Graphical Design of Integrated Reaction and Distillation in Dividing

Article pubs.acs.org/IECR

Graphical Design of Integrated Reaction and Distillation in Dividing Wall Columns D. Kang† and Jae W. Lee*,† †

Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Republic of Korea S Supporting Information *

ABSTRACT: This work introduces a geometric design approach for the integration of reaction and distillation in a heatintegrated wall-divided column. The behavior of composition trajectories in the reaction zone of the reactive dividing wall column (RDWC) is predicted by a graphical difference point method considering both reaction and separation terms. Through the visualization, the number of stages required, liquid and vapor molar compositions, and minimum reflux or reboil ratio can be precisely estimated before performing rigorous stage calculations. With the estimated operating conditions, the feasibility of the desired reaction with the recovery of pure components in a dividing wall column can also be evaluated under both reaction equilibrium and reaction kinetic constraints. This visualization method can provide design insights into a highly complex system of integrated reaction and separation in the RDWC.

1. INTRODUCTION Distillation has been one of the most widely used technologies in the chemical industry because of the requirement of product purity. However, gradual increases in fuel prices and CO2 emission have encouraged academic and industrial communities to develop energy-saving strategies for the distillation process. Reactive distillation and dividing wall column (DWC) are representative examples for reducing energy consumption in chemical processes. Reactive distillation integrates reaction and distillation units into a single reactive separation unit (Figure 1

distillation unit further developed by putting two connected Petlyuk columns into a single column.14 The main benefits of DWC are low capital and operating costs and high thermodynamic efficiency, which come from the decrease in the number of process units and the amount of the required heat utilities.15−18 Because both reactive distillation and DWC are the state of the art technologies for saving energy and overcoming phase and reaction equilibrium limitations, the integration of them may lead to further breakthrough in industrial processes by achieving advantages of both reactive distillation and DWC. This intensification is called a reactive dividing wall column (RDWC) (Figure 1c) and has been researched for potential applications.19−22 However, because the interaction between reaction and multiple distillation operations in the RDWC is complicated and the determination of design parameters such as the total number of trays and the minimum reflux is not a trivial task, only a few reaction systems have achieved the recovery of pure components through the RDWC. One way to gain insights into the intensification of reaction and distillation is visualizing the tray-by-tray calculation of the reactive distillation system in composition space.23−32 However, there has been no framework for understanding the RDWC by visualizing column behaviors. This is because not only the interaction between reaction and distillation but also multiple distillation operations in the dividing wall column should be considered for visualizing the tray-by-tray calculation of the RDWC. Therefore, a graphical method for the RDWC will be proposed in this study by deriving cascade difference points of integrated reaction and multiple distillation operations in the

Figure 1. Schematics of (a) RD, (b) DWC, and (c) RDWC (shaded regions are reaction zones).

a). The main advantages of reactive distillation are its potential for lower capital and operating costs, higher product yields, and elimination of equilibrium limitation.1−7 Because of these merits, reactive distillation has emerged as an attractive commercial process since the methyl acetate process was commercially launched.8 DWC can also save energy by integrating multiple distillation units into one single shell (Figure 1b). Following the introduction of Petlyuk distillation,9 several thermally coupled separation units have been investigated.10−13 DWC is a © 2015 American Chemical Society

Received: Revised: Accepted: Published: 3175

December 8, 2014 March 2, 2015 March 12, 2015 March 12, 2015 DOI: 10.1021/ie5047957 Ind. Eng. Chem. Res. 2015, 54, 3175−3185

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Industrial & Engineering Chemistry Research

Figure 2. Schematics of (a) three-column sequence, (b) Petlyuk column, and (c) RDWC.

