Ind. Eng. Chem. Res. 1992,31,2345-2362 Acid Moieties. Makromol. Chem., Rapid Commun. 1991, 12, 227-233. Kwon, I. C.; Bae, Y. H.; Okano, T.; Berner, B.; Kim, S. W. Stimuli Sensitive Polymers for Drug Delivery Systems. Makromol. Chem., Macromol. Symp. 1990,33,265-277. Okano, T.; Bae, Y. H.; Jacobs, H.; Kim, S. W. Thermally On-Off Switching Polymers for Drug Permeation and Release. J. Controlled Release 1990a,11, 255-265. Okano, T.; Bae, Y. H.; Kim, S. W. Temperature Responsive Controlled Drug Delivery. In Pulsed and Self-Regulated Drug Delivery; Kost, J., Ed.; CRC Press: Boca Raton, FL, 1990b;Chapter 2. Okano, T.; Yoshida, R.; Sakai, K.; Sakurai, Y. Thermo-Responsive Polymeric Hydrogels and Their Application to Pulsatile Drug Release. In Polymer Gelq DeRossi, D., Ed.; Plenum Press: New York, 1991;pp 299-308. Sakai, K.; Ozawa, K.; Mimura, R.; Ohashi, H. Comparison of Methods for Characterizing Microporous Membranes for Plasma Separation. J. Membr. Sci. 1987,32,3-17. Sato Matsuo, E.; Tanaka, T. Kinetics of Discontinuous VolumePhase Transition of Gels. J. Chem. Phys. 1988,89,1695-1703. Sawahata, K.; Hara, M.; Yasunaga, H.; Osada, Y. Electrically Controlled Drug Delivery System Using Polyelectrolyte Gels. J. Controlled Release 1990,14, 253-262.
2345
Siegel, R. A. pH-sensitive Gels: Swelling Equilibria, Kinetics, and Application for Drug Delivery. In Pulsed and Self-Regulated Drug Delivery; Kost, J., Ed.; CRC Press: Boca Raton, FL, 1990; Chapter 8. Tanaka, T.; Fillmore, D. J. Kinetics of Swelling of Gels. J. Chem. P h p . 1979, 70, 1214-1218. Verniory, A.; Du Bois, R.; Decoodt, P.; Gassee, J. P.; Lambert, P. P. Measurement of the Permeability of Biological Membranes. J. Gen. Physiol. 1973,62,489-507. Yoshida, R.; Sakai, K.; Okano, T.; Sakurai, Y. A New Model for Zero-Order Drug Release I. Hydrophobic Drug Release from Hydrophilic Polymeric Matrices. Polym. J. 1991a,23,1111-1121. Yoshida, R.; Sakai, K.; Okano, T.; Sakurai, Y.; Bae, Y. H.; Kim, S. W. Surface-Modulated Skin Layers of Thermal Responsive Hydrogels as "On-Off" Switches: I. Drug Release. J. Biomuter. Sci. Polymer Ed. 1991b,3, 155-162. Yoshida, R.; Sakai, K.; Okaao, T.; Sakurai, Y. Surface-Modulated Skin Layers of Thermal Responsive Hydrogels as "On-Off" Switches: 11. Drug Permeation. J. Biomater. Sci. Polymer Ed. 1992,3,243-252. Received for review December 23, 1991 Revised manuscript received April 20, 1992 Accepted July 21, 1992
SEPARATIONS The Product Composition Regions of Single-Feed Azeotropic Distillation Columns 0. M. Wahnschafft,*it J. W. Koehler,' E. Blass,' and A. W. Westerberg? Engineering Design Research Center and Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213,a n d Lehrstuhl A f u r Verfahrenstechnik, Technical university of Munich, Arcisstrasse 21, 8000 Munich 2, Germany
This paper shows how the limiting operating conditions, total reflux and thermodynamicallyoptimum operation, can be used to determine the feasibility of a desired separation by continuous distillation. *To assess feasibility, so-called pinch point trajectories are established as the limits of separations achievable in each column section. These trajectories may be determined graphically using residue curve maps. The feasibility criterion is generalized to result in a method to establish the ranges of top and bottom product compositions achievable by a single-feed distillation column for a given ternary feed. One particularly interesting application is to reveal where and to what extent distillation boundaries for azeotropic mixtures, derived for total reflux, can be surpassed in columns operated at finite reflux ratios. We present a criterion to estimate the maximum reflux for such separations and illustrate process schemes that exploit the possibility of crossing of total reflux boundaries to separate azeotrope-forming mixtures. Finally, we demonstrate how intermediate heat exchangers can be used to improve separations of azeotropic mixtures across total reflux boundaries.
Introduction Due to the well-known advantages of continuous distillation processes, azeotropic and extractive distillation continue to be among the most frequently used methods for the separation of azeotropic and nonideal close boiling mixtures, a task quite common in industrial practice (e.g., Malesinski, 1965;Horsley, 1973). Although it is possible to separate certain azeotrope-forming mixtures of three or more componente in a simple sequence of distillation
* To whom correspondence should be addressed. t Engineering Design Research Center, Carnegie Mellon
University. Technical University of Munich.
*
columns without introducing another species into the system and without change of operating pressures, separation by distillation in general requires the addition of an entrainer species and a more complex process scheme with recycle(s). The role of the mass separating agent is normally to facilitate separation either through the introduction of a new, extreme b o i i g azeotrope, or through the change of volatilities of the original components in presence of the entrainer (solvent). Depending on the physical property behavior of the original mixture and the way in which the mass separating agent is to enhance the separation, the entrainer stream can be mixed with the primary feed or has to be supplied separately to an azeotropic column. While heterogeneous azeotropic distillation
0888-5885/92/2631-2345$03.00~0 0 1992 American Chemical Society
2346 Ind. Eng. Chem. Res., Vol. 31, No. 10, 1992
processes imply the occurrence of a liquid-phase immiscibility that is exploited to subsequently recover the entrainer, entrainers for homogeneous azeotropic distillation are usually chosen such that they can be recovered by distillation (e.g., Hoffman, 1964; Doherty and Caldarola, 1985). The problem of the synthesis of such complex distillation processes can be decomposed into several stages: the selection or preliminary screening of entrainers, the conceptual design of suitable process configurations for a selected mass separating agent, and the detailed design of the individual separators and optimizationof the operating parameters. Until recently, the design and optimization tasks could only be handled by using rigorous simulation models in time-consuming trial and error procedures. Although new approaches for determining the minimum reflux (e.g., Levy et al., 1985; Julka and Doherty, 1990; Koehler et al., 1991) and for the design of nonideal multicomponent distillation columns (e.g., Van Dongen and Doherty, 1985; Fidkowski et al., 1991)have made the latter tasks much easier, it would still be very tedious to use design methods to synthesize process flowsheets or to evaluate candidate entrainers. More efficient systematic approaches for the conceptual design of processes separating a give mixture by means of a selected entrainer require the ability to identify quickly feasible separations in the resulting multicomponent system (Doherty and Caldarola, 1985; Knight and Doherty, 1989; Laroche et al., 1992; Wahnschafft et al., 1991). Since the products attainable in any single separation step depend on the composition of its feed(& the basic problem is to determine which separations can be accomplished for a fixed feed composition. In the case of multicomponent mixtures, this problem is not as trivial as for binary distillation where an increase of the reflux ratio always leads to improved separation and the extreme concentrations achievable require total reflux. Although it is known that, in the distillation of nonideal multicomponent mixtures, there are phenomena that do not occur in ideal distillation, e.g., that finite reflux ratios sometimes lead to a better separation than total reflux (e.g., Van Dongen, 1983; Laroche et al., 1990), a common practice has been to determine feasible product compositions based on the extreme operating condition of an infinite reflux ratio (Hoffman, 1964; Doherty and Caldarola, 1985; Stichlmair et al., 1989). Examples of exceptions are the work of Petlyuk (1978) and the dissertation of Van Dongen (1983), who not only observed that total reflux boundaries can be crossed but analyzed an example of a highly nonideal mixture to estimate the location of the absolute distillation boundaries. However, the objective of Van Dongen’s work also seems to have been to show that these boundaries can be reasonably well approximated by residue curve boundaries, and he did not develop a general procedure to establish the ranges of potential product compositions. Vogelpohl (1964) and Nikolaev et al. (1979) demonstrated that the location of product composition boundaries for continuous distillation is a function of the reflux ratio. In line with this observation, a method is presented here based on physical and geometrical considerations to determine feasible products of single-feed distillation columns with given ternary inlet composition. The approach entails the consideration of the two extreme operating conditions of a continuous distillation process: the condition of total reflux and that of thermodynamically optimum operation. Both are not practical for actual distillation columns because at total reflux no product can
