BRIEFS Summary of papers published in this month's research quarterly, IMEC Fundamentals
DEHYDROGENATION OF BUTANE AND BUTENES OVER CHROME-ALUMINA CATALYST
The forward and backward rates of reaction in a heterogeneous catalytic system characterized by a rate-determining step can be related to the stoichiometric number of this step. This number directly related the over-all kinetics to the chemical equilibrium constant. The present experimental study of butane and butene dehydrogenation was designed to investigate the existence and magnitude of such a number for this system. Good correlation was obtained consistent with a stoichiometric number of 2. Possible mechanisms are suggested to explain these results.
John H a j j e l , Hillard Blanck, and T . B. Hamill, New York University, Bronx, N . Y .
IND.ENG.CHEM.FUNDAMENTALS 5 , 289-294 (1966)
tration data, values of the velocities and affinities were coniputcd Cl2 = 2NOC1 and 2NOC1 for the two known reactions, 2 N 0 IZ = 2 N 0 2IC1. Under certain conditions of concentration, the second of these reactions was found to proceed with a negative affinity-velocity product, although the system as a whole displayed a positive entropy source term. The second reaction proceeded essentially to equilibrium during the experiment; the other remained substantially removed from equilibrium, with an A / R T value of approximately 10. In view of the significant departure from equilibrium, to quantitatively test the linear force and flux laws of irreversible thermodynamics was not possible. However, least squares analyses of the data definitely confirmed the existence of coupling, as shown by the nonzero values for the coupling coefficients, L I Zand L z l , and by the presence of the negative A V product. A conclusive test of the Onsager reciprocity relations could not be made.
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E. B. Nebeker and C. J . Pings, California Institute of Technology, Pasadena, Calif. PYROLYSIS OF ETHYLBENZENE WITH AND WITHOUT OXYGEN INITIATION
The effect of small quantities of oxygen (0 to 10%) on the thermal decomposition of ethylbenzene in the temperature range of 570' to 650' C. was investigated, utilizing a flow reactor with residence times on the order of 0.1 second. The runs made with oxygen excluded fit a half-order rate expression with an activation energy of 69 kcal. per gram mole. Small quantities of oxygen increase the rate of thermal decomposition, but this effect tapers off as the oxygen concentration is increased. With a n oxygen concentration of about 3%, the same level of conversion is achieved at a temperature 10" C. lower than that required when oxygen is excluded. T h e styrene yield selectivity increases from 74 mole without oxygen to 81 mole % with 10% oxygen. T h e presence of oxygen also lowers the apparent activation energy.
E. D. Hausmann and C. J . King, Univeisity of California, Berkeley, Calif. IND.ENG.CHEM.FUNDAMENTALS 5,295-301 (1966)
INFLUENCE OF THE GEOMETRIC FACTOR O N CATALYTIC PROPERTIES OF POTASSIUM GRAPHITE
All of the potassium graphites were prepared (KC*, KC24, KCa6, KC48, KC6o) and shown to possess high catalytic activity for double bond isomerization of 1-pentene. A geometric factor was clearly discernible, because distances between potassium layers increased in proceeding from high to low potassium concentration without significant changes in electrical properties of each layer. The layers in potassium-rich compounds were less effective because of steric hinderance, and unusual selectivity for lower olefins was demonstrated by KCs because of this effect.
Delbert M . Ottmers and Howard F. Rase, T h e University of Texas, Austin, Tex.
IND.ENG.CHEM.FUNDAMENTALS 5 , 302-310 (1966)
EXPERIMENTAL STUDY OF CHEMICAL COUPLING
Concentrations were measured photometrically as a function of time in a system comprised of the reactants NO, Clz, and 1 2 at atmospheric pressure and room temperature. From the concen-
IND.
