BRIEFS Summary of paflers published in this month's research quarterly, I@EC Fundamentals
DERIVATION OF HIGHER ORDER RECIPROCAL RELATIONS
The extension of irreversible thermodynamics past the range of validity of linear phenomenological laws is discussed. An extension of the Onsager reciprocal relation involving nonlinear coefficients is derived using the principle of microscopic reversibility. The phenomenological coefficients obey a hierarchy of equations, each expressible as a power series in a small parameter. The first two members of this hierarchy are displayed. The leading term in the first member is the familiar Onsager reciprocal relation, and that of the second member provides a relation between firstand second-order coefficients. This result is compared to those of several recent articles proposing macroscopic derivations of second-order reciprocal relations. Errors in some macroscopic derivations are pointed out, and some of the implications of a nonlinear theory are discussed.
Curtis F. Holmes and Robert G . Mortimer, Indiana University, Bloomington, Ind.
IND.ENG.CHEM.FUNDAMENTALS 6, 321-325 (1967)
CATALYSIS OF ALCOHOL AND ETHER DEHYDRATION ON GAMMA-ALUMINA
A recycling reactor was used for the experimental measurement of partial pressures of all products us. time in the dehydration of alcohol and ether over y-alumina catalysts. Data were observed at 220' to 374 O C. with alcohol and ether feeds under such conditions that diffusional effects were not important. A kinetic model is proposed and is shown to be effective in explaining the experimental observations. This model, the rate constants and activation energies of which are reported, is consistent with a single site interaction on the surface. The relationship of the model to recent mechanistic proposals is discussed.
Herman J . Solomon, Harding Bliss, and John B. Butt, Yale University, N e w Haven, Conn. IND.ENC. CHEM.FUNDAMENTALS 6, 325-333 (1967)
The catalyzed reaction between hydrogen chloride and vinyl chloride in a stirred reactor was studied at temperatures in the range of 164O to 299' F., mass-flow ratios of vinyl chloride to hydrogen chloride from 2.16 to 2.46, and catalyst exposure times up to 1800 hours. Zinc chloride carried on Celite was the catalyst, and regimes of fouling and nonfouling were observed. For the nonfouling case the rate of formation, rd, of the 1,l-dichloroethane
(
phpv
ip),
- -2
Robert G. Rinker and William H . Corcoran, California Institute of Technology, Pasadena, Calif. IND.ENC. CHEM.FUNDAMENTALS 6, 333-338 (1967) MULTICOMPONENT ION EXCHANGE IN FIXED BEDS. PROPERTIES OF EQUILIBRIUM SYSTEMS
OENERAL
A theoretical analysis of multicomponent ion exchange in fixed beds is presented. Equilibrium operation, uniform presaturation, and constant feed composition are assumed. Rules for outlining over-all concentration profiles, formulated in terms of dimensionless parameters, predict the number of composition changes (transitions) between zones of constant composition (plateau zones) ; whether these transitions exhibit constant or proportionate patterns; the order in which the concentrations of various components can become zero; and the proper selection of roots in calculating throughput-parameter values within transitions. Differences are discussed between the integral material-balance equation, applicable to abrupt composition changes, and the integrated differential material-balance equation applicable to gradual composition changes. Methods based on these material balances are developed for variable-separation-factor systems to calculate concentration-profile curves, the location of concentration discontinuities, and the composition of plateau zones. Where all of the components in a transition zone (boundary of chromatography) are also present in the adjacent plateau zones, approximate ideal extrapolation of the profile curves of one component to zero concentration facilitates calculation. Application of these methods is illustrated. The profiles obtained are readily convertible into effluent-concentration histories.
Gerhard Klein, Daniel Tondeur, and Theodore Vermeulen, University of California, Richmond, Calif. IND.ENO.CHEM.FUNDAMENTALS 6, 339-351 (1967) MULTICOMPONENT ION EXCHANGE IN FIXED BEDS. SEPARATION-FACTOR EQUILIBRIUM
CATALYTIC ADDITION OF HYDROGEN CHLORIDE TO VINYL CHLORIDE. STUDIES I N A STIRRED REACTOR
was found to follow the equation: rd = C
partial pressures, respectively, of hydrogen chloride, vinyl chloride, and 1,I-dichloroethane. A four-center reaction appeared to be the most probable mechanism.
