Methanol is an essential feed stock for the manufacture of many industrial products such as adhesives and paints and it is widely used as a solvent in many chemical reactions. Crude methanol is obtained from steam reforming of natural gas and then a purification process is needed since it contains smaller and larger degree of impurities. The purification process consists of two steps: a topping column used to remove the low boiling impurity called the light ends; and the remaining water methanol mixture is transferred to another column called the refining column where it is constantly boiled until separation occurs. Methanol rises to the top while the water accumulates in the bottom. This document focuses on methanol water separation. A detailed design study for the distillation column is conducted where the separation occurs at atmospheric pressure with a total condenser and a partial reboiler.

1. Building H - Faculty of Engineering – Holy Spirit University of Kaslik - B. P. 446 Jounieh, Lebanon
HOLY SPIRIT UNIVERSITY OF KASLIK
Faculty of Engineering
Department of Chemical Engineering
Separation Process GCH450
Year 2016/2017
Design of Methanol Water Distillation Column
Presented by:
Rita EL KHOURY Jean Noel SEMAAN
May 4, 2017

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Table of contents
Table of contents........................................................................................................................... 3
List of tables................................................................................................................................... 4
List of figures................................................................................................................................. 5
Abstract .......................................................................................................................................... 6
Introduction................................................................................................................................... 7
I. Design Procedure..................................................................................................................... 8
I.1.Design statement...............................................................................................................8
I.2.List of Assumptions..........................................................................................................8
II. Calculation Results.................................................................................................................. 9
III. Discussion .........................................................................................................................10
Conclusion....................................................................................................................................12
References ....................................................................................................................................13
Appendix A: Vapor Liquid Equilibrium Data.......................................................................14
Appendix B: Physical Properties for Methanol and Water.................................................17
Appendix C: Column Calculations..........................................................................................18
Appendix D: Duties of Condenser and Reboiler....................................................................26
Appendix E: Size Calculation ...................................................................................................28

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List of tables
Table 1 : Design specifications.............................................................................................. 7
Table 2 : Feed, bottom and distillate specifications................................................................ 9
Table 3 : Column stages ........................................................................................................ 9
Table 4 : Condenser and reboiler duties............................................................................... 10
Table 5 : Diameter size........................................................................................................ 10
Table A.1 : Vapor liquid equilibrium data for methanol water at 1 atm................................ 14
Table A.2 : Antoine equation constants ............................................................................... 14
Table E.1 : Size calculation results ...................................................................................... 30

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List of figures
Figure A.1 :Boiling points Excel calculation. ...................................................................... 15
Figure A.2 : McCabe-Thiele diagram for methanol water at 1 atm....................................... 16
Figure C.1 : Distillation column. ......................................................................................... 18
Figure C.2 : Fenske and Underwood calculations. ............................................................... 21
Figure C.3 : McCabe-Thiele diagram for Nmin and Rmin ................................................... 22
Figure C.4 : McCabe-Thiele diagram at finite reflux ratio. .................................................. 24
Figure E.1 : Feed section..................................................................................................... 29

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Abstract
Every year, the chemical industries produce a large amount of methanol due to the increase in
global demand. Methanol is an essential feedstock for the manufacture of many industrial
products such as adhesives and paints. It is also known that methanol is widely used as a
solvent in many chemical reactions. The manufacture process is based on the preparation of
syngas in order to synthesis the crude methanol and then a purification operation is needed to
remove the impurities especially the water present in the key product before it can be sold.
Water and methanol, having different boiling points, can be separated through distillation.
Distillation is the most well known separation technique used in the industry sector.
Therefore, the aim of this report is to design a distillation column for the separation of
methanol water mixture.
Key words: methanol, water, distillation, chemical industry.

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Introduction
Methanol is considered to be an important chemical commodity and a principal
energy source. It is a colorless liquid with high toxicity and flammability levels. The
exposure to this alcohol must be avoided as it can be extremely harmful to humans if
swallowed, inhaled or ingested.
There are many resources that serve as a feedstock for methanol production such as natural
gas, coal, and biomass. In fact, a significant advantage of methanol is that it can be produced
from any feedstock that can be converted first into syngas. However, the most common
method for methanol synthesis is through steam reforming of natural gas.
The crude methanol product contains smaller and larger degree of impurities. Therefore, the
purification process consists of two steps. The first step is about a topping column used to
remove the low boiling impurity called the light ends. The remaining water methanol mixture
is transferred to another column called the refining column where it is constantly boiled until
separation occurs. Methanol rises to the top while the water accumulates in the bottom.
This report will focus on methanol water separation. A detailed design study for the
distillation column is conducted through this paper. This distillation occurs at atmospheric
pressure with a total condenser and a partial reboiler. The design specifications are illustrated
in table 1.
Feed Saturated liquid
Feed composition 18 wt% methanol
82 wt% water
Distillate rate 100,000tons/year
Distillate composition 98 wt% methanol
Bottom composition 1 wt% methanol
Pressure 1 atm
Condenser Total
Reboiler Partial
Table 1: design specifications

