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Operation and Control of Dividing Wall Distillation Columns
0263±8762/98/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol 76, Part A, March 1998
OPERATION AND CONTROL OF DIVIDING WALL DISTILLATION COLUMNS Part 1: Degrees of Freedom and Dynamic Simulation M. I. ABDUL MUTALIB and R. SMITH (FELLOW) Department of Process Integration, UMIST, Manchester, UK
T
he dividing wall distillation column has been known now for some 50 years. Despite its potential to make major savings in energy and capital costs in distillation, it has not been widely used in practice. One of the major fears in applying the technology is uncertainty regarding the control and operation of the arrangement. This paper investigates theoretically the operation and control of the dividing wall column. A degrees of freedom analysis was performed to determine the number of control loops required. Possible control con® gurations were then investigated using Relative Gain Array Analysis and dynamic simulation. The results of these theoretical studies indicate that simple control schemes are capable of providing stable control. Keywords: dividing wall distillation; thermal coupling; dynamic simulation; control; pilot plant
Rudd1 2 , Cerda and Westerberg1 3 , Spadoni and Stramigioli1 4 , Nikolaides and Malone1 5 ). Recently, a design procedure which allows for optimization of the column has been proposed by Triantafyllou and Smith1 6 . By contrast, studies on the operational and control aspects of the Petyluk con® guration have received little attention in the past. Chavez et al.1 7 and Lin et al.1 8 reported multiple steady state solutions for the Petyluk con® guration. Using computer simulation, they presented four different solutions at a speci® ed re¯ ux which have different internal liquid and vapour ¯ ows between the prefractionator and the main column. As they reduced the re¯ ux ratio to a value beyond which no feasible solution existed, a unique solution was found. This is the optimum combination of the internal liquid and vapour ¯ ows which gives the minimum energy requirement. Wolff et al.1 9 , 2 0 performed control studies on the Petyluk con® guration using a three point and four point composition control. For the three point composition control, they set up a control con® guration which maintained the composition of the three main products of the column. Using one of the possible control schemes, they were able to achieve satisfactory control performance, given feed (¯ owrate and composition) and set point disturbances. For the four point composition control, they used the internal liquid split between the prefractionator and the main column to control the impurity ratio in the side draw as an additional control loop. They discovered that a problem can occur within a range of the internal liquid splits whereby the product speci® cations cannot be achieved. A similar result was observed when the vapour split was used in place of the liquid split. Morud and Skogestaad2 1 later provided an explanation for this using three dimensional plots displaying the variation of the reboiler duty and side draw impurity ratio against changes in the internal liquid and vapour splits.
INTRODUCTION Distillation remains the most important method used in the chemical industry for the separation of homogeneous mixtures, with the amount of energy used in distillation operations being considerable. Appropriate integration of the distillation column with the overall process can result in signi® cant energy savings (Linnhoff et al.1 , Smith and Linnhoff 2 ) but the scope for this is often limited. Other options involve the use of complex distillation arrangements such as the side-stripper, the side-recti® er or the fully thermally coupled (Petyluk) con® guration. Such complex arrangements can consume signi® cantly less energy when compared to a conventional arrangement. So far, the use of complex arrangements has largely been limited to crude oil distillation where the side stripper arrangement has been used extensively. The Petyluk con® guration (Figure 1a) was initially introduced some 50 years ago (Brugma3 ). Theoretical studies on a stand alone basis (Petyluk et al.4 , Fidskowski and Krolikowski5 , Glinos and Malone6 and Kaibel7 ) have shown that it is capable of achieving typically 30% of energy savings compared with a conventional sequence. In addition, the Petyluk arrangement can also be achieved by placing a vertical wall in the middle of the column (Figure 1b), separating the feed from the side draw (Wright8 , Kaibel9 ). Thus an overall reduction in capital cost can be expected through the elimination of a column shell, reboiler and condenser when compared with a conventional arrangement. Despite these advantages, industry has been reluctant to use the Petyluk and dividing wall con® gurations. This can largely be attributed to the lack of established design procedures and the fear of control problems. The design of the Petyluk con® guration has been studied by many researchers (Stupin1 0 , Fonyo et al.1 1 , Tedder and 308
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Figure 1. Fully thermally coupled columns. (a) Petyluk column; (b) Dividing wall column.
In this paper, the complexity of the dividing wall column will ® rstly be assessed by performing degrees of freedom analysis. The variables leading to the additional complexity of the column, when compared to the more established side draw column, will then be analysed to investigate the impact on the operation and control of the column. Dynamic simulation will also be used to investigate the controllability of the column from a theoretical point of view. Part 2 of this paper will discuss pilot plant control studies on such a column. DEGREES OF FREEDOM ANALYSIS 22
A method developed by Howard for analysing the degrees of freedom at unsteady state condition has been used for the dividing wall column. The method is based on the fact that the degrees of freedom for a system is equal to the sum of degrees of freedom of all the units in the system minus the sum of degrees of freedom for all the interconnecting streams. This requires the system to be torn apart into smaller units with inter-stream connections. When analysing the degrees of freedom for any of the units, hold up is included to account for the unsteady state. The way the method handles hold up is by treating it as a quantity stream with the same variables as the interconnecting stream, except that a hold up quantity is used instead of ¯ owrate. In a distillation column, the units consist of stages, condenser and accumulator, reboiler and stream splitters which are connected by interconnecting streams. Each of the interconnecting streams has degrees of freedom equal to NC + 2 where NC is the number of components present in the stream. These variables consist of NC-1 concentration variables, a rate or quantity variable and two other intensive variables i.e. temperature and pressure. A stage in a distillation column consists of four interconnecting streams, a quantity stream for the hold-up and a heat stream. Note that only the liquid hold-up is accounted for while the vapour hold-up is neglected. Since there are 5 streams present and each stream has NC + 2 variables, with a heat quantity term, Q, the number of variables in the unit is 5NC + 11. The relationships among the variables depends on the way in which the stage is de® ned. Suppose, the stage is considered to be a single Trans IChemE, Vol 76, Part A, March 1998
mixed pool with the liquid leaving having the same properties as the liquid on the stage, the number of relationships is equal to 3NC + 4. These relationships consist of a total material balance, an energy balance, NC-1 component balances, NC distribution relationships between the vapour and liquid phase, i.e. vapourliquid equilibrium, NC-1 concentration identities for liquid leaving and liquid on the stage, two temperature identities and two pressure identities for the vapour and liquid leaving and liquid on the stage. Hence the degrees of freedom for the unit are: No. of DOF
= No. of variables - No. of relationships
= 5NC + 11 - 3NC - 4 = 2NC + 7 The degrees of freedom for a cascade of N stages can then be easily determined by treating the cascade as a system. Since a cascade of N stages are interconnected by 2N-2 streams, the degrees of freedom are: No. of DOF for Sum of DOF Sum of DOF cascade of N units= for N units - 2N - 2 streams
= N(2NC + 7)- 2(N - 1)(NC + 2) = 3N + 2NC + 4
An extra degree of freedom has to be added to the above due to the choice for number of stages in the cascade. Thus the number of degrees of freedom for a cascade of N stages are 3N + 2NC + 5. In contrast to the conventional stage, the feed and side draw stages are slightly different. This is due to the fact that an extra stream is involved. For a feed stage, the number of degrees of freedom is equal to the number of degrees of freedom for a stage plus the number of degrees of freedom for a stream, thus giving 3NC + 9. A side draw stage can be represented by a stage connected to a splitter which divides between the side draw ¯ ow (either a vapour or liquid) and the ¯ ow to the next stage. Since stages can be attached to the cascade of stages prior to the side draw stage location, only the number of degrees of freedom for the splitter needs to be counted. Using the same approach as described for the conventional stage, with the exception that
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there is no hold up, the number of degrees of freedom for a splitter unit is found to be NC + 5. A condenser and accumulator unit consist of two ¯ ow streams, a quantity stream and a heat stream. Note that the liquid hold up is considered as the quantity stream. The number of variables in the unit comes from the three streams and a heat quantity term are 3NC + 7, while the number of relationships between the variables is 2NC + 2, i.e. total material balance, a heat balance, NC1 component balances and NC-1 concentration, a pressure and a temperature identities for liquid leaving the unit. Therefore, the of degrees of freedom for this unit are NC + 5. The reboiler unit consists of 3 ¯ ow streams, a quantity stream and a heat stream. Again, the liquid hold up is considered as a quantity stream. The number of variables in the unit which comes from the four streams and a heat quantity term are 4NC + 9. However, the number of relationships between the variables that can be derived for the unit is 3NC + 4 thus giving the number of degrees of freedom to be NC + 5 (which turns out to be the same as the condenser unit). The relationships between the variables that can be derived for the unit consist of a total material balance, a heat balance, NC-1 components balances, NC distribution relationships and NC-1 concentration, two pressure and two temperature identities for liquid and vapour leaving the unit. Table 1 summarizes the degrees of freedom for each of the units in a typical distillation column. The dividing wall column can be represented by the Petyluk con® guration as illustrated in Figure 2. The column is divided into 6 sections, each containing a number of cascaded trays. There are three feed and three side-draw trays located between the sections with a partial reboiler and total condenser at the top and bottom of the column. Table 2 gives details of the analysis of the degrees of freedom for the dividing wall column. Based on the analysis, the number of degrees of freedom for the column is thus 3(NS(1) + NS(2) + NS(3) + NS(4) + NS(5)+ NS(6))+ NC + 35 where NS(i) is the number of stages in section `i ’ . After taking into account of the inherent relationships and the product speci® cations, the number of degrees of freedom for the column is NC + 10. Because the feed composition, ¯ owrate and pressure are ® xed, the number of degrees of freedom left is 9. This means that only nine variables can be manipulated or speci® ed in order to fully control the system. The 9 variables involved are shown in Table 3. When comparing this to the more established side draw column, the dividing wall column has 2 Table 1. Degrees of freedom for various units in a distillation column. Unit 1. 2. 3. 4. 5. 6. 7.
