bluuebunny/crossref_metadata_2025 huggingface dataset:
A reduced state vapor‐pressure relationship and its application to hydrocarbons
Authors: Reynes Enrique G. , Thodos George
Published: June 2004

The Frost‐Kalkwarf vapor‐pressure equation has been modified to include as variables the reduced temperature and pressure of the substance. The resulting relationship was found to contain a universal constant δ = 0.1832 and three other constants α, β, and γ, which are characteristic of the substance. Relationships between α, β, and γ were found to exist, and thus a vapor‐pressure equation was produced which contains only one characteristic contant β and which is capable of predicting vapor pressures of pure substances up to the critical point.

This vapor‐pressure relationship has been applied to hydrocarbons of all types, including normal paraffins, isoparaffins, olefins, diolefins, acetylenes, naphthenes, and aromatics. In these calculations values of β were estimated from the molecular structure of the hydrocarbons. For hydrocarbons the approach developed in this study was found to reproduce experimental vapor pressures with an average deviation of 2.7% for 456 experimental points representing fifty four hydrocarbons.

This study indicates that if reliable vapor‐pressure data, however meager, are available for a hydrocarbon, these data can be used to obtain constants which enable the prediction of the critical temperature and the critical pressure of the substance.
Reduction of iron oxide in gas‐conveyed systems
Authors: Themelis N. J. , Gauvin W. H.
Published: June 2004

The model particles were prepared by oxidation of carbonyl iron spheres, followed by fractionation into cuts of very narrow size. A two‐wavelength radiation pyrometer was developed for measuring the temperature of the particles in flight, and special probes were designed for determining gas velocity and degree of reduction at different levels of the reactor.
Adsorption of methane and hydrogen on packed beds of activated carbon
Authors: Geser John J. , Canjar Lawrence N.
Published: June 2004

The adsorption of methane from mixtures of methane and hydrogen on fixed beds of activated carbon at −115°F. and 1 atm. has been studied. Inlet gas concentrations of 5.69, 7.58, and 10.65 mole % methane in hydrogen were employed over a gas flow rate range of from 3.24 to 16.3 std. cu. ft./hr. Activated carbon in sizes of 4 × 6 and 6 × 16 mesh and as 1/8‐ and 3/16‐in. pellets were employed as adsorbent.

The external diffusion of adsorbate to the surface can be correlated by the usual mass transfer expressions for packed beds, although coefficients obtained in this work are lower than those reported for other systems in the literature.

A new equation is presented for internal particle diffusion.
Liquid phase activity coefficients and standard state hypothetical liquid fugacities for hydrocarbons
Authors: Hoffman Dwight S. , Welker J. Reed , Felt Rowland E. , Weber James H.
Published: June 2004

One method of predicting vaporization equilibrium ratios for the components of a multicomponent mixture is through the use of standard state liquid fugacities, standard state vapor fugacities, liquid phase activity coefficients, and vapor phase activity coefficients. The relationship among these variables will be shown.

It is the purpose of this paper to present a method for evaluating the fugacities of the components of a multicomponent liquid mixture which is in equilibrium with its vapors; to present a method for evaluating the standard state fugacities of hypothetical liquids and to disclose these values for methane and ethane up to a reduced temperature of 1.6 and values for propane up to a reduced temperature of 1.3; to present the coincident derived values of the vaporization equilibrium constants, Z factors, and solubility parameters; and to show correlations of these values.
Power requirements and blend times in the agitation of pseudoplastic fluids
Authors: Godleski E. S. , Smith J. C.
Published: June 2004

Agitation and blending studies were made with solutions of Natrosol 250H, which were pseudoplastic fluids with nonconstant flow‐behavior indexes. The published power number‐Reynolds number correlation for pseudoplastic fluids having constant flow‐behavior indexes is valid for Natrosol solutions. Published correlations for blend times in Newtonian fluids do not apply to Natrosol solutions; the blend times are ten to fifty times longer than with Newtonian fluids of the same apparent viscosity. Blend times are shortest in unbaffled vessels when a vortex is formed and correlate well with the vortex depths. Insertion of radial baffles always lengthened the blend time.
Interrelation of packing and mixed phase flow parameters with liquid residence time distribution
Authors: Glaser M. B. , Lichtenstein Ira
Published: June 2004

Brine‐air and kerosene‐hydrogen systems were used for the mixed phase tests. No specific gas phase effects were detected. The measured variability, encompassing all three flow mechanisms, correlated well with particle Reynolds number for each system and decreased with increasing flow rate. However the variability component resulting solely from bulk liquid flow through the main bed channels was found to be relatively constant over a wide range of Reynolds number and independent of whether the bed was uniformly packed or contained large packing faults. The significance of these results to liquid‐solids contacting efficiency is discussed.
Pressure drops in the flow of gases through packed and distended beds of spherical particles
Authors: Wentz Charles A. , Thodos George
Published: June 2004

Pressure drop measurements were made across packed and distended beds having five layers of smooth plastic spheres, 1.23 in. in diamter, arranged in cubic, body‐centered cubic, and face‐centered cubic orientations of void fractions varying from 0.354 to 0.882. The distended beds were prepared by separating the spheres with permanently attached short lengths of fine rigid wire. Friction factors were calculated from the overall pressure drop measurements with the Ergun equation and were plotted against the corresponding modified Reynolds number which ranged from 2,550 to 64,900. A single relationship resulted for both types of beds which is independent of the geometric orientation and void fraction of the spheres of the bed.

