Design and control of acetic acid dehydration system via heterogeneous azeotropic distillation

Design and control of acetic acid dehydration system via heterogeneous azeotropic distillation

Chemical Engineering Science 59 (2004) 4547 – 4567 www.elsevier.com/locate/ces Design and control of acetic acid dehydration system via heterogeneous...

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Chemical Engineering Science 59 (2004) 4547 – 4567 www.elsevier.com/locate/ces

Design and control of acetic acid dehydration system via heterogeneous azeotropic distillation I.Lung Chien∗ , Kai-Luen Zeng, Huan-Yi Chao, Jun Hong Liu Department of Chemical Engineering, National Taiwan University of Science and Technology, 43, Keelung Road, Sec. 4, Taipei 10672, Taiwan Received 14 August 2003; received in revised form 14 March 2004; accepted 28 June 2004 Available online 21 August 2004

Abstract Acetic acid dehydration is an important operation in the production of aromatic acid, such as terephthalic acid or in the manufacture of cellulose acetate. Although acetic acid and water does not form azeotrope, but using simple distillation to separate these two components is not practical. The reason is because the system has tangent pinch on the pure water end, thus it is more customary in industry to use an entrainer via a heterogeneous azeotropic distillation column system for the separation. In this study, a suitable entrainer is selected from three candidate acetates through rigorous steady-state simulation of this system. Optimum process design and operating condition are determined to keep high-purity bottom acetic acid composition and also keep a small acetic acid loss through top aqueous draw. Furthermore, the overall control strategy of this column system is proposed to hold both bottom and top product specifications in spite of feed rate and feed composition load disturbances. The proposed overall control strategy is very simple requiring only one tray temperature control loop inside the heterogeneous azeotropic column. 䉷 2004 Elsevier Ltd. All rights reserved. Keywords: Acetic acid dehydration; Heterogeneous azeotropic distillation; Entrainer selection; Distillation column control

1. Introduction Acetic acid dehydration is an important operation in the production of aromatic acid, such as terephthalic acid or in the manufacture of cellulose acetate. Although acetic acid and water does not form azeotrope, but using simple distillation to separate these two components would require many equilibrium stages and thus is impractical. The reason is because the system has tangent pinch on the pure water end (see Fig. 1), thus it is more customary to use an entrainer via a heterogeneous azeotropic distillation column system for the separation. Heterogeneous azeotropic distillation column is commonly used in industry to separate mixtures of close relative volatility (such as the system studied in this paper) and also

∗ Corresponding author. Tel.: +886-2-27376652; 27376644. E-mail address: [email protected] (I.L. Chien).

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0009-2509/$ - see front matter 䉷 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.06.041

breaking azeotropes (such as ethanol or isopropyl alcohol dehydration). Nice review of this system by Widagdo and Seider (1996) showed that parametric sensitivity, multiple steady states, long transient and nonlinear dynamics were found by many authors using theoretical models, computer simulations and even experimental verifications. However, most of the literatures on this topic are concerned mainly with issues such as modeling, simulation, and system characteristics. There have been relatively few discussions about control of heterogeneous azeotropic distillation. Bozenhardt (1988) proposed control strategy involving average temperature control, on-line break point control, and five feedforward control loops for the ethanol + ether + water system. Rovaglio et al. (1993) proposed average temperature control and two feedforward control loops for the ethanol + benzene + water system. Both of the strategies above require either on-line composition measurement or a precise mathematical model of the system to precede with the feedforward controls. Chien et al. (1999b) proposed an inverse double temperature loop control strategy for the isopropyl

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1.0 0.9 0.8 0.7

y (H O)

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.6

0.7

0.8

0.9

1.0

x (H O)

Relative Volatility ( (yH O/xH O ) / (y

/x

))

2.2

2.0

1.8

1.6

1.4

1.2

1.0 0.0

0.1

0.2

0.3

0.4

0.5

x (H O)

Fig. 1. VLE and relative volatility for HAc and water system.

alcohol + cyclohexane + water system. Experimental verification of the above control strategy can be seen in Chien et al. (2000a). Chien et al. (2000b) proposed a simple operating procedure under inverse double loop control strategy to automatically adjust the column heat duty and organic reflux to be at optimum operating point and also proposed an improved decoupling control strategy for the double loops. Ulrich and Morari (2002) examine the influence of fourth component impurities on the operation and control of a heterogeneous azeotropic distillation column for dewatering a heavy-boiling organic using methyl tert-butyl ether as a light entrainer. None of the above papers studied the acetic acid dehydration system. Design of acetic acid dehydration system using an entrainer has been studied in several publications. In a review paper, Othmer (1963) described an azeotropic distillation system containing a dehydrating column, a decanter, and a water column for the separation of acetic acid and water. The entrainer used before 1932 was ethylene dichloride, and later normal propyl acetate and normal butyl acetate were used to reduce the organic reflux and heat duty used in the dehydrating column. In the paper by Pham and Doherty (1990), examples of using ethyl acetate (cf. Tanaka and

Yamada, 1972), n-propyl acetate (cf. Othmer, 1941), or nbutyl acetate (cf. Othmer, 1941; Tanaka and Yamada, 1972) as entrainer were listed in a table of examples of heterogeneous azeotropic separations. Siirola (1995) uses acetic acid dehydration as an example to demonstrate a systematic process synthesis technique to the conceptual design of process flowsheet. Ethyl acetate as entrainer was used in the paper by Siirola (1995) to design a complete acetic acid dehydration process with multiple effect azeotropic distillation and heat integration. More recently, Wasylkiewicz et al. (2000) proposed using geometric method for optimum process design of an acetic acid dehydration column with n-butyl acetate as entrainer. All of the above papers on acetic acid dehydration system are on the subject of process synthesis and design, very little discussion about control strategy of this system has been found in the literature. Luyben and Tyreus (1998) offered a realistic vinyl acetate monomer example for academic researchers pursuing simulation, design, and control studies. In this example, an azeotropic distillation column with decanter is presented. Although the flowsheet of this column system is similar to this study with components of acetic acid and water, but since vinyl acetate is a product of the overall process, an extra organic phase product is drawn-off from the decanter which is different from the system which will be studied in this paper. Kurooka et al. (2000) proposed a nonlinear control system for the acetic acid dehydration column with n-butyl acetate as entrainer. The thermodynamic model used in this work is questionable because a minimum-boiling azeotrope is predicted between n-butyl acetate and acetic acid though the mixture is zeotropic (cf. Horsley, 1973). In their study, complicated exact input–output linearization controller was used with values of some unmeasured state variables needed for the calculations. The resulting control performances under feed rate and composition changes are not desirable because of large fluctuations in the manipulated variables. Gaubert et al. (2001) studied operation of an unnamed organic acid dehydration in the industry using an immiscible entrainer. Multiple steady states are confirmed for the heterogeneous column by simulation and experimental data for the industrial unit. However, dynamics and control of this system is not studied in their paper. In this paper, a suitable entrainer for this acetic acid dehydration system will be selected from several candidate acetates. Steady-state tray by tray column simulation will be used to determine the best entrainer with minimum total annual cost. Optimum process design and operating condition will be determined to keep high-purity bottom acetic acid composition and also keep a small acetic acid loss through top aqueous draw. The overall control strategy of this column system will be proposed to hold both bottom and top product specifications in spite of feed rate and feed composition disturbances. In the control study, conventional control strategy using only tray temperature measurements will be considered so that the result of this study can easily be used directly in industry.

