bluuebunny/crossref_metadata_2025 huggingface dataset:
A theoretical‐empirical approach to the mechanism of particle entrainment from fluidized beds
Authors: Zenz F. A. , Weil N. A.
Published: June 2004

A means of calculating the rate of entrainment of solids from commercial‐size continuously operating fluidized beds was developed from the combined results of a theoretical and an empirical approach which through different channels arrived at the same fundamental mechanism. The calculation method shows agreement with data obtained from an apparatus simulating flow characteristics in large‐scale equipment and compares favorably with smaller scale tests reported in the literature at pressures up to 200 1b./sq. in. gauge.
Density: Reduced‐state correlations for the inert gases
Authors: Hamrin Charles E. , Thodos George
Published: June 2004

The principle of corresponding states has been adopted to the correlation of densities and found to be applicable for nonopolar substances when the critical compressibility factor is introduced as an independent parameter. For the inert gases, densities available in the literature for the gaseous and liquid states have been referred to their critical densities to produce reduced‐state correlations which are identical only when their corresponding critical compressibility factors are the same. As a result, a consolidated reduced density correlation forzc= 0.291 has been developed from experimental data for argon, krypton, and xenon. Although thezcvalues for helium and neon are essentially alike, different reduced‐state correlations for these substances were found to exist. This behavior is expected in view of the radical nature of helium, which can be accounted for by its excessive quantum deviation. Therefore the reduced density correlation for neon (zc= 0.307) is selected as representative of that class of substances having similarzcvalues.

The validity of both correlations has been extended beyond the monatomic gases to include substances having comparable critical compressibility factors. With the generalized chart forzc= 0.291 gaseous densities at elevated temperatures and pressures have been calculated for nitrogen, oxygen, carbon monoxide, and methane to produce an average deviation of 1.4% from reported values in the literature. For these substances the average deviation becomes 1.5% for densities in the liquid state. With the reduced density chart for neon (zc= 0.307) densities calculated for hydrogen (zc= 0.305) in the gaseous region produced an average deviation of 2.5% and covered pressures in excess of 500 atm. and temperatures as high as 500°C.
Compressibility of n‐hexane
Authors: Griskey Richard G. , Canjar Lawrence N.
Published: June 2004

Although a considerable amount of work has been done on the compressibility of n‐hexane, it has been impossible until now to compare or evaluate the work of the various investigators. There has also been a serious lack of information in the region above the critical temperature. It is the purpose of this work to make an extensive study of temperatures of 240° to 300°C. and of pressures up to 225 atm. in order to provide the lacking information and to overlap with the work of other investigators so that a proper evaluation of their work may be made.
Low‐temperature vapor‐liquid equilibria in ternary and quaternary systems containing hydrogen, nitrogen, methane, and ethane
Authors: Cosway Harry F. , Katz Donald L.
Published: June 2004

Experimental data are presented for three ternary systems and the quaternary at pressures of 500 and 1,000 1b./sq. in. abs. and at temperatures of −100° and −200°F. These data along with information in the literature were correlated to give charts of equilibrium ratios as a function of temperature, pressure, and composition.
Sublimation from sharp‐edged cylinders in axisymmetric flow, including influence of surface curvature
Authors: Christian William J. , Kezios Stothe P.
Published: June 2004

An experimental investigation was performed on the mass transfer by sublimation from the outer surfaces of hollow naphthalene cylinders, 0.75 and 1.00 in. in diam., in parallel air streams at velocities between 20 and 120 ft./sec. Local mass transfer rates on the cylinders were obtained by a profilometric technique consisting of accurate determinations of changes in radii of the subliming surfaces at points along elements of the cylinders.

Local coefficients of mass transfer obtained with laminar boundary layers for Reynolds numbers (based on axial length) between 12,000 and 100,000 were found to be up to 8% greater, because of surface curvature, than corresponding values for flat surfaces. Moreover comparison of the mass‐transfer data with a theoretical prediction for laminar skin friction on circular cylinders indicates an effect of surface curvature on the Chilton‐Colburn anology between momentum and mass transfer amounting to as much as 6% in the range of air velocity employed. For turbulent boundary layers obtained by artificial triggering of turbulence at the leading edges of the cylinders no effect of surface curvature was found. The results obtained for Reynolds numbers of 40,000 to 1,000,000 are lower than previously published correlations of turbulent heat, mass, and momentum transfer, when compared by the Boelter, Martinelli, and Jonassen form of the analogy.
Theoretical plate concept in chromatography: Part II
Authors: Said A. S.
Published: June 2004

Part A of this paper is essentially a continuation of a previous paper on the theoretical plate concept in chromatography (4). It deals with some special cases of eluting conditions and zone shapes. A more general equation, which combines both elution and deposition, is derived, and methods for approximating a continuous zone by means of a discontinuous one are discussed.

Part B discusses the effect of the finite size of samples and the dead free volume at the bottom of the column on the shape of elution curves. The effect of representative sample volumes is calculated, and the deviation between the experimental and the true elution curves is illustrated.

