WILLIAM L. BOLLES JAMES R. FAIR
ANNUAL REVIEW
Distillation Coverage o f t h e literature published in the period July 1967 t o June 1968 lthough there is not currently a great deal of fundase, there is much of a developmental nature that can be related to distillation. Thus, the distillation literature tends to follow two lines: reports on experimental and theoretical work in cognate areas, and review interpretations which bring these reports into focus for the distillation practitioner. This review attempts to follow the latter line in its coverage of the world’s literature appearing in the general period from July 1967 through June 1968, in sequence with the previous review (78). The emphasis is on the practitioner audience; more fundamental work is covered by past I&EC reviews of Mass Transfer (15), Process Control (175), and Fluid Dynamics (63), and in reviews of these subjects to be published shortly in I&EC, as well as in the review of Mixing (118 and p 24 of the November 1968 issue of I&EC).
A mental work dealing with distillation per
HIGHLIGHTS Large number of general worksbooks and reviews-on distillation Modern concepts of fluid mechanics, statistics, and mathematical modeling applied t o liquid distribution in packed columns and entrainment in plate columns Continued large-scale research on vapor-liquid contacting devices Renewed interest in analytical solutions o f stage separation calculations Rigorous, general models f o r batch distillation Revival of interest in design-oriented studies
General Works
This was a productive year for reviews and books dealing with distillation. The book by Van Winkle (769) presents a comprehensive treatment of all aspects of distillation theory and practice, and includes a great many worked-out examples to aid the student or practitioner. The two-volume set by Jordan (84) includes excellent chapters on vapor-liquid equilibria, pilot plant distillations, and gas absorption in packed and plate columns; it is oriented generally toward industrial needs for chemical process development. The book by Holland (75) is concerned with the analysis and the transient behavior of continuous and batch distillation columns, and presents supporting material for modeling both steady- and unsteady-state cases. Valentin ( I S @ , in his book on absorption in gas-liquid dispersions, reviews methods for integrating basic studies with the empirical demands of commercial equipment. The final book to VOL. 6 0
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mention is a small volume of distillation terms (167) with their equivalents in English, French, Spanish, Russian, Italian, and German; this is a product of the effective Working Party on Distillation, a subgroup of the European Federation of Chemical Engineering. Reviews on distillation were also numerous. Huebner (78) presents his usual annual review, in German, of literature up to mid-1967; as anticipated, his emphasis is on European publications. Holdsworth (74) covers the 1963-1967 literature somewhat lightly, but does include a tabulation of important studies of vapor-liquid equilibria. Three reviews cover the general aspects of scale-up and design of distillation equipment: Rigamonti et al. (138) relate (in Italian) their work to developments during the past decade; Heckmann (72) and Dietz and Kardos (48) discuss (in German) the general development and testing of distillation models; and the present authors (56) give some emphasis to the effective use of large computers in distillation design. Finally, mention should be made of the new journal, Separation Science, which is now in its third year. One’s initial impression was that this journal would publish little or nothing of interest to distillation practitioners ; this has proved not to be the case. Research
I n continuation of the trend, very few university theses on distillation were published during the year. Of 338 titles listed for the United States (36), only 13 dealt with distillation, five of them on column dynamics and control. A similar situation prevails in Japan (87). The situatibn is different in Russia, however; the “Second All-Union Inter-University Conference on Theory and Practice of Rectification” was held in May 1966 ( 7 ) ,and 52 papers were read and discussed. There were four main sections of this Russian conference : statics and thermodynamics of rectification in multicomponent systems ; hydrodynamics and mass transfer ; analysis, scale-up, and construction of equipment; and mathematical modeling, with control and optimization in mind. For each section, a principal review was given, and one review aroused such great interest that “. . . a resolution was passed recognizing that the derivation of reliable methods of scaling-up on the basis of similarity theory and modeling was an important line of investigation in the study of rectification equipment.” In fact, one infers from the literature that commercially oriented distillation research in Europe is quite active. As mentioned in last year’s review, a large test installation a t the Czechoslovak Academy of Science is producing valuable performance data on contacting devices. Another laboratory producing valuable data is that of Badische Anilin und Soda-Fabrik AG in Germany. Progress reports on both the Czech and German activities are given later in this review. I n the United States, Fractionation Research, Inc., continues to handle most of the large-scale research, but the only technical report on the activity was an indirect one covering packing tests (70). 30
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
Physical Properties
