Shortcut Method for the Design of Reactive Dividing Wall Column

Article pubs.acs.org/IECR

Shortcut Method for the Design of Reactive Dividing Wall Column Lanyi Sun* and Xinxin Bi State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Qingdao, Shandong 266580, China S Supporting Information *

ABSTRACT: The minimum vapor flow method and Vmin diagram are applied to the design of a reactive dividing wall column (RDWC) in this work. A shortcut design method for the conventional dividing wall columns based on the Underwood equations has been extended by introducing a new parameter that eliminates the effects of the reaction to allow conceptual design of the RDWC. Taking the syntheses of methyl tert-butyl ether (MTBE), ethyl tert-butyl ether (ETBE), and dimethyl ether (DME) as design cases, the results show that the minimum vapor flow method and the Vmin diagram can be well applied to the conceptual design of a RDWC in different reaction systems. first time, which were in agreement with those obtained using steady state simulations. Application of RDWC to the production of biodiesel11−14 was also studied with only 15% excess of methanol being added to completely convert the fatty acids feedstock. In the dimethyl ether production process, RDWC had a better performance of 12−58% energy savings, up to 60% CO2 emission reduction, and up to 30% lower total annual costs compared with the RD process.15 Although numerous studies had been done for the simulation of RDWC, the design issues went largely unnoticed by researchers. Most of the design approaches for thermally coupled reactive columns were performed by a trial-and-error procedure, with the exception for the graphical-method work of Kiss et al.5 Daniel et al.16 reported a novel approach for the conceptual design of RDWC using the graphically based boundary value method (BVM) with the chemical equilibrium on every reactive stage of the column being assumed. Nevertheless, graphical methods for designing the RDWC with more than four components became difficult or even infeasible. Gómez-Castro et al.17 proposed an approach considering the mass and energy balances and the use of Fenske−Underwood−Gilliland equations to determine the number of separation stages. Two strategies were employed: the first approach formulated the complete set of equations as a nonlinear programming (NLP) problem to minimize the heat duty, and the second strategy only formulated the mass and energy balances of the various sections of the column as a NLP problem, and then Fenske−Underwood−Gilliland equations were used to calculate the remaining design variables. The methods mentioned above were all available but appeared to be too complicated. A method based on the Underwood equations called minimum vapor flow method is presented in this work. The Underwood equations have been applied successfully by many authors for analysis of multicomponent distillation in the early literature. Minimum energy expressions for Petlyuk arrangements with three components

1. INTRODUCTION Recent research efforts in the development of production processes show an increasing concern for the reduction of environmental impact due to human activity. In those approaches, process intensification plays an important role. Process intensification, which is an area of chemical engineering, mainly focuses on the developing production alternatives to achieve the goal of reducing energy requirements and capital cost. To achieve that, strategies including multitask equipment and process integration have been employed. The reactive dividing wall column (RDWC), which combines the reactive distillation (RD) with the dividing wall column (DWC), is a highly integrated process leading to a step toward ultimate sustainability in process industries. The RDWC was first recognized and claimed by Kaibel in his 1984 patent.1 Up to now, just very few industrial applications of RDWC have been reported. However, this process has been theoretically analyzed by many scholars.2 Comprehensive papers on RDWC modeling were published by the group of Kenig.3,4 The performance of a RDWC was theoretically studied for different systems with the rate-based approach. It was found that RDWC had great advantages in high conversion, selectivity, and product purity and less energy consumption. Kiss et al.5 described a study undertaken to arrive at RDWC design for an industrial case within Akzo Nobel Chemicals, which indicated that savings with respect to conventional alternative would be 35% on capital and 15% on the energy side. Sun et al.6,7 reported the design, optimization, and control of a RDWC for the hydrolysis of methyl acetate. The results showed that energy savings of over 20% were possible. Lee et al.8 proposed a thermally coupled design for the production of isopropyl acetate to further reduce the energy requirement. The simulation results showed that the energy savings of more than 23% can be realized using the proposed thermally coupled design. The RD with thermal coupling was demonstrated by Cheng et al.9 for the synthesis of diphenyl carbonate, and the steady state simulation results revealed that not only the operating cost but also the capital cost could be decreased by using the thermal coupling technology. Delgado-Delgado et al.10 presented experimental results for the production of ethyl acetate in a RDWC for the © 2014 American Chemical Society

Received: Revised: Accepted: Published: 2340

July 8, 2013 January 5, 2014 January 17, 2014 January 17, 2014 dx.doi.org/10.1021/ie402157x | Ind. Eng. Chem. Res. 2014, 53, 2340−2347