To eliminate entrance and exit effects of the air flowing through the bed pressure drop measurements were also made across the middle layer of each distended bed. Again a single relationship between the corresponding friction factors and modified Reynolds number was obtained which is independent of the geometric orientation and void fraction of the bed.

From the two relationships between friction factors and modified Reynolds number the ratio Pk/fk for a packed or distended bed having five layers of spheres is 1.13. This ratio should decrease with increasing number of layers of spheres and approach the limiting value of 1 when the number of layers becomes very large.
Dispersed phase mixing: II. Measurements in organic dispersed systems
Authors: Miller R. S. , Ralph J. L. , Curl R. L. , Towell G. D.
Published: June 2004

When two liquid phases are contacted in a stirred tank reactor, dispersed phase mixing can affect average reaction rate and product selectivity in nonfirst order or mass transfer controlled reactions, as shown theoretically in Part I. This work is concerned with experimental measurement of the dispersed phase mixing rate. Various organic phase dispersions in water were studied in stirred tanks with a dye transfer light transmission technique. Batch experiments were performed in 0.30, 5.5, and 86‐gal. vessels. The variables studied were power input per unit volume, phase fraction, impeller type, and vessel scale. Dispersed phase mixing rates were found to be in the range where they can have significant effects on chemical reactions. A typical value of the mixing rate is 10 volumes of dispersed phase/min. at a power input of 10 hp./1,000 gal. The information given here and in Part I shows for the first time the importance of these effects in reactor design.
Enthalpies of methane‐light hydrocarbon binary mixtures in the vapor phase
Authors: Edmister Wayne C. , Yarborough Lyman
Published: June 2004

The isothermal effects of pressure and composition on the mixture and partial enthalpy differences of the methane‐propane binary were derived from PVTy data. A graphical and numerical technique was used to derive the enthalpy differences from 100° to 460°F. and 200 to 2,000 lb./sq. in. abs. for the complete composition range of the binary.

The isothermal effects of pressure and composition on the mixture enthalpy data of the methane‐propane binary were also calculated with the Benedict‐Webb‐Rubin and the Redlich‐Kwong equations of state. The results of the three methods of calculation are compared. The comparison showed that the two‐constant Redlich‐Kwong equation of state is as good as the eight‐constant Benedict equation of state in the superheated vapor region.

The data derived in this work were combined with other methane binary enthalpy data from the literature to construct a general correlation of the effect of pressure and composition on the enthalpy of methane‐light hydrocarbon binaries. The correlating parameters are the pseudo reduced temperature and pressure and a mole‐average acentric factor.
Optimum effectiveness factors for porous catalysts
Authors: Cunningham R. E. , Smith J. M.
Published: June 2004

In the manufacture of catalyst pellets from particles of powder, for example alumina, one of the parameters is pellet density. The opposing effects of density on surface available for reaction and on pore diffusion result in a specific pellet density for maximum reaction rate per unit volume of reactor. The method for predicting the optimum density and rate is presented for a first‐order reaction. The data required are pore volumes and pore‐size distributions as a function of density, as well as kinetic measurements. Such data are available for the ortho‐para hydrogen reaction using a nickel oxide‐on‐alumina catalyst. Using this system as an illustration, it can be seen that the optimum effectiveness factors are less than unity and range from about 0.68 for 1/8‐in. diam. spherical catalyst pellets to 0.29 for 1‐in. pellets. Corresponding optimum densities are from about 1.3 to 0.6 g./cc

The results demonstrate the possibility of a tailor‐made pelleted catalyst for optimum reaction rate.
Performance of packed columns VII. The effect of holdup on gas‐phase mass transfer rates
Authors: Shulman H. L. , Savini C. G. , Edwin R. V.
Published: June 2004

To account for the differences in the gas‐phase mass transfer coefficients obtained by the use of vaporization and absorption techniques, data were obtained for ring and saddle packings in a 12‐in. diam. column employing water vaporization and methanol absorption. The ratio of the vaporization to absorption coefficient, corrected for differences in diffusivity, is found to be directly proportional to the ratio of the total holdup to the operating holdup in confirmation of the proposed model in which the effective interfacial area for each type of operation is proportional to the holdup of the liquid active for that operation.
Diffusion resistances in alumina and silica catalysts
Authors: Rao M. Raja , Smith J. M.
Published: June 2004

Reaction‐rate measurements were made for the ortho‐para hydrogen conversion at −196°C. at 1 atm. pressure with nickel oxide catalysts using alumina and silica gel as carriers. Data were obtained for fine particles for which pore‐diffusion resistances were negligible, for large particles of silica catalysts containing only micropores, and for alumina pellets containing both micro‐ and macropores. From these data experimental effectiveness factors were evaluated.

