AN ABSTRACT OF THE THESIS OF
Travis J. Campbell for the degree of Master of Science in Chemical Engineering
presented on May 14, 2011
Title: Photochemical Reduction of Carbon Dioxide in Aqueous and Ionic Liquid
Solutions in a Microreactor with TiO2 Catalyst; Experiment and Modeling
Abstract approved:
Goran N. Jovanovic
Alexandre F. Yokochi
Microtechnology was used to study the chemical reduction of dissolved carbon
dioxide into useful products. A novel TiO2 photocatalyst was used to activate the reaction
under ultraviolet irradiation. CO2 was dissolved in aqueous and 50% BMIM-BF4 (ionic
liquid) solutions. The introduction of an ionic liquid increased the solubility of CO2 by
60%. Both solutions were pumped through a continuous photochemical microreactor and
analyzed for products.
The aqueous photochemical microreactor process produced 5x10-8-1x10-6 moles of
methane per liter of solution processed. These values vary with mean residence time
within the 0.016 mL microreactor volume. Serial reduction intermediates are likely
present in solution below the detection limits of our analytical instruments. The 50%
ionic liquid process produced 4x10-8-1x10-7 moles of methane per liter of solution
processed. Similarly, no intermediates were measured.
Mathematical models for the kinetic mechanism, momentum transfer, and mass
transfer within the reactor were developed. These models were added to a numerical
simulation and compared to experimental values. An optimization scheme was executed
to extract meaningful reaction rate constants from the simulation that best fit the
experimental data. Reaction rate constants reflect the feasibility of operating these
processes and the numerical models can be used as design tools.
©Copyright by Travis J. Campbell
May 14, 2013
All Rights Reserved
Photochemical Reduction of Carbon Dioxide in Aqueous and Ionic Liquid Solutions in a
Microreactor with TiO2 Catalyst; Experiment and Modeling
by
Travis J. Campbell
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Presented May 14, 2013
Commencement June 2013
Master of Science thesis of Travis J. Campbell presented on May 14, 2013.
APPROVED:
Co-Major Professor, representing Chemical Engineering
Co-Major Professor, representing Chemical Engineering
Head of the School of Chemical, Biological, and Environmental Engineering
Dean of the Graduate School
I understand that my thesis will become part of the permanent collection of Oregon
State University libraries. My signature below authorizes release of my thesis to
any reader upon request.
Travis J. Campbell, Author
ACKNOWLEDGEMENTS
Thank you, Dr. Jovanovic, for challenging me with this project and mentoring me
throughout the process.
Thank you, Dr. Yokochi, for your guidance, expertise, and remarkable patience.
I could not have finished without the help of Dr. Azizian, a humble and incredibly
talented man.
Special thanks to everyone at the Microproducts Breakthrough Institute (MBI), Oregon
State University, and the Petroleum Authority of Thailand (PTT) that created this
opportunity to explore a new frontier of chemical engineering.
To my fellow graduate students, I cannot thank you enough for everything.
Special thanks to Yu Miao (Tony), my lab partner, who deserves equal credit for this
work.
TABLE OF CONTENTS
Page
1. INTRODUCTION ...................................................................................................1
2. GOALS AND OBJECTIVES ..................................................................................3
3. THEORETICAL BACKGROUND AND TOOLS .................................................5
3.1 Kinetic Model ..............................................................................................5
3.2 Momentum Model .....................................................................................24
3.3 Mass Transfer Model .................................................................................28
3.4 Numerical Model .......................................................................................31
3.5 Numerical Optimization.............................................................................33
4. EXPERIMENTAL APPARATUS, METHODS AND MEASUREMENTS ........36
4.1 Experimental Apparatus.............................................................................36
4.2 Methods......................................................................................................41
4.3 Measurements ............................................................................................41
5. MATERIALS, METHODS, PROCEDURES .......................................................42
6. EXPERIMENTAL DATA .....................................................................................49
7. EXPERIMENTAL RESULTS...............................................................................51
8. CONTRIBUTION TO SCIENCE AND CONCLUSIONS ...................................54
9. RECOMMENDATIONS FOR FUTURE WORK ................................................56
BIBLIOGRAPHY ..................................................................................................57
APPENDICES .......................................................................................................60
LIST OF FIGURES
Figure
Page
3.1 Depiction of Chemical Reaction at a Photocatalyst Surface .......................................5
3.2 Depiction of Electron/Hole Pair Generation and Recombination................................6
3.3 Depiction of Surface Reaction Mechanism ...............................................................18
3.4 Depiction of Surface Adsorption ...............................................................................18
3.5 Depiction of Surface Desorption ...............................................................................19
3.6 Velocity Profile of Liquid in a Microchannel ............................................................24
3.7 Velocity Profile in the Microchannel .........................................................................27
3.8 Differential Fluid Element in a Microchannel ...........................................................28
3.9 COMSOL Contour Plot of Velocity in the Microreactor Cross Section ...................31
3.10 COMSOL Meshing in the Microreactor Numerical Model .......................................31
3.11 Example of Numerical Model Curves Compared to Experimental Data ..................32
3.12 Flowchart of Optimization Program ..........................................................................34
3.13 Plot of Objective Function vs. Iteration Number .......................................................34
3.14 Reaction Rate Constants vs. Iteration Number ..........................................................35
4.1 Photocatalytic Microreactor Process Schematic ........................................................36
4.2 Photocatalytic Microreactor Components..................................................................37
4.3 Schematic of Parallel Plate Photocatalytic Microreactor...........................................37
4.4 Design Drawing of Catalyst on Quartz Crystal .........................................................38
4.5 16,000x SEM Image of NanospringsTM .....................................................................38
4.6 Photon Counts Across the UV-Visual Spectra from Light Source ............................39
4.7 Light Intensity at 254 nm versus Distance from UV Source .....................................40
LIST OF FIGURES (Continued)
Figure
Page
5.1 CO2 Solubility in H2O versus Temperature1 ..............................................................43
5.2 Calibration Curve for Formic Acid Measurement .....................................................44
5.3 Example Peak Measurement – Formaldehyde Peak on Upper Right .......................45
5.4 Calibration Curve for Formaldehyde Measurement ..................................................45
5.5 Example Peak Measurement – Methanol Peak Third from Left ...............................46
5.6 Calibration Curve for Methanol Measurement ..........................................................47
5.7 Calibration Curve for Methane Measurement ...........................................................48
6.1 Methane Produced in the Aqueous Photocatalytic Microreactor Process .................49
6.2 Methane Produced in the 50% Ionic Liquid Process .................................................50
7.1 Aqueous Photocatalytic Microreactor Optimization Results.....................................51
7.2 50% Ionic Liquid in Water Photocatalytic Microreactor Optimization Results ........51
8.1 Predicted Values of All Compounds in Aqueous System from Model .....................54
LIST OF TABLES
Table
Page
3.1 Diffusion Coefficients Used in the Mass Transfer Model .........................................30
4.1 EDAX Elemental Analysis of Catalyst Surface.........................................................39
5.1 CO2 Solubility in H2O at Common Temperatures .....................................................43
6.1 Aqueous Photocatalytic Microreactor Experimental Results ....................................49
6.2 50% Ionic Liquid Experimental Results ....................................................................50
7.1 Reaction Rate Constants from Optimized Model ......................................................53
LIST OF SYMBOLS
Symbol
Units
-
e
Φ
Description
[6.02x10
-23
Electron
2
photons/m ·s]
“Moles” of incident photons per area per time
h
+
-
Positive hole, caused by electron absence
i(s)
-
Chemical species i adsorbed onto a surface (s)
i+
-
Electron-deficient species i
i*
-
Radical species i
i-
-
Electron-rich species i
Kh
-
Hydration constant
Ka1
-
First acid dissociation constant
CT
-
Number of catalyst sites total
C
-
Number of catalyst sites empty
C
-
Number of catalyst sites occupied
Ci, 
-
Number of catalyst sites occupied by species i
ri
[mol/m3·s]
Reaction rate of species i in the bulk
ri,s
[mol/m2·s]
Reaction rate of species i at the surface
[i]
[mol/m3]
σ
[m2]
Catalyst surface area
ν
[m3]
Catalyst volume
γ
[g/m2]
Reactor catalyst loading
α
[m2/g]
Available surface area per mass of catalyst
-1
s
[m ]
DiB
2
[m /s]
Mi
[g/mol]
Vi
[m3/mol]
φ
-
Concentration of species i
Ratio of σ to ν
Diffusion coefficient for species i into bulk
fluid B
Molecular weight of species i
Molal volume of species i
Association parameter in Wilke-Chang
LIST OF APPENDICES
Appendix
Page
Hardware Information ........................................................................................................60
A.1 Harvard Apparatus 975 Syringe Pump .........................................................60
A.2 (SG009660) SGE 50 mL Gas-tight, Glass Syringe.......................................60
A.3 Connection Detail 1 ......................................................................................61
A.4 Connection Detail 2 ......................................................................................61
A.5 Microreactor Components.............................................................................62
A.6 Quartz Crystal, Cut and Drilled by Technical Glass Products ......................63
A.7 Quartz Plate with Catalyst Applied ...............................................................63
Catalyst Characterization ...................................................................................................64
A.8 1,000x SEM image of TiO2-coated NanospringsTM .....................................64
A.9 2,000x SEM image of TiO2-coated NanospringsTM .....................................64
A.10 4,000x SEM image of TiO2-coated NanospringsTM .....................................65
A.11 4,000x SEM image of TiO2-coated NanospringsTM after Gold ALD ..........65
A.12 8,000x SEM image of TiO2-coated NanospringsTM after Gold ALD ..........66
A.13 16,000x SEM image of TiO2-coated NanospringsTM after Gold ALD ........66
A.14 30,000x SEM image of TiO2-coated NanospringsTM after Gold ALD ........67
A.15 60,000x SEM image of TiO2-coated NanospringsTM after Gold ALD ........67
T.1 Catalyst Thickness at Six Locations ..............................................................68
T.2 Catalyst Thickness Measurement Using 10x Optic.......................................68
T.3 Catalyst Thickness Measurement Using 20x Optic.......................................68
LIST OF APPENDICES (Continued)
Appendix
Page
Numerical Model ...............................................................................................................69
Numerical Optimization.....................................................................................................84
Statistical Methods .............................................................................................................85
T.4 Z-values for Various Levels of Confidence (LOC) .......................................85
Photochemical Reduction of Carbon Dioxide in Aqueous and Ionic Liquid Solutions in a
Microreactor with TiO2-Catalyst; Experiment and Modeling
CHAPTER 1
INTRODUCTION
CO2 is accountable for 50% of the greenhouse gas effect in earth’s atmosphere2. This
alarming realization provides a strong incentive to explore new processes for chemical
reduction of CO2. However, reduction is an energy intensive process. It is possible that in
the near future profit functions will evolve to include emissions of greenhouse gases.
With that in mind, we briefly review the available processes for CO2 reduction.
Electro catalytic processes provide one option for reduction of CO23. These systems
are subject to varying life cycles and do not address the net energy loss. Bioconversion is
another option, but the system is also energetically unfavorable. Some CO2 is used to
manufacture commodity chemicals, but total demand amounts to a small fraction of the
annual production4. A solution is required which circumvents the net energy loss by
employing renewable sources.
Another option for chemical reduction is photocatalysis. Light-activated catalysts
reduce the activation energy required for chemical conversion. This process has the
advantage of creating useful chemical products such as methane, methanol, and ethanol.
Photocatalysis may become energetically favorable by harnessing and coupling the
renewable power of solar energy5. In our studies, we demonstrate that photocatalysis is
possible under favorable conditions of ambient temperature and pressure, making the
process relatively safe.
There have been several successful demonstrations of CO2 reduction via
photocatalysis. One catalyst that is commonly used due to its abundance in nature is
titanium dioxide (TiO2). In fact, TiO2 has been used with dissolved CO2, ultraviolet light,
2
doped transition metals, and organic precursors to produce formaldehyde,6 methanol,6,
oxalic acid,7 methane,8 formic acid, and hydrogen9. These experiments all demonstrated
the capability of batch photo reduction processes. Applying a microreactor would allow
us to extend our study to the continuous operation of such processes.
Microreactors are sized to capitalize on the natural diffusion of molecules. Defined
with a characteristic length between 1-100 micrometers, a microreactor scales down
chemical processes such that diffusion will transport a molecule in solution from reactor
wall to wall in under one second. Molecules rapidly permeate porous media such as
packed beds and catalyst layers with relative ease. Applied specifically to catalytic
systems, the implication is that reaction rates will increase significantly.
The microreactor used in our study contains a unique catalyst that is mostly void space
with large surface area. The NanospringTM catalyst has an atomic layer-deposited
conformal coating of TiO2 on the surface to enable photocatalytic reduction of CO2. The
scale of this reactor combined with the unique catalyst architecture allows CO2 to rapidly
diffuse to the catalyst surface, where reaction occurs, and quickly diffuse back out where
convective mass transfer is dominant.
Additionally, an ionic liquid is added to the aqueous solvent to increase CO2
concentration within the microreactor. Ionic liquids are liquid salts that can form
complexes with dissolved CO2 and thus more can be absorbed into solution10. Complexes
have additional functionality in that they can to be susceptible chemical reduction. For
example, Rosen et al. demonstrated that an ionic liquid complex renders CO2 more
susceptible to electrochemical reduction. The result was that minimal over potential
beyond the net change in chemical potential was required to drive a reduction to carbon
monoxide11. We will apply the ionic liquid to our microreactor for study.
3
CHAPTER 2
GOALS AND OBJECTIVES
There are two major goals of this work:
1. Provide experimental and modeling/simulation evidence that photochemical
reduction of carbon dioxide in aqueous and ionic liquid solutions in a
microreactor with TiO2 catalyst is feasible.
2. Determine the reaction rate constants, which emerge from the chemical reaction
mechanism adopted in this thesis.
To achieve these goals, the following objectives have to be accomplished:
a. Define the reaction mechanism for the photochemical reduction of CO2 in
aqueous and ionic liquid solution on TiO2 catalyst.
b. Define a mathematical model based on the conservation of mass and momentum
transport variables, which can represent operation of a photochemical
microreactor.
c. Validate the model by performing initial simulation of the reactor performance.
d. Design, manufacture and assemble a photochemical microreactor.
e. Design and build a test-loop suitable for testing the photochemical microreactor.
f. Design and characterize the TiO2 catalyst suitable for the photochemical reduction
of CO2 in aqueous and ionic liquid solution.
g. Design an instrumentation system and perform necessary calibration and
validation.
h. Perform experiments
i. Determine the reaction rate constants pertinent for the adopted chemical reaction
mechanism. This objective is performed by comparing experimental data with a
mathematical model, using numerical simulation and optimization. When
convergence is achieved, the model will effectively become a tool for system
analysis and design.
4
j. Define recommendations for future study, development and commercialization of
the system.
5
CHAPTER 3
THEORETICAL BACKGROUND AND TOOLS
To characterize any chemical process, a sufficiently thorough understanding of the
physical system is required. This system is described by three physical models: kinetic,
momentum, and mass. All three are combined in one numerical model which is used to
simulate the physical system. Experimental results are compared to the model using an
optimization program until the model and experimental results converge. At convergence,
the numerical model’s reaction rate constants reflect the true behavior of the physical
system, and those rate constants can be effectively used for system analysis and design.
3.1 Kinetic Model
All reactions occur at the catalyst surface, and therefore, all reaction rates are expressed
as ri,s, which is the reaction rate of species i at the catalyst surface s.
Figure 3.1 Depiction of Chemical Reaction at a Photocatalyst Surface
In photocatalytic reduction, photons are absorbed by a catalyst, generating electron/hole
pairs.
6
k1
TiO2   
 e(s )  h(s )
(1)
Here, light energy flux is quantified with the symbol Φ [6.02x10-23 photons/m2·s].
Photons have been converted to “moles” for homogeneity with chemical species in these
expressions.
Electron/hole pairs may facilitate chemical reaction or recombine to release heat.


