Abstract
AbstractWe 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.
Highlights
Robust, computationally efficient and accurate phase splitting or flash calculations play a crucial role in many engineering disciplines, such as chemical-process and reservoir simulations
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
We have developed a Fortran implementation of the proposed flash algorithms for the four discussed isothermal and nonisothermal flash calculations, and tested it for a large number of different multicomponent mixtures and different cubic equation of states (EoS)
Summary
Computationally efficient and accurate phase splitting or flash calculations play a crucial role in many engineering disciplines, such as chemical-process and reservoir simulations. In Computational Fluid Dynamics (CFD) simulations of realistic multi-component vapor–liquid fluid flows, millions of phase equilibrium calculations are required every time step in the form of either the VT-flash or UV-flash, depending on the chosen formulation of the governing equations: The VT-flash is needed in cases where the overall specific volume, temperature and composition are known, such as for the carbon dioxide injection into subsurface reservoirs.[1,2] Methods that solve the compressible Navier–Stokes equations based on the conservation laws for mass, linear momentum and total energy, such as applied for the simulation of the trans-critical vaporization of liquid fuels,[3,4,5,6] require a UV-flash, where the input is the overall specific internal energy, volume, and composition.
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