Industrial & Engineering Chemistry Research

Article

⎡ di − 1 α z ⎤ i i ⎢ −∑ ⎥ ⎢ i = 1 αi − θd1 ⎥ ⎢ ⎥ ⎢ di − 1 α z ⎥ i i ⎢ −∑ ⎥ Z = ⎢ i = 1 αi − θd2 ⎥ ⎢ ⎥ ⋮ ⎢ ⎥ ⎢ di − 1 ⎥ αizi ⎢− ⎥ ⎢ ∑ α −θ ⎥ dNd − 1 ⎦ ⎣ i=1 i

had been presented by Fidkowski and Krolikowski18 and Carlberg and Westerberg.19,20 Then the minimum vapor flow method was applied to the conceptual design of DWC by Halvorsen.21 In this work a step further has been made by extending the validity of this rather simple and effective method to a RDWC.

2. DESCRIPTION OF THE MINIMUM VAPOR FLOW METHOD FOR THE DESIGN OF A RDWC 2.1. Minimum Vapor Flow Method in the Conventional Column. Halvorsen21 proposed a simplistic but surprisingly effective approach to the conceptual design of DWC in his thesis. Needed input parameters are feed composition, feed quality expressed by the liquid fraction, K values, and desired product purities or recoveries. The Underwood equations are then used to determine the minimum vapor flow, needed for separation of all possible pairs of feed components, to any achievable degree of purity. The computation procedures of minimum vapor flow method are as follows. The Underwood equation can be stated in the form Nc

V=

∑ i=1

αixi , D (αi − θ )

Nc

D=

∑ i=1

αiri , Dzi (αi − θ )

The elements in each column of M arise from the terms related to the distributing components in eq 1, and one row corresponds to each active root. Z contains the part of eq 1 arising from the nondistributing light components with the recovery one in the top. If the product split is specified as one degree of freedom, D/F is introduced as an extra variable. D/F =

αd2z d2 ⎡ αd1z d1 ⎢ αd2 − θd1 ⎢ αd1 − θd1 ⎢ α z αd2z d2 d1 d1 ⎢ ⎢ αd − θ d αd 2 − θ d 2 1 2 ⎢ ⎢ ⋮ ⋮ ⎢ α z α z d d d 1 1 2 d2 ⎢ ⎢ αd − θ d α θdNd − 1 − d2 Nd − 1 ⎢ 1 ⎢⎣ z d1 z d2

(1)

where F (kmol/h) is the molar feed flow rate, V (kmol/h) is the molar vapor flow rate, D (kmol/h) is the molar liquid flow rate, Nc is the number of components, αi is the relative volatility of component i to the key component, xi,D is the molar fraction of component i in the top of the column, ri,D is the recovery of component i in the top of the column, zi is the molar fraction of component i in the feed, and θ is the Underwood equation root of the rectifying section. A vector X is defined by containing the recoveries of distributing components and the normalized vapor flow in the top section:

⎡ di − 1 α z ⎤ i i ⎢ −∑ ⎥ ⎢ αi − θd1 ⎥ i=1 ⎢ ⎥ ⎢ di − 1 α z ⎥ i i ⎢ −∑ ⎥ ⎢ i = 1 αi − θd2 ⎥ ⎢ ⎥ =⎢ ⋮ ⎥ ⎢ di − 1 ⎥ αizi ⎢ ⎥ − ∑ ⎢ ⎥ α θ − i d Nd − 1 ⎥ ⎢ i=1 ⎢ ⎥ di − 1 ⎢ ⎥ − ∑ zi ⎢ ⎥ ⎣ ⎦ i=1

(2)

where the subscript T denotes the rectifying section, d is the distributing component, and Nd is the number of distributing components. Equation 1 can be written as a linear equation set in matrix form

with αd2z d2 ⎡ αd1z d1 ⎢ αd2 − θd1 ⎢ αd1 − θd1 ⎢ α z αd2z d2 d1 d1 ⎢ ⎢ αd 2 − θ d 2 M = αd1 − θd2 ⎢ ⎢ ⋮ ⋮ ⎢ α z αd2z d2 d1 d1 ⎢ ⎢⎣ αd − θd αd2 − θdNd−1 1 Nd − 1

··· ··· ⋮ ···

αdNdz dNd αdNd − θd1 αdNdz dNd αdNd − θd2 ⋮ αdNdz dNd αdNd − θdNd−1

(6)

