1.0 INTRODUCTION

We are assigned to design a reactor and a separator for the production of isobutylene by

performing reaction system analysis and sizing. In this project, we are required to produce as much as

100000 metric tonnes of isobutylene yearly through the process of MTBE cracking. There are several

steps or stages that have to be analysed and evaluated thoroughly. This includes performing overall

material mass and energy balance for the process, followed by reactor sizing by taking into

consideration the effect of diffusion and also side reactions, and finally, obtaining the weight of catalyst

used and other parameters concerned.

1.1 Background of Product- Isobutylene

Isobutylene (C4H8) as shown in the figure below is a hydrocarbon of industrial significance. It is a four-carbon branched alkene , which is one of the four isomers of butylene.

Figure 1.1.1 Isobutylene Molecular Structure

The melting point and boiling point of isobutylene are −140.3 °C and -6.9 °C respectively. It is insoluble in water. At standard temperature and pressure it is a colourless flammable gas with faint petroleum-like odour.

Isobutylene is a component of natural gas and crude oil found in porous rock formations in the upper strata of some areas of the Earth's crust. It is used as an intermediate in the production of a wide range of products. For instance, it is reacted with methanol and ethanol in the manufacture of the gasoline oxygenates methyl tert-butyl ether (MTBE) and ethyl tert-butyl ether (ETBE), respectively. Alkylation with butane produces isooctane, another fuel additive. Isobutylene is also used in the production of methacrolein. Antioxidants such as butylated hydroxytoluene (BHT) and butylated hydroxyanisole (BHA), two commonly used food preservatives are produced by Friedel-Crafts alkylation of phenols using isobutylene.

Isobutylene can be isolated from refinery streams by reaction with sulfuric acid, but the most common industrial method for its production is by catalytic dehydrogenation of isobutane. In the

1

1990s, the production of isobutylene increased dramatically as the demand for oxygenates such as MTBE grew.

Isobutylene is a highly flammable gas and presents an explosion danger. It is usually stored as a compressed, liquefied gas, if released it may produce an oxygen-deficient atmosphere that presents an asphyxiation hazard. Hence, it has to be handled with great care.

1.2 MTBE Cracking

Industrial plants designed for this operation have not yet been built. However, much development work already undertaken in the area serves to highlight the main characteristics of a technology based on the following cracking reaction:

(CH3)3C-O-CH3 (CH3)2C=CH2+CH3OHThis is an endothermic conversion, which takes place in the gas phase between 150 and 300 ◦C

(preferably at about 275◦C), at a pressure as low as possible, but sufficient to recover the isobutylene in the liquid phase by cooling with water, namely about 0.6x103 kPa absolute. To avoid dehydration side reactions, operations are conducted in the presence of steam, with a typical H2O/MTBE mole ratio at the reactor inlet of 5/1. As in the steam cracking of hydrocarbons, this procedure serves to reduce the partial pressure of the components and to facilitate the production of isobutylene and methanol.

The reaction takes place in the presence of an acid catalyst. The materials proposed for this include Dow 50x12 resins, polyphosphoric acids, both solid or deposited on kieselguhr, metallic oxides or alumina with a specific surface area of 200m2/g. These systems operate with a VHSV approaching 1; once-through conversions are as high as 95 to 98 per cent, and selectivities are even better, over 99.9 molar per cent in relation to the isobutylene and 94 per cent in relation to the methanol. Such performance tends to eliminate the need for MTBE recycling, which produces azeotropes of comparable boiling points (51.6 and 52.6◦C respectively at 0.1x103 kPa absolute) with methanol and water. In certain cases, however, where conversion does not exceed 65 per cent, this operation becomes necessary. In this case, the temperature is also lower (≈150◦C).

The main by-products of MTBE cracking are dimethyl ether obtained by methanol dehydration, the dimer and trimer of isobutylene, and t-butyl alcohol resulting from the polymerization and hydration of the olefin.

The flow sheet (Figure 1.6.2) of an industrial MTBE cracking facility comprises three main sections:

(a) Conversion, carried out in a tubular reactor of the heat exchanger type, in which a heat transfer fluid flows at the shell side, while the feedstock, and possibly a recycle stream, and the process steam enter the tubes after being preheated. After cooling, the effluent is condensed and separated into two liquid phases.

2

(b) Isobutylene purification, achieved by washing the hydrocarbon phase with water to eliminate soluble compoents such as methanol and t-butyl alcohol, followed by distillation in a series of three columns, where dimethyl ether, water, and heavy products such as the dimer of isobutylene and MTBE are removed in succession.

(c) Recovery of the methanol present in the aqueous phase and the wash waters by reconcentration in a distillation column.

