Operation of Dividing-Wall Columns. 1. A Simplified Temperature

Article pubs.acs.org/IECR

Operation of Dividing-Wall Columns. 1. A Simplified Temperature Difference Control Scheme Shujun Luan, Kejin Huang,* and Ning Wu College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ABSTRACT: A simplified temperature difference control (STDC) scheme, consisting of two temperature and two temperature difference control loops, is proposed for the operation of dividing-wall columns (DWCs). The two temperature control loops are located, respectively, in the rectifying and stripping sections of the main distillation column and work to maintain the top and bottom product qualities. The two temperature difference control loops are arranged, respectively, in each side of the dividing wall with their temperature measurements arranged above and below the locations for introducing feed to the prefractionator and for withdrawing the intermediate product from the main distillation column. These special arrangements serve to keep a certain degree of separation of the fed mixture in the prefractionator and the purity of the intermediate product, tightening product quality control and rendering the STDC scheme with high robustness to the changes in the thermodynamic properties of the ternary mixtures separated. Separation of three ideal ternary mixtures of hypothetical components, A, B, and C, with different ease of separation indexes (ESIs) is chosen as illustrative examples to evaluate the proposed STDC scheme and thorough comparison is conducted with the currently available temperature control (TC) and temperature difference control (TDC) schemes. It is found that the STDC scheme is much superior to the TC scheme irrespective of the great changes in the ESIs. Although with relatively lower instrumentation cost and smaller engineering effort, it can generally lead to performance comparable with the TDC scheme. Application of the STDC scheme to the DWC separating a ternary mixture of ethanol, propanol, and butanol is also attempted and similar outcomes are obtained. Since the STDC scheme behaves in good accordance with the working principle of the DWC, it should be viewed as a general and effective strategy for the operation of the DWC.

1. INTRODUCTION Despite the fact that dividing-wall columns (DWCs) are known to have around 30% or even higher degree of reduction in capital investment and utility requirements as compared with conventional direct and indirect distillation sequences in the separation of ternary mixtures, they have not yet found wide application in the chemical and petrochemical process industries.1−5 The major reason lies essentially in the lack of insights into process dynamics and controllability and reliable methods for the synthesis and design of decentralized control systems.6−10 Recently, increasingly more efforts have been seen in these aspects and relatively more papers have been published on the dynamics and operation of the DWC.11−20 In 1995, Wolff and Skogestad proposed, for the first time, two kinds of direct composition control schemes for the DWC.21 One involved three control loops controlling the purities of the three products, respectively, with the reflux flow rate, intermediate product flow rate, and vapor boilup rate as manipulated variables. The other included four control loops with the purities of the three products and the ratio between the two impurities in the intermediate product controlled, respectively, by the reflux flow rate, intermediate product flow rate, vapor boilup rate, and liquid split ratio. Though it was sometimes infeasible to pursue the four-point control of the DWC (i.e., the so-called black-hole problem), the issue could be completely circumvented by delicate process design.22,23 Through insightful steady-state analysis, Halvorsen and Skogestad pointed out the great importance of keeping the heaviest/lightest component from going out of the top/bottom of the prefractionator on the energy efficient operation of the DWC.24 A number of papers demonstrated that with the liquid split ratio to control the © 2013 American Chemical Society

composition of the heaviest component at the top of the prefractionator, not only could the composition of the three products be controlled at the desired specifications, but also the minimum utility consumption could be achieved irrespective of great changes in the feed flow rates and compositions.25 In the light of the same principle, indirect composition control (or temperature inferential control) was attempted for the operation of the DWC and these included temperature control (TC) and temperature difference control (TDC) schemes.26 For the TC scheme, four temperature measurements were located generally in the rectifying section, intermediate sections, stripping section, and top section of the prefractionator. For the TDC scheme, four additional temperature measurements were added to the TC scheme to infer more accurately the information about the qualities of the three products and the heaviest component composition at the top of the prefractionator. Owing to the widely different thermodynamic properties of the ternary mixtures separated and the possibly strong interactions between the prefractionator and main distillation column involved, greatly different choices of temperature measurements were likely to be recommended by sensitivity analysis or singular value decomposition, and these could lead to sharply different control schemes. For example, Wang and Wong, in terms of the separation of a ternary mixture of ethanol, n-propanol, and n-butanol, chose a temperature in the Received: Revised: Accepted: Published: 2642

October 30, 2012 January 11, 2013 January 15, 2013 January 15, 2013 dx.doi.org/10.1021/ie3029762 | Ind. Eng. Chem. Res. 2013, 52, 2642−2660

Industrial & Engineering Chemistry Research

Article

Table 1. Physical Properties and Design Specifications of the Three Examples Studied value parameter

example I

condenser pressure (bar) 3 stage pressure drop (bar) 6.8901 × 10−3 feed composition (mol %) A 33.33 B 33.33 C 33.34 feed flow rate (kmol/s) 1.0 feed thermal condition 1.0 relative volatility A:B:C 4:2:1 vapor pressure constants A(Avp/Bvp) 13.04/3862 B(Avp/Bvp) 12.34/3862 C(Avp/Bvp) 11.65/3862 product specifications (mol %) A 99 B 99 C 99

example II

example III

3 6.8901 × 10−3

3 6.8901 × 10−3

33.33 33.33 33.34 1.0 1.0 8:2:1

33.33 33.33 33.34 1.0 1.0 8:4:1

13.04/3862 11.65/3862 10.96/3862

13.04/3862 12.34/3862 10.96/3862

99 99 99

99 99 99

Figure 1. Petlyuk distillation column (a) and its thermodynamic equivalent DWC (b).

