Summary of papers published in this month’s research quarterly, I&EC Fundamentals
BEST OPERATING POINTS FOR STAGED SYSTEMS
Methods are presented here for finding the sequence of operating conditions for staged systems which maximize or minimize some measure of the over-all performance of the system. The systems may be staged discretely or continuously, either in position or in time. The methods will apply to such chemical processing problems as the design of best residence time sequences for cascades of continuous stirred tank reactors, of best temperature profiles and inlet concentrations for pipeline reactors, and of best addition rate schedules for batch reaction systems, in control systems studies, and in certain problems in the economic allocation of resources. The computations needed to solve problems of the size that may be anticipated in the engineering applications are well within the capacity of computing machines of moderate speed and memory. Mathematically, the present methods are grounded in the classical calculus of variations, and indeed represent analogs of the Weierstrass E condition and of certain transversality conditions. These methods appear to have for many purposes distinct computational advantages over direct use of methods of dynamic programming which have recently found application in so many contexts.
Stanley Kat,?, American Cyanamid co., Wuynt‘, N . J.
OPTIMUM TIME SCHEDULING OF KINETIC EXPERIMENTS
T h e design of kinetic experiments has been considered as a problem in selecting the best time intervals for measuring the composition of the reacting mixture. An approach based on transformation of the time variable to a dimensionless variable, e, is described. This transformation leads to a time schedule for making composition measurements which results in a reasonably close approach to equal changes in composition with successive integral changes in e throughout the entire time range of the experiment. This minimizes the number of measurements required for evaluating a rate constant to a desired level of accuracy, and permits facile calculation of the instantaneous reaction rate by methods of numerical differentiation. The method is extremely versatile and can be applied to almost any reaction, simple or complex, regardless of whether or not the form of the rate equation is known in advance.
Kenneth L. LindJay, Ethyl Corp., Baton Rouge, L a .
MULTIVARIABLE SYSTEMS. CONTROL SYNTHESIS
ANALYSIS AND FEEDFORWARD
Methods are developed for analyzing multivariable systems which may include feedforward and feedback control, and for designing feedforward controllers for such systems. These procedures are applicable to systems which can be described by linear time-in-
variant models and for which the control system goal is to maintain outputs constant. This approach provides a convenient framework for selecting variables to be monitored, manipulative inputs and outputs to be controlled.
R. E. Bollinger and D . E. Lamb, Department of Chemical Engineering, University of Delaware, Newark, Del.
DESIGN AND CONTROL OF FEED-EFFLUENT, EXCHANGER-REACTOR SYSTEMS
Simultaneous solutions of the steady-state heat and material balances for a first-order reaction occurring in a feed-effluent? exchanger-reactor system were obtained on an analog computer and used to calculate the values of exchanger and reactor lengths which minimized the equipment cost of the system. A dynamic study of the system indicated that the desired steady-state conditions were metastable. However, a feedback proportional controller could be used to stabilize the process. Computations were made to determine the effect of various controller gains, positions of the sensing element, and time lags in the feedback loop.
J . M . Douglas, Atlantic ReJning Co., Phiiadelphia, Pa.; J.C. Orcutt, Research Triangle Institute, Durham, N . C.; and P. W. Berthiaume, Electronic Associates, Inc., Princeton, N . J .
BUBBLE DYNAMICS AT THE SURFACE OF AN EXPONENTIALLY HEATED PLATE
The consequences of Zuber’s hypothesis, which states that at every instant the latent heat increase of a bubble growing at a heated surface is equal to the superheat energy of the liquid displaced by the bubble, are evaluated for an exponentially heated plate. For a bubble growing in saturated liquid, the radius increases initially as t3’2, a result in agreement with Zwick’s relationship for a buk’sle growing in liquid with exponential volume heat sources. The effect of plate thickness is also discussed.
S. G. Bankoff, Chemical Engineering Department, Northwestern Uniniversity, Evunston, Ill.
NATURAL CONVECTION IN HORIZONTAL CONCENTRIC CYLINDRICAL ANNULI
The problem of steady, laminar natural convection between horizontal concentric circular cylinders was attacked numerically via detailed difference equation approximations for the differential equations of conservation. No terms were eliminated by boundary layer arguments. The problem was solved with machine language on an IBM 650 digital computer for several diameter ratios and several Grashof numbers at a Prandtl number of 0.714. Computed results agree well with experiments reported in the literature. I n the appropriate limiting case, the computed results also accord with an derivation for creeping flow’
Lloyd Crawford and Robert Lemlich, Department of Chemical Engineering, University of Cincinnati, Cincinnati 27,Ohio VOL. 5 4
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BRIEFS INERTIAL IMPACTION ON SINGLE ELEMENTS
THERMAL CONDUCTIVITY OF ALUMINA CATALYST PELLETS
United States and foreign open literature and various unclassified technical reports on the inertial impaction of small aerosol particles are reviewed. T h e data presented herein have possible practical application to the design of dust filters, heat exchangers, and combustion devices. T h e information surveyed is presented in terms of an inertial impaction efficiency E as a function of a n inertia impaction parameter K , as originally defined by Langmuir. A third parameter rp is used to indicate deviations from Stokes' law of resistance at high particle Reynolds numbers. All data presented pertain to single elements, such as cylinders, spheres, plates, and airfoils, no attempt being made to describe behavior when these elements are in cascade arrangement. T h e theoretical treatments are based on the assumption of potential flow in the main body of fluid.
