Phase equilibrium calculations with quasi-Newton methods

摘要: The phase split problem, formulated as an unconstrained minimization of the Gibbs free energy, is commonly solved by second-order Newton method, preceded a number first-order successive substitutions. For difficult problems, convergence radius method may be small and high substitution iterations required before switch, or in repeated switch-backs. An interesting alternative given quasi-Newton methods, representing good compromise between complexity speed. BFGS exhibits super-linear rate (in some cases without step length control) rank two update Hessian matrix guarantees hereditary positive definiteness. In this work, scaling methodology proposed for finding appropriate change variables equilibrium problems; applied to two-phase resulting leads form H = I + D ND, where identity matrix, diagonal with elements vanishing at solution, ND effective low-rank matrix. results numerical experiments carried out on several test show that using more robust efficient than previous implementations (from literature open source codes). A two-parameter cubic equation state was used but any can used. methods are particularly suited thermodynamic models which costly obtain.