bluuebunny/crossref_metadata_2025 huggingface dataset:
Simultaneous mass transfer and equilibrium chemical reaction
Authors: Olander Donald R.
Published: June 2004

Equations predicting the effect of various types of equilibrium chemical reactions on the liquid‐phase mass transfer coefficient have been derived. In each case the reacting species were assumed to be present in equilibrium concentrations at all points along the diffusion path. Equations were derived for both the film and surface‐renewal theories of simple mass transfer in conjunction with these equilibrium reactions.

The well‐known Hatta equation for the rapid second‐order irreversible reaction was shown to be a limiting case of the general equilibrium reaction A + B ⇌ E.

The calculated mass transfer coefficients were found to be functions of the concentration driving force and the average concentration level over the diffusion path as well as of the magnitude of the equilibrium constant and the diffusivities of the reacting species.
The compressibility of carbon dioxide‐argon mixtures
Authors: Abraham William H. , Bennett C. O.
Published: June 2004

The compressibility factor has been measured at 50°C. and 50 to 1,000 atm. for each of seven mixtures of carbon dioxide and argon containing 12.9 to 83.1 mole % carbon dioxide. The compressibility factors are reported as smoothed values at even pressures and also in the form of empirical smoothing expressions which fit the experimental values with an average absolute deviation of 0.1%. Various methods of predicting gas‐mixture compressibility are tested, and activity coefficients calculated from the experimental data are reported.
Diffusion in compressed binary gaseous systems
Authors: Berry V. J. , Koeller R. C.
Published: June 2004

Apparatus is described for experimentally determining diffusion coefficients in dense‐gas systems to pressures of 15,000 lb./sq. in. abs. Tests were made with the hydrogen‐nitrogen and methane‐ethane systems at 104°, 139°, and 171°F. to 10,000 lb./sq. in. abs. and with the nitrogen‐methane and nitrogen‐ethane systems at 104°F. to 2,500 lb./sq. in. abs. In all cases it was found that diffusion coefficients predicted on the basis of the Lennard‐Jones model with Thorne's dense‐gas correction diverged below the experimental data in the high‐density region. Coefficients predicted from the Slattery‐Bird reduced‐state correlation showed better agreement with the experimental data. The temperature dependence of the results is better described by the exponential form for liquids than by the form of the dense‐gas theory.
Mechanisms by which ultrasonic energy affects transfer rates in liquid‐liquid extraction
Authors: Woodle H. A. , Vilbrandt F. C.
Published: June 2004

Concurrent and spray‐tower studies have been accomplished that illustrate the effects of ultrasonic insonation on transfer rates in liquid‐liquid extraction. Stage efficiencies and over‐all transfer rates in the system toluene‐methyl alcohol‐water were determined with and without insonation of the system at frequencies of 40 and 800 kc.

Insonation was shown to have a positive effect on mass transfer in both concurrent and spray‐tower operations. Insonation of the system provides for increased interfacial area between the two phases, removal of relatively stagnant liquid layers at the interface, and increased circulation currents within a single liquid phase. Low‐frequency insonation favors local agitation and mixing of the phases, and high‐frequency insonation favors induced circulation currents.
Momentum and heat transfer in laminar boundary‐layer flows of non‐Newtonian fluids past external surfaces
Authors: Acrivos Andreas , Shah M. J. , Petersen E. E.
Published: June 2004

A theoretical analysis for the laminar flow past arbitrary external surfaces of non‐Newtonian fluids of the power‐law model is presented. The main problem which is considered is how to predict the drag and the rate of heat transfer from an isothermal surface to the fluid. Inspectional analysis of the modified boundary‐layer equations yields a general relationship both for the drag coefficient and for the Nusselt number as functions of the generalized Reynolds and Prandtl numbers. The flow past a horizontal flat plate is studied in detail numerically.
Limiting velocities, holdup, and pressure drop at flooding in packed extraction columns
Authors: Venkataraman Gopal , Laddha G. S.
Published: June 2004

Criterion for flooding which was found to be reproducible in packed columns has been described. Limiting velocities, holdup, and pressure drop at flooding have been experimentally determined for binary liquid systems in a countercurrent extraction column packed with raschig rings, Berl saddles, Lessing rings, and spheres. Generalized correlations have been suggested, with the experimental data taken into account along with, published data of other workers for the estimation of limiting velocities, holdup, and pressure drop at flooding.
Longitudinal mixing in fluidization
Authors: Cairns E. J. , Prausnitz J. M.
Published: June 2004

Longitudinal mixing properties in liquid‐solid fluidized beds were investigated by means of a salt‐solution tracer technique. The electrical conductance breakthrough curves were measured with very small electrical conductivity probes for a step‐function input of salt‐solution tracer. Longitudinal eddy diffusivities were determined for 1.3‐ and 3.0‐mm. lead spheres and 3.2‐mm. glass spheres in 2‐ and 4‐in.–diameter beds at a distance of 5 bed diam. from the injector and for various radial positions.

