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SOME SURFACE TRANSPORT EFFECTS O N ACTIVITY I N DIFFUSIONALLY LIMITED CATALYTIC SYSTEMS

PRESSURE FLUCTUATIONS I N A FLUIDIZED BED WITH AND WITHOUT SCREEN CYLINDRICAL PACKINGS

The influence of surface diffusion on catalytic activity in isothermal and nonisothermal systems is investigated for cylindrical microcapillaries. Localized chemisorption in the Henry’s law region is used as a basis for the analysis; particular results are reported and discussed for simple, irreversible kinetics. Surface transport can have considerable effect on the apparent activity of a supported catalyst, particularly when significant thermal gradients occur. The similarity of the temperature behavior of surface transport rates to that of reaction rate hinders simple interpretation of diffusional limitation in terms of temperature dependence of apparent rate.

Pressure fluctuation data were obtained from an air-fluidized sand bed (-48 65 Tyler mesh) with open-ended cylindrical packing. The tests were made in a 5-inch diameter column, and with packings made from steel wire cloth 4-, 6-, or 14-mesh per inch and ‘ j z X I/z, 3 / 4 X 3 / 4 , and 1 X 1 inch in size. These data were analyzed to yield r.m.s. values, the probability density, and the normalized power spectral density functions. The r.m.s. values of the pressure fluctuations were lower for the packed fluidized beds than for the same bed fluidized with no packing. For each packing, a maximum was observed on a plot of r.m.s. us. flow rate or bed expansion. When no packing was used, r.m.s. values increased continuously with gas flow or bed expansion; the distributions were Gaussian at low flow rates, and skewed at high flow rates. The probability distributions of the differential pressure fluctuations were Gaussian for a fluidized bed containing packings over the whole flow range tested. The normalized power spectral density functions were similar for the packed and unpacked fluidized beds, though peak frequencies showed some dependence on packing dimensions.

Richard N . Foster and John B. Butt, Yale University, N e w Haven, Conn. IND.ENG. CHEM.FUNDAMENTALS 6,481-488 (1967)

THE RECYCLE REACTOR AS A MODEL OF INCOMPLETE MIXING

The residence time distribution for a recycle reactor is derived and the correspondence between this model for incomplete mixing and the tanks in series and longitudinal diffusion models is established by the equal variance condition to be n = 1 / R 1 = uL/2D. Danckwerts’ degree of segregation is evaluated for the recycle reactor and shown to be small compared with the degree of segregation in series of two and three well mixed tanks. Further examination of the age distributions in the reactor shows that the recycle reactor is in fact a “maximum mixedness” reactor. This is confirmed by the identity of the equations for conversion in the recycle reactor and the maximum mixedness reactor with the same residence time distribution. An expression is also given for the conversion in a completely segregated reactor with the recycle reactor residence time distribution.

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D. W. T. R$pin, Imperial College, London, England IND.END.CHEM.FUNDAMENTALS 6 , 488-492 (1967)

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W . K . Kang, J . P. Sutherland, and G. L. Osberg, National Research Council, Ottawa, Canada IND. END.C H E M . FUNDAMENTALS 6, 499-504 (1967)

EVAPORATION COEFFICIENT OF LlQUlDS

Thermal gradient calculations have been made in an attempt to place the technique of the jet tensimeter on a quantitative basis. Families of curves have been derived with which experimental data can be compared. Using the jet tensimeter, evaporation rates of water, isopropyl alcohol, carbon tetrachloride, and toluene have been examined a t various liquid temperatures, times of exposure, and back pressures of vapor. The experimental results agree satisfactorily with the thermal gradient calculations, making the assumption that the evaporation coefficient is unity. This shows that there is little or no resistance to molecules crossing the vaporliquid interface in addition to the natural resistance imposed by the gas laws. As a corollary, when any vapor molecule strikes a t the interface, the chance of failing to cross is small. No significant difference in the behavior of evaporation due to the difference in molecular structure or chemical properties was observed.

Jer Ru M a a , Rochester Institute of Technology, Rochester, N . Y . IND.END.CHEM.FUNDAMENTALS 6,504-518 (1967) VAPOR-LIQUID EQUILIBRIA AT HIGH PRESSURES. VAPOR-PHASE FUGACITY COEFFICIENTS I N NONPOLAR AND QUANTUM-GAS MIXTURES

Vapor-phase fugacity coefficients, calculated with the RedlichKwong equation, are in excellent agreement with experimental results when Redlich’s original mixing rule for constant a is modified by inclusion of one binary interaction constant. Such constants are reported here for 114 binary systems including several which contain hydrogen, neon, or helium. Quantum corrections for these gases are taken into consideration. T h e calculations are readily performed with an electronic computer and are useful for reduction and correlation of vapor-liquid equilibrium data a t high pressures.

