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Influences of Pressure on the Operation of Reactive Distillation Columns Involving Kinetically Controlled Exothermic Reactions Chao Wang,† Liang Zhang,† Kejin Huang,*,† Haisheng Chen,† Shaofeng Wang,† Wei Liu,† and Zhigang Lei‡ †

College of Information Science and Technology, and ‡State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China ABSTRACT: For the reactive distillation column involving a kinetically controlled exothermic reaction, operating pressure can present nonmonotonic influences on process dynamics and operation. While the enhancement of operating pressure benefits process dynamics and controllability in the lower part of its feasible region (which is confined by the temperature levels of the available cold and hot utilities), it turns to deteriorate process dynamics and controllability in the higher part of its feasible region. Three reactive distillation systems, including an ideal reactive distillation column performing a hypothetical exothermic reaction, kf

A+B⇀ ↽ C + D, and two real ones producing, respectively, methyl acetate from acetic acid and methanol and methyl tertiary kb

butyl ether (MTBE) from isobutylene and methanol, are thoroughly studied in this work, and the results confirm the existence of this unique phenomenon. The intricate behavior of such kind of reactive distillation columns is essentially governed by the conflicting effects of operating pressure on reaction rate and chemical equilibrium constant and determines actually a favorable region of operating pressure for process dynamics and operation. Because the region may or may not coincide with the one in terms of process synthesis and design, operating pressure can therefore serve as an important decision variable to trade-off process design and operation, rendering the resultant process design with balanced steady-state performance and process dynamics and controllability.

1. INTRODUCTION Operating pressure is one of the most important decision variables in the synthesis and design of reactive distillation columns because it can present a strong impact to not only the reaction operation and the separation operation involved but also their combination (i.e., the so-called process intensification).1,2 Recently, we systematically studied the complicated relationship between operating pressure and steady-state performance in terms of a variety of reactive distillation columns involving either equilibrium-limited or kinetically controlled reactions with endothermic or exothermic effect.3 It was found that for the reactive distillation column involving a kinetically controlled exothermic reaction, there existed a complicated relationship between operating pressure and steady-state performance. Whereas the enhancement of operating pressure reduced the heat duties of condenser and reboiler in the lower part of its feasible region (which is usually confined by the temperature levels of the available cold and hot utilities), it turned to increase the heat duties of condenser and reboiler in the higher part of its feasible region. This unique phenomenon was essentially dominated by the conflicting effects of operating pressure on reaction rate and chemical equilibrium constant and determined actually a favorable region of operating pressure for process synthesis and design. Because the conflicting effects of operating pressure on reaction rate and chemical equilibrium constant might also affect considerably process dynamics and controllability, it is therefore necessary to ascertain the detailed mechanism for such kind of reactive distillation columns. The obtained results could not only reveal the inherent characteristics of © 2012 American Chemical Society

their complicated interplay but also offer a potential way to balance process design and operation with operating pressure as an effective decision variable at the early stage of process development. Despite that operating pressure is an important decision variable for the developments of reactive distillation columns, only a few studies have been conducted so far about its detailed impacts on process dynamics and controllability. Al-Arfaj and Luyben once addressed the design and control of an olefin metathesis reactive distillation column to be operated, respectively, at low and high operating pressures.4 They noticed the strong effect of operating pressure on the steadystate and dynamic performance but gave no detailed explanations about its impacts on process dynamics and controllability. Kaymak addressed the design and operation of an ideal reactive distillation column performing a hypothetical kf

5 exothermic reaction, A + B ⇀ ↽ C + D. He demonstrated the

kb

existence of a nonmonotonic relationship between operating pressure and steady-state performance, but did not examine further the effect of operating pressure on process dynamics and controllability according to the characteristics of the relationship already obtained. Despite the fact that a certain degree of degradation in closed-loop responses had been Received: Revised: Accepted: Published: 3692

June 16, 2011 January 10, 2012 February 8, 2012 February 8, 2012 dx.doi.org/10.1021/ie202241p | Ind. Eng. Chem. Res. 2012, 51, 3692−3708

Industrial & Engineering Chemistry Research

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Figure 1. Optimal points for steady-state performance and process dynamics and controllability versus operating pressure for the reactive distillation columns involving kinetically controlled exothermic reactions.

observed with the enhancement of operating pressure from 8.5 to 10 bar, he did not further discuss the phenomenon and simply drew a conclusion that operating pressure did not lead to any improvement in process dynamics and controllability. Because of the complicated interaction between the reaction operation and the separation operation involved, the steady states adopted to explore the impact of operating pressure on process dynamics and controllability must be carefully chosen for the reactive distillation column involving a kinetically controlled exothermic reaction; otherwise, an incomplete and even wrong interpretation is quite likely to be generated. This, on the other hand, reflects again the special feature of this kind of reactive distillation columns. The current work attempts to examine the influences of operating pressure on the dynamics and controllability of the reactive distillation columns involving kinetically controlled exothermic reactions. Three reactive distillation systems, including an ideal reactive distillation column performing a

Figure 2. An ideal reactive distillation column performing a kf hypothetical exothermic reaction: A + B ⇀ ↽ C + D (ΔHR < 0) kb (example I).

kf

hypothetical exothermic reaction, A + B ⇀ ↽ C + D, and two real kb

with regard to its influences on the reaction operation involved. They lie mainly on the reaction rate and/or the constant of chemical equilibrium, affecting eventually the reaction conversion during process synthesis and design. Therefore, the variation of operating pressure can affect significantly the dynamics and controllability of the reaction operation involved. The reaction operation can pose further a strong impact to the combination between the reaction operation and the separation operation involved, which determines eventually the dynamics and controllability of the resultant reactive distillation columns. Figure 1 shows a typical relationship between operating pressure and steady-state performance for a reactive distillation column involving a kinetically controlled exothermic reaction. It is generated based on our previous work.3 In the left side of the dashed line (which corresponds to the minimum of the heat duty of condenser/reboiler), whereas the enhancement of operating pressure increases the reaction rate, it also decreases the constant of chemical equilibrium, both of which are caused by the resultant temperature elevation. Because the favorable effect of the former outweighs the unfavorable effect of the latter, the net result is the improvement of the steady-state performance. In the right side of the dotted line, because the favorable effect of the former is not as competitive as the unfavorable effect of the latter, the net result is the degradation of the steady-state performance. The nonmonotonic relationship between operating pressure and steady-state performance is further affected by the interaction between the reaction

ones producing, respectively, methyl acetate from acetic acid and methanol and methyl tertiary butyl ether (MTBE) from isobutylene and methanol, are selected as representative examples for this kind of reactive distillation columns and thoroughly studied in this work. The unique influences of operating pressure on process dynamics and controllability are demonstrated, and their implications on process design and operation are then highlighted. Some important conclusions are summarized in the last section of this Article.

