bluuebunny/crossref_metadata_2025 huggingface dataset:
The activated calcium sulfate‐water vapor sorption therm
Authors: Jury Stanley H. , Pollock Mark A. , Mattern James W.
Published: June 2004

The sorption isotherms are reported for the β‐soluble anhydrite form of calcium sulfate (Drierite) exposed to moist air at one atmosphere total pressure and 90, 100, 125, 150, 175, and 200°F. A concentration‐temperature coordinate has been identified which when plotted against the amount sorbed caused all isotherms to collapse into a single sorption therm. The latter has been fit by a three‐term expression based on a combination of sorption theories. A graphical comparison is made between a curve calculated from the analytical expression and actual experimental datum points.

Curve fitting was done by machine and involved minimizing the square of the deviations. Maximum deviations up to 4% are experienced in the high range. In the low range these tend to increase but so do the experimental errors.
Turbulent diffusion in the core of a pipe with uniform transverse flow at the walls
Authors: Suneja S. K. , Shea R. H. , Wasan D. T.
Published: June 2004

An analysis of point source turbulent diffusion of a gaseous tracer in the core of a circular straight porous pipe with uniform transverse flow at the walls is presented. Time averaged concentration distributions were measured at four distances downstream from a point source located at the axis of a fully developed turbulent flow of air in a 6‐in. pipe. Experiments were run at average velocities between 4.36 and 23.0 ft./sec. (corresponding to Reynolds numbers 12,000 to 66,000) with injection velocities ranging from 0 to 0.170 ft./sec. and suction velocities from 0 to 0.048 ft./sec. The highest injection rate corresponded to 58% by volume of the main stream. Good agreement is obtained between the expeimental and the calculated concentration profiles.

The present study shows that the plume width of the disperising tracer is considerably affected by the transverse flow. It also shows that the eddy diffusivity in the pipe core and the radial mass flux increase with fluid injection and decrease with suction through the pipe walls. Also, for increasing values of aspect ratio, they increase in the case of injection and decrease in the case of fluid suction.
Observations of early turbulence in the pipe flow of drag reducing polymer solutions
Authors: Forame P. C. , Hansen R. J. , Little R. C.
Published: June 2004

Early turbulence has for the first time been observed in the flow of very dilute polymer solutions in tubes larger than capillary size. Flow rate‐wall shear stress measurements were conducted in 0.553 and 0.660 cm. diameter pipes. Polyethylene oxide samples of two molecular weights were employed, dissolved in water‐glycerine mixtures with viscosities ranging from 0.0261 to 0.160 poise. The flow rate‐wall shear stress relationship for these solutions corresponded to Poiseuille's Law below a well‐defined onset wall shear stress, at which the Reynolds number was less than the transition value for Newtonian fluids. As the flow rate was increased from the onset condition, however, the wall shear stress became progessively larger than that predicted by the Poiseuille relationship. The onset wall shear stress for the phenomenon increased linearly with solvent viscosity. Its relationship to polymer concentration was dependent on the solvent viscosity. An explanation for early turbulence is suggested on the basis of these results, and the relationship of the phenomenon to turbulent flow drag reduction is discussed.
The use of secondary measurements to improve control
Authors: Weber Richard , Brosilow Coleman
Published: June 2004

Many industrial processes are difficult to control because product quality cannot be measured economically on line. One solution to this problem is to use secondary measurements in conjunction with a mathematical model of the process to estimate product quality. This paper presents a method for designing a static estimator which predicts product quality from a linear combination of process input and output measurements. The design method includes procedures for selecting a subset of the availble output measurements so as to obtain an estimator which is relatively insensitive to modeling errors and measurement noise. Application of the estimator to a simulated multicomponent distillation column shows that the composition control achieved with an estimator based on temperature, reflux, and steam flow measurements is comparable to that achieved with instantaneous composition measurements. The composition control using the estimator is far superior to the composition control achieved by attempting to maintain a constant temperature on any single stage of the column.
A mathematical model for heat transfer in a packed bed and a simplified solution thereof
Authors: Kim D. S. , Gates L. E. , Brodkey Robert S.
Published: June 2004

Heat transfer in packed beds can be mathematically modeled to account for the heat transfer between the particles and the gas phase, the conduction through the solid phase of particles, and the mixing or dispersion within the gas phase in the void structure of the porous media. To solve the resulting differential equations numerically is not easy. The solution for sinusoidal gas temperature input assumes linearity of the logarithm of the temperature with time. If, in addition, linearity with distance can be assumed, then the solution can be vastly simplified to finding the real root of a fourth‐order algebraic equation.
An experimental study of instabilities and other flow properties of a laminar pipe jet
Authors: Iribarne Agripina , Frantisak Frantisek , Hummel Richard L. , Smith James W.
Published: June 2004

Flow patterns in an axisymmetrical laminar pipe jet with a flat entering velocity profile and a diametrical expansion ratio of 1:2 was investigated using nondisturbing flow visualization. A wavelike instability was discovered in the detached shear layer even at the lowest Reynolds numbers, and for Reynolds numbers greater than 350 tangential motions were observed, resulting in considerable turbulence near the mean position of re‐attachment. This turbulence even at low Reynolds explains local high rates of mass and heat transfer. The mean re‐attachment position depends on Reynolds number.

