Honors Program Thesis Proposal
Lisa Nelson
Advised by Dr. Ross Taylor
Modeling Energy Efficient Complex Distillation Columns
Introduction
In the United States, the chemical industry represents 24% of manufacturing
energy use. Distillation processes account for about 55% of that [1]. Despite their
flexibility and widespread use, distillation columns have low energy efficiency. In recent
years there has been increased interest in more energy efficient columns. To this end,
complex arrangements such as dividing-wall columns (DWCs) have been developed.
The objective of this research is to investigate energy optimization of complicated
separator layouts, such as the DWC.
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Background Information and Literature Review
Using differences in boiling points, distillation can separate mixtures of chemicals
to a high degree of purity. However, this purity comes at the price of high energy input.
This energy is mainly due to irreversible work performed by heating in the reboiler and
cooling in the condenser of the column.
A distillation column consists of many stages where liquid and vapor come into
contact. This contact changes the compositions of the vapor and liquid. Stages in a
distillation column can be counted from the top downward or from the bottom upward.
Here, the bottom-up approach is used. The reboiler is labeled as stage 1, and the
condenser as stage N, as shown in Figure 1. The stages below the feed stage is known as
the stripping section, and the stages above the feed stage is the rectifying section.
Figure 1. A representation of a simple distillation column.
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Analysis of a Simple Column
In the preliminary conceptual design of a distillation column, it is often assumed
that the liquid streams and vapor streams in sections of the column remain constant. That
is, L j  L j 1 and V j  V j 1 from the reboiler to the feed stage, and from the feed stage to
the condenser. This is known as constant molar overflow[2].
Figure 2. A stage in a distillation column.
For stages with no feed stream, such as that shown in Figure 2, the material balance for
species i is:
L j xi , j  V j xi , j  L j 1 xi , j 1  V j 1 xi , j 1
(1)
Equation 1 applies for each component in the mixture. For a feed stage the material
balance must be modified to
L f xi , f  V f xi , f  L f 1 xi , f 1  V f 1 xi , f 1  Fxi , f
(2)
It is usual to assume that the vapor and liquid streams leaving a stage are in
equilibrium with each other. Vapor-liquid equilibrium is represented here by a simple
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relative volatility model. For the ternary system that will be considered, these equations
are
 1,3 
 2,3
y1 / x1
y 3 / x3
y /x
 2 2
y 3 / x3
(3)
where αi,j is the volatility of component i relative to that of component j.
The mole fractions in both the liquid and the vapor must sum to 1; so for every
stage
x1, j  x2, j  x3, j  1
y1, j  y 2, j  y3, j  1
(4)
Using Equation sets 3 and 4, the vapor mole fractions can be solved in terms of
the liquid mole fractions. For each stage,
y1, j 
 1,3 x1, j
 1,.3 x1, j   2,3 x 2, j  x3, j
y 2, j 
 2,3 x 2, j
 1,3x1, j   2,3 x 2, j  x3, j
y 3, j 
(5)
x 3, j
 1,3 x1, j   2,3 x 2, j  x3, j
For a simple distillation column with N stages and 3 components, there will be 3N
equations in the form of (1) or (2), and N of each of the relative volatility equations (5).
This gives a total of 6N equations to be solved so far.
A distillation column includes a condenser at the top and a reboiler at the bottom.
With a total condenser, both streams leaving have the same composition as the stream
entering. In a partial reboiler, the exiting streams are in equilibrium with each other.
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Important parameters in a distillation column are the reflux ratio, r, and the stripping or
boil-up ratio, s. For the flows leaving the condenser of the column, r is the ratio of the
liquid going back to the column to the flow taken as the top product.
LN  r D
(6)
Similarly, for the reboiler, s is the ratio of vapor returning to the column to liquid taken as
product.
V1  s B
(7)
r and s are also related by a balance around the whole column.
r  1 xi , F  xi , D

