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平板式微型甲醇蒸汽重組器熱質傳特性與流道設計之研究

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立交通大學

機械工程學系

平板式微型甲醇蒸汽重組器熱質傳特性

與流道設計之研究

Study on Heat and Mass Transfer Characteristics and Flow Channel

Design in a Plate Methanol Steam Micro-Reformer

研 究 生 : 薛清益

指導教授 : 陳俊勳 教授

曲新生 教授

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平板式微型甲醇蒸汽重組器熱質傳特性

與流道設計之研究

Study on Heat and Mass Transfer Characteristics and Flow Channel

Design in a Plate Methanol Steam Micro-Reformer

研 究 生 : 薛清益 Student : Ching-Yi Hsueh

指導教授 : 陳俊勳、曲新生 Advisor:

Chiun-Hsun Chen

Hsin-Sen Chu

國 立 交 通 大 學

機 械 工 程 學 系

博 士 論 文

A Thesis

Submitted to Department of Mechanical Engineering National Chiao Tung University

in partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy in

Mechanical Engineering

May 2010

Hsinchu, Taiwan, Republic of China

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平板式微型甲醇重組器熱質傳特性與流道設計之研究

學生 : 薛清益 指導教授 : 陳俊勳、曲新生

摘 要

本論文係以數值分析探討平板式微型甲醇蒸汽重組器(包含甲醇蒸汽重組器與甲醇 觸媒燃燒器)之熱質傳現象,本研究首先針對微型甲醇蒸汽重組器,探討幾何效應與熱 流效應對甲醇轉化率及氣體濃度分佈之影響,以俾獲得較佳的流道設計與操作條件,接 著並加入甲醇觸媒燃燒器,其結果可以提供平板式微型甲醇蒸汽重組器一個完整的設計 資訊。 本研究探討的議題主要分為二個部份:第一部份是以微型甲醇蒸汽重組器為主,並 不考慮甲醇觸媒燃燒器。首先建立一甲醇蒸汽重組器之二維流道數學模型,並探討幾何 參數與熱流參數對重組器性能與流道內熱質傳現象之影響。研究結果發現當壁面溫度由 200度升高至260度時,甲醇轉換效率約提升49%,結果也顯示當入口甲醇與水之燃料比 由1.0變為1.6時,流道出口之CO濃度會從1.72%降低至0.95%。而選用較長的流道長度、 較低的流道高度、較大的觸媒高度、較大的觸媒孔隙度、較高的壁面溫度與較低的雷諾 數等參數可以有效提升微型重組器之性能。接著建立甲醇蒸氣重組器之三維流道數學模 型,並探討不同流道高寬比與流道幾何尺寸對氣體傳輸現象與微型甲醇蒸汽重組器性能 之影響。結果顯示,壁面傳導效應對於模型之溫度分佈會有顯著的影響,因此在分析模 型中,必須考慮壁面傳導效應之影響。結果亦顯示,較低的流道高寬比會有較好的微型

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ii 型流道之微型甲醇蒸汽重組器,並利用數值方法探討壁面溫度、入口燃料比與雷諾數對 具蛇型流道之微型甲醇蒸汽重組器性能與傳輸現象之影響。結果顯示,藉由降低雷諾數 與提高入口燃料比可以有效提升甲醇轉換效率。而加熱壁面在蛇型流道之頂端(Y=1)或 底部(Y=0)時,吾人發現加熱壁面在流道頂端時,會有較佳的甲醇轉換率,此乃肇因於 加熱壁面在流道頂端時,會有較大的化學反應。 而本論文第二部份主要是利用數值方法針對微型甲醇蒸氣重組器並搭配觸媒燃燒 器之熱質傳特性與性能進行研究,首先建立甲醇蒸氣重組器搭配觸媒燃燒器之三維流道 數學模型,來探討不同流動形式與幾何參數對微型甲醇重組器性能之影響,結果顯示採 用逆向流比起平行流可以有效改善重組器10%的效能,主要是由於逆向流有較佳的熱管 理能力,因此能有效改善重組器之轉換效率,結果也顯示,適當的幾何參數會有較佳的 熱管理能力與甲醇轉換率,而當燃燒器有較大的雷諾數時,會有較大的壁面溫度,因此 能有效提升甲醇轉化率。接著建立具不同流道形狀(蛇型流道與直通流道)之三維甲醇蒸 汽重組器搭配甲醇觸媒燃燒器模型,並探討不同流道對甲醇轉化率與傳輸現象之影響。 結果顯示,具蛇型流道之微型甲醇蒸汽重組器與甲醇觸媒燃燒器會有最佳的甲醇轉換 率,此乃肇因於採用蛇型流道作為微型甲醇蒸汽重組器與甲醇觸媒燃燒器之流道時,會 有較佳的熱管理能力。本論文之數值模型可以有效的分析微型重組器內傳輸現象,其結 果將有助於今後平板式微型重組器之設計。

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Study on heat and mass transfer characteristics and channel design in a

plate methanol steam micro-reformer

Student: Ching-Yi Hsueh Advisor: Chiun-Hsun Chen

Hsin-Sen Chu

ABSTRACT

This dissertation aims to examine numerically heat and mass transport phenomena in the plate methanol steam micro-reformer (including methanol steam micro-reformer and methanol catalytic combustor). The first focus is to investigate the effects of geometric and thermo-fluid parameters on the methanol conversion and gas concentration distributions of the methanol steam micro-reformer in order to obtain better channel designs and operating conditions. Furthermore, a methanol steam micro-reformer with a methanol catalytic combustor is considered in the present work. The results can provide comprehensive information for designing the plate methanol steam micro-reformer.

This study can be divided into two parts. In the first part, the research only considered the plate methanol steam micro-reformer, namely the methanol catalytic combustor is not included in it. Firstly, a 2-dimensional channel model of the methanol steam micro-reformer is established to investigate effects of geometric and thermo-fluid parameters on performance and heat and mass transfer phenomena in micro-reformer channels. The results of the modeling suggest that the methanol conversion could be improved by 49 %-points by increasing the wall temperature from 200 to 260 . ℃ ℃ The results also show that the CO

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iv

Secondly, a 3-dimensional channel model of the methanol steam micro-reformer is developed to investigate the effects of various height and width ratios and channel geometric size on the reactant gas transport characteristics and micro-reformer performance. The predictions show that conduction through the wall plays a significant effect on the temperature distribution and must be considered in the modeling. The predicted results also demonstrated that better performance is noted for a micro-reformer with lower aspect-ratio channel. This is due to the larger the chemical reaction surface area for a lower aspect-ratio channel. The results indicate that the smaller channel size experiences a better methanol conversion. This is due to the fact that a smaller channel has a much more uniform temperature distribution, which in turn, fuel utilization efficiency is improved for a smaller channel reformer. Finally, the established 3-dimensional channel model of a plate methanol steam micro-reformer extends to be a plate methanol steam micro-reformer with serpentine flow field. A numerical investigation of the transport phenomena and performance of a plate methanol steam micro-reformer with serpentine flow field as a function of wall temperature, fuel ratio and Reynolds number are presented. The methanol conversion is improved by decreasing the Reynolds number or increasing the S/C molar ratio. When the serpentine flow field of the channel is heated either through top plate (Y=1) or the bottom plate (Y=0), we observe a higher degree of methanol conversion for the case with top plate heating. This is due to the stronger chemical reaction for the case with top plate heating.

