El Kanzi 1996

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ELSEVIER

Chemical Engineering and Processing 35 (1996) 131-139

Optimization of MTBE synthesis in a fixed-bed reactor system

E.M. Elkanzi

Department of Chemical and Petroleum Engineering, Faculty o f Engineering, UAE University, P.O. Box 17555, Al-Ah, United Arab Emirates

Received 12 April 1995; accepted 23 August 1995

Abstract

A fundamental fixed-bed catalytic reactor model has beendeveloped or use n selectingalternative operating strategies n a

commercialmethyl-t-butyl ether (MTBE) unit. The model is basedon generalchemicalengineering rinciplesand is tuned to

represent he operation of the reactor’s systemof a given MTBE unit. Constrainedoptimization techniques re used o determine

the optimum operating conditions of the reactor’s system hat give the maximum net profit. The model will enable he user to

predict the required bed temperature rises, the required recycle rate for specificsingle-pass onversion and the required heat

removal rate in the coolers of an existing unit. For optimization purposes, he model is used o investigate he effect on unit

profitability when variablessuchas he conversionper passor the total conversionweremodified. A computer program,MTBEC,

wasdeveloped or solving the model equations.Conversionper passwasvaried from 62.3% o 87.3% n increments f 5%. Based

on thesecases, onversionper passhigher than the original design alue of 72.3% s suggested. he optimum conversionper pass

value appears o be about 75.5% and represents n improvement of about 1.5%on daily net profit for the pricesquoted. These

resultsdemonstrate he useof the model n selectingmore economicallyattractive operating targets.The modelcan alsobe used

to investigate he effect of other variablesamenable o optimization, e.g. fresh feed stock quality, feed costsand bed temperature

profiles.

Keywords: MTBE synthesis;Fixed-bed reactor system; Catalytic reactor model; Constrained optimization techniques;Model

equations

1. Introduction

The use of MTBE as a gasoline octane blending

component is growing rapidly due to the phase out of

tetraethyl lead as an octane boaster. According to most

estimates, demand for MTBE could reach 24 million

tonne y-i in 1995 [l]. This follows the second phase of

reformulated gasoline in 1997 in the USA, plus the

potential later in Europe and elsewhere. Moreover,

there are some viable alternatives to MTBE, including

ethanol, ETBE, TAME and DIPE, and new technolo-

gies such as reactive distillation using a solid catalyst

where both chemical reaction and fractionation of

products can proceed simultaneously are already run-

ning. New MTBE plants wil l come on stream and the

existing plants will have to adjust themselves to the

current economic situation, The availability and cost of

raw materials may become a problem and the existing

plants have to improve their eff iciency and increase

their profitability rather than expand the plant. One

0255-2701/96/ 15.001996 ElsevierScience .A. All rights eserved

way of improving productivity per given reactor vol-

ume may be accomplished by optimizing the plant

operating conditions [2]. However, the optimization of

an existing producing unit is a different type of opti-

mization than that made by the original designer of the

unit. The original design is based on a given set of

product prices and capital equipment costs with given

feed and product specifications. All process equipment

are sized and rated to meet the design operation. After

a certain period of operation, the economics may

change significantly from the original design basis.

Certain pieces of equipment, feed and/or product

qualtities may become bottlenecks or constraints to the

most economic operation. In addition, new catalysts are

being developed whose activities and selectivities are

better than that used in the original design [3]. As such,

a process model is needed to predict optimum opera-

tions more economically. In its simplest form this

model may be a heuristic model developed by an oper-

ator through first-hand observation of the unit. How-

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132 EM. Elkanzi / Chemical Engineering and Processing 35 (1996) 131-139

ever such models cannot be relied upon for accurate

quantitative predictions and more rigorous models

based on basic chemical engineering principles - ma-

terial and energy balances,equilibrium thermodynamics

and kinetics - are needed to evaluate the subtle eco-

nomic trade-offs involved in process optimization.

The aim of this study is to maximize the profitability

of an existing MTBE reactor’s systemby maximizing

an objective function which includes the value of

MTBE produced, and the operating and feed costs.The

technical basis of a fundamental fixed-bed catalytic

reactor model to search for more economically desir-

able operation of the reactor’s system is described.

