RD Feasible Distillation Regions
Transcript of 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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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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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,
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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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