The product composition regions of azeotropic distillation columns. 2

Synthesis of Distillation Processes Using Thermodynamic Models and the Dortmund Data Bank. Jürgen Gmehling and Christian Möllmann. Industrial ...
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Ind. Eng. Chem. Res. 1993,32, 1108-1120

The Product Composition Regions of Azeotropic Distillation Columns. 2. Separability in Two-Feed Columns and Entrainer Selection Oliver M. Wahnschafft'vt and Arthur W. Westerberg Engineering Design Research Center and Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

A method to assess the product composition regions for distillation of ternary mixtures in singlefeed distillation columns, introduced in the first paper of this series, is generalized to account for the effect of introducing multiple feeds of different trays. The method relies on so-called fixed point curves which are trajectories in the compositions space. These trajectories describe the possible compositions of pinch points in each column section as functions of the energy supplied to a column, Le., for all conceivable values of the reflux ratio. Pinch point trajectories may be determined analytically or, for ternary mixtures, can be located graphically using residue curve maps. We carry out a mostly graphical analysis, using pinch point trajectories to establish separation feasibility ahead of design calculations. Our analysis also provides information on the minimum entrainer supply for a specified separation and visualizes the phenomenon of the occurrence of a maximum reflux ratio for separation in a column with a separate, extractive agent feed. The analysis is analogous to that for single-feed columns, only the critical pinch trajectories may be those for the extractive column section between the feeds. This analogy suggests the notion of a generalized extractive distillation process, for which new entrainer selection criteria are proposed.

Introduction The design of distillation systems for the separation of given multicomponent mixtures always requires some knowledge about the feasible splits or, in other words, the theoretically possible product compositions. For ideal mixtures it is sufficient to know the order of normal boiling points or the relative volatilities to determine, at least qualitatively, which splits are feasible. However, for mixtures with nonideal equilibrium behavior, i.e., composition-dependent relative volatilities, a more detailed analysis is required to determine existence and location of distillation boundaries. Because of its significance for synthesis and design of processes to separate azeotropic mixtures, the problem of determining the feasible separations of azeotropic mixtures has received much interest over the past three decades (e.g., see Levy (1985)for more references). Most publications on the subject of distillation boundaries have dealt with single-feed columns. Perhaps the most common approach has been to study the product composition limits of continuous distillation columns in comparison with residue curve and distillation line boundaries. These boundaries are determined for the limiting operating condition of totalreflux (e.g., Vogelpohl, 1964;Van Dongen, 1983;Stichlmair et al., 1989;Laroche et al., 1992a). While it has been shown repeatedly that there are cases where the product composition boundaries derived for total reflux can be surpassed at finite reflux ratios (e.g., Nikolaev et al., 1979;Van Dongen, 1983;Levy, 1985; Laroche et al., 1992a), theoretical analyses to determine the separability limits based on more fundamental insight have been provided only recently by Wahnschafft (1993),Wahnschafft et al. (1992)and Stichlmair and Herguijuela (1992). The method presented by Wahnschafft et al. (1992)in the first paper of this series is based on the fact that, for the distillation of ternary mixtures, all degrees of freedom may be used to specify the desired product compositions + Present address: Aspen Technology, Inc., Ten Canal Park, Cambridge, MA 02141.

rather than design parameters, such as the number of stages and the reflux ratio. Starting from the fiied product compositions, one can calculate suitable values of the design and operating parameters. This so-called "boundary value procedure" has been suggested initially by Van Dongen and Doherty (Van Dongen, 1983;Van Dongen and Doherty, 1985) and has been refined by Julka and Doherty (1993)and Fidkowski et al. (1991). However, as opposed to these design procedures, our method does not require solutions of the finite difference equations which describe the change of liquid composition from stage to stage. Wahnschafft et al. (1992)demonstrated that the composition profiles attainable in each column section are constrained by so called pinch point curves, which describe the compositions of the stationary points attainable at arbitrary reflux ratios. Thus, the course of the pinch point curves can be used to determine aheadof design calculations whether or not a given product specification is in principle feasible. A pinch point in a separation device is due to vanishing driving forces for mass exchange. In a distillation column, for example, a zone of constant compositions arises if the streams getting in contact on the trays approach equilibrium. If, and at which compositions, such pinch points occur depends on the energy supplied to the column, i.e., on the reflux and reboil ratio. A conventional adiabatic distillation column cannot be pinched throughout. However, the notion of a pinch point can be used to define the model of the thermodynamically optimum separationpath. To minimize the occurrence of irreversible processes, thermodynamic equilibrium must be approached throughout the column. Such operation could theoretically be attained in a column with an infinite number of stages and heat exchange on each tray. Physically, this model implies that the internal vapor and liquid flows are adjusted by incremental heating and cooling at intermediate temperature levels to ensure that the vapor and liquid phase getting into contact at each stage are in equilibrium. The resulting separation path corresponds to the compositions of pinch points for continuously increasing condenser and reboil duties.

0888-588519312632-1108$04.00/0 0 1993 American Chemical Society

"0:: Reflux condenser

--, 1

2

/

3

Rectifying

section

4

Accumulator

n+-n-'

?=+ "n

(Y*)

Ln.1

DL

Reflux ratlo = b / D internal reflux ratlo = L.1ID

Figure 1. Internal and product flows for top rectifying section. At a pinch point, the vapor rising from a tray and the liquid moving down from above are in equilibrium.

