Distillation Theory and Fundamentals A of the theory and fundamentals of distillation would more COMPLETE REVIEW
than fill the contents of a good-sized textbook. Such a large coverage is required because the topics of importance include such a wide range of fundamental knowledge. To understand the behavior of most distillation columns, a chemical engineer must be familiar with the principles of vapor-liquid equilibrium, of minimum reflux and theoretical tray requirements, of tray efficiency, and of mechanical and hydraulic design of columns. H e should
tance of having sound vapor-liquid equilibrium data. Multicomponent tray-to-tray calculations using computers will point the way to improved tower efficiencies
also be familiar with the unsteady state or transient behavior of columns if he is also concerned with the automatic control of these units. Such a comprehensive review will not be presented here; the treatment will be limited to the theoretical factors of most interest and importance. And, rather than present topics adequately covered in standard textbooks, this review will emphasize the areas where basic concepts have been developed and where knowledge of fundamentals has been widened in recent years.
Advances in the fundamentals of distillation were summarized by the writer in 1955 ( 3 9 ) ; more recent progress has been abstracted by Walsh in the annual unit operations reviews published by this journal (772). Geddes has recently outlined the important developments in distillation as well as the needs for future research in this area (38). The Association of British Chemical Manufacturers and the British Chemical Plant Manufacturers Association have released a joint report outlining the areas of distillation knowledge which require further researchLe., physical data for distillation systems, mass transfer, efficiency of contacting means, and automatic control ( 7 5 ) .
Special Notice This i s the concluding part of the series on theory, design, and application o f process equipment for the chemical industry. The group covers heat exchangers, pumps, and distillation equipment. Reprints of the complete series, 52 pages, may be obtained for $2.00 per copy. Address: Special Issue Sales American Chemical Society 1 1 55 Sixteenth St., N.W. Washington 6, D. C.
Prediction and Correlation of Vapor-liquid Equilibrium Data
Light Hydrocarbons. Much effort has been expended in corrrlation of equilibrium data for light hydrocarbons because of the need for such data in the design of refinery and petrochemical distillation units. Such data, usually expressed as I(-factors, may be computed at low and moderate pressures for each of the components concerned from VOL. 52,
NO. 8
AUGUST 1960
645
4 0
IIJ
z a
E
30
E
a ?I
z 0
t;
20
?
Y
IO 0
0 2 04 06 08 io MOLE FRACTION PROPANE I N LIQUID, METHANE-FREE BASIS
Figure 1. Mixture composition, a t moderate and high pressures, becomes an important variable affecting Kfactors for methane Experimental d a t a o f Rigas and others ( 9 5 ) for methane-propane-n-butane system a t 100' F.
knowledge of the vapor pressure and pressure - volume temperature relationships of each pure substance; the volumetric data may be experimental, or generalized charts may be used, such as the fugacity charts of Ehrett, Weber, and Hoffman ( 3 0 ) based upon recent compressibility factor correlations (67). However, a t moderate and high pressures, the mixture composition becomes a n important variable affecting the magnitude of the individual K-factors. This may be illustrated by the experimental data of Rigas, Mason, and Thodos (95) for the methane-propanen-butane system. Figure 1 shows experimental K-factors for methane at 100' F. as a function of system pressure and as a function of the relative amounts of propane and n-butane present in the liquid. The lines would be horizontal if the mixture composition were unimportant; the lines have the greatest slope as the critical region is approached. One widely used method for characterizing the effect of mixture composition is by means of its "convergence pressure," defined as the pressure at which, for a given mixture and temperature, the K-factors for all components converge to unity. Recent advances in the prediction and use of convergence pressure for light hydrocarbon mixtures are discussed in later paragraphs of this article. The ATatural Gasoline Association of America K-factor Committee has suggested that the mixture effect cannot be ignored if the operating pressure is more than 407, of the convergence pressure. A second method for characterizing the effect of mixture composition upon K-factors is by application of the Benedict equation of state (7, 8 ) . The equation was originally developed to represent volume temperature repressure
-
-
646
-
lationships for pure components as a function of eight empirical constants; after the constants have been determined from experimental data for the substance of interest, the equation has the ability to correlate with exceptional accuracy the volumetric behavior of both the gas and liquid phases up to the critical point. Values of the eight constants for each of the common light hydrocarbons applicable for pressures u p to about 4000 p s i have been given by Benedict ( 7 ) : and Sage and coworkers have more recently given values for these same constants which are applicable for volumetric prediction at pressures up to 10,000 p d . (82-84, 706). Benedict also proposed a method for combining the constants of various substances to arrive at a set of eight constants which, when substituted into the basic equation, correlate the volumetric behavior of the mixture. Such information, when used in the appropriate thermodynamic relations, is then sufficient to predict K-factors for each substance in the mixture. Unfortunately, the calculation procedure is unusually tedious, and Benedict, Webb, Rubin, and Friend abandoned the exact procedure and introduced the molal average normal boiling point of each phase as the composition variable ( 9 ) . This resulted in a series of about 300 graphs known as Kellogg or Polyco charts for predicting the K-factors for 12 light hydrocarbons at pressures up to 3600 p.s.i. and temperatures as low as -100' F. DePriester (26) then found a way of linearizing the relations between the two fugacity functions and pressure, and was able to consolidate-with but little loss of accuracy-the same information into 24 charts. Edmister and Ruby (28) also developed a procedure for consolidating the Kellogg charts. These authors showed that the correlated activity coefficient functions for the gas and the liquid phases of all components were each a unique function of the reduced temperature, the reduced pressure, and a phase composition parameter, taken as the ratio of the phase molal average normal boiling point to the component normal boiling point. The DePriester charts, the Edmister and Ruby charts, and the Lenoir and White convergence pressure charts (discussed later) are some of the most convenient correlations available today suitable for predicting light hydrocarbon behavior at elevated pressures. Gordon, Goodwill, and Paylor (48)determined the empirical constants in a regression equation suitable for representing the Edmister and Ruby charts; this permits K-factors to be calculated by a digital computer directly, a n essential part of any digital program for making tray-to-tray calculations. Hope still remains: however, that with the widespread availability of
INDUSTRIAL A N D ENGINEERING CHEMISTRY
