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Configuring Effectively Double Temperature Difference Control Schemes for Distillation Columns Yang Yuan, Kejin Huang, Haisheng Chen, Liang Zhang, and Shaofeng Wang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02542 • Publication Date (Web): 20 Jul 2017 Downloaded from http://pubs.acs.org on July 31, 2017

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Industrial & Engineering Chemistry Research

Configuring Effectively Double Temperature Difference Control Schemes for Distillation Columns

Yang Yuan, Kejin Huang∗, Haisheng Chen, Liang Zhang, and Shaofeng Wang College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, P. R. China

∗

Phone: +86–10–64437805. Fax: +86–10–64437805. E-mail: [email protected]. 1

ACS Paragon Plus Environment


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Abstract: The conventional method for configuring double temperature difference control (DTDC) schemes relies on sensitivity analysis (SA) and singular value decomposition (SVD) analysis, respectively, to determine sensitive and reference stages. Since no considerations are given at all to the interactions between the synthesized double temperature differences (DTDs) and to the coordination between the upper and lower temperature differences (TDs) subtracted in each synthesized DTD, the conventional method may lead to DTDC schemes that fail to secure tight product quality control of distillation columns. In this article, a novel method is proposed that employs a newly defined metric in our recent work, the averaged absolute variation magnitudes (ASVM), to determine the two reference stages in each DTDC loop. The ASVM measures the variations of TDs between the sensitive stage and the remaining ones with the assumption of complete rejection of all disturbances concerned and can thus reflect the inherent characteristics of coupling between the controlled product qualities. For each DTDC loop, while the first reference stage should be chosen to cope with its coupling with the other control loops, the second reference stage should be to coordinate the two TDs involved, thereby yielding a favorable effect to the inference of the controlled product qualities. Four example systems, including one conventional distillation column separating a binary mixture of ethanol and butanol, two conventional distillation columns separating a ternary mixture of ethanol, propanol, and butanol, and one dividing-wall distillation column separating a ternary mixture of ethanol, propanol, and butanol, are used to assess the proposed method by means of in-depth comparison with the conventional method. While they display comparable dynamic performances, the former leads to considerably smaller steady-state deviations in the controlled product qualities than the latter. These striking outcomes demonstrate evidently that the proposed method can be a promising alternative for the pursuit of tight temperature inferential control of various distillation columns.

Keywords: Distillation column; DTDC; SA; SVD; ASVM.

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1.

Introduction Owing to the involvement of more temperature measurements, double temperature difference control (DTDC)

schemes outperform generally temperature control schemes and temperature difference control schemes in the inferential control of various distillation columns. 1-3 Not only are the static offsets in the controlled product qualities reduced, but also the capability of rejecting feed composition disturbances is enhanced. Contrary to this common sense, we found recently in our studies about the operation of dividing-wall distillation columns (DWDCs) that some simplified DTDC schemes, which involved relatively a reduced set of temperature measurements, could still give quite similar or even better performance than the DTDC schemes.

4, 5

Gupta and Kaistha also indicated the reasonability and effectiveness of

employing simplified DTDC schemes to deal with the nonlinear effect of a benzene-toluene-xylene DWDC.

6

These

unexpected outcomes have reminded us of the drawbacks of the conventional method adopted for the synthesis and design of the DTDC schemes and stimulated us to trace the problems that caused such a deficiency. As a result, a more effective method that permits tight inferential control of various distillation columns is likely to be derived and this is the major purpose of the current study. The key for the derivation of a DTDC scheme lies in the construction of a set of effective double temperature differences (DTDs) to infer the product qualities to be controlled. Although four temperature measurements are, in principle, needed to construct a DTD, for the simplicity and economic reasons three temperature measurements are usually employed in practice, with one from the sensitive stage (SS) and two from the upper reference stage (URS) and the lower reference stage (LRS) chosen, namely, ∆2T = ∆TLRS – ∆TURS = (TLRS – TSS) – (TSS –TURS) = TLRS + TURS – 2TSS. The conventional method relies on sensitivity analysis (SA) and singular value decomposition (SVD) analysis to determine the sensitive stage and the upper and lower reference stages, respectively. For the identification of sensitive stages, many methods have been proposed so far

7, 8

and Luyben once gave a comprehensive review.

9

Generally speaking, SA is the

simplest and mostly-used method and can yield reliable outcomes for the synthesis and design of various temperature inferential control systems. Thus, the deficiency of the DTDC schemes seems to be not closely related to the identification of sensitive stages. For the determination of reference stages, no much attention has been given so far and they have frequently been determined via insightful operation analysis.

1, 2, 6

Based on SVD analysis Ling and Luyben suggested

locating their positions that yield the highest sensitivities between the temperature differences (TDs) thus formed with the given sensitive stages and the manipulated variables adopted.

10

By following exactly the same principle, Wu et al. 3



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determined the upper and lower reference stages and proposed consequently a DTDC scheme for the operation of DWDCs. 3

This represented essentially the conventional method for configuring the DTDC scheme and its deficiency should be

closely related to the determination of the upper and lower reference stages. In the remainder of this article, the drawbacks of the conventional method for configuring the DTDC scheme are firstly pointed out and a novel method that can avoid these drawbacks is then detailed in chapter 2. The advantages stem from the systematic consideration of the interactions between the synthesized DTDs and the coordination between the upper and lower temperature differences subtracted in each synthesized DTD. Four example systems, including one conventional distillation column (CDC) processing a binary mixture of ethanol and butanol, two CDCs processing a ternary mixture of ethanol, propanol, and butanol, and one DWDC processing also a ternary mixture of ethanol, propanol, and butanol, are employed to evaluate its reasonability and effectiveness through in-depth comparison with the conventional method from chapters 3 to 6. The merits and demerits of the novel method proposed are indicated in chapter 7, followed by some concluding remarks in chapter 8.

