LABORATORY OF APPLIED THERMODYNAMICS

Dr. Grigorios C. Koltsakis

Aristotle University Thessaloniki

Tutorial

DOC & DPF modeling

Contents

� Diesel oxidation catalyst modeling

� Single channel modeling

� Washcoat modeling

� DOC chemistry

� HC adsorption

� Diesel Particulate Filter (DPF) modeling

� Fundamentals, basic model equations

� Filtration, soot properties

� Soot thermal and catalytic oxidation

� Transport-reaction coupling

� “3-dimensional” effects

LABORATORY OF APPLIED THERMODYNAMICS

Tutorial

DOC & DPF modeling DOC modeling

Channel model

Basic 1-D model equations

( )sg

g

gg TTS

hx

Tv −⋅

⋅−=∂

∂

ερ

Gas energy balance Gas species balance

( ) ( )jsjgj

ggcc

Sk

x

cv,, −⋅

⋅−=∂

∂

ε

( ) ∑=

∆−

−−

−

+∂∂

=∂∂ kn

k

kksgs

ss

sps RHTTS

hx

T

t

TC

12

2

,1

1

1 εελρTransient energy

balance

( ) )(,, sjjsjgj

g

gcRcc

Sk

M=−

ε

ρ

Mass-transfer rate = reaction rate

Solid heat capacity Conduction Convection Reaction heat

Substrate Ts, ρs, vs Washcoat

O2, N2, CO, HC, NOx O2, N2, CO2, H2O

Gas Tg, ρg, vg

2-D axi-symmetric modeling

Basic concept

Filter

Insulating mat

Metal Can Z

R

Simulation of discrete

“representative” channels

Derivation of heat source terms

(convection, exothermy)

Solution of time dependent flow distribution

profile at catalyst inlet, as function of flow

resistance

(temperature distribution in the filter)

Sr

Tr

rrz

T

t

TC s

rss

zss

sps +

∂∂

∂∂

+∂∂

=∂∂

⋅1

,2

2

,, λλρ

Energy balanceEnergy balance

Substrate Ts, ρs, vs Washcoat

O2, N2, CO, HC, NOx O2, N2, CO2, H2O

Gas Tg, ρg, vg

Axial

heat conduction

Radial

heat conductionHeat capacity

Substrate

1-d washcoat model

Washcoat diffusivity

“mixed” (parallel pore) model

Intra-layer

Washcoat

Substrate

∑=

∂

∂

∂∂

−k

kkj

m

xj

xj Rcc

f

x

yf

xD ,

( ) ( ),1,1,1,1,11 jjsj

w

j yykdf

yvz

−=∂∂

− i

jmol

jid

DShk

,

,

⋅=

( ),,11

2

1

jw

s

j

wj yvz

dfx

yfD

∂∂

−=∂

∂− −−

0

2

=∂

∂

s

j

x

yBoundary conditions:

Washcoat:

Channel gas species balance:

Intra-layerIntra-layer

Washcoat

Substrate

∑=

∂

∂

∂∂

−k

kkj

m

xj

xj Rcc

f

x

yf

xD ,

( ) ( ),1,1,1,1,11 jjsj

w

j yykdf

yvz

−=∂∂

− i

jmol

jid

DShk

,

,

⋅=

( ),,11

2

1

jw

s

j

wj yvz

dfx

yfD

∂∂

−=∂

∂− −−

0

2

=∂

∂

s

j

x

yBoundary conditions:

Washcoat:

Channel gas species balance:

Applications

� “Thick” washcoats

� Extruded catalysts

� Multi-layer catalysts

+=

jknudjmolpjw DDD ,,,

111

ετ

j

p

jknudM

TdD

πℜ

=8

3,

7

Overview of 3-d catalyst modeling

( )