A simple expression for the number of theoretical plates utilizing the ratio between the maximum concentrations at the top and bottom of the column is derived and corrected for the effect of the finite size of samples.
Liquid viscosities of methane and propane
Authors: Swift G. W. , Christy J. A. , Kurata Fred
Published: June 2004

The theory and calibration procedure for a cylindrical falling body viscometer is presented.

Experimental viscosity data are given for liquid methane from −150°C. to the critical point and for liquid propane from −185° to +90°C. The maximum experimental error for methane data is ±8% and for propane data ±5%.
Mass transfer at low flow rates in a packed column
Authors: Dorweiler V. P. , Fahien R. W.
Published: June 2004

Mass transfer in packed columns has been investigated for a variety of column and packing sizes but at flow rates restricted to fully developed turbulent conditions. The present work was undertaken to investigate mass transfer at flow‐rate conditions in the transition and laminar regions.

A dual treatment of experimental data required a knowledge of the variation of concentration and velocity with radial position. A tracer‐injection technique was employed which consisted in the introduction of a tracer gas into the center of a bulk gas stream and the measurement of the tracer‐gas concentration at various radial positions downstream. The velocity distribution for the packed column was determined by means of a five‐loop, circular, hot‐wire anemometer. The test column was a vertical 4‐in, pipe. packed with 1/4‐in. spherical, ceramic catalyst‐support pellets.

Mass transfer diffusivity and Peclet number were determined from two solutions of the differential‐diffusion equation applied in previous investigations. An analytical solution in terms of Bessel functions was used to calculate values of average diffusivity and Peclet number and a seminumerical solution in terms of homogeneous linear‐difference equations to calculate values of point diffusivity and Peclet number.

Variation of diffusivity and Peclet number with radial position is shown, average diffusivity and Peclet number being correlated with Reynolds number. The interaction of molecular and eddy mass transfer mechanisms with decreasing mass velocity is illustrated by defining a molecular and an eddy Peclet number and correlating with Reynolds number. Eddy diffusivity is correlated as a function of local flow conditions.
Solubility of liquids in compressed hydrogen, nitrogen, and carbon dioxide
Authors: Prausnitz J. M. , Benson P. R.
Published: June 2004

The vapor‐phase solubilities of carbon tetrachloride, iso‐octane, toluene, and n‐decane were measured in compressed hydrogen, nitrogen, and carbon dioxide at 50° and 75°C. and at various pressures between 20 and 90 atm. The virial equation of state was used to describe the volumetric properties of the vapor mixtures, and the second virial cross coefficients were evaluated from the solubility data. The results indicate that the vapor phase departs from ideality very quickly for these systems as the pressure increases, particularly at pressures greater than 10 atm.
Turbulent flow of pseudoplastic polymer solutions in straight cylindrical tubes
Authors: Shaver Robert G. , Merrill Edward W.
Published: June 2004

Experimental studies are described concerning the fluid dynamics, particularly in the turbulent region, of dilute solutions of free‐draining, nonassociating, linear polymers; sodium carboxymethylcellulose, ammonium alginate, polyisobutylene, and carboxypolymethylene, all of which are pseudoplastic. These solutions were run in laminar, transition, and turbulent flow in a pipeline flow apparatus designed to permit measurement of dynamic pressure drop and impact pressure by radial traverse.

Photographic studies with dye injection used at the tube wall and at the tube center showed that turbulent flow of these pseudoplastic fluids has the following characteristics compared to Newtonian fluids: poor over‐all radial mixing, thicker nonturbulent layer at the wall, and decreased rate of formation of horseshoe vortices at the wall.
Heat transfer and fluid dynamics in mercury‐water spray columns
Authors: Pierce R. D. , Dwyer O. E. , Martin J. J.
Published: June 2004

Heat transfer and fluid dynamics were studied in columns in which hot mercury was sprayed into a rising stream of water. Volumetric and area heat transfer coefficients are presented which were found to be lower than those reported for heat transfer from fixed spheres.

It was observed that considerable water bypassed the stream of drops, while some surrounding the drops flowed downward. This behavior resulted in water temperatures at the base of the column which were considerably higher than the inlet water temperatures. Consequently the outlet mercury temperature did not approach the inlet water temperature as a limit. The very unconventional flow pattern of the water was unexpected and is believed to be an important factor in spray‐column heat transfer and mass transfer kinetics.
Effective diffusivity of packed bed
Authors: Kimura M. , Ueda K. , Ofuka T.
Published: June 2004

From time to time, A.I.Ch.E. Journal presents translations of certain technical articles written by our Japanese colleagues in their own language. These translations are made by Kenzi Etani, who received his B.S. in chemical engineering in 1953 at the Tokyo Institute of Technology and his M.S. in 1955 at M.I.T. He is associated with Stone & Webster and is an associate member of American Institute of Chemical Engineers. He is also a member of the Society of Chemical Engineers, Japan, and the Japan Oil Chemists' Society. His offer to help break down the language barrier is acknowledged.