be drawn off and thermodynamically optimum operation would require an infinite number of stages and intermediate condensers and reboilers (e.g., Petlyuk et al., 1965; Koehler et al., 1991). However, the ranges of product compositions achievable in distillative separations of a given feed into two products are confined by the limits for the separations feasible at minimum work consumption (optimum heat exchange distribution) and the limits for the separations achievable at maximum work consumption (total reflux). The method presented in the following to identify feasible products will be illustrated graphically. While, for the determination of product compositions feasible at total reflux, one should in principle use so-called distillation line diagrams, it turns out that the absolute product composition regions are often larger than the regions reachable at total reflux and should be determined using residue curve maps which provide the necessary information on the vapodiquid equilibrium behavior of ternary mixtures. Even in ideal distillation, there are always product compositions that can be obtained from columns operated at finite reflux ratios but not at total reflux. However, the difference between the product compositions attainable at high and at lower reflux is most relevant in azeotropic systems with total reflux boundaries that exhibit significant curvature. In such cases, distillation column sequences can be devised which are feasible only due to the possibility of crossing such a boundary in one column operated at finite reflux ratios. We present a criterion to determine the maximum reflux ratio of an adiabatic column achieving a specific separation across a total reflux boundary and demonstrate where, and by how much, curved total reflux boundaries can be surpassed. These insights are particularly useful if one deals with azeotrope-forming multicomponent mixtures which may become separable in a sequence of distillation columns without using an additional species as entrainer or shifting the location of a residue curve boundary by pressure change. An example is the separation of ethanol and water in presence of a large fraction of methanol (Hunek et al., 1989). If the concentration of the species playing the role of an entrainer is not already high enough in the feed, the cost of separation by distillation depends mainly on the recycle rates required within the overall process. The recycle flow in turn is determined by the extent of crossing of the residue curve boundary. As we will show in the final section, the flows through the columns of the sequence can be minimized using one or more intermediate heat exchangers in the main column to reduce the entrainer flow required to obtain sufficiently pure products in a process with a minimum number of units. As will be discussed in more detail in a subsequent paper (Wahnschafft and Westerberg, 19921,it should be pointed out that the curved residue curve or “distillation” boundaries are not contrived cases. Rather, the curvature simply reflects the selectivity with which components modify each others’ volatilities. Only in the case that there is no selectivity a t all, a total reflux boundary is a straight line. While it is in fact impossible to surpass a boundary which is straight in a continuousdistillation column, the situation is essentially the same if there is no such boundary, as is the case, for example, in a system with a binary minimum-boiling azeotrope and a high-boiling entrainer, but the candidate entrainer does not modify the volatilities of the species to be separated. Basic Concepts Since most distillation-based processes require an additional component, an entrainer, to separate at least two
Ind. Eng. Chem. Res., Vol. 31, No. 10,1992 2347 Reflux
condenser
-bQ
tv,
UD
3
Rectifying section
4
Accumulator DL
d '
section
dividual separation and mixing steps demand that inlet and outlet compositions are on straight lines, and the flow rates obey the so-called "lever rule" (e.g., Hoffman, 1964). A separation by distillation is feasible if the overall mass balance is satisfied and if there is at least one path of calculation accounting for material and energy balances and equilibrium relationships describing the individual stages of a column from the distillate to the bottoms (e.g., Hoffman, 1964). Such calculations are quite straightforward for conventional adiabatic distillation columns (Figure 1)operated at the limiting condition of total reflux which could be realized by condensing all of the vapor leaving the top stage and feeding it back as liquid reflux. Since no product is taken out, the material balance around a column section demands that the vapor rising from a tray must have the same composition as the liquid coming down from the tray above. Moreover, vapor and liquid are assumed to be in equilibrium on each tray. Thus the (liquid) concentration profiles of staged total reflux columns consist of a number of equilibriumsteps (tie lines) connecting the compositions of the liquid on each tray. Figure 2 shows an example of such a composition profile in a ternary diagram, obtained by simulation of a column separating an ideal mixture at almost total reflux (r = 100, N = 8 , =~1). Instead of joining the discrete concentrations by piecewise linear segments, Le., drawing a "tie line curve," total reflux profiles in staged columns have been represented by distillation lines (e.g., Stichlmair et al., 1989),smooth trajectories passing through the points of liquid compositions. However, it should be noted that the trajectories of both tie line curves and distillation lines are in principle dependent on the tray efficiency (Vogelpohl, 1964), which is typically simply assumed to be unity. Only the similar residue curves are uniquely defined in a thermodynamic sense. Residue curves are defined through the condition that, at any given liquid composition a, the vector joining the liquid and the equilibrium vapor in the multicomponent composition state space is tangent to the
. _
3 2
Reboil ratio 1
4
VOIR
-nv
Figure 1. Flows in conventional single-feed distillation column.
irregularly behaved species, the problem studied typically in the literature is that of the distillation of ternary mixtures. Separations of ternary mixtures can be visualized in composition triangles in which the (mole) fractions of any two components form a coordinate system. The fraction of the third component is dependent since the s u m of all fractions must be unity. Mass balances around in-
p = 1 bar
0
Hexane 68.7 "C
'
0.8
0.6
0A
Hexane
Figure 2. Composition profile of a staged distillation column operated close to total reflux.
0.2
96.4
2348 Ind. Eng. Chem. Res., Vol. 31, No. 10, 1992
Intermediate
Heavy
Figure 3. Relation between residue curves, tie line curves, and distillation lines in ternary distillation.