PARTICLE PRECIPITATION BY SPACE CHARGE I N TUBULAR FLOW

Precipitation of charged particles by their own space charge is investigated both theoretically and experimentally. Mathematical models are developed for the precipitation of charged particles from a gas moving through a cylindrical precipitator. Comparison of calculated results for plug-flow and turbulent-flow models demonstrates that precipitation rates may be satisfactorily predicted by the plug-flow model. Experimental points verify the calculations.

P. L.Chueh and J.M . Prausnitz, Uniuersity of California, Berkeley, Cql;f.

Larry E. Faath, Samir N . . Bustany, D. N. Hanson, and C. R. Wilke, University of California, Berkeley, Calq.

IND. ENG.CHEM.FUNDAMENTALS 6,492-498 (1967)

IND.ENG.CHEM.FUNDAMENTALS 6, 519-526 (1967) VOL. 5 9

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BRIEFS A FLUID MECHANICAL DESCRIPTION OF FLUIDIZED BEDS. EQUATIONS OF MOTION

NEW TIME-DOMAIN TECHNIQUE FOR IDENTIFICATION OF PROCESS DYNAMICS

Starting from the equations of motion of a single solid particle and the Navier-Stokes equations for fluid motion, a set of equations of motion is developed for a system of fluidized particles, and the result is compared with previously proposed equations.

A technique is developed for determination of process dynamic equations from experimental test data and simultaneous evaluation of reliability of the equations. T h e mathematical analysis is carried out entirely in the time domain. Identification of time constants was tested by using analog computer simulations of systems to which random noise was added. T h e technique appears to be a powerful tool for the direct experimental determination of linear approximations to chemical process dynamics.

T . B. Anderson and Roy Jackson, University of Edinburgh, Edinburgh, Scotland IND.

ENGC . H E M . FUNDAMENTALS 6,527-539 (1967)

Michael Heymann, M . L . McGuire, and C. M . Sliepcevich, UniLersity of Oklahoma, 'Torman, Okla.

IND. END.CHEM.FUNDAMENTALS 6 , 555-563 (1967) DETERMINATION OF RATE CONSTANTS FOR COMPLEX KINETICS MODELS

A method of determining kinetic rate coefficients for complex reactions by user-oriented iterative methods is described. T h e differential equations representing the reaction system may be nonlinear in the dependent variable but must be linear in the coefficients. Direct integration of the model for a sequence of time steps permits the model coefficients to b e estimated by maximizing the multivariate correlation coefficient, which is the same as minimizing the sum of the squares of the weighted deviations. Three weighting schemes are compared. Simulations studies and tests with actual data indicate that the proposed technique is effective.

STRUCTURAL ANALYSIS FOR MULTIVARIABLE PROCESS CONTROL

A method is introduced which retains internal structural information available from process models in feedforward and feedback control analysis of linear constant coefficient systems with the control objective of holding one or more outputs constant. Comparative examples illustrate some of the advantages of this approach over the corresponding terminal or external analysis.

D . M . Himmelblau, C. R. Jones, and K . B . Bischoy, University of Texas, Austin, T e x .

G. G. Greenfield and T . J . Ward, Clarkson College of Technology, Potsdam, 'V.Y.

IND.ENG.CHEM.FUNDAMENTALS 6, 539-543 (1967)

I N D .ENG.CHEM.FUNDAMENTALS 6 , 564-571 (1967)

ANOMALOUS OSMOSIS I N DIALYSIS OF ACIDS WITH ANION EXCHANGE MEMBRANES

STRUCTURAL AND TERMINAL ANALYSIS I N MULTIVARIABLE PROCESS CONTROL

The dialysis of four acids, (HCI, " 0 3 , H ~ S O I ,and HsPOI), through anion exchange membranes was studied. Anomalous negative osmosis-i.e., flow of solvent in direction opposite to the usual osmotic flow-was observed. TVhen these acids were dialyzed from a solution containing a nondiffusible species, the concentration of this species was increased during dialysis. Thus, the chief disadvantage of dialysis, dilution of the product, was overcome. The anomalous water transport and the increment in anomalous negative osmosis by the presence of a polyelectrolyte support the theory of Schlogl.

A method of control analysis for continuous multivariable processes uses a structural description of a process. It makes maximum use of available process information to yield optimum feedforward and feedback control configurations. Comparison is made with the corresponding terminal analysis method, and examples illustrate the significant advantages of the structural approach.

