Gibbs energy minimization using Lagrange method of undetermined multipliers for electrochemical and thermodynamic modeling of a MCFC with internal steam reforming

Precise determination of the chemical equilibrium state is important for electrochemical and thermodynamic modeling of a molten carbonate fuel cell (MCFC). One method for determining the equilibrium state of a MCFC with internal reforming is to compute the total Gibbs free energy of the system (G) and minimize it by adjusting the molar amounts of each substance. Multi-dimensional optimization algorithms can be used for this purpose. The Lagrange method of undetermined multipliers as a powerful analytical solution is used in the present work to estimate chemical equilibrium state. Under this condition, the effects on voltage losses, output voltage, stack power, efficiency and molar portions of the exhaust chemical species at the anode and cathode are investigated, separately of such parameters as current density, reaction temperature, stack pressure as well as fuel and carbon dioxide utilization ratios. A simulation of a MCFC stack performance by the Lagrange method at a specified state, results in an efficiency of 50.3% and output power of 554.3 kW.