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Department of Chemical & Biological Engineering
Illinois Institute of Technology
Modeling and Control of an
Autothermal Reforming (ATR) Reactor
for Fuel Cell Applications
Donald J. Chmielewski and Yongyou Hu
Department of Chemical & Biological Engineering
Illinois Institute of Technology, Chicago, IL
Dennis Papadias Chemical Engineering Division
Argonne National Laboratory, Argonne, IL
October 5th 2007
Chemistry Colloquium, Illinois Institute of Technology
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Polymer Electrolyte Membrane
Fuel Cell (PEMFC)
N2
N2
N2
H2
H2
H2
H2
H2
H2
O2
O2
O2
H+
e- e-
Anode
Electrolyte
Cathode
O2 N2
N2
O2
O2
H+
H+
H+
H2O
H2O
H2O
H2O
H2O
H2O
Generated power due to
enthalpy released by
the reaction:
H2 + ½ O2 H2O
(H ~ 58 kcal/mole H2)
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Polymer Electrolyte Membrane
Fuel Cell (PEMFC)
N2
N2
N2
H2
H2
H2
H2
H2
H2
O2
O2
O2
H+
e- e-
Anode
Electrolyte
Cathode
O2 N2
N2
O2
O2
H+
H+
H+
Transportation Applications
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Fuel Cell System
Fuel
Processor Fuel Cell
Stack
Spent-Fuel
Burner
Thermal & Water Management
Air
Air
Fuel
H2
Exhaust
H2O CO2
Electric Power
Conditioner
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Hydrogen Storage vs. On-Board Reforming
Transportation
Applications
PEMFCReformerLiquid Fuel
Storage Tank
Cm
Hn
H2
CO
H2O
CO2
PEMFCHydrogen
Storage Tank
H2
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Hydrogen Storage vs. On-Board Reforming
Transportation
Applications
PEMFCReformerLiquid Fuel
Storage Tank
Cm
Hn
H2
CO
H2O
CO2
PEMFCHydrogen
Storage Tank
H2
Department of Chemical & Biological Engineering
Illinois Institute of Technology
PEMFC and CO Poisoning
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Fuel Processing Reactors
PEMFCPreferential
Oxidation
(PrOx)
Water-
Gas
Shift
(WGS)
Reformer
Hydrocarbon Feed
Large Hydrocarbons Cracked:
Low H2 to CO ratio Most CO converted to CO2: ~ 1% CO remaining
CO levels down to ~ 10 ppm
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Partial Oxidation
Hydrocarbon Fuel
Air (at a sub-
stoichiometric rate)
PO
Reactor
Total Oxidation: OHnmCOOnmHC nm 222 2/)2/(
Steam Reforming: 22 )2/( HnmmCOOmHHC nm
Water Gas Shift: 222 HCOOHCO
22
2
COOH
COH
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Water Gas Shift Reaction
At High temperatures equilibrium favors:
222 HCOOHCO
At Low temperatures equilibrium favors:
222 HCOOHCO
More H2O in the feed will also favor the forward direction
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Autothermal Reforming
Hydrocarbon Fuel Air (at a sub-
stoichiometric rate)
ATR
Reactor
Oxidation: OHnmCOOnmHC nm 222 2/)2/(
Steam Reforming: 22 )2/( HnmmCOOmHHC nm
Water Gas Shift: 222 HCOOHCO
22
2
COOH
COH
Steam
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Autothermal Reforming
Hydrocarbon Fuel Air (at a sub-
stoichiometric rate)
ATR
Reactor
Oxidation: OHnmCOOnmHC nm 222 2/)2/(
Steam Reforming: 22 )2/( HnmmCOOmHHC nm
Water Gas Shift: 222 HCOOHCO
CO
H
Less
More 2
Steam 222 ,,, COOHCOH
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Outline
Introduction / Motivation
Reactor Modeling and Analysis
Classic Controller Design
Nonlinear Model Predictive Control
Reduced Order Modeling
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Fuel Processor System at Argonne
Water
WG
1
AirWater
Fuel
AirW
G2
WG
3
WG
4
PrO
x1
PrO
x2
PrO
x3
ATR
Water
WG
1
AirWater
Fuel
AirW
G2
WG
3
WG
4
PrO
x1
PrO
x2
PrO
x3
ATR
Department of Chemical & Biological Engineering
Illinois Institute of Technology
ATR Reactor at Argonne
Vaporized gasoline,
Steam
Liquid water
Heat exchangerAir (25 °C)
Hot air
Nozzle
7 m
m1
2 m
m1
2 m
m
96 mm
Catalyst bed
Heater rod
Thermocouple1 2 3 4
5 6 7
8 9 10
Metal wall
thickness=1.7 mm
High Space Velocity
(GHSV ~ 50,000/h)
Noble Metal Catalyst
(Rh on a Gd-CeO2 substrate).
