Design of Processes with Reactive Distillation Line Diagrams

Jun 15, 1997 - of the reactive distillation line diagrams, it can be decided whether a column with ... Block flow diagram for a conventional chemical ...
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Ind. Eng. Chem. Res. 1997, 36, 3032-3042

Design of Processes with Reactive Distillation Line Diagrams† B. Bessling,*,‡ G. Schembecker,§ and K. H. Simmrock§ Engineering R&D, BASF Ludwigshafen, 67056 Ludwigshafen, Germany, and Technical Chemistry A, Department of Chemical Engineering, University of Dortmund, D-44221 Dortmund, Germany

On the basis of the transformation of concentration coordinates, the concept of reactive distillation lines is developed. It is applied to study the feasibility of a reactive distillation with an equilibrium reaction on all trays of a distillation column. The singular points in the distillation line diagrams are characterized in terms of nodes and saddles. Depending on the characterization of the reactive distillation line diagrams, it can be decided whether a column with two feed stages is required. On the basis of the reaction space concept, a procedure for the identification of reactive distillation processes is developed, in which the reactive distillation column has to be divided into reactive and nonreactive sections. This can be necessary to overcome the limitations in separation which result from the chemical equilibrium. The concentration profile of this combined reactive/nonreactive distillation column is estimated using combined reactive/ nonreactive distillation lines. 1. Introduction In recent years many processes for basic and intermediate products were improved by a combination of reaction and distillation in a reactive distillation column. The conventional process has to be compared with the reactive distillation process to understand the possible improvements; see Figures 1 and 2. The conventional process consists of a reaction and a separation section. Two unitssusually connected by a recycle streamsare necessary to produce and to separate the products. In a reactive distillation column, it is possible to combine two operations in one unit, so that synergistic effects between distillation and reaction occur; see Figure 2. Examples are as follows: (a) shift of the chemical equilibrium by separation of the products and (b) utilization of the reaction heat for the separation of educts and products. These synergistic effects cause benefits of a reactive distillation process when compared to the conventional design: (a) lower capital investment, (b) lower energy consumption, and (c) higher product yields. Because of these benefits it is necessary to check during the development of a new process or during the reengineering of an existing process whether the process can be improved by reactive distillation. The obstacle to the synthesis of a reactive distillation process is to understand the interaction of reaction and distillation. Consider, for example, that a first simple reactive distillation process for methyl acetate was developed in 1921 by Backhaus (1921), but it took 60 years to reach the level of the Eastman Kodak Process patented by Agreda and Partin (1984). To fill this gap, the interaction of reaction and distillation has been a topic of intensive studies, for example, by Barbosa and Doherty (1988a) and Ung and Doherty (1995). This research, which is the basis for the work presented here, focuses on the basic principles of the interaction of reaction and distillation. Neverthe* To whom correspondence should be addressed. E-mail, [email protected]; telephone number, 0049/621/60/ 55446; Fax, 0049/621/60/52411. † Dedicated to Prof. Gilbert Froment on the occasion of his 65th birthday. ‡ BASF Ludwigshafen. § University of Dortmund. S0888-5885(96)00727-0 CCC: $14.00

Figure 1. Block flow diagram for a conventional chemical process.

Figure 2. General structure of a reactive distillation process.

less a strategy for the design of reactive distillation processes has not been published. We combine existing knowledge and new aspects to a method which takes into account important elements of an overall design strategy. This method applies heuristic rules and numeric routines. 2. Fundamentals 2.1. Reaction Spaces. Reactive distillation is usually applied to systems with equilibrium reactions. For the following discussion, it is assumed that the system is in chemical and physical equilibrium. Under this assumption, the degrees of freedom (FG) of a system are reduced by the number of independent chemical equilibrium reactions (Wales, 1985).

Gibbs phase rule:

FG ) 2 + n - π - r

(1)

In Table 1 an overview is given about the systems discussed in this paper. The following conditions were varied: (a) type of reaction, (b) presence of inerts, (c) number of components, and (d) type of phase equilibrium. The number of degrees of freedom is identical to the dimension of the concentration space in which the © 1997 American Chemical Society

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3033

Figure 3. Reaction: A a B. In a binary system with two phases at constant pressure or temperature the equilibrium is reached only at one point (marked by a cross).

Figure 5. Reaction: A a B in the presence of the inert components C an D. When another inert component D besides C is assumed, the reaction space is stretched between equilibrium concentration in the binary system AB and the inert components C and D (K ) 1).