computers the original form of the Benedict equation might find practical usefulness for predicting phase behavior of light hydrocarbons. Proper use of the original equation would not only provide greater accuracy in correlating phase behavior, but would also permit partial volumes and partial enthalpies of components in a complex mixture to be computed with accuracy (727, 723). The applicability of the original form of the Benedict equation for prediction of K-factors for light hydrocarbon mixtures has recently been investigated by Price, Leland, and Kobayashi (90). Deviations were computed between predicted K-factors and those determined experimentally by the same authors for the methane-ethane-propane system at F. and temperatures down to -200' pressures up to the critical. The deviations averaged 4.07, for the methane K-factors, 6.77, for the ethane Kfactors, and 13.5Yo for the propane Kfactors. The experimental data were also correlated in terms of DePriestertype charts, and it is recommended that these be used instead of DePriester's original charts in the low temperature region. Although Price, Leland, and Kobayashi found substantial deviations between their experimental K-factors and those predicted by the Benedict equation, this is no indication that the Benedict equation is unsound for characterizing thermodynamic behavior of mixtures : I t merely indicates that the simple rules given by Benedict for combining the pure component constants into mixture constants need to be reconsidered. This is illustrated by the work of Pings and Sage (87),who fit their experimental data for the methane-n-pentane system with the original Benedict equation at pressures up to 5000 p.s.i. and in the temperature range 100' to 460' F. Although the average relative error in volume at 50 mole 7 0 methane composition was 0.03 when Benedict's squareroot rule for obtaining mixture constants was used, the same error was only 0.003 w-hen interaction constants for the Benedict equation ~ c r obtained e empirically from the data. However, it was also shown that the error could be reduced almost to the same extent by experimental evaluation of only one of the eight constants, the second virial coefficient Bo. This same conclusion was noted by Hsieh and Zimmerman (53), who found that the accuracy of representing experimental compressibility factor data for various natural gas mixtures could be increased markedly if Bo were expressed by their recommended function of composition. Although this approach to better correlation of vapor-liquid data is promising, much additional work will be required before generalized relationships can be made available for interaction constants for the Benedict
DISTILLATION EQUIPMENT equation as a function of the nature of the components. The usefulness of convergence pressures as a means of characterizing the effect of mixture composition upon Kfactors has been previously mentioned. The standard methods for predicting convergence pressure are based upon experimental data from various binary systems; convergence pressures for multicomponent systems are obtained by treating the mixture as a fictitious binary (50, 64, 78, 707, 778). A computer program for computing convergence pressure by the Hadden method has recently been described (85). Lenoir and White have recently refined the procedures for predicting convergence pressure (65). They provide more definite rules for computing the effective boiling points of the two pseudo-components of the fictitious binary mixture, including procedures for handling mixtures containing aromatics, naphthenes, acetylenes, and nonhydrocarbons (such as hydrogen sulfide) ; they also recommend a method for handling mixtures containing only small amounts of the heaviest or lightest components. Once the effective boiling points of the two pseudo-components are computed, they are used to find the convergence pressure from correlation charts given in the article. Without doubt, the improved methods of Lenoir and White for predicting convergence pressure will greatly assist in improving the design of many types of distillation columns. Once the convergence pressure of a multicomponent mixture is known, various empirical rules are followed to extend the low-pressure, noncompositiondependent K-factors out into the high pressure region to the convergence pressure where the K-factors for all components become unity (50). An alternate to this procedure is to use the Lenoir and White K-factor charts (64) or nomograph (77) which give the Kfactors for any component as a function of pressure, convergence pressure, and the K-factor at 10 p.s.i.a. All prior discussion of equilibrium behavior has been limited to paraffin and olefin light hydrocarbons, and when naphthenes and aromatics are introduced, additional nonidealities become evident owing to differences in the chemical types present. Such differences are characterized by the magnitude of the liquid phase activity coefficients for each of the components; if the activity coefficients are unity, the mixtures have no nonideality owing to differences in chemical type. Extensive work by Myers (76) has shown that terminal activity coefficients for paraffin-aromatic systems range from about 1.3 to 1.8, while for naphthene-aromatic systems, they vary
from about 1.2 to 1.4. Narrow-boiling naphthene-paraffin mixtures were shown to be essentially ideal, but for wideboiling mixtures of this type, terminal activity coefficients can exceed 1.I. Black (77), utilizing the data of Sage and Lacey for the system l-butenen-butane (702), found this system to be slightly nonideal ; the terminal activity coefficients ranged from 1.01 to 1.03. The method of Lenoir and White for predicting K-factors cannot be applied directly to naphthenes for aromatics, although if these substances (or others) are present in a predominantly paraffin-olefin mixture, their effect upon the convergence pressure of the mixture can be computed (65). Lenoir has recently developed an empirical correlation of convergence pressure for closeboiling nonideal systems (62) ; but as this correlation is based upon experimental data for only 11 binary systems involving 10 different substances, its applicability should be further tested before being widely used. The critical behavior of two paraffinammonia binary systems has recently been determined by Kay and associates (58); as both systems form azeotropes, the critical locus lines exhibit unusual behavior. Many data have been accumulating in the past several years for hydrogenlight hydrocarbon system. Sources of data for binary, ternary, and one complex system are conveniently summarized by Benham, Katz, and Williams (70); an additional reference for the hydrogenn-hexane system is (79). Cosway and Katz have recently presented data for ternary and quaternary systems containing hydrogen, nitrogen, methane, and ethane (25). Correlation of these various data has presented quite a challenge because K-factors for hydrogen, unlike those for light hydrocarbons, increase with decreasing temperature at any given pressure. Benham, Katz, and Williams (70) attempted a number of generalized correlations in which the molal average boiling points of the vapor and liquid phases were used as correlating parameters; the mole fraction of hydrogen in the vapor phase was also used. The correlations were shown to be satisfactory for binary and certain ternary systems, but are not reliable for complex mixtures. Lenoir and Hipkin (63) have offered an explanation for the behavior of hydrogen-light hydrocarbon mixtures. They contend that because hydrogen is usually present at temperatures well above its critical temperature, K-factors for hydrogen are independent of temperature: the increase in K-factors for hydrogen with decreasing temperature is said to be caused not by a temperature effect, but by an increase in con-
