Dynamics and Control of Reactive Distillation Columns with Double

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Dynamics and Control of Reactive Distillation Columns with Double Reactive Sections: Feed-Splitting Influences Yang Cao, Kejin Huang,* Yang Yuan, Haisheng Chen, Liang Zhang, and Shaofeng Wang College of Information Science and Technology, Beijing University of Chemical Technology, Beijing 100029, People’s Republic of China S Supporting Information *

ABSTRACT: Reactive distillation columns with double reactive sections (RDCs-DRS) at the top and bottom are especially favorable for the separations of reacting mixtures featuring the most unfavorable ranking of relative volatilities. In this article, their dynamics and control are studied in great detail, with special attention given to the influences of feed splitting on process dynamics and controllability. Because of the totally refluxed and totally reboiled operation mode plus an intermediate-product withdrawal, the RDC-DRS is generally characterized by severe under-dampness between the intermediate-product compositions and the reboiler heat duty (i.e., the regulation path) and by severe asymmetry between the intermediate-product compositions and the heaviest reactant feed flow rate (i.e., the disturbance path), consequently posing a great challenge to tight product quality control. With feed splitting of the lightest and heaviest reactants in the RDC-DRS (RDC-DRSFS), the simultaneous suppression of the under-dampness in the regulation path and the asymmetry in the disturbance path is attained, thereby presenting favorable influences to process dynamics and controllability. Two reactive distillation systems, executing a hypothetical reversible reaction, A + B ↔ C + D (αA > αC > αD > αB), and the lactic acid esterification with methanol, are employed to inspect the dynamics and controllability of the RDC-DRS and RDC-DRSFS. Although the RDC-DRS can be maintained as stable, rather sluggish tracking responses are noticed because the under-damped and asymmetrical behaviors restrict tight controller tuning. The RDC-DRSFS, on the other hand, shows greatly improved tracking performance with even enhanced disturbance rejection capabilities. The comparison endorses the great significance of feed splitting for the RDC-DRS, namely, not only an effective strategy for process retrofitting but also a potential booster for process dynamics and controllability.

1. INTRODUCTION Reacting mixtures with the most unfavorable ranking of relative volatilities signify here those mixtures whose reactants are the lightest and heaviest with the generated products in between (for instance, A + B ↔ C + D with αA > αC > αD > αB). For the separations of such reacting mixtures, reactive distillation columns with a single reaction section (RDCs-SRS) generally fail to yield better economical performance than their conventional counterparts (e.g., a reactor combined with a series of conventional separators).1−3 The reason lies mainly in the rigidity aroused by the allowance of a single reaction section to react away the lightest reactant (LR) A and the heaviest reactant (HR) B fed and to simultaneously purify the generated intermediate products. There are two methodologies available to alleviate the drawback. One is to arrange a top−bottom external recycle to keep the LR A and the HR B in close contact, in the reactive section (such a scheme is, hereinafter, referred to as the RDC-TBER).4 Although the steady-state economics could be enhanced considerably, great difficulties might be encountered © XXXX American Chemical Society

in maintaining the LR A and the HR B in close contact in a dynamic state, thereby revealing rather complicated dynamics and deteriorated controllability of the RDC-SRS and RDCTBER.5 The other methodology is to fortify a reactive distillation column with double reactive sections (RDC-DRS) as sketched in Figure 1a.6 With the flexibility of arranging double reactive sections at the top and bottom (note that the condenser and reboiler are also contained), the LR A and the HR B can contact each other in a very easy way if they are introduced, respectively, into the reboiler and condenser, thereby enabling the RDC-DRS to require considerably smaller investment and operating expenditures than its conventional counterpart and the RDC-SRS.7 Recently, it was further demonstrated that, for the separations of reacting mixtures featuring even more complicated reaction Received: Revised: Accepted: Published: A

April 10, 2017 June 21, 2017 June 21, 2017 June 21, 2017 DOI: 10.1021/acs.iecr.7b01488 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Schemes and dynamic characteristics of the RDC-DRS and RDC-DRSFS: (a) RDC-DRS, (b) RDC-DRSFS, (c) regulation path of RDC-DRS, (d) disturbance path of RDC-DRS, (e) regulation path of RDC-DRSFS, and (f) disturbance path of RDC-DRSFS.