The longitudinal mixing properties are strongly affected by particle concentration; maximum mixing occurs at a fraction voids of 0.7. Longitudinal eddy diffusivity increases with particle density and with decreasing dp/D ratio. Velocity profiles markedly influence the eddy‐diffusivity profiles.
General short‐cut equation for equilibrium stage processes
Authors: Smith Buford D. , Brinkley W. K.
Published: June 2004

An equation for the prediction of the separation of a multicomponent mixture in equilibrium stage processes is presented. The equation is applicable to extraction processes with up to three feeds (an intermediate feed, a feed at the extract end, and the solvent feed at the raffinate end) and both raffinate and extract reflux. In its simplest form (simple extraction, stripping, or absorption) the equation reduces to the familiar Kremser equation. The use of the equation to solve multicomponent distillation and extraction problems is illustrated by examples.
Entrainment and pressure drop in concurrent gas ‐ liquid flow: I. Air ‐ water in horizontal flow
Authors: Wicks Moye , Dukler A. E.
Published: June 2004

Experimental equipment and data are reported for entrainment and energy loss in annular, two‐phase flow of water and air. Measurements were made with a sample withdrawal technique in 1‐ and 3‐in. horizontal tubes. A knowledge of entrainment is necessary to an understanding of various mass transfer, heat transfer, and separation problems in two‐phase flow. A preliminary correlation is presented.
On the steady state activity levels in a reactor‐regenerator system
Authors: Petersen E. E.
Published: June 2004

A method is proposed for computing the steady state activity levels at various points within a reactor‐regenerator system in which the residence time distribution functions in the reactor and regenerator, the permanent deactivation function, and the temporary deactivation and activation functions are arbitrarily specified. A particularly simple solution to these equations is obtained when the temporary activation and deactivation functions are of exponential form. The latter equations are used to calculate values of the mean activity in the reactor for the limiting cases of piston type of flow and complete mixing under a variety of conditions.
The kinetics of the absorption of phosgene into water and aqueous solutions
Authors: Manogue W. H. , Pigford R. L.
Published: June 2004

Pure phosgene gas was dissolved in short laminar jets of aqueous solution, and the results were interpreted with an unsteady state absorption‐plus‐reaction theory. Absorption rates of sulfur dioxide and carbon dioxide into water in the same equipment support this interpretation. The solubility of phosgene in water at 25°C. has been estimated from the absorption rates as 0.069 g.mole/(liter) (atm.). The estimated heat of solution is 6,800 cal./g.mole. At 16° and 25°C. the effect of a chemical reaction between phosgene and water on the absorption rate in a jet appears to be almost negligible, but at 45°C. a first‐order reaction rate constant of 75 sec.−1 can be derived from the absorption rates.

From absorption measurements with short jets and sodium hydroxide solutions so strong that a pseudo‐first‐order reaction accompanied absorption, the reaction rate constant for the bimolecular reaction between dissolved phosgene and the hydroxyl ion was estimated. A value of 1.6 × 104 liters/(g. mole) (sec.) was obtained at 25°C. in 1‐N sodium hydroxide; at 35°C. in the same solution the estimated value was 2.9 × 104. There appears to be a slight increase in the reaction‐rate constant with the ionic strength of the solution.
Axial diffusion of liquids in packed beds and end effects
Authors: Liles A. W. , Geankoplis C. J.
Published: June 2004

Experimental data were obtained on the effect of bed length of packed spheres on axial diffusion coefficients with the frequency response technique used. Lengths of packed section of 6 to 174 cm. were used. The end effects were eliminated by using a novel experimental technique for analyses of the inlet and outlet streams. No effects of length on DL were found.

When the end effects were artificially introduced by using void analytical sections at the two ends, then large effects of length on DL were found. These void sections were the cause of length effects found by other experimenters. The DL drops as the length of bed is increased. Above about 65 cm. length the DL remains constant with increase in length. The over‐all results are in general agreement with the data of others.
Heat and mass transfer transients in cylinder drying: Part I. Unfelted cyclinders
Authors: Nissan A. H. , Hansen David
Published: June 2004

An investigation has been made of transient heat transfer and water removal on an unfelted cylinder dryer. This investigation has included the development of a theory for describing conduction of heat in the drying material and an experimental testing of the adequacy of the theory.

The theory describes the heat transfer and evaporation of water in terms of a second‐order partial‐differential equation and appropriate boundary conditions. Numerical solutions obtained on a digital computer are presented.

The experimental work, performed on a specially constructed laboratory dryer, included measurements of temperatures at internal points in a drying sheet and also measurements of water removed during drying.

Good agreement was found between theory and experiment, and the usefulness of the theory is demonstrated in the analysis of water removal in some drying experiments.

