Sustainable production of Acrylic Acid
Distillation columns D-102 and D-103
CHEN30022: Design Project – Part 2
Adekola Adeoye
10191915
Group MT
April 2021
Table of Contents
1.
Introduction .............................................................................................................................................. 4
1.1 Design objectives and constraints .......................................................................................................... 4
1.2 Equipment Selection ............................................................................................................................... 5
1.3 Operating Conditions .............................................................................................................................. 5
1.3.1 Operating Pressure .......................................................................................................................... 5
1.3.2 Operating Temperature ................................................................................................................... 7
2. Short-cut Method ......................................................................................................................................... 8
2.1 Relative Volatility.................................................................................................................................... 8
2.2 Fenske Equation ...................................................................................................................................... 8
2.3 Underwood Equations ............................................................................................................................ 9
2.4 Gilliland Equation.................................................................................................................................... 9
2.5 Kirkbride Correlation .............................................................................................................................. 9
3.Rigorous simulation and Optimisation study ............................................................................................. 10
3.1 Fluid package selection ......................................................................................................................... 10
3.2 Optimum number of stages.................................................................................................................. 10
3.2.1 Capital cost ..................................................................................................................................... 10
3.2.2 Equipment sizing ............................................................................................................................ 11
3.2.3 Operating costs .............................................................................................................................. 12
3.3 Optimisation Analysis results ............................................................................................................... 13
3.3.1 Optimum feed stage location ........................................................................................................ 14
3.3.2 Optimum feed temperature .......................................................................................................... 15
4. Material and Energy Balances .................................................................................................................... 16
4.1 Material balance ................................................................................................................................... 16
4.2 Energy balance ...................................................................................................................................... 17
5. Internal Design ............................................................................................................................................ 17
5.1 Choice of trays or packing .................................................................................................................... 17
5.1.1 Column internals ............................................................................................................................ 18
5.2 Column Diameter .................................................................................................................................. 18
5.2.1 Flooding velocity ............................................................................................................................ 19
5.2.2 Liquid flow pattern ........................................................................................................................ 20
5.2.3 Provisional plate design................................................................................................................. 21
5.2.4 Weeping check ............................................................................................................................... 21
5.2.5 Plate pressure drop........................................................................................................................ 22
5.2.6 Downcomer design ........................................................................................................................ 23
5.2.7 Entrainment check ......................................................................................................................... 24
5.2.8 Perforated area .............................................................................................................................. 24
5.2.9 Plate efficiency ............................................................................................................................... 25
6. Mechanical Design ...................................................................................................................................... 25
6.1 Choice of material ................................................................................................................................. 25
6.2 Minimum wall thickness and critical pressure .................................................................................... 26
6.3 Choice of end closures .......................................................................................................................... 26
6.4 Stress Analysis ....................................................................................................................................... 26
6.4.1 Dead weight stress......................................................................................................................... 26
6.4.2 Bending stress ................................................................................................................................ 27
6.4.3 Pressure stress ............................................................................................................................... 28
6.4.4 Principal stress ............................................................................................................................... 28
6.4.5 Elastic stability check ..................................................................................................................... 28
6.5 Column Skirt .......................................................................................................................................... 29
7. Ancillary Design........................................................................................................................................... 29
7.1 Condenser, Reboiler and Cooler H-107 ................................................................................................ 30
7.2 Reflux Drum .......................................................................................................................................... 30
7.3 Reflux Pump .......................................................................................................................................... 30
7.4 Vacuum Pump ....................................................................................................................................... 30
8. Economic Analysis ....................................................................................................................................... 31
9. Safety........................................................................................................................................................... 32
10. Conclusion ................................................................................................................................................. 32
11. Specification Sheet ................................................................................................................................... 33
12. References ................................................................................................................................................. 34
DECLARATION
No part of the work referred to in this report has been submitted in support of an application for any
degree or other qualification at this, or any other university, or institute of learning.
Abstract
This report focuses on the chemical engineering design of vacuum distillation column, D-102, and standard
distillation column, D-103, as well as its ancillaries. Chemical engineering methods and software were used
throughout the report for modelling of the design of the rigorous columns, in order to appropriately
determine the overall costs and efficiencies. The rigorous model was further optimised prior to final
costing. An internal and mechanical design was conducted on the systems, to ensure a safe and feasible
operation. The optimised total annualised cost of the units was found to be approximately $2.3 million yr-1
and $740,000 yr-1.
1. Introduction
The purpose of this report is to provide a detailed, thorough analysis and optimisation of distillation
columns D-102 and D-103, including the internal and mechanical design of the columns as well as the
ancillaries and other pieces of equipment. Following this evaluation and optimisation of the column
designs, a sensitivity analysis will be performed on the columns and, the subsequent operating and capital
costs will be estimated.
The first column that will be designed in this report is distillation column D-102. A visual diagram is shown
in Figure 1. D-102 is the final column in the crude glycerol purification area, which will further purify the
crude glycerol from the bottoms of the first column, D-101. Glycerol is raw material needed to produce
acrylic acid, via a series of two reactions. The first reaction is glycerol to acrolein, which is facilitated in
reactor, R-101; and the second is acrolein to acrylic acid, which occurs in reactor, R-102. Therefore, the
design of this column is crucial to produce the desired intermediate, to hence ensure the sustainable
production of acrylic acid. After receiving the bottoms of D-101, this column will then separate out glycerol
from sulfuric acid to produce a highly-pure glycerol top product, a bottom product containing the other
impurities.
The next column that will be designed in this report is distillation column D-103. D-103 is employed to
recover the intermediate product, acrolein, so it can further react to produce the desired chemical, acrylic
acid. Also, it is employed to remove excess water to reduce volume sizes and molar flows for the
subsequent unit operations, lowering capital costs of the whole process plant. Column D-103 will receive
the effluent of reactor R-101, after it has been passed through condenser H-107. As stated in part 1 of the
report, the condenser will cool the vapour down to produce a mixed two-phase, liquid-gas flow, which is
then fed to D-103. This column will then produce a vapour distillate product, and a liquid bottoms product.
The top mainly consists of: acrolein, light gases (e.g. hydrogen, nitrogen, oxygen and carbon dioxide) and
some water, and the bottom product mainly comprises of the removed excess water. A diagram of this
process is shown in Figure 2.
Figure 1: Flow diagram of column D-102
Figure 2: Flow diagram of column D-103
1.1 Design objectives and constraints
As stated above, the design objective of this report is to provide a detailed chemical and mechanical
engineering design of distillation columns D-102 and D-103, and the surrounding equipment such as the
attached condensers and reboilers. The design objective of D-102 is such that there should be a goal of 99.9
mol% glycerol recovery in the distillate, so as to minimise the wastage of the raw material, and, as a result,
maximise the economics of the acrylic acid production process. From Part 1, the design objective of D-103
is the complete recovery of acrolein to the vapour top product, and 80 mol% water recovery to the
bottoms. When it comes to designing the distillation column there are a number of constraints that must
also be considered;
•
•
Control measures – the design must be able to easily respond to disturbances in the feed or in the
operating conditions of the column in order to continue operating at optimum conditions to ensure
the best separation is carried out.
Inherent safety of the design – the column must be designed in such a way that all potential hazards
are minimised following the as low as reasonably possible (ALARP) principle.
1.2 Equipment Selection
D-102
Table 1: Boiling points of various compounds at atmospheric pressure
Compound name
FAME (Methyl
Oleate)
Sulfuric Acid
Glycerol
Boiling point
351.4 ℃ [1]
337 ℃
290 ℃
[2]
[3]
As seen from Table 1, the components involved in the separation have very high boiling points at
atmospheric pressure. High-pressure (HP) steam is available at a maximum pressure of 40 bar, which
corresponds to a maximum reboiler temperature of 240 ℃ (assuming a minimum temperature difference
of 10 ℃). Therefore, vacuum distillation needs to be employed in order to lower boiling points of the
compounds, and keep the reboiler temperature below 240℃. In fact, vacuum distillation is the
conventional technology used for this separation [4]. For this separation; glycerol will be selected as the
light key (LK) because glycerol is the necessary raw material for the process to operate, and sulfuric acid will
be the heavy key (HK) because it has the next lowest boiling point and is the second most abundant
component, thus selecting this component will improve the separation efficiency.
D-103
Acrolein has a boiling point of 53℃ [3], which is significantly lower compared to the boiling point of water
of 100 ℃. This suggests that a flash separator could be implemented to exploit the vapour pressure
differences between the components. However, when this was simulated on Aspen HYSYS, it was found to
be extremely inefficient compared to a distillation column. Thus, a distillation column will be used, as
originally modelled in Part 1. A partial condenser will be employed, instead of a total condenser, due to the
presence of non-condensable compounds such as carbon dioxide, hydrogen, oxygen and nitrogen. For this
column; acrolein will be chosen to be the light key because the purpose of the column is to fully recover the
acrolein, and water will be the heavy key as the secondary objective is to remove excess water. Selecting
these two compounds as the key components will meet the objective of the column.
1.3 Operating Conditions
1.3.1 Operating Pressure
D-102
The operating pressure of a column is a critical parameter that needs to be selected, as the operating
pressure can affect the whole process. Generally speaking, as the pressure decreases, the relative volatility
increases and the minimum number of stages decreases. However, as the vessel is operating under
vacuum, the lower pressure, the more susceptible it is to implosion. This is because there’s a greater
pressure difference inside and outside the column. Also, additional costs are incurred when maintaining a
vessel under lower vacuum pressures. Therefore, there needs to be a balance between the safety of the
column, the cost and the ease of separation. The mean relative volatilities and the reboiler temperatures
were recorded at various column pressures using equations from Sections 1.3 and 2.1 to determine the
optimum pressure.
Table 2: Mean relative volatilities and reboiler temperature at different column pressures
Mean relative volatility, (αi,j )mean
Column pressure, P (kPa)
3
Water
Glycerol (LK)
Sulfuric Acid (HK)
FAME (Methyl Oleate)
Salt (NaCl)
Reboiler temperature (℃)
5
6
7
10
1059.7
832.8
765.0
712.4
604.5
2.38
2.64
2.73
2.80
2.95
1
1
1
1
1
0.72
0.74
0.75
0.76
0.77
1.88×10-15
5.57×10-15
8.17×10-15
1.13×10-14
2.36×10-14
216.8
230.9
236.1
240.7
251.6
As it can be seen from Table 2, there is no benefit from operating under lower vacuum pressures, contrary
to what was expected. This could because at lower pressures, the differences in saturated temperature
diminishes, hence a decreasing mean relative volatility between the light and heavy key components. The
optimum pressure for this column would be 6 kPa, as this is the maximum pressure at which the column
can operate, while still having a reboiler temperature below 240℃ . However, this produced a reboiler
temperature greater than 240 ℃ in the rigorous simulation on Aspen HYSYS, therefore the pressure was
changed to 5 kPa. In crude distillation, pressures as low as 1.3 kPa are used [5], therefore it is technically
feasible to operate at 5 kPa.
D-103
A similar analysis was conducted for column D-103, the column pressure was varied from the reactor
effluent at 280 kPa to atmospheric pressure at 101.325 kPa to determine the effect on the mean relative
volatility, and thus select the optimum pressure. Operating under vacuum could result in an easier
separation, however, the need for a vacuum pump can be quite expensive, therefore it wasn’t considered.
