1

PROCESS DESIGN AND OPTIMIZATION OF SOLID OXIDE FUEL CELLS AND PRE-REFORMER SYSTEM UTILIZING LIQUID HYDROCARBONS

By

TAE SEOK LEE

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

2008

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© 2008 Tae Seok Lee

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To my beloved wife and son

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ACKNOWLEDGMENTS

This research project would not have been possible without the support of many people. I

wish to express my gratitude to my supervisor, Dr. Chung, who was abundantly helpful and

offered invaluable assistance, support and guidance. Deepest gratitude also goes to the members

of the supervisory committee, Dr. Sherif and Dr. Ingley. Without their knowledge and assistance

this study would not have been successful.

Special thanks also go to all my colleagues and graduate friends, especially group member,

Yun Whan Na for invaluable advice and my contemporaries; Minki Hwang, Jung Hwan Kim,

Sung Jin Lee, and Gun Lee. Not forgetting to my bestfriends as well as UFMAEKR members

who always been there. Finally but not least, I would like to express my love and gratitude to my

beloved families; for their understanding and endless love, through the duration of my studies.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS ...............................................................................................................4

LIST OF TABLES...........................................................................................................................7

LIST OF FIGURES .........................................................................................................................8

ABSTRACT.....................................................................................................................................9

CHAPTER

1 INTRODUCTION AND BACKGROUND ...........................................................................11

Steam Reforming Reaction.....................................................................................................11 Solid-Oxide Fuel Cells ...........................................................................................................11 Chemical Reaction Equilibrium .............................................................................................12

Stoichiometry and Extent of Reaction.............................................................................12 Chemical Reaction Equilibrium and Equilibrium Constant............................................13

2 THERMODYNAMIC MODEL .............................................................................................16

Introduction.............................................................................................................................16 Assumption .............................................................................................................................17 Thermodynamic Properties of Chemical Species...................................................................17

Justification for Ideal Gas Assumption ...........................................................................17 Heat Capacity ..................................................................................................................18 Heat Capacity for Fuel (n-Dodecane)..............................................................................18

Molar Balance.........................................................................................................................19 Chemical Equilibrium at the Pre-Reformer.....................................................................19 SOFC Model....................................................................................................................20 Recycle Ratio...................................................................................................................22

Energy Balance.......................................................................................................................23

3 RESULTS AND OPTIMIZATION........................................................................................31

Results.....................................................................................................................................31 Chemical Equilibrium at Pre-Reformer and Optimum Pre-Reformer Temperature .......31 Fuel and Oxygen Consumption Results without Recirculation and CO2 Capture ..........31 Recycle Ratio and Water Management ...........................................................................32 Energy Balance and Efficiency Results without Recirculation and CO2 Capture ..........32 Carbon Dioxide Capture Effects .....................................................................................34 Recirculation Effects .......................................................................................................35

Optimization ...........................................................................................................................35

4 SUMMARY AND CONCLUSION .......................................................................................60

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LIST OF REFERENCES...............................................................................................................62

BIOGRAPHICAL SKETCH .........................................................................................................63

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LIST OF TABLES

Table page 1-1 Types of fuel cells, their characteristics.............................................................................15

2-1 Critical and reduced temperature and pressure..................................................................28

2-2 Heat capacities of gases in the ideal-gas state ...................................................................29

2-3 Coefficients for dodecane heat capacity in the ideal-gas state ..........................................30

3-1 Overall molar balance results.............................................................................................57

3-2 Dependency on CO2 adsorption percentage and recirculation ratio ..................................58

3-3 Maximum overall efficiencies for given SC and TSOFC with corresponding recirculation ratio and CO2 capture percent.......................................................................59

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LIST OF FIGURES

Figure page 2-1 Process flow diagram.........................................................................................................26

2-2 Effect of number of transfer units, NTU, on the effectiveness, ε, with several heat capacity ratios, Cr, for crossflow and both fluids mixed heat exchanger ..........................27

3-1 Reaction equilibrium results for steam reforming and water-gas shift reaction for several steam to carbon ratios ............................................................................................37

3-2 Produced hydrogen per consumed energy .........................................................................38

3-3 Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratio, where no CO2 capture and no recirculation..............................................................40

3-4 Effect of SOFC temperature on oxygen consumption rate with different steam to carbon ratio, where no CO2 capture and no recirculation..................................................41

3-5 AOG recycle percent versus SOFC temperature with different steam to carbon ratio, where no CO2 capture and no recirculation .......................................................................42

3-6 Effect of SOFC temperature on additional heat transferred rate for pre-reformer unit with different steam to carbon ratio, where no CO2 capture and no recirculation.............43

3-7 Effect of SOFC temperature on detailed additional heat transferred rate for pre-reformer unit with S/C =4, where no CO2 capture and no recirculation............................44

3-8 Effect of SOFC temperature on efficiency based on LHV with different steam to carbon ratio, where no CO2 capture and no recirculation..................................................45

3-9 Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratios and several CO2 adsorption percents, where no recirculation .................................46

3-10 Carbon dioxide capture effects on the depleted fuel consumption fraction for the several steam to carbon ratios, where no recirculation ......................................................47

3-11 Effect of SOFC temperature on fuel consumption rate with different steam to carbon ratio and several recirculation ratio, where no CO2 adsorption .........................................48

3-12 Recirculation effects on the depleted fuel consumption fraction for the several steam to carbon ratios, where no CO2 adsorption ........................................................................49

3-13 Efficiency based on LHV of fuel .......................................................................................50

3-14 Effects of SOFC temperature and SC on maximum system efficiency.............................56

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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

PROCESS DESIGN AND OPTIMIZATION OF SOLID OXIDE FUEL CELLS AND PRE-

REFORMER SYSTEM UTILIZING LIQUID HYDROCARBONS

By

Tae Seok Lee

December 2008 Chair: Jacob N. Chung Major: Mechanical Engineering

We conducted optimization for a flow process consisting of a typical direct internal

reforming Solid Oxide Fuel Cell (SOFC) utilizing synthesis gas (syngas) produced through

steam reforming of the liquid hydrocarbon inside the external reforming unit. The anode off gas

recycling system and after-burner unit are introduced to maximize its efficiency. The mass and

energy balance analysis for the whole system has been carried out. Mass balance (or molar

balance) analysis includes optimization for minimum fuel and oxygen consumption rates

corresponding to the temperatures of pre-reformer and SOFC, the steam to carbon ratio inside

the pre-reformer, recirculation ratio, and rate of CO2 capture. Studies on the reforming chemical

reactions and chemical equilibria are presented. The results include CO2 adsorption in the

adsorbent bed as well as recirculation. For the molar balance study, we provided dodecane

consumption rate and overall molar balance results. With the energy balance analysis, the

temperature distributions in the system are calculated by means of solving energy balance for

each device. However, energy is not perfectly balanced. So, another heat effect is introduced on

the pre-reformer unit. This could be either heat surplus or insufficient heat depending on SOFC

temperature. The temperature, which makes heat balanced without newly introduced heat effect

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on pre-reformer, is named as self-energy balanced operating temperature. It have been

investigated the total system efficiency based on the first law of thermodynamics. The overall

efficiency is defined as the total net power output divided by the lower heating value rate of fuel

input. Considering net power output, produced electrical work should reimburse insufficient heat

on the pre-reformer. It is also provided optimal case operating parameters. Thermodynamic

efficiency is mainly affected by CO2 adsorption percentage under low steam to carbon ratio

region, while efficiency is mainly affected by the recirculation rate under high temperature

operation. In accordance with simulation, recommend operating conditions are SC =2, 800 oC

SOFC temperature, 550 oC Pre-Reformer temperature, 0.35 recirculation ratio and 25% carbon

dioxide adsorption yielding the highest efficiency as 74.79%.

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CHAPTER 1 INTRODUCTION AND BACKGROUND

Steam Reforming Reaction

The catalytic conversion of hydrocarbons with water steam is one of the most widely used

industrial methods for production of hydrogen-containing gases. The first industrial steam

reformer was installed at Baton Rouge by Standard Oil of New Jersey and commissioned in 1930.

