Operation of Dividing-Wall Distillation Columns. 3. A Simplified Double

Article pubs.acs.org/IECR

Operation of Dividing-Wall Distillation Columns. 3. A Simplified Double Temperature Difference Control Scheme Yang Yuan and Kejin Huang* College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, P. R. China S Supporting Information *

ABSTRACT: Although the double temperature difference control (DTDC) scheme outperforms the temperature difference control (TDC) scheme in controlling dividing-wall distillation columns (DWDCs), four additional temperature measurements are required and result in a more expensive and complicated control structure. In order to overcome its drawbacks and still keep its advantages, we proposed a simplified DTDC (SDTDC) scheme, which includes two temperature control (TC) and two DTDC loops. While the two TC loops are designed, respectively, to regulate the top and bottom products, the two DTDC loops are designed to control tightly the prefractionator and intermediate product. The design strategy makes deliberately use of the operating characteristics of the DWDC and can consequently facilitate its product control and robustness to the operating condition changes. The control of a DWDC, fractionating a benzene/toluene/o-xylene mixture, is studied to compare the SDTDC scheme against the TDC and DTDC schemes. Although sharing an equal number of temperature measurements, the SDTDC scheme is superior to the TDC scheme with comparable or even reduced static offsets in the three products and enhanced capability of handling feed composition disturbances. The SDTDC scheme leaves slightly greater static offsets than the DTDC scheme, but its reduced cost and alleviated complication justify it to be a competitive alternative for the operation of the DWDC. The SDTDC scheme can be further reinforced through the formation of TDC loops in the rectifying and/or stripping sections with the available temperature measurements in the two sections along the dividing wall, and this increases the diversity of the proposed control strategy. A systematic approach is given to search for the tight control scheme for the DWDC with as a small number of temperature measurements as possible.

1. INTRODUCTION In the last paper, the double temperature difference control (DTDC) scheme was found to yield better control of dividingwall distillation columns (DWDCs) than the temperature difference control (TDC) scheme.1 Not only were the static offsets in the three products reduced simultaneously, but also the capability of rejecting feed composition disturbances was raised to 30% of the nominal static value of each component involved. (Remember the fact that the TDC scheme can only tolerate feed composition disturbances by 20% of the nominal static value of each component involved.) Although these represent substantial improvements in process operation, the DTDC scheme is still considered to have its inherent drawbacks. First, since four additional temperature measurements are required in the DTDC scheme, more engineering efforts must be expended in control system development in addition to the expended capital cost for temperature sensors. Second, since the four inferentially controlled variables, namely, the three product compositions plus the one from the top/bottom of the prefractionator,1−4 are essentially treated with equal importance in the DTDC scheme (this is well reflected from the fact that all control loops include uniformly three temperature measurements), the design philosophy is, however, not exactly in line with the working mechanism of the DWDC. For the effective operation of the DWDC, it is imperative to control strictly the two sections along the dividing wall because the separations of three components are primarily conducted there and can give strong influences to the rectifying and stripping sections (RSS) of the main distillation column (MDC). Therefore, it is advisable to adopt two DTDC loops to © 2014 American Chemical Society

control, respectively, the two sections along the dividing wall. For the RSS of the MDC, because they, in principle, deal with the separations of binary mixtures, it is usually unnecessary to control them with two DTDC loops, especially under the circumstance of tight control of the two sections along the dividing wall. The DTDC scheme is thus considered to have a redundancy problem in the employment of too many temperature measurements in control system synthesis and design. These two defects remind us of the possibility of simplifying the DTDC scheme with the purpose of retaining its advantages in the operation of the DWDC in terms of a relatively small number of temperature measurements. This gives rise to an interesting and yet challenging issue to be addressed. Although intensive researches have been conducted so far on the dynamics and operation of the DWDC, systematic studies on the development of temperature inferential control strategies are relatively few.5−7 The scarcity of systematic research is also regarded as one of the main reasons that restrict the DWDC from finding wide applications in the industrial sector. The current work aims to synthesize a simplified DTDC (SDTDC) scheme for the DWDC. The primary objective is to achieve tight product regulation with as small a number of temperature measurements as possible. The principle of the SDTDC scheme is introduced, and the control of a DWDC, fractionating Received: Revised: Accepted: Published: 15969

