Technical Memorandum No. CIT-CDS 93-001
January 28,1993
"Multiple Steady States in Homogeneous
Azeotropic Distillation"
Nikolaos Bekiaris, George
A.
Meski, Christian M. Radu, and Manfred Morari
Control and Dynamical Systems
California Institute of Technology
Pasadena,
CA
91
125
Multiple Steady States in Homogeneous Azeotropic
Distillation
Nikolaos Bekiaris
George
A.
Meski
Cristian
M.
Radu
Manfred Morari*
Chemical Engineering 2 10-4
1
California Institute of Technology
Pasadena,
CA
91125
CIT/CDS Technical Report No.
93-00
1
January
28,
1993
Abstract
In
this article we study multiple steady states in ternary homogeneous azeotropic
distillation. We show that in the case of infinite
reflux and an infinite number of trays
one can construct bifurcation diagrams on physical grounds with the distillate flow
as
the bifurcation parameter. Multiple steady states exist when the distillate flow varies
non-monotonically along the continuation path of the bifurcation diagram. We derive
a necessary and sufficient condition for the existence of these multiple steady states
based on the geometry of the distillation region boundaries. We also locate in the com-
position triangle the feed compositions that lead to these multiple steady states. We
further note that most of these results are independent of the thermodynamic model
used. We show that the prediction of the existence of multiple steady states in the case
of infinite
reflux and an infinite number of trays has relevant implications for columns
operating at finite
reflux and with a finite number of trays.
Using numerically con-
structed bifurcation diagrams for specific examples, we show that these multiplicities
tend to vanish for
small columns and/or for low reflux flows. Finally, we comment on
the effect of multiplicities on column design and operation for some specific examples.
KEYWORDS:
distillation, azeotropic distillation, multiplicity, distillation design,
extractive distillation.
'Author to whom correspondence should be addressed.
Phone:
(818) 356-4186.
Fax:
(818) 568-8743.
E-mail: MM@IMC.CALTECH.EDU.
1
Introduction
Azeotropic distillation is one of the most widely used and most important separation op-
erations in the
che+cal and the specialty chemical industry. Despite that, the design and
operation of azeotropic distillation columns are relatively poorly understood and little stud-
ied. Among their surprising features, it has been discovered that such columns can exhibit
multiple steady states
i.e. two or more steady states with different composition and temper-
ature profiles which correspond to the same set of operating parameters. In this article we
are only investigating this type of
multiplicities.
The study of multiplicities in distillation has a long history. Rosenbrock (1962) proved
that the steady state of distillation columns separating a binary mixture is unique under the
assumptions of
(3;
constant molar flows (i.e. neglecting the energy balances) and (2) that to
every value of vapor composition
y
there corresponds a unique value of liquid composition
x
in equilibrium with
y.
This assumption does not exclude the cases of nonideal vapor-liquid
equilibrium (including the cases where an
azelotrope is formed between the two components).
Petlyuk and Avetyan (1971) first conjectured the possibility of multiple steady states in
the distillation of ternary homogeneous systems under the assumptions of constant molar
flows and
nonideal vapor-liquid equilibrium (Wilson equation). They conjectured that mul-
tiple steady states exist when a distillation product region is a quadrangle. However, as we
will
show this condition is neither necessary nor sufficient for the existence of multiple steady
states. Moreover, they do not identify any physical mixture that
may lead to these multiple
steady states.
Magnussen et al. (1979) present simulation results that show the existence of three steady
states for the heterogeneous mixture of ethanol
-
water
-
benzene. In these calculations the
phase splitter is removed; instead, a second feed at the top of the column is considered (this
second feed is the same for all three steady states). Moreover, the liquid composition profiles
of all three steady states lie entirely in the single liquid phase region. Therefore, although
the mixture ethanol
-
water
-
benzene can exhibit liquid
-
liquid phase split, the multiplicities
presented in that article cannot be explained by the heterogeneity of the mixture. Hence,
the
explanation for the existence of the aforementioned multiplicities should be sought in
the regime of
homogeneous
azeotropic distillation. Finally, it should be noted that the
multiplicities were observed with the UNIQUAC and NRTL activity coefficient models but
a unique steady state was found with the
Wilson equation model.
Doherty and
Perkins (1982) considered the case of nonideal vapor
-
liquid equilibrium
and constant molar flows. They proved the stability of the unique steady state in binary
distillations (uniqueness was already proven by Rosenbrock, 1962). They also prove that
a unique steady state exists for single-staged "columns" of any multicomponent mixture.
Using the above results, they conclude that the multiplicity reported by Magnussen et al.
(1979) is a consequence of multiple components and multiple stages.
The "discoveries" by Magnussen et al. (1979) triggered great interest in multiple steady
states in distillation. The belief that heterogeneity is a possible cause for such multiple
steady states directed the attention towards heterogeneous azeotropic distillation. Conse-
quently, several articles were published
where the results of Magnussen et al. (1979) were
studied extensively and where multiplicities for other heterogeneous systems were reported
(Prokopakis and Seider, 1983; Kovach and Seider, 1987; Widagdo et al., 1989).
However, other types of systems have also been investigated. In a simulation study
Chavez et al.
(1986) and Lin et al.
