Recycle Selection for Homogeneous Azeotropic Distillation Sequences

May 24, 2005 - uses recycle streams to manipulate the feed composition ... In the problem specification step,3 the feed and ..... Therefore, a meaning...
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Ind. Eng. Chem. Res. 2005, 44, 4641-4655

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Recycle Selection for Homogeneous Azeotropic Distillation Sequences Guilian Liu,†,§ Megan Jobson,*,† Robin Smith,† and Oliver M. Wahnschafft‡ Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester, P. O. Box 88, Manchester M60 1QD, U.K., and Aspen Technology, Inc., Ten Canal Park, Cambridge, Massachusetts 02141

To recover all the pure components from a homogeneous azeotropic mixture using distillation, one or more recycles are needed. These recycles may have compositions close to those of singular points (i.e., pure components and azeotropes) or may have compositions of mixtures of singular points. The selection of the recycle structure and of the recycle flow rates for a given distillation sequence is a design challenge, as recycles impact on both the feasibility and performance (e.g., the number of stages and the reflux requirement) of separations. This work analyzes recycles with singular point compositions in terms of their effects on the feasibility and performance of splits. On the basis of this analysis, a set of rules and a systematic procedure are developed for selecting recycles with singular point compositions and for identifying promising recycles comprising a mixture of singular points. These rules and procedures allow the recycle structure to be proposed efficiently for a distillation sequence separating a multicomponent homogeneous azeotropic mixture into pure component products. Introduction Sequences separating homogeneous azeotropic mixtures into their pure component products need recycles, because components forming an azeotrope cannot be separated by distillation columns and because distillation and compartment boundaries1 constrain product compositions. The composition and flow rate of a proposed recycle may affect the feasibility and performance (e.g., the reflux ratio and number of stages required) of all the columns contained within the recycle loop. Recycles, therefore, pose a challenge for the synthesis of distillation sequences separating azeotropic mixtures. For ternary azeotropic mixtures, residue-curve and distillation-line maps can be used to aid the selection of recycles. However, no such graphical tools exist for multicomponent azeotropic mixtures, as these maps cannot be visualized. Wahnschafft et al.2 and Thong and Jobson3 proposed methods for the synthesis of distillation sequences with recycles. However, these methods cannot systematically and efficiently identify a suitable recycle structure for a distillation sequence separating a multicomponent homogeneous azeotropic mixture. Tao et al.4 proposed a systematic method for generating process alternatives with recycles, in which recycle alternatives are generated according to the feasibility and component recovery of separations. The work of Tao et al.4 does not consider the effects of different types of recycles on different types of splits. This paper proposes rules and systematic procedures for generating simplified recycle structures; the ap* To whom correspondence should be addressed. Tel.: +44(0)161 306 4381. Fax: +44(0)161 236 7439. E-mail: [email protected]. † University of Manchester Institute of Science and Technology. ‡ Aspen Technology, Inc. § Current address: Department of Chemical Engineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China.

proach incorporates insights into the effects of different types of recycles on the feasibility of different types of splits, on flowsheet performance, and on the recovery of azeotropic components. Using these rules and procedures, beneficial recycles with the compositions of either a singular point (i.e., a pure component or an azeotrope) or a mixture of singular points can be identified. Background Because of the existence of azeotropes, the composition space of an azeotropic mixture is generally separated into distillation regions and compartments.1 All residue curves within a distillation region have the same pair of initial and terminal singular points, which are unstable and stable nodes in the residue-curve map, respectively, while residue curves lying in different distillation regions have different stable or unstable nodes.5 Two adjacent distillation regions are separated by a distillation boundary, which imposes limitations on product compositions and composition profiles of distillation columns. At total reflux, a feasible separation must have two products lying in the same distillation region.6 A separation, with products in one region and the feed in another, may also be feasible if the feed lies on the concave side of the distillation boundary. Such a separation crosses the distillation boundary and is called a distillation-boundary crossing (DBC) split in this work. Although all residue curves within a distillation region begin at the same unstable node and end at the same stable node, sometimes they may approach (move toward and away from) different saddle points. In this case, the distillation region is generally separated into several “continuous distillation regions”7 or “compartments”.1 In each compartment, all residue curves start from the unstable node, approach saddle points one by one in the order of increasing boiling temperature, and end at the stable node. Residue curves can approach all the saddle points appearing within a compartment.1 This behavior is analogous to that in the composition

10.1021/ie049402w CCC: $30.25 © 2005 American Chemical Society Published on Web 05/24/2005

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Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 Table 1. Distillation Regions, Distillation Boundaries, Compartments and Compartment Boundaries in the Quaternary System Shown in Figure 1 1 distillation regions compartments

1-2-3-5-6 1-2-5-6 1-3-5-6

compartment boundaries

1-5-6

distillation boundary

Figure 1. Adjacency and reachability matrix of a quaternary mixture with three azeotropes. One distillation boundary and one compartment boundary are shown by shaded surfaces. Reprinted with permission from ref 1, copyright 2001 Elsevier; and from ref 13, copyright 2004 American Chemical Society.

space of non-azeotropic mixtures. Two neighboring compartments, which lie in the same distillation region, have different saddle points and are separated by a compartment boundary, or “continuous distillation boundary”.7 This boundary can be linearly approximated by connecting the common singular points of the two compartments using straight lines.1 Single-feed columns can sometimes cross a compartment boundary (i.e., the two products lie in adjacent compartments), and twofeed columns can further facilitate such a separation.1 Residue-curve maps allow a visual representation of distillation regions and compartments. However, for multicomponent azeotropic mixtures, the topology of the composition space (i.e., the existence and location of distillation regions and compartments and their boundaries) cannot be visualized. Fortunately, the approach of Knight and Doherty8 allows a mathematical representation of the topology. For a multicomponent azeotropic mixture, with singular points numbered in the order of increasing boiling temperature, an adjacency matrix, A, and a reachability matrix, R, can be defined.8 An element of the adjacency matrix is defined by ai,j ) 1 if a residue curve joins singular point i to singular point j; otherwise, ai,j ) 0. An element of the reachability matrix is defined by ri,j ) 1 if there is any path from i to j; otherwise, ri,j ) 0. Rooks et al.9 developed a general procedure for computing the adjacency and reachability matrices for multicomponent homogeneous mixtures. Using these matrices, algorithmic procedures can identify distillation regions9 and compartments,1 without relying on visualization tools. Distillation boundaries are linearly approximated by Rooks et al.,9 as are compartment boundaries by Thong and Jobson.1 Figure 1 illustrates the adjacency and reachability matrices of a quaternary mixture with three azeotropes. Using the procedures of Rooks et al.,9 it can be established that the whole composition space is separated into two distillation regions by distillation boundary 1-2-3-5. Two compartments in distillation region 1-2-3-5-6 and three in region 1-2-3-4-5-7 can be identified using the procedure of Thong and Jobson.1 The distillation regions, compartments, and corresponding boundaries are listed in Table 1.1 Previously published work on the synthesis of distillation sequences with recycles includes the sequential methodology of Wahnschafft et al.2 and the algorithmic procedure of Thong and Jobson.3 In the approach of Wahnschafft et al.,2 repeated process simulations are employed to identify all possible column sequences that can be used to separate a given mixture. Within these sequences, separations are combined according to stream

