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16
Enhanced Interval Analysis for Phase Stability: Cubic Equation of State Models
 IND. ENG. CHEM. RES
, 1998
"... The reliable prediction of phase stability is a challenging computational problem in chemical process simulation, optimization and design. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. Conventional solution meth ..."
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Cited by 30 (20 self)
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The reliable prediction of phase stability is a challenging computational problem in chemical process simulation, optimization and design. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. Conventional solution methods are initialization dependent, and may fail by converging to trivial or nonphysical solutions or to a point that is a local but not global minimum. Thus there has been considerable recent interest in developing more reliable techniques for stability analysis. Recently we have demonstrated, using cubic equation of state models, a technique that can solve the phase stability problem with complete reliability. The technique, which is based on interval analysis, is initialization independent, and if properly implemented provides a mathematical guarantee that the correct solution to the phase stability problem has been found. However, there is much room for improvement in the computational efficiency of the technique. In this paper we consider two means of enhancing the efficiency of the method, both based on sharpening the range of interval function evaluations. Results indicate that by using the enhanced method, computation times can be reduced by nearly an order of magnitude in some cases.
GLOPEQ: A New Computational Tool for the Phase and Chemical Equilibrium Problem
 Comput. Chem. Eng
, 1995
"... Calculation of phase and chemical equilibrium represents a crucial phase in the modeling of many separation processes. For conditions of constant temperature and pressure, a necessary and sufficient condition for the true equilibrium solution is that (i) the total Gibbs free energy of the system ..."
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Cited by 24 (4 self)
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Calculation of phase and chemical equilibrium represents a crucial phase in the modeling of many separation processes. For conditions of constant temperature and pressure, a necessary and sufficient condition for the true equilibrium solution is that (i) the total Gibbs free energy of the system be at its global minimum, or (ii) the minimum of the tangent plane distance function be nonnegative for all phase models used to represent the system. In this work, the goal is to obtain equilibrium solutions corresponding to a global minimum of the Gibbs free energy as efficiently as possible, for cases where the liquid phase or phases can be modeled by the NRTL, UNIQUAC, UNIFAC, Wilson, modified Wilson and ASOG equations. Vapor phases whose behavior can be described as ideal can also be handled. In achieving this goal, there are two distinct problems of relevance: (i) the minimization of the Gibbs free energy, denoted (G), and (ii) the minimization of the tangent plane distance fun...
Global Optimization for the Phase Stability Problem
 AIChE J
, 1994
"... The Gibbs tangent plane criterion has become an important tool in determining the quality of obtained solutions to the phase and chemical equilibrium problem. The ability to determine if a postulated solution is thermodynamically stable with respect to perturbations in any or all of the phases is ve ..."
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Cited by 20 (4 self)
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The Gibbs tangent plane criterion has become an important tool in determining the quality of obtained solutions to the phase and chemical equilibrium problem. The ability to determine if a postulated solution is thermodynamically stable with respect to perturbations in any or all of the phases is very useful in the search for the true equilibrium solution. Previous approaches have concentrated on finding the stationary points of the tangent plane distance function. However, no guarantee of obtaining all stationary points can be provided. These difficulties arise due to the complex and nonlinear nature of the models used to predict equilibrium. In this work, simpler formulations for the stability problem are presented for the special class of problems where nonideal liquid phases can be adequately modeled using the NRTL and UNIQUAC activity coefficient equations. It is shown how the global minimum of the tangent plane distance function can be obtained for this class of problems. The adv...
Global Optimization And Analysis For The Gibbs Free Energy Function Using The Unifac, Wilson And Asog Equations
 I&EC Res
, 1994
"... The Wilson equation for the excess Gibbs energy has found wide use in successfully representing the behavior of polar and nonpolar multicomponent mixtures with only binary parameters, but was incapable of predicting more than one liquid phase. The UNIFAC and ASOG group contribution methods do not ha ..."