2
e(s)
 h(s)

 heat
k
(2)
Figure 3.2 Depiction of Electron/Hole Pair Generation and Recombination
In this mechanism, TiO2 absorbs photons and CO2 is reduced to formic acid (HCOOH),
formaldehyde (HCHO), methanol (CH3OH), and methane (CH4) in series. The model is
adopted from similar work by B. Srinvas et al.7
7
To enable CO2 reduction, water is oxidized by electron holes to produce protons and
hydroxyl radicals. Hydroxyl radicals combine to form hydrogen peroxide (H2O2), which
is subsequently oxidized by electron holes to generate oxygen and protons.



3
H2O(s)  h(s)

 H(s)
 OH(s)
(3)

4
2OH(s)

 H 2O2(s)
(4)



5
H2O2(s)  h(s)

 O2(s)
 2H(s)
(5)


6
O2(s)
 h(s)

 O2(s)
(6)
k7
H 2O2( s )   
 2OH (s )
(7)
k
k
k
k
Upon dissolution in water, a small amount of CO2 forms carbonate and, subsequently,
carbonic acid (H2CO3, Kh = 1.7x10-3 , Ka1 = 2.5x10-4 M, pH = 4.4 at 25 ⁰C). Carbonic
acid dissociates and acidifies the bulk solution.
8
CO2(s)  H 2O(s) 
 H 2CO3(s)
(8)

2
9
H 2CO3(s) 
 2H(s)
 CO3(s)
(9)
k
k8
k
k9
The net effect of equations (3) - (7) is the generation of hydronium ions (H+) and
electrons (e-) that may go on to reduce CO2 or recombine to form hydrogen molecules.



10
H(s)
 e(s)

 H(s)
(10)

11
2H(s)

 H 2(s)
(11)
k
k
Some CO2 will adsorb to the catalyst surface where serial reduction occurs. Upon
adsorption, CO2 is reduced to an anionic radical.
8


12
CO2(s)  e(s)

 O  C   O(s)
k
(12)
Adsorbed, anionic radicals can combine with protons to yield formic acid, formaldehyde,
methanol, or methane in series, respectively.
k13
O  C  O(s )  H(s) 
O  C  OH( s)
k14
O  C  OH( s)  H(s ) 
O  CH  OH(s )
(13)
(formic acid)
(14)
k15
O  CH  OH( s)  e(s) 
OH  HC  O(s)
(15)
k16
OH  HC  O(s)  H(s) 
OH  HC  OH( s)
(16)
k17
OH  HC  OH(s)  e(s) 
OH  C() H  OH(s)
(17)
k18
OH  C() H  OH(s)  H(s) 
OH  CH2  OH(s)
(18)
k19
OH  CH2  OH( s) 
 H2O( s)  HCHO( s )
(19)
(formaldehyde)
k20
HCHO( s )  e(s ) 
 HC H  O(s )
(20)
k21
HC H  O(s )  H(s ) 
 HCH  OH( s )
(21)
k22
HC H  OH( s)  H(s) 
CH3OH( s)
(methanol)
k23
CH3OH( s )  H(s ) 
C H3( s)  H2O( s)
k24
C  H 3( s )  H (s ) 
 CH 4( s )
(22)
(23)
(methane)
(24)
A material balance is conducted using the equations above. The Quasi-Steady State
assumption is applied to determine the concentration of all compounds on the catalyst
surface [mol/m2]:
Concentration of carbon dioxide CO2 on the catalyst surface [mol/m2]:
d
CO2( s )   k12 e(s )  CO2( s )   k8 CO2( s )   H2O( s )   k8  H2CO3( s ) 
dt
(25)
9
Concentration of hydrogen H2 on the catalyst surface [mol/m2]:
(26)
2
d
 H2( s )   k11  H(s ) 
dt
Concentration of formic acid HCOOH on the catalyst surface [mol/m2]:
(27)
d
 HCOOH( s )   k14  H(s )  O  C  OH( s )   k15 e(s )   HCOOH( s) 
dt
Concentration of formaldehyde HCHO on the catalyst surface [mol/m2]:
(28)
d
 HCHO( s )   k19 OH  CH 2  OH ( s )   k20 e(s )   HCHO( s ) 
dt
Concentration of methanol CH3OH on the catalyst surface [mol/m2]:
(29)
d
CH3OH( s )   k22  HC H  OH( s )   H(s )   k23  H(s )  CH3OH( s) 
dt
Concentration of methane CH4 on the catalyst surface [mol/m2]:
(30)
d
CH 4( s )   k24 C  H 3( s )   H (s ) 
dt 
Concentration of holes h+ on the catalyst surface [mol/m2]:
(31)
d 
 h( s )   k1  k2  h(s )  e(s )   k3  H 2O( s )  h(s )   k5  H 2O2( s )  h(s ) 
dt  
k6 O2( s )   h(s ) 
Concentration of electrons e- on the catalyst surface [mol/m2]:
(32)
d 
e( s )   k1  k2 e(s )   h(s )   k10  H (s )  e(s )   k12 CO2( s )  e(s ) 
dt
k15  HCOOH ( s )  e(s )   k17 OH  HC   OH ( s )  e(s )   k20 e(s )   HCHO( s ) 
10
Concentration of hydrogen radicals H  on the catalyst surface [mol/m2]:
(33)
2
d
 H (s )   k10  H (s )  e(s )   k11  H (s )   k14  H (s )  O  C   OH ( s ) 
dt
k22  HC  H  OH ( s )   H (s )   k23  H (s )  CH 3OH ( s )   k24 C  H 3( s )   H (s ) 
Concentration of hydrogen ions H+ on the catalyst surface [mol/m2]:
(34)
d
 H (s )   k3  H 2O( s )   h(s )   2k5  H 2O2( s )   h(s )   2k9  H 2CO3( s ) 
dt 
2
k9  H (s )  CO3(2s )   k10  H (s )  e(s )   k13  H (s )  O  C   O(s ) 
k16  H (s )  OH  HC   O(s )   k18  H (s )  OH  C (  ) H  OH ( s ) 
k21  H (s )   HC  H  O(s ) 
Concentration of O  C  O on the catalyst surface [mol/m2]:
(35)
d
O  C  O(s )   k12 CO2( s )  e(s )   k13  H(s)  O  C   O(s) 
dt
Concentration of O  C  OH on the catalyst surface [mol/m2]:
(36)
d
O  C  OH( s )   k13  H(s )  O  C  O(s )   k14  H(s)  O  C  OH( s) 
dt 
Concentration of OH  HC  O on the catalyst surface [mol/m2]:
(37)
d
OH  HC  O(s )   k15  HCOOH( s )  e(s)   k16  H(s)  OH  HC  O(s) 
dt
Concentration of OH  HC  OH on the catalyst surface [mol/m2]:
d
OH  HC   OH ( s )   k16  H (s )  OH  HC   O(s ) 
dt
k17 OH  HC   OH ( s )  e(s ) 
(38)
11
Concentration of OH  C ( ) H  OH on the catalyst surface [mol/m2]:
(39)
d
OH  C (  ) H  OH ( s )   k17 OH  HC   OH ( s )  e(s ) 
dt
k18  H (s )  OH  C (  ) H  OH ( s ) 
Concentration of OH  CH2  OH on the catalyst surface [mol/m2]:
(40)
d
OH  CH 2  OH ( s )   k18  H (s )  OH  C (  ) H  OH ( s ) 
dt 
k19 OH  CH 2  OH ( s ) 
Concentration of HC  H  O on the catalyst surface [mol/m2]:
(41)
d
 HC H  O(s )   k20 e(s )   HCHO( s )   k21  H(s )   HC H  O(s ) 
dt
Concentration of HC H  OH on the catalyst surface [mol/m2]:
(42)
d
 HC H  OH( s )   k21  H(s )   HC H  O(s )   k22  HC H  OH( s )   H(s ) 
dt
Concentration of C H3 on the catalyst surface [mol/m2]:
(43)
d
C  H 3( s )   k23  H (s )  CH 3OH ( s )   k24 C  H 3( s)   H (s) 
dt
Concentration of OH  on the catalyst surface [mol/m2]:
(44)
2
d
OH (s )   k3  H 2O( s )  h(s )   k4 OH (s )   k7  H 2O2( s )  
dt
Concentration of H2O2 on the catalyst surface [mol/m2]:
(45)
12
2
d
 H 2O2( s )   k4 OH (s )   k5  H 2O2( s )  h(s )   k7  H 2O2( s )  
dt
Concentration of O2 on the catalyst surface [mol/m2]:
(46)
d
O2( s)   k5 H2O2( s)  h(s)   k6 O2( s)  h(s) 
dt
Concentration of O2 on the catalyst surface [mol/m2]:
(47)
d
O2( s )   k6 O2( s )  h(s ) 
dt
Concentration of H 2CO3 on the catalyst surface [mol/m2]:
(48)
d
 H 2CO3( s )   k8  H 2O( s )  CO2( s )   k8  H 2CO3( s )   k9  H 2CO3( s ) 
dt 
2
 k9  H (s )  CO3(2 s ) 
Concentration of CO32 on the catalyst surface [mol/m2]:
(49)
2
d
CO3(2s)   k9  H2CO3( s)   k9  H(s)  CO3(2s) 
dt
With equations for all concentrations at the catalyst surface, the kinetic model can be
built to determine rates of reaction at the catalyst surface.
Several assumptions are employed to simplify the model. They allow us to reduce the
model to its most significant variables and study their effects on the system:
1. Photocatalytic reduction is completed via e , H  and H  attack on CO2 .
13
2. The concentrations of h  and e are constant at steady state, and by employing the
Quasi-Steady-State Assumption (QSSA), their changes with time are negligible.
d 
d
 h   e   0
dt
dt
3. Recombination rate of h  and e is much faster than formation rate of hydroxyl
radicals.16
k2 e  h   k3 H2O( s)  h 
4. Recombination rate of h  and e is much faster than consumption rate of hydrogen
peroxide and formation rate of oxygen.
k2 e  h   k5  H2O2( s )  h   k6 O2( s)  h 
5. The concentrations of h  and e are equal.
 h   e 
6. Employing the Quasi-Steady-State Assumption, the concentrations of all radicals
are constant at steady state.
d
d
d
d
 H (s )    H (s )   OH (s )   O  C   O(s ) 
dt
dt
dt
dt
d
d
 O  C   OH ( s )   OH  HC   O(s ) 
dt
dt
d
d
 OH  HC   OH ( s )   OH  C (  ) H  OH ( s ) 
dt
dt
d
d
 OH  CH 2  OH ( s )    HC  H  O(s ) 
dt
dt
d
d
  HC  H  OH ( s )   C  H 3( s )   0
dt
dt
14
7. At steady state, the number of available catalyst sites is constant, as well as the
number of occupied/unoccupied catalyst sites.
C   Ci ,
CT  C  C  const
i
dCT
 0;
dt
dC
dC
0
 0;
dt
dt
8. The concentrations of hydrogen peroxide, carbonic acid and carbonate ions are
very low.
 H 2O2   0,  H 2CO3   0,
CO32   0
9. The low hydration constant of aqueous CO2 renders the carbonic acid equilibrium
reaction insignificant.
k 
k12 CO2( s )   1  
 k2 
0.5
k8 CO2( s )   H 2O( s )   k8  H 2CO3( s ) 
These assumptions are applied to the QSSA equations for each compound’s
concentration at the catalyst surface (eq. 25-49) to yield simplified expressions:
1. Applied assumptions [2], [3], [4] and [5] on equation (31) :
d 
 h( s )   k1  k2  h(s )  e(s )   k3  H 2O( s )   h(s )   k5  H 2O2( s )   h(s ) 
dt  
2
k6 O2( s )   h(s )   k1  k2 h(s )  e(s )   k1  k2 h(s )   0
k 
 e    h    1  
 k2 

(s)
0.5

(s)
2. Applied assumption [6] on equation (35) :
(50)
15
d
O  C  O(s )   k12 CO2( s )  e(s )   k13  H(s )  O  C  O(s )   0
dt
 O  C  O  


(s)
k12 CO2( s )  e(s ) 
k13  H(s ) 
(51)
3. Applied assumption [6] on equation (36) :
d
O  C   OH ( s )   k13  H (s )  O  C   O(s ) 
dt
k14  H (s )  O  C   OH ( s )   0
 O  C  OH ( s )  

k13  H (s )  O  C   O(s ) 
k14  H (s ) 
(52)
4. Applied assumption [6] on equation (37) :
d
OH  HC   O(s )   k15  HCOOH ( s )  e(s ) 
dt
k16  H (s )  OH  HC   O(s )   0
 OH  HC  O  


(s)
k15  HCOOH ( s )  e(s ) 
k16  H(s ) 
(53)
5. Applied assumption [6] on equation (38) :
d
OH  HC   OH ( s )   k16  H (s )  OH  HC   O(s ) 
dt
k17 OH  HC   OH ( s )  e(s )   0
 OH  HC  OH ( s )  

k16  H (s )  OH  HC   O(s ) 
k17 e(s ) 
6. Applied assumption [6] on equation (39) :
(54)
16
d
OH  C (  ) H  OH ( s )   k17 OH  HC   OH ( s )  e(s ) 
dt
k18  H (s )  OH  C (  ) H  OH ( s )   0
 OH  C
(  )
H  OH ( s )  
k17 OH  HC   OH ( s )  e(s ) 
k18  H (s ) 
(55)
7. Applied assumption [6] on equation (40) :
d
OH  CH 2  OH ( s )   k18  H (s )  OH  C (  ) H  OH ( s ) 
dt
k19 OH  CH 2  OH ( s )   0
 OH  CH 2  OH ( s )  
k18  H (s )  OH  C (  ) H  OH ( s ) 
k19
(56)
8. Applied assumption [6] on equation (41) :
d
 HC H  O(s )   k20 e(s )   HCHO( s )   k21  H(s )   HC H  O(s )   0
dt 
  HC H  O  


