Modeling and Control of an Autothermal Reforming (ATR...

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

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

Polymer Electrolyte Membrane

Fuel Cell (PEMFC)

Electrolyte

Cathode

Generated power due to

enthalpy released by

the reaction:

H2 + ½ O2 H2O

(H ~ 58 kcal/mole H2)

Polymer Electrolyte Membrane

Fuel Cell (PEMFC)

Electrolyte

Cathode

Transportation Applications

Fuel Cell System

Processor Fuel Cell

Spent-Fuel

Burner

Thermal & Water Management

Exhaust

H2O CO2

Electric Power

Conditioner

Hydrogen Storage vs. On-Board Reforming

Transportation

Applications

PEMFCReformerLiquid Fuel

Storage Tank

PEMFCHydrogen

Storage Tank

Hydrogen Storage vs. On-Board Reforming

Transportation

Applications

PEMFCReformerLiquid Fuel

Storage Tank

PEMFCHydrogen

Storage Tank

PEMFC and CO Poisoning

Fuel Processing Reactors

PEMFCPreferential

Oxidation

(PrOx)

Water-

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

Partial Oxidation

Hydrocarbon Fuel

Air (at a sub-

stoichiometric rate)

Reactor

Total Oxidation: OHnmCOOnmHC nm 222 2/)2/(

Steam Reforming: 22 )2/( HnmmCOOmHHC nm

Water Gas Shift: 222 HCOOHCO

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

Autothermal Reforming

Hydrocarbon Fuel Air (at a sub-

Reactor

Oxidation: OHnmCOOnmHC nm 222 2/)2/(

Autothermal Reforming

Hydrocarbon Fuel Air (at a sub-

Reactor

Oxidation: OHnmCOOnmHC nm 222 2/)2/(

More 2

Steam 222 ,,, COOHCOH

Outline

Introduction / Motivation

Reactor Modeling and Analysis

Classic Controller Design

Nonlinear Model Predictive Control

Reduced Order Modeling

Fuel Processor System at Argonne

AirWater

ATR Reactor at Argonne

Vaporized gasoline,

Liquid water

Heat exchangerAir (25 °C)

Hot air

Nozzle

Catalyst bed

Heater rod

Thermocouple1 2 3 4

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

Reactor Model (Axially Dependent, Nonlinear Dynamic Version)

)()()(,

jc rMk1

)()()(

)()()()(

)()( ˆ0 sggccc

pg TThA

)()()(

)()( )(ˆ wsw

pw TTxh

Mass Balances:

Catalyst Phase:

Gas Phase:

Energy Balances:

Gas Phase:

llreactor wa fer toHeat trans

)()()(

...)(1ˆ

Solid Phase:

Reactor Wall:

Model of Reaction Kinetics (1)

fuel yyAr

Total Oxidation Reaction :

OHnmCOOnmHC nm 222 2/)2/(

Rate Expression:

Oxidation rate is Fuel Diffusion Limited.

222 HCOOHCO

Water-Gas Shift Reaction:

Rate Expression:

029.22073)()(

33 10;22

yyyyeAr

Wheeler, Jhalani, Klein, Tummala, Schmidt, J. Catal. (2004).

Parameters Adapted from:

22 )2/( HnmmCOOmHHC nm

Steam Reforming Reaction:

Rate Expression:

yeKyyeAr

Activation Energies from:

Dubien, Schweich, Mabilon, Martin, Prigent, Chem. Eng. Sci. (1998).

A2 and K2: Fit to Experimental Data:

Micro-Reactor Tests (Steady-State Analysis)

0.75 1.25 1.75 2.25 2.75 3.25

H2O/C ratio (-)

O2/C=0.45

0.30 0.35 0.40 0.45 0.50 0.55 0.60

O2/C ratio (-)

H2O/C=1.5

Reactor Start-up: A 2 Step Procedure

Partial Oxidation Mode (to quickly increase temperature)

ATR Mode (for greater CO conversion)

Hydrocarbon Fuel Air

Reactor

Hydrocarbon Fuel

Reactor

Reactor Start-Up

20 40 60 80 100 120 140 160 180 200

Time (s)

Experimental Data

Simulation

@ 7 mm

@ 19 mm

Inlet temperature

Steady-State Axial Profiles

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)

CPOX Mode: ATR Mode:

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)

