Basic overall reaction for hydrogen powering

Fuel Cell Basics

Basic overall reaction for hydrogen powering 2H 2 + O 2 2H 2 O Hydrogen produces electrons, protons, heat and water

PEMFC Anode reaction: H 2 2H + + 2e Cathode reaction: (½)O 2 + 2H + + 2e H 2 O Overall: 2H 2 + O 2 2H 2 O

SOFC Anode reaction: H 2 + O 2 H 2 O + 2e Cathode reaction: (½)O 2 + 2e O 2 Overall: 2H 2 + O 2 2H 2 O

Open Circuit Voltage (OCV) Inputs and Outputs Hydrogen Energy Oxygen Energy Electric Energy, V I t Heat Water

Enthalpy of formation Enthalpy of formation of the product in a chemical reaction is the difference in enthalpy of the product and sum of enthalpy of all reactants

Enthalpy of formation Reference state is 25 C and 0.1 MPa. At this state the enthalpy of the reactants is zero. The enthalpy of the product at the reference state is then given by the net heat transfer and this is termed the enthalpy of formation of the product

Enthalpy of formation = H p = Q CV The enthalpy of formation can be determined by experiments but commonly statistical thermodynamics is used to determine it for various compounds. Table is provided.

Enthalpy of formation Enthalpy of formation of the components and compounds at any other state than the reference base state is estimated by adding the change in enthalpy between the given state and the reference state as ht p h C MPa h 0 (, ) f (25,0.1 ) 25 C,0.1 MPa T, p h 25C, 0.1MPa T,P c p (T)dT

Gibbs free energy of formation

Gibbs free energy of water at various temperatures and state Water Product Temperature, C Δg f, kj/mole Max EMF, V Efficiency limit % liquid 25 237.2 1.23 83 liquid 80 228.2 1.18 80 gas 100 225.3 1.17 79 gas 200 220.4 1.14 77 gas 400 210.3 1.09 74 gas 600 199.6 1.04 70 gas 800 188.6 0.98 66 gas 1000 177.4 0.92 62

Estimation of open circuit voltage, OCV Let e be the charge of one electron. As two electrons are produced by the considered reaction, the produced charge becomes: 2Ne = 2F Coulombs where N is the Avogadro number and F is the Faraday constant. The electrical work done by the fuel cell in moving two electrons around the circuit is found from: Electrical work = charge x voltage = 2FE Joule

Estimation of open circuit voltage, OCV

Efficiency

Influence of Pressure on Gibbs Energy and Reversible Voltage

Gibbs energy or function is defined as G = H TS or g = h Ts = u + pv Ts First law of thermodynamic states that du = q pdv = Tds pdv By combining these it is possible to find dg = vdp sdt or dg = Vdp SdT

Effect of gas concentration

Effect of gas concentration continued

Fuel Cell Reaction involving Hydrogen Oxygen

EMF values Depends on temperature Low temperature (40 C): EMF 1.2 V High temperature (800 C): EMF 1 V

EMF versus temperature

Operational losses

FC Ireversibilities, Voltage losses Activation loss Ohmic loss Concentration loss Cross over and short circuit losses

Fuel Cell Polarization Curve Losses: anode and cathode activation losses, ohmic losses, mass transfer losses, losses due to short circuit, losses due to reactant crossover The net fuel cell overpotential becomes:

Operational Voltage vs Current Density for an FC

Voltage losses Activation losses over potential Fuel crossover/internal current losses Ohmic losses Mass transport/concentration losses

Activation losses The activation losses are non linear with current. Typically the activation losses introduce a sharp initial drop in the cell open circuit EMF with increasing current load. The losses are different at each electrode (the anode and cathode) because the double layer configuration is different. These losses are directly related to the energy barrier (resistances) for oxidation and reduction at the electrodes.

Electrical Double Layer As a metal electrode is placed in an electrolyte, the charge of the metal will attract ions of opposite charge in the electrolyte. Then a layer of charge is formed both in the electrolyte and the metal. This layer is called the electrical double layer and a principle sketch is provided in the Figure below. The electrochemical reactions take place in this layer. All atoms or ions being reduced or oxidized have to pass through this layer. The kinetics of the electrode reaction is controlled by the possibility for ions to pass across this layer. The energy barrier for the electrode reaction, called the activation energy of the electrochemical reaction is situated in this electrical double layer

Principle of Activation Energy The activation energy has to be supplied to jump over the hill. If the probability of a molecule is low for having sufficient energy, the actual reaction will proceed slowly.

The slow reaction rates can be affected by a) using catalysts, b) increasing the temperature and c) increasing the electrode area (porous with microstructure). The reaction area involving the fuel or oxidant with the electrolyte and the electrode is sometimes called the three phase contact or triple phase boundary.

Activation losses The activation losses for the anode and cathode are given by the equations below: For a hydrogen oxygen FC, the cathodic activation loss is dominating and hence the anodic one is neglected.

