Design and Control of a Thermally Coupled Reactive Distillation

Article pubs.acs.org/IECR

Design and Control of a Thermally Coupled Reactive Distillation Process Synthesizing Diethyl Carbonate San-Jang Wang,*,† Shueh-Hen Cheng,‡ Pin-Hao Chiu,‡ and Kejin Huang§ †

Department of Applied Technology of Living, Ta Hwa University of Science and Technology, Chiunglin, Hsinchu 307, Taiwan Department of Chemical and Materials Engineering, Tunghai University, Taichung 40704, Taiwan § College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ‡

ABSTRACT: Diethyl carbonate (DEC) is a versatile material due to its excellent chemical and physical properties. Several chemical routes have been reported for the preparation of DEC. However, they suffer the drawbacks of using poisonous gases or attaining a low yield of DEC. In this study, a promising route by the transesterification of propylene carbonate and ethanol is used to coproduce DEC and propylene glycol. The transesterification reaction offers an excellent green chemical process. However, the reaction is a typically equilibrium-limited one. Reactive distillation (RD) with excess reactant is adopted in the study to improve reaction conversion and obtain high-purity products in the DEC synthesis. A base-case design, consisting of a RD column and a DEC purification column with its overhead unreacted ethanol stream recycled back to the RD column, is developed and optimized by minimizing the total annual cost. An alternative thermally coupled RD process is also developed which results in substantially reduced energy consumption. Further, steady-state analysis is used to design the control strategies of the thermally coupled RD process. It has been demonstrated that the proposed temperature control + constant reflux-ratio control scheme is sufficient to maintain not only feed ratio of the reactants but also product purities at or around their designed values for the RD process with thermal coupling.

1. INTRODUCTION Diethyl carbonate (DEC) is a versatile material due to its excellent chemical and physical properties. It has been considered as a promising fuel additive1 since DEC has higher oxygen content than methyl tert-butyl ether and has a more favorable gasoline/water distribution coefficient than dimethyl carbonate and ethanol. Besides being used as a fuel additive, DEC can be used as a reactive intermediate to produce urethanes, ureas, pharmaceuticals, and so on.2 DEC is also a safe solvent and an electrolyte for lithium ion batteries.3 In addition, DEC was also found to have applications as a raw material for manufacturing polycarbonate, an important engineering thermoplastic that has excellent mechanical and optical properties as well as electrical and heat resistance properties. Several synthetic routes of DEC were developed, including, for example, ethanolysis of phosgene, oxidative carbonylation of ethanol, carbonylation of ethyl nitrite, and alcoholysis of urea.4 They, however, had the drawbacks of either the use of poisonous gases or a low yield of DEC. Recently, a promising route5 by transesterification was developed using carbon dioxide and propylene epoxide or ethylene epoxide to produce an intermediate propylene carbonate (PC) or ethylene carbonate (EC). DEC was synthesized through the transesterification of PC or EC with ethanol (EtOH), coproducing useful propylene glycol (PG) or ethylene glycol. The transesterification reaction offers an excellent green chemical process. It changes the waste greenhouse gas, carbon dioxide, into the valuable chemical with a zero-discharge and a 100% atom economy.6 In this study, PC and EtOH are selected as reactants to synthesize DEC. Since the transesterification © 2014 American Chemical Society

reaction of PC and EtOH is a typically equilibrium-limited one, reactive distillation (RD) is adopted to improve conversion in the DEC synthesis reaction. RD has attracted much attention in the last two decades because of its potential for lower capital investment, improved selectivity, increased yield, and reduced energy consumption by combining reaction and separation into a single column. Doherty and Malone,7 Sundmacher and Kienle,8 and Luyben and Yu9 thoroughly reviewed the research on RD. More than 100 industrially or potentially important reactions applied to RD were surveyed in the book of Sundmacher and Kienle. Luyben and Yu in their book pointed out that there were 1105 related publications and 814 U.S. patents between 1971 and 2007. They also highlighted 236 reaction systems, which can be carried out by RD configuration. The above references clearly expressed the importance of RD technology in industrial applications. This useful technology is, in fact, being applied now to any scale of operation from manufacture of fine chemicals to that of bulk chemicals. The application domain of RD is still increasing and will continue to remain on the rising trend. Distillation is undoubtedly the most energy-intensive separation process in the chemical industry and needs approximately 3% of the energy in the world.10 Motivated by this large energy requirement, much research effort has been focused on the thermal coupling between the distillation Received: Revised: Accepted: Published: 5982

