Azeotropic Distillation in a Middle Vessel Batch Column. 3. Model

Ind. Eng. Chem. Res. 1999, 38, 1549-1564

1549

Azeotropic Distillation in a Middle Vessel Batch Column. 3. Model Validation Weiyang Cheong and Paul I. Barton* Department of Chemical Engineering and Energy Laboratory, 77 Massachusetts Avenue, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

A dimensional time model of the middle vessel batch distillation column (MVC) is developed in the ABACUSS process modeling environment, and simulations are conducted to validate the theoretical insights developed for the operation of the MVC based on a warped time model of the MVC. The qualitative dynamics of the MVC operated in the presence of linear separation boundaries are validated via simulations conducted on the ternary azeotropic mixture of acetone, chloroform, and methanol. It is also shown via simulation that the separation results obtained from a column with significant but reasonable amounts of holdup on the trays are not significantly different from a column in which holdup in the trays is assumed to be negligible. Theoretical operating policies for separating the azeotrope of acetone and chloroform using benzene as a batch entrainer are also validated using the ABACUSS model. Finally, we explore the advantages and disadvantages of different feasible operating policies for separating a mixture of acetone, benzene, and chloroform completely into its constituent pure components. Introduction This is the final paper in a three-part series of papers on the middle vessel (batch distillation) column (MVC). This paper validates the theoretical results developed in our previous work1,2 by simulating the operation of a MVC for the distillation of azeotropic mixtures. In our first paper,1 a mathematical model involving a system of differential-algebraic equations (DAEs) was developed for the MVC. Assumptions used in the model include (1) constant molar overflow (CMO) and (2) quasisteady state (QSS). In this paper, the model, of the MVC is coded in the ABACUSS [ABACUSS (Advanced Batch and Continuous Unsteady-Steady Simulator) process modeling software, a derivative work of gPROMS software, ©1992 by Imperial College of Science, Technology and Medicine.] language, and simulations are conducted using ABACUSS/DSL48S.3 This paper is in three sections. The first section of this paper presents the dimensional time model of the MVC used in our simulation analysis of the MVC. This differs from the dimensionless time model used in the theoretical derivation of the qualitative dynamics of the MVC, in that dimensional time rather than dimensionless time is used. Dimensional time makes the model more computationally tractable, but makes the model harder to analyze theoretically. The second section of this paper presents the simulation results obtained for the ternary azeotropic system of acetone, chloroform, and methanol, with three binary azeotropes, a ternary azeotrope, and four separatrices, of which only one is relatively straight. The results of these simulations serve to validate theoretical results in the presence of straight MVC distillation boundaries as obtained in our first paper.1 The third part of this paper summarizes simulation results obtained for the ternary azeotropic system of acetone, benzene, and chloroform. Simulations were * Corresponding author. Phone: +1-617-253-6526. Fax: +1-617-258-5042. E-mail: [email protected].

conducted to validate the theoretical operating policies proposed in our second paper2 for separating the acetone-chloroform azeotrope with benzene as the batchwise entrainer. Comparisons are also made between different feasible operating policies to highlight the trade-offs inherent in the choice between these policies. Mathematical Model of the MVC The equation describing the change in the liquid composition in the MVC still pot in vector notation was shown to be1

dxM ) xM - λxD - (1 - λ)xB dξ

(1)

where the x’s are NC vectors of composition, superscripts indicate location of the composition M for the MVC still pot, D for the distillate product, and B for the bottoms product), and ξ is the warped time variable (dimensionless time) defined in the interval [0, ∞) as

dξ ) -d(ln M)

(2)

such that ξ f ∞ as the still pot is boiled dry. The ABACUSS model was built in dimensional time to verify the results obtained from the analysis of the MVC obtained by introducing a dimensionless time. If the results obtained from the dimensional time model matched those predicted theoretically using the dimensionless time model of the MVC, its ability to predict the qualitative behavior of the MVC would have been validated. This then allows further analysis on the MVC using the dimensionless time model of the MVC, which is much more tractable for theoretical analyses than using the dimensional time model. Dimensional Time Model of the MVC. The schematic configuration of a MVC is shown in Figure 1. The model assumes constant molar overlow (CMO) and is based on a differential model of the rate of composition change in the middle vessel. The column has ND trays

10.1021/ie980471i CCC: $18.00 © 1999 American Chemical Society Published on Web 02/09/1999

1550 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999

dM ) Ld + Vb - Vd - Lb dt

(4)

while the overall component mass balance is given by

dMxM ) Ldx1 + VbyNB - VdyM - LbxM dt

(5)

Next, we consider the mass balances which can be written for the trays in the column. For the rectifying section, (envelope C in Figure 1):

Hnd

dxnd ) Ldxnd+1 + Vdynd-1 - Ldxnd - Vdynd dt ∀ 1 e nd e ND (6)

where y0 ) yM is the middle vessel vapor composition, and because of the total condenser assumption xND+1 ) yND ) xD. A mass balance around the condenser (envelope F) yields

Vd ) Ld + D

(7)

The vapor-liquid equilibrium (VLE) relationship on each tray and in the middle vessel can also be written as

yi ) yi(xi,T(xi,P),P)

∀ i ∈{nd},{nb},M

(8)

where yi is modeled using the NRTL local-composition activity coefficient model.4 A similar set of equations can also be obtained for the stripping section of the MVC, by considering envelopes E and G in Figure 1: Figure 1. Schematic configuration of a MVC.

and a total condenser in the rectifying section and NB trays and a total reboiler in the stripping section. To investigate the effect on the qualitative behavior of the MVC due to small amounts of holdup in the trays, we introduce a model that alllows for a small and constant amount of overall liquid holdup in each of the trays (1ND) in the rectifying section: Hnd for nd ∈{1...ND}, and in each of the trays (1-NB) in the stripping section: Hnb for nb ∈{1...NB} of the MVC. The mixture to be distilled has NC components and is characterized with nonideal VLE models such as the NRTL or Wilson liquid composition activity coefficient models. Total molar holdup in the middle vessel is M, and two diferent vapor and liquid flow rates exist respectively in the stipping and rectifying sections. In the rectifying section, the vapor and liquid flow rates are Vd and Ld, respectively, while in the stripping section, the corresponding vapor and liquid flow rates are Vb and Lb, respectively. The presence of the heat exchanger at the middle vessel allows for different flow vapor flow rates in the two sections of the column. Distillate is drawn at a flow rate of D from the total condenser, and a bottoms product is drawn at a flow rate of B from the total reboiler, with the dimensionless “middle vessel parameter” defined as λ ∈ [0, 1]:

D λ) D+B

(3)

First, from the overall mass balance for the middle vessel, we obtain the following “dimensional time equation”:

Hnb

dxnd ) Lbxnb+1 + Vbynb-1 - Lbxnb - Vbynb dt ∀ 1 e nb e NB (9)

where xNB+1 ) xM is the still pot liquid composition, and because of the total reboiler assumption y0 ) x1 ) xB.