Instantaneous mean velocity profiles and wall shear stresses were determined.
Systematic synthesis of separation schemes
Authors: Thompson Roger W. , King C. Judson
Published: June 2004

The paper reports efforts to automate the synthesis of separation processes. Heuristic and algorithmic programming are used to select both the sequence and types of processes used for the conversion of complex mixtures into specified products. Improved schemes are evolved using learning techniques. An illustrative example is included.
Using the dusty gas diffusion equation in catalyst pores smaller than 50 Å radius
Authors: Omata Hirokazu , Brown Lee F.
Published: June 2004

When the dusty gas diffusion equation is applied to materials containing pores with radii below 50 Å, the observed diffusion behavior in these smaller pore systems can be quite different from that predicted by the equation. Higher temperatures and in some cases higher pressures tend to lessen the deviations between prediction and experiment. The observed deviations are probably caused by surface transport and by momentum transfer between gas molecules and pore walls during molecular flight. For bimodal materials, an additional factor can be the inapplicability of the equation to systems of parallel micro‐ and macropores. Excellent agreement between theory and experiment occurs for large‐pore unimodal systems.
Computer control using optimal multivariable feedforward‐feedback algorithms
Authors: Newell Robert B. , Fisher D. Grant , Seborg Dale E.
Published: June 2004

This paper presents three methods of designing feedforward compensators which can be combined with multivariable feedback controllers in order to minimize or eliminate errors caused by sustained measurable disturbances. The designs are based on a linear, time‐invariant state‐space model of the process and minimize a quadratic function of the errors and/or constrain selected steady state offsets to zero. Simulated and experimental data from a computer controlled pilot‐plant evaporator show that multivariable feedback‐plus‐feedforward control is relatively simple to implement, is practical, and gives excellent control.
The effect of angular light intensity distribution on the performance of tubular flow photoreactors
Authors: Zolner William J. , Williams John A.
Published: June 2004

The angular light intensity distribution (ALID) at the surface of several elliptical reflector‐photoreactors was determined experimentally using the optically dense potassium ferrioxalate actinometer. The distributions were well correlated by the model

The correlating parameter β was a function of the ratio of the light source and photoreactor tube diameters.

The theoretical effect of ALID on reactor performance was determined for a reaction which proceeded via direct absorption by the reactant. The ALID effect on performance was most pronounced under conditions of high optical densities and low radial mixing rates of reactant.
A new model for granular porous media: Part II. Numerical solution of steady state incompressible Newtonian flow through periodically constricted tubes
Authors: Payatakes Alkiviades C. , Tien Chi , Turian Raffi M.
Published: June 2004

A numerical method for the solution of the problem of steady state, incompressible Newtonian flow through periodically constricted tubes is developed. All terms of the Navier‐Stokes equation are retained, including the nonlinear inertia terms.

Sample calculations for a uniform periodically constricted tube, the geometry of which is connected with the modeling of a packed bed of sand are given, including streamlines, axial and radial velocity profiles, pressure profiles, and the dimensionless pressure drop versus Reynolds number relation. The effect of some geometric characteristics of periodically constricted tubes on their friction factor is investigated numerically, and comparison of some existing experimental data with calculated ones is made.
An analysis of carrier‐facilitated transport
Authors: Smith Kenneth A. , Meldon Jerry H. , Colton Clark K.
Published: June 2004

The physical and mathematical characteristics of carrier‐facilitated transport in a liquid film are examined for a reaction scheme of the form A + B ⇄ AB, in which A is the permeating species and B and AB are diffusable species which are constrained not to leave the film. For thin films, a solution is developed as a perturbation from purely physical diffusion and is expressed as a second‐order power series. For thick films, a solution is developed as a perturbation from a state in which the species concentrations at any one point within the film are related by an equilibrium constraint. This development utilizes the techniques of matched asymptotic analysis. Taken together, these solutions provide an excellent estimate of the facilitation for a film of any thickness, as shown by comparison with numerical results.
Gasification: Part I. Isothermal, kinetic control model for a solid with a pore size distribution
Authors: Hashimoto Kenji , Silveston P. L.
Published: June 2004

A model describing the development of specific surface area, volume, porosity, and mean pore radius of a porous solid with extent of gasification is developed based on consideration of pore size growth, initiation of new pores, and coalescence of adjacent pores. Use of population balances and formulation of the properties as moments of the pore size distribution leads to a mathematically simple, closed set of equations for kinetically controlled gasification. The model successfully predicts maximums in specific surface area and number of pores observed by Kawahata and Walker (1962) in the activation of devolatilized anthracite by CO2 in a fluidized bed.
The thermodynamic approach to fluidized drying and moistening optimization
Authors: Sieniutycz Stanislaw
Published: June 2004

For drying and moistening processes in batch fluidization and fluidization in a horizontal exchanger, the overall mathematical model describing simultaneous heat and mass exchange is given. On this basis, the problem of finding the optimal temperatures of inlet gas is formulated and investigated for the case when inlet gas humidity is constant. It is explained that when unit economical values of gas and solid phases are linear with regard to unit available energies (exergies), the economical problem of minimum costs is equivalent to the thermodynamical problem of minimum available energy (exergy) dissipation. Therefore, the performance index expression in exergy terms is formulated as a functional of the Bolza form. The dynamic programming method is used to obtain results of optimal trajectories and decisions. The dependence of optimal process time on apparatus price, which is characterized here by a Lagrangian multiplier λ, is pointed out.

