bluuebunny/crossref_metadata_2025 huggingface dataset:
Cell model theory of homogeneous fluidization: Density and viscosity behavior
Authors: Saxton James A. , Fitton John B. , Vermeulen Theodore
Published: June 2004

As a step toward a unified treatment of particulately fluidized beds, a statistical‐thermodynamic approach has been investigated, with the smoothed potential cell theory of pure liquids used to establish an equation of state and a collisional‐viscosity relation. This treatment has correlated well with experimental data on liquid‐fluidized beds, and the same method gives reasonable predictions for gas‐fluidized beds. A parameter equivalent to thermodynamic temperature has been identified for fluidized beds, which depends solely upon fluid properties and includes the three‐halves power of superficial velocity. This approach should be of value for interpreting other liquidlike properties of fluidized systems.
The effect of turbulence on hot‐film anemometer response in viscoelastic fluids
Authors: Serth R. W. , Kiser K. M.
Published: June 2004

From studies of turbulence in round jets of Newtonian and non‐Newtonian fluids, it has been found that the response of wedge shaped, hot‐film probes can be influenced by the structure of the flow. In water and in weakly viscoelastic fluids the probe is little affected by turbulence, but for more highly viscoelastic fluids the rate of heat transfer from the hot film is markedly increased. Increases as great as 37% were found in this work; this corresponds to a 250% increase in apparent velocity. For this reason, care must be taken in interpreting measurements obtained with hot‐film wedges (and probably cylinders and cones also) in flows with both laminar and turbulent regimes.
A liquid‐phase adsorption study of the rate of diffusion of Phenol from aqueous solution into activated Carbon
Authors: Miller Conrad O. M. , Clump Curtis W.
Published: June 2004

The differential equation for diffusion of a solute in a quasi‐homogeneous, spherical, ion exchange particle, previously solved for time‐dependent boundary conditions, is applied to an activated carbon adsorption system. This solution differs from the infinite volume solution which assumes constant boundary conditions. The result is applied to experimental data and yields effective adsorbent‐phase diffusion coefficients. Equilibrium and rate studies were performed by using the aqueous phenol solution—activated carbon system. The rigorous solution to the diffusion equation is compared with a recently published frequency domain solution. Excellent agreement is obtained for values of the effective diffusion coefficient computed from the two rate equations.

It is recommended that the rigorous model be used for mechanism and diffusion coefficient determination. After the mass transfer parameters have been obtained, the simplified rate equation may be used for either lumped parameter or distributed parameter models for prediction of fixed‐bed adsorber response. Further studies are required to determine if the simplified model adequately describes fixed‐bed behavior.
The structuring of process optimization
Authors: Christensen James H.
Published: June 2004

The efficiency of process optimization by mathematical programming can be increased by tearing, that is, rearranging the design equations so as to reduce the number of equality constraints. The structure of a system of equations may be depicted as an undirected bipartite graph; algorithm I‐T utilizes this graph to determine an order of solution for the equations which requires no tears. If this is impossible, then algorithm II‐T uses indexing in conjunction with algorithm I‐T to produce an order which minimizes the number of torn equations. This procedure is extended to the problem of minimum recycle parameters, and the two‐way interaction between tearing and algebraic simplification is illustrated.
Conversion and temperature profiles for complex reactions in laminar and plug flow
Authors: Merrill Lavaun S. , Hamrin Charles E.
Published: June 2004

An investigation of the mass and heat transfer equations describing radial and axial profiles for tubular reactors in laminar and plug flow is reported. Reactor conditions evaluated were isothermal, constant wall temperature, and adiabatic. Both diffusion and nondiffusion were considered. The reaction investigated was the demethylation of toluene in the presence of hydrogen.

It was found that diffusion plays only a minor role in laminar flow for the conditions investigated. It was also found that isothermal and constant wall temperature reactor operation affected the temperature and concentration profiles very little when r/R was less than 0.6.
Simultaneous energy and mass transfer in the laminar boundary layer with large mass transfer rates toward the surface
Authors: Manganaro J. L. , Hanna O. T.
Published: June 2004

The laminar boundary‐layer equations are solved asymptotically for simultaneous mass and energy transfer in a variable property binary gas mixture when one component is rapidly transferred toward the surface. Flow is past a surface of arbitrary geometry, and both forced and free convection are studied. Advantage is taken of a mole fraction formulation of the boundary‐layer equations, which considerably simplifies the final results. General results are obtained for energy and mass transfer rates when physical properties are arbitrary functions of both temperature and composition. By considering two sets of property variations, representing extremes between which many actual variations lie, it is shown that in many forced convection problems the rates of energy and mass transfer can be expressed in a particularly simple form. The results also show that property variations are generally more important for free convection than for forced convection.
Upper and lower bounds on the drag coefficient of a sphere in an Ellis model fluid
Authors: Hopke Scott W. , Slattery John C.
Published: June 2004