( ) ( )jsjgj

gg

sg

g

gg

ccS

kx

cv

TTS

hx

Tv

,, −⋅

⋅−=∂

∂

−⋅

⋅−=∂

∂

ε

ερ

Sz

Tk

y

Tk

x

Tk

x

Tc s

zss

yss

xss

sps +∂∂

+∂∂

+∂∂

=∂∂

2

2

,2

2

,2

2

,,ρ

( )jisigj

g

gRcc

Sk

M=−⋅

,,ε

ρ

Intra-layer

Washcoat

Substrate

∑=

∂

∂

∂∂

−k

kkj

m

xj

xj Rcc

f

x

yf

xD ,

( ) ( ),1,1,1,1,11 jjsj

w

j yykdf

yvz

−=∂∂

− i

jmol

jid

DShk

,

,

⋅=

( ),,11

2

1

jw

s

j

wj yvz

dfx

yfD

∂∂

−=∂

∂− −−

0

2

=∂

∂

s

j

x

yBoundary conditions:

Washcoat:

Channel gas species balance:

Intra-layerIntra-layer

Washcoat

Substrate

∑=

∂

∂

∂∂

−k

kkj

m

xj

xj Rcc

f

x

yf

xD ,

( ) ( ),1,1,1,1,11 jjsj

w

j yykdf

yvz

−=∂∂

− i

jmol

jid

DShk

,

,

⋅=

( ),,11

2

1

jw

s

j

wj yvz

dfx

yfD

∂∂

−=∂

∂− −−

0

2

=∂

∂

s

j

x

yBoundary conditions:

Washcoat:

Channel gas species balance:

Multi-dimensional washcoat models

DOC global reaction scheme

� CO oxidation with O2

� HC oxidation with O2

� NO reversible oxidation

� CO oxidation with NO2

� HC oxidation with NO2

� HC / H2O adsorption

2221 COOCO+ →

24 222 OHy

xCOOy

xHC yx

+→

++

2

122 NOONO →←+

NOCOCO+NO +→ 22

22

2 222 OHy

NOxCONOy

xHC yx

++→

++

Global reaction rates (examples)

2221 COOCO+ →

2

1 2

1

G

cceAR

OCORT

E

⋅⋅⋅=

−

2

122 NOONO →←+

CO self inhibition effects

0

20

40

60

80

100

100 150 200 250 300

Temperature [°C]

Eff

iencie

ncy [%

]

CO computed

CO experimental

0

20

40

60

80

100

100 150 200 250 300

Temperature [°C]

Eff

iencie

ncy [%

]

CO computed

CO experimental

[CO]=576 ppm

0

20

40

60

80

100

100 150 200 250 300

Temperature [°C]

Eff

iencie

ncy [%

]

CO computed

CO experimental

[CO]=1536 ppm

T50 = 160 degC T50 = 190 degC

Hydrocarbon adsorption

Langmuir isotherm

Alternative adsorption models

Dubinin-Radushkevich isotherm

� D-R isotherm is applicable to multilayer adsorption in microporous solids (zeolites).

� The equation of the DR isotherm gives the adsorbed mass as function of temperature and partial pressure.

� A linear «driving force» is assummed to calculate the rates towards equilibrium.

� Adjustable parameters:

� W0 (micropore volume)

� A (micropore size distribution)

� β (affinity parameter)

� k (rate constant)

� The rate constant for desorption is an exponential function of temperature.

2

=

βRT

AD( )2

00 lnlnln

−=

p

pDWxeq ρ

( )xxkt

xR eq −⋅=

∂∂

=

How to model diesel exhaust hydrocarbons?

� Not possible with a single HC species

� Pontikakis et al. (2000) used 4 HC species

� Decane: fast oxidizing, easily adsorbable

� Toluene: fast oxidizing, less easily adsorbable

� Propene: fast oxidizing, practically non-

adsorbable

� Propane: slow oxidizing, practically non-

adsorbable

� Model calibration with SGB tests, validation in NEDC

100 150 200 250 300 350 400

Temperature [°C]

0

20

40

60

80

100

Eff

icie

ncy [

%]

Low GHSV, experimental

Low GHSV, computed

High GHSV, experimental

High GHSV, computed

100 150 200 250 300 350 400

Temperature [°C]

-20

0

20

40

60

80

100

Effic

iency [%

]

Low GHSV, experimental

Low GHSV, computed

High GHSV, experimental

High GHSV, computed4 HCs

HC prediction

NEDC instantaneous emissions

0 200 400 600 800 1000 1200

Time [s]

0.00E+0

2.50E-4

5.00E-4

7.50E-4

1.00E-3

1.25E-3

1.50E-3

Concentration

Inlet

Outlet, computed

Outlet, experimental

0 100 200 300 400 500 600 700 800

Time [s]