Lb ) Vb + B

(10)

The VLE relationships given by eq 8 also hold as before in the stripper trays. In the presence of finite reboil and reflux ratios, the reflux ratio (Rd) and reboil ratio (Rb) are defined accordingly as Rd ) Ld/D and Rb ) Vb/B. The tray holdup times in the rectifying (hnd) and stripping (hnb) sections of the column are defined respectively as hnd ) Hnd/D and hnb ) Hnb/B. Equations 6-10 are then modified to obtain for the rectifying section of the MVC

hnd

dxnd ) dt nd+1 Rdx + (Rd + 1)ynd-1 - Rdxnd - (Rd + 1)ynd ∀ 1 e nd e ND (11)

Similarly, for the stripping section of the MVC

hnb

dxnb ) dt (Rb + 1)xnb+1 + Rbynb-1 - (Rb + 1)xnb - Rbynb ∀ 1 e nb e NB (12)

Note that if all the tray holdups are set to zero, this

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1551

model reduces to the time domain analogue of the warped time model presented in part 1.1 Theoretical Results under the Assumption of Limiting Conditions and Linear Separation Boundaries First, operating the MVC under limiting conditions (zero holdup in trays, reboiler, and reflux drum; ND, NB f ∞; Rb, Rd f ∞), it was found that the distillate and bottoms products of the MVC are given by1

xD(ξ) ) R(xM(ξ))

(13)

xB(ξ) ) ω(xM(ξ))

(14)

Table 1. Composition of Fixed Points in the Acetone-Chloroform-Methanol System fixed point label

xAcetone

xChloroform

xMethanol

characteristic

A C M AC AM CM ACM

1.0 0.0 0.0 0.3455 0.7780 0.0 0.3396

0.0 1.0 0.0 0.6545 0.0 0.6579 0.2322

0.0 0.0 1.0 0.0 0.2220 0.3421 0.4282

saddle point saddle point stable node stable node unstable node unstable node saddle point

and

where R(xM(ξ)) and ω(xM(ξ)) denote the R and ω limit sets, respectively, of the current still pot composition given by xM(ξ).5 Furthermore, it was elucidated1 that the distillate and bottoms product compositions (being the R and ω limit sets, respectively, of the simple distillation residue curves) would be invariant in time, until the MVC still pot composition entered a different basic distillation region. These theoretical assertions will be validated by simulating the separation of a mixture of acetone, chloroform, and methanol in an MVC operated near limiting conditions. Second, eq 1 under these limiting conditions can then be written as

dxM ) xM(ξ) - xP(xM(ξ)) dξ

(15)

Figure 2. Batch distillation regions Y1-Y6 in the A-C-M system for the rectifier configuration.

where xP, the net product drawn from the column, is defined by

xP ) λxD - (1 - λ)xB M

(16) M

) λR(x ) - (1 - λ)ω(x )

(17)

Hence, the MVC still pot composition will move directly away from the net product xP, where xP is strictly dependent on the current R and ω limit sets and the value of λ. This prediction will also be validated by simulation of the MVC operation. Finally, the theory of MVC batch distillation regions is tested on the acetone-chloroform-methanol mixture. The MVC batch distillation regions are enumerated, and the qualitative dynamics of the MVC operating on a sample point in each of the MVC batch distillation regions will be studied via simulation. Results obtained via simulation are compared to dynamic behavior predicted by theoretical analysis of the MVC.1 Acetone-Chloroform-Methanol System. The acetone-chloroform-methanol system is one that exhibits a total of three binary azeotopes (two unstable nodes and one stable node) and one ternary azeotrope (saddle point); it is a 113-S system, as enumerated by Doherty and Caldarola.6 The system is characterized by some extremely curved separation boundaries, which results in some behavior not enountered in systems with straight separation boundaries. The purpose of using the acetone-chloroform-methanol system as an example is to show that the theoretical analysis developed for straight separation boundaries can also be applied with appropriate modifications, to an existing azeotropic

Figure 3. Batch distillation regions Z1-Z6 in the A-C-M system for the stripper configuration.

mixture with extremely curved separation boundaries. A summary of the fixed points for this ternary mixture is provided in Table 1. Because of the large number of fixed points in this ternary system, there also exist a large number of batch distillation regions for the system, for each of the stripper, rectifier, and middle vessel configurations. These batch distillation regions are shown as follows: Figure 2 for the batch rectifier column, Figure 3 for the batch stripper column and, finally, Figure 4 for the MVC.

1552 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 4. Product Sequences Expected for Each Region χ1 - χ24 in the Presence of Curved Boundaries, λ ) 1/2

Figure 4. Batch distillation regions χ1-χ24 in the A-C-M system for the middle vessel configuration, for λ ) 1/2. Table 2. Product Sequences for Regions Yi for i ) 1...6, in a Batch Rectifier for the A-C-M Mixture region

first cut

second cut

third cut

Y1 Y2 Y3 Y4 Y5 Y6

CM CM CM AM AM AM

C ACM-mix ACM ACM ACM-mix A

AC AC M M AC AC

Table 3. Product Sequences for Regions Zi for i ) 1...6, in a Batch Stripper for the A-C-M Mixture region

first cut

second cut

third cut

Z1 Z2 Z3 Z4 Z5 Z6

AC AC M M AC AC

C ACM ACM ACM-mix ACM-mix A

CM CM CM M AM AM

There are a total of six batch distillation regions for the batch rectifier, Y1-Y6, six batch distillation regions for the batch stripper, Z1-Z6, and a grand total of 24 MVC batch distillation regions, χ1-χ24. On the basis of theory developed for the limiting behavior of batch rectifiers and strippers,7,8 the expected product sequence for each of the enumerated batch distillation regions are tabulated in Table 2 (for the rectifier) and Table 3 (for the stripper). On the basis of the limiting analysis developed for the MVC by Cheong and Barton,1 the expected product sequences for each of the 24 enumerated batch distillation regions of the MVC are also tabulated in Table 4. In the tables, cuts which are followed by a suffix of “mix” indicate product cuts which are affected by curvature of the pot composition boundaries in the vicinity of the cut. This results in a varying composition in the cut drawn from the column as the still pot composition is forced to trace out a route along the curved boundary, and the product formed is governed by mass balance. The curved stable separatrices in the A-C-M system form pot composition boundaries for all values of λ in the MVC other than λ ) 0.1 Similarly, the curved unstable separatrices in the A-C-M system form pot composition boundaries for all values of λ in the MVC other than the value of λ ) 1. Thus, for a

region

first cut

second cut

third cut

χ1 χ2 χ3 χ4 χ5 χ6 χ7 χ8 χ9 χ10 χ11 χ12 χ13 χ14 χ15 χ16 χ17 χ18 χ19 χ20 χ21 χ22 χ23 χ24