vergence pressure. To show this quantitatively, it was necessary to have values of convergence pressure for the mixtures of interest. As these values are often as high as 70,000 p.s.i., and experimental values never exceeded 10,000 p.s.i., it was necessary to estimate many of the values by extrapolation of existing data. The resulting values permitted a correlation to be made of convergence pressure as a function of temperature and effective boiling point of the nonhydrogen components of the mixture. It was then possible to show that hydrogen K-factors for all mixtures, all temperatures, and all pressures could be expressed on one generalized plot as a function of only two variables-pressure and convergence pressure. The average deviation between predicted and experimental values was 11.3% for 375 comparisons made with hydrogenparaffin, hydrogen-olefin, and hydrogenparaffin-olefin mixtures. Nonideal Binary Mixtures. Unless the components to be separated are members of the same homologous series, they are likely to have deviations from ideality in the liquid phase even at low pressures. The extent of deviations from ideality is shown by the extent to which the liquidphase activity coefficients (y-values) differ from unity. If the y-values are no greater than about 8, the system is not likely to show any immiscibility; if the y-values are over 20. the maximum solubility of one component in the otherexpressed in mole fraction units-is approximately equal to l / y . Thus for highly immiscible systems, the y-values are extremely large. If y-values-plus vapor pressures and compressibility factors-are known for a given system, its vapor-liquid equilibrium behavior can be readily predicted ; unfortunately, y-values for any component vary widely depending upon the chemical nature of the other substance present in the mixture, and no comprehensive correlation exists to express this behavior. Methods are available, however, for extending a limited amount of solubility data, absorption equilibrium data, boiling point data, or azeotropic data into a fairly accurate prediction of vapor-liquid behavior over the entire composition range (22); the same methods also permit vapor-liquid equilibrium data available a t only a given temperature or pressure to be extended to other conditions of temperature and pressure. Because of difficulties in predicting nonideal binary behavior, it is important to the distillation design engineer to have ready access to a comprehensive compilation of existing literature data. One of the best of these is a recent translation of a book by Hala and others entitled “Vapour-Liquid Equilibrium” VOL. 52, NO. 8
AUGUST 1960
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(57). In addition to text material devoted to general thermodynamic principles, properties of solutions, and methods of representing data, a list is given of over 1000 original sources of equilibrium data covering the literature up to February 1957. Other useful sources of vapor-liquid equilibium data are the books by Chu and others (722) and by Timmermans (724). An important attempt to relate activity coefficients as a function of the molecular structure of the binary components has recently been offered by Pierotti, Deal, and Derr ( 8 6 ) . The correlations of these authors are limited to systems containing water, paraffins, or organic compounds containing only one functional group. However, they have been able to express quantitatively the y-behavior as a function of the nature of the functional group, the number of carbon chains in the molecule, and a relatively few interaction constants. This leads to the possibility of using data available for related binary systems to predict the behavior of an unknown binary. Of no small importance is the inclusion in this article of valuable new data for 275 binary systems. Gerster, Gorton, and Eklund have recently reported on the experimental behavior of 33 pentane-solvent and pentene-solvent binary mixtures (40). They found that for solvents which do not form hydrogen bonds, the ratio of the Margules binary constants for the two hydrocarbons at infinite dilution increased in a regular manner as the magnitude of either binary constant increased. Prediction of vapor-liquid behavior for binary systems is sometimes limited when compressibility factors for vapor mixtures are not a simple function of the pure component compressibility factors. This situation is aided by recent work of Prausnitz and Benson (89), and by that of Leland and Mueller (67). Nonideal Multicomponent Mixtures. The prediction of vapor-liquid equilibrium relationships for multicomponent mixtures which are nonideal in the Lquid phase can be accomplished by use of the binary and multicomponent forms of one of the several sets of thermodynamic equations such as the Margules or Van Laar ( 7 7 9 ) or the Redlich and Kister equations (94). The binary forms of these equations contain two or three “binary constants” which, when suitably evaluated from experimental binary data, allow the equations to describe the relationship between the binary liquid-phase activity coefficients and the liquid composition; the binary constants vary somewhat with temperature, so that knowledge of the binary behavior at several temperatures is desirable. Multicomponent liquid-phase activity coefficients may be predicted from the multicomponent equations,
648
which involve as variables the liquid compositions, the various binary constants, and higher order interaction terms. Fortunately, the higher order interaction terms are usually of negligible importance (707) so that multicomponent data can truly be predicted from binary data. Actually, the procedure is not quite as simple as just indicated. The difficulty comes about in choosing an equation form suitable for representing the activity coefficient behavior of all of the possible binary mixtures which comprise the multicomponent mixture of interest. If a moderately complex binary equation form is required to fit an unusually nonideal binary system, then the multicomponent equations become unusually tedious. And, when one of the binary pairs is immiscible, choice of the proper equation form cannot readily be made unless a few ternary data are available. The author’s experience has been that the three-suffix Margules equations as given by \Vohl (779) are suitable for more than half of the situations normally encountered, whereas Wohl’s four-suffix Margules equations are of sufficient complexity that nearly all of the remaining situations can be handled. Recent papers by Black ( 7 7 ) have introduced a modified form of the Van Laar-type equations in which highly associated binary mixtures can be represented with good precision. The binary equations contain three constants instead of the two constants found in the ordinary two-suffix Van Laar equations. The author utilizes a plot of (log yl)o.j us. (log y ~ ) O . 5 to obtain directly the optimum value of the three constants; in some cases where this relationship is linear, one of the three constants becomes zero. The multicomponent form of Black’s equations includes only coefficients derived from binary data. Thus multicomponent predictions can be made only if the binary coefficients are related to each other in a prescribed manner; this restriction is less severe: however, than that of the regular two-suffix Van Laar ternary equations [Equation 47 of reference ( 7 7 9 ) l . Black has shown, however, that a wide variety of multicomponent systems can be predicted from binary data by his equations. He has also sho\vn that his equations have advantages in representing the behavior of systems containing a large number of components when several of these components are of the same chemical type. Distribution of Products in Multicomponent Distillation Columns The availability of automatic computers has changed the habits of the average distillation design engineer. He is now less likely to rely upon short-cut methods
INDUSTRIAL AND ENGINEERING CHEMISTRY
lor determination of products distribution. usually preferring to work out tedious but exact solutions to his problems on a computer. This situation has resulted in an increased number of literature publications along two main lines of endeavor: development of computer solutions for handling existing design procedures and development of new exact procedures previously too complex to b:: practical.