0

5E-4

1E-3

2E-3

2E-3

HC

Concentr

ation a

t outlet

-1.0

0.0

1.0

Adsorb

ed H

C [m

ol]

Without HC adsorption

Experimental

With HC adsorption

Adsorbed HC

HC/H2O adsorption competition

0

50

100

150

200

250

300

350

400

450

6278 6478 6678 6878 7078 7278 7478 7678

Time[s]

HC

concentr

ation [ppm

]

T1_exp [

oC

]HC inHC out simulationHC out experimentalT1_exp

0

50

100

150

200

250

300

350

400

450

2967 3017 3067 3117 3167 3217 3267 3317 3367

Time[s]

HC

concentr

ation [ppm

]

T1_exp [

oC

]

HC in HC out simulation HC out experimental T1_exp

Decane adsorption desorption

w/o H2O in the feed

Decane adsorption desorption

with H2O in the feed

Water condensation/evaporation effect on thermal response

0 100 200 300 400 500

Time [s]

0

100

200

Tem

pera

ture

[°C

]

Core, exp.

Core, cmp.

Core, cmp., no H2O ads.

Periphery, exp.

Periphery, cmp.

Periphery, cmp., no H2O ads.

Chatterjee et al., SAE 2008-01-0867

Pontikakis et al., CaPoC 5, 2000

Hysteresis (history) effect

0

10

20

30

40

50

60

70

80

90

100

60 100 140 180 220 260 300 340 380 420 460

T [°C]

Convers

ion e

ffic

iency %

CO light off CO cool down NO light off NO cool down HC light off HC cool down

COCO

HCHC

NONO

LABORATORY OF APPLIED THERMODYNAMICS

Tutorial

DOC & DPF modeling DPF modeling

Definitions

Soot & wallSoot & wall

p1, T1, ρ1, v1

p2, T2, ρ2, v2

Ts, ρw, vw

Filter

Insulating mat

Metal Can Z

R

0-d

Representative channel

& axial uniformityRepresentative channel

(adiabatic, uniform inlet flow)

Axi-symmetric, non-segmented filter

(circular shape, symmetric flow distribution)

Random shape, segmentation

any flow distribution

Catalyst effects

soot layer properties

1-d

2-d 3-d

Intra-layer

The challenge of catalyzed DPF modeling

“Mixed reactor”

reactionreaction

reaction

Mass-transfer

reaction

Mass-transfer

reaction

“channel flow”

“wall flow”

Mass-transfer

reaction

“channel flow”

“wall flow”

Mass-transfer

LABORATORY OF APPLIED THERMODYNAMICS

Tutorial

DOC & DPF modeling

Species balance

Wall-scale equations

Species equations

quasi-steady, kw=infinite -> Yw (x)=Yf(x)

( )IvY

IIfwIIadv YvN ,, =

)(zYI

( )−IvY

( )IfIIIconv YYkN ,

*

, −=

IwIadv YvN =,

( )IIIIfIIIIconv YYkN −= ,

*

,

)(zYII

( )IIvY

( )−IIvY

Rx

YD

x

Yv

f

g

f

w =∂

∂−

∂

∂2

2

*

)(xY fIfY , IIfY ,

Inlet channel Wall Outlet channel

Extremely high species transfer rates inside the porous wall

Species equations

quasi-steady, kw=infinite (Yw=Yf)

( )IvY

IIfwIIadv YvN ,, =

)(zYI

( )−IvY

( )IfIIIconv YYkN ,

*

, −=

IwIadv YvN =,

( )IIIIfIIIIconv YYkN −= ,

*

,

)(zYII

( )IIvY

( )−IIvY

Rx

YD

x

Yv

f

g

f

w =∂

∂−

∂

∂2

2

*

)(xY fIfY , IIfY ,

IfwfIadv YvN ,,, =

IIfwfIIadv YvN ,,, =

fIdifN ,,fIIdifN ,,

( )x

YDYvYYkYv

f

gIfwwIIIw ∂

∂−=−+ *

,)( ,

*

IIIIfII

f

g YYkx

YD −=

∂

∂−

Haralampous O. A., Koltsakis G. C.: Industrial & Engineering Chemistry Research, Vol.43, Issue 4, p. 875-883, 2004.