Operating Temperature
~ 700 – 1000o C
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Reactor Model (Axially Dependent, Nonlinear Dynamic Version)
)()()(,
)()(
0s
jg
jg
jccc
gj
g
kAx
m
N
i
iijj
g
j
s
j
g
jc rMk1
)()()(
,0
)()()()(
)()( ˆ0 sggccc
gg
pg TThA
x
Tcm
)()()(
)()( )(ˆ wsw
w
ww
pw TTxh
t
TSc
Mass Balances:
Catalyst Phase:
Gas Phase:
Energy Balances:
Gas Phase:
n
1i
c
)()(
llreactor wa fer toHeat trans
)()()(
,
)()()(
...)(1ˆ
ii
sg
cc
sw
ww
s
axe
ss
p
s
rHTTh
TTxhx
T
xt
Tc
Solid Phase:
Reactor Wall:
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Model of Reaction Kinetics (1)
)()(
11 2
s
O
s
fuel yyAr
Total Oxidation Reaction :
OHnmCOOnmHC nm 222 2/)2/(
1A
Rate Expression:
where
Oxidation rate is Fuel Diffusion Limited.
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Model of Reaction Kinetics (2)
222 HCOOHCO
Water-Gas Shift Reaction:
Rate Expression:
029.22073)()(
)()(
33 10;22
2
3
T
e
e
s
CO
s
Hs
OH
s
CO
RT
E
KK
yyyyeAr
Wheeler, Jhalani, Klein, Tummala, Schmidt, J. Catal. (2004).
Parameters Adapted from:
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Model of Reaction Kinetics (3)
22 )2/( HnmmCOOmHHC nm
Steam Reforming Reaction:
Rate Expression:
2
)(
2
2)()(
22
2
2
2
1
s
fuel
RT
H
s
OH
s
fuel
RT
E
yeKyyeAr
Activation Energies from:
Dubien, Schweich, Mabilon, Martin, Prigent, Chem. Eng. Sci. (1998).