Figure 3. Optimum design (a) and temperature profiles (b) of the DWC (Example I). Figure 2. Proposed STDC scheme.

decentralized temperature control system for the DWC and reminded us of finding a simple and yet effective approach to tackle this issue in a unified manner. In the present work, a simplified temperature difference control (STDC) scheme, consisting of two temperature and two temperature difference control loops, is proposed for the operation of the DWC. While the two temperature control loops work to maintain the top and bottom product qualities, the two temperature difference control loops serve to keep a certain degree of separation in the prefractionator and the purity of the intermediate product. Since the STDC scheme fits well the working principle of the DWC, it could be effective for the operation of the DWC separating ternary mixtures with widely different thermodynamic properties.

bottom of the prefractionator and two temperatures in the rectifying and stripping sections of the main distillation column as controlled variables for the operation of the DWC.27 With reference to the separation of a ternary fatty alcohol of n-hexanol, n-octanol, and n-decanol, Buck et al. devised two temperature control schemes controlling a temperature in the bottom of the prefractionator and three temperatures in the rectifying section, intermediate sections, and stripping section of the main distillation column.28 Though the two control schemes differed from each other in control configurations, they delivered quite comparable control behaviors. These examples implied the great complexities encountered in the synthesis and design of 2643

dx.doi.org/10.1021/ie3029762 | Ind. Eng. Chem. Res. 2013, 52, 2642−2660


Article

Figure 4. Sensitivity analysis of the DWC (Example I): (a) prefractionator, (b) main distillation column.

two sections. Similarly, the liquid flow from section II to sections V and VI contains mostly components B and C and is separated into relatively pure components B and C in the latter two sections. In the light of this operation analysis, it is readily understood that keeping a certain degree of separation of the fed mixture in the prefractionator is a prerequisite for the smooth operation of the DWC. For the achievement of this purpose, a temperature difference control loop should be employed with its two temperature measurements located, respectively, above and below the feed location. A constant temperature difference between these two temperature measurements guarantees a certain degree of separation of the fed mixture to the prefractionator irrespective of the nonstationary changes encountered in operating conditions. In the main distillation column, the rectifying section (section III) and stripping section (section VI) can be roughly viewed as separating a binary mixture of A/B and B/C, respectively, in spite of the inevitable existence of a small amount of component C in the former and a small amount of component A in the latter. It is thus reasonable to employ two temperature control loops to maintain the top and bottom product qualities because a good corresponding relationship can be expected between the

To comprehensively evaluate the STDC scheme, we choose the separation of three ideal ternary mixtures of hypothetical components, A, B, and C, with different ease of separation indexes (ESIs) as illustrative examples. Both the steady-state analysis and dynamic evaluations are conducted in addition to the thorough comparison with the currently available TC and TDC schemes. The features of the STDC scheme are further analyzed and some conclusions are given in the last section of this article.

2. STDC SCHEME PROPOSED FOR THE OPERATION OF THE DWC As depicted in Figure 1, the Petlyuk distillation column and its thermodynamic equivalent DWC are divided into six sections by the locations of feed, intermediate product, and interconnecting flows between the prefractionator and main distillation column involved. Sections I and II constitute the prefractionator, and sections III−VI constitute the main distillation column. Suppose component A is the lightest, component B is the middle, and component C is the heaviest, then the vapor flow from section I to sections III and IV contains mostly components A and B and is separated into relatively pure components A and B in the latter 2644



Article

Figure 5. STDC (a), TC (b), and TDC (c) schemes (Example I).

Figure 6. Variations of temperatures and temperature differences of the DWC versus the changes in feed compositions of components A, B, and C (Example I): (a) prefractionator, (b) main distillation column.

temperatures and compositions in these two sections. Two major disturbances, coming possibly from the top and/or bottom effluents

of the prefractionator, can pose a detrimental effect to the quality of the intermediate product. For the effective inference of their effects, 2645



Article

Figure 7. STDC scheme by Aspen plus (Example I).

two temperature measurements should be located in sections IV and V, respectively, and they form another temperature difference control loop. Keeping a constant temperature difference between these two temperature measurements can counteract the influences of those two disturbances and serve to stabilize the composition of the intermediate product. Based on the above deductions, a STDC scheme is devised and shown in Figure 2. As can be seen, it involves four control loops, regulating, respectively, two temperatures, TR and TS, in the rectifying and stripping sections, and two temperature differences, ΔTI and ΔTP, in each side of the dividing-wall with the manipulations of reflux flow rate R/distillate flow rate D (note that this is closely dependent on the steady-state value of reflux ratio), reboiler heat duty QR, intermediate product flow rate I, and liquid split ratio RL. The selection of temperature measurements can be simply made in the light of sensitivity analysis29 and the detailed procedure is to be well illustrated in the examples studied in the following three sections. Besides its relatively low instrumentation cost and small engineering effort in control system synthesis and design as compared with the TDC scheme, the STDC scheme is expected to work well in the operation of the DWC in spite of the possibly complicated process dynamics caused by the separation of various ternary mixtures exhibiting different ESIs. Similar to the currently available TC and TDC schemes, the STDC scheme can also maintain energy efficient operation of the DWC because the top composition of component C or the bottom composition of component A can be strictly controlled with the temperature difference control loop in the prefractionator. In what follows, three DWC systems separating, respectively, three ideal ternary mixtures of hypothetical components, A, B, and C with the ESI ranging from 0.5 to 2 are chosen as illustrative examples to comprehensively evaluate the proposed STDC scheme. Both the steady-state analysis and dynamic studies are conducted in addition to the thorough comparison with the currently available TC and TDC schemes.

Table 2. Controller Parameters for the TC, STDC, and TDC Schemes (Example I) scheme TC

STDC

TDC

controller

manipulated variable

controlled variable

KC (−)

TI (min)

TC1 TC2 TC3 TC4 TC1 TC2 TC3 TC4 TC1 TC2 TC3 TC4

D I QR RL D I QR RL D I QR RL

T10 T35 T46 TP10 T10 T35−T14 T46 TP18−TP10 TP6−T10 T35−T26 T46−T40 TP10−TP2

44.68 11.96 4.82 8.15 46.84 2.1 4.35 2.01 2.74 0.81 0.36 0.48

30.36 18.48 6.6 22.44 30.36 17.16 7.92 10.56 31.68 19.78 10.56 21.12

3. EXAMPLE I: OPERATION OF A DWC SEPARATING AN IDEAL TERNARY MIXTURE OF HYPOTHETICAL COMPONENTS A, B, AND C WITH ESI = 1 3.1. Steady-State Process Design. Ideal vapor and liquid phase behaviors are assumed for the hypothetical ternary mixture separated, and the vapor−liquid equilibrium relationship can be expressed by Pj = xA , jPAs + xB , jPBs + xC , jPCs

yi , j = xi , jPis, j/Pj

1≤j≤N

i = A, B, C, and 1 ≤ j ≤ N

(1) (2)

The vapor saturation pressure is calculated via the following equation ln Pis, j = A vp , i − Bvp , i /Tj

i = A, B, C, and 1 ≤ j ≤ N (3)

The physical properties and design specifications are listed in Table 1 for the DWC to be developed, and the relative volatilities of the components A, B, and C make the ESI = αAB/αBC = 1 in this situation. The steady-state simulations make use of the rigorous models of distillation columns in the commercial software 2646



Article

Figure 8. Regulatory responses of Example I for a ± 5% step change in the feed compositions of component A, respectively.

