Design and Control of a Heat-Integrated Reactive Distillation System

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Ind. Eng. Chem. Res. 2010, 49, 7398–7411

Design and Control of a Heat-Integrated Reactive Distillation System for the Hydrolysis of Methyl Acetate Hao-Yeh Lee,† Yi-Chen Lee,† I-Lung Chien,†,‡ and Hsiao-Ping Huang*,† Department of Chemical Engineering, National Taiwan UniVersity, Taipei 106, Taiwan, and Department of Chemical Engineering, National Taiwan UniVersity of Science and Technology, Taipei 106, Taiwan

There is increasing interest in the heat-integrated reactive distillation systems, lately. In this Article, two types of heat-integrated reactive distillation systems for the hydrolysis of methyl acetate are investigated. One type is to use the concept of internally heat-integrated distillation column (HIDiC) as applied to the reactive distillation system. Another type for the heat integration is to use a multieffect distillation concept by splitting the feed to enter into two smaller reactive distillation columns operated at different pressures. Rigorous simulation study has been conducted to compare the optimal flowsheet of the above two designs. It is found that, although the first design can save operating costs by 8.05%, due to the high cost of the compressor needed in the system, the total annual cost is 33.13% higher than that of the base design without heat integration. On the contrary, the multieffect distillation design not only saves operating cost by 15.19%, but also saves the total annual cost by 6.42%. The overall control strategy of this proposed heat-integrated design has also been developed. Only tray temperature control loops are needed to properly reject feed disturbances. 1. Introduction By combining two important operations (reaction and separation) into a single vessel, reactive distillation has demonstrated its potential for capital productivity improvements, selectivity improvements, reduced energy use, and the reduction or elimination of solvents in the process (cf., Malone and Doherty1). From that review paper, there are a total of 562 publications of reactive distillation for the period of 1971-1999. An updated version of the literature survey (cf., Luyben and Yu2) shows that there were 1105 publications and 814 U.S. patents between 1971 and 2007. This shows the rapid progress of this technology sector in recent years. Also, in a book presenting the status and future directions of reactive distillation (cf., Sundmacher and Kienle3), a survey of chemical reaction systems that performed successfully in reactive distillation columns is given. In Tables 1.1 and 1.2 of this book, over 100 industrially or potentially important reactions for reactive distillation applications are given. An updated literature survey from Luyben and Yu2 shows a total of 236 reaction systems in the Appendix of this recent book. This illustrates the importance of this technology in industrial applications. For the exothermic reaction systems utilizing reactive distillation, the operating energy can be reduced by making use of this heat of reactions to partially supply vapor traffic inside the column. However, many endothermic reaction systems can still benefit from the reactive distillation technology for conversion and selectivity improvements purpose. For these endothermic reaction systems, operating the reactive distillation column at higher pressure (which means the system is operated at higher temperature condition) would benefit from the shifting of the reaction to the product side. Moreover, heat integration methods via pressurize operation in the open literature can be utilized to further save energy of these reactive distillation systems. In this Article, the heat integration methods used in regular column will be investigated in a reactive distillation system with endothermic reaction. * To whom correspondence should be addressed. Tel.: 886-2-23638999. Fax: 886-2-2362-3935. E-mail: [email protected]. † National Taiwan University. ‡ National Taiwan University of Science and Technology.

In 1950, Robinson and Gilliand4 listed two ways for doing heat integration in a distillation system. One is via multieffect distillation columns, and the other is via vapor recompression columns, which is a prototype of internally heat-integrated distillation column (HIDiC). For the multieffect distillations, heat integration utilizes the heat of top distillate vapor in one column to supply the heat to the reboiler of next column. To provide the necessary temperature difference, the columns are operated under different pressures. Andercovich and Westerberg5 studied the thermodynamics analysis for N multieffect distillation columns. By the T-Q diagram, they claimed energy decreasing is proportion to 1/N. Even though more columns in multieffect process can reduce more on energy consumption, it costs more on capital investments. Another practical problem with more columns is the unit placement in the plant. The industries generally select double-effect as a compromise to save energy but not cost more on capital investments and also to avoid the unit placement problem. On the unit operation level, one notable example of double-effect distillations is the feed split configuration of the heat-integrated distillation column5–8 where the feed is split into two streams and is fed separately to two heat-integrated columns; theoretically, an amount up to 50% energy can be saved. A study of Tsai et al.9 demonstrated that such an integration can be properly controlled for practical application. On this basis, the feed split for distillation is applied here to a reactive distillation system (denoted as a r-FS system) for further energy saving. On the other hand, to improve energy efficiency, the heat pump principle is another effective method for the reuse of the rejected heat. In this approach, it compresses the vapor from the overhead as the heat pumping fluid to support energy required for its reboiler in the bottom. In this way, it saves energy by reusing the energy removed. The HIDiC used this heat pump concept to integrate heat between the rectifying and the stripping sections. Since then, quite a few papers addressing this HIDiC system have been published (Mah et al.,10 Takamatsu et al.,11,12 Nakaiwa et al.,13–17 and Huang et al.18,19). Nakaiwa et al.20 and Naito et al.21 also demonstrated that not only an ideal system but also an experimental benzene/toluene HIDiC