Table 3: Mean relative volatilities at different column pressures for D-103
Mean relative volatility, (𝛼𝑖,𝑗 )𝑚𝑒𝑎𝑛
Column pressure, P (kPa)
280
200
101.325
Oxygen
737.95
867.47
1199.86
Nitrogen
792.47
936.29
1308.15
Hydrogen
721.66
868.7
1259.7
Carbon dioxide
188.13
211.20
266.6
Acetaldehyde
8.89
9.53
10.97
Acrolein (LK)
3.66
3.86
4.30
1
1
1
0.25
0.24
0.23
Glycerol
1.82×10-5
9.80×10-6
2.33×10-6
Sulfuric acid
1.25×10-4
1.04×10-4
7.19×10-5
Water (HK)
Acetol
5.26×10-5
Methyl Oleate
4.11×10-5
2.47×10-5
From Table 3, it is obvious to note that as the column pressure decreases, the mean relative volatility
increases. This is expected because; in the pressure ranges, the differences in saturated temperatures are
large, hence an increasing relative volatility. Distillation column D-103 will operate under atmospheric
pressure, as the mean relative volatility is the greatest. Consequently, a pressure drop will be incorporated
in the design of H-107.
1.3.2 Operating Temperature
The operating temperature is another critical parameter that needs determined, as this affects the type of
utility to be used, and hence the utility costs. In the case of D-102; a total condenser and a partial reboiler is
being employed, therefore the bubble and the dew points of their streams were calculated to determine the
temperatures respectively. The inlet stream to D-102 will be a saturated liquid, therefore the bubble point
of the stream needs to be calculated. For D-103; only the dew points were calculated, as a partial condenser
is being employed. The feed to D-103 is a vapour-liquid mixture, therefore no condition needs to be
calculated. Instead, a preliminary feed temperature of 70℃ was selected, this will later be optimised in
Section 3.3.2. It is important to note that the temperatures and pressures of any stream are interlinked,
therefore the temperatures were determined once the pressure had been selected. This was an iterative
process.
The vapour pressures, 𝑃𝑠𝑎𝑡 , were calculated for each component using the Antoine equation (Eq. 1), where
A, B and C are constants and were obtained from Yaws’ Handbook [6].
𝐵
log10 𝑃𝑠𝑎𝑡 = 𝐴 − 𝑇+𝐶
(Eq. 1)
The equilibrium constant, 𝐾𝑖 , were calculated for each component using knowledge of the selected column
pressure, P.
𝐾𝑖 =
𝑃𝑠𝑎𝑡
𝑃
(Eq. 2)
To calculate the bubble points, the mole fractions of each component were multiplied by their respective
equilibrium constants as shown in (Eq. 4). Using Excel Add-in Solver, the temperature of the stream was
varied until the summation was equal to unity.
𝐵𝑢𝑏𝑏𝑙𝑒 𝑝𝑜𝑖𝑛𝑡: ∑ 𝐾𝑖 𝑥𝑖 = ∑ 𝑦𝑖 = 1
(Eq. 4)
A similar process was utilised to calculate the dew points, the mole fractions of each component were
divided by their respective equilibrium constants as indicated by (Eq. 3). Using Excel Add-in Solver, the
temperature of the stream was varied until the summation was equal to unity.
𝑦
𝐷𝑒𝑤 𝑝𝑜𝑖𝑛𝑡: ∑ 𝐾𝑖 = ∑ 𝑥𝑖 = 1
(Eq. 3)
𝑖
Table 4: Feed, condenser, and reboiler temperatures for columns D-102 and D-103
Distillation column
Feed stream
temperature (℃)
Condenser temperature
(℃)
Reboiler temperature
(℃)
D-102
197.8
196
230.9
D-103
70
63.4
106.5
These values are subject to change depending on the rigorous simulation, but the fact that they strongly
agree with the temperatures calculated in the short-cut simulation on Aspen HYSYS, suggests that the
values are accurate. For both distillation columns, cooling water was chosen as the cold utility because the
temperature of the condenser was well above the cooling water temperature. For column D-102, HP steam
at 40 bar and 250℃ was selected as the hot utility, as intended in Section 1.2. For column D-103, LP steam
at 4 bar and 143℃ was selected for as the hot utility because this is the cheapest utility available that can
meet the heating demand.
2. Short-cut Method
For the design of the distillation columns, short-cut calculations were used as estimates before attempting
a rigorous simulation on Aspen HYSYS. The short-cut method utilises numerous equations to provide good
initial estimates for key variables in column designs such as the minimum number of stages and the
minimum reflux ratio required for the desired separation. The short-cut method assumes the following
information;
•
•
Constant relative volatility- the relative volatility between the components remains constant at
each stage
Constant molar overflow-the molar flowrates for the vapour and liquid is constant at each stage
Whilst these assumptions are vital for the method to work, they do not accurately represent the realistic
design of a distillation column, and hence the short-cut method will only be treated as an estimate. And, as
a consequence, the rigorous simulation on HYSYS may obtain results that differ from the ones found with
this method.
2.1 Relative Volatility
The first step of the short-cut method involves calculating the relative volatilities of the components. To do
this, the saturated vapour pressures were calculated using Eq. 1, and then the equilibrium constants were
calculated for each component using Eq. 2. These values are then used to calculate the relative volatility
using Eq. 5.
𝛼𝑖,𝑗 =
𝐾𝑖
𝐾𝑗
(Eq. 5)
This procedure can then be repeated for the top product stream and the bottom product stream at the
saturated conditions from the column, so that the geometric mean relative volatility can be determined
using Eq. 6
(𝛼𝑖,𝑗 )𝑚𝑒𝑎𝑛 = 3√(𝛼𝑖,𝑗 )𝑓𝑒𝑒𝑑 (𝛼𝑖,𝑗 )𝑡𝑜𝑝 (𝛼𝑖,𝑗 )𝑏𝑜𝑡𝑡𝑜𝑚
(Eq. 6)
The geometric mean is utilised, as it eliminates variance in the relative volatilities throughout the column,
and, thus, allows the assumption of constant relative volatility to become more reliable and valid.
2.2 Fenske Equation
The Fenske Equation (Eq. 7) is used to calculate the minimum number of stages required for the separation
of the light and heavy key components, given the known product compositions. This equation assumes
total reflux (i.e. an infinite reflux ratio)
𝐷 𝐵
log[ 𝐿 𝐻 ]
𝑁𝑚𝑖𝑛 = log(𝛼
𝐷𝐻 𝐵 𝐿
(Eq. 7)
𝐿,𝐻 )𝑚𝑒𝑎𝑛
L and H denote the light and heavy key component, and (𝛼𝐿,𝐻 )𝑚𝑒𝑎𝑛 denotes the relative volatility of the
light key.
Table 4: minimum number of stages for columns D-102 and D-103
Distillation Column
𝑁𝑚𝑖𝑛
D-102
8.89
D-103
5.92
2.3 Underwood Equations
The Underwood equation is used to estimate the minimum reflux ratio. The minimum reflux ratio
corresponds to an infinite number of stages. Eq. 8 was solved iteratively using Excel Add-in Solver to
determine theta, 𝜃, which is then substituted into Eq. 9, where the minimum reflux ratio, 𝑅𝑚𝑖𝑛 , was
calculated. For D-102; saturated feed conditions have been solved for a saturated liquid, therefore, the
feed condition, 𝑞, was determined to be 1. For D-103; the feed condition was taken to be 0.536 by Aspen
HYSYS.
1−𝑞 =∑
(𝛼𝑖,𝑗 )𝑚𝑒𝑎𝑛 𝑧𝐹,𝑖
(Eq. 8)
(𝛼𝑖,𝑗 )𝑚𝑒𝑎𝑛 −θ
𝑅𝑚𝑖𝑛 + 1 = ∑
(𝛼𝑖,𝑗 )𝑚𝑒𝑎𝑛 𝑥𝐷
(Eq. 9)
(𝛼𝑖,𝑗 )𝑚𝑒𝑎𝑛 −θ
Table 5: theta and the minimum reflux ratio for columns D-102 and D-103
Distillation Column
𝜃
𝑅𝑚𝑖𝑛
D-102
1.052
0.426
D-103
1306.4
0.152
The value of ϴ found must usually lie between the mean relative volatility of the light key and heavy key. As
noted in Table 5, this wasn’t the case for D-103, but as this is a preliminary calculation and it yielded a
reasonable minimum reflux ratio, the value was deemed acceptable.
2.4 Gilliland Equation
The Gilliland correlation was used to determine the actual number of theoretical stages. The reflux ratio, R,
was specified to be 1.3 times that of 𝑅𝑚𝑖𝑛 . This was used to determine 𝜑 from Eq. 11, which was then
substituted into Eq. 10 to determine the actual number of stages. The actual number of plates was rounded
up to the nearest whole number.
𝑁−𝑁𝑚𝑖𝑛
𝑁+1
1+54.5𝜑
𝜑−1
= 1 − exp [(11+117.2𝜑) ( 𝜑0.5 )]
(Eq. 10)
Where 𝜑 is defined as,
𝜑=
𝑅−𝑅𝑚𝑖𝑛
𝑅+1
(Eq. 11)
Table 6: Actual reflux ratio, 𝜑 and the actual number of theoretical stages for columns D-102 and D-103
Distillation column
R
𝜑
N
D-102
0.554
0.0822
23
D-103
0.198
0.0382
18
2.5 Kirkbride Correlation
The Kirkbride correlation was used to determine the optimal equilibrium stage for the feed to enter using
the compositions of the key components in the feed and products, and total product flow rates. It is
important to note that the actual number of stages takes into account a partial stage, therefore it was
subtracted by the number of partial stages, n, to determine the actual number of plates in the column as
indicated by Eq. 13. The feed enters the column in the last stage of the rectifying section.
𝑁
𝐵
𝑥
𝑥
2
Log 𝑁𝑟 = 0.206 log[(𝐷) ( 𝑥𝐻𝐾,𝑓) (𝑥 𝐿𝐾,𝑏 ) ]
𝑠
𝐿𝐾,𝑓
(Eq. 12)
𝐻𝐾,𝑑
𝑁 − 𝑛 = 𝑁𝑟 + 𝑁𝑠
(Eq. 13)
Table 7: number of rectifying, Nr, and stripping stages, Ns, for columns D-102 and D-103
Distillation column
n
𝑁𝑟
𝑁𝑠
Feed tray stage
D-102
1
6
16
6th
D-103
2
2
14
2nd
3.Rigorous simulation and Optimisation study
As mentioned before, the short-cut method is only used to provide the rigorous simulation with some
initial estimates. It is highly unsuitable for the actual design for column. Unlike the short-cut, the rigorous
simulation does not assume constant molar overflow and constant relative volatility, but solves material,
efficiency, summation and energy balances for every single stage, this is known as MESH equations [7].
Hence, the rigorous simulation accounts for the non-idealistic nature of the mixture and gives more
accurate results. For D-102; the objective of the optimisation study is to determine the optimum number of
stages and the feed tray location. For D-103; the objective of the study is to determine the optimum
number of stages, feed tray location and the optimum feed temperature.
