Brown Industries
GGBL Building
Ann Arbor, MI 48109-2136
DATE:
November 11, 2002
TO:
Richard Wagner, Plant Supervisor, Brown Industries
FROM:
Emma Wong, Team Leader, Brown Industries
Mario Fabiilli, Staff Engineer, Brown Industries
Jessica Garbern, Staff Engineer, Brown Industries
SUBJECT:
Final Report for the Methanol Recovery Optimization via Distillation: Rotation 2
REF:
Distillation work plan (10/21/02)
Rotation 1 final report (10/7/02)
Fogler memo (9/3/02)
Abstract
To investigate the feasibility of recovering of 97 vol% methanol from Brown Industries waste
streams (waste streams: 5-10 vol% methanol), we needed to characterize our packed bed
distillation column, assess and expand the flooding correlation provided by Rotation 1, and
develop a model to predict the column performance. We quantified the effects of feed flow rate
and feed temperature on product (methanol distillate) concentration (xD) and mass transfer
coefficient (KOG). We determined that as the feed rate increased, the x D increased while KOG
decreased. However, we found no correlation between feed temperature and x D or KOG. We
determined that there was no correlation between reflux ratio and flooding and found that the
correlation from Rotation 1 is accurate. To develop our model, we assumed the constant molar
overflow assumption is valid for this system because the latent heats of vaporization of
methanol and water are comparable (water: 35210 kJ/mol; methanol: 40657 kJ/mol). Our Excel
model predicts column performance by taking inputs of reflux ratio, reboiler power, feed
weight fraction, feed temperature, and distillate weight fraction and determining the optimum
flow rate at which to run the column to satisfy these conditions. To account for changes in K OG
at different column conditions, a correlation relating the KOG to feed flow rate and reflux ratio
was determined using Polymath (KOG = 2123.5·(feed flow rate)-0.933·(reflux ratio)-0.552). The
model also predicts whether or not flooding will occur using the Rotation 1 flooding
correlation. This model can be used to determine the appropriate operating conditions to purify
the methanol waste stream. Finally, we evaluated the online, tray distillation column designed
by the University of Tennessee. We conclude that the simulation is good and relatively easy to
use; however we also recommend a few changes we feel would improve the usability of the
column.
1
Introduction
Manufacturing processes at Brown Industries currently produce aqueous waste streams
containing 5-10 vol% methanol. If concentrated to at least 97 vol% methanol, these waste
streams can potentially be sold to outside vendors for a profit. On September 3, 2002, Dr.
Fogler requested that we investigate the feasibility of this methanol recovery process using the
packed-bed distillation column in the Brown Industries Lab. To help us meet the objectives for
Rotation 2, we used operational limits proposed by Rotation 1 on the pilot-scale methanolwater distillation column. Dr. Fogler also requested that we evaluate the online tray distillation
column designed by the University of Tennessee-Chattanooga.
We set the following objectives to meet these goals:






Quantify the effect of feed flow rate and feed temperature on product concentration (x D)
and mass transfer coefficient (KOG). (See Appendix A for variable definitions.)
Assess the effect of changing reflux ratio on flooding.
Evaluate the proposed flooding correlation from Rotation 1.
Determine whether the constant molal overflow assumption or the enthalpy-concentration
method is valid for this distillation column.
Develop a model to predict column performance that incorporates the following relevant
parameters:
– Feed flow rate
– Reflux ratio
– Reboiler power
– Changes in the mass transfer coefficient
– Flooding
Evaluate the online, tray distillation column designed by the University of Tennessee.
This report details our completed work for Rotation 2.
Theory and Data Analysis
Distillation is used to separate components in liquid solution. The separation is based on the
different boiling points of the components in the mixture. When the liquid mixture is heated, a
vapor forms, and the distribution of the components in the liquid and vapor phases will be
different because of the different boiling points. Vapor leaving the top of the column, called
distillate, is condensed. Part of the distillate is returned to the column as reflux, which allows
liquid to flow back down the column and creates the opportunity for mass transfer between
phases. The remaining distillate is removed as product. A reboiler also vaporizes some of the
falling liquid while the remaining liquid exits the column as bottoms.
Feed Conditions
Feed flow rate can affect mass transfer by causing either laminar or turbulent flow in the
column. At lower flow rates, the flow is laminar, which limits contact between the liquid and
2
vapor phases, leading to relatively low mass transfer. However, at higher flow rates, the flow
becomes turbulent, which improves mass transfer between phases.
Feed temperature affects the quality of the feed stream, where quality is the ratio of the amount
of heat needed to vaporize one mole of feed at the entering conditions to the molar latent heat
of vaporization of the feed. For a saturated liquid feed, q=1, while for a saturated vapor feed,
q=0. The quality of the feed affects the slope of the operating lines, as the enriching and
stripping operating lines intersect on the q-line (see “Constant Molal Overflow – McCabe
Thiele Method” for more details).
To quantify the effect of feed flow rate and feed temperature on the product concentration and
mass transfer coefficient, we constructed the following plots of our experimental data:
 Feed flow rate versus product concentration
 Feed flow rate versus mass transfer coefficient
 Feed temperature versus product concentration
 Feed temperature versus mass transfer coefficient
See Appendix B for detailed calculations involving KOG.
Flooding
Flooding occurs when the gas flow rate in the column is so great that the downward flow of
liquid is hindered. If the gas flow rate is great enough, the liquid may actually rise up the
column and exit in the distillate. We chose to examine reflux ratio because this value affects
flow rates within the column, and may have an effect on flooding. Rotation 1 has shown that at
small reflux ratios (i.e. producing a minimal increase in liquid flow compared to the feed rate),
increased reboiler power is necessary to cause flooding at lower flow rates compared to higher
flow rates. This may be because at low flow rates for a given reboiler power, there is less
liquid falling down the column; thus an increased gas flow rate is necessary to result in a large
enough liquid buildup to cause flooding.
There are several methods to develop a flooding correlation for a distillation column. We used
an empirical correlation to predict flooding as a function of feed flow rate, similar to Rotation
1. See Appendix C additional flooding correlations and Appendix D for detailed flooding
calculations. We plotted the reboiler power at which flooding occurred versus feed flow rate
(see Results - Flooding). Above this line results in flooding, while below this line indicates
normal (non-flooding) operation.
Constant Molal Overflow (McCabe-Thiele Method)4
We compared our data to predictions made by the McCabe-Thiele method to determine
whether or not this method accurately simulates this distillation column. This method provides
a graphical means of modeling the operation of a distillation column and can also be used to
determine distillate composition or feed flow rate for a given set of conditions. The McCabe
Thiele method assumes the following:
3



Equal latent heats of vaporization for all components
Negligible differences for the sensible heat
Constant molal overflow in each section of the column
Because the McCabe-Thiele method assumes constant molar overflow (Equation 1), this
results in straight operating lines.
Vn+1 + Ln-1 = Lv + Ln
(1)
With this assumption, the following equations for the enriching section operating line
(Equation 2), stripping-section operating line (Equation 3), and q-line (Equation 4) can be
derived, respectively4.
y n1 
x
R
xn  D
R 1
R 1
(2)
y
Lm
Wx
xm  w
Vm1
Vm1
(3)
y
x
q
x F
q 1
q 1
(4)
For a liquid feed, the slope of the q-line increases as feed temperature increases until it reaches
saturation (vertical q-line). If additional heat is added beyond saturated liquid, the feed
becomes a mixture of liquid and vapor and the slope of the q-line ranges from 1 to 0. The qline, enriching operating line, and stripping operating line all intersect at a single point.
Enthalpy-Concentration Method4
The enthalpy-concentration method accounts for differences in latent heats for each
component, heats of solution or mixing, differences in sensible heats of the components, and
does not assume constant molal flow. This results in curved operating lines. We determined
whether this method is necessary for this system by comparing the latent heats of vaporization
of methanol and water. This method would only me necessary if the latent heats are
significantly different. Equation 5 gives the enriching-section operating line and Equation 3
gives the stripping-section operating line.
y n1 
Ln
Dx D
xn 
Vn1
Vn1
(5)
A trial and error solution must be used to simulate a column with this approach. This method is
detailed in Appendix E4.
4
Distillation Model
We adapted a model provided by Rotation 1 to predict the performance of this column. This
model is both experimentally and theoretically derived, where theory was used to construct the
McCabe-Thiele plot, and empirical data was used to calculate the mass transfer coefficient. A
detailed description of this model is found in Appendix F. This model allows us to account for
changes in the mass transfer coefficient due to changes in column conditions, as well as predict
when flooding will occur.
Equipment2
The distillation apparatus we used to perform pilot-scale separation processes is shown in
Appendix G. The 30-inch tall packed-bed distillation column contains 1/4-inch Pro-Pack
stainless steel random packing within a 3-inch inner-diameter glass pipe. The apparatus has
two available feed tanks: a smaller tank for use during recycle-mode and a larger tank for use
during production-mode. We used the column in production-mode to remove the possibility
that the hot bottoms being returned to the recycle feed tank could change our results due to
additional feed preheating. The preheater heats the feed, which then enters the column in the
top, middle, or bottom feed port. The vapor exits the top of the column to be condensed then
sent to a distillate receiver. The distillate is returned to the column as reflux, returned to the
feed tank during recycle-mode, or collected in a distillate tank during production-mode. A
bottoms waste stream is removed from the reboiler and is either returned to the feed tank
during recycle-mode or held in a bottoms tank during production. Additionally, Appendix H
contains a MSDS for methanol.
Throughout the distillation column there are seventeen thermocouples to record temperatures
and four volumetric turbine flow meters to record feed, reflux, distillate, and bottoms flows.
All of these values are recorded on a computer through LabTech Control software. For
additional equipment operation instructions, see equipment manual2.
A gas chromatograph (GC) was used to analyze and determine the composition of various
streams. Samples of approximately 1 ml were removed with a syringe from the feed tank or
sample ports in the apparatus, transferred to a 1 ml Eppendorf tube, and quickly capped. Then,
using an injection syringe, a 0.2 l sample was placed in sample port B of the GC. The SOP
for operating the GC was followed2. Because the GC has a high degree of error, it was
calibrated before each use with the standard samples.
The online distillation column at the University of Tennessee – Chattanooga is a 12-tray
column. The operators can change the feed pump setting, reflux percentage, and reboiler
power. Four real time images of the column are present on the user interface. Additionally,
real time temperature profiles are given for each of the trays, feed, distillate, and reflux.
5
Experimental Design
There are five independent variables with the Brown Industries distillation column:





Feed flow rate
Feed temperature
Feed concentration
Reboiler power
Reflux ratio
Dependent variables consist of temperatures and compositions of the distillate and bottoms
streams, as well as the properties calculated from these values, including the mass transfer
coefficient.
Table 1 highlights the runs that we completed in order to determine the effects of feed flow rate
and feed temperature on product concentration and hence the mass transfer coefficient.
Table 1 – Experimental Runs
Run
1
2
3
4
5
6
7
8
9
Feed Flow Rate (mL/min)
131
326
530
146
330
533
150
350
550
Feed Temperature (C)
25.0
23.6
24.2
35.0
35.0
35.0
45.0
45.0
48.7
Colored blocks indicate sets of runs, where the colored variables were varied while the others
were held constant. The maximum feed rate and temperature were chosen based on maximum
values reported by Rotation 1. During these runs, the feed concentration, feed location,
reboiler power, and reflux ratio were set at 5.5  0.9 vol%, middle, 50% and 4.7, respectively.
To continue the flooding study initiated by Rotation 1, we varied feed flow rate and reflux ratio
according to the runs outlined in Table 2. For each run, the reboiler power was adjusted until
flooding was observed, according to the methodology of Rotation 1.
Table 2 –Runs to Determine Flooding Conditions
Run
10
11
12
13
Feed Flow Rate (mL/min)
67
152
350
597
Reflux Ratio
36.7
59.4
38.8
48.6
6
Since Rotation 1 conducted runs at a reflux ratio of 6.7, we decided to operate at higher reflux
ratios. We predicted that this variable would most affect the gas flow rate inside the column,
and hence cause flooding. The feed temperature, concentration, and location were set to 56.5 
12.1C, 5.5  0.9 vol%, and middle, respectively. Though there appears to be large variations
in the feed temperature and reflux ratio between runs (due to difficulty maintaining steady
state), we found that these fluctuations were insignificant and had no effect on determining a
correlation for flooding or confirming the data found by Rotation 1. Further details can be
found in the results and discussion sections.
The online distillation column at the University of Tennessee can test three independent
variables: feed pump setting, percent reflux, and reboiler power. Table 3 outlines the runs we
completed while evaluating this column. We chose to examine the effect of feed pump setting
on the methanol distillate composition. Distillate composition was determined by using the
temperature of the top tray of the column and assuming that the vapor is at the saturation point
on each tray. Due to equipment difficulties, we were unable to complete additional runs we
had planned to examine the effects of reflux and reboiler power on distillate composition.
Table 3 –Runs completed with UTC simulator
Run
14
15
16
17
Reflux (%)
80
80
80
80
Reboiler Power (W)
2000
2000
2000
4000
Feed Pump
1
3
5
3
Results
We performed runs using the experimental procedures described above to obtain the following
results.
Effect of Feed Flow Rate on Product Concentration and Mass Transfer Coefficient
Figures 1 and 2 respectively illustrate the dependence of methanol distillate (product)
concentration and the mass transfer coefficient on feed rate for feed temperatures of 25C,
35C, and 45C. Feed concentration, feed location, reboiler power, and reflux ratio were 5.5 
0.9 vol%, middle, 50% and 4.7, respectively. Linear fits relating product concentration and the
mass transfer coefficient to feed rate are displayed in Equations 6 - 11.
7
Product Concentration
(vol% MeOH)
Figure 1 – Product Concentration vs. Feed Rate
100
90
80
70
60
50
40
30
20
10
0
100
25C
45C
35C
Linear (35C)
Linear (45C)
Linear (25C)
200
300
400
500
600
Feed Rate (mL/min)
25C: (vol%) = 0.0013 · F + 0.1378 with R2 = 0.98
35C: (vol%) = 0.0012 · F + 0.1214 with R2 = 0.99
45C: (vol%) = 0.0010 · F + 0.2236 with R2 = 0.95
(6)
(7)
(8)
Figure 2 – Kog vs. Feed Rate
25C
12.00
45C
KOG (mol/cm)
10.00
35C
Linear (35C)
8.00
Linear (25C)
Linear (45C)
6.00
4.00
2.00
0.00
100
200
300
400
500
600
Feed Rate(mL/min)
25C: Kog = -0.0186 · F + 10.758 with R2 = 0.99
35C: Kog = -0.0238 · F + 13.918 with R2 = 0.95
45C: Kog = -0.0147 · F + 9.4990 with R2 = 0.99
(9)
(10)
(11)
8
Effect of Feed Temperature on Product Concentration and Mass Transfer Coefficient
Figures 3 and 4 respectively show product concentration and the mass transfer coefficient as a
function of feed temperature, where Equations 12 -17 show the correlations obtained for feed
flow rates of 150, 350, and 550 mL/min, respectively.
Figure 3 – Product Concentration vs. Feed Temperature
100
Product Concentration
(vol% MeOH)
90
80
70
150
60
350
50
550
40
Linear (150)
30
Linear (350)
20
Linear (550)
10
0
0
10
20
30
40
50
Feed Temperature(°C)
150 mL/min: (vol%) = 0.3211 · TF + 23.654 with R2 = 0.46
350 mL/min: (vol%) = -0.0457 · TF + 54.317 with R2 = 0.07
(13)
550 mL/min: (vol%) = -0.2729 · TF + 91.995 with R2 = 0.75
(14)
(12)
Figure 4 – Kog vs. Feed Temperature
9
12.00
KOG (mol/cm)
10.00
150
350
550
Linear (550)
Linear (350)
Linear (150)
8.00
6.00
4.00
2.00
0.00
0
10
20
30
40
50
Feed Temperature(C)
150 mL/min: Kog = 0.1238 · TF + 4.5584 with R2 = 0.42
350 mL/min: Kog = -2·10-5 · TF + 4.53 with R2 = 6·10-7
550 mL/min: Kog = -0.0144 · TF + 0.8247 with R2 = 0.49
(15)
(16)
(17)
Flooding
Figure 5 highlights flooding conditions that were obtained by Rotation 1 (reflux ratio of 6.7)
and Rotation 2 (average reflux ratio of 46). Conditions at and above these points will result in
column flooding. Flooding correlations at both reflux ratios relating feed flow rate and reboiler
power are given in Equations 18 and 19, respectively. Appendix I contains additional graphs
relating vapor flow rate to reboiler power and feed rate.
Figure 5 – Flooding Conditions
10
100
Reflux ratio = 6.7
Reflux ratio = 46
Reboiler power (%)
95
90
85
80
75
70
0
200
400
600
800
Feed rate (mL/min)
Rotation 1 (Reflux ratio = 6.7):
Reboiler power = -0.0483·(feed flow rate) + 101.43, with R2 = 0.9956
(18)
Rotation 2 (Reflux ratio = 46):
Reboiler power = -0.0499·(feed flow rate) + 102.31, with R2 = 0.9948
(19)
University of Tennessee Distillation Column: Feed Pump Setting versus Product Concentration
The data that was collected from the distillation column at the University of Tennessee is
plotted in Figure 6.
11
Figure 6 – Product Concentration vs. Feed Pump Speed
100
y = -5.125x 2 + 49.5x - 27.375
R2 = 1
Product Concentration
(vol% MeOH)
90
80
70
60
50
40
30
20
10
0
0
1
2
3
4
5
6
Feed Pump Speed
Discussion
We evaluated our experimental results according to our proposed objectives. In addition, we
identified sources of error in our data and evaluated the report submitted by Rotation 1.
Effect of Feed Flow Rate on Product Concentration
We found a linear, positive correlation between the feed flow rate and the product
concentration. This trend agrees with theory because as feed flow rate is increased, the flow
rate increases in turbulence. Mass transfer is improved with a more turbulent flow resulting in
increased distillate composition of product. Due to equipment problems, we were unable to
measure distillate composition when the flow rate was high enough to cause flooding to occur.
However, we would expect that distillate composition would continue to increase with
increasing flow rate until flooding. During flooding, the contact between the liquid and vapor
phases is dramatically decreased, therefore, we would expect mass transfer and hence distillate
composition to be decreased as well.
Effect of Feed Flow Rate on Mass Transfer Coefficient (Kog)
We found a linear, negative correlation between the feed flow rate and mass transfer
coefficient, which is also consistent with theory. This is because the mass transfer coefficient
as derived by6 is actually a resistance to mass transfer. Thus, as mass transfer capability
increases, the mass transfer coefficient should decrease.
12
Effect of Feed Temperature on Product Concentration and Mass Transfer Coefficient
Feed temperature did not have a significant effect on distillate composition or mass transfer
coefficient. All of our runs were completed only within the fairly small temperature range of
25-45˚C. This is due partly to equipment difficulties, preventing us from collecting additional
data at higher temperatures within the available time frame. Also, we chose 45˚C as the
maximum temperature because at high flow rates (550 mL/min), we were unable to reach
temperatures higher than 45˚C. Therefore, we maintained this temperature range to be
consistent across all flow rates. Because this temperature range is so small, it is possible that
there was just not a large enough difference to see any trend on a plot of feed temperature
versus product concentration or mass transfer coefficient.
Another possible explanation is that although at higher temperatures, there will be more vapor
flowing through the enriching section of the column, it is uncertain what the composition of
this vapor will be. While there may be increased total moles of methanol in the vapor phase,
there will also be increased total moles of water. Thus we are unable to predict whether the
product concentration should be significantly changed with different feed temperatures without
further experimentation. We recommend that future experimentation include obtaining data at
a wider range of temperatures for the low flow rate (150 mL/min).
Also, the reboiler adds a large amount of heat to the system. It is possible that the effects of
the changing feed temperature are insignificant compared to the heat provided by the reboiler.
This may also explain the lack of correlation we found from our results between feed
temperature and distillate composition (and mass transfer coefficient).
Flooding
We confirmed the findings of Rotation 1 that reboiler power and feed flow rate would have the
greatest effect on flooding. We also extended the experimentation completed by Rotation 1 by
testing the effect of reflux ratio on flooding. We found no difference in flooding conditions
between reflux ratios of 6.7 and 46. The data found by Rotation 1 was compared to the Wilkes
and Pro-pak flooding correlations (Appendix I). While the trends were similar, the actual
numbers were not. Rotation 1 attributes this to the numerous assumptions (constant densities
throughout column equal to the liquid and vapor densities at the top of the column, linear
combination of the densities of the mixtures valid, liquid and vapor have equal molar
compositions).
A possible source of error in our data is in our definition of flooding. Flooding was defined as
occurring when the liquid holdup reached 6 inches above the center feed, similar to Rotation 1.
This definition is fairly subjective and is difficult to expand to other distillation columns
without experimentation. Due to equipment limitations, we were unable to predict flooding as a
function of pressure drop. However, a correlation based on pressure drop would be more
useful if extending to other distillation columns. Therefore, we recommend in the future for
users to attempt to determine a flooding correlation that is based on the pressure drop, p.
13
Constant Molal Overflow Assumption versus Enthalpy-Concentration Method
We determined that the constant molal overflow assumption is valid for this distillation
column. This is because the latent heats of vaporization for methanol and water are nearly
equal (methanol: 40657 kJ/mol; water: 35210 kJ/mol). If this difference were significant, then
if the enthalpy-concentration method were used, this would result in curved operating lines.
We generated a T-x-y plot using a representative set of data with both the McCabe-Thiele
method (constant overflow assumption) and the enthalpy-concentration method (Appendix J).
Because these two graphs are very similar, with almost straight operating lines with the
enthalpy-concentration method, this confirmed the validity of the constant molal overflow
assumption.
Distillation Model
Rotation 1 provided a model to determine KOG using theoretical equations and to plot a
McCabe-Thiele diagram. We adapted this model to determine optimum flow rate for a
specified distillate composition. We also extended this model to better fit our data by first
calculating values for KOG theoretically, then fitting our experimental data to a regression
model using Polymath to determine KOG as a function of feed flow rate and reboiler power
(Equation 20). Feed flow rate and reboiler power were chosen because they appeared to have
the strongest effect on product concentration.
KOG = 2123.5·(feed flow rate)-0.933·(reflux ratio)-0.552
(20)
By fitting our data to a model, this allowed us to more realistically account for changes in KOG
due to changes in the column conditions. This model takes inputs of reflux ratio, reboiler
power, and distillate composition, and determines what flow rate the column should be set at to
achieve this distillate composition. It will provide warnings if this column is not capable of
reaching this distillate composition within the flow rates we tested (100-550 mL/min) or if
flooding will occur. A detailed description of the model is found in Appendix F.
Figure 7 compares experimental data (for Run 1) to data obtained using the model. This
confirms the validity of this model because the experimental and theoretical values are
comparable (within 25%)
14
Figure 7 – Experimental vs Model (for Run 1 Conditions)
1
Distillate Composition (vol%)
0.9
xd, model
0.8
xd, expt
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
100
200
300
400
500
600
Feed Flow Rate (mL/min)
Evaluation of University of Tennessee-Chattanooga Online Distillation Column
We assessed the usability of the online tray distillation column designed by the University of
Tennessee, Chattanooga (UTC). Overall, we found the column easy to use and were impressed
by the extensive real-time data available for us to download.
We felt the following changes would facilitate use of this column for diverse users:

Clarify the feed location on the diagram: The diagram looks as if the feed port is at the top of
the column. In addition, it looks as if there are two other possible feed ports (in the middle
and bottom). We were informed that the feed is currently at the middle, however. We
thought the actual location of the feed should be made clearer on the diagram. Also, we were
uncertain if it were possible to change the feed location if we contacted UTC or if the feed
location can only be in the middle.

Label and improve the lighting of the real-time pictures: We felt we would be able to
understand the pictures better if they were labeled with which part of the column they are.
Also, it is difficult to see the pictures unless either the room lights are on or the blinds are
open. We felt that if it were possible, improved lighting would also help clarify the pictures.

Provide a correlation to convert the feed pump scale to an actual flow rate: Currently, the
feed flow rate is indicated only by a unitless integer scale. In terms of data analysis, we felt
that it would be useful to either indicate what the actual flow rate is (in volume/time) on the
interface or to have a correlation to determine actual flow from the unitless scale.

Show reflux as reflux ratio rather than reflux percent (on the graphical control panel):
Because many theoretical equations use reflux ratio rather than reflux percent, we felt it
15
would helpful to express this variable as reflux ratio to facilitate data analysis and when
choosing what column settings to use.

Provide a better visual and/or audio alert at automatic column shut-down after 15 minutes of
use: An alert to inform the user that the column is shutting down would be helpful to prevent
having to re-establish steady-state if the user did not press start immediately after automatic
shut-down occurred.

