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Showing papers in "Aiche Journal in 1977"


Journal ArticleDOI
TL;DR: In this paper, a correlating equation for assisting convection was developed by combining correlating equations for pure free and pure forced convection, based on laminar boundary-layer theory for an isothermal, vertical plate.
Abstract: A correlating equation for assisting convection was developed by combining correlating equations for pure free and pure forced convection. These component equations are based on laminar boundary-layer theory for an isothermal, vertical plate. Theoretical values for assisting convection indicate that the third root of the sum of the third powers gives the best representation, as contrasted with the choice and rationalization of the second or fourth power by prior investigators. This expression was modified by the addition of a limiting value Nuo to obtain a better representation below the domain of boundary-layer theory and was generalized for uniform heating and for spheres and horizontal cylinders by the appropriate choice of the characteristic length.

238 citations


Journal ArticleDOI
TL;DR: In this paper, trajectories have been computed for two equal sized spherical particles in simple laminar shearing and in uniaxial extensional flows, and effects of interparticle attraction, electrostatic repulsion, and hydrodynamics were included.
Abstract: Trajectories have been computed for two equal sized spherical particles in simple laminar shearing and in uniaxial extensional flows. Effects of interparticle attraction, electrostatic repulsion, and hydrodynamics were included. The results are pertinent to questions of colloidal stability under various conditions of flow. Particulate dispersions can react in several different ways as the intensity of shearing is increased from zero: the dispersion can remain stable; it can be redispersed, if it had been initially flocculated into a weak secondary minimum in the interparticle potential curve; it can be flocculated into a strong primary minimum in the potential curve; or, in extreme cases, it can be redispersed from the primary minimum. Results are presented which illustrate criteria for flocculation or stability to both laminar shearing and extensional flow. It is shown that hydrodynamic effects can significantly alter the criteria developed for stability of dispersions to Brownian coagulation.

188 citations



Journal ArticleDOI
TL;DR: In this paper, the influence of Schmidt number on the rate of mass transfer between a turbulent fluid and a pipe wall is investigated. But the Schmidt number is only applicable to a vanishingly small portion of the concentration field as Sc → ∞.
Abstract: New measurements are presented on the influence of Schmidt number on the rate of mass transfer between a turbulent fluid and a pipe wall. It is found that for large Schmidt numbers the fully developed mass transfer coefficient is related to the friction velocity and the Schmidt number by the equation The experiments are accurate enough to rule out the Sc−2/3 or the Sc−2/3 relations commonly used, deduced from plausible limiting expressions for the eddy diffusivity close to a wall. It is argued that these expressions arevalid only over a vanishingly small portion of the concentration field as Sc → ∞.

168 citations


Journal ArticleDOI
TL;DR: In this article, a group contribution molecular model is developed for the thermodynamic properties of polar and nonpolar liquids and their solutions, including energy of vaporization, ρVT relations, excess properties, and activity coefficients.
Abstract: A group contribution molecular model is developed for the thermodynamic properties of polar and nonpolar liquids and their solutions, including energy of vaporization, ρVT relations, excess properties, and activity coefficients. The model is based on the cell theory in which the repulsive forces of molecules are expressed with a modified cell partition function derived from the Carnahan-Starling equation of state for hard spheres. The attractive forces are made up of group pair interaction contributions. Group and interaction properties have been determined for methyl, methylene, hydroxyl, and carbonyl. Extensive comparisons are made of predictions of the model with data for pure liquids and their solutions.

154 citations


Journal ArticleDOI
TL;DR: In this paper, the rigorous critical state criterion enunciated by Willard Gibbs can be used with a recently formulated two-parameter equation of state to obtain an analytical solution to the problem of predicting the critical properties of defined multicomponent mixtures.
Abstract: This paper shows how the rigorous critical state criterion enunciated by Willard Gibbs can be used with a recently formulated two-parameter equation of state to obtain an analytical solution to the problem of predicting the critical properties of defined multicomponent mixtures. Comparisons are made between predicted and experimental values for several systems containing paraffin hydrocarbons and related materials.