3.1 Fluid package selection
In Aspen HYSYS, a fluid package is a thermodynamic model used to calculate the physical properties of
chemicals after undergoing physical and/or chemical transformations during unit operations. The selection
of an appropriate fluid package is critical as the acrylic acid production plant process is predicated on this.
For both columns, D-102 and D-103, the components involved are mainly polar components, therefore
activity coefficient models were chosen as opposed to equations of state. This narrows down the selection
to NRTL, UNIQUAC and Wilson. UNIQUAC was selected for the rigorous simulation, this is because
UNIQUAC is a development on the NRTL model, and utilises group contributions to calculate the activity
coefficients [8], thus it is more accurate.
3.2 Optimum number of stages
When operating at Rmin the operating costs will be at their lowest, however the capital costs will be at their
maximum due to the fact that minimum reflux ratio corresponds to an infinite number of stages. A trade
off needs to be found between the reflux ratio and the number of stages, so that an optimal value can be
obtained that correlates to a minimum total annualised cost (operating costs plus capital costs) for the
distillation columns. The number of stages within the column was altered and the associated reflux ratio,
reboiler and condenser duties were recorded; a preliminary total annualised cost was then be found. In the
case of D-102; the two specifications were the product recovery (99.9 mol%) and the distillate rate (408.5
𝑘𝑚𝑜𝑙 ℎ−1 ), as this is the basis used in Part 1. The column pressure was fixed at 5 kPa and the feed inlet tray
was fixed as being the 4th tray from the top. For D-103; the two specifications were the complete recovery
of acrolein to the top product, and 80 mol% recovery of water to the bottoms, as stated in the design
objectives.
3.2.1 Capital cost
The capital cost includes the column vessel, trays, condenser and reboiler cost. Equation 13 shows the
general equation used to calculate the purchase cost of the different equipment. The following
assumptions were made in the capital cost for the columns;
•
•
The distillation columns will be estimated as a carbon steel pressure vessel
The trays will be sieve trays for column D-103
•
•
Structured packing will be used for column D-102
A U-tube shell & tube and a kettle reboiler were chosen for the preliminary costing of the
condenser and reboiler respectively for both columns
These assumptions were made to simplify the calculations for the capital cost. A detailed analysis on the
types of equipment and material will be further investigated in Section 5 and 6.
𝐶𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 = 𝑎 + 𝑏𝑆 𝑛
(Eq. 14)
Table 8: Size parameters and installation factors for each type of equipment [9]
Equipment
Units for Size,
S
a
b
n
Installation
factor, f
Vertical
pressure vessel
Shell mass, kg
10,000
29
0.85
4
Sieve trays
Diameter, m
110
380
1.8
2.5
Structured
packing
Volume, m3
0
6,900
1.0
4
U-tube shell &
tube
condenser
Area, m2
24,000
46
1.2
3.5
Kettle reboiler
Area, m2
25,000
340
0.9
3.5
The installed cost of the equipment was then calculated using equation 14, where f represents the
respective installation factors of the equipment. The purchase costs are based from the year 2010, hence it
had to be scaled up using the Chemical Engineering Plant Cost Index (CEPCI), as shown by Eq. 16. The
installed cost was scaled up to the year 2020 as that is the latest CEPCI available to date.
𝐶𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 = 𝑓 × 𝐶𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒
(Eq. 15)
𝐶𝐸𝑃𝐶𝐼 2020
𝐶𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑,2020 = 𝐶𝑖𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 × 𝐶𝐸𝑃𝐶𝐼 2010
(Eq. 16)
Where CEPCI 2010 is 532.9 and CEPCI 2020 is 596.2 [10]
The summation of all the equipment’s installed cost is the total capital cost of the plant. In order to
determine the amount that has to be paid out each year until the end of the plant life, the total capital cost
was annualised by using Eq. 17. This amount also includes the interest that was accumulated each year. The
assumptions made were an interest rate, I, of 5% and a plant life, n, of 20 years.
𝑖(1+𝑖)𝑛
𝐴𝑛𝑛𝑢𝑎𝑙𝑖𝑠𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = 𝑇𝑜𝑡𝑎𝑙 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 × (1+𝑖)𝑛 −1
(Eq. 17)
3.2.2 Equipment sizing
Distillation column and sieve tray sizing
The sizing unit of a pressure is its shell mass, hence the length, Lc, and diameter, Dc, of the column had to be
determined. A plate spacing, lt, of 0.5m was assumed. Using the assumed plate spacing value, the column
length was calculated using Eq. 18. The additional 2 m was put in place to account for the top and bottom
closures of the column.
𝐿𝑐 = (𝑁 × 𝑙𝑡 ) + 2
(Eq. 18)
Using Eq. 19, the maximum allowable superficial vapour velocity, 𝑢̂v, was calculated to ensure that no
calamities occur in the process. The liquid density, ρL, and the vapour density, ρV, were obtained by Aspen
HYSYS.
𝜌𝐿 −𝜌𝑉 0.5
)
𝜌𝑉
û𝑣 = (−0.17𝑙𝑡2 + 0.27𝑙𝑡 − 0.047)(
(Eq. 19)
Using Eq. 20 and the maximum allowable superficial vapour density, the column diameter, Dc, was then
calculated. The diameter calculated was also used as the sizing unit for sieve trays. The vapour mass
flowrate, Vw, was obtained by Aspen HYSYS.
̂𝑤
4𝑉
𝜋𝑢
𝑣 ̂𝑣
𝐷𝑐 = √𝜌
(Eq. 20)
In the preliminary costing, the wall thickness, tw, was assumed to be 10 mm. As the vessel was taken to be a
carbon steel, the density, ρ, was taken to be 7850 kg m-3
𝑠ℎ𝑒𝑙𝑙 𝑚𝑎𝑠𝑠 = 𝜌𝜋𝐷𝑐 𝐿𝑐 𝑡𝑤
(Eq. 21)
It can’t be further stressed that the values assumed were made in order to simplify the preliminary costing.
The tray spacing and the wall thickness will be further analysed in the mechanical design.
Condenser and Reboiler
The costs of the condensers and reboilers are based on the heat transfer area, A, of each equipment. This
was determined from Eq. 22. The log mean temperature difference, ΔTLM, was calculated using Eq. 23. The
following assumptions were made;
•
•
•
•
•
The overall heat transfer coefficient of the condensers is assumed to be 850 W m2 K-1
The overall heat transfer coefficient of the reboiler is assumed to be 1050 W m2 K-1
The inlet cooling water is assumed to be 30℃ and the increase in temperature is 20℃
The minimum approach temperature, ΔTmin, was assumed to be 10℃
Counter-current flow was assumed for both heat exchangers
These assumptions are justified in Section 7.1.
𝑄
𝐴 = 𝑈∆𝑇
(Eq. 22)
𝐿𝑀
∆𝑇𝐿𝑀 =
Where
(𝑇ℎ,𝑖𝑛 −𝑇𝑐,𝑜𝑢𝑡 )−(𝑇ℎ,𝑜𝑢𝑡 −𝑇𝑐,𝑖𝑛 )
𝑇
−𝑇𝑐,𝑜𝑢𝑡
ln( ℎ,𝑖𝑛
)
(Eq. 23)
𝑇ℎ,𝑜𝑢𝑡 −𝑇𝑐,𝑖𝑛
3.2.3 Operating costs
Steam cost
In order to generate high pressure steam required in the reboiler, natural gas is used as a fuel source, which
costs $2.63 mmBTU-1 in the USA [11]. Using Eq. 24 and Eq. 25; this was converted into the price of HP
steam, by assuming a boiler efficiency of 0.8 to determine the fuel requirement, and then multiplying by
the aforementioned price of natural gas. LP steam is usually half the price of HP steam [9].
𝐹𝑢𝑒𝑙 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 =
ℎ𝑤,40𝑏𝑎𝑟 −ℎ𝑤,20℃
0.8
𝐻𝑃 𝑠𝑡𝑒𝑎𝑚 𝑝𝑟𝑖𝑐𝑒 = 𝐹𝑢𝑒𝑙 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡 × 𝑁𝑎𝑡𝑢𝑟𝑎𝑙 𝑔𝑎𝑠 𝑝𝑟𝑖𝑐𝑒
Table 9: Steam pricing results
(Eq. 24)
(Eq. 25)
Specific enthalpy of saturated steam at 40 bar,
ℎ𝑤,40𝑏𝑎𝑟 (kJ kg-1)
2800 [12]
Specific enthalpy of water at 20℃, ℎ𝑤,20℃ (kJ kg-1)
83.95 [12]
Fuel requirement (kJ kg-1)
3395
HP steam price ($ kg-1)
0.00846
LP steam price ($ kg-1)
0.00423
To determine the steam cost of a reboiler, the mass flowrate of steam, 𝑀̇𝑠𝑡𝑒𝑎𝑚 , needs to be calculated first.
Using Eq. 26, and knowing the latent heat of vaporisation of steam, ΔHvap, the mass flowrate of steam was
established. ΔHvap is 1713kJ kg-1 at 40 bar and 2133 kJ kg-1 at 4 bar [12].
𝑄𝑟𝑒𝑏𝑜𝑖𝑙𝑒𝑟
𝑀̇𝑠𝑡𝑒𝑎𝑚 = ∆𝐻
(Eq. 26)
𝑣𝑎𝑝
This was then multiplied by the price of steam and the number of operating hours, which was assumed to
be 8000, to determine the annual cost of steam, as shown by Eq. 27
𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑠𝑡𝑒𝑎𝑚 ($ 𝑘𝑔−1 ) = 𝑀̇𝑠𝑡𝑒𝑎𝑚 × 𝑠𝑡𝑒𝑎𝑚 𝑝𝑟𝑖𝑐𝑒 × 8000
(Eq. 27)
Cooling water cost
Using Eq. 28 and taking the specific heat capacity of water, Cp, to be 4.18 kJ kg-1 K-1[12], the mass flow rate
of cooling water, 𝑀̇𝑐𝑤 , was obtained. As previously mentioned, the temperature difference, ΔT, was 20℃
𝑄
𝑀̇𝑐𝑤 = 𝑐𝑜𝑛𝑑𝑒𝑛𝑠𝑒𝑟
𝐶 ∆𝑇
(Eq. 28)
𝑝
This was then multiplied by the price of cooling water, which is $0.0000575 kg-1 in the USA [13], and the
number of operating hours to calculate the annual cost of cooling water, as indicated by Eq. 29
𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑤𝑎𝑡𝑒𝑟 ($ 𝑦𝑒𝑎𝑟 −1 ) = 𝑀̇𝑐𝑤 × 𝑐𝑜𝑜𝑙𝑖𝑛𝑔 𝑤𝑎𝑡𝑒𝑟 𝑝𝑟𝑖𝑐𝑒 × 8000 (Eq. 29)
3.3 Optimisation Analysis results
Annual costs against the number of stages
Annual costs against the number of stages
8000000
ACC
4500000
7000000
4000000
6000000
Total
operatin
g costs
Total
annualis
ed costs
5000000
4000000
3000000
2000000
Annual Costs ($/year)
Annual costs ($/year)
ACC
5000000
Total
operat
ing
costs
Total
annual
ised
costs
3500000
3000000
2500000
2000000
1500000
1000000
500000
1000000
0
0
9
15
21
27
Number of stages, N
Figure 3: Optimisation of the number of stages with
respect to the annual costs for column D-102
33
39
5
10
15
20
Number of stages, N
Figure 4: Optimisation of number of stages with
respect to the annual costs for column D-103
The number of stages were varied from 9 to 40 and the corresponding capital, operating and total
25
30
annualised costs were recorded to determine the optimum number of stages. It is important to note that
the column failed to converge below 9 stages, suggesting the minimum number of stages is indeed 9, and
thus the short-cut method provided an accurate estimate. As shown in Figure 2; the capital cost remained
relatively constant with a slight increase, because increasing the number of stages decreased the duties of
the reboiler and the condenser, thus decreased their capital costs, and hence the slight increase in the
annualised capital cost. The optimum number of stages was determined to be 18; because after this point,
the savings in the total annualised costs significantly diminishes, and one has to consider the associated
safety issues with a taller column, which is especially important as this column is operating under vacuum.