Thermal conductivities of pellets of alumina particles were measured as a function of pellet density (macropore volume fraction). Data were obtained under vacuum conditions from 100' to 300' F., and at 120' F. for the pores filled with helium and with air at 1-atm. pressure. Some results are also given for pellets made from powdered silver particles. From pore-size distribution measurements the variation in pellet density was observed to have little effect on the microporous particles and resulted in changes primarily in macropore volume. T h e thermal conductivities at vacuum conditions were unusually low, increasing linearly from 0.04 to 0.10 B.t.u./(hr. ft. OF.) with decreasing macropore volume fraction. T h e k. values for gas-filled pellets were greater than the vacuum results and exhibited the same increase with decreasing macrovoid fraction. The accurate Drediction of the effect of gas conductivity is by the influence Of pore radius on k , for pore in the Angstrom range. Data on accommodation coefficients for catalyst surfaces are needed to elucidate this situation. By comparison of the results for silver and alumina it is possible to make approximate predictions for the conductivity of any pelleted catalyst.
M . N . Golovin and A , A . Putnam, Battelle Memorial Institute, Columbus, Ohio
COLLECTION EFFICIEN2Y OF JET IMPACTORS AT REDUCED PRESSURES
T h e collection efficiencies of circular and rectangular jet impactors have been determined at reduced pressures using monodispersed, solid, homogeneous aerosols. Variables include particle size, jetto-slide spacing, jet size, jet velocity, and pressure. T h e data are compared with theoretical and experimental results by other investigators. Areas of agreement and disagreement are discussed. T h e experiments verify the significant role of the Cunningham correction for slip at reduced pressures.
R. A . Mischke and J. M . Smith, Northwestern University, Evan.rton, Ill.
S. C. Stern, H. W. Zeller, and A . I. Schekman, Electronics Groufi, General Mills, Inc., Minneapolis, Minn.
Two new generalized compressibility functions are defined and evaluated in terms of Pitzer's acentric factor for various reduced conditions. These new factors allow rapid estimation of those thermodynamic properties which involve the partial derivatives of volume with either temperature or pressure.
METHOD FOR RAPID DETERMINATION OF DIFFUSION COEFFICIENTS. THEORY AND APPLICATION
A method similar in operation to chromatographic techniques has been theoretically and experimentally extended for measuring a wide range of diffusion coefficients. Design of the experimental apparatus is guided by chromatographic theory. For very slow diffusion processes, such as those occurring in liquid systems, it is possible to magnify the over-all diffusion effect so that it is measurable after a very short period of time. T h e experimental work deals with gaseous diffusion coefficients measured at various flow velocities, concentration levels, etc. Where data are available for comparison, agreement with other methods is satisfactory. Although the potential speed of the method has not yet been developed, it appears that diffusional analysis by this method is already much more rapid than by most conventional methods of similar accuracy.
J . C. Giddings and S. L. Seager, Department of Chemistry, University of Utah, Salt Lake City, Utah.
DIFFUSION IN PACKED BEDS AT LOW FLOW RATES
DERIVATIVE COMPRESSIBILITY FACTORS
Robert C. Reid and Jon R. Valbert, Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
CRICONDENTHERMS AND CRICONDENBARS. THEIR PREDICTION FOR BINARY HYDROCARBON SYSTEMS
An empirical function has been developed relating the maximum temperature (cricondentherm) and the maximum pressure (cricondenbar) points of binary hydrocarbon systems to composition and the ratio of the absolute normal boiling points of the heavy and light constituents. T h e constants in the empirical function were determined from data for 13 systems. Except for systems containing methane, the average deviations of the calculated tcmperature and pressure at the cricondentherm point were 2.1 and 4.6%, respectively; for the cricondenbar they were 1.9 and 5.59r,, respectively.
Edward D. Silverman and George Thodos: The Technological Institute, Northwestern University, Evanston, Ill.
Diffusion rates were measured in a 2-inch I.D. column; packed with I/*- to 1/2-inch spherical particles and through which nitrogen flowed. Carbon dioxide was introduced into the center of the bed and its concentration measured 4.75 inches downstream. Measurements were made in the low range of modified Reynolds numbers, from 3 to 80, where data are scarce. Modified Peclet numbers were computed from the data by using a finite-source solution to the equation expressing the concentration as a function of position. For the range of conditions studied, the simpler point source solution would give results about 10% low. The importance of axial diffusion was analyzed by computing the effect of the magnitude of the axial diffusivity on the radial diffusivity. For the low Reynolds numbers employed in the present study the final results were obtained by assuming that the axial and radial diffusivities were equal.
