COMSOL 6.4 - Theory for Electrochemical Power Losses

Theory for Electrochemical Power Losses

Most Electrochemistry interfaces define power loss variables that can be used to analyze the performance of electrochemical cells. The power loss variables are derived using similar principles as for the electrochemical heat source variables, but with the fundamental difference that the power loss variables are based on interfacial changes and domain gradients in the Gibbs free energy, rather than the enthalpy. In the absence of entropy changes, the power loss and the heat source variables are identical.

Kinetic Activation Power Losses

On an electrode surface, the local power loss (A/m2) equals the local electrode reaction current density times the overpotential

(4-48)

whereas in a homogenized porous electrode model, the local power loss (A/m3) equals the volumetric electrode reaction current density times the overpotential

(4-49)

Electrolyte transport power losses

Power loss associated with transport is based on gradients in the chemical potentials of the transported species. (The chemical potential equals the Gibbs free energy per mole of that species). For an electrolyte species i, the electrochemical potential gradient (J/mol/m) is defined as

(4-50)

This definition assumes that the Nernst–Einstein equation applies for the definition of the electrolyte mobility, and that the equilibrium potential of all electrode reactions exhibit a Nernstian (logarithmic) concentration dependency. For non-ideal activities, the ci is replaced by ai.

The electrolyte power loss associated with the transport of the species i is then defined as

(4-51)

where Nmd,i is the migrative-diffusive flux of species i with respect to the mass-averaged, or solvent, convective velocity of the electrolyte which relates to the total molar flux Ntot,i as

(4-52)

where v is the velocity.

The total power loss due to electrolyte transport is defined as

(4-53)

Recognizing that the total electrolyte current vector equals

(4-54)

it is possible to split the total power loss into an entropic and ohmic part defined as

(4-55)

and

(4-56)

Electrolyte transport losses in the Hydrogen Fuel Cell and Water Electrolyzer interfaces

In the absence of membrane gas crossover and electroosmotic drag, the power loss is defined as for ploss,ohmic above.

When electroosmotic water drag is enabled in a membrane domain, this adds an additional term to the electrolyte transport power losses resulting in

(4-57)

Gas Crossover Transport Losses in the Hydrogen Fuel Cell and Water Electrolyzer Interfaces

When crossover of a gas species i is enabled, this adds a contribution according to

(4-58)

in the membrane domain.

For the case when the crossover species is either H2 or O2, and the same species is not present in the gas mixture at the recombining boundary (that is, at the O2 or H2 gas mixture boundary, respectively), the concentration of the crossover species is set to zero at the recombining boundary, and the resulting flux is used to compute the local current density of the recombination reaction. For this case, Green’s theorem is used to compute the combined power loss associated with both the electrode kinetics at the recombining boundary and the gas transport through the membrane, and this combined contribution is added to the gas crossover power loss variable for the membrane domain.

For the case of hydrogen crossover and oxidation at the oxygen mixture boundary, the resulting power loss at the oxygen boundary is

(4-59)

where

(4-60)

Equation 4-60 accounts for the adjustment to the open circuit voltage necessary as a result of the concentration of hydrogen equaling zero at the boundary. Equation 4-59 is summed with Equation 4-58 to get the total power loss from hydrogen crossover.

(4-61)

(4-62)