Abstracts, notation, literature cited, tables, and figure captions not published here appear in English in the original paper. No figure will be reproduced in these translations.

The following article was published in Chemical Engineering (Japan), 21, pages 17–25 (1957).
A Computer study of a free‐radical mechanism of ethane pyrolysis
Authors: Snow R. H. , Peck R. E. , Von Fredersdorff C. G.
Published: June 2004

The pyrolysis of ethane (including the equilibrium behavior and the tendency to form secondary products) has been reproduced by calculations based on a reaction mechanism which includes the reverse of the chain propagating reactions as well as other hitherto neglected elementary reactions. Reverse reactions are important even at low conversion (1%); hence previous investigations of initial reaction rate have doubtful fundamental significance. Values of rate constants used in the calculations were taken mostly from the literature. Consideration was limited to reactions of methyl, ethyl, and hydrogen free radicals with ethane and its primary pyrolysis products. The results can be incorporated into reactor performance calculations to replace empirical reaction rate correlations and thus widen the range of conditions over which the calculations are reliable.
Initiation of the homogeneous n‐butane oxidation
Authors: Skrivan J. F. , Hoelscher H. E.
Published: June 2004

Initiation of the oxidation of hydrocarbons, an important part of many flame systems' remains largely unsolved. This paper reports a study of the oxidation of butane under conditions that yield information on the homogeneous initiation reactions.

A sequential reaction mechanism is proposed involving activation of an oxygen molecule followed by attack on a butane. This leads to rate equations which accurately describe the observed butane decomposition rates. Activation energies have been calculated from experimental data with this equation and are found to check values obtained from the literature and from theoretical considerations.

The tentative initiation mechanism is used to explain the existence of three classes of products in the exit gases: hydrocarbons other than butene, butene, and oxygenated products.

Under some operating conditions periodic cool flame phenomena are observed, and their effect on the course of the reaction has been explained.
Ion exchange kinetics for systems of nonlinear equilibrium relationships
Authors: Tien Chi , Thodos George
Published: June 2004

Mathematical relationships based on material balance and rate equations have been derived for the study of ion exchange kinetics in a fixed‐bed operation. Numerical techniques for the solution of the systems possessing equilibrium relationships of the Freundlich‐adsorption isotherm type have been developed, and numerical results have been obtained with the use of a digital computer. The resulting numerical solutions have been found to be dependent on parameters involving time, position, and the relative resistances of the liquid and resion phases. The numerical solutions are presented in both tabular and graphical forms.
Studies of the cation exchange system Fe+++‐H+: I. Equilibrium studies
Authors: Vasishth R. C. , David M. M.
Published: June 2004

Equilibrium data are presented for the exchange of Fe+++ and H+ on a sulfonated polystyrene exchanger. The data cover solution concentrations from 0.05 N to 2 N in total cation for solutions having either nitrate or perchlorate ion as the common anion. The nitrate system shows irregular behavior because of complex ion formation, but for composition where such behavior is absent the equilibrium data can be correlated by equations based on the law of mass action. Equilibrium compositions for the perchlorate system can be correlated over the entire range studied by a single equation based on the law of mass action. Methods based on the law of mass action are presented for correlating or predicting equilibrium compositions for both systems.
Studies of the cation exchange system Fe+++−H+: II. Rate studies in concentrated solutions
Authors: Vasishth R. C. , David M. M.
Published: June 2004

Fixed‐bed kinetic studies were made for Fe+++ — H+ exchange, with perchlorate as the anion, covering concentrations from 0.5 N to 2.0 N in total cation, flow rates of 5 ml./min. sq. cm. to 45 ml./min. sq. cm. bed depth of 25 to 60 cm., and average resin particle diameters of 0.28 and 0.56 mm. The results are correlated on the assumption of internal diffusion as the rate‐controlling step and an essentially irreversible equilibrium.
Fluid dynamics and diffusion calculations for laminar liquid jets
Authors: Scriven L. E. , Pigford R. L.
Published: June 2004

In connection with a study of the mechanism of gas absorption the problem arose of predicting absorption rates into laminar liquid jets. A solution to the problem is presented in this paper, which provides an example of the application of fluid dynamics to the analysis of mass transfer in a complex flow system.

The water jets considered here issued from circular nozzles of about 1.5‐mm diameter, flowed intact downward through an atmosphere of solute gas at average velocities of from 75 to 550 cm./sec. over distances of 1 to 15 cm., and were collected in a receiver slightly larger in diameter than the nozzles. Equations describing the liquid flow near the jet surface are deduced from measurements of jet diameter and analogy to related flow situations. When one uses these equations, absorption rates are predicted from unsteady state diffusion theory with the assumption of interfacial equilibrium. The predicted rates for carbon dioxide at 25°C are in close agreement with experimental determinations over the observed range of contact time of the liquid with gas, namely 0.003 to 0.04 sec.
Film boiling of Helium I and other liquefied gases on single wires
Authors: Frederking T. H. K.
Published: June 2004

Heat transfer coefficients have been obtained for natural‐convection film boiling of helium I on single wires with a diameter ranging from 5 to 50 μ. The measurements covered temperature differences of 30° to 1,000 °K. between the heating surface and the saturated liquid under atmospheric pressure. The results are correlated in dimensionless from (Nusselt number vs. the product of the Grashof and Prandtl numbers) and compared with data for nitrogen and measurements of other investigators on film boiling of liquefied gases.
Evaporation rates of liquids to flowing gas streams
Authors: Severson D. E. , Madden A. J. , Piret Edgar L.
Published: June 2004

The influence of high concentration gradients and high evaporative velocities on rates of mass transfer was studied by evaporating liquids into low‐speed inert gas streams at pressures approaching the vapor pressure of the liquids.