1.3 Isobutylene Global Market Demand

In recent years, with the domestic gasoline and diesel prices continue rising, to get higher profits, chemical enterprise starts gasoline and diesel processing. The main processing raw material is MTBE, and isobutylene is also the main material to produce MTBE. Currently, the productivity of isobutylene production in refining enterprise is quite small, and market demand of isobutylene is smaller, thus, many chemical enterprises rush to purchase the isobutylene.

Additional sources of isobutylene will be needed in order to produce the large quantities of MTBE necessary to satisfy these requirements. Table 1.31 below shows the global MTBE demand to the year 2000 and the required increase in isobutylene capacity. The resulting increased isobutylene demand for the 1990s can only be satisfied by an increase in the dehydrogenation capacity, which in 10 years increased by almost an order of magnitude.

Table 1.31 World MTBE and Isobutylene demand (106t/yr)2

This shows the supply/demand situation for isobutylenes in 2010 and market projections for 2015. The focus of the study is the worldwide isobutylenes market, to evaluate the entire world supply of isobutylenes and the consumption of isobutylenes for production of chemicals and gasoline blending components, where data are available.

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Isobutylenes are four-carbon mono-olefins that find uses in fuel and chemical applications. Fuel markets account for about 85–90% of the world production of isobutylenes. The major fuel application is in the manufacture of gasoline blending components, such as gasoline alkylate, polymer gasoline and dimersol. Isobutylene serves as a raw material for the oxygenates, methyl tert-butyl ether (MTBE) and ethyl tert-butyl ether (ETBE), as well as for iso-octane. Isobutylenes may also be blended directly into gasoline for volatility control. They are also marketed with propane and butanes as liquefied petroleum gas (LPG).

At about 10–15% of the total worldwide market for isobutylenes, the size of the chemical market pales in comparison to that of the fuel market. n-Butenes are used as the precursor for sec-butyl alcohol, butadiene, butene-1 and other smaller applications. In industrialized regions—the United States, Western Europe and Japan—the chemical market for n-butnes is flat to declining. In developing regions such as Asia and Latin America, demand for butene-1 as a polyethylene comonomer and sec-butyl alcohol for MEK will gradually increase. Environmental regulations have slowed the growth of chemical markets for isobutylene in the United States and Japan with the cessation of MTBE use in reformulated gasoline. Other isobutylene derivatives such as butyl rubber and polybutenes represent mature markets in these regions and will experience only small growth. Stronger isobutylene demand in Other Asia, Central and South America, and Central and Eastern Europe is forecast through 2015.

Figure 1.31 : World Consumption of Isobutylenes in 2010

During 2010–2015, no significant deviations from the current conditions are expected to occur in the amount of isobutylenes generated from each process, with the exception of lower volumes recovered from steam crackers as a result of feedstock shifts in ethylene production. Quantities of MTBE will continue to be converted back into isobutylenes for chemical applications or ETBE in Europe. In the United States, overall isobutylenes supply will grow only slightly, with refineries and steam crackers providing the bulk of supply and on-purpose production playing a greater role during the forecast period.

Western European and Japanese markets, where steam cracking provides a significant portion of the isobutylenes supply, are expected to exhibit slower growth rates. Other Asia, Central and Eastern Europe, and the Middle East will experience somewhat higher growth rates.

1.4 Catalyst Chosen

4

The catalysts used in the process of the invention can be, for example, metal oxides, mixed metal oxides, in particular those containing silicon oxide and/or aluminum oxide, acids on metal oxide supports or metal salts. In the process of the invention, preference is given to using catalysts which formally consist of magnesium oxide, aluminium oxide, and silicon oxide for the cracking of MTBE into isobutylene and methanol in the gas phase.

Particular preference is given to using catalysts which formally comprise magnesium oxide, aluminium oxide and silicon dioxide and have a proportion of magnesium oxide of from 0.5 to 20% by mass, preferably from 5 to 15% by mass and more preferably from 10 to 15% by mass, a proportion of aluminium oxide of from 4 to 30% by mass, preferably from 10 to 20% by mass and a proportion of silicon dioxide of from 60 to 95% by mass, preferably from 70 to 90% by mass. The pore volume of the catalyst is preferably from 0.5 to 1.3 ml/g, more preferably from 0.65 to 1.1 ml/g. The average pore diameter of the catalyst is preferably from 5 to 20 nm, more preferably from 8 to 15 nm. Particular preference is given to at least 50%, preferably over 70%, of the total pore volume (sum of the pore volume of pores having a pore diameter greater than or equal to 3.5 nm determined by mercury porosimetry) of the catalyst being made up by pores having a diameter of from 3.5 to 50 nm.

