An algorithm is proposed for conducting the phase-equilibrium calculation for a given mixture with a specified pressure, enthalpy, and composition. We use a second-order optimization method to maximize entropy, With the individual phase compositions and enthalpies as the independent variables. At any point during the iterative solution procedure, the direction of the iterative step can be checked by ensuring an increase in entropy. During the iterations we allow phases to be split further into sub-phases to tackle the issue of a phase having multiple stable roots for the specified erithalpy. We successfully apply the method to calculate two-phase thermodynamic equilibrium for many hydrocarbon mixtures, some of which are known to have posed issues related to narrow-boiling. (C) 2017 Elsevier B.V. All rights reserved.