Figure 4. Reaction: A a B in the presence of the inert component C. In the presence of one inert component the equilibrium is located on a line between the equilibrium in the binary system AB and the inert component C (K ) 1). Table 1. Overview about the Systems Discussed in This Paper

reaction AaB AaB AaB A+BaC A+BaC A+BaC+D A+BaC+D A+AaE A+BaC A+BaC+D

inerts

type of phase equilibrium

no. of components

C C,D D

degrees of freedom F (P or T constant)

2 3 4 3 4 4 5

VLE VLE VLE VLE VLE VLE VLE

0 1 2 1 2 2 2

3 4

VLLE VLLE

0 1

equilibrium conditions are fulfilled. We define this part of the concentration space as reaction space. The reaction space is a subspace of the concentration space. The geometrical shape of the reaction space depends on the type of reaction, the position of the chemical equilibrium, and the presence of inert components. For the case study in Figures 3-10 it is assumed that the chemical equilibrium can be described by the following form of the mass action law: nc

K)

xiν ∏ i)1

i

(2)

As examples some important types of reaction were chosen. The reaction A a B is an example for isomerization (Figures 3-5), A + B a C for etherification (Figures 6 and 7), and A + B a C + D for esterification (Figure 8). Figures 9 and 10 depict systems with a miscibility gap, which reduces the reaction space. 2.2. Transformed Concentration Coordinates. The reduction of the degrees of freedom allows us to

Figure 6. Reaction: A + B a C. Chemical equilibrium with different equilibrium constants for an additive reaction.

Figure 7. Reaction: A + B a C in the presence of the inert component D. When an inert component is added, the reaction space is stretched between the chemical equilibrium in the reactive ternary system A, B, C and the inert component D (K ) 1).

simplify the representation of reacting systems. To get a structured representation of these systems, transformed concentration coordinates have been published by Barbosa and Doherty (1988a) and Espinosa et al. (1995a, 1995b). The chemical reaction is presented here as the following:

νAA + νBB + ... a νPP + νQQ + ... The transformed liquid and vapor coordinates for an arbitrary component i are given by Espinosa et al. (1995b):

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Figure 8. Reaction: A + B a C + D. The reaction space is stretched between the nonreacting binary systems AC, AD, BC, and BD (K ) 1).

Figure 9. Reaction: A + B a C (with two liquid phases). The two liquid phases with the concentrations x′ und x′′ are in chemical and physical equilibrium. Within the miscibility gap the reaction space has the dimension zero, outside the dimension one. An example is the reaction of isobutene with water to tert-butyl alcohol (Sakuth, 1995).

(3)

νiyP νP Yi ) νTyP 1νP

(4)

yi -

where P is the chosen reference component. When the transformation is applied, the transformed liquid and vapor mole fraction for component P is set to zero (i ) P; XP ) YP ) 0). The transformed composition coordinates fulfill the following contraints: nc

nc

(5)

The stoichiometric coefficient νT is defined as nc

νT )

∑ i)1

νi

Figure 11. Tranformation of the coordinates for the reaction A + B a C.

components being set to zero:

νI ) 0

νixP νP Xi ) νTxP 1νP xi -

X i ) ∑ Yi ) 1 ∑ i)1 i)1

Figure 10. Reaction: A + B a C + D (with two liquid phases). If the system AC has a miscibility gap, the reaction space will be reduced. Within the miscibility gap, the reaction space has the dimension one, outside the dimension two; see Table 1. An example is the esterification of n-pentyl alcohol and acetic acid to pentyl acetate and water.

(6)

Inert components can be included in that scheme, simply by the stoichiometric coefficient νI for inert

(7)

Consider, for example, a mixture of A, B, and C in which the equilibrium reaction A + B a C takes place. Using transformed concentration coordinates, we assume that C is completely decomposed to A and B and only the transformed concentration of A or B has to be specified; see Figure 11. By the transformation the total number of moles changes, if νT * 0. Transformed concentration coordi-

(

N h )N 1-

)

νTxP νP

(8)

nates can be used to derive the lever rule and the equations for the operating line for a reactive distillation column; see the work of Barbosa and Doherty (1988b) and Espinosa et al. (1995a). The overall and the component molar balance for the rectifying section of a reactive distillation column are as follows:

G)D+L+R

(9)

GyGi ) DxDi + LxLi + Ri

(10)

Using transformed composition coordinates, eqs 9 and 10 can be rewritten:

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In a similar way, transformed coordinates can be applied to derive the equations for the rectifying and stripping section of a reactive distillation column; see Figure 13. These equations are derived under the following assumptions: (a) chemical and vapor-liquid equilibrium is achieved on all stages and (b) the column operates at steady state. Using transformed flow rates and concentration coordinates, the overall balance and component balance for the rectifying section are as follows:

Figure 12. Lever rule for reacting systems.

Gn-1 ) Ln + D h

(17)

Gn-1Yn-1 ) LnXn + D h XD

(18)

The local reflux ratio on stage n for the rectifying section is defined as

( (

) )

νTxnP νP Ln v) ) D h νTxDP D 1νP Ln 1 -

(19)

Hence, the equation for the operating line in the rectifying section changes to

Yn-1 )

v 1 X + X v+1 n v+1 D

(20)

Analogously the operating line for the stripping section can be derived, using v* as the local reflux ratio on stage m in the stripping section: Figure 13. Material balance of a reactive distillation column.