residue curve through a. The trajectories that satisfy this condition can be obtained from integrating dx/ds = x - Y*(x) (1) with arbitrary liquid compositions as initial conditions. Experimentally, residue curves can be obtained as the composition of the liquid remaining in a still when vapor is continuously boiled off in an open simple distillation process (Schreinemakers,1901; Doherty and Perkins, 1978, 1979). At any time the change of the liquid composition with a differential amount of vapor being removed occurs along the direction of the vapor-liquid equilibrium vector. Figure 3 illustrates qualitatively the relation between residue curves and distillation lines with a residue curve and a distillation line (as well as the corresponding tie line profile) that pass through the point a of arbitrarily chosen liquid composition x. The vapor composition y* in equilibrium with x must be on the distillation line and must lie on the tangent to the residue curve in x. Thus, in wide boiling systems and regions of high curvature, total reflux profiles of staged columns are somewhat more bulged than residue curves. However, the difference between residue curves and distillation lines (or tie line curves, for that matter) is normally not very significant. Indeed, Vogelpohl(1964)showed that the set of differential equations describing the simple distillation process is identical to the one for the composition profiles of packed columns operated at total reflux when the mass-transfer efficiency is unity. Van Dongen and Doherty (1985) also demonstrated that the results yielded by a differential column model and by a stage-by-stage calculation are very similar. Thus,for practical purposes it should be legitimate to approximate the composition profiles of total reflux columna with a finite number of stages by residue curves. A collection of trajectories indicating the possible course of residue w e s in a ternary system provides information on the composition dependence of the vaporliquid phase equilibrium behavior and is termed a residue curve map. Irregular systems can exhibit residue curves that are qualitatively different; they start and/or end at different
nodes which are either pure components or azeotropic compositions. Thus the composition space can be divided into different regions by boundaries which limit product compositions achievable in columns operating at total reflux. As an example, Figure 4 shows the residue curve map for the system octane, ethylbenzene, and 2-ethoxyethanol which exhibits two binary minimum boiling azeotropes resulting in a residue curve boundary. It ought to be noted that residue curve boundaries do not necessarily coincide with valley or ridge lines of the boiling temperature surface, Le., with the curves of minimum or maximum ascent, as has long been believed. The idea that such valleys and ridges should limit the separations achievable in continuous distillation processes stemmed from the misconception that the boiling temperature would, for example, have to decrease if the separation was to cross a ridge line. However, composition profiles of distillation columns do not approach valleys or ridges in boiling point surface perpendicularly. Thus there can be paths across a ridge which continuously lead upward. For a more detailed analysis of the relation between the topology of residue curve maps and of the corresponding boiling temperature diagrams, see Vogelpohl (1964) or Van Dongen and Doherty (1984). Product Regions of Total Reflux Columns
A separation is feasible at total reflux if the bottoms and distillate composition are part of the same distillation line or, when residue curves are used to approximatethe total reflux trajectories, part of one residue curve. In ternary systems, the overall mass balance line representing such a separation must be a chord of this composition trajectory. Thus there cannot be any product inside the arc region of the total reflux curve passing through the feed composition if this trajedory has no inflection (Stichlmair et al., 1989). As an example, consider the residue curve map of the octane, ethylbenzene, and 2-ethoxyethanol system shown in Figure 5. According to the method described by Stichlmair et al., a distillation column with the feed (F,)
Ind. Eng. Chem. Rea., Vol. 31, No. 10,1992 2349
.
Octane 1'$5,5.a°C
Figure 4. Faample ternary nptem with a total reflux boundary. Octane 1 2 5 . 8 . ~ ~ . .
0
Feed
A
Distillate
0
Bottom product
0
Minimum
, 2-ethoxy-elhanol 136.2 9:
1
0.8
o.6
127.1'~
0.4
Ethylbenzene
0.2
0
135.1 "c
Figure 5. Examples of product compositionregions for total reflux columas separating mixtures of octane, ethylbenzsne, and Z-ethoxyethmol.
could only provide product concentrations indicated by the shaded areas labeled D,and B,,which is correct if only infink reflux ratios are considered. The two regions are enclosed by a part of a total reflux boundary, by the total reflux curve through the feed (the "feed residue curve'), and by mass balance lines through F1and the neighboring
mixture compositions with the lowest (odane/Z-ethoxy ethanol azeotrope) and highest boiling temperatures (2ethoxyethanol). The situation is somewhat more complicated if the vapor-liquid equilibrium behavior of a ternary system exhibits a nonideality resulting in inflections of the total
2360 Ind.
Eng. Chem. Rea., VoL 31, No.10.1992 C
Produn range bounday determined by the
'Tangent points" on the same residue curves a Feed
, E 1
0.8
0.6
0.4
0.2
0
'A
Figure 6. 'Tangent construction" of product regiona for total reflux columns in system with inflections of residue curves.
reflux trajectories. If the feed cornposition is located on a reaidue curve close to an inflexion point (like F2in Figwe 5), there may be curvea that can correspond to profiles of columns operated at total reflux on either side of the trajectory pawing through the feed concentration. Figure 5 also shows two examples of separations illustrating this fact. The totalreflux curve indicated by the dashed l i e connecting BZband Dzblies below the trajectory passing through the feed, whereas the one indicating the profile for the separation into B, and D, is above it. For a separation to be feasible at an infinite reflux ratio, the maea balance h e must intersect the feed residue curve twice, including the intersection at the feed point. Thus there are disjoint sets of feasible product compositions if the feed residue curve has an inflection. Moreover, the split into B, and Dz. demonstrates that, for nonideal mixtures, product regions are not necessarily limited by the mass balance lines through the compositions with the lowest and highest boiling points reachable with the given feed. Even at total reflux a wider range of intermediate separations may be feasible. Figures 6 and 7 illustrate a method to construct the complete product composition regions for total reflux columns. For the purpose of illustration, the residue curve map in these figures shows a boundary of extreme curvature. In Figure 6, the feed is located on the outside of the arc region. We shall say this feed is on the convex side of the total reflux boundary. The product regions shaded dark are those enclosed by the feed residue curve and the simple distillation boundary and the side of the composition t r i i l e , respectively. The border of the additional, lightly shaded regions can be determined by finding tangents to residue curves which point through the feed composition and marking the intersections of these mass balance lines with the corresponding residue curves on the opposite side of the feed. Again, it should be noted that, for determining product compositions feasible at total
reflux, we are using residue curves as approximationsof distillation lines. Since the only requirements for a separation to be feasible at infiiite reflux ratio are that the mass balance is satisfied and that there is a residue curve connecting the product compositions, there can also be products on either side of a curved distillation boundary if the feed composition is in the arc region of the boundary (Stichlmair, 1991). The product region limitson the convex side of the distillation boundary in Figure 7 were constructed by the enme method as employed for Figure 6, i.e., by searching for residue curves with tangents that point through the feed composition and following these residue curves to the second intersection with their tangents. For reasons to be explained in the following sections, we will call the trajectory of compositions a t which the equilibrium vector passes through the feed composition a "feed pinch point curve." As shown in Figures 6 and 7, in nonideal mixtures there may be more than one such trajectory. For the method described above to determine product regions of total reflux columns, it is generally useful to first locate these feed pinch point trajectories. So far we only dealt with separations feasible a t total reflux. Applying the knowledge of how to determine these product regions, we can already use the information contained in residue curve maps to develop processes to s e p arate ternary mixtures (or binary mixtures with an entrainer, respectively) by means of distillation. Doherty and Caldarola (1985)showed that it is impossible to devise a sequence of distillation columns to separate a mixture if the species lie in different regions divided by a residue curve boundary that does not exhibit a marked curvature. On the other hand, if a boundary is sufficiently curved, separation may be feasible in a sequence of columns even if all columns operate at very high (total) reflux (e.g., Stichlmair et aL, 1989;Laroche et al., 1992),as exemplified by the process separating a mixture (F) of acetone, chlo-
Ind. Eng. Chem. Res., Vol. 31, No. 10,1992 2361 C r
s
Tangent points
*
Corresponding compositions on the same residuecuwes
0
Feed
.
0
Product range boundaly determined by the '"tangentmethod"
,
0
B
A I
0.a
0.4
0.6
0.2
0
+X A
Figure I. Curved distillation boundaries aurpaasable even a t total reflux. Benzene 80.1 OC
p = 1 bar
Acnone 56.5 o c
Figure 8. Exploiting the curvature of a distillation boundary in an azeotropic distillation sequence.
roform, and benzene shown in Figure 8. The azeotropic boundary can be crossed hy recycle hecause the relative azeotropic composition changes in presence of benzene which acta aa entrainer. Since in this example enough
benzene is introducedwith the feed, no recycle is required other than the bottoms of the thud column. Note that, at total reflux, feaaihle producta of one column necessarily lie in the same distillation region. Thus
ID-[; "ot
2352 Ind. Eng.Chem. Res., Vol. 31,No. 10,1992 Reflux
c, condenser
2 3
Reetifylng *ecuon
t
v3
tL' 4
J-p
Accumulator
DI.