Computer Programs Utilizing Existing Design Methods. Most computer programs of this type use either the Lewis - Matheson method (66),the Thiele-Geddes method (770), or modifications thereof (54, 97). I n most cases, one starts with a specified number of trays, a given reflux, distillate, and feed rate, and a particular feed, and then computes the product distribution. Application of the Lewis-Matheson procedures to this problem requires an assumption for the top and bottoms products distribution, after which stepwise calculations are made from the top and bottom toward the feed tray; the validity of the assumed products distribution is proved when all compositions match a t the feed tray. The only difficulties encountered in this procedure are the development of a foolproof procedure for adjusting the trial values of products distribution so that successive trials converge rapidly upon the true solution and availability of a sound basis for choosing the initial trial values required Bonner has made a number of recommendations in this regard (73, 74). He suggests it should be assumed initially that no light components appear in the bottoms, no heavy components appear in the distillate. and then the resulting zero concentrations be replaced with 10-40 mole per hour; that a linear temperature profile be assumed, with limits taken as values which lie ivell outside the expected temperature range; and that vapor rates be assumed constant regardless of feed condition. The computer then bases its first plateto-plate calculation on these assumptions, and in succeeding trials, each of these three factors is recalculated on the assumption that the other two remain constant. Bonner states that “in spite of the apparent coarseness of the technique, convergence to a solution is cxtremely rapid.” After each trial Bonner adjusts the distillate and bottoms rate of each component by a factor related to the degree of “mismatch” of that component at the feed tray. A computer procedure recommended by Shelton and McIntire (708) is quite similar in its basic methods to that of Bonner. Rose has pointed out that difficulties are sometimes encountered in the computer procedures just discussed in the choice of successive trial values ( 9 9 ) .
D I S T I L L A T I O N EQUIPMENT An intensive study by Lyster and others (69) has resulted in a new recommended computer procedure which converges rapidly upon the true solution. These authors use a Thiele-Geddes procedure to compute trial values of bottoms-todistillate withdrawal rate ratios (b/d values) for each component, and these values are then corrected ’so that the required total distillate rate and all over-all balances are satisfied. The correction is made by use of a multiplier, 6, which is the same for all components, = 6 (b/d)ai,l. by relation (b/d),orreote~ Choice of the proper value of 6 to be employed uses a short computer subroutine in which Newton’s method is applied. Lyster and others also recommend the use of two “forcing procedures” which increase the rate at which the computer converges on the correct answer. T h e first is an improved procedure for adjusting the temperature profile, and the second is to compensate for deviations in calculated values of distillate rate which result in the third trial when enthalpy balances are introduced for the first time. Application of all of these modifications is straightforward, and rapidly converging solutions were obtained by the authors for more than 50 different examples. The extensive experience and good results underlying the Lyster method make it quite attractive for widespread application to most hydrocarbon distillations. Details are available on programming the Lyster method for an IBM 705 computer (68). A multicomponent distillation program designed especially for the IBM 704 computer has recently been described (49). This program employs assumed starting values of appropriate variables a t the top and bottom of the column and performs tray-to-tray calculations to obtain values of all other variables in the column. Discrepancies in material and heat balances at the feed tray are used to supply new estimates of the starting values using an appropriately framed form of Newton’s method. The authors state that at times the Newton method fails to converge, in which case corrections are made to the trial values in a way such that an improvement toward convergence is achieved. The article gives no specific example and only four or five types of problem appear to have been evaluated. However, the solution time for the problems considered on this large computer was apparently 12 minutes or less. Mills (73) described a program for handling u p to 10 components in a mixture where liquid-phase activity coefficients differed considerably from unity. I t was stated that manual intervention may be required to ensure con-
vergence. Rose and coworkers have given the results of their experience in computing tray requirements for a methanol-ethanol-water separation (98). Edmister has suggested that his effective absorption and stripping factor relationships be applied to a digital computer (27). Two recent articles recommended procedures for digital computation of stripper-stabilizers (70) and for plate-toplate calculations (77). O’Brien and Franks demonstrated the feasibility of using an analog computer for making plate-to-plate calculations for a column separating acetylene from ethylene by extractive distillation (80). New Computer Procedures for Multicomponent Design. An interesting new procedure for making exact multicomponent design calculations has been developed by Acrivos and Amundson ( 7 ) and has been adapted for a Remington Rand Univac Model 1103 computer by Amundson, Pontinen, and Tierney (2, 3 ) . These authors express in matrix form the set of heat and mass balance equations which apply to each tray of the column. The equations for the whole column are then solved simultaneously, component by component, based upon an assumed temperature gradient; a matrix inversion technique is used. If the assumed temperature gradient is not correct, the liquid compositions (x) on any tray will not add up to unity, nor will the summation of Kx values for all components on any tray add up to unity (where K is the equilibrium vaporization ratio). I n such a case, the compositions are normalized, and a new set of temperatures is computed such that the summation of Kx values-where the individual x values are the normalized values-for all trays equals unity. Complete solutions are usually obtained in four or five iterations, but of course the techniques for solving a large number of linear simultaneous algebraic equations require the services of a very large, fast computer. A second new design procedure for making multicomponent calculations is the relaxation method suggested by Rose, Sweeny, and Schrodt (99). In this method, calculations are made for the gradual change in all the plate and product compositions which occur in a column from initial start-up until steady state is achieved; batch distillation equations for the case of appreciable liquid holdup on the trays are used. The steady-state results obtained are independent of the starting compositions and holdup quantities used in the calculations, and the method has special value for complicated design problems where multiple columns, nonideal equilibrium behavior, or multiple draw-offs are encountered. The relaxation method does require repeated trials for cases