In the second part, a numerical study is performed to examine the characteristics of heat and mass transfer and the performance of a plate methanol steam micro-reformer with a methanol catalytic combustor. Firstly, a three-dimensional channel numerical model of a micro-reformer with combustor is developed to examine the effects of various flow configurations and geometric parameters on micro-reformer performance. Comparing the co- and counter-current flows via numerical simulation, the results show that the methanol

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conversion for counter-current flow could be improved by 10%. This is due to the fact that counter-current flow leads to a better thermal management, which in turn improves fuel conversion efficiency. The results also reveal that the appropriate geometric parameters exist for a micro-reformer with a combustor to obtain better thermal management and methanol conversion. With a higher Reynolds number on the combustor side, the wall temperature is increased and the methanol conversion can thus be enhanced. In addition, the three-dimensional models of a plate methanol steam micro-reformer and a methanol catalytic combustor with the parallel flow field and the serpentine flow field have been established to investigate the performance and transport phenomena in the micro-reformer. The methanol conversion of the micro-reformer with the serpentine flow field and the combustor with the serpentine flow field is the best due to a better thermal management in the micro-reformer. The numerical model provides an efficient way to characterize the transport phenomena within the micro-reformer, and the results will benefit the future design for the plate methanol steam micro-reformer.

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vi

ACKNOWLEDGEMENTS

首先感謝恩師 曲新生及陳俊勳教授,恩師除了在學術上悉心的指導我之外,在待 人處世方面更是值得我學習的典範。其次,感謝 顏維謀教授在交大求學過程中給予我 莫大的幫助,使我的博士論文能進行的十分順利。也很感謝口試委員翁政義、陳朝光、 林清發及陳慶耀諸位教授對於論文的建議及指導,使得本論文更加的嚴謹及完整。 此外,特別感謝交大曲新生師門與陳俊勳師門的學長、學姐、同學及學弟妹們在學 業及生活上的關心與照顧,幫助我在研究過程中解決許多困難。也感謝華梵大學熱流實 驗室的學長、學姐及學弟妹們為我的生活帶來了許多歡樂的回憶。 最後特別感謝我的家人,在這漫長的求學過程中,不斷給予我許多的支持及鼓勵, 陪伴我經歷了許多挫折及挑戰,僅以此論文獻給所有幫助、關心及照顧我的人。

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TABLE OF CONTENTS

CHINESE ABSTRACT ... i

ENGLISH ABSTRACT ...iii

ACKNOWLEDGEMENTS ... vi

TABLE OF CONTENTS ...vii

LIST OF TABLES... x

LIST OF FIGURES... xi

NOMENCLATURE ...xvii

CHAPTER 1 INTRODUCTION ... 1

1.1 Background...1 1.2 Literature Survey ...5 1.3 Objectives ...13

CHAPTER 2 MATHEMATICAL MODEL AND ANALYSIS ... 25

2.1 The Model of the Methanol Steam Micro-Reformer...25

2.1.1 Model Description ...25

2.1.2 Assumption ...26

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viii

2.2.1 Model Description ...31

2.3.2 Assumption ...33

2.3.3 Governing Equations ...33

2.3.4 Boundary Conditions...37

CHAPTER 3 METHOD OF SOLUTION ... 44

3.1 Flow Chart ...44

3.2 Numerical Method...45

CHAPTER 4 RESULTS AND DISCUSSION ... 48

4.1 Two-Dimensional Channel Model of a Plate Methanol Steam Micro-Reformer...48

4.1.1 Effects of the Geometric Parameters on the Heat and Mass Transfer and Methanol Conversion in a Micro-Reformer Channel...49

4.1.2 Effects of Thermo-Fluid Parameters on the Heat and Mass transfer and Methanol Conversion in a Micro-Reformer Channel...53

4.2 Three-Dimensional Channel Model of a Plate Methanol Steam Micro-Reformer ...55

4.2.1 Effects of Channel with Various Height and Width Ratios on Micro-Reformer Performance and Local Transport Phenomena...56

4.2.2 Effects of Geometric Size on the Transport Phenomena and Performance of Micro-Reformer...61

4.3 Three-Dimensional Model of a Plate Methanol Steam Micro-Reformer with Serpentine Flow Field Design ...62

4.3.1 Effects of Thermo-Fluid Parameters on the Plate Methanol Steam Micro-Reformer with Serpentine Flow Field Performance...63

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4.3.2 Effects of Various Heated Plates on Micro-Reformer Performance...66

4.4 Three-Dimensional Channel Model of a Plate Methanol Steam Micro-Reformer with Methanol Catalytic Combustor...67

4.4.1 Effects of Various Flow Configurations and Geometric Parameters on Micro-Reformer Performance ...68

4.4.2 Effects of the Reynolds Number (Re) on Heat and Mass Transfer Phenomena and Micro-Reformer Performance...71

4.5 Three-Dimensional Model of a Plate Methanol Steam Micro-Reformer with Methanol Catalytic Combustor for Parallel Flow Field and Serpentine Flow Field 73

CHAPTER 5 CONCLUSIONS AND RECOMMENDATION... 136

5-1 Conclusions ...136

5-2 Recommendations ...139

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x

LIST OF TABLES

Table 1-1 Energy density of various batteries and fuels [1] ...16 Table 1-2 Comparison of reforming technologies[4] ...17 Table 4-1 Parameters used in the two-dimensional channel model of a plate methanol steam

micro-reformer ...77 Table 4-2 Methanol mole fractions for the various grids ...78 Table 4-3 The cases with various aspect-ratio channels used in this work ...79 Table 4-4 Parameters used in the three-dimensional channel model of a plate methanol steam

micro-reformer ...80 Table 4-5 Mole fractions of methanol for the various grid tests at different axial locations....81 Table 4-6 Parameters used in the three-dimensional model of the plate methanol steam

micro-reformer with serpentine flow field design...82 Table 4-7 Temperature distributions (℃) for the various grid tests at different axial locations

...83 Table 4-8 Parameters used in the three-dimensional channel model of a plate methanol steam

micro-reformer with methanol catalytic combustor ...84 Table 4-9 Temperature distributions (ºC) for the various grid tests at different axial locations

...85 Table 4-10 Parameters used in the three-dimensional model of a plate methanol steam

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LIST OF FIGURES

Fig. 1-1 Applications of the fuel cell (ERL/ITRI)...18

Fig. 1-2 Photograph of the (a) small PEMFC and (b) micro-reformer [6]...19

Fig. 1-3 Schematic of fuel reforming process [7]...20

Fig. 1-4 Photograph of the plate methanol steam micro-reformer [7]...21

Fig. 1-5 Structure of micro-reformer [6] ...22

Fig. 1-6 Schematic of methanol reforming system [6]...23

Fig. 1-7 Schematic of PhD thesis structure ...24

Fig. 2-1 Schematic diagram of the two-dimensional channel model of a plate methanol steam micro-reformer ...39

Fig. 2-2 Schematic diagram of the three-dimensional channel model of a plate methanol steam micro-reformer ...40

Fig. 2-3 Schematic diagram of the three-dimensional model of a plate methanol steam micro-reformer with serpentine flow field design...41

Fig. 2-4 Schematic diagram of the three-dimensional channel model of a plate methanol steam micro-reformer with methanol catalytic combustor ...42

Fig. 2-5 (a) Schematic diagram of a plate methanol steam micro-reformer with methanol catalytic combustor, (b) Parallel Flow Field and (c) Serpentine Flow Field...43

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xii

Fig. 4-2 Effects of geometric parameters and wall temperature on (a) the methanol conversion and (b) the CO concentration (ppm) at the outlet...88 Fig. 4-3 Effects of geometric parameters and H2O/CH3OH molar ratio on the CO

concentration at (a)T w=200 °C and (b) T w=260 °C...89 Fig. 4-4 Effects of the channel heights on temperature distributions along the centerline of the

channel at T w=200 °C and T w=260 °C ...90 Fig. 4-5 Effects of wall temperature on the cross-sectioned temperature at different axial

locations for H=1.0mm. (a)T w=200 °C and (b) T w=260 °C ...91 Fig. 4-6 Effects of wall temperature on the cross-sectioned velocity at different axial locations for H=0.2mm. (a)T w=200 °C and (b) T w=260 °C...92 Fig. 4-7 Variations of the mole fraction of the various species along the channel (a)T w=200

°C and (b) T w=260 °C. ...93 Fig. 4-8 Effects of geometric parameters on the local CH3OH mole fraction along the channel

