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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
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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

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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.

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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

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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

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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

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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

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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

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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

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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

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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.

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Chapter 1

Introduction

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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

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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

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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

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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.

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Chapter 2

Literature review

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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

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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

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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

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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.

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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.

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• 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

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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.

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Chapter 3

Liquid phase zeolite catalyst process

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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.

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Fig. 3.1 process flowsheet for ethylbenzene production by liquid phase zeolite catalyst process

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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+ n D,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 = 499.50.999

= 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

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Material balance Chapter 3

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- 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 = 474.0250.9988

= 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

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Material balance Chapter 3

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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

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Material balance Chapter 3

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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

*All the flow

rates given are in ton/h Table 3.1 M

aterial balance data for the manufacturing of 400000 tons/year of ethylbenzene using liquid phase zeolite catalyst process.

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Chapter 4

Energy balance

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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×𝑇𝑇𝑟𝑟2 (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)

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Energy balance Chapter 4

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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− 𝑇𝑇𝐶𝐶3)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

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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)

�𝑇𝑇1𝑇𝑇𝑇𝑇�

= (𝑃𝑃𝑇𝑇𝑃𝑃1

)𝛾𝛾−1𝛾𝛾 (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 − 𝑎𝑎𝑇𝑇 (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.

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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 − 𝑎𝑎𝑇𝑇𝑇𝑇 − 1) �𝑃𝑃1𝑃𝑃2�

𝛾𝛾0−1𝛾𝛾0

= 𝑇𝑇𝑇𝑇(𝛾𝛾0 − 𝑎𝑎𝑇𝑇1 − 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 = � 𝐶𝐶𝑃𝑃𝑉𝑉 𝑑𝑑𝑇𝑇 = 𝐶𝐶1 ∗ (511.15 − 298) + 𝐶𝐶2𝐶𝐶3 ∗ (𝐶𝐶𝑇𝑇𝑊𝑊ℎ(𝐶𝐶3

511.15

511.15

298)

− 𝐶𝐶𝑇𝑇𝑊𝑊ℎ(𝐶𝐶3

298)) − 𝐶𝐶4𝐶𝐶5(𝑇𝑇𝑎𝑎𝑛𝑛ℎ �

𝐶𝐶5511.15�

− 𝑇𝑇𝑎𝑎𝑛𝑛ℎ(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:

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Energy balance Chapter 4

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𝑄𝑄𝑐𝑐 = 𝑛𝑛∆𝐻𝐻 = 460.8� 𝐶𝐶𝑝𝑝𝑣𝑣483

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 Ĥ𝑇𝑇 − �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 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇 + ʋ ∆P483

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

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Energy balance Chapter 4

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ʋ = �1 𝜌𝜌𝑖𝑖�𝑛𝑛

𝑛𝑛

𝑖𝑖=1

= � 𝐶𝐶2(1+(1−

𝑇𝑇𝑖𝑖𝐶𝐶3)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 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.128 ∗ 1924.7483

298

Ĥ1 = 79226.24 kJ/kmol

For ideal gas behavior pressure has no effect on the enthalpy of ethylene

Ĥ2 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐸𝐸) 𝑑𝑑𝑇𝑇483

298

Ĥ2 = 61925.47 kJ/kmol

Ĥ3 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇 + ʋ ∆P483

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 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.1565 ∗ 1874.05483

298

Ĥ4 = 79219.71 KJ/kmol

Ĥ5 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇 + ʋ ∆P483

298

Ĥ5 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.1565 ∗ 1874.05483

298

Fig. 4.2 Sketch of the alkylator along with fully defined streams.

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Ĥ5 = 27076.56 KJ/kmol

Ĥ6 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐷𝐷𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇 + ʋ ∆P483

298

Ĥ6 = Ĥ°𝑓𝑓 + � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.1172 ∗483

2981874.05

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).

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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

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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

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The heat of the reboiler is provided from saturated steam at 45 bar (258.5°C)

Amount of steam required = 10010.91675.85

= 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

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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 = 13494.0164.2∗(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

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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 = 13512.861675.85

= 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

Diethylbenzene 0 0 44.085 Ĥ2 44.085 Ĥ5

*Reference state, components at 86.43°C and 1.2 atm

Ĥ1 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇473.2

359.43= 25123.664

𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑇𝑇𝑘𝑘

Ĥ2 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐷𝐷𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇473.2

359.43= 31452.4

𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑇𝑇𝑘𝑘

Ĥ3 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇𝑇𝑇𝑜𝑜

359.43

Ĥ4 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇𝑇𝑇𝑜𝑜

359.43

Ĥ5 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐷𝐷𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇𝑇𝑇𝑜𝑜

359.43

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Energy balance:

�𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖 = �𝑛𝑛𝑜𝑜 Ĥ𝑇𝑇

1398191.183 = ∑ 𝑛𝑛𝑜𝑜 Ĥ𝑇𝑇 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/𝑘𝑘𝑇𝑇𝑘𝑘

∆𝐻𝐻𝑟𝑟 = −380𝑘𝑘𝑘𝑘

𝑘𝑘𝑘𝑘𝑇𝑇𝑘𝑘

The transalkylator reactor is adiabatic. The energy balance equation reduces to:

∆𝐻𝐻 = Ƹ ∆𝐻𝐻𝑟𝑟 + �𝑛𝑛𝑜𝑜 Ĥ𝑇𝑇 − �𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖 = 0

�𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖 − Ƹ ∆𝐻𝐻𝑟𝑟 = �𝑛𝑛𝑜𝑜 Ĥ𝑇𝑇 (4.10)

Where Ƹ is the extent of reaction

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Energy balance Chapter 4

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Ƹ =46.3925 − 0.5437

2= 22.9244 𝑘𝑘𝑘𝑘𝑇𝑇𝑘𝑘/ℎ

Ĥ1 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇 + ʋ ∆P493

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 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.0985 ∗ 1924.7493

298= 32517.872

𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑇𝑇𝑘𝑘

Ĥ2 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.1331 ∗ 1924.7493

298= 41992.3356

𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑇𝑇𝑘𝑘

Ĥ3 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐷𝐷𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.1699 ∗ 1924.7493

298= 51973.7255

𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑇𝑇𝑘𝑘

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 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.0985 ∗ 1874.05𝑇𝑇𝑜𝑜

298

Ĥ5 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.1331 ∗ 1874.05𝑇𝑇𝑜𝑜

298

Ĥ6 = � 𝐶𝐶𝑝𝑝𝐿𝐿(𝐷𝐷𝐸𝐸𝐵𝐵) 𝑑𝑑𝑇𝑇 + 0.1699 ∗ 1874.05𝑇𝑇𝑜𝑜

298

Ƹ ∆𝐻𝐻𝑟𝑟 = −380 ∗ 22.9244 = −8711.272 𝑘𝑘𝑘𝑘ℎ

Fig. 4.7 Sketch of the transalkylator along with fully defined

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Energy balance Chapter 4

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�𝑛𝑛𝑖𝑖 Ĥ𝑖𝑖 = 4962486.271 𝑘𝑘𝑘𝑘ℎ

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.

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.

Fig. 4.8 Process flow diagram

of the base case design including main equipm

ent and stream's designations.

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Energy balance Chapter 4

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Fig. 4.9 Aspen hysys ethylbenzene process sim

ulation

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Energy balance Chapter 4

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Table 4.8 Aspen hysys process w

orkbook.

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Chapter 5

Equipment design

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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 Ҳ11+117.2 Ҳ��

Ҳ−1Ҳ0.5�� (5.1)

Ү = 𝑁𝑁 − 𝑁𝑁𝑚𝑚𝑖𝑖𝑛𝑛

𝑁𝑁 + 1 (5.2)

Ҳ = 𝑅𝑅 − 𝑅𝑅𝑚𝑚𝑖𝑖𝑛𝑛

𝑅𝑅 + 1 (5.3)

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Equipment design Chapter 5

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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)

𝑁𝑁𝑚𝑚𝑖𝑖𝑛𝑛 = log � 𝑓𝑓𝐴𝐴,𝐷𝐷 𝑓𝑓𝐵𝐵,𝑊𝑊

�1−𝑓𝑓𝐴𝐴,𝐷𝐷 ��1−𝑓𝑓𝐵𝐵,𝑊𝑊��

log(𝛼𝛼𝐴𝐴𝐵𝐵)𝑎𝑎𝑣𝑣

(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

𝑎𝑎𝑘𝑘𝑇𝑇𝑎𝑎𝑛𝑛𝑑𝑑 𝑇𝑇𝑓𝑓 𝐴𝐴 𝑖𝑖𝑛𝑛 𝑑𝑑ℎ𝑒𝑒 𝑓𝑓𝑒𝑒𝑒𝑒𝑑𝑑 𝑓𝑓𝐵𝐵,𝑊𝑊 =

𝑊𝑊 𝑥𝑥𝐵𝐵,𝑊𝑊

𝑎𝑎𝑘𝑘𝑇𝑇𝑎𝑎𝑛𝑛𝑑𝑑 𝑇𝑇𝑓𝑓 𝐵𝐵 𝑖𝑖𝑛𝑛 𝑑𝑑ℎ𝑒𝑒 𝑓𝑓𝑒𝑒𝑒𝑒𝑑𝑑

(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).

(𝛼𝛼𝐴𝐴𝐵𝐵)𝑎𝑎𝑣𝑣 = �(𝛼𝛼𝐴𝐴𝐵𝐵)𝑇𝑇𝑜𝑜𝑝𝑝 ∗ (𝛼𝛼𝐴𝐴𝐵𝐵)𝐵𝐵𝑜𝑜𝐵𝐵𝐵𝐵𝑜𝑜𝑚𝑚 (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).

𝑅𝑅𝑚𝑚𝑖𝑖𝑛𝑛 = 𝑉𝑉𝑚𝑚𝑖𝑖𝑚𝑚𝐷𝐷

− 1 (5.6)

Vmin : Minimum vapor flow at the top stage corresponding to the minimum reflux. It can be calculated from (Eq.5.7).

𝑉𝑉𝑚𝑚𝑖𝑖𝑛𝑛 = ∑ 𝛼𝛼𝑖𝑖 𝐷𝐷 𝑥𝑥𝑖𝑖,𝐷𝐷𝛼𝛼𝑖𝑖 − 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 𝑧𝑧𝑖𝑖𝛼𝛼𝑖𝑖 − 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:

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𝑞𝑞 = ℎ𝑒𝑒𝑎𝑎𝑑𝑑 𝑟𝑟𝑒𝑒𝑞𝑞𝑎𝑎𝑖𝑖𝑟𝑟𝑒𝑒𝑑𝑑 𝑑𝑑𝑇𝑇 𝑐𝑐𝑇𝑇𝑛𝑛𝑣𝑣𝑒𝑒𝑟𝑟𝑑𝑑 1 𝑘𝑘𝑇𝑇𝑘𝑘𝑒𝑒 𝑇𝑇𝑓𝑓 𝑑𝑑ℎ𝑒𝑒 𝑓𝑓𝑒𝑒𝑒𝑒𝑑𝑑 𝑑𝑑𝑇𝑇 𝑊𝑊𝑎𝑎𝑑𝑑𝑎𝑎𝑟𝑟𝑎𝑎𝑑𝑑𝑒𝑒𝑑𝑑 𝑣𝑣𝑎𝑎𝑝𝑝𝑇𝑇𝑟𝑟

𝐿𝐿𝑎𝑎𝑑𝑑𝑒𝑒𝑛𝑛𝑑𝑑 ℎ𝑒𝑒𝑎𝑎𝑑𝑑 𝑇𝑇𝑓𝑓 𝑣𝑣𝑎𝑎𝑝𝑝𝑇𝑇𝑟𝑟𝑖𝑖𝑣𝑣𝑎𝑎𝑑𝑑𝑖𝑖𝑇𝑇𝑛𝑛 𝑇𝑇𝑓𝑓 𝑑𝑑ℎ𝑒𝑒 𝑊𝑊𝑎𝑎𝑑𝑑𝑎𝑎𝑟𝑟𝑎𝑎𝑑𝑑𝑒𝑒𝑑𝑑 𝑘𝑘𝑖𝑖𝑞𝑞𝑎𝑎𝑖𝑖𝑑𝑑

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) PvA (atm) PvB (atm) PvC 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, PvB 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 =(𝛼𝛼𝐴𝐴𝐵𝐵)𝑎𝑎𝑣𝑣 𝑣𝑣𝐴𝐴

(𝛼𝛼𝐴𝐴𝐵𝐵)𝑎𝑎𝑣𝑣 − ϕ+

(𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑣𝑣 𝑣𝑣𝐵𝐵(𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑣𝑣 − ϕ

+ (𝛼𝛼𝐶𝐶𝐵𝐵)𝑎𝑎𝑣𝑣 𝑣𝑣𝐶𝐶

(𝛼𝛼𝐶𝐶𝐵𝐵)𝑎𝑎𝑣𝑣 − ϕ

q = 1 (the feed is a saturated liquid) (𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑣𝑣 = 1 (𝛼𝛼𝐶𝐶𝐵𝐵)𝑎𝑎𝑣𝑣 = √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

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Since the (HNK) is not distrusted the value of ϕ should be between the value of (αAB)av and (𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑣𝑣 ((𝛼𝛼𝐵𝐵𝐵𝐵)𝑎𝑎𝑣𝑣 < ϕ < (αAB)av) [11]. ϕ = 1.57563 Use (Eq.5.7) to calculated Vmin

𝑉𝑉𝑚𝑚𝑖𝑖𝑛𝑛 =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)

𝑅𝑅𝑚𝑚𝑖𝑖𝑛𝑛 = 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 Ҳ11+117.2 Ҳ��

Ҳ−1Ҳ0.5��

Ҳ = 0.735 − 0.4896

0.735 + 1= 0.15

Substituting the value of Ҳ and Ү in (Eq.5.1).

Ү = 𝑁𝑁 − 8.737𝑁𝑁 + 1

= 0.502

N = 18.561 ideal tray The optimal feed tray location is determined using Kirkbride's equation (Eq.5.9).

