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Unformatted text preview: Reactions and Separations Visualizing the
Use this spreadsheet-based visualization
and interactive analysis of the
McCabe-Thiele diagram to understand the
foundations of distillation engineering. Paul M. Mathias
Fluor Corp. M ore than 80 years ago, McCabe and Thiele
developed a creative graphical solution technique based on Lewis’s assumption of constant
molal overﬂow (CMO) for the rational design of distillation columns (1). The McCabe-Thiele diagram enabled
decades of effective design and operational analysis of
distillation columns, and has been used to teach several
generations of chemical engineers to design and troubleshoot distillation and other cascaded processes.
Simpliﬁed methods such as McCabe-Thiele are rarely
used today for detailed design. Modern tools are based
on rigorous solution of the equations governing cascaded
separations, and properly deal with multicomponent systems, heat effects, chemical reactions and mass-transfer
limitations (2). Commercially available software enables
simulation of entire chemical plants for the purposes of
design, optimization and control — but it is important
to ensure the discriminating and competent use of these
sophisticated tools. The McCabe-Thiele visual approach
provides a powerful way to attain this judgment and
Software applications based on rigorous calculations
do not explain how distillation really works and how the
numerous process variables interact to yield a distillation column that is energy efﬁcient, stable, and produces
products with the desired purities. If the design engineer speciﬁes an impossible set of inputs, even the best
commercial software either crashes or returns vague and
unhelpful messages (e.g., “Tray j dried up”). Engineers
who have only performed simulations resort to arbitrary
and frantic changes in input variables to obtain a simulation with a feasible speciﬁcation. In addition, rigorous,
computerized calculations do not reveal design problems
Revised 1/15/10 36 www.aiche.org/cep December 2009 CEP such as composition pinches and unforgiving composition
proﬁles (i.e., a steep peak in the composition proﬁle of one
or more components in multicomponent distillation) —
until they are converged. For these reasons, textbooks on
staged separations stress the visual approach and present
the McCabe-Thiele diagram as an essential tool for understanding and analyzing cascaded operations. Experienced
process engineers often use McCabe-Thiele diagrams to
understand or help debug simulation results (3). Yet some
consider graphical techniques tools of the past, and as a
result, the distillation column has become a black box and
engineers’ understanding of distillation has suffered (4).
Even though the construction of McCabe-Thiele diagrams is straightforward, it is a tedious and error-prone
process. Hence, engineers rarely study the large number
of cases needed to understand the interactions of the many
process variables. This article introduces a spreadsheet-based
approach that readily produces McCabe-Thiele diagrams for
binary systems so that the interacting effect of process variables can be visualized easily and interactively; the Excel ﬁle
is provided as a supplement to the online version of this article (www.aiche.org/cep). Because it is based on the widely
available Excel software and uses standard techniques, this
method is a useful advance over existing software tools that
enable visualization of the McCabe-Thiele diagram.
Excel spreadsheets are increasingly used in chemical
engineering education and industrial practice (5). This
article demonstrates how Excel may be used for chemical
engineering computation and visualization. Through the
example presented in the sidebar, the article also demonstrates how the McCabe-Thiele method, and, in particular,
the spreadsheet application introduced here, answers typical design questions. Q Example: The Problem Statement
An existing distillation column consists of a total
condenser and 10 equilibrium stages, with the feed
inlet on the ﬁfth stage from the top. The 10 equilibrium
stages include a partial reboiler. The column needs to be
reused to separate an acetone-ethanol binary mixture
at a pressure of 1 atm. The feed is 20% vaporized and
contains 50 kmol/h acetone and 50 kmol/h ethanol. The
desired distillate and bottoms compositions of acetone
are 90 mole% and 3 mole%, respectively. Vapor-liquid
equilibrium (VLE) data are provided for this binary
system, and the enthalpies of vaporization of acetone
and ethanol may be assumed to be constant at 29.6 and
38.9 kJ/mol, respectively. Assume that the constantmolal-overﬂow (CMO) assumption applies.
a. Is the CMO approximation valid?
b. Calculate the number of stages needed at total
reﬂux. If the minimum number of stages exceeds 10, the
separation is impossible.
c. Your supervisor, a distillation expert, has
answered question b, and assures you that the minimum number of stages needed at total reﬂux is less
than 10. Calculate the reﬂux ratio needed to achieve the
desired separation. How does the reﬂux ratio change as
the thermal state of the feed is varied?
d. If it is possible to move the feed inlet stage, would
you recommend that this be done? What is the optimum
feed location? How is the separation affected as the
feed inlet is changed?
e. How should the design be changed if the tray
efﬁciency decreases below unity? The approach
As far as possible, this application uses Excel’s
standard capabilities. The exception is a function to
perform data interpolation, called Interp, which was
developed using Visual Basic for Applications (VBA)
and is provided as part of the online version of the article.