pure R and P2 are separated from the top and bottom of the lower distillation column, respectively. Therefore, pure P1, R, and P2 can be produced through the three-column sequence. Petlyuk column (Figure 2b) will operate in the same manner as the three-column sequence. The reactive distillation column and the two parallel nonreactive columns of the three-column sequence are integrated into one reactive prefractionator and the other nonreactive main column in the Petlyuk column. Therefore, pure P1, R, and P2 are recovered from the top, side, and bottom of the main column of the Petlyuk column. The behavior of the RDWC (Figure 2c) is identical to that of Petlyuk column. The forward and backward sections of the RDWC act as the prefractionator and the main column of Petlyuk column, respectively. Therefore, pure P1, P2, and R are separated through the single RDWC column. To recover pure products and unreacted reactant through the RDWC, the upper exchange streams between the forward and backward sections should not include P2. Because P2 is the heaviest component, if the upper exchange streams include P2, the side product stream may include P2 during the rectification in the backward section. Likewise, the lower exchange steams between the forward and backward sections should not contain P1. Because P1 is the lightest component, in case that the lower exchange stream contains P1, the side product stream may contain P1 during the stripping in the backward section. When the above description is visualized in composition space, the composition trajectory in the forward section approaches the R-P1 binary edge and moves away from the R-P2 binary edge in going up to upper stages (Figure 3). After that, the mixture of P1 and R is separated into pure P1 and R through the upper part of the backward section. At the same time, the composition trajectory in the forward section reaches the R-P2 binary edge and moves away from the R-P1 binary edge while moving down to lower stages (Figure 3). Then, pure R and P2 are recovered from the side and the bottom of the backward section. From the above criteria, the desired direction of the composition trajectory in the forward section is determined for recovering pure unreacted reactant and products through the RDWC. Therefore, we can evaluate the feasibility of the ternary decomposition reaction and determine the key design variables of the RDWC by visualizing the composition trajectory of the forward section in composition space.

RDWC. Different from previous graphical research which usually focuses only on reaction equilibrium of reactive distillation,23−32 this method can utilize both reaction equilibrium and reaction kinetic data for designing a RDWC. With the graphical understanding, the composition trajectory of the RDWC will be traced and its behavior will be identified. The feasibility of the RDWC under given conditions will be evaluated by this graphical tray-by-tray calculation. From the graphical interpretation, the number of needed stages, minimum reflux−reboil ratios, and liquid−vapor molar compositions of each stage will be estimated. The production of dimethyl ether from methanol dehydration in a RDWC will be employed as a real example and analyzed by this visual-aided method. Moreover, the result of the visual analysis will be compared with that of the rigorous computer-aided Aspen simulation for verifying the validity of the proposed method.

2. FEASIBILITY OF TERNARY ISOMOLAR REACTION IN A RDWC We consider the following ternary isomolar decomposition reaction in a RDWC. 2R(I) ↔ P1(L) + P2(H)

(1)

Here, R, P1, and P2 represent reactant, product 1, and product 2, respectively. Notations in the parentheses of eq 1 indicate the sequence of the relative volatilities; thus, I, L, and H are intermediate, low, and high boiling points. It is assumed that this reaction takes place in the liquid phase. Because one of the important advantages in employing the RDWC is the intensification of reaction and distillation in a single column, pure products and unreacted reactant should be recovered through a single RDWC. If not, additional separation units would be needed, and there is no economic benefit for using the RDWC in place of sequential reaction and distillation units. This feasibility criterion can be elucidated by tracing the composition trajectory in the RDWC and comparing it with the composition profile of the three-column sequence. In the threecolumn sequence (Figure 2 a), all of the light product (P1) and part of the intermediate reactant (R) are separated from the top of the reactive distillation column. Therefore, all of the heavy product (P2) and the rest of the intermediate reactant (R) are naturally recovered from the bottom of the reactive distillation column. After that, P1 and R are recovered from the top and bottom of the upper distillation column, respectively. Likewise, 3176

DOI: 10.1021/ie5047957 Ind. Eng. Chem. Res. 2015, 54, 3175−3185

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Industrial & Engineering Chemistry Research F xF = D xD + S x s + BxB − vξ

(3)

Here, ξ, vT, and v represent the overall reaction extent, the sum of the stoichiometric coefficients, and the stoichiometric vector, respectively. Because the pure unreacted reactant is recovered from the side stream of the RDWC, the molar composition of the side stream (xs) is equal to that of the feed stream (xF). To simplify eqs 2 and 3, the concepts of the pseudo feed (x F̂), the normalized reactant/product stoichiometric coefficient vectors (CR = [0,1,0], CP = [1/2,0,1/2]), and the overall reaction cascade difference point for the rectifying section (δRr)26,33,34 are employed. Therefore, eqs 2 and 3 are rearranged into eqs 4−8. Figure 3. Desired composition trajectory of the forward reactive section in a RDWC.