··· ··· ⋮ ··· ···

αdNdz dNd αdNd − θd1 αdNdz dNd αdNd − θd2 ⋮ αdNdz dNd αdNd − θdNd − 1 z dNd

⎤ −1 0 ⎥ ⎥⎡ rd1,T ⎤ ⎥ ⎥⎢ r ⎢ d ,T ⎥ − 1 0 ⎥⎢ 2 ⎥ ⎥ ⋮ ⎥ ⎥⎢ ⋮ ⋮ ⎥⎢ rdNd ,T ⎥ ⎥ ⎥⎢ ⎢ V /F ⎥ − 1 0 ⎥⎢ T ⎥ ⎥ ⎥⎣ D / F ⎦ 0 −1⎥⎦

(7)

The minimum-energy mountain diagram (Vmin diagram) can be plotted according to eq 7. From the Vmin diagram, the minimum vapor flow in each section of the column can be read directly. 2.2. Minimum Vapor Flow Method in a RDWC. For the design of a RD column, only the operating minimum reflux ratio and the number of theoretical stages in each section should be calculated. For the DWC, the interconnected stream flows also should be considered. The minimum vapor flow method, which has been tested to be available and simple in DWC by Halvorsen,21 is proved feasible to design a RDWC in this work. Figure 1 shows the configurations of the RDWC and the Petlyuk arrangement, with the shaded region being the infinite number of stages. It is assumed that the reaction occurs only in the top section of the prefractionator (column C1).22 In

(3)

M·X = Z

∑ ri ,Tzi

Then eq 3 can be extended to the form of eq 7.

F

⎡ V ⎤T X = ⎢rd1,T , rd2 ,T , ..., rdNd ,T , T ⎥ ⎣ F⎦

(5)

⎤ −1⎥ ⎥ ⎥ −1⎥ ⎥ ⎥ ⋮⎥ ⎥ −1⎥ ⎥⎦ (4) 2341

dx.doi.org/10.1021/ie402157x | Ind. Eng. Chem. Res. 2014, 53, 2340−2347


Article

The relative volatility can be calculated by eq 12. αi , ∞ = K i , ∞/K r , ∞

(12)

When the definition of relative volatility (with respect to the key component r) is incorporated, a new variable, ϕ = (1/ Kr,∞)(Lr,∞/V), called the absorption factor, is introduced. The sum of the compositions in the vapor stream must be 1, so eq 13 can be obtained. VT = D

(

αi , ∞ xi , D −

Nc

∑

νi ξk ,T −νk D

)

αi , ∞ − ϕ

i=1

(13)

A new variable related to the reaction, Ci, the reactant conversion or the production yield of component i, is introduced. Thus eq 14 can be obtained.

Figure 1. Configurations of the RDWC and the integrated Petlyuk arrangement.

Nc

VT =

addition, the mass balance envelope in the rectifying section of column C1 is presented in Figure 2.

∑

αi , ∞(xi , DD + CiziF ) (αi , ∞ − ϕ)

i=1

Nc

=

∑

αi , ∞(ri , DziF + CiziF ) (αi , ∞ − ϕ)

i=1

(14)

Equation 14 can be rearranged by introducing an expression representing the improved recovery r′i due to simultaneous reaction and distillation, defined as

ri′ = ri , D + Ci Nc

VT =

∑ i=1

(15)

αi , ∞ri′zi (αi , ∞ − ϕ)

F (16)

Equation 16 can be extended as eq 17. αd1z d1 αd2z d2 ⎡ ⎢ α ϕ α − d2 − ϕd1 ⎢ d1 d1 ⎢ αd1z d1 αd2z d2 ⎢ ⎢ αd − ϕ α d2 − ϕd2 d2 1 ⎢ ⎢ ⋮ ⋮ ⎢ α α z d1 d1 d2z d2 ⎢ ⎢α − ϕ αd2 − ϕd dNd − 1 Nd − 1 ⎢ d1 ⎢ z d1 z d2 ⎣

Figure 2. Mass balance envelope in the rectifying section of column C1.

