Mixtures Containing Inerts - American Chemical Society

Ind. Eng. Chem. Res. 1996, 35, 4537-4549

4537

Some Aspects in the Design of Multicomponent Reactive Distillation Columns with a Reacting Core: Mixtures Containing Inerts Jose´ Espinosa,† Pio Aguirre,* and Gustavo Pe´ rez INGAR, Instituto de Desarrollo y Disen˜ o, Avellaneda 3657, 3000 Santa Fe, Argentina

Some aspects related to the design of reactive distillation columns with a reacting core are addressed in this paper. A set of transformed composition variables proposed in a previous paper is used to develop both the design equations and the reactive residue curve maps for quaternary reacting mixtures. Also, conventional residue curve maps are employed to achieve a better physical and conceptual insight into the relationships between the different constitutive parts of a column with a reacting core. Limitations in product specifications of entirely reactive distillation columns are explained by means of reactive residue curve maps, and a new feasibility criterion of a given separation for reactive columns with a reacting core is also developed on the basis of the two extreme operation conditions of a column. Finally, the behavior of column profiles for both high-conversion and low-conversion cases is analyzed and optimal product specifications are suggested to obtain high purity products. As we concluded in previous works, the inerts have a central role in both the design and synthesis of a reactive distillation column. All the concepts are applied to azeotrope-forming mixtures. I. Introduction The design and synthesis of reactive distillation columns are the subjects of several works (Barbosa and Doherty, 1988a-c; Espinosa et al., 1993) for mixtures in which all species present in the feed stream participate in a single chemical reaction. Recent papers treat the relevant cases of feed streams to reactive columns containing nonreactive species (Ung and Doherty, 1995a; Espinosa et al., 1995a,b) and multiple chemical reactions (Ung and Doherty, 1995a). All the mentioned contributions employ transformed composition variables similar to those originally proposed by Barbosa and Doherty (1988b). By using the transformed model, problems as the design and the prediction of the products attainable for a given feed to a reactive column are easily performed in a manner similar to conventional distillation. Furthermore, the simultaneous phase-reaction equilibrium solved via transformed compositions permits the identification of reactive azeotropes (Barbosa and Doherty, 1988a,b) and, at the same time, the visualization of equilibrium states in a lower dimensional coordinates system. These works apply well when the equilibrium reaction occurs at all trays of the column. For this case, a parametric analysis of the composite phase-reaction equilibrium (Ung and Doherty, 1995a; Espinosa et al., 1995a) shows in general that it is impossible to obtain the pure reaction products because of the assumption that the reaction reaches equilibrium instantaneously. For systems where the simultaneous phase-reaction equilibrium permits the obtention of high purity products in a completely reactive column, small disturbances applied to the system during operation can result in a considerable diminution of the product purity (Espinosa et al., 1994). On the other hand, in a column with a reacting core it is possible to obtain high purity products because pure

rectifying and stripping are at both sides of the reactive part and, hence, the combination of the reaction-mass transfer process in a single apparatus produces a situation such that the thermodynamic constrains typical of each individual process can be eliminated (Serafimov et al., 1993). In addition, economic savings are possible with this configuration. The purpose of this paper is to delineate the most important characteristics of the design of columns with a reacting core whose feed stream contains nonreactive species. Also, a new criterion for determining the feasibility of a desired separation is given. II. Transformed Field and Residue Curve Maps for Reactive Systems Describing reactive distillation using transformed variables makes inlet and outlet product compositions fall on a straight line containing the feed composition. Therefore, the flow rates in the transformed field obey the lever rule. In this work, we use the following liquid and vapor composition variables (j ) 1, nc - 1; j * k) proposed in our previous paper (Espinosa et al., 1995b); however, those proposed by Ung and Doherty (1995a) can be useful, too:

Xj )

νkxj - νjxk νk - νtxk

XI )

νkxI νk - νtxk

(1)

Yj )

νkyj - νjyk νk - νtyk

YI )

νkyI νk - νtyk

(2)

where I is the index of the nonreactive species. The main advantages in using the transformed model are the following: (i) Easy identification of conventional and reactive azeotropes (Barbosa and Doherty, 1988a,b) by means of the following equalities:

Xj ) Yj * To whom correspondence should be addressed. † Next address (April 1997): Chemical Engineering Department, Technical University of Munich, Arcisstrasse 21, 81241 Munich, Germany.

S0888-5885(96)00355-7 CCC: $12.00

XI ) YI

(3)

(ii) Equilibrium visualization in a lower dimensional coordinate space (Espinosa et al., 1993; Ung and Doherty, 1995a). For example, the simultaneous phase© 1996 American Chemical Society

4538 Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996

reaction equilibrium of a quaternary reactive mixture can be represented in a three-dimensional space with two transformed compositions and the temperature as coordinates. (iii) Instantaneous mapping between “transformed” and “natural” variables when the simultaneous phasereaction equilibrium is solved using transformed compositions (Espinosa et al., 1994; Espinosa et al., 1995a,b). (iv) Derivation of a simple relationship between the external reflux and the external reboil ratios, and reduction of the order of the equation system (Barbosa and Doherty, 1988c; Espinosa et al., 1995a). In the same way as in conventional distillation, the synthesis of a reaction-mass transfer process in a single apparatus can be done with the aid of reactive residue curve maps. These maps will serve for determining some of the limitations of designing an entirely reactive distillation column. We present here the results obtained in Espinosa et al. (1995a,b) for two quaternary reacting systems. The residue curve maps are the result of the integration of the set of autonomous ordinary differential equations that model the dynamics of reactive simple distillation. They are trajectories in an n-dimensional space (where n is the number of differential equations) called “phase space”. Each trajectory is parametrized in terms of the transformed time variable. By using the existence and uniqueness theorem of differential equations, any initial condition X0 gives rise to a unique trajectory through X0. Moreover, as a consequence of such property, at every point X on the trajectory, the autonomous differential equation system assigns a unique tangent vector X-Y. There exist special degenerate trajectories in phase space that are just points because all the transformed compositions satisfy (j ) 1, nc; j * k):

Xj ) Yj

(4)

Such critical (singular) points correspond to reactive azeotropes (Barbosa and Doherty, 1988a,b; Doherty and Buzad, 1992), pure species, and nonreactive azeotropes. However, it is important to note that only some of the pure components and conventional azeotropes belong to phase space when an equilibrium chemical reaction occurs. Figure 1 shows the residue curve maps in the transformed field for an ideal mixture (γj ) 1) forming a reactive azeotrope and suffering a reaction of the type (Espinosa et al., 1995b)

A+BaC

Figure 1. Ideal reacting mixture showing a reactive azeotrope: residue curve maps.