September 5, 2013 March 7, 2014 March 20, 2014 March 20, 2014 dx.doi.org/10.1021/ie402923p | Ind. Eng. Chem. Res. 2014, 53, 5982−5995

Industrial & Engineering Chemistry Research

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Table 1. Parameter Values for UNIQUAC Modela

columns in series for the separation of multicomponent mixtures. Thermally coupled distillation can provide potential energy saving with respect to conventional distillation trains because of reduced remixing effects by interconnecting liquid and vapor streams between two columns.11 However, the tremendous mass and energy integration between columns complicates the design and control of thermally coupled structures.12−15 Recently, Dejanovic et al.16 gave a comprehensive overview of dividing-wall distillation (a configuration thermodynamically equivalent to the thermally coupled distillation) in the areas of theoretical and application studies. Yildirim et al.17 reviewed current applications of dividing-wall distillation in industry and related research activities. According to Schultz et al.,18 the dividing-wall distillation will become a standard distillation tool in the next 50 years. Process intensification is defined as a strategy for chemical process development that leads to a substantially smaller, cleaner, and more energy efficient technology.19 It is a revolutionary approach to the design, development, and implementation of chemical processes and has gained increasing attention not only in the industry but also in academic research. RD distillation and thermally coupled distillation are two promising technologies that can gain substantial economical benefits due to process intensification. However, they correspond to two different integration methods: reaction−separation and separation−separation, respectively. Recently, a new intensification scheme recognized as thermally coupled RD has been proposed by combining the technologies of RD and thermally coupled distillation. This novel technology has been studied in an ideal reaction system20 and many real reaction systems, such as methyl acetate hydrolysis,21 ethyl acetate synthesis,22 isopropyl acetate synthesis,23 DMC synthesis,24 fatty ester synthesis,25,26 and transesterification reactions.27−32 In this work, an excess reactant is used in the RD column for DEC synthesis in order to increase the reaction conversion and obtain high-purity products. Therefore a conventional separation column following the RD column is necessary to recover the excess reactant, which is then recycled back to the RD column. Thermally coupled RD technology is utilized in the study between the RD column and the conventional separation column to design the RD process for the DEC synthesis. The control strategy of the thermally coupled RD process is also explored. This paper is organized in the following fashion. The kinetic and thermodynamic models are given in the next section. The conventional RD process is designed to cogenerate high-purity DEC, EtOH, and PG in section 3. The optimum condition of the conventional RD process is searched by minimizing the total annual cost (TAC) under the requirements of reaction conversion and product purity specifications. In section 4, the thermally coupled RD process is designed by minimizing total reboiler duty. Its control strategy is investigated in section 5, and conclusions are given in the last section.

a

component j

Uij − Ujj

Uji − Uii

PC PC PC EtOH EtOH DEC

EtOH DEC PG DEC PG PG

367.49 −172.09 79.09 35.26 181.02 485.28

184.29 216.21 292.94 287.93 −57.82 −36.54

ChemCad UNIQUAC: N

ln γi = ln

N

Φi θ Φ z + qi ln i + li − i ∑ xjl j − qi ln(∑ θτ j ji) + qi 2 Φi xi xi j j

N ⎛ ⎞ θτ j ji ⎟ − qi∑ ⎜⎜ N ⎟ j ⎝ ∑k θkτki ⎠

where Φi = xiri/(∑xjrj), θi = xiqi/(∑xjqj), τij = exp[Aij − (Uij − Ujj)/ RT + Cij ln(T) + DijT], T = temperature (K), li = (z/2)(ri − qi) − ri + 1, z = 10 (coordination number), qi = van der Waals area parameter, ri = van der Waals volume parameter.

