RESEARCH RESULTS . . . . . . immediately available All papers listed are being considered for publication in I&EC or one of the I&EC Quarterlies. They are available in manuscript form, with the requirement that any reference to their content in a publication must have the author’s prior approval. Orders are processed within 24 hours of receipt, with shipment by first class mail. Prices for subscribers and nonsubscribers are listed with each manuscript. Please include Davment with order.
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A Generalized Newton-Raphson Method for Nonlinear Boundary Value Problems In Ordinary Differential Equations. A quasilinearization technique is shown to be an effective tool. Steady-state equations resulting from mass and energy balance in a tubular reactor with axial diffusion are solved. With very poor initial approximations, only seven iterations are needed for the correct answer.
E. S t a n l e ~Lee, Phillips Petroleum Company Ms. 66-575 15pages (Jfigures)
0
NONSUBSCRIBER
0
Quasilinearisation and Invariant Imbedding in Optimization.
A combined quasilinearization and invariant imbedding procedure is used to obtain the optimum temperature profile in a tubular reactor. This combined procedure is compared with the quasilinearization approach and also with those in the literature.
E. Stanley Lee, Phillips Petroleum Company Ms. 66-523
Subscribers $2.00
Subscribers $2.00 7 9 pages (7 figure, 2 tables)
Nonsubscribers $4.00
Nonsubscribers $4.00
Quasilinearization and the Estimation of Parameters in Differential Equations. The estimation problem is formulated as a tHo-point or multipoint boundary-value problem. T h e classical least squares criterion is used. T o illustrate the approach, the Peclet group and the reaction rate group in a tubular reactor u i t h axial mixing are obtained.
linear Programming-Z Transform Design of Digital Controllers for Regulator Systems. Linear programming coupled with Z-transform method permits designs based on performance criteria and classes of deterministic input functions not suitable for conventional design techniques. Method is described in detail and illustrated by an example.
E. Stanley Lee, Phillips Petroleum Company
C. I. Huber
Ms. 66-520 78 pages
Subscribers $2.00 Nonsubscribers 84.00
and R. K. Kermode, Carnqie Instilute oj’ Technology
M S . 66-526
Subscribers $3.00
28 pages (4figures)
Nonsubscribers $6.00
Invariant Imbedding and Boundary Value Problems. The invariant imbedding concept is used to obtain the missing initial condition of ordinary differential equations of the boundaryvalue type resulting from a tubular reactor with axial mixing. A predictor-corrector formula by combined use of invariant imbedding and quasilinearization is also formulated and discussed.
Combustion Phenomena in Industrial Flamer: Rosin Combustion Intensity Equation. Restates equation as an approximation of combustion chamber behavior against which significance of new research detail is seen more readily. Concerns calculated combustion intensities for coal and oil flames, and illustrates the prime importance of reaction rates.
E. Sfanley Lee, Phillips Pelroleum Company
R. H. Essenhigh, Pennsylvania State University
Ms. 66-527 22 pages ( 7 j g u r e , 7 tables)
Subscribers $3.00 Nonsubscribers $6.00
Invariant Imbedding, Nonlinear Filtering, and Parameter Estimation. T h e invariant imbedding concept is used to derive sequential estimator equations in the theory of nonlinear filtering and estimation. T h e reaction rate constant and the concentration of the reactant are estimated by these estimator equations. The least squares criterion is used.
E. Stanley Lee, Phillips Petrolcum Company Ms. 66-522 2 5 p a g e s (4jigures)
Ms. 66-52?
Subscribers $3.00
2 8 p a g e s (3jigures)
Nonsubscribers $6.00
Creep in Glass Fiber Reinforced Plastics. Mechanisms are considered taking into account the forces of molecular bonding in the resin, a t the interface via coupling agent, and those originating from resin shrinkage, thermal contractions, and externally applied bonds. Specific examples are considered. Methods for predicting creep behavior are outlined briefly.
T . R. Bolt and A . J. Barker, The University, Birmingham, Enpland Subscribers $3.00 Nonsubscribers $6.00
Ms. 66-528
Subscribers $2.00
2Opages (Ijgures, 7 table) VOL. 5 9
Nonsubscribers $4.00 NO. 3
MARCH 1967
63
RESEARCH RESULTS Prediction of Vapor Composilions in Gas-liquid
Systems.
A comparison of the Black and Wilson equations in predicting activity coefficients in multicomponent mixtures shows that the Wilson equation is more accurate. Temperature dependence of Black’s equation is shown. Parameters are evaluated by an optimization technique.
Ivars Neretnieks, Royal Institute of Technology, Stockholm, Su’eden
Ms. 66-529
Subscribers $3.00
2 3 p a g e s ( 2 f g u r e s , Q tables)
Nonsubscribers $6.00
A Fluidized Bed Ozonizer. The generation of ozone in fluidized beds of several different granular dielectric materials placed in the discharge region of a tubular ozonizer was investigated. Ozone concentrations and energy yields were appreciably greater with beds of glass beads or powdered alumina than when no bed was present.