Although the work was primarily concerned with a description of the paper drying process, the methods should apply equally well to the drying of other materials on heated cylinders.
A computational model for predicting and correlating the behavior of fixed‐bed reactors: I. Derivation of model for nonreactive systems
Authors: Deans H. A. , Lapidus Leon
Published: June 2004

A mathematical model is developed for predicting the mixing characteristics of fixed beds of spheres. The model is based on a two‐dimensional network of perfectly stirred tanks. By means of the conventional partial differential equation description of flow in fixed beds, the predictions of the new model are compared with experimentally observed axial and radial mixing characteristics. The introduction of a capacitance effect is shown to enable the model to predict the abnormally low axial Peclet numbers observed in liquid‐phase systems in the unsteady state.

The mathematical model developed in the first part of this paper is extended to cover chemical reaction in a cylindrical fixed bed of porous catalyst spheres. The mathematical effect on the model of various controlling rate steps, nonconstant property values, and multiple, non‐first‐order reactions is discussed. After the general discussion a simplified system is chosen to indicate the practical advantages of the model. A single, first‐order, irreversible, exothermic reaction is considered to proceed according to an effectively homogeneous rate expression, which varies exponentially with the inverse of absolute temperature. Both steady state and transient cases are calculated for a reactor, the walls of which are maintained at constant temperature.
Mixing in a jet‐stirred reactor
Authors: Bartok William , Heath Carl E. , Weiss Malcolm A.
Published: June 2004

Measurements were made of the over‐all mixing in a gas phase flow reactor stirred by the entering feed jets. The mixing was studied by following the decrease in exit concentration after sharp cutoff of a radioactive tracer gas krypton −85. The data showed that over the entire range of average residence times investigated, about 0.4 to 16 sec., the reactor behaved as though 85% of its volume was perfectly stirred and the remaining 15% was in piston flow in series with the stirred region. Relocation of the feed jets would probably increase the fraction of volume that is effectively perfectly stirred to about 95%.
A note on multicomponent diffusion
Authors: Shain Stephen A.
Published: June 2004

The problem of defining an average diffusion coefficient of a gas arises in the application of the film resistance model for mass transfer to systems involving multicomponent mixtures of simultaneously diffusing gases and in the application of mass, momentum, and heat transfer analogies in such systems. It is shown that, in some cases, integration of the diffusion equation with an average value of the diffusion coefficient will not be valid. An approximate solution of the diffusion equation is obtained with the concentration dependence of the diffusion coefficient taken into account. Some numerical examples are constructed for comparison of this method and several methods for defining an average diffusion coefficient with an exact solution of the Stefan‐Maxwell relations.
Phase relations of miscible displacement in oil recovery
Authors: Hutchinson C. A. , Braun Philip H.
Published: June 2004

Miscible displacement as an oil recovery process has received wide interest in the literature recently. Essentially three basic processes have been proposed for attaining miscible displacement in our oil reservoirs: high pressure gas, enriched gas, and miscible slug processes.

The present paper relates and compares the phase relations and mass transfer mechanisms of these various basic miscible displacement processes. It also discusses the effects of the various operating variables, such as pressure, temperature, injected gas composition, etc., on the applicability of the process and considers the pertinent conditions that restrict the application of each process. It is to be recognized that at times a miscible displacement may be attempted but not attained, or unforeseen conditions may destroy miscibility once it has been attained. The authors discuss the results of such conditions. The mechanisms of the miscible displacement processes are explained in a conceptual analysis based on the triangular phase diagram. Although the multicomponent reservoir fluid system cannot be represented rigorously from a thermodynamics standpoint by these diagrams, they are useful for cenceptual analysis. Their limitations are presented by the authors along with data supporting the concepts developed.
The effect of mixer design on the efficiency of a pump‐mix mixer‐settler
Authors: Davis A. T. , Colven T. J.
Published: June 2004

The mixing efficiency of simple and pitched paddles, marine propellers, and centrifugal and disk impellers was determined by a heat transfer method in a single stage of a large pump‐mix mixer‐settler. The mixing devices were from 3 to 5 in. in diameter and were tested with a refined kerosene as the organic phase and water as the aqueous phase.

A heat conductance was calculated from flow parameters and the efficiency and was correlated against impeller design and speed variables. For centrifugal and disk impellers UA was proportional to n1.2L3b0.3; for the paddles UA was proportional to n1.67L2.5b0.42. At normal operating speeds controlled variation of the internal recirculation of mixed phases through a centrifugal impeller did not change the efficiency.
Thermodynamics of solvent selectivity in extractive distillation of hydrocarbons
Authors: Prausnitz J. M. , Anderson Ralph
Published: June 2004