147 citations


Journal ArticleDOI
TL;DR: In this paper, pressure drop correlations for flow of slurries in pipelines were developed for each of the following four flow regimes: flow with a stationary bed, saltation flow, heterogeneous flow, and homogeneous flow.
Abstract: Pressure drop correlations for flow of slurries in pipelines were developed for each of the following four flow regimes: flow with a stationary bed, saltation flow, heterogeneous flow, and homogeneous flow. A total number of 2 848 data points, comprised of 1 912 collected from the published literature together with 936 taken using our own test pipelines and relating to ranges of the pertinent variables extensive enough to span all four flow regimes were used as the basis of these correlations. Also, these data were used in developing an associated quantitative regime delineation scheme. The correlations provide an improved predictive capability over previously available procedures and are also broader in scope. The delineation procedure developed here permits straightforward classification of the data according to the flow regime prevailing, and it is moreover inclusive of all the data and is self-consistent.

137 citations


Journal ArticleDOI
TL;DR: In this article, the distribution of drop sizes can be characterized by an upper limit, log normal function with only one of the three parameters, the volume median diameter, a strong function of flow conditions.
Abstract: The droplets that appear in annular gas-liquid flows are formed by the eruption of wavelets from the surface of the wall layer. Ninety per cent of the volume of this dispersed liquid is carried by only about 10% of the drops. We find, as suggested by Wicks and Dukler, that the distribution of drop sizes can be characterized by an upper limit, log normal function with only one of the three parameters, the volume median diameter, a strong function of flow conditions. A method for predicting the average diameter is suggested which is consistent with a theoretical interpretation based on a Kelvin-Helmholtz mechanism, whereby the destabilizing force is the pressure variation over the wavelets.

133 citations


Journal ArticleDOI
TL;DR: In this paper, a mathematical model and experimental data are presented for both a kaolin clay suspension and an oil in water chemically stabilized emulsion, and the model is used in conjunction with experimental data to separate the liquid film resistance adjacent to the filter cake which is determined by fluid shear and electric field from the cake and filter medium resistances which are influenced by electroosmosis.
Abstract: The cross flow/electrifiltration process combines migration of particles in the presence of electrical and shear fields to increase filtration rates. A mathematical model and the experimental data are presented for both a kaolin clay suspension and an oil in water chemically stabilized emulsion. When the filter is operated in a regime above the critical voltage, filtration rate-electric field strength dependence becomes linear, and both electroosmosis in the filtration medium and electrophoresis in the liquid film are the controlling mechanisms of transport. Both experimental data and the mathematical model indicate that the fluid circulation rate tangential to the filtration media does not necessarily increase filtration rate depending on the regime of operation. The model is used in conjunction with the experimental data to separate the liquid film resistance adjacent to the filter cake which is determined by fluid shear and electric field from the cake and filter medium resistances which are influenced by electroosmosis.

132 citations



Journal ArticleDOI
TL;DR: A simulation procedure is presented in this work which can analyze the behavior of any dispersed phase system consisting of particles whose random behavior is specified in terms of probability functions, and is an efficient alternative to the modeling of such systems.
Abstract: A simulation procedure is presented in this work which can analyze the behavior of any dispersed phase system consisting of particles whose random behavior is specified in terms of probability functions. The procedure distinguishes itself from its predecessors in being free from arbitrary discretization of time or any other parameter along which the system evolves, and its ability to predict the behavior of randomly behaving small populations. Where population balance equations, which describe the behavior of particulate systems, cannot be readily solved, the simulation technique presented herein represents an efficient alternative to the modeling of such systems. Tables and a flow chart are given which would enable the use of the method for any system with specified particle behavior.

