Showing papers in "Aiche Journal in 1970"

An eddy cell model of mass transfer into the surface of a turbulent liquid

Abstract: Experimental gas absorption studies for bubbles transported in turbulent pipe flow of water strongly indicate that liquid phase controlled mass transfer is due to surface renewal by turbulent eddies. Predictions of transport behavior from the conditions of turbulent flow cannot be made in support of this mechanism because no satisfactory theory of turbulent transport near a gas-liquid interface is available. This work considers a model of the hydrodynamic behavior near the surface which provides a link between the observed mass transfer behavior and the state of the turbulent field. In this model, the very small scales of turbulent motion are considered to be controlling. These motions are idealized, and their flow and mass transfer behavior are solved analytically. The overall result for eddies of various sizes is related to the turbulent energy spectrum by using only the easily accessible parameter ϵ, the energy dissipation rate. This model gives quantitative agreement to within a factor of 2 for three widely different experimental situations including gas-liquid and liquid-solid interfaces. However, the predicted Reynolds number dependence is somewhat higher than the experimental result. The model attempts to clearly define the basic physical process at the interface. Therefore, it indicates the direction for further experimentation needed to clarify the basic relationship between the mass transfer rates in the liquid phase and the hydrodynamic behavior of the turbulent liquid.

Kinetics of catalytic cracking selectivity in fixed, moving, and fluid bed reactors

Abstract: A kinetic mathematical model of catalytic cracking is described which accounts for conversion and gasoline yield in isothermal fixed, moving, and fluid bed reactors The model has been tested and verified by using laboratory moving bed data with a commercial gas oil and catalyst It is shown that under certain conditions, the selectivity behavior and maximum gasoline yield of fixed, fluid, and moving bed reactors will be identical Maximum gasoline yield is defined in terms of both the kinetic parameters and the process variables for fixed, moving, and fluid bed reactors

Analytical and experimental studies of facilitated transport

Abstract: Facilitated transport is a process in which permeation through a liquid film is chemically augmented. Because of the scientific and engineering interest in this phenomenon, the purpose of this work was to carry out a detailed mathematical and experimental investigation of facilitated transport. The differential equations describing facilitated transport are presented, and a generally applicable numerical solution recently developed by G. M. Roe for this type of boundary value problem is summarized. The experimental investigation consisted of measuring the steady state rate of transport of nitric oxide through thin films of ferrous chloride solution and of determining independently the values of the system parameters of which the nitric oxide flux was a function. The experimental results were accurately predicted by using the model developed by Roe. This is the first demonstration of a general quantitative understanding of facilitated transport.

Correlation and prediction of vapor‐liquid equilibria with the redlich‐kwong equation of state

Abstract: A modified Redlich-Kwong equation has been applied to the calculation of phase equilibria in multicomponent systems. The two parameters of the Redlich-Kwong equation are treated as temperature functions. They are obtained for each pure component from experimental vapor pressures and liquid densities with the help of a generalized fugacity coefficient correlation for saturated vapors. The need to submit coefficients for pure components is thus eliminated. At least one experimental vapor-liquid equilibrium point is required to establish an interaction constant for each binary system. Applications have been made to binary and multicomponent systems containing hydrocarbons, hydrogen, carbon dioxide, and hydrogen sulfide.

Light intensity profiles in a perfectly mixed photoreactor

Abstract: The light intensity distribution in a perfectly mixed photoreactor has been studied experimentally and analytically. Experimental measurements of intensities within the reactor were made with a specially designed light probe. These data were then used to test the validity of a model which treats the ultraviolet lamp as a linear source radiating in all directions. It was found that this model, which seems appropriate and allows reasonable computations, is somewhat in error owing to the neglect of the finite size of the lamp and the existence of reflection and refraction effects within the reactor. An empirical correction function was determined for use with the model which then yields predictions in close agreement with experimental data when the reactor is filled with a light absorbing liquid.

Numerical treatment of fully developed laminar flow in helically coiled tubes

Abstract: Laminar flow in helically coiled tubes is treated numerically. Fully developed axial and secondary velocities are calculated for both circular and elliptical cross sections. Only closely wrapped helices, that is, helices with modest pitch, are considered. Ten solutions with Deans numbers up to 200 have good accuracy. Two additional solutions with Deans numbers up to 280 are approximate.