Figure 2. (a) RDC-DRS and (b) RDC-DRSFS for a hypothetical reversible reaction A + B ↔ C + D (example I).

Table 1. Physicochemical Properties for Example I parameter

kinetics, i.e., the two-stage consecutive reversible reactions (A + B ↔ C + D and C + B ↔ E + D with αD > αB > αC > αA > αE) and the three-stage consecutive reversible reactions (the disproportionation of trichlorosilane to silane), the RDC-DRS also showed considerably improved steady-state economics as compared with the RDC-SRS.8,9 With reference to its unique process configuration and operation mechanism, Zhang et al. noticed the great impacts of feed locations of the LR A and the HR B on the steady-state performance of the RDC-DRS and advocated the adoption of feed splitting (FS) in process development (such a process is, hereinafter, referred to as the RDC-DRSFS), as is shown in Figure 1b.10−12 The simultaneous introduction of the LR A and the HR B into the condenser and reboiler served to coordinate the reaction conversions in the upper and lower reactive sections and consequently reduced the amount of the unconverted LR and HR passing through the stage where the intermediate product is withdrawn, thereby dramatically enhancing the steady-state economics of the RDC-DRSFS. Chen et al.

value

activation energy (kJ/kmol) specific reaction rate at 366 K [kmol/(s kmol)] relative volatility A:B:C:D heat of reaction (kJ/kmol) latent heat of vaporization (kJ/kmol) vapor pressure constants

forward backward forward backward

A (Avp/Bvp) B (Avp/Bvp) C (Avp/Bvp) D (Avp/Bvp)

50 208 71 128 0.008 0.004 8:1:4:2 −20 920 29 053.7 17.65/3862 15.57/3862 16.95/3862 16.26/3862

indicated recently that an external recycle could still be employed in the RDC-DRSFS and lead to improved steady-state performance that is even better than that of the RDC-TBER.13 Although the RDC-DRS and RDC-DRSFS are considerably superior to the RDC-SRS in the aspects of capital investment and B

DOI: 10.1021/acs.iecr.7b01488 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 3. Steady-state profiles of example I: (a) temperature, (b) vapor and liquid flow rates, (c) liquid composition, and (d) net reaction rates.

Figure 4. Open-loop responses of example I in the face of ±10% step changes in the reboiler heat duty: (a) C and (b) D.

Figure 5. Open-loop responses of example I in the face of ±20% step changes in the B feed flow rate: (a) C and (b) D.

operating cost, very few studies have been carried out so far on their dynamics and operation. Kaymak et al. recently studied the control of an RDC-DRS separating a two-stage consecutive reaction, A + B ↔ C + D and C + B ↔ E + D (αD > αB >

αC > αA > αE).14 They found that temperature inferential control could not work effectively unless it is with the involvement of the direct composition control of the lightest product D and the heaviest product E, simultaneously. Regarding the RDC-DRS C


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unique operation mechanisms (i.e., the totally refluxed and totally reboiled operation mode). The sharp uniqueness is likely to result in complicated process dynamics and consequently degrades process controllability. For effective and reliable process development, it is thus imperative to investigate in great detail the dynamics and operations of the RDC-DRS and RDCDRSFS as well as their close dependence on process synthesis and design. This essentially stands as the major purpose of this research. The rest of the paper is structured as follows: In Section 2, the dynamic characters of the RDC-DRS and RDC-DRSFS are analyzed and compared after a brief introduction of their process configurations and operation mechanisms. The separations of a hypothetical reversible reaction, A + B ↔ C + D (αA > αC > αD > αB), and of lactic acid esterification with methanol are employed in Sections 3 and 4, respectively, to inspect the dynamics and controllability of the RDC-DRS and RDC-DRSFS. Some concluding remarks are finally given in Section 5.

