Temperature Sequences for Categorizing All ... - ACS Publications

Ind. Eng. Chem. Res. 1997, 36, 1799-1811

1799

Temperature Sequences for Categorizing All Ternary Distillation Boundary Maps Eric J. Peterson† and Lee R. Partin* Eastman Chemical Company, P.O. Box 1972, Kingsport, Tennessee 37662-5150

Temperature sequences are formulated as a complete method of categorizing the feasible distillation boundary maps (DBMs) for ternary systems which commonly have unique binary and ternary azeotropes. DBMs are simplified versions of residue curve maps. The method requires the boiling temperatures at system pressure of pure components and azeotropes, if they exist. Seven position numbers are assigned to the pure components (three) and azeotropes (three binary, one ternary). The boiling temperatures are sorted to rank the position numbers. The temperature sequence is defined as the ranking of position numbers. The position numbers of missing azeotropes are excluded from the sequence. An algorithm searches all possible temperature sequences for feasible DBMs. The result is a complete listing of 125 DBMs, 307 temperature sequences, and 382 [temperature sequence, DBM] pairs. Lookup tables simplify the procedure for finding the DBM(s) for a temperature sequence or finding the temperature sequences for a DBM. Example applications are presented for applying the technique in the initial screening for distillation system synthesis. Introduction There exists a large body of published literature on the application of residue curve maps (RCMs) to the design of separation processes. RCMs are constructed by measuring or calculating the residue composition in a batch still without reflux (Schreinemakers, 1901). Most of the research has focused on ternary systems. The batch compositions are plotted on a triangular diagram. Figure 1 depicts an example of methanol, ethanol, and water at 1 bar pressure. The convention for this paper is to place the lowest boiler (L) at the right vertex, the intermediate boiler (I) at the top vertex, and the highest boiler (H) at the bottom left vertex. The RCM plot contains several curves over the composition space, with arrows pointing in the direction of increasing temperature for the boiling liquid. Figure 1 shows that the composition space is divided into two regions. The top section of residue curves starts at pure methanol and finishes at pure ethanol. The bottom section of residue curves starts at pure methanol and finishes at pure water. Fien and Liu (1994) reviewed the literature of RCM technology and its application in the synthesis and design phases of separation processes. The techniques provide a major advance in the methodology for flowsheet feasibility and preliminary process design in the separation of nonideal systems. The objective of this work is to fully categorize the occurrence of distillation boundaries within the RCMs of ternary systems and to apply the categorization system as a tool in the initial synthesis step of separation processes. The objective is achieved by inventing a new method of sequencing the boiling point temperatures within the ternary system and fully categorizing the potential distillation boundary maps (DBMs) that are feasible. Distillation Boundary Maps Distillation boundary maps (DBMs) are closely related to RCMs. A DBM applies knowledge of pure * Author to whom correspondence is addressed. Telephone: 423/229-5716. Fax: 423/229-3017. E-mail: lrpartin@ eastman.com. † E-mail: [email protected]. S0888-5885(96)00437-X CCC: $14.00

Figure 1. Residue curve map for a methanol-ethanol-water system at 1 bar pressure.

component and azeotrope temperatures to define the basic pattern of the RCM temperature directions and the distillation boundaries when they exist. Knowledge of azeotropic compositions is not necessary for defining the DBM, but it can be applied to draw a specific DBM for a given system. The distillation boundaries are approximated as straight lines. The RCM of Figure 1 translates into the DBM of Figure 2. The ternary system contains an ethanol-water binary azeotrope. The azeotrope forms a distillation boundary with the pure methanol node. The DBM shows the directions of increasing temperature on the triangle faces and the distillation boundary. Matsuyama and Nishimura (1977) developed the accepted naming scheme for DBMs. A number is associated with the azeotrope on each face of the triangle in the order of L-I, I-H, and L-H. The numbers describe azeotropes in terms of minimum, intermediate, or maximum boiling point and of node or saddle point. A node-type azeotrope has residue curves either start or finish at the azeotrope. Therefore, a node is either the highest or lowest temperature in its region. © 1997 American Chemical Society

1800 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997

Figure 2. Distillation boundary map for a methanol-ethanolwater system at 1 bar pressure.

A saddle-type azeotrope has an intermediate temperature for its region, and it resides at an intermediate point on a residue curve. The digits are as follows: 0, no azeotrope; 1, binary minimum-boiling azeotrope node; 2, binary minimum-boiling azeotrope saddle; 3, binary maximum-boiling azeotrope node; 4, binary maximum-boiling azeotrope saddle. When a ternary azeotrope exists, a letter follows the three-digit code: m, minimum-boiling azeotrope node; M, maximum-boiling azeotrope node; S, intermediateboiling azeotrope saddle. Therefore, the map in Figure 2 is the 020 DBM. The classification system assumes that only one azeotrope can exist per binary system or ternary system. The current work continues with this assumption. There is the potential for rare cases where multiple azeotropes exist (e.g., Gaw and Swinton, 1966, Wade and Taylor, 1973). An extension of the naming convention is required to fully document DBMs. In some cases, there are multiple DBMs possible when a ternary saddle is present. The method of Foucher et al. (1991) is then applied to distinguish the DBMs via new ternary codes of SH, SI, and SL. The meaning of the SH, SI, and SL codes is most easily provided in an example. The 433-S, 433SI, and 433-SL DBMs can exist as documented in Figure 8. The base code of 433-S is given to the map with only four boundaries. The 433-SI and 433-SL maps have five boundaries. The SI code for 433-SI is given to the only one of the three maps that has a boundary connected to the I node. The SL code for 433-SL is given to the only one of the three maps that has a boundary connected to the L node. The SH code is not needed for the example. All three maps have boundaries connected to the H node. DBM Temperature Sequence This paper presents a new method of fully characterizing the feasible DBMs through temperature sequences. Seven position numbers are assigned to the pure components, binary azeotropes, and ternary azeotrope as shown in Figure 3 {T1 ) TL, T2 ) TL-I azeotrope, T3 ) TI, T4 ) TI-H azeotrope, T5 ) TH, T6 ) TL-H azeotrope, T7 ) Tternary azeotrope}. The temperature sequence of a given ternary system is its position numbers as sorted