In the prefractionator, the mass balance equation for component i around the rectifying section of column C1 is ν VTyi , ∞ = L∞xi , ∞ + Dxi , D − i ξr ,T −νr (8)

⎡ di − 1 α z ⎤ i i ⎢ −∑ ⎥ ⎢ αi − ϕd ⎥ i=1 1 ⎢ ⎥ ⎢ di − 1 α z ⎥ i i ⎢ −∑ ⎥ ⎢ i = 1 αi − ϕd ⎥ 2 ⎢ ⎥ =⎢ ⎥ ⋮ ⎢ d −1 ⎥ i ⎢ ⎥ αizi ⎢− ∑ ⎥ α − ϕ dNd − 1 ⎥ ⎢ i=1 i ⎢ ⎥ di − 1 ⎢ ⎥ − ∑ zi ⎢ ⎥ ⎣ ⎦ i=1

with

V1yi ,1 = L1xi ,1 + Dxi , D

(9)

where L (kmol/h) is the molar liquid flow rate, xi is the liquid molar fraction of component i, yi is the molar vapor fraction of component i, ν is the stoichiometric coefficient, and ξ is the reaction extent; the index ∞ has been assigned to the streams coming from the section with an infinite number of stages. It is also considered that the liquid−vapor equilibrium on the last stage of the rectifying section is given by xi , ∞ = yi , ∞ /K i , ∞

yi , ∞

VT = D

αdNdz dNd αdNd − ϕd

1

··· ⋮ ··· ···

αdNdz dNd αdNd − ϕd

2

⋮ αdNdz dNd αdNd − ϕd z dNd

Nd − 1

⎤ −1 0 ⎥ ⎤ ⎡ ⎥⎢ rd′1,T ⎥ ⎥⎢ r′ ⎥ −1 0 ⎥⎢ d2 ,T ⎥ ⎥⎢ ⎥ ⎥⎢ ⋮ ⎥ ⋮ ⋮ ⎥⎢ rd′Nd ,T ⎥ ⎥⎢ ⎥ ⎥ −1 0 ⎥⎢ VT/F ⎥ ⎥ ⎢ ⎥⎣ D / F ⎦ ⎥ 0 −1⎦

(17)

Applying the material balance to the bottom section (stripping section) of column C1, eq 18 can be obtained.

(10)

where K is the vapor−liquid equilibrium constant. When eq 10 is substituted into eq 8 and is rearranged, ν ξ xi , D − −νi Dk ,T k 1 L∞ 1− K V i ,∞

···

−

VB = B

Nc

∑ i=1

αi′, ∞xi ,B αi′, ∞ − ϕ′

(18)

where the subscript B denotes the stripping section and B (kmol/h) is the molar flow rate of the bottom product.

(11) 2342



Article

Combining eq 13 and eq 18 and taking into account that αi,∞ = α′i,∞ and ϕ = ϕ′, eq 19 can be obtained. Nc

VT − VB =

∑

(

αi , ∞ Dxi , D −

νi ξ −νr r,T

)

+ Bxi ,B

αi , ∞ − ϕ

i=1

(19)

When the feed liquid fraction q is introduced, eq 20 can be obtained from the material balance on the feed stage of C1. VT − VB = F(1 − q)

(20)

The component mass balance equation for the whole column of C1 is shown as eq 21. ν Fzi = Dxi , D − i ξr ,T + Bxi , D −νr (21)

Figure 3. Simulation flowsheet for a RDWC process of etherification reaction in Aspen Plus.

Etherification takes place at 650 kPa, and the reaction is reversible. However, the reverse reaction effects are small and a yield higher than 90% can be obtained. The analyzed system includes three components involved in the reaction (IC4, MeOH, and MTBE). The two feed conditions are shown in Table 2. Here, we illustrate the calculation processes by applying the equations to feed I. The roots of the feed equation are θA = 1.73 and θB = 0.73, which can be calculated by eq 23 taking into account that q = 1. Assuming the sharp split between components A and B, one of the peak points can be figured out.

Combining eq 20 and eq 21, eq 22 can be obtained. Nc

1−q=

∑ i=1

αi , ∞zi αi , ∞ − ϕ

(22)

When ϕ is replaced by θ, we can get the feed equation of a RDWC as shown in eq 23. Nc

1−q=

∑ i=1

αizi αi − θ

(23)

The computation procedure to plot the Vmin diagram is as follows. First, the reaction extent ξ and the reactant conversion C are calculated. The equilibrium conversion is assumed in each stage in this work. Second, the roots of the feed equation are calculated, namely, eq 23. Finally, the Vmin diagram is plotted. The computation procedure for RDWC is similar to the conventional column. 2.3. Calculation of the Number of Stages. The minimum number of stages for each section of a RDWC is calculated through the Fenske equation in a way similar to that in the nonreactive case, which is a significant assumption and the main source of error in this method.

