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KineticModellingandReactorDesignMethanolSynthesis2013

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Kinetic Modelling and Reactor Design Methanol Synthesis

2013

Kelvin Obareti CE4005

4/26/2013

CE4005 | Abstract 1

Abstract The primary purpose of this project is to develop kinetic modelling methods and

approaches. A pseudo-homogeneous model was developed for a shell and tube

methanol reactor based on the reaction mechanisms and mass and energy balance

equations. Shell and tube reactor consist of tubes packed with catalyst particles and

operated in a vertical position. The catalyst particles are of spherical shape. Feed is

passed from the top of reactor in to the tubes; due to exothermic reaction the rate will

be relatively large at the entrances to the reactor tube owing to the high concentrations

of reactants existing there. It will become even higher as the reaction mixture moves a

short distance into the tube, because the heat liberated by the high rate of reaction is

greater than that which can be transferred to the cooling fluid as water at high pressure.

Hence the temperature of the reaction mixture will rise, causing an increase in the rate

of reaction. This continues as the mixture moves up the tubes, until the disappearance

of reactant has a larger effect on the rate than the increase in the temperature. Farther

along the tube the rate will decrease. Langmuir-Hinshelwood model was used to derive

a kinetic rate equation ( [ ]

) With the proposed mathematical

model, a plant scale reactor was simulated for a feed temperature of 475K with a feed

composition of 70mol% H2 and 30mol%CO. Properties of the reactor and the catalyst

bed was determined. The Reynolds number was calculated to be less than 2000 which

means the flow will be laminar and the velocity profile will be parabolic. This

contradicts the assumption of a steady state plug flow where reactor mixture of

different age will not mix.

The dimensions of the reactor were calculated based on information from specification,

literature and reasonable assumptions. The reactor worked out to be an adiabatic

cylindrical vessel, 15.95m long with a diameter of 3.19m with a pressure drop around

0.5 bar, the catalyst (assumed to be Cu/ZnO/Al2O3) weight was calculated to be

37257kg for the specified molar feed rate of 5947.66 mol/s. The sensitivity of the vessel

to allowable pressure drop was also investigated. This suggests that for a given amount

of catalyst, a reduced pressure drop can be obtained by reducing the bed depth at the

expense of increasing the bed diameter. Although reducing the pressure drop will

reduce the operating power cost, it will increase the vessel cost.

CE4005 | Abstract 2

The reactor simulation was repeated with three kinetic models from literature and

compared to the developed kinetic model. The kinetic equation proposed by Agny and

Takoudis (1985) fitted best with the experimental data and was closest to the proposed

kinetic data that was derived from the kinetic experimental data provided. The Agny

and Takoudis mathematical model was used to simulate the reactor for adiabatic and

non-adiabatic setup from the given kinetic data. The equilibrium conversion (highest

conversion possible for reversible reactions) was found to be 23% with a

corresponding equilibrium temperature of 550K, hence a coolant temperature of 550K

was recommended for the shell side of the reactor in order to be able to achieve the

equilibrium conversion. Interstage cooling was suggested in order to be able to achieve

higher conversion.

The modelling process was repeated on ASPEN in order to observe the temperature

profile and the effects of different feed composition as well as feed temperature. The

optimum feed composition was found to be 70mol% H2 and 30mol%CO as this

produced the highest amount of methanol under the same conditions. The ASPEN

simulation results also showed a conversion range between 20%-30% which is similar

to that of the equilibrium conversion obtained earlier. A sensitivity analysis was carried

out on Aspen to check the effect of varying the feed temperature on the rate of

production of methanol. The analysis showed that increasing the feed temperature will

lead to decrease in methanol production and vice versa. The optimum temperature

from the graph was 100 C (373K). This results follows from the strong exothermic

nature of the methanol synthesis. At equilibrium, the rate of backward reaction will

increase more relative to the rate of backward reaction with temperature rise which

means there will be less conversion of the reactants to products.

The high adiabatic temperature rise observed in all the simulation suggested that an

adiabatic reactor running at the specified condition is not suitable for the methanol

synthesis process and therefore an operation with an heat exchange medium should be

considered. An optimisation of the temperature regime was suggested. This can be

achieved by using a type of reactor where the temperature profile can be adjusted such

that the reaction mixture is allowed to be heated by the heat of reaction in the region

free of the effect of chemical equilibrium , to be later cooled by heat exchange in the

region effected strongly by chemical equilibrium.

CE4005 | Abstract 3

Table of Contents Abstract ..................................................................................................................................... 1

1. Introduction ...................................................................................................................... 7

2. Background ....................................................................................................................... 7

2.1. Available Process Routes .......................................................................................... 8

2.2. Reactor Model Description ..................................................................................... 12

3. Literature Review ........................................................................................................... 15

3.1. Process Description ................................................................................................. 15

3.2. Reaction Mechanisms and Kinetic Models ............................................................ 18

3.2.1. Mechanisms involving CO ................................................................................ 18

3.2.2. Mechanisms Involving CO2 ............................................................................. 19

3.3. Thermodynamic Equilibrium ................................................................................. 20

3.4. Selectivity ................................................................................................................. 22

3.5. Catalysts ................................................................................................................... 23

3.5.1. High-pressure Catalysts ................................................................................... 23

3.5.2. Low-pressure Catalysts ................................................................................... 24

3.6. Kinetic Models .......................................................................................................... 26

3.6.1. Natta et al (1953) ............................................................................................. 27

3.6.2. Rozovskii (1980) and Klier (1982) ................................................................ 27

3.6.3. Agny and Takoudis (1985) .............................................................................. 28

3.6.4. Skrzypek's (1985 and 1991) ........................................................................... 29

3.6.5. Lim (2009) ........................................................................................................ 31

3.6.6. Literature Review Conclusion ......................................................................... 34

4. Work Plan and Methodology ......................................................................................... 35

4.1. To develop a kinetic model for the synthesis of methanol from the synthetic

rate data given in Appendix 1 ........................................................................................... 35

4.1.1. Developing Langmuir-Hinshelwood Kinetic Model from Experimental Data

35

4.1.2. Experimental Data Incorporated into Kinetic Model From Literature ........ 36

4.2. Simulating a Plant-Scale Catalytic Reactor ............................................................ 39

4.2.1. Reactor Volume ................................................................................................ 40

4.2.2. Reactor Length and Diameter ......................................................................... 40

CE4005 | Abstract 4

4.2.3. Reactor Dome Closure ..................................................................................... 41

4.2.4. Catalyst Bed Characteristics ............................................................................ 42

4.3. Sensitivity to pressure drop ................................................................................... 43

4.4. Effect of Coolant Temperature ................................................................................... 43

4.5. Modelling with ASPEN Process Modelling Software. ........................................... 44

4.6. Gantt Chart ............................................................................................................... 44

5. Results and Discussion .................................................................................................. 44

5.1. Developing a kinetic model from experimental data ........................................... 44

5.1.1. Dependence on the product methanol ........................................................... 46

5.1.2. Dependence on Carbon Monoxide .................................................................. 47

5.1.3. Dependence on Hydrogen ............................................................................... 47

5.1.4. Finding k and K Values ..................................................................................... 48

5.2. Plant-Scale Catalytic Reactor Simulation ............................................................... 51

5.2.1. Reactor Dimension ........................................................................................... 59

5.3. Experimental Data Incorporated Into Kinetic Models from Literature .............. 66

5.4. Effect of Coolant Temperatures .............................................................................. 74

5.5. Modelling with ASPEN Process Modelling Software ............................................ 76

5.6. Further Discussion .................................................................................................. 81

6. Conclusion ....................................................................................................................... 82

7. Recommendations .......................................................................................................... 84

8. Nomenclature ................................................................................................................. 86

9. References ....................................................................................................................... 87

10. Appendices

10.1 Appendix 1: Data for Kinetic Analysis

10.2 Appendix 2: Possible Routes to Methanol

10.3 Appendix 3: Deriving non-adiabatic energy balance

10.4 Appendix 4: ASPEN Simulation Results

10.5 Appendix 5: Improved Gantt Chart

10.6 Appendix 6: Reactor Simulation Summary

10.7 Appendix 7: USB stick with ASPEN and Microsoft Excel Simulation and

Graphs

CE4005 | Abstract 5

List of Figures Figure 1 Structural formula of methanol ................................................................................... 7

Figure 2. The ICI-steam-raising reactor for low-pressure methanol synthesis [iv]. ................ 10

Figure 3 Simplified route to methanol production [].............................................................. 11

Figure 4 Production of methanol from atmospheric carbon dioxide or from neutral gas

(methane), and its use as a fuel. DMFC: direct methanol fuel cell [i]. .................................... 11

Figure 5 Schematic diagram of a plug flow reactor ................................................................. 12

Figure 6 Mass balance around a plug flow reactor ................................................................. 12

Figure 7. Essential process steps in Lurgi’s Low Pressure Methanol Process []. ..................... 16

Figure 8. Flow sheet of Lurgi's Methanol Synthesis Loop [xii] ................................................. 17

Figure 9. Thermodynamics of methanol synthesis. Variation of equilibrium constant kp with

temperature and pressure [iv] ................................................................................................. 21

Figure 10. Reaction temperature profile of adiabatic and non-adiabatic set up at conversion

between 0 and 0.9 ................................................................................................................... 59

Figure 11. Reactor hemispherical dome closure dimension ................................................... 61

Figure 12. Preliminary dimension of the plant-scale catalytic reactor .................................... 62

Figure 13. Reactor dimension sensitivity to pressure drop ..................................................... 66

Figure 14. Reaction rate as a function of degree of conversion in the adiabatic reactor. ...... 71

Figure 15. Relationship between temperature and degree of conversion in the adiabatic

reactor. ..................................................................................................................................... 71

Figure 16. Reaction rate as a function of degree of conversion in the non-adiabatic reactor.

.................................................................................................................................................. 73

Figure 17. Relationship between temperature and degree of conversion in the non-adiabatic

reactor. ..................................................................................................................................... 73

Figure 18. Plot of equilibrium conversion as a function of temperature. ............................... 75

Figure 19. Interstage cooling []. ............................................................................................... 76

Figure 20. Reactor model summary ......................................................................................... 77

Figure 21. Flow sheet with heat and material balance for ASPEN simulation at a feed inlet

temperature of 473K (200 C) ................................................................................................... 78

Figure 22. Temperature profile of the reactor at a feed composition of 70% H2 and 30% CO

.................................................................................................................................................. 79

Figure 23. Sensitivity of methanol production to different feed temperatures. ................... 80

CE4005 | Abstract 6

List of Tables Table 1. Catalysts proposed or used for industrial process [iv]. .............................................. 23

Table 2. Important rate expressions for methanol synthesis []. ............................................. 26

Table 3. Elementary Reactions for Cu/ZnO/Al2O3/ZrO2 catalysed methanol synthesis [] ....... 32

Table 4. Reaction rates for methanol synthesis reaction and DME production [xxvi]. ........... 33

Table 5. Methanol synthesis kinetic models to be compared to developed kinetic model .... 34

Table 6. Data for Kinetic Analysis ............................................................................................. 45

Table 7. Experiment 1 compared to experiment 5. ................................................................. 46

Table 8. Experiments to deduce the dependence on carbon monoxide ................................ 47

Table 9. Effect of decreasing the partial pressure of hydrogen on the rate of reaction. ........ 47

Table 10. Constant hydrogen partial pressure for kinetic parameter ..................................... 49

Table 11. Constant methanol partial pressure for kinetic parameter ..................................... 50

Table 12. Experimental data table modified to include values of VO , CA0, FA0 and ṁ ........... 55

Table 13. Experiment 12 reaction conditions 1 ....................................................................... 57

Table 14. Experiment 12 reaction conditions 2 ...................................................................... 57

Table 15. Reactor volume and temperature profiles for adiabatic and non-adiabatic setup at

conversion between 0 and 0.9................................................................................................. 58

Table 16. Summary of reactor cylindrical section dimension.................................................. 60

Table 17. Summary of overall rector dimension ..................................................................... 62

Table 18. Summary of catalyst bed characteristics. ................................................................ 64

Table 19. Reactor dimension sensitivity to pressure drop ...................................................... 65

Table 20. Methanol synthesis kinetic models and rate equation............................................ 66

Table 21. Comparison of kinetic model simulation results. .................................................... 67

Table 22. Summary of Agny and Takoudis model for an adiabatic reactor using the provided

experimental data .................................................................................................................... 69

Table 23. Summary of Agny and Takoudis model for non-adiabatic reactor setup using the

experimental data provided .................................................................................................... 72

Table 24. Results table for temperature-conversion relationship. ......................................... 74

CE4005 | Introduction 7

1. Introduction

The primary purpose of this project is to develop a kinetic model for the synthesis of

methanol from given set of synthetic rate data. The result of the kinetic model will then

be used to simulate a shell-and-tube reactor at specified conditions, using a simple one-

dimensional, plug-flow, pseudo homogeneous, nonisothermal reactor model. The

kinetic model developed will be compared to other kinetic models suggested by

literature and the best model will be used in the reactor design and to study the

performance of the reactor. This will provide an opportunity to demonstrate and apply

technical knowledge. Also, the ability in critical analysis will be demonstrated.

2. Background

The issue of sustainability is that which concerns many industries and given the option

of moving from the consumption of fossil fuels towards renewable/cleaner energy

makes the synthesis of methanol very important.

Methanol is the simplest alcohol (one carbon backbone). It is a clear, colourless liquid

with a characteristics alcohol odour.