Vapor-liquid equilibria. The year marked the appearance of the second edition of “Vapor-Liquid Equilibrium” by Hala et al. (68). This useful book has been revised and expanded to cover developments through mid-1965. Of some interest is the fact that the index to the world’s literature on vapor-liquid equilibria (VLE) now lists 2656 references, an increase of 1424 over the first edition published in 1958. Another important listing of VLE, directed toward cryogenic processing, has been prepared by the Low Temperature Working Party of the Institution of Chemical Engineers (750). The listing includes a reference to a n extensive bibliographb- of low-temperature VLE work published in Russia in 1963 (700). The previously mentioned review by Holdsworth (74) lists a number of VLE references together with the system identification. Many research papers on VLE continue to appear in the Journal of Chemical and Engzneering Data and in the Russian Journal of Applied Chemzstry. Diffusion coefficients. There continues to be much interest in the measurement and prediction of liquidphase diffusion coefficients. I t is beyond the scope of this review to note the many references on this subject, but since there are practical needs for the engineer to estimate diffusion coefficients as a part of the process of predicting mass transfer efficiencies, a few works will be cited. Cullinan, at the State University of New York, continues to be active in his quest for the reliable and general predictive model ; he has developed a predictive theory for dilute diffusion in mixed solvents (42) and has extended it to the concentrated case (41). In an experimental study of gas-liquid diffusion, Davies et al. (44) found that the 38-year old Arnold equation offered the best fit to their (dilute) data. I n a study of selfdiffusion in liquid carbon dioxide and propane, Robinson and Stewart (739) found that their data and those of others could be correlated on a reduced pressure-reduced temperature basis. Pratap (728) has developed a modification of the Eyring equation for liquid diffusion that, it is claimed, is useful for engineering approximations ; a key correlating parameter is related to the heat of vaporization of the solvent and is independent of solute. T h e general problem of accurate prediction of diffusion in concentrated liquid solutions still remains. Surface tension. Because of its likely effect on interfacial area, entrainment, and mass transfer efficiency, surface tension is a property of interest to distillation practitioners. Three articles dealing with surface tension prediction were noted. Schonhorn (752) developed a tentative correlation between liquid viscosity and surface tension, useful if viscosity data are available. Ramakrishna (733) developed further the Eberhart (57) method for predicting surface tension of mixtures. Finally, Rao et al. (735) have developed a simple method, based on structure alone, to predict surface tension of pure liquids at their boiling points; for 100 comparisons with measurements the average error was only 3.5y0. T h e capability of measuring and
predicting surface tension appears to have outdistanced the understanding of just how it affects distillation equipment performance. Stage Calculations
. Continuous distillation. A state-of-the-art review of mathematical modeling of stage calculations for continuous, multicomponent distillation was presented by Kafarov et al. (85). Included are discussions of the problem of inserting mass transfer into the stage calculation model, and the problem of nonequal plate efficiencies among components. A new model for continuous, plate-to-plate calculations was developed by Eckhart and Rose (52). This model differs from others in that it approximates the vapor-liquid equilibrium relationship by a series of tangents to the true VLE curve, of the 6 , rather than the usual expression y = form y = ax Kx. The new model was applied successfully to the solution of a number of cases for which the steady-state component, flow, and temperature distribution throughout the column were already known. Aristovich and Levin (4)described a new algorithm for achieving convergence for multicomponent distillation involving wideboiling and/or nonideal mixtures. For multicomponent calculations at total reflux, the equation of Fenske (57) was modified by Molokanov (712) so as to provide more convenient direct solutions for six different types of problems. The appearance of an article by Apelblat (3) proposing an improved method for calculating stagewise unit operations highlights a new trend toward analytical solutions to the problem of complex stage calculations. The author first solved a Riccati difference equation by special transformation, then used the analytical solution to describe a stagewise separation of a binary mixture. The case treated has curved operating and equilibrium lines. The resulting nonlinear equations characterizing the equilibrium and material balance relations are reduced to a set of linear equations with a tri-diagonal Jacobi matrix. The Apelblat work, following after and built on similar works in recent years, is worthy of reflection. I n the 1930’s there was much interest in analytical solutions of stagewise distillation calculations. The more important accomplishments of that period included development of the absorption factor concept by Kremser (96), the total reflux equation for multicomponent distillation by Fenske (57), and the analytical solution for binary distillation a t finite reflux ratios by Smoker (157). These analytical solutions were, of course, applicable to only certain special cases of the general problem. Further work in this area then died out, presumably because of the advent of the electronic computer which
+
AUTHORS Wzlliam L. Bolles is a Technologist and James R. Fazr is Manager of the Engineering Technology Area, Central Engineering Department, Monsanto Co., St. Louis, M o . 63766. The authors collaborated on last year’s review; Dr. Fair has prepared the review since 1962.
