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similar e uipment in which the equilibrium conditions between liquid an% vapor may be assumed to follow the relationships of ideal solutions. (2) That the over-all plate efficiency of natural gasoline stabilizers, at least of this type of construction and operating at a pressure of about 300 pounds per square inch absolute, is approximately 100 per cent.
comes the feed to the rectifying section and liquid overflowing becomes the feed to the stripping section
1, 2, 3, etc., = first, second, third, etc., plate of the column,
numbered from top downward K = equilibrium constant for a particular component (6) A = L / K V = absorption factor for a particular component S = K F / E = stripping factor for a particular component
Nomenclature F = moles of feed to column; used as subscript to signify feed B = moles of bottom product; used as subscript to signify
bottom product D = moles of distillate withdrawn as overhead product; used as subscript to signify overhead product V = moles of vapor rising from plate in rectifying section; used as subscript to signify vapor phase L = moles of liquid overflowing from plate in rectifying section; used as subscript to signify liquid phase = moles of vapor rising from plate in stripping section L = moles of liquid overflowing from plate in stripping section a, b, c, d, etc. = moles of individual components of which a is the most volatile; used as subscript to refer to individual com onents z = mole fraction any component in liquid y = mole fraction of any component in vapor n = number of theoretical plates above feed late; used as subscript to refer to any plate in rectiging section m = number of theoretical plates below feed plate; used as subscript to refer to any plate in stripping section f = feed plate-i. e., plate from which the vapor rising be-
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Acknowledgment The plant data used in this paper were kindly furnished by the Development Department of the Union Oil Company, Calif., through E. G. Ragata. Without these data complete demonstration of the application of the absorption factor method to commercial plant practice would have been impossible.
Literature Cited (1) Brown, Souders, and Nyland, IND.ENQ.CHEW,24, 522 (1932). (2) Katz and Brown, Ibid., 25, 1373 (1933). (3) Kremser, Natl. Petroleum News, 43 (May 21, 1930). (4) Lewis and Matheson, IXD. ENQ.CHEM.,24, 494 (1932). (5) Souders and Brown, Ibid., 24, 519 (1932). (6) Souders. Selheimer, and Brown, Ibid., 24, 517 (1932). (7) Underwood, A. J. V., Trans. Inst. Chem. Engrs. (London), 10 112 (1932).
RECEIVED January 28, 1935.
Application of Graphical Method of Ponchon to Distillation and Extraction E. W. THIELE Standard Oil Company (Ind.), Whiting, Ind.
QM
OST graphical methods for the computation of columns in the case of binary mix-
tures are based on the assumption that the overflow from plate to plate in each section of the column, (measured in appropriate units) is substantially constant, and it becomes quite inconvenient to apply when this condition is not fulfilled. Ordinarily the fact that there is a temperature gradient throughout the column produces some variation in the overflow, which may become large if the temperature differences are large. Any heat effects on mixing the pure liquid will also result in irregularities. Ponchon (7) presented some years ago a method which, while not so convenient where constant overflow can be assumed, takes account of any changes in the overflow. None of the descriptions of the method is conveniently located for American readers, and it will be desirable to present such a description before pointing out certain cases to which it is particularly applicable and showing how it can be extended to the analogous operation of extraction.
Description of Method The method requires a knowledge of how the total heat (enthalpy) of the saturated liquids and vapors varies with composition (at the pressure at which the column is to be operated). This is not a limitation of the method, since this information is necessary in a n y case if the overflow ratio is
The graphical method for the analysis of distillation columns devised by Ponchon is presented. In this method there is no assumption as to constancy of overflow from plate to plate. I t is therefore applicable where usual methods fail, as in distillations in the critical region. There is a close analogy between distillation and countercurrent liquid extraction, and by a suitable modification the method is applied to this operation. The usual operation of this type is conducted in the equivalent of the critical region with no rectifying section. The advantages of the use of a rectifying section, and of LL solvent in which neither constituent is completely miscible, are pointed out. to be computed. This information being given, a plot is made of total heat (per mole or other unit of quantity) us. composition (expressed in the same units). The standard state for the computation of the total heat may be arbitrary. The results will generally be similar to that shown in Figure 1, the saturated vapors being represented by one line extending across the diagram, which may be called the “dew line,” the boiling liquids by another line lower down which may be called the “boiling line.” Points representing liquids and vapors which are in equilibrium with each other may be connected by straight lines which are more or less analogous to the tie lines used in phase-rule diagrams. These lines are,
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of course, vertical at the ends of the diagram, which represent pure substances. The space between the lines represents mixtures of liquid and vapor. Above the dew line lie the superheated vapors; below the boiling line, liquids below their boiling points. An essential property of this type of d i a g r a m is that, if two mixtures repre-
i[,
,
,
,
,
I?