(a)T w=200 °C and (b) T w=260 °C...94 Fig. 4-9 Effects of geometric parameters on the local H2 mole fraction along the channel at T

w=200 °C and (b) T w=260 °C...95 Fig. 4-10 Effects of geometric parameters on the local CO mole fraction along the channel at

(a)T w=200 °C and (b) T w=260 °C...96 Fig. 4-11 Effects of thermo-fluid parameters on the local CH3OH mole fraction along the

channel at (a)T w=200 °C and (b) T w=260 °C ...97 Fig. 4-12 Effects of thermo-fluid parameters on the local H2 mole fraction along the channel

at (a)T w=200 °C and (b) T w=260 °C...98 Fig. 4-13 Effects of thermo-fluid parameters on the local CO mole fraction along the channel

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at (a)T w=200 °C and (b) T w=260 °C...99 Fig. 4-14 Comparisons of the predicted results with and without wall conduction effects for

the temperature and CH3OH mole fraction distributions along the centerline of the channel (Y=0.5)...100 Fig. 4-15 Comparison of predicted methanol conversion with previous experimental data of

Park et al. [16] ...101 Fig. 4-16 Variations of the mole fractions of the various species along the channel center line

(γ=0.5) ...102 Fig. 4-17 Effects of aspect ratios of channel and wall temperature on methanol conversion and CO concentration (ppm) at outlet of channel ...103 Fig. 4-18 Effects of aspect ratios of channel on local methanol conversion along center line of

channel at T w=200 °C and T w=260 °C ...104 Fig. 4-19 Effects of aspect ratios of channel at T w=200 °C and T w=260 °C on (a) local H2

mole fraction and (b) local CO mole fraction along center line of channel ...105 Fig. 4-20 Effects of aspect ratios of channel at T w=200 °C and T w=260°C on (a) local

velocity and (b) local pressure along center line of channel ...106 Fig. 4-21 Effects of aspect ratios of channel at T w=200 °C and T w=260 °C on (a) local

temperature along center line of channel and (b) local reaction rates of methanol steam reforming along interface between flow channel and catalyst layer...107 Fig. 4-22 Effects of aspect ratios of channel and Reynolds number on methanol conversion

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xiv

Fig. 4-24 Effects of geometric size of channel and Reynolds number on local CH3OH mole fraction along center line of channel at (a)T w=200 °C and (b) T w=260 °C... 110 Fig. 4-25 Effects of various wall temperatures on (a) the temperature distributions and (b) the

CH3OH mole fraction and H2 mole fraction distributions along the centerline of the serpentine flow field (Y=0.5). ... 111 Fig. 4-26 Effects of various wall temperatures on (a) the local velocity and (b) the local

pressure along the centerline of the serpentine flow field (Y=0.5). ... 112 Fig. 4-27 Effects of Reynolds numbers at Tw=230°C on (a) the temperature distributions and

(b) the CH3OH mole fraction and H2 mole fraction distributions along the center line of the serpentine flow field (Y=0.5) ... 113 Fig. 4-28 Effects of H2O/CH3OH molar ratio (S/C) at Tw=230°C on (a) the temperature

distributions and (b) the CH3OH mole fraction and CO mole fraction distributions along the center line of the serpentine flow field (Y=0.5) ... 114 Fig. 4-29 Local distributions of (a) CH3OH mole fraction, (b) H2 mole fraction and (c) CO

mole fraction along the cross-section of Y=0.5 at Tw=230°C ... 115 Fig. 4-30 Local distributions of (a) CH3OH mole fraction, (b) H2 mole fraction and (c) CO

mole fraction along the interface between the flow channel and catalyst layer

(Y=0.95) at Tw=230° ... 116 Fig. 4-31 Effects of wall temperature and inlet fuel Reynolds number on the methanol

conversion and H2 production rate ... 117 Fig. 4-32 Effects of heating different channel plates on the temperature and CH3OH mole

fraction distributions along the center line of the serpentine flow field (Y=0.5) ... 118 Fig. 4-33 Comparison of theoretical simulation of present results with previous experimental

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data by Won et al. [24]... 119 Fig. 4-34 Comparisons of the simulation results with and without wall conduction effects for

the temperature distributions and CH3OH mole fraction distributions along the centerline of the channel...120 Fig. 4-35 Effects of co- and counter-current flow configurations on (a) the temperature

distributions along different axial location lines and (b) the local distributions of the mole fractions of the various species along the center line of the reforming channel (Y=0.167) ...121 Fig. 4-36 Effects of the channel height of the combustor on (a) the temperature distributions

along the top centerline of the reforming channel and (b) the CH3OH mole fraction distributions along the center line of the reforming channel ...122 Fig. 4-37 Effects of the channel height of the reformer on (a) the temperature distributions

along the top centerline of the reforming channel and (b) the CH3OH mole fraction distributions along the center line of the reforming channel ...123 Fig. 4-38 Effects of the channel width on (a) the temperature distributions along the top

centerline of the reforming channel (Y=0.333) and (b) the CH3OH mole fraction distributions along the center line of the reforming channel (Y=0.167) ...124 Fig. 4-39 Effects of the steel widths on (a) the temperature distributions along the top

centerline of the reforming channel (Y=0.333) and (b) the CH3OH mole fraction distributions along the center line of the reforming channel (Y=0.167) ...125 Fig. 4-40 Effects of the Reynolds number (Re) for the combustor on (a) the temperature

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Fig. 4-41 Effects of the Reynolds number (Re) for the reformer on (a) the temperature distributions along the top centerline of the reforming channel (Y=0.333) and (b) the CH3OH mole fraction distributions along the center line of the reforming

channel (Y=0.167)...127 Fig. 4-42 Effects of the Reynolds number (Re) of the combustor on wall temperature and

methanol conversion...128 Fig. 4-43 Effects of the inlet flow rate (Q0,R) of the reformer and various flow field designs on

(a) wall temperature and (b) methanol conversion...129 Fig. 4-44 Effects of inlet flow rate (Q0,C) of the combustor and various flow field designs on

(a) wall temperature and (b) methanol conversion...130 Fig. 4-45 The temperature distributions on the top cross-section of the reforming channel for

reformer and combustor with various flow field designs ...131 Fig. 4-46 The CH3OH mole fraction distributions on the middle cross-section of the reforming channel for reformer and combustor with various flow field designs...132 Fig. 4-47 The H2 mole fraction distributions on the middle cross-section of the reforming

channel for reformer and combustor with various flow field designs...133 Fig. 4-48 The CO mole fraction distributions on the middle cross-section of the reforming

channel for reformer and combustor with various flow field designs...134 Fig. 4-49 Effects of the inlet flow rate (Q0,R) of the reformer and various flow field designs on

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NOMENCLATURE

Ci concentration of species i (mol m-3)

cp specific heat at constant pressure (kJ kg-1 K-1) D hydraulic diameter (m)

Deff effective mass diffusivity (m2 s-1) Dk mass diffusion coefficient (m2 s-1) Dp catalyst particle diameter (m) Ea activation energy (kJ mol-1) H channel height (m)

HC combustion flow channel (m) HR reforming flow channel (m) HW solidwall thickness (m)

SR

H

Δ Enthalpy of reaction for steam reforming (kJ mol-1)

rWGS

H

Δ Enthalpy of reaction for the reverse water gas shift (kJ mol-1)

MD

H

Δ Enthalpy of reaction for decomposition reaction (kJ mol-1) I, J, K grid points in the x, y and z directions, respectively keff effective thermal conductivity (W m-1K-1)

kf fluid phase thermal conductivity (W m-1K-1) kp permeability (m2)

ks solid medium thermal conductivity (W m-1K-1) k1 pre-exponential factor for steam reforming

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xviii

k-2 pre-exponential factor for the water gas shift L flow channel length (m)

Ls the total length from the serpentine flow channel inlet to outlet (m) Mi mole fraction of species i

Mw,i molecular weight of species i (kg mol-1) mi mass fraction of species i

p pressure (Pa)