(s)
k20  e(s )   HCHO( s ) 
k21  H (s ) 
(57)
9. Applied assumption [6] on equation (42) :
d
 HC  H  OH ( s )   k21  H (s )   HC  H  O(s ) 
dt
k22  HC  H  OH ( s )   H (s )   0
  HC H  OH ( s )  

k21  H (s )   HC  H  O(s ) 
k22  H (s ) 
10. Applied assumption [6] on equation (43) :
(58)
17
d
C  H3( s )   k23  H (s )  CH 3OH ( s )   k24 C  H 3( s )   H (s )   0
dt
 C  H 3( s )  
k23 CH 3OH ( s ) 
(59)
k24
11. Applied assumption [6] and [8] on equation (34) :
d
 H (s )   k3  H 2O( s )  h(s )   k10  H (s )  e(s )   k13  H (s )  O  C   O(s) 
dt
 k16  H (s )  OH  HC   O(s )   k18  H (s )  OH  C ( ) H  OH ( s ) 
 k21  H (s )   HC  H  O(s )   0
Substitute in equations (50), (51), (53), (54), (55), and (57)
k3  H 2O( s )   k10  H (s )   k12 CO2( s )   2k15  HCOOH ( s ) 
(60)
k20  HCHO( s )   0
12. Applied assumption (6) on Eq33:
2
d
 H (s )   k10  H (s )  e(s )   k11  H (s )   k14  H (s )  O  C   OH ( s ) 
dt
k22  HC  H  OH ( s )   H (s )   k23  H (s )  CH 3OH ( s )   k24 C  H 3( s )   H (s )   0
Substitute in equations (50), (51), (52), (57), (58), (59), and (60)
k 
k11  H   2k23  H  CH 3OH ( s )   2k12 CO2( s )   1  
 k2 

(s)
2
0.5
k 
k 
2k15  HCOOH ( s )   1    2k20  HCHO( s )   1  
 k2 
 k2 
k 
 k3  H 2O( s )   1  
 k2 
0.5

(s)
0.5
0
0.5
(61)
18
Species in the bulk fluid are adsorbed onto the catalyst surface. A fraction of the adsorbed
species react and are converted into other species, which can desorb back into the bulk12.
Taking CO2 as an example, the surface adsorption, reaction at the surface, and rate of
desorption are depicted below:
Figure 3.3 Depiction of Surface Reaction Mechanism
Figure 3.4 Depiction of Surface Adsorption

kads

CO2  Surface 
CO2( s )
kdes
rads,CO2 
1
Vfluid in reactor
dNi
 CO2  C   kads ,CO2 CO2 
 kads
dt
k
ads
 C  
 kads
19
Figure 3.5 Depiction of Surface Desorption
rdes ,CO2 
1
 catalyst surface
rs ,CO2  
d CO2( s ) 
dt
dNi
 kdes ,CO2 CO2( s ) 
dt
0.5
k 
 k12 CO2( s )   1    k8 CO2( s )   H 2O( s )   k8  H 2CO3( s ) 
 k2 
k 
 k12 CO2( s )   1  
 k2 
rads ,CO2 
0.5

r
r
     s    rdes,CO  rs,CO
 des ,CO s ,CO
2
2
2
2

0.5

 k1  
 kads ,CO2 CO2        s    kdes ,CO2  k12     CO2( s ) 

 k2  
(62)
In the previous equations, (σ) is catalyst surface area [m2], (ν) is catalyst volume [m3]
within the reactor, (γ) is reactor catalyst loading [g/m2], (α) is available surface area of
catalyst per mass of catalyst [m2/g], and s is the ratio (σ/ν) [m-1].
Using the same method for other species, for formic acid (HCOOH):
rHCOOH ( s )
k 
d
  HCOOH ( s )   k12 CO2( s )   k15  HCOOH ( s )   1  
dt
 k2 

rads , HCOOH      s    rdes , HCOOH  rs , HCOOH 

0.5
20
 kads , HCOOH  HCOOH        s  
0.5

 k1  
 kdes , HCOOH  HCOOH ( s )   k12 CO2( s )   k15  HCOOH ( s )     

 k2  

(63)

For formaldehyde (HCHO):
rHCHO ( s )
k 
d
  HCHO( s )   k15  HCOOH ( s )   k20  HCHO( s )   1  
dt
 k2 


0.5
rads , HCHO      s    rdes , HCHO  rs , HCHO 
 kads , HCHO  HCHO        s  
0.5

 k1  
 kdes , HCHO  HCHO( s )   k15  HCOOH ( s )   k20  HCHO( s )     

 k2  


(64)
For methanol (CH3OH):
rCH3OH ( s )
k 
d
 CH 3OH ( s )   k20  HCHO( s )   1  
dt
 k2 

rads ,CH3OH      s   rdes ,CH3OH  rs ,CH3OH
0.5
 k23 CH 3OH ( s )   H (s ) 

 kads ,CH3OH CH 3OH        s  
0.5

 (65)
 k1 
 kdes ,CH3OH CH 3OH ( s )   k20  HCHO( s )      k23 CH 3OH ( s )   H (s )  


 k2 
For methane (CH4):
rCH4 ( s) 
d
CH4( s )   k23 CH3OH( s)  H(s) 
dt 
21

rads ,CH4      s   rdes ,CH4  rs ,CH4


 kads ,CH4 CH 4       s   kdes ,CH4 CH 4( s )   k23 CH3OH ( s )   H (s ) 

(66)
For hydrogen (H2):
rH2 ( s) 
2
d
 H2( s)   k11  H(s) 
dt

rads , H2      s   rdes , H2  rs , H2


 kads , H2  H 2       s   kdes , H2  H 2( s )   k11  H (s ) 
2

(67)
In order to determine the reaction rate at the surface ri,s, we need to calculate the
concentrations of reactants and products by solving equations (61) – (67).
k 
k11  H   2k23  H  CH 3OH ( s )   2k12 CO2( s )   1  
 k2 

(s)
2
k 
2k15  HCOOH ( s )   1  
 k2 
k 
 k3  H 2O( s )   1  
 k2 
0.5

(s)
0.5
k 
 2k20  HCHO( s )   1  
 k2 
0.5
(61)
0.5
0
0.5

 k1  
kads ,CO2 CO2        s    kdes ,CO2  k12     CO2( s ) 

 k2  
(62)
kads , HCOOH  HCOOH        s  
0.5

 k1  
 kdes , HCOOH  HCOOH ( s )   k12 CO2( s )   k15  HCOOH ( s )     

 k2  


(63)
22
kads , HCHO  HCHO        s  
0.5

 k1  
 kdes , HCHO  HCHO( s )   k15  HCOOH ( s )   k20  HCHO( s )     

 k2  

(64)

kads ,CH3OH CH 3OH        s  
0.5

 (65)
 k1 
 kdes ,CH3OH CH 3OH ( s )   k20  HCHO( s )      k23 CH 3OH ( s )   H (s )  


 k2 

kads ,CH4 CH 4       s   kdes ,CH4 CH 4( s )   k23 CH3OH ( s )   H (s ) 

kads , H 2  H 2        s   kdes , H 2  H 2( s )   k11  H (s ) 
2

(66)

(67)
By transforming groups of variables the equations become more manageable.
k 
 A  k12  1  
 k2 
0.5
 D  kdes ,CO2   A
0.5
k 
 B  k15  1  
 k2 
 E   kdes , HCOOH   B
k 
G  k3  1    H 2O s  
 k2 
k
CO2 
CO2( s )   ads ,CO2
    s    D
0.5
k 
C   k20  1  
 k2 
0.5
 F   kdes , HCHO  C 
23
 HCOOH ( s )  
 HCHO( s )  
kads , HCOOH   D   HCOOH   kads ,CO2   A  CO2 
    s    D   E
kads , HCHO   D   E    HCHO   k ads , HCOOH   B   D   HCOOH 
     s    D   E    F 

 H (s )  
kads ,CO2   A   B  CO2 
     s    D   E    F 
kdes ,CH3OH
3k23
CH 3OH ( s )  
k ads ,CH OH   D   E    F   CH 3OH   k ads , HCHO  C    D   E    HCHO 
3
2
3

     s    D   E    F   kdes ,CH OH
3
kads , HCOOH   B  C    D   HCOOH   kads ,CO2   A   B  C   CO2 
2
    s    D   E   F   kdes ,CH3OH
3
1
CH 4( s )  

2   D   E    F        s   kdes ,CH 4
2   D   E    F   kads ,CH 4 CH 4   kads ,CH3OH   D   E    F   CH 3OH 



 kads , HCHO  C    D   E    HCHO   kads , HCOOH   B  C    D   HCOOH 


 kads ,CO2   A   B  C   CO2 

 kdes ,CH3OH 
kads , H 2  H 2        s   k11 

 3  k23 
 H 2( s )  
    s  kdes ,H2
2
24
Each of these expressions is included in the numerical model. The model requires a
known concentration of CO2 and estimates for each rate constant to calculate product
concentrations.
3.2 Momentum Model
The momentum model describes bulk fluid flow through the microchannel. Fluid
convection is the primary mechanism of CO2 delivery to the catalyst surface; it is,
therefore, a critical component of the system.
Figure 3.6 Velocity Profile of Liquid in a Microchannel
The following assumptions were made to simplify the momentum model:
1. System is at a steady-state
2. Liquid is incompressible
3. System is isothermal
4. Flow is fully developed along the entire microchannel
5. Gravity is negligible in all directions (gx = gy = 0)
6. There is no velocity in the y- direction
7. Velocity in the x-direction is function of y (height), only
8. Microreactor thickness is much greater than height, and the flow is symmetric in
the z-direction
25
The continuity equation was applied to the system:
 


   x     y     z   0
t x
y
z
Continuity was simplified using the aforementioned assumptions:
 


   x     y     z   0
t x
y
z
 x
0
x
The Navier-Stokes equation describing fluid flow in a rectangular channel was also
applied to the system:
x-component:
 x



 x x   y x  z x
x
y
z
 t

  2 x  2 x  2 x 

P




g


 2  2  2 

x
x
y
z 

 x
y-component:
  2 y  2 y  2 y
 y
 y
 y 
  y
P
 x
y
 z




g


 2  2  2

y

t

x

y

z

y
y
z


 x




z-component:
  2  2  2 
 z


 
P
 x z   y z  z z   
  g z    2z  2z  2z 
x
y
z 
z
y
z 
 t
 x

Navier-Stokes was simplified using the same assumptions:
26
x-component:
 2
P
  2x
x
y
y-component:
P
0
y
z-component:
P
0
z
Using separation of variables, the x-component was set equal to a constant, C, and
solved.
 2
P
 C   2x
x
y
The following boundary conditions apply:
At x = 0, P = P0
At x = L, P = PL
At y = 0,
 x
=0
y
At y = ±H, x = 0
Boundary conditions are used to integrate:
27
C
 P0  PL 
L
 x
C
 yD
y

D0
x  
E
x ( y) 
C 2
y E
2
C 2
H
2
 PL  P0 
2 L
y
2
H2
Figure 3.7 Velocity Profile in the Microchannel
28
3.3 Mass Transfer Model
Figure 3.8 Differential Fluid Element in a Microchannel
The mass balance was built with respect to species i in the following way:
Compound i entering at x by convection
x yz  Ci x t mol 
Compound i entering at x by diffusion
 DiB  yz 
Ci
t  mol 
x x
Compound i leaving at x+∆x by convection
x yz  Ci xx t mol 
Compound i leaving at x+∆x by diffusion
 DiB  yz 
Compound i entering at y by diffusion
Ci
x
t  mol 
x x
29
 DiB  xz 
Ci
t  mol 
y y
Compound i leaving at y+∆y by diffusion
 DiB  xz 
Ci
y
t  mol 
y y
No convection or diffusion occurs in the z-direction.
Input – Output + Generation = Accumulation
x
Ci
 2Ci
 2Ci Ci
 DiB

D

iB
x
x2
y 2
t
Assuming steady state operation, the equation is simplified accordingly:
 x
Ci
 2Ci
 2Ci
 DiB

D
0
iB
x
x 2
y 2
The following boundary conditions apply to this system:
At x = 0, Ci  0, y   Ci 0 ,
At x = L,
At y = 0,
At y = H,  DiB
Ci  0, y 
0
x
Ci  L, y 
0
x
Ci  x,0
0
y
Ci  x, H 
     rs
y
30
All reactions occur at the catalyst surface, and a bulk reaction term is defined per unit
area [m2] which is related to the catalyst surface area [m2] per reactor volume [m3] in the
following way:
rb 

rs       s   rs

Diffusion coefficients for CO2, CH4 and H2 at 298 K are obtained from literature.13
Diffusion coefficients for HCOOH, HCHO, and CH3OH are calculated using the WilkeChang correlation13
8
D12 2 7.4 10   M 2 

