Method for the Design of Azeotropic Distillation Columns - American

Ind. Eng. Chem. Res. 2007, 46, 6635-6644

6635

Method for the Design of Azeotropic Distillation Columns Claudia Gutie´ rrez-Antonio and Arturo Jime´ nez-Gutie´ rrez* Instituto Tecnolo´ gico de Celaya, Departamento de Ingenierı´a Quı´mica, AV. Tecnolo´ gico y Garcı´a Cubas s/n, 38010, Celaya, Guanajuato. Me´ xico

A tray-by-tray method for the design of azeotropic distillation columns is presented. The method uses distillation lines, solves the material balances (in the form of algebraic equations), and detects a feed tray location that minimizes the total number of stages. Several cases of study show that the placement of the feed, as suggested by this method, can provide better designs than those obtained using the boundary value method (BVM). 1. Introduction

Table 1. Azeotropic Mixtures Selected as Cases of Study

Azeotropic distillation is widely used in the petrochemical, chemical, and biochemical industries.1 Many important chemicals, such as acetone, benzene, methyl acetate, ethyl acetate, and isopropanol, among others, involve azeotropic distillation processes for their purification. The complex nature of azeotropic mixtures makes the design procedure more complicated than that for ideal mixtures. The first thing to address with azeotropic distillation problems is the feasibility of a desired split. Distillation boundaries divide the composition space for azeotropic mixtures, such that not all specified splits can be feasible. A separatrix cannot be crossed, except for some cases in which it has a pronounced curvature.1 A given split is feasible if the products and feed compositions are located in the same region of the composition space. Although the origin of azeotropic distillation has been traced back to 1903, one of first design methods for azeotropic distillation columns was published in 1985 by Van Dongen and Doherty,2 almost 40 years after the development of the Fenske, Underwood, and Gilliland equations.3 This observation shows the periodic attention that azeotropic distillation has received over the past several decades. Several aspects remain to be developed. For instance, Liu et al.4 noted the need of a reliable method to calculate the minimum number of stages in azeotropic distillation columns. Several methods have been proposed for the estimation of a minimum reflux ratio in azeotropic distillation. Levy et al.5 reported one method that requires the location of the saddle and feed pinch points, and the verification of the collinearity of these points with the feed composition. It is worth of mention that the collinearity criterion is exact for the separation of ideal mixtures, but it is only an approximation for azeotropic mixtures. Extensions to the procedure by Levy et al.5 have been reported. Basically, those methods use the collinearity criterion of the pinch points, with respect to the feed, to determine the minimum reflux ratio. Julka and Doherty6 made the extension to multicomponent mixtures to develop the zero-volume criterion (ZVC). In this procedure, the minimum reflux ratio is obtained when the feed composition is collinear with the C-1 pinch points located in a hyperplane, where C is the number of components. This method works only for direct and indirect splits, because the pinch points that determine minimum reflux ratio must be known a priori. Ko¨hler et al.7 proposed the minimum angle criterion (MAC). This criterion is empiric in nature and is based on the principle * To whom correspondence should be addressed. Tel.: (+52-461) 611-7575, Ext. 139. Fax: (+52-461) 611-7744. E-mail address: [email protected].

mixture

components (from light to heavy)

M1 M2 M3 M4

acetone-isopropanol-water acetone-chloroform-benzene ethanol-water-ethylene glycol methanol-isopropanol-water

that, under minimum reflux conditions, the angle between the feed composition and a pinch point for each section of the column must be a minimum. This criterion is equivalent to the collinearity criterion proposed by Levy et al.5 However, this method does not have a physical explanation for cases with more than three components. Po¨llman et al.8 reported the eigenvalue criterion (EC), which is a hybrid between the boundary value method (BVM)2 and the ZVC method.6 In this procedure, the profiles are calculated just after the pinch point with a tray-by-tray calculation in the direction of the unstable eigenvector of the pinch point. The minimum reflux ratio is the smallest value that provides the intersection of the profile of one section with a pinch point of the other section. However, when there is more than one unstable eigenvector in the pinch point, many profiles must be calculated, thus increasing the computational effort. Bausa et al.9 developed the rectification bodies method (RBM). A rectification body is a triangle that has been delimited by possible trajectories of pinch points, in the stripping or the rectification section, from products to the feed point. The minimum reflux ratio is observed when the rectification and stripping bodies intersect in one point. Also, the method makes a calculation of the generated entropy, to verify that the trajectories are thermodynamically consistent. Some methods for the design of azeotropic distillation columns have been developed. One of the first methods to be reported was the BVM method, by Van Dongen and Doherty.2 The method uses residue curves and is based on material balances in the form of differential equations to calculate the number of plates in each section of the column. The differential equations are solved from the outside to the inside of the column, finding the feed stage when the liquid compositions of both sections are equal. The BVM is simple to use, but the intersection of the operating profiles does not necessarily provide the optimal feed tray location, because the intersection of the operating profiles is not always close to the feed composition. As a result, in many cases, the composition of the feed tray is quite different from the feed composition. The method assumes constant molar flows, theoretical stages, and feed as saturated liquid. Stichlmair and Fair10 used tray-by-tray calculations to determine the number of stages in each section of the column. The