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Table 1 Experimental physical properties of three candidate acetates Acetate

Ethyl acetate iso-butyl acetate n-butyl acetate

Normal boiling point ( ◦ C)

Azeotropic component

Azeotropic temp. ( ◦ C)

Azeotropic composition (water, mol%)

Aqueous phase (acetate, mol%)

Organic phase (acetate, mol%)

Water

70.38

31.2%

117.2

Water

87.4

56.1%

126.2

Water

90.2

72.2%

1.40% (@40 ◦ C) 0.127% (@40 ◦ C) 0.3638% (@25 ◦ C)

83.5% (@40 ◦ C) 90.47% (@40 ◦ C) 86.31% (@25 ◦ C)

77.15

Table 2 Parameter values for the NRTL model i, j

Bij

Table 3 Parameter values for the NRTL model Bj i

1, 2 576.234 −322.424 1, 3 416.124 1024.50 2, 3 −211.310 652.995 (1) Ethyl acetate, (2) acetic acid, (3) water.

ij

i, j

0.3 0.3067 0.3

1, 2 194.416 90.268 1, 3 489.609 1809.079 2, 3 −211.310 652.995 (1) Iso-butyl acetate, (2) acetic acid, (3) water.

2. Process simulation and entrainer selection Three candidate acetates will be studied in detailed process simulation to demonstrate the factors needed to be considered in determining the suitable entrainer for this system. The three candidate acetates to be considered are: ethyl acetate, iso-butyl acetate, and n-butyl acetate. The important experimental physical properties of these three acetates at atmospheric pressure are listed in Table 1. The azeotropic data is from Horsley (1973), the vapor–liquid equilibrium data is from Gmehling and Onken (1977) with the VLE date for acetic acid–iso-butyl acetate system from Christensen and Olson (1992). For the binary and ternary liquid–liquid equilibrium data, they are from SZrensen and Arlt (1979, 1980). The nonrandom two-liquid (NRTL) activity coefficient model (Renon and Prausnitz, 1968) was used for the vapor–liquid–liquid equilibrium (VLLE) for the ternary system. The Hayden–O’Connell (Hayden and O’Connell, 1975) second virial coefficient model with association parameters was used to account for the dimerization of acetic acid in the vapor phase. The Aspen Plus䉸 (Aspen Technology, Inc., 2001) built-in association parameters were employed to compute fugacity coefficients. The extended Antoine equation is used to calculate the vapor pressure of each component in the system. The Aspen Plus䉸 built-in parameters were again used in the simulation. The set of NRTL parameters are obtained to be capable of describing well the binary and ternary, vapor–liquid equilibrium (VLE) and liquid–liquid equilibrium (LLE) data. The set of NRTL parameters for the ternary systems of acetic acid–ethyl acetate–water, acetic acid–iso-butyl acetate–water, and acetic acid–n-butyl acetate–water are listed in Tables 2–4. All three candidate entrainers form a minimum-boiling azeotrope with water. A heterogeneous azeotropic distilla-

Bij

Bj i

ij 0.3 0.2505 0.3

Table 4 Parameter values for the NRTL model i, j

Bij

Bj i

1, 2 397.85 −68.61 1, 3 354.31 2578.35 2, 3 −211.31 652.995 (1) n-Butyl acetate, (2) acetic acid, (3) water.

ij 0.3 0.219 0.3

tion column can be designed to obtain high-purity acetic acid product (b.p. of 118 ◦ C) at the column bottom while obtaining minimum boiling entrainer–water azeotrope at the top of the column. With this column design by adding entrainer into the system, the difficult tangent pinch of the pure water side can be avoided at the top of the column. Since this entrainer–water azeotrope is heterogeneous, the top column vapor stream forms two liquid phases after condensation in the decanter. The organic phase will be refluxed back to the heterogeneous azeotropic column to provide enough entrainer inside of the column. The aqueous phase containing mostly water will be assumed to be drawn out from the system for further treatment or discharge. Some of the aqueous phase can be refluxed back to the heterogeneous azeotropic column if the organic reflux is too small to fulfill the column specifications. The conceptual design of this heterogeneous azeotropic distillation column system is illustrated in Fig. 2. The residue curve maps with the binodal curve of the LLE of the three entrainer systems studied in this paper are shown in Figs. 3–5. By observing these three figures, the prediction for entrainer solubility in water and also the azeotropic temperature match well with the experimental data in Table 1. The azeotropic composition for the iso-butyl acetate system gives the most discrepancy in comparison with the experimental data in Table 1. The experimental

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Fig. 2. Conceptual design for the separation of acetic acid and water.

Fig. 3. Residual curve map for the system HAc–EtAc–H2 O.

azeotropic composition is at 43.9 mol% iso-butyl acetate but the simulation predicted at 36.8 mol%. This is mainly due to the compromise of obtaining the NRTL model parameters by fitting all binary and ternary VLE and LLE data while trying to predict well the azeotropic temperature and composition. The residue curve maps for the ethyl acetate and the isobutyl acetate systems are similar in nature with the twocomponent azeotrope as the lowest temperature in the system and acetic acid as the highest temperature in the system. The

Fig. 4. Residual curve map for the system HAc–iBuAc–H2 O.

residue curve map for the n-butyl acetate system is different than the other two systems. In the n-butyl acetate system, the highest temperature in the system is n-butyl acetate (b.p. 126.2 ◦ C), not acetic acid (b.p. 118 ◦ C). Slippage of entrainer into the bottom product stream is the situation needed to be avoided for this system. The other two systems do not need to worry about this situation because acetic acid is the highest temperature in the system which should come out of the column through bottom stream in ideal situation.

I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567

Fig. 5. Residual curve map for the system HAc–nBuAc–H2 O.

Rigorous process simulation is performed to find the optimum design and operating conditions of these three entrainer systems. The feed composition of 50 mol% acetic acid and 50 mol% water is considered for the Aspen Plus䉸 simulation. The feed rate is assumed to be 500 kg/h and it is saturated liquid phase. The column pressure is assumed to be at atmospheric pressure. The decanter temperature is at 40 ◦ C. In the Aspen Plus䉸 simulation, the column bottom product is kept at 99.9 mol% acetic acid high purity by varying the reboiler heat duty and the column top aqueous product is kept at 0.1 mol% acetic acid loss by varying the entrainer makeup flow rate. If the high purity specifications cannot be met, portions of the aqueous phase can be refluxed back to the column to fulfill the column specifications. This extra third degree of freedom (aqueous reflux flow rate) is fixed at a value which will meet both top and bottom product specifications while also minimize reboiler heat duty of the column system. Design variable of total number of trays is a compromise between the total equipment cost and the total utility cost. The optimum total number of trays and the feed tray location are determined to minimize Total Annual Cost (TAC). The calculation procedure of Douglas (1988) is followed with the annual capital charge factor of 1/3 was used. The utility cost is calculated the same way as in Chiang et al. (2002). The Aspen Plus䉸 simulation results for the three entrainers are summarized in Tables 5–7. Several observations can be made by comparing these three tables. Firstly, for the system of acetic acid–ethyl acetate–water, no aqueous reflux is necessary to meet the product specifications while the other two systems need aqueous reflux stream for the separation with higher aqueous reflux flow rate for the n-butyl acetate system. Secondly, the organic reflux flow rate and also the reboiler heat duty