Steam reforming is an essential process in the manufacture of synthesis gas (syngas) and

hydrogen from hydrocarbons [1, 2].

Solid-Oxide Fuel Cells

A fuel cell is an electrochemical energy conversion device that converts chemical energy

of fuel directly into electricity, promising power generation with high efficiency and low

environmental impact. Because the intermediate steps of producing heat and mechanical work

are avoided, fuel cells are not limited by thermodynamic limitations of heat engines such as the

Carnot efficiency. A fuel cell is similar to a battery in aspects that both have an electrolyte, and

negative and positive electrodes, and generate DC electricity through electrochemical reactions.

However, fuel cells continuously consume reactant, which must be replenished, whereas

batteries generate electricity by depleting materials in electrodes inside the batteries. Because of

this, batteries may be discharged, whereas fuel cells cannot be discharged as long as the reactants

are supplied [3, 4]. Fuel cells can be categorized by the type of electrolyte used in the cells:

• Polymer Electrolyte Fuel Cell (PEFC) • Alkaline Fuel Cell (AFC) • Phosphoric Acid Fuel Cell (PAFC) • Molten Carbonate Fuel Cell (MCFC) • Solid Oxide Fuel Cell (SOFC) Table 1-1 provides an overview of the key characteristics of the main fuel cell types.

Solid oxide fuel cells (SOFCs) have an electrolyte that is a solid, non-porous metal oxide.

The cell is constructed with two porous electrodes that sandwich an electrolyte. Air (or oxygen)

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flows along the cathode. When an oxygen molecule contacts the cathode/electrolyte interface, it

acquires electrons from the cathode. The oxygen ions diffuse into the electrolyte material and

migrate to the other side of the cell where they contact the anode. The oxygen ions encounter the

fuel at the anode/electrolyte interface and react catalytically, giving off water, carbon dioxide,

heat, and electrons. The electrons transport through the external circuit, providing electrical

energy [4].

Chemical Reaction Equilibrium

Stoichiometry and Extent of Reaction

The general chemical reaction may be written

1 1 2 2 3 3 4 4M M M Mν ν ν ν+ + → + + (1-1)

where |νi| is a stoichiometric coefficient, positive sign for a product and negative sign for a

reactant, and Mi stands for a chemical species i. As the reaction represented by Eq. (1-1)

progresses, the changes in the numbers of moles of species Mi, dni, are in direct proportion to the

stoichiometric numbers. Introducing variable ε, called the extent of reaction or progress variable,

it is possible to represent an amount of reaction. The general relation connecting the differential

change dni with dε is therefore:

or ii ii

dndn d dν ε εν

= = (1-2)

Integration of Eq. (1-2) from an initial un-reacted state to a state reached after an arbitrary

amount of reaction gives:

or iio

n

i i i io in odn d n n

εν ε ν ε= = +∫ ∫ (1-3)

The molar fractions of the species i, yi, are as follows:

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i io iii io i

i i i

n ny

n nν εε ν

+= =

+∑ ∑ ∑ (1-4)

Equation (1-4) represents molar fraction of the i-th species for an arbitrary amount of reaction.

However, in general, two or more independent chemical reactions occur simultaneously. So,

subscript j serves as the reaction index. The general equation analogous to Eq. (1-3) is as follow:

,i i j jj

dn dν ε=∑ (1-5)

where νi,j denotes the stoichiometric number of species i in reaction j. The number of moles of i-

th species may change because of several reactions, identified by subscript j. This is why Eq.

(1-5) contains summation for j. Integration of Eq. (1-5) from an initial un-reacted state to a state

reached after an arbitrary amount of reaction gives:

,i io i j jj

n n ν ε= +∑ (1-6)

Therefore, molar fraction of the i-th species in progress of multireaction can be expressed as

follow

,

,

io i j jji

ii

io i j jii j i

nny

n n

ν ε

ν ε

+= =

⎛ ⎞+ ⎜ ⎟

⎝ ⎠

∑∑ ∑ ∑ ∑

(1-7)

Chemical Reaction Equilibrium and Equilibrium Constant

Consider a closed system containing an arbitrary number of species and comprised of an

arbitrary number of phases in which the temperature and pressure are uniform. Combining the

first law with the second law of the thermodynamics yields

( ),

0 or 0t t t tT P

dU PdV TdS dG+ − ≤ ≤ (1-8)

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where superscript t denotes total properties of the system. This equation (1-8) represents that all

irreversible processes occurring at constant temperature and pressure proceed in such a direction

as to cause a decrease in the Gibbs energy of the system.

For the single-phase, open system, mixture, the total Gibbs energy (nG or Gt) of the system

becomes a function is the numbers of moles of the chemical species as well as pressure and

temperature. And its total differential is as follow

( ) ( ) ( ) i ii

d nG nV dP nS dT dnµ= − +∑ (1-9)

where µi is the chemical potential of species i in the mixture defined by

( )

, , j

ii P T n

nGn

µ⎡ ⎤∂

= ⎢ ⎥∂⎣ ⎦ (1-10)

Substituting Eq. (1-2) into Eq. (1-9) gives

( ) ( ) ( ) i ii

d nG nV dP nS dT dν µ ε= − +∑ (1-11)

The right hand side of Eq.(1-11), is an exact differential expression; whence,

( ) ( ), ,

t

i ii T P T P

GnGν µ

ε ε

⎡ ⎤∂⎡ ⎤∂⎢ ⎥= =⎢ ⎥∂ ∂⎢ ⎥⎣ ⎦ ⎣ ⎦

∑ (1-12)

Considering Eq. (1-8), a criterion of chemical reaction equilibrium is therefore:

0i iiν µ =∑ (1-13)

By assuming the equilibrium mixture behaves as an ideal gas, Eq. (1-13) becomes

( ) expi i

i ii

oi i

ii o o

i

GP Py KP RT P

ν νν

ν− −⎛ ⎞−∑ ∑⎛ ⎞ ⎛ ⎞⎜ ⎟= =⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎜ ⎟⎝ ⎠

∑∏ (1-14)

This expression is also the definition of the equilibrium constant, K [5, 6].

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Table 1-1. Types of fuel cells, their characteristics

PEFC AFC PAFC MCFC SOFC

Electrolyte

Hydrated Polymeric Ion

Exchange Membranes

Mobilized or Immobilized Potassium

Hydroxide in asbestos matrix

Immobilized Liquid

Phosphoric Acid in SiC

Immobilized Liquid Molten

Carbonate in LiAlO2

Porovskites (Ceramics)

Electrodes Carbon Transition metals Carbon Nickel and

Nickel Oxide

Perovskite and

perovskite / metal cermet

Catalyst Platinum Platinum Platinum Electrode material Electrode material

Interconnect Carbon or metal Metal Graphite Stainless steel

or Nickel

Nickel, ceramic, or

steel

Operating Temperature 40 – 80 °C 65 – 220 °C 205 °C 650 °C 600–1000 °C

Charge Carrier H

+ OH− H+ CO32− O2−

External Reformer HC Yes Yes Yes

No, for some fuels

No, for some fuels and cell

designs

External shift conversion of CO to H2

Yes, plus purification to remove trace

CO

Yes, plus purification to

remove CO and CO2

Yes No No

Prime Cell Components Carbon-based Carbon-based

Graphite-based

Stainless-based Ceramic

Product Water Management

Evaporative Evaporative Evaporative Gaseous Product Gaseous Product

Product Heat Management

Process Gas + Liquid

Cooling Medium

Process Gas + Electrolyte Circulation

Process Gas + Liquid cooling

medium or steam

generation

Internal Reforming + Process Gas

Internal Reforming + Process Gas

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CHAPTER 2 THERMODYNAMIC MODEL

