Strategies for the robust simulation of thermally coupled distillation sequences

Strategies for the robust simulation of thermally coupled distillation sequences

Computers and Chemical Engineering 36 (2012) 149–159 Contents lists available at ScienceDirect Computers and Chemical Engineering journal homepage: ...

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Computers and Chemical Engineering 36 (2012) 149–159

Contents lists available at ScienceDirect

Computers and Chemical Engineering journal homepage: www.elsevier.com/locate/compchemeng

Strategies for the robust simulation of thermally coupled distillation sequences Miguel A. Navarro a,∗ , Juan Javaloyes a , José A. Caballero a , Ignacio E. Grossmann b a b

Department of Chemical Engineering, University of Alicante, Ap Correos 99, 03080 Alicante, Spain Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Av., Pittsburgh, PA 15213, USA

a r t i c l e

i n f o

Article history: Received 21 February 2011 Received in revised form 17 June 2011 Accepted 22 June 2011 Available online 30 June 2011 Keywords: Distillation Simulation Thermally coupled distillation

a b s t r a c t This paper presents a novel strategy for the simulation of thermally coupled distillation sequences using process simulators. First, we show that the two side stream connections involved in a ‘thermal couple’ can be accurately substituted by a combination of a material stream and heat flow; enabling a sequence of thermally coupled distillation columns to be simulated without recycle streams, similar to conventional simulations of zeotropic distillation sequences. In fact, using this method, a sequence of thermally coupled distillation columns is not more difficult to converge than other distillation systems without recycles. Furthermore, in most cases, this approach introduces negligible errors, and provides excellent starting points for rigorous simulations of actual thermally coupled systems with recycle streams. Different examples, including mixtures of hydrocarbons (C4s–C5s–C6s), aromatics (BTX), alcohols, nonideal azeotropic systems (acetone, benzene, chloroform) and systems involving 4 or 5 components are presented. In addition, various thermodynamically equivalent configurations, corresponding to different alternatives for implementing this approach, are discussed. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction Sustainable process development encourages the pursuit of designs that make efficient use of energy. Distillation processes consume approximately 3% of the total global energy (Soave & Feliu, 2002). However, separation sequences using conventional columns (a single feed, two product streams, condenser and reboiler) suffer from an inherent inefficiency, caused by the thermodynamic irreversibility associated with stream mixing at the feed, top, and bottom of the column (Petlyuk, Platonov, & Slavinsk, 1965). This inefficiency is intrinsic to any separation that involves an intermediate boiling component, and can be generalized for an N-component mixture. Theoretical studies developed by Petlyuk et al. (1965) showed that this inefficiency can be improved by removing some heat exchangers, and by introducing thermal coupling between the columns. In fact, the fully thermally coupled configuration for separating a three component mixture is named a Petlyuk configuration, in honor of F. Petlyuk. However, since the advent of that pioneer work, interest in thermally coupled distillation (TCD) declined until the end of the 1980s, when the operation of a divided wall column (DWC) by BASF (Schultz et al., 2002) renewed interest in thermally coupled distillation. Moreover, several researchers (Fidkowski & Agrawal, 2001; Fidkowski & Krolikowski, 1987; Fidkowski, 2006; Shah & Kokossis, 2002;

∗ Corresponding author. E-mail address: [email protected] (M.A. Navarro). 0098-1354/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2011.06.014

