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DEHYDRATION OF ETHANOL OVER HZSM-S

bY

Cheng-Liang Chang

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemical Engineering

1985

I a

”VI“.

I.I “
‘

 

 

 

 

ABSTRACT
Dehydration of Ethanol Over HZSM-S
by

Cheng-Liang Chang

Steady state ethanol dehydration kinetics experiments
were carried out with a Mobil's proprietary ZSM-S class
catalyst in an integral reactor operated at atmospheric
pressure and temperatures of lSO'C to 360°C. The reactant
was diluted by helium with a molar ratio of 1:2 through out
the kinetics experiments. A set of liquid hourly space

velocities(LHSV) ranging from 0.46 to 98.9 was used.

The ethanol conversion on HZSM-S yielded a variety of
hydrocarbons ranging from methane and light olefins to
paraffins and aromatics. The selectivity of light olefins
was enhanced by increasing temperature. Excluding water
produced, the maximum yields of C3-C6 light olefins at 250,
300 and 360 'C were 23, 26 and 30 wt%, respectively. The
major products at 150 and 200°C were diethyle ether, water
and ethylene. At 300 and 360.C, the conversion of ethanol
was greater than 90% and trace amounts of ether were found
in the range of residence time used. Aromatics were major
products among the C6+ hydrocarbons when the temperature was

above 300'C.

Cheng—Liang Shana

A mathematical model of the dehydration kinetics (data)
was. developed using the lumping approach with a "built-in"
Langmuir-Hinshelwood type of rate expressions. A nonlinear
parameter estimation using least squares as the objective
function and quasilinearization was used to estimate rate
constants, adsorption equilibrium constants, and activation
energies. The _ Langmuir-Hinshelwood rate equations
successfully correlated the experimental data. The olefin

oligomerization reaction was found to be second order.

The kinetic expressions were utilized in a model
describing the steady state diffusion-reaction in a single
catalyst particle. Orthogonal collocation was used for
solution of the diffusion-reaction models. The single
particle study was extended to a heterogeneous model of an
isothermal Continuous Stirred Tank Reactor to investigate
the effects of varying catalyst properties and reaction

conditions such as temperature and pressure.

Empirical correlations between the selectivity and
reaction conditions reported by previous investigators are
explained by the kinetic model developed which indicates

that the lump reaction network is a good representation of

Caeng- ulwlg

ethanol conversion reactions. CSTR simulation showed that
the selectivity of light olefins can be enhanced by
increasing the temperature and reducing the system pressure.
However, the diffusion limitation influences the selectivity
of light olefins when the size of the catalyst pellets is

greater than 0.02 cm.

DII'CJJIE

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n. C. ... .. p. e C V t.
be a” a. w. «v «a kn nu an .u 3;
.4 i. e. t. C S. o. e 3. nu ab

 

 

ACKNOWLEDGEMENTS

I wish to thank my thesis advisors, Dr. Antonio L.
DeVera and Dr. Dennis J. Miller, for getting me involved
in such a fascinating, albeit at times frustrating, research

topic, and for allowing me to learn from my mistakes.

I also wish to thank Dr. Charles A. Petty for his
friendship and many helpful discussions throughout the

course of my work.

I am particularly indebted to my family and my friends
for their constant moral and spiritual support, which were
the backbone of my persistence in this endeavor. Their
encouragement and confidence in my abilities were

invaluable.

Most of all. I wish to thank my wife,Ching. Her

unfailing support was the source of my dedication and sense

of direction throught the completion of this research.

ii

TABLE OF CONTENTS

LI ST OF FI GURES O I O O O O O O O O O O O O O 0
LIST OF TABLES. . . . . . . . . . . . . . . . .
NOTATI CNS 0 O O O O O O O O O O O O O O O O O 0

CHAPTER
1 Introduction. . . . . . . . . . . . . . .

2 ZSM-S Catalyst and Alcohol Dehydration Catalysis.

2.1 Reaction Networks . .
2.2 The Catalyst. . . . .

2.3 Reaction Mechanism. . . . . . . . . .
2.4 Reaction Kinetics . ‘. . . . . .
2.5 Lumping Approach. . . . . . . . . .
3 Experimental. . . . . . . . . . . . . . .
3.1 Materials . . . . . . . . . . . . . .
3.2 Kinetics Experiments. . . . . . . . .
3.2.1 Equipment. . . . . . . . . . .
3.2.2 Procedure. . . . . . . . . . .
3.3 Intraphase and Interphase Gradients .
4 Results . . . . . . . . . . . . . . . . .
4.1 Experimental. . . . . . . . . . . . .
4. 2 Kinetic Modelling . . . . . . . . . .
4.2.1 The Lump Reaction Network. . .
4.2.2 The Kinetics Models. . . .
4.2.3 The Ordinary Differential Equat
the Integral Reactor . . . . .
4.2.4 Data Fitting . . . . . . . .
4.3 Diffusion- Reaction Modelling. . . .
4.4 CSTR Simulation . . . . . . . . . . .
4.4.1 Temperature Effect . . . . . .
4.4.2 Pressure Effect. . . . . . . .
4.4.3 Catalyst Size Effect . . . . .
4.4.4 Activity Distribution Effects.

5 DiSCUSSion. O O O O O I O O O O O O O O O
6 Conclusions and Recommendations . . . . .

BIBLIOGRAPHY. O O O O O O O O O I O O O O O O O

O O O O O O O O H. O O O O O O O O O O O O O O 0

APPENDIX A Calibrations and Sample Calculations

APPENDIX B Calculation of Possible Transport

iii

on

o o 0 01.0 o o e o o

O

o o o e o o o o I" o I o o o o e o o o o o e o

APPENDIX

APPENDIX

APPENDIX

APPENDIX

Limitation O O O 0 O O O O O O O O O O O O 171
Summary of Data from Kinetics Experiments. 175
Sample Calculation for Data Fitting. . . . 181

Sample Calculation for Diffusion Modelling
in CSTR. I O O O O O O I O O O O O O O O O 193

Summary of Results from CSTR Simulation. . 212

iv

Figure

Figure

Figure
Figure

Figure
Figure
Figure
Figure

Figure
Figure
Figure

Figure

Figure
Figure
Figure
Figure

Figure

2.1

2.2
2.3

3.1

3.7

3.8

4.1

LIST OF FIGURES

Schemes for reaction pathways in the

literature. .

Structure of ZSM-5. . . . . . .

Reaction mechanism for the ethanol
conversion to hydrocarbons. . .

Continuous flow apparatus design for

kinetics study

Photograph of apparatus. . . .

Schematic of the vaporizer. . .

Schematic of the reactor. . . .

Schematic of the water displacement tower

Typical gas chromatogram for CC analysis

of gas sample

Typical gas chromatogram for CC analysis

of gas sample

Typical gas chromatogram for CC analysis
of liquid sample. . . . . . . .

Lump reaction network . . . . .

o_e e e

4.2(a)Arrhenius plots for k},k},k. and K. in

Model I . . .

4.2(b)Arrhenius plots for k;,k},k. and k, in

4.3

4.4

Model I . . .

Concentrations
kinetics study

Concentrations
kinetics study

Concentrations
kinetics study

versus residence
using model I at

versus residence
using Model I at

versus residence
using Model I at

time for
150 C . .

time for
200'C . .

time for
250'C . .

. .22
.25

.35
. .43

.64

 

 

 

"I

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

4.12

4.13

4.14

4.15

4.16

4.17

4.18

4.19

time for
300 C O 0

versus residence
using model I at

Concentrations
kinetics study .71
time for
360'C . .

versus residence
using Model I at

Concentrations

kinetics study .72

time for
300°C . .

versus residence
using Model 11 at

Concentrations
kinetics study .73
versus residence time for

using model 11 at 360'C . .-

Concentrations
kinetics study .74
Concentrations versus residepce time for
reversible reaction 5 at 360 C . . . . . . .77
concentration profiles in catalyst
Profiles of ethylene and C3-C6
are decreasing along X/L-axis . . .

Typical
pellet.
olefins .83
concentration profiles in catalyst
Profiles of ethylene and C3-C6
have local maximum points . . . . .

Typical
pellet.
olefins .84
Bulk mole fraction of ethylene versus %
conversion of ethanol in CSTR for various
temperatures. L20.01 cm, P=1 atm . . . . . .88
Bulk mole fraction of C3-C6 olefins versus %
conversion of ethanol in CSTR for various
temperatures; L=0.01 cm, P=10 atm . . . . . .89
Bulk mole fraction of aromatics and C6+
aliphatics versus % conversion of ethanol in
CSTR for various temperatures;

L-0.01 cm, Po=1 atm . . . . . . . . . . . . .90
Selectivity of C3-C6 olefins over ethylene
versus % conversion of ethanol in CSTR for
various temperatures; L=0.01 cm, P=l atm. . .91
Selectivity of C3-C6 olefins over aromatics
and C6+ aliphatics versus % conversion of
ethanol in CSTR for various temperatures;
Ls0. 01 cm, P21 atm . . . . . . . . .
Selectivity of C2- C6 olefins over ether and
aromatics versus % conversion of ethanol in
CSTR for various temperatures;

L80.01 cm, Pal atm . . . . . . . . .

.92

O O O

Selectivity of C3-C6 olefins over other

vi

 

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. . . o .‘a
”I. nib ’5

a.

.4.

a:

 

nus

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Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

4.32

4.33

4.34

4.35

3.37

4.38

4.39

versus % conversion of ethanol in CSTR for
various pellet sizes; T8400‘C, P=1 atm. . . 108

Selectivity of C3-C6 olefins over aromatics

and C6+ aliphatics versus % conversion of
ethanol in CSTR for various pellet sizes
T2400'C, P=l atm. . . . . . . . . . . . . . 109

Selectivity of C2-C6 olefins over ether and
aromatics versus % conversion of ethanol in
CSTR for various pellet sizes;

T-400°C, Pal atm. . . . . . . . . . . . . . 110

Selectivity of C3-C6 olefins over other
products versus % conversion of ethanol in

CSTR for various pellet sizes;

T=400°C, Pal atm. . . . . . . . . . . . . . 111

Physical pictures of cases in step
distribution of catalyst activity . . . . . 113

Bulk mole fraction of ethylene versus %
conversion of ethanol in CSTR for step
activity distribution study;

L30.05 cm, T2400'C, P-l atm . . . . . . . . 114

Bulk mole fraction of C3-C6 olefins versus %
conversion of ethanol in CSTR for step
activity distribution study;

L-0.05 cm, T-400'C, Pal atm . . . . . . . . 115

Bulk mole fraction of aromatics and C6+
aliphatics versus % conversion of ethanol in
CSTR for step activity distribution study;
L-0.05 cm, T-400'C,.P-1 atm . . . . . . . . 116

Selectivity of C3-C6 olefins over ethylene
versus % conversion of ethanol in CSTR for

step activity distribution study;

L=0.05 cm, T8400'C, P=1 atm . . . . . . . . 118

Selectivity of C3-C6 olefins over aromatics

and C6+ aliphatics versus % conversion of
ethanol in CSTR for step activity

distribution study;

L-0.05 cm, T=400'C, P81 atm . . . . . . . . 119

Selectivity of C2-C6 olefins over ether and

aromatics versus % conversion of ethanol in
CSTR for step activity distribution study;

viii

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

5.1

5.3

5.4

5.5

5.6

5.8

5.9

5.10

5.11

L=0.05 cm, T=400°C, P=1 atm . . . . . . . .

Selectivity of C3-C6 olefins over other
products versus % conversion of ethanol in
CSTR for step activity distribution study;
L80.05 cm, T=400°C, P21 atm . . . . . . . .

Concentration profiles of ethylene in
catalyst pellet for various temperatures;
’Ts25 sec, L80.01 cm, P21 atm . . . . . .

Concentration profiles of C3-C6 olefins in
catalyst pellet for various temperatures;
'T-ZS sec, L30.01 cm, Pal atm . . . . . .

Concentration profiles of ethylene in
catalyst pellet for various pellet sizes;
’T-l sec, T=400 C, Pal atm. . . . . . . . .

Concentration profiles of C3-C6 olefins in
catalyst pellet for various pellet sizes;
'T-l sec, T-400'C, P-l atm. . . . . . . . .

Concentration profiles of aromatics and C6+
aliphatics in catalyst pellet for various
pellet sizes; 7'al sec, T2400 C, P21 atm. .

Concentration profiles of ethanol in
catalyst pellet for step activity
distribution study; T2400 C, P=1 atm. . . .

Concentration profiles of ethylene in
catalyst pellet for step activity
distribution study; T8400 C, Pal atm. . . .

Concentration profiles of C3- C6 olefins in
catalyst pellet for step activity
distribution study; T=400 C, P81 atm. . . .

Concentration profiles of aromatics and C6+
aliphatics in catalyst pellet for step
activity distribution study;

Ethanol conversion=40%, T=400' C, Pal atm. .

Concentration versus residence time for
kinetics study using single site model
at 1500C. O O O O O O O O O O O O O O O O 0

Concentration versus residence time for
kinetics study using single site model

ix

120

125

126

129

130

131

133

134

135

136

139

Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

"1323’
NH

.4

F.6

F08

F.9

at 200°C. . . . . . . . . . . . . .

Calibration curve for Matheson 601 tube

Calibration curve for Matheson 602 tube

Concentration versus residence time
CSTR study; T2300°C, L20.01 cm, P21

Concentration versus residence time
CSTR study on temperature effect;
T2350°C, L20.01 cm, P21 atm . . . .

Concentration versus residence time
CSTR study on temperature effect;
T2400'C, L20.01 cm, P21 atm . . . .

Concentration versus residence time
CSTR study on pressure effect;
P210 atm, T2400'C, L20.01 cm. . . .

Concentration versus residence time
for CSTR study on pressure effect;
P21 atm, T2400°C, L20.01 cm . . . .

Concentration versus residence time
CSTR study on pressure effect;
P20.1 atm, T2400°C, L20.01 cm . . .

residence time
size effect;
P'l atm. O O 0

Concentration versus
CSTR study on pellet
L20.001 cm, T2400 C,

Concentration versus residence time
CSTR study on pellet size effect;
L20.02 cm, T2400°C, P21 atm . ... .

Concentration versus residence time
CSTR study on pellet size effect;
L20.05 cm, T2400'C, P21 atm . . . .

Concentration versus residence time

for
atm

for

for

for CSTR study on pellet size effect;

Concentration versus residence time

CSTR study on step activity distribution

effect (case 1) . . . . . . . . . .

Concentration versus residence time

X

for

for

140
154
155

215

216

217

218

219

220

221

222

223

224

225

Figure F.l3

CSTR study on step activity distribution
effect (case II). 0 O O I O O O O O O O O O 226

Concentration versus residence time for

CSTR study on step activity distribution
effect (case III) . . . . . . . . . . . . . 227

xi

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table
Table

Table

4.1

4.2

4.8

4.9

4.10

Lumped Data
150 C O O O

Lumped Data
200.C I O O

Lumped Data
250.c O O O

Lumped Data
300‘C . . .

Lumped Data

of Kinetics

of Kinetics

of Kinetics

of Kinetics

of Kinetics

LIST OF TABLES

Experiments

Experiments

Experiments

Experiments

Experiments

at

360.C O O O O O O O O O O O O I O O O O 0 0
Normalized Distribution of C3-C6 Olefins. .

Estimated Rate Constants of Model I at
150.C and 200.C O O O O O O O O O O O O O 0

Estimated Rate Constants of Model II at
150.C and 200.C O O O O O I O I O O O O O 0

Estimated Rate Constants of Model I at
250,300 and 360.C O O O O O O C O O O O O 0

Estimated Rate Constants of Model II at
250,300 and 360.C O O O O O O O O O O O I O

Arrhenius Frequency Factors and Activation
Energies of Parameters in Model I . . . . .

Dimensionless Second Order O.D.E.s and
Boundary Conditions for Diffusion-Reaction
"Odelling O O O O O O O O I O O O O I O O 0

Estimated Rate Constants for Single Site
Model at 150 and 200'C. . . . . . . . . . .

FID Response Factor . . . . . . . . . . . .
Data for Run-1 at 300°C . . . . . . . . . .

Data for Kinetics Experiments at 150°C. . .

xii

Page

.46

.47

.48

.49

.50
.57

.61

.62

.65

.66

.75

.80

141
157
160
176

Table C.2
Table C.3
Table C.4
Table C.5

Data
Data
Data

Data

for
for
for

for

Kinetics Experiments
Kinetics Experiments
Kinetics Experiments

Kinetics Experiments

xiii

at

at

at

at

200°C.
250'c.
3oo'c.
360°C.

177
178
179
180

NOTATION

(Notations in APPENDIXES are not included. Comprehensive
definitions are given in the text)

Bi
Chg
Ci
Ci}
1»;

In;

hi
KL

k8

mass Biot number for species 1 ,kgé L/D
bulk concentration of species 1

local concentration of Species i

inlet concentration of species i
effective diffusivity of species }

diffusivity ratio of reactant(1) over species j,
Dal/Dgi

dimensionless adsorption equilibrium constant,K.Pb

adsorption-desorption equilibrium constant for
species 1, l/atm

forward reaction constant of the rate determining
step for elementary reaction i

backward reaction constant of the rate determining
step for elementary reaction 1

combined rate constant for dual site model,

which incorporates the adsorption equilibrium
constant for the reactant of the elementary
reaction i, the rate constant for the rate
determining step of the elementary reaction 1,

and a conversion factor to allow for the total
number of active sites per unit weight of catalyst

combined rate constant for Single site model
combined rate constant for the elementary reaction

i with the rate determining step to be chemisorption
of the reactant

external mass transfer coefficients for species i

half thickness of the catalyst slab

partial pressure of species i or pressure of
inlet stream

xiv

w.

a

V.

v...

 

 

Pb

Pb;
Qb
q;

y;

Fri

bulk pressure

bulk partial pressure of species i

outlet volumetric flow rate of CSTR

inlet volumetric flow rate of CSTR

gas constant

rate of formation of species i

reaction rate of elementary reaction 1

molar ratio of inlet stream over outlet stream

number of the unoccupied active sites per unit
weight of catalyst

number of the active sites occupied by species i
per unit weight of catalyst

total number of active sites per unit weight of
catalyst

time ratio of the system residence time over the
characteristic holding time in the catalyst pellet

residence time based on the volumetric flow rate -
of inlet gas stream in a PFR

reactor volume
local volumetric flow rate in PFR

distance from the center of the catalyst slab,
OéxeL

ratio of the local molar flow rate of Species i

to the total molar flow rate of the gas stream
entering a PFR or local mole fraction of species i
based on the bulk molar density in CSTR

bulk mole fraction of species j

inlet mole fraction of species j

XV

Greek Symbols

E

6

<12.

0
0
6
7.

dimensionless position variable, x/L
void fraction of the catalyst in the reactor

Thiele modulus based on the diffusivity of
reactant(1) for elementary reaction i

apparent density of catalyst, gcgt/volume of
catalyst

total external Surface area of catalyst pellet
in the reactor

a common fraction factor of the active sites covered
by different Species, 1/(1+2K;P,)

residence time based on the volumetric flow rate
of inlet gas stream in a CSTR

CHAPTER 1

Introduction

Although the alcohol dehydration reaction on solid
catalyst was discovered nearly two centuries ago [1], it was
not until the early 1970s that the industrial potential of
the reaction emerged. In view of the critical energy
situation around the world, coal, fermentation products, and
other non-petroleum materials are expected to become
important sources of fuels during the next several decades.
Since Mobil announced the invention of the
methanol-to-gasoline (MTG) process using ZSM-S class zeolite
in 1976 [10],‘ considerable efforts have been made in the
development of the process. Since the conversion of coal to
methanol is a well-established commerical technology,
coupling of the methanol process with this technology
provides a new route for the conversion of coal to gasoline.
This route provides a high quality gasoline which can be
used directly in automobiles without any of the
disadvantages normally associated with other coal conversion

process such as the Fischer-Tropsch process.

The Mobil process can also be used in converting
ethanol to high quality gasoline, and ethanol can be

produced by fermentation of farm products. In the
1

conversion of farm products to liquid fuel by fermentation,
large energy savings are possible if distillation to
anhydrous alcohol for gasoline blending is replaced by
gasoline production with the Mobil process [77].
Significant problems related to performance and reliability
of using the ethanol-gasoline blends in existing vehicles
would have to be solved. These problems include possible
phase separation in hot climate, corrosion effects on auto
parts, and required fuel storage modifications and are
addressed by Maiorellar [77]. Although alcohol from
fermentation is thus best converted to gasoline, the
commercial application is not presently economical. For
this reason, little effort has been made on the ethanol
conversion compared to the methanol case. As ethanol can be
produced easily in a fermentor and is an endless energy
resource, a small well-designed unit for farmer's use to
convert their home-grown corn into gasoline has commercial

potential in the future.

The reaction path for the alcohol conversion to
hydrocarbons has been shown to involve a sequence of steps
[11,12]. The kinetic study in such a complex reaction
network is difficult. Rational kinetic modelling and
reactor design on the alcohol conversion can not be found in

the literature. Commercial reactor design based on

 

 

a:

8..

 

 

empirical data can neither be efficient nor trustworthy. A
good example is shown in the monograph by Weekman [63] in

developing a lumped kinetic model for catalytic cracking.

The objective of this research is to obtain sufficient
data on the ethanol dehydration reaction using ZSM-S, and to
develop a reliable kinetic model which can fit the
experimental data and interpret the important observations
in the literature. The kinetic results are intended to form
the groundwork for subsequent studies under conditions close
to industrial conditions. The ultimate goal is the design
and operation of commercial alcohol conversion to

hydrocarbons process.

 

 

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ID

 

 

CHAPTER 2

ZSM-S Catalyst and Alcohol Dehydration Catalysis

The following section is a review of several important
background subjects, including alcohol dehydration reaction
network,the ZSM-S catalyst structure, the dehydration
reaction mechanism and kinetics, and the lumping approach in
a complex reaction system. This is not intended to be a
comprehensive review; references to more detailed

discussions are given.

2.1 Reaction Networks

When Bondt, Deiman, van Troostwyk and Lauwerenburg [1]
reported their discovery of forming ethylene by passing
ethanol or ether over heated alumina or silica in 1797,
alcohol dehydration became one of the first catalytic
reactions discovered and has been since studied for nearly
two centuries. This reaction has been the subject of several

excellent reviews [2,3,4]; only a few remarks are made here.

Both simple consecutive and parallel reactions were
first employed using the observed maximum ether
concentration as a function of the residence time and the

reversibility of the etherification reaction [5,6,7]. A

 

general parallel-consecutive reaction scheme has been
developed and widely accepted by gradual addition of further
steps to the original consecutive or parallel scheme [8], as
is shown in Figure 2.1(a). The relative participation of
the various steps depends on a number of factors such as the
reaction conditions, the structure of the starting alcohol,

the property of the catalyst, etc.

Although a variety of substances have been found to be
active in the dehydration reaction [2], most of the studies
have been done with alumina for two reasons: 1) alumina is
easy to prepare and does not readily poison, and 2) there is
only small need to prepare olefins from alcohols for
teaching and research purposes. Only a few studies on the
alcohol dehydration were conducted with zeolites[4,9]. A
methanol-to-gasoline(MTG) process using ZSM-S class zeolite
was announced by Mobil in l976[10]. The reaction path for
methanol conversion to gasoline using zeolites has been
shown to involve a sequence of steps [11,12], shown in
Figure 2.1(b). The primary olefins are converted to higher
hydrocarbons by oligomerization reactions on zeolites. The
aromatics and paraffins are formed in cyclization and

hydrogen transfer reactions.

 

A:

 

r:
0‘ ‘
\u .

 

(a) A general parallel-consecutive reaction scheme for
alcohol dehydration [8].
ether +H;0

2 alcohols olefin + alcohol + Hyo

2 olefins + 2H10

(b) A simplified reaction scheme for MTG process [11.12].

201430}! =:——:-= CH30CH3+H10

Cg-C, light olefins

)

Cg'olefins
paraffins
cycloparaffins
aromatics

Figure 2.1 Schemes for reaction pathways in the
literature [8.11.12].

It is the purpose of this section to point out the
importance of the strong acidic sites of the zeolite which
catalyze the primary olefins in scheme (a) of Figure 2.1 to
hydrocarbons. The shape selective nature of the catalyst
also provides the selectivity to important species. The
invention of the MTG process provides an indirect way to
convert synthesis gas to high quality gasoline with research
octane number of 90-100. It is better than the direct(but
poor in selectivity) Fischer-Tropsch process. Although
significant progress has been made in the development of the
MTG process [12,13], little effort has been made in the
dehydration of alcohols other than methanol using zeolite as

catalyst.
2.2 The Catalyst

An extensive list of the dehydration catalysts can be
found in the literatures [2,14]. The important groups of
the dehydration catalysts are oxides, aluminosilicates,
metal salts, and cation exchange resins. The structure and
chemistry of the aluminosilicates, the most important
catalysts in the petroleum industry, are well discribed in
the classic monographs of Breck [15] and Rabo [16]. Since

it was not the expectation of this investigation to provide

much new insight into the zeolite structure, only a brief
discription of the most effective catalyst, ZSM-S, used in

this research is given here.

Zeolite is composed of A101 and SiO4 tetrahetra which
are connected through shared oxygen atoms, forming a three
dimensional framework with a net negative charge. The
negative charge is balanced by cations M which leads to the

general representation for zeolite as follows:

Hz/n[ (”502% (5a 0;) ] 2/7'20

I

ZSM-S can be synthesized in the broad range of silica to
alumina ratio, 5<y/x<°’ . When MM is a proton, the zeolite
becomes a very strong Bronsted acid, which may be due to the

low aluminum content in the structure.

The chemistry and structural framework of ZSM-5 is
fairly well vknown[17-24]. In brief, ZSM-S possesses an
exceptionally high degree of thermal and acid stability and
low degree of coking. The characteristic configuration of
ZSM-5 consists of eight five-membered rings, as shown in
Figure 2.2(a). These units join through edges to form
chains which are connected to form sheets, and the linking
of the sheet lead to a three dimensional framework
structure(a channel system) as shown in Figure 2.2. The

unique channel system consists of two types of intersecting

a

 

A.

 

 

:5.

\n.

 

 

(a)Characteristic configuration (b)Chain from linkage of
in ZSM-5 (a) in ZSM-S

   

 

(c)Skeletal diagram of the (d)Channel Structure in
zsm- 5 unit cell zsm-S

Figure 2.2 Structure of ZSM-5

 

10

channels: ellipsoidal lO-membered ring straight channels
with openings of 5.4x~5.6 A and sinusoidal tortuous channels
with openings of 5.1% 5.4 A, as shown in Figure 2.2(d). The
unique pore dimensions cause a shape selectivity on reactant
and products in that formation of hydrocarbons larger than
C11 is inhibited and the intracrystalline coke deposition is

prevented[18,25,26].

The activity distribution inside the structure is also
an important factor on the performance of ZSM-5. The
activity has been attributed primarily to the surface
Bronsted acid sites [27,28]. The role for Lewis sites in
the initial step of forming dimethyl ether from methanol is
also suggested [29]. As mentioned in the previous
paragraph, the acidity of zeolite is due to the aluminum
content. This leads to an important question: are the
active sites homogeneously distributed in a ZSM-S particle?
Since the way the active sites are distributed affects the
performance of ZSM-5, studies of the aluminum distribution
have been conducted, resulting in different conclusions
[30-34]. Suib et a1 [30] and Dwyer et a1 [31] conclude that
the surface silica-to-alumina ratio of ZSM-5 is closed to
that of the bulk. Derouane et a1 [33] and van Ballmoos et
a1 [32] have found an enrichment of alumina at the surface

of ZSM-5. Hughes et al have found' a silicon-rich outer

11

surface and an aluminum-rich interior in their ZSM-S sample.
The different distributions can result from the variety of

ways to prepare the zeolite.

It is thus seen that there is a unique structure of
ZSM-5, and that the active sites are not necessary
homogeneously distributed in the ZSM-5 framework, a fact
which. could affect the performance of the catalyst to some

degree.
2.3 Reaction Mechanism

Most studies on the mechanism investigation, of the
initial alcohol dehydration reaction have been done with
alumina. Review of the mechanisms hypothesized can be found
in several articles [2,3,4]. A review of the mechanisms of
the initial reaction on zeolite suggested is given by Venuto
and Landis [9]. The mechanisms of the olefin
oligomerization, cyclization, and H-transfer over acidic
catalysts are well understood and proceed via classical
carbonium mechanisms [9,44]. The mechanism of the initial
C-C bond formation in the methanol dehydration reaction has
recieved much attention in the past decade. Different
mechanisms of the methanol conversion to dimethyl ether and

C2+olefins over ZSM-S, invoking carbenes [11,12,45], oxonium

12

ions [46-49], trimethyloxonium ion [40], surface alkoxyls
[50] and pentacoordinate carbon [51] have been postulated.
A comprehensive review of the major mechanistic aspects of
the methanol dehydration is given in the literature [52,53].
Since it is not the expectation of this investigation to
provide insight into the details of the mechanism, only a
brief overview of the major mechanisms suggested on ethanol

dehydration will be given here.