In the process of the invention, preference is given to using catalysts which have an average particle size (determined by sieve analysis) of from 10 μm to 10 mm, more preferably from 0.5 mm to 10 mm, particularly preferably an average particle size of from 1 to 5 mm. Preference is given to using solid catalysts which have an average particle size d50, of from 2 to 4 mm, in particular from 3 to 4 mm. 

In the process of the invention, the catalyst can be used as shaped bodies. The shaped bodies can have any shape. The catalyst is preferably used as shaped bodies in the form of spheres, extrudates or pellets. The shaped bodies preferably have the abovementioned average particles sizes. 

Throughout the above conditions, in the process of MTBE cracking for production of isobutylene, magnesium-aluminosilicate has been chosen as the catalyst in this case.

1.5 Fixed-Bed Reactor

In a fixed-bed reactor the catalyst pellets are held in place and do not move with respect to a fixed reference frame.

Fixed-bed reactors have long been used in process industries. They contain catalyst, typically in pellet form, packed in a static bed. The syngas is then passed through the bed, where the reactions are induced as the gases contact the catalyst. The species production rates in the bulk-fluid are essentially zero. That is the reason we are using a catalyst.

Originally, fixed-bed reactors were the only commercially viable reactor type due to technological limitations. However, they also presented drawbacks mainly in the constraints existing in

5

access to the catalyst material. Since the gas has to pass over the material the reaction is limited by the available surface area. This problem can be reduced by allowing more than one "bed" in the reactor for the gas to pass over, under, and/or through. The catalysts in fixed-bed reactors do not need to be as resilient, as they do not move in the bed. For the common situation encountered when a reaction process is exothermic, fixed-bed reactors demand cooling of the bed. If the excess heat is not dissipated from the reactor bed, it could eventually lead to deterioration and deactivation of the catalyst material. Fixed-bed reactors can be equipped with internal tubes where a heat transfer fluid, such as boiler feed water, can circulate inside the tubes to control the temperature rise in the reactor.

1.5.1 Why Fixed-Bed Reactor ?

In this project, we are using Fixed-bed reactor for isobutylene production through MTBE cracking. We do not need Moving bed reactor as the catalyst is not required to be recycled for the reaction process to proceed. Furthermore, Fixed-bed reactor is the commercially viable reactor nowadays due to technology limitations.

1.5.2 Considerations When Modelling The Reactor

Fixed-bed catalytic reaction is often complicated to model, because of the many phenomena that need to be taken into account in order to more accurately. These include:

rate-limiting diffusion of reactants and products to and from the catalyst surface the catalytic reaction itself; many such reactions involve a lot of species, and reaction rates must

be accurately quantified in order to predict the selectivity at different conditions correctly heat transfer through the bed and from the bed to the outside world.

In fact, to gain maximum benefit from modelling requires highly detailed models that take into account all of the phenomena.

One of the most troublesome is about the catalyst handling of Fixed-bed reactor. Catalyst handling is a highly specialized area of activity and is used widely throughout the petrochemical, pharmaceutical, agrochemical and processing industries. Catalysts must be safely and efficiently removed and (re)loaded in which expensive downtime is to be minimized.

Present-day reactors within chemical plants and refineries require the best available technical services. In the competitive petrochemical world, having the most reliable reactors with a minimum downtime and maximum runtime and performance are wanted by any production company. Catalyst handling is an important step in this process to gain maximal reactor performance. For instance; the smallest percentage of mal-distribution in catalyst beds can significantly decreases the reactor's performance and runtime.

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1.6 Production Technologies

Figure 1.6.1 Technologies Comparison

MMTBE MISOBUTYLENE

MMETHANOL

FBR SEPARATOR

Figure 1.6.2 Cracking of MTBE to Isobutylene. IFP Process

To convenient the calculations, the actual industrial MTBE cracking process as shown in Fig 1.6.2 has been mainly simplified into two parts which are Fixed Bed Reactor(FBR) and Separator.

In the FBR part, the technology used is adsorption between reactants and catalyst while in separator part, the technology used is distillation due to the different boiling point of components. Due

7

T=548KP=6 atm

Zeolite as catalyst

to the difference of boiling point of components, the desired and undesired product can be collected or separated easily in different phases.

2.0 OVERALL MASS AND ENERGY BALANCES

2.1 Material Balances

Figure 2.11 : Process Flow Diagram for Isobutylene Production

Main Reaction:

CH3OC(CH3)3 (CH3)2C=CH2 + CH3OH

MTBE Isobutylene Methanol

For this stage, 100% conversion is considered.

Isobutylene Production Rate:

100000Mtonyear

×1000 kgMton

×year

365days×

day24 hour

=11415.53kg /h

Conversion for Mole-Balance:

11415.53kghour

×kmol

56.11kg=203.45kmol/h

Feed :

According to stoichiometry, 1 mole of MTBE will produce 1 mole of Isobutylene and 1 mole of MTBE. Steam is feed with a ratio of 1:5 to MTBE to suppress side reaction.