Figure 3. Position numbers for defining temperature sequences.

by ascending boiling temperatures. When an azeotrope does not exist, the corresponding position number is left out of the temperature sequence. For example, the 020 DBM of Figure 2 is the 1435 temperature sequence since TL < TI-H azeotrope < TI < TH, which is the same as T1 < T4 < T3 < T5. All temperature sequences will contain position numbers 1, 3, and 5 that correspond to the three pure components. Temperature sequences will also contain an additional position number (2, 4, 6, or 7) for each corresponding binary or ternary azeotrope that exists. The temperature sequence is established by knowledge of the existence of azeotropes and of the related boiling temperatures at a specified pressure. Relationship of Temperature Sequences to DBMs The rules for sketching DBMs are fully documented (Foucher et al., 1991). The rules require knowledge of azeotrope existence and the related boiling temperatures, which is the same information as needed for temperature sequences. In fact, the rules require only the relative order of the boiling points as given in the temperature sequence. DBMs can be sketched from the temperature sequence without knowledge of the specific temperatures. It follows that all ternary systems with the same temperature sequence have the same DBM (or multiple feasible DBMs in some cases). Therefore, temperature sequences provide a categorization system for documenting all possible ternary systems by applying the DBM rules to permutations of temperature sequences to find feasible DBMs. Table 1 presents the results of the study in a listing of (temperature sequence, DBM) pairs. There are 125 DBMs, 307 temperature sequences, and 382 (temperature sequence, DBM) pairs. The task of determining the DBM for a given system is a simple table lookup of the DBM from its temperature sequence (e.g., 6135 ) 001 DBM, 461325 ) 312 or 411 DBM). Figures 4-8 contain graphs of all 125 DBMs for review once the DBM is determined. An algorithm was developed to find all of the feasible temperature sequences for Table 1. The algorithm was programmed in the Maple V Release 3 language. The program is available on the world wide web at http:// www.preferred.com/∼lpartin site. The algorithm applies the DBM rules for all potential temperature sequences as follows:

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1801 Table 1. Lookup Table for the Distillation Boundary Map Given the Temperature Sequence temp sequen

135 1325 1354 1356 1435 2135 6135 13254 13256 13524 13526 13542 13546 13547 13562 13564 13567 13725 13752 14325 14352 14356 14735 21354 21356 21435 24135 26135 41325 41735 42135 46135 61325 61354 61435 62135 64135 72135 76135 132546 132547 132564 132567 135246 135247 135264 135267 135426 135427 135462 135467 135624 135627 135642 135647 135724 135726 135742 135746 135762 135764

DBM name

000 400 030 003 020 100 001 430 403 430 403 340 043 040-M 304 034 004-M 300-S 300-S 320 410 320 023 010-S 130 103 120 120 102 410 010-S 210 012 401 031 021 201 021 200-m 002-m 443 440-M 434 404-M 443 440-M 434 404-M 443 440-M 344 044-M 434 404-M 344 044-M 330-S 303-S 330-S 033-S 303-S 033-S

temp sequen

DBM name

temp sequen

DBM name

137254 137256 137524 137526 137542 137562 143256

303-S 303-S 330-S 303-S 330-S 303-S 323 413 420-M 420-M 323 413 420-M 314 323 024-M 310-S 310-S 310-S 310-S 013-S 420-m 143 140-M 134 104-M 123 110-S 123 110-S 122 110-S 132 122 122 101-S 413 413 314 310-S 310-S 310-S 310-S 013-S 213 110-S 212 110-S 312 411 312 011-S 212 011-S 431 431 341 041-M 301-S 301-S 321 411 321 011-S

621354 621435 624135 627135 641325

231 221 221 101-S 321 411 321 011-S 221 011-S 420-m 230-m 203-m 220-m 220-m 202-m 420-m 220-m 022-m 402-m 032-m 022-m 202-m 022-m 444-M 444-M 433-S 433-SI 433-SL 433-S 433-SI 433-SL 444-M 444-M 433-S 433-SI 433-SL 433-S 433-SI 433-SL 444-M 444-M 343-S 343-SH 343-SI 343-S 343-SH 343-SI 444-M 444-M 334-S 334-SH 334-SL 334-S 334-SH 334-SL 343-SI 433-SI 433-SL 334-SL 433-SI 433-SL 343-SH 343-SI

143257 143275 143526 143527 143562 143567 143725 143752 147325 147352 147356 174325 213546 213547 213564 213567 214356 214735 241356 241735 246135 247135 261354 261435 264135 267135 413256 413526 413562 413725 413752 417325 417352 417356 421356 421735 426135 427135 461325 461352 461735 462135 467135 613254 613524 613542 613547 613725 613752 614325 614352 614735

641352 641735 642135 647135 714325 721354 721356 721435 724135 726135 741325 742135 746135 761325 761354 761435 762135 764135 1325467 1325647 1325746 1325764 1352467 1352647 1352746 1352764 1354267 1354627 1354726 1354762 1356247 1356427 1356724 1356742 1357246 1357264 1357426