2.

A Novel Method for Configuring the DTDC Scheme for Distillation Columns 2.1. Drawbacks of the conventional method for configuring the DTDC schemes. As indicated clearly in the

preceding section, the drawbacks of the conventional method for configuring the DTDC scheme stem essentially from the determination of the upper and lower reference stages. Although SVD analysis can guarantee the high sensitivity between the temperature differences, i.e., (TLRS – TSS) or (TSS – TURS), and the manipulated variable adopted in each control loop, it gives no account at all to the interactions between all the DTDs thus established. As a result, not only can the high sensitivity between ∆2T = (TLRS – TSS) – (TSS –TURS) and the corresponding manipulated variable not be guaranteed, but also their corresponding relationship is quite likely to be distorted. This should be the first drawback of the conventional method for configuring the DTDC scheme. Since the upper and lower temperature differences, ∆TLRS = (TLRS – TSS) and ∆TURS = (TSS – TURS), are determined separately (from the two sections just above and below the given sensitive stage) based on SVD analysis, no considerations are given at all to their coordination. This may result in the degradation not only in the sensitivity between ∆2T = (TLRS – TSS) – (TSS –TURS) and the corresponding manipulated variable but also in the corresponding relationship between ∆2T = (TLRS – TSS) – (TSS –TURS) and the corresponding product quality to be controlled.

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This should be the second drawback of the conventional method for configuring the DTDC scheme. 2.2. A novel method proposed for configuring the DTDC scheme. To address the first drawback of the conventional method for configuring the DTDC scheme, we may use the performance metric proposed in our recent work, the averaged absolute variation magnitudes (ASVM), to aid the determination of the upper and lower reference stages in each control loop. 5 The ASVM is defined as in Eq. 1, which calculates the distribution of temperature difference variations between the sensitive stage and the remaining ones for a specified control loop under the assumption of complete rejection of all kinds of feed composition disturbances encountered.

ASVM =

1 2 NC ai ∆ (T − TSS )i ∑ i 2 NC

(1)

where NC is the number of feed components, and αi (i =1, …, NC) are weighting coefficients that represent the relative importance of rejecting the disturbances from feed compositions by the control scheme to be developed. With the inclusion of positive and negative changes in each feed component, the total number of scenarios in feed composition variations is thus 2NC. If the rejection of one feed composition disturbance is more important than the rejection of the other ones, a weighting coefficient greater than one should be adopted in this situation. On the contrary, if the rejection of one feed composition disturbance is less important than the rejection of the other ones, a weighting coefficient smaller than one should be adopted. However, the summation of all αi (i=1, …, 2NC) should always be equal to 2NC. Figure 1 shows two typical curves of the ASVM for the rectifying section of a CDC. Here, the sensitive stage has a zero value and is marked with the symbol of a five-pointed star. Since the coupling comes exclusively from the stripping section (because the bottom product quality needs to be controlled strictly), thus the selection of reference stages should be initiated from the section that is below the sensitive stage. Note that the ASVM increases gradually as the stage moves away from the sensitive stage and at a certain place a turning point appears (i.e., the first turning point here). By further moving away from the sensitive stage, two representative situations occur. One case is sketched in Figure 1a, where the ASVM begins to decrease and reaches a local minimum at a certain stage (notice that the first turning point becomes essentially a local maximum in this situation). The drop of the ASVM is certainly aroused by the coupling from the bottom control loop and the stage corresponding to the local minimum should certainly be regarded as the lower reference stage in this situation because the advantages of this coupling can fully be taken into account. The other case is shown in Figure 1b, where the ASVM still increases until the arrival of the second turning point. Although the coupling from the bottom control 5



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loop can be observed from the appearance of the first turning point, no favorable coupling can be obtained in the section between the first and second turning points. Therefore, the stage corresponding to the first turning point should be taken as the lower reference stage in this situation because this option suppresses, to the greatest extent, the possibly unfavorable coupling from the bottom control loop. In the case that a sensitive stage has multiple couplings with the other column sections (because their corresponding product qualities need to be controlled simultaneously), the determination of the reference stages becomes a little bit more complicated because the other column sections must also be taken into account during the selection of the reference stages. The circumstance happens, for example, to the sensitive stages that reflect the qualities of intermediate products in a nonconventional distillation column with more than three products. The sensitive stages that reflect the qualities of the intermediate products and the top product of the prefractionator in a DWDC also belong to this circumstance. Because the couplings come from the column sections above and below, they should fully be taken into account to locate the reference stages according to the method outlined above. As a result, two candidate reference stages, including one upper reference stage and one lower reference stage, are determined. Since a small ASVM implies essentially a tight product quality control, the one with the smaller ASVM should be chosen here as one of the two reference stages of a DTD, which can be either the upper reference stage or the lower reference stage in this situation. To address the second drawback of the conventional method for configuring the DTDC scheme, one needs to find a stage on the other side of the sensitive stage that shares a quite similar ASVM with the reference stage determined above. This can simply be approached by drawing a horizontal line from the ASVM of the reference stage determined above. If the reference stage determined above works to be the lower reference stage, then the horizontal line should be drawn to the left, otherwise, it should be to the right. In Figure 1a and 1b, the horizontal lines (i.e., the red dashed line here) are all drawn to the left because the reference stages already determined serve to be the lower ones in these situations. The intersection of the horizontal line with the ASVM curve above the sensitive stage then gives two candidates for the upper reference stage. In most cases, the one with the ASVM closer to the lower reference stage below the sensitive stage should be chosen. The way to coordinate the upper and lower reference stages guarantees the high sensitivity between ∆2T = (TLRS – TSS) – (TSS –TURS) and the corresponding manipulated variable and meanwhile facilitates the corresponding relationship between ∆2T = (TLRS – TSS) – (TSS –TURS) and the product quality to be controlled.