8

Catalyst

PRODUCT

MTBE: 203.45kmol /h ; 203.45kmol

hour×

88.15kgkmol

=17934.1175 kg/h

Steam: 15×203.45

kmolh

=40.69kmol /h ; 40.69kmolhour

×18kgkmol

=732.42kg /h

Reactor-exit :

Isobutylene: 203.45kmol /h ; 203.45kmol

hour×

56.11 kgkmol

=11415.53 kg/h

Methanol : 203.45kmol /h ; 203.45kmol

hour×

32.04kgkmol

=6518.538kg/h

Steam : 15×203.45

kmolh

=40.69kmol /h ; 40.69kmolhour

×18kgkmol

=732.42kg /h

Separator: Assumed efficiency 100%

Product: 100% Purity

Isobutylene: 203.45kmol /h ; 203.45kmol

hour×

56.11 kgkmol

=11415.53 kg/h

Wastes:

Methanol : 203.45kmol /h ; 203.45kmol

hour×

32.04kgkmol

=6518.538kg/h

Steam : 15×203.45

kmolh

=40.69kmol /h ; 40.69kmolhour

×18kgkmol

=732.42kg /h

Table 2.1 : Summary of Material Balances

Feed Reactor-exit Product Waste

MTBE 17934.1175 /h 0kg /h 0kg /h 0kg /h

STEAM 732.42kg /h 732.42kg /h 0kg /h 732.42kg /h

ISOBUTYLENE

0kg /h 11415.53 kg/h 11415.53 kg/h 0kg /h

METHANOL 0kg /h 6518.538kg /h 0kg /h 6518.538 kg /h

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2.2 Energy Balances

Figure 2.21 : Flow Diagram of Materials

MISOBUTYLENE

MMTBE TF=513K

MMETHANOL

FBR SEPARATOR

Where MMTBE = Mass flow rate of methyl tert-butyl etherMISOBUTYLENE = Mass flow rate of isobutyleneMMETHANOL = Mass flow rate of methanol

Elements’ Heat Capacities Calculations :

Heat capacity, Cp = [A + BT + CT2 + DT3+ET4] (T in Kelvin, Cp in J/mol.K ) ( Eqn 1.0 )

Table 2.21 : Heat Capacity Parameters of Gase Phase Elements

Parameters MTBE Isobutylene Methanol

A 39.585 32.918 40.046

B 2.8849 ×10−1 1.8546×10−1 -3.8287 ×10−2

C 1.3825×10−4 7.7876×10−5 2.4529 ×10−4

D -2.5131×10−7 -1.4645×10−7 -2.1679×10−7

E 8.0807×10−11 4.6867×10−11 5.9909×10−11

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T=548KP=6 atm

Zeolite as catalyst

At Feed temperature, TF = 513K :

Enthalpy of MTBE :

= ∫298

513

Cp(MTBE)dT , by referring to Eqn 1.0 ;

=

∫298

513

[¿(39.585)+(2.8849×10−1)(T )+(1.3825×10−4)(T )2+(−2.5131×10−7)(T 3 )+8.0807×10−11(T 4)]kJ /kmol

88.15kgkmol

(molar mass of MTBE)¿

= 400.96 kJ/kg

Enthalpy of Isobutylene :

=∫298

548

Cp(isobutylene)dT , by referring to Eqn 1.0 ;

= ∫298

548

[¿(32.918)+(1.8546×10−1)(T )+7.7876×10−5T 2−1.4645×10−7T 3+4.6867×10−11T 4]kJ /kmol

56.106kgkmol

(molar massof Isobutylene)¿

=514.3 kJ/kg

Enthalpy of Methanol :

¿∫298

548

Cp(methanol)dT , by referring to Eqn 1.0 ;

=

∫298

548

[¿40.046+(−3.8287×10−2 ) (T )+ (2.4529×10−4 ) (T2 )+(−2.1679×10−7T 3 )+5.9909×10−11T 4]kJ /kmol

32.04kg /kmol (Molarmass of Methanol )¿

= 416.92kJ/kg

Energy Balances Calculations:

Table 2.22 : Heats of Formation at 25°C, [kJ/kg] for Elements (Gas Phase)

MTBE ISOBUTYLEN METHANOL

11

E-3216.1 -301.3 -200.66

H= H 298+∫T 0

T

C pdT (Eqn 2.0)

Inlet:

MTBE (513 K), HMTBE = (ΔHf 0) MTBE + ∫

298

513

Cp(MTBE)dT

= -3216.1 kJ/kg + (400.96 kJ/kg)