3.2. Synthesis and Design of the STDC Scheme. Sensitivity analysis is used to select the stage temperatures to be controlled. A very small change (i.e., 0.1% in the current work) is made, respectively, to the four manipulated variables (i.e., distillate flow rate D, intermediate product flow rate I, reboiler heat duty QR, and liquid split ratio RL) and the resultant temperature profiles are calculated with the commercial software Aspen Plus. The changes in stage temperatures divided by the changes in the manipulated variables yields the steady-state gain matrix. Figure 4a shows the outcomes of sensitivity analysis of the prefractionator. While the upper two graphs show the steady-state gains with respect to the distillate flow rate D and intermediate product flow rate I, the lower two graphs show the steady-state gains to the heat duty of reboiler QR and liquid split ratio RL. Stages 10 and 18 are found to be the sensitive stages in the two sections involved because of the greatest variations occurring there. Similarly, Figure 4b shows the outcomes of sensitivity analysis of the main distillation column. It is noted that four peaks are found, respectively, on stages 10, 14, 35, and 46, and they correspond actually to the sensitive stages in the four sections of the main distillation column. The STDC scheme can then be simply constructed as shown in Figure 5a. While in the prefractionator the temperature difference between stages 10 and 18 is controlled by the liquid split ratio RL, in the main distillation column the temperature on stage 10 is controlled by the distillate flow rate D (Since RR = 3.56 > 3.0, the reflux flow rate should be used to control the level of the reflux-drum and this can be beneficial to process dynamics and controllability), the temperature difference between stages 14 and 35 by the intermediate product flow rate I, and the temperature on stage 46 by the heat duty of reboiler QR.

Aspen Plus. The DWC is constructed by combining a rectifying column (with only a condenser), a stripping column (with only a reboiler), and two absorber columns in parallel (with neither reboiler nor condenser).25,26 The hypothetical components A, B, and C should first be defined followed by the selection of the physical property package to be used. These can be achieved according to the following procedure: (i) click Components on the left of the Data Browser window and fill in A, B, and C under Component ID, (ii) select IDEAL in the Property method, (iii) specify the parameters of the hypothetical components in the Pure Component. The parameters include the coefficients for the DIPPR ideal gas heat capacity equation, the DIPPR heat of vaporization equation, the DIPPR liquid viscosity equation, the DIPPR vapor viscosity equation, the DIPPR liquid surface tension equation, the extended Antoine vapor pressure equation, the IKCAPE model for liquid heat capacity, and so on. Figure 3a presents an optimum design of the DWC resulted from the minimization of total annual cost (TAC) in terms of a simple methodology proposed in our early work.30 The TAC combines actually operating cost and discounted capital investment. The operating pressure of condenser is set at 3 bar, and the pressure drop is assumed to be 6.8901 × 10−3 bar per stage. The resultant DWC contains a 27-stage prefractionator and a 53-stage main distillation column with the dividing-wall running from stage 13 down to stage 39. The feed processed is fed onto stage 15 in the prefractionator and the intermediate product is withdrawn from stage 23 on the other side of the dividing-wall. The liquid split ratio RL is 0.385, and the vapor split ratio RV is 0.61. Figure 3b depicts the temperature profiles of the DWC. 2647



Article

Figure 9. Closed-loop responses of the TC, STDC, and TDC for a ± 5% step change in the feed compositions of components A, B, and C, respectively, and for a ± 0.001 step change in the purities of the three products (Example I): (a) ± 5% step change in the feed compositions of component A, (b) ± 5% step change in the feed compositions of component B, (c) ± 5% step change in the feed compositions of component C, (d) ± 0.001 step change in the purities of the three products. Gray curves: negative responses; black curves: positive responses.

Under the condition of strictly keeping the three products on their specifications, respectively, the variations of some stage temperatures and temperature differences are shown in Figure 6a and b when the DWC is subject to changes in the feed compositions of components A, B, and C, respectively. One can readily note that the changes of the temperature differences are much smaller in magnitudes than the changes of the temperatures, implying the possibility that tighter control of the DWC can be expected with the STDC scheme than with the TC scheme. The STDC scheme is implemented with the commercial software Aspen Dynamics and the detailed configuration is shown in Figure 7. While the pressure at the top of the rectifying column is controlled by the heat removal from condenser, the other three pressures at the tops of the stripping column and the

two paralleled absorber columns are controlled, respectively, by the power of the corresponding compressors. The liquid levels of the condenser and reboiler are regulated, respectively, with the reflux flow rate (since RR > 3) and bottom product flow rate. The liquid levels in the bases of the rectifying column and two absorber columns are manipulated, respectively, by their bottom withdrawals. While the top ratio control loop is used to regulate the liquid flow rate from the rectifying column to the prefractionator, serving to maintain a constant liquid split ratio RL, the bottom ratio control loop is employed to regulate the vapor flow rate from the stripping column to the prefractionator, serving to maintain a constant vapor split ratio RV. A 1-min dead-time element has been included in all the temperature measurements, and the four temperature/temperature difference controllers are 2648



Article

control (CC) scheme by Ling and Luyben25 is also included here, which works mainly as a reference basis. Although the TC, STDC, and TDC schemes result in somewhat different reboiler duties, their values are actually quite close to each other and all lie around the one of the CC scheme. These results help to confirm the reasonability of employing the STDC scheme to the operation of the DWC.

tuned with the built-in Tyreus-Luyben tuning rule in a sequential manner.26 Namely, the QR loop is first tuned since it greatly can affect all of the other variables. Second, with the QR loop on automatic, the D loop is tuned. Third, with the QR and D loops on automatic, the I loop is tuned. Finally, with the QR, D, and I loops on automatic, the RL loop is tuned. Table 2 gives the resultant controller parameters of the STDC scheme.