A number of contradictory views have been published
concerning the structure of adsorbed alcohols and the nature
of adsorption sites [14]. A general form of the surface
complex is shown in Figure 2.3(a). The surface complex is
then decomposed to ethylene and water through a classical
fl -elimination process. The surface complex can also be
attacked by the second alcohol molecule either from the gas
phase or from an adjacent weakly adsorbed state. The
cooperation of acidic and basic sites seems to be necessary,
but no strong evidence is presently available. The
mechanisms of the elimination and etherification reactions
of ethanol are shown in Figure 2.3(b)(c). The mechanism of
the oligomerization or polymerization of olefins is
illustrated by ethylene polymerization employing a typical

carbonium ion type of mechanism, as shown in Figure 2.3(d).

of.

.— u

a .

 

 

 

‘zge
\us

13

(a) A general form of the surface complex for a ethanol
molecule absorbed on active site of zeolite

SH 86)
HQ - CHI—'- CH3

fie
\51/ \3/
(b) ethylene formation from decomposition of the absorbed
ethanol
so»,r’\ I \\ ,/' I I
.—-m—c— 0 —c=c-—
g. '2! —-~—— is
- 0 . 0 e

(c) ether formation from a Rideal-type bimolecular process

 

CH3 -- cxl— OH H\ H
/
Piio ”‘—"“ lie
(3 a 0 C)
\Si/ \Al/ \Si/ \Al/

(d) carbonium ion type of mechanism for ethylene
polymerization on zeolite

I
—" :C_ -—CC=
/ l l l I
139 2:22:33 0—8-— 2;:22? -c—hp-—c-—-c——
\ ~ 0 3/ 06 \ I 09 1 I
81/ \AI \Si/ \Al/ 81/ \Al/

Figure 2.3 Reaction mechanism for the ethanol conversion
to hydrocarbons

 

Ga

.3

.au

 

 

 

 

 

 

 

 

 

14

The purpose of this section is to briefly overview the
mechanisms of ethanol conversion suggested by other
researchers and point out that the goal of this research is
not to explain the validity of the mechanisms but to
determine the effect of process variables on product
selectivities, since such is the crucial part in the process

design of alcohol to hydrocarbons.

2.4 Reaction Kinetics

Alcohol dehydration involves a complicated reaction
scheme (Figure 2.1) which makes kinetic analysis rather
difficult. However, initial reaction rates can be obtained
separately for olefin and ether formation[4,35]. More
complete kinetic descriptions using a somewhat simplified
scheme have been attempted [36,37,381 for the reaction of
ethanol on the basis of data from different types of
reactors. A lumped kinetic study on reaction of methanol
at different reactor pressures is given by Chang and
coworkers [39,43]. Since the comprehensive kinetics for the
initial reactions is given in the literature [4], only a few

remarks on the initial reactions are given here.

15

The validity of the Langmuir-Hinshelwood or Eley-Rideal
type rate equations in heterogeneous alcohol dehydration has
been confirmed by many researchers, as mentioned in the
review by Beranek and Kraus [4]. The formation of olefin
from alcohol is first order with respect to alcohol
concentration in the numerator of both the
Langmuir-Hinshelwood and Eley-Rideal rate expression. The
power in the denominator depends on the assumption made on
the number of active sites involved in the hypothetical
mechanism. There is no general agreement in the literature
on the number of active sites involved. The
Langmuir-Hinshelwood rate expression for the ether formation
is not consistant from the literature. For the reaction of
diethyl ether giving either ethylene and ethanol or ethylene
and water, a dual site model is suggested by Solomon [37].
The first order of the oligomerization reaction of olefin is

suggested by van den Berg [40].

The lumped approach of methanol conversion presented by
Chang [39] has been conducted from the experimental data
obtained by keeping the reaction temperature the same and
varying the system pressure. In such a_case the correlation
between the rate constants and the temperature can not be

obtained. The correlation between the rate constants and

16

the pressure is interpreted in terms of sorption equilibria
and Langmuir-Hinshelwood isotherm. The pressure effect on
the methanol conversion observed by Chang et a1. [41]
indicates the enhancement of aromatics selectivity by
increasing pressure. Water addition to the feed is also

found to enhance the aromatics yield [42].

A more systematic study of the temperature and the SiO;
/A1.0, ratio effect on the methanol conversion has been done
by Chang et al. in 1984 [43]. It is found that the
selectivity to olefins can be enhanced by a cooperative
effect of increased temperature and increased SiOz /Al;Os
ratio. An A-B-C scheme is suggested where A 2 oxygenates,
B 2 olefins and C 2 aromatics+paraffins. The disappearance
rates of oxygenates and olefins are assumed to be
first-order. Little temperature dependence of aromatization
is found while a relatively strong temperature dependency is
found for olefin formation with an apparent activation
energy of 19.3 Kcal/mole. The ratio of the two first
order rate constants (K, /K2.) is found to be a linear
function of the effective SiOz/Alzog ratio. The linearity

is not explained in the article.

The purpose of this section is to briefly review the

kinetics for the initial 'reaction steps of alcohol

 

9.
.Au .

 

17

dehydration and some important observations reported in the
literature, and to point out that little effort has been
made on the development of a complete kinetics model for the

alcohol conversion to hydrocarbons.
2.5 Lumping Approach

Since the chemistry of the ethanol to hydrocarbons
process is quiet complex, it is necessary to group many of
the individual species into pseudo species and then to

develop kinetics based on the simplified reaction network.

Wei et al.[54,55,56] derived criteria for exact lumping
of monomolecular reaction systems. Their works were
extended by Ozawa [57], Bailey [48] and Liu et a1 [59].
Unfortunately, their analysis is applicable only to systems
in which the kinetics of both the individual and grouped
species are first order, and requires kinetics information
which is usually unavailable. Studies of errors involved in
the use of empirical rate expressions were presented by
Hutchinson and Luss [60,61]. Weekman [62,63] and Lee [64]
provided detailed discussions of the philosophy of kinetic

lumping in complex reaction systems.

18

The goal of the kinetic lumping of the ethanol
conversion in this investigation is to determine the
dehydration kinetics using a minimal number of lumped
species and a minimal number of reaction pathwagsbetween
lumps. The proper choice of the lumped species is based on
the thermodynamic and kinetic considerations of the
individual reaction pathway, and the empirical correlations

found in the experiments.

CHAPTER 3

EXPERIMENTAL
3.1 Materials

Ethanol of 99.8% purity (spectranal grade) was obtained
from Crescent Chemical Company and used without further
purification. Compounds for standardization use in GC
analysis were obtained from Aldrich (liquid compounds) and

Matheson(gaseous compounds).

Helium (grade 4.5 with purity of 99.995%) and air (dry
grade) cylinder gases were obtained from Airco and were used

as received.

The catalyst used in this research was an ammonium form
of ZSM-5 from Mobil research and development corporation
with SiOz/A1103 mole ratio of 70:1. This was compressed to
small pellets of 0.015 cm in thickness under a pressure of
16000 pounds per square inch and then crushed and sieved
before use. The ammonium form of ZSM-5 was converted to
hydrogen form by thermal decomposition of the ammonium ion

at 600°C for 6 hours.

19

 

 

 

(1

(7'

'fi F! m

'1

 

20
3.2 Kinetics Experiments

3.2.1 Equipment

A diagram of the continuous flow apparatus used for
determining dehydration kinetics is shown in Figure 3.1.
A photograph is also shown in Figure 3.2. Heating zones
including the preheater, vaporizer, and reactor were made
of 0.5 in 0.D. quartz tube and were wrapped by heating
tapes and then insulated with fiber glass layers. Quartz
tubing was used instead of stainless steel tubing to avoid
the possibility of reaction between reactant and metal.
One-quarter inch 0.D. stainless tube was used for the
carrier gas(helium) pipe line and connected to the preheater

by an Ultra-Torr fitting (Cajon).

The reactant feeds consisted of vaporized ethanol and
helium from cylinder. The pressure of helium was requlated
by a model 3500 high pressure regulator and model 715 low
pressure regulator from Matheson and was maintained at
6 psig. Helium flow rate was controlled by a high accuracy
valve and was measured with a rotameter from Matheson. Two
sets of rotameter tubes and valves, a 602 tube with valve
model 7943 and a 610 tube with valve model 7941, were used
for high flow rate range and low flow rate range
respectively. Both sets were calibrated to give accurate

helium flow rates, as are shown in Appendix A.

hczpm weaves“: how :mwmmp magnummnm BOHh mzozcflwcoo H.m ohsmwm

0:

mm<e que<mz :BHS Qmmm<m3 mzHA 1r+|T+ITlI$1F
mmoe<qzumm

   

 

 

 

 

 

 

 

 

 

 

 

 

 

mama mama

11 m>q<> wo<m=oo< on: on Smo\qoz<aomm-H SOH
2 _ 7 _ 1
mmemsaaom cam quqms<m [Ar] . I

v

a

mean u“

mosz»m u.

Sozazem mmNHmoa<> moeoemm a

K---~ \szsxkxx L

NV‘NN‘u‘V— J‘VVNVW‘N2V

.Owe .O.B

22

F
a.)

'4ng

 

Figure 3.2 Photograph of apparatus

23

Liquid ethanol was fed from a B-D glass syringe to the
system by a Sage syringe pump (model 341A) The syringe pump
was calibrated at several gear settings for three sizes of
syringes, as shown in Appendix A. The ethanol flowed
through a 10 inch 'long capillary tube (0.0625 in 0.D.

stainless steel) to a vaporizer.

The vaporizer was an 8.5 in length of 0.5 in 0.D.
quartz tubing into which a continuation of the capillary
feed line projected approximately 4 in (Figure 3.3).
Preheated helium gas entered the vaporizer at a 90 degee
angle and was mixed with the vaporized ethanol. The
preheater and vaporizer were wrapped by a heating tape which
was attached to an Athena temperature controller (model
20008). The temperature in the vaporizer was monitored and
controlled at reaction temperature via an Omega sheathed
iron constantan thermocouple. This thermocouple was
connected to the Athena controller. The thermocouple probe
was positioned perpendicular and placed near the center line
of the vaporizer. The thermocouple probe was covered with
a thin pyrex glass layer to avoid contacting the metal
with reactant. The shape of the pyrex glass layer was
designed to hold the thermocouple probe steady and fit

perfectly into the quartz wall to minimize the possible

 

()

f'

(7

(f

f)
1' V

 

 

(r
fit

24

dead volume due to the sensor probing in, as is shown in.

Figure 3.3.

The mixed vapor feed passed from the vaporizer to a 5
in length tube section to ensure adequate mixing of the
reactant and carrier gas before it entered the reactor. The
reactor was also a 0.5 in 0.D. quartz tube approximately 1
cm in length (Figure 3.4). It was packed with 9-10 mesh
catalyst pellets (0.015 cm in thickness) held in place with
two quartz frits. The reactor was heated externally by
a heating tape connected to a temperature controller
(Athena model 5000FC), and was surrounded by fiber glass
insulation. The reactor temperature was monitored with a
sheathed iron constantan thermocouple positioned at the
center of the reactor bed. The thermocouple was mounted on
the reactor exactly the same way as those for the vaporizer
and was sealed with an o-ring. The pressure in the system
was monitored with different feed rates passing through
the reactor before the experiment started. The flow rate
used in the experiments and the short reactor bed length in
the system ensure that the pressure drop across the reactor

was negligible.

The product vapor from the reactor flowed through two
cold traps in series. The first trap was immersed in an ice

bath placed in a dewar flask which kept the bath temperature

25

mSDm
mqumwm
Scam
ommm
Aoz¢rem

=m~eo.c

 

 

 

Lonwuomm> one Mo eavmsmnom m.m omswwm

 

 

 

 

 

 

 

 

a:
TA) :W o m
r [Iv
_ IV. (V. moeocmm
- a (1 ca

 

oszI

 

 

 

CODE

26

 

 

 

 

 

 

 

 

 

 

TOC.
,—
O-RING
CATALYST
FRITS PELLETS
0.5"
TO 1
ICE ‘_ *FROM
TRAP \ VAPORIZER‘
11nd [- T

 

 

Figure 3.4 Schematic of the reactor

27

at O‘C. Isopropanol/dry ice bath was used in the second
cold trap to maintain the bath temperature at -78 ’C.
The isopropanol/dry ice bath was prepared by adding the
crushed dry ice chips to isopropanol solvent until a slush

was formed.

The remaining gas from the second trap was then
collected in a 15” x 15” Tedlar gas sampling bag obtained
from Cole-Farmer instrument company. The volume of the gas
collected in the sampling bag was measured by a water
displacement tower. The water displacement tower was
actually a cylindrical tank made of acrylic glass (Figure
3.5). On top of the tower, an acrylic glass lid was mounted
by six screws and an O-ring lay in between to ensure it was
pressure tight. An empty sampling bag was mounted at the
center of the lid. The tower was filled up with water via a
side arm (a hose connector) located at bottom part of the
tower. A hose connector mounted on the edge of the lid
allowed the displaced water to flow out. The displaced

water was then collected in a container.

The volume of the remaining gas was estimated by
measuring the volume of the displaced water from the
displacement tower. The liquid products collected in
the cold traps were weighed by an electric balance.

The composition of both the gas products and liquid

28

 

DISPLACED
WATER CONNECTED TO
U OUT SAMPLING BAG

 

L"- < BUILD-IN ‘,
\ \ ‘GAS BAG ,. /

~~fi

WATER

 

 

 

“=3:
4

WATER IN

 

 

 

 

 

 

Figure 3.5 Schematic of the water displacement tower

29

products was analyzed by a Gas Chromotograph (Varian 3700)

and was recorded by an integrator (Hewlett Packard 3390A).
3.2.2 Procedure

Steady-state ethanol dehydration kinetics studies were
performed at 150.200.250.300 and 360 'c with a catalyst
charge of 0.5 g; a fresh catalyst charge was used whenever a
set of runs at one temperature was started. Before a run
started, the catalyst bed was heated to 500 °C with oxygen
flowing through for 8 hours to regenerate the catalyst from
coke poisoning, then purged with helium flow for 4 hours.
Next, the reactor was cooled to the desired temperature

under helium flow.

Experiments were begun by bringing the system to the
desired temperature with the desired helium flow rate. The
carrier gas flow rate was kept proportional to the desired
ethanol flow rate with a molar ratio of 2:1 which ensured
that the mole fraction of ethanol entering the reactor was
a constant (1/3). Then, the ethanol flow was started at
the desired rate to the vaporizer, and the systen was
allowed to reach steady state, which took about 1 hour.
After the system reached steady state, the cold traps and

the gas sampling bag were connected to the system. The

30

amount of ethanol injected was measured by recording the
elasped time after the connection was done, and was checked
by the scale reading on the syringe. When the desired
amount of ethanol had been injected, the cold traps and the
sampling bag were disconnected from the system
instantaneously. The ice bath and the isopropanol/dry ice
bath were then removed in sequence and the products
trapped in the cold traps and bag were allowed to reach
thermal equilibrium at room temperature. The volume of the
trapped gas in the bag and the weight of liquid products

were measured as described in the previous section.

The equipment was shut down, by first stopping the
liquid feed and then increasing the helium flow rate to
purge the remaining product mixture out of the system. This
purge was maintained at all times when experiments were not
performed. The heating elements of the reactor, vaporizer
and transfer line: were left on at all times except when a
fresh catalyst charge was necessary. To remove the used
catalyst and charge the fresh catalyst in the reactor. the
thermocouple set on the reactor was dismantled from the
system and the catalyst exchange was done by blowing the
used catalyst out and then pouring the fresh catalyst into

the reactor through the thermocouple port.

31

The gas samples from two cold traps and the sampling
bag were analyzed by G.C. without further dilution. The
liquid products in the traps were mixed and diluted with
known amount of methanol which was chosen as the solvent in
G.C. analysis. Separation of the reaction products was
achieved by a 12' 1/8” 0.D. stainless steel G.C. column
packed with Porapak Q,80/100 mesh, from Supelco. Porapak Q
is a non polar porous polymer composed of ethylvinylbenzene
cross-linked with divinylbenzene to form a uniform structure
of a distinct pore size, and is used primarily for efficient
separation of a wide variety of relatively low molecular
weight compounds. Owing to the molecular sieve nature of
the Porapak material, compounds with similar structure (or
molecular weight) are eluted in groups. The resolution of
the peaks in one group highly depends on the carrier gas
flow rate and the oven temperature program. In this
research, the G.C. column was temperature programmed at two
different rates. The first temperature program was from 120
'C to 240'C at 2°C/min., the products with carbon number
varing from 2 to 10 were separated into nine groups, as is
shown in figure 3.6 which is a typical gas chromatogram for
the gas sample analysis. Ethanol was eluted together with
n-butane at the same retention time(ll.55 min). Ether was

eluted together with n-heptene and i-heptane at the same

32

:Hs\ae on .ESHHS: .mmm Swampmo
0.02m on cae\o.m pa o.o~a .mSSPatmaemp aesaoo
name oo~\om .a xaaanom .mm ca mxaxpm ma .cezaoo

maasmm mmw mo mwmhamcm om mom sapwomeopno mam Hmowaze ©.m mmsmfim

 

 

 

 

 

 

.o in”
or» E. a
. . ...u .2 .
u w a ”we...
.5 r... m an
5 w“ r|’\III\ Il .
u I|I(|I\ use 400 . a
M wmo Rb N
«.0
mo mold I”
no-“ mo n
u n :01:
hmsum
m
we

 

89'

um

 

 

 

33

retention time(20.39 min). In order to measure the
quantities of ethanol and ether, another temperature program
was used. The second temperature program started from 80°C,
which was slightly higher than the boiling point of ethanol,
and was held for 45 min before the oven temperature was
raised linearly to 140°C at 1°C/min, as shown in Figure 3.7.
Ehanol was eluted right after the C4 group with a long
tailing. Ether was eluted together with n-pentane and
i-pentene instead of n-pentene. By comparing two
chromatograms, the quantities of ethanol and ether were then
determined. Elution shift usually happens whenever more
than one liquid phase is used in the packing material.
The reason why it happened in Porapak Q column is unknown,
and no attempt was made to investigate such. A typical
gas chromatogram for the liquid sample analysis is also
shown in Figure 3.8. Helium, air, and hydrogen flow rates
used in G.C. analysis were 30 ml/min., 300 ml/min, and
30 ml/min, respectively. The flame ionization detector can
not detect any quantity of water, therefor no water peak was
obtained. Peak areas were determined by digital integration
and converted to molar compositions with the use of
component response factors. Response factors for flame
ionization detector reported by Dietz[65] were used

directly.

34

CHE\HE om .SSAHm: .mmw moflmmmo
otoea op :ws\ota pm awe m: ode: otow .oSSHMLoQEoP cesaou
gate ooa\om .a Stetson .mm an m\sxpa ma .cszaoo

oaqsmm new no mflmzamcm ow mom smawopmsomno mam Havamze m.m omsmfim

 

 

 

 

 

_ r. _ _
_ U\ i
“ II.
no d m... so: m
u ooznooampmom o
:01:
so

 

 

 

6?“

"M
O

N
U

 

 

:HE\HE on .ESMHS: .mmw mmfinamo
o.osm op cas\o.m pa o.oma .mSSpanmaemp cesaoo
name ooa\om .c xaaanom .mm as w\atpa Na .cesaoo
oHQEmm pflsuwa mo mamAHmcm 00 now Emhmopmsomzo mam Hmowmze m.m omsmflm

 

HTS

'éé-‘A

35.

 

 

n. a u .1
a 6 6 . r: IKE ” W
H t u u
w
r-J\l|\ f 2! k! 2‘ k . {Ii
moo mmo mac moo mmo mao

 

 

ifil

Hocmnpoe

 

 

36

Overall product distribution was calculated by making
an overall mass balance, carbon balance, and oxygen balance
over the total feed and the products. The mass balance over
the system was made to evaluate the amount of gas
produced. Water in the gas Samples was assumed to be
negligible which made the evaluation of the gas product
distribution over three gas samples possible. The amount of
organic material in the liquid products was calculated from
the carbon balance over the system. The quantities of the
individual species in liquid products were then determined.
The overall product distribution was then obtained, and the
validity was checked by oxygen balance over the system. The
error in the oxygen balance was found to be less than 1%
throughout all the kinetics data. A sample calculation is

given in Appendix A.
3.3 Intraphase and Interphase Gradients

Ethanol dehydration involves complex kinetic rate
expressions with reaction order between 0 and 1 [35,40]
which leads to some difficulties in studying the transport
criteria for the system. A first order rate expression was
used in order to get a rough estimation of the possible

'transport limitations in the system.

37

Carberry (1964) and Mears (1971) showed that axial
mixing effects upon kinetics can be neglected for catalyst
bed with large length-to-particle diameter ratio [66,67].
An L/dp ratio > 30 has been suggested by these authers as
sufficiently large to guarantee plug flow. The thickness of
the catalyst used was 0.015 cm, and the bed length was 1 cm,
indicating that plug flow condition is most likely to

prevail.

According to Mears (1971), intraparticle diffusion
effects are a much more significant limitation than are
external diffusion effects. The effect of poSsible
intrapartical mass transfer limitations at low temperature
(150°C) was evaluated according to the method outlined in
Section 3.4 of Satterfield (1970), and the effectiveness
factor for the first order rate expression was virtually
unity, as is shown in Appendix B. The external diffusion
effect was also checked according to the criterion stated by
Carberry[69], and proved to be insignificant. At high
temperatures, 300°C and 360 'C, the consumption rate of
ethanol was high such that the reaction of ethanol to
ethylene was diffusion limited. It was assumed that ethanol
was converted to ethylene right after it entered the

catalyst bed and the successive formation_of light olefins

38

from ethylene became the reaction concerned. Since the
successive reaction was relatively slow, the effect of

internal diffusion was assumed to be insignificant.

CHAPTER 4
RESULTS

4.1 Experimental Results

A blank (empty reactor) run at 250°C confirmed lack of
catalytic activity of the reactor set up. Trace amounts of
acetaldehyde were detected at the beginning of the blank run
and tended to fade out eventually. It is suspected that the
formation of acetaldehyde was caused by the oxygen adsorbed

on the quartz tube which reacted with the reactant.

A Summary of the data from kinetics experiments is
shown in Appendix C. The major products in the lower
temperature range, 150 and 200°C, were diethyl ether, water
and ethylene. Difficulty was encounted reading the data
for trace amounts of C6+ hydrocarbons formation from the gas
chromatogram. This was speculated to be caused by the base
line drift arising from the temperature programming mode,
column bleeding, and bad resolution among the peaks which
are representative of these high molecular weight compounds.
The formation of C3+ hydrocarbons increased rapidly when the
ethylene formation approached the maximum value. The
magnitude and location of the maximum yield of ether tended
to decrease and shifted to the left respectively as the
reaction temperature increased, as shown in Figures 4.3

and 4.4 in Section 4.2.4.

39

40

At 250°C, the conversion of ethanol was typically
greater than 50% in the range of the residence time used in
the experiment. The yield of water leveled off as expected
when the residence time increased, as shown in Figure 4.5.
The yields of the light olefins, including ethylene and
C3+ olefins, had global maximum values located at different
residence times. A similar trend was found among the yields
of light olefins except ethylene, whose distinct maximum
yield was ahead of others, indicating that ethylene could be

an inactive initial intermidiate.

The conversions of ethanol were greater than 90% in the
higher temperature runs, 300 and 360°C, as are shown in
Figures 4.6 and 4.7. Aromatics became major species among
the C6+ hydrocarbons. The formations of light paraffins and
aromatics followed the same path which indicates a strong
correlation between the two. This correlation arises from
the hydrogen transfer mechanism. The molar ratio of
paraffins over aromatics was about 3:1. Only trace amounts

of ether were found in the runs with low residence time.

Excluding water produced, the maximum yields of C3-C6
light olefins at 250,300 and 360°C were 23, 26, and 30 wt%,
respectively. Due to the length of the experiment, only a

few runs were duplicated and proved to be reproducible.

41

4.2 Kinetic Modelling

The following sections discuss the kinetic modelling of
the ethanol-to-hydrocarbons reaction carried out in the
integral reactor. The differential condition is not
possible to approach in such a fast reaction system. A
lumping approach, similar to the one that was employed for
the kinetic modelling of cracking of petroleum reactions
over zeolite catalysts [63], was used to establish an order
in assisting the elucidation of the dehydration mechanism as
well as the kinetics. Here, the choice of the lumped
components was based on both thermodynamic and kinetic

considerations of the individual reaction pathway.

The Langmuir-Hinshelwood model is employed in many
heterogeneous systems involving gaseous reactions on solid
surfaces. The use of the complex model has frequently been
criticized as an attempt to read too much into a set of
kinetic data. The implicit results of such a misapplication
would lead to a proliferation of meaningless constants; this
would thus lead to unnecessary effort in data fitting and
interpretation, or to misleading interpolation or
extrapolation. Simplification of a complex model is then
necssary to reduce the danger of misleading and the

unnecessary effort in data fitting.

42

4.2.1 The Lump Reaction Network

The general consecutive and parallel reaction network
(Figure 2.1(a)) for alcohol dehydration mentioned in Chapter
2 needs to be simplified because of the mathematical
difficulty involved in data fitting. The successive
reactions including the formation of paraffins, higher
olifins, and aromatics, which is not included in the general
network, was suggested by several researchers [11,70], as
mentioned in Chapter 2. The simplified lump scheme (Figure
2.1(b)) consisting of groups of light olefins (CZ-C5) and
the other final products as an intermediate lump and a
terminal lump, respectively, is so oversimplified in that it

could lose insight for the chemistry involved.

A more plausible lump reaction network based on the
facts pointed out in the literature and the observations of
the experimental results was adopted here. This is shown in
Figure 4.1. This network consists of eight species,
including five individual species and three lumps. The five
individual species are ethanol, water, ether, ethylene and
ethane. The three lumps are C3-C6 light olefins, C3-C5
paraffins, and C6+ compounds including aromatics and C6+
aliphatics. Seven elementary reactions are involved in the
network. They are: (l) dehydration of ethanol to ethylene

and water; (2) condensation of ethanol to ether and water;

43

ethanol(l)
2 1
water(2)+ether(3) ethylene(4)+water
.1 I .\
ethanol(1)+ethylene(4) ethane(8)
4 4

 

)

03-05 olefins

7 x

03-0, aromatics
paraffins + Cfi’aliphatics
(7) (6)

Figure 4.1 Lump reaction network

44

(3) decomposition of ether to ethanol and ethylene; (4)
oligomerization of ethylene to C3-C6 olefins; (5)
oligomerization of light olefins to higher aliphatics and
aromatics; (6) hydrogenation of ethylene to ethane; (7)

hydrogenation of light olefins to light paraffins.

Several assumptions were made :

(1) All reactions are irreversible.

(2) The decomposition of ether to ethanol and ethylene
is more important than the hydration of ether to
ethanol.

(3) Ethylene is an initial inactive olefin and is not
included in the light olefins lump.

(4) The formation of paraffins is not related to the

formation of aromatics, which leads to three
parallel reactions (Reaction 5-7).

The assumption (1) can be valid if the equilibrium
constant of the reaction of concern is large or the
adsorption-desorption equilibriun constant of the product is
relatively smaller than the one for the reactant, which is
generally found to be true from the literature[35,70]. The
reason for making assumption (2) is mainly from the
modelling point of view. Because the two existing routes of
reforming alcohol from ether can cause difficulty in data
fitting, it is assumed that the decomposition one is more
feasible. A satisfactory explanation for assumption (3) is
provided by the result of the ethylene sudies done by

Dejaifve et a1 [70] who pointed out that desorption of

45

ethylene is faster than chemisorption of ethylene from the
gas phase. The hydrogen balance makes assumption (4) to be
unrealistic. It was made because the ethane is not included
in the paraffins lump, and is thus valid when there is no

other source of hydrogen in the system.

