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Heat transfer effects in microwave-heated heterogeneous catalytic reactions

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Heat Transfer Effects in Microwave-Heated Heterogeneous
Catalytic Reactions
BY
WILLIAM L. PERRY, m
B. S., Mechanical Engineering, Texas A&M University, 1991
M. S., Chemical Engineering, University o f New Mexico, 1994
!
D IS S E R T A T IO N
Submitted in Partial Fulfillment of the
Requirements for the Degree of
Doctor o f Philosophy
Engineering
The University o f New Mexico
Albuquerque. New Mexico
May, 1998
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UMI Number: 9826650
Copyright 1998 by
Perry, William Leroy, III
All rights reserved.
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W illiam L. Perry
Candidate
Chem ical and Nuclear Engineering
Department
This dissertation is approved, and it is acceptable in quality
and form for publication on microfilm:
Approved by the Dissertation Committee:
Chairperson
Accepted:
&
Dean. Graduate Schot
School
APR 1 5 1998
Date
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D ED ICA TIO N
For My Family
Marian, Felix, Ross, Gladys, Bill and Jane Ann
iii
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ACKNOWLEDGEMENTS
Brock Roberts (AMTECH)
Dan Rees (Los Alamos)
Mike Lynch (Los Alamos)
Tom Hardek (Los Alamos)
William Roybal (Los Alamos)
Frank Gac (Los Alamos)
Wayne Cooke (Los Alamos)
Mark Paffett (Los Alamos)
Anil Prinja (U. of NM)
Alan Portis (UC Berkely)
Materia] Science and Technology Division of Los Alamos National Laboratory
Los Alamos Nuetron Scattering Center
iv
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Heat Transfer Effects in Microwave-Heated Heterogeneous
Catalytic Reactions
BY
WILLIAM L. PERRY, HI
A B S T R A C T O F D IS S E R T A T IO N
Submitted in Partial Fulfillment o f the
Requirements for the Degree of
Doctor o f Philosophy
Engineering
The University o f New Mexico
Albuquerque. New Mexico
May, 1998
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Heat Transfer Effects in Microwave-Heated Heterogeneous
Catalytic Reactions
by
William L. Perry, III
B. S., Mechanical Engineering, Texas A&M University, 1991
M. S., Chemical Engineering, University of New Mexico, 1994
Ph. D., Chemical Engineering, University of New Mexico, 1998
ABSTRACT
The kinetics of the CO oxidation reaction on Pt/A fC ^ as well as Pd/ANC^ have
been m easured in a packed bed reactor heated by microwaves. The reaction rate was also
measured in an identical reactor that was heated conventionally. Insertion o f a
thermocouple after the microwaves were switched off provided the best m ethod for
temperature measurement in this study. However, large-scale temperature gradients must
be elim inated before this method can provide accurate temperature measurements. After
modifications in our packed bed reactor to eliminate non-isothermality, the reaction
kinetics for the microwave heated CO oxidation reaction were comparable to those for
the conventionally heated reactor. The CO oxidation reaction therefore serves as an insitu probe o f metal surface temperature. These observations suggest the Pt and Pd
crystallites in a supported catalyst are not significantly hotter than the alum ina support in
a microwave heated reactor.
A sim ple model is presented which estimates the temperature rise o f 1 and 100
nm metallic particles typically found in a supported metal catalyst structure. The model,
based on a simple steady-state energy balance, assumes that the particles only lose heat to
vi
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the gas-phase, not the support matrix. This represents a best-case scenario for a
temperature gradient relative to the surroundings. The model indicates that the
temperature gradient is insignificant and this conclusion is supported by an experiment in
which the microwave-driven carbon m onoxide reaction acts as an in-situ temperature
probe.
The methanol-steam reaction was used as a test reaction to study the effect of
microwave heating on endothermic catalytic reactions. Mathematical models were
derived and solved for: I ) a single catalyst pellet; 2) a one-dimensional tubular reactor;
and 3) the two-dimensional tubular reactor w here radial heat transfer effects were not
negligible. The single catalyst pellet model indicated at gas temperatures near the
operating limit of the catalyst, a significant increase in productivity could be achieved
using microwave heating. The one-dimensional model also showed how microwaves
could offer an advantage over interstage heating of adiabatic reactors for this endothermic
reaction. Finally, the two-dimensional model indicated the homogeneous nature of
microwave heating could minimize radial heat transfer effects. An energy balance on a
conventional reactor versus a microwave heated reactor indicated an efficiency advantage
for the microwave as axial heat transfer rates increased relative to the radial heat transfer
case.
vii
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TABLE OF CONTENTS
LIST OF FIGURES
x
LIST OF TABLES
xiii
CHAPTER 1: INTRODUCTION
I
Specific Objectives
4
Discussion of the Nature of Microwave Heating
Microwave Interactions with Ceramics
Microwave Interactions with Conductors
7
1
11
CHAPTER 2: KINETICS OF THE MICROWAVE-HEATED CO OXIDATION
REACTION OVER ALUMINA SUPPORTED PD AND PT CATALYSTS
15
Introduction
15
Experimental
18
Results
Kinetics in an Integral Bed Reactor
Kinetics in a Differential Bed Reactor
Kinetics in a Modified Differential Bed
22
22
Discussion
29
Summary and Conclusions
34
Thermocouple Correction and Error Analysis
35
23
26
CHAPTER 3: ON THE POSSIBILITY OF A SIGNIFICANT TEMPERATURE
GRADIENT IN SUPPORTED METAL CATALYSTS SUBJECTED TO
MICROWAVE HEATING
37
Introduction
37
Heat Transfer Model
39
Dielectric Loss in Metallic Particles
44
Estimating the Temperature Rise
46
Supporting Evidence
48
Conclusion
50
viii
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CHAPTER 4: THE APPLICATION OF MICROWAVE ENERGY TO THE
ENDOTHERMIC METHANOL/STEAM REFORMING REACTION
51
Introduction
51
Modeling
Single Catalyst Pellet Model
One-Dimensional Integral-Bed Reactor Model
Two-Dimensional, Non-adiabatic Packed-Bed Model
54
Experimental
Differential Conversion
One-Dimensional Packed Bed
Two-Dimensional Packed-Bed
57
63
68
91
93
95
97
Experimental Results
100
Discussion
104
Conclusion
107
Future Work
110
CHAPTER 5: CONCLUSIONS AND SIGNIFICANCE OF WORK
111
Conclusions
111
Significance of this work
115
TABLE OF SYMBOLS
116
APPENDIX A: ACRITICAL REVIEW OF KEY PAPERS FROM
CHAPTER 2
118
APPENDIX B: MATHEMATICA CODE FOR THE 1-D SPHERICAL
MODEL
122
APPENDIX C: MATHEMATICA MODEL FOR SOLVING THE 1-D AXIAL
MODEL
125
APPENDIX D: FORTRAN CODE FOR SOLVING THE 2-D TUBULAR FLOW
MODEL
127
BIBLIOGRAPHY
139
ix
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LIST OF FIGURES
Page
Figure 1.1. Electric and magnetic field intensities, and electric current in lossy
12
media.
Figure 1.2. Size dependent quasi-DC conductivity of small indium crystals versus
particle size.
14
Figure 2.1. Schematic o f the reactor system containing two identical reactors, one
heated by microwaves and the other via a conventional clam -shell furnace.
18
Figure 2.2. Correlation between reactor temperature m easured by the furnace
controller and the temperature extrapolated from a thermocouple.
20
Figure 2.3. Schematic o f an integral-type packed-bed reactor and the expected
temperature profile when heated by microwaves.
21
Figure 2.4. Thermal (infrared) image of microwave heated integral bed.
22
Figure 2.5. Arrhenius plot for CO oxidation obtained using the configuration
shown in Figure 2.3.
23
Figure 2.6. Schematic o f a differential packed-bed reactor and the expected
temperature profile when heated by microwaves.
24
Figure 2.7. Arrhenius plot for CO oxidation obtained using the configuration
shown in Figure 2.6.
25
Figure 2.8. Schematic of the modified differential-bed configuration with the
expected temperature profile.
26
Figure 2.9. Arrhenius plot for CO oxidation in the reactor configuration shown in
Figure 2.8.
27
Figure 2.10. Effect o f CO partial pressure on CO oxidation rates for microwave
and conventionally heated reactors.
28
Figure 3.1. A representation of a supported metal crystallite in a pore.
38
Figure 3.2. An illustration of a hypothetical metal crystallite which is suspended
in air inside a spherical cavity.
39
x
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Figure 3.3. Arrhenius plot from Chapter 2 which compares the rate o f the CO
oxidation reaction under microwave versus conventional heating.
49
Figure 4.1. Conceptual representation o f endothermic temperature profiles,
microwave heating profiles, and their superposition.
52
Figure 4.2. Numerical solution for the concentration o f methanol from the coupled
heat and mass transfer equations given in the text.
60
Figure 4.3. Numerical solution for the temperature from the coupled heat and mass
transfer equations.
61
Figure 4.4. a) Theoretical conversion profiles over C18HC catalyst for an inlet
temperature of 580 K and three different electric field strengths, b) Theoretical
temperature profiles for different electric field strengths.
66
Figure 4.5. Theoretical conversion as a function o f applied electric field strength.
67
Figure 4.6. Schematic of system to be analyzed to determined endothermic
reaction behavior where radial heat transfer effects are included.
68
Figure 4.7. Temperature profiles for the base case when the reactor is heated
conventionally.
80
Figure 4.8. Concentration profiles for the base case when the reactor is heated
conventionally.
80
Figure 4.9. Temperature profiles for the base case when the reactor is heated by
microwaves.
81
Figure 4.10. Concentration profiles for the base case when the reactor is heated by
microwaves.
81
Figure 4.11. Conversion versus normalized exit temperature for the case where the
flowrate is G. 1x the base case.
83
Figure 4.12. Conversion versus normalized exit temperature for the case where the
flowrate is the base case.
83
Figure 4.13. Conversion versus normalized exit temperature for the case where the
flowrate is 2 x the base case.
86
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Figure 4.14. Conversion versus normalized exit temperature for the case where the
flowrate is 5 x the base case.
84
Figure 4.15. Conversion versus normalized exit temperature for the case where the
flowrate is lOx the base case.
85
Figure 4.16. Summary of Figures 4.11-4.15 where the ratio of the efficiency of the
two processes is indicated.
86
Figure 4.17. Conversion versus normalized exit temperature for the case where the
thermal conductivity is lOx the base case.
87
Figure 4.18. Conversion versus normalized exit temperature for the base case.
88
Figure 4.19. Conversion versus normalized exit temperature for the case where the
thermal conductivity is 0 .2 x the base case.
88
Figure 4.20. Summary of Figs. 4.17-4.19 where the ratio of the efficiency o f the
two processes is indicated.
89
Figure 4.21. Schematic of feed system for the methanol + steam reaction.
92
Figure 4.22. Reactor configuration used for the differential experiment.
93
Figure 4.23. Reactor configuration for the 1-D integral-bed experiment.
96
Figure 4.24. Reactor configuration for the 2-D integral-bed experiment which was
heated conventionally.
98
Figure 4.25. Reactor configuration for the 2-D integral-bed experiment which was
heated by microwaves.
98
Figure 4.26. Arrhenius plot showing the reaction rate of methanol over 24.4 mg of
catalyst.
101
Figure 4.27. Plot shows results o f 10 runs where conversion was nominally 60%
for both microwave and conventional case.
102
xii
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LIST OF TABLES
Table 3.1. Numerical values used to estimate the temperature rise in small
metallic particles.
Table 4.1. Numerical values used in 2-D model calculations.
xiii
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CHAPTER 1: INTRODUCTION
This document describes the study o f microwave heating as a means o f delivering
energy to catalytically promoted reactions. Consider, for exam ple, any endothermic
catalytic reaction. In an adiabatic reactor, such a reaction quickly consumes the sensible
heat from the gas, limiting the total conversion achieved because transfer of heat to the
reactants becomes a limiting process. Several strategies are used to solve this problem
including interstage heating, heat transfer by wall conduction, or even the use of
exothermic reactions to provide energy to the principal reaction. One of the objectives of
this study was to explore the use of microwaves to provide the energy required for a
catalytic process.
In addition, this dissertation has examined differential heating of metal
crystallites in a supported catalyst structure. Microwave heating appears to alter the
selectivity o f some chemical reactions [1-3], which has been attributed to the effects of
preferential heating o f the catalytically active phase. However, heat transfer from small
metallic particles is very efficient, and I will show theoretically and experimentally that it
is unlikely that the crystallites were hotter than their surroundings.
The differences between microwave heating and conventional heating are well
known in our everyday experience. A conventional oven relies on conductive and
convective heat transfer, and heating occurs from the outside in. On the other hand,
microwave ovens heat directly by coupling with the internal structure of a material,
heating volumetrically. Furthermore, conventional ovens are material insensitive; this is
not the case with microwave heating. Different materials will heat differently depending
on their dielectric properties. The most obvious success o f microwave heating is our
1
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home microwave oven. The success directly results from the unique way that energy
dissipates in the interior of food and the advantages this method offers over conventional
cooking.
The use of microwave heating for chemical processing has been investigated [510], and has been shown to speed up liquid-phase chemical reactions. The reason for the
rate increase lies in the effective coupling of microwave energy directly into polar
organic and inorganic solvents. This is a volumetric heating process, analogous to the
idea of volumetrically dissipating energy into the catalytically active phase as described
before.
Recently, interest has arisen in the use o f microwave heating for heterogeneous
catalysisfl 1]. In April 1993, the Electric Power Research Institute (EPRI) and the
National Science Foundation (NSF) organized a workshop which exam ined the role of
microwave processing on chem istry in general, and microwave-driven catalysis in
particular [12-15]. At this workshop, there were reports o f significant microwave heating
enhancements on the activity and selectivity o f catalytic processes. A second workshop
was held in 1997.
In the literature, enhancements have been attributed to the selective heating
properties of microwave energy. In fact, several of the papers exam ined attributed
selectivity enhancements to the temperature gradients established within the packed bed
[1-3]. Other researchers [3,4] suggest that the small metal crystallites in a supported
metal catalyst may become hotter than their surroundings during microwave heating. Part
of the difficulty in assessing the value of microwave heating in catalysis stems from the
difficulty in accurately observing not only the temperature o f the catalyst surface, but also
2
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the nature and magnitude o f the thermal gradients that exist in a microwave-heated
packed bed.
3
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Specific Objectives
The objective of this research was to perform fundamental studies of microwaveassisted catalysis and develop an understanding o f the nature and magnitude o f the
temperature distributions which exist in a microwave heated system. T he main body of
this document contains the following: 1) Experimental evidence that small (1-10 nm)
supported metal crystallites do not attain a higher temperature than their surroundings
using the rate of CO oxidation as a temperature probe; 2) Heat transfer analysis of the
nanometer sized crystallites which are exposed to microwave energy which supports the
evidence of #1 above; and 3) Solution o f the equations which describe a single catalyst
pellet and a microwave-heated reactor for an endothermic reaction which show a
performance enhancement under some conditions. Experiments were also performed to
test the model.
The following is a detailed outline of the work performed during this research:
I. CO-Oxidation Reaction
As mentioned previously, there has been speculation that the catalytic reaction
surface was hotter than the surroundings [4]. As an assessment of these claims, I
used the CO oxidation reaction as a temperature probe. The com parative kinetics
of the CO oxidation reaction (microwave vs. conventional) suggested that the
crystallites were no hotter than their surroundings.
4
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II. Heat Transfer Effects in Small Metal Crystallites
A rigorous derivation has been performed which relates the temperature rise of
small metallic particles to the microwave power, estimated dielectric properties of
the particles and the microwave frequency. Assumptions which lead to the best
case for a temperature rise were employed. Given the likely range of dielectric
loss values, and the amount of power required to sustain a temperature rise, it is
unlikely that the small particles reach a temperature significantly greater than
their surroundings.
III. Application of M icrowaves to Endothermic Reactions
Based on theoretical and experimental evidence, it appears that the nature of
microwave heating can increase the overall efficiency of endothermic reactions
under demanding heat transfer conditions. Specifically, the methanol-water
reaction was used as a test of this hypothesis. An endothermic reaction which
occurs in a catalytic system consumes energy and gives rise to a temperature drop
along all coordinates away from a heat source. In contrast, microwaves dissipate
energy homogeneously and the superposition should tend to counteract the
temperature drop, thereby increasing the catalyst utilization (efficiency). I have
exam ined this effect in three ways.
5
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1 .1 have solved the coupled heat and mass transfer equations for a single catalyst
pellet using parameters for the methanol+steam reaction system. The results show
a volumetric reaction rate increase when the system is operated at the maximum
temperature that the catalyst can tolerate.
2 . 1 have solved the coupled heat and mass transfer equations that show the
conversion behavior obtainable from an adiabatic plug flow reactor and
conversion behavior when microwave energy is applied. Again, this was done
using parameters from the methanol+steam reaction. The model shows an
improvement in the conversion behavior when microwave energy is used.
3. The 2-D coupled heat and mass transfer equations were solved for a tubular
reactor using the parameters for the methanol+steam reaction. An experiment was
also performed to verify the qualitative behavior of the model. Both the
experiment and the model indicate that microwave heating was more efficient
than conventional heating, especially as radial heat transfer conditions were made
more demanding.
The remainder of this introductory section is devoted to a discussion o f the recent
literature that relates to microwave catalysis and a discussion o f microwave interactions
with matter and how heating occurs.
6
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Discussion of the Nature of Microwave Heating
In this research project, I am primarily concerned with microwave heating of
solids. A basic understanding o f how microwave energy interacts with metals and
ceramic catalyst materials was therefore essential. This discussion will focus on the
general interactions of microwaves with ceramic materials. These materials include the
catalyst support and typical materials used for microwave reaction vessels, and the
discussion will also focus on the interaction of microwaves with conductors.
Microwave Interactions with Ceramics.
Electromagnetic energy interacts with ceramics prim arily through polarization
and conductivity effects. The polarization effects include atomic, electronic, orientation,
ion-jump and space-charge polarization [16-18]. The characteristic frequencies of atomic
and electronic polarization are beyond the microwave range and will not be considered
further. Orientation polarization occurs in the presence o f permanent electric dipoles that
are not generally present in ceramic materials, and this is also not considered here.
Hence, for my purposes, ion-jum p and space charge polarization in addition to
conduction losses will be discussed.
In a crystal, ions o f greater or lesser valency than standard lattice ions (impurities)
often exist adjacent to a vacancy, and together the pair form a quasi-permanent dipole.
This dipole will tend to rotate under the influence of an external alternating field in much
the same way a permanent dipole rotates in an alternating field [19]. The term ?jum p?
arises from the need for the process to overcome a potential barrier, and thus the process
7
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is an activated process. Thus jum p polarization contributes to losses by dissipation of
rotational kinetic energy into the lattice [19].
In a polycrystalline material, such as y-alumina, space-charge polarization can
occur because charge carriers, such as mobile ions or vacancies, encounter physical
boundaries, such as grain boundaries. The magnitude of the polarization thus depends on
the relaxation time with respect to the characteristic duration of the field. During this
relaxation period, conduction losses occur that give rise to heating. The maximum loss
occurs when there is a match between the polarization relaxation time and the field
frequency. This qualitative behavior can be seen in the Debye equations [16]:
= г~ +
(g p -O
(l +Q)2r 2)
(1.1)
(e'o -e'S p iT
g; =
(l - t - o r r )
and
г
? г + /г
( 1.2 )
where i= V =i. e ? and e? refer to the real and imaginary parts of the dielectric constant,
respectively. e ?0 is the static dielectric constant and г? is the constant at high frequency.
