Showing papers in "Aiche Journal in 1955"

Correlation of diffusion coefficients in dilute solutions

Abstract: Equation i 1) is strictly applicable in ideal dilute solutions in which convective transport due to volume changes on mixing is negligible, and in which other possible modes of mass transfer are not operative. This paper represents an attempito generalize the relation of P to conveniently available properties of dilute solutions so as to permit estimation of diffusion coefficients for engineering purposes.

Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes

Abstract: The splitting of globules is an important phenomenon during the final stages of disintegration processes. Three basic types of deformation of globules and six types of flow patterns causing them are distinguished. The forces controlling deformation and breakup comprise two dimensionless groups: a Weber group NWe and a viscosity group NVi. Breakup occurs when NWe exceeds a critical value (NWe)crit. Three cases are studied in greater detail: (a) Taylor's experiments on the breakup of a drop in simple types of viscous flow, (b) breakup of a drop in an air stream, (c) emulsification in a turbulent flow. It is shown that (NWe)crit depends on the type of deformation and on the flow pattern around the globule. For case (a) (NWe)crit shows a minimum value ∼ 0.5 at a certain value of (NVi) and seems to increase indefinitely with either decreasing or increasing ratio between the viscosites of the two phases. For case (b) (NWe)crit varies between 13 and ∞, depending on NVi and on the way in which the relative air velocity varies with time, the lowest value refers to the true shock case and Nvi→0. For case (c) (NWe)crit, which determines the maximum drop size in the emulsion, amounts to ∼1, and the corresponding values of NVi appear to be small. A formula is derived for the maximum drop size.

Heat and mass transfer in packed beds

Abstract: Eddy mass diffusivities, effective thermal conductivities, and wall heat transfer coefficients were measured in an 8-in. tube packed with 1/2- and 3/4-in. glass spheres. Superficial mass velocities ranged from 110 to 1,640 Ib./(hr.) (sq. ft.), corresponding to modified Reynolds numbers of 100 to 2,000. Air was the main stream fluid in all cases. The modified Peclet group (DpV/E*td) was found to be constant at a value of about 12 in the region of fully developed turbulence. At lower Reynolds numbers this group varied with the flow rate. Effective thermal conductivities were correlated by an equation. Modified Peclet numbers for heat transfer were about 25% less than those for mass transfer. The wall heat transfer coefficient varied with the superficial mass velocity as hw = 0.090 (Go0.75). An explanation is suggested for the similarity in velocity dependence between these values and those for turbulent flow in an empty tube, based on channeling at the wall.

Flow of non‐newtonian fluids—correlation of the laminar, transition, and turbulent‐flow regions

Abstract: All available data on flow of non-Newtonians in pipes have been correlated on the conventional friction factor — Reynolds number plot for Newtonian fluids. This correlation, theoretically rigorous in the laminar flow region, was tested with data on 16 different non-Newtonian materials covering the 2.1 × 109 range of Reynolds numbers from 6.3 × 10−5 to 1.3 × 105. Pipe diameters varied from 1/8 to 12 in. As the correlation does not depend on the type of fluid encountered, it may be used with Newtonian and non-Newtonian fluids alike. In spite of the great range of the available experimetnal data, further work is necessary in the transition and turbulent-flow regions. No data at all were available on thixotropic, rheopectic, and dilatant fluids, and extension of the correlation to these materials should prove most illuminative from both theoretical and practical viewpoints.

Dynamics of vapor bubbles and boiling heat transfer

Abstract: Analytical expressions for bubble radii and growth rates derived by the authors are applied in an analysis of surface boiling at high heat transfer rates. It is shown that the product of bubble radius and radial velocity is a constant, independent of the bubble radius. This circumstance permits the formulation of a Reynolds number for the flow in the thin superheated liquid layer adjacent to the heating surface. The result of the analysis is then applied to maximal heat transfer rates in pool boiling.

Mechanism of heat transfer to fluidized beds

Abstract: In order to determine the nature of the resistance controlling heat transfer between fluidized beds and surfaces in contact with them, heat transfer measurements were made on the same solid constituents with several different fluidizing gases. The heat transfer coefficients obtained with fluidized beds are found to be proportional to the square root of the thermal conductivity of the quiescent beds. This result indicates that the process controlling fluidized heat transfer may be considered to be an unsteady-state diffusion of heat into mobile elements of quiescent bed material. This picture is analyzed mathematically to yield an equation for the heat transfer coefficient h = h wherein the effects of the bed thermal properties are separated from the effects of the stirring factor S, which accounts for bed motion and geometry. The mass transfer analogue is also derived and shown to correlate existing mass and heat transfer data reasonably well. It is concluded that the proposed mechanism yields a satisfactory picture of the fluidized heat transfer process and may provide the beginnings of a rational approach to the correlation and prediction of fluidized heat transfer in engineering work.

