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Comparing Temperature Difference Control Schemes for Dividing-Wall Distillation Columns
Krist V. Gernaey, Jakob K. Huusom and Rafiqul Gani (Eds.), 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering. 31 May – 4 June 2015, Copenhagen, Denmark © 2015 Elsevier B.V. All rights reserved.
Comparing Temperature Difference Control Schemes for Dividing-Wall Distillation Columns Yang Yuana, Haisheng Chena, Jieping Yua, and Kejin Huanga, * a
College of Information Science and Technology, Beijing University of Chemical Technology, 15 beisanhuan east road, chaoyang district, Beijing 100029, P.R. China *[email protected]
Abstract The operation of a DWDC, fractionating an ideal ternary mixture of hypothetical components A, B, and C, is studied to compare various temperature difference control schemes proposed so far, including temperature difference control (TDC) scheme, simplified temperature difference control (STDC) scheme, double temperature difference control (DTDC) scheme and simplified double temperature difference control (SDTDC) scheme. The nearly similar system performance of the STDC and SDTDC schemes to the TDC and DTDC schemes, respectively, indicates the great importance to control strictly the two sections along the dividing wall. With the two intermediate sections tightly controlled, the operation of the rectifying and stripping sections should then be tightened to improve further system performance. This gives rise to a novel SDTDC scheme involving two DTDC and two TDC loops, which enriches the potential alternatives to control the DWDC. Keywords: DWDC, temperature control, temperature difference control, double temperature difference control, simplified double temperature difference control.
1. Introduction Although dividing-wall distillation columns (DWDCs) can economize 30 % equipment investment and operation cost as compared with the conventional two-column separation sequences in the separations of ternary mixtures, their industrial applications are rather limited due to the complicated process dynamics and control difficulties involved. Many studies have conducted so far, but they focused merely on specific control problems (Kiss and Bildea, 2011; Wang and Wong, 2007). Ling and Luyben (2009) proposed a control structure with four manipulated variables (i.e., reflux flow rate, side-stream flow rate, reboiler heat duty, and liquid split ratio) to control the purities of the top, intermediate, and bottom products. Its major advantages lay in the capability of minimalizing reboiler heat duty. Later, they employed a temperature control (TC) and temperature difference control (TDC) schemes to achieve the same purpose. It was found that while the latter could tolerate 20 % feed composition disturbances the former could not (Ling and Luyben, 2010). Luan et al. (2013) indicated the importance of tight control of the two sections along the dividing wall and developed accordingly a simplified temperature difference control (STDC) scheme. Due to the addition of two temperature measurements, the STDC scheme was demonstrated to be superior to the TC scheme. Wu et al. (2013) devised a double temperature difference control (DTDC) scheme with 12 temperature measurements. It was characterized by great capability of suppressing steady-state deviations and rejecting feed composition disturbances. To reduce its temperature measurements, we recently proposed a simplified double temperature difference control (SDTDC) scheme with 8
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temperature measurements. Similar to the DTDC scheme, it still featured relatively great capability of suppressing steady-state deviations and rejecting feed composition disturbances (Yuan and Huang, 2014). In what follows, the operation of a DWDC separating an ideal ternary mixture of hypothetical components A, B, and C is studied. The purpose is to make a systematic comparison between the TDC, STDC, DTDC, and SDTDC schemes proposed so far and draw potentially useful guidelines for the synthesis and design of control systems for the DWDC.