(5)

The edges of the composition triangle in Figure 1 represent (i) the “pure reacting system, xI ) 0”, and (ii) the nonreactive mixtures between any of the reagents and the inert I (more volatile component in the example). This system shows a unique distillation region at total reflux since all the trajectories start at the nonreactive component vertex (an unstable node) and end at the reactive azeotrope (a stable node). In the vicinity of each of the reagents, some trajectories approach the critical point while others move away from it; therefore, such points are called “saddle points”. The maximum value of xC is located on the “pure reacting axis” for XA ) XB ) 0.5. The reaction product, unlike the reactants and the nonreactive species, is not a singular point because of the assumption that the reaction reaches

Figure 2. Parametric analysis of the phase-reaction equilibrium (ideal reacting mixture).

equilibrium instantaneously, which means that C (heaviest component in the example) can never be obtained since it will react immediately to give a mixture of all components. From a parametric analysis of the phasereaction equilibrium depicted in Figure 2, it is obvious that an entirely reactive distillation column cannot produce bottom compositions with more than 60% C. Note that the phase-reaction equilibrium permits the occurrence of nonreactive mixtures between A/I and B/I. For this reason, any feasible column could eventually have two parts: (i) a pure distillative rectifying section and (ii) a reactive section. As we will demonstrate, a pure distillative stripping section is the only way to produce a bottom stream richer in C. For this case, the combination of the reaction-mass transfer process in a single apparatus will produce a situation such that the thermodynamic constrains of the reaction process (i.e., to attain degrees of reagent conversion exceeding the thermodynamic equilibrium levels for the operation conditions) are eliminated. Figure 3 represents the residue curve maps at three atmospheres for the highly nonideal mixture forming a conventional azeotrope (Espinosa et al., 1995b); namely, the system isobutene-methanol-methyl tert-butyl ether (MTBE)-n-butane (inert). For this system, there exist two fundamentally different types of residue trajecto-

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4539

Figure 3. Highly nonideal reacting mixture showing a binary azeotrope: residue curve maps.

ries. In the first type, the residue curves emanate from regions rich in isobutene (unstable node), while in the second type, the residue curves have their starting point in the minimum boiling azeotrope between n-butane and methanol (unstable node). Both types of composition trajectories end at pure methanol (stable node). The different types of residue curves give rise to two different distillation regions at total reflux. The corresponding separatrix begins at the n-butane vertex (saddle node) and terminates at the methanol vertex (stable node). Similar behavior was encountered by Ung and Doherty (1995b) and by Jacobs and Krishna (1993) for systems having n-butane and n-butene as inert, respectively. For this system, the reaction product MTBE is not a singular point because pure MTBE can never be obtained since it will react inmediately to produce a mixture of MTBE, methanol, and isobutene. In line with this observation, the binary azeotropes methanolMTBE and isobutene-methanol are not singular points. The maximum in MTBE occurs in the edge of the simplex that represents the pure reacting mixture at Xisobutene ≈ 0.5. Note that several trajectories approach the “reactive edge” at approximately Xisobutene ≈ 0.5. As was mentioned in Ung and Doherty (1995a,b), this point can be considered as a pseudoreactive azeotrope for all practical purposes. III. Product Composition Limitations and Minimum Reflux Calculations in Entirely Reactive Columns Feasibility Criterion of a Desired Separation at Finite Reflux. Consider an entirely reactive column producing a distillate (D) and a bottom (B), as is shown in Figure 4 for the ideal mixture with a feed stream (F) that contains an excess of component B. At finite reflux, the top and bottom profiles do not follow their respective total reflux curves (residue curves) through the distillate or the bottom compositions. As in conventional distillation for a given reflux or reboil ratio, both profiles end at their respective “end pinch points”, which correspond to points where the tangent to residue curves (equilibrium vector) passes through (D) or (B). Such “end pinches” or “stationary points” are aligned with (D) or (B) because the direction of the material balance line and the direction of the

Figure 4. Infeasible separation in an entirely reactive distillation column (ideal reacting mixture).

equilibrium vector in each column section coincide, so that an infinite number of stages would be required to perform such a separation. At these points, the liquid and vapor have reached simultaneous vapor-liquid and chemical reaction equilibrium. Note that at this moment we do not deal with the feasibility of the mentioned separation (both profiles must intersect to lead to a feasible design). We just want to point out that for given values of reflux or reboil ratios there exist end pinches that can be encountered by solving the top and bottom profiles from the design equations (i.e., the plate to plate model). By changing the reflux or reboil ratio, other stationary points for both top and bottom profiles are reached. Alternatively, such points (curve) could be obtained graphically by finding tangents to residue curves that pass through the distillate or bottom. In Espinosa (1994), an optimization program for solving this problem is briefly explained, and in Aguirre and Espinosa (1996) a robust method based on homotopy continuation is proposed for multicomponent highly nonideal mixtures. The collection of these points yields curves that represent the thermodynamically optimum separation paths for the top and bottom products under consideration (Koehler et al., 1991; Wahnschafft et al., 1992; Espinosa et al., 1995b). The whole range of liquid compositions that could be achieved by composition profiles pertaining to the rectifying section is enclosed by two curves: the total reflux curve and the pinch point curve for the distillate. In an analogous way, the total reflux curve and the pinch point curve for the bottom act as limits for the all-possible composition profiles in the stripping section. Since there exist boundaries for the conceivable top and bottom profiles, the liquid composition profiles of a feasible column must meet somewhere in the region of overlap of both regions. If there is no overlap, the specified products are not feasible. Figure 4 shows for the given separation that if we specify the bottom composition being that corresponding to a maximum in the heavy species C, there is no overlap of the profile regions and, therefore, the separation is not feasible. Fortunately, as we will demonstrate later, such a separation will be possible if a pure stripping section is added to the column. For this case, the point on the composition simplex representing the bottom product will be a mixture containing (pure) C with traces of B, A, and I. A similar approach can be applied to the highly nonideal mixture.


Figure 5. Angle-minimization criterion by Koehler et al. (1991).