(1) Any given temperature sequence must be a subset of the list of position numbers. The first step is to determine the power set for the list of position numbers, {1, 2, 3, 4, 5, 6, 7}. The power set contains all possible subset combinations of numbers from the list. There are 128 entries in the power set. (2) Valid temperature sequences must contain the numbers 1, 3, and 5 for the L, I, and H components. Therefore, the next step is to purge the combinations that do not contain the numbers 1, 3, and 5. The

temp sequen 1357462 1357624 1357642 1372546 1372564 1375246 1375264 1375426 1375462 1375624 1375642 1432567 1432576 1432756 1435267 1435276 1435627 1435672 1435726 1435762 1437256 1437526 1437562 1473256 1473526 1473562 1743256 1743526 1743562 2135467 2135647 2135746 2135764 2143567 2147356 2413567 2417356 2461735 2467135 2471356 2476135 2613547 2614735 2641735 2647135

DBM name

temp sequen

DBM name

temp sequen

DBM name

433-SI 334-SH 343-SH 343-SI 334-SH 334-SL 433-SL 334-SH 334-SL 343-SH 343-SI 334-SL 343-SI 334-SL 343-SI 343-SI 334-SL 334-SL 324-M 414-M 423-M 423-M 423-M 324-M 414-M 423-M 423-M 324-M 414-M 423-M 324-M 313-S 313-S 313-S 313-S 313-S 313-S 313-S 313-S 423-m 423-m 324-m 144-M 144-M 133-S 133-S 124-M 113-S 124-M 113-S 112-SH 112-SH 112-SL 121-SH 113-S 112-S 112-SH 112-SL 142-M 112-SH 112-SH 112-SH 121-SH 121-SI

2671354 2671435

131-S 121-S 121-SH 121-SI 121-S 121-SH 121-SI 414-M 414-M 414-M 313-S 313-S 313-S 313-S 313-S 313-S 313-S 313-S 214-M 113-S 112-SH 112-SH 112-SL 211-SL 113-S 112-S 112-SH 112-SL 412-M 412-M 412-M 311-S 311-S 311-S 311-S 211-SI 112-SL 211-SI 211-SL 311-S 311-S 211-S 211-SI 211-SL 412-m 441-M 441-M 441-M 331-S 331-S 331-S 331-S 331-S 421-M 421-M 421-M 311-S 311-S 311-S 311-S 421-m 241-M 211-SI 211-SI

6247135

121-SH 121-SH 211-SI 131-S 121-S 121-SH 121-SI 121-S 121-SH 121-SI 421-M 421-M 421-M 311-S 311-S 311-S 311-S 211-SI 121-SI 211-SI 211-SL 311-S 311-S 211-S 211-SI 211-SL 421-m 421-m 423-m 423-m 324-m 243-m 234-m 223-m 223-m 222-m 232-m 222-m 222-m 423-m 423-m 324-m 223-m 222-m 322-m 412-m 421-m 322-m 222-m 432-m 432-m 342-m 322-m 412-m 421-m 322-m 232-m 222-m 222-m 322-m 412-m 421-m 322-m 222-m

2674135 4132567 4135267 4135627 4135726 4135762 4137256 4137526 4137562 4173256 4173526 4173562 4213567 4217356 4261735 4267135 4271356 4276135 4613257 4613275 4613527 4613725 4613752 4617325 4617352 4621735 4627135 4671325 4671352 4672135 4761325 6132547 6135247 6135427 6135724 6135742 6137254 6137524 6137542 6143257 6143275 6143527 6143725 6143752 6147325 6147352 6174325 6213547 6214735 6241735

6271354 6271435 6274135 6413257 6413275 6413527 6413725 6413752 6417325 6417352 6421735 6427135 6471325 6471352 6472135 6714325 6741325 7143256 7143526 7143562 7213546 7213564 7214356 7241356 7246135 7261354 7261435 7264135 7413256 7413526 7413562 7421356 7426135 7461325 7461352 7462135 7613254 7613524 7613542 7614325 7614352 7621354 7621435 7624135 7641325 7641352 7642135

remaining sets are {1, 3, 5}, {1, 2, 3, 5}, {1, 3, 4, 5}, {1, 3, 5, 6}, {1, 3, 5, 7}, {1, 2, 3, 4, 5}, {1, 2, 3, 5, 6}, {1, 3, 4, 5, 6}, {1, 2, 3, 5, 7}, {1, 3, 4, 5, 7}, {1, 3, 5, 6, 7}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 7}, {1, 2, 3, 5,6 ,7}, {1, 3, 4, 5, 6, 7} and {1, 2, 3, 4, 5, 6, 7}. Permutations of numbers from these sets may produce valid temperature sequences. (3) Determine all permutations of the 16 number sets from the previous step (e.g., the permutations of {1, 3, 5} are [1, 3, 5], [1, 5, 3], [3, 1, 5], [3, 5, 1], [5, 1, 3], and


Figure 4. Documentation of distillation boundary maps, part 1.