Development of an equation of state for gases

Abstract: More than a hundred equations of state relating the pressure, volume, and temperature of gases have been proposed according to Dodge ( 7 ) , but only a very few of them have attained any practical importance as the majority do not represent the data with sufficient accuracy. In this work the significant pressure-volume-temperature (hereafter referred to as P V T ) characteristics of pure gases have been examined in detail, and an equation has been developed to fit precisely the characteristics common t o different gases. PVT data may be plotted on different types of graphs, of which probably the oldest is that of pressure vs. volume with temperature as a parameter, as shown in Figure 1. From this graph van der Waals deduced two properties of the critical isotherm namely, that at the critical point the slope is zero and an inflection occurs.' Van der Waals expressed these two properties algebraically in the following well-known manner :

Chemical reactor stability and sensitivity

Abstract: The purpose of this paper is to consider the well agitated continuous reactor from the standpoint of stability of the steady state. It has been shown in the past that chemical-reaction systems may be unstable in the sense that on slight perturbation they tend to move to a more stable state or that they are stable in their steady states, small perturbations being self-correcting so that the system possesses autoregulation. In this paper methods of developing criteria for the quantitative determination of stability or instability or presented and applied to some simple problems. In order that the effect of large perturbations on the system may be determined, complete solutions of the rigorous equations are obtained on the analogue computer (R.E.A.C.). A complete plot of reaction paths in the concentration-temperature plane may be obtained in this manner. Because of the nonlinearity of the system one cannot predict with certainty what steady state will be approached after a given large perturbation, multiple steady states being assumed possible. From the phase plot of reaction paths the regions in the plane which lead to certain steady states are delineated. Also it is shown that the natural behavior of a reactor is not to approach an unstable state. So far as the reactor is concenrned, the unstable state does not exist. The stability of the system is important to the engineer, as control will be easy or difficult and product quality will be satisfactory or not depending upon the relative stability of the steady state. An unstable state would require more elaborate control than a stable state.

The fall of single liquid drops through water

Abstract: The steady motion of single drops of ten organic liquids falling through a stationary water field is discussed. A correlation is presented for nine systems with the exception of the aniline-water system, in the form of a single curve relating the drag coefficient, Weber number, Reynolds number, and a physical property group. The curve can be used directly to predict the terminal velocity, drag coefficient, Reynolds number, and Weber number for any given equivalent drop size. A break point in the curve serves to predict the peak velocity and its related quantities. The critical drop size is predicted from the pertinent physical properties alone. All these estimations were accurate within 10% for the systems used. The interfacial tensions ranged from 24 to 45 dynes/cm. and the drop densities from 1.100 to 2.947g./ml., the latter resulting in a twentyfold range of density differences. The drop viscosities had no apparent effect.

Surface tension and the principle of corresponding states

Abstract: Experimental surface-tension data for pure substances have been correlated successfully by the use of two recent modifications of the principle of corresponding states. The results are expressed in terms of simple analytical relations which allow one to calculate the surface-tension curves either from the critical constants Pc, Vc, and Tc or from Pc, Tc, and the boiling point Tb and also provide a method for estimating critical properties from surface-tension measurements. In addition, a method for estimating the surface tension of molten metals is suggested.

Numerical solution of two‐dimensional heat‐flow problems

Abstract: Two-dimensional heat flow frequently leads to problems not amenable to the methods of classical mathematical physics; thus, procedures for obtaining approximate solutions are desirable. A recently introduced finite-difference method, known to be applicable to problems in a rectangular region and involving much less calculation than previous methods, is extended by example to cases of more practical interest. Although all three examples given are steady state, unsteady state problems may also be attacked successfully by the method. The first example is that of flow around a corner and indicates that a more complicated region than a rectangle can be treated. Then a problem involving a radiation-boundray condition is given; as this condition is nonlinear, the method is extended to more general equations. The last example involves point heat sources and sinks in an elliptical region and so extends the method to treat curved boundaries (as distinguished from polygonal domains) and singular points. It is believed that materially less calculation is necessary by this method than for previous procedures.

