Showing papers in "Aiche Journal in 1979"
TL;DR: In this article, the relative motion correlations for dispersed two-phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model, and satisfactory agreements were obtained at wide ranges of the particle concentration and Reynolds number.
Abstract: Drag coefficient and relative motion correlations for dispersed two-phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model. The results are compared with a number of experimental data, and satisfactory agreements are obtained at wide ranges of the particle concentration and Reynolds number. Characteristics differences between fluid particle systems and solid particle systems at higher Reynolds numbers or at higher concentration regimes were successfully predicted by the model. Results showed that the drag law in various dispersed two-phase flows could be put on a general and unified base by the present method.
1,685 citations
TL;DR: In this article, a theory for predicting the effective axial and radial thermal conductivities and the apparent wall heat transfer coefficient for fluid flow through packed beds is derived from a two-phase continuum model containing the essential underlying and independently measurable heat transfer processes.
Abstract: A theory for predicting the effective axial and radial thermal conductivities and the apparent wall heat transfer coefficient for fluid flow through packed beds is derived from a two-phase continuum model containing the essential underlying and independently measurable heat transfer processes. The theory is shown to explain much of the confused literature and pinpoints the remaining major areas of uncertainty, further investigation of which is needed before secure prediction is possible.
388 citations
TL;DR: A review of macroscopic descriptions of deep bed filters and their analytical solutions can be found in this paper, with a focus on particle deposition and the relationship between the extent of deposition and filter bed characteristics.
Abstract: A review covers macroscopic descriptions of deep bed filters and their analytical solutions; parameter estimation methods; single-media vs. multimedia filters; particle deposition; trajectory calculation of particle deposition rate; some published trajectory calculation results; the contribution of Brownian diffusion to deposition; straining; the effect of surface interaction on deposition; theoretical studies on non-Brownian particles; Brownian diffusion of submicron particles; the effect of particle deposition on filter performance; deposit morphology; quantitative relationships between the extent of deposition and filter bed characteristics; filter design and optimization; pretreatment; the role of flocculants in depth filtration; optimal dosage determination; alum vs. polyelectrolytes; and highlights of Grutsch and Mallatt's study Vertical Bar3Vertical BarChem. Eng. Prog. 7.
318 citations
TL;DR: In this article, a new correlation was developed for the densities of saturated liquids and their mixtures, which is relatively easy to use and is applicable to a wide variety of liquids.
Abstract: A new correlation has been developed for the densities of saturated liquids and their mixtures. The correlation is relatively easy to use and is applicable to a wide variety of liquids. The saturated liquid density correlation is flexible and consistent and requires only reduced temperature, acentric factor, and a characteristic volume for each pure compound. Mixing rules are given. When tested against a data base of 2 657 points of pure compound liquid density data for 97 hydrocarbons and 1 851 points for 103 other compounds, the new correlation gave an average absolute error of 0.37% compared to 2.14% for the Yen-Woods correlation and 0.50% for the SDR equation as modified by Spencer and Danner. For 2 994 points of liquid mixture density data for 167 mixtures, the new correlation gave an average absolute error of 1.40% compared to 5.64% for the Yen-Woods correlation and 2.95% for the SDR equation. Characteristic volumes are listed for 200 compounds; they are generalized as functions of acentric factor for various types of compounds and are compared to critical volumes.
269 citations
TL;DR: In this paper, methods for estimating mutual diffusion coefficients for polymer-solvent systems are reviewed and procedures are recommended for the determination of the temperature, concentration, and molecular weight dependences of diffusivities both for dilute and concentrated solutions.
Abstract: Methods for estimating mutual diffusion coefficients for polymer-solvent systems are reviewed. Procedures are recommended for the determination of the temperature, concentration, and molecular weight dependences of diffusivities both for dilute and concentrated solutions.
199 citations
TL;DR: In this article, a new solution to the kinetics of a fixed-bed adsorber in response to a step change in feed concentration is obtained for a linear equilibrium system, considering the resistance to mass transfer in both the mobile and stationary phases.