is thermodynamically limited. A kinetic equation for this reversible reaction catalyzed by a homogeneous catalyst, sodium ethoxide, is given as follows:33 ⎛ −31293 ⎞ ⎟C rPC = 1.9689 × 104 exp⎜ − 9.7868 × 108 ⎝ RT ⎠ PC ⎛ −48156 ⎞ C DECC PG ⎟ exp⎜ ⎝ RT ⎠ C EtOH 2 (2)

where rPC is the reaction rate of PC in moles per liter per minute and Ci represents the concentration of the i component in moles per liter. This kinetic equation was obtained experimentally with the homogeneous catalyst of concentration 1 wt %. A rigorous distillation model provided by ChemCad software is used in the study to conduct the simulation of the RD process to synthesize DEC. The nonlinear vapor−liquid equilibrium relationship is described by the UNIQUAC activity coefficient model. There are six binary pairs in the transesterification reaction system. The UNIQUAC parameters for the EtOH−PG pair are built in the ChemCad data bank. The UNIQUAC parameters for PC−PG and EtOH−DEC pairs are calculated by regressing the vapor−liquid equilibrium data given in Mathuni et al.34 and Rodriguez et al.,35 respectively. The phase equilibrium data of the other missing pairs (PC− EtOH, PC−DEC, and DEC−PG) in literature are determined experimentally in the present study. The UNIQUAC parameters for these three pairs are regressed from the experimental vapor−liquid equilibrium data. Table 1 lists the UNIQUAC parameters for six binary pairs in the reaction system. The predicted T−xy and x−y plots are shown in Figure 1 together with the experimental data. The thermodynamic model agrees well with the experimental data in the reaction system except the PG−PC pair with relatively larger errors in T−xy data than other pairs. The kinetic and thermodynamic models given above are used in the following section to design the RD processes without and with thermal coupling for DEC synthesis.

2. KINETIC AND THERMODYNAMIC MODELS Both kinetic and thermodynamic models are necessary to be established in the design of a RD process. The transesterification reaction of PC and EtOH can be expressed as PC + 2EtOH ⇌ DEC + PG

component i

(1)

This reversible reaction is a weakly exothermal one with a molar reaction heat equal to −16.8 kJ mol−1. Its reaction extent 5983

dx.doi.org/10.1021/ie402923p | Ind. Eng. Chem. Res. 2014, 53, 5982−5995


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Figure 1. T−xy and x−y plots of the DEC synthesis system. 5984



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Figure 2. Flowsheet of the conventional RD process for DEC synthesis.

3. DESIGN OF THE CONVENTIONAL RD PROCESS TO SYNTHESIZE DEC The conventional RD process to synthesize DEC contains a RD column and a separation column. Figure 2 depicts the flowsheet of the conventional RD process. The RD column only has a rectification zone and reaction zone (shaded area) due to the use of a homogeneous catalyst (sodium ethoxide). To enhance the contact of both reactants, the high-boiling reactant (PC) together with the homogeneous catalyst is fed into the top of reaction zone and the low-boiling reactant (EtOH) is introduced into any tray near the RD column bottom. The column trays below the PC feed location are all reactive trays. The feed rate of the reactant PC is assumed to be 25 kmol/h. The reactant EtOH in a near stoichiometric ratio (49.953 kmol/h) is fed into the RD column at the beginning of the design. Reaction products are generated in the reaction zone. However, the high-boiling product PG with high purity cannot be obtained from the column bottom due to the low reaction conversion. In the reaction system, the order of the normal boiling-point temperature for the pure components is

intermediate ones. This means that the reaction system has the least favorable relative volatility ranking for a RD column. The reactants are much more easily removed from the reaction zone in the RD column than the products. It clearly indicates that this is a very difficult RD column to be operated. Some amounts of unconsumed reactant PC, the highest boiling-point component, can be found at the column bottom when these two reactants are fed to the column in a near stoichiometric ratio. To increase the reaction conversion of PC and prevent PC from being withdrawn from the column bottom, excess EtOH is introduced into the column to react away almost all the PC toward the column bottom. The PG product at a high purity of 99.9 mol % can then be obtained at the column bottom. A mixture comprising mainly unreacted EtOH and low-boiling product DEC is distillated from the RD column top and then fed into a distillation column for further separation. High-purity DEC (99.9 mol %) is produced from the bottom of the separation column. Very high-purity EtOH (99.97 mol %) obtained from the column top is recycled back to the fresh EtOH feed location in the RD column. The operating pressures of these two columns are all set at 1 atm. In the optimal design of the RD process to synthesize DEC, TAC is used in the study as the objective function to be minimized by changing some design parameters in the process. TAC includes operating cost and capital cost by a payback of three years. The detailed TAC calculation can refer to the