Show numerical values of additional temperatures on the figure (eg. the top tray temperature
and feed temperature): We thought it would be helpful to have numerical values of additional
temperatures displayed on the column diagram. Although it would probably seem too
cluttered if temperatures of all trays were provided on the screen, we thought it would be
useful to have the temperature of the top tray to enable the user to determine the distillate
concentration. It would also be helpful to have the feed temperature shown on the screen to
more easily determine the feed quality.
In general, we felt that this column was very well designed and clear to use.
We found a second order correlation between feed rate and composition with the Tennessee
column. This is in contrast to our experimental data collected in the Brown Industries lab.
One possible reason for this might be that we do not know the actual flow rates with the
Tennessee column and therefore it is difficult to determine whether we were operating at the
same ranges. We operated our column at conditions well below flooding. If the Tennessee
column were at or close to flooding at the higher flow rates, this would result in a leveling off
of the composition-feed rate curve due to limited mass transfer. Also, to determine the
distillate composition of the Tennessee column, we had to calculate the composition from the
top tray temperature, rather than analysis by a GC. This may also have resulted in the
difference between the Tennessee column and the Brown Industries data.
Error
In this rotation, we determined that the main source of error is in manually keeping the set
point values constant on the distillation column. On the distillation column, the set point for the
reflux ratio was hard to keep constant since the control was manual. Changes in the level of
distillate collected in the receiver made it difficult to maintain steady-state; this may have
affected our calculations. Another possible source of error is that because the feed tank was
not continuously stirred, there may have been a separation of methanol and water due to their
different densities (methanol: 0.79 g/cm3; water: 1 g/cm3). This would result in a non-constant
feed concentration leading to error in the concentration measurements and error in the model.
Lastly, the GC calibration and readings were inaccurate (+/- 2 vol% as determined by Rotation
1), and this would lead to inaccuracies in our calculations.
Critique of Rotation 1
The final report provided by Rotation 1 was overall very thorough and detailed. Each
objective was completed and presented in a planned and organized manner. Their error
16
analysis regarding the gas chromatograph was useful in determining the reliability and
accuracy of the instrument. Rotation 1’s flooding analysis was quite comprehensive,
especially their presentation of experimental versus theoretical (i.e. Wilkes) values.
We found three aspects of Rotation 1’s report that could be improved. First, the experimental
design regarding quantifying the effect of reflux ratio and reboiler power on the distillate
composition seems to be rather limited in scope. The ranges for both independent variables are
small and more useful correlations could have been developed for a wider range of values.
Second, Rotation 1 claimed that no correlation existed between distillate composition and
reboiler power. However, the reported higher reboiler power values (> 70%) are at or above
flooding conditions. By removing these points, a correlation between these variables can be
developed. Third, after analyzing the computer module that Rotation 1 developed to produce
McCabe-Thiele plots, it seems that their program determines the number of stages to step off
by determining how many stages are needed to reach the bottoms concentration (xw) calculated
by the mole balance rather than using the calculated value for NOG. They did not include a
check to ensure that the number of stages calculated by NOG equals the number of stages
needed to reach the calculated xw. Therefore, their model would only be accurate if all
parameters are set from empirical data, and they would not be able to determine if their
empirical data is flawed using their model.
Conclusions and Recommendations
To conclude, we were able to complete all of our objectives. For the concentration and mass
transfer coefficient, we found that as the feed rate was increased the concentration of methanol
increased and the mass transfer coefficient decreased, and there was no correlation with feed
temperature. Furthermore, we were able to correlate the feed flow rate and reflux ratio to the
mass transfer coefficient using Polymath. We also determined that there was no correlation
with reflux ratio to flooding and found that the correlation for flooding from Rotation 1 was
accurate. We decided that we can use the molar overflow assumption for our model because
the difference between the latent heats of vaporization of methanol and water is negligible.
Therefore, we were able to create a model on Excel where the reflux ratio, reboiler power, feed
weight fraction, feed temperature, and distillate weight fraction can be inputted, and the model
will calculate the changes in the mass transfer coefficient, whether or not flooding will occur
and the appropriate feed flow rate to be used. Lastly, when evaluating the online tray
distillation column simulation from the University of Tennessee, we have determined that it is
a good simulation, but there are some changes that can be made.
After completing our objectives, we have several recommendations. First, we suggest that the
column be run at a wider range of temperatures to find better correlations. Also, there should
be a stronger feed preheater, so the feed will be able to enter the distillation column at the
saturation point for higher flow rates. This would lead to a better correlation. Next, we suggest
that the feed placement in the distillation column be evaluated. Additionally, the feed tank
should be stirred more frequently to prevent separation of methanol and water due to the
difference in the densities of the components. Also, when trying to determine when steady state
has been reached, it should be determined by a constant level in the distillate receiver. We also
recommend for the determination of a flooding in the column be based on the pressure drop,
17
p. To facilitate this p measurement, the data acquisition should be faster so the change in
pressure can be read in smaller intervals. We also recommend that automatic controls be
installed to adjust the reflux and the distillate flow rates to minimize the fluctuation that occurs
when adjusting these values manually. This would prevent the inaccuracies in measurement
and identifying when steady state has been reached. We also recommend that a better GC with
less error be purchased in order to produce more accurate results.
References
1
Simons, E., Soares, S., and L. Soland Distillation Final Report – Rotation 1 10/7/02
2
Brown Industries. ChE 460 Equipment Manual: “Technovate Pilot-Scale Distillation Column.”
2002.
3
Wilkes, JO. Fluid Mechanics for Chemical Engineers. Prentice-Hall Inc. New Jersey. 1999.
4
Geankopolis, CJ. Transport Processes and Unit Operations, Third Edition. Prentice-Hall, Inc.
New Jersey. 1993.
5
Perry, RH and Green, DW. Perry’s Chemical Engineers’ Handbook Seventh Edition. McGrawHill. New York. 1997.
6
Lecture 1-Distillation, Fogler lecture notes from September 9, 2002
18
Appendix A: Nomenclature Table
Symbol
cp
D
Hsol
F
gc
H
h
Lm, Ln
m
Mg
Ml
n
q
qC
qR
R
T
Vm, Vn
W
x
XLG
y
YLG
Description
Heat capacity
Distillate flow rate
Heat of solution
Packing factor (Wilkes, 1999)
Conversion factor, 32.2
Enthalpy of vapor
Enthalpy of liquid
Liquid flow rate in column
Tray m in stripping section
Gas mass velocity
Liquid mass velocity
Tray n in enriching section
Quality of feed (q=1 when saturated liquid)
Energy removed by condenser
Reboiler duty
Reflux ratio
Temperature
Vapor flow rate
Bottoms flow rate
Liquid mole fraction
Independent variable on flooding curve
Vapor mole fraction
Dependent variable on flooding curve

L
g
l

Latent heat of vaporization
Liquid viscosity
Gas density
Liquid density
Density of water divided by density of liquid
Units
J/kg K
mol/hr
kJ/mol
--lbm ft/lbf s2
btu/lbm or kJ/kg
btu/lbm or kJ/kg
mol/hr
--lbm/ft2 s or kg/s m2
lbm/ft2 s or kg/s m2
----btu/hr or kJ/h
btu/hr or kJ/h
--°C
mol/hr
mol/hr
mol product/total mol liquid
--mol product/total mol vapor
(lbm/ft2 s)(cP0.2)/
[(lbm/ft3)2(lbm ft/lbf s2)]
kJ/kg mol
cP
lbm/ft3 or kg/m3
lbm/ft3 or kg/m3
---
19
Appendix B1: Explanation of Calculations
McCabe - Thiele Diagram and Mass Transfer Coefficient
We needed to calculate a mass transfer coefficient for all of our runs as well as generate a
McCabe-Thiele diagram. The following shows how we carried out these calculations and a
sample calculation. The sample calculation is based on the following conditions that were
observed in lab:
Reflux rate (ml/min)
Distillate rate (ml/min)
Feed concentration (vol%)
Feed rate (ml/min)
Top column temperature (°C)
Feed temperature (°C)
Reboiler Power %
Distillate concentration (vol%)
99
21
5.1%
530
83.1
24.22
50
86.6%
Table B.1: Data used in Sample calculations
First, we needed to calculate the quality of the feed stream. In order to do this we used the
following equation4.
q
Hv  H f
(B-1)
Hv  Hl
Hv= Enthalpy of feed as a vapor at saturation temperature.
Hf= Enthalpy of feed.
Hl= Enthalpy of feed as a liquid at saturation temperature.
To calculate Hv – Hf heat of mixing was neglected and the following equation was used.
 Tb

 Tb



H v  H f  n H 2O  C pH2O   vH 2O  nmethanol   C pmethanol   vmethanol 
T

T

 f

 f



H v  H l  n H 2O  vH 2O  nmethanol  vmethanol 
(B-2)
(B-3)
C pH 2O = Heat capacity of water= 2.33 + 7.82E-3 * T + 3.77E-5 * T2
C pmethanol =Heat capacity of methanol= 4.188 - 5.69E-4 * T - 8.49E-6 * T2
 vH 2O =Heat of vaporization of water=2481.8 - 1.821 * T- .004236 * T2
 vmethanol =Heat of vaporization of methanol=1218.4- 1.3849 * T- .006402* T2 (Binarysee below)
20
For the Cp and  v calculations T is in °C.
Sample Calculations:
For our system, using the equations above:
 94.64b

 94.64

H v  H f  n H 2O   C pH 2O   vH 2O   nmethanol   C pmethanol   vmethanol 


 24.22

 24.22

nmethanol= (converting volume fraction to mol fraction) .0234
nH2o= 1-.0234=.9766
(B-4)
Hv-Hf= 2521.71 kJ/kg


H v  H l  n H 2O  vH 2O  nmethanol  vmethanol 
with T=94.64°C (from TXY diagram)
Hv- Hl= 2231.6 kJ/kg
Therefore,
q= 1.13
We then used the values that we observed in lab for xD, D, L, F and xF to calculate xB, B and the
slope and intercepts of all the operating lines as described below.
 To calculate B and xB we used the following equations derived from a mass balance.
B= F-D
xB 