could be programmed to solve complex problems without complete analytical models. However, as internal models for describing the phenomena of phase equilibria, thermodynamics, and mass transfer became more and more complicated, computer machine time for the solution of practical problems became more critical. Hence, there is new interest in replacing the iterations required by existing methods with analytical solutions. This new trend in the 1960’s began with the work of Martin (703), continued with the research of Chen (38), and now results in further developments by Apelblat (3). Although these workers have not yet achieved the analytical solution of the general, nonideal, multicomponent problem, it is still noteworthy that they are making significant progress based on modero mathematical techniques. Batch distillation. An important contribution to the mathematical modeling and numerical integration of multicomponent batch distillation equations was made by Distefano (50). The only assumptions in this model are constant plate liquid holdup, negligible fluid dynamic lags, and the concept of theoretical trays. The algorithm consists of an iterative, plate-to-plate technique, using direct substitution with adaptive acceleration and damping. The plate holdup is expressed in volume, rather than the usual weight or molar units. The author investigated nine different numerical integration techniques, the results of which are reported. The basic model applies to a constant rate of distillate draw over an operational time increment. Programming of special distillate rate and reflux schedules can be handled by simulation of sequential increments, each with a different distillate rate. Barb and Holland (8) derived models for cyclic batch distillation. This study was prompted by the realization that most laboratory distillation columns operate on a cyclic basis because of the difficulty in flow control of small streams. T o study this problem properly the authors developed alternate models for four types of operation : total reflux (no distillate draw) ; stripping (no reflux) ; cyclic operation (alternating between total reflux and stripping) ; and continuous operation (both distillate draw and reflux). These models are for multicomponent distillation, are based on the absorption factor approach, and employ the e method for convergence. The authors include a comparison of model calculations with experimental results from a laboratory column. Also included are an example and discussion of the use of this batch model in optimization design. A study of batch distillation reflux policy was reported by Coward (40). By reflux policy is meant the schedule of reflux ratio us. time (or accumulated quantity of distillate drawoff) at constant boilup. One extreme reflux policy is to maintain, continuously, constant distillate composition by continuously adjusting the reflux ratio. The other extreme policy is to operate at constant reflux ratio, allowing distillate product composition to vary, and stopping the batch when the mixed, accumulated distillate product reaches the desired composition. Then there are, of course, an infinite number of other VOL 6 0
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reflux policies between these two extremes. The new contribution of these authors was to develop a model and algorithm whereby it is possible to find the minimum processing time for a given case and the corresponding optimum reflux policy. Numerical examples indicated that the time saved on a binary batch distillation, by using the optimal reflux policy rather than the constant overhead composition or constant reflux ratio policies, amounted to only a few per cent. Absorption and stripping. Burningham and Otto (26) studied stage calculations for absorbers by computer. Their principal concern was the convergence algorithm used in the computer program. Several different algorithms were studied and compared on the basis of achievement of convergence as well as required computer time. Cases studied included both simple and reboiled absorbers. Packed columns. Two articles appeared on the subject of the relationship between H T U and H E T P in packed columns. This was a popular subject several decades ago, when there was considerable controversy over the application of HETP to packed columns. I t is obvious, of course, that mass transfer in a packed column is a countercurrent, not