A Simplified Scheme of Externally Heat-Integrated Double Distillation

Ind. Eng. Chem. Res. 2010, 49, 3349–3364

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A Simplified Scheme of Externally Heat-Integrated Double Distillation Columns (EHIDDiC) with Three External Heat Exchangers Yun Wang, Kejin Huang,* and Shaofeng Wang College of Information Science and Technology, Beijing UniVersity of Chemical Technology, Beijing 100029, People’s Republic of China

A simplified scheme of the externally heat-integrated double distillation columns (EHIDDiC), termed SEHIDDiC in this paper, is proposed and studied. Only three external heat exchangers are used to approximate the external heat integration between the rectifying section of the high-pressure distillation column and the stripping section of the low-pressure distillation column. The locations and sizes of the three external heat exchangers are key decision variables and should be considered deliberately to maximize thermodynamic efficiency in process development. A sequential procedure is thus derived for process synthesis and design, and the SEHIDDiC is then evaluated through intensive comparison with conventional distillation columns and the EHIDDiC in terms of the separation of C2 and benzene/toluene binary mixtures. The results obtained indicate that the SEHIDDiC could be an excellent candidate to approximate the EHIDDiC with even a greater reduction in utility consumption and a lesser extent of capital investment. The SEHIDDiC offers essentially a much simple way to design and implement the concept of the EHIDDiC in separation processes. 1. Introduction Since distillation columns occupy a great proportion of utility consumption in the chemical and petrochemical process industries, both economical and environmental considerations have been the continuous impetus to encourage the development of thermodynamically efficient distillation systems. Heat integration is an effective way that has long been known and widely researched for this purpose.1-5 For instance, the ideal heatintegrated distillation column (Ideal HIDiC), as shown in Figure 1, is derived via the internal heat integration between the whole rectifying section and the whole stripping section of a simple distillation column and can operate with a much higher thermodynamic efficiency than a conventional distillation column.6-10 Unfortunately, it has not yet been widely used in the industrial sector because of its high capital investment and potential operation difficulties incurred by the employment of an expensive compressor and the complicated structure for internal heat integration. To avoid using the expensive compressor, one may arrange heat integration between the rectifying section and the stripping section of two individual distillation columns (it is thus called external heat integration in this regard), and the necessary temperature driving forces can be achieved with the adjustments of the system pressures (i.e., through the top condensers). This modification gives birth to a novel configuration of heat-integrated distillation systems, namely, the externally heat-integrated double distillation columns (EHIDDiC), as shown in Figure 2a. Recently, Huang et al. studied the EHIDDiC in the separation of an ideal ternary mixture and found that it could be more thermodynamically efficient than the corresponding conventional distillation systems with and without the condenser/reboiler type heat integration.11 With regard to the design and implementation of the concept of internal heat integration between the rectifying section and the stripping section, considerable effort has been attempted, and a number of schemes have been proposed and studied so far. Tung et al. once developed a plate-fin device for the parallel vertical flows in the alternating stripper and rectifier layers in * To whom correspondence should be addressed. Phone: +86 10 64434801. Fax: +86 10 64437805. E-mail: [email protected].

order to provide the heat transfer areas necessitated for internal heat integration.12 During their long effort to find an appropriate scheme for internal heat integration, Nakaiwa and his co-workers devised and experimentally studied two apparatuses: one is a concentric shell and tube scheme and the other a binding type shell and tube scheme.13,14 For a C3 splitter, Olujic et al. tried to fit heat transfer panels (elements) filled with the vapor flows from the rectifying section into the downcomers and/or the active tray areas in the stripping section.15 Kaeser and Pritchard invented a heat transfer sieve tray with one of the working fluids moving inside it.16 Although these devices appeared sharply different in their designs and were likely to meet the requirements for internal heat integration, they shared a common feature that heat integration was arranged within the ideal HIDiC, making the design and implementation of internal heat integration an extremely challenging issue because of the quite limited space in the column shell, the aroused difficulties and complexities in process design, and the possibly strong influences to the mass transfer between the liquid and vapor phases. To circumvent these difficulties, one may arrange the internal heat

Figure 1. Schematic of an ideal HIDiC.

10.1021/ie901534q  2010 American Chemical Society Published on Web 03/02/2010

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Ind. Eng. Chem. Res., Vol. 49, No. 7, 2010

the heat-integrated pairs of stages, simplifying considerably the design and implementation of the ideal HIDiC and the EHIDDiC as well. The primary objective of the current paper is to study a simplified scheme for the EHIDDiC (termed the SEHIDDiC hereafter), which employs only three external heat exchangers to approximate the external heat integration between the rectifying section of a high-pressure (HP) distillation column and the stripping section of a low-pressure (LP) distillation column. After a brief introduction of the principle of the EHIDDiC, the potential configurations of the SEHIDDiC are described, and a sequential procedure is developed to maximize thermodynamic efficiency during the synthesis and design of the SEHIDDiC. In terms of the separation of C2 and benzene/ toluene binary mixtures, the SEHIDDiC is evaluated through intensive comparison with the conventional distillation column (CDiC) and the EHIDDiC. The unique characteristics of the SEHIDDiC are then highlighted, and some concluding remarks are summarized in the last section of the article. 2. Principle and Configurations of the EHIDDiC

Figure 2. Schematics of the EHIDDiC: (a) a symmetrical EHIDDiC, (b) an asymmetrical EHIDDiC, (c) an asymmetrical EHIDDiC.

integration outside the column shells, and this also allows the employment of a much smaller number of heat exchangers than

Although the EHIDDiC can, in principle, separate either a common mixture or two different mixtures, the former case is studied here. As can be seen in Figure 2a, the EHIDDiC is comprised of HP and LP distillation columns, where heat is favorably transferred from the rectifying section of the former to the stripping section of the latter. Because of the external heat integration, the condenser of the HP distillation column and the reboiler of the LP distillation column can be omitted simultaneously. Apart from the pressure difference and external heat transfer areas between the HP and LP distillation columns, the feed ratio (or feed splitting ratio when separating a common mixture) is another key design variable, which can greatly affect the capital investment and operating cost. Since the schematic shown in Figure 2a features an equal number of stages in the rectifying section of the HP distillation column and the stripping section of the LP distillation column (termed therefore the symmetrical EHIDDiC hereafter), it can only be applied to some mixtures with specific thermodynamic properties and compositions. To extend its applications, one may choose a different number of stages in the rectifying section of the HP distillation column and the stripping section of the LP distillation column, giving rise to an asymmetrical EHIDDiC (c.f., Figure 2b and c). Note also that further improvement in thermodynamic efficiency can be made with the structure modification, and in process synthesis and design it is therefore imperative to determine cautiously the configuration of the external heat integration between the HP and LP distillation columns.17,18 Comparing Figures 2b and c, one may find that the arrangement of external heat integration depends upon the number of stages contained in the rectifying section/stripping section of the HP/LP distillation columns. If the stripping section of the LP distillation column contains fewer stages than the rectifying section of the HP distillation column, then external heat integration should be arranged from the top of the HP distillation column, serving to keep a reflux-free operation mode in the HP distillation column. Otherwise, it should be arranged from the bottom of the LP distillation column, serving to keep a reboil-free operation mode in the LP distillation column.