(B-5)
x f * F  xD * D
B
(B-6)
Since for all of our runs, the GC could not detect the concentration of methanol in the
bottoms, we assumed that xB <.02 for all runs, and checked this to ensure a proper mass
balance.
Sample Calculation:
For our system:
First we converted the volume concentrations and fractions to molar
concentrations and mol fractions. We assumed no change in volume in order to
do this.
B= 28.71 mol/min-.98 mol/min= 27.73 mol/min
.0234 * 28.71  .78 * .9766
xB 
 .0079molmethanol / moltotal
27.73
To calculate the equation for the q-line the following method was used:
The equation for the q-line is4:
x
q
y
x F
(B-7)
q 1
q 1
21
We found the slope and intercept for this line using the calculated value of q, the
experimental value of xF , and the equation above.
Sample Calculation:
q
1.13
Slope 

 8.63
q  1 1.13  1
intercept 

 x F  .0234

 .18
q  1 1.13  1
(B-8)
(B-9)
To calculate the equation for the enriching line the following method was used:
The equation for the enriching line is4:
y
x
R
x D
R 1
R 1
(B-10)
We found the slope and intercept for this line using the equation above, calculated values
for R (R=L/D), and experimental values for xD.
Sample Calculation:
R
4.7
slope 

 .82
R  1 4.7  1
intercept 

xD
.0234

 .13
R  1 4.7  1
(B-11)
(B-12)
To calculate the equation for the stripping line, the following method was used:
The equation for the stripping line is4:
y
Lm
B
x
xB
Gm
Gm
(B-13)
Lm  q * F  L
(B-14)
Gm  ( L  D)  (1  q) * F
(B-15)
We found the slope and intercept for the stripping line using the equations above along
with experimental values of xB, F and L and calculated values of q.
Sample Calculation:
Lm  q * F  L =1.13*28.71+5.48=37.92 mol/min
Gm  ( L  D)  (1  q) * F =(5.48+.9766)-(1-1.13)*28.71=7.79 mol/min
22
slope 
Lm 38.35

 4.87
Gm
7.79
B
29.17
* xB  
* .00703  .03
(B-16)
Gm
9.17
Once the equations for all the lines were generated, we checked to ensure that the lines
intersected at the same point, then verify the placement of the feed and also to determine xa, the
intersection of the stripping and enriching lines. We then plotted the lines on a Txy diagram
(using an excel spreadsheet) in order to generate a McCabe Thiele diagram.
intercept  
Sample Plot:
McCabe Thiele Diagram
1
0.9
0.8
0.7
y
0.6
0.5
0.4
equilibrium data
y1=x1
enriching line
stripping line
q-line
stages
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
Figure B.1: Sample McCabe Thiele Diagram
Once a McCabe- Thiele diagram was generated, we found Nog using the following equation4:
yD
N og 
dy
 y *y
(B-17)
yB
We found values of y and y* using the equations for the operating lines and the Txy diagram
1
respectively. We then used Simpson’s rule to integrate the area under the curve for
v y.
y  y*
For our data, we found a Nog value of 3.78.
23
We found Hog using the equation below
H og 
H
N og
(B-18)
Sample Calculation
For our data
H og 
H
76.2cm