Single phase streams Ideal stage Cascade of N ideal stages Feed stage Stream splitter (no hold up) Total condenser/accumulator Partial reboiler
Degrees of freedom NC + 2 2NC + 7 3N + 2NC + 5 3NC + 9 NC + 5 NC + 5 NC + 5
Figure 2. Layouts of the units in a dividing wall column.
additional degrees of freedom which are the liquid and vapour splits. In the implementation of the dividing wall column, it is impractical to manipulate the vapour split. Hence, the vapour split will be left to occur naturally. Therefore, a degree of freedom is lost here. Unlike the vapour split, the liquid split can be easily manipulated using a simple device, thus leaving the option open to the designer. The decision whether to employ it as a manipulated variable will be assessed later.
COLUMN CONFIG URATION The design of the dividing wall column can be treated similar to the design of the Petyluk con® guration (Triantafyllou2 3 ). However, there is one major difference between the two columns. This results from the ® xed position of the dividing wall which prevents the manipulation of the internal vapour split in the column. For the Petyluk con® guration, the vapour split was manipulated in most of the previous studies due to the separate shell arrangement. A steady state rigorous simulation model for the dividing wall column was developed using the ASPEN PLUST M package. The ternary mixture used for the separation consists of methanol, iso-propanol and butanol. The Wilson equation was used for the prediction of vapour liquid equilibrium. The con® guration of the dividing wall column was designed using the method proposed by Triantafyllou and Smith1 6 , using the option for minimizing the number of stages. The feed to the column has an equimolar composition and the products speci® ed to be 98.5 mol percent. The arrangement on the distribution of the number of stages at different sections inside the column, together with the operating parameter, are given in Figure 3. Trans IChemE, Vol 76, Part A, March 1998
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Table 2. Degrees of freedom analysis for dividing wall column. Units
Degrees of Freedom
Top Column Section. Condenser/accumulator. Re¯ ux splitter. Cascade of stages (Section 1). Vapour feed stage. Liquid draw stage.
NC + 5 NC + 5 3NT(1) + 2NC + 5 3NC + 9 NC + 5
Dividing Wall Section. Prefractionator side. Cascade of stages (Section 5). Feed stage Cascade of stages (Section 6).
3NT(5) + 2NC + 5 3NC + 9 3NT(6) + 2NC + 5
Main Side. Cascade of stages (Section 2). Liquid draw stage. Cascade of stages (Section 3).
3NT(2) + 2NC + 5 NC + 5 3NT(3) + 2NC + 5
Bottom Column Section. Liquid feed stage. Vapour draw stage. Cascade of stages (Section 4). Partial reboiler.
3NC + 9 NC + 5 3NT(4) + 2NC + 5 NC + 5
Total DOF
3(NT(1) + NT(2) + NT (3) + NT(4) + NT (5) + NT (6))+ 27NC + 87
Restriction from 26 interconnecting streams
- 26NC + 52 3(NT(1) + NT(2) + NT (3) + NT(4) + NT (5) + NT (6))+ NC + 35
Total column DOF
Restriction from inherent relationships, design speci® cations and uncontrolled variables. Pressures on all stages, reboiler, condenser and re¯ ux splitter. Heat leaks on all stages and splitters. Holdup on all stages. No. of plates at each section. Feed (composition, ¯ owrate and pressure).
NT(1) + NT (2) + ¼ + NT (6) + 9 NT(1) + NT (2) + ¼ + NT (6) + 7 NT(1) + NT (2) + ¼ + NT (6) + 3 6 NC + 1
Total DOF restricted
3(NT(1) + NT(2) + NT (3) + NT(4) + NT (5) + NT (6) + NC + 26
Degrees of freedom for the column
9
IMPAC T OF THE LIQUID SPLIT ON THE MIDDLE PRODUCT COMPOSITION In the practical implementation of the dividing wall column, the liquid split can easily be manipulated. One way of achieving this is by means of simple ¯ ow controller installed externally on both liquid streams returning to the top of each side of the dividing wall. A ratio controller can be used to ® x or to vary the two ¯ ows according to a speci® ed ratio. However, if a ® xed ratio is desired, an internal mechanism located at the top of the dividing wall can serve to divide the ¯ ows to each side of the wall
according to the set ratio used. Manipulating the liquid split at the top of the dividing wall is a way of manipulating the re¯ ux ratio on each side of the wall. Triantafyllou and Smith1 6 presented a procedure to optimize the re¯ ux ratio in different parts of the column in the initial design. Calculations were performed to ® nd the relation between the liquid split and the composition of the light key (methanol) as well as the middle key (iso-propanol) in the middle product. To achieve this, the liquid split was changed at different values while keeping the vapour split constant at base case value, i.e. 1.29. Note that the split is de® ned as the ratio between the ¯ ow on the product
Table 3. Controlled and manipulated variables for dividing wall column. Controlled variables 1. 2. 3. 4. 5. 6. 7. 8. 9.
Feed temperature Column pressure Top product composition Middle product composition Bottom product composition Condenser/accumulator holdup Reboiler holdup Light impurity in middle product Heavy impurity in middle product
Trans IChemE, Vol 76, Part A, March 1998
Manipulated variables Feed preheater duty Condenser cooling duty Re¯ ux ¯ owrate Distillate ¯ owrate Sidedraw ¯ owrate Reboiler duty Bottom product ¯ owrate Liquid split at top of dividing wall Vapour split at bottom of dividing wall
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ABDUL MUTALIB and SMITH The magnitude of changes for the methanol composition seems to be very small for most of the range used for the variation in the liquid split. Therefore, controlling the methanol concentration using the liquid split would require a large action in order to correct a small deviation. In addition, varying the liquid split also affects the isopropanol composition by a similar magnitude to the effect on the methanol composition. If the iso-propanol composition is controlled by another manipulated variable such as the side draw ¯ owrate, the two control loops are bound to interact signi® cantly.
Figure 3. The dividing wall column con® guration and the base case operating parameter.
side to the ¯ ow on the feed side of the dividing wall. The feed composition, ¯ owrate and temperature as well as the product ¯ owrates and reboiler duty were also kept constant. Figure 4 (i) shows the variation of methanol composition in the middle product, while Figure 4 (ii) shows the variation of iso-propanol composition in the middle product. Both were subjected to variation in the liquid split. The pattern of changes followed by the methanol composition exhibits a minimum point as the liquid split is varied. The signi® cance of this observation is that simple PID control cannot be applied to link these two variables to form a control loop. At two different locations along the curve, separated by the minimum point, the direction for the control action is different. Since it is not possible for a normal PID controller to recognize on which side of the curve the current operation is located, and it is not also possible for the controller to have a variable gain sign, applying the controller in such a situation will lead to failure.
IMPACT OF THE VAPOUR SPLIT ON THE MIDDLE PRODUCT COMPOSITION In the dividing wall column operation, manipulating the vapour splits would be impractical. The vapour split inside the column occurs naturally according to the pressure drop relation across the internals at each side of the dividing wall, which will be discussed later. Despite this, calculations were made to determine the effect of changing the vapour split on the middle product composition. The idea of doing this was to investigate whether ® xing the dividing wall would lead to any major bene® t being missed. Figure 5 (i) shows the variation of butanol composition in the middle product while Figure 5 (ii) shows the variation of iso-propanol composition in the middle product. Both were subjected to variation in the vapour split. This leads to the same conclusions as for the liquid split. From the analysis conducted for the liquid and vapour splits, it is clear that maintaining the two splits constant seems to be the preferred option. The same suggestion can also be extended to the Petyluk column. However, in doing so, the impurities and the main component compositions in the middle product cannot be controlled simultaneously.