QH2 hydrogen production rate at outlet (cm3 min-1)

QC inlet flow rate of the combustor QR inlet flow rate of the micro-reformer R universal gas constant (kJ kg-1 K-1)

RSR Arrhenius reaction rate coefficient for steam reforming (mol m-3 s-1) RrWSG Arrhenius reaction rate coefficient for the reverse water gas shift (mol m

-3 s-1) RMD Arrhenius reaction rate coefficient for decomposition reaction (mol m-3 s-1) RCombustion Arrhenius reaction rate coefficient for combustion reaction (mol m-3 s-1) Re Reynolds number, Re=ρuD/μ

ReC Reynolds number (Re) of the combustor ReR Reynolds number (Re) of the micro-reformer S/C molar ratio of H2O/CH3OH

T temperature ( )℃ Tw wall temperature ( )℃

u, v, w velocity components in the x, y and z directions, respectively, (m s-1) u0,C inlet flow velocity on the combustion channel side (m s-1)

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xs the length from the serpentine flow channel inlet to outlet (m) Y dimensionless coordinate, Y=y/H, Y= y/HC+δC+HW+HR+δR x, y, z coordinates (m)

WR channel width (m) WL steel width (m)

Greek symbols

β inertial loss coefficient

γ aspect ratio (height and width ratio, δ1+δ2/WR) δC combustion catalyst layer thickness (m) δR Reforming catalyst layer thickness (m) δ1 catalyst layer height (m)

δ2 flow channel height (m) ε porosity

θ dimensionless temperature, θ=(T-T0)/(Tw-T0) η methanol conversion

' i

λ the stoichometric coefficient for reactant i in reaction

" i

λ the stoichometric coefficient for product i in reaction τ tortuosity of the porous medium

μ viscosity (kg m-1 s-1)

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xx Subscripts eff effective u x-direction v y-direction w z-direction 0 inlet

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CHAPTER 1

INTRODUCTION

1.1 Background

The demand for power sources with superior performance has increased due to the rapid growth of the portable electronics market. Moreover, technology progresses over time have enabled developments in electronics to move us into a microelectronics age. When devices make smaller, new functionalities are added. However, power consumption rises alarmingly. Therefore, the power sources must produce adequate power output while at the same time maintaining criteria such as a very small volume and lightweight packaging. Primary and secondary batteries have been the energy storage solution for these devices. However, batteries are a chemical process, but they do not last long enough. Until recently, one innovative way is to utilize the hydrogen and feed it to a fuel cell, producing electricity. Kundu et al. [1] presented fuel cells promise to provide higher power density and longer durability than batteries (Table 1-1). In fuel cell, electricity and water are produced from hydrogen and oxygen in an electrochemical reaction. Besides, fuel cells are quiet, efficient and convert energy electrochemically rather than mechanically. Therefore, fuel cells are widely regarded as the most promising energy storage devices for mobiles, laptops, and personal digital assistants (PDA) in the 21st century due to their properties of high energy density, low noise, and low pollution.

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2

into electrons through a direct fuel cell system. In direct fuel cell system, the main studies focused on DMFC, but DMFC has still issues due to a low rate of oxidation and a high crossover rate. The PEMFC is highly attractive for both portable and stationary application due to its high operating efficiency and environmental friendliness. This gives the PEMFCs great flexibility of a wide range of applications, Fig 1-1. PEMFCs have been proposed as battery replacements. Ball and Wietschl [2] presentedapplications of PEMFC in portable power sources need to carry enough hydrogen fuel. However, the hydrogen storage problem is still difficult to overcome. To solve this technical difficulty, one possible solution is to employ a reformer. Indirect energy conversion systems is to first reform methanol, ethanol, gasoline followed by feeding the reformate gas into miniature PEM fuel cell. The reformers often have characteristic dimensions, such as channel gaps, which are on the micro-scale (typically<1000μm) or meso-scale (1000μm to a few centimeters) and will be referred to in this article as micro-reformers. These features are significantly smaller than many conventional reformers, and they can significantly enhance mass and heat transfer rates. Therefore, micro-reformers are being developed for using with the miniature PEMFCs, to overcome the high risk of carrying a large quantity of hydrogen.

In reforming systems, the electronic energy system is generated using concentrated hydrogen produced by reforming from a fuel such as methanol. Holladay et al. [3] showed methanol is an attractive fuel because of its low reforming temperatures, good miscibility with water and low content of sulfur compounds. From the technological point of view, methanol clearly has distinct advantages as a fuel for fuel cell applications. First, methanol is liquid at atmospheric conditions and has a high hydrogen-to-carbon ratio relative to gasoline. Secondly, it can be reformed to hydrogen at much lower temperatures (200-300℃), and is more efficient as compared to gasoline and methane (700-800℃). Finally, methanol is an environmentally friendly fuel, as it is readily biodegradable in air, soil and water. Therefore, methanol clearly

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has distinct advantages as a fuel for fuel cell applications due to its higher hydrogen-to-carbon ratio, low reforming temperature and greater environmental friendliness.

Holladay et al. [4] presented the majority of reformers currently being developed are designed to produce hydrogen from methanol. Three basic reforming technologies are steam reforming, partial oxidation, and autothermal reforming. Table 1-2 summarizes the advantages and challenges of each of these processes. Endothermic methanol steam reforming requires an external heat source. Partial oxidation is an alternative to steam reforming, where the reaction heat is provided by the partial combustion of the methanol with oxygen. The autothermal reforming process is a thermally neutral hybrid of steam reforming and partial oxidation. The partial oxidation and autothermal processes do not require an external heat source, but an expensive and complex oxygen separation unit is needed. Because of the steam reforming produces higher yields of hydrogen than autothermal reforming and partial oxidation of hydrocarbon fuels. The requirement of an external heat source can be addressed through the advanced heat and mass transfer provided by combustors. Hence, steam reforming is generally the preferred process for hydrogen production. A portable hydrogen production unit based on methanol steam reforming would be simpler and less costly than other alternatives.

The plate reformers have better performance than cylindrical reformers due to better heat and mass transfer is presented by Kolb et al. [5]. The plate methanol steam reformers are regarded as being micro-structured coated wall reformers, when patterning channels or similar fluid paths with a size below 1 mm. The advantages of micro-structured reformers enhanced heat and mass transfer are observed. Micro-structured reformers are much more suitable for

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4

multi-channel reformers work under laminar flow conditions demonstrating low pressure drop compared to randomly packed beds, and allow easy thermal integration of the processes involved. From the stated above, the plate methanol steam micro-reformer with small PEMFC has become a potential candidate for portable electronic products in the near future.

Fig. 1-2 shows a photograph of the micro-reformer and micro fuel cell, while Fig 1-3 shows the schematic of a system that consists of a methanol steam reformer and a fuel cell. First, methanol is fed with water and is heated by the vaporizer. The methanol is reformed by the reforming catalyst to generate hydrogen in the steam reformer. To supply heat to the steam reformer, part of methanol be fed to the combustor that generates sufficient amount of heat to sustain the steam reforming of methanol. For PEM fuel cells, the carbon monoxide levels need to be below 10 ppm. Therefore, a final polishing step (preferential oxidizer (PrOx) reactor) is used. Fig. 1-4 shows the photograph of the plate methanol steam micro-reformer including the etched glass wafers, the cross-section of the reformer, and the complete micro-reformer. Fig. 1-5 presents a simplified cross-sectional diagram of the plate methanol steam micro-reformer. The micro-reformer is composed of four units with vaporizers, catalytic combustor, and a CO remover. The functions are separated into two reaction systems. One reaction system is the hydrogen production system in which the methanol aqueous solution is fed and then vaporized at vaporizer 1, it is reformed to H2 with CO2 and a trace of CO at the methanol reformer; and finally the CO is preferentially oxidized at the CO remover. The other reaction system, the catalytic combustion system, is used to supply heat to the hydrogen production system. In this system, the methanol is vaporized at vaporizer 2 and then burned at the catalytic combustor. Fig. 1-6 shows a schematic of these two reaction systems.

