Showing papers on "Mass transfer published in 1985"

Fundamentals of Heat and Mass Transfer

Abstract: This undergraduate-level engineering text introduces the physical effects underlying heat and mass transfer phenomena and develops methodologies for solving a variety of real-world problems.

Chemical mass transfer in magmatic processes

Abstract: Thermodynamic and mathematical relations are presented to facilitate the description of an algorithm for the calculation of chemical mass transfer in magmatic systems. This algorithm extends the silicate liquid solution model of Ghiorso et al. (1983) to allow for the quantitative modelling of natural magmatic processes such as crystal fractionation, equilibrium crystallization, magma mixing and solid-phase assimilation. The algorithm incorporates a new method for determining the saturation surface of a non-ideal multicomponent solid-solution crystallizing from a melt. It utilizes a mathematical programming (optimization) approach to determine the stable heterogeneous (solids+liquid) equilibrium phase assemblage at a particular temperature and pressure in magmatic systems both closed and open to oxygen. Closed system equilibria are computed by direct minimization of the Gibbs free energy of the system. Open system equilibria are determined by minimization of the Korzhinskii potential (Thompson 1970), where oxygen is treated as a perfectly mobile component. Magmatic systems undergoing chemical mass transfer processes are modelled in a series of discrete steps in temperature, pressure or bulk composition, with each step characterized by heterogeneous solid-liquid equilibrium. A numerical implementation of the algorithm has been developed (in the form of a FORTRAN 77 computer program) and calculations demonstrating its utility are provided in an accompanying paper (Ghiorso and Carmichael 1985).

A Multiphase Approach to the Modeling of Porous Media Contamination by Organic Compounds: 1. Equation Development

Abstract: A multiphase approach to the modeling of aquifer contamination by organic compounds is developed. This approach makes it possible to describe the simultaneous transport of a chemical contaminant in three physical forms: as a nonaqueous phase, as a soluble component of an aqueous phase, and as a mobile fraction of a gas phase. The contaminant may be composed of, at most, two distinct components, one of which may be volatile and slightly water soluble and the other of which is both nonvolatile and insoluble in water. Equations which describe this complex system are derived from basic conservation of mass principles by the application of volume averaging techniques and the incorporation of various constitutive relations and approximations. Effects of matrix and fluid compressibilities, gravity, phase composition, interphase mass exchange, capillarity, diffusion, and dispersion are all considered. The resulting mathematical model consists of a system of three nonlinear partial differential equations subject to two equilibrium constraints. These equations relate five unknowns: two capillary pressures and three mass fractions.

Fundamentals of gas-liquid-solid fluidization

Abstract: The successful design and operation of a gas-liquid-solid fluidized-bed system depend on the ability to accurately predict the fundamental properties of the system, specifically, the hydrodynamics, the mixing of individual phases, and the heat and mass transfer properties. Identification of the flow regimes under which the system operates is crucial to an understanding of both the variations of these properties and overall system performance. This timely, comprehensive review describes in a systematic manner the status of fundamental gas-liquid-solid fluidization behavior. This review also discusses the areas in which current knowledge is deficient and further research is needed.

A Groundwater Mass Transport and Equilibrium Chemistry Model for Multicomponent Systems

Abstract: A mass transport model, TRANQL, for a multicomponent solution system has been developed. The equilibrium interaction chemistry is posed independently of the mass transport equations which leads to a set of algebraic equations for the chemistry coupled to a set of differential equations for the mass transport. Significant equilibrium chemical reactions such as complexation, ion exchange, competitive adsorption, and dissociation of water may be included in TRANQL. Here, a finite element solution is presented first for cadmium, chloride, and bromide transport in a one-dimensional column where complexation and sorption are considered. Second, binary and ternary ion exchange are modeled and compared to the results of other investigators. Results show TRANQL to be a versatile multicomponent transport model, with potential for extension to a wide range of equilibrium reactions.

Use of laboratory data in freeze drying process design: heat and mass transfer coefficients and the computer simulation of freeze drying.