Abstract: A new solution to the kinetics of a fixed-bed adsorber in response to a step change in feed concentration is obtained for a linear equilibrium system, considering the resistance to mass transfer in both the mobile and stationary phases. The differential equations of continuity and mass transfer are integrated by simulating the intraparticle concentration profile with a parabola. The results agree with Rosen's rigorous but complex solution.
180 citations
TL;DR: The controller developed is shown to have the same structure as the linear-quadratic optimal feedback controller for input delays and reduces to the Smith predictor (and the analytical predictor) for the special case of a single time delay.
Abstract: A multivariable, multidelay compensator, capable of handling general, linear time delay problems is derived in a form applicable both in continuous and discrete time. The controller developed is shown to have the same structure as the linear-quadratic optimal feedback controller for input delays and reduces to the Smith predictor (and the analytical predictor) for the special case of a single time delay. Some examples representative of engineering practice are used to demonstrate the effectiveness of the controller.
170 citations
TL;DR: In this paper, the equation of motion for the two phase flow within a bubble column, operated within the recirculation flow regime, has been solved, and the profile of liquid flow has been determined.
Abstract: The equation of motion for the two phase flow within a bubble column, operated within the recirculation flow regime, has been solved, and the profile of liquid flow has been determined. Nicklin's relation for the bubble flow regime has been extended to the recirculation flow regime.
Data analysis shows that the mean slip velocity between bubble and liquid is approximately constant and that the kinematic turbulent viscosity increases rapidly with increasing diameter of the column. These observations lead to the conclusion that scale-up has but little influence upon the mean gas holdup.
168 citations
TL;DR: In a Lagrangian frame of reference based on lamina (fluid filament) thickness and in a warped time scale based on a single, flow dependent quantity, mixing, diffusion, and reaction can be described in a relatively simple way.
Abstract: In a Lagrangian frame of reference based on lamina (fluid filament) thickness and in a warped time scale based on a single, flow dependent quantity, mixing, diffusion, and reaction can be described in a relatively simple way. Applications are presented for stretch and fold in taffy pull, egg beater and static mixer, shear stretch, stretch of laminae in a vortex, mixing with diffusion, reaction rate controlled by diffusion of reactant through a product layer, and very fast reactions in a turbulent flow.
163 citations
TL;DR: In this article, the semi-empirical Pitzer equation for modeling equilibrium in aqueous electrolyte systems has been extended in a thermodynamically consistent manner to allow for molecular as well as ionic solutes under limiting conditions.
Abstract: The semi-empirical Pitzer equation for modeling equilibrium in aqueous electrolyte systems has been extended in a thermodynamically consistent manner to allow for molecular as well as ionic solutes Under limiting conditions, the extended model reduces to the well-known Setschenow equation for the salting out effect of molecular solutes To test the validity of the model, correlations of vapor-liquid equilibrium data were carried out for three systems: the hydrochloric acid aqueous solution at 29815°K and concentrations up to 18 molal; the NH3-CO2 aqueous solution studied by Van Krevelen et al (1949) at 29315°K; and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process with temperatures from 34315°K to 41315°K and concentrations up to 40 weight percent equivalent potassium carbonate The success of the correlations suggests the validity of the model for aqueous electrolyte systems of industrial interest
160 citations
TL;DR: In this article, the authors investigated the characteristics of the gel layer of polyvinyl alcohol and ovalbumin aqueous solutions, using cellulose acetate tubular ultrafiltration membranes.
Abstract: Characteristics of the gel layer were investigated by direct measurement of its concentration treating polyvinylalcohol and ovalbumin aqueous solutions, using cellulose acetate tubular ultrafiltration membranes. The concentration of the gel layer was not constant but a function of bulk concentration and feed velocity. The mass transfer coefficient obtained agreed with Deissler correlation. There was a definite correlation between the resistance of the gel layer and its concentration.
