Energy-Efficient Designs of Thermally Coupled Distillation Sequences

Ind. Eng. Chem. Res. 2003, 42, 5157-5164

5157

Energy-Efficient Designs of Thermally Coupled Distillation Sequences for Four-Component Mixtures Juan Luis Blancarte-Palacios,† Marıá Nancy Bautista-Valde´ s,† Salvador Herna´ ndez,† Vicente Rico-Ramı´rez,‡ and Arturo Jime´ nez*,‡ Facultad de Quı´mica, Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., Me´ xico 36050, and Instituto Tecnolo´ gico de Celaya, Avenida Tecnolo´ gico y Garcıá Cubas s/n, Celaya, Gto., Me´ xico 38010

A design procedure for thermally coupled distillation sequences for the separation of fourcomponent mixtures is presented. The schemes analyzed include a sequence with a side rectifier and a side stripper and a sequence with a prefractionator (Petlyuk-type column). Initial designs for the thermally coupled distillation sequences are obtained from the tray distribution of a conventional distillation sequence and then optimized for energy consumption using two interconnecting flows as search variables. Several tray arrangements for each thermally coupled design were analyzed, and the results show that the sequence with side columns can reach a lower energy consumption. 1. Introduction The high share of energy in the yearly cost of distillation systems has motivated research on alternative schemes that provide a lower consumption of fossil energy. In particular, the case of separation systems for three-component mixtures has received special attention. One of the first works dealing with this problem was developed by Tedder and Rudd,1 who analyzed eight different alternatives for the separation of several threecomponent mixtures and reported optimality regions as a function of the feed composition and an ease of separation index. Three alternatives that have been further explored involve some recycle streams between columns and include a sequence with a side rectifier (Figure 1), a sequence with a side stripper (Figure 2), and a fully thermally coupled distillation column, or Petlyuk system (Figure 3). All of these structures showing vapor-liquid interconnections between two columns are referred to as thermally coupled distillation sequences (TCDSs), because each interconnection eliminates either a reboiler or a condenser of one of the columns. The TCDS schemes of Figures 1-3 have been shown to provide energy savings of up to 30% over the conventional direct and indirect distillation sequences.1-3 These types of results promoted the development of design methods for these integrated systems.4-6 Other integrated schemes have recently been proposed that aim to provide alternatives with more promising operating characteristics.7,8 Some extensions toward the design of integrated systems for mixtures of more than three components have recently been reported. Christiansen et al.9 showed how several conceptual extensions of the Petlyuk system can lead to new and potentially interesting designs. Rong et al.,10 using shortcut methods, have shown that arrangements with side strippers and side rectifiers for mixtures of five components offer economic incentives * To whom correspondence should be addressed. Tel.: (52-461) 611-7575 Ext. 139. Fax: (52-461) 611-7744. E-mail: [email protected]. † Universidad de Guanajuato. ‡ Instituto Tecnolo´gico de Celaya.

Figure 1. TCDS with side rectifier.

over sequences based on conventional distillation columns. Fidkowski and Agrawal11 presented a study of thermally coupled systems for multicomponent mixtures under minimum reflux conditions, and their results indicate that, for the case of quaternary mixtures, the fully thermally coupled system can offer energy savings in the range of 20-50% with respect to sequences based on conventional distillation columns. Formal design methods for such types of integrated systems, however, are still to be developed. In this work, we present a design method for two types of TCDSs for the separation of four-component mixtures. Although several arrangements can be conceptually designed, we have concentrated on two schemes that arise from natural extensions of the TCDSs shown in Figures 1-3. The first one includes the use of both a side rectifier and a side stripper (Figure 4), and the second is an extension of the Petlyuk system (Figure 5).

10.1021/ie030297k CCC: $25.00 © 2003 American Chemical Society Published on Web 09/09/2003

5158 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003

Figure 2. TCDS with side stripper. Figure 4. TCDS with side rectifier and side stripper (TCDSSR/SS).

Figure 3. Petlyuk system.