Hill's extremum principles are not directly applicable to an Ellis model fluid. A method of adapting Hill's principles to the Ellis model was developed and used to calculate upper and lower bounds on the drag coefficient for a sphere moving slowly through such a fluid. Available experimental data were compared with the average of the upper and lower bounds. Agreement was poor with Slattery's data and good with Turian's data. Some reasons to suspect Slattery's data have been pointed out.
A new simulation method for equilibrium stage processes
Authors: Tomich John F.
Published: June 2004

This paper presents a new, general method for mathematical simulation of equilibrium stage operations. The procedure solves component material balance equations with a tridiagonal matrix algorithm. Heat balances and summation equations are handled with Broyden's method. The unique feature of this procedure is that, in a mathematical sense, all equations are solved simultaneously. Therefore, the method can be used for all types of equilibrium stage processes. Additionally, the use of Broyden iteration insures solutions which are both stable and more rapid than current techniques. An exact solution for a twenty tray column with twenty components takes approximately 30 sec. on an IBM 360/65 computer. Successful simulations have been made for both absorption and distillation type of operations which have included complex columns with multiple feeds and side product streams. Design applications of the method cover a variety of equilibrium stage processes in the chemical and petroleum industries.
Single drop breakup in developing turbulent pipe flow
Authors: Swartz John E. , Kessler David P.
Published: June 2004

An experimental study was made on the breakup of a single drop in two phase liquid‐liquid developing turbulent pipe flow. The predominant breakup mechanism was controlled by dynamic pressure forces, and the drop breakup was characterized by one or two smaller drops breaking off a larger drop.

The effect on the increase in interfacial area and the resulting size distribution of the fragmented drops of drop velocity, interfacial tension, initial drop size, and the distance down the pipe was studied. Regression analysis was used to determine the significant effects. Most of these regression equations had significant cubic and two‐factor interactions, which is indicative of the complexity of drop breakup.

The size distribution of the fragmented drops can be approximated by a normal distribution. However, the steady state distribution was not fully developed in the work here.
Combined reactors: Formulation of criteria and operation of a mixed tubular semifluidized reactor
Authors: Rao Kothapalli Babu , Doraiswamy L. K.
Published: June 2004

Combined reactors in which the mixed reactor is followed by a tubular reactor can be optimal for a large number of simple adiabatic exothermal reactions. In the present paper, optimality criteria defined earlier for simple reactions involving a single reactant species have been extended to reactions involving two reactant species and for a system of consecutive reactions.

The oxidation of benzone has been studied in an adiabatic semifluidized mixed tubular (MT) reactor. A definite improvement is possible when the oxidation is carried out in this reactor, as observed by a comparison of the experimental results obtained in tubular, mixed, and MT reactors under adiabatic conditions.
Absorption and scattering of thermal radiation by a cloud of small particles
Authors: Nagy A. R. , Lenoir J. M.
Published: June 2004

An experimental investigation was made of the absorption and scattering of thermal radiation by a cloud of small, spherical, micronsized, aluminum oxide particles in a plane‐parallel enclosure. By using carbon tetrachloride and carbon disulphide as suspendign media, transmission measurements were made with collimated and diffuse sources for wavelengths from 2 to 11μ. By employing a two‐flux diffuse model, the data were correlated to obtain absorption and back‐scattering cross sections. From the diffuse and collimated data, a backscattering coefficient was found which varied linearly with relative refractive index. With the developed coefficients, the absorptivities of the cloud of particles were determined.
An optimal control algorithm using the Davidon‐Fletcher‐Powell method with the fibonacci search
Authors: Birta Louis G. , Trushel Peter J.
Published: June 2004

A numerical method for solving a class of nonlinear optimal control problems is presented. The approach reformulates the associated two‐point boundary value problem as a multidimensional minimization problem. This problem is, in turn, solved by using the method of Davidon‐Fletcher‐Powell. The one‐dimensional minimization problem implicit in the implementation of the Davidon‐Fletcher‐Powell algorithm is handled with the Fibonacci search technique. Several examples are presented to demonstrate the effectiveness of the method for problems with and without magnitude constraints on the control variable(s).
On the numerical solution of problems in multicomponent distillation at the steady state II
Authors: Billingsley D. S.
Published: June 2004

A modification is presented of the Kb method described by Holland. This modified procedure exhibits substantially improved convergence characteristics when compared with the unmodified procedure or with the classical bubble point approach. Further, it provides by far the fastest algorithm known to the author. A second procedure for determining stage temperatures is also given. In this method, flow equations as well as equilibrium relations are satisfied by the temperature profile at each iteration. Next, an improved scheme for handling nonideal mixtures is given. Finally, it is shown that a positive solution to the convergence acceleration equations of Holland may not exist when this procedure is applied to a purity specification.
Statistical models for surface renewal in heat and mass transfer. Part III: Residence times and age distributions at wall surface of a fluidized bed, application of spectral density
Authors: Koppel L. B. , Patel R. D. , Holmes J. T.
Published: June 2004

