固态氧化燃料电池建模：方法、程序与技术概览

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"Modeling Solid Oxide Fuel Cells: Methods, Procedures and Techniques 是一本关于固体氧化燃料电池的专业书籍，由Thomas Malkow撰写，Roberto Bove和Stefano Ubertini编辑。该书属于Fuel Cells and Hydrogen Energy系列，由Springer Netherlands出版，于2008年首次发行，全书共397页，包含了402页的技术内容。书中的语言为英文，ISBN号分别为978-1-4020-6994-9和978-1-4020-6995-6。这本书关注的是固体氧化燃料电池的建模、方法和技术，旨在为燃料电池和氢能领域的科研人员、工程师、技术专家、设计师、技术经理及研究生提供方便的信息检索。" 《Modeling Solid Oxide Fuel Cells》是燃料细胞和氢能研究领域的重要文献，它深入探讨了固体氧化燃料电池这一特殊类型的燃料电池。固体氧化燃料电池（Solid Oxide Fuel Cells, SOFC）是一种高效、清洁的能源转换装置，它们利用氧化还原反应将化学能转化为电能，而不依赖于液体或气体燃料，这使得它们在环保和能源效率方面具有显著优势。本书的内容涵盖了SOFC的多个关键方面： 1. **材料科学**：SOFC的工作依赖于特定的电解质和电极材料，如氧化锆陶瓷和金属合金等。书中可能详细讨论这些材料的性质、制备方法及其对电池性能的影响。 2. **工程设计**：包括燃料电池的结构设计、热管理和流场设计，这些都是提高燃料电池效率和稳定性的关键因素。 3. **制造工艺**：书中可能涵盖制造过程中的关键技术，如薄膜沉积、组件组装以及大规模生产策略。 4. **建模与仿真**：建模是理解和优化燃料电池性能的关键工具。书中可能会介绍不同层次的模型，从微观的电化学反应动力学到宏观的系统集成，以及如何使用计算机模拟来预测和分析电池性能。 5. **应用研究**：除了基础理论，书中还可能涉及SOFC在电力生成、分布式发电、移动电源等方面的实际应用案例。 6. **燃料处理**：由于SOFC通常可以使用多种燃料，包括氢气、天然气和生物燃料等，书中可能讨论了燃料重整过程，以优化燃料供应并减少有害排放。 7. **传感器技术**：为了监控燃料电池系统的运行状态，书中可能也涵盖了用于检测氢气、碳氢化合物和其他气体的传感器技术。通过这本书，读者可以系统地了解固体氧化燃料电池的各个方面，不仅能够深入理解其工作原理，还能掌握相关的建模技术和工程实践，从而在燃料电池和氢能领域开展更深入的研究和开发工作。

6 T. Malkow

Fig. 1.2 Principles, functions and schematic of a ﬂat planar SOFC where the PEN is stacked

between two bipolar plates (interconnect with gas ﬂow ﬁelds).

By stacking several cells in series or parallel, the voltage and power sought in

an application can be attained. It requires however another component, interconnect

or current collector. The interconnect material can be ceramic or metallic in nature.

The entire build up of the individual cells and interconnect is called the stack. Cur-

rently, two major stack designs – tubular and planar – are widely used both with

beneﬁts and drawbacks. For example, the tubular SOFC (TSOFC) as developed by

Siemens Power Generation (SPG) can be seal-less manufactured. It has however a

long current path around the circumference of the single cell tube which basically

limits the power density obtainable to typically 200 mW/cm

at 1,000

◦

C. A novel

high power density (HPD) design consisting of ﬂattened tubes is currently being de-

veloped by SPG to overcome this limitation. The HPD design employs internal ribs

made of the cathode material to mechanically stabilize the tubes and to shorten the

current path. Further improvements may come from the monolithic tubular structure

known as DELTA-N HPD. The major beneﬁt of TSOFC is its enhanced tolerance for

high thermal stresses which allows better resistance to thermal cycling. In addition,

the cathode can be made thinner, thereby reducing polarization. Other major tubular

stack geometries include the open-ended tubes design by TOTO, the segmented-in-

series thin ﬂat tube integrated planar design by Rolls-Royce (RR), the segmented or

staggered tubes design by Mitsubishi Heavy Industries (MHI) and the anode sup-

ported micro tubules concept by Acumentrics and Adelan.