Constrained optimization techniques are used to deter-

mine the key variables so as to satisfy the objective

function while maintaining the reactor’s temperatures

within safe limits.

2. Process description

2.1. Process chemistry

Methyl-t-butyl ether, or MTBE, is the equilibrium

product of the reaction of isobutylene (iC,) with

methanol in the presenceof an acid catalyst. The main

reaction is [4].

H

CI-4

H

CH,

I I I

H-C-OH + C=CH, H-C-0-C-CH,

(1)

I I I I

H CH, H CH,

This reaction is exothermic with 37.7 kJ of heat released

for each mole of isobutylene converted, the maximum

conversion being determined by a thermodynamic equi-

librium value [4-61. The reaction is also extremely

selective to isobutylene, i.e. other butenes are not con-

verted [7] other than under conditions of hot spots

when linear butenes can react [8]. Under design condi-

tions and using a sulfonated polystyrene resin (e.g.

polystyrene/divinylbenzene copolymer), essentially the

only hydrocarbon molecule to react is isobutylene. The

remaining hydrocarbons in the feed stream are almost

entirely inert. However, undesirable side-reactionsmay

take place side by side with the main reaction of Eq.

(1). The most important side-reaction is the dimeriza-

tion of isobutylene to a mixture of the isomers 2,4,4-

trimethyl-1-pentene (TMP-1) and 2,4,4-trimethyl-

2-pentene (TMP-2). Interaction of two molecules of

isobutylene produces the dimer [4],

CH, CH3 CH, CH,

I I I I

C=CH2 + C=CH, Z+ C=C-C-CH,

(2)

I

I

I I I

CH, CH,

CH, H CH,

At design conditions the isobutylene selectivity to form

these isomers is less than 0.5% [9]. Higher reaction

temperatures tend to produce more and should be

avoided.

Dimethyl ether (DME) can be formed by the interac-

tion of two methanol molecules in the presence of an

acid catalyst [9].

H H

H H

I

I I I

H-C-OH + H-C-OH +H-C-0-C-H+H1O

I I I I

H H H H

(3)

Reaction (3) is not only harmful by itself but the water

produced may also react with isobutylene to form

t-butyl alcohol (TBA) [9].

CK CH,

H,O + C=CH2 + HO-C-CH3 (4)

I I

CH, CH,

Production of TBA is not totally undesirable because

its blending octane number is lower than that of MTBE

but higher than that of base gasoline. Besides the

formation of TBA, water has another harmful effect in

that it reduces the acidity of the catalyst and thus

lowers its activity and a higher reaction temperature is

therefore required. This effect disappears when water is

converted into TBA and in fact only a few centimeters

at the reactor are affected by water [lo]. At design

conditions, the isobutylene selectivity to form TBA is

less hen 0.9% [ll].

2.2. Reaction kinetics

The direct addition of olefins catalyzed by ion-ex-

change resins to give ethers was investigated by Ancil-

lotti et al. [12]. They confirmed the high reactivity of

isobutylene with methanol compared to other olefins.

Several investigators [4,5,12- 171have studied the kinet-

ics of the reaction of Eq. (1) both in the liquid and

vapor phases, and generally two approaches were fol-

lowed for the analysis of the kinetic data. In the first

approach the reaction is considered as a homogeneous

catalytic reaction where the reactants are confined

within the gel-like resin. In the second approach, the

resin is treated like a solid catalyst and the reaction is

considered as a heterogeneouscatalytic reaction. In one

study [5], a first-order dependence with respect to

isobutene was found together with a -0.25 order de-

pendence with respect to methanol. In another study

[12], a power law rate expression with a zero-order

dependenceof rate on methanol concentrations of more

than 4 mall-’ was reported. In the same study, a

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E.M. Elkauzi 1 Chemical Engineering and Processing 3.5 (1996) 131-139

133

first-order dependence of the rate on the isobutylene

concentration with an activation energy of 17 kcal

mol-’ was also reported. In another study 1131, re-

versible rate expressions with a second-order depen-

dence of the forward reaction and a first-order

dependence of the reversible step have been sug-

gested.