10.1021/ie061329h CCC: $37.00 © 2007 American Chemical Society Published on Web 08/28/2007

6636

Ind. Eng. Chem. Res., Vol. 46, No. 20, 2007

Figure 1. Feasibility products zone for a given feed F; D denotes the distillate product, and B is the bottom product.

Figure 2. Rectifying section (1) and stripping section (2) for the application of the design model.

procedure begins in the bottom part of the column, and when the feed composition is attained, the equations for the rectifying section are applied. This method shows a disadvantage, in that it does not always reach the composition of the top product. To calculate the minimum reflux ratio, they use transition points, which are the compositions where the profiles change from a ternary mixture to a binary mixture. The pinch point of the feed is located on the line between the feed composition and the transition point. After the composition of the transition point is found, the minimum reflux ratio is calculated with a simple equation. The basis of the method is that, under minimum reflux conditions, the feed, the transition, and the feed pinch points are collinear, which is only an approximation for azeotropic mixtures. Liu et al.4 recently reported a method that was based on azeotropic regions called compartments. A distillation region has at least one stable node, one unstable node, and one saddle node. However, when there is more than one saddle node, the

distillation region can be divided into compartments. These compartments can be taken as ideal regions, such that by considering azeotropes as pseudo-components, one can use the Underwood-Gilliland3 equations to calculate the design variables. Liu et al.4 reported calculations of minimum reflux that show deviations of up to 22%, with respect to the calculations obtained with the HYSIS simulator. The reported differences in the number of stages attain values up to 30%. The use of design models for azeotropic distillation columns within optimization frameworks has also been reported. Bauer and Stichlmair14 developed a mixed-integer nonlinear programming (MINLP) formulation, in which a tray-by-tray model with MESH equations was used. The alternative, embedded in a superstructure with the minimum total annual cost, was determined with the MINLP model. Bauer and Stichlmair14 used binary variables to identify the optimal location of the feed tray, as implemented by Viswanathan and Grossmann15 for distillation systems with multiple feeds. From the available methods for designing azeotropic distillation systems, the method by Lui et al.4 is simple, but it does not seem reliable; the method by Stichlmair and Fair10 does not always satisfy the overall material balance; and the BVM design2 does not necessarily provide the best location for the feed stage. In this work, an alternative design method for homogeneous azeotropic distillation columns is proposed. The method is based on distillation lines and tray-by-tray calculations, and it detects a feed tray location that minimizes the total number of stages. 2. Design Method The first step of the design procedure is to check the feasibility of the split. The procedure by Stichlmair and Fair10 can be used for that purpose. The feasible zone for the bottom and top products for a given feed is delimited by the composition space, the distillation boundary, the distillation line through the feed, and the material balance lines for direct and indirect splits. Figure 1 illustrates how the feasible region can be identified in a ternary composition diagram. Given a feed point F, the feasible distillate products are located in the area delimited by the distillation line through the feed, the distillation boundary, and the material balance line for the

Ind. Eng. Chem. Res., Vol. 46, No. 20, 2007 6637

Figure 3. Operating profiles at the minimum reflux ratio.

Figure 4. Composition profiles for the rectifying section, case 1. Table 2. Split Specifications Case 1 (M1S1) A B C

Case 2 (M2S1)

Case 3 (M3S1)

Case 4 (M4S1)

zF

zD

zB

zF

zD

zB

zF

zD

zB

zF

zD

zB

0.63 0.07 0.30

0.93 0.02 0.05

0.02 0.1717 0.8083

0.50 0.20 0.30

0.997 0.0015 0.0015

0.30 0.2798 0.4202

0.33 0.33 0.34

0.5026 0.4973 1 x 10-4

1 x 10-6 9.999 x 10-3 0.99

0.33 0.33 0.34

0.99 0.006 0.004

1 x 10-5 0.492 0.50799

indirect split; the feasible bottom products are located in the area delimited by the material balance line for the direct split, the distillation line through the feed, and the composition space. If the desired split is not feasible, one can easily specify a new feasible split using this type of diagram. One must take into account that the bottom products (B) and the top products (D) must to be collinear with the feed, to satisfy the overall material balance.

