BRIEFS Summary of papers published in this month’s research quarterly, I&EC Fundamentals
THERMAL CONDUCTIVITY OF GASES. NORMAL PRESSURES
HYDROCARBONS AT
BUBBLE FORMATION IN VISCOUS LIQUIDS UNDER CONSTANT FLOW CONDITIONS
Thermal conductivity measurements, k*, obtained from the literature for gaseous hydrocarbons a t normal pressures have been used to obtain the product, k*X, where X = M 1 / n T ~ ~ e / P o zThis ~3. product represents the sum of the translational, rotational, and vibrational contributions. T h e translational contribution ( k * X ) t is identical to k*X for monatomic gases and is a unique function of TR. T h e difference k*X ( k * h ) $ = (k*X)? (k*X)u has been designated as X, and the ratio X / X T ~ - ~ when . ~ O related to T R produces relationships specific to aliphatics, olefins, acetylenes, naphthenes, and aromatics. Group contributions deveIoped in this study permitted the establishment of X ~ ~ ~ 1 for . 0 0 the calculation of thermal conductivities of 27 hydrocarbons. These values, when compared with corresponding experimental measurements, produced a n average deviation of 2.1 % for 109 points.
T h e formation of bubbles under constant gas flow conditions has been studied for viscous liquids. No equations have been reported earlier which predict the values of bubble volume a t low gas flow rates when surface tension effects are present. An equation based on a new model of bubble formation mechanism has been developed and verified, by which bubble volumes can be predicted with a n accuracy of &5%.
D+ak Roy and George Thodos, Northwestern University, Evanston, Ill.
Experimental data for the gas-particle heat transfer coefficient in packed beds a t Reynolds numbers between 2 and 100 were determined, using a model which takes into account axial dispersion of heat in the gas phase and axial conduction in the solid phase. Beds of copper, lead, and glass were used with particle sizes ranging from 0.0198 to 0.080 inch. Dynamic thermal conductivities of the solid phase in the direction of flow were measured simultaneously.
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IND.ENG.CHEM. FUNDAMENTALS 7,529-534 ( 1 968)
EFFECTS OF DIFFERENT STRUCTURES OF POROUS SOLIDS ON DIFFUSION OF GASES IN THE TRANSITION REGION
Experimental data were obtained for diffusion of gases a t constant pressures in porous pellets of compressed alumina powder. Diffusion occurred both in the Knudsen and in the transition region. While the micropore structure was kept approximately constant, the macropore radius and bulk density were varied over a wide range. Experimental data compared closely with those predicted by the random pore model. New equations were derived for a pore structure containing many sizes of macropores and for one containing two micropores. Experimental data in such solids checked the predictions. T h e transition in going from pure Knudsen to molecular diffusion occurs over a pressure range of about 5000 to 1, which appears greater than previously assumed.
R. S. Cunningham and C. J . Geankoplis, The Ohio State University, Columbus, Ohio 43270 IND.ENG.CHEM.FUNDAMENTALS 7,535-542 (1968)
S. Krishnamurthi, R. Kumar, and N . R. Kuloor, Department of Chemical Engineering, Indian Imtitute of Science, Bangalore- 12, India
IND.ENG.CHEM.FUNDAMENTALS 7,549-554 (1968) GAS-PARTICLE HEAT TRANSFER COEFFICIENTS IN PACKED BEDS AT LOW REYNOLDS NUMBERS
Howard Littman, Rensselaer Pohtechnic Institute, Troy, N . Y., R. G. Barile, ’Purdue University, Lafayette, Ind., and A . H. Pulsifer, Iowa State University, Ames, Iowa
IND.END.CHEM.FUNDAMENTALS 7, 554-561 (1968) PARTICLE-TO-FLUID NUCLEATE BOILING HEAT TRANSFER IN A WATER-FLUIDIZED SYSTEM
An experimental study was conducted of nucleate boiling heat transfer from stainless steel balls fluidized in a water system. T h e steel balls were heated by a radiofrequency induction heater. Regimes of particle, liquid, and vapor motion were defined a n d observed. T h e heat flux and saturation temperature difference could be correlated using a form of Rohsenow’s nucleate boiling equation. Cavitation observed as a result of flow through the Auidized medium is postulated to be the source of initial nucleation sites. As a result, vigorous nucleate boiling was observed a t saturation temperature excesses as low as 0.7’F.