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3.

Example I: Temperature Inferential Control of a CDC Processing a Binary Mixture of Ethanol (E) and Butanol

(B) 3.1. Steady-state design. Figure 2a shows the steady-state design of the CDC and Table 1 lists its relevant operating conditions and product specifications. The CDC has 30 stages and is fed onto stage 15. Overhead pressure is set at 1 atm with a pressure drop of 0.0068 atm per stage. Feed flow rate is 1 kmol/s with a composition of 40 mol % E and 60 mol % B. The top and bottom products are all specified to be 99 mol %. In accordance with Aspen notation, top condenser is designated here as stage 1 and bottom reboiler stage 30. Throughout the article, the RadFrac module in Aspen Plus is used to establish the steady-state models and the UNIFAC model is used to estimate liquid activities. After the tray sizing of the steady-state models is accomplished, it is then converted to dynamic model in Aspen Dynamics. While the DTDC scheme by the conventional method (i.e., the combined uses of SA and SVD analysis) is denoted the DTDC-SVD scheme, the one by the novel method proposed in the current work the DTDC-ASVM scheme. The dark lines indicate the responses to the positive variations in feed compositions and the gray lines the responses to the negative variations in feed compositions. In the calculations of the ASVM, αi (i =1, …, NC) are set to be one for all feed components. 3.2. Configuring the DTDC-SVD scheme. Because there are two products to be controlled, the DTDC scheme should involve two DTDC loops with distillate flow rate D and reboiler heat duty QREB as manipulated variables (Since no substantial differences are aroused by the choice of manipulated variable between distillate flow rate D and reflux flow rate R, the former is adopted uniformly as the manipulated variable in the top control loop in all of the four examples studied). According to the SA and SVD analysis given in Supporting Information (for the sake of conciseness, the SA and SVD analysis are all comprehended here for the four separation systems examined), two DTDs, ∆2T5 = (T14 – T5) – (T5 – T2) and ∆2T26 = (T29 – T26) – (T26 – T17) are constructed and paired with D and QREB, respectively, as shown in Figure 2b. 3.3. Configuring the DTDC-ASVM scheme. With stages 5 and 26 as sensitive stages for the rectifying and stripping sections, respectively, the curves of the ASVM are drawn in Figure 3 under the assumption of complete rejection of ±10 % feed composition disturbances. With reference to Figure 3a, one can clearly see that a turning point happens at stage 8 and the ASVM reaches a local minimum at stage 15. Thus, stage 15 should be chosen as the lower reference stage in order to tap the potential of the favorable coupling from the bottom control loop (throughout the work, the upper and lower reference stages are denoted with the symbol of a red triangle). For the determination of the upper reference stage, a red

7



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dashed horizontal line is drawn to the left from the ASVM of the lower reference stage and its intersection with the curve of the ASVM above the sensitive stage locates between stages 3 and 4. Since stage 3 has an ASVM closer to the one of the lower reference stage, it is chosen here as the upper reference stage. Similarly, in accordance with Figure 3b, stages 15 and 27 should be chosen as the upper and lower reference stages in order to tap the potential of the favorable coupling from the top control loop. Thus, a DTD, ∆2T5 = (T15 – T5) – (T5 – T3), is constructed for the top control loop and a DTD, ∆2T26 = (T27 – T26) – (T26 – T15) for the bottom control loop, which are paired, respectively, with D and QREB. The DTDC-ASVM scheme is sketched in Figure 2c. 3.4. DTDC-SVD scheme versus DTDC-ASVM scheme. While a proportional-plus-integral (PI) controller is applied to the feed flow control loop with a gain of 0.5 and integral time of 0.3 min, a PI controller with a gain of 20 and integral time of 12 min in the pressure control loop. Two proportional controllers are arranged in the reflux-drum and reboiler level control loops, respectively, with a gain of 2 each. PI controllers are utilized in all temperature related control loops and a measurement dead-time of 60 seconds is included in temperature measurements. The Tyreus-Luyben rule embedded in the commercial software Aspen Dynamics is followed to tune all temperature related control loops and the resultant controller parameters are tabulated in Table 2 for the DTDC-SVD and DTDC-ASVM schemes. In Figure 4, the transient responses of the CDC, incorporated with the DTDC-SVD and DTDC-ASVM schemes, respectively, are depicted for ±10 % step variations in E and B feed compositions. Although the DTDC-ASVM scheme shows slightly bigger peak variations in the bottom product composition than the DTDC-SVD scheme, the former shows not only much smaller peak deviations but also shorter settling times in the top product composition than the latter especially in face of the step variations in B feed composition. As far as the steady-state deviations in the two controlled product compositions are concerned, the DTDC-ASVM scheme shows obvious advantages over the DTDC-SVD scheme. In Table 3 the steady-state deviations of the DTDC-SVD and DTDC-ASVM schemes are summarized and the maximum deviations in the top and bottom products are highlighted here with bold numbers. It can readily be noticed that of the totally 8 scenarios, the DTDC-ASVM scheme secures 7 times of smaller discrepancies in the two controlled product compositions than does the DTDC-SVD scheme. Moreover, the former suppresses the maximum deviation of the controlled product compositions by 38 % as compared to the latter.

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4.