A2 and K2: Fit to Experimental Data:
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Micro-Reactor Tests (Steady-State Analysis)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.75 1.25 1.75 2.25 2.75 3.25
H2O/C ratio (-)
H2,
CO
2 m
ola
r fr
ac
tio
n (
dry
)
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
CO
mo
lar
fra
cti
on
(d
ry)
O2/C=0.45
CO2
CO
H2
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.30 0.35 0.40 0.45 0.50 0.55 0.60
O2/C ratio (-)
H2,
CO
2 m
ola
r fr
ac
tio
n (
dry
)
0.05
0.08
0.10
0.13
0.15
0.18
0.20
CO
mo
lar
fra
cti
on
(d
ry)
CO2
H2
CO
H2O/C=1.5
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Reactor Start-up: A 2 Step Procedure
Partial Oxidation Mode (to quickly increase temperature)
ATR Mode (for greater CO conversion)
Hydrocarbon Fuel Air
ATR
Reactor
Steam
Hydrocarbon Fuel
Air
PO
Reactor
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Reactor Start-Up
0
100
200
300
400
500
600
700
800
20 40 60 80 100 120 140 160 180 200
Time (s)
Te
mp
era
ture
(°C
)
Experimental Data
Simulation
@ 7 mm
@ 19 mm
Inlet temperature
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Steady-State Axial Profiles
0.00
0.05
0.10
0.15
0.20
0.25
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Dimensionless x-axis (x/L)
Mo
lar f
ra
cti
on
s w
et
(-)
H2
CO
H2O
CO2
Fuel
CPOX Mode: ATR Mode:
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Dimensionless x-axis (x/L)
Mo
lar f
ra
cti
on
s w
et
(-)
H2
CO
H2O
CO2
FuelO2
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Outline
Introduction / Motivation
Reactor Modeling and Analysis
Classic Controller Design
Nonlinear Model Predictive Control
Reduced Order Modeling
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Need for Temperature Regulation
Vaporized gasoline,
Steam
Liquid water
Heat exchangerAir (25 °C)
Hot air
Nozzle
7 m
m1
2 m
m1
2 m
m
96 mm
Catalyst bed
Heater rod
Thermocouple1 2 3 4
5 6 7
8 9 10
Metal wall
thickness=1.7 mm
0 200 400 600 800 10000
100
200
300
400
500
time (sec)
Inle
t A
ir T
em
pera
ture
(deg C
)
Inlet Air Temperature Trajectory
Primary Disturbance:
Inlet Temperature
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Open-Loop System
ATR
System T3
Inlet Air Flow
T4
T5
T2
T1
Inlet Air
Temperature
Inlet Steam Flow
} } Unmeasured
(but simulated)
Measured
(and simulated)
• Step Tests Performed Using the 1-D Nonlinear Model
Department of Chemical & Biological Engineering
Illinois Institute of Technology
First Order Plus Dead Time Modeling
0 20 40 60 80 100800
850
900
950
1000
1050
T3
T1
T2
T3
T4
T5
AT
R T
em
pera
ture
(oC
)
time (sec)0 20 40 60 80 100
800
850
900
950
1000
1050
time (sec)
AT
R T
em
pera
ture
(oC
) T1
T2
T3
T4
T5
0 20 40 60 80 100650
700
750
800
850
900
950
1000
1050
AT
R T
em
pera
ture
(oC
)
time (sec)
T2 T
1
T4
T5
T3
Air Flow Rate Inlet Temperature Steam Flow Rate
1,
s
eK
F
T
i
s
i
inAir
ii
1,
s
eK
T
T
i
s
i
inAir
ii
1,
s
eK
F
T
i
s
i
inSteam
ii
Department of Chemical & Biological Engineering
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Feedback Control
ATR
Reactor
T3 Inlet Air Flow
+ +
+ +
T4
T5
T2
T1
+
- PI
Control
T3, set point
Inlet Air Temperature
T3, measured
Sensor Noise
Temperature Fluctuations in Reactor
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Feedback Control
ATR
Reactor
T3 Inlet Air Flow
+ +
+ +
T4
T5
T2
T1
+
- PI
Control
T3, set point
Inlet Air Temperature
T3, measured
Sensor Noise
Temperature Fluctuations in Reactor
Manipulated
Variable
Control Variable
Disturbances
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Illinois Institute of Technology
Simulated Disturbances
0 200 400 600 800 10000
100
200
300
400
500
time (sec)
Inle
t A
ir T
em
pera
ture
(oC
)
Inlet Air Temperature Trajectory
0 200 400 600 800-80