F. M . Young, Lamar State College, Beaumont, Tex., and J . P. Holman, Southern Methodist University, Dallas Tex.
IND.ENG.CHEM.FUNDAMENTALS 7, 561-567 (1968) VISCOUS FLOW THROUGH PARTICLE ASSEMBLAGES AT INTERMEDIATE REYNOLDS NUMBERS. STEADY-STATE SOLUTIONS FOR FLOW THROUGH ASSEMBLAGES OF SPHERES
T h e complete Navier-Stokes equation has been solved for axisymmetric flows around spherical particles in a n assemblage. Reynolds numbers up to 1000 were investigated and particle interaction was accounted for using a “surface-interaction model.” Numerical results are presented in the form of surface vorticity and pressure distributions, standing vortex ring dimensions, and form, friction, and total drag. T h e agreement between predicted drag and experimental data for packed and fluidized beds is satisfactory.
HEAT TRANSFER FROM A SPRAY-COOLED ISOTHERMAL CYLINDER
T h e local heat transfer coefficients around the periphery of a n isothermal cylinder exposed to a cross-flow consisting of a water-in-air spray have been investigated analytically. T h e analysis is valid over the leading 160’ of the cylinder and considers integral forms of the continuity, momentum, and energy equations as applied to the liquid film which forms on the cylinder. All flow is considered incompressible and evaporation from the film is neglected. T h e theoretical results agree with experimental data.
B. P. LeClair and A . E. Hamielec, McMaster University, Hamilton, Ont., Canada
J . W . Hodgson, Mechanical and Aerospace Engineering Department, The University of Tennessee, Knoxville, Tenn., and J . Edward Sunderland, Mechanical and Aerospace Engineering Department, North Carolina State University, Raleigh, N . C. 27607
IND.END.CHEM.FUNDAMENTALS 7, 542-549 (1968)
IND.ENG.CHEM.FUNDAMENTALS 7,567-572 (1968) VOL. 6 0
NO. 1 1
NOVEMBER 1 9 6 8
63
BRIEFS
DISPLACEMENT OF LIQUIDS FROM RANDOM SPHERE PACKINGS
EFFECT OF INTRAPARTICLE DIFFUSION O N CATALYST FOULING
T h e theory previously applied to mercury penetration is generalized to determine the quantity of water displaced by air from packings of randomly arranged spheres as a function of pressure. Above the breakthrough pressure, the displacement curves for thick and thin aggregates are similar and the liquid tends to be uniformly distributed in the interior of the aggregate. T h e residual saturation at high pressure is due to groups of cells filled with liquid which are not connected to the surface of the porous body toward which the liquid is being displaced.
T h e problem of catalyst fouling influenced by intraparticle diffusion in a single pellet was studied theoretically and experimentally. Some theories were confirmed by experiment. Two reaction schemes were studied: parallel reaction and series reaction, When the intraparticle diffusion resistance is small, coke deposition occurs from the inner part of the pellet in the latter, while in the former it occurs from the outer part. With a large diffusion effect, deposition occurs from the outer part in both reaction schemes. A higher catalyst activity or greater diffusion resistance is accompanied by a more rapid degradation of the over-all reaction rate in both reaction schemes, but in the series reaction scheme with a large diffusion resistance, the rate of the production of the intermediate product does not decrease as much.