Introduction

The molar balance including chemical equilibrium is considered. After evaluating molar

composition of each steam, energy balance is solved for each device. Figure 2-1 shows the

process flow diagram which consists of recirculated direct internal reforming SOFC, pre-

reforming unit, recuperator, carbon dioxide adsorbent, pre-heater, flue gases condenser and

Anode off gas (AOG) recycling system. The AOG has, generally, high water content due to the

fact that water is only product of the electrochemical reaction which produces electrical power in

a SOFC. With appropriate AOG recycle, it is possible to maintain steam to carbon ratio (SC) as

preset value. If AOG does not contain enough water, water should be added with fuel to keep the

desired steam to carbon ratio. It is obvious that AOG compressor is required for this AOG

circulation system. From thermodynamics point of view, high temperature compressing process

requires more work than low temperature compression. Therefore, AOG should be cooled down

before the compressing process. After compressed, temperature of AOG is recuperated passing

through a heat exchanger. Un-recycled AOG is burned at the after-burner, instead of venting, on

purpose to not only provide heat to the reformer but also prevent wasting useful gases such as

hydrogen. Flue gases from after-burner could be used to heat up mixture of fuel and recycled

AOG or oxygen flows by passing through fuel pre-heater and/or condenser. As shown in Figure

2-1, each stream is labeled in two letters with combination of letter and number corresponding to

its molar composition and temperature. The first letter denotes molar composition or

concentration, while the second letter denotes temperature. Therefore, streams 1a and 1b are the

same molar composition but in different temperature.

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Assumption

The following assumptions are made in the analysis:

• Steady state operation

• All gaseous phases are ideal gas.

• Gas mixture at the exit is at chemical and thermal equilibrium.

• All devices are assumed perfect insulation.

• Fuel or hydrocarbon is reacted with water vapor and produces only carbon monoxide and hydrogen.

• Only hydrogen is electrochemically reacted inside SOFC.

• Pressure drop is ignored on calculation of molar balance or chemical equilibrium. This means pressure effect is ignored on equilibrium constant.

• Complete combustion occurs at the after-burner. So, it is assumed that flue gases consist of carbon dioxide, water vapor and excess oxygen.

• Temperature increase in compression process is neglected.

• 85% fuel utilization at the SOFC

• 85% of enthalpy change for electrochemical reaction is converted into electrical work instead of taking into account voltage losses consisting of activation, ohmic (or resistive), and concentration polarization.

Thermodynamic Properties of Chemical Species

Justification for Ideal Gas Assumption

As mentioned in assumption section, all gases are assumed as the ideal gases. This

condition should be justified before evaluating thermodynamic properties of chemical species. It

is well-known that all gases and vapors approach ideal-gas behavior under the low density

condition. At higher densities the behavior may deviate substantially from the ideal-gas equation

of state. By introducing compressibility factor, Z, this ambiguousness, low density, condition

could be cleared. Compressibility factors Z for different chemical species exhibit similar

behavior when correlated as a function of reduced temperature, Tr, and reduced pressure, Pr.

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Critical temperature and pressure as well as reduced temperature and pressure data are provided

in Table 2-1. Reduced temperatures in the Table 2-1 are evaluated at the lowest temperature, T2b,

in the process flow diagram. If the pressure is very low (that is, Pr 2), the ideal-gas model can be assumed with good accuracy to reduced

pressures as high as four or five [5, 6]. As shown in Table 2-1, reduced pressures are

significantly small, Pr ~ 10−2, so ideal gas assumption is reliable.

Heat Capacity

In this work, the empirical equation for heat capacity as a function of the temperature is

used. This relationship is as follow,

2 2PC A BT CT DTR

−= + + + (2-1)

where either C or D is zero, depending on the substance considered and T is in Kelvin. Equation

(2-1) is applied for Hydrogen, Water vapor, Methane, Carbon Monoxide and Carbon Dioxide.

The coefficients are presented in the Table 2-2 [5]. This empirical relationship is valid from

room temperature (298.15 K) to Tmax presented in Table 2-2.

Heat Capacity for Fuel (n-Dodecane)

The specific heat of dodecane is interpolated into 3rd order polynomial, Eq. (2-2), using

data achieved by Lemmon and Huber [7] and Span and Wagner [8].

2 3PC A BT CT DTR

= + + + (2-2)

Interpolation result is presented in Table 2-3.

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Molar Balance

Chemical Equilibrium at the Pre-Reformer

As shown in Fig. 2-1, pre-reformer unit consists of external reformer and after-burner. Pre-

heated mixture of fuel and recycled AOG is passing through reforming channel of the external

reformer. In the presence of catalysis, steam reforming reactions and water-gas shift (WGS)

reaction, which are shown in Eqs. (2-3)-(2-5), occur and find chemical equilibrium under the

given temperature and pressure [9].

4 2 23CH H O CO H+ ↔ + (2-3)

2 2 2CO H O H CO+ ↔ + (2-4)

4 2 2 22 4CH H O CO H+ ↔ + (2-5)

Reforming reactions (2-3) and (2-5) are strongly endothermic, so the forward reaction is

favored by high temperature, while the water-gas shift reaction (2-4) is exothermic and is

favored by low temperature. The overall reaction is endothermic, so heat should be supplied into

reforming channel in two ways; the sensible heat of AOG from SOFC and combustion heat from

the after-burner. Let the extents of reaction, which are defined as Eq. (1-5), be εR1, εR2, and εR3

for chemical equilibrium reactions (2-3), (2-4), and (2-5), respectively. Then equilibrium molar

fractions are expressed as follows;

22

, 1 2 3

1 3

22 2

o H O R R RH O

o R R

Fy

Fε ε εε ε

− − −=

+ + (2-6)

44

, 1 3

1 32 2o CH R R

CHo R R

Fy

Fε ε

ε ε− −

=+ +

(2-7)

22

, 1 2 3

1 3

3 42 2

o H R R RH

o R R

Fy

Fε ε εε ε

+ + +=

+ + (2-8)

20

, 1 21 32 2

o CO R RCO

o R R

Fy

Fε εε ε+ −

=+ +

(2-9)

22

, 2 3

1 32 2o CO R R

COo R R

Fy

Fε ε

ε ε+ +

=+ +

(2-10)

where, Fo and Fo,i denote inlet total molar flow rate, label 3b, and inlet molar flow rate of i

component, respectively. Once extents of reaction are obtained, evaluation of the equilibrium

molar fraction is straightforward. Therefore, one needs three equations to be solved

simultaneously to find εR1, εR2 and εR3 under equilibrium condition. These are the chemical

equilibrium equations corresponding to the steam reforming and water-gas shift reaction, as

following;

( ) 24 2

2 31

1 expH CO R

R oCH H O

y y GpK Tp y y RT

⎛ ⎞ −∆⎛ ⎞= =⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

(2-11)

( ) 2 22

0

22 exp

H CO RR o

H O CO

y y GpK Tp y y RT

⎛ ⎞ −∆⎛ ⎞= =⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

(2-12)

( ) 2 22 4

2 43

3 2 expH CO R

R oH O CH

y y GpK Tp y y RT

⎛ ⎞ −∆⎛ ⎞= =⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

(2-13)

The temperature dependent equilibrium constant is solved by the classical method in which

the change in Gibbs free energy of the reactions is used. After Gibbs energy difference obtained,

equilibrium molar fractions, Eqs. (2-6)-(2-10), are substituted into Eqs. (2-11)-(2-13) and then

the system of equations is solved by Newton-Rahpson method with 10−7 tolerance [10].

SOFC Model

In this work, direct internal reforming SOFC model is based on achievement done by

Colpan et al. [11]. The steam reforming reaction for methane, Eq. (2-3), water-gas shift reaction,

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Eq.(2-4), and electrochemical reaction, Eq.(2-14), occur simultaneously at the direct internal

reforming SOFC.

2 2 212

H O H O+ → (2-14)

The extent of reaction for electrochemical reaction, εS3, can be expressed using molar

balance, definition of molar fraction, and recirculation ratio [11].