0) refers to the applied field frequency and x refers to the relaxation time. The real
component of the dielectric function represents the ?polarizability? of a material, and the
complex term is the ?dielectric loss?. Clearly, the maximum loss occurs when co = 1/x. If
8
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conduction losses become important, an extension [5] o f M axw ell-W agner theory [19]
modifies the Debye equations such that:
(l -t-o
+ гU't")
rr2)
(1.3)
COг 0
where a is the d.c. conductivity o f the material. As an exam ple, at high temperatures, the
conductivity of alumina increases substantially by the thermal excitation of valence
electrons into the conduction band, and conduction losses becom e important [5],
Equations (1.1) and (1.3), in general, are not very accurate due to the multiplicity of
relaxation times present in real materials. In practice, the values are determined
experimentally. The ceramic materials o f interest in this research are y-alumina and a
copper-oxide, zinc-oxide, alumina mixture. The loss factor o f the oxide mixture lias not
been measured, and the loss factor of alumina can vary widely due to crystallite size
distribution and variation of impurity levels.
It is the loss term that is of primary interest in this context because it represents
the ability of a material to convert microwave energy into thermal energy. The equation
representing this conversion is [16,18]:
(1.4)
9
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where P/V (W /m3) represents the pow er dissipated per v o lu m e ,/is the microwave
frequency in Hz, E is the applied electric field in V/m, гo is the permittivity o f free space
(8.8 x 10'12 F/m), and e? is the dielectric loss.
In addition, it is important to qualitatively understand attenuation o f an electric
field in a dielectric [20]. In any material, the electric field decays to 1/e o f its original
value at a depth of 5= 1/a:
(1.5)
For a good insulator:
(
1 -6 )
and equation (1.5) reduces to
(1.7)
For alumina, 1/a is on the order of 109 meters for 915 MHz radiation. A more realistic
approximation can be made by using a = 0)гoг? . A typical dielectric loss for alumina is
0.001, and 1/abecom es 103.
10
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Microwave Interactions with Conductors.
The behavior of conductors exposed to microwaves differs substantially from the
behavior of insulators. M icrowave energy does not substantially penetrate into bulk
conductors due to the large population of free charge carriers, which tend to absorb the
propagating wave [20]. In typical bulk metals analyses, such as in a waveguide analysis,
the tangential electric field is generally taken as zero at the surface, and the normal
component is taken as unchanged. The use of these boundary conditions with M axwell?s
equations has allowed a precise determination of the field distributions inside waveguides
and other metal enclosures [16,20]. W hile these boundary conditions are convenient for
the solution o f the field distribution, they do not accurately represent the true situation at
the surface where there is dissipation of the microwave energy into the metal structure,
which is of more interest for this research project.
Figure 1.1 represents the situation when an electromagnetic wave is incident on a
lossy conductor [20].
11
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b? * ~ H
╗2 = 9f3.
╗ i = 10"1 S/m
Incident |
Figure 1.1. Electric and magnetic Field intensities, and electric current in lossy
media when a EM wave is incident normal to the surface [20],
The more rigorous boundary conditions include continuity of the tangential
electric Field across the surface, and the perpendicular electric Field drops by the
permittivity ratio of air-to-m etal. Stated mathem atically from M axwell?s equations
[20]:
0
( 1. 8 )
г2г 2n -г,'г,? = 0
(1.9)
12
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where the subscripts n and t refer to the normal and tangential com ponents. In the
tangential case, the field is attenuated in the metal through the m ovement o f electrons that
dissipate energy into the lattice through conduction losses. The decay o f the electric field
is given by [2 0 ]:
E(z) = E0 e x p (-z a )
(1 1 0 )
where a is given by equation (1.5) above. For good conductors [20]:
f &
?
╗ 1
(1.11)
vO Jг
and equation (1.5) reduces to [20]:
( 1. 1 2 )
Again, the penetration depth (skin) where the field falls to 1/e o f the surface value is 1/a.
The skin depth of platinum and palladium at 915 MHz is approxim ately 5 pm.
O f principal interest to this project is the behavior of small metal particles on the
order of 1-10 nm. These particles, in effect, are surfaces in their entirety, because over 10
nm ( л 8 ) the field has not decayed appreciably [21]. In addition, it appears that small
metallic particles do not experience conventional conduction losses due to a size-induced
13
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metal-to-insulator transition [22]. Figure 1.2 shows the conductivity behavior as a
function o f particle size. Small metal particle behavior will be discussed in more detail in
Chapter 3.
10
6
c la s s ic a l
10
&
/
/ ?
?
/
10░
Indium
IT; 300k t
?2
10
10
8
.7
10
10
6
10
x(m)
Figure 1.2. Size dependent quasi-DC conductivity o f small indium crystals versus particle
size. For comparison, the bulk conductivity and classical size effect are also shown [22],
14
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CHAPTER 2: KINETICS OF THE MICROWAVE-HEATED CO OXIDATION
REACTION OVER ALUMINA SUPPORTED PD AND PT CATALYSTS
The contents of this chapter are published in JOURNAL OF CATALYSIS , v. 171 (#2)
pp. 431-438 OCT 15, 1997.
Introduction
The benefits of microwave heating have been known for some tim e and have been
exploited by organic chemists for liquid phase chemical reactions carried out in the batch
mode [5-7]. Microwave batch reactors that are transparent to microwaves but can sustain
high internal pressures have also been designed [8 ] and result in faster reaction times due
to rapid heating. The potential o f microwave heating for heterogeneous catalysis
prompted the Electric Power Research Institute (EPRI) and the National Science
Foundation (NSF) to organize a workshop on microwave effects in April 1993 [11]. At
this workshop, there were several reports of how microwave heating could enhance the
rates as well as selectivity of chemical reactions. For example, Cha reported high removal
rates (98%) of SO: and NOx in a microwave heated char-bed [ 12 ], and rapid
devolatilization of char and coal in a microwave heated reactor [23]. There are several
other reports o f microwave-assisted heterogeneous catalysis in the literature [2,24,25].
The benefits derived from microwave heating of catalytic systems appear to fall
into one o f two categories: rapid heating and temperature gradients within the reactor. In
the liquid- phase batch mode experiments [5-7], rapid heating can be attributed to the
mode of energy transfer. In a conventionally heated system, heat must be transferred
from the source and into the reaction vessel via conduction and convection. In a
microwave-heated vessel, the microwave energy is converted to heat within the vessel
15
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through coupling with the polar solvents, bypassing conventional heat transfer
mechanisms. Sim ilar benefits are seen also in heterogeneous gas-phase processes: Cha
[12] and Cha and Kim [23] have shown that rapid heating occurs in a microwave-heated
char bed. Also, Wan and Koch [24] show kinetic plots where the product formation in the
ammonia synthesis o f HCN reaches a quasi-steady state in a matter o f seconds. In these
heterogeneous experiments, microwave energy is dissipated directly into the solid
catalyst. As with the liquid phase reactions, microwave heating bypasses the conventional
convective and conductive heat transfer modes with the result that heating is rapid.
In addition to rapid heating, microwave heated heterogeneous systems may
provide temperature gradients within the catalyst bed, with potentially beneficial effects.
The works by Cha [12] and Cha and Kim [23] suggested that large temperature gradients
may exist between the char particles and the gas stream in the packed bed with the result
that the decomposition of NOx and SO t occurs at a lower gas temperature. Ioffe, et al.
[25] also suggested that temperature gradients may have been responsible for their
observed selectivity o f >90% for acetylene formation from methane in a microwaveheated activated carbon bed. The authors suggest that the highly non-isothermai nature
of the packed bed might allow reaction intermediates formed on the surface to desorb into
a relatively cool gas stream where it follows a different reaction pathway than in an
isothermal reactor. A higher selectivity towards acetylene formation was also reported by
Chen, et al. [2] during oxidative coupling of methane in a microwave heated reactor. The
non-isothermal nature of the microwave heated catalyst and lower temperature during
reaction was thought to account for the improved selectivity.
16
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Tem perature gradients within a packed bed have been found to be beneficial in
several applications: microwave heated infiltration [26, 27], catalyst preparation [1, 28],
drying [29] and sintering [30]. M odeling of power/electric field density in heterogeneous
systems has also been performed [31-33]. Based on their heat transfer model for a
microwave heated fluidized bed, Roussy, et al. [32], suggest, contrary to comments in
[2,12,23, 25]], that the temperature of the catalyst is identical to that of the gas phase. A
very com plete review of the literature was done by Peterson [34].
In a microwave heated catalyst bed, temperature gradients could occur on two
length scales. Large-scale non-isothermalities can be measured via a thermal imaging
camera or an optical pyrometer. However, temperature gradients between the metal
particles and the gas phase or support are difficult to measure. It is possible that some of
the differences between microwave and conventionally heated reactors reported in the
literature may be a result of temperature nonuniformities and errors in temperature
measurement. Therefore, the primary objective of the present study was to perform
accurate tem perature measurements in a microwave heated reactor. The temperature
dependence o f the CO oxidation reaction over Pd and Pt on Y-AI2O 3 was studied in an
identical reactor heated via microwave as well as conventional heating. This reaction was
chosen because the reaction kinetics are well known [35, 36,37], Our results yield insight
into the nature of the thermal gradients in a packed bed reactor and the kinetic behavior
of the microwave-heated CO oxidation reaction.
17
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Experimental
The CO oxidation reaction was studied over Pt and Pd/y-AhOj in a specially
constructed microwave heated reaction system. The catalysts were obtained from
commercial vendors: 5wt% Pd/y-AIiOj Escat 14 from Engelhard and lwt% Pt/ y-AliCh
(300 m 2/g) Stk # 11797 lot E3 IB 13 from AESAR. Figure 2.1 is a schematic of the
experimental system that consists of two branches that are identical in every respect
except for the heating source. Each branch consists o f a stand-alone reactor, one of which
CO
P Sensor
Flow Controllers
Controller
gW
Source
T u b e Furnace
|iW
Power
Sensor
G a s Chromatograph
EXhaust
Figure 2.1. Schematic o f the reactor system containing two identical reactors, one
heated by microwaves and the other via a conventional clam-shell furnace.
is heated using microwaves, and the other heated conventionally. The reactors were
constructed using 8 mm diameter quartz tubing. The thermal reactor system was heated
18
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with a digitally controlled 1? resistive tube furnace. The microwave reactor was heated
by a magnetron based system operated on a continuous basis at 915 MHz. The power
incident on the microwave cavity was 850W to 1000W and was delivered to a resonant
applicator via a rectangular waveguide in the TEio mode. The cavity was structured so
that only a small fraction of the incident power was absorbed by the catalyst bed, the
remainder being dumped into a water load. The reactor tube, containing the catalyst, was
inserted through the rectangular resonant applicator parallel to the direction of the electric
field. Product analysis was performed using a Microsensor Technology, Inc. M200 gas
chromatograph using a 4m PoraPlot U column. Reactant ratios were fixed by mass flow
controllers, and the pressure was regulated by a bypass valve and monitored with a
capacitance manometer.
The reactants were mixed in a stoichiometric ratio for the Arrhenius experiment
using a 2 cc/s flow rate for CO and 1 cc/s for Oi; the reactor pressure was fixed at 1000
Torr. The dependency on CO partial pressure was found by using an excess of oxygen.
The oxygen flow rate was 30 cc/s and the CO flow rate was varied from 0.5- 3 cc/s, or a
CO partial pressure range of 35 - 95 Torr . The total reactor pressure was again held
constant at 1000 Torr and the reactor temperature was 408 K.
An infrared thermal imaging camera was used, primarily to determine the
temperature distributions in the packed bed. The spectral response of the system was such
that the quartz reactor tube was translucent. Hence, the measured temperature was an
average of that of the outer surface of the quartz tube and the catalyst inside [34]. In view
of the radial temperature gradient within the packed bed, we felt the method would be
unsuitable for accurate measurement of catalyst bed temperature Hence, thermal imaging
19
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was abandoned in favor of the thermocouple insertion technique. However, the thermal
imaging system did provide information on the spatial variation in temperature in the
axial direction.
Temperature was measured in the microwave system by inserting a thermocouple into the
bed after the microwave power was turned off. The temperature decay curve was
recorded on a strip chart recorder. The temperature versus time curve was linearized by
talcing the natural log of the data and extrapolated to zero time to determine operating bed
temperature. Since insertion of the thermocouple into the bed caused an initial cooling
that was too rapid to appear on the strip chart curve, a correction factor was necessary.
Therefore the procedure was repeated with a conventional tube furnace. The digitally
controlled tube furnace was allowed to reach a known temperature, the furnace power
300
U
<u
280
3
<U
Q.
B
tL>
JL>
"o
I?
C
o
U
260
240
220
200
180
o
o
o
o
o
o
o
o
o
Extrapolated Temperature (C)
Figure 2.2. Correlation between reactor temperature measured by the furnace
controller and the temperature extrapolated from a thermocouple inserted into the
furnace after heating had been switched off.
was terminated and the thermocouple inserted while the temperature was recorded as a
function of time. Figure 2.2 shows actual reactor temperature versus the extrapolated
20
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temperature after thermocouple insertion. This data was then used to apply a correction
factor for the temperature measurement during microwave heating. Further details of the
correction procedure and the error analysis are presented in a later section.
Initial experiments used an integral packed-bed configuration using 2 grams of
\% Pt/y-Ah 0 3 as shown in Figure 2.3. The configuration was such that the thermocouple
T h e rm o c o u p le
R eactor T ube
Active!
Figure 2.3. Schematic o f an integral-type packed bed reactor and the expected
temperature profile when heated by microwaves.
came into contact with the top of the packed bed after insertion. As we gained a better
understanding of the thermal gradients in the microwave heated reactor, the packed bed
configuration was modified. The evolution of the reactor configuration is described in
the results section. Subsequent experiments were performed with a differential bed
configuration using 5% Pd/AbCb as the catalyst.
21
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Results
Kinetics in an Integral Bed Reactor
We first present results obtained early in the experimental development, and how
these results led to the improper conclusion that a microwave-induced rate enhancement
was occurring. Figure 2.4 shows an Arrhenius plot obtained from the integral reactor
structure that used 2 grams of 1% Pt/AliC^. The thermocouple extrapolation technique
Figure 2.4. Thermal (infrared) image of microwave heated integral bed.
Temperatures shown are the average temperatures o f the areas outlined by the
boxes.
was used for this experiment and the probe was inserted such that it was in contact with
the top of the packed bed as shown in Figure 2.3. In addition to the thermocouple, an
infrared camera was used to obtain information about the temperature distributions in the
22
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packed bed. A typical infrared image from the microwave heated reactor is shown in
Figure 2.4. The observations indicated that temperature difference was approximately
Conventional
Microwave
c
- 5 .0
in
<n
i
i
cq
ei
is
cs
i
oo
<n
os
cs
1 0 0 0 /T (K )
Figure 2.5. Arrhenius plot for CO oxidation obtained using the configuration
shown in Figure 2.3. The increased reactivity under microwave heating can be
attributed to errors in temperature measurement inherent in the experimental
configuration of Figure 2.3. Reaction rate is in units o f (imoles/s/g.
20 K, such that the thermocouple was recording temperature in the coolest region while
most of the reaction was occurring on surfaces that were significantly hotter. The nonisothermal nature of this packed bed resulted in an apparent rate enhancement and altered
activation energy and pre-exponential factor, as shown in Figure 2.5.
Kinetics in a Differential Bed Reactor
Figure 2.6 shows a modified experimental design and the expected temperature
profile. In this experimental configuration, the catalyst bed was sandwiched between two
1 g masses o f inactive a-alum ina support. The catalyst bed contained 3 mg of active
23
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G u id e T u b e
R e a c to r T u b e
Pd/y-A LO
a-A LO
In su la tio n I
AT,
z
Figure 2.6. Schematic of a differential packed bed reactor and the expected
temperature profile when heated by microwaves.
catalyst (5 wt % Pd/y-A bC b) diluted in approximately 50 mg of y-alum ina support to
achieve radial uniformity of catalyst distribution across the packed bed. The packed bed
was insulated on the outside with microwave transparent sapphire wool. In addition, a
?guide tube? was added such that the thermocouple was inserted through the tube (see
Figure 2.6) until it came to rest in the hottest (active) part o f the bed.
Figure 2.7 shows an Arrhenius plot obtained from this differential-bed
configuration. The plot clearly shows an apparent rate enhancement for the microwave
24
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2.0
Microwave
Conventional
T3
0.0
a.
CN
-
h<y
2.0
-3.0
cX
c
oc
1000/T(K)
Figure 2.7. Arrhenius plot for CO oxidation obtained using the configuration
shown in Figure 2.6. The apparent rate enhancement resulted from thermal
gradients caused by differences in microwave coupling within the y and a
alumina portions of the differential bed. Reaction rate is in units of (imoles/s/g.
heated reactor. As was shown before with the integral bed, the apparent rate enhancement
could be caused by our inability to measure the reactor temperature properly. A blank
experiment demonstrated that Y-AI2O 3 absorbs microwave energy more efficiently than
OC-AI2O 3. Hence, the true temperature in the catalyst bed, which is composed o f Y-AI2O 3,
may be greater than the temperature of the a-alum ina that is used to sandwich the bed.
The larger mass of the a-alum ina (2g) versus that of the catalyst bed (0.05g) would make
it likely that the temperature recorded by the thermocouple is lower than the actual
temperature of the catalyst bed.
25
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Kinetics in a Modified Differential Bed
For the final set of experiments that revealed the true kinetics, the differential bed
was modified as described below. In this configuration, identical Y-AI2O 3 material was
used as the support as well as the insulating material surrounding the catalyst. Figure 2.8
shows a schematic and the expected temperature profile. An Arrhenius plot is shown in
Figure 2.9 for the oxidation of CO over PCI/Y-AI2O 3 in the modified differential bed. The
reaction rates were marginally greater, for microwave versus conventional heating, but
within the margin of experimental error. The slopes of the curves yield an activation
Guide T ube
Reactor Tube
Active
Inert
Inert
Insulation
T
AT
Figure 2.8. Schematic of the modified differential bed configuration with the
expected temperature profile.
26
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c
_o
o
3
-o
ot-l
4.0
M icrowave
.??i
3.0-
Conventional
CL
cs
O
U
?' + o
<D
c3
&
'c
2 .0 -
? ?i
0.0
vC
CN
c-i
1000/T(K)
Figure 2.9. Arrhenius plot for CO oxidation in the reactor configuration shown in
Figure 2.8. The marginal increase in rates for the microwave heated catalyst arise
due to errors in temperature measurement, as discussed in the text. Reaction rate
is in units of (imoles/s/g.
energy of 12.5 kcal/mol, which agrees with the results of Choi, et al. [37] for this
temperature range. The error bars on the microwave curve include the error in the
original measurement, and the propagated error from the correction procedure. The
details of the error analysis are presented in a later section. Also, as shown in Figure
2.10, the orders of reaction in CO are nearly identical with the best fit line slopes of -0.59
and -0.64 for conventional and microwave heating.
27
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c
_o
a
3
~a
ou.
3.0
M icrowave
Conventional
2.0
CU
CN
o
u
ллo
<u
C
3
'c
0.0
o
DC
rn
DC
ln(CO Partial Pressure)
Figure 2.10. Effect of CO partial pressure on CO oxidation rates for microwave
and conventionally heated reactors. The order o f reaction is 0.59 and 0.64 for the
conventional and microwave reactors, respectively. The reaction temperature for
the conventional reactor was 405 K; the temperature was not recorded for the
microwave heated reactor. Reaction rate is in units o f (imoles/s/g.
28
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Discussion
An important question in the study o f microwave catalysis is whether or not the
observed effects (altered reactivity and/or selectivity) can be explained by errors in
temperature measurement [34]. This would be the case if the observed effects are seen
also with conventionally heated catalysts, albeit at temperatures different from those seen
in the m icrowave heated catalyst. From our experim ents, the initial erroneous conclusion
was that the CO oxidation reaction was occurring at a higher rate when heated with
microwaves than with a conventional heat source (Figures 2.5 and 2.7). However, once
the temperature measurement errors in the reactor had been addressed, our final
conclusion was that there is no specific microwave effect in the CO oxidation reaction
over A fO j-supported Pd.
