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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 5 th 2007 Chemistry Colloquium, Illinois Institute of Technology

Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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Page 1: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 2: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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)

Page 3: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 4: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 5: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 6: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 7: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

PEMFC and CO Poisoning

Page 8: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 9: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 10: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 11: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 12: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 13: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 14: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 15: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 16: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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:

Page 17: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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.

Page 18: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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:

Page 19: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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:

Page 20: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 21: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 22: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 23: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 24: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 25: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 26: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 27: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 28: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 29: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 30: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

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

Page 31: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 32: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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)

-

Page 33: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 34: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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)

Page 35: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 36: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 37: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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.

Page 38: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 39: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 40: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

Advanced Process Control

Nonlinear Model Predictive Control (NMPC):

Gp(s) T Air Flow

Steam Flow Rate

(Measured)

NMPC

Process

Contraints

Feedback

Page 41: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 42: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

Challenges to Implementing NMPC

- Computational challenges

- Optimization based

- Small sample intervals

- Accurate model required

- Needed for feed-forward action

Page 43: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 44: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 45: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 46: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 47: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

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

Page 48: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 49: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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 )(),( )()(

Page 50: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 51: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 52: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 53: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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)

Page 54: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 55: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

Sampled Like Response of Gas

)(gT

tct

)(gm

tct

Page 56: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

)(gy

tct

Sampled Like Response of Gas Content

)(gm

tct

Page 57: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

)(gy

tct

ct

q

t

)(gT

tct

Sampled Like Response of

Heat Generation Term

Page 58: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

Validity of Sample & Hold?

)(sT

tctct

q

t

)(ˆ tqBAxx

)(ˆ)()( 11 kdkdk tqBtxAtx

Page 59: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 60: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

Department of Chemical & Biological Engineering

Illinois Institute of Technology

Impact of the Sample Time

ct

q

t

)(sT

tct2

ct2

q

t

)(sT

tct

Page 61: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 62: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 63: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

)(

Page 64: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

)(

Page 65: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 66: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 67: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 68: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 69: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 70: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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).

Page 71: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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

Page 72: Modeling and Control of an Autothermal Reforming (ATR ...mypages.iit.edu/.../seminar/IIT_ChemDept_Oct2007.pdf · Illinois Institute of Technology, Chicago, IL Dennis Papadias Chemical

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)