Evaluation of hydrogen and methane-fuelled solid oxide fuel cell systems for residential...

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 8 6 3 0 – 8 6 4 4

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Evaluation of hydrogen and methane-fuelled solid oxide fuelcell systems for residential applications: System designalternative and parameter study

P. Kazempoor a,b,*, V. Dorer a, F. Ommi b

a EMPA Swiss Federal Laboratories for Material Testing and Research, Building Technologies Laboratory, CH-8600 Dubendorf, Switzerlandb Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 14 June 2009

Received in revised form

24 July 2009

Accepted 31 July 2009

Available online 27 August 2009

Keywords:

Solid oxide fuel cell

Intermediate temperature

Hydrogen fuel

Methane fuel

System model

Residential application

Abbreviations: CHP, combined heat and ponegative electrode; SC, steam to carbon ratiophase boundary; WGS, water gas shift react

* Corresponding author. EMPA Swiss FederalDubendorf, Switzerland. Tel.: þ41 44 823 42

E-mail addresses: pejman.kazempoor@em0360-3199/$ – see front matter ª 2009 Profesdoi:10.1016/j.ijhydene.2009.07.119

a b s t r a c t

Design-point and part-load characteristics of a solid oxide fuel cell (SOFC) system, fuelled

by methane and hydrogen, are investigated for its prospective use in the residential

application. As a part of this activity, a detailed SOFC cell model is developed, evaluated

and extended to a stack model. Models of all the required balance of plant components are

also developed and are integrated to build a system model. Using this model, two system

base cases for methane and hydrogen fuels are introduced. Cogeneration relevant

performance figures are investigated for different system configurations and cell param-

eters i.e. fuel utilization, fuel flow rate, operation voltage and extent of internal fuel

reforming. The results show high combined heat and power efficiencies for both cases,

with higher thermal-to-electric ratio and lower electric efficiency for the hydrogen-fuelled

cases. Performance improvements with radiation air pre-heaters and anode gas recycling

are presented and the respective application limits discussed.

ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1. Introduction homes to large scale commercial buildings; SOFC systems are

Buildings worldwide contribute significantly to the high and

still increasing energy consumption. Therefore, measures for

reduction have received increasing attention. Building inte-

grated co- and polygeneration are emerging technologies with

the potential to reduce primary energy consumption and

associated greenhouse gas emissions. With their high electric

efficiency, high exhaust gas temperature and wide range of

capacity covering all types of buildings from single family

wer; CSTR, stirred tank r; SOFC, solid oxide fuel cion; RAP, radiation air prLaboratories for Material75; fax: þ41 44 823 40 09.

pa.ch, p_kazempoor@msor T. Nejat Veziroglu. Pu

expected to play an important role in distributed energy

generation and in building integrated co- and polygeneration.

However, there are a lot of uncertainties about the best layout

of the SOFC system in terms of feasibility, performance,

economics and controllability. Therefore, the development

and evaluation of building integrated micro- and small-scale

co- and polygeneration SOFC systems require experimental

setups or detailed models on cell, stack and system levels. A

few detailed SOFC system models have been developed for the

eactors; BoP, balance of plant; PEN, positive-electrode/electrolyte/ell; SR, steam reforming; TER, thermal-to-electric ratio; TPB, triplee-heater; PCU, power conditioning unit.Testing and Research, Building Technologies Laboratory, CH-8600

odares.ac.ir, [email protected] (P. Kazempoor).blished by Elsevier Ltd. All rights reserved.

mailto:[email protected]



http://www.elsevier.com/locate/he

http://www.sciencedirect.com

Nomenclature

Latin letters

A Area, m2

Ci Molar concentration of components i, mol m�3

Dh Hydraulic diameter, m

E0 Standard equilibrium potential, V_E Fuel and air enthalpy energy flow, J s�1

ECH4 Methane activation energy, J mol�1

F Faraday constant (¼96485 C mol�1)

f Friction factor

H Height, m

HHV Higher heating value, J mol�1

i Cell current, A

J Current density, A m�2

J0 Exchange current density, A

K Pre-exponential constant

Kc Flow conductance, kg pa�1 s�1

Keq,WGS Equilibrium coefficient for water gas shift reaction

KWGS Pre-exponential constant of water gas shift

reaction, mol s�1 m�2 Pa�1

L Length, m

LHV Lower heating value, J mol�1

_m Mass-flow rate, kg s�1

_Mfeed Feed flow rate to cell or stack, kg s�1

_n Molar flow rate, mol s�1

NCh Channel number

ne Number of electrons transferred per

electrochemical reaction_nH2 ;consumed H2 consumed in each channel, mol s�1

p Partial pressure, Pa

P Pressure, Pa

PAC,Net Net system AC power output, W_QCHP System output heat, J s�1

_q Heat flux, W m�2

R Gas constant, J k�1 mol�1

Re Reynolds number

Req,ohm Equivalent ohmic resistance, U

rj Rate of reaction j, mol m�2 s�1

T Temperature, K

Tex SOFC system exhaust gas temperature

t Thickness, m

uA Air velocity, m s�1

UF Fuel utilization

uF Fuel velocity, m s�1

VNernst Nernst cell potential, V

Vop Cell voltage, V

W Width, m

Wa Actual compressor work, W

WBlower Blower power, W

WComp Fuel compressor power, W

Ws Isentropic compressor work, W

Xi Molar fraction of specie i

Greek letters

b Electron transfer coefficient

G Non-dimensional parameter

d Thickness, m

DP Pressure drop, Pa

DX Length of discretized element, m

h Efficiency, %

hact Activation polarization, V

hdiff Diffusion polarization, V

hohm Ohmic polarization, V

lCell Air excess ratio

m Dynamic viscosity, kg m�1 s�1

ni,j Stoichiometric coefficient of component i in

reaction j

r Density, kg m�3

U Non-dimensional parameter

Super scripts

0 Open circuit/feed conditions (fuel and air channel

inlet)/standard condition

cond Conduction

conv Convection

Rad Radiation

Subscripts

A,Air Air

act Activation

An Anode

b Bulk

Ca Cathode

Ch Channel

Eff. Efficiency

El. Electrolyte

F,Fuel Fuel

Ic Interconnector

In Inlet

Out Outlet

Ox Oxidation

Red Reduction

Stack SOFC stack

Sy System

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 8 6 3 0 – 8 6 4 4 8631

building application, many models are more focused on gas

turbine–SOFC cycles performance analysis for a large systems.