Abstract: Freeze drying process development normally proceeds via an empirical “trial and error” experimental approach which is both time consuming and uncertain in reliable extrapolation to production equipment. This research describes the use of phenomenological theory, with key parameters determined by laboratory experiments, to guide the experimental program to optimize the primary drying stage of the process for a given product/container combination. The theoretical description of primary drying is a problem in coupled heat and mass transfer which can be satisfactorily described using a steady-state model where the heat flow is given by the product of the mass flow and the heat of sublimation. Generally, mass transfer is impeded by three barriers or resistances: resistance of the dried product layer, resistance of the semi-stoppered vial, and resistance of the chamber. Resistance, defined as a ratio of pressure difference to mass flow, is experimentally determined for each barrier. The resistance of the dried product normally increases with time as the thickness of dried product increases and typically accounts for over 90% of the total resistance to mass transfer. Heat flow from the shelf surface to the subliming ice is impeded by three barriers: the interface between the shelf surface and the bottom of the tray used to contain the vials, the interface between the tray and the vial bottom, and the ice between the bottom of the vial and the sublimation surface. Heat flow is described in terms of heat transfer coefficients, defined as the ratio of the heat flux to temperature difference, where the heat transfer coefficients are experimentally determined for each vial and tray of interest. Vial and tray heat transfer coefficients increase with increasing pressure and are quite sensitive to variations in degree of flatness of the vial or tray bottom. Steady-state transport theory is used to define six equations with eight variables where the equations contain mass transfer resistances and heat transfer coefficients which are determined from laboratory experiments. The variables are the sublimation rate and the pressures and temperatures throughout the system. Our procedure is to fix two of the variables (i.e., chamber pressure and shelf temperature) and solve, via a computer program, for the other six variables. Solutions are obtained for 0, 20, 40, 60, 80. and 100% completion of primary drying, thereby providing sublimation rate and the relevant temperatures and pressures as a function of time during the freeze-drying cycle defined by the input parameters chosen (i.e., the chamber pressure and shelf temperature profile with time). Thus, computer-generated freeze-drying cycles may be generated for any combination of product, container, and process parameters desired. Agreement between theoretical and experimental cycles is satisfactory. Use of this approach is demonstrated with the following applications: (1) a study of the effect of changes in chamber pressure and shelf temperature on drying time and product temperature: (2) the effect of shelf temperature variability and vial heat transfer coefficient variability on uniformity of drying: and (3) cycle optimization.

Particle Dynamics and Particle Heat and Mass Transfer in Thermal Plasmas. Part II. Particle Heat and Mass Transfer in Thermal Plasmas

Abstract: This paper is concerned with a review of heat and mass transfer between thermal plasmas and particulate matter. In this situation various effects which are not present in ordinary heat and mass transfer have to be considered, including unsteady conditions, modified convective heat transfer due to strongly varying plasma properties, radiation, internal conduction, particle shape, vaporization and evaporation, noncontinuum conditions, and particle charging. The results indicate that (i) convective heat transfer coefficients have to be modified due to strongly varying plasma properties; (ii) vaporization, defined as a mass transfer process corresponding to particle surface temperatures below the boiling point, describes a different particle heating history than that of the evaporation process which, however, is not a critical control mechanism for interphase mass transfer of particles injected into thermal plasmas; (iii) particle heat transfer under noncontinuum conditions is governed by individual contributions from the species in the plasma (electrons, ions, neutral species) and by particle charging effects.

Modeling liquid mass transfer in higee separation process

Abstract: Correspondence concerning this paper should be addressed to Professor Richard S.H. Mah. Hsien-Hsin Tung is now affiliated with Department of Chemical Engineering, California Institute of Technology Penetration theory is used to describe the liquid mass transfer in Higee separation process. Within a possible range of effective areas, it is shown that the predicted mass transfer coefficients are in reasonable agreement with the estimated mass transfer coefficients. The estimated coefficients were calculated from the experimental data and the possible effective areas. Hence it is concluded the penetration theory is generally applicable to describe liquid mass transfer in Higee separation process. The comparison also suggests that liquid mixing at the junctions of packing materials may be more complete in Higee process than in traditional process.

Heat and mass transfer in water-laden sandstone: microwave heating

Abstract: Our previous theoretical model was extended to predict the heat and mass transfer phenomena in microwave-heated porous materials. A water-filled sandstone was heated in microwaves and its drying rates and temperature profiles were measured. Predictions agree well with observations. Besides moisture loss rates and temperature profiles, the model also predicts local moisture content, gas densities, and pressure. These latter quantities were not measured in our work, but are of interest since they reveal the basic mechanisms of heat and mass transfer in internally heated porous media.

Effects of surface-active substances on gas holdup and gas-liquid mass transfer in bubble column

Abstract: The effects of surfactants and antifoam agent on the gas holdup e, the liquid-phase mass transfer coefficient kL and the volumetric liquid-phase mass transfer coefficient kLa in a bubble column were studied experimentally. An addition of surfactants such as n-alcohols to water increases e and decreases kL, and an addition of antifoam agent to water decreases e, kL and kLa. However, the degree of reduction of kL value by an addition of surfactant to water is lower for bubble swarms in a bubble column than that for a single bubble in stagnant liquid. Based on these observations, the previous model for estimating kL of a single bubble in aqueous solutions of surface-active substance is modified so as to be applicable to the estimation of kL for bubble swarms in a bubble column.