This function is used, for example, to interpolate vaporpressure and x-y equilibrium data. This feature enables
the spreadsheet application to accept x-y data from any
source, including experimental data, calculated values
derived from a thermodynamic model, or values from
Figure 1 is a schematic diagram of a distillation column with a total condenser and a partial reboiler. The partial reboiler is an equilibrium stage, but the total condenser
is not. The stages are counted from the top down, with
stage 1 at the top of the column where the reﬂux enters.
(Note that if a partial condenser is used, it will have to be
counted as the ﬁrst equilibrium stage.) According to the
CMO approximation, each stage is at phase equilibrium,
and the vapor and liquid ﬂows are constant in both the rectifying section (above the feed tray) and the stripping section (feed tray and below). Following the usual practice, QC V
(feed with q = 1) D
(heat rate required
to change its
to the specified q) N Q QR Q B Figure 1. The example distillation column has a total condenser, a partial
reboiler, and N stages; the ﬁrst stage is at the top of the column where the
reﬂux enters, and the Nth stage is the partial reboiler. the compositions refer to the more-volatile component.
The vapor and liquid ﬂows in the rectifying section (above
the feed tray) are denoted as V and L, respectively.
The equations resulting from the McCabe-Thiele
technique are available in textbooks on separations and
are only summarized here. The constant vapor and liquid
ﬂows resulting from the CMO approximation lead to the
following component-balance equation (or operating line)
in the rectifying section:
y j + 1 = V x j + (1 - V ) x D ^1 h The relationship between the reﬂux ratio (R = L/D)
and the liquid-to-vapor ﬂow ratio (L/V) is:
V = 1+R ^2 h Analogous to Eq. 1, the operating line for the stripping section is: yj+1 = L
x j + ( - 1) x B
V ^3 h The feed line, or “q-line,” starts from a point on the
x = y diagonal line where x = xF and has a slope based
on q or the liquid fraction of the feed. In the distillation
literature, q is usually referred to as the thermal state of
the feed. Note that q can be less than zero (superheated
vapor) or greater than unity (subcooled liquid). The slope
of the q-line is q/(q – 1).
The construction of the two operating lines and the
q-line is performed in Excel as follows:
1. The rectifying-section operating line is drawn using
Eqs. 1 and 2 and the speciﬁed values of xD and R.
CEP December 2009 www.aiche.org/cep 37 Reactions and Separations 2. The q-line is constructed by drawing a straight line
from (xF, xF) with a slope equal to q/(q – 1).
3. The stripping-section operating line is the straight
line from (xB, xB) to the intersection of the rectifyingsection operating line and the q-line.
The function Interp is useful in implementing the
operating lines and the q-lines even though all three are
straight lines. For the purpose of calculating equilibrium
compositions, x-y data have been entered as a table with
101 points (x_Data, y_Data). This spacing of data points
is expected to be adequate for accurate interpolation of
the acetone-ethanol x-y diagram. For another system with
an x-y diagram that has a more complex shape, more data
points in the table may be needed.
The McCabe-Thiele diagram is constructed by “stepping
off stages.” The starting point is (xD, xD), which is the vapor
composition ascending from tray 1. The liquid composition
descending from tray 1 is the mole fraction in equilibrium
with a vapor with composition xD, which is obtained using
the function Interp: x1 = Interp (xD, x_Data, y_Data, 0).
Next, the vapor composition rising from tray 2 is calculated
from the rectifying-section operating line (or componentbalance equation), again using Interp. The stepping off
of stages continues over the entire column, switching to
the stripping-section operating line at the feed tray. In this
way, the entire McCabe-Thiele diagram can be computed
and graphically represented using standard Excel charting
Standard Excel what-if analysis capability can be used
to evaluate design results. For example, Goal Seek or
Solver may be used to calculate the reﬂux ratio to obtain
the liquid composition (xB) descending from tray 10.
(Solver seems to converge more reliably and accurately
than Goal Seek.)
As was ﬁrst suggested by Murphree, the McCabeThiele procedure may be made more realistic by relaxing the approximation that vapor-liquid equilibrium
is achieved on each stage. The Murphrey efﬁciency is
deﬁned as: E ML = x j - x j-1
x* - x j - 1
j ^4 h In Eq. 4, xj* is the liquid mole fraction that is in equilibrium with the vapor ascending from tray j and xj is the
actual mole fraction of the liquid descending from tray j.