Consequently, safety issues, storage problems, and size or portability considerations make pure hydrogen feeding relatively difficult for electronic equipment applications. The combination of a methanol reformer with a PEMFC overcomes the high risk involved in

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carrying a large quantity of hydrogen, and is thus a promising choice for miniaturized portable electronic systems, and could soon become the new choice for portable fuel cell applications.

1.2 Literature Survey

The methanol steam micro-reformers have received much attention due to their compact sizes and great potential to be used in portable fuel cell systems as a hydrogen generation unit. Several experiments for methanol steam reformers are currently in progress. Various reformer types have been used as the foundation for methanol steam reformer designs, including packed-bed reformers and plate reformers. Several successfully fabricated packed bed reformers for hydrogen production have been reported [8-10]. Kolb and Hessel [11] presented that the plate reformers have better performance than the packed bed reformers due to better heat and mass transfers. Therefore, the channels were patterned on the plate methanol steam reformers by several investigators [12-18]. As a result of the steam reforming being an endothermic reaction, the researchers have used electrical heat sources to supply heat flux to steam micro-reformers. Seo et al. [12] used stainless steel as a substrate to fabricate a unit of reformer and vaporizer. The heat for the endothermic reaction is from the electric heater and the developed fuel processor can generate sufficient hydrogen for a fuel cell with power output of 10W. Kwon et al. [13] made a micro-reformer by using silicon wafer substrate and a ‘fill-and-dry’ method for catalyst coating. The stack of micro-reformer occupies 15 cm3 only and the maximum hydrogen production rate occurs about at 320 in their experiments.℃ Ha et al. [14] fabricated a PDMS (poly dimethylsiloxane) micro-reformer, and used a heater to

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6

approximately 78% conversion of methanol, with a hydrogen production rate of 3 L/h. Park et al. [16] fabricated a steam reformer and vaporizer, and then assembled a miniature reforming device. The micro-channels were patterned on the steam reformer and the vaporizer. Their experimental results showed about 90% conversion of the methanol, with a hydrogen production rate of 0.498 mol/h, enough to supply a 15 W fuel cell. Jeong et al. [17] studied the steam reforming of methanol over a series of Cu/Zn-based catalysts by a micro-reformer. They found that a micro-reformer coated with Cu/ZnO/ZrO2/Al2O3 catalyst with an undercoated Al2O3 buffer layer exhibits higher methanol conversion rate and lower CO concentration in the outlet gas. Kundu et al. [18] studied the stability and performance of microchannel reactor for methanol steam reforming with different sols as a binder in the coating of catalyst. They found the mixed sol of alumina and zirconia comparatively produced better performance.

The plate integrated fuel processor, consisting of the various micro structured modules, was developed to produce hydrogen for fuel cell systems. The fuel processor includes a fuel vaporizer, a catalytic combustor and a steam reformer. The catalytic combustor supplied heat to the steam reforming reaction, and the hydrogen was produced by the micro methanol steam reformer. Therefore, several studies have used catalytic burners to supply thermal energy to the entire micro-reformer [19-25]. Kwon et al. [19] utilized silicon fabrication technology to set up the reformer and the catalytic burner. Their results indicated that the methanol combustion reaction with the catalytic burner successfully generated heat to maintain reformer temperature. The methanol steam reformer combined with the catalytic burner produced 73% hydrogen with 65% conversion of the methanol. A micro methanol steam reformer which included a vaporizer, heat exchanger, catalytic combustor and steam reformer to produce hydrogen for a PEMFC was conducted experimentally by Park et al. [20, 21]. Their results showed that at a temperature of 250℃, the reformer could produce a gas flow

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rate of 450 ml/min, with a gas composition of 73.3% H2 at the micro channel outlet. Yoshida et al. [22] fabricated a micro channel methanol reformer integrated with a combustor and a micro channel vaporizer. An appropriate depth of the micro channel vaporizer could generate high yields of hydrogen was found in their work. Park et al. [23] fabricated a micro-structure reforming system including a methanol steam reformer, combustor and vaporizer. Catalytic combustion produced thermal energy which was used to supply the entire system. Their experimental results showed that enough hydrogen was produced by the reforming system for a 0.1 W PEMFC. Won et al. [24] fabricated a micro channel reactor including a vaporizer, methanol steam reformer and combustor, to produce hydrogen for a PEMFC. Their results indicated that at a temperature of 270℃, the reformer could produce a hydrogen flow rate of 3.9 l/h for 5.5 W fuel cell. A plate fuel processor was developed by Sohn et al. [25] for a 150W PEM fuel cell system. The fuel processor includes reformer, combustor, heat exchanger, and evaporator and could be operated without any external heat supply.

For the PEM fuel cell, the CO concentration must be less than 10 ppm, so a cleanup step is required after methanol steam reforming. The integration of the PrOx or water-gas-shift reaction equipment to reduce the CO concentration in the gas from the methanol steam reformer has been used by several researchers [26, 27]. Kwon et al. [26] used silicon to fabricate a reformer and preferential oxidizer (PrOx) reactor. The reactor produced hydrogen to supply the fuel cell. The experimental results showed that the reformer generated 27 cm3/min of hydrogen and that the CO was totally removed from the gas by the PrOx device. When the fuel cell was operated at 0.6 V, the power density was 230 mW/cm2.

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8

The characteristics of fluid flow and heat transfer in micro channel cooling passages have been examined numerically by Liu [29]. Chiu et al. [30] and Chiu and Yan [31] developed numerical model to study mixed convection heat transfer in horizontal ducts and inclined ducts, respectively, with radiation effects. Massive amount of works on heat and mass transfer have focused mainly on parallel plate channel [32,33] and rectangular ducts [34]. Recently, the investigation of forced convection heat and mass transfer in vertical rectangular duct with film evaporation has been numerically examined by Boukadida and Nasrallah [35]. Analysis of chemical reaction coupled mass and heat transport phenomena in a reactor duct has been performed in the past decade [36-37]. The effects of catalyst loading and reformer geometry on the circular methane micro-reformer were studied numerically by Stutz et al. [36]. Yuan et al. [37] developed a model of the plate methane reformer, including the momentum equation, energy equation and chemical reaction equations to explore the temperature and gas distributions in the reformer ducts.

There are many research works about the developed catalysts used in the reforming reaction using different kinetics of the methanol steam reforming reactions [38-43]. Methanol can be reformed by two overall reactions in a reformer filled with the catalyst CuO/ZnO/Al2O3 as described by Amphlett et al.[38]. Peppley et al. [39, 40] studied the reaction network for methanol steam reforming over a Cu/ZnO/Al2O3 catalyst form BASF. The steam reforming of methanol over a Cu/ZrO2/CeO3 catalyst was investigated by Mastalir et al. [41]. The kinetic model suggested for the transformation involved the reverse water-gas shift and methanol decomposition, in addition to the steam reforming methanol reaction. Lee et al. [42] carried out a kinetic study of methanol steam reforming over a commercial catalyst CuO/ZnO/Al2O3.

Computational simulation and modeling are used extensively in research and industrial applications to obtain a better understanding of the fundamental processes and to optimize

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designs before building prototypes for engineering applications. Therefore, more theoretical modeling for study of the methanol reformer is in progress. Known from the literature survey, several numerical models have been presented, with the simplest methods using a one-dimensional model to describe the methanol reformer conversion and the heat and mass transport phenomena [43-47]. Kawamura et al. [43] proposed a mathematical heat and mass model to analyze the transport phenomena in the plane methanol steam reformer channels. They successfully simulated methanol conversion and gas concentration distributions along the channel. Kim and Kwon [44] have numerically investigated the inner transport phenomena in the plate methanol steam reformer ducts. The results indicated that a lower inlet feed rate has a better methanol conversion. Their results also showed that smaller reformer volumes required a higher heat flux. Pattekar and Kothare et al. [45] developed one-dimensional models for radial and micro channel methanol reformers. The results demonstrated that a radial flow reformer had better hydrogen production rates and lower pressure drops than the micro channels of a plate reformer. Stamps and Gatzke [46] developed a reformer with a model PEMFC to study various design and operating parameters on system performance. They found that agreement of the theoretical and experimental results for the temperature, flow rate and CO concentration data. The simplest model to describe the methanol reformer conversion and the heat and mass transport phenomena was presented by Yoon et al.[47]. The results showed that appropriate reactor geometry can improve the reactant gas transport and the efficiency of thermal management.

