experimental and modeling of a non-isothermal cstr

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Experimental and modeling of a non-isothermal CSTR tond outparameter regions and conditions causing input multiplicity for acidcatalyzed hydrolysis of acetic anhydride

N.S. Jayakumar a,, Merlin Thomas b, J.N. Sahu a,c,a Department of Chemical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur 50603, Malaysiab Institute of Science & Technology for Advanced Studies & Research (ISTAR), Vallabh Vidyanagar, Anand, Gujarat 388120, Indiac Petroleum and Chemical Engineering Programme Area, Faculty of Engineering, Institut Teknologi Brunei, Tungku Gadong, P.O. Box 2909, Brunei Darussalam

a b s t r a c ta r t i c l e i n f o

Article history:

Received 22 April 2013

Received in revised form 21 April 2014

Accepted 21 April 2014

Available online 26 April 2014

Keywords:

Outputinput multiplicity

CSTR

Open loop behavior

Parametric sensitivity

The continuous stirred tank reactor (CSTR) presents challenging operational problems due to its complex

open-loop non-linear behaviorsuch as input and output multiplicities, ignition/extinction, parametric sensitivity,

non-linear oscillations and perhaps even chaos. Manyresearchers havestudied the non-linear dynamic behavior

of CSTR for several reaction schemes froma theoretical stand point. The present experimental studies are carried

out to identify the existence of input multiplicityin a non-isothermal CSTR. The sulfuric acidcatalyzed hydrolysis

of acetic anhydride reaction system has been chosen and the regions of existence of input multiplicity are theo-

retically identied. The reactor showed the same steady state temperature for two inputow rates of reaction

mixtures into the CSTR reactor and thus conrming the existence of input multiplicity for the sulfuric acid

catalyzed hydrolysis of acetic anhydride reaction system. It was observed that the time taken by the reactor

was too long at a low feed ow rate of reaction mixture than at a higher feed ow rate reaction mixture. The

model simulations of steady state temperatures were in close agreement with experimental data for the above

feedow rates of reaction mixture conditions.

2014 Elsevier B.V. All rights reserved.

1. Introduction

Non-linear phenomenon such as multiplicities and stability

problems are encountered in industrial chemical reactors, but ap-

parently proprietary considerations have prevented the disclosure

of data and specic reaction. The occurrence of multiple steady

states under the same operating conditions of a reactor is known

as output multiplicity whereas input multiplicity means that more

than one set of input variables causes the same output variable.

Non-linearity is a necessary condition for input and output multi-

plicities[1]. Non-linear systems can show a variety of dynamic pat-

terns ranging from stable operation at a unique stable steady state,

to unstable operation such as unstable steady state, oscillations,

and chaos. In general input multiplicities occur due to the presence

of competing effects in non-linear process or due to non-ideal

mixing with certain non-linear reaction kinetics or due to the recy-

cle structure of non-linear processes. Constraints placed on the

manipulated variable of non-linear process and increasing the num-

ber of controlled variables can eliminate input multiplicities [2 ].

However, one of the major difculties in dealing with non-linear

systems is the lack of unied mathematical theory for representing

various non-linear system characteristics. Most of the recent ad-

vances in the study and understanding of multiplicity in chemically

reacting systems have resulted from the applications of catastrophe

and singularity theories to situations which are relatively simple, i.e.

the number of intrinsic state variables involved are limited [3,4]. The

CSTR lumped reactor system with control has been reported by nu-

merous researchers[512] investigating various aspects such as sta-

bilization of CSTR, state and parameter estimation methods, design

and operability of the CSTR reactor and control of non-linear CSTR.

