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THREE-PARAMETER FORMULATION OF JOFFE EQUATION OF STATE
New temperature functions have been defined for the Joffe equation of state on a thrcc-parameter basis. Pitzer’s generalized correlations for the second virial coefficient and for the compressibility factor were used as guides in the fitting procedure. Sufficient care was taken in deriving the temperarue functions to permit the equation to yield reliable results for enthalpy as well as for compressibility. Coefficients for pure fluids are evaluated from the critical pressure, critical temperature, and acentric factor, and mixtures are handled by means of a previously established pseudocritical rule. T h e equation is tested for the computation of gas-phase density, fugacity, and enthalpy departure from the ideal gas. Acceptable results are obtained for nonpolar or slightly polar pure fluids and mixtures.
H. E. Barner and S.B. Adler, M . W . Kellogg Go., Piscataway, N . J . 08854
IND.ENG.CHEM.FUXDAMENTALS 9,521-530 (1970)
PREDICTION OF LIQUID-PHASE ENTHALPIES WITH THE REDLICH-KWONG EQUATION OF STATE
T h e Redlich-Kwong equation with temperature-dependent coefficients, previously used for predicting vapor-liquid equilibria, has been applied to the calculation of liquid-phase enthalpies of pure compounds a n d mixtures. The two parameters of the Redlich-Kwong equation, treated as temperature functions, are obtained for each component from its saturated pure liquid properties. Binary interaction constants are required for describing mixing behavior i n binary and multicomponent systems. These constants have been established for a number of systems as part of earlier work in utilizing this equation for predicting vapor-liquid equilibria. T h e proposed method for predicting enthalpies is compared with the pseudocritical method of Barner and Quinlan for several systems for which there are experimental enthalpy data.
Joseph Joffe and David Zudkeuitch, Esso Research and Engineering Co., Florham Park, N,J . 07932
IND.ENC.CHEM.FUNDAMENTALS 9,545-548 (1970)
ENTHALPY OF MIXTURES BY MODIFIED BWR EQUATION
T h e enthalpy behavior of methane-propane mixtures is predicted using a modified BWR equation for enthalpy developed to predict pure component enthalpy behavior. T h e use of geometric mixing rules for the thrcc new parameters introduced into the BTVR equation yields enthalpy predictions which are generally within 2 Btu per pound of experimental data for methane-propane mixtures. T h e use of specific values for unlike interaction parameters yields predicted mixture enthalpies that are somewhat more accurate than enthalpies calculated using geometric rules.
K . E. Starling and J . E. Powers, Uniuersib of ]Michigan, A n n Arbor, Mich. 48 103 IND.ENG.CHEM.FUNDAMENTALS 9,531-537 (1970)
CORRESPONDING STATES PRINCIPLE USING SHAPE FACTORS
PREDICTION OF VAPOR-LIQUID EQUILIBRIA AND ENTHALPIES OF MIXTURES AT LOW TEMPERATURES
I n a computerized system for prediction of vapor-liquid equilibria and enthalpies of multicomponent mixtures separate correlations are used for vapor and liquid phases; the virial equation of state is used to describe nonidealites of the vapor phase, and liquidphase activity coefficients are correlated with a four-suffix Margules equation. T h e reference state for pure-component, liquid-phase fugacities and enthalpies is the saturated liquid adjusted to zero pressure ; however, for highly supercritical components, the reference fugacities are given by Henry’s constants. Heat-of-mixing and pressure corrections are applied to liquid mixture enthalpies. Comparisons are made with experimental data for low temperature systems as encountered in liquefaction of natural gas and purification of hydrogen. The calculation procedure described is modular and can readily be extended to systems at higher temperatures.
Matthew G. Zellner and L. Carroll Claitor, Air Products and Chemicals, Inc., Allentown, Pa. 78105, and John LM. Prausnitz, UniversiQ of California, Berkely, Calif. 34720
T h e simple corresponding states principle provides for predicting properties of pure fluids and mixtures that are conformal with a reference. Slightly nonconformal substances (many important compounds) require a n extended CSP for satisfactory representation. An extension of the simple CSP involves additional parameters called shape factors, which modify the critical properties of nonconformal fluids so that they conform to the reference. Theory and comparisons with experimental data indicate that total thermodynamic properties of a mixture (enthalpy, fugacity, entropy) can be accurately calculated even a t low temperatures by CSP. Prediction of partial thermodynamic properties involves differentiation of CSP parameters with respect to composition and requires much greater accuracy in specifying the unlike pair interactions. Prediction of partial thermodynamic properties is now limited to reduced temperatures above 0.6 and mixtures having no large differences in molecular properties.