Inlet channel Wall Outlet channel

Species equations

quasi-steady, kw=infinite, kI=kII=0

IIfwIIadv YvN ,, =

inI YY =

IwIadv YvN =,

)(zYII

( )IIvY

( )−IIvY

Rx

YD

x

Yv

f

g

f

w =∂

∂−

∂

∂2

2

*

)(xY fIfY , IIfY ,

IfwfIadv YvN ,,, =

IIfwfIIadv YvN ,,, =

fIdifN ,,fIIdifN ,,

x

YDYvYv

f

gIfwIw ∂

∂−= *

,0* =

∂

∂−

x

YD

f

g

Inlet channel Wall Outlet channel

Neglecting the convective species transfer from channel gas to surface

(not justified, especially in catalyzed applications)

Species equations

quasi-steady, kw=infinite, kI=kII=0, Dg*=0

IIfwIIadv YvN ,, =

inI YY =

IwIadv YvN =,

)(zYII

( )IIvY

( )−IIvY

Rx

Yv

f

w =∂

∂

)(xY fIfY , IIfY ,

IfwfIadv YvN ,,, =

IIfwfIIadv YvN ,,, =

IfI YY ,=

Bissett E. J., Shadman F., AlChE Journal (Vol31, No5), p. 753, May 1985. ”0-d model”

Bissett E. J., Chemical Engineering Science Vol. 39, Nos 7/8, pp. 1233-1244 (1984). “1-d model”