In physical terms, due to the existence of input multiplicity phe-

nomena, there may be more than one set of manipulated variables

which can produce the same desired steady state in CSTR. Input

multiplicity can occur if at least one variable appears in a non-

linear fashion in the governing equation. The bounds on the values

of the manipulated variables have a strong impact on the number

of feasible inputs and a decrease in the range of values of the manip-

ulated variable tends to decrease the number of possible inputs for a

specied output. Although there have been developments in the un-

derstanding of the dynamic behavior of CSTR including investiga-

tions on the existence of input multiplicity for several reaction

Chemometrics and Intelligent Laboratory Systems 135 (2014) 213222

Cor responding author. Fax: +60 3 79675319.

Correspondence to: J.N. Sahu, Department of Chemical Engineering, Faculty of

Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia. Fax: +60 3 79675319.

E-mail addresses:[email protected](N.S. Jayakumar), [email protected]

(J.N. Sahu).

http://dx.doi.org/10.1016/j.chemolab.2014.04.017

0169-7439/ 2014 Elsevier B.V. All rights reserved.

Contents lists available atScienceDirect

Chemometrics and Intelligent Laboratory Systems

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schemes from a theoretical standpoint[14,1318,20], very few re-

action systems have been tried experimentally[1820]. In the ab-

sence of a unied mathematical theory can represent various non-linear system characteristics, it will be appropriate to study the

input multiplicity behavior of CSTR by means of experiments and

to link the acquired data to theoretical considerations for existence,

detection and elimination of operating problems. Multiplicity anal-ysis provides practical guidance for process redesign, including

CSTRC-3

ST-1 ST-2 ST-3

CHT-1 CHT-2 CHT-3

R-1 R-2

R-3

TS

C-1

C-2

T-1

T-2

Fig. 1.Experimental set up used for conducting reaction experiments.

Table 1

Process variable combinations causing input multiplicity.

Tf(C)

c CAf(mol/m3)

Ua W/C q 106 m3/s qc 106 m3/s

20.2 0.0027 38.34 0.2387 5000 16.930 1.3110 0.4367 10.50

3.360 1.3923 0.0887 12.00

20.2 0.0027 38.34 0.2865 6000 24.850 1.3110 0.6700 10.50

2.290 1.4595 0.0615 13.33

31.3 0.072 36.96 0.2300 5000 23.810 1.2131 2.722 8.833

0.478 1.3790 0.0546 11.67

31.3 0.072 36.96 0.2760 6000 30.760 1.2131 3.510 8.833

0.370 1.4840 0.0422 13.83

214 N.S. Jayakumar et al. / Chemometrics and Intelligent Laboratory Systems 135 (2014) 213222


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eliminating difcult operating regions associated with the input and

output multiplicities. These reasons justify the need for a systematic

experimental study of a non-isothermal CSTR for its multiplicity

behavior.

2. Experimental set-up and technique

The experimental set-up which includes a 330 ml stainless steel

reactor with four bafes and a stainless steel cooling coil of six turns

and a diameter 63 mm is as illustrated inFig. 1. The inlet temperatures

of the feed reactants and the reactor temperatures were measured with

the help of a RTD probe. The rpm of the stirrer was checked at regular

intervals using a tachometer and the speed (rpm) was regulated by

varying voltage to the stirrer motor. The constant temperature bath

and the feed tubes were insulated with Plaster of Paris to minimize

the heat losses. The reactants were allowed to ow through the coils

in the bath and through the feed lines into the collection tank for suf-

cient amount of time such that the reactants attained steady state feed

temperatures. When feed temperatures had attained constant values,

the drain tube of the reactor was closed. The reactor was then lled at

the same time with the feed mixtures with known composition and

inlet temperatures up to the level of the outletow tube. The stirring

was done immediately after pouring the reacting liquids into the reac-tor. The stirrer speed of the motor was regularly measured with the

help of a tachometer and was kept constant at 820 rpm with the help

of a variac connected to the motor. At the time of pouring reactants

into the reactor, the levels of liquid in the feed storage tanks were

noted. Empty overow collection tanks were used to collect the over-

ow from the constant head feed tanks. The experimental runs were

allowed to continue till the temperature of the reactor reached a steady

value. The transient reactor temperature with time readings is noted till

the CSTR reactor reached steady state reactor temperature. A series of

experimental runs were conducted for different feed concentrations,

feed temperature and other kinetic parameters, which were identied

theoretically for existence of input multiplicity. For each experimental

run, the time temperature prole of the reaction system was recorded

until steady state was obtained. The experimental conditions used inpresent study are shown inTable. 1.