[CM,M] [CM,M] [CM,M] [CM,M] [AM,M] [AM,M] [AM,M] [AM,M] [CM,AC] [CM,AC] [CM,AC] [CM,AC] [CM,AC] [CM,AC] [CM,AC] [CM,AC] [AM,AC] [AM,AC] [AM,AC] [AM,AC] [AM,AC] [AM,AC] [AM,AC] [AM,AC]

[ACM-mix,M] [ACM-mix,M] [CM,ACM-mix] [CM,ACM-mix] [ACM-mix,M] [ACM-mix,M] [AM,ACM-mix] [AM,ACM-mix] [CM,C] [CM,C] [C,AC] [C,AC] [CM,ACM-mix] [CM,ACM-mix] [ACM-mix,AC] [ACM-mix,AC] [ACM-mix,AC] [ACM-mix,AC] [AM,ACM-mix] [AM,ACM-mix] [AM,A] [AM,A] [A,AC] [A,AC]

[M,M] [ACM,ACM] [ACM,ACM] [CM,CM] [M,M] [ACM,ACM] [ACM,ACM] [AM,AM] [CM,CM] [C,C] [C,C] [AC,AC] [CM,CM] [ACM,ACM] [AC,AC] [ACM,ACM] [ACM,ACM] [AC,AC] [ACM,ACM] [AM,AM] [AM,AM] [A,A] [A,A] [AC,AC]

generic MVC not operating under the special cases of λ at 0 or 1, the separatirces, both stable and unstable, form pot composition boundaries for the MVC. As explained by Cheong and Barton,1 this implies that the MVC’s motion is more constrained at a fixed value of λ than either that of the stripper or the rectifier, but when λ is allowed to vary, the MVC is less constrained than both the stripper or the recitifier. Finally, it should be noted that the expected product cuts in each MVC batch distillation region, as denoted in Figure 4 and Table 4, were based on λ ) 1/2. Varying the value of λ would result in MVC batch distillation regions of different shapes and sizes, but the characteristic behavior associated with each of these regions would be unchanged. For all values of 0 < λ < 1, there would be 24 batch distillation regions of non-zero volume; only when λ ) 1 (batch rectifier) and λ ) 0 (batch stripper) are there six batch distillation regions of non-zero volume, as the other 18 regions deform into regions of zero volume. Operation of the MVC with the Operating Parameter at λ ) 1/2. In this section, the MVC is used for processing an initial composition point in which each of the 24 middle vessel batch distillation regions, at an operating value of λ ) 1/2. Simulations were conducted for a sample point within each of the 24 enumerated regions, and the results obtained for each of the sample points were indeed indicative of the behavior expected of the batch distillation region in which these sample points belonged. Results of initial compositions in regions χ1 and χ24 are presented. Region χ1 demonstrates the behavior of a ternary mixture separated in a MVC, in the presence of relatively straight boundaries. Region χ24 represents the separation of a ternary mixture in a MVC for which the batch distillation boundary (being the C-A edge) is completely straight. Results for all other regions are available in Cheong.9 Operating conditions for each simulation were kept constant so as to ensure that the results could be comparable to each other. The pertinent operating parameters used are summarized in Table 5. The behavior of the column as ND, NB f ∞ and the reflux

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1553 Table 5. Operating Conditions for the MVC Simulations operational parameter

numerical value

units

initial still plot holdup vapor flow rate (Vb) liquid flow rate (Ld) distillate product flow rate bottoms product flow rate resulting value of λ resulting reflux ratio (Rd) resulting reboil ratio (Rb) no. of trays in the rectifying section of column no. of trays in the stripping section of column operating pressure in column

100 10 10 0.01 0.01 1/ 2 1000 1000 50

mol mol/time mol/time mol/time mol/time dimensionless dimensionless dimensionless dimensionless

50

dimensionless

1

bar

Figure 5. Graph of distillate product composition against time.

Figure 6. Graph of bottoms product composition against time.

Figure 7. Plot of still pot motion in composition space.

and reboil ratios f ∞, was approximated by using a reflux/reboil ratio of 1000, and up to 100 trays with zero holdup in the entire column. (1) Analysis of the Results from Region χ1. The results are representative of the use of a MVC to separate a mixture of acetone, chloroform, and methanol, in which the still pot composition encounters a MVC batch distillation boundary (stable separatrix in this case) and travels along the stable separatrix to a stable node which forms the final R and ω set of the distillation process. The expected product sequence for region χ1 is ([CM,M], [ACM-mix,M], [M,M]). The initial still pot composition chosen to represent region χ1 was (xacetone ) 0.05, xchloroform ) 0.22, xmethanol ) 0.73). As shown in Figure 5, the distillate product cut from the MVC was (CM, ACM-mix, M), the respective R limit sets of the still pot composition, as expected. A slight curvature of the stable separatrix encountered resulted in a slight “mix” in the ACM cut, but when compared to the “mixed” cut that was obtained when the still pot composition encountered either the ACM-AC, ACMAM, or ACM-CM separatrices, this “mixing” is almost negligible. The bottoms product cut was predicted to be pure M (ω limit set of the still pot composition) and invariant throughout the operation of the column (the ω limit set remained unchanged as the still pot composition moved from one basic distillation region to another). This was indeed observed, as shown in Figure 6. The resulting motion of the still pot composition in the composition simplex is also illustrated in Figure 7. The still pot composition moved directly away from the combined net product (given by midpoint between fixed points of CM and M), until it encountered the curved stable separatrix between M and ACM. At this point, a change in the R limit set occurred, and the new products of the rectifying section of the MVC became the ACM azeotrope. The bottoms product was unchanging because the ω limit set of the still pot composition remained as pure M. The still pot then traced out the stable separatrix, drawing a net product that was


Figure 8. Graph of still pot composition against time.


tangent to the separatrix (at the point where the still pot composition was instantaneously located). This continued until the still pot composition finally entered the fixed point of pure M. Pure M was then drawn from the MVC for both the distillate and the bottoms product (since the still pot composition was pure M until the still pot ran dry (i.e., ξ f ∞). The still pot composition as a function of time is also presented in Figure 8 and can be referenced with Figure 5 to validate that the switch in the product compositions occurred at the points in time when the still pot composition moved from one basic distillation region to another. (2) Analysis of the Results from Region χ24. The results obtained from simulation of an initial MVC still pot composition in region χ24 is presented here. In this region, the still pot composition enters a straight middle vessel batch distillation boundary (composition edge A-C and moves toward a stable node which forms the final R and ω set of the process. The expected product sequence for region χ24 is ([AM,AC], [A,AC], [AC,AC]). The initial still pot composition chosen to represent region χ24 was given by (xacetone ) 0.55, xchloroform ) 0.40, xmethanol ) 0.05). As presented in Figure 9, the distillate product cut from the MVC was (AM, A, AC, which was as expected for the region. Straight distillation boundaries resulted in there being no “mixed” cuts obtained. The A cut was due to the R limit set of the still pot composition becoming that of pure A when the pot composition encountered the A-C edge. Finally, when the still pot composition became AC, AC was drawn as the distillate product as well, as it became the R limit set of the still pot composition. The bottoms product cut, on the other hand, was predicted to be invariant at AC, as the ω limit set of the still pot composition did not change throughout the operation. This again corresponded to the results obtained as shown in Figure 10. As in χ1, the product composition only underwent transitions when the still