2. INFLUENCES OF OPERATING PRESSURE ON THE DYNAMICS AND OPERATION OF REACTIVE DISTILLATION COLUMNS INVOLVING KINETICALLY CONTROLLED EXOTHERMIC REACTIONS For any kind of reactive distillation columns involving either equilibrium-limited or kinetically controlled reactions, operating pressure is one of the most important design variables that can affect simultaneously the reaction operation and the separation operation involved. Regarding its influences on the separation operation involved, they lie primarily on the relative volatilities between the reacting components, affecting, in general, the number of stages in the rectifying and/or stripping sections during process synthesis and design. Therefore, the variation of operating pressure usually cannot affect significantly the dynamics and controllability of the separation operation involved. However, the situation is quite different 3693

dx.doi.org/10.1021/ie202241p | Ind. Eng. Chem. Res. 2012, 51, 3692−3708


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Table 1. Physicochemical Properties and Operating Conditions of Example I parameter number of stages

stage holdup (kmol) activation energy (kJ kmol−1)

value rectifying section reactive section stripping section

forward backward specific reaction rate at 366 K forward (kmol s−1 kmol−1) backward feed flow rate of reactant A (kmol s−1) feed flow rate of reactant B (kmol s−1) feed location of reactant A feed location of reactant B thermal condition of FA thermal condition of FB relative volatility A:B:C:D heat of reaction (kJ kmol−1) latent heat of vaporization (kJ kmol−1) overhead product composition (C, mol %) bottom product composition (D, mol %) vapor pressure constants A(Avp/Bvp) B(Avp/Bvp) C(Avp/Bvp) D(Avp/Bvp)

7 6 7 1 125 520 167 360 0.008 0.004 0.0126 0.0126 14 9 1.0 1.0 4:2:8:1 −41 840 29 053.7 95 95 12.3463/3862 11.6531/3862 13.0394/3862 10.96/3862

Figure 4. A decentralized control scheme for example I.

Table 2. Controller Parameters for Example I operating pressure (bar) 6

6.7

9

12

15

KC

control loop top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry

3.25 5.34 7.25 6.25 6.46 7.68 6.65 1.21 9.50 6.52 1.24 8.68 6.35 1.27 8.46

× × × × × × × × × × × × × × ×

TI (min) −3

10 10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−3 10−3 10−2 10−3 10−3 10−2 10−3

84 60 44 48 44 32 44 33 44 38

kf

exothermic reaction, A + B ⇀ ↽ C + D, and two real ones kb

producing, respectively, methyl acetate from acetic acid and methanol and MTBE from isobutylene and methanol, are employed as representative examples to explore the influences of operating pressure on the dynamics and controllability of the reactive distillation columns involving kinetically controlled exothermic reactions.

Figure 3. Effect of operating pressure on the steady-state performance of example I.

operation and the separation operation involved and helps to determine a favorable region of operating pressure (i.e., the gray region in this case) in terms of process synthesis and design for the given reactive distillation column. Because the combination between the reaction operation and the separation operation involved can give a strong impact to process dynamics and controllability, it is quite likely that operating pressure may also present a nonmonotonic influence on process dynamics and controllability. More specifically, whereas the enhancement of operating pressure gives a favorable influence to process dynamics and controllability in the lower part of its feasible region, the reverse is true in the higher part of its feasible region. Confirming this unique behavior can certainly facilitate the simultaneous consideration of process design and operation with operating pressure as an effective decision variable at the early stage of process development. In what follows, three reactive distillation systems, including an ideal reactive distillation column performing a hypothetical

3. EXAMPLE I: AN IDEAL REACTIVE DISTILLATION COLUMN PERFORMING A HYPOTHETICAL kf

EXOTHERMIC REACTION A + B ⇀ ↽C+D kb

3.1. Process Description. The hypothetical ideal reactive distillation column was originally proposed by Luyben and his co-workers and has been studied intensively by a lot of researchers so far.6−11 As shown in Figure 2, a typical process design is chosen here, accommodating a three sectional structure, 7/6/7, that is, a rectifying section, a stripping section, and a reactive section between. It is equipped with a total condenser at the top and a partial reboiler at the bottom. Two pure reactant feeds, FA and FB, are fed onto the bottom and the 3694



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Figure 5. Regulatory responses of example I for a ±5% step change in the feed flow rate of reactant B, respectively (6/6.7/9 bar): (a) composition of component C in the top product, (b) reflux flow rate, (c) composition of component A on stage 14, (d) feed flow rate of reactant A, (e) composition of component D in the bottom product, and (f) bottom vapor flow rate. Gray curves, negative responses; black curves, positive responses.

The hypothetical reversible reaction occurring on reactive stages is

Table 3. IAE of Example I scenario Iincrease by 5% in the feed flow rate of reactant B decrease by 5% in the feed flow rate of reactant B increase by 50% in the feed flow rate of reactant B decrease by 15% in the feed flow rate of reactant B

operating pressure (bar) 6 6.7 9 6 6.7 9 9 12 15 9 12 15

distillate 7.132 1.554 9.945 7.277 1.456 1.012 1.411 1.579 2.133 2.958 2.974 3.273

× × × × × × × × × × × ×

10−2 10−2 10−3 10−2 10−2 10−2 10−1 10−1 10−1 10−2 10−2 10−2

bottom withdrawal 2.901 1.497 3.721 2.955 1.378 3.692 3.578 3.722 4.494 1.056 1.207 1.225

× × × × × × × × × × × ×

kf

A+B⇀ ↽C+D

10−2 10−2 10−3 10−2 10−2 10−3 10−2 10−2 10−2 10−2 10−2 10−2

kb

ΔHR = −41 840 kJ kmol−1 (1)

kf

where the symbol ⇀ ↽ indicates that the reaction is a kinetically kb

controlled one. The volatilities are such that the products C and D are the lightest and heaviest, respectively, in the reaction system. The net reaction rate for component i on stage j in the reactive section is given by

top of reactive section, respectively, and the specification of the top and bottom products is set to be 95 mol %.

ri , j = viHj(k f, jxA, jx B, j − k b, jxC, jx D, j) 3695

(2)



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Figure 6. Regulatory responses of example I for a +50% and −15% step change in the feed flow rate of reactant B, respectively (9/12/15 bar): (a) composition of component C in the top product, (b) reflux flow rate, (c) composition of component A on stage 14, (d) feed flow rate of reactant A, (e) composition of component D in the bottom product, and (f) bottom vapor flow rate. Gray curves, negative responses; black curves, positive responses.

where kf, j and kb, j are the forward and backward specific reaction rates and are given by k f, j = (k f )366 e−(Ef / R )(1/ Tj − 1/366)

(3)

k b, j = (k b)366 e−(Eb / R )(1/ Tj − 1/366)

(4)

Here, the liquid holdup Hj is an important design parameter that can reflect the amount of catalyst installed on a reactive stage. A large value represents an operating condition that a large amount of catalyst has been installed on a reactive stage, and vice versa.