Braun [1] investigated micro-cogeneration systems for resi-

dential applications. Presenting the effect of the different

system configurations on SOFC system performance, espe-

cially for cogeneration, Autissier [2] applied multi-objective

optimization methods to his system model. Finkenrath [3]

developed a system model for larger scale SOFC systems.

To bridge the still existing gap between the many more

sophisticated SOFC stack models and the few existing

system models, this paper presents SOFC cell, stack and

system models, some of them adapted and generalized

from existing literature, which are especially developed

for the analysis of building integrated co- and polygenera-

tion SOFC systems. In more detail, the goals of the paper

are:


(i) To compare methane- and hydrogen-fuelled SOFC

systems.

(ii) To evaluate varying system alternatives.

(iii) To gain knowledge on system behaviour by parametric

studies.

(iv) And finally to develop a model which can easily be used to

generate the input characteristic curves for the IEA ECBCS

Annex 42 fuel cell cogeneration model [4], which uses

a pragmatic ‘‘grey box’’ approach. For a specific device,

the grey box model has to be calibrated using perfor-

mance data gained from laboratory tests. However, these

model parameters can also be derived using a detailed

fuel cell system model.

Based on these goals, such a detailed SOFC cell model was

developed; based on the mass, momentum and energy conser-

vation equations (besides the electrochemical analysis and fuel

kinetic reaction). It is briefly presented here. The cell model is

extended to a system model. Models for the necessary balance

of plant (BoP) components were also developed and integrated

into an SOFC system model which can be used specifically for

co- and polygeneration. The system model is kept very flexible

and can be used to simulate both high and middle temperature

SOFC systems with any kind of fuel. In this paper, besides

the model description, two base cases for hydrogen and

methane fuel are introduced. For each case, design-point

and off-design-point operations, system design alternatives,

and also parametric analyses on cell and system levels in terms

of energy performance are presented and compared.

2. SOFC cell model description

2.1. Model definitions and assumptions

Many current stack designs in the range of the application

used in this research (1–20 kWe) are moving towards planar

Fig. 1 – Cell geometry and un

designs [1–3,5], the considered geometry for the SOFC cells is

therefore planar type with internal fuel and air manifolding.

A detailed quasi-2D SOFC channel model based on elec-

trochemical, mass and energy balances was developed and

extrapolated for the entire cell–stack. A schematic of the cell

model is shown in Fig. 1. As can be seen, the planar SOFC

channel is divided into series of piped-type volumes (cells),

where the number and dimensions can be defined by the user.

The finite volume method is used to discretize the governing

equations on each cell. The main assumptions of the model

are [1,6–8]: (i) uniform distribution of feed gases to each

individual cell in the stack and among the channels; (ii)

steady-state condition; (iii) 1D cell representation along the

streamwise direction (iv) each of the gas channels in the unit

cell acts as continuously stirred tank reactors (CSTR); (v)

lumped temperature of the solid cell structure: (vi) due to the

high conduction electrodes and current collector acts as iso-

potential surfaces; (vii) a constant Nusselt number is

assumed.

Any combination of H2, CO, CO2, H2O, CH4 and N2 is allowed

as fuel composition, and the oxygen fraction in the cathode

gas can be set to any value.

2.2. Model equations

2.2.1. Electrochemical modelThe Nernst equation for hydrogen, considering the complete

calculation of activation, ohmic and diffusion losses, Eqs. (1)

and (2), is used for modelling the electrochemical perfor-

mance of the SOFC.

Vop ¼ VNernst ��

hohm þ hact þ hdiff

�(1)

VNernst ¼ E0 þ RTPEN

neFln

XH2 ;b

�XO2 ;b

�0:5

XH2O;b

!þ RTPEN

2neFln

�PCa

P0

�(2)

The calculation of the ohmic voltage losses follows Ohm’s law:

it element configuration.


hohm ¼ iReq;ohm (3)

In the present model, the method presented in Ref. [6] is used

for the calculation of the ohmic equivalent resistance. In this

method it is assumed that the current flow path is directed

perpendicularly to the cell plane. Then the resistance of the

cell, estimated by subdividing the cell into three parts, namely

air channel interconnector, solid structure of anode, electro-

lyte and cathode layers (PEN), and fuel channel inter-

connector, all of which act as series of resistances.

The activation losses are due to the energy barrier to be

overcome in order for the electrochemical reaction to occur,

and can be characterized by the Butler–Volmer equation [9]:

J ¼ J0

�exp

�bneFhact

RTPEN

�� exp

� ð1� bÞneFhact

RTPEN

�(4)

The complete form of Eq. (4) with b¼ 0.5 is considered in the

present model [9]. The values and equations suggested in

Ref. [10] were selected to calculate the anode, J0,An, and

cathode, J0,Ca, exchange current densities as a function of the

gas compositions in the fuel and air channels and PEN

temperature.

The diffusion polarization can be described in a variety of

ways. In this research, two levels of diffusion phenomena

between the bulk gas phase to the electrode surface and

between electrode surface and triple phase boundary (TPB)

have been applied in the model as follows [11,12]:

hdiff;Ca ¼RTPEN

4Fln

�XO2 ;b

XO2 ;TPB

�(5)

hdiff;An ¼RTPEN

2Fln

�XH2bXH2O;TPB

XH2O;bXH2 ;TPB

�(6)

In the present model, binary diffusion is considered to calcu-

late the gas concentrations in the electrode surfaces. Both

ordinary diffusion and Knudsen diffusion may occur simul-

taneously in the porous media and the effect of these can be

considered with the effective diffusion coefficient [12].

Therefore, the diffusion between the surfaces and TPB is

calculated considering the effective diffusion coefficient.

2.2.2. Material balancesThe mass balance sub-model calculates the compositions in

the fuel and air channels due to the electrochemical reactions,

water–gas-shift reaction (WGS), mass transfer of the chemical

species, and internal methane steam reforming reaction (SR).