Robert D . Hansen and M . L . Anderson, Daw Chemical Go., Adidland, Mzch.

I K D .E K G .CHEM.FUKDAMENTALS 6, 571-580 (1967)

G. G. Greenjeld and T . J . W a r d , Clarkson College of Technology, Potsdam, N.Y.

IND.END.CHFM.FUNDAMENTALS 6 , 543-546 (1967)

ADSORPTION EQUILIBRIA I N THE METHANE-PROPANE-SILICA GEL SYSTEM AT HIGH PRESSURES

LAMINAR GAS JET IMPINGING O N A N INFINITE LIQUID SURFACE. NUMERICAL FINITE DIFFERENCE SOLUTION INVOLVING BOUNDARY AND FREE STREAMLINE DETERMINATIONS

Further improvements and application of the chromatographic technique for obtaining adsorption equilibrium data have been made. Adsorption data have been obtained a t high pressure for methane, propane, and several of their mixtures on silica gel, by using radioactive tracer pulsing. A method of obtaining adsorbed-phase volumes is introduced. T h e data are represented analytically using a two-dimensional virial equation of state truncated after the third virial coefficients.

Numerical solutions are presented for the problem of an irrotational gas jet impinging on and depressing a n infinite liquid surface. T h e solutions are shown to be consistent with prior experimental work, including the prediction of rippling of the liquid surface. T h e solutions involve the determination of both the jet free streamlines and the unknown boundary corresponding to the depressed liquid surface. The method of treatment of the boundary and of the free streamlines is discussed in detail.

J . J . Haq'del and Riki Kobayashi, William Marsh Rice Uniaersity, Houston, T e x .

E. B. Fagela-Alabastro and J . D . Hellums, Rice Unicersity, Houston, Tex .

IND.ENG.CHEM. FUKDAMENTAL 6 , 546-554 (1967)

IND. ENG.CIIEY.F U N D A M E K T A L S 6, 580-587 (1967)

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t N DUST RIAL A N D E N G I N E E R I N G CHEMISTRY

EXPERIMENTAL TECHNIQUE.

ON-LINE PARTICLE SIZE ANALYZER

Two new instruments for on-line measurement of particle fineness are described. Experimental results show that average particle size can be detected continuously within about 10 to 15 seconds and the cumulative oversize distribution curve obtained in less than 1 minute. Only particles from 100 to 500 microns are observed.

Y . Nakajima, K. Gotoh, and T. Tanaka, Department of Chemical Process Engineering, Hokkaido University, Sapporo, Japan IND.ENG..CHEM.FUNDAMENTALS 6 , 587-592 (1967)

EXPERIMENTAL TECHNIQUE.

HIGH-SPEED CINEPHOTOMICROGRAPHY

Techniques of high-speed photomicrography are presented. Attention is focused on the equipment and practices for taking motion pictures at framing rates up to 4000 p.p.s. Consideration is given to data accumulation from films and the error involved in velocity determinations.

D . F. Sherony, C. B. Tan, and R. C. Kintner, Illinois Institute of Technology, Chicago, Ill.

IND.ENG.CHEM.FUNDAMENTALS 6,592-595 (1967)

EXPERIMENTAL TECHNIQUE. LENGTH DISTRIBUTION

In experimental or commercial photochemistry, the Hanovia mercury vapor arc lamps listed below have induced ultraviolet radiation and near.visible violet and blue radiation in many photo-reactions. These Hanovia photochemical systems can be integrated easily into standard laboratory apparatus. And a built-in automatic protective system completely eliminates any hazard t o personnel or equipment. The complete, ruggedly-built systems include immersion wells, lamps and accessories. All available immediately from stock. For complete details, write today.

METHOD FOR MEASURING FIBER

A novel method has been devised for measuring length distribution of fibers which eliminates the time-consuming task of aligning fiber ends required by standard array methods. Projecting ends of parallel fibers arrayed on a bank of combs are removed by cutting. Under conditions described, the mean $ of the original fiber sample is related to the observed mean, X,of the cut sample by the equation $ = (3/2)X. The variances, uZ2and uhz, of the original and cut samples, respectively, are related by uZ2= 2 v i 2 - (X/2)2. Tests on known fiber distributions show good agreement with calculated values. A procedure for calculating fiber length distribution from wet-screening test data is outlined.