Figure 7. A reactive distillation column producing methyl acetate from acetate acid and methanol (example II). 3696



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Table 4. Physicochemical Properties and Operating Conditions of Example II parameter number of stages


liquid holdup (m3) activation energy (kJ kmol−1)

forward backward pre-exponential factor forward (kmol s−1 kgcat−1) backward feed flow rate of reactant HAc (kmol h−1) feed flow rate of reactant MeOH (kmol h−1) feed location of reactant HAc feed location of reactant MeOH thermal condition of FHAc thermal condition of FMeOH heat of reaction (kJ kmol−1, 100 kPa, 330 K) latent heat of H2O (kJ kmol−1, 100 kPa, 330 K) overhead product composition (MeAc, mol %) bottom product composition (H2O, mol %)

2 25 9 0.0379584 49 190 69 230 29 610 1 348 000 50 50 4 28 1.0 1.0 −33 566.80 42 657.62 95 95

Figure 9. A decentralized control scheme for example II.

Table 5. Controller Parameters for Example II operating pressure (atm)

control loop

KC

TI (min)

0.9

top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry

1.95 1.49 0.92 2.22 1.68 1.05 2.51 1.73 1.17 2.32 1.62 1.09 2.19 1.45 0.93

83.45 78.32

1.5

2.1

2.4

2.6

Ideal vapor and liquid phase behavior is assumed for the reaction system, and the vapor−liquid equilibrium relationship can be expressed as (5)

yi , j = xi , jPis, j/Pj

(6)

The vapor saturation pressure is calculated as lnPis, j = A vp, i − B vp, i /Tj

(7)

Equimolar overflow is assumed, so the liquid and vapor flow rates are constant in the nonreactive rectifying and stripping sections. Because the reaction is exothermic, ΔHR < 0, the vapor and liquid flow rates change from stage to stage in the reactive section because the thermal heat of reaction vaporizes a certain amount of liquid on each reactive stage. Vj = Vj + 1 − rj ,CΔHR /ΔHV

(8)

Lj = Lj − 1 + rj ,CΔHR /ΔHV

(9)

54.02 58.78 63.68 61.18 80.47 70.54

The physicochemical properties and nominal steady-state operating conditions for the hypothetical ideal reactive distillation column are summarized in Table 1, and other relevant information can be found in the corresponding references. Because constant relative volatilities are assumed between the reacting components, the variations of operating pressure will not affect the separation operation involved in this case. The steady-state and dynamic behaviors of the hypothetical ideal reactive distillation column can be well predicted with the first-principle models shown in Appendixes A and B, respectively. 3.2. Effect of Operating Pressure on Steady-State Performance. In Figure 3, the relationship between operating pressure and the steady-state performance of the hypothetical ideal reactive distillation column is illustrated. It is noted that it takes a shape somewhat similar to the one shown in Figure 1. The heat duties of condenser and reboiler reach simultaneously their minimum values at the operating pressure of 9 bar. Away from this value, they turn to increase monotonically in both directions, portraying a nonmonotonic relationship between operating pressure and steady-state performance. 3.3. Effect of Operating Pressure on Process Dynamics and Controllability. In the following subsections, the closed-loop control of the hypothetical ideal reactive distillation column is used to ascertain the effect of operating pressure on process dynamics and controllability. A decentralized

Figure 8. Effect of operating pressure on the steady-state performance of example II.

s s Pj = xA, jPA + x B, jP Bs + xC, jPCs + x D, jP D

59.67 64.45

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Figure 10. Regulatory responses of example II for a ±5% step change in the feed flow rate of acetate acid, respectively (0.9/1.5/2.1 atm): (a) composition of methyl acetate in the top product, (b) reflux flow rate, (c) composition of methanol on stage 28, (d) feed flow rate of methanol, (e) composition of water in the bottom product, and (f) heat duty of reboiler. Gray curves, negative responses; black curves, positive responses.

control structure shown in Figure 4 is adopted here, where the purities of the top and the bottom products are measured and controlled. Operating pressure is regulated with the heat removal of condenser and is assumed to be perfectly controlled. In the top product, the composition of component C is controlled by manipulating the reflux flow rate. In the bottom product, the composition of component D is controlled by manipulating the heat duty of reboiler. The concentration of reactant A on the lower feed stage (i.e., stage 14) is measured and controlled by manipulating the feed flow rate of reactant A (i.e., the so-called reactant stoichiometry control loop). The employment of direct composition control here avoids the drawbacks of the feedforward ratio control scheme, for example, the severe noises in flow rate measurements and failures to deal with feed composition changes. The feed flow rate of reactant B is the production rate handle and is flow controlled. The levels of the reflux-drum and bottom reboiler are controlled by the distillate and the bottom product flow

rates, respectively. The dynamics of concentration measurements is assumed to be two first-order lags of 30 s in series. While proportional-only (P) controllers are used for all level control loops, proportional plus integral (PI) controllers are adopted for the top and the bottom composition control loops. For the reactant stoichiometry control loop, a P controller (instead of a PI one) is chosen, and this cannot affect the stable operation of the hypothetical ideal reactive distillation column.7,10 The gains of the level controllers are assigned to be 2. All composition controllers are tuned according to the Tyreus−Luyben rule (i.e., KC = KCU/3 and TI = 2PCU), and slight adjustments are still necessary to get satisfactory responses.12 The obtained results are listed in Table 2. With reference to the optimum performance of the hypothetical ideal reactive distillation column shown in Figure 3, it is reasonable to divide the feasible region of operating pressure into two parts, the left (below 9 bar) and right (above 9 bar) subregions. To assess the influence of operating pressure on 3698



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increasingly great maximum deviations in the top and bottom product qualities regardless of the negative or positive changes in the feed flow rate of reactant B. The IAE for these circumstances is also calculated and listed in Table 3, confirming again the degradation of process dynamics and controllability incurred by the increase of operating pressure from 9 bar. The closed-loop simulation results show that the enhancement of operating pressure deteriorates process dynamics and controllability in the operation range above 9 bar. Moreover, at the newly reached steady states, the process operated at 9 bar maintains its higher thermodynamic efficiency than those operated at 12 and 15 bar.

