(616b) Pseudo-Extrapolation Algorithm for General Equation of State Model

Equation of state (EOS), such as general cubic EOS, may have root reduction situation where multiple compressibility roots (three for cubic EOS in general) reduce to single root. Such situation may cause non-smoothness issue on the solution path when Newton-Raphson type of solver is applied to phase equilibrium calculation. Same situation may also end up with trivial K-value, which would cause convergence failure or issue wrong solution.

Introduced here is a pseudo-extrapolation algorithm for general cubic EOS based on the original (true) cubic curve itself. Advantages can be expected including smoothness and reliability. The new extrapolation algorithm also ensures that by convergence, all real (non-zero flow) phases will have their compressibility roots landed on the original cubic curve.

Comparison with existing pseudo extrapolation techniques such as Mathias et. al., 1982, had also been illustrated to show that the new pseudo-extrapolation algorithm provides much natural smooth transition between the true and pseudo values of compressibility roots, which in general reduced the calculation cost other extrapolation technique requires.