stagewise, process. Thus, it would appear that packed columns should properly be described mathematically in terms of the number of transfer units and the HTU. Also, mathematical relations between mass transfer and packed height are most conveniently accomplished in terms of the height of a transfer unit. However, the equivalent number of theoretical plates, and the height equivalent to a theoretical plate, HETP, are advantageous for packed columns in some situations. One is absorption involving multicomponent systems, where the rigorous application of the H T U concept has not yet been completely developed. Another is where existing data are available in terms of HETP, not H T U . Thus, it is worthwhile to have a proper understanding of the true relationship between HETP and H T U . The new articles this year on this subject appear to be considerably more rigorous and are expressed in terms of more precise mathematics than those of two decades ago. Arkenbout and Smit (5) began by stating that the physical validity of the concepts of theoretical plate and transfer unit cannot be deduced from their definitions. They also maintained that although these two concepts have been discussed in the literature many times, an acceptable relation between the two has not heretofore been presented. The authors then proceeded to develop the concept of a “column equation” of general applicability, which same equation can be used to derive the relationship of either the theoretical plate or the transfer unit. I n this way, the concepts of H E T P and H T U were related on a rigorous mathematical basis. I t was concluded that the HETP concept can be rigorously applied to packed columns, provided the proper mathematical transformations are made. O n the same subject, Katayama and Yoshida (90) independently derived the relationship between HETP and H T U . They covered the cases where the equilib32
INDUSTRIAL A N D ENGINEERING C H E M I S T R Y
rium line is both straight and curved. One useful result of this study was that if mG/L lies between 0.5 and 2.0, the value of HETP may be estimated by:
1
”1/2
HETP -
-1+ LHOG
‘I
HOL
where : slope of the equilibrium curve molar gas rate molar liquid rate HOG height of an over-all transfer unit based on the gas phase HoL = height of an over-all transfer unit based on the liquid phase Yamada et al. (778) developed a correlation between packed height and reflux ratio for distillation cases. The correlation applies to packed columns much as the classical Gilliland correlation (64) applies to plate columns. Empirical models. A new nomograph for calculating the relationship between reflux ratio and theoretical trays was developed by Mapstone (702). This nomograph, which is based on the original correlation of Gilliland (64), represents only a slight modification of previously published nomographs of the same correlation. m
G L
= = = =
Hydrodynamics
Plate columns. Thomas and Campbell (165), in the introduction to their article on sieve trays (perforated trays with downcomers), present the hydrodynamic problem very clearly : “ I t is becoming increasingly apparent that investigations on distillation columns can yield meaningful results only if three major aspects of design are considered together. These are hydraulics, residence time, and mass transfer studies. The physicochemical nature of the system and the geometry of the apparatus establish the frame of reference for interpretation. “Plate and downcomer hydraulics are relatively incompletely studied and the literature on them is sparse. Difficulty of examination on the large scale is evident, and studies made on small columns are open to serious criticism. “The complexity of hydraulic studies on fluids in an aerated state has resulted in a seniiempirical approach of limited academic interest. Xevertheless, the importance of such studies lies not only in their intrinsic value but in the significance of mass transfer.” The authors present a state-of-the-art review based on the open literature. This is followed by a report on experiments conducted with a “large” (22-in. flow path), multiple-plate sieve tray simulator operating on air and a water-glj-cero1 solution. Measurements w-ere made, with varying vapor and liquid flow rates, of dry-tray pressure drop, total pressure drop, froth height, froth density, and hydraulic gradient. The results of experiments were compared with equations from the literature.