2. A DWDC Fractionating a Ternary Mixture of Hypothetical Components A, B, and C The vapor-liquid equilibrium relationship is expressed by
Pj
yi , j
x A, j PAs xB , j PBs xC , j PCs
xi , j Pi ,s j / Pj
M1
(1)
L $%&DQGM1
(2)
The vapor saturation pressure can be estimated with the following equation
lnPi ,sj
Avp ,i Bvp ,i / T j
L $%&DQGM1
(3)
Table 1 summarizes the operating conditions and design specifications for the DWDC to be developed. The commercial software Aspen Plus is used to perform steady-state simulation. A stripping distillation column with only a reboiler, two paralleled absorber distillation columns with neither reboiler nor condenser, and a rectifying distillation column with only a condenser are employed to construct the DWDC. The design of the DWDC is conducted via a simple search procedure proposed in our earlier work and the minimization of total annual cost is chosen as the objective function for process screening (Wang et al., 2011). The resultant DWDC is sketched in Figure 1a. Table 1. Operating Conditions and Design Specifications for the DWDC Parameter Condenser pressure (bar) Stage pressure drop (bar) Feed A compositions B (mol %) C Feed flow rate (kmol/s) Feed thermal condition (liquid fraction)
Value 3 6.8901×10–3 33.33 33.33 33.34 1
Parameter Vapor pressure constants Product specifications (mol %)
1
Relative volatility A:B:C
A(Avp/Bvp) B(Avp/Bvp) C(Avp/Bvp) A B C
Value 13.04/3862 12.34/3862 11.65/3862 99 99 99 4:2:1
3. Various Temperature Difference Control Schemes Proposed for the DWDC Figures 1b to 1e sketches, respectively, the TDC, STDC, DTDC, and SDTDC schemes to be studied in the current work. The TDC scheme contains four TDC loops. For the STDC scheme, while two TDC loops are used in the two sections along the dividing wall, two TC loops in the rectifying and striping sections, respectively. The DTDC scheme involves four DTDC loops. In the SDTDC scheme, while two DTDC loops are used in the two sections along the dividing wall, two TC loops in the rectifying and
Comparing Temperature Difference Control Schemes for Dividing-Wall Distillation Columns
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striping sections, respectively. In all these control schemes, the controlled variables are paired with the nearest manipulated variables in locations (i.e., TR/ǻTR/ǻ2TR–D, TS/ǻTS/ǻ2TS–QRǻ7I/ǻ2TI–I, and ǻ7P/ǻ2TP–RL). They are justified, however, by static and dynamic analysis and/or closed-loop operability studies and detailed outcomes can be found, elsewhere (Luan et al., 2013; Wu et al., 2013; Yuan and Huang, 2014). PC
P = 3 bar
RL 10
R = 1.19 kmol/s D = 0.335 kmol/s XD,A = 0.99 12 XD,B = 0.01 XD,C = 0 P13 13
RL = LP13/L12 = 0.385 F = 1 kmol/s q=1 A/B/C = 23 0.3333/0.3333/0.3334 P27
F
+
I = 0.33 kmol/s XI,A = 0.004 XI,B = 0.99 XI,C = 0.006
P39 39
TDC4 – ǻTP22
P22 35
FC
B = 0.335 kmol/s XB,A = 0 XB,B = 0.01 XB,C = 0.99
QR = 44.75 MW
40
– +
2 RL 10
+
P30
–
ǻT46
26
35
+ + – – +
35
– +
T46
46
ǻ2T35 DTDC2
F
DTDC4 ǻ2TP22
+ – –
P14
+
P30
B
(c)
LC1 R
D
35
46
B
+ –
39
FC
RL 10 T10
21
P22
2 + –– ǻ T46 DTDC3 +
LC2
TC2
LC2
RL 10
I
ǻT35 TDC1
FC
R
DTDC1
I
PC
D
P22
TDC3
B
+ – –
TC1
P14
+
TDC2
TDC2 ǻTP22
T10
LC1
ǻ2T10 21
39 40 46 52
FC
ǻT35
F
PC
R
P14 P18 P22
–
LC1
+ – –
I
(b)
PC
ǻ2TP22
TDC1
LC2
(a)
DTDC4
ǻT10
– 26
D
RL 10
+
46 +
52
R
D
P14 P18
40
F
LC1
R
RR = 3.56
2
RV = VP39/V40 = 0.61
PC LC1
QC = 44.33 MW
– +
TC1
DTDC2 I
ǻ2T35 DTDC2
T46
F
ǻ2TP22
+ – –
P14 P18 P22
+
P30
35 39
FC
40
TC3
LC2
21
46
B
D
+ ǻT10
– +
–
ǻ2T35
– +
TDC1 I
DTDC1
– ǻT46 TDC2 +
LC2
B
(d) (e) (f) Figure 1. (a) Optimum design of the DWDC, (b) TDC scheme, (c) STDC scheme, (d) DTDC scheme, (e) SDTDC scheme (f) novel SDTDC scheme Table 2. Controller Parameters for the TDC, STDC, DTDC, SDTDC DQG 16'7'& Schemes Scheme
Controller TDC1 TDC2 TDC TDC3 TDC4 DTDC1 DTDC2 DTDC DTDC3 DTDC4 TDC1 16'7'& TDC2
KC 0.279 0.745 0.365 0.524 0.123 0.202 0.040 0.700 0.208 0.359
TI (min) 14.520 17.160 10.560 19.800 14.520 17.160 10.560 19.800 13.200 9.240
Scheme
Controller TC1 TC2 STDC TDC1 TDC2 TC1 TC2 SDTDC DTDC1 DTDC2 DTDC1 16'7'& DTDC2
KC 3.632 4.020 0.731 0.508 0.123 0.040 0.202 0.700 0.195 0.752
TI (min) 13.200 7.920 18.480 21.120 14.520 10.160 17.160 19.800 17.160 19.800
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4. Comparison of Various Temperature Difference Control Schemes Proposed Closed-loop operations of the DWDC, controlled, respectively, with the TDC, STDC, DTDC, and SDTDC schemes are simulated with the commercial software Aspen Dynamics. All temperature sensors contain a 1-min dead-time element and all the temperature/temperature difference/double temperature difference loops are tuned with the built-in Tyreus-Luyben rule. The detailed parameters are summarized in Table 2.