The design method we outline in this paper is based on distillation lines, which constitute a more appropriate tool than residue curve lines for staged columns.10 The use of distillation lines allows the material balances to be written in algebraic form. As in the BVM design,2 the material balances are solved from the outside to the inside of the distillation column (see Figure 2), to ensure that the product compositions are met. Ideal stages and constant molar overflows are assumed. The following

6638


Table 3. Designs Obtained

proposed method BVM proposed method BVM

number of feed trays, NF

total number of trays, N

Case 1 12

17

12

19

Case 3 17

24

24

31

proposed method BVM proposed method BVM

number of feed trays, NF

total number of trays, N

Case 2 117

120

118

120

Case 4 9

71

8

To determine the location of the feed stage, we propose using a minimum difference criterion, in which a search is conducted for the tray with the minimum difference between the composition of each stage in the column and the feed composition. The search procedure for the minimum difference is performed for each section of the column, so that the number of stages in the stripping and the rectifying sections are obtained along with the location of the feed stage. The difference (or distance) between the compositions is calculated using eqs 6 and 7:

79

x∑ x∑ c

equations can be written for the rectifying section (1) and for the stripping section (2):

xn+1,i

n,i

(1)

D,i

n,i

(2)

where xj,i is the liquid-phase composition of component i in stage j, yj,i the vapor-phase composition of component i in stage j, r the reflux ratio (r ) L/D), s the boilup ratio (s ) V/B), zD,i the composition of component i in the distillate product, and zB,i the composition of component i in the bottom product. The mass balance equations must be used with a thermodynamic model that relates the vapor-liquid equilibrium conditions:

yn,i ) f(xn,i)

(3)

An analysis of the number of degrees of freedom indicates that 2C + 1 variables must be specified. Therefore, for a ternary mixture, seven variables are needed. One can conveniently specify the operating pressure, the reflux ratio, and five (independent) mole fractions (for instance, two feed and three product mole fractions) from which the complete set of feed and product streams compositions can be obtained from summation constraints and simple mass balances. For instance, if the set {zD,1,zD,2,zB,1} is specified for the products (see Figure 2), then zB,2 is calculated as

[

zF,1 - zB,1 zF,1 - zD,1

]

(4)

The reboil ratio (s) can be calculated from

s ) (r + q)

[

]

zB,1 - zF,1 + (q - 1) zF,1 - zD,1

(zF,i - yNR,i)2 ∑ i)1

(zF,i - xNS,i)2 +

(zF,i - yNS,i)2 ∑ i)1

i)1

dS )

i)1

B,i

zB,2 ) zF,2 + (zF,2 - zD,2)

c

(zF,i - xNR,i)2 +

c

(r +r 1)x + (r +1 1)z s 1 )( y +( z s + 1) s + 1)

yn+1,i )

dR )

(5)

where q is the thermal condition of the feed (q ) 1 for saturated liquids, q ) 0 for saturated vapors, and 0 < q < 1 for a liquid-vapor mixture). When the feed is a saturated liquid, eq 5 reduces to the expression reported by Van Dongen and Doherty.2 Equations 1 and 2 can be solved, together with the application of the vapor-liquid equilibrium model, to obtain the composition profiles for a given reflux ratio r. The intersection of the composition profiles anywhere in the composition space is a necessary and sufficient condition to establish the feasibility of the split.11 However, the intersection of the composition profiles does not necessarily provide a good criterion for the feed tray, because it does not always locate the plate with the composition closest to that of the feed.