As the efﬁciency EML decreases to values less than unity,
the decrease in liquid mole fraction from the distillate to the
bottom will be reduced. The concept of Murphree efﬁciency
is equally applicable to the vapor or liquid phase, and here
it is convenient to apply it to the liquid phase. Note that if
38 www.aiche.org/cep December 2009 CEP Eq. 4 is be applied, the use of Murphree efﬁciencies requires
a modiﬁcation in the way that the liquid mole fraction is
calculated from the vapor mole fraction.
It is useful to estimate heat effects consistent with the
CMO approximation. Here, it is assumed that sensible
heat effects and heats of mixing are negligible and that
heat duties are only associated with evaporating and condensing binary mixtures based on their (ﬁxed) enthalpies of vaporization. The condenser duty, QC, is the heat
removal rate required to condense a vapor with ﬂowrate V
and composition xD:
- Q C = V 6 x D DH 1 + (1 - x D) DH 2 @ ^5 h The CMO approximation implies that the sum of the
condenser and reboiler duties is zero for a saturated-liquid
feed (q = 1). The heat duty required to change the thermal
state of the feed from the saturated-liquid state is:
Q F = F (1 - q) 6 x F DH 1 + (1 - x F) DH 2 @ ^6 h The reboiler duty (QR) is calculated from QC and QF:
QR = - QC - QF ^ 7h Evaluating binary separations
A spreadsheet is used to analyze the separation of the
acetone-ethanol mixture and other binary mixtures using
the McCabe-Thiele approach.
The McCabe-Thiele diagram is constructed by interpolation of x-y data. These data may be obtained from
a variety of sources, such as standard thermodynamic
models or commercial process-simulation software. The
advantage of this approach is that the source may be
sophisticated models and databases that are difﬁcult and
time-consuming to program in Excel. However, x-y data
may not always be available for the system of interest, so
the use of Excel for regression of phase-equilibrium data
to generate the x-y data is demonstrated here.
VLE data for the acetone-ethanol system at 50°C,
71°C and 80°C (6, 7) have been used to regress the
parameters of the NRTL activity-coefﬁcient model.
Since the pressure is low (about 2 bar or less), pressure
effects on the liquid fugacity may be neglected and the
vapor phase can be treated as an ideal gas. Thus, the total
pressure of the binary mixture is given by Eq. 8, and the
vapor composition for the speciﬁed liquid composition
may be calculated from Eq. 9: The Role of the McCabe-Thiele Method in Distillation Engineering T he availability of digital computers and the intense
development of solution algorithms, beginning in about
1951, eliminated the need for approximate solutions in
equilibrium-stage distillation calculations and enabled more
rigorous simulations (11). A comprehensive suite of powerful
rigorous methods is available today in commercial software,
which has completely replaced simpliﬁed methods for the
design of distillation towers. Unfortunately, these rigorous,
computerized calculations are often used as a black box,
and the intuitive, visualization beneﬁts inherent in the simpliﬁed procedures are in danger of being lost. Kister noted that
despite the huge progress in distillation, the number of tower
malfunctions is not declining (12).
Experts recognize that an effective distillation design
and analysis toolkit must have more than the capability for
rigorous, computerized calculations. Accurate calculation of
thermodynamic properties (especially vapor-liquid equilibrium) is crucial to producing correct designs (13). Residue
curve maps (RCMs) (14) provide visualization of feasible and
infeasible separation sequences, and have been extended to
multicomponent systems and pressure variations. Graphical
techniques, like McCabe-Thiele and Hengstebeck diagrams,
multicomponent distillation proﬁles and RCMs, are excellent
troubleshooting tools because they uncover design problems, such as composition pinches and unforgiving composition proﬁles (15). Good plant data are difﬁcult to obtain, but P= y1 = sat
P 1 x 1 c1 + P 2 x 2 c 2 sat
P 1 x 1 c1
P ^8 h ^ 9h Any suitable activity-coefﬁcient model may be used
to represent the liquid nonideality, and here the NRTL
model has been chosen:
G 21 x21
G 12 x12
x 1 x 2 RT = x 1 + x 2 G 21 + x 2 + x 1 G 12 ^10h G 12 / exp (- ax12) and G 21 / exp (- ax21) ^11h x12 = A 12 + B 12 /T and x21 = A 21 + B 21 /T ^12h The equations for the resulting activity coefﬁcients
(γ1 and γ2) are available in standard references. At each
temperature, the vapor pressures of acetone and ethanol
have been estimated using the function Interp and
assuming that the logarithm of the vapor pressure is are well worth the time and effort required to collect them,
since they are the prime tool of the troubleshooter. Visualization tools capture the fundamentals of distillation. Such a
diverse and comprehensive toolkit gives engineers detailed
results, insight, and understanding to develop superior
designs, as well as the judgment to diagnose and resolve
Today, implementation of the McCabe-Thiele graphical
procedure does not require the CMO approximation, since
the diagram can easily be constructed from a rigorous distillation calculation. In addition, the McCabe-Thiele diagram
has been extended to multicomponent systems by Hengstebeck. When used in this manner, McCabe-Thiele/Hengstebeck diagrams are highly effective as design and troubleshooting tools for analyzing new energy-saving technologies
(16), designing steam-stripping systems (17), improving
energy efﬁciency (18), evaluating revamp improvements (19),
and explaining counter-intuitive observations in a multi-feed
distillation tower (20).
