dynamic modeling of reliability constraints in solid oxide ... · dynamic modeling of reliability...
TRANSCRIPT
Dynamic Modeling of Reliability Constraints in Solid Oxide Fuel
Cells and Implications for Advanced Control
AIChE Fall 2010 Annual Meeting
Benjamin Spivey
Advisor: Dr. Thomas F. Edgar
University of Texas at Austin
November 10, 2010
*GE, 2007
The University of Texas at Austin 2Benjamin James Spivey
Modeling and Controls Objective:
Maintain solid oxide fuel cell (SOFC) performance and operational integrity subject to load-following, efficiency maximization, and disturbances using advanced process control.
Agenda:
• Motivation and Overview of Tubular SOFC System
• Distributed-Parameter SOFC Modeling
• SS and Dynamic Simulations of Fuel Cell Operation
• Conclusion
Overview
The University of Texas at Austin 3Benjamin James Spivey
Benefits
• High efficiencies at full and partial load: 40-50% (LHV) for SOFC for 200 kW, 60-70% for GT-SOFC, 90%+ for cogeneration.
• Fuel flexibility:– Hydrogen, natural gas, propane
– Alcohols, biomass, coal gas
• Suitability for cogeneration with high exhaust temperatures
• Low noise and emission levels
Operational Challenges
• Micro-cracking, catalyst poisoning, and air & fuel starvation decrease the lifetime and increase cost of electricity.
• Majority of real plants have used SISO PID and PLC control –operations experience with advanced control is limited.
Research Motivation
The University of Texas at Austin 4Benjamin James Spivey
• The SOFC is often recommended to be coupled with a gas-turbine to utilize waste heat, maximize efficiencies, and supplement power production.
• Model of manipulated variables assumes an external variable speed compressor and recuperators.
Primary
Fuel
Secondary
Fuel from HX
Downstream
CHP BOP
Recuperator
Compressor
TurbineCombustor
Air Supply Tube
Tubular
SOFC
Internal
Reformer
Ejector
Inverter
Grid
Ambient
Air Cool AirHeated Air
Fuel
Spent Fuel
Electrical Current
HX
Generator
Pre-reformer
ACDC
~
SOFC system within a GT-SOFC Plant
SOFC System Overview
Distributed-Parameter SOFC Modeling
The University of Texas at Austin 6Benjamin James Spivey
Tubular SOFC Modeling
Type: high-temperature tubular SOFC
Structure: cathode-supported
Fuel: prereformation and direct
internal reformation of methane
Balance of Plant in Model: ejector and
prereformer
Pressurized to 3 bar
Based on a Siemens-Westinghouse
plant at National Fuel Cell Research
Center.
*Image from Singhal, S.C., 2006.
Tubular Solid Oxide Fuel Cell Assembly
Parameters and inlet conditions are well known in literature versus other SOFC designs
The University of Texas at Austin 7Benjamin James Spivey
Dynamic Modeling Challenges
• Distributed parameter approach produces a large number of states:
220 states for 10 finite volumes in the axial direction.
• Dynamic system of differential and algebraic equations to be solved
simultaneously (without algebraic loops).
• Algebraic equations are in an implicit form.
• Nonlinearities introduced by reaction and electrochemical terms.
• Multiple time scales varying from milliseconds to hours.
The University of Texas at Austin 8Benjamin James Spivey
Anode
Electrolyte
Cathode
Air Tube
rInner Air Chamber
Outer Air Chamber
Fuel Chamber
• Total States per Element = 22 : Tga, Tsa, Tse, Tsc, Tgc2, Tsat, Tgc1, Nga1-Nga7, Ngc21-Ngc27,
I (current)
• Total States per SS Model = 878
• Total States per Dynamic Model = 220
∆xGas Element States:
Tg, Ng1, …Ng7
Solid Element States:
TsH2, CH4, H2O, etc.