Therefore, to increase the inherent safety of the column, the number of stages in distillation column D-102
will be 18.
For the investigation of D-103, the number of stages were varied from 6 to 30 and the resulting capital,
operating and total annualised costs were recorded. As visualised in Figure 2, a minimum is produced when
the number of stages is 10. Therefore, the optimum number of trays in distillation column D-103 is 10, as
this corresponds to the minimum annual costs.
3.3.1 Optimum feed stage location
The feed stage location is a critical parameter as it can influence the condenser and reboiler duties. The
feed must enter the column at the tray where its composition is the most similar to that of the liquid on the
tray, thus reducing the energy required for mixing, which contributes to the operating costs. Hence, the
optimum feed stage was determined by changing the location of the feed stage and comparing the
condenser duty, reboiler duty, the reflux ratio, and the key components composition. For both columns,
this was conducted on the optimised number of stages.
D-102
Table 10: Optimisation of the feed tray location results for column D-102
Feed tray
location
Glycerol mole
fraction in tray
Sulfuric acid
mole fraction
in tray
Reflux ratio
Condenser
duty, kW
Reboiler duty,
kW
8
0.9154
0.06829
1.308
9980
10010
9
0.9109
0.07260
1.267
9803
9833
10
0.9051
0.07849
1.265
9793
9829
11
0.8959
0.0808
1.291
9906
9943
As shown in Table 10, the optimum feed tray location was the 10th tray from the top, because this results in
the lowest condenser and reboiler duties, and the lowest reflux ratio. It can also be seen that this tray that
matches the feed composition the closest, which is 89.92mol% glycerol and 7.37mol% sulfuric acid. The
optimum feed tray calculated from the Kirkbride correlation was the 6th tray out of 23. The difference
between the short-cut and rigorous simulation could be due to the assumptions made in the short-cut
calculation.
D-103
Table 11: Optimisation of the feed tray location results for column D-103
Feed tray
location
Acrolein
mole
fraction in
tray
Water
mole
fraction in
tray
Reflux ratio
Condenser duty,
kW
Reboiler duty,
kW
2
0.0683
0.8721
2.418
12260
15620
3
0.1761
0.6905
1.953
10017
13180
4
0.1019
0.8148
143.5
1.524 × 105
1.526 × 105
5
7.84
× 10−5
0.9924
2491
1.251 × 107
1.251 × 107
As indicated in table 11, the optimum feed tray position for column D-103 was an extremely sensitive
parameter, as it varied considerably between the feed trays. As highlighted in bold, the optimum feed tray
was the 3rd tray from the top, because it produced the lowest reboiler and condenser duties. This differs
from the Kirkbride correlation, which calculated a feed tray position of 2nd tray out of 18. Again, this
difference could be due to the assumptions made in the short-cut calculations.
3.3.2 Optimum feed temperature
For distillation column D-103, further analysis was conducted on the optimum feed temperature, as the
feed is a vapour-liquid mixture. This is an important parameter because the temperature affects the
fraction that is vapour in the vapour-liquid mixture, which can have a subsequent effect on the condenser
and reboiler duties. For column D-102, this was not necessary because the optimum feed temperature is
the saturated liquid point, which was calculated in Section 1.3. For this investigation, the feed temperature
was varied from 30℃ to 150℃, and the corresponding steam cost, cooling water cost and total operating
costs were noted. This was conducted on the optimised column of 10 stages, and the feed tray position
being the 3rd tray from the top, hence capital costs were ignored.
Annual costs against the feed temperature
8.00E+05
Annual costs ($/year)
7.00E+05
6.00E+05
5.00E+05
4.00E+05
3.00E+05
2.00E+05
1.00E+05
30
40
cost of steam
50
60
70
80
90 100 110 120 130 140 150
Feed temperature (℃)
cost of cooling water
total operating costs
Figure 5: Optimisation of the feed temperature with respect to the annual costs for column D-103
As shown in Figure 5, the annual cost of steam dominates the total operating costs. This is because LP
steam is more expensive than cooling water. In addition, a trend is revealed: as the feed temperature
increases, the annual cost of cooling water increases. This is because at a higher feed temperature, a
greater proportion of the feed is vapour, so more vapour flows to the top of the column, and hence more
energy is required to condense the mixture, thus the cost of cooling water increases. Overall, the total
operating costs decreases as the temperature increases, but plateaus after 90℃. The optimum feed
temperature was determined to be 100℃, as this is away from the point of plateau, so minor temperature
fluctuations will not impact the operating costs. Furthermore, 100℃ is the saturation temperature of water
– a key component in the separation- therefore the separation is easier.
4. Material and Energy Balances
A material and energy balance were performed on both distillation columns, based on the optimised case
and the specifications mentioned in Section 1.1.
4.1 Material balance
The following equations were applied for material balance, where F, D and B are molar flowrates of the
feed, distillate and bottom, and xF , xD and xB are mole fractions of components in the feed, distillate and
bottom respectively.
𝐹 =𝐷+𝐵
(Eq. 30)
𝐹𝑥𝐹 = 𝐷𝑥𝐷 + 𝐵𝑥𝐵
(Eq. 31)
Table 12: Material balance for column D-102
Component
Feed, F
(kmol h-1)
xF
Distillate, D
(kmol h-1)
xD
Bottom, B
(kmol h-1)
xB
Water
0.231
0.001
0.231
0.001
0
0
Glycerol
210.0119
0.8992
209.8019
0.9889
0.21
0.01
Sulfuric acid
17.2177
0.0737
2.0039
0.01
15.2138
0.7101
FAME
3.6377
0.0156
0.0902
0.0001
3.5475
0.1655
NaCl
2.4522
0.0105
0
0
2.4522
0.1144
Total
233.5505
1
212.127
1
21.4235
1
Table 13: Material balance for column D-103
Component
Feed, F
(kmol h-1)
xF
Distillate, D
(kmol h-1)
xD
Bottom, B
(kmol h-1)
xB
Oxygen
7.766
0.0086
7.766
0.0184
0
0
Nitrogen
63.586
0.0704
63.586
0.1510
0
0
Hydrogen
18.3990
0.0204
18.3990
0.0437
0
0
Carbon
dioxide
18.3990
0.0204
18.3990
0.0437
0
0
Acetaldehyde
18.3990
0.0204
18.3990
0.0437
0
0
Acrolein
180.011
0.1994
180.011
0.4276
0
0
Water
582.4944
0.6453
113.8121
0.2704
468.6823
0.9731
Acetol
10.995
0.0122
0.6288
0.0015
10.3662
0.0215
Glycerol
0.5082
0.0006
0
0
0.5082
0.001
Sulfuric acid
2.0039
0.0022
0
0
2.0039
0.0042
Methyl Oleate
0.0902
0.0001
0
0
0.0902
0.0002
Total
902.6517
1
421.0009
1
481.6508
1
4.2 Energy balance
For the energy balance, Eq. 31 was utilised where HF, HD, HB are the molar enthalpies of the feed, distillate
and bottom respectively, and QC and QR are the condenser and reboiler duties.
𝑄𝑅 + 𝐹𝐻𝐹 = 𝑄𝐶 + 𝐷𝐻𝐷 + 𝐵𝐻𝐵
(Eq. 31)
Table 14: Energy balance for column D-102
Heat flow
(kW)
Qc
QR
FHF
DHD
BHB
Overall
9793
9829
-41805.5
-37367.65
-4394.36
7.49
As shown in Table 14, the overall balance does not equal to zero, but when compared to the magnitude of
the other heat flows, it is safe to say that the imbalance is negligible, and the system satisfies the energy
balance equation.
Table 15: Energy balance for column D-103
Heat flow
(kW)
Qc
QR
FHF
DHD
BHB
Overall
11410.5
5848.4
-46331.3
-13837.7
-38055.7
0
5. Internal Design
The internal column design is essential for a safe and reliable operation. A good internal design will ensure
a high vapour and liquid contact in each stage, in addition to high mass transfer. This section will critically
analyse the internal structure of distillation columns D-102 and D-103.
5.1 Choice of trays or packing
The internal structure of a distillation column can be split into two categories; trays or packed. Packing is
usually more expensive than trays. However, it provides a lower pressure drop than trays [14], which is
especially important in the case of column D-102, as it operating under very low pressures. In addition, D102 involves the separation of corrosive substances such as sulfuric acid, packing is more suitable for the
use of corrosive components [15]. Therefore, packing will be employed as the internal structure of
distillation column D-102. Packing can be further split into random and structured packing. Structured
packing is extensively used in vacuum distillation [16], thus this type of packing will be selected. To be
specific, a ceramic structured packing named Boegger CSPS-03, Model 250Y, will be utilised for the
separation. This is because it has a high separation efficiency, can be used for large diameters, and is acid
resistance [17]. The packing factor, FP, for this particular packing was found to be 120 m-1 [8]. In the case of
column D-103, there is a large vapour flowrate than that of the liquid, therefore trays will be utilised for
this separation, as the use of packing may lead to flooding. Flooding is where the liquid is entrained in the
vapour up the column, this leads to a large pressure drop and a significant decrease in performance. Trays
can handle a large vapour flowrate, and are easier to clean [15]. There are 3 main plate types: sieve,
bubble-cap and valve plates. Sieve plates gives the lowest pressure drop across the column and is the
cheapest out of three [8]. Furthermore, the differences in plate efficiency between the plates is negligible
[8]. Therefore, after considering all the above-mentioned factors, sieve plates were selected for the internal
design of column D-103.
5.1.1 Column internals
Generally speaking, specific column internals would need be specified by the packing manufacturer and
would be purchased together as a package to ensure peak performance. This sub-section describes briefly
the types of internals required for column D-102 and their specific functions. Liquid distributors will be
installed, wherever an external liquid stream is introduced, to ensure uniform liquid distribution inside the
column. In this column, the liquid distributor will operate at the top of the column, as this is where the
reflux liquid re-enters the column. It is common for columns with more than 15 stages to employ a liquid
redistributor [18], to correct any poor distribution of liquid. A liquid redistributor will then be placed at the
feed stage due to the large liquid flowrate.
