by william jason harrington - university of...
TRANSCRIPT
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INVESTIGATION OF DIRECT METHANOL FUEL CELL VOLTAGE RESPONSE FOR
METHANOL CONCENTRATION SENSING
BY
WILLIAM JASON HARRINGTON
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
2012
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© 2012 William Jason Harrington
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To my wife Ashley, my parents Bill & Xinia and brother Jesse, thanks for your enduring love
and support
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ACKNOWLEDGMENTS
I thank the members of my committee Dr. William E. Lear, Dr. James H. Fletcher and Dr.
David W. Mikolaitis for their support and guidance on this thesis. I must also thank Dr. Joseph
L. Campbell, Dr. Philip Cox and Dr. Oscar D. Crisalle for their wisdom and advice. Finally, I
would like to thank all of my fellow colleagues in the University of North Florida Fuel Cell
Laboratory and University of Florida Energy Park for their encouragement and comradery.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS .............................................................................................................. 4
LIST OF TABLES .......................................................................................................................... 7
LIST OF FIGURES ........................................................................................................................ 8
ABSTRACT .................................................................................................................................. 11
CHAPTER
1 INTRODUCTION ................................................................................................................. 13
2 LITERATURE REVIEW ...................................................................................................... 17
Rechargeable Battery Technology Status .............................................................................. 17 Lithium-ion Battery Advantages .................................................................................... 17
Lithium-ion Battery Disadvantages ................................................................................ 17 Direct Methanol Fuel Cells .................................................................................................... 18
Effects of Methanol Concentration ................................................................................ 19 Methanol Sensing Technologies ............................................................................................ 21
Physical Property Type Methanol Sensing ..................................................................... 21
Capacitance-based sensors ...................................................................................... 21
Speed of sound-based sensors ................................................................................. 22 Refractive index-based sensors ............................................................................... 22 Infrared spectrum-based sensors ............................................................................. 23
Heat capacity-based sensors .................................................................................... 23 Viscosity-based sensors ........................................................................................... 24
Dynamic viscosity-based sensors ............................................................................ 24 Electrochemical Type Methanol Sensing ....................................................................... 25
3 EXPERIMENTATION AND DATA ANALYSIS ............................................................... 29
Test Station Description ........................................................................................................ 29 Fuel Cell Hardware ................................................................................................................ 31 Experimentation ..................................................................................................................... 32
Active Load Method .............................................................................................................. 33 Experimentation ............................................................................................................. 35 Results ............................................................................................................................ 36
Passive Load Method ............................................................................................................. 39 Experimentation ............................................................................................................. 39 Results ............................................................................................................................ 43
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4 VERIFICATION MODEL .................................................................................................... 52
Methanol Concentration Distribution .................................................................................... 52 Steady State Concentration Distribution ........................................................................ 52 Transient Concentration Distribution ............................................................................. 54
Transient Oxygen Concentration Distribution ....................................................................... 56 Modeling Summary ............................................................................................................... 57
5 SYSTEM INTEGRATION ................................................................................................... 58
Methanol Concentration Tracking ......................................................................................... 58 Methanol Consumption Model ....................................................................................... 58
Faradaic oxidation ................................................................................................... 59
Methanol crossover ................................................................................................. 60
Methanol Injection Model .............................................................................................. 61 Methanol Concentration Determination ......................................................................... 63
Brassboard Operation ............................................................................................................ 63
6 CONCLUSIONS ................................................................................................................... 65
APPENDIX
A DIFFUSION MODEL DEVELOPMENT ............................................................................. 68
Initial Conditions ................................................................................................................... 70 Anode Diffusion Layer (0 ≤ z ≤ zAD) ..................................................................................... 71
Anode Catalyst Layer (zAD ≤ z ≤ zAC) ................................................................................... 72 Membrane Layer (zAC ≤ z ≤ zM) ............................................................................................ 73
Cathode Catalyst Layer (zM ≤ z ≤ zCC) .................................................................................. 75 Homogenous Equations ......................................................................................................... 77 Steady State Equations .......................................................................................................... 80
B DIFFUSION MODEL MATLAB CODE ............................................................................. 84
LIST OF REFERENCES .............................................................................................................. 90
BIOGRAPHICAL SKETCH ........................................................................................................ 93
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LIST OF TABLES
Table page
3-1 OCV rise time at 0.60 M and 0.80 M. .............................................................................. 45
4-1 Summary of methanol crossover results from model for various feed methanol
concentrations with a current density of 150 mA/cm². ..................................................... 54
A-1 Matrix form of boundary equations for homogeneous equations. .................................... 80
A-2 Modified matrix of homogenous set of boundary equations. ........................................... 80
A-3 System of equations for homogeneous set of boundary conditions. ................................. 80
A-4 Boundary conditions for steady state, non-homogeneous boundary conditions............... 83
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LIST OF FIGURES
Figure page
2-1 The effect of methanol concentration on a typical DMFC at 75°C. ................................. 19
2-2 The effect of methanol concentration on a typical DMFC at low current densities. ........ 20
2-3 Transient behavior of DMFC with respect to methanol concentration ............................. 27
3-1 Screenshot of LabVIEW interface on University of North Florida Test Stations ............ 29
3-2 University of North Florida standard fuel cell test station. ............................................... 30
3-3 UNF Fuel Cell Test Station instantaneous methanol control attachment. ........................ 30
3-4 P&ID for University of North Florida standard test station and methanol control
attachment. ........................................................................................................................ 31
3-5 Compressed eight cell fuel cell stack. ............................................................................... 32
3-6 DMFC methanol concentration sensitivity with static loading......................................... 33
3-7 DMFC current density response with load change from 0.40 V to 0.35 V. ..................... 34
3-8 Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 0.20 M
and 50°C. .......................................................................................................................... 35
3-9 Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 0.60 M
and 50°C. .......................................................................................................................... 36
3-10 Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 1.60 M
and 50°C. .......................................................................................................................... 36
3-11 Unfiltered fuel cell transient response when electrically loaded from 0.40 V to 0.35
V at 50°C. ......................................................................................................................... 37
3-12 Unfiltered fuel cell transient response when electrically loaded from 0.35 V to 0.40
V at 50°C. ......................................................................................................................... 37
3-13 Filtered and normalized fuel cell transient response when electrically loaded from
0.40 V to 0.35 V at 50°C. ................................................................................................. 38
3-14 Filtered and normalized fuel cell transient response when electrically loaded from
0.35 V to 0.40 V at 50°C. ................................................................................................. 38
3-15 Current Density Transient Response Power Curve Fit Coefficients for 0.35 V and
0.40 V at 50°C. ................................................................................................................. 39
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3-16 Representative fuel cell voltage response from loaded to unloaded operating point. ...... 40
3-17 Fuel cell air starve cycle with 0.60, 0.80 and 1.60 molar concentration at 50 °C. ........... 41
3-18 Typical load cycle for DMFC OCV decay slope testing. ................................................. 42
3-19 OCV decay slope at 120 mA/cm² at various methanol concentrations with error bars
indicating first standard deviation. .................................................................................... 44
3-20 OCV decay slope at various current densities with 50°C stack temperature. ................... 45
3-21 OCV Decay slope with constant current density and variable concentration and
temperature. ...................................................................................................................... 47
3-22 Max OCV rise time at constant current density with varying temperature and
methanol concentration. .................................................................................................... 48
3-23 OCV Rise Slope held at constant current density (40 mA/cm²) with variable
concentration and stack temperature with error bars indicating single standard
deviation. ........................................................................................................................... 49
3-24 OCV Rise Slope held at constant current density (120 mA/cm²) with variable
concentration and stack temperature with error bars indicating single standard
deviation. ........................................................................................................................... 50
4-1 Results from model for MEA methanol concentration distribution for 0.80 M feed
concentration at a current density of 150 mA/cm². ........................................................... 53
4-2 Results from model for MEA methanol concentration distribution for various feed
concentrations at a current density of 150 mA/cm². ......................................................... 53
4-3 Results from model for MEA transient concentration distribution from a current
density of 120 mA/cm² to 0 mA/cm² at a feed concentration of 0.80 M. ......................... 54
4-4 Results from model for MEA transient concentration distribution from a current
density of 120 mA/cm² to 0 mA/cm² at a feed concentration of 1.60 M. ......................... 55
4-5 Model results for transient methanol concentration response at cathode catalyst layer
from a current density of 120 mA/cm² to 0 mA/cm². ....................................................... 55
4-6 Model results for the mean transient oxygen content in the cathode. ............................... 57
5-1 UNF 20 W DP4 brassboard fuel cell system. ................................................................... 58
5-2 Simplified methanol consumption and injection model for DP4...................................... 59
5-3 Representative methanol crossover current density for DP4 stack at various stack
temperatures, methanol concentrations and current densities. .......................................... 60
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5-4 Performance Curve for Single µBase Pump ..................................................................... 62
5-5 Comparison of µBase Pump Performance versus various inlet pressures. ....................... 62
5-6 UNF DP4 brassboard operation using sensor-less methanol sensing techniques. ............ 64
6-1 Ideal methanol concentration distribution at various load conditions. ............................. 68
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Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
INVESTIGATION OF DIRECT METHANOL FUEL CELL
VOLTAGE RESPONSE FOR METHANOL CONCENTRATION SENSING
By
William Jason Harrington
August 2012
Chair: William E. Lear, Jr.
Major: Mechanical Engineering
A Direct Methanol Fuel Cell (DMFC) was tested under various transient load conditions in
order to determine the sensitivity of response to methanol concentration. In addition to varying
load profiles, the DMFC was tested at several temperature and methanol concentration operating
conditions. The results demonstrated a strong correlation of open circuit voltage transient
response to methanol concentration with high repeatability and resolution in the methanol
concentration range of 0.60 - 1.60 M.
The findings and phenomena that were observed in the experiments were further studied
using a simple, 1-D, transient methanol diffusion model. The model represents the transient
methanol crossover within the membrane electrode assembly of the DMFC. The transient
methanol crossover values that were calculated using the model were used to approximate the
transient oxygen consumption for an open cathode system. The results generated by the
computer model exhibited similar timescales compared to what was observed during the DMFC
testing. This supports the theory of a cathode dominant response due to the change in methanol
crossover with various methanol feed concentrations.
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Finally, the measurements that were gathered during DMFC testing were applied in a
brassboard system. A table was generated allowing a DMFC open circuit transient voltage
response to be correlated to a methanol concentration. Due to the operation profile that a DMFC
must undergo, the open circuit transient voltage response could only be captured during
rest/rejuvenation cycles which typically occur every 10-20 minutes. Therefore, a secondary
model had to be created in order to track the methanol concentration between rest/rejuvenation
cycles by predicting the consumption (Faradaic, crossover) and addition (methanol injection) of
methanol in the system. Utilizing the transient open circuit voltage response with the methanol
concentration estimator allowed for over 20 hours of continuous operation in a brassboard
without the use of a secondary methanol sensor.
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CHAPTER 1
INTRODUCTION
The advances in multimedia (internet, social networking, multi-megapixel photos, high
definition video, high fidelity music, television programming, etc.) and wireless communications
(Wi-Fi, Bluetooth®, WWAN, 4G, LTE, 3G, etc.) have transformed the way people communicate
today. While the computing power in portable electronics such as laptops and cell phones
continues to double every two years [1], the energy density of the most common power source
found in these devices (lithium ion batteries) only doubles every thirteen years [2].Consumers
demand access to content and services at all times through devices with larger screens and faster
processors while achieving a lighter weight and a thinner profiles. The use of such devices with
existing battery technology has negatively impacted their run time. In addition to the deficiency
of the energy density found in lithium ion batteries, power density has also become a
technological limitation. As lithium ion batteries are pushed to higher power densities, the
combination of added heat generation and the limitations in manufacturing have resulted in an
increase of lithium ion battery related fires [3]. One of the most promising solutions that is being
considered as a potential replacement for battery technology is the direct methanol fuel cell
(DMFC) which offers advantages in both energy and power density.
Fuel cells are electrochemical devices that convert chemical energy into electrical energy.
The fuel cell is similar to a battery, as both operate through an electrochemical reaction; however
fuel cells have the advantage of storing the fuel and oxidant externally. This enables the fuel cell
to operate indefinitely provided that sufficient reactants are present. Because the energy
conversion process that takes place in a fuel cell is not based on the process that limits most
typical heat engines (Carnot cycle), the fuel cell is able to achieve high efficiencies at low
temperatures.
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The majority of PEM fuel cells accept hydrogen at the anode and oxygen at the cathode to
electrochemically produce power. A DMFC ultimately uses hydrogen at the anode, however a
methanol-water solution is electrochemically converted to hydrogen without the use of
intermediate steps or equipment. The use of methanol as a fuel has many advantages over
hydrogen including ease of storage, high availability and low cost. The DMFC has the distinct
advantage of higher energy density over a typical hydrogen-oxygen based fuel cell with low
power applications (< 100 W). The high energy density of methanol fuel and the ease of storage
and handling enable the DMFC to perform for longer periods of time given the same system
volume. This characteristic makes DMFC technology a prime candidate for portable electronic
applications.
1-1
1-2
1-3
The anode (1-1) and cathode (1-2) half reactions can be combined to form an overall
reaction (1-3) for the DMFC. Although there are many intermediate reactions that take place
before the overall reaction is completed, the half reactions are the most simplified way to
describe the processes that takes place within the fuel cell. At the anode, methanol and water are
electrochemically converted to hydrogen protons, electrons and carbon dioxide. In the cathode
reaction, oxygen and the hydrogen protons generated at the anode react to form water. One of the
most important operating parameters for a DMFC is the methanol concentration at the anode.
Operation of a DMFC using very low concentrations (less than 0.4 Molarity) of methanol can
result in reduced limiting current density, peak power and damage due to fuel starvation [4]. Due
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to the existing limitations of DMFC membrane technology, DMFCs should not operate using
equi-molar ratios of pure methanol and water as implied by Equation 1-1. When high
concentrations of methanol (greater than 1.0 Molarity) are exposed to the anode, excessive
permeation of methanol across the membrane occurs; this phenomenon has been termed
“methanol crossover”. The adverse effects of methanol crossover include depolarization at the
cathode and poor fuel utilization [5]. The methanol diffuses from the anode to the cathode across
the membrane, eventually reaching the platinum catalyst of the cathode, where it reacts with
oxygen from the air, creating waste heat. In order to minimize methanol crossover and maintain
reasonable DMFC output power levels, a DMFC will typically operate with an aqueous solution
of methanol (0.6-1.0 Molarity).