(6)

c

(7)

where dR is the distance between the equilibrium composition of a stage in the rectifying section and the feed composition, dS represents the distance between the equilibrium composition of the stage in the stripping section and the feed composition, zNR,i is the composition of component i in stage NR of the rectifying section, and zNS,i represents the composition of component i in stage NS of the stripping section. Notice that the balances given by eqs 1 and 2 are consistent in regard to the manner in which the method is applied, i.e., the trays are labeled from the top of the column for the rectifying section (until the feed is identified by minimizing eq 6), and from the bottom of the column for the stripping section (until the feed is identified by minimizing eq 7). Typically, the total number of equilibrium stages thus obtained will be equal to the number of ideal trays plus a partial reboiler (assuming that a total condenser is used). The minimum reflux ratio is calculated by trial and error until a pinch point for the operating profiles is detected, as illustrated in Figure 3. After the minimum reflux ratio is known, an operating reflux ratio can be fixed using a heuristic rule, or it can be optimized for some objective function (for instance, the minimization of the annual cost of the distillation column). The overall design procedure involves the following steps: (1) Fix the pressure P, the reflux ratio r, and five mole fractions (for instance, zF,1, zF,2, zD,1, zD,2, and zB,1). (2) Calculate the reboil ratio (s), using eq 5. (3) Complete the feed and products compositions data with mass balances (for instance, eq 4) and summation constraints. (4) Using the distillation lines map, determine the feasibility of the split (i.e., if the products and feed compositions are located in the same region of composition space). If the proposed split is feasible, then go to step 5; otherwise, go back to step 1 and set new products specifications. (5) Search for the minimum reflux ratio. For each search point, solve eqs 1 and 2, together with the liquid-vapor equilibrium model, until the composition profiles pinch each other. (6) With an operating reflux ratio above the minimum value, apply eq 1 and the equilibrium model for the rectifying section until the minimum difference criterion provided by eq 6 is detected. Apply a similar procedure with eq 2 and the equilibrium model for the stripping section until the minimum value of eq 7 is found. As a result, the number of stages for each section of the column, along with the feed tray location, is obtained.


Figure 5. Composition profiles for the stripping section, case 1.

Figure 6. Rectifying composition profiles for case 2.

The method as presented here applies for azeotropic distillation columns, but it can also be used for ideal and nonideal distillation cases with a suitable thermodynamic model. 3. Applications The mixtures reported in Table 1 were used as case studies. The azeotropic mixtures show only one distillation boundary at atmospheric pressure. Split specifications are given in

Table 2. All columns are assumed to operate at atmospheric pressure. For the equilibrium calculations, the nonrandom twoliquid (NRTL) model was used for the activity coefficients in the liquid phase, whereas ideal gas behavior was assumed for the vapor phase. The adjusted parameters for the NRTL model were taken from the Dechema collection.12 As suggested by Douglas,13 the operating reflux ratio was fixed as 1.1 times the minimum value. The feed was assumed to be saturated liquid.

6640


Figure 7. Stripping composition profiles for case 2.


Table 3 gives the designs obtained for each case study; results obtained with the BVM methodology2 are also given, for comparison purposes. A discussion on the results for each case of study follows. Case 1: Acetone-Isopropanol-Water Mixture. The first case consists of a mixture of acetone, isopropanol, and water. The desired objective is to obtain high-purity acetone as a top product. Figure 1 shows the application of the feasibility test by Stichlmair and Fair10 for the proposed split of the problem. Both the distillate point (D) and the bottoms point (B) fall into

their feasible regions, as explained previously in section 2. After the feasibility of the split has been verified, a search for the minimum reflux ratio is conducted. A trial-and-error procedure is used until a value for which the operating profiles intersect for the first time is obtained. The result of the search, shown in Figure 3, provides a minimum reflux ratio of r ) 0.6035. Taking an operating reflux ratio of r ) 0.66385 (equal to 1.1 times the minimum value), we can apply the design algorithm. Equations 1 and 2 are solved, together with the thermodynamic model for equilibrium calculations. The procedure provides the number



Figure 10. Operating composition profiles for case 3.

of stages for each section of the column when the differences given by eqs 6 and 7 are minimized. The design obtained with the proposed method shows two fewer stages than that calculated with the BVM process (see Table 3, where NF is the number of feed trays, as counted from the top of the column, and N is the total number of trays that includes a partial reboiler). In this case, the intersection of the operating profiles is very close to the feed, so both methods provide the same number of trays for the rectifying section. Figure 4 shows the composition profiles obtained for each component along the rectifying section of the column; one can see that a total of 12 trays are required

to reach the minimum of eq 6. When the design procedure is applied for the stripping section, two fewer stages are required, with respect to the BVM methodology. Figure 5 shows the composition profiles for the stripping section. The minimum distance criterion indicates that five stages are needed for this section, thus ending with a design of 17 total stages for the column. Case 2: Acetone-Chloroform-Benzene Mixture. The second case involves the separation of a mixture of acetone, chloroform, and benzene to provide high-purity acetone. The total number of stages obtained with both methods is the same,

6642




and the location of the feed tray differs by only one stage. Figure 6 shows the rectifying profile obtained with our design procedure, with the minimum distance (as defined in eq 6) found in stage 117; the BVM design places the feed in stage 118. Note that the rectifying profile has two pinch zones. The stripping profile is shown in Figure 7. One can observe that only 3 stages are needed to provide the minimum distance from the feed; the total number of stages for the column is then 120. One pinch zone is observed in the stripping profile.