June 23, 2014 September 18, 2014 September 22, 2014 September 22, 2014 dx.doi.org/10.1021/ie502516y | Ind. Eng. Chem. Res. 2014, 53, 15969−15979

Industrial & Engineering Chemistry Research

Article

Table 1. Operating Conditions and Prouduct Specifications for the DWDC Parameter Condenser pressure (atm) Stage pressure drop (atm) Feed compositions (mol %)

Value

Benzene Toluene o-Xylene

Feed flow rate (kmol/s) Feed thermal condition Relative volatility B:T:X Normal boiling points (K)

Product specifications (mol %)

Benzene Toluene o-Xylene Benzene Toluene o-Xylene

0.37 6.90 × 10−3 30 30 40 1.0 1.0 7.1:2.2:1 353 385 419 99 99 99

a benzene (B)/toluene (T)/o-xylene (X) mixture, is examined to compare the SDTDC scheme against the TDC and DTDC schemes. Potential strategies for further reinforcement of the SDTDC scheme are also pointed out, and a systematic approach is indicated for the tight control of the DWDC with as small a number of temperature measurements as possible. Some conclusions are finally reached.

Figure 1. Simplified double temperature difference control (SDTDC) scheme proposed for the operation of the DWDC.

2. A SDTDC SCHEME PROPOSED FOR THE DWDC With reference to the location of the dividing wall, it is reasonable to divide the DWDC into four sections, namely, rectifying section, stripping section, and the two sections along the dividing wall. The four sections interact with each other to effect a given separation. Because the two sections along the dividing wall deal primarily with the separation of ternary mixtures, their operations are quite likely to present strong influences to the RSS (which, on the other hand, deal primarily with the separations of binary mixtures) and affect consequently the control of the three products. For the effective control of the DWDC, it is therefore imperative to control more tightly these two sections than the RSS, and this represents essentially the key point for developing a control system for the DWDC. Many temperature inferential control schemes proposed so far, including, for example, temperature control (TC), TDC, and DTDC schemes, failed to

make use of this inherent operation characteristic and treated the two sections along the dividing wall with equal importance to the RSS. This may result in either the degradation of control system performance due to the unpredicted temperature measurement failures or the redundancy problem due to the employment of more temperature measurements than necessary in control system development. It is therefore worth exploring a way here to control the DWDC with as small a number of temperature measurements as possible. In terms of the inherent operation characteristic of the DWDC outlined above, the SDTDC scheme is devised as sketched in Figure 1. It can readily be noted that two TC loops (i.e., TC1 and TC2) and two DTDC loops (i.e., DTDC1 and DTDC2) are included apart from the necessary pressure and inventory control loops. The TC1 and TC2 loops regulate, respectively, the top and bottom products in terms of controlling the temperatures of

Table 2. Controller Parameters for the TDC, DTDC, SDTDC, and SDTDC-FR Schemes Scheme TDC

DTDC

SDTDC

SDTDC-FR

Controller

Manipulated variable

Range of manipulated variable

Controlled variable

Range of controlled variable (K)

KC (−)

TI (min)

TDC1 TDC2 TDC3 TDC4 DTDC1 DTDC2 DTDC3 DTDC4 TC1 DTDC1 TC2 DTDC2 TDC1 DTDC1 TC1 DTDC2

D (kmol/s) I (%) QR (MW) RL (−) D (kmol/s) I (%) QR (MW) RL (−) D (kmol/s) I (%) QR (MW) RL (−) D (kmol/s) I (%) QR (MW) RL (−)