Figure 4. Variation in middle product composition subject to changes in liquid split. (a) Methanol; (b) Iso-propanol.
Figure 5. Variation in middle product composition subject to changes in vapour split. (a) Iso-propanol; (b) Butanol.
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Figure 6. Generalized pressure drop correlation chart.
IMPACT OF THE LIQUID SPLIT ON THE VAPOUR SPLIT As mentioned earlier, the vapour divides to satisfy the pressure drop equalization between the sections on each side of the dividing wall. In the case where the number of stages are equal at each side of the dividing wall, the vapour split depends on the position of the dividing wall and the liquid loading of the two sections at each side of the dividing wall. The liquid loading of the two sections vary as the liquid split is changed. Before the impact of the liquid split on the vapour split can be assessed, some form of relation must be established between the changes in the liquid loading and the resulting changes in the pressure drop across a packing height or trays. In the present case, it was decided to demonstrate the study using packing as the internals. Figure 6 shows the Generalised Pressure Drop Correlation chart which is typically used for determining the pressure drop across a packed height for a given liquid and vapour loading. When considering the changes in the pressure drop with respect to the liquid loading, two regions can be identi® ed. In the ® rst region, which corresponds to low liquid loading, the pressure drop hardly changes with the liquid loading. In the second region, which corresponds to high liquid loading, the pressure drop changes more signi® cantly with the liquid loading. Based on the above observation, a number of conclusions can be made. If the dividing wall column is operated within the ® rst region, the liquid split changes should not affect the vapour split. Therefore, operating within this region should provide some ¯ exibility in changing the liquid split. Conversely, if the column is operated within the second region, the vapour split will vary as the liquid split changes, thus offering no ¯ exibility during the operation of the column. Following this, a correlation between the pressure drop and the liquid and vapour loadings for a speci® c type of packing (Gempak 4A, GLITSCH2 4 ), applicable within the ® rst region, was used to determine the relation between the position of the dividing wall (described by the area ratio between the product side to the feed side of the column) and the vapour split speci® ed. For a given cross sectional area of the column and the number of stages on each side of the dividing wall and using the information on liquid and vapour loading at each stage obtained from rigorous simulation for a speci® ed liquid and vapour split, the area ratio required to satisfy the pressure drop equalization criteria can be calculated. The criteria can be based on either the total pressure drop or the average pressure drop on both sides of the dividing wall. Trans IChemE, Vol 76, Part A, March 1998
Figure 7. Area ratio and vapour split relationship for pressure drop equalization between the two sides of the dividing wall. (Equal number of stages at both sides).
Figure 7 shows the plot obtained, which demonstrates a linear relation between the area ratio and the vapour split required. More signi® cantly, the area ratio was found to be almost the same as the vapour split speci® ed when equal number of stages were used on each side of the dividing wall. This indicates that in order to obtain the desired vapour split, the position of the dividing wall can be set to give the same area ratio as the required vapour split. DESIGNING FOR THE LIQUID AND THE VAPOUR SPLITS Having given all the arguments which led to the preference for operating the dividing wall column with a constant liquid and vapour split, it is then important to know how to design for the two splits. As it is always desirable to operate the column as close as possible to the optimal state, the sensitivity of the optimum location for the two splits with regard to changes in the feed composition and the product speci® cations needs to be assessed. IMPACT OF FEED COMPO SITION ON THE OPTIMUM LIQUID AND VAPOUR SPLITS Calculations were performed to determine the variation in the liquid and vapour splits required to maintain lowest energy consumption for changes in the feed composition. Three different feed compositions within the allowable range were tested and the value for the two splits that gave minimum energy consumption were found for each case using rigorous simulation. Note that the middle product impurities were not included in the product speci® cations as it has already been decided not to control them using the liquid and the vapour split. Table 4 presents the results obtained from the analysis. The optimum values for the liquid and vapour splits were found to be insensitive to the variation in the feed composition. IMPACT OF PRODUCT SPECIFICATION ON THE OPTIMUM LIQUID AND VAPOUR SPLITS Following the above, calculations were performed for different product speci® cations. Table 5 presents the results
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Table 4. Optimum liquid and vapour split for changes in feed composition. Feed composition
Optimum liquid split
Optimum vapour split
3.80
1.16
3.80
1.16
3.90
1.16
3.75
1.15
Table 5. Optimum liquid and vapour split for changes in product speci® cation. Product speci® cation
Feed 1 (0.333, 0.334, 0.333) Feed 2 (0.363, 0.334, 0.303) Feed 3 (0.303, 0.364, 0.333) Feed 4 (0.303, 0.334, 0.363)
obtained. The optimum values for the liquid and vapour splits were found to vary as the product speci® cations changed. Figure 8 shows three sets of plots where the difference in reboiler duty between the operation of the column at a speci® ed liquid or vapour split and operation at the optimum splits are plotted against the speci® ed liquid or vapour split. The plots cover the location within the optimum splits for three different product speci® cations. There are two plots for each product speci® cation. For the ® rst plot, the vapour split is kept constant at its optimum value while allowing liquid split to vary. For the second plot, the liquid split is kept constant at its optimum value while allowing the vapour split to vary. A comparison between the plots obtained for the different product speci® cations shows that the optimum location tends to be more sensitive to the changes in liquid and vapour splits as the product speci® cations were increased. This was shown by the extent of the ¯ at region within the optimum location which tended to reduce slowly as the product speci® cations were increased. Hence, it is important that the column is run close to the optimum liquid and vapour splits for the higher product speci® cations otherwise a high energy penalty will have to be paid.
98 mol percent 98.5 mol percent 99 mol percent
Optimum liquid split
Optimum vapour split
3.5 3.8 3.7
1.02 1.16 1.29
In the dividing wall column operation, the vapour split is largely ® xed by the position of the dividing wall but the liquid split has the ¯ exibility to be changed. However, as discussed earlier, manipulating the liquid split can lead to serious problem in the operation and control of the dividing wall column. Therefore, it is better to ® x the liquid split. Fixing the liquid and vapour split for a different feed composition will not be a problem as the optimum value for the liquid and the vapour split hardly change. However, it is not so straightforward when the product speci® cations are allowed to vary. In this case, the above ® nding can be used to help decision making. The obvious choice is to set the liquid and vapour splits at the optimum values for the highest product speci® cations designed for the column. The reason for this is because of the relative importance in operating the column with liquid and vapour splits close to the optimum values for higher product speci® cations compared with lower product speci® cations. Even if the column is operated to produce lower purity products, the penalty in terms of the energy consumption when operating the column with the optimum splits for the higher product speci® cations proves to be reasonably small. On the other hand, if the column is operated with the optimum liquid and vapour splits for lower product speci® cations and higher purity products are to be produced, the penalty in the energy consumption can be extremely high and, in certain cases, the higher product speci® cations might not
Figure 8. Plots of changes in reboiler duty requirement with different liquid and vapour splits.
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Table 6. Results from an example to illustrate the setting for the liquid and vapour splits for the dividing wall column operation. Operating liquid and vapour splits
Product speci® cation (0.98, 0.98, 0.98) (0.99, 0.99, 0.99)
3.7 3.5
Optimum liquid and vapour splits 1.29 1.02
be achieved even running the column at total re¯ ux. Table 6 illustrates the results from an example to explain the above.
COMPO SITION CONTRO L OF THE DIVIDING WALL COLUMN In order to study the control behaviour of the dividing wall column, a dynamic model was built using SPEEDUP T M . Similar con® gurations for the column as modelled previously using the ASPEN PLUST M package were used. The same feed and product speci® cations were employed. In line with the earlier suggestion, the liquid and vapour split were maintained at the optimum values obtained from the design method used (Triantafyllou and Smith1 6 ). The assumption of no heat transfer across the dividing wall was maintained and only decentralized control was used. The short cut dynamic model which is available in SPEEDUP T M was used. Assumptions involved in using the short cut model are perfect material balance, i.e. no accumulation of material in the system, and constant molal over¯ ow. In addition, since the short cut model solves stage equilibrium by lumping several stages together to form a section within the column, constant relative volatility within the section was assumed (but varied between sections). The maximum number of stages that can be lumped within a section must be kept within a reasonable number in order to keep the model within an acceptable accuracy for simulation purposes. The relative volatility within each section was speci® ed by taking the average value obtained for the relevant stages from the rigorous simulation done using ASPEN PLUST M .