(a)
(b)
(c) Figure 2. Comparison of various temperature difference control schemes in face of a ±30 % step change in feed compositions of components A, B, and C: (a) component A, (b) component B, (c) component C
Comparing Temperature Difference Control Schemes for Dividing-Wall Distillation Columns
1497
In Figure 2, the comparisons of the closed-loop responses of the DWDCs, controlled, respectively, with the TDC, STDC, DTDC, and SDTDC schemes are depicted after the processes have been subjected to a ±30 % step change in feed compositions of components A, B, and C. While the dark lines indicate the responses to the positive changes, the gray lines to the negative ones. The TDC scheme is failed to suppress the disturbances in the cases of positive change in feed compositions of components A and B and negative change in feed compositions of component C. The STDC scheme is unable to reject the disturbances in the case of positive change in feed compositions of component B and negative change in feed compositions of component C. With the inclusion of 4 and 2 temperature measurements, the DTDC and SDTDC schemes can do a better job because they can now suppress a ±30% step change in feed compositions of components A, B, and C. In particular, the DTDC scheme displays smaller steady-state deviations in the three products for step change in feed compositions of components A and C but slightly bigger ones for step change in feed compositions of component B than the SDTDC scheme. Table 3 shows the relative static errors in more detail. Table 3. Relative Static Errors for a ±30 % Step Change in Feed Compositions of Components A, B, and C Relative static error (%) Scenario Product STDC TDC SDTDC DTDC 16'7'& A –1.506 0.001 –0.895 0.106 0.652 +30% ZA B –1.649 –33.776 –0.198 –0.259 –0.445 C 0.127 –3.843 0.184 0.052 –0.143 A 0.498 –0.137 0.486 0.251 –0.154 –30% ZA B 0.305 0.365 0.192 0.241 0.277 C –0.114 0.082 –0.136 –0.036 0.127 A 0.323 –0.501 0.382 0.198 –0.061 +30% ZB B –0.645 –1.098 0.049 0.084 0.099 C 0.226 –0.106 0.257 0.108 –0.057 A –0.782 0.416 –0.791 –0.006 0.413 –30% ZB B 0.082 0.272 –0.033 0.018 0.031 C –0.361 0.222 –0.363 –0.104 0.167 A 0.243 0.101 0.159 0.057 –0.159 +30% ZC B 0.506 0.580 0.168 0.185 0.221 C –0.492 0.374 –0.603 –0.113 0.487 A –0.007 –5.734 –0.184 –0.001 0.187 –30% ZC B –29.316 –19.716 –0.092 –0.103 –0.122 C 0.467 –0.146 0.366 0.166 –0.116
5. Discussions Generally speaking, the SDTDC scheme can be described to lead to comparable regulatory control performance with the DTDC scheme for a ±30 % disturbance in feed compositions of components A, B, and C. Luan et al. (2013) once demonstrated that the STDC scheme could achieve similar regulatory control performances with the TDC scheme for a ±20 % step change in feed compositions of components A, B, and C. These combined results indicate that for the effective operation of the DWDC it is
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extremely important to give strict control of the two sections along the dividing wall and it should be ranked as the WRSSULRULW\LQFRQWUROV\VWHPV\QWKHVLVDQGGHVLJQ1RWH the fact that the SDTDC scheme is superior to the STDC scheme coincides also with this interpretation. In case of employing four or more temperature measurements to the two sections along the dividing wall, little enhancement can, however, be secured. Therefore, the DTDC loop should be the best option here. In Table 3, it can be further observed that the relative static errors in the three products of the DTDC/TDC schemes are smaller than those of the SDTDC/STDC schemes. The result reminds us of the fact that controlling strictly the rectifying and stripping sections helps to improve system performance and it should be taken into account if further improvement is expected from the control system performance of the SDTDC scheme. A novel SDTDC scheme 16'7'& ZLWK WZR TDC loops in the rectifying and stripping sections is thus derived as shown in Figure 1f. It yields slight improvement in control system performance in comparison with the SDTDC scheme and the detailed relative static errors are listed also in Table 3.