(

G 1-

(

G yGi -

) ( ) (

) ( ) (

) )

νTyGP νTxDP νTxLP )D 1+L 1νP νP νP

(11)

νiyGP νixDP νixLP ) D xDi + L xLi (12) νP νP νP

L/D )

( )

XDi - YGi YGi - XLi

1-

(13)

) )

νTxmP νP Lm ) v* ) B h νTxBP B 1νP Ym-1 )

Rewriting eqs 11 and 12 gives the following:

νTxDP νP νTxLP 1νP

( (

Lm 1 -

v* 1 X X v* - 1 m v* - 1 B

(21)

(22)

2.3. The Concept of Reactive Distillation Lines. Using transformed concentration coordinates and flow rates, the equations for the operating lines and the lever rule have the same structure as for systems without reaction. For infinite reflux ratio (v f ∞), the operating line can easily be calculated. The transformed liquid

The transformed flow rates are defined as the following:

( (

) )

νTxLP L h )L 1νP

(14)

νTxDP νP

(15)

D h )D 1-

Equation 12 can be rearranged with the help of eqs 14 and 15:

L h /D h )

XDi - YGi YGi - XLi

(16)

This is the lever rule for systems with one equilibrium reaction; see Figure 12.

Yn-1 ) Xn

(23)

Yn ) f(Xn,P)

(24)

composition X on stage n is identical to the transformed vapor concentration Y arising from stage n - 1. The vapor concentration is a function of the transformed liquid concentration and the pressure. Similar to nonreactive distillation (Stichlmair, 1988) these lines can be called reactive distillation lines. Top and bottom product for a reactive distillation column at infinite reflux must be located on the reactive distillation line and on the mass balance line; see Figure 14.

F h XFi ) D h XDi + B h XBi

(25)

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Figure 14. Concept of reactive distillation lines. XD and XB are located on a straight line that passes through the feed XF.

Figure 15. Reactive distillation lines for a system A + B a C in the presence of the inert component D (relative volatilities A/B/ C/D, 4/2/1/8, equilibrium constant, K ) 0,1; pressure, P ) 1.013 bar).

The arrow on the distillation line points in the direction of increasing low boiler concentrations and decreasing temperatures. Only algebraic equations have to be solved to calculate a distillation line. The concentration and temperature profiles calculated by a reactive distillation line can serve as a first estimate for the rigorous simulation with an equilibrium stage model. Using reactive distillation line diagrams, it is possible to explore the feasibility of a specific reactive distillation. The number of stages between the bottom and the top product is the minimum number of stages at infinite reflux. 3. Application of the Reactive Distillation Line Concept Applying the concept of reactive distillation lines, it is possible to represent concentration profiles at infinite reflux conditions in a reactive distillation column and to discuss the feasibility of a specific reactive distillation concept. In the following figures the influence of volatilities and equilibrium constants for different ideal systems will be studied. Then the discussion will be extended to an industrially important system. The presented simulations are based on the following assumptions: (a) chemical and vapor-liquid equilibrium is achieved on all stages; (b) the column operates at steady state; (c) the molar heat of vaporization for all components is equal; (d) heat losses and the heat of reaction are negligible; (e) the heat of mixing is negligible; (f) the sensible heat of the streams can be neglected; (g) all streams are fed into the column as saturated liquids. 3.1. Ideal Systems. One of the most important areas of application for reactive distillation is the etherification. Figure 15 presents the reactive distillation lines for a system with the reaction A + B a C in the presence of an inert component, D. Relative

Figure 16. Reactive distillation lines for a system A + B a C in the presence of the inert component D (relative volatilities A/B/ C/D, 4/2/1/8; equilibrium constant, K ) 10; pressure, P ) 1.013 bar).

volatilities and the equilibrium constant used in the calculation are given in the figure. (The temperatures correspond to parameters for the Antoine equation given in the Appendix. Ideal gas and liquid phase were assumed.) In this diagram, the edges AD and BD represent the binary nonreactive systems AD and BD. The edge AB represents the reactive system AB in chemical equilibrium with the component C (compare Figures 6 and 7). The concentration with the coordinates XB ) 0.5 and XD ) 0 has the maximum concentration of C in equilibrium with A and B. Notice, there is no point corresponding to the pure product C. All distillation lines start at the high-boiling component B and end at the low-boiling inert component D. Corresponding to the nonreactive distillation, we call the starting and end points of reactive distillation lines nodes and all other vertices saddles (Fien, 1994). The distillation lines indicate that two different reactive distillation designs are feasible. In design I, the component C decomposes and B is separated from A and D. Using design II, the component C is formed and the inert component D is separated from a mixture consisting of A and B in chemical equilibrium with C. To purify C, a nonreactive distillation section must be added. This nonreactive section purifies C and recycles the educts A and B to the reactive distillation zone. When the equilibrium constant is increased, a reactive azeotrope appears; see Figure 16. As defined by Ung and Doherty (1995), a reactive azeotrope has identical transformed vapor and liquid concentration coordinates.