3.5 3.7
Energy penalty (percent) 1.02 1.29
6.9 product specs. not achieved with the operating splits
INTERACTION ANALYSIS Two control schemes that can be used for controlling the dividing wall column were considered, i.e. L-S-V and D-S-V (where L, S, D and V refer to manipulation of the top re¯ ux, side draw, distillate ¯ ows and vapour ¯ ow from the reboiler respectively). These are shown in Figure 9. Relative Gain Array Analysis (Bristol2 5 ) was used to analyse the interaction as well as determining suitable pairings between controlled and manipulated variables in the two control schemes. Basically, the RGA is a matrix which consists of elements representing the steady state gain ratio between the respective controlled and manipulated variables when all other manipulated variables are constant, divided by the steady state gain ratio between the same controlled and manipulated variables when all other controlled variables are constant. This is represented by the equation: k
ij
= (¢y / ¢m ) i
j mi
/ (¢yi / ¢mj )yj
where k ij is the relative gain between controlled variable yi and manipulated variable mj . If k ij = 0 then yi does not respond to mj and mj should not be used to control yi . If k ij = 1 then yi only responds to mj and does not interact with other manipulated variables. This is the preferred case. If 0
Table 7. Results for the steady state gain array and the relative gain array. Scheme
Steady state gain array 2.433
L-S-V
- 0.003 - 2.401
2.433
D-S-V
- 0.003
0.014
Figure 9. Two composition control scheme for the dividing wall column.
Trans IChemE, Vol 76, Part A, March 1998
Relative gain array
- 0.274 - 2.659 0.019 - 2.672
11.736 0.001 - 10.736
- 0.274 - 2.659 0.019 - 2.672
0.891 0.001 0.107
0.297
0.014
2.665
0.001
- 10.057 - 0.679 0.011 11.045
0.988 0.691
0.100 0.007 0.892
0.008 0.992 0.001
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Figure 10 (i). Control run for scheme L-S-V with set point changes. (ii). Control run for scheme D-S-V with set point changes.
between the middle product and the bottom product control loops. This means that the middle product composition should be controlled by the vapour ¯ ow while the bottom product composition should be controlled by the side draw ¯ ow.
DYNAMIC SIMULATION Dynamic simulation was then performed to observe the behaviour of the two control schemes when subjected to set point changes and feed disturbances as shown in Trans IChemE, Vol 76, Part A, March 1998
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Figure 11 (i). Control run for scheme L-S-V with feed disturbance. (ii) Control run for scheme D-S-V with feed disturbance.
Table 8. The controllers were tuned using the open loop response curve method. Figure 10 (a) and (b) show the response of the controllers in the two schemes when subjected to set point changes. Both schemes were able to produce a stable control response. Figure 11 (a) and (b) Trans IChemE, Vol 76, Part A, March 1998
show the response of the controllers in the two schemes when subjected to feed disturbances. Again stable control response was produced by both schemes. Overall, the D-S-V scheme seemed to produce better response compared with the traditional L-S-V scheme and
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ABDUL MUTALIB and SMITH Table 8. Set point changes and feed disturbances used.
Set point changes Feed disturbances
Middle product composition IPA: 0.985±0.988 Combined feed composition and ¯ owrate Composition: MeoH ± 0.333 to 0.363 IPA ± 0.334 to 0.284 BuoH ± 0.333 to 0.353 Flowrate: 1.081 to 1.190 kmol/hr
this is in agreement with the results derived from the RGA analysis. More importantly, both schemes were able to produce satisfactory control. CONCLUSIONS In this paper, studies relating to aspects of the operation and control of the dividing wall column have been investigated. When compared to the side draw column, the dividing wall column has a more complex nature, shown through degrees of freedom analysis. This results from two additional manipulated variables, the liquid and vapour splits. However, it is impractical to manipulate the vapour split, which is ® xed by the position of the dividing wall. On the other hand, the liquid split can be easily varied but has been found to have little bene® t in comparison to the complication that will be added to the operation and control of the column. A linear PID controller cannot be used and severe interactions would occur between the control loops, particularly for controlling the composition of the middle product and its impurities. In the region of high liquid and vapour loading, varying the liquid split will also affect the vapour split considerably and this even affects the operation and control of the column further. Based on this account, it was suggested that the column should be operated and controlled with a constant liquid split in addition to the ® xed vapour split. Having made the suggestion, the column can then be operated and controlled in a similar manner as the more established side draw column. Nevertheless, the disadvantage of this proposal is that the impurities composition in the middle product cannot be controlled. The optimum location for the liquid and vapour splits was found to be insensitive to the variation in the feed composition but this is not so for the variation in the product speci® cation. From a sensitivity study, it was found that the lower product speci® cation has a ¯ atter optimum compared with the higher product speci® cations. Therefore, it was concluded that the design for the liquid and the vapour split should be based on the highest product speci® cation when the column is required to produce a range of product compositions. Two composition (three point) control scheme were
selected for demonstrating the control using simulation. The column was subjected to changes in product speci® cation and feed disturbances. Simulation results indicate that stable control was achievable by both control schemes. REFERENCES 1. Linhoff, B., Dunford, H and Smith, R., 1983, Chem Eng Sci, 38(8): 1175. 2. Smith, R. and Linhoff, B., 1988, Chem Eng Res Des, 66: 195. 3. Brugma, A. J., 1942, US Patent 2,295,256. 4. Petyluk, F. B, Platonov, V. M. and Slavinskii, D. M., 1965, Int Chem Eng, 5(3): 561. 5. Fidkowski, Z. and Krolikowski, L., 1987, AIChE J, 33(4): 643. 6. Glinos, K. and Malone, M. F., 1988, Chem Eng Res Des, 66 (3): 229. 7. Kaibel, G., 1988, IChemE Symp Series No. 109: 43. 8. Wright, R. O., 1945, US Patent 2,471,134. 9. Kaibel, G., 1987, Chem Eng Technol, 10: 92. 10. Stupin, W. J., 1970, The separation of multicomponent mixtures in thermally coupled distillation systems, PhD Diss (University of Southern California). 11. Fonyo, Z., Szabo, J. and Foldes, P., 1974, Acta Chim, 82: 235. 12. Tedder, D. W. and Rudd, D. F., 1978, AIChE J, 24(2): 303. 13. Cerda, J. and Westerberg, W., 1981, Ind Eng Chem Proc Des Dev, 20(3): 546. 14. Spadoni, G. and Stramigioli, C., 1983, 3rd Int Cong Computers and Chemical Engineering, Paris, No 27: 43. 15. Nikolaides, I. P. and Malone, M. F., 1987, Ind Eng Chem Res, 26(9): 1839. 16. Triantafyllou, C. and Smith, R., 1992, Trans IChemE, 70 (A2): 118. 17. Chavez, R., Seader, J. D. and Wayburn, T. L., 1986, Ind Eng Chem Fundam, 25(4): 566±576. 18. Lin, W. J., Seader, J. D. and Wayburn, T. L., 1987, AIChE J, 33: 886±897. 19. Wolff, E. A., Skogestad, S. and Havre, K., 1993, AIChE Ann Meet, St. Louis, paper 195a. 20. Wolff, E. A., Skogestad, S. and Havre, K., 1994, ESCAPE’ 4, Dublin, IChemE Symp Series No 133: 111±118. 21. Morud, J. and Skogestad, S., 1994, AIChE Ann Meet, San Francisco, paper 131d. 22. Howard, G. M., 1967, Ind Eng Chem Fundam, 6(1): 86. 23. Triantafyllou, C., 1991, The design optimisation and integration of dividing wall distillation columns, PhD Thesis (submitted to UMIST Manchester). 24. GLITSCH, 1992, (Private Communication.) 25. Bristol, E. H., 1966, IEEE Trans Autom Control, AC-11: 133±134.
ACKNOWLEDGEMENTS The authors would like to express their appreciation to the UK Department of Energy, Energy Ef® ciency Of® ce, BP, Exxon, Glitch, ICI, M. W. Kellogg, and Shell for ® nancial support of this project. The authors would also like to express their gratitude to Dr Frigyes Lestak for his contribution to the project.
ADDRESS Correspondence concerning this paper should be addressed to Professor R. Smith, Department of Process Integration, UMIST, PO Box 88, Manchester M60 1QD, UK. The manuscript was received 4 August 1997 and accepted for publication after revision 22 January 1998.