Figure 10. Graph of bottoms product composition against time.

pot composition encountered a new basic distillation region; it was almost invariant otherwise. The resulting motion of the still pot composition simplex is also illustrated in Figure 11. As before, the still pot composition moved away from the net product xP given by the midpoints (λ ) 1/2) between the respective R and ω limit sets of the current still pot compositions, with a change in the R limit set (to A) occurring when the still pot composition encountered the simplex edge of A-AC and a change in the ω limit set (to AC) occurring when the still pot composition entered the stable node of AC. The MVC still pot composition as a function of time is also shown in Figure 12 for reference with Figures 9 and 10. Comparison of Results in the Presence of Holdup in Trays. The purpose of this section is to validate that, in the absence of extensive molar holdup in each tray, the assumption of negligible holdup does not affect the qualitative results of the MVC significantly. A simulation was conducted in this spirit, to affirm that the results obtained for a column in which there was appreciable tray holdup is indeed similar (if not equivalent) to that obtained for a column in which tray holdup was assumed to be negligible (as we have done so far in all our analyses). For an initial MVC still pot composition starting in region χ24, a holdup of 0.1% of the entire charge to the column was assumed to be on each of the 100 trays. This corresponds to a total of 10% of the initial column charge accumulated on the trays other than those of the middle vessel. Using the same operating parameters given in Table 5, simulations were conducted using a modified model of the MVC, in which a constant total molar holdup of 0.1 mol was introduced onto each of the 100 trays (total initial holdup in the still pot of the column being 100 mol). An initial charge size of 110 mol with composition of (xacetone ) 0.5498, xchloroform ) 0.3939, xmethanol ) 0.0563) was chosen to represent region χ24. This was slightly different from the initial still pot composition chosen to represent region χ24 in the absence of holdup, which was (xacetone ) 0.55, xchloroform ) 0.0.40, xmethanol ) 0.05). This then allows us to compare the movement of the still pot between the two cases of (1) no holdup on the trays versus that of a (2) small amount of holdup on the trays, by starting the still pot composition at the same point. The expected product sequence for region χ24 is ([AM,AC], [A,AC], [AC,AC]), in the absence of holdup on the trays. As illustrated in Figure 13, the distillate product cut sequence of the MVC in the presence of significant holdup on the trays is exactly the same as that when there is no holdup on trays (Figure 9). It should be noted, however, that in the presence of substantial holdup on trays the transitions between cuts become


Figure 11. Plot of still pot motion composition space.

Figure 12. Graph of still pot composition against time.

seems conclusive there is no appreciable difference between the still pot composition paths for the two cases (no holdup on trays versus slight holdup on trays). From the results presented, it seems reasonable to conclude that the assumption of no holdup in the column is indeed valid as an approximation of a column in which the holdup is not unreasonably large on each tray. The analysis associated with the limiting behavior of the MVC1 thus remains applicable to well-designed columns where there is a reasonably small amount of holdup on each of the trays in the MVC. Other simulations were also conducted for each of the batch distillation regions (six for the stripper, six for the recitifier, and 24 for the MVC) enumerated for the ACM system, and the results are available as Supporting Information.1 Azeotropic Batch Distillations with a Middle Vessel Column in the Presence of Curved Separatrices


less sharp. Timing of the cuts are also different due to the differing initial composition of the total holdup in the column. The qualitative behavior does, however, remain the same. The bottoms product cut, on the other hand, was predicted to be invariant as AC, which again corresponded to results identical to those in Figure 10, so they are not repeated here. The resulting motion of the still pot composition in the composition simplex is illustrated in Figure 14, which plots the still pot composition motion in the case of no holdup (i.e., Figure 11), the still pot composition with holdup, and the total column composition with holdup on the same Gibbs diagram. From Figure 14, it

On the basis of the analysis regarding the influence of curved separatrices on batch distillation regions in a MVC, an operating procedure was developed for the separation of the ternary mixture of acetone, benzene, and chloroform when conducted in a MVC.2 This idea, in which an entrainer is added batchwise to the initial charge of the column, is completely different from that of adding an entrainer continuously over the course of the operation of the middle vessel column as suggested by Safrit et al.10,11 These operating procedures were tested using the ABACUSS model of the MVC, so as to validate the theory behind such an operating procedure. The results of the simulations are presented here. This section is in five parts. The first part revisits the basic concepts which result in the plausible separation of a mixture of acetone, benzene, and chloroform.2 The second part presents the operating policies in quantitative terms. The third part presents the simulation results using a quasistatic mode of operation with the addition of benzene as a batch entrainer (as opposed to a continuous entrainer12). The fourth part discusses the


Figure 14. Combined plot of still pot motion and total holdup motion in composition space, with and without holdup on trays.

advantages and disadvantages of adding an entrainer (mode a vs mode b), for a mixture with its original composition starting in region ν. Finally, the quasistate mode of operation is compared to that of a non quasistate mode of operation while separating an original mixture corresponding to the acetone-chloroform azeotrope. Separation of an Acetone-Benzene-Chloroform Mixture in a Middle Vessel Column. Revisiting Cheong and Barton,2 there were two modes of operation feasible: (a) the recycle of an azeotropic cut to the next batch (or discarded as waste) with no addition of benzene and (b) no/negligible recycle of azeotropic cuts, but with the addition of fresh benzene as a batch entrainer. For mode b, the region of desired initial pot composition, achieved via mixing, is given by σ as illustrated in Figure 15. By observing the location of the separatrix on the residue curves map, the line segment F was determined to be

xbenzene ) 0.8...1 xchloroform ) 0.2...0

(18)

xacetone ≈ 0 This implies that the region σ is bounded by the A-B edge, the line segment defined as F on the B-C edge, and the line segment joining A to the composition point given by (xacetone ) 0, xchloroform ) 0.8, xmethanol ) 0.2). An original composition corresponding to the acetonechloroform azeotrope Fazeotrope was chosen to illustrate the applicability of mode b, but not mode a of operation, to an azeotropic mixture. To illustrate the applicability of mode b of operation to all regions within the composition simplex, original charges Fµ and Fν from each of the regions µ and ν were also chosen and both operated under mode b. To compare the results of mode a versus mode b of operation, the original charge of Fν was operated under mode a (without mixing of benzene), and the results of

Figure 15. Initial composition of mixture to be separated, before and after benzene is added as the entrainer to the still pot.