A method was developed for estimating the age density of transporting elements at a transport surface by using the spectral density of the total element counts. Only total counts, and not individual element histories, need be observed. The method was compared with autocorrelation methods used in an earlier work. Residence times were measured for several sizes of particles at a paticular wall surface of a stirred fluidized bed and at various gas velocities using both spectral density and autocorrelation methods. A dimensionless plot brought all data points near a single curve, valid only for this surface in this bed. Checks of these residence times against values obtained by direct observation of individual particles confirmed the methods.
Acoustic isotherms for argon, nitrogen, methane, tetrafluoromethane, dichlorodifluoromethane, and their mixtures, plus derived interaction potential force constants
Authors: Nierode D. E. , Lewis J. L. , Gaggioli R. A. , Obert E. F.
Published: June 2004

Acoustic velocity data for various isotherms from 1 to 70 atm. are presented for argon (32°F.), nitrogen (32°F.), methane (32°, 70°F.) tetrafluoromethane (32°, 70° F), dichlorodifluoromethane (240°F., p < 30 atm.), and various mixtures (32°F.). Interaction potential force constants for the pure gases are derived from the acoustic data with values for tetrafluoromethane and dichlorodifluoromethane differing significantly from previous literature values. BWR constants are also reported for argon and tetrafluoromethane.
Birefringent flow visualization of transitional flow phenomena in an isosceles triangular duct
Authors: Hanks Richard W. , Brooks James C.
Published: June 2004

A flow visualization study was made with an optically birefringent solution of milling yellow dye in water flowing through a transparent duct of isoceles triangular cross section. The present data confirm a number of theoretical predictions concerning transitional phenomena in triangular ducts. One of the most interesting of these phenomena is the existence of a region of simultaneous laminar and turbulent flow in the duct. The present results, which agree with the theory, indicate an order of laminar and turbulent flow which is inverse to previous observations made with smoke filament tracings.
Evaluation of models for tubular, laminar flow reactors
Authors: Andersen Theodore S. , Coull James
Published: June 2004

Significant error can result when the plug flow model is applied to the analysis or design of luminar flow reactors due to nonconstant radial profiles of velocity, composition, and temperature.

An analysis and comparison of suitable models for the nonisothermal, homogeneous, first‐order, irreversible, laminar, gas flow reactor has shown the finite‐difference solution for radial profiles to be superior to the power‐series approximation of radial temperature and composition profiles.

New capabilities of the present computer solution include isothermal or adiabatic wall, dilute or concentrated feed, any stoichiometric product‐to‐reactant ratio. Chapman‐Enskog model for gas diffusivity, calculation of both heat transfer parameters, and a correction factor to apply to plug flow calculations.

The new, improved computer solution may be used in the basic design or analysis of tubular, laminar flow reactors.
Heterogeneous reactions in the photochlorination of propane
Authors: Boval Bruno , Smith J. M.
Published: June 2004

An experimental study of the photochlorination of propane was undertaken to assess the significance of heterogeneous termination steps (wall reactions). Data were obtained in 2‐ and 10‐mm. I.D. tubular flow reactors with varying oxygen concentrations. The results indicated that homogeneous terminations were dominant in the large reactor, and heterogeneous ones were dominant in the small unit. A kinetic scheme which explained the data was proposed. It included two parallel termination steps: a second‐order homogeneous reaction between C3H7. and oxygen and a first‐order heterogeneous reaction between C3H7. and the reactor wall.

Even though the data were taken in the laminar flow regime, the rate of reaction was a function of Reynolds number for the 10‐mm. reactor. Kinetic factors may explain these results, but the reasons are not clear. More research in this area is needed.

Data taken in the 10‐mm. reactor packed with quartz cylinders gave results similar to those for the 2‐mm. reactor. This provided confirming evidence for the proposed scheme of parallel, heterogeneous and homogeneous termination steps.
Purge dynamics of fuel cells
Authors: Gidaspow Dimitri , Sareen Sarvajit
Published: June 2004

An anisotropic porous media model has been suggested for fluid motion in fuel cell cavities and has been shown to be valid experimentally with an actual fuel cell plate. Analytical solutions for pressure, velocity, and stream function have been obtained for finite and for point sources and sinks in rectangular cavities. Constant purge time curves have been constructed.
Hemolysis in simple shear flows
Authors: Shapiro Stephen I. , Williams Michael C.
Published: June 2004

Whole human blood was sheared in the flow field of a concentric cylinder Couette viscometer in the hope of isolating the physical traumas specifically related to the escape of intracellular hemoglobin. The experimental results indicated that laminar shear stresses per se were not instrumental within the investigated range (up to 600 dynes/sq.cm.). This, plus the hematocrit dependence, evidenced the importance of interaction of individual red cells with a surface in the hemolytic event.
Heat and mass transfer in a channel with surface mass addition: Application to phase change processes
Authors: Sparrow E. M. , Yu H. S.
Published: June 2004