EtOH(78.3 °C) < DEC(126.8 °C) < PG(187.6 °C) < PC(241.7 °C)

One can note that two reactants are the lightest and heaviest components, respectively, while two products are the 5985



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location are determined. The operation variables contain the reboiler duty, the reflux ratio, and the EtOH recycled flow rate. The reboiler duty is adjusted to satisfy the PG product specification at the column bottom. In addition to the product purity, the reaction conversion should be considered in the design of the RD column to simplify the subsequent purification procedure and yield high-purity products from the RD process. The reflux ratio is adjusted to guarantee PC reaction conversion at 99.9%. Because the EtOH recycled flow rate has a significant effect on the PC reaction conversion and product purities, enough EtOH reactant is necessary to be introduced into the RD column in order to satisfy the specifications of both reaction conversion and product purities. Therefore, there are only three degrees of freedom (total number of trays, PC, and EtOH feed tray locations) available in the RD column to minimize the TAC. In the separation column, the design variables include the total number of trays and the feed tray location of EtOH/DEC mixture. The operation variables contain the reflux ratio and the reboiler duty. The overhead and bottom product specifications are satisfied by adjusting the reflux ratio and the reboiler duty, respectively. Thus, two degrees of freedom (total number of trays and feed tray location) are available in the separation column to minimize the TAC. Hence a total of five variables can be varied to find the optimal design in the conventional RD process. The design procedures of the process with the minimum total TAC are summarized as follows: (1) Set the total number of trays in the RD column (NT1). (2) Set the PC feed tray location (NF1,PC). (3) Set the EtOH feed tray location (NF1,EtOH). (4) Find the minimum EtOH recycled flow rate under the condition that the specifications of bottom PG product and PC reaction conversion are met by adjusting the reboiler duty (QR1) and the reflux ratio (RR1) in the RD column. Next calculate the TAC of the RD column. (5) Go back to step 3 and repeat step 4 until the TAC of the RD column is minimized. (6) Go back to step 2 and repeat steps 3 and 4 until the TAC of the RD column is minimized. (7) Set the total number of trays in the separation column (NT2). (8) Set the feed tray location of the separation column (NF2). (9) Change the reflux ratio (RR2) and the reboiler duty (QR2) in the separation column until the two product specifications are satisfied. Next calculate the TAC of the separation column. (10) Go back to step 8 and repeat step 9 until the TAC of the separation column is minimized. (11) Go back to step 7 and repeat steps 8 and 9 until the TAC of the separation column is minimized. (12) Go back to step 1 and repeat the steps for minimizing the TAC of the RD column and the separation column, respectively, until the total TAC of the RD process is at a minimum. A similar method to search for the optimal condition can also be found in Cheng et al.32 The above iterative optimization procedure is followed to obtain the optimal RD process. For each simulation run, the holdup in the reactive tray must be iteratively obtained to agree with the calculation of column sizing. Figure 3 shows a summary plot for the relationship between the TAC and the design variables in the RD process

Figure 3. Relationship between TAC and design variables near the optimal condition.

works in Wang et al.29 and Cheng et al.32 There are many design and operation variables in the RD process depicted in Figure 2. In the RD column, design variables include the total number of trays and the PC and EtOH feed tray locations. Because the PC reactant and the homogeneous catalyst are introduced into the same location, the number of trays in the rectification zone and reaction zone in the RD column can be calculated once the total number of trays and PC feed tray 5986



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Figure 4. Configuration of the thermally coupled RD process.