M easurem ent of catalyst temperature during microwave heating is a daunting task
[34,38]. An optical probe would appear to be a logical choice, however in our
experiments there was a problem with the optical probe we used. When an optical
pyrometer was used to measure temperature from the radial direction, a potential source
of error was that the observed temperature profile was averaged in the radial direction,
which is the direction of heat loss to the surroundings. Therefore, the measured
temperature would be an average of the reactor surface temperature and its internal
temperature. The temperature measurement would be further complicated by the
different emissivities of the various constituents o f the heterogeneous catalyst. Due to
these problem s with the optical probe, we decided to use a thermocouple for temperature
measurement.
29
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The advantage of a thermocouple is that it can be inserted into the catalyst bed.
While there are reports [32,33, 38] that a thermocouple introduced normal to the direction
of the microwave electric field does not influence the electrom agnetic field distribution,
other researchers ( e.g. Chen [2]) have concluded that the interference o f the
electromagnetic field with the metallic thermocouples makes them unsuitable for use in a
microwave heated reactor. Seyfreid, et al. [3] used a thermocouple in situ to measure the
bulk catalyst temperature. The authors determined the error in temperature was 5-8K
while considering "limitations inherent in the experimental setup." In addition, Roussy, et
al. [31], used a thermocouple in situ to measure the temperature in a fiuidized bed with no
apparent ill effects. However, our efforts to attain an accurate temperature measurement
using a thermocouple in situ were unsuccessful. Therefore, in our experiments, we
resorted to the use o f a thermocouple that is inserted into the reactor after switching off
the microwave field. Admittedly, this is not a perfect probe since a temperature
correction is necessary to account for the cooling of the catalyst bed upon contact with
the thermocouple . However, after applying the correction procedure (described in a
following section), the measured temperature is within ▒5 K o f the actual temperature.
Even with this method, it is important to eliminate large scale temperature
gradients within the reactor. The large temperature gradients seen by the thermal
imaging camera with an integral bed reactor, and the placement o f the thermocouple in
the bed, caused the temperature during microwave heating to be underestimated, leading
to the erroneous conclusion o f a microwave enhancement in the rate of CO oxidation
(Figure 2.4). When a small amount of catalyst was sandwiched between two beds of
inert a-alum ina to form a differential reactor bed, there were still problems in obtaining
30
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an accurate temperature measurement- The time required for the isolated Y-AI1O 3
particles to cool to the surrounding temperature would be much less than the time
required to insert the thermocouple. Because o f the rapid cooling, the temperature
recorded by the thermocouple would be weighted towards the larger mass of the aalumina, underestim ating the reaction temperature and yielding the apparent rate
enhancement shown in Figure 2.7.
These problems in temperature measurement prompted us to modify the
differential bed such that the catalyst was sandwiched between a large mass of identical
y-alumina support. The comparable dielectric properties o f the catalyst and the support
would reduce the temperature variations and make it easier for the thermocouple to read
the true catalyst temperature. W ith this modified differential bed reactor, our results show
that the reaction rate in the microwave heated reactor is marginally greater than the rate
in a conventional reactor. The reaction order in CO and the activation energy for the
reaction was also unaffected by microwave heating. Since the apparent kinetics are not
affected by the microwave field, it may be reasonable to assume that the CO oxidation
reaction serves as an indirect probe of the metal particle temperature. On this basis, the
marginally higher reaction rate in the microwave heated reactor could be caused by the
catalyst being 13K hotter than the temperature recorded by the thermocouple. There are
several possible explanations for the higher reaction rate during microwave heating. The
microwave heated reactor was insulated with quartz wool, and would be losing heat
outward in the radial direction. The conventional reactor, on the other hand, is heated
from the outside and hence, the temperature variation in the radial direction would be
expected to be less pronounced. This factor alone could cause the temperature recorded
31
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by the thermocouple insertion technique to be lower than the actual bed temperature. The
inability of the temperature correction procedure to correctly predict the bed temperature
could be another cause for the observed discrepancy. W e feel both these factors could
certainly explain the marginally higher reaction rates observed during microwave
heating.
Other reports in the literature [2,12,23,38] have also documented increased
reaction rates with microwave heating. For example, Chen, et al. [2] report that for
comparable conversion, their microwave-heated reactor operated at a lower temperature
than the conventional reactor. They used an infrared pyrom eter for temperature
measurement. As discussed above, a radial temperature profile (hotter interior and lower
surface temperature) may account for the observed lower operating temperature during
microwave heating. W hile experimental conditions and the methods of temperature
measurement differ among the various studies of m icrowave-assisted catalysis, we feel
that difficulties in temperature measurement could certainly result in an apparent increase
in reaction rates during microwave heating of heterogeneous catalysts. For example,
Gourari, et al. [38] also performed a comparative study (microwave versus conventional)
of ethylene oxidation and also found a temperature discrepancy, approximately 8 K. In
their case, the temperature was measured with a fine thermocouple inserted into a thin
silica tube transverse to the microwave electric field, and the true temperature derived via
a mathematical model. These authors suggest that the discrepancy was due to an
electrom agnetic effect on the kinetics of the reaction, while we feel our 13K discrepancy
is due to an indirect approach to temperature measurement and thermal gradients within
the catalyst bed. It should be noted that Gourari, et al. [38] were not able to directly
32
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measure the true surface temperature and had to rely on a mathematical model. The
direct measurement of temperature in a microwave heated catalyst still represents a
formidable challenge. A more complete critical review of key papers, the critisism being
based on lessons learned in this research, is presented in Appendix A.
O f greater interest are the reported selectivity differences during microwave
heating o f catalysts. These selectivity differences have been attributed to a temperature
gradient between the catalyst surface and the gas phase, which could modify the
selectivity for reactions such as oxidative coupling o f methane [2], W hile it is plausible
that the different dielectric properties o f the metal catalyst and the insulating support may
cause differential microwave absorption and heating, there is some question whether a
large gradient can be sustained between the catalyst surface and the gas phase or the
support. The work of Holstein and Boudart [39] shows, based on calculations, that no
appreciable temperature difference is possible between a metal crystallite and the
surrounding gas phase, even with the m ost exothermic reaction. Chapter 3 o f this
dissertation specifically addresses the case o f microwave absorption and cooling of small
metallic catalyst particles. While temperature gradients between the active catalyst and
the gas phase or the support seem unlikely, the unique mode of energy transfer may
represent one of the potential benefits o f microwave catalysis, particularly for an
endothermic reaction.
33
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Summary and Conclusions
The kinetics of CO oxidation have been studied using microwave and
conventional heating of an identical packed bed reactor. The temperature was measured
by insertion of a thermocouple into the bed after microwave power was switched off.
Optical probes were found to be unsuitable for temperature measurement under our
conditions. The reactor configuration and the non-isothermal nature o f the catalyst bed
influenced the accuracy of temperature measurement and two o f the three reactor
configurations led to the erroneous conclusion that microwave heating caused significant
rate enhancements for CO oxidation. From the standpoint of accurate temperature
measurement, the best configuration was a differential reactor bed containing the active
catalyst sandwiched between 1 g beds of blank y-alumina support. Our observations
indicate that there was no microwave specific effect on the kinetics o f CO oxidation on 5
wt% PCI/AI2O 3. The activation energy for CO oxidation as well as the order of reaction
with respect to CO was similar to that observed during conventional heating. At any
given temperature, the CO oxidation rate was marginally greater with microwave heating
than with a conventional clam-shell furnace. However, we feel that errors in temperature
measurement could easily account for the marginal increase in reactivity observed during
microwave heating. The CO oxidation reactivity serves as an in-situ probe of metal
particle temperature and suggests that the metal particles in the supported catalyst are no
hotter than their surroundings, during microwave heating.
34
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Thermocouple Correction and Error Analysis
As described previously, temperature measurements were made by quenching the
microwave field, and immediately inserting a thermocouple into the packed bed. The
temperature history was recorded on a strip chart recorder and the curve was extrapolated
to the initial temperature. Fundamentally, the cooling curve represents three processes: I)
the cooling of the packed bed due to insertion of the thermocouple, 2) heating o f the
thermocouple until equilibrium with the bed was achieved, and 3) cooling o f the
thermocouple/packed bed system. Therefore, extrapolation yields a false, but consistent,
temperature due to the presence o f the thermocouple. To account for the deviation, a
correction procedure was employed.
The conventional tube furnace was fitted such that the temperature could be
measured using the fixed controller thermocouple and also with the insertion apparatus.
To begin, the tube furnace was allowed to reach an equilibrium temperature as governed
by the temperature controller. The pow er was then doused, the furnace was opened to
expose the reactor tube to air, and the thermocouple was inserted. In the usual manner,
the temperature history was recorded and extrapolated to obtain the initial bed
temperature. In this manner, the known controller temperature could be plotted against
the unknown extrapolated temperature as shown in Figure 2.2. A best fit straight line
through these points yields the following corrective function:
T = 1.19T -1 5 .9 7
(3)
35
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where Tr is the true temperature and Te is the extrapolated temperature. This expression
was applied to all of the data obtained with the extrapolation technique.
An error analysis was performed by repeatedly measuring a fixed, known
temperature using the procedure described above. The furnace controller w as set to 260 C
and the measurement was repeated 10 times. This produced a maxim um range o f 5 C.
The total error was estimated to be +/- 5 C.
36
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CHAPTER 3: ON THE POSSIBILITY OF A SIGNIFICANT TEMPERATURE
GRADIENT IN SUPPORTED METAL CATALYSTS SUBJECTED TO
MICROWAVE HEATING
The contents of this chapter are published in CATALYSIS LETTERS , v. 47(#1) pp. 1-4
1997.
Introduction
The possibility of selectively heating the small metal crystallites in a supported
media has important consequences in some catalytic reactions. Often, undesirable gasphase reactions degrade the desired selectivity. If the small metal crystallites absorb
microwave energy at a substantially higher rate than their surroundings, there is the
possibility of establishing a temperature gradient from the reaction surface to the gas
phase. This may allow quenching o f the undesirable gas-phase reactions. An important
example is the oxidative coupling o f methane to higher hydrocarbons where the gasphase reactions of methyl radicals could yield economically unimportant products. It is
because of these important possibilities that we investigate the possibility of a
temperature rise in these supported metal crystallites. Figure 3.1 shows a sketch of a
supported metal catalyst system where microwave energy is being absorbed and
temperature differences may exist.
37
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Figure 3.1. A representation of a supported metal crystallite in a pore. The
sinusoids represent the presence of microwave energy. The Q terms represent the
rate of energy absorption by the crystallites and the support. The different T
subscripts represent gas, crystallite and support and in general Tg<Ts<Tc.
Previous work in the literature has suggested that a tem perature gradient may
exist from the surface to the gas-phase during microwave heating [24,35]. In this
previous work, the surface temperature has not been directly measured. However,
Chapter 2 revealed CO oxidation kinetics under microwave heating. O ur results suggest
that the reaction surface is not significantly hotter than the average bed temperature for
the catalyst system studied. It will be shown in this paper that it is highly unlikely that a
temperature gradient can be sustained from the particle surface to the surroundings.
38
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Heat Transfer Model
The analysis begins by considering a metal crystallite in a supported metal
catalyst subjected to microwave heating. A sim ilar analysis was performed by Holstein
and Boudart [39], where heat was provided to the catalyst via an exothermic chemical
reaction. These authors refuted the possibility of any temperature rise due to exothermic
reaction, but used a theory that is most appropriate when the Knudsen num ber is small
(mean free path / characteristic dimension = \ g/Dp л
1). We will use the theory
presented by Springer that [40] accounts for steady state heat transfer when the Knudsen
number is large, as is the case for a nanom eter sized crystallites in a micropore. Figure
3.2 shows a schematic of the system where energy is absorbed by the m etallic particle
and subsequently dissipated into the gas phase. First, we consider a steady-state energy
Figure 3.2. An illustration of a hypothetical metal crystallite that is suspended in
air inside a spherical cavity. Q<j represents the microwave energy that is dissipated
in the crystallite and Qi represents the heat loss into the gas by conduction.
39
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balance where the heat dissipated in the crystallite equals the heat lost only into the gas
phase. As per Holstein and Boudart [39], this represents the best opportunity for a
temperature gradient to be sustained; including the heat conduction into the support
would lower the tem perature gradient. Indeed, this is a reasonable approximation because
typical Pd or Pt particles are spheroids and only make a small area contact with the
support [41-44]. The steady-state energy balance is simply:
a
(3.1)
= Q
where the subscript d refers to dissipation via microwaves in the crystallite and / refers to
heat lost into the gas-phase. W hen the gas mean free path exceeds the particle size, the
term on the right may be written [40] as
ip M R T )
(3.2)
R\ is the radius of the crystallite, R2 is the radius of the pore, A is the surface area of the
crystallite, Cv is the m olar heat capacity of the gas, M is the m olecular weight o f the gas,
R is the molar gas constant, and P is the gas pressure. T is evaluated as the average of T\
and T2 at the respective surfaces, cq and a2 are the accommodation coefficients of the
two surfaces. A good discussion o f the accommodation coefficient is given in [40], but
suffice it to say that the coefficient is an empirical factor that indicates the efficiency of
molecular energy transfer to a surface; e.g. analogous to a sticking coefficient. Generally,
40
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engineering materials have accommodation coefficients in the range of 0.8-1 for common
gasses. Since we are examining the limiting case for poor heat transfer, we use both
coefficients = 0.8. Finally, the exponent b is a geometrical term, equal to 2 for concentric
spheres [40], For this simplified analysis, we assum e that the system consists of an
isolated metal sphere in a spherical cavity as shown in the Figure 3.2.
Equation (3.2) can be loosely interpreted in a simple way. The term containing the
accommodation coefficients indicates the efficiency with which gas molecules can gain
energy from surface 1 and deposit energy on surface 2. The pressure term, in brackets,
gives the collision frequency of molecules on the surface. Finally, the term containing the
heat capacity indicates the amount of energy stored in each molecule for energy transport.
The LHS of equation (3.1) was evaluated by using the expression for power
dissipated in a dielectric, non-magnetic material that is exposed to an electromagnetic
field [16]:
Qt = K V fE \e "
(3.3)
In this expression, V refers to the particle v o lu m e ,/is the microwave frequency, E is the
magnitude o f the electric field, гq is the permittivity o f free space (8.8 x 10'12 F/m) and
г" is the dielectric loss factor of the material. Substituting equation (3.2) and equation
(3.3) into (3.1) and solving for the temperature rise yields:
41
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//
(3.4)
6{ (IjzM R T 'f 2 } ^ 1 + % )
All of the parameters on the RHS of equation (3.4) are known, can be calculated, or
limiting case assumptions can be made. Numerical values o f the RHS terms for
calculating temperature rise are reported in Table 3.1.
The preceding analysis assumes that the mean free path o f the gas is larger than
the particle size. We now consider the case where the gas m ean free is the same order of
magnitude as the particle size, such that X - Dp. We choose a particle size of 100 nm
because this represents a practical upper limit in a typical supported metal catalyst. In the
transition regime, the heat loss in equation (3.2) is modified using [40]:
f faYT
(3.5)
where the subscript tr indicates the transition regime. For Ri = 100 nm, Rj = 200 nm, CC|
= 0.8 and X = 100 nm, the above expression is evaluated as 1.43. This value scales the
temperature rise, given by equation (3.4), such that ATu- = 0.7 AT.
Table 3.1 provides numerical values for the param eters in equations (3.4) and
(3.5). Using the parameters from Table 3.1, equation (3.4) becomes:
A T = (6.2xlQ ~5)Dpf e "
(3.6)
42
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for the case where the particle size is smaller than the mean free path, and
ATlr = (4.4 x l(T 5)г>?/г"
(3.7)
For the case where the particle size is approximately equal to the mean free path.
The crux of this analysis now lies in the determination o f e " .
Table 3.1. Numerical values used to estimate the temperature rise in small metallic
particles.
Value
Units
Justification
Electric Field
106
V/m
accommodation
coefficient
accommodation
Coefficient
Particle Radius
Pore Radius
Pressure
M olecular
W eight
Gas Constant
Average
Temperature
Heat Capacity
0.8
none
Breakdown of
Air
Optimized Heating
0.8
none
Optimized Heating
0.5x1 O'9
10x1 O'9
1.01x10s
28.97
m
m
kg/(m s2)
kg/kg-mol
Typical particle size
Typical pore size
Typical Pressure
MW o f Air
8314.4
500
J/(kg-mol K)
K
21000
J/(kg-mol K)
I O'9
m
Gas Constant
Typical Reaction
Temperature
Approximate Value
for Air at STP
Particle D iam eter
independent
variable
Hz
Variable
E
Definition
ai
Ri
r2
P
M
R
T
Cv
DP
f
Particle
Diameter
Electric Field
Frequency
Typical microwave
frequency
43
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Dielectric Loss in Metallic Particles
The preceding analysis yielded a relationship between commonly known or
determinable quantities, dielectric loss o f the metallic crystallites and their effect on a
temperature rise from the small metallic crystallites to the surroundings. The Drude [45]
theory of metals provides an estimate for the conductive loss of a metal:
(3.g)
=
1+ ty'r'
Q)г0
For metals, the room-temperature relaxation time t is 5-25 x 10-15 s and cor may be
neglected at frequencies up to the far infrared.
W agner [16,46] and Hamon [16,47] have examined a situation com parable to our
own study. In 1914 Wagner proposed a model for loss due to interfacial polarization
effects, the loss in a system composed o f a small volume-fraction o f a conducting phase
dispersed in a loss-free dielectric medium. The macroscopic dielectric loss is:
9 Vгl(<7/C0гn )
, COгn
[г(oo) + 2em]- + ( a / c o г 0 )
cr
Here u is the volume fraction o f the conducting phase, гm is the perm ittivity o f the
medium and is some fraction o f 9.34, the permittivity o f bulk alumina. The quantity a is
the low-frequency conductivity and e(░░) is the high-frequency permittivity o f the
metallic particles. The full expression in equation (3.9) increases at first linearly with a
44
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as in equation (3.8), goes through a maximum for a < coeo, and decreases as 1/a at higher
conductivity. At an operating frequency of 915 MHz, the conductivity at the maximum is
0.051 (Q -m )_1, far below metallic conductivities and allowing us to make the indicated
approximation. In 1953 Hamon [16,47] verified an equation similar to equation (3.9) by
measuring the dielectric loss o f copper pthalocyanine particles dispersed in a paraffin
matrix.
45
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Estimating the Temperature Rise
We estimate the specific loss factor:
-
=
u
(3-10)
CT( D ,)
where a is a function of particle diam eter Dp, the result of internal surface scattering
[48,49] :
o (D ) = _ г f a ▒ _
v pJ 1+A t,/D ?
(3.i o
The bulk conductivity a (░░)is taken as 107 (Q m)"1 and the electron mean free path A.e as
7.5 nm, representative of either Pd or Pt.
For particles 1 nm in diameter, the particle specific loss factor is 2.05 x 10'6 The
upper limit of the temperature rise is:
AT = (6.2 x i o ' 5) г ? / г " / u = 1 .6 x lO '10K
(3 1 2 )
and for particles 100 nm in diameter, the particle specific loss factor is 2.4 x 10'7 The
upper limit of the temperature rise is:
46
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A r = (4.3 X 10 ~*)ppf г ? t v = 1.1 x 10?'░K
(3.13)
This limiting case (optimal heating) analysis indicates that the particles are in thermal
equilibrium with their surroundings.
