Geometric analysis of thermodynamic equilibrium processes

We introduce a method for the analysis of the asymptotic behavior of thermodynamic equilibrium processes from a geometric viewpoint. In many of the previous studies the thermodynamic equilibrium conditions were enforced approximately or incorrectly. In this work, a geometric interpretation is given for the thermodynamics equilibrium conditions by proving that the global minimum of the Gibbs free energy is located on the convex hull of the molar Gibbs energy function. This geometric equivalence is extended to the general equilibrium defined by the maximization of entropy and the chemical phase equilibrium. The convex hulls for the thermodynamic functions are shown to be C1-smooth. As a result, the boundary between the single phase region and the multiple ones is also smooth. This property can be used to check the phase diagrams generated from numerical calculation. A phase number function defined on the domain of the convex hull is shown to be lower semi-continuous and is used to investigate the properties of the phase regions. In particular, the properties of the two phase regions are used in the stability analysis of the isothermal isobaric flash. Its dynamics are given a clear geometric explanation and it is shown to converge to a steady state. This analysis method is extended to the adiabatic flash and the reactive flash with equimolar reactions. Finally, the uniqueness of the steady state is analyzed for different flash processes.