END.CHEM. FUNDAMEN'TALS 5 , 310-317 (1966)
EFFECTIVENESS FACTOR FOR POROUS CATALYSTS. LANGMUIRHINSHELWOOD KINETIC EXPRESSIONS FOR BIMOLECULAR SURFACE REACTIONS
A generalized method of predicting the catalyst effectivenessfactor has been developed for kinetic expressions of the LangmuirHinshelwood (Hougen-Watson) type, for the case of two reactants that combine by a second-order surface process, where inhibiting effects of either reactants or products may be significant. The catalyst effectiveness factor may exceed unity under some isothermal conditions. A region where the effectiveness factor is not uniquely determined by specifying the reaction conditions at the outside surface of the catalyst also exists and the implications of this multiplicity are discussed. Generalized charts for computation are presented and the method is illustrated by a typical calculation. G. W. Roberts and C. N. Satterjeld, Massachusetts Institute of Technology, Cambridge, Mass. IND.END.CHEM.FUNDAMENTALS 5 , 317-325 (1966)
EFFECT OF GEOMETRY O N CATALYST EFFECTIVENESS FACTOR. LANOMUIR-HINSHELWOOD KINETICS
A generalized chart compares the catalyst effectiveness factor for spherical and slab catalyst shapes for kinetic expressions of the Langmuir-Hinshelwood type, covering the case of a single reactant in which adsorption of products or reactant may be significant. For a given value of the modulus @L, the maximum deviation between the value of the effectiveness factor for spherical and for slab geometry varies up to 34%, depending upon the kinetic expression.
C. W. Knudsen, G. W. Roberts, and C. IV. Satterjeld, Massnchujells Institute of Technology, Cambridge, Mass. IND.ENG.CHEM.FUNDAMENTALS 5 , 325-326 (1966) (Continued on page 92) VOL. 5 8
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BRIEFS DIFFUSION AND REACTION IN SOLIDS
Diffusion has been studied in single pellets at 108' to 125' C. for the inert phthalic anhydride-phthalylsulfathiazole system. The diffusion of phthalylsulfathiazole into phthalic anhydride was not measurable, but concentration profiles of phthalic anhydride in phthalylsulfathiazole were observed. By, applying a moving boundary technique to the data, diffusivities were calculated for three temperatures and two porosities. .4sharp increase in diffusivity with porosity was obtained, indicating the importance of pore surface diffusion. Such diffusivities are necessary to predict tile extent of conversion in reacting systems. For single cylindrical pellets of reactants (with their end faces in contact) equations have been developed showing the effects of diffusivity and reaction rate constant on the concentration profiles for combined diffusion and reaction. 4 second-order rate equation was assumed for the solid-solid reaction between reactants.
K ..7. Arioulsmith and J . M . Smith, University of California, D u ~ i sGal$. , 1 ~ 1 3 EXG, . CHEM.FUNDAMENTALS 5 , 327-335
(1966)
expressed by an equation which is derived using the shear strength theory of friction and the mathematical form of an adsorption isotherm.
A . J . Haltner and C'. S. Olioer, General Electric Research Laboratory, Schenectady, il'. Y . IND.
ENG.CHEM. FUNDAMENTALS 5 , 348-355 (1966)
MOLECULAR PARAMETERS FOR NORMAL FLUIDS. LENNARD-JONES 12-6 POTENTIAL
A test was made of the applicability of the Lennard-Jones 12-6 potential to normal fluids. The force constants, u and e, were evaluated for 14 such fluids by least-squares analysis of experimental viscosities and second virial Coefficients. Correspondingstates correlations of the force constants were also obtained, directly from the experimental data. The preferred correlations reproduce the viscosity data within a standard deviation of 2.13y', or the second virial coefficients within 34 cc. per mole.
Liong Seng Tee, Sukehir-o Gotoh, and Wurren E. Stewart, University of Wisconsin, Mudiron, Wis. INFLUENCE OF SEGREGATION O N MOLECULAR WEIGHT DISTRIBUTION IN CONTINUOUS LINEAR POLYMERIZATIONS
IND.ENC.CHEM.FUNDAMENTALS 5 , 356-363 (1966)
Molecular weight distributions resulting in continuous polymerizations in microscopically segregated, stirred tank reactors at steady state were calculated and compared with those in batch and homogeneous, continuous stirred tank reactors for three typical linear polymerization mechanisms : stepwise addition without termination, condensation, and chain addition with termination by combination. For chain lifetimes that are long compared with the mean residence time, the distribution in a segregated reactor is broader than in a batch reactor but narrower than in a continuous, homogeneous reactor; for short lifetimes it is broader than both. These conclusions are helpful in analyzing the influence of incomplete mixing on molecular weight distribution in potentially homogeneous continuous reactors.