10.1021/ie9016754  2010 American Chemical Society Published on Web 07/14/2010

Ind. Eng. Chem. Res., Vol. 49, No. 16, 2010 a

Table 1. UNIQUAC Model Parameters for the Studied Systems (i,j)

aji (K)

aij (K)

bij (K)

cij (K-1)

bji (K)

cji (K-1)

(1,2) -0.9704 2.0346 -390.26 -65.245 0.003061 -0.003157 (1,3) 0.4364 -1.1162 62.19 -81.848 -0.0002724 0.001331 (1,4) 0.05101 0.2936 -422.38 98.120 0.0002402 0.00007674 (2,3) 0.7101 -0.7248 -62.97 -326.20 -0.001167 0.002355 (2,4) -3.1453 2.0585 575.68 -219.04 0.006071 -0.007015 (3,4) -0.01014 -0.9630 -593.70 265.83 0.002161 -0.0002013 a

1, HAc; 2, MeOH; 3, MeAc; 4, H2O.UNIQUAC model:

ln γi ) ln

Φi θi Φi z + qi ln + l ixi 2 Φi xi

nc

∑xl + j j

[

j)1

nc

q′i 1 - ln(

where Φi )

rixi nc

∑r x

, θi )

k k

j ji

j)1

nc

∑ θ′τ

j)1

k kj

k)1

qixi nc

∑q x

, θi′ )

k k

k)1

θj′τij

nc

∑ θ ′τ ) - ∑

k)1

]

q′ixi nc

∑ q′ x

k k

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every mole of PVA produced. One way to convert methyl acetate back to acetic acid (raw materials of PVA plant) is via methyl acetate hydrolysis. Lin et al.22 summarized and compared the methyl acetate hydrolysis process to reactive distillation in the open literature. The best design of a reactive distillation process has been proposed by Lin23 and Lin et al.22 In the following, we will review the design of this process as a candidate for exploring the possibility of heat integration in a reactive distillation system with endothermic reaction. 2.1. Thermodynamic and Kinetic Models. There are four components in the studied system including two reactants: methyl acetate (MeAc) and water (H2O); and two products, acetic acid (HAc) and methanol (MeOH). The UNIQUAC model was used to calculate the liquid activity coefficient, and the Hayden and O’Connell (HOC)24 model was used to account for association in the vapor phase. The parameters for the UNIQUAC and HOC models are listed in Tables 1 and 2, respectively. The endothermic reversible reaction of the studied system is shown below:

k)1

kf

H2O + CH3COOCH3 y\z CH3COOH + CH3OH

and

system can be well-controlled without special difficulties, as compared to conventional distillation. Despite an increasing interest in the heat integration for reactive distillation systems, no comparison of the uses of the two integration approaches for reactive distillation has been addressed. In this Article, the application of r-HIDiC and r-FS to the reactive distillation for hydrolysis of methyl acetate will be studied and compared using one common case (without heat integration) as a basis. It is also desirable to know if the heatintegrated process could be controlled properly for practical use. Thus, the overall control strategy of the most favorable design flowsheet will also be developed and studied. 2. The Studied Reactive Distillation Process In a polyvinyl alcohol (PVA) plant, reaction stoichiometry indicates that equal molar of methyl acetate is generated for Table 2. Hayden and O’Connell Association Parameters component

HAc

MeOH

MeAc

H2O

HAc MeOH MeAc H2O

4.50 2.50 2.00 2.50

2.50 1.63 1.30 1.55

2.00 1.30 0.85 1.30

2.50 1.55 1.30 1.70

The kinetic model of the above reaction was found in Po¨pken et al.25,26 Heterogeneous catalyst of Amberlyst 15 was used in the study. Two kinetic model forms (pseudohomogeneous and adsorption-based) were used to fit the experimental data. It was found that the adsorption-based model fits the experimental data better. The information of this kinetic model based on activity can be found in Table 3. In the table, Mi [kg/kmol] is the molecular weight of component i, and R [)8.314 kJ/kmol/K] is the gas constant. Notice that the unit of the reaction constants is in kmol/kgcat/s, which will be converted to kmol/m3/s in the simulation study with the assumption of catalyst density at 770 kg/m3 and catalyst occupied one-half of the liquid holdup in the reactive tray. The equilibrium constants (Keq ) kf/kr) calculated at two different temperatures were also listed in Table 3. Because the value of the equilibrium constant is small, excess water design has been conducted in Lin23 and Lin et al.22 to drive methyl acetate to near complete conversion. Because the reaction is endothermic, the calculated equilibrium constant is more favorable at higher operating temperature (Keq ) 0.046 at 393 K vs Keq ) 0.039 at 333 K). However, there is an upper limit on the operating temperature for Amberlyst 15 at 120 °C. We will keep this information in mind in the later design study when higher pressure will be operated to achieve heat integration of the studied system. 2.2. Base Design Flowsheet of the Overall Process. There are two azeotropes in the studied system. The boiling point

Table 3. Kinetic Model and Parameters for the Studied System kinetic model (catalyst) adsorption-based model (Amberlyst 15) kfaMeAcaH2O - kraHAcaMeOH r ) mcat · (a′MeAc + a′H2O + a′HAc + a′MeOH)2 Kiai a′i ) ,K ) 4.15, KH2O ) 5.24, Mi MeAc KHAc ) 3.15, KMeOH ) 5.64