(1987) found multiple steady states in interlinked
distillation columns. The multiplicity they report is due to the interlinking and is not found
in single columns.
Sridhar and Lucia (1989) considered binary mixtures with nonideal VLE and included
energy
balances in the model. They showed that any binary homogeneous separation process,
in which the temperature and pressure profiles are specified, has a unique steady state.
Jacobsen and Skogestad (1991) present two different types of multiplicities in binary
distillation columns with ideal VLE:
-
Multiplicity in Input Transformations.
Constant molar flows are assumed. Multiplicities occur when some flows are specified
on a mass basis (instead of a molar basis) and are due to the nonlinear mass to molar
flow transformation.
-
Multiplicity when molar reflux and boilup are used as specifications (LV configuration).
Energy balances are included in the model. This type of multiplicity does not occur
for the case of constant molar flows.
Most recently, Kienle et
al.
(1992) reported multiple steady states for the ternary ho-
mogeneous mixture of acetone, chloroform and methanol. The starting point for the study
presented here were the multiple steady states reported by
Laroche et
al.
(1990, 1991, 1992)
for a homogeneous ternary mixture (acetone
-
heptane
-
benzene) with nonideal VLE and
constant molar
flows.
Background
The term "homogeneous azeotropic distillation" covers the general notion of distillation of
azeotrope forming mixtures where a single liquid phase exists in the region of interest. Usu-
ally, homogeneous azeotropic distillation units perform the separation of a binary azeotrope
into two pure components through the addition of an entrainer which alters the relative
volatility of the two azeotrope constituents without inducing liquid
-
liquid phase separa-
tion.
Unless stated otherwise, we use the following convention to refer to a given mixture:
L
(I,
H
respectively) corresponds to the component which has the lowest (intermediate, highest
resp.) boiling point; we also denote the entrainer by
E.
We use the same notation in italics
(L,
I,
H,
E)
to denote the corresponding flow rates of the components in the feed. The
locations of the feed, distillate and bottoms in the composition triangle are denoted by
F,
D
and
B
respectively. Again, the corresponding flowrates are denoted by the same letters in
italics
(F,
D,
B
and
R
for the reflux flow).
In
all
simulations presented in this paper, the column operates under atmospheric pres-
sure, there is no pressure drop in the column and the condenser is total. Moreover, constant
molar overflow and a tray efficiency of
1
are assumed. Vapor pressures are calculated using
the Antoine equation and liquid activity coefficients are calculated using the Van
Laar equa-
tion. The appendix contains
more information on the thermodynamic model as well as the
Antoine and Van Laar coefficients used in the examples. The tray counting starts from the
reboiler (number 0) and ends at the top. Finally, in all composition profile figures the
liquid
mole fractions are depicted.
A widely used concept for the description of azeotropic distillation is that of the simple
distillation residue curve (hereafter
called residue curve).
The
simple distillation process
involves charging a still with a liquid of composition
:
and gradual heating.
The vapor
formed is in equilibrium with the liquid left in the still; the vapor is continuously removed
from the still.
A residue curve is defined as the locus of the composition of the liquid remaining at any
given time in the still of
a
simple distillation process. Residue curves are governed by the
set of differential equations (Doherty and
Perkins, 1978):
where
i
is the component index,
C
is the number of pure components in the mixture,
y;
(x;)
is the mole fraction of component
i
in the vapor (liquid) phase, and
[
is the dimensionless
warped time.
At infinite
reflux, the differential equations which describe packed columns become iden-
tical to the residue curve equations. Thus residue curves coincide exactly with composition
profiles of packed columns operated at total
reflux, and they give a very good approximation
of composition
profiles of tray columns at infinite reflux.
A
distillation region
is a subset of the composition simplex in which
all
residue curves
originate from
a
locally lowest-boiling pure component or azeotrope and travel toward
a
locally highest-boiling one. The curves which separate different distillation regions are called
residue curve boundaries. The term distillation region boundary (or just boundary) is used
for both residue curve boundaries (interior boundaries) and for the edges of the composition
simplex.
Infinite Reflux and Infinite Number
of
Trays
In this section we present
an
extensive analysis of the case where the reflux and the number
of trays are infinite (the
oo/m
case hereafter). The idea for examining this situation came
from the multiplicities reported by
Laroche et
al.
(1990, 1991, 1992). The homogeneous
mixture under consideration is that of acetone (L), heptane
(H)
and benzene (I). In this case
there is only one binary azeotrope formed between acetone and heptane (93% acetone, 7%
heptane). Benzene, the intermediate boiler, is used as entrainer for the separation of the
acetone
-
heptane azeotrope. Figure
1
shows the residue curve map of this ternary mixture
(001 class according to the classification by Matsuyama and
Nishimura, 1977).
Figure 2 depicts the separation sequence
and information about the azeotropic column.
The feed composition and flows, the
number of trays and the distillate, bottom, reflux and
reboil flow rates are identical for both steady states. Figure 3 shows the two different stable
steady state profiles reported by Laroche et
aj.
(1990, 1991, 1992). In the first case (Figure
3a) the column yields 99% acetone
(L)
at the top and 95% heptane
(H)
at the bottom while
in the second case (Figure
3b), the top product is a mixture of 93% acetone and 7% heptane
(azeotropic mixture).
