process design and optimization of solid oxide ......solid-oxide fuel cells a fuel cell is an...
TRANSCRIPT
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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)
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, 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)
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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
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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)
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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 %
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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
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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%.
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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.
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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