T h e quasilattice theory advanced by Guggenheim and Barker, re-expressed in canonical partition function of group interactions, is applied to the representation of excess thermodynamic properties of n-alcohol-n-paraffin mixtures. Six exchange energies of the groups involved are determined by fitting the equations of excess enthalpy to experimental data on eight binary systems over the entire composition range. T h e exchange energies thus determined are employed to predict excess free energy and excess entropy for comparison with experimental data on two binary systems. Reasonable agreement is obtained for all three excess properties for the systems studied.
G. D . Fisher, ChemShare Corp., Houston, T e x . 77027, and T . W . Leland, Jr., Rice Uniuersity, Houston, T e x . 7 7 0 0 1
C . - M . Kuo, R. L. Robinson, Jr., and K.-C. Chao, Oklahoma State Universiy, Stillwater, Okla. 74074
I N D . ENG.CHEM.FUNDAMENTALS 9,537-544 (1970)
I N D . ENG.
96
INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
IND.ENG.CHEM.FUNDAMENTALS 9, 549-563 (1970) QUASILATTICE THEORY AND PARAFFIN-ALCOHOL
CHEM. FUNDAMENTALS 9,564-568 (1970)
SYSTEMS
EFFECT OF PRESSURE ON HEAT CAPACITY. TRIFLUOROMETHANE SYSTEM
CHARACTERISTICS OF LIQUID-SOLID REACTIONS. HYDROCHLORIC ACID-CALCIUM CARBONATE REACTION
NITROGEN-
A Workman-type heat exchange calorimeter was used to study the effect of pressure on the heat capacity of two mixtures of nitrogen and trifluoromethane. Pressures ranged from 1 to 140 atm and temperatures from - 20 a to 60 ‘C.
S.M . Balaban and L . A . Wenzel, Lehigh University, Bethlehem,
pa^
18015 IND.END.CHEM.FUNDAMENTALS 9,568-574 (1970)
VAPOR COMPOSITION OVER DECOMPOSING HYDROGEN PEROXIDE SOLUTIONS
A model was developed and experimentally verified to permit the computation of vapor composition over thick layers of decomposing aqueous HzOz. Vapors containing HzOz concentrations greater than the known flammability limits can be generated during the decomposition of solutions stronger than about 86 weight yGHzOz.
E. S.Shanlty and P. F. Strong, Arthur D . Lzttle, Inc., Acorn Park, Cambridge, Mass. 02140, and L . R.Darbee and N . D . Lee, F M C Coif., Princeton, N. J . 0 8 4 5 0
Techniques commonly used to determine reaction rates for heterogeneous liquid-solid reactions such as the hydrochloric acid-calcium carbonate reaction are mass transport-limited and do not reflect surface kinetics. A procedure where liquid flows through a channel composed of solid reactant is proposed for obtaining kinetic data. An exact solution for reaction rate with an arbitrary kinetic model is obtained by numerical methods based upon Duhamel’s theory, for first- and second-order reversible and irreversible reactions. The method is easily extended to other models. An exact boundary layer solution is given for the firstorder irreversible reaction and an approximate boundary layer technique for solution of the arbitrary reaction rate case is developed. The approximate technique yields simple solutions which are accurate under certain prescribed conditions. Existing experimental data for the hydrochloric acid-calcium carbonate reaction are analyzed in light of the proposed kinetic models.
B. B. Williams, J . L . Gidley, J . A . Guin, and R . S. Schechter, ESSO Production Research Co., Houston, Tex. 77001 IND. ENC.CHEM.FUNDAMENTALS 9, 589-596 (1970)
IND. END.CHEM.FUNDAMENTALS 9, 574-578 (1970) FLOW OF SINGLE-PHASE FLUIDS THROUGH FIBROUS BEDS THERMODYNAMIC AND TRANSPORT PROPERTIES OF WATER VAPOR AT LOW DENSITIES
Using statistical-mechanical equations and the Kihara-Stockmayer potential model, thermodynamic and transport properties of dilute to moderately dense water vapor were calculated to within experimental error. The potential parameters employed are the same as those used for calculating properties of aqueous vapor mixtures.
