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Evaluation of Control Structures for a Debutanizer Column
10th International Symposium on Process Systems Engineering - PSE2009 Rita Maria de Brito Alves, Claudio Augusto Oller do Nascimento and Evaristo Chalbaud Biscaia Jr. (Editors) © 2009 Elsevier B.V. All rights reserved.
1473
Evaluation of Control Structures for a Debutanizer Column Lilian R. Canabarro,a Mario C. M. M. Campos,b Enrique L. Limaa a
Programa de Engenharia Química/COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária, CP 68502, Rio de Janeiro, RJ, Brazil 21945-970 b PETROBRAS S.A. Av. Horacio Macedo, 950, Rio de Janeiro RJ, Brazil 21941-915
Abstract In this work is described the choice of the control structure for a specific industrial distillation column presenting a significant discrepancy between the inventories of the top and bottom sections. The studied distillation column showed to be an excellent research field, but looking for the balance between scientific development and industrial application it is always important to take into consideration the variable “time invested”. In this context, and searching for a satisfactory control structure, static analysis tools, as RGA and SVD, had been used in the characterization of a set of alternatives structures based on the primary composition control variables L, V, D and B, as well as some relations between them. With the reduction of the “time invested” kept in mind, it was used a rigorous dynamic simulator capable to deal with thermodynamic calculations for complex multicomponent mixtures, as those found in the processing units of crude oil and its fractions. Results have demonstrated the importance of rigorous dynamic simulation to solve design control problems in distillation columns which frequently presents unique characteristics and should be treated accordingly. Keywords: Distillation control, control structure selection, dynamic simulation
1. Introduction The interest on distillation control systems started in the decade of the 50s, significantly increasing along the time, with special emphasis in the 80s. One conclusion that can be drawn from the huge amount of technical and scientific literature produced in this period is that distillation is a difficult system to understand. The scientific research is continuously improving our knowledge on the subject, but the practice is still confronted with serious difficulties, because each distillation column seems to be different from other ones and, in such a way, requires a personalized treatment. Recently Skogestad (2007) wrote “Many books...and papers, including several of my own..., have been written on the merits of the various configurations, but it is probably safe to say that the importance of the choice of configuration (level control scheme) has been overemphasized”. These words are a good example of the knowledge (scientific or general) evolution process, as they clearly express the permanent and necessary substitution of old “truths” by new ones. Certainly this subject deserves much more deep thoughts, but the idea here is only to show that in complex cases, as certainly can be the distillation columns, many of the “general truths” that had been enunciated had not been confirmed in practice, requiring more specific approaches. In his contribution Skogestad (2007) proposed a distillation column control methodology with reasonable general application, bringing great contribution for the practical side of the problem. The focus of this work is on the control structure design for a specific debutanizer
L.R. Canabarro et al.
1474
column using simple and practical tools, complemented with rigorous dynamic simulation.