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3. Principle to Approximate the EHIDDiC with the SEHIDDiC The SEHIDDiC is aimed at approximating the EHIDDiC, facilitating the design and implementation of the latter through retaining its thermodynamic efficiency with the former. The former is similar in configuration to the latter except in the heatintegrated sections. Three external heat exchangers are used instead in the SEHIDDiC to approximate the external heat integration between the rectifying section of the HP distillation column and the stripping section of the LP distillation column. Figure 3a shows the configuration of a symmetrical SEHIDDiC. The top external heat exchanger is arranged between the tops of the rectifying section in the HP distillation column and the stripping section in the LP distillation column, enabling the HP distillation column to operate in a reflux-free operation mode. The intermediate external heat exchanger is located between the middles of the rectifying section in the HP distillation column and the stripping section in the LP distillation column, generating additional reflux flow for the rectifying section in the HP distillation column and vapor flow for the stripping section in the LP distillation column. The bottom external heat exchanger is fixed between the bottoms of the rectifying section in the HP distillation column and the stripping section in the LP distillation column, enabling the LP distillation column to operate in a reboil-free operation mode. As for the arrangement of the total heat transfer areas of the EHIDDiC, a simple way is to equally distribute them among the three external heat exchangers in the SEHIDDiC. In the case of an asymmetrical EHIDDiC, an asymmetrical SEHIDDiC can be constructed in a similar fashion, as shown in Figure 3b and c. It should be indicated here that Figure 3a, b, and c illustrate a rather coarse approximation to the EHIDDiC because the three external heat exchangers have simply been designed and placed between the tops, middles, and bottoms of the heat-integrated section. Theoretically speaking, there exist six location variables, i.e., H1∼H6 in Figure 3a, b, and c, which determine the structure of external heat integration in the SEHIDDiC. For the maintenance of the reflux-free and reboil-free operation modes simultaneously in the HP and LP distillation columns, the top and bottom external heat exchangers have to be connected to the top stage of the former and the bottom stage of the latter, and thus the location variables, H1 and H6, are already fixed (c.f., Figure 3). The other four location variables, i.e., H2∼H5, can then be employed to maximize the thermodynamic efficiency of the SEHIDDiC. After the determination of the configuration for external heat integration, the distribution of the external heat transfer areas can be attempted among the three external heat exchangers, thus being likely to improve further the thermodynamic efficiency. For the attainment of a satisfactory approximation to the EHIDDiC, it appears imperative to deal with the intricate relationship between the HP and LP distillation columns through the adjustments of the locations and sizes of the three external heat exchangers. An effective philosophy for the synthesis and design of the SEHIDDiC should therefore be developed. 4. A Sequential Philosophy for the Synthesis and Design of the SEHIDDiC The synthesis and design of the SEHIDDiC is much more complicated than those of a conventional distillation system because of the external heat integration between the HP and LP distillation columns. It involves primarily four issues to be solved, and they can be tackled in a sequential manner.

Figure 3. Schematics of the SEHIDDiC: (a) a symmetrical SEHIDDiC, (b) an asymmetrical SEHIDDiC, (c) an asymmetrical SEHIDDiC.

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First of all, the synthesis and design of the EHIDDiC is to be conducted, which provides a target to be approximated with the SEHIDDiC. The outcomes should include detailed information about the configuration and operating conditions of the EHIDDiC. In terms of the unique features of the structures for external heat integration mentioned in section 2, an iterative search procedure for the development of the EHIDDiC is derived and outlined in Appendix I. Because of the inclusion of the HP and LP distillation columns, the rigorous search appears rather complicated and time-consuming, and for the simplification of the algorithm, the total numbers of stages in both distillation columns, NHP and NLP, are estimated without consideration of their coupling. Remember the fact that the structure for external heat integration (note also that it has been carefully determined in the algorithm) dominates the performance of the EHIDDiC; the simplification could not cause significant deviation from the true optimum. Second, the approximation of the EHIDDiC with the SEHIDDiC is conducted. With reference to the developed EHIDDiC shown in Figure 2a, the SEHIDDiC is constructed, as shown in Figure 3a, using three external heat exchangers to represent the external heat integration in the EHIDDiC. The top external heat exchanger is placed between the tops of the rectifying section in the HP distillation column and the stripping section in the LP distillation column. The intermediate external heat exchanger is placed between the middles of the heatintegrated sections. The bottom external heat exchanger is located between the bottoms of the rectifying section in the HP distillation column and the stripping section in the LP distillation column. The total external heat transfer areas in the EHIDDiC are equally distributed among the three external heat exchangers in the SEHIDDiC. Similarly, for the developed EHIDDiC shown in Figure 2b and c, their corresponding SEHIDDiC can also be constructed as shown in Figure 3b and c. The SEHIDDiC thus obtained is termed the Base_SEHIDDiC hereafter. Third, the refinement of the Base_SEHIDDiC is conducted through the relocation of the three external heat exchangers. Since their locations determine the structure for external heat integration and can greatly affect the thermodynamic efficiency of the SEHIDDiC, their placement should be determined carefully in process synthesis and design. A heuristic procedure is thus developed and listed in Appendix II, where a sequential search is performed in the order of the bottom, top, and intermediate external heat exchangers. Although the coupling between the locations of these external heat exchangers is not explicitly considered in the algorithm, its impact is considered quite limited. The resultant SEHIDDiC is termed the Intermediate_SEHIDDiC hereafter. Last, further refinement of the Intermediate_SEHIDDiC should be performed through the redistribution of external heat transfer areas among the three external heat exchangers. Quite similarly in principle to the placement of the three external heat exchangers, their sizes can also affect the thermodynamic efficiency and should be determined carefully in process synthesis and design. Although the total external heat transfer areas of the three external heat exchangers should be subjected to a detailed optimization study due to the great variations in the structure of external heat integration from the EHIDDiC to the Intermediate_SEHIDDiC, its effect is considered marginal. To lay a fair basis for the comparison of the EHIDDiC and SEHIDDiC, we keep constant the total heat transfer areas of the external heat exchangers in the current work. The resultant SEHIDDiC is termed the Optimum_SEHIDDiC hereafter.