( )2, 1 2

3

3

1o H S S

S

U F

r rU

ε εε

+ +=

− + (2-15)

Here, r is the recirculation ratio, U is fuel utilization, εSi is reaction coordinates for i-th reaction

at the SOFC, respectively. Also, Fo denotes inlet of SOFC anode, label 5. With the above

assumptions and Eq. (2-15), molar fractions for all the species at the exit of the anode of fuel cell

are given as below :

44

, 1

12o CH S

CHo S

Fy

Fεε−

=+

(2-16)

2

2

2

, 1 2, 1 2

1

31

2

o H S So H O S S

H Oo S

FF U

r rUy

F

ε εε ε

ε

⎡ ⎤+ +⎛ ⎞+ − − +⎢ ⎥⎜ ⎟− +⎝ ⎠⎣ ⎦=

+ (2-17)

( )( )22

, 1 2

1

3 1 12 1

o H S SH

o S

F r Uy

F r rUε εε

+ + − −⎛ ⎞= ⎜ ⎟+ − +⎝ ⎠

(2-18)

, 1 212

o CO S SCO

o S

Fy

Fε εε

+ −=

+ (2-19)

22

, 2

12o CO S

COo S

Fy

Fεε+

=+

(2-20)

22

Here, εS1 and εS2 are only unknowns. Likewise chemical equilibrium at the external reformer,

molar fractions at the exit of SOFC anode, Eqs. (2-16)-(2-20), are evaluated using equilibrium

constants, Eqs. (2-11) and (2-12).

Recycle Ratio

In the molar balance aspect, the last step for AOG recycle system is determination of the

recycle ratio. The amount of recycled AOG is manipulated to maintain the desired SC value. The

AOG recycle ratio is defined as recycled AOG to pre-recycled AOG, Rc = F2/F1. The steam to

carbon ratio is defined as;

24

2,

2,

H O

CH f

FSC

F F NC=

+ (2-21)

where, Ff and NC denote molar flow rate of fuel and the number of carbon in the fuel e.g., for

methane NC = 1, for dodecane NC = 12. Substituting definition of recycle ratio into Eq. (2-21)

yields

2 41, 1,

0 1fH O CH

SCF NCRc

F SCF< = ≤

− (2-22)

The numerator of Eq. (2-22) denotes required amount of steam due to newly added fuel for

the given conditions and the denominator means amount of excess steam available before

recycling. The range of recycle AOG is between 0 and 1. It is obvious that recycle ratio is always

greater than zero because operator manipulates recycle ratio to regulate SC and SC is greater

than zero. Mathematically it, however, could be greater than 1. This means shortage of the water

content in AOG. In this case, recycle ratio should be set as unity, i.e. total recycle, and water

deficiency should be added with fuel at the injector. Un-recycled AOG comprises mostly water

vapor but also contains small fraction of un-reacted hydrogen as well as carbon monoxide which

can be utilized through the after-burner.

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Energy Balance

With the energy balance analysis, the temperature of the each stream and capacity of the

cooler can be calculated. Basically, it is assumed that all devices are adiabatic open systems

except SOFC, external reformer, and afterburner. As mentioned in the previous molar balance

section, temperature of flow leaving SOFC and pre-reformer unit is assumed thermal equilibrium

with these devices. Therefore, those temperatures are assumed equal to their operating

temperature. This means TSOFC = T1a = To3 and TPRE = T1b = T4 = Ta1. Concerning AOG

compressor work, low temperature is favored. In this work, temperature of the AOG compressor

is fixed (T2b = Tcomp=150 oC). The temperature of the feedstock, fuel and oxygen, is assumed

room temperature, Tf = To1 = T0 (= 298.15 K). The molar composition and temperature are

unchanged at the splitter where recycle ratio is determined, T1c = T2a = Tv. Now, temperature of

10 streams out of 18 streams is preset so unknown stream temperatures, T1c, T2c, T3a, T3b, T5, To2,

Ta2, and Ta3, should be evaluated with applying appropriate energy balance equations.

However, 6 devices are available for applying first law of thermodynamics (adsorbent,

condenser, cooler, injector, pre-heater, and recuperator). Unknown temperature and cooler duty

cannot be solved only applying first law of thermodynamics because number of unknowns are

larger than number of equations. This lack of equations could be overcome by applying ε-NTU

method to the heat exchanger, i.e. pre-heater and recuperator [12] because both outlet

temperature of each stream could be evaluated by means of this method. So, it is possible to

evaluate the temperature of T1c and T2c applying ε-NTU method to recuperator. Once the

temperature of injector outlet obtained, it is straightforward to compute both outlet temperature

of the pre-heater, T3b and Ta2, by applying ε-NTU method. Temperature of stream leaving

adsorbent, T5, and injector, T3a, and cooler duty could be computed by applying the first law of

thermodynamics to adsorbent, injector, and cooler, respectively. Now, temperatures of departing

24

from the pre-heater for oxygen, or condenser, are undetermined and these temperatures could be

obtained by the same method used for recuperator. However, it is assumed that oxygen stream is

heated up to SOFC operating temperature because there is no necessity to overheat for oxygen

flow. If flue gases leaving fuel pre-heater have not enough sensible heat to heat up oxygen flow,

pre-heater should be replaced with condenser.

For recuperator and fuel pre-heater, applied ε-NTU method is as follow (crossflow, both

fluids mixed);

( ) ( )1

1 exp 1 expr

r

NTUC NTUNTU

NTU C NTU

ε =+ −

− − − −

(2-23)

where, ε=q/qmax=q/Cmin(Th,i-Tc,i), Cr=Cmin/Cmax, and NTU=AUo/Cmin. It is assumed NTU as 4

despite of small overall heat transfer coefficient, Uo, for gases. This may be possible by means of

increasing total surface area, A, replenishing high conductivity porous material into the flow

channels. The effect of number of transfer units, NTU, on the effectiveness, ε, with several heat

capacity ratios, Cr, is shown in figure 2-2. The classical expression of the first law of

thermodynamics is applied into other devices, evidently, kinetic and potential energy terms are

neglected in this work. For calculation of the enthalpy difference, specific heats for ideal gas

mixture are integrated with respect to temperature. Regarding the reaction, heat of reaction for

occurring reactions for SOFC, external reformer, CO2 adsorbent, and after-burner is taking into

account as well as sensible heat. In this work, the value of heat of adsorption is used literature

value, −17000 J/mol [13]. It is assumed that heat of combustion from the after-burner is

completely transferred into external reformer to provide heat of reforming reaction which is

strongly endothermic. AOG recycle ratio, however, is controlled to maintain desired SC ratio not

to supply enough heat into the external reformer. This may cause energy imbalance on the

25

external reformer. To make energy balanced, additional heat transfer term is taking into account

on external reformer which could be surplus or insufficient. Once energy balance set, evaluation

of temperature carried out by Newton-Rahpson method with 10−7 tolerance.

26

Figure 2-1. Process flow diagram

27

0 1 2 3 4 50.0

0.2

0.4

0.6

0.8

1.0

Cr = 1.0

Cr = 0.8

Cr = 0.6

Cr = 0.4

Cr = 0.2Cr = 0

Ef

fect

iven

ess,

ε

No. of transfer Units, NTU

Figure 2-2. Effect of number of transfer units, NTU, on the effectiveness, ε, with several heat capacity ratios, Cr, for crossflow and both fluids mixed heat exchanger

28

Table 2-1. Critical and reduced temperature and pressure

Substance Formula Critical Temperature (K) Critical Pressure

(MPa) Reduced

Temperature Reduced Pressure

Hydrogen H2 33.2 1.30 1.2745 × 101 7.7942 × 10-2

Methane CH4 190.4 4.60 2.2224 × 100 2.2027 × 10-2

Water H2O 647.3 22.12 6.5372 × 10-1 4.5807 × 10-3

Carbon monoxide CO 132.9 3.50 3.1840 × 100 2.8950 × 10-2

Carbon Dioxide CO2 304.1 7.38 1.3915 × 100 1.3730 × 10-2

Dodecanea) C12H26 658.2 1.80 6.4289 × 10-1 5.6292 × 10-2

From Ref. [5]

a) Critical temperature and pressure data are from NIST chemistry webbook.