( -63730 RT ) -60470 k ) 7.862 × 10 exp( RT )

kf ) 1.000 × 104exp 4

r

∆H ) 3260 [kJ/kmol]

(1)

kr

bij z + cijT, li ) (ri - qi) - (ri - 1), z ) 10 τij)aij + T 2

kf at T ) 333 K, kf ) 1.01 × 10

Keq -6

[kmol/kgcat/s]

at T ) 393 K, kf ) 3.38 × 10-5[kmol/kgcat/s]

at T ) 333 K, Keq ) 0.039

at T ) 393 K, Keq ) 0.046

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Ind. Eng. Chem. Res., Vol. 49, No. 16, 2010

Table 4. Boiling Point Ranking at 1 and 4.6 atm components of boiling point ranking (from low to high)

1 atm

4.6 atm

MeAc/MeOH azeo. MeAc/H2O azeo. MeAc MeOH H2O HAc

53.65 (°C) (0.653/0.347) 56.43 (°C) (0.89/0.11) 57.05 (°C) 64.53 (°C) 100.02 (°C) 118.01 (°C)

101.73 (°C) (0.51/0.49) 106.16 (°C) (0.78/0.22) 109.00 (°C) 109.14 (°C) 149.29 (°C) 175.92 (°C)

ranking of the four components as well as the two azeotropes are shown in Table 4. It is found that, although one product (HAc) is the heavy-boiler, however, the other product is in the middle of the boiling point ranking. Thus, it is more difficult to come up with the overall design flowsheet. Lin23 proposed the overall design flowsheet as in Figure 1. The overall flowsheet includes a reactive distillation column and two other columns. The two fresh feeds are all entered into the reflux drum of the reactive distillation column under total reflux operation with the upper section of this column all as reaction section. All products and the excess water are all withdrawn from the column bottoms to downstream separation system consisting of two columns. Because there is negligible methyl acetate in this feed stream to the downstream system, the separation should be easy because of no azeotrope in the ternary system of acetic acid, water, and methanol. The design of the separation system is to separate out acetic acid (heavy product) from the bottom of the first column and to separate out methanol (light product) from the top of the second column. The bottom of the second column is designed to avoid tangent pinch at the pure water end; thus, it contains mostly water with some acetic acid component. This stream is designed to be recycled back to the reactive distillation column. The overall design flowsheet to minimize total annual cost is shown in Figure 1. An extended design flowsheet with mixed feed of MeAc and MeOH instead of pure MeAc feed has been proposed by Lin et al.,22 which used a similar design concept. In Figure 1, indirect sequence (heaviest out first) was used for the design of the separation system. Heat integration of this

Figure 2. Design flowsheet of the reactive distillation column for the methyl acetate hydrolysis process.

separation system is possible by using a prefractionator column and a main column with side draw, Petlyuk column, or column with dividing wall. We will investigate the potential of energy saving using the above-mentioned method in a separate paper. In this Article, we will focus our attention on the reactive distillation column and compare two possible heat-integration designs. 3. Heat-Integrated Design The flowsheet of the reactive distillation column alone is shown in Figure 2. Two heat-integration methods found in the literature will be extended to apply to the reactive distillation

Figure 1. Base design for the methyl acetate hydrolysis process using reactive distillation.


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Figure 3. Conceptual design of the internally heat-integrated reactive distillation system.

column next. Notice, in all of the design studies, the software package of Aspen Plus was used to conduct the rigorous simulation. Equilibrium stages were assumed in the column simulation. Total material, component, and energy balances were calculated in each column tray via RadFrac module in Aspen Plus. The modified Newton’s method of Broyden is chosen to obtain the steady-state solution for the system of algebraic equations. 3.1. Internally Heat-Integrated Distillation Column. The first heat-integration method is called the internally heatintegrated distillation column (HIDiC). This method makes use of the vapor compression to increase the operating pressure of the rectifying section of a simple column so that its temperature is higher than that of the stripping section. With heat transfer from the rectifying section into the stripping section, heat input from the reboiler and heat removal by the condenser can be reduced. This idea, if extended to the reactive distillation column as in Figure 2, will look like the design flowsheet in Figure 3. In this design (called r-HIDiC), the vapor from the stripping section is pressurized using a compressor and entered into the reaction section. Because the operating temperature at the reaction section is elevated, the heat can be transferred into the stripping section. The internally heat-integrated design proposed by Olujic´ et al.27,28 will be used in our study with the reaction section in the center with annular stripping section. The number of stages for the reaction section and the stripping section are assumed to be the same so that this annular structure can easily be constructed. The temperature difference between the corresponding stages of the reaction section and the stripping section is set to be greater than 10 °C for the heat transfer. The operating temperature in the reaction section has to be less than 120 °C to be in compliance with the requirement of Amberlyst 15 catalyst. Another limitation is on the operating pressure in the reaction section where it has to be less than 8 atm so that side reaction for methanol to form dimethyl ether can be avoided (Song et al.29). In the simulation of the reaction section, the catalyst loading occupied one-half of the total liquid holdup in a tray with weir height of 10 cm and tray spacing of 0.6096 m. In the reflux drum where reaction also takes place, a residence time of 5 min is assumed. The calculation of the heat transfer in the simulation can be explained by a flowchart as in Figure