A modified Redlich‐Kwong equation of state

Abstract: A new modification of the Redlich-Kwong equation of state is presented. The modification follows the procedure suggested by Redlich, Ackerman, et al., in which a deviation function (a function of temperature, pressure, and acentric factor) is added to the compressibility factor from the original equation to improve the agreement with data. The purpose of the present modification was to improve predictions of the Redlich-Kwong equation in the saturated vapor region up to the critical point while retaining a relatively simple form to make analytical relations for derived properties possible. The equation for pressure correction to vapor enthalpy, derived from the compressibility factor by standard thermodynamic procedures, is also presented. Comparisons of predicted vapor compressibility factors and vapor enthalpy pressure corrections with literature data are given, demonstrating the advantages of the proposed modification when the saturated vapor region is of principal interest.

Venturi and other atomizing scrubbers efficiency and pressure drop

Abstract: Particle collection efficiency and gas pressure drop for venturi and other atomizing scrubbers can be predicted by means of equations developed in this paper. The significance of the details of the liquid atomization process, the collection of particles on single drops, and the uncertainty regarding them are discussed. The role of drop holdup in the scrubber throat is also important.

Mass transfer in a nonuniform impinging jet: Part I. Stagnation flow-velocity and pressure distribution

Abstract: A theoretical solution for the impingement flow of a jet with a parabolic velocity distribution is given. Viscous generation and diffusion of vorticity in the jet were neglected. Experimental velocity and pressure distributions measured in an impinging jet of air originating with Poiseuille flow compare well with theory, thus justifying the assumption of inviscid flow. Pressure distributions on the deflecting surface were independent of nozzle height in the range 1 to 12 nozzle radii. For lower nozzle heights the effect of the constriction of flow between the nozzle and the surface followed the predicted behavior.

A statistical model of a porous medium with nonuniform pores

Abstract: A random network model of a porous medium with nonuniform pores has been constructed. Nonuniformity is achieved by assigning two-parameter distributions to pore radius and pore length. Statistical derivations result in expressions for bulk model properties which are consistent with known empirical behavior of porous media such as capillary pressure, hydraulic permeability, and longitudinal and transverse dispersion. A series of experiments is suggested whereby the parameters of porous media structure may be determined from observed macroscopic behavior by using the expressions developed in this paper.

Radial migration of spherical particles in couette systems

Abstract: Several studies have been made in Couette systems of the primary motion (angular translation and rotation) of spheres suspended in viscous liquids. Radial migration trajectories, however, have been unreported for single spheres. In this study, a prediction of radial migration is developed and compared with experimental measurements. The predicted trajectories were found to agree well with the measured ones. Ultimately, radially migrating spheres reached an equilibrium position located approximately midway between the cylinder walls. The model developed predicted an equilibrium position just slightly inside the midpoint, while measured equilibrium positions fell between the midpoint and 0.4, the annular thickness from the inner cylinder walls. The differences in equilibrium positions are attributed to the approximate nature of the model.

Self‐diffusion measurements in methane by pulsed nuclear magnetic resonance

Abstract: The self-diffusion coefficient of methane has been measured from 150° to 350°K. and from 200 to 5,000 lb./sq. in. abs. At constant temperature, the density-diffusivity product is constant up to neighborhood of critical density and decreases sharply above that density. The temperature dependence of the low density data agrees with Chapman-Enskog theory. The Lennard-Jones (6-12) parameters determined from the low density data (ϵ/k = 130°K., σ = 3.85A.) are in good agreement with those determined by other methods. A correlation for the self diffusion coefficient for methane has been developed which may provide predictions of other spherical nonpolar gases.

A model for the thixotropy of suspensions

Abstract: A model for the rheological behavior of thixotropic systems is presented. The model is intended for systems exhibiting no elastic or anisotropic effects. It is shown how the constants of the model can be determined by a systematic program of experimentation. It is also shown how the model can be tested and amended, if necessary, by the same program of experiments. The model is advanced for suspensions of rigid, solid particles in liquids; it is not expected to be valid for materials of polymeric constitution or for suspensions of elastic, deformable particles in liquids.

Two‐phase flow through porous media

Abstract: In the context of a previously proposed new description for multiphase flow through porous media, we examine constitutive equations for gi, the force per unit volume which phase i exerts upon the pore walls and other adjacent fluids. The principle of material difference is used to determine the most general dependence of gi upon saturation gradient for a nonoriented (no porosity gradient) permeable structure. Three problems are solved and the results compared with analyses based upon our interpretation of Muskat's equations. The first concerns a semi-infinite porous column in air, the bottom of which is saturated with a liquid. The same saturation distribution is found with our approach as with Muskat's equations. The analysis of the second problem indicates the relation between our relative permeability and that of Muskat. The jump balances for mass and for momentum at a surface of discontinuity (or shock wave) with respect to volume averaged variables are derived. The significance of solutions in which such surfaces of discontinuity appear is discussed. In the third problem, a plane surface of discontinuity with respect to local saturation moves through an infinite permeable structure. This is similar to the displacement of oil by an aqueous solution in a secondary recovery process. The results are comparable to those with Muskat's equations only in the limit where capillary pressure is neglected (the Buckley-Leverett case). When capillary pressure differs from zero, Muskat's equations do not admit a shock wave solution.