Example II: Temperature Inferential Control of a CDC Processing a Ternary Mixture of Ethanol (E), Propanol

(P), and Butanol (B) 4.1. Steady-state design. Figure 5a sketches the steady-state design of the CDC and Table 1 lists its relevant operating conditions and product specifications. The CDC has 40 stages and is fed onto stage 20. Overhead pressure is set at 1 atm with a pressure drop 0.0068 atm per stage. The feed flow rate is 1 kmol/s with a composition of 33.3 mol % E, 33.3 mol % P, and 33.4 mol % B. The top product is specified to be 99 mol % E and the bottom product 1 mol % E. 4.2. Configuring the DTDC-SVD scheme. According to the SA and SVD analysis given in Supporting Information, two DTDs, ∆2T10 = (T21 – T10) – (T10 – T2) and ∆2T32 = (T39 – T32) – (T32 – T20), are constructed and paired with D and QREB, respectively. The resultant DTDC-SVD scheme is sketched in Figure 5b. 4.3. Configuring the DTDC-ASVM scheme. With reference to the sensitive stages, 10 and 32, for the rectifying and stripping sections, respectively, Figure 6 gives the curves of the ASVM under the assumption of complete rejection of ±10 % feed composition disturbances. With reference to Figure 6a, stages 8 and 17 should be selected as the upper and lower reference stages and a DTD, ∆2T10 = (T17 – T10) – (T10 – T8), is constructed for the top control loop. With reference to Figure 6b, stages 19 and 33 should be selected as the upper and lower reference stages and a DTD, ∆2T32 = (T33 – T32) – (T32 – T19) is constructed for the bottom control loop. These two DTDs are paired with D and QREB, respectively and the resultant DTDC-ASVM scheme is sketched in Figure 5c. 4.4. DTDC-SVD scheme versus DTDC-ASVM scheme. The same settings of feed flow rate, pressure, and liquid level control loops as in Example I are applied here. Table 2 tabulates the resultant controller parameters of the DTDC-SVD and DTDC-ASVM schemes. Figure 7 illustrates the transient responses of the CDC, with the incorporation of the DTDC-SVD and DTDC-ASVM schemes, respectively, in face of ±10 % step variations in E, P, and B feed compositions. Although the DTDC-ASVM scheme shows slightly bigger peak deviations than the DTDC-SVD scheme in face of the step variations in E feed composition, the reverse is true in face of the step variations in P feed composition. With respect to the steady-state deviations in the two controlled product compositions, the DTDC-ASVM scheme shows again significant advantages over the DTDC-SVD schemes. In Table 4 the steady-state deviations of the DTDC-SVD and DTDC-ASVM schemes are summarized. It can readily be noticed that of the totally 12 scenarios, the DTDC-ASVM scheme secures 12 times of smaller discrepancies in the two controlled product compositions than does the DTDC-SVD

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scheme. Moreover, the DTDC-ASVM scheme reduces the maximum deviation of the controlled product compositions by 70.4 % as compared to the DTDC-SVD scheme.

5.

Example III: Temperature Inferential Control of a CDC Processing a Ternary Mixture of Ethanol (E),

Propanol (P), and Butanol (B) 5.1. Steady-state design. The same mixture as in Example II is processed here but with a different component segmentation. Figure 8a sketches the steady-state design of the CDC and Table 1 lists its relevant operating conditions and product specifications. Note that the top product is specified to be 1 mol % B and the bottom product 99 mol % B, hence representing a sharp different separation operation from Example II. 5.2. Configuring the DTDC-SVD scheme. As shown in Figure 8b, the DTDC-SVD scheme involves two DTDC loops, in which two DTDs, ∆2T9 = (T19 – T9) – (T9 – T2) and ∆2T32 = (T39 – T32) – (T32 – T20), are constructed and paired with D and QREB, respectively. 5.3. Configuring the DTDC-ASVM scheme. With reference to the sensitive stages, 9 and 32, for the rectifying and stripping sections, respectively, the curves of the ASVM are drawn in Figure 9 under the assumption of complete rejection of ±10 % feed composition disturbances. In terms of Figure 9a, stages 5 and 21 should be selected as the upper and lower reference stages and a DTD, ∆2T9 = (T21 – T9) – (T9 – T5), is constructed for the top control loop. Similarly, with reference to Figure 9b, stages 24 and 33 should be selected as the upper and lower reference stages and a DTD, ∆2T32 = (T33 – T32) – (T32 – T24), is constructed for the bottom control loop. These two DTDs are paired with the D and QREB, respectively, and the resultant DTDC-ASVM scheme is sketched in Figure 8c. 5.4. DTDC-SVD scheme versus DTDC-ASVM scheme. The same settings of feed flow rate, pressure, and liquid level control loops as in Example I are also applied here. Table 2 tabulates the resultant temperature controller parameters of the DTDC-SVD and DTDC-ASVM schemes. In Figure 10, the transient responses of the CDC, incorporated with the DTDC-SVD and DTDC-ASVM schemes, respectively, are shown in face of ±10 % step variations in E, P, and B feed compositions. While sharing quite close settling times, the DTDC-ASVM gives rise to comparable or even smaller peak deviations in the top and bottom product compositions than the DTDC-SVD scheme. As for the steady-state deviations in the top and bottom product compositions, the former is obviously advantageous over the latter. In Table 5 the steady-state

10


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deviations of the DTDC-SVD and DTDC-ASVM schemes are summarized. one can readily understand that of the totally 12 scenarios, the DTDC-ASVM scheme secures 12 times of smaller discrepancies in the two controlled product compositions than does the DTDC-SVD scheme. Moreover, the DTDC-ASVM scheme reduces the maximum deviation of the controlled product compositions by 83.3 % as compared to the DTDC-SVD scheme.

6.