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𝑁𝑁𝑅𝑅𝑁𝑁𝑆𝑆

= ��𝑧𝑧𝐻𝐻𝐻𝐻𝑧𝑧𝐿𝐿𝐻𝐻

� �𝑥𝑥𝐿𝐿𝐻𝐻,𝑊𝑊𝑥𝑥𝐻𝐻𝐻𝐻,𝐷𝐷

�𝑊𝑊𝐷𝐷�0.206

(5.9)

Where: NR : Number of trays in the rectifying section NS : Number of trays in the stripping section Substituting: 𝑁𝑁𝑅𝑅𝑁𝑁𝑆𝑆

= ��0.44050.5175

� �0.00110.001

� 506.81543.5

�0.206

𝑁𝑁𝑅𝑅𝑁𝑁𝑆𝑆

= 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).

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The flooding velocity for spray entrainment flooding is calculated from Souders-Brown equation (Eq.5.10) [23].

𝑎𝑎𝑠𝑠,𝑓𝑓𝑓𝑓 = 𝐶𝐶𝑆𝑆𝐵𝐵 �𝜌𝜌𝐿𝐿−𝜌𝜌𝐺𝐺𝜌𝜌𝐺𝐺

�12�

(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].

𝐶𝐶𝑆𝑆𝐵𝐵 = 0.144 �𝑑𝑑𝐻𝐻2 𝜎𝜎𝜌𝜌𝐿𝐿�0.125

�𝜌𝜌𝐺𝐺𝜌𝜌𝐿𝐿�0.1

� 𝑆𝑆ℎ𝑐𝑐𝑐𝑐�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)

ℎ𝑐𝑐𝐵𝐵 = (ℎ𝑐𝑐𝐵𝐵)𝑤𝑤 �62.2𝜌𝜌𝐿𝐿�0.5(1−0.0231𝑑𝑑𝐻𝐻𝑓𝑓ℎ

)

(5.12)

(ℎ𝑐𝑐𝐵𝐵)𝑤𝑤 = 0.29 𝑓𝑓ℎ−0.791𝑑𝑑𝐻𝐻

0.833

1+0.0036 𝑄𝑄𝐿𝐿−0.59𝑓𝑓ℎ

−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).

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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

= Aafa

(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).

𝐴𝐴𝑑𝑑𝐴𝐴𝑇𝑇

=𝜃𝜃 − sin(𝜃𝜃)

2𝜋𝜋

(5.14)

𝑘𝑘𝑤𝑤 = 2𝐷𝐷𝑐𝑐 sin �𝜃𝜃2�

(5.15)

Fig. 5.1 Simple geometric representation of the tray

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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

(ℎ𝑐𝑐𝐵𝐵)𝑤𝑤 = 0.29 𝑥𝑥 0.1−0.791 𝑥𝑥0.3750.833

1+0.0036 (22.482−0.59𝑥𝑥 0.1−1.79) = 0.7647 inch

From (Eq.5.12)

ℎ𝑐𝑐𝐵𝐵 = 0.7647 � 62.249.136

�0.5(1−0.02310.375

0.1 )= 0.862 inch

Now CSB can be calculated from (Eq.5.11)

𝐶𝐶𝑆𝑆𝐵𝐵 = 0.144 �0.3752 𝑥𝑥 16.9247.845

�0.125

�0.256147.845

�0.1

� 180.862

�0.5

= 0.268 ft/s

The flooding velocity is calculated from (Eq.5.10)

𝑎𝑎𝑠𝑠,𝑓𝑓𝑓𝑓 = 0.268 �47.845−0.25610.2561

�12� = 3.654 ft/s

- The gas velocity through the column cross section is calculated to check for the tower diameter suitability

𝐴𝐴𝑇𝑇 = 𝜋𝜋4

(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 = 759461.6862.83 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:

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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 ∗𝐴𝐴𝑑𝑑𝐴𝐴𝑇𝑇

= 1812𝑥𝑥 95.033𝑥𝑥0.05 = 7.127 ft3

Residence time = 𝐷𝐷𝑜𝑜𝑤𝑤𝑛𝑛 𝑐𝑐𝑜𝑜𝑚𝑚𝑐𝑐𝑟𝑟 𝑣𝑣𝑜𝑜𝑓𝑓𝑣𝑣𝑚𝑚𝑐𝑐𝑐𝑐𝑓𝑓𝑐𝑐𝑎𝑎𝑟𝑟 𝑓𝑓𝑖𝑖𝑙𝑙𝑣𝑣𝑖𝑖𝑑𝑑 𝑓𝑓𝑓𝑓𝑜𝑜𝑤𝑤

= 7.1272

= 3.56 𝑊𝑊 (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∗ �ℎ𝑇𝑇𝑘𝑘𝑒𝑒 𝑑𝑑𝑖𝑖𝑎𝑎𝑘𝑘𝑒𝑒𝑑𝑑𝑒𝑒𝑟𝑟ℎ𝑇𝑇𝑘𝑘𝑒𝑒 𝑝𝑝𝑖𝑖𝑑𝑑𝑐𝑐ℎ �

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

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• 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 + ℎ𝑜𝑜𝑤𝑤 + ∆ 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�

13�

(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

ℎ𝑜𝑜𝑤𝑤 = 1.43 ��203.8

3600 𝑥𝑥 1.097 � �2

9.81�13�

= 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).

ℎ𝑎𝑎𝑑𝑑 = 0.03 � 𝐿𝐿𝑣𝑣 100 𝐴𝐴𝑎𝑎𝑑𝑑

�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

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ℎ𝑎𝑎𝑑𝑑 = 0.03 � 897.3044100 𝑥𝑥 0.54

�2= 8.24 inch

c) Total gas pressure drop

The dry tray pressure drop is calculated using (Eq.5.21).

ℎ𝑑𝑑 = 0.186𝐶𝐶𝑜𝑜 2

�𝜌𝜌𝐺𝐺𝜌𝜌𝐿𝐿� 𝑎𝑎ℎ 2 (5.21)

Where:

uh: Gas velocity through holes. Co: Discharge coefficient. It can be obtained from appendix A (Figure A-1).

𝑎𝑎ℎ = 𝐺𝐺𝑣𝑣ℎ𝑜𝑜𝑓𝑓𝑐𝑐𝑠𝑠 𝑎𝑎𝑟𝑟𝑐𝑐𝑎𝑎

= 759461.6843600 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 = 0.1860.7352

�0.256147.845

� 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).

ℎ𝑓𝑓 = 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 = 𝑎𝑎𝑠𝑠,𝑏𝑏 (𝜌𝜌𝐺𝐺)1 2� = 𝐺𝐺𝑣𝑣𝐴𝐴𝑎𝑎,𝑏𝑏(𝜌𝜌𝐺𝐺)1 2� (5.22)

𝐹𝐹𝑠𝑠ℎ = 759461.68471.68 𝑥𝑥 3600 (0.2561)1 2� = 1.489

From figure A-2, 𝛽𝛽 = 0.6

ℎ𝑓𝑓 = 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).

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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 = 𝜌𝜌𝑓𝑓𝑟𝑟𝑜𝑜𝐵𝐵ℎ 𝜌𝜌𝐿𝐿� . For a sieve tray it rarely goes below 0.5 [11].

Taking the minimum value available in literature, ∅𝑑𝑑 = 0.5

ℎ𝑓𝑓 = 18.8870.5

= 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: 𝑣𝑣𝑠𝑠𝑣𝑣𝑠𝑠,𝑓𝑓𝑓𝑓

= 61.94% (acceptable)

Down comer's liquid velocity and residence Time are within accepted range. 𝑆𝑆2

= 18 𝑖𝑖𝑛𝑛 > ℎ𝑑𝑑𝑏𝑏

S + hw = 38.5 > hf

- Check for entrainment, weeping and turndown ratio

ℎ𝑑𝑑𝑏𝑏 = ℎ𝑐𝑐 + ℎ𝑎𝑎𝑑𝑑 + ℎ𝑑𝑑 (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

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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).

𝐿𝐿𝐺𝐺

(𝜌𝜌𝐺𝐺𝜌𝜌𝐿𝐿

)0.5 = 203.8 𝑥𝑥 766.4 (𝑘𝑘𝑘𝑘ℎ )

21505.56 𝑥𝑥 4.102 (𝑘𝑘𝑘𝑘ℎ ) (4.102766.4

)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 16.9247.845 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 �

0.256147.845�

𝑎𝑎ℎ 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 = 10.5567

= 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 𝜎𝜎𝜌𝜌𝐿𝐿 𝑑𝑑𝐻𝐻

(5.25)

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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: 𝑣𝑣𝑠𝑠𝑣𝑣𝑠𝑠,𝑓𝑓𝑓𝑓

= 63.05% (acceptable)

Down comer's liquid velocity and residence Time are within accepted range. 𝑆𝑆2

= 9 𝑖𝑖𝑛𝑛 > ℎ𝑑𝑑𝑏𝑏

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

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𝐿𝐿𝐺𝐺

(𝜌𝜌𝐺𝐺𝜌𝜌𝐿𝐿

)0.5 = 40.06 𝑥𝑥 794.756 (𝑘𝑘𝑘𝑘ℎ )

21505.56 𝑥𝑥 3.61 (𝑘𝑘𝑘𝑘ℎ ) ( 3.61794.756

)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 �

0.225449.615�

𝑎𝑎ℎ 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 = 10.6649

= 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].

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𝐸𝐸𝑀𝑀 = 𝑦𝑦𝑛𝑛 − 𝑦𝑦𝑛𝑛+1𝑦𝑦𝑛𝑛∗ − 𝑦𝑦𝑛𝑛+1

(5.26)

Where:

yn and yn+1 : Average concentration of gases leaving nth and (n+1) tray. yn* : Equilibrium concentration of the gas leaving nth tray. yn* is obtained from equilibrium data. It was experimentally demonstrated that benzene-ethylbenzene system perfectly obeys Raoult's law [27] (Eq.5.27).

𝑦𝑦𝑖𝑖𝑛𝑛∗ = 𝑃𝑃𝑖𝑖𝑣𝑣

𝑃𝑃 𝑥𝑥𝑖𝑖𝑛𝑛 (5.27)

Piv Vapor pressure of component i at particular temperature

The effect of entrainment can be accounted for in Murphree's equation and the final form is shown in (Eq.5.28).

𝐸𝐸𝑀𝑀𝐸𝐸 = 𝐸𝐸𝑀𝑀

1 + 𝐸𝐸𝑀𝑀(𝜑𝜑 1 − 𝜑𝜑)⁄ (5.28)

Where: φ Fractional entrainment = 0.064 and 0.0025 for rectifying and stripping sections respectively

The VLE data is obtained for each tray and the corresponding Murphree's efficiency is calculated; results are shown in appendix A (Table A-3).

The overall efficiency of the whole column (or a section in the column) can be obtained by many methods. Useful correlations are available that estimates the section efficiency. The widely used correlation is the one derived from O’Connell's chart (Eq.5.29) [28]. O’Connell's chart is shown in appendix A (Figure A-5).

𝐸𝐸𝑜𝑜 = 50.3 (𝜇𝜇𝐿𝐿𝛼𝛼)−0.226 (5.29)

Where:

Eo : Overall efficiency. 𝜇𝜇𝐿𝐿 : Viscosity of the feed at average section temperature. In cp. α: Average relative volatility of the LK to HK. A recently published modification to O’Connell's equation which was tested to be more accurate than the original correlation will be used (Eq.5.30) [29].

𝐸𝐸𝑜𝑜 = 0.503 𝜇𝜇𝐿𝐿−0.226𝜆𝜆−0.08 (5.30)

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Where 𝜆𝜆 is the stripping factor defined as the ratio of the slope of the equilibrium line to operating line. The efficiency is calculated for the rectifying and stripping sections separately and the average parameters are obtained from appendix A (Table A-4). The average values in rectifying section: 𝜇𝜇𝐿𝐿 = 0.27645 cp λ = 2.9488 Substituting, the modified O’Connell efficiency correlation (Eq.5.30). 𝐸𝐸𝑜𝑜 = 0.503 𝑥𝑥 0.27645−0.226𝑥𝑥2.9488−0.08 = 61.68%

The average values in stripping section: 𝜇𝜇𝐿𝐿 = 0.23148 cp λ = 1.9217 𝐸𝐸𝑜𝑜 = 0.503 𝑥𝑥 0.23148−0.226𝑥𝑥1.9217−0.08 = 66.45% - The actual number of trays is:

Rectifying section = 9.90.6168

= 16.05 = 17 trays Stripping section = 8.65

0.6645 = (13 trays + reboiler) = 14 trays

The feed is introduced onto the 17th tray from the top - The column height

• There are 13 tray spacing in the stripping section and 16 tray spacing in the rectifying section = 13 x 36 + 16 x 18 = 63 ft.

• Extra space added for the feed nozzle; add extra feed nozzles below and above the design feed tray in case of change in operation (i.e. tray 18 and 16), account for 0.5 ft for each nozzle = 0.5 x 3 = 1.5 ft.

• Add 0.75 ft spacing in the rectifying section at the tray provided with a manhole (due to small tray spacing).

• Provide 3 ft liquid depth at the bottom of the column and 6 ft clear space above that = 9 ft bottom space.

• Provide 4 ft above the top tray to accommodate the demister and exit nozzle. Total column height = 78.25 ft = 23.85 m

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- Total pressure drop The pressure drop expressed as liquid head can be converted to a more convenient unit (e.g. psi) using the following formula (Eq.5.31).