3. VISUALIZATION OF TERNARY ISOMOLAR REACTION UNDER REACTION EQUILIBRIUM Under the assumption of reaction equilibrium, the molar compositions of liquid and vapor are confined to liquid reaction equilibrium curves and their phase-equilibrated vapor curves in composition space. Because the total number of moles does not change during the isomolar reaction, a constant molar overflow (CMO) is assumed with a constant heat of vaporization and negligible sensible and reaction heat changes. 3.1. Reactive Rectifying Section. There are two types of RDWCs depending on the original type of Petlyuk column. One originates from the prefractionator (Figure 4), and the other originates from the postfractionator (Figure 5) of the Petlyuk column. However, when the reaction zone is located in the rectifying section of the RDWC, total material balances of both types are the same, and they are shown in eqs 2 and 3. F = D + S + B − vTξ (2)

(F − S)xF = B xB + DδR r

(4)

(D + S + B)(xF − x F̂) = −2ξ(C P − C R )

(5)

(D + S + B)(xF − x F̂) = −D(xD − δR r)

(6)

x F̂ = δR r =

D xD + S x s + BxB D+S+B

(7)

D xD + 2ξC R − 2ξC P D + 2ξ − 2ξ

(8)

The material balances of the enveloped rectifying section in both prefractionator (Figure 4) and postfractionator types (Figure 5) are the same and given in eqs 9−13. The reaction cascade difference point (δR,nr) for the enveloped rectifying section26,33,34 in Figures 4 and 5 is given below. Moreover, the concept of exchange cascade difference point for the rectifying section (δIr) is introduced. Vn + 1 + IV r = Ln + D + IL r − vTξn r

(9)

Vn + 1 yn + 1 + IV r yI r = Ln x n + D xD + IL r xI r − 2ξn r(CP − CR ) (10)

Figure 4. Balance envelope of the rectifying section in (a) Petlyuk column and (b) RDWC of prefractionator type. 3177


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Figure 5. Balance envelope of the rectifying section in (a) Petlyuk column and (b) RDWC of postfractionator type.

Vn + 1 yn + 1 + (IV r − IL r)δI r = Ln x n + DδR, n r

δI r =

(11)

IV r yI r − IL r xI r

δR, n r =

IV r − IL r

D xD + 2ξn r C R − 2ξn r C P D + 2ξn r − 2ξn r

(12)

(13)

Here, n is the number of stages counted from the top to stage n and ξnr represents the accumulated reaction extent from the top to stage n. To achieve the desired composition profile as shown in Figure 3, it is clear that vapor and liquid streams between the upper and lower parts of the backward section (yIr and xIr should contain only R. Therefore, the molar composition of δIr indicates also pure R (= xF = xs) from eq 12. Because the positions of yI, xI, and δIr are the R vertex (xs) in composition space, eq 11 is rearranged as follows. Vn + 1 yn + 1 + (IV r − IL r)x s = Ln x n + DδR, n r

(14)

As can be seen from Figure 6, we can gain insight into the stage composition behavior of the RDWC by visualizing eqs 4, 13, and 14 in composition space. The lever rule of eq 4 means that xF is between xB and δRr. Because the stoichiometric coefficients of P1 and P2 are the same and thus the equal amount of product is recovered from the top and bottom of the RDWC, it is clear that D is equal to B. Therefore, from xF and xB, as well as the lever rule of eq 4, δRr is easily determined in composition space (refer to Figure 6). We also know that the segment xDδR, n r is parallel to the line segment C R C P by rearranging eq 13. Because xD, CR, and CP are given, it is clear that δR,nr lies on the straight line passing δRr and xD, which is parallel to C R C P. When the desired forward reaction occurs in the reaction zone, the reaction extent from the top to n stage (ξnr) increases as the number of stages (n) increases. Therefore, δR,nr approaches δRr while moving down from the top to the feed stage in the forward section. When the