Design of cyclic fixed‐bed adsorption processes. Part I: Phenol adsorption on polymeric adsorbents

Abstract: A model for the adsorption of phenol in a fixed bed of a polymeric adsorbent is developed. Model parameters (equilibrium parameters, capacity factor, axial dispersion, film mass transfer coefficient, and intraparticle effective diffusivity) are experimentally determined from independent experiments. Numerical solution of the model equations uses the method of lines with double orthogonal collocation in finite elements. The model is used for the prediction of breakthrough curves and is part of a package for the design of cyclic processes.

Two‐dimensional, transient model for mass transport in laser surface alloying

Abstract: The process of alloy generation during laser surface alloying was examined. A numerical model was developed that solved the two‐dimensional, transient equation for convection diffusion of matter in the melt pool using the alternate‐diagonal implicit method. Velocity distributions used were for steels for a laser power of 1.5 kW, a 0.001‐m beam diameter and a traverse speed of 0.01 m/s. Calculations were made for a uniform surface mass flux of 5 and 10 kg m2 s−1 and values of 100 and 1000 for the Peclet number for diffusion. The results showed that powder particles injected into the melt pool melted practically instantaneously, that good mixing was determined by the pattern of fluid flow, that average solute contents increased linearly with increasing interaction time, and that a change in the solute diffusivity by a factor of 10 did not greatly alter the predicted solute distribution. Good mixing was also found with surface flux over only a part of the melt pool. The conclusions were that fluid flow dominates the process of mass transport and determines the nature of the solute distribution, that powder feed is an effective method for surface alloying, and that results of the model could be used to better understand the process of laser surface alloying.

Effects of intraparticle heat and mass transfer during devolatilization of a single coal particle

Abstract: The objective of the present work is to elucidate the influence of intraparticle mass and heat transfer phenomena on the overall rate and product yields during devolatilization of a single coal particle in an inert atmosphere. To this end a mathematical model has been formulated which covers transient devolatilization kinetics and intraparticle mass and heat transport. Secondary deposition reactions of tarry volatiles also are included. These specific features of the model allow a quantitative assessment to be made of the impact of major process conditions such as the coal particle size, the ambient pressure and the heating rate on the tar, gas and total volatile yield during devolatilization. Model predictions are compared to a limited number of experimental results, both from the present work and from various literature sources.

Gas-liquid mass transfer in fluidized particle beds

Abstract: Gas/liquid mass transfer has been studied in air/water fluidized beds of 0.05-8 mm glass spheres in a 0.14 m diameter reactor. The volumetric mass transfer coefficients kL a were independent of bed height, and, for particle diameters up to 1 mm, decreased linearly with solids concentration. Low solids loadings as well as large diameter particles significantly increased kL and a, respectively, as compared to the two-phase system.

Solid-liquid mass-transfer in packed-beds with cocurrent gas-liquid downflow

Abstract: Local instantaneous solid-liquid mass transfer coefficients were measured in two-phase gas-liquid downflow through packed columns for 3 X 3 mm and 6 X 6 mm cylinders. An electrochemical technique was used. Liquid flow rates from 3.0 to 26.6 kg/m/sup 2/ X s and gas flow rates from 0.07 to 1.16 kg/m/sup 2/ X s covered the gas-continuous, ripple, and pulse flow regimes. Time-averaged mass transfer coefficients in trickle flow and in pulse flow for the pulse proper and the base (outside the pulse) were found to increase with increasing gas and liquid rates. Correlations are presented in terms of liquid phase Reynolds numbers and in terms of Kolmogoroff numbers. The mass transfer coefficients in the pulse were found to correspond closely to the coefficients that would be attained in the dispersed bubble flow regime.

External Mass‐Transfer Rate in Fixed‐Bed Adsorption

Abstract: External mass-transfer coefficients are measured with organic compounds, p-nitrophenol and 2,4-dichlorophenol, under conditions representative of fixed-bed activated-carbon adsorption for water treatment. The superficial velocity was in the range 1.3 – 8.0 mm/s and the Reynolds number range was 0.8 – 5. The observed external transfer coefficients are compared with predicted values from four mass-transfer models; the relationship of Gnielinski bestpredicts the velocity dependence. The observed transfer coefficients in all cases exceeded the predictions based on ideal spherical geometry. Depending on the conditions and the choice of predictive model, the particle size correction factors ranged from 1.44 – 2.04. The data from previously published studies show deviations that are similar in direction, but smaller in magnitude.