4. The heat transferred from the reaction section to the stripping section at each stage is iteratively obtained to match the Q ) UA∆T calculation. The value of the overall heat-transfer coefficient U has been reported in Nakaiwa et al.21 and Olujic´ et al.28 to be between 0.6 and 1 kW m-2 K-1 for their benzene/ toluene and propylene/propane processes. We adopt a value of 0.85 kW m-2 K-1 for U, in this Article. The heat transfer area per stage is calculated as the circumferential area of the inner column. Its value is determined by πD times tray spacing (i.e., 6096 m). The design variables in the flowsheet of Figure 3 include the number of stages in the reaction section (recalled to be assumed as the same as the stripping section) and the compressor ∆P. The objective function for the optimization search is the total annual cost (TAC). The TAC includes the operating cost and the annualized capital cost. The operating cost includes the steam for the reboiler, the cooling water for the condenser, the catalyst cost, and the operating cost for the compressor. For estimating the catalyst cost, the unit price is assumed to be $3.50/lb and replaced every 3 months. The capital cost includes the column shell, internal trays, reboiler, condenser, and the compressor. A capital charge factor of 3 years is assumed in the calculation. The cost calculation can be seen from Appendix E of the Douglas30 process design book. There is only one degree of freedom for the flowsheet in Figure 3 because it is under total reflux operation with no distillate. The methyl acetate composition at column bottoms is set to be at 0.15 mol % by varying the reboiler duty. Figure 5 displays the TAC with varying total stages of the reaction section (NT) at three different compressor values ∆P of 2, 2.1, and 2.2 atm. It is observed that the 10 total stages all gave the least TAC. Increasing this number would add reactive holdup and also add heat transfer area for the internal heat transfer from the reaction section to the stripping section, thus further reducing the needed reboiler duty. However, more stages mean more capital cost and more catalyst cost, and thus the 10 total stages represent a trade-off among the above pros and cons. It is also observed from the figure that the compressor ∆P is smaller, which is better. This can be explained by the high compressor cost in the TAC calculations. The ∆P of 2 atm represents the

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Figure 6. TAC and energy saving versus ∆P for the r-HIDiC design.

lowest ∆P, which still gives the temperature difference between the two column sections to be greater than 10 °C. Figure 6 displays the TAC, annualized capital cost, operating cost, and the energy saving (%) of this process at different compressor ∆P. In the plot, the energy saving is defined as the total heat duty saved when using this internally heat-integrated design versus the original design flowsheet in Figure 2. It can be seen from this figure that the energy saving increases as the compressor ∆P increases. However, the TAC as well as the annualized capital cost and the operating cost also increase, and thus it is more beneficial to select compressor ∆P at its lowest value. Figure 7 shows the resulting optimal flowsheet for the internally heat-integrated design (r-HIDiC). The detailed comparison of this r-HIDiC design to the original design without heat integration is outlined in Table 5. Although the energy and the operating cost savings are at 26.88% and 8.05%, respecTable 5. Comparison of Optimal Design and Cost Information of Basic RD versus r-HIDiC

Figure 4. Flowchart for the heat transfer calculation in r-HIDiC simulation.

Figure 5. TAC plot versus operating pressure and NT at reaction section for the r-HIDiC design.

system

RD

r-HIDiC

total no. of trays no. of trays in reaction section (NRxn) no. of trays in stripping section (NS) reactive trays catalyst in reflux drum (m3) catalyst in each tray/sum (m3) acetate/water feed flow rate (kmol/h) recycle flow rate (kmol/h) (FR) molar feed ratio (water/acetate) bottom product flow rate (kmol/h) bottom composition (mole fraction)

31 22 9 22 2.85 0.089/1.95 50/50 220 4.59 320 HAc: 0.2813 MeOH: 0.1554 MeAc: 0.0015 H2O: 0.5618 1.57 -3245.91 3395.60 0 3395.6 0 114.01 238.7 352.71 0 0 455.54 455.54 0 808.25 0

20 10 10 10 2.604 0.06/0.6 50/50 220 4.59 320 HAc: 0.2813 MeOH: 0.1554 MeAc: 0.0015 H2O: 0.5618 1.29/1.56 -2435.9 2065.29 417.68 2483.01 26.88 76.07 248.254 324.324 8.05 465.107 286.593 751.7 -65.01 1076.023 -33.13

column diameter (m) condenser duty (kW) reboiler duty (kW) compressor duty (kW) total heat duty (kW) energy saving (%) catalyst cost ($1000/year) utility cost ($1000/year) operating cost ($1000/year) operating cost saving (%) compressor cost ($1000/year) column cost ($1000/year) capital cost ($1000/year) capital cost saving (%) total TAC ($1000/year) TAC saving (%)


Figure 7. Optimal flowsheet for the r-HIDiC design.