Figure 6. Visualization of the lever rule of stage calculation in the rectifying section under reaction equilibrium when IVr − ILr > 0. Hereafter, the dotted curve represents liquid-phase reaction equilibrium while the solid curve is its equilibrated vapor curve.

entire reaction zone is included in the enveloped rectifying section, δR,nr is equal to δRr. By visualizing eq 14 as shown in Figure 6, the liquid molar composition at stage n (xn) can be calculated from the given vapor molar composition at stage n+1 (yn+1). For example, when IVr − ILr is positive, eq 14 geometrically implies that the segments yn + 1x s and x nδR, n r intersect at a combined point (*) by the lever rule. Moreover, the length ratio of yn + 1* to *x s is the ratio of IVr − ILr to Vn+1 and that of x n* to *δR, n r is the ratio 3178


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Industrial & Engineering Chemistry Research of D to Ln. Because IVr − ILr can be calculated from the mass balance of the RDWC, the length ratio of IVr − ILr to Vn+1 is calculated from the given stream flows (refer to section S1 of Supporting Information). Likewise, the length ratio of D to Ln is calculated from a specified reflux ratio. Therefore, the combined point (*) is determined from the calculated length ratio of IVr − ILr to Vn+1 as well as known xs and yn+1. Because xn is confined to reaction equilibrium curves and possible δR,nr are on the straight line passing δRr and xD, we can locate δR,nr and xn from the calculated length ratio of D to Ln and the known combined point (*). Thus, the liquid molar composition and reaction extent of an arbitrary stage can be calculated from a given vapor molar composition at one stage below (Figure 6). Figure 7 visualizes eq 14 when IVr − ILr has a negative value. Compared with the case when IVr − ILr has a positive value,

Figure 8. Visualization of the tray-by-tray calculation of the rectifying section under reaction equilibrium when IVr − ILr < 0 (Ln/D = 7, Vn+1/ (ILr − IVr) = 8.3).

At the feed stage, the vapor molar composition, yf, is calculated from phase equilibrium of the given liquid molar composition, xf, and then the combined point of the above-feed stage (*f−1) is located from Vf /(IVr − ILr) by the lever rule of eq 14 as shown in Figure 9. Because the entire reaction zone in the rectifying section is included in the enveloped region at the above-feed stage, the reaction cascade difference point, δR,f−1r, is equal to the overall reaction cascade difference point for the rectifying section, δRr. Therefore, the liquid molar composition

Figure 7. Visualization of the lever rule of stage calculation in the rectifying section under reaction equilibrium when IVr − ILr < 0.

only the position of combined point (*) is changed. From the graphical illustration in Figures 6 and 7, the feed-to-top tray-bytray calculation of the forward section in the RDWC is possible using reaction and phase equilibrium data. Thus, we can determine the number of rectifying stages required for the forward section under given operating conditions to approach the R-P1 binary edge. If too many stages are needed to approach the desired binary edge, the operating conditions should be adjusted. Figure 8 portrays the tray-by-tray calculation when starting from stage 5 under the conditions that the length ratio of Ln to D is equal to 7 and the length ratio of Vn+1 to ILr − IVr is equal to 8.3. As can be seen, the number of stages required, reaction extent, and liquid and vapor molar compositions of each stage are calculated. Before starting the stage calculation from the feed to top stage, the minimum operating ratios can be calculated from the feasibility criterion that the composition trajectory should move away from the R-P2 binary edge and approach the R-P1 binary edge while going up to upper stages, as explained in section 2.