𝑃𝑃 (𝑖𝑖𝑛𝑛 𝑝𝑝𝑊𝑊𝑖𝑖) = ℎ𝑒𝑒𝑎𝑎𝑑𝑑 (𝑖𝑖𝑛𝑛 𝑓𝑓𝑑𝑑)𝑥𝑥 𝑆𝑆𝐺𝐺

2.31 (5.31)

Rectifying section = (2.97 12)⁄ 𝑋𝑋 17 𝑋𝑋 0.7947

2.31 = 1.4474 psi = 0.0985 atm

Stripping section = (6.6 12)⁄ 𝑋𝑋 14 𝑋𝑋 0.7664

2.31 = 2.554 psi = 0.174 atm

Condenser pressure = 1.2015 atm , Reboiler pressure = 1.474 atm The column data sheet is provided in (Table 5.4). Table 5.4 Benzene column – sieve tray data sheet Parameters Rectifying Stripping Overall Column ID (m) Operating pressure (atm) Operating temperature (°C) Fluid description Design Gas flow rate (m3/h)

Density (kg/m3) Design Liquid flow rate (m3/h)

Density (kg/m3) Surface tension (dyne/cm2)

Superficial Flooding velocity (ft/s) Down comer fluid velocity (ft/s) Down comer residence time (s) Column height (m) Number of trays Sieve tray data

Tray spacing (in) Weir height (in) Down comer clearance (in) Total number of holes Hole diameter (in) Fractional hole area Number of passes Weir length (ft)

3.353

1.2015 (top) 89.16 (top)

21505.56 3.61 40.06 794.7

19.085 4.094 0.059 9.625

- 17

18 1.5 1.1

9352 3/8 0.1 1

3.623

3.353

1.474(bottom) 150.17 (bottom)

Aromatic hydrocarbon

21505.56

4.102 203.8 766.4 16.92 5.12 0.14 7.5 -

14

36 2.5 2.3

6036 2/5 0.1 1

3.725

- - - - - - - - - - -

23.85 31 - - - - -

0.1 1 -

5.2 Design of the ethylbenzene distillation column The ethylbenzene column separates the ethylbenzene from diethylbenzene to yield final product of 99.88% ethylbenzene in the top; the concentration of benzene in the feed to

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the column is very low. Therefore, the column is assumed to be a binary system for EB and DEB.

5.2.1 Determination of the number of ideal stages and feed tray location For a binary multistage distillation, the most common method for the determination of the number of ideal stages is The McCabe-Thiele method [30]. The McCabe method is a graphical method that assumes constants vapor and liquid flows in the rectifying and stripping sections separately, this assumption doesn't hold perfectly in real life applications but in this process, it is a good approximation as there is no great variation in the flow rates throughout each section inside the column. The requirements for the graphical construction of the number of ideal stages are:

1. The equilibrium relations in the rectifying and stripping sections 2. The operating lines for the rectifying and stripping sections 3. The state of the feed

The equilibrium relation follows Raoult's law, the equilibrium line slope is obtained as an average between the top and feed mixtures for the rectifying section and between the feed and bottom mixtures for the stripping section. The data required is shown in (Table 5.5). The operating line for the rectifying and stripping section are obtained by performing a material balance over each section separately. The operating line equations are shown in (Eq.5.32) and (Eq.5.33) for the rectifying and stripping sections respectively. Table 5.5 Equilibrium constant for top, feed and bottom.

Temperature (°C) PvEB (atm) PTotal (atm) m = PvEB / PTotal 146 (top) 1.298 1.3 0.9985

151.56 (Feed) 1.492 1.4 1.0657 200.2 (bottom) 4.301 1.5 2.8673

* obtained for ethylbenzene.

𝑦𝑦𝑛𝑛+1 = 𝑅𝑅

𝑅𝑅 + 1 𝑥𝑥𝑛𝑛 + 𝑥𝑥𝐷𝐷

𝑅𝑅+ 1 (5.32)

𝑦𝑦𝑚𝑚+1 = 𝐿𝐿�

𝐿𝐿� −𝑊𝑊 𝑥𝑥𝑘𝑘 + 𝑤𝑤

𝐿𝐿� −𝑊𝑊 𝑥𝑥𝑤𝑤 (5.33)

Where:

yn+1 , ym+1: Mole fraction of the selected component in the vapor entering the nth and mth trays in the rectifying (n) and stripping (m) sections respectively. R: Reflux ratio.

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xD: Mole fraction of the selected component in the distillate. 𝐿𝐿�: Liquid molar flow in the stripping section. W: Molar flow of the bottom stream. The equilibrium curve is generated by taking slopes between the top and bottom equilibrium line slope. The feed line orientation is determined from the value of q defined as:

𝑞𝑞 = ℎ𝑒𝑒𝑎𝑎𝑑𝑑 𝑟𝑟𝑒𝑒𝑞𝑞𝑎𝑎𝑖𝑖𝑟𝑟𝑒𝑒𝑑𝑑 𝑑𝑑𝑇𝑇 𝑐𝑐𝑇𝑇𝑛𝑛𝑣𝑣𝑒𝑒𝑟𝑟𝑑𝑑 1 𝑘𝑘𝑇𝑇𝑘𝑘𝑒𝑒 𝑇𝑇𝑓𝑓 𝑑𝑑ℎ𝑒𝑒 𝑓𝑓𝑒𝑒𝑒𝑒𝑑𝑑 𝑑𝑑𝑇𝑇 𝑊𝑊𝑎𝑎𝑑𝑑𝑎𝑎𝑟𝑟𝑎𝑎𝑑𝑑𝑒𝑒𝑑𝑑 𝑣𝑣𝑎𝑎𝑝𝑝𝑇𝑇𝑟𝑟

𝐿𝐿𝑎𝑎𝑑𝑑𝑒𝑒𝑛𝑛𝑑𝑑 ℎ𝑒𝑒𝑎𝑎𝑑𝑑 𝑇𝑇𝑓𝑓 𝑣𝑣𝑎𝑎𝑝𝑝𝑇𝑇𝑟𝑟𝑖𝑖𝑣𝑣𝑎𝑎𝑑𝑑𝑖𝑖𝑇𝑇𝑛𝑛 𝑇𝑇𝑓𝑓 𝑑𝑑ℎ𝑒𝑒 𝑊𝑊𝑎𝑎𝑑𝑑𝑎𝑎𝑟𝑟𝑎𝑎𝑑𝑑𝑒𝑒𝑑𝑑 𝑘𝑘𝑖𝑖𝑞𝑞𝑎𝑎𝑖𝑖𝑑𝑑

q = 1 (the feed is a saturated liquid and the feed line is vertical) q = 0 (the feed is a saturated vapor and the feed line is horizontal) 0 > q > 1 ( the feed is a vapor-liquid mixture and the feed line has an angle between 0° and 90°) q > 1 ( the feed is a sub-cooled liquid and the feed line has an angle more than 90°) q < 0 ( the feed is a super-heated vapor and the feed line has an angle less than 0° [below the horizontal line since heat must be removed to convert a superheated vapor to saturated vapor]) saturated liquid feed is selected to minimize the column diameter (i.e. q=1). The feed line will be a vertical line passing through point (zf , zf) where z is the mole fraction of the selected component in the feed. Take the reflux ratio R = 2.7. Now that all the required data are available, the graphical construction is carried out.

• The feed line is vertical and passes through point (0.911, 0.911) • The rectifying section operating line joins the points (xD,xD) and the intersect

(xD/R+1). The points are (0.9988,0.9988) and (0, 0.2699). • The stripping section operating line joins the point (xw,xw) and the point of

intersection between the feed line and the rectifying section operating line. The graphical representation of the ethylbenzene column operation is shown in Figures 5.2 (a) and 5.2(b). The rectifying section has been isolated in smaller scale for more accurate determination of the number of stages.

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Fig. 5.2 Graphical construction of the number of ideal stages For (a) the rectifying section and (b) the stripping section.

From the graphs, the number of ideal stages is 10.8 stages and the feed is introduced onto the 4th tray from the top.

5.2.2 Determination of the column efficiency and column dimensions The overall efficiency is determined from (Eq.5.30). The average values are:

The average values in stripping section: 𝜇𝜇𝐿𝐿 = 0.19743cp λ = 1.578 𝐸𝐸𝑜𝑜 = 0.503 𝑥𝑥 0.19743−0.226𝑥𝑥1.578−0.08 = 69.97 %

Actual number of trays = 10.80.6997

= 15.44 = 16 tray

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The feed is introduced onto the 6th tray from the top.

The column diameter and height are then determined.

ρL = 45.71 lb/ft3

ρG = 0.284 lb/ft3

σ = 14.61 dyne/cm

Liquid volumetric flow rate Lv = 1309.85 gal/min

Vapor volumetric flow rate Gv = 1526928.765 ft3/h

The sizing parameters are shown in (Table 5.6).

Checking the design parameters: 𝑣𝑣𝑠𝑠𝑣𝑣𝑠𝑠,𝑓𝑓𝑓𝑓

= 63.73% (acceptable)

Down comer's liquid velocity and residence Time are within accepted range. 𝑆𝑆2

= 18 𝑖𝑖𝑛𝑛 > ℎ𝑑𝑑𝑏𝑏

S + hw = 38.8 > hf

The design is safe. Now proceed to sizing the tower. The column diameter is 4.57 m The column height:

• There are 15 tray spacing = 15 x 36 = 45 ft • Extra space added for the feed nozzle; add extra feed nozzles below and above

the design feed tray in case of change in operation (i.e. tray 18 and 16), account for 0.5 ft for each nozzle = 0.5 x 3 = 1.5 ft

• Provide 3 ft liquid depth at the bottom of the column and 6 ft clear space above that = 9 ft bottom space

• Provide 4 ft above the top tray to accommodate the demister and exit nozzle The column height = 45+1.5+9+4 = 59.5 ft = 18.136 m

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)

15

36

0.1

0.4

0.3722

4.708

3

0.165

18.2

2.8

6.31

17.649

35.299

Table 5.6 Design parameters of the ethylbenzene distillation column

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5.3 Design of alkylation reactor The differential form of the mole balance equation in terms of catalyst weight is given by (Eq.5.34) [31].

𝐹𝐹𝐸𝐸˳ 𝑑𝑑𝑑𝑑𝐸𝐸𝑑𝑑𝑊𝑊

= −𝑟𝑟𝐸𝐸 𝑘𝑘𝑘𝑘𝑇𝑇𝑘𝑘

𝑘𝑘𝑘𝑘 𝑐𝑐𝑎𝑎𝑑𝑑𝑎𝑎𝑘𝑘𝑦𝑦𝑊𝑊𝑑𝑑.ℎ (5.34)

Where −rE: Rate of consumption of ethylene, FE˳ : Inlet molar flow rate of ethylene, W :Amount of catalyst in kg, XE: Conversion of ethylene. There are two parallel reaction takes place in the alkylator. The main reaction is reaction of benzene with ethylene producing ethylbenzene. With a rate law which given by (Eq.5.35) [3]. − 𝑟𝑟𝐵𝐵 = 𝑘𝑘𝑟𝑟 𝐶𝐶𝐸𝐸

1+𝑘𝑘𝐸𝐸𝐵𝐵 𝐶𝐶𝐸𝐸𝐵𝐵 𝑘𝑘𝑚𝑚𝑜𝑜𝑓𝑓 𝑏𝑏𝑐𝑐𝑛𝑛𝑧𝑧𝑐𝑐𝑛𝑛𝑐𝑐

𝑘𝑘𝑘𝑘 𝑐𝑐𝑎𝑎𝐵𝐵𝑎𝑎𝑓𝑓𝑐𝑐𝑠𝑠𝐵𝐵.ℎ

(5.35)

𝑘𝑘𝑟𝑟 = 0.69 ∗ 106 𝑒𝑒𝑥𝑥𝑝𝑝−6.344 ∗ 104

𝑅𝑅𝑇𝑇

𝑘𝑘𝐸𝐸𝐵𝐵 = −1.5202 ∗ 10−2 𝑒𝑒𝑥𝑥𝑝𝑝−3.933 ∗ 103

𝑅𝑅𝑇𝑇

The side reaction is reaction of ethylbenzene with ethylene. With a rate law which given by (Eq.5.36) [3]. −𝑟𝑟𝐸𝐸𝐵𝐵 = 2.8 ∗ 10−2 exp �−4.7030∗104

𝑅𝑅𝑇𝑇� 𝐶𝐶𝐸𝐸𝐵𝐵𝐶𝐶𝐸𝐸 𝑘𝑘𝑚𝑚𝑜𝑜𝑓𝑓 𝐸𝐸𝐵𝐵

𝑘𝑘𝑘𝑘 𝑐𝑐𝑎𝑎𝐵𝐵𝑎𝑎𝑓𝑓𝑐𝑐𝑠𝑠𝐵𝐵.ℎ (5.36)

The rate of consumption of ethylene = rate of consumption of benzene in the main reaction plus that of ethylbenzene in the side reaction. −𝑟𝑟𝐸𝐸 = −𝑟𝑟𝐵𝐵 − 𝑟𝑟𝐸𝐸𝐵𝐵

−𝑟𝑟𝐸𝐸 =0.69 ∗ 106 𝑒𝑒𝑥𝑥𝑝𝑝 −6.344∗104

𝑅𝑅𝑇𝑇∗ 𝐶𝐶𝐸𝐸

1 − 1.5202 ∗ 10−2 𝑒𝑒𝑥𝑥𝑝𝑝 −3.933∗103

𝑅𝑅𝑇𝑇∗ 𝐶𝐶𝐸𝐸𝐵𝐵

+ 2.8 ∗ 10−2 exp�−4.7030 ∗ 104

𝑅𝑅𝑇𝑇�𝐶𝐶𝐸𝐸𝐵𝐵𝐶𝐶𝐸𝐸

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𝐹𝐹𝐸𝐸˳ 𝑑𝑑𝑑𝑑𝐸𝐸𝑑𝑑𝑊𝑊

=0.69 ∗ 106 𝑒𝑒𝑥𝑥𝑝𝑝 −6.344∗104

𝑅𝑅𝑇𝑇∗ 𝐶𝐶𝐸𝐸

1 − 1.5202 ∗ 10−2 𝑒𝑒𝑥𝑥𝑝𝑝 −3.933∗103

𝑅𝑅𝑇𝑇∗ 𝐶𝐶𝐸𝐸𝐵𝐵

+ 2.8 ∗ 10−2 exp�−4.7030 ∗ 104

𝑅𝑅𝑇𝑇�𝐶𝐶𝐸𝐸𝐵𝐵𝐶𝐶𝐸𝐸

𝐶𝐶𝐸𝐸 = 𝐶𝐶𝐸𝐸˳(1 − 𝑑𝑑𝐸𝐸) 𝐶𝐶𝐸𝐸𝐵𝐵 = 𝐶𝐶𝐸𝐸𝐵𝐵˳ + 0.95𝐶𝐶𝐸𝐸˳𝑑𝑑𝐸𝐸 − 0.05𝐶𝐶𝐸𝐸˳𝑑𝑑𝐸𝐸 Substituting for CE and CEB gives

𝐹𝐹𝐸𝐸˳ 𝑑𝑑𝑑𝑑𝐸𝐸𝑑𝑑𝑊𝑊

=0.69 ∗ 106 𝑒𝑒𝑥𝑥𝑝𝑝(−6.344∗104

𝑅𝑅𝑇𝑇) ∗ 𝐶𝐶𝐸𝐸˳(1 − 𝑑𝑑𝐸𝐸)

1 − 1.5202 ∗ 10−2 exp (−3.933∗103

𝑅𝑅𝑇𝑇) ∗ 𝐶𝐶𝐸𝐸˳(1 − 𝑑𝑑𝐸𝐸)

+ 2.8 ∗ 10−2 exp�−4.7030 ∗ 104

𝑅𝑅𝑇𝑇�

∗ �𝐶𝐶𝐸𝐸𝐵𝐵˳ + 0.85𝐶𝐶𝐸𝐸˳𝑑𝑑𝐸𝐸 − 0.15𝐶𝐶𝐸𝐸˳𝑑𝑑𝐸𝐸� ∗ 𝐶𝐶𝐸𝐸˳(1 − 𝑑𝑑𝐸𝐸) Separating variables and solving for the weight of catalyst, the equation is solved numerically with integration limits X=0 at W=0 and X=1 at W=W. W= 64433.655 kg The volume of the solid catalyst is then calculated from (Eq.5.37) [31].

