Modeling as a tool for understanding the MEA. Henrik Ekström Utö Summer School, June 22 nd 2010

Transcription

1 Modeling as a tool for understanding the MEA Henrik Ekström Utö Summer School, June 22 nd 2010

2 COMSOL Multiphysics and Electrochemistry Modeling The software is based on the finite element method A number of pre-defined interfaces, shipped within various modules, are available for solving a large number of common differential equations (Navier-Stokes, Laplace, Poissons,...) The user is also free to set up his own partial differential equations Various interfaces may be coupled together to enable multiphysics modeling, this approach is very suitable for electrochemical engineering modeling

3 Electrochemistry Modules A Batteries and Fuel Cells module is released this summer, with focus on PEMFCs SOFCs Li-Ion batteries NiMH and NiCd batteries Concentration distribution in a PEMFC. Model and picture courtesy: Center for Fuel Cell Technology (ZBT), Duisberg, Germany Heat analysis of a small PEM fuel cell for consumer electronics More electrochemistry modules are planned in the future Corrosion Electrolysis...

4 Today s lecture Some fundamental physics and equations to build a simple PEM MEA-model Charge conservation and porous electrodes Electrode kinetics Species transport, Stefan-Maxwell diffusion Momentum transport in porous media, Darcy s law Limitations of this model Simulations A base-case simulation Are gas pores really necessary? Is adding more catalyst always a good idea? An optimized MEA vs. the base case

5 Geometry (1D) Hydrogen oxidation Oxygen reduction Ground Cell potential Porous electrode (Anode) Membrane Porous electrode (Cathode)

6 Currents and Ohm s law In the porous electrode the carbon particle matrix acts as an ordinary electronic conductor and Ohm s law can be used for the electrode phase In the solid polymer electrolyte all charge is transported by protons (i.e. the transport number is unit), hence Ohm s law can also be used J J s l = σ φ = σ φ l s l s J, current density σ, conductivity φ, potential s, electrode phase l, electrolyte phase Note: The conductivity is at least one order of magnitude larger in the electrode than in the electrolyte

7 Charge conservation in the membrane and the porous electrodes In the membrane, the current only flows in the electrolyte phase, charge is conserved... J s = 0 ( ( J ) = l 0 In the porous electrodes, current will be transferred from one phase to the other due to the electrochemical reactions... ( J ( J s l ) = i ) = i v v i v, volumetric current density

8 Electrode kinetics The local current densities on the catalyst particles are modeled by Butler-Volmer kinetics: α afη /( RT ) iv = avi0( e e a, active surface area i 0 v α Fη /( RT ), exchange current density α and α, transfer coefficients ( a c c ) 0.5) The magnitude and direction of the overpotential will govern the magnitude and direction of the current... η = φ φ E s l 0 η, overpotential E 0, equillbrium potential of the electrode reaction

9 Electrode specific kinetics The exchange current density is concentration dependent i i H , anode = i0, H 2ref ( ) ch 2, ref 0, cathode = i 0, O2ref c c c O2 O2, ref Note that the hydrogen oxidation reaction is several orders of magnitude faster than the oxygen reduction reaction i 0, H 2ref i 0, O2ref 1000

10 Species transport The concentration dependence on the electrode kinetics introduces the need for a description of the species transport in the electrodes For mixtures where the reacting/produced species has low concentrations (<10%) with respect to the bulk, Ficks s law may be used... N = D c N, species flux D, Fick's diffusion coefficient...but this is seldom the case for gas diffusion electrodes Instead Stefan-Maxwell diffusion is used here

11 Stefan-Maxwell Diffusion Accounts for interactions between all species Binary diffusion coefficient, accounting for each species-species diffusion are used (i.e. at least two species are needed) The local species fluxes will depend on fluid velocity, pressure, temperature, density......where the source term is calculated by Faraday s law Species in this model: ν iiv Ri = M i nf R, volume mass source/sink of the species i i ν, stoichiometric coefficient in the electrode reaction i Anode: water and hydrogen Cathode: water, nitrogen and oxygen.