The results indicate that the constant gas inlet temperature policy commonly applied to the processes considered here prevents attainment of the process optimum. In fact, increasing inlet temperature until an admissible gas temperature is attained is the optimal policy.
Stability and uniqueness of a catalyst particle problem: Parameter optimization in Liapunov functions
Authors: Liou Ching‐Tien , Lim Henry C. , Weigand William A.
Published: June 2004

In the analysis of stability and uniqueness of steady state through the Liapunov functional technique, the Liapunov functional is not unique and different forms can lead to significantly different results. A method is proposed in which the state vector and/or the parameters in the weighting matrix S(x) are optimized to obtain less conservative results than those reported previously. For the problem of stability and uniqueness of the steady state of a chemical reaction occurring in a catalyst particle with slab geometry, several sufficient conditions for stability have been developed for both cases of unity and nonunity Lewis numbers in terms of the system parameters and steady state profiles, the system parameters and the catalyst center temperature, and the system parameters alone. These conditions are shown to be stronger than the previously reported results (Murphy and Crandall, 1970). Sufficient conditions for uniqueness have also been developed. For unity Lewis number our uniqueness condition is stronger than the previously reported result (Luss and Amundson, 1967), and for non‐unity Lewis number our uniqueness result is new.
An optimization algorithm for structured design systems
Authors: Westerberg Arthur W. , Debrosse Charles J.
Published: June 2004

Structured design systems are systems which may be represented by generally nonlinear equality and inequality constraints, each of which contains few of the variables in the system. Assuming the existence of an automatic capabity to derive and modify as needed effective solution procedures for sets of structured equality constraints, a two‐step strategy for optimizing design systems is presented in the form of two algorithms. An earlier paper presented an algorithm for locating a first feasible point, and this paper presents a companion algorithm based on the strategy known as restriction to optimize the system once feasible.

This companion algorithm divides the set of inequality constraints into three sets: the set of those currently being held as equality constraints, the set currently released but being used as search coordinates, and the set of all remaining constraints which are not currently part of the problem. Solution procedures are modified as inequality constraints and are moved from one set to another. Added constraints in the set being held tend to aid the optimization process by reducing the dimension of search space for what is usually a marginal added burden in solving an enlarged set of (structured) equations.

The strategy has proved remarkably effective on three relatively simple examples, including a nonlinear 31 constraint, 10 variable alkylation problem.
A critical evaluation of methods for the prediction of critical properties of hydrocarbons
Authors: Spencer Calvin F. , Daubert Thomas E.
Published: June 2004

A critical evaluation and modification of the available methods for the estimation of critical properties of pure hydrocarbons was undertaken to determine the most accurate method which has general applicability with minimum input data. As a result of the study, the method of Nokay as modified by the authors is recommended for the estimation of critical temperature while the method of Reidel is the best general method for critical volume. For critical pressure the Lydersen method is preferred for saturated hydrocarbons, while the method of Forman and Thodos is somewhat better for unsaturated hydrocarbons.
A critical review of correlations for the critical properties of defined mixtures
Authors: Spencer Calvin F. , Daubert Thomas E. , Danner Ronald P.
Published: June 2004

An extensive critical evaluation of available correlations for predicting critical properties of binary defined hydrocarbon as well as some multicomponent hydrocarbon and hydrocarbon‐nonhydrocarbon mixtures is presented using all available literature data. The Li method is recommended for critical temperature prediction based upon its accuracy and simplicity, although the Chueh‐Prausnitz method is equivalent in accuracy. The Kreglewski method is most accurate for critical pressure prediction. All methods evaluated yielded high errors for the critical properties of methane‐containing mixtures. Current correlations on critical volume are discussed, and correlational work on prediction using an excess volume approach is described.
Penetration of vapor jets submerged in subcooled liquids
Authors: Weimer J. C. , Faeth G. M. , Olson D. R.
Published: June 2004

An experimental investigation of the penetration distance required for complete condensation of a submerged turbulent vapor jet injected into a quiescent liquid bath of the same material was made. The bath was maintained in a subcooled condition at a temperature below the boiling temperature of the liquid at the bath pressure. The experiments were limited to choked injector Hows with the penetration regime such that buoyancy effects are negligible. Tests were run for water, ethylene glycol, and iso‐octane over a range of flow rates and bath pressures. A theoretical expression for the vapor penetration distance was developed utilizing a variable density single fluid model for the two‐phase flow, with the turbulent mixing process treated by an entrainment law. Corrections for the external expansion of the choked flow beyond the injector exit were also determined. This model was found to correlate the results of both the present experiments and those of earlier investigators over a wide range of operating conditions and injector geometries.
Volumetric properties of normal fluids at low temperatures: An extension of Pitzer's generalized correlation
Authors: Lu Benjamin C.‐Y. , Hsi Chu , Chang Shinn‐Der , Tsang Albert
Published: June 2004