It is noteworthy that the generalization of the feasibility criterion gives a method to obtain the complete product composition region attainable in a single-feed reactive distillation column (Wahnschafft et al., 1992; Espinosa et al., 1995b). This task must be executed before any attempt to design the column is done. Minimum Reflux for Entirely Reactive Distillation Columns. As in conventional distillation, there fundamentally are two approaches to the problem of designing an entirely reactive distillation column, namely, rigorous simulation with process simulators or alternatively with tray by tray procedures and, shortcut methods. Tray by tray procedures (Barbosa and Doherty, 1988c; Espinosa et al., 1995a) show that the “geometry” of the composition profiles at minimum reflux is similar to that studied in conventional distillation provided that convenient transformed variables have been used (Barbosa and Doherty, 1989c; Espinosa et al., 1995b). For this reason, shortcut methods for distillative columns are also applicable in reactive distillation. Barbosa and Doherty (1988c) developed an algebraic method similar to that proposed by Levy et al. (1985). Their procedure for constant-volatility systems finds the value of the reflux ratio which makes the feed pinch point, the saddle pinch point, and the feed composition collinear. In analogous way, the angle-minimization criterion developed by Koehler et al. (1991) is useful for highly nonideal reactive mixtures. The angle-minimization criterion is used to identify the physically meaningful pinch point pair (i.e., a saddle pinch and a feed pinch in Figure 5): the angle R between the two composition vectors connecting each of the two corresponding points on the reversible rectifying and stripping transformed profiles to the feed point is at a minimum value when the minimum reflux condition is reached. Both pinches must obey the energy balance around the reactive column. For this method, reversible paths (pinch point curves) for both products must be calculated. Aguirre and Espinosa (1996) presented a method based on homotopy continuation to deal with this problem. IV. Design of Reactive Distillation Columns with a Reacting Core Residue Curve Maps for Nonreactive Ternary Mixtures. Since the only way to produce pure reaction products is by adding a stripping section to the column, it is also useful to briefly analyze the residue curve maps for some combinations of the nonreactive mixtures. The analysis of the residue curve maps of the most significant ternary distillative mixtures is very useful at the stage of the design of a reactive distillation column with

Figure 6. Residue curve maps for the nonreactive ternary mixture A-B-C.

Figure 7. Residue curve maps for the nonreactive ternary mixture isobutene-methanol-MTBE.

a reacting core. Effectually, since a pure stripping section must be added, a sketch of the thermodynamic behavior permits that the designer determine whether the combination of the reaction-mass transfer process in a single apparatus will produce in principle the reaction products at the desired purity and the conditions for the occurrence of such a case. Figure 6 represents the ideal system A-B-C-(I ) 0). There exists a unique distillation region since all the trajectories emanate from the light species (A) and end at the heavy component (the reaction product C). Figure 6 also shows the “reaction curve” for the pure reacting mixture (xI ) 0). This curve is equivalent to the reactive edge in the simplex of transformed compositions. Figures 7 and 8 show the residue curve maps for the mixtures isobutene-methanol-MTBE-(n-butane ) 0) and n-butane-methanol-MTBE-(isobutene ) 0). In these figures, the conventional azeotropes methanolMTBE, isobutene-methanol, and n-butane-methanol at 3 atm pressure are also depicted. In addition, there exist two distillation regions, the upper section being rich in the reaction product MTBE. Note that the maximum in MTBE (Figure 7) belongs to the upper section.


νAA + νBB a νCC

Figure 8. Residue curve maps for the nonreactive ternary mixture n-butane-methanol-MTBE.

Minimum Reflux for Reactive Distillation Columns with a Reacting Core. In order to extend the methodology developed in the previous paper (Espinosa et al., 1995a), we have to restate the mass balance equations for the different column sections in terms of the transformed variables. As we will demonstrate, even though the equilibrium reaction does not occur at all the column trays it is possible to develop a transformed model. This model reproduces the situation at the ends of the reactive part. As an example, the model reproduces the fact that the liquid leaving the reactive part must be in chemical equilibrium. In addition, this liquid stream acts as a feed of the stripping section. For a quaternary reacting system, this situation can be seen as the intersection between a conventional stripping profile and a reactive surface. Such an intersection is easily computed by using transformed compositions. Along the following sections, the case of a feed stream entering the column at some stage into the reactive core is dealt with. Other single-feed topologies will be considered in a next paper together with multiple feed streams. To derive the design equations we suppose: (1) liquid boiling feed is present, (2) heat losses are negligible, (3) the molar heat of phase change for the mixture is constant, (4) the heat of mixing is negligible, (5) the heat capacity of the mixture is constant, (6) the reaction enthalpy change is negligible compared to the phase change enthalpy, (7) on each tray the equilibrium (phase equilibrium or phase-reaction equilibrium) is attained for the leaving streams, (8) the operating pressure is constant, and (9) the column operates with a partial condenser. The concepts developed in the next sections can be used in reactive distillation for a wide variety of multicomponent mixtures provided simultaneous phasereaction equilibrium or phase equilibrium takes place on each tray. However, in this work we demonstrate our approach by considering a ternary reacting system and one inert species “I”. The reason for this is that the design problem for such a system is similar to the corresponding formulation for three-component distillative mixtures. Provided that a tray contains the appropriate catalyst, the reacting species undergo an equilibrium reaction of type

(6)

Another important question is related to the first seven assumptions. As a consequence of these, the energy and mass balances can be decoupled and, hence, only the material balance and the equilibrium equations are used to compute the composition profiles for the column. Assuming a liquid boiling feed, the vapor flow rate remains constant in the three sections of the column and, on the other hand, the liquid flow rate varies only at the reactive part due to changes in the total number of moles by chemical reaction. Despite the simplicity of the model, this simplification will allow us to easily determine the composition profiles for all the sections of the column at different values of the reflux ratio and, hence, the geometry of the liquid profiles at minimum reflux. In a next paper we will relax the mentioned assumptions in order to consider a rigorous model with the energy balance at each tray of the column. Tray by Tray Equations. Pure Stripping Section. This section includes all the trays from the partial reboiler to the last plate without catalyst below the feed stream. The plate to plate equations for this area are (j ) 1, nc; n ) 1, Nstripping):

xj,n+1 )

s 1 y + x s + 1 j,n s + 1 j,B

(7)

where the external reboil ratio is defined as

s ) V/B

(8)

An intersection between the stripping profile and the reactive surface must occurs at the end of the pure stripping section, that is,

xj,Nstripping+1 ∈ reactive surface

(9)

At each point of the reactive surface, the liquid compositions are in chemical equilibrium and in vapor-liquid equilibrium with a vapor phase. Figure 9 shows two intersections between a pure stripping profile and the reactive curve for a bottom containing the three reacting species (xI ) 0). (For a ternary reactive mixture the reactive surface is a curve.) In the Appendix an algorithm is given to determine intersections between adiabatic profiles and reactive surfaces. Tray by Tray Equations. Reactive Stripping Section. For trays with catalyst the plate to plate equations in the transformed field are (j ) 1, nc; j * k and n ) Nstripping + 1, Nfeed):

Xj,n+1 )

s*n 1 Yj,n + Xj,B s* + 1 s* n n + 1

(10)

where the transformed reboil ratio at a tray n is defined by

νk - νtyk,n s* n ) s νk - νtxk,B

(11)

Note that eqs 10 and 11 are identical to those obtained by Barbosa and Doherty (1988c). However, at the first step in the calculation, the following equality must be employed:

Yj,n ) Yj,Nstripping+1 ) feq(XNstripping+1,p)

(12)


Figure 10. Equivalence between an entirely reactive distillation column and a column with a reactive core. Figure 9. Intersections between a stripping profile and a reactive curve for a bottom containing the three reacting components (ideal system without inert).