Figure 9. Minimum operating variables of the rectifying section under feed-pinch of reaction equilibrium. 3179


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Figure 10. Visualization of the lever rule of stage calculation in the rectifying section under the rate-based reaction model when (a) IVr − ILr > 0 or when (b) IVr − ILr < 0.

of the above-feed stage, xf−1, is easily determined from *f−1, δR,f−1r, and Lf−1/D by visualizing eq 14. The minimum operating ratios such as Lf−1/D and Vf/(IVr − ILr) are calculated when we assume that xf is equal to xf−1, which is called a feed-pinch. Under this feed-pinch assumption, because we know the positions of all points in eq 14, yf, δR,f−1r = δRr, xf−1 = xf, and xF = xS, the minimum operating ratios under the feed-pinch, (Lf−1/D)pinch and (Vf/(IVr − ILr))pinch, are determined from *f−1, which is the intersection point between xFyf and δR, f−1r x f−1. For example, when (Vf/(IVr − ILr))pinch has a positive value, the real operating value, Vf/(IVr − ILr), should be larger than (Vf/(IVr − ILr))pinch. Then, *f−1 is right-shifted on the line of xFyf and xf−1 is more distant from the R-P2 binary edge and closer to the R-P1 binary edge than xf, as can be seen in Figure 9. Moreover, the real operating value, Lf−1/D, naturally becomes larger than (Lf−1/D)pinch to satisfy the same criteria. Because CMO is assumed with a constant heat of vaporization and negligible sensible and reaction heat changes, the operating ratios calculated under feed-pinch such as (Vf/(IVr − ILr))pinch and (Lf−1/D)pinch can provide a guideline for these values in the stage calculation. Therefore, before starting the tray-by-tray calculation from the feed stage, the minimum operating ratios can be calculated through the visualization method. When the reaction zone is located in the stripping section of the RDWC, the derivations and visualizations of minimum operating ratios and stage calculations are shown in section S3 of Supporting Information.

reaction kinetic equation is needed for calculating the reaction extent instead of using reaction equilibrium information in addition to given operating conditions such as Ln/D and Vn+1/ (ILr − IVr) or Vm+1/B and Lm/(ILs − IVs). 4.1. Rectifying Section. In the rate-based reaction model, xn is not on the reaction equilibrium curve but can be located anywhere in composition space. Therefore, δR,nr should be calculated from the reaction kinetics, not from the reaction equilibrium. When the reaction occurs only in the rectifying section, because the length ratio of δR, n r xD to δR r xD is equal to the ratio of the accumulated reaction extent of stage n to the total reaction extent (ξnr/ξ) by eqs 8 and 13, δR,nr is determined by ξnr, which is different according to the catalyst holdup and reaction rate. When the feed-to-top stage calculation is performed from yn+1, the reaction extent (ξn+1r − ξnr) at stage n + 1 is calculated from the given reaction kinetics (reaction rate and reactive liquid holdup) as given below. ξn + 1r − ξn r = HL, n + 1*r = HL, n + 1*kC R1, n + 1aC R2, n + 1b

(15)

Here, HL,n+1 and k represent the liquid holdup of stage n + 1 and reaction rate constant, respectively. CR1,n+1 and CR2,n+1 are the concentrations of reactants at stage n + 1 which is calculated from xn+1. When starting from the feed stage, we can locate δR,nr by shifting as much as (ξn+1r − ξnr)/ξ from the known δR,n+1r in the direction of xD. Therefore, the accumulated reaction extents, ξfr = ξ = D or B, ξf−1r = ξfr − (ξfr − ξf−1r), ..., are calculated in sequence through the tray-by-tray calculation while going up to upper stages. After determining δR,nr, the combined point (*) is determined from the length ratio of IVr − ILr to Vn+1 as well as yn+1 and xs. Then, xn (refer to Figure 10) is located from the length ratio of D to Ln as well as the calculated combined point (*) and δR,nr by the lever rule of eq 14 (refer to Figure 10a). When IVr − ILr is positive or negative, the visualization of eq 14 in the rate-based reaction model is shown in panel a or b of Figure 10, respectively. The example of the stage calculation

4. VISUALIZATION OF TERNARY ISOMOLAR REACTION WITH A REACTION RATE-BASED MODEL Under the control of reaction rate, liquid molar compositions in the reaction zone are not confined to reaction equilibrium curves but determined by reaction kinetic. Therefore, the 3180