Figure 1 Structural formula of methanol

There are various means of producing methanol and these includes the anaerobic

metabolism of many varieties of bacteria (natural), pyrolysis of wood, and most

importantly from fossil fuel based synthesis gas, which is the main method of producing

methanol industrially.

According to the 1994 Nobel Prize in Chemistry winner, George Andrew Olah [i],

Methanol can replace fossil fuels as a means of energy storage, in what is now referred

CE4005 | Background 8

to as the methanol economy. Apart from the current use of methanol today as chemical

feedstock for producing useful chemical products like, acetic acid, formaldehyde (used

in construction and wooden boarding) and methyl tert-butyl ether (MBTE), due to its

high octane rating, and biodegradability, methanol can be used directly as a fuel in

hybrid vehicles and as a fuel in fuel cells which are renewable forms of energy

production.

2.1. Available Process Routes

From 1830 up until the mid-1920’s, wood de ived o natu al methanol was the main

source of methanol. The first commercial production of methanol was by the destructive

distillation of wood, hence methanol is sometimes called wood alcohol [ii]. Apart from

wood pyrolysis, there are various means of producing methanol and these includes the

anaerobic metabolism of many varieties of bacteria (natural), and most importantly

from fossil fuel based synthesis gas, which is the main method of producing methanol

industrially [iii].

The synthesis gas that was first used for the production of methanol was manufactured

by coke gasification. In recent times, the synthesis gas is now almost invariably

produced by steam reforming or partial oxidation of hydrocarbons, usually natural gas

[iv].

The production of methanol from synthesis gas occurs in two steps. The first step

involves the conversion of the feedstock natural gas (methane) into a synthesis gas

stream that consists of carbon monoxide (CO), carbon dioxide (CO2), water (H2O) and

hydrogen (H2). The first step is usually carried out by the catalytic steam reforming of

hydrocarbon feedstock or by non-catalytic partial oxidation of hydrocarbon or coal [iii].

Methanol produced via the catalytic hydrogenation of carbon monoxide and/or carbon

dioxide occurs via the three reactions given below [iv].

1. Hydrogenation of carbon monoxide:

CO + 2H2 CH3OH (ΔH298K = -90.64kJ/mol, ΔG°= -25.34kJ/mol) (2.1)

2. Hydrogenation of carbon dioxide:

CO2 + 3H2 CH3OH + H2O (ΔH298K = -49.47kJ/mol, ΔG°= +3.30kJ/mol) (2.2)


3. Water-gas shift reaction:

CO2 + H2 CO+ H2O (ΔH298K = -41.47kJ/mol, ΔG°= -28.64kJ/mol) (2.3)

Synthetic route for methanol production was first commercialised by BASF in Germany.

The process was based on the reaction of synthesis gas which is a mixture of hydrogen

and carbon oxides. The reaction occurred over a zinc chromite catalyst at relatively high

temperatures of 300 to 400°C and high pressures (250 to 350atm). Synthesis gas was

derived from coal via the water gas reaction [v]. By 1965, a state-of-the-art, high

pressure methanol unit typically had the following characteristics: Capacity, 70 to 150

thousand tonnes per year; Operating pressure, 350atm; Consumption, 11-12 million

kcal per tonne of methanol (130-140 ft3 of natural gas per gallon).

In 1966, Imperial Chemical Industries (ICI) developed the low pressure methanol

synthesis which was a significant breakthrough in methanol technology. The synthesis

was carried out over a proprietary based copper catalyst. This high activity catalyst

allowed the methanol synthesis reaction to proceed at commercially acceptable levels at

relatively low temperatures (220 - 280°C) which allowed operation at a notably

reduced pressure of 50 atm. Overall, the ICI low-pressure was more economical than

the high pressure system in terms of capital and operating cost [vi]. Figure 2 below

shows the ICI process which uses multi-bed synthesis reactors with feed gas quench

cooling.


Figure 2. The ICI-steam-raising reactor for low-pressure methanol synthesis [iv].

A, catalyst is charged and inspected through these manholes; B, the pressure vessel is of

simple design; C, cooling tubes are welded to a simple header system, F, embedded in

the catalyst bed; D, perforated catalyst support grids allow gas to be distributed along

the length of the catalyst bed; E, an upper header system collects steam from the tube

bundle, which then passes to the steam drum, I; H, boiler feed water enters the base of

the converter; G, gravity discharge of catalyst permits rapid preparation for

maintenance or recharging.


Figure 3 below shows some of the possible routes to methanol synthesis, a detailed

figure can be found in appendix 2.

Figure 3 Simplified route to methanol production [vii]

Based on the methanol economy, methanol can be prepared by direct oxidative

conversion of methane or the reductive conversion of atmospheric carbon dioxide with

hydrogen as shown in the figure below. Carbon dioxide is available as flue gas from

fossil fuel burning power plants, atmosphere and many industrial exhausts. The

conversion of carbon dioxide to methanol will recycle the harmful greenhouse gas to

useful fuel and also provide good source of hydrocarbons.

(2.4)

Figure 4 Production of methanol from atmospheric carbon dioxide or from neutral gas (methane), and its use as a fuel.

DMFC: direct methanol fuel cell [i].


2.2. Reactor Model Description

The reactor to be simulated is a simple one-dimensional, plug flow, pseudo

homogeneous, nonisothermal reactor model.

Due to the turbulence of gas phase reactions such as the methanol synthesis, they are

usually carried out in a plug flow reactor. The assumption made when choosing this

type of reactor is that there is no dispersion and no radial gradients in temperature,

velocity or concentration. The problem statement for this project states that ideal gas

law can be applied in all calculations, so the design equation can be written using the

ideal plug flow reactor model.

In an ideal plug flow reactor, velocity flow is assumed to be uniform or constant i.e. the

residence time is the same for every molecule throughout the flow. In this type of

reactor, there is no radial variation in velocity, concentration, temperature, or rate of

reaction [viii].

Figure 5 below shows a schematic diagram of a plug flow reactor. In this type of reactor,

there is no radial variation in velocity, concentration temperature, or rate of reaction.

Figure 5 Schematic diagram of a plug flow reactor

The design Equation of a PFR (plug flow reactor) operating at steady state is given

below.

Figure 6 Mass balance around a plug flow reactor


Where:

FAo is the entering molar flow

Co is the concentration in

v is the velocity of flow (i.e. volume flow)

V is the volume of reactor

C is concentration out.

Design Equation:

=

(2. ; Rate Law: -rA = kCA (2.6);

Stoichiometry: v=v0 (2.7)

v (2.8)

v (2.9)

CA=CA0 (1-X) (2.10)

Assuming a steady flow profile,

At steady state, there is no accumulation and for a differential element of volume, dV,

Input = output + disappearance by reaction. i.e.

FA = (FA + dFA) + (-rA) dV (2.11)

But dFA = d [FAo (1-XA)] = -FAo dXA (2.12)

FAo dXA = (- rA) dV (2.13)

dV/FAo = dXA/(- rA) (2.14)

By integration this becomes: ∫

∫

(2.15)

∫

(2.16)

Equation 2.16 above is the design equation for a plug flow reactor.

Knowing that v and dX = -dCA/CAo

The design equation can be written in terms of concentration, C as below:


V/vo = CAo ∫

= ∫

(2.17)

Where: V/vo = t (mean residence time of flowing material in the reactor)

Assuming a constant density system for simplicity, τ t= V/vo (2.18)

Where: t = τ is time needed to treat one reactor volume of feed,

t is mean residence time of flowing material in the reactor,

V is volume of the reactor,

vo is volumetric flow rate [ix ,x] .

The pseudo homogeneous part of the reactor specification describes the catalyst

system. In a pseudo homogeneous system, the small sized (approximately spherical)

unsupported catalyst particles are uniformly dispersed throughout the feed. As a result

of the particle size, the particles are suspended and exhibit properties similar to

colloidal solutions. Due to the exothermic nature of the methanol synthesis, a non-

isothermal reactor will be used. This means heat will vary along the length of the

reactor [xi].

CE4005 | Literature Review 15

3. Literature Review

This literature review will cover the methanol production process and some of the

previous kinetic models developed for methanol synthesis. The knowledge of the kinetic

mechanism of a chemical process presents a considerable importance in the reactions

which corresponds to the chemical equilibrium because this alone can allow the design

of the devices and sizing of the appliances needed to remove the heat conducted in

different parts of a reactor. Mathematical models of methanol synthesis are often

valuable tools that can be used in the evaluation of those systems. Any successful kinetic

model must include the rate equations of the reaction that accurately predict the effects

of process variable changes on reactor performance. Linear and nonlinear regression is

a method often used by many researchers to analyse data collected in order to produce

a reaction rate expression [ii]. The rate equations will vary depending on the assumed

mechanism and the role of each reactant in the reaction. In a case where a particular

reactant is weakly adsorbed to the surface of the catalyst used to catalyse the reaction,

such weakly adsorbed reactants are usually left out of the rate equation.

Before discussing the kinetic model, factors affecting the rate of the methanol synthesis

reaction will be discussed. Such factors are:

Reaction mechanism

Thermodynamic equilibrium

Process condition (Temperature, pressure)

Catalysts

3.1. Process Description

The methanol process consists mainly of three parts.

Synthesis gas preparation,

Methanol synthesis, and

Methanol distillation

As discussed earlier, methanol synthesis has improved from using high pressure to low

pressure which is more cost effective. Two low-pressure methanol synthesis processes

dominates the market; the ICI process which uses multi-bed synthesis reactors with

feed gas quench cooling and the Lurgi process [xii] that makes use of multitubular


synthesis reactors with internal cooling. The synthesis gas used in the production of

methanol is a mixture of CO, CO2 and H2. This synthesis gas can be produced from

various feedstock such as natural gas, higher hydrocarbons and coal. The synthesis gas

is produced conventionally via the steam reforming process but it can also be produced

from CO2 reforming, partial oxidation and auto thermal reforming. Figure 7 below

shows the essential steps of Lu gi’s Low Pressure Methanol Process with combined

reforming of oil associated natural gas. In the Lurgi reactor with typical operating

conditions of 523 K and 80 bar, the catalyst is packed in vertical tubes surrounded by

boiling water. Reaction heat is transferred to the boiling water to produce steam. Due to

the efficient heat transfer, very little temperature gradient is observed along the reactor.

The pressure of the boiling water helps to control the reactor temperature.

Figure 7. Essential p ocess steps in Lu gi’s Low P essu e Methanol P ocess [xiii].

Natural gas first undergoes desulphurization and gets saturated with process steam

then undergoes three steps of reforming (using Ni-based catalyst.):

Preforming - Higher hydrocarbons are converted to methane by steam reforming

and methanation in an adiabatic reactor

Steam reforming – parts of the methane gas are converted to synthesis gas by

the highly endothermic steam reforming reaction, reaction energy is supplied by

the burning of natural gas outside the catalyst tubes in a multitubular reactor.

Autothermal reforming – The remaining methane is converted into synthesis gas


The reactions occurring in the synthesis gas preparation are:

CnHm + nH2O nCO + (

) (3.1)

CH4 + H2O CO + 3H2 (ΔH,298K = -206kJ/mol) (3.2)

CH4 +

CO + 2H2 (ΔH,298K = 35kJ/mol) (3.3)

The water gas shift (equation 3) occurs in all the reforming steps.

In the methanol synthesis, synthesis gas is converted to methanol over a Cu/Zn/Al2O3

catalyst. Figure 8 below shows the Lu gi’s [xii] methanol synthesis loop.

Figure 8. Flow sheet of Lurgi's Methanol Synthesis Loop [xii]

Due to the quasi-isothermal reaction conditions and high catalyst selectivity, only small

amounts of by-products are produced during methanol synthesis. The methanol

synthesis loop consists of two parallel reactors with a common steam drum,

feed/effluent interchanger, a cooler, a methanol separator and a recycle compressor.

The methanol produced needs to be distilled to remove water, dissolved gases and

ethanol. Ethanol is the most difficult component to remove due to the small difference in


the volatility between ethanol and methanol. Firstly, the dissolved gases are separated

from the crude methanol by flashing at low pressure. Low and high boiling by-products

are removed in energy integrated three column distillation sequence. Ethanol is

removed in the side stream of the third of these columns [xiii].

3.2. Reaction Mechanisms and Kinetic Models

Two types of reaction mechanisms associated with methanol synthesis are discussed

below.

3.2.1. Mechanisms involving CO

Although many investigators support the carbon monoxide hydrogenation theory, the

source of methanol is still an open question. Is methanol synthesised from carbon

monoxide or carbon dioxide?

Herman et al., [xiv,xv] believes that carbon monoxide is adsorbed (with a carbon-metal

bond) and then successively hydrogenated to form formyl, hydroxycarbene and

hydroxyl-methyl species leading to methanol. Alternatively, Deluzarche et al., [xvi]

suggested that carbon monoxide is inserted into a surface hydroxyl group to form a

surface formate species (with an oxygen-metal bond), followed by hydrogenation and

dehydration to form a surface methoxide that leads to methanol. This mechanism

requires an oxygen bond to an active site. Although ICI investigators documented the

formation of a stable intermediate formate species, Kung et al., analysed the available

data [xvii] from the mechanisms proposed by Herman et al., and Deluzarche et al.,

sufficient evidence was found, which disprove those mechanisms. Kung found evidence

for carbon monoxide adsorption with the carbon end of the molecule towards the metal.

Agny and Takoudis [xviii] reiterated and refined a third mechanism that was proposed

by Henrici-Olive and Olive [xix]. This third mechanism introduced a new intermediate

between the formyl and methoxide species- surface bonded formaldehyde as shown in

equation 3.4 below.