Xi ) Yi

(26)

The reactive azeotrope and the inert component D are nodes; the components A and B are saddles. Corresponding to the normal nonreactive distillation, there is no reactive distillation border (Stichlmair et al., 1989) that divides the diagram into sections with different start or end points of the reactive distillation lines. All reactive distillation lines begin at that high-boiling reactive azeotrope and end at the low-boiling inert component D. Compared with Figure 15, it is not possible to realize design I (decomposition of C). Only design II (formation of C, separation D/A, B, C) is feasible. Another important type of reaction is the esterification. Many esterifications (Block, 1977) are carried out in reactive distillation columns. In the following figures the influence of the relative volatilities on the reactive distillation for this type of reaction (A + B a C + D) is studied.

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3037

Figure 17. Reactive distillation lines for a system A + B a C + D (relative volatilities A/B/C/D, 4/2/8/1; equilibrium constant, K ) 10; pressure, P ) 1.013 bar).

Figure 18. Concentration profile of a reactive distillation with 20 stages for the properties given in Figure 17. The input data for the simulation are molar ratio A/B ) 1:1; feed stage ) 10; reflux ratio v ) 3:1; pressure, P ) 1.013 bar. The resulting conversion of A is 99.7%.

For the representation of the quarternary system A, B, C, D a square diagram is used. The edges are the nonreactive binary systems. The diagonals AB and CD are the reactive binary systems; see Figures 8 and 17. An equilibrium constant of 10 is used in the calculation. In the first case (Figure 17), the educts A and B are medium boilers and the products C and D are low and high boilers, respectively. All distillation lines start at the high-boiling product and end at the low-boiling product. The products C and D are nodes in the diagram shown in Figure 17, and the educts A and B are saddles. From Figure 17 it can be seen that the production of C and D in one reactive distillation column is feasible. The reactive distillation line diagram represents the concentration profiles at infinite reflux. Figure 18 shows the concentration profile for the production of C and D at a finite reflux. The column has 20 stages and operates at a reflux ratio of 3:1. The equilibrium reaction takes place on all stages. The molar ratio distillate flow/bottom flow for the simulations with the reaction A + B f C + D is 1:1. Figure 19 illustrates the situation for the same system except that product D is a medium-boiling component. Then, product C, which is volatile, and educt B are nodes whereas product D and educt A are saddles. In that case, only with a large effort can a high conversion and high-product purity be achieved at a stoichiometric ratio of educts in one reactive distillation column. To show some effects, Figures 20-22 depict the concentration profiles of three simulations. In all cases the columns are equipped with 120 stages on which distillation and the equilibrium reaction take place. In the first case (Figure 20), a conversion of 83% can be achieved in a reactive distillation column with one feed stage and a reflux ratio of 1.2:1. In the second and third cases, the columns are also equipped with 120 stages, but they have two separate

Figure 19. Reactive distillation lines for a system A + B a C + D (relative volatilities A/B/C/D, 4/1/8/2; equilibrium constant, K ) 10; pressure, P ) 1.013 bar).

Figure 20. Concentration profile of a reactive distillation with 120 stages for the properties given in Figure 19. The input data for the simulation are molar ratio A/B ) 1:1; feed stage ) 50; reflux ratio v ) 1.2; pressure, P ) 1.013 bar. The resulting conversion of A is 83%.

Figure 21. Concentration profile of a reactive distillation with 120 stages for the properties given in Figure 19. The input data for the simulation are molar ratio A/B ) 1:1; feed stages ) 50 and 36; reflux ratio v ) 1.2; pressure, P ) 1.013 bar. The resulting conversion of A is 99%.

Figure 22. Concentration profile of a reactive distillation with 120 stages for the properties given in Figure 20. The input data for the simulation are molar ratio A/B ) 1:1; feed stages ) 50 and 36; reflux ratio v ) 2:1; pressure, P ) 1.013 bar. The resulting conversion of A is 90%.

feed stages. The second feed stage is one important possibility to increase the conversion. The high boiler is fed into the column above the low boiler to achieve countercurrent flow of the educts. A conversion of 99% can be achieved at a reflux ratio of 1.2:1, see Figure 21.

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Figure 23. Relation between reflux ratio and conversion. The relative volatilities and the column data are given in Figures 19 and 22.