In the equilibrium-based model of distillation, a pinch point can be calculated from the requirement that vapor and liquid compositions simultaneously satisfy the equilibrium relationship and the material balance equations. Instead of the rigorous mathematical model of such a process (e.g., Benedict, 1947;Petlyuk et al., 1965,Kaibel, 1987;Kohler, 1991; K6hler et al., 1991), we have used residue curve maps to graphically determine pinch point curves (Wahnschafft et al., 1992). The residue curve map of a ternary mixture is a convenient representation of the phase equilibrium behavior, derived from the open distillation process. Such maps reveal the occurrence of boundaries for distillation at total reflux and indicate the direction of the vapor-liquid equilibrium vector as a function of the liquid composition. For more information on residue curves see, for example, Doherty and Perkins (1978,1979) and Doherty and Caldarola (1985). Pinch point trajectories may be determined as the compositions for which the material balance and the equilibrium line coincide. For single-feed columns, this procedure is equivalent to finding the compositions at which the equilibrium vectors, Le., the tangents to the residue curves, point through the specified product compositions. As a reminder, Figure 1 depicts the flows pertinent to the material balance around the top section of an adiabatic column. At any stage in the rectifying section, the compositions V,, L,+l, and D must be on a straight line in a ternary diagram to satisfy the material balance V, = L,, + D (1) Since a pinch point also requires the vapor and liquid to be in thermodynamic equilibrium, the composition Vn must be located on a tangent to the residue curve passing through L-1. Similarly, at any stage in the stripping section, the liquid composition must lie on a straight line between the bottoms differencepoint and the composition of the vapor rising from the tray below

Lm = O,,

+B

(2) and again, at a pinch point, the two phase compositions must be in equilibrium. Figure 2 shows, for two arbitrarily chosen product compositions, the location of the pinch point trajectories and the regions of concentrations covered by the composition profiles that could conceivablybe obtained in an adiabatic distillation column rendering these products. These composition regions are enclosed by the trajectories for total reflux,which are approximated by residue curves, and by the product pinch point curves. The product specifications given in Figure 2 are feasible because the profile regions for the two column sections overlap. The

Ind. Eng. Chem. Res., Vol. 32,No. 6,1993 1109 overlap guarantees that there can be consistent paths of calculation, or composition profiles, respectively,leading to the given products. The criterion that the concentration profile regions determined for given product specificationsmust intersect is applicable regardless of the physical property behavior of a mixture. However, in azeotropic systems, the application of the criterion can become more complicated, as pinch point curves may exhibit bifurcations and multiple branches (e.g., Van Dongen, 1983;Fidkowski et al., 1991). Consider, for example, the separation of a mixture of acetone, chloroform, and benzene shown in Figure 3.For the bottoms composition there are two branches of pinch point curves which represent possible stationary points for composition profiles originating at B. As long as the reboil ratio is not too high, the composition profile will terminate on the pinch curve branch that traverses into the neighboring residue curve region. At too high values of reboil and reflux ratio, composition profiles will terminate on the disjointed pinch curve branch that ends at pure chloroform. Understanding the significance of the pinch point curves has enabled us to determine the maximum reflux ratio at which a separation across a residue curve or totalreflux boundary may be possible, as well as the maximum extent of separation (Wahnschafft et al., 1992). The crossing of the total reflux distillation boundary is enabled by an extractive effect due to the influence of benzene on the relative volatility between acetone and chloroform. Thus, benzene acts like a heavy, extractive entrainer while it is present in the feed. In the paper at hand, we will address the question what difference it makes with respect to the possibleseparations if there are multiple column feeds, each of which may be introduced onto a different tray. Multifeed columns have not received nearly as much attention in the literature as conventional columns have. An exception may be the classical extractive distillation in which a heavy entrainer is supplied close to the top of a column (e.g., Benedict and Rubin, 1945;Hoffman, 1964). However, the traditional extractive distillation process is just a special cme of the situations where one should or has to consider designing a column with separate feeds. Whenever two streams which are mixtures containing the same components,only in different composition, are to be separated in a single column, they should generally not be mixed to avoid unnecessary irreversibilities. More importantly, however, certain separations of azeotropic mixtures may only be feasible when entrainers are supplied as separate feeds. The objective of this paper is to provide a simple, semigraphical method to assess which separations of an azeotropic mixture mixture are in principle feasible when a separate entrainer feed is available. As part of this problem, we will clarify under which circumstances a separating agent should be introduced below or above an azeotropic feed. Even Levy (1985),who extended the boundary-valuedesign procedure proposed by Van Dongen (1983)to two-feed columns,did not address these questions from a synthesis point of view, although his design method could certainly be used to answer them through repeated application with varied operating and design parameters. However, the analysis presented here provides deeper insight into the complexphenomena occurring in nonideal distillation without requiring performance or design calculations. As a result, we arive at new criteria for the preliminary selection of entrainers to facilitate the separation of azeotropic mixtures by means of a generalized extractive distillation process.

1110 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993

0

. .

Feed Vapor compositions Liquid compobilions

Tangent points

Examples of

68.7 'C

'

..- -. ._ 0.8

0.6

0.4

0.2

98.4

+ 'man.

9:

Figure 2. Limiting regions for all adiabatic mlumn pmfiiss leading to the specified pmducta. The regions ere enclosed by curves (midue c w e a ) and by pinch point nwea.