Equation 12 indicates that the first transformed vapor composition is in phase-reaction equilibrium with the liquid composition resulting from the intersection between a pure stripping profile for a given value of the reboil ratio and column pressure and the reactive surface. Tray by Tray Equations. Reactive Rectifying Section. For trays with or without catalyst, the plate to plate equations in the transformed field are (j ) 1, nc; j * k and m ) Nfeed +1, N) (Note that, for the examples under consideration, the phase-reaction equilibrium includes the liquid-vapor equilibrium for binary mixtures between each one of the reagents and the nonreactive species.):

Yj,m-1 )

r*m 1 Xj,m + Yj,D r* + 1 r* m m + 1

(13)

where the transformed reflux ratio at a tray m is defined by

νk - νtxk,m Lm r* ; rm ) m ) rm νk - νtyk,D D

νk - νtyk,m-1 (r* + 1) νk - νtyk,N-1 ext

(15)

where the transformed external reflux ratio is related to the column reflux ratio by

νk - νtxk,D LN ; r) r*ext ) r νk - νtyk,D D

D(νk - νtyk,D) B(νk - νtxk,B)

)

Xj,B - Xj,F ; j ) 1..., nc - 1; j * k Xj,F - Yj,D (17)

XA,B - XA,F XB,B - XB,F ) XA,F - YA,D XB,F - YB,D

(16)

Figure 10 shows us the equivalence between a reactive column with a reacting core and an entirely reactive column. It must be noted that all the columns considered in this paper are fed at some tray into the reactive section. Obviously, before proceeding to compute the transformed profiles, an intersection between a pure stripping profile for a given value of s and the reactive surface must be obtained. Note, however, that now

(18)

Finally, the relationship between the external reboil and reflux ratios can be obtained after dividing and multiplying eq 17 by the vapor flow rate V and relating the ratio D/V to the transformed external reflux ratio from the material balance around the partial condenser

s(νk - νtyk,N-1) (r*ext + 1)(νk - νtxk,B)

(14)

The relationship between the transformed reflux ratio on a tray above the feed stage and the external one is related by

r* m + 1 )

there are no impediments to select a bottom composition rich in the reaction product because a stripping section has been added to the column. In a manner similar to the feed, the mole fractions of any bottom selected must be converted to transformed variables by using eqs 1. Overall Balances and Degree of Freedom of a Complete Column. From the overall mass balances the following relationships can be derived:

)

Xj,B - Xj,F ; j ) 1..., nc - 1; Xj,F - Yj,D j * k (19)

As can be seen from eqs 17-19, a quaternary reactive system is similar to a ternary distillative mixture and, hence, before we can solve eqs 7, 10, and 13 to find the composition profiles in the three sections of the column, we must first specify values for the design parameters. In our case, the degrees of freedom for the ternary reactive system with one inert component correspond exactly to those of a ternary nonreactive system. Then, the feed composition (liquid boiling), the column operation pressure, and three independent transformed compositions in the products streams must be specified (i.e., XA,B, XB,B, and YA,D) in adition to the external reflux ratio r. In order to univocally determine the bottom composition, it is convenient that one specify all the species mole fractions and then calculate the transformed mole fractions by means of eq 1. Note that for a bottom rich in C the transformed composition values approach XA,B ) XB,B ) 0.5. The design specifications lead to a feasible column only when the stripping and the rectifying profiles contain a tray with the same liquid composition; this

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4543 Table 1. Stream Results for an Operating Reflux Ratio, r ) 8.5 (Ideal Reacting Mixture) stream composition

flow rate

A

B

C

I

distillate 21.606 3.88E-07 0.074 335 78 612E-07 0.925 663 22 feed 100.000 0.39 0.41 0 0.20 bottom 39.394 1.00E-06 0.01 0.989 999 1.00E-10 transformed variable

distillate feed bottom

flow rate

XA

XB

XI

21.606 100 78.394

1.00E-06 0.39 0.497 488

0.074 336 0.41 0.502 512

0.925 663 0.20 5.00E-11

corresponds to the feed stage. To obtain a feasible column and once the overall balances have been done, we compute the pure-distillative operating line beginning from the bottom at the partial reboiler and going upward until we find a liquid composition in chemical reaction equilibrium. Once this step is performed, it is possible to compute the reactive stripping profile but now until we find an end pinch, for which no further progress in the liquid composition is noted. In the same way, the rectifying profile must be computed beginning from the partial condenser and going downward until an end pinch has been found. A feasible column design is found when the profiles of the equivalent column intersect in the concentration simplex. Thus, by solving the tray by tray model, the search for a feasible column design involves changing the external reflux ratio until an intersection is obtained. Furthermore, the minimum reflux condition demands that either the rectifying or the stripping profile or both together end with their end pinches just on the feed tray. For this reason, a reactive column under minimum reflux operation will require an infinite number of stages. It has to be noted that even when the profiles in the examples below were calculated with this simplified model, the adiabatic profiles were always found following reasonable patterns according to the other rigorous simulations cited in section VII. V. Examples Table 1 shows the overall results for the ideal mixture whose feed stream contains the reagents in quantity near the stoichiometric ratio. The distillate is a mixture between the inert and the excess reagent B, while the bottom stream contains a great amount of the reaction product and only 1 mol % component B. Note that the bottom specifications were made taking into account the volatility order of all the components of the quaternary mixture. Figure 11 shows the liquid profiles at minimum energy demand operation in the transformed field. As can be seen, the only way to produce an intersection between the top and bottom profiles is from a stripping profile that begins (first reactive tray) with a mixture with an excess of B (more exactly, with a composition greater than that of the reactive azeotrope) so that the liquids representing the trays in the reactive stripping part are confined in the neighboring region to that showed for the bottom in Figure 4. Note, however, that the reactive stripping profile terminates in a nonactive pinch of the bottom pinch point curve (Figures 4 and 11). Figure 12 exhibits the intersection between the pure stripping profile and the reactive curve at approximately

Figure 11. Composition profiles at minimum reflux for the separation specified in Table 1 (ideal reacting mixture, smin ) 4.94, rmin ) 8.0).