Table 1. Physical Properties and Design Specification of Example I parameter feed composition (mol %)

value ethylene ethane

83 17 988.034 246.150 1882.877 0.6 10 600 99.5 99.9

feed flow rate (kmol · h-1) feed temperature (K) feed pressure (kPa) heat transfer coefficient (kW · K-1 · m-2) heat transfer area (m2 · stage-1) pressure of the LP distillation column (kPa) product specification (mol %) ethylene ethane

Table 2. Economical Basis for Process Synthesis and Design for Example I parameter

value Condensers

heat transfer coefficient (kW · K-1 · m-2) temperature difference (K)

0.852 13.9

Reboilers heat transfer coefficient (kW · K-1 · m-2) temperature difference (K) energy cost of condenser ($/106 kJ) energy cost of reboiler ($/106 kJ) payback period (yr)

0.568 34.8 20.4833 (193 K) 0.148 3

In the above four steps, the minimization of total annual cost (TAC) can be taken as the objective function. The TAC is the sum of operating cost (OC) and annual capital investment (c.f., eq 1).19,20 The annual capital investment is assumed to be the capital investment (CI) divided by a payback period, and the cost of equipment and utilities is estimated with the formulas shown in Appendix III. TAC ) OC + CI/payback period

(1)

In the following sections, two example separation problems are studied to evaluate the feasibility of approximating the EHIDDiC with the SEHIDDiC. 5. Example I: Separation of a C2 Binary Mixture Since the separation of a C2 binary mixture is accompanied by the consumption of a great amount of expensive cold (refrigeration) utilities, it is employed to evaluate the SEHIDDiC in this section. Table 1 summarizes the physical properties and design specification of the example system, and Table 2 tabulates the economical basis for process synthesis and design. Here, the cost of the cold utility is listed only for the temperature of 193 K. When the cold utility of other temperatures is needed, its cost is calculated according to a detailed mechanic model developed. According to the principle shown in Appendix IV, the steady state models of the EHIDDiC and SEHIDDiC have been developed with the assumption of theoretical stages with perfect mixing. The Peng-Robinson equation of state is used to represent the vapor-liquid equilibrium relationship, and no heat loss is considered. These steady state models can be used effectively to aid process synthesis and design. 5.1. Synthesis and Design of the EHIDDiC. According to the grid-search procedure described in Appendix I, the synthesis and design of the EHIDDiC starts from an arbitrarily chosen process design with 85 stages in the HP and LP distillation columns, respectively, and the obtained results are shown in Figure 4. In column I, the relationship is displayed between the CI, OC, and TAC and the number of stages in the HP distillation column when the number of stages in the LP distillation column has been fixed at 85. The TAC is reduced gradually when the number of stages


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Figure 4. Relationships between the CI, OC, and TAC and the number of stages in the HP and LP distillation columns of the EHIDDiC (Example I): (I) effect of the number of stages in the HP distillation column, (II) effect of the number of stages in the LP distillation column.

in the HP distillation column is increased, and the minimum value is reached when the number of stages is around 100 in the HP distillation column. In column II, the relationship is displayed between the CI, OC, and TAC and the number of stages in the LP distillation column when the number of stages in the HP distillation column has been fixed at 100. The TAC is reduced when the number of stages in the LP distillation column is decreased from 85 and the minimum value is reached when the number of stages is around 60 in the LP distillation column. Therefore, the optimal design of the EHIDDiC corresponds to a distillation system that involves 100 and 60 stages in the HP and LP distillation columns, respectively, with the feed locations at stages 66 and 33. As shown in Figure 5a, the process involves an asymmetrical configuration with 27 stages heat-integrated, and its detailed design parameters and operating conditions are listed in Table 3. 5.2. Approximation of the EHIDDiC with the SEHIDDiC. With reference to the configuration of the obtained EHIDDiC, the Base_SEHIDDiC is constructed with three external heat exchangers to replace the external heat integration in the EHIDDiC. The total heat transfer areas (i.e., 27 × 10 m2) are equally distributed among the three external heat exchangers with each to be 90 m2. As shown

in Figure 5b, the top external heat exchanger is placed between the tops of the rectifying section in the HP distillation column and the stripping section in the LP distillation column (i.e., stages 1 and 34 in the HP and LP distillation columns, respectively). The intermediate external heat exchanger is arranged between the middles of the heat-integrated sections (i.e., stages 14 and 47 in the HP and LP distillation columns, respectively). The bottom external heat exchanger is placed between the bottom of the LP distillation column and the stage counted down from the top of the rectifying section by 27 stages in the HP distillation column (i.e., stages 27 and 60 of the HP and LP distillation columns, respectively). The steady state profiles of temperature, liquid composition, and vapor and liquid flow rates of the EHIDDiC and Base_ SEHIDDiC are compared in Figure 6. It is stipulated here that the numbers of 1-100 represent the stages in the HP distillation column and the numbers of 101-160 the stages in the LP distillation column. As can be seen, a good agreement has been reached in the profiles of temperature and liquid composition between the EHIDDiC and Base_SEHIDDiC. As for the vapor and liquid flow rates, sharp changes take place at the locations

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Figure 5. Schematics of the EHIDDiC, Base_SEHIDDiC, and Intermediate_SEHIDDiC (Example I): (a) EHIDDiC, (b) Base_SEHIDDiC, (c) Intermediate_SEHIDDiC.