Table 6. IAE of Example II scenario increase by 5% in the feed flow rate of acetate acid

decrease by 5% in the feed flow rate of acetate acid

increase by 0.01 in the top and bottom product purities simultaneously decrease by 0.01 in the top and bottom product purities simultaneously

operating pressure (atm) 0.9 1.5 2.1 2.4 2.6 0.9 1.5 2.1 2.4 2.6 2.1 2.4 2.6 2.1 2.4 2.6

distillate 9.875 6.314 7.250 9.958 4.890 9.932 5.214 3.979 4.807 3.752 1.755 4.459 7.757 1.369 1.997 4.103

× × × × × × × × × × × × × × × ×

10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−2 10−2 10−2 10−2 10−2 10−2

bottom withdrawal 1.643 1.186 1.273 1.614 1.131 1.539 9.394 1.052 1.039 6.062 1.838 4.672 8.324 1.378 1.889 4.060

× × × × × × × × × × × × × × × ×

10−2 10−2 10−2 10−2 10−2 10−2 10−3 10−2 10−2 10−3 10−2 10−2 10−2 10−2 10−2 10−2

4. EXAMPLE II: A REACTIVE DISTILLATION COLUMN PRODUCING METHYL ACETATE FROM ACETIC ACID AND METHANOL 4.1. Process Description. A methyl acetate reactive distillation column by Tang et al. is adopted here.13 The process incorporates a three sectional structure, 2/25/9, with the specification on the top and bottom products as 95 mol %, respectively (cf., Figure 7). The relevant physicochemical properties and nominal steady-state operating conditions are summarized in Table 4. The esterification reaction occurring on the reactive stages is

process dynamics and controllability, we choose, respectively, two values of operating pressure in these two subregions. While operating pressures of 6 and 6.7 bar are selected in the left subregion, they are chosen to be 12 and 15 bar in the right subregion. Together with the boundary point of 9 bar, these values form two groups of operating pressures: (i) 6, 6.7, and 9 bar, and (ii) 9, 12, and 15 bar, based on which the closed-loop responses of the hypothetical ideal reactive distillation columns are to be compared. 3.3.1. Comparison of Process Dynamics and Controllability between Operating Pressures, 6, 6.7, and 9 bar. In Figure 5, the regulatory responses of the hypothetical ideal reactive distillation column operated under different operating pressures (i.e., 6, 6.7, and 9 bar, respectively) are depicted when the feed flow rate of reactant B has been upset by ±5%, respectively. In case the operating pressure is fixed at 6 bar, the process exhibits rather sluggish responses and needs a long time to reach the new steady states. In particular, initial oscillations are found in the top and bottom product control loops. With the increase of operating pressure to 6.7 or 9 bar, the settling times are sharply reduced irrespective of the negative or positive changes in the feed flow rate of reactant B. As for the comparison of dynamic performance between those operated under 6.7 and 9 bar, the former appears inferior to the latter in both deviations of product qualities and settling times. Integral absolute error (IAE) is calculated and tabulated in Table 3. It is noted that a good accordance has been achieved with the above observations. The closed-loop simulation results demonstrate that the enhancement of operating pressure benefits process dynamics and controllability in the operation range below 9 bar. Moreover, the hypothetical ideal reactive distillation column operated under 9 bar can maintain its higher thermodynamic efficiency than those operated under 6 and 6.7 bar at the newly reached steady states. 3.3.2. Comparison of Process Dynamics and Controllability between Operating Pressures, 9, 12, and 15 bar. The regulatory responses of the hypothetical ideal reactive distillation column operated under different operating pressure (i.e., 9, 12, and 15 bar, respectively) are presented in Figure 6 when the feed flow rate of reactant B has been upset by +50% and −15%, respectively. With the increase of operating pressure, the process tends to display

methanol(MeOH) + acetic acid(HAc) kf

⇀ ↽ methyl acetate(MeAc) + water(H2O)ΔHR,330 kb

= −33 566.80 kJ kmol−1

(10)

kf


controlled one. The net reaction rate is expressed by the pseudohomogeneous model with components represented in terms of activity and catalyst weight-based kinetics. r MeAc = mcat(k f aHAcaMeOH − k baMeAcaH2O)

(11)

k f = (2.961 × 104)e−49 190/(RT )

(12)

k b = (1.348 × 106)e−69 230/(RT )

(13)

The steady-state and dynamic simulation of the methyl acetate reactive distillation column is performed using the commercial software ASPEN PLUS and ASPEN DYNAMICS, respectively, and the UNIQUAC model is used to calculate the activity coefficients accounting for the nonideal vapor−liquid equilibrium. The dimerization of acetic acid is described by the Hayden−O’Conell second virial coefficient model, and the ASPEN PLUS built-in association parameters are used to compute its fugacity coefficients. 4.2. Effect of Operating Pressure on Steady-State Performance. The effect of operating pressure on the steadystate performance of the methyl acetate reactive distillation column is illustrated in Figure 8 (it is slightly different from the one reported in ref 3 because of the minor adjustments of steady-state operating condition necessary for dynamic simulation with ASPEN DYNAMICS). It is readily noted that it again takes a shape somewhat similar to the one shown in Figure 1. The heat duties of condenser and reboiler first 3699



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Figure 11. Regulatory responses of example II for a ±5% step change in the feed flow rate of acetate acid, respectively (2.1/2.4/2.6 atm): (a) composition of methyl acetate in the top product, (b) reflux flow rate, (c) composition of methanol on stage 28, (d) feed flow rate of methanol, (e) composition of water in the bottom product, (f) heat duty of reboiler. Gray curves, negative responses; black curves, positive responses.

decrease with the enhancement of operating pressure and reach their minima when the operating pressure is 2.2 and 2.1 atm, respectively. Beyond the optimum points, the heat duties of condenser and reboiler turn to increase, delineating a nonmonotonic relationship between operating pressure and steady-state performance. 4.3. Effect of Operating Pressure on Process Dynamics and Controllability. As shown in Figure 9, a decentralized control system is adopted here. Operating pressure is again assumed to be perfectly controlled with the heat removal of condenser. The levels of the reflux-drum and reboiler are controlled, respectively, with the distillate and the bottom product flow rates, and two P controllers with gains of 2 are adopted. In the top product, the composition of methyl acetate is controlled by manipulating the reflux flow rate, and a PI controller is employed. In the bottom product, the composition of water is controlled by manipulating the heat duty of reboiler, and a PI controller is employed. The

concentration of methanol on the lower feed stage (i.e., stage 28) is measured and controlled by manipulating the feed flow rate of methanol, aiming to keep the stoichiometric balance between the reactants acetic acid and methanol, and a P controller is used. The feed flow rate of acetic acid is the production rate handle and is flow controlled. The dynamics of concentration measurements is assumed to be a pure time-delay of 3 min. All composition controllers are first tuned in terms of the relayfeedback tests and Ziegler−Nichols rule and then detuned somehow to take account of the interaction between different control loops. The obtained controller parameters are listed in Table 5. Analogous to the case of the hypothetical ideal reactive distillation column outlined in the preceding section, we divide the feasible region of operating pressure into two parts based on the optimum design of the methyl acetate reactive distillation column, the left (below 2.1 atm) and right (above 2.1 atm) subregions. In each of the subregions, three operating 3700