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for the ethyl acetate system are much larger in comparison with the other two systems. This high organic reflux flow rate in the ethyl acetate system can actually be predicted by the inner molar balance envelope in Fig. 2 with the residue curve map plot of the ethyl acetate system in Fig. 3. Assuming at ideal condition, the column top vapor composition should be at the ethyl acetate–water azeotrope and the column bottom composition should be very close to the pure acetic acid corner in Fig. 3. Because of the feed composition is at 50 mol% acetic acid and 50 mol% water and the other inlet stream to the column for the inner molar balance envelope in Fig. 2 is the organic reflux (recall that no aqueous reflux is necessary for this system), the interception of the two inlet and outlet molar balance lines can be used to estimate the organic reflux flow rate. Since the interception point is closer to the organic reflux composition point, the organic reflux flow rate is quite high. If the feed is much richer in acetic acid, the organic reflux flow rate will be lower than the current case. Another observation by comparing these three tables is that the makeup flow rate for the ethyl acetate system is the highest while for the iso-butyl acetate system is the lowest. This can be explained by the outer molar balance envelope in Fig. 2 with the knowledge of the aqueous phase composition in Fig. 3. Assuming ideal situation for the ethyl acetate system, the two outlet streams for the outer molar balance envelope are at the points of aqueous phase composition and pure acetic acid in Fig. 3. The two inlet streams are at the points of feed composition and pure ethyl acetate (entrainer makeup) point. How close the interception point of the two molar balance lines to the feed composition point can be used to determine the makeup flow rate since the feed flow rate is known. If this interception point is very close to the feed composition point, the makeup flow rate will be small. From this explanation, it is not difficult to conclude that the ethyl acetate system will have the highest makeup flow rate and the iso-butyl acetate system will have the lowest makeup flow rate. The comparison of the minimum attainable TAC for these three systems as well as the acetic acid dehydration system without any entrainer is shown in Table 8. From the table, one can observe that the no entrainer system required the most TAC and the iso-butyl acetate system is most favorable for this feed composition and product specification requirements. The TAC for the iso-butyl acetate system is only about 55% of the no entrainer system which represents large saving can be made by using the iso-butyl acetate system. Notice that this finding is in general agreement with the industrial applications. (See patents by Costantini et al., 1981 and by Parten and Ure, 1999). The above two patents also found iso-butyl acetate as a favorable entrainer for the separation of acetic acid and water. Another earlier patent by Othmer (1936) found n-propyl acetate to be useful as an entrainer for this system. The patent by Mitsui Petro-Chemical Industries, Ltd. (1980) found n-butyl acetate to be favorable for this system. Notice that in all the patents above, the

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Table 5 Stream information for the system acetic acid(HAc)–ethyl acetate(EtAc)–water(H2 O)

Flow rate (mol/min) HAc mole fraction H2 O mole fraction EtAc mole fraction Heat duty (KW)

Feed

Bottom product

Top product

Aqueous reflux

Organic reflux

Makeup stream

Reboiler energy

213.48

106.74

108.98

0

573.95

2.24



0.5

0.999

1.00×10−3



2.87×10−3

0



0.5

9.90×10−4

0.9785



0.17586

0



0.0

1.0×10−5

2.05×10−2



0.82127

1













401.17



Table 6 Stream information for the system acetic acid(HAc)–iso-butyl acetate(iBuAc)–water(H2 O)

Flow rate (mol/min) HAc mole fraction H2 O mole fraction iBuAc mole fraction Heat duty (KW)

Feed

Bottom product

Top product

Aqueous reflux

Organic reflux

Makeup stream

Reboiler energy

213.48

106.74

106.90

33.36

92.71

0.16



0.5

0.999

1.00×10−3

1.00×10−3

1.90×10−3

0



0.5

5.90×10−4

0.9979

0.9979

7.98×10−2

0



0.0

4.10×10−4

1.10×10−3

1.10×10−3

0.9183

1













167.01



Table 7 Stream information for the system acetic acid(HAc)–n-butyl acetate(nBuAc)–water(H2 O)

Flow rate (mol/min) HAc mole fraction H2 O mole fraction nBuAc mole fraction Heat duty (KW)

Feed

Bottom product

Top product

Aqueous reflux

Organic reflux

Makeup stream

Reboiler energy

213.48

106.74

107.44

98.78

102.32

0.70



0.5

0.999

1.00×10−3

1.00×10−3

1.50×10−3

0



0.5

7.48×10−4

0.9928

0.9928

0.1448

0



0.0

2.52×10−4

6.20×10−3

6.20×10−3

0.8537

1













259.68



Table 8 Comparison of total annual cost for the acetic acid dehydration systems Entrainer

Optimal total stages

Ethyl acetate iso-butyl acetate n-butyl acetate No entrainer

16 30

Optimal feed stage

Annualized capital cost

Utility cost

Entrainer cost

TAC($)

2 9

6.84×104 6.81×104

4.20×104 1.80×104

5.40×104 1.70×104

1.64×105 1.03×105

31

11

8.44×104

2.78×104

6.08×104

1.73×105

50

37

1.42×105

4.37×104

0

1.86×105

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column as explained above during estimating the organic reflux flow rate for the ethyl acetate system. From Figs. 3–5, the ethyl acetate is the worst entrainer if only considering this factor. 2.2. Azeotropic temperature The azeotropic temperature determines the temperature difference between the top and the bottom of the column. A large delta T of the azeotropic temperature to the pure acetic acid temperature implies a good separability. Less column stages will be needed for specific product purity specifications. In this regard, ethyl acetate is the best entrainer. This interpretation is confirmed by Table 8 because ethyl acetate system requires the least total number of stages for the same separation. 2.3. Aqueous phase composition and entrainer pricing Fig. 6. Vapor and liquid profiles for the optimum system HAc– iBuAc–H2 O.

designed feed compositions and the specified column bottom and top purities are all different from this paper, thus no direct comparison of results can be made. The vapor and liquid profiles inside the column for the optimized iso-butyl acetate system can be seen in Fig. 6. Notice that the column behaves as what was designed. The first five stages counting from the top of the column have two liquid phases. The combined liquid compositions for these five stages are plotted in this figure. Another thing worth mention in the figure is that the column composition profiles bypassing the corner of pure water which is the region for the tangent pinch to be avoided. From this study, some important factors in determining the suitable entrainer for the acetic acid dehydration system are summarized below. The information needed for this qualitative comparison can be illustrated by the residue curve maps with the binodal curve of the LLE as shown in Figs. 3–5. The suitability of the entrainer is actually a combination of the following factors. 2.1. Azeotropic composition and organic phase composition It is better to have the azeotropic composition containing more water in this mixture. This means that this entrainer is more capable of carrying water to the top of the column, thus less entrainer is needed inside of the column. The distance for the points between azeotropic composition and organic phase composition is better to be further apart. This means that besides that the azeotropic composition containing more water, the organic phase composition should contain more entrainer. The location of these two points in Figs. 3–5 have to do with the organic reflux flow rate into the heterogeneous

The aqueous phase should contain as little entrainer as feasible. The reason is because the aqueous phase stream will be drawn out of the system, thus any entrainer loss should be compensated by the makeup stream in Fig. 2. This will correspond to a stream cost of the system as seen in Table 8. The makeup flow rate can actually be estimated using the outer molar balance envelope in Fig. 2 during ideal situation as explained previously. In this regard, iso-butyl acetate system results in the least makeup flow rate while ethyl acetate system requires the most makeup flow rate. This is confirmed by Tables 5–7. The annual cost of this stream is not only related to its flow rate but also related to the entrainer pricing. In this regard, ethyl acetate is the cheapest and iso-butyl acetate is the most expensive entrainer. With the knowledge of the entrainer pricing and the calculation of the makeup flow rates for the three systems, the entrainer cost can be estimated as seen in Table 8 even without any rigorous simulation. Since the system with iso-butyl acetate as entrainer results in most economical process design, we will study the dynamic and control strategy of this system in detail in the next section. Before doing that, let us first explore the necessity of the aqueous reflux stream under various feed compositions for the system using iso-butyl acetate as entrainer. Fig. 7 shows the collection of many simulation results under various feed composition conditions. In all the simulation runs, the total numbers of stages for the column are all fixed the same as the one in Table 8 (30 stages including reboiler but not the condenser). The column bottom product is kept at 99.9 mol% acetic acid high purity by varying the reboiler heat duty and the column top aqueous product is kept at 0.1 mol% acetic acid loss by varying the entrainer makeup flow rate. The aqueous reflux flow rate is fixed at value which will meet both top and bottom product specifications while also minimize reboiler heat duty of this column system. From the figure, one can observed that for feed water