FuelO2

Outline

Need for Temperature Regulation

Vaporized gasoline,

Liquid water

Heat exchangerAir (25 °C)

Hot air

Nozzle

Catalyst bed

Heater rod

Thermocouple1 2 3 4

8 9 10

Metal wall

thickness=1.7 mm

0 200 400 600 800 10000

time (sec)

(deg C

Inlet Air Temperature Trajectory

Primary Disturbance:

Inlet Temperature

Open-Loop System

System T3

Inlet Air Flow

Inlet Air

Temperature

Inlet Steam Flow

} } Unmeasured

(but simulated)

Measured

(and simulated)

• Step Tests Performed Using the 1-D Nonlinear Model

First Order Plus Dead Time Modeling

0 20 40 60 80 100800

time (sec)0 20 40 60 80 100

time (sec)

0 20 40 60 80 100650

time (sec)

Air Flow Rate Inlet Temperature Steam Flow Rate

inSteam

Feedback Control

Reactor

T3 Inlet Air Flow

Control

T3, set point

Inlet Air Temperature

T3, measured

Sensor Noise

Temperature Fluctuations in Reactor

Feedback Control

Reactor

T3 Inlet Air Flow

Control

T3, set point

Inlet Air Temperature

T3, measured

Sensor Noise

Temperature Fluctuations in Reactor

Manipulated

Variable

Control Variable

Disturbances

Simulated Disturbances

0 200 400 600 800 10000

time (sec)

Inlet Air Temperature Trajectory

0 200 400 600 800-80

60Temperature Fluctuations and Sensor Noise

time (sec)

ance I

Analysis of the Feedback Controller

Regulation During ATR Mode:

0 200 400 600 800800

1200CV (T

3) Response: Open- vs. Closed-loop

time (sec)

Open-loop

Closed-loop

0 200 400 600 8000

200MV (Air Flow) Response: Open vs. Closed-loop

time (sec)

) Open-loop

Closed-loop

Transition from CPOX to ATR Mode

T3 Air Flow

T3, set point

Steam Flow Rate

0 50 100 150 2000

Reacto

(deg C

)Impact of Steam Injection

time (sec)

With Feedback Controller

Without Feedback Controller

Steam Flow Rate

0 50 100 150 200

0 50 100 150 2000

0 50 100 150 200

Impact of Steam Injection Rate

With Feedback Controller

Without Feedback Controller

Steam Flow Rate

time (sec)

Reacto

(deg C

Feed-forward Control

Gp(s) T3

Flow +

T3, set point

Steam Flow Rate

(Measured)

Gff(s)

)()( sH

Impact of Feed-forward Control

0 20 40 60 80 100500

Reacto

(deg C

time (sec)

Steam Injection: With and Without Feed-forward

Feedback Controller Only

Feed-forward / Feedback Controller

Model Mismatch in Feed-forward Control

Gp(s) T3

Flow +

T3, set point

Steam Flow Rate

(Measured)

Gff(s)

)()( sH

• If the Gd(s) or Gp(s) used to define Gff(s) are

different than the actual plant then mismatch occurs.

Impact of Model Mismatch

0 20 40 60 80 100400

time (sec)

Feed-forward Without

Model Mismatch

Feed-forward With Model Mismatch

Impact of Model Mismatch on Feed-forward

0 20 40 60 80 100200

Impact of Model Mismatch on Feed-forward

time (sec)

Feed-forward Without Model Mismatch

Feed-forward With

Model Mismatch

Outline

Advanced Process Control

Nonlinear Model Predictive Control (NMPC):

Gp(s) T Air Flow

Steam Flow Rate

(Measured)

Process

Contraints

Feedback

Why NMPC?

- Optimized Responses

- Start-up

- Load changes

- Enforcement of Process Constraints

- Can use Nonlinear Model

- Needed for feed-forward action

Challenges to Implementing NMPC

- Computational challenges

- Optimization based

- Small sample intervals

- Accurate model required

- Needed for feed-forward action

Model Validation

20 40 60 80 100 120 140 160 180 200

Time (s)

Inlet temperature

Papadias, et.al. (2006), Ind. Eng. Chem. Res.