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Figure 12. Servo responses of example II for a ±0.01 step change in the top and bottom product purities, respectively (2.1/2.4/2.6 atm): (a) composition of methyl acetate in the top product, (b) reflux flow rate, (c) composition of methanol on stage 28, (d) feed flow rate of methanol, (e) composition of water in the bottom product, and (f) heat duty of reboiler. Gray curves, negative responses; black curves, positive responses.

pressures are selected, and they are 0.9, 1.5, and 2.1 atm for the left one and 2.1, 2.4, and 2.6 atm for the right one. In terms of these operating pressures, the regulatory responses of the methyl acetate reactive distillation column are to be compared in the following subsections. 4.3.1. Comparison of Process Dynamics and Controllability between Operating Pressures, 0.9, 1.5, and 2.1 atm. Figure 10 displays the regulatory responses of the methyl acetate reactive distillation column operated under different operating pressures (i.e., 0.9, 1.5, and 2.1 atm, respectively) when the feed flow rate of acetic acid has been upset by ±5% at the instant of 0.5 h, respectively. As can readily be seen, the process displays increasingly small maximum deviations in the top and bottom product qualities with the enhancement of operating pressure, no matter whether negative or positive changes have been encountered in the feed flow rate of acetic acid.

Figure 13. A reactive distillation column producing MTBE from isobutylene and methanol (example III). 3701



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Table 7. Physicochemical Properties and Operating Conditions of Example III parameter number of stages

Table 8. Controller Parameters for Example III


stage holdup (kg) heat of reaction (kJ kmol−1, 1100 kPa, 298 K) latent heat of MTBE (kJ kmol−1, 1100 kPa, 298 K) mole fraction of C4 IC4 NC4 feed flow rate of reactant MeOH (mol s−1) feed flow rate of reactant C4 (mol s−1) feed location of reactant MeOH feed location of reactant C4 thermal condition of FC4 thermal condition of FMeOH overhead product composition (NBUT, mol %) bottom product composition (MTBE, mol %)

2 8 5 1800 −37 700 29 829 0.357 0.643 198 547 4 11 1.0 0.0 84 90

operating pressure (atm)

control loop

KC

TI (min)

6.5

top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry top composition bottom composition reactant stoichiometry

4.62 5.87 0.97 9.16 4.08 0.52 9.32 3.06 0.50 9.69 2.82 0.88 10.05 1.68 5.11

26.50 11.00

6.8

7.1

8.5

10.1

22.00 13.00 22.00 15.50 19.00 15.00 18.00 16.50

Table 9. IAE of Example III operating pressure (atm)

scenario increase by 5% in the feed flow rate of methanol

decrease by 5% in the feed flow rate of methanol

Figure 14. Effect of operating pressure on the steady-state performance of example III.

6.5 6.8 7.1 8.5 10.1 6.5 6.8 7.1 8.5 10.1

distillate 2.770 3.344 1.839 5.645 5.673 1.099 1.922 1.201 5.340 2.992

× × × × × × × × × ×

10−2 10−3 10−3 10−4 10−4 10−2 10−3 10−3 10−4 10−3

bottom withdrawal 3.061 7.802 5.889 1.508 6.764 9.627 3.869 2.957 1.562 2.284

× × × × × × × × × ×

10−2 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−3 10−2

The closed-loop simulation results obtained indicate a nonmonotonic effect of operating pressure on the dynamics and controllability of the methyl acetate reactive distillation column in the left subregion. 4.3.2. Comparison of Process Dynamics and Controllability between Operating Pressures, 2.1, 2.4, and 2.6 atm. The regulatory responses of the methyl acetate reactive distillation column operated under different operating pressures (i.e., 2.1, 2.4, and 2.6 atm, respectively) are showed in Figure 11 when the feed flow rate of acetic acid has been upset by ±5% at the instant of 0.5 h, respectively. Although the process displaysincreasingly small maximum deviations in the top and bottom product qualities with the enhancement of operating pressure, the settling times are extended considerably. In case the operating pressure has been fixed at 2.6 atm, the methyl acetate reactive distillation column exhibits initial inverse responses in the top product quality in addition to the strong oscillations in the bottom product quality, both phenomena signifying sharply deteriorated process dynamics and controllability in this situation. In Table 6, the IAE is also calculated and listed for the three circumstances. Despite the fact that the value of the IAE at the operating pressure of 2.6 atm appears to be the smallest one for both positive and negative responses, the operating condition should evidently be considered as the worst one in terms of process dynamics and controllability. Through the comparison of the other two circumstances, they show a good agreement with the observations made above; the enhancement of operating pressure deteriorates process dynamics and controllability in the operation range above 2.1 atm.

Figure 15. A decentralized control scheme for example III.

In the aspect of settling time, however, the opposite trends are found when the operating pressure increases from 1.5 to 2.1 atm. With the simultaneous consideration of these two performance indexes, it is reasonable to conclude that the methyl acetate reactive distillation column operated under 1.5 atm should be superior to those operated under 0.9 and 2.1 atm. The IAE is calculated and listed in Table 6, which justifies the above interpretations. 3702



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The kinetic model proposed by Rehfinger and Hoffmann is used in this study.15

To gain further insights into the intricate relationship between operating pressure and process dynamics and controllability, we also examined the servo responses of the methyl acetate reactive distillation columns operated under different operating pressures (i.e., 2.1, 2.4, and 2.6 atm, respectively). In Figure 12, the obtained results are illustrated when the process has been upset by a ±0.01 step change in the set-points of the top and bottom products at the instant of 0.5 h, respectively. With the enhancement of operating pressure from 2.1 to 2.4 atm, the settling time is greatly increased, implying a considerable reduction of tracking capability. When operating pressure is further increased to 2.6 atm, the settling time is further magnified in case that the set-points of the top and bottom products are reduced simultaneously to 0.94. In case that the set-points of the top and bottom products are increased simultaneously to 0.96, the process cannot move to the desired steady state, leaving a divergent oscillation in the bottom product. The IAE is also calculated and tabulated in Table 6, displaying a good agreement with the above observations. These closed-loop simulation results evidence definitely that the enhancement of operating pressure deteriorates the dynamics and controllability of the methyl acetate reactive distillation column in the right subregion.