 20.16cm
N og
3.78
We then calculated the mass transfer coefficient, Kog, using the following equation
K og  H og * G '
(B-19)
Sample Calculation
K og  H og * G ' =20.16cm*0.074 mol/cm^2=1.50 mol/cm
Source: “Binary Distillation Using Random Packing”
http://www.ualberta.ca/CMENG/courses/che454/handouts/jan2002/dist.doc.
University of Alberta. (Date accessed: September 20, 2002)
24
Appendix C: Flooding Correlations
Wilkes
A theoretical correlation to model flooding can be plotted with Equations C-1 and C-23.
X LG 
Ml
Mg
G
L
M g2 Fl0.2
YLG 
g l gc
(C-1)
(C-2)
The independent variable in Equation 1 is XLG, which is based on the relationship between the
gas and liquid velocities. The dependent variable, YLG, is the square of the gas mass velocity
multiplied by a constant that takes into account the fluid densities, the packing factor, and the
liquid viscosity. On a plot of YLG versus XLG, the region above the curve predicts conditions
when flooding occurs, while the region below the curve predicts normal conditions.
Pro-Pak
There is also a model found in the Pro-Pak packing material literature which relates the vapor
velocity to flooding (Equation C-3).
MG = 270(ρ1)0.58(ρ2)0.42
(C-3)
25
Appendix D1: Flooding Analysis and Sample Calculations
In order to compare the flooding points to data from literature, a number of calculations were
necessary. The following equations were used.
Molar flow rate of gas (G):
(D-1)
G  L D
L is the liquid from the reflux and D is the distillate.
Based on the top-column temperatures, the methanol concentration in the distillate and the reflux
was determined from the T-x-y diagram. The volumetric flow rates of reflux and distillate were
monitored.
Conversion between molar and volumetric methanol fraction:
1
v MeOH  x MeOH  MWMeOH 
(D-2)
 MeOH
MWMeOH is the molecular weight of methanol.
ρMeOH is the density of liquid methanol
Mass flow rate of gas (Mg):
M G  G xMeOH  MWMeOH  x H 2O  MWH 2O 
xi is the mole fraction in the distillate and reflux.
Molar flow rate of liquid (L):
RG
L
1 R
R is the reflux ratio
L
R
D
Mass flow rate of liquid (ML):
M L  Lx MeOH  MW MeOH  x H 2O  MW H 2O 
Mass fraction of MeOH (mMeOH):
xMEOH  MWMEOH
mMeOH 
xMeOH  MWMeOH  xH 2O  MWH 2O
(D-3)
(D-4)
(D-5)
(D-6)
(D-7)
Density of gas phase (ρG), assuming that density is independent of mixing and that each
component fraction is at its saturation point:
 G  mMeOH   MeOH ( g )  mH 2O   H 2O ( g )
(D-8)
ρi(g) is the density for saturated vapor.
26
Density of liquid phase (ρL), assuming that density is independent of mixing and that each
component fraction is at its saturation point:
 L  mMeOH   MeOH (l )  mH 2O   H 2O (l )
(D-9)
ρi(l) is the density for saturated liquid.
Flooding correlation from Pro Pack manual:
0.58
0.42
(D-10)
M G  270 L  G 
To compare this predicted value to the actual experimental results, the densities used were
calculated by using the measured mass fractions of methanol and water (see eq. D-8 and D-9)
The results were multiplied by relevant constants to ensure that the units were the same
Graphical correlation from Wilkes3
The independent variable on the graph is FLG
G
M
FLG  L
M G L
(D-11)
The dependent variable (ywilkes’) is calculated from eq. (D-12)
2
0.2
M F l
yW ilkes'  G
(D-12)
G  L g c
F is packing factor,    H 2O /  L , μl is liquid viscosity and gc = 32.2 lbmft/lbfs2
(conversion factor). [MG] = lbm/ft2s, [ρi] = lbm/ft3
For these experiments: F = 372 ft-1 [1], μl = 0.3 cP (value for water) [2]
Area of column (A):
2
 1.5in 
  0.05 ft 2
A    
 12in / ft 
The inner diameter of the column is 3 in.
(D-13)
Sample calculations
Table D.1 shows a set of data that is used in the sample calculations while Table D.2 is a list of
used constants.
Table D. 1: Experimental Data
Top column
temperature (ºC)
93.56
xMeOH
L (ml/min)
D (ml/min)
0.23
377.97
6.37
Table D.2: Table of used constants
3
Vapor densities (kg/m )
MeOH
H2O
1.222
0.5975
Liquid densities (kg/m3)
MeOH
H2O
751.0
958.39
Molecular weights (g/mole)
MeOH
H2O
32.04
18.016
27
Molar gas flow rate
G  16.67mole / min
M G  16.670.23  32.04  0.77  18.016  0.354kg / min  0.265lb /( ft 2 s)
calculating the final term by using the area of the column
377.97
R
 59.3
6.37
59.3  16.67
L
 16.4mole / min
1  59.3
M L  16.40.23  32.04  0.77 18.016  0.349kg / min
0.23  32.04
m MeOH 
 0.35
0.23  32.04  0.77  18.016
 G  0.35  1.222  0.65  0.5975  0.82kg / m 3  0.051lb / ft 3
 L  0.35  751.0  0.65  958.39  886.4kg / m 3  55.3lb / ft 3
Flooding correlation from Pro Pack manual (unit defined in manual):
0.58
0.42
M G  27055.3 0.051  791.6lb /( h  ft 2 )
Graphical correlation
Independent variable
0.348 0.814
FLG 
 0.0298
0.354 886.4
Dependent variable
958.39
0.264 2  372 
 0.30.2
886.4
yW ilkes' 
 0.245
0.051  55.3  32.2
28
Appendix E: Enthalpy-concentration method
Equations E-1 and E-2 give the enriching section operating line and stripping section operating
line, respectively
y n1 
y
Ln
Dx D
xn 
Vn1
Vn1
Lm
Wx
xm  w
Vm1
Vm1
(E-1)
(E-2)
Equation E-3 is used to determine values for Vn+1 and Ln
Vn1 H n1  (Vn1  D)hn  V1 H1  LhD
(E-3)
V1 and Ln can be calculated if the reflux ratio is first set. H1 and hD can be determined by
equations for the saturated vapor enthalpy (Equation E-4) and saturated liquid enthalpy
(Equation E-5), respectively.
H  y A [ A  c py A (T  T0 )  (1  y A )[ B  c pyB (T  T0 )]
(E-4)
h  xA c pA (T  T0 )  (1 x A )c pB (T  T0 )  H sol
(E-5)
Alternatively, this data can be obtained from an enthalpy-concentration plot which can be
constructed by methods previously described4.
A trial and error approach must then be used to determine Hn+1, which is necessary to plot the
operating line. Details describing the use of the enthalpy-concentration method to find
distillate composition can be found in Geankopolis4 and is summarized below:
1. Assume a value for xn. Assume Vn+1=V1=L+D and Ln=L. Use Equation E-1 to calculate
yn+1, assumed.
2. Using calculated yn+1 and assumed xn, determine values for Hn+1 and hn by Equations E-4
and E-5, respectively. Using these values, determine Vn+1 by Equation E-3. Determine
Ln by Equation E-6.
Vn1  Ln  D
(E-6)
3. Using calculated values, determine yn+1 by Equation E-1.
4. If the calculated value of yn+1 does not equal yn+1, assumed, then use the calculated value for
yn+1 and repeat steps 2 and 3. If the old calculated value for yn+1 is not close to the new
calculated value for yn+1, assume another value for xn and repeat steps 1-4.
29
5. Plot the curved enriching-section operating line (Equation E-1) using the value for Hn+1
determined by the trial and error approach.
The stripping-section operating line is given by Equation E-2 above. An enthalpy balance is
done on the stripping section, given by Equation E-74.
Vm1 H m1  (Vm1  W )hm  q R  Whw
(E-7)
An overall enthalpy balance on the entire system is given by Equation E-8.
q R  DhD  WhW  qC  FhF
(E-8)
Using a similar trial and error method as described for the enriching-section, the strippingsection operating line can be determined. As described by Geankopolis4, first, assume a value
for ym+1, then calculate xm with Equation E-2. Vm+1 and Lm are then calculated from Equations
E-7 and E-9, respectively.
Lm  W  Vm1
(E-9)
Equation E-2 is then used to determine xm. This calculated value for xm is then compared to
the assumed value for xm. If the values are close, then the calculated values for Vm+1 and Lm
can be used in the stripping-section operating line.
30
Appendix E (cont.): Enthalpy-concentration chart data
Data for Enthalpy-c oncentration c hart for methanol-w ater s ys tem
Cp (J/mol K)
kJ/mol
Component BP (deg C)
liq
v apor
latent heat of vap
methanol (A)
64.6
81.1
44.1
40.657
w ater (B)
100
75.3
33.6
35.21
referenc e T: 64.6
xA
yA
xB
0
Tbp
1
0
0.25
0.25
0.5
0.5
0.5
0.75
1
x, y
0
0.25
0.5
0.75
1
0
0.25
0.5
0.75
1
0.75
1
h
100
64.6
79.5
93
73.1
85
68.5
74
64.6
0
h (liquid)
H (vapor)
Tie lines
2665.62
1143.575
664.7
310.635
0
37875.62
39719.425
39948.63
40165.785
40657
0.1
0.418
2056.802
39873.451
0.3