Theoretical effectiveness factors predicted by using a previous theory (7) agreed well with the experimental results. The application of the theory requires pore‐geometry data. The measurement of these data and their use in predicting diffusion resistances are illustrated by experimental data and calculations for the several catalysts. It is shown that a satisfactory method of predicting the significance of diffusion within porous catalysts requires information on the pore volume and pore sizes.
Experimental study of laminar flow heat transfer with prescribed wall heat flux
Authors: Akins R. G. , Dranoff J. S.
Published: June 2004

Laminar‐flow heat transfer in a cylindrical tube was studied experimentally in order to test a recent analytical method of predicting temperature profiles (1). The experimental equipment was designed to measure wall temperatures to better than 0.1°C. and to utilize small radial heat fluxes so as to minimize effects of natural convection.

A series of experiments was carried out on five different types of prescribed wall heat flux with water flowing in a vertical tube. The measured wall temperatures in these experiments compared well with those predicted by the theoretical solution. Small deviations which did exist were explained in terms of experimental errors.

The agreement found indicates that the analytical method may be safely used in the study of experimental data in such heat transfer and analogous mass transfer problems.
A theoretical and experimental investigation of the effects of horizontal barriers in thermal diffusion columns
Authors: Fleming J. R. , Powers J. E.
Published: June 2004

A theoretical and experimental investigation of the effects of horizontal barriers on the separation of binary mixtures attained in thermogravitational thermal diffusion columns was undertaken in an attempt to further the understanding of these effects. The presence of horizontal barriers serves to reduce the internal convective flow and to divide tht column into a number of smaller columns with interconnecting end feeds. Equations developed from such a model serve to predict the effect of the number of barriers, temperature difference, barrier diameter, and other parameters on the steady state and transient behavior of a batch column and on the manner in which bulk flow through the column influences the steady state separation in continuous‐flow columns.

Data were taken in both batch and continuous columns to test the theory. Parameters varied experimentally (with an ethanol‐water system) were number of barriers, (N = 0, 2, 4, 8, 16, 50), temperature difference, and diameter of the cylindrical barriers. It was found that the theoretical developments were entirely adequate to explain the observed influence of number of barriers for both types of column operation. The slight dependence of steady state batch separation on temperature difference that was observed is consistent with data of other investigations, and the independence of this type of separation on barrier diameter is in agreement with theoretical predictions. The theoretical predictions with respect to changes in temperature difference and a semitheoretical analysis of the effect of barrier diameter making use of isothermal hydrodynamic determinations proved satisfactory in predicting the influence of changes in these two parameters on both the transient batch and steady state continuous‐flow column operation.
Unsteady state absorption of carbon dioxide by dilute sodium hydroxide solutions
Authors: Rehm T. R. , Moll A. J. , Babb A. L.
Published: June 2004

Rates of carbon dioxide absorption by 0.01, 0.05, and 0.1 molar sodium hydroxide solutions were measured at 25°C. for exposure times from 1.4 to 21.6 milliseconds with a laminar‐jet technique. Absorption rates were calculated with a model based on one‐dimensional diffusion occurring simultaneously with two consecutive irreversible chemical reactions. The resulting partial differential equations were solved with an IBM‐709 computer. The calculated absorption rates agreed within 5% of the experimental values.
Thermal diffusion of salt solutions in single‐stage cells and in continuous horizontal columns: The system copper sulfate‐cobalt sulfate‐water
Authors: Fisher G. T. , Prados John W. , Bosanquet L. P.
Published: June 2004

The application of thermal diffusion to the separation of a pair of salts in aqueous solution was investigated. Experiments were conducted with the system copper sulfate‐cobalt sulfate‐water with both static, single‐stage cells and continuous, countercurrent flow contactors (or columns) of the horizontal Jury‐Von Halle type which utilizes flow through a porous membrane. Design equations for the continuous columns were developed, based on an idealized representation of the combined hydrodynamic and diffusion problem. Data from the single‐stage experiments were used in conjunction with these equations to predict stage separation factors and transfer unit heights. These mass transfer parameters were measured under various operating conditions on continuous units of two different sizes.

The effects of size and operating conditions on the separation factor and transfer unit height were successfully predicted by use of the design equations. The accurate calculation of these quantities directly from single‐stage separation data was less successful, owing to the highly idealized nature of the mathematical model employed.
An engineering study of the rotary drum crystallizer
Authors: Chaty John C. , O'Hern Harold A.
Published: June 2004

In the rotary drum crystallizer, solids are deposited from a molten liquid mixture on the cooled surface of a drum. Rotation of the drum carries the solids from the melt to a scraper blade which removes the crystal deposit in a liquid free, convenient form. The object of this investigation was to obtain data on the separation of binary mixtures over a range of melt temperature, drum coolant temperature, drum rotational rate, concentration of impurity in the liquid, and agitation of the liquid. Four systems were studied: naphthalene‐benzoic acid, beta‐naphthol‐naphthalene,p‐xylene‐m‐xylene, water‐sodium chloride.