(3.4)

The presence of the surface-bonded formaldehyde was verified by others such as

Tawarah and Hansen [xx] and Edwards and Schrader [xxi].


Transmission infrared spectroscopy was used by Edward and Schrader to develop the

mechanism. However, they speculate that the formaldehyde might be formed by carbon

monoxide insertion into an adsorbed hydroxyl group to form a bidentate formate

species. The infrared studies conducted under reaction conditions also showed that the

CO is adsorbed on the Cu(I) sites of the catalyst used, but much of the reaction occurs on

the zinc oxide component [xxi].

3.2.2. Mechanisms Involving CO2

The thermodynamics of the reaction of carbon dioxide to methanol are very

unfavourable at typical reaction conditions. This made Kung et al. reach a conclusion

that it is very unlikely for any proposed mechanism involving carbon dioxide

hydrogenation to be the predominant one [xvii]. Nevertheless, a series of studies by

Kagan and Rozovskii [xxii,xxiii] led them to conclude that methanol forms only via

carbon monoxide hydrogenation, and that direct synthesis of methanol from carbon

monoxide and hydrogen does not occur at all. Chinchen et al., [xxiv] confirmed this

when he repeated the work of Kagan and Rozovskii.

Bowker et al., [xxv] and Chinchen et al., [xxiv] proposed mechanisms that are similar in

nature. In their mechanisms, carbon dioxide is hydrogenated to form a surface formate

species which is further hydrogenated to form a surface formate species that is further

hydrogenated to produce methanol. Bowker et al speculated that this hydrogenation

proceeds through the methoxide species.

Recent studies by the department of chemical engineering at Ajou University in Korea

investigated the influence of CO2 on hydrogenation. A kinetic model was developed for

methanol synthesis over Cu/ZnO/Al2O3/ZrO2 catalyst to evaluate the effect of carbon

dioxide on the rate of reaction due to its high activity and stability.

Detailed kinetic mechanism, on the basis of different sites on Cu for the adsorption of

carbon monoxide and carbon dioxide, was applied, and the water-gas shift reaction was

included in order to provide the relationship between the hydrogenations of carbon

monoxide and carbon dioxide. Parameter estimation results show that, among 48

reaction rates that was developed from different combinations of rate determining

steps in each reaction, the surface reaction of a methoxy species, the hydrogenation of a

formate intermediate HCO2, and the formation of a formate intermediate are the rate


determining step for CO and CO2 hydrogenations and the water gas shift reaction,

respectively. The result showed that the rate of CO2 hydrogenation is much lower than

that of CO hydrogenation and this affects the methanol production rate.

However, it was also found that carbon dioxide indirectly accelerates the production of

methanol because it decreases the rate of reaction of the water gas shift. A decrease in

the rate of reaction of the water gas shift prevents the conversion of methanol to

dimethyl ether [xxvi]. The rate of reaction for methanol synthesis and DME production

is summarised in Table 4.

3.3. Thermodynamic Equilibrium

Reactions (2.2) and (2.3) combined are equivalent to reaction (2.1) so that either or

both, of the carbon oxides can be the starting point for the synthesis of methanol. The

reverse water gas shift is an endothermic reaction; so generally, increase in

temperature will favour the forward reaction in reaction (2.3). Reactions (2.1) to (2.3)

are exothermic and reaction (2.1) and (2.2) leads to reduction in volume, thus the value

of equilibrium constant Kp for synthesis from carbon monoxide;

(3.4)

decreases with temperature as shown in the figure below.

Pi = partial pressure of component i.


Figure 9. Thermodynamics of methanol synthesis. Variation of equilibrium constant kp with temperature and pressure

[iv]

Increase in the value of equilibrium constant with pressure is due to non-ideality. Thus

if the catalyst is sufficiently active, high conversion of methanol will be obtained at high

pressures and low temperatures. The use of high pressure commercially is expensive

both of capital and gas compression. Therefore, with a very active catalyst, it is most

economical to use lower pressure and obtain the same conversions as at high pressures

but at lower temperatures. Figure 9 shows a variation of equilibrium constant with

temperature and pressures. It shows that a catalyst which is only active at 350°C or

above such as the ZnO/Cr catalyst will require an operating pressure of 300 bar to

achieve a conversion to methanol of 3% while a more active catalyst such as the

Cu/ZnO/Al2O3 catalyst will obtain the same conversion at 50 bar [iv].

Thermodynamic equilibrium limits the maximum yields of carbon oxides to methanol.

Due to the strongly non ideal behaviour of gases at conditions used commercially,

equilibrium equations necessarily involve fugacity. The equilibrium composition of any


mixture of carbon oxides, water, methanol, hydrogen and inert can be calculated using

the equations below. These equations corresponds to reactions in equation 3.1 and 3.3.

Kf1 = fCH3OH/fCOfH2 (3.5)

Kf2 = fCO2fH2/fCOfH2O (3.6)

Where fi is the fugacity of component i in atmospheres [ii].

3.4. Selectivity

Carbon monoxide and carbon dioxide can also react with hydrogen to produce by-

products such as ethers, hydrocarbons and higher alcohols.

CO +3H2 CH4 +H2O (ΔH298K = -206.17kJ/mol, ΔG°= -142.25kJ/mol)

(3.7)

2CO +4H2 CH3OCH3 +H2O (ΔH298K = -204.82kJ/mol, ΔG°= -67.20kJ/mol)

(3.8)

2CO +4H2 C2H5OH +H2O (ΔH298K = -2 . 8kJ/mol, ΔG°= -122.55kJ/mol)

(3.9)

These reactions (equation 3.7-3.9) are more exothermic than the methanol synthesis

reactions and their formation involves larger negative change of free energy. Methanol

is thermodynamically less stable and less likely to be formed from carbon monoxide and

hydrogen than the other possible products such as methane. Kinetic factors are used to

determine the product formed. A selective catalyst is used to favour a reaction path

leading to the desired product (methanol) with a minimum of by-products [iv].


3.5. Catalysts

The catalysts used for methanol synthesis can be divided into 2, high-pressure and low-

pressure catalysts.

Table 1. Catalysts proposed or used for industrial process [iv].

Catalyst Composition Active phase in methanol

synthesis

Properties and use

ZnO ZnO Original synthesis catalyst,

short life.

ZnO/Cr2O3 ZnO Standard high-pressure

catalyst

ZnO/MnO/Cr2O3 + alkali Alkalized ZnO (+ MnO?) Standard high-pressure

catalyst for methanol/higher

alcohol mixtures.

Cu/ZnO

Cu ZnO/Cr2O3

Cu Early low-pressure catalyst,

short life

Cu ZnO/Al2O3 Cu Industrial low-pressure

catalyst

Pd/SiO2

Pd/basic oxides

Pd Active; poorer selectivity than

copper catalystsb

Rh/SiO2

Rh/basic oxides

Rh Active; poorer selectivity than

copper catalystsb

Rh complexes Rh complex Low activity; poorer

selectivityc

a There is evidence that the active phases in the Cu, Pd and Rh catalysts, essentially the

metals are partially oxidised, either bulk or surface.

b Catalysts based on Group VIII metals, The by-products are mainly hydrocarbons.

c homogeneous catalysis with rhodium complexes gives ethylene glycol + methanol. No

hydrocarbons are formed.

3.5.1. High-pressure Catalysts

In the past, when methanol syntheses were carried out under high pressure, the catalyst

used in the original process was derived by empirical methods. This catalyst contains

zinc oxide and chromia and was used for about 40 years. Although Zinc Oxide alone was


a good catalyst for methanol synthesis at high temperature and temperatures above

350°C, it was not stable and it quickly lost it activities which means it has to be replaced

frequently. Through research, it was found that chromia acts as a stabilizer for zinc

oxide by preventing the growth of the zinc oxide crystals and by so doing preventing die

off. The Zinc oxide/chromia catalyst was tolerant of the impure synthesis gas and could

have a plant life of several of years. This catalyst was not very selective and depending

on synthesis conditions as much as 2% of the inlet carbon oxides could be converted to

methane and a similar proportion to dimethyl ether. The very exothermic nature of the

side reaction calls for a careful control of catalyst temperature [iv].

3.5.2. Low-pressure Catalysts

The low-pressure process is based on high activity catalysts. Copper oxide was found to

be very effective for methanol synthesis when added to zinc oxide. The zinc

oxide/chromia catalysts also showed increase in activity when Copper oxide was added

to it, so it could be used at temperatures as low as 300°C. However catalysts containing

copper were not stable and lost activity e.g. a Zn/Cu/Cr catalyst in atomic proportions

of 6: 3 : 1 lost 40% of its activity in 72 hours. The work of ICI on methanol synthesis

resulted in the production of more stable copper catalysts. In the modern copper/zinc

oxide/alumina synthesis catalysts, high activity and stability are obtained by optimizing

the composition and producing very small particles of the mixture in a very intimate

mixture precipitated at controlled pH in which the acidic and alkaline solutions are

mixed continuously. Catalysts made by the continuous process were used in the first

(1966) low-pressure methanol synthesis plants operating at 50 bar and they had lives

of more than 3 years as well as producing methanol of a higher purity than the high-

pressure process. Further development resulted in catalysts suitable for operation at

100 bar, around the optimum operating pressure for plants capable of producing 1000

tonnes per day of methanol. Zinc oxide/alumina is not sufficiently refractory as a

support at 100 bar, but a more refractory support is provided by using some of the zinc

component as a compound with the alumina component; as zinc spinel (ZnO.Al2O3),

which is produced in a finely divided state.

In recent years, some new catalysts and process configuration has been proposed.

Although not yet commercially viable, some aspects may form the basis of methanol

synthesis in the future. Two novel supported catalysts have been reported. ‘Raney


copper’ prepared by leaching ternary copper/zinc/aluminium alloys with strong

aqueous sodium hydroxide and ‘extremely active thorium compounds’. Future

developments of the conventional process are likely to be mainly capital savings and

improvements in energy efficiency. Catalysts of improved performance will doubtless

enable process designers to overcome chemical engineering constraints [iv].


3.6. Kinetic Models

Table 2. Important rate expressions for methanol synthesis [xxvii].


3.6.1. Natta et al (1953)

One of the earliest most influential works on methanol synthesis was that of Natta et al.

[xxviii]. His studies included measurements of the effects of composition, temperature

and pressure on methanol synthesis reaction rates. The kinetics of methanol synthesis

was studied in a continuous operating apparatus at temperatures between 300 and

400°C, pressure between 150 and 300atm and at different CO/H2 ratios in the feed

gases.

The surface reaction between one chemiadsorbed molecule of carbon monoxide and

two hydrogen molecules to produce one molecule of methanol chemiadsorbed on the

solid catalyst is the slowest intermediate step which controls the whole rate of reaction.

Natta’s wo k ep esents one of the widest anges of conditions in all published

methanol literature. Natta assumed that the rate-determining step was the trimolecular

reaction of carbon monoxide and hydrogen on the surface of the catalyst. From

experimental data, he expressed the correlation between reaction rate, fugacity of

components, and some constants (mainly depending upon the adsorption equilibrium

constants). That led to the correlation in equation (3.10) below.

/

( (3.10)

Where: r = rate of reaction, f = fugacity, Keq = equilibrium constant and A,B,C and D are

adsorption rate constants.

The established correlation allows calculating the quantity of methanol produced, as a

function of temperature, space velocity, and composition of feed gas [xxviii].

3.6.2. Rozovskii (1980) and Klier (1982)

Since Natta’s esea ch, catalysts have been imp oved continuously, esulting in

methanol synthesis plants that operate at lower pressures and temperatures. In recent

time, much kinetics have been proposed but unfortunately, difference in operating

conditions, catalyst used and feed gas composition has made it difficult to arrive at a

final conclusion on the kinetics and reaction mechanism.

The pioneering work by Natta has been expanded and improved by many other

researchers. Klier et al., [xxix] assumed that a small amount of carbon dioxide is


hydrogenated directly to methanol and the remaining carbon dioxide competes for

active sites on the surface of the catalyst with other reactants. They attempted to

formulate a mechanism and rate law encompassing all surface phenomena. The rate law

formulated based on those assumptions is given below:

/

(

k (p

) (3.11)

Where:

A is the rate constant,

pi is partial pressure of component i in atmospheres,

Keq is equilibrium constant for CO,

’eq is equilibrium constant for CO2,

kCO , kH2 , kCO2 are desorption and adsorption parameters.

This model is consistent with all the physical characteristics of the CuZnO catalysts and

supports earlier findings that an intermediate oxidation state of the catalyst is its active

state.

Based on the stoichiometry of equation (2.2), Rozovskii [xxx] contends that methanol

forms only via carbon dioxide hydrogenation and proposed the rate equation below:

(3.12)

According to Rozovskii’s mechanism, carbon dioxide also participates in the reverse

water-gas shift reaction as shown in equation (2.3) with the rate equation given below:

(3.13)

Values of rate constants A-D are still undetermined [xxx].

3.6.3. Agny and Takoudis (1985)

Using a U shaped fixed bed reactor and a CuO/ZnO/Al2O3 catalyst operated at a

pressure between 0.3 to 1.5Mpa and temperature between 523-563K, Agny and

Takoudis [xviii] made use of the Langmuir-Hinshelwood kinetic model, they proposed


that that the adsorbed CO molecule dissociatively adsorbs a hydrogen molecule to form

the formyl intermediate CHO- with H2/CO ratio of 0.5/1 which is present in the

( . term of the kinetic equation they came up with equation 3.14 below. n was

determined as -1.3 empirically.

k (P P

(P P

. (3.14)

Where:

K is reaction rate constant = 0.991*10-2 exp (-18330/RT)

Keq is the thermodynamic equilibrium constant of carbon monoxide

hydrogenation reaction (equation 2.1)

Pi is the partial pressure of component i in atmosphere,

n is empirical constant = 1.3 ± 0.03.