1-2-3-4-5-7 1-2-5-7 1-3-5-7 1-3-4-7 1-5-7 1-3-7 1-2-3-5

composition. Two types of recycles, primary and secondary recycles, are assigned. Primary recycles supply a separation agent, and secondary recycles are used to avoid redundant separations. After assigning recycles, the sequence is resimulated. Some iteration is required in the synthesis procedure, because the recycles affect the feed compositions to proposed separations. In principle, the approach of Wahnschafft et al.2 is applicable to multicomponent mixtures. However, obtaining appropriate recycle compositions becomes difficult for multicomponent mixtures, and it is difficult to converge flowsheet simulations. Also, since simulation at high reflux ratios is used to check the feasibility of proposed separations, this approach can miss separations only possible at lower reflux ratios.3 More recently, Thong and Jobson3 proposed an algorithmic procedure for generating distillation sequences and corresponding recycle superstructures separating multicomponent azeotropic mixtures. The procedure uses recycle streams to manipulate the feed composition to columns in the sequence. Rather than fully specifying the product compositions, Thong and Jobson3 used product regions to specify product compositions. A product region is the set of product compositions that satisfies a certain topological constraint.1 For example, in Figure 2a, a product lying close to the distillation boundary lies in product region 3-4-5; a product close to the pure acetone vertex lies in product region 1. The term split is used to denote a separation with products specified in terms of product regions. Ideal splits are assumed, meaning that the column products lie precisely within the specified product regions and contain no trace impurities. The procedure involves problem specification, preliminary screening of column sequences, and generation of recycle options for a sequence of columns. This paper develops further the method of Thong and Jobson,3 which is described in more detail below. In the problem specification step,3 the feed and desired product compositions are specified. For a given feed mixture, all the azeotropes that occur can be found,10 and the adjacency and reachability matrices,8

Figure 2. (a) Quaternary system of acetone, chloroform, benzene, and toluene. (b) Sequence to separate equimolar feed F into pure component products. In column C1, split 1/3-4-5 is a sharp split that breaks the azeotrope between acetone and chloroform.

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as well as the distillation regions and distillation boundaries9 and the compartments and compartment boundaries,1 can be computed. For a given set of desired products, it can then be determined whether the feed and products lie in the same or different distillation regions.3,11 After specifying the problem, all possible sequences can be identified. Each column in a sequence performs a specified split, where the compositions of the products are represented by product regions. The second step involves preliminary screening of column sequences. The adjacency and reachability matrices are used to identify feasible splits and potentially feasible splits, i.e., splits for which the feasibility is uncertain and needs further investigation.1 These splits are classified as type A, B, and C splits.1,3 Type A splits satisfy the common saddle criterion,9 which requires the rectifying and stripping composition profiles of a feasible column to approach (move toward and away from) the same saddle at high reflux. Type A splits are feasible for any pair of product compositions in the corresponding product regions. Type B splits are sharp splits between singular points that are not adjacent in volatility order; they do not satisfy the common saddle criterion and are only feasible for some ranges of product compositions in the product regions. Type A and B splits do not cross compartment boundaries but may cross a distillation boundary. Type C splits cross a compartment boundary: the product compositions lie in two different compartments. These splits do not satisfy the common saddle criterion. Type C splits are potentially feasible:1 in some cases there will be no feasible pairs of products lying in the corresponding product regions. Once all the splits have been identified, all possible column sequences are generated by recursive searching.3,11,12 For a C-component mixture, each sequence starts with (C-1)-dimensional splits. Only column sequences that recover as final products all the desired singular point products are accepted; the assumption of ideal splits ensures that maximum recovery is achieved in all separations. No recycling is considered at this stage. The third step generates recycle options for a sequence of columns using a simple procedure. First, a superstructure of recycling options is constructed for a given sequence.3 Every final or intermediate product of the sequence is a potential recycle stream. All feeds to columns are potential destinations for recycle streams. The size of this superstructure is then reduced using the following set of rules:3 1. Azeotropes can either be recovered as final products, partially recovered (and partially recycled), or recycled completely. 2. Never recycle a stream to the column that produces it. 3. Never mix a recycle stream with a feed to a column performing a split where the recycle stream contains one or more components that are not present in either product stream. 4. Never mix streams with compositions in different compartments. The exception to this is recycle streams to columns performing type C splits; these streams can lie in either compartment that the split traverses. The first rule accounts for different requirements, e.g., the azeotrope might be recycled to the reactor or might be recycled internally within the separation flowsheet.3 From the second and third rules, it follows that only

the downstream products of an ideal split can be recycled to the feed of a column. No such conclusion can be drawn for a nonideal split.3 These rules do not account for the effects of a given recycle on the performance of the splits in a sequence or on the recovery of azeotrope-forming components. There are many recycle options for each sequence, and appropriate recycle options can only be identified after the stream compositions, themselves dependent on the recycle structure and flow rates, have been determined. Thong and Jobson3 proposed an iterative procedure for determining the product compositions of each column. Once all stream compositions have been identified, appropriate recycle options are determined using a material balance across every column.3 The procedure for closing the mass balance was not systematic, and while feasibility was addressed in this work, optimality was not. The procedure of Thong and Jobson1,3 allows all feasible and potentially feasible sequences to be identified and a recycle superstructure to be proposed for each sequence. A very large number of alternative sequences can be used to separate a multicomponent azeotropic mixture. For example, 5001 sequences can be used to separate a five-component mixture of acetone, benzene, 1-propanol, toluene, and styrene (with mole fractions in the feed of 0.2, 0.16, 0.17, 0.27, and 0.2, respectively).13 Even using the shortcut column design method proposed by Liu et al.,13 the evaluation of the recycle options for each sequence is very time-consuming. A challenge that remains for distillation sequence synthesis is how to select suitable recycle connections and flow rates for each sequence, so that the resulting recycle flowsheet can be efficiently evaluated. Analysis of Distillation-Recycle Flowsheets Each column in a distillation sequence performs a specific split, where the split is specified in terms of product regions; we denote the split performed in column i by “split i”. The splits in a distillation sequence are interconnected: the product of one split may feed another column or be mixed with recycles and then feed another column. The concepts of upstream and downstream are defined as follows. If the feed of split i is or contains the distillate (or bottom product), or part thereof, of split j, split i is downstream of split j and split j is upstream of split i. The products of split i are called downstream products of split j, or downstream products of the distillate (or bottom product) of split j. A sharp split is a split between two singular points that do not coexist in the products or in the corresponding downstream products. Otherwise, the split is a sloppy split. For example, in the distillation sequence shown in Figure 2b, split 1/3-4-5 in column C1 can separate a quaternary mixture of acetone, chloroform, benzene, and toluene into a distillate (lying in product region 1) and a bottom product (lying in product region 3-4-5). The distillate contains only singular point 1, so it cannot be further separated. Bottom product 3-4-5 can be further separated into downstream products, namely the four singular points, 2, 3, 4, and 5. Since the distillate of split C1 has no singular points in common with the bottom product, split 1/3-4-5 is a sharp split. A sharp split between the constituents of an azeotrope is said to be the split breaking this azeotrope. Column C1 in Figure 2b is an example of such a split. Since the