The experimental results show that separation improved with increasing agitation, increasing coolant temperature, decreasing drum speed, and decreasing liquid impurity. For the naphthalene‐benzoic acid system, the major system studied, the maximum stage efficiency was 96%. The results indicate that the vigor of agitation and the drum coolant temperature are the two most important variables which affect the separation. It was possible to calculate the rate of solid deposition with heat transfer data.

The rotary drum crystallizer appears to be an effective device for industrial separation of organic chemicals.
Use of adiabatic experiments for kinetic studies in fixed catalyst beds
Authors: Schmidt J. P. , Mickley H. S. , Grotch S. L.
Published: June 2004

A method is presented for using an adiabatic reactor to study the kinetics of reactions of gases on solid catalysts. The method is based on measurement of the steady state axial profile of temperature or composition in a specially designed adiabatic packed bed reactor. Reaction rates are calculated from these measured profiles by graphical differentitation. The method is applicable for multireaction systems and for any type of kinetic behavior.

The method was demonstrated by an experimental study of cumene cracking an silica‐alumina catalyst at 420° to 480°C. The measured reaction rates are in satisfactory agreement with results obtained by other investigators who used isothermal reactors. Areas of application of the adiabatic method are suggested.
Turbulent motion and mixing in a pipe
Authors: Lee Jon , Brodkey Robert S.
Published: June 2004

Turbulent mixing of a dye solution injected at the center of a pipe was studied by means of a new light probe developed for the measurement of concentration fluctuations were made both along the axial distance and across the pipe. The concentration fluctuations persisted longer at the center‐line region than anywhere else; this suggested the use of the decay of intensity at the center as an upper limit. Approximately 99% of the initial intensity decayed within 7.5 ft. (30 L/d). The concentration spectra along the axial distance indicated that the eddies initially undergo a scalar energy cascade. Because of the huge difference in the kinematic viscosity and molecular diffusivities the concentration spectra extend much farther toward high wave numbers than the velocity spectrum. Apparently a state of imbalance resulted between the supply of small eddies and their dissipation; this was marked by the appearance of a small hump in the spectra. The phenomenological approximations of Corrsin and of Beek and Miller could be used for the practical problem of predicting the decay of the intensity of the concentration fluctuations or mixing in the pipe geometry studied.
Unsteady diffusion with first‐order reaction
Authors: Lightfoot E. N.
Published: June 2004

Outline below is a method for simplification of the solution of diffusion problems involving irreversible first‐order reactions. It permits writing the concentration profiles for reactive systems in terms of those for nonreactive systems of the same geometry and similar boundary conditions. The method is valid where fluid flow patterns and concentration boundary conditions are time independent and where the assumptions of constant density and mass diffusivity are acceptable. The useful results of this development are summarized in Equations (31) through (33) and represent a generalization of an earlier development by P. V. Danckwerts (1).
Semibatch operation of a recirculation reactor for the hydrogenation of ethylene
Authors: Leinroth J. P. , Sherwood T. K.
Published: June 2004

The purpose of this study was to develop the use of semibatch operation of a recirculation reactor in kinetic studies. Ethylene hydrogenation over a supported copper catalyst was studied experimentally. In semibatch operation one of the reactants is fed at the rate necessary to hold the total pressure in the reactor constant. In ethvlene hydrogenation the reaction rate is directly equal to the feed rate, and the kinetics can be studied at constant partial pressure of either of the reactants. Since ethane is inert, this technique permitted the study of reaction rate as a function of one variable at a time.

Although ethylene hydrogenation has been studied extensively, there is not general agreement regarding the kinetics over a copper catalyst. The results are themselves of interest because they indicate the reasons for the apparently conflicting data in the literature.
A generalized virial equation of state derived from experimental data
Authors: Gyorog Donald A. , Obert Edward F.
Published: June 2004

Generalized virial coefficients B*, C*, D*, and their derivatives have been established to satisfy experimental compressibility and Δuo, Δhodata for spherically‐symmetrical, nonpolar gases.
Statistical surface thermodynamics of simple liquid mixtures
Authors: Eckert C. A. , Prausnitz J. M.
Published: June 2004

The surface properties of nonpolar liquid mixtures are derived from the application of the grand partition function to a cell model of the vapor‐liquid interface. The surface tension and surface composition are expressed in terms of the activity coefficients in the bulk liquid and pure‐component properties. The results are in excellent agreement with existing data for the surface tension of mixtures. This treatment provides a sound theoretical basis for the prediction of surface properties of other liquid systems and is especially applicable to cryogenic mixtures.
An analysis of the equilibrium stage separations problem—formulation and convergence
Authors: Friday John R. , Smith Buford D.
Published: June 2004