Inert gas concentration in some experiments changed nearly fivefold across the boundary layer. The velocity normal to the surface (owing to evaporation), usually neglected in comparison with main‐stream velocity, varied from 0.038 to 19 times the main‐stream velocity.

The data for air‐water, air‐carbon tetrachloride, air‐chlorobenzene, and helium‐chlorobenzene systems were represented within experimental error over the Graetz number range of 0.1 to 1,800 by the flat‐duct equations of Butler and Plewes (2) and also by the usual dimensionless plots.
Some properties of polar substances: A survey
Authors: Bird R. Byron , Brock James R.
Published: June 2004

The current understanding of the macroscopic (bulk) properties of polar substances in terms of molecular theory, or the correlation of them in terms of corresponding‐states principles is summarized.
Expansion and contraction of an air‐water mixture in vertical flow
Authors: Petrick Michael , Swanson Bernet S.
Published: June 2004

An experimental two‐phase flow study was made on an air‐water system at atmospheric pressure to obtain information on the effect of expansion and contraction of flow area on the relative velocity of the two phases. The data show that the relative velocity and hence the mean void fraction of the air‐water mixture changed following either an expansion or contraction; however the magnitude of the change was not great and could be predicted by a semitheoretical equation. The air‐water data are also compared with data taken from a steam‐water system at 150 to 600 lb./sq. in. In addition, a photographic study was made of the transition zone, and phase distributions were obtained by the use of a radiation attenuation traversing technique.
Vaporization of superheated drops in liquids
Authors: Moore G. R.
Published: June 2004

The work reported in this paper is an outgrowth of an exploratory investigation of the feasibility of spray drying of materials in solution by using direct‐contact heat transfer from a hot liquid rather than a gas to vaporize the solvent from the drops. Unexpectedly, it was found that drops suspended in a hot liquid had to be superheated to a very extreme degree in order to initiate vaporization. This effect was of such interest that the investigation was modified to a fundamental study of the vaporization of drops containing no dissolved solids. The results are closely related to problems of bubble formation in boiling, cavitation, and in the evolution of gases from supersaturated solutions. The experimental technique developed in this study is believed to be unique and capable of giving quite accurate data on homogeneous nucleation in superheated drops. After a discussion of the theory of homogeneous nucleation in pure liquids, the theory is extended to the formation of bubbles in superheated drops. The theoretical predictions were found to be in close agreement with the experimental results.
The economic design of mixer‐settler extractors
Authors: Treybal Robert E.
Published: June 2004

Relationships are developed for establishing the most economic values of the major variables of a liquid‐extraction process, including the concentrations of solute in recycled solvent and rejected raffinate, the solvent‐to‐feed ratio, and for mixer‐settlers certain of the design features. Consideration is given to costs of extraction and solvent recovery, as well as to the value of unextracted solute and lost solvent. For the design of mixer settlers scale‐up relationships are developed to permit prediction of the stage efficiency of a large extractor from experimental data taken on a small scale. These are expressed in terms of a scale‐up index relating the relative size of the mixer with the volumetric rates of liquid flow. It is shown that the cost of multistage extractor increases with scale up in a different fashion from the stage efficiency, depending upon the scale‐up index used. A detailed study of the costs for a typical case led to the development of economic scale‐up indexes which, because they cover nearly a fivefold ratio of fixed to operating costs, are of fairly general utility. The common practice of scaling up with equal holding times on the large and small scale is shown to be amply safe from the point of view of stage efficiency to be realized on the large scale but usually uneconomic.

Simplification of the complete system of equations permits rapid estimation of the most economic circumstances for any type of countercurrent extractor of which the cost per stage is proportional to Qg.
The vapor‐phase catalytic hydration of ethylene oxide to glycols
Authors: Metzner A. B. , Ehrreich J. E.
Published: June 2004

The vapor‐phase reaction between ethylene oxide and water to form glycols has been carried out under a wide range of conditions with particles of polystyrene–sulfonic acid ion exchange resins used as catalysts. The rates observed appeared to be directly proportional to the product of the partial pressure of ethylene oxide and the amount of water sorbed by the resin. By use of the Brunauer, Emmett, and Teller equation to describe the amount of water sorbed by the resin, the experimental data were correlated over a sixty‐fold range of reaction rates with a mean deviation of 15%.