Mass transfer in packed beds

Abstract: Although considerable work has been done on the problem of heat transfer radially in fixed beds through which gases are flowing, the data available for mass transfer are limited to one pipe size and one packing size and refer to average diffusivities for the entire bed. The present study was undertaken to determine: (1) diffusivities over a range of pipe and packing sizes and (2) the effect of radial position in the bed. The measurements were made by introducing carbon dioxide into an air stream and analyzing the resultant mixture at various positions in the bed downstream from the point of injection. Pipe sizes of 2, 3, and 4 in. were packed with spherical particles of 5/32-, 1/4-, 3/8-, and 1/2-in. nominal diameter. The differential equation describing the concentration in a packed bed when diffusivity E and the velocity u are permitted to vary with radial position was solved by use of an I.B.M. card-programmed calculator for the computations. The results show that the Peclet number Dpu/E increases from the center towards the wall of the pipe and that the increase is significant when Dp/Dt is greater than 0.05. Empirical correlations are then presented for both point Peclet numbers, which vary with radial position, and average Peclet numbers for the entire bed. The variations in Peclet number with radius can be explained in terms of the corresponding variation in void fraction for 81% of the radius of the bed. At modified Reynolds numbers above 40 to 100 the equation Pe = 8.0 + 100 (δ — δ0) correlates the effects of pipe and packing size and radial position. At radial positions greater than 0.81 wall friction influences turbulence conditions and the Peclet number.

Performance of packed columns. I. Total, static, and operating holdups

Abstract: Total and static holdups have been measured for 1/2-, and 1-in. ceramic Berl saddles, 1/2-, 1-, and 1 1/2-in. ceramic Raschig rings, and 1-in. carbon Raschig rings with air rates from 100 to 1,000 1b./(hr.) (sq. ft.) and water rates from 1,000 to 10,000 1b./ (hr.) (sq. ft.). The holdup measurements and motion picture observations of the flow of dye solutions through packings provide an explanation for the great differences observed when gas-phase mass transfer rates are measured by absorption and vaporization methods. If the effective interfacial area for vaporization is assumed to be proportional to total holdup and the area for absorption is assumed proportional to operating holdup, the raio of the two mass transfer rates should be equal to the ratio of the two holdups. The departure from equality of the two ratios can be explained by the observation that the static holdup is displaced slowly, resulting in additional effective area for absorption over that expected from the operating holdup alone.

Kinetics of the methane‐steam reaction

Abstract: A kinetic study was made of the reaction of steam and natural gas over a reduced nickel catalyst at a temperature range of 637° to 1,180°F. The rate of reaction is first order with respect to methane. The effect of temperature could be expressed by an Arrhenius type of equation. Both carbon monoxide and carbon dioxide are formed as primary reaction products.

Performance of packed columns. II. Wetted and effective‐interfacial areas, gas ‐ and liquid‐phase mass transfer rates

Abstract: A study was made of separating the volumetric mass transfer coefficients, kGa and kLa, into their components kG, kL, and a so that the effects of variables might be determined separately for each component. Mass transfer rates for four packings, 1/2- and 1 1/2-in. Raschig rings and 1/2-in. and 1-in. Berl saddles, made of naphthalene, were determined by vaporization into air at gas rates from 100 to 1,000 1b./(hr.) (sq. ft.). The correlation for kGa was used to determine the wetted areas of those packings when irrigated with water and to calculate the effective interfacial areas, a, from Fellinger's data for ammonia absorption. These effective areas were then used to evaluate kL from previously published kLa data, and a correlation was obtained for all packings. The correlations for kGa and kLand the effective-interfacial-area data make possible a more rigorous method for the design of packed columns than was heretofore available.

Activity coefficients at infinite dilution

Abstract: Equations are derived for obtaining activity coefficients at infinite dilution in binary systems by use of one of the following: (1) an isobaric temperature—liquid composition diagram, (2) an isobaric temperature—vapor composition diagram, (3) an isothermal pressure—liquid composition diagram, or (4) an isothermal pressure—vapor composition diagram. The derived equations are thermodynamically exact, and application involves no doubtful extrapolation of experimental data, as has heretofore been the case. Each equation involves the slope of one of the diagrams at the point corresponding to the pure component. Attention is called to the fact that data on the compositions of both the vapor and liquid phases in equilibrium are not required. Use of the equations is illustrated.

Studies of thermal conductivity of liquids. Part I

Abstract: Values of thermal conductivity and temperature coefficients for fifty-three pure organic liquids, obtained with newly designed, extensively tested apparatus, are presented. For thirty-one of these liquids values of thermal conductivity or temperature coefficients have not been previously reported. The statisically determined maximum error in the presented values of thermal conductivity of liquids is ±1.50%. A method of correlating the thermal conductivity of liquids based on a modified statement of the theory of corresponding states is presented. Group contributions to the thermal conductivity were calculated. The thermal conductivity of liquids was predicted by this method and the average deviation of the calculated from the observed values for forty-seven liquids is ±1.50%. The proposed method of correlation permits the calculation of the thermal conductivity of a series of liquids at any temperature from a single known value.

