Calculation of chemical and phase equilibrium based on stability analysis by QBB algorithm: application to NRTL equation
文献类型：期刊论文
| 作者 | Zhu, YS; Inoue, K |
| 刊名 | CHEMICAL ENGINEERING SCIENCE
 |
| 出版日期 | 2001-12-01 |
| 卷号 | 56期号:24页码:6915-6931 |
| 关键词 | Gibbs free energy QBB phase equilibria stability analysis global optimization TPDF |
| ISSN号 | 0009-2509 |
| 其他题名 | Chem. Eng. Sci. |
| 中文摘要 | 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. |
| 英文摘要 | 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. |
| WOS标题词 | Science & Technology ; Technology |
| 类目[WOS] | Engineering, Chemical |
| 研究领域[WOS] | Engineering |
| 关键词[WOS] | GLOBAL 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 |
| 收录类别 | SCI |
| 原文出处 | |
| 语种 | 英语 |
| WOS记录号 | WOS:000172815800012 |
| 公开日期 | 2013-11-14 |
| 版本 | 出版稿 |
| 源URL | [http://ir.ipe.ac.cn/handle/122111/5734]  |
| 专题 | 过程工程研究所_研究所（批量导入） |
| 作者单位 | 1.Chinese Acad Sci, Inst Chem Met, Beijing 100080, Peoples R China 2.Saga Univ, Dept Appl Chem, Saga 8408502, Japan |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：过程工程研究所
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