[5, 3, 1]). The permutations become a set of potential temperature sequences. For example, [1, 3, 5] is the 135 temperature sequence. (4) Test the validity of the potential temperature sequences. Begin by finding the order of each position number where order is defined as its position in the sequence. For 135, order1 equals 1 since 1 is the first element, order3 equals 2, order5 equals 3, and the other order values are set to zero since they are missing from the temperature sequence. (4a) Test that the pure component temperatures have the proper temperature relationship, TL < TI < TH. Therefore, order1 < order3 < order5 for a valid temperature sequence. (4b) Test the validity of the binary azeotrope temperatures. A binary azeotrope boiling temperature must not be between the boiling temperatures of its pure components. It must be either minimum boiling or maximum boiling. Purge any permutations where

order1 < order2 < order3, order3 < order4 < order5, or order1 < order6 < order5. (5) The DBM sketching rules (Foucher et al., 1991) are next applied to the remaining permutations. The rules either discard the permutation as infeasible or determine the associated DBM(s) for a valid temperature sequence. (5a) Determine if position #1 is a node or saddle by tracking the directions of increasing temperature along the sides of the triangle at position #1. If temperature rises away from L along both the LI and LH sides, then it is a node. Likewise, if the temperature decreases away from L along both the LI and LH sides, then it is a node. Otherwise, position #1 is a saddle. Repeat the determination for positions #3 and #5. Calculate the number of pure component nodes as parameter N1 and the number of pure component saddles as S1. (5b) Count the number of binary azeotropes as parameter B.

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1803


(5c) Apply the rules for determining the type of ternary azeotrope. If the ternary azeotrope exists (i.e., order7 > 0), then it is a node (N3 ) 1 and S3 ) 0) if one or more of the following statements is true:

N1 + B < 4 order7 ) 1 or 2 order7 ) 3 and position #1 is a saddle and order1 < 3 order7 ) 3 and position #3 is a saddle and order3 < 3 order7 ) count or (count-1), where count is the number of elements in the temperature sequence order7 ) (count-2) and position #3 is a saddle and order3 > (count-2) order7 ) (count-2) and position #5 is a saddle and order5 > (count-2)

Otherwise, the ternary azeotrope is a saddle (N3 ) 0 and S3 ) 1). Now, the values of N3 and S3 are known. (5d) The initial breakthrough in residue curve map research (Doherty and Perkins, 1979) applied graph theory to relate the singular points of residue curves. The derived topological constraint is now used to determine the number of binary nodes and saddles:

N2 ) (2 + B - N1 - 2N3 + 2S3)/2 S2 ) B - N2 The values of N2 and S2 must be integers from the list [0, 1, 2, 3]. Delete any permutations that give other values for N2 or S2. Invalid temperature sequences can result in noninteger or negative values. (5e) Check the status of each binary azeotrope to determine the associated type code (0 ) none, 1 ) minimum-boiling node, 2 ) minimum-boiling saddle, 3 ) maximum-boiling node, 4 ) maximum-boiling saddle).



The analysis for the LI azeotrope (position #2) is as follows:

type ) 0 if order2 ) 0 since there is no azeotrope type ) 1 if order2 ) 1 since an azeotrope that is the lowest boiling temperature of the system must be a minimum-boiling azeotrope node type ) 3 if order2 ) count since an azeotrope that is the highest boiling temperature of the system must be a maximum-boiling azeotrope node otherwise, set type ) (12) if it is minimum boiling or set type ) (34) if it is maximum boiling since the status is yet unknown Similar rules are applied for positions #4 and #6. (5f) Verify that there are enough binary azeotropes of unknown status (i.e., types (12) and (34)) to fill the

requirement for the S2 value. If not, then the permutation is not a valid temperature sequence. (5g) If a ternary saddle azeotrope exists (S3 ) 1), then it will have two boundaries with temperatures increasing to the azeotrope and two boundaries with temperatures increasing away from the azeotrope. Also, the boundaries must alternate in temperature direction. Positions #1 through #6 are the possible connections for the boundaries except that pure-component saddles are excluded. A simple way to test a temperature sequence for available ternary saddle connections is to calculate the number of times that the temperature crosses above or below the ternary azeotrope while progressing through positions #1 to #6. The temperatures must cross the ternary azeotrope at least three times to provide the alternating boundary connections. For example, the 010-S DBM of Figure 4 has #1 below, #3 above, #4 below, and #5 above. If there are less than three temperature crosses, then the permutation is not a feasible temperature sequence.



(5h) Further determine the unknown status of binary azeotropes. If N2 equals B, then all of the binary azeotropes are nodes. Any type (12) binary azeotropes are changed to type 1, and any type (34) binary azeotropes are changed to type 3. Likewise, if S2 equals the number of unknown status azeotropes, then any type (12) binary azeotropes are changed to type 2 and any type (34) binary azeotropes are changed to type 4. (5i) Establish the type code (m, M, or S) for the ternary azeotrope from the N3 and S3 values. If N3 equals 1 and order7 is 3 or less, then it is a type m minimum-boiling ternary azeotrope. If N3 equals 1 and order7 is greater than (count-3), then it is a type M maximum-boiling ternary azeotrope. If S3 equals 1, then it is a type S ternary saddle azeotrope. (6) At this point, the DBM sketching rules have resolved most of the DBM names for the valid temperature sequences; for example, temperature sequence 2135 is the 100 DBM system. There are several names that are left unresolved, though. The problem is that

some temperature sequences can result in one of multiple DBMs. From Table 1, it is seen that temperature sequence 14325 can be either 320 or 410. At this point, the algorithm only knows that 14325 is a (34)(12)0 DBM and that one binary azeotrope is a node and the other is a saddle. Therefore, (34)(12)0 is either 320 or 410. The temperature sequence data are not sufficient to determine which DBM occurs. Experimental data or a validated vapor-liquid equilibrium model are required to determine the DBM. The algorithm continues by listing all possible combinations for the unknown systems. The combinations are presented in Table 2. (7a) Ternary azeotropes have an added degree of complexity. Section 5g introduced the test for valid boundary connections. Four temperatures from the pure-component nodes and binary azeotropes must be available for distillation boundary connections. When N1 + B equals 4, then the requirement is exactly satisfied. The complexity arises for some systems when