the separation compared to that of Fν were operated under mode b. Furthermore, it was determined that quasistatic operation of the column (after it crosses the separatrix) is superior2 because purity is maintained (with the consistently high reflux ratio) while operation time was decreased. Hence, only operation of the MVC with a quasistatic step was studied. Operating the column without a quasistatic step would just result in a longer time, with the qualitative results remaining the same. Operating Parameters, Feed/Mixture Composition, and Charge Sizes. Operating conditions for each simulation were kept constant so as to ensure comparable results. The pertinent operating parameters are thus summarized in Table 6. The qualitative behavior of the column as N f ∞ and the reflux/reboil ratios f ∞ was approximated by using a reflux/reboil ratio of 1000 and a total of 100 trays in the MVC. As before,

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1557 Table 6. Operating Conditions for the Rectifier and Stripper Simulations operational parameter

numerical value

units

vapor flow rate (stripping) liquid flow rate (rectifying) rectifying product flow rate stripping product flow rate resulting reflux ratio resulting reboil ratio no. of trays in the rectifying column no. of trays in the stripping column operating pressure in column

10 10 0.01 0.01 1000 1000 50 50 1

mol/time mol/time mol/time mol/time dimensionless dimensionless dimensionless dimensionless bar

the vapor-liquid equilibria relationships between the components are given by the NRTL local composition activity coefficient model, and the vapor pressure of the component is given by an extended Antoine equation from Aspen Plus.13 In our attempt to produce product qualities of 99.9% or better, the following operating policy was employed in each of the simulations: (1) With the original charge of the mixture to be separated, an appropriate amount of benzene was added to the charge, such that the ratio of benzene to chloroform in the initial still pot composition is

ratio of benzene to chloroform ) 4:1 This corresponds to the initial still pot composition lying on the edge of the region σ. (2) The middle vessel column is

operated at λ ) 1 (i.e., as a rectifier), until the following conditions are met:

xD acetone e 0.999 which corresponds to the still pot composition reaching the separatrix, resulting in a degradation of product purity (from 100% purity), as the R limit set switches from that of pure acetone to the azeotrope of AC. (3) The middle vessel column is then

operated at λ ) 0 (i.e., as a stripper), until the following conditions are met: M xM chloroform g xbenzene

which corresponds to the point where pure chloroform should also be drawn from the column. (4) At this point, a distillate product flow rate of 0.01 mol/time is reintroduced into the rectifying column, such that a reflux ratio of 1000 is again achieved in the rectifying section of the column, and such that benzene and chloroform will be exhausted in the still pot at the same point in time. This results in the column operated at

λ)

0.01 1 ) 0.01+0.01 2

or a quasistatic operation, until the following conditions are met: B (xD chloroform < 0.999) ∨ (xbenzene < 0.9999)

which corresponds to the degradation of products as the column finally runs out of benzene and chloroform, and the acetone concentration starts becoming significant in either the distillate or bottoms product. Operation is ceased at this point. The resulting purity of all three components recovered were in the region of 100.0%. The policy of drawing chloroform as near to the end of the operation as possible is due to the fact that even though the separatrix hugs the B-C edge at the point in time when the still pot encounters the separatrix and stops drawing acetone, there remains some acetone in the still pot. While its concentration is initially negligible (when the quantity of benzene and chloroform is substantial), it is no longer negligible as the still pot boils down. If the column was operated in a quasistatic state immediately after the still pot composition crossed the separatrix, it would be forced back onto the separatrix after a short period of operation. When the still pot composition is forced back onto the separatrix, the net product drawn will have to be from a location that is tangent to the separatrix. As the separatrix approaches but not quite reaches the B-C edge, this would imply that pure chloroform and benzene can no longer be drawn in a quasistatic operation if this occurs. As such, this is avoided by moving the MVC still pot composition toward the chloroform vertex (by drawing benzene in the stripping operation for a longer period of time), such that as the amount of acetone in the column becomes significant again, the still pot would move toward the acetone vertex within the region of µ and encounter the separatrix only at a much later point in time. The point in time when the still pot composition encounters the separatrix again is where the operation of the column is ceased. Finally, it should be noted that if the stripper operation was allowed to continue until the still pot encounters the C-AC edge, followed by a rectifying operation to recover the chloroform, the amount of pure products recovered from the column will be maximized. However, this results in a substantial increase in the processing time, which does not seem justifiable given the minute quantities of A, B, and C discarded as a result of using a quasistatic operation. This point is of importance because should the chemicals prove extremely valuable or waste treatment costs were very high, and time is not a concern, then a stripping operation, followed by a rectifying operation, as enumerated below would be the optimal policy. Steps 3 and 4 should then be substituted as follows: (a) The middle vessel column is then operated at

λ)0 (i.e., as a stripper), until the following conditions are met:

xM benzene e 0.001 which corresponds to the point where all pure benzene has been drawn. (b) At this point, the column is operated again as a rectifier, that is operated at

λ)1 until the following conditions are met:

xD chloroform < 0.999

1558 Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 Table 7. Molar Amounts of Original Charge, Benzene Added, and Resultant Initial Still Pot Charge component

Fµ

Fν

Fazeotrope

original charge of acetone original charge of benzene original charge of chloroform amount of benzene added resulting total charge

10 15 75 285 385

50 25 25 75 175

33.4 0.0 66.6 266.4 366.4

Figure 17. Bottoms composition for Fazeotrope.

Figure 16. Distillate composition for Fazeotrope.

which corresponds to the degradation of products as the still pot composition encounters the azeotropic fixed point, and the azeotrope starts coming out of the rectifying section of the column. Operation is ceased at this point. The purities of all three components recovered are again in the region of 100.0%. This operating policy will be simulated for the case of Fazeotrope to illustrate that the time savings of quasistatic operation largely outweighs the additional amount of products that can be recovered from the MVC if the operating policy of a stripper followed by a rectifier was used instead. Separation in the Middle Vessel Column Using Operation Mode b. The original charges, amount of benzene added to the charge, and resultant total charge are summarized in Table 7. The original composition and resultant initial still pot compositions of each operation are summarized in Table 8. (1) Simulation for the Separation of Fazeotrope. Results of the simulation performed for an original charge with a composition corresponding to the azeotrope of AC are presented. Total time required to separate the mixture was approximately 29 500 units of time. Purities for each of the cuts of acetone, benzene, and chloroform were >99.9%, as specified by the operating policy and illustrated in Figures 16 and 17. Figure 16 shows the change in product composition in the rectifying section, as the MVC still pot composition crosses over from region ν to region µ. Because of the specified limiting conditions, the transition is extremely sharp, and this sharp cut helps in maintaining the purity of the products. It should be noted that this transition need not be so sharp, as the chloroform product is not drawn until much later, when the amount of benzene remaining in the column equals the amount of chloroform remaining in the column. Next, variation of the still pot composition during the operation is presented as a function of time (Figure 18) and within the composition simplex (Figure 19). Figure

Figure 18. Still pot composition for Fazeotrope as a function of time.