Planar SOFC, in particular, monolithic designs (MHI) are capable of high (volu-

metric) power densities most favoured by direct and short current paths across the

stack components. The PEN is principally square, rectangular and circular (Ceramic

Fuel Cells Limited (CFCL), Mitsubishi Materials Corp., Sulzer Hexis) in shape with

active surface areas of 100–200 cm

(15.5–31 in

). A drawback of this design is that

it often necessitates the use of high temperature sealants for application at the in-

1 SOFC in Brief 7

terconnect edges to prevent premature air fuel mixing. The sealants could be rigid

or compressive. Materials mainly employed are insulating glass and glass ceram-

ics. However, these materials usually contain highly volatile and mobile alkali and

alkaline earth metals. Since hermeticity, creep and stability impose a challenge at

stack fabrication and operation conditions, some designs aim to avoid sealing all

together. In addition to sealants, a planar SOFC often requires the use of contact

materials such as ceramic layers at the cathode and metallic meshes at the anode to

ensure good adherence between the all ceramic PEN and the interconnect. The few

millimetres thick interconnect is sometimes called the bipolar plate as it functions

in addition to current collection and heat conduction as gas separator. Furthermore,

protective coatings are sometimes applied onto the bipolar plate to prevent excess-

ive corrosion, particularly evaporation of chromium species which are poisonous to

cathode activity.

The gas supply to the stack is accomplished using either external manifolds,

usually made of stainless steel, or internal manifolds (Versa Power Systems, HT-

ceramix). In the latter case, the manifolds are integrated into the cell design and

interconnect (Delphi).

Typically, TSOFC use co- and counter-ﬂow conﬁgurations whereas planar stacks

sometimes favour cross ﬂow simplifying manifolds attachment. The ﬂow of air usu-

ally provides cooling to a stack in either design as does internal reforming (Sulzer

Hexis). The ﬂow regime strongly affects the distribution of gas composition, mech-

anical stress, stack temperature and ultimately current density.

However, the mechanical self support of cells is basically provided by the thick-

est PEN layer; either one of the electrodes or the electrolyte (Sulzer Hexis, MHI,

RR, CFCL). Thick porous ceramic (RR, MHI) and metallic substrates and intercon-

nects (Ceres Power) onto which a thin PEN is applied have also been suggested to

provide the mechanical support required. The electrolyte and anode supported cells

are nowadays preferred in tubular and planar stacks.

The materials requirements for the cathode are high electronic and ionic con-

ductivity (mixed ionic electronic conductor, MIEC), sufﬁcient open porosity (20–

40 vol-%) for gas phase transport, to be catalytically active towards OOR, chem-

ically compatible with other stack components (electrolyte, interconnect, sealant)

as well as to have dimensional and thermodynamic stability in oxidizing atmo-

spheres. The preferred choice of material is strontium-doped lanthanum magnetite,

1−x

MnO

3−δ

(LSM) with typically x = 0.10–0.25. It has a thermal expansion

of around 11 × 10

−6

−1

between room temperature and operation temperature.

Other perovskites of type A

2−

such as rare earth and alkali iron-doped co-

baltite (i.e. La

0.5

Mn Co

0.8

0.2

3−δ

, BSCF) and lanthanum ferrite (preferably

A site doped by Sr, LSF) are mainly used at lower temperatures of 500

◦

C (932

◦

to 600

◦

C (1,112

◦

F). In LSM, oxide ion conduction proceeds via oxygen vacancies

incorporated by adding lower valence ions such as Sr (in Kröger Vink notation)

2La

+2SrO → 2Sr



··

+ La

(1.10)

8 T. Malkow

to the La sub-lattice providing for the deviation δ from stoichiometry. The electronic

conduction in LSM is due to hopping of electron holes between the Mn

/Mn

valence states. Similarly, the anode must be a mixed conductor too and be sufﬁ-

ciently porous, chemically compatible with the electrolyte and interconnect. It must

be stable in highly reducing atmospheres exhibiting oxygen partial pressures as low

as 10

−19

bar (10

−20

atm). Furthermore, the anode must catalyse the HOR in hydro-

gen fuelled SOFC and should exhibit catalytic activity towards steam reforming and

water gas shift in hydrocarbon fuelled SOFC. This is true for anodes containing a

transition metal (Ni, Fe, Co, Cr, Cu, Mo, V). In this case and for direct hydrocarbon

oxidation, the anode material should moreover resist coking due to gas phase carbon

deposition. Basically, carbon formation and subsequent deposition onto the anode

material, speciﬁcally metallic particles in the anode, is assisted by the Boudouard

reaction

2CO(g) ↔ CO

(g) +C(s) (1.11)

and for example, methane decomposition (cracking)

