Continuous Binary Distillation
University of Illinois
Continuous Binary Distillation
Lab Prep Report
Unit Operations Lab 2
January 24, 2011
Group 6
Sana Buch
Priya Chetty
Liliana Gutierrez
Linda Quan
Vijeta Patel
Lipi Vahanwala
Unit Operations ChE-382 Group No. 6
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
01/24/2011
Continuous Binary Distillation
University of Illinois
1. Introduction
Distillation is the most widely used separation process that separates a mixture
based on differences in the conditions required to change the phase of components of the
mixture. Distillation contributes to more than 50% of plant operating costs (Modeling &
Simulation of Binary Distillation Column). Distillation is used mainly for commercial
purposes, such as production of gasoline, distilled water, xylene, alcohol, paraffin, and
kerosene (Modelling & Simulation of Binary Distillation Column). In large chemical
complexes, the distillations are continuous with the feed entering at some point near the
middle of the column and the product being taken off the top and the bottom. Distillation
is very flexible and there are schemes which include multiple feeds to the column and the
take-off of multiple products. However, a distillation column can produce only two
products (the top and the bottom) which are of high purity. Sequences of distillation
columns are commonly used to produce numerous high-purity products.
The process of distillation can be categorized according to the following (Guzman
4).
1) Method of separation (Guzman 5)
a. Simple distillation is distillation without reflux, where no condensate is
allowed to return to the single stage still pot to contact the rising vapors.
b. Fractional distillation is distillation with reflux in which a portion of the
condensate is allowed to return to the distilling column to contact the
rising vapors.
2) Nature of the process feed (Guzman 5)
a. Binary component
b. Multi-component
3) Method of operation (Guzman 5)
a. Batch Column is the design of a batch column, which is more complex
than a continuous distillation column as it requires consideration of
unsteady-state behavior (Diweker, Madhvan 713). Batch distillation is
most often used with smaller volume products (“The Distillation Group,
Inc”). The batch column distillation column can be designed by keeping
two modes of operation (Diweker, Madhvan 713).
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Spring 2011
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Continuous Binary Distillation
University of Illinois
i. Variable reflux and constant product composition of all or one
component
ii. Constant reflux and variable product composition
b. Continuous Column, on the other side, is an ongoing distillation in which
a liquid mixture is continuously fed into the process and separated
fractions are removed continuously (M&S). The simulation of continuous
distillation for multi-component mixture is well developed in chemical
engineering due to its commercial importance. Continuous distillation is
most often used with big volume products like jet fuel, benzene, and
plastic monomers (“The Distillation Group, Inc”).
4) Types of columns used (Guzman 5)
a. Plate/staged column type provides each plate contact between vapor and
liquid in continuous countercurrent flow. Each plate constitutes a single
stage where there’s a simultaneous partial condensation of vapor and
partial vaporization of liquid.
b. Packed column type are plate columns containing packing columns that
provides high interfacial area for the exchange of the components
between the vapor and liquid phases.
This lab is mainly designed to separate binary components including methanol
and water using the fractional distillation method in the six stages batch column. The 32
liter mixture is created using 5vol% of 99.8% anhydrous methanol and water. Then
sufficient amount of steam is supplied to begin the process of distillation. After it starts
boiling, the feed reaches equilibrium and samples of liquid and vapor from each stage are
collected. The collected sample is observed under a refractometer, a device that measures
the index of refraction. The data obtained from the refractometer is compared with the
calibration data obtain at room temperature in order to determine the composition.
2. Literature Review/Theory
Distillation is the separation or partial separation of a liquid feed mixture into
components or fractions by selective boiling (or evaporation) and condensation (Wankat
Unit Operations ChE-382 Group No. 6
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
86). In a distillation column, the separation occurs because different components have
different volatilities. The component with more volatility is easy to vaporize therefore
the output vapor from distillation column will be enriched with more volatile component
while the output liquid phase will be more enriched with less volatile component
(Wankat 91). When a mixture reaches a specific temperature and pressure a certain
amount of the mixture moves into the vapor phase until the vapor reaches the mixture’s
vapor pressure (Wankat 98). This point is known as the vapor-liquid equilibrium.
Volatility is a measure of a pure component’s vapor pressure at a set pressure and
temperature in a specific mixture. It is incorrectly assumed that the components of a