2. Design and Optimization Strategy In principle, the design of the thermally coupled distillation systems could be modeled through superstructures suitable for optimization procedures with mathematical programming techniques. However, the task is complicated, requires extensive computing time, and is likely to fail to achieve convergence. Two efforts along these lines for the optimal design of TCDSs for three-component mixtures are worth mentioning. Du¨nnebier and Pantelides12 developed an MINLP approach for the optimal design of integrated schemes, but they were unable to obtain a global optimum solution from the model superstructure of that problem and reported numerical solutions that were obtained with a local optimization code. Caballero and Grossmann13 used disjunctive programming for the optimal design of thermally linked distillation columns; as many as eight

Figure 5. TCDS with prefractionator (TCDS-PR).

separation alternatives can be imbedded for a threecomponent mixture. The solution for their model was aided by the use of simple, shortcut cost correlations. For a four-component mixture, the problem is clearly more complicated as the combinatorial nature of the system gives rise to a superstructure that is significantly more complex to solve. To overcome the complexity of the simultaneous solution of the tray arrangement and energy consumption within a formal optimization algorithm, we decoupled the design problem into two stages. First, a basic structure for each integrated system is developed.

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5159

Figure 6. Uncoupled distillation sequence with prefractionator.

The basic design is then analyzed in terms of energy consumption to detect the conditions under which the most energy-efficient separation is obtained. Other tray arrangements are similarly analyzed, and the set of alternatives is compared in terms of energy consumption to identify a design that, for practical purposes, should provide an excellent choice. Our approach begins with the development of preliminary designs for the integrated systems shown in Figures 4 and 5 from the design aspects of a sequence based on conventional distillation columns (Figure 6). In this conventional sequence, column C-1 (a prefractionator) performs the split AB/CD (i.e., B is the light key and C is the heavy key component), whereas columns C-2 and C-3 perform the splits A/B and C/D, respectively. Recoveries of 98% of the key components are used for the binary separations. The recovery of the prefractionator, on the other hand, is a design specification that affects the tray distribution of the columns, and it is used in this work as an additional search variable. 2.1. Tray Configuration. The conventional sequence of Figure 6 shows six different tray sections; these sections are used as a basis for the arrangement of the tray structure of the integrated sequences through a section analogy procedure. Consider, for instance, the first column of the integrated sequence of Figure 4. The total number of trays above the feed tray is obtained by conceptually moving section 3 from the second column of the conventional sequence to the top of the first column; the condenser of the first column is replaced by a vapor-liquid interconnection, providing thermal coupling. The number of trays in the side stripper of the thermally coupled sequence that produces stream B is equal to the number of trays in section 4 of the conventional sequence. A similar procedure is

applied to the bottom section of the main column of the integrated sequence; section 6 of the conventional sequence is removed from the third column (along with the reboiler) and added to the first column, a vaporliquid interconnection between the columns provide thermal coupling that eliminates the need for the original reboiler of the first column, and the number of trays required by the side rectifier is equal to the number of trays in section 5 of the conventional sequence. The integrated arrangement with the tray section distribution obtained from the sections of the base conventional sequence is shown in Figure 4. For the design of the Petlyuk-like system, TCDS-PR, seven tray sections are identified. Six of them are provided by the combination of the three original columns from the conventiional sequence, with the substitution of vapor-liquid interconnections for the condenser and reboiler of the first column or prefractionator. The main column must be joined with an additional tray section between the main products B and C that does not exist within the conventional sequence because the split B/C is not performed in that sequence. The number of trays in such a section (section 7 in Figure 5) can be estimated through the design of the binary separation B/C at total reflux conditions. The total number of trays for the TCDS-PR is then completed, with the distribution for each tray section indicated in Figure 5. 2.2. Design Strategy. The design strategy is as follows. After the tray arrangements for the integrated designs have been obtained from the method described above, an optimization procedure is used to minimize the heat duty supplied to the reboilers of each coupled scheme, taking into account the constraints imposed by the required purity of the four product streams. Although the number of trays is not formally optimized, a parametric analysis can be carried out to test different tray arrangements by changing the recoveries of the key components of the prefractionator of the conventional sequence of Figure 6. When one lowers the recovery specification of the prefractionator, for instance, from 98 to 80%, the number of trays required by the prefractionator is reduced, which, in turn, affects the tray sections for the columns C-2 and C-3. Because the resulting sections serve as a basis for the tray arrangements of the integrated sequences, such a procedure allows for the comparison of different designs to detect, in principle, the design with superior performance in terms of energy conservation. In practice, the procedure is limited by the number of tray arrangements that the designer decides to consider (i.e., by the number of recovery values assumed for the prefractionator). After the tray arrangements and the design specifications are made, two degrees of freedom remain for each integrated sequence. In this work, we use the interconnecting flows of vapor (VF) and liquid (LF) as search variables within an optimization procedure to minimize the energy consumption for the separation task. The optimization procedure, shown schematically in Figure 7, consists of the following steps, which are applied to each of the two integrated sequences under consideration: (1) A base design for the TCDS scheme is obtained as described in section 2.1. The base design depends on the distribution of key components in the split AB/CD of the prefractionator of the conventional sequence; such a split distribution is treated as a search variable


