical-fluid extraction

Abstract: Extraction or leaching of a solute from a solid material is a process involving mass transfer in the solid matrix. When the solute content in the solid material is sufficiently large as compared to the solubility in fluid phase, the process is similar to that of irreversible desorption. The shrinking-core model was applied to the modeling of the extraction process. The model including axial dispersion in the extraction column was solved numerically. Quasi-steady-state solution without axial dispersion was derived, and the accuracy was discussed in comparison with the numerical solutions. The model calculations gave a good agreement with the experimental extraction curve reported in literature.

The influence of mass transfer characteristics and porous media heterogeneity on nonaqueous phase dissolution

Abstract: A two-dimensional multiphase flow and species transport model was developed and applied to the case of nonaqueous phase liquid (NAPL) emplacement and dissolution in both homogeneous and heterogeneous porous media systems. Simulations were performed to observe dissolution rate variations and the degree of NAPL-aqueous phase nonequilibrium as a function of two aqueous phase velocities and five forms of the NAPL-aqueous phase mass transfer formulation. An integrated form of the Damkohler number was introduced to analyze the degree of NAPL-aqueous phase nonequilibrium. Mass removal rates for homogeneous media were insensitive to the form of the NAPL-aqueous phase mass transfer formulation, yielding results similar to a local equilibrium approach for all but one mass transfer formulation. This latter formulation was most sensitive to NAPL saturation and yielded significant nonequilibrium behavior, which was manifested as a decrease in NAPL dissolution rates as the NAPL volume fraction decreased. Variations in mass elution rates between homogeneous and heterogeneous media were observed, with more significant variations found for variances in porous media properties than for horizontal correlation lengths. In heterogeneous media, decreases in dissolution rates were attributed to the existence of relatively immobile regions of NAPL with saturations greater than the residual saturation of the media, so-called NAPL pools. These results illustrate the importance of the statistical characteristics of heterogeneous porous media on NAPL distribution and dissolution processes.

A modified Maxwell-Stefan model for transport through inert membranes : the binary friction model

Abstract: This paper focuses mainly on the development of a model for permeation through inert membranes, as encountered in many cases in ultrafiltration and in gas permeation through inert porous plugs. The ultrafiltration model is made up of a boundary layer transport model and a porous membrane model in series, which are connected by an equilibrium relation. The boundary layer model is developed with the Vieth approximation for turbulent diffusivity. For the internal membrane transport, a modification of the Maxwell-Stefan-Lightfoot equation is derived (the binary friction model), which in a natural way includes both interspecies (diffusive) and species-wall forces. Application for the partial separation of PEG-3400 from aqueous solution shows that membrane friction coefficients can simply be estimated from membrane resistance measurements and mixture viscosity data. The only adjustable parameter to be determined is the distribution coefficient between the free solution and the membrane pores. The differences between the Lightfoot approach and the dusty gas model (DGM) are shown to stem from errors in the drivations of the latter, thus invalidating the dusty gas approach in the normal region in which viscous friction effects become important. For gases, the binary friction model is developed to include Knudsen and viscous wall friction terms as well as intermolecular diffusion. It is shown to give excellent coverage of the He-Ar diffusion data of Evans et al. (J. Appl. Phys., 33 (1962) 2682; 34 (1963) 2020), with wall friction coefficients derived directly from Knudsen coefficients and gas viscosity data. The apparent success of the DGM in describing the same phenomena is shown to be caused by the relatively small importance of the wall friction forces at elevated pressures, and by the correct transition to Knudsen flow at low pressures. In addition, it is shown that diffusive slip phenomena in capillaries can be described well by the binary friction model.

A re-examination of pressure effects on enantioselectivity in asymmetric catalytic hydrogenation

Abstract: Marked shifts in enantioselectivity in the asymmetric hydrogenation of several prochiral substrates were observed as a function of the availability of hydrogen to the catalyst in both heterogeneous and homogeneous catalytic reactions. The key kinetic parameter affecting enantioselectivity was found to be concentration of molecular hydrogen in the liquid phase, [H2], rather than hydrogen pressure in the gas phase, and it was observed that under typical reaction conditions, [H2] could differ widely from its equilibrium saturation value. It was demonstrated that the reported pressure dependence on enantioselectivity may in fact be reproduced at constant pressure for several systems by varying the rate of gas−liquid mass transfer. The general significance of the conclusions suggest that considerations of hydrogen diffusion limitations might be important in other asymmetric hydrogenation studies reported in the literature. For systems where enantioselectivity depends positively on hydrogen pressure, the intrin...

Macrotransport of a Biologically Reacting Solute Through Porous Media

Abstract: A physically based model is developed to study the transport of a solute utilized by microorganisms forming a biofilm coating on soil grains in a porous medium. A wavy-walled channel is used as a geometrical model of a porous medium and a biofilm is attached to the channel wall. Within the biofilm the solute is consumed according to a first-order volumetric rate. A numerical study is performed to obtain the dependence of the macrotransport coefficients on the Peclet number and Damkohler number. It is found that in some cases of practical importance the pore fluid is not well mixed, and mass transport limitations can control macroreaction rates. For diffusion-limited cases (large Damkohler numbers) increased solvent velocity can enhance the macroreaction rate by a factor of almost 3. Mean solute and mean solvent velocities are, in general, not equal, and mean solute velocities can exceed mean solvent velocities by 60% at high Damkohler numbers. These results agree qualitatively with those of a previous numerical study by Edwards et al. (1993). The results also suggest that due to the spatially variable pore geometry, the biomass nearest the pore throat is more effective at consuming the solute than biomass in the pore chamber. A comparison is made between mass transfer correlations and the results determined for the macroreaction rate coefficient. We find that over a limited range of Peclet numbers a macroscale Sherwood number follows the Pel/3 behavior determined from experimental mass transfer correlations and predicted by boundary layer theory.

