RD Feasible Distillation Regions

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Computers and Chemical Engineering 24 (2000) 20432054

Synthesis of distillation-based processes for non-ideal mixtures

Arthur W. Westerberg *, Jae Woo Lee, Steinar Hauan

Department of Chemical Engineering, Carnegie Mellon Uni6ersity, Pittsburgh, PA 15213, USA

Abstract

Our understanding of how to design distillation-based processes to separate mixtures displaying azeotropic behavior has grown

enormously in the past quarter century. We elegantly sketch distillation column behavior on a composition diagram where we

display VLE and column behavior using residue and distillation curves. In the presence of azeotropes, these curves partition

composition space into distillation regions that trap the performance of individual columns. We can view liquidliquid behavior

as a tearing of composition space, a tear that always spawns from a minimum binary azeotrope. A material balance across a

column section leads to a difference point, which we can use to understand column tray-by-tray and limiting behavior for

ordinary, extractive and even reactive distillation. We demonstrate how to synthesize alternative separation processes, concentrat-

ing on those that produce pure products. We use boundary curvature, solvent addition, extractive agents, liquidliquid behavior

and strategically placed reaction to step across distillation boundaries. We show that these processes always contain recycles to

gain feasibility but also to have economically attractive processes. 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Distillation based processes; Azeotropic behavior; Non-ideal mixtures; Reactive distillation; Difference points

www.elsevier.com/locate/compchemeng

1. Introduction

We were invited to prepare a paper on the synthesis

of distillation-based separation processes for the

CEPAC Workshop held September 2 and 3, 1999, at

INTEC in Santa Fe, Argentina. We elected to prepare

a tutorial paper that looks at the series of improve-

ments we have had in chemical engineering of our

understanding of these processes in the last 15 20

years. 20 years ago we had reasonable methods to aid

engineers to synthesize processes that separated rela-tively ideal mixtures, using a series of conventional two

product columns. We were just beginning to develop

visualization methods to aid us to find the better heat

integrated sequences, including the use of more com-

plex configurations such as side strippers and enrichers

and so-called Petlyuk configurations.

There were already at this time some very notable

publications guiding us to understand the behavior of

azeotropic mixtures the book by Hoffman (1964),

ex-Soviet Union literature (see the references in Pet-

lyuk, 1998) and papers by Doherty and Perkins (1978)

and then a large number of papers by Dohertys group

at the University of Massachusetts.

The theme for this paper will be visual insights,

which we strongly believe aid designers to be innova-

tive. Very powerful insights are often based on simple

approximate sketches that expose the essence of a de-

sign problem. The grand composite curve for heat

exchanger network synthesis is one example (described

in Chapter 10 in Biegler, Grossmann & Westerberg,1997). Another classic example is the McCabeThiele

diagram for binary distillation. We often teach our

students the mechanics for constructing a McCabe

Thiele diagram and show them how to determine the

number of trays for a column. However, determining

the number of trays is not the primary use for such a

diagram. We would almost always use a readily avail-

able computer program instead. Perhaps the most im-

portant use is when experienced engineers use it to

visualize how columns behave. For example, knowing

how the operating lines on a McCabeThiele diagram

shift when one preheats the feed allows one to decide if

preheating the feed is likely to useful for a given

column.

Paper presented at CEPEC, Santa Fe, Argentina, September 23,

1999.

* Corresponding author. Tel.: +1-412-2682344; fax: +1-412-

2687139.

E-mail address: [email protected] (A.W. Westerberg).

0098-1354/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved.

PII: S0098-1354(00)00575-5


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A.W. Westerberg et al. /Computers and Chemical Engineering 24 (2000) 204320542044

In this paper we shall focus on the development of

insights that have become available for separating mix-

tures that display azeotropic behavior. We shall end

this paper by presenting some of the recent insights that

are becoming available for reactive distillation. If these

are successful, we may at times be able to use sketches

to decide if we should use reactive distillation and, if so,

even where we should place the reaction within thecolumn.

We first present a number of fundamental concepts

to aid in the design of distillation-based separation

processes. We shall generally limit ourselves to ternary

mixtures so we can visualize the geometry. We shall use

a fairly informal writing style to be consistent with our

intent that this paper be tutorial and, hopefully, easy to

read.

2. Basics

In this section we shall review the use of composition

diagrams to display VL(L) behavior and to allow for

the geometric construction of the tray-by-tray behavior

of columns. Very recent developments allow us to

consider columns in which reaction is also occurring.

