Investigation of the Effect of the Vapor Split Ratio Decision in Design

Aug 6, 2014 - simulated to show the dependence of a total annualized cost (TAC) of the ... that the TAC is sensitive to the rv, and the extent of the ...
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Investigation of the Effect of the Vapor Split Ratio Decision in Design on Operability for DWC by Numerical Simulation Xiaolong Ge, Chen Ao, Xigang Yuan,* and Yiqing Luo State Key Laboratory of Chemical Engineering, School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China S Supporting Information *

ABSTRACT: The effect of the vapor split ratio on the operability of divided wall column (DWC) is numerically investigated. Four DWCs for separating a three-component mixture with, respectively, four different compositions are designed and then simulated to show the dependence of a total annualized cost (TAC) of the columns on the vapor split ratio, rv, which is subjected to change in operation for reason for either the design uncertainty or the possible change in the feed composition. It is shown that the TAC is sensitive to the rv, and the extent of the sensibility depends on the feed composition in the design. It is also demonstrated that the flexibilities of the four DWCs designed respectively for the different cases over the feed composition change exhibit differently, and a DWC designed for the feed with relatively higher concentration of the light component tends to have higher flexibility over the feed composition change. By the simulation the vapor split ratio is shown to be an important decision variable in the design of a DWC with uncertain feed composition.

1. INTRODUCTION The dividing-wall column (DWC) developed from the Petlyuk configuration for distillation is an attractive alternative to the conventional sequence of simple columns for separation of ternary mixtures.1,2 However, the industrial application of the DWC has been limited, and one of the reasons for this is its complexities in operation.3−5 The complexities are due to mainly the fact that a DWC has more freedom than a conventional distillation column. As shown in Figure 1b, the newly appeared freedoms of the DWC, compared to a simple column, include numbers of stages for the various column sections in the main column (sections 1, 2, 3, and 4), the mid product side-stream flow rate (S), the liquid split ratio (rl, the fraction of the liquid from the bottom of section 1 going to section 2), and the vapor split ratio (rv, the fraction of the vapor from the top of section 4 going to section 3). In the point of view of design, if the compositions for the key component in the mid component product is specified, the remaining free variables, together with the conventional ones (the numbers of stages of column sections 5 and 6, the boilup V and the reflux L for example) can be used for minimizing the total annualized cost (TAC) in the design of DWC. A large number of works have been published about the design of DWC,6−13 and a summary can be found in the book by A. A. Kiss.5 A basic principle for the design in most works has been the minimization of the vapor flow in the column based on the Underwood equation.14 An equivalent of this minimization for DWC design is the optimization of a parameter β, the recovery of component B in the top product of the prefractionator, which has been shown to be a function of rl, and rv, as has been recognized as early as by Fidkowski and Krolikowski8 and Carlberg and Westerberg.10 In other words, both rv and rl determine the total annualized cost of DWC if numbers of the stages, and the compositions for the key components in the three products are specified. © 2014 American Chemical Society

In the aspect of operation of a DWC, the liquid split ratio is easy to control as the liquid from the bottom of section 1 can be drawn out of the column and redistributed back to the two sides of the dividing wall as shown in Figure 1b. However, the vapor split ratio is usually fixed in the design by positioning the dividing wall, such that the ratio of the column cross-sectional areas of the two sides partitioned by the wall equals simply to the vapor split ratio. Such a design relies on the assumption that the vapor velocities in both sides are the same. Consequently, for a fully thermally coupled DWC, the vapor split ratio is practically predetermined in the design stage and is selfadjusting, so it cannot be utilized as a manipulated variable in operation.15 The vapor split ratio has been shown to be an important parameter determining the energy efficiency of the DWC.16,17 However, few works have concentrated on the influence of rv predetermined in the design on the operability of DWC. As analyzed by Maralani et al.,18 uncertainty on rv may exist in the following two scenarios: (a) the operational vapor split ratio is shifted from the optimally design value because of design defect and (b) the feed composition in operation is changed from the design specification. In either case, the optimum vapor split ratio in the operations may be significantly different from that optimally decided in the design for the DWC. Maralani et al.18 illustrated the relationship between the vapor split ratio and the total annualized cost of the column under condition of a fixed liquid split ratio of 50%. However, since both the liquid and the vapor split ratios have a strong impact on the cost of the column, the liquid split ratio must be optimized in the plot of Received: Revised: Accepted: Published: 13383