5.2 Column Diameter
The column diameter and pressure drop are interlinked, so the column diameter was determined once was
the pressure drop was selected. The column diameter was calculated above (rectifying section) and below
(stripping point) the feed point to obtain a suitable diameter to be used for the whole column. The pressure
drop per unit column length, Δp, must be selected such that the vapour velocity is well below the flooding
velocity. For this column, a pressure drop of 21 mm H2O per metre (205.9 Pa m-1) was selected based on
the literature guidance for vacuum distillation columns [8]. First, the flow factor, FLV, was calculated using
Eq. 32 and knowledge of the vapour and liquid mass flowrates, VW and LW, and the vapour and liquid
densities, ρv and ρL.
𝐿
𝜌
𝐹𝐿𝑉 = 𝑉𝑊 √ 𝜌𝑉
𝑊
(Eq. 32)
𝐿
Using the flow factor and with the help of a graphical correlation, the parameter, K4, was determined at the
selected pressure drop and at the flooding line. The flooding percentage can then be calculated using these
parameter values of K4, as described in Eq. 33. It is important to note that for structured packing the
flooding percentage, f%, should be within the range of 50-70% [19], to mitigate the risk of flooding.
𝐾4 𝑎𝑡 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 ∆𝑝
𝐾4 𝑎𝑡 𝑓𝑙𝑜𝑜𝑑𝑖𝑛𝑔 𝑙𝑖𝑛𝑒
𝑓% = √
× 100%
(Eq. 33)
Consequently, the vapour mass flow-rate per unit column cross sectional area, VW*, was then determined
using this parameter, Eq. 34 and the liquid viscosity, μL.
𝐾4 𝜌𝑉 (𝜌𝐿 −𝜌𝑉 )
∗
𝑉𝑊
=√
𝜇 0.1
13.1𝐹𝑝 𝐿
(Eq. 34)
𝜌𝐿
The column area, Ac, can then be computed using Eq. 35
𝐴𝑐 =
𝑉𝑊
∗
𝑉𝑊
(Eq. 35)
The column diameter, Dc, can then be determined from the area knowing that the structured packing has a
circular shape as described in Eq. 36
𝐷𝑐 = √
4𝐴𝑐
𝜋
(Eq. 36)
The calculated column diameter was rounded up to the nearest d.p. for vendor specifications. A new
flooding percentage, f%,new, was calculated, based on the new diameter, to ensure that it is still within the
suitable range, as shown in Eq. 37
𝑜𝑙𝑑 𝑎𝑟𝑒𝑎
𝑓%,𝑛𝑒𝑤 = 𝑓% × 𝑛𝑒𝑤 𝑎𝑟𝑒𝑎
(Eq. 37)
The required height of packing, H, in a column can be calculated using the number of theoretical stages, N,
required for the separation and the height equivalent of a theoretical plate (HETP), which accounts for the
height of packing required to achieve the same change in concentration as an equilibrium stage. This is
shown in Eq. 38
𝐻 = 𝑁 × 𝐻𝐸𝑇𝑃
(Eq. 38)
From the manufacturer specifications, for an F value of 2.44 Pa0.5, the HETP was found to be 0.27 m-1. This
results in a height of packing of 4.86 m. A further 2 m was added to account for the bottoms stump and the
overheads height, which results in a final column height of 6.86 m. From this, the total pressure drop across
the column, ΔP, can be obtained using Eq. 39
∆𝑃 = 𝐻 × ∆𝑝
(Eq. 39)
Table 16: Structured packing internal design results for column D-102
Rectifying section
Stripping section
Flow factor, FLV
0.133
0.281
Parameter, K4 (at the selected Δp)
0.74
0.6
Vapour mass flowrate per unit
column cross sectional area, VW*
(kg m-2 s-1)
0.402
0.389
Column diameter, Dc (m)
1.577
1.16
Rounded diameter, Dc (m)
1.6
1.2
Column cross-sectional area, Ac
(m2) (based on rounded diameter)
2.01
1.13
Old flooding (%)
55.5
57.7
New flooding (%)
53.9
54
Total pressure drop across the column, ΔP = 1412.5 Pa
As shown in Table 16, the column diameter calculated for the rectifying section is larger than the diameter
for the stripping section. This could be due to the larger vapour flowrates at the top of the column. The
larger column diameter of 1.6 m was chosen to ensure that the column is large enough for operation.
D-103
When designing sieve plates, an iterative approach is required. First, initial estimates of design parameters
are made, then these parameters are altered such to satisfy the key performance factors, such as weeping,
flooding, entrainment and pressure drop, to give a reliable operation for the plate, and thus the whole
distillation column.
5.2.1 Flooding velocity
Flooding is major factor when designing plates in distillation columns, as it can seriously impact
performance. The flooding velocity, uf, was determined using Eq. 40 by knowing the surface tension of the
mixture, σm, and the dimensionless parameter, K1
𝜎
𝜌𝐿 −𝜌𝑉
𝜌𝑉
𝑚 0.2
𝑢𝑓 = 𝐾1 (0.02
) √
(Eq. 40)
The parameter, K1, was obtained graphically from the flooding velocity of sieve plates [8]. A tray spacing of
0.6 m was assumed, based on design heuristics for distillation columns. According to design heuristics, the
vapour velocity, un, is typically 80-85% of the flooding velocity. Therefore, an initial estimate of 85% of the
flooding velocity was taken.
𝑢𝑛 = 0.85𝑢𝑓
(Eq. 41)
The net area, An, was calculated using Eq. 42 and the volumetric vapour flowrate, Qvap.
𝐴𝑛 =
𝑄𝑣𝑎𝑝
(Eq. 42)
𝑢𝑛
By assuming a downcomer area, Ad, of 12% of the cross-sectional area, Ac. This was recommended based
on design heuristics for distillation columns [8]. The column cross-sectional area, Ac, was determined using
Eq. 43. The column diameter, Dc, was also calculated using Eq. 36
𝐴𝑐 =
𝐴𝑛
𝐴
1−( 𝑑 )
(Eq. 43)
𝐴𝑐
These calculations were conducted for the rectifying section and stripping section of the optimised D-103
column with 10 trays, with the feed tray being the 3rd.
Table 17: Column diameter results for column D-103
Rectifying Section
Stripping Section
Liquid-vapour flow factor, FLV
0.015
0.055
K1
0.11
0.116
Flooding velocity, uf (m s-1)
4.83
5.20
Vapour velocity, un (m s-1)
4.11
4.42
Net area, An (m2)
2.64
1.02
Column cross-sectional area, AC
(m2)
3.005
1.16
Column diameter, Dc (m)
1.96
1.22
As shown in Table 17, the column diameter calculated for the rectifying section is much larger than the
diameter calculated for the stripping section. This could be due to the feed tray being placed quite high up
the column and the high vapour fraction in the feed. This leads to an uneven distribution of vapour in the
column, thus a much lower volumetric vapour flowrate in the stripping section, hence the difference in the
calculated diameters. Nevertheless, the larger diameter of 1.96 m was rounded up to the nearest standard
carbon steel vessel size of 2 m [20]. Results obtained in the following sections were based on a
column diameter of 2 m.
5.2.2 Liquid flow pattern
When designing trays in a column, internal flow pattern is an important factor, as it affects the
column efficiency. The liquid flow arrangement depends on the column diameter and the liquid
volumetric flowrate. The minimum and maximum volumetric liquid flowrates were obtained
from Aspen HYSYS, and were 0.00518 m3 s-1 and 0.0053 m3 s-1 respectively. This, coupled with
Figure 6: Singlepass liquid flow
pattern
the calculated column diameter from the above section, resulted in a single pass flow. This is shown in
Figure 6.
5.2.3 Provisional plate design
Table 18 shows details of the provisional plate design, which will be further checked for weeping,
entrainment and other performance factors to ensure that they do not fall below the acceptable range. The
net area, An, was calculated using Eq. 44, and the active area, Aa, was calculated using Eq. 45. The weir
length was obtained from a graphical correlation, relating the downcomer area and the weir length-tocolumn diameter ratio. The hole area, Ah, was assumed to be 10% of the active area; the weir height was
assumed to be 50mm, the hole diameter, dh, and plate thickness, tp, were assumed to be 5 mm each. These
assumptions were made based on the design heuristics for a carbon steel pressure vessel [8].
𝐴𝑛 = 𝐴𝑐 − 𝐴𝑑
(Eq. 44)
𝐴𝑎 = 𝐴𝑐 − 2𝐴𝑑
(Eq. 45)
Table 18: Provisional plate design values for column D-103
Column diameter, Dc (m)
2
Column Area, Ac (m2)
3.14
Downcomer area, Ad (m2)
0.377
Net area, An (m2)
2.76
Active area, Aa (m2)
2.39
Hole area, Ah (m2)
0.239
Weir length, lw (m)
1.54
Weir height, hw (mm)
50
Hole diameter, dh (mm)
5
Plate thickness, tp (mm)
5
5.2.4 Weeping check
Another key performance factor in the design of plate columns is weeping. Weeping is a phenomenon
whereby the vapour flowrate is much lower than the liquid flowrate, therefore it is unable to exert
sufficient pressure to hold the liquid on the tray, thus leading to the leakage of liquid through the holes. In
order to avoid this, a weeping check must be conducted to determine whether the hole area is appropriate
safe operation. First, the minimum weir liquid crest height, how,min, was calculated using Eq. 46. Assuming a
turn down ratio of 70%, the minimum liquid mass flow rate, Lw,min, was 70% of the maximum liquid mass
flow rate, Lw,max.
𝐿𝑤,𝑚𝑖𝑛 2
ℎ𝑜𝑤,𝑚𝑖𝑛 = 750(
𝜌𝐿 𝑙 𝑤
)3
(Eq. 46)
From this, a parameter, K2, was obtained from the weep point correlation graph. Using K2 and Eq. 47, the
minimum design vapour velocity, uh, was computed. It should be noted that the units for hole diameter, dh,
used in Eq. 47 is in millimetres.
𝑢ℎ =
𝐾2 −0.9(25.4−𝑑ℎ )
(𝜌𝑉 )0.5
(Eq. 47)
Following this, the actual minimum vapour velocity, umin, was determined using Eq. 48. The minimum
volumetric vapour flowrate, Qvap,min, was taken from the stripping section due to the uneven distribution of
the vapour in the column, this ensures a reliable operation throughout the distillation column.
𝑢𝑚𝑖𝑛 =
𝑄𝑣𝑎𝑝,𝑚𝑖𝑛
(Eq. 48)
𝐴ℎ
Table 19: Weeping check results for column D-103
Maximum liquid flowrate, Lw,max (kg s-1)
5.34
Minimum liquid flowrate, Lw,min (kg s-1)
3.74
Minimum weir liquid crest height, how,min (mm)
12.3
K2
30.3
Minimum design vapour velocity, uh (m s-1)
12.5
Actual minimum vapour velocity, umin (m s-1)
18.9
As seen in Table 19, it is evident that the actual minimum vapour velocity was greater than the minimum
design velocity, therefore there was no need to further reduce the hole area, which was set at 10% of the
active area, and thus, the weeping constraint is satisfied.
5.2.5 Plate pressure drop
Another important consideration in the design of sieve plates is the pressure drop. Pressure drop is a result
of two factors; the vapour flow through the perforations in the plate, and the liquid head in the plate. The
total plate pressure drop, also accounts for the residual losses, which takes into consideration that the
liquid head would contain some froth. The maximum vapour velocity, umax, through the holes was
determined using Eq. 48, utilizing the maximum volumetric vapour flowrate, Qvap,max. The maximum dryplate drop, hd, was calculated using Eq. 49. The orifice coefficient, Co, was obtained from the discharge
coefficient graph for sieve plates.