To obtain data of value in elucidating reaction mechanisms, the reactor was usually run under “differential” conditions, that is low conversions. However in a few runs conversions of as high as 54% were obtained for a contact time of 0.02 sec. The ratio of ethylene glycol to higher glycols (selectivity) obtained varied between 73 and 99% but was usually above 80% under conditions of high conversion. However it could also be reduced forcibly to produce higher glycols as the major product, if desired.
Transfer resistance and fluid mechanics
Authors: McCarter Robert J. , Stutzman Leroy F.
Published: June 2004

Pure liquids were evaporated in a wetted‐wall column into flowing streams of air to investigate the thickness and transfer resistance of gas films.

It was found necessary to express Reynolds number relative to the liquid surface to correlate transfer with gas flow.

Laminar and buffer layers in the gas phase were calculated from fluid‐flow principles and compared to the effective film thickness calculated from mass transfer and molecular diffusivity. Good agreement was obtained, indicating applicability of fluid mechanics to mass transfer problems.

Eddy diffusivity was indicated to have a negligible effect upon the total resistance to transfer. Consequently it might be concluded that in packed towers where distances in the turbulent phase are shorter transfer between phases depends almost entirely upon molecular diffusivity.
The mechanics of vertical moving liquid‐liquid fluidized systems: I. Interphase contacting of droplets passing through a second quiescent fluid
Authors: Weaver Robert E. C. , Lapidus Leon , Elgin J. C.
Published: June 2004

Previous publications have shown that for solid spheres fluidized in water a unique relationship exists between the slip velocity and the system holdup. With this work as a model a method is now presented for estimating the behavior of the liquid‐in‐liquid spray column in which droplets of one phase move through a second quiescent phase.

Combining the solids fluidization results with information on the single droplet terminal velocity one can obtain a design estimate of the holdup or interphase contact area for the liquid‐liquid spray column. This design estimate includes the particular nature of the liquid droplet of being susceptible to internal circulation, oscillation, and distortion.
Reaction rates in the synthesis of ammonia
Authors: Mills A. K. , Bennett C. O.
Published: June 2004

A study has been made of the reaction rates of mixtures of hydrogen and nitrogen to form ammonia over a doubly promoted iron catalyst at 400° and 450°C. and at pressures up to 1,000 atm. In this work particular care has been taken to obtain data representing the true kinetics of the reaction. The reactor used was essentially isothermal, and the effects of diffusion have been reduced to a minimum. The results have been correlated by the use of the mechanism proposed by Temkin and Pyschev (19) with moderate success.
Heterogeneous phase equilibria of the hydrogen sulfide–carbon dioxide system
Authors: Sobocinski D. P. , Kurata Fred
Published: June 2004

An experimental study on the system hydrogen sulfide‐carbon dioxide was performed from the critical region to the solid‐liquid‐vapor region. For seven mixtures individual phase diagrams were determined by the establishment of dew, volume percentage liquid, hubble, critical, and triple points. A splendid study of this system had been reported earlier by Bierlein and Kay (1) for temperatures above 32°F. However from a temperature point of view this earlier work represents about one half of the phase diagram from the critical locus to the locus of triple points. Hence in this study particular attention was devoted to the lower temperature regions.

Equilibrium constants were determined from 100 to 1,200 lb./sq. in. abs. Vapor and liquid equilibrium compositions from this investigation were compared with those obtained by Bierlein and Kay (1) at 20, 40, 60, and 80 atm.

Solid‐liquid‐vapor loci were found to meet at a minimum temperature, lower than either of the individual pure component triple points, due to the formation of a eutectic mixture consisting of 12.5 mole % carbon dioxide. Vapor and liquid compositions in equilibrium with solid were established along the vapor‐liquid‐solid carbon dioxide and vapor‐liquid‐solid hydrogen sulfide loci.
Evaporation from drops containing dissolved solids
Authors: Charlesworth D. H. , Marshall W. R.
Published: June 2004

A study was made of the evaporation from single drops containing solids. By means of a specially designed sensitive balance, drops were suspended over a hot‐air stream and their drying behavior was observed. Weight changes were measured during evaporation. Experimental data are presented on the time of appearance of the first solid phase and the formation of a solid crust for a wide range of drying conditions and materials. A theory is advanced for predicting the formation of a solid phase in drying a droplet containing a dissolved solid. This theory shows reasonable agreement with the experimental results. A tentative proposal for the application of the results to spray‐dryer performance is suggested.
The constant‐volume heat capacities of gaseous perfluorocyclobutane and propylene
Authors: De Nevers Noel , Martin Joseph J.
Published: June 2004

The constant‐volume heat capacities of gaseous perfluorocyclobutane and propylene have been measured over a considerable range of temperatures and densities with a new type of adiabatic calorimeter. This calorimeter differs from previous constant‐volume gas calorimeters in having very thin walls and being equipped with an internal motor stirrer to provide temperature uniformity. The experimental results have been compared with the predictions of the Benedict‐Webb‐Rubin and Martin‐Hou equations, by use of published values of the zero‐pressure‐constant‐volume heat capacity. The over‐all agreement is satisfactory, with a maximum difference between the experimental and calculated heat capacities of 6.7%; however the comparison reveals several interesting systematic differences between the experimental and calculated values of the derivatives of the constant‐volume heat capacity with respect to temperature and density.
Centrifugal filtration through beds of small spheres
Authors: Bingeman J. B. , Coates Jesse
Published: June 2004