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I. Design Procedure
I.1. Design statement
This report is developed to discuss the major aspects present in the design of a distillation
column required for the separation of the methanol water mixture. Two methods are adopted
in the calculation of some design parameters for this binary column distillation: the McCabe
and Thiele construction method (see [Sheet 1] & [Sheet 2]) and the approximate shortcut
methods (see [Sheet 3]). The calculations are done using Excel Spreadsheets and detailed in
appendix C.
Our report will follow the subsequent algorithm:
1- Vapor liquid equilibrium data for methanol water mixture – Appendix A
2- Physical data of methanol and water required – Appendix B
3- Material balance – Appendix C
4- Minimum number of stages – Appendix C
5- Minimum reflux ratio – Appendix C
6- Actual reflux ratio – Appendix C
7- Number of actual trays – Appendix C
8- Optimum feed tray location – Appendix C
9- Duties of the condenser and reboiler – Appendix D
10- Column size calculation – Appendix E
I.2. List of Assumptions
A number of assumptions were taken during the design of the distillation column:
- Adiabatic and well insulated column
- The constant molal overflow CMO are valid
- Constant relative volatility
- Mixture of methanol water is ideal
- Reflux is saturated liquid
- Ideal gas law is applicable for the vapor (for density calculation)

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II. Calculation Results
The detailed calculations are present in Appendix C. The design parameters obtained for the
distillation column operating at atmospheric pressure are tabulated as follow:
Parameter Value
Feed temperature 87 ͦ C
Top temperature 65.67 ͦ C
Bottom temperature 98.98 ͦ C
Feed rate 3 332.76 kmol/h
Distillate rate 361.823 kmol/h
Bottom rate 2970.936 kmol/h
Table 2: Feed, bottom and distillate specifications
Value
Parameter McCabe-Thiele
method
Shortcuts
method
Minimum number of trays 6 5.68
Minimum reflux ratio 1.61 2.5
Actual reflux ratio 2 2
Actual number of trays 12 12.03
Optimum feed tray location from condenser 8 7.68
Table 3: Column stages

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The column operates with a total condenser and a partial reboiler. The detailed calculation for
their duties is available in appendix D and the results are tabulated below.
Duties Value
Total condenser −38.28 × 106
𝑘𝐽/ℎ
Partial reboiler 37.63 × 106
𝑘𝐽/ℎ
Saturated steam rate 14 062 kg/h
Cooling water rate 702 772 kg/h
Table 4: Condenser and Reboiler duties
The calculation of the size of the distillation column is shown in Appendix E. the result is
tabulated below.
Diameter Value
Top column 1.45 m = 4.77 ft
Bottom column 0.86 m = 2.82 ft
Table 5: Diameter size
III. Discussion
The theoretical values obtained from McCabe-Thiele diagram and from Fenske, Underwood
and Gilliland equations and correlations are close proving that our design work is accurate.
The theoretical number of stages for the designed distillation column is 12 stages including
partial reboiler.
𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝐸 =
𝑁𝑡ℎ𝑒𝑜𝑟𝑎𝑡𝑖𝑐𝑎𝑙 − 1
𝑁𝑎𝑐𝑡𝑢𝑎𝑙
Assuming that our design is based on 75% overall efficiency, then we have 15 actual trays
plus partial reboiler. Since the diameter size is based on 32 cm tray spacing, the actual height
of the column is about 5 meters.