Due to the simplicity of operation at higher methanol concentrations, manufacturers are
working to mitigate issues encountered with methanol crossover by improving membrane
technology [6]. The essential task of producing a membrane that has a higher ion exchange
capacity while allowing less methanol to diffuse is difficult. PolyFuel Inc. developed a
hydrocarbon-based membrane to compete with DuPont’s widely used fluorocarbon based Nafion
117. PolyFuel claims that its family of membranes offers a 33 to 50 percent improvement in the
level of methanol crossover, water flux, and power density when compared to Nafion [7].
Although advancements in membrane technology are critical to improving DMFC power and
energy density, the methanol concentration will continue to be an essential factor for DMFC
performance.
In order to achieve optimum performance, the DMFC must operate in a tight methanol
concentration band. A number of technologies exist to measure the concentration of methanol,
however, few are able to meet the requirements (size, costs, weight, reliability, accuracy, etc.)
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and electrochemical sensing methods. Physical-type sensors correlate methanol concentration to
a physical property such as density or heat capacity. Some of these sensors are fairly robust;
however they usually do not package well for miniature applications and often require auxiliary
devices (pumps, heaters, complex sensing systems) which increase parasitic power loads on the
DMFC. Most electrochemical-type sensors work using the same principles found in DMFCs
where a signal can be interpreted based on electrochemical response. The most accessible
electrochemical sensor to integrate into a DMFC system is the fuel cell stack itself. With the
added benefit of reduced cost, weight and space, the stack is an ideal replacement for a methanol
sensor.
It is the goal of this thesis to correlate the transient voltage response of a DMFC to
methanol concentration in order to eliminate the requirement for a discrete methanol
concentration sensor in a DMFC system. Integration of a sensor-less (operation without a
methanol sensor) methanol sensing technique will significantly reduce system cost, weight and
complexity accelerating the movement of DMFC technology.
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CHAPTER 2
LITERATURE REVIEW
Rechargeable Battery Technology Status
Battery technology is the most prevalent form of portable power. Due to its convenience
and low operating cost, rechargeable batteries account for 85% of fiscal battery sales [9].
According to McAllister and Farrell, the annual electrical demand for the average household in
the state of California is 125 kWhr for rechargeable devices, which accounts for 2.3% of the total
electrical load [8]. Typically only 15% of the energy that is used to recharge batteries is stored,
while the remainder is wasted as heat [8]. The sales published by the Battery Association of
Japan show that lithium-ion battery technology is the most prevalent rechargeable battery
chemistry used today, accounting for 47% of the fiscal sales of all rechargeable batteries [9].
Lithium-ion Battery Advantages
Lithium-ion batteries have many advantages over other battery technologies. Lithium is the
lightest metal in the periodic table, therefore lithium-ion batteries are lighter than most other
battery chemistries. In addition to lithium’s light weight, the metal is also highly reactive with an
average open circuit potential of 3.7 Volts, resulting in one of the highest energy density battery
chemistries [10]. As published by Powers, lithium-ion battery technology also exceeds other
battery chemistries in maximum charge cycles and off-state discharge rates [10].
Lithium-ion Battery Disadvantages
However, lithium-ion battery technology has its drawbacks. Scrosati and Vetter both
observed accelerated degradation in the off state when storing lithium-ion batteries at elevated
temperatures [11, 12]. Shim published data for lithium ion battery testing at 60°C, where the
degradation was 15 times more than at 25°C (10% annually at 25°C) [13]. Researchers have
determined that the root cause of high temperature degradation for lithium ion batteries occurs
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within the morphology and composition of the solid electrolyte interface, which changes at
elevated temperatures [12].
In addition to degradation, elevated temperatures can adversely affect the stability and
safety of lithium ion batteries. To date, the Federal Aviation Administration has documented
over 28 lithium-ion related fires/explosions on commercial airline flights [14]. Due to the high
level of energy that can be stored in lithium-ion batteries, injury and/or death can occur due to
failure.
The major drawback for lithium-ion batteries is the rate at which they technologically
advance. Historically, lithium-ion technology advances at a rate of approximately 5% annually
while the microprocessors that most of these batteries power advance in processing speed at a
rate of 40% annually [1, 2]. This poses a major problem for the advancement of portable
electronics in general. A recent development in the energy density of batteries in portable
electronics has primarily been achieved by replacing off the shelf battery cells with custom fit,
non-user removable battery packs. Apple computers was one of the first major manufacturers to
incorporate this strategy resulting in a 30% increase in battery capacity [15]. Research institutes
such as Stanford University have reported advances (nanowire technology) in lithium-ion
technology, however the timeline for implementation of these breakthroughs is 5-10 years away
[16]. Without a power source that can meet the demands of tomorrow’s portable electronics, the
consumer will see a slowdown in the progression of portable technology that is available today.
Direct Methanol Fuel Cells
Direct methanol fuel cells have the potential to replace lithium-ion battery technology as a
power source in portable electronics. Direct methanol fuel cells (DMFCs) work on similar
principles to batteries. Both devices electrochemically convert fuel and oxidant into electricity;
however the fuel cell has the inherent advantage of storing its reactants externally. Instead of
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waiting for a battery to recharge, the fuel cell simply requires a new fuel cartridge of methanol to
continue producing power. The possibility of carrying multiple batteries is an option to extend
portable electronic runtimes; however the energy density of the liquid methanol that DMFCs use
exceeds all common battery technologies. It is this property that enables DMFCs to excel over
battery technology during extended durations (>10 hours). Direct methanol fuel cells are an
enabling technology which can give portable electronics manufacturers the flexibility to expand
the capabilities of portable devices without the risk of reducing portable operation duration.
Effects of Methanol Concentration
One of the major technological barriers that DMFCs must overcome are its sensitivity to
methanol concentration. The Nernst equation for the concentration polarization at the anode
suggests that the concentration losses can be minimized by increasing the limiting current
density. The limiting current density for the anode is directly related to the amount of methanol
(methanol concentration) that is present [17]. However, as shown in Figure 2-1, data presented
by Song suggests that the performance of a direct methanol fuel cell does not always increase
with increasing methanol concentration.
Figure 2-1. The effect of methanol concentration on a typical DMFC at 75°C [18].
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The effect of methanol concentration on DMFC performance indicates increased
performance with increasing methanol concentration until reaching a feed solution concentration
of 2.0 M. At high current densities (greater than 100 mA/cm²), the effect of methanol crossover
is less severe. Only until reaching 2.0 M do the benefits of reducing anode concentration losses
outweigh the voltage losses due to methanol crossover [18]. Primarily driven by concentration
and pressure gradients, as the concentration of methanol at the anode increases, more methanol
crosses the membrane depolarizing the cathode potential. Du, Zhao, and Yang report that the
resulting decline in cathode electrode performance is related primarily to the “poisoning” of the
cathode catalyst from methanol oxidation intermediates such as CO [19].
The effect of the feed methanol concentration on DMFC performance is most evident at
low current densities. As shown in Figure 2-2, Song presented data where a strong relationship
of fuel cell performance at low current densities with respect to feed methanol concentration was
established. With a low feed methanol concentration (0.25 M), the methanol crossover is reduced
allowing for the fuel cell to operate with a 12.5% increase in performance relative to a high
methanol concentration (4.0 M).
Figure 2-2. The effect of methanol concentration on a DMFC at low current densities [18].
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Methanol Sensing Technologies
There is strong evidence in the published literature that shows direct methanol fuel cell
performance is heavily dependent on the feed methanol concentration at the anode [4], [18], [23],
[20]. Therefore it is critical that the anode methanol concentration be kept at a level that is
optimized for DMFC power output and efficiency. In order to monitor the methanol
concentration in the DMFC, a methanol sensor can be used in the anode loop. A number of
different methanol sensing technologies exist each with its own advantages and disadvantages.
Most of the methanol sensors that are available today can be separated into physical property
type sensors or electrochemical type sensors.
Physical Property Type Methanol Sensing
Capacitance-based sensors
Doerner proposed a capacitance based methanol sensor utilizing impedance spectrum
analyzer electronics [21]. The sensor uses two planar sensing electrodes to measure the dielectric
constant (capacitance) of a test solution in order to determine the methanol concentration. The
sensor exhibited high signal to noise levels at low frequencies (>300 kHz) and a strong
relationship with respect to temperature. Capacitance-type sensors have been used in the past to
determine the concentration of methanol in gasoline-methanol fuel mixtures with reasonable
results due to the high disparity of dielectric constants for gasoline (2.0 [22]) and methanol (32.6
[22]). The distinction between the dielectric constants for water (80.4 [22]) and methanol (32.6
[22]) is much less. The resolution for measuring the dielectric constant of methanol solutions less
than 5.0 Molar is small. In addition to errors that may arise from measurement resolution, the
corrosion of electrodes, CO2 bubbles generated by the DMFC in the anode stream, or metallic
ions can severely impact capacitance measurements [23].
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Speed of sound-based sensors
A speed of sound-based methanol sensor was proposed in patent 6,748,793 by Rabinovich
and Tulimieri utilizing an ultrasonic sensor. According to the patent literature, the sound
propagation time is measured for a given distance in order to determine the speed of sound of the
mixture. Primarily based on the density and bulk modulus of elasticity of the test medium, the
speed of sound for methanol and water is 1580 m/s and 1150 m/s, respectively [23]. Like the
capacitance-type sensors, the disparity in sound velocities for methanol and water is not great
enough to provide high resolution measurements, particularly at elevated temperatures.
Temperature has a strong effect on the speed of sound of methanol-water solutions, therefore
Rabinovich and Tulimieri proposed a second measurement chamber for a calibration sample
(deionized water). This would allow the sensor to offset the temperature effects by compensating
with the output of the calibration sample. In addition to the low resolution provided by speed of
sound-type sensors, this type of sensor is not easily miniaturized and can also suffer from
measurement error due to anode CO2 generation.
Refractive index-based sensors
Longtin and Fan developed a refractive index-based concentration sensor that uses a one
mW 632.8 nm laser in conjunction with a semiconductor position sensor [24]. They were able to
achieve a highly accurate, small and inexpensive concentration sensor. However some
measurement error was observed attributed to vibration, air disturbances and laser fluctuations.
In addition, although the refractive index concept offers the most simple of designs, the change
in refractive index at low concentrations provides the least resolution among the discussed
concentration sensing methods. The refractive index for water is 1.333 [25] and the refractive
index for pure methanol is 1.329 [25].
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Infrared spectrum-based sensors
DuPont currently holds a patent for an infrared spectrum-based methanol sensor [26]. The
sensor works using similar principals found in the refractive index sensor. An IR source
transmits a non-visible light through a test medium where a photodetector analyzes the
transmitted light and a microprocessor converts the signal to a methanol concentration. A strong
relationship between absorption and methanol concentration can be determined from IR
wavelengths in the range of 9.8 to 9.9 µm. The infrared spectrum provides excellent resolution
for low methanol concentrations (less than 1.5 M), however measurement accuracy is still
effected by CO2 bubbles [23].
Heat capacity-based sensors
Siargo has developed a prototype heat capacity type methanol sensor utilizing their flow
measurement technology. The sensor requires a heat source, a constant flow rate and two
temperature sensors. The methanol solution temperature is measured using one of the
temperature sensors as heat is applied to the solution. The temperature of the solution
downstream of the heater is measured to determine the corresponding heat capacity. The isobaric
specific heat capacity for methanol and water is 78.81 J/mol·K [27] and 75.40 J/mol·K [27],
respectively. For aqueous methanol solutions, the heat capacity vs. methanol concentration curve
is non-linear. The heat capacity sharply increases until the molar concentration reaches 7.0
molarity, where it steadily starts to decrease with increasing methanol concentration. For a
solution flow rate of 100 mL/min, the difference in temperature rise for a solution changing from
0.5 Molarity to 1.0 Molarity is 2.0 °C [23]. Although this temperature difference is easily
measured, the accuracy of heat capacitance-type devices can be heavily influenced by
movement. At constant flow velocities, a convection coefficient can be determined for the
sensor. If the sensing device were to be abruptly shaken, the resulting convection coefficient
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would change resulting in a varied temperature rise across the heater. In addition to the
inaccuracies created by abrupt movements, the parasitic power from the heater and additional
pumping requirements must also be taken into consideration when dealing with portable power
applications.
Viscosity-based sensors
Siemens currently holds a US patent for a methanol sensor that measures the viscosity of a
methanol solution in order to determine its concentration [28]. The methanol solution is pumped
through a constriction and the pressure drop across the constriction is measured in order to
determine its viscosity using the Hagen-Poiseuille equation. At 20ºC, water is characterized with
a viscosity that is 1.5 times more than for methanol [29]. Interestingly, the viscosity of an
aqueous methanol solution increases with concentration until reaching a concentration of 12.0
molarity [23]. The large change in viscosity for low methanol concentrations provides excellent
resolution for correlating methanol concentration. Measuring the pressure drop across a flow
restriction provides one of the simplest methods for determining fluid viscosity.
Determination of methanol concentration using viscosity has its drawbacks. The CO2
bubbles that are introduced into the solution line by the fuel cell can create large errors in
viscosity determination. In addition, viscosity is a strong function of temperature. The viscosity
of water is nearly half at 50°C compared to its value at 20°C [29]. Therefore an accurate means
of temperature measurement would also be required.
Dynamic viscosity-based sensors
Integrated Sensing Systems (ISSYS) produces a methanol sensor that utilizes a micro-
machined resonating tube to measure kinematic viscosity [30]. Kinematic viscosity is composed
of density and the dynamic viscosity. As the density of the test solution changes, the effective
mass of the resonating tube shifts, therefore affecting the resonant frequency. Additionally, the
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damping effect on the resonator can be used to determine the dynamic viscosity. Kinematic
viscosity sensors work well with low flow applications such as fuel cells. However, these sensors
do not miniaturize well due to the requirement of a bulky counterbalance. In addition, previous
experience has shown that density-type sensors severely suffer from impact shock and
measurement drift over time.
