Determination of Material Parameters of Gas Diffusion Layers by Combining Pore-Morphology Method and Single Phase Simulations

(1)

Determination of Material Parameters of Gas Diffusion

Layers by Combining Pore-Morphology Method and

Single Phase Simulations

PEMSim Berlin, 18.-20.09.2006

Jürgen Becker, Oleg Iliev, Volker Schulz, Konrad Steiner,

Andreas Wiegmann

(2)

Introduction

Starting Point:

• three dimensional model of GDL fibre/pore structure given • origin of 3d model:

– reconstructed from a 3d tomography image – virtually created model

Aim

:

• determine saturation dependent effective material parameters: – capillary pressure pc(s) – permeability K(s) – diffusivity coefficients D(s) – thermal conductivities β(s)

Idea

:

• use pore morphology method to determine phase distributions • use single phase simulations to determine material parameters

(3)

Seite 3

Pore Morphology Method

ingredient 1:

– Young – Laplace equation

idea: a pore is filled with the NWP, if

non-wetting fluid

wetting fluid

r

(4)

Pore Morphology Method

ingredient 2:

– image analysis to determine pore sizes

: pore space

: structuring element (e.g. spheres of radius r) morphological opening:

phase distribution: non-wetting phase , wetting phase

(5)

Seite 5

Pore Morphology Method (Algorithm)

algorithm :

1. start configuration 2. erode pore space

3. eroded pore space has to be connected with non-wetting phase reservoir

4. dilate remaining pore space 5. final result

(6)

Wetting phase reservoir

Non-wetting phase reservoir

C

lo

se

d

Bubble point!

Pore Morphology Method (Drainage)

• starting point: pore space completely filled with wetting fluid

• determine pore space occupied by non-wetting fluid for increasing pressure (decreasing pore radius)

(7)

Seite 7

Pore Morphology Method (3D)

Assumptions:

• interface between wetting phase and non-wetting phase is assumed to be spherical (or a superposition of spheres)

• no residual wetting phase

• contact angles other than 0 are

reflected only by the “factor“ cos β in the Young-Laplace equation

porous media “imbibition” “drainage (top)” “drainage”: only pores connected to the NWP

reservoir are filled with the NWP

“imbibition” (or repeated drainage+imbibition) : all pores large enough are filled with the NWP

(8)

Using the Pore Morphology Method to Determine Saturation

Dependent Material Parameters

general approach:

first step:

– use pore morphology method to determine phase distributions for varying capillary pressures

for each cap. pressure:

– phase distribution is assumed to be stationary

– solve single-phase microscopic equations in the corresponding phase space – determine macroscopic material parameters via upscaling

(9)

Seite 9

Using the Pore Morphology Method to Determine Saturation

Dependent Material Parameters

capillary pressure curve pc(s) :

first step:

(10)

Using the Pore Morphology Method to Determine Saturation

Dependent Material Parameters

permeability (wetting phase):

first step:

– solve Stokes equation in the space occupied by the WP

(11)

Seite 11

Using the Pore Morphology Method to Determine Saturation

Dependent Material Parameters

permeability (non-wetting phase):

first step:

– solve Stokes equation in the space occupied by the NWP

(12)

Using the Pore Morphology Method to Determine Saturation

Dependent Material Parameters

diffusivity:

first step:

– solve Laplace equation in the space occupied by the WP. – determine macroscopic diffusivity coefficients D(s) via upscaling

(13)

Seite 13

Using the Pore Morphology Method to Determine Saturation

Dependent Material Parameters

thermal conductivities:

first step:

– solve heat transport equation in the complete space, with discontinuous coefficient (differs for gas, water and fibres).

(14)

Example: 3D tomography image of a Gas Diffusion Layer

•

material:

– carbon fibres of diameter ~ 7 µm – hydrophobic PTFE coating

– porosity 78%

– layer thickness ~ 200 µm • 3D data

– synchrotron tomography by ANKA GmbH (Karlsruhe)

– picture shows area of size 717x717 µm – resolution: 0.7 µm/voxel

(15)

Seite 15

GDL: Capillary Pressure – Saturation

used parameter:

• contact angle: 140°

results:

•bubble point (drainage): 8.8 kPa •saturation at bubble point: 20.8%

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 saturation (NWP) c a p . p re s s u re [ P a ] Drainage(z+) Imbibition

(16)

GDL: Thermal Conductivity (Results)

parameters used: – water :0.606 W/Km – air: 0.0262 W/Km – fibres: 17 W/Km 0 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 Saturation (NWP) C o n d u c ti v it y [ W / m K ] beta_11 beta_22 beta_33

• averaged results over 3 cut-outs with 256 x 256 x 300 voxels

(17)

Seite 19

A Reduced Model for Compression

(18)

GDL: Water Distribution (uncompressed and 40% compressed)

pc= 10.6 kPa (r=10.5 µm)

(19)

Seite 21

Capillary Pressure Curve

1.00 10.00 100.00 0 0.2 0.4 0.6 0.8 1 Sa turation (nw ) C a p . P re s s u re [ k P a ] uncompressed 20% compr. 40% compr. • Imbibition • 1024x1024x300

(20)

Permeability

0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1

Saturation (non-w etting phase)

P e rm e a b il it y [ d a rc y ] uncompresed 20% compr. 40% compr. 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1

Saturation (non-w etting phase)

P e rm e a b il it y [ d a rc y ] uncompressed 20% compr. 40% compr. •through-plane • 512x512x300 • imbibition

(21)

Seite 23

Diffusivity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.2 0.4 0.6 0.8 1 Satura tion (w a te r) D if fu s iv it y ( % ) uncompressed 20% compr. 40% compr. •through-plane • 512x512x300 • imbibition

(22)

Summary

• starting point:

– synchrotron tomography image – virtually generated fibre structure

• calculated effective material parameters: – pore size distribution

– bubble point

– capillary pressure – saturation relation – (relative) gas diffusivity tensor

– (relative) permeability (wetting and non-wetting phase) – (relative) thermal conductivities