The mass balance equations for both air and fuel channels can

be written as:

uFvCi;F

vx¼X

j

ni;jrj1

HFCi;Fjx¼0:0¼C0

i

i˛fCH4;CO2;CO;H2O;H2;N2g j˛fOx;WGS;SRg (7)

uAvCi;A

vx¼ ni;jrj

1

HACi;Ajx¼0:0 ¼ C0

i i˛fN2;O2g j˛fRedg (8)

Local rate of reactants and products to the electric current can

be calculated by Faraday’s law [7]:

rOx ¼ rRed ¼J

2F(9)

The following equations are used to calculate SR [10] and WGS

reactions [7,13]:

rSR ¼ KpCH4 exp

�� ECH4

RTF

�(10)

rWGS ¼ KWGSpCO

1� pCO2

pH2

Keq;WGSpCOpH2O

!(11)

2.2.3. Energy balancesIn the SOFC energy analysis, the different temperature

layers can be used to calculate the temperature profiles in

the SOFC. Different approaches with one to five tempera-

ture layers are presented in the literature [1,7,13]. However,

there are no guidelines available how to properly select

temperature layers [13]. To improve the accuracy of the

present model, five temperature layers have been consid-

ered, namely PEN, air channel, fuel channel, air inter-

connector and fuel interconnector. In the middle of

a planar SOFC stack, the air and fuel side interconnectors

of adjacent cells could be considered as one temperature

layer, but a separate temperature layer is used here for

future investigations of the cells at the boundaries of the

stack. A schematic of the energy flow for a unit element is

shown in Fig. 2.

In Fig. 2, _ERea, _EPro are the energies related to the mass

transfer of reaction products and to the reactants between

bulk gases and PEN or vice versa. _qRadPEN;Ic is the radiation heat

exchange between PEN and interconnector. It is calculated

based on Ref. [14].

2.2.4. Pressure losses in the SOFC fuel and air channelsIn the SOFC channels, the gas flow is not isothermal, but the

flow can be assumed to be laminar and fully developed due to

the small size of the channels [15]. The fully developed

laminar flow solutions of the Navier–Stokes equations or

steady Hagen–Poiseuille analysis can be used for the calcula-

tion of the pressure losses [16].

Considering the definition of the hydraulic diameter and

the related Reynolds number, the mass-flow rate in the

channel, in function of the net pressure difference from the

channel inlet to the outlet, is calculated as [16]:

_m ¼�

1Ref

DhACh

2LCh

r

m

�ðPIn � POutÞ ¼ KcðPIn � POutÞ (12)

where m is the dynamic viscosity of the fluid. The constant Kc,

flow conductance,

Kc ¼�

1Ref

DhACh

2LCh

r

m

�(13)

characterizes the proportionality between the mass-flow rate

in a channel and the net pressure difference from inlet to

outlet. In the present model, the flow conductance Kc is con-

structed based on the viscous effects in the channels.

2.2.5. Gas and solid material propertiesThe following methods are used to calculate the gas and solid

material properties:


(i) The enthalpy of the mixture is evaluated by a molar

mixing law [17] and the enthalpy of each species calcu-

lated based on the exact gas temperature.

(ii) The heat transfer coefficients, needed to solve the energy

balance equations, are calculated with a constant Nusselt

number, an assumption confirmed as a good approxi-

mation in the literature [1,6,7,13].

(iii) Due to the electrochemical reaction the mass transfer of

the reactants and products, the gas mixture composition

is not constant along the channel length. Therefore, the

dynamic viscosity and thermal conductivity of the

mixture vary. The kinetic theory of gases is used to

consider this effect [15].

(iv) Data presented in Ref. [5] have been assumed for the

temperature dependent specific resistivity of the solid

parts, needed for calculation of ohmic polarization.

(v) The Fuller equation is used to calculate the binary diffu-

sion coefficients [15]. The Knudsen diffusion coefficients

are calculated based on the average molecular speed of

each component [11]. The effective diffusion coefficients

are calculated based on the binary and Knudsen diffusion

coefficients, considering the mixing rule [11].

3. System components model description

The system component models are needed to model the

operation and to assess the SOFC system performance. In

the capacity range considered in this research, (1–20 kWe), the

following BoP components have been considered, taking into

account the specific requirements for the envisaged residen-

tial application, such as, system size, system simplicity and

also economic criteria [1–3,5]: Fuel compressor, air blower,

water pump, air and fuel ejector, external fuel pre-reformer,

gas to gas heat exchanger, gas to water heat exchanger, DC to

AC inverter, desulphurizer, RAP and air filter. Each component

was individually modelled in the present work. A brief

Fig. 2 – Energy flows f

introduction to these system component models is given in

the sub-sections below. Economics are also of great impor-

tance in any SOFC development. For systems’ evaluations

however, few reliable cost data are available. In the frame of

this paper, no economic evaluations were performed, but

economic criteria were considered to select the system

components and operating points, using the result of some

previous and similar systems [14].

3.1. Compressor, blower and pump models

In the system model; compressors, pump and blower have

been modelled in a similar way, based on the efficiencies

expressions:

hComp ¼Isentropic compressor work

Actual compressor work¼Ws

Wa(14)

3.2. Desulphurizer

A literature review showed that the desulphurizer model is

neglected in some SOFC system models [3,12]. However, some

of the available models demonstrate that at least the pressure

loss in the desulphurizer must be considered in the SOFC

system design [1,18]. In the present model, a constant pres-

sure drop value of 0.01 bar, as suggested in Ref. [19] for the

5 kWe SOFC system, and adiabatic conditions, are assumed.

3.3. Heat exchanger analysis

Three types of heat exchangers are considered in the present

research, namely fuel pre-heater, water boiler and air pre-

heater. For all three types, the hot fluid stream is the exhaust

burner gas. Because of the higher SOFC operation tempera-

ture, air and fuel pre-heaters might be used in any system

design, but a water boiler may not be needed when anode gas

recycling is applied.

or a unit element.

Fig. 3 – (a) RAP structure and its integration to the stack; (b)

energy flow for an RAP.


The Effectiveness–NTU method [20] has been applied to

calculate the output characteristic of the heat exchangers.

This method is more appropriate when the output tempera-

ture of the cold and hot streams is not defined.

3.4. Fuel and air ejectors

In SOFC systems, water must be added to the anodic stream

for hydrocarbon reforming. Since the anodic exhaust stream

is rich in steam (about 40–45% in mass) and poor in carbon

monoxide, the recirculation of a part of this gas produces

enough water vapour in the anodic inlet. A water line with

a specific pump and boiler can also be used for this purpose.

However, depending on the system size, the efficiency, oper-

ation life and capital costs of the system may be improved by

anode stream recycling. In SOFC systems, ejectors or tradi-

tional blowers can be used for recycling the anodic stream.

However, taking into account that the recirculation is carried

out at a temperature just over 650 �C while the temperature in

the stack is close to 1000 �C for SOFCs, the use of an ejector is

less risky.