The selectivity of a polar solvent is expressed in terms of an approximate theory of solutions. The theoretical results are insufficiently precise for the accurate prediction of activity coefficients, but the analysis shows that in the absence of chemical effects selectivity depends primarily on the difference in molar volumes of the hydrocarbons to be separated and on the polar energy density of the solvent. The effectiveness of a solvent is related to its polarity (which should be large) and to its molecular size (which should be small). In cases where chemical effects are important or where the molar volumes of the hydrocarbons to be separated are only slightly different, selectivity also depends on the relative ability of the hydrocarbons in acting as electron donors and on the ability of the solvent to act as an electron acceptor in forming acid‐base complexes. The theoretical conclusions, which are based on modern thermodynamics and on the theory of intermolecular forces, are in agreement with experimental observations. The results obtained in this work provide theoretical criteria for the selection of an optimum solvent for a given separation and give semiquantitative explanations of solution phenomena related to extractive distillation.
Vapor‐liquid equilibrium in ammonia complex systems
Authors: Muendel C. H. , Linford H. B. , Selke W. A.
Published: June 2004

The vapor‐liquid equilibrium in ammonia complex systems has been studied with a view toward design methods for separational and leaching processes. It is felt that the previously reported equilibrium constants for these systems are subject to considerable question with regard to the method used to measure the activity of the free ligand, or coordinating species. It is shown how this difficulty can be surmounted by the use of ammonia vapor pressure measurements and fugacities. A method of correlating complex equilibrium data from measurements of over‐all metal concentration and free metal ion concentration is proposed. Vapor liquid equilibrium measurements have been made on the systems copper hydroxide, ammonia, water, nitrogen and nickel hydroxide, ammonia, water, nitrogen at 40° and 60°C. under 1 atm. total pressure with a continuously recirculating batch contactor. The correlation method is illustrated with the data of these measurements.
Temperature depressions for evaporating spheres at low pressures
Authors: Madden A. J. , Halfen F. J.
Published: June 2004

The evaporation of naphthalene spheres into air in the micron pressure range may be accompanied by an appreciable surface temperature depression. The magnitude of the effect is shown to depend upon the geometry of the experimental system and the pressure level. Such effects are of interest in studies aimed at determining evaporation coefficients.
Heats of mixing: Alcohol‐ aromatic binary systems at 25°, 35°, and 45°c.
Authors: Mrazek Robert V. , Van Ness H. C.
Published: June 2004

A new isothermal calorimeter with no vapor space is described. It allows the accurate and rapid determination of heats of mixing of endothermic liquid systems. Data are presented for eighteen binary systems composed of a lower alcohol and a simple benzene derivative at 25°, 35°, and 45°C. Precise equations for representing these data are also presented.
Mass transfer between isobutanol and water in concurrent flow through a packed column
Authors: Leacock James A. , Churchill Stuart W.
Published: June 2004

Local and mean rates of transfer of isobutanol into the water‐rich phase and of water into the isobutanol‐rich phase were measured in concurrent upward flow through a column packed with glass spheres. The use of a two‐component system permitted determination of the individual‐phase coefficients. These are the first rate measurements for concurrent flow in a packed bed. Because the flow rates are not limited by flooding, much higher rates of transfer are attainable than in countercurrent flow.
Effect of mass transfer on solid‐catalyzed reactions: The dehydrogenation of cyclohexane to benzene
Authors: Barnett L. G. , Weaver R. E. C. , Gilkeson M. M.
Published: June 2004

The reaction of gaseous components at a solid catalytic surface has long been a subject of prime engineering interest. Generally speaking one expects the reaction velocity constant to follow the Arrhenius exponential temperature dependence. However as the reaction temperature increases, the intrinsic reactivity of the surface will increase and mass transfer begins to limit the rate of the reaction. In the case of a porous solid catalyst, where most of the active surface is on the catalyst pellet interior, the rate‐limiting process will frequently be internal diffusion, and in such a case the milder effect that temperature has on the diffusion process is the one observed in the gross kinetics, rather than the exponential Arrhenius dependence.

The study reported here has examined the kinetics of the dehydrogenation of cyclohexane to benzene over a platinum‐on‐alumina pelleted catalyst. This is a notorious problem system, and in seeking to describe the observed rate data the authors provided a stern test for an analytical model treating the coordinate diffusion and reaction mechanisms. In particular the parameter of particle size was studied over a temperature range of from 640° to 910°F. For these runs reactor pressure was held constant at essentially 200 lb./sq. in. gauge (14.7 atm.), und the feed was maintained at 20 mole % cyclohexane, 80 mole % hydrogen.
Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface
Authors: Sakiadis B. C.
Published: June 2004

The laminar boundary‐layer behavior on a moving continuous flat surface is investigated by two methods. One method involves the numerical solution of the boundary‐layer equations. The other is an integral method, based on an assumed velocity profile that satisfies the appropriate boundary conditions. Good agreement is obtained between the results of these two methods of solution. The turbulent boundary‐layer behavior on a moving continuous flat surface is investigated by the integral method only. Equations for the boundary‐layer thickness, displacement thickness, momentum thickness, and skin friction are presented for both laminar and turbulent boundary layers. Comparison is made with the boundary‐layer behavior over a flat plate of finite length.
The effect of vibration on natural convective mass transfer
Authors: Lemlich Robert , Levy Martin R.
Published: June 2004