Figure 8. Documentation of distillation boundary maps, part 5. Table 2. Resolution of Cases with Multiple DBM Solutions DBM systems to be resolved

potential DBMs

(34)(12)0 (34)(12)3 3(12)(34) (34)1(12) (34)(12)1 (12)(12)1-S (12)1(12)-S 1(12)(12)-S (34)(34)3-S (34)3(34)-S 3(34)(34)-S (34)(12)(12)-m & S2 ) 2 (34)(12)(34)-M & S2 ) 2

320, 410 323, 413 314, 323 312, 411 321, 411 121-S, 211-S 112-S, 211-S 112-S, 121-S 343-S, 433-S 334-S, 433-S 334-S, 343-S 322-m, 412-m, 421-m 324-M, 414-M, 423-M

N1 + B equals 6, and there are multiple ways to sketch the boundaries. Therefore, all of the ternary saddle azeotrope systems must be tested for multiple DBMs. The S, SH, SI, and SL tags are applied to distinguish

the DBMs. Table 3 presents the data for all of the ternary saddle azeotrope systems. (7b) The algorithm now has the multiple DBMs to match with the temperature sequence. For example, the 1357264 temperature sequence is determined as (34)(34)3-S. (34)(34)3-S includes the {343-S, 343-SH, 343-SI} and {433-S, 433-SI, 433-SL} sets. The 1357264 temperature sequence could be any one of these six DBMs. The final step is to verify that the temperature sequence matches with the temperature rise patterns of the DBM. Each distillation boundary within the DBM sets a temperature order constraint. The 343-S DBM has a boundary going from position #4 to position #7. Therefore, position #4 must be prior to position #7 in the temperature sequence and order4 is less than order7. Since position #4 is after position #7 for the 1357264 temperature sequence, 343-S is not valid for it. Each of the six possible DBMs is tested. The result from Table 1 is that the 1357264 temperature sequence has three possible DBMs (i.e., 334-SL, 433-SI, and 433-

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1807 Table 3. Analysis of Ternary Saddle DBMs base DBM

N1 + B

potential DBMs

010-S 011-S 013-S 033-S 101-S 110-S 112-S 113-S 121-S 131-S 133-S 211-S 300-S 301-S 303-S 310-S 311-S 313-S 330-S 331-S 334-S 343-S 433-S

4 4 4 4 4 4 6 4 6 4 4 6 4 4 4 4 4 4 4 4 6 6 6

010-S 011-S 013-S 033-S 101-S 110-S 112-S, 112-SH, 112-SL 113-S 121-S, 121-SH, 121-SI 131-S 133-S 211-S, 211-SI, 211-SL 300-S 301-S 303-S 310-S 311-S 313-S 330-S 331-S 334-S, 334-SH, 334-SL 343-S, 343-SH, 343-SI 433-S, 433-SI, 433-SL

SL). The order constraints for the algorithm are tabulated in Table 4. The algorithm has completely determined the feasible temperature sequences and their associated DBMs. It is now an easy task to find the DBM for a given ternary system. System temperatures are used to calculate the temperature sequence by sorting the position numbers by increasing boiling temperature. Then, Table 1 lists the DBM(s) associated with the temperature sequence. If multiple DBMs can exist, then experimental data or a validated vapor-equilibrium model is required to determine the proper DBM. Examples Three examples are given. The first example demonstrates the simplicity involved in looking up a DBM for a ternary system when all of the azeotropic data are known. The second example is more complicated in that all of the azeotropic data are not known. Therefore, multiple solutions are possible. The third example will demonstrate how to use the temperature sequenceDBM information to aid in selecting a mass separating agent for a binary system. The pure component data for the examples are taken from the databank by the Design Institute for Physical Property Research (DIPPR) from the American Institute of Chemical Engineers. The azeotropic data were found in Gmehling et al. (1994). Example 1. System: ethanol, benzene, water. Pressure ) 1.0 atm. This example assumes that all azeotropic information is known. Step 1: Write down the known pure-component and azeotropic boiling points. component data

position #

bp/azeotropic (°C)

ethanol benzene water ethanol-benzene benzene-water ethanol-water ethanol-benzene-water

1 3 5 2 4 6 7

78.2 80.0 100.0 68.1 69.3 78.1 64.9

Step 2: Sketch the boiling point data on a standard right triangle. See Figure 9.

Step 3: Write down the system’s temperature sequence for the known boiling points. The boiling points, in ascending order, are 64.9, 68.1, 69.3, 78.1, 78.2, 80.0, and 100.0 °C. These boiling points correspond to a temperature sequence of “7246135”. Step 4: Find the DBM for the given temperature sequence. The value of 7246135 is found in Table 1, and it corresponds to DBM 222-m. See Figure 10 for the mapping. Example 2. System: acetone, chloroform, ethanol. Pressure ) 1.0 atm. This example assumes that some azeotropic data are unknown. Step 1: Write down the known pure-component and azeotropic boiling points. component data

position #

bp/azeotropic (°C)

acetone chloroform ethanol acetone-chloroform chloroform-ethanol

1 3 5 2 4

acetone-ethanol acetone-chloroform-ethanol

6 7

56.2 61.1 78.2 64.5 minimum boiling azeotrope; boiling point unknown none unknown