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up dramatically for the cases with no aqueous reflux (70%, 80%, and 90% feed H2 O compositions). This implies that it may be better to add a preconcentrator column before the heterogeneous azeotropic column to increase the acetic acid content in the feed to the heterogeneous azeotropic column if the fresh feed water composition is too high. Another possible advantage may be to have extra degree of freedom (aqueous reflux) to be manipulated in the control strategy. The importance of the aqueous reflux stream for manipulation purpose will be shown in the next section.

1.0 0.9

Aqueous Reflux Fraction

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

3. Control strategy design

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Feed Water Composition

Fig. 7. Minimum aqueous reflux ratio under various feed compositions.

composition above 70 mol%, the aqueous reflux stream is not needed. For the feed composition studied in this paper, the aqueous reflux stream is necessary in order to properly hold the bottom and top product specifications. Table 9 shows the value of main operating variables in keeping the top and bottom product purity at their specifications under various feed composition conditions. In this table, the operating condition is not unique for feed water contents from 10% to 60%. For these feed composition cases, there are three degrees of freedom (extra one is the aqueous reflux) for the system with only two product purity specifications. The ones included in the table are the operating conditions that minimize reboiler heat duty by varying aqueous reflux flow rate. One important thing which needs to be pointed out from the table is that in order to hold product specifications, aqueous reflux flow rate needs to be adjusted in a very wide range. This means that this manipulated variable (aqueous reflux) should not be fixed in the control strategy when trying to reject unmeasured feed composition disturbance. This manipulated variable is preferable to be used in the inferred composition loop to hold product specifications. Another observation is that the reboiler duty goes

The heterogeneous azeotropic column system using isobutyl acetate as entrainer will be studied in detail in this section. The overall control strategy of this system will be developed in order to hold bottom and top product specifications in spite of feed flow rate and feed composition changes. In the control strategy development, we will assume no online composition measurement is available. The composition control loops will be inferred by some tray temperature control strategy. This type of control strategy can easily be implemented in industry for wider applications. The Aspen Plus䉸 steady state simulation in the last section is exported to the dynamic simulation of Aspen DynamicsTM . The tray sizing option in Aspen Plus䉸 is utilized to calculate the column diameter to be 0.3259 m with the tray spacing of 0.6096 m is assumed. Other equipment sizing recommended by Luyben (2002) is used here. The volume of the reboiler is sized to give 10 min holdup with 50% liquid level. The decanter is sized to be bigger to allow for two liquid phases to separate. The holdup time of 20 min is used in the dynamic simulation. Pressure-driven simulation in Aspen DynamicsTM is used with the top pressure of the azeotropic column controlled at 1.1 atm to allow for some pressure drop in the condenser and decanter to give the decanter at atmospheric pressure. The pressure drop inside the column is automatically calculated in Aspen DynamicsTM . Since the tray pressures in the columns are

Table 9 Desired operating conditions under various feed compositions Feed H2 O composition (mol%)

Aqueous reflux (mol/min)

Organic reflux (mol/min)

10 133 102 20 109 100 30 85 99 40 60 96 50 33 93 60 8 90 70 0 99 80 0 113 90 0 127 Product specifications: Bottom at 99.9 mol% HAc and aqueous draw at

Reboiler duty (KW)

Entrainer makeup (mol/min)

Aqueous draw (mol/min)

Bottom product (mol/min)

189 186 182 175 167 159 175 200 226 0.1 mol% HAc.

0.07 0.08 0.11 0.13 0.16 0.16 0.16 0.19 0.21

21 43 64 86 107 128 150 171 193

192 171 150 128 107 85 64 43 21

I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567 Table 10 Base case condition of the optimum flow sheet for dynamic tests

Bottom composition

99.89 mol% HAc 0.0665 mol% H2 O 0.0458 mol% iBuAc 106.89 mol/min

Top aqueous outlet composition

0.0997 mol% HAc 99.79 mol% H2 O 0.11 mol% iBuAc

130

120

110

100

Base case +0.1% -0.1%

90

80 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Stages 140

Heat Duty ±0.1% Change 130

120 o

Temp ( C)

Top aqueous outlet flow rate

Aqueous Reflux ±0.1% Change

o

30 (including reboiler but not including condenser) 9 (counting from the top tray) 213.48 mol/min 50 mol% HAc and 50 mol% H2 O 162.27 KW 92.21 mol/min 33.40 mol/min 0.165 mol/min 106.76 mol/min

140

Temp ( C)

Total number of stage for the azeotropic column Feed stage Fresh feed flow rate Fresh feed composition Column reboiler duty Organic reflux flow rate Aqueous reflux flow rate Entrainer makeup flow rate Bottom flow rate

4555

110

Base case +0.1% -0.1%

100

90

80 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Stages 140

Organic Reflux ±0.1% Change 130

120 o

Temp ( C)

different than the constant atmospheric pressure assumption used in steady-state simulation, the established base case condition in Aspen DynamicsTM will be slightly different than Table 6 in previous section. The final base case steady-state condition used for control study can be seen in Table 10. There are two inventory control strategies which can be used for this system. The first inventory control strategy (Inventory Strategy #1) uses entrainer makeup flow to control the organic phase level in the decanter. This inventory control strategy was successfully used in Chien et al. (1999b, 2000a) when controlling an isopropyl alcohol dehydration column. The second inventory control strategy (Inventory Strategy #2) uses organic reflux flow to control the organic phase level in the decanter. This second inventory control strategy is more intuitively sound because organic reflux flow rate is much larger than the entrainer makeup flow rate, thus the organic phase level control should be more effective. Other inventory control loops which use the same pairings for either of the above strategies are: using top aqueous product flow to control the aqueous phase level in the decanter; using bottom product flow to control the column bottom level. The column top pressure is controlled at 1.1 atm by manipulating the top vapor flow and the decanter temperature is controlled at 40 ◦ C by manipulating the condenser duty. After deciding the inventory control strategy, there are three variables left and can be used in some composition control strategy. The three candidate variables for Inventory Strategy #1 are: organic reflux flow, aqueous reflux flow, and the reboiler duty; while the three candidate variables for Inventory Strategy #2 are: entrainer makeup, aqueous reflux flow, and the reboiler duty. The control objective is to hold the bottom and the top aqueous product specifications at base case condition under ±10% feed flow and ±10% feed H2 O composition changes.

110

Base case +0.1% -0.1%

100

90

80 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Stages

Fig. 8. Sensitivity analysis of the three manipulated variables under Strategy #1.