where C is
an empirically determined rate constant, K p is the equilibrium constant referred to partial pressures, and p h , pu, and p d are the
CONSTANT-
A general analytical solution is provided for the simultaneous mateterial balance and constant-separation-factor equilibrium relations pertaining to zones of varying composition in multicomponent, fixed-bed ion-exchange columns. Uniform presaturation and a step change in feed composition are considered. Algebraic and numerical methods are presented for determining the constants occurring in the analytical solution, and for obtaining the over-all concentration profiles of three- and four-component systems. Criteria for classifying ternary pattern types are de-ie!oped to permit the rapid construction of schematic profiles. Numerical examples illustrate the calculation methods.
Daniel Tondeur and Gerhard Klein, University of California, Richmond, Calif.
IND. END.CHEM.FUNDAMENTALS 6, 351-361 (1967) (Continued on page 172) VOL. 5 9
NO. 8
AUGUST 1967
111
BRIEFS MULTICOMPONENT ION EXCHANGE IN FIXED BEDS. GENERALIZED EQUILIBRIUM THEORY FOR SYSTEMS WITH CONSTANT SEPARATION FACTORS
A general analytical solution for systems with arbitrary number of exchanging species is given for conditions of local equilibrium, absence of axial diffusion and dispersion, constant separation factors, uniform presaturation, and constant feed. T h e proof of the uniqueness of the solution, based on the new concept of coherence of chromatographic boundaries, is outlined. General properties of coherent boundaries, not restricted to particular initial and input conditions, are discussed.
F. G. Helfferich, Shell Development Go., Emeryville, Gal+, IND.ENC.CHEM.FUNDAMENTALS 6, 362-364 (1967) PREDICTION OF QUATERNARY LIQUID EQUILIBRIA
A wholly empirical method for predicting quaternary liquid-liquid equilibria in two-phase systems comprising two Type I ternaries, wherein quaternary tie lines are determined from the ternary tie lines by geometric construction, was suggested some years ago. Historically, this method was verified experimentally for only several quaternary systems. This paper describes a research study initiated to determine under what conditions, if any, the method could be extended to other quaternary systems. Predicted solubility and equilibrium data were compared with experimentally determined values for the systems pyridine-tolueneethanol-water and chloroform-acetone-formic acid-water at 25" C. and 1 atm. Good agreement was found for the former system; some appreciable discrepancies were found for the latter. The results are interpreted in terms of the nature of the quaternary solubility surface, and the effects of variable distribution coefficients.
R. W . Riebling, California Institute of Technology, Pasadena, Cal;f. J . J . Conti, Polytechnic Institute of Brooklyn, Brooklyn, N . Y . IND. END.CHEhf.
FUNDAMENTALS 6,364-370 (1967)
EXISTENCE OF TWO TYPES OF DRAG REDUCTION IN PIPE FLOW OF DILUTE POLYMER SOLUTIONS
Drag reduction in the pipe flow of polymer solutions is shown to b e of two types which apparently occur by two separate mechanisms. I n turbulent flow, drag reduction is probably caused by viscoelastic effects. The critical solvent Reynolds number a t the onset of drag reduction is proportional to about the first power of the diameter. Thus, the critical velocity is independent of tube diameter. Polymers dissolved in good solvents show more drag reduction than i n poor solvents. T h e other type of drag reduction occurs when the laminar region is extended to high Reynolds numbers. It is followed by a transition region and a turbulent region in which the drag is not affected.
H. C. Hershey and J . L.Zakin, University of Missouri, Rolla, Mo.
IKD. END.CHEM.FUNDAMENTALS 6 , 381-387 (1967)
EXPERIMENTAL EVALUATION OF VISCOELASTIC THEORIES
Viscoelastic theories due to Oldroyd, Pao, Bogue, and Bernstein, Kearsley, and Zapas (BKZ) are examined for their ability to correlate linear dynamic data with nonlinear viscosity and normal stress data. Data are presented for solutions of 107, polyisobutylene in Decalin and 12% polystyrene in Aroclor. I t is concluded that the three-constant Oldroyd and the Pao theories do not correlate the data quantitatively, the Pao theory producing a high shear rate viscosity plateau at too low a shear rate. T h e Bogue and BKZ theories, both of which contain an adjustable parameter in the forms used, are reasonably successful. Some comments on the essential experiments necessary to characterize viscoelastic fluids are made. J . 0. Doughty and D . C. Bogue, University of Tennessee, Knoxville, Tenn.