= - 2815.14 kJ/kg

Outlet:

ISOBUTYLENE (548 K), HISOBUTYLENE = (ΔHf 0) ISOBUTYLENE +∫

298

548

Cp ( isobutylene )dT

= -301.3 kJ/kg + (514.3 kJ/kg)

= 213 kJ/kg

METHANOL (548 K), HMETHANOL = (ΔHf 0) METHANOL + ∫

298

548

Cp (methanol )dT

= -200.66 kJ/kg + (416.92 kJ/kg)

= 216.26 kJ/kg

Energy balance, Q = ΔH = (ƩMout . Hout ) – (ƩMin . Hin) ( Eqn 3.0 )

Q = (MISOBUTYLENE *HISOBUTYLENE + MMETHANOL*HMETHANOL ) – (MMTBE*HMTBE )

Q =(213 x11415.53+216.26 x6518.538 )— 2815.14 x17934.1175 kJ /h

¿5.43 x107 kJ /h (Endothermic)

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3.0 REACTOR SIZING BY CONSIDERING THE ENERGY BALANCE & MAIN REACTION

In this chapter, we used the algorithm for PBR sizing to find the optimum conversion and the weight of catalyst needed for this heterogeneous catalytic conversion. The reaction is carried out in steady state so the volume or weights of catalyst does not change with time. Adiabatic reaction is used as isobutylene production reaction is endothermic reaction. No catalyst deactivation is considered in this stage of reactor sizing.

3.1 DESIGN EQUATION

Differential form of Packed Bed Reactor design equations is used in term of conversion as below:

F AOdXdW

=−r ' A

Where FA0 is the flow rate of reactant into the reactor, X denotes the conversion, W denotes weight of catalyst used, -r’A is the rate law of our reaction.

3.2 RATE LAW

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The rate of this MTBE cracking is surface reaction limited as supported by the rate of reaction retrieved from MTBE production. The way that catalyst proceeds at surface is Langmuir-Hinshelwood mechanism, as the rate of heterogeneous reaction is controlled by the reaction of the adsorbed molecules, and that all adsorption and desorption pressure are in equilibrium.

The reaction is carried out in the following manner:

k1

MTBE ISOBUTYLENE + METHANOL k2

We will now call MTBE as species A, Isobutylene as species B, and Methanol as species C. The term k1 is used represent the forward reaction rate constant and k2 is the backward reaction rate constant.

The forward and backward reactions are elementary, hence the rate law of MTBE cracking is :

−r 'A=rA=k ' 1C A−k ' 2CBCC

Where

k ' 1=1.464×1022 e

−129,600RT

ρc,(

m3

kg .h)

k ' 2=6.05×1016e

−85,400RT

ρc ,( m3

kg .h)

ρc is catalyst density in kg/m3.This rate law is adapted from MTBE production process from isobutylene as there is no information found regarding MTBE cracking.

3.3 STOICHIOMETRY

Stoichiometric table for a flow system:

Species Inlet Change Outlet Concentration

A MTBE F A0 −F A0 X F A=F A0(1−X ) C A=C A0( 1−X1+εX )(T 0

T ) yB Isobutylene F A0θB F A0 X FE=FA 0(θ¿¿B+X )¿ CB=C A 0( θB+X1+εX )(T0

T ) yC Methanol F A0θC F A0 X FH 2

=F A0(θ ¿¿C+X )¿ CC=C A0( θC+X1+εX )(T 0

T ) y

Where,

FA0, molar flowrate = 203450 mol/h

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T0 = 548 K

R = 8.3144 J/mol.K

P0 = 0.6x106 Pa

v0, volumetric flowrate = 4623.38 m3/h

C A0=FA 0

v0

θB=0

θC=0

y A 0=1

ε= y A0δ=1 (1+1−1 )=1

T0 is reactor inlet temperate and T is reactor outlet temperature, y is pressure drop ratio PP0

where P is

reactor outlet pressure and P0 is reactor inlet pressure.

3.4 PRESSURE DROP

Since MTBE cracking is carried out is gas phase,there will be pressure drop for flow through PBR. For ε ≠0 ,

Pressure Drop Parameters:

dydW

=−α2 y

(1+εX ) TT 0

Where:

α=2β0

Ac ρc (1−∅ )P0

And with Reynold Number of more than 2000, turbulent flow:

15

β0=G(1−∅ )ρ0gcDp∅

3 [1.75G ]

Parameters are defined as follow:

∅=porosity=void fraction=0.475

gc=1.0 formetric system

D p=Diameter of particle∈the bed=0.00034m

Ac=Cross sectional area of reactor=2m

u=superficial velocity= volumetric flowcross sectional area

=4623.38m3/h2m2 = 2311.69 m/h

ρo=gasdensity=3.879kg/m3

G=ρu=superficialmass velocity=3.879kg/m3 x 2311.69 m/h x 1h/3600s =

2.490829 kg/m2.s

ρc ,Catalyst density=1300kg /m3

3.5 ENERGY BALANCE FOR ADIABATIC OPERATION OF PBR:

Gas-phase heat capacity: Cp = A + BT + CT2 + DT3 + ET4 ( T in Kelvin, Cp in J/mol.K )

MTBE ISOBUTYLENE METHANOLA 39.585 32.918 40.046B 2.8849 x 10-1 1.8546 x 10-1 -3.8287 x 10-2

C 1.3825 x 10-4 7.7876 x 10-5 2.4529 x 10-4

D -2.5131 x 10-7 -1.4645 x 10-7 -2.1679 x 10-7

E 8.0807 x 10-11 4.6867 x 10-11 5.9909 x 10-11

Cp (MTBE) = 39.585 + (2.8849 x 10-1) (T) + (1.3825 x 10-4) (T)2 + (-2.5131 x 10-7) (T)3

+ (8.0807 x 10-11) (T)4 J/mol.K

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Cp (ISOBUTYLENE) = 32.918 + (1.8546 x 10-1) (T) + (7.7876 x 10-5) (T)2 + (-1.4645 x 10-7) (T)3

+ (4.6867 x 10-11) (T)4 J/mol.K

Cp (METHANOL) = 40.046 + (-3.8287 x 10-2) (T) + (2.4529 x 10-4) (T)2 + (-2.1679 x 10-7) (T)3

+ (5.9909 x 10-11) (T)4 J/mol.K

For adiabatic operation in PBR,

dTdW

=(r ' A)(∆H RX)

FA 0(ΣΘiCPi+ΔCP X )

Where,

∆C p = Cp (ISOBUTYLENE) + Cp (METHANOL) - Cp (MTBE)

∆ H °RX (TR) ;Temperature Reference = 298K

= (ΔHf 0) ISOBUTYLENE + (ΔHf

0) METHANOL - (ΔHf 0) MTBE

= (-301.3 J/g x 56.11 g/mol) – (200.66 J/g x 32.04 g/mol) – (-3216.1 J/g x 88.15 g/mol)

= 260173.3572 J/mol

∆ H RX (T )=∆ H °RX (T R )+∆CP(T−T R)

∑θi Cpi = Cp (MTBE) ; as only MTBE is reactant.

= 39.585 + (2.8849 x 10-1) (T) + (1.3825 x 10-4) (T)2 + (-2.5131 x 10-7) (T)3+ (8.0807

x 10-11) (T)4 J/mol.K

3.6 COMBINE

ODE Solver in Polymath is used in solving this reactor sizing and the following report has been obtained:

POLYMATH Report No Title Ordinary Differential Equations 13-Dec-2013

Calculated values of DEQ variables

  Variable

Initial value

Minimal value

Maximal value

Final value

1 a 0.0011161 0.0011161 0.0011161 0.0011161

2 Ac 2. 2. 2. 2.

3 b0 4.57E+05 4.57E+05 4.57E+05 4.57E+05

4 Ca 44.0046 19.8485 47.07949 19.8485

5 Ca0 44.0046 44.0046 44.0046 44.0046

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6 Cb 0 0 5.252181 2.50357

7 Cc 0 0 5.252181 2.50357

8 Cpa 205.1247 160.8004 205.1247 160.8004

9 Cpb 138.0624 109.9418 138.0624 109.9418

10

Cpc 7.869319 6.473114 7.869319 6.473114

11

Cpi 205.1247 160.8004 205.1247 160.8004

12

dCp -59.19302 -59.19302 -44.3855 -44.3855

13

Dp 3.0E-05 3.0E-05 3.0E-05 3.0E-05

14

Fa0 2.035E+05 2.035E+05 2.035E+05 2.035E+05

15

G 2.490829 2.490829 2.490829 2.490829

16

gc 1. 1. 1. 1.

17

HrxT 2.454E+05 2.454E+05 2.56E+05 2.56E+05

18

HrxTref 2.602E+05 2.602E+05 2.602E+05 2.602E+05

19

k1prime 4.994E+06 62.94675 4.994E+06 62.94675

20

k2prime 3.37E+05 199.1519 3.37E+05 199.1519

21

P0 6.0E+05 6.0E+05 6.0E+05 6.0E+05

22

p0 3.879 3.879 3.879 3.879

23

pc 1300. 1300. 1300. 1300.