[0, 2.717] [0, 100] [0, 61.872] [0, 1.143] [0, 2.717] [0, 100] [0, 61.872] [0, 1.143] [0, 2.717] [0, 100] [0, 61.872] [0, 1.143] [0, 2.717] [0, 100] [0, 61.872] [0, 1.143]

T7 − TP12 T26 − T31 T40 − T34 TP16 − TP12 (T2 − T7) − (T7 − TP12) (T19 − T26) − (T26 − T31) (T34 − T40) − (T40 − T45) (TP12 − TP16) − (TP16 − TP24) T7 (T19 − T26) − (T26 − T31) T40 (TP12 − TP16) − (TP16 − TP24) T7 − TP12 (T19 − T26) − (T26 − T31) T40 (TP12 − TP16) − (TP16 − TP24)

[0, 14.643] [0, 18.248] [0, 24.352] [0, 10.943] [0, 19.052] [0, 7.020] [0, 4.229] [0, 27.262] [273.150, 404.623] [0, 7.020] [273.150, 514.486] [0, 27.262] [0, 14.643] [0, 7.020] [273.150, 514.486] [0, 27.262]

0.180 0.585 2.140 0.763 0.152 0.401 0.105 0.266 2.171 0.386 4.951 1.143 0.233 0.150 4.949 1.166

10.560 10.560 11.880 22.440 14.520 17.160 10.560 22.440 14.200 17.160 7.920 19.800 13.200 17.160 7.920 21.120

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dx.doi.org/10.1021/ie502516y | Ind. Eng. Chem. Res. 2014, 53, 15969−15979


Article

Figure 2. Optimum design of the DWDC and its static temperature profiles: (a) DWDC; (b) static temperature profiles.

the sensitive stages in the RSS. By controlling two double temperature differences in the two sections along the dividing wall, the DTDC1 and DTDC2 loops serve, respectively, to keep a tight regulation of the prefractionator and counteract those disturbances (from the prefractionator) affecting the intermediate product. The design strategy permits tight control of the DWDC with the smallest number of temperature measurements in comparison with the DTDC scheme. Here, the controlled variables are simply paired with the nearest manipulated variables in locations (i.e., TR−D (R), TS−QR, Δ2TI−I, and Δ2TP−RL); the control configuration needs, however, to be carefully judged by static or dynamic analysis and/or closed-loop operability studies. For the determination of sensitive and reference stages, they should be conducted, respectively, in terms of sensitivity analysis and singular value decomposition (SVD) techniques; detailed principles can be found elsewhere.1,3,4 Although the SDTDC scheme shares an equal number of temperature measurements with the TDC scheme (both actually contain eight temperature measurements), the arrangement of two DTDC loops in the two sections along the dividing wall tightens greatly the operation of the DWDC and is quite likely to render the former to be better in control of system

Figure 3. Three control schemes examined: (a) TDC scheme; (b) DTDC scheme; (c) SDTDC scheme.

performance than the latter. In spite of the fact that the SDTDC scheme might be inferior to the DTDC scheme due to the removal of four temperature measurements from the RSS, the reduced capital cost and alleviated complication could still enable the former to be a rather competitive alternative to the latter. 15971



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Figure 4. DWDC along with the SDTDC scheme: (a) Aspen dynamics implementation; (b) controller faceplates.

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Figure 5. Transient responses of the DWDC incorporated with the SDTDC scheme after facing a ±10% feed flow rate variation.