N2, O2
2224
224
42
3
2
1
HCOOHCH
HCOOHCH
r
r
+→+
+→+
x
SOFC Cross-Section in Radial (r) and Axial (x) Directions
Quasi-2D SOFC Model Discretization
The University of Texas at Austin 9Benjamin James Spivey
( )
( )
( ) rxnesopps
s
i
sgiis
p
rxnr
i
gsiip
i jjiiinout
QTTAF
dx
dTkTTAh
dt
dTVc
QTTAhdx
dTcm
rvnn
i
i
,
4,
4
,0
+−+
+−=
+−+=
+=
∑
∑
∑ ∑
σε
ρ
&
&&
effr
cl
jc
al
ja
c
jcja
a
r
iR
ii
F
RT
ii
F
RT
ii
F
RT
ii
F
RT
F
GE
=
−+
−=
+
=
∆−=
η
η
ααη
,
,
,
,
0
,
0
,
0
1ln4
1ln2
ln4
ln2
2Electrochemical Model
VolK
XXXXkr
AreapRT
EAr
ps
COH
OHCO
CHsa
a
⋅
−=
⋅
−=
22
2
4
2
1 exp
Anode Steam Reformation ModelSpecies and Energy Balances
rcacell EV ηηη −−−=
+=
OH
OHavg
p
pp
F
RTEE
2
22
2/1
0 ln2
( )
0)(
),(0
),(..
,min
≥
=
=Ω∈
xh
uxg
uxfxts
uxJx
&
The complete SOFC model is solved simultaneously via constrained NLP using the APMonitor Modeling Language.
2224
224
42
3
2
1
HCOOHCH
HCOOHCH
r
r
+→+
+→+
Key SOFC Model Equations
The University of Texas at Austin 10Benjamin James Spivey
MAP for Electrolyte Temperature = 3.85%The mean absolute percentage (MAP) error is used to compare the models.
The tubular SOFC steady-state model is validated based upon experimental data and model data from standard practice (Campanari, 2004; Seume, 2009).
Model Results Campanari Model
∑ −=
t t
tt
A
PA
n
1MAP
SOFC Steady-State Model Validation
The University of Texas at Austin 11Benjamin James Spivey
Comparison of the concentration profiles also indicates that the steady-
state model matches well versus the standard models used for tubular,
high-temperature SOFC modeling.
Model Results Campanari Model
SOFC Steady-State Model Validation
The University of Texas at Austin 12Benjamin James Spivey
Radiation Analysis for Plant B : Air channel radiation is significant
Final Steady-State Model = Validated Campanari Model + Air Channel Radiation + Model Validation
Without Radiation With Radiation
Radiation Effects:
•Increased peak temperature
•Inlet air and solid PEN is closer in temperature
• Higher T gradients at outlet
• Molar flow exhibits no noticeable change.
SOFC Radiation Sensitivity
The University of Texas at Austin 13Benjamin James Spivey
SOFC Electrical Characterization
SS Electrical Characterization for Plant A: 120 kW, 1.05 bar
• LHV efficiencies are 45% and 38% for Plants A and B respectively - typical for 100-300 kW SOFC.
•Nominal efficiency is based upon provided inputs, not plant modeling.
• Fixed fuel flow rate condition
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 500 1000 1500 2000 2500 3000
Current Density [A/m^2]
Vo
ltage
[V
]
0
20
40
60
80
100
120
140
160
Po
we
r [W
]
Voltage Power
0%
20%
40%
60%
80%
100%
0 1000 2000 3000
Current Density [A/m^2]
Eff
icie
ncy
[%
]
0%
20%
40%
60%
80%
100%
Fuel U
tiliza
tion [
%]
Efficiency
Fuel Utilization
in,4CH4CHin,COCOin,O2HO2H NLHVNLHVNLHV
VI
+⋅+⋅
⋅=η
SS and Dynamic Simulations of Fuel Cell Operation
The University of Texas at Austin 15Benjamin James Spivey
Prereformer:
Quasi-Steady-State
ODE Model
8 States
Matlab
SOFC :
Dynamic
DAE Model
220 States
APMonitor
Ejector:
Quasi-Steady-State
Algebraic Model
9 States
Matlab
PT PC
FC
TT TC
PT PC
TT
FC
Air
FT
TC
SOFC Exhaust
Variable Speed
Compressor
Fuel
FC
FC
Fuel Tanks
MV MV
MV MV
MV
MV
MV
MV
..