of the three external heat exchangers, demonstrating a kind of reasonable approximation to the gradual changes of the vapor and liquid loads in the EHIDDiC. 5.3. Refinement of the SEHIDDiC through the Relocation of the Three External Heat Exchangers. In terms of the search procedure shown in Appendix II, the optimum location of the bottom external heat exchanger in the HP distillation column is first searched, and the results are illustrated in Figure 7a. With ascending gradually the location of the bottom external heat exchanger from stage 27 of the HP distillation column, the TAC reduces gradually and approaches its minimum value around stage 3. Next, the optimum location of the top external heat exchanger in the LP distillation column is searched, and the results are illustrated in Figure 7b. With descending gradually the location of the top external heat exchanger from stage 34 of the LP distillation column, the TAC reduces and reaches its minimum value around stage 43. With reference to the newly determined locations of the bottom and top external heat exchangers, the intermediate external heat exchanger has to be moved between them along the heights of the HP and LP distillation columns, respectively. Since the bottom and top external heat exchanger are placed respectively on stages 3 and 1 in the HP distillation column, the location of the intermediate external heat exchanger can only be arranged on stage 2. The feasible location of the intermediate external heat exchanger in the LP distillation column is between stages 43 and 60, and a heuristic search is illustrated in Figure 7c. With descending gradually the location of the intermediate external heat exchanger, the TAC reduces and reaches its minimum value around stage 59. The relocations of the three external heat exchangers are then finished, and the Intermediate_SEHIDDiC derived is sketched in Figure 5c. 5.4. Refinement of the SEHIDDiC through the Heat Transfer Area Redistribution among the Three External Heat Exchangers. So far, the external heat transfer areas for the three external heat exchangers have been assumed to be equal with each other, and they should be adjusted to maximize the thermodynamic efficiency of the Intermediate_SEHIDDiC. On the basis of a constrained steepest gradient method, the optimum distribution of the external heat transfer areas is searched among the three external heat exchangers. Since the utility cost of the top condenser in the LP distillation column ($20.4833/106 kJ) is much higher than that of the bottom reboiler in the HP distillation column ($0.148/106 kJ), the former is preferred to be employed as an index here, and the results are depicted in Figure 8. As can be readily seen, the heat duty of the top condenser in the LP distillation column reaches the minimum value when the external transfer areas are 99.074 m2, 71.562 m2, and 99.364 m2, respectively, for the top, intermediate, and bottom external heat exchangers. The steady state profiles of temperature, liquid composition, and vapor and liquid flow rates of the Optimum_SEHIDDiC are also depicted in Figure 6. It can be readily seen that a great reduction in the vapor and liquid flow rates has been achieved (in the nonheat-integrated sections), demonstrating the great importance of employing the locations and sizes of the three external heat exchangers as decision variables to maximize the thermodynamic efficiency in process synthesis and design. While gradual changes in the vapor and liquid flow rates take place at the top part of the rectifying section in the HP distillation column, sharp changes occur in the striping section of the LP distillation column, signifying the different impacts of external heat integration on the HP and LP distillation columns. The relocations of the three external heat exchangers and redistribu-


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Table 3. Comparison between the CDiC, EHIDDiC, Base_SEHIDDiC, Intermediate_SEHIDDiC, and Optimum_SEHIDDiC for the Separation of a C2 Binary Mixture parameter number of stages in the HP/LP distillation column heat transfer area (m2) number of the heat-integrated stages feed location of the HP/ LP distillation column pressure of the HP distillation column (kPa) pressure of the LP distillation column (kPa) feed splitting ratio reflux ratio in the HP distillation column reflux ratio in the LP distillation column condenser heat duty in the LP distillation column (kW) reboiler heat duty in the HP distillation column (kW) diameter of the HP distillation column (m) diameter of the LP distillation column (m) height of the HP distillation column (m) height of the LP distillation column (m) operating cost ($106/yr) capital investment ($106) TAC ($106/yr) comparison in the capital cost comparison in the operating cost

CDiC 93 58 1770.000

EHIDDiC

Base_SEHIDDiC

Intermediate_SEHIDDiC

Optimum_SEHIDDiC

100/60 10 27 66/33 1774.020 600 0.434

100/60 90/90/90 3 66/33 1748.000 600 0.453

100/60 90/90/90 3 66/33 1786.150 600 0.420

100/60 99.074/71.562/99.364 3 66/33 1781.700 600 0.421

1.998 4569.800 2460.920 1.494 1.907 73.148 43.889 2.435 3.048 3.451 144.523% 74.374%

2.133 4619.640 2563.630 1.528 1.918 73.148 43.889 2.462 2.611 3.333 123.803% 75.199%

1.873 4485.380 2336.700 1.459 1.890 73.148 43.889 2.390 2.537 3.236 120.294% 72.999%

1.875 4484.790 2337.260 1.459 1.890 73.148 43.889 2.390 2.536 3.235 120.247% 72.999%

2.776 8191.930 5567.470 2.253 68.028 3.274 2.109 3.977 100% 100%

tion of the external heat transfer areas give rise to a drastic change in the profiles of liquid composition. 5.5. Evaluation of the SEHIDDiC. Table 3 shows a detailed comparison between the CDiC, EHIDDiC, Base_SEHIDDiC, Intermediate_SEHIDDiC, and Optimum_SEHIDDiC for the C2 separation system. The CDiC is also derived with the minimization of the TAC as the objective function and serves here as a

baseline for the comparative studies. Because of the external heat integration between the rectifying section of the HP distillation column and the stripping section of the LP distillation column, the EHIDDiC cut the operating cost by 25.626% in comparison with the CDiC at the expense of an additional capital investment by 44.523%. The Base_SEHIDDiC secures a 24.801% reduction in operating cost with an additional capital

Figure 6. Steady state profiles of the EHIDDiC, Base_SEHIDDiC, and Optimum_SEHIDDiC (Example I): (a) temperature, (b) liquid composition, (c) vapor flow rate, (d) liquid flow rate.

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Ind. Eng. Chem. Res., Vol. 49, No. 7, 2010 Table 4. Physical Properties and Design Specification of Example II parameter feed composition (mol %)

value benzene toluene

feed flow rate (kmol · h-1) latent heat of vaporization (kJ · kmol-1) relative volatility feed thermal condition heat transfer coefficient (kW · K-1 · m-2) heat transfer area (m2 · stage-1) pressure of the LP distillation column (kPa) product specification (mol %) benzene toluene

50 50 500 30000 2.4 1 0.6 10 101.3 99.5 99.5

Table 5. Economical Basis for Process Synthesis and Design for Example II parameter

value Condensers

heat transfer coefficient (kW · K-1 · m-2) temperature difference (K)

0.852 13.9

Reboilers heat transfer coefficient (kW · K-1 · m-2) temperature difference (K) energy cost of condenser ($/106 kJ) energy cost of reboiler ($/106 kJ) payback period (yr)

0.568 34.8 0.02647 11.029 3

three external heat exchangers, the Intermediate_SEHIDDiC reduces the operating cost by 27.001%, which is even greater than that of the EHIDDiC. Moreover, the diameters of the HP and LP distillation columns are also diminished as compared with those of the EHIDDiC and Base_SEHIDDiC, leading to a further abated additional capital investment by 20.294%. The Optimum_SEHIDDiC results in a reduction of 27.001% in the operating cost with an additional capital investment by 20.247%, implying that redistributing the external heat transfer areas among the three external heat exchangers cannot greatly improve the thermodynamic efficiency posterior to the relocations of the three external heat exchangers. The reason is due to the fact that external heat integration between the HP and LP distillation columns is determined actually by the following relationship: QIN ) U × S × ∆T Figure 7. Relationships between the TAC and the locations of the three external heat exchangers (Example I).