47
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Supporting Evidence
The kinetics of the carbon m onoxide oxidation reaction over 59c Pd/AFC^ were
studied under conventional versus microwave heating in Chapter 2. The reaction
temperature was measured using a thermocouple that was inserted into the reaction zone
after the microwave energy was turned off. A temperature decay curve was recorded and
extrapolated back to the true reaction temperature. The process was calibrated and an
error analysis was performed. This method only allows observation of the bulk support
temperature. The metal particle temperature was not observable due to the low mass
fraction and rapid transient behavior of such small objects. However, the rate o f reaction
provides an indirect measure of the metal surface temperature. We would have expected
that the microwave-heated reaction rate would be higher than that for conventional
heating at a given temperature if a significant temperature gradient existed between the
metallic particles and their surroundings. The Arrhenius plot from Chapter 2 is repeated
here in Figure 3.3, and the rates o f reaction are found to be nearly identical within
experimental error at any given observed temperature. This indicates that the temperature
of the microwave-heated metallic particles is not significantly higher than the
surrounding support material.
48
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?
c
o^4
U
3
TJ
O
i_
(X
CN
o
4.0
M icrowave
.?-I
Conventional
3 .0
??I
2.0
u
<4 -1
o
<u
C3
w
'g
a ?i
0.0
u~*
CN
1000/T(K)
Figure 3.3. Arrhenius plot from Chapter 2 that compares the rate of the CO
oxidation reaction under microwave versus conventional heating. A
stoichiometric mixture of CO and O 2 was used with a 5 wt% Pd/alumina catalyst.
The reaction rate was insensitive to the mode o f heating, and therefore provides
indirect evidence that the surface temperature o f the metal crystallites is not
significantly hotter than their surrounding support.
49
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Conclusion
A best-case analysis has been presented for the largest possible temperature
gradient, relative to the surroundings, of small metallic particles that are exposed to
microwave energy. The analysis assumes that the metal particles are embedded in a lossfree dielectric support, hence the model is not intended for calculating the total power
consumption. The temperature difference between the metal particle and the
surroundings was calculated for two limiting cases: 1) gas mean free path greater than
the particle size and; 2) particle size comparable to the mean free path. In both cases, the
temperature rise was determined to be insignificant. W e do not believe it is possible to
cause a temperature gradient between metallic particles (1-100 nm) and their
surroundings in a typical supported metal catalyst structure (metal particles deposited on
a ceramic support) by using microwave energy. This conclusion was supported by the
observed reaction rates o f the microwave-heated CO oxidation reaction.
50
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CHAPTER 4: THE APPLICATION OF MICROWAVE ENERGY TO THE
ENDOTHERMIC METHANOL/STEAM REFORMING REACTION
Introduction
Endothermic reactions pose design challenges because energy consumed by the
reaction causes poor surface area utilization on both the individual pellet level and at the
reactor level. Conventional heating occurs by transferring heat through the surface of a
catalyst pellet, or reactor wall, resulting in a temperature drop as distance from the heat
source increases. As a result, surfaces far away from the heat source are poorly utilized
due to the decrease in reaction rate that results from the temperature drop. As an
alternative to a conventional heat source, microwaves heat volumetrically if the
penetration depth is large, such that the temperature drop due to an endothermic reaction
could be negated. This is shown qualitatively in Figure 4.1.
The methanol steam reaction (MSR) proceeds as follows:
MeOH + H 2O ? > CO 2 + 3 H 2
(4.1)
The MSR has been studied for producing H 2 to supply proton-exchange membrane fuel
cells [50, 51,52]. These fuel cells are the current favorite for use in electric cars and the
MSR is a good candidate for producing the requisite H 2. Unfortunately, limitations in
efficiency have been encountered due to the large endothermicity of the reaction [53].
These efficiency limitations affect the compactness o f the unit and the overall cost, partly
because of increased catalyst requirements. In addition, combustion o f methanol currently
51
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provides heat to the reaction. M icrowave heating could remedy these problems. As of
1984, the efficiency of
T
a)
MW
-AH
r
b)
Figure 4.1. a) Illustration o f how microwaves add energy along the length of an
adiabatic packed bed reactor where an endothermic reaction occurs. Curve a
represents the temperature profile when the reaction consumes the sensible heat
from the gas stream. Curve b shows the temperature profile when microwave
heating is added, b) Conceptual representation o f endothermic temperature
profiles, microwave heating profiles, and their superposition.
microwave heating of dielectric materials was approximately 80%, from the power
source to the load. The microwave heating method also avoids the burning of methanol,
the current method for providing heat to the reaction, which inhibits the process as a
"clean fuel technology".
This chapter will provide an analysis to show that under optimal conditions,
microwave energy can provide heat internally, and the available catalyst surface area is
52
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more effectively utilized. This has the added advantage o f decreasing the required mass
o f the catalyst bed that makes the system more attractive in terms of cost and
compactness. The theoretical analysis will be followed by experimental verification and a
discussion o f the experimental results. The theory provided here can be easily extended to
other important industrial endothermic reactions such as ammonia synthesis and the
reforming o f methane [54,55].
53
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Modeling
The nature and magnitude o f thermal gradients within a m icrowave heated
catalytic reactor has not been extensively studied. Therefore, a major goal o f this research
has been to gain a better understanding o f the thermal gradients through experiments as
well as a theoretical study.
I performed an extensive search of the literature for papers relevant to the
modeling of microwave heated packed-bed tubular reactors, and no references were
found. However, the mathematical model of a two-dimensional tubular packed-bed
reactor differs little from a conventionally heated reactor and many references exist that
analyze this configuration. Any model of a microwave-heated packed bed should
therefore begin with this previous work, which is discussed briefly here.
In 1971, De Wash and Froment [56] provided very general equations to solve this
problem. They develop the general two-dimensional coupled heat and mass transfer
equations according to mechanisms that were deemed important by Yagi and Kuni [57]
in 1957. These mechanisms include conduction through the particles, particle-particie
conduction through contact surfaces, conduction through the stagnant boundary layer,
radiation effects, fluid convection and conduction, transfer from fluid to solid and internal
particle (void) radiation. O f course, these equations also contain the non-linear Arrhenius
terms that account for the production/consumption o f heat and mass. In 1990, De
Azevado, Romero-Ogawa and W ardle [58] published a very thorough review of the
literature regarding modeling o f tubular packed-bed reactors. These authors indicate the
practical usage of these models that include scale-up, change o f feedstock, effect of
different process parameters, effect of transient trends, and optimization. The review
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provides the most general form of the equations and boundary conditions. This general
form includes inter- and intraparticle transport effects, transport properties for both the
solid and fluid phase and other realistic characteristics o f a tubular packed-bed reactor. In
1991, Lemcoff, Duarte, and Martinez published a complete treatise of Heat Transfer in
Packed-Beds in Reviews in Chemical Engineering [59]. This publication is text-book
style and includes information regarding estimation of heat-transfer parameters,
estimation o f pseudo-homogeneous heat transfer coefficients, solid-fluid heat transfer
effects, and heterogeneous heat transfer effects. Also, a chapter is included concerning
the effects o f the chemical reaction on the estimation of the heat transfer parameters.
Since De Azevado and coworkers published their paper in 1990, other papers that
consider this subject have been published. In 1991, Grigoriu, Balasanian and Sim iniceanu
[60] exam ined a model of a 2-D reactor to carry out the ammonia synthesis reaction.
Since the am m onia synthesis reaction is endothermic, this paper is of particular relevance
to this research. The authors developed a model that agreed with experimental data
acquired from a real industrial-scale reactor. They conclude their model was valid for
predicting the behavior of industrial reactors o f this type. In 1993, Wijngaarden and
Westerterp [61] published a paper detailing a 2-D heat transfer model that criticizes the
use of the pseudohomegenous approach for estimating transport properties. They avoid
using two radial parameters for both heat and mass transfer, the parallel approach, and
present a model that employs a series approach where transfer occurs from the fluid to
the solid and back to the fluid, etc. Also in 1993, Borkink, Borman, and W esterterp [62]
model a wall-cooled packed-bed. In this work, the authors reveal the confidence intervals
that result from using the pseudohomogeneous approach for calculating heat transfer
55
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parameters. They also examine the confidence intervals that result from the choice of
boundary conditions.
More recently, in 1995 Legawiec and Ziolkowski [63] simulated heat transfer in a
packed-bed tubular reactor while considering the inhomogeneity of the system. Models
prior to this considered the bed voidage to be radially uniform. The uniqueness of this
model arises by accounting for variations of the bed voidage in the radial direction. The
most recent article reviewed was published in 1996 by Bart, Germerdonk and Ning [64],
This work models a tubular activated carbon adsorber for the removal of toluene. The
model presented is two dimensional and includes the non-isothermal nature of toluene
adsorption. In addition, this considers ?maldistributed? flow, i.e. the existence of a radial
velocity profile.
The review of this literature has provided information to model a tubular packed
bed reactor over a wide range of complexity. One could model the entire reactor
assuming the packed bed and fluid within both have lumped effective transport properties
and the flow can be approximated by plug flow. Conversely, one could include radial
flow variations, inter- and intraparticle temperature and concentration variations. Also,
transport properties for both the solid and fluid phases could be used. There are obviously
many possibilities. The current work focuses on how microwave heating changes the
performance o f chemical reactors. In any model, the addition of a homogeneous energy
source term is required. Again, the complexity o f the model would dictate the nature of
this term; i.e. whether the term is completely homogeneous or whether the term is applied
only to the solid phase.
56
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Single Catalyst Pellet Model
The coupled heat and mass transfer equations have been numerically solved for a single
catalyst pellet that is subjected to microwave heating:
(4.2)
+ Q mW + Qnn(r )
where T is the temperature, C m is the concentration of methanol, k is the thermal
conductivity, D is the effective diffusion coefficient, RMaccounts for the consumption of
methanol by chemical reaction, Qrxn represents the heat generated by the reaction, Q^w is
the heat generated by microwave energy dissipation. The rate law for reaction over an
alumina/CuO/ZnO catalyst (C18HC CCI, Inc.) has been determined by Amphlett and
coworkers [52]:
R? = [l. 15x10s + In(лs,? > .4 1 x l0 s } ^ j e x p ( - | j ) c ? = k C ?
/
-E
(4.3)
\
(4.4)
57
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E^ is the activation energy, R is the gas constant, A is the pre-exponential factor, P is the
total pressure,
is the steam to methanol ratio (molar), and AH is the heat o f reaction.
Under the conditions of interest A = 30,1283.0. and Ea = 84100 J/(mol K). Combining
equations (4.2) and (4.4):
0 = D l _ ▒ l f K M(r)
- Aexp
r~ dr
dr
Ur(r)Jc "(r)
(4.5)
d r_2 dT(r) + QiUW+ AHrxAe x p - E ? \ I
0 = k ^1 ?
CM(r)
RT(r))
r 1 dr
dr
Useful physical insight is gained by non-dimensionalizing the equations. First,
introducing the following relationships for the dependent and independent variables,
respectively:
C*(r*) = ^ t^ ;
C.
1 d .2 d c \ r )
0 = - rr ? r r ?
r ?2 dr'
dr'
T(r)-T
0 ( r ?) =
. _ r_
r ~ R
(4.6)
1
\ a R2
-E?
C' ( r ' )
i ? exp
D
[ R KTs(Q(r ) + l)J
(4.7)
I
d
7^57
2 dQ(r')
[QMWR 2 l
\ c sAHrinR 2A_
J+{
a.
-E?
exp { RgTsm r ' )
C'{r)
+ \ )j
The second term in the RHS o f the concentration equation (4.7) is the Thiele Modulus
squared ( 0 2), and we will call the coefficient o f the exponential 0 2 ?. The third term in
the RHS o f the energy equation is a Damkohler Number (Da). Similarly, we will call the
58
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coefficient of the exponential D a?. The second term in the RHS o f the energy equation
relates the rate of microwave energy absorption to the rate o f energy conduction to the
surface of the pellet. This term is defined as the ?microwave? number, M W . Finally, by
defining gamma as E /R eT s, equation (4.7) can be written as:
1 d .idC'(r')
C( r ' )
0 = ~ - f - r r ? - _ v; - / -fc>2,]exp
dr'
r ' 2 dr'
[ (й(#" ) + D )
0=
If IMWI л
1
d
.idO(r')
r -2 dr'
dr'
.
.
(
?+ M W + [Z)a?]exp
~7
( 0 ( r ) +1)
\
(4.8)
C\r)
IDal > 1, concave up temperature profiles will develop due to the dominance
of the endothermic effects over the microwave heating effects. Conversely if IDal л
IMWI > 1, concave down temperature profiles will develop. For the cases where IDal =
IMWI or IDal л
1 and IMWI л
1, no significant temperature gradients exist, and the
concentration equation can be solved analytically for Q = 0. The condition IDal = IMWI
represents the condition where the energy per volume supplied by the microwave is
balanced with the energy consumed by the reaction occurring at the surface temperature.
This effectively zeros the net pow er input to the pellet and no temperature rise or drop
can occur.
These equations need four boundary conditions to obtain a unique solution. In
order to facilitate the numerical solution, we will use boundary conditions o f the first
kind at the pellet surface:
0 ( r ? = 1) = 0
C \ r = 1) =1
<4'9)
59
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For a numerical solution, the values o f the concentration and temperature, as well as the
values of the derivatives, must be specified at r* = 0. The derivatives are known to be
zero due to symmetry. However, the concentration and temperature are not known, and
an iterative procedure must be employed. To obtain the solutions presented here, the
Mathematica [65] program, which uses an adaptive Runge-Kutta routine, was used. To
Find the solution, a set of possible temperature and concentration values at r*=0 were
tested until the proper boundary conditions at r*=l were obtained. The Mathematica code
used for this analysis is provided in Appendix B.
Reference [66] gives all of the data necessary for calculating <p2 ? and D a?. For the
numerical calculations, <p2? = 2 x 10s , D a? = 2.7 x 107, and y = 16.3. In addition, a value
of MW = 0.6 was empirically found to satisfy the temperature leveling requirement.
Figures 4.2 and 4.3 show the concentration and temperature behavior for MW = 0.6 at a
1.250
M icrow ave Healed
C onventional H eating
0.000
й
o
d
й
o
й
IT ,
fN
o
Dimensionless Radius
Figure 4.2. Numerical solution for the concentration o f methanol from the
coupled heat and mass transfer equations given in the text. The inset is a
magnification of the near-boundary behavior and represents an overall reaction
rate increase of approximately 2x. The microwave curve is the lower curve.
60
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U .U IU
C
UJ
3
-i-j
cuO
>
<L>
0.000
Microwave
( 0 .010 )
Conventional
( 0 .020 )
г
TJ
<U
N
73
( 0 .0 3 0 )
( 0 .0 4 0 )
( 0 .0 5 0 )
Norm alized R adius
Figure 4.3. Numerical solution for the temperature from the coupled heat and
mass transfer equations given in the text. Microwave power was adjusted in the
model to make the temperature profile as flat as possible. The microwave curve is
the upper curve.
gas phase temperature of 600K. This temperature is chosen for illustration
and represents the upper operating temperature of the C18HC catalyst that is typically
used for this reaction. In addition, there are other terms to consider in the MW term to
show that 0.6 is a reasonable number. An order of magnitude estimate for the thermal
conductivity is 0.5 W/(m K), and a typical pellet radius is 3 mm. Using equation (1.4)
evaluated at 1 GHz and a dielectric loss o f 0.001 (an assumption based on the dielectric
loss of alumina), the required electric field is approximately 5 x 105 V/m. This represents
a reasonable value.
The overall reaction rate can be determ ined from the slope, representing the mass
flux, at the boundary of the pellet. The inset on Figure 4.2 shows that the slope (flux) is
higher for the case where MW = 0.6. This is the most significant conclusion o f this
61
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analysis: In an endotherm ic reaction occurring in a porous catalyst pellet, the reaction rate
in the microwave heated case will always exceed the rate in a conventionally heated
pellet. In fact, this particular analysis indicates a volumetric rate increase of
approximately 2.
This is an important conclusion in the context o f the autom otive fuel cell. As
mentioned previously, size and economy are tantamount issues. If the production of H,
can be increased by a factor of two on a volumetric basis, the required catalyst mass will
be substantially less. This has positive benefits in terms of weight, size, and energy
required for heating.
62
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One-Dimensional Integral-Bed Reactor Model
The previous analysis indicates that microwave heating can beneficially effect
endothermic catalytic reactions within a single pellet. In practice, the reactions are
carried out in an adiabatic packed-bed in which the gas is preheated. The sensible heat in
the gas is consum ed and the gas is then reheated using an interstage heater before each
reactor stage [67] such that the desired conversion is achieved. I will perform a
theoretical analysis on an adiabatic packed bed reactor, using the parameters from the
MSR assuming radial heat transfer effects are negligible. This provides a com parison
between a single stage endothermic tubular reactor and a single stage microwave reactor.
In addition, the experiment has utility in demonstrating the ability of the microwave to
?insert? energy into locations that are not readily accessible by conduction and
convection when the rate of endothermic energy consumption exceeds the rate o f heat
transfer. The theoretical comparison begins by performing a shell mass balance on a
tubular reactor that results in the following differential equation:
d.( y г y ) _ k c
dW
=Q
(410)
"
where v is the volumetric flow rate, W is the catalyst weight coordinate and k is the
specific reaction rate. The rate law, as mentioned previously, is first order in methanol
[52,66]. Volume change occurs during the M SR, therefore:
v = u0(l + fcX)?
(4.11)
63
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(4.12)
c? =cm {\-K X)^
k =
^ 4
(4.13)
^ )
where k is the parameter accounting for the volume change on reaction, X is the
conversion, and the ?0? subscripts refer to the conditions at the reactor inlet. Inserting
(4.11), (4.12), and (4.13) into equation (4.10):
dX
,
f - E aY l ~ X \ T
n
vo ?
^
p
\
?
r ; ? =░
dW
V R T A 1+ kX / Tn
(4.14)
An energy shell balance leads to an equation for the temperature profile:
- * w c,
+v
H eat
21 - m k C ╗ = 0
<4 - 15)
again using equations (4.11), (4.12), (4.13):
------------------ T
T0
L
K
----- +2(1 + kX ) T --------------- h------------------------------AHkCA0-,--------r ? = 0
dW
dW
p ca,
+ KX) T
J
(l
(4.16)
where To is the reactor inlet temperature, T is the temperature, and Cp is the heat capacity
of the fluid, which is assumed constant. The assumptions used for this derivation include
isobaric, adiabatic, plug flow, and constant density operation.
Q mw
is the power
64
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dissipated in the catalyst by the microwave. Equation (1.4), evaluated at 915 MHz and a
dielectric loss of 0.001, was used to calculate the power dissipation.
The adaptive Runge-Kutta routine found in M athem atica [65] was used to solve
these equations for the reaction occurring over 1 gram o f catalyst. The M athematica code
can be found in Appendix C. Figure 4.4 shows the reactor conversion and temperature
profiles for various applied microwave power levels and Figure 4.5 shows the
dependency of conversion on the applied microwave power. It is apparent that adding
heat volumetrically partially negates the energy consumption o f the endothermic reaction,
thereby increasing the overall conversion. The result bears a strong resemblance to the
case where heat is added along the length o f the reactor [71]. However, in that case, a
radial temperature profile would develop, which would not be present in the
65
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1
Field Strength
0.75
X
o
co
o>
ao
0.5
2.5 x to 5
5x I05
<J
0.25
T = 580 K
o
Catalyst W eight (g)
a)
600
550 -
0
3
500 -
2 .5 x I 0 5
5 x 10s
450 -
400
o
Catalyst W eight (g)
b)
Figure 4.4. a) Theoretical conversion profiles over C 18HC catalyst for an inlet
temperature o f 580 K and three different electric field strengths, b) Theoretical
temperature profiles for different electric field strengths. The upper lines belong
to 5 x 105 V/m, the middle belong to 2.5 x 105 V/m, and the lower belongs to 0
V/m.