Figure 8. Cost comparison (base design vs r-HIDiC).

tively, the TAC costs more than the original design due to high compressor cost. Figure 8 further highlights the importance of the costs associated with the compressor, which makes this r-HIDiC design inferior to the original design. The temperature profiles of this r-HIDiC design versus the original design can be seen in Figure 9. It is clear in Figure 9b that the tray temperatures at the reaction section were elevated by increasing the operating pressure so that internal heat transfer is possible between the reaction section and the stripping section. Figure 9b also shows that the minimum temperature difference is at 10.87 °C, which makes the internal heat transfer still feasible. The composition and the reaction profiles of this r-HIDiC design are shown in Figure 10. Because of total reflux operation, the compositions of two reactants (MeAc and H2O) were maintained at high concentrations in the reaction section to favor the hydrolysis reaction to take place. The shaded area in Figure 10 displays that most of the reaction happened at the reflux drum because the reaction holdup is much larger than the tray holdup.

Figure 9. Temperature profile: (a) base design and (b) r-HIDiC.

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Figure 12. Conceptual design of the multieffect reactive distillation system.

Figure 10. Composition profile of r-HIDiC design.

Figure 11. Vapor and liquid flow profile: (a) base design and (b) r-HIDiC.

The liquid and vapor flow rates inside the column are shown in Figure 11. When compared to the original design in Figure 11a, the r-HIDiC design could reduce the vapor flow rate at reboiler from 318.57 to 191.82 kmol/h because part of the energy requirement at the stripping section was fulfilled by the internal heat transfer.

3.2. The External Heat-Integration via Multieffect Distillation. The second heat-integration design is to use the multieffect distillation column concept by splitting the feed to enter into two smaller reactive distillation columns operated at different pressures. The operating pressure of the high-pressure column is determined so that the heat removal at the condenser of the high-pressure column can be matched by the heat input at the reboiler of the low-pressure column; thus, the energy at reboiler of the low-pressure column that originally needs to be supplied by steam can be saved with this heat-integrated design. Because we are making use of this feed-splitting design in the reactive distillation column, this design is abbreviated as r-FS. One other thing worth mentioning is that the boiling point ranking of this RD system should not be changed due to operating the RD column at higher pressure so that the original design concept carried over to the high-pressure RD column. Table 4 confirmed this point. There are quite a few design variables that need to be determined. Figure 12 shows the conceptual design flowsheet of this r-FS design. For simplification purposes, the low-pressure column is assumed to be operated at atmospheric pressure. In this flowsheet, the design variables include: operating pressure at high-pressure column, total stages at high-pressure column, reactive stages at high-pressure column, total stages at lowpressure column, reactive stages at low-pressure column, and the feed-splitting ratio. The methyl acetate composition at the combined column bottoms is specified at 0.15 mol % by varying the reboiler duty of the high-pressure column. The other limitations imposed in the r-HIDiC design study are still valid here. The operation pressure of the reactive distillation is kept below 8 atm to avoid a side reaction to form dimethyl ether. The operating temperature in the reaction section has to be lower than 120 °C to meet the catalyst (Amberlyst 15) requirement. The temperature difference for the heat exchanger served as the reboiler of the low-pressure column and also as the condenser of the high-pressure column, which was kept above 10 °C for feasible heat transfer. For determining the optimal values of this six design variables, iterative sequential optimization search procedure is performed. The objective function to be minimized is the total annual cost (TAC). The TAC includes the operating cost and the annualized capital cost. The operating cost includes the cooling water for the condenser of the low-pressure column, the steam for the reboiler of the high-pressure column, and the catalyst cost. In this Article, the steam prices of high-pressure column and low-pressure column are 3.04 ($/1000 lb) and 2.28 ($/1000 lb), respectively. For estimating the catalyst cost, the unit price is assumed to be $3.50/lb and replaced every 3


Figure 13. TAC versus design variable for the r-FS design.

months. The capital cost includes the column shell, internal trays, and condenser for the high-pressure column; the column shell, internal trays, and reboiler for the high-pressure column; and the heat exchanger served as reboiler for the low-pressure column and also as condenser for the high-pressure column. Capital charge factor of 3 years is assumed in the calculation.

Figure 14. Optimal flowsheet for the r-FS design.

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The cost calculation can be seen from Appendix E of the Douglas30 process design book. This iterative search procedure is outlined as follows: (1) fixed the pressure (PHigh) of the high-pressure column; (2) fixed the total stages (NT-HighP) of the high-pressure column; (3) fixed the reactive stages (NRxn-HighP) of the high-pressure column; (4) fixed the total stages (NT-LowP) of the low-pressure column; (5) fixed the reactive stages (NRxn-LowP) of the low-pressure column; (6) fixed the feed-splitting ratio (SR) until TAC is minimized; (7) varying reboiler duty to meet product specification; (8) go back to step (6) to change SR until TAC is minimized; (9) go back to step (5) to change NRxn-LowP until TAC is minimized; (10) go back to step (4) to change NT-LowP until TAC is minimized; (11) go back to step (3) to change NRxn-HighP until TAC is minimized; (12) go back to step (2) to change NT-HighP until TAC is minimized; and (13) go back to step (1) to change PHigh until TAC is minimized. The resulting optimal values for the six design variables are high-pressure column operated at 4.6 atm, total stages of the high-pressure column at 17, reactive stages of the high-pressure column at 2, total stages of the low-pressure column at 23, reactive stages of the low-pressure column at 15, and the feedsplitting ratio at 0.54. Figure 13 shows the effect of each design variable when the other variables maintained at optimal values. It is noticed that two design variables of PHigh and SR are the most sensitive ones. Small changes of these two design variables cause relatively larger changes of TAC. Figure 14 shows the resulting optimal flowsheet for this feedsplitting heat integration design (r-FS). The detailed comparison of this r-FS design to the original design without heat integration is outlined in Table 6. It is noticed that the energy saving and the operating cost saving of this heat integration design are at 38.26% and 15.19%, respectively. The annualized capital cost of this r-FS design only increases slightly, and the TAC is still lower than the original design without heat integration by 6.42%. The temperature profiles of the two reactive distillation columns are shown in Figure 15. The top temperature (113.19 °C) of the high-pressure column is still higher than the bottom temperature (98.26 °C) by as much as 14.93 °C, more than