In 1856 Darcy observed that water flowed through a sand bed at a rate proportional to the area of the bed and to the difference between the upstream and dowstream hydraulic heads and inversely proportional to the bed thickness. Since that time many investigators have accumulated masses of data in support of numerous theoretical and empirical relationships for correlating and predicting pressure drop, flow rate, and fluid and bed properties. Naturally certain areas of research have received less attention than others.

Among the areas receiving least attention are flow through beds composed of particles of identical shape but mixed size, flow through unconsolidated beds composed of small particles, and flow under the influence of a centrifugal driving force. Accordingly, the flow of liquids through unconsolidated beds of small spherical particles of mixed size was investigated in two laboratory centrifugal filters. Experimental conditions were such that the flow was laminar and the cakes were incompressible. While there was some difficulty in obtaining reproducibility of cakes, the data for any particular cake were correlated satisfactorily by the Darcy equation adapted for centrifugal filtration.
Calculation of equilibrium flash vaporization curves by an integration method
Authors: Bennett C. O. , Brasket C. J. , Tierney J. W.
Published: June 2004

Techniques for solving the equilibrium flash problem are reviewed and a new technique especially adapted for use on automatic digital computers is developed. Instead of a single equation with multiple roots being solved by an iterative process, as is usually done, the problem is rephrased as a differential equation, and a numerical integration is made. The isothermal and isobaric flash problems can be handled with essentially the same equations. The method is particularly advantageous when a complete flash curve is required and the equations can be used when a linear model of the equilibrium flash process is required.
Heat transfer characteristics of porous rocks
Authors: Kunii Daizo , Smith J. M.
Published: June 2004

Equations are derived for predicting the effective thermal conductivity of beds of unconsolidated particles containing stagnant fluid. The effective thermal conductivity at these conditions, called the stagnant conductivity, is a function of the thermal conductivities of the solid and fluid phases, the void fraction, and, if radiation is important, the emissivity, mean temperature, and diameter of the solid particles. Comparison with the available experimental data indicates that the equations are satisfactory for fluids and solid particles of both high and low thermal conductivities.

To extend the theory to beds of consolidated particles, it is supposed that consolidated beds are formed by partial clogging and cementing of beds of unconsolidated particles. With this assumption the theoretical equations for packed beds are extended to include such materials as sandstone and porous metals. The resulting expressions for the stagnant conductivity involve a consolidation parameter characteristic of the solid material. This quantity accounts for the heat transfer across the contact surfaces between cemented or clogged particles. The equations correctly predict the effect of void fraction and solid and fluid thermal conductivities on the heat transfer properties of sandstones and sintered metal systems.
Photographic study of solid‐gas fluidization
Authors: Massimilla Leopoldo , Westwater J. W.
Published: June 2004

Motion pictures at 2,000 frames/sec. were used to measure the movements of individual solid particles and gas bubbles in a fluidized bed. Air was used to fluidize 0.028‐in. glass spheres and 200‐mesh alumina in a 3.75‐in. glass column. Aggregates were very common, and each moved as a unit. Particles and aggregates near the wall showed pronounced alternations of fast and slow movements both upward and downward. Individual particles exhibited spin. Baffles increased the bed density and decreased the particle velocities. Small bubbles rose rapidly with little change in shape. Large cavities were slow and tended to collapse and reform elsewhere.
Mass transfer in liquid‐lithium systems
Authors: Gill William N. , Vanek Richard P. , Jelinek Robert V. , Grove C. S.
Published: June 2004

The behavior of type‐304 stainless steel in a forced‐convection closed‐loop lithium system was investigated over a wide range of temperatures and velocities. Fundamental information concerning the mechanism for mass transport has been obtained by examining solution and deposition effects along flat plates. The rate‐determining process for solution is transport from the solid to the interface, whereas deposition rates are liquid‐phase controlled.

Liquid‐phase mass transfer coefficients were correlated with a maximum deviation of approximately 15% by the use of von Kàrmàn's analysis of the turbulent boundary layer along a flat plate, combined with the Chilton‐Colburn empirical modification of the Schmidt group. In contrast no adequate model is available for the prediction of solution rate constants which must be determined experimentally. Mean values of the solution rate constants ranged from 0.154 to 0.750 × 10−5 cm./sec. at temperatures from 510° to 612°C. These values are on the order of 103 smaller than corresponding liquid‐phase mass transfer coefficients.
Plate efficiencies in multicomponent distillation
Authors: Toor H. L. , Burchard John K.
Published: June 2004

A first approximation to the multicomponent plate‐efficiency problem has been carried out with a film model combined with equations for steady state diffusion in a ternary gas mixture. Numerical integration of the equations through a plate yields the ternary efficiencies as functions of the binary efficiency.