TL;DR: In this paper, several methods are reviewed for determining compositions in multiphase, reacting mixtures at equilibrium. Wolfe's quadratic programming algorithm is applied and results compared with the Rand method (Dluzniewski and Adler 1972), NASA method (Gordon and McBride 1971) and the George et al. (1976) implementation of Powell's method.
Abstract: Several methods are reviewed for determining compositions in multiphase, reacting mixtures at equilibrium. Wolfe's quadratic programming algorithm is applied and results compared with the Rand method (Dluzniewski and Adler 1972), NASA method (Gordon and McBride 1971) and the George et al. (1976) implementation of Powell's method. For poor guesses in compositions, local and constrained minima in Gibbs free energy may arise, giving incorrect phase distributions.
TL;DR: In this paper, a simulation procedure for predicting the dynamic behavior of a deep bed filter over the entire practicable range of filter operation is developed, based on synthesizing available quantitative results relating to filtration, and to porous media flows.
Abstract: A simulation procedure for predicting the dynamic behavior of a deep bed filter over the entire practicable range of filter operation is developed. The method is based on synthesizing available quantitative results relating to filtration, and to porous media flows, within an overall framework which views the process to consist of two principal stages dominated by appropriate limiting deposition modes. Evaluation of the results through comparison with available data indicates, to the extent the nature of these types of data permits, that the method is surprisingly effective and even capable of predicting on satisfactorily quantitative basis some intricate details of observed filter behavior.
TL;DR: In this paper, the authors give thermodynamically consistent equations for gas absorption with chemical reaction at equilibrium, and preliminary design calculations for sweetening natural gases by absorption with mixed solvents suggest that mixed-solvent absorption may be more economical than using conventional aqueous alkanolamine.
Abstract: Solubilities of ethane, carbon dioxide, and hydrogen sulfide have been measured in propylene carbonate, N-methyl-2-pyrrolidone and tetramethylene sulfone (sulfolane); and in mixtures of these physical solvents with monoethanolamine and diglycolamine, in the range −10 to 100°C. Thermodynamically consistent equations are given for gas absorption with chemical reaction at equilibrium. Henry's law describes physical equilibrium between the acidic gas in the vapor phase and free acid solute in the liquid phase. Equilibrium constants describe chemical equilibria for the absorbed gas and the chemical solvent.
Preliminary design calculations for sweetening natural gases by absorption with mixed solvents suggest that, under some circumstances, mixed-solvent absorption may be more economical than using conventional aqueous alkanolamine.
TL;DR: In this paper, a procedure was developed for evaluating effectiveness factors for nonuniform boundary conditions existing when part of the particle surface is covered by gas, indicating a gas covered type of surface.
Abstract: Rates of hydrogenation of α-methyl styrene were measured at 40.6°C and 1 atm in a recycle, trickle-bed reactor using a palladium/aluminum oxide catalyst. Data for different hydrogen concentrations in the gas and liquid feed streams suggested that except, at high liquid flow rates, on part of the outer surface of the catalyst the mass transfer limitation was very small, indicating a gas covered type of surface. A procedure was developed for evaluating effectiveness factors for the nonuniform boundary conditions existing when part of the particle surface is covered by gas.
TL;DR: In this paper, the authors measured the absorption rate of pure carbon dioxide into aqueous monoethanolamine solution with a surface active agent of 60/sup 0/, 77/sup 1/F, 95/sup 2/F and 113/Sup 0/F in a liquid jet column and a wetted wall column.
Abstract: To obtain reliable data on the monoethanolamine system for removing carbon dioxide from gas streams, the rates of absorption of pure carbon dioxide into aqueous monoethanolamine solutions were measured with a surface active agent of 60/sup 0/, 77/sup 0/, 95/sup 0/, and 113/sup 0/F in a liquid jet column and a wetted wall column. Experimental results were analyzed with the chemical absorption theory based on the penetration model. The physical solubility of carbon dioxide in an aqueous MEA solution - as determined from the absorption rates measured in a near pseudo-first-order reaction regime - proved to be considerably larger than the physical solubility in water. The measured absorption rates were in good agreement with the theoretical predictions for gas absorption with an irreversible second-order reaction, when the variation of the physical solubility during the absorption process was taken into account.
