Showing papers in "Aiche Journal in 1968"

Local compositions in thermodynamic excess functions for liquid mixtures

Abstract: A critical discussion is given of the use of local compositions for representation of excess Gibbs energies of liquid mixtures. A new equation is derived, based on Scott's two-liquid model and on an assumption of nonrandomness similar to that used by Wilson. For the same activity coefficients at infinite dilution, the Gibbs energy of mixing is calculated with the new equation as well as the equations of van Laar, Wilson, and Heil; these four equations give similar results for mixtures of moderate nonideality but they differ appreciably for strongly nonideal systems, especially for those with limited miscibility. The new equation contains a nonrandomness parameter α12 which makes it applicable to a large variety of mixtures. By proper selection of α12, the new equation gives an excellent representation of many types of liquid mixtures while other local composition equations appear to be limited to specific types. Consideration is given to prediction of ternary vapor-liquid and ternary liquid-liquid equilibria based on binary data alone.

Longitudinal dispersion of liquid flowing through fixed and fluidized beds

Abstract: Longitudinal liquid mixing in fluidized and fixed beds was studied using sinusoidal and pulse response techniques. The tracer used was light emissive fluorescein dye. A systematical study of liquid phase dispersion by varying particle size, fluid velocity, fraction voids, and particle density was conducted. A generalized correlation applicable to both fixed bed and fluidized bed was obtained. The application of the correlation in predicting the effect of the dispersion on reactor performance was discussed.

Adsorption rate constants from chromatography

Abstract: A new method for determining adsorption equilibrium constants, rate constants, and intraparticle diffusivities is described and applied for the adsorption of ethane, propane, and n-butane on silica gel. The method rests upon recently developed theory for relating the moments of the effluent concentration wave from a bed of adsorbent particles to the rate constants associated with the various steps in the overall adsorption process. It is necessary to operate at concentrations of adsorbable gas such that the adsorption isotherm is linear. However, it is possible to take into account effects of longitudinal dispersion and diffusion to the particle surface as well as the intraparticle processes of diffusion and adsorption on the pore surface. The method gave reasonable values for intraparticle diffusivities and adsorption rate constants. Intraparticle diffusion was a major resistance for all particle sizes studied and for the largest size (R = 0.50 mm.) this step controlled the overall rate. From the constants determined chromatographically it is possible to predict breakthrough curves for the adsorption of these hydrocarbons on silica gel. The predicted curves agree well with experimentally established breakthrough curves.

Comparison of kinetic and diffusional models for solid-gas reactions.

Abstract: Kinetic and diffusion models for gas-solid reactions in spherical particle, comparing core shrinking mechanism and activation energies

Fluid flow through woven screens

Abstract: A packed bed model has been adopted to develop a general correlation applicable to the flow of Newtonian fluids through all types of woven metal screens. Both of the main theoretical approaches to studying pressure drop in packed systems have been used by visualizing the screen as a collection of submerged objects with surface area to unit volume ratio a for laminar flow, and as a bundle of tubes of diameter D for turbulent flow. In the usual manner viscous and inertial energy losses are added to give an expression for the total pressure loss. Rearrangement of the general equation to the form of a friction factor yields a unique definition of the Reynolds number for screens NRe = ρu/μa2D. Procedures are described for collection of pressure drop-velocity data for the flow of nitrogen and helium through plain square, full twill, fourdrinier, plain dutch, and twilled dutch weaves. The data are used to derive a viscous resistance coefficient α = 8.61 and an inertial resistance coefficient β = 0.52. The validity of the correlation equation is tested by using additional data from the literature. The correlation successfully predicts pressure drop for a Reynolds number range of 0.1 to 1,000, void fractions from 0.35 to 0.76, screen pore diameters from 5 to 550 μ, mesh sizes from 30 to 2,400 wires/in., and surface area to unit volume ratios from 1,200 to 29,000 ft.−1.

Drop formation at low velocities in liquid-liquid systems: Part I. Prediction of drop volume

Abstract: A correlation is presented for predicting the drop volume for injection at low velocities of one Newtonian liquid into a second stationary immiscible Newtonian liquid in the absence of surface active agents. The analysis, which is based on a two-stage process of drop formation, predicts drop volumes within an average error of 11% for fifteen liquid-liquid systems covering a wider range of variables than any previous study. Although the equation was tested primarily with mutually saturated liquids, if correctly predicted drop size for two systems where mass transfer was occurring.

Crystal size distributions in continuous crystallizers when growth rate is size dependent

Abstract: Empirical size-dependent growth rate models are studied for their effect on the population density distributions from a continuous, mixed suspension, mixed product removal (CMSMPR) crystallizer. The growth rate models and/or their corresponding population density distributions are examined for continuity, convergence of moments, versatility, and their ability to fit experimental data. A new empirical size-dependent growth rate model is proposed which has properties superior to those of previous models. Experimental steady state data are presented to illustrate the application of the model to actual CMSMPR crystallization systems.