Enrichment calculations in gaseous diffusion: Large separation factor

Abstract: A general method has been devised for calculating gaseous-diffusion-stage requirements to separate gases of widely differing molecular weights. For such a mixture the actual separation factor is shown to be less than the ideal separation factor, depending on the undiffused-gas composition and the ratio of absolute pressures on each side of the barrier. The equilibrium relationship between the compositions of the diffused- and undiffused-gas streams leaving any stage is also derived by means of the Rayleigh concept. Application of the method is illustrated with a diagram, like that of McCabe and Thiele for distillation, on which are stepped off the required number of theoretical stages to separate a particular hydrogen-nitrogen mixture.

Analysis of gas-fluidized solid systems by x-ray absorption

Abstract: X-ray absorption is presented as a unique tool for the study of the fundamentals of gas fludization. For example, bed-density profiles, valuable indexes of the quality of fluidization, are readily determined by means of X-ray absorption. No internal probes, to interfere with the normal action within a fluidized bed, are involved. As an initial application of X-ray absorption to fluidization, the results of a study of the effect of mode of distribution of gas to a fluidized bed are presented. The importance of this variable, only superficially discussed in previous literature, is clearly shown by these results. Application of X-ray absorption to other chemical engineering operations is readily conceivable.

Liquid films in viscous flow

Abstract: A trace of radioactive material dissolved in a liquid enables the thickness of a moving film to be determined by measurement of the radiation emitted. The method is rapid and accurate and an average thickness is obtained directly even though the surface of the film may be irregular. Six liquids, having viscosities ranging from 0.5 to 20 centipoises were observed in flow down the inner wall of a vertical tube. Liquids having viscosities of about 1 centipoise or less exhibit typical viscous behavior with respect to film thickness even when waves are present. Liquids having larger viscosities give values of the film thickness which are less than for true viscous flow. The departure from normal behavior increases with increasing viscosity and occurs only over the region where the liquid moves in wave flow. Surface tension is not a factor in either wave formation or wave flow. The wave motion appears at flow rates well within the viscous region and occurs when the Froude number exceeds unity. Equations derived for the viscous flow of liquid films on the inner wall of a vertical tube would be required where tube diameter is small or liquid viscosity large. Ordinarily the less complex equations for flow down a flat plate may be used. A theory of flow in the viscous region with waves present is suggested.

Turbulence in falling liquid films

Abstract: On the basis of fluid dynamic and heat transfer studies on falling-film towers by various investigators, it has been commonly accepted by most workers that the liquid flow is essentially streamline in nature for liquid-film Reynolds numbers under 1,800 to 2,000; conseuquently it would be expected that the rate of physical gas absorption in such liquid films could be predicted directly from a knowledge of molecular diffusion rates. Measurements of the absorption of pure gases in falling liquid films at low Reynolds numbers substantiated the findings of other investigators that the mass transfer rates were manyfold greater than could have been predicted if molecular diffusion were the only transfer process. Increased interfacial area due to rippling of the liquid films could not account for the large increase in mass transfer rates found, and experiments with the addition of a dye stream to the liquid at the freer interface indicated turbulence. Dissolution rates of slightly soluble solids coated on the tube wall to liquid films were measured and showed that the liquid film was not in laminar flow even for Reynolds numbers as low as 300. An explanation is proposed which resolves these apparently conflicting results between momentum and heat and mass transfer, based on the fact that mass transfer measurements provide a more sensitive test for the presence of turbulence than do momentum or heat transfer measurements.

Gas-solid contact in fluidized beds

Abstract: According to the concept of two-phase fluidization, a part of the gas in a fluidized reactor passes through the uniform dispersed solid-gas phase in the form of bubbles, channels, and slugs. Material transport by mixing or diffusion takes place at the phase boundaries. A mass transfer coefficient between the two phases may be used to evaluate the effectiveness of contact between the gas and solid. The reaction rate for the catalytic decomposition of nitrous oxide was determined in a fluidized bed of impregnated alumina particles and compared with the corresponding rate in a fixed bed. Simultaneous rate equations were established based on the assumption that the continuous phase is either completely unmixed or uniformly mixed, and the discontinuous phase passes without mixing. The effects of the velocity of the gas, the particle size, and the bed depth on the transfer coefficient were investigated. Applications to heat transfer in fluidized beds and equipment design are discussed.