(2)

On the basis of the above comparison, one can readily understand that the SEHIDDiC can be an excellent approximation to the EHIDDiC, with even a reduced capital investment and operating cost. 6. Example II: Separation of a Benzene/Toluene Binary Mixture

Figure 8. Relationship between the condenser duty and the heat transfer area of the three heat exchangers (Example I).

investment by 23.803%, indicating again a reasonable approximation to the EHIDDiC. Owing to the relocations of the

Separation of an equi-molar benzene/toluene binary mixture is employed as the second illustrative example. Table 4 summarizes the physical properties and design specification for the example system, and Table 5 shows the economical basis for process synthesis and design. According to the principle shown in Appendix IV, the steady state models of the EHIDDiC and SEHIDDiC have been developed under the assumption of theoretical stages with perfect mixing. A constant relative volatility of 2.4 is used to represent approximately the vapor-liquid equilibrium relationship. Constant overflows are assumed (in column sections without external heat integration), and sensible heat can be ignored in comparison with a latent one. These steady state models can be used effectively to aid process synthesis and design.


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Figure 9. Relationships between the CI, OC, and TAC and the number of stages of the HP and LP distillation columns for the EHIDDiC (Example II): (I) effect of the number of stages in the HP distillation column, (II) effect of the number of stages in the LP distillation column.

6.1. Synthesis and Design of the EHIDDiC. By means of the search procedure outlined in Appendix I, the synthesis and design of the EHIDDiC is performed starting from an arbitrarily chosen process design with 34 stages in the HP and LP distillation columns, respectively, and the obtained results are depicted in Figure 9. In column I, the effect of the number of stages in the HP distillation column is displayed, and the TAC reaches its minimum value around 36 stages in the HP distillation column. Likewise, the effect of the number of stages in the LP distillation column is illustrated in column II. The TAC reduces with the decrease in the number of stages and reaches its minimum value around 28 stages in the LP distillation column. These outcomes indicate that the optimal process design for the EHIDDiC contains two distillation columns with 36 and 28 stages, respectively, in the HP and LP distillation columns, and the feed locations are placed at stages 23 and 16, respectively, with in total 12 stages heat-integrated, as shown in Figure 10a. The detailed design parameters and operating conditions are listed in Table 6.

6.2. Approximation of the EHIDDiC with the SEHIDDiC. According to the configuration of the EHIDDiC obtained above, the Base_SEHIDDiC is simply constructed with the employment of three external heat exchangers. Since the total heat transfer areas are 12 × 10 m2 in the EHIDDiC, the heat transfer area of each external heat exchanger is set to be 40 m2 in the Base_SEHIDDiC. The top external heat exchanger is placed between the tops of the rectifying section in the HP distillation column and the stripping section in the LP distillation column (i.e., stages 1 and 17 in the HP and LP distillation columns, respectively). The intermediate external heat exchanger is placed between the middles of the heat-integrated section (i.e., stages 6 and 22 in the HP and LP distillation columns, respectively). The bottom external heat exchanger is placed between the bottom of the stripping section in the LP distillation column and the stage counted down from the top of the rectifying section by 12 stages in the HP distillation column (i.e., stages 12 and 28 in the HP and LP distillation columns, respectively). The resultant Basic_SEHIDDiC is shown in Figure 10b, and the

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Figure 10. Schematics of the EHIDDiC, Base_SEHIDDiC and Intermediate_SEHIDDiC (Example II): (a) EHIDDiC, (b) Base_SEHIDDiC, (c) Intermediate_SEHIDDiC.

steady state profiles of temperature, liquid composition, and vapor and liquid flow rates for the EHIDDiC and Base_SEHIDDiC are compared in Figure 11. It is stipulated here that the numbers 1-36 represent the stages of the HP distillation

column and the numbers 37-64 the stages of the LP distillation column. As can be seen, sharp changes in the vapor and liquid flow rates occur in the locations of the three external heat exchangers, demonstrating again a kind of reasonable approximation to the gradual changes in the vapor and liquid loads in the EHIDDiC. 6.3. Refinement of the SEHIDDiC through the Relocation of the Three External Heat Exchangers. The four variables about the locations of the three external heat exchangers are adjusted on the basis of the search procedure described in Appendix II. First, the effect of the location of the bottom external heat exchanger in the HP distillation column is examined, and the results are illustrated in Figure 12a. With ascending the location of the bottom external heat exchanger from the bottom of the heat-integrated section in the HP distillation column, the TAC reduces and reaches its minimum value around stage 5. Second, the effect of the location of the top external heat exchanger in the LP distillation column is illustrated in Figure 12b. With descending the location of the top external heat exchanger from the top of the stripping section in the LP distillation column, the TAC reduces and reaches its minimum value around stage 26. In terms of the newly determined locations of the bottom and top external heat exchangers, the feasible region where the intermediate external heat exchanger should be located can be identified. Since the top external heat exchanger is placed on stage 26 in the LP distillation column, the location of the intermediate external heat exchanger can only be stage 27 in the LP distillation column. The effect of the location of the intermediate external heat exchanger in the HP distillation column is illustrated in Figure 12c. With ascending the location of the intermediate external heat exchanger in the HP distillation column, the TAC reduces and reaches its minimum value around stage 2. Thus, the relocation of the three external heat exchangers gives rise to an Intermediate_SEHIDDiC, as shown in Figure 10c, and the detailed design parameters and operating conditions are tabulated in Table 6. 6.4. Refinement of the SEHIDDiC through the Heat Transfer Area Redistribution among the Three External Heat Exchangers. In virtue of the constrained steepest gradient search method, the optimal distribution of the external heat transfer areas among the three external heat exchangers is searched, aiming to improve the thermodynamic efficiency of the Intermediate_SEHIDDiC. Since the utility cost of the bottom reboiler in the HP distillation column ($11.029/106 kJ) is much higher than that of the top condenser in the LP distillation column ($0.02647/106 kJ), the former is preferred to be employed as an index here, and Figure 13 shows the search outcome. The heat duty of the bottom reboiler in the HP distillation column reaches its minimum value when the external transfer areas are 29.305 m2, 30.378 m2, and 60.317 m2, respectively, for the top, intermediate, and bottom external heat exchangers. The steady state profiles of temperature, liquid composition, and vapor and liquid flow rates of the Optimum_SEHIDDiC are also depicted in Figure 11. Again, a substantial reduction in the vapor and liquid flow rates has been achieved, demonstrating that modifying the locations and sizes of the three external heat exchangers can enhance considerably the thermodynamic efficiency of the Base_SEHIDDiC. While fairly sharp changes happen in the vapor and liquid flow rates in the rectifying section of the HP distillation column, gradual changes occur in the bottom part of the striping section in the LP