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azeotropic constituents, acetone (1) and chloroform (2), only appear in the distillate and downstream of the bottom product, respectively, this split breaks the azeotrope (3) between acetone and chloroform. For a given distillation sequence, recycles are generally necessary to recover all pure components of a homogeneous azeotropic mixture. There are three aims of using recycles. The first is to avoid repeated separation between the same two key components. For example, to avoid repeated separation, streams with the composition of the azeotrope are always recycled to the column that breaks this azeotrope. The second aim is to help with breaking the azeotrope so that all azeotropic constituents can be recovered. Recycle streams with the compositions of components that can act as mass separation agents are effective for this purpose. The third aim is to adjust the product composition and flow rate and, thus, adjust the feasibility of splits and the recovery of a desired component. These three aims are not independent. A recycle loop is formed by a recycle stream, together with all the columns for which the feed or product compositions are affected by this recycle. A recycle superstructure can be constructed by taking all product streams and all feeds of columns as possible recycles and possible destinations of recycles, respectively. However, such a recycle superstructure will contain very many recycles, and its evaluation will be extremely time-consuming. The general rules of Thong and Jobson3 reduce the size of the recycle superstructure. These rules indicate that only the downstream products of a sharp split in a distillation sequence can be recycled to its feed. This is consistent with the recycle reachability rule introduced by Tao et al.,4 which requires that there must be an exit point for each component not only for the entire process system but also within each recycle loop. When the product of a sharp or sloppy split i is recycled to the feed of its upstream split j, the splits contained in the resulting recycle loop are the upstream splits of split i lying between splits i and j in the sequence. Consider the separation of the equimolar quaternary mixture shown in Figure 3a. In the sequence of sharp splits shown in Figure 3b, the top product of column C2 has the composition of the azeotrope and is recycled to the feed of column C1, which is its upstream split; its recycle loop contains all the columns of the sequence. The top product of column C4 may be recycled to the feed of column C3. The two resulting recycle loops contain columns C3 and C4, as shown in Figure 3b. However, when the product of a split is recycled to the feed of a split that is not an upstream split, a bigger recycle loop will be formed. This recycle loop will contain all splits upstream of this recycle, as well as the split that is the destination of this recycle and all its downstream splits. This is illustrated in Figure 3c. If the top product of column C4 is recycled to the feed of column C2, which is not upstream of C4, to produce the same products, the whole sequence will be affected. Such a recycle will significantly increase the mass load of the sequence, compared to the case shown in Figure 3b, and is, therefore, unlikely to be economic. Note that the recycle reachability rule of Tao et al.4 also concludes that this stream should not be recycled. In this work, streams are only recycled to the feed of a column upstream of the source of the recycle. Recycle streams can be classified according to their compositions as singular point recycles and mixed

Figure 3. Examples of recycle loops (indicated by shaded columns) in a sequence of sharp splits: (a) four-component system with an equimolar feed; (b) recycle mixed with the feed of an upstream split; (c) recycle fed to a column that is not upstream.

recycles. A singular point recycle has a composition close to that of a singular point; a mixed recycle has the composition of a mixture of singular points. A singular point recycle cannot be further separated and, thus, must be the final product of a distillation sequence. It is relatively straightforward to analyze whether recycling a given singular point recycle will benefit a given split. Singular point recycles will be analyzed first from two aspects: the feasibility of different types of splits (type A, type B, and type C splits1) and the recovery of the azeotropic components. A mixed recycle is generally an intermediate stream of the distillation sequence of interest. The composition of such a recycle might change with the flow rate and composition of another recycle. It is difficult to directly analyze whether such a recycle stream is necessary or

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Figure 4. In a ternary azeotropic system, a distillation boundary limits the product compositions and flow rates of a distillation column.

beneficial. Mixed recycles will be analyzed by considering the findings for singular point recycles. In a distillation sequence, type A, B, and C splits have different feasibility characteristics, so they need different types of recycles to adjust their feasibility. Let us first consider only singular point recycles. The feasibility of each split and the recovery of constituents forming an azeotrope are addressed for each type of split. Distillation-boundary crossing splits have special requirements for recycles; these splits will be analyzed separately. Distillation-Boundary Crossing (DBC) Splits. One or more azeotropes, especially maximum-boiling azeotropes, may introduce a distillation boundary into the composition space. Such azeotropes lie on the resulting distillation boundary, while their constituents lie in different distillation regions. A distillation boundary always limits the compositions and flow rates of products of feasible columns and, thus, limits recovery of the azeotropic constituents. For example, in the ternary azeotropic system of acetone, chloroform, and benzene shown in Figure 4, the maximum-boiling acetone-chloroform azeotrope causes a distillation boundary. If there were no distillation boundary, a column could fully recover acetone in distillate D from a mixture with composition P1. The corresponding bottom product B would be a chloroform-benzene mixture. However, because of the distillation boundary, the maximum recovery of acetone corresponds to distillate D and bottom product B1, which lies on the distillation boundary and which contains a significant amount of acetone. To recover all the pure constituents of one or more azeotropes that introduce a distillation boundary, the distillation boundary must be crossed. A simple column can cross a curved distillation boundary if the feed is on its concave side.14 The greater the curvature of a distillation boundary, the easier it is to cross this boundary. A DBC split can be a type A or B split; its feed and products lie on the concave and convex sides, respectively, of the distillation boundary it crosses. A distillation boundary can be linearly approximated by connecting with straight lines the neighboring singular points that lie on the boundary. The linearly approximated distillation boundary, together with the actual distillation boundary, bounds the region of feasible feed compositions for DBC splits. In Figure 5, feed composition P1 lies in the region of feasible feed compositions. A DBC split with this feed has feasible product regions in the neighboring distillation region. On the other hand, P2 is not a feasible feed for a DBC split.

Figure 5. Curved boundary and the linearly approximated distillation boundary bound the region of feasible feed compositions for DBC splits, such as feed P1.

The products of a feasible DBC split lie in a different distillation region to that of the feed. Since the distillation boundary can only be crossed in one direction, from its concave side to its convex side, the products of the DBC split cannot be further separated into products that lie in the same distillation region as the feed to this DBC split. Only products and downstream products of a DBC split can be recycled to its feed or to the feed of an upstream split. Such recycles will affect the compositions of the feed and products of the DBC split, as well as its feasibility. Different types of singular point recycles have different effects on the feasibility of a DBC split. Some recycles can move the feed composition into the region of feasible feed compositions or move the feed composition toward the distillation boundary, thus increasing the feasibility or ease of separation of the DBC split. Other recycles will have the opposite effect. Singular point recycle streams which are products or downstream products of the DBC split of interest can be classified into (a) RP recycles, recycles with the composition of singular points lying on the convex side of the distillation boundary crossed by the DBC split, and (b) RB recycles, recycles with the composition of singular points lying on the distillation boundary crossed by the DBC split. These recycles can be mixed directly with the feed to the DBC split or can be mixed with the feed of a split upstream of the DBC split. Of special interest is an upstream split that breaks one of the azeotropes, giving rise to the distillation boundary crossed by the DBC split. A necessary condition for a DBC split to be feasible is that its feed composition lies in the region of feasible feed compositions. RB recycles will move the feed composition toward the singular point recycles. The feed composition of the DBC split of interest will move toward the linearly approximated distillation boundary but can never cross it. Whether the feed composition moves toward the actual curved distillation boundary depends on the original composition of the column feed. The geometry underlying this one-dimensional argument applies also to multicomponent systems. Consider the feed of a DBC split that lies in the region of feasible feed compositions, for example P1, shown in Figure 6a. The RB recycle with the composition of the azeotrope will move the feed composition P1 along the straight line RB-P1 toward the linearly approximated distillation boundary. If the DBC split of interest is a type A split, which is feasible for all pairs of product

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Figure 7. Effect of an RP recycle on the feasibility of a DBC split. The recycle is to be mixed with the feed of this DBC split, which lies inside the region of feasible feed compositions.