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Our design specifications are a saturated liquid feed, total condenser and partial reboiler.
Consequently, the duties of the condenser and reboiler must be approximately equal.
According to table 4, the duties of the condenser and reboiler obtained for our design are
close to each other which verify the calculations.
The difference in these two values is due to the heat loss since the assumption of an adiabatic
and well insulated column is theoretical. Practically, there’s always a small amount of heat
losses.
Moreover, the use of cooling water in the condenser is the most preferable due to the fact that
refrigeration is expensive. Thus, in designing a distillation column we should avoid the use of
refrigeration in the condenser.
On the other hand, the design size of the column should be evaluated in a way of avoiding
flooding caused by entrainment. The diameter at the top of the column is different than the
one at the bottom. Based on literature1
and as rule of thumb, if the feed is saturated liquid and
water is the heavy key, either bottom or top diameter can be larger. Furthermore, if the vapor
velocity changes on a relatively high scale, the diameters calculated will be quite different.
Our design conditions implicate having a top diameter larger than the bottom. A good
assumption would be to choose the larger diameter for the rest of the design work. However,
if a large change in diameter is faced the optimum way to design the column is by building it
in two sections of different diameters. The ultimate variations would be considered and
included in the design calculations.
1
“Separation process engineering includes mass transfer analysis”, 3rd
edition, chap. 10

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Conclusion
The design of a suitable separation unit for the purpose of separating methanol water
mixture has been kept simplified. An atmospheric distillation column is an effective
industrial unit for purifying methanol. From the bottom of the column pure water is removed.
At the top, the methanol vapors are pure, condensed in a heat exchanger and collected in a
reflux drum. Part of methanol serves as a reflux for the column while the product is stored
and recovered in a buffer tank. Methanol can be beneficial for reducing the operating cost if it
is re-injected into the process.
The studies and researches concerning the production and purification of methanol are of
great importance due to industrious importance of methanol.

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References
[1] Phillip C.Wankat, «Separation Process Engineering Includes Mass Transfer Analysis, »
third edition, Pearson Education International.
[2] Marc A.Burns, James C.Sung, « Design of separation units using spreadsheets »,
university of Michigan, Ann Arbor, MI 48109-2136.
[3] Robert H.Perry, « Perry’s chemical engineers handbook », seventh edition, McGraw- Hill.
[4] Richard M.Felder, Ronald W.Rousseau, « Elementary principles of chemical processes »,
third edition, John Wiley & sons, Inc, tables B.1, B.2, B.4, B.6, p 628-649.
[5] Cathy van Hoogstraten & Kevin Dunn, « The design of a distillation column», university
of Cape Town, department of chemical engineering, 18 September 1998.

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Appendix A: Vapor Liquid Equilibrium Data
The equilibrium measurements for the binary mixture of methanol and water at 1 atm are
taken from reference [1] and shown in table A.1 in molar fraction.
Methanol liquid Methanol Vapor Temp. ͦC
0 0 100
0.02 0.134 96.4
0.04 0.23 93.5
0.06 0.304 91.2
0.08 0.365 89.3
0.1 0.418 87.7
0.15 0.517 84.4
0.2 0.579 81.7
0.3 0.665 78
0.4 0.729 75.3
0.5 0.779 73.1
0.6 0.825 71.2
0.7 0.87 69.3
0.8 0.915 67.6
0.9 0.958 66
0.95 0.979 65
1 1 64.5
Table A.1: Vapor liquid equilibrium data for methanol water at 1 atm
The Antoine constants for methanol and water are obtained from Felder & Rousseau [4] and
listed in table A.2. Antoine equation where T in ͦ C and VP in mmHg is:
log( 𝑉𝑃) = 𝐴 −
𝐵
𝑇 + 𝐶
Compound A B C
Methanol 8.080897 1582.271 239.726
Water 8.10765 1750.286 235
Table A.2: Antoine equation constants

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According to these data, the boiling point of pure methanol and pure water are calculated in
the Excel Spreadsheets [Sheet 1] using Solver.
The result is in accordance with the theoretical values:
Figure A.1: Boiling points Excel calculation
Thus,
𝑇 𝑚𝑒𝑡ℎ𝑎𝑛𝑜𝑙
𝑏𝑝
= 64.55 ͦ 𝐶 𝑇 𝑤𝑎𝑡𝑒𝑟
𝑏𝑝
= 99.86 ͦ 𝐶
The feed, top and bottom temperature of the column are obtained by interpolating in the
composition-temperature data shown in table A.1. For the composition calculation, see
Appendix C.
- Feed temperature: 𝑧 𝑚 = 0.1098 → 𝑇𝑓𝑒𝑒𝑑 = 87 ͦ 𝐶
- Top temperature: 𝑥 𝑚,𝑑𝑖𝑠𝑡 = 0.965 → 𝑇𝑡𝑜𝑝 = 65.67 ͦ 𝐶
- Bottom temperature: 𝑥 𝑚,𝑏𝑜𝑡 = 0.005647 → 𝑇𝑏𝑜𝑡 = 98.98 ͦ 𝐶
The binary vapor liquid data tabulated in A.1 are represented graphically by plotting the mole
fraction of methanol, the more volatile component. The obtained y vs. x graph is called
McCabe-Thiele diagram.