The Problem The studied system is a 26 trays naphtha stabilizer column of a crude atmospheric distillation unit. The feed, coming from the top of the atmospheric tower and introduced in tray 13th (from the top), contains 30 components, including 2% of light components (methane, ethane, propane, butanes, pentanes, etc.), water and 20 pseudo-components. The bottom product of the column is used to preheat this feed. Because it is almost totally in the liquid phase, vapor and liquid flows in the stripping section are larger than in the rectifying section, and as a consequence the thermal load to the reboiler is larger than to the condenser. There are three products in the system: combustible gas and liquefied petroleum gas (LPG) in the vapor and liquid streams that leave a partial condenser; and stabilized naphtha in the bottom stream. The control objective is to obtain a top product with the highest purity, guaranteeing the LPG quality, without reducing the quality of the stabilized naphtha. As this is produced in a large amount, significant quality variations are not expected, so the top composition control was considered a priority. Technical-scientific literature shows that the Relative Gain Array (RGA) introduced by Bristol (1966) is still an important analysis and design tool for multivariate systems. Initially developed to determine static interaction in systems, allowing appropriate pairing between input and output variables in a control structure, its area of applicability was significantly extended later, both for static and dynamic conditions (Grossdidier et al., 1985). Considering the stationary case and using the system gain matrix K, the RGA matrix ȁ can be obtained as follows,
/
>O @ ij
>K > K @ @ 1 T
ij
ij
where Ȝij is the ratio of the static gain of the output variable i related to the input variable j, with all the other pairs in open loop, to the static gain of the same pair (i,j), with all the other pairs under perfect control. A RGA matrix close to identity indicates small interaction, determining the appropriated pairing. Another tool, sometimes complementary to the RGA, results from Singular Value Decomposition, SVD (Grossdidier et al., l985). Also considering the static case and starting from the gain matrix K, the SVD is defined as
K
U6V T
where U and V are unitary matrices, and 6 is a diagonal matrix with the singular values in descending order of magnitude. The ratio of the largest to the smallest singular value defines the Condition Number, Ȗ, a measure of the difficulty to control the associated system. As this number is dependent on variables units (scaling) it can take very different values for the same system. The correct way to take advantage of the information supplied by the condition number is to use the scaling that produces the minimum value, Ȗ* (scaling doesn’t change system’s characteristics). Research literature clearly shows limitations when evaluating a system operating in dynamic
Evaluation of Control Structures for a Debutanizer Column
1475
condition using static information. However, it is important to notice that in many practical cases it is difficult to get a reasonable dynamic description of the system, limiting the use of complex elaborated theoretical methods. An approach for calculating the gain matrices of different alternative control structures from the knowledge of only one aroused great interest in the end of the 80s and early 90s. The method introduced by Häggblom and Waller (1988) was based on transformations and relations of consistency derived from global and component mass balances. This approach seemed to be quite useful for simplifying the calculation of RGA and SDV of different control structures. Considering only the top and bottom distillation products quality control, there are 4 primary manipulated variables available: reflux (L), distillate (D), bottom (B) and vapor (V) flowrates. From these primary variables the literature reports a large number of combinations that generates secondary variables, allowing the design of a large number of control structures. Disregarding any one of them could be a difficult task, requiring significant testing work. This is facilitated by combining the use of appropriate indices, such as RGA and Ȗ (there are many others, with varying complexity), system knowledge and computer simulation.
2. Implementation A set of control structures was chosen for evaluation disregarding some literature recommendations (sometimes divergent), because they are commonly based on results obtained from very simplified systems. Due to the large bottom flowrate the popular LB structure was not considered. The structures chosen were: LV, DV and (L/D, V/B). A fourth structure was also chosen where, as suggested by Skogestad (2007), a fast tray temperature loop was include in the stripping section. In this structure, identified as LVcascade, the top composition is controlled by a cascade control system, manipulating a pump’s rotor speed, where the internal loop controls the reflux. The bottom composition is controlled by another cascade control system, manipulating V, where the internal loop controls the 19th tray temperature. Table 1 shows the values of K, RGA, Ȗ e Ȗ* for each control structure.
Structure
Table 1 Static gains, RGA and conditional numbers K ȁ
Ȗ
Ȗ*
LV
ª 1.023 « 6 ¬ 3.88e
0.5806 º » 1.12e 3 ¼
ª 1.0018 0.0018º « 0.0018 1.0018 » ¬ ¼
1259.5
1.0892
DV
ª 2.12 « 6 ¬ 6.86e
0.6014 º » 1.12e 3 ¼
ª 1.0017 0.0017º « 0.0017 1.0017 » ¬ ¼
2048.7
1.087
L/D V/B
ª 3.70e 2 « 8 ¬ 9.45e
5.6202 º » 1.08e 2 ¼
ª 1.0013 0.0013º « 0.0013 1.0013 » ¬ ¼
79155
1.0757
LV-Cascade
ª 2.1790 « 6 ¬ 8.37e
1.11e 2 º » 2.68e 6 ¼
ª 1.0162 0.0162º « 0.0162 1.0162 » ¬ ¼
826230
1.2887
The RGA and Ȗ* values indicate that the different structures should present similar behavior, in terms of insignificant interaction and good conditioning (although system scaling is weak). From this information it is possible to choose good variable pairing
L.R. Canabarro et al.