29

Table 2-2. Heat capacities of gases in the ideal-gas state

Substance Formula Tmax (K) A 103 B 106 C 10−5 D

Hydrogen H2 3000 3.249 0.422 0 0.083

Methane CH4 1500 1.702 9.081 −2.164 0

Water H2O 2000 3.470 1.450 0 0.121

Carbon monoxide CO 2500 3.376 0.557 0 −0.031

Carbon Dioxide CO2 2000 5.457 1.045 0 −1.157

30

Table 2-3. Coefficients for dodecane heat capacity in the ideal-gas state

Substance Formula A B C D

Dodecane C12H26 − 3.5966 0.1558 −1.0259 ×10−4 2.6471 ×10−8

31

CHAPTER 3 RESULTS AND OPTIMIZATION

Results

Chemical Equilibrium at Pre-Reformer and Optimum Pre-Reformer Temperature

Figure 3-1 shows reaction equilibrium results for steam reforming and water-gas shift

reaction. Steam to carbon ratio was adjusted by methane and water vapor. The dry molar fraction

is plotted versus reaction temperature with several SC ratios. Total fuel conversion and saturation

of hydrogen molar fraction can be achieved low temperature with increasing SC ratio. The dry

molar fractions of carbon monoxide and carbon dioxide appear in opposite manner with

increasing SC ratio. With regard to determination of the operating temperature of pre-reformer, it

should be considered energy requirement as well as produced amount of the hydrogen due to

endothermic reaction. The amount of created hydrogen per consumed energy is plotted in Figure

3-2 for two different input temperatures, 25 and 100 °C. In the energy efficiency aspect, it is

considered that operation of pre-reformer in temperature range from 500 °C to 600 °C is the

optimum case regardless of SC ratio. In this work, temperature of the pre-reformer unit is fixed

as 550 °C.

Fuel and Oxygen Consumption Results without Recirculation and CO2 Capture

A parametric study is performed to find the optimal operating condition such as

temperature of SOFC, SC ratio, recirculation ratio, and CO2 adsorption. Illustrative computations

are performed considering fixed electrical work output, 1 kW, from SOFC. It is assumed 25%

excess oxygen is supplied into the afterburner for complete combustion of un-recycled AOG.

Figures 3-3 and 3-4 demonstrate how fuel and oxygen consumption rates depend on variations of

the SOFC temperature as well as SC ratio without recirculation and CO2 capture. Regardless of

SC ratio, required fuel and oxygen rates increase with increasing SOFC operating temperature.

32

On the other hand, fuel and oxygen consumption rates always decreases with increasing SC ratio

in any temperature. Also, shape of the two graphs is quite similar to each other. This is evident

taking whole system as control volume. Apparent reaction is as follow taking into account

adsorbed carbon dioxide;

( )12 26 2 2 2 218.5 13 12C H x O H O CO xO+ + → + + (3-1)

Several overall molar balance results are provided in Table 3-1.

Recycle Ratio and Water Management

Figure 3-5 shows AOG recycle percentage, i.e. F2a/F1c×100. As mentioned in molar

balance section, AOG recycle percentage is determined to adjust SC ratio. AOG recycle percent

increases with increasing SC ratio. With fixed fuel input, AOG recycle percentage should be

doubled when SC ratio becomes doubled. As shown in Fig. 3-3, fuel consumption rate decreases

with SC ratio so AOG recycle percent does not increase by double with doubled SC ratio. AOG

recycle percent is independent with SOFC temperature despite of the fact that fuel requirement

increases with SOFC temperature. This means AOG water content increases with SOFC

temperature so it is possible to maintain SC ratio though fuel flow rate is increased with SOFC

temperature. Also, Fig 3-5 shows that AOG has enough water content to adjust SC ratio up to 5

by recycling. Therefore, water is self sufficient, in other words there is no necessity to add water

with fuel.

Energy Balance and Efficiency Results without Recirculation and CO2 Capture

As mentioned in energy balance section, un-recycled AOG acts an important role in energy

balance for external reformer, since un-recycled AOG is burned at the after-burner and provides

heat into external reformer for steam reforming reaction. Heat, however, is imbalanced on pre-

reformer unit. To make energy balanced, another heat effect, QPRE, is introduced on pre-reformer

33

unit. The amount of this newly introduced heat effect is dependent upon SOFC temperature. This

could be either heat surplus or insufficient heat depending on SOFC temperature. Figure 3-6

shows energy balance results for the external reformer. The negative QPRE means heat is rejected

from the external reformer, heat surplus, while the positive QPRE means heat from AOG and

after-burner is insufficient for heat of reforming reaction. From the energy and molar balance

results, high SC ratio case requires more heat of reforming reaction. Both excess heat and

insufficient heat cases are not favored in efficiency point of view. In Figure 3-7, detailed heat

analysis is presented for SC = 4. Shaded region named |∆HAOG| represents heat transferred from

sensible heat of AOG stream and under the shaded region denotes heat transferred from the after-

burner, |QAB|. The magnitude of heat requirement for reforming reactions, |∆HPRE|, is decreased

slightly with SOFC temperature. The magnitude of transferred heat from the after-burner

increases with SOFC temperature due to increasing of carbon monoxide content into the after-

burner. The major reason of changing from insufficient heat region to excess heat region is

sensible heat of AOG. Two different efficiencies, ηLHV and ηTh, are evaluated. The first

efficiency, ηLHV, is based on lower heating value of fuel, while the second efficiency, ηTh, is

based on total enthalpy change of Eq. (3-1). Seemingly, apparent chemical reaction, Eq. (3-1), is

similar to combustion process. In this work, efficiency based on lower heating value is used

despite of water condensing. Definition of efficiency considering heat imbalance for Pre-

reformer unit is as follows;

( )

( )

0

0

electPRE

fLHV

elect PREPRE

f

W QF LHV

W Q QF LHV

η

⎧ ⎪⎩

(3-2)

34

In insufficient heat case, heat deficiency at the pre-reformer unit is subtracted from SOFC

electrical work. Figure 3-8 demonstrates how the efficiency changes with variations of SOFC

temperature as well as SC ratio. Dotted lines in Fig. 3-8 represent efficiency under no

consideration of heat imbalance at pre-reformer unit and correspond with fuel consumption rate.

Figure 3-8 allows us to understand the significance of heat imbalance adjudging operation

conditions. System efficiency has the maximum value for given SC ratio. Considering energy

imbalance on pre-reformer, the temperature, which makes heat balanced without QPRE, is named

as self-energy balanced operating temperature. It is possible to obtain the maximum efficiency

operating SOFC with this self-energy balanced operating temperature. The higher temperature

operation yields the more fuel consumption. Lower temperature operation gives heat

insufficiency on the pre-reformer unit. Therefore, produced electrical work should reimburse this

insufficient heat on the pre-reformer.

Carbon Dioxide Capture Effects

In this work, it is assumed only hydrogen is electrochemically reacted and carbon

monoxide is converted to hydrogen and carbon dioxide by WGS reaction, Eq. (2-4), inside the

SOFC. Figure 3-1 is obtained assuming initially methane and water vapor corresponding to given

SC ratio. With recycling AOG, reforming channel inlet gases consist of all 5 chemical

components. After the equilibrium achieved inside the external reformer, outlet of reforming

channel contains unreacted methane. This unreacted methane is undergone reforming reaction,

Eq. (2-3), in SOFC. Both internal reforming and WGS reactions are limited by equilibrium. If it

is possible to manipulate both forward reactions getting over the equilibrium, fuel consumption

rate will decrease. With regard to concentration under constant temperature and pressure

condition, there are two ways getting over the equilibrium; to remove product of forward

reaction, and to add more reactant of forward reaction. The first concept is ineffective to steam

35

reforming reaction, Eq. (2-3), because products, CO and H2, are already consuming by WGS and

electrochemical reactions. For WGS reaction, CO2 capture corresponds to the first concept.

