Ethylbenzene Capstone Project, Mass balance, Energy balance, Equipment design, Heat exchanger, distillation column, Pump, Cost estimation & Process control

1. Production of ethylbenzene by liquid
alkylation of benzene using zeolite catalyst
This dissertation is submitted to the Department of Chemical Engineering
for the partial fulfillment of the requirements for the Bachelor of Science
in Chemical Engineering degree
By
Alaa Elgabry
Amr Mansi
Amr Nabil
Basma Ali
Karim Ashour
Supervisor
Prof. Dr. Mohamed Bassyouni
June 2019
Acknowledgement
Port Said University
Faculty of Engineering
Department of Chemical Engineering

2. 2
We have taken efforts in this project. However, it would not have been possible without
the kind support and help of our great professors. We would like to extend our sincere
thanks to all of them. We would like to express our great appreciation to our supervisor
and mentor, Professor Mohamed Bassyouni for his guidance and constant supervision
as well as for providing necessary information regarding the project, also for giving us
a great share of his precious time and knowledge. We would like to express our
gratitude towards our families for their great help and constant support over years which
have led us to this success.

3. i
Table of Contents
Chapter 1 Introduction...............................................................................................1
1. Introduction................................................................................................................2
1.1 History..................................................................................................................2
1.2 Physical and chemical properties of ethylbenzene...............................................2
1.3 Hazard assessment................................................................................................3
1.3.1 National Fire Protection Association fire diamond.......................................3
1.3.2 Ethylene safety considerations ......................................................................3
1.3.3 Benzene safety considerations.......................................................................4
1.3.4 Safety considerations of ethylbenzene ..........................................................4
1.3.5 Safety considerations of diethylbenzene .......................................................4
1.3.6 Safety considerations of Y-zeolite catalyst ...................................................4
1.4 Summary ..............................................................................................................5
Chapter 2 Literature review ......................................................................................6
2. Literature review........................................................................................................7
2.1 Reactions..............................................................................................................7
2.2 Liquid phase aluminum chloride catalyst process................................................7
2.2.1 Description.....................................................................................................7
2.2.2 Advantages ....................................................................................................8
2.2.3 Disadvantages................................................................................................8
2.3 Vapor -phase zeolite catalyst process...................................................................9
2.3.1 Description.....................................................................................................9
2.3.2 Advantages ....................................................................................................9
2.3.3 Disadvantages..............................................................................................10
2.4 Liquid phase zeolite catalyst process .................................................................10
2.4.1 Description...................................................................................................10
2.4.2 Advantages ..................................................................................................10
2.5 Mixed liquid-vapor phase zeolite catalyst process.............................................10
2.5.1 Description...................................................................................................11
2.5.2 Advantages ..................................................................................................11
2.6 Summary ............................................................................................................13
Chapter 3 Liquid phase zeolite catalyst process ....................................................14
3. Liquid phase zeolite catalyst process.......................................................................15
3.1 Process description.............................................................................................15

4. ii
3.2 Material balance.................................................................................................15
3.2.1 Available data and assumptions ..................................................................15
3.2.2 Alkylator mass balance................................................................................17
3.2.3 Material balance on the benzene distillation column ..................................17
3.2.4 Material balance on the ethylbenzene distillation column ..........................18
3.2.5 Material balance on the transalkylator.........................................................18
3.3 Summary ............................................................................................................19
Chapter 4 Energy balance........................................................................................21
4. Energy balance.........................................................................................................22
4.1 Data available.....................................................................................................22
4.2 Energy balance procedures.................................................................................24
4.2.1 Energy balance for ethylene compression...................................................24
4.2.2 Energy balance on the alkylator ..................................................................26
4.2.3 Energy balance on benzene distillation column ..........................................28
4.2.4 Energy balance on ethylbenzene distillation column ..................................31
4.2.5 Energy balance on transalkylator pre-mixing point ....................................33
4.2.6 Energy balance on the transalkylator...........................................................34
4.3 Summary ............................................................................................................36
Chapter 5 Equipment design ...................................................................................40
5. Equipment design.....................................................................................................41
5.1 Design of benzene distillation column...............................................................41
5.1.1 Determination of the number of ideal stages and feed tray location...........41
5.1.2 Tray design ..................................................................................................45
5.1.3 Tray efficiency and column height..............................................................55
5.2 Design of the ethylbenzene distillation column.................................................58
5.2.1 Determination of the number of ideal stages and feed tray location...........59
5.2.2 Determination of the column efficiency and column dimensions...............61
5.3 Design of alkylation reactor...............................................................................63
5.4 Design of heat exchanger...................................................................................67
5.4.1 Determination of the amount of water required and heat exchanger duty ..67
5.4.2 Determination of the tube-side heat transfer coefficient .............................69
5.4.3 Determination of the shell-side heat transfer coefficient.............................70
5.4.4 Determination of the overall heat transfer coefficient.................................71
5.4.5 Tube and shell side pressure drop................................................................72
5.4.6 Heat exchanger insulation ...........................................................................73

5. iii
5.5 Pump design.......................................................................................................74
5.6 Summary ............................................................................................................76
Chapter 6 Plant layout and plant location..............................................................77
6. Plant layout and plant location.................................................................................78
6.1 Plant location and site selection .........................................................................78
6.1.1 Marketing area.............................................................................................78
6.1.2 Raw materials ..............................................................................................78
6.1.3 Transport......................................................................................................79
6.1.4 Availability of labor.....................................................................................79
6.1.5 Utilities (Services).......................................................................................79
6.1.6 Environmental impact and effluent disposal ...............................................80
6.1.7 Local community considerations.................................................................80
6.1.8 Land (Site considerations)...........................................................................80
6.1.9 Climate.........................................................................................................80
6.1.10 Political and strategic considerations ........................................................80
6.2 Site layout...........................................................................................................82
6.3 Plant layout.........................................................................................................82
6.3.1 Costs ............................................................................................................83
6.3.2 Process Requirements..................................................................................83
6.3.3 Operation .....................................................................................................83
6.3.4 Maintenance.................................................................................................83
6.4.5 Safety...........................................................................................................83
6.3.6 Plant Expansion...........................................................................................83
6.3.7 General Considerations................................................................................83
6.4 Summary ............................................................................................................84
Chapter 7 Cost estimation........................................................................................85
7. Cost estimation.........................................................................................................86
7.1 Purchased equipment cost..................................................................................86
7.1.1 Heat exchangers...........................................................................................86
7.1.2 Alkylation reactor........................................................................................87
7.1.3 Transalkylation reactor................................................................................88
7.1.4 Benzene distillation column ........................................................................88
7.1.5 Ethylbenzene distillation column ................................................................88
7.1.6 Compressor cost ..........................................................................................89
7.1.7 Pumps cost...................................................................................................89

6. iv
7.2 Capital investment..............................................................................................90
7.3 Operating cost ....................................................................................................91
7.3.1 Variable operating costs ..............................................................................91
7.3.2 Fixed operating costs...................................................................................92
7.4 Depreciation cost................................................................................................93
7.5 Cash flow and cash flow diagram ......................................................................93
7.6 Summary ............................................................................................................96
Chapter 8 Process control ........................................................................................97
8. Process control.........................................................................................................98
8.1 Introduction to process control...........................................................................98
8.2 Control of liquid level in storage tanks..............................................................99
8.3 Control of heat exchanger ..................................................................................99
8.4 Control of the alkylation reactor ......................................................................100
8.5 Control of distillation column ..........................................................................101
8.6 Summary ..........................................................................................................103
Appendices................................................................................................................104
Appendix A Distillation design..............................................................................105
Appendix B Heat exchanger design.......................................................................109
Appendix C Cost estimation data...........................................................................113
Appendix D Similarity report.................................................................................115
References.................................................................................................................126

7. v
List of Figures
Figure 1.1 The NFPA fire diamond system illustration for hazards identification. ......3
Figure 1.2 Fire diamond of ethylene..............................................................................3
Figure 1.3 Fire diamond of benzene ..............................................................................4
Figure 2.1 Simplified flowsheet of Liquid phase aluminum chloride catalyst process.8
Figure 2.2 Simplified flowsheet of vapor -phase zeolite catalyst process.....................9
Figure 2.3 Simplified flowsheet of liquid phase zeolite catalyst process....................11
Figure 2.4 Simplified flowsheet of mixed liquid-vapor zeolite catalyst process.........12
Figure 3.1 process flowsheet for ethylbenzene production by liquid phase zeolite
catalyst process ............................................................................................................16
Figure 3.2 Sketch of the alkylation reactor..................................................................17
Figure 3.3 Sketch of the benzene distillation column..................................................18
Figure 3.4 Sketch of the ethylbenzene distillation column..........................................18
Figure 3.5 Sketch of the transalkylation reactor..........................................................19
Figure 4.1 Sketch of the ethylene pre-conditioning sequence.....................................26
Figure 4.2 Sketch of the alkylator along with fully defined streams...........................27
Figure 4.3 Total energy flow in a distillation column .................................................28
Figure 4.4 Sketch of benzene distillation column along with fully defined streams...29
Figure 4.5 Total energy flow around a distillation column condenser ........................30
Figure 4.6 Sketch of ethylbenzene distillation column with fully defined streams.....31
Figure 4.7 Sketch of the transalkylator along with fully defined ................................35
Figure 4.8 Process flow diagram of the base case design including main equipment and
stream's designations....................................................................................................37
Figure 4.9 Aspen hysys ethylbenzene process simulation...........................................38
Figure 5.1 Simple geometric representation of the tray...............................................47
Figure 5.2 Graphical construction of the number of ideal stages For (a) the rectifying
section and (b) the stripping section. ...........................................................................61
Figure 5.3 Illustration of the stresses affecting the welded joints of a pressurized
cylindrical wall.............................................................................................................65
Figure 5.4 Temperature profile of the alkylation reactor.............................................66
Figure 5.5 Sketch of the heat exchanger of concern....................................................67
Figure 5.6 Sketch of the pump concerned in the design.............................................74
Figure 6.1 Illustration of the plant layout. ...................................................................84
Figure 7.1 Cost of shell and tube heat exchangers.......................................................86
Figure 7.2 Cost of vertical pressure vessel. .................................................................88

8. vi
Figure 7.3 Cost of distillation column trays ................................................................88
Figure 7.4 Cumulative cash flow diagram...................................................................94
Figure 7.5 The variation with selling price of cumulative cash position (a), and of
ROROI (b). ..................................................................................................................95
Figure 8.1 Standard symbols for control elements. .....................................................98
Figure 8.2 Control scheme of liquid storage tank........................................................99
Figure 8.3 Control scheme of heat exchanger. ..........................................................100
Figure 8.4 Control scheme of the alkylation reactor..................................................101
Figure 8.5 Control scheme of distillation column .....................................................102

9. vii
List of Tables
Table 1.1 Physical properties of ethylbenzene ..............................................................2
Table 2.1 Comparison between the two modes of operation for alkylation reaction. .12
Table 3.1 Material balance data for the manufacturing of 400000 tons/year of
ethylbenzene using liquid phase zeolite catalyst process. ...........................................20
Table 4.1 Values of constants for calculating liquid and gas phase heat capacities....23
Table 4.2 Values of constants for calculating latent heats of vaporization at any boiling
temperatures.................................................................................................................23
Table 4.3 Values of Antoine's equation constants .......................................................24
Table 4.4 Constants for calculating densities of liquid pure components. In addition to
the normal boiling points and heats of formation........................................................24
Table 4.5 Enthalpies and molar flows for the inlet and outlet components of the
alkylator. ......................................................................................................................26
Table 4.6 Enthalpies and molar flows for the inlet and outlet components of the mixing
point. ............................................................................................................................33
Table 4.7 Enthalpies and molar flows for the inlet and outlet components of the
transalkylator................................................................................................................34
Table 4.8 Aspen hysys process workbook...................................................................39
Table 5.1 Relative volatilities of A,B and C at the top and bottom.............................43
Table 5.2 Design parameters of the stripping section..................................................52
Table 5.3 Design parameters of the rectifying section ................................................54
Table 5.4 Benzene column – sieve tray data sheet ......................................................58
Table 5.5 Equilibrium constant for top, feed and bottom............................................59
Table 5.6 Design parameters of the ethylbenzene distillation column ........................62
Table 6.1 comparison between the three considered sites according to the main factors.
......................................................................................................................................81
Table 7.1 Cost estimation of shell and tube heat exchangers ......................................87
Table 7.2 Cost of pumps..............................................................................................89
Table 7.3 Estimation of the total fixed capital investment ..........................................90
Table 7.4 Summary of operating costs. .......................................................................91
Table 7.5 Raw materials and utilities cost. ..................................................................91
Table 7.6 Non discounted cumulative cash flow.........................................................94

10. viii
Abstract
Ethylbenzene is a very important chemical utilized in industry as a raw material for the
production of styrene monomer. The aim of this work is the design of a plant for the
production of 400000 tons/year of ethylbenzene using Y-zeolite as a liquid phase
alkylation reaction catalyst. It is found that 294638 tons/year of benzene and 105721
tons/year of ethylene are required to produce 400000 tons/year of ethylbenzene.
Equipment design of all the process units including reactors, heat exchangers,
distillation columns, etc. is carried out based on the data calculated by material and
energy balance. The plant is planned to be located at Tahrir petrochemical complex in
Ain Sokhna, Egypt. This location is chosen because it is superior to other locations in
terms of raw materials availability, market and other economical and operational
aspects. The economic investigation of the plant construction and operation showed
that the project is profitable with a cumulative profit of 44.5 million USD. Finally, the
process control is established to maintain the safest and most economical operating
conditions. Styrene monomer that is produced from ethylbenzene is then polymerized
to polystyrene which is a highly versatile polymer used to make a wide variety of
products such as food packing, laboratory ware, electronics, automobile parts. Its foam
form can also be used as an insulating material and lightweight protective packaging.