66
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I
0.8
-
0.6
-
X
c
o
o>
c
o
u
0.4 -
0.2
+
L
L
J
N
O
E lectric Field Strength (V /m )
Figure 4.5. Theoretical conversion as a function of applied electric field strength.
Plot shows how microwave energy can increase conversion in an ?adiabatic?
packed bed reactor.
microwave heated case. In addition, the heat transfer surface area is relatively low if the
heat is added through the wall of the reactor. In the microwave case, the energy dissipates
over a high surface area, decreasing the magnitude of the local heat flux and eliminating
high wall temperatures. Again, the model suggests that microwave energy will dissipate
where the endothermic reaction consumes energy, without relying on convective and
conductive heat transfer.
67
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Two-Dimensional, Non-adiabatic Packed-Bed Model
A central hypothesis which has evolved in this research suggests that the
microwave energy required (Q mw) to achieve a given conversion (X) is less than the
conventional energy required (QCOnv) to achieve the same conversion when all other
conditions are identical. The effect is presumed to be most prevalent when the rate of
energy consumption by the endothermic reaction and the rate of axial heat transfer
exceeds the rate of heat transfer by radial conduction. To test this hypothesis, I chose a
tubular reactor where radial heat transfer effects were non-negligible as a theoretical test
platform. A schematic is shown in Figure 4.6. The most rigorous treatment
Feed
1 g catalyst
z= 0
z= L
Figure 4.6. Schematic of system to be analyzed to determined endothermic
reaction behavior where radial heat transfer effects are included.
begins with a model that accounts for the axial transport of heat and mass by convection,
and the radial transport of heat and mass by diffusion. Since the model must include an
endothermic reaction heat sink term and the temperature dependent reactant sink term,
68
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these two-dimensional equations for heat and mass transfer are coupled and non-linear.
This complexity precludes an analytical solution, but the general behavior can be
illustrated using a numerical approximation. The most general mathematical description
of a tubular packed bed reactor is given in the review article by De Azevado, et al. [68],
and Froment and Bischoff [69] provide a somewhat more specific model originally due to
De Wasch and Froment [56]. For the purposes of illuminating the fundamental
differences between the microwave and conventionally heated reactors, several
simplifying assumptions were made. I derived the model subject to the following
assumptions:
d 2C
1. axial dispersion is negligible: D - r r - =
oz~
d 2C
=0
oT~
2. Intra- and interparticle gradients were neglected.
3. The packed bed was assumed to be pseudohomogeneous in that overall
transport properties such as an effective thermal conductivity and radial
diffusivity were assumed.
4. Plug flow.
5. Negligible pressure drop.
6. No volume change on reaction (constant volumetric flow rate).
7. Constant properties such as gas density and heat capacity.
These assumptions lead to the following equations:
dT
d2r
i dr)
HW
iac^_
dC = eD
n d c
u ?
I dr2 + r dr ) ~ pBrM'░"
J dz
69
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(4.17)
where
' McOH
= A exp
I -E
I RT
(4.18)
C = C(r,z)
T = T(r,z)
In these equations, pe is the catalyst bed density, pg is the gas density, k is the radial
thermal conductivity, us is the gas velocity, Cp is the gas heat capacity, and e is the bed
voidage. As with the previous models, AH is the heat o f reaction and Q^v is the heat
supplied by the microwave. The equations were non-dim ensionalized using the following
dimensionless dependent variables:
where R and L are the radius and length of the reactor, respectively. Making the
appropriate substitutions and rearranging the physical parameters to make the equations
non-dimensional:
dC*
dz*
dT*
**
eDL
d'C *
u 5R 2 \ dr *2
1 dC*
r* dr*
d 2T *
R2?sPgCP d r * 2
Lk
ParMeOHL
? s C0
1 dT*
PB^HrSUOHL
Q,wL
r* dr*
usPgCPTo
usP*CrTo
The dim ensionless param eter groupings have familiar definitions:
70
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(4.20)
dC* _
dz*
1 3 r *dC*}
?Da,
Pe M r* dr * r dr*
dT
a
_ d r *'
dr*
dr'-
i
dz*
PeH
?Da? + Mw
(4.21)
where the dimensionless ratios are:
eD L
w
Lk
h
Dai = P s ^ ohR . Dci i = P b^ suohL
uC.
?<PxCpT0
QnwL
Mw =
(4.22)
u<PsCnTo
The boundary conditions are:
C * (0, r*) = 1
T * (0, r*) = 1
dT* I
dC*
rir
a r * I r*-=o
^r
ur *
dcdr*
(4.23)
=0
r*=R
qR_
dT*
dr *
=0
I r * -0
r ? =R
kTn
In order to numerically solve these equations, the equations were descretized by
determining the average value of the derivatives across a radial cell. The average value
per unit length of the concentration or temperature derivatives at any node i,j+l is found
71
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as follows. In this discussion, for brevity, the symbol <d will be used interchangeably for
T* or C*.
1 r░f 1
0.51j* ^
AA I*?
' 1 3
*
r * dr*
1
X./+I
2k_
^+0 5
AA
3 r:
p i+ 0 .5
M
= J i-0
/
,
5 2 K rd r =
,
?
a r* 3 0 * 'jIjtrdr
^
dr*)
30:
ri- 0. 5
1+05.y
+
i
3 r:
(4.24)
I-05./+I
\
(4.25)
r''- 0 5 '
where O represents either dimensionless temperature (T*) or concentration (C*), the
index i represents the descretized radial coordinate, and j is the descretized axial
coordinate. At the boundaries:
r i+ o 5 ? r x
30
3 r:
? R
iV.y+I
(4.26)
r i-0 5 ? 0
30:
3 r : !./+!
=0
Using a single point approximation to the derivatives in equation (4.26)
30*
dr*
f <*\+l.y+l - ^ ?./+l
1+
0
.5
\
Ar *
/
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( o ;./+I - o ; _ Ly+1}
<*D*
d r*
1-0.5
Ar
\
*
/
and the axial derivative was replaced with the following approximation:
<I╗ , - O
<&>*
Ik*
(4.28)
Az *
Substituting equations (4.24) - (4.28) into equations (4.21) and rearranging the
expressions such that all Q.J+i and T,.j+l are on the LHS and all other terms (source terms)
are on the R H S:
/+1 + X
n
о
(
4 -2 9 >
where 0 , is a generalized source term and can include the reaction term (Dai or Dan) and
the microwave source term (MW). The coefficients a , (3, yare:
_
aо, =
1 _l_
Az
y<t>, =
9z r1-0.5
2 (*1+0.S ~l~ ^1-0.5)
Pe*(rr^5 - r ^ 5)br
- 2 ri+Q.5
(4.30)
73
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With the application of the boundary conditions and indexed radius values:
ao>*
о < t> i ~
Y
on
=0
dr'
(4.31)
l.y + l
The equations can now be represented entirely in matrix form:
m
(4.32)
? <i>/+1 = [<f>; + 0 ;
where the d>.; are the source terms in the RHS of equation (4.29), and the O, H are the
unknowns to be found. The overbars indicate that O is a vector and it is N-dimensional.
The matrix M is tridiagonal and in general for both T* and C*:
7 * .
& 02
0
...
0
0
0
0
Yoz
0
...
.. .
>/V
Pos
0
0
P*2
7 < t> :
0
0
...
...
0
0
~p*l
7*1
^02
& Oi V
7^ ?Da? + Mw
?
T, ?Da? + Mw
Ti
=
Tv - Da,, + Mw; + j v p = _^_}
kTn
I
/+> J s . i-i
C," - Da,
~c;'
? cl
=
C\ - Da,
(4.33)
...
P
on
7+1 c;. 7+1
C,; - D a , + {VF = 0 }
Resuming the use of the general dependent variable O , the value at the j+1 node is found
by inverting the matrix M and m ultiplying the result by the source vector on the RHS of
equation (4.33):
74
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(4.34)
The algorithm for solving this equation was straightforward. First, a, b, and g
were loaded into separate arrays. Also, arrays of the entry condition for T* and C* were
built; i.e. O i=i_iV = 1.0. These values o f T* and C* were also used to calculate the
reaction term for that cell. The International Math Standards Library (IMSL) [70] routine
LSLTR was then called to invert M and solve equation (4.34). This algorithm uses T*
and C* information from the j index to calculate C* and T* at the j+1 index. Since the dz
step size was small and the C* dependency for each index was linear, this was o f little
concern. However, T* was imbedded in the non-linear (exponential) reaction term and
small changes between indices produced large errors. Therefore, iterations were
performed at each index in order to modify the temperature used in the reaction term
(T*?) until a suitable convergence was achieved. This criteria was:
(4.35)
N -2
The procedure was repeated with the j+1 arrays reassigned to the j arrays until the
procedure was completed. A complete listing of the FORTRAN code implemented for
this procedure is given in the Appendix D.
Recall that the goal of this numerical solution is to show that the addition of
volumetric microwave heating, represented by Mw, will lessen the severity o f the radial
75
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temperature profiles and will lead to more efficient conversion o f reactants, i.e. consume
less energy to produce the same conversion. More concisely, I wish to prove that under
some conditions, it requires less energy to induce the same conversion when the energy
is delivered in the form of microwaves versus conventional means. Mathematically:
(4.36)
Qmw < Qcon
where Qmw represents the driving energy supplied by microwaves and Qcon represents the
energy supplied through the tube walls in the conventional manner. In the model, this can
be calculated in two ways: 1) Direct calculation of the energy required in both cases: 2)
calculation of the average exit temperature in both cases. In this report, I choose to
calculate the exit temperature because this parameter is easier to observe experimentally
than measuring heat input.
An energy balance will illustrate the validity of this approach:
(4.37)
for the microwave case, and for the conventional case:
(4.38)
con
where Qin is the heat supplied to the reactor by convection, Q0Ut is the heat that leaves the
reactor by convection, and Qrxn is the heat consumed by the endothermic reaction. If the
76
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conversion is identical in both cases, the heat consumed by the endothermic reaction is
identical in both cases and:
?out.am +Q
Q,n
(4.39)
~Q
The Qin cancels if the inlet conditions are identical. The following substitutions are
appropriate:
Q?u,,on = ?CrT?
(4.40)
QoU
,.nm- = mCpTa
?out.ntw
p out .mw
where the T,
and TouU.on are the average exit temperatures. Making these
substitutions into the energy balance:
-m C p T o u tw + Q m
╗
- - , i l C p T ,,U,.cur.
+
Q cn r.
(4.41)
(4.42)
Equation (4.42) states that the difference between the exit temperatures in the two
reactors, scaled by mCp , is a direct indicator o f the difference in energy required for
each process. Thus model calculations, other than surface plots for the purpose of
visualization, are presented as Conversion (X) as a function of exit temperature using the
numerical values given in Table 4.1.
77
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Table 4.1. Numerical values used in 2-D model calculations.
Parameter
Value
Units (SI)
Comments
Eff. thermal conductivity, k
1.0
W /(m K)
Est. using Fig. 11.7.1-2 in [691
Pre-exponential, A
30,1283.0
m3/(s kg)
ref. [66]
Initial concentration, Co
12.2
mol/m3
50% molar ratio
Initial temperature, To
575
K
approaching upper limit for catalyst
Catalyst bed density, pb
1000
kg/m3
Estimated from data in [661
gas density, pg
0.75
kg/m3
Estimated using ideal gas law
particle diameter, dp
1 5 0 x 10*
m
measured
bed radius, Rb
4 x 10'3
m
known
bed length. Lb
15 x 10?3
m
known
Average gas velocity, v
0.2
m/s
measured in experiment
Activation Energy, Ea
84,100.0
J/mol
ref. [52], ref. [66]
Heat of Reaction, AH
-60,000
J/mol
ref. [66]
Heat Capacity
35.0
J/(kg K)
Est. from information in [66]
M ass Peclet number, PeM
23.0
none
Est. using Fig. 11.7.1-1 in [69]
Heat Peclet Number, Pen
0.2
none
Estimated from values in this table
Mass Damkohler Number, Dai
6.3r,vieOH
none
Estimated from values in this table
Heat Dam kohler Number, Dan
lOrMeOH
none
Estimated from values in this table
The dimensionless parameters summarized in Table 4.1 will henceforth be referred to as
the ?base case? and were used to generate the surface plots shown in Figure 4.7 - Figure
10 .
Figures 4.7 - 4.10 illuminate the stark differences between the two modes of
heating. In the conventional case heat must be transferred from the walls into the gas
stream and through the packed bed. Significant radial profiles will develop if the rate of
energy consumption by endothermic reaction exceeds the rate o f axial heat transport.
These relative rates are characterized by the dimensionless parameters in Table 4.1. Pe
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(mass or heat) indicates the relative importance of axial convection to radial diffusion.
Dal indicates the rate of mass consumption by reaction to the transfer of mass axially by
convection, and D ali gives the ratio o f the rate o f heat consumption by reaction to the
rate of heat transfer by axial conduction. Finally, the microwave number is a ratio of the
rate of heat dissipation by microwaves versus the rate o f axial heat transfer.
79
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Axial Coordinate xlOO
Figure 4.7. Temperature profiles from r*=0 to R (c.l. is to the left) for the base
case when the reactor is heated conventionally using 8.2 W atts. Conversion is
80%.
In н
coordinatexlOO/.
Figure 4.8. Concentration profiles from r*=0 to R (c.l. is to the left) for the base
case when the reactor is heated conventionally using 8.2 W atts. Conversion is
80%.
80
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Axial Coordinate xlOO
Figure 4.9. Tem perature profiles from r*=0 to R (c.l. is to the left) for the base
case when the reactor is heated by microwaves using 7.1 W atts. Conversion is
80%.
Axial Coordinate xlOO
Figure 4.10. Concentration profiles from r*=0 to R for the base case when the
reactor is heated by microwaves using 7.1 W atts. Conversion is 80%.
81
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A value of 0.2 for the Pen number, being an indicator o f the relative importance of
axial heat transfer versus radial heat transfer, indicates radial heat transfer dominates, but
not substantially. This is reflected by the moderate profiles in Figure 4.7. The magnitude
o f Dan is more difficult to ascertain because this parameter varies exponentially with
temperature and linearly with concentration. Its value can change drastically throughout
the reactor. Radial profiles develop for concentration in this case as well because of the
elevated temperatures at the walls. The reaction rate in the region o f the walls exceeds the
rate closer to the center o f the reactor. When the rate of reaction at the walls exceeds the
radial diffusion rate, the profiles will develop as shown in Figure 4.7.
The model for the microwave heated reactor shows no radial variation for either
heat or mass. As suggested by the original hypothesis, adding heat in this manner does
not rely on conduction or convection and the heat is dissipated hom ogeneously as it is
consumed by the chemical reaction. Axial variations exist because the consumption of
heat by reaction varies along the length of the reactor as the temperature and
concentration change while the energy dissipated from microwave heating remains
constant.
Figures 4.11 - 4.15 show how the conversion versus reactor exit temperature
varies for increasing axial flow rates. Lines have been added to indicate the temperature
for each case at 80% conversion. The model predicts that the exit temperatures for both
the microwave case and the conventional case increase with increasing flowrate.
However, the increase in exit temperature for the conventional case exceeds the increase
predicted for the microwave case. This result tends to support the hypothesis given by
equation (4.36).
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'?
!
Microwave
Conventional i
Relative Flowrate: 0.1
0.8
I 0.6
s
U
0.4
0.2
0.8
1.4
1.2
1.6
1.8
Normalized Exit Temperature
Figure 4.11. Conversion versus normalized exit temperature for the case where
the flowrate is 0.1 x the base case. In this case the difference is minimal.
Conventional
M icrowave
Relative Flowrate: I
0.8
c
0
0.4 -
0.8
1
1.2
1.4
1.6
1.8
2
Norm alized Exit T em p eratu re
Figure 4.12. Conversion versus normalized exit temperature for the case where
the flowrate is the base case. In this case, a difference in exit temperatures
becomes discemable.
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1.2
C onventional
M icrowave
j
Relative Flowrate: 2
s
л
0.6
-
c
c
y
0.2
0.8
1. 2
1.4
1.6
1.8
2
Normalized Exit Temperature
Figure 4.13. Conversion versus normalized exit temperature for the case where
the flowrate is 2x the base case.
j
M icrow ave
|
C o n v en tio n al!
Relative Flowrate: 5
0.8
|j 0.6
u
0.4
0.2
0.8
1.2
1.4
1.6
1.8
Normalized Exit Temperature
Figure 4.14. Conversion versus normalized exit temperature for the case where
the flowrate is 5x the base case. The difference in exit temperatures is substantial
at this flowrate.
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1.2
Conventional
Microwave
Relative Flowrate: 10
0.8
e
л
c
0.6
?
U
0.4 0.2
0
0.8
1.2
1.4
1.6
1.8
2
Normalized Exit Temperature
Figure 4.15. Conversion versus normalized exit temperature for the case where
the flowrate is lOx the base case. The trend towards a larger exit temperature
difference with increasing flowrate is clear. In this case, the range for T> 1.7 was
extrapolated for the conventional case because the model output was terminated
due to excessive wall temperatures.
Figure 4.16 summarizes the trend for exit temperature versus flowrates relative to
the base case. The microwave exit temperature increases linearly as shown by the dotted
line, while the conventional exit temperature increases in a non-linear fashion. The longdash line indicates the ratio of the microwave efficiency to the conventional efficiency.
The efficiency is defined as the ratio o f energy required by the reaction to the energy
supplied by the source, conventional or microwave.
(4.43)
Substituting the energy balance from equation (4.38) for Qs = Q mw or Qcon:
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substituting for the constants and defining an efficiency ratio of the conventional to the
microwave process:
2 = _= l+ 0 .8 5 9 ( C ,? - l)
(4.45)
1+0.859(7;;,^ - 0
% .
This expression was used to calculate the curve labeled ?efficiency ratio? in Figure 4.16.
The model indicates that the microwave process becomes increasingly more efficient as
the flowrate increases relative to the base case for 80% conversion.
Q8 ?
*
a60.4 <12 ---------------------------------------------------------- Q-------------------------------------------------------------0.1
1
10
Relative Flow Rate
Figure 4.16. Summary of Figures 4.11-4.15 showing the trend of exit temperature
versus relative flowrate for both the conventional and microwave cases at 80%
conversion. The ratio of the efficiency o f the two processes is also indicated.
To give a broader picture of the effect of microwave heating on endothermic
reactions, the model was also used to vary the radial thermal conductivity around the base
case. Figures 4.17 -4.19 show how the conversion versus reactor exit temperature vary
for various thermal conductivities. As with the flowrate model, this model predicts that
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the exit temperatures for the conventional case increases with increasing flowrate.
However, in contrast to the previous case, the exit temperature for the microwave reactor
did not vary with thermal conductivity and exit temperature for the conventional case
exceeds the exit temperature predicted for the microwave case. This result tends also
tends to support the hypothesis given by equation (4.36).
1.2
M icro w av e
i
C o n v e n tio n a l1
R elativ e therm al c o n d u c tiv ity : 10
0.8
s
o
'3
u
г 0.6
s
U
0.4
0.2
0
0.8
0.9
1.1
1.2
1.3
1.4
1.5
1.6
Normalized Exit Temperature
Figure 4.17. Conversion versus normalized exit temperature for the case where
the thermal conductivity is lOx the base case. The difference in exit temperatures
is negligible at this thermal conductivity.
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1.2
Conventional
Microwave
Relative therm al conductivity: 1
0.8
0.6
0.4
0.2
0
0.8
0.9
1. 1
1.2
1.3
1.4
1.5
1.6
Norm alized E xit T em p era tu re
Figure 4.18. Conversion versus normalized exit temperature for the base case . A
difference between the two processes becomes noticable for this case.
