ChE 305 - Process Separations Project
Ian Lutz
Tom Salerno
Michael Ocbo
Jimmy George
Stephen Tomczewski
Introduction:
A firm by the name of Chomical Chemical Company is planning to distill
dichloromethane, trichloromethane and carbon tetrachloride. The Separations Group has
been charged with the assignment to come up with a number of column designs and
associated operating conditions to see which is the most cost effective. From this data the
vice president will choose the design which is most economical.
Your manager, however, wants to get moving on this project immediately instead
of waiting a few years to get all of the data from the Separations team, and then need to
go through each design to find out which one is best. Thus he has charged us with the
assignment to get a rough idea of how this column will operate on his desk in a few days,
so that he might continue with his work while the research team is finalizing a more exact
analysis of the column. From the data he distributed to us, we came up with the following
schematic of what the column will look like.
Figure 1: Schematic of distillation column for Chomical Chemical Company
We are asked to find the optimum feed stage and the total number of equilibrium
contacts required. We are also instructed to make plots of temperature and composition
profiles. There are two main assumptions made to aid in the solution to this design
inquiry and they are that constant molal overflow applies and that the system will follow
ideal solution behavior. Constant molal overflow essentially states that there are equal
heats of vaporization, that there is no heat loss from the column to the surroundings and
that the specific heat changes are small compared to latent heat changes. The assumption
of ideal solution behavior gives us the following relationship the K value of each
component to their respective vapor pressures and the total pressure of the system.
Ki = V Pi / Ptot
Two solutions are shown in the body of this project. The first is an excel solution
with the appropriate hand calculations using the given relationship for Ki found in the
problem statement. The second solution is a simulation method completed using Aspen
design software assuming ideal gas behavior.
Results and Methodology:
Excel (Hand) Calculations:
We began solving this problem by doing external balances around the entire
column. The equations we developed are the overall mass balance, the balance of the LK
component (dichloromethane), and the balance of the HK component (chloroform).
(1)
F  BD
(2)
FzCH 2Cl2  BxB ,CH 2Cl2  DxD ,CH 2Cl2
(3)
FzCHCl3  BxB ,CHCl3  DxD ,CHCl3
(4)
z
C
i
i
1
C
x
i
B ,i
1
C
x
i
D ,i
1
However, for the external balances there were still six unknowns and only 5
independent equations. Thus our group made the assumption that all of the HNK (carbon
tetrachloride) would go to the bottoms. With this assumption we were able to write,
(5)
xD ,CCl4  0
We then solved Equations 1, 2, 3, 4 and 5 simultaneously and were able to
completely specify the feed stream, the bottom stream, and the distillate stream. After this
was completed we found the values for L, the liquid rate flowing down the column, and
V, the vapor rate flowing up the column, by using an overall balance around the
condenser and the definition of the reflux ratio.
(6)
L
L    D   Reflux ratio  D and V  L  D
D
We realized that although our assumption of all of the HNK going to the bottoms
is a good approximation, it is probably incorrect. The real value might be 10-4 , 10-6 etc.
Consequently, the percent error in xD ,CCl4 is probably very large, but the percent error in
xB ,CCl4 is probably very small. Thus we decided to step off stages starting from the
bottom, which is more accurately specified, and moving up.
Before we could step off stages, we needed a method to correlate the
compositions of passing streams, such a function would allow us to move from one stage
to the next. We found such a relation for the part of the column above the feed (the
enriching section) by performing mass balances around the top of the column and an
arbitrary stage j. From this we were able to construct the top equilibrium line as,
(7)
yi , j 1 
L
 L
xi , j  1   xi ,dist .
V
 V
We obtained another relation for the part of the column below the feed (the stripping
section) by performing mass balances around the bottom of the column and an arbitrary
stage j. From this we obtain our bottom equilibrium line as,
(8)
yi , j 1 
 L
L
xi , j  1   xi ,bot .
V
 V
From our external balances we were able to completely specify the liquid stream.
Thus our first step was to calculate the vapor compositions leaving this stage. To do this
we had to use our ideal gas relationship,
(9)
pi*
Ki 
ptot
where our vapor pressures ( pi* ) for each species at each temperature where found using
the Antoine Equation, to make the calculations in Excel easier. The constants for the
Antoine Equation were found from the text, Elementary Principles of Chemical Process.
The functional form of this equation is shown below,
(10)
 