IKD. ENG.CHEM.FUNDAMENTALS 6 , 388-393 (1967)
GENERAL SOLUTION TO THE PROBLEM OF HYDROGEN SULFIDE ABSORPTION I N ALKALINE SOLUTIONS
A4theoretical solution for the case of absorption followed by an instantaneous reversible ionic reaction is presented. T h e theory is particularly useful for the absorption of H2S in solutions of a salt of a strong base and a weak acid, inasmuch as the main reaction is a proton-transfer reaction and, therefore, it may be assumed instantaneous. The following cases of chemical absorption of HnS are reviewed: in hydroxide solutions, in alkaline buffer solutions, in monoethanolamine solutions, in aqueous solutions of a salt of a strong base and a weak acid-e.g., NaAc and NaSP04 -and i n inert solutions-cg., NaCl (inert as far as H2S absorption is concerned). T h e simultaneous absorption of HQS and COS in hydroxide solutions is also reviewed. Absorption data already published as well as original data show good agreement with theory.
This work was undertaken to define the conditions under which the Deborah number may become large enough to cause significant deviations from the usual drag coefficient-Reynolds number relationships for purely viscous fluids flowing through porous media under noninertial conditions. The analysis suggests that major effects may be expected at Deborah numbers in the range 0.1 to 1.0. Experimental studies using a porous medium support this analysis and yield a critical value of the Deborah number at which viscoelastic effects were first found to be measurable. The influences of a high Deborah number level upon the uniformity of the flow and upon the distribution of the fluid residence times in porous media are considered briefly.
Francesco Gioia and Gianni Astarita, Istituto di Chimica Industriale, University of IVaples, Naples, Italy
R. J . Marshall and A. B. Metzner, University Del.
IND. END.CHEM.FUNDAMENTALS 6 , 370-375 (1967)
IXD.END.CHEM.FUNDAMENTALS 6 , 393-400 (1967)
FLOW OF VISCOELASTIC FLUIDS THROUGH POROUS MEDIA
of
Delaware, Newark,
SIMULTANEOUS HEAT AND MASS TRANSFER IN LAMINAR FREE CONVECTION WITH A MOVING INTERFACE HOLDUP IN IRRIGATED RING-PACKED TOWERS BELOW THE LOADING POINT
A theoretical study has been made of simultaneous heat and mass transfer i n a laminar, free convection boundary layer at a vertical surface. Exact solutions over wide ranges of the parameters take into account density differences due to both concentration and temperature variations and which involve nonzero interfacial velocity components both normal and parallel to the interface. An asymptotic solution for high interfacial velocities has been extended to include mass and heat transfer coupling. An analysis of these and prior results shows that relatively simple theoretical expressions can represent the solutions over wide ranges of the parameters despite the apparent complexity of the problem.
Two limiting dynamic regimes for liquid flow on a n irrigated packing may b e distinguished: the gravity-viscosity regime at low Reynolds numbers and the gravity-inertia regime a t high values. Examination of simple models of the two modes suggests the form of the holdup relation for each case and gives order of magnitude estimates of the coefficients. Experimental results lie between the limits but are satisfactorily correlated by an interpolation formula.
D . V . Cardner and J . D.Hellums, Rice University, Houston, Tex.
Australia
IND. ENG.CHEM.FUNDAMENTALS 6 , 376-380 (1967)
IND.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
J. E. Buchanan, University of N e w South Wales, Kensington, N.S. W., ENO. CHEM. FUNDAhiENTALS 6 , 400-407 (1967)
LIQUID-LIQUID SPRAY COLUMN DROP SIZE, HOLDUP, AND CONTINUOUS PHASE MASS TRANSFER
PERFORMANCE AND STABILITY OF COUNTERCURRENT TWO-PHASE EXTRACTIVE TUBULAR REACTORS
Nozzle velocities for spray columns are usually higher than those covered by drop size correlations. T h e Null and Johnson correlation provides a good estimate of drop diameters at the relatively low nozzle velocities where the method is applicable. Dispersed phase holdups can be predicted as a function of the ratio of the dispersed phase superficial velocity to the terminal velocity for the drop. Continuous phase mass transfer coefficients for spray columns can be predicted from correlations for single drops if the ratio of the continuous to dispersed phase viscosity is less than one. If the viscosity ratio is greater than one, there appears to be a n interaction effect of the multiple drops that reduces the coefficient from that of a single drop.