M icrow ave
1
C o n v en tio n al,
Relative thermal conductivity: 0 2
0.8
a 0.6
0.4
0.8
0.9
1.2
1.3
1.4
1.5
1.6
Normalized Exit Temperature
Figure 4.19. Conversion versus normalized exit temperature for the case where
the thermal conductivity is 0.2x the base case. The difference in exit temperatures
is substantial at this thermal conductivity.
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Figure 4.20 summarizes the trend for exit temperature versus thermal conductivity
relative to the base case. The microwave exit temperature remains constant as shown by
the dotted line, while the conventional exit temperature increases in a non-linear fashion.
The long-dash line indicates the ratio o f the microwave efficiency to the conventional
efficiency. Equation (4.45) was again used to calculate the curve labeled ?efficiency
ratio? in Figure 4.20. The model indicates that the microwave process becom es
increasingly more efficient as the flowrate increases relative to the base case for 80%
conversion.
--------------------------------------Mr?
------------------------------------------;
?? M icrowave
?Conventional
- Efficiency Ratio
Z
uJ
3
ZJ
>
3
Sг
10
0.1
Relative Thermal Conductivity
Figure 4.20. Summary of Figs. 4.17-4.19 showing the trend of exit temperature
versus relative flowrate for both the conventional and microwave cases. The ratio
of the efficiency of the two processes is also indicated.
The model presented here suggests that the nature of microwave heating can be more
efficient than conventional radial heating when applied to a tubular packed-bed flow
reactor in which an endothermic reaction occurs. The model indicates the trend towards
increasing relative efficiency for the microwave case occurs as the dem and on fast radial
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heat transfer becomes more severe, such as the cases studied here: decreasing radial
thermal conductivity and increasing flow rates. I will now present experimental evidence
in order to corroborate the qualitative behavior predicted by the model.
90
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Experimental
The models suggest that during the MSR, there will be a tem perature drop at any
coordinate away from a heat source, which the dissipation o f microwave energy could
counteract. I performed experiments to test this conclusion by exam ining the heat transfer
behavior o f a cylindrical plug o f catalyst. To test the behavior of the 1-D reactor the plug
diameter was small, such that radial variations could be neglected in both the
conventional and microwave case. In the 2-D case, the plug diam eter was large enough so
that a temperature gradient would exist from a radial heat source (in the absence of
microwaves), and long enough so an axial temperature gradient would exist from the inlet
of the reactor. Specifically, a comparative experiment was run such that the conversion
and inlet conditions of the microwave heated reactor were identical to the conventionally
heated reactor. The exit temperatures were then compared.
Two boilers provide the methanol vapor and steam for reaction. This
configuration was chosen over a sparging system for economic reasons, and the
availability o f equipment. A schematic o f the system is shown in Figure 4.21. Heat is
added from regulated power supplies to the boilers C and D at a rate that provides the
desired mass flow rate. At the exit of the boilers, the vapors are superheated to avoid
condensation in the feed lines and to avoid condensation o f the w ater vapor upon mixing.
The vapor mixture then passes through a final reheater stage, which maintains the
superheated state, and provides the desired reactor inlet temperature. Conversion in all
cases was measured using a HP-5890A gas chromatograph fitted with a HayeSep P
(Alltech, Deerfield, IL) column.
91
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{So?-j_
Legend
Red - electrical
B lue - plum bing
G reen - h e a te rs
valve
A: S ta rtu p C o n d e n s e r
B: In e rt G as S u p p ly
C: M ethanol B oiler
D: W ater B oiler
E: W aveguide a n d MW h e a te r
F: W ater B oiler PS
G: M ethanol B oiler PS
H: F inal SH S u p p ly
1: E ffluent C o n d e n se r
J . K: P rim ary SH V a riac s
L: T e m p era tu re
M: P re ssu re
N: V acuum
Figure 4.21. Schematic o f feed system for the MSR.
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Differential Conversion
Before I made the comparison o f the adiabatic packed-bed reactor model to an
experiment, I first investigated w hether or not the kinetic expression o f the reaction
provided by Amphlette, et al. [52] applies equally well to the microwave heated catalyst
as is it does to a catalyst heated by conventional means. This will be done in a differential
isothermal m icro-reactor and a schematic of this reactor is shown in Figure 4.22.
Sapphire
wool
Insulation
W aveguide
^
G C Measurement
Figure 4.22. Reactor configuration used for the differential experim ent. Heat was
supplied to the reaction from sensible heat in the feedstream. The bed reaction
was run at a given temperature with microwaves either on or off.
In the reactor section the feed passed over the differential mass o f catalyst, and the
conversion was kept at less than 5%. This configuration was approxim ately isothermal
and will minimize the complications o f endothermicity and volume change. In addition,
during differential conversion, the rate behavior mostly depends on the temperature and
93
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only very weakly (linear, first order) on the conversion. A thorough discussion of
differential reactors can be found in Fogler [71] o r Weekman [72].
The differential reactor was loaded with 24.4 mg of crushed AliOs/CuO/ZnO
catalyst (C18HC, obtained from CCI). The oxides were present in a 40-50/35-40/8-15
ratio and copper was reduced to active reaction sites in-situ [66]. The reactant gases,
mixed at a 1:1 steam to methanol ratio (molar), were fed at 8 cc/s. These feed conditions
were typical for all the experiments, which include the 1 and 2-D integral-bed reactor
configurations. The experiments were performed over a temperature range o f 500 - 600K.
This was repeated for the two cases of 1) no applied microwave power, and 2) an electric
field strengths of 3x 105 V/m. The reactor configuration is shown in Figure 4.22, was such
that the mass of catalyst was heated by the sensible heat in the gas and could be exposed
to microwaves to examine case 2.
The electric field strength inside the waveguide was measured using a calibrated
antenna and a HP-8481A power meter. The antenna was calibrated using a vector
network analyzer (VNA) such that the free space electric field strength could be
determined using the scattering parameters. These parameters are discussed in Appendix
E. The antenna was inserted into the location where the differential mass o f catalyst was
to reside during the study of case 2 and the response was again measured using the VNA.
This measurement guarantees the existence of microwave energy at the differential-bed
location.
For the differential experiment, I collected data in the form of rate versus
temperature at constant feed conditions with no applied microwave power. Then the same
procedure was followed using an electric field strength of 3 x l0 5 V/m. An Arrhenius plot
94
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will yield the activation energy as the slope of the curve and the pre-exponential factor
from the linearized first order rate expression. Linearizing equation (4.3) for the case o f
low conversion:
ln ( f i? ) = ln ( A C ,,0 ) - ^ Y
(4.46)
This expression was then evaluated experimentally and compared to the expression given
by Amphlette, et al. [52].
One-Dimensional Packed Bed
The behavior of equations (4.14) and (4.16), shown in Figures 4.4 and 4.5, was to be
tested using an integral type reactor with 1 gram o f crushed catalyst. The reactant gases,
mixed at a 1:1 steam to methanol ratio, were fed at 8 cc/s. This was done at a temperature
of 580K. To maintain the 1-D assumption the tube diameter was chosen such that the Pe\i
was л
1. Using a tube diameter of 2.5 mm and length o f 60 mm, the Peclet number was
approximately 0.01. Conversion was then measured for no applied microwave power, and
varying electric field strengths up to 5 x 105 V/m. A schematic of the reactor
configuration for this experiment is shown in Figure 4.23.
95
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W aveguide
^
'
G C M easurem ent
Figure 4.23. Reactor configuration for the 1-D integral-bed experiment. Reaction
was driven either by the sensible heat in the feed, or by the dissipation of
microwave energy.
96
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Two-Dimensional Packed-Bed
The general behavior of the numerical solution o f equations (4.21) was tested
using a 2-D packed bed reactor. The radial dim ension o f this reactor is chosen such that
the Peclet num ber was significantly larger than the l-D approximation. The tube diameter
was chosen to be 4 mm in diameter and 15 mm in length. These dimensions gave a PeM
o f approximately 0.2. This is not an appreciably large value, but the model presented
previously indicates that appreciable radial temperature profiles would develop. Methanol
and steam were fed at 8 cc/s, molar ratio of 1:1, and temperature o f 575 K. Inlet
conditions and overall conversion were maintained constant while the exit temperature
was measured for the cases where the bed was heated 1) conventionally, and 2) by
microwaves.
The conventional heat was supplied radially by a Nichrome wrapping as shown in
Figure 4.24. For case 2, the reactor tube was moved down into the waveguide as shown
in Figure 4.25. In both cases the inlet temperature was measured by a thermocouple at the
top of the assembly, which was separated from the catalyst bed by approximately 1 cm of
sapphire wool as shown in the figures. For case I , the exit temperature was measured by
a separate thermocouple at the bottom of the bed. This T/C was pressed up against a 2 cm
long plug of sapphire wool used to support the catalyst. At this location, the lower
thermocouple was inside the waveguide, and located within the region of reactor tube that
was wrapped in 1? o f sapphire wool. The temperature difference between the two
measurement locations was recorded as -118 K while operating at the standard inlet
conditions and a conversion of 60%. For case 2, the thermocouple was moved down until
97
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Feed ?
O
1
2-D Integral Bed
Ni Chrom e
Heater
'
Sapphire
wool
Insulation
Waveguide
G C M easurem ent
Figure 4.24. Reactor configuration for the 2-D integral-bed experiment. This
configuration was heated conventionally by wire wrapped around the reactor tube.
Inlet and exit temperatures were measured.
2-D Integral Bed
Feed
Sapphire
wool
Insulation
Waveguide
GC M easurem ent
VC?
Figure 4.25. Reactor configuration for the 2-D integral-bed experiment. This
configuration was heated by microwaves. Inlet and exit temperatures were
measured.
98
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it was observed to be just outside the waveguide. It was then moved up exactly 20 mm.
The temperature difference between the original location and this new location was then
observed to be -61 K. The entire assembly was then moved down 20 mm such that the
entire catalyst bed was located inside the waveguide. The location of the upper
thermocouple was unchanged relative to the catalyst bed. This procedure was performed
without interrupting the reactor feed and the location o f the lower thermocouple was
visually verified to be approximately 1 mm below the inner surface of the waveguide.
The microwave pow er was then adjusted until the conversion was again observed to be
60% and the temperature of the lower thermocouple was observed. The exit temperature
for cases 1 and 2 were then compared by adding 61 K to the observations in case 2.
Potential error in this method and its significance are discussed in the Discussion section
of this chapter.
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Experimental Results
The first goal of these experiments was to confirm that the kinetics of the MSR
were identical whether heated conventionally or by microwaves. This was done using the
differential method described above to produce an Arrhenius plot. This plot is shown in
Figure 4.26. Equation (4.46) was used to determine the activation energy and preн
exponential factor, which were found to be 2.25 x 104 m3/s/kg and 80,563 J/mol,
respectively, using a linear least squares fit. These values were close enough to
Amphlette?s values [52] to establish that their expressions will serve as a rough estimate
for the kinetics of my system. In addition, the important result here is that the kinetics did
not appear to be affected by microwave heating . The design o f this experiment was twoн
fold: 1) to prove that the reaction was unaffected by the mode o f heating; and 2) show
that the use of Amphlette?s expression was valid for use in the models presented in this
paper. I concluded that the agreement was satisfactory for these purposes.
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1.7
A
1.75
1.8
1.85
1.9
1.95
2
2.05
? Conventional
a Microwave
-4.5 -
ia
зe
E
v
?c
uf
5
-6.5 -
1000/T(K)
Figure 4.26. Arrhenius plot showing the reaction rate of methanol over 24.4 mg of
catalyst. M icrowave and conventional reaction rates are compared and are nearly
identical. The activation energy is 80,563 J/mol K and the pre-exponential factor
is 2.25 x 104 m3/s/kg.
Having shown the reaction kinetics were unaffected by the mode o f heating, the results of
the 1-D and 2-D experiments can now be examined. The results o f the 1-D experiment,
unfortunately, were inconclusive. The crux assumption in the model was the dielectric
loss and I was unable to obtain a reliable measurement of this property. In addition, the
determination of the electric Field in the cavity was a key measurement. While the proper
method for determ ining the antenna coupling is outlined in Appendix E, the calibration
was done using an empty cavity. In reality, the effect o f the 1 gram dielectric load in the
cavity on the antenna behavior could not be neglected. The procedure outlined in the
appendix yielded electric field strengths in excess o f the breakdown voltage of air. In the
case of the differential bed, I claim the effect of the 24 mg of catalyst was small and that
the procedure gives a reasonable approximation to the electric field strength for that case.
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Recalibration of the antenna would be simple, but unfortunately, at the time this error was
discovered, the necessary equipment was no longer accessible.
The overriding goal of this research was to show that microwave energy could
reach regions not easily accessible by conventional means. The model for the 2-D case
supports this hypothesis. Figure 4.27 shows the results of the 2-D comparative
experiment. As predicted by the model, the exit temperature for the microwave-heated
case was lower than the exit temperature for the conventional case. At the same
conversion, the energy balance (equations (4.36-4.42)) indicates that less energy was
supplied by the microwave to produce the same conversion achieved by the conventional
source. This energy balance also provided an energy check for the model.
i
80
s
7
| ? C onventional!
J
' A Microwave
j
;
70
U
SS
50
C o n v en tio n al E x it T em p era tu re = 436 K
40
M icro w av e E x it T em p era tu re
< 415 K
30 4.
0
1
2
3
4
5
6
7
8
9
10
Run Number
Figure 4.27. Plot shows results of 10 runs where conversion was nominally 60%
for both microwave and conventional case. Exit temperature was measured in
both cases and found to be less in the microwave case. This result indicates
energy required for this conversion was less for the microwave case as suggested
by the energy balance in equation (4.36) and the results of the 2-D model.
By a calorimetry calculation, approximately 5 Watts were provided in both the
microwave and conventional case. A voltage/resistance power calculation on the
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conventional case indicated approximately 20 Watts were provided to the experiment.
This calculation did not include heat loss to the surroundings. These calculations bracket
the value of approximately 8 W atts which was determined by the model previously.
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Discussion
Three models of the endothermic M SR have been presented in this chapter: 1) a
1-D spherical model; 2) a 1-D axial model; and a 3) 2-D plug-flow model. All three of
these models were assumed to obey kinetic expression determined experimentally by
Amphlette and coworkers [52]. The results in Figure 4.26 shows this to be a reasonable
assumption. M any other assumptions were made in the development of these models
which underm ine their absolute predictive value. However, it is my opinion that these
models reveal valuable qualitative information about how microwaves will affect
endotherm ic reactions.
In the 1-D spherical case, an experim ent to verify the behavior was deem ed too
difficult to perform during this research project so experimental confirmation o f this
m odel?s behavior is not available. A m ajor deviation from reality for this model was the
exclusion o f the effects of volume change on reaction. This particular reaction goes from
2 moles to 4 moles and inclusion of this effect would certainly change the behavior
predicted by the model. Thus, the model may over or underestimate the increase in
reaction rate. It is unclear at this time what the effect of neglecting volume change may
have. Finally, the effect of external gradients, both concentration and temperature, were
neglected in this analysis and inclusion o f these effects will surely influence the behavior
of the model.
The 1-D axial model was more com plete than the others in that volume change
and tem perature effects on volume were included. However, the effects shown by the
single pellet model were not included in the analysis. This inclusion would require
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developing a functional relationship on concentration and temperature that would include
the mass and heat transfer effects shown by the model. M athem atically, this model was
identical to a one dimensional non-adiabatic axial model. This solution, without the
volume effects, can be found in Fogler, example 8-7 [71]. As an illustration, the model
presented in this chapter shows the differences between an endothermic reactor that
consumes heat from the gas feed, and one that consumes heat along the length, if radial
gradients are negligible. O f course, the real utility of this is difficult to determine for a
number of reasons. A thorough understanding of the distribution o f the electromagnetic
fields in a microwave reactor are needed before a real assessm ent can be made. Also,
there is the question of the efficiency and availability o f a microwave source that could
generate power and dissipate the energy evenly on an industrial scale. These are issues
that require further study.
The final experiment and theoretical study considered a 2-D reactor in which
radial heat transfer was not negligible. The theoretical study, while non-trivial, was
highly simplified. The entire reactor bed was treated as a homogeneous medium, which
of course is far from the real case. An effective diffusion coefficient and effective radial
thermal conductivity were assumed. In the real case, as has been discussed in the
literature, transport processes in both the solid and fluid medium must be considered for
the model to have more realistic results.
This model was developed in order to better understand an experimental
observation. The previous models had suggested that the microwave energy dissipation
mode could increase the productivity of the catalyst. As mentioned before, the pellet
model was deemed a difficult experiment to perform, and the 1-D axial model was such
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that radial conventional heat would produce the same result. I therefore hypothesized that
a reactor?s performance, in which radial heat transfer effects were non-negligible, would
show some form of improvement. The experimental result showed the exit temperature of
the microwave reactor was lower than the exit temperature of the conventional analog
and the energy balance of equation (4.36-4.42) indicated that less energy was required
from the source to achieve the same conversion. In addition, the data shown in the
Arrhenius plot o f Figure 4.26 indicates the microwaves do not affect the basic reaction
mechanism. The sum of this evidence strongly suggests the cause for this increased
efficiency was heat transfer effects. Thus, solving the 2-D coupled heat and mass transfer
equations indeed provided better insight into the process, and the resulting surface plots
and conversion versus flow and conductivity plots were very revealing as to the
qualitative differences between the two systems. It seems clear that in the conventional
case, the inefficiency arises from the heat leaving the reactor before being consumed by
the reaction. In other words, the low surface area wall heating process preferentially heats
the gas over supplying heat to the reaction. Conversely, the efficiency o f the microwave
reactor relies on heat dissipation over a high surface area near where the reaction occurs.
The microwave process, while also heating the gas, more effectively supplies heat to the
reaction before it exits the reactor.
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Conclusion
It was hypothesized that the homogeneous nature of m icrowave energy
dissipation could alleviate heat transfer difficulties often found with endothermic
catalytic reactions. The first test of this hypothesis was the solution o f the 1-dimensional,
spherical, coupled heat and mass transfer equation, which represented a single catalyst
pellet within which the M SR occurred. The behavior of the conventionally heated case
was compared to the microwave heated case. The analysis indicated a fairly uniform
temperature profile could be imposed on the pellet by microwaves and the resulting
overall reaction rate (including mass transfer effects) increased by approximately a factor
of two over the conventional case when the upper operating tem perature o f the catalyst
was imposed.
The next test was intended to examine a one-dimensional tubular reactor both
theoretically and experimentally. The situation illustrated how microwave heating might
offer an advantage over the typical industrial interstage heating technique. Unfortunately,
difficulties with the microwave apparatus yielded meaningless experimental results.
However, the model indicated improved conversion behavior when microwaves were
used. The model was analogous to the case where heat is added radially along the length
of a reactor suggesting that microwave heating is only advantageous when radial heat
transfer effects are not negligible where, in a real case, interstage heating would be
necessary. The lessons learned in this analysis prompted another experimental
investigation of a reactor configuration in which radial heat transfer effects were not
negligible.
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The final experim ent compared the behavior o f a tubular flow reactor that was
either heated radially or by microwaves. All other aspects, such as feed rate and feed
temperature, of the two configurations were identical. To exclude the possibility o f
anomalous reaction behavior in the microwave case, a comparative Arrhenius experim ent
was performed. In both the microwave and conventional cases, the kinetics were found to
be identical, and in reasonable agreement with values reported in the literature. The
results o f the subsequent heat transfer experiment, where radial transport effects were
non-negligible, indicated the temperature o f the effluent in the microwave case was
significantly less than the temperature of the effluent in the conventional case. A
subsequent energy balance indicated that the energy supplied by the microwave w'as less
than the energy supplied conventionally (radially) to achieve the same conversion. This
important result supports the hypothesis that microwave heating of an endothermic
reaction dissipates the energy homogeneously where it is consumed by the endothermic
reaction without the delay inherent in conductive and convective heat transport.