mixture will separate based on their boiling points when pure. Rather, the boiling point of
a mixture is based on the total vapor pressure of a mixture, which is a sum of the vapor
pressures of each individual component in the mixture. This is known as the Dalton’s law
and can be expressed as:
p sat  (vpa  vpb .....)
(1)
P sat  Vapor pressure of mixture (kPa)
vpa  Vapor pressure of component a (kPa)
vpb  Vapor pressure of component b (kPa)
This means that a component will not boil off “cleanly” meaning it is impossible through
distillation to obtain a pure substance. The vapor created above a mixture is also a
mixture of components. The composition of the vapor is based on the volatility of each of
the substances. Raoult’s law helps us to determine what the volatility, or “K value” of a
substance. This in turn allows us to find the mole fraction of a component in the vapor
phase.
Unit Operations ChE-382 Group No. 6
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
ya 
vpa * x a
(2)
p sat
y a  Mole fraction of component a in vapor phase (dimensionless)
vpa = Vapor pressure of component a (kPa)
xa = Mole fraction of component a in liquid phase (dimensionless)
Psat = Vapor pressure of mixture (kPa)
Equation 2 (Raoult’s law) holds true only for those components that do not form
azeotrope (J.M. Smith, H.C. Van Ness, M.M Abbott 350. Not all components obey
Raoult’s law because some components have high solubility with each other which leads
to the formation of azeotrope. An azeotrope is a mixture of two or more liquids in such a
ratio that its composition cannot be changed by simple distillation. This occurs because,
when an azeotrope is boiled, the resulting vapor has the same ratio of constituents as the
original mixture (Azeotrope). The simplest of all distillation techniques is called flash
distillation. Flash distillation occurs when a mixture at a specific temperature and
pressure is allowed to drop in pressure. This changes the vapor-liquid equilibrium of the
mixture and creates a vapor rich in the most volatile component(s). This is also the
crudest form of distillation and does not allow for refinement of the distillates.
A more complicated form of distillation is batch distillation. Batch distillation
uses both a boiler and a condenser, but only allows one separation, or cut, to be taken
from the mixture.
Continuous distillation is the most complicated and most common form. It has a
boiler, condenser and multiple trays or packing which allows the vapor to condense as it
moves up the column and cools. The trays or packing allows for a better separation of the
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
01/24/2011
Continuous Binary Distillation
University of Illinois
components in the mixture which in the end gives purer products. It also adds a lot of
complexity to the system.
Figure 1
The McCabe-Thiele method greatly simplified the process of determining the size
of the tower and the number of trays. The method uses a graphical representation of the
material balance equations as operating lines on a graph of the liquid composition (xaxis) and the vapor composition (y-axis). The bottom line in Figure 1 is the x-y line. This
starts at the origin and ends where x and y both equal 1.This line would represent a
distillation column that operated at total reflux and total boil-up, meaning that all of the
vapor and all of the liquid is recycled back into the system. The next line added is the
vapor –liquid equilibrium line for a binary system which is found experimentally. By
moving step-wise between the two lines we can find the number of theoretical plates
needed for a specific separation of a binary mixture and the liquid and vapor composition
at any point in the distillation column. These stage lines can be seen in Figure 1.
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Spring 2011
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Continuous Binary Distillation
University of Illinois
Figure 2: McCabe-Thiele diagram with operating lines and feed line added.
In practice, we want to draw a purified product out of the column in the form of
either a distillate (top of the column) or the bottoms product (bottom of the column) or
both. This requires a column that operates at a partial reflux and/or a partial boil-up ratio.
This means that we cannot use the x-y line for such a column. In Figure 2 we see the
addition of a line for reflux ratio (slope L/V) and a line for the boil-up (slope L’/V’). The
boil-up line’s slope increases as we increase the amount of bottoms product that we
remove from the system. Subsequently, as we remove more distillate as product we
decrease the slope of the top operating line, which is the line for the reflux ratio. By
changing the amount of liquid re-boiled, which is liquid returned to the column as a
vapor, or by changing the amount of vapor refluxed, returned to the column as a liquid,
we change the number of theoretical plates necessary for a given separation. The q
Unit Operations ChE-382 Group No. 6
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
(quality) line in Figure 4 is the feed line which is the composition of the stream entering
the distillation column. We can see from the diagram in Figure 4 that where that line
intersects with the two operating lines is the feed stage, or the tray at where the incoming
stream enters.
The quality q is defined as:
(3)
Where:

[=] quality of the feed (dimensionless)

[=] liquid flow rate below the feed (mole/hr)

L [=] liquid flow rate above the feed (kJ/kg)

F [=] feed flow rate (mole/hr)

H [=] saturated vapor enthalpy of feed (kJ/kg)

hf [=] enthalpy of feed (kJ/kg)

h [=] saturated liquid enthalpy of feed (kJ/kg)
The feed line can then be defined as:
(4)
Where:

y [=] vapor mole fraction of methanol (dimensionless)

q [=] quality of the feed (dimensionless)

x [= ] liquid mole fraction of methanol (dimensionless)

ZF [=] mole fraction of methanol in feed (dimensionless)
Unit Operations ChE-382 Group No. 6
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
The top operating line is defined as
(5)
Where:

y [=] vapor mole fraction of methanol (dimensionless)

L0 [=] liquid reflux rate into column (mole/hr)

D [=] distillate flow rate (mole/hr)

x [=] liquid mole fraction of methanol (dimensionless)

xD [=] mole fraction of methanol in distillate (dimensionless)
The McCabe-Thiele method is widely used for binary mixtures. Multi-component
distillation is much more complicated and the calculations involved are trial-and-error, so
it is convenient to do them on computers (Wankat 176).
3. Experimental
3.1 Apparatus
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University of Illinois
1
2
9
3
10
11
4
12
5
13
14
6
15
7
16
8
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
19
17
20
18
2
21
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
5
22
12
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
23
27
24
28
25
29
26
30
31
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Continuous Binary Distillation
33
34
University of Illinois
35
32
36
No. Manufacture Component
1
N/A
Condenser
2
N/A
Water supply
3
F&P Co
4
N/A
Liquid
Rotameter
Stages 1-6
5
N/A
Filling tank
6
N/A
Ladder
Description/Usage/Safety
Condenses the water.
A bulb valve used to fill the filling tank with
water. Be cautious of splashing water when
opening the valve.
Measures the flowrate of the water flowing into
the condenser.
There are 6 stages of the distillation column. At
each stage, both liquid and vapor can be
extracted. When extracting samples, be careful.
Use a ladder or the staircase. Do not climb on
the metal bars to extract samples.
The filling tank holds the methanol and water
until it can be drained into the round bottom flask
of the distillation column.
Used to fill the holding tank and to extract
Unit Operations ChE-382 Group No. 6 p. 14
Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
7
N/A
Ball valve for
draining
distillation
column
Fill/Drain
valve
8
N/A
9
N/A
Pressure gauge
10
N/A
11
N/A
12
Powerstat
Flow rate
control valve
Valve for
pressure gauge
Heater box
13
N/A
14
Newport
15
N/A
16
N/A
17
N/A
Valve to
release the
vapor
18
N/A
Tube for gas
19
N/A
Valve to
release the
liquid
20
N/A
Tube for liquid
21
N/A
Filling funnel
Thermometer
gauge
Digital
Thermometer
Large round
bottom flask
Reboiler
University of Illinois
samples at various stages of the distillation
column.
Ball valve is used to drain the distillation column
at the end of the experiment. Make sure the
system is cooled to room temperature before
draining; otherwise, it will break the glass.
Needle valve used to fill the distillation column
with the methanol and water solution from the
filling tank. When the knob is pointing towards
“fill” the filling tank can be filled with solution.
When the knob is pointing towards drain, the
filling tank will be drained of the solution and
transported into round bottom flask of the
distillation column.
Reads the pressure of the water flowing into the
condenser.
Needle valve used to control the flow rate of the
water flowing into the condenser.
Needle valve used to control the pressure of the
condenser.
Controls the boiler of the distillation column.
Team must ask instructor to unlock and turn on
the reboiler.
Reads temperature at the top of the distillation
column.
Reads the temperature at each thermocouple
