Linear Independence and Optimality Concepts Revisited in Thermodynamics and Kinetics

In this work, the concept of reaction linear independence is placed in a rigorous mathematical framework. It is shown that different conclusions may be reached regarding reaction independence depending on whether such independence is assessed in an equilibrium sense or in a kinetic sense. Mathematical techniques are proposed for the identification of independent reactions at equilibrium conditions. In the process of developing these results, necessary conditions for optimality are developed to assess reaction and phase equilibrium using a Gibbs Free Energy Minimization formulation. Case studies regarding natural gas reforming based hydrogen production utilizing a Gibbs equilibrium reaction model are presented. These case studies are used to quantify the carbon formation boundary of the reaction.