Example IV: Temperature Inferential Control of a DWDC Processing a Ternary Mixture of Ethanol (E),

Propanol (P), and Butanol (B) 6.1. Steady-state design. Figure 11a sketches the steady-state design of the DWDC and Table 1 lists its relevant operating conditions and product specifications. For easy reference, the steady-state composition of B at the top of the prefractionator is also included here. The DWDC has 64 stages with the dividing wall from stage 13 to stage 47. Overhead pressure is set at 1 atm with a pressure drop 0.0068 atm per stage. The ternary mixture is introduced onto stage P32 with a flow rate of 1 kmol/s and a composition of 33.3 mol % E, 33.3 mol % P, and 33.4 mol % B. The intermediate product is withdrawn from stage 26 and the top, intermediate, and bottom products are all specified to be 99 mol %. Because there is no available DWDC module in Aspen Plus, four RadFrac modules are combined together to establish the model of the DWDC, with two having neither condenser nor reboiler, one having only condenser, and one having only reboiler. 6.2. Configuring the DTDC-SVD scheme. As shown in Figure 11b, the DTDC-SVD scheme consists of four DTDC loops with D, intermediate product flow rate I, QREB, and liquid split ratio RL as manipulated variables. Four DTDs, ∆2T9 = (TP21 – T9) – (T9 – T2), ∆2T39 = (T48 – T39) – (T39 – T26), ∆2T56 = (T63 – T56) – (T56 – T48), and ∆2TP21 = (TP32 – TP21) – (TP21 – TP15), are constructed for the top, intermediate, bottom, and prefractionator’s control loops, respectively. 6.3. Configuring the DTDC-ASVM scheme. With reference to the sensitive stages, 9, 39, 56, and P21, for the common rectifying section, right section of the dividing-wall, common stripping section, and prefractionator, respectively, Figure 12 presents the curves of the ASVM under the assumption of complete rejection of ±10 % feed composition disturbances. In Figure 12a, the first turning point appears at stage P17 and the ASVM still increases as the stage moves downwards. Thus, stage P17 should be chosen as the lower reference stage and stage 7 the upper reference stage, in the top control loop. Although stage 13 corresponds to a local minimum, it is neglected here because of the highly nonlinear behaviors of the right section of the dividing wall.

3, 10

For the intermediate control loop (c.f. Figure 12b), because the

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couplings originate from the multiple sections above and below the sensitive stage 39, stages 14 and 56 are selected firstly as the two candidate reference stages. Since stage 14 corresponds to a smaller ASVM than stage 56, the former is finally selected as the upper reference stage; as a result, stage 45 is located as the lower reference stage following the principle described in section 2. With reference to Figures 12c and 12d, stages 48 and 57 should be selected as the upper and lower reference stages, respectively, for the bottom control loop, and stages P16 and P32 the upper and lower reference stages, respectively, for the prefractionator’s control loop. Therefore, four DTDs, ∆2T9 = (TP17 – T9) – (T9 – T7), ∆2T39 = (T45 – T39) – (T39 – T14), ∆2T56 = (T57 – T56) – (T56 – T48), and ∆2TP21 = (TP32 – TP21) – (TP21 – TP16), are constructed, giving rise to the DTDC-ASVM scheme as sketched in Figure 11c. 6.4. DTDC-SVD scheme versus DTDC-ASVM scheme. The same settings as in Example I are also applied to feed flow rate, pressure, and liquid level control loops here. Table 2 tabulates the resultant controller parameters of the DTDC-SVD and DTDC-ASVM schemes. In Figure 13, the transient responses of the DWDC, incorporated, respectively, with the DTDC-SVD and DTDC-ASVM schemes, are shown in face of ±10 % step variations in E, P, and B feed compositions. Both the control schemes work well to handle the feed composition disturbances. In particular, the DTDC-ASVM exhibits not only smaller peak variations but also shorter settling times than the DTDC-SVD in the scenarios of P feed composition changes. As for the steady-state deviations in the three controlled product compositions, the DTDC-ASVM scheme is quite superior to the DTDC-SVD scheme. In Table 6 the steady-state deviations of the DTDC-SVD and DTDC-ASVM schemes are summarized. It can readily be seen that of the totally 18 scenarios, the DTDC-ASVM scheme secure 15 times of smaller discrepancies in the three controlled product compositions than does the DTDC-SVD scheme. Moreover, the DTDC-ASVM scheme reduces the maximum deviation of the controlled product compositions by 58.2 % as compared to the DTDC-SVD scheme.

7.

Discussion With reference to the four separation systems studied, the novel method proposed in the current work has clearly been

demonstrated to be more effective than the conventional method for configuring the DTDC scheme. In despite of the fact that they differ not so much in dynamic responses, the DTDC-ASVM scheme secures considerably tighter product quality control than the DTDC-SVD scheme. In addition to more scenarios of reduced steady-state deviations, the maximum

12


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deviations have also been suppressed considerably in the controlled product compositions. These advantages have certainly been brought about by the careful consideration of the coupling between all the DTDs constructed and the effective coordination between the upper and lower temperature differences in each DTD. Table 7 lists the relative gain array (RGA) of the DTDC-SVD and DTDC-ASVM schemes for Examples I to IV, where the diagonal elements are highlighted with bold numbers. It can readily be identified that the couplings between the synthesized controlled variables have been alleviated in the DTDC-ASVM scheme for Examples I to III as compared to those in the DTDC-SVD scheme. For Example IV, it is hard to identify favorable variations in the couplings between the synthesized controlled variables, but the sharp improvement in control system behaviors has still justified the construction of the DTDs by the novel method proposed. Although it needs to calculate the curves of the ASVM, it is actually quite straightforward in principle and can be accomplished through several cases of steady-state simulation. Therefore, the novel method proposed shares approximately the same degree of computational complexity and requirements as the conventional method for configuring the DTDC scheme. Although a complete rejection of ±10 % feed composition disturbances is employed to sketch the ASVM curves in all of the four examples studied, changes to other magnitudes of feed composition disturbances lead only to very small variations in the ASVM curves. This feature allows the resultant DTDC scheme to be quite robust to the changes in operating conditions.