Triantafyllou & Smith, 1992) have since shown that TCDs are typically capable of achieving a 30% reduction in energy use compared to conventional systems. In addition, Halvorsen and Skogestad (2003a, 2003b, 2003c) proved that the minimum energy consumption for an ideal N component mixture is obtainable in fully thermally coupled configurations. However, from a structural point of view, thermally coupled configurations are much more complex than sequences of conventional columns. In a seminal paper, Agrawal (1996) established the theoretical basis behind fully thermally coupled (FTC) systems. If we take into account all possible alternatives, from conventional to FTC distillation systems, including all intermediate alternatives, the situation becomes even more complex. A method for the systematic generation of all of these alternatives was proposed by Caballero and Grossmann (2004, 2006), using logical relationships and mathematical programming; while Agrawal (2000a, 2003), and Rong et al. (Rong, Kraslawski, & Nystrom, 2000; Rong, Kraslawski, & Nystrom, 2001; Rong, Kraslawski, & Turunen, 2003), among others, proposed a method to accomplish the same task using alternative conceptual enumeration. In addition, different researchers have proposed alternatives that were not previously considered, such as: structures with a reduced number of column sections (Kaibel, 1987); structures with duplicate key components (Rong et al., 2003); structures with duplicate separation tasks (Grossmann, Aguirre, & Barttfeld, 2005); and modifications designed to enable better control, while maintaining nearly the same level of performance over a large range of operational conditions (Agrawal, 1999; Caballero & Grossmann, 2003). Other proposed modifica-

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tions include a reduction in column interconnections, which was hypothesized to provide better controllability (Agrawal, 2000b). However, later studies showed that reducing the number of interconnections does not necessarily provide operational advantages over modified and simpler structural designs (Jimenez et al., 2003; Segovia-Hernandez, Hernandez, & Jimenez, 2005). In particular, Segovia-Hernandez et al. (2005) compared the control properties of six alternative thermally coupled distillation schemes to the Petlyuk system; and found that reducing the number of interconnections in the Petlyuk configuration does not necessarily improve its controllability. The magnitude of the problem can be understood by considering that there are more than 105 alternatives for separating a 5 component mixture into its pure components (Caballero & Grossmann, 2006; Giridhar & Agrawal, 2010). An important reason why TCD systems were “forgotten”, in spite of their clear advantages, is the lack of confidence in the controllability of these systems. However, the controllability of TCD systems is similar to, and in some cases better than, systems consisting only of conventional columns. The controllability of these systems has been analyzed by many researchers (Alatiqi & Luyben, 1986; Jimenez et al., 2001; Luyben, 2006; SegoviaHernandez, Hernandez, & Jimenez, 2002; Segovia-Hernandez et al., 2004; Segovia-Hernandez et al., 2007a, 2007b; Serra, Espuna, & Puigjaner, 1999; Serra et al., 2000, 2001; Serra, Espuna, & Puigjaner, 2003). Most of the studies performed on TCD sequences were conducted using shortcut models, such as the Fenske–Underwood–Gilliland method (Underwood, 1948). Although these approaches are accurate enough to identify and compare promising alternatives; a more rigorous simulation is necessary to verify the accuracy of these shortcut models, and enable more detailed designs. Most chemical process simulators include side columns, or even Petlyuk-like configurations. However, simulation of thermally coupled systems involving more than two columns (and in some cases even with two columns) is difficult, because the two side flows connecting the columns produce systems with a large number of ‘recycle’ streams (in a modular simulator these recycles are converged through tear streams). Whatever the method used to converge the cyclic structure of the flowsheet (e.g. fixed point, Newton or quasi-Newton methods), good initial values approximating the final solution are mandatory to converge the system, while maintaining product specifications. The presence of a large number of tear streams slows down the simulation, making convergence difficult. For the remainder of the present study, we present a very straightforward procedure that enables simulation of these systems in such a way that they can be simulated with the same degree of difficulty as a sequence of conventional columns. It should be noted that, in this paper, we only deal with the problem of simulation, and not with the design or optimization of a TCD system. However, it is not difficult (although this is outside of the scope of this paper) to synthesize a TCD sequence using the procedure presented by Caballero, Milan-Yanez, and Grossmann (2005).