4. EXAMPLE II: OPERATION OF A DWC SEPARATING AN IDEAL TERNARY MIXTURE OF HYPOTHETICAL COMPONENTS A, B, AND C WITH ESI = 2 4.1. Steady-State Process Design. The physical properties and design specifications are also listed in Table 1 for the DWC to be developed here. Note that the relative volatilities of the components A, B, and C are modified now to give an ESI of 2 in this situation. The optimum design of the DWC is derived from the minimization of the TAC, and the resultant scheme is shown in Figure 10a, which accommodates 24 stages in the

Table 3. Relative Errors of the Three Product Qualities (Example I) relative error (%) disturbance

product

TC

STDC

TDC

+5% ZA

A B C A B C A B C A B C A B C A B C

−0.18 −0.3 0.01 0.15 0.21 −0.002 0.1 0.07 0.06 −0.11 −0.09 −0.06 0.05 0.15 −0.07 −0.06 −0.19 0.06

−0.11 0.03 0.03 0.1 −0.01 −0.03 0.08 0.005 0.05 −0.09 0.001 −0.05 0.02 −0.03 −0.08 −0.02 0.02 0.08

0.03 −0.1 −0.02 −0.03 0.08 0.01 −0.07 −0.09 −0.02 0.07 0.07 0.03 0.03 0.15 0.04 −0.04 −0.19 −0.04

−5% ZA

+5% ZB

−5% ZB

+5% ZC

−5% ZC

3.3. Closed-Loop Evaluation. Figure 8 displays the closedloop responses of the DWC in the face of a ± 5% step change in the feed compositions of component A, respectively. The ratio between the feed compositions of components B and C has been kept the same as in the nominal operating conditions. Fairly rapid and smooth regulations of the temperatures and temperature differences are achieved, leaving rather small peak deviations in the four controlled variables. Figure 9a−c detail the comparisons among the STDC, TC, and TDC schemes when the DWC has been disturbed by a ± 5% step change in the feed compositions of components A, B, and C, respectively. The TC and TDC schemes are designed according to the procedure by Ling and Luyben.26 The resultant configurations are shown in Figure 5b and c, respectively, and their corresponding controller parameters are also tabulated in Table 2. The relative steady-state errors in the three product purities are summarized in Table 3. It can be noted that the STDC scheme appears to be much better than the TC scheme despite the fact that the former sometimes delivers slightly greater steady-state deviations in the bottom product than the latter. Although the STDC scheme sometimes leads to somewhat greater steady-state deviations in the top and bottom products than the TDC scheme, the reverse is true in the intermediate product. Figure 9d makes the comparisons among the STDC, TC, and TDC schemes when the DWC has been disturbed by a ± 0.001 step change in the purities of the three products, simultaneously. Under these circumstances, the STDC scheme is found to exhibit responses quite similar to the TC and TDC schemes. It is worthwhile to examine further the performance of the STDC, TC, and TDC schemes in terms of the comparison of their reboiler duties in the newly reached steady states, and the detailed outcomes are tabulated in Table 8. The composition

Figure 10. Optimum design (a) and temperature profiles (b) of the DWC (Example II).

prefractionator and 45 stages in the main distillation column. The mixture processed is fed onto stage 15 in the prefractionator and the intermediate product is withdrawn from stage 17 in the main distillation column, with the dividing-wall running from stage 9 down to stage 32. The liquid split ratio RL is 0.415, and the vapor split ratio RV is 0.7. The temperature profiles of the DWC are delineated in Figure 10b. 4.2. Synthesis and Design of the STDC Scheme. Figure 11a shows the outcomes of sensitivity analysis of the prefractionator, and the sensitive stage should be stage 9. Figure 11b shows the sensitivity analysis of the main distillation column, and the sensitive stages should be stages 5, 28, and 38. Note that the number of sensitive stages is different from that of Example I, reflecting a certain extent of changes in operation characteristics by the variations of the thermodynamic properties of the ternary mixture separated. Stage 16 in the prefractionator and in the main distillation column is chosen as the reference stages to construct the temperature difference control loops in the both sides of the 2649



Article

Figure 11. Sensitivity analysis of the DWC (Example II): (a) prefractionator, (b) main distillation column.

Figure 12. STDC (a), TC (b), and TDC (c) schemes (Example II).

by the distillate flow rate D (because of the fact that RR = 3.2 > 3.0), the temperature difference between stages 16 and 28 by the intermediate product flow rate I, and the temperature on stage 38 by the heat duty of reboiler QR. Table 4 lists the

dividing-wall. The resultant STDC scheme is shown in Figure 12a. While in the prefractionator the temperature difference between stages 9 and 16 is controlled by the liquid split ratio RL, in the main distillation column the temperature on stage 5 is controlled 2650



Article

the DWC has been disturbed by a ± 5% step change in the feed compositions of components A, B, and C, respectively. The TC and TDC schemes are shown in Figure 12b and c, respectively, with their controller parameters also tabulated in Table 4. Table 5 summarizes the relative steady-state errors in the three product purities. It can readily be found that the STDC scheme is still superior to the TC scheme. Though the former sometimes leaves greater steady-state deviations in the bottom product than the latter, the reverse is true in the top and intermediate products. The STDC scheme is somewhat inferior to the TDC scheme, but the difference is actually rather small. Figure 14d depicts the comparisons among the STDC, TC, and TDC schemes when the DWC has been disturbed by a ± 0.002 step change in the purities of the three products, simultaneously. The STDC scheme exhibits again quite similar responses with the TC and TDC schemes. In Table 8, the reboiler duties of the three control schemes are also compared with reference to the one of the CC scheme. The STDC scheme leads again to reboiler duties that are quite close to the ones of the TC, TDC, and CC schemes.

Table 4. Controller Parameters for the TC, STDC, and TDC Schemes (Example II) scheme TC

STDC

TDC

controller


controlled variable

KC (−)

TI (min)


D I QR RL D I QR RL D I QR RL

T5 T28 T38 TP9 T5 T28−T16 T38 TP16−TP9 T8−T5 T32−T28 T38−T33 TP14−TP9

3.82 10.67 4.78 9.24 3.84 0.68 4.8 2.05 1.72 0.37 0.38 0.72

34.32 15.84 7.92 21.12 34.32 17.16 6.6 23.76 27.72 15.84 10.56 25.08

controller parameters of the resultant STDC scheme. Because the comparisons of the variation magnitudes between temperatures and temperature differences exhibit the same tendencies as those of Example I (c.f., Figure 6), the results are not shown here. 4.3. Closed-Loop Evaluation. Figure 13 displays the closed-loop responses of the DWC in the face of a ± 5% step change in the feed compositions of component A, respectively. The ratio between the feed compositions of components B and C has been kept the same as in the nominal operating conditions. Rapid and smooth regulations of the temperatures and temperature differences are achieved again, leaving rather small peak deviations in the four controlled variables. Figure 14a−c detail the comparisons among the STDC, TC, and TDC schemes when