Figure 6. Effect of (a) RB and (b) RP recycles on the feed composition (P) of a DBC split.

compositions in its corresponding product regions, the RB recycle will not improve its feasibility. An RB recycle can adjust the product compositions and, thus, change the feasibility of a type B split that is not feasible for all pairs of product compositions in its product regions. The characteristics of type A and type B splits will be introduced in detail later. If the feed of a DBC split lies outside the corresponding region of feasible feed compositions, such as P2 shown in Figure 6a, this DBC split is infeasible. An RB recycle will move the feed composition toward the linearly approximated distillation boundary (for example, from P2 to P2′) but not into the region of feasible feed compositions. The furthest the feed composition can move is to the azeotrope. Therefore, RB recycles can never move the feed of a DBC split from outside to inside the region of feasible feed compositions, and so they cannot make an infeasible DBC split become feasible. It can be concluded that only when a DBC split is a type B split with a feed that lies within the region of feasible feed compositions can mixing an RB recycle with the feed improve the feasibility of the split. On the other hand, RP recycles do not lie in the same distillation region as the feed of a DBC split. Mixing streams lying in two different distillation regions can move the composition of the feed to this DBC split toward, or even across, the corresponding distillation boundary. If only feasibility is considered, this type of recycle can certainly increase the feasibility or ease of separation of the DBC split, as shown in Figure 6b. However, this type of recycle does not always benefit the recovery of constituents of the azeotrope. The effect of an RP recycle on the DBC split depends on whether the feed lies in the region of feasible feed compositions. Figure 7 shows a feasible DBC split, for which the feed, P1, lies in the region of feasible feed compositions. Its distillate and bottom products are D1 and B1, respectively. With the RP recycle, the feed composition moves along the straight line RP-P1, toward both the recycle composition and the distillation boundary. If the recycle flow rate is great enough, the composition of the feed of the DBC split can cross the distillation boundary,

Figure 8. Four-column distillation sequence with RB recycle (3) and RP recycle (2). Molar flow rate of equimolar feed is F.

for example to point P1′. The composition of the bottom product, pure benzene, is treated as fixed; when the feed composition moves to P1′, the distillate product moves to D1′. Since composition D1′ lies in the same distillation region as RP and D1, one can obtain the recycle by further distillation. The RP recycle does not change the feasibility of this split, but as the feed composition moves toward the curved distillation boundary, the DBC split becomes easier. For example, in the feasible four-column sequence shown in Figure 2b, column C2 performs a DBC split and crosses the distillation boundary 3-4-5. Figure 8 shows the same sequence with two proposed recycles. The feed of column C2 lies in the region of feasible feed compositions. When only the bottom product of column C3 (3, an RB recycle) is recycled to the feed of column C1, with a flow rate of 0.2F (where F is the molar flow rate of the feed to the sequence, 100 kmol/h), the DBC split C2 and the sequence are feasible. Table 2 presents the parameters of each column designed by rigorous simulation using AspenPlus.15 The NRTL model, with the default model parameters,15 was used. In an alternative recycle configuration, pure chloroform, 2 (the distillate of column C3 and a downstream product of column C2), is recycled to the feed of column C2. Chloroform lies in a different distillation region from the feed to column C2, so this is an RP recycle. If this stream is also recycled to the feed of column C2 with a flow rate of 0.05F, as shown in Figure 8, the DBC split C2 and the sequence are still feasible. The number of stages in each column is chosen to be the same as in the flowsheet design shown in Table 2. The AspenPlus15 simulation results for the second flowsheet are shown in Table 3. Note that the recycles have not been converged in these flowsheet simulations, so that changes in recycle compositions, after simulation, do not influence the analysis.

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4647 Table 2. Rigorous Simulation Results Using AspenPlus for Columns Shown in Figure 8 (R2 ) 0, R3 ) 0.2F) column

C1

C2

C3

C4

reflux ratio no. stages [feed stagea] feed flow rate, kmol/h distillate flow rate, kmol/h reboiler duty, 106 kJ/h feed composition acetone chloroform benzene toluene distillate composition acetone chloroform benzene toluene bottom product composition acetone chloroform benzene toluene

7.09 53 [20] 120 25 6.277

2.7 57 [23] 95 45 5.143

5.63 48 [24] 45 25 4.883

1.50 26 [13] 50 25 1.949

0.262 0.317 0.212 0.208

0.068 0.401 0.268 0.263

0.144 0.836 0.020 0

0 0.008 0.492 0.500

1.000 0 0 0

0.144 0.836 0.020 0

0.003 0.997 0 0

0 0.017 0.969 0.014

0.068 0.401 0.268 0.263

0 0.008 0.492 0.500

0.321 0.635 0.044 0

0 0 0.015 0.985

a

Condenser is stage 0.

Table 3. Rigorous Simulation Results Using AspenPlus for Columns Shown in Figure 815 (R2 ) 0.05F, R3 ) 0.2F) column

C1

C2

C3

C4

reflux ratio no. stages [feed stagea] feed flow rate, kmol/h distillate flow rate, kmol/h reboiler duty, 106kJ/h feed composition acetone chloroform benzene toluene distillate composition acetone chloroform benzene toluene bottom product composition acetone chloroform benzene toluene

7.16 53 [20] 120 25 6.329

2.24 57 [23] 100 50 4.972

4.79 48 [24] 50 30 5.118

1.50 26 [13] 50 25 1.949

0.262 0.317 0.213 0.208

0.064 0.430 0.255 0.250

0.129 0.851 0.020 0

0 0.009 0.490 0.500

1.0 0 0 0

0.129 0.851 0.020 0

0.002 0.998 0 0

0 0.019 0.966 0.015

0.067 0.401 0.268 0.263

0 0.009 0.490 0.500

0.318 0.632 0.050 0.0

0 0 0.014 0.986

a

Condenser is stage 0.

Comparing the results shown in Tables 2 and 3, it can be seen that, with the RP recycle (Table 3), the required reflux ratio of the DBC split decreases from 2.70 to 2.24, corresponding to a reduction of reflux from 121.5 to 112 kmol/h. This example illustrates that the RP recycle can facilitate split C2. Without the RP recycle, the feed of the DBC split (column C2) lies in distillation region 1-3-4-5; with this recycle, the feed moves to distillation region 2-3-4-5, as confirmed using DISTIL.16 That is, the feed and products of column C2 lie on the same side of the distillation boundary and column C2 no longer crosses the boundary: the distillation boundary is crossed by mixing. Note that the flow rates of the recycles in the above example were specified and have not been optimized. Therefore, a meaningful comparison of the overall performance of the two flowsheets cannot be made. On the other hand, when the feed of a DBC split lies outside the region of feasible feed compositions, an RP recycle cannot be used to overcome the infeasibility of the DBC split. In the illustrative example shown in Figure 9, the split with feed composition P2 cannot cross

Figure 9. An RP recycle cannot make feasible an infeasible DBC split. Note that the overall mass balance (B2 - P2 - Azeotrope) does not hold.