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Industrial & Engineering Chemistry Research starting from stage 5 under the conditions that Ln/D = 6 and Vn+1/(ILr − IVr) = 5 is also visualized in Figure 11.

located outside the shaded region where the molar composition is closer to RP2 or more distant from RP1 than xf, which is called an infeasible region. To do this, Vf/(IVr − ILr) should be larger than (Vf/(ILr − IVr))pinch determined under the feed-pinch, which assumes that xf−1 is equal to xf. Then, *f−1 is right-shifted and xf−1 is located outside the infeasible region. After a ratio of Vf/(IVr − ILr) larger than (Vf/(ILr − IVr))pinch is specified, the minimum value of Lf−1/D is calculated from Figure 12b. To locate xf−1 outside the hatched region, Lf−1/D should be larger than (Lf−1/D)pinch. Then, *f − 1x f − 1 becomes shorter and xf−1 is located outside the infeasible region. Because CMO is assumed with a constant heat of vaporization and negligible sensible and reaction heat changes, the operating ratios calculated at the feed stage under feed-pinch such as (Vf/ (IVr − ILr))pinch and (Lf−1/D)pinch can provide guideline values of these ratios in the stage calculation. For the reaction zone located in the stripping section under the rate-based reaction model of the RDWC, the visualization method is shown in section S4 of Supporting Information.

5. RATE-BASED CASE STUDY: DIMETHYL ETHER SYNTHESIZED FROM METHANOL DEHYDRATION To validate the proposed visualization method under the ratebased reaction model, the synthesis of dimethyl ether (DME) by methanol (MeOH) dehydration in the RDWC22 was visualized through the above procedures, and the results of them were verified by ASPEN Plus simulation. The dehydration of MeOH produces DME and water (W) as follows.

Figure 11. Visualization of the tray-by-tray calculation of the rectifying section under the rate-based reaction model when IVr − ILr < 0 (Ln/D = 6, Vn+1/(ILr − IVr) = 5).

Like the equilibrium case, the composition trajectory should be away from the R-P2 binary edge and approach the R-P1 binary edge while going up to upper stages. From these constraints, the minimum operating variables such as Ln/D and Vn+1/(IVr − ILr) are calculated before starting tray-by-tray calculations. As can be seen in Figure 12(a), xf−1 should be

2MeOH(I) ↔ DME(L) + W(H)

(16)

The binary parameter set of UNIQAC35 was employed to calculate vapor−liquid equilibria, and it was determined that there are no azeotropes. When an ion-exchange resin is used for

Figure 12. Minimum operating variables under feed-pinch of the rate-based reaction model. The hatched region is the infeasible region for xf−1. 3181


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Figure 13. Schematic of the RDWC for the synthesis of dimethyl ether (DME) by methanol (MeOH) dehydration ((a), Petlyuk column, (b) RDWC).

set the value of Vm+1/B as 3. The summary of operating constraints with various values of xf is shown in Table 1.

MeOH dehydration in the liquid phase, the kinetic data were given in the same operating conditions as follows.35 r = kWcatC MeOH1.51C W −0.51

(17)

⎛ −E ⎞ k = A 0 exp⎜ a ⎟ ⎝ RT ⎠

(18)