5. EXAMPLE III: OPERATION OF A DWC SEPARATING AN IDEAL TERNARY MIXTURE OF HYPOTHETICAL COMPONENTS A, B, AND C WITH ESI = 0.5 5.1. Steady-State Process Design. Table 1 also summarizes the physical properties and design specifications of the DWC to be developed here. The relative volatilities of the components A, B, and C are modified now to give an ESI of 0.5 in this situation. The optimum process design is generated by the minimization of the TAC and the resultant scheme is sketched in Figure 15a including 24 and 44 stages in the prefractionator and

Figure 13. Regulatory responses of Example II for a ± 5% step change in the feed compositions of component A, respectively. 2651



Article

Figure 14. Closed-loop responses of the TC, STDC, and TDC for a ± 5% step change in the feed compositions of components A, B, and C, respectively, and for a ± 0.002 step change in the purities of the three products (Example II): (a) ± 5% step change in the feed compositions of component A, (b) ± 5% step change in the feed compositions of component B, (c) ± 5% step change in the feed compositions of component C, (d) ± 0.002 step change in the purities of the three products. Gray curves: negative responses; black curves: positive responses.

shown in Figure 17a, in which the temperature on stage 10 is controlled by the reflux flow rate R (since RR = 2.45 < 3.0, the distillate flow rate should be used to control the level of the reflux-drum and this can be beneficial to process dynamics and controllability), and the temperature on stage 41 by the reboiler heat duty QR. While the temperature difference between stages 6 and 15 in the prefractionator is controlled by the liquid split ratio RL, the temperature difference between stages 20 and 29 is controlled by the intermediate product flow rate I. Table 6 gives the controller parameters of the STDC scheme. Because the comparisons of the variation magnitudes between temperatures and temperature differences exhibit the same tendencies as those of Examples I and II (c.f., Figure 6), they are not shown here. 5.3. Closed-Loop Evaluation. Figure 18 displays the closed-loop responses of the DWC in the face of a ± 5% step change in the feed compositions of component A, respectively. The ratio between the feed compositions of components B and C

the main distillation column involved, respectively. The dividingwall is located between stage 14 and stage 37 with the mixture separated introduced onto stage 7 in the prefractionator and the intermediate product withdrawn from stage 28 in the main distillation column. The liquid split ratio RL is 0.379, and the vapor split ratio RV is 0.66. The temperature profiles of the DWC are shown in Figure 15b. 5.2. Synthesis and Design of the STDC Scheme. The outcomes of sensitivity analysis of the DWC are shown in Figure 16a and b, which indicate that stage 15 in the prefractionator and stages 10, 20, and 41 in the main distillation column are sensitive stages. The number of sensitive stages is still different from that of Example I, reflecting again a certain extent of changes in operation characteristics by the variations of the thermodynamic properties of the ternary mixture separated. Stage 6 in the prefractionator and stage 29 in the main distillation column are chosen as the reference stages. The resultant STDC scheme is 2652



Article

again advantageous over the TC scheme in spite of the fact that the former sometimes results in greater steady-state deviations in the top product than the latter. While the STDC scheme cannot compete with the TDC scheme in the aspect of steady-state deviations, the reverse is true in the aspect of dynamic behaviors because the TDC scheme sometimes exhibits much greater peak deviations and even severe oscillations in the product qualities. Figure 19d makes the comparisons among the STDC, TC, and TDC schemes when the DWC has been disturbed by a ± 2.5 × 10−3 step change in the purities of the three products, simultaneously. While the TDC scheme cannot maintain the three products at 99.25 mol % (in particular, the intermediate product shows a sudden drop at the time instant of 3.7 h), the TC scheme exhibits rather severe oscillations in the three products. The STDC scheme, on the other hand, can smoothly drive the DWC to the desired steady states. It is worth pointing out here the fact that while the TC scheme fails to reject a +10% step change in the feed compositions of component A, the TDC scheme is unable to handle a +10%/ −10% step change in the feed compositions of component A/B. The detailed results are shown in Figure 20, and it can be readily found that the STDC scheme still does a good job in these circumstances. The reason behind these phenomena is anticipated to be the extended time constant between the temperature measurement in the TC scheme/temperature measurements in the TDC scheme in section II and the liquid split ratio RL. The degraded process dynamics not only worsens the closed-loop behaviors of the TC and TDC schemes, but also confines their abilities to handle severe feed composition disturbances. The comparisons among the reboiler duties of the three control schemes are also made in Table 8 with the inclusion of the CC scheme as a reference basis. The STDC scheme leads again to reboiler duties that are quite close to the ones of the TC, TDC, and CC schemes.

Table 5. Relative Errors of the Three Product Qualities (Example II) relative error (%) disturbance

product

TC

STDC

TDC

+5% ZA


−0.08 −0.6 0.004 0.08 0.34 0.01 0.05 0.18 0.06 −0.05 −0.24 −0.07 0.03 0.2 −0.06 −0.03 −0.27 0.06

−0.06 −0.18 0.01 0.06 0.15 −0.01 0.05 0.16 0.06 −0.05 −0.19 −0.06 0.01 −0.01 −0.08 −0.01 0.006 0.07

0.03 0.05 −0.02 −0.03 −0.05 0.02 −0.02 0.09 −0.05 0.02 −0.09 0.05 −0.006 −0.14 0.08 0.005 0.15 −0.06

−5% ZA

+5% ZB

−5% ZB

+5% ZC

−5% ZC

6. DISCUSSION The three example systems studied in the current work have demonstrated that the STDC scheme can be employed for the operation of the DWC. Apart from the maintenance of stable operation, the steady-state deviations in the three product qualities are also acceptable. While the temperature difference control loop in the prefractionator serves to maintain a certain degree of separation of the fed mixture, the other one in the main distillation column works to keep the bottom and top effluents of the prefractionator from affecting the purity of the intermediate product. This is why it can be generally superior to the TC scheme regardless of the magnitudes of the feed composition disturbances encountered. In comparison with the TDC scheme, the STDC scheme appears slightly unfavorable in terms of the steady-state deviations in the three product qualities and this might be related to the simple temperature control strategies adopted in the rectifying and stripping sections of the main distillation column. Because of the multicomponent nature in these two sections, the simple temperature control loops cannot handle feed composition disturbances well and this slightly degrades the performance of the STDC scheme. Intensive simulation studies have already confirmed this interpretation. In the aspect of the robustness of the STDC scheme to the variations of the ESI, the STDC scheme appears to be advantageous over the TC and TDC schemes and this can easily be inferred from the severe deterioration in system behaviors of the latter two schemes in Example III. This property helps to ease, to a certain extent, the synthesis and design of the STDC scheme.