Reflux ratio I bID
"-1
"*- t v n ( y * ) L I W Internal reflux ratio I Ln., ID Figure 9. Flows in and out of the rectifying d o n of a simple Column.
the fact that there can be products on either side of the residue curve boundary has nothing to do with the phenomenon mentioned in the Introduction, namely the crossing of such boundaries in finite reflux columns. In order to illustrate how the curvature of a simple distiition boundary can actually be better exploited in a column with lower reflux designed to surpass the curved boundary from the concave side by as much as possible, we first have to consider the difference between the composition profiles of columna operated at infiiite and at f i i t e reflux ratios. Feasibility of a Desired Separation at Arbitrary Reflux As mentioned before, separation by didlation is feasible if there is at least one path of concentrations from the distillate to the bottoms composition which satisfies equilibrium and mass and enthalpy balance constraints (Hoffman, 1964). In this section, a criterion shall be derived to determine the feasibility of a desired separation based on mass balance and equilibrium considerations
only. For the examples presented here, the Wilson model (e.g., Reid et al., 1987)has been used to predict the activity coefficients of the species in nonideal mixtures. Pure component vapor pressures were calculated using a modified Antoine equation (Aspen Tech, 1991)or the Wagner equation (Blass, 1989). Quantitative results for composition profdes were obtained in either rigorous simulations with Aspen Plus (Aspen Tech, 1991) or with a program (Poellmann, 1989)based on the boundary value procedure proposed by Van Dongen and Doherty (1985). Finally, a program originally developed to determine the minimum reflux in nonideal multicomponentdistillation (Koehler et al., 1991) was used to produce the so-called fixed or pinch point curves which will play an important role in the analysis of cornposition profiles and determination of product composition limits. However, it should be pointed out that the latter tools are not required to apply the methods described here to the synthesis of azeotropic distillation processes. In principle, all one needs is a reasonably detailed residue curve map. Assume a column is to produce a distillate D from a given feed F. What could the composition profile in the rectifying section look like that yields this product? A material balance around the top section of the column (Figure 9), including the condenser, at an arbitrary stage n yields V, = , L +D (2) As illustrated in Figure 10,interpreted graphically, this equation means that at any point in the redifyingsection the vapor rising from a tray must be on a straight line between the distillate composition (the difference point) and the composition of the liquid on the next higher stage. How close the vapor composition is to the composition of the downcoming liquid depends on the reflux ratio. At finite reflux ratios, the profile does not quite follow the total reflux curve through the distillate composition but
Pentane 36.1 'C
Residue curve 0
Feed
.
Vapor compositions Liquid compositions
. Tangent points
68.7 "C
'
0.8
04
0.6
+ XH.X.".
02
98.4
"c
10. Possible campsition profdes in the Bections of a conventional singlefeed distillation column leading to two productfI in question.
Ind. Eng. Chem. Res., Vol. 31, No. 10,1992 23153 travels with higher curvature, crossing residue curves from the convex side until it reaches a composition where the tangent to the residue curve points through the difference point D (Figure 10). Since at this composition the downcomingliquid L,-l and the vapor V, rising from below have approached equilibrium, an infinite number of stages would be required for the composition profile to pass on. The driving force for mass transfer between the phases has become infinitesimally small, which is why this point is called a pinch or stationary point (e.g., King, 1980). In order to achieve a larger change of composition within the rectifying section, the energy available for separation has to be increased by changing the reflux ratio. In this case the whole profile starting at the top composition will have a different trajectory, but has to end again in a stationary point where the direction of the material balance line and of the equilibrium vector coincide. In the upper right corner of Figure 10,a schematic of a pinch situation is shown enlarged. The whole range of concentrations that could conceivably be covered by composition profiles of the rectifying section is shaded lightly in Figure 10. This composition region is enclosed by the total reflux curve through product D and the pinch point curve for product D. For the total reflux situation, we have again used the residue curve instead of the distillation line. However, we will see soon that this really makes no difference for the determination of feasible products. The pinch point curve for D can be constructed by finding the points on residue c w e s with their tangents passing through the product composition. The latter trajectory corresponds to the thermodynamically optimum separation path which could theoretically be obtained in the rectifying section of a column producing D with an infinite number of stages and continuous adjustment of the internal flows through condensers at each stage. Such nonadiabatic operation would be required to keep the driving forces for heat and mass transfer at a minimum throughout the column section (e.g., Petlyuk et al., 1965;Koehler et al., 1991). Let us now continue by determining the composition trajectories in the stripping section of an adiabatic column with the fixed distillate composition, a fixed reflux, and a certain number of stages n in the rectifying section (Figure 1). Below the feed stage, we have to account for the introduction of the stream F. One could now write an overall mass balance at an arbitrary stage in the stripping section, and include the feed and the top produd: + F = D + f;, (3) However, using the overall mass balance around the column, eq 3 is more conveniently written as e, = +B (4) Thus, the arguments outlined above apply in a complete analogy to the composition profiles in the stripping section: at any stage, the liquid composition must lie on a straight line between the bottoms difference point and the composition of the vapor rising from the tray below. If one wanta to test whether it will be possible to produce a desired bottoms composition B (which must lie on the overall mass balance line through feed and the assumed distillate), it has to be determined if the composition profiles that could be calculated from the ends of the two column sections can intersect. To answer this question using design calculations, one would have to vary parameters, such as the reflux ratio and the corresponding reboil ratio, until an intersection of the trajectories is found (if it is possible). The portions of the composition trajectories calculated beyond the point of intersection are then
physically meaningless (Van Dongen and Doherty, 1985). Fortunately, there is a simpler (necessary) criterion to determine the feasibility of a specified separation. All possible concentration profiles in the stripping section are confiied by the total reflux curve and the pinch point curve for the bottoms point in question. Although it is obvious that the separation depicted in Figure 10 will be possible since the profile region of the rectifying section already includes the composition B,the composition region for profiles of the stripping section are also indicated in the figure. For a feasible specification of products B and D,the liquid composition profiles of rectifying and stripping section must meet somewhere in the region of overlap. If the intersection occurs at a point corresponding to an integral number of stages of both column sections, the concentration at the intersection coincides with the composition of the liquid on the feed tray (which usually differs from the composition of the feed). While the profiles will generally not meet at exactly such a point, there will be a design that leads to the two desired products B and D as long as the profiles can intersect at all. However, the exact design may require a variation of the reflux, the number of stages in either column section, or the concentration of the trace species in a product. There may also be multiple solutions involving different combinations of the design parameters (Hoffman, 1964). It should be noted that the feasibility criterion demanding an overlap of the profile regions of possible concentration paths is in principle only a necessary, not a sufficient criterion for a separation to be feasible in an adiabatic column. Although we did not find examples where the fact that the overall enthalpy balance was neglected was relevant, there may be cases where it is impossible to produce an intersection of the diabatic profiles despite the overlap of the profile regions emanating from specified distillate and bottoms compositions. However, in such cases the overall energy balance could still be satisfied through strategic placement of intermediate heat exchangers. In view of the requirement that a continuous path of calculation exists from the top to the bottom product concentration, we can draw another intereating conclusion from Figure 10 there is not only a minimum reflux but also a maximum reflux above which it is impossible to design a column that will exactly produce the two products specified because they are not on the same total reflux m e . This observation is not as strange as it might appear at first sight; it is just a consequence of the limited degrees of freedom. If the specification was to obtain products with maximum allowable impurities (which would make more sense than specifying both product compositions exactly, anyway), there is no maximum reflux. Increased reflux would improve separation until both products lie on the same total reflux c w e at infinite reflux. The feasibility criterion presented here is not limited to ideal systems. Only the shape of the total reflux curves and the pinch point curves becomes more complicated, as exemplified in Figure 11. In this example, there is no overlap of the regions of potential composition profiles starting from the two specified products. Thus, thii specific split is not feasible. If the residue curve map of a mixture exhibits a separatrix which is not a straight line, it has been found that certain finite reflux ratios lead to better separation than total reflux if the material balance line of a desired separation is to cross the total reflux boundary from the concave side (e.g., Petlyuk, 1978;Van Dongen, 1983;Laroche et al., 1990). Reverting to the qualitative discussion of the
2354 Ind. Eng. Chem. Res., VoL 31, No. 10,1992
Rectifying
aed
p = i bar
ingent points
, Ethylene glycol 100 'C 1
0.8
0.4
0.8
0.2
197 "C
XW.1.l
Pigun 11. Example of an infeubile product speciiication.