The figure also shows the concentration profiles for the rectifying section, the section between the two feeds and the stripping section. Using two feed stages, the concentration profiles in the stripping and rectifying section are shifted in the direction of the desired products. When the reflux ratio is increased (Figure 22), the conversion decreases because the separation of the unreacted educt B is improved. This example illustrates the difficulties of reactive distillation if one of the products is a saddle in the reactive distillation line diagram. In Figure 23, the results of the case study are summarized. The low conversion on the left hand side of the maximum is caused by the insufficient separation of the educts. When the reflux ratio is increased up to about 1.2:1, the product purities and the conversion are improved. At reflux ratios higher than 1.2:1, the conversion decreases because the separation of the unreacted educt B is improved. In contrast to the situation in Figure 23, it is known from Wo¨rz and Mayer (1992) for examples similar to Figure 18 that by increasing the reflux ratio the conversion increases also. These relations between reflux ratio and conversion are important for the optimization and control of reactive distillation columns. From the discussion of these different systems some simple rules can be derived. Examples are as follows: Reactive distillation is a feasible and probably an economic operation if both products are connected by a reactive distillation line, the products are nodes in a reactive distillation line diagram, and the boiling point difference between the products is large. If one or both products are saddles, the concentration profile can be shifted in the direction of the saddle by using a column with two feed stages. 3.2. Highly Nonideal System. In this section the considerations are extended to a highly nonideal system. As an example the esterification of formic acid (FA) with methanol (MeOH) to methyl formate (MF) and water (H2O) is discussed:

FA + MeOH a MF +H2O

Kx ) 5

In the vapor phase formic acid dimerizes:

2FA a FADim The dimerization equilibrium is described by the chemical theory (Gmehling et al., 1979). In the systems there are five components and two equilibrium reactions. Therefore the system has 2 degrees of freedom at a given pressure or temperature.

Figure 24. Reaction: FA + MeOH a MF + H2O. Boiling point surface as a function of transformed liquid composition coordinates (P ) 3 bar).

Figure 25. Reactive distillation line diagram for the esterification of formic acid and methanol (P ) 3 bar).

Figures 24 and 25 depict the boiling point surface and the distillation line diagram for the system FA, MeOH, MF, H2O. The azeotrope formic acid/water has the highest boiling point and the azeotrope methyl formate/ methanol the lowest. All reactive distillation lines start at the azeotrope FA/H2O and end at the azeotrope MF/ H2O. The azeotropes are nodes in this system, and the pure components are saddles. The system has no reactive distillation borders. In Figure 26 the concentration profile of the reactive distillation is depicted. The high-boiling component (FA) is fed above the low-boiling component (MeOH) into the reactive distillation column. Formic acid and methanol are nearly completely converted into methyl formate and water. The products of this reactive distillation are not the nodes but the saddles. There are three reasons why this reactive distillation is easy: (a) the boiling point differences between the azeotropes FA/H2O and water on one side and the azeotrope MF/MeOH and methanol on the other side are small, so that the separation between the azeotropes (here the nodes) and the pure components (here the saddles) is difficult; (b) the boiling point difference between the desired products is large; (c) the chemical equilibrium lies on the side of the products (K ) 5). The other way around, these are the reasons why no economic design was found to produce formic acid and

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Figure 27. Combined distillation line. Reaction A a B in the presence of C as the inert component. Figure 26. Concentration profile of a reactive distillation with 22 stages for the physical properties given in the Appendix. The input data for the simulation are molar ratio FA/MeOH ) 1:1; feed stages ) 17(FA) and 10(MeOH); reflux ratio, v ) 2.5; pressure, P ) 3 bar. The resulting conversion of FA is 99.7%.

methanol from water and methyl formate in one reactive distillation column. From this and similar examples the following rule can be derived: If one or both products are saddles, a high conversion is required at a stoichiometric ratio of educts, the separation between the saddles (desired top to bottom product) and the nodes (undesired top to bottom product) is difficult, the boiling point difference between the products is large, no distillation border must be crossed, and the chemical equilibrium is on the side of the desired products, then the reactive distillation is a feasible and probably an economic operation. 4. The Combination of Reactive and Nonreactive Distillation 4.1. Combined Distillation Lines. The reactive distillation line concept allows us to discuss the feasibility of a reactive distillation, if on all stages distillation and the equilibrium reaction occur simultaneously. We call this design simple reactive distillation. In a simple reactive distillation the total concentration profile and the products are located in the reaction space; see Figures 3-10. If it is necessary to separate a product that is not in the reaction space, a section with nonreactive distillation trays must be added. Even for complex reacting systems, it is possible to decide whether a product is located in the reaction space. From the evaluation of the reaction spaces the following rules can be deduced: (a) all components which need a reactant for the forward or backward reaction are located in the reaction space (e.g., for the reaction A a B neither A nor B is located in the reaction space, whereas for the reaction A + B a C only C is not in the reaction space.); (b) all inert components are located in the reaction space. As an example, Table 2 shows the application of these rules for the systems discussed in the present paper. These rules can also be applied to other systems. It should be noted that it is necessary to consider not only the type of reaction but also the desired direction. For example, if for the system A + B a C the component C is the educt, a simple reactive distillation is feasible, whereas if C is a desired product, a combination of