The behavior of adiabatic two-phase countercurrent extractive tubular reactors was investigated. The possibility of the occurrence of multiple steady states, some of which are highly unstable, is demonstrated. The effect of various physical parameters on the performance and stability of the reactor has been investigated. The reactor may possess a hot spot with temperatures in excess of the adiabatic temperature of the reacting mixture. T h e optimum yield of the desired product often occurs for an unstable steady state. Transient numericalcomputations were carried out to determine the response of the system. A possible method is outlined for determining asymptotic stability from steady-state data alone.
G . A . Hughmark, Ethyl Corp., Baton Rouge, L a .
Dan Luss and N . R. Amundson, University of Minnesota, Minneapolis, Minn.
IND.ENG.CHEM.FUNDAMENTALS 6, 408-413 (1967)
IND.END.CHEM.FUNDAMENTALS 6,436-445 (1967)
EXPERIMENTAL TECHNIQUE. ENTRANCE EFFECTS AND WALL EFFECTS IN A N EXTRUSION RHEOMETER DURINO THE FLOW OF CONCENTRATED SUSPENSIONS
NUMERICAL DIFFERENTIATION OF EQUALLY SPACED AND NOT EQUALLY SPACED EXPERIMENTAL DATA
Procedures are given for smoothing and differentiating experimental data with both equal and nonequal spacing in the independent variable. Selection of the number of points to be included in the “movable strip” technique and of the degree of the polynomial is discussed. Equations are given for estimating the error by calculating a confidence interval on each slope. A technique for handling certain types of nonrandom errors is presented.
H. C . Hershey, J . L. Zakin, and Robert Simha, University of Missouri, Rolla, M o . INDENG.CHEM.FUNDAMENTALS 6, 413-421 (1967)
The flow properties of concentrated suspensions prepared from kaolinite PD-10 and distilled water have been investigated in a n extrusion-type rheometer using capillary tubes of different dimensions. Because of the presence of entrance losses and wall effects encountered during the flow of such suspensions, different flow curves result, depending on the dimensions of the tubes used. Entrance losses were determined using tubes of different lengths but the same diameter; wall effects, using tubes of different diameters but the same length. The wall phenomena and the slip coefficients have been analyzed in terms of structural characteristics of the suspensions. The results indicate that the wall phenomena affect flow curves more strongly than the entrance losses. 2. D . Jastrzebski, Lafayette College, Easton, Pa.
DESIGN AND EFFECTIVENESS OF FEEDFORWARD CONTROL SYSTEMS FOR MULTICOMPONENT DISTILLATION COLUMNS
The design and simulation of feedforward and feedback control systems fm a five-tray, single-feed distillation column have been carried out for the multicomponent system benzene-toluene-pxylene. For changes in feed composition, linear feedforward compensation may range from nearly perfect to detrimental, depending on column operating conditions.
T. W . Cadman, University of Maryland, College Park, M d . R. R. Rothfus and R. I. Kermode, Carnegie Institute of Technology, Pittsburgh, Pa. IND.END.CHEM.FUNDAMENTALS 6, 421-431 (1967)
IND.ENG.CHEM.FUNDAMENTALS 5, 445-454 (1967)
EXPERIMENTAL TECHNIQUE. INCLINED DIAPHRAGM CELL
CONVECTION AND TRANSPORT I N A N
If diffusion coefficients are measured in a cell with the diaphragm inclined to the horizontal, a flow arises because of the density difference between compartments. This flow is antisymmetric around the center of the diaphragm and is a maximum with a vertical diaphragm. The apparent diffusion coefficient is always increased by the flow, and an analysis of the phenomena gives results in accord with isothermal, binary experiments with both small and large inclinations. T h e analysis indicates that initial density differences less than 0.004 gram per cc. are required with a typical vertical diaphragm if the apparent diffusion coefficient is to be within 1yo of the true value.