Feasibility of Separations in Multifeed Columns

To investigate separation paths and the question of separation feasibility in a two-feed column, we will start by specifying feed and product compositions. Our objective is to obtain a quick feasibility assessment before trial-and-error calculationsare used to determine the reflux and the number of stages needed in each column section. Rigorous simulations or the boundary-value procedure proposed by Levy (1985) can render such information. However, such iterative design calculations can be atedious way to discover that a given design specification is simply infeasible. Material Balance Constraints for the Extractive Section. We first establish mass balances for the whole column and for vapor and liquid flows in the three column sections (Figure 4). The balance equations for the flows in the rectifying and stripping section are the same as for a single-feed column (eqs 1and 2). Hence, composition profiles in the rectifying and in the stripping section that are to lead to specified distillate and bottom products must be enclosed between the total reflux curves passing through these product compositionsand the corresponding product pinch point curves. If these two composition profile regions overlap, the assumed products can be obtained in a column without an extractive section or, in other words, in a simple column supplied with the mixed feed. To determine if an extractive column can make a desired separation feasible when a single-feed design cannot, we need to ask if the separation path in the extractive section can "connect" the composition profile regions of the rectifying and the stripping section. This "connection" will never be possible at total reflux because the column profile would have to follow a residue curve just as it would for a single-feed column. Hence, there must always be a maximum reflux ratio for a rational design of an extractive column (e.g., Tanaka and Yamada, 1965; Knapp and Doherty, 1991; Laroche et al., 1992a).

total reflux

To evaluate the mass balance constraints for the extractivesection between the two feeds, one has to decide which of the feeds should he the upper one and which the lower one. While normally a feed with a lower bubble point temperature issuppliedcloser tothe top ofacolumn, introducing the streams in reverse order of the volatilities can expand the range of feasible separations when an extractiveeffect occurs. There are also situationsin which feeding streams in reverse order of bubble points reduces the reflux requirementto accomplish the same separation (Levy, 1985). If the order of the feeds is not obvious, the following analysis may have to be performed for both possible configurations. overall mass balance:

F,+ Fl = D + B

(3)

balance for extractive section around the top part of the column:

vs-l- L, = D - F,

(4) balance for extractive section around the bottom half of the column: V8-l - La= Fl -B

(5)

Note that the index s for the stages in the extractive section is assumed to increase from 1at the lower feed tray upward. Equations 4 and 5 are valid a t any stage in the extractive section. Since the right-hand sides of these equations are not a function of the tray number, there is a difference point with constant composition also for this column section. From combining the two equations, it is apparent that, in a ternary diagram, this difference point must be the intersection point of the line that connects the compositions for F. and D with the line that connects those for FI and B. However, unlike the difference points

Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 1111 Benzene 80.1

56.5%

'

0.8

'c

0.6

X A ~ l ~ n i

Figure S. Separation of aeetane/chloroform/benzenemixhue. A total reflux boundary can be surpassed by distillation at finite reflux ration, an long the pinch curve for the product beyond the boundary can extend inta the neighboring distillationregion. In such canes the pinch point curve bifurcates into a branch describing stationary pointa for low values of the reflux ratio and one for higher reflux ration.

From the material balances around individual column sections it can be concluded that in the rectifying section the net vapor flow must be higher than the net liquid flow. Conversely, in the stripping section the net molar liquid flow is larger than the vapor flow. To decide which of the flows is larger in the extractive section, however, we have to the make a distinction. Using eq 4, we can distinguish

Rectifying section

_ I

I

Sbipping section

T'+,

2. D < F,:

It, = V8.1 + (F,- D)

BL

Figure 4. Flowa in the sectionn of a column with two feedn.

for the rectifying and the stripping section which correspond to the specified product compositions,the difference point A for the graphical construction of the compcmition profile in the extractive section is located outside the composition diagram.

= Le (D - FJ

(6a)

(6b) For case 1,the difference point is found by continuing the connection line between F. and D beyond D, whereas in the second case it is located on the continuation beyond F,. Accordingly, it is either the composition of the vapor rising from below that must he situated on the line between the difference point and the liquid composition or the liquid composition that is between the difference point and the compositionof the vapor. Thus, we can locate the difference point and analyze qualitatively how the composition profile calculation would have to proceed in the extractive section, as determined by the material balance constaints and the vapor-liquid equilibrium behavior indicated by the residue curves. Pinch Point Curves for the Middle Section. A ternary system used as an example in the previous paper (Wahnschafftet al., 1992),namelythesystem2-propanol, water, and ethylene glycol, shall serve to illustrate the role of the difference point for the extractive section. Figure 5 shows the residue curve diagram of this system. Assume therearetwoseparatefeeds,F,andFI,whose hypothetical total inlet composition is Ft. One would like to know if it is theoretically possible to produce D as distillate and B as bottoms. Because the concentration profile regions for the stripping and the rectifying section do not overlap, these products cannot be realized in a single-feedcolumn.

-yT[; Reboiler

+

1. D > F,: and

1112 Ind. Eng. Chem. Res., Vol. 32, No. 6,1993

\

Isopropanol 8 2 0 ~

\

\

\ \

~ = bar 1

\

ch polnt trajectories for A -

motive section

0

water iO0"C 1

Eihvlene aiveol 0.8

0.4

0.6

+xwaIer

0.2

0

197OC

Figure 6. Residue curve diagram of 2-propanollwaterlethyleneglycol system. For a column with more than one feed, we have to trace the possible composition trajectories in each column section and determine whether a consistent path can exist between the specified products. The product specification shown in the figure turns out to be feasible when ethylene glycol is added as a heavy entrainer above the Z-propanolwater mixture.

Since for the given feed and product specifications the distillate flow rate D is greater than the supply of the assumed upper feed (FJ, the difference point A is found on the extension of the line connecting F, and D beyond D. In Figure 5 it is indicated that this difference point will he rather far out to the upper left of the composition triangle. The point corresponds to the intersection of two balance lines: one that includes the upper feed and the distillate and one which includes the lower feed and the bottoms product. As discussed before, the composition profiles in the rectifying and in the stripping section that are to lead to specified products are confined by total reflux curves and by pinch point trajectories determined for the specified product compositions. These pinch point curves were found as the trajectories of compositions at which the tangents to the residue curves aim at the composition of the difference points. By analogy, knowing the location of the difference point for the extractive section, we can now determine graphically whether and where there are pinch trajectories along which the equilibrium vectors point at A. As sketched in Figure 5, in the case of ow example problem, one can find two such trajectories. As forthe rectifyingandthe stripping section (e.g., Fidkowski et al., 1991),these trajectories originate at the nodes and saddlesand theresiduecurvemap, i.e.,atpurecomponents and azeotropic compositions. The pinch point trajectories divide the composition space into regions in which the separationpaths that could conceivably he accomplished in the extractive section are qualitatively different. Let us first consider the composition region between the two pinch trajectories for the extractive section. Because D > F,, the graphical construction of the composition profile requires that the composition of the vapor rising from below is located between the liquid