Figure 12. Intersection between the stripping profile at minimum boilup and the reactive surface (ideal reacting mixture, only the intersection giving a feasible profile is shown).

xI ) 0. Only the trays from the bottom until that corresponding to the intersection must be considered. For this example, two intersections occur with the reactive surface for the same boilup, but only one produces a feasible column (Figure 11). As can be seen from Figure 6, a boilup of considerable magnitude can be expected to produce a feasible column since it is the only way to obtain an intersection with the reactive surface whose maximum in C is about 60%. Figures 13 and 14 display the approximate liquid profiles for all components in the three sections of the column and the reaction coordinate vs the column height for a feasible column of 60 theoretical trays working at a reflux ratio of 8.5 and fed at stage 33 from the top. From this Figures, the following conclusions can be obtained: (i) At both ends of the column in the pure-rectifying (trays from 1 to 19) and pure-stripping sections (trays from 43 to 60), the inert I and the reaction product C are separated from the excess reactant B, respectively. The plateau or “zone of constant composition” at the top of the column indicates that the rectifying profile passes


Figure 13. Shape of the profiles for the separation specified in Table 1 (ideal reacting mixture, s ) 5.21, r ) 8.5).

Figure 14. Reaction coordinate vs column height for the separation specified in Table 1 (ideal reacting mixture, s ) 5.21, r ) 8.5).

near a conventional saddle point. By changing the product specification at the bottom (i.e., diminishing the concentration of A) also a plateau for the stripping profile can be expected. (ii) In the reactive section (trays from 20 to 42) C is produced while the limiting reagent A is totally eliminated by chemical reaction. The concentration of the reaction product reaches a maximum whose value remains below the maximum allowed by the chemical reaction. The product (C) is generated in a great amount in the feed plate, and on the other hand, an inversion in the reaction occurs at the end of the reactive section. Two important questions can be now elucidated by newly analyzing Figure 11. At minimum reflux condition (Figure 11), the reactive stripping profile does not pass near a saddle pinch even when the first reactive tray only contains traces of the inert component. In reality, for the given bottom transformed composition and the minimum boilup value, there exists a pinch belonging to the reactive edge. However, in Figure 11 such a pinch is located between the bottom (B) and the reactive species A vertex. Because of this fact, the minimum angle criterion as presented by Koehler et al. (1991) has to be used considering the two end pinchs. In such a case, a poor estimation of the minimum vapor flow is obtained: VMAC ) 91.8, Vmin ) 194.6, giving a relative error of -53%.

In addition, both feasible and infeasible bottom profiles terminate in the same pinch point of the thermodynamically optimum separation path. The reason for this is that, for a specified bottom and column pressure, only one additional variable has to be set to determine the pinch condition (Koehler et al., 1991; Aguirre and Espinosa, 1996); therefore, for the specified value of the boilup at least one physically meaningful solution of the pinch equations exists. Due to the topology of the pinch point curve in Figure 11, the boilup monotonically varies from zero at the bottom composition to infinite at the inert species vertex. Only one physically meaningful solution exists for a given boilup; hence, both adiabatic profiles must reach the same end pinch. From a mathematical point of view, since the bottom end pinch is only boilup dependent, a small difference between the last stripping tray composition (calculated via the tray by tray procedure) and the first reactive tray mole fraction (interpolated value) will produce a small error in the shape of the profile because it must terminate at the end pinch. Therefore, we expect that the estimated values of the minimum reflux calculated from the tray by tray procedure will be reliable values. Anyway, it is always possible to obtain an exact intersection between the stripping profile and the reactive surface by slightly varying the product specification. From an operational standpoint, it is noteworthy that a bottom stream rich in the reaction product can be obtained by adding a pure stripping section (Figure 6), and an originally infeasible separation (Figure 4) can now be converted to a feasible one. Thus, a reactive distillation column with a reacting core is more advantageous than an entirely reactive column because it produces a wide variety of products and an enhancement in the reagent conversion. The overall results for the highly nonideal mixture whose feed stream contains 20 mol % n-butane and a methanol:isobutene ratio of 1.15 are listed in Table 2. The distillate composition is near that of the minimum boiling azeotrope between n-butane and methanol. On the other hand, the bottom is a mixture between the excess reagent methanol and 90% MTBE. The bottom specifications were made taking into account the volatility order of all the species of the quaternary mixture corresponding to the upper region of Figures 7 and 8. Figure 15 shows the minimum reflux operation in the triangular diagram (transformed field). An infinite number of trays in the bottom section are necessary for this separation. Also, the bottom pinch point curve and the residue curve maps (total reflux curves) can be seen in Figure 15. The first reactive tray at the bottom is a mixture of all species and contains an excess of methanol. Due to the substantial difference between the temperatures of both column products, a low value for the minimum reflux can be expected. Values of the reflux ratio above 3 can be considered near total reflux. For this reason, both profiles approximately follow their respective residue curves. In the case of the stripping, the residue curve that must be considered is that which passes through the composition of the first reactive tray. Figure 16 displays the approximate liquid profiles for all species in the three column sections for a feasible column of 20 theoretical trays working at a reflux ratio of 0.9 and fed at stage 11 from the top. Three purerectifying stages and eight pure-stripping trays are necessary to obtain the high purity bottom stream. The feasible column profiles obtained via tray by tray

Ind. Eng. Chem. Res., Vol. 35, No. 12, 1996 4545 Table 2. Stream Results for an Operating Reflux Ratio, r ) 0.90 (MTBE System) stream composition distillate feed bottom

flow rate

isobutene

methanol

MTBE

n-butane

21.08 100.00 41.67

5.19E-06 0.3725 7.60E-06

0.051 641 64 0.4275 0.105 878 007

0.000 094 82 0 0.893 925

0.948 258 35 0.20 0.000 189 393

transformed variable distillate feed bottom

flow rate

Xisobutane

Xmethanol

Xn-butane

21.085 100.000 78.915

1.00E-04 0.372 5 0.472

0.051 73 0.427 5 0.527 9

0.948 17 0.20 1.00E-04

Figure 15. Composition profiles at minimum reflux for the separation specified in Table 2 (MTBE system, smin ) 0.9361, rmin ) 0.85).