Case 3: Ethanol-Water-Ethylene Glycol. The third case of study involves a mixture of ethanol, water, and ethylene glycol, to obtain a bottom product with high-purity ethylene glycol. The design obtained with the new approach shows seven fewer stages than that obtained with the BVM procedure. Both designs have the same number of stages in the stripping section. By locating the optimal feed tray, one obtains 17 stages for the rectifying section, while application of the BVM methodology gives 7 more stages (Figure 8). One can see that, for stage 24 (the feed tray predicted by BVM), the value of the difference

Ind. Eng. Chem. Res., Vol. 46, No. 20, 2007 6643 Table 4. Validation of the Designs Using Aspen Plus mole fraction

mole fraction

Case 1: Acetone proposed method 0.91163 BVM 0.91341

Case 2: Acetone proposed method 0.99999 BVM 0.99999

Case 3: Ethylene Glycol proposed method 0.99009 BVM 0.99009

Case 4: Methanol proposed method 0.98422 BVM 0.97768

or distance is ∼1.5 times the minimum value. The rectifying profile has two pinch zones; one can observe how stage 24 (the feed stage, according to the BVM procedure) is inside the second pinch zone. There are some stages that are not improving the separation, but they are taken into consideration by the BVM design, as a consequence of the use of the intersection of the composition profiles to locate the feed tray. For the stripping profile (Figure 9), both design procedures give 7 stages. One can observe that the stripping profile has one pinch zone. Figure 10 shows how the intersection of the profiles happens quite far from the feed point. Case 4: Methanol-Isopropanol-Water. A mixture of methanol, isopropanol, and water was taken as the fourth case of study, with methanol as the main product. The design obtained with the proposed method shows fewer stages than that obtained with the BVM design. In fact, the number of stages of the rectifying section alone for the BVM design equals the total number of stages obtained with the new procedure. Figure 11 shows the rectifying composition profile; the minimum distance value corresponds to stage 9. The BVM method gives 8 stages for this section. Note that the rectifying profile has one pinch zone. The stripping profile is shown in Figure 12; the minimum distance criterion provides 62 stages, for a total of 71 trays for the column. The BVM design gives 71 stages for the stripping section, and the difference in composition, with respect to the feed, is 2.58 times the minimum value. Moreover, stage 71 is near a second pinch zone. Simulations. Finally, we used Aspen Plus 10.2.1 software to perform rigorous simulations of the resulting designs. Table 4 shows the results. The composition of the component of interest of the azeotropic mixture in its corresponding product stream is given (acetone and methanol as top products, ethylene glycol as a bottoms product). For the first case of study, the acetone compositions are very similar, so the design with two fewer stages provided by the proposed method could be chosen. For the second case, the resulting acetone compositions are greater than the specified compositions for both designs. For the third case, the design with seven fewer stages provides the same product composition as that obtained with the BVM methodology; in this case, there are some stages in the stripping profile of the BVM design inside a pinch zone, which are not necessary to improve the separation. For the fourth case, the methanol composition reached with the design provided by the proposed method is slightly greater than the composition given by the BVM procedure. Such an improvement is obtained despite the use of a design with fewer stages. The last two cases show how determination of the location of the feed stage, using the minimum difference criterion with eqs 6 and 7, improves the efficiency of the design. 4. Concluding Remarks A method for the design of azeotropic distillation columns has been presented. The method uses distillation lines with algebraic mass balances for each section of the column and solves the equations from the outside of the column to the inside