Research into the hydrodynamics of sieve trays was reported by Sterbacek (763). Based on new experimental data, new models for weep point, flood point, clear liquid height, froth height, and pressure drop Were proposed. All of the models are empirical, with independent variables being liquid velocity, vapor velocity, weir height, proportionate open area, and system properties. T h e experimental data were obtained on 2-ft square plates and 2-ft diameter round plates. Systems studied were air-water, air-brine (7y0, 12.570, 25y0), air-0.9 sp gr oil, and combustion gaswater suspension of A1203. Operating pressures (unreported) are presumably atmospheric. Experiments were statistically designed. Froth and foam height studies in a small perforated plate column were reported by Redwine, Flint, and Van Winkle (736). These investigators used 4-in. square and 6-in. round glass columns, and employed a photographic method for evaluating froth height, reproducible to k 0 . 2 5 in. Systems studied included airwater ; air-water, 1-butanol; air-water, 3-heptanol ; acetone-1-butanol ; and methyl ethyl ketone-toluene. Froth heights varied from 1.4 to 2.5 in. Qualitative conclusions were drawn with respect to the relationship among variables. I n a study of sieve-tray weepage, Zenz, Stone, and Crane (779) developed a new correlation for predicting weepage rates for sieve trays operated below normal design vapor and liquid loads. The new correlation is based on experimental data obtained with the air-water system in a single-plate simulator. T h e experiments covered hole diameters of 1/16, 1/8, and 1/4 in., and open areas from 5 to 3oy0. Submergence was varied by changing overflow weir height and liquid circulation rate. For a n investigation of dual flow trays (perforated plates without downconiers), Steiner and Standart (167) reported on pressure drop. Based on new data, a semitheoretical model for the prediction of pressure drop was developed. T h e model was based on about 1000 experimental data points, obtained on 22 different plate geometries, including openings round, square, oval, and rectangular, various sizes, and open areas from 4 to 20y0. T h e column consisted of one plate, 4 in. X 8 in. T h e systems studied all involved air as the gas. T h e liquids were glycerol, kerosine, water, and water plus a wetting agent. I t was gratifying to note considerable hydrodynamic research activity on valve trays, a n important area heretofore largely neglected except by proprietary firms. Hoppe (76) reported on measurement of pressure drop with the air-ammonia-water system in valve-tray columns 24 and 31 in. in diameter. Equations were derived for calculation of pressure drop. Nencetti and coworkers studied valve trays from the standpoint of liquid and froth holdup (7 74) and pressure drop ( 7 76). Models were suggested for correlation and prediction. Nitschke et al. ( 7 77) also derived empirical relationships for pressure drop in valve trays.
Azbel and Narazhenko (6) reported on the development of a new model for estimating the amount of entrainment under intensive bubbling conditions. I t was noted that in the gas many liquid droplets of different sizes move a t various velocities. The authors derived a model based on a n application of probability theory, for entrainment as a function of elevation above the tray, tray spacing, initial drop escape velocity, and dispersion of drop velocities. The parameters for the model were calculated from experimental data on the systems airwater, methane-water, Freon 12-water, and airkerosine. The model was found to fit the data with a deviation of f10%. Packed columns. I n December 1964, the previously mentioned Working Party on Distillation held a discussion meeting on “problems associated with largediameter packed columns.” One conclusion of this meeting was that the loss of efficiency in large-diameter columns is associated with liquid maldistribution in the packed bed (34). This problem was indeed the subject of a large number of studies reported in the past year. I n a series of three papers, Porter and coworkers investigated liquid flow in packed columns. In the first part ( 7 2 4 a theoretical model is presented for the liquid flow pattern in a randomly packed column. The liquid is assumed to run over the packing in the form of rivulets which sometimes merge and coalesce to larger rivulets, and sometimes divide into smaller rivulets. At the column wall, rivulets