T
V10.6
1/2
Table 3.1 Diffusion Coefficients Used in the Mass Transfer Model
Species
Di,H2O [m2/sec]
CO2
1.92E-09
CH4
1.49E-09
H2
4.50E-09
HCOOH
1.71E-09
HCHO
2.09E-09
CH3OH
1.64E-09
O2
2.10E-09
31
3.4 Numerical Model
The 3 previous models are combined in one numerical model using COMSOL software.
This enables simulation of the physical system and comparison with experimental values
to extract meaningful reaction rate constants.
Figure 3.9 COMSOL Contour Plot of Velocity in the Microreactor Cross Section
Figure 3.10 COMSOL Meshing in the Microreactor Numerical Model
32
10
Concentration (mol/m3)
9
8
7
CO2
6
HCOOH
5
HCHO
4
CH3OH
3
CH4
2
H2
1
0
0
10
20
30
40
50
Mean Resident Time (sec)
Figure 3.11 Example of Numerical Model Curves Compared to Experimental Data
33
3.5 Numerical Optimization
Model results are compared to experimental data for numerical optimization. We apply
an objective function that sums the squared differences of experimental and model results.
That function is defined here:
J  Wi Ci ,experiment  Ci ,mod el 
N
2
i 1
where Wi is the respective weighting factor.
The numerical modeling program (COMSOL) can be saved as a Matlab file (M-file) and
inserted as code within a Matlab function file. In this way, the model can be simulated
with reaction rate estimates and the function file determines the objective function value.
Matlab offers flexibility for choosing an optimization scheme. In this study, we use
the simplex minimization object (fminsearch) to estimate a change to the initial reaction
rate constants that will result in a lower objective function value. The COMSOL model
runs within the function file to return simulation results, the results are used to calculate
the objective function value, and the M-file object iterates this procedure until an
acceptably low objective function is achieved.
34
Figure 3.12 Flowchart of Optimization Program
Figure 3.13 Objective Function vs. Iteration Number
Reaction Rate Constant, ki
35
k1/k2
k
3
k11
k12
k15
k
20
k23
Iteration, K
Figure 3.14 Reaction Rate Constants vs. Iteration Number
36
CHAPTER 4
EXPERIMENTAL APPARATUS, METHODS AND MEASUREMENTS
4.1 Experimental Apparatus
The photocatalytic microeactor process has five components: reactant delivery,
microreactor, ultraviolet light source, collection vessel, and connections.
Figure 4.1 Photocatalytic Microreactor Process Schematic
Reactant delivery:
A Harvard Apparatus 975 syringe pump delivered CO2-saturated water to the
microreactor. The pump delivered liquid at rates between 0.2-46 mL/hr. A gas-tight, glass
syringe was used to contain the reactants.
Microreactor:
Functional components of the photocatalytic microreactor are housed between two
aluminum plates. The front plate has one inlet port and one outlet port. Neoprene gaskets
seal the plates to quartz crystals. Crystals are 1/8” thick that have been cut and drilled to
fit the plates. Between crystals is a PTFE spacer that seals the crystals and forms the
reactor volume. Four screws that have been tightened to 30 cN·m to seal the reactor.
37
Figure 4.2 Photocatalytic Microreactor Components
Figure 4.3 Schematic of Parallel Plate Photocatalytic Microreactor
One crystal is coated with silica Nanosprings,TM a proprietary catalyst support structure.
The Department of Physics at the University of Idaho adds the springs and coats them
with TiO2 via atomic layer deposition. The catalyst layer is approximately 26 microns
thick.
38
Figure 4.4 Design Drawing of Catalyst on Quartz Crystal
Figure 4.5 16,000x SEM Image of NanospringsTM
39
Table 4.1 EDAX Elemental Analysis of Catalyst Surface
Ultraviolet light source:
The UV source is a 48W mercury gas bulb with peak intensity at 254 nm.
Figure 4.6 Photon Counts Across the UV-Visual Spectra from Light Source
40
No Quartz
Behind 1/8" Quartz
Photons per Optic Area
20500
20000
19500
19000
18500
18000
17500
17000
0
0.5
1
1.5
2
Distance From Source [inches]
Figure 4.7 Light Intensity at 254 nm versus Distance from UV Source
Collection Vessel:
A 10 mL gas-tight, glass syringe was connected to the reactor outlet to collect products.
Connections:
All fittings are male or female luer lock connections screwed onto 1/8” male nuts with
ferrules. PEEK HPLC tubing connects the fittings. This tubing was small (0.02” ID) and
could withstand very high pressure (>2,000 psi).
4.2 Methods
CO2 was bubbled through HPLC-grade water provided by OSU’s chemistry store for at
least 30 minutes to remove dissolved oxygen and saturate with CO2. pH of this solution
was 3.71. The liquid was immediately transferred into a gas-tight glass syringe. Care was
41
taken to avoid excessive agitation that might promote CO2 dissolution. The syringe was
immediately connected to the photocatalytic microreactor process. The ultraviolet light
source was allowed sufficient time to warm up (10 minutes) and the syringe pump setting
was selected for the desired mean residence time. A second collection syringe was
attached and wrapped with a paper towel to prevent stray UV light from oxidizing
products. The catalyst was primed by running 15 mL of CO2-saturated solution before
any samples were collected. This allowed full loading and enabled the steady-state
assumption.
For 50% (w/v) ionic liquid experiments, the same procedure was followed with the
mixture replacing water.
4.3 Measurements
All samples were collected in a 10 mL gas-tight syringe and immediately transferred into
a 12 mL sealed headspace vial for analysis.
42
CHAPTER 5
MATERIALS, METHODS, PROCEDURES
Five compounds were measured: carbon dioxide (CO2), formic acid (HCOOH),
formaldehyde (CH2O), methanol (CH3OH), and methane (CH4).
Carbon Dioxide (CO2):
Solution pH was measured using a pH probe after undergoing a two-point calibration at
pH = 4.0 and 7.0. The pH can be used to calculate dissolved CO2 using the following
method:
Kh = 1.7x10-3 = [H2CO3]/[CO2]
Ka1 = 2.5x10-4 = [H+][HCO3-]/[H2CO3]
Step1. Measure pH
Step 2. Calculate [H+]
[H+] = 10-pH
Step 3. Calculate [H2CO3]
[H2CO3] ~ [H+]2/Ka1
Step 4. Calculate [CO2]
[CO2] = [H2CO3]/Kh
43
Figure 5.1 CO2 Solubility in H2O versus Temperature1
Table 5.1 CO2 Solubility in H2O at Common Temperatures
Temp. [⁰C]
[g/kg]
[mol/L]
10
2.5
5.7E-02
20
1.7
3.9E-02
25
1.5
3.4E-02
30
1.25
2.8E-02
44
Formic Acid (HCOOH):
Formic acid was measured as dissolved formate using ion chromatography.
Peak Area of Potassium Formate (μS▪min)
9
8
y = 0.0833x
R² = 0.9997
7
6
5
4
3
2
1
0
0
20
40
60
80
100
Concentration of Formate Anion (or Formic Acid) (ppm)
Figure 5.2 Calibration Curve for Formic Acid Measurement
Formaldehyde (CH2O):
Formaldehyde was measured using gas chromatography equipped with a flame ionization
detector. A 6-foot Porapak QS column was used with the following settings:
Oven Temp: 70 ⁰C, ramp 30 ⁰C/min for 6 min
Detector Temp: 240 ⁰C
Injection Volume: 10 µL
Retention Time: ~5.5 min
45
Measure: total peak area
Figure 5.3 Example Peak Measurement – Formaldehyde Peak on Upper Right
25
Peak Area
20
15
10
y = 6.6948ln(x) - 26.652
R² = 0.9998
5
0
0
200
400
600
800
1,000
ppm
Figure 5.4 Calibration Curve for Formaldehyde Measurement
46
Methanol (CH3OH):
Methanol was measured using gas chromatography equipped with a flame ionization
detector. A 6-foot Porapak QS column was used with the following settings:
Oven Temp: 135 ⁰C for 10 min
Detector Temp: 240 ⁰C
Injection Volume: 1 µL
Retention Time: ~1.25 min
Measure: peak height
Figure 5.5 Example Peak Measurement – Methanol Peak Third from Left
47
14
y = 0.0102x - 0.2125
R² = 0.9956
12
Peak Height
10
8
6
4
2
0
0
200
400
600
800
1000
1200
PPM
Figure 5.6 Calibration Curve for Methanol Measurement
Methane (CH4)
Methane was measured using gas chromatography equipped with a flame ionization
detector. A 6-foot Porapak Q column was used with the following settings:
Injector Temp: 200 ⁰C
Oven Temp: 50 ⁰C, ramp 30 ⁰C/min for 6 min
Detector Temp: 200 ⁰C
Injection Volume: varied
Retention Time: 0.3 min
Measure: total peak area
(Note: this is a gas measurement, where all others were liquid samples)
48
1.E+04
y = 2.78E+13x - 7.57E+01
R² = 1.00E+00
9.E+03
8.E+03
Peak Area
7.E+03
6.E+03
5.E+03
4.E+03
3.E+03
2.E+03
1.E+03
0.E+00
0.E+00
5.E-11
1.E-10
2.E-10
2.E-10
Moles CH4
Figure 5.7 Calibration Curve for Methane Measurement
3.E-10
49
CHAPTER 6
EXPERIMENTAL DATA
The photocatalytic microreactor process exhibited high selectivity for the production of
methane, in agreement with similar batch studies cited in literature14. No other products
were present in measurable amounts.
Table 6.1 Aqueous Photocatalytic Microreactor Experimental Results
Mol CH4,
Measured
2.54E-10
4.11E-10
7.59E-10
1.72E-09
2.60E-09
4.13E-09
6.61E-09
Methane, CH4
Vol. Run
[mL]
5
5
5
5
5
5
5
[mol/L]
5.08E-08
8.23E-08
1.52E-07
3.44E-07
5.19E-07
8.26E-07
1.32E-06
Carbon Dioxide, CO2
CH4 Concentration [mol/L]
1.6E-06
9.E-02
8.E-02
7.E-02
6.E-02
5.E-02
4.E-02
3.E-02
2.E-02
1.E-02
0.E+00
1.4E-06
1.2E-06
1.0E-06
8.0E-07
6.0E-07
4.0E-07
2.0E-07
0.0E+00
0
20
40
60
CO2 Concentration [mol/L]
MRT
[sec]
1.3
2.5
4.8
9.5
19
37
72
80
MRT [sec]
Figure 6.1 Methane Produced in the Aqueous Photocatalytic Microreactor Process
50
The addition of 50% ionic liquid (w/v) to the photocatalytic microreactor process yielded
methane concentrations lower than the aqueous system with similarly high selectivity for
methane production. Below MRT = 37 [sec], no product was detected.
Table 6.2 50% Ionic Liquid Experimental Results
Mol CH4,
Measured
N/A
N/A
N/A
N/A
N/A
1.99E-10
2.56E-10
3.96E-10
6.85E-10
CH4 Concentration [mol/L]
Methane, CH4
Vol. Run
[mL]
5
5
5
5
5
5
5
5
5
[mol/L]
N/A
N/A
N/A
N/A
N/A
3.98E-08
5.12E-08
7.92E-08
1.37E-07
Carbon Dioxide, CO2
1.8E-07
1.6E-01
1.6E-07
1.4E-01
1.4E-07
1.2E-01
1.2E-07
1.0E-01
1.0E-07
8.0E-02
8.0E-08
6.0E-02
6.0E-08
4.0E-08
4.0E-02
2.0E-08
2.0E-02
0.0E+00
0.0E+00
0
50
100
150
200
250
300
MRT [sec]
Figure 6.2 Methane Produced in the 50% Ionic Liquid Process
CO2 Concentration [mol/L]
MRT
[sec]
1.3
2.5
4.8
9.5
19
37
72
141
276
51
CHAPTER 7
EXPERIMENTAL RESULTS
Data were used to optimize the numerical model using the scheme introduced in Chapter
CH4, Experimental
CH4, Model
CO2, Experimental
CO2, Model
2.5E-06
1.E-01
2.0E-06
8.E-02
1.5E-06
6.E-02
1.0E-06
4.E-02
5.0E-07
2.E-02
0.0E+00
0.E+00
0
20
40
60
CO2 Concentration [mol/L]
CH4 Concentration [mol/L]
3. Results gave the following best fit (lowest value of the objective function):
80
MRT [sec]
Figure 7.1 Aqueous Photocatalytic Microreactor Optimization Results
CH4, Model
CO2, Model
2.0E-07
1.5E-01
1.5E-07
1.0E-01
1.0E-07
5.0E-02
5.0E-08
0.0E+00
0.0E+00
0
50
100
150
200
250
CO2 Concentration [mol/L]
CH4 Concentration [mol/L]
CH4, Experimental
CO2, Experimental
300
MRT [sec]
Figure 7.2 50% Ionic Liquid in Water Photocatalytic Microreactor Optimization Results
52
The following reaction rate constants were obtained from the optimization scheme:
Table 7.1 Reaction Rate Constants from Optimized Model
Ionic Liquid System
Value
Units
Ratio
Aq/IL
k11
Aqueous System
Value
4.87E-04
5.38E-04
[m2/mol·s]
0.90
k12
6.04E-03
4.08E-03
[m2/mol·s]
1.48
k15
1.19E+00
1.30E+00
[m2/mol·s]
0.92
k20
1.46E+00
k23
1.60E+00
1.68E+00
k1_k2
4.66E-01
3.21E-01
Constant
1.60E+00
2
0.91
2
[m /mol·s]
0.95
[mol·s/m2]
1.45
[m /mol·s]
2
G
5.68E-05
6.54E-05
[mol·s/m ]
0.87
kads_CO2
2.02E-05
4.47E-07
[1/s]
45.33
kdes_CO2
2.19E-04
2.17E-04
[1/s]
1.01
kads_HCOOH
1.18E-01
1.80E-01
[1/s]
0.66
kdes_HCOOH
4.54E-05
6.69E-05
[1/s]
0.68
kads_HCHO
1.07E-01
1.20E-01
[1/s]
0.89
kdes_HCHO
1.62E-04
1.76E-04
[1/s]
0.92
kads_CH3OH
1.41E-01
1.62E-01
[1/s]
0.87
kdes_CH3OH
5.37E-04
5.56E-04
[1/s]
0.96
kads_H2
7.03E-01
6.88E-01
[1/s]
1.02
kdes_H2
5.01E-04
5.58E-04
[1/s]
0.90
kads_CH4
1.15E-02
1.25E-02
[1/s]
0.92
kdes_CH4
1.12E+00
1.20E+00
[1/s]
0.93
kads_O2
1.39E+00
1.42E+00
[1/s]
0.98
kdes_O2
8.22E-06
8.86E-06
[1/s]
0.93
53
These rate constants apply to the models developed in Chapter 3, but two general
conclusions can be inferred about the physical system. First, the adsorption rate of CO2 to
the catalyst surface is very low. For the ionic liquid system, CO2 adsorption is the lowest
rate obtained. For the aqueous system, CO2 adsorption rate is larger than only oxygen
desorption. This suggests that the system’s CO2 conversion rate is limited by the rate of
adsorption to the catalyst surface. Second, ratios on the table’s rightmost column
