In this work, we build a new uniqueness and stability proof on the geometric insight. The computationally challenging problem of finding the global minimum of the system Gibbs energy is equivalent to the geometrically intuitive problem of constructing the convex hull for all the Gibbs energy functions of candidate phases. Analytically, a convex hull is defined with Caratheodary theorem (Rockafellar 1970). The infimum operator in the theorem can be dropped under mild assumptions. The two-phase region on the convex hull is proved to a ruled surface. Its projection onto the component space is also endowed with the special structure, which allows the use of an extended level rule for the phase distribution relation. The uniqueness problem is transformed into the determination of intersection points of two trajectories. The stability proof is constructed with help of Lyapunov theorem. A ternary T-P flash is used as an example to demonstrate the idea of geometric analysis employed in this work. Future work includes the extension of the analysis in this work to reactive flash reactors and multi-staged systems.
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