19 shows that while the MVC was operated as a rectifier, the initial still pot composition moves directly away from the acetone fixed point, encounters the separatrix near the B-C edge (in region F), and changes its operation to that of a stripper. The still pot composition than moves directly away from the fixed point of M pure benzene, until the xM benzene ) xchloroform, at which point the “quasi static” operation of the column begins. However, because of the presence of residual acetone in the column, the operation is not strictly quasi static, as the acetone that is not drawn out of the column causes the still pot composition to move toward the acetone vertex. Finally, the still pot composition encounters the separatrix, and operation is ceased. The corresponding holdup of the components in the still pot, and accumulation of each of the distillate and bottoms cuts, are illustrated in Figures 20-22. As shown in Figure 21, the two cuts of acetone and the chloroform drawn from the rectifying section of the column are sufficiently apart in time. Resolution of the cuts should not pose a problem. Even if the column was not limiting and the cuts not as sharp as those simulated by our limiting column, complete separation should be possible. As expected, the bottoms cut is composed of pure benzene. At the end of the operation, only a trickle of a mixture of acetone, benzene, and chloroform remains in the column (Figure 20). A summary of the inventory of each of the components at the end of the operation is presented in Table 9. Each of the cuts of acetone (distillate first cut), benzene (bottoms cut), and chloroform (distillate second cut) have near 100% purities. Only 1.20% of the acetone and 5.08% of the chloroform were unrecoverable; 1.32% of the benzene added as the entrainer was also discarded.

Table 8. Compositions of Original Charge and Initial Composition of Still Pot Given as (xAcetone, xBenzene, xChloroform) component

Fµ

Fν

Fazeotrope

original charge composition initial still pot composition

(0.10,0.15,0.75) (0.026,0.779,0.195)

(0.50,0.25,0.25) (0.286,0.571,0.143)

(0.334,0.0,0.666) (0.091,0.727,0.182)


Figure 19. Still pot composition for Fazeotrope in composition space.

Figure 20. Still pot molar holdup for Fazeotrope as a function of time.

Figure 22. Bottoms molar holdup for Fazeotrope as a function of time. Table 9. Final Inventory (mol) of Components for Fazeotrope Using Mode b Operation

Figure 21. Distillate molar holdup for Fazeotrope as a function of time.

This is negligible compared to the recovery of 98.8% of the acetone and 94.2% of the chloroform that was charged as the azeotrope; 98.68% of the benzene introduced as the entrainer was also recovered at near 100% purity, which means that it can be recycled for use in other parts of the plant or resold at market value. Finally, a plot of the middle vessel parameter as a function of time is also provided in Figure 23. (2) Simulation for the Separation of Fµ. In this section, the results of the simulation performed for an original charge from the composition space of the region

component

acetone

benzene

chloroform

initial still pot final still pot percentage of initial (%) distillate first cut percentage of initial (%) distillate second cut percentage of initial (%) bottoms cut percentage of initial (%)

33.4 0.40 (1.20) 33.0 (98.8) 0.0 (0.0) 0.0 (0.0)

266.4 3.52 (1.32) 0.0 (0.0) 0.0 (0.0) 262.88 (98.68)

66.6 3.38 (5.08) 0.0 (0.0) 63.22 (94.92) 0.0 (0.0)

µ are presented. Total time required for the separation of this mixture was 31 000 units of time. Purities of each of the cuts of acetone, benzene, and chloroform were >99.9% (Figures 24 and 25). Figure 24 also shows the change in product composition in the rectifying section, as the still pot composition crosses over from region ν to region µ. Graphs of the still pot composition as a function of time and its path in the composition simplex, of the molar accumulation and holdups in each of the cuts and the still pot, and of the variation of λ with time are all similar in nature to that obtained for Fazeotrope, and as such are detailed in Cheong.9 Of interest, however, is the quality of the separation and the amount of acetone, benzene, and chloroform recovered with respect to the


Figure 23. Middle vessel parameter, λ, for Fazeotrope as a function of time.

Figure 26. Distillate composition for Fν.

Figure 27. Bottoms composition for Fν. Figure 24. Distillate composition for Fµ.

Figure 25. Bottoms composition for Fµ. Table 10. Final Inventory (mol) of Components for Fµ Using Mode b Operation component

acetone

benzene

chloroform


10 (0.44) (4.4) 9.56 (95.6) 0.0 (0.0) 0.0 (0.0)

300 (3.96) (1.32) 0.0 (0.0) 0.0 (0.0) 296.04 (98.68)

75 (3.81) (5.08) 0.0 (0.0) 71.19 (94.92) 0.0 (0.0)

initial amount of acetone, benzene, and chloroform added. This information is summarized in Table 10. As seen in Table 10, each of the cuts of acetone (distillate first cut), benzene (bottoms cut), and chloroform (distillate second cut) are again of near 100% purity. Only 4.4% of the acetone and 5.08% of the chloroform were not recoverable; 1.32% of the benzene added as the entrainer was also discarded. This is negligible compared to the recovery of 95.6% of the acetone and 94.2% of the chloroform that was charged as the azeotrope; 98.68% of the benzene introduced as the entrainer was also recovered at 100% purity, which means that it can be recycled for use or resold at market

value. The percentage of benzene and chloroform recovered are the same as those of Fazeotrope because the operating policies separating benzene and chloroform (after most of the acetone was removed) were exactly the same. The percentage of acetone not recovered is larger in this case because of the larger initial charge of benzene and chloroform that was present in the still pot, which results in a larger amount of acetone retaining in the still pot when the separatrix is encountered. (3) Simulation for the Separation of Fν. In this section, the results of the simulation performed for an original charge from the composition space of the region ν are presented. Total time required for the separation of this mixture was 14 500 units of time. Purities of each of the cuts of acetone, benzene, and chloroform were again >99.9%, as illustrated by Figures 26 and 27. Figure 26 also shows the change in product composition in the rectifying section, as the still pot composition crosses over region ν to region µ. Graphs of the still pot composition as a function of time and its path in the composition simplex, of the molar accumulation and holdups in each of the cuts and the still pot, and of the variation of λ with time are again all similar in nature to that for Fazeotrope, and as such are detailed in Cheong.9 The quality of separation and the amount of acetone, benzene, and chloroform recovered with respect to the initial amount of acetone, benzene, and chloroform added is summarized in Table 11. Each of the cuts of acetone (distillate first cut), benzene (bottoms cut), and chloroform (distillate second cut) are again of 100% purities. Only 0.3% of the acetone and 5.08% of the chloroform were not recoverable; 1.32% of the benzene added as the entrainer was also discarded. This is again negligible compared to the recovery of 95.6% of the acetone and 94.2% of the chloroform that was charged as the azeotrope; 98.68% of benzene introduced as the entrainer was also recovered at near 100% purity. The percentage of benzene and chloroform