As in the previous example, by adding a purestripping profile it is possible to attain degrees of reagent conversion exceeding the thermodynamic equilibrium levels for the operation conditions (see Figure 7). In this example, both product compositions (in the natural field) belong to the same distillation region at total reflux (upper section in Figure 8) but also feasible designs are possible for distillates near the minimum boiling azeotrope in the lower section of Figure 8. Therefore, in a reactive distillation column with a reacting core it is possible to obtain product streams at distinct sides of conventional total reflux boundaries. This fact can be explained as follows: both types of distillate specifications give a first reactive tray composition belonging to the same distillation region in Figure 15 (the region with residue trajectories starting at the minimum boiling azeotrope); therefore, an intersection between top and bottom profiles (similar to that of Figure 15) is possible at least for some bottom specifications. Finally, unlike the previous example, two active pinches appear at the minimum energy demand operation in Figure 15: a stripping end pinch and a conventional saddle rectifying pinch. Therefore, the MAC to estimate minimum flows in the transformed field can be now used without any modification. The value obtained with MAC is VMAC ) 46 whereas the minimum vapor flow calculated by means of the tray by tray model is Vmin ) 39, giving an error of 18%. VI. A New Feasibility Criterion of a Given Separation at Finite Reflux in Reactive Columns with a Reacting Core

Figure 16. Shape of the profiles for the separation specified in Table 2 (MTBE system, s ) 0.9614, r ) 0.9).

procedure reveal the most important characteristic present in the production of ethers via reactive distillation. At the top, the minimum boiling azeotrope between the inert (n-butane or n-butene or both of them) and the alcohol is obtained, while at the bottom, the ether is separated from the excess reagent (methanol) and the inert (in traces). The isobutene practically disappears in the reactive part of the column. Only some traces of the limiting reagent are present in both product streams. For the given specifications, the reaction mainly occurs at the feed tray and a little decomposition of MTBE in the last tray is present.

Returning to the first example, it can be seen from Figure 9 (ternary reacting mixture) that, for a given value of the boilup, two intersections exist between the pure-stripping profile and the reactive curve. This occurs because the bottom stripping profiles in Figure 9 are enclosed by the bottom total reflux curve (bottom residue curve) and by the bottom pinch point curve, with the last curve near the A-C axis. Since the inert is the more volatile component, bottoms containing all the species (with xI,B ∼ 0, xA,B ∼ 0, and xI,B < xA,B) will produce, for each value of the boilup, two intersections between a pure-stripping profile and the reactive surface (Figure 11). At infinite boilup, the two corresponding intersections will give two reactive stripping profiles that closely follow their respective residue trajectories. This occurs because s*n in eq 10 tends to infinity when s tends to infinity, too. In both cases, the residue curves that must be considered are the residue trajectories that pass through the corresponding compositions of the first reactive trays. Therefore, all the conceivable reactive stripping profiles for the bottom of Figure 11 are enclosed by the two


Figure 17. New feasibility criterion of a given separation at finite reflux: ideal reacting mixture (separation specified in Table 1).

residue curves of Figure 17. However, all profiles have the same bottom pinch point curve (see Figures 11 and 17). (This curve was obtained by using the homotopycontinuation method developed by Aguirre and Espinosa (1996).) It is obvious that, for the problem under consideration, there exist two different types of reactive stripping profiles. The region labeled I in Figure 17 corresponds to reactive stripping profiles enclosed by the “left residue curve” and by the bottom pinch point curve. In a similar manner, the reactive stripping profiles enclosed by the “right residue curve”and by the bottom pinch point curve (region labeled II in Figure 17) constitutes another region. The two extreme operating conditions of a column can serve to determine the feasibility of a desired separation (at finite values of the reflux ratio). Since there exist boundaries for the allpossible top and bottom profiles, the liquid composition profiles of a feasible column must meet somewhere in the region of overlap of both regions. As pointed out by Wahnschafft et al. (1992) and Espinosa et al. (1995b), the mentioned criterion is a necessary but not sufficient feasibility condition. An overlap exists between the distillate region and the left (I) bottom region of Figure 17, and therefore, the separation is (in principle) feasible. Figure 18 shows us that the separation given in Table 2 is (in principle) also feasible. The residue curve that passes through the bottom composition is also depicted in this figure to demonstrate that both column products pertain to distinct distillation regions at total reflux (see Figure 3). Hence, in a reactive column with a reacting core it is also possible to produce product streams at distinct sides of a “transformed” total reflux boundary. VII. Comparative Results and Optimal Design Specifications At this point, a comparative analysis of our results with those of other works based on rigorous simulations and experimental developments will be done. The aim of this section is to produce a discussion toward the concept of optimal design specifications based on all the available information. In their study on catalytic distillation process, Yuxiang and Xien (1992a,b) obtained composition profiles at other operating parameters; however, the shape of their profiles looks very similar to those depicted in

Figure 18. New feasibility criterion of a given separation at finite reflux: MTBE system (separation specified in Table 2).

Figure 19. Feasible separation specified in Table 3: lowconversion case (MTBE system, s ) 8.37, r ) 6.74).

Figure 16. The major difference occurs at the reactive part due to the different distribution of the reaction along the trays when two feeds are employed. In addition, their column has 21 trays and works at a reflux value of 2. Jacobs and Krishna (1993) studied multiple solutions in reactive distillation for MTBE synthesis with the aid of residue curve maps for simultaneous physical and chemical equilibrium and the flowsheet simulator ASPEN PLUS (see Venkataraman et al., 1990). They concluded that the reactive stages of a high composition profile follow a path that is similar to a residue curve starting in the vicinity of the inert-alcohol minimum boiling azeotrope (see Figures 5 and 6 of that paper). This is clearly the behavior presented for the reactive trays in Figure 15. Figure 19 and Table 3 present a case where the design specifications give rise to a low isobutene conversion. As can be seen, several reactive stages belong to the total reflux region with residue curves starting at pure isobutene vertex. This behavior was also encountered by rigorous simulation with ASPEN PLUS by Jacobs and Krishna (1993). By using our approach, this observation becomes obvious, since low isobutene conversion cases correspond to total mass balance lines pointing out the methanol vertex. In a manner similar


Figure 20. Column composition profile for the separation specified in Table 3 (MTBE system).

Figure 21. Composition profiles at minimum reflux for the nonoptimal product specification (MTBE system).