Batch heat loss experiments were carried out to determine the

overall heat transfer coefcients at various coolant ow rates owing

through cooling coil. The reactor was lled with preheated water of

80 C and stirred at 820 rpm. The time versus temperature fall of the

CSTR vessel due to heat loss were noted. From the slope of the plot of

time versus log of the difference between temperature of the reactor

and air temperature, theoverall heat transfer coefcient Ua for a cooling

water ow rate qc was determined. Severalheat loss experiments were

conducted and an empirical equation relating Ua and qcis obtained

from overall heat transfer coefcient and the coolant ow rate as

shown in Table 2. An empirical correlation relating overall heat transfer

coefcient, Ua with coolant ow rate, qc using the various experimental

data is given as

Ua 2:290 105

qc0:45

1

Table 2

The results of batch heat loss experiments to obtain heat transfer coefcient at different coolant ow rates.

Cooling water ow rate, qc 106 m3/s I nitial temp eratu re of the reactor, C R oom temper ature, C Overa ll heat transf er coef cient, Ua (W/C)

1.333 80 34 0.5190

1.667 80 34 0.5743

3.667 80 34 11.73

5.167 80 34 13.68

7.167 80 34 15.85

9.167 80 34 17.71

10.500 80 34 18.8312.083 80 34 20.05

16.667 80 34 23.05

Table 3

List of dimensionless variables.

Items Name

qVk0exp E=RT f Dimensionless ow rate

H CAf

Cp T f Dimensionless heat of reaction or exothermicity parameter UaCp Vk0exp E=RT f Dimensionless heat transfer coefcient

TT f T f Dimensionless reactor temperature

X exp 1 = Dimensionless temperature variable ERT f Dimensionless activation energy

Fig. 2.Region of existence of input multiplicity (T f= 20.2 C, = 0.235, = 37.85,

= 16.93 & 3.36, CAf= 5000 mol/m

3

,C= 0.0027).

215N.S. Jayakumar et al. / Chemometrics and Intelligent Laboratory Systems 135 (2014) 213222


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3. Reaction system

The acid catalyzed hydrolysis of acetic anhydride was chosen forstudying the dynamics of a CSTR reactor. Theoverall hydrolysis of acetic

anhydride reaction can be represented as:

CH3CO 2OAceticanhydride

H2OH2SO4Catalyst

acetic acid solvent2CH3COOH

Acetic acid

: 2

The mechanisms of the hydrolysis of acetic anhydride are well doc-

umented. It is well known that the reaction proceeds via a substitution,

in which an attacking nucleophile replaces a substituent group on the

central carbon.

The reaction is of therst order with respect to acetic anhydride. The

batch reaction kinetic equation for acid catalyzed hydrolysis of acetic

anhydride as given by[20]is:

rA 1:85 1010

Csexp 11; 243:9=T

CA and

H 58520 RTD probe J=mol:

3

The kinetic parameters of the above reaction system obtained by

[20]are used to simulate the CSTR reactor.

4. Modeling of non-isothermal CSTR

The conditions necessary for the occurrence of input multiplicity

for the system under study are theoretically determined using the

same approach as that of a previous work by [2]. They have predicted

methods for the determination of parametric regions with a number

of solutions. To control theexit temperature andthe conversion through

manipulating theow rate (q) and the coolant ow rate (qc), both the

manipulated variables q and qc should satisfy steady state mass and

energy balance equations for any feasible values of concentration (CA)

and absolute temperature (T), hence input multiplicity cannot occur

for any set of parameters.