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Figure A.2: McCabe-Thiele diagram for methanol water at 1 atm.

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Appendix B: Physical Properties for Methanol and Water
The physical data used in this report are obtained from references [3] and [4].
Molecular weight
For methanol: 32.04 g/mol
For water: 18.015 g/mol
Heat capacities
For methanol: 𝐶 𝑝𝐿 = 75.86 + 0.1683 𝑇
𝐽
𝑚𝑜𝑙 ͦ 𝐶
𝐶 𝑝𝑣 = 42.93 + 0.08301 𝑇 − 1.87 × 10−5
𝑇2
− 8.03 × 10−9
𝑇3 𝐽
𝑚𝑜𝑙 ͦ 𝐶
For water: 𝐶 𝑝𝐿 = 75.4
𝐽
𝑚𝑜𝑙 ͦ 𝐶
𝐶 𝑝𝑣 = 33.46 + 0.006880𝑇 + 0.7604 × 10−5
𝑇2
− 3.593 × 10−9
𝑇3 𝐽
𝑚𝑜𝑙 ͦ 𝐶
Latent heat of vaporization
For methanol: λ = 35.27 kJ/mol at boiling point
For water: λ = 40.656 kJ/mol at boiling point
For steam: ∆𝐻𝑣𝑎𝑝,𝑠 = 2676
𝑘𝐽
𝑘𝑔
= 48.208 𝑘𝐽/𝑚𝑜𝑙
Density
For liquid density: 𝜌𝐿,𝑓𝑒𝑒𝑑 = 954.72
𝑘𝑔
𝑚3 𝜌𝐿,𝑡𝑜𝑝 = 799.17
𝑘𝑔
𝑚3 𝜌𝐿,𝑏𝑜𝑡 = 997.37
𝑘𝑔
𝑚3
For vapor density: 𝜌 𝑣,𝑓𝑒𝑒𝑑 = 0.808
𝑘𝑔
𝑚3 𝜌 𝑣,𝑡𝑜𝑝 = 1.134
𝑘𝑔
𝑚3 𝜌 𝑣,𝑏𝑜𝑡 = 0.59
𝑘𝑔
𝑚3
The calculations are detailed in Excel Spreadsheet [sheet 1]. The vapor and liquid densities
are calculated at the feed, top and bottom of the column.

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Appendix C: Column Calculations
Methanol, designated by the index m, is the more volatile component. Thus, the most of it
will appear in the distillate while water, designated by the index w, will accumulate in the
bottom. The design calculations fit a production rate of 100,000 tons per year of 98% pure
methanol.
Figure C.1: Distillation column
The given data are the following:
- Feed F:
 Saturated liquid q = 1
 𝑧 𝑚 = 0.18 𝑤𝑡
- Distillate D:
 Production rate D= 100,000 tones/year
 𝑥 𝑚.𝑑𝑖𝑠𝑡 = 𝑥 𝐷 = 0.98 𝑤𝑡
- Bottom B:
 𝑥 𝑚,𝑏𝑜𝑡 = 𝑥 𝐵 = 0.01 𝑤𝑡
- Total condenser:
 𝑦 𝑚,1 = 𝑥 𝑚,𝑑𝑖𝑠𝑡 = 𝑥 𝐷
- Partial reboiler