“Perry’s Chemical Engineers’ Handbook” (21) states:
“With the widespread availability of computers, the preferred
approach to design is equation based … Nevertheless,
diagrams are useful for quick approximations, for interpreting
results of equation-based methods, and for demonstrating
the effect of various design variables. The x-y diagram is the
most convenient for these purposes.” linear in reciprocal temperature.
The optimum values of the NRTL parameters
(A12, A21, B12 and B21) have been determined using Solver
to minimize the sum-squared error between the measured
and calculated total pressures (i.e., Barker’s method).
The optimum values of the NRTL parameters are:
α = 0.3; A12 = 0.724358; B12 = –159.176; A21 = –2.33876;
B21 = 921.128.
Using the NRTL model with Eqs. 8–12, an x-y diagram is generated. At each value of x, the temperature
must be found such that the total pressure (Eq. 8) is equal
to the stage pressure (constant at 1 atm or 101.325 kPa).
Although Goal Seek may be used to solve this equation, it is tedious, since the calculation will have to be
repeated 101 times. A better approach is to calculate the
sum-squared error of the difference between the calculated pressures and 101.325 kPa, and then use Solver to
minimize the sum-squared error by changing the 101 cells
that contain the temperatures corresponding to the liquid
compositions. The latter methodology (provided with the
online article) is efﬁcient in terms of human effort, since
a single Excel step generates the entire x-y table. Total reﬂux
The total-reﬂux calculation, which corresponds to
inﬁnite reﬂux ratio, is useful because it determines the
minimum number of stages needed for the target separaCEP December 2009 www.aiche.org/cep 39 Reactions and Separations
1 0.9 xF 0.7
0.6 0.0300 QC, GJ/h –4.984 1.00 xB 0.03 QR, GJ/h 4.299 2.025 5 xB-error 4 0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x = Mole Fraction of Acetone in Liquid Figure 2. Acetone-ethanol separation at 1 atm and total reﬂux requires
between six and seven stages to achieve xD = 0.09 and xB = 0.03. tion. At inﬁnite reﬂux, both operating lines reduce to
the diagonal (x = y) line. The total-reﬂux diagram for
acetone-ethanol is presented as Figure 2, which indicates
that between six and seven stages are needed to achieve
xD = 0.9 and xB = 0.03. Hence, it is possible to use a distillation column with 10 stages for the desired separation. Effect of q and comparison with rigorous calculation
Figure 3 presents the reﬂux ratio needed to achieve
the desired separation. As shown in the ﬁgure, the desired
reﬂux ratio is readily calculated using Solver to determine
the reﬂux ratio that gives the target bottom concentration,
xB = 0.03.
Figure 3 demonstrates that the optimum feed location
is tray 6 rather than tray 5, but the penalty for the nonoptimum feed location is fairly small.
A study of the effect of varying the thermal state of
the feed is summarized in Table 1 (using the optimum
feed location, tray 6). The required reﬂux ratio decreases
as the thermal state of the feed (q) increases, and the
reboiler duty (QR) increases as q increases. The reboiler
duty in Table 1 is not the entire heat load, since it does
not include any heat treatment of the feed. Thus, the table
includes QR + QF, where QF is the heat load required to
modify the thermal state of the feed from q = 1 (saturated
liquid). (Based on the Lewis CMO approximation,
QR + QF is exactly equal to –QC.) On this basis, the total
heat load decreases as q increases.
