Integrated column designs for minimum
energy and entropy requirements in multicomponent distillation
Ivar J. Halvorsen and Sigurd Skogestad
Department of Chemical
Engineering
Norwegian University of Science and Technology
(NTNU)
N7491 Trondheim
Norway
What is the minimum energy requirement for separating a given
multicomponent mixture by distillation? This is a fundamental
question of significant practical importance, yet it remains
unsolved even for the case of ideal mixtures, at least when we
consider the practical case with adiabatic column sections. We
conjecture that, with constant pressure and without internal heat
integration, the generalized Petlyuk arrangement requires less
energy than any other adiabatic arrangement. The energy requirement
is then easily computed as the being equal to the most difficult
binary split(!). The minimum energy requirement when we allow for
internal heat exchange remains unknown.
However, minimum energy (1st law) is by itself not sufficient as
a measure, because also the quality (temperature) of the energy
matters. Specifically, we prefer a process where the energy may be
supplied at a low temperature and cooling may be supplied at a high
temperature. To take this into account, we also consider the entropy
production or lost work (2nd law). This leads us to the reversible
Petlyuk arrangement. The total required heat supply is higher than
for the adiabatic Petlyuk arrangements, but the reversible
arrangement has a potential for further energy reduction by use of
internal heat integration. This principle can also be applied to
general arrangements (not only reversible).
We here consider the separation of ideal mixtures for which we
may assume constant relative volatility and constant molar flows. We
assume infinite number of stages because resulting minimum vapor
rate Vmin provides a lower bound on the energy requirement for ideal
mixtures. In practice, with a finite number of stages, the actual
energy requirement may be about 10% higher.
To illustrate the results we consider the energy requirement
(given in terms of the vapor rate Vmin/F) and entropy production
(given in terms of the relative entropy production Sr= Stotal/S
where S is the entropy of mixing) for a specific case, namely the
separation of an equimolar ternary mixture (components A, B and C)
with relative volatilities 4 and 2 into its three pure products.
Let us first consider the conventional "direct split" arrangement
with two columns. Here we in the first column take A as the top
product and B/C as the bottom product. The second column separates B
and C, and we get B in the top and C in the bottom. The combined
energy requirements in the two column reboilers is Vmin/F=2.072 and
the entropy production is Sr=0.59.
Some energy reduction may be achieved in this case with the
"indirect split" where we in the first column take C as the bottom
product and A/B as a vapor top product. The second column separates
A and B. Here Vmin/F=2.032, but the entropy production is higher,
Sr=1.21, because the temperature difference between heat supply and
cooling is larger.
The adiabatic directly coupled Petlyuk column with a single
reboiler achieves more than 30% energy reduction, Vmin/F=1.366. This
is the best adiabatic arrangement in terms of energy. However, the
entropy production remains high, Sr=0.72, because all the heat is
supplied at the highest temperature (boiling point of component C)
and all the cooling is at the lowest temperature (boiling point of
component A). To further reduce the energy requirements we must
allow for internal heat exchange. For example, for this specific
mixture we may in the Petlyuk column preheat the feed with the
sidestream product and achieve Vmin/F=1.181 and Sr=0.49, but it is
not known whether further reductions are possible.
To significantly reduce the energy consumption further we must
allow for non-adiabatic sections with continuous heat exchange. For
example, for this specific mixture, if we allow for heat exchange
between the middle four sections in the Petlyuk column, then we may
achieve Vmin/F=1.000 and Sr=0.26.
To achieve further reductions let us consider reversible
distillation where the entropy production is zero, Sr=0. There are
many possible reversible configurations, all of which require
nonadiabatic column sections. One is the reversible Petlyuk column
where Vmin/F=1.566, so its energy requirement is higher than for the
adiabatic Petlyuk column (Vmin/F=1.366), which is no big surprise
since we no longer supply all the heat at the highest temperature.
To reduce the energy requirements we may introduce internal heat
pumps so that again all heat supply is at the highest temperature.
In this way we may reduce the energy requirement to Vmin/F=0.793,
which is the theoretical minimum for the separation of this mixture
by distillation at constant pressure.
In the paper we derive general expressions for computing the
energy and entropy, and also discuss practical issues related to
operation.