Ind. Eng. Chem. Res., Vol. 38, No. 4, 1999 1561 Table 11. Final Inventory (mol) of Components for Fν Using Mode b Operation component

acetone

benzene

chloroform


50 0.15 (0.3) 49.85 (99.7) 0.0 (0.0) 0.0 (0.0)

100 1.32 (1.32) 0.0 (0.0) 0.0 (0.0) 98.68 (98.68)

25 1.27 (5.08) 0.0 (0.0) 23.73 (94.92) 0.0 (0.0)

recovered are again the same as those of Fazeotrope, for reasons as explained in the earlier subsection. The percentage of acetone not recovered is smaller in this case because of the smaller initial charge of benzene and chloroform that was present in the still pot, which allows a lower acetone content in the still pot before the separatrix is encountered. Comparison of Mode a of Operation versus Mode b of Operation. To highlight the differences between mode a of operation versus mode b of operation for an original mixture within the region ν, Fν was also operated under mode a of operation. The results of that simulation are presented in this section and compared to the results obtained earlier. The operating procedure for mode a to obtain product cuts with purity greater than 99.9%, is given as the following: (1) The middle vessel column is operated at

Figure 28. Distillate composition for Fν, mode a.

Figure 29. Bottoms composition for Fν, mode a.

λ)1 (i.e., as a rectifier), until the following conditions are met:

xD acetone e 0.999 (still pot composition reaching the separatrix, resulting in a degradation of product purity as the R limit set switches from that of pure acetone to the azeotrope AC). (2) The middle vessel column is then operated at

λ)0 (i.e., as a stripper), until the following conditions are met:

MxM benzene e 0.01 (all benzene effectively removed from column, and the still pot composition is essentially a point on the C-AC edge). (3) At this point, a distillate product flow rate is reintroduced into the rectifying section, such that the operating λ in the column will be given by

operated at λ )

xazeotrope - xM A A xazeotrope A

which results in a quasi static operation, drawing the azeotrope and chloroform in the appropriate proportions such that the still pot composition remains stationary, until the following conditions are met:

∑B,D (total accumulation) g 99 which corresponds to the still pot running dry, and

Figure 30. Still pot composition for Fazeotrope as a function of time, mode a.

operation is ceased at this point. The resulting purity of all three components recovered will all be in the region of 100.0%. Following the above procedure, the results of the simulation performed for Fν are presented. Total time required for the separation of this mixture was 10 000 units of time. This was in comparison to the 14 500 units of time required if mode b was used, a time savings by mode a of up to 1/3 of the time required by mode b, achieved at the cost of a larger resulting azeotropic recycle/discard cut which may be undesirable. As illustrated by Figures 28 and 29, purities of each of the cuts of acetone, benzene, and chloroform were again >99.9%. Figure 28 shows the change in product composition in the rectifying section, as the still pot composition crosses over from region ν to region µ. Figure 29 shows the change over in the ω limit set from pure B to that of the azeotrope AC as the still pot composition encounters the C-AC edge. Variation of the still pot composition during the operation is presented as a function of time (Figure 30) and within the composition simplex (Figure 31). While operated as a rectifier, the initial still pot composition moves directly away from the acetone fixed point,


Figure 31. Still pot composition for Fν in composition space, mode a.

Figure 32. Still pot molar holdup for Fν as a function of time, mode a.

Figure 34. Bottoms molar holdup for Fν as a function of time, mode a. Table 12. Final Inventory (mol) of Components for Fν Using Mode a Operation

Figure 33. Distillate molar holdup for Fν as a function of time, mode a.

encounters the separatrix near the B-C edge (within the line segment of F), and changes its operation to that of a stripper. The still pot composition than moves directly away from the fixed point of pure benzene, until it encounters the C-AC edge, at which point the “quasi static” operation of the column begins. The corresponding holdup of the components in the still pot, and the accumulation of each of the distillate and bottoms cuts, are illustrated in Figures 32-34. The first bottoms cuts is composed entirely of pure benzene as shown in Figure 34, while the second bottoms (azeotropic) cut was sufficiently small and can be

component

acetone

benzene

chloroform

initial still pot final still pot percentage of initial (%) distillate first cut percentage of initial (%) distillate second cut percentage of initial (%) bottoms first cut percentage of initial (%) bottoms second cut percentage of initial (%)

50 0.15 (0.24) 46.81 (93.62) 0.0 (0.0) 0.0 (0.0) 3.07 (7.14)

25 0.0 (0.0) 0.0 (0.0) 0.0 (0.0) 25.00 (100.0) 0.0 (0.0)

25 0.88 (3.54) 0.0 (0.0) 18.24 (72.96) 0.0 (0.0) 5.88 (23.52)

discarded without much lost or recycled to the next batch. At the end of the operation, only a trickle of a mixture of acetone, benzene, and chloroform remains in the column (Figure 32). The quality and quantity of separation achieved and the amount of acetone, benzene, and chloroform recovered with respect to the initial amount of acetone, benzene, and chloroform added is summarized in Table 12. As seen in Table 12, each of the cuts of acetone (distillate first cut), benzene (bottoms cut), and chloroform (distillate second cut) are again of near 100% purities, However, up to as much as 7.26% acetone and 27.04% chloroform were unrecoverable (lost in either the


Figure 35. Distillate composition for Fazeotrope, nonquasistatic.

Figure 37. Still pot composition for Fazeotrope, nonquasistatic. Table 13. Final Inventory (mol) of Components for Fazeotrope Using Mode b Operation, Nonquasistatic

Figure 36. Bottoms composition for Fazeotrope, nonquasitstatic.

azeotropic cut or as the residue in the still pot). None of the benzene added as the entrainer was discarded, with near 100% obtained as a pure benzene cut, which can be recycled or resold. This is relatively large in comparison to the 0.3% acetone and 5.08% chloroform lost in mode b. It should be noted, however, that less of the benzene added (none) is lost when compared to the 1.32% benzene lost in mode b. Thus, the use of a mode a operation of the middle vessel column results in a shorter separation time, but a larger portion of original feed is discarded. Thus, a trade-off exists between a shorter separation time versus a smaller portion of waste. Depending on the costs of operation, raw materials, and waste disposal, an appropriate trade-off can then be reached, in which perhaps less benzene is added (such that ratio of benzene to chloroform in the initial still pot composition is less than 4:1), but a larger cut of the azeotrope is recycled, resulting in a moderate operating time. Comparison of a Quasi Static Operation for Fazeotrope Versus a Non Quasi Static Operation. Lastly, a mode b operation with a quasi static operation phase is compared to one which does not have a quasi static operation phase. The operating schedule for an operation which does not have a quasi static phase was enumerated earlier. The results of the simulation are summarized in this section and compared to the results obtained earlier for the quasi static operation of Fazeotrope using mode b. The total time required to separate the mixture was approximately 36 500 units of time, about 7 000 units of time more than with quasi static operation, or up to 25% more time is required for the non quasi static operation of the column. Purities of each of the cuts of acetone, benzene, and chloroform were >99.9%, as specified by the operating policy, and illustrated in Figures 35 and 36. It should be noted that the azeotropic cut appearing in the bottoms product (Figure 36) was not withdrawn from

component

acetone

benzene

chloroform


33.4 0.39 (1.17) 33.02 (98.83) 0.0 (0.0) 0.0 (0.0)