location at each stage of the distillation column.
Holds the methanol and water solution while the
boiler heats it up.
Heats up the round bottom flask containing the
methanol and water solution.
For each stage there is a ball valve labeled
“GAS” and the stage number. This releases the
vapor into a tube in which a vapor sample at that
stage can be collected.
A clear tube is connected to a valve in order to
transfer the vapor from the distillation column to
a small test tube.
For each stage this is a ball valve labeled “LIQ”
with the stage number. This releases the liquid
into a tube in which the liquid sample at that
stage can be collected.
A clear tube connected to the liquid valve allows
for an easy transfer of the liquid from the
distillation column to a small test tube.
There if a funnel located at the mouth of the
Unit Operations ChE-382 Group No. 6 p. 15
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Spring 2011
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Continuous Binary Distillation
22
N/A
Filling tank
valve
23
24
Eyepiece
Thermometer
25
26
Light switch
Adjusting
Knob
Refocusing
knob
Light source
Scale
illumination
Illuminating
Prism
27
28
29
30
31
32
33
34
35
36
37
University of Illinois
filling tank in which water and methanol can be
easily poured into the tank.
A green valve that drains the fluid out of the
tank. When the green valve is facing the left
side, the solution is contained in the tank. When
the green valve is facing the right side, the
solution is transported through the pipes and into
the distillation column.
Used to see the sample.
Reads the temperature of the water flowing into
the refractometer from the ice bath.
Turns on the light source of the refractometer.
Used to align the horizontal refracting line to the
center of the X.
Used to focus the refracting line.
This button makes the refractor index scale
appear. Read the top numbers.
A small droplet of the sample is placed here. Be
sure to clean the lens using distilled water and
kimwipes in between samples.
Tubing for cold The cold water from the ice bath is transported
water
through the refractometer.
Ice bath
Used to keep the water flowing through the
refractometer cold.
Capacity
Controls the amount of fluid flowing through the
Controller
refractometer.
Temperature
Controls the heating coil that melts the ice to
controller
form water which flows through the
refractometer.
On/Off Switch Turns the ice bath machine on and off.
Digital
Reads the temperature of the ice bath.
thermometer
Heating coil
Melts the ice into water which flows through the
refractometer.
3.2 Materials and Supplies
No. Materials/Supplies
1
Goggles
2
Gloves
Description/Use
Used to protect the eyes
Used to protect your hands from Methanol because it can
dry out your hands.
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Continuous Binary Distillation
3
Tap Water
4
Methanol
5
6
7
Graduated
Cylinders
Ladder
Small test tubes
8
9
10
Distilled water
Kimwipes
Ice
11
Digital
Thermometer
Refractometer
12
University of Illinois
Used to make the 5 wt % methanol and supplied to the
condenser
99.8% anhydrous methanol used to make the 5wt% watermethanol solution that is then fed into the distillation
column.
Measure the amount of Methanol needed to make
methanol solutions.
Used to add methanol to the filling tank.
Used to collect samples of the liquid and vapor at each stage
of the distillation column.
Used to clean the refractometer in between readings.
Used to clean and dry off the refractometer.
Used in the ice bath for the refractometer to maintain the
temperature at approximately 33°F
Used to read the temperature of the ice bath.
Used in the experiment to obtain the refractive index that be
used to calculate density once calibrated.
3.3 Experimental Procedure
Starting the batch distillation column:
1. Make sure the filling tank is closed and the knob of the Fill/Drain valve is
pointing in the direction of “Fill”.