the distillation boundary. If the bottom product, B2, is pure benzene, which lies on the distillation boundary, the distillate corresponding to the maximum recovery of benzene is D2, which lies in the same distillation region as feed P2. When the RP recycle is mixed with P2, the feed composition of the split of interest will move along the straight line RP-P2, toward the distillation boundary, e.g., to P2′, and into the region of feasible feed compositions. Thus, the DBC split apparently becomes feasible. However, unless the DBC split is already feasible, the RP recycle cannot be produced downstream of the DBC split. In other words, the mass balance for the distillation-recycle loop with feed P2 and products B2 and the azeotrope does not hold. It can be concluded that only when the feed of a DBC split lies in the region of feasible feed compositions can an RP recycle be beneficial. This conclusion is in good agreement with the work of both Doherty and Caldarola14 and Thong and Jobson.3 Recycles mixed with the feed to a DBC split have been addressed. Next, we consider recycles mixed with the feed to a split upstream of a DBC split. In this case, the feed composition of the DBC split will be affected, so these recycles may affect the feasibility of the DBC split. We consider first singular point downstream products and then immediate products of the DBC split. When the downstream products of a DBC split are recycled to the feed of an upstream split, the effect of these recycles on the feasibility of the DBC split is the same as that of recycling them directly to the feed of this DBC split. For example, the four-column sequence shown in Figure 10 can be used to recover all pure components of the quaternary feed mixture shown in Figure 2a. Split C3 crosses the distillation boundary 3-4-5; splits C1 and C2 are its upstream splits. Downstream products (3, RB recycle; 2, RP recycle) can be mixed with the feed of columns C1, C2, and C3; the effect on the feed and product compositions of column C3 does not depend on the recycle destination, but it will affect the product compositions of the upstream splits included in the recycle loops. The immediate products of the DBC split (e.g., 4, an RB recycle in Figure 10) can also be recycled to the feeds of upstream splits. These recycles will not affect the product compositions of the DBC split but will affect its feed composition. The effect of such a recycle on the DBC split depends on its type (RB or RP) but not on its origin (i.e., whether it is a product or a downstream product of the DBC). A DBC split may have several upstream splits; accounting for all possible recycle streams to all upstream column feeds is a potentially enormous task.

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Figure 10. All possible recycles of singular point products downstream of column C3, the DBC split in a four-column sequence separating an acetone-chloroform-benzene-toluene mixture.

Therefore, it is proposed to identify the destinations that will allow recycles to have the best effect on the sequence. The effect of an RB or RP recycle on a DBC split (in terms of mass balance) does not depend on the upstream recycle destination. Therefore, which destinations are best does not depend on the effect of recycles on the DBC split but does depend on the effect on its upstream splits. First, we note that one of the splits upstream of the DBC must break one of the azeotropes, giving rise to the boundary crossed by the DBC split (i.e., it must perform a sharp split between the constituents of an azeotrope). The DBC split does not break the azeotrope itself, since the products and downstream products of the DBC split can only lie on the same, convex, side of the distillation boundary. RB and RP recycles can act as mass separation agents (i.e., material added to facilitate the separation, e.g., by favorably altering relative volatilities) to break an azeotrope in a distillation sequence separating an azeotropic mixture. Those recycles which will facilitate the breaking of the azeotrope should be retained as candidates to be recycled upstream of the DBC split. As discussed previously, recycle loops including more columns are likely to be less economic that those with fewer columns, for the same choice of recycle. A summary of which recycles should be mixed with the feed of the azeotrope-breaking split is presented in Table 4. For example, in the sequence shown in Figure 10, column C2 breaks the azeotrope. Therefore, candidate recycles should mix with the feed of column C2. Recycles mixed with the feed of column C1 will increase the total cost of the sequence without improving the performance of column C2. Only if an RB or RP recycle can help this upstream split to break the azeotrope can the recovery of the azeotrope constituents be improved. The effects of RB and RP recycles are different and will be analyzed using an illustrative example, the separation of a mixture of acetone, chloroform, benzene, and toluene. Figure 11 illustrates the effect of an RB recycle. Split C1 (1/3-4-5) separates F1 into distillate D1 and bottom product B1 and breaks the azeotrope between acetone and chloroform. B1 is on the curved distillation boundary and can be further separated by a DBC split and its

downstream splits into four products 2, 3, 4, and 5. One downstream product of B1 has the composition of the azeotrope (3), which lies on the distillation boundary, and can be recycled to F1 as an RB recycle. Suppose this recycle moves the feed composition of split C1 to F2. If the composition and flow rate of the distillate D1 do not change, the bottom product of split C1 will change to B2, which is not on the curved distillation boundary but lies in the region of feasible feed compositions of the DBC split. Therefore, the DBC split with feed B2 would still be feasible, and the feed composition would be the same as if 3 were recycled directly to the DBC split. That is, the RB recycle to the feed of the upstream split would not affect the feasibility of the DBC split. However, the RB recycle would move the bottom product composition of split C1 away from the curved distillation boundary, as shown in Figure 11. A bottom product on the curved distillation boundary could be obtained, increasing the recovery of azeotropic components. For example, the bottom product composition of split C1 could be specified as B3 on the curved distillation boundary. As the bottom product moved from B2 to B3, the flow rate of the distillate product, acetone, would increase. It can be concluded that recycling an RB recycle to the feed of the split breaking an azeotrope causing the distillation boundary, upstream of the DBC split, can improve the recovery of a constituent of an azeotrope giving rise to the boundary. The effect of RP recycles on a column upstream of the DBC split are considered next, using the same illustrative example. Figure 12 illustrates the effects of an RP recycle recycled to the feed of split C1, F1. This RP recycle is a downstream product of B1 with the composition of singular point 2. For a given recycle flow rate, the feed composition of split C1 will move along the straight line F1-RP to F2, as shown in Figure 12. If the composition and flow rate of the distillate D1 do not change, the bottom product of split C1 should change to B2. However, B2 does not lie in the same region as distillate D1, so split C1 is infeasible; a bottom product that lies on the distillation boundary, such as B3, is achievable but results in a reduced recovery of acetone. It follows that recycling RP recycles to the feed of an upstream split cannot benefit the recovery of azeotropic constituents. The effect of recycles on DBC splits has been analyzed in terms of the feasibility of the DBC split and the recovery of azeotropic components. A DBC split depends on one or more of its upstream splits to produce a feed lying in the region of feasible feed compositions. Recycles to the feed of the DBC split cannot make an infeasible DBC split feasible. RP recycles can make the split easier, while RB recycles will only benefit feasibility for a type B DBC split. The products or downstream products of the DBC split of interest can be recycled to the feed of an upstream split. The best destination for these recycles is the feed of the upstream split that breaks an azeotrope associated with the distillation boundary crossed. Recycling an RB recycle to the feed of the upstream split that breaks the azeotrope can improve the recovery of the azeotrope constituents in the DBC split. The effect of the RB recycle on the DBC split is the same as that of directly recycling it to the feed of the DBC split. On the other hand, RP recycles should not be recycled to

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4649 Table 4. Effects of RB and RP Recycle Destination on Sequence Performancea recycle destination

conclusion

feed of azeotrope-breaking split

recycle may help to break the azeotrope

allow

upstream of azeotrope-breaking split

recycle can help to break the azeotrope; upstream flows increased without benefiting feasibility recycle cannot help break the azeotrope

reject

downstream of azeotrope-breaking split a

consequence

reject

Note: All splits are upstream splits of the DBC split of interest; the azeotrope is one giving rise to the crossed distillation boundary.