The experimental data are reorganized and tabulated
according to the reaction network. These are shown in

Tables 4.1-4.5.
4.2.2. The Kinetics Models

In order for a heterogeneous catalytic reaction to
occur, several physical and chemical steps must proceed on a
molecular scale. These are : (1) mass transfer of reactant
from the bulk of the fluid to the exterior surface of the
catalyst particle; (2) diffusioin of the reactant from the
exterior surface of the catalyst particle into the interior
pore structure; (3) chemisorption of the reactant on the
catalyst surface (active site); (4) reaction on the surface
which can be reaction between either two adjacent adsorbed
species or an adsorbed species and an empty active site
adjacent to it; (5) desorption of surface species, both
reactant and products; (6) diffusion of products from the
pores to the external surface of the catalyst particle; (7)

mass transfer of products from the external surface to the

TABLE 4.1

Lumped Data of Kinetics Experiments at 150°C

Residence .12 .22 .71 1.51 4.35

time(sec)
y. .2773 .2434 .1223 .0665 .0311
y; .0290 .0456 .1327 .2040 .2865
y3 .0270 .0443 .0783 .0529 .0157
y“ .0015 .0013 .0538 .1392 .2643
Y: .0001 .0001 .0001 .0004 .0011
y‘ .0000 .0000 .0000 .0001 .0003
Y1 .0000 .0000 .0002 .0003 .0007
y) .0000 .0000 .0000 .0004 .0012
where subscripts [l] 2 ethanol [5] 2 C,-C, olefins
[2] 2 water [6] 2 aromatics+Cflaliphatics
[3] 2 ether [7] 2 C3-Cgparaffins
[4] 2 ethylene [8] 2'ethane

47

TABLE 4 . 2

Lumped Data of Kinetics Experiments at 200°C

Residence .02 .03 .05 .13 .25 .78
Time(sec)

y, .2600 .2260 .2029 .1254 .0776 .0266
y; .0407 .0624 .0834 .1682 .2295 .3057
y3 .0326 .0449 .0474 .0397 .0263 .0010
y» .0080 .0175 .0364 .1281 .2005 .2929
y, .0000 .0000 .0000 .0001 .0007 .0033
y‘ .0000 .0000 .0000 .0002 .0001 .0006
y7 .0000 .0000 .0000 .0000 .0004 .0017
y, .0000 .0000 .0000 .0001 .0003 .0005

where all the subscripts are previously stated in TABLE 4.1

48

TABLE 4.3

Lumped Data of Kinetics Experiments at 250°C

Residence .03 .05 .12 .22 .71 1.42 3.51

Time(sec)
y, .1311 .0942 .0062 .0024 .0002 .0001 .0000
y; .1890 .2313 .3270 .3309 .3331 .3332 .3333
Y3 .0133 .0078 .0002 .0000 .0000 .0000 .0000
Y4 .1740 .2182 .2805 .2216 .1025 .0679 .0277
y: .0005 .0013 .0151 .0281 .0371 .0338 .0270
y‘ .0000 .0003 .0022 .0080 .0205 .0230 .0145
Y7 .0003 .0007 .0052 .0131 .0377 .0552 .1005
y, .0001 .0001 .0005 .0008 .0016 .0029. .0038

where all the subscripts are previously stated in TABLE 4.1

49

TABLE 4 . 4

Lumped Data of Kinetics Experiments at 300°C

Residence .11 .20 .65 1.34 3.20.

Time(sec)
y, .0004 .0001 .0000 .0000 .0000
y; .3300 .3276 .3230 .3211 .3196
y3 .0000 .0000 .0000 .0000 .0000
y; .1850 .1143 .0387 .0159 .0156
y} .0418 .0474 .0330 .0224 .0186
y‘ .0078 .0134 .0223 .0260 .0234
y7 .0209 .0405 .0758 .0908 .1045
y, .0007 .0011 .0021 .0026 .0052

where all the subscripts

are previously stated in TABLE 4.1

 

TABLE 4 . 5

Lumped Data of Kinetics Experiments at 360°C

Residence .11 .18 .58 1.22 2.91

Time(sec)
y, .0001 .0000 .0000 .0000 .0000
y; .3289 .3271 .3233 .3215 .3178
y3 .0000 .0000 .0000 .0000 .0000
y4 .1337 .0935 .0468 .0276 .0272
y, .0589 .0578 .0421 .0335 .0310
y‘ .0094 .0142 .0250 .0304 .0260
y7 .0313 .0442 .0664 .0778 .1103
y, .0011 .0015 .0036 .0042 .0083

where all the subscripts

are previously stated in TABLE 4.1

51

bulk of the fluid. Any one of the steps mentioned above may
be sufficiently slow to control the overall rate of

reaction.

External concentration gradient beween the bulk of
fluid and the exterior surface of the catalyst particle and
internal concentration gradient caused by the intraparticle
diffusion should be avoided in developing of intrinsic rate
expressions for heterogeneous catalytic reactions by
increasing the fluid flow rate and reducing the size of the
catalyst particle. The Langmuir-Hinshelwood type of the
reaction rate expression is widely used in deriving a"
mathematical expression for the intrinsic
adsorption-desorption reaction. The Langmuir isotherm
corresponds to an idealized type of adsorption and is based
on the following assumptions: (1) molecules are adsorbed at
discrete sites on the surface and each site is capable of
accommodating only one adsorbed species; (2) the
intermolecular force between adjacent molecules is
negligible; (3) the maximum amount of absorption is that
which corresponds to a monolayer; (4) the desorption rate
depends only on the concentration of adsorbate. Based on
these assumptions, the concentrations of unoccupied active
site and the adsorbed species can be derived in terms of the
adsorption-desorption equilibriun constants and partial

pressures as follows:

52

5 = .S.//r2'k.'Pc ”-1)

52 .5. KaPc/szaf’.‘ (4-2)

where So is the total number of active sites per unit weight
of catalyst;
S is the number of the unoccupied active site per unit
weight of catalyst.
Si is the number of the active sites occupied by
species i per unit weight of catalyst.
Ki is the adsorption-desorption equilibrium constant
for species 1.

when the expressions for the various Si are substituted into

a rate equation of the form
' x a:
r: 7'5): 5: ""' (4-3)

a Langmuir-Hinshelwood or Hougen-Watson rate expression
is obtained, which may be valid when surface reaction is

the rate limiting step.

The surface reaction as the limiting step is widely
accepted by most researchers in this area[4]. The only
arguement is on the rate limiting step of the successive
reactions involving formation of light olefins from ethylene
and aromatics from light olefins. According to Dejaifve et
al.[18], the reaction of CzH} (ads) is faster than its
desorption as ethylene, and desorption is faster than
chemisorption of ethylene from the gas phase which implies
that chemisorption is the limiting Step for the reaction of
ethylene to light olefins. Pending the attainment of more

convincing evidences on the relative rate of the three

53

steps, two plausible kinetics models were considered in

attempting to correlate the data of Tables 4.1-4.5.

As an illustration of the derivation of a LHHW rate
equation, it will be shown how the following equation can be
derived from a plausible mechanism for the reaction 1 in the

reaction network:
r t 591*! Kjfl - 522 *1 k2 k‘ffi f4 ‘
‘ (If/(7ft *lof‘rfi kgfg+hfefkyfg+kl°5fk7fr+Kt?!) (4-4)

where r. is the rate of conversion of ethanol (1) to
eth lene (4) and water (2);
k,, 7 are forward and backward surface reaction
constants respectively;
Ki,Pi are adsorption-desorption equilibrium constant
and partial pressure res ctively for species i. These
species can be ethanol(l§fwater(2),ether(3),ethylene(4),
light o1efins(5),C6+ hydrocarbons(6),light paraffins(7)
and ethane(8).

Equation (4.4) describes a process involving adsorption
of ethanol(C;H;OH), reversible surface reaction between the
adsorbed ethanol (C,H;OH§Z°) and an empty active site(H° 2°)
, and desorption of products (CzHe-and°H10). That is, it

may be derived as follows for the sequence of step belows:

CzHJOH 1- HZ é ( ask/504,32" ) (LP-5)

(re Hear/{2"} + HZ —-°-;_'——-—"' ( far/HZ’) + (H40*z°)(4-6)
2

mo. + HZ #2 cu/Hz’ (4-7)

H30 +HZ ’9 (H.o*z°) (4-8)

 

 

Now, designate Equation (4-6) as the rate limiting step
which implies that:
r, = 4,3,5 — 4,5,5. (“-9)

54

Substituting (4-1) and (4-2) into Equation (4-9), the

desired equation (4-4) can be obtained:

502*[kIPI “5.31.! kzklfltfi‘ (4-4)

[1" z
(/+ é’kifa)

Equation (4-4) can be simplified by applying the
following two assumptions: (8) all adsorption terms are not
important except the one for reactant (K.Pa) which implies
the adsorption-desorption equilibrium constants of the
products are small compared to K.or the partial pressures of
the products are relatively small; (b) k.is much smaller
than k which leads to irreversibility of the reaction. From
the literature, it can be concluded that both assumptions
can be true under the experimental conditions in this
research. Thus, a simplified rate equation can be derived

as follows:
5.2 fiak’ P
r. (1+ MHz (4-10)

If the rate determining step does not involve the adjacent
empty active site, the power of So and the denomenator will

be one instead of two.

Applying a similar 'technique to all the elementary
reactions involved, two kinetic models based on different

assumptions on the reaction of olefins can be developed.

55
Model I

The assumptions in this model include:

(1) the adsorption equilibrium for each species is maintained
at all times and the rate-determing step for each elementary
process is the rate of reaction on the surface;

(2) all elementary reactions in the network are irreversible;

(3) the concentration of hydrogen in the acidic catalyst is
high enough to be treated as a constant in the rate
expression for the hydrogenation reaction (Reaction 6 and 7).

Hence the elementary rate expressions can be written as follows:

r. - i, P. 8‘ (4-11)
r, - R. 38‘ (4-12)
1', . E; P; 9° (4'13)
r42 K4 PIO’ (4'14)
1:, . E.p;e' (4-15)
I." 3 E4 P4 9° (4‘16)
{'1' E7 P; 6° (4'17)

where 6 is l/(1+K.P.) which can be interpretated as a
fraction factor of the active sites covered by
different species.

k; is the combined rate constant, which incorporates
the adsorption equilibrium constant for the reactant
of the elementary reaction 1, the rate constant

for the rate determining step of the elementary
reaction i, and a conversion reactor to allow for the
total number of active sites per unit weight of
catalyst.

Model I I
A different assumption made in this model is that the rate
determining step for the reaction of olefins is the rate of

chemisorption which leads to the following different rate

expressions for reactions 4-7:

”9

(‘8 “P46 (4-18)
:32 fine (4-19)
r.2 k:P.9 (4-20)
r73 fi;PIe (4-21)

where k: is also a combined rate constant for elgmentary
reaction i which has units different from ki.

56

The rate of formation of each species can then be
derived by the combination of the rate expressions for the

seven elementary reactions as follows:

R; I ‘1‘. '21’; +133 (4'22)
R;‘ r. +172 (4‘23)
R52 rz-r; (4—24)
R42 r,+r,-2r,-r4 (4-25)
R52 r,-2r:-r7 (4-26)
R48 r; (4-27)
R1. r7 (4'28)
R33 I" (4‘29)

where R is the rate of formation of species i.

A word of caution is warranted concerning the use of
stoichiometric coefficients to relate the formations of
lumped species in reaction 4 and 5. Recall that the light
olefins lump includes C3-C6 olefins which indicates the
stoichiometric coefficient of forming light olefins from
ethylene is not really 2. It can be larger or smaller than 2
depending upon how the light olefins are distributed in the
lump. The same situation happens_in the formation of higher
hydrocarbons from light olefins. If the distribution of the
species in one lump does not change much in all experimental
results, the factor of the difference will be built in the
rate constants found from data fitting. Table 4.6 shows the
normalized distributions of C3-C6 olefins at 250 'C, 300 °C

and 360 °C. One can conclude that the stoichiometric

57

TABLE 4.6

Normalized Distribution of C3-C601efins

250’c

Residence

Time(sec) .03 .05 .12 .22 .71 1.42 3.51
Propene .7191 .6506 .5651 .4732 .3841 .4975 .4438
Butenes .1114 .1527 .3119 .3385 .3602 .3104 .3149
Heptenes .0000 .0476 .0964 .1427 .1816 .1275 .1559
Hexenes .1695 .1491 .0266 .0452 .0742 .0646 .0854
300'c

Residence

Time(sec) .11 .20 .65 1.34 3.20

Propene .5648 .5433 .4889 .4143 .3979

Butenes .2977 .2799 .2097 .1448 .0840

Heptenes .1079 .1428 .2602 .3945 .4674

Hexenes .0296 .0340 .0413 .0473 .0507

360°C

Residence

Time(sec) .11 .18 .58 1.22 2.91

Propene .6735 .6418 .6711 .5930 .5758

Butenes .2363 .2427 .1900 .1995 .2269

Heptenes .0766 .0996 .1252 .1891 .1833

Hexenes .0136 .0519 .0137 .0184 .0140

58

coefficients assigned are generally acceptable although the

slight deviations do exist.

4.2.3. The Ordinary Differential Equations for the Integral
Reactor

The steady state differential equation for species i
can be derived by making° material balance of species i
around a small controlled volume in the tubular reactor. It
is:

6(Cglr
alV

 

Where C1 is the concentration of species i,
v is the local volumetric gas flow rate;
V is the differential volume of the reactor;
P is the apparent density of the catalyst;
e is the void fraction of the catalyst in the reactor.

Assuming that the ideal gas law applies at the reaction
conditions(P2l atm,T21150°C), Equation (4-30) can be

rewritten for the isothermal constant pressure reactor as :

41; _. _J§L__ . _
M F (a R. (4 31)
where y, is the ratio of the local molar flow rate of
species i to the total molar flow rate of the
gas stream entering the reator;
t is the residence time based on the volumetric flow
rate of inlet gas stream;
R is the gas constant;
T,P are the reactor temperature and pressure,
respectively.

Eight ordinary differential equations in the form of

Equation (4-31) for the eight species, involving seven

 

 

'3
m
m
(I
(V

‘
O
"
W
.5

4.2.4

fOun
and

inhe
Stif
qUas

equa

ini
819
is
in:
Sue

cf

59

reaction constants and one adsorption constant, are the

working equations to correlate the data of Tables 4.1-4.5.
4.2.4. Data Fitting

A quasilinearization method was employed with the eight
ordinary differential equations to determine the best set of
the eight parameters for each model to fit the experimental
data. Details of the method are shown in Appendix D. There
are a number of examples of parameter estimation in
O.D.E.s using quasilinearization in the literature,
, [71,72]. A 'more comprehensive discussion can be
found in the book by Lee [73]. (Two Fortran programs, DGEAR
and LEQTlF from IMSL library were used. The stiffness
inherent in the models led to the use of DGEAR (based on the
stiff method of Gearf for the integration part of the
quasilinearization technique. The final linear algebraic

equations were solved by applying LEQTlF.

The quasilinearization method requires a good set of
initial guesses of parameters for convergence of the
algorithm. Since the range of a good set of initial guesses
is inherently narrow, enormous effort had been put on the
initial guesses searching. Once the right set of initial
guesses is found, it is not difficult to obtain a good fit

of almost any data set to a mathematic expression. The

60

parameter values obtained should comply with the following
general criteria . (Kittell, 1970) to be physically
meaningful:(a) the rate and adsorption constants should be
positive; (b) a plot of the logarithm of the rate constant
(or adsorption constant) versus reciprocal absolute
temperature (Arrhenius plot) should be linear with a

negative slope (or positive slope).

Since the major products at 150 °C and 200 °C were
ethylene, water and ether, comparison between the two models
which have same rate expressions of reaction 1-3 can not be
made in the low temperature range. Tables 4.7 and 4.8 show
the parameters of the two models which gave the ”best” fit
to the data at 150°C and 200°C. At 250°C, the conversion of
ethanol was fairly high and the concentration of ether was
so low in the range of the residence time used that it falls
within the tail end part of the overall concentration
profile of ether, and thus reliable values of 1'1. i2, [(3 and
K1 can not be found. The values of 12, ES and K1
extrapolated from the Arrhenius plot (Figure 4.2(a)),based
on the results at two low temperatures, were instead used.
The Arrhenius plots of kl,k2,k3, and K1 are shown in Figure
4.2(a). At 300°C and 360 °C, the extrapolated values of
kl,k2,k3 and K1 were used,since conversion of ethanol was

greater than 90%. Tables 4.9 and 4.10 list the rate

constants and adsorption constants at 250 C , 300 C and 360

 

"I

m

I FF"

¢ 6....
.

 

"he:

 

 

 

 

Estimated Rate Constants of Model I at 150°C and 200°C

Temperature(°C)

61

TABLE 4.7

F, mole/gag sec atm
k, mole/gar sec atm‘
TE, mole/get sec atm
k", mole/g“, sec atma
k, mole/g“, sec atm°
R; mole/gar sec atm
k1 mole/g“, sec atm
K. l/atm
where k,2 Sdk,K. k,- sdkst
[L2 So’k.K,' 1?;- 56k: K4
IE,- Sd'kgK; 1?,- SdkyK:

E4, . Sdk‘ K4°

150
3.68E-5
6.43E-4
9.26E-5
7.43E‘6
2.73E-2
1.98E-7
3.16E-5
4.73

So 2 mole sites/9c"
k; 2 gar/mole sec

200
1.35E-4
2.27E-3
1.188-3
1.71E-5
2.84E-2
3.08E-7
9.14E-5
2.17

 

('1

"he:

 

 

 

62

TABLE 4 . 8

Estimated Rate Constants of Model II at 150°C and 200°C

Temperature(°C) 150 200
k, mole/g“;- sec atm 3.68E-5 1.34E-4
R, mole/g“, sec atmz 6.38E-4 2.33E-3
I, mole/gm sec atm 9.29E-5 1.22E-3
’12: mole/gm sec atm 1.08E-6 3.19E-6
k: mole/gar sec atm 3.78E-5 6.02E-5
k: mole/g.“ sec atm 1.93E-7 2.92E-7
I; mole/g“; sec atm 2.62E-5 8.268-5
K, l/atm 4.69 2.23

where k ,‘k, ,k, and X. are defined in TABLE 4.8
1 2 So ki ,i24,-~,7

 

 

 

 

‘2
—3_. a
E -4. °
8
:4
‘5 l r l
.0077 .0019 .0027 . .0023 .0025

l/T

Figure 4.2 (a) Arrliienius plots for If. .13. ,E, and K. in Model I
n l
at E1
5 a -
0 Km 10 °

64

 

.. 317—2} 0
/ (1'.
:1
I. 6‘
‘4‘ 0
44-418"
5

LOG (k)

 

 

 

 

"‘ 6 r I. I I
.00/5 .00/7 .00/9 .002/ .0023 . 0025

l/T

Figure (4.2 (b) Arrienius plots for 12, ink} and E, in Model I
U .

x 12,; 10"
21 EM 10
° 7

65

TABLE 4 . 9

Estimated Rate Constants of Model I at 250,300 and 360°C

Temperature(°C) 250 300 360
E, 8.48E-4 2.28E-3° 7.09a-3°
E. 6.29E-3! 1.46E-2° 3.36E-2!
I, 9.248-33 5.05E-2! 2.72E-1!
24 2.6lE-4! 8.338-49 9.918-49
R, 5.518-4 1.83E-4 8.94E-4
E, 7.44E-7 1.75E-6 1.98E-6
I, 4.83E-5 1.64E-4 9.81E-5
x, 1.1539 0.68! 0.41!

gextrapolated value from the low temperature results

TABLE 4 . 10

Estimated Rate Constants for Model II at 250,300 and 360°C

Temperature(°C) 250 300 360
E. 8.22E-4 9.03E-4° 2.12E-3°
E, 6.64E-3° 1.58E-2° 3.76E-3°
k, 9.83E-3° 5.50E-2° 3.03E-l°
k: 3.64E-5 1.19E-4 1.50E-4
E; 1.93E-5 5.008-5 3.63E-5
‘K: 1.37E-6 3.77E-6 6.51E-6
121' 5.93E-5 1.54E-4 1.015—4
x. 1.22! 0.75! 0.462

!extrapolated value from the low temperature results

67

°C for two models. The concentration profiles predicted by
model I at five different temperatures are shown in Figures
4.3 - 4.7. The concentration profiles predicted by model II

at 300°C and 360°C are shown in Figures 4.8 and 4.9.

Without statistical study, it is seen that the
model I gave a better fit at 300 °C and 360°C , by
comparing Figure 4.6 and 4.7 to Figure 4.8 and 4.9. Since
model I is the best choice, it is the only one for which the
activation energies and the Arrhenius frequency factors of
all parameters were calculated, as shown in Table 4.11

and Figures 4.2(a) and 4.2(b).

As mentioned in section 4.1, the magnitude of C6 +
hydrocarbons yield at low temperature was small that it led
to the erroneous values of :5 at 150 and 200°C. These were
not included in calculation of activation energy and
Arrhenius frequency factor for :5. The trend of ether yield
with respect to the temperature mentioned in section 4.1 can
be explained by the large negative activation energy of E3.
The adsorption constant Kahas a positive activation energy
since the adsorption-desorption reaction is an endothermic

reaction.

There was an apparent discrepancy in data fitting of

the light olefins yield for reaction condition of low

68

 

.46?

“35“

END-

.22?- .

JR?-

./5-‘

MOLE FRACTION

./0-

$25-'

 

/° 0

 

 

C73 ‘[ 7 _
~2.20 —I80 -/.40 -/00 -o.60 -0.20 0.20 0-60 I

LOG (RESIDENCE TIME), SEC

Figure “-3 Concentrations versus residence time for
kinetics study using model I at 150°C

0 ethanol 0 03-06 olefins

A water 4: aromatics + C60 aliphatics
O ether y CB-CS paraffins

x ethylene z ethane

0,457.2 are not shown in the figures since
low yields of these compounds were found at
low temperature ‘

 

 

 

 

 

 

22.352 ES 1....
T.

 

 

59

 

.30“

. 25-

.20-7

MOLE FRACTION

 

01

'2.20 -/ 80 -/40 -/-100 -0.60 -020 0.20 0.60

Figure 14. 1+

 

 

 

LOG (RESIDENCE TIME) SEC

Concentrations versus residence time for
kinetics study using model I at 200° C

0 ethanol 0 C3-C6 olefins

Awater 45 aromatics +C6+ aliphatics
O ether X CB-CS paraffins

x ethylene z ethane

0,45. Xzare not Shown in the figures since
low yields of these compounds were found at
low temperature

/

 

 

 

23 ~ 935:;

:4 A .2

 

 

.4‘
T.

 

.40

7O

 

..35-

.30 -

 

 

0 I

MOLE FRACTION
Us
l

\
»

 

I»
>

 

-—_

-2.20 -/.80 -/.40 -/.00 -0.60 -0.20 0.20 060 ’

LOG (RESIDENCE TIME), SEC

Figure 4.5 Concentrations versus residence time for
kinetics study using model I at 250 C

0 ethanol

A water
0 ether

x ethylene

O C3-C6 olefins

4 aromatics + C6+ aliphatics
y: C3-C5 paraffins

z ethane

 

 

 

 

1::
0‘ ‘

?.
2: ~ ._CC<I_.~ 2432

 

 

71

 

 

MOLE FRACTION

 

.20 -
.l5-
. I0-
.05- o

04 AAA;

'220 ‘/.80 ‘/.40 'l 00 -060 '0.20 020 060

 

LOG (RESIDENCE TIME), SEC

Figure 4.6 Concentrations versus residence time for
kinetics study using model I at 300°C

0 ethanol 0 C3-C6 olefins
A water 43 aromatics + C6+ aliphatics
O ether 3: 03-C5 paraffins

x ethylene z. ethane

 

/

72

 

.35d

 

.30-
.25-

.20-

MOLE FRACTION

 

 

I ° _ -
-2.20 -/.80 -/.40 -/.00 " 060 ‘020 020 0.60

LOG (RESIDENCE TIME). SEC

Figure 4.7 Concentrations versus residence time for
kinetics study using model I at 360 C

0 ethanol 0 03-06 olefins
A water 45 aromatics + C6+ aliphatics
O ether ,7 X C3-C5 paraffins

X ethylene ' zethane

/

 

73

 

.40

.35-

 

.30“

.25“

.20- ‘
./5-

./0-

X
X
\ .
\ 4‘
(2% _ 4“; —“!!!!!!E$:‘aj% °§
l l °° ' ° °
-2.20-1.87 -/.40 -/.00 ‘060 -0.20 0.20 0.60

MOLE FRACTION

 

 

 

 

LOG (RESIDENCE TIME) . SEC

Figure 4.8 Concentrations versus residence timeofor
kinetics study using model II at 300 C

0 ethanol C3-C6 olefins
A water aromatics + C6+ aliphatics
Q ether 7; C3-C5 paraffins

x ethylene z ethane

 

 

 

 

z~v~ Lsnv<¥~3~

14:2

 

44*
\:

 

MOLE FRACTION

.40

.35"

.20-

./5-‘

74

 

 

 

 

 

)_i

 

 

o , , _ - .. I
~2.2o 480 -/.40 -/.00 -0.60 -0.20 0.20' 0.60

LOG (RESIDENCE TIME), SEC

Figure 4.9 Concentrations versus residence time for

kinetics study using model 11 at 360°C

oethanol O C3-C6 olefins
A water 45 aromatics + C6+ aliphatics
Oether $1 C3-C5 paraffins

x ethylene Z ethane

I

 

75

TABLE 4.11
Arrhenius Frequency Factors and Activation Energies of

Parameters in Model I

Parameter Frequency Factor Activation Energy(cal/g-mole)

E. 369.92 13661.68
I, 97.14 10023.92
1, 2642883.95 21445.17
4, 114.10 14056.65
1, .01246 2910.96
‘2, .0003414 6364.44
E, .001457 3013.19

K. .002945 -6204.53

76

ethanol feed rate and high temperature, as shown in
Figure 4.6 and 4.7. The reason for the discrepancy could be
the combination of the following possibilities: (a) improper
lump of the light olefins which covers a wide range of
molecular weight (C3-C6); (b) reaction 5 could be reversible
instead of irreversible; (c) catalyst could be poisoned

since the collection time was long for the low feed rate.

Table 4.6 shows the normalized distributions of the
C3-C6 light olefins at 250, 300 and 360°C. The yield
of propene and butene had a tendency to decrease while the
yield of heptene and hexene had a tendency to increase
when the residence time increased. The variation of the
normalized distribution with respect to residence time was
less significant at higher temperature which indicates that
the improper lumping of the light olefins could not be

responsible for the descrepancy.

An attempt was made to take the reversibility of
reaction 5 into account. Figure 4.10 shows the resulting
concentration profiles at 360 °C. The difference between
Figure 4.7 and Figure 4.10 is minor, and the reversibility
of reaction 5 can not likewise explain the discrepancy. The
most possible reason is therefore that catalyst poisoning

decreased the catalyst activity and led to the erroneous

77

 

 

 

MOLE FRACTION

O

X
.05" \b A .
0 l ' ‘ ”——_° _° ;
‘220 ‘(80 ‘/.40 '/.00 “0.50 ’020 020 050 /

 

LOG (RESIDENCE TIME) . SEC

Figure 4.10 Concentrations versus residence time with
reversible reaction 5 at 360 C

Oethanol 003-06 olefins
Awater 4 aromatics + C6+ aliphatics
O ether X C3-C5 paraffins

x ethylene 2, ethane

 

78

results of the experiments at high temperatures and high

residence time.

4.3 Diffusion-Reaction Modelling

In developing the intrinsic rate expressions, the
interparticle and intraparticle mass transfer limitations
were avoided by careful disign of the reactor and the
reaction conditions which are not practical in a commercial
situation. Since the dehydration reaction of alcohol
involves a variety of products, direct use of the intrinsic
kinetic model can result in wrong prediction of product
yields in a commercial reactor. For completeness, an
isothermal one-dimensional diffusion model was considered

and the possible effects of diffusion were investigated.

If a catalyst pellet has the width and the length much
larger than the thickness, i.e. a semi-infinite slab
geometry, a one-dimensional diffusion-reaction model can be

described by the following second order differential

equation:
13°“: ('22.: '5'?" 2 - Mi ,c‘=/,"'./V <4-32)

where N 2 number of species.
Assumed Knudsen diffusion appilies on the mass transfer

in a porous media and the diffusivity is not a function of

79

concentrations and position, we have
8
A 6'
0,. 775' = ~86.- 01-33)
or

2‘8:

41" = - £77030 (4'34)

on:
with boundary conditions

Du; 4%? ‘1‘“) = *1. [Pbc‘f’t‘m’]

where k9; is the external mass transfer coefficient for
species i;
P», is the bulk partical pressure of species 1;
L is the half thickness of the catalyst slab.
Applying equations (4-33),(4-34)and (4-35) to all the
species concerned in the system,six dimensionless second order
O.D.E.s with corresponding dimensionless boundary conditions

can be derived, as shown in Table 4.12, by introducing

the following dimensionless quantities:

—‘—‘— _Lc' __0 , _. JILL
f = L 7 7‘- : F5 5 £6 = I 82' — ‘

(‘2‘: L°K7F/ D“. 9 7 A“ /' 3

~ 3 .
(74‘. L‘tzrrfl / De, ) . c= 4‘45

7f). = KI/Db

80

TABLE 4 . 12
Dimensionless Second Order O.D.E.: and Boundary Conditions

for Diffusion-Reaction Modelling

 

 

O.D.E. Boundary Condition
1 it???“ °3°iyfil°'°°z' E y' $11333. [ym-y, (1)]
2 gjytahahggf 4:2.) 24. §::E3;:31[Y81‘Y1(1)]
3 %=M&f;§,y’-;;y, +2¢:Y.°+.15¢;y35+’ £11333. [mu-y3 (1)]
4 ai$!_hhafgigyiy.‘+z.as4:31;;4 2:216:23. [yM-y, (1)]
5

d° _h.5(-¢‘ ‘) _ y'(l)-B [y -y (1)]

3?: TEL—W. “*5 xvi-(0)0 °‘ ’

6 d“ -h. (-34>‘ ‘) _._ y'(l)2B [y -y (1)]
3?“ °1I+5;y:)"°" y::(0)20° °‘ ‘

where chi-(Ear: nip/13..)i .i-l.3
dag-(EtL’RTp/D..fi(l=b)= .122,4.s
th-Da/Dtjj-Z, . . . , 6
1'1"“an
Bf-kgjL/ch» ,j-1,...,6
yu-bulk mole fraction of i,i21,...,6

81

Water was not included in the calculation since the
yield of water could be evaluated stoichiometrically from
the conversion of ethanol and the yield of ether. Ethane
and other light paraffins were treated as one species and
their yield was constrained by the formation of
aromatics. A ratio of paraffins/aromatics to be 3:1 here
was assigned. Difficulty was encountered with the
consumption rates of ethylene and other light olefins due to
the formation of paraffins from them, a distribution of
0.15:2.85 was assigned respectively based on the

experimental data at high temperatures(300and 360°C).