′ , rB,T ′ ] = [1, 0] PAB: [rA,T

(25)

⎡ αAzA ⎤ [D/F , VT,min /F ] = ⎢zA , ⎥ = [0.3, 0.712] αA − θA ⎦ ⎣

(26)

Similarly, we can get other peak points at the operation of the sharp split between B and C and the sharp split between A and C. ′ , rC,T ′ ] = [1, 0] PBC: [rB,T

(27)

⎡ αBz B ⎤ αAzA [D/F , VT,min /F ] = ⎢zA + z B , + ⎥ = [0.7, 1.856] αA − θA αB − θB ⎦ ⎣

(28)

′ , rC,T ′ ] = [1, 0] PAC: [rA,T

3. CASE STUDY Three reactive systems are investigated to demonstrate the effectiveness of the proposed method on the RDWC design, and different feed compositions are also tested for each system. In all cases, the column feed is assumed to be saturated liquid, and 1.05Rmin is used to fix the operating reflux ratio. Given the pressure and temperature conditions, the reactions occur in a single liquid phase; thus, only the vapor−liquid equilibrium (VLE) calculations are considered for the phase equilibrium. The simulation flowsheet of the etherification reaction in the RDWC is shown in Figure 3, and a detailed analysis of each case study is presented in the following subsections. 3.1. Synthesis of Methyl tert-Butyl Ether. The first case study is the synthesis of methyl tert-butyl ether (MTBE), and the chemical reaction proceeds as indicated by eq 24.

(29)

⎡ α βz ⎤ αAzA [D/F , VT,min /F ] = ⎢zA + βz B , + B B ⎥ αA − θB αB − θB ⎦ ⎣ (30)

with β=−

αAzA(αB − θA )(αB − θB) = 0.158 αBz B(αA − θA )(αA − θB)

(31)

The Vmin diagrams of the RDWC for the two feed conditions are shown in Figure 4. All of these preceding equations are derived without taking any consideration of the influence of azeotropes. However, two azeotropes exist in this system at the operation pressure. The azeotropes have no influence on the VLE of the column with the assumption that the azeotropes will leave the column once they formed. The compositions of azeotropes obtained with the UNIQUAC model equations are shown in Table 1. The reaction−separation process takes place in the prefractionator in RDWC. When column C1 operates at the point PAC (preferred split point), MTBE does not exist in the

IC4(C4H8) + MeOH(CH3OH) ↔ MTBE(C5H12O) (24)

where IC4 (A) stands for isobutene and MeOH (B) and MTBE (C) represent methanol and methyl tert-butyl ether, respectively. When relative volatility is calculated by using eq 12, methanol is the reference component for the reaction. 2343



Article

Figure 4. Vmin diagrams of the RDWC for the MTBE synthesis: (a) feed I; (b) feed II.

The RDWC is simulated by Aspen Plus using the UNIQUAC model equations. The operation parameters are optimized with the least energy requirement. In the MTBE system, the increase of light component (IC4) brings a lower reboiler duty, which can be certified by decreasing the reflux ratio in the main column as shown in Table 2. In addition, it is shown that the proposed shortcut method can be available in the design of RDWC for the synthesis of MTBE in spite of the little relative error when compared with the results obtained by a rigorous method using Aspen Plus. 3.2. Synthesis of Ethyl tert-Butyl Ether. Since its interesting physicochemical properties for enhancing octane number and decreasing fuel vaporization losses, the production of ethyl tert-butyl ether (ETBE) has been studied. The synthesis of ETBE can be described as

Table 1. Azeotrope Compositions for the Ternary Mixture at 650 kPa mole fraction binary azeotrope

temp (K)

IC4

MeOH

MTBE

IC4−MeOH MeOH−MTBE

325.35 286.12

0.9461

0.0539 0.5474

0.4526

vapor stream and neither does isobutene in the liquid stream leaving C1. Thus the Vmin diagram of the sections C21 and C22 in the main column is just at the left and right sides of the operation point PAC. The minimum reflux ratio, Rmin, is 0.725 when the prefractionator is operated at the preferred split. With a finite number of stages, however, the actual minimum reflux ratio (Rmin,real) has to be slightly higher. Suggesting that Rmin,real is 1.05 times as large as Rmin; then Rmin,real = 1.05Rmin = 0.761.21 If the equilibrium conversion of the reaction in the prefractionator is 90%, the composition both in the top and bottom of column C1 can be obtained. Assuming the 0.1% impurity of A and C at the bottom and the top, respectively, the number of theoretical stages can be calculated using the Fenske equation. The separation process takes place in the main column where two azeotropes exist. The composition at the top of C21 can be obtained by assuming that the azeotrope of isobutene and methanol forms on the first stage. Likewise, it is suggested that the azeotrope of methanol and MTBE forms on the stage where the side product leaves. It is assumed that the actual number of stages is two times as large as the minimum number of stages which can be calculated by Fenske equation. The operation parameters of the RDWC calculated by the minimum vapor flow method and the simulation results from both methods are shown in Table 2.