Chromatographic study of surface diffusion

Abstract: A new method, based upon chromatography, was used to measure surface diffusion coefficients for ethane, propane, and n-butane on silica gel. The diffusivities correspond to very low surface coverages (fraction of a monolayer of the order of 10−4) and hence should represent limiting values. A survey of available surface diffusion information, all at higher coverages, indicated that the results reported here are at the lower end of the range of diffusivities. The activation energy and heat of adsorption, for example, for n-butane, were 4.4 and −7.8 k cal./mole, respectively. Surface diffusion was a significant fraction of the total intraparticle mass transport, in part because in the small pores in silica gel gas phase diffusion was solely by the Knudsen mechanism. For propane, surface migration was 73% of the total transport at 50°C. and 61.5% at 125°C.

Kinetics of thiophene hydrogenolysis on a cobalt molybdate catalyst

Abstract: The intrinsic kinetics of the hydrogenolysis of thiophene on a cobalt molybdate catalyst were studied in a differential reactor with recirculation, at a total pressure of about 1 atm. and temperatures of 235° to 265°C. Retardation of the reaction by both thiophene and hydrogen sulfide was significant and the rate of thiophene disappearance was correlated by a Langmuir-Hinshelwood type of kinetic equation. Hydrogenation of the butene intermediate was inhibited by both butene and hydrogen sulfide and the rate of this reaction was also described with a Langmuir-Hinshelwood rate equation. The forms of the kinetic expressions obtained imply that the butene is not hydrogenated at the original desulfurization site.

Studies of intramembrane transport: A phenomenological approach

Abstract: The intramembrane transport properties of carbohydrates were investigated in cellophane. The experiments performed were the measurement of net volume transfer under a concentration and pressure gradient and the solute transfer due to a concentration difference together with the physical properties of the membrane. The matrix of phenomenological coefficients characteristic to the transport was established after the phase boundary contributions were extricated from the experimental transport data. These thermodynamic coefficients were then interpreted through the Spiegler-Kedem-Katchalsky frictional model. The analysis of the frictional coefficients clearly indicated the importance of solute-polymer interactions. The magnitude of solute-solvent frictional coefficients in the membrane were compared with the corresponding interactions in free solutions. Their differences were explained in terms of the interaction of the solute with the macromolecular network and were quantitatively expressed by introducing two reduced frictional coefficients. The tortuosity factor was shown to be related to these interactions and not a simple geometric property of the membrane. The temperature dependence of the frictional coefficients was established.

Laminar liquid jet diffusion studies

Abstract: A rigorous analysis of jet hydrodynamics is used to develop a technique for determining diffusion coefficients from laminar liquid jet absorption experiments, and the influence of the jet fluid mechanics on the absorption process is clarified. The new technique is used to determine the diffusivities of carbon dioxide, oxygen, argon, nitrous oxide, ethylene, and propylene in water within the temperature range 25° to 40°C. A critical analysis of available diffusivity data for these gases indicates that there is no conclusive evidence that demonstrates the existence of a significant interfacial resistance in uncontaminated laminar jet experiments. In addition, comparison of existing data shows that the commonly accepted diffusivities for the oxygen-water system may be significantly higher than the actual values. It is concluded that the laminar jet experiment is a rapid, accurate method of obtaining diffusion coefficients of dissolved gases in liquids.

Mathematical modeling and numerical integration of multicomponent batch distillation equations

Abstract: A mathematical model for multicomponent batch distillation was derived, and a FORTRAN IV program was written for solution on a digital computer. The program has been used in the simulation of several commercial batch distillation columns. A calculation procedure for the numerical solution of batch distillation equations starting from total reflux steady state conditions was developed, and the step-by-step procedure is presented here. Also included is a discussion of the stability and relative computational effectiveness of various numerical integration techniques when applied to transient distillation calculations. The discussion applies equally well to both batch distillation and unsteady state continuous distillation.

The rates of evaporation of sprays

Abstract: This paper reports a computational study of the evaporation rates of sprays of pure liquid drops having negligible velocity with respect to the air, and for drop velocities great enough to affect the evaporation rate. The principle parameters considered were the mean diameter and distribution of drop sizes in the initial spray, ratio of air to spray, initial temperature difference between air and spray, initial drop velocity, and air velocity.