of the column to meet the overall material balance. The design procedure is easy to implement and provides a quick design. As opposed to the concept of the intersection of the two operating profiles, the method optimizes the feed location by searching for the minimum difference in composition between any given tray and the feed point. Even when the intersection of the operating profiles is a necessary and sufficient condition to establish the feasibility of a split, it does not necessarily provide the optimal feed location. The examples show that the proposed method provided the same or fewer stages than the boundary volume method (BVM), and the rigorous simulations show that more-efficient designs were detected, because the reduction in the number of stages was not translated into a deterioration of the product compositions. Also, this modeling strategy could be implemented into mixed-integer nonlinear programming (MINLP) models of the type presented by Bauer and Stichlmair14 for the optimization of azeotropic distillation systems; in particular, the selection of the feed tray location, using the approach presented here, could be used effectively to reduce the search space for the optimization problem, with respect to the implementation of binary variables in MINLP models. Nomenclature B ) bottoms flow rate (lb mol/h) C ) number of components D ) distillate flow rate (lb mol/h) d ) distance between the feed and the equilibrium compositions in one stage L ) liquid flow rate (lb mol/h) P ) pressure (psia) q ) thermal condition of the feed r ) reflux ratio s ) reboil ratio V ) vapor flow rate (lb mol/h) x ) composition of liquid phase y ) composition of vapor phase z ) composition (liquid or vapor phase) Subscripts B ) bottom D ) distillate F ) feed j,i ) component i, stage j n ) stage NR ) equilibrium stage in rectifying section NS ) equilibrium stage in stripping section R ) rectifying section S ) stripping section Acknowledgment Financial support from CONACYT, Mexico, for the development of this project (Grant No. SEP-2003-C02-43898) is gratefully acknowledged. Also, C.G.-A. was supported through a scholarship from CONACYT. Literature Cited (1) Doherty, M. F.; Malone, M. F. Conceptual Design of Distillation Systems; McGraw-Hill: New York, 2001. (2) Van Dongen, D. B.; Doherty, M. F. Design and Synthesis of Homogeneous Azeotropic Distillations. 1. Problem Formulation for a Single Column. Ind. Eng. Chem. Fundam. 1985, 24, 454-463. (3) Henley, E. J.; Seader, J. D. Equilibrium Stage Separation Operations in Chemical Engineering; Wiley: New York, 1981.

6644


(4) Liu, G.; Jobson, M.; Smith, R.; Wahnschafft, O. M. Shortcut Design Method for Columns Separating Azeotropic Mixtures. Ind. Eng. Chem. Res. 2004, 43, 3908-3923. (5) Levy, S. G.; Van Dongen, D. B.; Doherty, M. F. Design and Synthesis of Homogeneous Azeotropic Distillations. 2. Minimum Reflux Calculations for Nonideal and Azeotropic Columns. Ind. Eng. Chem. Fundam. 1985, 24, 463-474. (6) Julka, V.; Doherty, M. F. Geometric Behavior and Minimum Flows for Nonideal Multicomponent Distillation. Chem. Eng. Sci. 1990, 45, 18011822. (7) Ko¨hler, J.; Aguirre, P.; Blass, E. Minimum Reflux Calculations for Nonideal Mixtures Using the Reversible Distillation Model. Chem. Eng. Sci. 1991, 46, 3007-3021. (8) Poellmann, P.; Glanz, S.; Blass, E. Calculating Minimum Reflux of Nonideal Multicomponent Distillation Using Eigenvalue Theory. Comput. Chem. Eng. 1994, 18 (Suppl.), S49-S53. (9) Bausa, J.; Watzdorf, R. V.; Marquardt, W. Shortcut Methods for Nonideal Multicomponent Distillation:1. Simple Columns. AIChE J. 1998, 44, 2181-2198. (10) Stichlmair, J. G.; Fair, J. R. Distillation: Principles and Practice; Wiley: Hoboken, NJ, 1998.

(11) Castillo, F. J. L.; Thong, D. Y. C.; Towler, G. P. Homogeneous Azeotropic Distillation. 1. Design Procedure for Single-Feed Columns at Nontotal Reflux. Ind. Eng. Chem. Res. 1998, 37, 987-997. (12) Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection, Dechema; Chemistry Data Series; DECHEMA: Frankfurt/Main, Germany, 1977. (13) Douglas, J. M. Conceptual Design of Chemical Processes; McGrawHill: New York, 1988. (14) Bauer, M. H.; Stichlmair, J. Design and Economic Optimization of Azeotropic Distillation Processes Using Mixed-Integer Nonlinear Programming. Comput. Chem. Eng. 1998, 22 (9), 1271-1286. (15) Viswanathan, J.; Grossmann, I. E. Optimal Feed Locations and Number of Trays for Distillation Columns with Multiple Feeds. Ind. Eng. Chem. Res. 1993, 32, 2942-2949.

ReceiVed for reView October 16, 2006 ReVised manuscript receiVed May 16, 2007 Accepted August 7, 2007 IE061329H

Method for the Design of Azeotropic Distillation Columns - American

Recommend Documents