266.4 0.21 (0.08) 0.0 (0.0) 0.0 (0.0) 266.19 (99.92)

66.6 1.26 (1.89) 0.0 (0.0) 65.34 (98.11) 0.0 (0.0)

Table 14. Percentage of Acetone, Benzene, and Chloroform Lost, Quasistatic Operation vs Nonquasistatic Operation component percentage lost quasistatic (%) percentage lost nonquasistatic (%) percentage improvement (%)

acetone benzene chloroform 1.20 1.17 0.03

1.32 0.08 1.24

5.08 1.26 3.82

the column because the product flow rate at the bottom of the column was set to zero at that point in time (operated as pure rectifier). Graphs of the still pot composition during the operation as a function of time and as its path within the composition simplex are also illustrated in Figures 37 and 38. Graphs of the molar accumulations in the cuts and the still pot, and of the operating λ, are in Cheong.9 They are similar to that obtained for Fazeotrope under mode b of operation. Of greater interest are the benefits from operating the MVC under non quasi static operation, traded off against the 25% increase in operating time. This benefit comes from a slight increase in the amount of pure products recovered from the separation. A summary of the inventory at the end of the operation for each of the components is presented in Table 13. As seen in Table 13, each of the cuts of acetone (distillate first cut), benzene (bottoms cut), and chloroform (distillate second cut) had 100% purities. A comparison of the amounts of acetone, benzene, and chloroform lost in the two operation schemes (quasi static, and non quasi static) are presented in Table 14. The improvements in the amount of pure products obtained is in the order of a few percent, as compared to the 25% increase in the operating time required. Unless raw materials and/or disposal waste costs dominate the cost of operation absolutely, there is no incentive to operate the MVC in a non quasi static mode, as it only improves the separation achievable slightly. Conclusions A “dimensional time” mathematical model of a middle vessel batch distillation column was presented, based


Figure 38. Still pot composition motion for Fazeotrope, nonquasistatic, in composition space.

on the simplifying assumption of constant molar overflow. This model was coded using the ABACUSS language, and simulations were solved using ABACUSS/ DSL48S. Theory on the limiting behavior of the MVC1 was validated by simulating the separation of an azeotropic ternary mixture of acetone, chloroform, and methanol. It was confirmed that when the MVC was operated under limiting conditions, the distillate product was given by the R limit set of the current still pot composition, and the bottoms product was given by the ω limit set of the current still pot composition. This product composition was also found to be invariant with xM as long as xM remained in the same basic distillation region. The MVC still pot composition moved away from the net product xP drawn from the column (as defined by eq 17), exactly as predicted by the theoretical analysis of the MVC. Finally, the bifurcations of batch distillation regions for the MVC was also validated via simulations. Theoretical operating procedures developed for the separation of a ternary azeotropic mixture of acetone, benzene, and chloroform2 were also validated via simulations. This separation can be interpreted as the use of benzene as a batch entrainer for the separation of the acetone-chloroform azeotrope. Different operating policies were also studied (mode a vs mode b, quasi static operation vs non quasi static operation), and the advantages and disadvantages of each policy highlighted. Thus, the theory developed by Cheong and Barton1,2 describing the qualitative dynamics of the MVC was validated by the simulations of the MVC model in the ABACUSS process modeling environment. Acknowledgment This work was supported by the U.S. Department of Energy under Grant DE-FG02-94ER14447 and the MIT Undergraduate Research Opportunities Program. Supporting Information Available: Bifurcation behavior in MVC batch distillation regions. This mate-

rial is available free of charge via the Internet at http:// pubs.acs.org. Literature Cited (1) Cheong, W.; Barton, P. I. Azeotropic distillation in a middle vessel batch column. 1. Model formulation and linear separation boundaries. Ind. Eng. Chem. Res. 1999, 38, 1504-1530. (2) Cheong, W.; Barton, P. I. Azeotropic distillation in a middle vessel batch column. 2. Nonlinear separation boundaries. Ind. Eng. Chem. Res. 1999, 38, 1531-1548. (3) Feehery, W. F.; Tolsma, J. E.; Barton, P. I. Efficient sensitivity analysis of large-scale differential algebraic systems. Appl. Numer. Math. 1997, 25 (1), 41-54. (4) Renon, H.; Prausnitz, J. M. Local compositions in thermodynamic excess functions for liquid mixtures. AIChE J. 1968, 14 (1), 135-144. (5) Ahmad, B. S.; Barton, P. I. Homogeneous multicomponent azeotropic batch distillation. AIChE J. 1996, 42, 3419-3433. (6) Doherty, M. F.; Caldarola, G. A. Design and synthesis of homogeneous azeotropic distillations. 3. The sequencing of columns for azeotropic and extractive distillations. Ind. Eng. Chem. Fundam. 1985, 24, 474-485. (7) Van Dongen, D. B.; Doherty, M. F. On the dynamics of distillation processes VI: Batch distillation. Chem. Eng. Sci. 1985, 40, 2087-2093. (8) Bernot, C.; Doherty, M. F.; Malone, M. F. Feasibility and separation sequencing in multi-component batch distillation. Chem. Eng. Sci. 1991, 46, 1311-1326. (9) Cheong, W. Simulation and analysis of a middle vessel batch distillation column. Bachelor’s thesis, Massachusetts Institute of Technology, May 1998. (10) Safrit, B. T.; Westerberg, A. W.; Diwekar, U.; Wahnschafft, O. M. Extending continuous conventional and extractive distillation feasibility insights to batch distillation. Ind. Eng. Chem. Res. 1995, 34, 3257-3264. (11) Safrit, B. T.; Westerberg, A. W. Improved operational policies for batch extractive distillation columns. Ind. Eng. Chem. Res. 1997, 36, 436-443. (12) Lelkes, Z.; Lang, P.; Benadda, B.; Moszkowicz, P. Feasibility of extractive distillation in a batch rectifier. AIChE J. 1998, 44, 810-822. (13) Aspen Technology. ASPEN Plus User Manual Release 9; Aspen Technology Inc.: Cambridge, MA, 1995.

Received for review July 17, 1998 Revised manuscript received December 17, 1998 Accepted December 18, 1998 IE980471I

Azeotropic Distillation in a Middle Vessel Batch Column. 3. Model

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