Step 2: Sketch the boiling point data on a standard right triangle. See Figure 11. Step 3: Write down the system’s temperature sequence for the known boiling points. The known boiling points, in ascending order, are 56.2, 61.1, 64.5, and 78.2 °C. These boiling points correspond to a temperature sequence of “1325”. Step 4: Modify or create additional temperature sequences to include unknown azeotropic data. The chloroform-ethanol azeotrope (#4) is minimum boiling and therefore must boil below 61.1 °C. Including “4” in the temperature sequence produces two new temperature sequences: (1) “41325” (if the chloroform-ethanol azeotrope boils below 56.2 °C); (2) “14325” (if the chloroform-ethanol azeotrope boils above 56.2 °C). It is unknown whether an acetone-chloroformethanol azeotrope (#7) exists. Therefore, a “7” must be included in the above temperature sequences in all possible locations. Also, the initial two temperature sequences must be kept in case the ternary azeotrope does not exist. The following 14 temperature sequences result: “41325”, “741325”, “471325”, “417325”, “413725”, “413275”, “413257”, “14325”, “714325”, “174325”, “147325”, “143725”, “143275”, “143257”. Step 5: Find the corresponding DBM for the given temperature sequences. Look up these 14 temperature sequences in Table 1 to check their validity. If not found in Table 1, the temperature sequence is impossible. temperature sequence

Table 1 lookup result

“41325” “741325” “471325” “417325” “413725” “413275” “413257” “14325” “714325” “174325” “147325” “143725” “143275” “143257”

DBM 410 DBM 420-m impossible DBM 310-S DBM 310-S impossible impossible DBM 410 or DBM 320 DBM 420-m DBM 420-m DBM 310-S DBM 310-S DBM 420-M DBM 420-M

1808 Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 Table 4. Position Order Constraints for Resolving Multiple DBM Solutions DBM

temperature order constraints

312 314 320 321 323 410 411 413 112-S 112-SH 112-SL 121-S 121-SH 121-SI 211-S 211-SI 211-SL 322-m 324-M 334-S 334-SH 334-SL 343-S 343-SH 343-SI 412-m 414-M 421-m 423-M 433-S 433-SI 433-SL

order4 < order6 order6 < order2 order1 < order4 order6 < order4 order1 < order4 order2 < order5 order2 < order5 order2 < order6 order2 < order7, order7 < order3, order4 < order7, order7 < order6 order2 < order6, order2 < order7, order7 < order3, order4 < order7, order7 < order5 order7 < order1, order2 < order7, order7 < order3, order4 < order7, order4 < order6 order7 < order1, order2 < order7, order7 < order4, order6 < order7 order7 < order1, order2 < order7, order2 < order4, order7 < order5, order6 < order7 order7 < order1, order2 < order7, order7 < order3, order6 < order4, order6 < order7 order7 < order2, order4 < order7, order7 < order5, order6 < order7 order6 < order2, order7 < order3, order4 < order7, order7 < order5, order6 < order7 order4 < order2, order4 < order7, order7 < order5, order6 < order7, order7 < order1 order7 < order4, order7 < order6 order1 < order4, order6 < order7 order7 < order2, order3 < order7, order7 < order4, order6 < order7 order6 < order2, order7 < order2, order3 < order7, order7 < order4, order5 < order7 order1 < order7, order7 < order2, order3 < order7, order7 < order4, order6 < order4 order1 < order7, order7 < order2, order4 < order7, order7 < order6 order1 < order7, order7 < order2, order4 < order2, order5 < order7, order7 < order6 order1 < order7, order7 < order2, order3 < order7, order4 < order6, order7 < order6 order2 < order5, order7 < order6 order2 < order7, order6 < order7 order2 < order5, order7 < order4 order1 < order4, order2 < order7 order2 < order7, order7 < order4, order5 < order7, order7 < order6 order2 < order6, order3 < order7, order7 < order4, order5 < order7, order7 < order6 order2 < order4, order7 < order4, order5 < order7, order7 < order6, order1 < order7

Figure 9. Boiling point sketch for example 1.

Figure 10. DBM for example 1.

Three of these temperature sequences are not found in Table 1 and are therefore impossible. Ten of the temperature sequences are found in Table 1 and correspond to a single DBM. The other temperature sequence (“14325”) is in Table 1 but is indeterminate (i.e., corresponds to more than one DBM). If this is the actual case, then it cannot be determined which DBM is the actual one without doing some experimental work. As you can see, even with all of the above scenarios, there are only five possible DBMs. See Figure 12. If the ternary azeotrope does not exist, then either DBM 410 or DBM 320 results. The selection between them depends on the relative boiling points of the chloroform-ethanol azeotrope and acetone. If the chloroform-ethanol azeotrope boils lower than acetone (56.2 °C), then DBM 410 results. If the chloroform-ethanol azeotrope boils higher than acetone (56.2 °C), then it is

impossible to determine whether DBM 410 or DBM 320 is the correct DBM without doing experimental work. If the ternary azeotrope does exist, then either DBM 420-M, DBM 420-m, or DBM 310-S results. The selection between them depends on the ternary azeotrope’s boiling point relative to the other boiling points. If the ternary azeotrope is minimum boiling, then DBM 420-m results. If the ternary azeotrope is maximum boiling, then DBM 420-M results. If the ternary azeotrope is intermediate boiling (i.e., a saddle), then DBM 310-S results. Note: The chloroform-ethanol azeotrope actually boils at 59.3 °C, and there is a ternary saddle azeotrope that boils at 63.2 °C. Therefore, the correct temperature sequence and DBM are “143725” and 310-S, respectively. See Figure 13. Example 3. System: acetone, n-heptane. Pressure ) 1.0 atm. This example is different from the first two

Ind. Eng. Chem. Res., Vol. 36, No. 5, 1997 1809 Table 5. Lookup Table for Finding the Temperature Sequences That Produce a Given DBM DBM name