In the following section, the control of a DWDC fractionating a B/T/X mixture is studied to assess the SDTDC scheme

proposed. The example is taken from the papers of Ling and Luyben2,3 and also studied by other researchers.8 15973



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Table 3. Relative Static Errors for a ±10% Step Change in Feed Flow Rate and a ±30% Step Change in Feed Compositions of Benzene, Toluene, and o-Xylene Relative Error (%) Scenario +10% F

−10% F

+30% ZB

−30% ZB

+30% ZT

−30% ZT

+30% ZX

−30% ZX

Product

TDC

DTDC

SDTDC

SDTDC-FR

B T X B T X B T X B T X B T X B T X B T X B T X

0.051 −0.032 −0.041 −0.056 0.029 0.038 0.277 0.001 −0.081 −0.276 −0.006 0.089 −0.432 0.553 −0.279 0.280 −0.266 0.504 −49.580 −89.032 1.010 −0.168 0.522 −0.229

0.048 0.005 −0.006 −0.052 −0.005 0.006 −0.073 −0.131 0.040 0.119 0.138 −0.024 0.098 0.054 0.101 −0.039 0.002 −0.037 0.051 0.154 −0.018 −0.019 −0.088 0.193

0.059 0.004 −0.042 −0.064 −0.004 0.042 −0.668 −0.131 0.168 0.359 0.129 −0.158 0.283 0.056 0.301 −0.530 −0.018 −0.462 0.121 0.124 −0.840 −0.135 −0.079 0.470

0.035 0.004 −0.042 −0.037 −0.005 0.042 0.302 −0.126 0.168 −0.254 0.136 −0.158 −0.143 0.064 0.301 0.290 −0.011 −0.461 −0.059 0.123 −0.840 0.089 −0.082 0.471

in which the choice of sensitive and reference stages is also demonstrated. 3.2. Closed-Loop Evaluations of the SDTDC Proposed. The TDC, DTDC, and SDTDC schemes are sketched, respectively, in parts a−c of Figure 3. The DWDC is constructed along with the SDTDC scheme proposed using Aspen Dynamics (cf., Figure 4a), and the controller faceplates are shown in Figure 4b. A measurement delay of 60 s is involved in each temperature sensor, and all temperature related control loops are tuned by the embedded Tyreus−-Luyben rule (cf., Table 2). Figure 5 plots the transient responses of the DWDC incorporated with the SDTDC scheme proposed after facing a ±10% feed flow rate variation. The scenarios can represent generally the regulatory performance of the SDTDC scheme proposed. Note that stable control of the DWDC is achieved, giving small peak deviations and settling times in the four controlled variables. Figure 6 shows the comparisons between the DWDCs incorporated with the TDC, DTDC, and SDTDC schemes after facing a ±10% feed flow rate variation. While the dark lines indicate the responses to the positive variations, the gray lines indicate the responses to the negative ones. Negligible differences are observed between the responses of the top product. In the case of the intermediate product, oscillatory responses occur with the peak deviations in an increasing order as the TDC, DTDC, and SDTDC schemes. In the newly reached steady states, while the TDC scheme results in the greatest offsets, the other two lead to negligible ones. For the bottom product, while the TDC scheme results in the greatest peak deviations, the DTDC and SDTDC schemes leave comparable ones. In the newly reached steady states, while the DTDC scheme results in the smallest offsets, the DTDC and SDTDC schemes leave comparable ones. Table 3 shows the relative static offsets. The TDC scheme retains all

Figure 6. Comparison between the DWDCs incorporated with the TDC, DTDC, and SDTDC schemes after facing a ±10% feed flow rate variation.

3. CONTROL OF A DWDC FRACTIONATING A B/T/X MIXTURE WITH THE SDTDC SCHEME PROPOSED 3.1. Problem Description and Process Development. In Table 1, the relevant operating conditions and product specifications are tabulated. Aspen Plus is adopted to simulate the DWDC, and the Chao-Seader model to predict the vapor−liquid equilibrium relationship. As sketched in Figure 2a, the optimum DWDC is yielded as per a simple search procedure from our earlier work.9 (It is actually extremely similar to the one derived by Ling and Luyben.) The temperature profiles of the prefractionator and MDC involved are delineated in Figure 2b, 15974



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Figure 7. Transient responses of the DWDC incorporated with the SDTDC scheme after facing a ±30% variation in benzene feed composition.