MOLECULAR PARAMETERS FOR NORMAL FLUIDS. POTENTIAL WITH SPHERICAL CORE
Zehijv 'radmor and Joseph A . Biesenbeiger, Stevens Institute of Technology, Fhboken, AT. J .
Liong Seng Tee, Sukehiro Gotoh, and Warren E. Stewart, Uninioersity Wisconsin, Madison, W i s .
I N n . p,UG. C H E M . F U X D A M E N l ~ . A L5 ,
336- 343 (1966)
THE KIHARA
' l h e usefulness of the Kihara spherical-core potential model for the prediction of viscosities and second virial coefficients of normal fluids is investigated. Kihara force constants of 14 normal fluids are determined from experimental viscosities and/or second virial coefficients. Corresponding-states correlations are developed for prediction of force constants of other normal fluids. In comparison with the Lennard-Jones 12-6 potential, the Kihara potential predicts second virial coefficients with considerably better accuracy; however, the prediction of viscosities is only of comparable accuracy. of
IND. ENG.CHEM.FUNDAMENTAI.S 5 , 363-367 (1966) BOUNDARY LAYER EFFECTS IN REVERSE OSMOSIS DESALINATION
CALCULATION OF DISSOCIATION PRESSURES OF GAS HYDRATES USING THE KIHARA MODEL
A potential function based on the Kihara niodel is presented for the rodlike molecules encaged in a cell. The parameters of the derived function are dctcrmined so as to agree with the experimental dissociation pressure for nitrogen hydrate, while the Kihara model for a spherical core ir used to calculate the dissociation pressure of methane hydrate. 4 comparison of predicted dissociation pressures for the methane-nitrogen-water svstem obtained by using the Kihara model and the Lennard-Jones potential with cxpcriInexital data shows that the Kihara model, taking int.0 account the shape and size of a caged molecule, is superior to the less realistic Idennard-Jonespotential. I,rumu lVu,euia and R i k i Kobayashi, Rice University, Houston, T e x . { N D . b h G , GHEM. F U N D A h f E N T A L S
5 , 344--348 (1966)
EFFECT OF WATER VAPOR O N THE FRICTION OF MOLYBDENUM DISULFIDE
.Z dctailed study has been made of the effect of water vapor on the friction of a n MoSz compact sliding against a rubbed film of MoSz on copper in an atmosphere of nitrogen. Associated with the friction increase in the presence of water vapor is a surface oxidation of MoSz to produce H2S. T h e data are consistent with a picture which assumes that frictional forces arise from processes that occur at the surfaces of MoS2 crystallitcs. The variation of friction of MoS2 with the partial pressure of water vapor can be 92
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
Predicted average production rates based on a detailed analysis of brineside liquid-phase diffusional behavior of continuous reverse osmosis in a parallel plate channel are compared with the experimental data of Merten, Lonsdale, and Riley. The agreement obtained is good and tends to bolster confidence in the method of analysis, which accounts for nonlinear effects.
William Gill, Clarkson College of Technology, Potsdam, LV. Y., and Dale Zeh and Chi Tien, Syracuse University, Syracuse, N . Y . A\r.
IKD.
ENG.CHEII. FVNDAZCEKTALS 5 , 367-370 (1966)
CORRELATION OF HEAT AND MASS TRANSFER DATA FOR HIGH SCHMIDT AND REYNOLDS NUMBERS
Turbulent mass transfer in rectangular ducts was studied via diffusion-controlled reduction of potassium ferricyanide in excess caustic. Observations were made at Schmidt numbers from 1700 to 30,000 and Reynolds numbers from 7000 to 60,000 by variation of temperature, caustic concentration, and flow rate. Results agreed more closely with the Chilton-Colburn analogy than with available semi-empirical expressions, and tend to cast doubt on the latter. Values of dln hTu/dln Sc varied from an average of 0.367 at R e = 60,000 to 0.300 at R e = 7000, and values of dln Nu/dlnJ from about 0.8 at Sc = 1700 to about 0.3 at Sc = 30,000.