where the number of trays or feed tray location is unknown ; but each trial does give an exact answer for the chosen conditions. The rate of approach toward steady-state compositions is rapid at first, but extremely slow toward the end; thus a n approximate solution can be obtained quickly, but an exact solution takes longer unless one is willing to calculate only the first portion of the compositiontime curve, and extrapolate this to steady state. Baer, Seader, and Crozier have adapted the Bachelor minimum reflux method (4)to a Datatron 205 computer ( 5 ) . The Bachelor minimum reflux method applies absorption and stripping factor equations to each section of a distillation column operating with infinite trays at the minimum reflux condition. As the calculations are applied successively to the various trays, it is possible to allow for local variations in flow rates and relative volatilities. An iterative procedure is followed to converge upon the true value of minimum reflux.
Tray Efficiency Reports are now available describing the results obtained from a 5-year study of tray efficiencies coordinated by the Research Committee of the American Institute of Chemical Engineers (77, 47, 704, 775). The recommended procedures for prediction of tray efficiencies are based on comprehensive efficiency data which were obtained over a wide range of operating variables, system variables, and tray design variables. I t is impossible to summarize here the large mass of material contained in these reports. However, it should be of interest to compare and interpret recent tray efficiency data from the literature with the recommendations of the A.1.Ch.E. reports. Recent Literature on Tray Efficiency. Manning, Marple, and Hinds (72) have reported on the efficiency and capacity of a 5-foot diameter bubbletray column. The single cross-flow trays contained five rows of 6-inch round caps on 8.5-inch triangular spacing. The outlet weir height was 1 7 / 8 inches and the tray spacing was 24 inches. Values of Murphree efficiency were reported for the iso-octane-toluene system at total reflux, a top tower pressure of 5 p.s.i.g. and throughput rates ranging from 13 to 7470 of flooding. The experimental efficiency results are compared with those predicted by the A.1.Ch.E. procedures in the table. Agreement between predicted and experimental efficiencies is good except for the lowest gas rate condition (Run 2 ) which was 13% of flooding. As the prediction equations are limited to the case of a uniformly bubbling tray, it is VOL. 52,
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AUGUST 1960
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Comparison of Experimental Iso-octane-Toluene Tray Efficiencies in 5-Foot Diameter Column" with Efficiencies Predicted b y A.1.Ch.E. Report* Shows Good Agreement 2
R u n Nuinher 1 3
10
I?xperimental Efficiencies Av. tower pressure, p.s.i.g. Av. tower temperature, "F. Av. liquid composition, mole 7ciso-octane Gas rate expressed as F-factor (it?) Liquid rate, g.p.m./(foot of average column width) Capacity, % of flooding Av. Murphree liquid plate efficiency, E M L ,yo
5.4 237 45 0.344 5.35 13 61
5.4 237 48 0.895 13.9 34 77
5.4 237 48 1.49 23.2 56 82
5.4 237 48 1.97 30.7 74 78
1.89 1.16 41.3 16.3 0.58 66.5
1.70 1.19 14.3 8.96 0.88 65.5
1.50 1.22 7.56 6.66 0.88 65.0
1.34 1.26 5.10
5.52 0.88 65.0
88.6
87.0
86.3
86.3
88.6
86.7
54.0
76.2
87
e5
82
74
Predicted Efficiencies Liquid holdup on tray, inches of tray liquid [Eq. S-2 of
(4z)J
Number of gas-phase transfer units [Eq. S-1 of (4.2) 1 Liquid contact time on tray, sec. [Eq. S-3 of (@)I Number of liquid-phase transfer units [Eq. S-4 of I)@( Slope of equilibrium curve Point efficiency, Yo, [Eq. S-5 of I)@( Murphree efficiency (not including effect of entrainment), E v v , ?& [Eqs. s - 6 , s - 7 , and Fig. 11-2 of (4211 Murphree efficiency (including effect of entrainment), Ewr , % [Figs. 9 and 1 1 and Eq. 24 of (IQ)] Final predicted Murphree liquid plate efficiency, E a r L , % [Eq. S-24 of (43)l a Reference 7 1 Reference 42
likely that for this case poor gas distribution caused the experimental efficiency to be so low. The table also shows that the difference between the efficiency of the entire tray (ETITr) was over 20 efficiency 7 0 greater than the point efficiency. Thus incomplete mixing of the liquid on the tray is seen to have a very important effect upon the magnitude of the efficiency. Manning. Marple. and Hinds (72) found the flooding point of their column to be reached at a n Ffactor of 2.84 when the liquid rate was 30 g.p.m. per foot: the A.1.Ch.E. 2-foot test column flooded at F = 2.7 to 2.8 a t the same condition. Robin has presented performance data for the new Glitsch ballast tray (96). This is a valve-type tray in which cach bubble cap is replaced with a 2-inch outside diameter unit. The unit consists of an opening in the tray floor and a horizontal, weighted disk placed over the opening which is free to rise and fall within an enclosing shroud as the vapor loading changes. Because the slot opening varies automatically to suit the vapor flow and gives nearly a constant slot velocity, the tray operates in a completely stable manner down to 1170 of its normal design loading. According to Robin, this flexibility is about double that of a well-designed, bubble-cap tray; he also emphasizes that for vacuum service this type of tray can show less than 3.0 mm. of mercury pressure drop while still retaining a 1.5-inch liquid seal and good tray efficiency. Figure 2 indicates the efficiency data obtained by Robin for the ballast tray. The data were obtained in a 4-foot tower for the cyclohexane-n-heptane system
650