The effects of diffusional interactions in a distillation column were studied by computing the efficiencies on each plate when a column is designed to separate a ternary mixture. In the example studied, the average column efficiency was 39% less than the binary efficiency.

Some criteria are suggested for comparing other multicomponent systems to the one studied in order to estimate the uncertainty in the use of binary correlations for these systems.
Correlating vapor pressures and heats of solution for the ammonium nitrate—water system: An enthalpy–concentration diagram
Authors: Othmer Donald F. , Frohlich Gerhard J.
Published: June 2004

The usual tedious method of construction of enthalpy‐concentration charts for solutions of solids requires data seldom available. A new, simple method is therefore presented that utilizes more readily available data, that is vapor pressures of the solutions. These plot as straight lines on a logarithmic‐reference substance plot. Differences from unity of the slopes of these lines represent heats of solution, and when this difference function is integrated between concentration limits the integral heat of solution is obtained. The enthalpy chart is then readily constructed by use of the specific heats of liquid and solid.

Ammonium nitrate is the solid used in this example, and water is the liquid because of the industrial importance of aqueous solutions. Vapor pressures were carefully determined experimentally, and the enthalpy chart was developed from the straight lines of the logarithmic plot and available heat data. Constants for the vapor‐pressure curves for ammonium nitrate solutions and equations for enthalpies of solid ammonium nitrate are given for the temperature range 0° to 170°C.
Hydrocarbon vapor‐liquid equilibria and solubility parameter
Authors: Prausnitz J. M. , Edmister W. C. , Chao K. C.
Published: June 2004

Hydrocarbon vapor‐liquid equilibria are expressed in terms of K values, which are functions of composition, as well as pressure and temperature. The composition effect in the liquid phase is calculated by the Hildebrand‐Scatchard equation for regular solutions. The parameters in this equation, called solubility parameters, can be calculated simply from heat of vaporization for the heavier hydrocarbons, but an indirect method of calculation must be used for the lighter components. Solubility parameters for hydrogen, methane, ethane, and propane were computed from gas‐solubility data in several hydrocarbon solvents at various temperatures and pressures. This computation also yielded simultaneously the fugacities of the hypothetical liquid‐standard states.

The results presented are not complete for practical applications, owing to the scarcity of suitable solubility data, especially at high temperatures and pressures. However solubility parameters appear to give the right liquid‐phase corrections in the correlation and prediction of hydrocarbon phase equilibria. Calculated K values for light hydrocarbons in paraffinic, naphthenic, and aromatic absorption oils are compared with experimental results. The average deviation for the forty‐two values tested is 13%.
Mass transfer from a solid soluble sphere to a flowing liquid stream
Authors: Steinberger Robert L. , Treybal Robert E.
Published: June 2004

Solution rates of 1/2‐, 3/4‐, and 1‐in. cast benzoic acid spheres were measured under natural‐and forced‐convection conditions. Upward‐flowing streams of water and aqueous propylene glycol, in laminar and turbulent flow, were used to contact single spheres in either a 1.50‐ or 4.00‐in.‐ diameter column. Sphere Reynolds numbers ranged from 10 to 16,920; Schmidt numbers from 987 to 69,680; sphere‐ to column‐diameter ratios, ds/dc, from 0.123 to 0.497; and Grashof numbers from 5,130 to 125,200.

The Sherwood number was found independent of the laminar‐turbulent transition for pipe flow and the sphere‐ to column‐diameter ratio when the Reynolds number is based on the average fluid velocity and sphere diameter.

A correlation of the data based on the additivity of the natural and forced convection processes is proposed, and statistical analyses of the new experimental data result in equations which correlate other heat and mass transfer data for single spheres immersed in bounded and free‐jet streams of gases and liquids for NRe, S from 1 to 30,000 and NSe from 0.6 to 3,000, within an average deviation of about 20%.
Modified law of corresponding states for gases
Authors: Bloomer Oscar T. , Peck Ralph E.
Published: June 2004

A new correlation is presented for predicting the pressure‐volume temperature relations of nonpolar (and slightly polar) gases. The correlation modifies the law of corresponding states in which a third parameter, the slope of the pseudocritical isometric in dimensionless form, is introduced. This parameter is introduced in a simple manner by multiplying the reduced pressure and temperature of the gas by a factor which can be easily calculated or read from a graphs. This gives the corrected reduced pressure and temperature which can then be used with a generalized compressibility factor chart in place of the true values. The correlation is accurate for densities up to about 1.2 times the critical density.

A detailed comparison of the method with data on twelve pure gases showed that by introducing this parameter into the law of corresponding states the average error was decreased from 1.598 to 0.320%. The parameter S can readily be determined from experimental PVT data, and only one isotherm is required. S is related to the vapor‐pressure curve for a substance as characterized by the critical pressure and the ratio of the critical temperature to the normal boiling temperature, and a simple method is proposed for predicting S when no experimental data are available.