Davis W . Hubbard and E. N. Lightfoot, 1Jniversity qf Wisconsin, Madison, Wis. IND.
ENG.CHE?d.
FUXD4SlEKTALS
5 , 370--379 (1966)
GRAVITATIONAL THINNING OF FILMS. VISCOSITY AND SURFACE ELASTICITY
EFFECT OF SURFACE
The effect of surface viscosity and surface elasticity on the thinning of soap films has been analyzed mathematically. Two special cases of interfacial mass transfer were considered : kinetically controlled transfer between the surface and a substrate of constant concentration, and equilibrium between the surface and a substrate of varying concentration due to convective transport. The first case illustrates the role of the Marangoni effect in foam stabilization, while the second case illustrates the Gibbs effect. Both effects give rise to an “elastic” type of behavior, and the calculated drainage rates indicate that the Gibbs effect is by far the more important.
Stephen Whitaker, Unrversity of California, Davis, Calif. I N D .ENG.CHEM.FUNDAMENTALS 5, 379-388 (1966)
more accurate type of linearization. An improved method for controlling distributed parameter systems involving nonlinear feedback is illustrated for proportional control,
L. B. Koppel, Purdue University, Lafayette, Ind. IND.ENC. CHEM.FUNDAMENTALS 5, 403-413 (1966)
CONTROL OF TUBULAR HEAT EXCHANGERS AND CHEMICAL REACTORS BY PIECEWISE CONSTANT MANIPULATION OF FLOW RATE
Control of a class of tubular heat exchangers and chemical reactors by piecewise-constant (switched) manipulation of flow rate provides efficient algorithms for driving the process from one steadystate condition to another. Switching times for minimizing various performance criteria are derived from exact and linearized dynamics, and found to compare closely. Time-optimum control of the transfer function (1 - e P ) / s is shown to require infinite switching.
TURBULENT PIPE FLOW OF MAGNESIA PARTICLES I N AIR
L . B. Koppel, Purdue University, Lafayette, Ind.
Results on concentration and mass flow distributions in turbulent gas-solid pipe flow are presented. T h e system consists of nominal 30-micron magnesium oxide particles in air. Experimental range includes mass ratios up to 3 pounds of solids per pound of air at Reynolds numbers from 1.3 X lo5 to 2.95 X lo5. The density distribution of solid particles is strongly influenced by their average charge to mass ratio, while the velocity distribution of the particles remains in the range where the collision among the solid particles is negligible.
IND.ENG.CHEM.FUNDAMENTALS 5,413-422 (1966)
S . L. So0 and G. J. Trerek, University of Illinois, Urbana, Ill. IND.END.CHEM.FUNDAMENTALS 5,388-392 (1966)
EFFECT OF DIFFERENTIAL PRESSURE O N FLOW OF GRANULAR SOLIDS THROUGH ORIFICES
The effect of differential pressure on the flow rate of several freeflowing granular solids through horizontal orifices has been investigated experimentally. An equation developed from energy balance considerations describes the experimental results. Two parameters appear in this equation, one that is a function onlv of the particle properties and one that is a function of particle properties and the orifice diameter. The two parameters behave as would be predicted from the factors that define them.
Wzlliam Resnick, Yztshak Heled, Aharon Klezn, and Ephratm Palm, Department of Chemical Engineering, Israel Institute of Technology, Haifa, Israel IND.ENG.CHEM.FUNDAMENTALS 5, 392-396 (1966)
OPTIMUM CROSSCURRENT EXTRACTION WITH MISCIBLE SOLVENTS
The optimal solvent distribution in staged crosscurrent extraction with miscible solvents is determined by a modified maximum-principle algorithm. For the case of linear equilibria an analytical solution is developed which enables the amount of the second solvent to be chosen such that the total profit is maximized. The comparison of the numerical results with an earlier publication confirms the accuracy of the data obtained by a numerical technique.