Neglecting diffusion in the wall-flow direction

Energy equations

( )Ip vTC ρ

( ) IIfpwIIadv TCvH ,, ρ=

)(zTI

( )−Ip vTC ρ

( )IwIIIconv TThH ,

*

, −=

( ) IpwIadv TCvH ρ=,

( )IIIIwIIIIconv TThH −= ,

*

,

)(zTII

( )IIp vTC ρ

( )−IIp vTC ρ

( ) ( )fwww

f

g

f

pw TTShx

Tk

x

TCv −=

∂

∂−

∂

∂2

2

*ρ

( ) ( ) reactw

wwfww

wp Hx

TkTTSh

t

TC +

∂∂

+−=∂∂

2

2

ρ

)(xT f

)(xTw

IfT , IIfT ,

IwT , IIwT ,

( )wfwwconv TThH −=,

Inlet channel Wall Outlet channel

Energy equations

( )Ip vTC ρ

( ) IIfpwIIadv TCvH ,, ρ=

)(zTI

( )−Ip vTC ρ

( )IwIIIconv TThH ,

*

, −=

( ) IpwIadv TCvH ρ=,

( )IIIIwIIIIconv TThH −= ,

*

,

)(zTII

( )IIp vTC ρ

( )−IIp vTC ρ

( ) ( )fwww

f

g

f

pw TTShx

Tk

x

TCv −=

∂

∂−

∂

∂2

2

*ρ

( ) ( ) reactw

wwfww

wp Hx

TkTTSh

t

TC +

∂∂

+−=∂∂

2

2

ρ

)(xT f

)(xTw

IfT , IIfT ,

IwT , IIwT ,

( ) IfpwfIadv TCvH ,,, ρ=

( ) IIfpwfIIadv TCvH ,,, ρ=

fIcondH ,, fIIcondH ,,

wIcondH ,, wIIcondH ,,

( ) ( )x

TkTCvTCv

f

gIfpwIpw ∂

∂−= *

,ρρ 0* =∂

∂−

x

Tk

f

g

( )wx

wwIIIIwIIx

TkTTh

=∂∂

−=−,

*( )0

,

*

=∂∂

−=−x

wwIwII

x

TkTTh

( )wfwwconv TThH −=,

Energy equations

neglecting gas conduction term kg* =0

( )Ip vTC ρ

( ) IIfpwIIadv TCvH ,, ρ=

( )−Ip vTC ρ

( )IwIIIconv TThH ,

*

, −=

( ) IpwIadv TCvH ρ=,

( )IIIIwIIIIconv TThH −= ,

*

,

)(zTII

( )IIp vTC ρ

( )−IIp vTC ρ

( ) ( )fwww

f

pw TTShx

TCv −=

∂

∂ρ

( ) ( ) reactw

wwfww

wp Hx

TkTTSh

t

TC +

∂∂

+−=∂∂

2

2

ρ

)(xT f

)(xTw

IfT , IIfT ,

IwT , IIwT ,

( ) IfpwfIadv TCvH ,,, ρ=

( ) IIfpwfIIadv TCvH ,,, ρ=

wIcondH ,, wIIcondH ,,

IfI TT ,= 0* =∂

∂−

x

Tk

f

g

( )wx

wwIIIIwIIx

TkTTh

=∂∂

−=−,

*( )0

,

*

=∂∂

−=−x

wwIwII

x

TkTTh

( )wfwwconv TThH −=,

)(zTI

Haralampous O., Koltsakis G. C.: Chemical Engineering Science, Volume 57, Issue 13, July 2002, Pages 2345-2355.

Energy equations

simplification, hw infinite, Tf=Tw after dx

( ) wpwIIadv TCvH ρ=,( ) IpwIadv TCvH ρ=,

( ) IIconvIconvreactwconvw

wp HHHHt

TC ,,, +++=

∂∂

ρ

wf TxT =)(

ww TxT =)(

IfT , wIIf TT =,

IfI TT ,=

( ) ( )IIfIfpwwconv TTCvH ,,, −= ρIT IIT

( )IwIIIconv TThH ,

*

, −= ( )IIIIwIIIIconv TThH −= ,

*

,

Bissett E. J., Chemical Engineering Science Vol. 39, Nos 7/8, pp. 1233-1244 (1984). “1-d model”

Koltsakis G. C., Stamatelos A. M., Ind. Eng. Chem. Res., 1997 Vol. 36 p. 4155-4165. “catalytic 1-d model, modified energy balance”

wIIf TT =,

In Bissett’s 1984 model: Tf,I = Tw

Summary of model equations

( ) ( ) ww

i

iii vdvdz

ρρ∂∂

412 −=

( ) 2

1

2 / iiiii dvv

zz

pµαρ

∂∂

∂∂

−=+

( )11

11

11,

4TT

dh

z

TvC szgp −=

∂∂

ρ

( )2,22

22,

4)( TTd

vChz

TvC swwgpzgp −+=

∂∂

ρρ

Channel scale: gas balancesMass/momentum/energy/species

( ) ( )jjsj

w

jw

w

j yykdf

yvdf

yvz

,1,1,1,12,11

11−+−=

∂∂

−−

( ) ( )jjsj

w

jsw

w

j yykdf

yvdf

yvz

ss

,2,2,2,22,22

11−+=

∂∂

Sz

Tk

y

Tk

x

Tk

t

TC s

zss

yss

xss

sps +∂∂

+∂∂

+∂∂

=∂∂

⋅2

2

,2

2

,2

2

,,ρ

Filter scale: 3-d solid energy balance

radreactwallconv HHHHS +++=

Sz

Tk

y

Tk

x

Tk

t

TC s

zss

yss

xss

sps +∂∂

+∂∂

+∂∂

=∂∂

⋅2

2

,2

2

,2

2

,,ρ

Filter scale: 3-d solid energy balance

radreactwallconv HHHHS +++=

∑=

∂

∂

∂∂

−∂

∂

k

kkj

m

xj

xj

j

w Rcc

f

x

yf

xD

x

yv ,

pwwFkp

pvsRm

dt

mdµρ+′−= ∑ˆ

ˆ

( )pk

xv

dx

dp µ=

Wall/soot scale balancesMomentum/soot/ species

LABORATORY OF APPLIED THERMODYNAMICS

Tutorial

DOC & DPF modeling Filtration and soot deposition

Clean filter filtration modeling

32

45.0−

= PecleanD ηη

25.13 RcleanR ηη =

RDg ηηη +=0,

p

p

p

grain dd

−=

0,

0,

0,

1

2

3

ε

ε

part

grainw

D

duPe

0,=

0,

2

grain

part

d

DR =

Diffusion mechanism

Interception mechanism

Grain diameter Total grain efficiency (without soot)

wupd

: Initial wall porosity

: Wall mean pore size

: Gas wall velocity

: Particle diameter

: Calibration parameter

0,pε

partD

cleann

Loaded wall filtration efficiency

Semi-empirical approaches

Open issuesSoot morphological properties inside the wall

Does the unit-cell approach apply to wall-flow filter structure?