% L e s s l/olat/le Component
FIGURE 1. POXCHON TOTAL HEAT-COMPOSITION DIAGRAM
393
means of determining the composition of the vapor rising from a plate when the composition of the liquid descending to the plate is given, or vice versa. The tie lines afford a means (assuming the plates to be 100 per cent efficient) for determining the composition of the liquid on a tray, &-henthe composition of the vapor rising from it is known, or vice versa. Starting for example from A , which represents the vapors rising from the top plate, S, the other end of the tie line through B represents the liquid on the first theoreticallv Derfeci tray (which descends to thk iray below). A straight line through H and S intersects the condensation line at B, the composition of the vapor rising from the second tray. The tie line through B fixes the composition of the liquid on the second tray, represented by point T. By drawing H T , point C is determined, which represents the vapor rising from the third tray, and so on. Hence the whole course of the distillation above the feed can be followed. I n a similar way, we may draw sections through the column below the feed plate. Past each of these sections the same net bottoms product and the same net total heat are passing. Hence we can say that a t any section, if the bottoms product obtained in a given time (imagined as cooled to a certain temperature), were added to the vapors rising through the section in the same time, the result would be
sented by two different points on the diagram are blended, the point representing the composition and total heat of the resulting blend will lie on the straight line connecting ,erhead Cbmpositlon the points. Now consider a s e c t i o n d r a w n t h r o u g h a c o n t i n u o u s rectifying column, operating on a binary mixt u r e , j u s t a b o v e the top plate. Vapors leave past this section, and reflux in suine form returns to the column past the section Because of the constancy of operation it follows i that the amount of net product in P 9 unit time, added to the amount of iJ FIGURE 2. PONCHON'S METHOD reflux in that time, will exactly reproa $ duce the vapors, in quantity and composition. At the same time there will be a difference in the exactly equal t o the total heat of the liquid and vapor, which represents the net l i q u i d p a s s i n g down amount of heat leaving the section. If, therefore, we could through the section, not ff take a quantity of the net product equal to that produced per only in q u a n t i t y and L ' " ' " " ' M o l e % Heptane unit time and heat i t so that its total heat equals the net heat composition but also in leaving the column, and add this to the corresponding amount total heat. Except for FIGURE 3. PENTANE-HEPTANE SYSTEM AT 30 ATMOSPHERES of reflux, the vapors would be exactly reproduced as to quanthe effect of heat losses tity, composition, and heat content. There is therefore from the column sides, (Figure 2 ) a point, N,lying in a straight line n-ith A and R the temperature to which the bottoms would have to be cooled which stand for the vapors and reflux, respectively, that reprewould be the same at all points. Hence there is a single point, sents this imaginary heated product. The abscissa of this K , on the diagram, which represents this imaginary cooled point is fixed by the composition of the product; the ordinate bottom product; i t lies in the same straight line as the points by the amount and temperature of the reflux. representing the vapors rising from and the liquid descending If a section is next drawn below the top plate, it is equally to any tray below the feed. The abscissa of this point is fixed true there that the addition of the product to the liquid reflux by the composition of the bottom product, the ordinate by will reproduce the vapors both in quantity and $composition. the heat added to the still per unit of bottoms. Likewise, since there is no heat accumulation betv een the I n Figure 2 , since the bottom product normally has the two sections (the heat loss from the column walls is assumed same composition as the still contents, point 2 may represent to be negligible), the net total heat passing the section below the latter. Tie line %iV gives the composition of the next the tray will be the same as the net total heat passing the vapor, line MK is then drawn to find X, which represents the section above the tray. Hence the point H will also lie in a next liquid, and so on. Thus the behavior of the whole straight line with B and S, which represent, respectively, the column can be computed. vapor rising from the second tray and the liquid descending to It can be shown that F , which represents the composition the second tray. Similar remarks apply to all the other trays and total heat of the feed, lies on the straight line joining H in the rectifying section. and K (neglecting heat loss from the column). An azeoPoint H , therefore, the position of which is fixed by the tropic mixture is represented by a vertical tie line. Minicomposition of the overhead product and the amount of heat mum reflux is fixed by the intersection of the tie line (protaken out of the top of the column (or reflux ratio), affords a longed) with vertical lines representing product composition.