2. DYNAMIC CHARACTERISTICS OF THE RDC-DRS AND RDC-DRSFS As sketched in Figure 1a, the RDC-DRS is configured in such a way that two reactive sections are arranged deliberately at the top and bottom (which include not only the condenser and reboiler but also some stages in the upper and lower sections divided by the stage for withdrawing the reaction products) to counteract the fact that the LR A and the HR B tend to move upward and downward and accumulate, respectively, at the corresponding ends. The LR A and the HR B are fed, respectively, into the reboiler and condenser with the light product C and the heavy product D withdrawn together as an intermediate product. It is noted that this arrangement leaves the RDC-DRS in a totally refluxed and totally reboiled operation mode. Since the reboiler heat duty exhibits much quicker dynamics than the reflux flow rate and intermediate-product flow rate, the former should be used to maintain the C and D compositions of the intermediate product, and the latter two should be used to maintain the inventories of the condenser and reboiler. The very unusual process configuration and operation mechanism actually lend the RDC-DRS very unique process dynamics that can have profound influences on process controllability. First, the regulation path is to be analyzed. The reboiler heat duty actually has two routines to affect the C and D compositions of the intermediate product. Once a change occurs in the reboiler heat duty, it arouses an immediate variation in the vapor flow rate and has its first impact on the C and D compositions of the intermediate product (cf., Figure 1c). After the change moves upward and enters into the condenser, the totally refluxed operation mode transfers it completely into a perturbation in the liquid flow rate. After it reaches the stage for withdrawing the intermediate product, the perturbed liquid flow rate then presents the second impact on the C and D product compositions. It is noted that the first and second impacts are along opposite directions, and their net effect is the occurrence of an open-loop, under-damped behavior. Apparently, the unique phenomenon is closely related to the totally refluxed operation mode; more specifically, when the inventory in the condenser is larger, the degree of under-dampness becomes more severe, which presents definitely detrimental influences to process controllability.15,16 Apart from the intensification of interaction with the other control loop (i.e., the stoichiometric-balance

Figure 6. Control scheme for example I: (a) RDC-DRS and (b) RDCDRSFS.

and RDC-DRSFS, they feature not only very unique process configurations (i.e., with double reactive sections at the top and bottom and an intermediate-product withdrawal) but also very D


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Industrial & Engineering Chemistry Research Table 2. Controller Parameters for Examples I and II example I

example II

RDC-DRS control loop

KC (−)

reboiler-inventory control loop reflux-drum-inventory control loop stoichiometric-balance control loop intermediate-product control loop

0.01 1 12 249 750

RDC-DRSFS

TI (min)

KC (−)

120

0.01 1 20 770 000

RDC-DRS

TI (min)

KC (−)

480

2 10 1.29 0.11

RDC-DRSFS

TI (min)

KC (−)

TI (min)

34.32 27.72

2 10 0.25 1.52

73.92 23.76

Figure 7. Servo responses of example I in the face of ±0.005 step changes in the set point of the intermediate-product control loop: (a) C, (b) D, (c) reboiler heat duty, and (d) A feed flow rate.

Table 3. IAE for Examples I and II example I servo response RDC-DRS RDC-DRSFS

example II regulatory response

servo response

regulatory response

+0.005

−0.005

+20%

−20%

+0.0001

−0.0001

+20%

−20%

2.9150 1.2258

1.8810 0.8206

1.2638 0.6373

0.9771 0.9335

1.1735 0.1558

0.8921 0.1764

4.9806 0.5843

4.4634 0.7774

control loop), the under-damped behavior of the RDC-DRS also poses additional restrictions to tightening controller tuning. Second, the disturbance path is to be analyzed. The primary disturbance essentially originates from the B feed flow rate (and this assumes implicitly that it is taken as the production rate handle). Because of the totally reboiled operation mode, the open-loop under-damped behavior should still prevail despite that the intermediate-product flow rate is supposed to regulate the reboiler inventory here.17 Nonetheless, the severity of the under-dampness should be alleviated substantially because of there being no changes at all in the reboiler heat duty (the vapor flow rate involves few changes in this situation). In addition, a severe asymmetry between the positive and negative responses is also expected in the disturbance path, and two factors are responsible for such an unusual behavior (cf., Figure 1d). One