11. Chapter 1
Introduction

12. IntroductionChapter 1
2
1. Introduction
Ethylbenzene is an organic compound with the chemical formula C6H5CH2CH3. This
aromatic compound (which is also known as phenyl ethane and ethylbenzol) has
various applications; it is used in the production of styrene which is further converted
to polystyrene. Moreover, ethylbenzene is used as a solvent in many industries such as
rubber manufacturing, paint manufacturing, paper coating, and as a constituent of
asphalt and naphtha, and in fuels [1,2]. Ethylbenzene is manufactured by the acid-
catalyzed reaction of benzene and ethylene followed by distillation to obtain the desired
ethylbenzene and recover the unreacted benzene [3].
1.1 History
Currently, almost all ethylbenzene (EB) is produced commercially by alkylating
benzene with ethylene, primarily via two routes: in the liquid phase with aluminum
chloride catalyst, the vapor phase with a synthetic Zeolite catalyst. The alkylation of
aromatic hydrocarbons with olefins in the presence of aluminum chloride catalyst was
first practiced by M. Balshon in 1879. however, Charles Friedel and James M. crafts
pioneered much of the early research on alkylation and aluminum chloride catalysis. In
1965 ca. 10% of the United States ethylbenzene production was from the super
fractionation of the mixed xylenes stream produced by the catalytic reforming of
naphtha. In 1986, the amount of ethylbenzene derived from this source was
insignificant because of the escalating cost of energy [4].
1.2 Physical and chemical properties of ethylbenzene
There are various chemical and physical properties of ethylbenzene.
o The physical properties of ethylbenzene are shown in (Table 1.1) [2,4].
o The most important reaction of EB is its catalyzed dehydrogenation to styrene
shown in (Eq.1.1) [5].
(1)
Table 1.1 Physical properties of ethylbenzene
Property Value
Molar mass 106.17 g.mol-1
Density 871.39 Kg/m3
at 15°C, 862.62 Kg/cm3
at 25°C
Normal boiling point 136.186°C
Latent heat of vaporization 335 kJ/kg
Specific heat capacity
1.169 KJ/Kg.k (ideal gas at 25°C)
1.725 KJ/Kg.K (liquid at 25°C)
Vapor pressure 9.53 mm Hg at 25°C

13. IntroductionChapter 1
3
1.3 Hazard assessment
The hazard assessment should be stated before the beginning of the design to account
for safety considerations; these considerations include the safety of workers in the field
from accidents and toxic materials and safety of nearby citizens.
1.3.1 National Fire Protection Association fire diamond
The National Fire Protection Association (NFPA) established a standard system for the
identification of the hazards of materials for emergency response. The system is
diamond separated into four sections (shown in figure 1.1), each section identifies a
specific hazard of the material and the how severe this hazard is [6]. This system helps
in determining whether a special materials of construction should be used, procedures
followed during emergencies and safety precautions related to process materials.
Fig. 1.1 The NFPA fire diamond system illustration for hazards identification.
1.3.2 Ethylene safety considerations
The fire diamond of ethylene is shown in (Figure 1.2). Ethylene is a colorless gas at
standard temperature and pressure, it is extremely flammable. Ethylene has a lower and
upper explosion limit of 3.1% and 32% by volume in air
respectively. Therefore, high levels of safety must be
established in the compression and reaction of this gas.
Ethylene is considered a simple asphyxiant, it is neither toxic
nor carcinogenic. There is no health concern if released into the
atmosphere other than it explodes if present in the flammable
range. Moreover, the gaseous nature of ethylene necessitate the
storage under high pressure which introduce higher risks of
explosion.
Fig. 1.2 Fire diamond of ethylene

14. IntroductionChapter 1
4
1.3.3 Benzene safety considerations
The fire diamond of benzene is shown in (Figure 1.3). Benzene is a clear liquid at
standard temperature and pressure and produces. Benzene vapors are flammable, it has
a lower and upper explosion limit of 1.0% and 6.7% by volume in air respectively.
Benzene can cause extreme health concerns to the plant
workers if not handled properly. Benzene is reported to
be carcinogenic and can damage the central nervous
system under moderate exposure periods [7]. Boiling
point of benzene under standard conditions is 80.1°C and
it is immiscible with water. Therefore, a firefighting
system using foam or CO2 as the extinguishing fluid must
be installed at places where high amounts of benzene is
located such as the alkylation reactor and storage tanks.
1.3.4 Safety considerations of ethylbenzene
Ethylbenzene is a clear colorless liquid at standard temperature and pressure, it has very
similar properties to benzene. It is immiscible with water and has similar flammability
limits. It has higher boiling point than benzene which means it has a lower chance of
spreading to the atmosphere. Acute (short-term) exposure to ethylbenzene in humans
results in respiratory effects, such as throat irritation and chest constriction, irritation of
the eyes, and neurological effects such as dizziness. The reference concentration for
ethylbenzene toxicity is 1 mg.m-3
.The reference dose for ethylbenzene is 0.1 milligrams
per kilogram body weight per day.
1.3.5 Safety considerations of diethylbenzene
Diethylbenzene is treated in the same manner as benzene and ethylbenzene. In fact, all
the three aromatic compounds have the same fire diamond and very similar health
impacts. However, increasing the number of ethyl group connected to the benzene ring
increases the boiling point and greatly reduces the volatility.
1.3.6 Safety considerations of Y-zeolite catalyst
The catalyst used in this process belongs to the Y-zeolite family. The catalyst is
developed by Honeywell UOP company. It is named EBZ-500 and EBZ-100 for
alkylation and transalkylation respectively [8]. The catalyst doesn't pose any safety
concerns; it is inert, stable and safe to dispose into the environment.
Fig. 1.3 Fire diamond of benzene

15. IntroductionChapter 1
5
1.4 Summary
In this chapter, the manufacturing process of ethylbenzene by liquid phase alkylation
of benzene using Y-zeolite catalyst is introduced. Early processes used aluminum
chloride as a catalyst but it was replaced by zeolites to avoid corrosion problems.
Ethylbenzene is the raw material for the manufacturing of styrene which is then
polymerized to obtain ,the widely used polymer, polystyrene. Physical and chemical
properties of ethylbenzene are summarized. The toxicity and safety related to every
material present in the process are addressed. All the organic materials available are
flammable, benzene is carcinogenic, ethyl and diethylbenzene are also carcinogenic but
are less active and offer lower risk than benzene. The catalyst is safe to use in the
process and offers no environmental impact on disposal.

16. Chapter 2
Literature review

17. Literature reviewChapter 2
7
2. Literature review
There are different manufacturing processes available for Ethylbenzene. Some of
these are listed below [2,9]:
• Liquid phase aluminum chloride catalyst process
• Vapor-phase zeolite catalyst process
• Liquid phase zeolite catalyst process
• Mixed Liquid-Vapor Phase zeolite Catalyst process
2.1 Reactions
The main reaction is the liquid phase reaction of benzene with ethylene (Eq.2.1) [3].
(2.1)
However, an undesired reaction occurs in which ethylbenzene reacts with ethylene to
form diethyl benzene (Eq.2.2). The generation of diethyl benzene must be kept to
minimum not only because it consumes the desired product but also due to the fact that
it in styrene production.
(2.2)
A third reaction also occurs, in which diethyl benzene reacts with benzene to form
ethylbenzene (Eq.2.3).
(2.3)
2.2 Liquid phase aluminum chloride catalyst process
Liquid phase aluminum chloride processes have been the dominant source
of Ethylbenzene since the 1930s to about 1980.
2.2.1 Description
Alkylation of benzene in the presence of an aluminum chloride catalyst complex is
exothermic (ΔH=-114 kJ/mol). In the conventional AlCl3 process three phases are
present in the reactor. Aromatic liquid, ethylene gas, and a liquid catalyst complex
phase (a reddish-brown material called red oil). Process flowsheet is shown in (Figure
2.1). A mixture of catalyst complex, dry benzene, and recycled polyalkylbenzenes is
continuously fed to the reactor and agitated to disperse the catalyst complex phase in
the aromatic phase. Ethylene and the catalyst promoter are injected into the reaction
mixture through spargers. The liquid reactor effluent is cooled and discharged into a

18. Literature reviewChapter 2
8
settler, where the heavy catalyst phase is decanted from the organic liquid phase and
recycled. The organic phase is washed with water and caustic to remove dissolved
AlCl3 and promoter. The aqueous phase from these treatment steps in first neutralized
and then recovered as a saturated aluminum chloride solution and wet aluminum
hydroxide sludge. The unreacted benzene is recovered by the first columns as an
overhead distillate. The second column separates the ethylbenzene product from the
heavier polyalkylated components. The bottoms product of the second column is fed to
a final column, where the recyclable polyalkylbenzenes are stripped from non-
recyclable high molecular mass residue compounds. The residue or flux oil, consisting
primarily of polycyclic aromatics, is burned as fuel.
Fig. 2.1 Simplified flowsheet of Liquid phase aluminum chloride catalyst process
2.2.2 Advantages
• The aluminum chloride present in alkylation reactor effluent catalyst
transalkylation reaction
• Reaction is very fast in presence of aluminum chloride & produces almost
stoichiometric yields of ethylbenzene.
• Essentially 100% of ethylene is converted
2.2.3 Disadvantages
• Handling and disposal of aluminum chloride catalyst and waste has become
increasingly costlier and more complicated because of environmental
considerations
• Equipment and piping corrosion and fouling along with related environmental
issues led to development of EB process based on solid acid heterogeneous catalysts
• Major equipment pieces needed to be replaced on regular schedule because
of corrosion which results in extensive turnarounds poor plant on-stream efficiency
and thus are primary contributors to the high operating costs associated with
aluminum chloride

19. Literature reviewChapter 2
9
2.3 Vapor -phase zeolite catalyst process
2.3.1 Description
The reactor typically operates at 400-450°C and 2-3 MPa (20-30 bars). At this
temperature, more than 99% of the net process heat input and exothermic heat of
reaction can be recovered as steam. Process flowsheet is shown in (Figure 2.2). The
reaction section includes two parallel multi bed reactors, a fired heater, and heat
recovery equipment. The high-activity catalyst allows trans alkylation and alkylation to
occur simultaneously in a single reactor. Because the catalyst slowly deactivates as a
result of coke formation and requires periodic regeneration, two reactors are included
to allow uninterrupted production: one is on stream while the other is regenerated.
Regeneration takes 36 hrs and is necessary after 6-8weeks of operation. The reactor
effluent passes to the purification section as a hot vapor. This steam is used as the heat
source for the first distillation column, which recovers the bulk of the unreacted
benzene. The remaining benzene is recovered from a second distillation column. The
Ethyl benzene product is taken as the overhead product from the third column. The
bottoms product from this column is sent to the last column, where the recyclable alkyl
benzenes and poly alkyl benzenes are separated from heavy no recyclable residue.
Fig. 2.2 Simplified flowsheet of vapor -phase zeolite catalyst process
2.3.2 Advantages
• Use of zeolite catalyst that eliminated issues associated with corrosion and
waste disposal of aluminum chloride
• The original vapor phase design accomplished the alkylation and trans
alkylation reactions in single reactor
• The third generation technology is capable of achieving EB yield greater
than99%
• The third generation technology offered significant benefits in purity, capital
cost