8.

Conclusion The derivation of the DTDs to be controlled represents the most important step towards the synthesis and design of

the DTDC scheme for distillation columns. Although SVD analysis guarantees the high sensitivities between the upper and lower temperature differences chosen and the manipulated variable adopted for each control loop, it cannot guarantee the resultant DTD to be in high sensitivity with the manipulated variable. Neither the coupling between the DTDs nor the coordination between the upper and lower temperature differences in each control loop has been taken into account. These are the primary pitfalls of the conventional method that can compromise substantially the performance of the resultant DTDC scheme. By means of the ASVM developed in our earlier work, a novel method has been proposed for configuring the DTDC scheme. It permits not only careful consideration of the coupling between all the DTDs but also effective coordination between the upper and lower temperature differences in each control loop, thereby being capable of enhancing

13



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Page 14 of 38

the accuracy of the DTDs constructed to infer the product qualities to be controlled. In terms of four example systems, the effectiveness of the novel method proposed has been evaluated in terms of thorough comparison with the conventional method. The obtained results have confirmed that the former can render tight inferential control of product qualities than the latter. Not only have more scenarios of reduced steady-state deviations been achieved but also the maximum deviations have been suppressed in the controlled product qualities. These advantages have corroborated definitely that the proposed method can be an effective alternative for the synthesis and design of the DTDC scheme for various distillation columns.

Supporting Information Sensitivity analysis and SVD analysis of Examples I-IV.

Acknowledgements The research is supported by National Nature Science Foundation of China (21076015, 21376018, 21576014, and 21676011) and Fundamental Research Funds for Central Universities (ZY1503).

Literature Cited (1)

Luyben, W. L. Feedback Control of Distillation Columns by Double Differential Temperature Control. Ind. Eng. Chem. Res. 1969, 8, 739.

(2)

Yu, C. C.; Luyben W. L. Use of Multiple Temperatures for the Control of Multicomponent Distillation Columns. Ind. Eng. Chem. Process Des. Dev. 1984, 23, 590.

(3)

Wu N.; Huang K.; Luan S. Operation of Dividing-Wall Distillation Columns. 2. A Double Temperature Difference Control Scheme. Ind. Eng. Chem. Res. 2013, 52, 5365.

(4)

Yuan Y.; Huang K. Operation of Dividing-Wall Distillation Columns. 3. A Simplified Double Temperature Difference Control Scheme. Ind. Eng. Chem. Res. 2014, 53, 15969.

(5)

Yuan Y.; Huang K.; Chen H.; Zhang L.; Wang S. Asymmetrical Temperature Control of a BTX Dividing-Wall Distillation Column. Chem. Eng. Res. Des. 2017, 123, 84.

(6)

Gupta R.; Kaistha N. Role of Nonlinear Effects in Benzene-Toluene-Xylene Dividing Wall Column Control

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System Design. Ind. Eng. Chem. Res. 2015, 54, 9407. (7)

Luyben W. L. Practical Distillation Control; Van Nostrand Reinhold: New York, 1992.

(8)

Hori E. S.; Skogestad S. Selection of Control Structure and Temperature Location for Two-Product Distillation Columns. Chem. Eng. Res. Des. 2007, 85, 293.

(9)

Luyben W. L. Evaluation of Criteria for Selecting Temperature Control Trays in Distillation Columns. J. Process Control. 2006, 16, 115

(10)

Ling H.; Luyben W. L. Temperature Control of the BTX Divided-Wall Column. Ind. Eng. Chem. Res. 2010, 49, 189.

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Figure Legends Figure 1.

Selection of the upper and lower reference stages in terms of the ASVM.

Figure 2.

Steady-state design of Example I and its DTDC schemes: (a) process design, (b) DTDC-SVD scheme, (c) DTDC-ASVM scheme.

Figure 3.

ASVMs in face of ±10 % variations in feed compositions (Example I): (a) top loop, (b) bottom loop.

Figure 4.

Comparison between the DTDC-SVD and DTDC-ASVM schemes after ±10 % variations in feed compositions (Example I): (a) E, (b) B.

Figure 5.

Steady-state design of Example II and its DTDC schemes: (a) process design, (b) DTDC-SVD scheme, (c) DTDC-ASVM scheme.

Figure 6.

ASVMs in face of ±10 % variations in feed compositions (Example II): (a) top loop, (b) bottom loop.

Figure 7.

Comparison between the DTDC-SVD and DTDC-ASVM schemes after ±10 % variations in feed compositions (Example II): (a) E, (b) P, (c) B.

Figure 8.

Steady-state design of Example III and its DTDC schemes: (a) process design, (b) DTDC-SVD scheme, (c) DTDC-ASVM scheme.

Figure 9.

ASVMs in face of ±10 % variations in feed compositions (Example III): (a) top loop, (b) bottom loop.

Figure 10.

Comparison between the DTDC-SVD and DTDC-ASVM schemes after ±10 % variations in feed compositions (Example III): (a) E, (b) P, (c) B.

Figure 11.

Steady-state design of Example IV and its DTDC schemes: (a) process design, (b) DTDC-SVD scheme, (c) DTDC-ASVM scheme.

Figure 12.

ASVMs in face of ±10 % variations in feed compositions (Example IV): (a) top loop, (b) intermediate loop, (c) bottom loop, (d) prefractionator’s loop.

Figure 13.