factor is the introduction of the LR A and the HR B into the bottom and top, respectively, which results in sharply different reaction conversions by the positive and negative variations in the B feed flow rate. The other factor is the totally refluxed and totally reboiled operation mode. In the case of an increase in the B feed flow rate, the increased liquid flow rate and reboilerinventory control loop tend to lower the C composition of the intermediate product. On the contrary, in the case of a decrease in the B feed flow rate, only the decreased liquid flow rate tends to lower the C composition of the intermediate product, while the reboiler-inventory control loop works in an opposite direction. For the D composition of the intermediate product, quite similar scenarios can be expected but with opposite changing directions. Still, this unique phenomenon is closely related to the amount of inventory in the reboiler; more specifically, when E


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Figure 8. Regulatory responses of example I in the face of ±20% step changes in the B feed flow rate: (a) C, (b) D, (c) reboiler heat duty, and (d) A feed flow rate.

methanol, are used to examine the insights on the dynamics and controllability of the RDC-DRS and RDC-DRSFS.

the the inventory in the reboiler is larger, the the degree of the asymmetry becomes more severe. It is evident that the severe asymmetry between the positive and negative responses calls for additional requirements on the control of the C and D compositions in the intermediate product. With the adoption of FS in process revamp, the exploited two degrees of freedom can generally lead to a great improvement in the steady-state performance of the RDC-DRSFS.11,12 As sketched in Figure 1b, the LR A is now simultaneously fed into the condenser and reboiler in a carefully determined ratio βA, and so is the HR B fed in a carefully determined ratio βB. Relatively low vapor and liquid heat loads are now solicited by the RDC-DRSFS, which are marked by two arrows that are narrower than those in Figure 1a. In the regulation path, although the second impact to the intermediate-product composition by a change in the reboiler heat duty shows few variations to the process modification, the first impact to the intermediateproduct compositions of C and D is considerably suppressed because of the fact that reaction conversions have now been well-coordinated between the upper reactive section and the lower reactive section (cf., Figure 1e). Therefore,the severity of open-loop under-dampness should be greatly abated in the RDC-DRSFS. In the disturbance path, the alleviation of the open-loop under-dampness behavior can still be expected. As for the asymmetry between the positive and negative responses, the same conclusion can be held because FS reduces the difference in reaction conversions by the positive and negative variations in the B feed flow rate (cf., Figure 1f). The improvement of openloop process dynamics will certainly present favorable influences to the tight control of the C and D compositions in the intermediate product. In the following, two reactive distillation systems, including the separations of a hypothetical reversible reaction, A + B ↔ C + D (αA > αC > αD > αB), and of the lactic acid esterification with

3. EXAMPLE I: SEPARATING A HYPOTHETICAL REVERSIBLE REACTION, A + B ↔ C + D (αA > αC > α D > α B) 3.1. Process Studied. As shown in Figure 2, the two reactive distillation systems, i.e., the RDC-DRS and RDC-DRSFS, are taken from Zhang et al., which separate a hypothetical reversible reaction.11 A+B↔C+D

ΔHR = −20 920 kJ/kmol

(1)

Table 1 lists the main physicochemical properties, and other relevant information can be found in the same reference. The net reaction rate is defined as ri , j = υi RHoldup( k x x − kB, jxC, jx D, j) j F, j A, j B, j

(2.1)

where kF,j and kB,j are the rate constants for the forward and backward specific reactions, respectively, and are calculated as kF, j = aF exp( −E F /RTj)

(2.2)

kB, j = aB exp( −E B /RTj)

(2.3)

In the reactive sections, the reaction thermal effect changes the vapor and liquid flow rates in the following fashion: Vj = Vj + 1 − rC, j(ΔHR /ΔHV )

(3.1)

Lj = Lj − 1 + rC, j(ΔHR /ΔHV )

(3.2)

In the nonreactive sections, the vapor and liquid flow rates involve no changes at all.