demonstrate a significantly lower rate of CO2 adsorption for the ionic liquid system. The
reason for this may be the complex formed between ionic liquid and dissolved CO2,
which increases solubility, but decreases adsorption rate to the catalyst surface.
With so many parameters being reported, it is important to comment on the
significance of each number. The reactions that are rate-limiting (kads_CO2) are most
significant. Changing non-rate limiting reaction rate constants would not affect the
numerical model’s results as significantly as the same change to kads_CO2. For that reason,
the rates of CO2 adsorption to the catalyst surface are most accurate and represent what
this photocatalytic microreactor process is capable of.
54
CHAPTER 8
CONTRIBUTION TO SCIENCE AND CONCLUSIONS
The photocatalytic microreactor process has been used to reduce dissolved carbon
dioxide and form methane, demonstrating a novel application in microtechnology. A
model has been developed that describes the microreactor’s performance and can be used
to scale as appropriate. Reaction rate constants have been determined for two systems,
the aqueous and partial ionic liquid, which represent the feasibility of implementing such
processes.
The aqueous microreactor process yielded low concentrations of methane only.
Reduction did not have a measurable effect on the concentration of dissolved CO2. It is
not clear if intermediates were formed (HCOOH, HCHO, CH3OH) because they would
be present at concentrations below our detection limits (1-100 ppm) according to the
Formic Acid, HCOOH
Formaldehyde, HCHO
Methane, CH4
Carbon Dioxide, CO2
Methanol, CH3OH
2.0E-06
0.1
1.8E-06
0.09
1.6E-06
0.08
1.4E-06
0.07
1.2E-06
0.06
1.0E-06
0.05
8.0E-07
0.04
6.0E-07
0.03
4.0E-07
0.02
2.0E-07
0.01
0.0E+00
CO2 Concentration [mol/L]
Product Concentrations [mol/L]
numerical model results.
0
0
10
20
30
40
50
60
70
MRT [sec]
Figure 8.1 Predicted Values of All Compounds in Aqueous System from Model
55
Addition of 50% ionic liquid increased the solubility of CO2 by 60%. However, the
system exhibited no measurable intermediates and produced lower concentrations of
methane (approximately 4.4% of the aqueous system). There are two reasons this could
occur; for one, the ionic liquid mixture could have greater methane solubility, making
headspace measurement less accurate. The Henry’s law constant for methane in water is
3.44x10-2 ([mol/Laq]/[mol/Lgas]) and this value must increase by a factor of 900 when
adding ionic liquid to account for the difference in methane production. The second
reason is that the complex formed between BMIM-BF4 and CO211 may adsorb less
effectively to the catalyst surface.
56
CHAPTER 9
RECOMMENDATIONS FOR FUTURE WORK
There are several areas for future work, including catalyst modification, liquid mixture
optimization, and general yield improvement.
Literature suggests that product selectivity can be modified by doping the TiO2
catalyst with a second metal. Reported values imply that the utilization of electron/hole
pairs can be significantly increased by making this modification with copper7 or
ruthenium9. TiO2 is just one catalyst option and significant resources are actively
exploring the application of other elements.
A second opportunity for future development is the optimization of liquid mixtures. It
was stated previously that the ionic liquid presents a benefit in the increased solubility of
CO2. Addition of a hole scavenger such as sodium hydroxide or isopropanol has
successfully extended the separation of electron/hole pairs and modified the product mix7,
9, 14
. It is not ideal to add more chemicals to this process, because it deviates from the
environmentally benign operation, but functionality may outweigh this cost.
General yield improvement brings the reader back to the motivation for this work,
mitigation of environmentally hazardous atmospheric CO2. Introduction of separation and
recycle streams will theoretically improve yield. Coupling microseparators to remove
methane and/or micromixers to re-dissolve CO2 create more opportunities to demonstrate
microtechnology and improve process efficacy.
57
BIBLIOGRAPHY
1
Engineering Toolbox Online. Web. 19 Feb. 2013 < http://www.engineeringtoolbox.com/gases-solubility-
water-d_1148.html>.
2
Malati, M. A. “Mitigation of CO2 greenhouse effect. Combined disposal and utilization by photo
catalysis.” Energ. Convers. Manage. 37 (1996): 1345–1350. Print.
3
Angamuthu, R., et al. “Electro catalytic CO2 conversion to oxalate by a copper complex.” Science 327
(2010): 313–315. Print.
4
Armor, J. N. “Addressing the CO2 dilemma.” Catal. Lett.
114 (2007): 115–121. Print.
5
Usubharatana, P., et al. “Photocatalytic process for CO2 emission reduction from industrial flue gas
streams.” Ind. Eng. Chem. Res. 45 (2006): 2558–2568. Print.
6
Inoue, T., et al. “Photoelectrocatalytic reduction of carbon dioxide in aqueous suspensions of
semiconductor powders.” Nature 277 (1979): 637–638. Print.
7
Srinvas, B., et al. “Photocatalytic Reduction of CO2 over Cu-TiO2/Molecular Sieve 5A Composite.”
Photochemistry and Photobiology 87 (2011): 995-1001. Print.
8
Anpo, M., et al. “Photocatalytic reduction of CO2 with H2O on various titanium oxide catalysts.” Journal
of Electroanalytical Chemistry 396 (1995): 21-26. Print.
9
Sasirekha, N., J. S. B. Sheikh, and S. Kannan. “Photocatalytic performance of Ru doped anatase mounted
on silica for reduction of carbon dioxide.” Applied Catalysis B: Environemntal 62 (2006): 169-180. Print.
10
Hou, Y., and R. E. Baltus. “Experimental Measurement of the Solubility and Diffusivity of CO2 in
Room-Temperature Ionic Liquids Using a Transient Thin-Liquid-Film Method.” Ind. Eng. Chem. Res. 46
(2007): 8166-8175. Print.
11
B. A. Rosen, et al. “Ionic Liquid-Mediated Selective Conversion of CO2 to CO at Low Overpotentials.”
Science 334 (2011): 643-644. Print.
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12
Du, Erdeng, Yuxian Zhang, and Lu Zheng. "Photocatalytic degradation of dimethyl phthalate in aqueous
TiO2 suspension: a modified Langmuir-Hinshelwood model." Reac. Kinet. Catal. Lett. 97. (2009): 83-90.
Print.
13
Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems. Cambridge: University Press, 2009. Print.
14
Dey, G. R., Belapurkar, A. D., Kishore, K.; Photo-catalytic reduction of carbon dioxide to methane using
TiO2 as suspension in water. Journal of Photochemistry and Photobiology A: Chemistry 2004, 503-508.
15
National Climatic Data Center. “Global Climate Change Indicators.” National Oceanic and Atmospheric
Administration. National Climatic Data Center, 2013. Web. 4 April 2013.
< http://www.ncdc.noaa.gov/indicators/>
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17
Cerrano, C. et al. “Red coral extinction risk enhanced by oceanic acidification.” Sci Rep. 3 (2013): 1457.
Print.
18
Jitaru, M. “Electro chemical carbon dioxide reduction—fundamentals and applied topics.” J. Univ.
Chemi. Technol. Metallurgy 42 (2007): 333–344. Print.
19
Benson, E. E., et al. “Electro catalytic and homogeneous approaches to conversion of CO2 to liquid
fuels.” Chem. Soc. Rev. 38 (2009): 89–99. Print.
20
Rothenberger, Guido, Jacques Moser, et al. "Charge Carrier Trapping and Recombination Dynamics in
Small Semiconductor Particles." J.Am.Chem.Soc. 107. (1985): 8054-59. Print.
21
Hori, H., et al. “Efficient photo catalytic CO2 reduction using [Re(bpy)(CO)3{P(OEt)3}]+.” J.
Photochem. Photobiol. A 96 (1996): 171–174. Print.
22
Ikeue, K., H. Yamashita, and M. Anpo. “Photo catalytic reduction of CO2 with H2O on titanium oxides
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Yamashita, H., et al. “In situ XAFS studies on the effects of the hydrophobic-hydrophilic properties of Ti-
Beta zeolites in the photocatalytic reduction of CO2 with H2O.” Top. Catal. 18 (2002): 95–100. Print.
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24
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60
APPENDICES
HARDWARE INFORMATION
Figure A.1 Harvard Apparatus 975 Syringe Pump
Figure A.2 (SG009660) SGE 50 mL Gas-tight, Glass Syringe
61
Figure A.3 Connection Detail 1
(Z227293) Supelco 1/16” OD / 0.02” ID HPLC PEEK tubing
(P-202X) Upchurch ¼-28 flangeless Delrin nuts for 1/16” OD tubing
(P-200X) Upchurch flangeless ETFE ferrules for 1/16” OD tubing
Figure A.4 Connection Detail 2
(P-655) Upchurch PEEK female ¼”-28 to male luer
(P-658) Upchurch PEEK female ¼”-28 to female luer
62
Figure A.5 Microreactor Components
(0005-599) ICL SL-3 liquid spectrophotometer cell front with dispersive (rectangular)
aperture
(0001-1397) Neoprene gasket – 38.5 x 19.5 mm.
(0001-3396W) PTFE spacer – 38.5 x 19.5 mm, 0.2 mm path length
(0005-600) ICL SL-3 liquid spectrophotometer cell back with dispersive (rectangular)
aperture
(0005-598) SL-3 screws (not pictured)
63
Figure A.6 Quartz Crystal, Cut and Drilled by Technical Glass Products
Figure A.7 Quartz Plate with Catalyst Applied
64
CATALYST CHARACTERIZATION
Figure A.8 1,000x SEM image of TiO2-coated NanospringsTM
Figure A.9 2,000x SEM image of TiO2-coated NanospringsTM
65
Figure A.10 4,000x SEM image of TiO2-coated NanospringsTM
Figure A.11 4,000x SEM image of TiO2-coated NanospringsTM after Gold ALD
66
Figure A.12 8,000x SEM image of TiO2-coated NanospringsTM after Gold ALD
Figure A.13 16,000x SEM image of TiO2-coated NanospringsTM after Gold ALD
67
Figure A.14 30,000x SEM image of TiO2-coated NanospringsTM after Gold ALD
Figure A.15 60,000x SEM image of TiO2-coated NanospringsTM after Gold ALD
68
Table T.1 Catalyst Thickness at Six Locations
Optic Measurement
Zoom from base to
Equivalent distance
focus
(microns)
10x
1
9.0
22.9
10x
2
12.0
30.5
10x
3
10.4
26.4
20x
4
8.0
20.3
20x
5
10.4
26.4
20x
6
12.1
30.7
Catalyst thickness calculation:
̅
√
Table T.2 Catalyst Thickness Measurement Using 10x Optic
AVG
STDEV
SE
Z
Upper
Lower
26.6
3.8
2.2
3
33.2
20.0
Table T.3 Catalyst Thickness Measurement Using 20x Optic
AVG
STDEV
SE
Z
Upper
Lower
25.8
5.2
3.0
3
34.9
16.8
69
NUMERICAL MODEL
function f = M051013AQ(k)
%
% M051013AQ.m
%
% Model exported on May 9 2013, 11:11 by COMSOL 4.3.0.233.
import com.comsol.model.*
import com.comsol.model.util.*
model = ModelUtil.create('Model');
model.modelPath('Z:\Windows.Documents\Desktop\Final Work');
model.name('051013AQ.mph');
k11 = k(1);
k12 = k(2);
k15 = k(3);
k20 = k(4);
k23 = k(5);
k1_k2 = k(6);
G = k(7);
kads_CO2 = k(8);
kdes_CO2 = k(9);
kads_HCOOH = k(10);
kdes_HCOOH = k(11);
kads_HCHO = k(12);
kdes_HCHO = k(13);
kads_CH3OH = k(14);
kdes_CH3OH = k(15);
kads_H2 = k(16);
kdes_H2 = k(17);
kads_CH4 = k(18);
kdes_CH4 = k(19);
kads_O2 = k(20);
kdes_O2 = k(21);
k11 = abs(k11);
k12 = abs(k12);
k15 = abs(k15);
k20 = abs(k20);
k23 = abs(k23);
k1_k2 = abs(k1_k2);
G = abs(G);
kads_CO2 = abs(kads_CO2);
kdes_CO2 = abs(kdes_CO2);
kads_HCOOH = abs(kads_HCOOH);
kdes_HCOOH = abs(kdes_HCOOH);
kads_HCHO = abs(kads_HCHO);
kdes_HCHO = abs(kdes_HCHO);
70
kads_CH3OH = abs(kads_CH3OH);
kdes_CH3OH = abs(kdes_CH3OH);
kads_H2 = abs(kads_H2);
kdes_H2 = abs(kdes_H2);
kads_CH4 = abs(kads_CH4);
kdes_CH4 = abs(kdes_CH4);
kads_O2 = abs(kads_O2);
kdes_O2 = abs(kdes_O2);
model.param.set('k11', k11);
model.param.set('k12', k12);
model.param.set('k15', k15);
model.param.set('k20', k20);
model.param.set('k23', k23);
model.param.set('k1_k2', k1_k2);
model.param.set('G', G);
model.param.set('kads_CO2', kads_CO2);
model.param.set('kdes_CO2', kdes_CO2);
model.param.set('kads_HCOOH', kads_HCOOH);
model.param.set('kdes_HCOOH', kdes_HCOOH);
model.param.set('kads_HCHO', kads_HCHO);
model.param.set('kdes_HCHO', kdes_HCHO);
model.param.set('kads_CH3OH', kads_CH3OH);
model.param.set('kdes_CH3OH', kdes_CH3OH);
model.param.set('kads_H2', kads_H2);
model.param.set('kdes_H2', kdes_H2);
model.param.set('kads_CH4', kads_CH4);
model.param.set('kdes_CH4', kdes_CH4);
model.param.set('kads_O2', kads_O2);
model.param.set('kdes_O2', kdes_O2);
model.param.set('velocity', '3.07e-4[m/s]', 'Average fluid velocity');
model.param.set('press', '101300[Pa]', 'Outlet pressure');
model.param.set('DCO2', '1.92e-9[m^2/s]', 'Diff coef of CO2');
model.param.set('DHCOOH', '1.72e-9[m^2/s]', 'Diff coef of HCOOH');
model.param.set('DHCHO', '2.1e-9[m^2/s]', 'Diff coef of HCHO');
model.param.set('DCH3OH', '1.65e-9[m^2/s]', 'Diff coef of CH3OH');
