A Robust and Efficient Algorithm for Computing Reactive Equilibria in Single and Multiphase Systems

Prediction of liquid–liquid phase equilibria in reacting systems is important in many applications such as reactive extraction. This problem poses several numerical challenges. These systems are governed by highly nonlinear algebraic equations and are plagued by the issue of nonconvergence of iterative algorithms. They exhibit strong sensitivity to the choice of the initial values or starting guesses for the variables. The nonconvergence stems primarily from the wide range of concentrations of various species at equilibrium. In this work, a new methodology for predicting thermodynamic equilibria of multiphase reacting systems is proposed. The mathematical formulation and solution are based on the use of the logarithms of the concentrations as the dependent variables. The proposed algorithm shows rapid convergence even when the initial guesses are far from equilibrium. The efficiency of the method is demonstrated by predicting the equilibrium concentrations of species in three systems of varying degrees of complexity.