Electrochemical Type Methanol Sensing
An electrochemical-based methanol sensor was developed at the Jet Propulsion Laboratory
based on the electro-oxidation of methanol to carbon dioxide on a platinum-ruthenium catalyst
[31]. The proposed methanol sensor operates on the same principles found in DMFCs. The anode
potential is set at a constant voltage and the oxidation current is measured. At lower methanol
concentrations, the oxidation current is limited by the transport of methanol to the electrode
surface. Electrochemical-based methanol sensors offer strong measurement resolution and are
less sensitive to CO2 compared to other methanol sensing technologies. In addition,
electrochemical-based methanol sensors can easily be constructed and miniaturized due to their
simplicity and similarities to fuel cells. However, electrochemical-based sensors suffer from
nearly all issues encountered by DMFCs including contamination, degradation, catalyst
deterioration and slow response time [23].
Other electrochemical-based methanol sensors have been developed including one from
the Institute of Nuclear Energy Research in Taoyuan County, Taiwan. The sensing method
utilizes the fuel cell stack by measuring an operating characteristic such as voltage, current or
power and applies a control strategy for the methanol injection pump accordingly. Based on the
performance of the stack, a certain amount of methanol is required in order for the methanol
concentration in the system to remain constant. If a slightly higher amount of methanol is
precisely metered into the system than what the system consumes, the methanol concentration
26
will increase. Response of the fuel cell stack can be analyzed in order to determine whether the
system methanol concentration increased closer or further away from the optimal operating
point. One inherent advantage to this control strategy is that the methanol concentration can be
optimized for a stack that has suffered from performance degradation [32]. However, operating
close to the optimal methanol concentration poses a risk for fuel starvation due to the proximity
of the optimal methanol concentration operating point to the fuel starvation point.
One of the largest manufacturers of commercial DMFC systems is Smart Fuel Cells
Energy Inc. They have developed many systems utilizing sensorless technology. Although the
exact method for methanol concentration determination is undetermined, it is believed that a
lookup table is used in order to determine the methanol concentration within the system based on
key system parameters (fuel cell voltage, current, temperature, etc.). One of the major drawbacks
to using a lookup table in a DMFC is the measurement error that is introduced when the fuel cell
stack experiences a non-standard degradation mechanism. In addition, repeated start-up and shut-
downs can pose a major problem for methanol concentration determination due to the lack of
operation time resulting in minimal feedback of methanol concentration. This can lead to damage
of the stack due to excessive methanol concentration or fuel starvation [33].
Differences in electrochemical response with respect to methanol concentration can also be
seen in the transient behavior of direct methanol fuel cells. Essentially, the transient behavior of
the fuel cell is characterized by the transport properties of methanol through the anode diffusion
layer and membrane. The relationship of methanol crossover relative to feed methanol
concentration is nearly linear [34]. When the fuel cell is operated under constant load, a certain
quantity of methanol diffuses through the diffusion layer to the anode catalyst. The concentration
27
gradient across the anode is different at varying load levels. When the load is abruptly changed,
it takes time for the concentration gradient to reach equilibrium.
Figure 2-3. Transient behavior of DMFC with respect to methanol concentration. [35]
As shown in Figure 2-3, the load on the DMFC oscillates from a loaded condition to open
circuit. When the load on the fuel cell is removed, less methanol is required for the reaction to
take place. At this very moment, when the load is changed, the local concentration at the cathode
catalyst is relatively low. The decreased load also allows for an increase in the amount of
methanol that is available at the anode catalyst. The combination of low methanol concentration
at the cathode (decreased methanol crossover) and high methanol concentration at the anode
(decreased anode concentration overpotential) is ideal. As a result, the transient voltage
performance when switching from a loaded to non-loaded condition sharply increases until the
diffusion of methanol is able to equilibrate. As shown in Figure 2-3, the dynamic behavior for
each methanol concentration varies. Analysis of the effect of methanol concentration on the
28
transient electrochemical performance will be used in order to determine the feed solution
methanol concentration in a direct methanol fuel cell.
29
CHAPTER 3
EXPERIMENTATION AND DATA ANALYSIS
Test Station Description
In order to analyze the transient behavior of a direct methanol fuel cell relative to methanol
concentration, a test station had to be developed that would provide accurate, repeatable data for
analysis. The University of North Florida acquired a number of disassembled, incomplete, Fuel
Cell Technologies, Inc. test stations. These test stations were refurbished utilizing the existing
electric load banks, temperature controllers and enclosures. All other components (data
acquisition, cathode mass flow controller, signal conditioning, anode solution heater and pump,
computer, etc.) were procured and selected based on the engineering requirements.
Figure 3-1. Screenshot of LabVIEW interface on University of North Florida Test Stations
As shown in the screenshot in Figure 3-1, a new LabVIEW interface was written in order
to control all of the applicable test station components. As shown in Figure 3-2, the University of
North Florida standard test station is fully equipped including:
Fuel cell load control
Fuel cell voltage and current measurements
Anode solution flow control
Anode solution temperature control and measurement
30
Fuel cell temperature control and measurement
Fuel cell cathode flow rate control and measurement
Customized LabVIEW interface
Script enabled test operation
Figure 3-2. University of North Florida standard fuel cell test station.
In addition to the standard fuel cell test station, an attachment was developed in order to
precisely control the methanol feed concentration delivered to the fuel cell. As shown in Figure
3-3, a PDS-100 dual head precision piston pump was mounted to an aluminum substructure with
a USB enabled data acquisition controller.
Figure 3-3. UNF Fuel Cell Test Station instantaneous methanol control attachment.
31
The use of the methanol control attachment with the standard test station (P&ID shown in
Figure 3-4) enabled repeatable, accurate data collection with the flexibility of instantaneous
methanol concentration control.
PDS-100 Pump Head A
PDS-100 Pump Head B
10% Methanol
Deionized Water
T
Thermocouple
Direct Methanol
Fuel Cell
Waste Container
T
Thermocouple
TThermocouple
Computer
DAQ
T-1
T-2
T-3
AR-1
AR-2
AR-6
AR-3
Solution
Heater AR-7
AR-8
AW-2
AW-1
AR-5
AR-4
FCV-1
CV-1
CV-2
CV-3
ACP-2AC ACP-1
Fuel Cell Test Stand
FCL-1 CR-1
ComputerCI-1
CI-2
Multimeter
FCI-1
P-1
Figure 3-4. P&ID for University of North Florida standard test station and methanol control
attachment.
Fuel Cell Hardware
The eight cell stack shown in Figure 3-5 with an active area of 15.5 cm² per cell was used
to analyze the variation in transient performance relative to the feed methanol concentration. The
MEA is composed of an in-house hydrocarbon based membrane with a catalyst loading of 3.7
mg/cm² on the anode and two mg/cm² on the cathode. The composition of the catalyst on the
anode is a 50/50 atomic ratio mixture of platinum/ruthenium, while the catalyst on the cathode is
a solitary platinum catalyst.
A flow channel plate is placed between each MEA in order to deliver various
concentrations of methanol to the anode and oxygen (air) to the cathode. The anode and cathode
32
each have a unique flow pattern that has been optimized for reactant delivery. The anode side of
the flow channel plate is characterized with a serpentine flow channel, while the cathode has an
open straight channel design. The simplicity of the open cathode allows for easy heat removal,
however the cathode is typically subjected to operation at ambient conditions (pressure,
temperature, humidity). In order to acquire repeatable, consistent data, a PID temperature
controller was used with a solution heater to preheat the anode solution entering the stack so that
a uniform stack temperature could be achieved. For all of the testing that was conducted, the
minimum stoichiometric flow rates for the anode and cathode were ten and three respectively.
Figure 3-5. Compressed eight cell fuel cell stack.
Experimentation
Based on the data that is presented in Figure 3-6, the DMFC performance has a strong
correlation relative to the feed methanol concentration. However, the optimal methanol
concentration for these data is approximately 0.70 M. Without a reference of which side of the
optimal concentration that the fuel cell is operating at, it is very difficult to determine the
methanol concentration based on a static load measurement. Therefore, the transient response of
the DMFC was evaluated for sensitivity to methanol concentration.
33
Figure 3-6. DMFC methanol concentration sensitivity with static loading.
Active Load Method
During the literature review, Argyropoulos, Scott and Taama [35] revealed a variation in
the cell voltage response with respect to methanol concentration when a DMFC was brought
from a loaded to an unloaded (OCV) condition. It is less than desirable to interrupt fuel cell
power production every time the methanol concentration needs to be determined. With the
intention of eliminating the unloaded condition to determine methanol concentration, an active
load approach was tested initially. In order to determine if a measurable correlation between
methanol concentration and the transient behavior of the fuel cell exists, the fuel cell was
operated with various transient electrical loads. Initially, the load was oscillated in constant
voltage mode at different frequencies and magnitudes. By comparison, the published literature
conducted their testing in constant current mode. In order to prevent cell reversal, constant
60.0
70.0
80.0
90.0
100.0
110.0
120.0
130.0
140.0
150.0
160.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
Cu
rre
nt
De
nsi
ty (
mA
/cm
²)
Solution Concentration (Moles/Liter)
Current Density vs. Solution Concentration (Cv=0.35 V)
55.0 50.0 45.0
34
voltage load steps were used. An exemplar transient load profile shown in Figure 3-7 identifies
the critical points and terminology for data analysis.
Figure 3-7. DMFC current density response with load change from 0.40 V to 0.35 V.
As shown in Figure 3-7, the fuel cell was electrically loaded from a constant voltage of
0.40 V to 0.35 V. The transient fuel cell current that corresponds to the voltage load steps was
analyzed. Immediately after the electrical load is changed, the fuel cell current experiences a
rapid transient. Due to the actuation speed of the electrical load bank, the initial peak, identified
as the peak cutoff in Figure 3-7, is more than likely an artifact of the electrical load bank
overshooting its target voltage. Therefore, any of the transient data prior to this peak was
disregarded for data analysis. In addition to the peak cutoff point, the maxima and minima for
each voltage step is labeled.
35
Experimentation
An algorithm was developed in LabVIEW to determine the cutoff point, maximum and
minimum current for each electrical load change. The data that exists between these two points
was used to perform the analysis for methanol concentration sensitivity. During operation, the
DMFC is typically operated at a voltage between 0.35 and 0.40 V in order to maximize output
power and efficiency. Therefore, the load changes for experimentation were oscillated between
0.35 and 0.40 V. Furthermore, 10 seconds (5 seconds for each load step) were used for the load
oscillation period in order to obtain frequent concentration measurements. The DMFC was tested
at various methanol concentrations ranging from 0.20 M – 1.60 M in 0.20 M increments.
The DMFC was tested for ten minutes for each methanol concentration setpoint. As shown
in Figure 3-8, for low methanol concentrations (0.20 M), a very erratic behavior exists. Figure
3-9, with an operation methanol concentration of 0.60 M, indicates a substantial change in the
transient current density response relative to the 0.20 M sample. Finally, Figure 3-10 represents
the upper level of methanol concentration setpoints, with a more subtle change with respect to
the 0.60 M test case.
Figure 3-8. Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 0.20 M
and 50°C.
36
Figure 3-9. Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 0.60 M
and 50°C.
Figure 3-10. Transient current for a DMFC with load oscillations from 0.35 V to 0.40 V at 1.60
M and 50°C.
Results
The data presented in Figure 3-11 and Figure 3-12 represent one instance of the unfiltered
(peak cutoff not removed) fuel cell current with load changes to 0.35 V and 0.40 V respectively.
Figure 3-13 and Figure 3-14 are the same data that was presented in Figure 3-11 and Figure 3-12,
however the data has been filtered and normalized in order to facilitate data analysis. Based on
an initial qualitative analysis, are large disparity forms between methanol concentration less than
37
0.50 M and greater than 0.50 M. For the 0.35 V case, the test that were conducted with the lower
concentrations (<0.50 M) decreased, while the testing that was conducted with the higher
methanol concentrations increased. For the 0.40 V testing, the opposite relationship was
established. With both the 0.35 V and 0.40 V cases, the difference between the transient response
with methanol concentrations greater than 0.80 M was minimal.
Figure 3-11. Unfiltered fuel cell transient response when electrically loaded from 0.40 V to 0.35
V at 50°C.
Figure 3-12. Unfiltered fuel cell transient response when electrically loaded from 0.35 V to 0.40
V at 50°C.
60
80
100
120
140
160
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Cu
rre
nt
De
nsi
ty (
mA
/cm
²)
Elapsed Time (s)
Fuel Cell Current Transient Response at 0.35 V
0.2 M 0.4 M 0.6 M 0.8 M 1.0 M 1.2 M 1.4 M 1.6 M
0
50
100
150
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Cu
rre
nt
De
nsi
ty (
mA
/cm
²)
Elapsed Time (s)
Fuel Cell Current Transient Response at 0.40 V
0.2 M 0.4 M 0.6 M 0.8 M 1.0 M 1.2 M 1.4 M 1.6 M
38
Figure 3-13. Filtered and normalized fuel cell transient response when electrically loaded from
0.40 V to 0.35 V at 50°C.
Figure 3-14. Filtered and normalized fuel cell transient response when electrically loaded from
0.35 V to 0.40 V at 50°C.
For each oscillation, a power curve fit was established of the form listed in Equation 3-1.
The exponential b-coefficient is representative of the slope of the curve. The power curve fit
coefficients for each methanol concentration cycle was average and is shown in Figure 3-15. The
active load measurement provides an acceptable resolution with concentrations ranging from 0.2
to 0.8 M, however this limited range for use in a DMFC is unsatisfactory for robust operation.