TL;DR: An iteration technique has been developed to solve the equations of motion for flow of an incompressible Newtonian fluid through circular tube with a radius which varies sinusoidally in the axial direction as mentioned in this paper.
Abstract: An iteration technique has been developed to solve the equations of motion for flow of an incompressible Newtonian fluid through circular tube with a radius which varies sinusoidally in the axial direction. The iteration is essentially geometric; one proceeds from a solution for flow through a tube in which the waveleneth of diameter chance in the axial direction is
TL;DR: In this paper, the authors found that switching between carbon monoxide/argon and oxygen/argon mixtures to a gradientless reactor significantly increased the average reaction rate as compared to the steady state rate, when the time averaged feed concentrations in both cases are stoichiometric.
Abstract: Periodic feed switching between carbon monoxide/argon and oxygen/argon mixtures to a gradientless reactor has been found to significantly increase the average reaction rate as compared to the steady state rate, when the time averaged feed concentrations in both cases are stoichiometric. The rate enhancement achieved during periodic reactor operation is attributed to the attainment of more desirable surface concentrations on the platinum catalyst which dramatically increase the surface rate processes leading to carbon dioxide production.
TL;DR: In this paper, a theoretical study was conducted to investigate the effects of large temperature differences on the rate of pure heat transfer from a very hot gas to stationary spheres using finite difference techniques.
Abstract: A theoretical study has been conducted to investigate the effects of large temperature differences on the rate of pure heat transfer from a very hot gas to stationary spheres.
In the numerical analysis, the momentum and energy equations for variable property flow past a sphere were solved simultaneously, using finite difference techniques. Results were obtained for Reynolds numbers up to 50 and surface temperature to gas temperature ratios varying between 0.25 and unity. These ranges cover most of the conditions commonly encountered in heterogeneous plasmas, transferred arc, and other high temperature chemical engineering processes. The flow behavior, drag coefficients, and Nusselt number were calculated for each case.
The constant property solutions were in excellent agreement with numerical and experimental results reported in the literature, thus justifying the validity of the model and of the underlying assumptions. In general, the effect of variable properties was to drastically increase the flow velocity, vorticity, and temperature and vorticity gradients near the surface.
A generalized heat transfer correlation was derived which, in addition to constant property conditions, included the effect of large variations in the physical properties of the fluid as a result of large temperature differences.
TL;DR: In this article, an experimental and theoretical study of horizontal stratified gas-liquid two-phase flow in a circular tube is performed, where both phases are considered to be in turbulent flow, and the liquid phase flow field is modeled by applying eddy viscosity expressions developed for single phase flow.
Abstract: This paper is an experimental and theoretical study of horizontal stratified gas-liquid two phase flow in a circular tube. Both phases are considered to be in turbulent flow, and the liquid phase flow field is modeled by applying eddy viscosity expressions developed for single phase flow. The pressure drop and in situ volume of liquid are predicted from the gas and liquid flow rates, physical properties, and pipe size by means of an iterative procedure which terminates when calculated gas and liquid pressure drops match. The iterative design procedure is compared with new data for air-water flow in a smooth tube of 63.5 mm ID and with data available in the literature. For conditions corresponding to small amplitude interfacial waves, the average deviation between predicted and experimental results is 24.3% for the pressure drop and 7.7% for the holdup. For roll wave conditions, the corresponding average deviations are 4.6 and 26.4% for pressure drop and holdup, respectively. These results are substantially better than the predictions obtained using the Lockhart-Martinelli correlations.