Table 3. Stream Results for an Operating Reflux Ratio, r ) 6.74 (MTBE System, Low-Conversion Case) stream compositions flow rate isobutene methanol distillate feed bottom

46.51 100.00 43.00

MTBE

n-butane

0.569 928 1.00E-06 5.00E-05 0.430 021 0.372 5 0.427 5 0 0.20 0.005 807 0.750 199 0.243 993 1.00E-06 transformed variables

distillate feed bottom

flow rate

Xisobutene

Xmethanol

Xn-butane

46.51 100.00 53.49

0.569 95 0.372 5 0.200 805

5.03E-05 0.427 5 0.799 195

0.430 00 0.20 9.97E-07

to that of Jacobs and Krishna (1993), Figure 20 illustrates that, for the lower conversion case, crossing of a conventional distillation boundary does occur. In Figure 20, and for the sake of simplicity, both n-butane and isobutene were lumped into one component. In their work on multiplicity with the aid of ASPEN PLUS, Hauan et al. (1995) developed a hypothesis yielding a qualitative understanding of the multiplicity phenomenon. As the reaction mixture is diluted with inert (i.e., the reaction mixture in the lower part of the reactive zone must be sufficiently diluted with nbutane), it will be possible to prevent MTBE decomposition at the end of the reactive section. This occurs because the more inert, the lower temperature in the catalyst section, and therefore, the equilibrium constant increases avoiding MTBE decomposition. From the mentioned authors, the above condition must be met in order to achieve high conversion of the limiting reagent. The approximate profile for n-butane shown in Figure 16 demonstrates that the concentration of inert in the last reactive tray is about 25 mol %. However, it must be noted that unlike Hauan et al.’s (1995) claim, high conversion profiles can be obtained for nondiluted reaction mixtures (see Figure 13) provided the column has a sufficient number of trays with catalyst (as is the case for entirely reactive columns). This effect was not encountered by their simulations because the number of stages of the three constitutive column sections were fixed at low values. The column specifications corresponding to the minimum reflux situation of Figure 21 are very similar to that of Table 2, but the bottom mole fractions of the lighter species are interchanged. The same bottom

Figure 22. Shape of the profiles at r ) 0.9 for the nonoptimal product specification (MTBE system).

specification for the heavy components are selected, and a similar value for the minimum reflux is obtained. Figure 22 presents the approximate column liquid profiles. Despite the feasibility of the separation, it must be noted that the design specifications are not appropiate due to the following reasons: (i) A great number of trays with catalyst must be employed to achieve the column specifications. (ii) MTBE decomposition occurs at the end of the reactive section. (iii) The inert is exhausted in the reactive section. Taking into account the foregoing results, it is clear that an optimal design requires, for both ideal and nonideal examples, a bottom specification with a ratio inert/limiting reagent greater than unity. With this specification, a saving in the number of trays with catalyst is obtained, product decomposition is avoided by effect of dilution, and the inert is exhausted by distillation. In line with Hauan et al.’s (1995) observations, the mean temperature in the reactive part for a diluted reaction mixture (design specifications of Figure 16) is 312.5 K, while the mean temperature (trays with catalyst, nondiluted reaction mixture) for the nonoptimal design is about 327.25 K. From our previous work (Espinosa et al., 1995a) we concluded that in an entirely reactive distillation column the only way to produce a bottom stream rich in MTBE


was by specifying the concentration of the inert at the bottom equal to zero with the transformed mole fractions for the reagents near to 0.5. Note that the absolute maximum for xMTBE is achieved at the bottom for values of the reagent transformed compositions equal to 0.5 (see the reactive curve in Figure 7). The bottom will be a mixture of MTBE, methanol, and isobutene at chemical equilibrium. For feed streams with an excess of alcohol, the distillate will be a mixture between the inert and methanol. Therefore, both in pure reactive distillation columns and in columns with a reacting core, the nonreactive component plays the same role because most of the methanol in excess will appears as n-butane/methanol azeotrope at the top of the column. However, the addition of pure stripping permits a wide variety of product and reagent conversions. In addition, optimal designs can be performed through an appropriate specification of the concentrations of the more volatile species at the bottom. Note that, in columns with a reacting core, we are free to specify the ratio inert/limiting reagent greater as well as less than unity. This characteristic gives this operation a great flexibility with respect to entirely reactive distillation columns. Finally, a recent paper by Ung and Doherty (1995c) shows that it is possible to produce column sequencing with the aid of conventional and reactive residue curve maps and the overall balance line in the transformed field. Their concepts apply to the cases of the presence of nonreactive species and occurrence of multiple chemical reactions in columns with a reacting core. Although the mentioned approach is useful in the synthesis of distinct column configurations, we resort to our own method for the design of each column. A design method, as it is proposed here, must consider (a) the thermodynamic insight from the analysis of the residue curve maps, (b) the feasibility of a given separation at finite reflux as a consequence of the analysis of the two extreme operation conditions of the column, and (c) the results obtained from simulations. VIII. Conclusions Some aspects related to the design of reactive distillation columns with a reacting core are studied with the aid of both “conventional” and “transformed” residue curve maps and design equations. This approach intends to achieve a better physical and conceptual insight into the relationships between the different constitutive parts of a column with a reacting core. The results obtained show that using an apparatus with three sections it is possible to obtain high purity products; therefore, the combination of the reactionmass transfer process in a single column produces a situation such that the thermodynamic constraints typical of each individual process can be eliminated. Limitations in product specifications of entirely reactive distillation columns are explained by means of “transformed” residue curve maps, and a new feasibility criterion of a given separation for reactive columns with a reacting core is also developed on the basis of the two extreme operation conditions of a column. The behavior of column profiles for both high-conversion and low-conversion cases is analyzed, and optimal product specifications are suggested to obtain a reactive distillation column with high purity products. For sharp distillation in columns with a reacting core, the minimum reflux structure differs from those of entirely reactive columns and conventional columns. Rough

estimations of minimum flows can be obtained by using shortcut methods. As we concluded in previous works, the inerts have a central role in the design of a reactive distillation column. Acknowledgment The authors gratefully acknowledge the financial support of CONICET (Consejo Nacional de Investigaciones Cientı´ficas y Tećnicas de Argentina) and U.N.L. (Universidad Nacional del Litoral). Nomenclature A, B, C, I ) generic chemical species B ) bottom, bottom molar flow rate D ) distillate, distillate molar flow rate F ) feed stream L ) internal liquid molar flow rate MAC ) minimum angle criterion N ) number of column trays nc ) number of components p ) column pressure q, q1, q2 ) parameters defined in the Appendix r ) external reflux ratio s ) external reboil ratio T ) temperature V ) internal vapor molar flow rate xj ) molar fraction of component j in the liquid phase Xj ) transformed composition of component j in the liquid phase yj ) molar fraction of component j in the vapor phase Yj ) transformed composition of component j in the vapor phase Greek Letters β ) Euclidean norm between liquid mole fractions defined by eq A1 γj ) liquid phase activity coefficient of component j λ ) parameter that varies between zero and unity νj ) stoichiometric coefficient of component j νt ) sum of the stoichiometric coefficients of the reacting species Subscripts A, B, C, I ) components A, B, C, I, respectively B ) bottom D ) distillate eq ) equilibrium value F ) feed MAC ) minimum angle criterion m ) generic tray above the feed tray min ) minimum n ) generic tray below the feed tray t ) tray 0 ) initial condition 0, 1, 2 ) first point, second point, third point Superscript * ) transformed value

Appendix. Determination of Intersections between an Adiabatic Profile and a Reactive Surface The algorithm employed in this paper is based on the following aspects: Given the liquid compositions on a tray, xt, (i) Values for transformed compositions Xt, can be calculated from eqs 1.