are used for the processes without and with thermal coupling. Figure 4 depicts the thermally coupled process where liquid and vapor are directly interchanged between the top of the RD column and the feed of the separation column. The condenser in the RD column can then be eliminated by conducting thermal coupling. Figure 5 gives the configuration which is thermodynamically equivalent to that in Figure 4. The thermally coupled RD process in Figure 5 contains a RD column and a side stripper column. The high-boiling product, PG, with a purity of 99.9 mol %, is withdrawn from the bottoms of the RD column. Very high-purity EtOH (99.97 mol %) is distilled from the top of the RD column and recycled back to the fresh EtOH feed location in the RD column. Part liquid from the RD column is fed to the side stripper column for the DEC purification. Vapor from the top of the side stripper column is wholly introduced to the RD column. High-purity DEC with 99.9 mol % is obtained from the bottom of the side stripper column. The thermally coupled RD process given in Figure 5 has four design degrees of freedom: two reboiler duties, the reflux ratio of the RD column, and the liquid split ratio (LSR). Product specifications of PG, DEC, and EtOH from three outlet streams are satisfied by adjusting two reboiler duties and the reflux ratio. LSR is the only remaining variable used to minimize the total reboiler duty of the process. It is defined as the liquid flow directed to the RD column divided by the liquid flow directed to the side stripper column. Under the optimal condition, the LSR is equal to 9.12. The corresponding reflux ratio and

near the optimal condition. It should be noted that the trays in the RD and separation columns are numbered from top to bottom with the condenser as the first tray and the reboiler as the last tray. It is found that there are no solutions to satisfy the specifications of the bottom PG purity and PC reaction conversion in the RD column when the trays between EtOH feed and column bottom are less than three or the PC feed is located above the fourth tray. The minimum total TAC ($2.645 × 106 per year) of the RD process occurs when NT1, NF1,PC, and NF1,EtOH in the RD column are equal to 17, 4, and 14, respectively, and when NT2 and NF2 in the separation column are equal to 47 and 40, respectively. The corresponding TACs of the RD column and separation column are $9.208 × 105 per year and $1.724 × 106 per year, respectively. Under the optimal condition, the reboiler duties of the RD column and separation column are 4508.2 kW and 9793.6 kW, respectively, when the reflux ratios of the RD column and separation column are 0.185 and 2.14, respectively. The stream information and optimal condition of the conventional RD process are also provided in Figure 2.

4. DESIGN OF THE RD PROCESS WITH THERMAL COUPLING The conventional RD process designed in section 3 can be improved upon in terms of its energy consumption if thermal coupling is implemented between the RD column and the separation column depicted in Figure 2. To have a fair comparison in energy consumption, the same numbers of trays 5987



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Figure 5. Configuration of the thermally coupled RD process thermodynamically equivalent to that in Figure 4

In the side stripper column, almost only EtOH and DEC exist and high-purity DEC can easily be obtained at the bottom. The control strategy of the thermally coupled RD process is investigated in the following section.

reboiler duty of the RD column and reboiler duty of the side stripper column are 2.146, 4544.5 kW, and 5738.5 kW, respectively. The reboiler duty (9793.6 kW) of the separation column in the conventional RD process can be substantially reduced by conducting the thermal coupling between the RD column and the separation column, while there are only small variations in the reboiler duty of the RD column. A decrease of the total reboiler duty by 28.1% is obtained for the thermally coupled RD process. The stream information and operating condition for the thermally coupled RD process are also given in Figure 5. Figure 6 displays the temperature and composition profiles of the RD column and the side stripper column in the thermally coupled RD process. In the rectifying section of the RD column, only very small amount of PC and PG exists, and the separation of EtOH and DEC is performed. At the trays near the column bottom, PC is almost completely reacted away by excess EtOH, and then EtOH and PG can easily be separated. The temperature profile in these trays changes substantially due to the large boiling-point difference of EtOH and PG.

5. CONTROL OF THE THERMALLY COUPLED RD PROCESS In the control of a thermally coupled RD process, stoichiometric balance between reactants and product purities must be maintained under disturbances. The feed ratio scheme is the simplest method to maintain stoichiometric balance between reactants. However, the desired feed ratio cannot be kept by this scheme when measurement bias exists in the feed flow rate. To overcome this problem, Al-Arfaj and Luyben36 suggested the use of a composition loop to maintain some reactant inventory in the RD column by adjusting some reactant feed flow rate. However, the use of composition control suffers from some disadvantages, including large measurement delay, high investment cost, and high maintenance cost for most product analyzers. In the study, only 5988



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Figure 6. Temperature and composition profiles of (a) the RD column and (b) the side stripper column in the thermally coupled RD process.