Vj = Vj + 1 F

(4.1) DOI: 10.1021/acs.iecr.7b01488 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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intermediate product. It is noted that the C composition of the intermediate product competes intensively with the D composition of the intermediate product, giving rise to quite similar responses but with opposite changing directions. For the RDCDRSFS, FS makes it exhibit a degree of under-dampness that is considerably reduced as compared with that in the RDC-DRS, implying a favorable influence on process dynamics by such a process revamp. Figure 5 depicts the open-loop responses of the RDC-DRS and RDC-DRSFS after ±20% step changes are introduced, separately, into the B feed flow rate. For both the positive and negative perturbations, the RDC-DRS displays under-damped behaviors with a fairly severe asymmetry between the two opposite scenarios. With the adoption of FS, both the underdamped behaviors and the asymmetry between the two opposite scenarios are subdued in the RDC-DRSFS, implying again a favorable influence on process dynamics by such a process revamp. The fact should be indicated here that the same amount of inventories in the condenser and reboiler has been assumed between the dynamic models of the RDC-DRS and RDC-DRSFS. Thus, the differences in the under-dampness and asymmetry are considered to be rather conservatively estimated in the above simulation study. 3.3. Closed-Loop Operation. Direct composition control schemes are employed here as shown in Figure 6. Column pressure is regulated with the condenser heat removal, and the inventories of the reflux drum and reboiler are regulated with the reflux and intermediate-product flow rates, respectively, via a P-only controller. Since the total amounts of liquid in the reboiler and the condenser are taken as the controlled variables, a much smaller controller gain than the common practice of 2 is adopted here (cf., Table 2). The C composition of the intermediate product is regulated by the reboiler heat duty via a PI controller, leaving the D composition of the intermediate product uncontrolled. As per the characteristics of the composition profiles sketched in Figure 3c, the A feed flow rate is employed to control the composition of A on stage 5 in the RDC-DRS and on stage 10 in the RDC-DRSFS, serving to keep the stoichiometric ratio between the LR A and the HR B. Although a P-only composition controller or a PI composition controller can be used here, for the sake of simplicity, the former option is chosen. The B feed flow rate is flow-controlled and works as the production rate handle. FS ratios are kept by two ratio controllers in the RDC-DRSFS. The composition controllers, designed in-line with the Tyreus− Luyben tuning rule, are also listed in Table 2. The fact is noted that two very large controller gains are obtained for the RDC-DRS and RDC-DRSFS because of their extremely small process gains between the intermediate-product composition and reboiler heat duty. In particular, the controller gain of the C-composition control loop is increased by a factor of 3.08 from the RDC-DRS to the RDC-DRSFS, implying the great influences of FS on controller tuning. Although the integral time is also increased here by a factor of 4, it affects mainly the tracking speed of the C composition of the intermediate product. Composition measurement devices are assumed to act like a firstorder process with a 5 min time constant, and control valves are all set at the half-open position in the nominal steady state. The servo responses of the RDC-DRS and RDC-DRSFS are delineated in Figure 7, after the C-composition control loop’s set point is disturbed, respectively, by ±0.5 mol % in magnitude. For the RDC-DRS, a rather sluggish tracking performance is noticed, with more than 90 and 100 h, respectively, for the C and D com-

Figure 9. (a) RDC-DRS and (b) RDC-DRSFS for the esterification of lactic acid with methanol (example II).