Table 1. Operating Constraints with Various Values of xf case xf

Here, the Arrhenius factor, A0, is equal to 5.19 × 109 m3 kg cat−1 s−1 and the activation energy, Ea, is equal to 133.8 kJ mol−1. As the relative volatility between DME and MeOH is larger than that between MeOH and W, the reaction zone was located in the stripping section.26 We employed the main column with the postfractionator model (Figure S5 of Supporting Information) following previous work.22 The schematic of this process is shown in Figure 13. Before the tray-by-tray calculation was performed, the minimum values of Vm+1/B and Lm/(ILs − IVs) were calculated from the vapor and liquid molar compositions of the feed stage, yf and xf. Although we could not predict the exact values of yf and xf, it could be estimated that xf is almost pure MeOH and includes a negligible amount of W because pure liquid MeOH was supplied to the feed stage and the composition trajectory approaches the MeOH−DME binary edge at the feed stage. In this case, we chose three different points of xf = [0.92, 0.075, 0.005]T, [0.90, 0.095, 0.005]T, and [0.88, 0.115, 0.005]T (=[MeOH, DME, W]T). From the proposed method in section S4 of Supporting Information, the minimum value of Lm/(ILs − IVs) was calculated as 0.31, 0.37, and 0.5, respectively. To increase the value of Lm/(ILs − IVs) from the minimum value, we can increase Lm or decrease ILs − IVs. Because the large value of Lm is related to the high operating cost, it is more economical to decrease ILs − IVs than to increase Lm. Therefore, we set ILs − IVs as zero because it was easy to visualize. After the value of Lm/(ILs − IVs) was determined, the minimum value of Vm+1/B was also calculated as 2.95, 2.63, and 2.53 through the proposed method in section S4 of Supporting Information. Therefore, we

min. Lm/(ILs − IVs) set Lm/(ILs − IVs) min. Vm+1/B set Vm+1/B

1

2

3

[0.92, 0.075, 0.005] 0.31

[0.90, 0.095, 0.005] 0.37

[0.88, 0.115, 0.005] 0.5

∞ 2.95 3

∞ 2.63 3

∞ 2.53 3

Under the selected operating conditions and the starting points above, the tray-by-tray calculations in composition space were done for the stripping section under the rate-based model (for the material balance equations, refer to section S4 of Supporting Information). The detail of the tray-by-tray calculation of case 1 is shown in Figure 14. Other tray-bytray calculations are portrayed in section S5 of Supporting Information. As can be seen, they had nearly identical liquid and vapor trajectories and 24 stages in total were needed to approach the desired binary edge in all of the cases. From this similarity, the estimation of xf could be validated. To prove the validity of the proposed graphical method, the computer-aided simulation using ASPEN Plus was also done (Table 2). During the simulation, the amount of interchange streams and reflux ratio were specified to maintain similar to those of the tray-by-tray calculation in Figure 14 for the fair comparison. Although the CMO assumption could not completely be valid during the computer-aided simulation, Vm+1/B and ILs − IVs had slight deviations compared to that of the visual-aided case (Figure 14) throughout the entire stages of the reactive section (Table 1). The liquid and vapor composition trajectories and reaction extents of the visualization method and the computer-aided 3182


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Figure 15. Visualization of the ASPEN Plus simulation for the DME synthesis by MeOH dehydration.

Figure 14. Visualization of the tray-by-tray calculation for the DME synthesis by MeOH dehydration (case 1 in Table 1).

Table 2. Design Parameters and Main Results of ASPEN Simulation system no. of divided stages divided stage MeOH feed stage exchange streams (from forward to backward section) reaction zone operating pressure (bar) (ILs − IVs)/Lm Vm+1/B MeOH conversion DME purity (mole frac) water purity (mole frac) MeOH purity (mole frac)

composition trajectory and reaction extents in the reaction zone can be precisely predicted before performing rigorous calculations. Moreover, design insights into the minimum operating ratios and required number of stages in the reaction zone can be obtained with this proposed method. The application of this method for the dimethyl ether production system clearly elucidated the validity of this visualization method. When starting from the selected operating conditions based on the calculated minimum values of them, the number of stages required for the desired extent of reaction was reliably estimated in the dimethyl ether production system. Therefore, the proposed method can be used for understanding the behavior of composition trajectory, evaluating the feasibility of the desired reaction, and determining operating variables when designing the RDWC before doing detailed experiments. However, this method has been applied only to the ternary isomolar reaction with the intermediate volatile reactant. Therefore, the scope of the graphical design method will be enlarged to develop a general form of this method. Using the concept of reaction difference point and projected composition space, we will extend it to its general form by accommodating various systems such as nonisomolar reaction and multicomponent cases in a dividing wall column.