..
TT
TT
TT
..
.
CV
CV
Cell
Temperatures
Power &
Efficiency
MV Voltage
CV
Air/Fuel Utilization
Steam-Carbon Ratio
Manipulated and controlled variables are chosen based upon the SOFC+BOP system
SOFC and Balance of Plant (BOP) System
The University of Texas at Austin 16Benjamin James Spivey
Relevance of Controlled Variables
Objective or Risk Controlled Variable
DC Power Delivery Power (W)
Efficiency (%)
Thermal Stress Minimization Minimum Stack Temperature (K)
Radial Thermal Gradient (K/m)
Avoid Catalyst Poisoning Steam-to-Carbon Ratio
Avoid Air and Fuel Starvation Air and Fuel Utilization (%)
Recent studies report that the minimum stack temperature and radial thermal gradient are responsible for the highest and second-highest thermal stress levels
(Seume, 2009).
The University of Texas at Austin 17Benjamin James Spivey
-2,500
-2,000
-1,500
-1,000
-500
0
500
1,000
0.15 0.3 0.45 0.6 0.75 0.9 1.05 1.2 1.35 1.5
dT
dx
(K/m
)
Length (m)
Radial
Axial
Radial versus Axial Temperature Gradient
The radial gradient is negative near the fuel inlet placing the anode in tension. The radial gradient is several times the axial gradient.
Simulation results agree with prior studies indicating that radial thermal gradients are most significant.
The University of Texas at Austin 18Benjamin James Spivey
Tstack, min (K)
Radial ∆T/L, max
(K/m)
Power (W)
CVs
Air Mass Flow
(kg/s)
System Pressure
(bar)Voltage (V)
Air Inlet
Temperature (K)
Fuel Inlet Pressure
(bar)
Fuel Inlet
Temperature (K)MVs
All scales are consistent for a given CV to compare slopes.
Variable Steady-State Gains
• Most MVs affect the minimum stack temperature.
• Air temperature and voltage affect the radial gradient significantly.
• Fuel pressure and temperature have most affect on power in this operating region.
Manipulated variables (MVs) are adjusted 10-20% of nominal on both sides of the nominal
value. Nominal is close to Plant B conditions.
800
1150
0 5
800
1150
0.55 0.7
800
1150
500 1500
800
1150
5 10
800
1150
200 500
800
1150
0.3 0.9
1000
3500
0.3 0.9
1000
3500
0 5
1000
3500
0.55 0.7
1000
3500
500 1500
1000
3500
5 10
1000
3500
200 500
140
165
0.3 0.9
140
165
0 5140
165
0.55 0.7140
165
500 1500
140
165
5 10
140
165
200 500
The University of Texas at Austin 19Benjamin James Spivey
Air Utilization (%)
Fuel Utilization
(%)
Steam-Carbon
Ratio
CVs
Air Mass Flow
(kg/s)
System Pressure
(bar)Voltage (V)
Air Inlet
Temperature (K)
Fuel Inlet Pressure
(bar)
Fuel Inlet
Temperature (K)MVs
Variable Steady-State Gains
• Air mass flow is a key MV for managing air utilization.
• Fuel temperature and system pressure manage fuel utilization.
• Fuel pressure and temperature and system pressure significantly affect
the steam-to-carbon ratio.
15
40
0.3 0.9
15
40
0 5
15
40
0.55 0.7
15
40
500 1500
15
40
5 10
15
40
200 500
40
100
0.3 0.9
40
100
0 5
40
100
0.55 0.7
40
100
500 1500
40
100
5 10
40
100
200 500
0
8
0.55 0.70
8
0.3 0.9
0
8
0 5
0
8
500 1500
0
8
5 10
0
8
200 500
The University of Texas at Austin 20Benjamin James Spivey
Simulation Time Discretization: Power Response to Voltage Step
• Decreasing time steps below 1 s yields little change in dynamic response.