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Convert to molar units
The general form applied for all the given data is the following:
𝑥 𝑚 [ 𝑚𝑜𝑙 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛] =
𝑥 𝑚[𝑤𝑡]
𝑀𝑊𝑚
(
𝑥 𝑚[𝑤𝑡]
𝑀𝑊𝑚
) + (
𝑥 𝑤[𝑤𝑡]
𝑀𝑊𝑤
)
𝐷 [
𝑘𝑚𝑜𝑙
ℎ
] =
𝐷 [
𝑘𝑔
ℎ
]
𝑀𝑊𝐷
̅̅̅̅̅̅̅
𝑤ℎ𝑒𝑟𝑒 𝑀𝑊𝐷
̅̅̅̅̅̅̅ = 𝑥 𝑚,𝑑𝑖𝑠𝑡 × 𝑀𝑊𝑚 + 𝑥 𝑤,𝑑𝑖𝑠𝑡 × 𝑀𝑊𝑤
Thus the mol fraction in the distillate, bottom and feed are:
𝑥 𝐷 = 0.965
𝑥 𝐵 = 0.005647
𝑧 𝑚 = 0.1098
The distillate rate is equal to 100,000 tons/year which is equivalent to 11 415.52 kg/h.
applying the conversion equation 𝐷 =
11415.52
31.55
= 361.823 𝑘𝑚𝑜𝑙/ℎ
Material balance
- Overall material balance:
𝐹 = 𝐵 + 𝐷
- Methanol balance:
𝐹 𝑧 𝑚 = 𝐵 𝑥 𝐵 + 𝐷 𝑥 𝐷
Thus, solving these two equations with two unknowns gives:
𝐹 = 3 332.76 𝑘𝑚𝑜𝑙/ℎ
𝐵 = 2970.936 𝑘𝑚𝑜𝑙/ℎ

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Minimum number of trays
For this separation, the minimum number of stages required is obtained at total reflux using
two methods:
- McCabe-Thiele construction method:
The graphical construction is illustrated on the Excel Spreadsheet [Sheet 1]. The
procedure adopted in stepping off stages from the total condenser is:
 Starting point 𝑥 𝐷 = 𝑦 𝑚,1 = 0.965 and then 𝑥 𝑚,1 is found by interpolating
from the VLE data according to ref [2]: 𝑥 = 𝑥 𝑏𝑒𝑙𝑜𝑤 +
(𝑥 𝑎𝑏𝑜𝑣𝑒−𝑥 𝑏𝑒𝑙𝑜𝑤)(𝑦−𝑦 𝑏𝑒𝑙𝑜𝑤)
𝑦 𝑎𝑏𝑜𝑣𝑒−𝑦 𝑏𝑒𝑙𝑜𝑤
 The y = x line is used then where 𝑦 𝑚,𝑗+1 = 𝑥 𝑚,𝑗
The diagram is illustrated in figure C.3 where we can read that 𝑁 𝑚𝑖𝑛 = 6 𝑠𝑡𝑎𝑔𝑒𝑠
- Fenske equation:
For binary mixture, Fenske equation is as follow
𝑁 𝑚𝑖𝑛 =
ln((
𝑥 𝑚,𝑑𝑖𝑠𝑡
𝑥 𝑤,𝑑𝑖𝑠𝑡
)/(
𝑥 𝑚,𝑏𝑜𝑡
𝑥 𝑤,𝑏𝑜𝑡
))
ln 𝛼 𝑚−𝑤
The relative volatility for methanol water is estimated using the geometric average.
The calculations are detailed in the Excel Spreadsheet [Sheet 3] and it’s is assumed to
be constant: 𝛼 𝑚−𝑤 = 4.44
 𝑁 𝑚𝑖𝑛 = 5.68 𝑠𝑡𝑎𝑔𝑒𝑠
Minimum reflux ratio
- McCabe-Thiele construction method:
The minimum reflux ratio is related to an infinite number of stages. Thus, the
construction method requires that the intersection of the rectifying line and the feed
line occurs at the pinch point A (0.1098; 0.4374) as shown in figure C.3.
Feed is saturated liquid  vertical q-line
Rectifying line  𝑦 =
𝑅 𝑚𝑖𝑛
𝑅 𝑚𝑖𝑛+1
𝑥 +
1
𝑅 𝑚𝑖𝑛+1
𝑥 𝐷
𝑠𝑙𝑜𝑝𝑒 = 0.617 =
𝑅 𝑚𝑖𝑛
𝑅 𝑚𝑖𝑛+1
 𝑅 𝑚𝑖𝑛 = 1.61