February 20, 2014 July 31, 2014 August 6, 2014 August 6, 2014 dx.doi.org/10.1021/ie500686p | Ind. Eng. Chem. Res. 2014, 53, 13383−13390

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three components in the feed mixture in the present work are chosen as A: pentane, B: hexane, and C: heptane, the ESI of which is 1.034 according to the relative volatilities given in Table 1. The input and output of the column system are also Table 1. Feed Conditions and Products’ Specifications variable name

value

relative volatility (A/B/C) feed mole flow (kmol·h−1) feed pressure (atm) feed vapor fraction product purity requirement

αi= [7.37, 2.67, 1] F = 300 1 0.44 xtop, A = 0.987, xside, B = 0.980, xbot, C = 0.987

defined in Table 1. The pressure of the column is chosen as 1 atm in the design of DWCs so that cooling water can be used in the overhead condenser. The operability of the DWC is analyzed by employing the four cases defined, respectively, by the four different feed compositions as shown in Table 2. The Table 2. Definitions for the Cases case

definition

case 1

feed composition with equal mole fraction of the components (A = 0.333, B = 0.333, C = 0.333) feed composition with higher mole fraction for light component (A = 0.5, B = 0.25, C = 0.25) feed composition with higher mole fraction for mid component (A = 0.25, B = 0.5, C = 0.25) feed composition with higher mole fraction for heavy component (A = 0.25, B = 0.25, C = 0.5)

case 2 case 3 case 4

Figure 1. Fully thermally coupled distillation arrangement for separating a three-component mixture.

four cases (four different feed compositions) employed have been so selected that they covered the central part of the triangle diagram for the feed composition (this can be seen in Figure 9), covering hopefully the range of common applications of DWC. The columns are first designed using a shortcut method based on the Fenske-Underwood-Gilliland-Kirkbride equations with the following assumptions: (i) equilibrium stages with constant relative volatilities, (ii) constant molar flows, and (iii) no heat transfer through the dividing wall. Then the results of the shortcut calculation are used to initialize the rigorous simulations of the DWC with the RadFrac model in Aspen Plus software. The feed locations, the positions of the thermally coupling streams for each of the cases, are obtained in the simulation by using the sensitivity analysis in Aspen Plus. The columns are then optimized by varying the vapor and liquid split ratios to achieve the minimum costs for each of the DWCs. A key issue in the design of the DWC by means of simulation is the determination of the optimal vapor and liquid split ratios. To do this, we employed an enumeration approach to search in the two-variable space for the optimal rv and rl to minimize the total annualized cost (TAC), which is defined by the sum of the operating cost and the investment cost of the column. The results for the designs of the four DWCs for each of the four cases are listed in Table 3. It should be noted that in the operability analysis for the DWCs in the following sections, the TAC was defined as the sum of the capital investment cost of the installation including column, reboilers, and condensers etc. and the operating cost on the hot and cold utilities’ basis. The diameters of various column sections (i.e., sections 1−6 in Figure 1b) were calculated carefully so that they could be incorporated in the

relationship between the vapor split ratio and the total annualized cost of dividing-wall column for the analysis. In the present work, the processes of DWCs for separating three-component mixtures are numerically simulated using commercial software (Aspen Plus). By the results of our simulations, we first show how the plot of rv vs TAC changes if the rl is changed, then the optimal value of the liquid split ratio is plotted against the variation of the vapor split ratio. We also show the sensitivity of the DWC operation to its vapor split ratio, the extent to which the split ratio could be feasible for the DWC to fulfill the separation task, and the dependence of these sensibility and feasibility on the feed composition. By examining the rv -TAC relationships for different feed compositions, the flexibility of a DWC over feed composition change is investigated, and the decision on the rv for uncertain feed composition is discussed.