Thus, a suitable ejector model must be included in the

SOFC system model. In order to keep the model as generic as

possible in regard to overall system performance, a lumped

model method as suggested in Ref. [21] is applied, considering

(i) steady-state situation, (ii) constant cross-section mixing,

and (iii) isentropic expansion of the actuating fluid.

In this work, the amount of recycle is defined as the frac-

tion of the anode outlet molar flow that is recirculated back to

the pre-reformer inlet.

Besides the anode gas recycling (AGR), an ejector is also

used for recycling the cathodic stream. Using cathode gas

recycling (CGR) can effectively decrease the air access ratio to

the system and consequently size and cost of the air pre-

heater.

3.5. Pre-reformer

In a reformer, at high temperatures (700–1100 �C) and in the

presence of a metal-based catalyst (nickel), steam reacts with

methane to yield CO and H2. The carbon monoxide can also be

converted to CO2 and H2 by WGS reaction. Thus, the following

processes are considered in the pre-reformer of the present

model:

(i) Pre-heating of the fuel mixture to the desired pre-

reformer and inlet SOFC fuel temperature. In fact, in the

present model the fuel pre-heating is coupled with the

pre-reformer.

(ii) Conversion of higher hydrocarbons to methane and

partial conversion of methane to hydrogen.

(iii) WGS reaction

Considering a steady-state and adiabatic pre-reformer

operation, the material balance equations were written for

each component [12]. To solve the set of equations governed

by material balances, two additional equations must be

added. In the pre-reformer, the SR and WGS reactions are

considered in equilibrium conditions and the two additional

equations are added to the material balance equations [12].

3.6. Radiation air pre-heater

In the SOFC operation efficiency range (electric efficiency

about 30–55% LHV), the amount of waste heat is notable and

must be considered in any system design [22]. Radiation air

pre-heater (RAP) [22] and indirect internal reformer (IIR) [12]

are promising components to manage waste heat. Both of

them are built in such way that radiation is the governing

transfer mechanism for waste heat from the stack.

An example of an RAP design and its integration into the

stack are shown in Fig. 3(a). As can be seen, two RAP elements

are attached to the stack. The stack is cooled by conduction to

the external stack wall, radiation to the adjacent RAP walls,

and convection to a reduced airflow through the RAP.

In an SOFC system, a high air excess ratio is needed to cool

the SOFC stack. The high airflow ratio leads to increased size

and cost of the system components, especially the air pre-

heater. Therefore, in this research, an RAP is considered to

reduce the air pre-heater heat exchanger size and thus cost.

The following advantages can also be allocated to RAPs [22]:

(i) As RAPs are designed to selectively remove the heat from

the hottest parts of the stack, the cell performance can be

improved. The results of a well-designed RAP are

a smooth temperature distribution inside the stack and

a longer stack life.

(ii) Lower air access ratio may be used for the system.

(iii) RAPs can easily be used in the SOFC network, to increase

the system compactness and modularization capacity.

The same and practical configuration that has been sug-

gested in Ref [22] is used here. Two RAPs are used in this

configuration for each stack. The horizontal airflow in the RAP


is arranged so that the relatively cold RAP inlet air is opposite

to the potentially hot air outlet/fuel outlet quadrant of the

stack. The panels are opposite to the fuel inlet and outlet sides

of the stack. The panel airflow is perpendicular to the stacking

direction and counter to the airflow in the cells.

A 1D finite volume model, considering the mass, energy and

momentum conservation laws, has been developed to calculate

the RAP heat transfer and flow characteristics. A schematic of

the energy flows for the RAPs is shown in Fig. 3(b). The main

assumptions used inthe model are: steady-state condition: one-

dimensional cell representationalong the streamwisedirection:

adiabatic boundaries at the left and right hand sides of the

computational domain; adiabatic wall surface for the outer RAP

wall; heat exchange between the stack and the inner wall of the

RAP assumed to be dominated by radiative heat transfer.

3.7. Burner

An ideal model is considered for the burner. This means that

all of the methane, hydrogen and carbon monoxide will be

converted to carbon dioxide and steam. Adiabatic condition or

constant heat losses can be used to calculate the exhaust gas

temperature [12].

In the burner model it is assumed that at least the stoi-

chiometric rate of oxygen is available. Else the outlet oxygen

mole fraction of the model will turn negative.

3.8. Power conditioning unit

The power conditioning unit (PCU) has been modelled

considering a constant efficiency as shown in Table 1.

3.9. Cell-to-stack model

The stack performance is modelled by extending the results of

the cell model (described in Section 2 above), and considering

the stack pressure losses and the radiative heat transfer effect

from the stack to the airflow.

A generic model which accounts for the pressure losses in

the stack certainly has its limitations and shortcomings, as

SOFC stack analysis is very much dependant on the actual

design. Up to now, a number of studies concerning experi-

mental and mathematical modelling have been presented for

calculation of the pressure losses in SOFC stacks. A general

model based on dimensionless groups has been developed in

Ref. [14]. The model solves mass and momentum equations to

predict pressure drop and flow uniformity within individual

channels. By formulating the problem in dimensionless vari-

ables, the solutions are generalized in terms of the two non-

dimensional groups and can be used for any particular

applications. The two non-dimensional groups are [14]:

G ¼�

PCh

2DhmRef

�LCh

_mCh

U ¼ Kc _mCh

rA2Ch

(15)

After some calculations and considering a well-designed

manifold which works in the uniform-flow region, the pres-

sure losses in the SOFC cell headers and manifolds can be

calculated as [14]:

DP ¼_M

2

feed

KcNCh(16)

Eq. (16) is general and can be used to calculate the pressure

losses of any kind of manifold e.g. the stack manifolds (inlet and

outlet), and the cell feed header. In the case of cell pressure

losses calculation, _Mfeed is the feed flow rate to the cell feed

header and for thestack pressure losses calculation it is thefeed

flow to the inlet and outlet fuel and air manifolds respectively.

The method given in Ref. [16], as mentionedabove, was used

in the present model for the calculation of the stack pressure

drop. Therefore, the stack pressure drop is the sum of (i) the

fuel and air header pressure losses and (ii) the feed fuel and air

manifold pressure losses. Both can be calculated using Eq. (16).

To consider the radiative heat transfer from the stack to

the airflow, a constant temperature based on the average cell

temperature was selected for the stack. As outlined in Section

3.6, the heat exchange between the stack and the inner wall of

the RAP is assumed to be dominated by radiative heat trans-

fer. The energy balance equations are written for the RAP

compartments as shown in Fig. 3b. Based on these equations,

the heat exchange from the stack to the RAP can be calculated.

