(321bd) Reliable Computation of Density Roots, Phase Stability and Phase Equilibrium Using Saft Equation of State

Statistical association fluid theory is an important thermodynamic tool to model the system containing associating and chain like molecules. Reliable computation of the phase behavior through SAFT equation of state is very critical to predict the number of phases and phase compositions accurately.

We demonstrate an application of homotopy continuation method to reliably compute the density roots, phase stability and phase equilibrium of system involving associating molecules using SAFT equation of state. The predictive step of the continuation method is applied to all unknowns except the internal variables. After each predictive step, the newton correction is applied which has to be modified when the equation of state is applied to the system containing associating molecules to solve for the internal variables. The internal variables are solved after each step of newton correction on compositions and density. We also apply internal iteration to solve for the internal variables while computing the jacobian of each newton correction of the homotopy continuation method. This methodology is applied to binary and ternary system involving both self and cross associating molecules. The well known two stage strategy is followed for the phase equilibrium computations. The density root is calculated first and then the phase is tested for stability. For both computations, homotopy continuation method is applied. The phase split problem is then solved locally with the guess values provided by the global phase stability computations.