Comparison between the DTDC-SVD and DTDC-ASVM schemes after ±10 % variations in feed compositions (Example IV): (a) E, (b) P, (c) B.

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(a)

(b)

Figure 1 Yang Yuan, Kejin Huang, Haisheng Chen, Liang Zhang, and Shaofeng Wang Configuring Effectively Double Temperature Difference Control Schemes for Distillation Columns 17



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(a)

(b)

(c)



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(a)

(b)

Figure 3 Yang Yuan, Kejin Huang, Haisheng Chen, Liang Zhang, and Shaofeng Wang Configuring Effectively Double Temperature Difference Control Schemes for Distillation Columns

19



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(a)

(b)



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(a)

(b)

(c)




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(a)

(b)



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(a)

(b)

(c)




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(a)

(b)

(c)



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(a)

(b)




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(a)

(b)

(c)



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(a)

PC

LC1

R

D 2 RL 9

– + –

∆2T9

DTDC1

DTDC4 ∆2TP21

F

– + – +

P15 +

P21 P32

I

26

–

39

+ –

48 56 63

+ – + – +

FC

∆2T39

∆2T56

DTDC2

DTDC3

LC2

B

(b)

(c)




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(a)

(b)

(c)

(d)



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(a)

(b)

(c)




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 38

Table Legends Table 1.

Operating Conditions and Product Specifications (Examples I-IV)

Table 2.

Controller Parameters of the DTDC-SVD and DTDC-ASVM Schemes (Examples I-IV)

Table 3.

Steady-State Deviations for ±10 % Step Changes in Feed Compositions of E and B (Example I)

Table 4.

Steady-State Deviations for ±10 % Step Changes in Feed Compositions of E, P, and B (Example II)

Table 5.

Steady-State Deviations for ±10 % Step Changes in Feed Compositions of E, P, and B (Example III)

Table 6.

Steady-State Deviations for ±10 % Step Changes in Feed Compositions of E, P, and B (Example IV)

Table 7.

RGA of the DTDC-SVD and DTDC-ASVM schemes (Examples I-IV)

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Table 1. Operating Conditions and Product Specifications (Examples I to IV) System

Parameter Top pressure (atm)

Example I

Value 1.0

Bottom pressure (atm)

1.1972

Feed flow rate (kmol/s)

1.0

Distillate flow rate (kmol/s)

0.398

Reflux flow rate (kmol/s)

0.417

Feed compositions E:B (mol %)

40:60

Product specifications E:B (mol %)

99:99

Top pressure (atm)

1.0


1.2652


1.0


0.33


0.855

Example II Feed compositions E:P:B (mol %)

33.3:33.3:33.4

Distillate specification E (mol %)

99

Bottom specification E (mol %)

1

Top pressure (atm)

1.0


1.2652


1.0


0.669


0.713

Example III Feed compositions E:P:B (mol %)

33.3:33.3:33.4

Distillate specification B (mol %)

1

Bottom specification B (mol %)

99

Top pressure (atm)

1.0


1.4284


1.0


0.335


1.35

Example IV Feed compositions E:P:B (mol %) Product specifications E:P:B (mol %) Prefractionator’s top composition B (mol %)

33.3:33.3:33.4 99:99:99 0.0166

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Table 2. Controller Parameters of the DTDC-SVD and DTDC-ASVM Schemes (Examples I to IV) System

Scheme DTDC-SVD

Controller

Manipulated variable

Controlled variable

KC

TI (min)

DTDC1

D

(T14 – T5) – (T5 – T2)

0.17

35.64

DTDC2

QREB

(T29 – T26) – (T26 – T17)

0.07

10.56

Example I DTDC-ASVM

DTDC-SVD

DTDC1

D

(T15 – T5) – (T5 – T3)

0.26

38.28

DTDC2

QREB

(T27 – T26) – (T26 – T15)

0.22

11.88

DTDC1

D

(T21 – T10) – (T10 – T2)

1.05

38.28

DTDC2

QREB

(T39 – T32) – (T32 – T20)

0.05

19.80

DTDC1

D

(T17 – T10) – (T10 – T8)

1.35

48.84

DTDC2

QREB

(T33 – T32) – (T32 – T19)

0.45

23.76

Example II DTDC-ASVM

DTDC-SVD

DTDC1

D

(T19 – T9) – (T9 – T2)

0.43

54.12

DTDC2

QREB

(T39 – T32) – (T32 – T20)

0.30

15.84

DTDC1

D

(T21 – T9) – (T9 – T5)

1.13

50.16

DTDC2

QREB

(T33 – T32) – (T32 – T24)

0.90

10.56

DTDC1

D

(TP21 – T9) – (T9 – T2)

0.33

36.96

DTDC2

I

(T48 – T39) – (T39 – T26)

0.06

25.08

DTDC3

QREB

(T63 – T56) – (T56 – T48)

0.04

10.56

DTDC4

RL

(TP32 – TP21) – (TP21 – TP15)

0.18

30.36

DTDC1

D

(TP17 – T9) – (T9 – T7)

0.91

36.96

DTDC2

I

(T45 – T39) – (T39 – T14)

0.75

23.76

DTDC3

QREB

(T57 – T56) – (T56 – T48)

0.36

10.56

DTDC4

RL

(TP32 – TP21) – (TP21 – TP16)

0.31

30.36

Example III DTDC-ASVM

DTDC-SVD

Example IV

DTDC-ASVM

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Table 3. Steady-State Deviations for ±10 % Step Changes in Feed Compositions of E and B (Example I) Steady-state deviation Scenario