Semi-empirical cake formation modeling

0

20

40

60

80

100

0 1 2 3

Wall filtration Cake filtration

A

Transition

Mechanism 1: Wall saturation Mechanism 2: Impenetrable cake

0%

20%

40%

60%

80%

100%

Cake soot mass/filtration area [kg/m²]

Cake filtr

ation e

ffic

iency [-]

-50%0%50%100%

Wall porosity [-]

Cake filtr

ation e

ffic

iency [-]

0%

20%

40%

60%

80%

100%

Mechanism 1

Mechanism 2

Soot loading [g/l]

Filtr

ation e

ffic

iency [%

]

Prediction of filtration efficiency

Wall structure effect

Low Flow Rate (100 kg/h)

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500

Time [s]

Filtr

ation E

ffic

iency [%

]

0

0.5

1

1.5

2

2.5

3

Soot M

ass [g]

Dots: Measurement

Lines: Simulation

LP: filtration

ΗP: filtration

ΗP: Wall Soot

LP: Wall Soot

LP: Soot

HP: Soot

Prediction of the filtration efficiency

depending on the wall structure

Estimation of soot in the wall

depending on the wall structure

High Flow Rate (300 kg/h)

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500

Time [s]

Filtr

ation E

ffic

iency [%

]

0

1

2

3

4

5

6

Soot M

ass [g]

Dots: Measurement

Lines: Simulation

LP: filtration

ΗP: filtration

ΗP: Wall Soot

LP: Wall Soot

LP: Soot

HP: Soot

Prediction of filtration efficiency

Flow rate effect

Low Flow Rate (100 kg/h)

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 2500

Time [s]

Filtr

ation E

ffic

iency [%

]

0

0.5

1

1.5

2

2.5

3

Soot M

ass [g]

Dots: Measurement

Lines: Simulation

LP: filtration

ΗP: filtration

ΗP: Wall Soot

LP: Wall Soot

LP: Soot

HP: Soot

Prediction of the filtration efficiency

depending on the flow rate

Estimation of soot in the wall

depending on the flow rate

Soot cake properties

Effect of Peclet number on ρ x k

Effect of pressure drop on porosity

Compressible soot cake modeling

single-channel studies

2 g/l

5 g/l

9 g/l

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14 16

Velocity [cm/s]

Mean d

ensity [kg/m

³]

1.5-3.0 g/l

4-6 g/l

7.5-10.5 g/l

2 g/l Calculated

5 g/l Calculated

9 g/l Calculated

Before compression

m=50 kg/h

After compression

m=170 kg/h

Pressure drop “hysteresis”

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Soot Mass [g/l]

Pre

ssu

re D

rop [

mbar]

Initial loading

Depth filtration of soot in the wall contributes strongly to pressure drop.

Pressure drop “hysteresis”

Wall-scale effects

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Soot Mass [g/l]

Pre

ssu

re D

rop [

mbar]

Initial loading

Depth filtration of soot in the wall contributes strongly to pressure drop.

Pressure drop “hysteresis”

Wall-scale effects

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Soot Mass [g/l]

Pre

ssu

re D

rop [

mbar]

Initial loading

Depth filtration of soot in the wall contributes strongly to pressure drop.

Pressure drop “hysteresis”

Wall-scale effects

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Soot Mass [g/l]

Pre

ssu

re D

rop [

mbar]

Initial loading

Partial re

generation

After partial regeneration, oxidation of soot in the wall reduces pressure drop for same

soot mass, compared to initial loading.

Pressure drop “hysteresis”

Wall-scale effects

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Soot Mass [g/l]

Pre

ssu

re D

rop [

mbar]

Initial loading

Partial re

generation

After partial regeneration, oxidation of soot in the wall reduces pressure drop for same

soot mass, compared to initial loading.

Pressure drop “hysteresis”

Wall-scale effects

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Soot Mass [g/l]

Pre

ssure

Dro

p [

mba

r]

Initial loading

Partial re

generation

Reloading

Incoming soot does not re-penetrate the wall. The correlation of pressure drop vs soot

loading is depends on partial regeneration history.