The analysis demonstrates that the effect of an
increase in q results in a decrease in capital costs (due to
a lower reﬂux ratio and column ﬂows and hence a smaller
column diameter), as well as a decrease in operating
costs (mainly a lower heating duty, which is usually the
40 xB Stage 10 0.90 Reﬂux Ratio 3 xD Calculated Feed Stage 0.8 EML XD 0.5 q 2
0.8 www.aiche.org/cep December 2009 CEP y = Mole Fraction of Acetone in Vapor y = Mole Fraction of Acetone in Vapor 1 8.9 E–23 1
6 3 2 1 5 7 0.5 Top
Line 8 0.4 11
0.2 Feed Line 0.1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x = Mole Fraction of Acetone in Liquid Figure 3. The McCabe-Thiele diagram for acetone-ethanol at 1 atm
shows the input variables (design speciﬁcations) and key calculated
variables. xB-error is the square of the difference between the desired and
calculated values of xB. Solver is used to vary reﬂux ratio to drive xB-error to
a minimum value (effectively zero).
Table 1. The thermal state of the feed affects the
reﬂux ratio and the reboiler and condenser duties.
xF = 0.5, xD = 0.9, xB = 0.03, EML = 1.0
(QR + QF) is the reboiler duty plus the heat required to raise
the feed from a saturated liquid to its feed thermal state.
Tray Q R,
GJ/h Q C,
GJ/h Q R + Q F,
GJ/h –0.1 2.54 6 2.06 –5.83 5.83 0 2.44 6 2.25 –5.68 5.68 0.2 2.27 6 2.65 –5.39 5.39 0.4 2.12 6 3.09 –5.15 5.15 0.6 2.00 6 3.56 –4.93 4.93 0.8 1.89 6 4.07 –4.75 4.75 1 1.79 6 4.60 –4.60 4.60 1.1 1.75 6 4.88 –4.53 4.53 major operating cost). The value of this analysis is that
the design engineer can easily understand the beneﬁts of
varying q and make the best design choice.
This McCabe-Thiele method was tested by comparing
its calculated q variations with rigorous results from the
Aspen Plus process simulator. The Aspen Plus simulation
uses the same thermodynamic model (ideal vapor phase,
no pressure effects on the liquid fugacity, and the NRTL
activity-coefﬁcient model), but rigorously deals with heat
effects. It does not make the Lewis approximations (constant molal overﬂow or constant heat of vaporization even
as the liquid composition changes, and negligible sensible Error bars show ±10% variance
from rigorous calculation
Rigorous x = Mole Fraction of
Acetone in Liquid Reflux Ratio 3.2
1.6 McCabe-Thiele 0 0.2 0.4
q = Thermal Quality of Feed 0.8 1 1
Rigorous 0 Figure 4. The required reﬂux ratio is a function of the thermal quality
of the feed. 2 4
Tray Number 8 10 Figure 6. The liquid composition proﬁles obtained using the McCabeThiele techinique and rigorous calculations are similar. 5 200
Rigorous 4 Vapor 175 3
2 McCabe-Thiele Error bars show ±15%
variance from rigorous calculation 1
0 0.2 0.4 0.6 0.8 1 Flow, kmol/h Reboiler Duty, GJ/h 6 150
Liquid 125 Rigorous: Solid lines
McCabe-Thiele: Dashed lines 100 q = Thermal Quality of Feed 75
0 2 4
Tray Number Figure 5. The reboiler duty is a function of the thermal quality
of the feed. Effect of feed location
Figure 8 shows the effect of nonoptimum feed
tray location on the required reboiler duty. Note that a
severely nonoptimum feed location (e.g., tray 9 vs. tray
6) will require the reboiler duty to be doubled in order
to achieve the target separation. Figure 9 illustrates the
pinch point that occurs when the feed point is too low.
Figure 10 provides further illustration of the pinch point,
showing that the liquid mole fraction reaches an asymp- 10 Reboiler Duty, GJ/h Figure 7. There is poor agreement between the Lewis approximations
and rigorous calculations for the column ﬂow proﬁles.
3 4 5 6 7 8 9 Feed Tray Figure 8. A nonoptimum feed tray location (such as tray 3 or 9) would
require a larger reboiler duty to achieve the target separation.
y = Mole Fraction of Acetone in Vapor heat and heat of mixing), and hence provides a way to
estimate the errors caused by the approximations.
Figures 4 and 5 indicate that the Lewis approximations cause errors of about 10% in the reﬂux ratio and up
to 15% in the reboiler duty. The Lewis approximations
are in excellent agreement with the rigorous calculation
for the liquid composition proﬁle (Figure 6), but poor
agreement with the rigorous calculation for the ﬂow
proﬁles (Figure 7).
Today, rigorous calculations rather than shortcut methods are used for detailed design of distillation columns.