(15)

k f = (3.67 × 1012)e−11 110/ T

(16)

K eq = 284e f (T )

(17)

⎛1 ⎛T ⎞ 1⎞ f (T ) = A1⎜ − ⎟ + A2 ln⎜ ⎟ + A3(T − T0) T0 ⎠ ⎝T ⎝ T0 ⎠ + A 4 (T 2 − T02) + A5(T 3 − T03) + A 6(T 4 − T0 4)

(18)

where T0 = 298.15 K, A1 = −1.49277 × 103 K, A2 = −77.4002, A3 = 0.507563 K−1, A4 = −9.12739 × 10−4 K−2, A5 = 1.10649 × 10−6 K−3, and A6 = −6.27996 × 10−10 K−4. The steady-state and dynamic simulation of the MTBE reactive distillation column is carried out using the commercial software ASPEN PLUS and ASPEN DYNAMICS, respectively, and the liquid phase activities are calculated using the UNIQUAC model with the binary interaction parameters reported by Rehfinger and Hoffmann.15 5.2. Effect of Operating Pressure on Steady-State Performance. Figure 14 displays the effect of operating pressure on the steady-state performance of the MTBE reactive distillation column. It is noted that it again takes a shape somewhat similar to the one shown in Figure 1. The increase of operating pressure leads to reductions in the heat duties of condenser and reboiler, and the minima locate at the operating pressure of 7.2 and 7.1 atm, respectively. Beyond the optimum points, the heat duties of condenser and reboiler begin to increase with the enhancement of operating pressure, thereby depicting a nonmonotonic relationship between operating pressure and steady-state performance. 5.3. Effect of Operating Pressure on Process Dynamics and Controllability. The decentralized control scheme for the MTBE reactive distillation column is sketched in Figure 15. Operating pressure is again assumed to be perfectly controlled with the heat removal of condenser. The levels of condenser and reboiler are controlled, respectively, with the distillate and the bottom product flow rates, and two P controllers with gains of 2 are adopted here. The top composition of NBUT is controlled with the reflux flow rate, and a PI controller is employed. The bottom composition of MTBE is controlled with the heat duty of reboiler, and a PI controller is employed. The isobutylene composition on the lower feed stage (i.e., stage 11) is controlled with the feed flow rate of C4, serving to keep the stoichiometric balance between the reactants, and a P controller is used. The feed flow rate of methanol is the production rate handle and is flow controlled. The dynamics of concentration measurements is assumed to be a pure time-delay of 3 min. The composition controllers are tuned sequentially in terms of relay-feedback tests and Ziegler− Nichols tuning method.16 Table 8 lists the obtained controller parameters for the MTBE reactive distillation column operated under different operating pressures. In light of the optimum operating pressure of the MTBE reactive distillation column shown in Figure 14, the feasible

5. EXAMPLE III: A REACTIVE DISTILLATION COLUMN PRODUCING MTBE FROM ISOBUTYLENE AND METHANOL 5.1. Process Description. MTBE is produced by a reversible exothermic reaction of methanol and isobutylene in the presence of either a heterogeneous catalyst, for example, a strong acidic ion-exchange resin, or a homogeneous catalyst, for example, sulfuric acid. In this work, the reaction catalyzed by sulfuric acid is to be investigated. Instead of being assumed to be an equilibrium-limited reaction as shown in our previous work,3,14 it is now taken as a kinetically controlled one. The reactive distillation column shown in Figure 13 is employed here. A C4 vapor at 350 K (qC4 = 0), comprised of 36 mol % isobutylene and 64 mol % inert n-butene (NBUT), is employed to react with a pure methanol liquid at 320 K (qMEOH = 1). The process possesses a three sectional configuration: 2/8/5, that is, a rectifying section, a stripping section, and a reactive section between, in addition to a total condenser at the top and a partial reboiler at the bottom. The top and bottom products are specified to be 84 and 90 mol % for NBUT and MTBE, respectively. Other relevant physicochemical properties and nominal steady-state operating conditions are summarized in Table 7. The reaction occurring on the reactive stages is methanol(MeOH) + isobutylene(IBUT) kf

⇀ ↽ methyl tertiary butyl ether(MTBE)ΔHR,298 kb

= −37 700 kJ kmol−1

⎞ ⎛ aIB aMTBE ⎟ ⎜ r MTBE = mcatqacidk f − ⎜a K eqa2 MeOH ⎟⎠ ⎝ MeOH

(14)

kf


controlled one. 3703



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Figure 16. Regulatory responses of example III for a ±5% step change in the feed flow rate of methanol, respectively (6.5/6.8/7.1 atm): (a) composition of NBUT in the top product, (b) reflux flow rate, (c) composition of isobutylene on stage 11, (d) feed flow rate of C4, (e) composition of MTBE in the bottom product, and (f) heat duty of reboiler. Gray curves, negative responses; black curves, positive responses.

region of operating pressure is divided into two parts, the left (below 7.1 atm) and right (above 7.1 atm) subregions. In each of the subregions, three operating pressures are selected, and they are 6.5, 6.8, and 7.1 atm for the left one and 7.1, 8.5, and 10.1 atm for the right one. In terms of these operating pressures, the regulatory responses of the MTBE reactive distillation column are to be examined in the following subsections. 5.3.1. Comparison of Process Dynamics and Controllability between Operating Pressures, 6.5, 6.8, and 7.1 atm. In Figure 16, the regulatory responses of the MTBE reactive distillation column operated under different operating pressures (i.e., 6.5, 6.8, and 7.1 atm, respectively) are shown, when the feed flow rate of methanol has been upset by ±5% at the instant of 0.5 h, respectively. With the enhancement of operating pressure, the process exhibits increasingly improved dynamic responses in the top and bottom product qualities no matter whether negative or positive changes have been encountered in

the feed flow rate of methanol. This can easily be identified through the comparison of maximum deviations and settling times. In particular, the MTBE reactive distillation column, when operated at 6.5 atm, fails to overcome the positive disturbance and exhibits divergent oscillations in the top and bottom product qualities. After operating pressure has been raised to 6.8 or 7.1 atm, the oscillations completely disappeared. The IAE is calculated and listed in Table 9, which justifies the above observations. The closed-loop simulation results evidence that the enhancement of operating pressure benefits the dynamics and controllability of the MTBE reactive distillation column in the left subregion. 5.3.2. Comparison of Process Dynamics and Controllability between Operating Pressures, 7.1, 8.5, and 10.1 atm. Figure 17 details the regulatory responses of the MTBE reactive distillation column operated under different operating pressures (i.e., 7.1, 8.5, and 10.1 atm, respectively) when the feed flow 3704



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Figure 17. Regulatory responses of example III for a ±5% step change in the feed flow rate of methanol, respectively (7.1/8.5/10.1 atm): (a) composition of NBUT in the top product, (b) reflux flow rate, (c) composition of isobutylene on stage 11, (d) feed flow rate of C4, (e) composition of MTBE in the bottom product, and (f) heat duty of reboiler. Gray curves, negative responses; black curves, positive responses.

rate of methanol has been upset by ±5% at the instant of 0.5 h, respectively. Of the dynamic responses at the three operating pressures, one can easily conclude that the one at 8.5 atm should be the best in light of process dynamics and controllability. In case the operating pressure has been fixed at 10.1 atm, the process exhibits inverse responses in the top and bottom product qualities, and it even fails to overcome the negative disturbance, implying sharply deteriorated process dynamics and controllability under this operating condition. In Table 9, the IAE is also calculated and listed for these circumstances, which shows a good accordance with the above observations. The closed-loop simulation results obtained indicate a nonmonotonic effect of operating pressure on the dynamics and controllability of the MTBE reactive distillation column in the right subregion.