The mathematical equations characterizing the dynamic behavior of

the non-isothermal CSTR are modeled using the unsteady state material

and energy balance and Arrhenius relation. The unsteady state material

and energy balance for a single CSTR are given as:

VdCAdt

q CAfCA VkCA 4

CpVdT

dt qCp T fT Ua TcT VH k CA: 5

The temperature dependency of rate of reaction according to

Arrhenius theory is k = k0exp(E/RT).

The steady state material and energy balances for the reaction in

study are:

q CAfCA Vk0 expE=RT CA 0 6

q Cp T fT Ua TcT VH k0 expE=RT CA 0: 7

Consider a case where the temperature in the reactor is controlled

by manipulating the ow rate, by eliminating the concentration term

Fig. 3. Region of existence of input multiplicity (Tf= 24 C, = 0.235, = 37.85,

= 20.74 & 1.65, CAf= 5000 mol/m3).

Fig. 4.Region of existence of input multiplicity (Tf= 31.3 C, = 0.235, = 37.85,

= 23.81 &0.478, CAf= 5000 mol/m

3

,C= 0.072).

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from Eqs. (6) and (7) and by introducing dimensionless variables as and

can be rewritten and shown inTable 3.

The mass balance in dimensionless can be written as:

CAfCA

1 eE TT f

RTTf

8

X 1

eE TT f

TT f

: 9

The energy balance is rearranged to get the dimensional form

equations into dimensionless form as given below:

e ERT fT fe

ERT fT e

TCe

T BT fe ERT

CACAf

0 10a

e ERT fT fe

ERT fT e

TCe

T BT fe ERT 1

1

e

0

10b

e ERT fT fe

ERT fT e

TCe

T BT fe

ERT

1 X

0 10c

e

T fe

T e

TCe

T BT fe

ERT

1 X

0 10d

T

T f

c

1

1

BeTRT

e X 0 10e

c

1

1

BX

X 0 10f

c

BX

X 0 10g

c

BX

X 0 10h

C

BX

X 0 10i

C

BX

X 0 10j

c X

X 0: 11

A single steady state equation relating the dimensionless tempera-

ture T and the dimensionless ow rate is obtained by eliminating

the concentration term from the steady state mass and energy balance

equations for a perfectly mixed CSTR for a rst order exothermic reac-

tion is as in Eq.(11).Table

4

S

teadystatetemperatureofCSTRundervariousprocessconditions(Tf=

20.2C).

Feedtemperature,Tf(C)

20.2

Initialreactortemperature,Ti(C)

20.6

20.6

32.0

32.0

40.0

40.0

Processvariables

Expt.steadystatetemperature(C)

Steadystate

predictedtemp(C)

Expt.steadystate

temperature(C)

Steadystatepredicted

temp(C)

Expt.steadystate

temperature(C)

Steadystate

predictedtemp(C)

CAfmol/m

3

q106

m3/s

qc

106

m3/s

5000

0.4367

10.50

23.00

24.2

23.00

24.24

23.00

24.16

5000

0.0937

12.00

23.00

24.6

23.00

24.57

23.00

24.72

6000

0.6700

10.50

24.96

24.7

24.92

24.62

24.92

24.35

6000

0.0615

13.33

25.10

25.0

25.10

25.02

25.10

25.03



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5. Results and discussion

5.1. Input multiplicity region

Eq. (11) is quadraticin , sothat atmost two valuesof mayexist for

any specied dimensionless temperature,. This implies the existence

of a single steady state temperature for two manipulating ow rates.

Using the kinetic parameters for the hydrolysis of acetic anhydride

[20],the dimensionless quantities are calculated for various conditions.