2. DWC MODEL AND SIMULATION Since the DWC can be considered as a fully thermally coupled distillation system and thermodynamically equivalent with the Petlyuk configuration, DWCs in our simulations are considered as a combination of simple columns connected by thermally coupling streams to facilitate the simulation of the column by the use of an available package (Aspen Plus is used in the present work). According to previous works, the DWC has been shown to be more efficient than the conventional cascaded simple columns for separation of ternary mixtures when the Ease of Separation Index19 (ESI, defined as the ratio of the relative volatility of A/B to that of B/C) of the system is equal approximately to one. In order to be representative, the 13384

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by optimally partitioning the column sectional areas of the two sides of the dividing wall in the design for the original feed composition. 3.1. Effect of rv and rl on the TAC. Halvorsen et al.4,20 demonstrated the variation of the energy consumption of a DWC with values of rv and rl by a shape of a ship in a threedimensional diagram. Similarly, we interpret the effect of rv and rl on the TAC in the operation of DWC but with twodimensional graphs to facilitate our analysis in the following sections. In order to do so, the DWC for case 1 is simulated, and the corresponding TAC is evaluated for different values of rv and rl. The simulation results are shown in Figure 2. It can be seen from Figure 2 that, for the specified separation task, the variations of TAC with rl are very different for different values of rv.

Table 3. Results of the Designs of the DWCs for the Four Cases variable trays no. for main column trays no. for prefrationator feed tray location of connect streams (FL/Fv) location of side product stream (S) rl/rv reflux ratio, R

case 1

case 2

case 3

case 4

40

45

39

40

19

20

20

21

12 10,11/28,29

13 13,14/35,36

10 9,10/29,30

15 8,9/30,31

20

20

17

18

0.51/0.36 4.701

0.57/0.41 3.750

0.67/0.54 5.619

0.54/0.40 2.849

same column shell. In our following analysis for any of the cases, the optimum column diameter is fixed as what was decided in the stage of design, whereas the sizes of the reboiler and condenser are allowed to vary because any change in the vapor split ratio may lead to a change in heat load, which should not be restricted by the size of heat exchangers. This is why we chose to use the TAC, instead of the operating cost, as the criterion in our analysis.

3. RESULTS AND DISCUSSION The analysis in the following subsections will be concentrated on the operability for the four DWCs designed for the feed conditions of the four cases respectively given in Table 2, with the specifications in Table 1. As the results of the designs, the main parameters are shown in Table 3. In the following analysis, the two scenarios defined by Maralani et al.18 are considered: Scenario (a): the operational rv is different from the value in Table 3 because the real resistances of the two sides of the dividing wall to the vapor are different due to the uncertainties either in the manufacturing of the column and the internals (trays, packing, fluid collector/distributer, etc.) or in the estimation of the resistances in the design. In the design of a DWC, the vapor split ratio can be fixed by positioning the dividing wall, such that the ratio of the column cross section areas of the two sides partitioned by the wall equals simply to the vapor split ratio. Such a design relies on the assumption that the vapor velocities in both sides are the same, or equivalently, the resistances of the two sides to the vapor are the same. However, the resistance of any of the two sides depends on the number and the type of the trays or the height and the type of packing and column internals, liquid loads, etc. in that side and so is difficult to estimate precisely in the stage of design. As a result, the resistances of the two sides of the dividing wall in a DWC so designed cannot be guaranteed equal. In the operation of the DWC, the vapor split ratio is automatically adjusted so that the pressure drops for both sides are equal. Thus, if the resistances of the two sides of the dividing wall are different, the rv in the real operation will be shifted away from the design value, and this would lower the performance, even lead to failure in fulfilling the specified separation task. Scenario (b): the feed composition in the operation is changed from the value that is used in the design of the DWC. In this case, the optimum vapor split ratio for the changed feed composition could be significantly different from what was fixed

Figure 2. Dependence of economic behavior of DWC on the vapor and the liquid split ratio for case 1.

For different vapor split ratios, the corresponding optimal liquid split ratios and the feasible regions for operation are different. Note that, in Figure 2, the minimal point (point A) of the curve at rv = 0.36 corresponds to the optimal design of the DWC for case 1, the result of which is given in Table 3. Figure 2 suggests that, if the vapor split ratio deviates from its optimally design value of 0.36 to, for example, 0.34 in operation for reason for scenario (a) as stated above, and the liquid split ratio remains at the design value, namely 0.51, an significant rise in TAC (from 1.42 × 106 to about 1.45 × 106) is inevitable because the change of TAC with rv now obeys the curve of rv = 0.34 (point B). In this case, however, changing the liquid split ratio to the value of 0.5 that is at the minimum of the curve of rv = 0.34 (point C), as can be seen from Figure 2, the rise of the cost can be much less (to only about 1.43 × 106). In other words, in the operation of a DWC, if the vapor split ratio is shifted from the optimally design value in case of scenario (a), the liquid split ratio should be changed accordingly to minimize the cost. Tracing the minimal values of the curves at every values of rv in Figure 2, we can get the plot of rv vs rl (trajectory of the optimal), as shown in Figure 3. Figure 3 indicates the way that the liquid split ratio should be changed to get a minimal cost of the operation of the DWC if the vapor split ratio is changed in operation due to scenario (a). Note that points A, B, and C in Figure 2 are also marked in Figure 3, and point B is not on the curve because its rl is not optimized when rv is changed from 0.361 (abscissa of A) to 0.34 (abscissa of B and C, respectively). However, the vapor split ratio of a DWC can hardly be measured in operation. In such a case, the liquid split ratio 13385