The three‐parameter tabular correlation of Pitzer et al. for calculating the compressibility factor of pure components has been extended to lower temperatures in the region where Tr is from 0.5 to 0.80 and Pr is from 0 to 9. The compressibility‐factor is expressed linearly in the acentric factor Z = Z(0) + ωZ(1) with values of Z(0) and Z(1) tabulated in terms of Tr and Pr. The generalized correlation has been tested for 21 compounds with a total number of 463 data points. The average deviations in the calculated compressibility factors are 1.63% for the compressed liquids and 0.67% for the gases.
Catalytic oxidation of hydrogen chloride in a fluid bed reactor
Authors: Furusaki Shintaro
Published: June 2004

The Deacon reaction (HCI + 1/4 O2 ⇋ 1/2 Cl2 + 1/2 H2O) was studied in a catalytic fluid bed reactor. Reaction rates found from measurements in differential and integral reactors were represented by the Langmuir‐Hinshelwood type rate equation. Considering the effect of catalysts in the dilute phase, it was found that conversions in a fluid bed reactor can be calculated without any modifying parameters. It is pointed out that the wake fraction, which has been necessary to consider for fast reactions in a fluid bed reactor, is attributed to the dilute phase effect.
Gas chromatographic determination of thermodynamic properties of polymer solutions at high pressure
Authors: Brockmeier Norman F. , Carlson Ronald E. , McCoy Robert W.
Published: June 2004

The gas chromatographic (GC) method for thermodynamic measurements of polymer‐solvent systems at finite concentration has been improved to extend its operating range from atmospheric pressure to over 70 atm and over 240°C. This paper describes the design and opertion of the equipment and the mathematical treatment of the GC data, and presents experimental results for n‐hexane and isooctane in high density polyethylene. These results include the solubility isotherms, activity coefficients, and polymer‐solvent interaction parameters. The activity coefficients covering a range from 4 to 70 atm for n‐hexane in the polymer solution were correlated successfully as a function of composition using a two‐parameter segment interaction equation.
A theoretical model for enzymatic catalysis using asymmetric hollow fiber membranes
Authors: Waterland Larry R. , Michaels Alan S. , Robertson Channing R.
Published: June 2004

The behavior of an immobilized enzyme reactor utilizing asymmetric hollow fibers is simulated using a theoretical model. In this reactor, an enzyme solution contained within the annular open‐cell porous support structure of the fiber is separated from a substrate flowing through the fiber lumen by an ultrathin dense membrane impermeable to enzyme but permeable to substrate and product. The coupled set of model equations describing the behavior of this reactor represents an extended Graetz problem in the fiber lumen, with diffusion through the ultrathin fiber skin and reaction in the microporous sponge region. Exact analytic expressions for substrate concentration profiles throughout an idealized fiber which incorporate the membrane and hydrodynamic mass transfer resistances are obtained for a first‐order enzyme reaction, and numerical techniques for their evaluation are given. This analysis is extended to yield a numerical finite difference solution for nonlinear Michaelis‐Menten reaction kinetics, which is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).
On the oxidation of fuel nitrogen in a diffusion flame
Authors: Sternling C. V. , Wendt J. O. L.
Published: June 2004

The kinetic mechanisms of fuel nitrogen conversion to NO and N2 in a diffusion flame were investigated. A simple model of a diffusion flame in which the reaction zone has a finite thickness was developed. The purpose of this model was to allow the testing of complex kinetic mechanisms of pollutant formation under conditions where the fuel and oxidant feed rates are controlled by diffusion. A simple kinetic mechanism in which fuel nitrogen was simulated by nitrogen atoms showed the correct functional dependence of nitric oxide emissions on fuel nitrogen content. The model also predicts a significant effect of combustion intensity and temperature on fuel nitrogen conversion. For the hydrogen air diffusion flame the Zeldovich reaction mechanism could account for the production of N2 as well as NO.
Steady state multiplicity and stability in an adiabatic controlled cycled stirred tank reactor
Authors: Ausikaitis J. , Engel A. J.
Published: June 2004

Steady state multiplicity in exothermic adiabatic reaction systems has previously been demonstrated by a number of authors. Specifically, the work of Root and Schmitz proved the existence of multiple steady states in a loop reactor, but difficulty was encountered in controlling such a reaction system at the intermediate steady states.

Since a close analogy can be demonstrated between loop reactors and controlled cycled reactors (CCTR), it appeared reasonable to attempt to achieve steady state multiplicity in a CCTR. When the chemical reaction of Root and Schmitz was carried out in a CCTR, it proved relatively easy to obtain experimental values of intermediate steady statesf and to control the reactor at these conditions by means of a simple on‐off temperature controller.