simulation 24 8−31 8 L8 (LI in Figure 13); V31(V I in Figure 13) 9−30 10 −0.00489 ∼ −0.00673 2.56−3.34 51.35 1.000 0.996 0.996

simulation are shown in Figures 14 and 15, respectively. As can be seen from these figures, the composition trajectory can approach the desired binary edges at the top exchange stream (MeOH−DME at stage 8) and the bottom exchange stream (MeOH−W at stage 31). Moreover, when the same number of stages was used, the liquid and vapor molar compositions and reaction extent of an arbitrary stage have almost identical values in both cases. Therefore, it can be concluded that the feasibility of the RDWC for the desired reaction can be evaluated through the visual-aided method. Furthermore, the number of needed stages in the reactive zone, the behavior of the composition trajectory, and the minimum operating conditions can be estimated through the proposed visualization of the tray-by-tray calculation before performing rigorous simulations.

■

ASSOCIATED CONTENT

S Supporting Information *

Additional information on the determination of reactive stripping material balances and minimum operating ratios. This material is available free of charge via the Internet at http://pubs.acs.org.

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6. CONCLUSION We have developed a graphical method for designing a RDWC and demonstrated the visualization method using both reaction equilibrium and rate-based constraints. The behavior of the

AUTHOR INFORMATION

Corresponding Author

*Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, 3183


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Industrial & Engineering Chemistry Research Greek Letters

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v = stoichiometric coefficient vector vT = sum of stoichiometric coefficients ξ = overall molar reaction extent ξnr = accumulated molar reaction extent of the rectifying section from the top to stage n ξm+1s = accumulated molar reaction extent of the stripping section from the bottom to stage m + 1 δRr = total reaction cascade difference vector of the rectifying section δR,nr = partial reaction cascade difference vector of the rectifying section at stage n δIr = exchange cascade difference vector of the rectifying section δRs = total reaction cascade difference vector of the stripping section δR,m+1s = partial reaction cascade difference vector of the stripping section at stage m + 1 δIs = exchange cascade difference vector of the stripping section

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by both the Midcareer Researcher Program through NRF grant (2014R1A2A2A01007076) and the Advanced Biomass R&D Center (ABC-20110031354) as the Global Frontier Project funded by the Ministry of Science, ICT and Future Planning.

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NOMENCLATURE A0 = Arrhenius factor B = molar flow rate of a bottom product Ci,n = molar concentration of component i at stage n CP = normalized product stoichiometric coefficient vector CR = normalized reactant stoichiometric coefficient vector D = molar flow rate of a distillate Ea = activation energy F = molar flow rate of a feed f = fraction vaporized of the feed HL,n = molar liquid holdup of stage n ILr = molar flow rate of a liquid leaving the rectifying section at backward section ILs = molar flow rate of a liquid entering the stripping section at backward section IVr = molar flow rate of a vapor entering the rectifying section at backward section IVs = molar flow rate of a vapor leaving the stripping section at backward section k = rate constant LF = molar flow rate of a liquid in the feed Ln = molar flow rate of a liquid leaving stage n LI = molar flow rate of a upper exchange liquid L̅ I = molar flow rate of a lower exchange liquid q = fraction liquefied of the feed R = gas constant S = molar flow rate of a side stream T = temperature VF = molar flow rate of a vapor in the feed Vn = molar flow rate of a vapor leaving stage n VI = molar flow rate of a upper exchange vapor V̅ I = molar flow rate of a lower exchange vapor xB = molar composition vector of a bottom product xD = molar composition vector of a distillate xF = molar composition vector of a feed xf = molar composition vector of a liquid leaving feed stage x F̂ = molar composition vector of a pseudo feed xIr = molar composition vector of a liquid leaving the rectifying section at backward section xIs = molar composition vector of a liquid leaving the stripping section at backward section xn = molar composition vector of a liquid leaving stage n xs = molar composition vector of a side stream yf = molar composition vector of a vapor leaving feed stage yIr = molar composition vector of a vapor entering the rectifying section at backward section yIs = molar composition vector of a vapor leaving the stripping section at backward section yn = molar composition vector of a vapor leaving stage n

Abbreviations

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DME = dimethyl ether MeOH = methanol W = water

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Graphical Design of Integrated Reaction and Distillation in Dividing

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