J . P. O’Connell, Unzuersity of Florzda, Garnesville, Fla., 32607, and J . M . Prausnitt, University OJ CaliJornia, Berkeley, Calif. 94720 IND.ENG.CHEM.FUNDAMENTALS 9,579-584 (1970)
A pore model for the flow of a single-phase fluid through a bed of random fibers is proposed. An effective pore number, Are, accounts for the influence of dead space on flow; deflection number, N , , characterizes the effect of fiber deflection on pressure drop. Experimental data were obtained with glass, nylon, and Dacron fibers of 8- to 28-micron diameter and with fluids of viscosity ranging from 1 to 22 cp. A generalized friction factor-Reynolds number equation is presented. The effects of dead space in a fibrous bed on flow and of fiber deflection on pressure drop have no parallels in a granular bed.
C. P. Kyan, D . T . Wasan, and R. C. Kzntner, Illinois Institute of Technology, Chicago, Ill. 606 76 IND. ENG.CHEM.FUNDAMENTALS 9, 596-603 (1970)
JOULE-THOMSON INVERSION CURVE, CORRESPONDING STATES, AND SIMPLER EQUATIONS OF STATE
Existing Joule-Thomson inversion data show a good corresponding states correlation in terms of T , and P,. The maximum inversion temperature is 5.0, the (extrapolated) minimum inversion temperature is 0.8, and the maximum Pv = 11.75 occurs a t T , = 2.25. The reduced inversion curve can be described by the empirical equation, P, = 24.21 - (18.54/T,) - 0.825 T,2. Although the Redlich-Kwong is somewhat better than the others, none of the better simpler equations of state (van der Waals, generalized Dieterici, generalized Redlich-Kwong, or Martin) adequately characterizes the inversion curve. Agreement with the inversion curve is a severe test of equations of state.
EXPERIMENTAL OBSERVATIONS OF SPHERE MIGRATION IN COUETTE SYSTEMS
Experimental measurements of the radial migration of spheres in Couette systems are reported. This migration carries the sphere to an equilibrium position near the midpoint of the annular region. The observed migrations varied from extremely rapid motions with overshooting of the midpoint to extremely slow migrations requiring many revolutions of the sphere about the Couette axis to reach equilibrium. With a correlation of the experimental data based on theoretical considerations, migration effects in Couette systems can be easily estimated.
D . G. Miller, Lawrence Radiation Laboratory, University of CaliJornia, Livermore, Calif. 94550
J . S.Halow and G. B. Wills, Virginia Polytechnic Institute, Blacksburg, Va. 24061
IND. ENC.CHEM.FUNDAMENTALS 9,585-589 (1970)
IND.END.CHEM.FCJNDAMENTALS 9,603-607 (1970) VOL. 6 2
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NOVEMBER 1 9 7 0
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BRIEFS
VISCOUS FLOW THROUGH PARTICLE ASSEMBLAGES AT INTERMEDIATE REYNOLDS NUMBERS. STEADY-STATE SOLUTIONS FOR FLOW THROUGH ASSEMBLAGES OF CYLINDERS
maximum time step which ensures stability while minimizing computing time.
J . M . Wheeler, Eastman Kodak Co., Rochester, N . Y., 14650, and Stanely Middieman, L’niuersity of Massachusetts, Amherst, Mass. 01002
Numerical solutions have been obtained for incompressible, Newtonian flow normal to a n assemblage of uniform circular cylinders for the Reynolds number range 0 to 500, and the porosity range 0.4 to 1.0. Tube interaction has been accounted for, using one of the many possible surface-interaction models. T h e numerical results show the effects of variation in Reynolds number and porosity on surface vorticity distribution; surface pressure distribution; form, friction: and total drag coefficients; and standing vortex ring dimensions. Predicted drag and heat transfer coefficients for assemblages of cylinders are compared with experimental data for fiber bundles and tube banks. The agreement is satisfactory.
T h e Volterra series in discrete form forms the basis for a n algorithm for identifying unknown nonlinear processes in the presence of contaminating input fluctuations. Simulation of the model of a n ore-crushing rod mill is used to test out the feasibility of the algorithm. T h e method is extremely promising for this type of nonlinear identification or model building.