This work suggests that chemical systems displaying steady state multiplicity can be experimentally investigated in a CCTR and that cyclic operation may be the best way for controlling such reactions systems.
Fully developed viscous—flow heat transfer in curved circular tubes with uniform wall temperature
Authors: Kalb Charles E. , Seader J. D.
Published: June 2004

Fully developed forced‐convective heat transfer to viscous flow of a constant‐property Newtonian fluid in curved circular tubes was studied theoretically for a uniform‐wall‐temperature boundary condition. Numerical solutions were obtained over a wide range of Prandtl numbers for Dean numbers as large as 1,200. The curvature ratio (radius of bend/inside radius of tube) was included as an independent parameter and, for values as small as 10, was found to have a negligible effect on the peripherally averaged Nusselt number. The average Nusselt numbers for the important Prandtl number range of 0.7 to 5 were correlated by NNu = 0.836 NDe0.5 NPr0.1 for NDe ≥ 80.
Carbon dioxide‐ethane phase equilibrium and densities from experimental measurements and the B‐W‐R equation
Authors: Gugnoni R. J. , Eldridge J. W. , Okay V. C. , Lee T. J.
Published: June 2004

Liquid composition‐total pressure and liquid composition‐liquid density data for the carbon dioxide‐ethane system were measured at −31.7°, −17.8°, −3.9°, and 10.0°C (−25°, 0°, 25°, and 50°F ± 0.02°F), from 0 to 80 mole % CO2 at 10°C and 0 to 100% CO2 for the other isotherms. The Benedict‐Webb‐Rubin equation of state with a modified A0 mixing rule was used to correlate the composition‐pressure data, with deviations in predicted pressures of only 0.8% average and 2% maximum. Vapor‐liquid equilibrium compositions and component K values y/x were then predicted for this minimum boiling azeotrope system from 10° down to −56.7°C (50° to −70°F).
Effect of diffusional limitations on lineweaver‐burk plots for immobilized enzymes
Authors: Hamilton Bruce K. , Gardner Colin R. , Colton Clark K.
Published: June 2004

Lineweaver‐Burk plots of reaction rate data obtained with immobilized enzymes need not be linear even when intrinsic enzyme kinetics follow the simple Michaelis‐Menten rate expression. Theoretical calculations show that mass transfer effects may cause curvature which is concave or convex to the abscissa, depending upon experimental conditions. Consequently, graphical procedures commonly employed for analysis of soluble enzyme kinetics may yield misleading results when applied to immobilized enzymes. Three approaches which follow from the behavior of numerical and asymptotic solutions to the problem are proposed for extraction of intrinsic kinetic information.
Transient modeling of a catalytic converter to reduce nitric oxide in automobile exhaust
Authors: Ferguson Noble B. , Finlayson Bruce A.
Published: June 2004

Mathematical models are developed to study the catalytic reduction of nitric oxide contained in automobile exhaust in which the temperature, flow rate, and concentrations of various species vary widely with time. The quasi‐static approximation is compared to the fully dynamic model. In the quasi‐static model all processes are steady state except for the solid temperature and inlet conditions. Suggestions are given for deciding a priori if the quasi‐static model is appropriate. Suggestions are also given for integrating the quasi‐static equations in order to minimize errors compared to the dynamic model. The performance of three different catalysts is examined with the mathematical model, when the inlet conditions correspond to typical values of temperature, flow rate, and concentration when the automobile is operated according to the Federal Test Procedure.
Absorption in packed towers with concurrent upward flow
Authors: Specchia Vito , Sicardi Silvio , Gianetto Agostino
Published: June 2004

In a previous paper hydrodynamic conditions, interfacial areas and mass transfer coefficients in a packed tower with concurrent downward flows were measured. In this work a packed column with concurrent upward flow has been examined.

The results show greater area and liquid mass transfer coefficient values than with downward flow. In concurrent upward flow the increase of power consumption was less than proportional to the mass transfer increase.

The experimental data show some factors which affect the increase of area and of the liquid mass transfer coefficient.

Energy correlations of mass transfer parameters were proposed.
Intraparticle mass transport in liquid‐filled pores
Authors: Komiyama Hiroshi , Smith J. M.
Published: June 2004

Adsorption rate data were measured at 25° to 75°C for benzaldehyde on polymeric, porous Amberlite particles. When the benzaldehyde is dissolved in methanol, the adsorption capacity is very low. Data for methanol solutions gave reasonable values for intraparticle diffusivities based solely on transport in the pore volume. For adsorption from aqueous solution (where the adsorption capacity was high), the contribution of surface diffusion was important.

From the two sets of data it was possible to evaluate average effective surface diffusivities by using a model based upon both pore‐volume and surface transport. These values were about 10−8 cm2/s and were sufficiently sensitive to temperature to give activation energies of 7 to 9 k cal/mole.

For the more hydrophobic Amberlite, XAD‐4, surface transport was many times as large as pore‐volume diffusion.
Analysis and optimization of the Williams‐Otto process by geometric programming
Authors: Rijckaert M. J. , Martens X. M.
Published: June 2004

This paper applies the principles of geometric programming to the optimization of the well‐known Williams‐Otto process. Following the trend of the articles published on this subject, two different objective functions are considered and the results are compared to those of other investigators.