Rate of fall of single liquid droplets

Abstract: A study was made of the terminal velocities of fall of liquid droplets in another phase liquid under stationary conditions. The studies include dimensional analysis, experimental work for collection of fall-velocity data, and photographic studies of the drop behavior. Six systems were studied for organic liquids insoluble in and heavier than water. The experimental conditions and procedure have been standardized. For any given system, as the drop size was increased the fall velocities of the droplets increased gradually, reached a maximum, and then fell off asymptotically. Two mechanisms have been postulated, (1) for the range where the fall velocities increased with an increase of drop size and (2) for the range where the fall velocities decreased with an increase of drop size, with the maximum velocity region corresponding to the transition from region 1 and 2.

Entrainment removal by a wire-mesh separator

Abstract: The efficiency of a wire-mesh separator as an entrainment eliminator has been experimentally determined in an evaporator employing a sodium chloride brine to trace the entrainment throughout the system. Superficial linear velocities have been tested with efficiencies ranging from less than 80% at lower velocities up to 99.9% at 17 ft./sec. Higher superficial linear velocities were explored, but the results were erratic, with reentrainment from the separator visually evident. The experimental data have been correlated by the assumption, and development, of a proposed mechanism for the capture of the entrainment particles by the wires in the separator. This mechanism is developed from a theoretical derivation by Langmuir and Blodgett used for correlating the stoppage of mist particles by the leading edges of airplanes and has been found to correlate the experimental data very well, so that predictions in unworked ranges may be made. The separator as applied in this experimental work behaved as an impingement-type, inertial entrainment eliminator. The use of the presently developed equations permits the recommendation of specifications to be used in the fabrication of a separator for its most efficient performance if the nature of the entrainment and conditions of operation are known.

Estimation of ternary vapor‐liquid equilibrium

Abstract: Isothermal vapor-liquid equilibrium measurements were made at 50°C. for the ternary systems acetone-methanol-chloroform, acetone-methanol-carbon tetrachloride, and acetone-methanol-methyl acetate, by means of an improved vapor-recirculation type of apparatus. The complete range of concentrations was investigated, including six of the seven constituent binary systems. Chemical methods, supplemented by density and refractive-index measurements, were used for analysis. Results are presented in the form of activity coefficients γ as a function of various concentrations. Binary and ternary constants for the three-suffix Margules equations were determined by plots of (log γ) / (1-x)2 as a function of the mole fraction x. Such equations have been found to represent both the binary and the ternary data adequately except in the system containing both methanol and carbon tetrachloride. For these mixtures a simplified four-suffix equation, including a single ternary constant, correlates binary and ternary equilibrium data. The data indicate that reliable estimates of ternary equilibria can be based on the assumption that the ternary constant C* is zero for mixtures in which all deviations from Raoult's Law are positive. This is interpreted as indicating that the probability of existence of trimolecular aggregates, two- or three-component, in ternary solutions is no greater than the average of probabilities of existence of trimolecular aggregates in the constituent binary systems. Based on equations of the Margules type, a procedure is outlined for determining binary constants rapidly and for planning experiments whereby a ternary system may be completely investigated with the aid of very few measurements. The composition changes that the accompany differential distillation of the three ternary mixtures are described qualitatively in terms of the shape of the vapor-pressure-composition surfaces.

Capacity factors in the performance of perforated plate columns

Abstract: A study was made of factors affecting the vapor-handling capacity of perforated-plate liquid-vapor contacting columns. Vapor-phase pressure drop across plates, liquid entrainment upward from plate to plate, and plate stability were investigated as functions of operational and geometric column parameters. Gas-phase pressure drop across dry perforated plates was observed to follow functional relationships predicted from available information for single perforations. The presence of liquid on a plate increased the total pressure drop by the equivalent clear-liquid head plus a small residue which is nearly constant for a given liquid. Entrainment was observed to be a function of column gas velocity, independent of gas velocity in the perforations. Weight rate of entrainment was also found to be proportional to the gas density, independent of liquid density, and inversely proportional to the liquid-surface tension. For a given system, entrainment was observed to be proportional to approximately the third power of the group, gas velocity divided by the distance between the liquid surface and the plate above. The stability of perforated plates was observed to be adequate for many industrial and experimental applications, as also reported in recently published studies, but contrary to qualitative statements found in the earlier literature. Stability was found to increase with decreasing perforation diameter and decreasing total perforation area relative to column cross-sectional area; to increase with greater gas density, liquid surface tension, and liquid wetting power; and to be virtually independent of liquid density and viscosity. Operating limits of vapor and liquid throughput are shown for a typical application of perforated plates in liquid-vapor contacting columns.