IC4(C4H8) + EtOH(C2H5OH) ↔ ETBE(C6H14O) (32)

where IC4 (A) stands for isobutene and EtOH (B) and ETBE(C) represent ethanol and ethyl tert-butyl ether, respectively. When relative volatility is calculated using eq 12, ethanol is the reference component for the reaction. Etherification takes place at 1100 kPa, and the reaction is reversible. However, the reverse reaction effects are small, and a yield higher than 90% can be obtained. The analyzed system includes three components involved in the reaction (IC4, EtOH, and ETBE). There are no azeotropes existing in this reactive mixture, whose thermodynamic properties are calculated using the UNIQUAC model. The calculation procedures for this case are the same as those for the MTBE synthesis, and the Vmin diagrams of the RDWC

Table 2. Comparison of the Results Obtained by Two Methods for the Synthesis of MTBE operation parameters column C1 Feed I NT1 NF RR1 Feed II NT1 NF RR1

shortcut

main column

Aspen Plus

component (mol %)

feed

top

side

bottom

top

side

bottom

32 25 0.761

NT NF1 NF2

32 7 25

NS RR2

17 1.206

IC4 MeOH MTBE

30.0 40.0 30.0

94.6 5.4 0.0

0.3 54.6 45.1

0.0 3.7 96.3

95.2 4.8 0.0

0.3 58.7 41.0

0.0 12.9 87.1

36 31 0.682

NT NF1 NF2

44 7 35

NS RR2

17 1.074

IC4 MeOH MTBE

35.0 35.0 30.0

94.3 5.7 0.0

1.0 50.7 41.9

0.0 0.2 99.8

95.0 4.2 0.8

1.0 54.3 44.8

0.0 0.3 99.7

2344



Article

Figure 5. Vmin diagrams of the RDWC for the ETBE synthesis: (a) feed I; (b) feed II.

Table 3. Comparison of the Results Obtained by Two Methods for the Synthesis of ETBE operation parameters column C1

shortcut

main column

component (mol %)

Aspen Plus

feed

top

side

bottom

top

side

bottom

30.0 40.0 30.0

98.0 2.0 0.0

0.6 99.4 0.04

0.0 2.0 98.0

89.4 10.5 0.1

0.6 91.0 8.4

0.5 2.2 97.3

30.0 50.0 20.0

98.0 2.0 0.0

0.2 99.7 0.1

0.0 2.0 98.0

94.2 5.7 0.1

9.3 90.6 0.1

0.8 8.2 91.0

Feed I NT1 NF RR1

28 23 0.313

NT NF1 NF2

54 5 46

NS RR2

17 0.876

NT1 NF RR1

28 23 0.304

NT NF1 NF2

50 5 41

NS RR2

13 0.777

IC4 EtOH ETBE Feed II IC4 EtOH ETBE

Figure 6. Vmin diagrams of the RDWC for the DME synthesis: (a) feed I; (b) feed II.

Table 4. Comparison of the Results Obtained by Two Methods for the Synthesis of DME operation parameters column C1

shortcut

main column

component (mol %)

Aspen Plus

feed

top

side

bottom

top

side

bottom

33.3 33.3 33.3

99.9 0.1 0.0

0.4 99.3 0.3

0.0 5.0 95.0

93.3 5.0 1.7

5.2 89.5 5.3

4.1 8.9 87.0

30.0 50.0 20.0

99.9 0.1 0.0

0.2 99.6 0.2

0.0 5.0 95.0

99.9 0.1 0.0

0.2 99.8 0.0

0.0 1.0 99.0

Feed I NT1 NF RR1

24 17 0.27

NT2 NF1 NF2

47 5 40

NS RR2

15 0.96

NT1 NF RR1

18 17 0.29

NT2 NF1 NF2

48 5 39

NS RR2

15 0.88

DME MeOH water Feed II DME MeOH water

are shown in Figure 5. Details of the feed conditions and simulation results are reported in Table 3. As shown in Table 3, a satisfactory agreement is obtained between the ETBE compositions calculated by shortcut and detailed models. In particular, the ETBE purities obtained using the two approaches are very similar, with a relative difference of

7.14%. Therefore, the shortcut design method proposed in this study can be considered reliable enough to be used for the purposes of conceptual design of a RDWC. 3.3. Synthesis of Dimethyl Ether. Dimethyl ether (DME) is of great industrial interest due to its use as a clean fuel for diesel engines or in combustion cells. Conventionally, high 2345



Article

Notes

purity DME is synthesized by dehydration of methanol. The chemical reaction proceeds as indicated by eq 33.