𝑣𝑣𝑇𝑇𝑘𝑘𝑎𝑎𝑘𝑘𝑒𝑒 𝑇𝑇𝑓𝑓 𝑊𝑊𝑇𝑇𝑘𝑘𝑖𝑖𝑑𝑑 𝑐𝑐𝑎𝑎𝑑𝑑𝑎𝑎𝑘𝑘𝑦𝑦𝑊𝑊𝑑𝑑 =𝑤𝑤𝑒𝑒𝑖𝑖𝑘𝑘ℎ𝑑𝑑 𝑇𝑇𝑓𝑓 𝑑𝑑ℎ𝑒𝑒 𝑐𝑐𝑎𝑎𝑑𝑑𝑎𝑎𝑘𝑘𝑦𝑦𝑊𝑊𝑑𝑑

𝑑𝑑𝑒𝑒𝑛𝑛𝑊𝑊𝑖𝑖𝑑𝑑𝑦𝑦 𝑇𝑇𝑓𝑓 𝑐𝑐𝑎𝑎𝑑𝑑𝑎𝑎𝑘𝑘𝑦𝑦𝑊𝑊𝑑𝑑

(5.37)

Where density of zeolite (ρ) = 740 kg/m3 [32]. So, volume of solid catalyst= 87.07 m3

𝑏𝑏𝑎𝑎𝑘𝑘𝑘𝑘 𝑣𝑣𝑇𝑇𝑘𝑘𝑎𝑎𝑘𝑘𝑒𝑒 𝑇𝑇𝑐𝑐𝑐𝑐𝑎𝑎𝑝𝑝𝑖𝑖𝑒𝑒𝑑𝑑 𝑏𝑏𝑦𝑦 𝑐𝑐𝑎𝑎𝑑𝑑𝑎𝑎𝑘𝑘𝑊𝑊𝑑𝑑 =𝑣𝑣𝑇𝑇𝑘𝑘𝑎𝑎𝑘𝑘𝑒𝑒 𝑇𝑇𝑓𝑓 𝑊𝑊𝑇𝑇𝑘𝑘𝑖𝑖𝑑𝑑 𝑐𝑐𝑎𝑎𝑑𝑑𝑎𝑎𝑘𝑘𝑦𝑦𝑊𝑊𝑑𝑑 1 − 𝑝𝑝𝑇𝑇𝑟𝑟𝑇𝑇𝑊𝑊𝑖𝑖𝑑𝑑𝑦𝑦 𝑇𝑇𝑓𝑓 𝑐𝑐𝑎𝑎𝑑𝑑𝑎𝑎𝑘𝑘𝑦𝑦𝑊𝑊𝑑𝑑

(5.38)

Where the porosity of zeolite catalyst = 0.15 [33] Substituting for porosity and volume of solid catalyst: Bulk volume occupied by the catalyst= 102.43 m3 Distributing the catalyst onto 2 beds, 0.5 m is allowed between each bed and the same for entrance and exit of fluid. So, the volume of the reactor available for feed flow (assuming the feed is introduced below the ellipsoidal head) = volume of the catalyst + volume between beds + entrance and exit volume

п4𝐷𝐷2𝐿𝐿 = 102.43 + 0.5 ∗

п4𝐷𝐷2 + 2 ∗ 0.5 ∗

п4𝐷𝐷2

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Where D and L are diameter and height of the cylindrical reactor walls respectively.

Substituting for L using aspect ratio (𝐿𝐿𝐷𝐷

= 1.25) and solving for D gives

D= 5.144 m & L= 1.25*D= 6.43 m

So, the volume of the reactor = 133.6 m3

The residence time is related to the void volume by (Eq.5.39).

residence time (τ) =void volume

volumetric flow rate

(5.39)

Void volume = 133.6-87.07= 46.53 m3

Volumetric flow rate = 110.93 m3/h

Substituting in eq.5.33

𝜏𝜏 = 0.42 ℎ = 25 min

Knowing the dimension, the reactor thickness is now calculated. Choose 316 stainless steel due to its high corrosion resistance and good mechanical and thermal properties. The cylindrical wall thickness can be calculated from (Eq.5.40) based on the theory of thin cylinders [34].

𝑑𝑑 =𝑃𝑃𝑖𝑖 𝑑𝑑𝑖𝑖

2 𝜎𝜎𝑎𝑎𝑓𝑓𝑓𝑓 𝜂𝜂𝐽𝐽 − 𝑃𝑃𝑖𝑖+ 𝐶𝐶 (5.40)

Where: t : Wall thickness. In mm Pi : Design pressure. In MPa (taken as 2.2 MPa) di : Inner diameter of the reactor. In mm 𝜎𝜎𝑎𝑎𝑓𝑓𝑓𝑓 ∶ Allowable tensile stress for the reactor material. It is based on the yield strength of the material with a suitable factor of safety. For 316 stainless steel the yield strength is equal to 205 MPa. For a factor of safety=1.5, the allowable tensile stress is equal to 205/1.5 = 136.667 MPa. 𝜂𝜂𝐽𝐽: Longitudinal joints efficiency which depends on the efficiency of welding (Illustrated in figure 5.3). Taken as 85% C: Corrosion allowance (taken as 1 mm) The thickness is therefore calculated:

𝑑𝑑 =2.2 𝑥𝑥 5140

2 𝑥𝑥136.667𝑥𝑥 0.85 − 2.2+ 1 = 50.17 𝑘𝑘𝑘𝑘

Fig. 5.3 Illustration of the stresses affecting the welded joints of a pressurized cylindrical wall. From [35]

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The reactor head cover is chosen to be semi-elliptical. The thickness of the head can be determined from (Eq.5.41).

𝑑𝑑ℎ =𝐾𝐾𝑓𝑓𝑃𝑃𝑖𝑖 𝑑𝑑𝑖𝑖

2 𝜎𝜎𝑎𝑎𝑓𝑓𝑓𝑓 𝜂𝜂𝐽𝐽 − 0.2𝑃𝑃𝑖𝑖+ 𝐶𝐶

(5.41)

Where: th : Head thickness. In mm Kf : Stress intensification factor defined as: 𝑘𝑘𝑓𝑓 = 1

6 (2 + 𝑘𝑘𝑖𝑖 2)

Where ki is the ratio of the major axis to minor axis of the ellipsoidal head (commonly taken as 2). Therefore, Kf = 1

Take C= 0.3 (less susceptible to corrosion)

th = 41.7 mm

Now the cooling configuration of the reactor is determined. First a cooling jacket is considered. In a previous study of a reactor for the same system and overall heat transfer coefficient of 850 W/m2.k [36], the reactor cooling was previously defined in chapter 4. Temperature profile of the reactor is shown in (Figure 5.4). The flow inside the reactor is assumed to be analogues to flow inside a one shell pass- two tube pass reactor (Co-current in a section and counter current in the other section). The overall heat transfer equation (Eq.5.42).

Where:

U: Overall heat transfer coefficient. A: Heat transfer area required. ∆𝑇𝑇𝑚𝑚: Logarithmic mean temperature difference. F: Temperature correction factor, obtained from appendix B (Figure B-1) [37]. The parameters required for the determination of F are:

S = 123.25−25210−25

= 0.531

R = 210−210123.25−25

= 0 F = 0.98

𝑄𝑄 = 𝑈𝑈𝐴𝐴∆𝑇𝑇𝑚𝑚𝐹𝐹 (5.42)

Fig. 5.4 Temperature profile of the alkylation reactor

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∆𝑇𝑇𝑚𝑚 = (210−123.25)−(210−25)

ln(210−123.25210−25 )

= 129.73 °C

Substituting into (Eq.5.42) neglecting the heat loss to the reactor walls. Q = 14553.25 x 103 = 850x A x 122.84 x 0.98 A = 134.6 m2 The external surface area of the reactor is then determined, the outer diameter of the reactor = 5.144+0.05 = 5.194 m and the height = 6.43 m A = 𝜋𝜋

4 5.1942 𝑥𝑥 6.43 = 136.22 m2

Since the external surface of the reactor is larger than the area required for cooling, a cooling jacket would be a suitable cooling configuration.

5.4 Design of heat exchanger The heat exchanger is shown in (Figure 5.5). The hydrocarbon feed is directed into the shell side and cooling water is directed into the tube side as it is the more corrosive and fouling fluid. Cooling water is available at 25°C and is allowed to heat up to 50°C.

Fig. 5.5 Sketch of the heat exchanger of concern

Assumptions:

- The properties of the fluids will be taken as constant average values throughout the design

- Only the heat transfer in the lateral direction in the tubes would be considered ( other two dimensions heat transfer is neglected)

5.4.1 Determination of the amount of water required and heat exchanger duty The heat exchanger duty is calculated by performing energy balance over the shell side.

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𝑄𝑄 = 𝑛𝑛∆𝐻𝐻

𝑛𝑛∆𝐻𝐻 = 𝑛𝑛𝐵𝐵 � 𝐶𝐶𝑝𝑝𝐿𝐿 (𝐵𝐵)

437.05

383.2 𝑑𝑑𝑑𝑑 + 𝑛𝑛𝐸𝐸𝐵𝐵 � 𝐶𝐶𝑝𝑝𝐿𝐿 (𝐸𝐸𝐵𝐵)

437.05

383.2 𝑑𝑑𝑑𝑑 + 𝑛𝑛𝐷𝐷𝐸𝐸𝐵𝐵 � 𝐶𝐶𝑝𝑝𝐿𝐿 (𝐷𝐷𝐸𝐸𝐵𝐵)

437.05

383.2 𝑑𝑑𝑑𝑑

Substituting using equations (4.1 and 4.2) and the data available in tables (3.1 and 4.1) we obtain:

Q = 6208.3638 kw

Q = mw Cpw (Tco – Tci)

6208.3638 = mw * 4.2 (50-25)

mw = 59.127 kg/s

The design of the heat exchanger will follow Kern's method [37,38].

First determine the area of heat transfer using (Eq.5.42).

Use one shell pass-two tube pass heat exchanger, from (Figure B-1).

S = 50−25

211.54−25 = 0.134

R = 211.54−107.21

50−25 = 4.173

F = 0.96

∆𝑇𝑇𝑚𝑚 = (211.54−50)−(107.21−25)

ln(211.54−50107.21−25)

= 117.42 °C

From (Table B-1) in appendix B use U = 350 W/m2.°C as basic estimate. Substitute into (Eq.5.42) Q = 6208.363 x 103 = 350 x A x 117.42 x 0.96 A = 157.36 m2

Choose stainless steel tube, 20 mm outer diameter, 16 mm i.d., 4.88-m-long (3/4 in×16 ft). Allowing for tube-sheet thickness, take L= 4.83 m External surface area of one tube = 𝜋𝜋 ×4.83 × 20 × 10-3 = 0.303 m2

Number Of Tubes = 157.36/0.303 = 519.34 = 520 tube

Arrange the tubes in a 1 in square pitch.

From (Tables B-2) in appendix B,

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Standard number of tubes = 526 tubes

Inner diameter of the shell = 29 in = 0.737 m

Tube per pass = 526/2 = 263 tube

5.4.2 Determination of the tube-side heat transfer coefficient

Mean water temperature = 50+252

= 37.5 °C Tube cross sectional area = 𝜋𝜋

4 𝑥𝑥 162 = 201 mm2

Total flow area = 263×201×10−6= 0.05286 𝑘𝑘2 Water mass velocity (Gsw) =

59.1270.05286

= 1118.5 kg/m2.s Water density = 995 kg/𝑘𝑘3

Water linear velocity (u) = 𝑀𝑀𝑎𝑎𝑠𝑠𝑠𝑠 𝑣𝑣𝑐𝑐𝑓𝑓𝑜𝑜𝑐𝑐𝑖𝑖𝐵𝐵𝑐𝑐𝑚𝑚𝑎𝑎𝑠𝑠𝑠𝑠 𝑑𝑑𝑒𝑒𝑛𝑛𝑊𝑊𝑖𝑖𝑑𝑑𝑦𝑦 =

1118.5995 = 1.124 m/s

The tube side heat transfer coefficient can be determined from (Eq.5.43).