Raymond P. Iczkowski, Research Division, Allis-Chalmers, Milwaukee, Wis. 5320 7
IND. ENG.CHEM.FUNDAMENTALS 7,572-576 (1968)
Yuichi Murakami, Takeshi Kobaqashi, Tadashi Hattori, and Moriyoshi Masuda, Nagoqa University, Nagcya, Japan DEFORMATION AND BREAKUP OF LIQUID DROPLETS IN A SIMPLE SHEAR FIELD
Theoretical factors involved in deformation and breakup of liquid droplets in a simple shear field are discussed. The theoretical formulas were checked experimentally; excellent agreement was obtained. Internal circulation within a drop was observed to make it more stable. T h e practical significance of the results is discussed in terms of the formation of suspensions.
H. J . Karam and J . C. Bellinger, The Dow Chemical Co., Midland, Mich. IND.END.CHEM.FUNDAMENTALS 7,576-581 (1968)
EXPERIMENTAL STUDY OF CONTINUOUS THICKENING OF A FLOCCULATED SILICA SLURRY
T h e continuous thickening behavior of a superfine grade of silica pulp flocculated with lime was observed on a pilot scale thickener of 28-sq foot area and compared with that predicted by static batch setting tests, Talmage and Fitch, and other methods. Solids throughput and density profile compared reasonably well with predictions, the second method proving the most reliable. T h e observed deviations from accepted theory reveal the limitations of various means of obtaining the experimental solids flux curve and confirm the presence and effect of different types of nonideal settling behavior in flocculated slurries, such as channeling and compaction settling. A singly humped discontinuous reduced flux curve affords a rational means of identifying the concentration zones which exhibit this anomalous behavior and thus relates fairly closely the batch and continuous thickening of real slurries.
Keith J . Scott, Chemical Engineering Group, S.A. Council for Scient& and Industrial Research, Pretoria, South Africa IND.END.CHEM.FUKDAMENTALS 7, 582-595 (1968)
IND.
ENG.CHEM. FUNDAMENTALS 7, 599-605 (1968)
KINETIC EXPRESSION WITH DIFFUSION CORRECTION FOR AMMONIA SYNTHESIS O N INDUSTRIAL CATALYST
T h e expression for the rate of formation of ammonia at pressures from 150 to 300 atm derived here is the simplest available for a modern catalyst, is suitable for design, optimization, and control studies, and is believed to be as accurate as the most complex expressions in the composition, temperature, and pressure regions of commercial importance. T h e rate expression is based on the Temkin and Pyzhev expression corrected for high pressures and fitted to recently reported kinetic measurements of Nielsen, Kjaer, and Hansen for a n industrially used catalyst. I n addition, simple expressions permit rapid calculation of effectiveness factors for 6to IO-mm particles for the process conditions found in modern synthesis units.
D. C. Dyson and J . M . Simon, Rice University, Houston, Tex. 77001 IND.ENG.CHEM.FUNDAMENTALS 7, 605-610 (1968) QUANTITATIVE RATE COEFFICIENTS FROM PULSED MICROCATALYTIC REACTORS. ETHYLENE HYDROGENATION OVER ALUMINA
T h e use of pulsed microcatalytic reactors could be broadened considerably if quantitative rate coefficients could be extracted from the conversion data. Until recently it has not been clear how this could be done except for first-order kinetics. T h e problem is solved numerically for the case of a concentration pulse which does not broaden in the reactor. T h e results of calculations for several nonlinear rate equations are presented. Essentially the same amount of kinetic information can be extracted from the over-all conversion during a pulse run as from a steady-state flow run. There is potentially more kinetic information in the shape of the output pulse. I n the hydrogenation of ethylene over alumina close agreement was found for rate coefficients derived from pulse and flow reactors.
W. A . Blanton, Jr., C. H. Byers, and R. P. Merrill, University of California, Berkeley, Calif. 94720 EXCESS PRESSURE DROP IN LAMINAR FLOW THROUGH SUDDEN CONTRACTION. NON-NEWTONIAN LIQUIDS
Excess pressure drops for laminar flow of non-Newtonian liquids, both weakly and highly elastic, have been measured. When plotted in the appropriate dimensionless form, the data show that there are no conspicuous non-Newtonian or elastic effects. T h e dimensionless pressure drop is inversely proportional to the Reynolds number, the constant of proportional being a function of the flow index. Values both larger and smaller than the corresponding Newtonian values have been observed.