Although the hypothesis was well supported by this experimental result, it was
difficult to ascertain exactly how this increase in efficiency occurred. In order to better
understand the different behavior observed in the two reactors, the 2-D coupled heat and
mass transfer equations that represented the experim ent were solved. The results
indicated that during conventional heating, as the axial heat transfer rate increased
relative to the radial heat transfer rate, increasingly more energy exited the reactor before
consumption by the reaction. Conversely, the microwave reactor displayed no radial
thermal gradients, indicating there was no delay in radial heat transport due to
convection and conduction. Therefore, as a final statement on this matter: The evidence
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presented, both experimental and theoretical, very strongly supports the original
hypothesis that microwave energy bypasses the spatial delay inherent in conductive and
convective heat transfer processes, such that the energy dissipates exactly where it is
consumed by the endothermic reaction.
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Future Work
This work provided useful insight into the behavior of heat transfer effects in a
microwave heated reaction system. However, steps could certainly be made towards
making both the 2-D experiment and the 2-D model more quantitatively accurate. The
experiment was originally designed to be radially insulated by an effectively adiabatic
vacuum jacket. In addition to simplifying the analysis, this feature would improve the
exit temperature measurements because no temperature drop would exist from the end of
the catalyst bed to the temperature probe. Although my attempt at this feature failed, it
has been successfully used in the past for microwave heat insulation [73.74],
Also, the model could be more reflective of the real case, where the solid and gas
thermal and diffusive properties could be accounted for properly. In addition, changes in
volume, pressure and heat capacity would be a logical next step the development o f the
model.
Finally, the global energy balance issue is unresolved. Certainly large high power
microwave power sources exist, but what is the real feasibility of industrial usage? What
are the consequences of the electric field distribution, wavelength, penetration depth on
larger-than-experimental scales? Is this a technique that will only have a ?niche? for
smaller portable systems? These questions are unanswered at this time.
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CHAPTER 5: CONCLUSIONS AND SIGNIFICANCE OF WORK
Conclusions
The original intent of this research project was to study microwaves as an energy
delivery mechanism for catalytic reactions. The literature revealed exciting possibilities
that include fast heating rates and altered reaction behavior. The fast heating rate
phenomenon was understood to result from the way microwave energy couples to the
substance being heated, heating from the outside in, rather than inside out. The altered
reaction behavior was not as well understood.
The general consensus in the literature was the altered reaction behavior resulted
from the existence of microwave-induced thermal gradients. However, the nature and
magnitude of these thermal gradients were not well understood. Therefore, the main
focus of this research endeavored to understand these thermal gradients and their effect
on catalytic reaction behavior. The study has been largely successful through
experimentation with the CO oxidation and MSR, and through theoretical analysis of
heat transfer on a nano-scale and on a global reactor scale.
Kinetics of the CO oxidation were initially studied in an integral bed reactor and
the results yielded altered reaction behavior when the temperature was measured using
the thermocouple insertion technique. Observations using a thermal imaging camera
revealed a highly non-isothermal temperature profile in the integral-bed. Refinement of
the experimental design led to a reactor configuration in which the active catalyst mass
was sandwiched between two inactive masses of catalyst support. The support material
was largely identical in composition such that the microwaves were absorbed
homogeneously and the temperature was approximately uniform across the active portion
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o f the bed. The thermocouple insertion technique was again used and the temperature o f
the active portion of the bed was measured. In this configuration, the kinetics in the
microwave reactor were found to be virtually identically to the kinetics in the
conventional reactor.
Two conclusions were drawn from these observations. Most obviously, reactor
scale temperature gradients caused the erroneous kinetics that were observed in the
integral-bed experiment. More subtly, the fact that the kinetics in the modified
differential bed experiment were identical suggested that there was no temperature
gradient from reaction surface to the surrounding catalyst support. The temperature o f the
reaction surface was not observable, and a relatively hot reaction surface would have
caused the observed kinetics to differ. This was the most important result of this phase of
the work and led to further work to substantiate this experimental observation.
The next phase of the work was a theoretical examination of heat transfer away
from a hypothetical system intended to represent the small metallic catalyst crystallites
found in the PCI/AI2 O 3 and Pt/A^Ch when heated by microwaves. The analysis began with
an analysis of the rate o f heat transfer from the 1-100 nm crystallites considering the
molecular flow character of the system and was tailored to represent the largest possible
temperature rise in the particles. The resulting expression was solved for the temperature
rise. The only unknown parameter in this equation was the dielectric loss of the metallic
crystallites. The dielectric behavior of the small crystallites was examined theoretically
and it was found that 1-100 nm metallic particles behave very much like insulators at this
small scale. The result of the analysis indicated an appreciable temperature rise in the
small metallic particles was very unlikely. Thus, the results o f the CO oxidation reaction
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along with this theoretical result combine to make a very com pelling argument against a
localized microwave-induced high temperature on the reaction surface.
The third and final phase of this research theoretically and experimentally
examined the M SR as a platform for the study of microwave effects on endothermic
catalytic chemical reactions. During this phase of the research, microwave heat transfer
effects have been shown to improve the productivity o f the endothermic MSR for three
cases. 1) A single catalyst pellet; 2) a 1-D tubular reactor; 3) a 2-D tubular reactor. The
magnitude of the benefit in all cases was determined by the relative importance of three
processes: the consumption of heat by reaction , the supply o f heat by radial conduction
and the supply of heat by axial convection. If the rate o f heat supply by radial conduction
sufficiently exceeded the rate o f heat consumption by reaction and axial convection, then
the microwave heating was of little benefit. However, if heat consumption by reaction
and transport of heat by axial convection exceeded radial heat transfer rates, the
homogeneous nature of microwave heating was shown to minimize radial thermal
gradients because the energy was dissipated where it was consum ed by the reaction.
Finally, and most importantly, the 2-D experiment and model in conjunction with the
energy balance indicated that the energy required from the microwave source was less
than the energy required from the conventional source to achieve the same conversion,
indicating the microwave reactor was more efficient than the conventional reactor. The
model indicated relative efficiency of the microwave reactor to the conventional reactor
increased as the conditions on heat transfer were made more demanding, indicating that
as the axial heat transfer rate increased relative to the radial heat transfer rate,
increasingly more o f the energy left the reactor before being consum ed by the reaction.
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Changing the relative importance o f these two heat transfer processes was irrelevant in
the microwave case, because this mode of heating essentially eliminated heat transfer in
the radial direction entirely. Finally, to restate the most important conclusion of this
phase of the research: The evidence presented, both experim ental and theoretical,
supports the original hypothesis that microwave energy bypasses the spatial delay
inherent in conductive and convective heat transfer processes, such that the energy
dissipates exactly where it is consumed by the endothermic reaction.
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Significance of this work
Catalytic processes account for up to 30% o f the US GNP. Any increase in overall
efficiency o f industrially important reactions could have an enormous economic and
environmental impact. The microwave, at the very least, offers an alternative method for
driving chemical reactions. Given the advantages that were shown in this document for
endothermic reactions, and the great potential for a positive impact on society, industry
and the environment, a thorough study is certainly warranted.
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Table of Symbols
Symbol
Units
Definition
Optical Dielectric Permittivity
A
Pre-exponential Factor
A
Surface Area
rrr
C
Concentration
mo I/m3
C*
Dimensionless Concentration
Co
Initial concentration,
mol/m3
Co
Reactor Inlet Concentration
mol/m3
Cv, Cp
D
Heat Capacity
Diffusion Coefficient
J/(kg-mol K)
m'/s
Dai
Dan
Dp
dp,R
Mass D am kohler Number
Heat D am kohler Number,
Particle D iam eter
particle diameter,
m
m
E
Ea
Electric Field
Activation Energy
V/m
J/mol/K
f
>d
k
Electric Field Frequency
Mesh Indices
Hz
Effective Thermal Conductivity,
W/m/K
Lb,L
Packed Bed Length
m
M
MW
P
P
PeH
M olecular W eight
Dimensionless Microwave Source Term
Pressure
Total or Partial Pressure
Heat Peclet Number,
kg/kg-mol
Pe.M
Mass Peclet number,
Heat Flux
W/m2
Power
W/m3
R
r
Gas Constant
Dimensionless Radius
J/(kg-mol K)
R.
R2
Rb,R
Particle Radius
Pore Radius
bed radius
m
m
t*MeOH
Rate of M ethanol Consumption by Reaction
mol/s/kg
q
Q
*
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kg/(m s2)
Pa
T
T
Average Tem perature
Temperature
K
K
To
Initial temperature
K
To
Reactor Inlet Temperature
K
v, us
Average gas velocity,
m/s
z
Dimensionless Axial Coordinate
AH
Heat of Reaction
cl>
N
General Dimensionless Dependend Variable, Represents
Either T* or C
Number o f Radial Nodes
T*
Dimensionless Temperature
'F
Generalized Dimensionless Mass or Heat Flux
Gt|
(X2
a , (3, y
Accommodation Coefficient
Accommodation Coefficient
Tri-diagonal Matrix Elements
e
Bed Voidage
e?
e ?n
г?
гn
гm
0
r\
Dielectric Permittivity
Static Dielectric Permittivity
Dielectric Loss
Permittivity of Free Space
Dielectric Permittivity of Alumina Support
Thiele Modulus
Thermal Efficiency
K
parameter accounting for volume change on reaction.
Xe
X
pb
Electron M ean Free Path
Gas Mean Free Path
Catalyst bed density,
m
m
kg/m
pg
gas density,
kg/m3
a
t
u
\)
to
Conductivity
Relaxation Time
Volumetric Flow Rate
Volume Fraction o f Conducting Phase
Microwave Angular Frequency
(г2-m )'?
s
m 7s
J/mol
none
none
m '1
117
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F/m
rad/s
Appendix A: ACritical Review of Key Papers from Chapter 2
In 1995 Chen, et al. [2] comparatively examined oxidative coupling o f methane
reaction in conventional versus microwave heating. The authors observed sim ilar
conversion of methane in these reactors, however the microwave reactor operated at 400
C lower. Also, the product distribution of the two reactors differed somewhat. In these
experiments, the temperature was measured using an infrared pyrometer. Unfortunately,
details of the pyrom eter were not given, making the validity o f the measurements difficult
to ascertain. It is possible for the spectral response of an infrared pyrom eter to be such
that the quartz is transparent, opaque, or somewhere in between, to the infrared radiation.
It is therefore possible that the temperature reported was the tem perature o f the outer
surface of the quartz reactor such that the indicated temperature was significantly lower
than the reaction temperature. In light of this possibility and the lack o f information
regarding the response of the pyrometer, the results presented are difficult to interpret.
In 1993 Cha and Kim [] published a paper indicating there was an
electromagnetic enhancem ent o f chemical reactions, namely, the devolatilization of coal
in a char bed. The paper describes a process whereby the endothermic devolatilization of
char occurs in a microwave heated reactor. The authors allude to a temperature
measurement, but neither the device nor the procedure are discussed. This is a serious
deficiency because o f the pivotal nature of temperature measurement in microwave
heated chemistry. Furthermore, it is stated ?...microwave energy does provide very high
temperature gradients between the gas phase and char particles...? In all likelihood, this
was true for micron and greater size particles. However, the great m ajority o f reaction
surface present in a carbon system is found in the pore network. Typically the size of
118
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these pores is less than the mean free path o f gasses at standard conditions and thus a
temperature gradient was unlikely. The paper discusses an important process, and clearly
the microwave energy was suitable for the application. However, the author?s conclusion
that ?....the devolitalization of char is enhanced by microwave energy...? was
unsubstantiated with out more information regarding temperature and the significance of
their energy calculations.
In 1995, Ioffe and coworkers [] studied the selective production of acetylene from
the reaction of methane over carbon. The authors reported a high selectivity to C2H2,
certainly an important result. As with the work by Cha and Kim [], this paper makes the
statement ?...intermediates formed on the catalyst surface are thermally desorbed during
the RF or microwave pulse absorption and quenched in a relatively cool gas phase...?
Again, it was unlikely, due to pore dimensions, that this mechanism played a significant
role. It is more likely the pulsed nature o f the energy supply caused a rapid surface
heating - reaction - rapid cooling and quenching o f the intermediates. Also, temperature
measurement was not measured. Unfortunately, tem perature measurement of these short
time scale transients would undoubtedly be very difficult. However, much could be
learned from a transient heat and mass transfer analysis o f the system, which would also
be a challenging task.
Seyfried, et al. [] described microwave effects on reform ing catalysts in a 1994
article. In this paper, the authors describe the reaction o f hexane over Pt/Alumina
catalysts to produce a distribution of isomers. They describe selectivity differences as a
function of the reaction temperature for a com parison between a microwave heating
system and a conventional system. The selectivity differences occur for two cases: 1)
119
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
mode of heating during reaction; 2) mode o f heating during catalyst preparation. In all
cases the temperature was measured by a small thermocouple attached to the outer wall
of the reactor tube. This w ould normally be cause for concern, due to the possibility of
large radial temperature gradient. However, the authors indicate the reactor is ?lagged" so
that ?the differences of temperature into the bulk of the catalyst and the heat losses to the
cavity are attenuated.? Presumably, this refers to radial insulation, however, without
explicit information to this effect, the results presented in the paper are suspect. The mal
effects of radial heat transfer were shown in Chapter 2 o f this dissertation.
Bond, et al. [] reported in 1993 beneficial effects o f microwave energy on the
oxidative coupling of methane. In this publication, the authors report observing similar
product distributions between a reactor heated conventionally and a reactor heated by
microwaves. However, the microwave reactor produced this product distribution at 400 C
lower. They conclude that local temperature non-uniformities were responsible for this
behavior. As shown in Chapter 3, heat transfer is very rapid at very small dimensions.
Therefore, there would have to be very large differences in the rate o f microwave energy
absorption for these non-uniformities to be significant. Once again, molecular flow heat
transfer inside the catalyst pellet becomes an issue. Other than the composition, sodium
aluminate, the article does not give any information regarding the catalyst so pore size
was unknown. However, as stated in previous paragraphs, interpore gradients are not
likely, however, if the catalyst particles (or pellets) were large enough, internal gradients
would be likely. In this manner, perhaps the interior temperatures o f the catalyst were
significantly higher; a possible explanation for the observed behavior. The authors do
raise an interesting issue regarding temperatures of sharp comers found on the catalyst
120
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that could be analyzed using the methods presented in Chapter 4, only using cartesian
coordinates. In this papers, the authors adm it the hypothesis concerning hot-spots remains
unproven, and this is common to all the papers reviewed here. It therefore remains a task
for the microwave research community to investigate these issues further.
121
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Appendix B: Mathematica Code for the 1-D Spherical Model
Mathematica [65] Code for Solving the 1-D Spherical Pellet Model
Da=200 10A6
MWI= 0.22 2.75
MWH= 27 10A6
Ts=575
Rg=8.314
E A =84100.0
alpha=EA/(Rg Ts)
Q = 5 10A6
Qterm = 0
ICCsave = -999
ICTsave = -999
flag = -999
firstC = 0.38
IastC = 0.4
stepC = 0.001
initC = firstC
firstT = 0.025
lastT = 0.04
stepT = 0.001
DeleteFile["result"]
While[ flag != 1 && FirstT <= lastT,
[
FirstC = initC,
While[ flag != 1 && FirstC <= IastC,
[
sol = NDSolve[
[
C"[r] + 2/(r+0.0001) C'[r]
Da C[r] Exp[-alpha/(T[r]+l)] = 0,
(T"[r] + 2/(r+0.0001) T'[r])
- MWH C[r] Exp[-alpha/(T[r]+1)] + MWI == 0,
122
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C[0] = FirstC, C?[0] = 0,
T[0] = firstT, T'[0] = 0
],
[C ,T ],
[r, 0, 1],
M axSteps -> 300
],
BCClst = Evaluate[C [l] /. sol],
BCTlst = Evaluate[T[l] /. sol],
BCC = BCClst[[ 1]],
BCT = BCTlst[[ 1]],
Print["initC = ", firstC ,", BC(C) = ", B C C ," :: initT
= ", FirstT,", BC(T) = ", BCT, "b"],
(*answer = [ firstC, BCC, firstT, BCT] ╗ > result,*)
If[BCC > 0.99 && BCC < 1.01 && BCT > -0.01 && BCTcO.Ol,
[
ICCsave = firstC,
ICTsave = firstT,
Print["initial concentration = ",ICCsave. ",
initial temperature = ",ICTsave],
flag = 1
1,
flag = 0
1,
firstC = firstC + stepC
]
].
firstT = firstT + stepT
]
]
If[flag = 0, [Print[" "],Print["nothing found"]], flag = 0]
123
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
If[flag = 0,
[
Plot[Evaluate[C[r] /. soI,[r,0,l],PIotRange->[0,2]]],
Plot[Evaluate[T[r] /. sol,[r,0,l],PlotR ange->[-l,2]]],
Print["max flux", EvaIuate[C '[l] /. sol]], л r e s u lt,
Cdata = TabIeForm[Table[Evaluate[C[r] /. sol],[r,0,1,.05]]],
Tdata = TableForm[Table[Evaluate[T[r] /. sol],[r,0,1,.05]]],
TableForm [C data]╗ M ail/Cdatfil,
TableForm[Tdata] ╗ Mail/Tdatfil
],
flag = 0
]
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix C: Mathematica Model for Solving the 1-D Axial Model
Mathematica [65] Code for Solving the 1-D Integral-Bed Model
Tc =
A =
H =
AE =
R =
580
(* K *)
1.532 10*6 (* m3 / (s kg *)
60000 (* J/mol *)
81400
(* J/mol *)
8.314 (* J/(mol K)
*)
v = 5 10*-6
(* m 3 /s *)
Cp = 1911 (* J / ( k g K) *)
rho = 0 . 6 7 2
(* kg/m3 *)
rhocat = 1 2 8 0 (* kg/m3 *)
eps = 0.7
Co = 2 1
(* mol/m3 *)
eta = 0.8
f = 10*9
(* Hz *)
eo = 8.8 10*-12 (* F/ m *)
epp = 0.001
EF = 5 10*5
(* V / m *)
Q = 2 3.14 f EF*2 eo epp (* W/m3
P = (Q/rhocat) 0.75
*)
sol = NDSoive[
[ - v X '[w] + A E x p [- A E / ( R (T[w]))] (1 - X[w])/(i +
eta X[w]) Tc/T[w] == 0,
-rho v Cp/Tc (T[w]*2 eta X ? [w] + (1+eta X [ w ] ) 2 T[w]
T ' [ w ] ) + (Q/rhocat) \
eps - H A E x p [-AE/(R (T[w]))] Co (1 - X[w])/(1 + eta
X [ w ] ) Tc/T[w] == 0,
X[0] == 0, T [0 ] == Tc], [X, T] , [w, 0, 0.001]]
P l o t [ E v a l u a t e [[100 X [ w ] , T[w]]
> [0,600]]
/. % ] , [w,0 ,0.001],PlotRange-
Cdata = T a bl eFo rm [Table [Evaluate [X [w] /.
s o l ] , [w,0,0.001,.00005]]] Tdata = \
TableForm[Table[Evaluate[T[w] /. s o l ] , [w,0,0.001,.00005]]]
125
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TableForm[Cdata]
TableForm[Tdata]
>> Mail/C da tfi l
>> Mail/T da tfi l
126
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX D: FORTRAN Code for Solving the 2-D Tubular Flow Model
FORTRAN PROGRAM
FOR SOLVING TH E 2-D COUPLED HEAT AND MASS TRA N SFER WITH
ENDOTHERM IC REACTION.
INTEGER I,J,I_LIM IT, J_LIM IT, ICOUNTER, JCOUNTER, SCOUNTER,
J_LIM IT_IN
REAL DZ,DZO, DR, PM, PT, DI, DII, MW, FLUX, FLUX_IN, X, TARG_X, TO
REAL CO, A, RXN, S, R, STEPPER,SDENOM, DENOM _C,DENOM _T,
R_I,AV
REAL R_I_LEVHT, RP, RM, CORRECTOR, EA, RG, PD, PCLIM , B, C, SIG_T.