6. Conclusions In the current study, the operation of a DWDC separating an ideal ternary mixture of hypothetical components A, B, and C has been examined with the TDC, STDC, DTDC, and SDTDC schemes, respectively. Two conclusions have been drawn on the synthesis and design of the control schemes for the DWDC. Firstly, top priority should be given to the control of the two sections along the dividing wall and usually the DTDC loops should be employed to yield tight control outcomes. Secondly, tightening the operations of the rectifying and stripping sections should then be considered if further improvement in control performance has been required. With the replacement the two TC loops in the SDTDC scheme by two TDC loops, a novel SDTDC scheme has been derived. It enriches the potential alternatives to control the DWDC.
References S. J. Wang, Wong, D. S. H., 2007, Controllability and Energy Efficiency of High Purity Divided Wall Column, Chemical Engineering Science, 62, 1010. A. A. Kiss, Bildea, C. S., 2011, A Control Perspective on Process Intensification in DividingWall Columns, Chemical Engineering and Processing: Process Intensification, 50, 281. H. Ling, Luyben, W. L., 2009, 1HZControl Structure for Divided-Wall Columns, Industrial and Engineering Chemistry Research, 48, 6034. H. Ling, Luyben, W. L., 2010, Temperature Control of the BTX Divided-Wall Column, Industrial and Engineering Chemistry Research, 49, 189. 6 /XDQ +XDQJ . :X 1 2SHUDWLRQ RI 'LYLGLQJ-Wall Distillation Columns. 1. A Simplified Temperature Difference Control Scheme, Industrial and Engineering Chemistry Research, 52, 2642. 1 :X +XDQJ . /XDQ 6 2SHUDWLRQ RI 'LYLGLQJ-Wall Distillation Columns. 2. A Double Temperature Difference Control Scheme, Industrial and Engineering Chemistry Research, 52, 5365. Y. Yuan, Huang, K., 2014, Operation of Dividing-Wall Distillation Columns. 3. A Simplified Double Temperature Difference Control Scheme, Industrial and Engineering Chemistry Research, 53, 15969. P. Wang, Chen, H., Wang, Y., Zhang, L., Huang, K., Wang, S. J., 2011, A Simple Algorithm for the Design of Fully Thermally Coupled Distillation Columns (FTCDC), Chemical Engineering Communication, 199, 608.
Comparing Temperature Difference Control Schemes for Dividing-Wall Distillation Columns Yang Yuana, Haisheng Chena, Jieping Yua, and Kejin Huanga, * a
College of Information Science and Technology, Beijing University of Chemical Technology, 15 beisanhuan east road, chaoyang district, Beijing 100029, P.R. China *[email protected]
Abstract The operation of a DWDC, fractionating an ideal ternary mixture of hypothetical components A, B, and C, is studied to compare various temperature difference control schemes proposed so far, including temperature difference control (TDC) scheme, simplified temperature difference control (STDC) scheme, double temperature difference control (DTDC) scheme and simplified double temperature difference control (SDTDC) scheme. The nearly similar system performance of the STDC and SDTDC schemes to the TDC and DTDC schemes, respectively, indicates the great importance to control strictly the two sections along the dividing wall. With the two intermediate sections tightly controlled, the operation of the rectifying and stripping sections should then be tightened to improve further system performance. This gives rise to a novel SDTDC scheme involving two DTDC and two TDC loops, which enriches the potential alternatives to control the DWDC. Keywords: DWDC, temperature control, temperature difference control, double temperature difference control, simplified double temperature difference control.
