Phase Stability with Cubic Equations of State: A Global Optimization Approach

Calculation of phase and chemical equilibria is of fundamental importance for the design and simulation of chemical processes. Methods that minimize the Gibbs free energy provide equilibrium solutions that are only candidates for the true equilibrium solution. This is because the number and type of phases must be assumed before the Gibbs energy minimization problem can be formulated. The tangent plane stability criterion is a means of determining the stability of a candidate equilibrium solution. The Gibbs energy minimization problem and the tangent plane stability problem are very challenging due to the highly nonlinear thermodynamic functions that are used. In this work the goal is to develop a global optimization approach for the tangent plane stability problem that (i) provides a theoretical guarantee about the stability of the candidate equilibrium solution and (ii) is computationally eecient. Cubic equations of state are used in this approach due to their ability to accurately predict the behavior of nonideal vapor and liquid phases across a broad range of pressures. The mathematical form of the stability problem is analyzed and nonlinear functions with special structure are identiied. These special structures are exploited to achieve faster convergence of the algorithm. The proposed approach has been applied to the SRK, Peng-Robinson, and van der Waals cubic equations of state and can address a variety of mixing rules. Results for several example problems, including an eight component problem, are presented.