The dual geometric program is used to provide an answer to the question of why the optimal value of the objective function remains unchanged for perturbations in a certain variable.
Joule‐Thomson coefficients of argon‐carbon dioxide mixtures
Authors: Strakey Joseph P. , Bennett Carroll O. , Dodge Barnett F.
Published: June 2004

Adiabatic Joule‐Thomson coefficients are presented for argon and two argon‐carbon dioxide mixtures (46.4% CO2and 75.4% CO2) in the single‐phase part of the range: −120 <T<110°C,P< 190 atm. Results are analyzed in terms of the virial equation (including terms to account for the quadrupole moment of CO2), several forms of the Redlich‐Kwong equation, and the Benedict‐Webb‐Rubin equation. In general, the best results were obtained by the Redlich‐Kwong equation as modified by Barner et al. (1966).
Three‐phase equilibria using equations of state
Authors: Heidemann Robert A.
Published: June 2004

It is demonstrated that a single equation of state may be used to describe all three phases in liquid‐liquid‐vapor equilibrium situations. Wilson's version of the Redlich‐Kwong equation is shown to predict accurately the water solubility in normal paraffins with interaction parameters k12 = 0.50. A simple procedure for three‐phase flash computations is presented. Results obtained using this procedure for the system methane, n‐butane, water exhibit many of the characteristics of the experimental data of McKetta and Katz (1948). In particular, the water content of the vapor phase and the liquid hydrocarbon phase are accurately predicted.
Synthesis of distillation systems with energy integration
Authors: Rathore Ram N. S. , Vanwormer Kenneth A. , Powers Gary J.
Published: June 2004

A formal method is described for the synthesis of multicomponent distillation systems when energy integration is considered between streams both within the separation sequence and in other parts of the process. The pressure in each column is considered as an optimization variable for both the energy integration and column sizing computations. Four rules are used to enumerate all feasible energy matches between the streams associated with the distillation columns. A bounding strategy which uses both upper and lower bounds is combined with dynamic programming to synthesize the optimal distillation sequence with energy integration. A five‐component separation problem demonstrates the effectiveness of the methods.
Single particle studies of binary and ternary cation exchange kinetics
Authors: Bajpai R. K. , Gupta A. K. , Rao M. Gopala
Published: June 2004

Extensive ternary ion‐exchange rate data for cases where particle‐diffusion is important are presented. Experimental rate data, using a single‐particle radioactive‐tracer technique, were obtained for the following systems in Dowex 50W‐X8 resin: Mn‐Cs‐Na, Ba‐Mn‐Na, and Sr‐Mn‐Cs. Nernst‐Planck equations have been used to describe the ternary ion‐exchange kinetics. The Nernst‐Planck model, when used for the correlation of binary and various types of ternary exchange data obtained under unfavorable equilibrium conditions, usually cannot afford to disregard liquid‐film resistance. The model incorporating the film effects correlated satisfactorily most of the experimental data, and even in cases where the correlation was not good, it interpreted adequately the trend of the results.
Relative contribution of variables affecting the reaction in fluid bed contactors
Authors: Miyauchi Terukatsu , Furusaki Shintaro
Published: June 2004

Simplified expressions to calculate the extent of reaction in a fluid bed show good agreement with the experimental data of Lewis et al. (1959) and Swaay and Zuiderweg (1972). The contribution of the dilute phase seems more important than that of the jetting zone or reaction factor (Hatta number) in usual fluid bed operations. The effect of the dilute phase is discussed. It is profitable to use the dilute phase for the consecutive isothermal and endothermic reaction, but unprofitable for the exothermic reaction. These characteristics depend upon the nature of reactions and careful considerations as to the choice of the gas velocity, particle characteristics, and reactor design will be necessary.
Solubilities of gases in high‐boiling hydrocarbon solvents
Authors: Chappelow C. C. , Prausnitz J. M.
Published: June 2004

Low‐pressure solubilities of methane, ethane, propane, n‐butane, iso‐butane, and hydrogen have been measured in n‐hexadecane, n‐eicosane, squalane, bicyclohexyl, octamethylcyclotetrasiloxane, diphenylmethane, and 1‐methylnaphthalene over the temperature range 25° to 200°C. The accuracy of these measurements is better than 1%. The data for the hydrocarbon gases have been correlated with a generalized configurational entropy and a van Laar‐type interaction parameter. The entropic component of that parameter is related to the free volume of the solvent as suggested by Flory's equation‐of‐state theory of fluid mixtures. The accuracy of the correlation is about ±15%.
Effect of London forces upon the rate of deposition of Brownian particles
Authors: Prieve Dennis C. , Ruckenstein Eli
Published: June 2004

Rates of deposition of particles onto a spherical collector, immersed in a creeping fluid, are calculated as a function of Peclet number, aspect ratio, and the ratio of Hamaker's constant to kT for all cases of practical importance involving convective‐diffusion and London forces. Boundaries of regions where London forces or Brownian motion may be neglected are established in terms of the above dimensionless groups. Gravitational forces were included in the calculations for some representative conditions but may be neglected for small or neutrally buoyant particles or for high flow rates.