composition and the difference point (eq 6a). Thus, we can pick an arbitrary composition in the region between the pinch trajectories and visualizehow the calculation of the composition profile would have to proceed. We follow alternate equilibriumandmaterial balance steps beginning in the composition region reachable by the stripping profile. In the example, stepping up the hypothetical trays in the extractive section leads to compositions that move toward the 2-propanol-ethylene glycol axis. This separation path is consistent with those achievable in the bottom stripping section and in the top rectifying section-the separation can proceed from the high-hailing bottoms composition toward the distillate along a path with constantlydecreasingtemperature. Hence, the given product specifications are in principle feasible when ethylene glycol is added as an extractive agent (feed FJ. Minimum and Maximum Reflux Ratio. Note that if we assumed the composition in the extractive section to he outside of the region between its pinch trajectories, stepping up in the extractive section in a graphical construction like the one illustrated in Figure 5 would imply an increase of the water fraction. Thus, the composition profiles in the rectifying and in the stripping section, determined by starting from the specifiedproduct compositions for a specific reflux and reboil ratio, must reach into the region between the extractive section pinch trajectories. This requirement defines lower and upper bounds for the reflux ratio at which the specified separationcould possibly heaccomplished. Attoo highareflux, the composition profile in either the stripping or the rectifying section will end at a pinch outaide the composition region for which the extractive section can make the desired separation feasible. Possible Separation Sequences for a Given Entrainer. In early papers and textbooks on extractive distillation, one can find the statement that a high-boiling

Ind. Eng. Chem. Res., Vol. 32,No.6, 1993 1113

A

Born.

I I

Mimm

mM (ASPENPLUS1

Tb-S.5G

1

Q ,T ~ = ,

55.5 G

0.6 +xlolaOJ

az

0 Tb=U.7 OC

Figure 6. Product composition regions for a single-feed column distilling a mixture of acetone, methanol, and water. None,of of the wmtropic constituents can be produced in pure form in a single-feed column.

entrainer will allow one to produce the lighter-boiling component as pure distillate. It is known now that this is not generally correct. Which component(s)can appear in the distillate depends not only on the pure component boiling points, but also on the nonideal molecular interactions between the entrainer and the components to be separated (e.g., Berg and Yeh, 1985). By increasing the relative volatility of the heavier azeotropic constituent, it is quite possible that an entrainer takes the lighter componentto the bottom. However, it has not been shown how the existing design options can be inferred from the trajectories of residue curves, and one may even wonder if both options could be feasible for a certain entrainer. Larocbe et al. (1991)used rigorous simulations to study designs of extractive distillation columns. For a selected entrainer, they found that it was only possible to design a column that would produce either the lighter- or the intermediate-boilingcomponent as pure distillate. Using our pinch point analysis, we can now investigate which design could be realized without having to rely on simulations. Moreover, we want to address the question of how much of the entrainer will be needed to accomplish a specified separation of an azeotropic mixture. As an example, let us consider the separation of the acetone/ methanol azeotrope with water as an entrainer. Figure 6 presents product compositions obtained using the RADFRAC model of Aspen Plus (Aspen Tech, 1991) for numerous possible designs of a single-feed column supplied with a mixture of acetone, methanol, and water as feed. The shaded areas correspond to the theoretically feasible product composition regions one can determine using the method we presented in the previous paper (Wahnschafft et al., 1992). We notice that, for a singlefeed column, the best possible separation between acetone and methanol entails the split into water and methanol as bottoms and a near-azeotropic mixture of acetone and methanol as distillate. In Figure 7a, the main feed (FI)is acetone and methanol at practically azeotropic composition, while now an

arbitrarily chosen amount of pure water is to be used as the higher-boiling upper entrainer feed Fu. Having fixed product specifications for the separation into acetone as distillateandwaterandmethanolasbottoms,wecanlocate the composition profile regions for the three column sections. The bold arrows in Figure 7a indicate the 'direction" the composition profiles in the three column sections could follow with decreasing temperature. The profile region for the stripping section allows for removal of acetone, 80 that water and methanol can be produced as bottoms. On the other hand, the separation in the rectifying sectionthatcan lead to acetone as distillate is restricted to a path along the acetone/water axis. In other words, if methanol appears above the upper feed tray, it cannot be separated from acetone in the rectifying section-it will escape into the distillate. Thus, the extractivesectionmust accomplish the separationthrough the composition region between the pinch curve for the stripping section and the acetone/water axis. From the feed and product specifications, we find that this time the difference point A for the extractive section is on the entrainer-rich,upperright side of the composition diagram. There are again two pinch trajectories for this difference point. Since the distillate flow rate is smaller than that ofthe upper feed, the composition profile in the extractive sectionhas to be constructed such that the liquid composition on a stages is located between the difference point and the composition of the vapor rising from below (see eq 6b). By testing some arbitrary liquid and vapor compositions in the region between the pinch curves for the extractive section (Figure 7a), one can verify that the compositionprofile in the extractive section must traverse toward the water-acetone axis. Thus, there is a path from the assumed bottoms composition all the way to the postulated distillate along which the boiling temperature decreases monotonically-the specified produds are feasible! Figure 7b shows the composition profile of a

1114

Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 W.lw

r,

/To"{:

1m.o4:

I

' /

M.th.nd Tb= €4.7 4:

' 0.6

0.b

02

M.th.nol 0 Tb= 64.7 4:

4- .n-=

Figure I. Separating an azeotropic mixture of acetone and methanol using water. (a, top) If water is supplied an a heavy extractive agent closer to the top of the column, it becomes possihle to recover acetone an pure distillate. The extractive section is required to ensure that no methanol appeas at the top. (b. bottom) Result of a rigorous simulation run verifying the analysis. The compositionprofile in the extractive section reaches the acetonewater axis.

distillation column accomplishing this separation, determined by an Aspen Plus simulation run (Aspen Tech, 1991). If we increased the amount of water added as the upper feed, the total feed composition would he closer to the entrainer edge. For theseparationintoacetoneasdistillate

and water and methanol as bottoms, the difference point A would thus also move closer to the entrainer edge, approaching it from outside the composition diagram. As the difference point is closer to the entrainer edge, the composition region between the pinch trajectories for the extractive section broadens. Consider now the limiting

Ind. Eng. Chem. Res., Vol. 32,No. 6, 1993 1115 case of an infinite entrainer-to-feed ratio. The column would practically be filled with water and perform the separation into acetone as distillate and a bottoms that containsall the methanoland the water with a composition very close to the water edge. For this case, the difference point A practically coincides with the water edge of the diagram. In the limit, the upper pinch trajectory will lie on the water-methanol axis, while the other pinch curve for the extractive section would coincide with a so-called isouolatility curue (Laroche et al., 1991). In general, an isovolatility curve is a trajectory along which the volatilities (K-values)of two species are equal. The isovolatility curve shown in Figure 7 is the one for acetone and methanol. In a residue curve map, isovolatility curves can be identified by finding compositions at which the equilibrium vector, i.e., the tangent to a residue curve, points through a vertex of the composition diagram because along such a line the relative composition between two species is constant. In our example, the isovolatilitycurve comprisesthe compositionsat which the equilibriumvector passes through the entrainer (water) vertex. The isovolatility curve divides the compositionspacein regionswhere the components have a different volatility order (Laroche et al., 1991). In the example system, methanol is more volatile below the curve, while acetone is more volatile than methanol in the rest of the composition space. While isovolatility curves appeared long ago in the distillation literature, their significance as the theoretical limits for the location of pinch point curves has not been recognized previously. The fact that methanol becomes more volatile than acetone in the acetone-rich corner is the reason why it is only possible to reach pure acetone via a separation path along the acetonelwater axis. Accordingly, the entrainer feed must not be contaminated with the component it is supposed to attract, Le., with methanol, because water is rapidly depleted in the column section above the entrainer feed, and the methanol would have to appear in the distillate. The Minimum EntrainerRatio. Instead of increasing the supply of water beyond the amount that was used for the situation shown in Figure 7, we can also perform a second thought experiment in which we reduce the ratio between water supplied as the extractive agent and the azeotropicfeed. As we still specify separationsinto acetone as distillate and water and methanol as desired bottom products, the difference point moves away from the entrainer edge to infinity. It continues by jumping to the other side of the composition diagram when the distillate flow D exceeds that of the upper feed F,. By reducing the amount of entrainer, the composition region between the extractive section pinch curves is made narrower until, at a minimum entrainer-to-feed ratio, the gap between the pinch curves becomes very small. The gap closes when the difference point A is located on a tangent to a residue curve at its point of inflection. Thus, just like the criterion presented in our earlier paper (Wahnschafft et al., 1992) to locate the maximum separation beyond a total boundary for the case of a single-feed column, the requirement that the separation path can progress throughout the extractive section means that the difference point A may not be situated on a tangent of a residue curve at an inflexion point. Again, this criterion could be used to determine the minimum entrainer concentration required for a specified separation by calculating pinch point curves. However,because the difference points are located outside the composition diagram, the graphical method to deter-

mine the minimum entrainer flow for effective separation in the extractive section is rather cumbersome. Finally, let us investigate if it could be possible to design a column that would produce methanol as distillate and a bottoms product consistingof acetone and water. These specifications are shown in Figure 8 for an arbitrarily picked amount of water used as entrainer. The bold arrows in Figure 8 indicate how the separation paths would have to proceed in the three column sections with decreasing temperature. The composition profile region for the rectifyingsection that could conceivablyproduce methanol as distillate is restricted to the water-methanol axis. On the other hand, following the residue curve map in the direction of decreasing temperature from the assumed bottoms composition, the concentration path in the stripping section could only move toward acetone and the acetone/methanol azeotrope. The difference point A for the extractive section is located toward the upper left side of the triangle. In this case, there is only one pinch trajectory for the extractive section, as shown in Figure 8. According to the product specification, the mass balance eq 6b demands that the liquid composition on a tray in the extractive section is between the difference point and the composition of the vapor rising from below, so that the composition profile in the extractive section has to move toward the acetone-water axis with decreasing boiling temperature. One realizes that there is no consistent path of separation that could make the given product specifications feasible. The extractive section cannot bridge the composition space between the regions for the rectifying and the stripping sections because its concentration path would allow only for enrichment in acetone toward the upper feed tray. Summary. In summary, the feasibility of a specified separation in a column with more than one feed can be examined without trial-and-error calculations,just as we demonstrated previously for single-feed columns (Wahnschafft et al., 1992). The underlying idea is to construct the composition regions in which separation can occur in the individual column sections. For this purpose, one has to locate the possible pinch compositionsfor the difference points derived from the design specification in question, which can be done graphicallyor by calculation. The liquid composition profile must be able to traverse through these concentration regions along a separation path with monotonically decreasing temperature. Thus, the presence of an extractive section can make the overall separation feasible if (1) a composition region remains between its pinch point trajectories, (2)that region overlaps with the rectifying and stripping section profile regions, and (3) the separation path can be consistent with the separations in the rectifyingand the stripping sections that are to lead to the specified products. By examining the pinch trajectories for the extractive section qualitatively, we also demonstrated that, for a specified separation of an azeotropic mixture, the size of the composition region in which the extractive section can accomplishseparationdecreasesas the amount of entrainer is reduced. At the minimum entrainer ratio, below which the extractive section cannot make a specified separation feasible anymore, the pinch trajectories for this column section approach each other. The pinch trajectories actually touch (or bifurcate) when the difference point A is located on a tangent to a residue curve at its point of inflection.