-60
-40
-20
0
20
40
60Temperature Fluctuations and Sensor Noise
time (sec)
Dis
turb
ance I
nput
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Analysis of the Feedback Controller
Regulation During ATR Mode:
0 200 400 600 800800
900
1000
1100
1200CV (T
3) Response: Open- vs. Closed-loop
time (sec)
Tem
per
atu
re (
oC
)
Open-loop
Closed-loop
0 200 400 600 8000
50
100
150
200MV (Air Flow) Response: Open vs. Closed-loop
time (sec)
Inle
t A
ir F
low
Rate
(sl
pm
) Open-loop
Closed-loop
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Transition from CPOX to ATR Mode
Gp(s)
T3 Air Flow
+ + +
- PI
T3, set point
Steam Flow Rate
+ +
Gd(s)
-
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Transition from CPOX to ATR Mode
0 50 100 150 2000
400
600
800
0 50 100 150 2000
50
100
Reacto
r T
em
pera
ture
(deg C
)Impact of Steam Injection
Ste
am
Flo
w R
ate
(g/m
in)
time (sec)
With Feedback Controller
Without Feedback Controller
Steam Flow Rate
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Transition from CPOX to ATR Mode
0 50 100 150 200
400
600
800
0 50 100 150 2000
50
100
0 50 100 150 200
Impact of Steam Injection Rate
With Feedback Controller
Without Feedback Controller
Steam Flow Rate
time (sec)
Reacto
r T
em
pera
ture
(deg C
)
Ste
am
Flo
w R
ate
(g/m
in)
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Feed-forward Control
Gp(s) T3
Air
Flow +
+ +
- PI
T3, set point
Steam Flow Rate
(Measured)
+ +
Gd(s)
Gff(s)
-
)()(
)()( sH
sG
sGsG
p
d
ff
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Impact of Feed-forward Control
0 20 40 60 80 100500
600
700
800
900
Reacto
r T
em
pera
ture
(deg C
)
time (sec)
Steam Injection: With and Without Feed-forward
Feedback Controller Only
Feed-forward / Feedback Controller
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Model Mismatch in Feed-forward Control
Gp(s) T3
Air
Flow +
+ +
- PI
T3, set point
Steam Flow Rate
(Measured)
+ +
Gd(s)
Gff(s)
-
)()(
)()( sH
sG
sGsG
p
d
ff
• If the Gd(s) or Gp(s) used to define Gff(s) are
different than the actual plant then mismatch occurs.
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Impact of Model Mismatch
0 20 40 60 80 100400
600
800
1000
1200
time (sec)
T3 T
em
pera
ture
(oC
)
Feedback Controller Only
Feed-forward Without
Model Mismatch
Feed-forward With Model Mismatch
Impact of Model Mismatch on Feed-forward
0 20 40 60 80 100200
400
600
800
1000
T3 T
em
pera
ture
(oC
)
Impact of Model Mismatch on Feed-forward
time (sec)
Feed-forward Without Model Mismatch
Feedback Controller Only
Feed-forward With
Model Mismatch
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Outline
Introduction / Motivation
Reactor Modeling and Analysis
Classic Controller Design
Nonlinear Model Predictive Control
Reduced Order Modeling
Department of Chemical & Biological Engineering
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Advanced Process Control
Nonlinear Model Predictive Control (NMPC):
Gp(s) T Air Flow
Steam Flow Rate
(Measured)
NMPC
Process
Contraints
Feedback
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Why NMPC?
- Optimized Responses
- Start-up
- Load changes
- Enforcement of Process Constraints
- Can use Nonlinear Model
- Needed for feed-forward action
Department of Chemical & Biological Engineering
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Challenges to Implementing NMPC
- Computational challenges
- Optimization based
- Small sample intervals
- Accurate model required
- Needed for feed-forward action
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Model Validation
0
100
200
300
400
500
600
700
800
20 40 60 80 100 120 140 160 180 200
Time (s)
Te
mp
era
ture
(°C
)
7 mm
19 mm
Inlet temperature
30 mm
Papadias, et.al. (2006), Ind. Eng. Chem. Res.