model.param.set('DCH4', '1.49e-9[m^2/s]', 'Diff coef of CH4');
model.param.set('DH2', '4.5e-9[m^2/s]', 'Diff coef of H2');
model.param.set('DO2', '2.1e-9[m^2/s]', 'Diff coef of O2');
model.param.set('c0CO2', '85.4[mol/m^3]', 'Initial concentration of
CO2');
%model.param.set('k11', '5e-4[m^2/(mol*s)]', 'Rate constant for
production of H2');
%model.param.set('k12', '3e-2[m^2/(mol*s)]', 'Rate constant for
consumption of CO2');
%model.param.set('k15', '1[m^2/(mol*s)]', 'Rate constant for
consumption of HCOOH');
%model.param.set('k20', '1[m^2/(mol*s)]', 'Rate constant for
consumption of HCHO');
%model.param.set('k23', '1[m^2/(mol*s)]', 'Rate constant for
consumption of CH3OH');
%model.param.set('k1_k2', '1[mol*s/(m^2)]', '=k1/k2');
71
%model.param.set('G', '5e-5[mol/(s*m^2)]', '=k3*(k1*I/k2)^0.5*cH2Os');
%model.param.set('kads_CO2', '1.861e-4[1/s]', 'Adsorption rate c of
CO2');
%model.param.set('kdes_CO2', '1e-4[1/s]', 'Desorption rate c of CO2');
%model.param.set('kads_HCOOH', '0.1[1/s]', 'Adsorption rate c of
HCOOH');
%model.param.set('kdes_HCOOH', '2e-4[1/s]', 'Desorption rate c of
HCOOH');
%model.param.set('kads_HCHO', '0.1[1/s]', 'Adsorption rate c of HCHO');
%model.param.set('kdes_HCHO', '2e-4[1/s]', 'Desorption rate c of
HCHO');
%model.param.set('kads_CH3OH', '0.1[1/s]', 'Adsorption rate c of
CH3OH');
%model.param.set('kdes_CH3OH', '5e-4[1/s]', 'Desorption rate c of
CH3OH');
%model.param.set('kads_H2', '0.6[1/s]', 'Adsorption rate c of H2');
%model.param.set('kdes_H2', '5e-4[1/s]', 'Desorption rate c of H2');
%model.param.set('kads_CH4', '0.01[1/s]', 'Adsorption rate c of CH4');
%model.param.set('kdes_CH4', '1[1/s]', 'Desorption rate c of CH4');
%model.param.set('kads_O2', '0.9[1/s]', 'Adsorption rate c of O2');
%model.param.set('kdes_O2', '1e-5[1/s]', 'Desorption rate c of O2');
model.param.set('g', '1[g/m^2]', 'Reactor catalyst loading');
model.param.set('a', '1[m^2/g]', 'Catalyst specific surface');
model.param.set('s_area', '1000[m^2/m^3]', 'Reactor surface to volume
ratio');
model.param.set('I', '4.03e-9[mol/(s*m^2)]', 'Light intensity');
model.param.set('sol_CH4', '0.023[g/kg]', 'Solubility of CH4');
model.param.set('sol_H2', '0.0016[g/kg]', 'Solubility of H2');
model.param.set('sol_O2', '0.044[g/kg]', 'Solubility of O2');
model.param.set('rho', '1000[kg/m^3]', 'Density of water');
model.param.set('M_CH4', '16[g/mol]', 'Molecular weight of CH4');
model.param.set('M_H2', '2[g/mol]', 'Molecular weight of H2');
model.param.set('M_O2', '32[g/mol]', 'Molecular weight of O2');
model.modelNode.create('mod1');
model.geom.create('geom1', 2);
model.geom('geom1').lengthUnit('mm');
model.geom('geom1').feature.create('r1', 'Rectangle');
model.geom('geom1').feature('r1').set('pos', {'0.5' '0'});
model.geom('geom1').feature('r1').set('size', {'22' '0.074'});
model.geom('geom1').run;
model.variable.create('var1');
model.variable('var1').model('mod1');
model.variable('var1').set('A', 'k12*(k1_k2*I)^0.5');
model.variable('var1').set('B', 'k15*(k1_k2*I)^0.5');
model.variable('var1').set('C', 'k20*(k1_k2*I)^0.5');
model.variable('var1').set('D', 'kdes_CO2-A');
model.variable('var1').set('E', 'kdes_HCOOH-B');
model.variable('var1').set('F', 'kdes_HCHO-C');
model.variable('var1').set('rCO2', '-A*cCO2s', 'Rate of dis. of CO2');
72
model.variable('var1').set('rHCOOH', 'A*cCO2s-B*cHCOOHs', 'Rate of pro.
of HCOOH');
model.variable('var1').set('rHCHO', 'B*cHCOOHs-C*cHCHOs', 'Rate of pro.
of HCHO');
model.variable('var1').set('rCH3OH', '(C*cHCHOs)(k23*cCH3OHs*cH_radical)', 'Rate of pro. of CH3OH');
model.variable('var1').set('rCH4', 'k23*cCH3OHs*cH_radical', 'Rate of
pro. of CH4');
model.variable('var1').set('rH2', 'k11*(cH_radical)^2', 'Rate of pro.
of H2');
model.variable('var1').set('rO2', 'G');
model.variable('var1').set('cCO2s', '(kads_CO2*cCO2)/(g*a*s_area*D)',
'Concentration of CO2 at surface');
model.variable('var1').set('cHCOOHs', '(kads_HCOOH*D*cHCOOHkads_CO2*A*cCO2)/(g*a*s_area*D*E)', 'Concentration of HCOOH at
surface');
model.variable('var1').set('cHCHOs', '(kads_HCHO*D*E*cHCHOkads_HCOOH*B*D*cHCOOH+kads_CO2*A*B*cCO2)/(g*a*s_area*D*E*F)',
'Concentration of HCHO at surface');
model.variable('var1').set('cCH3OHs',
'epsilon/(g*a*s_area*D*E*F*(kdes_CH3OH-k23*cH_radical))',
'Concentration of CH3OH at surface');
model.variable('var1').set('epsilon', 'kads_CH3OH*D*E*F*cCH3OHkads_HCHO*C*D*E*cHCHO+kads_HCOOH*B*C*D*cHCOOH-kads_CO2*A*B*C*cCO2');
model.variable('var1').set('cH_radical', '-beta/(3*alpha)',
'Concentration of Hydrogen radical at surface');
model.variable('var1').set('cH2s', 'kads_H2*cH2/(g*a*s_area*kdes_H2)(k11*cH_radical^2/kdes_H2)', 'Concentration of H2 at surface');
model.variable('var1').set('cCH4s',
'kads_CH4*cCH4/(g*a*s_area*kdes_CH4)(k23*cCH3OHs*cH_radical/kdes_CH4)', 'Concentration of CH4 at surface');
model.variable('var1').set('cO2s', '(kads_O2*cO2g*a*s_area*G)/(kdes_O2*g*a*s_area)');
model.variable('var1').set('alpha', '(g*a*s_area)*D*E*F*k11*k23');
model.variable('var1').set('beta', '(g*a*s_area)*D*E*F*kdes_CH3OH*k11');
model.variable('var1').set('gamma', 'k23*(2*kads_CO2*A*(2*B*CB*F+E*F)*cCO2+2*kads_HCOOH*B*D*(F-2*C)*cHCOOH+4*kads_HCHO*C*D*E*cHCHO2*kads_CH3OH*D*E*F*cCH3OH-g*a*s_area*D*E*F*G)');
model.variable('var1').set('delta', '-kdes_CH3OH*(2*kads_CO2*A*(B*CB*F+E*F)*cCO2+2*kads_HCOOH*B*D*(F-C)*cHCOOH+2*kads_HCHO*C*D*E*cHCHOg*a*s_area*D*E*F*G)');
model.variable('var1').set('Z', 'cCO2+cHCOOH+cHCHO+cCH3OH+cCH4', 'Sum
of carbon species');
model.variable('var1').set('C_CH4', '(rho*sol_CH4)/M_CH4', 'Solubility
of CH4');
model.variable('var1').set('C_H2', '(rho*sol_H2)/M_H2', 'Solubility of
H2');
model.variable('var1').set('C_O2', '(rho*sol_O2)/M_O2', 'Solubility of
O2');
model.material.create('mat1');
73
model.physics.create('spf', 'LaminarFlow', 'geom1');
model.physics('spf').feature.create('inl1', 'Inlet', 1);
model.physics('spf').feature('inl1').selection.set([1]);
model.physics('spf').feature.create('out1', 'Outlet', 1);
model.physics('spf').feature('out1').selection.set([4]);
model.physics.create('chds', 'DilutedSpecies', 'geom1');
model.physics('chds').field('concentration').field('cCO2');
model.physics('chds').field('concentration').component({'cCO2' 'cHCOOH'
'cHCHO' 'cCH3OH' 'cCH4' 'cH2' 'cO2'});
model.physics('chds').feature.create('fl1', 'Fluxes', 1);
model.physics('chds').feature('fl1').selection.set([2]);
model.physics('chds').feature.create('in1', 'Inflow', 1);
model.physics('chds').feature('in1').selection.set([1]);
model.physics('chds').feature.create('out1', 'Outflow', 1);
model.physics('chds').feature('out1').selection.set([4]);
model.physics('chds').feature.create('fl2', 'Fluxes', 1);
model.physics('chds').feature('fl2').selection.set([3]);
model.physics('chds').feature.create('reac1', 'Reactions', 2);
model.physics('chds').feature('reac1').selection.set([1]);
model.mesh.create('mesh1', 'geom1');
model.mesh('mesh1').feature.create('size1', 'Size');
model.mesh('mesh1').feature('size1').selection.geom('geom1', 1);
model.mesh('mesh1').feature('size1').selection.set([2 3]);
model.mesh('mesh1').feature.create('ftri1', 'FreeTri');
model.mesh('mesh1').feature('ftri1').selection.geom('geom1', 2);
model.mesh('mesh1').feature('ftri1').selection.set([1]);
model.mesh('mesh1').feature.create('bl1', 'BndLayer');
model.mesh('mesh1').feature('bl1').selection.geom('geom1', 2);
model.mesh('mesh1').feature('bl1').selection.set([1]);
model.mesh('mesh1').feature('bl1').feature.create('blp1',
'BndLayerProp');
model.mesh('mesh1').feature('bl1').feature('blp1').selection.set([2
3]);
model.mesh('mesh1').feature.create('ftri2', 'FreeTri');
model.result.table.create('tbl1',
model.result.table.create('tbl2',
model.result.table.create('tbl3',
model.result.table.create('tbl4',
model.result.table.create('tbl5',
model.result.table.create('tbl6',
model.result.table.create('tbl7',
'Table');
'Table');
'Table');
'Table');
'Table');
'Table');
'Table');
model.view('view1').axis.set('xmin',
model.view('view1').axis.set('xmax',
model.view('view1').axis.set('ymin',
model.view('view1').axis.set('ymax',
'22.382186889648438');
'22.57434844970703');
'-0.0645522028207779');
'0.1479654610157013');
model.material('mat1').name('Water');
model.material('mat1').propertyGroup('def').func.name('Functions');
model.material('mat1').propertyGroup('def').set('density', '1000');
74
model.material('mat1').propertyGroup('def').set('dynamicviscosity',
'8.94e-4');
model.physics('spf').prop('PseudoTimeProperty').set('locCFL',
'1.3^min(niterCMP-1,9)+if(niterCMP>25,9*1.3^min(niterCMP25,9),0)+if(niterCMP>50,90*1.3^min(niterCMP-50,9),0)');
model.physics('spf').feature('fp1').set('minput_velocity_src',
'root.mod1.u');
model.physics('spf').feature('inl1').set('BoundaryCondition',
'LaminarInflow');
model.physics('spf').feature('inl1').set('U0in', 'velo_soln');
model.physics('spf').feature('inl1').set('Uav', 'velocity');
model.physics('spf').feature('inl1').set('Lentr', '0.5');
model.physics('spf').feature('out1').set('p0', 'press');
model.physics('chds').feature('cdm1').set('u_src', 'root.mod1.u');
model.physics('chds').feature('cdm1').set('D_0', {'DCO2'; '0'; '0';
'0'; 'DCO2'; '0'; '0'; '0'; 'DCO2'});
model.physics('chds').feature('cdm1').set('DiffusionMaterialList',
'mat1');
model.physics('chds').feature('cdm1').set('minput_concentration_src',
'root.mod1.cO2');
model.physics('chds').feature('cdm1').set('D_1', {'DHCOOH'; '0'; '0';
'0'; 'DHCOOH'; '0'; '0'; '0'; 'DHCOOH'});
model.physics('chds').feature('cdm1').set('D_2', {'DHCHO'; '0'; '0';
'0'; 'DHCHO'; '0'; '0'; '0'; 'DHCHO'});
model.physics('chds').feature('cdm1').set('D_3', {'DCH3OH'; '0'; '0';
'0'; 'DCH3OH'; '0'; '0'; '0'; 'DCH3OH'});
model.physics('chds').feature('cdm1').set('D_4', {'DCH4'; '0'; '0';
'0'; 'DCH4'; '0'; '0'; '0'; 'DCH4'});
model.physics('chds').feature('cdm1').set('D_5', {'DH2'; '0'; '0'; '0';
'DH2'; '0'; '0'; '0'; 'DH2'});
model.physics('chds').feature('cdm1').set('D_6', {'DO2'; '0'; '0'; '0';
'DO2'; '0'; '0'; '0'; 'DO2'});
model.physics('chds').feature('fl1').set('species', {'1'; '1'; '1';
'1'; '1'; '1'; '0'});
model.physics('chds').feature('fl1').set('N0', {'(g*a)*rCO2';
'(g*a)*rHCOOH'; '(g*a)*rHCHO'; '(g*a)*rCH3OH'; '(g*a)*rCH4';
'(g*a)*rH2'; '0'});
model.physics('chds').feature('in1').set('c0', {'c0CO2'; '0'; '0'; '0';
'0'; '0'; '0'});
model.physics('chds').feature('fl2').set('species', {'0'; '0'; '0';
'0'; '0'; '0'; '1'});
model.physics('chds').feature('fl2').set('N0', {'0'; '0'; '0'; '0';
'0'; '0'; '(g*a)*rO2'});
model.mesh('mesh1').feature('size').set('table', 'cfd');
model.mesh('mesh1').feature('size').set('hauto', 6);
model.mesh('mesh1').feature('size1').set('table', 'cfd');
model.mesh('mesh1').feature('bl1').feature('blp1').set('blnlayers',
'2');
model.mesh('mesh1').feature('bl1').feature('blp1').set('blhminfact',
'5');
model.mesh('mesh1').run;
75
model.frame('material1').sorder(1);
model.result.table('tbl1').comments('CH4_1
model.result.table('tbl2').comments('CH4_2
model.result.table('tbl3').comments('CH4_3
model.result.table('tbl4').comments('CH4_4
model.result.table('tbl5').comments('CH4_5
model.result.table('tbl6').comments('CH4_6
model.result.table('tbl7').comments('CH4_7
(cCH4)');
(cCH4)');
(cCH4)');
(cCH4)');
(cCH4)');
(cCH4)');
(cCH4)');
model.study.create('std1');
model.study('std1').feature.create('stat', 'Stationary');
model.sol.create('sol1');
model.sol('sol1').study('std1');
model.sol('sol1').attach('std1');
model.sol('sol1').feature.create('st1', 'StudyStep');
model.sol('sol1').feature.create('v1', 'Variables');
model.sol('sol1').feature.create('s1', 'Stationary');
model.sol('sol1').feature('s1').feature.create('fc1', 'FullyCoupled');
model.sol('sol1').feature('s1').feature.create('d1', 'Direct');
model.sol('sol1').feature('s1').feature.remove('fcDef');
model.result.dataset.create('cln2', 'CutLine2D');
model.result.dataset.create('cln3', 'CutLine2D');
model.result.dataset.create('cln4', 'CutLine2D');
model.result.dataset.create('cln13', 'CutLine2D');
model.result.dataset.create('cln6', 'CutLine2D');
model.result.dataset.create('cln7', 'CutLine2D');
model.result.dataset.create('cln8', 'CutLine2D');
model.result.dataset.create('cln9', 'CutLine2D');
model.result.dataset.create('cln10', 'CutLine2D');
model.result.dataset.create('cln11', 'CutLine2D');
model.result.numerical.create('int14', 'IntLine');