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Table 6. Comparison of Optimal Design and Cost Information of Basic RD versus r-FS r-FS system total no. of trays (NT) no. of trays in reaction section (NRxn) no. of trays in stripping section (NS) reactive trays catalyst in reflux drum (m3) catalyst in each tray/sum (m3) acetate/water feed flow rate (kmol/h) recycle flow rate (kmol/h) (FR) molar feed ratio (water/acetate) bottom product flow rate (kmol/h) bottom composition (mole fraction)

RD

high P

low P

31 22

17 2

23 15

9

15

8

22 2.85

2 1.817

15 1.466

0.089/1.95

0.03/0.06

0.046/0.69

50/50

27/27

23/23

220

118.8

101.2

4.59

4.59

4.59

320

172.8

147.2

HAc: 0.28103 MeOH: 0.15513 MeAc: 0.00181 H2O: 0.56140 0.925 (1793.97) 2096.5 2096.5 38.26 95.85 203.29 299.14 15.19 455.54 -0.38 756.4 6.42

HAc: 0.28166 MeOH: 0.15577 MeAc: 0.00117 H2O: 0.56203 1.13 -1747.78 (1793.79)

HAc: 0.2813 MeOH: 0.1554 MeAc: 0.0015 H2O: 0.5618 column diameter (m) 1.57 condenser duty (kW) -3245.91 reboiler duty (kW) 3395.60 total heat duty (kW) 3395.6 energy saving (%) 0 catalyst cost ($1000/year) 114.01 utility cost ($1000/year) 238.7 operating cost ($1000/year) 352.71 operating cost saving (%) 0 capital cost ($1000/year) 455.54 capital cost saving (%) 0 total TAC ($1000/year) 808.25 TAC saving (%) 0

enough for providing efficient heat transfer in the heat exchanger. The composition and reaction profiles of the two columns are shown in Figure 16. For each column, most of the reaction takes place at the reflux drum, the same as in the r-HIDiC design. The MeAc composition diminishes at column bottoms as was specified. Notice, under the optimal condition, the shaded area in Figure 16 displays that over 90% of reaction takes place in the high-pressure reflux drum; however, only about 70% of reaction takes place in the low-pressure reflux drum. 3.3. Comparison of r-FS and r-HIDiC. The design studies in this section can be summarized as in Figure 17. Both heatintegration methods saved energy in this system. As in Figure 17a, r-FS saved the most at 38.26%, while r-HIDiC saved 26.88%. The comparison of TAC, capital cost, and operating cost can be seen in Figure 17b. In this plot, the cost ratio of the base design with no heat integration was assumed to be unity. It is found that r-HIDiC, although saving at the operating cost, had a capital cost that was much higher due to the compressor equipment. The heat-integration method of r-FS is a better way to pursuit, which saved both operating cost by 15.19% and TAC by 6.42%. 4. Overall Control Strategy In the following, we will investigate the proper overall control strategy for the most promising heat-integrated design flowsheet in Figure 14 together with the two separation columns in the downstream of the overall process (see Figure 1). Only tray temperature control loop(s) will be used in the overall control strategy for wider industrial applications. In the dynamic simulation, the pressure of high-pressure column should be floating and the energy supply to the low pressure column is determined by the equation Q ) UA∆T. According to Luyben’s study,31 the overall heat-transfer coefficients of U can be

Figure 15. Temperature profile: (a) high-pressure RD and (b) low-pressure RD.

assumed as 0.00306 GJ h-1 m-2 °C-1. The heat duty and temperature difference in the condenser/reboiler are known from the result of steady-state design. So, the heat transfer area can be calculated and fixed as 141.9301 m2. During the dynamic simulation, the pressure in the high-pressure column would change along with temperature in the condenser/reboiler to supply the heat called for by the temperature controller. The overall control strategy of this process is shown in Figure 18. In all of the closed-loop simulation runs, the P-only controller is used in all level loops. The reason for using the P-only controller is to provide maximum flow smoothing and also because maintaining a liquid level at set-point value is often not necessary. Kc ) 2 as suggested in Luyben32 is used in most of the level loops. For all of the column pressure control loops, tight PI controllers with tuning parameters of Kc ) 20 and τI ) 12 min are used. Notice that the “variable step implicit Euler” method is used to solve the system of ordinary differential equations for dynamic simulation. The minimum and maximum integration steps are setting as 0.0001 and 0.005, respectively. All of the initial conditions are given from the steady-state results of Aspen Plus.


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Figure 17. Energy and cost comparison for the base design versus r-HIDiC and r-FS. Figure 16. Composition profile: (a) high-pressure RD and (b) low-pressure RD.