Figure 7. Optimization strategy.

because it provides a systematic way to test different tray arrangements. Each design of the conventional sequence is completed with the binary splits A/B and C/D, for which recoveries of 98% for key components are used. (2) A value for the interconnecting vapor flow (VF) is assumed. (3) A value for the interconnecting liquid flow (LF) is assumed. (4) A rigorous model for the simulation of the TCDS with the proposed tray arrangement is solved. We used Aspen Plus 10.1 for that purpose. The first solution of the rigorous model serves also to validate the base design. If the product compositions are obtained, then the design is kept; otherwise, proper adjustments in the tray arrangement are made until the adjusted design meets the specified separation task. Because the designs are evolved from different recovery values assumed for the prefractionator of a conventional sequence (Figure 6), it is convenient that any adjustment in the trays of the integrated systems that might arise from the validation process be made for any of the other sections of such systems (3 to 6 for TCDS-SR/SS of Figure 4, 3 to 7 for TCDS-PR of Figure 5).

The resulting design (either base or adjusted) is subjected to a search for minimum energy consumption. (5) The value of LF is changed, going back to step 4 until a local minimum in energy consumption for the assumed value of VF is detected. (6) The value of VF is modified, going back to step 3 until the minimum energy supplied to the reboilers is obtained. This result implies that an optimum value has been detected for the design of the TCDS scheme (which depends on the assumed distribution for the split AB/ CD of the conventional sequence that was taken as a basis for the design of the integrated sequence). (7) A new recovery in the split AB/CD is assumed, which provides a new tray arrangement for the integrated sequence. The new design is tested by steps 2 through 6. The process is repeated until an overall optimum energy consumption is detected. The following case study illustrates the use of the design procedure. 3. Case Study An equimolar mixture of n-pentane, n-hexane, nheptane, and n-octane with a feed flow rate of 45.5

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5161

Figure 8. Response surface of TCDS-SR/SS for recoveries of 98% of the key components in the split AB/CD.

kmol/h as saturated liquid was considered. Both TCDSSR/SS and TCDS-PR schemes were designed, and the results are presented as a function of different recoveries for the split AB/CD assumed for the prefractionator of the sequence of Figure 6. Heuristic rules were used to fix the design pressure and reflux ratios. A design pressure of 21.17 psia was used for all columns, with a pressure drop of 5 psia; this choice allows for the use of cooling water in the condenser of each unit. The number of trays for each section of the conventional sequence (which provides the tray arrangements for the TCDS schemes) was obtained using a reflux ratio of 1.3 times the minimum value for each separation. Three recovery levels for the design of the prefractionator were considered, thus providing three different base designs for each TCDS. The values were chosen to reflect a high recovery (98%), an intermediate recovery (80%), and a fairly low recovery value (70%). The performance of each case with respect to energy consumption is discussed in the following sections. 3.1. Recovery of 98% in the Split AB/CD. When the design of the conventional sequence was carried out with a specification of 98% recovery for the prefractionator (i.e., for the split AB/CD), 20 trays were obtained for the first column (with a distribution in sections 1 and 2 of S1 ) 11 and S2 ) 9, see Figure 6), 17 for the column performing the split A/B (with S3 ) 9 and S4 ) 8), and 18 for the column that separates C/D (with S5 ) 11 and S6 ) 7). The structure of the TCDS-SR/SS was then implemented as indicated in Figure 4; for the TCDS-PR alternative, 20 trays were used for the prefractionator and 47 for the main column (after the addition of the section between the main streams B and C, see Figure 5). Both designs were then subjected to a search procedure for minimum energy consumption. Figure 8 displays the response surface for the optimization of the TCDS-SR/SS option. The response surface shows an interesting effect of the search variables. The design is very sensitive, in terms of its energy consumption, to changes in the interconnecting liquid flow (LF) once a value for the vapor flow is set. On the other hand, there is a region in which the energy consumption does not vary significantly with VF for a