The regions of existence of input multiplicity were identied for various

combinations of process variables (temperature, concentration and

kinetic parameters) by drawing graphs of (dimensionless heat

transfer coefcient) versus(dimensionless temperature). The input

multiplicity region enclosed within the curve is shown inFigs. 24.

For a different feed reactor temperature the region of input multiplicity

is plotted and is shown inFigs. 24for different feed reactor tempera-

tures of 20.2, 24.0 and 31.3 C respectively. For thereaction experiments

on the hydrolysis of acetic anhydride in non-isothermal CSTR, the pro-

cess variables causing input multiplicity are calculated theoretically

from the above region and these are summarized inTable 1.

5.2. Experimental study

The experiments concerning the sulfuric acid catalyzed hydrolysisofacetic anhydride reaction were carried out with various process vari-

ables chosen to observe the existence of input multiplicity, as shown

in Table 1. In each case, the input multiplicity was conrmed by observ-

ing the same steady state temperature in CSTR with two different feed

ow rates (q values), while all other variables remained the same, and

the experimental values of steady state temperature for the two feed

ow rates were also found to be in close agreement.

The experimental results showed that the effect of initial reactor

temperature was almost nil on the steady state temperature. For the

three different initial reactor temperatures, the value of steady state

temperature was almost the same. For feed temperature 20.2 C, the

experiments were carried out at three different initial reactor tempera-

tures of 20.6 C, 32 C and 40 C. The steady state temperature for each

case wasalmost the sameat a particular feed concentration as shown in

Tables 4 and 5. Similar results were obtained for the other feed temper-

atures. The time versus temperature proleof reactionfor all the sets of

process variable combinations were also recorded. The transient time

versus temperature prole obtained for the experiments representing

different feed temperatures and feed concentrations are shown in

Figs. 5 and 6. For a particular process variable combination where

input multiplicity was observed, the time taken for reaching the steady

state temperature was much higher for the lower ow rate in compar-

ison to the higher ow rate. For example, in case of Tf= 20.2 0C,

Ti= 40 C, CAf= 6000 mol/m3 (Fig. 5), the steady state temperature

for q = 0.0615 106 m3/s was obtained after 300 min whereas for

q = 0.67 106 m3/s, the steady state is reached before 50 min. The

same observation was obtained when the initial reactor temperature,

Ti = 32 C at feed temperature Tf= 24 C and feed concentration of

acetic anhydride CAf= 5000 mol/m3 conditions, as shown inFig. 6.

The experimental time taken to steady state temperatures for feed tem-peratures, Tf, = 20.2 C, 24 C and 31.3 C are as shown inTables 68.

It was observed that the time taken by the reactor was too long at a

low feed ow rate of reaction mixture than at a higher feedow rate re-

action mixture and is shown in Tables 68. It was found experimentally

that the reactor started with higher initial temperatures that reached

Table 5

Steady state temperature of CSTR under various process conditions (T f= 31.3 C).

Feed temperature, Tf(C) 31.3

Initial reactor temperature, Ti(C) 32.0 32.0 40.0 40.0

Process variables Expt. steady state temperature (C) Steady state predicted temp.

(C)

Expt steady state temperature (C) Steady state predicted temp.

(C)CAfmol/m

3 q 106 m3/s qc 106 m3/s

5000 2.7210 0.8333 44.1 37.69 44.1 36.88

5000 0.0546 11.6667 44.0 38.46 44.0 37.50

6000 3.5160 8.8333 56.2 37.30 56.25 37.02

6000 0.0422 13.8333 56.0 37.88 56.10 37.52

q = 0.670x 10-6m3/s

q = 0.062x 10-6m3/s

40

35

25

30

20

Temperature,T

(C)

0 100 200 300 400

Time, t (min)

Fig. 5. Time versus temperature prole(Tf= 20.2 C, Ti = 40 C,CAf= 6000 mol/m3 and

q = 0.0615 10

6

m

3

/s and 0.670 10

6

m

3

/s).

q = 0.889x 10-6m3/s

q = 0.072x 10-6m3/s37

32

27

220 50 100 150 200 250 300

Time, t (min)

Temperature,

T(C)

Fig. 6.Time versus temperature prole (Tf= 24 C, Ti= 32 C, CAf= 5000 mol/m3 and

q = 0.0715 10

6

m

3

/s and 0.8880 10

6

m

3

/s).