TL;DR: In this article, a series of bottlenecks from the viewpoint of energy conservation is sequentially found by a thermodynamic analysis using a heat availability diagram, and modified systems are evolutionally synthesized as the result of debottlenecking.
Abstract: Starting from a conventional distillation system without heat integration, a series of bottlenecks from the viewpoint of energy conservation is sequentially found by a thermodynamic analysis using a heat availability diagram, and modified systems are evolutionally synthesized as the result of debottlenecking. The present approach has made possible a unified interpretation of various energy integrated distillation systems with multieffect columns, intercondensers/interreboilers, heat pumps, etc.
TL;DR: In this article, a method for predicting absorption rates for liquid layers flowing along a wall is presented based on results presently available in the literature as well as on the results of studies we recently carried out on the rate of oxygen absorption from a flowing air stream into water layers on the bottom of a horizontal enclosed channel and on the inside of a vertical pipe.
Abstract: A method is presented for predicting absorption rates for liquid layers flowing along a wall. It is based on results presently available in the literature as well as on the results of studies we recently carried out on the rate of oxygen absorption from a flowing air stream into water layers on the bottom of a horizontal enclosed channel and on the inside of a vertical pipe. Absorption measurements can be interpreted by assuming that the process is controlled by eddies whose length and velocity are characterized by bulk turbulence properties and that in a region of thickness δ close to the interface the turbulence is dampened by viscosity.
TL;DR: In this article, three modes or types of sedimentation are recognized in flocculent suspensions: clarification, where floccules are separated and settle independently, zone settling, and compression or compaction, in which the solids structure is strong enough to exhibit a compressive yield value.
Abstract: Three modes or types of sedimentation are recognized in flocculent suspensions: Clarification, in which floccules are separated and settle independently; zone settling, in which floccules are incorporated into some solids structure so that all are constrained to subside at more or less the same rate; and compression or compaction, in which the solids structure is strong enough to exhibit a compressive yield value. Current models for sedimentation in the three modes are reviewed, with particular emphasis on their use and reliability (or lack of it) for sedimentation basin design. Most models of thickening presented in the literature derive from a basic partial differential equation for force balance. Models differ in which terms of the equation are disregarded. Several of the theories of compaction are essentially equivalent solutions for the same model, but with different sets of independent variables.
TL;DR: For every viscoelastic fluid studied in the contraction geometry, it was found that increasing the flow rate beyond a certain limit resulted in disturbance to the stable entry flow patterns described in Parts I and II as discussed by the authors.
Abstract: For every viscoelastic fluid studied in the contraction geometry, it was found that increasing the flow rate beyond a certain limit resulted in disturbance to the stable entry flow patterns described in Parts I and II. An examination of the development of the entry flow disturbances was carried out using still and cine photography. Still photographs are presented to illustrate the characteristics of the unstable flow patterns. The time varying nature of the flow has been recorded on a cine film Flow Patterns in Abrupt Entry Flow of Viscoelastic Fluids which is available for loan. Critical condition criteria for the onset of the periodic flow disturbances were obtained in terms of the fundamental fluid properties and are presented and compared with other suggested criteria for the onset of unstable entry flow of viscoelastic fluids.
TL;DR: In this paper, the operation of a periodically forced chemostat (CSTR) in which two microbial populations compete for the same nutrient has been examined, using the Floquet stability theory.
Abstract: The operation of a periodically forced chemostat (CSTR) in which two microbial populations compete for the same nutrient has been examined. Easily implemented criteria for the stability of the resulting cycles have been obtained, using the Floquet stability theory. After examining several possibilities it was found that stable periodic trajectories of coexistence can be achieved: (a) when the dilution rate of the chemostat is properly varied in a periodic manner between two values so chosen that the growth of one population is favored by the first and the growth of the other population is favored by the second, (b) when a certain percentage of biomass and growing medium is harvested periodically from the chemostat, and (c) when both the dilution rate and the concentration of the substrate in the feed are varied simultaneously and in a periodic manner.