(g) ↔ 2H

(g) +C(s). (1.12)

In case of hydrogen-fed SOFC, cermets made of yttria-doped zirconia (YSZ) with

30–50 mol-% nickel are mainly used. Such 30% Ni cermets have a thermal ex-

pansion of about 12.5 × 10

−6

−1

while exhibiting electronic conductivities of

500–1,800 S/cm in the temperature and partial pressure range anticipated in SOFC

operation. For the latter case, nickel could partly be replaced by copper or Cu-Ni

alloys in addition to small amounts of ceria and molybdena, added to circumvent

coking of Ni particles. Moreover, Cu is less susceptible to deactivation by sulphur,

an impurity often present in hydrocarbon fuels. However, fuel loss, for example at

high utilization (large H

O/H

ratio), has to be avoided to prevent oxidation of the

metal particles in the anode. Usually, such oxidation is accompanied by an undesired

volume expansion which can be fatal for ceramic materials. Alternative anode ma-

terials include cermets made of ceria usually doped with 10–20% samarium (SDC)

and gadolinium (CGO) and single phase MIEC such as titania modiﬁed YSZ (YTZ)

and chromium doped LSM (LSCM). As opposed to the electrodes, the electrolyte

should ideally be a pure ionic conductor, be sufﬁciently dense, gas tight and as thin

as possible not to compromise on the required conductivity. It must also be chemic-

ally compatible with anode and cathode materials in addition to be thermodynamic-

ally stable in oxidising and reducing environments. The electrolyte shall have high

mechanical strength and toughness to withstand dynamic mechanical and thermal

loads. For high temperature operations, the ultimate materials choice is so far YSZ

containing 8 mol-% (13 wt-%) Y

(8YSZ) to stabilize zirconia in its face-centred

cubic ﬂuorite structure down to room temperature. Such material is polycrystalline

in nature and exhibits an ionic conductivity of about 0.1 S/cm at 1,000

◦

C but falling

to 0.03 S/cm at 800

◦

C. Its thermal expansion is about 10.5×10

−6

−1

,ratherclose

to that of the anode. Importantly, YSZ reacts with LSM at the electrode/electrolyte

interface to form insulating La

. Measures to combat pyrozirconate forma-

tion include the use of La-deﬁcient LSM with excess of Mn and the application of

1 SOFC in Brief 9

a barrier layer at this interface. In addition, glass impurities such as SiO

may se-

gregate at grain boundaries thereby increasing electrolyte resistivity. Scandia doped

zirconia (SSZ), SDC, CGO are useful alternative electrolytes. In case of the latter

two materials, ceria exhibits a Ce

/Ce

reduction in reducing atmospheres, res-

ulting in an increase in electronic conductivity but accompanied by a deleterious

volume expansion. The application of a thin YSZ layer between the doped ceria

and the anode may inhibit such an effect. Similarly, operation temperatures below

600

◦

C would retard such a reduction reaction. Moreover, doped lanthanum gallate

(La

0.9

0.1

0.8

0.2

3−δ

, LSGM) is suggested as an electrolyte for intermedi-

ate temperature SOFC (ITSOFC) operating at 650

◦

C–750

◦

C (1,202

◦

F–1,382

◦

F).

But, LSGM suffers from grain boundary coarsening and it reacts readily with Ni to

form volatile metallic phases. Apparently, the use of single phase MIEC electrodes,

for example anodes made of SDC, CGO, YTZ, doped LSC and cathodes made of

1−x

1−y

3−δ

(A = Sr, Ba, Ca and B = Fe, Cu, Ni) is a new trend gaining

more and wider acceptance. Their entire electrode surface can be used advantage-

ously for the cell reactions as compared to a much smaller active surface in con-

ventional electrode/electrolyte material pairs. The use of MIEC certainly increases

reaction rate though the determining step is likely to change.