2. Application of the proposed simulation strategy: “acyclic system simulation” The basic idea behind the simulation strategy presented in the present study is to avoid the recycle structure that appears in TCD systems in a modular simulator. This idea is based on the works by Carlberg and Westerberg (1989a, 1989b), who proved, in the context of Underwood’s shortcut method, that in a TCD system, the two side streams connecting the rectifying section of column 1 (see Fig. 1a) with column 2 are equivalent to a superheated vapor

stream, whose flow is the net flow (i.e. the difference between vapor exiting the column and liquid entering the column) (Fig. 1b). If the two side streams connect the stripping section of the first column with the second column, then they are equivalent to a single subcooled liquid stream, whose flow is the net flow (in this case the liquid minus the vapor flows) (see Fig. 1c and d). However, in general, this approach cannot be implemented in modular process simulators, because the degree of superheating and/or subcooling can be so large that it might produce results without physical meaning, and thus the simulator may fail to converge. A simple example will illustrate this last point. Assume that we have a mixture of benzene, toluene and p-xylene, with a molar fraction composition of 0.3, 0.4 and 0.3. If we want to use a Petlyuk configuration, which is thermodynamically equivalent to a divided wall column, we can simulate this system using two (or maybe three) conventional columns (see Fig. 2). A complete discussion of thermodynamically equivalent configurations and their implications with respect to cost and operability for systems with 3 or more components can be found in Agrawal (1999), Caballero and Grossmann (2003) and Agrawal and Fidkowski (1998). However, to illustrate this point, we will focus only on the first column. Assume also that we have 20 theoretical trays, with the feed in tray 10 (a non-optimized column). In order to avoid recycled streams, we follow the Carlberg and Westerberg strategy and use a conventional column with a partial reboiler to obtain a saturated vapor distillate stream. Using a feed flowrate of 100 kmol/h as a basis for calculation, and specifying 99.9% benzene recovery in the top of the column and 99.9% p-xylene recovery in the bottom stream, we obtain by Aspen-Hysys (HYSYS, 2002) (using a Peng Robinson equation of state, a constant pressure of 1 atm and default parameters): Distillate: Saturated vapor, 45.84 kmol/h; molar fractions of benzene, toluene and xylene, 0.6538, 0.3456 and 0.0006, respectively; temperature 93.8 ◦ C. Bottoms: Saturated liquid, 54.16 kmol/h; molar fractions of benzene, toluene and xylene, 0.0005, 0.4461 and 0.5534, respectively; temperature 123.6 ◦ C. The heat flow that must be removed in the condenser is 478.7 kW. And the heat flow added in the reboiler is 918.5 kW. With the above data and a simple energy balance, it is easy to calculate that, according to the procedure suggested by Carlberg and Westerberg, the temperature of the equivalent distillate stream should be 350 ◦ C! Thus, Hysys fails to properly calculate the temperature of the bottoms stream, because the energy balance predicts temperatures below −273.15 ◦ C (0 K!), which of course has no physical meaning. Fortunately, it is possible to solve this problem by substituting the superheating or subcooling streams with a combination of a material stream and an energy stream. In the rectifying section, the material stream is vapor at its dew point and the energy stream is equivalent to the energy removed if we include a partial condenser to provide reflux to the first column (see Fig. 1e). In the stripping section, the material stream is liquid at its bubble point, and the energy stream is equivalent to the energy added if we include a reboiler to provide vapor to the first column (see Fig. 1f). The main source of error encountered when using the Carlberg and Westerberg approximation is the assumption that the introduction of a liquid stream in a column does not modify the flow of the vapor stream; and that the introduction of a vapor stream does not modify the flow of the liquid stream. (These assumptions are discussed in the original paper, and for further details the interested reader is referred to the original work (Carlberg & Westerberg, 1989a, 1989b).) Consider, for example, that in Fig. 3, the only possiC2 bility for stream VC1 1 to mix with stream V1 without modifying

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Fig. 1. (a, b and e) Equivalent configurations. (c, d and f) Equivalent configurations.

Fig. 2. Petlyuk configuration and the thermodynamically equivalent divided wall column.