reactive and nonreactive distillation is necessary. This consideration is independent of the stoichiometric coefficients if νi * 0. As an extension to the reactive distillation line concept presented above, a combined distillation line concept was developed to estimate the concentration profiles at total reflux for a distillation column with a reactive and a nonreactive distillation section. Consider for example the reactive distillation problem in Figure 27 with the reaction A a B. The component B reacts to the desired product A. The feed is a mixture of B and the inert component C. A is the high-, B the medium-, and C is the low-boiling component. According to the rules the product is not in the reaction space. To produce A and to separate the inert component C, the column is divided into two sections. Because the product A is a high-boiling component, the nonreactive section must be located in the stripping section. To estimate the concentration profile, a nonreactive distillation line (Stichlmair, 1988) can be used.

yn-1 ) xn

(27)

yn ) f(xn,P)

(28)

As a starting point a concentration in the vicinity of A is taken (stage 1, Figure 27). Stepwise the concentrations on higher stages in the nonreacting zone of the stripping section are calculated (stages 2, 3, 4′). The vapor arising from stage 3 has the concentration 4′. However the concentration 4′ is on the “wrong” side of the chemical equilibrium line. Therefore the reactive distillation line concept has to be applied. This switch corresponds to the transition from 4′ to 4. To estimate the concentration profile in the reactive distillation section, a reactive distillation line was calculated with the concentration 4 as starting point. This combined reactive distillation line concept is now applied to the example in Figure 16, the reaction of A + B a C in the presence of D as an inert component. In the column, A and B are converted to C in the presence of D. Figure 28 shows the reaction space and the concentration profile for this reactive distillation. It is assumed that A and B are medium-boiling components, C is a high-boiling component, and D is a low-boiling component. The chemical equilibrium is on the side of the products (K ) 10). Using a column with a reactive distillation section above the feed stage and a section with distillation only below the feed stage, it is possible to separate the inert component D as the top and C as the bottom product. Using a simple reactive distillation,

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Figure 28. Reaction space and concentration profile for the reactive distillation of A, B, and D with D as inert component. A and B are converted to C. The equilibrium constant is K ) 10. The relative volatilities of the components A/B/C/D are 4/2/1/8. The pressure is P ) 1.013 bar. Table 2. Guideline for the Combination of Reactive and Nonreactive Distillation in One Reactive Distillation Column

reaction

inerts

AaB AaB

C

AaB

C,D

A+BaC A+BaC A+BaC+D

D

desired products

section only with distillation required

A or B B/C A/C BC/D; BD/C; B/CD AC/D; AD/C; A/CD C A/B C/D AD/B; A/BD A/B C/D

+ + + + + + + -

the product concentration is limited by the chemical equilibrium. Because the desired product C is not located in the reaction space, the column must be divided into one reactive distillation and one nonreactive distillation section. To separate the inert component D, it is not necessary to interrupt the reactive distillation in the rectifying section because D is located in the reaction space. The evaluation of the liquid concentration profile indicates that the upper part of the concentration profile in the rectifying section is on a nonreactive edge CD. Therefore it is not necessary to have a reactive distillation zone in the whole rectifying section. If the desired reaction is the decomposition of C to A and B, it is not necessary to divide the column into a reactive distillation and a distillation section (compare Table 2). All products are located in the reaction space. But the decomposition in one simple reactive distillation only is possible, if the chemical equilibrium is on the side of the decomposition product (compare Figures 15 and 16). Concentration and temperature profile calculated with a combined reactive distillation line can serve as a starting point for rigorous simulation. Using this approach, difficulties with convergence and multiplicity analyzed for example by Jacobs and Krishna (1993) and Nijhuis et al. (1993) for the methyl tert-butyl ether (MTBE) system can be minimized. 4.2. Impact on the Process Design. A reactive distillation column can be divided into sections with reactive distillation and in sections with only distillation

Figure 29. Process for the design problem as in Figure 28. It is supposed that a homogeneous high-boiling catalyst is applied.