0.665
1047.8
39765.266
0.5
0.779
644.7
40222.766
0.7
0.87
381.448
40122.354
0.9
0.958
124.254
40574.476
0.02
0.134
2543.8564
38863.899
lambdaB
H
2665.62
36686.18
37875.62
36686.18
39719.425
36686.18
39948.63
1143.575
664.7
310.635
36686.18
0
40165.785
40657 pure methanol
Perry 's T-x -y data:
Temp (C)
x1
100
96.4
93.5
91.2
89.3
87.7
84.4
81.7
78
75.3
73.1
71.2
69.3
67.5
65.9
65.1
64.5
y1
y 1=x1
0
0.02
0.04
0.06
0.08
0.1
0.15
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.95
1
0
0.134
0.23
0.304
0.365
0.418
0.517
0.579
0.665
0.729
0.779
0.825
0.87
0.915
0.958
0.979
1
0.25
0.75
0.04541
0.442
0.1414
0.662
0.8925
0.25
0.75
0.5
0
0.02
0.04
0.06
0.08
0.1
0.15
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.95
1
31
Appendix E (cont.): Enthalpy-concentration chart for methanol-water
Enthalpy concentration plot for
methanol (A)-water (B)
enthalpy of mixture (kJ/mol)
45000
40000
35000
30000
h (liquid)
H (vapor)
Tie lines
25000
20000
15000
10000
5000
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
xA, yA
32
Appendix E (cont.): Enthalpy concentration method calculation for Run 3
Vm+1,calc
(mol/min)
Lm, calc
(mol/min)
ym+1, calc
(mol frac)
yn+1, calc
(mol frac)
0.11
0.20
0.37
0.54
0.71
0.80
0.88
0.97
hm (J/mol)
Ln, calc
(mol/min)
123
119
112
111
109
108
107
105
Hm+1
(J/mol)
Vn+1,calc
(mol/min)
143
139
132
131
129
128
127
125
qC (J)
hn (J/mol)
2500
2400
1000
665
300
225
150
0
hF (J/mol)
Hn+1
(J/mol)
38000
39000
39800
39900
40000
40250
40500
41000
hw (J/mol)
hD (J/mol)
-2364
-2364
-2364
-2364
-2364
-2364
-2364
-2364
hm (J/mol)
H1 (J/mol)
40827
40827
40827
40827
40827
40827
40827
40827
Hm+1
(J/mol)
F (mol/min)
550
550
550
550
550
550
550
550
F (mol/min)
xD (wt frac)
0.866
0.866
0.866
0.866
0.866
0.866
0.866
0.866
qR (J)
mD (mol
frac)
0.785
0.785
0.785
0.785
0.785
0.785
0.785
0.785
xw (mol frac)
D (mol/min)
20
20
20
20
20
20
20
20
W
Vn+1=V1
(mol/min)
120
120
120
120
120
120
120
120
Vm+1
Ln
(mol/min)
100
100
100
100
100
100
100
100
Lm
xn
0
0.1
0.3
0.5
0.7
0.8
0.9
1
xm
0.131
0.214
0.381
0.547
0.714
0.797
0.881
0.964
ym+1
yn+1
Tref=64.6 deg C
0.008
0.024
0.055
0.087
0.119
0.151
0.167
0
0.1
0.3
0.5
0.7
0.9
1
100
100
100
100
100
100
100
630
630
630
630
630
630
630
530
530
530
530
530
530
530
0.00931
0.00931
0.00931
0.00931
0.00931
0.00931
0.00931
5E+06
5E+06
5E+06
5E+06
5E+06
5E+06
5E+06
550
550
550
550
550
550
550
36334
36426
36609
36793
36977
37160
37252
-2229
-2246
-2280
-2315
-2349
-2383
-2401
-3436
-3436
-3436
-3436
-3436
-3436
-3436
-2989
-2989
-2989
-2989
-2989
-2989
-2989
4862943
4862943
4862943
4862943
4862943
4862943
4862943
35500
36000
38500
39500
39800
39900
40000
2500
2400
1000
665
300
150
0
243
237
193
182
174
170
167
773
767
723
712
704
700
697
-0.02
0.30
1.10
1.93
2.81
3.67
4.14
33
Appendix F: Distillation Model (Excel)
Distillation Model
INPUTS
Feed Flow Rate
Distillate Flow rate
Reflux Flow rate
Feed wt fraction
Feed temp
Distillate wt fraction
Reboiler Power
Warning (flooding)
Feed vol fraction
Distillate vol fraction
Quality
Feed mol flowrate
Distillate mol flowrate
Reflux mol flowrate
Feed mol fraction
Disitillate mol fraction
Reflux Ratio
Bottoms Flow (mol)
Bottoms concentration
q-line
slope
intercept
Bounds
Value
100
20
100
0.05
25
0.6
50
0.061875
0.65274725
1.13
13.76
0.70
3.52
0.03
0.46
5.00
13.05
0.005611
Units
ml/min
ml/min
ml/min
g methanol/g total
oC
g methanol/g total
%
volmeth/totalvol
volmeth/totalvol
mol/min
mol/min
mol/min
molmeth/totalmol
molmeth/totalmol
8.80
-0.22
x
Reboiler Power
y
3.18
-0.01
x
y
0.01
0.11
0.83
0.08
x
G'
HOG
NOG
xw, calcd by Kog
abs(xwMB-xwKOG)
optimum F
min error, xw
status
yintersection
0.04
0.04
0.04
1.45
45.72 cm
31.47 cm
2.91 mol/cm
74.04
0.76
0.46
-39.64%
x
xtoy
0.05
0.46
0.46
0.84
Flooding Conditions
88.9203 %
Experimentally Determined
4.893416061 mol/cm
0.11
0.11
0.11
top + bottom
Nog2
Ve
Hog
Kog
1.91
76.20 cm
39.98 cm
3.70 mol/cm
q-line y
0.27
0.46
0.092653935 mol/(min*cm^2)
52.81390443 cm
1.442801869 plates
0.23
-0.04
1
Nstages, expt correlation (integer)
0.119857108
0.114246 (error)
259.000000 mL/min
0.000014 molmeth/totalmol
these conditions should work! (for error(xw) < 0.01)
y
0.46
0.04
Reference:
Density of methanol
Density of water
KOG
0.03
0.11
0.01
0.04
Enriching Line
slope
Intercept
Bounds
Distillation point
slope enriching
Rmin
mol/min
molmeth/totalmol
0.03
0.04
Stripping line
slope
intercept
Bounds
xintersection
q-line/strip inter
qline/enrich inter
strip/enrich inter
only top
Nog
Ve
Hog
Kog
Top temperature
equil y
y from GC
Error
0.46
0.11
0.79 g/cm^3
0.99 g/cm^3
34
Appendix F: Distillation Model (Visual Basic Code)
Module 1
'TXY data
' This declares the array
Dim txy(17, 3)
Sub start()
'This procedure declares the array
'This section puts the TXY Data
'in the form (a,b) the a stands for the row number
'and the b stands for the column
'
'**IMPORTANT***, this procedure will interpolate data within the
'table, it will not give data at the endpoints or extrapolate data
'Declares the T data
txy(1, 1) = 100
txy(2, 1) = 96.4
txy(3, 1) = 93.5
txy(4, 1) = 91.2
txy(5, 1) = 89.3
txy(6, 1) = 87.7
txy(7, 1) = 84.4
txy(8, 1) = 81.7
txy(9, 1) = 78
txy(10, 1) = 75.3
txy(11, 1) = 73.1
txy(12, 1) = 71.2
txy(13, 1) = 69.3
txy(14, 1) = 67.5
txy(15, 1) = 65.9
txy(16, 1) = 65.1
txy(17, 1) = 64.5
'Declares the X data
txy(1, 2) = 0
txy(2, 2) = 0.02
txy(3, 2) = 0.04
txy(4, 2) = 0.06
txy(5, 2) = 0.08
txy(6, 2) = 0.1
txy(7, 2) = 0.15
txy(8, 2) = 0.2
txy(9, 2) = 0.3
txy(10, 2) = 0.4
txy(11, 2) = 0.5
txy(12, 2) = 0.6
txy(13, 2) = 0.7
txy(14, 2) = 0.8
txy(15, 2) = 0.9
txy(16, 2) = 0.95
txy(17, 2) = 1
35
'Declared the Y data
txy(1, 3) = 0
txy(2, 3) = 0.134
txy(3, 3) = 0.23
txy(4, 3) = 0.304
txy(5, 3) = 0.365
txy(6, 3) = 0.418
txy(7, 3) = 0.517
txy(8, 3) = 0.579
txy(9, 3) = 0.665
txy(10, 3) = 0.729
txy(11, 3) = 0.779
txy(12, 3) = 0.825
txy(13, 3) = 0.87
txy(14, 3) = 0.915
txy(15, 3) = 0.958
txy(16, 3) = 0.979
txy(17, 3) = 1
End Sub
'Converts a T value to an X value
Function ttox(Tvalue)
start
trigger = 0
'initiallizes the values to dummy values
x1 = 10
x2 = 0
t2 = 10
t1 = 0
' loops down the rows
x=2
For x = 2 To 17
If trigger = 0 Then
If (Tvalue >= txy(x, 1)) Then
t1 = txy(x, 1)
t2 = txy(x - 1, 1)
x1 = txy(x, 2)
x2 = txy(x - 1, 2)
trigger = 1
End If
End If
Next x
ttox = (x2 - x1) / (t2 - t1) * (Tvalue - t1) + x1
' interpolates the data and sends it back to the cell
End Function
'Converts a temperature to a y value
Function ttoy(Tvalue)
start
trigger = 0
36
'initiallizes the values to dummy values
y1 = 10
y2 = 0
x2 = 10
x1 = 0
' loops down the rows
For x = 2 To 17
If trigger = 0 Then
If (Tvalue >= txy(x, 1)) Then
x1 = txy(x, 1)
x2 = txy(x - 1, 1)
y1 = txy(x, 3)
y2 = txy(x - 1, 3)
trigger = 1
End If
End If
Next x
' interpolates the equilibrium data and sends it back to the cell
ttoy = (y2 - y1) / (x2 - x1) * (Tvalue - x1) + y1
End Function
'Converts x values to y values
Function xtoy(xvalue)
start
trigger = 0
'initiallizes the values to dummy values
y1 = 10
y2 = 0
x2 = 10
x1 = 0
' loops down the rows
For x = 2 To 17
If trigger = 0 Then
If (xvalue <= txy(x, 2)) Then
x1 = txy(x, 2)
x2 = txy(x - 1, 2)
y1 = txy(x, 3)
y2 = txy(x - 1, 3)
trigger = 1
End If
End If
Next x
' interpolates the equilibrium data and sends it back to the cell
xtoy = (y2 - y1) / (x2 - x1) * (xvalue - x1) + y1
End Function
'Converts y values to x values
37
Function ytox(yvalue)
start
trigger = 0
'initiallizes the values to dummy values
y1 = 10
y2 = 0
x2 = 10
x1 = 0
' loops down the rows
For x = 2 To 17
If trigger = 0 Then
If (yvalue <= txy(x, 3)) Then
x1 = txy(x, 3)
x2 = txy(x - 1, 3)
y1 = txy(x, 2)
y2 = txy(x - 1, 2)
trigger = 1
End If
End If
Next x
' interpolates the equilibrium data and sends it back to the cell
ytox = (y2 - y1) / (x2 - x1) * (yvalue - x1) + y1
End Function
'Converts x value to T value
Function xtot(xvalue)
start
trigger = 0
'initiallizes the values to dummy values
x1 = 10
x2 = 0
t2 = 10
t1 = 0
' loops down the rows
x=2
For x = 2 To 17
If trigger = 0 Then
If (xvalue <= txy(x, 2)) Then
t1 = txy(x, 1)