model.result.numerical('int14').set('probetag', 'none');
model.result.numerical.create('int15', 'IntLine');
model.result.numerical('int15').set('probetag', 'none');
model.result.numerical.create('int16', 'IntLine');
model.result.numerical('int16').set('probetag', 'none');
model.result.numerical.create('int17', 'IntLine');
model.result.numerical('int17').set('probetag', 'none');
model.result.numerical.create('int18', 'IntLine');
model.result.numerical('int18').set('probetag', 'none');
model.result.numerical.create('int19', 'IntLine');
model.result.numerical('int19').set('probetag', 'none');
model.result.numerical.create('int20', 'IntLine');
model.result.numerical('int20').set('probetag', 'none');
model.result.numerical.create('int21', 'IntLine');
model.result.numerical('int21').set('probetag', 'none');
model.result.numerical.create('int22', 'IntLine');
model.result.numerical('int22').set('probetag', 'none');
model.result.numerical.create('int23', 'IntLine');
76
model.result.numerical('int23').set('probetag', 'none');
model.result.numerical.create('int24', 'IntLine');
model.result.numerical('int24').set('probetag', 'none');
model.result.numerical.create('int25', 'IntLine');
model.result.numerical('int25').set('probetag', 'none');
model.result.numerical.create('int26', 'IntLine');
model.result.numerical('int26').set('probetag', 'none');
model.result.numerical.create('int27', 'IntLine');
model.result.numerical('int27').set('probetag', 'none');
model.result.create('pg1', 'PlotGroup2D');
model.result('pg1').feature.create('surf1', 'Surface');
model.result.create('pg2', 'PlotGroup2D');
model.result('pg2').feature.create('con', 'Contour');
model.result.create('pg3', 'PlotGroup2D');
model.result('pg3').feature.create('surf1', 'Surface');
model.result.create('pg4', 'PlotGroup1D');
model.result('pg4').set('probetag', 'none');
model.result('pg4').feature.create('lngr5', 'LineGraph');
model.result('pg4').feature.create('lngr6', 'LineGraph');
model.result('pg4').feature.create('lngr3', 'LineGraph');
model.result('pg4').feature.create('lngr2', 'LineGraph');
model.result('pg4').feature.create('lngr4', 'LineGraph');
model.result('pg4').feature.create('lngr7', 'LineGraph');
model.result('pg4').feature.create('lngr1', 'LineGraph');
model.result('pg4').feature.create('lngr8', 'LineGraph');
model.result('pg4').feature.create('lngr9', 'LineGraph');
model.result('pg4').feature.create('lngr10', 'LineGraph');
model.result('pg4').feature.create('lngr11', 'LineGraph');
model.result.create('pg6', 'PlotGroup1D');
model.result('pg6').set('probetag', 'none');
model.result('pg6').feature.create('lngr1', 'LineGraph');
model.result('pg6').feature.create('lngr4', 'LineGraph');
model.result.create('pg7', 'PlotGroup1D');
model.result('pg7').set('probetag', 'none');
model.result('pg7').feature.create('lngr1', 'LineGraph');
model.sol('sol1').attach('std1');
model.sol('sol1').feature('st1').name('Compile Equations: Stationary');
model.sol('sol1').feature('st1').set('studystep', 'stat');
model.sol('sol1').feature('v1').set('control', 'stat');
model.sol('sol1').feature('v1').feature('mod1_cO2').set('variables',
'mod1_cCO27');
model.sol('sol1').feature('s1').set('control', 'stat');
model.sol('sol1').feature('s1').set('stol', '0.010');
model.sol('sol1').feature('s1').feature('fc1').set('initstep', '0.01');
model.sol('sol1').feature('s1').feature('fc1').set('minstep', '1.0E6');
model.sol('sol1').feature('s1').feature('fc1').set('maxiter', '1000');
model.sol('sol1').feature('s1').feature('fc1').set('probesel',
'manual');
model.sol('sol1').feature('s1').feature('d1').set('linsolver',
'pardiso');
model.sol('sol1').runAll;
77
model.result.dataset('cln2').name('y=0.0mm');
model.result.dataset('cln2').set('genpoints', {'0.5' '0.0'; '22.5'
'0.0'});
model.result.dataset('cln3').name('Beginning');
model.result.dataset('cln3').set('genpoints', {'0.5' '0'; '0.5'
'0.074'});
model.result.dataset('cln4').name('End');
model.result.dataset('cln4').set('genpoints', {'20' '0'; '20'
'0.074'});
model.result.dataset('cln13').name('MRT 1.26');
model.result.dataset('cln13').set('genpoints', {'0.887' '0'; '0.887'
'.074'});
model.result.dataset('cln13').set('spacevars', {'cln6x'});
model.result.dataset('cln6').name('MRT 2.47');
model.result.dataset('cln6').set('genpoints', {'1.259' '0'; '1.259'
'.074'});
model.result.dataset('cln7').name('MRT 4.85');
model.result.dataset('cln7').set('genpoints', {'1.988' '0'; '1.988'
'.074'});
model.result.dataset('cln8').name('MRT 9.51');
model.result.dataset('cln8').set('genpoints', {'3.419' '0'; '3.419'
'.074'});
model.result.dataset('cln9').name('MRT 18.7');
model.result.dataset('cln9').set('genpoints', {'6.226' '0'; '6.226'
'.074'});
model.result.dataset('cln10').name('MRT 36.5');
model.result.dataset('cln10').set('genpoints', {'11.72' '0'; '11.72'
'.074'});
model.result.dataset('cln11').name('MRT 71.7');
model.result.dataset('cln11').set('genpoints', {'22.5' '0'; '22.5'
'.074'});
model.result.numerical('int14').name('CH4_1');
model.result.numerical('int14').set('data', 'cln13');
model.result.numerical('int14').set('table', 'tbl1');
model.result.numerical('int14').set('expr', 'cCH4');
model.result.numerical('int14').set('unit', 'mol/m^2');
model.result.numerical('int14').set('descr', 'Concentration');
model.result.numerical('int15').name('CH4_2');
model.result.numerical('int15').set('data', 'cln6');
model.result.numerical('int15').set('table', 'tbl2');
model.result.numerical('int15').set('expr', 'cCH4');
model.result.numerical('int15').set('unit', 'mol/m^2');
model.result.numerical('int15').set('descr', 'Concentration');
model.result.numerical('int16').name('CH4_3');
model.result.numerical('int16').set('data', 'cln7');
model.result.numerical('int16').set('table', 'tbl3');
model.result.numerical('int16').set('expr', 'cCH4');
model.result.numerical('int16').set('unit', 'mol/m^2');
model.result.numerical('int16').set('descr', 'Concentration');
model.result.numerical('int17').name('CH4_4');
model.result.numerical('int17').set('data', 'cln8');
model.result.numerical('int17').set('table', 'tbl4');
78
model.result.numerical('int17').set('expr', 'cCH4');
model.result.numerical('int17').set('unit', 'mol/m^2');
model.result.numerical('int17').set('descr', 'Concentration');
model.result.numerical('int18').name('CH4_5');
model.result.numerical('int18').set('data', 'cln9');
model.result.numerical('int18').set('table', 'tbl5');
model.result.numerical('int18').set('expr', 'cCH4');
model.result.numerical('int18').set('unit', 'mol/m^2');
model.result.numerical('int18').set('descr', 'Concentration');
model.result.numerical('int19').name('CH4_6');
model.result.numerical('int19').set('data', 'cln10');
model.result.numerical('int19').set('table', 'tbl6');
model.result.numerical('int19').set('expr', 'cCH4');
model.result.numerical('int19').set('unit', 'mol/m^2');
model.result.numerical('int19').set('descr', 'Concentration');
model.result.numerical('int20').name('CH4_7');
model.result.numerical('int20').set('data', 'cln11');
model.result.numerical('int20').set('table', 'tbl7');
model.result.numerical('int20').set('expr', 'cCH4');
model.result.numerical('int20').set('unit', 'mol/m^2');
model.result.numerical('int20').set('descr', 'Concentration');
model.result.numerical('int21').name('CO2_1');
model.result.numerical('int21').set('data', 'cln13');
model.result.numerical('int21').set('table', 'tbl1');
model.result.numerical('int21').set('expr', 'cCO2');
model.result.numerical('int21').set('unit', 'mol/m^2');
model.result.numerical('int21').set('descr', 'Concentration');
model.result.numerical('int22').name('CO2_2');
model.result.numerical('int22').set('data', 'cln6');
model.result.numerical('int22').set('table', 'tbl2');
model.result.numerical('int22').set('expr', 'cCO2');
model.result.numerical('int22').set('unit', 'mol/m^2');
model.result.numerical('int22').set('descr', 'Concentration');
model.result.numerical('int23').name('CO2_3');
model.result.numerical('int23').set('data', 'cln7');
model.result.numerical('int23').set('table', 'tbl3');
model.result.numerical('int23').set('expr', 'cCO2');
model.result.numerical('int23').set('unit', 'mol/m^2');
model.result.numerical('int23').set('descr', 'Concentration');
model.result.numerical('int24').name('CO2_4');
model.result.numerical('int24').set('data', 'cln8');
model.result.numerical('int24').set('table', 'tbl4');
model.result.numerical('int24').set('expr', 'cCO2');
model.result.numerical('int24').set('unit', 'mol/m^2');
model.result.numerical('int24').set('descr', 'Concentration');
model.result.numerical('int25').name('CO2_5');
model.result.numerical('int25').set('data', 'cln9');
model.result.numerical('int25').set('table', 'tbl5');
model.result.numerical('int25').set('expr', 'cCO2');
model.result.numerical('int25').set('unit', 'mol/m^2');
model.result.numerical('int25').set('descr', 'Concentration');
model.result.numerical('int26').name('CO2_6');
model.result.numerical('int26').set('data', 'cln10');
model.result.numerical('int26').set('table', 'tbl6');
79
model.result.numerical('int26').set('expr', 'cCO2');
model.result.numerical('int26').set('unit', 'mol/m^2');
model.result.numerical('int26').set('descr', 'Concentration');
model.result.numerical('int27').name('CO2_7');
model.result.numerical('int27').set('data', 'cln11');
model.result.numerical('int27').set('table', 'tbl7');
model.result.numerical('int27').set('expr', 'cCO2');
model.result.numerical('int27').set('unit', 'mol/m^2');
model.result.numerical('int27').set('descr', 'Concentration');
model.result.numerical('int14').setResult;
model.result.numerical('int15').setResult;
model.result.numerical('int16').setResult;
model.result.numerical('int17').setResult;
model.result.numerical('int18').setResult;
model.result.numerical('int19').setResult;
model.result.numerical('int20').setResult;
model.result.numerical('int21').appendResult;
model.result.numerical('int22').appendResult;
model.result.numerical('int23').appendResult;
model.result.numerical('int24').appendResult;
model.result.numerical('int25').appendResult;
model.result.numerical('int26').appendResult;
model.result.numerical('int27').appendResult;
model.result('pg1').name('Velocity (spf)');
model.result('pg1').set('title', 'Velocity (m/s)');
model.result('pg1').set('frametype', 'spatial');
model.result('pg1').set('titletype', 'manual');
model.result('pg1').feature('surf1').set('data', 'dset1');
model.result('pg2').name('Pressure (spf)');
model.result('pg2').set('frametype', 'spatial');
model.result('pg2').feature('con').set('expr', 'p');
model.result('pg2').feature('con').set('unit', 'Pa');
model.result('pg2').feature('con').set('descr', 'Pressure');
model.result('pg2').feature('con').set('number', '40');
model.result('pg3').name('Concentration (chds)');
model.result('pg3').feature('surf1').set('expr', 'cCO2');
model.result('pg3').feature('surf1').set('unit', 'mol/m^3');
model.result('pg3').feature('surf1').set('descr', 'Concentration');
model.result('pg4').name('Concentration Profiles');
model.result('pg4').set('data', 'cln2');
model.result('pg4').set('title', 'Concentration Profile
(v_avg=5.25e-4 m/sec)');
model.result('pg4').set('xlabel', 'Length of the Reactor (mm)');
model.result('pg4').set('xlabelactive', true);
model.result('pg4').set('ylabel', 'Concentration (mol/m³)');
model.result('pg4').set('ylabelactive', true);
model.result('pg4').set('axislimits', 'on');
model.result('pg4').set('xmin', '-0.2100019007921219');
model.result('pg4').set('xmax', '22.');
model.result('pg4').set('ymin', '-0.09999999403953552');
model.result('pg4').set('ymax', '100');
model.result('pg4').set('titletype', 'manual');
model.result('pg4').feature('lngr5').set('data', 'cln2');
model.result('pg4').feature('lngr5').set('expr', 'cCO2');
80
model.result('pg4').feature('lngr5').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr5').set('descr', 'Concentration');
model.result('pg4').feature('lngr5').set('legend', true);
model.result('pg4').feature('lngr5').set('legendmethod', 'manual');
model.result('pg4').feature('lngr5').set('legends', {'CO2'});
model.result('pg4').feature('lngr5').set('smooth', 'none');
model.result('pg4').feature('lngr6').set('data', 'cln2');
model.result('pg4').feature('lngr6').set('expr', 'cHCOOH');
model.result('pg4').feature('lngr6').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr6').set('descr', 'Concentration');