Figure 9. Response surface of TCDS-PR for recoveries of 98% of the key components in the split AB/CD.

given value of LF. This observation might reduce the numerical search for the optimum value, as one can fix a reasonable value for VF and then carry out a search procedure over a single variable, LF, to obtain an excellent near-optimal solution. Another implication of this observation has to do with operational considerations. Minor changes in the operating conditions of the thermally coupled system can lead to a significant deterioration of its energy consumption. The control design of this system, therefore, appears to be an important task to develop. When the TCDS-PR was designed and optimized for energy consumption, the results shown in Figure 9 were obtained. If one compares the effect of each search variable, one might notice again that LF affects energy cosumption more noticeably than VF, although the shape of the response surface suggests a lower sensitivity of energy consumption to changes in operating conditions than for the system with two side columns. The TCDS-SR/SS system shows a minimum energy consumption of 1541 kW, whereas the corresponding value for the TCDS-PR system is 926 kW, 40% lower than that of the TCDS-SR/SS system. 3.2. Recovery of 80% in the Split AB/CD. The specification of the recovery for the prefractionator of the conventional sequence was then lowered to 80%. This new recovery level reduced the number of trays needed for the first split to 13 (S1 ) 8 and S2 ) 5), while the trays required for the splits A/B and C/D were, respectively, 17 (S3 ) 9 and S4 ) 8) and 19 (S5 ) 11 and S6 ) 8). When the TCDS-SR/SS scheme was analyzed, the results shown in Figure 10 were obtained after the optimization process for energy consumption. The shape of the response surface is fairly similar to that obtained for the previous case. The minimum energy required for the new design amounts to 773 kW, which is lower than the value obtained for the previous case. When the structure of the TCDS-PR system was considered (with a total number of trays equal to 50 for the main column), the results of Figure 11 show that a minimum energy consumption of 851 kW was obtained; this result is 10% higher than the energy required for the TCDS-SR/SS system.



Figure 11. Response surface of TCDS-PR for recoveries of 80% of the key components in the split AB/CD.

3.3. Recovery of 70% in the Split AB/CD. Figures 12 and 13 show the response surfaces obtained for the energy optimization of each thermally coupled system when their designs were based on a recovery of 70% in the prefractionator that performs the split AB/CD. A minimum energy requirement of 1740 kW was obtained for the TCDS-SR/SS system; the Petlyuk-type column shows a corresponding value of 937 kW, or 46% lower than the system with side columns. The response surfaces in this case show sharp differences. In contrast to the other cases analyzed, the response surface for the TCDS-SR/SS system shows that its energy consumption depends strongly on changes in both LF and VF. This observation suggests that the system with side columns might be more sensitive to changes in operating conditions than the Petlyuk-type system. We observe that the energy consumption for both systems improved when the recovery for the split AB/ CD in the prefractionator of the conventional sequence was changed from 98 to 80%; it then increased when


Figure 13. Response surface of TCDS-PR for recoveries of 70% of the key components in the split AB/CD. Table 1. Optimum Energy Requirements (kW) for All of the Recoveries Assumed in the Splits AB/CD recovery (%) sequence