This overall control strategy is to determine the control structure of the two separation columns first. For the acetic acid product column, the inventory control loops are control of reflux drum level by manipulating the distillate; control of bottom level by manipulating acetic acid product flow; and control of column pressure by manipulating the condenser duty. The reflux ratio of this column is also maintained at constant. Reboiler duty is the remaining manipulated variable, which will be used to control a tray temperature. For the methanol product column, the inventory control loops are control of reflux drum level by manipulating the distillate; control of bottom level by manipulating the fresh water feed flow; and control of column pressure by manipulating the condenser duty. The reason for using the fresh water feed flow as the manipulated variable for the bottom level control is to prevent the snowballing effect from the water recycle flow back to the RD columns. The manipulated variable reserved for the tray temperature control is the reflux ratio; thus, the reboiled ratio (reboiler duty/bottom flow) is kept constant. Open-loop sensitivity analysis was used to determine the controlled tray temperature for the above two columns. Figure 19a shows the deviation of tray temperatures with (0.01% changes of the reboiler duty of this column. The tray temperature with the largest deviation with almost linear behavior is at 13th

stage; thus, this location is selected as the control point. Similarly, Figure 19b shows the deviation of tray temperatures with (0.01% changes of the reflux ratio of this column. The 16th stage is selected as the control point. After the control structures of the two separation columns have been determined, the next step is to determine the control structure of the two RD columns. The inventory control loops are determined first. Both columns are operated under total reflux with no distillate stream; thus, both reflux drum levels are all controlled by manipulating their reflux flows. Both bottom levels are all controlled by manipulating their bottom flows. The pressure of the low-pressure column is controlled by manipulating the condenser duty. Because the condenser is replaced by a heat exchanger, the pressure of the high-pressure column is controlled by manipulating the top vapor flow. The “total water” flow rate into the two RD columns is maintained at a constant ratio with the flow rate of MeAc fresh feed. The “total water” stream is the sum of the fresh water feed stream and the bottom recycle stream from the water product column. The MeAc fresh feed flow rate is under flow control and assigned as the throughput manipulator to handle production changes. The remaining two manipulated variables are the feeds (MeAc and water) split ratio and the reboiler duty of the high-pressure column. These two manipulated variables can be used to control one tray temperature at low-pressure

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Figure 18. Proposed overall control strategy for the methyl acetate hydrolysis process.

column and another tray temperature at high-pressure column. Open-loop sensitivity analysis is again used for determining these two control points. Figure 20 displays the results with (0.01% changes of the reboiler duty or the split ratio. For either of the changes, the largest temperature deviation for the highpressure column is at the 14th stage, and that of the low-pressure column is at the 21st stage. The pairing of the two temperature loops was determined by the relative gain array (RGA) analysis. The resulting RGA is: QHighPSR 0.4179 0.5821 TLowP, 21 Λ) 0.5821 0.4179 THighP, 14

[

Figure 19. Open-loop sensitivity plot: (a) acetic acid product column and (b) methanol product column.

]

(2)

The suggested pairings are 21st stage temperature in the lowpressure column to pair with the split ratio and 14th stage temperature in the high-pressure column to pair with the reboiler duty. Because the pressure at the high-pressure column is “floating”, a control arrangement similar to the “pressurecompensated temperature” in Luyben32 is implemented so that the set-point of the 14th stage temperature will be adjusted according to the pressure measurement. As for the most important four tray temperature control loops, the PI tuning constants are all determined using relay feedback test provided in Aspen Dynamics with Tyreus and Luyben tuning rules.33 The iterative tuning procedure was to tune the loop at acetic acid product column first, then the one at water product column, and then the one at high-pressure RD column, and finally the one at the low-pressure RD column. The procedure is repeated until the tuning parameters from relay feedback test converged. The resulting tuning constants for the four tray temperature loops can be found in Table 7. Two types of disturbances will be used to test the proposed control strategy. The first one is the production rate changes. To make these changes, the set-point of the MeAc fresh feed flow loop is changed by (20% at time ) 1 h. With proper


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Figure 20. Open-loop sensitivity plot for the two RD columns. Table 7. Tuning Constants for the Tray Temperature Control Loops controlled variables

manipulated variables

tuning parameters

THighP,14 TLowP,21 TSep1,13 TSep2,16

QHighP SR QSep1 RRSep2

KC,1 ) 9.1276, τI,1 ) 9.6 (min) KC,2 ) 3.5663, τI,2 ) 33.6 (min) KC,3 ) 17.3095, τI,3 ) 6.6 (min) KC,4 ) 6.4754, τI,4 ) 13.2 (min)

overall control strategy, all variables in the design flowsheet should be increased or decreased accordingly but still maintain the two product compositions. Figure 21 shows the closed-loop simulation results for the proposed control strategy. The four tray temperature control loops are displayed in the last two rows of Figure 21. All temperature control loops are performed nicely by forcing the temperatures to quickly return to their set-points. The MeAc compositions at the two RD column bottoms (third row, first, and second columns of Figure 21) are all maintained at very low values, indicating nearly complete conversion of MeAc. The two product flow rates (first and second rows, second columns of Figure 21) are all increased or decreased as planned with the two product compositions (second row, third and fourth columns of Figure 21) maintained at high purity. The second disturbance is the MeAc feed composition changes. The -5 or -10 mol % changes in the fresh MeAc feed composition are introduced at time ) 1 h. The -5% mol % change means that the feed composition is changed from pure MeAc to 95 mol % MeAc and 5 mol % MeOH. For these unmeasured disturbance changes, the control strategy should allow the fresh water to decrease accordingly to compensate the MeAc composition changes so that