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Cited by 16 (5 self)
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The Wilson equation for the excess Gibbs energy has found wide use in successfully representing the behavior of polar and nonpolar multicomponent mixtures with only binary parameters, but was incapable of predicting more than one liquid phase. The UNIFAC and ASOG group contribution methods do not have this limitation and can predict the presence of multiple liquid phases. The most important area of application of all these equations is in the prediction of phase equilibrium. The calculation of phase equilibrium involves two important problems: (i) the minimization of the Gibbs free energy, and (ii) the tangent plane stability criterion. Problem (ii), which can be implemented as the minimization of the tangent plane distance function, has found wide application in aiding the search for the global minimum of the Gibbs free energy. However, a drawback of all previous approaches is that they could not provide theoretical guarantees that the true equilibrium solution will be obtained. The g...
Reliable Computation of Phase Stability Using Interval Analysis: Cubic Equation of State Models
 Comput. Chem. Eng
, 1998
"... The reliable prediction of phase stability is a challenging computational problem in chemical process simulation, optimization and design. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. Conventional solution meth ..."
Abstract

Cited by 15 (9 self)
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The reliable prediction of phase stability is a challenging computational problem in chemical process simulation, optimization and design. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. Conventional solution methods are initialization dependent, and may fail by converging to trivial or nonphysical solutions or to a point that is a local but not global minimum. Thus there has been considerable recent interest in developing more reliable techniques for stability analysis. In this paper we demonstrate, using cubic equation of state models, a technique that can solve the phase stability problem with complete reliability. The technique, which is based on interval analysis, is initialization independent, and if properly implemented provides a mathematical guarantee that the correct solution to the phase stability problem has been found. 1
Reliable phase stability analysis for excess Gibbs energy models
 CHEM. ENG. SCI
, 2000
"... Because models used to represent the Gibbs energy of mixing are typically highly nonlinear, the reliable prediction of phase stability from such models is a challenging computational problem. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear ..."
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Cited by 13 (9 self)
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Because models used to represent the Gibbs energy of mixing are typically highly nonlinear, the reliable prediction of phase stability from such models is a challenging computational problem. The phase stability problem can be formulated either as a minimization problem or as an equivalent nonlinear equation solving problem. However, conventional solution methods are initialization dependent, and may fail by converging to trivial or nonphysical solutions or to a point that is a local but not global minimum. Since the correct prediction of phase stability is critical in the design and analysis of separation processes, there has been considerable recent interest in developing more reliable techniques for stability analysis. Recently we have demonstrated a technique that can solve the phase stability problem with complete reliability. The technique, which is based on interval analysis, is initialization independent, and if properly implemented provides a mathematical guarantee that the correct solution to the phase stability problem has been found. In this paper, we demonstrate the use of this technique in connection with excess Gibbs energy models. The NRTL and UNIQUAC models are used in examples, and larger problems than previously considered are solved. We also consider two means of enhancing the efficiency of the method, both based on sharpening the range of interval function evaluations. Results indicate that by using the enhanced method, computation times can be substantially reduced, especially for the larger problems.
Deterministic Global Optimization In Design, Control, And Computational Chemistry
 IMA Volumes in Mathematics and its Applications : Large Scale Optimization with Applications, Part II
, 1997
"... . This paper presents an overview of the deterministic global optimization approaches and their applications in the areas of Process Design, Control, and Computational Chemistry. The focus is on (i) decompositionbased primal dual methods, (ii) methods for generalized geometric programming problems, ..."
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Cited by 10 (7 self)
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. This paper presents an overview of the deterministic global optimization approaches and their applications in the areas of Process Design, Control, and Computational Chemistry. The focus is on (i) decompositionbased primal dual methods, (ii) methods for generalized geometric programming problems, and (iii) global optimization methods for general nonlinear programming problems. The classes of mathematical problems that are addressed range from indefinite quadratic programming to concave programs, to quadratically constrained problems, to polynomials, to general twice continuously differentiable nonlinear optimization problems. For the majority of the presented methods nondistributed global optimization approaches are discussed with the exception of decompositionbased methods where a distributed global optimization approach is presented. 1. Background. A significant effort has been expended in the last five decades toward theoretical and algorithmic studies of applications that arise...