Interconnects must be good electronic and thermal conductors, chemically com-

patible with electrode materials, high temperature corrosion resistant in oxidising

and reducing atmospheres (including carbon containing gases), and have thermal

expansion matching those of other cell components. For planar stacks, the bipolar

plate must be dense, have high mechanical strength and toughness and be able to be

easily machined (ﬂow channel incorporation). Metallic interconnects such as engin-

eered Cr-based alloys and ferritic stainless steels with thermal expansions of 11.5–

12.5 ×10

−6

−1

form scales of iron oxides and chromia when subjected to SOFC

conditions. It hinders electronic conduction particularly for scales which can be sev-

eral tens of and even more than 100 microns thick. In addition, Cr (oxy-hydroxide)

species evaporating from the plate metallic surface, or from these scales, poison the

cathode when deposited on it; thereby reduce its activity signiﬁcantly. Measures to

combat these effects include applying protective layers of perovskites onto the bi-

polar plate. However, additional layers complicate stack manufacture and are likely

to introduce additional contacts and issues related to changing materials behaviour

during operation. In TSOFC, Sr- and Mg-doped lanthanum chromites, La

1−x

(Sr,

Mg)

(LSMC) with 10

−5

−1

thermal expansion are used as the interconnects.

Such materials are also used in some planar stack designs. Drawbacks of LSMC are

poor sinterability in air below 1,350

◦

C (2,462

◦

F) and possible formation of volatile

Cr species.

PEN fabrication particularly for planar stacks, is usually carried out in layers us-

ing popular deposition methods such as screen printing, wet spraying, tape casting

and calendering at room temperature followed by (intermediate) ﬁring at high tem-

peratures between 1,300

◦

C (2,372

◦

F) and 1,700

◦

C (3,092

◦

F), respectively to sinter

the PEN and ceramic interconnect. Elevated temperature fabrication techniques in-

clude plasma spraying, electrophoresis deposition (EPD) and chemical vapour de-

position (CVD) for both principle designs. Moreover, co-fabrication is sometimes

10 T. Malkow

employed to minimize process steps, thereby reducing costs and automating com-

ponent manufacture. It should be noted that reaction layers may form between the

cell assembly components already during PEN fabrication and stack manufacture

due to inter-diffusion, which can be deleterious to stack performance. It is now com-

mon practice to employ bi-layer composite cathodes composed of a thin functional

layer, made of the actual cathode material, and the electrolyte sandwiched between

the latter and a thick layer made exclusively of cathode material. In a similar way,

anode functional layers can be applied. Such arrangement obviously enhances the

respective TPB zones. Furthermore, stack developers increasingly use barrier layers

between the PEN components and interconnect and graded cell structures to en-

large stack performance and durability. The former approach protects cell materials

from deterioration in environments harmful to otherwise well-performing materi-

als. The use of graded materials primarily aims to increase component functional-

ity. For example, electrode porosity may gradually be dominated by smaller sized,

more compact pores near the electrolyte to facilitate molecular diffusion and en-

hance electrochemical activity. A more coarse and open porous electrode structure

may prevail near the gas channel to enhance mass transport (gas phase diffusion

and convection). Similarly, the chemical compatibility of the PEN components and

interconnect can be tailored; though it certainly necessitates the use of suitable and

cost effective co-fabrication and co-ﬁring techniques. However, it would result in

material anisotropy.

Interestingly, research has started on single chamber SOFC (SC-SOFC) con-

cepts. However, the SC-SOFC exhibits inherently low power density and is therefore

primarily of academic interest. It has the potential to relax cell component require-

ments and probably to ease manufacture. The principle of SC-SOFC is that it is fed

by an air fuel mixture which ﬂows onto the PEN contained in a single compartment,

avoiding the use of gas separator plates and high temperature sealants. The ﬂuid

may ﬂow simultaneously or sequentially along the electrodes. Both electrodes are

either built onto the same side of the electrolyte some distance apart or on oppos-

ite sides. Low temperature operation would apparently suppress direct combustion

of the air fuel mixture provided the electrode materials chosen are highly selective

towards their respective catalytic reactions. SC-SOFC stacks may hold prospects in

speciﬁc applications where the reaction products are the prime focus.

More recently, protonic ceramic fuel cells (PCFC) have emerged as an alternative

SOFC technology. Such fuel cells have the advantage that fuel is not diluted by

water which is produced at the cathode rather than the anode as for conventional

SOFC. This is of great interest when operating on hydrocarbon fuels to allow their

direct conversion in addition to steam reforming. The electrolyte in the PCFC is

a high temperature proton conductor such as barium and strontium zirconates as

well as their cerates. Doping of alkaline cerate with rare earth oxides, for example,

gadolinia forms oxide ion vacancies

2Ce

+ Gd

→ 2Gd



+ V

··

+2CeO

(1.13)

and alternatively, electron holes

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