Figure 11. An RB recycle recycled to the feed of the split that is breaking the azeotrope and is upstream of the DBC split can enhance the recovery of a constituent of the azeotrope giving rise to the distillation boundary.

Figure 13. Simple recycle structure and optimum recycle flow rates for a four-column distillation sequence separating an acetonechloroform-benzene-toluene mixture. (F ) 100 kmol/h).

Figure 12. The effect of an RP recycle when it is returned to the feed of a split upstream of the DBC split reduces the recovery of a constituent of the azeotrope giving rise to the distillation boundary.

the feed of a split upstream of a DBC, because they will decrease the recovery of the azeotropic constituents. The effects on a DBC split of different recycles, to its feed and to the feed of its upstream splits, have been analyzed with respect to feasibility and component recovery and are summarized below: 1. An RB recycle can be recycled to the feed of a DBC split that is a type B split where the feed composition lies within the region of feasible feed compositions. 2. An RB recycle can be recycled to the feed of a split that breaks an azeotrope causing the distillation boundary crossed and which is upstream of a DBC split. 3. An RP recycle can be recycled to the feed of the DBC split when its feed composition lies within the region of feasible feed compositions. Note that this analysis addresses feasibility and recovery only, not process economics or operability. Type A Splits. Type A splits satisfy the common saddle criterion, which requires the liquid composition profiles of both the rectifying and stripping sections to approach (move toward and away from) the same saddle point.9 These splits are always feasible.1 Therefore, the feasibility of a type A split in a distillation sequence does not need to be adjusted by recycles. Nevertheless, type A splits sometimes need recycles to improve component recoveries. Returning an RB recycle of a DBC split to the upstream split that breaks an azeotrope causing the crossed distillation boundary can improve the recovery of azeotropic constituents. Therefore, when a type A split is such an azeotrope-breaking split, RB recycles are beneficial.

An illustrative example supports these findings. In the distillation sequence shown in Figure 13, all splits are type A splits. Split 2-3/4, in column C3, crosses the distillation boundary; the upstream split performed by column C2, 1/3-4, breaks the azeotrope. On the basis of the above analysis, an RP recycle can be recycled to the feed of split 2-3/4, while an RB recycle can be recycled to the feed of split 1/3-4. The resulting recycle structure of this sequence, shown in Figure 13, is clearly simpler than the recycle superstructure shown in Figure 10, where more singular point recycles are considered. The two recycle structures are evaluated using the procedure proposed by Liu et al.:13 recycle options are exhaustively assessed, within a specified range, in steps of 0.2F, where F is the molar flow rate of the process feed. The set of recycle flow rates that corresponds to the best flowsheet performance, shown in Figure 13, is the same for the two structures. Table 5 presents the corresponding column design parameters. Type B Splits. Type B splits are different from type A splits in that they do not satisfy the common saddle criterion: the stripping and rectifying section profiles approach two different saddle points lying in the same compartment. This work defines these two saddle points as difference saddle points of the type B split; the lighter and heavier difference saddle points are abbreviated as LDSP and HDSP, respectively. The rectifying section composition profile of a type B split approaches the HDSP; the stripping section profile approaches the LDSP. Figure 14 shows examples of type B composition profiles at total reflux; the rectifying section profiles approach saddle point 4, while the stripping section profile approaches saddle point 3. The singular point that is the HDSP must appear in the distillate, or both section profiles of this split will approach the LDSP and the split will not be a type B split. Similarly, the

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Table 5. Design Parameters for Columns Shown in Figure 13

a

column

C1

C2

C3

C4

reflux ratio no. stages energy cost, £/yr capital cost, £ total cost,a £/yr total cost of the sequence, £/yr feed mole composition and flow rate, kmol/h acetone chloroform benzene toluene flow rate distillate mole composition and flow rate, kmol/h acetone chloroform benzene toluene flow rate bottom mole composition and flow rate, kmol/h acetone chloroform benzene toluene flow rate

1.21 24 220 457 286 936 316 102 1 296 000

6.14 55 205 648 396 376 337 773

2.33 53 180 677 379 689 307 240

6.42 49 210 036 374 126 334 745

0.255 0 0.251 3 0.242 5 0.251 3 100

0.333 2 0.406 3 0.259 2 0.001 5 95

0.098 6 0.547 9 0.351 4 0.002 1 70

0.153 4 0.843 9 0.002 2 0.000 4 45

0.340 0 0.335 0 0.320 0 0.005 0 75

0.99 0.01 0.001 0 25

0.153 4 0.843 9 0.022 0.000 4 45

0.01 0.99 0 0 25

0 0 0.01 0.99 25

0.098 6 0.547 9 0.351 4 0.002 1 70

0 0.015 0.980 0.005 25

0.332 7 0.661 3 0.005 0.001 20

Annualization factor for capital cost is 0.33.

Figure 14. A type B split is not feasible for all pairs of product compositions lying in the corresponding product regions.

singular point that is the LDSP must appear in the bottom product of a type B split. A type B split is feasible for some, but not all, pairs of products lying in the specified product regions. For example, split 1-3-4/3-4-5 shown in Figure 14 is a type B split. Composition B lies in bottom product region 3-4-5, and compositions D1 and D2 both lie in distillate product region 1-3-4. Using the boundary value method, it is found that the product pair D1-B is feasible but D2-B is not. The concentrations of the LDSP and HDSP in the products are key to the feasibility of a type B split, affecting the likelihood that the rectifying and stripping profiles intersect. Recycles allow product compositions of a type B split to be adjusted, facilitating the split. Consider the case that the bottom product composition is fixed and a recycle is used to adjust the distillate composition within a product region. If the mole fraction of the HDSP is decreased or the mole fraction of the LDSP is increased in the distillate, the distillate composition will move away from the HDSP, and the corresponding rectifying profile could approach the LDSP rather than the HDSP. These two section profiles will become more likely to intersect, indicating a feasible split. The converse is also generally true. It follows that recycling a downstream product of the distillate with the composition of the LDSP, or recycling the downstream product of the bottom product with the composition of the HDSP, can significantly increase the feasi-

Figure 15. (a) Sequence separating an acetone-chloroformbenzene-toluene mixture. (b) Type B split (1-3-4-5/3-4-5) with all possible recycles. Table 6. Feed and Product Compositions of Type B Split 1-3-4/3-4-5 Shown in Figure 15 mole fraction

feed

distillate 1-3-4

bottoms 3-4-5

acetone chloroform benzene toluene total flow rate (kmol/h)

0.2812 0.4060 0.1567 0.1600 160

0.3907 0.4386 0.1700 0.0010 72.5

0.1905 0.3789 0.1457 0.2849 87.5

bility of a type B split. It is convenient to represent azeotropes as pseudocomponents, using the composition transformation method introduced by Liu et al.13 In the acetone-chloroform-benzene-toluene system shown in Figure 14, the distillation sequence shown in Figure 15a can be used to separate the feed mixture into its pure components. The first column performs the feasible type B split 1-3-4/3-4-5 shown in Figure 14. The distillate 1-3-4 can be further separated into three streams with the compositions of singular points 1, 3, and 4. Bottom product 3-4-5 can be further separated into streams with the compositions of singular points 2, 3, 4, and 5. Feasible product compositions are shown in Table 6. To analyze the effect of different recycles on the feasibility of this split, various downstream recycles with singular point compositions (shown in a simplified