Trans IChemE, Vol 76, Part A, March 1998
OPERATION AND CONTROL OF DIVIDING WALL DISTILLATION COLUMNS Part 1: Degrees of Freedom and Dynamic Simulation M. I. ABDUL MUTALIB and R. SMITH (FELLOW) Department of Process Integration, UMIST, Manchester, UK
T
he dividing wall distillation column has been known now for some 50 years. Despite its potential to make major savings in energy and capital costs in distillation, it has not been widely used in practice. One of the major fears in applying the technology is uncertainty regarding the control and operation of the arrangement. This paper investigates theoretically the operation and control of the dividing wall column. A degrees of freedom analysis was performed to determine the number of control loops required. Possible control con® gurations were then investigated using Relative Gain Array Analysis and dynamic simulation. The results of these theoretical studies indicate that simple control schemes are capable of providing stable control. Keywords: dividing wall distillation; thermal coupling; dynamic simulation; control; pilot plant
Rudd1 2 , Cerda and Westerberg1 3 , Spadoni and Stramigioli1 4 , Nikolaides and Malone1 5 ). Recently, a design procedure which allows for optimization of the column has been proposed by Triantafyllou and Smith1 6 . By contrast, studies on the operational and control aspects of the Petyluk con® guration have received little attention in the past. Chavez et al.1 7 and Lin et al.1 8 reported multiple steady state solutions for the Petyluk con® guration. Using computer simulation, they presented four different solutions at a speci® ed re¯ ux which have different internal liquid and vapour ¯ ows between the prefractionator and the main column. As they reduced the re¯ ux ratio to a value beyond which no feasible solution existed, a unique solution was found. This is the optimum combination of the internal liquid and vapour ¯ ows which gives the minimum energy requirement. Wolff et al.1 9 , 2 0 performed control studies on the Petyluk con® guration using a three point and four point composition control. For the three point composition control, they set up a control con® guration which maintained the composition of the three main products of the column. Using one of the possible control schemes, they were able to achieve satisfactory control performance, given feed (¯ owrate and composition) and set point disturbances. For the four point composition control, they used the internal liquid split between the prefractionator and the main column to control the impurity ratio in the side draw as an additional control loop. They discovered that a problem can occur within a range of the internal liquid splits whereby the product speci® cations cannot be achieved. A similar result was observed when the vapour split was used in place of the liquid split. Morud and Skogestaad2 1 later provided an explanation for this using three dimensional plots displaying the variation of the reboiler duty and side draw impurity ratio against changes in the internal liquid and vapour splits.
INTRODUCTION Distillation remains the most important method used in the chemical industry for the separation of homogeneous mixtures, with the amount of energy used in distillation operations being considerable. Appropriate integration of the distillation column with the overall process can result in signi® cant energy savings (Linnhoff et al.1 , Smith and Linnhoff 2 ) but the scope for this is often limited. Other options involve the use of complex distillation arrangements such as the side-stripper, the side-recti® er or the fully thermally coupled (Petyluk) con® guration. Such complex arrangements can consume signi® cantly less energy when compared to a conventional arrangement. So far, the use of complex arrangements has largely been limited to crude oil distillation where the side stripper arrangement has been used extensively. The Petyluk con® guration (Figure 1a) was initially introduced some 50 years ago (Brugma3 ). Theoretical studies on a stand alone basis (Petyluk et al.4 , Fidskowski and Krolikowski5 , Glinos and Malone6 and Kaibel7 ) have shown that it is capable of achieving typically 30% of energy savings compared with a conventional sequence. In addition, the Petyluk arrangement can also be achieved by placing a vertical wall in the middle of the column (Figure 1b), separating the feed from the side draw (Wright8 , Kaibel9 ). Thus an overall reduction in capital cost can be expected through the elimination of a column shell, reboiler and condenser when compared with a conventional arrangement. Despite these advantages, industry has been reluctant to use the Petyluk and dividing wall con® gurations. This can largely be attributed to the lack of established design procedures and the fear of control problems. The design of the Petyluk con® guration has been studied by many researchers (Stupin1 0 , Fonyo et al.1 1 , Tedder and 308
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309
Figure 1. Fully thermally coupled columns. (a) Petyluk column; (b) Dividing wall column.
In this paper, the complexity of the dividing wall column will ® rstly be assessed by performing degrees of freedom analysis. The variables leading to the additional complexity of the column, when compared to the more established side draw column, will then be analysed to investigate the impact on the operation and control of the column. Dynamic simulation will also be used to investigate the controllability of the column from a theoretical point of view. Part 2 of this paper will discuss pilot plant control studies on such a column. DEGREES OF FREEDOM ANALYSIS 22
A method developed by Howard for analysing the degrees of freedom at unsteady state condition has been used for the dividing wall column. The method is based on the fact that the degrees of freedom for a system is equal to the sum of degrees of freedom of all the units in the system minus the sum of degrees of freedom for all the interconnecting streams. This requires the system to be torn apart into smaller units with inter-stream connections. When analysing the degrees of freedom for any of the units, hold up is included to account for the unsteady state. The way the method handles hold up is by treating it as a quantity stream with the same variables as the interconnecting stream, except that a hold up quantity is used instead of ¯ owrate. In a distillation column, the units consist of stages, condenser and accumulator, reboiler and stream splitters which are connected by interconnecting streams. Each of the interconnecting streams has degrees of freedom equal to NC + 2 where NC is the number of components present in the stream. These variables consist of NC-1 concentration variables, a rate or quantity variable and two other intensive variables i.e. temperature and pressure. A stage in a distillation column consists of four interconnecting streams, a quantity stream for the hold-up and a heat stream. Note that only the liquid hold-up is accounted for while the vapour hold-up is neglected. Since there are 5 streams present and each stream has NC + 2 variables, with a heat quantity term, Q, the number of variables in the unit is 5NC + 11. The relationships among the variables depends on the way in which the stage is de® ned. Suppose, the stage is considered to be a single Trans IChemE, Vol 76, Part A, March 1998
mixed pool with the liquid leaving having the same properties as the liquid on the stage, the number of relationships is equal to 3NC + 4. These relationships consist of a total material balance, an energy balance, NC-1 component balances, NC distribution relationships between the vapour and liquid phase, i.e. vapourliquid equilibrium, NC-1 concentration identities for liquid leaving and liquid on the stage, two temperature identities and two pressure identities for the vapour and liquid leaving and liquid on the stage. Hence the degrees of freedom for the unit are: No. of DOF
= No. of variables - No. of relationships
= 5NC + 11 - 3NC - 4 = 2NC + 7 The degrees of freedom for a cascade of N stages can then be easily determined by treating the cascade as a system. Since a cascade of N stages are interconnected by 2N-2 streams, the degrees of freedom are: No. of DOF for Sum of DOF Sum of DOF cascade of N units= for N units - 2N - 2 streams
= N(2NC + 7)- 2(N - 1)(NC + 2) = 3N + 2NC + 4
An extra degree of freedom has to be added to the above due to the choice for number of stages in the cascade. Thus the number of degrees of freedom for a cascade of N stages are 3N + 2NC + 5. In contrast to the conventional stage, the feed and side draw stages are slightly different. This is due to the fact that an extra stream is involved. For a feed stage, the number of degrees of freedom is equal to the number of degrees of freedom for a stage plus the number of degrees of freedom for a stream, thus giving 3NC + 9. A side draw stage can be represented by a stage connected to a splitter which divides between the side draw ¯ ow (either a vapour or liquid) and the ¯ ow to the next stage. Since stages can be attached to the cascade of stages prior to the side draw stage location, only the number of degrees of freedom for the splitter needs to be counted. Using the same approach as described for the conventional stage, with the exception that
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there is no hold up, the number of degrees of freedom for a splitter unit is found to be NC + 5. A condenser and accumulator unit consist of two ¯ ow streams, a quantity stream and a heat stream. Note that the liquid hold up is considered as the quantity stream. The number of variables in the unit comes from the three streams and a heat quantity term are 3NC + 7, while the number of relationships between the variables is 2NC + 2, i.e. total material balance, a heat balance, NC1 component balances and NC-1 concentration, a pressure and a temperature identities for liquid leaving the unit. Therefore, the of degrees of freedom for this unit are NC + 5. The reboiler unit consists of 3 ¯ ow streams, a quantity stream and a heat stream. Again, the liquid hold up is considered as a quantity stream. The number of variables in the unit which comes from the four streams and a heat quantity term are 4NC + 9. However, the number of relationships between the variables that can be derived for the unit is 3NC + 4 thus giving the number of degrees of freedom to be NC + 5 (which turns out to be the same as the condenser unit). The relationships between the variables that can be derived for the unit consist of a total material balance, a heat balance, NC-1 components balances, NC distribution relationships and NC-1 concentration, two pressure and two temperature identities for liquid and vapour leaving the unit. Table 1 summarizes the degrees of freedom for each of the units in a typical distillation column. The dividing wall column can be represented by the Petyluk con® guration as illustrated in Figure 2. The column is divided into 6 sections, each containing a number of cascaded trays. There are three feed and three side-draw trays located between the sections with a partial reboiler and total condenser at the top and bottom of the column. Table 2 gives details of the analysis of the degrees of freedom for the dividing wall column. Based on the analysis, the number of degrees of freedom for the column is thus 3(NS(1) + NS(2) + NS(3) + NS(4) + NS(5)+ NS(6))+ NC + 35 where NS(i) is the number of stages in section `i ’ . After taking into account of the inherent relationships and the product speci® cations, the number of degrees of freedom for the column is NC + 10. Because the feed composition, ¯ owrate and pressure are ® xed, the number of degrees of freedom left is 9. This means that only nine variables can be manipulated or speci® ed in order to fully control the system. The 9 variables involved are shown in Table 3. When comparing this to the more established side draw column, the dividing wall column has 2 Table 1. Degrees of freedom for various units in a distillation column. Unit 1. 2. 3. 4. 5. 6. 7.