from the packing are assumed to coalesce with the liquid on the wall, and new rivulets are generated a t a rate proportional to the flow a t the wall. The second part (725) presents new experimental data on the flow of water in columns packed with 1/2-in. ceramic Raschig rings and 1/2-in. ceramic Intalox saddles. The liquid spreads by a probability mechanism, and agreement between experiment and theory depends upon the size of the sampling area used to measure the spread. T h e results are compared with the predictions of the rivulet model of Part I. In Part I11 (727), experimental measurements were presented on the quantity of liquid flowing down the walls of columns packed with 1/2-in. Raschig rings. Column diameters varied between 2 and 12 in. Large wall flows were found; up to 50% of the total liquid fed to the Gin. diameter column appeared on the wall. Another discussion of distribution in packed columns was presented by Jameson (83),who noted that it has long been speculated that maldistribution of liquid has an adverse effect on the performance of packed absorption columns. I t is commonly thought that the ratio of the column diameter to the packing diameter should exceed eight to achieve reasonable distribution, and that redistribution may be necessary if the packed height exceeds 15 ft. Various devices have been tried to minimize the wall effect, including liquid redistributors and < opan, 5,20’(19&7). (112) Molokanov, Y . K., “Calculation of Product Com osition durin Operation of Column under T o t a l Reflux Conditions,” Theor. Pound. Chem. 8ng. (USSR, Engl. trans.), 1, 261 (1967). (113) Murray, R. M . and Wright J. E “Ap roaches t o Trouble-Free Startup (ofDistillation Colukns),” Chem. hng. dogr., 6$ (12), 40 (1967). (114) Nencetti, G. F., et al., “On Behavior of Plate Columns. Role of Geometric Factors and of Operating Conditions on Foam-, Liquid- and Gas-Holdup i n Valve Plates,” Quaderni Zng. Chim. Ztal., 3, 169 (1967). (115) Nencetti, G . F., et al., “On the Determination of Interface Areas i n Bubble C a u Travs.” tbtd.. D 122. (116) Nencetti, G . F., et a[., “On the Operation of Plate Columns. Pressure Drop through Valve Trays,” ibid., p 202. (117) Nitschke, K., et al., “Determination of Pressure Loss of Valve Trays,” Chem. Tech., 20, 23 (1968). (118) Oldshue, J. Y., ‘‘Annual Review-Mixing,” IND.ENC. CHEM.,59, (121, 5 8 (1967). (119) Onda, K., Sada, E., and Takeuchi, H., “Gas Absorption with Chemical Reaction in Packed Columns,” J . Chem. Eng. Japan, 1, 62 (1968). (120) O n d a K Takeuchi H and Okumoto Y . ,,:‘Mass Transfer Coefficients between d a s ahd Liquid $has& in Packed Col;mns, zbtd., p 56. (121) Peacock, , D . G., “Selection of Test Mixtures for Distillation Columns,” Chem. Eng. Sct., 22, 957 (1967). (122) Ponter A. B Davies G. A Beaton W and Ross, T. K., “Wetting of Packings i; Distiiiation: influenze of CoAtact‘kngle,” Trans. Inst. Chem. Engrr. (London), 45, T345 (1967). (123) Popov, V. V., and Po ova L. M . “Design of Tray-Type Mass Transfer 197 (1667). Equipment,” Intern. Chem. &E., (124) Porter, K . E., “ L i uid Flow in Packed Columns. Part I: Rivulet Model,” Trans.Inst. Chem. Eng. &ondon), 46, T69 (1968). (125) Porter, K . E. Barnett V. D and Templeman J. J., “Liquid Flow i n Packed Columns. Part i I : S p r e i d of Ciquid over Randdm Packings,” ibid., p T74. (126) Porter, K. E., Davies, B. J., and Wong, P. F. Y., “Mass Transfer and Bubble Sizes in Cellular Foams and Froths,” ibid., p T265. (127) Porter, K. E., and Templeman, J. J., “Liquid Flow in Packed Columns. Part 111: Wall Flow,” ibid., p T86. (128) Pratap, R . “Equation for Estimating Liquid Diffusivities,” Indian J . Tech. 5 (5), 145 (196j). (129) Rafal, M . D., and Stevens, W. F., “Discrete Dynamic Optimization Applied t o On-Line Optimal Control of Small Distillation Unit,” A.Z.Ch.E. J., 14, 85 (1968). (130) Raichle, L., and Billet R “Efficiency Loading, and Pressure Drop of Thormann Travs.” Chem.-Znd.-T8ch.. 35. 831 d963). (131) Raichle, L‘, and Billet,-R., “Overall Efficiency of Thormann Trays,” Erdoel. Kohie, Erdgan Petrochemie, 17, 715 (1964). (132) Raichle, L., and Billet, R., “Rectification Efficiency of Valve Trays,” Chom.Zne.-Tech.., 37., 669 11965). . , (1337, Ramakrishna, V., and Suri, S. K., “Surface Tension of Liquid Mixtures,” Indian J . Chem., 5 (7), 310 (1967).
5,
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_
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,
I
li,
.