Concerning the second concept, it is effective for both WGS and steam reforming reactions to

put in more water vapor into the anode which can be achieved by recirculation of AOG back into

anode inlet due to high water content of AOG. Carbon dioxide capture effects on fuel

consumption rate are illustrated in Fig. 3-9 for several SC ratios. For the comparison, decreased

fuel consumption rate due to CO2 capture is expressed in a fraction to the fuel consumption rate

for the same condition, expect CO2 capture. These reduced fractions are depicted in Fig. 3-10.

Fuel consumption rate is definitely decreased with CO2 capture but decreased amount is not

directly proportional to CO2 capture. From the Fig. 3-10, it is found that CO2 capture effects are

conspicuous in high temperature region and low SC ratio rather than low temperature and high

SC ratio.

Recirculation Effects

In Figure 3-11, fuel consumption rate is calculated with variations of the recirculation ratio

as well as SOFC temperature and SC ratio. And reduced fractions compared with no

recirculation case are illustrated in Fig. 3-12. Fuel consumption rate decreases with increasing

recirculation ratio. In this simulation, recirculation ratio is limited up to 0.5 because current

density is affected by recirculation ratio. It can be verified that recirculation effects are

conspicuous in high temperature region and low SC ratio rather than low temperature and high

SC ratio.

Optimization

Concerning efficiency, heat imbalance on the pre-reformer should be considered with CO2

capture rate and recirculation ratio. Total 4620 cases of parametric studies had been conducted

36

concerning efficiency with variations of SC, TSOFC, CO2 capture and recirculation ratio.

Parameters for optimization are as follows;

• SC: 2, 3, 4, and 5 • TSOFC: 600, 700, 800, 900 and 1000 °C • CO2 capture: 21 cases (0 ~ 100 %) • Recirculation ratio: 11 cases (0 ~ 0.5)

Concerning maximum efficiency, these parametric studies could be classified 6 unique

types according to dependency on CO2 adsorption and recirculation;

a) high CO2 adsorption and low recirculation b) moderate CO2 adsorption and low recirculation c) low CO2 adsorption and low recirculation d) low CO2 adsorption and high recirculation e) moderate CO2 adsorption and high recirculation f) high CO2 adsorption and high recirculation

Distribution map for those 6 categories is provided in the Table 3-2. Representative overall

efficiencies of the each category, depending on CO2 capture and recirculation ratio at given SC

and TSOFC, are illustrated in Figure 3-13. Among all 4620 cases, 20 maximum efficiencies for

given SC and TSOFC are presented in the Table 3-3 and Figure 3-14. Data in the Table 3-3 and

Figure 3-14 is representation of the highest efficiency with given SC and TSOFC. In the Table 3-3,

carbon dioxide capture and recirculation effects appear in opposite manner although they have a

common tendency for dependency on SC and temperature. Low temperature cases prefer

maximum CO2 capture and no recirculation, while maximum recirculation and low CO2 capture

are preferred in high temperature.

37

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

350 400 450 500 550 600 650 700 7500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

350 400 450 500 550 600 650 700 7500.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9(d)(c)

(b)(a)

S/C = 5S/C = 4

S/C = 3S/C = 2

H2 CH4 CO CO2

mol

ar fr

actio

n, y

i,DR

Y [-]

mol

ar fr

actio

n, y

i,DR

Y [-]

mol

ar fr

actio

n, y

i,DR

Y [-]

Temperature [oC]

mol

ar fr

actio

n, y

i,DR

Y [-]

Figure 3-1. Reaction equilibrium results for steam reforming and water-gas shift reaction for

several steam to carbon ratios

38

300 350 400 450 500 550 600 650 700 750 800

5

6

7

8

9

10

11

12

TR = 25 oC

H

ydro

gen

outp

ut /

requ

ired

heat

[mm

ol/k

J]

Pre-Reformer Temperature, [oC]

S/C = 2 S/C = 3 S/C = 4 S/C = 5

A

Figure 3-2. Produced hydrogen per consumed energy A) TR = 25 °C, B) TR = 100 °C

39

300 350 400 450 500 550 600 650 700 750 800

5

6

7

8

9

10

11

12

TR = 100 oC

Hyd

roge

n ou

tput

/ re

quire

d he

at [m

mol

/kJ]

Pre-Reformer Temperature, [oC]

S/C = 2 S/C = 3 S/C = 4 S/C = 5

B

Figure 3-2. Continued

40

600 650 700 750 800 850 900 950 10001.65

1.70

1.75

1.80

1.85

1.90

1.95

2.00

2.05

2.10

TPR = 550 oC

U = 0.85ηFC = 0.85no CO2 capturer = 0

S/C = 5S/C = 4

S/C = 3S/C = 2

D

odec

ane

cons

umpt

ion

rate

for 1

kW

ope

ratio

n [g

/min

]

SOFC Temperature, TS [oC]

Figure 3-3. Effect of SOFC temperature on fuel consumption rate with different steam to carbon

ratio, where no CO2 capture and no recirculation

41

600 650 700 750 800 850 900 950 10005.8

6.0

6.2

6.4

6.6

6.8

7.0

7.2

7.4 TPR = 550 oC

U = 0.85ηFC = 0.85no CO2 capturer = 0

S/C = 5S/C = 4

S/C = 3S/C = 2

Oxy

gen

cons

umpt

ion

rate

for 1

kW

ope

ratio

n [g

/min

]

SOFC Temperature, TS [oC]

Figure 3-4. Effect of SOFC temperature on oxygen consumption rate with different steam to

carbon ratio, where no CO2 capture and no recirculation

42

600 650 700 750 800 850 900 950 1000

66

68

70

72

74

76

78

80

82

84 TPR = 550 oC

U = 0.85ηFC = 0.85no CO2 capturer = 0

S/C = 5

S/C = 4

S/C = 3

S/C = 2

AO

G R

ecyc

le p

erce

nt [%

]

SOFC Temperature, TS [oC]

Figure 3-5. AOG recycle percent versus SOFC temperature with different steam to carbon ratio,

where no CO2 capture and no recirculation

43

600 650 700 750 800 850 900 950 1000

-300

-250

-200

-150

-100

-50

0

50

100

150

200

250

300

surplus Heat region

insufficient Heat region

TPR = 550 oC

U = 0.85ηFC = 0.85no CO2 capturer = 0

S/C = 5S/C = 4

S/C = 3S/C = 2

QPR

E [W

att]

SOFC Temperature, TS [oC]

Figure 3-6. Effect of SOFC temperature on additional heat transferred rate for pre-reformer unit

with different steam to carbon ratio, where no CO2 capture and no recirculation

44

600 650 700 750 800 850 900 950 10000

100

200

300

400

500

600|∆HAOG|+|QAB|

Insufficient Heat

Excess Heat|∆HPRE|

|∆HAOG|

|QAB|

SOFC temperature, TS [oC]

TPR = 550 oC

U = 0.85ηFC = 0.85S/C = 4no CO2 capturer = 0

Rat

e of

requ

ired

and

trans

ferre

d he

at [W

att]

Figure 3-7. Effect of SOFC temperature on detailed additional heat transferred rate for pre-

reformer unit with S/C =4, where no CO2 capture and no recirculation

45

600 650 700 750 800 850 900 950 1000

57

60

63

66

69

72

75

78

81

TPR = 550 oC

U = 0.85ηFC = 0.85no CO2 capturer = 0

S/C = 2S/C = 3S/C = 4S/C = 5

η L

HV [

%]

SOFC Temperature, TS [oC]

Figure 3-8. Effect of SOFC temperature on efficiency based on LHV with different steam to

carbon ratio, where no CO2 capture and no recirculation

46

600 650 700 750 800 850 900 950 10001.65

1.70

1.75

1.80

1.85

1.90

1.95

2.00

2.05

2.10

Line color S/C = 2 S/C = 3.5 S/C = 5

CO2 capture 0 % 50 % 100 %

TPR = 550 oC

U = 0.85ηFC = 0.85r = 0

D

odec

ane

cons

umpt

ion

rate

[g/m

in]