to leave the reaction space by (a) using distillation trays with a high-residence time in the reactive distillation section and with a low-residence time in the distillation section; (b) choosing the feed stage for the catalyst and selecting a catalyst with a suitable boiling point; (c) fixing a heterogeneous catalyst in the reactive distillation section of the column (see for example the patents of Jones (1991), Ghelfi and Stringaro (1993), and Smith (1990)). These methods can be applied separately or can be combined. Often the chemical reaction in the column must be catalyzed. The type of catalyst has a large impact on the process design. Assume, for example, that it is possible to use two different types of catalyst for the example in Figure 28: (a) a homogeneous catalyst, which is the highest-boiling component in the system, and (b) a heterogeneous catalyst, which can be fixed inside the column. If the reaction is fast in the presence of the catalyst, the homogeneous catalyst must be separated to produce C; see Figure 29. In the first reactive distillation column the inert component D can be separated as the top product. The mixture of the catalyst and C in chemical equilibrium with A and B is the bottom product. In the second distillation A, B, and C must be separated from the catalyst. According to the rules of Schoenmakers (1982) C will be partially decomposed into the educts A

Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997 3041

and B in a undesired reaction in the stripping section of this distillation column. Now it is possible in a third distillation to separate C and to recycle the unconverted educts A and B. When a heterogeneous catalyst which can be fixed in the reactive distillation column is applied, the whole process can be performed in a reactive distillation column; see Figure 28. An example of the impact of catalyst selection on the process design is the synthesis of MTBE. It is possible to catalyze the reaction with sulfuric acid and with strong acid ion-exchange resins. The process with the heterogeneous catalysis corresponds to the process in Figure 28, the process with the homogeneous catalyst to the process in Figure 29. The comparison of these to flow sheets (Figures 28 and 29) indicates that it is very important that the catalyst is really fixed in the reactive distillation section in the process depicted in Figure 29. Otherwise, this process is not feasible. 5. Summary and Future Development In this paper the main elements of a design procedure for reactive distillation processes with an equilibrium reaction were identified. These elements are as follows: (a) Evaluation of the reaction space. When the reaction space is analyzed, it can be decided whether a reactive distillation must be combined with a nonreactive distillation. (b) Evaluation of the reactive distillation line diagrams. The interpretation of the reactive distillation line diagrams supports the decision on the feasibility of a reactive distillation process. The characteristics of the distillation line diagram give hints on the basic column design. The necessity of two feed stages can be predicted. (c) Application of combined reactive/nonreactive distillation lines. The combined reactive/nonreactive distillation line concept allows us to check the proposed column design. (d) Rigorous simulation and optimization. The information collected above is the starting point for the rigorous simulation and optimization. This design procedure will be integrated in the heuristic numeric system PROSYN for process synthesis; see the work of Schembecker et al. (1994) and Schembecker and Simmrock (1996). Notation a, b, c ) parameters of the Antoine equation B ) mole flow of bottom product B h ) transformed mole flow of bottom product FG ) degrees of freedom F ) mole flow of feed F h ) transformed mole flow of feed D ) mole flow of distillate D h ) transformed mole flow of distillate G ) mole flow of vapor G h ) transformed mole flow of vapor K ) equilibrium constant (in this work defined as nc νi K ) ∏i)1 xi L ) mole flow of liquid L h ) transformed mole flow of liquid P ) pressure nc ) number of components N ) number of moles N h ) transformed number of moles r ) number of independent chemical equilibrium reactions R ) reaction Xi ) transformed liquid phase composition of component i vL ) liquid molar volume [cm3/mol]

Table 3 Antoine parameters volatility

a

b[°C]

c[°C]

8 4 2 1

14.044 13.351 12.658 11.965

3984.923 3984.923 3984.923 3984.923

233.426 233.426 233.426 233.426

Table 4 Antoine parameters

liquid molar volume

component

a

b [°C]

c [°C]

vL (cm3/mol)

water (H2O) methyl formate (MF) methanol (MeOH) formic acid (FA)

11.9647 10.2965 11.9869 9.3703

3984.9228 2801.0487 3643.3136 2982.4463

233.426 240.37 239.726 218

18.07 61.54 40.73 37.91

xi ) mole fraction of component i in the liquid Yi ) transformed vapor phase composition of component i yi ) mole fraction of component i in the vapor v ) reflux ratio Greek Letters νI ) stoichiometric coefficient of component i νT ) the sum of the stoichiometric coefficients nc νi νT ) ∑i)1 π ) number of phases Subscripts β ) bottom product D ) distillate Dim ) dimer i ) component i I ) inert component L ) liquid P ) reference component (Barbosa and Doherty, 1988a; Espinosa et al., 1995b) m ) stage m (stripping section) n ) stage n (rectifying section) Abbreviations Cat ) catalyst FA ) formic acid MeOH ) methanol MF ) methyl formate

Appendix Physical Properties. For the calculations of the vapor-liquid equilibrium the parameters listed in Tables 3 (Figures 15-23 and 28) and 4 (Figures 24 and 25) were used. The Antoine equation is defined as follows:

ln(P) ) a -

b ; P [bar] T+c

Parameters for the Wilson equation (Gmehling et al., 1979) are as follows: a12 ) 2001.7 a13 ) 515.9 a14 ) -194.6 Λ24 ) 1 a23 ) 151.7973 Λ34 ) 1

a21 ) 80.1 a31 ) 74.5 a41 ) 758.5 Λ42 ) 1 a32 ) 907.572 Λ43 ) 1

Chemical Theory. The dimerization of formic acid in the vapor phase was taken into account by the