These second order O.D.E.s need to be solved
numerically since a closed form solution is not available.
An optimal ”Galerkin with quadrature” method was used to
estimate the solution. The collocation points were
determined by finding the roots of Jacobi polynomial . Once
the optimal collocation points were determined, a set of
Lagrange interpolation polynomials was used for the
approximated solution yu,i21,2,....,6. The node values were
then determined by subsitituting yhbinto the O.D.E.s,
linearizing the resulting nonlinear algebraic equations and
solving the linear algebraic equations. Details of the

calculation technique are shown in Appendix E.

82

In general, it i s impossible to ascertain when a
given accuracy has been reached since the exact
solution is unknown. A estimate of approximation accuracy
is suggested in Section 2.3.5 of Villadsen and
Michelsen[74]. The approximation order N should at least

safisfy

Z a
4N>¢a° "‘ 4’";

Thus the results for N28 are only expected to reliable up to
4’: 2 256. The magnitudes of the largest and smallest 4p; in
the system have a difference up to 5th order, and it appears
that a choice has to be made between the reliability of the
approximation and the length of the computation time in
some critical cases. For cases with half thickness L
greater than 0.02 cm and the temperature greater than 300°C,
the Thiele moduli <5: ,9: and 43: are greater than 256,and the

accuracy of the approximation could be questionable.

A general performance index can not be defined for the
purpose of the diffusion effect study in such a complicated
.reaction system, and the diffusion effect will be studied on

a case by case basis as discussed in the following sections.

Two typical concentration profiles inside the catalyst

slab are shown in Figures 4.11 and 4.12. The concentration

 

 

 

 

 

 

 

 

 

 

«25
.2d ethylene
./5-
z:
o
H
94
0
<2
Ix
Ex...
m .l-
,4
o
2:
.c15-
C3-C‘ olefins
other compoun;;‘—-“~.‘~._-~—-==-—
0 F=I$?"'l

o .2 .4 p .6 .8 /
X/L

Figure 4.11 Typical concentration profiles in catalyst pellet.
Profiles of Ethylene and C,-C‘ olefins are
decreasing along X/L-axis

84

 

“25-

  
  
 

‘2. ethanol

MOLE FRACTION
G
l

.I- light paraffins

 

 

 

aromatics

 

 

 

(3
it
41
03+
00

X/L

Figure 4.12 Typical concentration profiles in catalyst pellet.
Profiles of ethylene and 03-C5 olefins have
local maximum points

85

profile of intermediate such as ethylene and light olefins
may have a maximum point when the catalyst thickness is
large making the consumption rate of the intermediate higher

than the formation rate near the maximum .
4.4 CSTR Simulation

The mathematical diffusion model described in the
section 4.3 involves 23 parameters including 5 Thiele moduli,
6 mass Biot numbers,5 diffusion ratios,6 bulk concentrations
and one dimensionless adsorption constant. To simplify the
problem, a CSTR simulation with preset reaction conditions
was performed in order to study the possible effects of some

important design parameters.

A fluid phase balance was added in the mathematical

model as follows:

3662'; _ 3‘ c". _. (3’0? —:°(-%L (ta-Z.) = 0 (4-36)

where q; and q. are the inlet and outlet volumetric flow
rates, respectively;
Cij and Csj are the inlet and outlet concentrations of
species j, respectively.

If the amount of catalyst in the system is fixed, the total
external surface area E°is inversely proportional to the
catalyst pellet thickness L.

4' V’fi
- - 7
‘p L (4 3 )

 

where V is the reactor volume;

86

E is the volume ratio of catalyst to reactor;
Equation (4-36) can be rewritten in a dimensionless

form as follows:

' ° ,. ._ . __ Qu'VZ' dz; _. _-
ioPa 1‘} I"! 551‘ at? (7") 0

01'

. g . “77‘ -
.740. Km??- -— 7'7. 7;- ( $27) = o (4 38)

where Rm 2 qipz/qbpb which is the molar ratio of inlet stream
over outlet stream;
T 2 (V/q,)/(L°/D¢;£ ) which is a time ratio of the
residence time over the characteristic holding time in
the catalyst pellet.

Using Equation (4-38), the boundary conditions at f2L listed

in Table 4.12 can be rewritten as

1124397) — °’°[°°°°°[ ° £070] (4-39)
A? / 7" 5; Tr;

By specifying the reaction conditions, the performance
of the ethanol dehydration reaction in a CSTR reactor can be
investigated. The numerical method described in the previous
section was employed, and the details of the calculation
technique are shown in Appendix E. Temperature, pressure,
pellet thickness,and catalyst activity distribution are four
important parameters affecting the selectivity of light
olefins and will be studied one by one in the following

sections.

4.4.1 Temperature Effects 87

Temperature effects on the reactant conversion, product
yields,and selectivity to light olefins were investigated at
300, 350 and 400°C. The resulting bulk mole fractions as
functions of the residence time are shown in Appendix F.
The yields of ethylene, light olefins and Czhydrocarbons are
plotted versus the conversion of ethanol in Figures
4.13-4.15. The ethylene yield decreases as the reactor
temperature increases. The light olefins yield increases as
the reactor temperature increases. With the same
conversion, the yield of C6+ hydrocarbons increases as the

temperature increases.

Four different selectivities of interest were evaluated
and plotted versus ethanol conversion. These are shown
in Figures 4.16-4.19. The selectivity of light olefins over
ethylene (y4/y3) with respect to the ethanol conversion
increases as the reactor temperature increases. The
selectivity of light olefins over C6+ hydrocarbons (y4/y5)
decreases as the temperature increases. The selectivity of
olefins including ethylene and C3-C6 light olefins over
ether and C6+ hydrocarbons,(y3+y4)/(y2+y5), can be improved
by increasing temperature if the ethanol conversion is less
than 60%. The selectivity of C3-C6 light olefins over other
products,' y4/(y2+y3+y5+y6), increases as the reactor

temperature increases.

88

 

.l6-

.08-

BULK MOLE FRACTION

.04-

 

300°C

 

 

 

_J.

I 7 I I

20 40 60 80 I00

% ETHANOL CONVERSION

Figure 4.13 Bulk mole fraction of ethylene versus % conversion

of ethanol in CSTR for various temperatures
L20.01 cm
P =1 atm

 

 

 

 

 

.05
.04-
400°C
5 03-1 °°°0°
E; ° 300°C
3":
Ch
8
g .02") ).
a '.
B
49/-
,1”
,2:
(91"gr l 'T’ I I
0 20 40 ~- 60 80 /00

% ETHANOL CONVERSION

Figure 4.14 Bulk mole fraction of 03‘C5 olefins versus
% conversion of ethanol in CSTR for various
temperatures
L=0.01 cm
P =10 atm

 

 

.03

.024-

8 .0/8—
'3
ES
8‘.
S

:29 .0/2"
6d
I4
2

.006-

o-I

0

Figure 4.15

 

 

 

 

% ETHANOL CONVERSION

Bulk mole fraction of aromatics and Cgialiphatics
versus % conversion of ethanol in CSTR for
various temperatures

L2O.01 cm

P 21 atm

91

 

 

 

 

 

.75
.63-
» ‘45"
E-‘
S
E
O
8
8 .3-
./5-
0 r r I r
0 20 40 60 80 /00

% ETHANOL CONVERSION

Figure 4.16 Selectivity of C3-C‘ olefins over ethylene versus

% conversion of ethanol in CSTR for various
temperatures

L=0.01 cm

P =1 atm

 

>LL> a ECmfFLT.

 

 

92

 

 

 

 

.25
400°C
.2C3-
[5-
>4
E
H
>
E a
o 350 C
S
g l(3-
300°C
5...
(7 I *r* I I
0 20 40 60 80 IOO
% ETHANOL CONVERSION
Figure 4.17 Selectivity of Cg‘C‘ olefins over aromatics

and C? aliphatics versus % conversion of ethanol
in CSTR for various temperatures

L=0.01 cm

P =1 atm

93

 

 

 

 

50
40-
\\
400‘
g 30-
E
E
83
n—‘J
5% 20-
350°
[0‘ 3000C
0 I I r . .
0 20 4O 50 6’0 l00

% ETHANOL CONVERSION

Figure u.18 Selectivity of C;-C5 olefins over ether and
aromatics versus % conversion of ethanol in
CSTR for various temperatures
L=0.01 cm
P =1 atm

90

 

 

 

 

 

.25
.2?-
: '5‘
H
>
H
a
o
m
if:
m .l-
400°C
350°C
.05“
300°C
C) ‘I *r’ I I
0 20 4O 60 6’0 IOO
% ETHANOL CONVERSION
Figure 4.19 Selectivity of Cg-C‘ olefins over other products

versus % conversion of ethanol in CSTR for
various temperatures

L=0.01 cm
P =1 atm

95

4.4.2 Pressure Effects

Pressure effects on the yields and the selectivities
were investigated at 400 °C. The resulting bulk mole
fractions with respect to the residence time for different
system pressures, 10, l and 0.1 atm, are shown in Appendix
F. Figures 4.20-4.22 show the yields of ethylene, light
olefins and C6+ hydrocarbons, respectively, with respect to
the ethanol conversion. The ethylene yield decreases as the
reactor pressure increases. The light olefins yield has the
same trend as the ethylene yield if the ethanol conversion
is greater than 80%. For the conversion less than 40%, the
yield of light olefins increases as the reactor pressure
increases. A transition region exists between 40% and 80%
conversion. An optimal reactor pressure may be found in the
transition region. In the present study, the medium
pressure (1 atm) case has the best yield of light olefins in
the transition region, the high pressure case (10 atm) the
second, the low pressure case (0.1 atm) the third. The C6+

hydrocarbons yield increases as the pressure increases.

Figures 4.23-4.26 show the selectivities with respect
to the ethanol conversion. y4/y3 increases as the pressure

increases. y4/y5 decreases as the pressure increases.

 

 

 

0.1 atm
./6-*

z 1 atm
S. ./2-
e«
o
.<
m
a.
53 10 atm
g .05" I
m / I,

/ /

004-.l / ’l /
/ /
// /
/
C’/
0;"
#9
0'? T I
0 20 80

% ETHANOL CONVERSION

Figure 4.20 Bulk mole fractiOn of ethylene versus %
conversion of ethanol in CSTR for various

pressures
L=0.01 cm
T=hOO°C

 

{N
-l
/

 

 

 

 

 

.05
001 a ‘0
.04d
1 atm

g S.
H .03“
5‘
o
a?
In. 10 atm
g l
g .02-
a:
d L
:2)
m

.0/1

t
4
x‘~"
C*+‘Eflb— l I I I
0 20 40 60 6’0 /00
% ETHANOL CONVERSION

Figure 4.21 Bulk mole fractiOn of C,-C. olefins versus

% conversion of ethanol in CSTR for various
pressures

L=0.01 cm

T=HOO°C

98

 

 

 

 

 

 

.05

.04-
2:
<3
H
8 .03-
<
c:
[in
a:
h:
S
a: 'C22'
,4
D
m

.0/- 10 atm

1 atm
OJ—‘h—H— T I
0 20 40 60 80 IOO
% ETHANOL CONVERSION

Figure 4.22 Bulk mole fraction of aromatics and C;+aliphatics

versus % conversion of ethanol in CSTR for
various pressures

L=0.01 cm

T=400°C

99

 

 

 

 

 

 

.75
.6-
.45-I
Z
S
E
B
E: .3-
m
0’5- I 10 atm
1 atm
0.1 atm"f
C7 I I I TI
0 20 4O 60 80 IOO

% ETHANOL CONVERSION

Figure 4.23 Selectivity of C3-C6 olefins over ethylene versus
% conversion of ethanol in CSTR for various
pressures
L=0.01 cm
T=400°C

IOO

 

 

 

 

 

 

 

/50
I20-
0.1 atm

90‘
>I
9‘
'51
E
g 60~
m

30-

1 atm
0 10 L131?!
l l l I
0 20 40 60 80 / 00

% ETHANOL CONVERSION

Figure 4.24 Selectivity of C3-C6 olefins over aromatics and
C6+aliphatics versus % conversion of ethanol in
CSTR for various pressures
L=0.01 cm
T=400°C

lOl

 

 

 

 

 

 

 

800

640-
% 480-
9+
:2
a 320- 0 . 1 atm
m

/60-

1 atm_
0 :M I r
0 20 40 60 80 /00

% ETHANOL CONVERSION

Figure 4.25 Selectivity of Cg’Cé olefins over ether and

aromatics versus % conversion of ethanol in
CSTR for various pressures

L=0.01 cm
T=400°C

102

 

 

 

 

 

 

.35
.28-
.2/-
E
E
3
ES
53 ./4-
a:
10 atm
.07_ 1 atm ‘*
0.1 atm
0 I I I I I
0 20 40 60 80 /00

% ETHANOL CONVERSION

Figure 4.26 Selectivity of C,-C‘ olefins over other
products versus % conversion of ethanol in
CSTR for various pressures
L=0.01 cm
T=400°C

103

(y3+y4)/(y2+y5) decreases as the pressure increases.
y4/(y2+y3+y5+y6) decreases as the pressure increases if the
conversion is greater than 90%, while it increases if the
conversion is less than 70%. Again, there is a transition
regiOn where the medium pressure case has better selectivity

to light olefins.
4.4.3 Catalyst Size Effects

With equal amount of catalyst inside the reactor, the
performance of the CSTR was simulated at 400 iC with
different sizes of catalyst pellet. This was done by
holding the void fraction the same and varying the thickness
of the catalyst pellet. The characteristic holding time
in catalyst (Lz/Dc;£ ) was varied proportional to the
thickness square. Five different sizes of catalyst pellect
were investigated: 0.001, 0.01, 0.02, 0.05 and 0.1 cm.
The resulting bulk mole fractions with respect to the
residence time are shown in Appendix F. Figures 4.27-4.29
again show the yields with respect to the conversion. The
ethylene yield decreases as the pellet size increases. The
yield of light olefins decreases as the pellet size
increases if the conversion is greater than 85 %. It
increases if the conversion is lower than 40%. Again, a

transition region exists for the yield of light olefins.

104

 

.001 cm

BULK MOLE FRACTION

 

 

 

 

% ETHANOL CONVERSION

Figure 4.27 Bulk mole fraction of ethylene versus %
conversion of ethanol in CSTR for various
pellet sizes
T=400°C
P=1 atm

lOS

 

 

.06
.048-
.036-

Z
O
5
ES
m .024-
23
S
E
m .0/2-
04
0

 

.001 cm

 

 

 

 

I 7
80 /00

% ETHANOL CONVERSION

Figure 4.28 Bulk mole fraction of C3-C5 olefins versus

% conversion of ethanol in CSTR for various
pellet sizes

T=UOO°C

P=1 atm

106

 

 

 

 

 

 

 

.03

.024-

§ .0/8-
64
52
95.
[3.]

g 00/2.l
S
55
8

.006-

<91

0

 

% ETHANOL CONVERSION

Figure 4.29 Bulk mole fraction of aromatics and Cyraliphatics
versus % conversion of ethanol in CSTR for various
pellet sizes
T=400°C
P=1atm

107

The yield of C6+ hydrocarbons increases as the pellet size

increases.

Figures 4.30-4.33 show the selectivities. The relative
magnitude of product diffusivities plays important role in
determining the selectivity of a specific species. The
selectivity. of a species depends on how fast it can diffuse
out of catalyst pellet and the relative rate of formaton and
consumption of the species. The trend of seleCtivity is
more complicated to interpret. In general, y4/y3 increases
as the pellet size increases. For the convesion higher than
45%, y4/y5 decreases as the pellet size increases. For the
conversion lower than 40%, y4/y5 with L-O.l cm is greater
than the ones with L=0.02 cm and L=0.05 cm which indicates
the existance of a local minimum of the selectivity with
respect to the pellet size. The quantity (y3+y4)/(y2+y5)
decreases as the pellet size increases if the conversion is
higher than 60%. For the conversion less than 60%, the trend
of the selectivity is complcated but a local maximum exists
around L=0.05 cm. The quantity y4/(y2+y3+y5+y6) decreases as
the pellet size increases if the conversion is greater than
85%. For the conversion less than 85%, the selectivity, in

general, increases as the pellet size increases.

 

 

 

 

 

.75
AS“
.45- /
>4
94
H
>
3
fig .43-
In
[:1
0)
.l5‘
.010"
,z/’ .001 cm
, .1 cm
'05 .02 cm
C) V T r I
0 20 40 60 8O /00
% ETHANOL CONVERSION
Figure 4.30 Selectivity of Qg‘06 olefins over ethylene

versus % conversion of ethanol in CSTR for
various pellet sizes

T=400°C

P=1 atm

109

 

 

 

 

 

 

9
.01 cm
.001
.1 cm
7.2-
.02
.05 cm
‘3 5.41
>
E:
8
a
m 3.64
1.84
0 I I I I u
0 20 40 60 80 /00

% ETHANOL CONVERSION

Figure 4.31 Selectivity of C§-C5 olefins over aromatics and
Ci'aliphatics versus % conversion of ethanol in
CSTR for various pellet sizes
T=400°C
P=1 atm

llO

 

 

 

 

IOO
.001 cm
80-
.1 cm
E 6 O-I
E: .05 cm
94
Ed
R
”7 ‘4(?- - ~‘\\
.02 cm .0 cm
20-
0 I I I I
'0 20 40 60 80 /00

% ETHANOL CONVERSION

Figure 4.32 Selectivity of Cg‘C‘ olefins over ether and
aromatics versus % conversion of ethanol in
CSTR for various pellet sizes
T=400°C
P=1 atm

lll

 

0001 O

.01 cm

 

./5-

SELECTIVITY

.02 cm

 

005 C“
.1 cm

 

 

 

(9 I ‘T’ I

0 20 40 so 85 100

% ETHANOL CONVERSION

Figure 4.33 Selectivity of C,-C6 olefins over other products
versus % conversion of ethanol in CSTR for
various pellet sizes
T=400°C
P=1 atm

112

4.4.4 Activity Distribution Effects

Nonuniform activity distribution can also affect the
yields and the selectivities. Three simplified cases were
studied to investigate the activity distribution effects.
The physical pictures of the simplified cases are shown in
Figure 4.34. A brief description of them is given as
follows:

Case l:dual distribution with dense catalytic outer layer
and inert inner layer.

Case 2:dual distribution with dense catalytic inner layer
and inert outer layer. Diffusivities are the same
for both layers.

Case 3:same as Case 2 except that the values of
diffusivities in the invert outer layer are twice as
large as those in the catalytic inner layer.

The working equation of boundary condition for Case 2 and

Case 3 has different expression than Case 1. For Case 2 and

3, the boundary condition is:

I
4,6 D' at I
TI W =-—I::z I—‘m-I w

where Deixand Dei‘are diffusivities of species i in regions
I and II, respectively.

The resulting bulk mole fractions with respect to the
residence time are shown in Appendix F. Comparisons of
yields between the distributed cases and the uniform one are

shown in Figures 4.35-4.37. The difference between the case

113

 

 

 

 

 

 

 

 

 

 

 

 

l~—-L——w*-L
1.4
II I I II II I I I II
a 7%
(a)Case 1: (b)Case[2:
dense catalytic outer dense catalytic
layer and inert inner inner layer and
layer inert outer
D?=D? layer
03:0:

II I I I, II
/ /
27 /

(c)Case 3: (d) Uniform Case
dense catalytic inner
layer and inert outer
layer
D? =DI’ u

 

 

 

 

 

 

 

 

 

 

_R

 

inert area

 

 

 

 

 

//;//' I, uniform catalytic area

 

 

 

 

dense atal tic area
// ° 3*

 

 

Figure 4.34 Physical pictures of cases in step distribution
of catalyst activity

114

 

 

./5

I21

5 .09-I
E
I?
CL.
(11

23 .06-
S
53
E

.03-

0

0

 

 

 

 

case 1
uniform
case 3
case 2%
2'0 40 6'0 85 100

% ETHANOL CONVERSION

Figure 4.35 Bulk mole fraction of ethylene versus %

conversion of ethanol in CSTR for step
activity distribution study

L=0.05 cm

T=400'C

P=1 atm

 

 

 

 

 

.035
.028-
E
5 .02/-
as: unifo 0
EL.
g case 1
2 .0/4-
5
53 - - 3
.007“ . caseN
(7% ' I I I
0 20 4O 50 80 /00

% ETHANOL CONVERSION

Figure 4.36 Bulk mole fraction of C,-Ca olefins versus %
conversion of ethanol in CSTR for step activity
distribution study
L=0.05 cm
T=400'C
P=1 atm

 

ll6

 

 

.035

.020-
z

S .02/4
E4
O
:5
CL.
S

S .0/ 4-
fi
5

.00 7-

0
0
Figure 4.37

 

 

 

 

20 40 60 8'0 /00

% ETHANOL CONVERSION

Bulk mole fraction of aromatics and C? aliphatics
versus % conversion of ethanol in CSTR for step
activity distribution study

L=0.05 cm

T=400‘C

P=1 atm

117

I and the uniform case is minor. Case 2 and Case 3 exhibit
the drastic suppressive effect of the inert outer layer on
the yields of ethylene and other light olefins. Figures
4.38-4.41 show the comparison in selectivities. Generally
speaking, the inert outer layer increases the selectivity of

terminal species.

118

 

 

 

 

.5
I
.4-
case 2
>4 .34 case 3
eI
I:
E:
533
Efl “2-
m uniform
case 1
./ -
C3 I r I If
0 20 40 60 80 /00

Figure 4.38 Selectivity of C5-C. olefins over ethylene

% ETHANOL CONVERSION

versus % conversion of ethanol in CSTR for step

activity distribution study

L=0.05 cm
T=400°C
P=1 atm

 

 

 

 

 

 

 

7.5
6..
a 4.5-1
2
5
£3
53 3-
/.5-
C7 ' ' I I I
0 20 40 . 50 80 /00

% ETHANOL CONVERSION

Figure 4.39 Selectivity of Cg'C‘ olefins over aromatics and
Ci’aliphatics versus % conversion of ethanol in

CSTR for step activity distribution study
L=0.05 cm

T=400°C

P=1 atm

120

 

75

uniform

60-

case

SELECTIVITY

l5-

 

 

 

 

 

 

C)‘ I I
0 2'0 40 60 80 I00

% ETHANOL CONVERSION

Figure 4.40 Selectivity of Cz-Cs olefins over ether and
aromatics versus % conversion of ethanol in
CSTR for step activity distribution study
L=0.05 cm
T=400°C
P=1 atm

121

 

 

 

 

 

 

 

.035
.028-
.02/-
E:
#1 uniform
>.
g k
B .0/4" case 1
£12]
m case 3
'00?“ ca“
(7+ ' I I I
O 20 40 50 80
% ETHANOL CONVERSION
Figure 4.41 Selectivity of Cr-C‘ olefins over other

products versus % conversion of ethanol
in CSTR for step activity distribution
study

L=0.05 cm

T=400°C

P=1 atm

lOO

Chapter 5

Discussion

Althouth the alcohol dehydration reaction has been
studied for nearly two centuries and a enormous number of
papers have been published on the manufacture of gasoline
from methanol, relatively little has been published to date
on the kinetics of hydrocarbon formation from alcohols. Two
possible reasons are : 1) in view of the complexity of the
reaction, a rigorous kinetics study is difficult to
approach, and 2) the empirical' correlations can satisfy
industrial needs. From an engineer point of view, a reactor
built on the basis of empirical data can neither be
efficient nor trustworthy. A good example is shown in the
monograph by Weekman [63] in developing a lumped kinetic
model for catalytic cracking. A compromise can be made by
the lumping approach which simiplifies a complicated
reaction network down to an accessible kinetic model which
can be used to correlate the reactor performance to the
reaction parameters such as temperature, pressure, residence
time, and catalyst properties. For this reason, the
objective of this research is to obtain sufficient data on
the ethanol dehydration reaction using ZSM-S, and to develop
a reliable kinetic model which can fit the experimental data

and interpret the important observations in the literature

122

123

in order to justify the importance of a complete kinetic
study. The following discussion will aim at the
justification of the validity of the lumped kinetic model

obtained in this research for ethanol dehydration.

The reaction temperature used in the experiments covers
a broad range, 150-360 'C, commonly used by other
researchers. The goodness of the data fitting presented in
the previous section indicates that the kinetic model
obtained is reliable in the range of the temperature used.
The order of the oligomerization of ethylene is found to be
second order in the lumped model which is inconsistant with
the first order reported in the literature [40]. The
inconsistancy can be a result from the following reasons: 1)
the reaction product is a lump of C3-C6 olefins which may
implicitly affect the result in determing the reaction
parameters from data fitting and lead to the conclusion of
second order kinetics, and 2) the 8-coupled first order
O.D.E.s used in the data fitting involve seven rate
expressions for seven elementary reactions. Any assumptions
made for the individual elementary step may affect each
other. It is not proper to make any judgement on the
inconsistancy at present. More data should be obtained and
tested with the models before a significant statement can be

made.

124

The temperature effect on the selectivity of light
olefins in the CSTR simulation presented in Section 4.4.1
has general agreement with that reported by Chang et al.[43]
for the methanol conversion. The selectivity of olefin is
enhanced by increasing the temperature in the
alcohol-to-hydrocarbons process. The trend can be
interpreted by the relative magnitude of the rate constants
of olefins formation and consumption as function of
temperature [43]. At low conversion, the performance of a
CSTR is closed to the performance of a PFR used by Chang et
a1. Thus,it is not surprising that the trend of the olefins
selectivity in a CSTR is the same as what observed in a PFR.
However, the CSTR simulation shows that the olefins
selectivity decreases by increasing the temperature if the
ethanol conversion is greater than 60%. As mentioned in
Section 4.4.1, the yield of ethylene decreases and the yield
of C3-C6 olefins increase as the temperature increases. At
high conversion of ethanol, the yield of C3-C6 olefins is
affected by the diffusion limitation inside the catalyst
pellet. The comparison of the concentration profiles of
ethylene and C3-C6 olefins for different temperatures at
T-ZS sec are shown in Figures 5-1 and 5-2. The concentration
profile of ethylene does not change much along the X-axis.

However, the concentration of C3-C6 olefins is built up so

125

 

 

 

 

 

 

 

 

.2
./6-
300°C
.l 2— \
2:
<3
H
§ 350°C L.
‘____________,
g3 .CLS
a:
23 .
.Cl4-
C) l I I I
<7 ..2 4 .(3 A8 /
X/L
Figure 5.1 Concentration profile of ethylene in catalyst

pellet for various temperatures
7:25 sec

L=0.01 cm

P=1 atm

126

 

 

 

 

 

 

 

.036
.033-
2:
<3
H
e+
ca
é
Ex.
a:
#3
a
E .03-
.027 , , , r
O 2 4 . 6 8
X/L
Figure 5.2 Concentration profile of C;-C6 olefins in

catalyst pellet for various temperatures
7325 sec

L=0.01 cm

P=1 atm

 

127

high that the consumption rate of olefin is highly enhanced
by the diffusion limitation. Thus, the different trend of
the selectivity of C2-C6 olefins at high ethanol conversion
can be explained by the low. yield of ethylene and the

diffusion effect built in the simulation.

The pressure effect on the selectivity of aromatics in
methanol conversion is reported by Chang et al.[4l,43]. The
selectivity of aromatics is enhanced by increasing the
pressure. An interpretation is made by Chang [39] in terms
of sorption equilibria. The study of the pressure effect in
the CSTR simulation shows an obvious trend of suppression on
the olefin yield by increasing the system pressure which
leads to the enhancement of aromatics selectivity. The
pressure effect can be explained by the change of the Thiele
moduli values. As shown in Table 4.12, the Thiele moduliq’oz
and ¢¥ are linear function of the system pressure. Thus, the
enhancement of the aromatics selectivity with increasing
pressure is as expected. The selectivity of C2-C6 olefins is
again affected by diffusion which caused an unexpected trend
of the selectivity with respect to ethanol conversion, as

shown in Figure 4.26.