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Table 6

Experimental time taken to reach steady state reactor temperature (T f= 20.2 C, CAf= 5000 mol/m3).

Feed temperature, Tf(C) 20.2Initial reactor temperature, Ti(C) 20.6 32.0

Process variables Expt. time taken to reach steady state (min) Expt. time taken to reach steady state (min)

CAfmol/m3 q 106 m3/s qc 10

6 m3/s

5000 0.4367 10.50 80 34

5000 0.0937 12.00 166 112

6000 0.6700 10.50 62 22

6000 0.0615 13.33 380 126

Table 7

Experimental time taken to reach steady state reactor temperature (T f= 24 C, CAf= 5000 mol/m3).

Feed temperature, Tf(C) 24

Initial reactor temperature, Ti(C) 25 32.0


CAfmol/m

3

q 10

6

m

3

/s qc 10

6

m

3

/s5000 0.8997 9.833 51 20

5000 0.0715 11.66 294 82

6000 1.21 9.833 42 14

6000 0.0528 12.0 372 200


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steady state temperature faster than that with the low initial reactor

temperature.

5.3. Parametric variation

CSTR parameters such as cooling water ow rate, feed ow rate of

reaction mixture, reactor feed temperature, and initial reactor tempera-

ture were varied in the region of input multiplicity by simulating the

dynamic equations for parameter sensitivity in CSTR.

The governing equations of the CSTR reactor system with i = qc as

parameter can be rewritten as:

dCAdt

q CA0CA

V kCA F1 12

dT

dt

qCp T fT

VCp ws

H VkCAVCp ws

Ua TTc VCp ws

F2 13

dTcdt

Ua TTc

VccCpc

qcVc

TcinTc F3 14

d

dt

dCAdqc

F1CA

F1T

F1Tc

dCA

dqc

dT

dqc

dTcdqc

T F1qc

15

d

dt

dT

dqc

F2CA

F2T

F2Tc

dCA

dqc

dT

dqc

dTcdqc

T F2qc

16

d

dt

dTcdqc

F3CA

F3T

F3Tc

dCA

dqc

dT

dqc

dTcdqc

T F3qc

: 17

The above Eqs.(12)(17)were simulated and the results of simula-tions for parameter such as q, qc, Tf, Ti were shownin Fig. 7. The variation

of parameters such as q, qcand Tiwithin the range of 2% about the oper-

ating conditions do not show any signicant effect on both CSTR steady

state and transient reactor temperatures shown in Figs. 79. Buthowever

the feed temperature seems to affect the transient reactor temperatures

and steady state temperature is greatly inuenced by a variation in

reactor feed temperature, Tf, as shown inFig. 10.

6. Conclusions

Theregions of existenceof input multiplicity have been theoretically

identied for a non-isothermal CSTR with sulfuric acid catalyzed hydro-

lysis of acetic anhydride reaction system. Experimental investigations

were conductedin theidentied regionsand theexistence of input mul-tiplicity was conrmed for the above reaction system. Wherever input

multiplicity was observed for the system, it was found that the initial

reactor temperature did not affect the steady state temperature in the

non-isothermal CSTR. For a particular process variable combination

Table 8

Experimental time taken to reach steady state reactor temperature (T f= 31.3 C, CAf= 5000 mol/m3).