Figure 15. Optimum design (a) and temperature profiles (b) of the DWC (Example III).

has been kept the same as in the nominal operating conditions. Rapid and smooth regulations of the temperatures and temperature differences are again achieved, leaving rather small peak deviations in the four controlled variables. Figure 19a−c depicts the comparisons among the STDC, TC, and TDC schemes when the DWC has been disturbed by a ± 5% step change in the feed compositions of components A, B, and C, respectively. The TC and TDC schemes are shown in Figure 17b and c, respectively, with their controller parameters also tabulated in Table 6. Table 7 summarizes the relative steadystate errors of the three product purities. The STDC scheme is 2653



Article

Figure 16. Sensitivity analysis of the DWC (Example III): (a) prefractionator, (b) main distillation column.

Figure 17. STDC (a), TC (b), and TDC (c) schemes (Example III).

It is interesting to examine the variations of temperature measurement locations in the STDC scheme with respect to the changes in the ESI. In the case of the ESI equal to 1 (Example I), four sensitive stages are found, respectively, in sections I, II, IV

and V, as shown in Figure 4. The existence of two sensitive stages in sections I and II implies that controlling the compositions of components A and C in the bottom and top, respectively, is equally important because they can both affect the composition 2654



Article

of the intermediate product. Similarly, the existence of two sensitive stages in sections IV and V implies that suppressing the disturbances from the bottom and top of the prefractionator is also equally important to the control of the composition of the intermediate product. The employment of two temperature difference control loops in both sides of the dividing-wall can thus meet this purpose and keep the bottom and top effluents of the prefractionator from affecting the purity of the intermediate product. In the case of the ESI greater than 1 (Example II), there are only two sensitive stages, respectively, in sections I and V, as shown in Figure 11. The existence of one sensitive stage in the prefractionator implies that controlling the composition of

component C at the top is more important than controlling the composition of component A at the bottom under this circumstance. Similarly, the existence of one sensitive stage in section V implies that suppressing the disturbances from the bottom of the prefractionator is more important than suppressing the Table 7. Relative Errors of the Three Product Qualities (Example III) relative error (%)

Table 6. Controller Parameters for the TC, STDC, and TDC Schemes (Example III) scheme TC

STDC

TDC

controller


controlled variable

KC (−)

TI (min)


R I QR RL R I QR RL R I QR RL

T10 T20 T41 TP15 T10 T29−T20 T41 TP15−TP6 T10−T2 T20−T14 T41−T39 TP15−TP13

4.61 6.17 0.95 8.75 4.59 0.67 0.85 0.48 0.42 0.75 0.27 0.66

13.2 50.16 9.24 21.12 13.2 46.2 7.92 83.16 14.52 52.8 7.92 25.08

disturbance

product

TC

STDC

TDC

+5% ZA


−0.09 0.2 0.03 0.08 −0.6 −0.03 0.09 −0.3 0.02 −0.1 0.11 −0.02 −0.008 −0.15 −0.05 0.009 0.12 0.05

−0.1 0.13 0.03 0.1 −0.37 −0.02 0.1 −0.25 0.03 −0.1 0.08 −0.03 −0.005 −0.05 −0.05 0.005 0.05 0.05

−0.12 0.05 −0.02 0.11 −0.26 0.02 0.11 −0.19 −0.02 −0.13 0.04 0.02 −3 × 10−4 −0.02 0.04 7 × 10−4 0.01 −0.03

−5% ZA

+5% ZB

−5% ZB

+5% ZC

−5% ZC

Figure 18. Regulatory responses of Example III for a ± 5% step change in the feed compositions of component A, respectively. 2655



Article

Figure 19. Closed-loop responses of the TC, STDC, and TDC for a ± 5% step change in the feed compositions of components A, B, and C, respectively, and for a ± 2.5 × 10−3 step change in the purities of the three products (Example III): (a) ± 5% step change in the feed compositions of component A, (b) ± 5% step change in the feed compositions of component B, (c) ± 5% step change in the feed compositions of component C, (d) ± 2.5 × 10−3 step change in the purities of the three products. Gray curves: negative responses; black curves: positive responses.

disturbances in process operation. In fact, when encountering a ± 20% step change in the feed flow rate, the STDC scheme still works much better than the TC scheme and gives performance comparable to the TDC scheme in Examples I−III.31 With respect to the robustness of the STDC scheme to temperature measurement errors, similar conclusions can be reached as in the cases of suppressing feed composition and flow rate disturbances.31 The STDC scheme is also examined in the operation of the DWC separating ternary mixtures with widely different compositions (i.e., rather than equi-molar mixtures), no exception has ever been found as compared with the TC and TDC schemes.31 To demonstrate the application of the STDC scheme in the operation of the DWC separating real ternary mixtures, we choose here the separation of an equi-molar mixture of ethanol (E), propanol (P), and butanol (B). Figure 21a sketches an optimum design generated by the minimization of the TAC, and its temperature profiles are shown in Figure 21b. Figure 22 details the comparisons

disturbances from the top of the prefractionator. With the selection of two reference stages near the feed and the intermediate product, respectively, the STDC scheme can meet its purpose. In the case of the ESI smaller than 1 (Example III), there are two sensitive stages, respectively, in sections II and IV, as shown in Figure 16. In terms of the same deduction as in Example II, the feasibility of the STDC scheme can also be clarified. The above explanations indicate the adaptation mechanism of the STDC scheme to the variations in the thermodynamic properties of the ternary mixtures separated. It stands for the essential reason that renders the control structure with relatively high robustness in comparison with the TC and TDC schemes. In the current work, only the rejection of various disturbances from feed composition has been considered in the evaluation of the proposed STDC scheme, however, it never signifies the insignificance of examining its performance in face of feed flow rate disturbances because they also represent one of the major 2656



Article

Figure 20. Closed-loop responses of the TC, STDC, and TDC for a ± 10% step change in the feed compositions of components A and B, respectively (Example III): (a) ± 10% step change in the feed compositions of component A, (b) ± 10% step change in the feed compositions of component B. Gray curves: negative responses; black curves: positive responses.