Report of the catalyst pellet size effects on the

selectivity of alcohol conversion to hydrocarbons can not be

128

found in the literature. According to the results of the
CSTR simulation presented in Section 4.4.3, the catalyst
pellet size does play an important role in the selectivity.
The order of the diffusivities of ethylene,C3-C6 olefins and
aromatics is: ethylene > C3 -C6 olefins > aromatics.
Increasing the pellet size will favor the aromatics
formation. Both the formation rate and consumption rate of
C2-C6 olefins are enhanced by increasing the pellet size.
These competing effects complicate the resulting selectivity
in the CSTR siumlation. Local minimum of C3-C6 olefins over
aromatics and local maximum of C2-C6 olefins over other
products with respect to the pellet size are predicted in
the CSTR simulation at low conversion of ethanol. Figures
5.3-5.5 show the comparisons of the concentration profiles
of ethylene, C3-C6 olefins, and aromatics for different
pellet sizes at‘T-l sec. The concentration profiles of
ethylene and C3-C6 olefins have local maximum points near
the external surface of catalyst pellet( except the smallest
size (L- .001 cm)) which indicates the consumption rates of
these olefins are higher than the formation rates through
most of the catalyst pellet space. However, the formation
rate and the consumption rate of these olefins are
comparable, leading to the complexity of the selectivity
study. The concentration of' aromatics builds up in the

pellet due to the low diffusivity. As the ethanol

129

 

 

 

 

 

 

 

 

 

 

.2
.001 cm
./5;
.l2-
5
E
a:
“F .08-
a:
.4
2-
.04-
0 I I I
0 .25 .5 .75 /

X/L

Figure 5.3 Concentration profile of ethylene in Catalyst
pellet for various pellet sizes
=1 sec
T=400‘C
P=1 atm

130

 

 

 

 

 

 

 

 

 

.05
.02 cm
.04-
.001 cm
5 .034
E
3
‘35.
a .024
S
.0!-
0 I I I I I
0 .2 .4 .6 .8 /

X/L

Figure 5.4 Concentration profile of C,-C‘ olefins in catalyst
pellet for various pellet sizes
T=1 sec
T=400°C
P=1 atm

131

 

 

 

 

 

 

 

.06
.1 cm
.05« .05 cm
.04-
5: .2 cm
2
S: .03-
E.
a:
E
5 .02-
.CH'
.001 cm
0 , I I I
0 .2 .4 .6 ,8 /

X/L

Figure 5.5 Concentration profile of aromatics and Cgaliphatics
in catalyst pellet for various pellet sizes
751 sec
T=400°C
P=1 atm

132

conversion increases, the trend of the selectivity to light
olefins becomes more obvious since the formation rate of
ethylene becomes less important compared with the
consumption rate of ethylene. With the consumption rate of
light olefins dominating the reaction in the pellet, the
selectivity of light olefins decreases when the pellet size

increases as is predicted.

Report of the catalyst activity distribution effects on
the selectivity of alcohol conversion can not be found in
the literature. The results of the CSTR simulation in
Section 4.4.4 show that the addition of an external inert
layer on the catalyst pellet has a drastic suppressive
effect on the yield of ethylene and C3-C6 olefins. The
comparisons of .the concentration profiles of ethanol,
ethylene, C3-C6 olefins and aromatics for different activity
distributions are shown in Figure 5.6-5.9. The inert outer
layer reduces the flux of the ethanol coming in the catalyst
pellet which leads to low formation rate of ethylene.
Because the consumption rate of ethylene remains high
compared to the low formation rate of ethylene in the
catalyst pellet, the ethylene yield stay low through the
entire range of the residence time studied The same
explanation can be applied on the yield of C3-C6 light

olefins. Thus, the selectivity of terminal products

133

 

 

 

 

 

 

 

 

,2
./5-
2:
<3
E J-
o
<
E.
[:1
I:
<3
2:
.05-
case 2 case 3 uniform
0 I I I I
0 .2 .4 .6 .8
X/L

Figure 5.6 Concentration profile of ethanol in catalyst
pellet for step activity distribution study
Ethanol conversion=40%
T=400°C
P=1 atm

134

 

 

 

 

./5
uniform
./-
8
E
U
3:”
[51.2.
3
2 case 3
.05m
case 2
0 I I I I
0 .2 .4 I .6 .8
x/L

Figure 5.7 Concentration profile of ethylene in catalyst
pellet for step activity distribution study
Ethanol conversion=40 %
T=400°C
P=1 atm

 

135

 

uniform

case 3

 

. 02-

MOLE FRACTION

case

.Ol-

 

 

 

X/L

Figure 5.8 Concentration profile of C3-C5 olefins in catalyst
pellet for step activity distribution study
Ethanol conversion=40%
T=400°C
P=1 atm

136

 

 

 

 

 

.05

C) uniform

. 4-

case 2 '

s .03-
3 case
0
g
a.
a:
g 002‘
E:

.0!-

o I I I I I

(7 .2 u4 .6' .8 I
X/L

Figure 5.9 Concentration profile of aromatics and Cz'aliphatics
in catalyst pellet for step activity distribution
study
Ethanol conversion=40%

T=400°C
P=1 atm

137

(aromatics and paraffins) is enhanced by The external

resistance.

The 510, /A110, ratio effects on the decoupling of olefin
formation from aromatization reported by Chang et al.[43]
can be explained by means of the number of active sites
invOlved in each step. As mentioned in Section 4.2.4, the
single site rate expression has a similar form as the dual
site rate expression except that the power in the
denominator in the single site model is one instead of two
and the combined rate constant'P'is directly proportional to
So (2 number of active sites per unit catalyst weight)
instead of Sd’in the dual site model. Thus, the ratio of if
to E;will be approximately linearly proportional to the
reciprocal of So. The acidity of ZSM-5 is dictated by the
Sim/Alp, ratio: the higher the ratio, the lower the acidity.
If the acidity(represented by So) is a linear function of
the reciprocal of the SiO;/A1105ratio [76], if /k§ (which is
similar to k. /kz in the article by Chang et al) will be
linear function of the SiOz/A1203ratio. 'This linearity has
been reported by Chang et al. In such a case, the
olefinization reaction can be decoupled from the
aromatization reaction if the 5102 /A12 03 ratio can be
infinitely increased. This is possible with the ZSM-S class

catalyst. Report on the $102 /Al;03 ratio effects on the

138

selectivity of ethanol conversion can not be found in the

literature.

An attempt was made to apply the single site model to
the initial reaction steps (Reaction 1-3 in the network).
The power of e in Equations (4-11),(4-12), and (4-13) was
changed from two to one. The results of data fitting using
the single site rate expressions at 150 and 200°C are shown
in Figures 5.10-5.11 and Table 5.1. A discrimination
between the dual site model and single site model can not be
made since both of them fit the experimental data very well.
More data should be obtained and tested with the models
statistically before a significent statement can be made.
The study of the effect of the.SiO;/Al;05 ratio would also
help to discriminate between the single site and dual site

models.

The influence of the water addition in the feed on the
enhancement of the aromatics formation from ethanol
conversion is reported by Qudejans et a1. [42]. The
experiments were conducted by keeping the space velocity the
same and varying the water/ethanol feed composition at T8578
'K. Since the partial pressure of ethanol in the feed was

not constant for each run, the statement on the influence of

water content is doubtful. Water as co-feed_ is also

 

MOLE FRACTION

  

 

 

 

0‘1 l If_I'"—_"I'
“2.20 - L80 '/.40 '/.00 “C260 '020 0.20 0,60 /
LOG (RESIDENCE TIME) 0 SEC

Figure 5.10 Concentrations versus residence time for
kinetics study using single site model

at 150°C
0 ethanol 0 C3-C6, olefins+
Awater 4) aromatics 1- C6 aliphatics
Oether X C3-C5 paraffins

x ethylene z ethane

 

,40

.35“

.30-

.25-

MOLE FRACTION

 

 

 

 

l I
-2.20 '480 -/.40 -l.00 '060 0.20 0.20 060

L00 (RESIDENCE TIME). SEC

Figure 5.11 Concnetrations versus residence time for
kinetics study using Single site model

at 200 'C
0 ethanol OC3- C6 olefins
A water 4: aromatics + C6 aliphatics
o ether XCB- C 5 paraffins

X ethylene z ethane

 

TABLE 5.1

Estimated Rate Constants for Single Site Model at 150 and

zoo‘c
Temperature(°C) 150 200

Sok,K 4.843-5 1.508‘4
SOsz 6.733‘4 2.403'3
SokgK 9.918-5 1.278-3
SOk4 1.503'6 3.823‘6
50k: 5.238-5 7.33E'5
Saks 2.67E-7 3.473-7
Sokr 3.603'5 9.513‘5
K. 16.37 6.10

142

reported to decrease the rate of catalyst deactivation. A
contradictory statement is made by Maiorella [77]. An
attempt was made to include the water adsorption in the
Langmuir-Hinshelwood type of rate expressions in this
research. As a result a negative value of the water
adsorption constant was obtained. The influence of the
water addition can not be predicted from the kinetic model

obtained in this research.

CHAPTER 6

Conclusions and Recommendations

The results of the experiments, kinetics modelling and
CSTR simulation in ethanol conversion on HZSM-S lead to the

following conclusions:

(1) Ethanol can be readily converted to hydrocarbons
ranging from methane and light olefins to paraffins and
aromatics on the' ZSM-S class catalyst. The yield and
hydrocarbon distribution are similar to those for the more
studied methanol case. The similarity is expected since the
reaction pathways become identical for both cases after the
initial dehydration steps. Excluding water produced, the
maximum yields of the C3-C6 light olefins at 250, 300 and
360 °C were 23,26 and 30 wt%, respectively, from the
experimental data. Light paraffins and C6+ aromatics are
the terminal products. The yields of light paraffins and
C6+ aromatics are correlated due to hydrogen transfer
mechanism. Thus, the gasoline yield can not exceed 60 wt%.
The initial dehydration of ethanol to ethylene associated
with a bimolecular etherification reaction can be described
by the classical fl-elimination mechanism. The successive
reactions including olefin polymerization, aromatization,

and cracking can be described by the carbonium mechaism.

lfi3

144

(2) A lump reaction network has been developed and
proven to be feasible in determining the ethanol conversion
kinetics. Seven elementary reactions are involved in the
network. They are: (l) dehydration of ethanol to ethylene
and water; (2) condensation of ethanol to ether and water;
(3) decomposition of ether to ethanol and ethylene; (4)
oligomerization of light olefins to higher aliphatics and
aromatics: (6) hydrogenation of ethylene to ethane; (7)
hydrogenation of light olefins to light paraffins. The
network involves the initial dehydration steps which are not
considered by Chang et a1. [11]. Ethylene is an initial
inactive olefin and is not included in the light olefins

lump.

(3) Rate equations of the Langmuir-Hinshelwood type
have been developed to correlate the data and parameters
were evaluated with a quasilinearization method. The
results of this analysis indicate the polymerization of
ethylene is second order which is in contrast to the first
order observation reported in the literature [40]. The
inconsistancy could be a result from the lump network used
in this research. The first order kinetics reported is
based on the consumption rate of ethylene. The influence of

Sio1 /A1; Ogratio on methanol conversion studied by Chang et

145

al. [43] strongly suggests that the olefination and
aromatization reactions in. the alcohol conversion network
involve a different number of active sites. In this
research, the discrimination between the single site model
and the dual site model can not be made since both correlate
the experimental data fairly well. Although the ethanol
conversion process is similar to the methanol process, the
effect of SiO,/Alp,ratio on the selectivity of olefins from
ethanol conversion can be different from that observed in
the methanol conversion since a different mechanism is
involved in the initial dehydration steps. More studies

need to be done.

(4) The kinetics model was utilized in a model
describing the steady state diffusion-reaction in a single
catalyst particle. The single particle study was extended
. to a heterogeneous model of an isothermal CSTR to
investigate the effects of varying the reaction conditions
and the catalyst properties. The results of the CSTR

simulation need to be justified by experiment.

(5) The results of the CSTR study indicate the
selectivity of light olefins can be enhanced by increasing
the reaction temperature and reducing the reactor pressure

as is reported in the literature. However, the diffusion

146

limitation also plays an important role in the selectivity
which leads to the unexpected trends in the olefin
selectivity with respect to the conversion of ethanol. An
inert outer layer on the catalyst pellet drastically reduces
the selectivity of olefins. This decrease is explained by a
reduced reactant flux and product hold-up in the catalyst

pellet.

The following recommendations are suggested for future

studies:

(1)The isothermal study should be extended to include
the non-isothermal behavior by including an energy equation
in the mathematical models. The heat transfer effects are
neglected in the CSTR simulation. Unlike the methanol case,
the initial reaction step in the ethanol dehydration is
endothermic, which balances some of the heat generated in
the successive exothermic polymerization reactions. It is
interesting to study the intraparticle heat transfer effect

in such a case.

(2) The Knudsen diffusion theory was employed in this
diffusion modelling, i.e. the diffusitivity was assumed to
be constant in the catalyst pellet. Realizing the effective

diffusivity in the porous media can be a function of gas

147

mixture composition, and that diffusion effects the
selectivity, the study taking the concentration dependency
on diffusion into account would be an interesting topic in

the future investigation of the ethanol conversion.

0(3) The CSTR study should be extended to simulate the
performance of a PPR by conncecting a number of CSTR's in
series. The theoretical and experimental studies on the
"long range” effect of varying the reaction conditions and
catalyst properties in a PFR are important topics in the

future_investigation.

(4) Since the initial reaction step in the ethanol
dehydration is endothermic,a thermally balanced fluidized
bed ehathanol reactor can be designed. 'Owing to the
complicated transfer phenomena involved in the fluidized bed
reactor, study on the application of the complex kinetics
obtained to a fluidized bed reactor design for the ethanol

conversion process can be a challenge in the future.

BIBLIOGRAPHY

BIBLIOGRAPHY
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Pines,H., ”The Chemistry of Catalytic Hydrocarbon
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Lee, E.S.,”Quasi1inearization and Invariant Imbedding",
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17,581 1982). .

APPENDIX A

Calibrations and Sample

Calculations

APPENDIX A

Calibrations and Sample Calculations
A.1 Rotameter Calibrations

The Matheson rotameters were calibrated at atmospheric
pressure with a soap film flowmeter for helium flow. The
calibration curves are shown in Figures A.1 and A.2 for 610

tube and 602 tube, respectively.

A.2 Syringe Pump Calibration

The Sage syringe pump was calibrated at several gear
settings by filling the syringe with water, starting the
pump, and measuring the elution time of a 3 m1 sample. The
average of three runs was used as the flow rate at each gear
setting. The volumeteric flow rate at each of the gear

settings used in the experiments are listed below:

B-D syringe size pump setting volumetric flow rate

20 C.C. 5 0.93

11 10.91

30 C.C. 2 0.37

6 1.86

9 6.00

3* 28.94

50 C.C. 3* 44.31

4* 79.12

* gear setting in ml/min mode

153.

154

 

 

 

 

ISO
/ 00‘
E
8
U)
a?
5"
a?
' a
53 50-
g
01 l I I I
0 20 40 60 80 IOO

SCALE READING

Figure A.1 Calibration curve for Matheson 601 tube

155

 

 

 

 

/ 000

800~
§ 66!)? 8.5.
U)
é
a?
3
E5 ‘4CX7‘
:33

200- glass
(7‘ - , lj ___.
0 50 [00 ISO

S CALE READ ING

Figure A.2 Calibration curve for Matheson 602 tube

156

A.3 Gas Chromatograph Calibration

Peak areas of compounds determined by digital
integration are not directly proportional to the percent
composition, i.e., different compounds have different
detector responses: therefore, it is necessary to determine
these response factors. An excellent reference for response
factors for flame ionization detector is the article by
Dietz [65]. Response factors for several products which
were not reported by Dietz were determined experimentally by
analyzing mixtures of known compositions according to the
method outlined by McNair and Bonelli (1968)[75]. Once

determined, these response factors were used to calculate

the percent composition. For example,

AMMJ9/Fh

Wt 3A-
: ’4'“/Fufars

x 100

A list of the response factors needed for this research

is shown in Table A.1.

A.4. Sample Calculation for Kinetics Experiments

Mass balance and carbon balance were made over the
total feed and products to obtain the overall product
distribution, and the validity of the calculation was then
checked by the oxygen balance. The calculation was so

complicated such that a computer program was written and

Compound
Methane
Ethylene
Ethane
Propylene
Propane
I-butane
Butenes
N-butane
Butadiene
Heptenes
Heptanes
Hexenes
Other C6 HCs
C7 HCS

C8 HCs
C9+ HCs

Ethanol

Ether

157

TABLE A.1

Response Factor

FID Response Factor

0.97
1.02
0.97
1.00
0.98
1.09
1.00
1.09
1.00
1.04
1.04
0.99
1.03
1.00
1.03
1.00

0.46
0.60

158

used for each run to avoid the calculation error. The
calculation technique is described as follows:

(1)1nput data includes weights of the ethanol feed and the
liquid product (SWT,LWT), volumes of the sampling bag,
ice trap and isopropanol/dry ice trap (TVB,VT1,VT2),
volumes of the gas samples injected to GC from the
sampling bag, ice trap and isopropanol/dry ice trap (SVB,
SVl,SV2), peak areas of compounds analyzed by the
integrator for each sample and the corresponding response
factors of compounds, carbon number and molecular weight
of each compound.

(2)Use the response factors with the peak areas to evaluate
the normalized weight composition for each sample. Sums
of the corrected peak areas are also calculated and
multiplied by the volume ratios of the sampling bag, ice
trap and isopropanol/dry ice trap over their respective
gas samples to obtain the corresponding intensities of
the gas product.

(3)Ca1culate the normalized molar composition for each
sample.

(4)Total amount of gas produced is determined by the weight
difference between the total feed and liquid product. .
Amounts of gas product distributed in the bag and traps
are determined by the relative magnitudes of the
respective intensities calculated in step (2).

(5)Ca1culate weight and number of moles of each compound in
gas product from the normal weight compositions,normal
molar compositions and corresponding distributed weights
of gas in the sampling bag, ice trap and isopropanol/dry
ice trap.

(6)Calculate total number of carbon atoms in feed and gas
product. Total number of carbon atoms in liquid product
is then determined by a carbon balance.

(7)Calcu1ate the normalized carbon distribution in the
liquid product from the normalized liquid molar
composition. Individual number of carbon atoms of each
species in the liquid product is then determined from
the normalized carbon distribution and the total number
of carbon atoms in the liquid product calculated from
step (6). Number of moles of each species in the liquid
product can then be determined.

159

(8)Calculate the weight of the organic compounds in the
liquid product. From this the amount of water is then
determined.

(9)Knowing the weight and number of moles of each species
in the gas and liquid samples, the overall weight and
molar compositions can then be detemined.

(10)Calculate total number of oxygen atoms in ethanol, ether

and water. Compare the oxygen number in products to the

oxygen number originally in feed in order to check the
validity of the previous calculation.

The computer program based on the calculation technique
described above is shown in the following pages. Input and
output of the computer calculation for run-1 (at 300° C is
also shown for illustration purpose. A more comprehensive

data list is shown in Table A.2.

160

Table A.2

Data for Run-1 at 300°C

ethanol flow rate-10.91 ml/hr
flow rate-146.33 ml/min

Helium
amount
Volume
Weight
Volume
Volume
Volume
Volume
Volume

of
of
of
of
of
of
of
of

ethanol fed in-6 ml=4.7104g

sampling bag-6568m1

liquid product-2.07159

vapor in ice trap-106ml

vapor in isopropanol/dry ice trap-257ml

gas sample from bag-0.5ml

gas sample from ice trap-0.5m1

gas sample from isopropanol/dry ice trap-0.5ml

Peak areas:

Gas sample Gas sample Gas sample Liquid sample

Methane
Ethene
Ethane
Propene
Propane
I-butene
Butenes
ijutane
C5+i C5
I cs‘+cs
Hexenes
Hexanes
C7 HCs
C8 HCs
C9+ HCs
cascxo
Unknown
Ethanol
Ether

ice trap CO trap bag mixture
1.268E+4 3.628E+0 1.347E+4 0.000
2.910E+7 1.27OE+7 6.4SSE+7 1.503E+7
1.972E+5 1.222E+5 2.47SE+5 0.000
7.094E+6 3.047E+7 1.004E+7 0.000
1.585E+6 5.715E+6 1.616E+6 0.000
3.870E+6 5.237E+7 3.495E+6 7.856E+5
4.598E+6 7.503E+7 4.515E+6 1.928E+6
2.967E+6 4.528E+7 2.841E+6 9.981E+5
3.362E+6 3.407E+7 1.942E+6 1.837E+6
4.126E+6 3.019E+7 2.27ZE+6 2.539E+6
1.595E+6 4.705E+6 7.1308+5 2.539E+6
3.085E+6 5.489E+6 1.342E+6 2.884E+6
1.977E+6 1.0BOE+6 9.090E+5 5.849E+6
5.541E+5 1.580E+5 1.817E+5 1.090E+7
2.538E+5 0.000 0.000 1.352E+7
3.548E+4 1.671E+5 2.342E+4 0.000
1.265E+6 1.97ZE+7 1.078E+6 7.097E+5
0.000 0.000 0.000 2.846E+5
0.000 0.000 0.000 0.000

nnnnnnnnnnnnnnnnnnnnnnnnnnnnn

000

161

THIS PROGRAM IS TO CALCULATE THE OVERALL PRODUCT DISTRIBUTION FROM
THE GC ANALYSIS DATA OF FOUR SAMPLES IN THE KINETIC EXPERIMENTS,
INVOKING OVERALL MASS BALANCE, CARBON BALANCE AND OXYGEN BALANCE.

T'TEMPERATURE

PRFETHANOL PLOW RATE

FC'HELIUM FLOW RATE

TVB- TOTAL VOLUME OF SAMPLING BAG

VB-ESTIMATED VOLUME OP GAS PRODUCT IN THE SAMPLING BAG
SWT'WEIGHT OF ETHANOL INJECTED

LWT'WEIGHT OP LIQUID PRODUCT

VTISVOLUME OP GAS IN ICE TRAP

VTZBVOLUME OP GAS IN ISOPROPANOL/DRY ICE TRAP

SVlISIZE OF GAS SAMPLE PROM ICE TRAP INJECTED TO GC

SVZ'SIZE OP GAS SAMPLE FROM I-PROPANOL/DRY ICE TRAP INJECTED TO GC
SVB-SIZE OF GAS SAMPLE PROM SAMPLING BAG INJECTED TO GC
O(I,J)'PEAK AREA OF SPECIES J OF GROUP 0 IN SAMPLE I
A(I,J)'PEAK AREA OF SPECIES J OF GROUP A IN SAMPLE I
P(I,J)=PEAK AREA OP SPECIES J OF GROUP P IN SAMPLE I
EL(I)'PEAK AREA OF ETHANOL IN SAMPLE I

ER(I)'PEAK AREA OF ETHER IN SAMPLE I
FO(I),PA(J),PP(K)IRESPONSE FACTORS OP I,J,X IN GROUPS O,A,P
MO(I),MA(J),MP(K)=MOLECULAR WEIGHTS OP I,J,K IN GROUPS O,A,P
CO(I),CA(J),CP(K)=CARBON NO CARRIED BY I,J,K IN GROUPS O,A,P
FEL,PER'RESPONSE FACTORS OF ETHANOL AND ETHER
MEL,MER-MOLECULAR WEIGHTS OP ETHANOL AND ETHER
CEL,CER-CARBON NO CARRIED BY ETHANOL AND ETHER

PROGRAM KARENB

REAL AM(4,9),PM(4,9),OM(4,9),ERM(4),ELM(4),EL(4),ER(4),PO(9)
REAL PA(9).FP(9),A(4,9),P(4,9),O(4,9),MO(9),MP(9),MA(9),TA(9)
REAL TMA(9).TP(9),TMP(9),TO(9),TMO(9),MER,MEL,CA(9),CP(9),CO(9)
REAL SP(4).LWT,TOPW(9),TAPW(9),TPPW(9)

OPEN(5,PILEI'DATA290')

OPEN(6,PILE8'YI')

 

 

READ INPUT DATA

READ(5'*)T,FR,FC,TVB,VB,SWT,LWT,VT1,VT2,5V1,5V2,SVB
RBAD(50*)(O(IIJ)IJ'1I9)
m(5:*)(A(laJ)oJ'J-r9)
READ(SI*)(P(1;J)IJ.IIQ)
READ<S,*)EL(1);ER(1)
READ(5,*)(O(2,J),J=1,9)
READ(51*)(A(2rJ)IJ'119)
READ(5,*)(P(2,J),J=1,9)
READ(5'*)EL(2):ER(2)
READ(5,*)(O(3,J),J‘1,9)
READ(5,*)(A(3,J),J81,9)

90

95

100

110
120
125
130

140

162

READ(5,*)(P(3,J),J=1,9)
asan(5.*)st(3).za(3)
READ(5,*)(O(4,J),J=1,9)
READ(5.*)(A(4.J).J-1.9)
READ(5,*)(P(4,J),J-1,9)
Raan(5.*)EL(4).BR(4)

WRITE(6,90)
WRITE(6,100)T,FR,SWT,LWT,VT1,VT2
warra(6,95)
WRITE(6,100)PC,TVB,VB,SV1,SV2,SVB
ronuar('1',4x,'axn Taur',3x,'rszn RATE',4X,'TOTAL raun',4x,'txo WT
+',4X,'TRAP1 von',3x,'TRA22 VOL')
roannm(' ',sx,'aa RATE',4X,'TOTAL VB',3X,'EAG von',9x,'sv1',9x,'sv
+2',10x,'sva')

roannr('o',6312.4.//)

no 130 1-1,4

warra(6,110)1

WRITE (6,120) (0(I,J).J-1,9)

warrr (6,120) (A(I,J),J-1,9)

warts (6,120) (P(I,J),J-1,9)

warms (6,125) EL(I),ER(I)
roxnar('o',/,' DATA or SAMPLE xo',12,/)
ronnnr(' ',9F10.0)

ronnnr(' ',2212.2)

CONTINUE

------ SET RESPONSE PACTORS,MOLECULAR WEIGHTS AND CARBON NO-------

DO 140 I-l.9
PP(I)'1.0
CA(I)'1.0
MA(I)'1.0
CP(I)'1.0
CO(I)=1.0
PA(I)-1.0
MP(I)'1.0
PO(I)'1.0
MO(I)'1.0
CONTINUE
CA(1)-2.
CA(2)'2.
CA(3)'3.
CA(4)'3.
CA(5)'4.
CA(6)'4.
CA(7)-4.
CA(8)'5.
CP(1)=S.
CP(2)'6.
CP(3)'6.