Drop‐size distributions produced by turbulen pipe flow of immiscible liquids

Abstract: Drop-size distributions in turbulently flowing dispersion of immiscible liquids were investigated. The observed drop-size distributions were actually a composite of two superimposed distributions. One is the distribution produced by the injection nozzle and the other is that produced by breakup in the turbulent flow field. A mathematical model was developed which predicted both the shape of the observed distributions and kinetics of the droplet breakup process for the distribution produced by the turbulent flow field. The flowing dispersion composed of water and insoluble organic phase was photographed at 27, 209, 421, and 576 pipe diameters below the mixing jet and at distances of 0.05, 0.1, and 0.4 diam. from the wall. Average flow rates varied from 14 to 20 ft./sec. in the 0.750-in. I.D. tube. Three organic phases were studied at concentrations ranging from 0.6 to 10% by volume. Dispersed phase viscosity and interfacial tension varied from 1 to 18 cp. and 13 to 40 dynes/cm. No distribution law with any theoretical basis could be found which correlated experimental distributions. The stochastic model describing the breakup process postulates that each breakup event leads to two daughter drops with uniformly distributed volume ratios and a very small satellite droplet. An empirical correlation exists to predict only one of the three parameters of the model.

The periodic viscous sublayer in turbulent flow

Abstract: The model of the fluctuating viscous sublayer proposed by Einstein and Li was modified by treating some of the objections to the original formulation without greatly altering the essential simplicity of the concept. The applicability of this model to the description of the important features of turbulent flow and heat transfer in ducts and of the Toms phenomenon was evaluated by comparison of predictions of the model with experimental measurements. The mean period for growth and decay of the sublayer and the magnitudes of the wall-pressure fluctuations and wall-temperature fluctuations were compared for the flow of air and liquids. Quantitative spatial features of the periodic sublayer, that is, minimum and maximum sublayer thickness and patch size in the directions normal and parallel to the flow direction, were determined.

A diffusion model for reactions with turbulent mixing

Abstract: A diffusion model based on the simultaneous interdiffusion and reaction between alternate slabs of reactants is used to simulate the data of Vassilatos and Toor After slab sizes are chosen to fit the conversion data for very rapid reactions in a stoichiometric mixture, reasonably good predictions are obtained of the effect of stoichiometry and reaction velocity constant on conversion The results are close to the predictions of Kattan and Adler's stochastic mixing model, and the similar behavior of these disparate models implies that conversion is insensitive to the details of the mixing

An experimental study of steady state multiplicity and stability in an adiabatic stirred reactor

Abstract: Steady state and transient characteristics of an adiabatic, continuous flow, stirred reactor were studied in experiments employing the exothermic reaction between sodium thiosulfate and hydrogen peroxide in aqueous solution. Results illustrate the multiplicity of steady states in this system over a range of residence times. Temperatures of unstable states were attained experimentally by observing the effect of perturbations from stable temperatures. The observed steady states of the reactor under various mixing conditions are shown to be in good agreement with the predictions of a mathematical model which is based on the assumptions that mixing is perfect and that a single independent chemical reaction occurs. Less exact quantitative agreement between theoretical and experimental unsteady performance is accounted for in terms of the sensitivity of the unsteady state to small errors in the system parameters and the existence of appreciable extraneous heat capacities of the experimental equipment.

Evaporation and drying of drops in superheated vapors

Abstract: The evaporation of pure liquid drops and the drying of drops containing suspended and dissolved solids in an atmosphere of superheated vapor were studied. Changes in the weight and temperature of approximately 2 μliter drops of four food products, five miscellaneous materials, and pure water were measured as evaporation and drying proceeded at different drying temperatures. Evaporation of water was found to take place more slowly in superheated steam than in air. However, the medium, in which faster drying occurred, depended upon the material being dried. No major differences between the final products were observed for these two drying media except that some materials yielded denser particles in superheated steam than in air.