Small horizontal cylinders subliming to room air were vibrated in a vertical direction at 20 to 118 cycles/sec. Increases of up to 660% in the coefficient of mass transfer were thus obtained. The coefficient increased with both frequency and amplitude, the latter having the more pronounced effect. Results are correlated in terms of the stretched vibrational Reynolds number introduced in an earlier study and compared with the analogous case of natural convective heat transfer.
Effective thermal conductivity in packed beds
Authors: Gopalarathnam C. D. , Hoelscher H. E. , Laddha G. S.
Published: June 2004

Values of the effective thermal conductivity Ke for liquids in packed beds have been obtained from heat transfer studies in such beds. The method applied by Yagi and Kunii for gases is darified, their model is extended and is then applied to liquids. Experimental data for three different packings, glass, steel, and aluminum, with spheres of DP/DT ratio from 0.07 to 0.33 have been correlated. A brief comparison of the results from this analysis with previously published results from similar studies is presented.
Optimization of process performance
Authors: Lapidus Leon , Shapiro Eugene , Shapiro Saul , Stillman R. E.
Published: June 2004

The growing availability of fast, large memory digital computers has made it practical to consider the physical implementation of control system designs incorporating appropriate strategies for automatic process optimization. The control system is taken to consist of the process to be optimized together with the interconnected digital computer. The control strategy is realized in the program of the digital computer. In the present paper a number of such programs or algorithms are discussed for carrying out a search of the possible settings of the process input (independent) variables in such a way as to locate an extremal of the possible values of a chosen objective function. The magnitude of these variables is determined from measurements taken of the dependent variables in the process. It is shown that for the particular process used as an example it is desirable to alter the search strategy as the optimization proceeds in order to locate the extremal in a minimum amount of time. The emphasis at the beginning of the search is on speed in moving towards the optimum and at the end on accuracy.

Further, a computational technique is described whereby the dynamic response of the process to the various search steps (or settings) is under time‐optimal control. This procedure is important for the fast execution of the search programs and consequent rapid location of the extremal of the chosen objective function.
Solid‐liquid phase behavior of binary solutions at elevated pressures
Authors: Winnick Jack , Powers J. E.
Published: June 2004

The formation of a solid phase as the result of isothermally increasing pressure on a binary solution is analyzed from a thermodynamic point of view. Exact thermodynamic equations are presented for the case in which there are no more than one liquid and one solid phase in equilibrium for the entire range of compositions. Approximate relations incorporating the additional assumption of ideality in both solid and liquid phases are also presented. Experimental data for the system ethylene bromide‐ethylene chloride are reported and compared with predicted values. Incomplete data for the system benzene‐n‐heptane are also reported.
Relationship between pellet size and performance of catalysts
Authors: Beek John
Published: June 2004

The effect of mass transfer resistance in reducing the effectiveness of porous catalysts has been known since the publication of Thiele's classical paper in 1939. The variation in temperature caused by resistance to heat transfer may bring about equally significant changes in effectiveness in some cases. An extension of Thiele's treatment to take exact account of heat transfer resistance leads to a set of nonlinear differential equations that can only be solved numerically.

This paper presents an approximate treatment of the simulataneous effects of resistances to mass and heat transfer. With the limitations imposed by linearizing the equations the formulas derived give the activity and selectivity for any combination of reactions. The use of the results is illustrated by three examples. It is shown that the principal effects are associated with the variation of concentration within the pellet of catalyst and with the difference in temperature between the surface of the pellet and the bulk fluid.
Isothermal growth of hydrogen bubbles during electrolysis
Authors: Westerheide D. E. , Westwater J. W.
Published: June 2004

The investigation was concerned with measuring growth rates of bubbles in an isothermal medium where growth is controlled by mass diffusion. The conditions were met by generating hydrogen bubbles at a platinum cathode during the electrolysis of water. Growth data were obtained by motion picture photography at 800 to 2,400 frames/sec. taken through a microscope to produce an enlargement of 30X on the film.

Growth took place in 0.1 normal and 1.0 normal sulfuric acid in water at 77°F. Current densities between 0.1 and 0.2 amp./sq. cm. were used. The observed diameters were all less than 0.006 in., and the growth times were less than 2 sec. Beside growth phenomena interesting features recorded included the coalescence of bubbles, the jumping of bubbles off the solid and then back again, and the slip of the bubble contact at the solid surface.