000 001 002-m 003 004-M 010-S 011-S

012 013-S 020 021 022-m 023 024-M 030 031 032-m 033-S 034 040-M 041-M 043 044-M 100 101-S 102 103 104-M 110-S

112-S 112-SH

112-SL

113-S

temp sequen

135 6135 76135 1356 13567 14735 41735 461735 467135 614735 641735 647135 46135 147356 417356 1435 61435 64135 746135 761435 764135 14356 143567 1354 61354 761354 135746 135764 13564 13547 613547 13546 135467 135647 2135 267135 627135 26135 21356 213567 214735 241735 247135 421735 427135 2476135 4276135 2461735 2467135 2476135 2614735 2641735 2647135 4261735 4267135 4276135 2467135 2476135 4267135 4276135 4627135 2147356

DBM name

120 121-S

121-SH

121-SI

122 123 124-M 130 131-S 132 133-S 134 140-M 142-M 143 144-M 200-m 201 202-m 203-m 210 211-S 211-SI

211-SL

temp sequen 2417356 2471356 4217356 4271356 21435 24135 2671435 2674135 6271435 6274135 2467135 2647135 2671435 2674135 6247135 6271435 6274135 2647135 2671435 2674135 6247135 6271435 6274135 6427135 246135 261435 264135 214356 241356 2143567 2413567 21354 2671354 6271354 261354 2135746 2135764 213564 213547 2613547 213546 2135467 2135647 72135 62135 726135 762135 721356 42135 4672135 6472135 4621735 4627135 4672135 6214735 6241735 6247135 6421735 6427135 6472135 4267135 4627135 4672135 6427135

DBM name 212 213 214-M 220-m 221 222-m

223-m 230-m 231 232-m 234-m 241-M 243-m 300-S 301-S 303-S

304 310-S

311-S

312

temp sequen 6472135 426135 462135 421356 4213567 721435 724135 742135 621435 624135 642135 7246135 7261435 7264135 7426135 7462135 7621435 7624135 7642135 7214356 7241356 7421356 721354 621354 7261354 7621354 7213564 6213547 7213546 13725 13752 613725 613752 135726 135762 137256 137526 137562 13562 143725 143752 147325 147352 413725 413752 417325 417352 4613725 4613752 4617325 4617352 4671325 4671352 6143725 6143752 6147325 6147352 6413725 6413752 6417325 6417352 6471325 6471352 461325

examples in that we are starting with a binary system rather than a ternary system. In this example the temperature sequence-DBM method will be used as an aid for selecting a mass separating agent. We will work backward by selecting a desired DBM and then finding the temperature sequence that would produce this DBM. The temperature sequence will indicate what physical properties (i.e., boiling point range, formation of azeotropes, etc.) the mass separating agent must have.

DBM name 313-S

314 320 321

322-m

323 324-M

324-m 330-S

331-S

334-S 334-SH

334-SL

temp sequen 461352 1435726 1435762 1437256 1437526 1437562 1473256 1473526 1473562 4135726 4135762 4137256 4137526 4137562 4173256 4173526 4173562 143562 413562 14325 14352 614325 614352 641325 641352 7461325 7461352 7614325 7614352 7641325 7641352 143256 143526 143562 1432567 1435267 1435627 1435672 1743562 7143562 7413562 135724 135742 137254 137524 137542 6135724 6135742 6137254 6137524 6137542 1356724 1356742 1356724 1356742 1357462 1357624 1357642 1356724 1356742 1357264 1357624 1357642 1372564

DBM name

340 341 342-m 343-S 343-SH

343-SI

344 400 401 402-m 403 404-M 410 411 412-M 412-m

413

414-M

420-M 420-m 421-M

temp sequen 1375264 1375624 1375642 13542 613542 7613542 1354726 1354762 1354726 1354762 1357426 1357462 1357642 1354726 1354762 1357246 1357426 1357462 1372546 1375246 1375426 1375462 135462 135642 1325 61325 761325 13256 13526 132567 135267 135627 14325 41325 461325 614325 641325 4613257 4613275 4613527 4761325 7461325 7614325 7641325 143256 143526 413256 413526 1432567 1435267 1435627 4132567 4135267 4135627 143257 143275 143527 174325 714325 741325 6143257 6143275 6143527 6413257

DBM name

421-m

423-M

423-m

430 431 432-m 433-S

433-SI

433-SL

434 440-M 441-M 443 444-M

temp sequen 6413275 6413527 6174325 6714325 6741325 7461325 7614325 7641325 1432567 1432576 1432756 1435267 1435276 1435627 1743256 1743526 7143256 7143526 7413256 7413526 13254 13524 613254 613524 7613254 7613524 1325746 1325764 1352746 1352764 1325746 1325764 1352746 1352764 1357246 1357264 1357426 1325746 1325764 1352746 1352764 1357246 1357264 1357624 132564 135264 135624 132547 135247 135427 6132547 6135247 6135427 132546 135246 135426 1325467 1325647 1352467 1352647 1354267 1354627 1356247 1356427

The acetone-heptane system has a homogeneous minimum-boiling binary azeotrope, and therefore it cannot be separated with a single distillation column or a decanter. Typical solutions for breaking such an azeotrope involve selecting a mass separating agent (MSA) to aid in the separation. Oftentimes an MSA is selected so that either an extractive or azeotropic distillation could be carried out. For this example we will search for an MSA for a less used distillation technique. This technique involves adding an MSA such



Figure 11. Boiling point sketch for example 2.

boundaries; (b) have a minimum-boiling binary (acetone/ heptane) azeotrope; and (c) make at least one of the original pure components (acetone or heptane) a node. The DBMs with no internal boundaries are 000, 001, 003, 030, 031, 100, 103, and 130. See Figures 4-8. DBM 000 has no azeotropes so it is rejected by criteria b. DBMs 003 and 030 have only a maximum-boiling azeotrope so they are also rejected by criteria b. DBMs 031, 100, 103, and 130 fail criteria c because both acetone and heptane are saddles (i.e., not nodes) in the DBMs. Only DBM 001 matches all the criteria! Step 3: Find the temperature sequence for the given DBM. The DBM value of “001” is found in Table 5 and it corresponds to temperature sequence “6135”. Position #6 corresponds to the acetone-heptane binary azeotrope. Position #1 and #5 correspond to acetone and heptane. Therefore, position #3 must correspond to the MSA. Step 4: Find a MSA that meets the criteria. The MSA must not form an azeotrope with acetone or heptane, and it must have a normal boiling point between acetone and heptane. Benzene meets these criteria and will be chosen as our MSA. Step 5: Verify that the ternary system corresponds to the proper DBM.