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- Underwood equation
The first Underwood equation is used to find the value of 𝜑
∆𝑉𝑓𝑒𝑒𝑑 = 𝑉 𝑚𝑖𝑛 − 𝑉̅ 𝑚𝑖𝑛 = 𝐹(1 − 𝑞) = ∑
𝛼𝑖−𝑟𝑒𝑓 𝐹 𝑧𝑖
𝛼𝑖−𝑟𝑒𝑓 − 𝜑
2
𝑖=0
The second Underwood equation is used to find 𝑉 𝑚𝑖𝑛
𝑉 𝑚𝑖𝑛 = ∑
𝛼𝑖−𝑟𝑒𝑓 𝐷 𝑥𝑖,𝑑𝑖𝑠𝑡
𝛼𝑖−𝑟𝑒𝑓 − 𝜑
2
𝑖=0
Then,
𝐿 𝑚𝑖𝑛 = 𝑉 𝑚𝑖𝑛 − 𝐷
 𝑅 𝑚𝑖𝑛 =
𝐿 𝑚𝑖𝑛
𝐷
Water is the reference components, so 𝛼 𝑚−𝑤 = 4.44 and 𝛼 𝑤−𝑤 = 1
Using the Excel Spreadsheet [Sheet 3], the calculation results are the following:
Figure C.2: Fenske and Underwood calculation
 𝑹 𝒎𝒊𝒏 = 𝟐. 𝟓

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Figure C.3: McCabe-Thiele diagram for 𝑵 𝒎𝒊𝒏 and 𝑹 𝒎𝒊𝒏

23. 23 | P a g e
Actual reflux ratio
Our design will be based on a reflux ratio of 1.25 𝑅 𝑚𝑖𝑛 => 𝑅 = 1.25 × 1.6 = 2
Actual number of trays
- McCabe-Thiele construction method:
The rectifying line equation is
𝑦 =
𝑅
𝑅 + 1
𝑥 +
1
𝑅 + 1
𝑥 𝐷 = 0.6638𝑥 + 0.324
The stripping line equation is
𝑦 =
𝐿̅
𝑉̅
𝑥 −
𝐵
𝑉̅
𝑥 𝐵
Since the feed is saturated liquid  𝑉 = 𝑉̅
From the reflux ratio  𝐿 = 𝑅 × 𝐷 = 2 × 361.283 = 723.646 𝑘𝑚𝑜𝑙/ℎ
Then, 𝑉 = 𝐿 + 𝐷 = 723.646 + 361.823 = 1085.469 𝑘𝑚𝑜𝑙/ℎ
And 𝐿̅ = 𝐿 + 𝑞 𝐹 = 723.646 + 3332.76 = 4056.406 𝑘𝑚𝑜𝑙/ℎ
 𝑦 = 3.737 𝑥 − 2.737
The graphical construction is illustrated on the Excel Spreadsheet [Sheet 2]. The
procedure adopted in stepping off stages from the condenser is:
 Starting point 𝑥 𝐷 = 𝑦 𝑚,1 = 0.965 and then 𝑥 𝑚,1 is found by interpolating
from the VLE data according to ref [2]: 𝑥 = 𝑥 𝑏𝑒𝑙𝑜𝑤 +
(𝑥 𝑎𝑏𝑜𝑣𝑒−𝑥 𝑏𝑒𝑙𝑜𝑤)(𝑦−𝑦 𝑏𝑒𝑙𝑜𝑤)
𝑦 𝑎𝑏𝑜𝑣𝑒−𝑦 𝑏𝑒𝑙𝑜𝑤
 Top operating line is used then to calculate 𝑦 𝑚,𝑗+1 until we reach the feed
stage.
 Bottom operating line is then used to calculate 𝑦 𝑚,𝑗+1 until 𝑥 𝑤,𝑗+1 > 𝑥 𝑤,𝑏𝑜𝑡
The result in figure C.4 is 12 stages including the reboiler and the feed tray is at
stage 8 from the condenser.

24. 24 | P a g e
Figure C.4: McCabe-Thiele diagram at finite reflux ratio

25. 25 | P a g e
- Gilliland correlations
We have 𝑁 𝑚𝑖𝑛 = 5.68 and 𝑅 𝑚𝑖𝑛 = 1.6 and R = 2
 The abscissa 𝑥 =
𝑅−𝑅 𝑚𝑖𝑛
𝑅+1
= 0.133
 From the correlation
𝑁−𝑁 𝑚𝑖𝑛
𝑁+1
= 0.545827 − 0.591422𝑥 +
0.002743
𝑥
= 0.487
 N = 12.03 stages
The optimum feed tray location is found as follow
𝑁𝐹,𝑚𝑖𝑛 =
ln
𝑥 𝑚,𝑑𝑖𝑠𝑡 /𝑥 𝑤,𝑑𝑖𝑠𝑡
𝑧 𝑚/𝑧 𝑤
ln 𝛼 𝑚−𝑤
= 3.628
 𝑁𝐹 = 𝑁
𝑁 𝐹,𝑚𝑖𝑛
𝑁 𝑚𝑖𝑛
= 7.688 𝑠𝑡𝑎𝑔𝑒