As for the two-dimensional simulation about the methanol reformers, the literature survey has existed in the past decade [48-51]. Suh et al. [48, 49] employed a cylindrical

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methanol conversion. The effects of the methanol steam reforming rate in both a packed bed reformer and a wall coated reformer were examined by Karim et al. [50, 51]. The results showed that a wall coated reformer had better heat and mass transfer limitations and higher catalyst activity than a packed bed reformer. Their results also showed that the minimum reformer diameter yielded the highest catalyst activity and smallest temperature gradient.

There are many three-dimensional simulations of methanol reformers in the literature [7, 19, 27, 52-57]. Kwon et al. [19] investigated the pressure and velocity distributions in the micro-reformer channels by using computational fluid dynamics (CFD). The results show the reformer of 17 parallel micro-channels has a much more uniform velocity distribution than that of 36 parallel micro-channels. A uniform velocity distribution may have a better chemical reaction. A three-dimensional model of a micro-scale reactor to investigate velocity and pressure distributions was developed by Pattekar and Kothare [52]. Kim and Kown [27] developed a novel reforming channel to study the pressure, velocity, temperature and hydrogen mole fraction distributions in the reformer. The results show that the novel flow field had better performance than the serpentine flow field. A cylindrical model of the reformer which comprised of a methanol steam reformer and a CO methanator to simulate the conversion and temperature distributions in the reformer was investigated by Cao et al. [53]. Their results showed that the appropriate insulation thickness could reduce the heat losses and achieve a small volume and a high power density. Park et al. [54] developed 3-D, quasi-3-D and 1D models to study reformer performance. There was good agreement between the experimental and analytical results. Cao et al. [55] presented kinetic rate expressions and developed a homogenous model of a micro channel reformer to simulate the temperature distributions in a micro channel. Hsueh et al. [56] employed a numerical channel model to analyze various height and width ratios on the plate micro-reformer performance and reactant gas transport characteristics. The results indicated that a reduction in aspect ratio would

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improve H2 production rate and methanol conversion. Chen et al. [57] used a mathematical model of the plate-type reformer to investigate the heat and mass transfer in a reformer. The results showed that the CO concentration could reduce with lower temperature, larger H2O/CH3OH molar ratio and aspect ratio. Kim [7] developed a micro-reformer model to simulate the conversion and temperature distributions in the reformer. The results revealed that the methanol conversion increased with increasing the reformer temperature and decreasing the feed rate.

More theoretical modeling of steam reforming coupled with catalytic combustion for the plate reactors is currently in progress. A reactor model that combines a steam reformer and catalytic combustor was recently examined by several researchers [58-67]. The systems are fed by hydrocarbons which convert the hydrogen and generate heat, and studies have developed numerical models of a micro-reformer with a combustor to explore the heat and mass transport phenomena and fuel conversion efficiency. A two-dimensional model of a plate methane reformer with methane combustor to investigate thermo-fluid parameters and geometric parameters was developed by Zanfir and Gavriilidis [58]. Their results showed that the micro-reformers have better performance than traditional reformers due to their better heat and mass transfer. The results also showed that a higher channel height produces a lower conversion and much more uniform temperature distribution. More theoretical modeling of steam reforming couples with catalytic combustion for the plate reactors are currently in progress. Lattner and Harold [59] have numerically and experimentally investigated a bench-scale fixed-bed methanol reformer for autothermal reforming. This system was also used by Pepply et al. [40] and Reitz [60] who presented kinetic rate expressions for the

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production. The results show that the H2 production rate and the temperatures generated via the C3H8 combustion both increase as the flow rate of ammonia increases. The results also show that the co-current flow configuration has a lower reactor temperature and allows a wider spectrum of materials to be used than the counter-current flow configuration. A micro-channel model of the thermal integration of a steam reformer and a catalytic combustor was established by Arzamendi and collaborators [63-64]. Using the hydrogen produced by the reforming reaction from methanol and methane, the results showed the short diffusion distance and higher area to volume ratio required for using the micro reactor. The results also indicated that complete combustion of methane takes place over a very short distance. The reforming fuel is rapidly heated and then the methane reactor has a more uniform temperature distribution. Pan and collaborators [65, 66] developed the numerical models for a plate-fin methanol steam reformer and a bench-scale methanol autothermal reformer. A plate-fin reformer integrated endothermic and exothermic reactions into one unit. The combustor supplied the heat for the methanol steam reformer. Their numerical model accurately predicted the methanol conversion rate and the gas distributions. Varesano et al. [67] used an one-dimensional transient mathematical model to study the transport behavior in a steam reforming reactor with a burner that supplies heat. The transient characteristics of the reformer were examined in detail.

The flow field design in a fuel cell is one of the most important issues for PEMFC. An appropriate flow field design in the fuel cell can improve the reactant transport, the thermal and water management. To this end, different flow field configurations, including parallel, serpentine and interdigitated have been developed. Many efforts have been devoted to optimize the flow field design to improve cell performance [68-71]. In recent years, several studies based on the flow field designs theory are applied to the plate methanol reformer design. Different types of flow field designs for plate methanol micro-reformers have been

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used to achieve more efficient methanol conversion. Kundu et al. [72] used different flow configurations, including serpentine and parallel flow fields, to improve plate methanol reformer performance.

1.3 Objectives

In the present study, the objective of this work is to investigate the transport phenomena and performance of the plate methanol steam micro-reformer (only including methanol steam micro-reformer and methanol catalytic combustor). Fig. 1-7 shows the structure of PhD thesis. The study is divided into five parts. Firstly, there have been various numerical studies of the fluid flow in plate methanol steam reformer channels [19, 52]. In order to simplify the analysis, many studies have considered the numerical model of methanol steam reformers, only including energy equation and concentration equations with chemical reaction [43-44, 46, 48-51, 53, 55]. Furthermore, the continuity equation, momentum equation, energy equation and species equations with chemical reaction were employed to explore the temperature and gas concentration distributions in the reformer by several researchers [7, 27, 54]. In this work, an attempt is made to examine the detailed fluid flow, heat and mass transfer coupled with chemical reactions in the plate methanol steam micro-reformer channels. Therefore, we develop a two-dimensional channel model of the plate methanol steam reformer to study the methanol conversion and local heat and mass transfer in the channel of a plate micro-reformer. The effects of geometric and thermo-fluid parameters on the plate methanol steam micro-reformer performance and the heat and mass transfer are numerically investigated in detailed.

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issues. Appropriate reactor geometry can improve the reactant gas transport and the efficiency of thermal management [36-37, 47, 50-51, 73-75]. As stated above literature survey, while many studies have investigated the effects of reactor radius on cylindrical reactor performance [36, 47, 50-51, 73-75], few studies have reported on the flow channel designs of plate methanol steam micro-reformers. Therefore, based on flow channel designs, various aspect ratios of channels on plate methanol steam micro-reformers can potentially enhance fuel utilization. In this work, flow channels with various aspect ratios (height and width ratios) and geometric size are numerically examined the transport phenomena in a channel reformer. In addition, the thermo-fluid parameters (Reynolds number and wall temperature) are also investigated to examine their effects on the methanol conversion and efficiency of channel reformers.

Thirdly, the literature cited above has shown that micro-reformer performance can be enhanced by suitable thermo-fluid parameters. However, several researchers have studied plate steam reformers with a parallel flow field which is attractive due to its simplicity [44, 56-57]. There has been a limited amount of work investigating the effects of the different flow field designs on thermo-fluid parameters, especially for the serpentine flow field. Therefore, the objective of this section is to establish a three-dimensional serpentine flow field model of the plate methanol steam micro-reformer to investigate its transport phenomena and methanol conversion efficiency.