1. Introduction Although dividing-wall distillation columns (DWDCs) can economize 30 % equipment investment and operation cost as compared with the conventional two-column separation sequences in the separations of ternary mixtures, their industrial applications are rather limited due to the complicated process dynamics and control difficulties involved. Many studies have conducted so far, but they focused merely on specific control problems (Kiss and Bildea, 2011; Wang and Wong, 2007). Ling and Luyben (2009) proposed a control structure with four manipulated variables (i.e., reflux flow rate, side-stream flow rate, reboiler heat duty, and liquid split ratio) to control the purities of the top, intermediate, and bottom products. Its major advantages lay in the capability of minimalizing reboiler heat duty. Later, they employed a temperature control (TC) and temperature difference control (TDC) schemes to achieve the same purpose. It was found that while the latter could tolerate 20 % feed composition disturbances the former could not (Ling and Luyben, 2010). Luan et al. (2013) indicated the importance of tight control of the two sections along the dividing wall and developed accordingly a simplified temperature difference control (STDC) scheme. Due to the addition of two temperature measurements, the STDC scheme was demonstrated to be superior to the TC scheme. Wu et al. (2013) devised a double temperature difference control (DTDC) scheme with 12 temperature measurements. It was characterized by great capability of suppressing steady-state deviations and rejecting feed composition disturbances. To reduce its temperature measurements, we recently proposed a simplified double temperature difference control (SDTDC) scheme with 8
1494
Y. Yuan et al.
temperature measurements. Similar to the DTDC scheme, it still featured relatively great capability of suppressing steady-state deviations and rejecting feed composition disturbances (Yuan and Huang, 2014). In what follows, the operation of a DWDC separating an ideal ternary mixture of hypothetical components A, B, and C is studied. The purpose is to make a systematic comparison between the TDC, STDC, DTDC, and SDTDC schemes proposed so far and draw potentially useful guidelines for the synthesis and design of control systems for the DWDC.
2. A DWDC Fractionating a Ternary Mixture of Hypothetical Components A, B, and C The vapor-liquid equilibrium relationship is expressed by
Pj
yi , j
x A, j PAs xB , j PBs xC , j PCs
xi , j Pi ,s j / Pj
M1
(1)
L $%&DQGM1
(2)
The vapor saturation pressure can be estimated with the following equation
lnPi ,sj
Avp ,i Bvp ,i / T j
L $%&DQGM1
(3)
Table 1 summarizes the operating conditions and design specifications for the DWDC to be developed. The commercial software Aspen Plus is used to perform steady-state simulation. A stripping distillation column with only a reboiler, two paralleled absorber distillation columns with neither reboiler nor condenser, and a rectifying distillation column with only a condenser are employed to construct the DWDC. The design of the DWDC is conducted via a simple search procedure proposed in our earlier work and the minimization of total annual cost is chosen as the objective function for process screening (Wang et al., 2011). The resultant DWDC is sketched in Figure 1a. Table 1. Operating Conditions and Design Specifications for the DWDC Parameter Condenser pressure (bar) Stage pressure drop (bar) Feed A compositions B (mol %) C Feed flow rate (kmol/s) Feed thermal condition (liquid fraction)
