Aftertreatment Modeling with Computationally Efficient Q-S Solver

Syed Wahiduzzaman, GTI and

Jean-Nicolas Cassez, PSA Peugeot-Citroën

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Quasi-Steady Solver Overview

• Very fast solver: can simulate 10 to 100 times faster than real time

• Now available (build # 6) for both DPF and kinetics templates

• Makes parameter identification very efficient

• Use of built-in direct optimization (e.g. Brent Optimizer) highly suitable

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Governing Equations of Quasi-Steady Based Flow Solver

• Quasi-steady assumption with fluid phase

• Transient wall thermal model

• Transient surface coverage (solutions are carried out via decoupling with gas phase species with error control)

ambssggs

sbs

sbsbpsb qhTTAhz

TA

t

TAC

)(

2

2

,

Y

U

H

utz,

n

n

y

y

y

y

1

2

1

Y

UGUF

0

zwhere and

ss TCFdt

d,,

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Simulation Workflowfrom reactor data to emission prediction

Start

GT-POWER model

GT-POWER solver

Online sensors/controls evaluating objective

Built-in DoE or

direct optimizer

Initial parameters

Values

objective function

Yes/no

End

before after cycle emissions predictionApply to a TWC:

All in a one integrated environment

Altered parameters

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Application of Q-S solver

• PSA Peugeot-Citroën wants to benchmark GTI aftertreatment modeling capabilities and provided data for DOC and SCR for the purpose

• Two datasets were used– Calibration tests for identification of reaction

mechanisms and parameters– Transient tests for validation of driving cycle

emission data

• Transient test emission results were withheld until simulation results were provided

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Modeling of a Diesel Oxidation Catalyst (DOC)

*Balance consists of N2

13O2 (Vol.-%)

5CO2 (Vol.-%)

5H2O (Vol.-%)

300NO (ppm)

12.5C3H8 (ppm)

37.5C3H6 (ppm)

167H2 (ppm)

500CO (ppm)Inlet Gas

• Inlet Conditions:– Mass flow constant at 0.375 g/s– Temperature increase at rate of 1K/s– Constant Inlet Concentrations (see table)

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Modeling of a Diesel Oxidation Catalyst (DOC)

• Experimental Conversion Data:

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Modeling of a Diesel Oxidation Catalyst (DOC)

• Reaction Scheme:

=> CO2=> 3CO2 + 3H2O=> 3CO2 + 4H2O=> CO2 + 0.5N2=> H2O=> NO2=> NO+0.5O2

CO + 0.5O2C3H6 + 4.5O2

C3H8 + 5O2CO + NO

H2 + 0.5O2NO+0.5O2

NO2

R1:R2:R3:R4:R5:R6:R7:

1

/

1

12

1

G

yyeAr

OCO

TE w

1

/

2

2263

2

G

yyeAr

OHC

TE w

1

/

3

3283

3

G

yyeAr

OHC

TE w

2

13.03.04.1/

4

42

4

G

yyyeAr

NOOCO

TE w

1

/

5

522

5

G

yyeAr

OH

TE w

2

6 /

66 ONO

TEyyeAr w

2

7 /

77 NO

TEyeAr w

• Reaction Rates:

• Inhibition Functions:

7.0

4

22

3

2

211

1

1

1

63

63

CO

HCCO

HCCOw

yK

yyK

yKyKTG

2

52 1 COyKG

wTeK/961

1 5.65 wTeK

/361

2 2080 wTeK

/11611

3 98.3

wTeK/3733

4 479000

wTeK/5.654

5 86.19

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Parameter Identification

• Calibration performed using built in Brent Optimizer

• Independent Variables:– Pre-Exponent Multiplier (A)– Activation Energy (E)

Rate = A Tb exp(E/T) {conc} f(G) g(Ө)

• Dependent Variable:– Error Function defined by:

K

i

t

iiiEA

dtyy1

0

2expcal

,min

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Simulation Workflowfrom microreactor data to emission prediction

Start

GT-POWER model

GT-POWER solver

Online sensors/controls evaluating objective

Built-in DoE or

direct optimizer

parameters to vary

objective function

Yes/no

End

before after cycle emissions predictionApply to a TWC:

All in a single executable environment

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Modeling of a Diesel Oxidation Catalyst (DOC)

• Calibrated DOC model:

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Modeling of a Diesel Oxidation Catalyst (DOC)

• Calibrated DOC model used for Transient NDEC cycle

• Cumulative mass conversions predicted to be:CO = 61%HC = 49%NO = 6%

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Modeling of a Diesel Oxidation Catalyst (DOC)

• Simulations were performed on a Pentium 4 3.4GHz processor with 1 GB of RAM

7112000.25Step 2: Prediction

113270.25Step 1: Calibration

ComputationalTime (s)

SimulationTime (s)

Time StepSize (s)

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Modeling a Zeolite Based SCR

• Experimental data was provided by PSA Peugeot Citroën

• Five sets of calibration data aimed at determination of parameters involving:

– Test 1: Storage capacity, absorption/desorption * + NH3 < = > *NH3

– Test 2: Ammonia oxidation 4NH3 + 3O2 => 2N2 + 6H2O

– Test 3: “Standard” SCR reaction4NH3 + 4NO + O2 =>4N2 + 6H2O

– Test 4: “Slow” SCR reaction8NH3 + 6NO2 = > 7N2 + 12H2O

– Test 5: “Fast” SCR reaction4NH3 + 2NO + 2NO2 => 4N2 + 6H2O

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Other Reactions

• Nitrous Oxide– 4NH3 + 4O2 => 2N2O + 6H2O– 2NH3 + 2NO2 => N2O + N2 + 3H2O– 4NH3 + 4NO + 3O2 => 4N2O + 6H20– NH3 + HNO3 => N2O + 2H2O

• Nitric acid– NH3 + HNO3 NH4NO3– 2NO2 + H2O HONO + HNO3– HONO + NH3 N2 + 2H2O

• Reactions considered but not included in the present analysis based measured on exit concentration and experimental conditions. H 2O inhibits selective catalytic oxidation of ammonia (SCO)

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Experimental Procedure for SCR Kinetics Identification

Con

cen

trat

ion

s

Purge under N2

Start NH3 Injection

Stop NH3and

Begin NOxintroduction

Time

Temperatu

re

780K

460K

TemperatureRamp (TPD)

1840s 3650s

N2

NOx

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Processed Sensor Data

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Calculation of Storage Capacity

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Storage Capacity (cont.)• Experimental results suggest more NH 3 desorbed

than could be accounted for by storage• Two possibilities exist:

1. experimental error in one or both NH 3 sensors2. NH3 is pre-stored

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Storage Capacity (cont.)

• The onset of saturation and shape of saturation curve indicated by the exit NH 3sensor seemed to be consistent

• Optimization was performed to determine:– storage capacity– pre-stored NH3 (if any)

• Optimization goal:– conserve NH3 mass – conserve onset/shape of NH3 saturation

curve• Built-in Brent direct optimizer was used

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Storage Capacity (cont.)

• A pre-storage corresponding to 45% coverage and a storage capacity of 4.9E-3gmole/m^2 were determined

• These generally agree with all experiments

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

NH3 Oxidation Reaction

4NH3 + 3O2 => 2N2 + 6H2O

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Standard Reaction

4NH3 + 4NO + O2 =>4N2 + 6H2O

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Fast Reaction

4NH3 + 2NO + 2NO2 => 4N2 + 6H2O

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

SCR NOX Selectivity Study

• NOX conversion should be highest at NO2/NOX ratio of 0.5 (or NO:NO2 = 1:1)

• Study was performed using– Vary NO2/NOX ratio from 0-1– Vary temperature from 400-700K– 10 ppm NH3 slip– 150 ppm NOX, NH3 (variable), 10% H2O,

10% O2, balance N2

– Constant volume flow rate = 0.55 liter/s

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

SCR NOX Selectivity Study

• Original Calibration:

• R3: 4NH3 + 3O2 => 2N2 + 6H2O (too fast)• R6: 4NH3 + 2NO + 2NO2 => 4N2 + 6H2O (too slow)

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

SCR NOX Selectivity Study

• Adjusted Calibration:

• R3: decreased pre-exponent multiplier• R6: increased pre-exponent multiplier

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Transient Emission Predictions

• Calibrated SCR model used for Transient NDEC cycle

• Model ran under two conditions:– Absorption site 100% “open” (no NH3

prestorage)– Absorption site 0.0% “open”

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Emission Predictions (cont.)• All sites “open” (no NH3 prestored)

• Cumulative Mass Changes:NO = -28% NOX = -37%NO2 = -49% NH3 = -100%NOx (measured) = -38%

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Emission Predictions (cont.)• All sites “covered” (NH3 prestored to full capacity)

• Cumulative Mass Changes:NO = -48% NOX = -67%NO2 = -90% NH3 = -68%

*NOx measurement not available for comparison

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Modeling a Zeolite Based SCR

• Simulations were performed on a Pentium 4 3.4GHz processor with 1 GB of RAM

4336540.50Abs/Des with O2

4536540.50Standard Reaction

4936540.50Slow Reaction

5736540.50Fast Reaction

8511660.25Transient without NH3 prestored

8711660.25Transient with NH3 prestored

3136540.50Abs/Des without O2

ComputationalTime (s)

SimulationTime (s)

Time StepSize (s)

Overview

Q-S Solver

Identification

Applications

DOC

Calibration

Prediction

SCR

Data

Calibration

Prediction

Conclusions

All information contained in this document is confidential and cannot be reproduced or transmitted in any form or by any means, electronic or mechanical, for any purpose, without the express written permission of Gamma Technologies, Inc. © 2007 Gamma Technologies, Inc.

Conclusions

• Fast running Quasi-Steady solver is introduced

• The solver exhibited excellent computational efficiency while preserving the accuracy of the implicit solver

• Use of built-in direct optimizer (Brent) is demonstrated for kinetic parameter identification

• Validity of the technique was confirmed using literature and PSA supplied DOC and SCR data

• Transient prediction of DOC and SCR were performed for comparison with experimental data