Single phase streams Ideal stage Cascade of N ideal stages Feed stage Stream splitter (no hold up) Total condenser/accumulator Partial reboiler
Degrees of freedom NC + 2 2NC + 7 3N + 2NC + 5 3NC + 9 NC + 5 NC + 5 NC + 5
Figure 2. Layouts of the units in a dividing wall column.
additional degrees of freedom which are the liquid and vapour splits. In the implementation of the dividing wall column, it is impractical to manipulate the vapour split. Hence, the vapour split will be left to occur naturally. Therefore, a degree of freedom is lost here. Unlike the vapour split, the liquid split can be easily manipulated using a simple device, thus leaving the option open to the designer. The decision whether to employ it as a manipulated variable will be assessed later.
COLUMN CONFIG URATION The design of the dividing wall column can be treated similar to the design of the Petyluk con® guration (Triantafyllou2 3 ). However, there is one major difference between the two columns. This results from the ® xed position of the dividing wall which prevents the manipulation of the internal vapour split in the column. For the Petyluk con® guration, the vapour split was manipulated in most of the previous studies due to the separate shell arrangement. A steady state rigorous simulation model for the dividing wall column was developed using the ASPEN PLUST M package. The ternary mixture used for the separation consists of methanol, iso-propanol and butanol. The Wilson equation was used for the prediction of vapour liquid equilibrium. The con® guration of the dividing wall column was designed using the method proposed by Triantafyllou and Smith1 6 , using the option for minimizing the number of stages. The feed to the column has an equimolar composition and the products speci® ed to be 98.5 mol percent. The arrangement on the distribution of the number of stages at different sections inside the column, together with the operating parameter, are given in Figure 3. Trans IChemE, Vol 76, Part A, March 1998
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Table 2. Degrees of freedom analysis for dividing wall column. Units
Degrees of Freedom
Top Column Section. Condenser/accumulator. Re¯ ux splitter. Cascade of stages (Section 1). Vapour feed stage. Liquid draw stage.
NC + 5 NC + 5 3NT(1) + 2NC + 5 3NC + 9 NC + 5
Dividing Wall Section. Prefractionator side. Cascade of stages (Section 5). Feed stage Cascade of stages (Section 6).
3NT(5) + 2NC + 5 3NC + 9 3NT(6) + 2NC + 5
Main Side. Cascade of stages (Section 2). Liquid draw stage. Cascade of stages (Section 3).
3NT(2) + 2NC + 5 NC + 5 3NT(3) + 2NC + 5
Bottom Column Section. Liquid feed stage. Vapour draw stage. Cascade of stages (Section 4). Partial reboiler.
3NC + 9 NC + 5 3NT(4) + 2NC + 5 NC + 5
Total DOF
3(NT(1) + NT(2) + NT (3) + NT(4) + NT (5) + NT (6))+ 27NC + 87
Restriction from 26 interconnecting streams
- 26NC + 52 3(NT(1) + NT(2) + NT (3) + NT(4) + NT (5) + NT (6))+ NC + 35
Total column DOF
Restriction from inherent relationships, design speci® cations and uncontrolled variables. Pressures on all stages, reboiler, condenser and re¯ ux splitter. Heat leaks on all stages and splitters. Holdup on all stages. No. of plates at each section. Feed (composition, ¯ owrate and pressure).
NT(1) + NT (2) + ¼ + NT (6) + 9 NT(1) + NT (2) + ¼ + NT (6) + 7 NT(1) + NT (2) + ¼ + NT (6) + 3 6 NC + 1
Total DOF restricted
3(NT(1) + NT(2) + NT (3) + NT(4) + NT (5) + NT (6) + NC + 26
Degrees of freedom for the column
9
IMPAC T OF THE LIQUID SPLIT ON THE MIDDLE PRODUCT COMPOSITION In the practical implementation of the dividing wall column, the liquid split can easily be manipulated. One way of achieving this is by means of simple ¯ ow controller installed externally on both liquid streams returning to the top of each side of the dividing wall. A ratio controller can be used to ® x or to vary the two ¯ ows according to a speci® ed ratio. However, if a ® xed ratio is desired, an internal mechanism located at the top of the dividing wall can serve to divide the ¯ ows to each side of the wall
according to the set ratio used. Manipulating the liquid split at the top of the dividing wall is a way of manipulating the re¯ ux ratio on each side of the wall. Triantafyllou and Smith1 6 presented a procedure to optimize the re¯ ux ratio in different parts of the column in the initial design. Calculations were performed to ® nd the relation between the liquid split and the composition of the light key (methanol) as well as the middle key (iso-propanol) in the middle product. To achieve this, the liquid split was changed at different values while keeping the vapour split constant at base case value, i.e. 1.29. Note that the split is de® ned as the ratio between the ¯ ow on the product
Table 3. Controlled and manipulated variables for dividing wall column. Controlled variables 1. 2. 3. 4. 5. 6. 7. 8. 9.
Feed temperature Column pressure Top product composition Middle product composition Bottom product composition Condenser/accumulator holdup Reboiler holdup Light impurity in middle product Heavy impurity in middle product
Trans IChemE, Vol 76, Part A, March 1998
Manipulated variables Feed preheater duty Condenser cooling duty Re¯ ux ¯ owrate Distillate ¯ owrate Sidedraw ¯ owrate Reboiler duty Bottom product ¯ owrate Liquid split at top of dividing wall Vapour split at bottom of dividing wall
312
ABDUL MUTALIB and SMITH The magnitude of changes for the methanol composition seems to be very small for most of the range used for the variation in the liquid split. Therefore, controlling the methanol concentration using the liquid split would require a large action in order to correct a small deviation. In addition, varying the liquid split also affects the isopropanol composition by a similar magnitude to the effect on the methanol composition. If the iso-propanol composition is controlled by another manipulated variable such as the side draw ¯ owrate, the two control loops are bound to interact signi® cantly.
Figure 3. The dividing wall column con® guration and the base case operating parameter.
side to the ¯ ow on the feed side of the dividing wall. The feed composition, ¯ owrate and temperature as well as the product ¯ owrates and reboiler duty were also kept constant. Figure 4 (i) shows the variation of methanol composition in the middle product, while Figure 4 (ii) shows the variation of iso-propanol composition in the middle product. Both were subjected to variation in the liquid split. The pattern of changes followed by the methanol composition exhibits a minimum point as the liquid split is varied. The signi® cance of this observation is that simple PID control cannot be applied to link these two variables to form a control loop. At two different locations along the curve, separated by the minimum point, the direction for the control action is different. Since it is not possible for a normal PID controller to recognize on which side of the curve the current operation is located, and it is not also possible for the controller to have a variable gain sign, applying the controller in such a situation will lead to failure.
IMPACT OF THE VAPOUR SPLIT ON THE MIDDLE PRODUCT COMPOSITION In the dividing wall column operation, manipulating the vapour splits would be impractical. The vapour split inside the column occurs naturally according to the pressure drop relation across the internals at each side of the dividing wall, which will be discussed later. Despite this, calculations were made to determine the effect of changing the vapour split on the middle product composition. The idea of doing this was to investigate whether ® xing the dividing wall would lead to any major bene® t being missed. Figure 5 (i) shows the variation of butanol composition in the middle product while Figure 5 (ii) shows the variation of iso-propanol composition in the middle product. Both were subjected to variation in the vapour split. This leads to the same conclusions as for the liquid split. From the analysis conducted for the liquid and vapour splits, it is clear that maintaining the two splits constant seems to be the preferred option. The same suggestion can also be extended to the Petyluk column. However, in doing so, the impurities and the main component compositions in the middle product cannot be controlled simultaneously.