Fig. 3. Details of the connection between columns, “cyclic system simulation”.

C1 C2 stream LC2 2 is if the net stream V1 + V1 is in equilibrium with C2 L2 . Fortunately, this situation is generally found in any thermally coupled system. The introduction of an energy stream and a saturated stream is completely equivalent to the Carlberg and Westerberg methodology, if the heat of vaporization is independent of the composition, and if the heat of mixture can be neglected. Consider, for example Fig. 4, where the introduction of an energy stream results in partial vaporization of the liquid stream LC2 1 . Fortunately, all of the implied vapor and liquid streams are either in equilibrium (an ideal case in which the Carlberg and Westerberg approach does not introduce any error) or very close to equilibrium (generally found in real situations) and therefore the dependence of the heat of vaporization on the composition and heat of mixture can be neglected. As will be demonstrated in the remainder of the paper, even in the worst possible scenario, the values obtained with this tech-

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tional streams that form a thermal couple), for example, if those initial values come from any previous process synthesis step, the procedure proposed here is not really necessary, and we can converge directly the actual system. Note, however, that if a change is introduced in the system (i.e. changes in the feed composition, feed state, pressure, etc.) is not uncommon that the system presents convergence difficulties. In this case the proposed approach is an easy strategy to recover convergence. 3. Examples and results

Fig. 4. Details of the connection between columns, “acyclic system simulation”.

nique provide excellent initial points to enable convergence of the rigorous simulations of the original system. It is worth noting that some researchers have proposed the use of a single saturated stream to simulate a thermal couple, rather than the two bidirectional streams (vapor and liquid streams) (Triantafyllou & Smith, 1992) that characterize a thermal couple. However, this approach introduces considerable errors and should be avoided. A detailed discussion can be found in Vaca, Jimenez, and Álvarez-Ramírez (2009). It is important to remark that if good initial values are available for each of the tear streams (vapor or liquid streams in the bidirec-

In this section, a range of different examples are presented: including mixtures of hydrocarbons (C4s–C5s–C6s), aromatics (BTX), alcohols, non-ideal azeotropic systems (acetone, benzene, chloroform) and systems involving 4 or 5 components. In addition, various thermodynamic equivalent configurations, corresponding to different alternatives for implementing this approach are also discussed. All simulations were performed using ASPEN-HYSYS. Reboiler and condenser duties, as well as vapor/liquid internal flows were studied to compare the results between cyclic and acyclic simulations. 3.1. Separations of three component mixtures Four systems involving the separation of a three component mixture were studied: a mixture of aromatics (benzene, toluene, p-xylene); alcohols (methanol, ethanol, butanol); hydrocarbons (n-hexane, n-heptane, n-octane); and a difficult separation of a

Fig. 5. Residue curve maps of the four component systems studied: (a) i-butane, n-butane, cyclobutane; (b) n-hexane, n-heptane, n-octane; (c) benzene, toluene, p-xylene; (d) methanol, ethanol, butanol.

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Fig. 6. Calculation of tray columns using “short cut distillation”.

mixture of three compounds with similar volatilities (i-butane, nbutane, cyclobutane). As can be seen in the residue curve maps (see Fig. 5), in all cases, the separations are theoretically easy to carry out. Furthermore, the methodology is the same in all the cases. We will only discuss the first case in detail, but the other three cases are solved in a similar manner. First, we calculated the number of trays and the feed tray required in each column for a desired separation. To do this, we use a shortcut model: either Underwood–Fenske for near ideal systems; or simple trial and error for non-ideal systems. Note that we are not interested in optimizing the column, but only in developing an easy and reliable simulation (see Fig. 6 and Table 1). Next, we simulated the acyclic sequence, where each thermal couple is substituted by a mass and energy stream, using conventional distillation columns (see Fig. 7a). In this configuration, we connect the mass and energy streams that leave the condenser of the first column in the same tray of the second column. In the same way, the mass and energy streams that leave the reboiler of the first column are connected to the same tray of the second column. Finally, we converge the acyclic sequence. In this first example, we assume that the first column has 17 trays, with the feed in tray 9. The distillate stream (saturated vapor) and the energy stream are introduced in the second column in tray 14, which is simulated with 68 trays. The bottom stream from the first column (saturated liquid) is introduced in tray 51. From this tray (tray 51), an energy stream with exactly the same energy consumed in the reboiler of the first column is withdrawn. Specifications used to converge the first column were 0.9999 recovery of benzene in the distillate and 0.9999 recovery of xylene in the bottoms; while for the second column we specified a 0.999 recovery for each component. Toluene is withdrawn from tray 31. The results from this acyclic simulation were then used as initial points in the actual system (with a cyclic structure). In particular,

