Abstract
The matrix of binary interaction coefficients appearing in the van der Waals mixing rules for cubic equations of state is often rank-deficient. If the rank is sufficiently low, phase equilibrium algorithms can take advantage of the Sherman-Morrison-Woodbury formula to solve the linear system of equations appearing in the Newton iterations more economically than using LU- or Cholesky factorization. Frequently, many binary interaction coefficients are very small, implying that a good approximation of even lower rank may exist. Using the low-rank approximation when generating the Jacobian and Hessian matrices leads to a quasi-Newton method. The approach reduces the cost of applying the Sherman-Morrison-Woodbury formula. The results of a series of bench-marks show that the Sherman-Morrison-Woodbury formula can significantly speed-up phase equilibrium calculations in mixtures with a large number of components.