The heat and mass transfer processes in a binary mixture flowing in a parallel plate channel with mass addition at the bounding surfaces are investigated analytically. The rate of mass addition, the temperature, and the mass fraction are arbitrarily prescribed at each of the bounding walls. Similarity solutions are evaluated numerically to yield pressure gradient, Nusselt number, and Sherwood number results for a wide range of each of three governing parameters. It is found that increasingly strong surface mass addition markedly increases the magnitude of the axial pressure gradient. Mass addition decreases the Nusselt and Sherwood numbers at the channel wall at which the injection is strongest but may actually increase these moduli at the opposite wall. A generalizing analysis is performed to accommodate phase change processes as well as to accommodate the specification of plenum conditions rather than wall surface conditions. Application is made to the evaporation of liquid water by an air stream. It is shown that the rate of evaporation is augmented as the rate of air injection increases, but the extent of the augmentation is less than the causative increase in the air flow rate.
Analysis of kinetic parameters from batch and integral reaction experiments
Authors: Seinfeld John H. , Gavalas George R.
Published: June 2004

The estimation of chemical reaction rate constants from experimental batch or integral reactor data is examined. Consideration is given to the effect on the accuracy of the parameter estimates of the number of concentrations measured, extending the range of measurements to higher conversions, and experimental errors. The study is based on estimates of two rate constants obtained by quasilinearization in the pyrolytic dehydrogenation of benzene. It is found that if fewer than the number of independent components are to be measured, certain components produce better parameter estimates than others. The level of experimental errors is by far the most significant factor in obtaining reliable parameter estimates.
Predicting fractionator dynamics by using a frequency domain solution technique
Authors: Bollinger R. E.
Published: June 2004

Methods are described for predicting the dynamic behavior of high purity fractionators. The paper shows how to model both the composition and hydraulic response in towers with many trays and in towers which are subject to a variety of disturbances. The technique involves the transformation of the linear dynamic equations to the frequency domain and the solution of the resulting complex algebraic equations for specific values of frequency. The paper includes a description of the model formulation, solution, and validation, and applications including the design of feedforward controllers.
Small surface waves and gas absorption
Authors: Dick G. F. , Marchello J. M.
Published: June 2004

Surface renewal models based on wave induced drift currents are proposed to explain gas absorption data in deep tanks. A model assuming plug surface flow was found to best represent the available data for the absorption of carbon dioxide, oxygen, propylene, and helium into water. Velocities obtained by fitting the mass transfer data agree with experimental velocities obtained from dye studies.
Optimization of a continuous through‐circulation dryer
Authors: Thygeson J. R. , Grossmann E. D.
Published: June 2004

A mathematical model of a through‐circulation packed bed dryer is presented in this paper. The semitheoretical model treats the case of constant rate drying in a deep bed of granular solids under initially uniform drying conditions. Experimental data for drying in superheated steam, mixtures of superheated steam and air, and air alone showed good agreement with predictions of the model.

Based on the model, a static optimization method is developed for optimal operation of a continuous through‐circulation dryer subject to the inequality constraints of maximum permissible air‐horsepower per unit bed area and maximum permissible local final moisture content in the bed. A nonlinear capacity function is defined in terms of the independent drying variables and is maximized under the above nonlinear restraints.
High velocity compressible viscous flow
Authors: Schwartzberg Henry G. , Gurevich Michael
Published: June 2004

Pressure drops were measured for the high velocity isothermal viscous flow of steam in circular tubes. For the velocities tested, up to 0.48 times the isothermal sonic velocity, these flows obeyed the following equation with an average deviation of 2.4%.

This equation differs from the Poiseuille‐Meyer equation commonly used to correlate isothermal viscous flow in that it includes the term (NRe/3) In (P1/P2) which accounts for the change in momentum caused by expansion. In deriving this equation, the mean velocity, mean squared velocity, and wall shear stress were obtained from the parabolic velocity distribution for normal viscous flow. The velocity profile should flatten as the isothermal Mach number increases, and it is therefore anticipated that somewhere above the range tested the equation will no longer prove applicable. Variants of the equation, which take into account the flattening of the velocity profile in the range tested, did not fit the experimental data quite as well.
A new technique for chemical kinetics at high pressures
Authors: Grieger R. A. , Eckert C. A.
Published: June 2004

Information about the transition state of a chemical reaction is quite useful for the determination of mechanisms and for design of solvents for the reaction. High pressure kinetic studies, if sufficiently accurate, provide the required data. This work reports a new technique developed for measuring rates of chemical reactions in solution at high pressure. This method involves in situ mixing of reactants under pressure and direct sampling for analysis, eliminating large errors of temperature equilibration and time measurement inherent in existing techniques, and thus yielding more accurate results. Experimental results for the Diels‐Alder reaction of isoprene and maleic anhydride are reported at pressures up to more than 6,000 atm.
The periodic viscous sublayer in turbulent flow
Authors: Meek Ronald L. , Baer Alva D.
Published: June 2004