The formulation of a solution method for the equilibrium stage model equations involves six major decisions. Each of these decisions is analyzed and the proper choices indicated. One major contribution of the analysis was a clearer understanding of why any one solution method is not convergent on both distillation and absorber types of problems. A correct solution method is formulated for absorption and extraction problems. This method when programed in parallel with a distillation method works all but a few unusual problems with a minimum of computer time. Another contribution was the development of a procedure for solving the concentration or component rate matrix equations which avoids the computational difficulties of the Lewis‐Matheson and Thiele‐Geddes methods; that is the procedure avoids truncation error build up, does not require mesh points, works equally well for any number of feeds and side streams, and handles nondistributed components in the same way as distributed ones.
Velocity profiles of thoria suspensions in turbulent pipe flow
Authors: Eissenberg D. M. , Bogue D. C.
Published: June 2004

Velocity profiles and friction factors of non‐Newtonian fluids in turbulent pipe flow can be displayed with the semiempirical forms developed for Newtonian fluids in which the apparent viscosity evaluated at the wall shear stress is used.

Friction factors and velocity profiles were obtained for a dilute and a concentration aqueous thoria suspension and compared with the Newtonian correlations and with previous data obtained from widely different non‐Newtonian fluids including a viscoelastic fluid. A relationship is shown between the decrease of the friction factor and the change in the velocity distribution towards a more laminar profile.

A generalized method of deriving the friction factor‐Reynolds number plot from the velocity profile based on the von Kármán relationship for Newtonian fluids is derived and compared with the data.
Turbulence energy and intensity spectra in a baffled, stirred vessel
Authors: Kim W. J. , Manning F. S.
Published: June 2004

The radial components of the turbulence energy and intensity spectra within a stirred, baffled tank are measured with a transducer probe of the type developed by Eagleson et al. (9). The spectra are normalized because absolute levels of the intensity in these high intensity velocity fields cannot be measured with the present technique. Average velocities are also measured with Pitot and Prandtl tubes.

Range of measured energy and intensity spectra was 19 to 1,100 cycles/sec. The measured energy spectra show a k−5/3‐relation in the low wave number range where the wave number k is less than 100 ft.−1 and a k−10/3‐relation in the wave number range of 100 to 1,000 ft.−1. This behavior is found regardless of impeller size, motor speed, and position in tank, in particular radial distance, indicating that the decay of energy spectra is self‐preserving. Increasing the viscosity from 0.80 to 103 centipoises results in a progressively steeper slope in the high wave number range. The shape of the intensity spectra is the same as that of the concentration spectra measured by Manning (26, 27).
Kinetics of sulfochlorination of cyclohexane in carbon tetrachloride induced by gamma radiation
Authors: Schneider Alfred , Chu Ju Chin
Published: June 2004

Solutions of cyclohexane, chlorine, and sulfur dioxide in carbon tetrachloride were irradiated in an oxygen‐free system with gamma rays from uranium fission products contained in spent fuel elements. Reaction rates, equivalent to the rate of disappearance of free chlorine, were determined spectrophotometrically at 4,000Å. The reaction products were cyclohexanesulfonyl chloride and hydrochloric acid in nearly stoichiometric quantities. An empirical rate equation was derived, in which the rate of disappearance of chlorine was shown to be proportional to the square root of the product of the product of absorbed radiation, chlorine and cyclohexane concentrations, and independent of the concentration of sulfur dioxide. A chain mechanism was proposed, and the rate equation derived from this scheme was found to be in excellent agreement with the empirical rate equation. The reaction proceeded by a free radical mechanism, as evidenced by the strong inhibiting effect of oxygen. G numbers were of the order of 105, corresponding to an estimated chain length of 5,000, which is of the same order as the quantum yield of the photochemical sulfochlorination.
Dynamic optimization of a two‐stage reactor system
Authors: Thibodeau Robert D. , Stevens William F.
Published: June 2004

With the development of relatively inexpensive control computers and on‐stream analyzers, on‐line dynamic optimization of nonlinear, multistage systems has become more feasible. Investigators have been concerned with the static optimization and control of single‐stage and multistage systems, but few have considered the optimization of a multistage system whose behavior is nonstatic owing to stochastic changes in its input and environment, and whose optimal control policy is time varying.

This paper looks at the problem of dynamic optimization as it applies to the analysis of a multistage continuous stirred‐tank reactor system. A variational approach, in which the physical restraints on the manipulatable variables are included by a parametric representation, led to a bang‐bang, sampled‐data, optimal control law, or an equivalent analytical expression for continuous optimal control. Inclusion of the inequality relationships, specifying amplitude constraints on the manipulatable variables by a penalty function, resulted in a set of nonlinear Euler‐Lagrange equations specifying the control law.
A study of interstitial liquid flow in foam. Part I. Theoretical model and application to foam fractionation
Authors: Leonard Ralph A. , Lemlich Robert
Published: June 2004