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Figure 8. Comparison between the DWDCs incorporated with the TDC, DTDC, and SDTDC schemes after facing a ±30% variation in feed compositions: (a) benzene, (b) toluene, (c) o-xylene.

products within 99% ± 0.056%, the DTDC scheme within 99% ± 0.052%, and the SDTDC scheme within 99% ± 0.064%. Despite the fact that the SDTDC scheme shows a slightly larger variability than the TDC scheme, they deliver actually quite comparable performance. In Figure 7, the transient responses of the DWDC, incorporated with the SDTDC scheme proposed, are displayed after it has been subjected to a ±30% variation in benzene feed composition. The other components remain at the same ratio as in the nominal steady state. The so large disturbances are chosen here to ascertain mainly the regulation capability of the SDTDC scheme proposed. Stable regulations of the DWDC are again attained. In Figure 8, the comparisons between the transient responses of the DWDCs, incorporated with the TDC, DTDC, and SDTDC schemes, are performed after the processes have been subjected to a ±30% variation in feed compositions. Here, those components unperturbed remain at the same ratio as in the nominal steady state. For the positive variation in o-xylene feed composition, the TDC scheme is unable to attenuate the disturbance and gives great sudden drops in the top and intermediate products and a great sudden rise in the bottom product. The DTDC and SDTDC schemes, nevertheless, still do a good job and maintain stable operations of the DWDC. The SDTDC

scheme gives rise to slightly greater static offsets than the TDC scheme in the top and bottom products. In the face of variation in benzene feed composition while the same tendency occurs in the intermediate product, the reverse is true in the face of variations in toluene and o-xylene feed compositions. In comparison with the DTDC scheme, the SDTDC scheme leads to almost the same static offsets in the intermediate product but slightly amplified ones in the other products. Table 3 lists also the relative static offsets. The TDC scheme retains all products within 99% ± 89.032%, the DTDC scheme within 99% ± 0.193%, and the SDTDC scheme within 99% ± 0.84%.

4. DISCUSSION With reference to the DWDC studied, the SDTDC scheme has been found to be superior to the TDC scheme. Although they share an equal number of temperature measurements, the SDTDC scheme leads to not only comparable or even reduced static offsets in the three products but also enhanced capabilities of rejecting feed composition disturbances. The improvements are considered to stem from the strict control of the two sections along the dividing wall. One may argue that through subtle controller tuning, the TDC scheme can also have the same capabilities of rejecting feed composition disturbances. There certainly 15976



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exists such a possibility; however, the related work on controller tuning could be extremely troublesome and time-consuming. The comparison reveals again the merits of the SDTDC scheme proposed here. The SDTDC scheme is also found to be slightly inferior to the DTDC scheme, and this is aroused definitely by the adoption of two TC loops in the RSS. In view of the reduced capital cost and alleviated complication in the control configuration, the SDTDC scheme should be considered as a competitive alternative to the DTDC scheme. It is worth indicating here that the SDTDC scheme can be further reinforced through the formation of one or two TDC loops in the RSS with the available temperature measurements in the two sections along the dividing wall. This can not only improve control system performance but also add to the diversity of the proposed control strategy. One of the schemes (i.e., the SDTDC-FR scheme) is found to be effective for the DWDC studied and sketched in Figure 9. The SDTDC-FR scheme forms one TDC loop with the top temperature measurement in the prefractionator (indicated here by bold dashed lines). The temperature related controllers are retuned (cf., Table 2). The transient responses of the DWDC, incorporated with the SDTDC and SDTDC-FR schemes, are depicted in Figure 10, after encountering a ±30% feed composition variation. The reinforcement results in relatively smaller static offsets in the top product

Figure 9. Further reinforcement of the SDTDC scheme (SDTDC-FR).