s
xi , B  xi , F
(8)
Usually either r or s is specified for the column. Other specifications that are
needed are two of the feed stream mole fractions (the third is found using Equation 4),
and three more mole fractions from the two product stream. An overall material balance
for the column (Equation 9 below) is used to solve for the last composition. The feed
flowrate is also specified.
F xi , f  D xi , D  B xi , B
(9)
In a simple column with the boil-up ratio and the bottom stream compositions
specified, the composition on each stage of the column can be solved for using the
“stage-to-stage” approach as follows. Using Equation 5, the vapor composition yi,1
leaving the reboiler is found. Since there is no vapor stream entering the reboiler,
Equation 1 is modified and rearranged to give Equation 10. Since B is known, V1 can be
determined from Equation 7 and L2 from an overall material balance around the reboiler.
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xi , 2 
V1 y i ,1  Bx i , B
L2
(10)
Once the liquid composition is found, the vapor compositions can be found. Equation 1
is solved for xi,j+1 to obtain Equation 11. With constant molar overflow, L j  L j 1  L2
and V j  V j 1  V1 .
xi , j 1 
L j xi , j  V j y i , j  V j 1 y i , j 1
L j 1
(11)
Composition profiles can be completed in a column by alternating between the
material balance Equation 11 and the vapor-liquid equilibrium Equation 5. A plot of the
mole fraction of component 1 as it varies with respect to another mole fraction is the
stripping line. An example is shown in Figure 3. If there are enough stages, the
compositions will reach what is known as a pinch point. The change in composition
between stages decreases, and reaches a point where no more change will occur, even if
more stages are added, as shown in Figure 3.
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Figure 3. Composition profile in stripping section of a distillation column.
Once the pinch point is found from the bottom-up, similar calculations are carried
out starting at the top of the column. Because the total condenser is condensing all of the
vapor, the composition leaving will be the same as entering. xi , N  x i , D . LN is
determined from Equation 6, and VN-1 from a material balance around the condenser.
From constant molar overflow, L j  L j 1  L N and V j  V j 1  V N 1 .
Now, the relative volatility equations are used to solve for xi,j based on yi,j, and the
material balances are used to find yi,j-1. The new vapor-liquid equilibrium equations are
x1, j 
x 2, j 
x 3, j 
 2,3 y1, j
 2,3 y1, j   1,3 y 2, j  1,3 2,3 y 3, j
 1,3 y 2, j
 2,3 y1, j   1,3 y 2, j  1,3 2,3 y 3, j
 2,3 y1, j
(12)
 1,3 2,3 y 3, j
  1,3 y 2, j  1,3 2,3 y 3, j
The material balance (Equation 1) is solved for yi,j-1 to give Equation 13.
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y i , j 1 
L j xi , j  V j y j  L j 1 xi , j 1
V j 1
(13)
Alternating between the material balance and the liquid-vapor equilibrium
equations allows the stage compositions to be solved down to the feed stage. This forms
the rectifying line. Once again, given a sufficient number of stages, a pinch point will be
reached. If the distillation column is feasible, then the two composition profiles must
cross, as shown in Figure 4.
Figure 4. The composition profiles cross, so the separation is feasible.
Underwood and Minimum Reflux
At minimum reflux in a column, the rectifying and stripping lines do not cross;
instead they just touch at a pinch point as shown in Figure 5. This is the smallest reflux
ratio where the column will perform the desired separation.
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Figure 5. At minimum reflux, the reflux and stripping lines just touch.
Underwood [3] developed equations to calculate the minimum reflux ratio. The
following summary of Underwood’s method is adapted from [2]. In his method, Kvalues are used for liquid vapor equilibrium, where  i  K i / K ref . Constant molar
overflow is assumed, with the flows in the top of the column called L and V, and in the
bottom called L and V . At the pinch point, the compositions between stages are constant.
This means
xi , j 1  xi , j  xi , j 1 and y i , j 1  y i , j  y i , j 1
(14)
By writing a balance around the rectifying section of the column, Equation 15 is
obtained. Using the relative volatility and solving for Vmin yi,j+1 gives Equation 16.
Vmin yi , j 1 
Lmin
yi , j 1  D xi , D
Ki
(15)
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Vmin yi , j 1 
 i D x i,D
(16)
Lmin
i 
Vmin K ref
Summing Equation 16 over all components gives the total vapor flowrate in the
rectifying section at minimum reflux. The stripping section can be analyzed in a similar
fashion. Equations 17 and 18 are obtained.
Vmin


c
  i D xi , D
 
Lmin
i 1
  i 
Vmin K ref

 V min








  i B xi , B
 
i 1
  i  L min

V min K ref

New variables  
c
(17)







(18)
Lmin
L min
and  
are introduced. If constant molar
Vmin K ref
V min K ref
overflow and constant relative volatilities are assumed, then Equations 17 and 18 have
common roots and the first Underwood equation (Equation 19) can be written.
c
  i F xi , F
V feed  Vmin  V min   
i 1   i  