trajectories of composition profiles in rectifying and stripping sections, the phenomenon of crossing of total reflux boundaries is readily explained. As illustrated above, the trajectories of composition profiles at finite reflux are more curved than total reflux profiles, always crossing residue curves from the convex side when moving from the product toward the feed composition. An example is given in Figure E a , which shows the concentration profde of a distillation column whose bottom product is located beyond the residue curve boundary in the acetone/chloroform/benzene system. Figure 12b shows the result of the application of the feasibility criterion to this s p d i c separation. It was mid before that finite reflux composition trajectories are enclosed by total reflux curves through the assumed product composition and by the corresponding pinch point curves. However, as illustrated in Figure 12b, profdes emanating from a product situated just beyond a total reflux boundary may move toward the distillation region in which the feed lies or may remain in the neighboring region if the reflux is too high. In such a case there is a disjoint branch of pinch points located in the same region as the product composition B. This curve describes stationary points of stripping section profiles starting from B that are attainable at high values of the reflux ratio only (Nikolaev et al., 1979; Van Dongen, 1983). Thus the previous statement has to be generalized: all possible concentration profdes leading to a certain product composition are enclosed by the total reflux curve through the product composition and by the branches of product pinch point curves which can correspond to stationary points of fmite reflux profdes. A pinch point curve may have more than one branch if the product composition is located on a residue curve with an inflection such that there is another tangent to this residue curve which points through the product. If a product in question is located beyond the convex side of a residue curve boundary and the corresponding
pinch point curve has two branches, there must be a maximum value of the energy provided to the column, above which the separation is not feasible. If the reflux (or reboil) ratio is too high, the composition profile originating from the product cannot traverse into the distillation region of the feed any more. The composition profde calculated starting from the hypothetical product composition will always terminate at a stationary point in the wrong simple distillation region if more than the amount of energy is provided which is needed for the composition profile to reach the disjoint branch of the pinch point curve. Since protiles in adiabatic columnstend to follow closely the total reflux curves through the product compositions and then bend sharply, the disjoint branch of the pinch point curve must start at (or at least very close to) the residue curve which passes through the product composition in question (point a in Figure 12b). Thus,the maximum reflux or reboil ratio can be determined without trial and error by tracking the product residue c w e to locate the composition x of this pinch point. Because at this point equilibrium is reached (like at any pinch point), the composition y* of the vapor can be established in a simple flash calculation. Depending on whether it is a distillate or a bottoms product which is located beyond a residue curve boundary, a component mass balance is written for the rectifying or the stripping section. For the rectifying section (Figure 9) we obtain V&* = &,Xi
+ DXi,
(5)
Using the overall mass balance, eq 5 becomes
(L,,
+ D)yi* = L,-,zi + DziD
(6)
Dividing by D and rearranging yields
L,,
r m - - - =D-
xia
- Yi*
yi* - 2 i
(7)
Ind. Eng. Chem. Res., Vol. 31, No. 10,1992 2365 Benzene 80.1 o c -
0
0
Acetone 1
56.5OC
0.8
0.6
*
0.4
61.2%
0.2
XA~u~ne
Benzene 80.1 O c
0
Acetone SSS~C
1
0.8
OB
*
04
0.2
O
612%
XAcstons
Figure 12. (a) Example of the a w i n g of a total reflux boundary achieved in a column operated at f ~ t reflux e ratio. (b) Pinch point can bifurcate at a certain reflux ratio in nonideal mixturea.
CUN-
The index D denotes the fraction of component i in the distillate product; the other mole fractions are thcme at the pinch point and the equlibrium vapor composition. Note that, at constant molal overflow, the ratio of the flow of liquid (Ln.J to that of the product equals exactly the extemal reflux ratio L,/D. In cases where constant molal overtlow is not a good aeaumption, it is always possible to
obtain the maximum reflux ratio through an enthalpy balance around the column section up to the pinch point. Using the analogous expression to eq 7 derived from the stripping section, excellent was obtained between the theoretical value of the maximum reboil, s and the maximum value at which the stripping profile calculated starting at the bottoms product of Figure 12b still txavema
2356 Ind. Eng. Chem. Res., Vol. 31, No. 10, 1992
into the left distillation region. It should be noted that the fact that there can be multiple branches of stationary points does not imply that the column operation is unstable. It simply means that a certain separation can only be accomplished within a range of reflux ratios. In our example, incrsasing the reboil ratio s of an actual column beyond the value, s of about 10 would force the bottoms product to lie closer to the residue curve boundary, and hence decrease the extent of separation. In summary, the composition profiles for each column section are constrained by two distinct trajectories, or operating conditions, respectively. The first condition is that of total reflux, at which composition profiles closely follow the trajectories of residue curves. From the thermodynamical point of view, total reflux is the worst way of operating a column since the distance between operating and equilibrium lines is maximized (and actually no real separation effect is produced). The other extreme is the thermodynamically optimum distillation, for which parts of the composition profiles correspond to the pinch point curves discussed in this section. This operation is also inherently impractical. In order to realize a composition profile along which the driving force for mass transfer between the vapor and the liquid phase is always infinitesimally small, an infinite number of stages and of intermediate reboilers and condensers would be required. To be accurate, it should be noted that the distillation process could be completely reversible only if the tie line at the feed composition points in the direction of the mass balance line between the desired products, which means that the pinch point trajectories intersect at the feed composition. Otherwise, it is inevitable that mixing of streams of different compositions occurs at the feed tray (e.g., Petlyuk et al., 1965). We now have a criterion to assess whether or not a desired separation is feasible in a conventional column, which can help avoid unsuccessful design attempts. The composition profiles of the rectifying and the stripping section, determined by starting at each column end, must intersect. Thus, if the profile regions emanating from the desired product compositions overlap, one knows the product specifications are in principle feasible without having to determine the design parameters, i.e., a suitable number of stages, feed location, reflux, and product flow rates. Based on the qualitative analysis of the course of composition profiles in adiabatic distillation columns, it also was explained why curved total reflux boundaries can be crossed in a continuous distillation process, and a criterion was derived to determine the maximum reflux or reboil ratios for such separations.