163

CP(4)-7.
cp<s>=a.
cp(6)-9.
cp(7)=2.
cp(a)-4.
cp(9)-1.
can-4.
GEL-2.
ra<1>=1.02
FA(2)-.97
ra<3>-1.
ra<4>-.9a
FA(5)-l.09
FA(6)-1.00
FA(7)'1.09
nn(a)-1.04
FEL-.46
FER-.60
rp(1)-1.04
rp(2)-.99
rp<3>-1.03
ar(4)=1.oo
pp<5)-1.03
FP(6)-1.00
92(7)-.so
FP(8)-1.00
32(9)-o.97
MA(l)-28.05
MA(2)-30.07
xA(3)-42.oa
MA(4)-44.09
MA(5)-sa.12
MA<6>=56.10
MA(7)-58.12
MA(8)-70.l3
MEL=46.07
Man-74.13
xp(1>-72.5
up(2)-a4.13
MP(3)-86.l7
MP(4)-100.2
MP(5)-114.22
MP(6)-128.0
MP(7)=44.05
MP(6)-54.os
up(9)-16.o:
R-82.057
T2298.0

*--- CALIBRATE PEAK AREA AND NORMALIZE THE WEIGHT DISTRIBUTIONS-'-

170

700

190

200

220

231

C
C
C

240

164

W'0.0

DO 170 131,4

CALL XB(P,O,A,EL,ER,PP,PO,PA,PEL,PER,TOT,I,W)
SP(I)=TOT

CONTINUE

 

—CALCULATE NORMALIZED MOLE DISTRIBUTIONS

 

WRITE(6,700)TVB

PORMAT('1',//,SX,'SAMLING BAG VOL I',P10.2,//)
DO 200 131,4

DO 190 J81,9

AM(I.J)-A(Io3)

PM(I;J)'P(I.J)

OM(I,J)'O(I,J)

CONTINUE

ERM(I)'ER(I)

ELM(I)-EL(I)

CONTINUE

TOT-0.0

Wi0.0

DO 220 131,4

CALL KB(AM,PM,OM,ERM,ELM,MA,MP,MO,MER,MEL,TOT,I,W)
CONTINUE

------ -CALCULATE GAS WEIGHT DISTRIBUTION IN BAG AND TRAPS--------

Gwr-sz-Lwr

rwr1-vr1/sv1*sp(1)

TWTZ-VT2/5V2*5P(2)

awI-Tva/sva*sp(3)

Iwrsrwri+rwrz+awr

TWTlITWTl/TWT*GWT

TWTZsTWTZ/TWT'GWT

awI-awr/Twr*cwr

WRITE(6,231)BWT,TWT1,TWT2

FORMAT(' './/.' GAS WEIGHT IN BAG-',F8.4,/,' GAS WEIGHT IN ICE TRA

+PI',P8.4,/,' GAS WEIGHT IN I-PROPANOL+DRY ICE TRAP-',P8.4,/)

 

 

CALCULATE THE TOTAL WEIGHT OF EACH SPEICIES

no 240 J-l,9

TA(J)- A(1,J)*TWT1 + A(2,J)*TWT2 + A(3,J)*BWT
TMA(J)-TA(J) / MA(J)

TP(J)-P(1,J)*TWT1 + P(2,J)*TWT2 + P(3,J)*8WT
TMP(J)-TP(J) / MP(J)

TO(J)- 0(1,J)*TWT1 + O(2,J)*TWT2 + 0(3,J)*EWT
TMD(J)- TO(J) / MO(J)

CONTINUE

f)()()

250

rzrzr:

255

C
C
C

260

()flrl

270

165

TER- ER(1)*TWT1 + ER(2)*TWT2 + ER(3)*EWT
TMER- TER / MER
TEL: EL(1)*TWT1 + EL(2)*TWT2 + EL(3)*BWT
TMEL- TEL / MEL

 

CALCULATE THE NUMBER or CAREONS IN GAS SAMPLES ---------

TC80.O

DO 250 J'1,9

TC-TMA(J)*CA(J) + TMP(J)'CP(J) + TMO(J)*CO(J) * TC
CONTINUE

TC‘TMER'CER + TMEL*CEL + TC

-------CALCULATE THE NUMBER OF CARBONS IN THE LIQUID PRODUCT ------

TC58( SWT / MEL ) * 2.0

TCL. TCS - TC

WRITE(6,255)TCS,TC,TCL

PORMAT('0',/,' C IN FEED-',P10.7,/,' C IN GASI',P10.7,/,' C IN LIQ

+-',F10.7,//)

----CALCULATE THE CARBONS OP EACH SPECIES IN THE LIQUID PRODUCT--

184

Wil.

TOT'O.

CALL KB(AM,PM,OM,ERM,ELM,CA,CP,CO,CER,CEL,TOT,I,W)
1'4

DO 260 J'1,9
AM(I,J)¢AM(I,J)*TCL
PM(I,J)'PM(I,J)*TCL
0M(I.J)-OM(IpJ)*TCL
CONTINUE
ERM(I)'ERM(I) * TCL
ELM(I)'ELM(I) * TCL

--CALCULATE THE NUMBER OF MOLES OP EACH SPECIES IN LIQUID PRODUCT-

DO 270 6-1,9
AM(I.J)-AM(I.J)/CA(J)
PM<IIJ)'PM(IIJ)/CP(J)
OM(I.J)-OM(I.J)/CO(J)
CONTINUE
ERM(I)=ERM(I)/CER
ELM(I)=ELM(I)/CEL
OER=TMER+ERM(I)
OELsTMEL+ELM(I)
OACsTMP<7>+PM(4,7)

-----CALCULATE THE WEIGHT OP HC SPECIES IN THE LIQUID PRODUCT -----

166

CWL'0.0

DO 280 J31,9

“(II-I). “(1:3) * ”((1)

PM(I.J)'PM(IpJ) * MP(J)

OM(IpJ)' OM(IpJ) * MO(J)

CWL'AM(I,J) + PM(I,J) * OM(I,J) + CWL
280 CONTINUE

ERM(I)' ERM(I) * HER

ELM(I)' ELM(I) * MEL

CWL'I ERM(I) + ELMCI) + CWL

 

C CALCULATE WEIGHT AND MOLES OP WATER PRODUCED
WWT' LWT - CWL
WM- WWT / 18.016

 

 

GOO

CALCULATE OVERALL WEIGHT AND MOLE DISTRIBUTIONS ---------

Two-0.0
TMMO-0.0
no 550 J-1,9
TA(J)-TA(J)+AM(4.J)
TMA(J)-TA(J)/MA(J)
TP(J)-TP(J)+PM(4,J)
TMP(J)-TP(J)/MP(J)
TO<J>=TO<J>+OM(4.J)
TMO(J)-TO(J)/MO(J)
Two-TA(J)+TP(J)+TO(J)+Two
TMMOsTMA<J>+TMP<J>+TMO<J>+TMMO
sso CONTINUE
TER-TER-I-ERM( 4)
TMER=TER/MER
TEL=TEL+ELM( 4)
TMELaTEL/MEL
TWO=TER+TEL+WWT+TWO
TMMOaTMER+TMEL+WM+TMMO
OIRTWssz-Two
wRITE(6,555)OIRTw

555 FORMAT(' ','WEIGHT DIF-‘,F10.7,/)
WRITE(6,236)

236 FORMAT('0','WT PERCENT OF MCS ',12x,'MOLE PERCENT OF acs‘)
O0 560 3-1,9
TARW(J)-TA(J)/Two*loo.o
TMA(J)=TMA(J)/TMMO*100.0
TPPW(J)-TP(J)/Two*100.o
TMP(J)=TMP(J)/TMMO*100.0
TOPW(J)=TO(J)/TWO*100.0
TMO<J>=TMO(J)/TMMO*100.0
WRITE(6,23S)TAPW(J),TPPW(J),TMA(J),TMP(J)

235 FORMAT('0‘,2F12.7,5X,2F12.7)

560

234

257

500

000000

10

15

167

CONTINUE

TELPW‘TEL/TWO'100.0

TMER-TMER/TMMO*100.0

TERPW=TER/TWO*100.0

TMELITMEL/TMMO'100.0

TWWT‘WWT/TWO*100.0

TWM=WM/TMMO*100.0

WRITE(6,234)

PORMAT('0','WT OP ETHER ETOH',BX,'MOLE OP ETHER ETOH')
WRITE(6,235)TERPW,TELPW,TMER,TMEL .
WRITE(6,257)TWWT,TWM

PORMAT('0','WT OP WATER-',P12.7,5X,'MOLE OP WATER",P12.7)
OS‘ SWT / MEL

DIP=(OS-OER-OEL-OAC-WM)*100.0/OS

WRITE (6,500)DIP

PORMAT('0','PERCENT DIP IN 0 MOLE BALANCE”',P10.7)

STOP

END

THIS SUBROUTINE IS TO MULTIPLY(W'1.) OR DIVIDE(W'0.) FACTORS AND
THEN NORMALIZE A DISTRIBUTION INTERESTED.

SUBROUTINE KB (A,D.C.D,E,MA,MB,MC,MD,ME,TOT,I,W)
REAL 3(4v9).8(4.9).C(4.9).D(4).E(4).MA(9).MB(9).MC(9).ME.MD
IF ( W .20. 1.0) GOTO 6

TOT-0.0 .

DO 5 J-1,9

A(I.J)-A(I.J) / MA(J)

B(I,J)=B(I,J) / MB(J)

C(I.J)=C(I.J) / MC(J)

TOT- A(I,J) + B(I,J) + C(I,J) + TOT
CONTINUE

D(I)” D(I) /MD

E(I)- E(I) /ME

TOT- TOT + D(I) + E(I)

GOTO 15

CONTINUE

TOT-0.0

Do 10'J-1,9

A(I.J)- A(I.J) * MA(J)

D(I.3)- E(I.J) * MB(J)

C(I.J)= C(I.J) * MC(J)

TOT- A(I,J) + B(I,J) + C(I,J) + TOT
CONTINUE

D(I)- D(I) * MD

E(I)- E(I) * ME

TOT! TOT + D(I) + E(I)

CONTINUE

168

D0 20 J'l,9

3(I0J)' A(IoJ) / TOT

B(I,J)' E(IIJ) / TOT

C(I,J)- C(IpJ) / TOT
20 CONTINUE

D(I). D(I) / TOT

E(I)‘ E(I) / TOT

RETURN

END

 

INPUT DATA

 

300.10.43,146.33.6568,1518,4.7104,2.0715,106,257,0.5,0.5,0.5
OO'OO'OO'OO’O.'OO'OO'OO'OO
29104000,197210.7094100,1584500,3870400,4598100,2967400,3361600,0.
4126000,1594550,3085135,1977110,554067,253760,35480,1265200,12683.
0.,0.

o.'00'00'00'00'00'00'00'00
12695000,122240,30470000,5714700,52367000,75029000,45276000,34070000,0.
30185000,4705280,5489350,1079960,158022,0.,167100,19718000,4628.
00,00

o.'OO'OO'OO'OO'OO'OO'OO'O.
64554000,247540,10037000,1616000,3494500,4514700.2481300,1941700,0.
2272300,712960,1342404,908974,181733,0.,23415,1077500,13473.

00,0. .

o.'OO'OO’OO'OO'OO'OO’OO'OO
150270,0.,0.,0.,785613,1927979,998147,1836700,0.
2538700,1096920,2884412,5848640,10896590,13516440,0.,709709,0.
284643,0.

 

COMPUTER OUTPUT

 

RXN TEMP PEER RATE TOTAL Pflflfl LIQ WT TRAPl VOL TRAP2 V

300.0000 10.4300 4.7104 2.0715 106.0000 257.000
HE RATE TOTAL VB BAG VOL 5V1 5V2 SVB
146.3300 6568.0000 1518.0000 .5000 .5000 .500

DATA OP SAMPLE NO 1

0. 0. 0. 0. 0. 0. 0.

29104000. 197210. 7094100. 1584500. 3870400. 4598100. 2967400.

4126000. 1594550. 3085135. 1977110. 554067. 253760.. 35480.
.00 .00

DATA OP SAMPLE NO 2

169

00 o. O. 00 00 0.
12695000. 122240. 30470000. 5714700. 52367000. 75029000.
30185000. 4705280. 5489350. 1079960. 158022. 0.

.00 .00
DATA OP SAMPLE NO 3
o. o. o. o. o. 0.
64554000. 247540. 10037000. 1616000. 3494500. 4514700.
2272300. 712960. 1342404. 908974. 181733. 0.
.00 .00
DATA OP SAMPLE NO 4
o. o. o. o. o. 00
150270. 0. 0. 0. 785613. 1927979.
2538700. 1096920. 2884412. 5848640. 10896590. 13516440.
284643.00 .00
SAMLING BAG VOL 8 6568.00
GAS WEIGHT IN BAG!I 2.3161
GAS WEIGHT IN ICE TRAP- .0257
GAS WEIGHT IN I-PROPANOL+DR! ICE TRAPa .2971
C IN PEED- .2044888
C IN GAS= .1871932
C IN LIQ. .0172956
WEIGHT DIP- .0000000
WT PERCENT OP HCS MOLE PERCENT OP HCS
33.7890019 2.0773683 31.5370822 .7501610
.1384831 .6252955 .1205708 .1945868
5.9638169 1.1620594 3.7104586 .3530622
1.0006055 1.2307546 .5941578 .3215754
2.7919137 1.3917757 1.2576373 .3190113
4.1913456 1.6519645 1.9560035 .3378857
2.1861629 .0320973 .9847726 .0190766
1.8984651 1.0694722 .7087251 .5180275
.0000000 .0075114 .0000000 .0122601
WT OP ETHER ETOH MOLE OP ETHER ETOH
.0000000 .0755292 .0000000 .0429216

0.
45276000.
167100.

0.
2481300.
23415.

0.
998147.
0.

170

WT OP WATER- 38.7163771 MOLE OP WATER8 56.2620240
PERCENT DIP IN 0 MOLE BALANCES .8864892

APPENDIX B
Calculation of Possible

Transport Limitation

APPENDIX B

Calculation of Possible Transport Limitations

8.1 Intraparticle Mass Transfer

The effects of possible intraparticle mass transfer
limitations is evaluated according to the method outlined in
Section 3.4 Of Satterfield (l970)[68]. The reaction rate is

assumed to be first order.

The modified Thiele modulus, (p, , fOr flat plate

geometry is:
2

 

5 0"; V6 dt 65 (3‘1)

The quantity in parentheses is the observed rate of
reaction per unit volume of catalyst pellets. At 150°C for
16.8% conversion, the rate of reaction of ethanol is 8.72x10+
gmole/sec. The volume of the catalyst pellects (Vc) is
about 0.25 cm3 . Thus, the described rate is 3.488x10¢5

gmole/cm’of catalyst sec.
The half thickness of the catalyst pellets, L, is

0.0075 cm. Thus,
2 '5 1
L a 5.625x10 cm

171

172

The concentration of ethanol at the catalyst surface,
CS, is the bulk concentration of ethanol if the external

resistance is negligible.

Cs , _Efl_ _ (0.33;?!)(l-JJI)

-4 3
_ = . 77/ x/o m/e 6"
RT ( azagxaza) 7 i /

The effective diffusivity.. Dgff .. is a combination of
molecular and Knudsen diffusion coefficients. Since the
Knudsen diffusion coefficient, D; is much smaller than the
molecular diffusion coeficient, D47: is approximately equal
to D‘ which is calculated according to the method in Section

1.7 of Satterfield (l970)[68]. Thus,

5Q

-7 -2 3/
DefF - 0* .-.-.- 7710(2mxxo ) (27;,— .-. /./7é x/o an sec

-7
where 4.0x10 is an estimate of the catalyst pore radius in
cm. According to a article by Heering [78],the tortuosity
factor and the void fraction for the catalyst used in this

research are 2.5 and 0.4, respectively. Thus,

.1 _3 2
D , - (/./7éX/a )(I.4) = fly"? x /& ém/sx
‘ff 2.:

Substituting all values into Equation (8.1), the

modified Thiele modulus is Obtained:

173

-J’ ‘5
(dilzsx/o )(§.4//x/J )

-‘ = 0./5
(Alldx/o") (177/x” )

*Ps -

- Using Figures 3.4-3.7 in Satterfield (1970), Ps-0.13
gives an effectiveness factor I of virtually unity, and
intraparticle mass transfer effects may be neglected if the

first order reaction assumption is acceptable.

8.2 External Mass Transfer

The external mass transfer effect is less signigicant
than the intraparticle transfer effect. According to
Carberry [69], the criterion for the absence Of interphase
concentration gradient in an isothermal first order reaction
system, with effectiveness factor greater than 0.95, is :

nk

W

The first-order rate constant per unit particle volume,

K, can be estimated as follows:

'5. —/ -/
k - (-—‘— 4’95— )/ =3,#J’/XM /7,€7///fl = 4.4355- 5“
Vt, di’ 6,

The catalyst pellet size is 9-10 mesh(about 0.2cm) with
thickness 0.015cm. Thus, the external surface to the volume
ratio, A, is:

3 —/
A = -20!“ 4 40.2)(aa/f) = AL} a”

(49.2 1 (0.2) (AI/S")

174

The mass transfer coefficient,km, is function of the
particle geometry, fluid flow rate and temperature. With
the reaction condition used, the smallest value of km at 150

°C is approximately 0.5 cm/sec. Thus,

 

fl— : <l)<d'3‘$)__‘ = 4’57 < 0./
kin/'1 (1.5) (M's)

The absence Of the external resistance can be true
under the reaction condition used in the kinetics

experiments.

APJEIDIX C
Summary of Data From

{inetics Experiments

APPENDIX C

Summary of Data from Kinetics Experiments

Table C.l-C.5 list the product distribution data at
150,200,250,300 and 360 °C with different residence times.
Since the definition of the mole fraction (yi) used in
Equation(5-30) is different from what is used here, the data
are further processed and rearranged according to the new
definition and the lump scheme mentioned in Section 4.2.1.

The processed data are listed in Tables 4.1-4.5.

175

176

TABLE C.1

Data for Kinetics Experiments at 150°C

Run-l Run-2 Runé3 Run-4 Run-5

Penman/n7) 10 . 91 6. 00 1.86 .889 . 37
Fullym) 150.57 84.20 25.85 11.96 5.22
LHSV 13.64 7.50 2.32 1.11 .46
T(seC) .12 .22 .71 1.51 4.35

Mole Percentage

Methane .00 .00 .00 .00 .00
Ethene .43 .38 13.88 31.15 45.38
Ethane .00 .00 .00 .09 .19
Propene .01 .00 .01 .03 .06
Propane .00 .00 .00 .00 .01
I-butane .05 .01 .03 .00 .00
Butenes .01 .00 .01 .03 .04
N;butane .01 .00 .02 .50 .ll
C3+iCr .00 .00 .00 .00 .00
iC;+C, .00 .00 .00 .00 .00
Hexenes .00 .00 .01 .01 .03
Hexanes .00 .00 .00 .01 .02
C.HCs .00 .00 .00 .00 .01
CoHCs .00 .00 .00 .01 .02
C7-rHCs .00 .00 .00 .00 .01
CH.CHO .00 .00 .02 .08 .16
Unknown .00 .00 .01 .03 .06
Ethanol 82.77 72.73 31.54 12.14 2.97
Ether 8.06 13.23 20.22 12.41 2.29
Water 8.66 13.64 34.26 43.98 48.65

F E: emu/h)
PM. (Ml/min ’
LHSV
1(sec)

Methane
Ethene
Ethane
Propene
Propane
I-butane
Butenes
N;butane
Cr+1Cc
1C;+C:
Hexenes
Rexanes
C7HCS
C,HCs
C§HCs
CHsCHO
Unknown
Ethanol
Ether
Water

177

TABLE

C.2

Data for Kinetics Experiments at 200°C

Run-l

79.12
1118.2
98.90
.02

.00
2.35
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.01
.00
76.15
9.56
11.92

Run-2

44.31
589.2
55.39
.03

Run-3

28.94
403.3
36.21
.05

Run-4

10.91
151.3
13.64
.13

Mole Percentage

.00
4.98
.01
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.01
.00
64.42
12.80
17.79

.00
9.84
.01
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.01
.00
54.86
12.71
22.57

.00
27.74
.03
.01
.00
.00
.00
.01
.00
.00
.00
.00
.00
.00
.00
.01
.01
27.15
8.59
36.44

Run-5

6.00
84.1
7.52
.25

Run-6

1.86
25.7
2.32
.78

.00
46.33
.08
.32
.05
.03
.09
.15
.04
.03
.02
.01
.01
.03
.04
.13
.07
4.07
.15
48.36

F EEOWnl/M)

FHQ (“y-fin)

LHSV
T(sec)

Methane
Ethene
Ethane
Propene
Propane

I-butane

Butenes

N-butane

C;:1Cy
iC;+C:
Hexenes
Hexanes
CrHCS
CgHCS
CiHCs
CHQCHO
Unknown
Ethanol
Ether
Water

178

TABLE C.3

Data for Kinetics Experiments at 250°C

Run-l

44.31
630.6
55.39
.03

.00
34.23
.02
.06
.01
.01
.01
.03
.01
.00
.01
.00
.00
.00
.00
.04
.02
25. 75
2. 61
37.19

Run-2

28.94
402.0
36.10
.05

Mole

.00
39.39
.02
.13
.01
.03
.03
.06
.03
.01
.03
.01
.01
.01
.03
.06
.03
16.94
1.41
41.76

Run-3 Run-4
10.91 6.00
150.5 83.44
13.64 7.50
.12 .22
Percentage
.00 .00
44.11 36.78
.07 .13
1.24 2.08
.11 .34
.24 .62
.68 1.49
.27 .70
.18 .50
.21 .63
.06 .20
.10 .34
.07 .52
.08 .34
.10 .14
.06 .03
.16 .27
.91 .36
.02 .00
51.31 54.53

Run-5

1.86
25.62
2.32
.71

.02
19. 46

2.49
1.42
2.79
2.34
1.41
1.52
1.17
.48

.63

.98
1. 41
.00
.57
.04

.00
62.09

Run-6

.93
12.86
1.16
1.42

.05
13. 37
.58
3.11
3.23
4.46
1.94
1. 60
1.53
.80
.40
.46

1.18
2.04
.00
.40
.02
.00
63.97

Run-7

.37
5.21

3. 51

.13
5.60
.76
2. 29
6.18
8.63
1.62
2.65
2.73
.80
.44
.39
.59
.69
1/25
.00
.31
.01
.00
64.92

179

TABLE C.4

Data for Kinetics Experiments at 300°C

Run-1 Run-2 Run-3 Run-4 Run-5
Penman/u) 10.91 6.00 1.86 .89 .37
Fm(n.¢/.,-‘) 146.3 83.0 25.8 12.4 5.3
LHSV 13.04 7.51 2.32 1.11 .46
7(sec) .11 .20 .65 1.34 3.20

Mole Percentage

Methane .01 .03 .10 .20 .88
Ethene 31.54 20.99 7.82 3.312 3.21
Ethane .12 .20 .42 .54 1.07
Propene 3.71 4.46 3.50 2.49 2.18
Propane .59 1.31 3.78 5.37 8.58
I-butane 1.26 3.30 7.19 8.44 7.16
Butenes 1.96 2.30 1.50 .87 .46
N-butane .98 1.63 2.39 2.58 2.28
C;+ic: O71 1017 1086 2037 2.56
iC§+C¢ .75 1.00 .97 .74 .73
Hexenes .19 .28 .30 .28 .28
Hexanes .35 .53 .63 .66 .62
CrHCS .32 .67 1.31 1.66 1.52
C.HCs .32 .69 1.47 1.85 1.58
CfHCs .34 .57 1.10 1.28 1.09
CH.CHO .02 .01 .00 .00 .00
Unknown .52 .68 .49 .29 .17
Ethanol .04 .01 .00 .00 .00
Ether .00 .00 .00 .00 .00
Water 56.26 60.18 65.27 67.07 65.64

180

TABLE C.5

Data for Kinetics Experiments at 360°C

Run-1 Run-2 Run-3 Run-4 Run-5
Fuomru/nr) 10.91 6.00 1.86 .89 .37
me/w 141.9 84.9 25.8 12.4 5.2
LHSV 13.03 7.50 2.32 1.11 .46
T(sec) .11 .18 .58 1.22 2.91

Mole Percentage

Methane .07 .14 1.06 2.48 7.86
Ethene 23.90 16.77 9.24 5.59 5.03
Ethane 20 .28 .70 .84 1.53
Propene 6.46 6.24 5.41 4.00 3.41
PrOpane 1.25 1.99 4.48 4.62 5.45
I-butane 1.99 3.07 4.44 4.95 4.14
Butenes 2.27 2.36 1.53 1.35 1.34
N-butane 1.52 1.89 2.10 2.29 1.95
C}+ng .73 .96 1.01 1.27 1.09
1C;+Cy .90 .99 .67 .74 .56
Hexenes .13 .16 .11 .12 .08
Hexanes .39 .56 .64 .86 .71
C7HCs .42 .98 1.71 2.17 1.92
CnHCs .51 1.06 1.79 2.19 1.95
CrHCs .24 .44 .79 .93 .93
CH,CHO .01 .01 .00 .00 .00
Unknown .74 .83 .57 .57 .39
Ethanol .00 .00 .00 .00 .00
Ether .00 .00 .00 .00 .00
Water 58.25 61.27 63.75 65.03 61.65

APPENDIX D
Sample Calculation

for Data Fitting

APPENDIX D

Sample Calculation for Data Fitting

A quasilinearization method was employed with the eight
ordinary differential equations, mentioned in Section 4.2.3,
to determine the best set Of the eight parameters, including
seven surface reaction constants and one adsorption
constant, to fit the experimental data. This is a more
favored approach than the method of steepest descent since
it converges rapidly. The algorithm is basically following
the one outlined in Section 7.6.2 of Seinfeld and Lapidus

(1974)[72].

Consider again the O.D.E. model

all;
att

 

= f2 ($224.),- cho) = 1,, , c'-/,.2,.-.,2(O-1)

where gran 8 dimensional concentration vector
[scan 8 dimensional parameter vector

Define the following l6-dimensional vectors:

.4 f.
2" 3 5 i=[g] (O-2)

Since k is constant,
441
.d.t

a 0 (O-3)

 

181

182

Adjoin (D-3)to (D-1) and use (D-Z), we have

=Z(t:£) (D-4a)
2“ (O) = x60 ; C. = // 2; °“I g
(D-4b)
Z; (a) -'-' ‘? = 7, /a, ---,/6

The problem is to find Zi(0), i-9,10,..,16, to minimize

the following least squares criterion

R T
5=Z [ L10 4.; (tr; zwm] Eur-Warsaw») (0-5)
rs: -

where g (t:§(0)) is the solution to the O.D.E. model
corresponding to a particular set of Zi(0),i-9,..,16;
y is an 8 dimensional vector of observed concentrations
h is an 8 dimensional vector of predicted concentrations
2 is weighting matrix.
First, make an initial guess of the unknown
parameters, ki-Zn+i(0),i-1,2,...,8. Then integrate (D-4a)
numerically from t-O to t-tr. This solution corresponding
)
to the first guess of k, may be indicated by Z?(t). Next,
linearize (D-4a) to a first order about the nominal trajectory

(a!
Z (t). Thus,

 

:z.‘ -:«:[z ’ ]+[ 3% II]

’

 

97 .
where [ 7; J (0) =5- '4 " ’6 matrix whose elements are i)
‘- Z ‘22:
. - I
evaluated at z = Z (a)

Notice that (D-6) is simply a set of 16-coupled linear

183

O.D.E.s where a closed form solution is readily available.
The analytical solution is the sum of a particular solution
and 16 homogeneous solutions.

Let P_m(t) a particular solution of (D-6)

Hence, the general solution tO (D-6) can be written as

c )
2010‘): fl()(f)§u + P(I)<t) (D-7)

()
where the 16x16 matrix §'(t) is the solution of the

matrix homogeneous equation,

‘21: (U

. (U M
25 J2“) = (t) (D-8)

g (t):[

I
and 3"(t) is the soultion of

. (I)

p"’ut) = flg‘”, t] + [ 325—12w” m - fin] (ID-10)

I) .
The 16 dimensional vector 5; is simply a set of arbitrary
coefficients for the 16 homogeneous solutions of (D-61
The key step is the assignment Of boundary conditions
to (D-lO). These are arbitrarily set as follows:
1;. , i= /,2,---,é’
F.(o) = (9‘11)
4
0 ) O = 71/01-.-’ /é
This choice makes-<i - 0, i=1,2,..,8. Hence, the solution

given by (D-7) can be written as

184

a) (n I‘
Z (I) = P (t) + Z .4- Mia‘) (O-12)
._ ._ 3:,
where the 16-dimensiona1 vector 735 (t) satisfy
. 9}
,2". = [ 7; J2“, 216" (t) ’ 6. =7’ /0,‘°', /é (ID-13)

 

subject to the initial conditions

~= 2 ‘= , K (D-14)
7%; ‘3 (Sgi ) ‘ 75/5' '/ . J, "2 /

Now, use the final piece of information, namely,
)
minimize s by choice of 8 values ofggu:
— = O 6: 7’ /p’ --',/é (D'IS)
adall) I
This equation is just a set of 8-coupled linear algebraic

(I)
equations for the0<i .

The set ofg has special meaning at this point. If we
evaluate (D-12) at t . 0, we have

/1
(o) =- Pm(0) 4' Z “’6' 7’16 (a)
._ .. i=7

(I)

01'

z‘; (a) = 2" + d, 2”; (0) + “/0 %/"‘(a) + "' + 4‘ ”/‘l‘. (0)

f : /,J, n“, 6’

Z. (a) = #7 71!”!- (a) + 04’” 216" - (o) + --- + a“ 71!,

a ‘4' (.2

d. = 7, /0/ ".1 /é

However,from (D-14)

185

(I)

21 (a)

6

36.0 6' - // .2, "'1 i

I

(I)

2d. (a) = 0?. I Jg7l/p’--',/g

) . .0)
Therefore 5,” represent the new estimates of _k_. Once the <1

are Obtained, these values are used as the next guess of the
initial cdnditions Zi(0), i-9,10,..,16, and the procedure is

repeated.

Summarizing, the algorithem is used as follows:
1. Select a first guess Zi(0), i-9,10,..,16, and integrate
(D-4a), (D-lO) and (D-13) simultaneously with initial
conditions (D-4b), (D-ll) and (D-14).

2. Solve the algebraic equations resulting from (D-15) to

determine K‘ , «an... 4,2”. Replace Zi(O) by Ki‘fi’i-9,...,16.
3. Return tO step 1 with the new set of 5(0).
u:

(6») [I
4. Continue untill the sum of [-<i --<i J/[Ki’ ],i-9,..,16, is
less than some preset criterion.

This algorithm, if it converges, will dO so rapidly.
As with most iterative estimation technique, convergence
depends on a reasonable starting guess which is usually
difficult to get.