However, Figures 4 and 5 clearly demonstrate that the
McCabe-Thiele method captures the trends reasonably
well, and hence remains important for understanding the
foundations of distillation engineering. As discussed in
the sidebar on p. 39 (“The Role of the McCabe-Thiele
Method in Distillation Engineering”), the McCabe-Thiele
diagram, without the CMO approximation, has excellent
present-day value as a design and troubleshooting tool. 8 1
Line 2 1 3
9 0 0.1 Top
Feed Line 0.2 0.3 0.4 0.5 0.6 0.7 0.8
x = Mole Fraction of Acetone in Liquid 0.9 1 Figure 9. A pinch point occurs when a feed point is too low, such as
tray 9 rather than the optimum tray 6. CEP December 2009 www.aiche.org/cep 41 Liquid Mole Fraction Reactions and Separations 1.0
0 Table 2. The Murphree efﬁciency (EML) affects the reﬂux
ratio and reboiler duty.
xF = 0.5, xD = 0.9, xB = 0.03, q = 1.0
EML Reﬂux Ratio Optimum Tray QR, GJ/h 1.00 1.89 6 4.07 0.95 2.10 6 4.42 0.90 2.41 6 4.93 0.85 2.88 6 5.71 0.80 3.70 6 7.05 Figure 10. When the feed point is too low (tray 9 rather than the
optimum tray 6), the liquid composition reaches an asymptotic value. 0.75 5.38 6 9.83 0.74 5.95 6 10.8 totic value of about 0.09 at tray 9, and the addition of
more stages above the feed will have no effect on improving product purities.
The Excel ﬁle can be used to further study the analogous
detrimental effect that occurs if the feed point is too high. 0.73 6.68 6 12.0 0.72 7.57 5 13.4 0.71 8.81 5 15.5 0.70 10.6 5 18.4 0.69 13.3 5 22.9 Effect of reduced tray efﬁciency
It is usually recommended that the sectional column
efﬁciency be deﬁned as the ratio of the theoretical number of stages to the actual number of stages to achieve
a particular separation (8). Since efﬁciencies vary from
one section to another, it is best to apply the efﬁciency
separately for each section (i.e., rectifying and stripping).
The concept of Murphree efﬁciency (EML, Eq. 4) has been
used to investigate the effect of tray efﬁciency. Table 2 and
Figure 11 show that the required reﬂux ratio and the resulting
reboiler duty increase substantially as EML decreases below
unity. Note also that the optimum feed location changes as
efﬁciency changes, although the results are insensitive to the
feed location when the reﬂux ratio is high.
Figure 12 presents the McCabe-Thiele diagram for the
case where EML = 0.7. The reduced Murphree efﬁciency
effectively reduces the relative volatility, which makes the
separation more difﬁcult, requiring a higher reﬂux ratio. In
fact, the desired separation is barely possible for EML = 0.67,
and further reduction in the efﬁciency will make the desired
separation impossible, even at total reﬂux.
It should be emphasized that the Murphree efﬁciency
is only a crude description of the performance of real
trays, and hence the effect of varying EML should be
interpreted with caution. The effects shown here are only
qualitatively applicable, but useful to illustrate the effects
of reduced tray efﬁciency. 0.68 18.2 5 30.9 0.67 28.8 5 48.1 2 6
Tray Number 8 10 Solution to the acetone-ethanol example problem
a. Constant molal overﬂow is a reasonably good
approximation even for this case, where the enthalpy of
vaporization of ethanol is 32% higher than that of acetone.
The CMO approximation is especially useful because it
42 www.aiche.org/cep December 2009 CEP 20
Reflux Ratio 0 15
0.65 0.70 0.75 0.80
Efficiency 0.90 0.95 1.00 Figure 11. The Murphree efﬁciency (EML) substantially decreases with a
higher reﬂux ratio. captures trends, and thus serves as an aid to understand the
fundamentals of distillation engineering. But CMO does
not yield reliably accurate results, and is not recommended
for detailed design calculations, especially since software
employing rigorous methods is widely available.
b. The number of stages needed at total reﬂux is
between six and seven. Thus, the available 10-stage column is likely to be adequate for the desired separation.
c. The reﬂux ratio needed for the speciﬁed separation
is 2.0. The reﬂux ratio decreases with increasing q, and the
total heat duty (QR + QF) decreases as q increases. Therefore,
it is preferable to operate the column at high values of q.
d. The existing feed location (tray 5) is only slightly
suboptimal, with a required reﬂux ratio of 2.0, compared
with 1.9 if the feed location is lowered to tray 6. Figure 8
shows the negative effects that will occur for a poorly
located feed stage.
e. The separation becomes far more difﬁcult as EML
decreases below unity (Figure 11). Note also that low y = Mole Fraction of Acetone in Vapor 1
x = Mole Fraction of Acetone in Liquid Nomenclature
A12, A21, B12, B21 = B
G12, G21 =
= Figure 12. The effective equilibrium curve (green) at the reduced efﬁciency of EML = 0.7 on the McCabe-Thiele diagram reveals that the required
reﬂux ratio increases from 1.89 (EML = 1.0, optimum feed location) to 10.6. ΔH1vap, ΔH2vap = L = values of EML may cause pinch points that do not exist at
higher efﬁciencies. L = 1 P Other binary separations
Other binary systems may easily be studied by replacing the x-y table used here for the acetone-ethanol binary
mixture. The Excel ﬁle supplied online provides two
additional examples of x-y diagrams for binary systems.