100.0102.5105.0107.5110.0112.5115.0117.5120.0122.5125.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Current Density Responses at 0.35 V
0.20 M 0.40 M 0.60 M 0.80 M 1.00 M 1.20 M 1.40 M 1.60 M
110.0
120.0
130.0
140.0
150.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Current Density Responses at 0.40 V
0.20 M 0.40 M 0.60 M 0.80 M 1.00 M 1.20 M 1.40 M 1.60 M
39
3-1
Figure 3-15. Current Density Transient Response Power Curve Fit Coefficients for 0.35 V and
0.40 V at 50°C.
Passive Load Method
Based on the reviewed literature [35] and the results from the active method, it was
determined that the load profile that could provide the greatest resolution for methanol
concentration determination is when the stack is operated from a loaded (120-150 mA/cm²) to an
unloaded (OCV) operating point. This load profile is a realistic option for DMFC system
integration. In order to minimize on-state degradation due to cathode catalyst oxidation, a DMFC
is subjected to a periodic rest cycle during operation. This cycle involves removing the load from
the fuel cell stack, allowing the stack voltage to reach OCV and then reapplying the load with no
oxygen flow to the cathode so that the cathode potential is reduced.
Experimentation
In order to gain a better understanding of the voltage response, the stack was operated at
various methanol concentrations. The initial experiments revealed three distinct paths for
determining a correlation between the transient voltage response and methanol concentration. In
-1.0E-02-7.5E-03-5.0E-03-2.5E-030.0E+002.5E-035.0E-037.5E-031.0E-021.3E-021.5E-02
-3.E-02
-1.E-02
1.E-02
3.E-02
5.E-02
7.E-02
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80
0.3
5 V
Po
we
r C
urv
e F
it C
oe
ffic
ien
t
0.4
0 V
Po
we
r C
urv
e F
it C
oe
ffic
ien
t
Current Density Transient Response Power Curve Fit Coefficients
0.40 V Power Curve Fit Coefficient 0.35 V Power Curve Fit Coefficient
40
Figure 3-16, a representative voltage response is shown with the Max OCV, Max OCV rise time
and OCV decay slope identified.
Figure 3-16. Representative fuel cell voltage response from loaded to unloaded operating point.
As shown in Figure 3-17, a clear discrepancy is visible for methanol concentrations from
0.60 M to 1.60 M. Based on a qualitative analysis, the rise time provided the least amount of
resolution for determining methanol concentration. The time to reach max open circuit voltage
varied from three to 10 seconds. However, at higher methanol concentrations (CFeed > 1.0 M), the
difference between rise times was less significant providing less measurement resolution.
The Max OCV provides greater resolution than the MAX OCV rise time especially when
comparing concentrations from 0.80 M to 1.60 M. Unfortunately, the degradation that occurs
within the stack during operation has an intermediate effect on the open circuit voltage.
41
Therefore, it was determined that Max OCV is not ideal for long term methanol concentration
determination. Finally, the OCV decay slope was chosen as a primary candidate for data
analysis. This method for methanol determination provides a distinct variation for the various
methanol concentrations providing great resolution.
Figure 3-17. Fuel cell air starve cycle with 0.60, 0.80 and 1.60 molar concentration at 50 °C.
The fuel cell stack was operated at eight different methanol concentrations in order to
determine a relationship with respect to OCV decay slope. For each concentration that was
tested, the stack was operated at three different temperatures and four different current densities.
The fuel cell stack was operated for ten cycles on an accelerated rest cycle for each configuration
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0
Ce
ll V
olt
age
(V
)
Elapsed Time (s)
DMFC OCV Response with No Air Flow
0.60 M 0.80 M 1.00 M 1.20 M 1.40 M 1.60 M
42
of methanol concentration, temperature and current density. The abbreviated rest cycle is shown
in Figure 3-18, which consists of four distinct sub-cycles.
Figure 3-18. Typical load cycle for DMFC OCV decay slope testing.
The cycle begins with a constant current density step (sub-cycle 1) for two minutes. The
next step following sub-cycle one is the OCV response step (sub-cycle 2) with the oxygen flow
rate set to zero. The duration of this cycle varied based on the methanol concentration from 15 –
90 seconds. The data that was gathered during this sub-cycle was used for all of the data
analysis. During sub-cycle 3, the voltage on the stack is “pulled down” to a low voltage (<0.10
V) for thirty seconds in order to reduce the potential on the cathode. Sub-cycle four is where the
oxygen flow rate is turned back on and the voltage climbs back to open circuit voltage. The OCV
response in sub-cycle four has a different shape compared to the OCV response in sub-cycle 2.
43
The presence of continuously flowing oxygen during sub-cycle four allows for the OCV to
continue climbing while the absence of oxygen flow during sub-cycle two reduces the cell
voltage. Finally the cycle returns back to the beginning at sub-cycle 1. The iteration of this cycle
occurred over one thousand times in order to collect data for the various operating conditions
(temperature, current density, feed methanol concentration).
Results
The variation in OCV response is believed to be driven primarily by the consumption of
oxygen at the cathode. Based on the concentration of methanol at the cathode catalyst layer, the
oxygen will be consumed proportionally and subsequently the cell voltage will decay. However,
if oxygen continues to flow to the cathode, similar to the second OCV sub-cycle, the oxygen will
never be entirely consumed resulting in a less dramatic signal for methanol concentration
determination. Therefore, the first OCV sub-cycle, where the flow of oxygen is brought to zero,
was used for the OCV decay slope analysis.
A strategy was developed in LabVIEW in order to determine the OCV decay slope. For
each OCV response sub-cycle, a linear regression was performed shortly after the peak OCV was
achieved. The linear regression is composed of two coefficients. The “b” coefficient from
Equation 3-2 defines the slope of the line, while the “c” coefficient defines the offset on the y-
axis. The “b” coefficient for any of the linear regressions that were performed will now be
referred to as the OCV decay slope.
3-2
In Figure 3-19, the OCV decay slope for methanol concentrations from 0.60 M to 2.0 M
are shown at a nominal load and operating temperature. The OCV decay slopes have been made
44
positive for enhanced viewing on the logarithmic scale. The error bars display the first standard
deviation based on the ten cycles that were performed for each setpoint.
Figure 3-19. OCV decay slope at 120 mA/cm² at various methanol concentrations with error bars
indicating first standard deviation for the measurements that were conducted for each
cycle.
The OCV decay slope increases at nearly an order of magnitude with every 0.20 M change
in methanol concentration. Although less severe than what was observed for the active load
measurements, as the concentration approaches 1.60 M, the growth in the OCV decay slope
tapers off; the amount of methanol found at the cathode catalyst layer reaches a saturation point,
due primarily to the diffusion properties of methanol through the MEA.
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Ab
solu
te V
alu
e o
f O
CV
De
cay
Slo
pe
(V
/s)
Solution Concentration (M)
OCV Decay Slope at 120 mA/cm² at 50°C
45
Figure 3-20. OCV decay slope at various current densities with 50°C stack temperature.
Figure 3-20 indicates a weak function of OCV decay slope with respect to current density.
With the exception of the discrepancies at 0.80 M, the curves for all current densities follow a
similar trend. One of the key differences between the 40 and 80 mA/cm² current densities
compared to the 120 and 140 mA/cm² current densities at 0.80 M are the max OCV rise times.
As shown in Table 3-1, the OCV rise time for 120 and 140 mA/cm² is an order of magnitude
different when compared to the OCV rise time at 40, 80 mA/cm² and all of the data points
collected at 0.60 M.
Table 3-1. OCV rise time at 0.60 M and 0.80 M.
Current Density (mA/cm²) OCV Rise Time (s)
0.60 M 0.80 M
40 83.7 35.2
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20
OC
V D
eca
y Sl
op
e (
V/s
)
Solution Concentration (M)
OCV Decay Slope at Various Current Densities at 50°C
40 mA/cm² 80 mA/cm² 120 mA/cm² 140 mA/cm²
46
Current Density (mA/cm²) OCV Rise Time (s)
0.60 M 0.80 M
80 78.0 12.4
120 73.4 8.0
140 75.1 7.2
One potential explanation for the divergence in data points is localized flooding at the
cathode. With increasing methanol concentration, the amount of methanol crossover (internal
heating) also increases, therefore increasing the amount of cooling air required by the stack to
maintain constant temperature. In addition, with increasing current density, the cooling
requirements for the stack are also increased. At lower cathode flow rates, the stack is more
prone to flooding [36], resulting in blocked reaction sites at the cathode. Any reduction of
reaction sites would reduce the effective reactivity with oxygen and therefore the consumption
rate of oxygen at the cathode. At the prescribed concentrations and current densities, it is
believed that the DMFC is operating on a knife edge with the two competing effects of cathode
flooding and oxygen consumption.
The curves presented in Figure 3-21 display a similar trend to what has been observed in
Figure 3-19 and Figure 3-20, with the OCV decay slope increasing with methanol concentration.
The stack current density was held constant at 120 mA/cm² while varying the stack temperature
and concentration. A noticeable change in OCV decay slope is visible for varying temperature.
With increasing temperature, the OCV decay slope (diffusion) also increases. This agrees well
with other diffusion experiments that indicate methanol crossover’s high dependency on
temperature [37]. Similar to what was described for Figure 3-19, at higher methanol
concentrations, the diffusion of methanol through the MEA appeared to reach a maximum at
1.80 M irrespective of temperature.
The use of OCV decay slope provides a repeatable, accurate measurement for the
determination of methanol concentration in a DMFC. In addition, this measurement technique
47
can easily be integrated into any existing DMFC system with little system reconfiguration. In
order to reduce on-state degradation, a rest (air starve) is conducted multiple times per hour to
remove any buildup of oxides on the cathode catalyst layer [38]. This would be an ideal time to
determine methanol concentration because generally the stack voltage is allowed to go to OCV
before entering the air starved load condition. However, at reduced temperatures and methanol
concentrations, the OCV decay slope can require as much as 100 seconds to be determined. In
order to implement such a methanol sensing technique, the OCV rise time should not be greater
than 15 seconds for most operating conditions. This time is typical for DMFC OCV rest cycles.
As shown in Figure 3-22, the max OCV rise time falls in an acceptable range for methanol
concentrations 1.0 M and greater. In order to operate with rest cycles less than 15 seconds,
another technique must be used in order to determine the methanol concentration at lower
temperatures or methanol concentrations.
Figure 3-21. OCV Decay slope with constant current density and variable concentration and
temperature.
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20
OC
V D
eca
y Sl
op
e (
V/s
)
Solution Concentration (M)
OCV Decay Slope at 120 mA/cm²
45 °C 50 °C 55 °C
48
Figure 3-22. Max OCV rise time at constant current density with varying temperature and
methanol concentration.
For all previous measurements, the OCV decay slope was the method used to determine
methanol concentration. However, due to the unacceptable rise time for Max OCV at low
temperatures and methanol concentrations, the rise slope OCV was evaluated as an alternative to
measuring OCV decay slope. For the experiment, the maximum OCV rise time was defined at 15
seconds. If the max OCV was not reached within 15 seconds, the OCV rise slope was determined
for the last three seconds of OCV. For each temperature, methanol concentration and current
density configuration, the OCV rise slope was evaluated ten times.
As shown in Figure 3-23, the OCV rise slope at 40 mA/cm² is characterized with a linear
relationship relative to methanol concentration. However, as indicated by the error bars, the first
standard deviation for the sample is considerably higher than the measured OCV decay slopes. In
addition, the point with a solution concentration of 1.0 M and a stack temperature of 45°C
0
10
20
30
40
50
60
70
80
90
100
110
120
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Max
OC
V R
ise
Tim
e (
s)
Solution Concentration (M)
Max OCV Rise Time at 80 mA/cm²
45°C 50°C 55°C
49
exceeds an order of magnitude of the linear trend that is established by the existing points. As
previously discussed, these anomalies could very well be caused by the fuel cell stack operating
on a knife edge. At this condition, the stack could potentially be experiencing flooding, which
would affect OCV response.
Figure 3-23. OCV Rise Slope held at constant current density (40 mA/cm²) with variable
concentration and stack temperature with error bars indicating single standard
deviation.
The OCV rise slope at a current density of 40 mA/cm² provides much uncertainty in
methanol concentration determination. At a current density of 120 mA/cm², the uncertainty in
methanol concentration determination increased with a weaker correlation between methanol
concentration and OCV rise slope. The combination of weak correlation, with respect to
methanol concentration and high uncertainty, make the OCV rise slope an unsatisfactory method
for determining methanol concentration.
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
0.5 0.6 0.7 0.8 0.9 1.0 1.1
OC
V R
ise
Slo
pe
(V
/s)
Solution Concentration (M)
OCV Rise Slope at 40 mA/cm²
45°C 40°C 35°C
50
Figure 3-24. OCV Rise Slope held at constant current density (120 mA/cm²) with variable
concentration and stack temperature with error bars indicating single standard
deviation.
The failure of the OCV decay slope to provide reliable measurements for methanol
concentration determination leaves only a few methods for improving OCV decay slope response
time. One possibility is to operate the fuel cell stack at an elevated temperature just before rest.
Operation at an elevated temperature (55-60°C) can significantly shorten the max OCV rise time
to durations that would be acceptable for methanol concentration determination in a DMFC
system.
Another method for improving the max OCV rise time is to operate at an elevated
methanol concentration. At an elevated methanol concentration (CFeed > 1.0 M), the ratio of
methanol to oxygen at the cathode catalyst layer would exist at a considerably higher level than
for 0.60 M or 0.8 M. As previous data suggests, the OCV rise time would be significantly less.
However, with an increase in methanol concentration, the stack would operate at a less efficient
point resulting in less net power and poor fuel utilization.
0.0E+00
1.0E-03
2.0E-03
3.0E-03
4.0E-03
5.0E-03
6.0E-03
0.5 0.6 0.7 0.8 0.9 1.0 1.1
OC
V R
ise
Slo
pe
(V
/s)
Solution Concentration (M)
OCV Rise Slope at 120 mA/cm²
45°C 40°C 35°C
51
The last method for improving the max OCV rise time at reduced concentrations and
temperatures would involve the modification of the MEA. The supporting theory for long
duration max OCV rise times is the lack of oxygen consumption at the cathode catalyst due to
poor diffusion and flooding. A single MEA on the stack could be optimized for oxygen transport,
methanol crossover and reduced flooding effects. This would promote the consumption of
oxygen at the cathode catalyst layer with reduced max OCV rise times.