• The QSS gas transport assumption is only valid to 1s time steps.
153.2
153.6
154
154.4
154.8
155.2
155.6
0 200 400 600 800
Po
we
r (W
)
Time (s)
1 s
0.5 s
60 s
Transport Time Delays
• Three transport time delays are added to the QSS gas transport models to improve dynamic accuracy.
• Delays are important for sub-60 s response.
• Delays are updated by mass flows
153.2
153.6
154
154.4
154.8
155.2
155.6
0 20 40 60 80
Po
we
r (W
)
Time (s)
All Time Delays
No Time Delays
Dynamic Simulation Design
The University of Texas at Austin 21Benjamin James Spivey
110
120
130
140
150
160
170
180
0 500 1000 1500 2000
Po
we
r (W
)
Time (s)
110
120
130
140
150
160
170
180
0 500 1000 1500 2000
Po
we
r (W
)
Time (s)
110
120
130
140
150
160
170
180
0 500 1000 1500 2000
Pow
er (W
)
Time (s)
Fuel Pressure
Fuel Temperature
Voltage
MV:
• Staircase tests are run over 5 minutes in response to MV steps over 1 s.
• Increasing gains further from the nominal illustrate non-linearity.
• Decreasing the voltage to 0.55 V reduces power output – crossed peak voltage and shows nonlinear V-P relationship.
5.0
6.0
7.0
8.0
9.0
10.0
11.0
0 1000 2000
Pfu
el (
ba
r)
Time (s)
Staircase Dynamic Simulations: Power Plots
Example of staircase input:
The University of Texas at Austin 22Benjamin James Spivey
110
610
1110
1610
2110
2610
3110
3610
0 500 1000 1500 2000
dT
rad
,ma
x (K
/m)
Time (s)
110
610
1110
1610
2110
2610
3110
3610
0 500 1000 1500 2000
dTr
ad,m
ax
(K/m
)
Time (s)
110
610
1110
1610
2110
2610
3110
3610
0 500 1000 1500 2000
dT
rad
,ma
x (
K/m
)
Time (s)
Fuel Pressure
Fuel Temperature
Air Mass Flow
MV:
• Numerator dynamics response is real and due to quickly changing anode chamber gas conditions.
• Discontinuous curves can result between step changes when location of max gradient changes.
• The maximum radial thermal gradient does not change quickly due to varying cathode-side conditions.
Staircase Dynamic Simulations: Max Radial dTdr Plots
The University of Texas at Austin 23Benjamin James Spivey
Electrolyte Temperature and Radial Gradients
Power Increase
Dynamic Evolution of the Temperature Profile
Open-Loop Fuel Pressure Step Increase
-Lower Min Cell Temp.
-Higher Max dTdr
Increased Thermal Stresses
5.0
6.0
7.0
8.0
9.0
10.0
11.0
0 200 400 600
Pfu
el (
ba
r)
Time (s)
110
130
150
170
190
0 200 400 600
Po
we
r (W
)
Time (s)
Minimum temperature and radial gradients undergo unique dynamics
The University of Texas at Austin 24Benjamin James Spivey
Conclusions
• Modeling:
Distributed parameter modeling for SOFC is critical to accurately
capture overall performance as well as local gradients and minimum
temperatures – key reliability criteria.
• Simulation
- Radial thermal gradients may increase quickly in response to
changing input conditions. Control algorithms should account for
dynamics of minimum cell temperature and maximum radial
gradients.
- Most properties have an initial rise time < 1 min in response to 1 s
input steps despite final settling times of hours. Control input
intervals should be several times less than the rise time.
The University of Texas at Austin 25Benjamin James Spivey
Acknowledgments
• Dr. Thomas Edgar
• Dr. John Hedengren
• Dr. Jeremy Meyers
• Dr. Dongmei Chen
• APMonitor Modeling Language
• Labmates