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Table 6. Comparison between the CDiC, EHIDDiC, Base_SEHIDDiC, Intermediate_SEHIDDiC, and Optimum_SEHIDDiC for the Separation of a Benzene/Toluene Binary Mixture parameter number of stages in the HP/LP distillation column heat transfer area (m2) number of the heat-integrated stages feed locations of the HP/LP distillation columns pressure of the HP distillation column (kPa) pressure of the LP distillation column (kPa) feed splitting ratio reflux ratio in the HP distillation column reflux ratio in the LP distillation column condenser heat duty in the LP distillation column (kW) reboiler heat duty in the HP distillation column (kW) diameter of the HP distillation column (m) diameter of the LP distillation column (m) height of the HP distillation column (m) height of the LP distillation column (m) operating cost ($106/yr) capital cost ($106) TAC ($106/yr) comparison in the capital cost comparison in the operating cost

CDiC 40 23 101.300 1.421 5043.770 5043.770 1.993 29.259 1.445 1.217 1.851 100% 100%

EHIDDiC

Base_SEHIDDiC

Intermediate_SEHIDDiC

Optimum_SEHIDDiC

36/28 10 12 23/16 437.039 101.300 0.676

36/28 40/40/40 3 23/16 428.350 101.300 0.685

36/28 40/40/40 3 23/16 448.058 101.300 0.638

36/28 29.305/30.378/60.317 3 23/16 448.463 101.300 0.637

2.155 1408.710 3537.960 1.323 1.295 26.333 20.482 1.012 1.375 1.471 112.983% 70.035%

2.292 1426.830 3588.70 1.337 1.305 26.333 20.482 1.027 1.235 1.438 101.479% 71.073%

1.609 1330.370 3296.730 1.272 1.244 26.333 20.482 0.943 1.184 1.338 97.288% 65.260%

1.600 1326.920 3293.640 1.271 1.244 26.333 20.482 0.942 1.181 1.336 97.042% 65.190%

distillation column, reflecting the different effect of external heat integration on the HP and LP distillation columns. 6.5. Evaluation of the SEHIDDiC. Table 6 shows a detailed comparison between the CDiC, EHIDDiC, Base_SEHIDDiC, Intermediate_SEHIDDiC, and Optimum_SEHIDDiC for the separation of the benzene/toluene binary mixture. As compared with the CDiC, the EHIDDiC reduces the operating cost by

29.965% with an additional capital investment of 12.983%. The Base_SEHIDDiC results in a reduction of 28.927% in the operating cost with an additional capital investment of 1.479%, representing evidently an excellent approximation of the EHIDDiC. The Intermediate_SEHIDDiC derived through the relocation of the three external heat exchangers abates the operating cost by 34.740% and meanwhile reduces the capital

Figure 11. Steady state profiles of the EHIDDiC, Base_SEHIDDiC, and Optimum_SEHIDDiC (Example II): (a) temperature, (b) liquid composition, (c) vapor flow rate, (d) liquid flow rate.

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Figure 14. Further simplification of the SEHIDDiC: (a) Example I, (b) Example II.

Figure 12. Relationships between the TAC and the locations of the three external heat exchangers (Example II).

external heat exchangers results in a reduction of 34.810% in the operating cost and a reduction of 2.958% in the capital investment. The marginal difference between the Intermediate_ SEHIDDiC and Optimum_SEHIDDiC indicates again that redistributing the external heat transfer areas among the three external heat exchangers cannot greatly improve the thermodynamic efficiency after the relocation of the three external heat exchangers. The above comparison confirms the fact that the Optimum_SEHIDDiC can be advantageous over the CDiC and EHIDDiC in the aspect of capital investment and thermodynamic efficiency, demonstrating that the SEHIDDiC is an excellent candidate to approximate the EHIDDiC in separation operations. 7. Discussion

Figure 13. Relationship between the reboiler duty and the heat transfer areas of the three external heat exchangers (Example II).

investment by 2.712%. The Optimum_SEHIDDiC obtained by redistributing the external heat transfer area among the three

It is interesting to note with the obtained outcomes that the SEHIDDiC needs a smaller capital investment and appears to be more thermodynamically efficient than the EHIDDiC. It is considered that two factors are actually responsible for the occurrences of this phenomenon. One is the potential drawback of the external heat integration between the rectifying section of the HP distillation column and the stripping section of the


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Table 7. Comparison between the CDiC, Condenser/Reboiler Type Heat-Integrated Distillation System, EHIDDiC, and Optimum_SEHIDDiC for the Separation of a C2 Binary Mixture parameter number of stages in the HP/LP distillation column heat transfer area (m2) number of the heat-integrated stages feed locations of the HP/LP distillation columns pressure of the HP distillation column (kPa) pressure of the LP distillation column (kPa) feed splitting ratio reflux ratio in the HP distillation column reflux ratio in the LP distillation column condenser heat duty in the LP distillation column (kW) reboiler heat duty in the HP distillation column (kW) diameter of the HP distillation column (m) diameter of the LP distillation column (m) height of the HP distillation column (m) height of the LP distillation column (m) operating cost ($106/yr) capital cost ($106) TAC ($106/yr) comparison in the capital cost comparison in the operating cost

CDiC 93 58 1770.000 2.776 8191.930 5567.470 2.253 68.028 3.274 2.109 3.977 100% 100%

CRHIDiS

EHIDDiC

Optimum_SEHIDDiC

100/60

100/60 10 27 66/33 1774.020 600 0.434

100/60 99.074/71.562/99.364 3 66/33 1781.700 600 0.421

1.998 4569.800 2460.920 1.494 1.907 73.148 43.889 2.435 3.048 3.451 144.523% 74.374%

1.875 4484.790 2337.260 1.459 1.890 73.148 43.889 2.390 2.536 3.235 120.247% 72.999%

1 66/33 1774.020 600 0.347 2.766 1.863 5038.31 1921.81 1.324 2.002 73.148 43.889 2.682 2.357 3.468 111.759% 81.918%