temperature control is restricted to be used in the indirect maintenance of composition for the purpose of wider industrial application. Hence, there are two candidates (PC and EtOH feed flows) for the manipulated variable in the temperature control loop to maintain the stoichiometric balance between two reactants in the DEC synthesis column. Owing to the interaction between reaction and separation, RD can often exhibit intricate nonlinear phenomena, such as input multiplicity which increases operation and control difficulties. Input multiplicity refers to the situation when the fixed output variable corresponds to a multiple set of input variables. In relation to a control structure, an input variable is the one that can be manipulated by a control valve or other actuating device. An output variable is the one that is either controlled or measured to describe the process condition. Thus, in the temperature control to maintain reactant stoichiometric balance, the tray temperature selected as the controlled variable in the loop should have a sufficiently high sensitivity and no multiplicity relationship with respect to the reactant feed flow rate. Figure 7 displays the open-loop sensitivity analysis between tray temperatures and feed flow rates of PC reactant and EtOH reactant, respectively, in the thermally coupled RD

process. Input multiplicity occurs just around the nominal operating condition between PC feed and temperatures of trays 3 to 5 in the side stripper column. However, there is no input multiplicity between EtOH and tray temperatures in the thermally coupled RD process. Wang et al.37 showed that input or interaction multiplicity is one of the most important considerations in choosing the manipulated variable. The tray temperatures having input multiplicity or interaction multiplicity with manipulated variables should not be selected as controlled variables in order to avoid the problem of control stability. Hence, EtOH feed flow is chosen as the manipulated variable in the temperature loop to maintain the stoichiometric balance between reactants. In addition to the maintenance of the stoichiometric balance between reactants, two temperature loops are used to keep high-purity PG and DEC at the bottoms of the RD column and side stripper column, respectively, by manipulating the reboiler duties of the two columns. Two tray temperatures should be selected as controlled variables in these two loops. Figure 8 displays the open-loop sensitivity analysis between tray temperatures and reboiler duties of the RD column and side stripper column, respectively, in the thermally coupled RD 5989



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Figure 7. Open-loop sensitivity analysis between tray temperatures and feed flow rates of (a) PC reactant and (b) EtOH reactant, respectively, in the thermally coupled RD process.

process. No input multiplicity occurs between tray temperatures and these two reboiler duties. In the RD column with thermal coupling, the specification of overhead EtOH purity also needs to be satisfied in addition to the bottom PG purity. Instead of controlling overhead and bottom product purities of the column by two temperature loops, it may be possible in some processes to only control one product and overpurify the other product. Single-end control is simpler and easier to tune and gives faster response than double-end control because of the reduced interaction among control loops. Hence simple constant reflux-ratio control is utilized in the study to maintain high-purity EtOH at the top of the RD column. Obviously three tray temperatures need to be chosen as controlled variables in order to maintain stoichiometric balance between reactants and product purities in the control of the thermally coupled RD process. Singular value decomposition (SVD) method38 is used in the study to select the most appropriate location for temperature control. This method requires a steady-state gain matrix. These steady-state gains are calculated from the open-loop sensitivity analysis given in Figures 7 and 8. The controlled temperatures selected by the

SVD method are located at trays 47 (T47_1), 54 (T54_1) of the RD column, and tray 4 (T4_2) of the side stripper column. Relative gain array (RGA) analysis can then be used for variable pairing once the controlled and manipulated variables are determined. Table 2 gives the RGA analysis of controlled tray temperatures and manipulated variables. m1, m2, and m3 denote the reboiler duty of RD column, reboiler duty of side stripper column, and EtOH feed flow, respectively. This analysis indicates that the temperatures at trays 47 and 54 in the RD column and tray 4 in the side stripper column are controlled using the EtOH feed flow, reboiler duty of the RD column, and reboiler duty of the side stripper column, respectively. In the following investigation of control performance, the same procedures as those used by Wang et al.29 to tune the controller parameters are also adopted in the study. In their study, a sequential relay feedback test39,40 is performed to find the ultimate gain (KCU) and ultimate period (PU). Then the tuning constants of PI controllers are calculated by the following equations known as Tyreus−Luyben tuning. K C = K CU /3 5990

(3)



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Figure 8. Open-loop sensitivity analysis between tray temperatures and reboiler duties of the (a) RD column and (b) side stripper column, respectively, in the thermally coupled RD process.