A theoretical model for interstitial liquid flow in a stationary or moving foam was devised by relating the physical structure of the foam to the physical properties of the surfactant and the foam movement. This was accomplished through a differential momentum balance within a typical capillary (Plateau border) of noncircular cross section with finite surface viscosity at its boundaries. Velocity profiles were then calculated and integrated numerically for the randomly oriented capillaries so as to obtain the overall liquid flow through the foam in terms of the pertinent variables. Results are presented in a form suitable for estimating concentrations and flow rates of product and waste streams in foam fractionation.
Some molecular transport characteristics in binary homogeneous systems
Authors: Longwell P. A. , Sage B. H.
Published: June 2004

The behaviors of several diffusion coefficients are shown for the methane‐n‐butane system under conditions such that solutions are very nonideal and the concentrations of both components are significant. The coefficient proposed by Chapman and Cowling shows the least variation with state and is recommended for use under such conditions in hydrocarbon systems. Several other coefficients commonly used show large variations with state and coefficients using concentrations as a potential are even negative in certain regions.
Mass transfer in a sparged contactor: Part I. Physical mechanisms and controlling parameters
Authors: Braulick W. J. , Fair J. R. , Lerner B. J.
Published: June 2004

Studies of the air oxidation of aquoeus sodium sulfite solutions were made in simple bubble contacting columns of 3‐, 4‐, and 6‐in. diameter. Superficial gas rates up to 300 lb./hr.‐sq.ft. were used. Contacting action is described in detail, and comparisons with air‐water data show the marked influence of small, ionic bubbles. Mass transfer and dynamic gas holdup data are presented, and the former are compared with mass transfer data for bubble‐cap trays.
On the stability of a detailed packed‐bed reactor
Authors: McGuire M. L. , Lapidus Leon
Published: June 2004

An analysis of the stability of a packed‐bed reactor is presented subject to a model including axial and radial gradients in the interparticle field and gradients plus reaction in the intraparticle field. The stability of the entire reactor is characterized in terms of various stable and unstable conditions inside the porous particles. Simplifications in the mathematical model are shown to be invalid in many situations.
The friction factor–Reynolds number relation for the steady flow of pseudoplastic fluids through rectangular ducts. Part II. Experimental results
Authors: Wheeler John A. , Wissler Eugene H.
Published: June 2004

The friction factor and Reynolds number were measured for sodium carboxymethylcellulose (cmc) flowing through a rectangular duct. Measured values were compared with values calculated in Part I of this paper. Both a pipe viscometer and a Couette viscometer were used to evaluate the rheological parameters for the fluids. Calculations were based on a power law model. The agreement between theoretical and experimental values was excellent.
Mixing and chemical reaction in turbulent flow reactors
Authors: Keeler R. Norris , Petersen E. E. , Prausnitz J. M.
Published: June 2004

Mixing and a rapid, second‐order irreversible chemical reaction were studied in a turbulent chemical flow reactor, with a point conductivity probe used to detect changes in concentration. From the mathematical theory of Toor, it is shown experimentally that data on the mixing of a passive scalar additive in a nonreactive system may be used accurately to predict the yield of a rapid, irreversible second‐order reaction when the hydrodynamics and initial conditions on mixing for the reactive system are identical to those of the nonreactive system. Increasing the bulk average concentration of one reactant is shown to have a strong effect on the overall reaction yield.
Foam columns for countercurrent surface—liquid extraction of surface‐active solutes
Authors: Haas Paul A. , Johnson H. F.
Published: June 2004

The foam separation process uses differences in surface activity to separate components of a solution. Stable foams can flow upward countercurrent to liquid to give countercurrent differential separations with stripping, enrichment, or scrubbing similar to solvent extraction.

Six‐ and 24‐in. I.D. foam columns were operated with sodium dodecylbenzenesulfonate solutions to measure height of transfer unit (HTU) values and foam densities and to develop satisfactory gas spargers, liquid feed distributors, foam drainage conditions, and foam condensation equipment. The HTU values for stripping of Sr‐89 were about 1 cm. for the best conditions of uniform foams, liquid flows of 100 gal./sq.ft.hr. or less, and uniform liquid feed distribution with low inlet velocities. Variations of countercurrent column lengths within 10 to 28 cm. caused little variation in HTU values. The foams were condensed, with four types of pneumatic or mechanical foam breakers used. A pilot plant was designed for decontamination of a low level radioactive waste.
Constitutive equations for viscoelastic fluids with application to rapid external flows
Authors: White J. L. , Metzner A. B.
Published: June 2004

A major problem in the analysis of complex flows of viscoelastic fluids lies in the development of a suitable constitutive equation relating stresses to the kinematics of deformation. In this paper an equation is developed from successive approximations to a very general theory of viscoelasticity. This equation, which predicts both a non‐Newtonian viscosity coefficient and normal stress effects in simple laminar shearing flows, appears to reflect a reasonable compromise between simplicity and useful applicability to real materials.