The ﬁrst example is representative of the benzenetoluene system and assumes constant relative volatility, α: sat, P1 sat P2 =
1 + (a - 1) x ^13h ^14h The value of the simple constant-α system is that the
effects of close-boiling and wide-boiling systems may
easily be studied. Detailed study of this system is left as
an exercise for the reader.
In the second example, x-y data from an external source
are used — x-y data for the ethanol-water binary system at
1 atm from the Aspen Plus process simulator. The McCabeThiele diagram indicates that, with xF = 0.4, xD = 0.83,
xB = 0.01 and q = 1, (1) a reﬂux ratio of 5.4 is required
for the target separation, and (2) the optimum feed tray is
low in the column because the separation is very difﬁcult
at high ethanol concentrations due to the formation of
an azeotrope (at x ≈ 0.9). Hence, more stages are needed
above the feed stage. The reader is urged to perform
another calculation by increasing xD slightly, from 0.83 to
0.84 (leaving xB unchanged at 0.01). The required reﬂux
ratio almost doubles (to 10.2), which highlights the difﬁculty of achieving higher product purity in the vicinity of Q
= V =
= x* = y y= y/x
(1 - y) / (1 - x) = x a/ q = Greek Letters
α = α
γ1, γ2 =
= τ = Subscripts
= CEP temperature-dependence
parameters in NRTL model
bottom ﬂowrate, kmol/h
distillate ﬂowrate, kmol/h
Murphree efﬁciency, applied to
the liquid compositions (Eq. 4)
excess Gibbs energy (Eq. 10)
terms in NRTL model
(Eqs. 10 and 11)
enthalpy of vaporization of
components 1 and 2, kJ/mol
liquid ﬂowrate in rectifying
liquid ﬂowrate in stripping
vapor pressures of components
1 and 2, kPa
liquid fraction or thermal state
of the feed; q = 1 corresponds to
heat rate, GJ/h
vapor ﬂowrate in rectifying
vapor ﬂowrate in
stripping section, kmol/h
liquid mole fraction (of the morevolatile component)
liquid composition in equilibrium
with y (Eq. 4)
vapor mole fraction (of the morevolatile component) nonrandomness parameter in
NRTL model (Eq. 11)
relative volatility (Eq. 13)
activity coefﬁcients of
components 1 and 2
interaction-energy parameter in
NRTL model (Eq. 10) components 1 and 2
reboiler December 2009 www.aiche.org/cep 43 Reactions and Separations the azeotrope. The visual approach clearly provides insight
and understanding of the special considerations required
for the puriﬁcation of a mixture that forms an azeotrope. Closing thoughts
The ability to easily vary input speciﬁcations in the
Excel spreadsheet and to visualize the effects on column
performance has signiﬁcant value in teaching distillation
fundamentals. Engineers are better able to grasp the effects
of various inputs, and they become better design engineers
and more competent, discriminating users of commercial
software. The understanding gained from the spreadsheet
is a valuable ﬁrst step in using a rigorous simulation as a
design and troubleshooting tool.
But how robust is the McCabe-Thiele approach, which
is the foundation of this Excel application? In particular,
can it give results that will confuse or even mislead? In the
author’s experience, the McCabe-Thiele approach captures
trends well and thus is a valid and useful teaching tool.
So, should this tool be extended to improve accuracy
by eliminating the poor approximations and thus become
applicable to more realistic distillation situations (e.g., heat
effects, complex column conﬁgurations, multi-component
systems, mass transfer limitations, chemical reactions and
kinetics, etc.)? Extensions should be limited and should
be done with caution. Rigorous modeling methods are
very powerful for describing real distillation systems. The
computer code based on these methods supports ﬂexible
design requirements very well. Thus, the best use of the
spreadsheet method presented here is to produce engineers
who understand the fundamentals, have good engineering
judgment, and become discriminating users of sophisticated detailed methodologies.