In the heterogeneous catalytic reaction approach,

the kinetic data analysis was based on classical mod-

els such as the Langmuir-Hinshelwood-Hougen-

Watson (LHHW) models [4,5,13-171. A typical

LHHW model of the reaction is of the form:

Pa)

Under industrial conditions the forward reaction goes

almost to completion (96% conversion of iso-

butylene). Moreover, the reported [4] ratio of k,/kl at

60 “C is about 0.03 and the corresponding activation

energies ratio is about 1.6. Thus the reversible step

may be neglected and Eq. (4a) reduces to a first-or-

der dependence on the isobutylene concentration. In

fact, the analysis of the kinetic data of Subramanian

and Bhatia [13] based on first-order kinetics gives a

better fit of the data than the assumed second-order

forward step and the reversible first-order one. Based

on the above argument and on the results of Ancil-

lotti et al. [12] and on the analysis of industrial data,

a heterogeneous rate expression for the first-order de-

pendence on isobutylene concentration with an acti-

vation energy of 17.4 kcal mol-’ will be used in this

study.

2.3. The seactor system

In the idealized process involving the flow diagram

shown schematically in Fig. 1, the reactor system in-

cludes the catalytic reactors, coolers and static mix-

ers. The fresh feed enters a static mixer where

methanol and isobutylene liquids are blended. The

combined fresh feed (FF) then mixes with the first

reactors effluent recycle (R*) and passes through a

Fig. 1. Schematic flow diagram for the reactor system.

Table 1

Normal reactor system operation

Parameter

LHSV, s-’

Inlet temp., K

AT, K

iC, conversion, % based on

feed to reactor

Reactor I

2.94 x 1O-3

321

14.2(q)

72.3(X,)

Reactor II

7.5 x 10-4

314.7

3.2(%)

55.5(X,)

iC, conversion, % based on

fresh feed

MTBE selectiv ity, %

Recycle ratio

Pressure, bar

Catalyst volume, m3

QR> W

QE>

W

Products:

MTBE, kg/s

TMP, kg/s

MeOH, kg/s

ic,, kg/s

91(X,) 96(X,)

87.3

91.4

2.88 -

25 25

29.3

29.3

1.3x103 -

8.5 x 10’

4.16

4.9

0.0072 0.01

0.25 0.83

0.64 0.2

second static mixer where it is thoroughly blended to

ensure a homogeneous mixture - in the stoichiomet-

ric proportions of both reactants - before entering

the firs t reactor. In industrial practice, a 10% excess

to methanol is used in order to reduce mainly

isobutylene dimers by product fermentation. The re-

actors are operated near adiabatic conditions and the

reaction produces a significant amount of heat, caus-

ing a temperature rise across the catalytic bed. This

temperature is controlled by circulating a portion of

the first reactor’s effluent (E*) to the reactor inlet.

The circulating pumps take suction from the first re-

actor’s outlet and develop enough discharge head to

circulate the effluent through the recycle cooler and

combine it with the fresh feed. The remaining effluent

(EE) is cooled before entering the second reactor

where the remaining unconverted isobutylene reacts

to form MTBE, as in the firs t reactor, so that 96%

of the isobutylene contained in the fresh feed to the

reactor’s system is converted.

Table 2

Price assumptions

Feeds:

iC,(mixed butenes)

MeOH

Products:

MTBE

Utilities

Water cooling (11.1 K rise), m3

Electricity, kWh

Power, pumping

17.5 per BBL

23.9 per BBL

45.2 per BBL

14 per kg MTBE

2.2 per kg MTBE

SO.07 per BHP h-’

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Table 3

Base case economics

Product Quantity Unit value S per day

MTBE

3780.7 BBL d-’ S45.2 per BBL 170 888

Feeds:

iC4 2993.4 BBL d-’ 17.5 per BBL 52 385

MeOH 1290 BBL d-’ 23.9 per BBL 30 828

Operating costs:

Pumping

2532

Cooling 7597

Other? 34 445

Total cost

127 787

Net profit per day

43 100

Net profit per BBL 11.4

MTBE

a Others include: operating costs other than reactor sys -

tem + freight to USA + sales/delivery + fixed costs + import duty +

depreciation.