A new set of generalized compressibility factor and fugacity to pressure ratio charts is presented for use with the proposed correlation. A method is also presented for determining the thermodynamics functions.
Miniature hydroclones as slurry concentrators
Authors: Engel F. C. , Weisman Joel
Published: June 2004

Miniature hydroclones were evaluated for use with thoria‐urania slurries being considered as fuels for one type of homogeneous nuclear reactor. In addition to extensive room temperature data on concentrating performance, the results of tests with thoria slurries at a pressure of 2,000 lb./sq. in. and temperatures up to 550°F. are given. The data correlation presented allows prediction of the concentrating performance of a given clone provided that the properties and particle size distribution of the slurry feed are known.
Burning rates of solid propellants
Authors: Smith J. M.
Published: June 2004

A model is proposed for the burning of solid propellants which takes into account heat transfer, diffusion, and chemical reaction processes. The chemical step influencing the rate is postulated to be a reaction between a gaseous molecule and a solid component occurring at the solid‐gas interface. The combination of expressions for the rates of the heat transfer, diffusion, and reaction steps leads to relatively simple equations for the burning rate in terms of (1) the physical properties of the propellant; (2) the transport coefficients; (3) the operating conditions of the burning process, temperatures, and pressure; and (4) chemical characteristics of the gas‐solid reaction, activation energy, frequency factor, and heat of reaction.

The well‐established facts concerning burning rates, the effect of pressure and initial temperature, and the phenomenon of erosive burning are predicted by the proposed theory. Also specific experimental data for burning potassium and ammonium perchlorate composite propellants can be predicted from the theory. The values of the variables necessary to obtain agreement between observed and predicted results are generally realistic. However it should be emphasized that conclusions regarding the detailed mechanism of the burning process cannot be obtained from comparison with burning‐rate data. Elucidation of the kinetic steps in the process will require experimental investigation of the intermediate products of combustion and a detailed study of the burning surface and gaseous flame zone.
The mechanics of vertical moving fluidized systems: IV. Application to batch‐fluidized systems with mixed particle sizes
Authors: Hoffman Robert F. , Lapidus Leon , Elgin J. C.
Published: June 2004

The present paper extends the previous investigations from this laboratory on ideal fluidized systems to a system which is somewhat nonideal. Mixtures of different but well‐defined glass spheres are fluidized by water to ascertain whether the principles developed for a single particle size still hold. The analysis indicates that the ideal prediction method gives a reasonable representation of the batch‐expansion curves for mixed sizes.
Radiological study of liquid holdup and flow distribution in packed gas‐absorption columns
Authors: Hwa C. S. , Beckmann R. B.
Published: June 2004

A radiological method has been developed to study the local flow characteristics in two‐phase contacting equipment. The method presented permits the evaluation of both the vertical and horizontal components of the liquid holdup and flow distribution and can also be used to study the performance of a wide variety of two‐phase contacting apparatus. An external source of radiation is used, and hence neither phase is contaminated by the radioactive material.

The application of this method is illustrated in the specific case of air‐water contact in a countercurrent packed column.
Pressure drop and liquid holdup in concurrent gas absorption
Authors: Dodds W. S. , Stutzman L. F. , Sollami B. J. , McCarter R. J.
Published: June 2004

This work presents initial information useful to concurrent gas‐absorption design. Data are reported on the variation of pressure drop and liquid holdup obtained with various flow rates, packings, and liquids.
Extractive reaction: Batch and continuous‐flow chemical reaction systems dilute case
Authors: Piret Edgar L. , Penney W. H. , Trambouze P. J.
Published: June 2004

A reaction process occurring simultaneously with an extraction by an immiscible phase is referred to herein as extractive reaction.

Quantitative relations are developed which show how the rate of reaction, volumetric efficiency, and reactant conversion of a single‐phase batch reaction can be enhanced by deliberately adding to the batch a second phase such as an immiscible solvent or an inert gas.

Analytical solutions are also obtained for continuous‐flow extractive reactions of first order and of simple or complex stoichiometry occurring in single‐ or multistage stirred‐tank reactors. The effect of recirculated or side streams is included.

Dilute systems and several types of reactions are considered. The equations are applicable, for instance, to liquid‐liquid systems and solid‐liquid or gas‐liquid processes wherein reaction occurs in either the vapor or condensed phase.
Liquid, gas, and dense‐fluid viscosity of propane
Authors: Starling Kenneth E. , Eakin Bert E. , Ellington Rex T.
Published: June 2004

Experimental data, believed accurate within ±0.5%, are presented for pressures of 100 to 8,000 Ib./sq. in. abs. for nine temperatures from 77° to 280°F. One isotherm, within 1° of the critical, indicates the detail required in further investigation of the critical region. These data were combined with the available literature values to prepare a table of recommended viscosity values with maximum uncertainty of ±2% for temperatures from 70° to 460°F. Two generalized correlations and the Enskog viscosity theory for dense gases exhibit significant errors in predicting the data. Methods are suggested for extrapolation of the values to higher temperatures and pressures.