Fast and robust algorithm for calculation of two-phase equilibria at given volume, temperature, and moles

General algorithm for multiphase equilibria calculation at given volume, temperature, and moles

“…In the previous work [9], the non-uniqueness in determining the equilibrium state using the PT variables has been observed only in pure components at saturation pressure in two phases. Extending the results to three phases for CO 2 -H 2 O system under geologic carbon storage conditions, the behaviour similar to that of pure components has been observed in [10].…”

“…In the previous work [22,23,9], we dealt with the single-phase stability analysis and the two-phase split calculation, both at constant volume, temperature, and moles. Now, we extend these results and present a general strategy for -phase equilibrium computation at constant volume, temperature, and moles in a multicomponent mixture, where ∈ N is the number of phases which is now not known a priori.…”

“…., . Similarly to the algorithm presented in [9], the numerical procedure is based on transferring an n-dimensional problem of minimization of a twicecontinuously differentiable objective function subject to a set of t linear equality constraints into an unconstrained minimization problem with the same objective function, but a lower dimension n − t. The constraint equations (4) and (5) can be written in the matrix form as Ax = b, or (13) where A ∈ R (n+1)× (n+1) is the matrix formed by blocks of the identity matrix in R n+1 which is denoted by I n+1 , x ∈ R (n+1) is the vector of unknowns, which is given as…”

“…In [9] we have proposed a numerical algorithm for constantvolume two-phase split calculation which is based on the constrained minimization of the total Helmholtz energy of the mixture. The algorithm uses the Newton-Raphson method with line-search and the modified Cholesky decomposition of the Hessian matrix to produce a sequence of states with decreasing values of the total Helmholtz energy.…”

Acceleration of the NVT Flash Calculation for Multicomponent Mixtures Using Deep Neural Network Models

“…Despite the fact that the isothermal-isobaric phase equilibrium calculation is the most commonly used flash technique in compositional simulators, numerous efforts have been made to improve the computing performance of isothermal-isochoric phase equilibrium calculations and also extend its applications. Jindrová and Mikyška [18] developed a fast and robust NVTflash algorithm for two-phase equilibria problems by directly minimizing the total Helmholtz free energy. Subsequently, they extended their research to multiphase systems and investigated the equilibrium problem involving aqueous phase through the Cubic-Plus-Association EOS [19].…”