20. Literature reviewChapter 2
10
2.3.3 Disadvantages
• The significant extent of isomerization reactions and catalyst deactivation by
deposition of carbonaceous material are most important problems associated
with high temperature
• The length of time between regeneration can vary from as little as 2months to
slightly more than 1 year depending on specific plant design and operating
conditions
• Because the reactors must be taken offline for regeneration consequently
increasing the capital and operating costs for vapor phase plant.
• Additional equipment may be required for regeneration procedure depending
on specific plant design which adds capital cost to plant
2.4 Liquid phase zeolite catalyst process
2.4.1 Description
The alkylation reactor is maintained in liquid phase and uses multiple bed catalyst beds
ethylene injection. The ethylene conversion is essentially 100% in the alkylator reactors
and the reactor nearly operates isothermally. The exothermic heat of reaction is
recovered and used to produce steams or as heat duty in the distillation columns.
Process flowsheet is shown in (Figure 2.3). The alkylation and transalkylation reactor
effluent stream are sent to the distillation section which consist of primarily of three
distillation columns. The first column is a benzene column and it separates unconverted
benzene into the overhead stream for recycle to the reactors. The benzene column
bottom stream feeds the EB column. The EB column recovers the EB product in the
overhead stream and the bottom stream of the EB column feeds the PEB column where
PEB is fractionated overhead and recycle to the transalkylation reactor. The bottom
stream of the PEB column is removed as the residue stream and is generally used as
fuel in an integrated styrene.
2.4.2 Advantages
• The liquid phase zeolite catalyst process operates at substantially lower
temperature which decreased side reactions dramatically resulting in ultra-high
purity EB product.
• The plant achieves high on stream efficiency often greater than 99% which results
in low turnaround & maintenance cost.
• Catalyst regeneration is mild carbon burn procedure that is relatively inexpensive
2.5 Mixed liquid-vapor phase zeolite catalyst process
The process is based on mixed liquid-vapor phase alkylation reactor section. The design
of commercial plant is similar to the liquid phase technologies except for the design of
the alkylation reactor which combines catalytic reaction with distillation into a single
operation.

21. Literature reviewChapter 2
11
2.5.1 Description
This process operates under alkylation reactor, which combines catalytic reaction with
distillation into a single operation. Reaction temperature is 150-195 ̊C and operating
pressure of 1.6-2.1 MPa. The selectivity was above 83% (only benzene feed) and even
higher than 99% (benzene plus transalkylation feed).
Fig. 2.3 Simplified flowsheet of liquid phase zeolite catalyst process
Flow diagram of mixed liquid-vapor phase zeolite catalyst process is shown in (Figure
2.4). The process can be conveniently split into 3 major sections: Alkylation,
transalkylation and distillation section The alkylation reactor consists of two sections
catalytic distillation and standard distillation section. Benzene is fed at the top of the
reactor and ethylene is fed as a vapor at the bottom in catalytic distillation section
creating counter-current flow of reactants in the catalytic distillation section. In this
section, ethylene dissolves into the liquid phase rapidly heat of reaction creates the
vaporization necessary to affect the distillation. The alkylation products mainly
ethylbenzene, di-ethylbenzene and other products are continuously fractioned and
removed from the catalytic distillation section. In bottom section standard distillation
occurs and bottom stream exits containing ethylbenzene, PEB and other products.
Transalkylation reaction occurs on fixed beds of the catalyst using a vapor–liquid
mixture of benzene and other impurities like cyclohexane. Transalkylation occurs at the
temperature in the range of 220-250 ̊C. The benzene is used in stoichiometric excess
which gives 50% conversion of PEB to ethylbenzene per pass. The main reaction is the
alkylation of benzene to give ethylbenzene. The above reaction is carried out at 190 ̊C
in the presence of Zeolite Catalyst. Finally, PEB and ethylbenzene proceed to benzene
stripping section which operates in the temperature range of 295-325 ̊C depending upon
the pressure. Fired heater (or hot oil) provides heat for thermal duty. The stripping heat
input also decreases the alkylation temperature thus improving the alkylation rate of
reaction and minimizes the use of catalyst required.
2.5.2 Advantages
• Purity of product is more than other manufacturing process.

22. Literature reviewChapter 2
12
• Less pure ethylene & benzene is used.
• Low operating conditions.
• Cost of production is lower than other process.
Fig. 2.4 Simplified flowsheet of mixed liquid-vapor zeolite catalyst process
The liquid phase alkylation process was found to be more cost effective and safer to
operate than other processes. Therefore, it was chosen for further investigation. A
comparison between liquid and gas phase alkylation is shown in (Table 2.1) [10]. In the
following chapters the liquid phase process will be intensively investigated.
Table 2.1 Comparison between the two modes of operation for alkylation reaction.
Gas phase Production Using Zeolite
Catalysts
Liquid phase Production Using Zeolite
Catalyst
Extreme operating conditions between
675-725 K and 200-400 psig resulting in
higher risk.
Moderate operating temperatures and
pressures between 420-470 K and 70-
150psig
Benzene/ethylene ratio is approximately
8-16 by mole fraction.
benzene/ethylene alkylator feed ratios
range from 1.5-2.0 on a molar basis
Two reactors in parallel are used,
Alkylation and transalkylation take place
in the same reactor, while the other is for
regeneration
Requires both alkylation and trans-
alkylation reactors put in series.
Higher cost of operation
Large savings available in operational
costs.
The catalyst requires regeneration every
two to four weeks
catalyst life is approximately from two to
five years for the alkylator and the
transalkylator

23. Literature reviewChapter 2
13
2.6 Summary
In this chapter, all the processes that had been proposed for the production of
ethylbenzene are reviewed. The processes are categorized based on the catalyst used
and/or the reactants' phase in the alkylation reactor into five processes. Two processes
utilize aluminum chloride as catalyst for the reaction in liquid or gas phase. The three
remaining processes utilize zeolite as catalyst for the reaction in liquid phase, gas phase
or mixed phases in a reactive distillation system. The process selection is carried out
between the liquid phase alkylation using zeolite catalyst and the mixed phases process,
other processes are eliminated. The liquid phase process is chosen over the mixed
phases process because the reactive distillation system in the mixed phases process is
extremely difficult to control which can lead to the formation of many undesired by-
products; greatly decreasing selectivity and increasing the complexity of the process.

24. Chapter 3
Liquid phase zeolite catalyst process

25. Material balanceChapter 3
15
3. Liquid phase zeolite catalyst process
3.1 Process description
Process flowsheet of the base case of this study is shown in (Figure 3.1). Ethylbenzene
is being produced from benzene and ethylene by liquid phase alkylation in a packed
bed reactor, fitted with a fixed bed of zeolite used as catalyst. Gaseous ethylene is
sparged into the liquid phase of benzene mixture (fresh benzene and recycled benzene
from benzene distillation column) in the first reactor (alkylator). Both reactors operate
at high pressure (20 atm) to maintain the liquid phase in the reactor at high temperatures
required for reasonable reaction rates. Alkylator operates at 210°C and ethylene
conversion is 100%. The reaction is exothermic under isothermal condition. The
effluent from first reactor (alkylator) and second reactor (transalkylator) are fed to
benzene distillation column. It separates a distillate that is mixture of benzene and
ethylbenzene but it is mostly benzene (purity 99.9%) which is recycled to alkylator and
transalkylator. Bottom stream ,a mixture of ethylbenzene and diethylbenzene, is fed to
a second distillation column. It produces ethylbenzene as a distillate (purity 99.88%)
and a diethylbenzene bottom is recycled back to transalkylator. In the transalkylator
diethylbenzene reacts with benzene to produce ethylbenzene which is mixed with the
effluent from the alkylator and sent for purification in benzene and ethylbenzene
columns.
3.2 Material balance
Material balance for this process has been carried out to determine the amount of
benzene and ethylene required per hour to produce ethylbenzene with a target quantity
of 400000 tons/year (461.7 kmol/h).
3.2.1 Available data and assumptions
- Benzene fed to the process is pure at 25°C and 1 atm.
- Ethylene fed to the process is pure and at 25ׄ°C and 1 atm.
- Alkylator feed ratio ( Benzene to ethylene) is assumed to be 2.
- The limiting reactant is ethylene with overall conversion of 100% [3].
- 95% of the total ethylene fed are converted in the first reaction to form
ethylbenzene. The other 5% are completely consumed by the second reaction to
form diethylbenzene [3].
- Benzene recycle stream to alkylator is assumed to be equal to 85% of total
benzene recycle stream from benzene column.
- Benzene column distillate contains 0.999 of total benzene fed with a purity of
99.9% and the balance is ethylbenzene.
- Conversion of diethylbenzene in the transalkylator is 52% [3].
- Ethylbenzene column distillate contains 0.999 of total ethylbenzene fed with a
purity of 99.88% as a final product.
- The operation year is set to be 340 days.

26. Material balanceChapter 3
16
Fig.3.1processflowsheetforethylbenzeneproductionbyliquidphasezeolitecatalystprocess

27. Material balanceChapter 3
17
3.2.2 Alkylator mass balance
First, material balance over the alkylator is
carried out (Figure 3.2). Assuming basis 400
kmol/h fresh benzene and alkylator benzene
recycle of 600 kmol/h.
Mixed benzene = 1000 kmol/h
Ethylene feed = 1000 / 2= 500 kmol/h
Ethylene out = (1-1)*500 = 0
Ethylene reacted = 500 kmol/h
Where
X1 and
X2 are
the conversions in the first and second reactions
respectively.
From the stoichiometry:
y = 500 x 0.95 = 475 kmol EB/h
z = 500 x (1-0.95) x 1 = 25 kmol DEB/h
Reacted benzene must equal the amount produced of EB and DEB.
Reacted benzene = 500 kmol/h
Unreacted benzene = 1000-500 = 500 kmol/h
3.2.3 Material balance on the benzene distillation column
The benzene distillation column is shown in (Figure 3.3).
Perform component mass balance (C.M.B) on benzene
B,B+ nD,Bn=500
And nB,D = 0.999 of total benzene in the feed
B in the distillate = 0.999 x 500 = 499.5 kmol/h
B in the bottom = 500 – 499.5 = 0.5 kmol/h
The purity of benzene in the distillate = 99.9%
Molar flow of the distillate =
499.5
0.999
= 500 kmol/h
1 kmol 1 kmol 1 kmol
500 (1-X1)X2 Z kmol
1 kmol 1 kmol 1 kmol
500 X1 y kmol
Fig. 3.2 Sketch of the alkylation reactor

28. Material balanceChapter 3
18
- Component material balance on EB
475 = nEB,D + nEB,B
Mole fraction of EB in the distillate = 0.001
EB in the distillate = 0.001 x 500= 0.5 kmol/h
EB in the bottom = 475 – 0.5 = 474.5 kmol/h
DEB in the bottom = DEB in the feed
DEB in the bottom = 25 kmol/h
Benzene in the distillate is recycled back to the alkylator. However, the amount recycled
to the alkylator based on the above calculations = 0.85 x 499.5 = 424.575 which is lower
than the assumed value (600 kmol/h). The values will be corrected after performing
mass balance on all of the process units.
3.2.4 Material balance on the ethylbenzene distillation column
EB recovered in the distillate = 99.9 % of ethylbenzene fed
nEB,D = 0.999 * 474.5 = 474.0255 kmol/h
Distillate =
474.025
0.9988
= 474.595 kmol/h
All benzene fed is recovered in the distillate
nB,D = 0.5 kmol/h
And, nDEB,D = 474.7459-474.025-0.5
= 0.2209 kmol/h
The bottom streams are then determined:
nEB,B = 474.5 – 474.025 = 0.475 kmol/h
nDEB,B = 25 – 0.2209 = 24.7791 kmol/h
3.2.5 Material balance on the
transalkylator
The transalkylator is shown in (Figure 3.5).
Conversion of DEB in the transalkylator = 52%
DEB reacted = 24.7791 x 0.52 = 13 kmol/h
Fig. 3.3 Sketch of the benzene distillation column
Fig. 3.4 Sketch of the ethylbenzene distillation column

