Equations Used in Dynamic Model

Species Conservation:

Volume multiplied by the time derivative of the species concentration is the moles of that species at the inlet minus the moles at the oulet plus the number of moles created
Momentum Conservation:
Volume multiplied by the time derivative of the quantity of density times nu-bar is the inlet pressure times inlet area minus the outlet pressure times the outlet area minus the force on the system

Nernst Equation:

The cell EMF is the standard electrochemical potential plus the quantity of RT divided by the number of electrons that participate in the reaction and the Faraday constant, multiplied by the natural log of the concentration of hydrogen times the square root of the concentration of oxygen times the concentration of carbon dioxide f times the square root of the total pressure, divided by the concentration of water times the concentration of carbon dioxide rho

Electrochemical losses:

Ohmic polarization is the cell resistance multiplied by current density
Activation polarization is RT divided by the quantity of participating electrons times Faradays constant times catalyst surface area and multiplied by the natural log of the ratio of current density to exchange current density
Concentration polarization is negative RT divided by the quantity of number of participating electrons times Faraday’s constant and multiplied by the natural log of one minus the ratio of current density to limiting current density

Cell voltage:

Cell voltage is the open-circuit cell voltage minus the ohmic, activation, and concentration polarizations

Sample mass conservation equations:

Outlet concentration is the outlet pressure divded by RT
The number of moles out is the number of moles in plus the number of moles created minus the time derivative of the outlet concentration times volume

Mass fraction of hydrogen is the number of moles in times mass fraction of hydrogen in plus the amount of hydrogen created minus the time derivative of hydrogen concentration times volume, all divided by the number of moles out

Mass fraction of carbon dioxide is the number of moles in times mass fraction of carbon dioxide in plus the amount of carbon dioxide created minus the time derivative of carbon dioxide concentration times volume, all divided by the number of moles out

Mass fraction of water is the number of moles in times mass fraction of water in plus the amount of water created minus the time derivative of water concentration times volume, all divided by the number of moles out

Mass fraction of nitrogen is the number of moles in times mass fraction of nitrogen in minus the time derivative of nitrogen concentration times volume, all divided by the number of moles out