2. Make a 5% of 99.8% anhydrous methanol solution by mixing it with water in the
13 gallon feed tank using graduated cylinders for measurement.
3. Pour the methanol-water mixture into the feed container and turn on the water
valve and fill the filling tank to the 32 liter mark, indicated by the black line.
4. Once the filling tank is full, turn off the water supply and carefully climb back
down to ground level. Turn the Fill/Drain valve so that the knob is pointing in the
direction of “Drain”. Make sure the yellow ball valve of the distillation column is
closed which is indicated by the knob facing perpendicular to the pipe.
Unit Operations ChE-382 Group No. 6 p. 17
Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
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Continuous Binary Distillation
University of Illinois
5. Open the filling tank valve by turning the green knob all the way to the right. The
solution should start to fill the round bottom flask of the distillation column.
6. Once filling tank is completely drained, close the filling tank valve by turning the
green knob all the way to the left.
7. Call the instructor or the TA to turn on the reboiler.
8. Record the temperature of thermocouples at each stage every 20 minutes until the
temperature has reached steady-state.
9. Obtain samples of liquid and vapor at each stage.
10. Use the refractometer to determine the refractive index for each of the sample.
Instructions are listed below.
Using the refractometer:
1. Make solutions of 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 wt% methanol
solutions and cover each solution with parafilm.
2. Obtain ice from the CHE office on the 2nd floor.
3. Turn on the ice bath and add ice to cool the water to approximately 32 or 33°F.
Try to maintain this temperature throughout the experiment.
4. Turn on the light switch for the refractometer.
5. Open the illuminating prism and add a droplet of solution or sample. Close the
illuminating prism. And adjust the light source upwards.
6. While looking into the eyepiece, use the refocusing knob to obtain a clearly
defined horizontal line in which the bottom is green and the top is white.
7. Use the adjusting knob to raise or lower the line until it is exactly centered at the
middle of the X.
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Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
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Continuous Binary Distillation
University of Illinois
8. Press the scale illumination button to make the refraction index scale appear.
Record the value.
9. Repeat these steps for all the solutions of the calibration curve and the liquid and
vapor solutions from the distillation column after it has reached steady-state.
4. Anticipated Results
In this lab experiment, the mixture of methanol and water will be distilled using a
six stage batch distillation system at total reflux. The liquid and vapor compositions of
each stage will be determined using the refractometer, which will be calibrated using the
samples of known composition at constant temperature. From the values of refraction
index (n) of the known composition of methanol-water mixture, a second order
polynomial will be constructed. The vapor and liquid compositions for the each stage will
be calculated using the polynomial equation. The polynomial equation (ax2+bx+c) will
give two solutions for each refraction index. The correct refraction index will be
determined using the temperature of each stage.
From the collected data, the McCabe-Thiele diagram for the methanol-water
system will be constructed. This data will be compared to the theoretical VLE (vaporliquid-equilibrium) data of methanol-water system. Using this plot, the number of stages
and the fraction of the distillate will be calculated. The feed will be saturated vapor.
Using the Murphee plate efficiency equation, the efficiency of each stage will be
calculated.
(6)
Where,