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3.3. Operability of DWC for Changed Feed Compositions. As for scenario (b), if the feed composition in operation is different from what the DWC was designed for, the optimal operational rv is different from the design value that was set by proper partitioning of the column sectional areas of the two sides of the dividing wall. We simulated the operation of the DWC we design for the feed composition of case 1 but, by introducing as feed the mixtures for the feeds of cases 2, 3, and 4, estimated the TAC at different rv values and plotted the variations of TAC with rv for all four feeds in Figure 5(a). Note that, to produce Figure 5(a), we followed the same procedure as stated in section 3.1, i.e. a value of the TAC at any value of rv and at any curve is minimized by adjusting the liquid split ratio. Since the DWC was designed for the feed of case 1, the vapor split ratio should be expected to be within the gray region (Figure 5) in the operation if the column is free from major design deficit (scenario (a) does not happen). It can be seen from Figure 5(a) that the DWC designed for case 1 can safely operate if the mole fraction of component A in the feed increases to 0.5 (the feed for case 2), or if component B increases to 0.5 (the feed for case 3), but, in either of the cases, the TAC would increase significantly. Figure 5(a) indicates, however, that if the component C in the feed is increased (the feed for case 4), the operation of the DWC originally designed for case 1 would become very unstable because the TAC would change sharply even with minor uncertainty in the operational rv. Similar with Figure 3, the variations of the optimal rl values with respect to rv values are plotted in Figure 5(b), which shows how the rl should be changed if the feed composition is changed. Again, it can be found from Figure 5(b) that the region of the feasible operability of the DWC designed for case 1 could be quite narrow if the feed composition is changed to that of case 4. Figure 5 indicates that the DWC designed for case 1 could tolerate a feed with a higher concentration of the light or intermediate component, with of course a higher costs, but could be not suitable or even fail to operate with a feed of higher heavy component. Following the same steps, we simulated the operability for the DWCs designed for cases 2, 3, and 4 with the shifted feed conditions and plotted the results in Figures 6, 7, and 8, respectively. These figures demonstrate the flexibilities of the three DWCs over the feed composition. Generally, it can be seen from these figures that the DWCs designed for different feed compositions may behave very differently if the feed compositions are changed, and no a DWC can tolerate all the feed composition changes tested in our simulation. The DWC designed for case 2 (Figure 6(a)) could give a feasible separation for both the feed with the equal mole fractions for the three components (the feed of case 1) and that with higher concentration of component B (the feed of case 3). Whereas the DWCs designed for feed conditions of case 3 (Figure 7(a)) and case 4 (Figure 8(a)) could only operate for the feed changes to those of case 1 and case 2, respectively. The variations for the liquid split ratio in case of feed condition changes for the DWCs designed for the four cases are respectively shown in Figures 5(b), 6(b), 7(b), and 8(b). It is interesting, but expected, to note that the slopes for all rl−rv curves, which appear linear, are approximately the same. Also the curves can be represented by eq 1, and the corresponding parameters are shown in the Supporting Information. Figures 5−8 show the feasibilities of the DWCs over the feed compositions corresponding to just the four cases defined in

Figure 3. Variation of the optimum liquid split ratio with the vapor split ratio for case 1.

should be adjusted to reach the minimum cost, and the trajectory given in Figure 3 can be used to estimate the vapor split ratio in the operation. Note that the TAC is more sensitive to rl than rv, and the variation of rl with rv is approximately linear, which can be given by the following expression:

rl = a + brv

(1)

For case 1, the parameters a and b in eq 1 are estimated as 0.297 and 0.640, respectively, with an adjusted squared correlation coefficient (adj.R2) of 0.964. 3.2. Effect of rv on TAC. By projecting the minimal of all the curves for different rv given in Figure 2 onto the rv-TAC space, we can get a plot of the TAC against rv for case 1 as shown in Figure 4, in which the rv-TAC curves for all other

