Isochoric Phase Stability Testing for Hydrocarbon Mixtures

Abstract

A method for global phase stability testing at isotherm-isochoric specifications has been developed. The formulation of the tangent plane distance (TPD) criterion in terms of the Helmholtz free energy density (calculated from a general two-parameter cubic equation of state) with component molar density as independent variables is used. An unconstrained minimization problem of a smooth function is solved using the tunneling global optimization method. Calculations are carried out for several representative mixtures; special attention is paid to the performance of the algorithm for near-critical conditions and the vicinities of phase boundaries. The test examples show the robustness and efficiency of the proposed method, and its high reliability in solving the isochoric phase stability problem.

A simple approximate density-based phase envelope construction method

“…( 11) can be used for both VTN (at volume, temperature and moles) [16,17,21,23] and volume-based PT phase stability testing [20,22,24]. The volume-based phase stability problem is a bound-and linear inequality-constrained minimization of the TPD function usually solved by local minimization (using modifications of the Newton method) [16,17,20,21,24], constrained optimization (by formulation of phase stability as a dual optimization problem) [35,36] or global optimization methods [22,23]. In phase envelope construction, this TPD function is used in…”

“…Michelsen [14] expressed the TPD function in mole fractions and molar volume and later Mikyška and Firoozabadi [16] and Castier [21] derived the TPD function in terms of mole numbers and volume. Several volume-based phase stability testing methods were proposed, at PT or VTN specifications, using global [22,23] and local (modified Newton) [16,17,20,21,24] optimization methods.…”

Robustness and efficiency of phase stability testing at VTN and UVN conditions

“…The VTN stability and PT volume-based stability problems were solved using various methods, such as global optimization methods (Tunneling, Nichita et al [20,21], Castier [6] , Branch and bound, Smejkal and Mikyška [22]), standard Newton method (Mikyska and Firoozabadi [17]), modified Newton methods (Nagarajan et al [15], Castier [6], Nichita [18,19]), constrained optimization methods (Pereira et al. [23,24]), Sherman-Morrison iterations (Smejkal and Mikyška [25]) and evolutionary methods (S. Sun's group [26][27][28]).…”

Vapor-liquid equilibrium calculations at specified composition, density and temperature with the perturbed chain statistical associating fluid theory (PC-SAFT) equation of state

“…In addition, for pressure-explicit EoS this approach would also avoid the need for an iterative process to find the density from pressure, as the pressure becomes then an output of the minimisation process. This approach was then implemented for the stability testing of hydrocarbon mixtures 29 using the SRK and the PR EoS with the tunnelling method 30 . Following work used the successive substitution iteration (SSI) method and the PR EoS for the flash problem 31 .…”