Consequences for Entrainer Selection The insights into the phenomena that govern feasibility of separation in single-feed and two-feed distillation

1116 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993

p = 1 bar Wilron

e Acetone Tb= 56.5"C

Figure 8. Another specification for separating acetone and methanol. It is impossible to use water a8 a separating agent to produce pure methanol from the given feed. Water increases the volatility of acetone relative to methanol. Thus, there is no consistent separation path between the composition profde regions determined for the three column sections.

columnspresented here and in the first paper of this series have a number of implications for the synthesis and design of homogeneous azeotropic distillation processes, in particular for processes in which entrainers are used that do not introduce additional azeotropes and are thus readily recovered by distillation. Entrainers that do introduce additional azeotropes in homogeneous azeotropic distillation require either relatively high recycle ratios (e.g., Laroche et al., 1992a) or recovery by some method other than simple distillation. As suggested by Knapp and Doherty (1992),one possibility for the entrainer recovery step is a pressure-swing distillation, but their investigation of this technique essentially confirmed that such processes are only competitive if the species used as entrainers are already present in the mixtures to be separated. Thus, we will not deal with such entrainers here. It should be pointed out, however, that the process synthesis methodology proposed in the third paper of this series (Wahnschafft et al., 1993) takes into account such separating agents, as it aims at developing processes which make as much use as possible of species present in a problem to separate azeotropic multicomponent mixtures. Processes based on entrainers that do not introduce additional azeotropes are not restricted to classical extractive distillation. As in the example of the acetonel chloroformtbenzene system, species can act as extractive entrainers even when they are not supplied as separate feeds. Moreover, feasible entrainers do not always have to be higher-boiling (e.g., Hoffman, 1964; Doherty and Caldarola, 1985; Stichlmair et al., 1989; Laroche et al., 1991,1992b). Thus, we suggest denoting processes such as these, which are not traditional extractive distillation schemes, as generalized extractive distillation schemes to distinguish them from the more general concept of homogeneous azeotropic distillation (Doherty and Caldarola, 1985). How these processes work cannotbe inferred

from the presence or absence of residue curve boundaries alone. In principle, which separations are feasible can only be determined in arigorous analysis. However, there are simple indicators for situations in which total reflux boundaries can be surpassed. Moreover, as Laroche et al. (1991, 1992a) pointed out, the reverse may occur; i.e., separability may not be guaranteed even if there is no simple distillation boundary between the azeotropic components in the ternary system. Both effects can usually be predicted on the basis of the relative volatilities at infinite dilution, as we shall discuss now. First of all, when trying to separate a binary azeotropeforming mixture, one should distinguish according to the type of azeotrope to be separated. This distinction is important with regard to where in a homogeneous azeotropic distillation column the most difficult part of the separation must occur between the original azeotropic mixture constituents. The differences are apparent by consideringthe distillation of the binary azeotropic mixture without the entrainer. Consider distilling a binary mixture which exhibits a minimum-boiling azeotrope but which is not at the azeotropic composition. It is possible to obtain one component pure in the bottom of the column, while the composition profile approaches the azeotropic composition in the column section above the feed. Which component could be produced pure depends on the feed concentration, as indicated schematically in Figure 9a,b. Figure 9c,d shows the possible situations for a binary maximum-boiling azeotrope. The letters inside the columns represent the volatilities of the individual species. For the separation of a minimum-boiling azeotrope, a high-boiling entrainer used to modify the volatilities of the azeotrope-forming species must be present in sufficiently high concentration in the section above the azeotropic feed, and hence has to be supplied close to the top of the column. This process corresponds to classical

Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 1117 Mlnimum-bolllng azeotrope A/B

I -A I B

AI B

A/ B

Maxlmum-boiling azeotrope

Figure 9. Scheme showing distillation of a binary mixture. By analyzing the volatility order obtained in the distillation of binary azeotropicmixtures,we can tell where an entrainer component must be supplied, depending on the type of azeotrope to be separated and the boiling point of the entrainer relative to that of the azeotrope.

extractive distillation where the critical separation occurs in the extractive section. An example is the separation of acetone and methanol with water as extractive entrainer. For the separation of high-boiling azeotropes, the situation is reversed. In the binary distillation, a pure component would come overhead while the bottom composition is limited by the azeotrope (Figure 9c,d). When a heavier component is to be used as entrainer, it can in principle be supplied with the azeotropic feed because it is really only needed in the stripping section,provided the azeotrope-forming species do not reverse their volatility order in the column section with low entrainer concentration. An example of the application of a higher-boiling entrainer to separate a maximum-boiling azeotrope has been discussed at length in the previous paper (Wahnschafft et al., 1992),namely the separation of acetone and chloroform using benzene. Benzeneincreasesthe relative volatility between acetone and chloroform. In terms of the classification given in Figure 9, this problem would correspond to the situation in Figure 9c, with A representing acetone and B representing chloroform. In the rectifyingsection,acetoneis more volatile than chloroform anyway. While supplying the entrainer (benzene) at a higher stage would result in increased relative volatilities throughout the extractivesection and the stripping section, it would also incur higher thermodynamic losses-a tradeoff which can really only be resolved by rigorous optimization. Most importantly, we note that the entrainer does not have to be fed at a stage above the feed.