t2 = txy(x - 1, 1)
x1 = txy(x, 2)
x2 = txy(x - 1, 2)
trigger = 1
End If
End If
38
Next x
xtot = (t2 - t1) / (x2 - x1) * (xvalue - x1) + t1
' interpolates the equilibrium data and sends it back to the cell
End Function
'Converts y value to T value
Function ytot(ytalue)
start
trigger = 0
'initiallizes the values to dummy values
y1 = 10
y2 = 0
t2 = 10
t1 = 0
' loops down the rows
x=2
For x = 2 To 17
If trigger = 0 Then
If (yvalue <= txy(x, 3)) Then
t1 = txy(x, 1)
t2 = txy(x - 1, 1)
y1 = txy(x, 3)
y2 = txy(x - 1, 3)
trigger = 1
End If
End If
Next x
ytot = (t2 - t1) / (y2 - y1) * (yvalue - y1) + t1
' interpolates the equilibrium data and sends it back to the cell
End Function
'Determines the quality of a feed given the temperature and concentration
Function quality1(FeedTemp, FeedConc)
start
FeedX = molfrac(FeedConc)
FeedsatTV = xtot(FeedX)
FeedsatTL = ytot(FeedX)
MethHeatV = 1218.4 - 1.3849 * FeedsatTV - 0.006402 * FeedsatTV ^ 2
H20HeatV = 2481.8 - 1.821 * FeedsatTV - 0.004236 * FeedsatTV ^ 2
CpH20 = 4.188 * (FeedTemp - FeedsatTV) - 0.5 * 0.000569 * (FeedTemp ^ 2 - FeedsatTV ^ 2) - (1 / 3) *
0.00000849 * (FeedTemp ^ 3 - FeedsatTV ^ 3)
Cpmeth = 2.33 * (FeedTemp - FeedsatTV) + 0.5 * 0.00782 * (FeedTemp ^ 2 - FeedsatTV ^ 2) + 0.0000377 * (1 / 3)
* (FeedTemp ^ 3 - FeedsatTV ^ 3)
Hvhf = -CpH20 * (1 - FeedX) - Cpmeth * FeedX + MethHeatV * FeedX + H20HeatV * (1 - FeedX)
Hvhl = FeedX * MethHeatV + (1 - FeedX) * H20HeatV
quality1 = Hvhf / Hvhl
39
End Function
'Determined the hog using only enriching side
Function Hog(Slopedist, interdist, xa, xd)
Dim t(10100)
start
x = xa
numsteps = 10000
Height = (xd - xa) / numsteps
For N = 0 To numsteps
ystar = xtoy(xa + N * Height)
y = Slopedist * (xa + N * Height) + interdist
t(N) = (1 / (ystar - y))
Next N
H=0
g=2
int1 = 0
Do While g <= numsteps - 2
H = 4 * t(g)
int1 = int1 + H
g=g+2
Loop
H=0
int2 = 0
R=1
Do While R <= numsteps - 1
H = 2 * t(R)
int2 = int2 + H
R=R+2
Loop
inttotal = int1 + int2 + t(0) + t(numsteps)
Hog = (1 / 3) * Height * inttotal
End Function
'Calculates the HOg using both stripping and enriching lines
Function Hog2(Slopestrip, interstrip, Slopedist, interdist, xb, xa, xd)
Dim t(10100)
start
numsteps = 10000
Height = (xd - xb) / numsteps
For N = 0 To numsteps
xu = xb + N * Height
ystar = xtoy(xu)
If xu < xa Then
y = Slopestrip * (xu) + interstrip
End If
If xu > xa Then
y = Slopedist * (xu) + interdist
40
End If
t(N) = (1 / (ystar - y))
Next N
H=0
g=2
int1 = 0
Do While g <= numsteps - 2
H = 4 * t(g)
int1 = int1 + H
g=g+2
Loop
H=0
int2 = 0
R=1
Do While R <= numsteps - 1
H = 2 * t(R)
int2 = int2 + H
R=R+2
Loop
inttotal = int1 + int2 + t(0) + t(numsteps)
Hog2 = (1 / 3) * Height * inttotal
End Function
Module 2
Function molfrac(volconc)
rhoh20 = 0.99
rhometh = 0.79
molesh20 = (1 - volconc) * rhoh20 / 18
molesmeth = volconc * rhometh / 32.04
molfrac = molesmeth / (molesmeth + molesh20)
End Function
Function molvol(volflowrate, volconc)
rhoh20 = 0.99
rhometh = 0.79
massh20 = (volflowrate * (1 - volconc)) * rhoh20
massmeth = (volflowrate * volconc) * rhometh
molh20 = massh20 / 18
molmeth = massmeth / 32.04
molvol = molh20 + molmeth
End Function
Function volfrac(massconc)
rhoh20 = 0.99
rhometh = 0.79
volh20 = (1 - massconc) / rhoh20
volmeth = massconc / rhometh
41
volfrac = volmeth / (volh20 + volmeth)
End Function
Function intersx(slope1, inter1, slope2, inter2)
intersx = (inter2 - inter1) / (slope1 - slope2)
End Function
Function intersy(slope1, inter1, slope2, inter2)
inters = intersx(slope1, inter1, slope2, inter2)
intersy = slope2 * inters + inter2
End Function
Module 3
Sub GoalSeekRmin()
'
' GoalSeekRmin Macro
' Macro recorded 10/3/2002 by Smeeta
'
'
Range("I20").GoalSeek Goal:=0, ChangingCell:=Range("F20")
End Sub
Module 4
'TXY data
' This declares the array
Dim xstage(16)
Sub start()
'This procedure declares the array
'This section puts the X-stage Data
'in the form (a,b) the a stands for the row number
'and the b stands for the column
'
'**IMPORTANT***, this procedure will interpolate data within the
'table, it will not give data at the endpoints or extrapolate data
'set dummy variables to zero
xstage(1) = 0
xstage(2) = 0
xstage(3) = 0
xstage(4) = 0
xstage(5) = 0
xstage(6) = 0
xstage(7) = 0
xstage(8) = 0
xstage(9) = 0
xstage(10) = 0
xstage(11) = 0
42
xstage(12) = 0
xstage(13) = 0
xstage(14) = 0
xstage(15) = 0
xstage(16) = 0
End Sub
' determines bottoms concentration (xw) calculated by stepping off stages
Function xwstages(xstage1, xstage2, xstage3, xstage4, xstage5, xstage6, xstage7, xstage8, xstage9, xstage10,
xstage11, xstage12, xstage13, xstage14, xstage15, xstage16, N)
start
'define equilibrium x values for each stage as an array
xstage(1) = xstage1
xstage(2) = xstage2
xstage(3) = xstage3
xstage(4) = xstage4
xstage(5) = xstage5
xstage(6) = xstage6
xstage(7) = xstage7
xstage(8) = xstage8
xstage(9) = xstage9
xstage(10) = xstage10
xstage(11) = xstage11
xstage(12) = xstage12
xstage(13) = xstage13
xstage(14) = xstage14
xstage(15) = xstage15
xstage(16) = xstage16
'set dummy variables
trigger = 0
For x = 1 To 16
If trigger = 0 Then
If x = N Then
xwstages = xstage(x)
trigger = 1
End If
End If
Next x
End Function
Module 5
Sub findf()
'initialize variables
ffinal = 0
43
bottomsmin = 1
bottomsset = 10
trigger = 0
For F = 100 To 550
If (trigger = 0) Then
'set F on spreadsheet to current value of F
Range("B3").Select
ActiveCell.FormulaR1C1 = F
'get value for difference between xwMB and xwKog
bottomsmin = Range("F45")
If (bottomsmin <= bottomsset) Then
'if value in cell (bottomsmin) is less than
'the set min in this fxn (bottomsset) then
'set bottomsset to the lower cell value
bottomsset = bottomsmin
'set the flow rate at which the current
'bottomsset corresponds to
ffinal = F
'display current minimum error and optimum F
Range("F49").Select
ActiveCell.Value = bottomsset
Range("F48").Select
ActiveCell.FormulaR1C1 = ffinal
End If
stopvalue = Range("F39")
If (stopvalue = 0) Then
trigger = 1
End If
End If
Next F
If (bottomsset < 0.01) Then
Range("F50").Select
ActiveCell.FormulaR1C1 = "these conditions should work! (for error(xw) < 0.01)"
Range("B3").Select
ActiveCell.FormulaR1C1 = ffinal
44
Else
Range("F50").Select
ActiveCell.FormulaR1C1 = "distillate composition not attainable for these conditions (between F=100-550 mL/s)"
End If
End Sub
45
Appendix G: Equipment Diagram
16
14
Thermocouple
s
13
9
Sample Port
Q-3
C onde
nser
7
Cooling
Wat er
8
Feed Port
6
Fee d
Prehe ater
Turbine Flow-meter
Column
F
PRV
V-1
F
s
Reflu x
Prehe ater
5
4
Q-2
F-4
s
Disti llate
Rece iver
3
2
Q-1
F
F-5
Graduat ed
flow meter
1
Reboiler
0
B-1
s
R-3
R-4
10
12
B-2
11
Alternate
Bott oms
tank
D-3
Alternate
Dist illate
tank
C-1
D-4
Feed Tank
Feed Pump
F-1
F
R-6
s
B-3
D-2
15
R-1
s
F-2
Alternate
Fee d Ta nk
R-2
Ref lux Pump
D-1
46
Appendix H: MSDS of Methanol
47
Appendix I: Flooding Conditions
Figure I-1: Vapor flow rate vs. Reboiler Power
Vapor flow rate (kg/min)
0.43
R = 6.7
Pro Pack (R = 6.7)
R = 46
Pro Pack (R = 46)
0.41
0.39
0.37
0.35
0.33
0.31
0.29
0.27
0.25
70
75
80
85
90
95
100
Reboiler power (%)
*The flooding data from a reflux ratio of 6.7 is from Rotation 1.
Figure I-2: Vapor flow rate vs. Feed Rate
0.45
R = 6.7
Pro Pack (R = 6.7)
Vapor flow rate (kg/min)
0.43
0.41
R = 46
Pro Pack (R = 46)
0.39
0.37
0.35
0.33
0.31
0.29
0.27
0.25
60
160
260
360
460
560
660
Feed rate (ml/min)
48
Appendix I (cont.): Flooding Conditions
Figure I-3: Wilkes vs. Experimental Flooding Conditions for reflux ratios of 6.7 and 46
1
Y axis Wilkes
0.01
0.1
R = 6.7
Wilkes
R = 46
1
0.1
F LG
49
Appendix J: Constant Molal Overflow versus Enthalpy Concentration Method
Figure J-1: McCabe Thiele Method
Constant Molal Overflow Assumption
(McCabe-Thiele Method)
1
y(methanol)
0.8
0.6
Equilibrium
y1=x1
Enriching
stripping
q-line
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x(methanol)
Figure J-2: Enthalpy Concentration Method
Enthalpy Concentration Method
1
y(methanol)
0.8
0.6
0.4
Enriching
Stripping
0.2
Equilibrium
y=x
q-line
0
0
0.2
0.4
0.6
0.8
1
x(methanol)
50
51