60
www.cepmagazine.org
December 2002
CEP
Reactions and Separations
t is often necessary to develop data for a range of
operating conditions, so that the optimum con-
figuration of a distillation tower can be found.
There are two conventional methods to perform such
a task, either graphically by hand (which is some-
what inaccurate and time-consuming) or by any of a
number of commercial simulations that are faster, but
costly to license. A third alternative is presented
here: Merging the graphical and manual computa-
tional methods so that the inaccuracies of the former
are compensated for by the speed of the computa-
tions. The calculations can be run by any spreadsheet
program, such as Microsoft Excel, eliminating the
need for employing expensive simulation software
and for laboring over hand calculations. Further, the
time involved from a programmer’s point of view is
no more (or considerably less) than that required to
learn how to use a commercial simulation package.
The method presented here is easy to learn, and
offers a quick way to make preliminary estimates of
the tower diameter and height, number of stages,
energy consumption, and reflux ratio. Although the
calculation procedure is intended for binary sys-
tems, ternary systems can also be modeled if the
third component is less than 10% by volume and its
volatility is not drastically different from the those
of the remaining two components.
Spreadsheet calculation procedure
The first step in any binary distillation calcula-
tion (apart from performing the mass balance
around the column), is determining the vapor/liquid
equilibrium (VLE) data. Raoult’s law is used to cal-
culate the saturation pressure for the pure compo-
nents. Since most systems are non-ideal, the Van
Laar equation is then applied to determine the liq-
uid and vapor compositions. This equation includes
the activity coefficients for a mixture, making it
suitable for non-ideal systems (
(1)
, p. 32). An
ethanol/water system is used to illustrate the
overall method.
Apply Raoult’s law and the Van Laar equation
Use Raoult’s law to find the saturated vapor pres-
sure for each component. Published data are avail-
able for various compounds (
(2)
, p. 10-141). The sat-
urated vapor pressure of each component is
expressed as:
P
1
sat
= 10
[
A
–
B
/(
T
+
C
)]
(1)
where
P
1
sat
is the saturated vapor pressure of compo-
nent 1 (mm Hg),
T
is the temperature (°C), and
A
,
B
and
C
are the Raoult’s law constants for each com-
pound. For ethanol,
A
= 8.32109,
B
= 1,718.1 and
C
= 237.52. The values for water are:
A
= 8.07131,
B
=
1,730.63 and
C
= 233.42. To calculate the saturation
pressure of a component, simply substitute the value
of the temperature. In these calculations, 1 refers to
ethanol and 2 is for water.
This method uses a numerical solution to a
McCabe-Thiele diagram to find the theoretical
number of stages for binary and pseudo-binary
systems, then calculates the actual number of
stages, reflux ratio and column dimensions.