stoichiometric ratio between MeAc and water into the system is maintained. The closed-loop simulation results with these feed composition disturbances are shown in Figure 22. From the first row and third column of this figure, it is shown that the fresh water flow rate decreased to desirable values. The MeOH product flow rate (first row, second column of Figure 22) is larger than the HAc product flow rate (second row, second column of Figure 22) because of the extra MeOH impurity coming into the system through the MeAc feed stream. The MeAc compositions at the two RD column bottoms (third row, first and second columns of Figure 22) are all maintained at very low values, indicating nearly complete conversion of MeAc is achieved. The two product compositions (second row, third and fourth columns of Figure 22) are all maintained at high purity. 5. Conclusions In this Article, the optimal designs of two types of heatintegrated reactive distillation systems for the hydrolysis of methyl acetate are studied. Both heat-integrated methods (rHIDiC and r-FS) make use of the elevated operating pressure to save energy in operation of the reactive distillation column. Because the reactive distillation column needs to be operated at higher pressure (resulting in higher operating temperature), this makes endothermic reaction of methyl acetate hydrolysis a good candidate for this investigation. The optimal design flowsheets of both r-HIDiC and r-FS are obtained by minimizing the total annual cost (TAC) of the processes. The TAC of the r-HIDiC design is 33.13%

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Figure 21. Closed-loop responses with (20% MeAc feed rate changes (solid, +20%; dashed, -20%).

Figure 22. Closed-loop responses with -5% or -10% MeAc feed composition changes (solid, -5%; dashed, -10%).


more than the base design without heat integration. This inferior result is mainly due to expansive compressor necessary in the design flowsheet. The r-FS design splits the feeds into two smaller reactive distillation columns, one operated at higher pressure and another operated at atmospheric pressure. By combining the reboiler of the lowpressure column and the condenser of the high-pressure column into one heat-exchanger, the operating cost can be saved by as much as 15.19% with also a TAC saving of 6.42%. The overall control strategy of this r-FS system is proposed with only one tray temperature control loop in each column. Large variations in the feed composition and also throughput changes can be handled by this proposed control strategy. All product compositions are maintained at high purity despite feed disturbances. Acknowledgment This work is supported by the Ministry of Economic Affairs of the R.O.C. under grant no. 98-EC-17-A-09-S1-019. Literature Cited (1) Malone, M F.; Doherty, M. F. Reactive distillation. Ind. Eng. Chem. Res. 2000, 39, 3953. (2) Luyben, W. L.; Yu, C. C. ReactiVe Distillation Design and Control; John Wiley & Sons, Inc.: Hoboken, NJ, 2008. (3) Sundmacher, K., Kienle, A., Eds. ReactiVe Distillation: Status and Future Directions; Wiley-VCH Verlag CmbH & Co. KgaA: Weiheim, Germany, 2003. (4) Robinson, C. S.; Gilliland, E. R. Elements of Fractional Distillation, 4th ed.; McGraw-Hill: New York, 1950. (5) Andrecovich, M. J.; Westerberg, A. W. A simple synthesis method based on utility bounding for heat-integrated distillation sequences. AIChE J. 1985, 31, 363. (6) King, C. J. Separation Processes, 2nd ed.; McGraw-Hill: New York, 1980. (7) Chiang, T. P.; Luyben, W. L. Comparison of energy consumption in five heat-integration distillation configurations. Ind. Eng. Chem. Process Des. DeV. 1983, 22, 175. (8) Chiang, T. P.; Luyben, W. L. Comparison of the dynamic performance of three heat-integrated distillation configurations. Ind. Eng. Chem. Res. 1988, 27, 99. (9) Tai, W. H.; Huang, H. P.; Yu, C. C. Control structure design for parallel processes: Application to heat-integrated distillation. Trans. IChemE, Part A 2005, 83, 153. (10) Mah, R.; Nichoas, J. J.; Wodnik, R. B. Distillation with secondary reflux and vaporization: A comparative evaluations. AIChE J. 1977, 23, 651. (11) Takamatsu, T.; Lueprasitsakul, V.; Nakaiwa, M. Modeling and design method for internal heat-integrated packed distillation column. J. Chem. Eng. Jpn. 1988, 21, 595. (12) Takamatsu, T.; Nakaiwa, M.; Huang, K.; Noda, H.; Nakanishi, T.; Aso, K. Simulation oriented development of a new heat-integrated distillation column and its characteristics for energy saving. Comput. Chem. Eng. 1997, 21, S243. (13) Nakaiwa, M.; Hunag, K.; Owa, M.; Akiya, T.; Nakane, T.; Sata, M.; Takamatsu, T. Engergy savings in heat-integrated distillation columns. Energy 1997, 22, 621.

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ReceiVed for reView October 27, 2009 ReVised manuscript receiVed April 14, 2010 Accepted June 28, 2010 IE9016754

Design and Control of a Heat-Integrated Reactive Distillation System

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