Running time for
180 s :
~ 2 min for
FEMLAB on PC
with P4 2.0G
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Outline
Introduction / Motivation
Reactor Modeling and Analysis
Classic Controller Design
Nonlinear Model Predictive Control
Reduced Order Modeling
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Temperature profile
0 0.2 0.4 0.6 0.8 1700
750
800
850
900
950
Dimensionless,x/L1
Te
mp
era
ture
, oC
Solid
Gas
Oxidation
Reforming WGS
Department of Chemical & Biological Engineering
Illinois Institute of Technology
1-D CFD Dynamic Model
)()()ˆ( )()()()(
gs
ccs
g
z
g
gp TThz
Tv
t
Tc
Energy balance model
)()ˆ(
)()()1()ˆ(
)()()(
)()()()(
2
)(2
,
)(
ws
www
w
wp
i
iir
ws
wws
gs
ccs
s
axe
s
sp
TTht
Tc
rHTThTThz
T
t
Tc
62,1
)(1
)()(
)(
j
rMz
wv
t
w an
i
iijjcs
g
j
z
g
jg
Mass balance model
Vaporized gasoline,
steam
Liquid water Heat
exchanger
Air (25 °C)
Hot air
Nozzle
Catalyst bed
Heater rod Thermocouple
Metal wall, thickness, 1.7 mm
96 mm
7 mm 12 mm 12 mm
Resultant gases
Department of Chemical & Biological Engineering
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Infinite Dimensional Energy Balances
)(
)(
)()()(
)()(
2
)(2)(
ws
sw
w
sw
ws
s
s
s
TTt
T
qTTz
T
t
T
i
iirs
sg
gs rHTTtzq )(),( )()(
Catalyst Support
Reactor Wall
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Applying
Glerkin Approximation
N
j
j
s
j
s ztxtzT1
)()( )()(),(
N
j
j
w
j
w ztxtzT1
)()( )()(),(
)(ˆ tqBAxx
Tw
N
wws
N
ss xxxxxxx ],;,[ )()(
2
)(
1
)()(
2
)(
1
We arrive at the finite dimensional model
with a dimension of 2N
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Calculation of Heat Flux from Gas
)()ˆ( )()()(
gs
ccsc
g
gp TThAdz
dTcm
N
j
j
s
j
s ztxtzT1
)()( )()(),(
Energy Balance at Gas
i
iirs
sg
gs rHTTtzq )(),( )()(
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Calculation of Heat Flux from Gas
))()(()ˆ( )(
1
)()(
gN
j
j
s
jccsc
g
gp TztxhAdz
dTcm
in
sg TmMxmMtzT )()(),( 2
)(
1
)(
)( )()( sg
gs TT
Integration this ODE yields
and allows the calculation of
But, is time-dependent m
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Calculation of Reaction Heat
i
iirs
sg
gs rHTTtzq )(),( )()(
))(
()(
))(
1(
)(
)(
)(
2)(
33
2)(
2)(
22
2)(
11
22
22
2
2
2
2
2
2
s
eHCO
HCO
OHCO
OHCOs
C
C
s
a
OHC
OHC
s
OC
OC
s
TKMM
ww
MM
wwMTkr
wM
MTk
ww
MM
MTkr
wwMM
MTkr
m
m
m
m
m
m
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Calculation of Reaction Heat
))(
()(
))(
1(
)(
)(
)(
2)(
33
2)(
2)(
22
2)(
11
22
22
2
2
2
2
2
2
s
eHCO
HCO
OHCO
OHCOs
C
C
s
a
OHC
OHC
s
OC
OC
s
TKMM
ww
MM
wwMTkr
wM
MTk
ww
MM
MTkr
wwMM
MTkr
m
m
m
m
m
m
})4
({
})2
{(
}{
}2
{
}{
}{
16
)(
325
)(
324
)(
3213
)(
312
)(
211
)(
2
2
2
2
rn
mdz
dw
rrn
mdz
dw
rmrdz
dw
rmrrn
dz
dw
rmrdz
dw
rrdz
dw
g
O
g
H
g
CO
g
OH
g
CO
g
Cm
The ODE system is highly nonlinear
Numeric Integration is the only Option
m
MA jcsc
j
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Discrete-time Model
)(ˆ)(
)(ˆ)(
)(ˆ)()(
11
1
)(
1
)(
1
1
1
kdkd
k
t
t
tA
k
tA
t
t
tA
k
tA
k
tqBtxA
tqdetxe
dqetxetx
k
k
kc
k
k
kc
Applying Sample & Hold discretization for
)(ˆ tqBAxx
We find the discrete-time model:
(tc - controller sample time)
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Validity of Sample & Hold?