Product Composition Regions for Continuous Distillation Let us now apply the feasibility criterion presented in the previous section to establish the regions of feasible top and bottom product compositions for a given feed, starting again with an example of an ideal mixture (Figure 10). Instead of fixing both product compositions, we might ask what are feasible bottom products for the fixed distillate composition D? All posaible bottom product compositions have to satisfy the overall mass balance, i.e., have to lie on the line through the fixed distillate and the feed between the composition of the feed and the lower binary axis of the diagram (Figure 10). AB discussed before, one can state immediately that all compositions on the section of this line that is in the lightly shaded area must be feasible bottom products since they can be reached directly by the r e c t w section profile. Compositions “below”the
total reflux curve through D are also reachable (at finite reflux) because the pinch point curves through such bottom products still bend toward the light species and hence resemble the pinch point curve for B. However, there is no feasible counterproduct between the feed and the point labeled Bmh,which marks the intersection of the pinch point curve for D with the mass balance line. Compositions between the feed and B- cannot be reached by the rectifying profile, and the regions covered by the stripping profilea starting from any potential bottom product therein cannot overlap with the profile region of the rectifying section. We can also ask the reverse question, namely: what are feasible distillates for the fixed bottom product B? All compositions on the mass balance line between the feed and the binary axis of light and intermediate component will lead to an overlap of the composition profile regions. Thus, the only section of the mass balance line shown in Figure 10 where no product can be situated lies between the feed and the pinch point B- This point is a possible stationary point not only for the rectifying profile through D but for any distillate composition on the mass balance line in question, up to the feed point itself. Repeating the considerations for products on a mass balance line with a different slope, one realizes that the only section of the material balance line where there is no feasible product is between the feed and the pinch point at which the product pinch point curves intersect. At this point, the tangent to the residue curve has to coincide with the direction of the overall material balance line through the feed composition. Thus we can directly determine the “feed pinch point curve” to be all compositions at which the tangent to the residue curve points through the feed composition. The compositiona along this trajectory can satisfy the material balance around either column section simultaneously with the condition that the liquid entering a tray is in equilibrium with the vapor leaving the tray. A separation is feasible if and only if the mass balance line connecting the specified products intersects this curve twice, including the intersection at the feed point itself. Hence all possible orientations of mass balance lines are found by following the trajectory of the feed pinch point curve in both directions. For the example of an ideal mixture, the product composition regions for which this criterion is satisfied are shaded in Figure 13. The lightly shaded regions are those in which no product can be obtained from columns operated at total reflux. According to the above analysis, in the case of an ideal mixture, all splits realizable in a single-feed column can theoretically be carried out in distillative separations with composition profiles following pinch point curves in parts of the columns. However, as we will see now, this observation does not generally hold for nonideal systems. Thus it can be necessary to consider both limiting conditions, namely total reflux and thermodynamically optimum operation, to determine the absolute product composition limits. If the residue curve map of a mixture exhibits a separatrix which is not a straight line, and the feed is situated on the convex side of this boundary, the product composition region cannot extend into the neighboring distillation region. Whenever the material balance line of a separation is such that a curved total reflux boundary is approached from the convex side, low reflux ratios cause composition profiles originating from a potential product close to the boundary to move in the wrong direction. Thus the product compositions along convex sides of residue curve boundaries can be reached in columns with high reflux
Ind. Eng. Chem. Res., Vol. 31,No. 10,1992 2367 Pentane 36.1 .
.
'c
D
, Hemane 0.8
0.6
04 f-
XHeiane
02
98.4%
Figare 13. 'Absoluts" product mmpositiou regions of an example system with ideal physical property behavior. Product coucantratiomare limitad by the 'feed pinch point curve" rather than by a total reflux trajectory though the feed composition.
only, and the limiting condition is total reflux. If, on the other hand, the material balance line of a desired separation is to cross the total reflux boundary from the concaue side, we have Been that fmite reflux can lead to better separations than total reflux. While the phenomenon of crossing of residue curve boundaries and of multiple branches of product pinch point curves has been discussed repeatedly in the literature, e.g., by Nikclaev et al. (1979)and in the dissertation of Van Dongen (1983),no general conclusions concerning the maximum separations feasible at fmite reflux have been drawn. Using the feasibility criterion presented above, it is now possible to derive the conditions describing the product composition boundaries. The absolute limit for the location of a product in a neighboring simple distillation region is given by the compositions whose pinch point trajectories do not reach the distillation region of the feed because then all compositoin profiles emanating from such a product remain in the wrong distillation region. Hence, the product composition limit for the case of wssing of a simple distillation boundary from the concave to the convex side correspond to the liiita realizable in thermodynamically optimum distillation. The product pinch point curve can only traverse into the simple distiition region of the feed and the other product if it does not arrive at an inflection of the residue curves in ita region before reaching the residue curve boundary. Thus,feasible product compositions are those that do not lie on a tangent to a residue curue at its point of inflection. Figure 14 shows the pinch point curvea belonging to two hypothetical product compositions located on the convex side of a residue curve boundary. While D, would be reachable in a column with fmite reflux, the pinch point curve for product D2reaches an inflection point of a residue curve, after which it turns toward the stable node of the wrong distillation e o n . Thus all p i b l e composition
trajectories originatingfrom D, remain in this region, too. A simpler, necessary, but not sufficient condition limiting the location of produds beyond a residue curve boundary is that there must be a tangent to the boundary which points through the product composition. If not, there is no way for the corresponding product pinch point trajectory to move toward the distillation region of the feed. In order to construct the product compositionlimit along the convex side of a residue curve boundary for a iixed feed composition, one has to apply the inflection point criterion repeatedly, generating an envelope for the compositions whose pinch point curves completely remain in one distillation region. This procedure is illustrated in Figure 15. The other distinct curve limiting the product compositions in this figure is the feed pinch point curve, r e p resenting the compositions in which the tangents to residue curves point through the feed. This curve has the same significance in a nonideal mixture as in the ideal case discussed before: it can be used to determine all possible orientations of mass balance lines. Moreover, the composition profiles leading to desired producta can intersect only if the overall material balance line intersects with the feed pinch point line at least twice. Figure 16 shows, as an example for an actual problem, the product composition regions for a mixture of amtone, chloroform, and toluene, a ternary system with a residue curve boundary extending between the maximum-boiling azeotrope and the heaviest species, toluene. The product composition points obtained by rigorous simulations of widely different designs performed with the simulation package Aspen Plus (Aspen Tech, 1991) cover the theoretically predicted regions, in this case the region between the feed pinch point curve and the inflection p i n t tangent envelope on the convex side of the residue curve boundary. The column composition profile shown for one particular design demonstrates that separation acrm a residue curve boundary can actually reach the side of the composition
2358 Ind. Eng. Chem. Rea., Vol. 31, No. 10,1992
1
0.8
0.6
0.4
0.2
0
+XA
Pigum 14. Role of infleetion points in the determination of abaolute distillation boundaries. C
1
0.8
0.4
0.5
f'XA
F b m 15. Product composition boundary, an envelope of inflection point tangents.
0.2
0
Ind. Eng. Chem. Res., Vol. 31, No.10,1992 2369 Toluene T -110.80C b-L
0
-
Acetone T= , 56.5 OC
Figure 16. Product composition regions for an acetone/chloroform/toluene mixture. From Blania (1992).