Figure 10. Comparison between the DWDCs incorporated with the SDTDC and SDTDC-FR schemes after facing a ±30% variation in feed compositions: (a) benzene, (b) toluene, and (c) o-xylene. 15977



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5. CONCLUSION In the current study, a SDTDC scheme has been devised for the DWDC, which comprises two TC and two DTDC loops. While the two TC loops are designed for controlling the top and bottom products, the two DTDC loops are designed for the tight regulation of the prefractionator and intermediate product. This design philosophy can allow tight control of the DWDC with the smallest number of temperature measurements and consequently the smallest engineering efforts in control system development (as far as the DTDC scheme is concerned). In terms of the establishment of TDC loops in the RSS with the available temperature measurements in the other sections, the performance of the SDTDC scheme can be further enhanced, and this enriches the variety of the proposed control strategy. A systematic approach is given finally for seeking tight control of the DWDC with as a small number of temperature measurements as small a number. In terms of the DWDC fractionating a B/T/X mixture, the SDTDC scheme is found to outperform the TDC scheme. Not only are comparable or even reduced static offsets obtained in the three products, but also enhanced capability of handling feed composition disturbances is gained. Despite the fact that the SDTDC scheme presents slightly greater static offsets than the DTDC scheme in the three products, the differences are actually rather small. These properties render the SDTDC scheme to be a competitive alternative for the control of the DWDC.

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ASSOCIATED CONTENT

S Supporting Information *

Problem description and process design, and closed-loop evalutations and further reinforcement of the SDTDC proposed. This material is available free of charge via the Internet at http:// pubs.acs.org.

Figure 11. Systematic approach to control system development for the DWDC.

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than before, and the detailed relatively static offsets of the SDTDC−-FR schemes can also be found in Table 3. This outcome indicates that it is frequently beneficial to consider such reinforcement in the control system synthesis and design. Because the DTDC scheme involves uniformly three temperature measurements in each control loop, it belongs to a kind of symmetrical control structure. On the contrary, the SDTDC scheme belongs to a kind of asymmetrical control structure. With the knowledge of symmetrical and asymmetrical control structures for the DWDC, we can now address the issue of securing tight product control of the DWDC with as small a number of temperature measurements as possible. No studies have been found to focus on this issue so far. A systematic approach to the development of the DTDC (or SDTDC) scheme is devised and shown in Figure 11. Note that the design of the DTDC scheme should start from the corresponding asymmetrical control structure because it needs the smallest number of temperature measurements. Only when the asymmetrical control structure fails to meet the required performance (e.g., maximal and static deviations in the three products) should the reinforcement be considered through the formation of the TDC or DTDC loops in the RSS with the available temperature measurements in the other sections or the addition of new temperature measurements. The conservativeness guarantees the tight control of the DWDC with as small a number of temperature measurements as possible. The approach can also be employed for the development of the TDC scheme in a straightforward manner.

AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research funding is from the National Science Foundation of China (21076015 and 21376018) and the Doctoral Programs Foundation of the Ministry of Education of China (20100010110008). Valuable comments and suggestions by the anonymous reviewers resulted in a much improved paper.

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REFERENCES

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(6) Diggelen, R. C.; Kiss, A. A.; Heemink, A. W. Comparison of Control Strategies for Dividing-Wall Columns. Ind. Eng. Chem. Res. 2010, 49, 288. (7) Kiss, A. A.; Bildea, C. S. A Control Perspective on Process Intensification in Dividing-Wall Columns. Chem. Eng. Proc. 2011, 50, 281. (8) Zavala-Guzmán, A. M.; Hernández-Escoto, H.; Hernández, S.; Segovia-Hernández, J. G. Conventional Proportional-Integral (PI) Control of Dividing Wall Distillation Columns: Systematic Tuning. Ind. Eng. Chem. Res. 2012, 51, 10869. (9) 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.

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Operation of Dividing-Wall Distillation Columns. 3. A Simplified Double

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