f
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If the reflux is infinite, the lines corresponding to H T , MK, etc., are vertical. It is evident that this diagram makes possible the graphical design of columns for binary mixtures without any restriction Toluene
FIGURE 4. THE SYSTEMWATER-ACETIC ACIDTOLUENE as to constancy of reflux ratio. That restriction amounts to assuming that the dew line and boiling line as here presented are straight and parallel, which is practically never exactly the case, although ordinarily it is a satisfactory approximation if moles or latent heat units are used. The Ponchon diagram does not require the use of any special unit; weight percentages and total heats per unit weight may be used. It may also be noted that, by the use of a solid diagram, problems for ternary mixtures may be handled. This was shown by Savarit (9); probably the practical value of this fact is not great.
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Analogy between Extraction and Distillation Saal and van Dijck (8) have already pointed out an analogy between the separation of two components of a mixed liquid by extraction with another liquid and a separation by distillation. I n both cases the separation is effected by means of the difference in the proportions of the two components in two phases. In the case of distillation the two phases are formed by heat; in the case of extraction the solvent causes the formation of two phases. It is not, unreasonable therefore that a t least some of the same methods might be applied, and this has been found to be the case. In principle, any graphical m e t h o d which is useful for distillation could be employed; but in practice the analog of c o n s t a n t over6 flow is usually no an a l l o w a b l e assumption, so that t h e m e t h o d of Ponchon becomes especially suitable.
Application to Ex traction
Figure 4 shows a t y p i c a l triangular diagram b a s e d o n the data of Woodm a n (10) f o r t h e system acetic acidtoluene a t 25' C. Suppose acetic acid is to be separated from water by exApplication in Critical Region traction with toluene; an extraction Diagrams of this type are especially useful in understanding of t h i s k i n d (but what takes place when rectification in the critical region is using petroleum attempted. Cummings and others (3, 4 ) have pointed out cuts) is a c t u a l l y some of the phenomena and have given data for the pentaneFIGURE5. PONCIION DIAGRAM FOR EXTRACTION OF AQUEOUS ACETIC made in the celluheptane system, but some of the relationships have apparently ACIDWITH TOLUENE lose a c e t a t e innot been pointed out. Figure 3 shows the type of diagram d u s t r y according that will be obtained with the pentane-heptane system a t 30 to Clotsworthy (1). The calculations would be as follow; atmospheres. Although quantitative data on the total heat A plot is made in which abscissas represent the fraction relationships are lacking so that actual calculation is not pos(weight acetic acid) divided by (weight acetic acid plus sible, the fact that the latent heat becomes zero a t the critical water) in any mixture, the ordinates representing (weight point helps to fix the approximate shape. The boiling and toluene) divided by (weight acetic acid plus ,water) in the dew lines become continuous a t the critical point. Though same mixture. The resulting diagram is Flgure 5. Any the liquid and vapor phases become identical in compositon, possible mixture will be represented by a point, and the this is plainly a very different case from that of the ordinary point representing a blend always lies on a straight line conazeotropic mixture. Because the latent heat becomes so necting the components. The tie lines connect mixtures small, the reflux ratio can become very great, and separation, which are in equilibrium. The so far as it is possible a t all, can d i a g r a m r e s e m b l e s Figure 3 be achieved with a m o d e r a t e closely. heat i n p u t . It may also be Figure 6 shows diagrammatiseen that a section of column cally a t w o - s t a g e continuous below the feed would be of little countercurrent extraction using use in this case, and that nearly pure toluene. It is evident that, everything that can be done is when a steady state has been done with the rectifying secreached, thenet flow past each of tion only. the dotted sections is the same The curves m a y of c o u r s e and consists of a flow of extracted assume other forms in the critiwater with residual acetic acid cal region, b u t t h e general and some toluene in one direcprinciples which have been given FIGURE 6. TWOSTAGE COUNTERCURRENT tion, and a flow of toluene with EXTRACTION will apply.
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acetic acid and some water in the other direction. We may look upon this net flow as consisting of a single (imaginary) mixture, flowing in the direction of the water and having a negative toluene content. It will be represented by point K So/m n t
Compone,iC A
CompMent 8
FIGURE 7. PHASE-RULE DIAGRAM Neither component to be separated is oompletely miscible with solvent.