Considering an identical heat release from each cell, the total

heat transfer from the stack is evenly distributed and allo-

cated to the individual cells and the resulting value subtracted

in the cell interconnector energy balance equations.

3.10. System pressure losses

In the SOFC system; a significant part of the SOFC system

power output might be used to power the system auxiliaries

(about 20%). Therefore, the pressure losses and related pump

and blower power should be analysed carefully. Although an

approach assuming constant pressure losses may be accept-

able for the design-point dimensioning, for part-load investi-

gation and parameter sensitivity analysis a more detailed

approach is required.

In the model, the following approaches are used to calcu-

late the components pressure losses:

(i) A detailed pressure losses analysis based on the mass and

momentum conservation equations has been applied for

the cells, stack, RAP and ejectors. Therefore, for each

system operation point the pressure losses of the

mentioned components can be calculated directly using

the conservation equations.

(ii) Constant values are considered for the burner (20 mbar),

desulphurizer (100 mbar), air filter (5 mbar) and pipe lines

(25 mbar).

(iii) Pressure loss curves as a function of the system volu-

metric flow rate are considered for the heat exchanger,

based on the experimental data presented in Ref. [23].

4. SOFC system model performanceparameters

The following performance parameters are considered for cell

and system evaluations: SOFC cell fuel utilization, air excess

Table 1 – Input parameters for the base cases.

Parameters Value Parameters Value

SOFC stack input parameters

Anode thickness (m) 500� 10�6 Average current

density (A m�2)

5000

Cathode thickness (m) 50� 10�6 Air excess ratio Case (A): 10

Case (B): 12.5

Electrolyte thickness (m) 20� 10�6 Max. PEN allowable

temperature increase (K)

<100

Interconnector thickness (m) 0.5� 10�3 Stack configuration Co-flow

Cell active

area (width�height) (mm2)

100� 120 Air and fuel

inlet temperatures

to cells (K)

1023

Channel height,

fuel and air sides (m)

1� 10�3 Number of channels,

fuel and air sides

25

Channel width,

fuel and air sides (m)

3� 10�3 Number of cells 150

Fuel utilization (%) 80 Cell electrochemical

and thermal

properties (Eqs. (1)–(6) parameters)

Ref. [7]

System input parameters – base cases

Anode recycling

ratio (%)

Case (A): 0 Fuel and air input

temperature to system (�C)

15

Case (B): 60

Extent of methane

reforming

(percent of external reforming)

0 Cathode recycling

ratio (%)

0

Compressor efficiency (%) 68 Steam to carbon

ratio to cells

and reformer

>2

Blower efficiency (%) 73 Whole system

exhaust gas temperature (�C)

50

DC/AC convertor

efficiency (%)

92 System heat

losses (W)

5% of AC power

Air feed 21% O2, 79% N2 Inlet pressure (Pa) 101,325

Fuel feed

to the systems

Case (A): 95% H2þ 5% H2O

Case (B): 100% CH4


ratio, cell–stack efficiency, electric efficiency and CHP effi-

ciency respectively. They are defined as:

UF;Ch ¼_nH2 ;consumed�

4 _nCH4þ _nCO þ _nH2

�An;In

(17)

lCell ¼�

_nO2

�Ca;In�

2 _nCH4 þ 0:5ð _nCO þ _nH2Þ

An;In

(18)

hCell–Stack ¼PDC

ð _nFHHVFÞAn;In

(19)

hSy;E ¼PAC;Net

ð _nFHHVFÞSy;In

(20)

hCHP ¼PAC;Net þ _QCHP

ð _nFHHVFÞSy;In

(21)

For the calculation of the CHP efficiency, the amount of heat

available from the SOFC system for a constant exhaust gas

temperature after the exhaust/water heat exchanger of 50 �C

was considered. In reality, the efficiency depends of course on

the temperature level of the heat extraction fluid cycle. Some

real SOFC devices like the Hexis micro-CHP device even allow

for condensation in the exhaust gas, e.g. in low temperature

space heating applications, thus increasing the CHP efficiency.

On the other hand, when coupling an SOFC device to a ther-

mally driven chiller, heat normally has to be provided at

temperatures of at least 75 �C.

The thermal-to-electric ratio (TER) is another parameter

that can be used for the evaluation in residential applica-

tion. This parameter shows the thermal energy load to the

base electricity demand of a home. It is highly dependent

on some parameters like location, building type, design

usage patterns [1]. The annual hourly average domestic hot

water TER for a modest (200 m2) home in the US can range

from 0.7 to 1.0 [1] and the requested hot water temperature

is about 60 �C.

5. System configuration and parameters

All of the components models presented in the previous

sections are implemented in the EES software [24] to build the

system model. An example of the model input data is shown

in Table 1.


Although, as mentioned, both SOFC temperature opera-

tions can be investigated using the present model; the inter-

mediate temperature SOFC cell design is considered here. This

design is being developed for lower temperature operation to

mitigate the problems of materials degradation [5].

Except the cell geometrical parameters, the data presented

in Ref. [7] for the material properties of an intermediate

temperature direct internal reforming (IT-DIR) SOFC were

used as input values to the cell model. The remaining input

data are shown in Table 1. The most important operational

constraints for the SOFC stack are the maximum cell

allowable temperature increase (DTPEN¼ (TPEN,max� TPEN,min)

<100 K) and the steam to carbon ratio (SC) of the fuel input to

the stack (SC> 2).

The amount of AGR is determined from the specification of

the SC of the fresh fuel–AGR mixture. In methane-fuelled

systems incorporating AGR, the SC ratio is defined as,

SC ¼_nH2O;AGR

_nCH4 ;Sy þ _nCO;AGR þ _nCH4 ;AGR(22)

To avoid any carbon decomposition (SC> 2), about 60% of the

anodic stream must be recirculated. As a starting point for the

parameter variation, two base cases were selected: Case (A)

a simple SOFC system for hydrogen fuel (Fig. 5), Case (B) an

SOFC system for methane fuel and with anode gas recycling

only (Fig. 6).

The anode gas recycling was selected instead of the water

line for the methane-fuelled system because of its significant

role in improving the efficiency and reducing the cost of an

SOFC system [1,5,18]. Table 1 shows the input data and the

assumptions made for these base cases.

Besides the base cases, different system alternatives were

examined, incorporating additional components to the base

cases. The effect of the different cell parameters was inves-

tigated and parameter values for an optimised system were

identified. Based on literature [1–3,18], the following parame-

ters were considered for a comprehensive study of the cell

operating parameters on the system performance: extent of

methane external reforming (by system design alternatives),

fuel utilization, fuel flow rate, and cell operational voltage.

