Multiphysics Modeling for Exhaust Gas Treatment

Henrik von Schenck, COMSOL AB, Sweden

© COPYRIGHT 2008, COMSOL, Inc

Contents

• What is Multiphysics?• Capabilities and opportunities of COMSOL Multiphysics• Multiphysics modeling for exhaust gas treatment

– Case 1: Selective catalytic reduction of NO– Case 2: Abatement of VOC in a packed bed– Case 2: Abatement of VOC in a packed bed– Case 3: Diesel particulate filter (DPF)

• Concluding Remarks

COMSOL

• Started in 1986 with agency products, markets only own products now.• Released COMSOL Multiphysics in1998.• 180 employees worldwide.• 16 offices, 12 in Europe, 3 in the US and 1 in India.• Distributors worldwide.

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What is Multiphysics?

• Reliable simulation requires accurate mathematical modelsElectromagnetics:

Maxwell’s equations

Structural Mechanics:Newton’s laws of motion

Thermal Analysis:Heat transfer equation

Fluid Flow:Navier-Stokes’ equations

• “Single physics” approach is limited since no phenomenon is isolated

• Today’s engineering challenges demand that multiphysics be addressed

Newton’s laws of motion Navier-Stokes’ equations

The Multiphysics Approach

Mass, Energy and Momentum Transport

Mass, Energy and Momentum Transport

Select from

Mass, Energy and Momentum Transport

Select from predefined modeling interfaces

Select from

Create your multiphysics model

Mass, Energy and Momentum Transport

Select from predefined modeling interfaces

model

Predefined Modeling Interfaces – Fluid Flow

• Example - Navier-Stokes equations for fluid flow

( ) ( )( )[ ] FuuIuuu +∇+∇+−⋅∇=∇⋅+

∂∂ Tpt

ηρρ

( )∂ρ ( ) 0=⋅∇+∂∂

uρρt

Predefined Modeling Interfaces – Fluid Flow

• Couplings– Transport properties (ρ, η) dependent

upon• Temperature• Fluid composition

– Flow field affects– Flow field affects• Convective mass and energy

transport• Turbulent mixing

Predefined Modeling Interfaces – Mass Transport

• Example - Convection, diffusion and reaction

( ) iiiii cRcDt

c ∇⋅−=∇−⋅∇+∂∂

ut∂

Predefined Modeling Interfaces – Mass Transport

• Couplings– Affected by

• Convective transport (u)• Temperature (reaction rates, Di)

– Affects• Local mixture composition• Chemical reactions generate or

consume energy

Predefined Modeling Interfaces – Heat Transfer

• Example – Energy transport by convection and conduction

( ) TCQTkt

TC pp ∇⋅−=∇−⋅∇+

∂∂

uρρt∂

Predefined Modeling Interfaces – Heat Transfer

• Couplings– Affected by

• Convective transport (u)• Chemical composition• Exothermic/endothermic reactions

– Temperature affects– Temperature affects• Reaction rate• Transport properties

Coupled Transport Processes

Flow

HeatMass

Convectivetransport

Chemical reactions

Exothermic reactions

Reaction rates

Gas expansion

Equation Based Modeling

• Enter any PDE in general or coefficient form

FΓ =⋅∇+∂∂+

∂∂

tt

φφ2

2

NO Reduction in a Catalytic Converter

• Competing reactions– NO reduction by NH3

– NH3 oxidation

• Eley-Rideal kinetics3

3

111NH

NHNO ac

acckr

+=

322 NHckr = )//(22

2 TRgEeAk −=

)//(11

1 TRgEeAk −=

• Honeycomb monolith with V2O5/TiO2 catalyst

• A single monolith channel• Circular cross-section

approximation

NO Reduction in a Catalytic Converter

approximation

catalytic wash-coat

channel inlet

0.36 m

Model Equations

• Fluid flow– Coupled free and porous media

flow– Navier-Stokes equations– Brinkman equations

Free flow

Porous media flow

Model Equations

• Mass transport– N2, NO, NH3, O2, and H2O

transport through convection and diffusion in the open channel

– Diffusion and chemical reaction in the catalytic wash-coat

Non-reactive transport

the catalytic wash-coat

• Energy transport– Convection and conduction in the

open channel– Conduction and heat source due to

reaction in the porous structure

Chemical reaction

Modeling in COMSOL Multiphysics

VOC Abatement in a Packed Bed Reactor

• Parallel reactions– Hydrocarbon conversion– CO oxidation

OHCOOHC 22263 6692 +→+

22 22 COOCO →+

• Kinetic expressions2

11 )1(

6363

2

HCHCcoco

COCO

cKcK

cckr

++=

2

22 )1(

6363

263

HCHCcoco

COHC

cKcK

cckr

++=

• Reactor Equations– Mass balance on the macro-scale;

convection, diffusion and reaction

Model Equations

( ) iiii cRcD ∇⋅−=∇−⋅∇ u

reactor pore scale ~mm

– Ri depends on the transport in the pellets, i.e. the flux into at the pellet surface times surface area per unit volume

– A pellet mass balance is required to calculate the flux

Model Equations

• Pellet Equations– Mass balance on the micro-scale;

diffusion and reaction

( ) iii RcD ′=′∇′−⋅∇

rp

pellet pore scale ~µm

– Boundary conditions

– The concentration distribution in the pellet gives the flux at all r => the reaction term for the catalyst bed is given by the solution of the micro-scale mass balance

0=⋅′∇′− nii cD 0=r

ii cc ε=′prr =

Model Equations

• 2 geometries– Reactor– Pellet

• Coupling variables connect the mass transport equations on mass transport equations on each geometry

– Reactor bulk concentrations are coupled to pellet surface concentrations.