Lj = Lj − 1

(4.2)

The commercial software Mathematica is used in process simulation, and the steady-state distributions of temperature, vapor and liquid flow rates, liquid compositions, and net reaction rates are delineated in Figure 3. Because too much more of the catalyst was contained in the condenser and reboiler than in those stages in the two reactive sections, the reaction occurs mainly at the top and bottom. In comparison with the RDCDRS, the RDC-DRSFS reduces the reboiler heat duty by a factor of 3.37, highlighting the great potential of FS in process revamp. In this article, the dashed and solid lines stand for the outputs of the RDC-DRS and RDC-DRSFS, respectively, with black for the negative changes and gray for the positive changes in operating conditions. 3.2. Open-Loop Dynamic Characters. Figure 4 depicts the open-loop responses of the RDC-DRS and RDC-DRSFS after they encounter ±10% step disturbances in the reboiler heat duty, separately. For both the positive and the negative perturbations, the RDC-DRS shows seriously under-damped responses in the C (cf., Figure 4a) and D (cf., Figure 4b) compositions of the G


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Figure 10. Steady-state profiles of example II: (a) temperature, (b) vapor and liquid flow rates, (c) liquid composition, and (d) net reaction rates.

Figure 11. Open-loop responses of example II in the face of ±10% step changes in the reboiler heat duty: (a) MLA and (b) W.

Figure 12. Open-loop responses of example II in the face of ±20% step changes in the LA feed flow rate: (a) MLA and (b) W.

positions in the intermediate product to settle down completely to their new steady states. With the adoption of FS, the RDC-DRSFS displays much quicker tracking responses than the RDC-DRS, with around 20 and 40 h, respectively, for the

C and D compositions in the intermediate product to settle down completely to their new steady states. The advantages of the RDC-DRSFS over the RDC-DRS can also be confirmed by the integral absolute error (IAE) summarized in Table 3. It is noted here that the data tabulated are the sums of the values of the H


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disturbance. While the C composition of the intermediate product returns to its set point earlier than that in the RDC-DRS, the D composition of the intermediate product shares almost the same settling times as those in the RDC-DRS. In light of the IAE in Table 3, the RDC-DRSFS is clarified to slightly outperform the RDC-DRS. Also shown in the Supporting Information are the regulatory responses of the RDC-DRS and RDC-DRSFS after they experience a −20% step change in the B feed composition (A, 20 mol %; B, 80 mol %). The latter system is found again to be advantageous over the former in this situation.

4. EXAMPLE II: SEPARATING THE ESTERIFICATION OF LACTIC ACID WITH METHANOL 4.1. Process Studied. As shown in Figure 9, the two reactive distillation systems, i.e., the RDC-DRS and RDC-DRSFS, are again taken from Zhang et al. with the following reaction kinetics:11 lactic acid (LA) + methanol (MeOH) ↔ methyl lactate (MLA) + water (W)

(5)

ri , j = kF exp( −E F /RTj)(αLA, jαMeOH, j) − kB exp( −E B /RTj)(αMLA, jαW, j)

(6)

Although the aqueous solution of LA is usually adopted as a reactant in practice, the pure LA is used here because it makes the system become more complicated and challengeable in process operation. Other relevant information can be found in the same reference. The commercial software Aspen Dynamics is used for process simulation, and the steady-state distributions of temperature, vapor and liquid flow rates, liquid compositions, and net reaction rates are delineated in Figure 10 for the RDC-DRS and RDC-DRSFS. It is noted again that the reaction proceeds mainly in the condenser and reboiler. In comparison with the former, the latter reduces the reboiler heat duty by a factor of 70.3, highlighting again the great potential of FS in process revamp. 4.2. Open-Loop Dynamic Characters. Figure 11 depicts the open-loop responses of the RDC-DRS and RDC-DRSFS in the face of ±10% step changes in the reboiler heat duty, separately. Again, the RDC-DRS shows seriously under-damped responses in the MLA (cf., Figure 11a) and W (cf., Figure 11b) compositions of the intermediate product for both the positive and negative perturbations. In particular, the MLA composition of the intermediate product interacts intensively with the W composition of the intermediate product, giving rise to quite similar responses but with opposite changing directions. With the adoption of FS, the RDC-DRSFS displays a considerably suppressed degree of under-dampness, implying a favorable influence on process dynamics by such a process revamp. The open-loop responses of the RDC-DRS and RDC-DRSFS are shown in Figure 12, in the face of ±20% step disturbances, separately, in the LA feed flow rate. In addition to the great under-dampness, the RDC-DRS also displays an extremely severe asymmetry between the two opposite scenarios. With the adoption of FS, both the under-damped behaviors and the asymmetry between the two opposite scenarios are overwhelmingly subdued in the RDC-DRSFS, implying again a favorable influence on process dynamics by such a process revamp. Since the reductions in the amount of inventories in the condenser and reboiler caused by FS have been taken into account in the dynamic models of the RDC-DRS and RDC-DRSFS, such

Figure 13. Control scheme for example II: (a) RDC-DRS and (b) RDCDRSFS.