As Kister noted, “the two can coexist” (4). In fact, it is
good practice to beneﬁt from both the accuracy and ﬂexibility of rigorous calculations and the insight and understanding gained by visualization of the venerable
PAUL M. MATHIAS is a technical director at Fluor Corp. (47 Discovery, Irvine,
CA 92618; Phone: (949) 349-3595; Fax: (949) 349-5058); E-mail: Paul.
Mathias@Fluor.com), and previously worked on the ASPEN Project
(MIT), at Air Products and Chemicals, and at Aspen Technology. He is
a chemical technologist with more than 30 years of broad experience,
specializing in properties and process modeling. He has 50 publications and 75 presentations at technical conferences, and has been a
member of the editorial advisory boards of two journals: Chemical &
Engineering Data and Industrial & Engineering Chemistry Research.
He occasionally teaches chemical engineering courses at the Univ. of
California, Irvine. He is a member of AIChE. He earned a BTech from
the Indian Institute of Technology, Madras and a PhD from the Univ. of
Florida, both in chemical engineering. Acknowledgment
The author is grateful to Henry Kister for reviewing this article and offering
suggestions for improvement. 44 www.aiche.org/cep December 2009 CEP Literature Cited
5. 6. 7. 8. 9. 10.
16. 17. 18.
19. 20. 21. McCabe, W. L., and E. W. Thiele, “Graphical Design of
Fractionating Columns,” Ind. Eng. Chem., 17, pp. 605–611
Taylor, R., et al., “Real-World Modeling of Distillation,”
Chem. Eng. Progress, 99 (7), pp. 28–39 (2003).
Wankat, P. C., “Teaching Separations: Why, What and
When,” Chem. Eng. Education, 35 (3), pp. 168–171 (2001).
Kister, H. Z., “Distillation Design,” McGraw-Hill, New York,
Burns, M. A., and J. C. Sung, “Design of Separation Units
Using Spreadsheets," Chem. Eng. Education, 30, pp. 62–69
Lee, M.-J., and C.-H. Hu, “Isothermal Vapor-Liquid Equilibria for Mixtures of Ethanol, Acetone, and Diisopropyl Ether,”
Fluid Phase Equilibria, 109, pp. 83–98 (1995).
Chaudhry, M. M., et al., “Excess Thermodynamic Functions for Ternary Systems. 6. Total-Pressure Data and GE for
Acetone-Ethanol-Water at 50°C,” J. Chem. Eng. Data, 25,
pp. 254–257 (1980).
Kister, H. Z., “Effects of Design on Tray Efﬁciency in Commercial Towers,” Chem. Eng. Progress, 104 (6), pp. 39–47
Egloff, G., and C. D. Lowry, Jr., “Distillation Methods,
Ancient and Modern,” Ind. Eng. Chem., 21, pp. 920–923
Sorel, E., “Sur la Rectiﬁcaton de l’alcool,” Comptes Rendus,
58, p. 1128 (1889).
Seader, J. D., “The B. C. (Before Computers) and A. D. of
Equilibrium-Stage Operations,” Chem. Eng. Education,
19 (2), pp. 88–103 (1985).
Kister, H. Z., “What Caused Tower Malfunctions in the Last
50 Years?,” Trans. IChemE., 81A, pp. 5–26 (2003).
Carlson, E. C., “Don’t Gamble With Physical Properties
for Simulations,” Chem. Eng. Progress, 97 (10), pp. 42–46
Doherty, M. F., and M. F. Malone, “Conceptual Design of
Distillation Systems,” McGraw-Hill, New York, NY (2001).
Kister, H. Z., “Can We Believe the Simulation Results?,”
Chem. Eng. Progress, 103 (10), pp. 52–58 (2002).
Ohe, S., “Energy-Saving Distillation Through Internal Heat
Exchange (HiDiC),” in “Distillation 2007,” Topical Conference Proceedings, AIChE Spring National Meeting, Houston,
TX, p. 13 (Apr. 22–26, 2007).
Zygula, T. M., “A Design Review of Steam Stripping Columns for Wastewater Service,” in “Distillation 2007,” Topical
Conference Proceedings, AIChE Spring National Meeting,
Houston, Texas, p. 609 (Apr. 22–26, 2007).
Kister, H. Z, “Distillation Troubleshooting,” Wiley, Hoboken,
Love, D. L., et al., “Rethink Column Internals for Improved
Product Separation,” Hydrocarbon Processing, pp. 97–105
Bellner, S. P., et al., “Hydraulic Analysis is Key to Effective,
Low-Cost Demethanizer Debottleneck,” Oil & Gas Journal,
102 (44), pp. 56–61, (2004).
Green, D. W., and R. H. Perry, “Perry’s Chemical Engineers’
Handbook,” 8th ed., p. 13–17, McGraw-Hill, New York, NY
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