Product DTDC-SVD

DTDC-ASVM

–4

–0.36 × 10–4

B

6.22 × 10–4

0.61 × 10–4

E

2.75 × 10–4

2.16 × 10–4

B

–4.56 × 10–4

3.02 × 10–4

E

4.60 × 10–4

3.76 × 10–4

B

–5.80 × 10–4

6.01 × 10–4

E

–1.23 × 10–4

0.20 × 10–4

B

9.70 × 10–4

2.02 × 10–4

Maximum deviation (%)

100

62.0

Comparison

0/8

7/8

E +10 % ZE

–10 % ZE

+10 % ZB

–10 % ZB

–1.30 × 10

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Page 34 of 38

Table 4. Steady-State Deviations for ±10 % Step Changes in Feed Compositions of E, P, and B (Example II) Steady-state deviation Scenario

Product DTDC-SVD

DTDC-ASVM

E

–0.37 × 10

–3

1.01 × 10–4

E

–1.00 × 10–3

1.62 × 10–4

E

0.56 × 10–3

2.35 × 10–4

E

1.01 × 10–3

–5.04 × 10–4

E

1.33 × 10–3

4.69 × 10–4

E

1.56 × 10–3

–4.83 × 10–4

E

–1.70 × 10–3

–4.02 × 10–4

E

–1.49 × 10–3

2.30 × 10–4

E

–1.06 × 10–3

–3.86 × 10–4

E

–0.49 × 10–3

0.13 × 10–4

E

0.97 × 10–3

3.45 × 10–4

E

0.55 × 10–3

–0.54 × 10–4


100

29.6

Comparison

0/12

12/12

+10 % ZE

–10 % ZE

+10 % ZP

–10 % ZP

+10 % ZB

–10 % ZB

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Table 5. Steady-State Deviations for ±10 % Step Changes in Feed Compositions of E, P, and B (Example III) Steady-state deviation Scenario

Product DTDC-SVD

DTDC-ASVM

B

–0.67 × 10

–3

1.85 × 10–4

B

–0.58 × 10–3

–0.88 × 10–4

B

0.80 × 10–3

–1.74 × 10–4

B

0.56 × 10–3

0.98 × 10–4

B

1.41 × 10–3

–1.91 × 10–4

B

1.23 × 10–3

2.61 × 10–4

B

–1.29 × 10–3

–0.51 × 10–4

B

–1.57 × 10–3

–2.07 × 10–4

B

–0.63 × 10–3

–2.07 × 10–4

B

–0.78 × 10–3

–0.16 × 10–4

B

0.61 × 10–3

–0.08 × 10–4

B

0.83 × 10–3

2.62 × 10–4


100

16.7

Comparison

0/12

12/12

+10 % ZE

–10 % ZE

+10 % ZP

–10 % ZP

+10 % ZB

–10 % ZB

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Page 36 of 38

Table 6. Steady-State Deviations for ±10 % Step Changes in Feed Compositions of E, P, and B (Example IV) Steady-state deviation Scenario

Product DTDC-SVD

DTDC-ASVM

E

–0.78 × 10

–4

3.65 × 10–4

P

–7.86 × 10–4

–0.78 × 10–4

B

2.75 × 10–4

0.53 × 10–4

E

1.87 × 10–4

–2.01 × 10–4

P

3.66 × 10–4

–1.52 × 10–4

B

–2.81 × 10–4

–0.50 × 10–4

E

4.42 × 10–4

–1.87 × 10–4

P

–0.42 × 10–4

–3.42 × 10–4

B

5.91 × 10–4

1.39 × 10–4

E

–4.13 × 10–4

3.72 × 10–4

P

–2.27 × 10–4

1.40 × 10–4

B

–6.29 × 10–4

–0.73 × 10–4

E

–2.90 × 10–4

0.21 × 10–4

P

5.09 × 10–4

3.03 × 10–4

B

–8.90 × 10–4

–0.55 × 10–4

E

3.00 × 10–4

0.29 × 10–4

P

–4.07 × 10–4

–0.70 × 10–4

B

8.91 × 10–4

2.52 × 10–4


100

41.8

Comparison

0/18

15/18

+10 % ZE

–10 % ZE

+10 % ZP

–10 % ZP

+10 % ZB

–10 % ZB

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Table 7. RGA of the DTDC-SVD and DTDC-ASVM schemes (Examples I to IV) Example I

Example II D

DTDC-SVD

DTDC-ASVM

QREB

D

2

∆ T5

0.7674

0.2326

∆2T26

0.2326

0.7674

∆2T5

0.7688

0.2312

2

∆ T26

0.2312

0.7688

2

DTDC-SVD

DTDC-ASVM

Example III QREB

∆ T10

0.5495

0.4505

∆2T32

0.4505

0.5495

∆2T10

0.5893

0.4107

2

∆ T32

0.4107

DTDC-SVD

DTDC-ASVM

0.5893

D

QREB

2

∆ T9

0.4341

0.5659

∆2T32

0.5659

0.4341

∆2T9

0.4071

0.5929

0.5929

0.4071

2

∆ T32

Example IV D

DTDC-SVD

I

QREB

RL

D

I

0.0150

2

∆ T9

0.9614

–0.0007

0.0141

0.0252

–0.0007

∆2T39

–0.0007

0.2469

0.7545

–0.0007

∆2T56

0.0232

0.8126

0.2106

–0.0464

0.0161

–0.0588

0.0208

1.0219

2

∆ T9

0.9840

–0.0083

0.0093

∆2T39

–0.0008

0.2442

0.7573

∆2T56

0.0018

0.8305

0.2109

–0.0432

2

∆ TP21

0.0149

–0.0664

0.0226

1.0289

DTDC-ASVM

2

∆ TP21

QREB

RL

37



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Configuring Effectively Double Temperature ... - ACS Publications

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