)(gm
tct
Mass Flow Rate is the
MV of the Controller
a Sampled in Time
Structure
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Sampled Like Response of Gas
)(gT
tct
)(gm
tct
Department of Chemical & Biological Engineering
Illinois Institute of Technology
)(gy
tct
Sampled Like Response of Gas Content
)(gm
tct
Department of Chemical & Biological Engineering
Illinois Institute of Technology
)(gy
tct
ct
q
t
)(gT
tct
Sampled Like Response of
Heat Generation Term
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Validity of Sample & Hold?
)(sT
tctct
q
t
)(ˆ tqBAxx
)(ˆ)()( 11 kdkdk tqBtxAtx
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Solid Temperatures at Steady State
Figure 2 Comparisons on temperatures with different sample time
0 0.2 0.4 0.6 0.8 1800
850
900
950
1000
x/L1
Solid
Tem
pera
ture
, oC
CFD
Reduced ( tc=1s)
Reduced ( tc=2s)
air = 165 SLPM
fuel = 40 g/min
steam = 90 g/min
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Impact of the Sample Time
ct
q
t
)(sT
tct2
ct2
q
t
)(sT
tct
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Table 1. Comparisons on time cost for different models
Model
Name 1D-CFD
1D-PFR
(6ODEs)
ODE solver -- ode15s
Running time*, s 130 68
* Prediction Horizon is 180s
* Personal Computer with P4 2.0G Hz CPU and 512M RAM
Calculation Performance
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Oxidation reaction is mass-transfer limited
Oxidation Reaction Rate
2
22
)4/(
)()(
,
1
O
g
O
g
Occ
Mnm
wkr
zKg
O
g
O eww 1
22)0()()(
)(
116
)(
2
2 )4/()(
g
O
g
OwKrnm
dz
wd
zKerr 1)0(11
Department of Chemical & Biological Engineering
Illinois Institute of Technology
1st Reduction in Mass Balances
})4
({
})2
{(
}{
}2
{
}{
}{
16
)(
325
)(
324
)(
3213
)(
312
)(
211
)(
2
2
2
2
rn
mdz
dw
rrn
mdz
dw
rmrdz
dw
rmrrn
dz
dw
rmrdz
dw
rrdz
dw
g
O
g
H
g
CO
g
OH
g
CO
g
Cm
zKg
O
g
O
g
H
g
CO
g
OH
g
CO
g
C
eww
rrn
mdz
dw
rmrdz
dw
rmrrn
dz
dw
rmrdz
dw
rrdz
dwm
1
22
2
2
2
)0(
})2
{(
}{
}2
{
}{
}{
)()(
325
)(
324
)(
3213
)(
312
)(
211
)(
Department of Chemical & Biological Engineering
Illinois Institute of Technology
2nd Reduction in Mass Balances
zKg
O
g
O
g
H
g
C
g
CO
g
OH
g
CO
g
H
g
C
g
H
g
H
g
C
g
C
eww
zbw
wA
w
w
w
wwzfdz
dw
wwzfdz
dw
m
m
m
m
1
22
2
2
2
2
2
2
)0(
)(
),,(
),,(
)()(
)(
)(
)(
)(
)(
)()(
5
)(
)()(
1
)(
zKg
O
g
O
g
H
g
CO
g
OH
g
CO
g
C
eww
rrn
mdz
dw
rmrdz
dw
rmrrn
dz
dw
rmrdz
dw
rrdz
dwm
1
22
2
2
2
)0(
})2
{(
}{
}2
{
}{
}{
)()(
325
)(
324
)(
3213
)(
312
)(
211
)(
Department of Chemical & Biological Engineering
Illinois Institute of Technology
ATR Mode at Steady State
Figure 3 Comparisons on temperatures with different models
0 0.2 0.4 0.6 0.8 1800
850
900
950
1000
x/L1
Solid
Tem
pera
ture
, oC
CFD
Reduced
air = 165 SLPM
fuel = 40 g/min