Close agreement was noted between deposition rates calculated by summing individual contributions from each transport mechanism and deposition rates calculated from a rigorous consideration of their combined effect. Thus the additivity rule was verified for the cases studied.
Vapor‐liquid equilibrium: Part III. Data reduction with precise expressions for GE
Authors: Abbott M. M. , Van Ness H. C.
Published: June 2004

Through an empirical but rational appraoch to the development of equations to represent the composition dependence of the excess Gibbs function for binary liquid systems, it has been found possible to correlate VLE data precisely, even for highly nonideal systems. This makes possible the application of Barker's method to the reduction of VLE data on a routine basis. The validity of the method is demonstrated through application to several sets of data from the literature, and new experimental data are presented for six diverse binary systems in vapor‐liquid equilibrium at 50°C.
Membranes with common ion pumping
Authors: Caracciolo Frank , Cussler E. L. , Evans D. Fennell
Published: June 2004

Liquid membranes containing a macrocyclic polyether can move or pump a specific cation against its concentration gradient. The cation flux is not proportional to the difference of the cation concentration but to the difference of the product of cation and anion concentrations across the membrane. The results are inconsistent with existing theories of ion transport, but can be explained in terms of ion pairs.
Onset of fluidization and slugging in beds of uniform particles
Authors: Broadhurst T. E. , Becker H. A.
Published: June 2004

A comprehensive investigation has been made of the boundaries of the regime of bubbling aggregative fluidization. Experiments were done with sand, glass beads, clover seed, and iron shot fluidized with helium, air, and freon‐12 in columns 2.5, 5, 10, and 21 cm in diameter. Bed heights ranged from 1 to 60 column diameters, particle diameters from 0.07 to 1.1 mm, particle densities from 1300 to 7600 kg/m3, and gas densities from 0.17 to 5.2 kg/m3. Correlations are presented for the void fraction at the minimum bubbling point and for the superficial fluid velocity at the points of minimum fluidization, minimum bubbling, and minimum slugging.
A comparison of theoretical predictions with published experimental measurements on the blown film process
Authors: Petrie C. J. S.
Published: June 2004

The equations governing the shape and velocity of the polymer melt in the bubble blowing part of the blown film process are derived for non‐isothermal Newtonian and isothermal elastic material behavior. Measured bubble shapes (Ast, 1973; Farber, 1973) can be reproduced quite well, lying between elastic and viscous predictions. Velocity and strain rate predictions appear more sensitive to details of temperature profile and melt rheology. The results also include bubble pressure predictions or equivalently apparent viscosities for bubble blowing. The main lines of development suggested are the modeling of heat transfer and the use of a viscoelastic constitutive equation.
Contact nucleation of various crystal types
Authors: Tai C. Y. , McCabe W. L. , Rousseau R. W.
Published: June 2004

The purpose of this study was to investigate contact nucleation for various types of crystalline materials. Selected were aqueous solutions of two hydrated inorganic salts (MgSO4 · 7H2O and KAl(SO4)2 · 12H2O), one nonhydrated inorganic salt (K2SO4) and one organic substance (citric acid). Nucleation data were determined as number of nuclei generated per contact as a function of supersaturation and impact energy. Both of these variables strongly influenced the number of nuclei generated per contact. These data show that crystal growth and contact nucleation are related, with more rapidly growing substances giving higher yields of nuclei.
Particle‐gas dispersion effects in confined coaxial jets
Authors: Hedman Paul O. , Smoot L. Douglas
Published: June 2004

The objective of this study was to determine the mixing characteristics of two‐phase, confined, coaxial jets. Gas composition, gas velocity, and particle mass flux radial profiles were obtained at different axial stations using 20% by weight of 6 or 30 μm spherical aluminum particles in the primary stream. Additional tests were conducted without particles. Radial profiles for gas composition, velocity, and particle flux were correlated using the principle of similarity. In the gas phase, mass mixed more rapidly than momentum, and the 6 μm particles mixed less rapidly than mass or momentum. Systems with low primary density and low secondary velocity mixed most rapidly. An implicit numerical model was developed to predict the rate of mixing of the gas/particle mixture. The model included coupled dynamic and thermal nonequilibrium effects between the gas and solid phases. Comparisons of model predictions and experimental results were good.
On the statistical sensitivity analysis of models for chemical kinetics
Authors: Atherton R. W. , Schainker R. B. , Ducot E. R.
Published: June 2004

The differential equations governing the propagation in time of the sensitivity matrix for a mathematical model given by a system of ordinary differential equations are derived. These equations are used to perform a statistical sensitivity analysis of models for chemical reactors. The behavior of the sensitivities at equilibrium is analyzed. It is shown that the sensitivity equations for linear kinetics may be solved using an analytic representation. The numerical solution of these equations is discussed, and illustrative examples are presented. The lognormal distribution is presented as being representative of errors in rate constants.
Analysis of the high pressure polyethylene tubular reactor with axial mixing
Authors: Agrawal Satish , Han Chang Dae
Published: June 2004