The model of the fluctuating viscous sublayer proposed by Einstein and Li was modified by treating some of the objections to the original formulation without greatly altering the essential simplicity of the concept. The applicability of this model to the description of the important features of turbulent flow and heat transfer in ducts and of the Toms phenomenon was evaluated by comparison of predictions of the model with experimental measurements. The mean period for growth and decay of the sublayer and the magnitudes of the wall‐pressure fluctuations and wall‐temperature fluctuations were compared for the flow of air and liquids. Quantitative spatial features of the periodic sublayer, that is, minimum and maximum sublayer thickness and patch size in the directions normal and parallel to the flow direction, were determined.
Experimental determinations of several thermal properties of a mixture containing 51 mole percent Propane in Methane
Authors: Yesavage V. F. , Katz D. L. , Powers J. E.
Published: June 2004

Results of calorimetric determinations are reported for a mixture containing approximately 51 mole % propane in methane. Measurements were made with both isobaric and throttling flow calorimeters in the liquid, critical, gaseous, and two‐phase regions in the temperature range from −250° to +300°F. at pressures of between 100 and 2,000 lb./sq. in. abs. Tables of experimental values of heat capacity, Joule‐Thomson coefficient, and isothermal throttling coefficient are presented, and the values of Cp and ϕ are summarized on parametric plots.

Experimental values of enthalpy differences within the two‐phase region determined under both isobaric and isothermal conditions are also reported together with the experimentally determined phase boundary data. A skeleton enthalpy table is presented which is based almost entirely on experimental data obtained in this investigation. Comparisons are made with other published calorimetric data and with calculations based on PVT data.
Optimal feedforward control of concurrent tubular reactors
Authors: Bertran David R. , Chang Kun S.
Published: June 2004

Optimal control of concurrent nonlinear tubular reactors for complex reaction system is studied. The jacket side temperature is allowed to vary along the reactor length and with time. The optimal control possesses feedforward component only, and the nonlinear gain may be precomputed. For a Denbigh type of reaction system, if the heat generation is negligible, the control temperature is insensitive to feed concentration variations. With heat generation effect present, the optimal control is time dependent, and the nonlinear feedforward gain is obtained. The gain may be approximated by a linear function to construct a simple linear feedforward control loop which contains a synchronized time delay.
Mixing in viscous liquids
Authors: Coyle C. K. , Hirschland H. E. , Michel B. J. , Oldshue J. Y.
Published: June 2004

Detailed data are reported for blend time and turnover time with a 17‐in. impeller operating in an 18‐in. diameter tank. Above 1,500 centipoises, viscosity had no effect on blend time at constant speed. Blend time was inversely proportional to speed.

The inner flight of a helical impeller is of value when blending pseudoplastic fluids but has no effect on blend time with Newtonian fluids. The ratio of blend time to turnover time is given, as well as the effect of several different helical impeller geometry variables.
Optimal probability partial control of linear inventory systems
Authors: Kim S. M. , Wilde Douglass J.
Published: June 2004

Most processes have more storage levels to control than there are production rates for changing inventories, a situation known as partial controllability. Necessary and sufficient conditions under which all levels can be held within predetermined limits are presented. A control law maximizing the probability of satisfactory operation is developed, together with the computational steps required for its implementation. A simple numerical example is given.
The effect on conversion of flow rate variations in a heterogeneous catalytic reactor
Authors: Denis G. H. , Kabel R. L.
Published: June 2004

The unsteady state behavior of a tubular heterogeneous catalytic reactor, in which significant adsorption effects occur, has been investigated theoretically and experimentally. Transient responses of conversion to step increases and decreases of flow rate as well as to periodic variations in flow rate are considered. A simplified procedure for anticipating gross effects in cyclic processes is suggested.
Effect of fouling on stability of adiabatic packed bed reactors
Authors: Ervin Michael A. , Luss Dan
Published: June 2004

The effect of catalyst fouling on the stability and operation of adiabatic packed bed reactors was investigated for two poisoning mechanisms. The effect of fouling was found to be most predominant for packed beds in which nonunique pseudo steady states can exist. Fouling may cause the reactor to misbehave suddenly, with a violent temperature rise, after a long period of pacific operation.
Pore‐diffusion Mechanisms during vapor‐phase adsorption
Authors: Nemeth Edward J. , Stuart Edward B.
Published: June 2004

The mechanism of diffusion in an absorbent pore was studied by applying adsorption rate data to the Damköhler equation. Most of the data were taken in the multimolecular region of the nitrogen‐silica gel adsorption isotherm. Vapor‐phase and adsorbed‐phase contributions to the total transport were separated. Vapor‐phase transport increased with temperature and was most dominant at relative pressures of 0.4 to 0.6. Adsorbed‐phase diffusivities were of the order of 10−2 — 10−3 sq. cm./sec. and showed some dependence on the amount adsorbed at surface coverages greater than 1.5 molecular layers.
Photodecomposition kinetics of formic acid in aqueous solution
Authors: Matsuura Takeshi , Smith J. M.
Published: June 2004

The photodecomposition of aqueous solutions of formic acid was studied as a model reaction for removing organic pollutants from water. The process was carried out in a tubular‐flow reactor, operated continuously. The cylindrical reactor was irradiated from the outside by placing the cylindrical lamp and the reactor at the foci of an elliptical reflector. Measurements made at differential operating conditions permitted calculation of rates of reaction as a function of formic acid concentration and light intensity for the temperature range 25° to 60°C. Carbon dioxide and carbon monoxide were the only observed products of the decomposition.