Value 3 6.8901×10–3 33.33 33.33 33.34 1
Parameter Vapor pressure constants Product specifications (mol %)
1
Relative volatility A:B:C
A(Avp/Bvp) B(Avp/Bvp) C(Avp/Bvp) A B C
Value 13.04/3862 12.34/3862 11.65/3862 99 99 99 4:2:1
3. Various Temperature Difference Control Schemes Proposed for the DWDC Figures 1b to 1e sketches, respectively, the TDC, STDC, DTDC, and SDTDC schemes to be studied in the current work. The TDC scheme contains four TDC loops. For the STDC scheme, while two TDC loops are used in the two sections along the dividing wall, two TC loops in the rectifying and striping sections, respectively. The DTDC scheme involves four DTDC loops. In the SDTDC scheme, while two DTDC loops are used in the two sections along the dividing wall, two TC loops in the rectifying and
Comparing Temperature Difference Control Schemes for Dividing-Wall Distillation Columns
1495
striping sections, respectively. In all these control schemes, the controlled variables are paired with the nearest manipulated variables in locations (i.e., TR/ǻTR/ǻ2TR–D, TS/ǻTS/ǻ2TS–QRǻ7I/ǻ2TI–I, and ǻ7P/ǻ2TP–RL). They are justified, however, by static and dynamic analysis and/or closed-loop operability studies and detailed outcomes can be found, elsewhere (Luan et al., 2013; Wu et al., 2013; Yuan and Huang, 2014). PC
P = 3 bar
RL 10
R = 1.19 kmol/s D = 0.335 kmol/s XD,A = 0.99 12 XD,B = 0.01 XD,C = 0 P13 13
RL = LP13/L12 = 0.385 F = 1 kmol/s q=1 A/B/C = 23 0.3333/0.3333/0.3334 P27
F
+
I = 0.33 kmol/s XI,A = 0.004 XI,B = 0.99 XI,C = 0.006
P39 39
TDC4 – ǻTP22
P22 35
FC
B = 0.335 kmol/s XB,A = 0 XB,B = 0.01 XB,C = 0.99
QR = 44.75 MW
40
– +
2 RL 10
+
P30
–
ǻT46
26
35
+ + – – +
35
– +
T46
46
ǻ2T35 DTDC2
F
DTDC4 ǻ2TP22
+ – –
P14
+
P30
B
(c)
LC1 R
D
35
46
B
+ –
39
FC
RL 10 T10
21
P22
2 + –– ǻ T46 DTDC3 +
LC2
TC2
LC2
RL 10
I
ǻT35 TDC1
FC
R
DTDC1
I
PC
D
P22
TDC3
B
+ – –
TC1
P14
+
TDC2
TDC2 ǻTP22
T10
LC1
ǻ2T10 21
39 40 46 52
FC
ǻT35
F
PC
R
P14 P18 P22
–
LC1
+ – –
I
(b)
PC
ǻ2TP22
TDC1
LC2
(a)
DTDC4
ǻT10
– 26
D
RL 10
+
46 +
52
R
D
P14 P18
40
F
LC1
R
RR = 3.56
2
RV = VP39/V40 = 0.61
PC LC1
QC = 44.33 MW
– +
TC1
DTDC2 I
ǻ2T35 DTDC2
T46
F
ǻ2TP22
+ – –
P14 P18 P22
+
P30
35 39
FC
40
TC3
LC2
21
46
B
D
+ ǻT10
– +
–
ǻ2T35
– +
TDC1 I
DTDC1
– ǻT46 TDC2 +
LC2
B
(d) (e) (f) Figure 1. (a) Optimum design of the DWDC, (b) TDC scheme, (c) STDC scheme, (d) DTDC scheme, (e) SDTDC scheme (f) novel SDTDC scheme Table 2. Controller Parameters for the TDC, STDC, DTDC, SDTDC DQG 16'7'& Schemes Scheme
Controller TDC1 TDC2 TDC TDC3 TDC4 DTDC1 DTDC2 DTDC DTDC3 DTDC4 TDC1 16'7'& TDC2
KC 0.279 0.745 0.365 0.524 0.123 0.202 0.040 0.700 0.208 0.359
TI (min) 14.520 17.160 10.560 19.800 14.520 17.160 10.560 19.800 13.200 9.240
Scheme
Controller TC1 TC2 STDC TDC1 TDC2 TC1 TC2 SDTDC DTDC1 DTDC2 DTDC1 16'7'& DTDC2
KC 3.632 4.020 0.731 0.508 0.123 0.040 0.202 0.700 0.195 0.752
TI (min) 13.200 7.920 18.480 21.120 14.520 10.160 17.160 19.800 17.160 19.800
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4. Comparison of Various Temperature Difference Control Schemes Proposed Closed-loop operations of the DWDC, controlled, respectively, with the TDC, STDC, DTDC, and SDTDC schemes are simulated with the commercial software Aspen Dynamics. All temperature sensors contain a 1-min dead-time element and all the temperature/temperature difference/double temperature difference loops are tuned with the built-in Tyreus-Luyben rule. The detailed parameters are summarized in Table 2.