ℎ𝑖𝑖𝑑𝑑𝑖𝑖𝑘𝑘𝑓𝑓

= 𝑘𝑘ℎ 𝑅𝑅𝑒𝑒 𝑃𝑃𝑟𝑟0.33 �𝜇𝜇𝜇𝜇𝑤𝑤�0.14

(5.43)

Where:

hi : Tube side heat transfer coefficient di : Tube inside diameter kf : Thermal conductivity of the fluid, 0.59 W/m.°C for water Jh : Heat transfer factor, can be obtained from appendix B (Figure B-2). Re : Reynold's number, can be obtained from (Eq.5.44). Pr : Prandtl's number, can be obtained from (Eq.5.45). 𝜇𝜇 : Fluid viscosity at the bulk fluid temperature, 0.8 mN.s/m2 for water. 𝜇𝜇𝑤𝑤 : fluid viscosity at the wall.

𝑅𝑅𝑒𝑒 =𝜌𝜌 𝑎𝑎 𝑑𝑑𝑖𝑖 𝜇𝜇

(5.44)

𝑃𝑃𝑟𝑟 =

𝑐𝑐𝑝𝑝𝜇𝜇 𝑘𝑘𝑓𝑓

(5.45)

𝑅𝑅𝑒𝑒 = 995×1.124×16×10−3

0.8×10−3= 22367.6

𝑃𝑃𝑟𝑟 = 4.2𝑥𝑥103𝑥𝑥 0.8 𝑥𝑥 10−3

0.59 = 5.695

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The term � 𝜇𝜇𝜇𝜇𝑤𝑤�0.14

is usually very small and therefore neglected 𝐿𝐿𝑑𝑑𝑖𝑖

=4.83 × 103

16= 302

From Figure (B-2) jh = 3.9 x 10-3

Substituting into (Eq.5.43).

hi = 0.5916 𝑥𝑥 10−3

× 3.9 × 10−3 × 22367.6 × 5.70.33= 5743.22 W/m2.°C

5.4.3 Determination of the shell-side heat transfer coefficient Tube pitch = 1.25 × do = 1.25 x 20 = 25 mm The shell flow area can be determined from (Eq.5.46).

𝐴𝐴𝑠𝑠 =(𝑝𝑝𝐵𝐵 − 𝑑𝑑𝑜𝑜)𝐷𝐷𝑠𝑠𝑘𝑘𝐵𝐵

𝑝𝑝𝐵𝐵 (5.46)

Where:

do : Tube outer diameter. pt : Tube pitch, 1.25do = 25 mm. DS : Shell inside diameter. lB : Baffle spacing Baffle spacing value should be within the range of (DS ≥ lB ≥ DS/5). After checking the calculations by trial and error the value of lB = DS/2 is chosen = 368.5 mm.

Shell flow area (As) = (25−20)

25 × 737 × 368.5 × 10−6 = 0.0543 𝑘𝑘2

The equivalent diameter for flowing through the shell can be obtained from (Eq.5.47).

𝑑𝑑𝑒𝑒 = 1.27𝑑𝑑𝑜𝑜

(𝑝𝑝𝐵𝐵2 − 0.785𝑑𝑑𝑜𝑜2) ( 47.5 )

de =

1.120

(252 − 0.917 × 202) = 19.75 mm Mean shell side temperature = 211.54+107.21

2= 159.375 °C

Mixture density = 662.5 kg/m3

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Viscosity = 0.1117 mN.s/m2 Heat capacity = 2.495 kJ/kg.°C Thermal conductivity = 0.08376 W/m.k From eq.5.44.

𝑅𝑅𝑒𝑒 = 𝜌𝜌 𝑎𝑎 𝑑𝑑𝑖𝑖 𝜇𝜇

= 𝐺𝐺𝑠𝑠𝑑𝑑𝑐𝑐𝜇𝜇

= 𝑘𝑘𝑑𝑑𝑐𝑐𝐴𝐴𝑠𝑠 𝜇𝜇

𝑅𝑅𝑒𝑒 = 27.08×19.75×10−3

0.0543 𝑥𝑥 0.1117×10−3= 88144.4

From eq.5.45.

Pr = 𝑐𝑐𝑝𝑝𝜇𝜇 𝑘𝑘𝑓𝑓

= 2.495 𝑥𝑥 103𝑥𝑥 0.1117 𝑥𝑥 10−3

0.08376 = 3.33

Jh for shell side can be obtained from (Figure B-3) in appendix B. Choose 25 per cent baffle cut, Jh = 2.6 x 10-3

Substitute into eq.5.43 for shell side coefficient ho : ℎ𝑜𝑜 = 0.08376

19.75 𝑥𝑥10−3× 2.6 × 10−3 × 88144.4 × (3.33)0.33 = 1423.2 W/m2.°C

5.4.4 Determination of the overall heat transfer coefficient The overall heat transfer coefficient can be determined using (Eq.5.48) without accounting for fouling resistance and neglecting the tube wall resistance.

1𝑈𝑈𝑐𝑐

= 1ℎ𝑖𝑖𝑜𝑜

+1ℎ𝑜𝑜

(5.48)

Where hio = ℎ𝑖𝑖 𝑑𝑑𝑖𝑖𝑑𝑑𝑜𝑜

= 5743.22 x 1620

= 4594.6 W/m2.°C Substituting Uc = 1086.62 W/m2.°C Now the fouling resistance is checked, the fouling resistance is related to the design heat transfer coefficient UD by (Eq.5.49).

𝑅𝑅𝑑𝑑 =1𝑈𝑈𝐷𝐷

−1𝑈𝑈𝑐𝑐

(5.49)

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Calculate the new heat transfer area based on the corrected number of tubes A = Nt x Tube area = 526 x 0.3034 =159.63 m2

UD = 6208.363 𝑋𝑋 103

117.42 𝑋𝑋 159.63 = 331.22 W/m2.°C

𝑅𝑅𝑑𝑑 = 1

331.22− 1

1086.62 = 2.099 x 10-3 m2.°C/W

From (Table B-3) in appendix B, the allowed fouling factor of the system Rd,all = 0.001+0.001 = 0.002 Since Rd > Rd,all , the design is safe.

5.4.5 Tube and shell side pressure drop The pressure drop in the tube side can be calculated using (Eq.5.50).

∆𝑃𝑃𝐵𝐵 = 𝑁𝑁𝑝𝑝 [8 𝑘𝑘𝑓𝑓(𝐿𝐿𝑑𝑑𝑖𝑖

)(µ

µ w)−𝑚𝑚 + 2.5]

ρ 𝑎𝑎𝐵𝐵2

2 (5.50)

Where:

∆Pt : Tube-side pressure drop Np : Number of tube passes ut : Tube-side velocity JF : Tube friction factor, can be obtained from appendix B (Figure B-4) = 3.8 x 10−3 m : A constant dependent on the flow type (laminar or turbulent). The viscosity term is neglected ∆𝑃𝑃𝐵𝐵 = 2 [8 × 3.8 × 10−3(4.83×103

16) + 2.5) 995×1.1242

2 = 14678.68 Pa = 14.68 kPa

The tube side pressure drop is acceptable as the maximum allowable tube side pressure drop is 35 kpa. The shell side pressure drop can be calculated using (Eq.5.51).

∆𝑃𝑃𝑠𝑠 = 8𝑘𝑘𝑓𝑓𝑠𝑠(𝐷𝐷𝑠𝑠𝑑𝑑𝑐𝑐

)(𝐿𝐿𝑘𝑘𝐵𝐵

) ρ 𝑎𝑎𝑠𝑠 2

2(

µ𝜇𝜇𝑤𝑤

)−0.14 (5.51)

Where:

∆𝑃𝑃𝑠𝑠 : Shell side pressure drop. 𝑘𝑘𝑓𝑓𝑠𝑠 : Shell side friction factor, can be obtained from appendix B (Figure B-5). For 25% baffle cut, 𝑘𝑘𝑓𝑓𝑠𝑠 = 3.85 x 10-2 us : Shell linear velocity. The viscosity term is neglected. Linear velocity =

𝐺𝐺𝑠𝑠𝜌𝜌

= 27.080.0543 𝑥𝑥 662.5

= 0.7525 m/s

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∆𝑃𝑃𝑠𝑠 = 8 𝑥𝑥 3.85 𝑥𝑥 10−2𝑥𝑥 ( 737

19.75)(4.83 𝑥𝑥 103

368.5) 662.5 𝑥𝑥 0.75252

2 = 28262 pa = 28.26 Kpa

The shell side pressure drop is acceptable as the maximum allowable shell side pressure drop is 70 kpa.

5.4.6 Heat exchanger insulation The mean shell temperature is 159.4 °C which is not safe to touch. Therefore, the external surface of the heat exchanger is insulated to obtain a safe to touch temperature of 50°C and reduce the heat loss. The insulation thickness can be obtained using the principles of conduction heat transfer in a cylindrical wall (Eq.5.52) [39]. There are three resistances to heat flow considered named the thickness of the shell, the thickness of insulation and convective heat transfer of air surrounding the exchanger.

𝑄𝑄 = 2𝜋𝜋𝐿𝐿 (𝑇𝑇𝑖𝑖 − 𝑇𝑇𝑇𝑇)

∑ �ln�𝒓𝒓𝒏𝒏 𝒓𝒓𝒏𝒏−𝟏𝟏� �

𝐾𝐾𝑛𝑛�+ 1

𝑟𝑟𝑛𝑛 ℎ𝑇𝑇𝑛𝑛𝑖𝑖=1

(5.52)

Where:

Q: Heat transferred to the surroundings. Ti : Temperature of the shell. To : Ambient temperature (taken as 25°C). kn : Thermal conductivity of the material n. rn : Radius of the material n relative to a common center. ho : Heat transfer coefficient of the air layer surrounding the exchanger, commonly found to be 5 W/m2.°C [40].

The thickness of the shell must be determined. Consider the shell to be a pressure vessel of a diameter 0.737 m and holds 11 atm of pressure. Use 0.5% low carbon steel as the shell material ( yield strength = 370 MPa, σall = 370/1.5 = 246.67 MPa , K = 54 W/m.°C) allow for 0.3 mm corrosion and Longitudinal joints efficiency of 90%, the thickness is obtained using (Eq.5.40).

𝑑𝑑 = 1.1 𝑥𝑥 7372 𝑥𝑥 246.67 𝑥𝑥 0.9−1.1

+ 0.3 = 2.12 mm

Fiber glass ( k = 0.048 W/m.°C) will be used as an insulating material as it is cheap and has a wide range of working temperatures.

Substitute into (Eq.5.52).

𝑄𝑄 = 2𝜋𝜋 𝑥𝑥 4.83 𝑥𝑥 (159.4−25)

�ln�370.62

368.5� �

54 �+�ln�370.62+𝑟𝑟𝑖𝑖𝑛𝑛𝑊𝑊

370.62� �

0.048 �+ 1�370.62+𝑟𝑟𝑖𝑖𝑛𝑛𝑊𝑊�𝑥𝑥0.005

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It is apparent that the value of heat transferred to the surroundings is a function of the insulation thickness. Therefore, a proper thickness is chosen to achieve a low heat loss of 4 kw.

Substituting Q = 4 kw , rins = 9 mm.

5.5 Pump design The benzene recycle to transalkylator pump (P-102) is chosen for the design; a sketch of the pump is shown in (Figure 5.6).

Fig. 5.6 Sketch of the pump concerned in the design.

Axial flow centrifugal pump is chosen for the design for several reasons [41,42]:

- Suitable for high volumetric flow rates with high turndown ratio. - Lower viscosity fluid. - Low pressure operations and low pressure ratio (5:1). - Suitable for clean liquids with no entrained vapors or suspended solids.

For a given flow rate and pressure ratio the pump head is estimated and the corresponding power required is then calculated. The pump duty along with the pressure ratio and flow rate give a basic prediction on which pump to be obtained from the manufacturer [42].

The pump head can be calculated using (Eq.5.53).

𝐻𝐻 = (𝑃𝑃𝑑𝑑−𝑃𝑃𝑠𝑠) 𝑥𝑥 10.197𝑆𝑆𝐺𝐺

+ ℎ𝑘𝑘𝑇𝑇𝑊𝑊𝑊𝑊 (5.53)

Where:

H : Total Pump head, in meters. Pd , Ps : Discharge and suction pressures respectively, in bar. SG: Specific gravity of the liquid = 0.803. hLoss : Head loss due to friction and valves and fittings, in m. The head loss can be calculated from Darcy-Weisbach (Eq.5.54).

ℎ𝐿𝐿𝑜𝑜𝑠𝑠𝑠𝑠 = 𝑓𝑓 𝐿𝐿𝑑𝑑

𝑎𝑎2

2𝑘𝑘 (5.54)

Where:

𝑓𝑓 : Pipe friction factor L : Equivalent length of the pipe

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d : Pipe diameter u : Liquid velocity in the pipe g : Acceleration of gravity

The equivalent length of the pipe is determined from the total pipe length plus the fittings; there are two valves installed before and after the pump to control the flow, the equivalent length of each valve will be taken as 1 m (head loss due to flow through the valve is equivalent to the head loss due to flow through one meter of the pipe). Assume total pipe length of 8 meters.

Equivalent length = 1 + 1 + 8 = 10 m

The pipe diameter will be taken as 3 inch (0.0762 m ).

The liquid velocity = 𝑉𝑉𝑜𝑜𝑓𝑓𝑣𝑣𝑚𝑚𝑐𝑐𝐵𝐵𝑟𝑟𝑖𝑖𝑐𝑐 𝑓𝑓𝑓𝑓𝑜𝑜𝑤𝑤 𝑟𝑟𝑎𝑎𝐵𝐵𝑐𝑐𝐹𝐹𝑓𝑓𝑜𝑜𝑤𝑤 𝑎𝑎𝑟𝑟𝑐𝑐𝑎𝑎

= 7.923600 𝑥𝑥 �𝜋𝜋 4� � 𝑥𝑥 0.07622

= 0.482 m/s

The pipe friction factor depends on Reynold's number and the pipe roughness [43]. Choose commercial steel pipe with roughness ε = 0.046.

From (Eq.5.44).

Re = 803 𝑥𝑥 0.0762 𝑥𝑥 0.4820.00029

= 101595.037

For a turbulent flow in a rough pipe, the friction factor is calculated using (Eq.5.55) [43].