98

80

70

TCDS-SR/SS TCDS-PR

1541.2 926.0

773.0 851.1

1739.7 936.8

the value was further lowered to 70%, as summarized in Table 1. The best design for each type of thermally coupled system, based on the search points considered, was then obtained when an 80% recovery value of key components in the prefractionator of the conventional sequence was assumed; details for the integrated designs are given in Table 2. The temperatures obtained for the product streams, along with their corresponding product compositions, are shown in Table 3. (The minor differences observed for the intermediate components are due to the specific position of the stream extraction point, which is affected by the assumed pressure drop

Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 5163 Table 2. Optimum Design of the Thermally Coupled Distillation Sequences TCDS-SR/SS

TCDS-PR

column CA-1 reflux ratio ) 8.27 reboiler duty ) 679.6 kW LF ) 28.60 kmol/h VF ) 56.75 kmol/h

column CA-1 reflux ratio ) 11.59 reboiler duty ) 851.1 kW liquid side product ) 11.29 kmol/h LF ) 31.78 kmol/h VF ) 54.48 kmol/h

column CA-2 reboiler duty ) 93.47 kW column CA-3 reflux ratio ) 1.90

carried out in a single shell, in which the prefractionator task is performed by an internal division. The thermally coupled structure with a side stripper and a side rectifier can also be implemented in a single column; Agrawal16 has recently shown how a column with two partitions can be used to provide an equivalent arrangement. Given the potential savings in both energy and capital investment, the thermally coupled structures are therefore likely to provide choices with lower yearly costs than the conventional distillation sequences. 4. Concluding Remarks

Table 3. Temperatures (°C) and Purities for Each of the Stream Products temperature (°C)

purity

product

TCDS-SR/SS

TCDS-PR

mole fraction

A B C D

120 186 235 292

120 185 240 292

0.98 0.96 0.96 0.98

within the column.) Clearly, the procedure can be repeated for other values of the recovery in the prefractionator, to identify another tray arrangement that might provide a further improvement in energy consumption. Judging from the points analyzed, the system with two side columns provides the highest energy savings, although it can be noted that it also shows higher variations in minimum energy consumption for the three different tray arrangements that were considered. One detail is worth highlighting. As the recovery of AB/CD in the prefractionator is reduced, there is a point at which the binary columns of the conventional sequence used as a basis for the design of the integrated schemes cannot produce the specified product composition of the intermediate components B and C. (The lightest and the heaviest component do not show such a problem.) It should be stressed that this does not create any inconsistency in our procedure because such a conventional design is not subject to any further analysis; the only information taken from such a test is the tray distribution from which a new design for the integrated scheme is obtained. Such a design is validated (i.e., the integrated design should meet the specified product streams composition) and then optimized for energy consumption. This means that a search on the operating conditions for the integrated system (with a fixed design as far as its tray arrangement) is carried out to detect values for which a minimum energy consumption is obtained; within the search procedure, as the values for the interconnecting streams change, all other internal conditions of the system must adjust so as to produce the desired purities. Therefore, all thermally coupled arrangements presented in this work meet the same design specification for the product composition shown in Table 3. The study presented here on TCDS schemes for fourcomponent mixtures can be extended with an evaluation of their thermodynamic efficiencies, as shown by Agrawal and Fidkowski14 for separation systems for mixtures of three components. In addition to the energy savings, TCDS schemes can provide a reduction in capital investment. In particular, the Petlyuk-type structure analyzed in this work can be implemented through the dividing-wall column proposed by Kaibel;15 the whole separation system is

