Reliable computation of phase stability and equilibrium using interval methods

Abstract

The reliable calculation of phase equilibrium is a critical issue in the simulation, optimization and design of a wide variety of industrial processes, especially those involving separation operations such as distillation and extraction. However, even when accurate models of the necessary thermodynamic properties are available, it is often very difficult to actually solve the phase equilibrium problem reliably. In this paper, we will discuss a deterministic method, based on interval analysis, that provides a mathematical and computational guarantee that the phase equilibrium problem has been correctly solved, and will highlight recent results using such an approach. Cases are considered in which published computational results are shown to be incorrect.

Application of interval analysis for gibbs and helmholtz free energy global minimization in phase stability analysis

“…A reliable and robust method for this is given by the interval for the Newton/generalized bisection algorithm, based on interval analysis and interval arithmetic (Stadtherr, et al, 1995;Kearfott, 1996). The main advantage of this method is that it finds with certainty all the roots of the nonlinear set of equations, proving that each solution is enclosed within some bounds.…”

Intelligent route planning system based on interval computing

“…The role of compact intervals as independent objects is continuously increasing in numerical analysis when verifying or enclosing solutions of various mathematical problems or when proving that such problems cannot have a solution within a given domain. Interval arithmetic has been successfully used in chemical engineering [52], in the domain of spacecraft systems [28], in economics [26], in the simulation of physical and diagnostic reasoning, in the analysis and control of structural systems [17]. Nowadays, application areas of interval methods include electrical engineering, industrial engineering, control theory, remote sensing, experimental and computational physics, chaotic systems, celestial mechanics, signal processing, computer graphics, robotics, computer-assisted proofs, power systems, finance, route planning etc.…”

Region of attraction estimation of biological continuous Boolean models

“…Interval arithmetic has been used to achieve numerical certification of the kinematic calibration of a parallel robots [12], reliably calculate phase stability and equilibrium in industrial processes [36], global optimization of molecular structures [25], to verify the existence of the Lorenz attractor [42], and to estimate regions of attraction [45].…”