Table 8. Comparison between the CDiC, Condenser/Reboiler Type Heat-Integrated Distillation System, EHIDDiC, and Optimum_SEHIDDiC for the Separation of a Benzene/Toluene Binary Mixture parameter number of stages in the HP/LP distillation column heat transfer area (m2) number of the heat-integrated stages feed locations of the HP/LP distillation columns pressure of the HP distillation column (kPa) pressure of the LP distillation column (kPa) feed splitting ratio reflux ratio in the HP distillation column reflux ratio in the LP distillation column condenser heat duty in the LP distillation column (kW) reboiler heat duty in the HP distillation column (kW) diameter of the HP distillation column (m) diameter of the LP distillation column (m) height of the HP distillation column (m) height of the LP distillation column (m) operating cost ($106/yr) capital cost ($106) TAC ($106/yr) comparison in the capital cost comparison in the operating cost

CDiC 40 23 101.300 1.421 5043.770 5043.770 1.993 29.259 1.445 1.217 1.851 100% 100%

LP distillation column. Although it is effective to enhance the thermodynamic efficiency of separation operation, it is extremely difficult to guarantee that every pair of stages that are heatintegrated present their favorable effect in an efficient way. Recently, Gadalla et al. analyzed internal heat integration in a C3 splitter and found the same shortcoming in terms of pinch analysis.21 The other is the extended flexibility offered by the configuration of external heat integration with three external heat exchangers. The adjustments of the locations and sizes of the three external heat exchangers give additional degrees of freedom to process synthesis and design, leading therefore to a higher thermodynamic efficiency and smaller capital investment than those of the EHIDDiC. These realities lend evidently strong support to the reasonability of approximating external heat integration with three external heat exchangers in the EHIDDiC. Closely examining the two Optimum_SEHIDDiC’s derived in the two example systems, one could find that the locations of the three external heat exchangers are all at the top part of the rectifying section in the HP distillation column and bottom part of the stripping section in the LP distillation column. In particular, two external heat exchangers are located adjacent to each other on two consecutive stages in the HP and LP distillation columns, respectively, for instance, the intermediate and bottom external heat exchangers in the process design shown in Figure 5c and the top and intermediate external heat

CRHIDiS

EHIDDiC

Optimum_SEHIDDiC

36/28

36/28 10 12 23/16 437.039 101.300 0.676

36/28 29.305/30.378/60.317 3 23/16 448.463 101.300 0.637

2.155 1408.710 3537.960 1.323 1.295 26.333 20.482 1.012 1.375 1.471 112.983% 70.035%

1.600 1326.920 3293.640 1.271 1.244 26.333 20.482 0.942 1.181 1.336 97.042% 65.190%

1 23/16 437.039 101.300 0.501 1.475 1.586 2571.860 2571.860 1.142 1.440 26.333 20.482 0.737 1.290 1.167 105.998% 51.003%

exchangers in the process design shown in Figure 10c. These kinds of arrangements reflect actually a careful compromise between the effects of reflux and reboil flow rates and the utility consumption caused by the pressure elevation from the LP to HP distillation columns. They also present valuable clues to the further simplification of the SEHIDDiC, i.e., the employment of two external heat exchangers (rather than three of them) to represent external heat integration between the HP and LP distillation columns and direct use of the distillate from the HP distillation column to heat the stripping section in the LP distillation column. Two resultant process configurations are thus derived and illustrated in Figure 14a and b, and their static behaviors are worth studying in the near future. In Tables 7 and 8, the comparison is conducted between the CDiC, condenser/reboiler type heat-integrated distillation system (CRHIDiS), EHIDDiC, and Optimum_SEHIDDiC for the separation of a C2 and benzene/toluene binary mixture, respectively. For the former, the obtained results indicate that the EHIDDiC and optimal_SEHIDDiC are superior to the CRHIDiS in thermodynamic efficiency. For the latter, the results indicate that the reverse is true. These outcomes are actually in good accordance with the conclusion of our previous study. Namely, whether or not the EHIDDiC and optimal_SEHIDDiC are advantageous over the CRHIDiS depends heavily on the relative costs of utility and capital investment.11

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Figure 15. External heat integration in various double-effect distillation systems: (a) DEPDS, (b) DEDDS, (c) DEIDS, (d) SEHIDDiC for the DEPDS, (e) SEHIDDiC for the DEDDS, (f) SEHIDDiC for the DEIDS.

In this work, the SEHIDDiC is used to separate a common binary mixture, and it is actually quite similar in configuration to a double-effect distillation system.22,23 Because the double-effect distillation systems can offer not only relatively high thermodynamic efficiency but also enhanced separation ability through the double reduced-height distillation columns, they have been widely used in the chemical and petrochemical process industries. For example, C3 separation may need around 200-240 stages, and the resultant conventional distillation column is too high (possibly between 85 and 90 m). The double-effect arrangement helps to alleviate the drawback. The wide use of the double-effect distillation columns offers great opportunities for the applications of the SEHIDDiC. In Figure 15a, b, and c, three double-effect distillation systems, i.e., a double-effect parallel distillation system (DEPDS), a double-effect direct distillation system (DEDDS), and a doubleeffect indirect distillation system (DEIDS), are sketched, and their corresponding SEHIDDiCs are shown respectively in Figure 15d, e, and f.

and studied with the arrangement of the heat transfer elements in the outside of the column shell, leading to a much simplified scheme termed the SEHIDDiC in the current paper. The SEHIDDiC features only three external heat exchangers to approximate the external heat integration between the rectifying section of the HP distillation column and the stripping section of the LP distillation column, and their locations and sizes have to be carefully determined in order to exploit the full potentials of process simplification. A sequential procedure is thus derived for process synthesis and design. Two example systems, i.e., the separation of C2 and benzene/ toluene binary mixtures, are employed to evaluate the proposed philosophy for process simplification. The obtained results have shown that the SEHIDDiC is really advantageous over the EHIDDiC in not only capital investment but also operating cost, evidencing that the former could be an excellent alternative to the latter. The sequential procedure derived for process synthesis and design is also found to be reliable and effective.

8. Conclusion

Acknowledgment

Finding an effective way to design and implement external heat integration between the rectifying section of the HP distillation column and the stripping section of the LP distillation column is one of the most challenging issues encountered in the development of the EHIDDiC. A novel attempt is proposed

The project is financially supported by the National High Technology Research and Development Program of China (i.e., 863 Program under the Grant Number of 2007AA05Z210) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.