29. Material balanceChapter 3
19
From the stoichiometry:
Benzene reacted = 13 kmol/h
EB produced = 2*13 = 26 kmol/h
The reactor outlet is then determined:
DEBout = 24.7991 – 13 = 11.7991 kmol/h
EBout = 26 + 0.55 = 26.55 kmol/h
Bout = 74.925 – 13 = 71.925 kmol/h
3.3 Summary
In this chapter, the liquid phase alkylation of benzene using zeolite catalyst for the
production of 400000 tons/year of ethylbenzene was described. Detailed calculations
of the quantities of raw materials required and the flow of every component in the
process were performed on the basis of mass balance principles. The hand calculations
were performed without accounting for the recycle streams. The corrected values of the
flow rates are evaluated using Microsoft excel software and the results are shown
collectively in (Table 3.1).
1 kmol 1 kmol 2 kmol
13 kmol x kmol y kmol
Fig. 3.5 Sketch of the transalkylation reactor

30. Material balanceChapter 3
20
Total
DEB
EB
Ethylene
Benzene
Stream
No.
Total
DEB
EB
Ethylene
Benzene
Stream
No.
42.468
0.000
0.058
0.000
42.410
15
36.108
0.000
0.000
0.000
36.108
1
55.030
5.919
49.069
0.000
0.042
16
12.956
0.000
0.000
12.956
0.000
2
49.064
0.002
42.020
0.000
0.042
17
72.206
0.000
0.049
0.000
72.156
3
5.966
5.917
0.049
0.000
0.000
18
12.956
0.000
0.000
12.956
0.000
4
5.966
5.917
0.049
0.000
0.000
19
72.206
0.000
0.049
0.000
72.156
5
6.371
0.000
0.009
0.000
6.362
20
12.956
0.000
0.000
12.956
0.000
6
36.098
0.000
0.049
0.000
36.049
21
72.206
0.000
0.049
0.000
72.156
7
6.371
0.000
0.009
0.000
6.362
22
6.478
0.000
0.000
6.478
0.000
8
12.336
5.917
44.201
0.000
6.362
23
6.478
0.000
0.000
6.478
0.000
9
12.336
5.917
44.201
0.000
6.362
24
85.161
3.078
44.201
0.000
37.882
10
12.336
5.917
44.201
0.000
6.362
25
97.498
5.919
49.126
0.000
42.453
11
12.336
2.840
4.925
0.000
4.571
26
97.498
5.919
49.126
0.000
42.453
12
97.498
5.919
49.126
0.000
42.453
13
97.498
5.919
49.126
0.000
42.453
14
*Alltheflowratesgivenareinton/h
Table3.1Materialbalancedataforthemanufacturingof400000tons/yearofethylbenzeneusingliquidphasezeolitecatalystprocess.

31. Chapter 4
Energy balance

32. Energy balanceChapter 4
22
4. Energy balance
4.1 Data available
1. The specific heat capacity data are obtained from tabulated data found in Perry's
chemical engineering handbook [10]. The heat capacity is calculated for liquid
phase using (Eq.4.1) and for gas phase using (Eq.4.2).
CPL = C1 + C2 x T + C3 x T2
+ C4 x T3
+ C5 x T4 (4.1)
CPv = C1 + C2 �
C3 T⁄
sinh (C3 T⁄ )
�
2
+ C4 �
C5 T⁄
cosh(C5 T⁄ )
�
2
(4.2)
Where:
C1:C5: constants obtained from tabulated data.
Cp: specific heat capacity in (J/kmol.k).
T: absolute temperature.
The values of the different heat capacity constants for each component are shown in
(Table 4.1).
2. Heats of vaporization at any boiling temperature are obtained from (Eq.4.3).
∆𝐻𝐻𝑉𝑉 = 𝐶𝐶1 × (1 − 𝑇𝑇𝑟𝑟)𝐶𝐶2+𝐶𝐶3×𝑇𝑇𝑟𝑟+𝐶𝐶4×𝑇𝑇𝑟𝑟
2
(4.3)
Where:
C1:C4 : Constants obtained from tabulated data.
∆Hv: Latent heat of vaporization in (J/kmol).
Tr: Reduced temperature (T/Tc).
Tc: Critical temperature.
The values of the different heats of vaporization constants for each component are
shown in (Table 4.2).
3. Boiling points at 25°C and atmospheric pressure are available. Boiling points other
than the standard are obtained using Antoine's equation .
4. Antoine constants for benzene and ethylbenzene are obtained from [11] which
correspond to (Eq.4.4) and the constants for diethylbenzene are obtained from [12]
which correspond to (Eq.4.5).
ln(𝑝𝑝𝑣𝑣) = 𝐴𝐴 −
𝐵𝐵
𝐶𝐶 + 𝑇𝑇
(4.4)

33. Energy balanceChapter 4
23
Where:
Pv: Vapor pressure in mm Hg and T is in °C.
log10(𝑝𝑝𝑉𝑉) = 𝐴𝐴 −
𝐵𝐵
𝐶𝐶 + 𝑇𝑇
(4.5)
Where:
Pv is in bar and T in K.
The values of the constants are shown in (Table 4.3).
5. Standard heats of formation are obtained from [13] at 25°C and 1 atm.
6. Densities of the pure components are available as a function of temperature as shown
in (Eq.4.6).
𝜌𝜌 =
𝐶𝐶1
𝐶𝐶2(1+(1−
𝑇𝑇
𝐶𝐶3
)𝐶𝐶4
(4.6)
Where:
ρ: Density in kmol/m3
C1:C4: Constants available in tabulated data.
The values of the different density constants for each component are shown in (Table
4.4) along with normal boiling points and heats of formation.
There has been no available tabulated data for diethylbenzene. Therefore, the liquid
phase heat capacity relation and the densities at different temperatures are generated
from aspen hysys software.
Table 4.1 Values of constants for calculating liquid and gas phase heat capacities. obtained from [10].
Components Phase C1 C2 C3 C4 C5
Ethylene G 33380 94790 1596 55100 740.8
L
Benzene G 44420 232050 1494.9 17213 -678.15
L 129440 -169.5 0.64781 0 0
Ethylbenzene G 78440 339900 1559 242600 -702
L 133160 44.507 0.39645 0 0
Diethylbenzene G
L 44427 557.34 0 0 0
Table 4.2 Constants for calculating latent heats of vaporization at any boiling temperatures. From [10].
Components C1 C2 C3 C4
Benzene 47500000 0.45238 0.0534 0.1181
Ethyl benzene 5.464 0.392 0 0

34. Energy balanceChapter 4
24
Table 4.3 Values of Antoine's equation constants. From [11,12].
Component A B C
Benzene 15.9037 2789.01 220.79
Ethylbenzene 16.04305 3291.66 213.8
diethylbenzene 4.12544 1589.273 -71.131
Table 4.4 Values of constants for calculating densities of liquid pure components. In addition to the
normal boiling points and heats of formation. From [10.13].
components C1 C2 C3 C4
Hf
(kJ/mol)
N.B.P
(°C)
Ethylene 52.28 (g) -103.9
Benzene 1.0162 0.2655 562.16 0.28212 48.66 (L) 80.1
Ethylbenzene 0.6952 0.26037 617.2 0.2844 -12.46 (L) 136.2
Diethylbenzene -73.2 (L) 183.7
4.2 Energy balance procedures
A step by step energy balance is developed for the liquid phase zeolite catalyst process
to obtain the streams temperature and required heating or cooling duties.
The first stream to be evaluated is the ethylene feed to the reactor. Ethylene is
available at 25°C and 1 atm. The desired reactor operating conditions are 20 atm and
210°C to keep the benzene in liquid state at the inlet and to allow the reaction to proceed
at a reasonable rate [3].
4.2.1 Energy balance for ethylene compression
Assume ideal gas behavior, For a reversible adiabatic process the temperature is related
to pressure by (Eq.4.7)
�
𝑇𝑇1
𝑇𝑇𝑇𝑇
� = (
𝑃𝑃𝑃𝑃
𝑃𝑃1
)
𝛾𝛾−1
𝛾𝛾 (4.7)
Where γ is the heat capacity ratio (Cp/Cv).
The above equation is valid only if γ is constant. However, this is not the case with
ethylene and another relation must be obtained to correct the variation of γ with
temperature. The heat capacity ratio was previously confirmed to vary linearly with
temperature as shown in (Eq.4.8) [14].
𝛾𝛾 = 𝛾𝛾𝑜𝑜 − 𝑎𝑎𝑎𝑎 (4.8)
Where γo and a are constants that can be obtained by linear curve fitting.
Three different values for γ at 182,288 and 373k where obtained for ethylene [10] and
curve fitting yields.

35. Energy balanceChapter 4
25
γo = 1.5117
a = 0.00089 k-1
According to [15, 16], a suitable engineering approximation to the reversible adiabatic
process with variable γ can be made, this process can be divided into infinitesimal
processes, for all of which the adiabatic exponent γ can be regarded as constant. The
final equation for reversible adiabatic process with variable γ can be expressed as
(Eq.4.9).
𝑇𝑇1(𝛾𝛾0 − 𝑎𝑎𝑎𝑎𝑎𝑎 − 1) �
𝑃𝑃1
𝑃𝑃2
�
𝛾𝛾0−1
𝛾𝛾0
= 𝑇𝑇𝑇𝑇(𝛾𝛾0 − 𝑎𝑎𝑎𝑎1 − 1) (4.9)
Now substituting T0 = 298K, γo = 1.5117 and a =0.00089 k-1
T1s = 511.15 K
Apply energy balance over the compressor assuming negligible kinetic and potential
energy.
−𝑊𝑊𝑊𝑊 = 𝑛𝑛∆𝐻𝐻
Taking reference state as the state of the inlet feed and integrating (Eq.4.2).
∆𝐻𝐻 = � 𝐶𝐶𝑃𝑃𝑃𝑃 𝑑𝑑𝑑𝑑 = 𝐶𝐶1 ∗ (511.15 − 298) + 𝐶𝐶2𝐶𝐶3 ∗ (𝐶𝐶𝐶𝐶𝐶𝐶ℎ(
𝐶𝐶3
511.15
511.15
298
)
− 𝐶𝐶𝐶𝐶𝐶𝐶ℎ(
𝐶𝐶3
298
)) − 𝐶𝐶4𝐶𝐶5(𝑇𝑇𝑇𝑇𝑇𝑇ℎ �
𝐶𝐶5
511.15
� − 𝑇𝑇𝑇𝑇𝑇𝑇ℎ(
𝐶𝐶5
298
))
Substituting the values of the constants we obtain ∆H = 11397.417 kJ/kmol
The total isentropic work Ws = n∆H = 461.89*∆H = 5264.353 MJ/h = 1.462 MW
The actual outlet temperature is obtained by assuming a suitable compressor efficiency
of 75% [17].
Wactual = Ws /0.75 = 7019.137 MJ/h = 1.9452 MW
And the actual outlet temperature can be obtained by the same energy balance
procedure.
T1 = 568.76 K = 295.76 °C
The ethylene feed must therefore be cooled to 210°C. The flow arrangement is shown
in (Figure 4.1).
The cooler duty to cool ethylene from 568.76 K to 483 K is then calculated:

36. Energy balanceChapter 4
26
𝑄𝑄𝑐𝑐 = 𝑛𝑛∆𝐻𝐻 = 460.8 � 𝐶𝐶𝑝𝑝𝑝𝑝
483
568.76
𝑑𝑑𝑑𝑑
QC = 2564 MJ/h = 0.7122 MW
Cooling is performed by generating saturated steam at 2.2 bar from cooling water
available at 25°C. Taking Cp for water 4.2 kJ/kg.k, Tsteam = 123.25°C and latent heat of
vaporization = 2193 kJ/kg (from steam tables).
QC = mCp∆T + m∆Hv
0.7122*103
= mw*4.2*(123.25-
25)+2193*mw
mw = 0.273 kg/s steam generated
4.2.2 Energy balance on the alkylator
The fresh feed to the reactor is at 20 atm and 210°C. The reactor is operated
isothermally to prevent undesired vaporization of components and elevated
temperatures. Sketch of the alkylator along with the stream notations is shown in
(Figure 4.2). Reference state of 1 atm and 25°C is chosen; the enthalpies of each
component relative to the reference state are listed in (Table 4.5).
For isothermal reaction neglecting potential energy, kinetic energy and any work other
than flow work, the energy balance equation is reduced to:
𝑄𝑄 = ∆𝐻𝐻
∆𝐻𝐻 = � 𝑛𝑛𝑜𝑜 Ĥ𝑜𝑜 − � 𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖
Table 4.5 Enthalpies and molar flows for the inlet and outlet components of the alkylator.
Component
Feed product
ni (kmol/h) Ĥi (kJ/kmol) no (kmol/h) Ĥo (kJ/kmol)
Benzene 923.7800 Ĥ1 484.9845 Ĥ4
Ethylene 461.8900 Ĥ2 0 0
Ethylbenzene 0.4620 Ĥ3 416.3219 Ĥ5
Diethyl benzene 0 0 22.9356 Ĥ6
* Reference state, 25°C and 1 atm.
Ĥ1 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑 + ʋ ∆P
483
298
Where ʋ is the average specific molar volume between the reference and process
temperatures. The average specific volumes are then calculated (Eq.4.10).
Fig. 4.1 Sketch of the ethylene pre-conditioning sequence