Activation loss For equal charge coefficients, i.e., α a = α c = α It can be found based on Butler Volmer equation η act =

Exchange current density and charge transfer coefficient. A large value of means low electrode losses. n, F and R cannot be changed for a given reaction. Increase in T and increase of the reactant concentration C can lead to higher values of.

Minimizing activation losses High operational temperature, i 0 goes up Catalytic presence a) Rough catalysts mean more contact area, b) increase operational pressure, c) selection of catalytic material, Ni, Pt used commonly otherwise Pd better.

Ohmic losses These occur due to resistance to the flow of electrons in the interconnect, anode and cathode Directly proportional to the current Major loss in both low and high temperature fuel cells

Ohmic losses

Mass transport/concentration losses For low and high temperature fuel cells Particularly at high current densities Loss of high concentration of either fuel (at anode) or oxygen (at cathode) Fuel or oxygen is used faster than supplied

Mass transport loss The balance between the rate of transport of species and the rate of consumption at the interface determines the maximum current.the key transport processes are convection, diffusion and migration. Migration means transport of ionic species toward or away from the electrode due to the effect of an electric field. A high electric field gives high migration rate. Diffusion means transport of reactant or product species because of a concentration gradient. Convection means transport of reactant or product species by bulk fluid motion driven by natural or applied mechanical forces.

Mass transport loss

Concentration losses For reaction kinetics and based on the Butler Volmer equation it can be derived η conc,k =

Concentration losses Concentration effects can found by using the Nernst equation η conc,n =

Concentration losses η conc = η conc,k + η conc,n = (1 + 1/α)

Reactant crossover and internal currents The electrolyte of a fuel cell mainly conducts ions but it is not completely insulated from electrons. It will be able to support a small amount of electron conduction. This electron conduction in the electrolyte or internal current creates a net loss of current to external load. Also some reactants will diffuse from one electrode to another through the electrolyte where reactions occur without external electron transfer.

Fuel cross over/internal current loss Losses throughout the electrolyte a) Fuel is leaking through the electrode b) Electrons are leaking through the electrode Fuel leakage most severe but has a significant effect only at low temperature

j L j L is the maximum current density or limiting current density. At this all reactant gas has been consumed and the output cell voltage is zero.

PEMFC Cell voltage, volt 1.2 1.0 0.8 0.6 0.4 0.2 No loss voltage of 1.2 volts Even the open circuit voltage is less than the theoretical no loss value Rapid initial fall in voltage Region where voltage falls slowly and graph is fairly linear Rapid fall at higher currents 0 0 200 400 600 800 1000 Current density, ma cm -2

SOFC Cell voltage, volt 1.2 1.0 0.8 0.6 0.4 0.2 No loss voltage of 1.0 volts Very small initial fall on voltage, OCV almost equals to the theoretical value Graph mostly linear Rapid fall at higher currents, as with low temp. cells 0 0 200 400 600 800 1000 Current density, ma cm -2

Butler Volmer equation A key issue in the physical understanding, modeling and simulation of fuel cells is to determine the current generated by a cell. The most common method is to apply the so called Butler Volmer equation which relates the current density to the activation overpotential at each electrode/electrolyte interface. It reads:

Butler Volmer equation

Typical parameters for PEMFC and SOFC Parameters PEMFC SOFC Open circuit voltage (V) 1.22 1.06 1 x 10 4 0.1 1.5 1.5 0.002 0.002 0.03 0.09 A (V) 0.05 0.03 B(V) 0.06 0.08

Oxygen Hydrogen Water Flow Rates

Direct oxygen consumption The total charge current I is given by where is the number of electrons per mole of oxygen, F the Faraday constant and is the number of mol/s of oxygen.

Direct oxygen consumption For a stack of N c number of cells the oxygen consumption is given by In terms of mass flow rate (kg/s) we have

Direct oxygen consumption The power consumption in a single cell and in a stack can be expressed as P c = I V c P t = N c P c = N c I V c Then the mass flow rates can be expressed as:

Direct oxygen consumption For stack: For cell:

Oxygen consumption as air Let the mol fraction of oxygen in air be The the number of moles of oxygen per kilogram air is: The consumption of air for a cathodic reaction is then

Oxygen consumption as air Commonly an excess amount of oxygen is supplied and the excess air supply is defined in terms of a stochiometric factor ξ air Then the supply air mass flow rate (stack) is given by

Oxygen consumption as air The exit air flow rate is then simply

Hydrogen consumption and supply rates Similarly it is possible to estimate the hydrogen mole consumption in an anodic reaction as (cell): For a stack:

Hydrogen consumption and supply rates Mass flow rates of hydrogen: Stack cell

Water production rate Consider a hydrogen oxygen FC and then 1 mol of water is produced for every two electron charges. The water production rate is given by:

Water production rate Mass flow rate

Heat Generation Rate