1476
and to have a feeling of the control viability of the different structures, but it is not enough to define which structure is the best. To this end dynamic simulation (gPROMS®, Multiflash®) was used, comparing the behavior of the different structures when the system is perturbed by the most common disturbances in distillation columns: changes in feed flowrate, temperature and composition. Before presenting the simulation results, it is important to shortly comment about the experience we have with the transformations method (Häggblom e Waller, 1988). Using the gain matrix of the LV structure the method was used in order to calculate the gain matrices of the other ones. As can be seen in Table 2, there was no consistence in the obtained results. Table 2 RGA by transformations from LV Structure ȁ L/D V/B
ª 2.4442 3.4442 º « 3.4442 2.4442» ¬ ¼
DV
ª 1.0002 0.0002º « 0.0002 1.0002 » ¬ ¼
Although the result obtained for DV was similar to the one obtained from data specifically acquired for this structure (Table 1), the result obtained for (L/D,V/B) was completely different. This could be an indication that the assumptions on which the method is based are not satisfied in this case. As in practice this disagreement can be quite common, it may justify the little impact of the method observed in research literature after some initial popularity. The papers studying the transformation method were certainly of great value to improve the knowledge on distillation columns, but their use in practical problems requires a careful preliminary analysis. Some old “truths” must probably be re-evaluated to be put in their real dimension. Searching for the best control structure for the studied column the behavior of each structure was simulated against feed flowrate (+/- 10%), temperature (+/- 1%; the system is highly sensitive to this disturbance) and composition (+/- 10%) disturbances. Controllers were tuned in such way as to get the best performance for each structure. Results in Figure 1 were obtained for the top of the column against the positive flowrate and composition disturbances, and the negative temperature disturbance. In addition to the controlled variables responses, the behavior of primary manipulated variables is also shown. Figure 2 displays similar results for the bottom of the column. Considering the top (Figure 1), where composition control was more rigorous, it can be notice that there are close relations between the disturbances effects on the composition. The effect of 10% variation in feed flowrate was almost equivalent to -1% variation in feed temperature, while the effect of +10% variation in feed composition was less significant and in the opposite direction. The differences observed in the magnitude of the initial reflux flowrate have been attributed to the larger vapor amount required by the addition of the temperature control loop in the LV-cascade structure. But the fact that after 1% reduction in the feed temperature all the structures lead to the same reflux flowrate value still requires justification. There are large performance differences between the best (LV-cascade and [L/D,V/B]) and the worse (DV and LV) structures. Observing the light top mass fraction responses it can be verified that the best structures succeed in keeping the setpoint, with a minor advantage for the LV-cascade structure.
Evaluation of Control Structures for a Debutanizer Column
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Figure 1. LV (+), DV (o), [L/D,V/B] (x) and LV-cascade (-) responses for feed flowrate (a, d), temperature (b, e) and composition (c, f) disturbances; sum of distillate light components mass fractions (a, b, c), reflux mass flowrate (d, e, f).
Figure 2. LV (+), DV(o), [L/D,V/B] (x) and LV-cascade (-) responses for feed flowrate (a, d), temperature (b, e) and composition (c, f) disturbances; sum of bottom’s light components mass fractions (zoom) (a, b, c) and vapor mass flowrate coming from the reboiler (d, e, f).
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L.R. Canabarro et al.