37. Energy balanceChapter 4
27
ʋ = �
1
𝜌𝜌𝑖𝑖
�
𝑛𝑛
𝑛𝑛
𝑖𝑖=1
= �
𝐶𝐶2(1+(1−
𝑇𝑇𝑖𝑖
𝐶𝐶3
)𝐶𝐶4
𝐶𝐶1
𝑛𝑛
𝑖𝑖=1
(4.10)
For the inlet feed the average specific volumes are then calculated
ʋB = 0.1288 m3
/ kmol
ʋEB = 0.1565 m3
/ kmol
And that for the DEB produced, ʋDEB= 0.1172 m3
/ kmol
∆P is the change in pressure between the process and reference states in kPa = (20-
1)*1.013*102
= 1924.7 kPa
Ĥ1 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑 + 0.128 ∗ 1924.7
483
298
Ĥ1 = 79226.24 kJ/kmol
For ideal gas behavior pressure has no effect on
the enthalpy of ethylene
Ĥ2 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐸𝐸) 𝑑𝑑𝑑𝑑
483
298
Ĥ2 = 61925.47 kJ/kmol
Ĥ3 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐸𝐸𝐸𝐸) 𝑑𝑑𝑑𝑑 + ʋ ∆P
483
298
Ĥ3 =27084.49 kJ/kmol
For products the pressure drop is taken as 0.5
atm
∆P= (19.5-1)*1.013*102
=1874.05 kPa
Ĥ4 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑 + 0.1565 ∗ 1874.05
483
298
Ĥ4 = 79219.71 KJ/kmol
Ĥ5 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐸𝐸𝐸𝐸) 𝑑𝑑𝑑𝑑 + ʋ ∆P
483
298
Ĥ5 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑 + 0.1565 ∗ 1874.05
483
298
Fig. 4.2 Sketch of the alkylator along with fully defined
streams.

38. Energy balanceChapter 4
28
Ĥ5 = 27076.56 KJ/kmol
Ĥ6 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐷𝐷𝐷𝐷𝐷𝐷) 𝑑𝑑𝑑𝑑 + ʋ ∆P
483
298
Ĥ6 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑 + 0.1172 ∗
483
298
1874.05
Ĥ6 = −12283.25 kJ/kmol
Q = -52391705.56 kJ/h = -14553.25 kw
In order to maintain isothermal conditions, 14553.25kw of heat must be removed
from the reactor
Cooling is carried out using cooling water at 25°C and produce saturated steam at 2.2
bar.
The amount of water required =
14553.25
4.2∗(123.25−25)+2193
= 5.585 kg/s
4.2.3 Energy balance on benzene distillation column
At steady state, the energy balance over the entire system is illustrated in (Figure 4.3).
Fig. 4.3 Total energy flow in a distillation column
HF + QB = QC+HD+HW
The kinetic and potential energy of the process streams will be small and can be
neglected. Sketch of benzene distillation column along with fully defined streams is
shown in (Figure 4.4).

39. Energy balanceChapter 4
29
Fig. 4.4 Sketch of benzene distillation column along with fully defined streams
The temperature of the feed, top tray product and bottom tray product are calculated
from Antoine's equation
- The feed and bottom product are saturated liquids and the top tray vapor is
also saturated
- Tf is calculated from Antoine's equation at 1.3 atm = 107.21°C
- Temperature of the top tray product is calculated at 1.2atm =86.43°C
- The vapors are condensed and exits from the condenser as a saturated liquid at
86.43°C.
- Temperature of the bottom tray product is calculated at 1.4atm =151.56°C
HF =nB*[CpB*(Tf -Tref) + ʋB ∆Pf] + nEB*[CpEB*( Tf -Tref) + ʋEB ∆Pf] + nDEB*[CpDEB*(
Tf – Tref) + ʋDEB ∆Pf]
Take liquid components at 86.43 °C and 1 atm as a reference condition.
For the inlet feed the average specific volumes are then calculated
ʋB = 0.103 m3
/ kmol
ʋEB = 0.135 m3
/ kmol
ʋDEB = 0.117 m3
/ kmol
∆P = (1.3-1)*1.013*102
= 30.39 kPa
HF = 3948270.83 kJ/h

40. Energy balanceChapter 4
30
QC is determined by performing energy balance over the condenser (Figure 4.5).
HV = QC + HL + HD
Take reflux ratio = 1
L = D = V/2
V = 1085.914 kmol/h B + 1.087kmol/h EB
HV = nB*Hfg B + nEB*Hfg EB
Where Hfg is latent heat of vaporization
Hfg (B) = 30218 kJ/kmole
Hfg (EB) = 35222 kJ/kmole
HV =16426225.5 kJ/h
HD= ʋB ∆PD + ʋEB ∆PD
HD = 1095.55 kJ/h
HL = 1095.55 kJ/h
QC = 32852435.57 kJ/h = 9125.677 kW
Condensation is carried out using cooling water at 25°C and heating up to 50°C
The amount of water required =
9125.677
4.2∗(50−25)
= 86.911 kg/s
For the bottom product the average specific volumes are calculated
ʋB = 0.112 m3
/ kmol
ʋEB = 0.1429 m3
/ kmol
ʋDEB = 0.117 m3
/ kmol
∆P = (1.4-1)*1.013*102
= 40.52 kPa
Performing energy balance over the whole column
QB + HF = QC+ HD+ HW
HW = nB*[CpB*(T-Tref) + ʋB ∆Pw] + nEB*[CpEB*(T-Tref) + ʋEB ∆Pw] + nDEB*[CpDEB*(
T – Tref) + ʋDEB ∆Pw]
HW= 7135078.547 kJ/h
QB= QC+HD+HW -HF
QB= 36039252.29 kJ/h = 10010.9 kW
Fig. 4.5 Total energy flow around a distillation column
condenser

41. Energy balanceChapter 4
31
The heat of the reboiler is provided from saturated steam at 45 bar (258.5°C)
Amount of steam required =
10010.9
1675.85
= 5.973 kg/s
4.2.4 Energy balance on ethylbenzene distillation column
A sketch of benzene distillation column along with fully defined streams is shown in
(Figure 4.6).The procedure is the same as that of benzene distillation column.
Fig. 4.6 Sketch of ethylbenzene distillation column with fully defined streams
Balance over complete system is
HF +QB= QC+HD+HW
The temperature of the feed, top tray product and bottom tray product are calculated
from Antoine's equation
- The feed and bottom product are saturated liquids and the top tray vapor is
also saturated
- Tf is calculated at 1.25 atm = 156.23 °C
- Temperature of the top tray product is calculated at 1.4 atm = 151.56°C
- The vapors are condensed and exits from the condenser as a saturated liquid at
146.05°C.
- Temperature of the bottom tray product is calculated at 1.5 atm =200.23 °C
HF =nB*[CpB*(Tf -Tref) + ʋB ∆Pf] + nEB*[CpEB*( Tf -Tref) + ʋEB ∆Pf] + nDEB*[CpDEB*(
Tf – Tref) + ʋDEB ∆Pf]
Take liquid components at 146.05 °C and 1 atm as a reference condition.
For the inlet feed the average specific volumes are calculated

42. Energy balanceChapter 4
32
ʋB = 0.1121 m3
/ kmol
ʋEB = 0.1427 m3
/ kmol
ʋDEB = 0.1171 m3
/ kmol
∆Pf = (1.4-1)*1.013*102
= 40.52kPa
HF = 637851.919 kJ/h
QC is determined by taking balance round the condenser (same as in the benzene
distillation column)
HV = QC + HL +HD
Take reflux ratio = 2
L = 2D
V = L + D = 3D = 1.63 kmol/h B + 1385.126 kmol/h EB + 0.034 kmol/h DEB
HV = nB*Hfg B + nEB*Hfg EB
Where Hfg is latent heat of vaporization
Hfg (B) = 30088 kJ/kmole
Hfg (EB) = 35038 kJ/kmole
Hfg (DEB) = 39837 kJ/kmole
HV = 48582442.41 kJ/h
HD= ʋB ∆PD + ʋEB ∆PD
HD = 1990.85 kJ/h
HL = 1990.85 kJ/h
QC = 48578460.71 kJ/h = 13494.016 kW
Condensation is carried out using cooling water at 25°C and heating up to 50°C
The amount of water required =
13494.016
4.2∗(50−25)
= 128.5144 kg/s
For the bottom product the average specific volumes are then calculated
ʋEB = 0.154 m3
/ kmol
ʋDEB = 0.117 m3
/ kmol
∆P = (1.5-1)*1.013*102
= 50.65kPa

43. Energy balanceChapter 4
33
HW = nEB*[CpEB*(T-Tref) + ʋEB ∆Pw] + nDEB*[CpDEB*(T-Tref) + ʋDEB ∆Pw]
HW= 705694.838 kJ/h
QB= QC+HD+HW -HF
QB= 48646303.63 kJ/h = 13512.86 kW
The heat of the reboiler is provided from saturated steam at 45 bar (258.5°C).
Amount of steam required =
13512.86
1675.85
= 8.06 kg/s
4.2.5 Energy balance on transalkylator pre-mixing point
The enthalpies of each component relative to the reference state are shown in (Table
4.6).
Table 4.6 Enthalpies and molar flows for the inlet and outlet components of the mixing point.
Component Benzene recycle DEB recycle Mixed product
ni1
(kmol/h
)
Ĥi
(kJ/kmol
)
ni2
(kmol/h
)
Ĥi
(kJ/kmol
)
no
(kmol/h
)
Ĥo
(kJ/kmol
)
Benzene 81.444 0 0 0 81.444 Ĥ3
Ethylbenzene 0.082 0 0.4622 Ĥ1 0.5437 Ĥ4
Diethylbenzen
e
0 0 44.085 Ĥ2 44.085 Ĥ5
*Reference state, components at 86.43°C and 1.2 atm
Ĥ1 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐸𝐸𝐸𝐸) 𝑑𝑑𝑑𝑑
473.2
359.43
= 25123.664
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
Ĥ2 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐷𝐷𝐷𝐷𝐷𝐷) 𝑑𝑑𝑑𝑑
473.2
359.43
= 31452.4
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
Ĥ3 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑
𝑇𝑇𝑇𝑇
359.43
Ĥ4 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐸𝐸𝐸𝐸) 𝑑𝑑𝑑𝑑
𝑇𝑇𝑇𝑇
359.43
Ĥ5 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐷𝐷𝐷𝐷𝐷𝐷) 𝑑𝑑𝑑𝑑
𝑇𝑇𝑇𝑇
359.43

44. Energy balanceChapter 4
34
Energy balance:
� 𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖 = � 𝑛𝑛𝑜𝑜 Ĥ𝑜𝑜
1398191.183 = ∑ 𝑛𝑛𝑜𝑜 Ĥ𝑜𝑜
Solving for To we obtain:
To = 142.961 °C
4.2.6 Energy balance on the transalkylator
The fresh feed to the reactor is at 20 atm and 220°C. The reactor is operated
adiabatically. Sketch of the transalkylator along with the stream notations is shown in
(Figure 4.7). Reference state of 1 atm and 25°C is chosen; the enthalpies of each
component relative to the reference state are listed in (Table 4.7).
Table 4.7 Enthalpies and molar flows for the inlet and outlet components of the transalkylator
Component DEB reactor feed product
ni (kmol/h) Ĥi (kJ/kmol) no (kmol/h) Ĥo (kJ/kmol)
Benzene 81.4436 Ĥ1 58.5163 Ĥ4
Ethylbenzene 0.5437 Ĥ2 46.3925 Ĥ5
Diethylbenzene 44.0854 Ĥ3 21.161 Ĥ6
*Reference state, components at 25°C and 1 atm
∆𝐻𝐻𝑟𝑟 = ∑ 𝑣𝑣𝑖𝑖 ∆Ĥ𝐹𝐹 = (2 ∗ −12.46) − (1 ∗ 48.66 + 1 ∗ −73.2) = −0.38 𝑘𝑘𝑘𝑘/𝑚𝑚𝑚𝑚𝑚𝑚
∆𝐻𝐻𝑟𝑟 = −380
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
The transalkylator reactor is adiabatic. The energy balance equation reduces to:
∆𝐻𝐻 = Ƹ ∆𝐻𝐻𝑟𝑟 + � 𝑛𝑛𝑜𝑜 Ĥ𝑜𝑜 − � 𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖 = 0
� 𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖 − Ƹ ∆𝐻𝐻𝑟𝑟 = � 𝑛𝑛𝑜𝑜 Ĥ𝑜𝑜 (4.10)
Where Ƹ is the extent of reaction

