Marie Curie Workshop 2007

Transkript

1 Marie Curie Workshop 2007 Flow and transport in technical porous media: Modelling the water management in Polymer Electrolyt Membrane Fuel Cells ( PEMFCs ) Steffen Ochs, Rainer Helmig, Holger Class In cooperation with Stefan Dwenger, Ulrich Nieken and Majid Hassanizadeh

2 Motivation Soil Deformation CO 2 Storage Fuel Cells Materials: Concrete, Wood,... Deformable Soils Intervertebrate Disks, Brain, Liver,... Sand, Rock Plants, Top Soil,... Membranes, Filters, Paper,... Non-linear coupled flow and transport processes in heterogeneous porous media

3 Definition: Fuel Cell Definition (1894) (Wilhelm Ostwald): A fuel cell is an electrochemical device which continuously converts the chemical energy of a fuel and an oxidant in electrical energy... fuel cell is a factory that takes fuel as input and produces electricity as output Applications (2007): Mobile Portable Stationary

4 Functionality of Fuel Cells + - H 2 H2 4 H + 4 e 2 O + 4 H + 4e H O 2 2 O 2 H 2 H + HO 2 Anode Membrane Cathode

5 Motivation Fuel cells are considered as alternative power supplies in many applications. Polymer Electrolyte membrane fuel cells (PEMFC) are intensively investigated for mobile use. - small installation size ( C ) - low operating temperature ( W/kg - high power-density (~ high degree of efficiency -no C0 2 emission in operation

6 Subsurface Technical Porous Media Know-How: sophisticated??? Dimensions: m m Measurements: local integral

7 International Research Training Group NUPUS Fundamentals / theory: - upscaling - stochastic methods Utrecht Delft Eindhoven Numerical methods: - efficiency - robustness Stuttgart Conceptual models for selected applications: -CO 2 sequestration -swelling of clay -fuel cell

8 Fuel Cell Research in NUPUS Project C1: Transport interactions in thin hydrophobic porous media - Experiment with mixed wettable porous media - Determination of constitutive relations for DL => Nieken, Eigenberger, Dwenger Project C2: Simulation of multiphase / multicomponent processes PEMFCs ( DL ) - Model concept for porous gas diffusion layer - Coupling strategies DL-gas distributor - Implementation of constitutive relations for mixed wettable DL (p c (S), k r (S)). => Ochs, Class, Helmig In cooperation with Majid Hassanizadeh

9 electric current Assembly of PEMFC Stack endplate with integrated flow field / gas distributor anode diffusion layer membrane cathode diffusion layer bipolar plate MEA cell hydrogen (H 2 ) oxygen (O 2 ) / air

10 Assembly of PEMFC Stack electric current cross-section endplate with integrated flow field / gas distributor anode diffusion layer membrane cathode diffusion layer bipolar plate MEA cell oxygen (O 2 ) / air hydrogen (H 2 )

11 Cross-section of PEM Fuel Cell Anode PEM Cathode GD DL R R DL GD GD: Gas Distributor; DL: Diffusion Layer; R: Reaction Layer; PEM: Membrane

12 Parts of PEMFC Proton Exchange Membrane Functionality: Anode PEM Cathode - Proton transport GD DL R R DL GD - Gas separation Material: - Membrane with ionic groups ( Ionomer ) ( DuPont ) - e.g. Nafion Dimension: μm

13 Parts of PEMFC Reaction Layer Functionality: GD Anode DL R PEM R DL Cathode GD - Electrochemical reactions Material: ( Pt ) - Catalyst - Ionomer Dimension: ~10 μm

14 Parts of PEMFC ( Backing ) Diffusion Layer Functionality: Anode PEM Cathode - Gas transport GD DL R R DL GD - Water discharge - mech. protection Material: fleece - Carbon cloth / - hydrophobic Dimension: μm

15 Parts of PEMFC Gas Distributor Functionality: Anode PEM Cathode - Gas transport GD DL R R DL GD - Water discharge - electrical contact Material: plate - Metal / graphite with flow field Dimension: cm channel mm plate

16 Role of Water in Fuel Cells Water formed at the cathode constrains the oxygen transport in the DL (D g >>D w ). Oxygen supply of the cathode RL is a limiting factor for the performance of PEMFC. Water flooding of PEMFC stacks frequently observed. Water is required for proton transport. Nam & Kaviany, 2003 Efficient water management necessary!

17 Schematic Water Distribution in FC + - H 2 H2 4 H + 4 e O + 4 H + 4e 2 H O 2 2 O 2 H 2 H + HO 2 Anode Membrane Cathode

18 Schematic Water Distribution at Cathode + - O + 4 H + 4e 2 H O 2 2 O 2 HO 2 ne Cathode water is produced in the reaction layer

19 Numerical Investigations Objective: efficient water management necessary! Benefits: - develop process understanding - identification of relevant processes and parameter - optimization of the gas / water budget in fuel cell maximize power output

20 Dimensions and Scales typical length scale typical pore radius Kaviany, Eurotherm 2007

21 Validity Concept of REV? modified, after Bear 1972

22 Scale Definitions

23 Scales and Processes

24 Model Concept Two phases: liquid, gaseous ( 2002 (Class, Helmig Three components: water, nitrogen, oxygen

25 Darcy / Multiphase Darcy Darcy Law: H.P.G. Darcy (1856) found an empirical relation for describing single phase flow in sand columns. Multiphase Darcy: E. Buckingham (1907) extended Darcy's Law to multiphase flow in porous media.