= the composition in equilibrium with xn
 η = efficiency of the stage
 y = vapor fraction of methanol
The overall efficiency can be calculated from the equation below (Wankat 133):
Unit Operations ChE-382 Group No. 6 p. 19
Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
(7)
Where,

= the overall efficiency of the column

= number of the equilibrium stages

= actual number of the stage required
The overall energy balance for the distillation after it reaches the steady state can
be written as below:
(8)
Where,



m = mass of the component entering in the column at the top (kg)
= heat capacity of water at constant pressure (J/kg*K)
= the difference between inlet and outlet temperature of condenser (K)
From the above equation q of the distillation system will be calculated.
Unit Operations ChE-382 Group No. 6 p. 20
Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
5. References
1.
“Azeotrope” < http://en.wikipedia.org/wiki/Azeotrope >
2. Diwekar, Urmila M., and K. P. Madhavan. "Multicomponent Batch Distillation
Column Design." Industrial & Engineering Chemistry Research 30.4 (1991): 71321. Print.
3. Guzman, Manuel De. Distillation. Scribed. Electronic.
4. Introduction to Chemical Engineering Thermodynamics (7th Ed.), J.M. Smith,
H.C. Van Ness., M.M. Abbott. McGraw-Hill, 2005. Pages 350-353.
5. MODELLING & SIMULATION OF BINARY DISTILLATION COLUMN.
Working paper. Scribed. Print.
6. Separation Process Engineering (2nd Ed.), Wankat, Phillip, Prentice Hall, 2007.
Pages 86-105.
7. "The Distillation Group, Inc. Distillation." The Distillation Group, Inc
Distillation. The Distillation Group, Inc, 11 Jan. 2002. Web. 23 Jan. 2011.
<http://www.distillationgroup.com/distill.htm>.
8. Website: < http://www.chemsep.com/downloads/data/fri_1982_tr.png>
9. Website: http://commons.wikimedia.org/wiki/File:McCabe-Thiele_diagram.png>
REFERENCES for this Lab Report Template:
Final Report Template Fall 2009, Department of Chemical Engineering, University of
Illinois at Chicago, Chicago, Illinois.
CHE4162 Syllabus Spring 2010, Department of Chemical Engineering, Louisiana State
University, Baton Rouge, LA.
Unit Operations ChE-382 Group No. 6 p. 21
Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
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Continuous Binary Distillation
University of Illinois
6. Appendix I: Job Safety Analysis (formerly called WP &C)
What is the purpose of this experiment?
The purpose of this experiment is to separate a mixture of a 5% (by volume) methanolwater solution in a binary distillation column. Methanol-water mixture will be introduced
into the round bottom flask of the column and the column will operate at temperatures
ranging from 0-100oC. Water will be used to condense the methanol rich product. The
column will be run and allowed to reach steady state. Samples from the six stages will
then be obtained and tested with a Refractometer to eventually obtain the methanol
concentration in each stage.
What are the hazards associated with the experiment?
1. Methanol is a relatively toxic fluid. It can cause eye, skin and respiratory tract
irritation when carelessly exposed to lab personnel.
2. The persistent use of fluids like water and methanol could lead to fluid spillage. If
lab personnel were to walk over an affected area, they run the risk of injuries due to
a fall
How will the experiment be conducted in a safe manner?
1. Lab personnel should wear gloves, goggles, slip resistant shoes, and a facemask
when conducting experiment especially when handling the methanol.
2. Paper towels or task wipers should be in close proximity to clean up any fluid spills
that may occur during experiment.
3. The Distillation column should not be heated until the mixture has reached the
Reboiler section of unit.
What safety controls are in place?
1. There is a failsafe valve present that allows the removal of fluids incase the unit
gets flooded.
Describe safe and unsafe ranges of operations.
1. The operating flow rates of water should be between 0-2 GPM. All relevant data
can be obtained in this range. An increase flow rate between 3-10 GPM could be
hazardous due to increased pressure.
I have read relevant background material for the Unit Operations Laboratory entitled:
“Batch Distillation” and understand the hazards associated with conducting this
experiment. I have planned out my experimental work in accordance to standards and
acceptable safety practices and will conduct all of my experimental work in a careful and
Unit Operations ChE-382 Group No. 6 p. 22
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Spring 2011
01/24/2011
Continuous Binary Distillation
University of Illinois
safe manner. I will also be aware of my surroundings, my group members, and other lab
students, and will look out for their safety as well.
Signatures: _Sana Buch______________________________________
_Priya Chetty____________________________________
_Liliana Gutierrez_________________________________
_Vijeta Patel_____________________________________
_Linda Quan_____________________________________
_Lipi Vahnwala__________________________________
Unit Operations ChE-382 Group No. 6 p. 23
Buch, Chetty, Gutierrez, Patel, Quan, Vahanwala
Spring 2011
01/24/2011