3. Optimization model

3.1. Reactor equations

Commercial MTBE synthesis reactors are operated

near adiabatic conditions and are approximately plug

flow in nature, resulting in temperature and concentra-

tion gradients through the catalytic bed. Since tempera-

ture and concentration are the key driving forces in the

reaction rate expressions, a model which represents the

reactor by individual catalyst bed must integrate the

reaction rate and its related heat balance along the

catalyst bed. Only a model with such detail will enable

the user to predict the required bed inlet temperature,

the bed temperature rises, the required recycle rate for

a specific single pass and overall conversions and the

required heat removal rate in the coolers.

The detailed reactor model consists of differential

material and energy balances over adiabatic fixed-bed

reactors. These balances are coupled with physical

property and heat-transfer correlations. For the opti-

mal operation of the reactor’s system, optimization

variables such as the recycle ratio and the reactor’s inlet

temperatures are related to the objective function. The

details of the balances around the firs t reactor with

reference to the notation in Fig. 1 and to the nomencla-

ture are:

s

s

t; = Fi

dXi

0 Cmyi)

(5)

where

.

(-r,)=k,k,exp FF *Cy

01

Xl

I

‘=l+RR(l-XI)

I

>

(6)

Heat balance yields (datum = 298 K):

CpidT- t ET

s

T

C,i dT- FiA.H~X’= 0

i=l 298

(7)

and

QR= i RT

“CpidT

i-l

s

T

For the second reactor:

s

2

VI, = EEi

dXi

0 CBri>

and

x

2

= 0.96 -X,

1 -x,

Heat balance yields:

n

OTT- , I

(8)

(9)

(10)

C,,dT- 2 Pi

i=l

s

T T

X

Cpi dT- EEiAHgX2/= 0

(11)

298

and

QE = i EEi

‘TO Cpi dT

i=l

s

T

w

The variables to be determined from these balances

are the recycle ratio, RR, second reactor inlet tempera-

ture TT,, and heat removal rates, QR and QE, for given

values of X,, X0 and To.

3.2. Objective function and constraints

Optimization of the MTBE reactor’s system opera-

tion implies the maximization of unit profit. Within the

optimization model this is stated as an objective func-

tion defined by [2].

Profit = (product value) - (feed costs) -(operating costs)

(13)

The model is to be used to investigate the effect on

unit profitability when variables such as conversion per

pass, total conversion or feed quality are modified. This

leads to optimization of heat removal from the coolers

and recycle rates. These, in turn, determine the external

heat flux and recycle ratio which maximize the net

profit while maintaining the reactor’s temperature

within safe limits. Assuming that the product value,

feed costs and those components of the operating cost

which are not related to the reactor sysem are con-

stants, the net profit will then only be a function of the

reactor’s system operating costs. These operating costs

are effectively determined by the recycle pumping cost

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135

0.2 -

/

O.l- d

I I I

I

I I I

2 2.2

2.4 2.6 2.8 3.0 3.2 3.4 3.6

RECYCLE RATIO

Fig. 2. Variation of conversions with recycle ratio.

and external heat removal cost. Both recycle and heat

removal costs are functions of conversion. These rates

are used, therefore, to represent the reactor system

operating costs in the objective function. Thus, there is

an optimal reactor’s system operating conditions for

which the optimal operating cost gives a globally maxi-

mum profit. The operating cost itself is thus an opti-

mization variable. In general, the optimization of the

reactor’s system operating conditions is therefore a

continuous variable optimization within a single-

parameter (operating cost) optimization.

The objective function of Eq. (13) is subject to the

following implicit constraints:

ATI < E,

(14)

ATzG%

(15)

where E, and % are limits based on the consideration of

the reaction kinetics and MTBE selectivity (typical safe

values of these limits are shown in Table 1). It is further

assumed that the reactor system is operating against no

mechanical constraints, i.e. there is additional capacity

on the recycle and cooling water pumps.