The CH-O intermediate was postulated to be the abundant surface intermediate. The

rate determining step was the surface reaction between the adsorbed hydrogen and

methoxy intermediate CH3O-. They also suggested that trace amount of carbon dioxide

detected at the reactor effluent stream was produced from the water gas shift reaction

(equation 3.3) and the redox reaction from the oxidised state to the reduced state of the

catalyst. A carbon dioxide free synthesis gas was used as feed; therefore no term

corresponding to carbon dioxide was incorporated in the rate equation.

The value of the pre-exponential factor and the overall activation energy at 523k are

13600 mol/(s atm gcat) and 34000 cal/gmol respectively [xviii].

3.6.4. Skrzypek's (1985 and 1991)

Skrzypek et.al (1985) [ xxxi ] carried out the Analysis of the low-temperature methanol

synthesis in a single commercial isothermal Cu-Zn-Al catalyst pellet using the dusty-gas

diffusion model. They came up with a rate equation of

kp . P

(1

) (3.15)


Where:

r is the rate of reaction,

k is the reaction rate constant = 0.830 exp (-23750/RT)

(3.16),

pi is partial pressure of component i in atmosphere and

keq = thermodynamic equilibrium constant.

In 1991, they further investigated the kinetics of methanol synthesis over commercial

copper/zinc oxide/alumina catalysts at a temperature between 187-277°C and pressure

between 30-90 bar. A wide range of parameters was applied, especially that of the inlet

concentrations of reactant. They concluded that methanol synthesis occurs from CO2

rather than from CO and that the basic reactions are:

CO2+3H2⇄CH3OH+H2O and CO2+H2⇄CO+H2O (3.17)

They also demonstrated experimentally that methanol cannot be formed from hydrogen

and carbon monoxide without the presence of water.

Langmuir-Hinshelwood mechanism where CO2 and H2 react on the surface with few

intermediate steps was used. The rate determining step came out to be

CO2* + H2 * ⇄ H2CO2* (3.18)

(* denotes adsorbed species). The resulting rate equations this time around based on

equation 2.2 and 2.3 are:

( (

)(

))

(3.19)

( (

)( ))

(3.20)

den 1 p p p p p (3.21)

This kinetic model is based on measurements on a deactivated catalyst, and the effect of

deactivation is not accounted for. Hence, the reaction rates are probably too slow [xxxi].


3.6.5. Lim (2009)

The theory by Klier et.al (1982) that copper is reduced or oxidised by the adsorption of

CO and CO2, suggests that there are different adsorption sites for CO and CO2. Analysing

published reports shows that there are conflicting viewpoints on the identity of the

active sites on Cu containing catalysts for the methanol synthesis. In most published

reports, CO hydrogenation (Equation 2.1) has been considered to be the most

significant reaction for methanol production. A possible reason for the difference in

results is that CO2 hydrogenation also occurs to some extent under certain reaction

conditions. To solve this problem, Lim et al., took into account the hydrogenation of

both CO and CO2 and studied the kinetics of methanol synthesis over

Cu/ZnO/Al2O3/ZrO2 catalyst that was developed and selected to evaluate the effect of

carbon dioxide on the reaction rates due to its high activity and stability.

A kinetic mechanism where CO and CO2 are assumed to adsorb on different sites of Cu

was suggested for the development of hydrogenation reaction rates, while hydrogen is

supposed to be adsorbed on the site of ZnO. Since each overall reaction is made up of

several elementary steps, they developed various rate determining steps and estimated

to find the best fit model for methanol synthesis by using experimental data. The

experimental data in their study suggested the augmentation of additional reactions

other than the three main reactions (Equation 2.1, 2.2 and 2.3).

The resulting rate equations from this study is given below.

Where : ln .

29.07 (3.26)

ln .

5.639 (3.27)

KPC = KPA * KPB (3.28)

(3.22)

(3.23)

(3.24)

(3.25)


KDME =0.106 exp ( .

(3.29)

Table 3. Elementary Reactions for Cu/ZnO/Al2O3/ZrO2 catalysed methanol synthesis [xxxii]


Table 4. Reaction rates for methanol synthesis reaction and DME production [xxvi].


3.6.6. Literature Review Conclusion

Three of the kinetic models developed by other researchers will be used to analyse the

experimental data provided for the kinetic modelling and reactor design for methanol

synthesis. Agny and Takoudis (1985), Skrzypek (1985) and lim (2009) kinetic model all

considered the hydrogenation of carbon monoxide as the main reaction for methanol

synthesis. The three selected kinetic models carried out the methanol synthesis over a

common catalyst (Cu/ZnO/Al2O3). Langmuir – Hinshelwood model was used by the

three researchers to deduce a rate law consistent with their experimental observation,

hence a Langmuir – Hinshelwood type of kinetics will be developed from the

experimental data provided in the brief (see appendix 1) and the results will be

compared to those from literature.

Table 5. Methanol synthesis kinetic models to be compared to developed kinetic model

Model Catalyst Used Rate Equation

Agny and Takoudis Cu/ZnO/Al2O3 (

(

.

Skrzypek Cu/ZnO/Al2O3

. (1

)

Lim Cu/ZnO/Al2O3/ZrO2

. (

)

(1 (1 .

.

CE4005 | Work Plan and Methodology 35

4. Work Plan and Methodology

After reviewing the details of other kinetics for methanol synthesis, the following tasks

will be completed.

4.1. To develop a kinetic model for the synthesis of methanol from the synthetic

rate data given in Appendix 1

The above will be carried out by deducing a rate equation consistent with the provided

experimental data using the Langmuir-Hinshelwood kinetics. From the rate equation

deduced, the dimension of the reactor will be determined using the design equation of a

plug flow reactor (PFR) and the given specification.

The kinetic modelling will be repeated, and this time the experimental data will be

incorporated into suitable kinetic models from literature. The rate of the reaction and

the weight of catalyst required which will be deduced and this will then be used to work

out the reactor dimension and other properties of the reactor including the catalyst bed

characteristics and the sensitivity to pressure drop.

4.1.1. Developing Langmuir-Hinshelwood Kinetic Model from Experimental Data

Langmuir – Hinshelwood model can be used to deduce a rate law consistent with

experimental observation. Combining surface reaction rate laws with the Langmuir

expression gives the Langmuir-Hinshelwood (LH) rate laws for surface catalysed

reactions [ix].

e.g. for the overall reaction: A B

Rate of reaction (-rA) = kθA (4.1)

Where: k = reaction rate constant and

θ , f action of the su face cove ed by adso bed species

(4.2)

Hence,

(4.3)

In terms of partial pressure, the rate expression (equation 5.4) becomes:

(4.4)


Where

(4.5)

ka is adsorption rate constant,

kd is desorption rate constant,

pi is partial pressure of component i ,

CA is gas composition of component A,

CB is gas composition of component B.

The following assumptions will be used to deduce rate law consistent with the

experimental data provided.

1. Surface reaction is first order.

2. Reaction is essentially irreversible.

Conclusion can be drawn from the rate of disappearance of H2, on the partial

pressure of hydrogen, carbon monoxide and methanol.

Analyse the experimental data to find dependence on the product methanol.

Analyse the experimental data to find dependence on carbon monoxide.

Analyse the experimental data to find dependence on hydrogen.

Deduce Langmuir-Hinshelwood type rate equation from the analysis above.

Find the kinetic parameters, k and K values.

4.1.2. Experimental Data Incorporated into Kinetic Model From Literature

Sample Model: Agny and Takoudis Kinetic Model

k (P P

(P P

. (4.6)

k = 0.991*10-2 exp (-18330/RT). (4.7)

Log10Keq = (3921/T) – 7.971 log10T + 0.002499 T – (2.953*10-7)T2 + 10.2

(dimensionless). (4.8)

rmethanol is rate of reaction,

k is reaction rate constant ,

Pi is the partial pressure of component i (atmosphere),

n is the empirical constant,


Keq is the thermodynamic equilibrium constant and

T is temperature.

For Adiabatic PFR , the energy balance can be written as:

[(

] (4.9)

For nonadiabatic PFR, the energy balance can be written as:

[(

] (4.10)

The design equation of a FBCR,

∫

(

(4.11)

Where:

Tad is adiabatic temperature rise,

T is reaction temperature,

TO is reactor inlet temperature,

Ts is surrounding temperature/temperature of coolant,

ΔHreaction = Heat of reaction

FA0 is molar flow,

is specific mass flow rate,

CP is specific heat of the system.

W is weight of catalyst,

XA is fractional conversion and

-rA is the rate of reaction.

The weight of the catalyst calculated by simultaneous numerical solution of the material

and energy balance will be used to calculate the reactor dimension by following the

steps below:

1. Choose a value of conversion, X.

2. Depending on the desired reactor set up, calculate T from equation 4.9 for adiabatic

and 4.10 for non-adiabatic.


3. Calculate the kinetic parameters k and Keq from equation 4.6 and 4.7. (Other kinetic

model will have different kinetic parameters).

4. Substitute the partial pressure, Pi values into the kinetic model rate equation

5. Calculate –rA (rate of reaction) using the kinetic model rate equation

6. Calculate

( (4.12)

7. Repeat step (1) to (6) for values of conversion X between 0 and 0.9

8. Calculate ∑ (4.13)

Where G* is the average of two successive values of G and is the increment.

9. Plot the results with temperature on the y-axis and conversion on the x-axis.


4.2. Simulating a Plant-Scale Catalytic Reactor

Using the kinetic model result obtained from section 4.1, the dimension of a catalytic

scale reactor will be determined.

Find FAo , CAo and which a e some of the values needed to find the eacto

dimension.

From the material balance, FAo = voCAo (4.14)

Space velocity = 10000m3/hr/m3 of reactor volume

Space velocity =

=

hence, =

(4.15)

= 10000m3/hr , = 1 * 10-4

V = 1m3

v =

v = 10000

2.78

PV = nRT (4.16)

P n

P = ΣPi (4.17)

and

= CAo (4.18)

Hence, CAo =

(4.19)

Composition: 70 mol% H2; 30 mol% CO; r.m.m H2 = 2 , CO = 28

[(mola composition (H2) * r.m.m (H2) * FAo)+( molar composition of CO * r.m.m of

CO * FAo)]/1000 (4.20)

where:

FAo is molar flow at reactor inlet,


vo is volumetric flow rate,

CAo is initial concentration; is residence time,

is specific mass flow ate; P is pressure,

Pi is partial pressure of component i; n is number of moles,

V is reactor volume,

R is molar gas constant and

T is temperature.

4.2.1. Reactor Volume

For the shell and tube reactor, assuming the catalyst bed occupies 1/3 of the reactor

volume i.e. 1/3VReactor = VCatalyst, i.e. the catalyst will occupy a third of the reactor

volume. Another third of the reactor volume will be occupied by the shell space and the

final third will be occupied by the space between the catalyst bed and the top and

bottom dome heads. This assumption will help to calculate the dimension of reactor

needed without too much complication.

The volume of the reactor will be determined from the catalyst weight using the

equation: VC = WC/ρC = 1/3VReactor (4.21)

Where:

VC is the volume of catalyst

WC is weight of catalyst,

ρC is the bulk density of catalyst,

VReactor is the volume of cylindrical section of reactor

om the volume, the eacto length, diamete and the catalyst bed’s cha acte istics can

be determined.

The total volume of reactor is the volume of cylindrical section + volume of dome

closures.

4.2.2. Reactor Length and Diameter

For a cylindrical vessel, the relationship between the length and the volume of a

cylinder is given as: VR =

(4.22)


Where:

VR = volume of the reactor

D = diameter of reactor

= length of reactor

(Note: The reactor volume does not include the volume occupied by the dome head

closures).

Total length of reactor = length of cylindrical section + length of hemispherical head

closure

Assumption

Assuming a diameter to length ratio (D : ) of 1:4

Hence: 4 (4.23)

The volume of the reactor can be rewritten as:

VR =

4 (4.24)

VR πD3 (4.25)

Rearrange to get D

D = √

(4.26)

4.2.3. Reactor Dome Closure

The reactor is cylindrical and there are four principal types of ends used for a cylindrical

vessel.

1. Torispherical heads.

2. Hemispherical heads.

3. Ellipsoidal heads.

4. Flat plates and formed flat heads.


The reactor has a top and bottom head closure, the choice of head closure used in this

design is the hemispherical type. These have been chosen as they can withstand very

high pressure, and since the reactor design pressure will be higher than the operating

pressure, it is viable to use this type of head closure [xxxiii].

The dimensions of hemispheres are very simple, since it is half of a circle; the radius

from the centre of the circle to all edges of the hemisphere will be the same.

Volume of hemispherical head closure =

(4.27)

There are 2 closures (top and bottom) so total volume of closures = 2 (

)

4.2.4. Catalyst Bed Characteristics

Shell and tube reactor consist of tubes packed with catalyst particles and operated in a

vertical position. The catalyst particles are of spherical shape. Feed is passed from the

top of reactor in to the tubes. The number of catalyst tubes required will be calculated

from the equation below.