The choice of these parameters is dependent on which

parameters can be regulated with active control measures and

Fig. 4 – Current density and PEN temperature profiles along

the cell length, input data from Ref. [7].

also on how much the manipulation of these parameters

results in changes in performance indices, such as cell power

and efficiency.

The air excess ratio to the system could also be considered

as an operating parameter but here it was not investigated

separately. Here, for each change of operational parameter,

the air excess ratio was varied such to control the

DTPEN< 100 K condition.

6. Results

6.1. Cell model evaluation

As the SOFC stack is an important component in the system,

the cell model should be evaluated. The data presented for the

two sets of benchmark test (BMT) for high temperature (HT)

SOFC cell design [25] (based on [26]), and for an IT SOFC [7]

were selected for the model evaluation. In Table 2, as an

example, present model results are compared with results in

Ref. [7] for an IT SOFC in both co- and counter-flow cell

designs. The results show good accuracy of the present model

for both cell designs. Different cell modelling approaches are

identified as the source of the few discrepancies observed in

comparison with results in Ref. [7]. However, the present

model results are expected to be more accurate than those

given in Ref. [7], as in the 1D SOFC model presented in Ref. [7],

the interconnector rib effect was not considered. Due to this

rib effect the present results for the cell performance param-

eters like power output and cell efficiency show lower values

than data presented in Ref. [7] (an example of the distributed

parameters is shown in Fig. 4).

6.2. Base cases results

Considering the data presented in Table 1, examples of the

systems process flow diagram for both base cases, described

in Section 5, are shown in Figs. 5 and 6. As mentioned, Case (A)

is a hydrogen-fuelled SOFC system. Hydrogen can be supplied

to the system in different ways. In the present model, a low

pressure hydrogen fuel mixture (95% H2þ 5% H2O) and air

(21% O2þ 79% N2) at 15 �C enter to the system and are

compressed in the fuel compressor and blower respectively.

Before entering the SOFC stack, both flow streams are pre-

heated to the cell operation temperature (750 �C). The burner

exhaust gas is used here to pre-heat both streams (an air

bypass line is used to prevent the burner temperature rising

above 950 �C, in order to allow for lower burner material cost).

After pre-heating, the remaining thermal energy of the burner

exhaust gas can be used for co- or polygeneration in a heat

recovery heat exchanger. As shown in Fig. 5, the SOFC module

operating at 0.78 V produces about 7.02 kW of DC power and

5.27 kW of net AC power. The cell–stack, electric efficiency

and CHP efficiency for this system are about 42.5%, 31.7% and

79.5% (HHV) respectively. Considering 50 �C as the whole

system exhaust gas temperature, about 6.46 kW amount of

heat is available for co- and polygeneration.

Fig. 6 shows the process flow diagram of Case (B), i.e. the

methane-fuelled SOFC system. Pure methane (100% CH4) and

air (21% O2þ 79% N2) at 15 �C enter the system and are

Fig. 5 – Process flow-sheet diagram of hydrogen-fuelled base case (Case (A)).


compressed in the fuel compressor and blower respectively.

To avoid any carbon decomposition (SC> 2), an ejector is used

to recycle about 60% of the anode exhaust gas. The extent of

the fuel external pre-reforming is considered as 100% (100%

external fuel reforming). The inlet stack flow temperature is

750 �C for both sides. Therefore, before entering the SOFC

stack, both flow streams are pre-heated. The burner exhaust

gas is used here to pre-heat both streams. After pre-heating,

the remaining thermal energy of the burner exhaust gas can

be used for co- or polygeneration in a heat recovery heat

exchanger. The SOFC module operating at 0.735 V produces

about 6.62 kW of DC power and 4.60 kW of net AC power. The

cell–stack, electric efficiency and CHP efficiency for this

system are about 38.8%, 40.3% and 67% (HHV) respectively.

Considering 50 �C as the whole system exhaust gas tempera-

ture, about 3.05 kW amount of heat is available for co- and

polygeneration.

Table 2 – Evaluation of the model results in comparisonto [7].

Co-flow/counter-flow(present model)

Co-flow/counter-flow (Ref. [7])

Cell–stack

eff. (%)

46.09/54.28 46.08/54.54

Voltage (V) 0.654/0.7698 0.663/0.771

Min. PEN

temp. (K)

711.4/756 708/757

Max. PEN

temp. (K)

845/895 862/900

Average

power

density

(Wm�2)

3269/3849 3320/3860

A very basic calculation from the overall methane

reforming reaction shows that 4 moles of hydrogen are

produced for every mole of methane supplied to the system.

Thus, considering the higher heating value for hydrogen

(286 kJ mol�1) and methane (890.8 kJ mol�1), the ratio of

system fuel energy inputs ðð _nH2 HHVH2 Þ=ð _nCH4 HHVCH4 ÞÞ for

hydrogen to methane-fuelled systems is 1.28. Therefore, for

a given current and fuel utilization, the hydrogen system

requires 28% greater fuel energy input as compared to

methane-fuelled systems and thus has 28% lower electrical

efficiency. However, as shown in Figs. 5 and 6, due to the

higher electrochemical performance and lower system auxil-

iary power consumption for the hydrogen-fuelled system, the

efficiency difference is smaller than 28%. The increase in

system fuel energy input and the lack of any energy needed

for fuel processing, lead to the higher thermal energy poten-

tial for co- and polygeneration.

6.3. System design alternatives

The presented SOFC system model allows for the examination

of a variety of system alternatives. With the integration of CGR

and RAP to the base Case (A), two other system configurations

can be designed. Therefore, the following practical cases are

considered: Case (A1) hydrogen-fuelled base case with RAP

and Case (A2) hydrogen-fuelled base case with 60% cathode

gas recycling (CGR). For the new system alternatives, Case (A)

is modified adding the new components pressure losses and

also considering new air excess ratio to the system to satisfy

DTPEN< 100 K and SC> 2. Besides the data presented in Table

1, applied data for these cases are shown in Table 3.

The simulation results for new alternatives are shown in

Table 4. As can be seen, because of the higher cell voltage

polarization due to the lower oxygen concentration in the

cathode side, the operational voltage and stack efficiency are

Fig. 6 – Process flow-sheet diagram of methane-fuelled base case (Case (B)).

Table 3 – System alternatives input parameter besidedata presented in Table 1.