The control efforts showed by changes in manipulate variables are almost equal, with a notable exception in the case of the (L/D, V/B) structure submitted to a disturbance in F, were the manipulated variable presents an inverse behavior. There is no simple explanation to this fact, but it is important to remind that the complex multicomponent feed, with small amounts of light component, could produce complex thermodynamic effects. Considering the bottom, where the tuning was less rigid, it can still be observed the best performance of LV-cascade and (L/D,V/B), but now it is not possible to distinguish any clear difference between them. It should be note that in this case disturbances effects are very small due to non-significant light components concentration.
3. Conclusions The information obtained from simple static indexes was not sufficient to determine a best control structure. RGA results agreed with Shinskey (1984), apparently showing that the (L/D, V/B) structure has better decoupling characteristics than DV, and this than LV. Although there is not enough room for a detailed presentation, it is worth mentioning that setpoint top composition changes produced larger interaction effects in the structure (L/D, V/B) than in DV, in opposition to the previous statement. Moreover, the best performance during the simulation tests was obtained for the LV-cascade structure, whose index Ȗ* was the worst. It is interesting to note that, for the studied case, the positive characteristics of the “general” structure proposed by Skogestad (2007) were confirmed. The main conclusion that can be extracted form this work is that every effort should be made to have accurate dynamic simulators to aid the design of distillation columns control structures.
Acknowledgment The authors are grateful to CNPq and Petrobras for their support.
References E. H. Bristol, 1966, On a New Measure of Interaction for Multivariável Process Control, IEEE Trans. Auto. Con., AC-11, pp.133-134. P. Grossdidier, M. Morari, B. R. Holt, 1985, Closed-Loop Properties from Steady-State Gain Information, Ind. Eng. Chem. Fundam., 24, pp. 221-235. K. E. Häggblom, K. V. Waller, 1988, Transformations and Consistency Relations for Distillation Control Structures, AIChE Journal, 34, 1634-1648. F. G. Shinskey, 1984, Distillation Control, McGraw-Hill, New York. S. Skogestad, 2007, The Dos and Don´ts of Distillation Column Control, Trans IChemE, Part A, 85(A1), pp. 13-23.
1473
Evaluation of Control Structures for a Debutanizer Column Lilian R. Canabarro,a Mario C. M. M. Campos,b Enrique L. Limaa a
Programa de Engenharia Química/COPPE, Universidade Federal do Rio de Janeiro, Cidade Universitária, CP 68502, Rio de Janeiro, RJ, Brazil 21945-970 b PETROBRAS S.A. Av. Horacio Macedo, 950, Rio de Janeiro RJ, Brazil 21941-915
Abstract In this work is described the choice of the control structure for a specific industrial distillation column presenting a significant discrepancy between the inventories of the top and bottom sections. The studied distillation column showed to be an excellent research field, but looking for the balance between scientific development and industrial application it is always important to take into consideration the variable “time invested”. In this context, and searching for a satisfactory control structure, static analysis tools, as RGA and SVD, had been used in the characterization of a set of alternatives structures based on the primary composition control variables L, V, D and B, as well as some relations between them. With the reduction of the “time invested” kept in mind, it was used a rigorous dynamic simulator capable to deal with thermodynamic calculations for complex multicomponent mixtures, as those found in the processing units of crude oil and its fractions. Results have demonstrated the importance of rigorous dynamic simulation to solve design control problems in distillation columns which frequently presents unique characteristics and should be treated accordingly. Keywords: Distillation control, control structure selection, dynamic simulation
1. Introduction The interest on distillation control systems started in the decade of the 50s, significantly increasing along the time, with special emphasis in the 80s. One conclusion that can be drawn from the huge amount of technical and scientific literature produced in this period is that distillation is a difficult system to understand. The scientific research is continuously improving our knowledge on the subject, but the practice is still confronted with serious difficulties, because each distillation column seems to be different from other ones and, in such a way, requires a personalized treatment. Recently Skogestad (2007) wrote “Many books...and papers, including several of my own..., have been written on the merits of the various configurations, but it is probably safe to say that the importance of the choice of configuration (level control scheme) has been overemphasized”. These words are a good example of the knowledge (scientific or general) evolution process, as they clearly express the permanent and necessary substitution of old “truths” by new ones. Certainly this subject deserves much more deep thoughts, but the idea here is only to show that in complex cases, as certainly can be the distillation columns, many of the “general truths” that had been enunciated had not been confirmed in practice, requiring more specific approaches. In his contribution Skogestad (2007) proposed a distillation column control methodology with reasonable general application, bringing great contribution for the practical side of the problem. The focus of this work is on the control structure design for a specific debutanizer
L.R. Canabarro et al.