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4651 Table 7. Effects of Different Recycles on the Feasibility of the Type B Split 1-3-4/3-4-5 Shown in Figure 15 (Maximum Recycle Flow Rate Investigated ) 1.5F) only recycle downstream product of distillate 1-3-4 singular point base case recycle flow rate (F4 ) 0, F5 ) 0, F6 ) 0)

F1

F2

F3

feasible?

comments

3 (LDSP) 0 0 0 to 1.5F 0 0 0.5F to 1.5F 0 0.9F to 1.5F

1 0 0 0 0.1F to 1.5F 0.9F to 1.5F 0 1.4F to 1.5F 0

4 (HDSP) 0 0.1F to 1.5F 0 0 0.1F 0.1F 0.2F 0.2F

yes no yes yes yes yes yes yes

recycling HDSP product downstream of distillate reduces feasibility recycling downstream products of distillate other than HDSP increases feasibility

only recycle downstream product of bottom product 3-4-5 singular point base case recycle flow rate (F1 ) 0, F2 ) 0, F3 ) 0)

F4

F5

F6

feasible?

comments

3 (LDSP) 0 0 to 1.5F 0 0 0.1F 0.1F 0.2F 0.2F

4 0 0 0.1F to 0.4F 0 0.1F to 0.6F 0 0.1F to 1.5F 0

5 0 0 0 0 to 1.5F 0 0.3F to 1.5F 0 0.7F to 1.5F

yes no yes yes yes yes yes yes

recycling LDSP product downstream of bottom product reduces feasibility recycling downstream product of bottom product other than LDSP increases feasibility

form in Figure 15b) are evaluated using the boundary value method.17 Table 7 shows the results of this analysis and supports the generalizations made above. Table 7 also shows that recycling the LDSP downstream of the distillate is better than recycling another (non-HDSP) downstream product. For example, when the flow rate of recycle F3 (the HDSP) is 0.1F, the separation becomes feasible for a lower flow rate of recycle F1 (the LDSP) than that of F2. Similarly, recycling the HDSP downstream of the bottom product is better than recycling another downstream (nonLDSP) product, which is also as expected. If a type B split breaks an azeotrope causing the distillation boundary crossed by a downstream DBC split, RB recycles of the DBC split can also be recycled to the type B split, as discussed previously. Type C Splits. Type C splits are unlike type A and type B splits in that they cross compartment boundaries and do not satisfy the common saddle criterion. They may be feasible for a limited range of product compositions or not feasible at all. Recycling downstream products of a type C split can adjust the distillate and bottom product compositions; in some cases, this enhances feasibility. The singular points lying on a compartment boundary include a stable node, an unstable node, and, sometimes, saddle points common to the two compartments. The difference saddle points of the type C split appear in only one of the two neighboring compartments. Composition profiles of a type C split generally lie in different compartments and approach the light and heavy difference saddle points of this split. The set of all feasible liquid composition profiles for a given product composition,18 also known as the operation leaf,19 is also constrained to lie approximately within the compartment containing the product. Because operation leaves generally cannot cross the compartment boundary by very much, any intersection of composition profiles will be close to the compartment boundary. For example, the ternary system shown in Figure 16 has two compartments, 1-3-4 and 1-2-4. Four bottom

products, B1, B2, B3, and B4, are proposed for type C split 1-2/3-4: their stripping operation leaves lie in compartment 1-3-4 and approach saddle point 3. The rectifying operation leaves of the proposed distillate compositions, D1 and D2, lie mainly within compartment 1-2-4 and approach saddle point 2. Note that the rectifying operation leaf corresponding to D1 does cross the compartment boundary. The only overlap of the rectifying and stripping operation leaves is for the products that lie closest to the compartment boundary, D2 and B4. It follows that recycles that move the product compositions of a type C split toward the compartment boundary can increase feasibility of the split. The downstream products of a given type C split that have the composition of singular points can be classified as RBC recycles, which lie on the compartment boundary, and RNBC recycles, which do not. RBC and RNBC recycles will move the products toward, and away from, respectively, the compartment boundary. Only RBC recycles of a type C split increase its feasibility. Consider the sharp type C split 1-2/3-4 shown in Figure 16 with feed composition F1, bottom product composition B4, and distillate D1, which is to be further

Figure 16. Operation leaves corresponding to proposed distillate (D1 and D2) and bottom products (B1, B2, B3, and B4) of type C split 1-2/3-4.

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separated into products 1 and 2. The proposed split is infeasible. Recycling downstream product 1, which lies on the compartment boundary, could move the composition of the distillate toward the compartment boundary, to D2, for the same bottom product composition and, thus, make the separation feasible by the use of an RBC recycle. Screening Singular Point Recycles. The requirements of different types of splits of singular point recycles have been analyzed with respect to the feasibility of splits and the recovery of azeotropic components. The rules for selecting recycles in distillation sequences can be summarized: 1. For a DBC split with the feed composition lying in the region of feasible feed compositions, RP recycles can be returned to the feed. Type B DBC splits can also benefit from RB recycles. 2. A type A split that breaks an azeotrope which causes the distillation boundary crossed by a downstream DBC split can benefit from RB recycles returned to the feed. Otherwise, type A splits do not benefit from recycles. 3. For a type B split, the non-HDSP downstream products of the distillate and the non-LDSP downstream products of the bottom product can be recycled to the feed. If the type B split is upstream of a DBC split and breaks an azeotrope that causes the crossed distillation boundary, RB recycles of this DBC split can be returned to the feed of the type B split. 4. For a type C split, RBC recycles can increase feasibility. If the type C split is upstream of a DBC split and breaks an azeotrope that causes the crossed distillation boundary, RB recycles can be returned to the feed of the type C split. These rules allow a systematic procedure to be generated for screening recycles with singular point compositions for a distillation sequence, as follows: 1. Specify a distillation sequence from the sequences generated using the method of Thong and Jobson.3 2. Select a split from the sequence. 3. Identify whether the selected split is the final split. If it is, no recycles to its feed are needed; go to step 9. Otherwise, classify this split (azeotrope-breaking or DBC; type A, B, or C7); go to step 4. 4. If it is a DBC split, identify its RB and RP recycles. If it is also a type A split, allow RP recycles to the feed. Otherwise, allow both RB and RP recycles to the feed. Go to step 9. 5. If it is a type A split, no recycles to its feed are needed; go to step 8. 6. If it is a type B split, identify the corresponding LDSP and HDSP. Allow the non-HDSP downstream products of the distillate and non-LDSP downstream products of the bottom product to recycle to the feed. Go to step 8. 7. If it is a type C split, allow RBC recycles to the feed. Go to step 8. 8. If the split is upstream of a DBC split and breaks an azeotrope that causes the crossed distillation boundary, allow RB recycles to the feed of this azeotropebreaking split. 9. If some splits in the sequence have not been analyzed, select one of these splits and go to step 3. 10. End the screening procedure. This procedure is applied to generate the recycle structure of a distillation sequence separating a quaternary mixture of acetone, chloroform, benzene, and

Figure 17. Recycle structures for a four-column sequence separating an acetone-benzene-chloroform-toluene mixture: (a) simplified recycle structure identified using the new screening procedure; (b) recycle superstructure including all possible recycles with singular point compositions. Reprinted with permission from ref 3, copyright 2001 Elsevier.