A design procedure for thermally coupled distillation systems that separate four-component mixtures has been presented. The method is based on a section analogy procedure with respect to the characteristics of a conventional distillation sequence that consists of a prefractionator followed by two binary separations. Variations in the assumed recoveries of the prefractionator of the conventional sequence provide a systematic method for testing different tray arrangements of the integrated columns. When different designs were optimized for energy consumption, the results showed that the system with two side columns can provide higher energy savings, although the minimum energy consumption of the Petlyuk-type column was less sensitive to the changes implemented in the tray arrangements. Although a more formal study on the dynamic aspects of these integrated systems is required, the response surfaces obtained for each design seem to indicate that the system with side columns is more sensitive to changes in operating conditions than the Petlyuk arrangement. Acknowledgment Financial support from CONCyTEG and CONACyT, Mexico, is gratefully acknowledged. Nomenclature ABCD ) four-component mixture C-1 ) uncoupled distillation column C-1 C-2 ) uncoupled distillation column C-2 C-3 ) uncoupled distillation column C-3 CA-1 ) coupled distillation column CA-1 CA-2 ) coupled distillation column CA-2 CA-3 ) coupled distillation column CA-3 LF ) interconnecting liquid flow VF ) interconnecting vapor flow QR ) heat duty supplied to the reboiler

Literature Cited (1) Tedder, D. W.; Rudd, D. F. Parametric Studies in Industrial Distillation: Part I. Design Comparisons. AIChE J. 1978, 24, 303. (2) Alatiqi, I. M.; Luyben, W. L. Alternative Distillation Configurations for Separating Ternary Mixtures with Small Concentration of Intermediate in the Feed. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 500. (3) Finn, A. J. Consider Thermally Coupled Distillation. Chem. Eng. Prog. 1993, 10, 41. (4) Triantafyllou, C.; Smith, R. The Design and Optimization of Fully Thermally Coupled Distillation Columns. Trans. Inst. Chem. Eng. 1992, 70, 118. (5) Hernańdez, S.; Jimeńez, A. Design of Optimal ThermallyCoupled Distillation Systems Using a Dynamic Model. Trans Inst. Chem. Eng. 1996, 74, 357. (6) Hernańdez, S.; Jimeńez, A. Design of Energy-Efficient Petlyuk Systems. Comput. Chem. Eng. 1999, 23, 1005.

5164 Ind. Eng. Chem. Res., Vol. 42, No. 21, 2003 (7) Agrawal, R.; Fidkowski, Z. T. More Operable Arrangements of Fully Thermally Coupled Distillation Columns. AIChE J. 1998, 44, 2265. (8) Agrawal, R.; Fidkowski, Z. T. New Thermally Coupled Schemes for Ternary Distillation. AIChE J. 1999, 45, 485. (9) Christiansen, A. C.; Skogestad, S.; Lien, K. Complex Distillation Arrangements: Extending the Petlyuk Ideas. Comput. Chem. Eng. 1997, 21, S237. (10) Rong, B.; Kraslawski, A.; Nystro¨m, L. The Synthesis of Thermally Coupled Distillation Flowsheets for Separations of FiveComponent Mixtures. Comput. Chem. Eng. 2000, 24, 247. (11) Fidkowski, Z. T.; Agrawal, R. Multicomponent Thermally Coupled Systems of Distillation Columns at Minimum Reflux. AIChE J. 2001, 47, 2713. (12) Du¨nneiber, G.; Pantelides, C. Optimal Design of Thermally Coupled Distillation Columns. Ind. Eng. Chem. Res. 1999, 38, 162.

(13) Caballero, A. J.; Grossmann, I. E. Generalized Disjunctive Programming Models for the Optimal Synthesis of Thermally Linked Distillation Columns. Ind. Eng. Chem. Res. 2001, 40, 2260. (14) Agrawal, R.; Fidkowski, Z. T. Are Thermally Coupled Distillation Columns Always Thermodynamically More Efficient for Ternary Distillations? Ind. Eng. Chem. Res. 1998, 37, 3444. (15) Kaibel, G. Distillation Columns with Vertical Partitions. Chem. Eng. Technol. 1987, 10, 92. (16) Agrawal, R. Multicomponent Distillation Columns with Partitions and Multiple Reboilers and Condensers. Ind. Eng. Chem. Res. 2001, 40, 4258.

Resubmitted for review April 7, 2003 Revised manuscript received June 30, 2003 Accepted August 7, 2003 IE030297K

Energy-Efficient Designs of Thermally Coupled Distillation Sequences

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