Journal ArticleDOI
TL;DR: In this article, single-pore behavior in a porous pellet of reactant is used to develop a new model for predicting the conversion-time relationship for gas-solid non-catalytic reactions.
Abstract: Analysis of single-pore behavior in a porous pellet of reactant is used to develop a new model for predicting the conversion-time relationship for gas-solid noncatalytic reactions. The model accounts for the influence of pore diffusion, diffusion through the product layer which builds upon the pore walls, and surface reaction. By focusing attention on one pore, it is possible to include the effects of the changes in pore geometry that occur during reaction. Thus, both pore-mouth clocure and uniform deposition of product throughout the pellet can be predicted by using appropriate values for the diffusional and physical properties of the reaction system. The key parameters of the model are the effective pore length and effective diffusivity in the product layer. Numerical values of these quantities can be approximated from measurements of the pore volume and surface are of the unreacted and reacted forms of the pellet, or they may be evaluated from a limited amount of conversion vs. time data. The use of the model for predicting conversion-time curves is illustrated with available data for the reduction of nickel oxide pellets with carbon monoxide and for the reaction of sulfur dioxide with calcium carbonate.


Journal ArticleDOI
TL;DR: In this article, closed-form expressions for predicting vertical concentration distribution of the dispersed phase in the turbulent core of pipe and channel flow are presented for spherical particles, of mean diameter d50 comparable to the Kolmogorov microscale.
Abstract: Closed-form expressions are presented for predicting vertical concentration distribution of the dispersed phase in the turbulent core of pipe and channel flow. Experimental data obtained with spherical particles, of mean diameter d50 comparable to the Kolmogorov microscale, are in good agreement with model predictions. The average value of dimensionless lateral particle diffusivity, ζ = e/Ru*, determined from these data is approximately 0.25, that is, fairly close to previously reported measurements with much coarser particles.

Journal ArticleDOI
TL;DR: In this article, stable isothermal multiplicities were observed during carbon monoxide oxidation in an integral reactor, filled with alumina supported platinum catalysts, in the conversion-temperature, conversion-inlet carbon dioxide concentration and conversion-mass flow rate domains.
Abstract: Stable isothermal multiplicities were observed during carbon monoxide oxidation in an integral reactor, filled with alumina supported platinum catalysts. The multiplicities were investigated in the conversion-temperature, conversion-inlet carbon monoxide concentration and conversion-mass flow rate domains. The region of multiplicities was found to widen significantly upon catalyst aging which enhanced the pellets' diffusive resistances. Several intermediate stable steady states were found between the highest and lowest steady states, both experimentally and theoretically. All the above phenomena could be well interpreted by the interactions of the kinetics of carbon monoxide oxidation with intrapellet diffusion resistances.

Journal ArticleDOI
TL;DR: The chromatographic method has been used to study the sorption and diffusion of methane, ethane, propane, and cyclopropane in 5A molecular sieve as mentioned in this paper.
Abstract: The chromatographic method has been used to study the sorption and diffusion of methane, ethane, propane, and cyclopropane in 5A molecular sieve. Both the equilibrium isotherms and the time constants for zeolitic diffusion, obtained from the chromatographic peaks, agree well with the values obtained previously by the gravimetric method, thus confirming the validity of the experimental technique. The results obtained in several previously reported chromatographic studies are reviewed, and it is shown that the apparent discrepancies between chromatographic and gravimetric data arise mainly from differences in the way in which the micropore diffusivity is defined. The relative advantages and disadvantages of the gravimetric and chromatographic methods are briefly considered.

Journal ArticleDOI
TL;DR: In this paper, the authors measured gas holdup and the ratio of the turbulent regime mechanical power consumed in aerated compared to that in nonaerated aqueous phases were measured in two laboratory sized tanks.
Abstract: Gas holdup and the ratio of the turbulent regime mechanical power consumed in aerated compared to that in nonaerated aqueous phases were measured in two laboratory sized tanks. Standard six-blade turbine (D/T = 1/3), six-blade paddle (D/T = 1/3), and four-blade paddle (D/T = 2/3) impellers were used over a wide range of impeller rotational speed and gas sparging rate. For all systems, the power ratio results were found to fit a semitheoretical correlation (derived from dimensional analysis) involving the impeller Weber number, the aeration number, and the ratio of dispersion and liquid densities. Empirical correlations for gas holdup in water, aqueous solutions of nonelectrolytes, and an aqueous electrolyte solution are given. The overall results lead to the conclusion that power ratio and gas holdup correlations are highly specific to a particular impeller type and are also dependent on the tank size and the liquid phase physicochemical properties.