Transient behaviors of stirred tank reactors caused by the flow variations were analytically and numerically investigated. The knowledge of such transients is of practical importance for plant start-up and plant automation.
George Roemer, J . S. Dranoff3 and J. M . Smith, Northwestern University, Evanston, Ill.
Liang-tseng Fan and Pu-Shan Chu, Department of Chemical Engineering, Kansas State University, Manhattan, Kan.
COMMUNICATION. TRANSIENTS CAUSED BY FLOW VARIATION IN STIRRED TANK REACTORS
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L
RESEAR
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Velocity Protlles in Turbulent Pipe Flow: Newtonian and NonNewtonian Fluids
behavior of explosive devices which depend upon the rate of gas production. An additional benefit of this project is the effect of the area to volume ratio in bomb chamber work.
D . C. Bogue and A . B. Metzner, Unioerszly of Delaware
M s . 62-214
Velocity profile measurements are reported for the turbulent core region of viscous Newtonian and non-Kewtonian fluids, Turbulent velocity profiles for purely viscous non-Newtonian fluids are essentially the same as for Newtonian fluids when normalized with mean velociry or expressed using velocity defect parameter. Ms. 62-794
33pages, inchding Bfigures, 1 table
84.00
Initial Instability of a Viscous Fluid InterFace
William E. Ranz and William M . Dreier, Jr., Uniuersity of Minnesota Microsecond photomicrographs of liquid column being injected into another liquid obtained, showing typical behavior of common liquid pairs. A theoretical treatment by Taylor has been extended and a semiempirical model developed.
Ms. 62-205
30 pages, including 10figures
$3.00
W. R. Wilcox, PaciJic Semiconductors, Inc.
81.00
Dynamics of an Adaptive Optimizing Chemical Process
V. Rajaraman, University of Wisconsin Block-diagram method of analvzing time-varying systems used to determine dynamic characteristics of an adaptive optimizing chemical process. Adaptive feature of over-all system described by simple mathematical model which has configuration of a servomechanism. Ms. 6 2 - 2 1 2
30 Pages, including 9 figures
Mass Transfer Characteristics of a Venturi Liquid-Gas Contastod
W . G. Bauer, A . G. Fredrickson, and €I. M . Tsuchiya, University of Minnesota An experimental study of a mass transfer device n.hich eliminates certain undesirable features of conventional apparatus. Liquid culture can be pumped through this simple meter-type venturi, and gas can be introduced at the throat, resulting in a mixture of finely dispersed bubbles in the liquid culture. Has noteworthy advantages in a waste treatment process or for fermentation.
IMS.62-277
4 3 p a g e s , including 19figures
Polymer Sulfonation Without Cross-linking; phate System
55.00
?he SOa-Phos-
A . F. Turbak, ESSG Research and Eqineering Company
Ms. 62-279
Distillation is shown to be effective method for ultra-high purity materials. Special equations derived for batch distillation of low impurity-content materials are much simpler than the usual. Total and minimum reflux conditions are considered. 70 pages, including 7 k u r e
$2.00
High molecular weight polyaromatics can be reproducibly sulfonated to water soluble products by use of an organo-soluble SOa-phosphate complex. The activity of SO3 can now be controlled over a wide range with a single complexing agent.
Ultrapuritlcation by Distillation
M s . 62-2 7 7
72 pages, includang Zfigures, 2 tables
83.0U
72pages. Including ?figure, 4 tables
82.00
Design of Polyether Urethane Elostic Sealants
A . Damusis, J . M . McClellan, H . G. Wissman, C . W . Hamilton, and K . C. Frisch, Wyandotte Chemicals Corl,oration Data on design of sealants with wide range of physical properties, with comparisons using molecular weight per triol cross-link as common parameter. Accelerated aging studies also made on a large number of sealing compounds. Biological test program on selected formulations carried out to determine susceptibility to attack by microorganisms commonly encountered. Sealants studied show promise for use in many applications.
M s . 62-220
29jiages, including 7 j g u r z s , 8 tables
83.00
Comparative Reacrivities of Petroleum Cokes C. F . Gray and W . J . Metrailer, flumumble Oil and Rejning Company
Gaseous “Freeze Out” Temperatures. A Method of Estimating the “Freeze Out“ Temperalure of Solid Propellant Gases
J . E. Sinclair and Gary D . Hutton, Nacal Postgraduaie School A method has been developed that makes the estimation of “freeze out” temperatures from solid propellant combustion rapid and easy. This property is of value in predicting the
Reactivity data on nine commercially available cokes determined by exposing calcined samples to a flowing stream of (20% at 1742’ F. Data on granular cakes and molded carbon bodies included. Process used to prepare coke a major factor in reactivity, with ash and iron content of secondary importance.
Ms. 62-224
72pages, including S.figures, 2 tables
82.00
(Conlinued on page 747)
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