Comparison between Random and Structured Packings for Dehumidification of Air by Lithium Chloride Solutions in a Packed Column and Their Heat and Mass Transfer Correlations

Abstract: Random and structured packings were compared for their efficiency in dehumidification of air in a packed column using lithium chloride solutions. Experiments were conducted with cross corrugated ce...

Control of iron nitride layers growth kinetics in the binary Fe-N system

Abstract: This study is within the framework of a research program dedicated to defining the optimal conditions for the nitriding of iron and steels at atmospheric pressure by using various mixtures, NH3-N2-H2 and NH3-Ar. After studying the mechanisms of phase formation and mass transfer at the gas-solid interface, a mathematical model is developed in order to predict the nitrogen transfer rate in the solid, the nitride layer growth rate, and the nitrogen concentration profiles. In order to validate the model and to show its possibilities, it is compared with thermogravimetric experiments, analyses, and metallurgical observations (X-ray diffraction, optical microscopy, and electron microprobe anal-ysis). The results obtained allow us to demonstrate the sound correlation between the experimental results and the theoretical predictions. By applying the model to the iron-nitrogen binary system, when the e/γ/α configuration referred to the Fe-N phase diagram is formed, we have experimentally determined the effective diffusion coefficient of nitrogen in the e phase. The latter is constant for a composition of the e nitride between 8 and 9.5 wt pct nitrogen. All the results obtained show that it is possible, by means of dynamic gas flow regulation, to eliminate the incubation period and to control the thickness, composition, and structure of the compound layer at the beginning of the treatment.

A modelling study for moisture diffusivities and moisture transfer coefficients in drying of solid objects

Abstract: This article presents an effective analytical model for determining the moisture diffusivities and moisture transfer coefficients for solid objects (namely, infinite slab, infinite cylinder, sphere; and also for irregularly shaped objects, by using a shape factor) subject to drying applications in a medium. The unsteady-state moisture diffusion analysis is used on the basis of two important criteria: 0.1 100. The drying coefficients and lag factors were employed. The analytical models are then verified using available experimental data taken from the literature. The results show that the method presented here can be used to determine the moisture diffusion coefficients and moisture transfer coefficients for such solid objects in a simple and accurate manner for a variety of drying applications.

Modeling Colloid Transport in Unsaturated Porous Media and Validation with Laboratory Column Data

Abstract: Colloidal particles can act as carriers to enhance the transport of contaminants in porous media by reducing retardation effects. When colloids are present, especially in the vadose zone, the system can be treated as consisting of four phases: an aqueous phase, the stationary soild matrix phase, a carrier (colloidal particles) phase, and a stagnant air phase. In the work reported a mathematical model based on mass balance equations was developed to describe the transport and fate of colloids in an unsaturated porous medium. Colloidal particles can sorb onto the air-water interface as well as to the solid matrix surfaces. Colloid/matrix mass transfer rate is represented by first-order kinetics, while the colloid/air-water interface mass transfer mechanism is formulated by second-order kinetics. The model was applied to simulate the migration of colloids through an unsaturated finite column. Numerical solutions were obtained to provide estimates of colloidal concentrations. A sensitivity analysis of the transport model was utilized to assess the effect of several parameters on model behavior. The aqueous phase colloid concentration is quite sensitive to changes in the rate coefficient of colloidal deposition on the solid matrix. However, the colloidal capture on the air-water interface is affected by the fraction of air-water interface available for particle deposition as well as by the rate coefficient of colloidal capture on the air-water interface, k3. As k3 increases, the available sorption site reduces quickly. Furthermore, increasing colloidal sorption capacity significantly retards the colloidal migration. The model results match successfully with experimental data of Wan and Wilson [1994a] and Wan et al. [1994]. A comparison between the breakthrough curves of hydrophobic and hydrophilic colloids suggests that the hydrophobic colloids have less affinity for both solid matrix and the air-water interface. Experimental data and model results show that the presence of the air-water interface retards the colloid transport very significantly. Finally, the proposed model is extended to simulate the colloid transport under transient water flow conditions. Simulations show that aqueous phase colloid concentration varies along the column following a trend similar to the saturation profile for both hydrophobic and hydrophilic colloids. However, the migration profile of hydrophilic colloid suspension is faster than the hydrophobic one.

The dynamics of heat

Abstract: From Metaphors to Models of Heat.- Processes, Energy, and Dynamical Models.- Storage and Flow of Fluids and Electricity.- Energy in Physical Processes.- Transport and Balance of Momentum.- Thermal and Chemical Processes.- Storage, Flow, and Production of Heat.- The Response of Simple Materials to Heat.- Transformation and Transport of Substances.- The Transport of Heat.- Flow Systems and Convective Transports.- Minimization of Entropy Production.- A Dynamical Theory of Heat.- Thermodynamics of Spatially Uniform Systems.- Thermodynamics of Continuous Systems.- Thermodynamics and Radiative Transfer.- Special Processes and Systems.- Conduction and Coupled Transports.- Convective Heat Transfer.- Phase Change, Mixtures, and Engines.- Solar Radiation.