𝑓𝑓 = 0.25

�𝑓𝑓𝑜𝑜𝑘𝑘�� 𝜀𝜀3.7𝑑𝑑�+( 5.74

𝑅𝑅𝑅𝑅0.9)��2 (5.55)

Substituting:

𝑓𝑓 = 0.25

�𝑓𝑓𝑜𝑜𝑘𝑘�� 0.0463.7×0.0762�+�

5.74101595.0370.9���

2 = 0.4037

Substituting (Eq.5.54) into (Eq.5.53):

H = (5−1.2) 𝑥𝑥 1.01325 𝑥𝑥 10.197

0.803+ 0.437 𝑥𝑥

10

0.0762 𝑥𝑥

0.4822

2 𝑥𝑥 9.81 = 49.517 m

Now the power is calculated (Eq.5.56).

𝑃𝑃𝐻𝐻 = 𝑄𝑄 𝑥𝑥 𝜌𝜌 𝑥𝑥 𝑘𝑘 𝑥𝑥 𝐻𝐻3.6 𝑥𝑥 106 𝜂𝜂

(5.56)

Where:

PH : Hydraulic power, in kW. Q : Volumetric flow rate, in m3/h.

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𝜂𝜂 : Pump efficiency, the efficiency is obtained from the pump performance curve which is characteristic for each pump type and varies from one manufacturer to another. For axial flow centrifugal pump it has a range of (20% to 40%). It will be taken as 35%.

Substituting:

𝑃𝑃𝐻𝐻 = 7.92 𝑥𝑥 803 𝑥𝑥 9.81 𝑥𝑥 49.5173.6 𝑥𝑥 106 𝑥𝑥 0.35

= 2.452 kW

5.6 Summary In this chapter, a detailed design of the process equipment is carried out. Calculations of all design parameters were performed for Benzene distillation column, ethylbenzene distillation column, a heat exchanger, Alkylation reactor, and a Pump. For benzene column, calculations are made on the two sections of the column and shows that the rectifying section has 17 sieve type trays and the stripping section consists of 14 trays with tray efficiency of 61.68%. The column diameter is 11 ft and the column height is 78.25 ft with reflux ratio of 0.758. Design is applied for ethylbenzene column so that the column can separates the ethylbenzene from diethylbenzene to yield final product of 99.88% ethylbenzene as a top product. The column diameter is 15 ft and the height is 59.5 ft with reflux ratio of 2.7. It has 16 trays with the feed introduced in the 6th tray from the top and tray efficiency of 69.97%. Detailed tray design for the two columns is provided in the chapter. For the alkylation reactor, the weight of required catalyst for the reaction is determined by using molar balance and kinetic equations and is found to be 64433.6 kg which is distributed on 2 beds. The required residence time for the reaction is 25 min. The reactor is 5.14 m in diameter and 6.43 m in length. For the heat exchanger, a one shell pass-two tube passes exchanger having 526 tubes is chosen. The design overall heat transfer coefficient is 331.22 W/m2.°C and the corresponding heat transfer area is 159.63 m2. The overall fouling factor is 0.00209 m2. °C/W and the pressure drop is 14.68 kPa and 28.3 Kpa for tube side and shell side respectively which are well below the maximum allowable values. Finally, the pump selection and design is carried out based on the highest pressure ratio in the process (20 atm:1 atm), volumetric flow rates and the properties of flowing materials, centrifugal pumps are found to be suitable for the operation. The pump design operates with total head of 49.51 m and power 2.45 kw.

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Chapter 6

Plant layout and plant location

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6. Plant layout and plant location 6.1 Plant location and site selection

The location of the plant can have a crucial effect on the profitability of a project and the scope for future expansion. Many factors must be considered when selecting a suitable site, and only a brief review of the principal factors will be given in this section. The principal factors to consider are:

1) Location, with respect to the marketing area; 2) Raw material supply; 3) Transport facilities; 4) Availability of labor; 5) Availability of utilities: water, fuel, power; 6) Availability of suitable land; 7) Environmental impact, including effluent disposal; 8) Local community considerations; 9) Climate; 10) Political and strategic considerations.

6.1.1 Marketing area

Every company is expected to serve its customers by providing goods and services at the time needed and at reasonable price organizations may choose to locate facilities close to the market or away from the market depending upon the product. When the buyers for the product are concentrated, it is advisable to locate the facilities close to the market. Locating nearer to the market is preferred if The products are delicate and susceptible to spoilage. After sales services are promptly required very often. Transportation cost is high and increase the cost significantly. Shelf life of the product is short.

Nearness to the market ensures a consistent supply of goods to customers and reduces the cost of transportation. For materials that are produced in bulk quantities, such as cement, mineral acids, and fertilizers, where the cost of the product per metric ton is relatively low and the cost of transport is a significant fraction of the sales price, the plant should be located close to the primary market. This consideration is much less important for low-volume production and high-priced products, such as pharmaceuticals.

6.1.2 Raw materials It is essential for the organization to get raw material in right qualities and time in order to have an uninterrupted production. This factor becomes very important if the materials are perishable and cost of transportation is very high. General guidelines regarding effects of raw materials on plant location are:

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When a single raw material is used without loss of weight, locate the plant at the raw material source, at the market or at any point in between.

When weight loosing raw material is demanded, locate the plant at the raw material source.

When raw material is universally available, locate close to the market area. If the raw materials are processed from variety of locations, the plant may be

situated so as to minimize total transportation costs.

Nearness to raw material is important in case of industries such as sugar, cement, jute and cotton textiles. The availability and price of suitable raw materials will often determine the site location. Plants that produce bulk chemicals are best located close to the source of the major raw material, as long as the costs of shipping product are not greater than the cost of shipping feed. For example, at the time of writing much of the new ethylene capacity that is being added worldwide is being built in the Middle East, close to supplies of cheap ethane from natural gas. Oil refineries, on the other hand, tend to be located close to major population centers, as an oil refinery produces many grades of fuel, which are expensive to ship separately.

6.1.3 Transport The transport of materials and products to and from the plant can be an overriding consideration in site selection. If practicable, a site should be selected that is close to at least two major forms of transport: road, rail, waterway (canal or river), or a seaport. Road transport is increasingly used and is suitable for local distribution from a central warehouse. Rail transport is usually cheaper for the long-distance transport of bulk chemicals. Air transport is convenient and efficient for the movement of personnel and essential equipment and supplies, and the proximity of the site to a major airport should be considered.

6.1.4 Availability of labor Labor will be needed for construction of the plant and its operation. Skilled construction workers are usually brought in from outside the site area, but there should be an adequate pool of unskilled labor available locally, and labor suitable for training to operate the plant. Skilled craft workers such as electricians, welders, and pipe fitters will be needed for plant maintenance. Local labor laws, trade union customs, and restrictive practices must be considered when assessing the availability and suitability of the local labor for recruitment and training.

6.1.5 Utilities (Services) The basic infrastructure facilities like power and water etc., become the prominent factors in deciding the location. Chemical processes invariably require large quantities of water for cooling and general process use, and the plant must be located near a source of water of suitable quality. Process water may be drawn from a river, from wells, or purchased from a local authority. At some sites, the cooling water required can be taken from a river or lake, or from the sea; at other locations cooling towers will be needed. Electrical power is needed at all sites. Electrochemical processes (for example, chlorine manufacture or aluminum smelting) require large quantities of power and must be located close to a cheap source of power where uninterrupted power supply is assured

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throughout the year. A competitively priced fuel must be available on site for steam and power generation.

6.1.6 Environmental impact and effluent disposal A waste disposal facility for process industries is an important factor, which influences the plant location. All industrial processes produce waste products, and full consideration must be given to the difficulties and cost of their disposal. The disposal of toxic and harmful effluents will be covered by local regulations, and the appropriate authorities must be consulted during the initial site survey to determine the standards that must be met. An environmental impact assessment should be made for each new project or major modification or addition to an existing process.

6.1.7 Local community considerations The proposed plant must fit in with and be acceptable to the local community. Full consideration must be given to the safe location of the plant so that it does not impose a significant additional risk to the local population. Plants should generally be sited so as not to be upwind of residential areas under the prevailing wind. On a new site, the local community must be able to provide adequate facilities for the plant personnel: schools, banks, housing, and recreational and cultural facilities. The local community must also be consulted about plant water consumption and discharge and the effect of the plant on local traffic. Some communities welcome new plant construction as a source of new jobs and economic prosperity. More affluent communities generally do less to encourage the building of new manufacturing plants and in some cases may actively discourage chemical plant construction.

6.1.8 Land (Site considerations) Sufficient suitable land must be available for the proposed plant and for future expansion. The land should ideally be flat, well drained, and have suitable load-bearing characteristics. A full site evaluation should be made to determine the need for piling or other special foundations. Particular care must be taken when building plants on reclaimed land near the ocean in earthquake zones because of the poor seismic character of such land.

6.1.9 Climate Adverse climatic conditions at a site will increase costs. Abnormally low temperatures require the provision of additional insulation and special heating for equipment and pipe runs. Stronger structures are needed at locations subject to high winds (cyclone/ hurricane areas) or earthquakes.

6.1.10 Political and strategic considerations Capital grants, tax concessions, and other inducements are often given by governments to direct new investment to preferred locations, such as areas of high unemployment. The availability of such grants can be the overriding consideration in site selection. In a globalized economy, there may be an advantage to be gained by locating the plant within an area with preferential tariff agreements [44].

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A comparison between three industrial regions (Alexandria port, Tahrir petrochemicals complex and Damietta port according to the main factors is shown in (Table 6.1). The table shows that Tahrir Petrochemical Complex is the suitable site for building the ethylbenzene plant because of its high weight of raw material supply and marketing compared with the two other sites. The complex will contain cracking and reforming units which will provide the raw materials required. Three polystyrene production units will be built which are considered as the market, [45]. Alex port has a source for raw material represented by refineries but it doesn't have a market for ethylbenzene. On the other hand Damietta has neither raw material supply nor marketing. The three places have the same weight in terms of transport as they are located near a waterway which also used as a source for cooling water. The labor is more available in Alex and Damietta ports as they are both located near towns; Tahrir complex on the other hand is rather far from towns and consequently has lower availability of labor. The cost of land in Tahrir complex has moderate weight [46-48], this is expected because the complex is being built on 5 million square meters of land and the cost per square meter is comparably low to encourage investors. The climate is quite similar in the three locations but Alexandria has the lowest weight as its weather is more extreme in cold times, heavy rain (and sometimes snow) is encountered [49-51]. Water disposal has the same weight in the three locations, water is either threated in site or a specialized company load the wastewater on trucks and treat it elsewhere.

Table 6.1 comparison between the three considered sites according to the main factors.

Factors Weight Alexandria port

Tahrir Petrochemical

Complex Damietta port

1 Raw material supply 100 90 100 50

2 Marketing 100 50 90 50

3 Transport 70 65 65 65

4 Availability of Labor 70 55 40 60

5 Water supply 50 50 45 50

6 Land 50 25 35 40

7 Climate 50 35 40 45

8 Waste disposal 50 40 40 40

Total 540 410 455 400

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6.2 Site layout The process units and ancillary buildings should be laid out to give the most economical flow of materials and personnel around the site. Hazardous processes must be located at a safe distance from other buildings. Consideration must also be given to the future expansion of the site. The ancillary buildings and services required on a site, in addition to the main processing units include:

1. Storage for raw materials and products: tank farms and warehouses; 2. Maintenance workshops; 3. Stores, for maintenance and operating supplies; 4. Laboratories for process quality control; 5. Fire stations and other emergency services; 6. Utilities: steam boilers, compressed air, power generation, refrigeration,

transformer stations; 7. Effluent disposal plant: wastewater treatment, solid and or liquid waste

collection; 8. Offices for general administration; 9. Canteens and other amenity buildings, such as medical centers; 10. Parking lots.

When the preliminary site layout is roughed out, the process units are normally sited first and arranged to give a smooth flow of materials through the various processing steps, from raw material to final product storage. Process units are normally spaced at least 30m apart; greater spacing may be needed for hazardous processes. The location of the principal ancillary buildings should then be decided. They should be arranged so as to minimize the time spent by personnel in traveling between buildings. Administration offices and laboratories, in which a relatively large number of people will be working, should be located well away from potentially hazardous processes. Control rooms are normally located adjacent to the processing units, but those with potentially hazardous processes may have to be sited at a safer distance. The siting of the main process units determines the layout of the plant roads, pipe alleys, and drains. Access roads to each building are needed for construction and for operation and maintenance. Utility buildings should be sited to give the most economical run of pipes to and from the process units. Cooling towers should be sited so that, under the prevailing wind, the plume of condensate spray drifts away from the plant area and adjacent properties. The main storage areas should be placed between the loading and unloading facilities and the process units they serve. Storage tanks containing hazardous materials should be sited at least 70m (200 ft) from the site boundary.

6.3 Plant layout The economic construction and efficient operation of a process unit will depend on how well the plant and equipment specified on the process flow sheet is laid out. The principal factors to be considered are:

1. Economic considerations: construction and operating costs; 2. The process requirements; 3. Convenience of operation;

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4. Convenience of maintenance; 5. Safety; 6. Future expansion; 7. General consideration

6.3.1 Costs The cost of construction can be minimized by adopting a layout that gives the shortest run of connecting pipe between equipment and the least amount of structural steel work; however, this will not necessarily be the best arrangement for operation and maintenance.

6.3.2 Process Requirements An example of the need to take into account process considerations is the need to elevate the base of columns to provide the necessary net positive suction head to a pump

6.3.3 Operation Equipment that needs to have frequent operator attention should be located convenient to the control room. Valves, sample points, and instruments should be located at convenient positions and heights. Sufficient working space and headroom must be provided to allow easy access to equipment. If it is anticipated that equipment will need replacement, then sufficient space must be allowed to permit access for lifting equipment.