model.result('pg4').feature('lngr6').set('legend', true);
model.result('pg4').feature('lngr6').set('legendmethod', 'manual');
model.result('pg4').feature('lngr6').set('legends', {'HCOOH'});
model.result('pg4').feature('lngr6').set('smooth', 'none');
model.result('pg4').feature('lngr3').set('data', 'cln2');
model.result('pg4').feature('lngr3').set('expr', 'cHCHO');
model.result('pg4').feature('lngr3').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr3').set('descr', 'Concentration');
model.result('pg4').feature('lngr3').set('legend', true);
model.result('pg4').feature('lngr3').set('legendmethod', 'manual');
model.result('pg4').feature('lngr3').set('legends', {'HCHO'});
model.result('pg4').feature('lngr3').set('smooth', 'none');
model.result('pg4').feature('lngr2').set('data', 'cln2');
model.result('pg4').feature('lngr2').set('expr', 'cCH3OH');
model.result('pg4').feature('lngr2').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr2').set('descr', 'Concentration');
model.result('pg4').feature('lngr2').set('legend', true);
model.result('pg4').feature('lngr2').set('legendmethod', 'manual');
model.result('pg4').feature('lngr2').set('legends', {'CH3OH'});
model.result('pg4').feature('lngr2').set('smooth', 'none');
model.result('pg4').feature('lngr4').set('data', 'cln2');
model.result('pg4').feature('lngr4').set('expr', 'cCH4');
model.result('pg4').feature('lngr4').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr4').set('descr', 'Concentration');
model.result('pg4').feature('lngr4').set('legend', true);
model.result('pg4').feature('lngr4').set('legendmethod', 'manual');
model.result('pg4').feature('lngr4').set('legends', {'CH4'});
model.result('pg4').feature('lngr4').set('smooth', 'none');
model.result('pg4').feature('lngr7').set('data', 'cln2');
model.result('pg4').feature('lngr7').set('expr', 'Z');
model.result('pg4').feature('lngr7').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr7').set('descr', '');
model.result('pg4').feature('lngr7').set('linestyle', 'dotted');
model.result('pg4').feature('lngr7').set('linecolor', 'black');
model.result('pg4').feature('lngr7').set('smooth', 'none');
model.result('pg4').feature('lngr1').active(false);
model.result('pg4').feature('lngr1').set('data', 'cln2');
model.result('pg4').feature('lngr1').set('expr', 'cH2');
model.result('pg4').feature('lngr1').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr1').set('descr', 'Concentration');
model.result('pg4').feature('lngr1').set('legend', true);
model.result('pg4').feature('lngr1').set('legendmethod', 'manual');
model.result('pg4').feature('lngr1').set('legends', {'H2'});
model.result('pg4').feature('lngr1').set('smooth', 'none');
81
model.result('pg4').feature('lngr8').active(false);
model.result('pg4').feature('lngr8').set('data', 'cln2');
model.result('pg4').feature('lngr8').set('expr', 'C_CH4');
model.result('pg4').feature('lngr8').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr8').set('descr', 'Solubility of CH4');
model.result('pg4').feature('lngr8').set('linestyle', 'dashed');
model.result('pg4').feature('lngr8').set('linecolor', 'cyan');
model.result('pg4').feature('lngr8').set('smooth', 'none');
model.result('pg4').feature('lngr9').active(false);
model.result('pg4').feature('lngr9').set('data', 'cln2');
model.result('pg4').feature('lngr9').set('expr', 'C_H2');
model.result('pg4').feature('lngr9').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr9').set('descr', 'Solubility of H2');
model.result('pg4').feature('lngr9').set('linestyle', 'dashed');
model.result('pg4').feature('lngr9').set('linecolor', 'blue');
model.result('pg4').feature('lngr9').set('smooth', 'none');
model.result('pg4').feature('lngr10').active(false);
model.result('pg4').feature('lngr10').set('data', 'cln2');
model.result('pg4').feature('lngr10').set('expr', 'cO2');
model.result('pg4').feature('lngr10').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr10').set('descr', 'Concentration');
model.result('pg4').feature('lngr10').set('linecolor', 'black');
model.result('pg4').feature('lngr10').set('legend', true);
model.result('pg4').feature('lngr10').set('legendmethod', 'manual');
model.result('pg4').feature('lngr10').set('legends', {'O2'});
model.result('pg4').feature('lngr10').set('smooth', 'none');
model.result('pg4').feature('lngr11').active(false);
model.result('pg4').feature('lngr11').set('expr', 'C_O2');
model.result('pg4').feature('lngr11').set('unit', 'mol/m^3');
model.result('pg4').feature('lngr11').set('descr', 'Solubility of O2');
model.result('pg4').feature('lngr11').set('linestyle', 'dashed');
model.result('pg4').feature('lngr11').set('linecolor', 'black');
model.result('pg4').feature('lngr11').set('smooth', 'none');
model.result('pg6').name('CO2 concentration');
model.result('pg6').set('title', 'Line Graph: Concentration of CO2
(mol/m³)');
model.result('pg6').set('xlabel', 'y direction');
model.result('pg6').set('xlabelactive', true);
model.result('pg6').set('ylabel', 'Concentration (mol/m³)');
model.result('pg6').set('axislimits', 'on');
model.result('pg6').set('xmin', '-0.0020000000949949026');
model.result('pg6').set('xmax', '0.20200000703334808');
model.result('pg6').set('ymin', '7.716928851364085E-5');
model.result('pg6').set('ymax', '200');
model.result('pg6').set('ylog', true);
model.result('pg6').set('titletype', 'manual');
model.result('pg6').set('ylabelactive', false);
model.result('pg6').feature('lngr1').set('data', 'cln3');
model.result('pg6').feature('lngr1').set('expr', 'cCO2');
model.result('pg6').feature('lngr1').set('unit', 'mol/m^3');
model.result('pg6').feature('lngr1').set('descr', 'Concentration');
model.result('pg6').feature('lngr1').set('legend', true);
model.result('pg6').feature('lngr1').set('legendmethod', 'manual');
model.result('pg6').feature('lngr1').set('legends', {'Beginning'});
82
model.result('pg6').feature('lngr1').set('smooth', 'none');
model.result('pg6').feature('lngr4').set('data', 'cln4');
model.result('pg6').feature('lngr4').set('expr', 'cCO2');
model.result('pg6').feature('lngr4').set('unit', 'mol/m^3');
model.result('pg6').feature('lngr4').set('descr', 'Concentration');
model.result('pg6').feature('lngr4').set('legend', true);
model.result('pg6').feature('lngr4').set('legendmethod', 'manual');
model.result('pg6').feature('lngr4').set('legends', {'End'});
model.result('pg6').feature('lngr4').set('smooth', 'none');
model.result('pg7').set('xlabel', 'Arc length');
model.result('pg7').set('ylabel', 'Velocity magnitude (m/s)');
model.result('pg7').set('xlabelactive', false);
model.result('pg7').set('ylabelactive', false);
model.result('pg7').feature('lngr1').set('data', 'cln3');
cCH4_1(1)=mphinterp(model,'cCH4','coord',[0.887;0.0148]);
cCH4_1(2)=mphinterp(model,'cCH4','coord',[0.887;0.0296]);
cCH4_1(3)=mphinterp(model,'cCH4','coord',[0.887;0.0444]);
cCH4_1(4)=mphinterp(model,'cCH4','coord',[0.887;0.0592]);
cCH4_2(1)=mphinterp(model,'cCH4','coord',[1.259;0.0148]);
cCH4_2(2)=mphinterp(model,'cCH4','coord',[1.259;0.0296]);
cCH4_2(3)=mphinterp(model,'cCH4','coord',[1.259;0.0444]);
cCH4_2(4)=mphinterp(model,'cCH4','coord',[1.259;0.0592]);
cCH4_3(1)=mphinterp(model,'cCH4','coord',[1.988;0.0148]);
cCH4_3(2)=mphinterp(model,'cCH4','coord',[1.988;0.0296]);
cCH4_3(3)=mphinterp(model,'cCH4','coord',[1.988;0.0444]);
cCH4_3(4)=mphinterp(model,'cCH4','coord',[1.988;0.0592]);
cCH4_4(1)=mphinterp(model,'cCH4','coord',[3.419;0.0148]);
cCH4_4(2)=mphinterp(model,'cCH4','coord',[3.419;0.0296]);
cCH4_4(3)=mphinterp(model,'cCH4','coord',[3.419;0.0444]);
cCH4_4(4)=mphinterp(model,'cCH4','coord',[3.419;0.0592]);
cCH4_5(1)=mphinterp(model,'cCH4','coord',[6.226;0.0148]);
cCH4_5(2)=mphinterp(model,'cCH4','coord',[6.226;0.0296]);
cCH4_5(3)=mphinterp(model,'cCH4','coord',[6.226;0.0444]);
cCH4_5(4)=mphinterp(model,'cCH4','coord',[6.226;0.0592]);
cCH4_6(1)=mphinterp(model,'cCH4','coord',[11.72;0.0148]);
cCH4_6(2)=mphinterp(model,'cCH4','coord',[11.72;0.0296]);
cCH4_6(3)=mphinterp(model,'cCH4','coord',[11.72;0.0444]);
cCH4_6(4)=mphinterp(model,'cCH4','coord',[11.72;0.0592]);
cCH4_7(1)=mphinterp(model,'cCH4','coord',[22.5;0.0148]);
cCH4_7(2)=mphinterp(model,'cCH4','coord',[22.5;0.0296]);
cCH4_7(3)=mphinterp(model,'cCH4','coord',[22.5;0.0444]);
cCH4_7(4)=mphinterp(model,'cCH4','coord',[22.5;0.0592]);
cCH4_1m
cCH4_2m
cCH4_3m
cCH4_4m
cCH4_5m
cCH4_6m
cCH4_7m
=
=
=
=
=
=
=
mean([cCH4_1(1)
mean([cCH4_2(1)
mean([cCH4_3(1)
mean([cCH4_4(1)
mean([cCH4_5(1)
mean([cCH4_6(1)
mean([cCH4_7(1)
cCH4_1(2)
cCH4_2(2)
cCH4_3(2)
cCH4_4(2)
cCH4_5(2)
cCH4_6(2)
cCH4_7(2)
cCH4_1(3)
cCH4_2(3)
cCH4_3(3)
cCH4_4(3)
cCH4_5(3)
cCH4_6(3)
cCH4_7(3)
cCH4_1(4)]);
cCH4_2(4)]);
cCH4_3(4)]);
cCH4_4(4)]);
cCH4_5(4)]);
cCH4_6(4)]);
cCH4_7(4)]);
cCH4_ex = [5.08e-5 8.23e-5 1.52e-4 3.44e-4 5.19e-4 8.26e-4 1.32e-3];
83
cCO2_1(1)=mphinterp(model,'cCO2','coord',[0.887;0.0148]);
cCO2_1(2)=mphinterp(model,'cCO2','coord',[0.887;0.0296]);
cCO2_1(3)=mphinterp(model,'cCO2','coord',[0.887;0.0444]);
cCO2_1(4)=mphinterp(model,'cCO2','coord',[0.887;0.0592]);
cCO2_2(1)=mphinterp(model,'cCO2','coord',[1.259;0.0148]);
cCO2_2(2)=mphinterp(model,'cCO2','coord',[1.259;0.0296]);
cCO2_2(3)=mphinterp(model,'cCO2','coord',[1.259;0.0444]);
cCO2_2(4)=mphinterp(model,'cCO2','coord',[1.259;0.0592]);
cCO2_3(1)=mphinterp(model,'cCO2','coord',[1.988;0.0148]);
cCO2_3(2)=mphinterp(model,'cCO2','coord',[1.988;0.0296]);
cCO2_3(3)=mphinterp(model,'cCO2','coord',[1.988;0.0444]);
cCO2_3(4)=mphinterp(model,'cCO2','coord',[1.988;0.0592]);
cCO2_4(1)=mphinterp(model,'cCO2','coord',[3.419;0.0148]);
cCO2_4(2)=mphinterp(model,'cCO2','coord',[3.419;0.0296]);
cCO2_4(3)=mphinterp(model,'cCO2','coord',[3.419;0.0444]);
cCO2_4(4)=mphinterp(model,'cCO2','coord',[3.419;0.0592]);
cCO2_5(1)=mphinterp(model,'cCO2','coord',[6.226;0.0148]);
cCO2_5(2)=mphinterp(model,'cCO2','coord',[6.226;0.0296]);
cCO2_5(3)=mphinterp(model,'cCO2','coord',[6.226;0.0444]);
cCO2_5(4)=mphinterp(model,'cCO2','coord',[6.226;0.0592]);
cCO2_6(1)=mphinterp(model,'cCO2','coord',[11.72;0.0148]);
cCO2_6(2)=mphinterp(model,'cCO2','coord',[11.72;0.0296]);
cCO2_6(3)=mphinterp(model,'cCO2','coord',[11.72;0.0444]);
cCO2_6(4)=mphinterp(model,'cCO2','coord',[11.72;0.0592]);
cCO2_7(1)=mphinterp(model,'cCO2','coord',[22.5;0.0148]);
cCO2_7(2)=mphinterp(model,'cCO2','coord',[22.5;0.0296]);
cCO2_7(3)=mphinterp(model,'cCO2','coord',[22.5;0.0444]);
cCO2_7(4)=mphinterp(model,'cCO2','coord',[22.5;0.0592]);
cCO2_1m
cCO2_2m
cCO2_3m
cCO2_4m
cCO2_5m
cCO2_6m
cCO2_7m
=
=
=
=
=
=
=
mean([cCO2_1(1)
mean([cCO2_2(1)
mean([cCO2_3(1)
mean([cCO2_4(1)
mean([cCO2_5(1)
mean([cCO2_6(1)
mean([cCO2_7(1)
cCO2_1(2)
cCO2_2(2)
cCO2_3(2)
cCO2_4(2)
cCO2_5(2)
cCO2_6(2)
cCO2_7(2)
cCO2_1(3)
cCO2_2(3)
cCO2_3(3)
cCO2_4(3)
cCO2_5(3)
cCO2_6(3)
cCO2_7(3)
cCO2_1(4)]);
cCO2_2(4)]);
cCO2_3(4)]);
cCO2_4(4)]);
cCO2_5(4)]);
cCO2_6(4)]);
cCO2_7(4)]);
cCO2_ex = [85.4 85.4 85.4 85.4 85.4 85.4 85.4];
constants = k
f = 3.88e11*(cCH4_1m-cCH4_ex(1))^2+1.48e11*(cCH4_2mcCH4_ex(2))^2+4.34e10*(cCH4_3m-cCH4_ex(3))^2+8.44e9*(cCH4_4mcCH4_ex(4))^2+3.71e9*(cCH4_5m-cCH4_ex(5))^2+1.47e9*(cCH4_6mcCH4_ex(6))^2+6.18e8*(cCH4_7m-cCH4_ex(7))^2+(cCO2_1mcCO2_ex(1))^2+(cCO2_2m-cCO2_ex(2))^2+(cCO2_3m-cCO2_ex(3))^2+(cCO2_4mcCO2_ex(4))^2+(cCO2_5m-cCO2_ex(5))^2+(cCO2_6m-cCO2_ex(6))^2+(cCO2_7mcCO2_ex(7))^2
out = model;
84
NUMERICAL OPTIMIZATION
% fminsearch: find minimum of function using
% derivative-free method on transformed variables
clear all, format compact
global k0
% Starting point
k0 = [4.8694e-04
6.0384e-03
1.1903e+00
1.4553e+00
1.6038e+00
4.6551e-01
5.6810e-05
2.0242e-05
2.1885e-04
1.1809e-01
4.5392e-05
1.0749e-01
1.6193e-04
1.4122e-01
5.3685e-04
7.0346e-01
5.0067e-04
1.1530e-02
1.1185e+00
1.3926e+00
8.2161e-06];
% Options setting
options =
optimset('Display','iter','PlotFcns',@optimplotfval,'TolFun',1,'MaxIter
',500);
% k = the reaction rate constant
% fval = value of objective function
% exitflag = describe the exit condition of fminsearch
[k,fval,exitflag,output] = fminsearch('M051013AQ',k0,options);
85
STATISTICAL METHODS
Average:
X
X1  X 2 
N
 XN
Standard deviation:
N
 X

i 1
X
i
2
N 1
Standard error:
m 

N
Confidence intervals:
X  Z  m
Table T.4 Z-values for Various Levels of Confidence
LOC
Z
99.9%
3.3
99.0%
2.577
98.5%
2.43
97.5%
2.243
95.0%
1.96
90.0%
1.645
85.0%
1.439
75.0%
1.151