SOFC Temperature, TS [oC]

Figure 3-9. Effect of SOFC temperature on fuel consumption rate with different steam to carbon

ratios and several CO2 adsorption percents, where no recirculation

47

600 650 700 750 800 850 900 950 10000.94

0.96

0.98

1.00Line color S/C = 2 S/C = 3.5 S/C = 5

CO2 capture 50 % 100 %

TPR = 550 oC

U = 0.85ηFC = 0.85r = 0

D

odec

ane

cons

umpt

ion

rate

ratio

to n

o C

O2 c

aptu

re

SOFC Temperature, TS [oC]

Figure 3-10. Carbon dioxide capture effects on the depleted fuel consumption fraction for the several steam to carbon ratios, where no recirculation

48

600 650 700 750 800 850 900 950 10001.65

1.70

1.75

1.80

1.85

1.90

1.95

2.00

2.05

2.10

Line color S/C = 2 S/C = 3.5 S/C = 5

recirculation, r r = 0 r = 0.25 r = 0.5

S/C = 5, r = 0S/C = 3.5, r = 0.25S/C = 2, r = 0.5

TPR = 550 oC

U = 0.85ηFC = 0.85no CO2 capture

D

odec

ane

cons

umpt

ion

rate

[g/m

in]

SOFC Temperature, TS [oC]

Figure 3-11. Effect of SOFC temperature on fuel consumption rate with different steam to

carbon ratio and several recirculation ratio, where no CO2 adsorption

49

600 650 700 750 800 850 900 950 10000.94

0.96

0.98

1.00Line color S/C = 2 S/C = 3.5 S/C = 5

recirculation ratio, r 0.25 0.5

TPR = 550 oC

U = 0.85ηFC = 0.85no CO2 capture

D

odec

ane

cons

umpt

ion

rate

ratio

to n

o re

circ

ulat

ion

SOFC Temperature, TS [oC]

Figure 3-12. Recirculation effects on the depleted fuel consumption fraction for the several

steam to carbon ratios, where no CO2 adsorption

50

70.2370.77

71.32

71.86

72.41

69.6869.14

72.95

68.59

0.0 0.1 0.2 0.3 0.4 0.50

20

40

60

80

100

Recirculation ratio, r [-]

CO

2 Ads

orpt

ion

perc

ent [

%]

67.5068.0568.5969.1469.6870.2370.7771.3271.8672.4172.9573.50

Figure 3-13. Efficiency based on LHV of fuel; A) S/C = 2, TSOFC=600 oC (example (a), low

temperature region), B) S/C = 3, TSOFC=700 oC (example (b), low or moderate temperature region), C) S/C = 4, TSOFC=800 °C (example (c), moderate temperature and medium to high S/C region), D) S/C = 5, TSOFC=900 oC (example (d), moderate or high temperature and high S/C region), E) S/C = 5, TSOFC=1000 oC (example (e), high temperature and high S/C region), and F) S/C = 2, TSOFC=900 oC (example (f), high temperature and low S/C region)

51

69.77

69.41

69.05

68.68

68.32

70.14

67.95

67.59

0.0 0.1 0.2 0.3 0.4 0.50

20

40

60

80

100

Recirculation ratio, r [-]

CO

2 Ads

orpt

ion

perc

ent [

%]

66.5066.8667.2367.5967.9568.3268.6869.0569.4169.7770.1470.50

B

Figure 3-13. Continued

52

72.73

72.09

71.45

70.8270.18

69.55

68.9168.27

67.64

0.0 0.1 0.2 0.3 0.4 0.50

20

40

60

80

100

Recirculation ratio, r [-]

CO

2 Ads

orpt

ion

perc

ent [

%]

67.0067.6468.2768.9169.5570.1870.8271.4572.0972.7373.3674.00

C

Figure 3-13. Continued

53

72.82

73.55

73.5572.82

72.09

71.3670.64

69.91

69.18

68.45

74.27

0.0 0.1 0.2 0.3 0.4 0.50

20

40

60

80

100

Recirculation ratio, r [-]

CO

2 Ads

orpt

ion

perc

ent [

%]

67.0067.7368.4569.1869.9170.6471.3672.0972.8273.5574.2775.00

D

Figure 3-13. Continued

54

70.09 70.4570.8271.18

71.55

71.9172.27

71.91

71.5571.18

72.64

70.82

0.0 0.1 0.2 0.3 0.4 0.50

20

40

60

80

100

Recirculation ratio, r [-]

CO

2 Ads

orpt

ion

perc

ent [

%]

69.0069.3669.7370.0970.4570.8271.1871.5571.9172.2772.6473.00

E

Figure 3-13. Continued

55

69.5070.00 70.50

71.0071.50

72.00

72.5073.00

73.50

0.0 0.1 0.2 0.3 0.4 0.50

20

40

60

80

100

Recirculation ratio, r [-]

CO

2 Ads

orpt

ion

perc

ent [

%]

68.5069.0069.5070.0070.5071.0071.5072.0072.5073.0073.5074.00

F

Figure 3-13. Continued

56

73.20

72.27

71.33

70.40

69.47

68.53

67.60

73.20

66.67

74.13

74.13

600 650 700 750 800 850 900 950 10002.0

2.5

3.0

3.5

4.0

4.5

5.0

SOFC temperature, TS [oC]

Stea

m to

car

bon

ratio

, S/C

62.0062.9363.8764.8065.7366.6767.6068.5369.4770.4071.3372.2773.2074.1375.0776.00

Figure 3-14. Effects of SOFC temperature and SC on maximum system efficiency

57

Table 3-1. Overall molar balance results Input Output

CO2/C12H26 S/C TSOFC [oC]

C12H26 [mmol/sec] O2/C12H26 H2O/C12H26 O2/C12H26 total adsorbed output

2 700 0.1783 18.88 13.00 0.38 12.00 0.00 12.00

3 700 0.1748 18.79 13.00 0.29 12.00 0.00 12.00

4 700 0.1727 18.74 13.00 0.24 12.00 0.00 12.00

2 900 0.1942 18.99 13.00 0.49 12.00 0.00 12.00

3 900 0.1895 18.89 13.00 0.39 12.00 0.00 12.00

4 900 0.1865 18.82 13.00 0.32 12.00 0.00 12.00

2 700 0.1752 18.80 13.00 0.30 12.00 6.79 5.21

3 700 0.1721 18.72 13.00 0.22 12.00 8.05 3.95

4 700 0.1703 18.68 13.00 0.18 12.00 8.87 3.13

2 900 0.1881 18.85 13.00 0.35 12.00 6.72 5.28

3 900 0.1839 18.76 13.00 0.26 12.00 8.00 4.00

4 900 0.1815 18.70 13.00 0.20 12.00 8.84 3.16

58

Table 3-2. Dependency on CO2 adsorption percentage and recirculation ratio

TSOFC S/C 600

oC 700 oC 800 oC 900 oC 1000 oC

2 (a) (b) (a) or (d) (f) (f)

3 (a) (b) (c) (d) (f)

4 (a) (b) (c) (d) (e)

5 (a) (b) (c) (d) (e)

59

Table 3-3. Maximum overall efficiencies for given SC and TSOFC with corresponding

recirculation ratio and CO2 capture percent TSOFC

S/C 600 oC 700 oC 800 oC 900 oC 1000 oC

5 62.20 % r = 0.0

C = 100 %

64.96 % r = 0.0

C = 35 %

72.51 % r = 0.0

C = 0 %

74.63 % r = 0.5

C = 5 %

72.96 % r = 0.5

C = 50 %

4 65.15 % r = 0.0

C = 100 %

67.30 % r = 0.0

C = 40 %

73.67 % r = 0.0

C = 0 %

74.18 % r = 0.5

C = 5 %

72.65 % r = 0.5

C = 55 %

3 68.76 % r = 0.0

C = 100 %

70.34 % r = 0.0

C = 40 %

74.18 % r = 0.05

C = 10 %

74.01 % r = 0.5

C = 20 %

72.37 % r = 0.5

C = 85 %

2 73.23 % r = 0.0

C = 100 %

74.40 % r = 0.0

C = 30 %

74.79 % r = 0.35

C = 25 %

73.89 % r = 0.5

C = 80 %

71.62 % r = 0.5

C = 100 %

60

CHAPTER 4 SUMMARY AND CONCLUSION

In this thermodynamics and chemical equilibrium model of 1 kW SOFC system utilizing

liquid hydrocarbon, the individual effect of each parameter is analyzed. n-Dodecane, saturated

hydrocarbon containing 12 carbons, is selected for simulation as a representation of diesel fuel.