Journal ArticleDOI
TL;DR: In this article, the authors measured the absorption rate of pure sulfur dioxide into aqueous bisulfite, sodium hydroxide, and sodium sulfite solutions with and without a surface active agent using a liquid jet column.
Abstract: The rates of absorption of pure sulfur dioxide into aqueous sodium bisulfite, sodium hydroxide, and sodium sulfite solutions with and without a surface active agent were measured at 25°C using a liquid jet column. For the sulfur dioxide-sodium hydroxide system, the rate of absorption into the solution without surface active agent was higher than that into the solution with surface active agent, indicating the existence of the interfacial turbulence. The absorption rates obtained for the present system under the conditions of no interfacial turbulence were in good agreement with the theoretical predictions based on the penetration theory.

Journal ArticleDOI
TL;DR: In this article, the absolute evaporation flux from clean surfaces was measured for diethylene glycol, glycerine, dibutyl phthalate, and oleic acid.
Abstract: A method was developed for providing continuously wiped and, therefore, clean liquid surfaces in vacuo. By means of a mass spectrometer detector, the absolute evaporation flux from such clean surfaces was measured for diethylene glycol, glycerine, dibutyl phthalate, and oleic acid. The molecular flux from equilibrium vapor was also measured by the same detector. The ratio of the former to the latter, the evaporation coefficient, was found in each case to be close to unity and independent of the temperature.

Journal ArticleDOI
TL;DR: A cylindrical, light carrying, optical fiber coated with a catalyst layer is evaluated as a novel configuration for all such light assisted catalysis in this article, where an effectiveness factor eta/sub I/ for heterogeneous photo assisted catalysts is determined for reactions which are first order in intensity and without mass transport limitations.
Abstract: Recently reported varieties of photoassisted heterogeneous catalysts are summarized. A cylindrical, light carrying, optical fiber coated with a catalyst layer is evaluated as a novel configuration for all such light assisted catalysis. Equations are obtained which describe the light intensity in the fiber and its surrounding catalyst layer. A dimensionless group of the form phi = (4..cap alpha../sub c/..beta../sub c/dL)/(d/sub f/) (d = d/sub c/ for d/sub c/lambda) determines the relative influence of light loss by all absorption and scattering to light transported in the fiber length. An effectiveness factor eta/sub I/ for heterogeneous photoassisted catalysis is determined for reactions which are first order in intensity and without mass transport limitations. Asymptotic forms of eta/sub I/ are eta/sub I/ = 1.0 (phi > ..integral..1.0). 58 references.

Journal ArticleDOI
TL;DR: In this article, the Thiele modulus, incomplete external wetting (B), and fractional pore fill-up (C) were derived to predict catalyst effectiveness.
Abstract: Catalyst effectiveness factor in trickle bed reactors, (e.g., for hydrocarbon hydrodesulfurization) is a function of the Thiele modulus (A), incomplete external wetting (B), and fractional pore fill-up (C). An approximate formula is derived, which accounts for all three variables. This indicates that the evaluation of contacting efficiencies by applying reactor performance equations to reaction studies is prone to numerous errors. To predict catalyst effectiveness factors, some independent means of evaluating B and C have to be used. In general, existing correlations for B are unsatisfactory, and correlations for C are nonexistent. Fractional pore fill-up will depend on catalyst pore structure and physical properties (particularly surface tensions) of the gas-liquid-solid system involved. Failure to recognize that either B or C, depending on the range of A, are the primary variables affecting catalyst effectiveness in trickle bed reactors may explain the difficulties previously encountered in interpreting trickle bed data. Table, graph, and 19 references.

Journal ArticleDOI
TL;DR: In this paper, the spin line tension, diameter attenuation, and the onset of the draw resonance instability are determined for a viscoelastic polymer melt, taking into account the changes in physical properties resulting from cooling of the filament.
Abstract: Spin line tension, diameter attenuation, and the onset of the draw resonance instability are determined for a viscoelastic polymer melt, taking into account the changes in physical properties resulting from cooling of the filament. The theory predicts the experimentally observed stabilization of very short and very long filaments.