(a)
(b)
(c) Figure 2. Comparison of various temperature difference control schemes in face of a ±30 % step change in feed compositions of components A, B, and C: (a) component A, (b) component B, (c) component C
Comparing Temperature Difference Control Schemes for Dividing-Wall Distillation Columns
1497
In Figure 2, the comparisons of the closed-loop responses of the DWDCs, controlled, respectively, with the TDC, STDC, DTDC, and SDTDC schemes are depicted after the processes have been subjected to a ±30 % step change in feed compositions of components A, B, and C. While the dark lines indicate the responses to the positive changes, the gray lines to the negative ones. The TDC scheme is failed to suppress the disturbances in the cases of positive change in feed compositions of components A and B and negative change in feed compositions of component C. The STDC scheme is unable to reject the disturbances in the case of positive change in feed compositions of component B and negative change in feed compositions of component C. With the inclusion of 4 and 2 temperature measurements, the DTDC and SDTDC schemes can do a better job because they can now suppress a ±30% step change in feed compositions of components A, B, and C. In particular, the DTDC scheme displays smaller steady-state deviations in the three products for step change in feed compositions of components A and C but slightly bigger ones for step change in feed compositions of component B than the SDTDC scheme. Table 3 shows the relative static errors in more detail. Table 3. Relative Static Errors for a ±30 % Step Change in Feed Compositions of Components A, B, and C Relative static error (%) Scenario Product STDC TDC SDTDC DTDC 16'7'& A –1.506 0.001 –0.895 0.106 0.652 +30% ZA B –1.649 –33.776 –0.198 –0.259 –0.445 C 0.127 –3.843 0.184 0.052 –0.143 A 0.498 –0.137 0.486 0.251 –0.154 –30% ZA B 0.305 0.365 0.192 0.241 0.277 C –0.114 0.082 –0.136 –0.036 0.127 A 0.323 –0.501 0.382 0.198 –0.061 +30% ZB B –0.645 –1.098 0.049 0.084 0.099 C 0.226 –0.106 0.257 0.108 –0.057 A –0.782 0.416 –0.791 –0.006 0.413 –30% ZB B 0.082 0.272 –0.033 0.018 0.031 C –0.361 0.222 –0.363 –0.104 0.167 A 0.243 0.101 0.159 0.057 –0.159 +30% ZC B 0.506 0.580 0.168 0.185 0.221 C –0.492 0.374 –0.603 –0.113 0.487 A –0.007 –5.734 –0.184 –0.001 0.187 –30% ZC B –29.316 –19.716 –0.092 –0.103 –0.122 C 0.467 –0.146 0.366 0.166 –0.116
5. Discussions Generally speaking, the SDTDC scheme can be described to lead to comparable regulatory control performance with the DTDC scheme for a ±30 % disturbance in feed compositions of components A, B, and C. Luan et al. (2013) once demonstrated that the STDC scheme could achieve similar regulatory control performances with the TDC scheme for a ±20 % step change in feed compositions of components A, B, and C. These combined results indicate that for the effective operation of the DWDC it is
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Y. Yuan et al.
extremely important to give strict control of the two sections along the dividing wall and it should be ranked as the WRSSULRULW\LQFRQWUROV\VWHPV\QWKHVLVDQGGHVLJQ1RWH the fact that the SDTDC scheme is superior to the STDC scheme coincides also with this interpretation. In case of employing four or more temperature measurements to the two sections along the dividing wall, little enhancement can, however, be secured. Therefore, the DTDC loop should be the best option here. In Table 3, it can be further observed that the relative static errors in the three products of the DTDC/TDC schemes are smaller than those of the SDTDC/STDC schemes. The result reminds us of the fact that controlling strictly the rectifying and stripping sections helps to improve system performance and it should be taken into account if further improvement is expected from the control system performance of the SDTDC scheme. A novel SDTDC scheme 16'7'& ZLWK WZR TDC loops in the rectifying and stripping sections is thus derived as shown in Figure 1f. It yields slight improvement in control system performance in comparison with the SDTDC scheme and the detailed relative static errors are listed also in Table 3.
6. Conclusions In the current study, the operation of a DWDC separating an ideal ternary mixture of hypothetical components A, B, and C has been examined with the TDC, STDC, DTDC, and SDTDC schemes, respectively. Two conclusions have been drawn on the synthesis and design of the control schemes for the DWDC. Firstly, top priority should be given to the control of the two sections along the dividing wall and usually the DTDC loops should be employed to yield tight control outcomes. Secondly, tightening the operations of the rectifying and stripping sections should then be considered if further improvement in control performance has been required. With the replacement the two TC loops in the SDTDC scheme by two TDC loops, a novel SDTDC scheme has been derived. It enriches the potential alternatives to control the DWDC.
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