1474
column using simple and practical tools, complemented with rigorous dynamic simulation.
The Problem The studied system is a 26 trays naphtha stabilizer column of a crude atmospheric distillation unit. The feed, coming from the top of the atmospheric tower and introduced in tray 13th (from the top), contains 30 components, including 2% of light components (methane, ethane, propane, butanes, pentanes, etc.), water and 20 pseudo-components. The bottom product of the column is used to preheat this feed. Because it is almost totally in the liquid phase, vapor and liquid flows in the stripping section are larger than in the rectifying section, and as a consequence the thermal load to the reboiler is larger than to the condenser. There are three products in the system: combustible gas and liquefied petroleum gas (LPG) in the vapor and liquid streams that leave a partial condenser; and stabilized naphtha in the bottom stream. The control objective is to obtain a top product with the highest purity, guaranteeing the LPG quality, without reducing the quality of the stabilized naphtha. As this is produced in a large amount, significant quality variations are not expected, so the top composition control was considered a priority. Technical-scientific literature shows that the Relative Gain Array (RGA) introduced by Bristol (1966) is still an important analysis and design tool for multivariate systems. Initially developed to determine static interaction in systems, allowing appropriate pairing between input and output variables in a control structure, its area of applicability was significantly extended later, both for static and dynamic conditions (Grossdidier et al., 1985). Considering the stationary case and using the system gain matrix K, the RGA matrix ȁ can be obtained as follows,
/
>O @ ij
>K > K @ @ 1 T
ij
ij
where Ȝij is the ratio of the static gain of the output variable i related to the input variable j, with all the other pairs in open loop, to the static gain of the same pair (i,j), with all the other pairs under perfect control. A RGA matrix close to identity indicates small interaction, determining the appropriated pairing. Another tool, sometimes complementary to the RGA, results from Singular Value Decomposition, SVD (Grossdidier et al., l985). Also considering the static case and starting from the gain matrix K, the SVD is defined as
K
U6V T
where U and V are unitary matrices, and 6 is a diagonal matrix with the singular values in descending order of magnitude. The ratio of the largest to the smallest singular value defines the Condition Number, Ȗ, a measure of the difficulty to control the associated system. As this number is dependent on variables units (scaling) it can take very different values for the same system. The correct way to take advantage of the information supplied by the condition number is to use the scaling that produces the minimum value, Ȗ* (scaling doesn’t change system’s characteristics). Research literature clearly shows limitations when evaluating a system operating in dynamic
Evaluation of Control Structures for a Debutanizer Column
1475
condition using static information. However, it is important to notice that in many practical cases it is difficult to get a reasonable dynamic description of the system, limiting the use of complex elaborated theoretical methods. An approach for calculating the gain matrices of different alternative control structures from the knowledge of only one aroused great interest in the end of the 80s and early 90s. The method introduced by Häggblom and Waller (1988) was based on transformations and relations of consistency derived from global and component mass balances. This approach seemed to be quite useful for simplifying the calculation of RGA and SDV of different control structures. Considering only the top and bottom distillation products quality control, there are 4 primary manipulated variables available: reflux (L), distillate (D), bottom (B) and vapor (V) flowrates. From these primary variables the literature reports a large number of combinations that generates secondary variables, allowing the design of a large number of control structures. Disregarding any one of them could be a difficult task, requiring significant testing work. This is facilitated by combining the use of appropriate indices, such as RGA and Ȗ (there are many others, with varying complexity), system knowledge and computer simulation.