A Fortran program was uSed according to the algorithm
described above, as is shown in the following pages. The
program employed IMSL subroutines DGEAR for the integration
part and LEQTlF for solving the lineal algebraic equations.
An example for 150°C data fitting using model I is also

giving in the succeeding pages.

000000000000000000000000000000000000000

186

THIS PROGRAM IS TO FIND RATE CONSTANTS OF ETHANOL DEHYDRATION RXN
QUSILINEARIZATION METHOD HAS BEEN APPLIED TO FIND PARAMETERS OF
NONLINEAR RATE EXPRESSION IN INTEGRATION MODE. THE INTEGRATION IS
DONE BY IMSL SUBROUTINE DGEAR IN MSU. THE SOLUTION OP THE LINEAR
ALGEBRAIC EQUATIONS IS DONE BY IMSL SUBROUTINE LEQTlF.

METH,MITER,INDEX,IWK(I),WK(I),IER,TOL,XEND,X,H,N AND Y(I) ARE INPUT
OF SUBROUTINE DGEAR.

T'INDEPENDENT VARIABLE ; RESIDENCE TIME

YI-INITIAL VALUES OP DEPENDENT VARIABLES;VECTOR OP CONCENTRATIONS
AND RATE CONSTANTS

QIWEIGHTS

28EXPERIMENTAL DATA

P3PARTICULAR SOLUTION OP LINEARIZED DIFFERENTIAL EQNS
CM=HOMOGENEOUS SOLUTION OP LINEARIZED D.E.
O'PREDICTED VALUES OF DEPENDENT VARIABLES BY INITIAL GUESSES.
A,B,WKAREA(I) ARE INPUT OP LEQTlF TO SOLVE AX=B
NXSNO. OF VARIABLES:CONCENTRATIONS'IX

NDINO. OF RESIDENCE TIME

NKBNO. OF PARAMETER53RATE CONSTANTSSIK

NZ‘LENGTH OP VECTOR YIINX+NKSIZ

N'TOTAL NO OF FIRST ORDER D.E. TO BE SOLVED BY DGEAR

YtDEPENDENT VARIABLES TO BE SOLVED BY DGEAR,VECTOR OF LENGTH N

 

PROGRAM MODEL

INTEGER N,METH,MITER,INDEX,IWK(88),IER

REAL Y(88),WK(968).X,TOL,XEND,H

REAL T(8).YI(16).0(8).Z(8.7).P(8.7).CM(8.8.7).0<8.7)
REAL 6(9,9),A(9,9),waREA(269)

ExTERNAL FCN,FCNJ

OPEN(5,FILE='DATA8')

OREN(6,EILE-'0UTPUT')

 

 

SET NX,ND AND NR
N338
ND'7

15

999

25

10

187

NK=8
NZINX+NK

DO 55 I=1,8
T(I)=0.0
Q(I)=0.0

DO 55 J=1,7
Z(I,J)'0.0
P(I,J)=0.0
O(I,J)=0.0
DO 55 K=1,NK
CM(K,I,J)=0.0
CONTINUE

 

 

READ DATA YI,Q,T AND 2
READ(5'*) (YI(I)11319NZ)

READ(5,*)(Q(I),I=1,NX)

READ(5,*)(T(K),K81,ND)

DO 15 IIl,NX

READ(5,*)(Z(I,K),K81,ND)

CONTINUE

NIT81

CONTINUE

N'NX*2+NK*(NX+1)

 

 

SET INITIAL VARIABLES OF Y
DO 25 I'LNZ
Y(I)=YI(I)
CONTINUE

DO 10 1‘1,NX
J'NZ+I

Y(J)=Y(I)
CONTINUE

OO 20 I'NZ+NX*1,N
Y(I)’0.0

CONTINUE

 

SET INPUT VALUES OF DGEAR AND CALL DGEAR -----
X80.0

TOL8.000001

H-.000001

METH'Z

MITER83

INDEX=1

DO 30 K81,ND

XEND=T(K)

CALL DGEAR(N,FCN,PCNJ,X,H,Y,XEND,TOL,METH,MITER,INDEX,IWK,WK,IER)
IF(IER.GT.128)GO TO 40

 

 

STORE Y INTO 0,? AND CM
DO 50 J31,NK

LL'NZ+NX+(J-1)'NX

DO 50 131,NX

O(I,K)=Y(I)

P(IIK)=Y(I+NZ)

50
30

60

70

90

100

888

188

M8LL+I
04(J,I.K)=Y(M)
CONTINUE
CONTINUE

 

 

SET UP MATRIX A AND B
JBSNK+1

D0 60 181,JB

DO 60 J81,JB

A(I,J)'0.0

B(I,J)'0.0

CONTINUE

DO 70 I31,NK

B(I,I)'1.0

CONTINUE

DO 80 MI1,NK

DO 80 J'1,NK

DO 80 K81,ND

DO 80 I-1,NX
IF(I.EQ.2.0R.K.EQ.0.0R.X.EQ.0.0R.X.EQ.O)GO TO 80
IF(J.EQ.1)THEN
3(MIJB).B(MIJB)+Q(I)*CM(M0IIK)*(Z(IIK)-P(I'K))
END IF

A(M,J)8A(M,J)+Q(I)*CM(M,I,X)*CM(J,I,K)

CONTINUE

 

—CALL LEQTIF TO SOLVE AXSB

 

N-NK

M-JB

IA=JB

IDGT'1

CALL LEQT1F(A,M,N,IA,B,IDGT,WKAREA,IER)

 

 

ITERATION CRITERIA
SUM'0.0

DO 90 I31,NK

J81+NX

Y(J)=B(I,JB)
SUM‘SUM+ABS((Y(J)-YI(J))/YI(J))
YI(J)=Y(J)

CONTINUE
IF(SUM.LE.0.01.0R.NIT.EQ.5)THEN
WRITE(6,*)(Y(J),J8NX+1,NZ)
WRITE(6,100)((0(I,K),KI1,ND),I=1,NX)
FORMAT(1X,7F9.7)

GO TO 888

ELSE

WRITE(6,*)(Y(J),J=NX+1,NZ)
WRITE(6,100)((O(I,K),X81,ND),I=1,NX)
NIT=NIT+1

GO TO 999

END IF

STOP

40

00000000000000000000000

0000

189

CONTINUE
WRITE(6,*)IER,INDEX,X,XEND
STOP

END

 

 

SUBROUTINE FCN
YPRIME‘DERIVATIVE OF Y

PY'PARTIAL PRESSURE

RN-NUMERATOR OF RATE EXPRESSION
RIDERIVATIVE OF RN W.R.T. PY

GP'JOCOBIAN

RP'DERIVATIVE OF RN W.R.T. Y

TEM'TEMPERATURE

‘IR-NO. OP RXN

IX'NX'NO. OP VARIABLES;CONCENTRATIONS

IXINK‘NO. OP RATE CONSTANTS

 

SUBROUTINE PCN(N,X,Y,YPRIME)

INTEGER N

REAL Y(N).YPRIME(N).X

REAL PY(8).RN(7),R(7,16),GP(8,16),RP(7,8)

 

 

BEGIN TO FIT IN MODEL

 

 

SET TEM,IR,IX AND IN
TEM-523.

IR-7

1X88

IK=8

IZSIX+IK

IN'IX*2+IX'(IX+1)
SPD'.66667+Y(1)+Y(2)+Y(3)+Y(4)+Y(5)+Y(6)+Y(7)+Y(8)
DO 8 I-1,IX

PY(I)=Y(I)

Y(I)'Y(I)/SPD

CONTINUE

‘SD31.+Y(1)*Y(16)

DD-1./(SD**1.)
TO3-1o/(SD**2.)

 

 

CACULATE RN

0N

190

RN(1)=Y(9)*Y(1)/SD
RN(2)'Y(10)*Y(1)**2./SD
RN(3)=Y(11)*Y(3)/SD
RN(4)=Y(12)*Y(4)
RN(5)=Y(13)*Y(5)
RN(6)'Y(14)*Y(4)
RN(7)=Y(15)*Y(5)

 

CACULATE YPRIME OF CONCENTRATIONS ----------
YPRIME(1)=(-RN(1)'2.*RN(2)+RN(3))‘DD

YPRIME(2)=(RN(1)+RN(2))*DD

YPRIME(3)'(RN(2)-RN(3))*DD
YPRIME(4)=(RN(1)+RN(3)-2.*RN(4)-RN(6))‘DD
YPRIME(5)'(RN(4)-RN(5)*2.-RN(7))*DD

YPRIME(6)8RN(S)*DD

YPRIME(7)'RN(7)*DD

YPRIME(8)=RN(6)*DD

 

 

YPRIME OF RATE CONSTANTS'G
DO 2 I'IX+1,IZ

YPRIME(I)'0.0

CONTINUE

 

 

CACULATE R'RP AND G?
DO 3 I31,IR

DO 3 331,12

E(IIJ).OOO

CONTINUE

DO 4 131,7
R(Iol)'Y(16)*RN(I)*TD
R(I'16).Y(l)*RN(I)*TD
IF(I.LE.3)THEN

R(I,1)32.*R(I,1)
R(1916)'2.*R(I:16)

END IF

CONTINUE
E(l,1)‘R(1,1)+Y(9)*DD**2.
R(l,9)'R(1,9)+Y(l)*DD**2.
R(2,1)‘R(2,1)+2.*Y(1)*Y(10)*DD**2.
R(2,10)'R(2,10)+Y(1)**2.*DD**2.
R(3o3)‘R(3,3)+Y(11)*DD**2.
R(3,11)‘R(3,11)+Y(3)*DD**2.
R(4p‘)'R(4p4)+Y(12)*DD
R(4,12)'R(4,12)+Y(4)*DD
R(5,5)‘R(5.5)+Y(13)*DD
R(5,13)'R(5,13)+Y(5)'DD
3(694)'R(5p4)*Y(l4)*DD
R(6,14)3R(5,14)+Y(4)*DD
'R(7,5)=R(7,5)+Y(15)*DD
R(7,15)3R(7,15)*Y(5)*DD

DO 13 I31,IR

DO 13 3'1,IX

RP(I,J)=0.0

13

14

16

191

CONTINUE

DO 14 131,1R

DO 14 J31,IX

DO 14 M31,IX

IF(M.EQ.J)THEN
RP(I,J)=RP(I,J)+R(I,M)*(5PD-PY(M))/SPD**2.
ELSE
RP(I,J)3RP(I,J)-R(I,M)*PY(M)/SPD**2.
END IF

CONTINUE

DO 16 131,1R

DO 15 J'l,IX

R<IIJ).RP(IIJ)

CONTINUE

DO 5 131,12
GP(1!I)"R(10I)‘2.'R(201)+R(3II)
GP(2,I)'R(1,I)+R(Z,I)
GP(3,I)'R(2,I)-R(3,I)
GP(4,I)=R(1,I)+R(3.I)-2.*R(4,I)'R(6,I)
GP(5,I)'R(4,I)-R(5,I)'2.-R(7,I)
GP(6'I)'R(501)

GP(711)3R(711)

GP(8,I)'R(6,I)

CONTINUE

 

 

YPRIME OF P AND CM
DO 6 IIIZ+1,IZ+IX

YPRIME(I)'YPRIME(I-IZ)

DO 6 J81,IZ

IP(J.LE.IX)THEN
YPRIME(I)8YPRIME(I)+GP(I-IZ,J)*(Y(J+IZ)-PY(J))
ELSE

YPRIME(I)'YPRIME(I)-GP(I-IZ,J)*Y(J)

END IF

CONTINUE

DO 7 IIl,IX

DO 7 J81,IX

L=IZ+IX*I+J

YPRIME(L)'GP(J,I+IX)

DO 7 MIl,IX
YPRIME(L)'YPRIME(L)+GP(J,M)*Y(L-J+M)

CONTINUE

 

—OTHER OPERATIONS FOR THIS MODEL --------
Do 9 I-I,Ix

Y(I)=PY(I)

CONTINUE

DO 11 1:1,1N

YPRIME(I)=YPRIME(I)*26820.0938*TEM/523.

CONTINUE

 

RETURN

END

192

SUBROUTINE FCNJ(N,X,Y,PD)
INTEGER N
REAL Y(N),PD(N,N),X
RETURN

END

 

INPUT DATA

 

.33333'00'00'00'00'00'00'00,
.00003684,

.0006380.

.00009288,
.000001079,
.00003787,
.0000001933,
.00002618,

4.6932

1,1,1,1,1,1,1,1
.1209,.2173,.7059,1.5086,4.346
.2773074,.2434112,.1222510,.0664453,.O311115
.0289997,.0456346,.1327264,.2040124,.2864664
.0269921,.0442696,.0783309,.0628629,.0157223
.0014451,.0012656,.0537623,.1391636,.2643393
.0000666,.0000160,.0001300,.0004156,.0011328
.0000000,.0000008,.0000061,.0000823,.0003211
.0000324,.0000440,.0001890,.0002512,.0007170
.OOOOOOO,.OOOOOOO,.OOOOO31,.0004328,.0011904

 

COMPUTER OUTPUT

 

NEW SET OF PARAMETERS

.00003682678074741 .0006379933009321 .00009289164091339 .000001079294475
.00003784943126556 1.933631903033E-7 .00002617087049939 4.692968597685
THEORETICAL VALUES

.2765395
.0311732
.0256174
.0055489
.0000031
.0000000
.0000000
.0000006

.2379573
.0531878
.0421849
.0109777
.0000108
.0000003
.0000002
.0000021

.1221811
.1317350
.0794139
.0518753
.0001611
.0000161
.0000112
.0000366

.0717216
.1989179
.0626949
.1332383
.0007926
.0002137
.0001477
.0002450

.0250154
.2996480
.0086727
.2659447
.0026328
.0032886
.0022736
.0020571

APPENDIX E
Sample Calculation for

Diffusion Modelling in CSTR

APPENDI X E

‘Sample Calculation for Diffusion Modelling_in CSTR

An optimal ”Galerkin with quadrature" method was
employed to estimate the solution of the six coupled second
order ordinary differential equations and twelve boundary
conditions, mentioned in Section 4.3.1. The orthogonal
properties of Jacobi polynomial was used to determine the
collocation points following the method outlined in Chapters
2 and 3 of Villadsen and Michelsen (l978)[74].

Consider the second order O.D.E. model

1.,
= . = I "3 4 8-1

with boundary conditions

7%(7fl) =Bi[7ba‘7z‘7")] (8'2).

:—#7-—‘ (If: a): 0 , g°=/,2,“vé (Bi-3)
Let u 8 f1, (E-l),(E-2) and (8-3) can be rewritten as
2 . .
.3112. + 2 4‘51”— : f" (E-4)
u

411. dd

2. :—-—f:—‘ (u=/) = adju-yb-(us/d (E-S)

193

194

a( ' .
_L‘ (“=a) = o I ¢=/,2,---,é (3-6)
A!“
We now consider the trial solutions
A/ .
d" .
31. == / + ("NZ 4." a , z=/,z,--~,é
No . d
4"
Replace yi by yyi in equation (8-4) and denote the residual
as Rui. The Galerkin method given the following N relations
for each equation:

I

I .-
f. IQ”; {/‘u) a] d“ = 0 (33"?)
a ‘= Aua‘",/V
or I <¥
j W(“)§.(u)a(u =0 , J'LZV’WV (El-8)

where W(u) - weight function . l-u;

._ 1"

EM) -- ’Qflé u
Since the nonlinearity Of the O.D.E.s, equation (8-7)
normally has to be evaluated numerically and an explicit
solution in aij can not be obtained. It appears that we
have to choose between the easily applicable but in general
rather inaccurate collocation method and the trustworthy but
cumbersome Galerkin method. A compromise is, however,
possible. The integral in equation (E-B) may be approximated

by a numerical quadrature.

l

M
[WW-(«Mu ~ 2 wJ-W (3-9)
0 J 4:] J

195

For a weight function W(u) - ufi (l-uf‘there exist an
optimal choice of quadrature points in the sense that the
highest power of u in a power series expanflon of F(u) is
correctly integrated when these u-value are used as
quadrature points. The optimal quadrature points are zeros
of a:¢1u) which is a Jacobi polynomial of degree M in u that

satisfies the following relation:
I .
d’ an ) ,
f “pH-K) “’5‘ f (a) d“ =0 , i=0,/,"'/fi‘/ (3-10)
0

The quadrature is exact when E(u) is a polynomial Of
degree 5 ZM-l in u and in general the terms in a power
series expansion of E(u) are correctly integrated up to and
including qu-’. A discussion of the properties of
orthogonal polynomials P:%1u) and the proof of the optimality
of the proposed quadrature are given in chapter 3 of

Villasen and Michelsen.

Choosing M-N, the following N equations are Obtained:

N .
d-/
E W: 54h) = i M. km. a, = o (E-II)
fl" *=/ /=/,2,-“, A/
The N equations can be satisfied when
KN. = 0 M: “I; “Z; -." “M (3-12)
G
('1')
where “1 are zeros of Pp(u).

Notice that the best approximate Galerkin method is now

196

a collocation method, provided we choose as collocation
points the roots of éy?u)-0.

Once the Optimal interior collocation points are
determined, together with the exterior collocation point
usl, Lagrange interpolation polynomial can be used for the

Nth-degree polynomial approximation y~i:

N1"
in = Z lo; £44“) I &'=/,.2,---, 4 (3‘13)
4'"
where y? - y‘.(u¢-), i-l,2,..,6, j-1.2...,N+l.
The N+l polynomial lJ(u) are all of degree N:
~T/ -
L-(u) = 7T —“ ”* (IE-14)
J *3/11. L?’H*

where the notation k-l,j means that the product consists
of all factors (u-ufl/(ui -u,), k-l,2,..,N+l, except k-j.

Equations (E-l) and (3-2) can then be rewritten as

MN AH/
n /
4 “NZ Ie-IJ- (”A) + 2:: 771/09») =15 ([19) (E-Is)
J., J ‘ '3,
.¢=/,2,-~,~ , [swan-,4
M“

Z Z Liz/(mull) = 8‘; [ib13- z (“W/)J (8-16)
dz, is /,Z,-'-. 4

where y(k)-y;(u«), i-1,2,...,6:
1 '(uk) and 1;"(u*) are the first and second
derivatives of l}(u) evaluated at “k“

197

The left hand sides of (8-15) and (8-16) are linear
functions of y , isl,2,..,6, j-l,2,..,N+l. Combine

and rearrange (E-lS) and (316), we have

fgfil‘zz" (E-Iv)
where E ' (in 1,2 ”7,”, ’31 yumizml "’ ’64”! Barn”!
2' (firzmn) film.” ,mlmwy) saw-1mm”
T
( (KN) {I (0(a)) -—-
f1 1 2 Z ) (MN) x /
.5
' s
9 ' o ‘2
§§ éowzhéww)
where? is an N+1 N+l submatrix with elements 3.“ as
allows: I
4064:!) (“13+41jw‘fi) , J. =/,2,"';Nf’
fl =/:ZI--'JN

5,“ , .
2.12““) :,}=/.2,~-.NH
xeN+I
The problem now is to find 2,, ial,2,..,6(N+l), by

solving equation (8-17). Owing to the nonlinearity of the

elements in g, equation (E-l7) have to be linearized as

follows:
-a)+ Quiz“; EU5'0 (E-18)
or
(oi (0)
(0) ’3f (0)
where J a ['7;;_
... 4w+nx£(A/+/)

198

(0) (I)
z I z - 2

Equation (E-19) is simply a set of 6(N+l)-coupled linear

algebraic equations for 2i which can be solved by the IMSL

subroutine LEQTlF,,mentioned in APPENDIX D. To find Zi,

i-l,2,..,6(N+l),to be zero, an iteration procedure need to

be used with some preset criterion. Once the grid values

zd,i-l,2,...,6(N+l), are determined, the solution yi of

equation (E-l) can then be approximated by equation (E-13).

Summarizing, the algorithm is used as follows:

Choose the number of interior collocation points, N.
Determine the Optimal collocation points by finding the
roots of the Jacobi polynomial E$”(u).

Evaluate li'(u*) and lj'(U4), j-1,2,..,N+l, k-l,2,..,N+l.
Select a first guess 2;? i-l,2,...,6(N+l), and evaluate
§“’and g‘”.

Solve the algebraic equations resulting from equation
(E-19) to determine zf7i=l,2,.......,6(N+l). Replace zi
by (23525).

Return to step 3 with the new set of gwi
Continue until the sum of liti-l,2,.....,6(N+l), is less
than some preset criterion.

A Fortran program was written according to the algorithm

described above. This is shown in the following pages. The

program employed the subroutines JACOBI,DFOPR and INTRP

described in chapter 3 of Villasen and Michelsen. The

01’
subroutine JACOBI calculates the zeros of R:(u) and also the

first, second and third derivatives of the node polynomial'

199

Pm,(u) - (U‘U')(U"Uz) ------- (u-uwfl

at the interpolation points. The subroutine DFOPR with data
obtained in JACOBI calculates lj'(u*) or 1;"(uk)'
j-l,2,..,N+l, k-l,2,..,N+l. The subroutine INTRP calculates
the interpolation weight 15(U)' j-l,2,..,N+l, which are then
used with z to evaluate yui, i-l,2,.....,6. An example
calculation using this program is also given in the

following pages.

nnnnnnnnnnnnnnnnnnnnnnnnnnnn

000

11

200

THIS PROGRAM IS TO SIMULATE THE PERFORMANCE OF A CSTR TAKING
DIFFUSION INTO ACCOUNT IN THE ETHANOL CONVERSION PROCESS. AN
OPTIMAL GALERKIN WITH QUADRATURE METHOD IS EMPLOYED TO ESTIMATE
SIX COUPLED SECOND ORDER O.D.E.S WITH TWELVE B.C.S.

 

SLIHALF THICKNESS OF CATALYST PELLET

TEMBTEMPERATURE

DEN=APPARENT DENSITY OF CATALYST

QI,QB=VOLUMETRIC FLOW RATES OF INLET AND OUTLET STRESM
PI,PB=PRESSURES OF INLET AND OUTLET

SA'EXTERNAL SURFACE AREA OF CATALYST PER UNIT VOLUME OF REACTOR
VT'REACTOR VOLUME

YI=INLET CONCENTRATION

BI=EXTERNAL MASS TRANSFER COEFFICIENT AT INPUT;BIOT NO AT OUTPUT
HDtDIFFUSIVITY AT INPUT; DIFFUSIVITY RATIO WRT D1 AT OUTPUT
AF'ARRHENIUS FREQUENCY FACTOR

AE‘ACTIVATION ENERGY {-E/R)

N8NO OF INTERIOR COLLOCATION POINTS

NXSNO OF SPECIES OR NO OF EQUATIONS

NN'NO OF PARAMETERS

NR'NO OF ELEMENTARY RXNS INVOLVED

THI'THIELE MODULUS WRT TO D1

VARIABLES USED IN SUBROUTINES ARE THE SAME AS THOSE USED IN THE
TEXT BY VILLADSEN AND MICHELSEN.

 

PROGRAM CSTR
DIMENSION DIF1(10),DIF2(10),DIF3(10).ROOT(10),V1(10).V2(10),XINTP(

+10),Z(54),AMAT(SS,55),BMAT(SS,55),CMAT(55,55),WKAREA(400)

REAL YI(6).YB(6),BI(6),HD(6),THI(7),F(54),W(6),AF(8),AE(8),HTR(6)
OPEN(5,FILEI'DATA8')

OPEN(6,FILE='DETAIL')

OPEN(7,FILE='ELTA')

OPEN(8,FILE8'MOLE')

OPEN(9,FILE='FLUX')

OPEN(10,FILE8'RATE')

OPEN(11,FILE='SELE')

 

 

READ INPUT DATA

READ(5,*)N,NX,NK,NR

IF(N.EQ.O)GO TO 99

IRUN'O

NKT‘NK+1

READ(5,*)ALFA,BETA
READ(S,*)SL,TEM,DEN,QI,PI,QB,PB,SA,VT
READ(5,*)(YI(I),I=1,NX)
READ(5,*)(BI(I),I=1,NX)

GOO

000

100

12

210
220
225
230
240
250
260
270

17

201

READ(S,*)(HD(I),I=1,NX)
READ(5,*)(AF(I),I=1,NKT)
READ(5,*)(AE(I),I=1,NKT)
WRITE(6,100)N,ALFA,BETA

WRITE(6,210)

WRITE(6,*)NX,NK,NR

WRITE(6,220)
WRITE(6,*)SL,TEM,DEN,QI,PI,QB,PB,SA,VT
WRITE(6,225)

WRITE(6,*)(YI(I),I=1,NX)

WRITE(6,230)

WRITE(6,*)(BI(I),I=1,NX)

WRITE(6,240)

WRITE(6,*)(HD(I),II1,NX)

WRITE(6,250)

WRITE(6,*)(AF(I),I=1,NNT)

WRITE(6.260)

WRITE(6,*)(AE(I),I-1,NKT)
FORMAT(1HI,'NO. OF COLLOCATION POINTSI',I4,//,1x,'ALFAS',F4.1,3X,'

+BETAI',F4.1)

 

 

CACULATE RATE CONSTANTS

DO 12 1'1,NK

THI(I)=AF(I)*EXP(AE(I)/TEM)

CONTINUE

AK'AF(NKT)*EXP(AE(NKT)/TEM)

WRITE(6,270)

WRITE(6,160)(THI(I),I=1,NK)

WRITE(6.*)AK

FORMAT(1HO,'SYSTEM PARAMETERS (NX, NK,NR)')
FORMAT(IHO,' SL TEM DEN 01 PI QB PB SA VT')
FORMAT(IHO,'INLET MOLE FRACTIONS')
FORMAT(1HO,'MASS TRANSFER COEFFICIENTS (KG)')
FORMAT(1HO,'INTERNAL EFFECTIVE DIFFUSIVITIES (D)')
FORMAT(IHO,'KO IN ARRHENIUS EQN')
FORMAT(1HO,'ACTIVATION ENERGY')

FORMAT(1HO,'RATE CONSTANTS (K)')

 

 

:CACULATE DIMENSIOBLESS PARAMETERS

no 17 I-1,Nx
THI(I)=82.05*TEM*DEN*THI(I)*SL**2./HD(1)*SQRT(423./TEM)
IF(I.EQ.2.0R.I.EQ.4.0R.I.EQ.S)THEN '
THI(I)=THI(I)*PB

END IF

CONTINUE

RM'QI*PI/QB/PB

DE-HD(1)

DO 27 I=1,Nx

nnn

nnn

non

27

200

30

10

999

110

202

BI(I)'BI(I)*SL/HD(I)*(423./TEM)**0.32
HTR(I)=HD(I)*SA'VT/SL/QB*SQRT(TEM/423.)
HD(I)=DE/HD(I)

CONTINUE

AK‘AK'PB

 

 

IMPORTANT INDEXES

NT8N+1
NTD=NX*NT
ML-NTD+1
IA8ML
IDGT'S

 

 

FIND COLLOCATION POINTS

CALL JACOBI(10,N,O,1,ALFA,BETA,DIF1,DIF2,DIF3,ROOT)
WRITE(6,200)(ROOT(I).181,NT)
FORMAT(1HO,'COLLOCATION POINTS IN SQUARE OF X ARE',/,1OF8.4)

 

 

SET UP LAPLACIAN MATRIX

DO 30 J81,NTD

DO 30 III,NTD

AMAT(J,I)=0.0

CONTINUE

DO 10 J31,NT

CALL DFOPR(10,N,O,1,J,1,DIF1,DIF2,DIF3,ROOT,V1)
CALL DFOPR(10,N,O,1,J,2,DIF1,DIF2,DIF3,ROOT,V2)
DO 10 M!1,NX

DO 10 I=I,NT

IF(J.EQ.NT)V2(I)=0.0

K!J+(M-1)*NT

L=I+(M-1)*NT
AMAT(K,L)-4.*ROOT(J)*V2(I)+2.*V1(I)

CONTINUE

 

CONTINUE

WRITE(6,110)
WRITE(6,160)(BI(I),I=I,NX)
WRITE(6,120)
WRITE(6,160)(HD(I),I=1,NX)
WRITE(6,130)
WRITE(6,160)(THI(I),I=1,NK)
WRITE(6,140)

WRITE(6,*)AK
WRITE(6,410)QB
WRITE(6,150)RM
WRITE(6,160)(HTR(I),I=I,NX)
FORMAT(1H1,'BIOT NUMBERS')

nnn

nnn

000

000

120
130
140
150

160

20

51

60

SO

40

80

41

300

203

FORMAT(IHO,'DIFFUSIVITY RATIOS')

FORMAT(1HO,'THIELE MODULUS')

FORMAT(IHO,'ADSORPTION CONSTANTS * PB')

FORMAT(1HO,'RATIO OF MOLAR FLOW RATE8 ',F10.2,/,' HOLDING TIME RAT

+IO')

FORMAT(1X,7E11.3)

 

 

INITIAL ESTIMATE OF SOLUTION VECTOR Z

DO 20 ISI,NTD
E(I)-0.0
CONTINUE

----EVALUTE F VECTOR AND DERIVATIVES OF VECTER F WRT VECTER Z -----

IQBIO

INTO'O

IFLAG‘O

CALL MODEL(N,ML,NTD,NX,NK,NR,YI,HD,BI,THI,F,CMAT,Z,AK,HTR,RM)
DO 50 J31,NTD

EMAT(J,ML)'0.0

DO 60 I31,NTD

EMAT(J,I)'0.0
IF(J.EQ.I)BMAT(J,J)=1.0
BMAT(J,ML)IBMAT(J,ML)+AMAT(J,I)*Z(I)
CONTINUE

BMAT(J,ML)=EMAT(J,ML)-F(J)

CONTINUE .