Appendix I: A Search Procedure for the Synthesis and Design of the EHIDDiC With the applications of the steady state models shown in Appendix IV, the following grid-search philosophy can be employed for the synthesis and design of the EHIDDiC separating a given binary mixture. (i) Given an arbitrarily chosen structure of the EHIDDiC and the desired product specifications. (ii) Vary the number of stages in the HP distillation column, NHP. (iii) Vary the feed location for the LP distillation column, NFLP. (iv) In terms of the unique features of the structures for external heat integration, calculate the number of stages that should be heat-integrated, NHI ) min (NFHP - 1, NLP - NFLP). (v) Conduct the steady state simulation and calculate the TAC using the formulas in Appendix III. (vi) Check if the TAC is minimal with respect to the feed location for the LP distillation column, NFLP. If yes, go to next step; otherwise, go to step iii. (vii) Vary the feed location for the HP distillation column, NFHP. (viii) Repeat iv-v and check if the TAC is minimal with respect to the feed location for the HP distillation column, NFHP. If yes, go to next step; otherwise, go to step vii. (ix) Check if the TAC is minimal with respect to the number of stages in the HP distillation column, NHP. If yes, go to next step; otherwise, go to step ii. (x) Vary the number of stages in the LP distillation column, NLP. (xi) Repeat iii-viii to determine the optimal feed locations of the HP and LP distillation columns, NFHP and NFLP. (xii) Check if the TAC is minimal with respect to the number of stages in the LP distillation column, NLP. If yes, go to next step; otherwise, go to step x. (xiii) Summarize the synthesis and design results, and stop. Appendix II: A Search Procedure for the Relocation of the Three External Heat Exchangers The locations of the three external heat exchangers can be determined in a sequential manner. Since the top and bottom external heat exchangers determine the favorable region for external heat integration, their locations should be first decided. (i) Given the configuration and operating conditions of the Base_SEHIDDiC. (ii) Vary the location of the bottom external heat exchanger in the HP distillation column until the minimum TAC has been reached. (iii) Vary the location of the top external heat exchanger in the LP distillation column until the minimum TAC has been reached. (iv) In light of the resultant locations of the bottom and top external heat exchangers, the feasible region for the intermediate external heat integration can be identified. (v) Vary the locations of the intermediate external heat exchanger in the HP and LP distillation columns until the minimum TAC has been reached. (vi) Summarize the synthesis and design results, and stop.

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The heat transfer areas of the reboiler and condenser are calculated using the following equations: SREB ) QREB/(UREB × ∆TREB)

(A3)

SCON ) QCON/(UCON × ∆TCON)

(A4)

In terms of the above size estimations, the capital and energy costs of a distillation column are estimated using the following equations: column shell cost ) 17640 × D1.066 × Ht0.802

(A5)

tray cost ) 229 × D1.55 × N

(A6)

0.65 total heat exchanger cost ) 7296 × S0.65 REB + 7296 × SCON + HI

∑ (7296 × S

0.65 i )

(A7)

i)1

capital investment ) column shell cost + tray cost + total heat exchanger cost (A8) operating cost ) QCON × condenscost × 24 × 300 + QREB × reboilcost × 24 × 300

(A9)

Appendix IV: Steady State Models of the EHIDDiC and SEHIDDiC In terms of the principle of mass and energy conservation in conjunction with the given vapor-liquid equilibrium relationship, the steady state models of the EHIDDiC and SEHIDDiC have been developed. In these steady state models, four decision variables, i.e., the reflux flow rate in the LP distillation column, the bottom reboiler heat duty in the HP distillation column, the pressure of the HP distillation column, and the feed splitting ratio, are used to maintain the top and bottom products on their specifications. A modified Newton-Raphson method is employed to solve the resultant nonlinear equations, and the satisfaction of component mass balance equations (eqs A10 and A13) combined with the attainment of product specifications (eqs A11, A12, A14, and A15) is taken as the convergence criterion. Given the flow rate and composition of the mixture to be separated, the topological information of the process configurations, and the desired product specifications, the four decision variables can be readily obtained. The steady state models appear quite robust and can be employed to aid process synthesis and design. HP distillation column: |Lj-1xi,j-1 + Vj+1yi,j+1 - Ljxi,j - Vjyi,j + Fjzi,j | e ε (A10)

Appendix III: Sizing and Economic Basis of Distillation Columns

sp |xtop,HP - xtop,HP | eε

(A11)

Assuming an F factor of 1 in engineering units, the diameter of the distillation column is calculated via the equation

sp |xbot,HP - xbot,HP | eε

(A12)

0.5 D ) 0.01735 × (MW × T/P)0.25 × VNT

(A1)

The height of a distillation column is calculated by the equation Ht ) N × 2 × 1.2/3.281

(A2)

LP distillation column: |Lj-1xi,j-1 + Vj+1yi,j+1 - Ljxi,j - Vjyi,j + Fjzi,j | e ε (A13)

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Ind. Eng. Chem. Res., Vol. 49, No. 7, 2010 sp |xtop,LP - xtop,LP | eε

(A14)

sp |xbot,LP - xbot,LP | eε

(A15)

Nomenclature A ) component B ) component Base_SEHIDDiC ) SEHIDDiC without the adjustments of the locations and sizes of the external heat exchangers CDiC ) conventional distillation column CI ) capital investment ($) condenscost ) energy cost for condensing ($/106 kJ) CRHIDiS ) condenser/reboiler heat-integrated distillation system D ) diameter (m) DEDDS ) double effect direct distillation system DEIDS ) double effect indirect distillation system DEPDS ) double effect parallel distillation system EHIDDiC ) externally heat-integrated double distillation columns F ) feed flow rate (kmol · h-1) H1∼H6 ) locations of the external heat exchangers HIDiC ) heat-integrated distillation column HP ) high pressure (kPa) Ht ) height (m) Intermediate_SEHIDDiC ) SEHIDDiC with the adjustments of the locations of the external heat exchangers LP ) low pressure (kPa) MW ) molecular weight of a mixture (g · mol-1) N ) number of stages NF ) feed stage OC ) operating cost ($ · yr-1) Optimum_SEHIDDiC ) SEHIDDiC with the adjustments of the locations and sizes of the external heat exchangers P ) pressure (kPa) Q ) heat duty (kW) reboilcost ) energy cost for reboiling ($/106 kJ) S ) heat transfer area (m2) s ) feed splitting ratio SEHIDDiC ) simplified externally heat-integrated double distillation columns T ) temperature (K) TAC ) total annual cost ($ · yr-1) U ) overall heat transfer coefficient (kW · K-1 · m-2) VNT ) maximal vapor flow rate of a distillation column (mol · s-1) x ) liquid composition Greek letters ε ) error tolerance ∆ ) perturbation Superscripts sp ) product specification Subscripts CON ) condenser HI ) heat integration HP ) high pressure LP ) low pressure REB ) reboiler top ) top of a distillation column bot ) bottom of a distillation column

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ReceiVed for reView September 30, 2009 ReVised manuscript receiVed January 26, 2010 Accepted February 15, 2010 IE901534Q

A Simplified Scheme of Externally Heat-Integrated Double Distillation

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