Non-Equilibrium Thermodynamics: Foundations and Applications. Lecture 9: Modelling the polymer electrolyte fuel cell

Transcription

1 Non-Equilibrium Thermodynamics: Foundations and Applications. Lecture 9: Modelling the polymer electrolyte fuel cell Signe Kjelstrup Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway and Engineering Thermodynamics Department of Process and Energy, TU Delft

2 Non-Equilibrium Thermodynamics: Foundations and Applications

3 Non-Equilibrium Thermodynamics: Foundations and Applications Lecture 9. Transport heat, mass and charge in fuel cells Chapter 19 Lecture aims Scetch solution procedure for one-dimensional model and present some results Present an idea for more energy- and material-efficient design

4 PEM fuel cell challenges Too expensive Lifetime lower than competing technology Efficiency high, but can be higher P. Mock, J. Power Sources (2009)

5 PEMFC Description Design must consider Catalyst nanoporous layer Microporous support layer Gas supply system Water removal system Anode Flow Channel e H Fuel cell models must consider 2 Heat transport H + Electron production Proton and water transport Gas access Cathode Flow Channel O 2 e Water removal

6 Slide title PEMFC Description The catalyst a nanoporous agglomerate

7 PEMFC Description The microporous layers Edge View

8 Another common design

9 Working procedure for one-dimensional model 1. The entropy production of five separate layers 2. The fluxes and conjugate forces 3. The coefficients from experiments 4. Electric work from chemical energy in the cell 5. The dissipation of energy; lost work Limitations in this study: One-dimensional transports No pressure gradients

10 Transport of heat, mass and charge across five parallell layers Possible questions: Nernst equation is: ΔG = -nfe What is the local potential profile? Is there any temperature profile? In which contexts are concentration profiles important? What is the entropy production?

11 A systematic way to describe transport processes 2.law, local formulation Example: The PEM fuel cell s= å JX i i > i 0 Onsager s symmetry relations must be obeyed for any subsystem: J = L X + L X J 2 = L 2 1 X L 2 2 X 2.

12 Three ways to find the lost work: 1. By integrating over σ 2. By calculating J s in J s out 3. By measuring the heat production ò s dx = J -J out s in s é 1 out out = J ' + å J S out êët é 1 in in ù - J' in q+ å Ji Si êët úû q i i ù úû The cell potential as function of the current density shows 3 distinct regimes (Eg. Weber and Newman, review, 2004)

13 Energy is conserved! Thermoneutral potential (squares), polarisation curve (triangles) electric power (circles) as functions of current density in a fuel cell operated at 323 K, 1 atm, with oxygen and hydrogen Burheim et al. Electrochim. Acta. 55 (2010) E / V b) Nafion 115 j / Acm P / W cm -2 E TN Ecell P

14 Excess properties of the electrode surface according to Gibbs backing surface membrane Pt H(s) H 2 O H 2 HM Gibbs equation: å U = TS +g da+ m dn s s s j j

15 The entropy production for the cathode surface We use: Mass balances, first law, Gibbs equation One flux-force pair for each variable Reversible conditions give Nernst equation for the electrode! ' ms, æ1ö ' sc, æ1ö s= Jq D m, s + Jq D ç s, c èt ø çèt ø mæ 1 ö cæ 1 ö + J w - Dm, sm w, T + J w - Ds, cm ç w, T è T ø çè T ø é c 1 æ D G öù + j mc, ê - D j+ T ç F çè øú ë û

16 Part of the problem: Thermal osmosis (cf. Lecture 6) J - J = JDH ' ma, ' a q q J - J =-JDH ' c ' m, c q q Energy balance T-profile Concentration profile ( q ) ma, a 1 ' a * s T - T =- ` J - q J s l dt 1 ' m * m =- m ( Jq - q J) dx l c m, c 1 ' c * s T - T =- ` J - q J s l ( q ) ma, * s RT q D m =- J - D Dc T am, T s s, a m, a am, * m dm T 1 q c dt =- J m - dx D T RT dx mc, * s RT q D m =- J - D Dc T mc, T s s, c m, c mc, T T