H. L . Toor, Carnegie Institute of Technology, Pittsburgh, Pa. STABILITY ANALYSIS BY LIAPUNOV’S DIRECT METHODS. INVESTIGATION AND EXTENSION OF KRASOVSKII’S THEOREM
IND.ENG.CHEM.FUNDAMENTALS 6, 454-457 (1967)
Krasovskii’s theorem, by which a quadratic Liapunov function of the form u = XTAX is constructed for the nonlinear vector system, x = X(x),X(0) = 0, is investigated and extended. A sufficient condition that this v prove asymptotic stability of the origin over the entire space is that the matrix J =
($)
has
eigenvalues with only negative real parts over the entire space. A method is presented for finding the largest stable region of attraction of the origin defined by Krasovskii’s function for a system not satisfying the global conditions. Two example problems of the stability of a chemical reactor demonstrate how to determine the maximum stable region and illustrate some of the limitations of Krasovskii’s theorem.
R. H. Luecke and M . L. McGuire, University of Oklahoma, Norman, Okla. IND.END.CHEM.FUNDAMENTALS 6, 432-435 (1967)
COMMUNICATION. UNIQUENESS OF STEADY STATE FOR AN ISOTHERMAL POROUS CATALYST
For certain kinetic rate expressions a nonunique steady-state solution may be obtained for a reaction in an isothermal catalyst particle. This note investigates for what kinds of kinetic expressions this phenomenon is impossible. Sufficient conditions are presented under which a unique steady state can exist for an arbitrary kinetic rate expression.
Dan Luss and N . R. Amundson, University of Minnessta, Minneapolis, Minn.
IND. END.CHEM.FUNDAMENTALS 6, 457-459 (1967) (Continued on page 176) VOL. 5 9
NO. 8
AUGUST 1967
113
I-
J
ale
steel” New “ h configuration gives you all the fullbatch mixing efficiency of the former D-style baffle, while greatly increasing efficiency in partial batches, especially during filling and emptying. The reason is the added ballling surface that the secondary ann of the ‘%” puts down near the impeller. The result is greater flow deflection and turbulence. Excellent control of swirl, vortex and air entrapment. Plus p o w e h l top-to-bottom tumover. This is better mixing-one more reason to specify Pfaudler Glasteel reactors, your proven answer to processes that involve corrosive, ultra-pure, or stic!q materials.
114
INDUSTRIAL A N D ENGINEERING CHEMISTRY . .
baffles
. ..
The new h - b d e plus the agitator and access covers on a Glasteel reactor are made of Pfaudler Nucerite,@a ceramic-metal material that gives you all the corrosion resistance of Glasteel, plus four times its resistance to abrasion, twice its impact strength. The h-style baffle is standard now on all Glasteel reactors from 5 gallons through 4,000 gallons. Its small-radius restricted tip increases the response and accuracy of batch temperature measurements. For complete information on the Nucerite h - b d e , request Data Sheet 88.Write: The Pfaudler Co., Dept.IEC-87, Rochester, N. Y. 14603. Or call (718) 235-1OOO.
Glasteel reactors from
... PFAUDLERb 0N.OF RITTER PFAUDLER CORPORATION
Circle N h 14
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e
RIICR' S i n i c l CIfd VOL 5 9
NO. 8 A U G U S T 1 9 6 7
115
BRIEFS COMMUNICATION. HEAT OF ADSORPTION OF CARBON MONOXIDE O N COPRECIPITATED NICKEL OXIDE-SILICA CATALYST
T h e heat of adsorption of carbon monoxide on lithium-doped nickel oxide-silica coprecipitated catalyst was determined. T h e value obtained was 5.5 kcal. per gram mole, which is slightly higher than the value obtained for adsorption of carbon monoxide on pure silica gel (3.7 kcal. per gram mole). This unexpected similarity is explained by the formation of a silica skin which inhibits adsorption of carbon monoxide on nickel sites.
Sarah Skurnik and Menachem Steinberg, T h e Hebrew University, Jerusalem, Israel
COMMUNICATION. EXPERIMENTAL INVESTIGATION OF THE LAMINAR-TURBULENT TRANSITION FOR NEWTONIAN FLOW IN RECTANGULAR DUCTS
Experimental data obtained in four ducts of differing rectangular cross section provide quantitative verification of previous theoretical predictions of a minimum in the curve of critical Reynolds number as a function of duct aspect ratio. T h e possibility that the minimum was shallower than theoretically predicted as indicated by previous data is clearly refuted. T h e theoretical predictions are thus firmly proved.