C and D compositions in the intermediate product, i.e., IAE = IAE(C) + IAE(D). The regulatory responses of the RDC-DRS and RDC-DRSFS are illustrated in Figure 8, after ±20% step changes are introduced into the B feed flow rate, separately. Slight oscillations occur in the RDC-DRSFS, especially in the face of negative I


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Figure 14. Servo responses of example II in the face of ±0.0001 step changes in the set point of the intermediate-product control loop: (a) MLA, (b) W, (c) reboiler heat duty, and (d) MeOH feed flow rate.

Figure 15. Regulatory responses of example II in the face of ±20% step changes in the LA feed flow rate: (a) MLA, (b) W, (c) reboiler heat duty, and (d) MeOH feed flow rate.

RDC-DRS and RDC-DRSFS are developed as shown in Figure 13. The MeOH composition on stage 3 is controlled in the stoichiometric-balance control loop, and the resultant controller parameters are listed in Table 2. Although the intermediate-product composition also has a very small process gain with respect to the reboiler heat duty, the very severe

variations in inventories also greatly affect their dynamic behaviors, and this is why the differences in the under-dampness and asymmetry between the RDC-DRS and RDC-DRSFS in example II appear to be much more pronounced than those in example I. 4.3. Closed-Loop Operation. In terms of the same principle as that in Figure 6, the decentralized control systems for the J


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alleviate the inherent drawbacks and therefore presents favorable influences to process dynamics and controllability.

under-dampness poses additional restrictions to tightening controller tuning, and this leads to a much smaller controller gain than in example I for the RDC-DRS and RDC-DRSFS. The controller gain and integral time of the MLA-composition control loop are increased and decreased, respectively, by a factor of 13.8 and 0.86 from the RDC-DRS to the RDC-DRSFS, obviously implying the great influences of FS on controller tuning. The servo responses of the RDC-DRS and RDC-DRSFS are illustrated in Figure 14, after the MLA-composition control loop’s set point is varied, separately, by ±0.01 mol % in magnitude. For the RDC-DRS, both the MLA and the W compositions in the intermediate product exhibit extremely sluggish tracking behaviors and fail to reach the expected set points within 300 h. As for the RDC-DRSFS, the adoption of FS drastically improves the situation. Both the MLA and the W compositions in the intermediate product exhibit relatively quick tracking behaviors and can reach the expected set points within 200 h. The advantages of the RDC-DRSFS over the RDC-DRS are also certified by the IAE tabulated in Table 3. Figure 15 presents the regulatory responses of the RDC-DRS and RDC-DRSFS, after ±20% step changes are introduced, separately, into the LA feed flow rate. The RDC-DRS yields, in most cases, very great peak deviations in the MLA and W compositions of the intermediate product and needs about 30 h for these to return to their set points. On the contrary, the RDC-DRSFS shows a similar degree of initial oscillations and only needs about 5 h for the MLA and W compositions of the intermediate product to return to their set points. The IAE tabulated in Table 3 also endorses the comparison between the RDC-DRS and RDC-DRSFS. Also given in the Supporting Information are the regulatory responses of the RDC-DRS and RDC-DRSFS after they encounter a −20 mol % step change in the LA feed composition (MeOH, 20 mol %; LA, 80 mol %). One can readily note that the latter system is superior to the former in this situation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b01488. Regulatory responses of example I in the face of a −20% step change in the B feed composition (A, 20 mol %; B, 80 mol %), and regulatory responses of example II in the face of a −20% step change in the LA feed composition (MeOH, 20 mol %; LA, 80 mol %) (PDF)

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AUTHOR INFORMATION

Corresponding Author

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

Kejin Huang: 0000-0003-2649-0223 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The research is supported by National Natural Science Foundation of China (21076015, 21376018, 21576014, and 21676011) and Fundamental Research Funds for the Central Universities (ZY1503).