Figure 12. Potential DBMs for example 2.

that the resulting ternary system has no internal boundaries and one of the initial two initial components is a node. If such a ternary system can be found, then the components can be directly distilled in a series of two simple distillation columns. Step 1: Write down the known pure-component and azeotropic boiling points. The position numbers depend on the boiling point of the MSA which is unknown at this point. component data

position #

bp/azeotropic (°C)

acetone heptane acetone-heptane

1 or 3 3 or 5 2, 4, or 6

56.2 98.4 55.9

Step 2: Examine all 125 DBM to find any that meet all of the following criteria: (a) do not have any internal

component data

position #

bp/azeotropic (°C)

acetone benzene heptane acetone-benzene benzene-heptane acetone-heptane acetone-benzene-heptane

1 3 5 2 4 6 7

56.2 80.0 98.4 none none 55.9 none

The known boiling points, in ascending order, are 55.9, 56.2, 80.0, and 98.4 °C. These boiling points correspond to a temperature sequence of “6135”. Look up “6135” in Table 1. It corresponds to DBM 001. As expected, this is the DBM we wanted! See Figure 14. Separation will be accomplished by adding the MSA (benzene) to the feed (acetone-heptane azeotrope). Pure heptane can be removed out the bottom of the first column. The top of the column will contain an acetonebenzene mixture that is sent to a second distillation column. The second column removes acetone out the top and benzene out the bottom. Benzene is recycled to the first column. Figure 15 shows the mass balance lines for the separation of acetone from heptane.


synthesis of distillation systems for separating chemicals. The first example demonstrated the methods simplicity when all azeotropic data are known. The second example demonstrated how the method can be used even when missing or incomplete pure-component or azeotropic data exist. The third example demonstrated how the method can be used to aid in the selection of mass separating agents. The procedures can be easily automated within a computer program to further simplify the task as was done by the authors. Future research plans are centered on the flowsheet synthesis area. Generic flowsheets can be developed for each DBM to document feasible separation tasks. Nomenclature


B ) number of binary azeotropes count ) number of elements in a temperature sequence H ) heaviest boiling pure component I ) intermediate boiling pure component L ) lightest boiling pure component N1 ) number of pure component nodes (0, 1, 2, or 3) N2 ) number of binary nodes (0, 1, 2, or 3) N3 ) number of ternary nodes (0 or 1) orderi ) order of position #i in a temperature sequence S1 ) number of pure component saddles (0, 1, 2, or 3) S2 ) number of binary saddles (0, 1, 2, or 3) S3 ) number of ternary saddles (0 or 1)

Literature Cited

Figure 15. Mass balance lines for the separation system of example 3.

Conclusions Temperature sequences have been developed as a new method for completely characterizing the distillation boundary maps of ternary systems. The only required data for determining temperature sequences are the component boiling points and the azeotrope data. The temperature sequences are determined by ranking the boiling point temperatures of the pure components and azeotropes. There are 307 unique temperature sequences. Each temperature sequence matches with one or more appropriate distillation boundary maps for a total of 382 [temperature sequence, DBM] pairs. The results are documented in lookup tables for easy determination of the DBMs for a given temperature sequence. Examples were presented to demonstrate the usefulness of the method in DBM determination and in the

Doherty, M. F.; Perkins, J. D. On the dynamics of distillation processesIII. The topological structure of ternary residue curve maps. Chem. Eng. Sci. 1979, 34, 1401. Fien, G.-J. A. F.; Liu, Y. A. Heuristic Synthesis and Shortcut Design of Separation Processes Using Residue Curve Maps: A Review. Ind. Eng. Chem. Res. 1994, 33, 2505. Foucher, E. R.; Doherty, M. F.; Malone, M. F. Automatic Screening of Entrainers for Homogeneous Azeotropic Distillation. Ind. Eng. Chem. Res. 1991, 30, 760. Gaw, W. J.; Swinton, F. L. Occurrence of a Double Azeotrope in the Binary System of Hexafluorobenzene and Benzene. Nature 1966, 212, 283. Gmehling, J.; Menke, J.; Krafczykm, J.; Fischer, K. Azeotropic Data; VCH,:Weinheim, Federal Republic of Germany, 1994. Matsuyama, H.; Nishimura, H. Topological and Thermodynamic Classification of Ternary Vapor-Liquid Equilibria. J. Chem. Eng. Jpn. 1977, 10, 181. Schreinemakers, F. A. H. Z. Phys. Chem., Stoechiom. Verwandtschafsl. 1901, 36, 257. Wade, J. C.; Taylor, Z. L. Vapor-Liquid Equilibrium in Perfluorobenzene-Benzene-Methylcyclohexane System. J. Chem. Eng. Data 1973, 18, 424.

Received for review July 24, 1996 Revised manuscript received January 3, 1997 Accepted January 5, 1997X IE9604379

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

Temperature Sequences for Categorizing All ... - ACS Publications

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