at 24 p.s.i.a. pressure. The gas rates on this figure, expressed as a n F-factor, have been rccomputed based upon the bubbling area of the tray estimated to be 75Oj, of the total coIumn cross-sectional area. Also shown on the figure are data o l Robin for a bubble-cap tray measured under simiIar conditions. And, data of Fractionation Research, Inc., as reported in reference (46),are also shown on this figure for a bubblecap tray which employed the same system, the same tower diameter, and the same tower pressure. Inspection of the figure shows that the ballast tray may not have an efficiency superiority of more than about 5 efficiency Yo in the normal operating range, while the difference is not much greater at F-factors as low as 1.O. The higher flooding point for the ballast tray-about 1570 greater than the FRI column-is doubtless made possible by the lower gas pressure drops through the trays which in turn cause lower backup of liquid in the downpipes. And, these same factors promote lower froth heights on the tray and thus lower entrainment; this probably explains the source of the efficiency advantage of the ballast tray-indeed, if the F R I efficiency data are corrected to a no-entrainment basis, thcy coincide with the Ballast Tray results. Garner, Ellis, and associates ( 3 7 , 37) have determined air humidification and oxygen desorption efficiencies for the following types of trays: bubble-cap, sieve, grid, and Kaskade. The bubblecap tray tested with the air-water system was contained in a 5-fOOt diameter column, but the maximum gas rate cmployed (F-factor = 1.03) and the
INDUSTRIAL AND ENGINEERING CHEMISTRY
maximum liquid rate employed (7 gallons per minute per foot) were the lowest values studied in the A.1.Ch.E. program (78). At this condition, and for the 3.35 in. outlet weir employed, the experimental gas-phase efficiency from Figure 8 of (37) was 707,, whereas the corresponding value predicted by the A.1.Ch.E. correlation (42) is 737,. T h e sieve, grid, and Kaskade tray tests were carried out in small columns having cross sectional areas of 16 square inches or less, and although the data are valuable? the flow rates employed are too low for the results to have general industrial applicability. Efficiencies for the n-octane-toluene system have been reported for 3- and 6-inch diameter sieve tray columns by Hellums and others (52); these results are also useful as a source of performance data for small columns. Efficiency data for a 1-inch sieve-tray column operated without downcomers has also been recently made available (75)J open areas ranged from 19 to 35%. The effect of liquid viscosity upon gasphase efficiency was determined by Barker and Choudhury (6) in the same 5-foot diameter bubble-tray apparatus used by Garner, Ellis, and Freshwater (37). Measurements were made of the degree of humidification of air contacted in the apparatus with water which contained varying amounts of dissolved sugar. Solutions containing up to 50 wt. 70 sugar were employed; at this latter concentration, the liquid viscosity was 15.5 cp. and the liquid density was 1.23 grams per cc. All data were obtained with an air rate of 2.28 feet per second (F-factor 0.63) and with a liquid rate of 5 g.p.m. per foot. The results showed essentially no change in performance as the liquid viscosity was increased from 1 cp. (no sugar) to =
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os
io
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20
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F- FACTOR
Figure 2. Comparison of tray efficiency for Glitsch ballast tray (96), bubble-cap tray of Robin (96)and Fractionation Research, Inc., bubble-cap tray (46)explains source of efficiency advantage o f ballast tray Cyclohexane-n-heptane 4-foot tower
system a t 24 p.s.i.a. in
4 cp.; a t higher viscosities, the number of gas-phase transfer units was proportional to the liquid viscosity raised to the -0.60 power. This lowering of performance with increasing liquid viscosity is contrary to results determined in the A.1.Ch.E. program for the absorption of pure carbon dioxide in cyclohexanol on a small bubble tray (705). In these latter studies where the liquid viscosity was as high as 135 cp., the change in performance caused by the high viscosity of the liquid could be accounted for through its effect upon the liquid diffusivity. I t appears to this writer that the decrease in efficiency found by Barker and Choudhury is not due to a decrease in interfacial area as claimed by them but rather to one or both of the following factors : (1) plug flow of vapors upward through the liquid was assumed; if an increased liquid viscosity increased the degree of gas mixing in the bubbling mass on the tray, the efficiency would be lowered; and (2) although the equilibrium partial pressure of water vapor over sugar solutions is essentially the same as that over pure liquid water, the mass transfer rate of liquid water molecules through the solution to the interface might not be infinitely fast, as was assumed by Barker. For these reasons, further study of the problem is indicated. An interesting bit of related information obtained by Barker was the observation that entrainment from his sugar solutions was found to be proportional to the liquid viscosity raised to the -0.23 power. Kirschbaum has reported some new efficiency data for the ethyl alcohol-water system a t various gas rates, submergences, and total pressures for both bubble cap and sieve trays (59). Liquid Mixing on Bubble Trays. Equations presented in one of the A.1.Ch.E. tray efficiency reports (42) relate the point efficiency to the efficiency of the entire tray in terms of three variables: the length of liquid path, the average time of contact of the liquid on the tray, and an eddy diffusion coefficient ( D E ) . This latter coefficient varies with the degree of liquid mixing on a tray and was evaluated experimentally in this same report. A correlation was presented which showed that the pertinent variables affecting D E were gas and liquid rates and tray design. As this correlation was limited to bubblecap trays, however, it is of interest to examine some heretofore unpublished data of Robinson (97) for eddy diffusion coefficients on perforated trays. The trays used had s/16-inch diameter holes on 17/az-inch triangular spacing, giving a 10.6% free area. The system was airwater at 25’ C . ; F-factors ranged from 0.95 to 1.91; liquid rates were from 10 to 40 g.p.m. per foot; and outlet weir