6.3.4 Maintenance Heat exchangers need to be sited so that the tube bundles can be easily withdrawn for cleaning and tube replacement. Vessels that require frequent replacement of catalyst or packing should be located on the outside of buildings. Equipment that requires dismantling for maintenance, such as compressors and large pumps, should be placed under cover.

6.4.5 Safety Blast walls may be needed to isolate potentially hazardous equipment and confine the effects of an explosion. At least two escape routes for operators must be provided from each level in process buildings.

6.3.6 Plant Expansion Equipment should be located so that it can be conveniently tied in with any future expansion of the process. Space should be left on pipe racks for future needs, and service pipes should be oversized to allow for future requirements.

6.3.7 General Considerations Open, structural-steelwork buildings are normally used for process equipment. Closed buildings are used for process operations that require protection from the weather, for small plants, or for processes that require ventilation with scrubbing of the vent gas. The arrangement of the major items of equipment often follows the sequence given on the process flow sheet: with the columns and vessels arranged in rows and the ancillary equipment, such as heat exchangers and pumps, positioned along the outside.

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Based on the previous considerations, the plant layout is planned and the result is shown in (Figure 6.1).

Fig. 6.1 Illustration of the plant layout.

6.4 Summary Plant location is determined based on several factors including marketing area, raw materials, transport, availability of labor, water supply, etc. Three different locations are compared based on the selection factors; Tahrir Petrochemical Complex is found to be the most suitable location. The plant layout is constructed in a way that minimizes the cost of piping, provide safety for workers in the field and offices, facilitate transport within the plant and direct the process exhausts away from the offices and nearby residents.

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Chapter 7

Cost estimation

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7. Cost estimation 7.1 Purchased equipment cost After the process equipment have been designed and sized in the previous chapters, the cost of each piece of equipment is now evaluated as a first step in estimating the cost required for plant erection

7.1.1 Heat exchangers The cost of a shell and tube heat exchanger is based mainly on the area of heat transfer. Normal heat exchangers were sized using the technique applied in chapter 5, condensers and reboilers were sized using techniques obtained from [52,53]. The cost is obtained from (Figure 7.1); the data in figure 7.1 is based on the cost data in 1998 [53]. Therefore, the cost must be corrected to the current value. Marshall-Swift index will be used for the correction, the values of Marshall-Swift index is available in appendix C (Table C-1).

Fig. 7.1 Cost of shell and tube heat exchangers.

The current cost can be obtained using the following expressions

Purchased exchanger cost = (bare cost from figure)* Type factor * Pressure factor

Current cost = original cost �index value at present time

index value at time original cost was obtained�

From table C-1 the index values are 1061.8 (in 1998) and 1638.2 (in 2018). The total cost of exchangers in shown in (Table 7.1).

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Table 7.1 Cost estimation of shell and tube heat exchangers

Equipment code

Heat transfer

area (m2)

Material factor

Pressure factor Type factor

Equipment cost (USD)

Current equipment cost (USD)

H-101 194.22 2 1.3 1 78000 120342

H-102 16.3 3 1.1 1 13200 20366

H-103 23.06 2 1.3 1 16900 26074

H-104 159.6 3 1.1 1 110000 169714

C-101 250.01 3 1 0.8 120000 185142

C-102 250.01 3 1 0.8 120000 185142

B-101 212.4 2 1.3 1.3 101400 156445

B-102

424.9 2 1.3 1.3 169000 260742

Total - - - - 728500 1123968

7.1.2 Alkylation reactor The cost of the reactor is equivalent to the cost of a stainless steel vertical pressure vessel with a diameter of 5.14m and height of 6.43m, operating at 20 atm. The cost for a vertical pressure vessel is obtained from (Figure 7.2) by extrapolation [53], the cost of the catalyst is accounted for later.

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Fig. 7.2 Cost of vertical pressure vessel.

Purchased reactor cost = 40000 x 2 x 1.4 = $112000

Current cost = 112000 x 1638.21061.8

= $172800

7.1.3 Transalkylation reactor For stainless steel pressure vessel with a diameter of 2.96m and height of 3.7m, operating at 20 atm.

Purchased cost =10000 x 2 x 1.4 = $28000

Current cost = 28000 x 1638.21061.8

= $43200

7.1.4 Benzene distillation column The cost of a distillation column is composed of the cost of the trays and the cost of the column itself. The cost of the trays can be obtained from (Figure 7.3) [53]. For 30 carbon steel sieve trays of 3.35m diameter:

Cost per tray = $1800 Total trays cost = 1800 x 30 = $54000

Fig. 7.3 Cost of distillation column trays

The cost of the column is obtained from figure 7.2. For 23.8m height carbon steel column operating nearly at atmospheric pressure, the cost = $135000

Total column cost = $189000

Current benzene distillation column cost = 189000 x 1638.21061.8

= $291600

7.1.5 Ethylbenzene distillation column The procedure for this column is the same as previous. For 16 carbon steel sieve trays of 4.57m diameter. The column is 18.1m height and made of carbon steel.

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Total column cost = 16 x 2700 + 160000 = $203200

7.1.6 Compressor cost

The compressor cost can be obtained from (Eq.7.1) [53].

𝐶𝐶𝑒𝑒 = 𝐶𝐶𝑆𝑆𝑛𝑛 (7.1)

Where:

Ce : Equipment cost, in USD S : Characteristic parameter of the equipment C and n : Constants S, C and n can be obtained from appendix C (Table C-2).

For centrifugal compressor with a required power of 1500 kW:

C = $960 n = 0.8 S = 500

Maximum power available is 500 kw (The cost of three compressors would be a good approximation) Ce = 960 x 5000.8 = $139000 Total cost = 139000 x 3 = $417000

Current cost = 417000 x 1638.21061.8

= $643400

7.1.7 Pumps cost Based on the calculated head and pump power the pumps are selected. Pumps from XQST (model TIZ) is chosen [54]. This pump type offers a maximum head of 125m. Therefore in some cases two successive pumps may be required. The cost of each pump is shown in (Table 7.2).

Table 7.2 Cost of pumps

Original pump code

Pressure range (atm) Head (m) Power (kW) Cost (USD)

P-101 1-10 111 66 613

P-101 10-20 120 67 613

P-102 1.2-5 49.5 2.2 360

P-103 5-12 96 10.29 400

P-103 12-20 110 11.4 400

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P-104 1.5-5 48 2 360

Total - - - 2746

7.2 Capital investment

The cost of equipment required for the plant operation has been calculated in the previous section. However, other expense such as service facilities, piping, buildings, etc. must be obligated in order for the plant to start up. Moreover, it is necessary to have money available for the payment of expenses involved in the plant operation. The capital needed to erect the plant is the fixed capital investment, while that necessary for the start of the plant operation is the working capital investment. The sum of the fixed capital and working capital is the total capital investment required.

The fixed capital investment is obtained from the purchased equipment cost. The method includes giving every cost element a certain percentage of the total fixed capital so that the sum of all is 100%. Typical values are presented in appendix C (Table C-3) and the calculations of the fixed capital is shown in (Table 7.3) [55].

Purchased equipment cost = $2481000

Table 7.3 Estimation of the total fixed capital investment

Cost element Assumed of total% Cost Rationed of total%

Purchased equipment 25 2481000 23

Purchased –equipment installation 9 895317 8.3

Instrumentation (installed) 7 690365 6.4

Piping(installed) 8 787448 7.3

Electrical(installed) 5 496200 4.6

Buildings (including services) 5 496200 4.6

Yard improvements 2 194165 1.8

Services facilities (installed) 15 1488600 13.8

Land 1 97083 0.9 Engineering and

supervision 10 992400 9.2

Construction expense 12 1186565 11

Contractor's fee 2 194165 1.8

Contingency 8 787448 7.3

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Fixed capital investment 109 10786957 100

The working capital is taken as 10% of the fixed capital investment.

Working capital = 0.1 x 107869257 = $1078696

7.3 Operating cost The operating cost is the cost required for the operation of the plant (after startup). The operating cost elements are summarized in (Table 7.4) [53].

Table 7.4 Summary of operating costs.

7.3.1 Variable operating costs The raw materials and utility costs are shown in (Table 7.5). The flow rates were obtained from material and energy balance. The utility costs available are only rough estimates for initial cost estimation. The cost of water and fuels are highly dependent on the plant location and the current fuel prices in the production country [56-59].

Table 7.5 Raw materials and utilities cost.

Raw materials cost

Consumption rate (kg/yr)

Unit Cost ($/ton) Annual cost ($/yr)

Benzene 294638184.9 844 248674628

Ethylene 105721078.3 419 44297131.82

Utility cost

Cooling water 6338753280 0.067 424696.4698 High pressure

Steam 571891968 16.64 9516282.348

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*The working year is taken as 340 days.

The other miscellaneous materials (safety clothing, helmets, safety glasses, pipe gaskets, cleaning materials, etc.) is calculated in the following section. No shipping or packing are required because the product will be stored and used on-site.

7.3.2 Fixed operating costs - Maintenance cost = 0.05 x 10786957 = $540000/yr - Miscellaneous materials cost = 10% of maintenance = $54000/yr - For the operating labour, assume the plant would require 20 workers per shift and

the work would be divided into two shifts (40 total workers) with an average yearly wage of $9000/yr. The operating labour cost = 40 * 9000 = $360000/yr

- Take laboratory costs as 30% of the operating labour = $108000/yr - The cost of supervision mentioned in table 7.4 is related to the wages paid for site

mangers and foremen, it is taken as 20% of the operating labour = $72000/yr - Plant overheads includes plant security, safety, general management, medical care,

canteen and general clerical staff. It is taken as 50% of the operating labour = $180000/yr

- Capital charges are related to the capital recovered for the equipment depreciation

or to repay a loan if the If the money for the investment is borrowed. It will be taken as 10% of the fixed capital for now and will be explained further in section 7.4. Capital charges = $1078696/yr

- Insurance cost of the plant is taken as 1% of the fixed capital = $107870/yr - Local taxes = 2% of the fixed capital = $215740/yr - Royalties are paid if the process used has not been developed exclusively by the

operating company, which is true in this plant, it will be paid as annual fees of 1% of the fixed capital = $107870/yr

The direct production cost is the sum of the variable and fixed operating cost. Direct production cost = $305142912/yr The other expenses such as the general overheads and research and development would be taken as 20% of the direct production cost = $61028582/yr

Finally the total production cost is equal to the sum of all operating costs

Annual production cost = $366171495/yr

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The production cost per ton of ethylbenzene is now calculated

Production rate of ethylbenzene = 400000 ton/yr

Production cost per ton = 366171495400000

= $915/ton This price is convenient because the average global selling price is $1000/ton. The global price is quite high because in Egypt the wages, taxes and fuel prices are low compared to other industrial countries.

7.4 Depreciation cost The cost for equipment depreciation has been accounted for in the operating cost previously under the heading of capital charges. However, there are numerous methods available for the determination of depreciation, the linear method is chosen. The linear method is explained in (Eq.7.2).

Annual depreciation expense =equipment Cost − Solvage value

Useful life of the equipment (7.2)

The life of the project is typically taken as 10 years

The equipment cost = $2481000

salvage value = 10% of equipment cost = 248100

Annual depreciation expenses = 2481000 −24810010

= $223290/yr

The depreciation cost is recovered in five years period to account for any unplanned accidents.

7.5 Cash flow and cash flow diagram The cash flow is estimated on non-discounted basis; the cumulative cash position at the end of the project life, the payback period and the rate of return on investment are calculated to estimate the profitability of the project. The annual cumulative cash flow is calculated and the results are presented in (Table 7.6). The cash flow diagram is shown in (Figure 7.4).

The selling price is set to $930/ton The taxes on production is taken as 20% Revenue = total income = 930 x 400000 = $3.72 x 108 /yr Profit = (revenue – depreciation – production cost) x (1- taxes) + depreciation

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The cost of catalyst is 5000$/ton, 64433.65 kg are required in the alkylator and 11320.1 kg in the transalkylator with a combined cost of 378768$ every five years [60].

The cost of land is $117/m2. The area required for the plant is estimated to be 1000 m2, the total cost of land is 117000$.

The plant is constructed in two years, in the first year 40% of the fixed capital is paid and the other 60% in the second year plus the working capital. The plant startup is at year 3.

Table 7.6 Non discounted cumulative cash flow.

year Investment depreciation Revenue Production Cost profit Cash

flow Cumulative Cash flow

0 -0.117 0 0 0 0 -0.117 -0.117 1 -4.31 0 0 0 0 -4.31 -4.432 2 -7.55 0 0 0 0 -7.55 -11.983 3 0 0.477 372 365.47 5.62 5.62 -6.671 4 0 0.477 372 365.092 5.62 5.62 -1.056 5 0 0.477 372 365.092 5.62 5.62 4.560 6 0 0.477 372 365.092 5.62 5.62 10.175 7 0 0.477 372 365.092 5.62 5.62 15.790 8 0 0 372 365.47 5.53 5.53 21.012 9 0 0 372 365.092 5.53 5.53 26.538 10 0 0 372 365.092 5.53 5.53 32.064 11 0 0 372 365.092 5.53 5.53 37.590 12 1.2 0 372 365.092 5.72 6.92 44.510

* All the values are in $ million * The negative values indicates investment or no profit

Fig. 7.4 Cumulative cash flow diagram.

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The payback period is the time required after startup to recover the fixed capital investment without the cost of land (FCIL).

Payback period = 1+10.78−5.6155.615

= 1.97 year

The cumulative cash position is the total worth of the project at the end of its lifetime.

Cumulative cash position = $44.509 x 106

The rate of return on investment (ROROI) is calculated using (Eq.7.3).

ROROI =Average annual net profit

FCIL (7.3)

Where:

Average annual net profit: sum of the profit (without adding the depreciation) divided by the lifetime of the project.

Average annual net profit = ∑ profit – ∑ depreciation10

i=110i=1

Life time =

5.53 𝑥𝑥 107−2.23 𝑥𝑥 106

10

Average annual net profit = $5.3 x 106

ROROI = 5.37 x 106

1.08 𝑥𝑥 107 x 100 = 49.19%

The variation in the cumulative cash position and the ROROI with the selling price are shown in (Figure 7.5).