26. 26 | P a g e
Appendix D: Duties of Condenser and Reboiler
The calculations are found on Excel Spreadsheet [Sheet 4].
Assume a reference temperature for methanol 𝑇𝑟𝑒𝑓 = 64.5 ͦ 𝐶 and for water 𝑇𝑟𝑒𝑓 = 100 ͦ 𝐶.
Total condenser
The energy balance around the condenser:
𝑉1 𝐻1 + 𝑄𝑐 = 𝐷ℎ 𝐷 + 𝐿0ℎ0
 𝑄𝑐 = (1 +
𝐿0
𝐷
) 𝐷(ℎ 𝐷 − 𝐻1)
Since the reflux is saturated liquid:
𝐻1 − ℎ 𝐷 = 𝜆 𝑚
Thus, 𝑄𝑐 = −(1 + 𝑅) 𝐷 𝜆 𝑚 = −38.28 × 106
𝑘𝐽/ℎ
Partial reboiler
The energy balance around entire column:
𝐹ℎ 𝐹 + 𝑄𝑐 + 𝑄 𝑅 = 𝐷ℎ 𝐷 + 𝐵ℎ 𝐵
 𝑄 𝑅 = 𝐷ℎ 𝐷 + 𝐵ℎ 𝐵 − 𝐹ℎ 𝐹 − 𝑄𝑐
 For the feed
ℎ 𝐹 = 𝑧 𝑚 𝐶 𝑝,𝐿,𝑚(𝑇𝐹 − 𝑇𝑟𝑒𝑓) + 𝑧 𝑤 𝐶 𝑝,𝐿,𝑤(𝑇𝐹 − 𝑇𝑟𝑒𝑓)
From appendix A, the feed temperature is 𝑇𝐹 = 87 ͦ 𝐶
From appendix B, the heat capacities are found at
𝑇𝑎𝑣𝑔,𝑚 =
64.5+87
2
= 75.75 ͦ 𝐶 𝑎𝑛𝑑 𝑇𝑎𝑣𝑔,𝑤 =
100+87
2
= 93.5 ͦ 𝐶
 ℎ 𝐹 = 1383.74 𝐽/𝑚𝑜𝑙

27. 27 | P a g e
 For the distillate
ℎ 𝐷 = 𝑥 𝐷 𝐶 𝑝,𝐿,𝑚(𝑇𝑑𝑖𝑠𝑡 − 𝑇𝑟𝑒𝑓,𝑚)
From appendix A, the top temperature is 𝑇𝑑𝑖𝑠𝑡 = 65.67 ͦ 𝐶
From appendix B, the heat capacity 𝐶 𝑝,𝐿,𝑚 is found at 𝑇𝑎𝑣𝑔,𝑚 =
64.5+65.67
2
= 65.085 ͦ 𝐶
 ℎ 𝐷 = 98 𝐽/𝑚𝑜𝑙
 For the bottom
ℎ 𝐵 = 𝑥 𝐵 𝐶 𝑝,𝐿,𝑤(𝑇𝑏𝑜𝑡 − 𝑇𝑟𝑒𝑓,𝑤)
From appendix A, the bottom temperature is 𝑇𝑏𝑜𝑡 = 98.98 ͦ 𝐶
From appendix B, the heat capacity 𝐶 𝑝,𝐿,𝑤 = 75. 4 𝐽/𝑚𝑜𝑙 ͦ 𝐶
 ℎ 𝐵 = −76.47 𝐽/𝑚𝑜𝑙
Thus, 𝑄 𝑅 = 37.63 × 106
𝑘𝐽/ℎ
Saturated steam rate
It is calculated from:
𝑚 𝑠 =
𝑀𝑠 𝑄 𝑅
∆𝐻𝑣𝑎𝑝,𝑠
=
18.015 × 37.63 × 106
48.208
= 14 062 𝑘𝑔/ℎ
Cooling water rate
Assume that the available cooling water is at 22 ͦ C and the outlet temperature from the
condenser is 35 ͦ C. The rate is calculated from:
𝑚 𝑐𝑤 =
𝑄𝑐
𝐶 𝑝,𝐻2 𝑂( 𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛)
=
38.28 × 106
4.19(35 − 22)
= 702 772 𝑘𝑔/ℎ