TL;DR: In this paper, the over-all catalyst effectiveness in a trickle-bed reactor was determined by two approximate solutions, which account for partial wetting of the catalyst particles at low liquid rates and for interphase transport effects in reactions where the limiting reactant is in the gas phase or in the liquid phase.
Abstract: The over-all catalyst effectiveness factors (g/sub o/) in trickle-bed reactors can be determined by two approximate solutions, which account for partial wetting of the catalyst particles at low liquid rates and for interphase transport effects in reactions where the limiting reactant is in the gas phase (e.g., the removal of a pollutant from a liquid by catalytic oxidation with air in a trickle-bed reactor) or in the liquid phase (e.g., hydrodesulfurization in a trickle-bed reactor under some conditions). A two-dimensional model of a porous particle in an isothermal system with a reaction assumed to be first order and irreversible in the limiting reactant is used with an approximate explicit solution and a numerical solution to the relevant equations. These approximation methods, when tested on a published data for the hydrogenation of ..cap alpha..-methylstyrene over palladium/alumina particles in a trickle-bed reactor at 40.6/sup 0/ C and 1 atm, gave a reasonable estimate of the effectiveness factor.
TL;DR: In this paper, a free radical mechanism, with initiation of an electrophilic reaction for the formation of catechyl radical, has been proposed to explain the experimental data for phenol-ozone reaction in aqueous solutions.
Abstract: The present research concerns mechanism and rate of reaction between dissolved ozone and phenol in homogeneous solutions. The stopped-flow technique was employed to obtain absorbances during reactions; the kinetic experiments were conducted at temperatures varying from 5° to 35°C in aqueous solutions with pH values ranging from 1.5 to 5.2.
The kinetic data indicated that the absorbance of a mixed solution increased rapidly in the very early portion of the reaction and then declined slowly in the remaining period. The rate of reaction in the early period was first order with respect to both phenol and ozone concentrations. The rate constant increased with pH value and temperature, and an activation energy of 5.74 K cal/mole was obtained. Further tests showed that the dissolved ozone was consumed completely in the first period and that in the second period the intermediate products were decomposed without depletion of ozone. Catechol, o-quinone, hydroquinone, oxalic acid, humic acid, and a dimer were identified from mass spectra as products of the ozonization reaction.
A free radical mechanism, with initiation of an electrophilic reaction for the formation of catechyl radical, has been proposed to explain the experimental data for phenol-ozone reaction in aqueous solutions. According to the proposed mechanism, the reaction path through the attachment to ortho position is much more favorable compared with that through the paraposition because of geometric advantage, though quinones and hydroxyphenol can be formed through parallel paths. The products of reaction detected in this research, therefore, are accountable by this mechanism. A rate equation derived on the basis of this mechanism also agrees well with that observed from the kinetic experiments.
TL;DR: In this article, the analysis of solid-solid reactions is discussed, including fundamental considerations, experimental techniques, analysis of pellet-pellet reactions, mixed powder reactions, role of the gas phase, and reactor design.
Abstract: This paper reviews some important aspects of the analysis of solid-solid reactions which include: fundamental considerations, experimental techniques, analysis of pellet-pellet reactions, analysis of mixed powder reactions, role of the gas phase, and reactor design. Illustrations are given wherever necessary. Examples of industrial applications, important systems studied, and the models used are tabulated.
TL;DR: In this paper, a phase-splitting algorithm is coupled with the Rand method to improve its efficiency and reliability when the phase distribution is unknown at equilibrium, and the coupled algorithm works well to give phasesplits in the metastable region where most stability tests fail.
Abstract: A phase-splitting algorithm is coupled with the Rand method to improve its efficiency and reliability when the phase distribution is unknown at equilibrium. The coupled algorithm works well to give phase-splits in the metastable region where most stability tests fail. Exhaustive tests show fine performance in the region near liquid-liquid phase envelopes for systems with at least one partially miscible binary pair.