Fig. 7. Simulations of (A) acyclic and (B) cyclic system configurations.

the initial flow rate of the liquid stream entering the top of the first column (tear stream Liq to C1 in Fig. 7b) is assumed to be the flow entering the first column from the partial condenser in Fig. 7a (136.022 kmol/h). The composition of this stream can then be read from the liquid composition exiting tray 14 in column 2 of Fig. 7a. A similar procedure is followed to estimate the flow and composition of the vapor stream “Vap to C1” in Fig. 7b. A list of the results obtained using the above, and the characteristics of the different columns are shown in Table 2. It is important to note that the distillate of the first column is equivalent to a saturated vapor stream plus an energy stream; hence, we are adding heat to the upper part of the second column. However, the bottoms stream is equivalent to a saturated liquid stream minus a heat stream, and therefore, we are actually removing heat from the second column. In addition, the sign of the energy stream added must be taken into account, since a negative sign in Hysys means that we are removing heat, which is in fact what we want in the lower part of the second column. This is achieved in Hysys by means of a set operation that simply multiplies the reboiler heat load in the first column by minus one. The results obtained were very good in all cases: average errors in internal flows and energy consumption were lower than 1.5% and 1%, respectively; and in both simulations the maximum errors were between 3% and 5%. The results obtained in these systems are shown in Table 3. As a representative example, internal flows for the benzene–toluene–xylene 3-component separation are shown in Fig. 8.

Table 1 Characteristics of different feeds to each column.

Feed D1 R1

P (atm)

T (◦ C)

Molar flow (kmol/h)

1 1 1

103.3 95.3 124.7

200.00 97.51 102.49

Composition Benzene

Toluene

p-Xylene

0.30 0.61 5.8E−04

0.40 0.38 0.41

0.30 6.2E−04 0.58

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Fig. 8. Comparison of flows for BTX separation: (a) liquid flow-column 1; (b) vapor flow-column 1; (c) liquid flow-column 2; (d) vapor flow-column 2.

Table 2 Characteristics of short cut columns and conventional columns. N◦ trays Short cut columns 17 SC1 31 SC2 SC3 37 Conventional columns-acyclic system C1 17 C2 68 Conventional columns-cyclic system 17 C1 C2 68

Feed tray

Condenser energy (kWh)

Reboiler energy (kWh)

9 14 20

1777.9 5685.0 4561.6

2710.3 4830.2 4583.7

9 Tray D1—14Tray R1—51

– 3214.7

– 3315.3

9 Tray D1—14Tray R1—51

– 3220.7

– 3319.6

3.2. Difficult separations of three component mixtures Here we refer to difficult separations not in the usual sense (i.e. mixtures of components with very similar volatilities), but rather systems that present other theoretical difficulties, such as azeotropic systems (benzene–acetone–chloroform), multicomponent mixtures that must be separated in groups (i.e. groups of C3s, C4s and C5s), or non-ideal mixtures (acetone–acetic acid–acetic anhydride). To perform the separation of an azeotropic mixture, we first studied its residue curve map to determine a feasible separation route. In the following example (benzene–acetone–chloroform), there is a distillation boundary. A possible sequence to obtain the three pure components is shown in Figs. 9 and 10.