IND.ENG.CHEM.FUNDAMENTALS 7,611-617 (1968) MAXIMUM PRINCIPLE AND DISCRETE SYSTEMS
A steady-state discrete-staged system is optimized by considering the staged system as evolving in time, each stage variable being a n element in the overall state vector. This introduces a convexing effect and allows the continuous maximum principle to be used. Two famous examples which have been used to illustrate the defects of the discrete approach are analyzed by the present method with positive results.
Gianni Astarita, Guido Greco, Jr., and Luigi Peluso, Istituto di Elettrochimica, Uniuersitci di h'apoli, Xaples, I t a b
Okan Gurel, I B M Cor@.,New York, N . Y., and Leon Lafiidus, Princeton Uniuersip, Princeton, N . J . 08540
IND.ENG.CHEM.FUNDAMENTALS 7,595-598 (1968)
IKD.END.CHEM.FUNDAMENTALS 7,617-622 (1968)
64
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
ESTIMATION OF MORSE POTENTIAL PARAMETERS FROM THE CRITICAL CONSTANTS AND THE ACENTRIC FACTOR
EXPERIMENTAL TECHNIQUE. THERMISTOR ANEMOMETER FOR MEASUREMENT OF LOW FLUID VELOCITIES
Reliable estimates of the most likely Morse potential parameters are obtained from the same data ( T o ,P,, and a single vapor pressure datum) needed to calculate Pitzer’s acentric factor, w, by invoking corresponding states arguments. The errors in reproducing experimental viscosities and second virial coefficients are typically 1.5 times larger for the estimated potentials than for the most likely ones. For normal fluids these properties are reproduced with comparable efficacy by Morse and Kihara potentials which are estimated from corresponding states relations. The estimated parameters e and Y, for the two potentials agree within 5% for substances whose acentric factor is in the range 0 5 w 5 0.3.
Developmcnt and calibration of a low-speed, sclf-heated thermistor a~icmoineterare discussed. Tcrnperature gradients in the fluid can be tolerated, since temperature compensation is accomplished by a second measurement of the sensor. Thrc.shold values of the \docity mcasuremenr are 0.1 cm per second in air and 0.02 cm per second in water. Satural con1,ection causes anemometer rcadings to dcpend on the direction of fluid rlow.
D. E. .VurpJo and R. E. Sparks, Case
~ l ~ ~ ~ f cResene s r ~ r ? ~UnkzrriQ,
Clnriand, Ohio J1706 IND. ENC.
CHEM. FUXDAIICXTALS 7,642-645 (1968)
D . D.Konowalow and S.L. Guberman, State University of New York at Binghamton, iV. Y,73901
IND.END.CHEM.FUNDAMENTALS 7,622-625 (1968).
EXPERIMENTAL TECHNIQUE. MEASUREMENT OF ENTHALPY DIFFERENCES WITH A FLOW CALORIMETER
GENERALIZED LINEAR PROGRAMMING SOLUTION TO SEPARATION-BLENDING PROBLEMS
.\ flow calorimeter has been developrd for determining enthalpy difrerences of natural gases in the range of -3203 to T1OO°F for pressures up to 2000 psia. Pro\,isions for measurcment of integral isothcrmal, intcgral isobaric, and total cnthalpy diffcrcnces are included. Measuremcnrs are made by heat transfer hetween a referrnce fluid and/or heaters and the test material stream. Operatiny capability and an accuracy charactcrisric as a function of test strciam energy throughput \vert. establishcd from runs on nitrogen.
Separation-blending problems with variable coefficients in the constraint matrix are solved through the generalized linear programming procedure. The optimization technique is described and illustrated through a numerical example. Some aspects of the work required to solve the problem on the computer are discussed.