2.1. Composition diagrams

Composition diagrams are particularly useful to visu-

alize the performance of distillation columns, especially

ternary diagrams as we can readily sketch them on asheet of paper. A ternary diagram is triangular in

shape, and it lies entirely within a plane. A four-compo-

nent diagram forms a tetrahedron in three-space a

bit difficult for visualization while a binary diagram

is simply a line which does not convey too much

insight. A composition diagram for nc components has

nc1 degrees of freedom as the compositions all must

add to unity, which is, for example, why a three compo-

nent diagram lies in a two-dimensional plane. When we

examine difference points later, we shall find individual

component compositions that lie outside the range 01;

these add some interesting geometry to these diagrams.

2.2. Residue cur6es

It is useful to sketch the vapor liquid (VL) equi-

librium behavior of a set of species on a composition

diagram. There are two characterizations commonly

used: residue curves and distillation curves. The former

relates to boiling a liquid in a pot while the latter

corresponds to liquid compositions we would see in astaged distillation column.

For residue curves, consider having the pot of boiling

liquid shown in Fig. 1. We can determine the composi-

tion of the liquid remaining in the pot. We write the

following component material balance

dxiM

dt=xi

dM

dt+M

dxi

dt=yiV (1)

We note that dM/dt is V. We also define a dimen-

sion-less time ~=tV/M. Eq. (1) then becomes

dxd~=x

6y

6

(2)

Assuming the vapor compositions y6

are in equi-

librium with the liquid compositions x6, and if we plot

the trajectory for the liquid compositions x6 on a com-

position diagram, we get what is termed a residue

curve, i.e. the composition trajectory for the residue

that is left in a boiling pot as we boil away the liquid

versus time. Looking at this last equation as a vector

equation, we see that the direction for the vapor com-

position y6

in equilibrium with the liquid composition in

the pot x6

lies on the tangent line that touches theresidue curve at x6.

2.3. Distillation cur6es

The other type of curve we can draw, which gener-

ates a very similar diagram, is the curve passing

through the tray-by-tray liquid compositions in a

staged distillation column operating at total reflux.

Looking at Fig. 2, material balance requires that the

two streams are identical that flow counter to each

other between any two stages. Assume the vapor leav-

ing a tray is in equilibrium with the liquid leaving. To

step from tray to tray, we start with any arbitrary

composition xn. We compute yn in equilibrium with xn,

a bubble point computation. We then set xn1=yn. We

compute yn1 in equilibrium with xn1, set xn2=

yn1, etc. Thus a series of bubble point calculations will

move us up the column. In a similar fashion, we can

use a series of dew point calculations to move down the

column.

Just where will these curves head that we produce?

With increasing time, a residue curve will move upward

in temperature, terminating ultimately at a local maxi-mum temperature. Such a point is called a stable node

as the time trajectory ends there as time goes to infinity.Fig. 1. Batch still.


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A.W. Westerberg et al. /Computers and Chemical Engineering 24 (2000) 20432054 2045

Fig. 2. Total reflux column.

from this previous bubble point computation. Repeat-

ing enough times will generate a set of points leading to

the unstable node from which the curve emanates.

When close enough to this unstable node, return to the

original liquid composition and carry out a dew point

calculation for it. Repeat this step by carrying out a

dew point computation for the liquid resulting from

this previous dew point computation. Eventually thepoints will approach the stable node towards which this

curve is moving. When close enough to the stable node,

this curve is complete. Develop another curve by plac-

ing another first composition point in the composition

diagram and develop, as above, the curve for it. Repeat

until curves are developed throughout the composition

diagram.

2.4. Distillation regions

Fig. 3 illustrates the shape of residue curves for a

ternary mixture of ethanol, water and glycol. All trajec-

tories start at the unstable node the minimum

boiling azeotrope between water and ethanol, move

toward the components having intermediate boiling

points (toward water or ethanol, depending on which

direction we move away from the minimum boiling

azeotrope) and then towards the stable node corre-

sponding to pure glycol where they terminate. Points

like those for pure water and ethanol are called saddle

points as each has a trajectory that enters it, turns, and

leaves in another direction. For water for example, the

trajectory enters from the right along the lower edge,turns and leaves along the left edge toward glycol.

Of interest are topologies where there are two or

more stable and/or unstable nodes. Fig. 4 illustrates a

rather complicated composition diagram. Here there

are two unstable nodes (at local minimum temperatures

of 120C at the top and 155C along the bottom edge)

Fig. 3. Trajectories for composition in still pot.

Fig. 4. Complicated distillation or residue curve diagram.

Stepping down a column will create a set of points that

move upward in temperature, also ending at a stablenode. Integrating the differential equations for the

residue curve backwards in time or heading upward in

a column will lead downward in temperature, ulti-

mately to a local minimum point in temperature. Such

a point is known as an unstable node for the residue

curve as all curves will leave such a point as time

increases.