N olume of catalyst bed/(

i. d Length of catalyst tube (4.28)

Diameter of the reactor D, = Catalyst bed diameter

Bed depth, L

(4.29)

Mass velocity, G

u ρ (4.30)

For a spherical particle, the effective particle diameter d’p= diameter of particle dp =

0.0381m

eynolds numbe , e

(4.31)

r r

h

CE4005 | Effect of Coolant Temperature 43

Pressure drop ( P

(4.32)

Friction factor, f [1.7 (

] (

(4.33)

Fluid density ρ (

)

(4.34)

Superficial linear velocity, u

(4.35)

4.3. Sensitivity to pressure drop

Calculate pressure drop, from equation 4.32

Choose values of around that calculated in the step above.

Calculate the bed depth, L for the selected from equation 4.17

Rearrange equation 4.20 to give (

(4.36)

Calculate the diameter from

√

(4.37)

Tabulate the result

Plot a graph of on the y-axis, Diameter and bed depth on the x-axis

Observe the trend in D and L as pressure drop increase or drop.

Draw a conclusion on the trend above.

4.4. Effect of Coolant Temperature

Due to the exothermic nature of the methanol synthesis reaction (CO + 2H2 CH3OH

ΔH298K = -90.64kJ/mol) there is a need to take out the heat of the reaction. Cooling

water can be used to take out the heat of the reaction. The temperature of the cooling

water required can be found graphically by following the steps below.

Find the equilibrium conversion, Xe from the equation:

(

( (4.38)

Where Ke is the thermodynamic equilibrium constant and T is the equilibrium

temperature.

CE4005 | Results and Discussion 44

Plot a graph of equilibrium conversion Xe and conversion X on the y-axis against

temperature, T on the x-axis.

The intersection of the equilibrium conversion as a function of temperature with

temperature-conversion relationships suggests a reasonable coolant

temperature for the shell side in order to achieve the equilibrium conversion.

4.5. Modelling with ASPEN Process Modelling Software.

ASPEN, process simulation software will be used to model the methanol synthesis

process. The reactor will be modelled as an adiabatic plug flow reactor. The reactor is

big and therefore will approach adiabatic regime without the need for special insulation

due to negligible heat loss. Rate of chemical reaction also governs this. The faster the

rate of the chemical reaction, the easier it is to obtain adiabatic regime.

The adiabatic reactor can be controlled by the inlet composition of the reaction mixture

and the inlet temperature (473K). The composition of the inlet mixture for the

methanol synthesis given in the specification sheet is 70mol% H2; 30mol% CO.

A kinetic model will be selected and modelled on ASPEN using the data for kinetic

analysis provided. The composition and the reactor inlet temperature will be varied in

order to test the performance of the reactor. A sensitivity analysis will also be carried

out to check the effect of feed temperature on methanol production.

4.6. Gantt Chart

An academic supervisor will monitor the progress of this project. A Gantt chart will be

used to monitor and control the progress of this project against the schedule. Time

management is important in order to provide a project that will be of good quality and

that will be delivered on time. A Gantt chart containing the project schedule has been

attached to appendix 5.

5. Results and Discussion

5.1. Developing a kinetic model from experimental data

From the experimental data provided in Table 6 below, a kinetic model will be

developed for methanol synthesis. “ he data we e gene ated fo the ove all eaction as

it would occur in a back mixed, gradient less, experimental reactor at realistic reaction


conditions. The final data set is from a statistically designed, central composite set of

simulated experiments, to which 5% random error was added. It comprises a total of 27

simulated esults”[xxxiv].

2H2 + CO CH3OH (5.1)

Feed gas composition: 70 mol% H2; 30 mol% CO.

Table 6. Data for Kinetic Analysis

Experiment Rate mol/m3.s

Temp (K)

Partial Pressure (kPa)

Methanol CO Hydrogen

1 6.573 495 1013 4052 8509

2 4.819 495 1013 4052 5906

3 6.27 495 1013 1530 8509

4 4.928 495 1013 1530 5906

5 10.115 495 253 4052 8509

6 7.585 495 253 4052 5906

7 9.393 495 253 1530 8509

8 7.124 495 253 1530 5906

9 1.768 475 1013 4052 8509

10 1.177 475 1013 4052 5906

11 1.621 475 1013 1530 8509

12 1.293 475 1013 1530 5906

13 2.827 475 253 4052 8509

14 2.125 475 253 4052 5906

15 2.883 475 253 1530 8509

16 2.035 475 253 1530 5906

17 4.03 485 507 2533 7091

18 3.925 485 507 2533 7091

19 3.938 485 507 2533 7091

20 10.561 500 507 2533 7091

21 1.396 470 507 2533 7091

22 2.452 485 1520 2533 7091

23 5.252 485 172 2533 7091

24 3.731 485 507 4862 7091

25 3.599 485 507 1276 7091

26 5.085 485 507 2533 9330

27 3.202 485 507 2533 5369

Langmuir – Hinshelwood model can be used to deduce a rate law consistent with

experimental observation. Combining surface reaction rate laws with the Langmuir


expression gives the Langmuir-Hinshelwood (LH) rate laws for surface catalysed

reactions [ix].

The following assumptions will be used to deduce rate law consistent with the

experimental data provided in Table 6 above.

Surface reaction is first order

Reaction can be assumed to be essentially irreversible

Conclusion can be drawn from the rate of disappearance of H2, on the partial

pressure of hydrogen carbon monoxide and methanol.

5.1.1. Dependence on the product methanol

If methanol is adsorbed on the surface of the solid catalyst, the partial pressure of

methanol would appear in the denominator of the rate expression. The resulting rate

equation will be in the form of [

.. (5.7)

i.e. rate is inversely proportional to methanol concentration.

Experiments 1-8:

4 fold decrease in methanol concentration (partial pressure) almost doubled the rate

(experiment 1 compared to 5) as shown in Table 7 below.

Table 7. Experiment 1 compared to experiment 5.

Experiment Rate

mol/m3.s

Temp

(K)



1 6.573 495 1013 4052 8509

5 10.115 495 253 4052 8509

This result suggests that methanol is adsorbed on the catalyst surface i.e.

[

. (5.8)


5.1.2. Dependence on Carbon Monoxide

Table 8. Experiments to deduce the dependence on carbon monoxide

Experiment Rate

mol/m3.s

Temp

(K)



1 6.573 495 1013 4052 8509

3 6.27 495 1013 1530 8509

5 10.115 495 253 4052 8509

7 9.393 495 253 1530 8509

Experiments 1 and 3, 5 and 7, 9 and 11 shows that almost 3 folds increase in the partial

pressure of carbon monoxide has little effect on the rate of the reaction. This suggests

that carbon monoxide is very weakly adsorbed or goes directly into gas phase.

i.e. 1 (5.9)

5.1.3. Dependence on Hydrogen

Experiments 1 and 2, 3 and 4, 5 & 6, 7 & 8, 9 & 10, 13 & 14, 15 & 16 shows that rate

decrease with decrease in the partial pressure of hydrogen when the partial pressure of

methanol and carbon monoxide is kept constant as shown on Table 9 below.

Table 9. Effect of decreasing the partial pressure of hydrogen on the rate of reaction.

Experiment Rate

mol/m3.s

Temp

(K)



1 6.573 495 1013 4052 8509

2 4.819 495 1013 4052 5906

This suggests that hydrogen is strongly adsorbed on the catalyst surface, hence

[

. (5.10)

Combining equations 5.8, 5.9 and 5.10 suggests that the rate law is of the form:

[

(5.11)

Equation 5.11 can be rewritten as:


[

whe e

(5.12)

Where:

is ate of disappea ance of hyd ogen ate of fo mation of methanol,

k is the methanol synthesis rate constant,

Pi is partial pressure of component i,

KM is methanol adsorption equilibrium constant and

is hydrogen adsorption equilibrium constant.

5.1.4. Finding k and K Values

The rate law deduced from the experimental data provided (equation 5.12) is given

below:

To evaluate the reaction rate constant, k and the rate law parameters and

Rearrange equation 5.12.

(5.13)

This can be re-written as:

(5.14)

(Equation of a straight line) (5.15)

Appropriate data points will be selected from the experimental data available on Table

6 to plot a graph of y against x

Where:

y

, P /P (5.16)

c

(5.17)


m

/

(5.18)

Since the reaction rate constant and adsorption parameters, Ki are functions of

temperature, they should be found at constant temperature.

To find k and at constant temperature, vary and keep constant.

Table 10. Constant hydrogen partial pressure for kinetic parameter

y-axis X-axis

T PH2/-rH2 PH2

(kPa)

PM

(kPa)

475 4812.783 8509 1013

475 3009.904 8509 253

y = 2.3722x + 2409.7

1

1 2409.7

y = 2.3722x + 2409.7

0

1000

2000

3000

4000

5000

6000

0 200 400 600 800 1000 1200

PH

2/-

r H2

PM

KM

Linear (KM)


1 1

2409.7 4.1 10

2. 7 1

2. 7

4.1 10

2. 7 4.1 10 9.84 10

To find k and at constant temperature, vary and keep constant.

Table 11. Constant methanol partial pressure for kinetic parameter

y-axis X-axis

T PH2/-rH2 PH2

(kPa)

PM

(kPa)

475 5249.229 8509 1013

475 4567.672 5906 1013

y = 0.2618x + 3021.3

y = 0.2618x + 3021.3

4500

4600

4700

4800

4900

5000

5100

5200

5300

0 2000 4000 6000 8000 10000

PH

2/-

r H2

KH2

KH2

Linear (KH2)


c 1

k2 021.

k2 1

021. . 1 10 mol kpa m s

m 0.2618 k2

0.2618

. 1 10

0.2618 . 1 10 8.67 10

The value of k will lie between k1 and k2, hence k = (k1 + k2)/2

k = (4.1 10 . 1 10 )/2 = .7 10 mol kpa m s

The spread sheet used for the calculation has been attached to the appendix.

5.2. Plant-Scale Catalytic Reactor Simulation

“ inetic models based on experimental data are being used more frequently in the

chemical industry for the design of catalytic reactors, but the modelling process itself

can influence the final reactor design and its ultimate performance by incorporating

different interp etations of e pe imental design into the basic kinetic models.”

The kinetic model developed above will be used to simulate a plant scale catalytic

reactor using the specified reaction conditions, thermodynamic and physical data

provided below [xxxiv].

Reactor:

Type: Shell and tube

Tubes: 3000; 38.1 mm i.d * 12m

Coolant: boiling water is on shell side; assume coolant temperature constant at 483K

Overall heat transfer coefficient, U assumed to be 631 W/m2K

Catalyst Description:


Shape: Approximately spherical

Diameter: 2.87mm

Effective catalyst bed void fraction: 40%

Diffusional resistance: may be ignored

Process Conditions:

Feed gas:

Composition: 70 mol% H2; 30 mol% CO

Space velocity: 10,000 standard cubic meters per hour per cubic meter of reactor

volume.

Reactor inlet pressure: 10.13 MPa

Reactor inlet temperature: 473K

Reactor coolant temperature: 483K (constant)

Physical property and thermodynamic information:

Prandtl number of gas: 0.70 (assume constant)

Heat capacity of gas: 29.31 J/g mol.K (assume constant)

Heat of reaction: -97.97 kJ/mol methanol formed

Thermodynamic equilibrium constant: (T in K)

Log10Keq = (3921/T) – 7.971 log10T + 0.002499 T – (-2.953*10-7)T2 + 10.2

(dimensionless).

The reactor will be simulated using a simple one-dimensional, plug-flow, pseudo


The continuity equation for a pseudo homogeneous, one-dimensional plug flow is:

(

( 0


In terms of fractional conversion XA:

since

(1

( ( )

(

0

Where:

U is linear velocity,

CA is concentration,

v0 is volumetric flow,

FA is final molar flow ,

FAo is inlet molar flow,

XA is fractional conversion of A,

-rA is rate of reaction,

ρB is bulk density of the bed,

r is reactor cylindrical section radius,

But, ρ ρ π and d

So,

( 0 or w ∫

(

(design equation for an FBCR pseudo

homogeneous 1-dimensional plug flow).

The design equation for an FBCR is of the same form as equation for the volume V of a

PFR ( ∫

) [xxxiv].

Since (-rA) depends on temperature as well as on fA0, energy equation is needed in

addition to the continuity equation in order to obtain the weight (W). Effect of pressure

drop is neglected in obtaining W, because the pressure drop is usually relatively small.

However the pressure drop is important in determining the vessel diameter and bed

depth from the catalyst weight W [viii].


Using experiment 12 as an example,

From the material balance, FAo = voCAo

Space velocity =

=

hence, =

= 10000m3/hr , = 1 * 10-4

V = 1m3

=

= 10000

2.78

CAo =

. 21 9.4 /

FAo = voCAo = 2.78

21 9.4 / = 5947.66mol/s

Composition: 70 mol% H2; 30 mol% CO; r.m.m H2 = 2 , CO = 28

[(0.7*2* 5947.66) + (0.3*28* 5947.66)]/1000 = 58.28 kg/s

The values of VO , CA0, FA0 and fo e periment 1-27 are tabulated below.