45. Energy balanceChapter 4
35
Ƹ =
46.3925 − 0.5437
2
= 22.9244 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘/ℎ
Ĥ1 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑 + ʋ ∆P
493
298
Where ʋ is the average specific molar volume between
the reference and process temperatures.
For the inlet feed the average specific volumes are then
calculated:
ʋB = 0.0985 m3
/ kmol
ʋEB = 0.1331 m3
/ kmol
ʋDEB = 0.1699 m3
/ kmol
∆P is the change in pressure between the process and reference states in kPa = (20-
1)*1.013*102
= 1924.7 kPa
Ĥ1 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑 + 0.0985 ∗ 1924.7
493
298
= 32517.872
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
Ĥ2 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐸𝐸𝐸𝐸) 𝑑𝑑𝑑𝑑 + 0.1331 ∗ 1924.7
493
298
= 41992.3356
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
Ĥ3 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐷𝐷𝐷𝐷𝐷𝐷) 𝑑𝑑𝑑𝑑 + 0.1699 ∗ 1924.7
493
298
= 51973.7255
𝑘𝑘𝑘𝑘
𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘
Taking the same average specific molar volume for the outlet components and
assuming pressure drop of 0.5 atm we calculate the outlet enthalpies:
Ĥ4 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑑𝑑 + 0.0985 ∗ 1874.05
𝑇𝑇𝑇𝑇
298
Ĥ5 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐸𝐸𝐸𝐸) 𝑑𝑑𝑑𝑑 + 0.1331 ∗ 1874.05
𝑇𝑇𝑇𝑇
298
Ĥ6 = � 𝐶𝐶𝐶𝐶𝐿𝐿(𝐷𝐷𝐷𝐷𝐷𝐷) 𝑑𝑑𝑑𝑑 + 0.1699 ∗ 1874.05
𝑇𝑇𝑇𝑇
298
Ƹ ∆𝐻𝐻𝑟𝑟 = −380 ∗ 22.9244 = −8711.272
𝑘𝑘𝑘𝑘
ℎ
Fig. 4.7 Sketch of the transalkylator along with fully
defined

46. Energy balanceChapter 4
36
� 𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖 = 4962486.271
𝑘𝑘𝑘𝑘
ℎ
Substituting in (Eq.4.10) and solving for the reactor outlet temperature:
To = 220.7 °C
The change in temperature is finite due to the minute effect of the heat of reaction.
Now after the temperatures and duties of the main units have been obtained; the
complete process is synthesized and the result is shown in (Figure 4.8).
In order to check the mass and energy balance calculations, the process is simulated
using Aspen hysys software. The simulation scheme is shown in (Figure 4.9). and
obtained streams data in (Table 4.8).
4.3 Summary
In this chapter, detailed energy balance on the main process units is performed. The
main streams temperatures and heat flow throughout the process have been calculated
and the amount of heating steam or cooling water required have been evaluated. The
final process flowsheet is constructed based on the process heuristics. The hand
calculations are approved using Aspen hysys software, the calculations error in the main
streams considered is found not to exceed 0.1% which proves the accuracy of hand
calculations.

47. Energy balanceChapter 4
37
.
Fig.4.8Processflowdiagramofthebasecasedesignincludingmainequipmentandstream'sdesignations.

48. Energy balanceChapter 4
38
Fig.4.9Aspenhysysethylbenzeneprocesssimulation

49. Energy balanceChapter 4
39
Table4.8Aspenhysysprocessworkbook.

50. Chapter 5
Equipment design

51. Equipment designChapter 5
41
5. Equipment design
In this chapter, the design of the main process equipment will be established in detail.
The chapter is concerned with the design of the following units:
- Benzene and ethylbenzene distillation columns.
- The heat exchanger located before the benzene distillation.
- Alkylation reactor.
- Pump.
5.1 Design of benzene distillation column
The flow rates and full composition of the feed, distillate and bottom streams have been
previously calculated in chapter 3. In addition, the temperatures of the streams and the
corresponding condenser's and reboiler's duties have been evaluated in chapter 4 from
energy balance; using these obtained data the design of the distillation column was
carried out.
5.1.1 Determination of the number of ideal stages and feed tray
location
The number of ideal stages is evaluated by using a highly accurate approximate method
based on rigorous tray-by-tray calculations; this method is collectively referred to as
Fenske's-Underwood-Gilliland method (or simply FUG) [18,19].
Benzene would be taken as the light key (LK) component, ethylbenzene as the heavy
key (HK) component and diethylbenzene as the heavy non-key component (HNK)
which is assumed to be too heavy to be distributed (i.e. all diethylbenzene go to the
bottom stream.
In 1940, Gilliland proposed a graphical correlation based on the minimum required
number of trays (i.e. total reflux case) , proposed by Fenske, and the case of minimum
reflux ,proposed by Underwood, [20]. This correlation is still used till today as a short
cut method for the determination of the number of trays. However, the graphical form
is rarely used, instead many mathematical models has been established describe
Gilliland's correlation. The empirical equation established by Seader and Henley [21]
will be used in this work (Eq. 5.1).
Ү = 1 − 𝑒𝑒
��
1+54.4 Ҳ
11+117.2 Ҳ
��
Ҳ−1
Ҳ0.5�� (5.1)
Ү =
𝑁𝑁 − 𝑁𝑁𝑚𝑚𝑚𝑚𝑚𝑚
𝑁𝑁 + 1
(5.2)
Ҳ =
𝑅𝑅 − 𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚
𝑅𝑅 + 1
(5.3)

52. Equipment designChapter 5
42
Where:
N: Ideal number of trays.
Nmin: Minimum number of ideal trays obtained at total reflux condition from Fenske's
equation for the separation of two key components from a multi-component mixture
(Eq. 5.4)
𝑁𝑁𝑚𝑚𝑚𝑚𝑚𝑚 =
log �
𝑓𝑓 𝐴𝐴,𝐷𝐷 𝑓𝑓 𝐵𝐵,𝑊𝑊
�1−𝑓𝑓 𝐴𝐴,𝐷𝐷 ��1−𝑓𝑓 𝐵𝐵,𝑊𝑊�
�
log(𝛼𝛼𝐴𝐴𝐴𝐴)𝑎𝑎𝑎𝑎
(5.4)
fA,D : Fraction of one of the keys that is transferred to the distillate
fB,w : Fraction of the second key that is transferred to the bottom
𝑓𝑓𝐴𝐴,𝐷𝐷 =
𝐷𝐷 𝑥𝑥𝐴𝐴,𝐷𝐷
𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝐴𝐴 𝑖𝑖𝑖𝑖 𝑡𝑡ℎ𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
𝑓𝑓𝐵𝐵,𝑊𝑊 =
𝑊𝑊 𝑥𝑥𝐵𝐵,𝑊𝑊
𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 𝑜𝑜𝑜𝑜 𝐵𝐵 𝑖𝑖𝑖𝑖 𝑡𝑡ℎ𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓
(αAB)av : Geometric average of the relative volatilities between the two keys at the
conditions at the top and bottom stages of the column. The geometric mean is
mathematically defined as (Eq. 5.5).
(𝛼𝛼𝐴𝐴𝐴𝐴)𝑎𝑎𝑎𝑎 = �(𝛼𝛼𝐴𝐴𝐴𝐴)𝑇𝑇𝑇𝑇𝑇𝑇 ∗ (𝛼𝛼𝐴𝐴𝐴𝐴)𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 (5.5)
R: Actual reflux ratio
Rmin: Minimum reflux ratio at which the separation can be achieved. It can be calculated
by performing material balance over the condenser at minimum reflux (Eq. 5.6).
𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚 =
𝑉𝑉 𝑚𝑚𝑚𝑚 𝑚𝑚
𝐷𝐷
− 1 (5.6)
Vmin : Minimum vapor flow at the top stage corresponding to the minimum reflux. It
can be calculated from (Eq.5.7).
𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚 = ∑
𝛼𝛼𝑖𝑖 𝐷𝐷 𝑥𝑥𝑖𝑖, 𝐷𝐷
𝛼𝛼𝑖𝑖 − 𝜙𝜙𝑖𝑖 (5.7)
αi : Geometric mean of relative volatilities of a component i relative to the heavy key.
ϕ : Parameter defined as Lmin /(Vmin kHK), where KHK is the equilibrium vaporization
ratio of the heavy key component. ϕ can be alternatively calculated from (Eq. 5.8)
1 − 𝑞𝑞 = ∑
𝛼𝛼𝑖𝑖 𝑧𝑧𝑖𝑖
𝛼𝛼𝑖𝑖 − 𝜙𝜙𝑖𝑖 (5.8)
zi: Mole fraction of a component i in the feed ( the designation z is commonly used in
distillation to donate the feed composition).
q: donates the amount of liquid phase in the feed, it can be physically defined as:

53. Equipment designChapter 5
43
𝑞𝑞 =
ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑣𝑣𝑒𝑒𝑒𝑒𝑒𝑒 1 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑜𝑜𝑜𝑜 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣 𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙
Using the set of equations given above the ideal number of trays can be calculated.
• Calculation of the minimum number of tray
Let Benzene be (A), ethylbenzene be (B) and diethylbenzene be (C). The relative
volatilities of the components in top and bottom are given in (Table 5.1) assuming
nearly ideal solution behaviour.
fA,D = 0.999
fB,W = 0.99883
(αAB)av = √5.7327 𝑥𝑥 3.9737 = 4.7728
Substituting in (Eq.5.4) to obtain:
Nmin = 8.737 (7.737 ideal trays + the reboiler)
Table 5.1 Relative volatilities of A,B and C at the top and bottom.
Temperature (°C) Pv
A (atm) Pv
B (atm) Pv
C αAB αCB
86.43(top) 1.2119 0.2114 0.0407 5.7327 0.1925
151.56 (bottom) 5.9304 1.4924 0.4217 3.9737 0.2825
* Pv
A, Pv
B and Pv
C are obtained from Antoine's equation
• Calculation of the minimum reflux ratio
Using (Eq.5.8) to calculate ϕ taking:
1 − 𝑞𝑞 =
(𝛼𝛼𝐴𝐴𝐴𝐴)𝑎𝑎𝑎𝑎 𝑧𝑧𝐴𝐴
(𝛼𝛼𝐴𝐴𝐴𝐴)𝑎𝑎𝑎𝑎 − ϕ
+
(𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑎𝑎 𝑧𝑧𝐵𝐵
(𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑎𝑎 − ϕ
+
(𝛼𝛼𝐶𝐶𝐶𝐶)𝑎𝑎𝑎𝑎
𝑧𝑧𝐶𝐶
(𝛼𝛼𝐶𝐶𝐶𝐶)𝑎𝑎𝑎𝑎
− ϕ
q = 1 (the feed is a saturated liquid)
(𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑎𝑎 = 1
(𝛼𝛼𝐶𝐶𝐶𝐶)𝑎𝑎𝑎𝑎 = √0.1925 𝑥𝑥 0.2825 = 0.2332
zA, zB, zC are calculated from (Table 3.1)
Substituting:
1 − 1 =
4.7728 𝑥𝑥 0.5175
4.7728 − ϕ
+
0.4405
1 − ϕ
+
0.2332 𝑥𝑥 0.042
0.2332 − ϕ
Solving for ϕ : ϕ = 1.57563 or ϕ = 0.2419

54. Equipment designChapter 5
44
Since the (HNK) is not distrusted the value of ϕ should be between the value of (αAB)av
and (𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑎𝑎 ((𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑎𝑎 < ϕ < (αAB)av) [11].
ϕ = 1.57563
Use (Eq.5.7) to calculated Vmin
𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚 =
4.7728 𝐷𝐷 𝑥𝑥𝐴𝐴,𝐷𝐷
4.7728 − ϕ
+
𝐷𝐷 𝑥𝑥𝐵𝐵,𝐷𝐷
1 − ϕ
+
0.2332 𝐷𝐷 𝑥𝑥𝐶𝐶,𝐷𝐷
0.2332 − ϕ
From (Table 3.1): D xA,D = 542.9573, D xB,D = 0.5435, D xC,D = 0
Substituting to obtain Vmin :
Vmin = 809.5934 kmol/h
The minimum reflux ratio is calculated from (Eq.5.6)
𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚 =
809.5934
542.9573 + 0.5435
− 1
Rmin = 0.49
Take the operation reflux ratio as 1.55 Rmin [22].
R = 1.55 x 0.48959 = 0.76
Finally, the required ideal number of trays is calculated from (Eq.5.1).
Ү = 1 − 𝑒𝑒
��
1+54.4 Ҳ
11+117.2 Ҳ
��
Ҳ−1
Ҳ0.5��
Ҳ =
0.735 − 0.4896
0.735 + 1
= 0.15
Substituting the value of Ҳ and Ү in (Eq.5.1).
Ү =
𝑁𝑁 − 8.737
𝑁𝑁 + 1
= 0.502
N = 18.561 ideal tray
The optimal feed tray location is determined using Kirkbride's equation (Eq.5.9).