We can develop distillation curves by repeatedly us-

ing bubble and dew point flash computations, such as

available in commercial simulators. Pick an arbitrary

composition somewhere in the composition diagram.Do a bubble point calculation for it. Repeat this step

by finding the bubble point for the vapor composition


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Fig. 5. Vaporliquidliquid behavior on a ternary diagram.

liquidliquid behavior to be computed. Also attach two

liquid product steams to the flash unit.

Select an arbitrary overall liquid composition (point

x). If it lies in the VLL (vapor liquid liquid) equi-

librium region, a bubble point flash computation will

produce two liquid products with differing composi-

tions (points a and b) and a vapor composition (point

c) in equilibrium with both of them. The two liquidcompositions must lie at the end of a tie-line that passes

through the overall liquid composition x (a bubble

point produces no vapor so the original mixture parti-

tions into the two liquid phases). If we choose any

other liquid composition on that same tie-line, say x*,

we will again produce the exact same compositions a, b,

and c. Only the amount of the liquids having composi-

tions a and b will differ to satisfy the lever rule. Thus to

discover the structure of the VLL region, we need only

place one liquid composition on each tie-line of interest.

If the vapor composition happens to lie on precisely the

same tie-line as the overall liquid composition that

produced it, then it corresponds to a ternary azeotrope.

We could have selected an overall liquid composition

equal to that vapor composition and produced a calcu-

lation in which the overall liquid composition is the

same as the vapor composition produced from it-which

is the definition of an azeotrope.

All the vapor compositions in the VLL region will lie

along a single line. If we select our overall liquid

compositions closer and closer to the lower edge, the

vapor composition must also approach that edge as in

the limit we will have only a binary mixture of speciesA and B. That vapor composition will be an azeotrope

as it lies on the tie-line that produced it. It will, in fact,

be the minimum boiling azeotrope that must occur

between species A and B. If we start with a liquid

composition outside the VLL region, then we may

produce a vapor that lies within that region if it were

condensed. Thus the distillation curve we are discover-

ing using bubble point computations would move inside

the VLL region and immediately jump to be on the

vapor line we described above. We can approach the

VLL region from either side of it, jumping to the vapor

line once we enter it. Thus one can think of the VLL

region as a tear i.e. a fissure in the composition

space for the components.

As an exercise, think what the geometry will be if

there are three liquid phases in equilibrium with a single

vapor, i.e. a VLLL problem. Also think about how

many liquid compositions are needed to establish its

geometry.

2.6. Reachable products for a simple distillation column

Once we know the structure of the VL(L(L)) behav-ior as displayed on a ternary composition diagram, we

can approximate the behavior of conventional distilla-

and two stable nodes at local maximum temperaturesof 160 and 170C at the lower right and left. This

diagram has four different distillation regions. In region

I, residue curves emanate from the upper unstable node

and terminate at the lower left stable node. Region II

has the same unstable node, but all of its residue curves

head to the lower right stable node. Regions III and IV

have trajectories that start from the second unstable

node.

The ternary azeotrope in the middle is a saddle point

with the trajectories coming from the unstable nodes,

turning, and leaving toward the stable nodes.

Discovering distillation regions by plotting residue or

distillation curves is one of the most important geomet-

ric insights we can get from them. Experience with such

diagrams has told us that we cannot design conven-

tional distillation columns to operate such that their

distillate and bottoms products are in two different

regions (Doherty & Perkins, 1978). These regions essen-

tially trap where the products can lie as a result. The

trick to designing separation processes for species dis-

playing this type of complex behavior is to figure out

ways to cross these boundaries.

2.5. Liquidliquid beha6ior

It is interesting to think about what will happen

when a mixture of three components breaks into two or

more liquid phases that are in equilibrium with a single

vapor phase. We will use Fig. 5 to illustrate. Liquid

liquid behavior occurs when the Gibbs free energy of a

mixture decreases if the material breaks into two liquid

phases. (A discussion of this behavior is in most chem-

ical engineering thermodynamics textbooks see for

example, Smith and Van Ness (1987). It also appears inBiegler et al. (1997)). When generating a distillation

curve, select a physical property option that allows


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tion columns, i.e. a column with a single feed and a top

(distillate) product and a bottoms product (Westerberg

& Wahnschafft, 1996; Biegler et al., 1997; Stichlmair &

Fair, 1998). Because the feed is the sum of the two

products by material balance, we know that the feed

composition must lie on a straight line between the top

and bottom product compositions. Also the lever rule

tells us just where along this line the feed compositionlies. In Fig. 6, the line lengths a, b, and a+b are

proportional to the flowrates for B, D and F,

respectively.