Log10 pi*  A 
B
.
T C
With Equation 10, our process was to guess a temperature, calculate the vapor pressures
of each component, find the K values of each component, find the vapor composition of
each component using,
(11)
yi  Ki xi
C
and then see if
y
i
i
function in Excel.
 1 . We performed this process through the use of Goalseek, a
Next, we needed to calculate the vapor composition for each component using
both Equations 7 and 8. In order to decide which operating line to use we had to make
another assumption. As we move up from stage to stage, the optimal feed stage will make
the vapor composition of the LK increase the fastest, and also make the vapor
composition of the HK decrease the fastest. With this approximation of the optimal feed
stage we know that if our calculations of the next stage up the column we obtain,
(12)
 yCH 2Cl2 , j 1 
 yCH 2Cl2 , j 1 




 yCHCl , j 1 
 yCHCl , j 1 
3
3

top op eqn 
bot op eqn
then we continue to use the bottom operating line, and have not yet reached the feed
stage. However, if instead we obtain,
(13)
 yCH 2Cl2 , j 1 
 yCH 2Cl2 , j 1 




 yCHCl , j 1 


3

top op eqn  yCHCl3 , j 1 bot op eqn
then for that next stage, we use the top operating equation and we have reached our feed
stage. After reaching the feed stage we also need to check if we have enough stages to
complete the required separation. Thus for each stage above the feed we will see if
(14)
yCH 2Cl2 , j  yCH 2Cl2 ,dist .
If this is the case, then we have obtained the required separation, and j is the total number
of contacts required. If, however, Equation 14 is not satisfied we must continue to move
up stages.
We performed this entire procedure in Excel, the results, as well as, the hand
calculations showing every step are attached.
A summary of our Excel calculations are shown below
Table 1: Summary of results from Excel calculations
The raw data from our Excel file and the associated hand calculations follow
immediately.
Aspen (Simulator) Calculations:
After finishing our Excel calculations, our group wanted to obtain more
confidence in our rough sketch of the distillation column for Chomical Chemical
Company, and thus decided to try and solve their separation problem using Aspen.
The first step in this process was to find the number of stages and the optimal feed
stage for the required separation of Figure 1. To do this we designed a DIST column in
Aspen. This design required us to first solve all of the external balances, which we had
previously done in Excel. We also specified Aspen to use IDEAL relationships in its
calculations and allowed it to use its own stored thermodynamic data. Once this data was
plugged into Aspen, it generated results for the total number of equilibrium contacts, the
optimal feed stage, and the Distillate to Feed ratio. Along with this output came many
other parameters, which were not of vital importance in our rough design. However, this
design did not provide us with the Temperature and Liquid Composition Profiles we also
needed for our design.
Thus we needed to design another column, this time we used RADFRAC. The
inputs required for this column were: first, a completely specified feed stream which was
given in the problem statement; next the number of stages; operating pressure; reflux
ratio; and the Distillate to Feed ratio. All of this data was collected from either the
problem statement or from our previous Aspen column using DIST. After this data was
plugged in and we again specified using IDEAL relationships for their calculations,
Aspen was able to spit out the results of this column. The results here included our final
set of data, the temperature and liquid composition profiles of our column.
The results of these calculations in Aspen are as follows.
From the DIST column, we obtained:
282
26664
293
1
26664
3
2
300
B1
3
26664
2
1
Minimum reflux ratio:
Actual reflux ratio:
Minimum number of stages:
Number of actual stages:
Feed stage:
Distillate temperature:
Bottom temperature:
Distillate to feed fraction:
MIN_REFLUX
ACT_REFLUX
MIN_STAGES
ACT_STAGES
FEED_LOCATN
DISTIL_TEMP
BOTTOM_TEMP
DIST_VS_FEED
Table 2: Results from DIST column
From the RADFRAC column, we obtained:
282
26664
1
216
200
B4
3
11
10
300
26664
2
Temp erature (K)
Pressu re (N/sq m)
Mass Flo w R ate (k g /sec)
12
1.45763792
50
5.3462861
5.53188951 6 stages
3.72313855 4th from top
282.059597 K
300.2507 K
0.32117838
Liquid Composition Profile - Mole Fractions
DICHL-01
CHLOR-01
CARBO-01
6
0.786
0.208
5
0.613
0.369
4
0.408
0.543
3
0.231
0.662
2
0.115
0.701
1
0.051
0.657
Temperature Profile - degrees Celsius
Stage
Temperature - Aspen
6
9.68
5
12.40
4
16.09
3
20.22
2
23.82
1
26.91
Stage
Table 3: Profiles from RADFRAC column
0.006
0.018
0.049
0.107
0.184
0.292
Comparison of Methods
The two methods used to solve this distillation problem both have their
advantages and disadvantages. Both solutions methods used the same assumptions:
Constant Molal Overflow, the system is adiabatic, and that all of the LNK’s and HNK’s
go to the top or bottom. The results from both methods accurately agree showing that the
actual number of stages is 6 and the optimum feed location is at Stage 4, when numbered
from the top. As it is said, the results are only as good as the equilibrium data given.
Therefore, the simulator’s result is thought to be more accurate because it retrieves its
data from the program’s highly precise properties package whereas the Excel method
uses the Antoine equation to calculate the K-values.
In comparison, the main difference between the Excel and simulator solution is
that of convenience. Engineers who are well acquainted with programs such as HYSYS,
SIMSCI, and Aspen can yield results quickly and accurately by just inputting initial
conditions and letting the program do all the calculations. Of course longer and more
complex processes will require a greater amount of time even with these simulators, but it
would still be faster than manually typing in all the calculations into Excel. Another
advantage to simulator programs is the wide variety of scientific tools that are readily
accessible within their interfaces. With the click of a mouse, property packages provide
the user with physical, thermodynamic, and transport data which would have to be looked
up if Excel was being used.
The output of results that simulators compile shows
everything from flow rate values to estimated power requirements for the system’s
condenser and reboiler. However, the main drawback to simulator programs is their price
tags. Companies and universities spend thousands of dollars to have these tools and keep
them updated. Many times companies spend money on training program for employees
which add to the overall cost.
The Excel solution method is somewhat tedious in setting up the problem,
however, after the first stage calculation is completed, a macro can be written to solve the
rest of the problem. Another disadvantage to using Excel is the error-making
opportunities the program creates. Unless the engineer’s spreadsheet is well-organized,
numbers can easily get confused or equations easily mistyped. As most engineers know,
the time needed to debug a spreadsheet is exponentially related to the complexity of the
problem it is solving. However, it remains that Excel is a widely used tool available to
most people and not nearly as expensive as software programs, so for these reasons
engineers will continue to use it.
Overall, both methods are useful. It is simply a matter of analyzing the problem at
hand and deciding which method will get the job done most effectively. However,
businesses that want to stay as competitive as possible will always equip themselves with
the best tools available and so, simulator programs will always have a place in
engineering.
Summary and Conclusions:
Both the Excel calculation method and the Aspen simulator method of solving
this problem suggests that the number of equilibrium contacts is 6, with the optimum feed
stage being on stage 4 from the top. Thus our group can confidently say that the column
needed will require 5 plates and a partial reboiler, and that the feed stage should be on
plate the 4th plate from the top.
The stage by stage profiles for the Excel calculations differ from those given from
the Aspen simulator, however, their values are very similar, with an average error of only
10%. The small differences between these values are probably due to the fact that each
method uses different thermodynamic data. For the Excel calculations, we used the
Antoine equation to estimate the vapor pressures of each component at each temperature,
while Aspen used its own thermodynamic library to calculate these values. The
difference in the thermodynamic data thus leads to small differences in the stage by stage
results. Since we don’t know which thermodynamic data is better, our group decided to
use the average of the two as a good estimate for the temperature and liquid composition
profiles of our column.
Our overall solution is as follows: the column has 6 equilibrium contacts, 5
stages plus a partial reboiler; the feed stage should be located on the fourth stage from
the top; the temperature profile lies somewhere in between the following curves (Excel
solution, Aspen solution, average)
Tem perature Profile
30
Temperature (deg C)
25
20
Temperature - Excel
15
Temperature - Aspen
Temperature - Average
10
5
0
0
1
2
3
4
5
6
7
Stage (Reboiler = Stage 1)
Figure 3: Temperature profile
and the liquid composition profiles lie somewhere between the following curves (Excel
solution, Aspen solution, average)
Liquid Com position Profiles
0.900
0.800
0.700
CH2Cl2 - Excel
CH2Cl2 - Aspen
Mole Fraction
0.600
CH2Cl2 - Average
CHCl3 - Excel
0.500
CHCl3 - Aspen
0.400
CHCl3 - Average
CCl4 - Excel
0.300
CCl4 - Aspen
CCl4 - Average
0.200
0.100
0.000
0
1
2
3
4
5
6
Stage (Reboiler = Stage 1)
Figure 4: Liquid composition profiles
7