Fourthly, from the literature survey presented above, it was found that some literature is available on mathematical models of the methanol steam micro-reformer, but little information is available on mathematical models of a micro-reformer with a catalytic combustor. Therefore, the objective of the present study is to investigate the transport phenomena and the fuel conversion efficiency in a methanol steam micro-reformer with methanol catalytic combustor. A three-dimensional numerical model of a micro-reformer with

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combustor is developed to examine the effects of various flow configurations and geometric parameters on micro-reformer performance.

Finally, from the literatures cited above, it is shown that the methanol conversion can be enhanced by a suitable flow channel design. However, there is only a limited amount of work to investigate the effect of different flow field designs on the performance especially for the serpentine flow field. Therefore, the objective of this section is to establish a three-dimensional computational model of the plate methanol micro-reformer with methanol catalytic combustor to investigate the performance and transport phenomena of the micro-reformer with various flow fields (parallel flow field and serpentine flow field). In this study, micro-reformer performance and gas transport phenomena can be accurately predicted from our simulation. Therefore, this model is useful and can be reduce the design time of a new plate methanol steam micro-reformer. Thus this can provide sufficient information for designing micro-reformer system.

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Table 1-1 Energy density of various batteries and fuels [1]

Fuel Energy density (Wh kg−1) Comments

BB-2590 81 Secondary

BA-5590 150 Primary

BA-5390 235 Primary

BA-8180 345 Primary Zn–Air battery, large unit Compressed hydrogen 500~1000 5000 psig, value includes container weight Sodium borohydride 3600 [NaBH4 +2H2O] weight only

Methanol 5500 Based on lower heating value of fuel Most liquid hydrocarbons ~12,400 Based on lower heating value of fuel

Hydrogen gas 33,200 Unpacked

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Table 1-2 Comparison of reforming technologies [4]

Technology Advantages Disadvantages

1. Most extensive industrial experience 1. Highest air emissions 2. Oxygen not required

3. Lowest process temperature Steam reforming

4. Best H2/CO ratio for H2 production

1. Lower process temperature than POX 1. Limited commercial experience Autothermal reforming

2. Low methane slip 2. Requires air or oxygen 1. Decreased desulfurization requirement 1. Low H2/CO ratio

2. No catalyst required 2. Very high processing temperatures Partial oxidaiton

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Fig. 1-1 Applications of the fuel cell (ERL/ITRI)

Micro fuel cells 1~50W

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Fig. 1-2 Photograph of the (a) small PEMFC and (b) micro-reformer [6]

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20 Vaporizer PrOx Steam reformer Combustor Heat CH3OH Cartridge H2O Cartridge Air Cathode Electrolyte Anode H2 Electricity Pump

Fuel reforming module Fuel cell module

H2O

Target of present study

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Fig. 1-4 Photograph of the plate methanol steam micro-reformer [7]

(a) (b)

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22 Catalytic Combustor Methanol Reformer CO remover Vaporizer 1 Vaporizer 2

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CHAPTER 2

MATHEMATICAL MODEL AND ANALYSIS

2.1 The Model of the Methanol Steam Micro-Reformer

2.1.1 Model Description

In this section, the research only considered the plate methanol steam micro-reformer, namely the methanol catalytic combustor is not included in it. Firstly, a 2-dimensional channel model of the plate methanol steam micro-reformer would be established to study the methanol conversion and local heat and mass transfer in the channel of a plate methanol steam micro-reformer. Figure 2-1 presents a schematic of the two-dimensional channel geometry of the plate methanol steam micro-reformer used in the present work.

Then, the research extended my previous study to be a three-dimensional channel model of the plate methanol steam micro-reformer to analyze the local transport phenomena and micro-reformer performance. The channel is comprised of the flow channel, catalyst layer and solid wall. The governing equations include mass, momentum, energy and species equations. To reduce the computing time, the symmetric channel is considered only in this work. The schematic diagram of this work is shown in Fig. 2-2.

Finally, a three-dimensional computational model of heat and mass transfer in a micro-reformer with a serpentine flow field is proposed. The serpentine flow field has eight turns. A schematic illustration of the coordinate system is shown in Fig. 2-3. The channel of

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2.1.2 Assumption

To simplify the analysis, the following assumptions are made: (1) The flow is steady state;

(2) The inlet fuel is an ideal gas;

(3) The flow is laminar and incompressible; (4) The catalyst layer is isotropic;

(5) The chemical reaction occurs only in the catalyst layer;

(6) Thermal radiation and conduction in the gas phase are negligible compared to convection.

2.1.3 Governing Equations

According to the descriptions and assumptions above, the basic transport equations for the two-dimensional and three-dimensional plate methanol steam micro-reformer are as follows: Continuity equation: u v w 0 x y z ∂ ++= ∂ ∂ ∂ (2-1) X-momentum equation: 2 2 2 u 2 2 2 u u u p u u u u v w S x y z x x y z ⎛ ⎞ ⎛ ∂ ∂ ∂ ⎞ ∂ ∂ ∂ ∂ ερ + + = −ε + εμ + + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ (2-2) Y-momentum equation: 2 2 2 v 2 2 2 v v v p v v v u v w S x y z y x y z ⎛ ⎞ ⎛ ∂ ∂ ∂ ⎞ ∂ ∂ ∂ ∂ ερ + + = −ε + εμ + + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ (2-3) Z-momentum equation:

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2 2 2 w 2 2 2 w w w p w w w u v w S x y z z x y z ⎛ ⎞ ⎛ ∂ ∂ ∂ ⎞ ∂ ∂ ∂ ∂ ερ + + = −ε + εμ + + + ∂ ∂ ∂ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ (2-4)

In the momentum equations, ε is the porosity of the medium. Su, Sv and Sw are corrected terms for the reactant gas flow in the porous material of the catalyst layer of the micro-reformer. The Su, Sv and Sw are zero in the flow channel region. While in the catalyst layer, Su, Sv and Sw are different in each computation domain due to the difference in pressure when fluids pass through a porous medium. So, Su, Sv and Sw in the catalyst layer are [76]:

2 2 2 u p u u S u v w k 2 μ β ρ = − − + + (2-5) 2 2 2 v p v v S u v w k 2 μ β ρ = − − + + (2-6) 2 2 2 w p w w S u v w k 2 μ β ρ = − − + + (2-7)

where kp is the permeability and β is the inertial loss coefficient in each component direction[76]. 2 3 p p 2 D k 150(1 ) ε = − ε (2-8) 3 p 3.5(1 ) D − ε β = ε (2-9)

and where Dp is the catalyst particle diameter.

The viscosity of the gas mixture can be calculated from Wilke’s mixture rule [77] as follows:

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28 2 1 1 2 4 w, j i j w,i ij 1 i 2 w,i w, j M 1 M M 8 1 M ⎡ ⎞ ⎛ ⎤ ⎞ μ ⎢ + ⎜ ⎟ ⎜ ⎥ ⎢ ⎜μ ⎟ ⎜ ⎥ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦ φ = ⎡ ⎛ ⎞⎤ + ⎢ ⎜⎥ ⎢ ⎝ ⎠⎥ ⎣ ⎦

(2-11) Species equation: 2 2 2 i i i i i i eff 2 2 2 S c m m m m m m u v w D (1 ) S x y z x y z ⎛ ⎞ ⎛ ∂ ++ ∂ ⎞=+++ − ε ρ ⎜ ⎟ ⎜ ⎝ ⎠ ⎝ ⎠ (2-12)

In the species equation, mi denotes the mass fraction of the ith species; the calculations have included CH3OH, H2O, H2, CO2 and CO. In this work, the porosity ε is expressed as 0.38 and 1.00, in the catalyst layer and the flow channel, respectively. In Eq(2-12), Deff is the effective diffusion coefficient based on the Stefan-Maxwell equations [51]. Eq(2-13) is employed to describe the influence of the porosity on the diffusion coefficient

eff k

D =D ε τ (2-13)

The diffusion coefficient Dk for the methanol steam micro-reformer was derived from the Stefan-Maxwell equations which were used to calculate the mean effective binary diffusivity [51].