(19)
V feed is the change in vapor flowrate at the feed stage. If q, the vapor fraction of
the feed is known, then V feed  F 1  q  . Values for  are found which satisfy
Equation 19, which are then used to find Vmin. Lmin is then found from Lmin  Vmin  D ,
and the minimum reflux is found from rmin 
Lmin
.
D
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While Underwood’s method is useful for finding the minimum reflux of a
column, it has limitations. Most importantly, it does not give exact results for non-ideal
systems for which the simple relative volatility model, used here for illustration only,
does not hold.
Complex Distillation Columns
Ways to decrease the large energy input required for distillation include
modifying existing columns by updating equipment or adding a prestripper before the
main column [4]. Thermal coupling is another way to reduce energy use.
Several investigators [5,6] have analyzed possible configurations of thermally
coupled columns and the energy savings associated with them. Figure 6 shows the
transition from a system of non-thermally coupled columns (the transition split), into the
fully thermally coupled Petyluk arrangement, and finally the dividing-wall column. A
transition split configuration requires three reboilers and three condensers. The Petyluk
arrangement uses a section called the prefractionator to begin the separation of
components, and uses only one condenser and one reboiler. The DWC places both the
prefractionator and the main column in the same outer shell to save on construction costs.
A more detailed picture is shown if Figure 6. Companies using DWC’s have reported
savings of up to 30% in both capital and energy costs [6].
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Figure 6. a) Transition split arrangement (adapted from [7]) b) Petyluk arrangement
c) Dividing-wall column [6]
Figure 7. A representation of a dividing wall column (DWC).
When comparing the energy use of different column arrangements, the analysis
should be between columns at the minimum reflux required for the desired separation.
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At minimum reflux, the column is using the least amount of energy for a given
configuration and product purity.
In a simple column configuration, Underwood’s method can be used to minimize
energy use by minimizing vapor flow. Several methods [8,9,10,11,12] propose
modifications to Underwood's equations so they can be applied to some complex column
configurations. Several different thermally coupled arrangements can be analyzed this
way [11]. It has been shown that "the least minimum vapor flow at minimum reflux
conditions ... is achieved in TCS (thermally coupled systems).”[12] However,
Underwood’s method is not easily applied to fully coupled configurations.
It has been shown by Lucia and coworkers[13] that the length of the stripping line
corresponds to the amount of energy used by for the separation. The shortest stripping
line in a simple column is found by minimizing
Ns
D   x j
(20)
 s 
 1 
x j  
yj  xj  
xB

 s  1
 s  1
(21)
j 1
where
However, the stripping line is not well defined in complex distillation
arrangements. The stripping line in a simple column is easily seen, but the
prefractionator complicates things. The stripping line could be from the reboiler, through
the prefractionator to the feed stage, or it could remain in the main column and end at
where the middle product is removed.
Research Done
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Maple code has been written that has successfully represented a DWC with
several stages and connecting streams. Using liquid-vapor equilibrium and mass balance
equations, a large collection of equations are obtained that must be solved. Various
methods were examined for solving the system of equations. Figure 7 shows an example
of the composition profiles found using the simulation. Each point shows the liquid
composition in a tray in the column.
Figure 7: Composition profile of a dividing-wall column.
The bottom-up approach to the column is currently being evaluated, instead of
solving all of the equations en masse. This way, the column will be solved stage-bystage and the stripping line can be more easily seen. The first goal is to learn which of
the three possible definitions of the stripping line applies in complex distillation
configurations.
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Future Work
This model will be improved and expanded to include complex column
arrangements other than dividing-wall and to improve calculation speed. The results will
be used to evaluate and optimize the energy efficiency of complex distillation columns.
Timeline
May-August 2008
Continue work on model,
Collect numerical data, data analysis
Initial writing – chapters 1, 2, 3, abstract
September 2008
Initial writing – chapters 4, 5
October-December 2008
Finish chapters 1-3, continue 4, 5
Work on chapter 6
January 2009
Complete writing, work on presentation
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References
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Technology: Research Opportunities for Energy and Emissions Reduction.
Report prepared for the Industrial Technologies Program, U.S. Department of
Energy, Energy Efficiency and Renewable Energy, April 2005.
[2] Wankat, P.C. Separation Process Engineering, 2nd ed. 2007. p210-215.
[3] Underwood, A.J.V. Fractional Distillation of Multicomponent Mixtures. Chemical
Engineering Process. 1948, 44, 603-613.
[4] Demirel, Y. Separation Science and Technology. 2004, 39, 3897-3942.
[5] Rév, E. et al. Computers and Chemical Engineering. 2001, 25, 119-140.
[6] Dünnebier, G. and C.C. Pantelides. Optimal Design of Thermally Coupled
Distillation Columns. Ind. Eng. Chem Res. 1999, 38, 162-176.
[7] Muralikrishna, K., K.P. Madhavan, S.S. Shah. Trans IChemE, 2002, 80A, 155-166.
[8] McDonough, J.A. and Holland, C.D. Figure Separations the New Way – Part 9.
Hydrocarbon Process. Pet. Refin. 1962, 41, 153-160.
[9] Lee, E.S. Estimation of Minimum Reflux in Distillation and Multipoint Boundary
Value Problems. Chem. Eng. Sci. 1974, 29, 871-875.
[10] Cerda, J. and Westerberg, A.W. Shortcut Methods for Complex Distillation
Columns 1. Minimum Reflux. Ind. Eng. Chem. Process Des. Dev. 1981, 20,
546-557.
[11] Fidkowski, Z. and Krolikowski, L. Minimum Energy Requirements of Thermally
Coupled Distillation Systems. AIChE J. 1987, 33, 643-653.
[12] Fidkowski, Z. and Krolikowski, L. Energy Requirements of Nonconventional
Distillation Systems. AIChE J. 1990, 36, 1275-1278.
[13] Lucia, A., A. Amale and R. Taylor. Ind. Eng. Chem. Res., 2006, 45, 8319-8328.