55. Equipment designChapter 5
45
𝑁𝑁𝑅𝑅
𝑁𝑁𝑆𝑆
= ��
𝑧𝑧 𝐻𝐻𝐻𝐻
𝑧𝑧𝐿𝐿𝐿𝐿
� �
𝑥𝑥𝐿𝐿𝐿𝐿,𝑊𝑊
𝑥𝑥 𝐻𝐻𝐻𝐻,𝐷𝐷
�
𝑊𝑊
𝐷𝐷
�
0.206
(5.9)
Where:
NR : Number of trays in the rectifying section
NS : Number of trays in the stripping section
Substituting:
𝑁𝑁𝑅𝑅
𝑁𝑁𝑆𝑆
= ��
0.4405
0.5175
� �
0.0011
0.001
�
506.81
543.5
�
0.206
𝑁𝑁𝑅𝑅
𝑁𝑁𝑆𝑆
= 0.873
Also, NR + NS = 18.561
Solving the two equations simultaneously to obtain:
NR = 9.9
NS = 8.65
The feed is added to the 10th
ideal feed from the top
Tray-by-tray calculations have been performed using aspen-hysys software and the
results are shown in appendix A (Table A-1).
5.1.2 Tray design
Sieve tray Is chosen for the tower as it offers low pressure drop and lower cost than
other tray types. Moreover, a high turndown ratio is not required in this process.
Based on the data in appendix A (Table A-1), the vapor flow rates does not vary
widely throughout the column. However, the liquid rates vary greatly between the
rectifying and stripping sections. Therefore, the distillation tower is going to be
designed with two sections both having the same diameter but different tray design.
The highest vapor flow in the rectifying section upon which the tray is designed is found
to occur at the second tray from the top and has a value of 20963.96 m3
/h; the highest
liquid occurs at the first tray and has a value of 40.06 m3
/h. In the stripping section, the
highest vapor flow occurs at tray 18 and has a value of 21505.56 m3
/h and the highest
liquid rate occurs at tray 18 and has a value of 203.8 m3
/h.
The required diameter of the column is determined from flooding considerations (i.e.
maintaining a gas flow velocity below a limiting flow velocity above which liquid
entrainment is high enough to case entrainment flooding).

56. Equipment designChapter 5
46
The flooding velocity for spray entrainment flooding is calculated from Souders-Brown
equation (Eq.5.10) [23].
𝑢𝑢𝑠𝑠,𝑓𝑓𝑓𝑓 = 𝐶𝐶𝑆𝑆𝑆𝑆 �
𝜌𝜌𝐿𝐿−𝜌𝜌𝐺𝐺
𝜌𝜌𝐺𝐺
�
1
2�
(5.10)
Where:
us,fl : Superficial gas velocity that will cause flooding
ρL and ρG : Liquid and Gas mass densities respectively.
CSB : Souders-Brown constant
In reality CSB is not a constant; it depends upon tray spacing, liquid load, fractional
hole area and hole diameter of the sieve tray. There are many correlations available for
the calculation of CSB. In this work, the Kister and Haas Correlation is used (Eq.5.11)
[24].
𝐶𝐶𝑆𝑆𝑆𝑆 = 0.144 �
𝑑𝑑 𝐻𝐻
2
𝜎𝜎
𝜌𝜌𝐿𝐿
�
0.125
�
𝜌𝜌𝐺𝐺
𝜌𝜌𝐿𝐿
�
0.1
�
𝑆𝑆
ℎ𝑐𝑐𝑐𝑐
�
0.5
(5.11)
Where:
dH : Hole diameter, in inch
σ : Surface tension, in dyne/cm
ρL, ρG : Liquid and Vapor densities, in lb/ft3
S : Tray spacing in inch
hct : Clear liquid height at the transition from froth to spray regimes, in inch
The parameter hct can be calculated using equations (Eq.5.12) and (Eq.5.13)
ℎ𝑐𝑐𝑐𝑐 = (ℎ𝑐𝑐𝑐𝑐)𝑤𝑤 �
62.2
𝜌𝜌𝐿𝐿
�
0.5(1−0.0231
𝑑𝑑 𝐻𝐻
𝑓𝑓ℎ
)
(5.12)
(ℎ𝑐𝑐𝑐𝑐)𝑤𝑤 =
0.29 𝑓𝑓ℎ
−0.791
𝑑𝑑 𝐻𝐻
0.833
1+0.0036 𝑄𝑄𝐿𝐿
−0.59 𝑓𝑓ℎ
−1.79
(5.13)
fh : Fractional hole area = (hole area) / (active tray area)
QL : Liquid flow rate per unit segmental weir length at the downcomer entry, in
gal/min.in.
The segmental weir length at the downcomer entry can be calculated from the tray
geometry as shown in (Figure 5.1).

57. Equipment designChapter 5
47
From the geometry, the following equations can be
Derived, (Eq.5.14) and (Eq.5.15).
Where:
Ad , AT : Downcomer and tower cross sectional
areas respectively
Dc : Column diameter
Once CSB is calculated the flooding velocity is calculated from (Eq.5.10) and the
allowable vapor velocity should be between (60% to 80%) of the flooding velocity. The
active flow area can then be determined and the tower cross sectional area is then
determined by adding into account the area occupied by the down comers on both sides
of the tray (Eq.5.16).
AT =
Gv
�fl us,fl� fa
=
Aa
fa (5.16)
Where:
Gv : Gas volumetric flow rate
Aa : Active tray area
fL : Fractional approach to flooding velocity ( taken as 0.7)
fa : Fractional active area of the tray = (1 – 2Ad / AT)
it is apparent that the Kister-Hass correlation contains parameters that are not known
before the tray is designed. Therefore, a trial and error procedure is adopted to solve
this correlation. The properties required for the calculations are obtained from aspen-
hysys software and are presented in appendix A (Table A-2).
(a) Stripping section tray design
In the stripping section, the highest vapor flow occurs at tray 18 and has a value of
21505.56 m3
/h and the highest liquid rate occurs at the same tray and has a value of
203.8 m3
/h.
The properties are taken as an average between the first and final trays in the stripping
section (i.e. feed and bottom trays).
𝐴𝐴𝑑𝑑
𝐴𝐴𝑇𝑇
=
𝜃𝜃 − sin(𝜃𝜃)
2𝜋𝜋
(5.14)
𝑙𝑙𝑤𝑤 = 2𝐷𝐷𝑐𝑐 sin �
𝜃𝜃
2
� (5.15)
Fig. 5.1 Simple geometric representation
of the tray

58. Equipment designChapter 5
48
ρL = 47.845 lb/ft3
ρG = 0.2561 lb/ft3
σ = 16.92 dyne/cm
Liquid volumetric flow rate Lv = 897.3044 gal/min
Vapor volumetric flow rate Gv = 759461.684 ft3
/h
Initial assumptions: Dc = 10 ft, Ad / AT = 0.1, dH = 3/8 inch, S= 18 inch, fh = 0.1
From (Eq.5.14): θ – sin (θ) = 0.1*2* π
θ = 19.14°
From (Eq.5.15): Lw = 10 x 2 sin(19.14/2) = 3.326 ft
QL = Lv / lw = 897.304 / (3.326*12) = 22.482 gal/min.in
Using (Eq.5.13) to find (hct)w
(ℎ𝑐𝑐𝑐𝑐)𝑤𝑤 =
0.29 𝑥𝑥 0.1−0.791 𝑥𝑥0.3750.833
1+0.0036 (22.482−0.59 𝑥𝑥 0.1−1.79)
= 0.7647 inch
From (Eq.5.12)
ℎ𝑐𝑐𝑐𝑐 = 0.7647 �
62.2
49.136
�
0.5(1−0.0231
0.375
0.1
)
= 0.862 inch
Now CSB can be calculated from (Eq.5.11)
𝐶𝐶𝑆𝑆𝑆𝑆 = 0.144 �
0.3752 𝑥𝑥 16.92
47.845
�
0.125
�
0.2561
47.845
�
0.1
�
18
0.862
�
0.5
= 0.268 ft/s
The flooding velocity is calculated from (Eq.5.10)
𝑢𝑢𝑠𝑠,𝑓𝑓𝑓𝑓 = 0.268 �
47.845−0.2561
0.2561
�
1
2�
= 3.654 ft/s
- The gas velocity through the column cross section is calculated to check for the
tower diameter suitability
𝐴𝐴𝑇𝑇 =
𝜋𝜋
4
(10)2
= 78.54 ft2
Active tray area Aa is obtained from (Eq.5.16)
𝐴𝐴𝑎𝑎 = 78.54 (1 − 2 ∗ 0.1) = 62.83 ft2
The superficial gas velocity us =
759461.68
62.83 𝑥𝑥 3600
= 3.654 ft/s
The gas velocity is higher than the flooding velocity and the tower diameter must be
therefore increased to attain a suitable velocity.
Iterations were performed using Microsoft excel software and the final suitable design
parameters are:

59. Equipment designChapter 5
49
DC = 11 ft
Ad / AT = 0.05
us = 2.466 ft/s = 67.45% of the flooding velocity (acceptable)
- Check for the down comer liquid residence time
Clear liquid flow into the down comer = 897.304 x 0.00223 = 2 ft3
/s (acceptable)
Down comer volume = 𝑆𝑆 ∗ 𝐴𝐴𝑇𝑇 ∗
𝐴𝐴𝑑𝑑
𝐴𝐴𝑇𝑇
=
18
12
𝑥𝑥 95.033𝑥𝑥0.05 = 7.127 ft3
Residence time =
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣𝑣
𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 𝑓𝑓𝑓𝑓 𝑓𝑓𝑓𝑓
=
7.127
2
= 3.56 𝑠𝑠 (acceptable)
Now that the column diameter is successfully adjusted other design parameters are
calculated.
- Estimate the effective bubbling area and holes layout
The effective bubbling area is a little less than the active tray area (85.53 ft2
) due to the
accounting for flow clearance and tray support. Tray support ring to which the tray is
bolted and fixed to the column wall is used; a ring of 2 inch radial width is used which
has an approximate area covering active parts of the tray of 2.86 ft2
. Also, 4 inch
calming zone after the inlet down comer and before the outlet down comer is allowed.
The estimated overall dead area without holes is 13.85 ft2
.
The effective bubbling area Aa,b = 85.53-13.85 = 71.68ft2
The holes are placed on a triangular pitch of (pitch = 3dH ). The fractional hole area can
be calculated based on the pitch shape from (Eq.5.17).
𝑓𝑓ℎ = 𝑘𝑘∗
�
ℎ𝑜𝑜𝑜𝑜𝑜𝑜 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑
ℎ𝑜𝑜𝑜𝑜𝑜𝑜 𝑝𝑝𝑝𝑝𝑝𝑝𝑐𝑐ℎ
�
2
(5.17)
Where k*
is a constant dependent on the pitch type, equals 0.905 for triangular pitch.
fh = 0.905 x (1/3)2
= 0.1005 ~ the assumed value is 0.1 (acceptable)
Total holes area = fh * active tray area after correction (from definition)
Total holes area = 0.1 x 71.68 = 7.168 ft3
- Check for down comer back up
Now that the tower diameter has been calculated based on entrainment flooding, the
possibility for down comer flooding must be checked. The down comer flooding is
checked by calculating the liquid pressure head in the down comer (called down comer
backup). The down comer back up balances the sum of three terms:
• The clear liquid height on the tray
• The head loss for liquid flow under the down comer's plate