– Pellet species surface flux is coupled to reactor mass source term

ii cc ε=′ nN ⋅== )( pipi rrAR

• Reactor mass transport– C3H6, CO, CO2, H2O, and O2

– Convection, diffusion and reaction

Modeling in COMSOL Multiphysics

( ) cRcD ∇⋅−=∇−⋅∇ u( ) iiii cRcD ∇⋅−=∇−⋅∇ u

Modeling in COMSOL Multiphysics

• Coupling variables– Couple dependent

variables on different geometries

– Pellet =>reactor

nN ⋅== )( pipi rrAR

Modeling in COMSOL Multiphysics

• Pellet mass transport– C3H6, CO, CO2, H2O, and O2

– Diffusion and reaction

( ) iii RcD ′=′∇′−⋅∇ ( ) iii RcD ′=′∇′−⋅∇

Modeling in COMSOL Multiphysics

• Coupling variables– Couple dependent

variables on different geometries

– Pellet =>reactor

– Reactor=>pellet

nN ⋅== )( pipi rrAR

ii cc ε=′

Results – Reactor Species Distribution

Results – Pellet Species Distribution

Results

xr

Capture and Combustion of Soot in a DPF

5.86x4.66x8 inches

Model Equations

• Fluid flow– 1000’s of channels– Assume fully developed laminar

flow in the channels– Average flow field if proportional

u1

u2w

Hp1

p2

H/2 ∆xvm

to the pressure difference– Overall mass balance gives the

velocity in the channels– The channels are connected by

mass transfer across the porous membrane

( ) mvH

pkt 1111 4 ρρρ −=∇−⋅∇+

∂∂

( ) mvH

pkt 1222 4 ρρρ =∇−⋅∇+

∂∂

( )21 ppvm

m −=ηδ

κ

Model Equations

• Soot balance– Soot enters channel 1– Deposition at the membrane

results in a sink term

u1

u2w

Hp1

p2

H/2 ∆xvm

( ) smsss cv

HccD

t

c 41 −=+∇−⋅∇+

∂∂

u

Model Equations

• Species mass balances– O2, CO, and CO2

– O2 sink terms– Soot oxidation– Transfer across membrane

u1

u2w

Hp1

p2

H/2 ∆xvm

– Transfer across membrane

( ) sOmOOoO R

Hcv

HccD

t

c 441,211,21,22

1,2 −−=+∇−⋅∇+∂

∂u

( ) 2,222,22,222,2 4

OmOOOO cv

HccD

t

c=+∇−⋅∇+

∂∂

u

Model Equations

• Soot layer thickness, δs

– Decreases through oxidation– Increases by deposition of soot

particles in the exhaust gas– Affects vm

u1

u2w

Hp1

p2

H/2 ∆xvm

ms

ss

s

ss vc

RM

t ρρδ +−=∂

∂

Model Equations

• Energy balances– Channels– Filter walls; this temperature field

is connected for the entire system such that heat flow between channels

u1

u2w

Hp1

p2

H/2 ∆xvm

channels

( ) ( )11111111111

11

444TTh

HQ

HTvC

HTCTk

t

TC msmppp −++−=+∇−⋅∇+

∂∂ ρρρ u

( ) ( )22222222222

22

44TTh

HTvC

HTCTk

t

TC mmppp −+=+∇−⋅∇+

∂∂ ρρρ u

( ) ( ) ( )2111122 2 TTTh

TCTCv

Tkt

TC m

mpmp

m

mmm

mpmm −−+−−=∇−⋅∇+

∂∂

δρρ

δρ

Predefined Modeling Interfaces

• 9 coupled partial differential equations

• Use predefined modeling interfaces

– Pressure driven flow; Darcy’s – Pressure driven flow; Darcy’s Law interface

– Mass transport; Convection and Diffusion interface

– Energy transport; Convection and Conduction interface

The General Form PDE

• The general form PDE

• The equation for the soot

FΓ =⋅∇+∂∂+

∂∂

tt

φφ2

2

• The equation for the soot layer thickness

ms

ss

s

ss vc

RM

t ρρδ +−=∂

∂

Equation System View

• All predefined equations are viewable and editable

– Modify anisotropic transport properties; permeability and thermal conductivities

• PDEs displayed on a general form

FΓ =⋅∇+∂∂+

∂∂

tt

φφ2

2

Results – Flow Field

Results – Temperature Distribution

Results – Oxygen Concentration

Results – Soot layer in a central channel

Results – Soot layer in a peripheral channel

Concluding Remarks

• COMSOL offers a simulation environment for unlimited Multiphysics couplings

• The Chemical Engineering Module provides many of the Module provides many of the equations describing fluid flow, mass, and energy transport in predefined modeling interfaces

• You can also type in your own equations directly into the graphical user intefarce

• Model library– NO reduction, VOC abatement,

DPF– Model set up and solved + Model

doc

Resources and Contact

– COMSOL Multiphysics + Chemical Engineering Module ~100 models

• Introduction to Chemical Engineering Simulations CD

• COMSOL Conference CD 2008• Contact, software trial, training and

support

Resources and Contact

support– www.comsol.com– support@comsol.com

Thank you for your attention!