Table 12. Experimental data table modified to include values of VO , CA0, FA0 and

Expt Rate (mol/m3.s)

T (K)

Pi (atm) Pi (Pa) Σpi (pa

Vo (m3/s)

CA0 (mol/m3) FA0

CH3OH CO H2 CH3OH CO H2

1 6.573 495 9.99 39.99 83.97 1013000 4052000 8509000 13574000 2.78 3298.32 9169.33 89.85

2 4.819 495 9.99 39.99 58.28 1013000 4052000 5906000 10971000 2.78 2665.82 7410.98 72.62

3 6.27 495 9.99 15.09 83.97 1013000 1530000 8509000 11052000 2.78 2685.50 7465.69 73.16

4 4.928 495 9.99 15.09 58.28 1013000 1530000 5906000 8449000 2.78 2053.00 5707.36 55.93

5 10.115 495 2.49 39.99 83.97 253000 4052000 8509000 12814000 2.78 3113.65 8655.94 84.82

6 7.585 495 2.49 39.99 58.28 253000 4052000 5906000 10211000 2.78 2481.15 6897.59 67.59

7 9.393 495 2.49 15.09 83.97 253000 1530000 8509000 10292000 2.78 2500.83 6952.31 68.13

8 7.124 495 2.49 15.09 58.28 253000 1530000 5906000 7689000 2.78 1868.34 5193.97 50.90

9 1.768 475 9.99 39.99 83.97 1013000 4052000 8509000 13574000 2.78 3437.19 9555.40 93.64

10 1.177 475 9.99 39.99 58.28 1013000 4052000 5906000 10971000 2.78 2778.07 7723.02 75.68

11 1.621 475 9.99 15.09 83.97 1013000 1530000 8509000 11052000 2.78 2798.58 7780.04 76.24

12 1.293 475 9.99 15.09 58.28 1013000 1530000 5906000 8449000 2.78 2139.45 5947.66 58.28

13 2.827 475 2.49 39.99 83.97 253000 4052000 8509000 12814000 2.78 3244.75 9020.40 88.39

14 2.125 475 2.49 39.99 58.28 253000 4052000 5906000 10211000 2.78 2585.62 7188.02 70.44

15 2.883 475 2.49 15.09 83.97 253000 1530000 8509000 10292000 2.78 2606.13 7245.04 71.00

16 2.035 475 2.49 15.09 58.28 253000 1530000 5906000 7689000 2.78 1947.0 5412.67 53.04

17 4.03 485 5.00 24.99 69.98 507000 2533000 7091000 10131000 2.78 2512.47 6984.66 68.45

18 3.925 485 5.00 24.99 69.98 507000 2533000 7091000 10131000 2.78 2512.47 6984.66 68.45

19 3.938 485 5.00 24.99 69.98 507000 2533000 7091000 10131000 2.78 2512.47 6984.66 68.45

20 10.561 500 5.00 24.99 69.98 507000 2533000 7091000 10131000 2.78 2437.09 6775.12 66.39

21 1.396 470 5.00 24.99 69.98 507000 2533000 7091000 10131000 2.78 2592.65 7207.58 70.63

22 2.452 485 15.00 24.99 69.98 1520000 2533000 7091000 11144000 2.78 2763.69 7683.06 75.29

23 5.252 485 1.69 24.99 69.98 172000 2533000 7091000 9796000 2.78 2429.39 6753.70 66.19

24 3.731 485 5.00 47.98 69.98 507000 4862000 7091000 12460000 2.78 3090.06 8590.35 84.19

25 3.599 485 5.00 12.59 69.98 507000 1276000 7091000 8874000 2.78 2200.74 6118.04 59.96


Experimental 12 data (in bold on Table 12) was used to simulate the plan-scale catalytic reactor.

26 5.085 485 5.00 24.99 92.07 507000 2533000 9330000 12370000 2.78 3067.74 8528.31 83.58

27 3.202 485 5.00 24.99 52.98 507000 2533000 5369000 8409000 2.78 2085.42 5797.46 56.82


The rate law deduced from the experimental data provided (equation 5.12) is given

below:

Assuming conversion X is 90% = 0.9,

∫

(Design equation for a PFR)

[

0.90

Table 13. Experiment 12 reaction conditions 1

To (K) H (kJ/mol Fao (mol/s) (kg/s Cp (kJ/Kg mol.K

475 97.97 5947.66 58.28 29.31

Table 14. Experiment 12 reaction conditions 2

PH2

(kpa)

PM

(kpa)

k

(mol kpa-1 m-3 s-1)

KH2 KM U

(W/m2)

h

(m)

Ts

(K)

∏

5906 1013 0.00037 8.66514E-05 0.00098 631 12 483 3.1415

Sample calculation (X= 0.9) :

.

. . 0.877982 mol/m3.s

[

.

. 0.9 6096.82m

Values of X between 0 and 0.9 were tabulated in order to see the volume needed at

different conversions and the reaction temperature for adiabatic and non-adiabatic

setup. The results are tabulated on Table 15 below.


Table 15. Reactor volume and temperature profiles for adiabatic and non-adiabatic setup at conversion between 0 and 0.9

X -rH2(mol/m3.s) V(m3) Adiabatic T (K) Non-Adiabatic T(K)

0 0.88 0 475 483

0.1 0.88 677.42 509.10 485.04

0.2 0.88 1354.85 543.22 487.08

0.3 0.88 2032.27 577.32 489.12

0.4 0.88 2709.69 611.43 491.16

0.5 0.88 3387.12 645.54 493.19

0.6 0.88 4064.54 679.65 495.23

0.7 0.88 4741.97 713.75 497.27

0.8 0.88 5419.39 747.86 499.31

0.9 0.88 6096.82 781.97 501.35

For adiabatic PFR, the energy balance can be written as:

[(

] 47 [

( . .

. . ] 0.9 781.97

For non-adiabatic PFR, the energy balance can be written as:

[(

] 48 [

( . .

( ( . . ] 0.9 01. K

Where:

Tad is adiabatic temperature rise (K),

T is reaction temperature (K),

TO is reactor inlet temperature (K),

Ts is surrounding temperature/temperature of coolant (K),

ΔHreaction is Heat of reaction (kJ/mol)

FA0 is molar flow (mol/s),

is specific mass flow rate (kg/s),

CP is specific heat of the system (J/g mol.K)

XA is fractional conversion,

-rH2 is rate of reaction (mol/m3.s)

V is the volume of reactor (m3)

U is the heat transfer coefficient (w/m2.K)


h is the height of the catalyst bed (m)

Figure 10. Reaction temperature profile of adiabatic and non-adiabatic set up at conversion between 0 and 0.9

The adiabatic temperature rise is one of the most important characteristics of a reaction

mixture. It is the temperature difference by which the reaction mixture would increase

if the mixture reacted adiabatically from zero to unit degree of conversion. The graph

above shows that for the adiabatic configuration, the temperature increases with

conversion down the length of the reactor as expected for an adiabatic PFR when the

reaction is exothermic. There is no heat exchange device in the adiabatic configuration

so the heat released by reaction will be absorbed by the reaction mixture (no heat

exchange with the surroundings) which is what lead to the temperature increase.

For the non-adiabatic configuration, the temperature down the length of the reactor

remains constant. This can achieved by using a cooling medium which takes out the

heat generated from the exothermic reaction (equation 2.1).

5.2.1. Reactor Dimension

To get a reactor dimension in the specified range, the reactor volume in Table 15 above

will be scaled down by 60.

The new reactor volume will be 6096.82/60 = 101.61m3.

0

100

200

300

400

500

600

700

800

900

0 0.2 0.4 0.6 0.8 1

Rea

ctio

n T

emp

erat

ure

(K

)

Conversion

Graph of Reaction Temperature Against Conversion

Adiabatic

Nonadiabatic


Table 16. Summary of reactor cylindrical section dimension

Reactor Cylindrical Section Dimension

Reactor

Volume(m3)

Catalyst bed

Volume (m3)

Reactor

Diameter (m)

Reactor

Length (m)

Catalyst bed diameter

(m)

101.61 33.87 3.19 12.76 3.19

Assumptions

Diameter to length ratio (D : l) of 1:4; Hence l 4D

The catalyst bed occupies 1/3 of the reactor volume.

VCatalyst = 1/3VReactor = 1/3 * 101.61 = 33.87m3

For a cylindrical vessel, V = πD2L/4

(Note: The reactor volume does not include the volume occupied by the dome head

closures).

Given that the reactor is cylindrical, the volume of the reactor was calculated to be

101.61 m3

From this, the length of the reactor can be calculated. The relationship between the

length and the volume of a cylinder is given as: VR =

l

Where:

VR = volume of the reactor

D = diameter of reactor

l = length of reactor

The volume of the reactor can be rewritten as:

VR =

4D

VR πD3

Rearrange to get D


Diameter of the reactor, D = √

= √

.

= 3.19m

Length = 4D.

Hence length of the reactor l = 4*3.19 = 12.76m (cylindrical section)

5.2.1.1. Reactor Dome Closure

The reactor has a top and bottom head closure, the choice of head closure used in this

design is the hemispherical type. These have been chosen as they can withstand very

high pressure, and since the reactor design pressure will be higher than the operating

pressure, it is viable to use this type of head closure [xxxv].

The dimensions of hemispheres are very simple, since it is half of a circle; the radius

from the centre of the circle to all edges of the hemisphere will be the same. The reactor

diameter was calculated earlier to be 3.19 metres; hence the radius of the hemisphere

will be 1.595 metres. The dimension of the hemispherical head closure is shown below

accordingly.

Figure 11. Reactor hemispherical dome closure dimension

Volume of Hemisphere =

r = 1.595m

Volume of hemispherical head closure =

(1. 9 = 8.49m3

There are 2 closures (top and bottom) so total volume of closures = 8.49 m3 * 2 = 16.98

m3

The total volume of reactor = volume of the cylindrical section + volume of dome

closure = 101.61m3 +16.98 m3 = 118.59m3


Length of cylindrical section = 12.76m

Length of hemispherical head = (1.595+1.595)m = 3.19m

Total length of reactor = length of cylindrical section + length of hemispherical head

closures = (12.76+3.19) m = 15.95m.

Table 17. Summary of overall rector dimension

Reactor Dimension (Cylindrical section and Closure)

Reactor Volume(m3)

Catalyst bed Volume (m3)

Reactor Diameter (m)

Reactor Length (m)

Catalyst bed diameter (m)

118.59 33.87 3.19 15.95 3.19

The preliminary dimension of the plant-scale catalytic reactor is shown in Figure 12

below. The specification sheet stated that the length of the catalyst tube is 12m, the

reactor cylindrical section is 12.76m and will therefore be able to fit the catalyst tubes.

Figure 12. Preliminary dimension of the plant-scale catalytic reactor


5.2.1.2. Catalyst Bed Characteristics

5.2.1.2.1. Catalyst Weight

Assuming a Cu/ZnO/Al2O3 catalyst is used, The bulk density, ρb of the catalyst is 1100

kg/m3 [xxxvi ]

WC = VC * ρb = 33.87 m3 * 1100 kg/m3 = 37257kg

Where: WC is weight of catalyst; VC is volume of catalyst and ρb is the catalyst bulk

density.

5.2.1.2.2. Number of tubes required for the catalyst

N olume of catalyst bed/(

i. d Length of catalyst tubes

N .87

π4 0.0 8

12 2489 tubes

5.2.1.2.3. Bed Depth

Weight of catalyst, Wc = 37257kg

Diameter of the reactor (D) = Catalyst bed diameter= 3.19m,

atalyst bulk density, ρ 1100kg/m3

Bed depth, L

. 4.2 m

5.2.1.2.4. Mass Velocity

Mass velocity, G

.

. 7.29 kgs m

5.2.1.2.5. Reynolds Number

For a spherical particle, the effective particle diameter, d’p= diameter of particle, dp =

0.00287m [ix]

e d G

0.00287 7.29

1.6 10 1 08

Re < 2000 hence the flow will be laminar and the profile of velocity will be parabolic.

5.2.1.2.6. Pressure Drop

Pressure drop ( P


Friction factor, f [1.7 (

] (

[1.7

( .

] ( .

. 17.0

Fluid density ρ (

)

P = inlet pressure = 10.13*106pa

= 756.86 kg/s

FA0 = 77230.2 mol/s

R = 8.314 J/mol/K

T = 473K

ρ 10.1 10 (

8.28 947.66

)

8. 14 47 2 .24 kgm

G u ρ

u G

ρ 7.29

2 .24 0.29ms

Hence, Pressure drop ( P . . . .

. 467.97pa = 0.53 bar

Table 18. Summary of catalyst bed characteristics.

Catalyst Bed Characteristics

Catalyst

Weight (kg)

Catalyst bed

depth, L (m)

ρb (kg/m3) No. of tubes

Nt

dp ρf

37257 4.25 1100 2489 0.00287 25.24

Mass Velocity,

G (kg/m2.s)

Reynolds

Number, Re

Friction

factor, f

Superficial

linear

velocity

u (m/s)

Pressure

drop (Pa)

Pressure

drop

(bar)

7.29 1308 17.05 0.29 53467.97 0.53


5.2.1.2.6.1. Sensitivity to pressure drop

The sensitivity of the reactor dimension to a given pressure drop can be used for

operating power cost and vessel cost studies. Therefore a sensitivity analysis will be

carried out for the rector dimension obtained from the plant-scale catalytic reactor

simulation.

Pressure drop, ( P

Bed depth, L (

. .

. . . 4.2 m

D

D √

√

. .18m

Ranges of pressure drop have been selected around the calculated pressure drop. The

sensitivity result is tabulated in Table 19 below.

Table 19. Reactor dimension sensitivity to pressure drop

Pressure drop

(Pa)

Bed Depth

L (m)

D^2 Diameter

D (m)

10000 0.795122107 54.23839605 7.364672162

20000 1.590244214 27.11919802 5.207609627

30000 2.385366321 18.07946535 4.251995455

40000 3.180488428 13.55959901 3.682336081

53467.97 4.251356496 10.14409114 3.184978985

60000 4.770732642 9.039732675 3.00661482

70000 5.565854749 7.748342293 2.783584432

80000 6.360976856 6.779799506 2.603804813

Figure 13 below shows the sensitivity of the reactor dimension to pressure drop.