52
CHAPTER 4
VERIFICATION MODEL
A basic 1-D transient model was created in order to gain a better understanding of the
diffusion phenomena and transients measured with the fuel cell test station. The direct methanol
fuel cell has many side reactions and transport dependencies that take place within the MEA,
therefore many of the complex, secondary factors (membrane swelling, two phase flow, electro
osmotic drag, catalyst loading, etc.) that contribute to DMFC performance have been neglected
in order to simplify the model. The formulation of the model and all supporting boundary
conditions and assumptions are outlined in Appendix A.
The formulas that have been compiled to solve the 1-D non-homogeneous transient model
were entered into MATLAB. This model enabled the prediction of methanol and oxygen
concentration transient behavior through the MEA. The MATLAB code for the model can be
found in Appendix B.
Methanol Concentration Distribution
Steady State Concentration Distribution
The model was initially assessed in a steady state configuration. As shown in Figure 4-1,
the model was tested at a fuel cell current density of 150 mA/cm² with a feed concentration of
0.80 M. The model reveals a non-linear methanol concentration gradient across the anode
catalyst layer. The non-linear portion is a result of the methanol that is consumed for electrical
power production by the fuel cell at 150 mA/cm². At the cathode catalyst layer, the methanol
concentration approaches zero. The methanol crossover can be calculated based on the methanol
concentration gradient across the cathode catalyst layer or membrane layer.
In Figure 4-2, the model was executed for various feed concentration at 150 mA/cm². For a
feed concentration of 0.40 or lower, the methanol concentration at the anode catalyst layer is
53
below 0, which would result in a fuel starvation condition due to insufficient methanol. If the
effects of relatively low stoichiometric ratios were taken into account, a fuel starvation condition
would be realized at the end of the cell due to reduced feed methanol concentration relative to
the beginning of the cell. The variation of methanol concentration at the entrance of the cathode
catalyst layer is an indication of the variation in methanol crossover for various concentrations.
The methanol crossover for each methanol concentration is summarized in Table 4-1.
Figure 4-1. Results from model for MEA methanol concentration distribution for 0.80 M feed
concentration at a current density of 150 mA/cm².
Figure 4-2. Results from model for MEA methanol concentration distribution for various feed
concentrations at a current density of 150 mA/cm².
0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
MEA Position (cm)
Meth
an
ol C
on
cen
trati
on
(M
)
MEA Methanol Concentration Distribution for 0.80 M Feed Concentration at 150 mA/cm²
0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
MEA Position (cm)
Meth
an
ol C
on
cen
trati
on
(M
)
MEA Methanol Concentration Distribution for Various Feed Concentrations at 150 mA/cm²
0.40 M
0.60 M
0.80 M
1.00 M
1.20 M
1.40 M
1.60 M
Anode Diffusion Layer
Anode Catalyst Layer
Membrane Layer
Cathode Catalyst Layer
54
Table 4-1. Summary of methanol crossover results from model for various feed methanol
concentrations with a current density of 150 mA/cm². Feed Concentration (M) Crossover Current Density (mA/cm²)
0.6 8.2
0.8 20.1
1.0 32.0
1.2 43.9
1.4 55.8
1.6 67.7
Transient Concentration Distribution
The next set of test conditions that were executed using the model evaluated the transient
response of the methanol concentration distribution. The model was used to determine the
methanol concentration response with a load profile where the load is instantly removed. As
shown in Figure 4-3, the methanol concentration distribution requires approximately 75 seconds
to reach equilibrium. At the cathode catalyst layer, the non-linear concentration gradient is
evident when the load is still engaged at t = 0 s. Once the load is removed (t > 0), the methanol
concentration quickly increases and a linear concentration gradient is visible.
Figure 4-3. Results from model for MEA transient concentration distribution from a current
density of 120 mA/cm² to 0 mA/cm² at a feed concentration of 0.80 M.
The transient methanol concentration distribution for relatively high feed methanol
concentrations is shown in Figure 4-4. For a feed methanol concentration of 1.60 M, the
0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
MEA Position (cm)
Meth
an
ol C
on
cen
trati
on
(M
)
MEA Methanol Concentration Distribution from 120 mA/cm² to 0 mA/cm² at 0.80 M
0.0 s (120 mA/cm²)
15.0 s (0 mA/cm²)
30.0 s (0 mA/cm²)
45.0 s (0 mA/cm²)
60.0 s (0 mA/cm²)
75.0 s (0 mA/cm²)
55
methanol consumption for electrical power production is less significant. Therefore, the
methanol concentration at the cathode catalyst is similar to that for the unloaded points and is
relatively high.
Figure 4-4. Results from model for MEA transient concentration distribution from a current
density of 120 mA/cm² to 0 mA/cm² at a feed concentration of 1.60 M.
The response of the methanol concentration at the cathode catalyst layers are shown in
Figure 4-5. For each feed concentration, the response is similar in shape however the magnitude
of the concentration is more than double for a feed concentration of 1.6 compared to 0.80 M.
Figure 4-5. Model results for transient methanol concentration response at cathode catalyst layer
from a current density of 120 mA/cm² to 0 mA/cm².
0 0.005 0.01 0.015 0.02 0.025 0.03 0.0350
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
MEA Position (cm)
Meth
an
ol C
on
cen
trati
on
(M
)
MEA Methanol Concentration Distribution from 120 mA/cm² to 0 mA/cm² at 1.60 M
0.0 s (120 mA/cm²)
15.0 s (0 mA/cm²)
30.0 s (0 mA/cm²)
45.0 s (0 mA/cm²)
60.0 s (0 mA/cm²)
75.0 s (0 mA/cm²)
0
0.02
0.04
0.06
0.08
0.1
0.12
0 10 20 30 40 50 60 70 80
Me
than
ol C
on
cen
trat
ion
(M
)
Elapsed Time (s)
Transient Methanol Concentration Response at the Cathode Catalyst Layer from 120 mA/cm² to 0 mA/cm²
0.80 M 1.60 M
56
Transient Oxygen Concentration Distribution
Due to the relatively slow response of the methanol concentration distribution, the effect of
the transient methanol concentration distribution alone is not a viable means for methanol
concentration determination. However, if the flow of cathode air is removed from the fuel cell,
the oxygen on the cathode would quickly be consumed due to the methanol crossover. Using the
methanol crossover model that has been developed, a basic oxygen consumption model was
established in order to determine if the transient response of the cathode would provide a more
rapid response. Based on the methanol concentration response and the diffusion coefficient at the
cathode catalyst layer, the transient diffusion of methanol (methanol crossover) can be
calculated. Assuming that for each mole of methanol that is consumed at the cathode catalyst
layer, 1.5 moles of oxygen is consumed; the mean oxygen content at the cathode can be
calculated.
Even though an active air source is not present, the oxygen that is consumed at the cathode
can be replenished by means of natural convection or diffusion, due to the open cathode design
of the modeled fuel cell. A basic linear model was used to accommodate for the oxygen that is
replenished based on open cathode passive fuel cells. In addition to the replenished oxygen, the
amount of oxygen stored in the cathode flow channels was also taken into account. As shown in
Figure 4-6, the oxygen that is consumed at the cathode catalyst layer due to methanol crossover
occurs relatively fast. With increasing methanol concentration, the consumption rate of oxygen
on the cathode increases, resulting in shorter durations of high oxygen content. However, the
timescales for oxygen consumption for an open cathode are long compared to a closed cathode
where replenished oxygen would not be available. In order to emphasize the transient oxygen
concentration response for all methanol concentrations, a logarithmic time scale was used on the
x-axis.
57
Figure 4-6. Model results for the mean transient oxygen content in the cathode.
The cathode potential on a DMFC is strongly dependent on the concentration of oxygen at
the cathode [36]. The higher the partial pressure of oxygen at the cathode, the higher the cathode
potential. Therefore with a transient response in the concentration of oxygen at the cathode, the
voltage of the DMFC will also experience a dramatic transient.
Modeling Summary
Data provided by the model suggests that the dynamic behavior of the methanol
concentration distribution is not rapid enough for practical use in a DMFC as a sensor-less
measurement technique. Therefore, the air flow was removed from the cathode in the model in
order to accelerate the effects of methanol on the DMFC performance. The data from the
transient 1-D model agrees with the data that was collected experimentally and highlights the
importance of the removal of an active oxygen supply at the cathode. Furthermore, the model
showed that the feed methanol concentration has a greater influence on the anode methanol
concentration distribution than the operating current density.
0.0%
5.0%
10.0%
15.0%
20.0%
25.0%
0.1 1 10 100
Oxy
gen
Co
nce
ntr
atio
n
Elapsed Time (s)
Transient Mean Cathode Oxygen Concentration
1.6 M 1.4 M 1.2 M 1.0 M 0.8 M 0.6 M 0.4 M
58
CHAPTER 5
SYSTEM INTEGRATION
The University of North Florida has the capability to operate an unpackaged DMFC
system in a brassboard configuration. The brassboard platform shown in Figure 5-1 enables
maximum flexibility for in-situ testing of components and system control strategies. The OCV
decay slope method was implemented into the brassboard system in order to determine methanol
concentration during operation. The DP4 (demonstration prototype 4) brassboard was designed
to operate on ten minute rest cycles. Assuming the methanol concentration can be determined
during each rest cycle, the methanol concentration must be determined during non-rest operation.
Figure 5-1. UNF 20 W DP4 brassboard fuel cell system.
Methanol Concentration Tracking
Methanol Consumption Model
As highlighted in Figure 5-2, the methanol consumed by the stack to produce electrical
current and the methanol consumed at the cathode catalyst due to methanol crossover are the two
major contributors to methanol consumption in the DP4 system. The minor sources of methanol
consumption include leakage through the CO2 gas liquid separator and the solution storage tank.
59
However, these sources of methanol consumption are negligible relative to the rates of methanol
consumption due to crossover and power production.
A
N
O
D
E
M
E
M
B
R
A
N
E
C
A
T
H
O
D
E
Figure 5-2. Simplified methanol consumption and injection model for DP4.
Faradaic oxidation
The calculation of methanol consumption due to electrical current is a straightforward
calculation based on the anode half reaction. Equation 5-1 states that for every six moles of
electrons that are used, one mole of methanol is consumed. Using Faraday’s constant, the
conversion from amperes to moles of electrons can be made. Using these two factors, the final
conversion from amperes to methanol consumption equals 1.73E-6 Moles of
CH3OH/(s·Ampere·cell).
5-1
M
E
T
H
A
N
O
L
C
R
O
S
S
O
V
E
R
CH3OH
60
Methanol crossover
The methanol consumption due to methanol crossover was calculated based on the amount
of CO2 that was measured on the cathode exhaust using a CO2 analyzer. Carbon dioxide is a
product of the methanol that crosses over to the cathode catalyst and the oxygen that is delivered
to the cathode for the fuel cell reaction. For every mole of methanol that is oxidized at the
cathode catalyst, one mole of CO2 is released into the cathode stream. The methanol
consumption is converted to an equivalent crossover current density in order to simplify
comparison to the stack current density.
Figure 5-3. Representative methanol crossover current density for DP4 stack at various stack
temperatures, methanol concentrations and current densities.
15.0
25.0
35.0
45.0
55.0
65.0
75.0
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
Stac
k C
urr
en
t D
en
sity
(m
A/c
m²)
Crossover Current Density (mA/cm²)
Methanol Crossover at Various Stack Temperature, Concentration and Current Densities
0.8 M at 45 °C 1.0 M at 45 °C 1.5 M at 45 °C 0.8 M at 50 °C 1.0 M at 50 °C
1.5 M at 50 °C 0.8 M at 55 °C 1.0 M at 55 °C 1.5 M at 55 °C
61
Methanol crossover is primarily a function of current density, temperature and methanol
concentration. Therefore, these parameters were varied in order to determine the methanol
crossover for the fuel cell stack. The crossover current measurements in Figure 5-3 exhibit a
strong linear function with respect to stack current density. As the stack current density
approaches 0 mA/cm² (OCV), the availability of methanol at the cathode catalyst reaches a
maximum resulting in a maximum of crossover current density. With increased temperature, the
diffusion coefficient for methanol across the MEA also increases resulting in higher methanol
levels at the cathode catalyst layer. The last variable that was tested in order to determine the
amount of methanol crossover rates in the MEA was the sensitivity to methanol concentration.
With increasing methanol concentrations at the anode, the available methanol at the cathode
catalyst would only increase, resulting in a higher methanol crossover rate. The values from
Figure 5-3 were compiled in a 2-D matrix where they could be used in a lookup table.
Methanol Injection Model
In order to accurately track the methanol concentration within the brassboard, the amount
of methanol that is injected into the anode stream must be accounted for in addition to the
methanol that is consumed. Methanol is injected into the brassboard using a single piezoelectric
pump controlled by pulse width modulation (PWM). The pump was characterized at several duty
cycles using a mass balance. As shown in Figure 5-4, the pump has a strong linear relationship
with respect to PWM duty cycle.
During preliminary testing, the accuracy of the methanol injection pump appeared to vary
based on the fuel reservoir level. The fuel reservoir where the methanol is stored is a 500 mL
container. The difference in pressure head for when the fuel reservoir is full, compared to when it
is empty, can be as much as six inches of methanol. In order to more accurately predict the
amount of methanol injected into the system, the pump was characterized at two additional fuel
62
levels. As shown in Figure 5-5, the pump is strongly affected by the pressure head that is applied
to the inlet.
Figure 5-4. Performance Curve for Single µBase Pump
Figure 5-5. Comparison of µBase Pump Performance versus various inlet pressures.
0.0
0.2
0.4
0.6
0.8
0 5 10 15 20 25 30 35 40 45 50
Me
than
ol I
nje
ctio
n P
um
p F
low
Rat
e
(mL/
min
)
Pump Duty Cycle (%)
µBase Pump Performance
0.0
0.2
0.4
0.6
0.8
0 5 10 15 20 25 30 35 40 45 50
Me
than
ol I
nje
ctio
n P
um
p F
low
Rat
e
(mL/
min
)
Pump Duty Cycle (%)
µBase Pump Performance vs. Inlet Pressures
No Inlet Head 4" of Negative Inlet Head
63
Methanol Concentration Determination
The empirical data that was collected for methanol crossover and the methanol injection
pump were used in conjunction with the methanol consumption model based on electrical current
in order to determine a net mass balance of methanol for the system. To determine the methanol
concentration within the system, an accurate model must be used to determine both the quantity
of methanol and water in the system.