2. Implementation A set of control structures was chosen for evaluation disregarding some literature recommendations (sometimes divergent), because they are commonly based on results obtained from very simplified systems. Due to the large bottom flowrate the popular LB structure was not considered. The structures chosen were: LV, DV and (L/D, V/B). A fourth structure was also chosen where, as suggested by Skogestad (2007), a fast tray temperature loop was include in the stripping section. In this structure, identified as LVcascade, the top composition is controlled by a cascade control system, manipulating a pump’s rotor speed, where the internal loop controls the reflux. The bottom composition is controlled by another cascade control system, manipulating V, where the internal loop controls the 19th tray temperature. Table 1 shows the values of K, RGA, Ȗ e Ȗ* for each control structure.
Structure
Table 1 Static gains, RGA and conditional numbers K ȁ
Ȗ
Ȗ*
LV
ª 1.023 « 6 ¬ 3.88e
0.5806 º » 1.12e 3 ¼
ª 1.0018 0.0018º « 0.0018 1.0018 » ¬ ¼
1259.5
1.0892
DV
ª 2.12 « 6 ¬ 6.86e
0.6014 º » 1.12e 3 ¼
ª 1.0017 0.0017º « 0.0017 1.0017 » ¬ ¼
2048.7
1.087
L/D V/B
ª 3.70e 2 « 8 ¬ 9.45e
5.6202 º » 1.08e 2 ¼
ª 1.0013 0.0013º « 0.0013 1.0013 » ¬ ¼
79155
1.0757
LV-Cascade
ª 2.1790 « 6 ¬ 8.37e
1.11e 2 º » 2.68e 6 ¼
ª 1.0162 0.0162º « 0.0162 1.0162 » ¬ ¼
826230
1.2887
The RGA and Ȗ* values indicate that the different structures should present similar behavior, in terms of insignificant interaction and good conditioning (although system scaling is weak). From this information it is possible to choose good variable pairing
L.R. Canabarro et al.
1476
and to have a feeling of the control viability of the different structures, but it is not enough to define which structure is the best. To this end dynamic simulation (gPROMS®, Multiflash®) was used, comparing the behavior of the different structures when the system is perturbed by the most common disturbances in distillation columns: changes in feed flowrate, temperature and composition. Before presenting the simulation results, it is important to shortly comment about the experience we have with the transformations method (Häggblom e Waller, 1988). Using the gain matrix of the LV structure the method was used in order to calculate the gain matrices of the other ones. As can be seen in Table 2, there was no consistence in the obtained results. Table 2 RGA by transformations from LV Structure ȁ L/D V/B
ª 2.4442 3.4442 º « 3.4442 2.4442» ¬ ¼
DV
ª 1.0002 0.0002º « 0.0002 1.0002 » ¬ ¼
Although the result obtained for DV was similar to the one obtained from data specifically acquired for this structure (Table 1), the result obtained for (L/D,V/B) was completely different. This could be an indication that the assumptions on which the method is based are not satisfied in this case. As in practice this disagreement can be quite common, it may justify the little impact of the method observed in research literature after some initial popularity. The papers studying the transformation method were certainly of great value to improve the knowledge on distillation columns, but their use in practical problems requires a careful preliminary analysis. Some old “truths” must probably be re-evaluated to be put in their real dimension. Searching for the best control structure for the studied column the behavior of each structure was simulated against feed flowrate (+/- 10%), temperature (+/- 1%; the system is highly sensitive to this disturbance) and composition (+/- 10%) disturbances. Controllers were tuned in such way as to get the best performance for each structure. Results in Figure 1 were obtained for the top of the column against the positive flowrate and composition disturbances, and the negative temperature disturbance. In addition to the controlled variables responses, the behavior of primary manipulated variables is also shown. Figure 2 displays similar results for the bottom of the column. Considering the top (Figure 1), where composition control was more rigorous, it can be notice that there are close relations between the disturbances effects on the composition. The effect of 10% variation in feed flowrate was almost equivalent to -1% variation in feed temperature, while the effect of +10% variation in feed composition was less significant and in the opposite direction. The differences observed in the magnitude of the initial reflux flowrate have been attributed to the larger vapor amount required by the addition of the temperature control loop in the LV-cascade structure. But the fact that after 1% reduction in the feed temperature all the structures lead to the same reflux flowrate value still requires justification. There are large performance differences between the best (LV-cascade and [L/D,V/B]) and the worse (DV and LV) structures. Observing the light top mass fraction responses it can be verified that the best structures succeed in keeping the setpoint, with a minor advantage for the LV-cascade structure.