B. P. LeClair and A. E. Hamielec, McMaster University, Hamilton, Ontario, Canada
Y. Bard, I B M Cor)., 1Veu York, N. Y . 10017, and Leon Lapidus, Princeton University, Princeton, N.J . 08540
IND. ENG.CHEM. FUNDAMENTALS 9, 608-613 (1970)
IND.ENG.CHEM.FUNDAMENTALS 9,628-633 (1970)
IND.
ENG.C H E M . FUNDAMENTALS 9,624-627 (1970)
NONLINEAR SYSTEM IDENTIFICATION
DETERMINATION OF START-UP CONDITIONS FOR CHEMICAL REACTOR STABILITY MASS TRANSFER CHARACTERISTICS OF WOVEN-WIRE SCREEN CATALYSTS
The rate of oxidation of hexene or toluene in excess air on platinum screen catalysts under mass transfer-controlled conditions was used to calculate j u factors. Previous literature data on heat and mass transfer were reexamined and recorrelated and the transport characteristics of screen catalysts shown to be very similar to those of infinite cylinders. There is no positive evidence that any of the hydrocarbon oxidation in these studies or of the ammonia oxidation on Pt gauze under industrial conditions occurs a s a homogeneous process.
C. “V. SatterJield and D.H . Cortet: LMassachusettsInstitute o j Technology, Cambridge, M a s s . 02139 IND. ENG.CHEM. FUNDAMENTALS 9, 613-620 (1970)
FIXED BED ADSORPTION KINETICS WITH PORE DIFFUSION CONTROL
.\ general analytic solution has been obtained for the time-depen-
dent behavior of a fixed-bed absorption or ion exchange column under rhe conditions of pore diffusion control and irreversible equilibrium, without the constant pattern assumption. This is a single dimensionless solution which does not depend explicitly o n the column or rate parameters, hut only on two dimensionless combinations of them. T h e constant pattern as calculated by Hall is fully developed in a finite time and finite column length.
R. S. Cooper and D . A . Liberman, Universily o j CalqoTnia Los Alamos Scientz$c Laboratoiy, Los Alamos, iV. M . 87544 IND.
Frequency domain stability criteria are used to determine the set of initial states which lead reactor outputs to a desired equilibrium state when there are multiple equilibrium states. ils a n example, the system of stirred-tank reactors is considered i n which a firstorder irreversible, exothermic reaction A + B takes place, giving rise to three equilibrium states. T h e system equations are represented by two single-loop feedback systems; then the region of initial states for asymptotic stability of the reactor is determined. This type of analysis is important to the start-up of chemical reactors.
C. D . Han, Polytechnic Institute o j Brookbn, Brookbn, IV. Y.11201 IND.
ENG. CHEM. FUNDAMENTALS 9, 6 3 4 6 4 0 (1970)
OPTIMAL CONTROL OF A PLUG-FLOW HEAT EXCHANGER WITH CONTROL PRODUCED BY WALL FLUX OR WALL TEMPERATURE
An optimization technique is applied to a plug flow heat exchanger with wall flux and wall temperature controlling. The optimal unconstrained open loop control function subject to a quadratic performance index is obtained by employing techniques of functional analysis. T h e state of the system and the controlling function are related by a bounded linear operator, the problem is reduced to minimization in Hilbert space, and necessary conditions in the form of Fredholm integral equations of the second kind are produced, thereby avoiding the two-point boundary value problem produced by the maximum principle. Both analytical and numerical solutions and a method for a good suboptimal control are presented.
W . A. Weigand, Purdue L’nimsiQ, Lafajette, Ind. 47907 IND. ENG.CHEM. FUNDAMENTALS 9,641-651 (1970)
ENG.CHEM. FUNDAMENTALS 9, 620-623 (1970) CONTROL OF PLUG FLOW TUBULAR REACTORS BY VARIATION OF FLOW RATE
MACHINE COMPUTATION OF TRANSIENTS IN FIXED BEDS WITH INTRAPARTICLE DIFFUSION AND NONLINEAR KINETICS
T h e dynamics of fixed-bed performance was studied numerically. T h e model ignores axial diffusion in the fluid phase, but accounts for intraparticle diffusion and particle to fluid convective mass transfer. .A homogeneous chemical reaction is assumed to occur within the particles, the rate being governed by a nonlinear MichaelisMenten expression. The algorithm proposed for numerical solution lends itself readily to use with the IBM 360 continuous systems modeling program. h stability analysis gives good estimates of a 98
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
T h e control of isothermal and adiabatic plug flow tubular reactors by variation of flow- rate was studied. Proportional feedback, feedforward, and optimal control responses were compared for the regulation of reactor conversion in the presence of inlet disturbances. T h e optimal control, consisting of a singular solution in each case, produces a considerably improved response over both feedforward and proportional feedback control.