Figure 4. Variation in middle product composition subject to changes in liquid split. (a) Methanol; (b) Iso-propanol.
Figure 5. Variation in middle product composition subject to changes in vapour split. (a) Iso-propanol; (b) Butanol.
Trans IChemE, Vol 76, Part A, March 1998
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Figure 6. Generalized pressure drop correlation chart.
IMPACT OF THE LIQUID SPLIT ON THE VAPOUR SPLIT As mentioned earlier, the vapour divides to satisfy the pressure drop equalization between the sections on each side of the dividing wall. In the case where the number of stages are equal at each side of the dividing wall, the vapour split depends on the position of the dividing wall and the liquid loading of the two sections at each side of the dividing wall. The liquid loading of the two sections vary as the liquid split is changed. Before the impact of the liquid split on the vapour split can be assessed, some form of relation must be established between the changes in the liquid loading and the resulting changes in the pressure drop across a packing height or trays. In the present case, it was decided to demonstrate the study using packing as the internals. Figure 6 shows the Generalised Pressure Drop Correlation chart which is typically used for determining the pressure drop across a packed height for a given liquid and vapour loading. When considering the changes in the pressure drop with respect to the liquid loading, two regions can be identi® ed. In the ® rst region, which corresponds to low liquid loading, the pressure drop hardly changes with the liquid loading. In the second region, which corresponds to high liquid loading, the pressure drop changes more signi® cantly with the liquid loading. Based on the above observation, a number of conclusions can be made. If the dividing wall column is operated within the ® rst region, the liquid split changes should not affect the vapour split. Therefore, operating within this region should provide some ¯ exibility in changing the liquid split. Conversely, if the column is operated within the second region, the vapour split will vary as the liquid split changes, thus offering no ¯ exibility during the operation of the column. Following this, a correlation between the pressure drop and the liquid and vapour loadings for a speci® c type of packing (Gempak 4A, GLITSCH2 4 ), applicable within the ® rst region, was used to determine the relation between the position of the dividing wall (described by the area ratio between the product side to the feed side of the column) and the vapour split speci® ed. For a given cross sectional area of the column and the number of stages on each side of the dividing wall and using the information on liquid and vapour loading at each stage obtained from rigorous simulation for a speci® ed liquid and vapour split, the area ratio required to satisfy the pressure drop equalization criteria can be calculated. The criteria can be based on either the total pressure drop or the average pressure drop on both sides of the dividing wall. Trans IChemE, Vol 76, Part A, March 1998
Figure 7. Area ratio and vapour split relationship for pressure drop equalization between the two sides of the dividing wall. (Equal number of stages at both sides).
Figure 7 shows the plot obtained, which demonstrates a linear relation between the area ratio and the vapour split required. More signi® cantly, the area ratio was found to be almost the same as the vapour split speci® ed when equal number of stages were used on each side of the dividing wall. This indicates that in order to obtain the desired vapour split, the position of the dividing wall can be set to give the same area ratio as the required vapour split. DESIGNING FOR THE LIQUID AND THE VAPOUR SPLITS Having given all the arguments which led to the preference for operating the dividing wall column with a constant liquid and vapour split, it is then important to know how to design for the two splits. As it is always desirable to operate the column as close as possible to the optimal state, the sensitivity of the optimum location for the two splits with regard to changes in the feed composition and the product speci® cations needs to be assessed. IMPACT OF FEED COMPO SITION ON THE OPTIMUM LIQUID AND VAPOUR SPLITS Calculations were performed to determine the variation in the liquid and vapour splits required to maintain lowest energy consumption for changes in the feed composition. Three different feed compositions within the allowable range were tested and the value for the two splits that gave minimum energy consumption were found for each case using rigorous simulation. Note that the middle product impurities were not included in the product speci® cations as it has already been decided not to control them using the liquid and the vapour split. Table 4 presents the results obtained from the analysis. The optimum values for the liquid and vapour splits were found to be insensitive to the variation in the feed composition. IMPACT OF PRODUCT SPECIFICATION ON THE OPTIMUM LIQUID AND VAPOUR SPLITS Following the above, calculations were performed for different product speci® cations. Table 5 presents the results
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Table 4. Optimum liquid and vapour split for changes in feed composition. Feed composition
Optimum liquid split
Optimum vapour split
3.80
1.16
3.80
1.16
3.90
1.16
3.75
1.15
Table 5. Optimum liquid and vapour split for changes in product speci® cation. Product speci® cation
Feed 1 (0.333, 0.334, 0.333) Feed 2 (0.363, 0.334, 0.303) Feed 3 (0.303, 0.364, 0.333) Feed 4 (0.303, 0.334, 0.363)
obtained. The optimum values for the liquid and vapour splits were found to vary as the product speci® cations changed. Figure 8 shows three sets of plots where the difference in reboiler duty between the operation of the column at a speci® ed liquid or vapour split and operation at the optimum splits are plotted against the speci® ed liquid or vapour split. The plots cover the location within the optimum splits for three different product speci® cations. There are two plots for each product speci® cation. For the ® rst plot, the vapour split is kept constant at its optimum value while allowing liquid split to vary. For the second plot, the liquid split is kept constant at its optimum value while allowing the vapour split to vary. A comparison between the plots obtained for the different product speci® cations shows that the optimum location tends to be more sensitive to the changes in liquid and vapour splits as the product speci® cations were increased. This was shown by the extent of the ¯ at region within the optimum location which tended to reduce slowly as the product speci® cations were increased. Hence, it is important that the column is run close to the optimum liquid and vapour splits for the higher product speci® cations otherwise a high energy penalty will have to be paid.
98 mol percent 98.5 mol percent 99 mol percent
Optimum liquid split
Optimum vapour split
3.5 3.8 3.7
1.02 1.16 1.29
In the dividing wall column operation, the vapour split is largely ® xed by the position of the dividing wall but the liquid split has the ¯ exibility to be changed. However, as discussed earlier, manipulating the liquid split can lead to serious problem in the operation and control of the dividing wall column. Therefore, it is better to ® x the liquid split. Fixing the liquid and vapour split for a different feed composition will not be a problem as the optimum value for the liquid and the vapour split hardly change. However, it is not so straightforward when the product speci® cations are allowed to vary. In this case, the above ® nding can be used to help decision making. The obvious choice is to set the liquid and vapour splits at the optimum values for the highest product speci® cations designed for the column. The reason for this is because of the relative importance in operating the column with liquid and vapour splits close to the optimum values for higher product speci® cations compared with lower product speci® cations. Even if the column is operated to produce lower purity products, the penalty in terms of the energy consumption when operating the column with the optimum splits for the higher product speci® cations proves to be reasonably small. On the other hand, if the column is operated with the optimum liquid and vapour splits for lower product speci® cations and higher purity products are to be produced, the penalty in the energy consumption can be extremely high and, in certain cases, the higher product speci® cations might not
Figure 8. Plots of changes in reboiler duty requirement with different liquid and vapour splits.
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315
Table 6. Results from an example to illustrate the setting for the liquid and vapour splits for the dividing wall column operation. Operating liquid and vapour splits
Product speci® cation (0.98, 0.98, 0.98) (0.99, 0.99, 0.99)
3.7 3.5
Optimum liquid and vapour splits 1.29 1.02
be achieved even running the column at total re¯ ux. Table 6 illustrates the results from an example to explain the above.
COMPO SITION CONTRO L OF THE DIVIDING WALL COLUMN In order to study the control behaviour of the dividing wall column, a dynamic model was built using SPEEDUP T M . Similar con® gurations for the column as modelled previously using the ASPEN PLUST M package were used. The same feed and product speci® cations were employed. In line with the earlier suggestion, the liquid and vapour split were maintained at the optimum values obtained from the design method used (Triantafyllou and Smith1 6 ). The assumption of no heat transfer across the dividing wall was maintained and only decentralized control was used. The short cut dynamic model which is available in SPEEDUP T M was used. Assumptions involved in using the short cut model are perfect material balance, i.e. no accumulation of material in the system, and constant molal over¯ ow. In addition, since the short cut model solves stage equilibrium by lumping several stages together to form a section within the column, constant relative volatility within the section was assumed (but varied between sections). The maximum number of stages that can be lumped within a section must be kept within a reasonable number in order to keep the model within an acceptable accuracy for simulation purposes. The relative volatility within each section was speci® ed by taking the average value obtained for the relevant stages from the rigorous simulation done using ASPEN PLUST M .