A theoretical study was carried out for the analysis of the high pressure polyethylene tubular reactor with axial mixing (TRAM). In the study, the Contraction Mapping Theorem in the square‐integrable function space L2[0, 1] was first used to derive a uniqueness criterion for the existence of the steady state solution of the polyethylene TRAM. Then, an algorithm was derived which enabled us to compute the profiles of reactor temperature and concentration. Details of reactor performance were investigated in terms of the reactor operating and design variables: heat transfer coefficient, feed temperature and concentration, axial mixing, the length of reactor, and the distribution of preheating and cooling zones of the reactor. Also investigated in this study was the product quality in terms of the number‐average molecular weight and molecular weight distribution as affected by change in reactor operating conditions and by the chain transfer reactions.
Temperature excursions in catalytic monoliths
Authors: Hegedus L. Louis
Published: June 2004

The application of monolithic catalysts to automotive emission control has frequently been complicated by unexplained thermal degradation phenomena. This paper reports experimental and theoretical studies aimed at the understanding of how heat is generated and distributed in catalytic monoliths during an exothermal, mass transfer limited reaction.

Theoretical considerations indicate that under certain operating conditions the steady state solid catalyst temperature can exceed the adiabatic reaction temperature. It is also shown that the catalyst overtemperature is influenced by the nature of the reactive species and by the geometry of the catalyst. These predictions have been verified by experiments in a novel tubular reactor.
Experimental investigation of models for fluidized bed catalytic reactors
Authors: Fryer Colin , Potter Owen E.
Published: June 2004

The countercurrent backmixing model of a fluidized bed reactor predicts axial concentration profiles quite different from those suggested by simple two‐phase models. The models can also be distinguished in terms of the dependence of conversion on operating variables.

An experimental study of ozone decomposition in a reactor of 22.9 cm diameter has provided extensive data for comparison with backmixing and two‐phase models which incorporate bubble size variation. The measured profiles show a minimum concentration within the bed at gas velocities above a critical value, as predicted only by the backmixing model. The effect of operating variables on the shape of the profiles is also well accounted for by this model. The backmixing model is further supported by good agreement between predicted and measured reactant conversion. In particular, the variation of conversion with rate constant and gas velocity is fitted more accurately by the backmixing model than by two‐phase models.
Instabilities in polymer processing
Authors: Petrie Christopher J. S. , Denn Morton M.
Published: June 2004

Instabilities which arise in shear and extensional flows in the processing of polymeric liquids are reviewed. The experimental observations and the extent of theoretical understanding of the instabilities are discussed.
A comprehensive correlating equation for forced convection from flat plates
Authors: Churchill Stuart W.
Published: June 2004

A correlating equation was developed which provides a continuous representation for all Pr and Re. Different constants are suggested for the local and mean Nusselt numbers and for uniform wall temperature and heating. These constants are based on the best available theoretical and experimental results.
Heat transfer and curing in polymer reaction molding
Authors: Broyer Ephriam , Macosko Christopher W.
Published: June 2004

A theoretical model is proposed for curing in polymer reaction molding operations like casting, potting, lamination, thermoset molding, or reaction injection molding. In many cases, convection and mass diffusion can be neglected. The resulting unsteady heat equation with temperature dependent generation is solved numerically. Temperature and property profiles, gel point, sol fraction, and modulus are presented for a typical urethane system under several conditions. Two dimensionless groups, the adiabatic temperature rise and the ratio of polymerization rate to heat conduction rate, are most significant. Process design criteria are discussed.
Fluid and particle entrainment into vertical jets in fluidized beds
Authors: Merry J. M. D.
Published: June 2004

The flow of particles and fluid in the vicinity of vertical jets in fluidized beds was studied by using a two‐dimensional bed of lead shot fluidized by water. It was found that both interstitial fluid and solid particles are entrained into the jet as it expands and penetrates into the bed. An approximate mathematical model is developed to describe the particle and fluid flow fields observed experimentally; from this, an expression is derived for rates of entrainment into vertical jets in fluidized beds, and a model is postulated for the flow fields around grid jets.
The role of n‐butane in hydrate formation
Authors: Ng Heng‐Joo , Robinson Donald B.
Published: June 2004

The role of n‐butane in the formation of hydrates has been a matter of some uncertainty. The experimental measurements resulting from this work have shown conclusively that n‐butane does enter the hydrate lattice when hydrates are formed in the presence of methane at pressures from about 1 000 to 10 000 kPa over a temperature range from 0° to about 13°C. At higher pressures and temperatures, n‐butane ceases to enter the crystal and behaves like a nonhydrate former.
A flow model for gas movement in spouted beds
Authors: Lim C. J. , Mathur K. B.
Published: June 2004

A two‐region model of a spouted bed, postulating vertical plug flow of gas in the spout and dispersed plug flow along curved streamlines in the annulus, is proposed. The extent of axial dispersion is accounted for by a coefficient D which is an adjustable parameter of the model. Experimental support for the theory is provided by residence time‐distribution data obtained by using helium gas as tracer, covering a wide range of conditions. Values of the coefficient D, determined from a comparison between predicted and observed RTD curves, are generally higher than those reported for packed beds but much smaller than those for fluidized beds.