24

phi 0.475 0.475 0.475 0.475

25

R 8.3144 8.3144 8.3144 8.3144

26

rAprime -2.198E+08 -2.198E+08 -1.141589 -1.141589

27

T 548. 392.3767 548. 392.3767

28

T0 548. 548. 548. 548.

29

v0 4623.38 4623.38 4623.38 4623.38

30

w 0 0 2000. 2000.

18

31

X 0 0 0.1120062 0.1120062

32

y 1. 0.4044357 1. 0.4044357

Differential equations 1 d(X)/d(w) = (-rAprime) / Fa0

2 d(y)/d(w) = -(a / 2 * y) * (1 + X) * (T / T0)

3 d(T)/d(w) = (rAprime*HrxT)/(Fa0*(Cpi+dCp*X))

Explicit equations 1 Fa0 = 203450

  mol/h

2 T0 = 548

  K

3 R = 8.3144

  J/mol.K

4 P0 = 0.6e6

  Pa

5 v0 = 4623.38

  m3/h

6 Cpa = ((39.585) + ((2.8849 * 10 ^ -1) * T) + ((1.3825 * 10 ^ -4) * T ^ 2) + ((-2.5131 * 10 ^ -7) * T ^ 3) + ((8.0807 * 10 ^ -11) * T ^ 4))

  J/mol.K

7 HrxTref = 260173.3572

  J/mol

8 Cpb = ((32.918) + ((1.8546 * 10 ^ -1) * T) + ((7.7876 * 10 ^ -5) * T ^ 2) + ((-1.4645 * 10 ^ -7) * T ^ 3) + ((4.6867 * 10 ^ -11) * T ^ 4))

  J/mol.K

9 Cpc = (2.211) + ((12.216 * 10 ^ -3) * T) + ((-3.45 * 10 ^ -6) * T ^ 2)

  J/mol.K

10 dCp = Cpb+Cpc-Cpa

11 HrxT = HrxTref+(dCp*(T-298))

12 Cpi = ((39.585) + ((2.8849 * 10 ^ -1) * T) + ((1.3825 * 10 ^ -4) * T ^ 2) + ((-2.5131 * 10 ^ -7) * T ^ 3) + ((8.0807 * 10 ^ -11) * T ^ 4))

  J/mol.K

13 pc = 1300

  Catalyst density, kg/m3

14 Ca0 = Fa0 / (v0)

  mol/m3

15 Ca = Ca0 * (1 - X) / (1 + X) * (T0 / T) * y

16 Cb = Ca0 * (X) / (1 + X) * (T0 / T) * y

17 Cc = Ca0 * (X) / (1 + X) * (T0 / T) * y

18 k2prime = (6.05e16 * exp(-85400 / (R * T)))/pc

  m3/kg.h

19

19 k1prime = (1.464e22 * exp(-129600 / (R * T)))/pc

  m3/kg.h

20 Dp = 0.00003

  Zeolite diameter,m

21 gc = 1.0

  Conversion factor,metric system

22 G = 2.490829

  Superficial mass velocity #kg/m2.s

23 Ac = 2

  Cross sectional area,m2

24 rAprime = -((k1prime * Ca) - (k2prime * Cb * Cc))

25 phi = 0.475

  porosity

26 p0 = 3.879

  MTBE gas density,kg/m3

27 b0 = (G * (1 - phi) * (1.75*G) )/ (p0 * gc * Dp * phi ^ 3)

28 a = (2 * b0) / (Ac * pc * (1 - phi) * P0)

20

From the graph plotted from Polymath Result, we can see that the reactor needed 40.07884 kg/h to produce Isobutylene from MTBE at a conversion of 10.03633%. This weight is chosen as we can see that the pressure drop is still very small during this conversion, and when the catalyst is added is not increasing conversion. It is believed with the lack of reaction kinetic from experiment and journals, this cracking is carried out in a reversible manner and low conversion is achieved. The molar flow rate 203450 mol/h we considered here is producing target 100000 metric tonnes per year if conversion is 100%, since from Polymath the conversion is 9.8684 %, we need to scale up our molar flow inlet to 2027135.417 mol/h or 178691.987kg/h.

When conversion is 10.03633%

Actual Flow = Ideal FlowConversion

=203450mol /h0.1003633

=2027135.417mol /h

¿2027135.417molh×

1kmol1000mol

×88.15kgkmol

=178691.987kgh

21

4.0 Estimation of Diffusion- and Reaction-Limited Regimes

In many industrial reactions, the overall rate of reaction is limitedby the rate of mass transfer of reactants between the bulk fluid and the catalytic surface. By mass transfer, we mean any process in which diffusion plays a role. In the rate laws and catalytic reaction steps described in last stage, weneglected the diffusion steps by saying we were operating under conditionswhere these steps are fast when compared to the other steps and thus could be neglected. We now examine the assumption that diffusion can be neglected.