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5. CONCLUSIONS The unusual process configuration and operation mechanism, i.e., the totally refluxed and totally reboiled operation mode plus an intermediate-product withdrawal, lend the RDC-DRS very unique process dynamics. While in the regulation path, seriously under-damped behaviors could occur between the light or heavy product compositions of the intermediate product and the reboiler heat duty; in the disturbance path, a high degree of asymmetry could happen between the light or heavy product compositions of the intermediate product and the HR feed flow rate. These dynamic characteristics are likely to pose great difficulties for the tight quality control of the intermediate product. With the adoption of FS in the RDC-DRSFS, the reaction conversion is carefully coordinated between the upper reactive section and the lower reactive section, and this leads to not only the enhancement of steady-state performance but also the suppression of those unfavorable dynamic characteristics aroused by the totally refluxed and the totally reboiled operation mode plus an intermediate-product withdrawal. Two reactive distillation systems, carrying out a hypothetical reversible reaction, A + B ↔ C + D (αA > αC > αD > αB), and the esterification of LA with MeOH, have been employed to scrutinize the dynamics and control of the RDC-DRS and RDC-DRSFS. All of the obtained results have confirmed that the RDC-DRS features serious under-dampness in its regulation path and a high degree of asymmetry in its disturbance path. The adoption of FS in the RDC-DRSFS helps to substantially K

NOTATION a = pre-exponential factor A, B, C, D = hypothetical reacting components Avp, Bvp = vapor pressure constants, kPa CC = composition controller E = activation energy, kJ/kmol F = feed flow rate, kmol/s FC = flow controller FS = feed splitting Holdup = kinetic holdup in condenser or reboiler, kmol HR = heaviest reactant KC = controller gain k = rate constant, m3/(gcat min mol) L = liquid flow rate, kmol/s LA = lactic acid LC = level controller LR = lightest reactant MeOH = methanol MLA = methyl lactate P = pressure, kPa PC = pressure controller Q = heat duty, kW R = ideal gas law constant, kJ/(kmol K) r = reaction rate, kmol/s RDC-DRS = reactive distillation column with double reactive sections RDC-DRSFS = reactive distillation column with double reactive sections plus feed splitting RDC-SRS = reactive distillation column with a single reactive section RDC-TBER = reactive distillation column with double reactive sections plus a top−bottom external recycle RHoldup = kinetic holdup on a reactive stage, kmol DOI: 10.1021/acs.iecr.7b01488 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research RR = reflux flow rate, kmol/s S = intermediate-product flow rate, kmol/s T = temperature, K TI = reset time, min V = vapor flow rate, kmol/s W = water x = liquid composition ΔHR = reaction heat, kJ/kmol ΔHV = vaporization heat, kJ/kmol α = relative volatility β = feed-splitting ratio υ = stoichiometric coefficient of a reaction

(15) Huang, K.; Zhu, F.; Ding, W.; Wang, S. J. Control of a High-Purity Ethylene Glycol Reactive Distillation Column with Insights of Process Dynamics. AIChE J. 2009, 55, 2106. (16) Liu, W.; Huang, K.; Zhang, L.; Chen, H.; Wang, S. J. Dynamics and Control of Totally Refluxed Reactive Distillation Columns. J. Process Control 2012, 22, 1182. (17) Huang, K.; Yuan, Y.; Zhang, L.; Chen, H.; Wang, S.; Liu, N. Unique Influences of Reboiler Inventory Control on the Operation of Totally Reboiled Reactive Distillation Columns. Chin. J. Chem. Eng. 2017, 25, 103.

Subscripts

B = backward COND = condenser F = forward i = component index int = intermediate product j = stage index REB = reboiler

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Dynamics and Control of Reactive Distillation Columns with Double

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