diagram, as in this case a complete separation between the lightest and the heaviest species, acetone and toluene, is realized. Improving Separations by Intermediate Heat Exchange It was investigated here under what conditions finite reflux ratios can lead to better separation than total reflux in single-feed columns and how the absolute distillation boundaries can be determined. To demonstrate consequences of these theoretical considerations for synthesis and design of azeotropic distillation processes, let us consider the problem of the separation of the mixture of acetone, chloroform, and benzene shown in Figure 8. Because the residue curve boundary can be surpassed in a column operated at finite reflux, it is possible to recover all three components in essentially pure form in a process using two distillation columns only. The process requires an increase of the concentration of benzene in a first column through a recycle 80 that acetone can be separated almoet completely from benzene and chloroform. In this process, benzene acta as a heavy entrainer. The economics of this scheme depend on the recycle flow required, i.e., on the minimum concentration of benzene needed for a sufficiently high recovery of acetone in the distillate of the f i t column. In general, since the enuelope of inflection point tangents represents the product cornposition limit for any separation with one product on the concave side of the boundary, it dictates the theoretical minimum entrainer requirement for a specified separation across the total reflux boundary. Figure 17 presents results of simulations used to investigate the effect of the reflux ratio and of the distribution of the energy supplied to a column by means of intermediate heat exchangers on the extent of boundary croeeing. The composition profiles shown in these figures were determined in rigorous simulations using the
RADFRAC model of Aspen Plus (Aspen Tech, 1991). The vapor-liquid equilibria were calculated according to the Wilson model, which generally seems to predict lower curvatures of residue curve boundaries than other important methods, such as UNIFAC. Thus, one should expect that crossing of a curved simple distillation boundary is indeed poesible if it is predicted by simulations based on the Wilson model. A final assessment of the extent of boundary crossing, however, will require finetuning of the vapor-liquid equilibrium data correlations, just like the design of a conventional extractive distillation column does. Figure 17a demonstrates that, even with the feed composition M entering column 1,the bottoms product of the second column would contain about 6% acetone if the total reflux boundary could not be crossed in the f i t column. Varying the reflux ratio of an adiabatic column with 50 theoretical stages to determine the maximum separation for the feed composition M verified that a clearly better separation is possible at f i i t e reflux ratios. The composition profile shown in Figure 17a corresponds to the column design providing the best separation obtained in this way, Le., the one with the lowest fraction of acetone in the bottoms product of the first column. However, even after this optimization the concentration of benzene in F’ is still too low to obtain sufficiently pure chloroform (>99%) as the distillate of the second column. As discussed before, thermodynamically optimum sep aration guarantees that one reaches the maximum separation if a residue curve boundary is crossed from the concave side. Thus, instead of trying to improve the separation further through lowering the reflux and increasing the number of stages, an intermediate heat exchanger, in this case a reboiler, can be used to approach the thermodynamicallyoptimum separation path in the stripping section. The intermediate reboiler allow the energy supplied to the column to be distributed in a way
2360 Ind. Eng. Chem. Res., Vol. 31, No. 10,1992 Benzene 80.1 %
N N,
= 50 = 25
r = 8 D:F= 0.2
Total Reboil Duty = 0.54E10 watts ov
+
o Feed
p I1 bar
tal reflux In col. 1
0
Acetone 0.8
0.6
56.5 "C
+
0.4
0.2
Acetone
61.2 'C
Benzene 80.1 OC
= 50 N, = 25 D:F = 0.2 N
Total Reboll Duty = 0.65 E10 Watts
56.5 "C
'
0.8
0.6
0.4
Acetone
0.2
61.2 OC
Figure 17. (a) Composition profile croseing a total reflux boundary obtained in an adiabatic column. (b) Intermediate heat exchangere can improve separations in single-feed azeotropic distillation columns.
that the composition profile in the stripping section rapidly movea toward the left distillation region because of the low reboil ratio. The result of a rigorous simulation run demonstrating this behavior is shown in Figure 17b. Since some of the energy is supplied at a higher stage before the profile ends at a stationary point, the separation
path can continue without. reaching points of inflection of the residue curves. Although the reflux ratio and the total reboil duty of the column with intermediate heat exchanger is about 20% higher than for the column that achieved the best separation under adiabatic conditions, the use of the reboiler not only has the typical advantages
Ind. Eng. Chem. Res., Vol. 31, No. 10,1992 2361 of using intermediate heat exchange, namely a reduction of thermodynamic losses and increased heat integration opportunith, but it also improves the extent of separation, in this case mostly in the rectifyingsection. As a net result, the overall benzene recycle rate can be reduced, too, allowing for smaller column diameters and lower energy requirementa. The use of intermediate heat exchangers in a single-feed distillation column to maximize separation across a total reflux boundary accounts for the trade-off between the "normal" effect of improved separation at higher reflux and the positive effect of approaching a thermodynamically optimum operation in the column section in which the concentration profile actually traverses from one simple distillation region to the other. In the example problem analyzed here, the intermediate reboiler mostly improves the separation in the rectifyingsection due to the increased reflux. This usage of intermediate heat exchangers has become subject of a patent application (Wahnschafft and Westerberg, 1991). It can be considered counterintuitive, since intermediate heat exchangers are conventionally installed to remedy thermodynamic losses, i.e., where the composition changes are most drastic because of large driving forces between material balance line and equilibrium, but are not thought to have anything to do with the extent of separation possible. Although no economic analysis was carried out here, it is conceivable that the lower entrainer ratios achievable through the use of intermediate heat exchangers increase the attractiveness of certain azeotropic distillation process alternatives, especially when it is possible to employ species present in a feed stream more economically as separating agents. Since installation of intermediate heat exchangers is one of the simplest retrofitting options, even existing processes may be candidates for improvement by the technique described.
Summary and Conclusions In this paper we presented a method to determine the product composition regions of conventional single-feed distillation columns separating ideal and highly nonideal, azeotropic ternary mixtures. This method is based on a feasibility criterion which is applicable regardless of the physical property behavior. Our approach is to consider simultaneously the two extreme operating conditions of such columns: the condition of total reflux and that of thermodynamically optimum separation. It is shown where the consideration of total reflux alone is insufficient, and that even the product ranges of total reflux columns have not been described accurately before for certain types of nonideal mixtures. The difference between the product compositions attainable in continuous distillation columns with total reflux and with finite reflux ratios is particularly relevant in systems with simple distillation boundaries of marked curvature, for which we showed where and by how much such boundaries can be crossed in a column operated at finite reflux ratios. We also derived a criterion to determine the maximum reflux or reboil ratio of such columns and showed how the separation in a column with a fixed number of stages can be improved by means of intermediate heat exchangers. The paper at hand is the first of a series of papers which address the problem of the synthesis of distillation-based separation systems for azeotropic mixtures. In subsequent papers (Wahnschafft and Westerberg, 1992; Wahnschafft et al., 1992; see also Wahnschafft, 1992a,b),the analysis presented here will be generalized to columns with multiple feeds and consequences for the selection of entrainers for homogeneous azeotropic distillation will be discussed. Finally, a procedure for the systematic synthesis of com-
plex separation schemes will be presented which makes use of the information on separation feasibility for each step.
Acknowledgment We thank the Engineering Design Research Center (ERDC), 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 deutachen Vokes" are also acknowledged. Furthermore, thanks are due to the German National Research Agency (DFG, Deutache Forschungsgemeinschaft) for financing the distillation design project No. 82/21-1 and for providing funds for two research visita of J.K.to the EDRC. Finally, we thank Aspen Technology Inc. for providing us with the Aspen Plus simulation program.
Nomenclature B = bottom product flow rate or composition B = bottom product composition D = distillate product flow rate D = distillate product composition F = feed flow rate F = feed composition L = liquid flow rate r = reflux ratio Lo/D s = reboil ratio Vo/B V = vapor flow rate x = liquid composition vector (mole fraction) y = vapor composition vector (mole fraction) y* = vapor equilibrium composition (mole fraction) Literature Cited Aspen Tech. Aspen Plus User Guide to Release 8.3. Aspen Technology Inc., 251 Vassar St., Cambridge, MA 02139,1991. Blania, P. Produktbereiche der azeotropen Mehrkomponentenrektifikation mit einem Zulauf. Diploma Thesis, Technical University of Munich, Germany, 1992). Blass, E. Entwicklung verfahrenstechnischer Prozesse. Salle und Sauerlbder; Frankfurt, 1989. Doherty, M. F., Perkins, J. D. On the Dynamics of Distillation Processes-I (The Simple Distillation of Multicomponent NonReacting Homogeneous Liquid Mixturea). Chem. Eng. Sci. 1978, 33, 281-301.
