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Phase equilibrium calculations are often involved in the design, simulation, and optimization of chemical processes. Reported methods for these calculations are based on either equation-solving or Gibbs free energy minimization approaches. The main objective of this work is to compare selected methods for these two approaches, in terms of reliability to find the correct solution, computational time, and number of K-value evaluations. For this, four equation-solving and three free minimization methods have been selected and applied to commonly encountered vapour–liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), and vapour–liquid–liquid equilibrium (VLLE) examples involving multiple components and popular thermodynamic models. Detailed results show that the equation-solving method based on the Rachford–Rice formulation accompanied by mean value theorem and Wegstein's projection is …