Richard A . Pelers and Thomas D . Tl’heelock, Iolia State liniiersiiy of Science and irechnolofv .Ms. 67-5
35 pages (12Jgures, 2 cables) Analysis of the Control Potential of the Copolymerization Equalion by Analog Simulalion. T h e copolymerization equation is solved on a n analog computer. T h e solution is combined with a simulated control configuration, leading to a model which predicts and controls product composition. T h e limitations and potentialities of the model, and its probable successors, are discussed.
K. I . Mummk, L‘niuersily of Maine
.Vonsubscnbers $8.00
Whisker Orienlation in Variable Malrix Composite Filaments. Short fibers or whiskers, added to a desirable intermediate matrix and dra\vn or extruded into easily handled filaments or \vires, have a high degree of alignment among the long axis of the filament. Their use in composite laminates should mean substantial \\-eight savings and improved products.
Robert A . Cliflon, Jr., Bureau of .Mines
Ms. 66-535
Subscribers 52.00
7 7 p a g e s ( 6 f g u r e s , 2 tables)
Nonsubscrt bers 84.00
Initial Rate Studies for Vapor Phase Partial Oxidalion of Ethanol to Acelaldehyde over Silver Catalysl. Variables were : catalyst service time, alcohol flow rate, molal alcohol/air ratio, and catalyst bed temperature. Conversion increased with alcohol concentration or molal alcohol/air ratio. Initial rate was related to the ratio of partial pressures of alcohol and oxygen.
N . C. Roy, A . C. Gupta, and A . K. Chaudhuri, Indian Inslitu2e of Technology, Kharagjur, India
M s . 66-539
Subscribers 52.00 Nonsubscribers 54.00
7 9 p a g e s ( 7 f g u r e s , 2 tables)
Ms. 67-7 14 pages ( 5 j g u r e s )
The Response of a Tubular Heal Exchanger to large Slap Changes in Spatially Uniform Secondary Conditions. A method of calculating the response of a tubular heat exchanger to large step changes in spatially uniform secondary conditions is presented. T h e method, which is based on experimentally obtained response curves, is compared with possible mechanistic methods.
Samuel W . Sinderson, J r . , and John W. Tierney, UniuersiLy of Pittsburgh
Ms. 66-540
Subscribers $4.00
Subscribers $2.00 Nonsubscribers 54.00
The laminar Gas Jet Impinging on an Infinite liquid Surface. A Numerical Finile Difference Solulion Involving Boundary and Free Streamline Determinations. Numerical solutions are presented for the problem of a n irrotational gas jet impinging on and depressinq a n infinite liquid surface. T h e solutions involve the determination of both the jet free streamlines and the unknou n boundary corresponding to the depressed liquid surface.
Eslrelia B. Fagela-dlabastro and J . D. Heilurnns, Rice Uniz~ersiiy .Ms. 67-0
24pages (6jgures)
Subscribers $3.00 hhnsubscribers 36.00
Noninteracting Process Conlrol. New design technique handles constraint conditions on control variables and can be applied to nonlinear problems. Two examples are given, one concerning a nonisothermal chemical reactor, the other with control of a plate-type absorption column.
Shean-fin Liu, .Mobil Oil Corporation .MS.6 7 - 1 0
3 5 p a g e s ( 7 2 j g u r e s , 2 fables)
Subscribers 54.00 .Vonsubsrri bers SS.00
Nonsubscribers $8.00
40pages ( 6 j p r e s )
Analysis and Calibralion of Tubular Flow Meters. A tubular flow meter was calibrated for helium using rounded-entrance meter theory and a solution for developing f o w in tubes. Good results were obtained directly and excellent results were obtained using a n experimentally determined correction factor.
The Dimensionless parameters of Eleclrostatic Precipitalion. The methods of dimensional analysis are used to determine the efficiency of a n electrostatic precipitator for \\ hich the direct analytic approach is inadequate. Assuming 25 relevant electrical and mechanical variables, 19 dimensionless groups are derived and their physical significance discussed.
D . A . Willoughby and P. A . Kittle, Rohm
.Myron Robinson, Research-Cotfrell, Inc.
Ms. 66-543 Q p a g e s ( 2 f g u r e s , 1 table)
&?
H a a s Co. Subscribers 81.00 Nonsubscribers 82.00
longitudinal Dispersion for Turbulent Flow in Pipes. A onedimensional modpl was valid for describing longitudinal dispersion for Reynolds numbers greater than 4 X lo4. I n fully developed turbulent flow, the dispersion coefficient was independent of pipe length. Effect of diameter and fluid velocity was predicted by Taylor’s equation.
