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Calculation of chemical and phase equilibrium based on stability analysis by QBB algorithm: application to NRTL equation
Alternative TitleChem. Eng. Sci.
Zhu, YS; Inoue, K
2001-12-01
Source PublicationCHEMICAL ENGINEERING SCIENCE
ISSN0009-2509
Volume56Issue:24Pages:6915-6931
AbstractThe Gibbs tangent plane criterion is of crucial importance to confirm the reliability of the solution obtained for the chemical and phase equilibrium (CPE) problem, and it consequently facilitates the search for the true equilibrium state if a postulated solution is thermodynamically unstable. However, the nonconvex and nonlinear natures of the thermodynamic models, which are the necessary conditions in order to describe the chemical and phase equilibrium problems, make the application of the deterministic global optimization techniques to minimize the tangent plane distance function (TPDF) become very difficult. In this paper, a general quadratic underestimation function based branch and bound (QBB) algorithm is developed by the construction of a rigorous underestimator for TPDF, which is the sum of the original convex part in the TPDF and a quadratic underestimation function of the generic nonconvex part upon the basis of the maximal eigenvalue estimation of its interval Hessian matrix. The linear constraints, especially the simplex feasible region, provide the novel compact partition in the above framework and mathematically guarantee the epsilon -global convergence of this global optimization algorithm together with the rigorous underestimator obtained by interval analysis. The phase equilibrium compositions are then calculated by the Newton-Raphson method. The preliminary results for three ternary systems with up to two or three phases described by NRTL activity coefficient equation showed that the novel QBB algorithm could solve the global stability problem effectively. (C) 2001 Elsevier Science Ltd. All rights reserved.; The Gibbs tangent plane criterion is of crucial importance to confirm the reliability of the solution obtained for the chemical and phase equilibrium (CPE) problem, and it consequently facilitates the search for the true equilibrium state if a postulated solution is thermodynamically unstable. However, the nonconvex and nonlinear natures of the thermodynamic models, which are the necessary conditions in order to describe the chemical and phase equilibrium problems, make the application of the deterministic global optimization techniques to minimize the tangent plane distance function (TPDF) become very difficult. In this paper, a general quadratic underestimation function based branch and bound (QBB) algorithm is developed by the construction of a rigorous underestimator for TPDF, which is the sum of the original convex part in the TPDF and a quadratic underestimation function of the generic nonconvex part upon the basis of the maximal eigenvalue estimation of its interval Hessian matrix. The linear constraints, especially the simplex feasible region, provide the novel compact partition in the above framework and mathematically guarantee the epsilon -global convergence of this global optimization algorithm together with the rigorous underestimator obtained by interval analysis. The phase equilibrium compositions are then calculated by the Newton-Raphson method. The preliminary results for three ternary systems with up to two or three phases described by NRTL activity coefficient equation showed that the novel QBB algorithm could solve the global stability problem effectively. (C) 2001 Elsevier Science Ltd. All rights reserved.
KeywordGibbs Free Energy Qbb Phase Equilibria Stability Analysis Global Optimization Tpdf
SubtypeArticle
WOS HeadingsScience & Technology ; Technology
URL查看原文
Indexed BySCI
Language英语
WOS KeywordGLOBAL OPTIMIZATION METHOD ; EQUAL-AREA RULE ; DIFFERENTIABLE CONSTRAINED NLPS ; THERMODYNAMIC ENERGY ANALYSIS ; CRITICAL-POINT CALCULATIONS ; LIQUID-LIQUID EQUILIBRIUM ; ISOTHERMAL FLASH PROBLEM ; GIBBS FREE-ENERGY ; ALPHA-BB ; MULTIPHASE EQUILIBRIA
WOS Research AreaEngineering
WOS SubjectEngineering, Chemical
WOS IDWOS:000172815800012
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Cited Times:17[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Version出版稿
Identifierhttp://ir.ipe.ac.cn/handle/122111/5734
Collection研究所(批量导入)
Affiliation1.Chinese Acad Sci, Inst Chem Met, Beijing 100080, Peoples R China
2.Saga Univ, Dept Appl Chem, Saga 8408502, Japan
Recommended Citation
GB/T 7714
Zhu, YS,Inoue, K. Calculation of chemical and phase equilibrium based on stability analysis by QBB algorithm: application to NRTL equation[J]. CHEMICAL ENGINEERING SCIENCE,2001,56(24):6915-6931.
APA Zhu, YS,&Inoue, K.(2001).Calculation of chemical and phase equilibrium based on stability analysis by QBB algorithm: application to NRTL equation.CHEMICAL ENGINEERING SCIENCE,56(24),6915-6931.
MLA Zhu, YS,et al."Calculation of chemical and phase equilibrium based on stability analysis by QBB algorithm: application to NRTL equation".CHEMICAL ENGINEERING SCIENCE 56.24(2001):6915-6931.
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