26 Macro Scale Mass Balance

27 Macro Scale Energy Balance

28 Closur Relations Simplifying Assumptions: Local thermodynamic equilibrium Equations of State: ( Antoine ) Saturation vapor pressure Constitutive Relations:

29 Properties of Fluids / Porous Medium Fluid Properties: density, viscosity Porous Medium Properties: porosity permeability thermal conductivity availability constitutive relations

30 Constitutive Relations p c (S) relation: - hydrophobic DL - hysteresis? - mixed wettable porous media?? - change in wettability of porous media???

31 Electrochemical Processes Cell Voltage: ( Wieser:2001 (after

32 Electrochemical Processes Local current density:

33 Electrochemical Processes Local current density:

34 Electrochemical Processes Oxygen consumptions: Water production: Osmotic drag from membrane: Energy production:

35 Simulation Plattform MUFTE_UG

36 Implementaion Issues Box method: Variable substitution: Newton method:

37 Coupled, nonlinear PDE ( Newton-Raphson ) linearization Solution Methods Solution of linearized equations different options available in MUFTE_UG e.g., direct solvers, BICGStab, ILU, Multigrid Applying the multigrid method for varying phase states ( 2002 Bastian, (Class, Helmig, Prolongation: Coarse grid corrections linear approximation Phase states

38 Application of the Multigrid Method Coarse Grid: 400 elements NAPL saturation and temperature after 3 hours: NAPL-contaminated domain Steam-air injection Change of phase state NWG WG

39 Application of the Multigrid Method Different solution methods for the linearized problem: 1. Nested iteration, muligrid cycle (V) as preconditioner, BICGStab on finest grid, direct solver on the coarse grid desired optimum: convergence rate ( h independent of grid size 2. Same as Case 1, but nested iteration only for computation of first time step 3. Same as Case 2, but ILU as preconditioner (expected convergence rate: 1- O(h)) ( 2002 Bastian, (Class, Helmig, 1600, 6400, elements = 1, 2, 3 refinement levels

40 Case Study: Flow Fields Objectives: - Research the influence of different flow fields for the gas distributor on the system behavior. - Improve the understanding of relevant processes and parameters in the DL of PEMFC with a focus on the water management in the cathode DL of PEMFC. - Test the model under realistic conditions.

41 Researched Domain of FC

42 ( FFs ) Researched Flow Fields Conventional oxygen transport mainly diffusive Interdigitated oxygen transport advective, diffusive

43 Boundary Conditions: Conventional FF Neumann = 0 ( w,o,n,h ) Dirichlet S wr, p in,t in, X o in components: w: water o: oxygen n: nitrogen h: energy Neumann = 0 electochemical reactions Neumann = 0 Neumann = 0 ( w,o,n,h ) Dirichlet S wr, p in,t in, X o in

44 Results: Conventional Flow Field

45 Results: Conventional Flow Field

46 Boundary Conditions: Interdigitated FF Neumann = 0 Dirichlet (w, h) S wr,t in ( n Neumann (o, components: w: water o: oxygen n: nitrogen h: energy Neumann = 0 electochemical reactions Neumann = 0 Neumann = 0 ( w,o,n,h ) Dirichlet S wr, p out,t in, X o out

47 Results: Interdigitated Flow Field

48 Results: Interdigitated Flow Field

49 Conventional vs. Interdigitated Flow Field

50 Conventional vs. Interdigitated Flow Field

51 Résumé Case Study Flow Field Macroscopic multiphase / multicomponent model for DL of a PEMFC successfully tested. Basic system behavior could be reproduced for conventional and interdigitated Flow Field. Interdigitated GD leads to a better oxygen supply of the reaction layer and thus an improved performance. The study showed that the results depend strongly on the p c (S) / kr(s)-relation and the boundary conditions.

52 Outlook - Derive constitutive equations for hydrophobic / hydrophilic-hydrophobic porous media in cooperation with ICVT at. - Benchmark the model by modeling well defined experiments. - Coupling of porous media with channel flow for proper description of DL-GD interface

53 Coupling: Diffusion Layer- Gas Channel 3D multiphase / multicomponent model for DL - multiphase extension of Darcy s Law - component balance / energy balance -LEA - constitutive equations adequate coupling conditions: - mechanism of water discharge - impact cross-section DL-GD - gaseous / liquid state? - continuity of pg channel / pipe-flow model for GD - 1D Darcy Weisbach (laminar / turbulent) for gas phase. ( liquid - water transport (gaseous /

54 Thank you for your attention! Rainer Helmig, Steffen Oliver Ochs,