Some bubbles grew with their radii proportional to the square root of time as predicted theoretically by Scriven. For these bubbles the calculated supersaturation of hydrogen in the solution was found to be from eight to twenty‐four times the concentration at saturation.
A study of entrainment, perforated plate column—air‐water system
Authors: Bain Jesse L. , Van Winkle Matthew
Published: June 2004

A correlation has been developed interrelating entrainment as a function of plate spacing, weir height, hole size, liquid rate, and gas rate with a section of a 30‐in. diameter column and the air‐water system. The correlation is empirical, but approximately 90% of the over 900 points of data fall within ± 25% of the correlation. Hole diameters of 1/16 to 1/4 in., weir heights from 0 to 2 in., plate spacing from 12 to 24 in., gas rates from 770 to 1,700 lb./hr./sq. ft., and liquid rates from 2,800 to 12,000 lb./hr./ft. of weir length were studied as variable. Entrainment was found to increase with gas rate, decrease with weir height, increase with hole size, decrease with plate spacing, and could increase or decrease because of interaction effects as the liquid rate increases.
A study of iterative optimization
Authors: Rudd Dale F. , Aris Rutherford , Amundson Neal R.
Published: June 2004

A process is considered in which the inputs to the system are stationary random ergodic functions. From the spectral densitities of the inputs and cross‐spectral densities of inputs and outputs a local linearized model of the process is obtained through the transfer function. There results then a maximum problem involving an objective function and constraints imposed by the model and the physical and arbitrary restraining conditions. Two special cases are solved in detail in which the maximum problem reduces to a linear programing problem. Other methods are needed for the general problem.
Application of the Kihara potential to high pressure phase equilibria
Authors: Prausnitz J. M. , Keeler R. N.
Published: June 2004

This paper is concerned with the virial equation of state as applied to vapor mixtures at moderate densities. The required virial coefficients for small molecules can usually be estimated from generalized corresponding states correlations, but these correlations are not sufficient for mixtures which contain one very heavy and one very light component. It is shown that for such mixtures the necessary virial coefficients can be calculated by statistical thermodynamics with a potential function proposed by Kihara. This type of calculation is especially useful at low temperatures where virial coefficients have not been measured because of large experimental difficulties. Application of the Kihara potential is demonstrated with the computation of K values for heavy components for several mixtures at advanced pressures; good agreement with experimental results is obtained.

The virial equation may in some cases be used to test data for thermodynamic consistency, and for illustration it is shown that recently reported K data for propane in compressed hydrogen are thermodynamically inconsistent and too large by about two orders of magnitude.
Saturated liquid densities for binary hydrocarbon systems
Authors: Phillips Edward M. , Thodos George
Published: June 2004

The extension of the rules proposed by Cailletet and Mathias for the sum of the saturated vapor and liquid densities and by Guggenheim for the difference of these densities enabled the development of a method for the prediction of liquid densities for binary hydrocarbon systems at saturated conditions. The theorem by corresponding states indicated that unique relationships should exist between the reduced temperature and the sum and difference of the reduced saturated liquid density and the reduced saturated vapor density.

Density data reported by Kay for the systemsn‐butane—n‐heptane, ethane—n‐butane, ethane—n‐heptane, and ethane—cyclohexane were used to determine the exponents and the coefficients of the resulting equations. The exponents were found to be functions of two temperature parameters, which take into account both the components and composition of the mixture, while their coefficients have been found to depend only on their exponents.

It has been previously shown that critical temperatures of binary hydrocarbon systems can be predicted with the two temperature parameters. In this study it has been found that these two parameters can also be applied to determine the critical densities for these binary hydrocarbon systems. Using these critical properties one can directly obtain the saturated liquid densities of binary systems from the two reduced‐density relationship.

The method developed in this work reproduces the saturated liquid densities of the four systems within 4.8%. In addition saturated densities have been calculated for the ethylene—n‐heptane system and checked the experimental values within 3.2%.

Because saturated vapor densities are small compared with the saturated liquid densities for conditions removed from the critical point, the sum and difference of the liquid and vapor densities are approximately the same. Thus this method cannot be used with any reliability to determine the densities of saturated vapors.

At present this method can be applied only to hydrocarbon mixtures whose atmospheric dew point does not exceed twice its atmospheric boiling point.
Mass transfer in the flow of gases through fluidized beds
Authors: Riccetti Richard E. , Thodos George
Published: June 2004

Mass transfer studies were conducted for the flow of air through fluidized beds. These studies were concerned with the sublimation of p‐dichlorobenzene spherical particles, approximately 0.04 to 0.08 in. in diameter, and with the evaporation of nitrobenzene and water from alumina spheres. 0.1168 in. in diameter.

Void volumes for these fluidized beds were calculated from pressure‐drop measurements. The results of this investigation were used to establish mass transfer factors which were in agreement with values obtained for fixed beds for corresponding modified Reynolds numbers, DpG/μ(1‐ε).
The laminar nonisothermal flow of non‐Newtonian fluids
Authors: Hanks Richard W. , Christiansen Ernest B.
Published: June 2004

The equations which describe the process of simultaneous heat and momentum transport are solved to obtain the pressure loss‐flow rate relation for the laminar flow of pseudoplastic liquids through a smooth heated pipe. The rheology of the liquids is characterized by a temperature‐reduced form of the empirical Ostwald‐deWaele or power law equation.

Two solutions to the basic equations are presented, a numerical integration of the heat conduction differential equation and an approximate solution based upon a simplified model of the temperature profile.