Journal ArticleDOI
TL;DR: In this paper, the shadow effect due to deposited particles and the singular and random behavior of approaching particles are discussed and a new theory of particle deposition is proposed and procedures for the simulation of deposition process outlined.
Abstract: Two concepts concerning the deposition of particles from suspension onto a collector, the shadow effect due to deposited particles and the singular and random behavior of approaching particles, are presented and discussed. Based on these concepts, a new theory of particle deposition is proposed and procedures for the simulation of deposition process outlined. The simulation results give the rate of deposition and the deposit morphology. Potential applications of this model to a number of technical problems are outlined.

Journal ArticleDOI
TL;DR: In the course of daily operation of a petroleum refinery or chemical complex, many thousands of items of infor-mation are generated, gathered, and recorded, and these data are, in turn, used to plan, schedule, control, and evaluate process operations.
Abstract: In the course of daily operation of a petroleum refinery or chemical complex, many thousands of items of infor-mation are generated, gathered, and recorded. These data are, in turn, used to plan, schedule, control, and evaluate process operations. Because of the highly integrated nature of modern processes, inaccurate data taken from one part of the process can easily lead to poor decisions that affect other parts of the processes. For instance, if inventory and production data on one product are inaccurate, the manufacturer may be forced to substitute a premium grade product to meet his delivery, thereby incurring a quality giveaway and creating an additional demand for the substitute product. Or, he may have to procure the supply from some other sources at additional costs. Or, he may accumulate unnecessarily large inventory, thereby tying up production and storage facilities needed for other products. Because of the immense scale of operations, even a small percentage change in inventory or flow may make a substantial difference in revenues or profits. The availability of accurate and consistent process data is therefore crucial to all process analyses.

Journal ArticleDOI
TL;DR: An algorithmic-evolutionary approach to the systematic synthesis of minimum cost networks of exchangers, heaters, and coolers for industrial crude unit preheat recovery is proposed, providing an explicit theoretical guidance on the optimal exchange among hot and cold streams and on the optimum locations of heating and cooling utilities in the network.
Abstract: An algorithmic-evolutionary approach to the systematic synthesis of minimum cost networks of exchangers, heaters, and coolers is proposed. The new approach is easy to apply by hand calculations, requiring no special mathematical background and computational skill from the user. In addition to generating many cheaper networks for sample problems ranging in size from 4 to 10 streams as compared to previous studies, the proposed method provides an explicit theoretical guidance on the optimal exchange among hot and cold streams and on the optimal locations of heating and cooling utilities in the network. It also has a provision for the use of stream splitting and for generating a cyclic network. The new method is particularly effective in the synthesis of minimum cost networks for industrial crude unit preheat recovery.

Journal ArticleDOI
E. Talmor1
TL;DR: In this article, a flow map for nonfoaming and foaming two-phase downflow through catalyst beds was correlated in terms of the superficial volumetric gas-to-liquid ratio and a force ratio relating inertia plus gravity forces to viscous plus interphase forces.
Abstract: Flow regimes for nonfoaming and foaming two-phase downflow through catalyst beds were correlated in terms of the superficial volumetric gas-to-liquid ratio and a force ratio relating inertia plus gravity forces to viscous plus interphase forces. For nonfoaming systems, the resulting flow map identified five regimes: two continuous phases (trickling flow), gas continuous (spray or blurring flow), liquid continuous (dispersed bubble), pulsing, and bubbling/pulsing; for foaming systems, the regimes were two continuous phases, gas continuous, foaming, and pulsing with and without foaming. Several orders of magnitude variations in the Froude, Weber, and Reynolds numbers were covered by data obtained in a 29.2 cm dia bed for aqueous 0-46% glycerol solutions and literature data obtained during downflow in smaller diameter beds for nonfoaming systems, including air/diethylene glycol, natural gas/lubricating oil, carbon dioxide/lubricating oil, and Freon 12/silicone oil and for foaming systems, including air/silicone oil and natural gas/kerosine. In the pulsing flow regime, the frequency of pulses leaving large (29.2 cm) and small (6.58 cm) dia beds were correlated with the flow map coordinates. The results are applicable to existing or new pilot and commercial reactors. Diagram, graphs, and 17 references.