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obviously lrnmaterial to the argument. The “reflux” can be formed in several ways. Part of the solvent may be removed from the product layer, say by distillation, and the remainder separated into two layers, one of which is returned to the system; this is analogous to the partial condenser. Or the whole of the solvent may be removed and part of the product returned; this is analogous to pump-back. Or the product layer may be caused to separate into two layers by appropriate heating or cooling; for this there is no exact analog in distillation, although compression of the overhead vapors approximates it. The method of extraction which has just been discussed using a single solvent and a “rectifying section” has apparently not been employed. Similar results can be obtained by the use of two immiscible solvents. This method has actually been employed (2), although in practice the necessity for separating two solvents from the products and from each other adds considerably t o the difficulty of the operation, Graphical analysis of this more complicated case will require, in general, a solid diagram unless, as may happen with small concentrations of the materials to be separated as compared with the solvents, the former can be treated separately.
.4dvantages of an Immiscible Solvent
The use of a “rectifying” section is not absolutely restricted in Figure 5, and a straight line through the points representing to cases where both constituents are partly miscible with the the two liquids passing any of the sections will pass through solvent, but i t is most likely to be found useful in this case, this point K , which must lie vertically below the pbint reprewhich should be realized when the two constituents are rather senting the composition of the extracted product. alike. It would therefore be most suitable for difficult sepaIt is plain that, given the degree to which the water is t o be rations-for example, in separating pure compounds from exhausted of acetic acid and the ratio of fresh toluene to expetroleum. Ordinarily in searching for a selective solvent, hausted water, point K can be fixed. A line through K and one is sought in which the constituents to be separated are as F (which represents the feed) will intersect the curve at differently soluble as possible; but the present discussion point H representing the composition of the extract layer as which is essentially that of Saal and van Dijck (8) indicates it leaves the system. Assuming that equilibrium is attained, that for the most perfect separation a solvent can be too the tie line will give point S, representing the composition of selective. the aqueous layer passing to the next stage. The straight While the use of separate stages of mixing and settling line through S and K will intersect the curve a t point B , which represents the composition of the toluene layer traveling (corresponding to bubble plates) has been discussed here, it is obvious that continuous contacting devices, exactly analogous the other direction, and so on, exactly as in the rase of distillation, eachstage correspondingto a plate. Two papers (6, 8 ) have presented a method for making this type of calculation which is essentially identical wi& the adaptation of Ponchort’s Fresh Solvent c method, but which makes use of the ordinary triangular diagram. I n practice, sometimes one method and sometimes the other will be found most convenient, but the location of points such as K will be found somewhat harder to comprehend in the arrangement using the triangular diagram. I n the toluene-acetic acid-water case the distillation analogy would be a stripping column only, and a rectification section would be of Product little use. It is not possible to prepare pure FIGURE8. COUNTERCURRENT EXTRACTION WITH RECTIFICATION acetic acid with toluene at 25” C. because the two-phase region does not extend to pure toluene-acetic acid to (indeed identical with) the packed tower, are possible. mixtures, and most of the three-component, two-phase sysThe concept of H. E. T. P.(height equivalent to a theoretical tems which have been studied are of this type. However, plate) is the same in each case. suppose a system like the one shown diagrammatically in The case of the separation of three constituent> could be Figure 7 , in which neither constituent of the mixture is comtreated by a solid diagram, exactly as in distillation. pletely miscible with the solvent. When this type of system In the case of extraction, variation in temperature from is converted to Ponchon coordinates by the method described plate to plate introduces a complication (and also an opporabove, it is evident that a diagram exactly like that of Figure 2 tunity for improving results) to which there is no analog in will result, and that, when analogous processes are used, distillation. The means of handling it ha1-e been considered any desired degree of separation can be obtained just as in by Hunter and S a s h distillation. The processes involved are shown in Figure 8; It is plain that there is nothing in the method which rethe number of intermediate stages on each side of the feed is quires the phases to be liquid. In practice, however, solid
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phases, even if they form mixed crystals, cannot be treated by these methods because equilibrium is reached so slowly. Either or both of the constituents to be separated may, however, be solid. The case of liquid and vapor, unless the interchange of material is very small, is usually accompanied by such considerable heat effects that the simple procedure is not satisfactory, and a solid diagram is required. If the quantity 3f one constit