The anode solution reservoir tank for the system features a tank level sensor that utilizes
twelve points of conduction in order to determine the amount of solution in the reservoir tank. In
addition to the reservoir tank, anode solution is stored in the fuel cell stack, gas liquid separator,
methanol sensor and the silicone lines that are used to connect each of the components. The fuel
cell stack generates CO2 gas in the anode stream during power production, therefore the
displacement of gas in the components must be taken into consideration in order to accurately
account for the solution volume in the system.
Based on the liquid inventory , the previous methanol concentration ( , the methanol
consumption due to electrical current ( ̇ and methanol crossover ( ̇ , the methanol injected
by the feed pump ( ̇ , the molar mass of methanol and the amount of time
between the concentration measurements, the new calculated methanol concentration can
be calculated.
( ̇ ̇ ̇ )
5-2
Brassboard Operation
The results shown in Figure 5-6 are operation data from the brassboard using the sensor-
less OCV decay slope methanol sensing technique. The system was able to maintain a constant
methanol concentration without methanol excursions greater than 0.15 M for greater than
64
eighteen hours. This data suggests that sensor-less methanol sensing techniques are a feasible
method for continuous, reliable DMFC operation.
Figure 5-6. UNF DP4 brassboard operation using sensor-less methanol sensing techniques.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 2 4 6 8 10 12 14 16 18 20
Me
than
ol C
on
cen
trat
ion
(M
)
Elapsed Time (Hrs)
Actual Concentration (M) Sensorless Concentration (M)
65
CHAPTER 6
CONCLUSIONS
A new method for determining methanol concentration in a direct methanol fuel cell
(DMFC) system was evaluated at the University of North Florida Fuel Cell Laboratory. In this
study, a multilevel approach was used to move from concept to implementation. Initially, a
literature review revealed the sensitivity of DMFC transient open circuit voltage (OCV) response
with respect to methanol concentration.
Initial testing was performed to evaluate various parameters of the DMFC transient OCV
and their sensitivity to feed methanol concentration. Preliminary testing revealed that the OCV
decay slope offered the greatest resolution for methanol concentrations from 0.60 M to 1.60 M.
All future testing used OCV decay slope as a metric for methanol concentration determination.
The OCV decay slope was mapped for eight different concentrations, four different current
densities and three different operating temperatures, resulting in 96 unique operating points. For
each operating point, the DMFC was cycled 10 times in approximately three minute cycles. The
testing revealed a high resolution and repeatability in the OCV decay slope for methanol
concentrations ranging from 0.60 M to 2.00 M. For each change in methanol concentration of
0.20 M, the OCV decay slope changed by nearly one order of magnitude, while the first standard
deviation of the sample set remained relatively low, with less than 5% measurement error.
The sensitivity of OCV decay slope with respect to current density was quite low with the
exception of the points at reduced current densities and methanol concentrations. It is believed
that the irregularity in the OCV decay response is a result of localized flooding in the cathode. At
lower current densities and feed methanol concentrations, the amount of cathode cooling air that
is required to maintain the same operating temperature is less, therefore increasing the likelihood
of localized flooding at the cathode.
66
The sensitivity of OCV decay slope with respect to operating temperature was much higher
when compared to the sensitivity to current density. With increasing temperature, the OCV
decay slope also increased due to the higher level of diffusion.
The use of OCV decay slope provides a repeatable, accurate measurement for the
determination of methanol concentration in a DMFC. However, the acquisition time for OCV
decay slope can be as much as 90 seconds for low methanol concentrations (CFeed < 0.80 M) at
reduced operating temperatures (T < 50°C). The OCV rise slope was used as an alternative
measurement technique to reduce the acquisition time for operation at low methanol
concentrations with reduced stack temperatures. Unfortunately, there was a very weak
correlation between methanol concentration and OCV rise slope with very poor repeatability.
Other techniques were recommended, however they were not tested. They included changing the
DMFC operating profile to higher methanol concentrations and/or temperature during sensor-less
methanol detection, or optimization of the MEA cathode for OCV decay measurements.
A simplified 1-D transient model was developed to approximate the transient methanol
concentration distribution and verify the findings that were observed in previous experiments.
The initial model revealed a sluggish response time for the methanol concentration distribution
in the MEA. In order to better capture the phenomena that were occurring with respect to
methanol concentration, the computer model was modified to account for an open cathode with
the active air supply removed. The lack of an active air supply accelerated the depletion of
oxygen on the cathode due to methanol crossover resulting in timescales that were compliant
with the DMFC open circuit voltage response times measured. These results agreed well with the
measured data.
67
The final level of testing was implementation of the sensor-less OCV decay technique into
a 20 W DMFC brassboard system. Integration of OCV decay measurements into a DMFC
system is trivial. During operation, the DMFC must undergo a periodic rest to remove the oxides
that have accumulated on the cathode catalyst. This is achieved by removing the active air supply
from the cathode and pulling the voltage down on the DMFC. The OCV decay measurement is
in essence a free signal that can be gathered during an essential part of the DMFC’s operation
profile. The only drawback to this measurement strategy is the frequency that the DMFC enters a
rest period. Typically the time period between rest cycles is 10-20 minutes, therefore the
methanol concentration must be tracked between rests.
Methanol is consumed by the fuel cell stack through electrical power production and
methanol crossover. The methanol that is consumed for electrical power production can be
calculated based on the DMFC anode half reaction while the methanol that is consumed through
methanol crossover was measured at various methanol concentrations, temperatures and current
densities in order to develop an empirical model to predict methanol concentration. In addition to
the methanol that is consumed, a model was also developed to predict the amount of methanol
that is injected into the system via the methanol injection pump. One last model was created to
monitor the amount of solution within the system. By determining the net methanol intake for the
DMFC system and the level of anode solution, the methanol concentration can be tracked with
reasonable accuracy. The combination of the transient OCV decay measurement technique and
the methanol consumption model enabled the 20 W DMFC brassboard to successfully operate
without a methanol sensor for over 18 hours with methanol concentration excursions less than
0.15 M. Integration of this sensor-less methanol sensing technique will significantly reduce
system cost, weight and complexity accelerating the movement of DMFC technology.
68
APPENDIX A
DIFFUSION MODEL DEVELOPMENT
Figure A-1. Ideal methanol concentration distribution at various load conditions.
The MEA is typically composed of five distinct layers. The anode electrode is
characterized with a diffusion and catalyst layer. At the diffusion layer, the methanol-water
solution diffuses in the direction of the membrane, while the CO2 gas generated by the anode
reaction exits in the opposite direction. The catalyst layer at the anode is where the majority of
the methanol is consumed [20]. However, some methanol continues to migrate across the
membrane to the cathode catalyst layer. In an oxygen and catalyst rich environment, the
methanol is quickly consumed at the cathode catalyst layer [39]. Due to the assumption of
complete methanol oxidation at the cathode catalyst layer, the effects of the cathode diffusion
layer were neglected. In addition, due to the limitations of the simplified 1-D model, the effects
due to stoichiometric ratios between methanol consumption rates and methanol feed rate are
neglected.
The following assumptions were used to create the unsteady diffusion model:
1. Uniform material and reactant properties.
2. Negligible diffusion contact resistance.
z-axis
Met
han
ol c
on
cen
trat
ion
69
3. Consumption of methanol at the anode catalyst layer based purely on
electrochemical conversion.
4. Complete consumption of methanol at the cathode catalyst layer regardless of
concentration.
5. Concentration at the beginning (z = 0) of the anode diffusion layer is equal to the
feed methanol concentration.
6. Methanol concentration at the interface between the anode diffusion and catalyst
layers (z = zAD) is equal.
7. Diffusion of methanol at the interface between the anode diffusion and anode
catalyst layers (z = zAD) is equal.
8. Methanol concentration at the interface between the anode catalyst and membrane
layers (z = zAC) is equal.
9. Diffusion of methanol at the interface between the anode catalyst and membrane
layers (z = zAC) is equal.
10. Methanol concentration at the interface between the membrane and cathode catalyst
layers (z = zM) is equal.
11. Diffusion of methanol at the interface between the membrane and cathode catalyst
layers (z = zM) is equal.
12. Methanol concentration at the end of the cathode catalyst layer (z = zCC) is zero.
13. Negligible effects from cathode diffusion layer.
The foundation of any diffusion model starts with Fick’s First Law of Diffusion. The
concentration flux (J) is equal to the diffusion coefficient (D) times the concentration gradient,
.
A-1
In addition to Fick’s First Law of Diffusion, Fick’s Second Law of Diffusion provides a
means for solving unsteady diffusion problems.
A-2
At the anode and cathode catalyst layers, methanol is consumed through an oxidation
reaction. At the anode catalyst layer, the methanol is electrochemically consumed based on the
amount of electrical current that is generated by the fuel cell. At the cathode catalyst layer, the
crossover methanol from the anode and the oxygen from the cathode are readily consumed in the
catalyst enriched environment.
70
A-3
The reaction term “r”, which accounts for the methanol that is consumed
electrochemically, was added to Fick’s Second Law resulting in a second order, non-
homogeneous, linear, partial differential equation. In order to simultaneously solve for the
methanol concentration distribution across all four layers, the method of separation of variables
and the orthogonal expansion technique were used. For each layer, the differential equations
were divided into a homogeneous and non-homogeneous set of equations as shown in Equation
A-4. Equations A-7 through A-53 summarize the mass balance, boundary and initial condition
equations.
A-4
The model that is presented is an attempt to simulate the methanol concentration
distribution for varying fuel cell load levels. The simplified, ideal, 1-D model is used primarily
for data verification and phenomena understanding. The model assumes that the fuel cell has
been instantaneously loaded from an initial condition with a current density io to a final load
condition with a current density of if.
Initial Conditions
Initial Condition 1
The methanol concentration in all of the MEA layers at t=0 is equal to the steady state
methanol concentration at the initial current density (io), solution feed concentration and
temperature. The steady state equation is only a function of space, methanol feed concentration,
temperature and current density. Therefore the homogenous equation inherits the entire portion
of the initial condition.
71
A-5
A-6
Anode Diffusion Layer (0 ≤ z ≤ zAD)
The anode diffusion layer is where the feed methanol solution enters. No reaction is
present, therefore at steady state, a linear concentration gradient occurs across the diffusion layer.
For the anode diffusion layer, the formation of the homogeneous and non-homogeneous
equations are summarized in equations A-7 through A-10.
Mass Balance Equations
A-7
A-8
A-9
A-10
The equations that apply to the boundary condition at the interface at the beginning of the
anode diffusion layer are shown in equations A-11 through A-14.
Boundary Conditions
Boundary condition 1
The methanol concentration at the anode diffusion layer inlet is equal to the feed methanol
concentration. The boundary condition for the homogeneous set of equations is equal to zero.
A-11
72
A-12
A-13
A-14
Anode Catalyst Layer (zAD ≤ z ≤ zAC)
The anode catalyst layer is where the majority of the methanol in the fuel cell is consumed.
The amount of methanol that is consumed at the anode catalyst layer (rAC) is based entirely on
the amount of electrical current that the fuel cell is producing. The mass balance equation for this
region is defined in equations A-15 through A-18. A non-linear distribution can be expected at
the anode catalyst layer at steady state due to the methanol that is consumed at the anode catalyst
layer.
Mass Balance Equations
A-15
A-16
A-17
A-18
Steady State Boundary Equations
The boundary condition for the interface between the anode diffusion layer and the anode
catalyst layer are defined in Equations A-19 through A-26.
73
Boundary condition 2
The methanol concentration at the anode diffusion layer exit is equal to the methanol
concentration at the inlet of the anode catalyst layer.
A-19
A-20
A-21
A-22
Boundary condition 3
The methanol concentration flux at the exit of the anode diffusion layer is equal to the
methanol flux at the inlet anode catalyst layer.
|
|
A-23
|
|
|
|
A-24
|
|
A-25
|
|
A-26
Membrane Layer (zAC ≤ z ≤ zM)
The membrane layer is what separates the anode and cathode reactions. However,
crossover methanol migrates across this layer and subsequent layers. It is assumed that the
74
consumption of methanol at the membrane is zero, therefore a linear methanol concentration
gradient can be expected after steady state is reached.
Mass Balance Equations
A-27
A-28
A-29
A-30
Boundary Equations
The boundary condition for the interface between the anode catalyst layer and the
membrane layer are defined in Equations A-31 through A-38.
Boundary condition 4
The methanol concentration at the exit of the anode catalyst layer is equal to the methanol
concentration at the inlet of the membrane.
A-31
A-32
A-33
A-34
75
Boundary condition 5
The methanol concentration flux at the exit of the anode catalyst layer is equal to the
methanol flux at the inlet of the membrane.
|
|
A-35
|
|
|
|
A-36
|
|
A-37
|
|
A-38
Cathode Catalyst Layer (zM ≤ z ≤ zCC)
The cathode catalyst layer is not the final layer found in a typical MEA, however it has
been assumed that due to the presence of the cathode catalyst, the methanol is entirely oxidized
with the oxygen from the cathode. The consumption of the methanol in the cathode catalyst layer
is defined by rcc, where the rate of methanol consumption is heavily dependent upon the local
concentration at the cathode catalyst layer. The resulting steady state distribution of methanol
concentration is non-linear.
Mass Balance Equations
A-39
76
A-40
A-41
A-42
Boundary Equations
The boundary conditions six and seven are defined at the interface between the membrane
and cathode catalyst layers, while boundary equation eight defines the condition at the exit of the
cathode catalyst layer.
Boundary condition 6
The concentration at the exit of the membrane layer is equal to the inlet at the cathode
catalyst layer.
A-43
A-44
A-45
A-46
Boundary condition 7
The concentration flux at the exit of the membrane is equal to the inlet at the cathode
catalyst layer.
|
|
A-47
77
|
|
|
|
A-48
|
|
A-49
|
|
A-50
Boundary condition 8
The concentration of methanol at the exit of the cathode catalyst layer is equal to zero.