𝑢𝑚𝑎𝑥 2 𝜌𝑣
)
𝐶𝑜
𝜌𝐿
ℎ𝑑 = 51(
(Eq. 49)
The residual head, hr, was determined using Eq. 50.
ℎ𝑟 =
12,500
𝜌𝐿
(Eq. 50)
Using the maximum weir liquid crest height, how,max, calculated from Eq. 46, the total plate drop, ht, was
found with the help of Eq. 51
ℎ𝑡 = ℎ𝑑 + (ℎ𝑤 + ℎ𝑜𝑤,𝑚𝑎𝑥 ) + ℎ𝑟
(Eq. 51)
The total plate pressure drop, ΔPt, was obtained using Eq. 52. The total pressure drop, ΔP, experienced
across the column was computed as the product of the total plate pressure drop and the number of plates
in the column.
∆𝑃𝑡 = 9.81 × 10−3 ℎ𝑡 𝜌𝐿
(Eq. 52)
Table 20: Plate pressure drop results for column D-103
Maximum vapour velocity, umax (m s-1)
45.5
Orifice coefficient, Co
0.84
Maximum dry-plate drop, hd (mm)
119.4
Residual head, hr (mm)
10.8
Maximum weir liquid crest height, how,max (mm)
15.6
Total plate drop, ht (mm)
195.8
Total plate pressure drop, ΔPt (kPa)
2.22
The total pressure drop across the column, ΔP
(kPa)
22.2
5.2.6 Downcomer design
When designing sieve trays, it is c to consider the downcomer design, as a poor downcomer design could
result in flooding. This occurs when the total height of liquid and froth in the downcomer exceeds the top
of the outlet weir of the previous tray. Thus, the general heuristic is to ensure that the height of the liquid
back-up in the downcomer, hb, is no more than half of the summation of plate spacing plus weir height.
This constraint is shown in Eq. 53.
1
ℎ𝑏 ≤ 2 (𝑙𝑡 + ℎ𝑤 )
(Eq. 53)
In order to determine the height of liquid back-up; the area of clearance under the downcomer, Aap, was
calculated using Eq. 54. The distance from the bottom edge of the apron to the plate, hap, was assumed to
be 40 mm, as to overdesign for the liquid back-up [8].
𝐴𝑎𝑝 = ℎ𝑎𝑝 𝑙𝑤
(Eq. 54)
The head loss in the downcomer, hdc, was computed, knowing the downcomer liquid flowrate, Lw,d, and
using Eq. 55
𝐿
ℎ𝑑𝑐 = 166(𝜌 𝑤.𝑑
)2
𝐴
(Eq. 55)
𝐿 𝑎𝑝
The height of liquid back-up was then determined using Eq. 56. The maximum weir liquid crest height,
how,max, was used to overdesign to ensure the constraint is fully met throughout the column.
ℎ𝑏 = ℎ𝑑𝑐 + (ℎ𝑤 + ℎ𝑜𝑤,𝑚𝑎𝑥 ) + ℎ𝑡
(Eq. 56)
In order to prevent the entrained vapour from being carried over to the next tray by the liquid, design
heuristics suggest a residence time of at least 3 seconds to allow time for the vapour to separate from the
liquid [8]. The downcomer residence time, tr, was calculated using Eq. 57
𝑡𝑟 =
𝐴𝑑 ℎ𝑏 𝜌𝐿
𝐿𝑤,𝑑
(Eq. 57)
Table 21: Downcomer design results for column D-103
Clearance area of the downcomer, Aap (m2)
0.062
Downcomer head loss, hdc (mm)
6.44
Downcomer liquid back-up, hb (mm)
267.8
0.5(lt + hw) (mm)
325
Downcomer residence time, tr (s)
8.30
As shown in Table 21, the constraint shown in Eq. 53 was met, therefore there was no need to alter the tray
spacing. Also, the downcomer residence time was greater than 3 s, thus the design was deemed
satisfactory
5.2.7 Entrainment check
The flooding percentage was checked to ensure it is below 85% of the flooding velocity, uf, and within the
suitable range, as a low vapour velocity is detrimental for the plate efficiency. The actual vapour velocity,
un, was calculated using Eq. 58.
𝑢𝑛 =
𝑄𝑣𝑎𝑝,𝑚𝑎𝑥
(Eq. 58)
𝐴𝑛
The flooding percentage, f%, was then determined using Eq. 59
𝑢
𝑓% = 𝑢𝑛 × 100%
𝑓
(Eq. 59)
The flooding percentage was calculated to be 81.3%, which below the initial assumption of 85%, and within
the suitable range, therefore there was no need to alter the column diameter.
In addition, with an FLV value of 0.05, the fractional entrainment, ψ, obtained from the graph of
entrainment correlation for sieve plates was 0.05. This was deemed satisfactory, as to achieve higher plate
efficiencies, the fractional entrainment should be less than 0.1 [8].
5.2.8 Perforated area
The active area, Aa, calculated previously did not take into account the space needed to install support
rings, and the use of calming zones - unperforated strips that surround the active area. The width of the
strips, ws, was assumed to be 0.1 m, based on heuristics for column diameters larger than 1.5 m [8]. The
mean length of the unperforated edge strips, Le, was obtained using Eq. 60, the angle subtended by the
unperforated edge strips, ϴe, is the adjacent angle to the angle subtended by the weir length, ϴc. ϴc was
found using a graphical correlation.
𝜃
𝑒
𝐿𝑒 = 180
𝜋(𝐷𝑐 − 𝑤𝑠 )
(Eq. 60)
The area of the unperforated edge strips, Ae, was then determined
𝐴𝑒 = 𝐿𝑒 𝑤𝑠
(Eq. 61)
The mean length of the calming zone, Lz, was computed using Eq. 62
𝐿𝑧 = 𝑙𝑤 + 𝑤𝑠
(Eq. 62)
The area of the calming zones, Az, was determined using Eq. 63
𝐴𝑧 = 2𝐿𝑧 𝑤𝑠
(Eq. 63)
The total area of perforation, Ap, was found by subtracting the area of unperforated strips and the area of
the calming zones from the previously calculated active area, as described in Eq. 64
𝐴𝑝 = 𝐴𝑎 − 𝐴𝑒 − 𝐴𝑧
(Eq. 64)
The number holes punched into the perforated area was calculated using Eq. 65 and the area of one hole,
ah .
𝐴
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 ℎ𝑜𝑙𝑒𝑠 = 𝑎ℎ
ℎ
The hole pitch, lh, to hole diameter, dh, ratio was determined using Eq. 66
(Eq. 65)
𝑙ℎ
𝑑ℎ
=√
0.9𝐴𝑝
(Eq. 66)
𝐴ℎ
Table 22: Perforation area design results
Angle subtended by the edge of the plate, ϴe
95
Mean length of unperforated edge strips, Le (m)
3.15
Area of unperforated edge strips, Ae (m)
0.315
Mean length of calming zone, Lz (m)
1.64
Area of calming zone, Az (m2)
0.328
Total area of perforation, Ap (m2)
1.74
Hole area to perforated area ratio, Ah/Ap
0.137
Hole pitch to hole diameter ratio, lh/dh
2.56
Number of holes
12160
The hole pitch to hole diameter ratio should typically be in the range of 2.5 to 4, hence the ratio calculated
in Table 22 was deemed acceptable.
5.2.9 Plate efficiency
The optimised number of theoretical stages was 10 trays for column D-103. However, this assumes 100%
plate efficiency, meaning that the vapour and liquid on all trays was assumed to be in equilibrium, which is
not the case for real life operations. Factors that affect the plate efficiency are insufficient time of contact
between the liquid and the vapour, and poor degree of mixing. Due to the reduced efficiency, in order to
achieve the same desired separation, more trays will be required. The AIChE Method for determining the
plate efficiency could not be used, as this is only applicable for binary mixtures [21]. In addition, a binary
system assumption could not be made because 11 components are involved in this separation, and the key
components only make up 84 mol% of the feed. Instead, the plate efficiency was assumed to be 70%
because this is common in industry [21]. Furthermore, the actual vapour velocity was between 80-85% of
the flooding velocity, this made the assumption more valid. Assuming a plate efficiency of 70%, results in
the actual number of trays needed to perform this separation to be 15 trays. Also, this increases the total
pressure drop across the column, ΔP, to 33.4 kPa.
6. Mechanical Design
The mechanical design involves the analysis of the stresses on the columns, so that it does exceed the
maximum allowable stress. The mechanical design of the columns is essential to ensure safe design and
plant longevity. The columns should be designed to withstand higher operating conditions, and extreme
weather conditions. This design is critical in the case of D-102 as it is operating under vacuum.
6.1 Choice of material
Column D-102 involves the separation of corrosive components such as sulfuric acid, therefore the choice
of material will need to be resistant to this acid. A nickel-molybdenum alloy will be selected as the material
of construction for this column due to its acid-resistant properties and strong mechanical properties [22].
Ni-Mo alloys have been used as vessels in chemical industry [22], therefore the design is feasible. The
maximum allowable stress, S, for this alloy was determined to be 120.4 MPa at 260 ℃ (15% higher than the
maximum temperature in the column) [22]. The density of the material, ρm, was taken to be 9200 kg m-3
[22]. In the case of D-103, most of the compounds are non-corrosive, and the system contains are a large
amount of water. Carbon steel vessels are commonly used for systems containing water [21]. Therefore,
carbon steel will be employed as the vessel material for this column. The maximum allowable stress, S, for
carbon steel is 88.9 MPa at 260 ℃, which is much greater than the maximum temperature experienced in
the column. This was conducted as an over-precaution to ensure mechanical failure does not occur. The
density of the material, ρm, is 7850 kg m-3.
Mineral wool will be chosen as the insulation material for both distillation columns because it is moistureresistant and fire-resistant [23], therefore it is a good insulator and ensures the longevity of the columns. In
addition, a carbon steel skirt will be the choice of support for both columns because it is commonly used for
distillation columns, as it does not contribute any additional loads to the vessel [21].
6.2 Minimum wall thickness and critical pressure
The minimum wall thickness, tw, was calculated assuming a 20% increase in the internal pressure, Pi, and
using the diameters calculated in Section 5 as the internal diameters, Di. The joint efficiency, E, was
assumed to be 0.85. This shown in Eq. 67
𝑃𝐷
𝑖 𝑖
𝑡𝑤 = 2𝑆𝐸−1.2𝑃
𝑖
(Eq. 67)
The minimum vessel thickness was calculated to be 0.047 mm and 1.61 mm for columns D-102 and D-103
respectively. However, these values seemed unreasonable. Therefore, the minimum vessel thickness was
taken to be 7 mm and 9 mm for D-102 and D-103, based on the minimum practical wall thickness for the
column diameters [21]. It is important to note that these values include a 2 mm corrosion allowance.
