Rapid multi‐component phase‐split calculations using volume functions and reduction methods

Abstract

We present a new family of fast and robust methods for the calculation of the vapor-liquid equilibrium at isobaric-isothermal (PT-flash), isochoric-isothermal (VT-flash), isenthalpic-isobaric (HP-flash), and isoenergetic-isochoric (UV-flash) conditions. The framework is provided by formulating phase-equilibrium conditions for multi-component mixtures in an effectively reduced space based on the molar specific value of the recently introduced volume function derived from the Helmholtz free energy. The proposed algorithmic implementation can fully exploit the optimum quadratic convergence of a Newton method with the analytical Jacobian matrix. This article provides all required exact analytic expressions for the general cubic equation of state. Computational results demonstrate the effectivity and efficiency of the new methods. Compared to conventional methods, the proposed reduced-space iteration leads to a considerable speed-up as well as to improved robustness and better convergence behavior near the spinodal and coexistence curves of multi-component mixtures, where the preconditioning by the reduction method is most effective.

Numerical Simulations of Real-Fluid Reacting Sprays at Transcritical Pressures Using Multiphase Thermodynamics

“…To solve the VLE equations, we utilize the newly introduced method of Fathi and Hickel [3] that performs UV-flash calculations very fast and robust via Newton iterations with the exact Jacobian based on an effective reduction method. We note that tabulation methods are a suitable alternative for non-reacting flows.…”

“…For a comprehensive review and practical implementation guidelines, readers are referred to Ref. [3].…”

A unified presentation of phase stability analysis including all major specifications

“…As for PHN stability, no detailed analysis was provided in the literature. UVN (isochoric-isoenergetic) phase equilibrium (consisting of the maximization of entropy at given internal energy, volume and moles) [1][2][3][51][52][53][54][55][56][57] is applied in rigorous dynamic simulation of distillation columns; simulating two-phase pipe flow, filling tank, venting and leaks from pressure vessels, etc. A derivation of the TPD function at UVN conditions was apparently first given by Castier [52], who also showed that a PT stability testing can be carried out to assess UVN stability.…”