A-51
A-52
A-53
Homogenous Equations
The boundary conditions and the differential equations for the steady state and
homogeneous portions have been defined. The homogenous equations were solved using the
orthogonal expansion technique. The general solution for each layer is defined in Equations A-54
through A-57 where βn is the eigen-function and the coefficients A and B for each equation
represent constants.
(
√
) (
√
) A-54
78
(
√
) (
√
) A-55
(
√
) (
√
) A-56
(
√
) (
√
) A-57
In order to solve for the eight unknowns, eight equations were defined using the boundary
equations. The eight boundary conditions are defined in general solution form in Equations A-58
through A-65.
Boundary condition 1
(
√
) (
√
) A-58
Boundary condition 2
(
√
) (
√
) (
√
) A-59
Boundary condition 3
√ (
√
)
√ (
√
) √ (
√
)
A-60
79
Boundary condition 4
(
√
) (
√
) (
√
)
(
√
)
A-61
Boundary condition 5
√ (
√
) √ (
√
)
√ (
√
) √ (
√
)
A-62
Boundary condition 6
(
√
) (
√
) (
√
) (
√
) A-63
Boundary condition 7
√ (
√
) √ (
√
)
√ (
√
) √ (
√
)
A-64
Boundary condition 8
(
√
) (
√
) A-65
Boundary condition equations one through eight are defined in matrix form under Table A-
1. In order to avoid a trivial solution, the matrix from Table A-1 was modified assuming AAD is
equal to unity resulting in Table A-2.
80
Table A-1. Matrix form of boundary equations for homogeneous equations. (
√
) (
√
) (
√
) 0 0 0 0 0
√ (
√
) √ (
√
) √ (
√
) 0 0 0 0 0
0 (
√
) (
√
) (
√
) (
√
) 0 0 0
0 √ (
√
) √ (
√
) √ (
√
) √ (
√
) 0 0 X = 0
0 0 0 (
√
) (
√
) (
√
) (
√
) 0
0 0 0 √ (
√
) √ (
√
) √ (
√
) √ (
√
) 0
0 0 0 0 0 (
√
) (
√
) 0
Table A-2. Modified matrix of homogenous set of boundary equations. (
√
) (
√
) (
√
) 0 0 0 0 0
√ (
√
) √ (
√
) √ (
√
) 0 0 0 0 0
0 (
√
) (
√
) (
√
) (
√
) 0 0 0
0 √ (
√
) √ (
√
) √ (
√
) √ (
√
) 0 0 X = 0
0 0 0 (
√
) (
√
) (
√
) (
√
) 0
0 0 0 √ (
√
) √ (
√
) √ (
√
) √ (
√
) 0
0 0 0 0 0 (
√
) (
√
) 0
The resulting system of equations is shown in Table A-3. The unique solution for each
system of equations was solved for the first thirty eigenvalues.
Table A-3. System of equations for homogeneous set of boundary conditions. (
√
) (
√
) 0 0 0 0 (
√
)
√ (
√
) √ (
√
) 0 0 0 0 √ (
√
)
(
√
) (
√
) (
√
) (
√
) 0 0
X
=
0
√ (
√
) √ (
√
) √ (
√
) √ (
√
) 0 0 0
0 0 (
√
) (
√
) (
√
) (
√
) 0
0 0 √ (
√
) √ (
√
) √ (
√
) √ (
√
) 0
Steady State Equations
Previously, the homogeneous equations were solved using the orthogonal expansion
technique. The other half of the overall solution is characterized with non-homogeneous
boundary conditions. These steady state equations were solved using the differential
relationships defined by Equations A-7 through A-53. The equations labeled A-66 through A-69
81
are characterized with eight unknowns. Therefore eight equations were defined using the
boundary conditions.
A-66
A-67
A-68
√
√
A-69
The boundary equations for the steady state, non-homogeneous conditions are listed as
Equations A-70 through A-84.
Boundary condition 1
A-70
Boundary condition 2
A-71
A-72
Boundary condition 3
A-73
A-74
Boundary condition 4
A-75
82
A-76
Boundary condition 5
A-77
A-78
Boundary condition 6
√
√
A-79
√
√
A-80
Boundary condition 7
√
√
√
√
A-81
√
√
√
√
A-82
Boundary condition 8
A-83
√
√
A-84
In order to facilitate calculations using MATLAB software, the boundary equations were
formatted into a matrix as shown in Table A-4.
83
Table A-4. Boundary conditions for steady state, non-homogeneous boundary conditions.
0 1 0 0 0 0 0 0
1 -1
0 0 0 0
0 0 0 0 0 0
0 0 1 -1
0 0 x
=
0 0 0 0 0 0
0 0 0 0 1 √
√
0 0 0 0 0 √
√
√
√
0 0 0 0 0 0 √
√
84
APPENDIX B
DIFFUSION MODEL MATLAB CODE
clear
T=50; %Cell Temperature (°C) C_FEED = 0.4; %Feed methanol concentration (Moles/Liter) i_o = 120; %Initial Current Density (mA/cm²) i_f = 0; %Final Current Density (mA/cm²)
T=T+273.15; %Convert from ºC to K. C_FEED=C_FEED/1000; %Convert from Moles/Liter to Moles/cm³
Beta_n_precision= 10; %Number of decimal places to apply to eigenvalues (14
is the max). n_max = 30; %Max number of n iterations for the summation of orthogonal
functions. t_max = 75; %The number of seconds to evaluate the function for. (s) t_d = 6; %The number of divisions for the time space specified by t_max. z_d =200; %The number of z divisions for the thickness of the MEA.
D_AD = 1.1175e-005; %Anode Diffusion Layer Diffusion Coefficient (cm²/s) t_AD = 0.015; %Anode Diffusion Layer Thickness (cm)
D_AC = 2.8*10^-5*exp(2436*(1/353-1/T)); %Anode Catalyst Layer Diffusion
Coefficient (cm²/s) t_AC = 0.0023; %Anode Catalyst Layer Thickness (cm) r_AC_o = i_o/1000/96485/6/t_AC; %Anode Catalyst Layer Reaction Coefficient
before load change. [Moles of methanol/(cm³*s), where i is the current
density in mA/cm²] r_AC_f = i_f/1000/96485/6/t_AC; %Anode Catalyst Layer Reaction Coefficient
after load change. [Moles of methanol/(cm³*s), where i is the current density
in mA/cm²]
D_M = (4.9*10^-6*exp(2436*(1/333-1/T))); %Membrane Layer Diffusion
Coefficient (cm²/s) "Determination of methanol diffusion and electro-
osmotic drag coefficients in proton-exchange-membranes for DMFC" t_M = 0.018; %Membrane Layer Thickness (cm) [Alex's Model]
D_CC = 2.8*10^-5*exp(2436*(1/353-1/T)); %Cathode Catalyst Layer Diffusion
Coefficient (cm²/s) t_CC = 0.0023; %Cathode Catalyst Layer Thickness (cm) [Alex's Model] r_CC = 70/1000/96485/6/t_CC; %Cathode Catalyst Layer Reaction Coefficient
z_AD = t_AD; %Distance in the z-direction to end of the anode diffusion layer
starting from the anode side. (cm) z_AC = t_AD+t_AC; %Distance in the z-direction to to end of the anode
catalyst layer starting from the the anode side. (cm) z_M = t_AD+t_AC+t_M; %Distance in the z-direction to to end of the membrane
layer starting from the the anode side. (cm) z_CC = t_AD+t_AC+t_M+t_CC; %Distance in the z-direction to to end of the
cathode catalyst layer starting from the the anode side. (cm)
85
A_S = [0, 1, 0, 0, 0, 0, 0, 0; %Boundary Condition at Beginning of Anode
Diffusion Layer (Concentration) z_AD, 1, -z_AD, -1, 0, 0, 0, 0; %Boundary Condition between Anode
Diffusion and Catalyst Layers (Concentration) D_AD, 0, -D_AC, 0, 0, 0, 0, 0; %Boundary Condition between Anode
Diffusion and Catalyst Layers (Diffusion of Methanol) 0, 0, z_AC, 1, -z_AC, -1, 0, 0; %Boundary Condition between Anode
Catalyst Layer and Membrane Layer (Concentration) 0, 0, D_AC, 0, -D_M, 0, 0, 0; %Boundary Condition between Anode Catalyst
Layer and Membrane Layer (Diffusion of Methanol) 0, 0, 0, 0, z_M, 1, -exp(sqrt(r_CC/D_CC)*z_M), -exp(-
sqrt(r_CC/D_CC)*z_M); %Boundary Condition between Membrane Layer and Cathode
Catalyst Layer (Concentration) 0, 0, 0, 0, D_M, 0, -D_CC*sqrt(r_CC/D_CC)*exp(sqrt(r_CC/D_CC)*z_M),
D_CC*sqrt(r_CC/D_CC)*exp(-sqrt(r_CC/D_CC)*z_M); %Boundary Condition between
Membrane Layer and Cathode Catalyst Layer (Diffusion of Methanol) 0, 0, 0, 0, 0, 0, exp(sqrt(r_CC/D_CC)*z_CC), exp(-sqrt(r_CC/D_CC)*z_CC)];
%Boundary Condition at exit of cathode catalyst layer. (Concentration)
%Non_Homogeneous Conditions for Steady State ODEs at the initial condition. B_o_S = [C_FEED; %Boundary Condition at Beginning of Anode Diffusion Layer
(Concentration) r_AC_o*z_AD^2/2/D_AC; %Boundary Condition between Anode Diffusion and
Catalyst Layers (Concentration) r_AC_o*z_AD; %Boundary Condition between Anode Diffusion and Catalyst
Layers (Diffusion of Methanol) -r_AC_o*z_AC^2/2/D_AC; %Boundary Condition between Anode Catalyst Layer
and Membrane Layer (Concentration) -r_AC_o*z_AC; %Boundary Condition between Anode Catalyst Layer and
Membrane Layer (Diffusion of Methanol) 0; %Boundary Condition between Membrane Layer and Cathode Catalyst Layer
(Concentration) 0; %Boundary Condition between Membrane Layer and Cathode Catalyst Layer
(Diffusion of Methanol) 0]; %Boundary Condition at exit of cathode catalyst layer.
(Concentration)
%Non_Homogeneous Conditions for Steady State ODEs at the final condition. B_f_S = [C_FEED; %Boundary Condition at Beginning of Anode Diffusion Layer
(Concentration) r_AC_f*z_AD^2/2/D_AC; %Boundary Condition between Anode Diffusion and
Catalyst Layers (Concentration) r_AC_f*z_AD; %Boundary Condition between Anode Diffusion and Catalyst
Layers (Diffusion of Methanol) -r_AC_f*z_AC^2/2/D_AC; %Boundary Condition between Anode Catalyst Layer
and Membrane Layer (Concentration) -r_AC_f*z_AC; %Boundary Condition between Anode Catalyst Layer and
Membrane Layer (Diffusion of Methanol) 0; %Boundary Condition between Membrane Layer and Cathode Catalyst Layer
(Concentration) 0; %Boundary Condition between Membrane Layer and Cathode Catalyst Layer
(Diffusion of Methanol) 0]; %Boundary Condition at exit of cathode catalyst layer.
(Concentration)
86
k_o = A_S\B_o_S; %Steady State Coefficients for concentration gradient before
load change. k_f = A_S\B_f_S; %Steady State Coefficients for concentration gradient after
load change.
syms z
C_AD_S = sym((k_f(1)*z+k_f(2))); %Steady state concentration gradient at
anode diffusion layer after load change. C_AC_S = sym((r_AC_f/2/D_AC*z^2+k_f(3)*z+k_f(4))); %Steady state
concentration gradient at anode catalyst layer after load change. C_M_S = sym((k_f(5)*z+k_f(6))); %Steady state concentration gradient at
membrane layer after load change. C_CC_S = sym(k_f(7)*exp(sqrt(r_CC/D_CC)*z)+k_f(8)*exp(-sqrt(r_CC/D_CC)*z));
F_AD = sym((k_o(1)*z+k_o(2)))-C_AD_S; %Initial condition for Anode Diffusion
Layer. F_AC = sym((r_AC_o/2/D_AC*z^2+k_o(3)*z+k_o(4)))-C_AC_S; %Initial condition
for Anode Catalyst Layer. F_M = sym((k_o(5)*z+k_o(6)))-C_M_S; %Initial condition for Membrane Layer. F_CC = sym(k_o(7)*exp(sqrt(r_CC/D_CC)*z)+k_o(8)*exp(-sqrt(r_CC/D_CC)*z))-
C_CC_S; %Inital condition for Cathode Catalyst Layer.