Figure 23. Euclidean norm β vs tray temperature.

(ii) Solving the reactive bubble point for Xt, liquid mole fractions xeq in chemical equilibrium are obtained. (iii) The Euclidean norm β of the difference vector between xt and xeq, that is,

β ) ||xt - xeq||

(A1)

is zero when an intersection occurs between the adiabatic profile and the reactive surface. (iv) Detections of intersections can be done on a graphic of β vs tray temperature (see Figure 23). The algorithm needs three points [(T0, β0), (T1, β1), (T2, β2)] for determining an extreme through the equation:

q ) q1 × q2 q1 )

(A2)

β1 - β0 β2 - β1 ∧ q2 ) T1 - T0 T2 - T1

Provided that q < 0 and β (β ) min[βi], i ) 1, 2, 3) e set_value; a golden search method for x ) x0 + λx2 (with λ values between 0 and 1) is employed in order to achieve an exact solution. Literature Cited Aguirre, P.; Espinosa, J. A Robust Method to Solve Mass Balances in Reversible Column Sections. Ind. Eng. Chem. Res. 1996, 35, 559-572. Barbosa, D.; Doherty, M. F. The Influence of Equilibrium Chemical Reactions on Vapor-Liquid Phase Diagrams. Chem. Eng. Sci. 1988a, 43, 529-540. Barbosa, D.; Doherty, M. F. The Simple Distillation of Homogeneous Reactive Mixtures. Chem. Eng. Sci. 1988b, 43, 541-550. Barbosa, D.; Doherty, M. F. Design and Minimum-Reflux Calculations for Single-Feed Multicomponent Reactive Distillation Columns. Chem. Eng. Sci. 1988c, 43, 1523-1537.

Doherty, M. F.; Buzad, G. Reactive Distillation by Design. Trans. Inst. Chem. Eng. 1992, 70A, 448-458. Espinosa, J. Disenõ, Sıńtesis y Simulacioń de Torres Reactivas. Ph.D. Dissertation, Universidad Nacional del Litoral, Santa Fe, Argentina, 1994. Espinosa, J.; Scenna, N.; Pe´rez, G. Graphical Procedure for Reactive Distillation Systems. Chem. Eng. Commun. 1993, 119, 109-124. Espinosa, J.; Martıńez, E.; Pe´rez, G. Dynamic Behavior of Reactive Distillation Columns. Equilibrium Systems. Chem. Eng. Commun. 1994, 128, 19-42. Espinosa, J.; Aguirre, P.; Pe´rez, G. Some Aspects in the Design of Multicomponent Reactive Distillation Columns Including Non Reactive Species. Chem. Eng. Sci. 1995a, 50 (3), 469-484. Espinosa, J.; Aguirre, P.; Pe´rez, G. The Product Composition Regions of Single-Feed Reactive Distillation Columns: Mixtures Containing Inerts. Ind. Eng. Chem. Res. 1995b, 34, 853-861. Hauan, S.; Hertzberg, T.; Lien, K. M. Multiplicity in Reactive Distillation of MTBE. Comput. Chem. Eng. 1995, 19, S327S332. Jacobs, R.; Krishna, R. Multiple Solutions in Reactive Distillation for Methyl tert-Butyl Ether Synthesis. Ind. Eng. Chem. Res. 1993, 32, 1706-1709. Koehler, J.; Aguirre, P.; Blass, E. Minimum Reflux Calculations for Nonideal Mixtures using the Reversible Distillation Model. Chem. Eng. Sci. 1991, 46, 3007-3021. Levy, S. G.; van Dongen, D. B.; Doherty, M. F. Distillation and Synthesis of Homogeneous Azeotropic Distillations: 2. Minimum Reflux Calculations for Nonideal and Azeotropic Columns. Ind. Eng. Chem. Fundam. 1985, 24, 463-474. Serafimov, L. A.; Pisarenko, Yu.A.; Timofeev, V. S. Reaction-Mass Transfer Processes: Problems and Prospects. Theor. Found. Chem. Eng. 1993, 27 (1), 1-10. Ung, S.; Doherty, M. F. Vapor-Liquid Phase Equilibrium in Systems with Multiple Chemical Reactions. Chem. Eng. Sci. 1995a, 50 (1), 23-48. Ung, S.; Doherty, M. F. Necessary and Sufficient Conditions for Reactive Azeotropes in Multireaction Mixtures. AIChE J. 1995b, 41 (11), 2383-2392. Ung, S.; Doherty, M. F. Synthesis of Reactive Distillation Systems with Multiple Chemical Reactions. Ind. Eng. Chem. Res. 1995c, 34, 2555-2565. Venkataraman, S.; Chan, W. K.; Boston, J. F. Reactive Distillation Using ASPEN PLUS. Chem. Eng. Prog. 1990, 86 (8), 45-54. Wahnschafft, O. M.; Koehler, J.; Blass, E.; Westerberg, A. W. The Product Composition Regions of Single-Feed Azeotropic Distillation Columns. Ind. Eng. Chem. Res. 1992, 31, 2345-2362. Zheng Yuxiang and Xu Xien. Study On Catalytic Distillation Processes: Part I. Mass Transfer Characteristics in Catalyst Bed within the Column. Trans. Inst. Chem. Eng. 1992a, 70A, 459-464. Zheng Yuxiang and Xu Xien. Study On Catalytic Distillation Processes: Part II. Simulation of Catalytic Distillation Processes. Trans. Inst. Chem. Eng. 1992b, 70A, 465-470.

Received for review June 18, 1996 Revised manuscript received September 9, 1996 Accepted September 9, 1996X IE960355K

X Abstract published in Advance ACS Abstracts, October 15, 1996.

Mixtures Containing Inerts - American Chemical Society

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