The authors declare no competing financial interest.

■

2MeOH(CH3OH) ↔ DME(C2H6O) + water(H 2O)

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant 21276279) and the Development of Key Technologies Project of Qingdao Economic and Technological Development Zone under Grant 2013-1-57. Further, we are grateful to the editor and the anonymous reviewers for their helpful comments and constructive suggestions with regard to the revision of the paper.

(33)

where DME (A) stands for dimethyl ether and MeOH (B) represents methanol. When relative volatility is calculated using eq 12, methanol is the reference component for the reaction. Etherification takes place at 1000 kPa, and the conversion of MeOH is 50% for this reversible reaction. The analyzed system includes three components involved in the reaction (MeOH, DME, and H2O). The calculation results are obtained through the same calculation processes used in the MTBE synthesis. The Vmin diagrams of the RDWC are shown in Figure 6. The results shown in Table 4 indicate that the key component purities in the top and bottom of the column obtained from Aspen Plus and those obtained from the proposed design methodology are in good agreement. In summary, the proposed method appears to be capable of dealing with different compositions. Although this shortcut method cannot guarantee the optimal design, it can be used for a preliminary process design or as the initial case for a rigorous optimization. The calculation method of the number of stages may be the main source of error, since the method is strictly valid for the nonreactive case only. Further analysis is required to modify the Fenske equation for the reaction system. Also the reaction kinetics should be considered for the rate-controlled system.

■

B C D K L Nc Nd q r ri r′i V VB VT x y z

4. CONCLUSION A shortcut design method for a RDWC based only on Underwood equations is presented. The minimum vapor flow method and Vmin diagram applying to the conventional column are extended to the RDWC. Considering the influence of the reaction and the distillation, the corrected recovery ri′ is introduced to simplify the calculations. Taking the RDWC processes for the syntheses of MTBE, ETBE, and DME as industrially relevant base cases, the column parameters are calculated and the rigorous simulations are finished based on these parameters using Aspen Plus. The changes in feed compositions do not limit the application of the proposed shortcut method in the conceptual design of a RDWC. Furthermore, it can be seen that the results calculated by the minimum vapor flow method are highly consistent with those obtained through the rigorous simulation method with Aspen Plus. Namely, the proposed shortcut method can provide a perfect initial guess for the rigorous simulation.

■

Greek Letters

α θ ν ξ φ

■

relative volatility common root of Underwood equations stoichiometric coefficient reaction extent Underwood equation root of the rectifying section

REFERENCES

(1) Kaibel, G. Method of carrying out chemical reactions and for the simultaneous fractionation of a mixture into several fractions by a distillation column. EP 0126288 A2, 1984. (2) Yildirim, Ö .; Kiss, A. A.; Kenig, E. Y. Dividing Wall Columns in Chemical Process Industry: A Review on Current Activities. Sep. Purif. Technol. 2011, 80, 403. (3) Mueller, I.; Pech, C.; Bhatia, D.; Kenig, E. Y. Rate-based Analysis of Reactive Distillation Sequences with Different Degrees of Integration. Chem. Eng. Sci. 2007, 62, 7327. (4) Mueller, I.; Kenig, E. Y. Reactive Distillation in a Dividing Wall Column: Rate-Based Modeling and Simulation. Ind. Eng. Chem. Res. 2007, 46, 3709. (5) Kiss, A. A.; Pragt, J. J.; Van Strien, C. J. G. Reactive Dividing-Wall ColumnsHow to Get More with Less Resources. Chem. Eng. Commun. 2009, 196, 1366. (6) Sun, L. Y.; Qi, C. X.; Li, J.; Li, Q. S. Design of Catalytic Divided Wall Column. Adv. Mater. Res. 2011, 219, 1589. (7) Sun, L. Y.; Qi, C. X.; Li, J.; Li, Q. S. Control of Catalytic Divided Wall Column. Adv. Mater. Res. 2011, 225, 496. (8) Lee, H. Y.; Lai, I. K.; Huang, H. P.; Chien, I. L. Design and Control of Thermally Coupled Reactive Distillation for the Production of Isopropyl Acetate. Ind. Eng. Chem. Res. 2012, 51, 11753. (9) Cheng, K.; Wang, S. J.; Wong, D. S. H. Steady-State Design of Thermally Coupled Reactive Distillation Process for the Synthesis of Diphenyl Carbonate. Comput. Chem. Eng. 2013, 52, 262. (10) Delgado-Delgado, R.; Hernández, S.; Barroso-Muñoz, F. O.; Segovia-Hernández, J. G.; Castro-Montoya, A. J. From Simulation