60. Equipment designChapter 5
50
• The total gas pressure drop which is the sum of dry tray pressure drop and the
pressure drop for passage of gas through the liquid
a) The clear liquid height
The clear liquid height is calculated using (Eq.5.18)
ℎ𝑐𝑐 = ℎ𝑤𝑤 + ℎ𝑜𝑜𝑜𝑜 + ∆ 2⁄ (5.18)
Where:
hw Weir height (taken as 2 inch)
how : Liquid height over the weir. how can be calculated using Francis' weir equation
(Eq.5.19) [25].
∆ : Hydraulic gradient, in inch (it can be neglected for a sieve tray).
how = 1.43 �
�
Lv
lw
� �
2
g
�
1
3�
(5.19)
Where: all the parameters are in SI units and g is the acceleration of gravity = 9.81 m/s2
.
The revised weir length lw = 3.6 ft = 1.097 m
ℎ𝑜𝑜𝑜𝑜 = 1.43 �
�203.8
3600 𝑥𝑥 1.097� �
2
9.81
�
1
3�
= 0.0925 m = 3.645 inch
The clear liquid height (hC) = 2+3.645 = 5.645 inch
b) Head loss for flow of liquid under the down comer plate
It can be calculated using (Eq.5.20).
ℎ𝑎𝑎𝑎𝑎 = 0.03 �
𝐿𝐿𝑣𝑣
100 𝐴𝐴𝑎𝑎𝑎𝑎
�
2
(5.20)
Where Lv is in gal/min and Aad is the available area for flow under the down comer in
ft2
.
Select 1.8 inch clearance under the down comer
Aad = (1.8/12) x 3.6 = 0.54 ft2

61. Equipment designChapter 5
51
ℎ𝑎𝑎𝑎𝑎 = 0.03 �
897.3044
100 𝑥𝑥 0.54
�
2
= 8.24 inch
c) Total gas pressure drop
The dry tray pressure drop is calculated using (Eq.5.21).
ℎ𝑑𝑑 =
0.186
𝐶𝐶𝑜𝑜
2 �
𝜌𝜌𝐺𝐺
𝜌𝜌𝐿𝐿
� 𝑢𝑢ℎ
2
(5.21)
Where:
uh: Gas velocity through holes.
Co: Discharge coefficient. It can be obtained from appendix A (Figure A-1).
𝑢𝑢ℎ =
𝐺𝐺𝑣𝑣
ℎ𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎
=
759461.684
3600 𝑥𝑥 7.168
= 29.341 ft/s
Select tray thickness of 0.2 inch, tray thickness / hole diameter = 0.533
From figure A-1 the discharge coefficient Co = 0.74
ℎ𝑑𝑑 =
0.186
0.7352 �
0.2561
47.845
� 29.3412
= 1.6 inch
The pressure drop due to flow of gas through the liquid can be calculated as function
of the clear liquid height hc (Eq.5.22).
ℎ𝑙𝑙 = 𝛽𝛽 ℎ𝑐𝑐 (5.21)
Where 𝛽𝛽 is the aeration factor and can be calculated from appendix A (Figure A-2).
The parameter Fsh used to evaluate 𝛽𝛽 is a function of the superficial vapor velocity
based on the effective bubbling area (Eq.5.22).
𝐹𝐹𝑠𝑠ℎ = 𝑢𝑢𝑠𝑠,𝑏𝑏 (𝜌𝜌𝐺𝐺)
1
2�
=
𝐺𝐺𝑣𝑣
𝐴𝐴𝑎𝑎,𝑏𝑏
(𝜌𝜌𝐺𝐺)
1
2�
(5.22)
𝐹𝐹𝑠𝑠ℎ =
759461.684
71.68 𝑥𝑥 3600
(0.2561)
1
2�
= 1.489
From figure A-2, 𝛽𝛽 = 0.6
ℎ𝑙𝑙 = 0.6 𝑥𝑥 4.876 = 3.387 inch
The total gas pressure drop ht = 1.6 + 3.387 = 4.96 inch
Now the down comer backup can be calculated by summing the three terms mentioned
earlier (Eq.5.23).

62. Equipment designChapter 5
52
hdb = 5.644 + 8.284 + 4.96 = 18.887 inch
The down comer flooding is checked by calculating the froth height over the tray floor
(hf). Down comer flooding occurs if (hf ≥ S + hw). The froth height is calculated from
(Eq.5.24). Also, the down comer backup is preferably maintained lower than half of the
tray spacing (i.e. hdb < S/2)
Where: ∅𝑑𝑑 Relative froth density in the down comer =
𝜌𝜌𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓ℎ
𝜌𝜌𝐿𝐿
� . For a sieve tray it
rarely goes below 0.5 [11].
Taking the minimum value available in literature, ∅𝑑𝑑 = 0.5
ℎ𝑓𝑓 =
18.887
0.5
= 37.774 inch
Which is way higher than the quantity (S + hw). Therefore, the design parameters must
be adjusted to prevent down comer flooding. The design parameters have been adjusted
and re-calculated using Microsoft excel software and the final design parameters for
the stripping section are presented in the following table (Table 5.2).
Checking the new design parameters:
𝑢𝑢𝑠𝑠
𝑢𝑢𝑠𝑠,𝑓𝑓𝑓𝑓
= 61.94% (acceptable)
Down comer's liquid velocity and residence
Time are within accepted range.
𝑆𝑆
2
= 18 𝑖𝑖𝑖𝑖 > ℎ𝑑𝑑𝑑𝑑
S + hw = 38.5 > hf
- Check for entrainment, weeping and turndown ratio
ℎ𝑑𝑑𝑑𝑑 = ℎ𝑐𝑐 + ℎ𝑎𝑎𝑎𝑎 + ℎ𝑡𝑡 (5.23)
ℎ𝑓𝑓 =
ℎ𝑑𝑑𝑑𝑑
∅𝑑𝑑
(5.24)
Column diameter DC (ft)
Tray spacing S (in)
Ad / AT
Hole diameter (in)
CSB
Flooding velocity us,fl (ft/s)
Superficial gas velocity us (ft/s)
Down comer liquid velocity (ft/s)
Down comer residence time (s)
Weir height hw (in)
Total gas pressure drop (in)
Down comer backup hdb (in)
Froth height hf (in)
11
36
0.15
0.4
0.3756
5.12
3.171
0.14
21.39
2.5
6.6
17.4
34.801
Table 5.2 Design parameters of the stripping section

63. Equipment designChapter 5
53
Rate of entrainment can be calculated from Fair's plot knowing the mass flow rates and
densities. The plot is available in appendix A (Figure A-3).
𝐿𝐿
𝐺𝐺
(
𝜌𝜌𝐺𝐺
𝜌𝜌𝐿𝐿
)0.5
=
203.8 𝑥𝑥 766.4 (
𝑘𝑘𝑘𝑘
ℎ
)
21505.56 𝑥𝑥 4.102 (
𝑘𝑘𝑘𝑘
ℎ
)
(
4.102
766.4
)0.5
= 0.1295
From Fair's plot, the rate of entrainment Ψ = 0.01 mol per mol gross downflow. Since
Ψ is less than 0.1, the entrainment is acceptable.
The weeping is checked using Fair's weep point chart, appendix A (Figure A-4).
Required parameters are: hw + how = hc = 6.0662 , hd = 3 and hσ can be calculated from
(Eq.5.25).
Substituting: ℎ𝜎𝜎 =
0.04 𝑥𝑥 16.92
47.845 𝑥𝑥 0.4
= 0.0354
hd + hσ = 3.0354
The point (6.0662,3.0354) lies pretty much above the weep point curve in figure A-4
for fh = 0.1. Therefore weeping will not occur.
The turndown ratio is determined by calculating the turndown ratio at which the tray
will weep. From Fair's weep point plot at hc = 6.0662 the weep point is obtained by
extrapolation and is found to occur at (hd + hσ = 0.97)
hd = 0.97 – hσ = 0.97 – 0.0354 = 0.9346 inch
The corresponding vapor velocity through the holes at weep point is calculated from
(Eq.5.21)
ℎ𝑑𝑑 = 0.9346 =
0.186
0.74082
�
0.2561
47.845
� 𝑢𝑢ℎ
2
uh = 22.697 ft/s
The calculated vapor velocity through holes at weeping is 22.697/40.051 = 55.67% of
the design velocity through holes
The column turndown ratio =
1
0.5567
= 1.7645 (acceptable for a sieve tray).
The column can operate at 56.67% of the design capacity without weeping.
(b) Rectifying section tray design
ℎ𝜎𝜎 =
0.04 𝜎𝜎
𝜌𝜌𝐿𝐿 𝑑𝑑 𝐻𝐻
(5.25)

64. Equipment designChapter 5
54
The rectifying section is designed based on the highest vapor flow in the tower (i.e.
21505.56 m3
/h). The highest liquid flow occurs top tray and has a value of 40.06 m3
/h.
The column diameter is constant.
ρL = 49.543 lb/ft3
ρG = 0.2256 lb/ft3
σ = 19 dyne/cm
Liquid volumetric flow rate Lv = 176.379 gal/min
Vapor volumetric flow rate Gv = 928373.85 ft3
/h
The design of rectifying section follows the same procedure as that of the stripping
section. The design is carried out using Microsoft excel software and the final design
parameters for the rectifying section are presented in the following table (Table 5.3).
Checking the design parameters:
𝑢𝑢𝑠𝑠
𝑢𝑢𝑠𝑠,𝑓𝑓𝑓𝑓
= 63.05% (acceptable)
Down comer's liquid velocity and residence
Time are within accepted range.
𝑆𝑆
2
= 9 𝑖𝑖𝑖𝑖 > ℎ𝑑𝑑𝑑𝑑
S + hw = 19.5 > hf
The design is safe. Now check for entrainment,
weeping and turndown ratio.
Rate of entrainment can be calculated from Fair's plot (Figure A-3) knowing the mass
flow rates and densities
Column diameter DC (ft)
Tray spacing S (in)
Ad / AT
Hole diameter (in)
CSB
Flooding velocity us,fl (ft/s)
Superficial gas velocity us (ft/s)
Down comer liquid velocity (ft/s)
Down comer residence time (s)
Weir height hw (in)
Total gas pressure drop (in)
Down comer backup hdb (in)
Froth height hf (in)
11
18
0.07
0.375
0.2766
4.094
2.5812
0.059
25.3
1.5
2.97
6.541
13.082
Table 5.3 Design parameters of the rectifying section

65. Equipment designChapter 5
55
𝐿𝐿
𝐺𝐺
(
𝜌𝜌𝐺𝐺
𝜌𝜌𝐿𝐿
)0.5
=
40.06 𝑥𝑥 794.756 (
𝑘𝑘𝑘𝑘
ℎ
)
21505.56 𝑥𝑥 3.61 (
𝑘𝑘𝑘𝑘
ℎ
)
(
3.61
794.756
)0.5
= 0.0276
From Fair's plot, the rate of entrainment Ψ = 0.064 mol per mol gross downflow. Since
Ψ is less than 0.1, the entrainment is acceptable.
The weeping is checked using Fair's weep point chart (Figure A-4).
Required parameters are: hw + how = hc = 2.727 , hd = 1.3 and hσ can be calculated from
(Eq.5.25).
ℎ𝜎𝜎 =
0.04 𝑥𝑥 19.085
49.615 𝑥𝑥 0.375
= 0.041
hd + hσ = 1.441
The point (2.727,1.441) lies above the weep point curve in figure A-4 for fh = 0.1.
Therefore weeping will not occur.
The turndown ratio is determined by calculating the turndown ratio at which the tray
will weep. From Fair's weep point plot at hc = 2.727 the weep point is found to occur at
(hd + hσ = 0.62)
hd = 0.62 – hσ = 0.62 – 0.0411 = 0.5789 inch
The corresponding vapor velocity through the holes at weep point is calculated from
(Eq.5.21)
ℎ𝑑𝑑 = 0.5889 =
0.186
0.74082
�
0.2254
49.615
� 𝑢𝑢ℎ
2
uh = 19.556 ft/s
The calculated vapor velocity through holes at weeping is 19.556/ 29.411 = 66.49% of
the design velocity through holes
The column turndown ratio =
1
0.6649
= 1.5 (acceptable for a sieve tray).
As a result, the column as whole can operate at 66.49% of the design capacity without
weeping at any section of the column.
5.1.3 Tray efficiency and column height
Murphree defined an efficiency that estimates the performance of a tray. The
Murphree's efficiency is shown in (Eq.5.26) [26].