heights were 2.5 and 6.0 inches. Experimental values of D E are plotted in Figure 3 as a function of the previous results obtained for 3-inch round bubble caps on 4.5-inch triangular spacing (45). T h e slope of the line is 1.128, indicating that DE values for perforated trays are greater than the corresponding values for 3-inch bubble-cap trays by a factor of 1.27. These new sieve-tray mixing data are usefuk in analyzing the experimental efficiency data of Rush and Stirba (700). These authors distilled methyl isobutyl
the equilibrium c;rve was 200 and the slope of the operating line was 4.94. In a test made where the average liquid seal was 0.95 inch, the liquid rate was 10 g.p.m. per foot, and the F-factor was 1.4, the measured Murphree vapor efficiency, E M V , was 15%. The point efficiency for this case ( E o o ) is predicted by the A.1.Ch.E. method to be 6.9%. Taking D E from Figure 3 as 0.0402 square feet per second, one uses Figure 11-2 of (44) to find the predicted value of EMv/EoG as 2.7. This is a tremendous difference between the point and Murphree efficiency, but as the point efficiency is predicted to be only 6.970, the Murphree efficiency is predicted to be only 2.7 X 6.9 or 18.6yc, a value comparing favorably with the experimental value. Johnson and Marangozis (55) also determined mixing parameters for a perforated plate. They measured the degree of liquid splashing upstream or downstream from a 3 X 3 inch active tray area, and derived equations relating p, their mixing factor due to liquid splashing, to EMv and EOO. Their correlation for p involved not only gas and liquid rates and weir height, but also liquid density and viscosity. I n applying their correlation to the Rush and Stirba MIBK-water example above, p is found to be 0.41 and E M v is predicted to be 3370; if the liquid were totally unmixed, EMVwould have been predicted as 38Yc. Apparently much less mixing is predicted by Johnson and Marangozis’ correlation than is actually present in this particular case where E M , was found to be 15y0. Other information on liquid mixing on bubble trays may be found in the literature (33,47,87). Multicomponent Tray Efficiencies. The A.1.Ch.E. tray efficiency report did not include any experimental data for multicomponent systems, although the correlations were shown to apply to a few industrial columns where more than two components were present. In these cases, however, the components were similar in their physical properties.
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Figure 3. Values for eddy diffusion coefficient ( D E )for sieve trays (97)are greater than the corresponding 3-inch round bubble-cap trays from A.1.Ch.E. tray efficiency research program (45)
This report did indicate that each component in a multicomponent system would likely have a different tray efficiency if each had significantly different diffusional properties. Experimental and theoretical work on this problem is currently in progress a t the University of Delaware, and some other information of this type has recently been made available (34, 7 7 7 ) . Toor and Burchard ( 7 7 7 ) used the simplified concept of gas-phase diffusion through an effective gas film o r barrier gas to develop relationships between binary and ternary efficiencies. They showed that for the methanolisopropanol-water system, the gas-phase ternary efficiency of the isopropanol under some conditions could be markedly different from its gas-phase binary efficiency, whereas the binary and ternary efficiencies of the other two components were essentially the same. The differences in behavior are due to differences in the various binary diffusivities. Although significant contributions to the problem have been made, much more effort is required before generalized conclusions can be formed. Diffusivity Data. Any sound prediction of tray efficiency requires accurate knowledge of the pertinent gas- and liquid-phase diffusivities, although Friend and Adler have pointed out that such accuracy is less important a t low than at high efficiencies (35). Wilke and Lee (774) have evaluated various methods for predicting gasphase diffusivity, and their recommendations are most useful. The method of Slattery and Bird, which appeared subsequently, is also of value (709). Tabulated values of the collision integral as a function of T*, required in the calculaVOL. 52, NO. 8
0
AUGUST 1960
651
tion of gas-phase diffusivity by the Hirschfelder method ( 7 7 4 , have been reduced to equation form by Chen (2.1). The correlation of Chang and \Vilke (23) is simple to use for the prediction of liquid-phase diffusivity ( D L ) , but it is subject to a feiv limitations. Experimental values for the liquid diffusivity of oxygen through aqueous sucrose and glycerol solutions (57) show that DI, values decrease by a factor of 10 when the viscosity increases by a factor of 100 for sucrose solutions or by a factor of 50 in glycerol solutions. O n the other hand, Chang and Wilke’s correlation would predict the diffusivity values to be inversely proportional to viscosity. ’lhe Chang and Wilke correlation is also in error by a factor of 10 when predicting the liquid diffusivity of methane through a 340-molecular weight white oil at 40’ F. where the liquid viscosity is over 100 cp. ( 9 2 ) ; it satisfactorily predicts DL for methane in pentane over the temperature range 40’ to 280’ F. (92). Reamer and Sage have summarized their experimental D L data for methane in various paraffins ranging from propane to a 340-molecular weight oil ( 9 3 ) , but prefer not to suggest any generalized correlation of the results just yet. A comprehensive summary of current knowledge in the area of liquid diffusivity has appeared (56); there is also another extensive bibliography ( 2 0 ) . An important factor requiring much additional study is the effect of composition upon liquid diffusivity for nonideal mixtures; for example, for the methanol-benzene system at 27’ C., values of D L at 0, 50; and 100 mole yo methanol are 3.8, 0.9, and 2.8 sq.cm. per second (27). Entrainment a n d Mechanical Design of Trays. Entrainment is an important factor affecting the maynitude of tray efficiency, yer a need still exism for additional theoretical and experimental research work in this area. T w o correlations of entrainment have recently appeared (29, 32), but they are based upon existing literature data. 9 e w information on entrainment from sieve trays at low tray spacings has just become available (36). Design procedures are well established for the mechanical design of traysthat is, choice of cap and tray layouts so that gas and liquid distributions are uniform, and so that maximum throughput rates and pressure drops can be predicted. Procedures similar to those of Bolles (72) or Munk (74) are usually followed.