ASSOCIATED CONTENT

S Supporting Information *

Text describing the application of the Underwood equations in a RDWC and the detailed calculation procedures for other cases and figures showing the prefractionator of a Petlyuk arrangement for RDWC, the Vmin diagram for the prefractionator in the RDWC, and the fully thermally coupled reactive column. This material is available free of charge via the Internet at http://pubs.acs.org.

■

NOMENCLATURE molar flow rate of the bottom product, kmol/h reactant conversion molar flow rate of the distillate, kmol/h vapor−Liquid equilibrium constant liquid molar flow rate, kmol/h number of components number of distributed components liquid fraction of feed relative component recovery corrected recovery vapor molar flow rate, kmol/h vapor molar flow rate in the stripping section, kmol/h vapor molar flow rate in the rectifying section, kmol/h component molar fraction of liquid phase component molar fraction of vapor phase component molar fraction of feed

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86 13854208340. Fax: +86 0532 86981787. E-mail: [email protected]. 2346



Article

Studies to Experimental Tests in a Reactive Dividing Wall Distillation Column. Chem. Eng. Res. Des. 2012, 90, 855. (11) Nguyen, N.; Demirel, Y. Using Thermally Coupled Reactive Distillation Columns in Biodiesel Production. Energy 2011, 36, 4838. (12) Cossio-Vargas, E.; Barroso-Muñoz, F. O.; Hernandez, S.; Segovia-Hernandez, J. G.; Cano-Rodriguez, M. I. Thermally Coupled Distillation Sequences: Steady State Simulation of the Esterification of Fatty Organic Acids. Chem. Eng. Process. 2012, 62, 176. (13) Kiss, A. A.; Segovia-Hernández, J. G.; Bildea, C. S.; MirandaGalindo, E. Y.; Hernández, S. Reactive DWC Leading the Way to FAME and Fortune. Fuel 2012, 95, 352. (14) Kiss, A. A.; Segovia-Hernández, J. G.; Bildea, C. S.; MirandaGalindo, E. Y.; Hernández, S. Towards FAME and Fortune by Reactive DWC. Procedia Eng. 2012, 42, 1908. (15) Kiss, A. A.; Suszwalak, D. J. P. C. Innovative Dimethyl Ether Synthesis in a Reactive Dividing-Wall Column. Comput. Chem. Eng. 2012, 38, 74. (16) Daniel, G.; Patil, P.; Dragomir, R.; Jobson, M. Conceptual Design of Reactive Dividing Wall Columns. Inst. Chem. Eng. Symp. Ser. 2006, 152, 364. (17) Gómez-Castro, F. I.; Rico-Ramírez, V.; Segovia-Hernández, J. G.; Hernández-Castro, S.; González-Alatorre, G.; El-Halwagi, M. M. Simplified Methodology for the Design and Optimization of Thermally Coupled Reactive Distillation Systems. Ind. Eng. Chem. Res. 2012, 51, 11717. (18) Fidkowski, Z.; Krolikowski, L. Thermally Coupled System of Distillation Columns: Optimization Procedure. AIChE J. 1986, 32, 537. (19) Carlberg, N. A.; Westerberg, A. W. Temperature-Heat Diagrams for Complex Columns. 2. Underwood’s Method for Side Strippers and Enrichers. Ind. Eng. Chem. Res. 1989, 28, 1379. (20) Carlberg, N. A.; Westerberg, A. W. Temperature-Heat Diagrams for Complex Columns. 3. Underwood’s Method for the Petlyuk Configuration. Ind. Eng. Chem. Res. 1989, 28, 1386. (21) Halvorsen, I. J. Minimum energy requirements in complex distillation arrangements. Ph.D. Thesis, Norwegian University of Science and Technology (NTNU), Trondheim, Norway, 2001. (22) Huerta-Garrido, M. E.; Rico-Ramirez, V.; Hernandez-Castro, S. Simplified Design of Batch Reactive Distillation Columns. Ind. Eng. Chem. Res. 2004, 43, 4000.

2347


Shortcut Method for the Design of Reactive Dividing Wall Column

Recommend Documents