If we assume the column operates at total reflux, the

product compositions must also both lie on the same

distillation curve. We normally would also like to get

fairly pure products from a column. We would get fairly

pure products if the column has a large number of

stages, which is well approximated by assuming an

infinite number of stages. Thus the bottom end will be

close to a stable node or the top to an unstable node.Fig. 7 illustrates the products regions we can expect. For

one option, we place the distillate product at the un-

stable node and draw a straight line from it through the

feed to the opposite edge of the region containing the

distillate top product to locate approximately the corre-

sponding bottom product. For the other option, we

place the bottom product at the stable node and draw

a straight line from it through the feed and onward to

the opposite side of the region containing the bottomproduct to locate approximately the corresponding top

product. We get a bow-tie shaped region as shown in

Fig. 7. It is possible to argue that any products lying in

the shaded region and along a straight line through the

feed can correspond to a feasible distillation column.

The usual way to assess quickly the possible products

is to assume either (1) the stable node is the bottom

product (b1) or the unstable node the top product (d2).

The other product for each of these two cases (d1 or b2)

is then that which is most distant along the straight line

through the feed and in the same distillation region.

The feed does not have to lie in the same region as the

two products. When it does not, the feed tray composi-

tion must be different from the feed composition. The

feed tray composition will lie in the same region as the

products as will all the liquid tray composition

while the feed composition lies in the other region. One

can always have the feed and feed tray composition

more or less the same for a binary column but not in

general for columns having three or more components

in them.

2.7. Difference points the geometry of componentmaterial balances

The next interesting geometric insight we can observe

for a distillation column is the notion of a difference

point (Westerberg & Wahnschafft, 1996; Biegler et al.,

1997; Hauan, Ciric, Westerberg & Lien, 2000). In Fig.

8 we write the overall material balance for the top

section of an ordinary distillation column. We see the

form for the balance suggests that the entering vapor,

Vn+1, is the sum of the distillate product and the liquid

flow leaving, Ln. Thus the composition for Vn+1 lies on

a straight line between the compositions for D and Ln.

Assume the species are A, B and C, with A being the

most volatile and that we want our distillate product to

be relatively pure A. We sketch this geometry for an

arbitrary composition for Ln. The level rule says we

place Vn+1 such that the line segments DVn+1,Vn+1Ln and DLn are proportional to D, Ln and

Vn+1, respectively. Ln/D is the reflux ratio for the

column so, if we set the reflux ratio, we know exactly

where to place Vn+1 along this line. This line represents

a material balance. It allows us to find the composition

for the vapor flowing counter to the liquid between twostages just as the operating line does on a McCabe

Thiele diagram for a binary column.

Fig. 6. Lever rule on composition diagrams.

Fig. 7. Bow-tie shaped reachable region for a two-product column

operating at total reflux.

Fig. 8. Difference point for top part of ordinary distillation column.


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Fig. 9. Difference point for an extractive distillation column.

exactly where as the line lengths DD, DS and

DS, must correspond to the ratio of the flows of S, D

and D, respectively. If the solvent flow is nearly zero,

the composition ofD is very close to D. As the flow of

solvent increases, it will eventually be equal to D. At

that point the composition for D will have moved out

along the line to infinity. When S increases past D, the

flow D becomes negative, and its composition jumps toinfinity at the other end of the line. As S increases, the

composition for D moves towards that for S, which it

equals when S has an infinite flow.

In Fig. 9 we construct a material balance line to find

Vn+1; only this time we use the compositions for Lnand D.

2.8. The reaction difference point for a column (Hauan,Westerberg & Lien, 1999)

We are now ready to examine the impact of reaction

on a column. Reaction can be viewed as two flows. The

reactants flow out from the stage while the products

flow into it. If we were to do our material balances

using mass flows rather than molar flows, there would

be no loss or gain in material because of reaction. In

other words, 1 kg of reactants will always produce 1 kg

of products (disallowing nuclear reactions). However,

we can easily gain or lose moles. For example, the

reaction A+BUC converts two moles into one mole

each time the reaction turns over as written. We charac-

terize the rate of reaction as a turnover, which is a

flowrate (e.g. mol s1

) corresponding to the flowrate atwhich the reaction occurs as written. We designate

reaction turnover by the symbol x.