Diameter (D) decreases and the bed depth (L) increases. This suggests that for a given

amount of catalyst, a reduced pressure drop can be obtained by reducing the bed depth

at the expense of increasing the bed diameter. Although reducing the pressure drop will

reduce the operating power cost, it will increase the vessel cost.


Figure 13. Reactor dimension sensitivity to pressure drop

5.3. Experimental Data Incorporated Into Kinetic Models from Literature

As discussed under the conclusion section of the literature review, the experimental

data provided for the kinetic analysis of methanol (table 5) synthesis was tested on

three kinetic models from literature that only deals with the hydrogenation of carbon

monoxide, used similar catalyst (Cu/ZnO/Al2O3), follow the Langmuir-Hinshelwood

model and therefore do not have a CO2 adsorption term in their final kinetic rate

equation like the others suggested in literature. The aim is to identify which kinetic

model will fit best with the experimental data and the developed kinetic model in order

to be able to find more of the properties of the simulated reactor.

Table 20. Methanol synthesis kinetic models and rate equation

Model Catalyst Used Rate Equation

Developed kinetic

model

Cu/ZnO/Al2O3

(assumed)

k P 1 P P

Agny and Takoudis Cu/ZnO/Al2O3 k (P P

P

(P P

.

Skrzypek Cu/ZnO/Al2O3 kp

. P (1

P

k P P )

Lim Cu/ZnO/Al2O3/ZrO2

. (P P

P

)

(1 P (1 . P

. P

0

20000

40000

60000

80000

100000

0 2 4 6 8

Pre

ssu

re d

rop

(p

a)

Bed Diameter, Depth (m)

Graph of pressure drop against Diameter and Depth of bed

Diameter

Bed depth


Table 21. Comparison of kinetic model simulation results.

Developed Kinetic Model

Kinetic Models from literature Adiabatic

Kinetic Models from literature Non-Adiabatic

Agny and Takoudis

Skrzypek Lim Agny and Takoudis

Skrzypek Lim

Scaling factor to meet specification - 50 500 1000 100 750 800 Catalyst Weight (kg) 37257 39377 37875 37977 38626 38859 38304 Catalyst Bed Volume (m3) 33.87 35.79 34.43 34.52 35.11 35.33 34.82 Reactor Volume excluding dome closure (m3)

101.61 107.39 103.29 103.57 105.34 105.98 104.46

Reactor Length (m3) 12.76 12.98 12.81 12.83 12.89 12.92 12.86 Reactor Diameter (m3) 3.19 3.25 3.20 3.20 3.22 3.23 3.22 Catalyst Bed Depth (m) 4.25 4.33 4.27 4.28 4.29 4.31 4.29 Number of catalyst tubes 2500 2600 2500 2500 2600 2600 2500 Mass velocity (kg/m2.s) 7.29 7.05 7.23 7.22 7.14 7.10 7.18 Reynolds number 1308 1264 1297 1295 1280 1275 1287 Pressure drop (bar) 0.53 0.51 0.53 0.52 0.52 0.51 0.52

Number of catalyst tube (Nt) is approximated to the nearest hundred and other values in Table 21 above are rounded up to two decimal

places where appropriate (non-rounded figures are available in the appendix).


Experiment 12 data (see Table 13 and Table 14) was used to simulate a plant scale

catalytic reaction at the specified reaction conditions, thermodynamic and physical

property.

The Agny and Takoudis kinetic model came out to be the best fit with the experimental

data as it required the least scaling factor (*50) in order to be similar to the results from

the simulation using the developed kinetic model. Agny and Takoudis model will

therefore be examined in detail and used later for Aspen modelling. The full results from

Skrzpek and Lim kinetic model can be found in appendix 6.

Using experiment 12 from the provided kinetic data, and following the steps in the

methodology (section 4.1.2), the kinetic simulation using the Agny and Takoudis kinetic

model is given in Table 22 below. The catalyst bed characteristics and sensitivity to

pressure drop will not be shown here as they are similar to those calculated in chapter

5.2 above (same trend and therefore same justification) but have been attached to

appendix 6. Values in Table 22 have been rounded up to two decimal place where

appropriate and therefore slightly differs from the corresponding table in the appendix.


Table 22. Summary of Agny and Takoudis model for an adiabatic reactor using the provided experimental data

Table 22 shows the evaluation of the kinetic parameters which was used to calculate the weight of catalyst required. The results from

this table will be used to investigate the effect of conversion on the adiabatic temperature rise and the rate of reaction. A maximum rate

was observed at a conversion of 0.4. After a conversion of 0.6, the rate started to become negative which means there is a shift in

equilibrium which favours the backward reaction of equation 2.1 (carbon monoxide hydrogenation).

To (K) H (kJ/mol FA0 (mol/s) (kg/s)

Cp (kJ/Kg mol.K)

PCO

(atm) PH2 (atm) PCH3OH (atm) R

(J/mol/K)

475 97.97 5947.66 58.29 29.31 39.99 83.98 2.49 8.314

XA Tad (K)

k [mol/(s atm gcat)]

log10Keq Keq rmethanol

(mol/(gcat s) G (g)

G* (g)

G* (g G* (kg Xe

0 475 9.56E-05 -1.76 0.017 0.013 475600.1 0.89

0.1 509 0.00013 -2.48 0.003 0.017 349246.6 412423.32 41242.332 41.24 0.63

0.2 543 0.00017 -3.11 0.0007 0.022 268466.3 308856.44 30885.644 30.89 0.29

0.3 577 0.00022 -3.68 0.0002 0.027 217945.1 243205.69 24320.569 24.32 0.11

0.4 611 0.00027 -4.18 6.61E-05 0.031 194828.5 206386.77 20638.677 20.64 0.04

0.5 646 0.00033 -4.63 2.32E-05 0.026 225302.9 210065.7 21006.57 21.01 0.01

0.6 680 0.00039 -5.04 9.02E-06 0.00092 6468631 3346966.9 334696.69 334.69 0.0060

0.7 714 0.00045 -5.42 3.81E-06 -0.078 -76068 3196281.4 319628.14 319.63 0.0027

0.8 748 0.00052 -5.76 1.74E-06 -0.279 -21313.9 -48690.98 -4869.0979 -4.867 0.0013

Catalyst Weight : ∑ 787.55


Sample Calculation

Following the steps in the methodology for a chosen conversion of 0.5 (in bold on

Table 22) and experiment 12 data,

Adiabatic temperature rise, [(

] 47 [

( . .

. . ]

0. 646

k = 0.991*10-2 exp (-18330/RTad) = 0.991*10-2 exp (-180330/8.314 * 646) =0.00033

mol/(s atm gcat)

Log10Keq = (3921/646) – (7.971* log10646) + (0.002499 *646) – (2.953*10-7)* 6462 +

10.2 = -4.63

Keq = 10-4.63 = 2.3*10-5

k (P P

(P P

. 0.000 ( 9.9 8 .98 – .

. ( 9.9

8 .98 . . = 0.026 mol/(gcat.s).

G

( .

. 2287 6.1 g

The catalyst weight, W is calculated from equation 4.13.

∑

Where G* is the average of two successive values of G and is the increment.

Note : The differences in value is as a result of approximation used in the table above.

non approximated values are in the tables available in the appendix.


0

0.1

0.2

0.3 0.4

0.5

0.6 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 0.5 1

rate

(m

ol/

(gca

t s)

conversion

Rate vs Conversion

Rate vsConversion

0

200

400

600

800

0 0.2 0.4 0.6 0.8 1

Tem

per

atu

re (

K)

Conversion

Graph of Adiabatic Temperature Rise Against Conversion

T Vs X

In exothermic reactions, increasing the degree of conversion decreases the concentration of the reactants while the concentration of the

product increases, this leads to a decrease in the rate of reaction as shown in Figure 14 above. On the other hand, because the heat of

reaction is being absorbed by the reaction mixture, temperature increases with increase in the degree of conversion as shown on Figure

15 and thereby enhances the reaction. These opposite influences lead to the maximum observed on Figure 14 above. At low

conversions, the reaction rate increases with the degree of conversion. On the other side of the maximum, the reaction rate decreases

with the degree of conversion because the controlling effect is that of the shortage of reactants in the reaction mixture. Increase in

temperature can no longer offset the shortage of reactants at these high degrees of conversion.

Figure 15. Relationship between temperature and degree of conversion in the adiabatic reactor.

Figure 14. Reaction rate as a function of degree of conversion in the adiabatic reactor.


Table 23. Summary of Agny and Takoudis model for non-adiabatic reactor setup using the experimental data provided

To (K) Ts (K) H (kJ/mol Fao (mol/s) (kg/s Cp (kJ/Kg mol.K) PCO (atm) PH2 (atm) PCH3OH (atm) R (J/mol/K) U (W/m2)

475 483 97.97 5947.66 58.29 29.31 39.99 83.9 2.49 8.314 631

h ∏

12 3.142

XA T (K) k [mol/(s atm gcat)] log10Keq Keq Rate (mol/(gcat s)

Rate (mol/(kgcat s)

G (g) G* (g) G* (g G* (kg

0 483 0.000103 -1.94 0.012 0.0135 1.35E-05 440520.1

0.1 483.6 0.000104 -1.95 0.011 0.0135 1.36E-05 437945.7 439232.9 43923.29 43.92

0.2 484.2 0.000104 -1.96 0.010 0.0137 1.37E-05 435393.2 436669.4 43666.94 43.67

0.3 484.9 0.000105 -1.98 0.010 0.0137 1.37E-05 432862.5 434127.8 43412.78 43.41

0.4 485.5 0.000106 -1.992 0.010 0.0138 1.38E-05 430353.2 431607.8 43160.78 43.16

0.5 486.1 0.000106 -2.005 0.0099 0.0139 1.39E-05 427865.3 429109.2 42910.92 42.91

0.6 486.7 0.000107 -2.018 0.0095 0.0139 1.39E-05 425398.4 426631.8 42663.18 42.66

0.7 487.4 0.000108 -2.032 0.0092 0.0141 1.41E-05 422952.4 424175.4 42417.54 42.42

0.8 487.9 0.000108 -2.045 0.0090 0.0141 1.41E-05 420527 421739.7 42173.97 42.17

0.9 488.6 0.000109 -2.058 0.0087 0.0142 1.42E-05 418122 419324.5 41932.45 41.93

Catalyst Weight: ∑ 386.26


0

100

200

300

400

500

600

0 0.2 0.4 0.6 0.8 1

Tem

per

atu

re (

K)

Conversion

Graph of Non-Adiabatic Temperature Against Conversion

T vs X

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0 0.5 1

rate

(m

ol/

(gca

t s)

conversion

Rate vs Conversion

Rate vs Conversion

Unlike in the adiabatic reactor where there is no heat loss to the surrounding, non-adiabatic reactors have heat exchange devise which

helps to take out the heat of reaction. A cooling medium can be used to maintain the heat of reaction and hence keep the temperature in

the reactor constant as the reacting mixture will not absorb the heat produced from the reaction. The temperature will be constant

down the length of the reactor as suggested by Figure 16 and this will also keep the rate of the rate of reaction constant because the rate

of reaction is a function of the degree of conversion and temperature. See Figure 17. At higher conversion, the rate of reaction is greater

in the non-adiabatic setup than in the adiabatic set up.

Figure 16. Reaction rate as a function of degree of conversion in the non-adiabatic reactor.

Figure 17. Relationship between temperature and degree of conversion in the non-adiabatic reactor.


5.4. Effect of Coolant Temperatures

Understanding the effect of coolant temperatures can be used to suggest a cooling water

temperature for the methanol synthesis. In the construction of adiabatic reactors, there

is no need for heat exchange equipment between the mixture and a coolant; adiabatic

reactors therefore usually need an auxiliary heat exchanger to control the temperature

of the feed mixture before it enters the reactor. The highest conversion that can be

achieved in reversible reactions is the equilibrium conversion [viii]. For exothermic

reactions, the equilibrium conversion decreases with increasing temperature. For an

adiabatic reactor set up, the maximum conversion of an exothermic reaction can be

determined by finding the intersection of the equilibrium conversion as a function of

temperature with temperature-conversion relationships from the energy balance as

shown in Table 24 below. Using the results from Table 22, the equilibrium conversion Xe

was calculated from equation 4.38.

(

( .

Table 24. Results table for temperature-conversion relationship.

Sample Calculation

At a fractional conversion XA = 0.5,

(

(

.

. = 0.01

Table 24 above shows that as the inlet temperature increase due to the adiabatic

temperature rise, the adiabatic equilibrium conversion decreases. The results are

plotted on the graph in Figure 18 below.

XA Tad (K)

Keq Xe

0 475 0.017 0.89

0.1 509 0.003 0.63

0.2 543 0.0007 0.29

0.3 577 0.0002 0.11

0.4 611 6.61E-05 0.04

0.5 646 2.32E-05 0.01

0.6 680 9.02E-06 0.0060

0.7 714 3.81E-06 0.0027

0.8 748 1.74E-06 0.0013


Figure 18. Plot of equilibrium conversion as a function of temperature.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600 700 800

Xe

q, X

Temperature (K)

Graph of Equilibrium Conversion Against Temperature

Xe against T

X against T


Figure 18 shows that for a feed temperature of 475K, the adiabatic temperature

equilibrium is about 550K and the equilibrium conversion is 23% therefore a cooling

water temperature of 550K will be required on the shell side of the reactor to keep the

reaction at the equilibrium conversion (highest conversion that can be achieved) .