Heat and momentum transfer to particles in thermal plasma flows

Abstract: In this review effects exerted on the motion and on heat and mass transfer of a particle injected into a thermal plasma are discussed, including an assessment of their relative importance in the context of thermal plasma processing of materials. Results of computer experiments are shown for particle sizes ranging from 5 tm to 50 m, and for alumina and tungsten as sample materials. The results indicate that (i) the correction terms required for the viscous drag and the convective heat transfer due to strongly vary— ing properties are the most important factors; (ii) non—continuum effects are important for particle sizes < 10 im at atmospheric pressure and these effects will be enhanced for smaller particles and/or reduced pressures; (iii) the Basset history term is negligible, unless relatively large and light particles are considered over long processing distances; (iv) thermophoresis is not crucial for the injection of particles into thermal plasmas; (v) turbulent dispersion becomes important for particle < 10 m in diameter; (vi) vaporization describes a different particle heating history than that of the evaporation process which, however, is not a critical control mechanism for interphase mass transfer of particles injected into thermal plasmas.

Gas-liquid mass transfer characteristics in a bubble column with suspended sparingly soluble fine particles

Abstract: (To investigate the influence of suspended particles on mass transfer characteristics in a slurry bubble column, physical and chemical absorptions were performed into aqueous slurries of fine calcium hydroxide particles ca. 7 ..mu..m in average size. Such mass transfer parameters as volumetric liquid-side mass transfer coefficient, specific gas-liquid interfacial area, and hence liquid-side mass transfer coefficient were determined under various electrolyte concentrations, solid concentrations, and gas flow rates.) and K /SUB L/ /SUP o/ a could be correlated by the gas flow rate. (The volumetric gas-side mass transfer coefficient was determined and correlated by the gas flow rate. The enhancement factors during absorption of dilute carbon dioxide into aqueous calcium hydroxide slurries were compared with the theoretical predictions based on the film theoryincorporating a finite slurry concept.)

Effect of organic substances on mass transfer in bubble aeration

Abstract: Dispersion of gas bubbles in water has a wide application in aeration and ozonation processes. The rate of mass transfer in such systems depends strongly on the wastewater quality as well as on the design and operational characteristics of gas liquid contact units. Small amounts of surface active compounds in water were shown to reduce the overall mass transfer coefficient, kLa, in single bubble systems1,2,3 and in swarms of bubbles.4 This effect was attributed to the decrease in the liquid-phase mass transfer coefficient, kL.l~5 The adsorption of the large molecules of surfactants reduced the surface tension of water,1,467 reduced the bubble size,1,3,4,8 lowered the terminal velocity of bub bles,9-11 and increased the drag coefficient.5,10 Accordingly, surfactants were believed to reduce the kL by depressing the hydrodynamic activity, and by offering additional barriers for the passage of gas molecules at the gas-liquid interface. Higher concentrations of the surfactants improved kLa\ this was attributed to the increase in the interfacial area caused by the formation of smaller bubbles.1,4 On the other hand, Zieminski and his co-workers8,12"14 reported a definite improvement in kLa in the presence of various alcohols and carboxylic acids. The authors stated the principle action of such substances to be prevention of bubble coalescence. This study was undertaken to investigate the effects of various organic substances on the characteristics of oxygen transfer from air bubbles to water. The compounds listed in Table 1 were chosen to represent various groups of water contaminants. To elucidate the effective mechanisms, experi ments were conducted by using either a fritted glass diffuser or a capillary for gas dispersion. The effects of gas flow rate, pH, and ionic strength were also examined.

Heat transfer to a particle under plasma conditions with vapor contamination from the particle

Abstract: Heat transfer to a copper particle immersed into an argon plasma is considered in this paper, including the effects of contamination of the plasma (transport coefficients) by copper vapor from the particle. Except for cases of high plasma temperatures, the vapor content in the plasma is shown to have a considerable influence on heat transfer to a nonevaporating particle, and, to a lesser extent, on heat transfer to an evaporating particle. Evaporation itself reduces heat transfer to a particle substantially as shown in a previous paper [Xi Chen and E. Pfender, Plasma Chem. Plasma Process.,2, 185 (1982)]. Comparisons of the calculated results with those based on a method suggested in the above reference show that the simplified assumptions employed, i.e., that the surface temperature is equal to the boiling point and that plasma properties based on a fixed composition are applicable, can be employed to simplify calculations for many cases. This study reveals that a considerable portion of a particle must be vaporized before a steady concentration distribution is established around the particle.