12 Momentum transfer A momentum transfer model for the velocity field and pressure is always needed when modeling Stefan-Maxwell transport For porous electrodes Darcy s law is usually suitable for 1D. The velocity is assumed to be directly related to the pressure gradient according to κ v = p u κ, permeability u, dynamic viscosity For more complex modeling in 2D and 3D, when coupling to flow in GDLs and channels, Brinkman's equations can be a better choice

13 Porous electrode reactions and momentum transfer Due to the electrochemical reactions, mass will typically not be conserved within the gas phase. With R tot being the total mass sink/source due to the electrochemical reactions we get... ( ρ v ) = R tot

14 Additional considerations Water drag we assume every proton to be accompanied by a fixed number of water molecules in the electrolyte (here 1), i.e. every proton created will drag a water molecule from the gas phase at the anode, and deliver one water molecule at the cathode Bruggeman correction to the transport parameters (Diffusion coefficients, Conductivities) in the porous electrodes σ eff i, j, eff = ε 3/ 2 D = ε σ 3/ 2 D i, j ε, porosity

15 END OF EQUATIONS!

16 Boundary conditions Anode No electrode current Continuity in electrolyte potential No gas phase mass flow No gas phase species flux Electrode ground Inlet mass fractions Given cell potential Atmospheric Inlet mass fractions pressure Atmospheric pressure Membrane Cathode 1 D model three domains, four boundaries

17 Limitations of this model Transport No liquid water, only vapor phase Water transport through membrane limited to water drag, should also include diffusion No cross diffusion of hydrogen and oxygen through membrane No side reactions such as peroxide formation, carbon oxidation and platinum oxidation/dissolution Membrane conductivity depends on local humidity

18 Limitations Electrode kinetics An agglomerate model including inter-particle diffusion within the porous electrodes may better describe the mass-transfer coupled kinetics If cross diffusion through membrane is added, accompanying electrode reactions on each side also needed Due to the surface coverage of platinum oxides, oxygen reduction cannot be described by a simple Butler-Volmer equation

19 Base case simulation Standard set of parameters with orders of magnitude from literature (tweaked a little to get reasonable MEA performance for this lecture) Parameters that we will try to optimize: Parameter Value Description L_cathode 10 um Cathode thickness eps_l_cathode 0.4 Electrolyte volume fraction, cathode

20

21

22

23

24

25 Base case results

26 Base case electrolyte potential

27 Base case anode electric potential The potential drop in the electrode is one order of magnitude lower than in the electrolyte...

28 Parametric studies We choose 0.7 V as an operating point to investigate further...

29 Are gas pores necessary? Assume a constant volume fraction of electrode material, 0.3 Perform a parametric study with the electrolyte volume fraction going from 0.3 to 0.69 on the cathode (implying that the gas pore volume fraction goes from 0.4 to 0.01 at the same time).

30 Pore volume result, current density So only 10% of gas pores is ok?

31 Oxygen concentration dependence on electrolyte filling level Almost no effect until the gas pore volume goes below 5%. Is this correct?

32 Back-of-the-envelope check Use Fick s law to calculate a limiting current for a boundary layer with the same thickness as the electrode i cat,limiting 4FDc = 10 A/m L L cat O2, bulk 7 2 The limiting current for oxygen transport is about 1000 times the operating current for a unit porosity /2 =1/1000 no large gradients in oxygen concentration are to be expected for ε g >0.1 our simulation result seems reasonable, we choose ε l >0.6 as an optimized parameter

33 Is adding more catalyst always a good idea? Perform a parametric study on the cathode, with the thickness increasing from 5 um to 100 um (Due to our previous result we now increase the electrolyte volume fraction to 0.6)

34 Cathode thickness result There is a maximum thickness beyond which adding more electrode material does not increase the cell performance, why?

35 Comparing activation and resistive losses At a cathode thickness above 40 um the resistive losses increase more than the activation losses decrees

36 Base case vs. optimized cathode An approximate 40% increase in current at 0.7 V with optimized parameters achieved (however to a quadrupled catalyst cost)

37 Final remarks Even a quite basic model can provide new insights Start with a simple model, then expand it Do you really need to include everything? Which phenomena may be ignored? Always compare your results with analytic calculations as well as experiments A pen, a paper and a pocket calculator is a very powerful modeling tool Your model will never be more precise than the quality of your input data!

38 Thank you for listening!