Case(A1)

Case(A2)

Case(B1)

Case(B2)

Case(B3)

Case(B4)

Case(B5)

Anode

recycling

ratio (%)

0 0 60 60 60 60 60

Extent of

methane

reforming

(%)

0 0 30 0 0 30 30

Cathode

recycling

ratio (%)

0 60 0 0 60 0 60

Air excess

ratio (–)

8 4.12 8.6 10 5.77 6.5 4.05


lower for the two new cases. Although the new components

i.e. RAP and air ejector pressure losses are added to the new

case models, the lower airflow rate leads to the lower auxiliary

power consumption in air line. For both air and fuel lines the

total pressure losses are shown in Table 4. The lower system

auxiliary power consumption can improve the system

performance parameters, i.e. net AC power output and CHP

efficiencies. Since the radiation heat transfer from the stack to

the RAP is limited, the results also show that the incorporation

of CGR to the system is more effective than an RAP. The TER

values clearly indicate that a higher thermal-to-electric ratio

can be achieved by the hydrogen-fuelled system, but with the

disadvantage of a lower electric efficiency.

With the integration of CGR, DIR, AGR and RAP (separately or

simultaneously) to the base Case (B), several other system

configurations can be designed. However, to avoid any

complexity and to reduce the system cost, some of them are not

practical e.g. only one option between the CGR and RAP might be

used. Therefore, the following practical cases are considered:

Case (B1) methane-fuelled base case with 70% internal reform-

ing (IR); Case (B2) methane-fuelled base case with RAP; Case (B3)

methane-fuelled base case with 60% CGR; Case (B4) methane-

fuelled base case with RAP and 70% IR; and finally Case (B5)

methane-fuelled base case with 60% CGR and 70% IR. To model

these new system alternatives, Case (B) is modified adding the

new components pressure losses and also considering new air

excess ratio to the system to satisfy the requirements

DTPEN< 100 K and SC> 2. The power consumption for the fuel

processing also must be added in the model when it is applied.

Besides the data presented in Table 1, data applied for these

alternative cases are shown in Table 3. The results of the present

simulation for the above mentioned methane-fuelled cases are

given in Table 4. They show that the cell operational voltages for

all of the additional cases are lower in comparison to the base

case (B) due to the higher cell polarization. The comparison also

shows that partial methane internal reforming can improve the

cell–stack, electric efficiency and CHP efficiency effectively

whereas the cell operational voltage and power output are

decreased.

Also the system performance parameters are improved for

all of the additional cases in comparison to the Case (B).

System performance parameters are significantly improved in

Case (B4) and Case (B5) where anode gas recycling and IR,

besides CGR or RAP, are employed. However, adding CGR is

more effective in regard to system performance parameters

i.e. net AC power, electric efficiency and CHP efficiency. The

TER values vary between 0.63 and 0.74 for these cases and thus

show the higher system potential for electricity generation.

As discussed in the previous section, the results also

clearly indicate that the hydrogen-fuelled systems do not offer

any electric efficiency advantages over methane-fuelled

systems. Stack output parameters, amount of air excess ratio

and system pressure losses might be accounted as the main

differences between system alternatives results.

Table 4 – Simulation results for the base cases and the system alternative cases.

Systemconfiguration

Vop

(V)PDC

(W)WBlower

(W)WComp

(W)PAC,Net

(W)hcell–stack (%)

HHVhSy,E (%)

HHVhCHP (%)

HHVTER(–)

Tex

(K)DP air line

(mbar)DP fuel line

(mbar)

Hydrogen-fuelled SOFC system

Base case (A) 0.78 7023 1115 35.5 5271 42.45 31.67 70.49 1.226 201 227 187

Case (A1) 0.779 7016 955.3 35.5 5464 42.4 32.83 72.13 1.197 242 256 187

Case (A2) 0.778 7002 739.2 35.5 5667 42.32 34.05 75.69 1.223 426 407 187

Methane-fuelled SOFC system

Base case (B) 0.735 6617 1469 14.9 4604 38.83 40.32 67.0 0.66 109 251 406

Case (B1) 0.695 6251 960.8 14.9 4709 42.93 41.82 72.27 0.728 148 238 406

Case (B2) 0.734 6606 1250 14.9 4813 38.76 42.14 70.01 0.661 127 270 406

Case (B3) 0.733 6604 889.1 14.9 5171 38.75 45.28 76.57 0.691 217 396 406

Case (B4) 0.683 6149 703.2 14.9 4939 42.22 43.25 75.26 0.740 191 242 406

Case (B5) 0.692 6229 534.5 14.9 5181 42.78 45.37 78.86 0.738 300 332 406


6.4. Parameter study

6.4.1. Influence of fuel utilization factorThe influence of fuel utilization factor on net AC power,

electric efficiency and CHP efficiency is shown in Figs. 7 and 8

respectively for two cases with a constant inlet fuel flow rate

(0.1728 gr/s for the hydrogen-fuelled cases and 0.2058 gr/s for

the methane-fuelled cases). These methane-fuelled cases are

selected because of the higher system performance and

hereafter they will be used for parameters sensitivity analysis.

Although, in general, higher fuel utilization can increase

the reaction rate of the exothermic electrochemical oxidation

and sequentially the cell temperature and air excess ratio to

the system, increasing the stack power output dominates the

increasing auxiliary power consumption. Therefore, as shown

in Figs. 7 and 8, increasing the fuel utilization factor can

effectively increase the efficiency, except in the high fuel

utilization region (about <90%). The efficiency increases at

higher rate for the hydrogen-fuelled cases than for the

methane-fuelled cases, but decreases in the high fuel utili-

zation operating region for all the cases. In this region, the cell

performance is mass transfer limited, which dramatically

increases the cell polarization, resulting in a reduced

maximum power and, consequentially, efficiency.

Fig. 7 – Net AC power; electric efficiency and CHP efficiency

vs. fuel utilization factor, for the hydrogen-fuelled cases.

Figs. 7 and 8 also show the CHP efficiency as a function of

the fuel utilization. As can be seen; the higher the fuel utili-

zation, the lower the CHP efficiency. This is because of (i) the

lower amount of fuel which is supplied to the burner (leading

to lower both burner exhaust gas temperature and thermal

energy potential), and (ii) higher air excess ratio and auxiliary

power consumption.

For lower fuel utilization, also a lower air excess ratio is

needed to control the cell temperature. In this research, the

minimum allowable air excess ratio is 2. Therefore, especially

for the methane-fuelled cases, the slope of the CHP efficien-

cies curves decreases between 35% and 45% fuel utilization.