,
I
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i,
(134). Rao, M . V. R., “Estimate Optimum Gas Velocity in Turbogrid Trays,” Brit. Chem. Ena., - 13,. 257 (1968). (135) Rao, M . V. R., Reddy, K . A., a n d Sastri, S. R . S., “New Method t o Find Surface Tension,” Hydrocarbon Process. Petrol. Refmer, 17 ( l ) , 151 (1968). (136) Redwine D. A Flint E. M and Van Winkle M “Froth and Foam Height Studies. &all Pe;forateh P l a i i Distillation Colimg)’ TND. END. CHEM., PnoCESS DES. DEVELOP., 6, 525 (1967). (137) Reiss, L. P., “Cocurrent Gas-Liquid Contacting i n Packed Columns;’ IND. 6,486 (1967). ENO.CHEM.,PROCESS DES.DEVELOP., (138) Rigamonti, R., Fasoli U and Berbotto G., “Gas-Li uid Mass Transfer in Non-Conventional Ap a;atu; and by Norhonventiona? Procedures,” Chim. Ind. (Milan), 50 ( l ) , 7 8 9 6 8 ) . (139) Robinson R . C and Stewart, W. E. “Self-Diffusion in Liquid Carbon 7,90 (1968). Dioxide and Fkopane;” IND.ENG.CHEM.,FUADAM., (140) Rodionov, A. I., and Kashnikov, A. M., “Determining Interface Contact Area by Light Beam Reflection Method,” Khim. Prom., 43, 209 (1967). (141) Rodionov, A,., I., and Radikovskii, V. M “Mass Transfer in Gas Phase on Bubble Trays, Zh. Prikl. Khim., 40, 1491 ( l i k 7 ) . (142) Rodionov, A. I., and Vinter A. A “Investigation of Interfacial Surface Area on Sieve Trays by a Chemicai Meth;d,” Intern. Chem. Eng., 7 , 468 (1967). (143) Rodionov A. I Vinter A. A and Shabdanbekov U “Investigation of Phase Contaci Area?n Separation S i a c e of a Sieve-Plate bollmn,’’ Theor. Found. Chem. Eng. (USSR, English trans.), I, 87 (1967). (144) .Rolf, S., “Distillation-Mechanisms of Foam Stabilization and Antifoaming Action, Chem. Eng. Progr., 63 (91, 41 (1967). (145) Rozen, A. M., Aksel’rod, L. S., and Dil’man, V. V., “Some Scale Problems i n Designing Mass-Transfer Equipment,” Theor. Found. Chem. Eng. (USSR, Engl. trans.), 1, 363 (1967). (146) Rozen, A. M., and Krylov, V. S., “Problems of Scaling-Up Mass Transfer Apparatus,” ibid., p 232. (147) Rubin, E., LaMantia, C. R., and Gaden, E. L., Jr., “Properties of Dynamic Foam Columns,” Chem. Eng. Sci., 22, 1 1 17 (1967). (148) Ruckenstein, E., and Smi elschi, O., “Thermal Theory and Plate Efficiency,” Can. J . Chem. Eng., 45,834 (1967). (149) Rudov, G. Y., and Planovskii, A. N., “Kinetics of Mass Exchange i n Rectification of Binary Dilute Solutions in Sieve-Plate Column,” Theor. Found. Chem. Eng. (USSR, Engl. trans.), 1, 267 (1967). (150) Ruhemann M and Harmens A “Bibliography of Va or Liquid Equilibrium of Low Bbi& Mixtures a n d N&es on K-Value Corre&ns,” Chem. Eng. (London), 213, CE 254 (1967). (15;) Sauter, W: A., and Ward, T. J., “Use of Time Delays in Packed Gas-Absorption Column Simulation,” A.Z.Ch.E. J., 13, 1211 (1967). (152) Schonhorn H. “Surface Tension-Viscosity Relationship for Liquids,” J . Chem. Ene. d a t a -, i2. 524 , (1967). . . (153) Shih F. S. and Lemlich, R . “Study of Interstitial Liquid Flow in Foam. Part 111.’ Tes;ofTheory,” A.I.Ch.E. J., 13,751 (1967). (154) Shmelev, Yu. S., and Shabalin, K . N., “Effect of Geometric Parameters of Ap aratus and of Packing on Mass Transfer and Hydrodynamics i n Packed CoLmns,” Khim. Prom., 42,694 (1966). (155) Shulman, H. L., and Mellish, W. G., “Performance of Packed Columns: Part V I I I . Liquid Flow Patterns and Velocities in Packed Beds,” A.Z.Ch.E. J., 13, 1137 (1967). (156) Skorikov, I. E., Kafarov, V. V., and Boyarinov, A. I., “Use of a Mathematical Model for 0 timizing Control of a Fractionating Column,” Khim. i Tekhnol. Topliu i Masef13, 29 (1968). (157) Smoker, E. H., “Analytic Determination of Plates in Fractionating Columns,” Trans. A.Z.Ch.E. J . , 34, 165 (1938). (158) Solomakha G. P and Prokhorov V. P “Eflect of Directed Flow of Gas into Li uid on’ H driulics and Mass’TransFer during Bubbling,” Chem. Tech. Fuels Oi%, 12 (lo), v31 (1967). (159) Sommerfeld, J. 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