The rate was first order in absorbed light intensity and between zero and first order in formic acid. These results correspond to a combination of chain and non‐chain kinetics occurring simultaneously. Rate constant ratios and quantum yields were calculated from the data and the kinetics model.

A few measurements were made by adding ferric chloride and ferrous chloride to the feed to the reactor. An order of magnitude increase in rate was observed with these sensitizers.
Behavior of countercurrent liquid‐liquid columns with a liquid metal
Authors: Johnson T. R. , Pierce R. D. , Teats F. G. , Johnston E. F.
Published: June 2004

Packed columns are being considered for contacting liquid metals with molten salts to extract fission products from spent nuclear fuel. Extraction rates between a liquid cadmium alloy and a liquid chloride salt were measured at 530°C. in a prototype column. With a system of water and a low melting metal alloy, measurements of the pressure drop, limiting flow rates, and hold‐up were made and compared with the predictions of existing correlations. These data indicate that packed columns might be effective contacting devices for pyrochemical processes.
Heat and mass transfer in the wall region of turbulent pipe flow
Authors: Hughmark G. A.
Published: June 2004

Models for the laminar sublayer of turbulent pipe flow are reviewed. The observations of the sublayer by Popovich and Hummel and the experimental fluctuation frequencies obtained by Shaw and Hanratty are used with the models to evaluate experimental heat and mass transfer data. The eddy diffusivity model and a parallel conductance model appear to be consistent with the experimental data.
Ultrafiltration of proteins in stagnation flow
Authors: Kozinski A. A. , Lightfoot E. N.
Published: June 2004

The effect of viscosity and diffusivity variations on concentration polarization during the ultrafiltration of protein solutions in two‐dimensional stagnation flows is investigated by numerical integration of the equations of continuity and motion. It is found that these effects are surprisingly small and insensitive to the forms of concentration dependence postulated. The high Schmidt numbers and low permeation rates characteristic of these systems result in considerable simplification of the analysis and permit use of a modified Chilton‐Colburn relation for predicting the onset of sludge formation at the membrane‐solution interface. The predicted dependence on Schmidt number agrees with published experimental data for other boundary‐layer flows and suggests the possibility of improved prediction of equipment performance.
Interfacial mass and heat transfer during evaporation: II. Effect of monomolecular films on natural convection in water
Authors: Navon Uri , Fenn John B.
Published: June 2004

The reduction in evaporation from a water substrate and the accompanying change in heat transport through the water induced by monolayers of cetyl alcohol and stearic acid are investigated. Evaporation resistance of the monolayer and Nusselt number in the water are determined at 2° to 22°C. The evaporation resistance increases with increasing surface pressure of the monolayer. In the presence of natural convection in the water, the Nusselt number decreases during monolayer compression. This reduction is larger than could be expected just from the lowered evaporative heat flux and the resulting reduction in the Rayleigh number. It may be due to a change in the surface hydrodynamic characteristics caused by the monolayer.
Parametric pumping: Modeling direct thermal separations of sodium chloride‐water in open and closed systems
Authors: Sweed Norman H. , Gregory R. Alan
Published: June 2004

Direct thermal parametric pumping separations of a NaCl‐H2O‐ion retardation resin system have been investigated. Experimental breakthrough curves and batch parapump runs were used to determine the lumped‐parameter mass transfer coefficient λ and its dependence on velocity and temperature. Computer simulation of additional batch runs verified both the model and the STOP‐GO algorithm used to solve it. Computer estimates of open‐system behavior are presented.
Bubble coalescence in viscous fluids
Authors: de Nevers Noel , Wu Jen‐Liang
Published: June 2004

The gravity‐driven coalescence of 1‐ to 2‐cm. diameter air bubbles in glycerine and in water has been studied by high‐speed cinematography. The resulting coalescence behavior can be correlated by a simple model which assumes that each bubble trails a wake, and that the bubble coalescing from below accelerates when it enters the wake of the preceding bubble and thus overtakes the first bubble. The predictions of the model are not significantly altered by different assumed wake configurations.
Viscoelastic behavior of molten polymers in porous media
Authors: Siskovic Nandor , Gregory Dale R. , Griskey Richard G.
Published: June 2004

The modification of the Blake‐Kozeny equation for porous media flow using the power law has been shown to hold for molten polymers as well as for the previous cases for polymer solutions. The present work extended the correlation of friction factor with Reynolds number an additional three decades.

It was also shown, however, that the modified Blake‐Kozeny equation broke down when bed shear rates were in the range of excessive curvature on the polymer flow curves (shear stress‐shear rate). In such cases it is suggested that the Newtonian Blake‐Kozeny equation, together with apparent viscosity data, could be used to correlate such porous media flow of non‐Newtonians.