J. Wronski, Raybestos-Manhattan, Inc., Manheim, Pa. IND.ENG.CHEM.FUNDAMENTALS 6 , 595-599 (1967)

COMMUNICATION. CAPILLARY TUBES

PRESSURE DROP ACROSS SHARP END

The general expression for the pressure drop across sharp end tubes has been refined to include laminar flow and analytically derived pressure loss coefficients. These coefficients consider the effect of a nonuniform velocity distribution on the total pressure loss. Experimentally determined pressure drops across sharp end capillary tubes for Reynolds numbers less than 2100 were found to be in excellent agreement with calculated values using the refined equation.

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David Rimberg, Health and Safety Laboratory, U. S. Atomic Energy Commission, New York, N . Y .

IND.ENG.CHEM.FUNDAMENTALS 6,599-603 (1967) Circle No.

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BRIEFS

ESTIMATE

COMMUNICATION.

Bubbles come only from specific points in a hot surface, and these points initially contain vapor only intermittently. To explain this, two conditions have been considered: one is a location particularly favorable to forming or holding a vapor and/or dissolved gas nucleus; the other is a sufficient degree of superheat, either to form the nucleus, or to allow the repeated budding of a residual nucleus. These two factors alone do not adequately explain the experimental results, but call for a third factor. This is the presence of pressure fluctuations, generated by the bubbles themselves, which tend, sometimes to suppress, and sometimes to favor nucleation at either adjacent side. A hypothesis is presented suggesting when this third factor should come into play, and experimental results testing the hypothesis are analyzed. These experimental results tend to confirm details of the hypothesis that cannot be readily explained by the current theories involving only the two factors noted earlier.

This convenient simple-to-use graph, the first of i t s kind, is a useful tool for determining overall cost, including equipment investment, labor, fuel and power. For most spray drying applications i t by-passes the sizing and pricing steps normally required. Rough cost estimates can be made even if drying characteristics of the product are not known. Send for your free copy of t h e

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SEE US I N BOOTH 2144, CHEMICAL INDUSTRIES EXPOSITION Circle No. 34 on Readers’ Service Card

John J . Henley and Richard L. Hummel, Department of Chemical Engineering, Universzty of Toronto, Toronto, Canada

IND.ENG.CHEM.FUNDAMENTALS 6, 603-606 (1967) COMMUNICATION. VAPOR MIXTURE

GROWTH OF LIQUID DROP IN SUBCOOLED

T h e Boltzmann transformation is shown to provide a similarity variable for the equations describing the spherically symmetric, diffusion controlled growth of a new phase in an infinite medium, whose density and transport properties are temperature and composition dependent. T h e position of the phase front is thus proportional to the square root of time even though a velocity is induced by the change of volume on phase transition and the change of volume on mixing. An analytical solution is given for the special case of isothermal phase growth when the diffusivities are constant and the density depends on concentration in such a way that the change of volume on mixing is zero.

L. E. Johns, Jr., Dozer Chemical Go., Midland, Mich. IND.ENG.CHEM.FUNDAMENTALS 6, 607-609 (1967) COMMUNICATION. MEASUREMENT OF CONCENTRATION-DEPENDENT DIFFUSION COEFFICIENTS. THE EXPONENTIAL CASE

The diffusion equation has been solved for a diffusion coefficient varying exponentially with concentration for boundary conditions corresponding to those used in the absorption and desorption methods of evaluating diffusion coefficients. Comparison of these solutions with those for a constant diffusion coefficient yields simple correction factors for rapid calculation of true diffusion coefficients by these methods. Very serious errors are made when concentration dependence is neglected, as demonstrated by diffusion data for methanol, ethylene glycol monomethyl ether, chlorobenzene, and cyclohexanone in poly(viny1 acetate). Practical aspects of this type of diffusion are discussed.

Charles M . Hansen, Technical University of Denmark, Copenhagen, Denmark

IND.END.CHEM. FUNDAMENTALS 6, 609-614 (1967) CORRESPONDENCE

Comments on a published article on predictive theory for multicomponent diffusion coefficients and a rebuttal.

Alain Vignes, Uniuersity of Nancy, Nancy, France Harry T. Cullinan, Jr., State University of New York, Buffalo, N .

Y.

IKD.ENG.CHEM.FUNDAMENTALS 6, 614-616 (1967) CORRESPONDENCE

Comments on a published article on diffusion in a homogeneous fluidized bed and a reply.

Gerald Houghton, Florida State University, Tallahassee, Fla. E. Ruckenstein, Polytechnical Institute, Bucharest, Romania

IND.EKG.CHEH.FUNDAMENTALS 6, 617-619 (1967) Circle No. 10 on Readers’ Service Card

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INDUSTRIAL A N D ENGINEERING CHEMISTRY