J . H. Seinfeld, G. R. Gaualas, and AQungkyu Hwang, CalijFornia Institute of Technology, Pasadena, CalijF. 91 109 IND.
ENG.C H E M . FUNDAMENTALS 9,651-655 (1970)
MODIFIED NEY-ARMISTEAD CELL FOR GAS DIFFUSION MEASUREMENTS
A two-bulb gas diffusion cell is described which is suitable for measurements over a wide range of temperature and pressure, and is completely and easily accessible for cleaning and inspection. T h e new cell equation was tested experimentally using the carbon dioxide-nitrogen system.
Arvo Lannus and E. D. Grossmann, Drexel University, Philadelphia, Pa. 19104
shown to correlate the thermodynamic properties of 15 simple liquids very well.
K . K. Bhatia and T . M . Reed 111, Uniuersaty of Florida, Gainesuille, Fla. 32601 IND.ENG.CHEM.FUNDAMENTALS 9,670-671 (1970)
COMMUNICATION
IND. ENG.CHEM.FUNDAMENTALS 9,655-657 (1970) SOLUTION OF BLOCK-BAND MATRICES SIZE ANALYSIS OF IRREGULARLY SHAPED PARTICLES IN SIEVING COMPARISON WITH THE COULTER COUNTER
A study was made with a Coulter counter, using potassium sulfate crystals to determine the average size of particles in nine sieve cuts ranging from 60 to 400 U. S. standard mesh. T h e average equivalent spherical diameter of particles in a sieve cut can be greater than the average opening of the sieve screens. A modification of the Coulter counter sampling equipment is used for measuring particle sizes above 100 microns.
H. N . Rosen and H. M . Hulburt, Northwestern UniversiQ, Evanston, Ill. 60201
An algorithm suitable for the solution of general “block-band” matrices is presented. T h e method is equivalent to Gaussian elimination with partial pivoting. T h e method is-applicable to any system of simultaneous, linear equations and fails only if Gaussian elimination with partial pivoting fails. T h e method is illustrated with a simple numerical example.
James W . Gentry, University of Maryland, College Park, M d . 20742 IND.ENG.CHEM.FUNDAMENTALS 9, 671-673 (1970)
COMMUNICATION
IND.END.CHEM.FUNDAMENTALS 9,658-661 (1970) ELECTRICAL CONDUCTIVITY OF PARTIALLY SATURATED POROUS SOLIDS CONTINUOUS GAS CHROMATOGRAPHY OF MULTICOMPONENT HYDROCARBON MIXTURES
A continuous gas chromatograph was used to analyze ternary and quaternary light hydrocarbon mixtures. Sample mixture is fed continuously to the instrument. A sinusoidal variation in sample concentration is imparted to the feed stream before it enters the column by a piston driven in simple harmonic motion. For a n n-component mixture, n - 1 measurements of phase relative to the input are made a t downstream points in the column. T h e composition of the sample is calculated from these measurements. T h e instrument is intended for process stream monitoring and control applications.
D.E. Carter and G . L . Esterson, Washington Unzuersity, St. Louis, Mo. 63130 IND.ENG.CHEM.FUNDAMENTALS 9, 661-666 (1970)
IMPROVEMENTS TO MERCURY-SEAL PISTON FLOWMETER
T h e mercury-seal piston flowmeter is particularly suitable for the measurement of low rates of gas flow (1 to l o 3 cm3 sec-l) with high accuracy and it may be used as a primary standard. This paper describes modifications to the basic piston flowmeter which reduce and even out the backpressure from the meter, permit continuous flow measurement, and provide a simple and easily adjusted electronic timing system.
T h e typical decrease in electrical conductivity as electrolyte is displaced from a porous solid by a gas can be accounted for as a random breaking of conducting paths in a resistance network in which the cavities play the part of resistances.