Doherty, M. F.; Perkins, J. D. On the Dynamics of Distillation Proceeses-111 (The Topological Structure of Ternary Residue Curve Maps). Chem. Eng. Sci. 1979,34,1401-1414. Doherty, M. F.; Caldarola, G. A. Design and Synthesis of Homogeneous Azeotropic Distillations. 3. The Sequencing of Columns for Azeotropic and Extractive Distillations. Znd. Eng. Chem. Fundam. 1986,24,474-485. Fidkowski, Z. T.; Malone, M. F.; Doherty, M. F. Nonideal Multicomponent Distillation: Use of Bifurcation Theory for Design. AIChE J. 1991,37 (12), 1761-1779. Hoffman, E. J. Azeotropic and Extractiue Dietillation; Wiley Interscience: New York, 1964; Chapter V. Horsley, L. H. Azeotropic Data ZZfi Advances in Chemical Series 116; American Chemical Society Washington, DC, 1973. Hunek, J; Gal, 5.;Posel, F.; Gavic, P. Separation of an Azeotropic Mixture by Reverse Extractive Distillation. AIChE J. 1 9 8 9 , s (7), 1207-1210.
Julka, V.; Doherty, M. F. Geometric Behavior and Minimum Flows for Nonideal Multicomponent Distillation. Chem. Eng. Sci. 1990, 45, 1801-1822.
King, C. J. Separation Processes, 2nd ed.;McGraw-Hill: New York, 1980.
Knight, J. R.; Doherty, M. F. Optimal Design and Synthesis of He mogeneous Azeotropic Distillation Sequences. Znd. Eng. Chem. Res. 1989,28,564-572. Koehler, J. W.; Aguirre, P.; Blass, E. Minimum Reflux Calculations for Nonideal Mixtures Using the Reversible Distillation Model. Chem. Eng. Sci. 1991, in press.
Ind. Eng. Chem. Res. 1992,31,2362-2369
2362
Laroche, L.; Bekiaris, N.; Andersen, H. W.; Morari, M. The Curious Behavior of Homogeneous Azeotropic Distillation-Implications for Entrainer Selection. AIChE J. 1990,in press. Laroche, L.; Bekiaris, N.; Andersen, H. W.; Morairi, M. Homogeneous Azeotropic Distillation: Separability and Flowsheet Synthesis. Znd. Eng. Chem. Res. 1992,31, 2190-2209. Levy,S.G.; Van Dongen, D. B.; Doherty, M. F. Design and Synthesis of Homogeneous Azeotropic Distillations. 2. Minimum Reflux Calculations for Nonideal and Azeotropic Columns. Znd. Eng. Chem. Fundam. 1985,24,463-473. Malesineki, W. Azeotropy and Other Theoretical Problems of Vapour-liquid Equilibrium; Interscience: New York, 1965. Nikolaev, N. 5.;Kiva, V. N.; Mozzhukhin, A. S.; Serafiiov, L. A,; Goloborodkin, S. I. Utilization of Functional Operators for Determining the Regions of Continuous Rectification. Theor. Found. Chem. Eng. 1979,13,418-423. Petlyuk, F. B. Rectification of Zeotropic, Azeotropic, and Continuous Mixtures in Simple and Complex Infinite Columns with Finite Reflux. Theor. Found. Chem. Eng. 1978,12,671-678. Petlyuk, F. B.; Platonov, V. M.; Slavinsii, D. M. Thermodynamically Optimal Method for Separating Multicomponent Mixtures. Znt. Chem. Eng. 1966,5(2),309-317. Poellmann, P. Untersuchung dea Trennverlaufs bei der Rektiihtion realer Mehrstoffgemieche. Diploma Thesis, Technical University of Munich, Germany, 1989. Reid, R. C.; Prausnitz, J. M.; Poling, B.E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. Schreinemakers, F. A. H. 2.Phys. Chem. 1901,36,257. Stichlmair, J. Personal communication, 1991. Stichlmair, J.; Fair, J. R.; Bravo, J. L. Separation of Azeotropic Mixtures via Enhanced Distillation. Chem. Eng. h o g . 1989,85 (l),63-69. Van Dongen, D. B. Distillation of Azeotropic Mixtures. The Application of SimplaDistillation Theory to the Design of Continuous Processes. Ph.D. Dissertation, University of Massachusetts, Amherst, MA, 1983. Van Dongen, D. B., Doherty, M. F. On the Dynamics of Distillation
Processes-V (The Topology of the Boiling Temperature Surface and its Relation to Azeotropic Distillation). Chem. Eng. Sci. 1984, 39,883-892. Van Dongen, D. B.; Doherty, M. F. Design and Synthesis of Homogeneous Azeotropic Distillations. 1. Problem Formulation for a Single Column. Znd. Eng. Chem. Fundam. 1986,24, 454-463. Vogelpohl, A. Rektifikation von Dreietoffgemischen. Teil 1: Rektifikation als Stoffaustauschvorgang und Rektifikationslinien idealer Gemische. Chem.-Zng.-Tech. 1964,36 (lo), 1033-1045. Wahnschafft, 0. M. "Syntheaisof Separation System for Azeotropic Mixtures with an Emphasis on Distillation-Based Methods; Research Report, Engineering Design Research Center, Carnegie Mellon University: Pittsburgh, P A 15213,1992a. Wahnschafft, 0.M. Synthese von Trennprozessen zur Zerlegung azeotroper Vielstoffgemhhe unter beaonderer Berueckeichtigung der Rektifikation. Ph.D. Dissertation, Department of Chemical Engineering, Technical University of Munich, Germany, 1992b. Wahnschafft, 0. M.; Westerberg, A. W. Improving the Economics of Azeotropic Distillation Processes through Intermediate Heat Exchange. Document prepared for US. patent application, Carnegie Mellon University, Pittsburgh, 1991. Wahnschafft, 0. M.; Westerberg, A. W. The Product Composition Regions of Azeotropic Distillation Columns. 11. Separability in Multi-Feed Columns and Entrainer Selection. Submitted for publication in Znd. Eng. Chem. Res. 1992. Wahnschafft, 0. M.; Jurain, T. P.; Westerberg, A. W. SPLIT a Separation Process Designer. Comput. Chem. Eng. 1991,15 (8), 565-581. Wahnechafft, 0.M.; LeRudulier, J. P.; Westerberg,A. W. A Problem DecompositionApproach for the Syntheais of Complex Separation Processes. Submitted for publication in Znd. Eng. Chem. Res. 1992. Received for review August 9,1991 Revised manuscript received November 1,1991 Accepted July 16, 1992
GENERALRESEARCH Prediction of Enthalpies of Formation for Ionic Compounds C. Dianne Ratkey and B. Keith Harrison* Chemical Engineering Department, University of South Alabama, Mobile, Alabama 36688
An improved generalized correlation for the prediction of enthalpies of formation of ionic compounds was developed. Four correlations were examined: (1)the Wilcox/Bromley/Brandenbug method (WBB), (2)an empirical model based on Hisham and Benson's method, (3) the Kapustinskii-based method (KBM), and (4) a modified lattice energy method (MLE). The WBB method was not modified by the authors; however, the other three represent either generalizations of specialized methods or, in the last case, a modified lattice energy method. The MLE method exhibited the highest degree of accuracy of the four methods tested with an average absolute error of 23.8 kJ/mol for a database of 806 compounds. This represents about a 50% improvement to the WBB method while using fewer parameters. Additional inorganic compounds were examined to test the predictive abilities of the modified lattice energy method. The enthalpies of formation for these compounds were predicted with an average absolute error of 31.4 kJ/mol. Introduction Chemical engineers have become accustomed to routinely and somewh& confidently predicting themochemical properties for organic chemicals when experimental
* Author to whom correspondence should be addressed.
data are not available. In contrast to the situation for organic c h d & COm~ativelY work been done in develop@ generalized predictive methods for them* chemicalproprties for inorganic molecdea. For instancey current correlations for ionic heats of formation suffer from a lack of generality (being restricted to a small number of compounds) or from a lack of accuracy. When the Am-
08sS-5~5/92/2631-2362$03.00/0 0 1992 American Chemical Society