Figure 4. Economic behaviors and feasibility in the operation of the DWCs with the shifted vapor split ratio.

cases are plotted as well. Figure 4 demonstrates the cost rises if the rv is changed due to scenario (a) for each of the four DWCs designed in section 2. Since the rl is optimized at any vapor split ratio value, the curves in Figure 4 represent the best situations in terms of the TAC if the rv is shifted in the operation of the DWC. In Figure 4, the feasible operation regions for the vapor split ratios are shown to be limited, and the TAC is sensitive to the variation of rv for all four cases. Figure 4 shows that the TAC of the DWC tends to increase with the increase of the concentration of the middle component in the feed and that the TAC of case 1 is more sensitive to underestimation of the vapor split ratio in the design (i.e., rv in the real operation is probably higher than the design value). 13386

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Figure 5. (a) Economic behaviors and feasibility of DWC for the shifted vapor split ratio in case of changes in feed composition for column 1. (b) Variation tendency of the optimum liquid split ratio as the vapor split ratio changes in case of changes in feed composition for column 1.

Figure 6. (a) Economic behaviors and feasibility of DWC for the shifted vapor split ratio in case of changes in feed composition for column 2. (b) Variation tendency of the optimum liquid split ratio as the vapor split ratio changes in case of changes in feed composition for column 2.

Figure 7. (a) Economic behaviors and feasibility of DWC for the shifted vapor split ratio in case of changes in feed composition for column 3. (b) Variation tendency of the optimum liquid split ratio as the vapor split ratio changes in case of changes in feed composition for column 3.

Table 1. In fact, by employing the simulation procedure presented in the present work using more variations of feed composition, a map of the flexibility of a DWC over feed conditions can be obtained. For example, some feasibility fronts, as presented in Figure 9, can be drawn according to the

limited results given in Figures 5−8. Figure 9(a) shows a segment of the feasibility frontier, which excludes the feed composition of case 4 from the feasible operation region of the DWC designed for case 1. For the other three DWCs designed for cases 2, 3, and 4, corresponding segments of frontiers are 13387

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Figure 8. (a) Economic behaviors and feasibility of DWC for the shifted vapor split ratio in case of changes in feed composition for column 4. (b) Variation tendency of the optimum liquid split ratio as the vapor split ratio changes in case of changes in feed composition for column 4.

Figure 9. Flexibilities over feed composition change for the DWC designed for the four cases.

can see that the column designed for feed of case 4 has the most number of stages for the rectifying section of the prefractionator (column section 5 in Figure 1); this indicates that separating the feed with higher concentration of component C needs a higher value of β, fractional recovery of component B in the top product of the prefractionator to lower the TAC. This restricts the DWC’s ability of feasible operation for cases 1 and 3, but it can separate feasibly the feed for case 2 (Figure 9(d)), as such a separation needs also a higher number of the rectification stages. However, inversely, the column designed for case 2 cannot be suitable for

drawn in Figures 9(b), 9(c), and 9(d). For any of Figures 9 (a)−(d), if the simulation is continued by scattering the feed compositions around the design point, a feasible region of feed composition for the DWC can be obtained. Such a map may give a direct view of the flexibility of a DWC over the feed condition. Comparing Figures 9(a) and (b) to (c) and (d) suggests that a DWC designed for the feed with relatively higher concentration of the light component tends to have higher flexibility over the feed composition change. Explanations can be found in the design parameters given in Table 3. First, we 13388

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to be the optimum but maybe not, because of uncertainties coming from either the design or the operation. 2) Design defects in terms of the vapor split ratio (scenario (a)) may give rise to significant cost increase in operation of the DWC. Such design defects refer to those that may result in under- or overestimation of the vapor split ratio in the design; and at the same time, the sensibilities of the cost to such a defect may depend on the feed composition, based on which the DWC is designed. If this happens, according to conclusion 1, the cost rise could be reduced by adjusting the liquid split ratio in the operation. 3) A DWC can tolerate some changes in the feed composition (scenario (b)). A region of flexibility over the feed composition of a DWC can be drawn following the simulation procedure presented in this paper. The DWCs designed for feeds with relatively higher concentration of the light component tend to be more flexible over the feed composition change. 4) In case of uncertain feed composition around a given composition (scenario (b)), a right vapor split ratio, other than the optimal one for the given composition, should be chosen in the design of DWC so that it can operate feasibly for probably changed feed compositions. Again, the rl should be changed accordingly to match the new value of rv, as suggested by conclusion 1. It should be noted that the relative volatilities of the system play an important role in the behaviors of the dividing wall columns, and a different choice of system may lead to different results of the analysis and then different operating strategies for dividing wall columns; so it should be of interest to investigate further the dependencies of the DWCs’ operability on the vapor split ratio, which is fixed a priori in the design, for systems with different ternary mixtures.