As column D-102 is operating under vacuum, the critical pressure was calculated to ensure the column can
withstand an external pressure of at least 1 atm. In order to determine this, the outer diameter, Do, was
calculated using Eq. 68
𝐷𝑜 = 𝐷𝑖 + 2𝑡𝑤
(Eq. 68)
The critical pressure, Pc, was computed using Eq. 69. The collapse coefficient, Kc, was obtained a graphical
correlation, and the Young’s modulus, EY, of the Ni-Mo alloy was taken to be 217 GPa [22].
𝑡
𝑃𝑐 = 𝐾𝑐 𝐸𝑌 (𝐷𝑤 )3
𝑜
(Eq. 69)
The critical pressure calculated was 911 kPa, which is well above the atmospheric pressure, therefore, the
column design is appropriate to withstand atmospheric pressure.
6.3 Choice of end closures
A torispherical head was chosen as the closure for both distillation columns because it is the most
economical, and commonly used head for column pressures below atmospheric pressure [21]. The
thickness of the torispherical head, th, was calculated using Eq. 70. The crown radius, RC, was assumed to be
equal to the column diameter, based on mechanical heuristics for columns.
𝑡ℎ =
0.885𝑃𝑖 𝑅𝑐
𝑆𝐸−0.1𝑃𝑖
(Eq. 70)
The thickness of the head was calculated to be 0.1 mm and 2.28 mm for columns D-102 and D-103
respectively. As these values are too small, it was decided to design the head closures with the same
thickness as the vessel.
6.4 Stress Analysis
6.4.1 Dead weight stress
The dead weight stress of the column includes the stresses caused by the weights of the vessel, plates and
the insulation. The weight of the vessel, Wv, was calculated using Eq. 71; where the factor, Cv, is 1.15 for
distillation columns [21], Dm is the mean diameter of the column and Hv is the length of the cylindrical
section of the column.
𝑊𝑣 = 𝐶𝑤 𝜋𝜌𝑚 𝐷𝑚 𝑔(𝐻𝑣 + 0.8𝐷𝑚 )𝑡𝑤
(Eq. 71)
The weight of the plates, Wp, was calculated using Eq. 72. Even though, the internal structure of D-102 was
selected to be packing, for this analysis, they will be treated as plates, as to overdesign for the column.
𝑊𝑝 = 1.2𝑁𝐴𝑐
(Eq. 72)
The weight of the mineral wool, Wins, was calculated using Eq. 73. The thickness of the mineral wool, tins,
was assumed to be 50 mm, and the density of the mineral wool, ρins, was taken to be 130 kg m-3 [21].
𝑊𝑖𝑛𝑠 = 2𝜋𝐷𝑐 𝐻𝑣 𝑡𝑖𝑛𝑠 𝜌𝑖𝑛𝑠 𝑔
(Eq. 73)
Using the calculated weights and Eq. 74, the total weight of the vessel, Wt, was obtained. This value was
subsequently used to calculate the dead weight stress, σw, shown in Eq. 75
𝑊𝑡 = 𝑊𝑣 + 𝑊𝑃 + 𝑊𝑖𝑛𝑠
(Eq. 74)
𝑊
𝜎𝑤 = 𝜋(𝐷 +𝑡𝑡
(Eq. 75)
𝑤 )𝑡𝑤
𝑖
Table 23: Dead weight stress analysis results
D-102
D-103
Dead weight of the vessel, Wv
(kN)
29.9
63.4
Weight of the plates, Wp (kN)
43.4
56.5
Weight of the insulation, Wins
(kN)
4.40
8.81
Total weight of the vessel, Wt
(kN)
77.7
128.8
Dead weight stress, σw (MPa)
2.20
2.27
6.4.2 Bending stress
The bending stress, σb, was calculated using Eq. 76, where M is the total bending moment given by Eq. 77,
and Iv is the vessel’s second moment of area given by Eq. 78. Deff represents the mean diameter of the
column with insulation. The wind speed, uw, was assumed to be 160 km h-1, as to overdesign for worst-case
scenarios. The plus/minus sign in Eq. 76 is to indicate that the bending stress can be considered to be
compressive or tensile.
𝑀 𝐷
𝐼𝑣 2
𝜎𝑏 = ± ( 𝑖 + 𝑡)
𝑀=
(Eq. 76)
0.05𝑢𝑤 2 𝐷𝑒𝑓𝑓 𝐻𝑣 2
(Eq. 77)
2
𝜋
𝐼𝑣 = 64 (𝐷𝑂 4 − 𝐷𝑖 4 )
(Eq. 78)
Table 24: Bending stress analysis results
D-102
D-103
Bending moment, M (N m)
48400
155580
Second moment of area, Iv (m4)
0.0114
0.0287
Bending stress, σb (MPa)
±3.42
±5.48
6.4.3 Pressure stress
The pressure stresses include the longitudinal stress, σL, and the hoop stress, σh, which were calculated
using Eq. 79 and Eq. 80 respectively.
𝑃𝐷
𝜎𝐿 = 4𝑡 𝑖
(Eq. 79)
𝑤
𝑃𝐷
𝜎ℎ = 2𝑡 𝑖
(Eq. 80)
𝑤
Table 25: Pressure stress analysis results
D-102
D-103
Longitudinal stress, σL (MPa)
0.286
5.63
Hoop stress, σh (MPa)
0.571
11.3
6.4.4 Principal stress
The resultant longitudinal stress, σz, is known as the principal stress. This was calculated using Eq. 81. The
upwind resultant stress occurs when the bending stress is positive (tensile), and the downwind resultant
stress occurs when the bending stress is negative (compressive). In addition, an absolute difference of the
longitudinal stresses was calculated to check it is below the maximum allowable stress of the material.
𝜎𝑧 = 𝜎𝐿 − 𝜎𝑤 ± 𝜎𝑏
(Eq. 81)
Table 26: Principal stress analysis results
D-102
D-103
Upwind resultant longitudinal
stress, σz (MPa)
1.51
8.84
Downwind resultant longitudinal
stress, σz (MPa)
5.34
2.11
Downwind absolute difference of
the longitudinal stresses
5.91
13.4
As shown in Table 26, the greatest absolute difference of the longitudinal stress was well below the
maximum allowable stress of both materials, therefore the design was deemed mechanically safe
6.4.5 Elastic stability check
An elastic stability check was performed to ensure that the column does not buckle when the compressive
stress is at a maximum. The critical buckling stress, σc, was calculated using Eq. 82. The maximum
compressive stress is the summation of the dead weight stress and the compressive bending stress, as the
pressure stresses are tensile.
𝑡
𝜎𝑐 = 2 × 104 (𝐷𝑤 )
𝑜
(Eq. 82)
Table 27: Elastic stability check results
D-102
D-103
Critical buckling stress, σc (MPa)
86.7
89.2
Maximum compressive stress
(MPa)
5.62
7.74
As presented in Table 27, the maximum compressive stress was significantly below the critical buckling
stress, therefore the design was satisfactory.
6.5 Column Skirt
The bending stress, σbs, and dead weight stress, σws, of the skirt were determined using Eq. 83 and Eq. 84
respectively, where Ms is the maximum bending moment, and Wt is the total weight of the vessel, tsk is the
thickness of the skirt, and Ds is the diameter of the skirt (assumed to be same as the internal diameter). The
skirt height was assumed to be 3 m, and the skirt thickness was assumed to be 10 mm – as an initial
estimate.
4𝑀𝑠
𝑠𝑘 )𝑡𝑠𝑘 𝐷𝑠
𝜎𝑏𝑠 = 𝜋(𝐷 +𝑡
𝑠
(Eq. 83)
𝑊
𝜎𝑤𝑠 = 𝜋(𝐷 +𝑡𝑡
(Eq. 84)
𝑠𝑘 )𝑡𝑠𝑘
𝑠
For a skirt design to be safe, the following two criteria have to be met:
𝑡𝑠𝑘
) sin 𝜃𝑠
𝐷𝑠
𝜎̂
𝑠,𝑐 < 0.125𝐸𝑌 (
(Eq. 85)
𝜎̂
𝑠,𝑡 < 𝑆𝑠 𝐸 sin 𝜃𝑠
(Eq. 86)
Where Ss is the maximum allowable design stress for the skirt, and ϴs is the conical skirt base angle, which
was assumed to be 90◦, as an overdesign. The tensile stress, 𝜎̂
𝑠,𝑡 , is the difference between the bending
stress and the dead weight stress. The compressive stress, 𝜎̂
𝑠,𝑐 , is the sum of the two previously mentioned
stresses.
Table 28: Column skirt design results
D-102
D-103
Compressive 𝜎̂𝑠 (MPa)
2.00
2.37
Tensile 𝜎̂𝑠 (MPa)
-1.07
-1.63
139.7
111.7
𝑡𝑠𝑘
) sin 𝜃𝑠
𝐷𝑠
0.125𝐸𝑌 (
(MPa)
𝑆𝑠 𝐸 sin 𝜃𝑠 (MPa)
67.5
As shown in Table 28, the constraints shown in Eq. 85 and 86 were met when the skirt thickness was 10
mm. Therefore, the column skirt will have a thickness of 10 mm, which will also include a 2 mm corrosion
allowance, ensuring a mechanically safe operation of the columns.
7. Ancillary Design
The ancillary design comprises of a shell & tube condenser, a kettle reboiler, a reflux drum and a pump for
both columns. In addition, a vacuum pump and cooler H-107 will be designed for columns D-102 and D-103
respectively.
7.1 Condenser, Reboiler and Cooler H-107
The heat transfer area, A, of the heat exchangers were determined using Eq. 22 from Section 3.2.2. The
overall heat transfer coefficients, U, for the condensers, reboilers and the cooler were assumed to be 850,
1050 and 950 W m-2 K-1 respectively, based on the hot stream and cold stream components [21]. Also, the
minimum approach temperature, ΔTmin, was assumed to be 10℃, as this is the standard value in chemical
industry [8].
Table 29: Heat exchanger area results
Equipment Unit
Duty, Q (kW)
Area, A (m2)
D-102: Condenser
9793
74.7
D-102: Reboiler
9829
637.0
D-103: Condenser
11410.5
508.5
D-103: Reboiler
5848.4
221.3
H-107
2552
18.8
7.2 Reflux Drum
The purpose of the reflux drum is to act as a temporary holding tank for a holding time, tr, before pumping
it back to the column, while the rest is taken as the distillate, D (or in the case of D-103, the vapour
product). The volume of the reflux drum, V, was calculated using Eq. 87. A contingency of 20% was added,
in the event of unexpected surges in the flowrates. The holing time was assumed to be 10 minutes.
𝑉=
(𝑅+1)𝐷
𝜌𝐿
𝑡𝑟
(Eq. 87)
The volume of the reflux drum was calculated to be 5.44 m3 and 5.46 m3 for columns D-102 and D-103
respectively, which includes a 20% contingency.
7.3 Reflux Pump
The condenser and reboiler for both columns will be placed on the ground to avoid additional costs for
their supports. The optimum diameter, di,o, was calculated using Eq. 88. Using this the pressure drop due to
friction, ΔPf, was computed using Eq. 89, where L is the length of the column and f is the fanning friction
factor. The pumping power requirement was determined using Eq. 90, where ΔP is the pressure drop in the
system. The height difference, Δz, was assumed to be the length of the column, and the pump efficiency, η,
was assumed to 0.6.