6. DISCUSSION In terms of the hypothetical ideal reactive distillation column, the methyl acetate reactive distillation column, and the MTBE reactive distillation columns studied, we have demonstrated the existence of a nonmonotonic relationship between operating pressure and process dynamics and controllability. More specifically, whereas the enhancement of operating pressure is favorable to process dynamics and controllability in the lower part of its feasible region, it is likely to present an adverse effect in the higher part of its feasible region. Although it is extremely difficult to prove this intricate phenomenon on a pure theoretical basis, the findings of the current work are considered to be of general significance, revealing a relevant and yet uncommon feature of the reactive distillation columns involving kinetically controlled exothermic reactions. Because for any chemical processes unique process dynamics and controllability are generally caused by the interactions between 3705



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Figure 18. Optimal points for steady-state performance and process dynamics and controllability versus operating pressure for the reactive distillation columns involving kinetically controlled exothermic reactions: (a) optimal point for steady-state performance is at the right side of the one for process dynamics and controllability, and (b) optimal point for steady-state performance is at the left side of the one for process dynamics and controllability.

hand, the combination between the reaction operation and the separation operation involved, from which the deviation in operating pressure finally resulted. Understanding the unique effect of operating pressure on process dynamics and controllability is especially important for the developments of reactive distillation columns involving kinetically controlled exothermic reactions, because it offers a potential way to trade-off steady-state performance and process dynamics and controllability with operating pressure as a potential decision variable at the early stage of process synthesis and design. If, for a reactive distillation column involving a kinetically controlled exothermic reaction, operating pressure gives a correspondent effect on steady-state performance and process dynamics and controllability, as in the case of the hypothetical ideal reactive distillation column studied, then its favorable operating pressure should be located around the point of the most economical design, the gray region shown in Figure 1. If, for a reactive distillation column involving a kinetically controlled exothermic reaction, operating pressure does not present a correspondent effect on steady-state performance and process dynamics and controllability, as in the cases of the methyl acetate or MTBE reactive distillation columns studied, then its favorable operating pressure should be located between the two optimum points for steady-state performance and process dynamics and controllability, respectively, the gray regions shown in Figure 18a and b.

conflicting or competing factors, it seems reasonable to think that the conflicting effects of operating pressure on reaction rate and chemical equilibrium constant are responsible for such a complicated phenomenon. It is worth mentioning here the minor difference in the relationship between operating pressure and process dynamics and controllability for the three reactive distillation columns studied. For the hypothetical ideal reactive distillation column, the relationship between operating pressure and process dynamics and controllability shares a strict correspondence with the one between operating pressure and steady-state performance. For instance, at the operating pressure of 9 bar, the hypothetical ideal reactive distillation column exhibits the optimum steady-state performance with the most favorable process dynamics and controllability. For the other two reactive distillation columns, the situations are, however, different. In the case of the methyl acetate reactive distillation column, while the optimal steady-state performance is gained at the operating pressure of 2.1 atm, the most favorable process dynamics and controllability appears actually at an operating pressure less than it (i.e., around 1.5 atm). In the case of the MTBE reactive distillation column, while the optimal steady-state performance is gained at the operating pressure of 7.1 atm, the most favorable process dynamics and controllability appears actually at an operating pressure greater than it (i.e., around 8.5 atm). The deviations in operating pressure are anticipated to have been caused by the high degree of nonlinearities in the vapor− liquid equilibrium and enthalpy−composition relationships of the reacting mixture separated. It should, however, be borne in mind that the high degree of nonlinearities affects, on the first

7. CONCLUSIONS In this work, the influences of operating pressure on the dynamics and controllability of the reactive distillation columns involving a kinetically controlled exothermic reaction have been 3706



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|Lj − 1xi , j − 1 + Vj + 1yi , j + 1 − Ljxi , j − Vjyi , j + Fjz i , j δj , m

examined in terms of the three reactive distillation systems studied, including an ideal reactive distillation column performkf

kb

(A3)

APPENDIX B: DYNAMIC MODEL OF THE HYPOTHETICAL IDEAL REACTIVE DISTILLATION COLUMN In terms of the principle of mass and energy conservation in conjunction with the given vapor−liquid equilibrium relationship, a first-principle dynamic model is developed for the ideal reactive distillation column performing a hypothetical exother-

two real ones producing, respectively, methyl acetate from acetic acid and methanol and MTBE from isobutylene and methanol. It has been found that operating pressure can present nonmonotonic influences on process dynamics and controllability, just like its impact on the steady-state performance. While the enhancement of operating pressure benefits process dynamics and controllability in the lower part of its feasible region, it turns to deteriorate process dynamics and controllability in the higher part of its feasible region. The intricate behavior of the reactive distillation columns involving kinetically controlled exothermic reactions is essentially governed by the conflicting effects of operating pressure on reaction rate and chemical equilibrium constant and is useful to identify a favorable region of operating pressure from the viewpoint of process dynamics and controllability. Because the region may or may not coincide with the one for process synthesis and design, operating pressure can therefore serve as a potential decision variable to trade-off process design and operation, helping to make a process design with satisfactory steady-state performance, process dynamics, and controllability. Future work will be centered on analyzing the effect of operating pressure on the dynamics and controllability of the reactive distillation columns involving kinetically controlled exothermic reactions in terms of multivariable control theories.

■

+ ri , j| ≤ ε

■

ing a hypothetical exothermic reaction, A + B ⇀ ↽ C + D, and

kf

mic reaction, A + B ⇀ ↽ C + D. Besides the reaction kinetics, kb

vapor−liquid equilibrium relationship, and energy balance equations described by eqs 2−9, the following equations are included. Total mass balance equation on stage j (1 ≤ j ≤ n): dM j dt

nc

= Vj + 1 − Vj + Lj − 1 − Lj + Fj δj , m +

∑ ri , j i=1 (B1)

Component mass balance equation on stage j (1 ≤ i ≤ nc, 1 ≤ j ≤ n): dMjxi , j dt

= Vj + 1yi , j + 1 − Vjyi , j + Lj − 1xi , j − 1 − Ljxi , j + Fj δj , mz i , j + ri , j

(B2)

Stage hydraulic equation on stage j (2 ≤ j ≤ n − 1):

APPENDIX A: STEADY-STATE MODEL OF THE HYPOTHETICAL IDEAL REACTIVE DISTILLATION COLUMN

Lj − Ljs =

kf

hypothetical exothermic reaction, A + B ⇀ ↽ C + D, a steadykb

state model is developed in terms of the principle of mass and energy conservation in conjunction with the given vapor−liquid equilibrium relationship. As shown in eqs A1 and A2, two additional constraints have been imposed on the top and bottom product qualities within the steady-state model, which guarantee a predetermined conversion rate of reactants and thus lay a fair basis for the comparative studies of various process designs operated under different operating pressures. The steady-state model is solved using a modified Newton− Raphson method, and the satisfaction of component mass balance equations, (i.e., eq A3), as well as the attainment of the product specifications (i.e., eqs A1 and A2), is taken as the convergence criterion. The commercial software Mathematica is employed to compile and debug the program of the steadystate model. It appears to be quite robust and can approach a solution fairly quickly for the various hypothetical ideal reactive distillation columns operated under different operating pressures. (A1)

|x bot − x bot sp| ≤ ε

(A2)

(B3)

It is noted that a linearized stage hydraulic equation is employed here for the simplification of the complicated calculations. The dynamic model is solved using the commercial software Mathematica, and the solution can well represent the general behavior of the hypothetical ideal reactive distillation column. It is therefore reasonable to use it as a substitute to study process dynamics and controllability.