Journal ArticleDOI
TL;DR: In this article, a generalized version of the particle dendrite growth model was developed, and the use and behavior of this model was demonstrated in the simple case of deposition by pure interception.
Abstract: When a suspension of fine solid particles in a gaseous medium flows through a fibrous filter, particles deposit on the fibers forming chainlike agglomerates known as dendrites. This deposition pattern is responsible for the intrinsically transient behavior of the filter, leading to drastic increases of the filtration efficiency and of the pressure drop. Related phenomena are observed when aerosols flow through other types of porous media (for example, granular beds), or next to duct walls, around immersed objects, etc. A theoretical model of the particle dendrite growth was proposed recently by Payatakes and Tien. Here a revised and generalized version of that model is developed. The following major revisions are made: allowance is made for collisions with a particle in a given dendrite layer that lead to retension in the same layer, radial as well as angular contributions to deposition are considered, and the dendrite layer adjacent to the collector is allowed to contain more than one particle. These changes lead to a substantially more realistic theoretical model. Expressions for the transient behavior of a filter of differential thickness are obtained, based entirely on first principles. These, as it has been shown in a previous publication, can be used to predict the dynamic behavior of a macroscopic fibrous filter. The use and behavior of this model is demonstrated in the simple case of deposition by pure interception. The present treatment of deposition by pure interception is more rigorous than and supersedes that adopted in previous works.

Journal ArticleDOI
TL;DR: In this article, a flow type of apparatus is built to give equilibrium gas and liquid samples at elevated pressures and temperatures while minimizing thermal decomposition, and Saturated vapor and liquid compositions and K values are determined with this apparatus for the binary system hydrogen/tetralin (1,2,3,4-tetrahydronaphthalene) at four temperatures from 189.6° to 389.1°C, and seven pressures from 20 to 250 atm.
Abstract: A flow type of apparatus is built to give equilibrium gas and liquid samples at elevated pressures and temperatures while minimizing thermal decomposition. Saturated vapor and liquid compositions and K values are determined with this apparatus for the binary system hydrogen/tetralin (1,2,3,4-tetrahydronaphthalene) at four temperatures from 189.6° to 389.1°C, and seven pressures from 20 to 250 atm. Vapor pressures of tetralin are determined with the same apparatus, and values are reported at the four temperatures of this work.

Journal ArticleDOI
TL;DR: In this paper, the effects of temperature on the kinetics of crystallization of potassium nitrate were investigated in a continuous mixed-suspension, mixed-product-removal (MPM) crystallizer.
Abstract: A laboratory continuous mixed-suspension, mixed-product-removal crystallizer was used to study the effects of temperature on the kinetics of crystallization of potassium nitrate. A differential refractometer was used to continuously monitor the supersaturation permitting the measurement of supersaturation levels of order 10−3Kg solute/Kg water. The nucleation rate exhibited an inverse relationship with temperature.

Journal ArticleDOI
TL;DR: In this paper, diffusional mass transfer across membranes with uniform but low pore densities was studied experimentally as a function of stirring rate and pore area fraction, and the results were analyzed in terms of a stagnant film boundary-layer model specially formulated for a heterogeneous membrane containing discrete pores.
Abstract: Diffusional mass transfer across membranes with uniform but low pore densities was studied experimentally as a function of stirring rate and pore area fraction. The results were analyzed in terms of a stagnant film boundary-layer model specially formulated for a heterogeneous membrane containing discrete pores. The overall membrane diffusional resistance is linearly related to the inverse of the pore area fraction of the membranes for a constant stirring rate. An equivalent boundary-layer thickness can be defined which is independent of membrane properties but a unique function of stirrer speed. These experimental boundary-layer thicknesses are greater by a factor of 3 than those predicted by a published Sherwood number correlation determined for homogeneous surfaces, but the stirring rate dependence is in excellent agreement with this same correlation.