Feed temperature, Tf(C) 31.3

Initial reactor temperature, Ti(C) 32.0 40.0


CAfmol/m3 q 106 m3/s qc 10

6 m3/s

5000 2.7210 0.8333 30 12

5000 0.0546 11.6667 348 100

6000 3.5160 8.8333 12 10

6000 0.0422 13.8333 412 112

20.65

20.6

20.55

20.5

20.45

20.4

20.35

20.3

20.25

0 50 100 150

time, t

Temperature,T

q= 0.088275e-6

q= 0.089167e-6

q= 0.900583e-6

Fig. 7.Effect of

ow rate of reaction mixture, q variation in the region of input multiplicity (CAf= 5000 mol/m

3

, Tf= 20.2 C, qc= 1.050e

5

m

3

/s).



9/10

where input multiplicity was observed, the time taken for reaching

the steady state temperature was much higher for the lowerow rate

in comparison to the higher ow rate. The simulation study on the

variation of parameters in the region of input multiplicity has shown

that the parameters such as feedow rate of reaction mixture, cooling

water ow rate and initial temperature has no signicant effect affect-

ing input multiplicity. The variation in reactor feed temperature, T f, in

the range of 2% about operating feed temperature equal to 20.2 C has

shown to affect both t the steady state and transient temperature of

the reactor.

Nomenclature

a area of heat exchange, m2

CP specic heat capacity of the reaction mixture, J/(kg C)

E activation energy, J/mol

CAf feed concentration of acetic anhydride, mol/m3

CS concentration of sulfuric acid, mol/m3

CA concentration of acetic anhydride in the reactor, mol/m3

(H) heat of reaction, J/mol

k rate constant of reaction, s1

k0 frequency factor, s1

qA feedow rate of acetic anhydride, m3/s

qB feedow rate of acetic acidwater mixture, m3/s

q feedow rate (qA+ qB) in m3/s

qC coolant waterow rate, m3/s

R universal gas constant

rA rate of reaction, mol/(s-m3)

T temperature of reactor, C

Tf Feed Temperature, C

Ti initial reactor temperature, C

Tc Temperature of coolant, C

U overall heat transfer coefcient, W/(m2 C)

V volume of the reactor, m3

20.65

20.6

20.55

20.5

20.45

20.4

20.35

20.3

20.25

0 50 100 150

time, t

Temp

erature,

T

qc=1.0395e-5

qc=1.0500e-5

qc=1.6050e-5

Fig. 8.Effect of cooling water ow rate, qc, variation in the region of input multiplicity (CAf= 5000 mol/m3, Tf= 20.2 C, q = 0.089167e

6 m3/s).

20.9

20.8

20.7

20.6

20.5

20.4

20.3

0 50 100 150

time, t

Temp

erature,

T

Ti=20.394

Ti=20.600

Ti=20.806

Fig. 9.Effect of initial reactor temperature, Ti, variation in the region of input multiplicity (CAf= 5000 mol/m

3

, Tf= 20.2 C, q = 0.089167e

6

m

3

/s, qc= 1.050e

5

m

3

/s).



10/10

Greek notations

dimensionless exothermicity parameter, H CAfCpT f

dimensionless heat transfer coefcient, UaCpVk0exp E=RT f

dimensionless activation energy, ERT f dimensionless temperature, TT f T fc dimensionless temperaturebasedreference coolant tempera-

ture, TcT f T f dimensionless ow rate, qVk0exp E=RT f density, gm/ml

Conict of interest

We don't have conict of interest.

Acknowledgment

This work was supported by the University of Malaya for fully

funding under HIR-MOHE (UM/MOHE HIR, Grant No. D000020-16001).

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20.65

20.6

20.55

20.5

20.45

20.4

20.35

20.3

20.25

0 50 100 150

time, t

Tempe

rature,

T

Ti=19.998

Ti=20.200

Ti=20.402

Fig. 10.Effect of feed temperature, Tf, variation in the region of input multiplicity (CAf= 5000 mol/m3, Ti= 20.6 C, q = 0.089167e

6 m3/s, qc= 1.050e5 m3/s).

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