This limitation also affects the performance of the Case (A1)

and Case (A4) where the RAP is integrated to the system.

6.4.2. Influence of inlet fuel flow rateSince the rate of the electrochemical reaction and the cell

current are almost proportional to the fuel flow rate, a lower

cell voltage results when increasing the fuel flow rate due to

the higher cell ohmic and activation polarization. The present

results show that the cell voltage decreases about 24% for the

hydrogen-fuelled systems and about 27% for the methane-

fuelled systems when increasing the fuel flow rate from 0.1 to


vs. fuel utilization factor, for the methane-fuelled cases.

Fig. 10 – Net AC power; electric efficiency and CHP

efficiency vs. fuel flow rate to the system, for the methane-

fuelled cases.


0.4 gr/s (at constant fuel utilization i.e. 80%). Although the cell

voltage is lower for the higher flow rate, the cell and stack

power outputs increase due to the higher cell reaction rate and

current. A higher cell reaction rate increases the cell

maximum temperature and therefore, a higher air excess

ratio is needed to control the cell temperature gradient.

Figs. 9 and 10 illustrate the net AC power as a function of

the fuel flow rate for both fuel cases. As can be seen, although

a higher airflow rate and consequentially a higher blower

power is needed for increased fuel flow rates, the net AC

power output increases when increasing the fuel flow rate.

However, the increase rate is more pronounced until the

middle of the selected domain and it is nearly zero at the end

due to the higher blower power consumption. The cases in

Fig. 9 show quite a similar variation pattern except Case (A1).

Since a constant geometry, based on the system design point,

is considered for the RAP in Case (A1), the RAP pressure losses

become very high where for air excess ratios exceeding about

12 (for the selected methane-fuelled system). This parameter

is lower because of the IR. Therefore, for an SOFC system,

the RAP geometry should be designed not only based on the

design point but also on part-load operation points. The

results indicate that an integrated SOFC system with RAP is

not very suitable for systems operating within a broad power

range.

Figs. 9 and 10 also illustrate the electric and CHP efficien-

cies as a function of fuel utilization factor. As can be seen,

lower electric and CHP efficiencies can be expected for higher

fuel flow rate. However, the increasing rate is higher for the

methane-fuelled systems due to the higher voltage decreasing

rate.

6.4.3. Influence of cell operational voltageConsidering constant fuel utilization (80%, which is controlled

by the airflow rate to the system during load variation), the

results presented in the previous section can be extended to

show how the system performance parameters change during

the part-load operation or changing operational voltage. As

mentioned, the cell voltage, electric efficiency and CHP


vs. fuel flow rate to the system, for the hydrogen-fuelled

cases.

efficiency are lower for increased inlet fuel flow rates. There-

fore, at lower cell voltage, lower electric and CHP efficiencies

and higher fuel flow rate and net AC power output are

expected. Figs. 11 and 12 show net AC power, electric effi-

ciency and CHP efficiency as a function of the cell voltage for

both fuel cases. The limitations concerning the RAP dimen-

sioning apply also here.

7. Conclusions

Generalized SOFC system models were presented which are

specifically developed for the analysis the building integrated

co- and polygeneration SOFC system. As a part of this activity,

a detailed SOFC cell model was developed and was introduced

here in brief. The cell model was evaluated for both HT and IT

cell designs and an example of the evaluation cases was


efficiency vs. cell voltage, for the hydrogen-fuelled cases.


efficiency vs. cell voltage, for the methane-fuelled cases.


presented here. The cell model was extended to the stack

model and integrated into a generic SOFC system model. The

model was employed to analyse two base case SOFC systems

fuelled by hydrogen and methane respectively. System

configurations were varied by incorporating internal reform-

ing, anode recycling, cathode recycling, and RAP, and evalu-

ated for optimal efficiencies. Results of variation studies for cell

parameters i.e. fuel utilization, inlet fuel flow rate, and opera-

tional voltage were show optimised system operation points.

The main conclusions of this research are:

1 Lower electric efficiency, higher TER and higher cell–stack

efficiency were observed for all of the hydrogen-fuelled

cases in comparison to the methane-fuelled cases.

2 The stack output parameters, amount of air excess ratio

and system pressure losses might be accounted as the

main differences between the system alternatives results.

3 For both fuel cases, the incorporation of cathode gas

recycling to the base cases effectively improved the elec-

tric and CHP efficiencies. For the hydrogen-fuelled base

case about 7% higher electric and CHP efficiencies and for

the methane-fuelled base case about 11% and 12% higher

electric and CHP efficiencies respectively were observed

4 Although internal reforming can decrease the cell opera-

tion voltage and stack power output, higher electric and

CHP efficiencies resulted due to the lower auxiliary power

consumption.

5 The incorporation of RAPs to the system is an effective way

to decrease the air excess ratio rate and consequentially

the auxiliary power consumption. Since the RAP is

designed based on the design-point characteristic in this

research, it has been observed that there are some uncer-

tainties about how to dimension and operate the RAP when

the cell parameters deviate much from the design values,

especially because high pressure losses may arise in the

RAP.

6 The cell parameter sensitivity analysis showed (i) higher

net AC power and lower electrical efficiency and CHP effi-

ciency for fuel flow rates above the design value; (ii) higher

AC power and electric efficiency and lower CHP efficiency

for higher fuel utilizations (except at fuel utilizations above

90% for the methane-fuelled cases); and (iii) higher electric

and CHP efficiencies, and lower power output in the part-

load operation or for the higher voltage values.

The work presented clearly showed the problems and

limitations related to SOFC polygeneration performance eval-

uation using a generic SOFC model. However, such approach

proved to be a relatively easy and straightforward way to

optimize different SOFC cell and system configurations. Such,

the model may contribute to bridge the still existing gap

between the more sophisticated SOFC stack and system

models on the one hand, and the simple black box models,

often used in building simulation tools, on the other hand.

In an ongoing research, the results of this study have been

employed to derive SOFC system performance data for energy

and environmental impact studies of building integrated

SOFC co- and polygeneration systems, using transient whole

building and plant simulation tools.

Acknowledgements

Mr. Kazempoor would like to thank Dr. M. Santarelli (Asso-

ciate Professor, Dipartimento di Energetica, Politecnico di

Torino) and Dr. N. Woudstra (Associate Professor, Process &

Energy Lab., Delft University of Technology) for helpful

discussions. The support of the Iran Renewable Energies

Organization, Fuel cell Steering Committee for this work is

acknowledged.

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