Pressure drop hysteresis effect

Experimental validation

0

5

10

15

20

25

30

35

40

45

50

0 0.5 1 1.5 2 2.5 3 3.5 4

Soot Mass [g/l]

DP

[m

bar]

∆p Initial loading

∆p loading after partial regeneration

dots: measurement

lines: simulation

Following an incomplete regeneration, the cake soot does not allow the incoming soot to-

penetrate the wall. The pressure drop correlation with soot loading changes dramatically.

Uncatalyzed soot oxidation reactions

( )COCOOC 12 2

12 12121 ααα −+

−→+

OO22 NONO22

Fuel additive effects

0.1

1

10

100

1000

1.1 1.2 1.3 1.4 1.5 1.6 1.7

1000/T [1/K]

Reaction R

ate

[m

g/g

s]

Eolys 2% wt.

E=119±13 kJ/mole

No additive

E=152±5 kJ/mole

Eolys 1% wt.

E=121±9 kJ/mole

Eolys 2%wt. Protocol B

E=122±4 kJ/mole

Direct soot catalysis

Indirect soot catalysis

Soot is consumed in NO2-rich regions

NO2 is produced in the catalyzed wall

NO2 diffuses back to the soot layer

Soot density NO2 concentration

( ) ( )jjsj

w

jw

w

j yykdf

yvdf

yvz

,1,1,1,12,11

11−+−=

∂∂

−−

( ) ( )jjsj

w

jsw

w

j yykdf

yvdf

yvz

ss

,2,2,2,22,22

11−+=

∂∂

Convective species transfer in channelsConvective species transfer in channels

( ) ( )jjsj

w

jw

w

j yykdf

yvdf

yvz

,1,1,1,12,11

11−+−=

∂∂

−−

( ) ( )jjsj

w

jsw

w

j yykdf

yvdf

yvz

ss

,2,2,2,22,22

11−+=

∂∂

Convective species transfer in channelsConvective species transfer in channels

∑=

∂

∂

∂∂

−∂

∂

k

kkj

m

xj

xj

j

w Rcc

f

x

yf

xD

x

yv ,

IntraIntra--layer reactionlayer reaction--diffusion couplingdiffusion coupling

∑=

∂

∂

∂∂

−∂

∂

k

kkj

m

xj

xj

j

w Rcc

f

x

yf

xD

x

yv ,

IntraIntra--layer reactionlayer reaction--diffusion couplingdiffusion coupling

Haralampous O. A., Koltsakis G. C.: Industrial & Engineering Chemistry Research, Vol.43, Issue 4, p. 875-883, 2004.

O2 transfer from channel gas to soot surface

O2

O2 consumption

O2 gradientO2

O2 consumption

O2 gradient

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 20 40 60 80 100 120 140 160

Length [mm ]

Co

nc

en

tra

tio

n [

-]

0

0.05

0.1

0.15

0.2

0.25

O2 in outlet channel

O2 in inlet channel

Soot layer thickness

Wall flow

Due to concentration gradient, O2 is transferred from the axial flow to the soot layer and

increases local availability and reaction ratesHaralampous O. A., Koltsakis G. C.: AIChE Journal, Vol. 50, No. 9, p. 2008, 2004

Importance of O2 transfer for the prediction of filter temperature

Ignoring O2 mass-transfer effects (diffusive-convective) leads to serious under-prediction

of peak temperatures

800

900

1000

1100

1200

1300

1400

4 6 8 10 12 14 16

Soot loading [g/l]

Maxim

um

tem

pera

ture

[°C

]Measured

Computed with diffusion

Computed without diffusion

Test conditions: Gas burner, cordierite filter, Tin=600°C

800

900

1000

1100

1200

1300

1400

4 6 8 10 12 14 16

Soot loading [g/l]

Maxim

um

tem

pera

ture

[°C

]Measured

Computed with diffusion

Computed without diffusion

Test conditions: Gas burner, cordierite filter, Tin=600°C

Importance of O2 transfer for the prediction of filter temperature

Ignoring O2 mass-transfer effects (diffusive-convective) leads to serious under-prediction

of peak temperatures

800

900

1000

1100

1200

1300

1400

4 6 8 10 12 14 16

Soot loading [g/l]