 

 

SET UP JACOEIAN MATRIX

DO 40 III,NTD

DO 40 J81,NTD
CMAT(I,J)8AMAT(I,J)-CMAT(I,J)
CONTINUE

 

 

ITERATION ON VECTOR Z STARTS

CALL LEQT1F(CMAT,ML,NTD,IA,EMAT,IDGT,WKAREA,IER)
RES'0.0

DO 80 I'l,NTD

2(1)=Z(I)‘BMAT(IpML)

RESiRES+BMAT(I,ML)**2

INTOSINTO+1

IF(ITNO.GT.10)GO TO 41

IF(RES.GT.1.E-16)GO TO 51

WRITE(6,300)INTO,RES

WRITE(6,400)(Z(I),I=1,NTD)

FORMAT(//,1X,'NO. OF ITERATION=',I4,5X,'RESIDUAL=',E14.8//,' SOLUT

+ION AT COLLOCATION POINTS',/)

GOO

nnnn

000

204

400 EORMAT<1x,9R8.:)
-------- EVALUATE FLUX AT BOUNDARY AND BULK MOLE FRACTIONS---------

DO 70 L81,NX
W(L)'0.0
70 CONTINUE
DO 67 M=l,NX
DO 65 J81,NT
KIJ+(M-1)*NT
W(M)*W(M)+Vl(J)*Z(K)
65 CONTINUE-
YB(M)=RM*YI(M)'HTR(M)*W(M)*2.
67 CONTINUE

---EVALUATE QB BY OVERALL ME AND COMPARE WITH RREVIOUS 03. START
ITERATION ON QB.

 

QBNnQI*PI/PB—QB*(HTR(3)*W(3)+HTR(4)*W(4)+HTR(5)*W(S)+HTR(6)*W(6))
IP(ABS((QBN-QB)/QB).LE.1.E-5)THEN
wRITE(6,410)QE
410 FORMAT(lHO,'QB-',P12.2)
wRITE(6,150)RN
wRITE(6,160)(HTR(I).I=1.NX)
ELSE IP(IQB.EQ.3)THEN
wRITE(6,420)IQE
420 FORMAT(IHO,'QB DOES NOT CONVERGE AFTER',12,' ITERATIONS')
wRITE(6,410)QE
WRITE(6,150)RM
wRITE(6,160)(HTR(I),I=I,Nx)
ELSE
RM-RM*QB/QBN
DO 73 I-I,Nx
HTR<I>=HTR(I)*QB/QBN
78 CONTINUE
QE-QDN
wRITE(6,410)oE
WRITE(6,150)RM
wRITE(6,160)(HTR(I),I=1,NX)
IOE=IQE+I
INTOuo
GO TO 51
END IF
WRITE(6,440)
WRITE(6,160)(YB(I),I=1,NX) ,
4:0 FORMAT(lHO,'BULK MOLE FRACTIONS')

 

 

CONCENTRATION PROFILE

WRITE(6.500)

nnn

205

500 FORMAT(//.' CONCENTRATIONS AT FIXED GRIDPOINTS',//,3X,'X',7X,'Yl',
+9x,'YZ',9X,'Y3',9X,'Y4',9X,'YS',QX,'Y6',/)
Do 95 1:1,11
x=(I-1)/10.o
CALL INTRP(10,NT,X*X,ROOT,DIF1,XINTP)
Do 85 L-I,Nx
W(L)-0.0
85 CONTINUE
DO 92 M-l,NX
DO 90 J=I,NT
x-J+(N-1)*NT
w(N)=W(M>+x1NTF(J)*2(x)
9o CONTINUE
IF(w(M).LT.-1.E-IO)IFLAO-I
92 CONTINUE
WRITE(6,600)X,(W(L),L-l,NX)
600 FORMAT<1X,F4.2,6FII.5)
95 CONTINUE

 

 

EVALUATE THE EFFECTIVENESS FACTORS

DO 71 L81,Nx
W(L)-0.o

71 CONTINUE
DO 68 Mel,Nx
DO 68 JIl,NT
K-J+(M-1)*NT
W(M)*W(M)+V1(J)*Z(K)

68 CONTINUE
DN-1./((1.+YB(1)*AK)**2.)
R1=THI(1)*YB(1)
R2=THI(2)*YB(1)**2.
R3=THI(3)*YB(2)
R4-THI(4)*YB(3)**2.
R5=THI(5)*YB(4)**2.

R680.15*R5

R7-2.85*RS

P(1)-HD(1)*(R1+2.*Rz-R3)*DN
P(2)=HD(2)*(-R2+R3)*DN
F(3)-HD(3)*(-Rl-R3+2.*R4+R6)*DN
F(4)=HD(4)*(-R4+2.*R5+R7)*DN
F(5)=-HD(5)*RS*DN

P(6)=-HD(6)*(R6+R7)*DN

IRUNIIRUN+1
WRITE(9,900)IRUN,SL,THI(1),BI(1),(W(I),I=1,NX)
WRITE(10,900)IRUN,SL,THI(1),BI(1).(F(I),I=1,NX)
DO 75 M-1,Nx

F(M)=2.*W(M)/P(M)

7S CONTINUE
WRITE(6,800)

206

800 FORMAT(1H0,'EFFECTIVENESS FACTORS')

900

700

88

89

99

()()(1

()()()()()()()()

WRITE(6,160)(F(I).I=1,NX)
WRITE(8,900)IRUN,SL,THI(1),BI(1),(YB(I),I=1,NX)
SELl=YB(4)/YB(3)

SEL2=YB(4)/YB(S)
SEL3=(YB(3)+YB(4))/(YB(2)+YB(5))
SEL4=YB(4)/(YB(2)+Y8(3)+YB(5)+YB(6))
WRITE(11,900)IRUN,SL,RM,HTR(1),SEL1,SEL2,SEL3,SEL4
WRITE(7,900)IRUN,SL,THI(1),BI(1),(F(I),I=1,NX)
FORMAT(1X,IZ,F5.3,2F9.3,6E9.3)

WRITE(6,700)

FORMAI(//" alas-38838888....scat-saccsncsasssssaanaaas:"//)
IF(IFLAG.EQ.2.0R.IRUN.EQ.1)GO TO 11
SLN'SL+0.001

DO 88 1'1,NN

THI(I)'THI(I)*(SLN/SL)**2.

CONTINUE

DO 89 I'l,NX

BI(I)=BI(I)*SLN/SL

HTR(I)3HTR(I)*(SL/SLN)**2.

CONTINUE

SL'SLN

GO TO 999

STOP

END

 

 

SUBROUTINE JACOBI

SUBROUTINE JACOBI(ND,N,N0,N1,AL,BE,DIF1,DIF2,DIF3,ROOT)
DIMENSION DIF1(ND),DIF2(ND),DIF3(ND),ROOT(ND)

EVALUATION OF ROOTS AND DERIVATIVES OF JACOBI POLYNOMIALS
P(N) (AL.BE) , MACHINE ACCURACY 16 D,

FIRST EVALUATION OF COEFFICIENTS IN RECURSION FORMULAS
RECURSION COEFFICIENTS ARE STORED IN DIFI AND DIF2

AB 3 AL + BE

AD i BE AL

AP 8 BE * AL

DIF1(1) (AD/(AB+2)+l)/2
DIF2(1) 0.

IF(N.LT.2) GOTO 15

DO 10 I 8 2,N

21 I I-1

Z I AB+2*ZI

DIF1(I) 3 (AB*AD/Z/(Z+2)+1)/2
IF(I.NE.2) GOTO 11 '
DIF2(I) ' (AB+AP+ZI)/Z/Z/(Z+1)

nnnn.

GOO

000

11

10

15

25

30

22
21

20

31

35

207

GOTO 10

Z 8 2'2

Y 8 ZI*(AB+ZI)

Y 8 Y*(AP+Y)
DIF2(I) 8 Y/Z/(Z-l)
CONTINUE

ROOT DETERMINATION BY NEWTON METHOD WITH SUPPRESSION
OF PREVIOUSLY DETERMINED ROOTS

DO 30 J 8 1,N

XP 8 (DIF1(J)-X)*XN-DIF2(J)*XD
XP1 8 (DIF1(J)-X)*XN1-DIF2(J)*XDl-XN
ND 8 EN

XD1 8 XN1

EN 8 XP

XN1 8 XP1

EC 8 1.

Z 8 XN/XNI

IF(I.EQ.1) GOTO 21

DO 22 J 8 2,1

ZC 8 ZC-Z/(X-ROOT(J-1))
282/ZC

X 8 X-Z

IF(ABS(Z).GT.1E-09) GOTO 25

ROOT(I) 8 X
X 8 X+.0001
CONTINUE

ADD EVENTUAL INTERPOLATION POINTS AT X80 OR X81

NT 8 N+N0+N1

IF(N0.EQ.0) GOTO 35

DO 31 I 8 1,N

J 8 N+1-I

ROOT(J+1) 8 ROOT(J)
ROOT(I) 8 0.

IF(N1.EQ.1) ROOT(NT) 8 1.

NOW EVALUATE DERIVATIVES OF POLYNOMIAL
DO 40 I 8 1,NT

x 8 ROOT(I)
DIF1(I) 8 1.

 

000

0000000

40

21

20

10

25

60
50

208

DIF2(I) 8 0.

DIF3(I) 8 0.

DO 40 J 8 1,NT

IF(J.EQ.I) GOTO 40

Y 8 X-ROOT(J)

DIF3(I) 8 Y*DIF3(I) + 3 ’ DIF2(I)
DIF2(I) 8 Y'DIF2(I) + 2 * DIF1(I)
DIF1(I) 8 Y'DIF1(I)

CONTINUE

RETURN

END

 

 

S UTINE DFOPR

SUBROUTINE DFOPR(ND,N,N0,N1,I,ID,DIF1,DIF2,DIF3,ROOT,VECT)
DIMENSION DIF1(ND),DIF2(ND),DIF3(ND),ROOT(ND),VECT(ND)

SUBROUTINE EVALUATES DISCRETIZATION MATRICES AND
GAUSSIAN QUADRATURE WEIGHTS, NORMALIZED TO SUM 1
ID 8 1 , DISCRETIZATION MATRIX FOR Y(1) (X)

ID 8 2 , DISCRETIZATION MATRIX FOR Y(2) (X)

ID 8 3 , GAUSSIAN QUADRATURE WEIGHTS

NT 8 N+NO+N1

IF(ID.EQ.3) GOTO 10

DO 20 J 8 1,NT

IF(J.NE.I) GOTO 21
IF(ID.NE.1) GOTO 5

VECT(I) 8 DIF2(I)/DIF1(I)/2.
GOTO 20

VECT(I) 8 DIP3(I)/DIP1(I)/3.
GOTO 20

Y 8 ROOT(I)-ROOT(J)

VECT(J) 8 DIF1(I)/DIF1(J)/Y
IF(ID.EQ.2) VECT(J)8VECT(J)*(DIF2(I)/DIF1(I)-2/Y)
CONTINUE

GOTO 50

Y 8 0.

DO 25 J 8 1,NT

x 8 ROOT(J)

AX 8 X * (l-X)

IP(N0.EQ.0) AX8AX/X/X
IF(N1.EQ.0) AX8AX/(1-X)/(1-X)
VECT(J) 8 AX/DIFI(J)**2

Y 8 Y+VECT(J)

DO 60 J 8 1,NT

VECT(J) 8 VECT(J)/Y

RETURN

END

000

000

10

20

30

209

 

 

SUBROUTINE INTRP

SUBROUTINE INTRP(ND,NT,X,ROOT,DIF1,XINTP)
DIMENSION ROOT(ND).DIF1(ND),XINTP(ND)

EVALUATION OF LAGRANGIAN INTERPOLATION COEFFICIENTS

POL 8 1.

DO 5 I 8 1,NT

Y 8 X-ROOT(I)

XINTP(I) 8 0.
IF(Y.EQ.0.D0) XINTP(I)81.
POL 8 POL'Y
IF(POL.EQ.0.D0) GOTO 10
DO 6 I 8 1,NT

XINTP(I) 8 POL/DIF1(I)/(X-ROOT(I))
RETURN

END

--SUEROUTINE EVALUATES VECTER F AND ITS DERIVATIVES WRT VECTER Z--

SUBROUTINE MODEL(N,ML,NTD,NX,NK,NR,YI,HD,BI,THI,F,CMAT,Z,AN,HTR,RM
+)

INTEGER N,NTD,ML,NX,NK,NR

REAL YI(NX),HD(NX),BI(NX),THI(NK),F(NTD),CMAT(ML,ML),Z(NTD),HTR(NX
4')

REAL RN(7).R(7,6),Y(6)

INT8N+1

DO 10 I81,NTD

DO 10 J81,NTD

CMAT(I,J)8O.0

CONTINUE

DO 20 M81,NX

K8M'INT
F(K)8BI(M)*(RM*YI(M)-Z(K))/(1.+BI(M)*HTR(M))
CONTINUE

DO 40 X81,N

DO 30 J81,NX

JJ8(J-1)*INT+K

Y(J)8Z(JJ)

CONTINUE

SD81.+Y(1)*AK

DD81./(SD**2.)

TD8-2./(SD**3.)

RN(1)8THI(1)*Y(1)

RN(2)8THI(2)*Y(1)**2.

RN(3)8THI(3)*Y(2)

RN(4)8THI(4)*Y(3)**2.

RN(5)8THI(S)*Y(4)**2.

RN(6)80.15*RN(5)

60

65

40

210

RN(7)82.85*RN(5)

LA=K

LB8K+INT

LC8K+2*INT

LD8K+3*INT

LE8K+4*INT

LF8K+5*INT
F(LA)8HD(1)*(RN(1)+2.*RN(2)'RN(3))*DD
F(LB)8HD(2)'(‘RN(2)+RN(3))‘DD
F(LC)'HD(3)*('RN(1)'RN(3)+2.*RN(4)+RN(6))*DD
F(LD)8HD(4)*(‘RN(4)+RN(5)*2.+RN(7))*DD
F(LE)8-HD(S)*RN(5)'DD
F(LF)8-HD(6)'(RN(6)+RN(7))*DD

DO 60 I81,NR

DO 60 L81,NX

R(I,L)80.0

CONTINUE

DO 65 I81,NR

R(Ip1)'AK*RN(I)*TD

CONTINUE

R(1,1)8R(1,1)+THI(1)*DD
R(2,1)8R(2,1)+2.*Y(1)*THI(2)*DD
R(3'2).R(3p2)+THI(3)*DD
R(8,3)8R(4,3)+THI(4)*DD*2.*Y(3)
R(5,4)8R(5,‘)*THI(5)*DD*2.*Y(4)
R(6,4)8R(6,4)*THI(5)*DD*2.*Y(4)*0.15
R(7,4)8R(7,4)*THI(5)*DD*2.*Y(4)*2.85

DO ‘0 M81,NX

NK'(M'1)*INT+K
CMAT<LA,KK)8HD(1)*(R(1,M)+2.*R(2,M)-R(3,M))
CMAT(LB,KK)8HD(2)*(-R(2,M)+R(3,M))
CMAT(LC,KK)BHD(3)*(-R(1,M)'R(3,M)+2.*R(4,M)+R(6,M))
CMAT(LD,KK)8HD(4)*(-R(4,M)+R(S,M)*2.+R(7,M))
CMAT(LE:KK)8-HD(5)*R(5pM)
CHAT(LFIKK)--HD(6)*(R(6'M)+R(7IN))

CONTINUE

DO 80 K81,NX

KK8K*INT
04AT(NK,Kx)--EI(K)/(1.+DI(K>*HTR(K))

80 CONTINUE

RETURN
END

 

INPUT DATA

 

8,6,7,7

1,0

.01,673,2,200,0.1,200,0.1,0.4,1000

211

.33333,0,0,0,0,0

100,100,100,100,100,100

.0019,.0015,.0024,.0017,.0012,.0024
369.9174,97.1388,2642883.946,114.104,.01246,.0003414,.001457,.002945
-6875.53,-5044.75,-10183.51,-7074.31,-1465.0,-3203.04,-1516.45,3122.56

 

COMPUTER OUTPUT

 

NO. OF COLLOCATION POINTS8 8

ALFA8 1.0 BETA8 .0
SYSTEM PARAMETERS (NX, NK,NR)
6 7 7
SL TEM DEN QI PI QB PB SA VT
101 673. 2. 200. .1 200. .1 .4 1000.
INLET MOLE FRACTIONS
.33333 0. 0. 0. 0. 0. °
MASS TRANSFER COEFFICIENTS (KG)
100. 100. 100. 100. 100. 100.
INTERNAL EFFECTIVE DIFFUSIVITIES (D)
.0019 .0015 .0024 .0017 .0012 .0024
K0 IN ARRHENIUS EQN
369.9174 97.1388 2642883.946 114.104 .01246 .0003414 .001457 .002945
ACTIVATION ENERGY
-6875.53 '5044.75 -10183.51 -7074.31 -1465. -3203.04 -1516.45 3122.56
RATE CONSTANTS (K)
.135E-01 .539E-01 .709E+00 .311E-02 .141E-02 .293E-05 .153E-03
.304865615821
COLLOCATION POINTS IN SQUARE OF X ARE
.0178 .0913 .2143 .3719 .5452 .7132 .8556 .9554 1.0000
BIOT NUMBERS
.454E+03 .575E+03 .359E+03 .507E+03 .718E+03 .359E+03
DIFFUSIVITY RATIOS
.100E+01 .127E+01 .792E+00 .112E+01 .158E+01 .792E+00
THIELE MODULUS
.623E+02 .249E+02 .327E+04 .143E+01 .651E+00 .135E-01 .705E+00
ADSORPTION CONSTANTS * PB
.0304865615821
QB8 200.00
RATIO OF MOLAR FLOW RATE8 1.00
HOLDING TIME RATIO
.479E+00 .378E+00 .605E+00 .429E+00 .303E+00 .605E+00

NO. OF ITERATION8 6 RESIDUAL8 .302219158-27

SOLUTION AT COLLOCATION POINTS

212

.0001 .0003 .0010 .0031 .0087 .0201 .0380
.0000 .0000 .0000 .0000 .0000 .0000 .0000
.2055 .2089 .2143 .2205 .2249 .2245 .2178
.0580 .0560 .0525 .0478 .0425 .0372 .0327
.0022 .0021 .0019 .0017 .0014 .0011 .0010
.0045 .0043 .0040 .0036 .0032 .0029 .0026
QB8 223.08
RATIO OF MOLAR FLOW RATE8 .90
HOLDING TIME RATIO
.430E+00 .339E+00 .543E+00 .384E+00 .271E+00
NO. OF ITERATI0N8 4 RESIDUAL8 .1139044SE-26
SOLUTION AT COLLOCATION POINTS
.0001 .0003 .0010 .0031 .0085 .0196 .0371
.0000 .0000 .0000 .0000 .0000 .0000 .0000
.1922 .1952 .1998 .2050 .2084 .2071 .1997
.0491 .0473 .0441 .0399 .0352 .0304 .0264
.0015 .0014 .0013 .0011 .0009 .0008 .0006
.0030 .0029 .0027 .0024 .0021 .0019 .0017
QB8 222.90
RATIO OF MOLAR FLOW RATE8 .90
HOLDING TIME RATIO
.430E+00 .340E+00 .543E+00 .385E+00 .27ZE+00
NO. OF ITERATION8 3 RESIDUAL8 .20140677E-26
SOLUTION AT COLLOCATION POINTS
.0001 .0003 .0010 .0031 .0085 .0196 .0371
.0000 .0000 .0000 .0000 .0000 .0000 .0000
.1923 .1953 .1999 .2051 .2085 .2072 .1998
.0492 .0473 .0442 .0400 .0352 .0305 .0264
.0015 .0014 .0013 .0011 .0009 .0008 .0006
.0030 .0029 .0027 .0024 .0021 .0019 .0017
Q88 222.90
RATIO OF MOLAR FLOW RATE8 .90
HOLDING TIME RATIO
.430E+00 .340E+00 .543E+00 .385E+00 .272E+00
BULK MOLE FRACTIONS
.685E-01 .245E-04 .181E+00 .221E-01 .484E-03
CONCENTRATIONS AT FIXED GRIDPOINTS
X Y1 Y2 Y3 Y4 Y5

.0576
.0000
.2074
.0294
.0008
.0024

.543E+00

.0563
.0000
.1890
.0235
.0005
.0015

543E+00

.0563
.0000
.1891
.0235
.0005
.0015

.543E+00

.145E-02

Y6

.0690
.0000
.2008
.0280
.0008
.0023

.0674
.0000
.1823
.0222
.0005
.0015

.0674
.0000
.1824
.0222
.0005
.0015

.00
.10
.20
.30
.40
.50
.60
.70
.80
.90
1.00

.00005
.00007
.00013
.00027
.00059
.00129
.00284
.00627
.01381
.03047
.06737

EFFECTIVENESS FACTORS

.122E+00

.156E-02

213

.00000 .19160 .04965 .00156 .00307
.00000 .19201 .04940 .00155 .00305
.00000 .19322 .04864 .00151 .00299
.00000 .19521 .04738 .00145 .00290
.00000 .19792 .04558 .00136 .00277
.00000 .20123 .04322 .00125 .00261
.00000 .20477 .04029 .00113 .00242
.00000 .20780 .03674 .00099 .00221
.00000 .20853 .03255 .00083 .00197
.00001 .20302 .02770 .00066 .00172
.00002 .18240 .02224 .00049 .00146
.995E-01 .113E+01 .355E+01 .355E+01

33mmsmmmmax

APPENDIX F
Summary of Results from

CSTR Simulation

 

APPENDIX F.

Summary of Results from CSTR Simulation

Figures F.1-F.3 show the bulk mole fractions yi with
respect to residence time at 300, 350 and 400°C. Based on
Figures F.1-F.3, Figures 4.13-4.19 were constructed and
discussed in Section 4.4.1 on the topic of temperature

effects.

Figures F.4-F.6 show the bulk mole fractions yi with
respect to residence time at 10,1 and 0.1 atm, respectively.
Figures 4.20-4.26 are based on the information from Figures
F.4-F.6 and discussed in Section 4.4.2 on the pressure

effects.

Figures F.7-F.10 Show the diffusion effets with
different catalyst pellet Sizes in a CSTR at 400°C. Figures
4.27-4.33 discussed in Section 4.4.3 are based on these

figures.
Figures F.11-F.13 show the effects of step distribution

of catalyst activity at 400 °C. Based on these figures,

Figures 4.35-4.41 were constructed.

214

215

 

 

ethanol

ethylene

light

paraffins

= A aromatics-

““9“ 05'0\

 

 

 

n3
.ékfl-
./8-
E
E
E;
3‘. J2-
it}
a
2
$5
a .06-
(D
-/
Figure F.1

O—i
N~

LOG (RESIDENCE TIME). SEC

Concentrations versus residence time for
CSTR study on temperature effect

T=3OO°C
L=0.01 cm
P=1 atm

0N

216

 

 

 

 

 

.3
24-
z:
3 ’8‘ ethanol
Pa
:2
<2
m
a.
‘3 eth lene
2 /2- Y
a light .
D paraffins
CD
(96%
=_ = aromatic
CB C6 N
C) *1 r
-/ C? I ‘2 .5

LOG (RESIDENCE TIME). SEC

Figure F-Z Concentrations versus residence time for
CSTR study on temperature effect

T-350 t
L-0.0l cm
P81 atm

 

 

 

217

 

 

 

 

 

”3
J24-
2:
<3
H
E3 ./8~
<:
c:
a.
3 ethanol
<3
2:
33 -’3"
D light
‘3 ethylene paraffins
196-
C: = aromatics
(7 z z

 

“I C? / ,2 3
LOG (RESIDENCE TIME), SEC

Figure F.3 Concentrations versus residence time for
CSTR study on temperature effect

T-uoo°C
L-0.0l cm
P=1 atm

218

 

 

 

 

 

.2
./6-
ethanol
5
g: J42“
L:
<3
0:
a.
a aromatic
ethyle r
g .08~
::
.4
D
CD
light
.04. - paraffins
C: 3-06 "‘
I ether
0 x
-/ 0I I 2

LOG (RESIDENCE TIME), SEC

Figure F.“ Concentrations versus residence time for
CSTR study on pressure effect

P=lO atm
T=400'C
230.01 cm

 

219

 

 

 

 

 

 

425
u2~
ethanol
2’3 .15«-
H
53
3:: ethylene
E24
a:
fig ./4
fi aroma --
D
:n
'05" . _ light
paraffin?
Cg‘C- ‘ \
(7 " ‘1
“/ C? / ‘2 ‘3

LOG (RESIDENCE TIME). SEC

Figure F-S Concentrations versus residence time for
CSTR study on pressure effect

P=1 atm
T-400°C
L-0.0l cm

220

 

 

 

 

 

 

.25
ethanol
‘2.
ethylene

.l5-
Z
S
Ea
:3
‘<
E:
m .l‘
.4
<3
2:
:c
g aromatics
°° .05- _ \

= = C -C
C3-06 3
0 , I r
-/ 0 / 2

LOG (RESIDENCE TIME). SEC

Figure F.6 Concentrations versus residence time for
CSTR study on pressure effect

P=O.l°atm
T=4OO C
L-0.0l cm

221

 

 

 

.3

.24-1
2
a ./8. ethylene
54
:2
<2
o:
a.
£21
*3
2, .L2‘
E
3 ethanol aromatic

. C=-C=
'06 - 3 6 light
'I paraffins

 

 

 

 

LOG (RESIDENCE TIME). SEC

Figure F.7 Concentrations versus residence time for
CSTR study on pellet Size effect

IFO.OOl cm
T=400"C
P-l atm

 

 

 

 

 

 

.3
.241
ethanol
2
3
Ed .l8-
L)
.¢
:1
£2...
a:
.4
g
5‘: ./2q ethylene
,4
D
:n
aromatics ,
.05q . light
paraffins
\
€3-06
(7 I I '
- I 0 /

2 3
LOG (RESIDENCE TIME). SEC

Figure F.8 Concentrations versus residence time for
CSTR study on pellet size effect

L=0.02 cm
T2400‘C
P-l atm

 

223

 

 

 

 

 

 

.3
.24“
ethanol
2
.9.
ES .l8-
4<
c:
a.
a:
.4
2
)4 ’l2- ethylene
Q
D
m
aromatic
.05-*
= = Q
CB-CéA
C) " l l

-/ 0 l 2

LOG (RESIDENCE TIME). SEC

Figure F.9 Concentrations versus residence time for
CSTR study on pellet size effect

IF0.05 cm
T=L+oo °C
P=1 atm

224

 

.24-

ethanol

5 .18-

H

e.

D

«<

.z

EL.

53

2 .l2-

:4

.4

D

m aromatics

ethylene‘\

.06-

c“

r
2 3

 

 

C)
.1
i
\
\—

LOG (RESIDENCE TIME), SEC

Figure F.1O Concentrations versus residence time for
CSTR study on pellet size effect

L=O.l cm
Tsuoo'c
P=1 atm

 

 

225

 

ethanol

ethyle ; aromatics

 

 

425'

”2-
z

.9. 15‘
e.
o
<
c:
Cm.
a:
a”

2 -"
:4
.4
D
m

195~

(D
‘/
Figure F.11

 

C)
n04
(a

LOG (RESIDENCE TIME), SEC

Concentrations versus residence time for
CSTR study on step activity distribution
effect (case 1)

 

226

 

 

 

 

.25
.2-
2:
<3
5 .AS‘
O
E
[1.
a:
.4
g .I‘
s:
.4
D
m
.05-
O
“I
Figure F.12

I

0

 

ethanol
aromatic C '05 \
ethylene 3
CI
‘ I
/ 2

LOG (RESIDENCE TIME). SEC

Concentrations versus residence time for
CSTR study on step activity distribution

effect (case 2)

 

 

 

227

 

.25

.21

ethanol

BULK MOLE FRACTION

.05-

aromatic

ethylene\
C=-CZ~—~

3 #4.;

 

 

 

 

 

 

-! 0 I 2

LOG (RESIDENCE TIME). SEC

Figure F.13 Concentrations versus residence time for
CSTR study on step activity distribution
effect (case 3)