Thermocapillary flow around hemispherical bubble

Abstract: A hemispherical bubble, attached to a plate, is surrounded by an initially quiescent and isothermal liquid. By suddenly heating the plate, a thermal gradient over the bubble surface results. Because surface tension is temperature dependent, tangential stresses arise at the bubble surface. The liquid is viscous, and motion in the liquid phase begins. Such motion is an example of thermocapillary flow. This problem, besides being of interest from a fundamental point of view, is of possible concern in the design of space vehicles capable of storing cryogenic fluids for long periods of time in a weightless condition. Solutions to the problem are developed by numerical treatment of the governing equations. Flow and temperature fields, which depend upon the Prandtl and Marangoni numbers, were obtained for Prandtl numbers 1 and 5 and Marangoni numbers from 0 to 100,000. Results show that liquid is pulled toward the intersection of the bubble and the plate, then flows around the bubble surface, and leaves the bubble as a jet. The extent of the jet increases with increasing Marangoni number and decreases with increasing Prandtl number. Thermocapillary flow increases heat transfer (Nusselt number) over that obtained from conduction, but the increase is modest. The Nusselt number increases with the Marangoni number and is insensitive to the Prandtl number. At a Marangoni number of 40,000, the local Nusselt number was increased by a factor of 2. In order for thermocapillary flow to become a dominant heat transfer mechanism, the Marangoni number must exceed 100,000.

A new simulation method for equilibrium stage processes

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

Mass transfer in a nonuniform impinging jet: Part II. Boundary layer flow‐mass transfer

Abstract: Exact solutions of the boundary layer equations were used to calculate the local mass transfer coefficients for an impinging jet with a parabolic velocity distribution. Boundary conditions were obtained from an inviscid flow solution and also from experimental pressure distributions. Experimental data for the air/naphthalene system were in good agreement with theoretical results. Mass transfer from the impingement surface was independent of nozzle height in the range 0.5 to 12 nozzle radii. For lower nozzle heights the effect of the constriction of flow between the nozzle and the surface led to increased transfer rates near the nozzle wall; data followed the predicted behavior.

A correlation for the prediction of interaction energy parameters for mixtures of small molecules

Abstract: Low temperature, phase-equilibria data for binary systems containing hydrogen, helium, and neon were used to develop a correlation relating deviations from the geometric mean combining rule for the characteristic energy parameter to the ionization potentials of the component species. With the exception of oxygen systems, this relatively simple relationship correctly predicts published deviations, determined by different methods, for a number of systems within expected uncertainties. It is shown that consideration of attractive forces only, as done by Hudson and McCoubrey, is inadequate for such predictions.

Simultaneous heat and mass transfer in free convection boundary layers

Abstract: Expressions are derived for the heat and mass transfer coefficients for laminar free convection driven by simultaneous differences in temperature and composition for the asymptotic cases of equal Schmidt and Prandtl numbers approaching zero, equal Schmidt and Prandtl numbers approaching infinity, Schmidt number approaching infinity and Prandtl number approaching zero, and Schmidt number larger than Prandtl number and Prandtl number approaching infinity. The results are applicable for horizontal cylinders or vertical axisymmetric bodies with arbitrary body contours insofar as the approximations of boundary-layer theory are valid. The results compare favorably with existing solutions and experimental results for particular conditions.

Stabilizing effects of surface-active agents on a film flow

Abstract: The effects of surface-active agents on the stability of a liquid film is reinvestigated. The present analysis differs from the previous works in the treatment of the surface boundary conditions. The well-known damping and stabilizing effects of surface-active agents are shown to be due to the redistribution of surface material caused by wave motions and diffusion. The equations of neutral stability for both cases of soluble and insoluble surface-active agents are obtained.

Viscosity of nonpolar gaseous mixtures at normal pressures

Abstract: The relationship between μ*ξ and TR for nonpolar gases at normal pressures is used to predict the viscosity for their mixtures. For such mixtures, pseudocritical temperatures are used to obtain TR. To establish ξm for a mixture, a binary interaction model has been applied that utilizes composition and the ξ values of the pure components. Viscosities have been calculated for twenty binary systems which include helium and hydrogen. These calculated values produce an average deviation of 1.97% for 148 compositions. This method was also applied to the helium-neon-argon ternary system at 100°C. to obtain for four mixtures examined an average deviation of 2.2%.

Laminar flow in the entrance region of a cylindrical tube: Part I. Newtonian fluids

Abstract: The laminar flow of dilute aqueous polymer solutions was studied in the entrance region of a cylindrical tube. In laminar, fully developed, steady tube flow, elastic and inelastic fluids were indistinguishable. Viscoelastic fluids exhibited much higher entrance pressure losses than did inelastic fluids with comparable viscous properties. A method has been developed for separating the elastic portion of the overall entrance loss and shows that in some cases the elastic contribution represents as much as 80% of the total. An analysis is also presented which allows calculation of the elastic entrance loss in terms of a Hookean shear modulus.