R. W . Hanks and D . S. Song, Brigham Young University, Provo, Utah
IND.ENG.CHEM.FUNDAMENTALS 6, 472-473 (1967)
IND.ENG.CHEM.FUNDAMENTALS 6,459-460 (1967) COMMUNICATION.
COMMUNICATION. ESTIMATION OF UNKNOWN CONSTANTS FROM MULTIRESPONSE DATA
T h e analysis of data when only a single response variable is measured has been discussed extensively in the chemical and chemical engineering literature. Frequently in practice, however, data are obtained not on a single response alone but on two or more responses simultaneously. Several different criteria that have been used for fitting such data are discussed, and their limitations are indicated.
W . G. Hunter, University of Wisconsin, Madison, W i s . IND.ENG.CHEM.FUNDAMENTALS 6 , 461-463 (1967)
HEAT STORAGE IN TUNNEL WALLS
T h e heat capacity of the walls of underground personnel shelters enters as a significant factor in the over-all problem of heating and cooling such shelters. T h e rise in temperature of the wall surface with time is calculated for a cylindrical shelter with walls of finite thickness and for a constant heat flux into the wall. The results are presented in dimensionless form and are applied to two specific cases. C. D . Scott, Oak Ridge National Laboratory, Oak Ridge, Tenn J . S. Newman, University of California, Berkeley, Calif.
IND.ENG.CHEM.FUNDAMENTALS 6, 473-474 (1967)
CORRESPONDENCE
Comments on a published article on determination of best-fit rate constants in chemical kinetics and a reply.
John D . Wright, Pace Co., Houston, Tex. William E. Ball, Wasliington University, St. Louis, M o . IND.EKG.CHEM.FUXDAMENTALS 6,475-476 (1967) COMMUNICATION. DISPERSION OF MATTER IN NONNEWTONIAN FLOW AT LOW FLOW RATES
This paper gives an expression for the Taylor diffusion coefficient representing longitudinal dispersion accompanying laminar flow in a tube, for a non-Newtonian fluid which obeys the Casson shear stress-shear rate relationship. The virtual diffusion coefficient depends on the ratio of the fluid’s yield stress to the wall stress and reaches a maximum value a t a certain value of the ratio. A comparison of the results for various non-Newtonian fluid models is also given.
CORRESPONDENCE
Comments on a published article on velocity profile in the Stefan diffusion tube and two rebuttals.
Stephen Whitaker, University of California, Davis, Calif. S. S. Rao and C. 0. Bennett, University of Connecticut, Storrs, Conn. D . T. Wasan, Illinois Institute of Technology, Chicago, Ill.
IND. ENG.CHEM.FUNDAMENTALS 6,476-477 (1967) CORRESPONDENCE
M . E. Erdogan, Technical University of Istanbul, Istanbul, Turkey
Comments on a published article on effectiveness factors for porous catalysts.
IND. ENG.CHEM.FUNDAMENTALS 6, 463-469 (1967)
Warren E. Stewart, University o j Wisconsin, Madison, W i s .
IND.ENG.CHEM.FUNDAMENTALS 6, 478 (1967) CORRESPONDENCE
COMMUNICATION. TURBULENT HEAT TRANSFER I N VISCOELASTIC LIQUIDS
Experimental results of heat transfer for turbulent flow of viscoelastic liquids in tubes are compared with momentum transfer results under the same conditions. A marked decrease of the heat transfer efficiency is observed with respect to the Newtonian case, even larger than the corresponding drag reduction phenomenon.
Comments on a published note on hydrodynamic stability of a fluidized bed.
T. B. Anderson and R. Jackson, University of Edinburgh, Edinburgh, Scotland IND.ENG.CHEM.FUNDAMENTALS 6, 478 (1967) CORRESPONDENCE
Comments on a published article on heat transfer in liquid-film flow and a reply.
Giusefipe Marrucci and Gianni Astarita, University of Nafiles, Naples, Italy
%jam 0. Wallgren, AB Rosenblads Patenter, Stockholm, Sweden R. W . F. Tail, University of Adelaide, Adelaide, South Australia
IND.ENG. CHEM.FUNDAMENTALS 6, 470-471 (1967)
IND.ENC. CHEM.FUNDAMENTALS 6, 479-480 (1967)
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INDUSTRIAL A N D ENGINEERING CHEMISTRY