For the ideal reactive distillation column performing a

|x top − x topsp| ≤ ε

Mj − M js τ

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 10 64434801. Fax: +86 10 64437805. E-mail: [email protected].

■

ACKNOWLEDGMENTS The project is financially supported by the Doctoral Programs Foundation of Ministry of Education of China (Grant no. 20100010110008) and thereby is acknowledged. We also thank the State Key Laboratory of Chemical Resource Engineering at Beijing University of Chemical Technology for providing computing facilities.

■ 3707

NOTATION A = component a = liquid activity Avp = vapor pressure constant, Pa B = component Bvp = vapor pressure constant, Pa K dx.doi.org/10.1021/ie202241p | Ind. Eng. Chem. Res. 2012, 51, 3692−3708


Article

Recycle Systems for Different Chemical Equilibrium Constants. Ind. Eng. Chem. Res. 2004, 43, 2493. (3) Wang, S.; Huang, K.; Lin, Q.; Wang, S. J. Understanding the Impact of Operating Pressure on Process Intensification in Reactive Distillation Columns. Ind. Eng. Chem. Res. 2010, 49, 4269. (4) Al-Arfaj, M. A.; Luyben, W. L. Design and Control of an Olefin Metathesis Reactive Distillation Column. Chem. Eng. Sci. 2002, 57, 715. (5) Kaymak, D. B. Impact of Process Design on Dynamic Controllability of a Generic Reactive Distillation Column. Presented at the AIChE 2009 Annual Meeting, 2009. (6) Luyben, W. L. Economic and Dynamic Impact of the Use of Excess Reactant in Reactive Distillation Systems. Ind. Eng. Chem. Res. 2000, 39, 2935. (7) Al-Arfaj, M. A.; Luyben, W. L. Comparison of Alternative Control Structures for an Ideal Two-Product Reactive Distillation Column. Ind. Eng. Chem. Res. 2000, 39, 3298. (8) Kaymak, D. B.; Luyben, W. L. Comparison of Two Types of Two-Temperature Control Structures for Reactive Distillation Columns. Ind. Eng. Chem. Res. 2005, 44, 4625. (9) Huang, K.; Nakaiwa, M.; Tsutsumi, A. Towards Further Internal Heat Integration in Design of Reactive Distillation Columns − Part I: The Design Principle. Chem. Eng. Sci. 2005, 60, 4901. (10) Huang, K.; Nakaiwa, M.; Tsutsumi, A. Towards Further Internal Heat Integration in Design of Reactive Distillation Columns − Part II: The Process Dynamics and Operation. Chem. Eng. Sci. 2006, 61, 5377. (11) Huang, K.; Lin, Q.; Shao, H.; Wang, C.; Wang, S. A Fundamental Principle and Systematic Procedures for Process Intensification in Reactive Distillation Columns. Chem. Eng. Process. 2010, 49, 294. (12) Tyreus, B. D.; Luyben, W. L. Tuning PI Controllers for Integrator/Dead Time Processes. Ind. Eng. Chem. Res. 1992, 31, 2625. (13) Tang, Y. T.; Chen, Y. W.; Huang, H. P.; Yu, C. C.; Hung, S. B.; Lee, M. J. Design of Reactive Distillation for Acetic and Esterification. AIChE J. 2005, 51, 1683. (14) Huang, K.; Wang, S. J.; Ding, W. Towards Further Internal Heat Integration in Design of Reactive Distillation Columns − Part III: Application to a MTBE Reactive Distillation Column. Chem. Eng. Sci. 2008, 63, 2119. (15) Rehfinger, A.; Hoffmann, U. Kinetics of Methyl Tertiary Butyl Ether Liquid Phase Synthesis Catalyzed by Ion Exchange Resin − I. Intrinsic Rate Expression in Liquid Phase Activities. Chem. Eng. Sci. 1990, 45, 1605. (16) Lin, Y. D.; Huang, H. P.; Yu, C. C. Relay Feedback Tests for Highly Nonlinear Processes: Reactive Distillation. Ind. Eng. Chem. Res. 2006, 45, 4081.

C = component CC = composition controller D = component E = activation energy of a reaction, kJ kmol−1 F = feed flow rate of reactants, kmol s−1 FC = flow rate controller H = stage holdup, kmol ΔHR = thermal heat of a reaction, kJ kmol−1 ΔHV = heat of vaporization, kJ kmol−1 k = specific reaction rate, kmol s−1 kmol−1 KC = proportional gain KCU = ultimate gain Keq = equilibrium constant L = liquid flow rate, kmol s−1 LC = level controller M = stage holdup, kmol mcat = catalyst weight, kg n = number of stages nc = number of components P = pressure, Pa PCU = ultimate period, s qacid = ion-exchange capacity of the catalyst, equiv(H+) kg−1 Qreb = reboiler duty, kW R = ideal gas law constant, kJ kmol−1 K−1 r = net reaction rate, kmol s−1 RR = reflux rate, kmol s−1 t = time, s T = temperature, K TI = integral time, s V = vapor flow rate, kmol s−1 Vnt = bottom vapor flow rate, kmol s−1 x = liquid composition y = vapor composition z = feed composition Greek Letters

δ = Kronecker function ε = error tolerance τ = stage hydraulics time constant, s ν = stoichiometric coefficients of a reaction Subscripts

A = component index b = backward reaction bot = bottom product B = component index C = component index D = component index f = forward reaction IB = isobutylene i = component index j = stage index m = feed stage index top = top product Superscripts

s = saturation or steady state sp = product specification

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REFERENCES

(1) Luyben, W. L. Effect of Kinetic and Design Parameters on Ternary Reactive Distillation Columns. Ind. Eng. Chem. Res. 2007, 21, 6977. (2) Kaymak, D. B.; Luyben, W. L. Quantitative Comparison of Reactive Distillation with Conventional Multiunit Reactor/Column/ 3708


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