Fig. 7.5 The variation with selling price of cumulative cash position (a), and of ROROI (b).

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7.6 Summary In this chapter, detailed cost estimation for plant erection and operation is carried out. Purchased equipment cost is based on the sizing and design data obtained previously. The current cost of equipment is evaluated using Marshall-Swift index. The overall estimated capital required for plant erection is 10.8 million USD. The cost of plant operation includes the cost of raw materials, utilities, wages, maintenance, etc. The estimated annual operation cost is $3.66 x 108/yr. The selling price of ethylbenzene at the breakeven point is $915/ton which is lower than the global selling price, $1000/ton. The selling price is set at $930/ton which corresponds to an annual revenue of $3.72 x 108 /yr. Cumulative cash flow diagram is then construed and it is found that the payback period is approximately 2 years and the total worth of the project at the end of 10 years lifetime is 44.5 million USD.

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Chapter 8

Process control

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8. Process control 8.1 Introduction to process control The purpose of process control is to maintain the different process variables at steady state condition. Under normal operating conditions there is no variation in the amounts being produced, temperature or pressure. However, in industrial operations many disturbances can drive the system away from steady state. The process control is therefore installed to eliminate disturbances [61]. There are four main measurable variables that are controlled in industrial processes:

- Liquid level - Pressure - Temperature - Flow rate

The main control objective can be to control any of those variables or to control another variable by measuring one of the main four variables. Example of the later is to monitor the compositions in distillation columns by measuring the tray temperature; This type of process control is called inferential control [62]. The control elements are shown qualitatively in a flow diagram, Piping and instrumentation diagrams (P& ID), using standard symbols shown in (Figure 8.1) [63,64].

Fig. 8.1 Standard symbols for control elements.

In the following sections , control schemes of the main process units are established for the different disturbances that can occur in each process.

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8.2 Control of liquid level in storage tanks The objective of the storage tanks control would be to maintain the liquid level within previously determine limits. The control scheme of a liquid tank is shown in (Figure 8.2). The external disturbance that can affect the liquid level is the flow rate of the inlet stream. Two different measuring elements are utilized to ensure the safety of the operation, flow and level controls.

Fig. 8.2 Control scheme of liquid storage tank

To explain the symbols used in figure 8.2, the level control loop is considered. A level sensing element (LE) is located on the tank. The sensed level is converted into an electrical signal by the level transmitter (LT), the electrical signal is expressed by dashed lines. The electrical signal is sent to a level controller which in turn send an electrical signal to an instrument that computes the correct valve position and in turn sends a pneumatic signal (designated by a solid line with alternating double slashes) to activate the control valve (LCV). The controller and the computing instrument are expressed by (LC) symbol. In order to warn operators of potential errors, two alarms are placed in the control room. These are a low-level alarm (LAL) and a high-level alarm (LAH) and they receive the same signal from the level transmitter. If the level in the tank increases the (LCV) opening increases slightly to bring the level back to steady state condition.

8.3 Control of heat exchanger Consider the heat exchanger shown in (Figure 8.3). The shell side fluid is the process fluid that is required to be cooled to a certain temperature. The resulting temperature is measured at the outlet of the heat exchanger. Cooling is achieved by passing water through the tube side. The more water passing through the tubes, the more heat is transferred to it, and vice versa. The control objective is to maintain process fluid outlet temperature at steady state value by varying the water flowrate.

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Fig. 8.3 Control scheme of heat exchanger.

Three major disturbances can affect the process fluid outlet temperature:

- Changes in process fluid flow rate - Changes in process fluid inlet temperature - Change in water flow rate

The control loop follows the same sequence as explained in the liquid level control. The low and high level alarms are not shown in the exchanger control system and won't be shown in the following systems.

8.4 Control of the alkylation reactor Fixed bed reactors control is challenging, especially in the case of strongly exothermic reactions. These reactors cannot be operated in excessive temperatures, since disturbances in inlet conditions can generate hot spots, with undesired consequences, such as thermal decontrolling, by-product formation from secondary reactions and catalyst deactivation [65]. In fixed bed reactors where strongly exothermic reactions are carried out, it is necessary to control the temperature peak and exit concentrations simultaneously, to prevent excessive temperature elevations along the reactor and to guarantee the product specifications. Maintaining the reactor at the required process temperature requires the monitoring of this variable in some key positions [66]. In several industrial processes, it is impossible to measure the controlled variable with sufficient speed. This is the case, for example, for the concentration of chemical species in the exit of a fixed bed reactor. The measurement of this variable in real time is relatively expensive and demands periodic calibration and maintenance of analyzers. Moreover, sampling rates are relatively slow due to the time required to purge the line connected to the reactor and the necessary time to the chromatography analysis [67]. Therefore, the concentration can be controlled by strictly maintaining the flow rate of ethylene and the reactor temperature near steady state conditions. The selectivity is improved by keeping low ethylene to benzene ratio in the reactor.

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The pressure of the reactor must also be controlled because increasing the pressure will lead to buckling and may lead to explosion of the reactor and decreasing it will lead to reverse flow. When the pressure decreases the flow rate of ethylene must be increased to bring the pressure back to steady state. On the other hand, if the pressure increases, the valve opening is reduced to increase the pressure drop and bring the pressure back to steady state. The control scheme of the reactor along with its auxiliaries is shown in (Figure 8.4).

Fig. 8.4 Control scheme of the alkylation reactor

8.5 Control of distillation column The main task in the operation and control of distillation columns is the regulation of the products distillate and residual composition despite load disturbances. In practice, composition regulation is approached via indirect methodologies where a specified tray temperature is regulated at a given set point, which, in principle, corresponds to the desired composition value [68]. It is desirable to maximize the purity of the top and/or bottom products. Normally in industry, the control variables are set manually by human operators. Control is carried out using dual composition control, (i.e. automatic control for top and bottom). The column pressure and re-boiler and condenser levels must be controlled very carefully to maintain stable operation.

The LV configuration is the most common method that is used in controlling the composition of top and bottom products, where the reflux flow rate (L) is used to

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control the composition of the top product and the boil-up (V) is used to control the composition of the bottom product. In this case, the distillate flow rate and bottom product flow rate are used to control the levels of the condenser and reboiler respectively [69]. Column pressure has a direct effect on the relative volatility of the key components in the column. Thus, changes in the column pressure can significantly affect product compositions [70]. The control scheme of the distillation column is shown in (Figure 8.5).

Fig. 8.5 Control scheme of distillation column

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8.6 Summary In this chapter, a detailed process control for the main equipment is established to maintain the process at steady state. Control is applied to four equipment which are liquid storage tank, alkylation reactor, distillation column, and heat exchanger. For the liquid storage tank the controlled variable is the liquid level in the tank which can be disturbed by the inlet flow rate. If the level in the tank increases, a level control valve at the outlet bring the level back to steady state conditions. The objective of heat exchanger control is to maintain the process fluid temperature at steady state by cooling it using water directed into the tube side. Disturbances that can affect the process fluid outlet temperature are changes in process fluid flow rate, temperature and change in water flow rate. All these disturbances can be manipulated by changing the water flow rate as the more water passing through the tubes, the more heat is transferred to it and vice versa. The difficulty of alkylation reactor control is due to the highly exothermic reactions. The controlled variables are the selectivity of the reaction which is controlled by inferential control system using ethylene flow rate as a secondary measurement. The selectivity may be disturbed by a change in the flow rate of benzene in the feed and/or system temperature. The flow rate of ethylene is varied to bring the concentration back to steady state. The other controlled variable is the pressure of the reactor; the main disturbance is the flow rate of inlet gas stream (i.e. ethylene). Varying ethylene flow can help maintain the pressure in safe operating limits. However, if the pressure increases to a dangerous limit, venting the gas maybe desired. The main target in distillation control is controlling the purity of the top product which is performed by controlling the top tray temperature. An increase in the temperature is controlled by decreasing the reflux temperature by increasing cooling water flow rate. A decrease in the temperature is controlled by increasing the boil up temperature by increasing the flow rate of steam. The feed pressure must be controlled to assure proper flashing of the feed. The level control in the kettle reboiler is necessary to maintain efficient vapor-liquid separation and protect the equipment from failure.

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Appendices

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Appendix A Distillation design Table A-1 tray-by-tray calculations for benzene distillation column using aspen hysys software.

Tray no. Temperature (°C)

Net liquid flow (kmol/h)

Net vapor flow (kmol/h)

1 89.158 409.822 949.425 2 89.550 407.801 953.238 3 90.183 403.999 951.217 4 91.271 397.217 947.416 5 93.120 386.496 940.634 6 95.987 372.600 929.913 7 99.718 358.654 916.017 8 103.601 347.518 902.071 9 106.935 338.399 890.934 10 109.837 1385.958 881.816 11 113.553 1370.305 879.102 12 120.413 1355.690 863.449 13 129.804 1357.877 848.834 14 138.615 1377.171 851.021 15 144.484 1397.667 870.315 16 147.613 1410.642 890.811 17 149.174 1416.377 903.785 18 150.169 1415.037 909.521

Reboiler 151.588 506.856 908.181

Table A-2 properties required for the design of a sieve tray

Property Gas density (lb/ft3)

Liquid density (lb/ft3)

Surface tension (dyne/cm)

Top tray 0.2208 49.97 19.64 9th tray 0.23 49.26 18.53

Feed tray 0.2313 49.12 18.36 Bottom tray 0.2807 46.57 15.48

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Table A-3 VLE data for benzene-ethylbenzene system and the corresponding Murphree efficiency. The component of interest is the light key (i.e. Benzene)

Tray no. T (°C) 𝜇𝜇𝐿𝐿(cp) m Liq. Flow

(kmol/h) Vap. Flow (kmol/h) λ

1 87.83 0.28666 1.0041 409.82 949.43 2.3262 2 88.22 0.28574 1.0108 407.80 953.24 2.3627 3 88.81 0.28446 1.0246 404.00 951.22 2.4125 4 89.80 0.28243 1.0522 397.22 947.42 2.5097 5 91.41 0.27928 1.1039 386.50 940.63 2.6867 6 93.88 0.27466 1.1908 372.60 929.91 2.9720 7 97.15 0.26889 1.3133 358.65 916.02 3.3541 8 100.85 0.26356 1.4508 347.52 902.07 3.7658 9 104.80 0.26238 1.5761 338.40 890.93 4.1496 10 110.42 0.27143 1.6906 1385.96 881.82 1.0757 11 113.67 0.26551 1.8484 1370.31 879.10 1.1858 12 120.20 0.25397 2.1760 1355.69 863.45 1.3859 13 130.00 0.23758 2.6965 1357.88 848.83 1.6856 14 139.90 0.22223 3.2626 1377.17 851.02 2.0161 15 146.70 0.21244 3.6793 1397.67 870.32 2.2911 16 150.37 0.20759 3.9085 1410.64 890.81 2.4682 17 152.39 0.20587 4.0176 1416.38 903.79 2.5636 18 154.53 0.20671 4.0817 1415.04 909.52 2.6235

Table A-4 data required for the determination of the overall section efficiency Tray no. T (°C) Piv

(atm) yn yn+1 xn yn*

=(Piv/p)xn EM EME

1 89.158 1.313 0.9990 0.997 0.995 0.9992 0.88 0.833 2 89.550 1.328 0.9973 0.994 0.987 0.9978 0.88 0.834 3 90.183 1.352 0.9939 0.987 0.971 0.9949 0.88 0.826 4 91.271 1.395 0.9871 0.974 0.940 0.9890 0.87 0.819 5 93.120 1.471 0.9741 0.952 0.886 0.9776 0.86 0.814 6 95.987 1.594 0.9519 0.920 0.804 0.9574 0.85 0.806 7 99.718 1.766 0.9197 0.883 0.706 0.9273 0.83 0.785 8 103.601 1.960 0.8825 0.849 0.615 0.8920 0.78 0.739 9 106.935 2.139 0.8492 0.825 0.546 0.8600 0.69 0.658 10 109.837 2.305 0.8250 0.779 0.495 0.8364 0.80 0.800 11 113.553 2.531 0.7793 0.680 0.429 0.7926 0.88 0.880 12 120.413 2.993 0.6799 0.511 0.320 0.6964 0.91 0.909 13 129.804 3.726 0.5105 0.313 0.196 0.5294 0.91 0.911 14 138.615 4.528 0.3126 0.159 0.101 0.3287 0.91 0.903 15 144.484 5.129 0.1588 0.071 0.046 0.1687 0.90 0.897 16 147.613 5.473 0.0713 0.030 0.019 0.0762 0.90 0.893 17 149.174 5.651 0.0298 0.012 0.008 0.0319 0.89 0.893 18 150.169 5.766 0.0118 0.004 0.003 0.0126 0.90 0.896

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Fig. A-1 Hole discharge coefficient chart

Fig. A-2 Sieve tray aeration factor chart

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Fig. A-3 Sieve tray fractional entrainment chart (Fair's plot)

Fig. A-4 Fair's weep point plot for weeping and turndown ratio check

Fig. A-5 O’Connell's chart for the determination of distillation section efficiency

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Appendix B Heat exchanger design

Table B-1 Basic estimates of the overall heat transfer coefficient of some common systems.

Table B-2 Standard number of tubes for different type arrangements and the corresponding shell

diameter.

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Table B-3 (a) Fouling factors for common types of cooling water

Table B-3 (b) Fouling factors for some organic materials

Fig. B-1 Temperature correction factor: one shell pass; two or more even tube passes

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Fig. B-2 Tube-side heat-transfer factor

Fig. B-3 Shell-side heat-transfer factors, segmental baffles

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Fig. B-4 Tube-side friction factors

Fig. B-5 Shell-side friction factors, segmental baffles

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Appendix C Cost estimation data

Table C-1 Marshall-Swift index values for different years

* The values presented as publiished by Marshall Swift valuation services 01/2018.

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Table C-2 Values of constants for the estimation of miscellaneaous equipment cost.

* Values are based on the cost data in 1998.

Table C-3 Typical percentage of contribution of each cost element in the total fixed capital.

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Similarity report Appendix D

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Appendix D Similarity report

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