3.3. Solution methodology

Each set of equations [(5)-(7) and (9)-( 1 )] must be

solved simultaneously in order to determine the re-

quired recycle ratio and cooler heat loads for various

values of a single-pass conversion. These equations

were written in forms that were appropriate for solu-

tion using a finite-difference approach. It was found

convenient to consider the reactor as consisting of a

series of elements of volume and employing these equa-

tions by incrementing the known volume of the reactor.

The difference equations were solved with iterative con-

vergence on the conversion at each increment. Integra-

tion is continued until the reactor volume slightly

exceeds the design value and the conversion simulta-

neously matches with the current value.

The objective function [Eq. (13)] and constraints

[Eqs. (14) and (15)] were evaluated between each evalu-

ation of the recycle ratio and cooler heat loads in order

to determine a new search direction. The optimization

search was continued until a maximum profit (or mini-

mum operating cost) was determined. A computer pro-

gram, MTBEC, was developed for solving the model

equations. The algorithm for solving MTBEC was cou-

pled with the method for finding a maximum profit.

The model has two main modes of operation; it updates

the initial design operating conditions and predicts new

operating conditions imposed by the current economic

situation. In the update mode, commercial unit test run

data are input. These data include observed catalyst

bed temperature, liquid feed and recycle rates, cooler

heat loads, liquid feed, and product qualities and yields.

The model calculates both the conversion per pass and

total conversion, and updates all other design parame-

ters. In the predict mode the updated parameters are

utilized to solve cases after the user defines the problem.

Typically the user specifies the feed rates and qualities,

total and per pass conversion levels, current feed costs

and product value. The model firs t iterates to find the

required bed temperature rises, the recycle rates, the

cooler heat loads and the product yields. Additionally,

the predict mode calculations are performed until a

maximum profit is achieved.

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I I

I I

I

I

I

I

I

)

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 d

RECYCLE RATIO

Fig. 3. Variationof heat emoval ateswith recycle atio.

0

3.4. Model use example

To provide a specific example of the model’s use in

optimizing an actual unit, an MTBE reactor system was

modelled and a predict case was made to investigate

changes in some independence process parameters. The

schematic of the reactor system was as shown in Fig. 1.

In updating, the model was tuned using a test run

representing normal (or base case) operation of the

reactor system. This operation is shown in Table 1. The

unit produces 444 tonne d-l MTBE and the prices to

be used in selecting more optimum operations are as

shown in Table 2 [ 1, 18,191. The profit for the base case

(assuming a Middle East location for the unit) is shown

in Table 3.

The conversion per pass was varied from 62.3% to

87.3% and Fig. 2 shows the variation of the conversions

(X,, X, and X,) with recycle ratio. The model was run

to investigate the effect on unit profitability when this

variable was modified. Fig. 3 shows the variation of the

heat removal rates with recycle ratio. As part of the

reactor’s operating cost, it can be seen that the mini-

mum heat removal cost would occur at a recycle ratio

of about 2.33. However, at this value of the recycle

ratio the constraint of Eq. (14) is not satisfied and the

calculated temperature rise of 16.7 “C exceeds the safe

value. When coupled with the cost of the pumping

recycle rate, the variation of the reactor’s operating cost

with recycle ratio is as displayed in Fig, 4. From this

figure it can be seen that the minimum cost occurs at a

recycle ratio o f about 2.7, corresponding to a conver-

sion per pass of 75.4% (see Fig. 2). At this value the

constraints of Eqs. (14) and (15) are both satisfied as

displayed in Fig. 5 which shows the temperature profi-

les along the reactor length under optimal conditions.

At these optimal operating conditions the improvement

in daily net profit, for the prices quoted, is about 1.5%

higher than the base case conditions.

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EM. Elkanzi 1 Chemical Engineering and Processing 35 (1996) 131-139

300

u

0.2 0.4 0.6 0.8

DIMENSIONLESS AXIAL DISTANCE

Fig. 5. Temperature profiles under optimum conditions.

LO

P

reactor II effluent stream, kmol s-l

Q

rate of heat removal, kW

R* recycle rate, kmol s-l

p-“l,

recycle ratio

rate of reaction, kmol s-l mm3

T, +T temperature of first and second reactor, K

V reactor volume, m3

x conversion

& temperature difference limit, K

Subscripts

E effluent

i

component

ii

inlet

recycle

S

per pass

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