3.1. Dual temperature loop control strategy Since product specifications at both bottom and top ends are specified, we will consider dual-point temperature control structure first. The sensitivity analysis with small perturbation of the manipulated variables will be performed next in order to determine the two temperature control points. Fig. 8 shows the sensitivity analysis of the three manipulated variable changes under Inventory Strategy #1 and Fig. 9 shows the sensitivity analysis of the three manipulated variable changes under Inventory Strategy #2. The numbering of the stage in this column is counting from top to bottom

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I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567

140

0.3

Aqueous Reflux ±0.1% Change 130

0.2

110

100

Base Case +0.1% -0.1%

90

Zi = |U1i| - |U2i|

Temp ( C)

120

0.1

0.0

-0.1 80 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Stages

-0.2

140

5

10

15

20

25

30

Stages

Heat Duty ±0.1% Change 130

Fig. 10. Plot of Zi for control structure CS1. Temp ( C)

120

110

100

Base Case +0.1% -0.1%

90

80 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Stages 140

Makeup Flow ±10% Change 130

Temp ( C)

120

110

also indicates that dynamically a large inverse response was also observed for column stages between stages #13 to column bottom. Since the numbers of the candidate manipulated variables for each inventory control strategy are “three”, there will be three alternative temperature control structures for each inventory control strategy. From the open-loop data in Figs. 8 and 9, steady-state gain matrix for each alternative overall control strategy can be obtained by averaging the positive and negative manipulated variable changes. Each elements of the steady-state gain matrix is made to be dimensionless by the spans of the temperature sensors and the manipulated variables. Singular-value decomposition (SVD) as described by Moore (1992) can be made on the steady-state gain matrices as follows:

100

Base Case +10% -10%

90

80 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Stages

Fig. 9. Sensitivity analysis of the three manipulated variables under Strategy #2.

with stage #1 as the top stage and stage #30 as the reboiler. When perturbing one manipulated variable, the other two manipulated variables are fixed at base case condition. The final steady-state conditions of Figs. 8 and 9 are obtained by running dynamic simulation with the above mentioned perturbations and then wait until the dynamic simulation to reach final steady-state. For organic reflux changes in Fig. 8, a process gain sign reversing is observed between stages #12 and #13. Dynamically, a large inverse response was observed for column stages between stages #13 to column bottom. Similarly for entrainer makeup changes in Fig. 9, a process gain sign reversing is also observed between stages #12 and #13. This

K = UVT ,

(1)

where K is a 30×2 steady-state gain matrix for each control strategy. U = [U1 |U2 ] is an 30×2 orthonormal matrix, the columns of which are called the left singular vectors. VT is a 2×2 orthonormal matrix, the columns of which are called the right singular vectors.  is a 2×2 diagonal matrix of scalars called the singular values and organized in descending order. To trade off between sensor sensitivity and loop interaction, a function was defined by the difference between the absolute values of the elements of the U vectors as:

Zi = |U1i | − |U2i |.

(2)

The maximum and the minimum of this function as suggested by Moore (1992) are selected as the two tray locations for the temperature control points. For an example, Fig. 10 shows the Zi for the Inventory Strategy #1 with two manipulated variables of aqueous reflux and reboiler duty. From this figure, temperatures at stages #6 and #16 are selected for the two controlled variables for the above two manipulated variables. To compare among the alternative control structures, condition number (CN) and relative gain array

I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567

4557

Table 11 SVD and RGA analysis for each control structure Control structure

Controller pairing

Singular values

CS1 (Inventory Strategy #1) CS2 (Inventory Strategy #1) CS3 (Inventory Strategy #1) CS4 (Inventory Strategy #2) CS5 (Inventory Strategy #2) CS6 (Inventory Strategy #2)

T16 ↔aqueous reflux T6 ↔reboiler duty T7 ↔organic reflux T17 ↔reboiler duty T16 ↔aqueous reflux T7 ↔organic reflux T6 ↔aqueous reflux T15 ↔reboiler duty T7 ↔entrainer makeup T16 ↔reboiler duty T16 ↔aqueous reflux T6 ↔entrainer makeup

1 = 102.9 2 = 10.24 1 = 112.2 2 = 35.76 1 = 60.72 2 = 18.57 1 = 108.0 2 = 13.68 1 = 101.6 2 = 0.192 1 = 38.93 2 = 0.138

(RGA) are also calculated for each control structure. The candidate control structures are listed below: CS1: using Inventory Strategy #1 with reboiler duty and aqueous reflux as two manipulated variables for dualpoint temperature control. CS2: using Inventory Strategy #1 with reboiler duty and organic reflux as two manipulated variables for dualpoint temperature control. CS3: using Inventory Strategy #1 with aqueous reflux and organic reflux as two manipulated variables for dualpoint temperature control. CS4: using Inventory Strategy #2 with reboiler duty and aqueous reflux as two manipulated variables for dualpoint temperature control. CS5: using Inventory Strategy #2 with reboiler duty and entrainer makeup as two manipulated variables for dual-point temperature control. CS6: using Inventory Strategy #2 with aqueous reflux and entrainer makeup as two manipulated variables for dual-point temperature control. Table 11 summarizes the results of SVD and RGA analysis for the above six control structures. From the results of this table, several guidelines as suggested in Moore (1992) are followed to screen out the undesirable control structures from this steady-state analysis. The guidelines are: to select the smallest singular value as large as possible; to select the CN as small as possible; and to select the RGA(11 ) as close to unity as possible. From these guidelines, CS5 and CS6 are dropped for further comparison. For the remaining four control structures (CS1–4), further closed-loop dynamic evaluation will be made to determine which control structure is the best. For the manipulated variables not used for temperature control purpose, it is preferable to design some kind of ratio scheme in order to move these manipulated variables according to the disturbance changes. For example, with control structure CS1, constant ratio of organic reflux flow rate

CN

RGA(11 )

10.05

2.64

3.14

0.673

3.27

0.874

7.89

2.24

529.2

0.594

282.1

0.595

to feed flow rate is maintained throughout the closed-loop simulation run. In order to compensate the feed disturbance effect dynamically, a first-order lag with adjustable time constant is also included in the ratio scheme. Table 11 only shows the steady-state characteristics of each control structure. However, good steady-state characteristics are not a sufficient condition for good dynamic control system performance. Thus, Aspen DynamicsTM will be used to evaluate the control system performance for the alternative control structures. Since the ±10% unmeasured feed composition changes are the more severe closed-loop test in comparison with the feed rate changes, these load changes will be made in the closed-loop dynamic simulations for comparison. All level loops are assumed to be controlled by P-only controller in order to smooth out their manipulated variables in the system. Controller gain of 2.0 as suggested in Luyben (2002) is used in all the level loops. The PID tuning constants for all the stage temperature control loops are tuned using the same multiloop tuning guideline (cf. Chien et al., 1999a), thus fair comparison can be made on the closed-loop dynamic responses among the four candidate control structures. Besides the dynamic response, the evaluation of which control structure is adequate will emphasis more on the observation at final steady-state if the candidate control structure will actually meet the final product specifications in spite of the load disturbances. The closed-loop dynamic responses of control structures CS1–CS4 with ±10% changes in the feed H2 O composition are shown in Figs. 11–14, respectively. The disturbances are introduced at time = 0.5 h. With Inventory Strategy #1 (organic phase level to manipulate the entrainer makeup flow), the maximum makeup flow is assumed to be larger than twice of the steady-state flow rate in order to have better control of the organic phase level when this level is dropping. Since the control loop pairing of CS1 is unconventional (reboiler duty to control temperature at a stage closer to the top of the column), it is very difficult to find proper tuning constants for the two temperature control loops. The tuning guideline in Chien et al. (1999a) has to be further detuned

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108 106

164 Feed H O +10% Change Feed H O -10% Change

T ( C)

102 100 98

162

Reboiler Duty (KW)