Table 8. Comparisons among the Reboiler Duties of the CC, TC, STDC, and TDC Schemes for the Three Examples Studied reboiler duties (MW) example Example I

Example II

Example III

disturbance

CC

TC

STDC

TDC

+5% ZA −5% ZA +5% ZB −5% ZB +5% ZC −5% ZC +5% ZA −5% ZA +5% ZB −5% ZB +5% ZC −5% ZC +5% ZA −5% ZA +5% ZB −5% ZB +5% ZC −5% ZC

38.77 39.03 39.35 38.42 38.55 39.23 38.58 39.2 39.41 38.34 38.66 39.1 31.2 30.53 30.91 30.8 30.42 31.22

38.07 39.91 39.71 38.14 39 38.76 37.76 40.46 40.04 37.9 39.08 38.67 31.25 30.33 30.97 30.64 30.19 31.43

38.82 39.03 39.47 38.35 38.45 39.37 38.27 39.56 39.94 37.98 38.57 39.21 31.16 30.56 31.12 30.59 30.23 31.39

38.51 39.27 39.06 38.69 39.07 38.68 38.67 39.11 39.58 38.23 38.48 39.4 31.05 30.57 31.11 30.51 30.27 31.35

Figure 21. Optimum design (a) and temperature profiles (b) of the DWC separating an equi-molar mixture of ethanol, propanol, and butanol (Real example).

among the STDC, TC, and TDC schemes in terms of their regulatory responses to a ± 10% step change in the feed flow rate and feed compositions of ethanol, propanol, and butanol, respectively. Again, the STDC scheme works much better than the TC scheme and gives performance comparable to the TDC scheme. Regarding the servo responses and robustness to temperature measurement errors, quite similar conclusions are obtained as those obtained in the three hypothetical examples studied and are not shown here. The derivation of the STDC augments the methods to operate the DWC. To achieve effective control of the DWC, one therefore needs to carefully discriminate these alternatives during control system synthesis and design and this may be conducted

in terms of the trade-off between their performance and complexities. If the TC scheme is likely to meet the operation requirements, then it should first be considered in control system synthesis and design, otherwise, the STDC scheme should be adopted as an alternative. If the STDC scheme still fails, then the TDC scheme or even more complicated control schemes, e.g., the double temperature difference control (DTDC) scheme should be considered. The DTDC scheme is to be addressed in the second paper of this series.32 2657



Article

Figure 22. Closed-loop responses of the TC, STDC, and TDC for a ± 10% step change in the feed flow rate and feed compositions of ethanol, propanol, and butanol, respectively (Real example): (a) ± 10% step change in the feed flow rate, (b) ± 10% step change in the feed compositions of ethanol, (c) ± 10% step change in the feed compositions of propanol, (d) ± 10% step change in the feed compositions of butanol. Gray curves: negative responses; black curves: positive responses.

7. CONCLUSIONS In this work, a STDC scheme has been devised for the operation of the DWC. It is composed of two temperature and two temperature difference control loops and thus needs relatively lower instrumentation cost and smaller engineering effort than the TDC scheme. The two temperature control loops are arranged, respectively, in the rectifying and stripping sections of the main distillation column and serve to maintain the top and bottom product qualities. One temperature difference control loop is located in the prefractionator with the two temperature measurements arranged above and below the feed location; this helps to maintain a certain degree of separation of the fed mixture in the prefractionator. The other temperature difference control loop is located in the main distillation column with the two temperature measurements arranged above and below the location for withdrawing the intermediate product; this favors the rejection

of the disturbances coming, respectively, from the top and bottom of the prefractionator. The special arrangements of the control loops not only enable the STDC scheme to be a general and effective strategy for the operation of the DWC, but also facilitate the control of the three products. Separation of three ideal ternary mixtures of hypothetical components, A, B, and C with different ESIs has been chosen as illustrative examples to evaluate the STDC scheme proposed, and thorough comparison has been made with the currently available TC and TDC schemes. Irrespective of the great changes in the thermodynamic properties of the ternary mixtures separated, the STDC scheme appears to be always superior to the TC scheme and presents performance comparable with the TDC scheme. Application of the STDC scheme to the DWC separating a ternary mixture of ethanol, propanol, and butanol has also been examined and similar findings have been obtained. These outcomes stem from 2658



Article

TAC = total annual cost, no. of dollars TDC = temperature difference control V = vapor flow rate, kmol/s x = liquid composition y = vapor composition z = feed composition

the fact that the STDC scheme is devised in good accordance with the working principle of the DWC, which permits it to have relatively high adaptation ability to the variations in the thermodynamic properties of the ternary mixtures separated. Although the STDC and TDC schemes render stricter control of the three product qualities of the DWC than the TC scheme, they still exhibit somewhat great steady-state offsets. For the further enhancement of the closed-loop system performance, more complicated temperature inferential control systems should be attempted for the DWC and one of the potential control schemes is the DTDC scheme. It is to be addressed in the second paper of this series.32

■

Greek letters

α = relative volatility Subscripts

A = component index B = component index or bottom product C = component index D = distillate product I = intermediate product or intermediate sections P = prefractionator or stage index of the prefractionator R = rectifying section S = stripping section i = stage index of the main distillation column

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 10 64434801. Fax: +86 10 64437805. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

Superscripts

ACKNOWLEDGMENTS The current work is financially supported by The National Science Foundation of China under grant 21076015 and The Doctoral Programs Foundation of Ministry of Education of China under grant 20100010110008.