AVT
REAL TJM 1(101), CJM 1(101), TJ(101), RX NT(10l),RX N C( 101)
REAL CJ(101), T J P l(lO l), CJP 1(101)
REAL ALPHA_C( 101), BETA_C( 101), GAMMA_C( 101),
ALPHA_T( 101 ),BETA_T( 101), GAMMA_T( 101)
REAL TEMP, DTJP1, DCJP1, DTDR, ERROR, SIGMA, UP_M ULT,
DOWN_MULT,
DIFF
1DIRS NAM E(LSLTR="lsltr")
EXTERNAL LSLTR
S T E P P E R = 10
PCLIM = 1.0E5
I_LIMIT = 100
J_LIMIT = 1000
DZ = 0 .0 0 10000000000
DR = 0.010000000000
R_I_LEMIT = 100.000000000000
DECREASE COND.
PM = 23.0
PT = 0.2
127
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
DI = 6.3
DU = 10.0
M W = 0.0
FLUX = 0.0
X = O.OEOO
TA RG _X = 0.4
TO = 575.0
CO = 24.4/2.0
EA = 8.41E4
RG = 8.314E0
A = 3.01283E5
TR X N = 0.0
RXN = 0.0
S = 0.0
R = 0.0
ICOUNTER = 0
JCOUNTER = 0
CORRECTOR = 0.00001
SOLVE THE EQUATIONS
!
DO WHELE(X.LT.0.81)
'.**** SET THE INITIAL CONDITIONS
DO 5 1= 1,I_LIMIT
5
CJ(I) = 1.0000000000
TJ(I) = 1.0000000000
TJP1(I) = 0.0
CJP1(I) = 0.0
RXNT(I) = 1.0
RXNC(I) = 1.0
END DO
W RITE(*,505)J,TJ( 1),TJ( 10),TJ(20),TJ(20),TJ(40),TJ(50),TJ(60),TJ(70),TJ(80),
TJ(90),TJ(100)
i
W RITE(*,505)J,CJ(1),CJ(10),CJ(20),CJ(20),CJ(40),CJ(50),CJ(60),CJ(70),CJ(80),
CJ(90),CJ(100)
! **** INITIALIZE COUNTERS
128
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ICOUNTER = 0
JCOUNTER = 1
SCOUNTER = 0
ERROR = 1.0
! **** BEGIN BY BUILDING COEFFICIENT ARRAYS ALPHA, BETA AND
GAMMA
DO 400 J = l J J J M I T
UP_M U LT= 1.00001
DOWN_MULT = 0.99999
DO WHELE(ERROR.GT. 1.0E-3)
R_I = 1.0
DO 100 1= 1,I_LIMIT
RP = (R_I+0.5)/R_I_LIM IT
RM = (R_I-0.5)/R_I_LIM IT
DENOM_T = PT*DR*(RP**2-RM**2)
DENOM_C = PM*DR*(RP**2-RM**2)
ALPHA_C(I) = -2.0*RM/DENOM_C
GAMMA_C(I) = -2.0*RP/DENOM_C
BETA_C(I) = 1.0/DZ - (ALPHA_C(I) + GAMMA_C(I))
ALPHA_T(I) = -2.0*RM /DENOM_T
GAMMA_T(I) = -2.0*RP/DENOM _T
BETA_T(I) = 1.0/DZ - (ALPHA_T(I) + GAMMA_T(I))
R_I = R _ I+ 1.0
100
END DO
! **** TAKE CARE OF I = I AND I = I LIMIT AS SPECIAL CASES
RP = 2.5/R_I_LIMIT
ALPHA_C( 1) = 0.0
ALPHA_T( 1) = 0.0
129
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
GAM M A_T(1) = -2.0/(RP*DR*PT)
GAM M A_C(1) = -2.0/(RP*DR*PM )
BETA_T( 1) = 1.0/DZ - GAM M A_T( 1)
BETA_C( 1) = 1.0/DZ - GAM M A_C( 1)
RM = (R_I_LIM IT-0.5)/R_I_LIM IT
ALPHA_T(I_LIM IT) = -2.0*RM /(PT*DR*(1.0-RM **2))
ALPHA_C(I_LEMIT) = -2.0*RM /(PM *DR*(1.0-RM **2))
BETA_T(I_LIM IT) = 1.0/DZ - ALPHA_T(I_LIM IT)
BETA_C(I_LIM IT) = 1.0/DZ - ALPHA_C(I_LIM IT)
GAM M A_C(I_LIM IT) = 0.0
GAM M A_T(I_LIM IT) = 0.0
! **** LOAD THE RHS VECTORS EXCEPT FOR THE BOUNDARY
DO 2 0 0 1 = 1,I_LIMIT-1
S = -EA/(RG*T0*RXNT(I))
RXN = A*C0*CJ(I)*EXP(S)
CJP1(D = CJ(I)/DZ - DI*RXN
TJP1(I) = TJ(I)/DZ - DII*RXN + MW
200
END DO
! **** BOUNDARY CONDITIONS NEED SPECIAL ATTENTION: INCLUDE FLUX
S = -EA/(RG*T0*RXNT(I_LIM IT))
RXN = A*C0*CJ(I_L1MIT)*EXP(S)
C JP l(L L IM IT ) = CJ(I_LIM IT)/DZ - DI*RXN
TJP1(I_LIM IT) = TJ(I_LIM IT)/DZ - DII*RXN + FLUX + MW
, **** INITIAL RHS VECTORS ARE BUILT ABOVE. ALL OTHERS ARE BUILT
AT THE
!
END O F THIS LOOP. THESE VECTORS ARE CJ(I), TJ(I).
!
W RITE(*,500) 0 ,T JP I(1 ),TJP 1(20),TJP 1(40),TJP 1(60),TJP 1(80),TJP 1(100)
130
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CALL LSLTR(I_LIMIT, A L P H A .C , BETA_C, GAMMA_C, CJP1)
CALL LSLTR(I_LIMIT, A L P H A .T , BETA_T, G A M M A .T, TJP1)
! **** CALCULATE THE STANDARD ERROR
ERROR = 0.0
SIGM A = 0.0
DO 6 0 0 1 = 1,I_LIM IT
SIGM A = SIGMA + ((TJP1(I) - RXNT(I))**2)
IF(TJP 1(I).GT.RXNT(I)) THEN
RXNT(I) = RXNT (I) * UP_M ULT
ELSE IF(TJP 1(I).LT.RXNT(I)) THEN
RXNT(I) = RXNT(I)*DOW N_M ULT
END IF
600
END DO
!*** M ODIFY THE SCALING FACTOR DURING CONVERGENCE
ERROR = SQRT(SIGM A/(R_I_LIMIT-2.0))
IF(ERROR.GT.O.OOOOO 1) THEN
U P_M U LT= 1.0000000001
DOWN_MULT = l.0/U P_M U LT
END IF
IF(ERROR.GT.O.OOOO 1) THEN
UP_MULT = 1.00000001
DOWN_MULT = 1.0/UP_MULT
END IF
IF(ERROR.GT.O.OOOl) THEN
UP_MULT = 1.0000001
131
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
DOWN_MULT = 1.0/UP_MULT
END IF
IF(ERROR.GT.O.OOO I ) TH EN
UP_MULT = 1.00001
DOWN_MULT = 1.0/UP_MULT
END IF
IF(ERROR.GT.O.Ol) TH EN
UP_MULT =1.0001
DOW N_M ULT = 1.0/UP_MULT
END IF
EF(ERROR.GT.O.1) THEN
UP_MULT =1.001
DO W N _M ULT= 1.0/UP_MULT
END IF
ENDW HILE
END DO
W RITE(*,601) ERROR
ERROR = 1.0
EF(JCOUNTER.EQ.STEPPER) THEN
W RITE(*,505)J,TJP 1(1 ),TJP 1(10),TJP 1(20),TJP 1(20),TJP 1(40),TJP 1(50).TJP 1(6
0),TJP 1(70),TJP 1(80),TJP 1(90),TJP 1(100)
i
W RITE(*,505)0,C JP 1(1 ),CJP 1(10),CJP 1(20),CJP 1(20),CJP 1(40),CJP 1(50),CJP 1(
60),CJP 1(70),CJP 1(80),CJP 1(90),CJP 1(100)
JCOUNTER = 0
END IF
JCOUNTER = JCOUNTER + 1
DO 3 0 0 1 = 1,I_UM IT
TJ(I) = TJP1(I)
CJ(I) = CJP I (I)
RXNC(I) = CJP1(D
300
END DO
601
FORMAT(F10.8)
132
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ALL JS ARE DONE; REACTOR DONE.
400
END DO
! **** CALCULATE CONVERSION BASED ON AVERAGE CONCENTRATION
SIGMA = 0.0
SIG_T = 0.0
DO 501 1= 1,I_LIMIT
501
SIGMA = SIGM A + CJP 1(1)
SIG_T = SIG_T + TJP1(I)
END DO
AVT = SIG_T/I_LIMIT
AV = SIGM A/IJL IM IT
X = 1.0-AV
WRITE(*,512) X, FLUX, MW, AVT
DO 3 0 2 1 = 1,I_LIMIT
WRITE(*,301) I, CJP 1(1)
302
END DO
!
MW = MW + 0.05
FLUX = FLUX + 10.0
!
'
END WHILE
END DO
512
FO RM ATfCO N VERSIO N : ",F8.4," FLUX: ?,F15.10, " MW: ", F15.10. " AV
T: ", F10.7)
WRITE(*,515) PM, PT, DI,DII
WRITE(*,516) TO, CO
301
FORMAT(I5,",",F10.5)
505
FORMAT(I5,",",F7.5,",",F7.5,",",F7.5,",",F7.5,",",F7.5,",",F7.5,",",F7.5,",",F7.5,"
,",F7.5,",",F7.5,",",F7.5)
510
FORMAT(I5,F8.4,F8.4)
515
FORMAT("Pem: ",F8.4," Peh:",F8.4," Dal: ",F8.4," D ali: ?,F8.4)
516
FORMAT("T IN: ",F8.4," C IN: ",F8.4)
9999 END
133
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Appendix E: Cavity Electric Field Measurements
Electric field strength was measered using an HP 8481A power meter. T he device
was coupled to a small antenna inside the heating cavity that dissipated a small am ount of
cavity power upon excitation by the electric field. The power disspated by the antenna
was related to the power in the cavity by a calibration factor that was determ ined using an
HP-8510A Vector Network Analyzer. The cavity was removed from the m icrowave
source and a waveguide signal launcher was attatched to the coupling iris. The scattering
parameters of the two coupling apertures was then measured. The scattering param eters
have been defined by [75]:
? .2 _ Power _ Reflected _ from _ Input
Power _ Incident _ on _ Input
,
.2
Power _ Reflected _ from _ Output
Power _ Incident _ o n _ Output
(BP)
|S21|~ = Transmission _ Gain
The loaded cavity Q was then calculated using the S 21 parameter:
q _
Energy _ Stored _ in _ Cavity _ f c
Power _ Dissipated _ per _ cycle 2A/
where fc is the cavity resonant frequency (frequency of maximum power stored on
transmission) and 2Af is the bandwidth at the 3db points on the S 21 versus frequency
measurement of the cavity. The Q of the unloaded cavity was then found to be 3536.
134
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The S 22 parameter was used to calibrate the antenna, such that the power read
from the display on the HP 8481A power m eter was related to the electric field strength
in the cavity. The definition of S 22 contains information about the power reflected from
the antenna. I assum e losses of the antenna are negligible such that
T = 1- R
where T is the power transmitted from the antenna to the cavity and R is the power
reflected from the antenna back to the analyzer:
forw ard _ power
reflected _ power
2
The transmission properties are independent o f the transmission direction, so the
transmission coefficient applies to the fraction o f the power inside the cavity that was
coupled into the antenna. Now:
pantenna = t
pcavity = n' - f 212 1' ? pcavity
The cavity power term is:
P c a u ,y
= < !> -W sw m ,
135
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where co is the radiation angular frequency and Wstored is the energy stored in the cavity in
the form of the electromagnetic wave. Balanis [20] section 8.3.1 describes the derivation
of the stored energy as a function o f cavity geometry and electric field strength. The
cavity operates in the TEioi mode, and this leads to the following expression for the
stored energy:
i
|A o i|
12
^
(
k
X
abc
stored ( magnetic .electric )
Where a and b are the width and height o f the waveguide, 0.248 m and 0.124 m
respectively, c is Vi the guide wavelength. Aioi is found from Balanis, equation 8-81 [20]:
Where p are the eigenvalues. In the geometry considered ( z is the direction of energy
propogation), the terms that are a function of x and y are both unity, and the following
results:
г v = - - ^ - A 101 sin (P:z) = - ? Am sin (fi.z)
г
гa
136
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This may now be substituted into the expression for stored energy:
2
eE..
W.stored ( magnetic,electric)
a
1
'
k sin(/?.z)
г
2
" abc
8
abc
(E
1
1
8 ^ ' sin(/3.z) t
In the case of my measurements, the antenna was displaced along the z axis from
the maximum of the electric field:
sin(0.z)
such that
nr
W
stored {magnetic.eleitrtc)
abc F~
rO
? c _____
g
ma
Finally, inserting this result into the equation for antenna power:
Solving for the Electric field strength:
137
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E m ax
=
abc
Pantenna is related to the reading on the pow er meter. This relationship includes the power
reduction by
calibrated attenuators and the offset in the meter. Therefore:
P.F..
E m ax =
(1 - S ^ ) C O г
abc
W here Pr was the reading on the power meter, and Fatt was the attenuation factor. Here, co
is
2
k
x 915 MHz. e is the permittivity air, which is very close to that o f free space, 8.84 x
10'12 F/m. Finally, S 22 was measured to be 0.9160. The relationship between the electric
field and the power m eter reading in the differential case, using a m eter offset of 79 db
and 60 db of attenuation, was:
г?,=Vf'3-4lxl░3
and for the integral case, using 79 db offset and 16 db attenuation:
'5 .4 1 x 1 0 s .
138
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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143
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IMAGE EVALUATION
TEST TARGET ( Q A - 3 )
I .0
11
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Li
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гr u* ill2-2
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1653 E ast Main S treet
R ochester, NY 14609 USA
Phone: 716/482-0300
Fax: 716/288-5989
O 1993. Applied linage. Inc.. All Rights R eserved
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
microwave case. In the 2-D case, the plug diam eter was large enough so
that a temperature gradient would exist from a radial heat source (in the absence of
microwaves), and long enough so an axial temperature gradient would exist from the inlet
of the reactor. Specifically, a comparative experiment was run such that the conversion
and inlet conditions of the microwave heated reactor were identical to the conventionally
heated reactor. The exit temperatures were then compared.
Two boilers provide the methanol vapor and steam for reaction. This
configuration was chosen over a sparging system for economic reasons, and the
availability o f equipment. A schematic o f the system is shown in Figure 4.21. Heat is
added from regulated power supplies to the boilers C and D at a rate that provides the
desired mass flow rate. At the exit of the boilers, the vapors are superheated to avoid
condensation in the feed lines and to avoid condensation o f the w ater vapor upon mixing.
The vapor mixture then passes through a final reheater stage, which maintains the
superheated state, and provides the desired reactor inlet temperature. Conversion in all
cases was measured using a HP-5890A gas chromatograph fitted with a HayeSep P
(Alltech, Deerfield, IL) column.
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
{So?-j_
Legend
Red - electrical
B lue - plum bing
G reen - h e a te rs
valve
A: S ta rtu p C o n d e n s e r
B: In e rt G as S u p p ly
C: M ethanol B oiler
D: W ater B oiler
E: W aveguide a n d MW h e a te r
F: W ater B oiler PS
G: M ethanol B oiler PS
H: F inal SH S u p p ly
1: E ffluent C o n d e n se r
J . K: P rim ary SH V a riac s
L: T e m p era tu re
M: P re ssu re
N: V acuum
Figure 4.21. Schematic o f feed system for the MSR.
92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Differential Conversion
Before I made the comparison o f the adiabatic packed-bed reactor model to an
experiment, I first investigated w hether or not the kinetic expression o f the reaction
provided by Amphlette, et al. [52] applies equally well to the microwave heated catalyst
as is it does to a catalyst heated by conventional means. This will be done in a differential
isothermal m icro-reactor and a schematic of this reactor is shown in Figure 4.22.
Sapphire
wool
Insulation
W aveguide
^
G C Measurement
Figure 4.22. Reactor configuration used for the differential experim ent. Heat was
supplied to the reaction from sensible heat in the feedstream. The bed reaction
was run at a given temperature with microwaves either on or off.
In the reactor section the feed passed over the differential mass o f catalyst, and the
conversion was kept at less than 5%. This configuration was approxim ately isothermal
and will minimize the complications o f endothermicity and volume change. In addition,
during differential conversion, the rate behavior mostly depends on the temperature and
93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
only very weakly (linear, first order) on the conversion. A thorough discussion of
differential reactors can be found in Fogler [71] o r Weekman [72].
The differential reactor was loaded with 24.4 mg of crushed AliOs/CuO/ZnO
catalyst (C18HC, obtained from CCI). The oxides were present in a 40-50/35-40/8-15
ratio and copper was reduced to active reaction sites in-situ [66]. The reactant gases,
mixed at a 1:1 steam to methanol ratio (molar), were fed at 8 cc/s. These feed conditions
were typical for all the experiments, which include the 1 and 2-D integral-bed reactor
configurations. The experiments were performed over a temperature range o f 500 - 600K.
This was repeated for the two cases of 1) no applied microwave power, and 2) an electric
field strengths of 3x 105 V/m. The reactor configuration is shown in Figure 4.22, was such
that the mass of catalyst was heated by the sensible heat in the gas and could be exposed
to microwaves to examine case 2.
The electric field strength inside the waveguide was measured using a calibrated
antenna and a HP-8481A power meter. The antenna was calibrated using a vector
network analyzer (VNA) such that the free space electric field strength could be
determined using the scattering parameters. These parameters are discussed in Appendix
E. The antenna was inserted into the location where the differential mass o f catalyst was
to reside during the study of case 2 and the response was again measured using the VNA.
This measurement guarantees the existence of microwave energy at the differential-bed
location.
For the differential experiment, I collected data in the form of rate versus
temperature at constant feed conditions with no applied microwave power. Then the same
procedure was followed using an electric field strength of 3 x l0 5 V/m. An Arrhenius plot
94
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will yield the activation energy as the slope of the curve and the pre-exponential factor
from the linearized first order rate expression. Linearizing equation (4.3) for the case o f
low conversion:
ln ( f i? ) = ln ( A C ,,0 ) - ^ Y
(4.46)
This expression was then evaluated experimentally and compared to the expression given
by Amphlette, et al. [52].
One-Dimensional Packed Bed
The behavior of equations (4.14) and (4.16), shown in Figures 4.4 and 4.5, was to be
tested using an integral type reactor with 1 gram o f crushed catalyst. The reactant gases,
mixed at a 1:1 steam to methanol ratio, were fed at 8 cc/s. This was done at a temperature
of 580K. To maintain the 1-D assumption the tube diameter was chosen such that the Pe\i
was л
1. Using a tube diameter of 2.5 mm and length o f 60 mm, the Peclet number was
approximately 0.01. Conversion was then measured for no applied microwave power, and
varying electric field strengths up to 5 x 105 V/m. A schematic of the reactor
configuration for this experiment is shown in Figure 4.23.
95
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
W aveguide
^
'
G C M easurem ent
Figure 4.23. Reactor configuration for the 1-D integral-bed experiment. Reaction
was driven either by the sensible heat in the feed, or by the dissipation of
microwave energy.
96
Reproduced with permission of the copyrig
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