syms Beta_n A_AD A_AC B_AC A_M B_M A_CC B_CC
A_H = [sin(Beta_n*z_AD/D_AC^0.5), cos(Beta_n*z_AD/D_AC^0.5), 0, 0, 0, 0; Beta_n*D_AC^0.5*cos(Beta_n*z_AD/D_AC^0.5), -
Beta_n*D_AC^0.5*sin(Beta_n*z_AD/D_AC^0.5), 0, 0, 0, 0; sin(Beta_n*z_AC/D_AC^0.5), cos(Beta_n*z_AC/D_AC^0.5), -
sin(Beta_n*z_AC/D_M^0.5), -cos(Beta_n*z_AC/D_M^0.5), 0, 0; Beta_n*D_AC^0.5*cos(Beta_n*z_AC/D_AC^0.5), -
Beta_n*D_AC^0.5*sin(Beta_n*z_AC/D_AC^0.5), -
Beta_n*D_M^0.5*cos(Beta_n*z_AC/D_M^0.5),
Beta_n*D_M^0.5*sin(Beta_n*z_AC/D_M^0.5), 0, 0; 0, 0, sin(Beta_n*z_M/D_M^0.5), cos(Beta_n*z_M/D_M^0.5), -
sin(Beta_n*z_M/D_CC^0.5), -cos(Beta_n*z_M/D_CC^0.5); 0, 0, Beta_n*D_M^0.5*cos(Beta_n*z_M/D_M^0.5), -
Beta_n*D_M^0.5*sin(Beta_n*z_M/D_M^0.5), -
Beta_n*D_CC^0.5*cos(Beta_n*z_M/D_CC^0.5),
Beta_n*D_CC^0.5*sin(Beta_n*z_M/D_CC^0.5)];
B_H = [sin(Beta_n*z_AD/D_AD^0.5); Beta_n*D_AD^0.5*cos(Beta_n*z_AD/D_AD^0.5); 0; 0; 0; 0];
Psi_AD_n = sym(A_AD*sin(Beta_n*z/D_AD^0.5)); Psi_AC_n = sym(A_AC*sin(Beta_n*z/D_AC^0.5)+B_AC*cos(Beta_n*z/D_AC^0.5)); Psi_M_n = sym(A_M*sin(Beta_n*z/D_M^0.5)+B_M*cos(Beta_n*z/D_M^.5)); Psi_CC_n = sym(A_CC*sin(Beta_n*z/D_CC^0.5)+B_CC*cos(Beta_n*z/D_CC^0.5));
k_H = simple(A_H\B_H);
87
syms Beta_n_t
%Homogenous Equations for Unsteady PDEs in matrix form to solve for
Eigenvalues. A_H_E = [sin(Beta_n_t*z_AD/D_AD^0.5), -sin(Beta_n_t*z_AD/D_AC^0.5), -
cos(Beta_n_t*z_AD/D_AC^.5), 0, 0, 0, 0; Beta_n_t*D_AD^0.5*cos(Beta_n_t*z_AD/D_AD^0.5), -
Beta_n_t*D_AC^0.5*cos(Beta_n_t*z_AD/D_AC^0.5),
Beta_n_t*D_AC^0.5*sin(Beta_n_t*z_AD/D_AC^0.5), 0, 0, 0, 0; 0, sin(Beta_n_t*z_AC/D_AC^0.5), cos(Beta_n_t*z_AC/D_AC^0.5), -
sin(Beta_n_t*z_AC/D_M^0.5), -cos(Beta_n_t*z_AC/D_M^0.5), 0, 0; 0, Beta_n_t*D_AC^0.5*cos(Beta_n_t*z_AC/D_AC^0.5), -
Beta_n_t*D_AC^0.5*sin(Beta_n_t*z_AC/D_AC^0.5), -
Beta_n_t*D_M^0.5*cos(Beta_n_t*z_AC/D_M^0.5),
Beta_n_t*D_M^0.5*sin(Beta_n_t*z_AC/D_M^0.5), 0, 0; 0, 0, 0, sin(Beta_n_t*z_M/D_M^0.5), cos(Beta_n_t*z_M/D_M^0.5), -
sin(Beta_n_t*z_M/D_CC^0.5), -cos(Beta_n_t*z_M/D_CC^0.5); 0, 0, 0, Beta_n_t*D_M^0.5*cos(Beta_n_t*z_M/D_M^0.5), -
Beta_n_t*D_M^0.5*sin(Beta_n_t*z_M/D_M^0.5), -
Beta_n_t*D_CC^0.5*cos(Beta_n_t*z_M/D_CC^0.5),
Beta_n_t*D_CC^0.5*sin(Beta_n_t*z_M/D_CC^0.5); 0, 0, 0, 0, 0, sin(Beta_n_t*z_CC/D_CC^0.5), cos(Beta_n_t*z_CC/D_CC^0.5)];
P = simple(det(A_H_E));
%Solve for Eigenvalues Beta_n_t = 1/10^Beta_n_precision;
for n = 1:1:n_max n_max-n+1 delta = 1;
while delta >= 1/10^Beta_n_precision Test_b = subs(P) >= 0; Beta_n_t = Beta_n_t + delta; Test_a = subs(P) >= 0;
if Test_a ~= Test_b Beta_n_t = Beta_n_t-delta; delta = delta/10; end end Beta_n_array(n) = Beta_n_t-delta/2*10; Beta_n_t = Beta_n_t + delta*10; end
t_array = linspace(0,t_max,t_d); z_array = linspace(0,z_CC,z_d);
for n=1:1:n_max Beta_n = Beta_n_array(n);
n_max-n
A_AD = 1;
88
A_AC = subs(k_H(1)); B_AC = subs(k_H(2)); A_M = subs(k_H(3)); B_M = subs(k_H(4)); A_CC = subs(k_H(5)); B_CC = subs(k_H(6));
N_n =
subs(int(Psi_AD_n^2,0,z_AD))+subs(int(Psi_AC_n^2,z_AD,z_AC))+subs(int(Psi_M_n
^2,z_AC,z_M))+subs(int(Psi_CC_n^2,z_M,z_CC)); tail =
subs(int(Psi_AD_n*F_AD,0,z_AD))+subs(int(Psi_AC_n*F_AC,z_AD,z_AC))+subs(int(P
si_M_n*F_M,z_AC,z_M))+subs(int(Psi_CC_n*F_CC,z_M,z_CC));
for j=1:1:t_d t=t_array(j) nose = subs(1/N_n*exp(-Beta_n^2*t)); for i=1:1:z_d z=z_array(i);
if j == 1
if z <= z_AD C_S(i) = subs(C_AD_S);
elseif z <= z_AC & z_AD < z C_S(i) = subs(C_AC_S);
elseif z <= z_M & z_AC < z C_S(i) = subs(C_M_S);
elseif z <= z_CC & z_M < z C_S(i) = subs(C_CC_S); end end
if z <= z_AD C_H_n(i,j,n) = subs(nose*Psi_AD_n*tail);
elseif z <= z_AC & z_AD < z C_H_n(i,j,n) = subs(nose*Psi_AC_n*tail);
elseif z <= z_M & z_AC < z C_H_n(i,j,n) = subs(nose*Psi_M_n*tail);
elseif z <= z_CC & z_M < z C_H_n(i,j,n) = subs(nose*Psi_CC_n*tail); end
if n == n_max C_H(i,j) = sum(C_H_n(i,j,:)); C(i,j) = C_H(i,j) + C_S(i); end end
89
end end
plot(z_array,C*1000,'linewidth',2) axis([0 z_CC 0 1.8]) set(gca,'FontSize',16) xlabel('MEA Position (cm)','FontSize',16,'FontWeight', 'Bold') ylabel('Methanol Concentration (M)','FontSize',16,'FontWeight', 'Bold') Chart_Title = sprintf('MEA Methanol Concentration Distribution from %d mA/cm²
to %d mA/cm² at %0.2f M',i_o, i_f,C_FEED*1000); title(Chart_Title,'FontSize',24,'FontWeight','Bold') leg1=sprintf('%0.1f s (%d mA/cm²)',0*t_max/(t_d-1),i_o); leg2=sprintf('%0.1f s (%d mA/cm²)',1*t_max/(t_d-1),i_f); leg3=sprintf('%0.1f s (%d mA/cm²)',2*t_max/(t_d-1),i_f); leg4=sprintf('%0.1f s (%d mA/cm²)',3*t_max/(t_d-1),i_f); leg5=sprintf('%0.1f s (%d mA/cm²)',4*t_max/(t_d-1),i_f); leg6=sprintf('%0.1f s (%d mA/cm²)',5*t_max/(t_d-1),i_f); legh=legend(leg1,leg2,leg3,leg4,leg5,leg6); set(legh, 'Position', [.733,.663,.145,.22]) line([z_AC z_AC],[0 1.8],'linestyle','--','color','black') line([z_AD z_AD],[0 1.8],'linestyle','--','color','black') line([z_M z_M],[0 1.8],'linestyle','--','color','black')
format short g Total_CH3OH=(C_FEED-C(80,1))/z_array(80)*D_AD*96485*6*1000 XO_CH3OH=(C(188,1)-C(200,1))/(z_array(200)-z_array(188))*D_CC*96485*6*1000 CH3OH_Ratio=XO_CH3OH/((C(188,2)-C(200,2))/(z_array(200)-
z_array(188))*D_CC*96485*6*1000) format long poo=[C_FEED; i_o; D_AD; D_AC; r_AC_o; D_M; D_CC; r_CC; Total_CH3OH; XO_CH3OH;
CH3OH_Ratio] format short
90
LIST OF REFERENCES
[1] Moore's Law: Made real by Intel® innovation: 2009; Available at:
http://www.intel.com/technology/mooreslaw/. Accessed 07/21, 2009.
[2] M. Broussely, G. Archdale, J.Power Sources, 136 (2004) 386-394.
[3] http://www.faa.gov/about/office_org/headquarters_offices/ash/ash_programs/hazmat/aircarri
er_info/media/Battery_incident_chart.pdf
[4] J.G. Liu, T.S. Zhao, R. Chen, C.W. Wong, Electrochemistry Communications, 7 (2005) 288-
294.
[5] A. Heinzel, V.M. Barragán, J.Power Sources, 84 (1999) 70-74.
[6] M. Walker, K.-M. Baumgärtner, M. Kaiser, J. Kerres, A. Ullrich, E. Räuchle, J Appl Polym
Sci, 74 (1999) 67-73.
[7] ATP Project Brief - 00-00-7744: Available at:
http://jazz.nist.gov/atpcf/prjbriefs/prjbrief.cfm?ProjectNumber=00-00-7744. Accessed
07/23, 2009.
[8] J.A. McAllister, A.E. Farrell, Energy, 32 (2007) 1177-1184.
[9] BAJ Website | Total battery production statistics: 2011; Available at:
http://www.baj.or.jp/e/statistics/01.html. Accessed 08/11, 2011.
[10] R.A. Powers, Proceedings of the IEEE, 83 (1995) 687-693.
[11] B. Scrosati, Electrochim.Acta, 45 (2000) 2461-2466.
[12] J. Vetter, P. Novák, M.R. Wagner, C. Veit, K.-. Möller, J.O. Besenhard, M. Winter, M.
Wohlfahrt-Mehrens, C. Vogler, A. Hammouche, J.Power Sources, 147 (2005) 269-281.
[13] J. Shim, R. Kostecki, T. Richardson, X. Song, K.A. Striebel, J.Power Sources, 112 (2002)
222-230.
[14] J. McLaughlin, (2008).
[15] Ackerman D. New Apple MacBooks demystified. 06/08/09; Available at:
http://news.cnet.com/8301-17938_105-10260001-1.html?tag=rb_content;contentMain.
Accessed 08/19, 2011.
[16] Stanford University. New Nanowire Battery Holds 10 Times The Charge Of Existing Ones.
2007; Available at: http://www.sciencedaily.com/releases/2007/12/071219103105.htm.
Accessed 08/19, 2011.
91
[17] K. Scott, W.M. Taama, S. Kramer, P. Argyropoulos, K. Sundmacher, Electrochim.Acta, 45
(1999) 945-957.
[18] S. Song, W. Zhou, W. Li, G. Sun, Q. Xin, S. Kontou, P. Tsiakaras, Ionics, 10 (2004) 458-
462.
[19] C.Y. Du, T.S. Zhao, W.W. Yang, Electrochim.Acta, 52 (2007) 5266-5271.
[20] B. Gurau, E.S. Smotkin, J.Power Sources, 112 (2002) 339-352.
[21] S. Doerner, T. Schultz, T. Schneider, K. Sundmacher, P. Hauptmann, Sensors, 2004.
Proceedings of IEEE, (2004) 639-641 vol.2.
[22] Dielectric Constants of Materials: 2008; Available at:
http://clippercontrols.com/info/dielectric_constants.html#D. Accessed 07/24, 2009.
[23] H. Zhao, J. Shen, J. Zhang, H. Wang, D.P. Wilkinson, C.E. Gu, J.Power Sources, 159
(2006) 626-636.
[24] J.P. Longtin, C.H. Fan, Microscale Thermophysical Engineering, 2 (1998) 261-272.
[25] CRC handbook of chemistry and physics, CRC Press; 1978, pp. 8-70.
[26] A. Rabinovich, E. Diatzikis, J. Mullen, D. Tulimieri, US patent 6,815,682 (2003).
[27] G.C. Benson, P.J. D'Arcy, Journal of Chemical & Engineering Data, 27 (1982) 439-442.
[28] M. Baldauf, W. Preidel, US Patent 6,536,262
[29] F.M. White, Fluid mechanics, 6th ed., McGraw-Hill Higher Education, Boston, MA; 2008,
pp. 864.
[30] D. Sparks, R. Smith, V. Cruz, N. Tran, A. Chimbayo, D. Riley, N. Najafi, Sensors and
Actuators A: Physical, 149 (2009) 38-41.
[31] S.R. Narayanan, T.I. Valdez, W. Chun, Electrochem.Solid-State Lett., 3 (2000) 117-120.
[32] C.L. Chang, C.Y. Chen, C.C. Sung, D.H. Liou, J.Power Sources, 164 (2007) 606-613.
[33] J. Cristiani, N. Sifer, E. Bostic, P. Fomin, D. Reckar, Annual Meeting of the American
Institute of Chemical Engineers, (2005).
[34] E. Antolini, R.R. Passos, E.A. Ticianelli, J.Appl.Electrochem., 32 (2002) 383-388.
[35] P. Argyropoulos, K. Scott, W.M. Taama, Electrochim.Acta, 45 (2000) 1983-1998.
[36] Q. Ye, T.S. Zhao, H. Yang, J. Prabhuram, Electrochem.Solid-State Lett., 8 (2005) A52-A54.
92
[37] A. Casalegno, P. Grassini, R. Marchesi, Appl.Therm.Eng., 27 (2007) 748-754.
[38] C. Eickes, P. Piela, J. Davey, P. Zelenay, J.Electrochem.Soc., 153 (2006) A171-A178.
[39] F. Liu, C. Wang, J.Electrochem.Soc., 154 (2007) B514-B522.
93
BIOGRAPHICAL SKETCH
William “Jason” Harrington was born in Quepos, Costa Rica where at the age of one year
he moved with his family to Ormond Beach, Florida. In the spring of 2006, Jason graduated with
his Bachelor of Science in mechanical engineering from the University of North Florida. There,
he developed an interest in clean and renewable energy while working under Dr. James Fletcher
as a laboratory assistant. In 2010, he began working as a systems engineer for direct methanol
fuel cells with the University of North Florida. Jason graduated with his Master of Science in
mechanical engineering in the summer of 2012.