Transient natural convection in a vertical cylinder

Abstract: An experimental and analytical study is reported of transient natural convection in a vertical cylinder. For the experiments a cylinder was partially filled with liquid and subjected to a uniform heat flux at the walls. Thermocouples were used to measure the unsteady temperature field within the liquid; dye tracers were used to study flow patterns. Parameters that were varied included the test liquid (water-glycerin mixtures), the liquid depth, and the wall heat flux. A range of Prandtl number from 2 to 8,000, L/D ratio from 1 to 3, and Grashof number from 103 to 1011 were studied, encompassing both laminar and turbulent flow regimes. An analytical model was developed by dividing the system into three regions: a thin boundary layer rising along the heated walls, a mixing region at the top where the boundary layer discharges and mixes with the upper core fluid, and a main core region which slowly falls in plug flow. The temperature of the core fluid was assumed to vary in the vertical direction but not in the horizontal direction. Natural convection boundary-layer equations were modified to allow for a temperature variation at the outer edge of the boundary layer. The model may be used with a step-by-step computational procedure to predict the temperature distribution in the fluid as a function of time for an arbitrary set of conditions. Results computed by using the model were in good agreement with the experimental data.

Pool boiling heat transfer to cryogenic liquids; I. Nucleate regime data and a test of some nucleate boiling correlations

Abstract: Pool nucleate boiling heat transfer curves for pure nitrogen, oxygen, argon, methane, and carbon tetrafluoride have been measured on a horizontal, flat, circular, platinum plated disk for saturation pressures ranging from 1 atm. or less to the immediate vicinity of the critical pressure for each liquid. The results have been compared with various suggested nucleate boiling correlations, and the correlations of McNelly, of Kutateladze, and of Borishanskiy-Minchenko are found to be roughly equally successful and all distinctly superior to those of Rohsenow, of Gilmour, and of Forster and his collaborators for these liquids. For oxygen, argon, methane, and carbon tetrafluoride, boiling hysteresis of a type not previously reported was observed at intermediate and high saturation pressures on this surface.

Mechanism of interfacial mass transfer in membrane transport

Abstract: Dialysis of binary aqueous solutions of several sugars through a cellophane membrane was studied in a stirred batch dialyzer. Sherwood numbers describing mass transfer resistance in the fluid adjacent to the membrane were determined as a function of the corresponding Reynolds and Schmidt numbers. The results establish a reproducible environment for membrane testing in which a known controllable and small interfacial resistance is placed in series with that of the membrane. The results are also shown to support, for this geometry, the postulation of a third power relationship between eddy diffusivity and dimensionless distance from the phase boundary as well as the Sherwood-Ryan nondimensionalization of this distance.

Creeping flow of power‐law fluid over newtonian fluid sphere

Abstract: A technique which is a combination of Galerkin's method and variational principle was developed and used for the approximate solution of creeping flow of power-law fluid over a Newtonian fluid sphere. The stream functions (both internal and external) and drag coefficient are expressed in terms of three parameters: the flow behavior index of the power law fluid, the external Reynolds number, and a viscosity ratio parameter . Comparisons with existing experimental data are also given.

The synthesis of system designs: I. Elementary decomposition theory

Abstract: A system synthesis principle is proposed from which processes can be composed to perform an assigned task. Synthesis is performed by the sequential decomposition of the design problem into subproblems which eventually reach the level of available technology.

Analysis of steady state shearing and stress relaxation in the Maxwell orthogonal rheometer

Abstract: A nonlinear, integral viscoelastic model is used to predict the stresses in the Maxwell orthogonal rheometer The resulting expressions indicate that the instrument yields data on material functions not heretofore measured, and also show how the data may be analyzed to get the complex viscosity Expressions are given for stress relaxation after cessation of shearing Some experimental data are analyzed to give model parameters

Turbulent heat transfer in drag reducing fluids

Abstract: An analysis is presented which extends the analogy between energy and momentum transport for turbulent pipe flow of purely viscous fluids to include drag reducing, non-Newtonian fluids. The correlation by Meyer is used to predict friction factor and sublayer thickness for the drag reducing fluids. The use of the friction factor correlation with the heat transfer analogy makes it possible to predict heat transfer rates from simple measurements of pressure drop and flow rate for the drag reducing fluids. Some recent experimental data for two effective drag reducing fluids and for water are compared with the predicted heat transfer rates, and the mean deviation in Nusselt number is found to be +8.5% for all of the data. The heat transfer analysis predicts a reduction in Nusselt number accompanying a reduction in friction factor for a given Reynolds number and for Prandtl numbers greater than 1.

Discrete dynamic optimization applied to on-line optimal control

Abstract: A general method has been developed for controlling deterministic systems described by linear or linearized dynamics. The discrete problem has been treated in detail. Step-by-step optimal controls for a quadratic performance index have been derived. The method accommodates upper and lower limits on the components of the control vector. A small binary distillation unit was considered as a typical application of the method. The control vector was made up of feed rate, reflux ratio, and reboiler heat load. Control to a desired state and about a load upset was effected. Calculations are performed quite rapidly and only grow significantly with an increase in the dimension of the control vector. Extension to much larger distillation units with the same controls thus seems practical.