Reliable Computation of Phase Stability and Equilibrium from the SAFT Equation of State
 Industrial & Engineering Chemistry Research
, 2001
"... In recent years, molecularlybased equations of state, as typified by the SAFT (statistical associating fluid theory) approach, have become increasingly popular tools for the modeling of phase behavior. However, whether using this, or even much simpler models, the reliable calculation of phase behav ..."
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Cited by 9 (6 self)
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In recent years, molecularlybased equations of state, as typified by the SAFT (statistical associating fluid theory) approach, have become increasingly popular tools for the modeling of phase behavior. However, whether using this, or even much simpler models, the reliable calculation of phase behavior from a given model can be a very challenging computational problem. A new methodology is described that is the first completely reliable technique for computing phase stability and equilibrium from the SAFT model. The method is based on interval analysis, in particular an interval Newton/generalized bisection algorithm, which provides a mathematical and computational guarantee of reliability, and is demonstrated using nonassociating, selfassociating, and crossassociating systems. New techniques are presented that can also be exploited when conventional pointvalued solution methods are used. These include the use of a volumebased problem formulation, in which the core thermodynamic function for phase equilibrium at constant temperature and pressure is the Helmholtz energy, and an approach for dealing with the internal iteration needed when there are association effects. This provides for direct, as opposed to iterative, determination of the derivatives of the internal variables. 1
Global Optimization of Chemical Processes using Stochastic Algorithms
 IN "STATE OF THE ART IN GLOBAL OPTIMIZATION", CA FLOUDAS AND PM PARDALOS (EDS
, 1996
"... Many systems in chemical engineering are difficult to optimize using gradientbased algorithms. These include process models with multimodalobjective functions and discontinuities. Herein, a stochastic algorithm is applied for the optimal design of a fermentation process, to determine multiphase equ ..."
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Cited by 8 (2 self)
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Many systems in chemical engineering are difficult to optimize using gradientbased algorithms. These include process models with multimodalobjective functions and discontinuities. Herein, a stochastic algorithm is applied for the optimal design of a fermentation process, to determine multiphase equilibria, for the optimal control of a penicillin reactor, for the optimal control of a nondifferentiable system, and for the optimization of a catalyst blend in a tubular reactor. The advantages of the algorithm for the efficient and reliable location of global optima are examined. The properties of these algorithms, as applied to chemical processes, are considered, with emphasis on the ease of handling constraints and the ease of implementation and interpretation of results. For the five processes, the efficiency of computation is improved compared with selected stochastic and deterministic algorithms. Results closer to the global optimum are reported for the optimal control of the penicillin reactor and the nondifferentiable system.
Phase Stability with Cubic Equations of State: A Global Optimization Approach
 AIChE J
, 2000
"... Calculation of phase and chemical equilibria is of fundamental importance for the design and simulation of chemical processes. Methods that minimize the Gibbs free energy provide equilibrium solutions that are only candidates for the true equilibrium solution. This is because the number and type of ..."
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Cited by 7 (0 self)
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Calculation of phase and chemical equilibria is of fundamental importance for the design and simulation of chemical processes. Methods that minimize the Gibbs free energy provide equilibrium solutions that are only candidates for the true equilibrium solution. This is because the number and type of phases must be assumed before the Gibbs energy minimization problem can be formulated. The tangent plane stability criterion is a means of determining the stability of a candidate equilibrium solution. The Gibbs energy minimization problem and the tangent plane stability problem are very challenging due to the highly nonlinear thermodynamic functions that are used. In this work the goal is to develop a global optimization approach for the tangent plane stability problem that (i) provides a theoretical guarantee about the stability of the candidate equilibrium solution and (ii) is computationally efficient. Cubic equations of state are used in this approach due to their ability to accurately ...