It is also possible to employ intermediate-boiling entrainers, as has been suggested already by Hoffman (19641, but it is usually difficult to find species that boil in the narrow temperature range between azeotropeforming components and do not introduce additional azeotropes. If there are such components, however, they offer much flexibility in the design of suitable separation sequences (Laroche et al., 1991). Since intermediateboiling species lead to residue curve maps in which the azeotrope and one of the azeotropic constituents are the extreme boiling, stable nodes, there are residue curves that pass from the azeotrope to the first azeotropic constituent, on to the intermediate-boiling entrainer, and end at the other azeotropic species. Figure 10 illustrates the topology of the residue curve map for a system with an intermediate-boiling entrainer. One could say the azeotropic components are connected by a single residue curve in the ternary system, so that the mixture can be separated in a sequenceof columns operated at totalreflux, and even in a singlecolumn when the loss of a small amount of entrainer is tolerable. The intermediate-boiling component can reach very high concentration levels within the column, even if its fraction in the feed is almost negligible. Similarly, a component which introduces an azeotrope that is a saddle in the resulting residue curve map (i.e., the azeotropeboils between the pure component boiling temperatures) could function as an entrainer in a column operated close to total reflux. Finally, we want to consider lower-boiling entrainers. In the case of a minimum-boiling azeotrope, a low-boiling entrainer produces a residue curve map with a boundary while there is none in a system with a maximum-boiling azeotrope. In neither case the azeotropicconstituents are connected by a residue curve. However, what matters here is whether or not the low-boiling entrainer can alter the relative volatilities between the azeotropic species. If it does, it could be mixed with the main feed to separate a minimum-boiling azeotrope while, for the separation of a maximum-boiling azeotrope, it would have to be fed close to the bottom of the column. An example of the separation of a minimum-boiling azeotrope by means of a lower-boilingentrainer has been provided by Hunek et al. (1989), who demonstrated that a complete separation between ethanol and water is possible in the presence of a large fraction of methanol in the feed. Hunek et al. denoted this phenomenon, which they also verified experimentally, as “reverseextractive distillation”. Laroche et al. (1991) also discussed the possibility of using lighter entrainers but did not point out that one can expect them to be of little practical interest for the separation of maximum-boiling azeotropes. Extractive agents must modify the volatilities throughnonideal interactionswhich usually occur mostly in the liquid phase, while light entrainers have the tendency to strongly accumulate in the vapor phase when much heavier species are present. From the above discussion it becomes apparent that there are two fundamentally different situations in the separation of a binary azeotropic mixture by distillation in presence of an entrainer. Entrainers that result in residue curve maps in which the original azeotropic constituents are “connected” by residue curves enable separation by means of columns operated at high or total reflux. However, in most entrainerlazeotrope combinations the azeotropic species are not situated on a single residue curve in the ternary system, which implies that there must be a “total reflux boundary” between them,

1118 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 Entrainor Tb= 70.0 OC

0

A Tb= 80.0 O C

B 1 1

0.8 0.8 T&' T&' 555.0 OC 0.6

f

xA

0.4

0 Tb= 60.0 oc

02

Figure 10. Type of residue curve map topology arising from use of an intermediate-boiling entrainer component. The important point is that there are residue curves in the multicomponent system that pass along both azeotropic component vertices. Thus, such an entrainer could conceivably be used to even separate the two azeotropic species by means of a single column when small entrainer losses are not prohibitive (Laroche et al., 1992a,b).

although not necessarily a residue curve boundary. Here, the extractive effect needed to surpass the relative azeotropic composition does not reach a maximum a t total reflux but at some finite reflux ratio, as discussed in this and in the previous paper. Where such extractive entrainers can be supplied to the column depends on the type of azeotrope to be separated and on the boiling point of the entrainer relative to that of the azeotrope. Azeotrope Prediction and Preliminary Screening of Entrainers. In the generalized extractive distillation process discussed here, separability depends on the effect of the separating agent on the relative volatility between the azeotropic components, in particular when higherboiling or lower-boiling entrainers are used. The influence of an entrainer candidate on the volatilities of the species to be separated usually is reflected in the K-values a t infinite dilution. For binary mixtures, these data are also useful to predict the formation of azeotropes. As an example, Figure 11 shows the bubble and dew point curves of a binary mixture that exhibits a maximumboiling azeotrope. From the ratio of the fraction in the vapor phase (dew point curve) to that in the liquid phase (bubble point curve), we determine that the K-value of acetone at infinite dilution in chloroform is smaller than 1. On the other hand, theK-value of chloroform in acetone is also less than 1. Analogously, for a binary mixture with a minimum-boiling azeotrope, both K-values of the infinitely dilute species must be larger than 1. A mixture is zeotropic if one infinite dilution K-value is larger and one is smaller than 1. While there are binary mixtures with multiple azeotropes, such complex phemomena are extremely rare (Gmehling, 19921,so that the criteria for the identification of maximum- and minimum-boiling azeotropes based on the K-values at infinite dilution summarized in Table I

-

64

62

60 O C

58

56

54

0

Ace to ne

0.2

0.4

0.6

0.8

1

Chloroform

Figure 11. Bubble and dew point curve8 of the acetone-chlorofom system. The maximum-boiling azeotrope is reflected in the fact that the volatilities (K-values) of the components at infinite dilution in each other are below one. Table I. Correspondence between Aaeotropy and Infinite Dilution K-Values ~____ ~_______ minimum-boiling azeotrope K1, < 1andK2, < 1 maximum-boiling azetrope K1, > 1and&, > 1 heteroazeotrope Ki, > 10 and Kz, > 10 ~~~

are quite reliable. However, it should be noted that the criterion for identification of a binary heterogeneous minimum-boiling azeotrope is merely a heuristic. According to numerous cases studies, a partial immiscibility is possible if one K-valueis greater than 10and one greater than 5, and heterogeneity is almost certain if both K-values

Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 1119 Table 11. K-Values at Infinite Dilution for the Acetone/ ChloroformDenzene Syrtem at 1 bar acetone chloroform benzene acetone 1.0 0.4 0.7 chloroform 0.6 1.0 0.4 benzene 3.0 1.5 1.0

we studied. With further improvements of the group contribution methods under way (Gmehling, 1992), one may thus well resort to such methods for the prediction of azeotropes and for the preliminary screening of entrainers based on residue curve maps and relative volatility data.

are larger than 10.