Appropriate thermodynamic properties of chemical species are applied. Especially, heat capacity

of n-Dodecane is obtained from interpolation of previous literature value.

From not only chemical equilibrium results but also energy efficiency point of view,

optimum pre-reformer temperature is suggested. AOG recycle ratio and water management

analysis are considered. Water is self-sufficient by means of recycling AOG up to SC 5, so there

is no necessity to add water with fuel. The effects of SOFC temperature and steam to carbon

ratio on fuel and oxygen consumption rates are presented. Fuel and oxygen consumption rates

show similar inclination. From the molar (or mass) balance point of view, low SOFC

temperature and high SC are preferred. Overall species balance is considered, so overall

chemical reaction equation is indicated. It looks like combustion reaction of fuel. Also, overall

chemical species balance result is presented. Carbon dioxide capture and recirculation effects are

examined on purpose to produce more hydrogen than chemical equilibrium limitation under

given SOFC temperature condition. CO2 capture and recirculation effects on fuel consumption

rate have the similar tendency. The higher temperature and the smaller SC yield the less fuel

consumption.

Concerning energy balance, heat is imbalanced on pre-reformer unit. To make energy

balanced, another heat effect, QPRE, is introduced on pre-reformer unit. The amount of this newly

introduced heat effect is dependent upon SOFC temperature. This could be either heat surplus or

insufficient heat depending on SOFC temperature. The temperature, which makes heat balanced

61

without newly introduced heat effect on pre-reformer, is named as self-energy balanced

operating temperature. It is possible to obtain the maximum efficiency operating SOFC with this

self-energy balanced operating temperature. The higher temperature operation yields the more

fuel consumption. Lower temperature operation gives heat insufficiency on the pre-reformer unit.

Therefore, produced electrical work should reimburse this insufficient heat on the pre-reformer.

Parametric study is conducted for 4620 cases, 4 cases of SC ratio, 5 cases of SOFC

temperature, 21 cases of CO2 capture percentage, and 11 cases of recirculation ratio. Parametric

study results are classified into 6 unique types according to dependency on CO2 capture and

recirculation ratio. It is also categorized by dependency on SC ratio and SOFC temperature.

Distribution map for 6 categories over SC and SOFC temperature is presented. Also, the

maximum efficiencies depending on recirculation ratio as well as CO2 capture are presented for

given SC and SOFC temperature. In the maximum efficiency table, carbon dioxide capture and

recirculation effects appear in opposite manner although they have a common tendency for

dependency on SC and temperature. Low temperature cases prefer maximum CO2 capture and no

recirculation, while maximum recirculation and low CO2 capture are preferred in high

temperature. Among these maximum efficiencies, SC =2 and 800 oC SOFC temperature case

under 0.35 recirculation ratio and 25% carbon dioxide adsorption yields the highest efficiency as

74.79%.

62

LIST OF REFERENCES

1. Rostrup-Nielsen, J.R., 1984, Catalytic Steam Reforming, Springer-Verlag, Berlin, Heidelberg, Germany.

2. Imperial Chemical Industries, 1970, Catalyst handbook: with special reference to unit processes in ammonia and hydrogen manufacture, Wolfe Scientific Books, London, UK.

3. EG&G Technical Services, Inc., 2004, Fuel Cell Handbook (Seventh Edition), U.S. Department of Energy, Morgantown, West Virginia.

4. Barbir, F., 2005, PEM Fuel Cells: Theory and Practice, Elsevier Academic Press, London, UK.

5. Smith, J.M., Van Ness, H.C., and Abbott, M.M., Introduction to Chemical Engineering Thermodynamics, McGraw-Hill, New York, NY.

6. Sonntag, R.E., and Van Wylen, G.J., 1991, Introduction to Thermodynamics Classical and Statistical, John Wiley & Sons, Hoboken, NJ.

7. Lemmon, E.W., and Huber, M.L., 2004, “Thermodynamic Properties of n-Dodecane,” Energy & Fuels, 18, pp. 960-967.

8. Span, R., Wagner, W., 2003, “Equations of State for Technical Applications. I. Simultaneously Optimized Functional Forms for Nonpolar and Polar Fluids,” International Journal of Thermophysics, 24, pp. 1-39.

9. Xu, J., and Froment, G.F., 1989, “Methane Steam Reforming, Methanation and Water-Gas Shift: I. Intrinsic Kinetics,” AIChE Journal, 35(1), pp. 88-96.

10. Chapra, S.C, and Canale, R.P., 1998, Numerical Methods for Engineers: with programming and software applications, McGraw-Hill, New York, NY.

11. Colpan, C.O., Dincer, I., and Hamdullahpur, F., 2007, “Thermodynamic Modeling of Direct Internal Reforming Solid Oxide Fuel Cells Operating with Syngas,” International Journal of Hydrogen Energy, 32(7), pp. 787-795.

12. Kays, W.M., and London, A.L., 1984, Compact Heat Exchangers, McGraw-Hill, New York, NY.

13. Ding, Y., and Alpay, E., 2000, “Adsorption-enhanced steam-methane reforming,” Chemical Engineering Science, 55, pp. 3929-3940.

BIOGRAPHICAL SKETCH

Tae Seok Lee was born in 1977, in Seoul, Republic of Korea. He matriculated in

Department of Chemical Engineering, University of Seoul, Korea in 1996. After completing his

sophomore, he had joined Korea Military Service as a Field Artillery for 26 months. After

completing his military duty, Tae Seok went back to University. In his senior year, Tae Seok

won the bronze medal in the Transport Phenomena national competition held by Korea Institute

of Chemical Engineering, KIChE. And he had earned his B.S. in Chemical Engineering,

University of Seoul in 2003. After graduating, he worked at Korea Institute of Science and

Technology, KIST, as a commissioned research scientist. Tae Seok joined Department of

Mechanical and Aerospace Engineering at University of Florida in Fall 2005 as a graduate

student. Upon graduation he plans to pursue Ph.D. in the same research area.

ACKNOWLEDGMENTSLIST OF TABLESLIST OF FIGURESINTRODUCTION AND BACKGROUNDSteam Reforming ReactionSolid-Oxide Fuel CellsChemical Reaction EquilibriumStoichiometry and Extent of ReactionChemical Reaction Equilibrium and Equilibrium Constant

THERMODYNAMIC MODELIntroductionAssumptionThermodynamic Properties of Chemical SpeciesJustification for Ideal Gas AssumptionHeat CapacityHeat Capacity for Fuel (n-Dodecane)

Molar BalanceChemical Equilibrium at the Pre-ReformerSOFC ModelRecycle Ratio

Energy Balance

RESULTS AND OPTIMIZATIONResultsChemical Equilibrium at Pre-Reformer and Optimum Pre-ReformeFuel and Oxygen Consumption Results without Recirculation anRecycle Ratio and Water ManagementEnergy Balance and Efficiency Results without Recirculation Carbon Dioxide Capture EffectsRecirculation Effects

Optimization

SUMMARY AND CONCLUSIONLIST OF REFERENCESBIOGRAPHICAL SKETCH