3.5 3.7
Energy penalty (percent) 1.02 1.29
6.9 product specs. not achieved with the operating splits
INTERACTION ANALYSIS Two control schemes that can be used for controlling the dividing wall column were considered, i.e. L-S-V and D-S-V (where L, S, D and V refer to manipulation of the top re¯ ux, side draw, distillate ¯ ows and vapour ¯ ow from the reboiler respectively). These are shown in Figure 9. Relative Gain Array Analysis (Bristol2 5 ) was used to analyse the interaction as well as determining suitable pairings between controlled and manipulated variables in the two control schemes. Basically, the RGA is a matrix which consists of elements representing the steady state gain ratio between the respective controlled and manipulated variables when all other manipulated variables are constant, divided by the steady state gain ratio between the same controlled and manipulated variables when all other controlled variables are constant. This is represented by the equation: k
ij
= (¢y / ¢m ) i
j mi
/ (¢yi / ¢mj )yj
where k ij is the relative gain between controlled variable yi and manipulated variable mj . If k ij = 0 then yi does not respond to mj and mj should not be used to control yi . If k ij = 1 then yi only responds to mj and does not interact with other manipulated variables. This is the preferred case. If 0
Table 7. Results for the steady state gain array and the relative gain array. Scheme
Steady state gain array 2.433
L-S-V
- 0.003 - 2.401
2.433
D-S-V
- 0.003
0.014
Figure 9. Two composition control scheme for the dividing wall column.
Trans IChemE, Vol 76, Part A, March 1998
Relative gain array
- 0.274 - 2.659 0.019 - 2.672
11.736 0.001 - 10.736
- 0.274 - 2.659 0.019 - 2.672
0.891 0.001 0.107
0.297
0.014
2.665
0.001
- 10.057 - 0.679 0.011 11.045
0.988 0.691
0.100 0.007 0.892
0.008 0.992 0.001
316
ABDUL MUTALIB and SMITH
Figure 10 (i). Control run for scheme L-S-V with set point changes. (ii). Control run for scheme D-S-V with set point changes.
between the middle product and the bottom product control loops. This means that the middle product composition should be controlled by the vapour ¯ ow while the bottom product composition should be controlled by the side draw ¯ ow.
DYNAMIC SIMULATION Dynamic simulation was then performed to observe the behaviour of the two control schemes when subjected to set point changes and feed disturbances as shown in Trans IChemE, Vol 76, Part A, March 1998
OPERATION AND CONTROL OF DIVIDING WALL DISTILLATION COLUMNS: PART 1
317
Figure 11 (i). Control run for scheme L-S-V with feed disturbance. (ii) Control run for scheme D-S-V with feed disturbance.
Table 8. The controllers were tuned using the open loop response curve method. Figure 10 (a) and (b) show the response of the controllers in the two schemes when subjected to set point changes. Both schemes were able to produce a stable control response. Figure 11 (a) and (b) Trans IChemE, Vol 76, Part A, March 1998
show the response of the controllers in the two schemes when subjected to feed disturbances. Again stable control response was produced by both schemes. Overall, the D-S-V scheme seemed to produce better response compared with the traditional L-S-V scheme and
318
ABDUL MUTALIB and SMITH Table 8. Set point changes and feed disturbances used.
Set point changes Feed disturbances
Middle product composition IPA: 0.985±0.988 Combined feed composition and ¯ owrate Composition: MeoH ± 0.333 to 0.363 IPA ± 0.334 to 0.284 BuoH ± 0.333 to 0.353 Flowrate: 1.081 to 1.190 kmol/hr
this is in agreement with the results derived from the RGA analysis. More importantly, both schemes were able to produce satisfactory control. CONCLUSIONS In this paper, studies relating to aspects of the operation and control of the dividing wall column have been investigated. When compared to the side draw column, the dividing wall column has a more complex nature, shown through degrees of freedom analysis. This results from two additional manipulated variables, the liquid and vapour splits. However, it is impractical to manipulate the vapour split, which is ® xed by the position of the dividing wall. On the other hand, the liquid split can be easily varied but has been found to have little bene® t in comparison to the complication that will be added to the operation and control of the column. A linear PID controller cannot be used and severe interactions would occur between the control loops, particularly for controlling the composition of the middle product and its impurities. In the region of high liquid and vapour loading, varying the liquid split will also affect the vapour split considerably and this even affects the operation and control of the column further. Based on this account, it was suggested that the column should be operated and controlled with a constant liquid split in addition to the ® xed vapour split. Having made the suggestion, the column can then be operated and controlled in a similar manner as the more established side draw column. Nevertheless, the disadvantage of this proposal is that the impurities composition in the middle product cannot be controlled. The optimum location for the liquid and vapour splits was found to be insensitive to the variation in the feed composition but this is not so for the variation in the product speci® cation. From a sensitivity study, it was found that the lower product speci® cation has a ¯ atter optimum compared with the higher product speci® cations. Therefore, it was concluded that the design for the liquid and the vapour split should be based on the highest product speci® cation when the column is required to produce a range of product compositions. Two composition (three point) control scheme were
selected for demonstrating the control using simulation. The column was subjected to changes in product speci® cation and feed disturbances. Simulation results indicate that stable control was achievable by both control schemes. REFERENCES 1. Linhoff, B., Dunford, H and Smith, R., 1983, Chem Eng Sci, 38(8): 1175. 2. Smith, R. and Linhoff, B., 1988, Chem Eng Res Des, 66: 195. 3. Brugma, A. J., 1942, US Patent 2,295,256. 4. Petyluk, F. B, Platonov, V. M. and Slavinskii, D. M., 1965, Int Chem Eng, 5(3): 561. 5. Fidkowski, Z. and Krolikowski, L., 1987, AIChE J, 33(4): 643. 6. Glinos, K. and Malone, M. F., 1988, Chem Eng Res Des, 66 (3): 229. 7. Kaibel, G., 1988, IChemE Symp Series No. 109: 43. 8. Wright, R. O., 1945, US Patent 2,471,134. 9. Kaibel, G., 1987, Chem Eng Technol, 10: 92. 10. Stupin, W. J., 1970, The separation of multicomponent mixtures in thermally coupled distillation systems, PhD Diss (University of Southern California). 11. Fonyo, Z., Szabo, J. and Foldes, P., 1974, Acta Chim, 82: 235. 12. Tedder, D. W. and Rudd, D. F., 1978, AIChE J, 24(2): 303. 13. Cerda, J. and Westerberg, W., 1981, Ind Eng Chem Proc Des Dev, 20(3): 546. 14. Spadoni, G. and Stramigioli, C., 1983, 3rd Int Cong Computers and Chemical Engineering, Paris, No 27: 43. 15. Nikolaides, I. P. and Malone, M. F., 1987, Ind Eng Chem Res, 26(9): 1839. 16. Triantafyllou, C. and Smith, R., 1992, Trans IChemE, 70 (A2): 118. 17. Chavez, R., Seader, J. D. and Wayburn, T. L., 1986, Ind Eng Chem Fundam, 25(4): 566±576. 18. Lin, W. J., Seader, J. D. and Wayburn, T. L., 1987, AIChE J, 33: 886±897. 19. Wolff, E. A., Skogestad, S. and Havre, K., 1993, AIChE Ann Meet, St. Louis, paper 195a. 20. Wolff, E. A., Skogestad, S. and Havre, K., 1994, ESCAPE’ 4, Dublin, IChemE Symp Series No 133: 111±118. 21. Morud, J. and Skogestad, S., 1994, AIChE Ann Meet, San Francisco, paper 131d. 22. Howard, G. M., 1967, Ind Eng Chem Fundam, 6(1): 86. 23. Triantafyllou, C., 1991, The design optimisation and integration of dividing wall distillation columns, PhD Thesis (submitted to UMIST Manchester). 24. GLITSCH, 1992, (Private Communication.) 25. Bristol, E. H., 1966, IEEE Trans Autom Control, AC-11: 133±134.
ACKNOWLEDGEMENTS The authors would like to express their appreciation to the UK Department of Energy, Energy Ef® ciency Of® ce, BP, Exxon, Glitch, ICI, M. W. Kellogg, and Shell for ® nancial support of this project. The authors would also like to express their gratitude to Dr Frigyes Lestak for his contribution to the project.
ADDRESS Correspondence concerning this paper should be addressed to Professor R. Smith, Department of Process Integration, UMIST, PO Box 88, Manchester M60 1QD, UK. The manuscript was received 4 August 1997 and accepted for publication after revision 22 January 1998.
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