Some remarks on this last example. The separation benzene–acetone–chloroform can be performed using a system involving only two columns. However, this example has been selected to study the error propagation in a very non-ideal system, and therefore the three column sequence is presented here. On other side, it is known that Benzene cannot be used due to environmental concerns (carcinogenic and tumorigenic), and it can be substituted by other solvents like 1-hexanal or amyl methyl ether (Hostrup, Harper, & Gani, 1999). We have selected this example because is a well documented and easy to reproduce case of study; see for example the text book by Doherty and Malone (2001). The simulations performed here are different from those presented in the previous sections, because of the requirements of

Table 3 Results obtained with systems 3 compounds. Internal flow

3 Component mixtures i-Butane–n-butane–cyclobutane Hexane–heptane–octane Methanol–ethanol–butanol Benzene–toluene–xylene

Energy

Max. error

Average error

St. deviation

Max. error

3.42% 3.47% 3.94% 4.55%

0.74% 0.96% 0.86% 1.46%

0.87% 0.96% 0.92% 1.40%

0.04% 0.08% 0.08% 0.19%

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Fig. 9. Residue curve map (azeotropic mixture).

using three columns to obtain pure components, and the need to recycle the azeotropic stream and mix it with the feed stream. However, this simulation has the same level of difficulty as the previous examples; because, although the number of columns is increased, the number of recycle streams remains constant. Therefore, the complexity of the problem is not increased and consequently the error obtained is similar to that calculated previously. The multi-component separation of groups of C3s, C4s and C5s can be compared with a simple separation of a mixture of 3 components (as in the previous examples). As such, the methodology is the same as that used previously. However, the error obtained is slightly larger than the error associated with a 3-component mix-

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Fig. 11. Curve residue map acetone–acetic acid–acetic anhydride (AAA).

ture because increasing the number of components increases the complexity of the separation. Note that the case of a 3-component mixture acetone–acetic acid–acetic anhydride (AAA) is special, as can be seen from its residue curve map (Fig. 11). In particular, all residue curves are partly over the acetic acid–acetic anhydride binary mixture, which is problematic because any small change in the concentration of acetone in the residue causes significant changes in the concentrations of acid and anhydride. As a consequence, the small error introduced by the substitution of the two streams in a thermal couple with a material stream and an energy stream, can induce large errors compared to rigorous and approximate simulations.

Fig. 10. Simulations of acyclic (a) and cyclic (b) system configurations (azeotropic mixture).

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Fig. 12. Comparison of flows for AAA separation: (a) liquid flow-column 1; (b) vapor flow-column 1; (c) liquid flow-column 2; (d) vapor flow-column 2.

As expected, the results obtained were worse than those from the previously described examples. However, in all the cases, the outcomes obtained using our novel strategy still provided excellent initial points for use in rigorous simulations. Furthermore, the average errors in internal flow and energy consumption were less than 4% and 1%, respectively; and the maximum error between both simulations was between 4% and 18%. The results obtained in these systems are shown in Table 4. The internal flows for the worst case studied (acetone–acetic acid–acetic anhydride) are shown in Fig. 12. 3.3. Separation of 4 and 5 component mixtures Application of our proposed strategy to the separation of 4 component mixtures was also studied for butane–pentane–hexane–heptane, in a sequence with 16 thermodynamically equivalents configurations. In this case, 3 configurations were studied using the same methodology (see Fig. 13). Finally, the separation of a 5 component mixture was evaluated. In this case, only one configuration was studied using the same methodology described above (see Fig. 14). Although the results obtained were worse than any of the previously studied cases, they still remained very good. As expected, Fig. 14. Configuration separation system 5 compounds.

Fig. 13. Thermodynamically equivalents configurations-system 4 compounds: (a) configuration 1; (b) configuration 2; (c) configuration 3.