104

160

158 Feed H O +10% Change 156

Feed H O -10% Change

96 154

94

152

92 0

1

2

3

4

5

6

7

8

0

9 10 11 12 13 14 15 16 17 18 19 20

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Time (hr) 50

126 Feed H O +10% Change

124

45

Aqueous Reflux (mol/min)

Feed H O -10% Change 122

118

T

( C)

120

116 114

40 Feed H O +10% Change

35

Feed H O -10% Change 30

25

20

112

15

110 0

1

2

3

4

5

6

7

8

0

9 10 11 12 13 14 15 16 17 18 19 20

1

2

3

4

5

6

7

8

1.8

0.75

1.6

Feed H O +10% Change

1.4

Feed H O -10% Change

0.65 0.60 0.55 Feed H O +10% Change 0.50

Feed H O -10% Change

Makeup Flow (mol/min)

0.80

0.70

Organic Level (m)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Time (hr)

1.2 1.0 0.8 0.6 0.4 0.2

0.45 0.0 0.40 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Fig. 11. Closed-loop dynamic simulation using control structure CS1 with ±10% changes in the feed H2 O composition.

in order to make the system stabilized. Notice that for feed H2 O −10% change in Fig. 11, entrainer makeup flow valve has to be fully open at time = 2.4 h and stayed fully open until time = 10.2 h. The controlled temperature points are not steady yet at final simulation time of 20 h. For CS2 in Fig. 12, the dynamic response of −10% feed H2 O change is quite satisfactory. Two controlled temperature points are returned back to setpoints well before time = 20 h. However, the dynamic response is unacceptable for +10% feed H2 O change. Although two controlled temperature points reach their setpoints at final simulation time, the dynamic response of organic phase level is very bad. Its manipu-

lated variable switches from fully close to fully open for the entire simulation run. Similar unacceptable dynamic responses are observed in Fig. 13 for CS3. In comparison with the other three control structures, it is quite obvious from Fig. 14 that CS4 is the best control structure in terms of the dynamic response. All controlled and manipulated variables reach new steady-state within 8 h. The organic phase level is also maintained much better than the other three control structures. Although not shown in this paper, dynamic closed-loop tests for CS5 and CS6 are also performed for ±10% changes in the feed H2 O composition. The closed-loop performance

I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567 112

130 Feed H O +10% Change

110

Feed H O -10% Change

108

Feed H O +10% Change

Organic Reflux (mol/min)

120

106 104

T ( C)

4559

102 100 98 96

Feed H O -10% Change

110

100

90

94 92

80

90 0

1

2

3

4

5

6

7

8

0

9 10 11 12 13 14 15 16 17 18 19 20

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Time (hr) 200 120.4

Feed H O +10% Change 190 Feed H O -10% Change

Reboiler Duty (KW)

120.2

( C)

120.0

T

119.8 119.6

180

170

160

119.4 Feed H O +10% Change 150

Feed H O -10% Change

119.2

140

119.0 0

1

2

3

4

5

6

7

8

0

9 10 11 12 13 14 15 16 17 18 19 20

1

2

3

4

5

6

7

8

1.0

1.8 Feed H O +10% Change

1.6

Feed H O -10% Change

1.4

Makeup Flow (mol/min)

0.8

Organic Level (m)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Time (hr)

0.6

0.4

1.2 Feed H O +10% Change

1.0

Feed H O -10% Change

0.8 0.6 0.4

0.2

0.2

0.0

-0.2

0.0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Fig. 12. Closed-loop dynamic simulation using control structure CS2 with ±10% changes in the feed H2 O composition.

is also not satisfactory particularly for the temperature loop using entrainer makeup flow as the manipulated variable. This ineffectiveness of the entrainer makeup flow on the controlled tray temperature can actually be seen in previous sensitivity plot (Fig. 9). Large ±10% changes in the entrainer makeup only give comparable tray temperature perturbations to ±0.1% changes in the aqueous reflux flow. The large variations on the entrainer makeup flow rate as well as the controlled tray temperature have detrimental effect on the product composition specifications. One thing worth mention is that although the closed-loop dynamic response of CS6 is much worse than CS4 but it is performed somewhat better than CS1, CS2, and CS3. This is another proof that good

steady-state characteristics are not a sufficient condition for good dynamic control system performance of nonlinear systems. The condition number of CS6 (282.1 in Table 11) is much larger than CS1–CS3 but gives better dynamic control performance. The final objective of the alternative control structures is to maintain the bottom and top products specifications in spite of the load disturbances. Figs. 15 and 16 compare the dynamic responses of these four control structures with +10% and −10% feed H2 O composition changes, respectively. It is obvious from these two figures that CS4 is the best control structure to reject feed H2 O composition disturbances. Both bottom and top product compositions are

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130

110 108

120

Organic Reflux (mol/min)

106

T ( C)

104 102 100 98 96 Feed H O +10% Change

94

110 Feed H O +10% Change 100

Feed H O -10% Change

90

Feed H O -10% Change

92 90

80 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

Time (hr) 125

60

50

Aqueous Reflux (mol/min)

120

110

T

( C)

115

Feed H O +10% Change

105

Feed H O -10% Change 100

40 Feed H O +10% Change

30

Feed H O -10% Change 20

10

0

95

-10 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

Time (hr)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

1.2

1.4 Feed H O +10% Change

1.0

1.2

Makeup Flow (mol/min)

Feed H O -10% Change

Organic Level (m)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0.8

0.6

0.4

Feed H O +10% Change

1.0

Feed H O -10% Change 0.8 0.6 0.4 0.2

0.2 0.0 0.0

-0.2 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Fig. 13. Closed-loop dynamic simulation using control structure CS3 with ±10% changes in the feed H2 O composition.

quickly returned back to specifications much faster than the other three alternative control structures. Control structure CS3 dynamically departs the furthest for both bottom and top product compositions to their specifications for +10% feed H2 O composition change and control structure CS1 dynamically departs the furthest for −10% feed H2 O composition change. In terms of the final steady-state value, control structure CS2 departs the furthest to bottom product specification (see Fig. 16). This control structure of CS2 makes the aqueous reflux flow rate fixed during the dynamic runs thus lose the ability to adjust the aqueous flow rate upward or downward to cope with the feed H2 O composition changes. Attempts have been made to introduce a

ratio scheme to maintain constant aqueous reflux ratio instead of ratio to feed flow. The dynamic results are even worse than fixing the aqueous reflux flow rate during load disturbances. Another important closed-loop test for this control system is the feed flow rate changes. These changes are necessary in order to adjust the production rate upward or downward. Fig. 17 shows the dynamic responses for the proposed control structure CS4 under ±10% feed rate changes. Notice again that the closed-loop dynamic response is very satisfactory. Although not shown in the paper, both product specifications are maintained in spite of the production rate changes.

I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567 99

4561

50

T ( C)

Feed H O -10% Change

97

96

Aqueous Reflux (mol/min)

45 Feed H O +10% Change

98

40 Feed H O +10% Change 35

Feed H O -10% Change

30

25

95

20 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

Time (hr)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

170

118

168 Feed H O +10% Change

Feed H O +10% Change

Feed H O -10% Change

166

Reboiler Duty (KW)

116

T

( C)

117

Feed H O -10% Change 164

162

160

115

158

114

156 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

Time (hr)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr) 98

0.728 Feed H O +10% Change Feed H O -10% Change

0.724

0.722

Organic Reflux (mol/min)

Organic Level (m)

Feed H O +10% Change

96

0.726

Feed H O -10% Change 94

92

90

0.720 88 0.718 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Fig. 14. Closed-loop dynamic simulation using control structure CS4 with ±10% changes in the feed H2 O composition.