3042 Ind. Eng. Chem. Res., Vol. 36, No. 8, 1997

chemical theory (Gmehling et al., 1979). The parameters are A ) -18.12 and B ) 7099 K. Literature Cited Agreda, V. H.; Partin L. R. Reactive distillation process for the production of methyl acetate. U.S. Patent 4,435,595, 1984. Backhaus, A. A. Continuous process for the manufacture of esters. U.S. Patent 1,400,849, 1921. Barbosa, D.; Doherty, M. F. The simple distillation of homogeneous reactive mixtures. Chem. Eng. Sci. 1988a, 43, 541-550. Barbosa, D.; Doherty, M. F. Design of Minimum Reflux Calculations for Single-Feed Multicomponent Reactive Distillation Columns. Chem. Eng. Sci. 1988b, 43 (7), 1523-1537. Block, U. Carrying Out Continuous Reactions with Superposed Distillation. Chem.-Ing.-Tech. 1977, 49 (2), 151. Espinosa, J.; Aguirre, P. A.; Perez G. A. Some Aspects in the design of multicomponent reactive distillation columns including nonreactive species. Chem. Eng. Sci. 1995a, 50 (3), 469-468. Espinosa, J.; Aguirre, P. A.; Perez, G. A. Product Composition Regions of Single-Feed Reactive Distillation Columns: Mixtures Containing Inerts. Ind. Eng. Chem. Res. 1995b, 34, 853-861. Fien, L. Heuristic Synthesis and Short Design of Separation Processes Using Residue Curve Mapes: A Review. Ind. Eng. Chem. Res. 1994, 33, 2505-2522. Ghelfi, L.; Stringaro, J. P. Katalysierender Festbettreaktor. EP 93-810612, 1993. Gmehling, J.; Onken, U.; Arlt, W. Vapor-Liquid Equilibrium Data Collection. Chemistry Data Series; DECHEMA: Frankfurt, FRG, 1979. Jakobs, R.; Krishna, R. Multiple Solutions in Reactive Distillation for Methyl tert-Butyl Ether Synthesis. Ind. Eng. Chem. Res. 1993, 32, 1706-1709. Jones E. M. Catalytic distillation reactor. EP 91305245.2, 1991. Nijhuis, S. A.; Kerkhof, F. P. J. M.; Mak, A. N. S. Multiple Steady States during Reactive Distillation of Methyl tert-Butylether. Ind. Eng. Chem. Res. 1993, 32, 2767-2774.

Sakuth, P. Verfahren zur Spaltung von Tertia¨rbutylalkohol in einer Reaktionskolonne. DE 195 04 555.6 A1, 1995. Schembecker, G.; Simmrock, K. H.; Wolff, A. Synthesis of Chemical Process Flowsheets by means of Cooperating Knowledge Integrating Systems. Proceedings from the Fourth European Symposium on Computer Aided Process Engineering, IChemE Symposium Series No. 133, Warwick, U.K., 1994; pp 333-341. Schembecker, G.; Simmrock, K. H. Heuristic-Numeric Process Synthesis with PROSYN. AIChE Symp. Ser. No. 312 1996, 92, 275-278. Schoenmakers, H. Possibilities of Suppressing Undesired Reactions in Distillation Columns. Chem.-Ing.-Tech. 1982, 54 (12), 1196-1197. Smith, L. A. Catalytic distillation. EP 90113680.4, 1990. Stichlmair, J. Separation of Ternary Mixtures by Rectification. Chem.-Ing.-Tech. 1988, 60 (10), 747-754. Stichlmair, J.; Fair, J. R.; Bravo, J. L. Separation of Azeotropic Mixtures via Enhanced Distillation. Chem. Eng. Prog. 1989, 85 (1), 63-69. Ung, S.; Doherty, M. F. Necessary and Sufficient Conditions for Reactive Azeotropes in Multicomponents Mixtures. AIChE J. 1995, 41 (11), 2383-2392. Wales, S. M. Phase Equilibrium Chemical Engineering; Butterworth: Boston, MA, 1985. Wo¨rz, O.; Mayer, H. H. In Ullmann’s Encyclopedia of Industrial Chemistry, VCH Verlagsgesellschaft: Weinheim, Germany, 1992; Vol. B4 (Reaction columns).

Received for review November 14, 1996 Revised manuscript received February 3, 1997 Accepted February 4, 1997X IE960727P

X Abstract published in Advance ACS Abstracts, June 15, 1997.