Thimmappiah Prabhakar, Union Carbide Cor$., South Charleston, W . Va. 25303
J . P. Dolan, D . E. Ea’obin, and R. I;. Bukacel.., lnrtifute of Gas Technolo&,, Chicago, Ill. 60676 I K D . ENG. CHEM.
FCNDAIiEKrALS 7, 643-651 (1968)
IND.ENG.CHEM.FUNDAMENTALS 7, 626-632 (1968) EXPERIMENTAL TECHNIQUE. FLOWMETER CALIBRATED FOR ANY GAS IN THE RANGE OF 1 TO 500 LITERS PER HOUR OSCILLATORY OPERATION OF JACKETED TUBULAR REACTORS
Optimal control is studied of the cooling jacket water temperature of a n empty tubular reactor in which consecutive (Bilous-Amundson) reactions are carried out, subject to sinusoidal perturbations of the feed concentration. In this particular system, second-order effects on the desired outlet concentration were small, and could be either positive or negative, depending upon the frequency and parametric effects. T h e improvements seemed to be principally due to the zero-frequency effect, based upon the curvature of the steady-state response surface to inlet concentration, using optimal cooling water temperatures. Dynamic effects decreased the performance. Parametric studies were made of the effects of heat transfer coefficientand heat of reaction.
The prediction of flowmeter performance, commonplace in industrial practice, is difficult at the low gas flow rates frequently met in small scale laboratory experiments. However, if a flowmeter empIoying a conicaI entrance orifice is used, the flow rate of any gas or gas mixture may be predicted from a n experimentally determined calibration on a single gas, by means of a simple density correction only. New experimental data are measurements of discharge characteristics of conical entrance orifices, ranging from 0.018 to 0.076 cm in diameter, determined using hydrogen, helium, methane, nitrogen, ethylene, argon, and propane at pressure differentials from 1- to 120-cm water gage.
S. B. Reed and M . P. Sprange, Gas Council, London S.W. 6, England
IND.ENG.CHEM.FUNDAMENTALS 7, 651-655 (7968)
K. S. Chang and S. G. Bankoj, Northwestern University, Evanston, Ill. 6020 1
IND.ENG.CHEM.FUNDAMENTALS 7, 633-639 (1968)
EXPERIMENTAL TECHNIQUE. BATCH RECYCLE REACTOR FOR SLOW PHOTOCHEMICAL REACTIONS
A batch-type recycle reactor was developed for studying the
T h e d.c. plasma jet has an average composition very different from that predicted from its average enthalpy and the assumption of chemical equilibrium. An empirical “two-step” hot-core model eliminates the discrepancy within attainable experimental accuracy.
kinetics of slow photochemical processes. The equipment performed satisfactorily when tested with acetone photolysis. Solvable operating problems were encountered due to pressure fluctuations caused by the recycle pump. I n particular, air leakage in minute amounts induced photooxidation. Enough experimental data were obtained to establish the main products of the photooxidation and photolysis reactions. At the operating conditions (870 m m of Hg, 97OC, and 4 to 17Yo acetone in helium) the rate of ethane formation was less than first-order in acetone.
M . P. Freeman and J. E. Longjield, American Cyanamid Co., Stamford, Conn. 02739
A. E. Cassano, Takeshi Matsuura, and J . M . Smith, University of California, Davis, Calif.
IND.ENG.CHEM.FUNDAMENTALS 7, 640-641 (1968)
IND.END.CIIEM.FUNDAMENTALS 7, 655-660 (1968)
A PLASMA JET AS A SOURCE OF NONEQUlLlBRlUM CHEMICAL SPECIES. NEW TWO-STEP MODEL
VOL. 6 0
NO. 1 1
NOVEMBER 1 9 6 8
65
BRIEFS
COMMUNICATION. POLE LOCATION AND IMPORTANCE IN SIMPLE DEAD-TIME CONTROL SYSTEMS
The location of poles and their significance in simple feedback control systems in which the plant contains a dead-time lag are treated. Such control systems have a n infinite number of poles. If a system is designed by assuming that one pair of complex conjugate poles dominates, in certain cases real poles or low frequency complex poles occur which also contribute significantly to the closed-loop dynamic behavior. A suggestion for improving control system performance is made.