Automatic Control of Distillation Columns The design of a distillation column is not complete until procedures for its control have been worked out. Design of an optimum control system requires
652
knowledge of the transient behavior of the distillation column and its auxiliaries-knowledge of its unsteady-state response characzeristics ivhen subjected to changes in feed composition, feed rate, reboiler steam pressure, and the like. Information of this type may be obtaiiicd from experimentation with existing plant units or by simulation of column transient behavior through analog computer studies. IYoods (720) has described the procedures which he followed to obtain proper controller settings for a plant column separating monoethylene glycol from water. A step change in the reflux ratio was imposed upon the plant column, and from the transient response curve obtained, the frequency response of the column was computed; from this information, standard techniques were then available for computation of the closed-loop response as a function of load changes (16, 777). Schechter and Wissler have recently presented a mathematical procedure for computing frequency response from step input response (703); although strictly valid only for linear sy-stems, the techniques apply to many nonlinear systems if the srep change is small in magnitude. Gse of a large analog- computer enabled Lamb and Pigford (60)to predict the frequency response and transient behavior of a 16-tray column; they also summarized mathematical procedures and analog studies previously developed by others for distillation columns. No completely general results were obtained by these authors, indicating the need for many more studies of this type. Williams has attempted to correlate the available theoretical and experimental information on distillation column transient behavior to develop an optimum control scheme for a distillation column ( 7 7 6 ) . For maximum flexibility: he suggests that the control system should maintain constant the overhead composition and the ratio of boil-up rate and feed rate. Sampling of the top plate should give the best control, according to T4illiams, providing, of course; that the sampling device has suitable sensitivity. An excellent description of the control scheme used for three consecutive hydrocarbon columns is given by Wherry and Berger ( 7 73). Infrared analysis was used in the depropanizer and deisobutanizer, and a gas refractometer was used in the debutanizer. Results of the continuous sample analysis effected a change in the set point of the flowrate controller in the reboiler steam line. The sampling dead time was 1 minute, and the process dead time was 3 minutes; the latter was the time elapsed between variation of heat input to the reboiler and arrival of the changed vapor rate at the sample tray (41 trays above). Experimentation with the plant unit
INDUSTRIAL AND ENGINEERINGCHEMISTRY
showed that when a composition step change was made in the set point of the controller, about 25 to 35 minutes was required to nearly complete the step change. Much of this “inertia” in the control system was said to be due to the large and poorlv mixed reflux accumulator; Williams also recommended the use of a small condenser holdup ( 7 76). Pink has suggested that an analog computer be used to control a distillation column (88). The computer would receive information on the feed analysis, feed rate: and column temperatures, and compute top and bottom temperatures necessary to produce spccification products as a function of feed composition. The appropriate control settings to produce these temperatures at the required times would then be calculated and transmitted to the controllers, a procedure which would anticipate a change in product composition before it could occur. Williams, however, states that good column control can he achieved without the complexity and expense of a computer ( 7 16).
Literature Cited (1) Acrivos, A,, Amundson, N. R., IND. ENG.CHEM.47, 1533 (1955). ( 2 ) Amundson, N. R., Pontinen, A. J., Ibid., 50, 730 (1958). (3) Amundson, N. R., Pontinen, .4. J., Tierney, J. W., A.I.Ch.E. Journal 5 , 295 (1959). (4) Bachelor, J. B., Petroleum ReJiner, 36, No. 6, 161 (1957). (5) Baer, R. M.,Seader, J. D., Crozier, K.D.. Chem. Ene. P r o u . 55. No. 12, 88 (1959j. (6) Barker. P. E.. Choudhurv. M. H., Brit. Chek. ~ ~ 4,g348. (195oj.’ (7) Benedict, M., Webb, G. B., Rubin, L. C.,Chem. Eng. Progr. 47, 410, 449 (1951). (8) Benedict, M., Webb, G. B., Rubin, L. C., J. Chem. Phys. 8, 334 (1940); Ibid., 10, 747 (1942). ( 9 ) Benedict, M., Webb, G. B., Rubin, L. C., Friend, L., Chem. Eng. Progr.47, 571, 609 (1951). (10) Benham, A. L., Katz, D. L . , Williams, R. B., A.I.CI1.E. Journal 3, 236 (1957). (11) Black, C.,IND.ENG.CHEW51, 211 (1959); Ihid., 50, 391, 403 (1958). (12) Bolles, W. L., Petrol. Processing,11,No. 2, 64; No, 3, 82; No. 4, 72; and No, 5, 109 (1956). (13) Bonner, J. S.,Cfiem. En,