28. 28 | P a g e
Appendix E: Size Calculation
The top and bottom diameter calculation of the column are to be found in this appendix. The
column diameter is selected in order to avoid flooding.
Our design is based on 32 cm tray spacing which is equivalent to 1 ft. The calculations are
done on Excel Spreadsheet [Sheet 5].
Top column diameter
A set of equations is used in order to evaluate the required parameters for diameter
calculation:
- The flooding velocity 𝑢 𝑓 = 𝐾√
𝜌 𝐿−𝜌 𝑣
𝜌 𝑣
in ft/s
- The constant K is calculated in ft/s using a correlation according to reference [5]
𝐾 =
0.26𝑡−0.029𝑡2
√1+6𝐹𝐿𝑉
2 𝑡0.7498
where tray spacing t = 1ft.
- The flow parameter 𝐹𝐿𝑉 =
𝐿 𝑤
𝑉 𝑤
√
𝜌 𝑣
𝜌 𝐿
- The liquid mass flow rate 𝐿 𝑤 = 𝐿 × 𝑀𝑊𝑑𝑖𝑠𝑡
̅̅̅̅̅̅̅̅̅̅ in kg/s
- The vapor mass flow rate 𝑉𝑤 = 𝑉 × 𝑀𝑊𝑑𝑖𝑠𝑡
̅̅̅̅̅̅̅̅̅̅ in kg/s
- The vapor density at the top is the average 𝜌 𝑣 =
𝜌 𝑣,𝑓𝑒𝑒𝑑+𝜌 𝑣,𝑡𝑜𝑝
2
in kg/mᶟ
- The liquid density at the top is the average 𝜌𝐿 =
𝜌 𝐿,𝑓𝑒𝑒𝑑+𝜌 𝐿,𝑡𝑜𝑝
2
in kg/mᶟ
See appendix B for the values of vapor and liquid densities.
- The vapor volumetric flow rate 𝑉𝑉 =
𝑉 𝑤
𝜌 𝑣
in mᶟ/s
- The top column area 𝐴 𝑡𝑜𝑝 =
𝑉 𝑉
0.85 𝑢 𝑓
in m²
- The top column diameter 𝐷𝑡𝑜𝑝 = √
4 𝐴 𝑡𝑜𝑝
𝜋
in m
The obtained values are tabulated in table E.1

29. 29 | P a g e
Bottom column diameter
Same analysis and equations are applied. However since the feed is saturated liquid and the
CMO are valid, some considerations are to be taken in the stripping section:
Figure E.1: feed section
 𝐿 𝑤 = 𝐿 + 𝐹
 𝑉𝑤 = 𝑉
The set of equations is similar to the one applied for the calculation of top diameter where:
- The vapor density in the bottom is the average 𝜌 𝑣 =
𝜌 𝑣,𝑓𝑒𝑒𝑑+𝜌 𝑣,𝑏𝑜𝑡
2
in kg/mᶟ
- The liquid density in the bottom is the average 𝜌𝐿 =
𝜌 𝐿,𝑓𝑒𝑒𝑑+𝜌 𝐿,𝑏𝑜𝑡
2
in kg/mᶟ
See appendix B for the values of vapor and liquid densities.
- The liquid volumetric flow rate 𝐿 𝑉 =
𝐿 𝑤
𝜌 𝐿
in mᶟ/s
- The bottom column area 𝐴 𝑏𝑜𝑡 =
𝐿 𝑉
0.85 𝑢 𝑓
in m²
- The bottom column diameter 𝐷 𝑏𝑜𝑡 = √
4 𝐴 𝑏𝑜𝑡
𝜋
in m
The obtained values are tabulated in table E.1

30. 30 | P a g e
The results for all the calculations are shown in table E.1
Unit Top Bottom
𝝆 𝑳 kg/mᶟ 876.945 976.045
𝝆 𝒗 kg/mᶟ 0.971 0.7
𝑳 𝒘 kg/s 6.34 20.38
𝑽 𝒘 kg/s 9.51 5.45
𝑭 𝑳𝑽 0.02 0.1
𝑲 ft/s 0.230 0.224
𝒖 𝒇 ft/s 6.92 8.38
𝑽 𝑽 mᶟ/s 9.8
𝑳 𝑽 mᶟ/s 4.15
𝑨 𝒄 m² 1.66 0.58
𝑫 m 1.45 0.86
Table E.1: Size calculation results