𝐺
𝑑𝑖.𝑜 = 3.2(𝜌 )0.5
(Eq. 88)
𝐿
∆𝑃𝑓 =
𝑃𝑜𝑤𝑒𝑟 =
8𝑓𝜌𝐿 𝑢2 𝐿
2𝑑𝑖,𝑜
𝑚̇
[𝑔∆𝑧
𝜂
+
(Eq. 89)
∆𝑃−∆𝑃𝑓
𝜌𝐿
]
(Eq. 90)
This produced a power of 0.676 kW and 0.307 kW for the pumps of columns D-102 and D-103 respectively
7.4 Vacuum Pump
A liquid ring pump was selected as the pump to maintain D-102 under vacuum, because they are commonly
used in chemical industry [21]. These pumps are rated on their Actual Cubic Feet per Minute (ACFM)
values, which obtained using Eq. 88 and knowing their Standard Cubic Feet per Minute (SCFM). Data
suggests that a SCFM value of 70 ft3 min-1[24] is sufficient enough to maintain a vacuum of 5 kPa. P1 and P2
are the standard and actual pressures in the column in psia, while T1 and T2 are the standard and actual
temperatures in the column in Rankine. The standard temperature and pressures of the City of Industry,
the plant’s location, are 525.4◦R and 14.7 psia [25].
𝐴𝐶𝐹𝑀 = 𝑆𝐶𝐹𝑀 ×
𝑃1
𝑃2
×
𝑇2
𝑇1
(Eq. 88)
This obtained an ACFM value of 2300 ft3 min-1, which is equivalent to 1.09 m3 s-1.
8. Economic Analysis
A more accurate cost estimate of the designed columns was made. The costing was calculated using the
equations described in Section 3. The Ni-Mo alloy vessel is approximately 5 times more expensive than a
carbon steel vessel [22], hence the installation factor, f, was changed to 20 to reflect this. The operating
costs for the pumps were determined knowing that the price of electricity in California is $0.13 kWh-1 [26],
and the annual operating hours is 8000.
Table 30: Capital and operating costs for columns D-102 and D-103
Distillation
Equipment
S
a
b
n
f
Purchase
cost ($)
Installed
costs, 2010
($)
Installed
costs, 2020
($)
Operating
costs
($/year)
Shell, Ni-Mo alloy
29,331 kg
10000
29
0.85
20
191,813
3,836,268
4,097,586
N/A
Ceramic
structured
packing
3.84 m3
0
6900
1
4
26,468
105,874
11,305.5
N/A
Condenser
74.7 m2
24000
46
1.2
3.5
32,142
112,498
120,161
193,986
Kettle reboiler
637 m2
25000
340
0.9
3.5
138,554
484,941
517,974
1,398,025
Reflux drum
653 m2
10000
29
0.85
4
17,161
68,643
73,319
N/A
Reflux pump
5.56 L s-1
6900
206
0.9
4
7,865
31,462
33,605
703.3
Vacuum pump
1085 L s-1
6900
206
0.9
4
118,056
472,225
504,392
204,259
5,460,122
1,796,973
Column
D-102
TOTAL
D-103
Shell, CS
21,337 kg
10000
29
0.85
4
148,937
595,748
636,330
N/A
Sieve trays
2m
110
380
1.8
2.5
21,499
53,746
57,407
N/A
Condenser
509 m2
24000
46
1.2
3.5
105,340
368,692
393,806
226,026
Kettle reboiler
221 m2
25000
340
0.9
3.5
68,849
240,972
257,387
334,031
Reflux drum
655 m3
10000
29
0.85
4
17,183
68,733
73,415
N/A
Reflux pump
4.28 L s-1
6900
206
0.9
4
7,662
30,650
32,738
319.3
H-107 Condenser
18.8 m2
24000
46
1.2
3.5
25,555
89,442
95,535
50,552
1,546,618
610,928
TOTAL
The total installed costs were multiplied by 1.07, the location factor for the West Coast of the USA, and
annualised using Eq. 17 assuming an interest of 5% and plant life of 20 years. This results in a total
annualised cost of $2,265,776 yr-1 and $743,720 yr-1 for distillation columns D-102 and D-103.
9. Safety
The standard start-up procedure of any distillation column operation is to first perform a hydraulic testing
to detect any leakages, then purge the column of oxygen to prevent the possibility of combustion [21]. This
is known as line-blowing. Next, normal operation can commence. In the case of D-102, the column must be
evacuated to create a vacuum in the system. The feed is then fed into the column until a specific level has
been achieved, then reboiler and condenser operation can begin. To shut down the columns, the flowrate
of the feed and reflux rate should gradually decrease. After, the reboiler operation must cease to prevent
the formation of vapour. By the time the feed flowrate reaches zero, all the condensed liquid will be
collected in the reflux drum. When this occurs, the condenser must be stopped as well. Valves and other
smaller pieces of equipment should be flushed, so no residuals are present. For maintenance, the
distillation columns should be shut-down every 2 years. Trays, packing and internal column should be
checked for fouling and corrosion. Extra care should be taken when handling ceramics, as they are delicate.
It is crucial the maintenance team are fully certified, trained and equipped with PPE before carrying out any
maintenance work.
10. Conclusion
The report covers the optimisation, detailed internal and mechanical design of distillation columns D-102
and D-103. Vacuum distillation at a pressure of 5 kPa was chosen for D-102, due to the high boiling points
of the components involved in the separation, and the constraint on the hot utility temperature. Whereas,
column D-102 will operate at atmospheric pressure, as this was determined to be the best pressure. The
optimisation of the two columns was performed on Aspen HYSYS, using the UNIQUAC fluid package, with
the objective to find the optimum number of stages, feed stage location and feed temperature (in the case
of D-103), based on the annual costs of the columns. A detailed internal design was followed by this; which
recommended that a ceramic structured packing should be utilised for column D-102, due to the corrosive
key component, and the column being operated at vacuum, and sieve trays be used for column D-103.
Column D-103 was then critically checked weeping, flooding, entrainment, and other calamities that could
potentially decrease the efficiency, and cause operational failure. Consequently, the number of trays in
column D-103 was increased from 10 to 15, to account for the tray inefficiency. A mechanical design was
then performed on both columns which recommended the use of a Ni-Mo alloy for column D-102, due to
its acid-resistant properties. In addition, the ancillaries attached to the columns was rated and designed. A
more accurate economic analysis was conducted on both columns to determine the total annualised cost of
the designed distillation columns. A more rigorous safety analysis of the columns, and the whole process
will be examined in Part 3 of the report.
11. Specification Sheet
Project Name
Sustainable Production of Acrylic Acid
Project Part
Purification of Crude Glycerol
REV
DATE
BY
APVD
REV
DATE
1 ######## AA
21/04/2021
GROUP MT
Design Project 2021
COLUMN D-102 SPECIFICATION SHEET
Equipment Label
D-102
Equipment Name
Distillation Column D-102
Design Code
-
Volume
48.9
Plant Location
BY
APVD
City of Industy, CA, USA
3
m
PROCESS STREAM DATA
FEED
11
TOP PRODUCT
13
-1
Stream No.
BOTTOMS
12
Total Fluid Flow
kg hr
22260
19550
2707
Density
Dynamic Viscosity
kg m
mN s m-2
-3
929.9
2.549
972.2
3.116
960.7
0.4062
Specific Heat
kJ kg-1 K-1
2.846
2.968
2.011
Latent Heat
Temperature
Absolute Pressure
Nominal Diameter of Pipe
kJ kg-1
°C
kPa
mm
1868
200.8
5
200
786.4
199.8
5
200
1617
235
5
200
mol%
0.001
0.8992
0.0737
0.0156
0.0105
mol%
0.0011
0.989
0.0094
0.0004
0
mol%
0
0.0098
0.7101
0.1655
0.1145
Stream Compositions
Component
Water
Glycerol
Sulfuric acid
Methyl Oleate (FAME)
NaCl
MECHANICAL SPECIFICATION
Column Design
Shell Material
Wall Thickness
Insulation
Insulation Thickness
External Diameter
Head Type
Operating Pressure (Bottom)
Predicted Pressure Drop
Plate Design
Ni-Mo alloy
7 mm
Mineral wool
50 mm
1.614 m
Torispherical
5 kPa
1.413 kPa
Plate Type
Plate Material
No. stages
Packing height
Column Support
Structured packing
Ceramic
18
4.86
m
Estimated Column Mass
Support Type
Support Material
Support Height
Support Base Diameter
Support Thickness
29331
Skirt
Carbon Steel
3.00
1.60
10.0
kg
m
m
mm
Project Name
Sustainable Production of Acrylic Acid
Project Part
Acrolein Recovery
REV
DATE
BY
APVD
REV
DATE
1 ######## AA
21/04/2021
GROUP MT
Design Project 2021
COLUMN D-103 SPECIFICATION SHEET
Equipment Label
Design Code
D-103
-
Equipment Name
Volume
Distillation Column D-103
67.2
m3
Plant Location
BY
APVD
City of Industry, CA, USA
PROCESS STREAM DATA
kg hr
FEED
22
25361.7
VAPOUR PRODUCT
23
15880
kg hr-1
24970
15880
-
-1
391.7
0.9254
1.349
9481.7
-
0.0102
0.3114
1.626
1.35
1340
67.7
101.325
400
3.993
2280
100
101.325
400
2225
100.2
101.325
400
mol%
0.0086
0.0704
0.0204
0.0204
0.0204
0.1994
0.6453
0.0122
0.0006
0.0022
0.0001
mol%
0.0184
0.151
0.0437
0.0437
0.0437
0.4276
0.2703
0.0015
0
0
0
mol%
0
0
0
0
0
0
0.9731
0.0215
0.0011
0.0042
0.0002
Stream No.
Total Fluid Flow
Total Vapour Flow
Total Liquid Flow
Density
kg hr
kg m-3
Dynamic Viscosity
mN s m-2
-1
-1
Specific Heat
Latent Heat
Temperature
Absolute Pressure
Nominal Diameter of Pipe
Stream Compositions
kJ kg K
kJ kg-1
°C
kPa
mm
Component
Oxygen
Nitrogen
Hydrogen
Carbon Dioxide
Acetaldehye
Acrolein
Water
Acetol
Glycerol
Sulfuric acid
Methyl Oleate
-1
BOTTOMS
24
9481.7
956.4
MECHANICAL SPECIFICATION
Column Design
Shell Material
Internal Diameter
Wall Thickness
Insulation
Insulation Thickness
External Diameter
Head Type
Operating Pressure (Bottom)
Predicted Pressure Drop
Plate Design
Carbon Steel
2.00
9.0
Mineral Wool
50.0
2.018
Torispherical
101.33
33.400000
m
mm
mm
m
kPa
kPa
Plate Type
Plate Material
No. Plates
Plate Spacing
Plate Thickness
Wier Length
Calming Zone Width
Unperforated Edge Strip Width
Wier Height
Hole Diameter
No. Holes per Plate
Pitch
Pitch Length
Column Support
Sieve
Carbon Steel
15
0.60
5.00
1.54
50.0
100.0
50.0
5.00
12160
Triangular
12.8
m
mm
m
mm
mm
mm
mm
Estimated Column Mass
Support Type
Support Material
Support Height
Support Base Diameter
Support Thickness
21337
Conical Skirt
Carbon Steel
3.00
2.00
10.0
mm
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