Maxim

um

tem

pera

ture

[°C

]Measured

Computed with diffusion

Computed without diffusion

Test conditions: Gas burner, cordierite filter, Tin=600°C

800

900

1000

1100

1200

1300

1400

4 6 8 10 12 14 16

Soot loading [g/l]

Maxim

um

tem

pera

ture

[°C

]Measured

Computed with diffusion

Computed without diffusion

Test conditions: Gas burner, cordierite filter, Tin=600°C

Importance of O2 transfer for the prediction of filter temperature

800

900

1000

1100

1200

1300

1400

4 6 8 10 12 14 16

Soot loading [g/l]

Maxim

um

tem

pera

ture

[°C

]Measured

Computed with diffusion

Computed without diffusion

Test conditions: Gas burner, cordierite filter, Tin=600°C

Ignoring O2 mass-transfer effects (diffusive-convective) leads to serious under-prediction

of peak temperatures

Catalyzed DPF simulation

Catalyst zoning (Precious Metal saving concept)

� Uncoated DPF

� “Axial” zoning

� More PGM in front part

� Better cold-start performance

� “Intra-wall” zoning

� More catalyst close to soot layer

� Better passive regeneration

performance

Transport/reaction coupling necessary to account

for catalyst zoning

Uncatalyzed wall

Catalyzed with high PGM

Catalyzed with low PGM

Soot layer

Computed concentration profiles in catalyzed filters @ T=150°C

65

70

75

80

85

90

95

100

105

0 20 40 60 80 100 120 140 160

Filter Length [mm]

CO

[ppm

]

F-DPF in F-DPF out R-DPF in R-DPF out Z-DPF in Z-DPF out

COCO gradient

CO

zoned

high-PGM

low-PGM

high-PGM

low-PGM

zoned

Koltsakis, G. C., Dardiotis, C. K., Samaras, Z. C., Frey, M., Wenninger, G., Krutzsch, B., Haralampous, O. A., SAE 2008-01-0445, 2008

LABORATORY OF APPLIED THERMODYNAMICS

3-d effects

3-d DPF regeneration simulationSources of “3-dimensionality”

t=50 s t=60 s t=70 s t=80 s t=90 s

Soo

tT

empe

ratu

reF

low

“3-d effects”

Heat losses, segmentation, asymmetric inlet temperature/flow, oval DPF geometry

Flow, soot and temperature distribution effects due to inlet cone shape

Temperature (°C)

Soot loading (g/l)

Flow distribution (kg/sm2)

t=48 s

t=100 s

t=140 s

t=180 s

t=500 s

Koltsakis, G. C., Samaras, Z. C., Echtle H., Chatterjee D.,Markou P., Haralampous O., SAE paper 2009-01-1280, 2009

Model validation – centerline channel

Initial soot loading: 8 g/l

300

400

500

600

700

800

900

1000

0 50 100 150 200

Time [s]

Tem

pera

ture

[°C

]

1Inlet

2

3

1

23

11

2233

Post-Injection Idle Post-Injection

Dots: Measurement, Lines: Model

Koltsakis G.C, Haralampous O. A, Margaritis N., Samaras Z. C., Vogt C.D., Ohara E., Watanabe Y., Mizutani T.:, SAE Transactions,, 2005

Stress analysis

Temperature σZσX

NastranTMaxitrapTM

Deformation

Complete system simulation: Soot limit investigation

Koltsakis et al., FAD Conference-2007 (LAT-IAV GmbH-Exothermia)

62

3-d system temperature simulation

“Worst-case” DPF regeneration case

0

100

200

300

400

500

600

700

800

900

1000

0 50 100 150 200 250 300

Time [s]

Te

mp

era

ture

[C

]

DOC-out

CDPF-max

CDPF-out

SCR-max

SCR-out

Initial soot loading: 6 g/l

Full-load Idle

Test data for model input from IAV engine bench (SAE 2007-01-1127)

DOC CDPF SCR

t=10s

t=70s

t=130s

t=190s

t=250s

Koltsakis et al., FAD Conference-2007 (LAT-IAV GmbH-Exothermia)

LABORATORY OF APPLIED THERMODYNAMICS

Grigorios Koltsakis Thank you for your attention!