Fig. 10 aids in understanding the following ideas. We

can write the reaction A+BUC in the form A

B+C=0. The vector of stoichiometric coefficients w

for this reaction is the transpose of [1, 1, 1]. If the

turnover of the reaction as written is x mol s1, then

the net flow due to reaction into the column is wtotx=

1x, i.e. there will be two moles leaving and one

entering for a net of 1x mol s1 entering. The

composition of this flow is 1 mol s1 of A, 1 mol

s1 of B and +1mol s1 of C, rescaled to add to

unity, i.e. w/wtot= [1, 1, 1]T. We illustrate this compo-

sition in Fig. 10. Note it is on the line where the

compositions for A and B are one and C is negative

one. (To see this, note that the composition of A is 1 in

the lower left corner of the composition triangle and

zero all along the right edge of the triangle. Lines of

constant A are parallel to each other so along the line

joining D and the reaction difference point the compo-

sition of A is one.)

There is an interesting significance to this reaction

composition. It is a difference point for reaction. Selectany arbitrary composition within the composition tri-

angle and draw a straight line through it and the

Fig. 10. Difference point when reaction occurs.

The point D is called a difference point. The distillateD is the fixed difference (Vn+1Ln) for all stages n

above the feed in the column. Thus all material balance

lines such as we have constructed are straight lines that

pass through this single point for the top section of our

column.

Let us now add a solvent as an extractive agent to

our column (see Fig. 9). Let us assume it is the heaviest

species in the mixture, component C, which lies at the

upper corner of our composition diagram. The solvent

is a second feed to the column. We examine the mate-

rial balance for trays just below this feed.Again we write a material balance around the top

section, but this time the constant difference point is

DS rather than D. As is routinely done in the

textbooks, we call this difference D. We see that D is the

difference between D and S rather than the sum. If the

solvent flow S is very small relative to D, then D is

positive, and we can move S to the other side, giving us

D=S+D, with all flows being positive. Thus the com-

position for D should lie between the compositions for

S and D. However, D lies in the lower left corner, and

S lies at the upper corner. How can D lie between Sand D? The composition for D must lie outside the

feasible composition diagram. The lever rule tells us


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reaction composition point. All points along this line

within the composition triangle can be converted into

each other by carrying out the reaction to different

extents. The projections developed by Doherty (e.g.

Barbosa & Doherty, 1987) and his students map all the

points on one of these lines onto a single point using his

projection equations (Stichlmair & Fair, 1998). The

projection for A+BUC+D results in a two-dimen-sional square (see Fig. 11). To understand why it

becomes a square, construct a tetrahedron out of paper.

The reaction difference point is at infinity for this

reaction, as there are moles that are neither created nor

destroyed. The lines passing through this infinite differ-

ence point are parallel to the line going from a 5050

mixture of A and B that reacts to become a 5050

mixture of C and D. Viewed from the difference point

at infinity, the tetrahedron projects into a square.

We now return to the material balance equations

written at the top of Fig. 10. We see that D forextractive distillation is replaced by Dwtotx for extrac-

tive distillation with reaction. D has a fixed composition

and flow. However, the reaction extent can change

from tray to tray. The flow wtotx varies as x (in mol

s1) varies. We locate the composition for the flow

Dwtotx by drawing a line between the composition for

D and for the reaction (both fixed). We split this line

using the lever rule to give line length ratios that

correspond to the ratio for the two flows D and wtotx.

As both of these flows are positive for this example, the

resulting difference point here lies between their two

compositions. The composition for Vn+1 must then lieon a straight line connecting this composition to that

for Ln. The point can move as we step from tray to tray

because the reaction flow, wtotx, is the total of all the

reaction occurring within the stages around which we

have written our material balance.

We now point out one reason this construction is

interesting. Examine Fig. 12. Pick an arbitrary point for

the composition of Ln in the column. The composition

for Vn is on the line tangent to the residue curve passing

though Ln (or along the distillation line passing through

Ln). For an ordinary column, Vn+1 will be along a line

passing through the composition for the distillate, D. If

we introduce an extractive agent and/or reaction, we

move the difference point. We show it moving as for a

case in which we have reaction occurring. We see that

Vn+1 is to the left of Vn for an ordinary column and to

the right for a reactive column. We have caused the

direction the compositions change from tray-to-tray to

reverse. The trays below this tray continue to use this

same difference point if they do not have any reaction

occurring on them. Thus we can have a non-reactive

tray in which the compositions seem to change in a

direction that is the reverse of what we expect. Thetemperature could actually decrease as we move down

the column.

3. Using geometric insights to aid design

The above insights can help us to design separation

processes. We will emphasize separation tasks that in-

volve mixtures displaying azeotropic behavior. We will

present this section using examples. The purpose is not

to be all-inclusive but rather to explain why the geome-

try is suggesting these solutions. Thus it is hoped the

reader will see other alternatives based on similar rea-

soning for these and other problems.