Cooling the feed down to 400K will shift the energy balance line to the left and increase

the equilibrium conversion. Interstage cooling can be used to achieve higher

conversions.

Figure 19. Interstage cooling [xxxvii].

Interstage cooling can be used to get the best result from the reaction rate and reactant

conversion. Conversion is much less at lower temperature, this means catalyst mass and

volume must be much greater. It is very expensive to operate reactors at high

temperature and pressure, so smaller volume of reactor will be cost effective. The

cooler allows the temperature during a reaction to drop whilst not affecting the

pressure or the stream composition. This significant property is a good way of

increasing conversion and maximising productivity without an increase in overall

reactor volume [xxxvii].

5.5. Modelling with ASPEN Process Modelling Software

Using the thermodynamic and physical property data provided in the brief as well as

results from the reactor simulation from the developed kinetic rate equation, an

adiabatic reactor was modelled on ASPEN. The PSRK property method was selected as

it is suitable for reversible exothermic reactions at high temperature and pressure such

as the methanol synthesis reaction. The reactor model summary is provided below.


Figure 20. Reactor model summary

The flow sheet and the stream results from the simulation for a feed composition of

70% H2 and 30% CO entering the reactor at 473K (200 C) is given below.


Figure 21. Flow sheet with heat and material balance for ASPEN simulation at a feed inlet temperature of 473K (200 C)

An adiabatic reactor can be controlled by either the composition of the feed or the feed

temperature. Varying the composition showed that a feed composition of 70% H2 and

30% CO is optimum for methanol synthesis under the specified conditions. A conversion

of 29% was achieved (mole flow of methanol produced/ mole flow of feed *100 =

[{6238.968/21412.800} *100]) the results of varying the feed composition and the

temperature and composition profile resulting from such variation has been attached to

the appendix. In order for the reaction to occur, the molar composition of H2 must

always be greater than that of CO following from the stoichiometry of equation 2.1

(carbon monoxide hydrogenation).

PFRB2 B3

1 2 3 4

Heat and Material Balance Table

Stream ID 1 2 3 4

Temperature C 199.8 199.8 1182.7 1182.7

Pressure bar 101.300 101.300 101.300 100.800

Vapor Frac 1.000 1.000 1.000 1.000

Mole Flow kmol/hr 21412.800 21412.800 8934.864 8934.864

Mass Flow kg/hr 210150.271 210150.271 210150.271 210150.271

Volume Flow cum/hr 8977.323 8977.323 11067.410 11120.577

Enthalpy Gcal/hr -142.218 -142.218 -142.218 -142.218

Mole Flow kmol/hr

CO 6423.840 6423.840 184.872 184.872

H2 14988.960 14988.960 2511.024 2511.024

CH4O 6238.968 6238.968


Figure 22. Temperature profile of the reactor at a feed composition of 70% H2 and 30% CO

The temperature profile above shows that most of the reaction occurs at the entrance of the reactor. This points towards the need for a

cooling medium to cool the reactant down so that conversion to methanol can occur slowly along the length of the reactor. The adiabatic

temperature rise in this simulation is very high and therefore, there is a need to understand the effect that various feed temperature will

have on this simulation. This vital information can be obtained from a sensitivity analysis with varying feed temperature.


A sensitivity analysis was performed to see the effect of feed temperature on the

production of methanol.

Figure 23. Sensitivity of methanol production to different feed temperatures.

The sensitivity analysis shows that increasing the feed temperature will lead to

decrease in methanol production and vice versa. The optimum temperature from the

graph is 100 C (373K). This results follows from the strong exothermic nature of the

methanol synthesis. At equilibrium, the rate of backward reaction will increase more

relative to the rate of backward reaction with temperature rise which means there will

be less conversion of the reactants to products.

he high tempe atu e ise obse ved f om this simulation that’s illust ated on Figure 22

(almost double that of simulation on excel which might be due to error in the kinetics

specification on ASPEN) suggests that an adiabatic reactor running at the specified

condition is not suitable for the methanol synthesis process and therefore an operation

with an heat exchange medium should be considered. More results that validates the

suggestion for a cooling medium have been attached to the appendix. The simulation

also shows a conversion range between 20%-30%, as discussed earlier, interstage

cooling can be used to improve this conversion.


5.6. Further Discussion

To describe the behaviour of a chemical reactor, the composition and temperature at

each point of the reactor throughout the course of the chemical reaction must be known.

Concentration of species however can change at any point either due to disappearance

by chemical reaction or via mass transfer. Analogously, the temperature at any point

may change because heat is being absorbed or released by chemical reaction or by heat

transfer. Hence the concentration and temperature of a given spot in a reactor is

affected by the rate of the chemical reaction as well as the heat and mass transfer.

Reaction rate is determined by the micro kinetic properties which influence the

outcome of a process through the kinetics of heat and mass transfer.

A continuous adiabatic plug flow reactor (PFR) does not have the effect of macro kinetic

properties, hence the size and shape of the reactor is immaterial from the viewpoint of

chemical reaction. This makes direct data transfer possible i.e. the possibility to carry

out an experiment in a small laboratory scale reactor and transfer the result to a full

plant-scale industrial reactor of the same type preserving identical external reaction

conditions and inlet composition of the reaction mixture [xxxviii].

With regards to the developed kinetics, it was assumed that the reaction is irreversible

which isn’t the case as the methanol synthesis eaction is indeed eve sible. At the

operating conditions used for the methanol synthesis, the ideality assumed will be

invalid due to the non-ideal behaviour of gases at these conditions, the non ideality will

require fugacity parameters to be included in the kinetic rate equation to be in the

formed developed by Natta et.al (1953). Other side reactions discussed in the literature

review such as the water gas shift reaction and formation of DME are also very likely to

occur and these will have an impact on the rate of reaction. These factors put a lot of

limit to the developed kinetic rate equation and hence the performance of the reactor

simulated from that kinetic model.

CE4005 | Conclusion 82

6. Conclusion The primary objectives of this research project is to develop a kinetic model and reactor

design for the synthesis of methanol. Using the kinetic analysis data provided for

methanol synthesis, a Langmuir-Hinshelwood type of kinetics was developed. The

developed kinetic rate equation was used to simulate a plant scale catalytic reactor at

specified reaction conditions similar to that used in the chemical industry for methanol

synthesis. The reactor was simulated as a simple, one-dimensional, plug-flow, pseudo


Plug flow is an idealised flow of fluids under which all particles on a given cross section

will have identical velocity and direction of motion. This excludes mixing in the

direction of motion. Ideal gas law was assumed for all calculations in this report. Under

plug flow, particles of different age do not mix, as the particles that enter the reactor at

the same time must leave simultaneously. In real reactors, the flow of fluids can only

approximate to plug flow. The Reynolds number was calculated to be less than 2000 (Re

< 2000) which means the flow is laminar and this will result in a velocity p ofile that’s

parabolic. In a parabolic velocity profile, the molecules on a given cross section do not

move at the same velocity so particles of different age will therefore mix to some extent.

The effect of mixing can be regarded as negligible if the mixing does not significantly

alter the concentration field induced by chemical reaction given that there are no

appreciable longitudinal gradients of conversion within the reactor. However, because

the length of the tube along which the major portion of the reactant has been converted

to methanol is much larger than the tube diameter (ratio of 1:315), the concept of plug

flow is realistic. The maximum adiabatic temperature on the excel simulation was 748K,

when the simulation was repeated on ASPEN, this value doubled for the same feed

composition and specification. It is not advisable to use adiabatic reactors for reactions

whose adiabatic temperature rise is very large. Isothermal operation will be preferable

as this will allow the reaction to take place at a lower temperature which is more

favourable from the point of view of chemical equilibrium. The reactor was also

modelled to operate non-adiabatically and higher rate was observed at higher

conversion values than in the adiabatic setup. The non-adiabatic temperature profile

which allows for heat transfer agrees more with the admissible temperature range from

literature and the temperature at which the experimental data used was carried out.

The equilibrium conversion for the earlier simulation for the adiabatic setup was 23%

CE4005 | Conclusion 83

for a feed temperature of 473K. ASPEN confirms this result as the range of methanol

conversion lies between 20% and 30 %. Interstage cooling was suggested in order to

achieve higher conversion of the reactants to methanol. Adiabatic plug flow reactor can

only be used if the temperature rise corresponding to the outlet degree of conversion

remains smaller than the operating temperature region of the reactor. The operating

temperature of the methanol synthesis is between 400-700K from literature, see Table

2. The adiabatic temperature rise from the reactor simulation exceeds this value at the

specified conditions. It is important to optimise the temperature regime due to the

effect of temperature on the rate of reaction. Optimisation of the temperature regime

will be discussed further under the recommendation section.

The objectives of this research project were met and I had the opportunity to develop

kinetic modelling methods and approaches, on this basis this research can be concluded

as being successful.

CE4005 | Recommendations 84

7. Recommendations At equilibrium, the rate of forward reaction is equal to the rate of backward reaction.

For exothermic reactions, the rate of backward reaction will increase more relative to

the rate of backward reaction with temperature rise, therefore lowering the equilibrium

conversion and subsequently the rate of reaction. For a gas reversible exothermic

reaction such as the methanol synthesis, the productivity of the reactor for a given inlet

composition is at its maximum if the state of the reaction mixture follows the path of

maximum productivity. This path is approached neither by the adiabatic nor the

isothermal temperature regime. For the adiabatic setup, increase in temperature of the

reaction mixture favours the rate of the reaction but the productivity is low because the

reaction mixture rapidly approaches the region of the effect of thermodynamic

equilibrium at high temperature. In an isothermal reactor, the reaction can take place at

lower temperature which is more favourable from the point of view of chemical

equilibrium. However the reactor productivity will remain low because of the low

reaction rate in the region free of the effect of chemical equilibrium.

In a eacto that’s neither adiabatic nor isothermal, the temperature profile can be

adjusted such that the reaction mixture is allowed to be heated by the heat of reaction in

the region free of the effect of chemical equilibrium, to be later cooled by heat exchange

in the region affected strongly by chemical equilibrium. This leads to interstage cooling.

Low conversion is sometimes overcome by using several adiabatic reactors with

interstage cooling. Several reactors, with heat exchangers for cooling between them, are

run up to near the maximum reaction rate until satisfactory conversion is attained. This

is a common technique used in methanol synthesis from syngas. Interstage cooling

helps to achieve high conversion and extract reaction heat. Usually, up to three adiabatic

reactors with interstage cooling are sufficient to achieve good conversion [xxxix].

The optimum temperature regime for the methanol synthesis and other reversible

exothermic reaction will be that which approaches as closely as possible to the path of

maximum productivity without exceeding either the upper or the lower limit of the

admissible temperature range.

One of the advantages of the plug flow reactor which makes it suitable for gas phase

reactions is that it has no moving parts and therefore easy to maintain. Also, plug flow

reactors produce the highest conversion per reactor volume of any of the flow reactors.

CE4005 | Recommendations 85

However, for exothermic reactions, the temperature control is difficult and hotspots

might occur. Although the cost of the reactor and catalyst regeneration is high, using a

fluidised bed reactor can eliminate problems with hotspots as the contents in a fluidised

bed reactor are well mixed, resulting in a uniform temperature. A fluidised bed reactor

can handle large amounts of feed and solids and therefore will be suitable for the

methanol synthesis.

Finally, the method of obtaining the kinetic parameters can be improved by solving

them numerically with software package such as POLYMATH or MATLAB. This will give

an improved kinetic model and hence reduce errors in the reactor design and

performance.

CE4005 | Nomenclature 86

8. Nomenclature Symbol Definition Unit ρB Catalyst bed bulok density kg/m3 C Concentration mol/m3 Co Initial concentration mol/m3 ρC Bulk density of catalyst kg/m3 D Diameter m d’p Effective particle diameter m dp Particle diameter m dx Differential of x Bed voidage f Friction factor FA Molar flow mol/s FAo Inlet molar flow mol/s fi Fugacity of component i atm, bar Fluid density kg/m3 G ratio of molar flow to rate of reaction g, kg G* average of two successive values of G same unit as G ΔG° Measure of free energy kJ/mol h Height m ΔH Heat of reaction kJ/mol k Reaction rate constant mol/(gcat.s atm) ka Adsorption rate constant kd Desorption rate constant Ki Adsorption rate constant of component i Kp, Keq Thermodynamic equilibrium constant dimensionless l Length m L Bed depth Specific mass flow rate kg/s n Number of moles mol n Empirical constant Nt Number of catalyst tubes action of the su face cove ed by adso bed species P Pressure atm/Pa/kPa/bar Pi Partial pressure of component i atm/Pa/kPa Pressure drop Pa/kPa/bar r Radius m -rA Rate of reaction mol A / (kg cat.s) R Molar gas constant J/mol/K Re Reynolds number T Temperature K Tad Adiabatic temperature rise K TO Reactor inlet temperature K Ts Surrounding temperature/temperature of coolant K Mean residence time s u velocity m/s U Overall heat transfer coefficient W/m2K V Volume m3 Vc Volume of catalyst m3 v0 Volumetric flow m3/s VR Volume of reactor m3 Wc Weight of catalyst g, kg X Conversion

CE4005 | References 87

Xe Equilibrium conversion

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xiv R. G Herman, K. Klier, G. W. Simmons, B. P. Finn, J.B Bulko, and T. P. Kobylinski,

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