Experimental data obtained with eighteen different pseudoplastic solutions and the limited data available from the literature are compared with theoretical predictions and are correlated over a 5,000‐fold range of friction factors and pseudoplastic Reynolds numbers with a standard deviation of 7.9%.
Swirling flow in cylinders
Authors: Nissan Alfred H. , Bresan V. P.
Published: June 2004

The presence of vortex motion in a vertical cylinder in which water is passed upward can result in three types of velocity profiles: net upward motion at all points in the tube, an ascending outer annulus and a descending central core, and outer annulus and central core ascending and an intermediate annulus descending.

All three types of velocity profiles are functions of three factors: the tangential velocity, the manner of decay of the tangential velocity, and the wall pressure drop. A fourth factor, boundarylayer growth, is proposed to explain the third type of profile. Experimental work was carried out to prove the mechanisms proposed for the first two types of profiles. Photographic observations were taken showing the existence of the third type.
Kinetics of reduction of ferrous oxide with hydrogen in a fluidized bed at steady state
Authors: Feinman Jerome , Drexler Thomas D.
Published: June 2004

The kinetics of the reduction of ferrous oxide with hydrogen in a steady state fluidized bed have been correlated with a rate equation based on a reaction controlled at the oxide‐metal interface and on a differential material balance which assumes that a close approach to piston flow prevails. The correlation gives an enthalpy of activation of 29,500 b.t.u./lb. mole for the reaction, which is in good agreement with McKewan's reported value of 27,500 b.t.u./lb. mole. The relationships developed are used to predict the effect of the important independent variables on the over‐all kinetics of the system.
Heat transfer from acoustically resonating gas flames in a cylindrical burner
Authors: Zartman W. N. , Churchill S. W.
Published: June 2004

Heat transfer from premixed propane‐air flames to the cooled wall of a 5‐in. I.D. ramjet type of burner was studied with and without flame‐generated, sonic oscillations. Frequency and amplitude measurements revealed that both transverse and longitudinal waves were resonant. The heat flux to the wall was increased significantly by the oscillations, but the gas temperature profile was changed very little. The local heat transfer coefficient was found to be a linear function of the sound pressure amplitude and independent of the mode and frequency of the resonant oscillations.
The viscosity of nonpolar gases at normal pressures
Authors: Stiel Leonard I. , Thodos George
Published: June 2004

Experimental viscosity data available in the literature for fifty‐two nonpolar gases have been utilized in conjunction with a dimensional analysis approach to relate the viscosity at atmospheric pressure to temperature. The substances investigated are both simple and complex and include the inert and diatomic gases, carbon dioxide, carbon disulfide, carbon tetrachloride, and the hydrocarbons up ton‐nonane, including normal and isoparaffins, olefins, acetylenes, naphthenes, and aromatics. The dependence of the product μ*ξ on reduced temperature was found to be the same for all of these substances, except helium and hydrogen.

Both theoretical considerations and dimensional analysis indicate that the viscosity product of a gas might depend on the compressibility factor at the critical point. However the results of this study show that for these nonpolar substances this viscosity product at normal pressure is independent ofzcand depends only on temperature.

The only information required for the calculation of viscosity with the relationships developed in this study is the molecular weight, critical temperature, and critical pressure of the substance. Values calculated with these relationships have been compared with 785 experimental points from all reliable sources of experimental data and produced an average deviation of 1.77%. Comparisons have also been made with the values calculated with the Licht‐Stechert and Bromley‐Wilke equations.
The measurement of rapid surface temperature fluctuations during nucleate boiling of water
Authors: Moore Franklin D. , Mesler Russell B.
Published: June 2004

The surface temperature during nucleate boiling was measured with a special thermocouple so designed as to measure the temperature of a small area and to have an extremely rapid response time. The surface temperature was found to drop occasionally 20° to 30°F. in about 2 msec. during the boiling of water. This indicates a rapid extraction of heat during a short time interval. The significance of this observation is that it provides an important new clue to an understanding of nucleate boiling. A hypothesis is advanced to explain these observations.
The effect of organic substances on the transfer of oxygen from air bubbles in water
Authors: Eckenfelder W. Wesley , Barnhart Edwin L.
Published: June 2004

The liquid film coefficient is related to bubble diameter and velocity in pure water and to the physical properties of the liquid. The addition to water of organic substances which influence the surface tension and viscosity will decrease the size of the air bubble released from a diffuser and reduce the transfer of oxygen into the solution. The maximum reduction in oxygen transfer occurs in the region of maximum surface tension change. The effect of the addition of several organic substances on the oxygen transfer characteristics are shown.
Energy balances in solar distillers
Authors: Lof G. O. G. , Eibling J. A. , Bloemer J. W.
Published: June 2004

There has been considerable doubt as to the manner in which the productivity of solar stills is affected by many of the designs and operating variables. To assist in designing solar stills of improved performance, theoretical equations are derived to describe the complete energy and mass transfer relationships involved in the operation of the basin type of solar still. These are supplemented with data from field operation of a 2,500‐sq. ft. still. With these relationships and the aid of a digital computer, the effects of variations of design parameters on the performance of solar stills is predicted. Distiller productivity is correlated with atmospheric temperature, wind velocity, solar radiation, absorptivity and slope of transparent cover, and other variables. Curves showing the magnitude of the effects of design changes on cover temperature, brine temperature, and productivity are presented.
A thermodynamic correlation of gas solubilities
Authors: Prausnitz J. M. , Shair F. H.
Published: June 2004