3.1.1. Summary of dynamic simulation runs Some concluding remarks can be made after the above dynamic runs. Firstly, good steady-state characteristics on CS1–CS3 (see Table 11) are not a sufficient condition for good dynamic control system performance of nonlinear systems. These three control structures gave much unacceptable closed-loop performance than CS4. Secondly, dynamic simulations show that it is better to avoid using entrainer makeup flow as the manipulated variable for either of the organic phase level loop (CS1–CS3) or the controlled tray temperature loop (CS5 and CS6). In this system, there are “three” “free” manipulated variables that can be cho-

sen for the dual temperature loop. If including the organic phase level loop, there are total of “four” manipulated variables that can be chosen from. Thus, it is possible to select a control strategy not using entrainer makeup flow as manipulated variable. This entrainer makeup flow rate is fixed at the base case value and ratio to fresh feed rate changes. Fixing this entrainer makeup flow at base case value under various feed composition changes can still meet product purity specifications. This can be demonstrated by some steady-state simulation runs as in previous Table 9. In that table, desirable entrainer makeup flow rate is at 0.16 mol/min

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I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567

0.16

0.12 0.10

Top Acetic Acid Composition

Top Acetic Acid Composition

0.020

CS1 CS2 CS3 CS4

0.14

0.08 0.06 0.04 0.02

CS1 CS2 CS3 CS4

0.015

0.010

0.005

0.00

0.000 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

Time(hr)

9 10 11 12 13 14 15 16 17 18 19 20

Time(hr)

1.02

1.005

0.98 0.96

CS1 CS2 CS3 CS4

0.94 0.92 0.90 0.88

Bottom Acetic Acid Composition

Bottom Acetic Acid Composition

1.00

1.000

0.995

CS1 CS2 CS3 CS4

0.990

0.985

0.980

0.975

0.86 0.84 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time(hr)

Fig. 15. Comparison of bottom product acetic acid compositions for the four control structures with +10% feed H2 O composition change.

for 50% feed H2 O composition. If feed H2 O composition is changed to 40%, from the table, the desirable entrainer makeup flow rate is at 0.13 mol/min. This does not mean that entrainer makeup flow rate has to be at this value to meet two product purity specifications. As mentioned previously, there are multiple steady-state conditions which can meet both product purity specifications because there are “three” degrees of freedom. In fact, a steady-state run at 40% feed H2 O composition can be made with fixing of the two product purity specifications by varying reboiler duty and aqueous reflux and also fixing the entrainer makeup flow rate at 0.16 mol/min. The resulting steady-state condition gave a little bit more on the value of the reboiler duty (176 KW vs. 175 KW in Table 9) but still holding two product purity specifications. Also, noticeably the impurity of the bottom product shifted to more in iBuAc and less in H2 O but the total impurity (iBuAc+H2 O) is still at 0.1 mol% as desired. This demonstrates that control structure to fix entrainer makeup flow rate is workable. Since the existence of this extra degree of freedom (aqueous reflux) to let the entrainer makeup flow released from controlling the organic phase level or tray temperature, it is desirable to have this extra degree of freedom in the sys-

0.970 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time(hr)

Fig. 16. Comparison of bottom product acetic acid compositions for the four control structures with −10% feed H2 O composition change.

tem. This extra degree of freedom can provide desirable closed-loop dynamic response, thus if the feed composition is rich in water (70 mol% H2 O), it is preferable to add a preconcentrator column before the feed stream to improve the dynamic behavior. This suggestion is supported from previous Fig. 7 and the dynamic simulation runs in this section. From the dynamic responses of CS4 (Fig. 14), another important observation can be made. With disturbances like ±10% changes in the feed H2 O composition, the aqueous reflux flow rate will be adjusted upward or downward accordingly in order to maintain about the same overall H2 O composition into the column. However, the reboiler duty is actually returned back close to their original steady-state after some dynamic transients. This inspires the thinking if simpler single temperature control strategy will work or not? The attempts of using single temperature control strategy will be explored next. 3.2. Simpler single temperature loop control strategy The idea of the simpler single temperature loop control strategy is to use aqueous reflux flow rate to hold some tray

I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567

4563

38

T ( C)

Feed Rate +10% Change Feed Rate -10% Change

97

Aqueous Reflux (mol/min)

37 36 35 Feed Rate +10% Change Feed Rate -10% Change

34 33 32 31 30

0

1

2

3

4

5

6

7

8

0

9 10 11 12 13 14 15 16 17 18 19 20

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Time (hr) 120

190

119 180

T ( C)

Feed Rate -10% Change 117

116

115

Reboiler Duty (KW)

Feed Rate +10% Change

118

Feed Rate +10% Change Feed Rate -10% Change

170

160

150 114

113

140 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

Time (hr)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0.735

104 102 100

Feed Rate +10% Change Feed Rate -10% Change

0.725

0.720

0.715

Organic Reflux (mol/min)

Organic Level (m)

0.730

98 Feed Rate +10% Change Feed Rate -10% Change

96 94 92 90 88 86 84 82 80

0.710 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Time (hr)

Fig. 17. Closed-loop dynamic simulation using control structure CS4 with ±10% changes in the feed flow rate.

temperature inside the column and to keep the other two “free” manipulated variables (reboiler duty and entrainer makeup) to maintain ratioed to the feed flow rate. From the earlier sensitivity analysis in Fig. 9, the most sensitive control point inside the column is stage #6 which is closer to the top of the column. Since the main acetic acid product is drawn from the bottom of the column, an alternative control point is to select the second most sensitive control point which is closer to the bottom of the column. This alternative control point will be stage #16. Thus two single loop control structures will be deduced for closed-loop dynamic

test. They are: CS7: using Inventory Strategy #2 in the previous subsection with temperature at stage #6 controlled by manipulating aqueous reflux flow, while the other two manipulated variables, reboiler duty and entrainer makeup, maintain constant ratios to the feed flow rate. CS8: using Inventory Strategy #2 in the previous subsection with temperature at stage #16 controlled by manipulating aqueous reflux flow, while the other two manipulated variables, reboiler duty and entrainer

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50

99

Feed H O -10% Change

T ( C)

98

97

96

Aqueous Reflux (mol/min)

45 Feed H O +10% Change

40

Feed H O +10% Change

35

Feed H O -10% Change 30

95

25

94

20 0

1

2

3

4

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7

8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

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5

6

7

8

Time (hr)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0.7250

Feed H O +10% Change

0.7245

Feed H O -10% Change

0.7240 0.7235 0.7230 0.7225

93.6 93.4 93.2

Organic Reflux (mol/min)

Organic Level (m)

0.7255 Feed H O +10% Change Feed H O -10% Change

93.0 92.8 92.6 92.4 92.2 92.0 91.8 91.6 91.4 91.2 91.0 90.8

0.7220

90.6 90.4

0.7215 0

1

2

3

4

5

6

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8

9 10 11 12 13 14 15 16 17 18 19 20

0

1

2

3

4

5

6

7

8

Time (hr)

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Fig. 18. Closed-loop dynamic simulation using control structure CS7 with ±10% changes in the feed H2 O composition.

124

50

45 Feed H O +10% Change Feed H O -10% Change

118

T

( C)

120

116

Aqueous Reflux (mol/min)

122

40 Feed H O +10% Change

35

Feed H O -10% Change 30

25

114 20 112

15 0

1

2

3

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9 10 11 12 13 14 15 16 17 18 19 20

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9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0.7250 93.2 Feed H O +10% Change

93.0

Feed H O -10% Change

92.8

0.7240

0.7235

0.7230

0.7225

Organic Reflux (mol/min)

Organic Level (m)

0.7245

Feed H O +10% Change Feed H O -10% Change

92.6 92.4 92.2 92.0 91.8 91.6 91.4 91.2 91.0 90.8

0.7220

90.6 0

1

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8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0

1

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3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

Fig. 19. Closed-loop dynamic simulation using control structure CS8 with ±10% changes in the feed H2 O composition.