Appearance of viscoelastic effects at the critical Deborah number value of 0.05 predicted earlier were not found to hold. The data of the present investigation show that such a critical value must be at least 0.19 or even higher. This result helps to resolve partially the anomalous results obtained by previous investigators.
Crystallization: Kinetics and design considerations
Authors: Timm D. C. , Cooper T. R.
Published: June 2004

The following nucleation rate and growth rate relationships for the aqueous, continuous, cooling crystallization of potassium dichromate were determined from experimental crystal size distributions: J = 3.9 × 1010 (C – Ceq)0.9; r = 3.0 × 103 (C – Ceq)1.7. Since nucleation rate is of lower kinetic order than growth rate, higher levels of supersaturation will yield crystal distributions with a larger mean size. Therefore for this system, batch or plug‐flow reactors are preferred to continuous‐stirred tanks.
Heterogeneous phase behavior of solid carbon dioxide in light hydrocarbons at cryogenic temperatures
Authors: Jensen Robert H. , Kurata Fred
Published: June 2004

Solubilities of solid carbon dioxide in liquid ethane, propane, and n‐butane were measured from the hydrocarbon triple point or mixture eutectic point to the triple point of carbon dioxide, and an experimental uncertainty was determined for each data point. A eutectic point was discovered in the carbon dioxide–n‐butane system at approximately 134°K., with a eutectic composition of approximately 0.25 mole % carbon dioxide. A nonlinear least squares analysis was used to fit the binary solubility data and carbon dioxide‐methane data from the literature to the Wilson equation for the liquid‐phase carbon dioxide activity coefficient. Better agreement with experimental data was obtained by adding two empirical constants to the Wilson equation. This study shows that the Wilson equation is an excellent model for solid carbon dioxide solubility in liquid methane, ethane, propane, and n‐butane, over the entire composition range, and that the Wilson equation provides a better model than do corrections based on regular solution theory.

The ternary system carbon dioxide‐methane‐ethane was also studied, and liquid and vapor compositions were measured for each of ten ternary mixtures in solid‐liquid‐vapor equilibrium. Ternary phase diagrams were constructed, and an empirical correlation was derived for solid carbon dioxide solubility in methane‐ethane mixtures above 166°K. An important finding was that solid carbon dioxide is more soluble in some mixtures of methane and ethane than in either of the pure components.
Optimal control policies for tubular reactors experiencing catalyst decay: II. Multiple‐bed semiregenerative reactors
Authors: Ogunye A. F. , Ray W. H.
Published: June 2004

The optimal control problem for multiple beds is formulated and a distributed maximum principle derived. Gradient methods are then used to synthesize the optimal control policies for some examples in three‐bed isothermal and adiabatic reactors. Finally, examples are worked to illustrate the computational algorithm in adiabatic beds when optimal catalyst loading is to be determined, and when it is desired to distribute the feed in an optimal fashion between the beds. Reasonably good convergence was obtained in all the examples, so that the method appears quite feasible for determining optimal control policies in multiple reactors subject to catalyst decay.
Blood‐gas transfer in an axial flow annular exchanger
Authors: Chang Hsin‐Kang , Mockros Lyle F.
Published: June 2004

The rates of hemoglobin saturation and carbon dioxide reduction in blood flowing in an annular‐shaped membrane exchanger were studied theoretically by considering two limiting cases: the fluid‐limited case and the wall‐limited case. The blood is assumed to flow axially with a fully developed laminar profile. In the fluid‐limited analysis the membrane wall is assumed to be infinitely permeable, so the efficiency of the oxygenator depends solely on the rate of gas transport within the blood. In the wall‐limited case the blood is assumed to have infinite transport ability, thus the efficiency of the oxygenator is limited by the diffusion rate through the wall. For realistic radii ratio, the oxygenator is fluid limited, thus suggesting the need for enhanced blood mixing. In the fluid‐limited case the rate of gas transport depends on the radii ratio and a dimensionless length, which is independent of the cylinder sizes. IfPO2= 715 mm. Hg andPCO2= 0 mm. Hg are maintained at both walls, oxygenation is the slower process. For the same flow rate the length required for complete hemoglobin saturation in the annulus with an inner to outer radius ratio of 0.95 is 1/65 of that required in a circular tube.
Precipitate flotation of chromium
Authors: Bhattacharyya Dibakar , Carlton J. Andrew , Grieves Robert B.
Published: June 2004

A three‐stage procexsss of reduction of acid chromate (HCrO4−), with NaHSO3followed by precipitation of Cr(III) with NaOH followed by flotation with an anionic surfactant, provides 97% removal of chromium from aqueous suspensions containing 48.3 mg./liter Cr (0.929 mM). The required dosage of surfactant (sodium laurylsulfate) is 0.093 mole SLS/mole Cr, compared to a dosage of 1.1 mole cationic surfactant/mole Cr, used to ion float soluble acid chromate. The precipitate flotation process is pH dependent: below pH 6.3, soluble chromium species become appreciable and the flotation results agree with calculated soluble chromium concentrations; above pH 9.7, the charge of the precipitate is reversed, as indicated by surface potential measurements. The optimum pH range for flotation is 7.0 to 8.8. The effect of initial surfactant concentration on the flotation efficiency is established. Small quantities of calcium enhance the flotation of Cr, while higher concentrations, 0.5 mM and greater, decrease flotation efficiency. For suspensions with a doubled chromium concentration (96.6 mg./liter), the optimum pH range for flotation is lowered and narrowed to 6.3 to 6.5, indicating modifications in particle surface characteristics validated by measurements of surface potential and surfactant adsorption. Eighty‐seven percent flotation is achieved at a 0.093 mole/mole ratio.
Mathematical analysis of sorption experiments
Authors: Duda J. L. , Vrentas J. S.
Published: June 2004