Running time for

180 s :

~ 2 min for

FEMLAB on PC

with P4 2.0G

Outline

Temperature profile

0 0.2 0.4 0.6 0.8 1700

Dimensionless,x/L1

Oxidation

Reforming WGS

1-D CFD Dynamic Model

)()()ˆ( )()()()(

gp TThz

Energy balance model

)()ˆ(

)()()1()ˆ(

)()()(

)()()()(

rHTThTThz

iijjcs

Mass balance model

Vaporized gasoline,

Liquid water Heat

exchanger

Air (25 °C)

Hot air

Nozzle

Catalyst bed

Heater rod Thermocouple

Metal wall, thickness, 1.7 mm

7 mm 12 mm 12 mm

Resultant gases

Infinite Dimensional Energy Balances

)()()(

gs rHTTtzq )(),( )()(

Catalyst Support

Reactor Wall

Applying

Glerkin Approximation

s ztxtzT1

)()( )()(),(

w ztxtzT1

)()( )()(),(

)(ˆ tqBAxx

ss xxxxxxx ],;,[ )()(

We arrive at the finite dimensional model

with a dimension of 2N

Calculation of Heat Flux from Gas

)()ˆ( )()()(

gp TThAdz

s ztxtzT1

)()( )()(),(

Energy Balance at Gas

Calculation of Heat Flux from Gas

))()(()ˆ( )(

gp TztxhAdz

sg TmMxmMtzT )()(),( 2

)( )()( sg

Integration this ODE yields

and allows the calculation of

But, is time-dependent m

Calculation of Reaction Heat

wwMTkr

Calculation of Reaction Heat

wwMTkr

The ODE system is highly nonlinear

Numeric Integration is the only Option

MA jcsc

Discrete-time Model

)(ˆ)(

)(ˆ)()(

tqBtxA

tqdetxe

dqetxetx

Applying Sample & Hold discretization for

)(ˆ tqBAxx

We find the discrete-time model:

(tc - controller sample time)

Validity of Sample & Hold?

Mass Flow Rate is the

MV of the Controller

a Sampled in Time

Structure

Sampled Like Response of Gas

Sampled Like Response of Gas Content

Sampled Like Response of

Heat Generation Term

Validity of Sample & Hold?

)(ˆ tqBAxx

)(ˆ)()( 11 kdkdk tqBtxAtx

Solid Temperatures at Steady State

Figure 2 Comparisons on temperatures with different sample time

0 0.2 0.4 0.6 0.8 1800

Reduced ( tc=1s)

Reduced ( tc=2s)

air = 165 SLPM

fuel = 40 g/min

steam = 90 g/min

Impact of the Sample Time

Table 1. Comparisons on time cost for different models

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

Oxidation reaction is mass-transfer limited

Oxidation Reaction Rate

O eww 1

22)0()()(

2 )4/()(

OwKrnm

zKerr 1)0(11

1st Reduction in Mass Balances

2nd Reduction in Mass Balances

wwzfdz

ATR Mode at Steady State

Figure 3 Comparisons on temperatures with different models

0 0.2 0.4 0.6 0.8 1800

Reduced

air = 165 SLPM

fuel = 40 g/min

steam = 90 g/min

0 0.2 0.4 0.6 0.8 1700

Reduced

air = 165 SLPM

fuel = 40 g/min

steam = 90 g/min

Name 1D-CFD

1D-PFR

(6ODEs)

Reduced

(2ODEs)

ODE solver -- ode15s ode15s

Running time*, s 130 68 15

Name 1D-CFD

1D-PFR

(6ODEs)

Reduced

(2ODEs)

ODE solver -- ode15s ode15s Adam-Moulton

Running

time*, s 130 68 15

ATR Mode at Steady State

Figure 4 Comparisons on temperatures with different ODE solvers

0 0.2 0.4 0.6 0.8 1700

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

Reduced (ode15s)

Reuced (AM method)

air = 165 SLPM

fuel = 40 g/min

steam = 90 g/min

Dynamics for ATR Mode

Figure 5 Comparison on dynamics based on Adam-Moulton method

50 100 150 2000

Time,s

Reduced

0 100 200 300 400

0 100 200 300 400165170175180

Time, s

Reduced

@ 7 mm

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).

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

ATR Reactor Model

20 40 60 80 100 120 140 160 180

Time (s)

Inlet temperature

Partial Oxidation Start-up: (Liquid Water Spray at 75 s)

Modeling and Control of an Autothermal Reforming (ATR...

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