I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567 0.0013

0.006

0.0011

0.0010

0.0009

CS7 CS8 CS4

0.005

Top Acetic Acid Composition

CS7 CS8 CS4

0.0012

Top Acetic Acid Composition

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0.004

0.003

0.002

0.001

0.0008

0.000 0.0007 0

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9 10 11 12 13 14 15 16 17 18 19 20

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0.9994

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0.9992

0.9988

0.9990 0.9988

CS7 CS8 CS4

0.9986

9 10 11 12 13 14 15 16 17 18 19 20

Time(hr)

0.9984 0.9982 0.9980

Bottom Acetic Acid Composition

Bottom Acetic Acid Composition

Time (hr)

0.9986 0.9984 0.9982

CS7 CS8 CS4

0.9980 0.9978 0.9976 0.9974

0.9978

0.9972 0

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8

9 10 11 12 13 14 15 16 17 18 19 20

Time (hr)

0

1

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7

8

9 10 11 12 13 14 15 16 17 18 19 20

Time(hr)

Fig. 20. Comparison of bottom product acetic acid compositions for the double loop control structure of CS4 with single loop control structures of CS7 and CS8 with +10% feed H2 O composition change.

Fig. 21. Comparison of bottom product acetic acid compositions for the double loop control structure of CS4 with single loop control structures of CS7 and CS8 with −10% feed H2 O composition change.

makeup, maintain constant ratios to the feed flow rate.

the temperature loop and the organic level loop are shown in Fig. 22. All controlled and manipulated variables reach new steady-state values after a short dynamic transient. Although not shown in the paper, both product compositions are also maintained at tight specifications. The final proposed simple single temperature loop control structure of CS7 is shown in Fig. 23. Although the two product purities are assumed not to be measured on-line, but if they can be measured infrequently in quality lab, small trimming of the controlled temperature setpoint or small changes of the reboiler heat duty can be made to even more precisely to hold the product purities at their specifications during sustained feed disturbances.

Figs. 18 and 19 show the closed-loop dynamic responses for CS7 and CS8 under ±10% feed H2 O composition changes, respectively. Notice that the dynamic responses are all quite satisfactory with all variables settled out at new steady-state values even faster than CS4 (comparing to Fig. 14). The dynamic responses of the most important bottom and top product compositions are shown in Figs. 20 and 21 for +10% and −10% changes in the feed H2 O composition, respectively. Notice first that the scaling of Figs. 20 and 21 are much smaller than previous Figs. 15 and 16 indicating these two single loop control structures perform much better than previous CS1, CS2, and CS3. Comparing to more complex double loop control structure CS4, CS7 performs very satisfactory. Both product compositions are maintained at tight specifications even the control point is far away from the column bottom. On the contrary, the acetic acid loss through the column top cannot be maintained at tight specification for control structure CS8. The proposed control structure CS7 also performs very well for ±10% feed rate disturbances. The dynamic responses for

4. Conclusions Three candidate entrainers (ethyl acetate, iso-butyl acetate, and n-butyl acetate) are considered for acetic acid dehydration via heterogeneous azeotriopic distillation. The factors needed to be considered in selecting the proper entrainer are illustrated for this example system. Optimum column designs and operating conditions are obtained for these

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T ( C)

Feed Rate +10% Change Feed Rate -10% Change

98

96

Aqueous Reflux (mol/min)

Feed Rate +10% Change

100

Feed Rate -10% Change

40

35

30

25

94

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9 10 11 12 13 14 15 16 17 18 19 20

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9 10 11 12 13 14 15 16 17 18 19 20

Time (hr) 110

0.74

Feed Rate +10% Change

Feed Rate +10% Change Feed Rate -10% Change

105

Organic Reflux (mol/min)

Organic Level (m)

Feed Rate -10% Change

0.73

0.72

0.71

100

95

90

85

80

75 0

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9 10 11 12 13 14 15 16 17 18 19 20

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Fig. 22. Closed-loop dynamic simulation using control structure CS7 with ±10% changes in the feed flow rate.

Fig. 23. Schematic diagram of the proposed control structure CS7.

I.L. Chien et al. / Chemical Engineering Science 59 (2004) 4547 – 4567

three candidate systems using rigorous process simulation. Total Annual Cost (TAC) is used as the objective function in determining the optimum column designs and operating conditions for these three candidate systems. Iso-butyl acetate was found to be the best entrainer with resulting TAC only about 55% of the system with no entrainer. The optimum overall control strategy is also proposed for this column system to hold both bottom and top product specifications in spite of ±10% feed rate and ±10% feed H2 O composition load disturbances. Several alternative control structures are compared using dynamic simulation. The proposed overall control strategy is very simple requiring only one tray temperature control loop inside the column. This simple overall control strategy can easily be implemented in industry for wider applications. Acknowledgements This work is supported by National Science Council of R. O. C. under grant nos. NSC 89-2214-E-011-025 and NSC 90-2214-E-011-013. Helpful suggestions from anonymous reviewers are gratefully acknowledged. References Aspen Technology, Inc., 2001. Aspen Plus User’s Manual 11.1. Aspen Technology, Inc., Cambridge. Bozenhardt, H.F., 1988. Modern control tricks solve distillation problems. Hydrocarbon Processing 67 (6), 47–50. Chiang, S.F., Kuo, C.L., Yu, C.C., Wong, D.S.H., 2002. Design alternatives for the amyl acetate process: coupled reactor/column and reactive distillation. Industrial and Engineering Chemistry Research 41 (13), 3233–3246. Chien, I.L., Huang, H.P., Yang, J.C., 1999a. A simple multiloop tuning method for PID controllers with no proportional kick. Industrial and Engineering Chemistry Research 38 (4), 1456–1468. Chien, I.L., Wang, C.J., Wong, D.S.H., 1999b. Dynamics and control of a heterogeneous azeotropic distillation column: conventional control approach. Industrial and Engineering Chemistry Research 38 (2), 468–478. Chien, I.L., Wang, C.J., Wong, D.S.H., Lee, C.H., Cheng, S.H., Shih, R.F., Liu, W.T., Tsai, C.S., 2000a. Experimental investigation of conventional control strategies for a heterogeneous azeotropic distillation column. Journal of Process Control 10 (4), 333–340. Chien, I.L., Chen, W.H., Chang, T.S., 2000b. Operation and decoupling control of a heterogeneous azeotropic distillation column. Computers and Chemical Engineering 24 (2–7), 893–899. Christensen, S.P., Olson, J.D., 1992. Phase equilibria and multiple azeotrope of the acetic acid–isobutyl acetate system. Fluid Phase Equilibria 79, 187–199. Costantini, G., Serafini, M., Paoli, P., 1981. Process for the recovery of the solvent and of the by-produced methylacetate in the synthesis of terephthalic acid. U.S. Patent 4, 250, 330. Douglas, J.M., 1988. Conceptual Process Design. McGraw-Hill, New York. Gaubert, M.A., Gerbaud, V., Joulia, X., Peyrigain, P.S., Pons, M., 2001. Analysis and multiple steady states of an industrial heterogeneous azeotropic distillation. Industrial and Engineering Chemistry Research 40 (13), 2914–2924.

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