Low‐pressure solubility data have been correlated for eleven gases in nine solvents over a wide temperature range by considering the dissolution process in two steps. First the gas is condensed isothermally to a hypothetical liquid at 1 atm. pressure, and then this hypothetical liquid is dissolved in the solvent. The free energy of the first step depends only on the properties of the solute, which in the case of nonpolar gases can be adequately described by the theorem of corresponding states. The second step depends on the properties of both solute and solvent and, in the case of nonpolar systems, can be described by the theory of regular solutions. The correlation depends on three solute parameters: the solubility parameter, the molar volume, and the fugacity of the hypothetical liquid; the last of these has been plotted as a generalized function for the reduced temperature range of 0.7 to 3.2. A separate plot is given for hydrogen. These parameters may be used to make good estimates of low‐pressure gas solubilities (or K values) in nonpolar solvents over a wide range of temperature.

A semiempirical method for correlating the solubilities of gases in polar solvents is also described and illustrated for several cases.

Since the correlation presented in this paper covers a wide temperature range, it is possible to make estimates of the heats of solution of gases in liquids. These may be useful in enthalpyblance calculations as required in certain phase‐separation operations.
Temperature gradients in turbulent gas streams: Effect of viscous dissipation on evaluation of total conductivity
Authors: Venezian Emilio , Sage B. H.
Published: June 2004

Values of the total conductivity in a turbulently flowing air stream were originally reported without regard to the effects of viscous dissipation upon the results. By utilizing measurements of the shear taken at the time of the original study, the reported values of total conductivity were corrected for the effect of viscous dissipation. The effect of such dissipation upon the values of total conductivity is the greatest under conditions involving small temperature gradients and high Reynolds numbers.
Temperatures and partial pressures at the surfaces of catalyst particles
Authors: Yoshida Fumitake , Ramaswami D. , Hougen O. A.
Published: June 2004

Numerical and graphical methods are presented for estimating the temperatures and partial pressures at the surfaces of catalyst particles for gaseous reactions in flow systems. The errors resulting in the interpretation of catalytic reaction‐rate data, where surface conditions are assumed to be those of the ambient gas stream, are presented. A numerical method of evaluating the reaction model with nonisothermal surface conditions is indicated.
Kinetics of particle growth in a fluidized calciner
Authors: Lee B. S. , Chu Ju Chin , Jonke A. A. , Lawroski Stephen
Published: June 2004

This study of the factors underlying the mechanisms of particle growth in a fluidized calciner was conducted in a 3‐in. diameter column. In such a calciner radioactive waste liquor from nuclear fuel reprocessing can be converted to a granular solid for disposal. To simulate the octual waste, aluminum oxide as bed material and aqueous aluminum nitrate solution as feed were used. Particle growth was traced through the addition of radiactive seeds. The effects on the growth rate of operating variables and physical properties of the feed were investigated. Statistical analysis of the data substantiated the proposed growth mechanism, and the resulting growth coefficient was correlated with the variables studied.
Mass transfer in dilute turbulent and non‐turbulent systems with rapid irreversible reactions and equal diffusivities
Authors: Toor H. L.
Published: June 2004

Studies of mass transfer with rapid, homogeneous, irreversible reactions between dilute species with equal difusivities are carried out with a device which reduces the system of mass transfer‐reaction equations to the equations for mass transfer in the absence of reaction.

A relationship which gives the rate of transfer into stagnant, laminar, or turbulent reacting systems is developed. Under some conditions the reaction increases the transfer rates by a constant factor, while under other conditions the reaction increases the individual or over‐all mass transfer coefficients by a constant factor.

Calculations of concentration profiles, conversion, etc. are carried out for the Graetz problem with a homogeneous reaction between a dilute species in the fluid and a dilute species diffusing from the tube wall. Reaction completion times for various stagnant elements in infinite media are given.

Although the flux into a turbulent reacting fluid is related to the time average behavior in the absence of reaction, the time average concentrations depend also upon the relative intensity of the concentration fluctuations in the absence of reaction. This latter dependence is obtained from a relationship of Hawthorne, et al.

Surfaces on which the time average composition is stoichiometric and the reactant concentrations are proportional to the relative intensity of the concentration fluctuations in the absence of reaction are obtained for turbulent flow in a tube with a homogeneous reaction between the fluid and wall. Distances for almost complete reaction are estimated.

The time average conversion is related to the accomplished mixing for the case in which two dilute reactants are turbulently mixed. In a uniform, stoichiometric mixture the fractional conversion equals the accomplished mixing. Calculations are carried out for uniform, nonstoichiometric mixtures.