A new technique is derived for determining the concentration dependence of diffusion coefficients from sorption experiments. In this analysis the diffusion equation including the effects of phase volume change and volume change on mixing is solved by a weighted residual method to produce approximate analytical expressions which describe the sorption process. It is possible to deduce the concentration dependence of the diffusion coefficient from a single sorption experiment without assuming the form of the diffusivity‐concentration relationship. A direct evaluation of the technique is obtained from the analysis of test data generated by finite‐difference solutions of the equations which portray the sorption process.
Polymerization in a tubular reactor
Authors: Lynn Scott , Huff James E.
Published: June 2004

A mathematical model has been developed to predict the variations in temperature, velocity, and composition which occur during anionic polymerization in laminar flow in a tubular reactor. It is found that very large radial gradients in all three are to be expected when a solution containing only solvent and monomer is polymerized. Recycle of part of the product or prepolymerization in stirred‐tank reactors may be used to reduce greatly the distortion of the radial profiles.
Improvement of the performance of a fixed‐bed catalytic reactor by relaxed steady state operation
Authors: Bailey J. E. , Horn F. J. M.
Published: June 2004

The relaxed steady state operation of a tubular fixed‐bed catalytic reactor under control of the inlet composition is investigated. It is shown that the performance of such a reactor can be improved under certain conditions by periodically varying inlet concentrations rather than keeping these concentrations time invariant.
Eqation of state for phase equilibrium: I. Pure component
Authors: Yang Chang‐Lee , Yendall E. F.
Published: June 2004

An equation of state for the two‐phase region whose constants depend only on the critical pressure, the critical temperature, the normal boiling temperature, and the latent heat at the normal boiling point is shown to describe vapor pressure, latent heat, and saturation volumes of methane well.
Performance of packed columns: IX. Simulation of a packed column
Authors: Shulman H. L. , Mellish W. G. , Lyman W. H.
Published: June 2004

A model is described which may be used to simulate a packed column for countercurrent gas‐phase controlled absorption with liquid‐phase reaction. The model consists of a number of continuous stirred‐tank reactors in parallel with equal volumes and mass transfer areas. A distribution is presented which uses one parameter to determine the fraction of total liquid throughput going to each reactor. The model successfully predicts all responses, including those of Kga versus time for no reaction, Kga versus inlet acid normality, and Kga versus inlet gas concentration for liquid‐phase reaction for the systems ammonia‐water and ammonia‐sulfuric acid. It also explains the increase in mass transfer obtained by pulsing and controlled cycling.
Suboptimal control of nonlinear systems: I. Unconstrained
Authors: Weber A. P. J. , Lapidus L.
Published: June 2004

An algorithm for suboptimal control of nonlinear unconstrained systems is developed. The result is closed loop, uses the familiar linear‐quadratic optimal approach, and minimizes computational time and effort. Numerous examples are presented.
Pressure‐volume‐temperature behavior of carbon tetrafluoride using a variable‐volume cell of bellows design
Authors: Martin J. J. , Bhada R. K.
Published: June 2004

This paper presents data observed for the pressure‐volume‐temperature (P‐V‐T) behavior of carbon tetrafluoride (CF4) below room temperature, and uses these data in conjunction with higher temperature data from the literature to evaluate an equation of state. The P‐V‐T measurements were made via a variable‐volume technique without using a confining liquid. The variable‐volume design makes it possible to cover a range of specific volumes with a single charge, resulting in an efficient operating procedure.

A unique bellows design with a 14‐fold volume variation was developed. The bellows contained the compound under study (CF4) and was surrounded by a hydraulic liquid whose pressure could be varied causing the bellows to expand or contract. The volume of the bellows was determined by measuring the volume of the hydraulic liquid. Calibrations were made using a gas (CO2) of known thermodynamic properties. Pressure measurements were made via a differential pressure transducer on three Heise gauges calibrated in place against a Ruska dead‐weight tester. The bellows cell was maintained in a well‐agitated bath whose temperature was measured by a platinum resistance thermometer.

The data were taken by charging a known amount of the compound into the bellows and observing the pressure‐volume relationship at a fixed bath temperature. At the end of a run, the charge was recovered, the amount recovered agreeing within 0.01% with the amount charged.

The observed data were analyzed graphically on pressure‐volume, pressure‐temperature, and compressibility diagrams. Very good consistency was observed with the higher temperature data from literature. The data were correlated analytically with the Martin equation of state. This equation represents all the data with an average deviation of 0.25%.