toluene. Only singular point recycles are considered at this stage. The resulting recycle structure, shown in Figure 17a, may be seen to be significantly simpler to evaluate than the superstructure of recycles with singular point compositions proposed by Thong and Jobson,3 shown in Figure 17b. According to the method of Thong and Jobson,3 one of the four products of columns C3 and C4 should not be recycled. However, no systematic method exists to select this stream. In Figure 17b, the distillate of column C3 is chosen because it is a desired product of a difficult split crossing the distillation boundary. Recycles with the Composition of a Mixture of Singular Points. Recycles with the compositions of the mixtures of singular points (mixed recycles) can also be used in a distillation sequence. These recycles are

Ind. Eng. Chem. Res., Vol. 44, No. 13, 2005 4653

Figure 18. Four-column sequence with singular point and mixed recycles; optimum flow rates were determined using the methods of Liu et al.13

generally intermediate streams, rather than final products, of a distillation sequence. Mixed recycles may allow the cost of a sequence to be reduced, compared to the case of singular point recycles, because the recycle loop can contain fewer columns. There are many potential mixed recycles within a distillation sequence, and several possible destinations for each recycle candidate. The evaluation of these many options is greatly facilitated using the analysis for singular point recycles. A candidate mixed recycle should be allowed as a recycle to the feed of a split only if all of its downstream singular point products are also allowed as recycles. The logic behind this rule is that recycling pure components or singular points within a mixed recycle that should not be recycled may reduce, or even completely counteract, the benefit of recycling the other singular points. The following procedure for selecting mixed recycles is proposed: 1. Screen all singular point recycles. 2. Select an intermediate product of the distillation sequence (i.e., a candidate mixed recycle). 3. Identify all the singular points this stream includes. 4. On the basis of the simplified recycle structure with only singular point recycles, check whether there is a feed to which all downstream products of the candidate can be recycled. Only if there is such a feed can the candidate be recycled to this feed. 5. If some intermediate streams have not been analyzed, select another stream for analysis; go to step 3. 6. End the procedure. For example, in the sequence shown in Figure 17a, the bottom product of column C2 is a mixture of singular points 4 and 5. Since products 4 and 5 can both be recycled to the feed of column C1, the bottom product of column C2 (4-5) can also be recycled to the same destination. On the other hand, the distillate of column C2 cannot be recycled to the feed of column C1, since it contains singular point 2, which should not be recycled to the feed of column C1. Figure 18 shows the simplified recycle structure of this sequence, including both singular point and mixed recycles. The flow rates and connections of beneficial recycles can be identified using the sequence evaluation procedure of Liu et al.13 to minimize the total annualized cost of the flowsheet. An exhaustive search, in steps of 0.2F,

Figure 19. Distillation sequence for the separation of the fivecomponent azeotropic mixture of acetone, benzene, 1-propanol, toluene, and styrene.

where F is the molar flow rate of the feed, is used to set the recycle flow rates. The resulting recycle flow rates are shown in Figure 18. It is found that the only recycle has the composition of singular point 3 and a flow rate of 0.2F. In this case, the mixed recycle, containing singular points 4 and 5, is not beneficial. Illustrative Example The new procedures are used to generate the recycle structure of the distillation sequence shown in Figure 19a, in which the pure component products are recovered from a five-component mixture. Table 8 lists all

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Table 8. Singular Points in the Five-Component Azeotropic Mixture of Acetone, Benzene, 1-Propanol, Toluene, and Styrene cingular point

component or azeotrope

boiling point (°C)

1 2 3 4 5 6 7

acetone benzene-1-propanol benzene 1-propanol-toluene 1-propanol toluene styrene

55.68 75.28 78.32 92.66 96.83 110.18 144.95

Table 9. Designs of Columns Shown in Figure 19 Obtained Using Shortcut Methods13 column

C1

C2

C3

C4

C5

C6

split 1-2-3/4-6-7 1/2-3 2/3 4-5/6-7 4/5 6/7 reflux ratio 1.06 2.97 2.13 1.0 4.28 3.06 no. of stages 1446 27 30 44 31 17

quences separating homogeneous azeotropic mixtures with any number of components. Opportunities to exploit the pressure sensitivity of azeotropes and distillation boundaries are not addressed in this work. This work analyzes recycle options with respect to the feasibility of the distillation-boundary crossing split and the recovery of azeotropic constituents. The operating and capital costs of the flowsheet are not considered; the arguments presented treat feasibility and effective recovery of desired components as essential, ahead of cost considerations. Once the recycle structure of a distillation sequence has been generated, the total cost of the flowsheet can be minimized by optimizing all recycle flow rates and column designs.21 The optimization step requires more or less rigorous modeling of all the columns in the sequence to evaluate feasibility and cost. Methods such as the boundary value method17,20 and the shortcut models of Liu et al.13 may be applied for this purpose.

the singular points calculated using DISTIL16 with the Wilson model and the default model parameters. Using the procedure proposed by Rooks et al.9 and Thong and Jobson,1 it can be determined that the whole composition space of this system is a single distillation region that is separated into three compartments, namely compartments 1-2-3-6-7, 1-2-4-5-7, and 1-2-46-7. It can be established, for example, using the composition transformation procedure of Liu et al.,13 that the mixture to be separated, with composition XF ) [0.2 0.16 0.17 0.27 0.2]T, lies in compartment 1-24-6-7. The separation sequence shown in Figure 19a is identified as a potentially feasible sequence using the method of Thong and Jobson.3,13 The recycle structure that is generated is shown in Figure 19b. The flow rate of each of the recycle streams shown in Figure 19b is allowed to vary from 0 to 2F, with a step length 0.2F. The evaluation procedure of Liu et al.13 identifies the best set of recycle flow rates, corresponding to the minimum total annualized cost of the flowsheet, as shown in Figure 19b. The corresponding column design results are shown in Table 9.

DBC ) distillation-boundary crossing HDSP ) heavy-difference singular point LDSP ) light-difference singular point RB ) recycle on simple distillation boundary RBC ) recycle on compartment boundary RNBC ) recycle not on compartment boundary RP ) recycle not on distillation boundary

Conclusions

Literature Cited

Recycles are generally needed in a distillation sequence separating a homogeneous azeotropic mixture. They allow repeated separation tasks to be avoided within a sequence, can help to break azeotropes, and can adjust product and feed compositions of a separation to enhance feasibility. Because the choice and flow rate of recycles affects the feasibility and performance of several columns within a distillation sequence, the problem of flowsheet evaluation may become intractable. This work develops a methodology for efficiently selecting candidate recycle structures for a given distillation sequence. Recycles can be classified in terms of composition as singular point recycles and mixed recycles. The impact of singular point recycles on splits crossing distillation boundaries and on type A, type B, and type C splits7 is analyzed. These splits have different feasibility characteristics and, thus, need different types of recycles. Rules for screening mixed recycles are based on the analysis of singular point recycles. Procedures are proposed for systematically selecting singular point and mixed recycles. These recycles will benefit the feasibility of splits or the recovery of azeotrope constituents. The screening procedures are applicable to distillation se-

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Nomenclature ai,j ) element of adjacency matrix in row i and column j A ) adjacency matrix B ) molar flow rate of bottom product D ) molar flow rate of distillate F ) molar flow rate of feed ri,j ) element of reachability matrix in row i and column j R ) reachability matrix Acronyms

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Received for review July 8, 2004 Revised manuscript received January 10, 2005 Accepted April 15, 2005 IE049402W