steam = 90 g/min
0 0.2 0.4 0.6 0.8 1700
750
800
850
900
950
1000
x/L1
Gas T
em
pera
ture
, oC
CFD
Reduced
air = 165 SLPM
fuel = 40 g/min
steam = 90 g/min
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Table 1. Comparisons on time cost for different models
Model
Name 1D-CFD
1D-PFR
(6ODEs)
Reduced
(2ODEs)
ODE solver -- ode15s ode15s
Running time*, s 130 68 15
* Prediction Horizon is 180s
* Personal Computer with P4 2.0G Hz CPU and 512M RAM
Calculation Performance
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Table 2. Comparisons on time cost for different models
Model
Name 1D-CFD
1D-PFR
(6ODEs)
Reduced
(2ODEs)
ODE solver -- ode15s ode15s Adam-Moulton
Running
time*, s 130 68 15
* Prediction Horizon is 180s
* Personal Computer with P4 2.0G Hz CPU and 512M RAM
Calculation Performance
0.8
Department of Chemical & Biological Engineering
Illinois Institute of Technology
ATR Mode at Steady State
Figure 4 Comparisons on temperatures with different ODE solvers
0 0.2 0.4 0.6 0.8 1700
750
800
850
900
950
1000
x/L1
Gas T
em
pera
ture
, oC
CFD
Reduced (ode15s)
Reduced (AM method)
air = 165 SLPM
fuel = 40 g/min
steam = 90 g/min
0 0.2 0.4 0.6 0.8 1800
850
900
950
1000
x/L1
Solid
Tem
pera
ture
, oC
CFD
Reduced (ode15s)
Reuced (AM method)
air = 165 SLPM
fuel = 40 g/min
steam = 90 g/min
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Dynamics for ATR Mode
Figure 5 Comparison on dynamics based on Adam-Moulton method
50 100 150 2000
200
400
600
800
1000
Time,s
Solid
Tem
pera
ture
,oC
Reduced
CFD
@7 mm
0 100 200 300 400
800
850
900
950
Gas t
em
pera
ture
, oC
0 100 200 300 400165170175180
Time, s
Air f
low
rate
, S
LP
M
CFD
Reduced
@ 7 mm
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Conclusions
• Feedback Control (CPOX and ATR Modes)
– Good performance w.r.t. inlet conditions and sensor noise.
– Good performance during CPOX to ATR Transition, if transition is
slow enough.
• Feed-forward Control
– Model mis-match is a major concern
• Model Reduction
– Exploit pseudo steady-state assumption.
– Use analytic solutions wherever possible (minimize numeric schemes).
Department of Chemical & Biological Engineering
Illinois Institute of Technology
Acknowledgements
Collaborators
Shabbir Ahmed (ANL) Sheldon Lee (ANL)
Herek Clack (IIT) Jai Prakash (IIT)
Students
Kevin Lauzze (IIT)
Funding
Argonne National Laboratory
Graduate College, IIT
Armour College of Engineering, IIT
Chemical & Environmental Engineering Dept, IIT
Department of Chemical & Biological Engineering
Illinois Institute of Technology
ATR Reactor Model
0
100
200
300
400
500
600
700
800
900
20 40 60 80 100 120 140 160 180
Time (s)
Tem
pera
ture
(°C
)
7 mm
19 mm
Inlet temperature
Partial Oxidation Start-up: (Liquid Water Spray at 75 s)