4.1 Catalyst Deactivation

In designing fixed and ideal fluidized-bed catalytic reactors, we have assumed up to now that the activity of the catalyst remains constant throughout the catalyst’s life. However, the loss of catalytic activity that occurs as the reaction takes place on the catalyst. It is found out that decay reaction is in first order.

a=e−βw/Us

Where, β = decay rate constant (s-1) = 0.212W = catalyst weight (kg)= 2000Us = catalyst mass flow rate go through the catalyst bed (kg/s)=4981

a=e−(0.212)(2000)/(4981)

=0.9184

4.2 External Diffusion Effects

In this section we consider the external resistance to diffusion by using Mears’ Criterion.Thoenes-Kramers and Colburn J correlation are employed to get mass transfer coefficient value, kc.

4.2.1 Thoenes-Kramers correlation:

Parameters:

Cross sectional area, Ac 2 m2

Catalyst density,ρc 1300 kg/m3

Porosity, ϕ 0.475MTBE gas density,ρb 3.879 kg/m3

Zeolite diameter, Dp 0.00034 mRadius of catalyst particle, R 1.7 x 10-4 m

Volumetric flow rate,vo 4623.38 m3/hSurface area of the catalyst per unit mass of catalyst, Sa

750000 m2/kg cat

22

Superficial velocity,U=V o

Ac

¿4623.38 /2

¿2311.69 m/h

¿0.6421 m/s

ℜ=U dpV

¿(0.00003 x 0.6421)/(4.7 x10−7)

¿40.985

ℜ’= ℜ(1−φ) y

¿40.985 /(1−0.475)

¿78.067

Sc= VDAB

¿(4.7 x10−7) /(0.0792 x10−4)

¿0.05934

Since Re’ is within 40<Re’<4000 and φ is within 0.25< φ<0.50, but the Sc value is not within 1<Sc<4000, hence Thoenes-Kramers correlation cannot be used.

4.2.2 Colburn J factor correlation:

ℜ=U dpV

¿(0.00003 x 0.6421)/(4.7 x10−7)

¿40.985

JD=¿]/( φ)

JD=¿]/(0.475)

¿0.26

JD=Sh

Sc13 ℜ

23

0.26= Sh

0.0593413 x 40.985

Sh=4.156

Sh=kc d p

DAB

4.156=k c(0.00003)0.0792 x10−4

k c=1.097m /s

Since Re > 10 for gas phase, hence Colburn J factor can be used.

4.2.3 Mears’ Criterion

Cao = F Ao

vo

¿203450mol/h4623.38m3/h

=44.004mol /m3

k' = k1

ρc

¿ 125.14 s−1

1300kg/m3 =0.0963m3 /kg . s [ k1 = 356.2084

3600 m3/kg.s ]

-rA = k '×Cao (1−X )

1+εX; whereε= ya0δ=1× (1+1−1 )=1

¿0.0963×44.004 (1−0.1)

1+1(0.1)

= 3.467 mol/kg.s

ρb=ρc (1-ϕ)

= 1300(1-0.475) = 682.5 kg/m3

CM = −r A ρb RnkcCAb

24

¿3.467

molkg . s

×682.5kg

m3×(0.000015m)×1

(1.097ms)(44.004

molm3 )

¿7.353 x10−4 (<0.15)

According to Mears’s criterion,for CM is smaller than 0.15, external diffusion does not exist.

4.3 Internal Diffusion Effects:

In this section we consider the external resistance to diffusion by using Weisz-Prater Criterion.

4.3.1 Weisz-Prater Criterion

k 1¿ Ae

−ERT

¿ (1.464×1022 )e(−129600

8.314 x 411)h−1×

1h3600 s

=125.14 s−1

ϕs1¿ R√ k1

De

¿(0.00003/2)√ 125.140.4×10−7=0.839

η ¿ 3

ϕ12¿

¿ 3

(0.839)2 [0.8391

tanh (0.839)−1]=0.956

CWP =η×ϕ12

=0.956×0.8392=0.673 (<1)

According to Weisz-Prater criterion,for CM is smaller than 1, internal diffusion does not exist.

25

5.0 Conclusion

After we analyse the conversion profiles of MTBE cracking process,we can conclude that to produce target 100000 metric tonnes per year isobutylene with single pass conversion through the reactor of 9.8684 %, we need 178691.987kg/h of MTBE. The cracking process is a heterogeneous catalytic conversion that followed Langmuir-Hinshelwood kinetics. The conversion is reasonably low as this reaction is backward favourable, as in commercial production, isobutylene and methanol are used in MTBE production.

Since both the internal and external diffussion are not rate determining step (RDS), so the MTBE cracking process is surface reaction limited.

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