A subdivision algorithm for phase equilibrium calculations at high pressures

Abstract

-Phase equilibrium calculations at high pressures have been a continuous challenge for scientists and engineers. Traditionally, this task has been performed by solving a system of nonlinear algebraic equations originating from isofugacity equations. The reliability and accuracy of the solutions are strongly dependent on the initial guess, especially due to the fact that the phase equilibrium problems frequently have multiple roots. This work is focused on the application of a subdivision algorithm for thermodynamic calculations at high pressures. The subdivision algorithm consists in the application of successive subdivisions at a given initial interval (rectangle) of variables and a systematic test to verify the existence of roots in each subinterval. If the interval checked passes in the test, then it is retained; otherwise it is discharged. The algorithm was applied for vapor-liquid, solid-fluid and solid-vapor-liquid equilibrium as well as for phase stability calculations for binary and multicomponent systems. The results show that the proposed algorithm was capable of finding all roots of all high-pressure thermodynamic problems investigated, independent of the initial guess used.

Phase stability analysis of liquid-liquid equilibrium with stochastic methods

“…The results obtained were quite satisfactory (Corazza et al, 2007). It may be interesting to note that, to our knowledge, an application of a subdivision algorithm to liquid-liquid equilibrium calculations is not available in the literature.…”

“…In this context, the aim of this work is to provide a systematic comparison between the two mentioned strategies for phase stability analysis: Simulated Annealing (Press et al, 1992), wich is a global optimization procedure, and a subdivision method (Smiley and Chun, 2001;Corazza et al, 2007) -henceforth denominated SubDivNL -employed for solution of the stationary points on TPD of liquid mixtures modeled by the NRTL activity coefficient model (Renon and Prausnitz, 1968). Comparison of the approach used in this work with Interval Newton analysis is also provided.…”

Phase Stability Analysis with Equations of State—A Fresh Look from a Different Perspective

“…Local methods include reformulations of Newton’s method. Global methods are either stochastic (based on the application of exploration and exploitation strategies, which have been developed from principles of natural phenomena and artificial intelligence) or deterministic optimization methods and guarantee, at least theoretically, that the optimum is obtained irrespective of the starting point. , The number of papers and reviews devoted to the application of different optimization methods to the solution of the phase stability problem, in the past decade only, is considerable. − The references cited here are given rather as an illustration of the amount of work performed and of the wide variety of optimization methods used by the different research groups than with the ambition to be exhaustive. Interested readers are prompted to acquaint with the recent excellent and extensive review of Zhang et al who examine the state-of-the art of global optimization methods.…”

A reliable procedure to predict salt precipitation in pure phases

“…Commonly used stochastic methods include simulated annealing (e.g., Bonilla-Petriciolet et al, 2008), genetic algorithms (e.g., Alvarez et al, 2008), and particle swarm (e.g., Rahman et al, 2009). Deterministic methods generally include a procedure to subdivide the root search area and systematically discard regions that do not contain a root (e.g., Corazza et al, 2007, Simoni et al, 2007.…”