3.1. Example: sol6ent selection to break a binary

azeotrope

Our goal here is to find a third component that will

allow us to break a binary azeotrope. The approach we

shall investigate is to find a third component that will

allow us to step around the azeotrope using conven-

tional distillation. Fig. 13 illustrates the situation whenthe binary species A and B form a minimum boiling

azeotrope. We note that A has the lower normal boiling

Fig. 11. A square projection for A+BUC+D.

Fig. 12. Strategic use of difference point placement to steer plate-by-

plate composition trajectories in a column.

Fig. 13. Node behavior for a minimum binary azeotrope.


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Fig. 14. Breaking a binary azeotrope with an intermediate boiler.

is no B in this top product; we distill it to separate A

from the entrainer. We recycle the entrainer. It should

not be difficult now to describe the characteristics of an

entrainer to break a maximum boiling azeotrope. The

entrainer can form azeotropes with A and B; we need

only to have a single region in which A becomes a

saddle.

Doherty and Caldarola (1985) and Stichlmair andFair (1998) present an extensive set of rules for picking

a suitable entrainer to break binary azeotropes. They

involve this type of thinking.

3.2. Example: crossing distillation boundaries to break

an azeotrope

Another way to think about breaking an azeotrope is

to add a third component that converts the azeotrope

into a saddle. If the azeotrope is a minimum boiling

azeotrope, we need to select a light entrainer (Fig. 15).

This species will cause a distillation boundary to exist

that connects the entrainer with the azeotrope. We

want this boundary to be very curved, so we have a

second requirement: namely, that in regions where the

entrainer concentration is high (near the entrainer cor-

ner of the triangle), the two species have a very differ-

ent volatility. Here species A is much more volatile that

B. When that happens distillation curves leave the

entrainer (a stable node) and head toward the species

that is acting like the intermediate boiler-here A. They

then turn toward the high boiler as shown. As a result,

the distillation boundary is very curved as shown.We first mix the entrainer and the azeotrope, moving

the feed for the first column well into the three compo-

nent part of the diagram so as to take maximum

advantage of the curvature of the boundary. We distill,

getting species B as the bottom product. The distillate is

close to the distillation boundary. This distillate be-

comes the feed to the second column. While the feed is

in the right region, we can have both products in the

left region at the same time that both lie on a straight

line through the feed. As noted earlier, only the prod-

ucts have to be in the same distillation region. A third

column recovers A and azeotrope. We recycle the

azeotrope back to the feed.

This type of reasoning is involved in inventing sepa-

ration processes for the acetone, chloroform and ben-

zene system described in Westerberg and Wahnschafft

(1996) and Biegler et al. (1997).

3.3. Decantation

If we have a three component mixture to separate

where the species have a region in which there is

liquidliquid behavior, we often can readily develop aseparation process. Separating pyridine, toluene and

water is an example. Fig. 16 shows the structure of the

Fig. 15. Breaking a minimum boiling azeotrope with a low boiling

entrainer that forms a strongly curved distillation boundary.

point for the two components. Because the azeotrope is

a minimum one, it will typically lie closer to the lowerboiling component, as shown.

If we can alter our problem so A, B and the

azeotrope are all in the same distillation region, we will

be able to break the azeotrope using distillation. To be

in the same distillation region, we must have only one

stable and one unstable node. We have to convert at

least one of these nodes to a saddle. For example, we

can convert A into a saddle in the three component

composition diagram by picking a third component

that forms no azeotrope with them and that has a

boiling point that is between that for A and B. We

would get the behavior shown in Fig. 14. In thisdiagram, the binary azeotrope remains the unstable

node. B remains a stable node, while A and C are

saddles. All distillation curves will emanate from the

azeotrope and end up at pure B.

To invent a separation process, we could first mix

our entrainer with the azeotropic mixture, forming a

mixture that is away from the lower edge of the compo-

sition diagram. In the three component region, we can

have a column whose bottom product is the stable

node, species B, the highest boiling component in the

distillation region. The top product is along the straightline passing through the feed and as far as the furthest

edge of the distillation region, here the left edge. There


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distillation (or residue) curve map. The two phase

region boundary can either correspond to having a

vapor phase in equilibrium, or it can be the result of

cooling the liquid well below this point and having only

two liquid phases present. The more one cools, the

larger the two liquid phase region typically is.