separating the feed of case 4 (Figure 9(b)). This is because the more stages in section 5 (also in section 1, the rectification section of the main column) are required for separating efficiently the lightest component that is the most abundant in the feed, and, at the same time, their loading capacity is low and not enough to support the high value of β that is needed in separating the feed of case 4. As for Figure 9(c), the flexibility of the DWC for case 3 is small because it has the least number of stages in the rectifying section, which are needed in separating both the feeds of cases 2 and 4. 3.4. Decision of rv Considering Uncertain Feed Composition. Systematic design of processes with uncertainty should be done by optimizing all the decision variables and needs to know the probability distribution of the uncertain parameter,21,22 which is beyond the scope of the present paper. However, Figures 5−8 can give useful information on how to make a decision on the vapor split ratio rv, which has a strong impact on the economic behavior of a DWC, in the design with uncertain feed composition. For example, in the design of the DWC for the feed of case 1, as shown in Figure 5(a), if the feed composition with higher concentration of component C (the feed of case 4) would probably present as the feed uncertainty, the design value of rv should be moved from the gray region leftward to somewhere in the shadow region as shown in Figure 5(a), so that the DWC can feasibly operate if component C in the feed is increased up to 0.5 (mole fraction). The distance of the leftward movement of the value of rv along the abscissa in Figure 5(a) depends on the probability of the presence of the feed composition with higher C concentration. Again, as shown in Figure 5(b), the liquid split ratio must be changed if the feed composition is changed in operation. It should be pointed out that, for some cases, it is difficult to cover the feed uncertainty by adjusting only the design value of rv. For example, if in Figure 8 the feed for case 1 is envisaged in the feed uncertainty, and if we move the design value of rv rightward and into the common feasible region of rv for both the feeds of cases 4 and 1 as shown by the shadow ribbon in Figure 8(a), the operation will be found to be unstable because the magnitude of the slopes of both the curves are high; and at the same time, the margin to tolerate uncertainties from other sources (from scenario (a) for example) would become narrow. In such a case, in addition to rv, the other decision variables as listed in Table 3 should be optimized in the uncertain design.

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ASSOCIATED CONTENT

S Supporting Information *

Additional information is about the parameters of equation for all the simulated relationships of vapor and liquid split ratio. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

4. CONCLUSION Operability of DWCs designed respectively for four different feed conditions are examined by simulation for two scenarios that may be encountered in practical operations: (a) the operational vapor split is shifted because of design defect and (b) the feed composition in operation is changed. The investigation was done by demonstrating the relationship between liquid and vapor split ratios and their impact on the total annualized cost as well as the operation feasibilities of the diving-wall columns. The following conclusions can be drawn from the investigation: 1) The economic behavior (the TAC) of a DWC depends on both the liquid and vapor split ratios; for any given feasible value of rv, there exists a corresponding value of rl that minimize the TAC. The importance of knowing this is that the rl in operation could be adjusted to get a minimum cost for the present rv, which is nonadjustable in the operation and expected

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ACKNOWLEDGMENTS The authors acknowledge support from the National Supporting Research Program of China under Grant 2013BAA03B01.

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REFERENCES

(1) Kaibel, G. Distillation columns with vertical partitions. Chem. Eng. Technol. 1987, 10, 92−98. (2) Dejanović, I.; Matijašević, L.; Olujić, Ž . Dividing wall columnA breakthrough towards sustainable distilling. Chem. Eng. Process. 2010, 49, 559−580. (3) Wolff, E. A.; Skogestad, S. Operation of Integrated ThreeProduct (Petlyuk) Distillation Columns. Ind. Eng. Chem. Res. 1995, 34, 2094−2103. (4) Halvorsen, I. J.; Skogestad, S. Optimal operation of Petlyuk distillation: steady-state behavior. J. Process Control 1999, 9, 407−424. 13389

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dx.doi.org/10.1021/ie500686p | Ind. Eng. Chem. Res. 2014, 53, 13383−13390