R. P. Iczkowski, Allas-Chalmers, Greendale, W i s . 53120 IND.ENG.CHEM.FUNDAMENTALS 9,674-676 (1970)
COMMUNICATION CURRENTS LIMITED BY GAS SOLUBILITY
” T h e discrepancy between Slendyk’s polarographic limiting currents in 0.01M HC1 solutions and predictions of the effect of ionic migration is attributed to the formation of hydrogen gas a t the electrode and the consequent perturbation of the convective velocity. Negle‘ct of activity coefficient variations in the earlier calculations cannot account for the discrepancy. Diffusion coefficients of some gases in electrolytic solutions could conceivably be measured with a n electrode a t the upper end of a stagnant capillary by taking advantage of the limited solubility.
John Newman and Lzmin Hsueh, Unaversat_v of California, Berkeley, Calaf. 94720 IND.ENG.CHEM.FUNDAMENTALS 9,677-679 (1970)
S. B. Reed and M . P. Sprange, Gas Council, London, S. W. 6, England IND.END.CHEM.FUNDAMENTALS 9,666-669 (1970)
COMMUNICATION
COMMUNICATION
EFFECTS OF FREQUENCY ON MODELING HIGH-FREQUENCY ELECTRIC DISCHARGE REACTORS
ATTRACTING HARD SPHERES PAIR POTENTIAL IN THE SMOOTHED POTENTIAL CELL MODEL
A study was made of the effect of variations i n driving frequency on the spatial distributions of electron concentration, electric field strength, and reaction rate i n a high-frequency electric discharge.
The smoothed potential cell model using attracting hard spheres pair potential with attraction interaction varying as r + yields equations which were originally obtained empirically and were
Alexis T . Bell, University of California, Beikeley, Calif. 94720
IND. E:NG. CHEM. FUNDAMENTALS 9,679-681 (1970) VOL. 6 2
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NOVEMBER 1 9 7 0
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BRIEFS
COMMUNICATION CORRELATION OF KINETIC DATA FROM LAMINAR FLOW-TUBULAR REACTORS
By expressing the residence time of annular elements of the fluid in a laminar flow reactor as a function of reactor length and radial position, it is possible to relate the fractional conversion of reactant to dimensionless groups containing the rate constant, inlet concentrations, reactor volume, and flow rate. T h e functional dependence will vary with the order of the kinetic expression relating the rate of disappearance of reactant to concentration. For kinetic orders other than zero, the fractional conversion obtained in the laminar flow reactor will be less than that calculated by the plug-flow assumption. This analysis extends the previous treatments to include the general nth-order rate expression and firstorder consecutive reaction rate expressions.
M . .M. Johnson, Phdlips Petroleum Go., BartlesLille, Okla. 74003 IND.ENG.CHEM.FUNDAMENTALS 9, 681-684 (1970)
CORRESPONDENCE
Comments on a n article on parametric pumping and cycling zone adsorption.
Twenty-five papers from a symposium by the Division o f Inorganic Chemistry and the Division of Nuclear Chemistry of the American Chemical Society, chaired by Paul R . Fields and Therald Moeller. The two chemistries are intimately associated because their elements are of the f transition type and thus formally comparable with each other and different from other elements. In addition t o their chemical similarities, the two series also share the properties of magnetism and radiant energy absorption and emission characteristic of f.electron species. This volume contains thirteen papers on the lanthanides, twelve on the actinides, surveying current research in these series.
Paul R. Harris, Stauffer Chemical Go., Dobbs Ferry, N. Y . 70522 Burke Bakpr III, Shell Oil Go., Deer Park, Tex. 77536 Norman H . h e e d , Befit. of Chemical Engineering, Princeton Unioersity, Princeton, AV.J . 08540 IND.
ENC.C H E M . FUKDAMENTALS 9, 684-687 (1970)
CORRESPONDENCE
Comments on a n article on estimation of model parameters using quasilinearization.
Brian L . Ramaker, Cecil L . Smith, and Paul M7. M u r r i l l , Louisiana State C'niaersiiy, Baton Rouge, La. 70803 IND.
ENG.C H E M .
FUNDAMENTALS
9, 687 (1970)
CORRESPONDENCE
Comments on a n article on prediction of polystyrene melt tensile behavior.
Roger I . Tanner, Brown University, Providence, R. I . 0 2 9 7 2
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ENG.C H E M .
FUNDAMENTALS
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