C. N . Stttel, Jr., 1V. D . Threadgill, and K. B. Schnelle, Jr., Vanderhilt Uniaersity
MS. 67- 7 29 pages ( 3 j g u r e s )
64
Subscribers 54.00
Subscribers $3.00 Nonsubscribers $6.00
INDUSTRIAL A N D ENGINEERING CHEMISTRY
M s . 67- 1 1 27 pages ( I table)
Subscribers $3.00 .Vonsubscr2bers 56.00
Extension of Rigid Urethane Foams Using Alkoxyloled Wood Derivatives. Alkoxylated derivatives of low cost wood based byproducts were incorporated into rigid urethane foam systems with excellent results. These foams were lower in cost, superior in physical properties, and more easily flame retarded than equivalent conventional polyether based products.
1ViIliam C. Darr and John K . Backus, Mobay Chemical Company
Ms. 6 7 - 7 3 1 3 p a e e s ( 1 1 tables)
Subscribers $2.00 Nonsubscribers 54.00
RESEARCH RESULTS Tray Efficiencies i n Distillation of Acetone-Methanol-Water.
Correlation of binary tray efficiencies based on data obtained in a laboratory column are used to predict ternary efficiencies obtained in same column. Correlation of binary efficiencies shows liquid viscosity, gas holdup, and “F-factor” the principal variables affecting number of gas-phase transfer units.
D.-4.
Diener and
J. A.
Cerster, LSliversity of Delumare
M s . 67-14
Subscribers $4.00
37 pages ( 4 j p r e s , 2 tables)
Nonsubscribers$8.00
Coke Formation Kinetics on Silica-Alumina Catalyst. 1. M’eight of coke was measured continuously by a thermogravimetric system at atmospheric pressure, 350 to 500’ C. Rapid initial coke formation was indicated. Low per cent coke had no significant effect on surface area or effective diffusivity of catalyst. Yuichi Ozawa and Kenneth B.
Bischoff,
Uniuersily of Texas Subscribers 82.00
M s . 67- 79
79pages (4jgures, 5 tables)
Nonsubscribers$4.00
PUMP
LIQUIDS, GASES OR SOLIDS IN SOLUTION THROUGH FLEXIBLE TUBING
WITH FINGER PRESSURE OR KINETIC CLAMP
t
FINGER PUMP
Wave like m o t i o n o f steel fingers moves material t h r o u g h t u b i n g Capacities 005 m l / r n i n to 4 5 GPM Sigmamotor finger p u m p s provide t h e flexibility of h a n d l i n g up t o 4 tubes a t a time. T u b i n g size can be varied for proportioning, m e t e r i n g o r mixing.
KINETIC CLAMP Clamping pressure m o v i n g i n a circular pattern forces material t h r o u g h a single tube. Kinetic Clamp P u m p s are smaller a n d light weight Capacities 1 5 r n l / d a y to 12 Iiters/hr.
Coke Formation Kinetics on Silica-Alumina Catalyst. II. A n a l ysis. An approximate linear function for decline of catalyst
NO CORROSION NO CONTAMINATION Both types of Pumps are available in variable or fixed flow.
activity with coke level adequately represents observed effects except for initial period of veryrapid activity decline. Rate constants followed Arrhenius formula over the 150’ C. range. A simple interpretation based on Langmuir-Hinshelwood-HougenWatson concepts is presented for the fouling parameter.
WRITE FOR CATALOG
Yuichi Orawa and Kenneth B. Bischofj, Lhiversity of TexaJ
S I G M A M O T O R , INC.
.Ms.67-20
67NORTH MAIN ST., MIDDLEPORT, N.Y. 14105
Subscribers $3.00
30pages (8jgures, 1 table)
Nonsubscribers $6.00
Circle No. 21 on Readers’ Service Card
Mechanism OF Sulfur-Alkyllead Antagonism. Engine results with several fuels containing different sulfur compounds are consistent with the dual mechanism of sulfur antagonism: decomposition of alkylleads and deactivation of P b O by SOz. Further Tvork needed to elucidate details of deactivation process. Rodney L. M i e v i l l e and Garbid H. Meguerian, American O i l Company
M s . 67-21
Subscribers $2.00
20 pages (5jigures, 4 tables)
.\’onsu
bscribers $4.00
Pressure Drop Across Sharp End Capillary Tubes. The general expression has been refined to include laminar flow and analytically derived pressure loss coefficients. Experimentally determined pressure drops across sharp end capillary tubes for Reynolds numbers less than 2100 were in excellent agreement \vith calculated values using the refined equation. Dauid Rimberg,
U.S. Atomic
M s . 67-23 23pages (Jjgures, 1 table)
Energy Commission Subscribers $3.00 A’onsubscribers $6.00
.
. . how Millipore filters solve many problems by removing particulate and microbiological contaminants, by precise size, from liquids and gases for analysis, sterility or ultracleanliness. Write for a copy of Folder MT-1 which outlines elements of Millipore technology and lists technical application literature available free of charge. Millipore Corporation, Bedford, Massachusetts 01730.
Circle
No. 14 on Readers’ Service Card VOL. 5 9
NO. 3
MARCH 1967
65