We start by decanting the feed, to form water- and

toluene-rich phases. We can then distill each of thephases to get pure water and pure toluene bottoms

products, respectively. Mixing the distillate products,

which lie along the distillation boundaries shown, pro-

duces a mixture in the distillation region where we can

distill to recover pyridine, which we do. The distillate

from this distillation lies somewhere in the two-phase

region; we recycle it to the decanter. Here the appear-

ance of a VLL region allows us to use decanting to

cross distillation boundaries and thus to develop a

process fairly easily. Using this type of reasoning, we

can invent other possible processes for this feed.

3.4. Extracti6e distillation

We can also use extractive distillation to effect a

separation. What are the geometric clues that would

suggest this approach? Consider trying to break the

waterisopropylalcohol (IPA) binary azeotrope. Fig. 17

shows a typical extractive distillation column. In such a

column, we usually select a very heavy solvent one

that boils at a much higher temperature than either of

the other two species. We also want a solvent in which

the two species will have very different volatilities; i.e.

we want a solvent that is increases the activity coeffi-

cient of one of the species much more than it does for

the other. The species with an increased activity coeffi-

cient becomes relatively much more volatile. We can

detect this behavior by examining infinite dilution K-

values for the water and IPA in the presence of anumber of candidate solvents. If volatilities in a high

concentration of solvent are very different, we have a

candidate solvent.

In a matter of a few seconds, we can readily examine

thousands of components using a computer, provided

we have the appropriate data on each to allow us to

estimate physical properties. We should find ethylene

glycol to be a good candidate here. It is readily avail-

able, fairly safe to handle, boils at a much higher

temperature than either water or IPA, and it has a large

infinite dilution activity coefficient with IPA. The com-

position diagram in Fig. 17 illustrates the shape of the

distillation curves for these components. Examine the

portion of the composition diagram to the right of the

curve ab where EG is in high concentration. The shape

of the distillation curves in this region suggests that

water is the intermediate component while IPA is the

light or most volatile component. Only when the curves

are near the minimum azeotrope do they bend to move

toward the minimum boiling azeotrope, which here is

the unstable node.

The shape on the right suggests that water is the

intermediate and IPA is the light component. If thisshape appears in high concentrations of a proposed

solvent, then extractive distillation will allow us to

break the azeotrope.

We note that the IPA corner is a saddle yet, with

extractive distillation, we can have it as the top

product. To understand this, return to our earlier dis-

cussion on difference points for extractive distillation.

The D point (see Fig. 9) for extractive distillation will

lie on the straight lines that pass through the IPA

product and EG feed compositions. It will lie outside

the composition triangle. If the solvent flow is less than

the distillate product flow, it will be in the direction

shown. If the solvent flow is larger than the distillate, it

will wrap around and be below and to the right of the

EG corner along this same straight line. In either case,

if we take a tray-by-tray step, as shown in Fig. 12,

somewhere along the curve ab, we would find move-

ment up the extractive column just below the EG feed

would be toward the IPA/EG edge of the composition

space. We could get arbitrarily close to that edge,

effectively eliminating all the water from the top part of

the column. The top of the column above the EG feed

is then separating IPA from EG, a binary separationthat is done in one or two trays as EG is much heavier

than IPA.

Fig. 16. A process to separate species having a region with VLL

behavior.

Fig. 17. Extractive distillation example.


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Fig. 18. McCabeThiele diagram for column having reaction on

stages 2 and 3 from the top.

we have B+A=0 and the stoichiometric coeffi-

cients are [1, 1]. Here wtot=1+1=0 as there are

no net moles lost or produced as this reaction proceeds.

The reaction difference point is at infinity.

We shall construct a McCabe Thiele diagram for

this system (Lee, Hauan & Westerberg, 2000a). Our

goal is to discover how reaction alters this diagram. If

we write a material balance around the top of a column(as in Fig. 10) for the component A, we get

Vn+1yn+1, A=Lnxn, A+DxD, Ax

=Lnxn+D

xD, Ax

D

(3)

Since there is no net production or loss of moles,Vn+1=Ln+D. If we let yn+1=xn to find where this

operating line intersects the 45 line, we find that it

occurs when

xA=xD, A xD

(4)

Thus the intersection point shifts down by the fraction

the reaction turnover (flowrate) is of the distillation top

product flowrate. For example, if we feed 10 mol s1 of

B along with some A and run the column to convert

50% of the B in the feed into A, the turnover will be 5

mol s1 for the entire column.

Fig. 18 is a McCabe Thiele diagram (McCabe &

Thiele, 1925), where we have allowed reaction to occur.