distributor. The PC feed is flow controlled. In the inventor control of the side stripper column, the base level is maintained by adjusting bottom flow rate. In addition to inventory control, three temperature control loops designed by the above steadystate analysis are used for the quality control of the thermally coupled RD process. For a distillation column, the control of pressure, level, and flow belongs to the inventory control that maintains the basic column operation. Hence in the following discussion, emphasis is put on the response of temperature control + constant reflux-ratio control strategy used to maintain product purities and reactant feed ratio. The PI tuning parameters (KC/TI) are 3.33/154.9(min), 1.01/105.2(min), and 1.32/134.8(min) for the temperature loops used to maintain stoichiometric balance between reactants, PG purity at the RD column bottom, and DEC purity at the side stripper column bottom, respectively. The temperature transmitter spans are all set to be 40 °C in the study. Once the control structure is established, the control scheme is tested by introducing disturbances to investigate its control effectiveness. Figure 10 shows the closed-loop responses of controlled tray temperatures, product purities, EtOH feed flow, and reflux ratio under temperature control + constant reflux-

Table 2. RGA Analysis between Controlled Tray Temperatures and Manipulated Variables for the Thermally Coupled Process T47_1 T54_1 T4_2

TI = 2PU

m1

m2

m3

−5.16 5.78 0.38

0.55 −1.22 1.67

5.61 −3.56 −1.05

(4)

where KC and TI represent proportional gain and integral time, respectively. Figure 9 depicts the proposed control scheme, consisting of inventory control and quality control, for the thermally coupled RD process. The inventory control strategy used by Wang et al.29 is adopted in the study. In the inventory control of the RD column, coolant flow rate is manipulated to control column pressure. Levels of reflux-drum and base are maintained by adjusting reflux flow rate and bottom flow rate, respectively. The reflux ratio is kept constant by changing distillate flow rate to maintain the overhead EtOH purity. Liquid split ratio is maintained by using a liquid flow 5991



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Figure 9. Proposed control scheme (L/D, V1, V2 configuration) for the thermally coupled RD process.

ratio control for ±10% changes in PC feed flow. The controlled tray temperatures are held at their corresponding set points. Feed ratio and reflux ratio are also maintained at their corresponding designed values. Only a very small steady-state offset is observed in the PG product composition at the bottoms of the RD column. EtOH and DEC product compositions can almost be brought back to their desired operating values under the proposed control strategy. Temperature control alone does not guarantee composition control. In such cases, temperature + composition cascade control is commonly proposed. However, dynamic simulation results reveal that the proposed temperature control + constant reflux-ratio control scheme can maintain not only a reactant

feed ratio but also product purities at or around their desired values. Hence, temperature + composition cascade control is not used in the study.

6. CONCLUSIONS A promising route is utilized to synthesize DEC by the transesterification of PC and EtOH. However, the transesterification reaction has an unfavorable reaction kinetic and the least favorable relative volatility ranking (products are intermediate keys) for a RD column. Therefore, a RD process consisting of a RD column with a large excess of reactant EtOH and a separation column is used to gain high PC reaction 5992



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Figure 10. Closed-loop responses of controlled tray temperatures, product purities, EtOH feed flow, and reflux ratio under temperature control + constant reflux-ratio control for ± 10% changes in PC feed flow.

conversion and high-purity products. The optimal RD process is designed by minimizing the total TAC. A thermally coupled

RD process is also derived by interchanging liquid and vapor between these two columns. Steady-state simulation results 5993



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demonstrate that the process with thermal coupling provides a much more economical design than the process without thermal coupling. In developing the control scheme, temperature control strategies are designed by using steady-state analysis for the thermally coupled RD process. EtOH feed having no input multiplicity with tray temperatures is used to maintain the reactant feed ratio in the RD column. The placement of temperature sensors is analyzed by the SVD method and the pairing of manipulated and controlled variables is done by using the RGA analysis. Dynamic simulation results reveal that the temperature control + constant reflux-ratio control scheme can maintain not only reactant feed ratio but also product purities at or around their desired values in face of the changes in reactant feed rate.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +886-3-5927700 ext. 2853. Fax: +886-3-5927310. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Science Council of Taiwan under Grant No. NSC 101-2221-E-233-009-MY2

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REFERENCES

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Design and Control of a Thermally Coupled Reactive Distillation

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