Evaluation of Control Structures for a Debutanizer Column
1477
Figure 1. LV (+), DV (o), [L/D,V/B] (x) and LV-cascade (-) responses for feed flowrate (a, d), temperature (b, e) and composition (c, f) disturbances; sum of distillate light components mass fractions (a, b, c), reflux mass flowrate (d, e, f).
Figure 2. LV (+), DV(o), [L/D,V/B] (x) and LV-cascade (-) responses for feed flowrate (a, d), temperature (b, e) and composition (c, f) disturbances; sum of bottom’s light components mass fractions (zoom) (a, b, c) and vapor mass flowrate coming from the reboiler (d, e, f).
1478
L.R. Canabarro et al.
The control efforts showed by changes in manipulate variables are almost equal, with a notable exception in the case of the (L/D, V/B) structure submitted to a disturbance in F, were the manipulated variable presents an inverse behavior. There is no simple explanation to this fact, but it is important to remind that the complex multicomponent feed, with small amounts of light component, could produce complex thermodynamic effects. Considering the bottom, where the tuning was less rigid, it can still be observed the best performance of LV-cascade and (L/D,V/B), but now it is not possible to distinguish any clear difference between them. It should be note that in this case disturbances effects are very small due to non-significant light components concentration.
3. Conclusions The information obtained from simple static indexes was not sufficient to determine a best control structure. RGA results agreed with Shinskey (1984), apparently showing that the (L/D, V/B) structure has better decoupling characteristics than DV, and this than LV. Although there is not enough room for a detailed presentation, it is worth mentioning that setpoint top composition changes produced larger interaction effects in the structure (L/D, V/B) than in DV, in opposition to the previous statement. Moreover, the best performance during the simulation tests was obtained for the LV-cascade structure, whose index Ȗ* was the worst. It is interesting to note that, for the studied case, the positive characteristics of the “general” structure proposed by Skogestad (2007) were confirmed. The main conclusion that can be extracted form this work is that every effort should be made to have accurate dynamic simulators to aid the design of distillation columns control structures.
Acknowledgment The authors are grateful to CNPq and Petrobras for their support.
References E. H. Bristol, 1966, On a New Measure of Interaction for Multivariável Process Control, IEEE Trans. Auto. Con., AC-11, pp.133-134. P. Grossdidier, M. Morari, B. R. Holt, 1985, Closed-Loop Properties from Steady-State Gain Information, Ind. Eng. Chem. Fundam., 24, pp. 221-235. K. E. Häggblom, K. V. Waller, 1988, Transformations and Consistency Relations for Distillation Control Structures, AIChE Journal, 34, 1634-1648. F. G. Shinskey, 1984, Distillation Control, McGraw-Hill, New York. S. Skogestad, 2007, The Dos and Don´ts of Distillation Column Control, Trans IChemE, Part A, 85(A1), pp. 13-23.