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18
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 ..."
Abstract

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...
Floudas, Global Optimization and Analysis for the Gibbs Free Energy Function for the UNIFAC
 and ASOG Equations, Industrial and Engineering Chemistry Research 34
, 1995
"... ..."
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 ..."
Abstract

Cited by 14 (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...
Global Optimization of Chemical Processes using Stochastic Algorithms
 IN &QUOT;STATE OF THE ART IN GLOBAL OPTIMIZATION&QUOT;, 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 9 (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.
Reliable computation of phase stability and equilibrium from the SAFT equation of state
 Industrial and Engineering Chemistry Research
, 2002
"... ..."
A Generic Global Optimization Algorithm for the Chemical and Phase Equilibrium Problem
 J. Global Optim
, 1998
"... . This paper addresses the problem of finding the number, K, of phases present at equilibrium and their composition, in a chemical mixture of ns substances. This corresponds to the global minimum of the Gibbs free energy of the system, subject to constraints representing m b independent conserved q ..."
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Cited by 7 (0 self)
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. This paper addresses the problem of finding the number, K, of phases present at equilibrium and their composition, in a chemical mixture of ns substances. This corresponds to the global minimum of the Gibbs free energy of the system, subject to constraints representing m b independent conserved quantities, where m b = ns when no reaction is possible and m b ne + 1 when reaction is possible and ne is the number of elements present. After surveying previous work in the field and pointing out the main issues, we extend the necessary and sufficient condition for global optimality based on the "reaction tangentplane criterion", to the case involving different thermodynamical models (multiple phase classes). We then present an algorithmic approach that reduces this global optimization problem (involving a search space of m b (ns \Gamma 1) dimensions) to a finite sequence of local optimization steps in K(ns \Gamma 1)space, K m b , and global optimization steps in (ns \Gamma 1)space. T...