Sc represents the source terms due to the chemical reaction in the catalyst layer. Therefore, Sc is zero in the flow channel. Furthermore, Sc differs according to the reactant gases in the catalyst layer.

'' ' c w,i SR rWGS i i S =M (R +R )(λ − λ ) (2-14) where ' i λ and " i

λ are the stoichometric coefficient for reactant i and product i, respectively, in the reaction.

According to the chemical kinetics of Hotz et al. [78], the steam reforming reaction is much faster than the decomposition and water-gas shift reaction. Purnama et al. [79] and

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Agrell et al. [80] proposed that using a Cu/ZnO/AlO3 catalyst for methanol steam reforming gives rise to two main chemical reactions, the steam reforming and the reverse water gas shift reactions. They also indicated that CO was generated by the reverse water gas shift reaction. Therefore, only the steam reforming reaction, Eq. (2-15), and the reverse water-gas shift reaction, Eq. (2-16), are considered in this study.

1 k 3 2 2 2 CH OH H O+ ⎯⎯→CO +3H (2-15) 2 2 k 2 2 k 2 CO H CO H O − + ←⎯⎯→ + (2-16)

In this study, the model for methanol steam reforming is that used by Hsueh and collaborators [56, 57], and the Arrhenius equation is used to calculate the concentration of reactant gases generated by the chemical reaction.

3 2 0.6 0.4 a SR 1 CH OH H O E R k C C exp( ) RT = − (2-17) 2 2 2 a a rWGS 2 CO H 2 CO H O E E R k C C exp( ) k C C exp( ) RT − RT = − − − (2-18)

where the steam reforming reaction is a non-reversible reaction and the reverse water-gas shift reaction is reversible. The constants k1 and k2 are the forward rate constants for the steam reforming reaction and the reverse water-gas shift reaction, respectively. The constant k-2 is the backward rate constant for the water-gas shift reaction.

To calculate the local temperature, the energy equations must be solved. Energy equation: 2 2 2 p eff 2 2 2 t T T T T T T c u v w k S x y z x y z ⎛ ⎞ ⎛ ∂ ∂ ∂ ⎞ ∂ ∂ ∂ ρ + + = + + + ε ∂ ∂ ∂ ∂ ∂ ∂ ⎝ ⎠ ⎝ ⎠ (2-19)

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30

eff f s

k = ε + − εk (1 )k (2-20) where kf is the fluid phase thermal conductivity, ks the solid medium thermal conductivity and ε the porosity of the medium.

In the energy equation, St is the source term due to the chemical reactions, which in the channel is zero. The catalyst layer experiences exothermic and endothermic chemical reactions, so St can be described as:

t SR SR rWGS rWGS

S = − Δ( H R + ΔH R ) (2-21) where ΔHSR is the enthalpy of reaction of the steam reforming reaction, and ΔHrWGS is the enthalpy of reaction of the reverse water-gas shift reaction.

In the solid regions, the energy transport equation can be written as

2 2 2 2 2 2 T T T 0 x y z ∂ ++= ∂ ∂ ∂ (2-22)

2.1.4 Boundary Conditions

The boundary conditions of the present computation include those at the inlet, outlet, wall, and the interfaces between the flow channel and the catalyst layer.

(1) The boundary conditions for inlets at the flow channel and the catalyst layer: The inlet flow velocity is constant, the inlet gas composition is constant, and the inlet temperature is constant.

(2) The boundary conditions for outlets at the flow channel and the catalyst layer: The gauge pressure is zero.

(3) The boundary conditions for the interface between the solid wall and the insulated walls: The temperature gradients are zero.

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walls: The velocities, temperature, temperature gradient, species concentration and species flux are zero.

(5) The boundary conditions for the interface between the flow channel and solid wall. No slip and zero fluxes hold the velocities and the concentration gradients at zero. (6) The boundary conditions for the interface between the flow channel and the catalyst

layer: The velocities, temperature, species concentration and species flux are continuous.

(7) The boundary conditions for the interface between the heated wall and the catalyst layers: The velocities and the concentration gradient are assumed to be zero, and the temperature is assumed to be equal to the constant wall temperature.

2.2 The Model of a Plate Methanol Steam Micro-Reformer with Methanol

Catalytic Combustor

2.2.1 Model Description

In order to simplify the multifarious changes due to the wall temperature variation, the model above did not consider the wall thermal boundary condition to be a non-uniform temperature. To keep everything isothermal there must be a continual input of heat because the reaction is endothermic. However, in actual experimental operations, a key design consideration for the reformer is how to supply the heat for the reaction. The supply of heat will result in a non-uniform temperature along the length of the flow channel. The heat consumed by the reaction will cause the temperature to decrease near the inlet of the channel

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32

which is probably the most important results we could obtain from the reactor analysis. Consequently, a methanol steam micro-reformer with a methanol catalytic combustor would be considered in order to simulate the characteristics of the non-uniform temperature along the channel. Now, a reactor model with consideration of the methanol steam micro-reformer and methanol catalytic combustor has been developing.

This study extends the established 3-dimensional channel model of methanol steam micro-reformer to a reactor channel model with consideration of the methanol steam micro-reformer and methanol catalytic combustor in 3-dimensional model. The reactor consists of a methanol steam micro-reformer and a methanol catalytic combustion chamber. A schematic diagram of the physical system under consideration is shown in Fig. 2-4. The system consists of the solid wall, two catalyst layers and two flow channels each at the catalytic combustion/steam reforming side. It is seen that the methanol catalytic combustion chamber and the methanol steam reforming chamber are separated by a solid wall. Both sides of each channel are coated with a combustion catalyst layer and a steam reforming catalyst layer. The heat from the combustion reaction is used to drive the steam reforming reaction.

Next, the three-dimensional computational models with various flow fields have been established for methanol steam micro-reformer with methanol catalytic combustor. The flow fields in the methanol steam micro-reformer and methanol catalytic combustor include the parallel flow field and the serpentine flow field. The parallel flow field has five parallel channels and the serpentine flow field has one channel with four turns. A schematic illustration of these flow fields and associated coordinate system are shown in Fig. 2-5. The parallel flow field has five flow channels and each channel is 40mm in length. The serpentine flow field has one flow channel, the total flow channel length is five times the length of a channel in the parallel flow field, and there are four turning points. In this study, constant flow rate approach is utilized to investigate the effect of flow field on the performance of

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micro-reformer. The u, v, and w are the velocity components in the x-, y -, and z-directions, respectively. The reactor consists of the solid wall, a steam reforming flow channel, a steam reforming catalyst layer, a catalytic combustion catalyst layer and a catalytic combustion flow channel.

2.3.2 Assumption

To simplify the analysis for the present study, the flowing assumptions are made: (1) The flow is steady state;

(2) The inlet fuel is an ideal gas;

(3) The flow is laminar and incompressible; (4) The catalyst layer is isotropic;

(5) The chemical reaction occurs only in the catalyst layer;

(6)Thermal radiation and conduction in the gas phase are negligible compared to convection.

2.3.3 Governing Equations

With the above assumptions, the gas transport equations for the three-dimensional reactor can be described as follows.

Continuity equation:

u v w

0

++=

數據

Fig. 2-1 Schematic diagram of the two-dimensional channel model of a plate methanol steam  micro-reformer
Fig. 2-2 Schematic diagram of the three-dimensional channel model of a plate methanol steam  micro-reformer
Fig. 2-4 Schematic diagram of the three-dimensional channel model of a plate methanol steam  micro-reformer with methanol catalytic combustor
Fig. 2-5 (a) Schematic diagram of a plate methanol steam micro-reformer with methanol
+7

參考文獻

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