We start at the top tray where we specify that the

composition of A to be recovered in the distillate to be0.95. The original top operating line intersects the 45

line at this composition. We (arbitrarily) specify that we

shall have no reaction on the top stage; we step off this

stage using this original operating line. We place cata-

lyst on stage 2 so that we can get a reaction turnover of

x2. The operating line shifts downward. We step to this

operating line below stage 2. Let us suppose that we

also place catalyst on stage 3. We again shift the

operating line down as shown. Note that x3 as shown is

the sum of the turnover rates on and above stage 3 (the

material balance has to account for all stages above the

tray of interest). If we choose to put catalyst on no

other stages, we should then use this last operating line

for all stages below stage 4 and above the feed tray. We

analyze the bottom of the column as we would for a

non-reactive column.

We note that each time we allow reaction, the operat-

ing line moves down. Having reaction in the top of the

column makes our separation task easier. We ask next

what happens to our diagram if we allow reaction for

this case to occur in the bottom of the column.

We carry out a similar analysis, but this time we

place reaction in on a bottom stage of a column. Weconstruct the resulting McCabeThiele diagram in Fig.

19 for the same case for which we constructed Fig. 18.

Fig. 19. McCabe Thiele diagram when placing reaction in bottom

section.

4. Reactive distillation

We will complete this paper by looking at interesting

geometry for reactive distillation. In particular we shall

look at the geometry for binary columns. We have

already examined the use of a difference point for

reaction in ternary systems. We start by supposing we

have one component that can rearrange to form the

other; thus our system can be reactive and binary. Weshall assume the reactant is the less volatile species and

write our reaction as B A. Written in standard form,


11/12


This time we shall number from the bottom of the

column. Assume reaction occurs only on the second

stage from the bottom. When we allow reaction and

because of the sign changes that occur in the analysis,

the intersection point for the operating line and the 45

line moves downward here also. However, doing so

now shifts the new operating line upward, leading to a

more difficult separation; indeed, we can make theoperating line move above the equilibrium curve, which

would cause us to reverse the direction we separate the

mixture, i.e. we would start to step back to the left. The

second dashed operating line illustrates a shifted oper-

ating line that just touches the equilibrium curve lead-

ing to a pinch situation. Thus we can conclude that, for

this case of the heavy species forming the light species,

we make the separation task easier by having the

reaction occur in the top section of the column (Lee,

Hauan, Lien & Westerberg, 2000b).

4.1. Stepping past a binary azeotrope (Lee, Hauan &

Westerberg, 2000c)

Again consider the reaction B A. Only this time

we have two species that form a maximum boiling

azeotrope as shown in Fig. 20. Note that the equi-

librium curve crosses the 45 line. This shape is indica-

tive of a maximum boiling azeotrope. In the upper part

of the diagram A is more volatile while in the bottom,

B is. We start at the top where we again ask for 95%

pure A as the top product. Arbitrarily, we do not allowreaction to occur on the top stage. We place catalyst on

stages 2 and 3, each time causing the indicated reaction

turnover and shifting downward of the operating line.

The operating line is, by this time, well below the 45

line. We find we can now step past the azeotrope as the

operating line is also well below the equilibrium line

even though the equilibrium line is below the 45 line.

We can observe several interesting things about this

diagram. First, if we had used total reflux to decide

how to design this column, the operating line would

coincide with the 45 line, and we would not be able to

step past the azeotrope. Thus, it is our use of a finite

reflux ratio that gives us this possibility. Second, westep past the azeotrope below the trays where reaction

occurs. Once past the azeotrope, the more volatile

species, B, is enriching as we go down the column. This

behavior is similar to the behavior we discussed earlier

for a ternary diagram when we add reaction and possi-

bly an extractive agent flow to the column. As before

this enrichment says the temperature is decreasing on

non-reactive trays as we step down the column. This

behavior is very counter-intuitive for most chemical

engineers. It is occurring because reaction has altered

the material balance for the column, here dramatically.

5. Conclusion

We have examined some of the very interesting ge-

ometry associated with analyzing distillation processes.

In particular we first looked at residue and distillation

curves to expose VL(L) equilibrium phase behavior. We

next showed that difference points are how we account

geometrically for the material balances of a column. We

then looked at altering material balances for a column

by adding a solvent feed to and/or allowing reactionwithin the column and showed we could make the

tray-by-tray behavior of a column change directions

and even reverse directions.

We also showed how to use these insights to discover

useful column designs that can break binary

azeotropes. Finally we looked at binary reactive distil-

lation and showed that we can construct and use a

McCabe Thiele diagram for this situation. Again we

showed that altering the material balance by having

reaction occur within the column can lead to some very

interesting and we think not so intuitive behavior. We

could also derive a rule of thumb from just a sketchthat tells us where to place the reaction in the column.

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