The use of this equation is illustrated by means of a study of rapid flows about submerged objects. The results of this study are compared with the usual boundary‐layer theory for Newtonian fluids, and the implications of this comparison are discussed in some detail.
Correlation of latent heats of vaporization
Authors: Martin Joseph J. , Edwards John B.
Published: June 2004

Generalized equations for vapor pressure and PVT behavior are used to develop a functional relationship between latent heat of vaporization and reduced temperature and pressure. This function leads to a graphical correlation which utilizes the slope M of the vapor‐pressure curve at the critical point. The correlation gives the latent heat of vaporization at any temperature in the two‐phase region for any substance for which the critical point and one vapor‐pressure point are known. The correlation is particularly useful for prediction of latent heat of vaporization near the critical point by the use of information for removed from the critical. Included in the study are polar, nonpolar, organic, inorganic, and metallic substances. General predictions of latent heat as a function of temperature are within a few percent wherever comparisons can be made with experimental data.
Mass transfer in horizontally moving stable aqueous foams
Authors: Weissman Eugene Y. , Calvert Seymour
Published: June 2004

An efficient gas absorption device has been developed based on a stable aqueous foam moving in a horizontal duct, with a gas‐liquid interaction that causes only negligible pressure drops.

The study of a liquid‐phase and a mostly gas‐phase‐controlled system has indicated that their mass transfer performance can be predicted. This is based on hydrodynamic data for flowing foams, obtained in a preliminary study published elsewhere.

The influence of geometry, foaming solution properties, and surfactant‐caused interfacial resistance are included in the analysis.
Significance of pressure gradients in porous materials: Part III. Effect of pressure gradients on the effectiveness of porous catalysts
Authors: Otani Seiya , Wakao Noriaki , Smith J. M.
Published: June 2004

The effect of a change in moles, due to reaction, on the effectiveness of a catalytic reaction is analyzed by calculating the concentration profile along a capillary whose wall surface acts as a catalyst and within a spherical, porous, catalyst pellet. The effectiveness factor E is influenced most when the diffusion is predominately of the bulk type and none at all for Knudsen diffusion. For an increase in moles, the diffusion of reactant into the pellet is suppressed because of the opposing pressure gradient. The result is a decrease in E.

Application to a typical bidisperse catalyst pellet such as alumina indicates that the reduction in E due to an increase in moles is not likely to be large. The effect can be important only if the change in moles exceeds 1 or 2, and the pellet is of the low‐density type with large macropores.

In contrast the pressure gradient is large only when mass transfer is by the Knudsen process.
A matrix method for location of cycles of a directed graph
Authors: Norman R. L.
Published: June 2004

A matrix method is given for determining the nests of cycles of a directed graph. This has been applied to determining the recycle loops of a chemical process flow diagram.
Normal stress and viscosity measurements for polymer solutions in steady cone‐and‐plate shear
Authors: Williams Michael C.
Published: June 2004

Normal stress and viscometric measurements were made on nine polymer solutions with cone‐and‐plate instruments. Temperature, concentration, molecular weight, and chemical structure were varied. Zero‐shear viscosities, obtained by extrapolation of falling‐sphere data, ranged from 0.7 to 380 poise.

A brief description is given of a normal stress‐measurement apparatus, incorporating fast‐response strain gauge pressure transducers. Measurements were made at shear rates between 5 and 2,800 sec.−1, sometimes necessitating a considerable correction for inertial forces.

Non‐Newtonian viscosity, normal stress, recoverable shear strain, and elastic modulus are presented in terms of modified Ferry reduced variables.
An analytical solution for the nonlinear frequency response of radiant heat transfer
Authors: Blum Edward H.
Published: June 2004

An analytical solution is presented for the nonlinear frequency response of a system in which radiant heat transfer is coupled with conduction. The model is that of an object inside an evacuated enclosure whose wall temperature oscillates about a mean. A perturbation analysis solves the describing equations for oscillatory amplitudes less than one‐tent the mean wall temperature. An exact solution to a Ricatti differential equation verifies the perturbation analysis. These solutions show that, contrary to linear experience, the average object temperature over an oscillatory cycle exceeds the mean at the wall.

The complete solution for the frequency response can be divided into three regimes. In the first, at low frequencies, all response is truly linear. In the second, higher harmonics become important, but the response remains that of a lumped parameter systems. In the third, response changes with distance from the object surface and the response at the surface dominates. Nonlinearities are important in the second and third regimes. The solution has several applications.
Unsteady heat transfer to slug flows: Effect of axial conduction
Authors: Chu S. C. , Bankoff S. G.
Published: June 2004

Solutions are obtained for three illustrative cases of unsteady heat transfer to slug flows, taking axial conduction into account. The magnitude of the correction to the solutions neglecting this effect is shown to be quite appreciable near the leading edge. In agreement with previous steady state estimates, the axial conduction correction becomes negligible for Peclet numbers in excess of 100.
Water‐oil displacements from porous media utilizing transient adhesion‐tension alterations
Authors: Michaels Alan S. , Porter Marcellus C.
Published: June 2004

Previous laboratory studies have demonstrated that the injection of small quantities of reverse‐wetting agents during water displacement can increase oil recovery from unconsolidated porous media. Hexylamine is a suitable reverse‐wetting agent. It has been found that the effectiveness of this treatment increases with the quantity of amine injected (slug volume and/or amine concentration in the slug), and that treatments sufficient to stimulate oil production at high water flow rates did not do so at low flow rates. It has been established that the stimulation of oil production by this technique is accomplished by transient adhesion‐tension alterations, resulting in the spontaneous accumulation of oil into large continuous masses which are subsequently mobilized.