Summary

When the vapor-phase nonideality can be neglected, the infinite dilution K-values depend only on vapor pressures and activity coefficientsat infinite dilution (eq 7). As mentioned before, such K-values are useful not only for the prediction of azeotropic behavior but for the selection of entrainers for generalized extractive distillation. Table I1 lists the infinite dilution K-values for the example system of acetone, chloroform, and benzene. According to these values, the acetonelbenzene and chloroformJbenzenemixtures are not azeotropic, which we have seen before (Figure 3). Benzene increases the relative volatility, i.e., the ratio of K-values, between the azeotropic components acetone and chloroform so that the distillate can be enriched in acetone, while chloroform is attracted to the bottoms by the heavier species benzene. The residue curve map of the ternary system has a boundary whose curvature reflects this influence of benzene on the relative volatility between the azeotropic components (Figure 3). It should be noted that a relative volatility of 2 at dilution in the entrainer is not very large so that one can expect to find much stronger boundary curvatures for components with better selectivities. In general, the relative volatility at infinite dilution in an entrainer defines the design options(s) and gives an indication regardingthe minimum entrainer ratio needed. The larger the relative volatility at infinite dilution in an entrainer, the more significant will be the curvature of a boundary, if one exists, and, in turn, the lower will be the minimum entrainer-to-feed ratio. However, as Laroche et al. (1991) point out, comparison based on relative volatilities can only be made between entrainer candidates that would offer the same design options, i.e., lead to the same volatility order, because an evaluation of different separation sequences may involve more complex tradeoffs. When comparing entrainers, a table with K-values at infinite dilution like Table I1 can also be used to ensure that a candidate separating agent is easily separable from the azeotropic components over the whole composition range, which has an impact on the minimum reflux ratio for the azeotropic and the entrainer recovery column. For example, from Table I1 we determine that the relative volatility between chloroformand benzene ranges between 1.5 at infinite dilution in benzene and V0.4 = 2 at infinite dilution in chloroform. The relative volatility between acetone and benzene is 3.0 at high benzene concentrations and about 1.43 1/0.7 at infinite dilution in acetone.Thus, the recovery of benzene is readily accomplished by distillation. All data on volatilitiesgiven here were determined using the UNIFAC method (e.g., Fredenslund et al., 1977) as implemented in the simulationpackageAspen Plus (Aspen Tech, 1991). The predictions of mixture nonidealities based on this data have been found to be surprisingly accurate, as they never failed to predict, at least qualitatively, the behavior of the broad spectrum of mixtures

In this paper, we presented a method to assess the feasibility of product specificationsfor distillation columns with multiple feeds. This method is based on geometrical interpretations of the equations governingthe distillation process in an equilibrium-basedmodel formulation. Using graphical representations of vapor-liquid equilibrium (residue curves) and of mass balances, it has been possible to show how the separationpaths, Le., compositionprofiles, are constrained in the individual column sections. Pinch point curves have been identified as the limiting trajectories,which mathematicallyare uniquely definedthrough the mass balances and the requirement that the vapor and liquid getting in contact at any stage must be in equilibrium. By determining these limiting trajectories, either by calculation or graphically using reasonably detailed residue curve maps, it is thus possible to decide without column simulationsor design calculationswhether the specified products are in principle feasible. Lastly, being able to perform this analysis for columns with one and with more feeds, we derived an expanded set of criteria for the preliminary screening of entrainer candidates for the generalized extractive distillation discussed here. Having taken a detailed look at the use of distillation for the separation of azeotrope-forming mixtures, there will be one more paper in this series, in which we address in depth the practical consequences and applications of the methods and results presented so far. This last paper (Wahnschafft et al., 1993) deals with the problem of the conceptual design of the complex separation systems typically needed for azeotropicmulticomponentmixtures.

Acknowledgment The authors would like to thank the Engineering Design Research Center, an NSF-sponsored center at Carnegie Mellon University, and the Eastman Chemicals Division of the Eastman Kodak Company for their support of the work reported here. Funds provided to O.M.W. by the Ernest-Solvay Foundation and the ‘Studienstiftung des deutschenVolkes”are also acknowledged. Finally, we wish to thank Aspen Technology Inc. for providing us with the Aspen Plus simulation program.

Nomenclature B = bottom product flow rate B = vector of bottom product component flow rates D = distillate product flow rate D = vector of distillate component flow rates F = feed flow rate F = vector of feed component flow rates L = liquid flow rate L = vector of component molar flows in the liquid r = reflux ratio LdD s = reboil ratio VoIB V = vapor flow rate V = vector of component molar flows in the vapor x = liquid composition vector (mole fraction) l c i j = fraction of component i or j in mixture y = vapor composition vector (mole fraction)

1120 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993

A = net composition of the difference point for the extractive section Indices

B = bottoms D = distillate F = feed (stage) i, j = component indices m = stage in stripping section n = stage in rectifying section s = stage in extractive section

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Received for reuiew October 5, 1992 Accepted February 16, 1993