T . C. Chen and N . E. Ceaglske, University of Minnesota, Minneapolis, Minn. IND.ENG.CHEM.FUNDAMENTALS 5, 422-426 (1966)
EFFECT OF MASS TRANSFER ON THE STABILITY OF MISCIBLE DISPLACEMENT FRONTS I N POROUS MEDIA
Perturbation methods are applied to the equations describiiig miscible displacement processes in porous media under conditions where mass transfer is occurring. A criterion for hydrodynamic stability is thereby derived for both Cartesian and cylindrical coordinates. The criterion shows that mass transfer tends to stabilize miscible displacement fronts. A method for determining the initial response of system variables to a perturbation in axial velocity is illustrated.
D. 0. Cooney, University of Wisconsin, Madison, W i s . IND.ENG.CHEM.FUNDAMENTALS 5,426-430 (1 966) SAMPLED-DATA CONTROL OF UNSTABLE PROCESSES
Settings are presented for proportional and proportional-integral control of unstable processes such as exothermic chemical reactors in sampled-data systems. It is assumed that the instability may be adequately modeled by a negative time constant. The effects of time delay and additional process dynamics are discussed.
L. B. Koppel, Purdue University, Lafayette, Ind. IND.ENO.CHEM.FUNDAMENTALS 5,396-402 (1966)
DYNAMICS AND CONTROL OF A CLASS OF NONLINEAR, TUBULAR, PARAMETRICALLY FORCED HEAT EXCHANGERS AND CHEMICAL REACTORS
Earlier work on the dynamics of distributed parameter models of heat exchangers and chemical reactors is extended by defining a
COMMUNICATION. RADIAL MIXING DURING TWO-PHASE COUNTERCURRENT FLOW THROUGH A PACKED COLUMN
By use of a continuous point source of tracer, radial dispersion coefficients (expressed as radial Peclet numbers) have been measured for the dispersed water phase in a packed column. Air, flowing countercurrently to the water, was varied in flow rate from zero to near flooding conditions at each of four water rates. T h e Peclet number decreased (increased dispersion) with increase in either liquid or gas rate. A single correlation is presented for all of the results.
K . L. Anderson, 0. M . Stokke, and R. E. Gilbert, University of .\.cbraska, Lincoln, Neb. IND.ENG.CHEM.FUNDAMENTALS 5, 430-432 (1966).
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BRIEFS
THE C*HEMISTRY OF INTERFACES
COMMUNICATION. INDEPENDENCE OF THE PERFORMANCE OF A N ION EXCHANGE COLUMN ON ITS SHAPE
I&FX announces t h e publication of a hard-cover volume reprinted f r o m our pages. T h e chapters a r e t h e p a p e r s presented a t The Interface Symposium, held i n Washington, D. C., in J u n e of 1964 and then expanded f o r publication. T h e first of these articles appeared i n t h e September, 1964, issue of I&EC. The l a s t appeared i n September, 1965. This symposium was organized by Sydney Ross, Professor of Colloid Science, Rensselaer Polytechnic Institute. H e deliberately designed t h e symposium to provide a teaching insti,ument f o r industrial chemists faced w i t h practical pmblems in surface chemistry-a much-needed item. According t o Dr. Ross, no b e t t e r t e x t is available f o r those involved i n problems of surface chemistry, whether i n ind u s t r y or i n advanced classes a t universities. The 177-page book, printed in two colors, is bound i n hard eovei’s. It is available now, a n d includes a 5-page subject index. Price-$7.50 The topics a n d their a u t h o r s a r e a s follows:
Gene rui
Solid-liquid i n t e r f a c e s
Frederick M. Fowkes: Atti active Forces a t Intel faces
J. I-’.Olivier:
Liquid-liquid und liq wid-gasi n t e y f a c e s \Taller Drost-Hansen: Aqueous InterfacesMethods of S t u d y a n d S t r u c t u r a l Properties Parts 1 and2 Sydney Ross a n d E. S. Chen: Adsorption and Thermodynamics a t t h e Liquid-Liquid Interface
J . J. Bikerman: F o a m s a n d EmulsionsFormation, Properties and Breakdown Pait 1---Foams P a r t 2--Em~11sions
E. G. Schwarz and JV.