The present investigation has attempted to investigate the effect of other variables thought to be important in this system in order to clarify the mechanism by which increased oil recovery is effected. Specifically, the mechanism by which large oil masses are formed and propagated was studied.

Displacement studies conducted in a glass‐grid micromodel, under cinemicrographic observation, revealed that large oil masses form as a consequence of restoration of water wettability (amine desorption) but only if the local oil saturation exceeds the irreducible minimum value (under water‐wet conditions). Mobilization of these oil masses was observed under the influence of a favorable wettability gradient.

Displacement studies were also performed in unconsolidated silica sand beds, under conditions of varying oil‐water viscosity ratio, hydraulic permeability, flow rate, and time at which the amine was injected. In the range of the variables investigated, the additional oil recovered (by treatment) increased as the viscosity ratio increased oil recovery. Water‐oil displacement efficiencies enhanced by amine treatment were found to correlate satisfactorily with a parameter representing the ratio of the hydraulic forces to the capillary forces within the medium.
Deposits formed beneath bubbles during nucleate boiling of radioactive calcium sulfate solutions
Authors: Hospeti Narayan B. , Mesler Russell B.
Published: June 2004

Moore and Mesler postulated microlayer evaporation beneath a bubble to explain the sudden temperature drops observed by them during nucleate boiling of water.

A method was devised to estimate the microlayer thickness from the deposit formed by a series of bubbles during nucleate boiling of saturated calcium sulfate solution containing radioactive sulfur‐35. The results support the microlayer evaporation hypothesis.
A pitot tube method for measuring the first normal stress difference and its influence on laminar velocity profile determinations
Authors: Savins J. G.
Published: June 2004

A scheme is outlined which enables the calculation of the normal stress difference P11‐P22 in fluids undergoing steady Poiseuille flow from measurements with a pitot tube of local velocity distributions. This new technique should enable measurements in a region of shear rate comparable to that encountered in the torsional and circular flow methods. A particularly interesting consequence of the method is it leads one to the inescapable conclusion that the presence of finite normal stresses should produce significant aberrations on the measurement of the velocity profile in the laminar flow of viscoelastic fluids. The presence of a P11‐P22 induced aberration on the velocity profile measurement suggests that caution be exercised in the practice of deducing estimates of the thickness of a boundary layer in the nonlaminar flow of these fluids.
Optimum design of conventional and complex distillation columns
Authors: Srygley J. M. , Holland C. D.
Published: June 2004

A method is proposed for achieving the optimum design, in the sense of minimum plates, for conventional and complex distillation columns for any set of specifications directly dependent on product purity which might be imposed by the designer. The method uses the calculational procedure of Theiele and Geddes, the θ‐method of convergence, and sequential‐search procedures. Illustrative examples chosen from a large number of design problems solved by this method are presented.
The study of multicomponent gas‐solid equilibrium at high pressures by gas chromatography: Part II. Generalization of the theory and application to the methane‐propane‐silica gel system
Authors: Gilmer H. B. , Kobayashi Riki
Published: June 2004

The mathematical relation for the retention volume for elution chromatography has been extended to include the case of a multicomponent elution gas mixture in which all the components are adsorbed appreciably on the adsorbent. The total adsorption, component adsorption, and the K values or the ratio of the gas‐phase concentration to the adsorbed‐phase concentration for each component are related to the retention volume for the components as measured by a technique which distinguishes the molecules in the elution gas from those in the perturbing sample. Radioactively traced hydrocarbons are used in the application to obtain the retention volumes appropriate for the theory.

The relations derived were applied in studying the adsorption of methane‐propane mixtures on silica gel up to a pressure of 1,000 lb./sq. in. abs. The internal consistency of the propane adsorption data with the propane infinite dilution data and the methane data with the pure methane adsorption data obtained by a gravimetric method is demonstrated.
Measurement of the void fraction in two‐phase flow by x‐ray attenuation
Authors: Pike R. W. , Wilkins Bert , Ward H. C.
Published: June 2004

The use of an x‐ray tube that emits a spectrum of energy was shown to be an effective source of monoenergetic radiaton for the measurement of the void fraction in two‐phase, steam‐water flow with the proper selection of the tube wall thickness, x‐ray tube operating conditions, collimation, and traverse time. Assuming monoenergetic radiation, equations were derived for the local and average void fraction and the statistical error associated with the measurement, and were confirmed to be applicable by using the mock‐up technique. This consisted of simulating the two‐phase, steam‐water flow patterns of the experimental system with mock‐ups of Lucite and air. Exprimental data are presented to show that confidence could be placed in the measurements to within the probable statistical error, as all deviations of the measured values of the void fraction from the actual values were less than the probable error. Local and average void fractions for steam‐water, two‐phase flow are given. Application to other systems can be inferred from these results.