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Fig. 15. Comparison of flows for 5 compounds separation: (a) liquid flow-column 1; (b) vapor flow-column 1; (c) liquid flow-column 2; (d) vapor flow-column 2; (e) liquid flow-column 3; (f) vapor flow-column 3; (g) liquid flow-column 4; (h) vapor flow-column 4.

Table 4 Results of difficult separation systems with 3 compounds. Internal flow

3 compounds Azeotropic distillation C4s–C5s–C6s Acetone–acetic acid–acetic anhydride

Energy

Max. error

Average error

St. deviation

Max. error

4.04% 6.72% 18.40%

1.09% 1.43% 3.91%

0.98% 1.72% 4.61%

0.36% 0.05% 0.91%

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Table 5 Results for the systems with 4 compounds. Internal flow Max. error 4 compounds (butane–pentane–hexane–heptane) 21.16% Configuration 1 22.42% Configuration 2 22.42% Configuration 3 5 compounds (butane–pentane–hexane–heptane–octane) 79.27% Configuration 1

Energy Average error

St. deviation

Max. error

4.88% 5.03% 4.86%

6.00% 6.16% 6.07%

0.41% 0.12% 0.41%

23.61%

31.46%

0.19%

when the number of columns and recycle streams are increased, small errors propagate throughout the system. However, in any case, the results obtained with our proposed strategy still provide excellent initial points for use in rigorous simulations. The average errors in internal flow and energy consumption were less than 5% and 1%, respectively, for the separation of a 4 component mixture; and were less than 25% and 1%, respectively, for the separation of a 5 component mixture. The results obtained in these systems are shown in Table 5. Internal flows for the worst case studied (separation of a 5 component mixture) are depicted in Fig. 15. 4. Conclusions We evaluated the application of a novel strategy for the simulation of thermally coupled distillation sequences using process simulators. Several case studies were presented to demonstrate that the results obtained with this acyclic sequence technique are very close to those obtained with recycle calculations, with average errors below 2% for 3 component mixtures. The average error increases slightly with the number of components, due to error propagation as a consequence of the larger number of thermally coupled columns in the system. However, in all cases, “acyclic simulation” produces excellent results, which are comparable to those of the actual system. Furthermore, this new strategy yields very good starting points to converge rigorous simulations of these systems. In conclusion, our proposed technique enables thermally coupled distillation systems for the separation of 3, 4 or 5 component mixtures to be studied rapidly and easily. Acknowledgements The authors gratefully acknowledge financial support from the Spanish “Ministerio de Ciencia e Innovación” under project CTQ2009-14420-C02-01. References Agrawal, R. (1996). Synthesis of distillation column configurations for a multicomponent separation. Industrial & Engineering Chemistry Research, 35(4), 1059–1071. Agrawal, R. (1999). More operable fully thermally coupled distribution column configurations for multicomponent distillation. Chemical Engineering Research & Design, 77(A6), 543–553. Agrawal, R. (2000a). A method to draw fully thermally coupled distillation column configurations for multicomponent distillation. Chemical Engineering Research & Design, 78(A3), 454–464. Agrawal, R. (2000b). Thermally coupled distillation with reduced number of intercolumn vapor transfers. AIChE Journal, 46(11), 2198–2210. Agrawal, R. (2003). Synthesis of multicomponent distillation column configurations. AIChE Journal, 49(2), 379–401. Agrawal, R., & Fidkowski, Z. T. (1998). More operable arrangements of fully thermally coupled distillation columns. AIChE Journal, 44(11), 2565–2568. Alatiqi, I. M., & Luyben, W. L. (1986). Control of a complex sidestream column/stripper distillation configuration. Industrial & Engineering Chemical Process Design and Development, 25(3). Caballero, J. A., & Grossmann, I. E. (2003). Thermodynamically equivalent configurations for thermally coupled distillation. AIChE Journal, 49(11), 2864–2884.

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