17 Flux-force relations - cathode surface Temperature jumps: Changes in chemical potential of water: 1 é ' mc, *, mæ m m jö m jù D ms, T =- J s q -q Jw-t w -p l ê ç m F ë è ø mú û é æ ö D = p l ë 1 ' cm, *, c c c j c sc, T J s q q Jw tw ê çè c F ø *, c c c sc, wt,, sc, T çj cm s w tw çè mm j ù mú û q 1 æ j ö D m =- D - ç - T l F ø q 1 æ j ö D m =- D - ç - T l F ø *, m m m ms, wt,, ms, T çj mc s w tw çè mm The jump in electric potential across the surface Thermal osmosis and electro-osmosis! m c c p p Dmc, j+d G =- D m ms, T- D c sc, T FT FT m c tw tw - Dmc, mwt, - Dso, mwt, - F F s r j

18 To do for each of the five subsystems: Solve J = L X for fluxes of heat, water and electric current Boundary conditions used: Constant j, J w,, T a = T c =370 K Results 1: Mole fractions of water (left) and oxygen (right) 1. S.Kjelstrup and A. Røsjorde, J. Phys. Chem. B, 109 (2005) 9020

19 Results for water concentration profile in the membrane Water content, Dimensionless position in membrane The surface jump: q 1 æ jö D m = Dl l =- D - ç - T l F ø *, c * c c sc, wt, RT /, sc, T çj cm s w tw çè mm

20 Temperature profiles P E M F C T(x) Potential profiles J q (x) E(x)

21 Lost work and accumulated entropy production ds irr /dt cel l The cell potential as a function of j Accumulated entropy production

22 The problem: Losses are unevenly distributed across the membrane! Cf. Lecture 10

23 Entropy production in the human lung Flow regime E. R. Weibel, Am. J. Physiol. (1991) 261 Diffusional regime 1 The entropy production (and the driving force) is constant in each of the flow regimes S. Gheorghiu, S. Kjelstrup, P. Pfeifer and M.-O. Coppens (2005), Fractals in Biology and Medicine, Vol. IV (Losa et al., ed. Birkhäuser Verlag, Basel), pp

24 Can we make more energy efficient designs? A fractal injector in fluidized beds gives higher yield per unit time (Coppens, US patent) *US Patent

25 Highest thermodynamic efficiency with constant local entropy production and uniform feed over the area; or: Cf, Lectures 10,11 A fractal injector gives a uniform 2D distribution* Tondeur et al Right angles: OK when pressure losses are small!

26 The reaction can be limited by diffusion in the nanoporous part d Effective 1-D diffusion w Reaction/diffusion Stationary state Porosity 2 c D( ) k(1 ) c( y) 0 2 y d d w E. Johannessen, G. Wang, M.-O. Coppens. Ind. Eng. Chem. Res. (2007) E. Johannessen, G. Wang, C.R. Kleijn, M.-O. Coppens. Ind. Eng. Chem. Res. (2007)

27 =c 0 D gas 510 m/s D nano Given a constant production with efficiency factor Thiele modulus What is the optimal macroporosity ε and heigth H of the layer?

28 Find the minimum catalyst volume for a given current 0 Vcat (1 ) HLM J J LM Kjelstrup, Coppens, Pharoah, Pfeifer, Energy and Fuels (2010)

29 Improving the material- and energy efficiency. By uniform feed distribution and increasing access to the catalyst

30 ETEK Elat: 0.5 mg Pt/cm 2 Numerical example: Pure oxygen 353 K, 1 bar Current density / Am Transfer factor Butler-Volmer Overpotential / V Rate coefficient /s -1 Rate coefficient /s -1 Optimal layer height/ µm Energy dissipation reduced by mv % Pt cost reduced by a factor 8

31 Summary The coupling of transport phenomena in fuel cells is large The entropy production can be studied by calorimetry of fuel cells and by modeling The theory provides fundamental insight, and may help practical designs of experiments and equipments The entropy balance is not yet widely used in a systematic study of fuel cells. It can be used to find better designs (cf. Lectures 10,11).

32 On a road towards the hydrogen society. Where does H 2 come from? H 2 from natural gas Electrolysis of water Geothermal sources wind hydro geo