■

s = saturation

REFERENCES

(1) Dunnebier, G.; Pantelides, C. C. Optimal Design of Thermally Coupled Distillation Columns. Ind. Eng. Chem. Res. 1999, 38, 162. (2) Kolbe, B.; Wenzel, S. Novel Distillation Concepts Using One-Shell Columns. Chem. Eng. Process. 2004, 43, 339. (3) Errico, M.; Tola, G.; Rong, B.; Demurtas, D.; Turunen, I. Energy Saving and Capital Cost Evaluation in Distillation Column Sequences with a Divided Wall Column. Chem. Eng. Res. Des. 2009, 87, 1649. (4) Dejanovic, I.; Matijasevic, L.; Olujic, Z. Dividing Wall Column-A Breakthrough towards Sustainable Distilling. Chem. Eng. Process. 2010, 49, 559. (5) Sangal, V. K.; Kumar, V.; Mishra, I. M. Optimization of Structural and Operational Variables for the Energy Efficiency of a Divided Wall Distillation Column. Comput. Chem. Eng. 2012, 40, 33. (6) Abdul Mutalib, M. I.; Smith, R. Operation and Control of Dividing Wall Distillation Columns, Part 1: Degrees of Freedom and Dynamic Simulation. Chem. Eng. Res. Des. 1998, 76, 308. (7) Abdul Mutalib, M. I.; Zeglam, A. O.; Smith, R. Operation and Control of Dividing Wall Distillation Columns, Part 2: Simulation and Pilot Plant Studies Using Temperature Control. Chem. Eng. Res. Des. 1998, 76, 319. (8) Serra, M.; Espuna, A.; Puigjaner, L. Controllability of Different Multicomponent Distillation Arrangements. Ind. Eng. Chem. Res. 2003, 42, 1773. (9) Adrian, T.; Schoenmakers, H.; Boll, M. Model Predictive Control of Integrated Unit Operations: Control of a Divided Wall Column. Chem. Eng. Process. 2004, 43, 347. (10) Gomez-Castro, F. I.; Segovia-Hernandez, J. G.; Hernandez, S.; Gutierrez-Antonio, S.; Briones-Ramirez, A. Dividing Wall Distillation Columns: Optimization and Control Properties. Chem. Eng. Technol. 2008, 31, 1246. (11) Cho, Y.; Kim, B.; Kim, D.; Han, M.; Lee, M. Operation of Divided Wall Column with Vapor Sidedraw Using Profile Position Control. J. Process Contr. 2009, 19, 932. (12) Van Diggelen, R. C.; Kiss, A. A.; Heemink, A. W. Comparison of Control Strategies for Dividing-Wall Columns. Ind. Eng. Chem. Res. 2010, 49, 288. (13) Barroso-Munoz, F. O.; Hernandez, S.; Hernandez-Escoto, H.; Segovia-Hernandez, J. G.; Rico-Ramirez, V.; Chavez, R. Experimental Study on Pressure Drops in a Dividing Wall Distillation Column. Chem. Eng. Process. 2010, 49, 177. (14) Kiss, A. A.; Bildea, C. S. A Control Perspective on Process Intensification in Dividing-Wall Columns. Chem. Eng. Process. 2011, 50, 281.

■

NOTATION A = hypothetical component Avp = vapor pressure constant, Pa B = hypothetical component or bottom product flow rate, kmol/s Bvp = vapor pressure constant, Pa·K C = hypothetical component CC = composition control COMP = compressor D = distillate flow rate, kmol/s DWC = dividing-wall column ESI = ease of separation index F = feed flow rate, kmol/s FC = flow rate controller i = component index I = intermediate product flow rate, kmol/s j = stage index KC = proportional gain L = liquid flow rate, kmol/s LC = level controller N = number of stages P = pressure, Pa PC = pressure controller QC = heat duty of condenser, MW QR = heat duty of reboiler, MW q = feed thermal condition R = reflux flow rate, kmol/s RC = ratio controller RL = liquid split ratio RR = reflux ratio RV = vapor split ratio STDC = simplified temperature difference control T = temperature, K TC = temperature controller or temperature control ΔT = temperature difference, K, or time delay, min TI = integral time, min 2659



Article

(15) Yildirim, O.; Kiss, A. A.; Kenig, E. Y. Dividing Wall Columns in Chemical Process Industry: A Review on Current Activities. Sep. Purif. Technol. 2011, 80, 403. (16) Buck, C.; Hiller, C.; Fieg, G. Applying Model Predictive Control to Dividing Wall Columns. Chem. Eng. Technol. 2011, 34, 663. (17) Kiss, A. A.; Rewagad, R. R. Energy Efficient Control of a BTX Dividing-Wall Column. Comput. Chem. Eng. 2011, 35, 2896. (18) Ling, H.; Cai, Z.; Wu, H.; Wang, J.; Shen, B. Remixing Control for Divided-Wall Columns. Ind. Eng. Chem. Res. 2011, 50, 12694. (19) Rewagad, R. R.; Kiss, A. A. Dynamic Optimization of a DividingWall Column Using Model Predictive Control. Chem. Eng. Sci. 2012, 68, 132. (20) Niggemann, G.; Fieg, G. Validation of Dividing-Wall Columns Based on Experimental Data and Dynamic Simulations: Pilot-Plant and Production-Scale Columns. Ind. Eng. Chem. Res. 2012, 51, 931. (21) Wolff, E. A.; Skogestad, S. Operation of Integrated Three-Product (Petlyuk) Distillation Columns. Ind. Eng. Chem. Res. 1995, 34, 2094. (22) Wang, Y.; Huang, K.; Luan, S.; Chen, W.; Wang, S. J.; Wong, D. S. H. Circumventing the Black-Hole Problem in Design and Control of Dividing-Wall Distillation Columns. Ind. Eng. Chem. Res. 2012, 51, 14771. (23) Gao, J.; Huang, K.; Luan, S.; Jiao, Y.; Li, S. Avoiding the BlackHole Problem by the Arrangements of Multiple Intermediate Products to Dividing-Wall Distillation Columns. Ind. Eng. Chem. Res. 2013, under revision. (24) Halvorsen, I. J.; Skogestad, S. Optimal Operation of Petlyuk Distillation: Steady-State Behavior. J. Process Contr. 1999, 9, 407. (25) Ling, H.; Luyben, W. L. New Control Structure for Divided-Wall Columns. Ind. Eng. Chem. Res. 2009, 48, 6034. (26) Ling, H.; Luyben, W. L. Temperature Control of the BTX Divided-Wall Column. Ind. Eng. Chem. Res. 2010, 49, 189. (27) Wang, S.; Wong, D. Controllability and Energy Efficiency of a High-Purity Divided Wall Column. Chem. Eng. Sci. 2007, 62, 1010. (28) Buck, C.; Hiller, C.; Fieg, G. Decentralized Temperature Control of a Pilot Dividing Wall Column. Chem. Eng. Process. 2011, 50, 167. (29) Luyben, W. L. Distillation Design and Control Using Aspen Simulation; Wiley: New York, 2006. (30) Wang, P.; Chen, H.; Wang, Y.; Zhang, L.; Huang, K.; Wang, S. J. A Simple Algorithm for the Design of Fully Thermally Coupled Distillation Columns (FTCDC). Chem. Eng. Commun. 2011, 199, 608. (31) Luan, S. A Simplified Temperature Difference Control (STDC) Scheme for the Dividing-Wall Columns. MS Thesis, Beijing University of Chemical Technology, 2013. (32) Wu, N.; Huang, K.; Luan, S. Operation of Dividing-Wall Distillation Columns. 2. Application of Double Temperature Difference Control Principle. Ind. Eng. Chem. Res. 2013, submitted.

2660


Operation of Dividing-Wall Columns. 1. A Simplified Temperature

Recommend Documents