\ymrocess mrollem
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CHEMl CAL ENGINEERING CATALOG
T . J. McAvoj and E. F. Johnson, Princeton Universify, Princeton, N. J. IND.ENC.CHEM.FUNDAMENTALS 7,661-664 (1968) COMMUNICATION. REACTIONS
EFFECTIVENESS FACTORS FOR REVERSIBLE
T h e generalized graphical methods presented in previous papers for calculating catalyst effectiveness factors are extended to a simple reversible reaction A e X. Illustrative calculations demonstrate use of the method.
H. S.-P. Kao, Princeton University, Princeton, N . J . , and C. A’. SatterJield, Massachusetts Institute of Technology, Cambridge, Mass. 02139 IND.ENG.CHEM.FUNDAMENTALS 7,664-667 (1968) COMMUNICATION. SYMMETRY OF CERTAIN THERMODYNAMIC FUNCTIONS AND THE VlRlAL EXPANSION OF THE LIQUID
Evidence derived from experimental data seems to support the concept that the thermodynamic quantity T - ( d T / d P ) V P is a symmetric function of density and that the state behavior of the liquid is expressible by the virial expansion: P = RTf(d) [l B ( d , - d ) C(d, - d)2 . . . I , where d = density, d, = density of the crystal at the triple point, B, C . . . . = temperature-dependent virial coefficients, a n d f ( d ) = function of density, independent of temperature. At the triple point, tp, the expansion reduces to B t , = (Ad)-l where Ad is the density change on melting. Second virial coefficients calculated by this formula agree reasonably well with values derived from low density data.
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G. J . Auslaender, Institute Petrochim., Ploesti, Romania
IND.ENG.CHEWFUNDAMENTALS 7, 668-669 (1968) COMMUNICATION. NONIDEAL GASES
COMPACT SONIC VELOCITY EQUATION FOR
Following the idea presented in a previous communication where the sonic velocity, a, is introduced as a thermodynamic variable replacing the specific volume, the equation az = -@RT is derived, a not too obvious modification of the ideal gas relationship, a2 = r R T . T h e equation applies accurately for z values at least down to 0.80, thus covering many gaseous systems of practical importance.
G. E. Goring, TriniQ UniversiQ, San Antonio, Tex. 78272 IND.ENG.CHEM.FUNDAMENTALS 7, 669-670 (1968) CORRESPONDENCE
Comments on a n article on viscous heating in plane and circular Aow between moving surfaces.
A . B. Metmer, University of Delaware, Newark, Del.
steel and PVC Pat
IND.END.CHEM.FUNDAMENTALS 7, 670 (1968) CORRESPONDENCE
Comments on a n article on gaseous diffusion and flow in commercial catalysts at pressure levels above atmospheric.
Sun-Tak Hwang and Karl Kammermeyer, University of Iowa, Iowa City, Zowa. IND.END.CHEM.FUNDAMENTALS 7, 671-672 (1968) 66
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
Developed a new Dimensionless Group lately? If you have, and you’re just about to call it the Humperdinck Number, hold on a
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In these t w o articles, Georae D. Fulforc of the University of I.,ter.~o, Ontario, and J o h n .P. Ct.?chpole of England‘s Admiralty Materials Laboratory have listed alphabetically a total .of 285 dimensionless groups together with their symbols, definitions, fields of significance and use, and original references. What’s more, specially compiled tables list the groups b y the variables of which they are composed and the exponents to which they are raised.
So if you‘ve come up with the group D+’v+’p+’p-? a quick check of these tables will tell you that Osborne Reynolds got there before you. Sorry about that, Dr. Humperdinckl
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