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Calculation of liquid-liquid equilibrium based on the global stability analysis for ternary mixtures by using a novel branch and bound algorithm: Application to UNIQUAC equation | |
Alternative Title | Ind. Eng. Chem. Res. |
Zhu, YS; Xu, ZH | |
1999-09-01 | |
Source Publication | INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH |
ISSN | 0888-5885 |
Volume | 38Issue:9Pages:3549-3556 |
Abstract | In this paper, a novel branch and bound algorithm based on the idea of Horst (Math Program. 1976, 10, 312) was developed to minimize the tangent plane distance function (TPDF) of the stability analysis problem where nonideal liquid phases are described by the UNIQUAC activity coefficient equation. Some simple transformations were used to construct the DC (i.e., difference of two convex functions) programming of TPDF that does not rely on any newly introduced parameters except the inner ones of the UNIQUAC equation. A compact partition of the feasible space and a valid underestimation function of the TPDF depending on the linear characteristics of the stability analysis problem were developed to guarantee the new branch and bound algorithm obtaining the epsilon-global convergence to the global solution of the TPDF. In comparison with the algorithms presented by Sun and Seider (Fluid Phase Equilib. 1995, 103, 213) and McDonald and Floudas (AlChE J. 1995, 41, 1798), the novel branch and bound algorithm is slightly slower; however, it can provide complete reliability for solving the phase stability analysis problem. Liquid-liquid equilibrium compositions were then calculated by the Newton-Raphson method (Fluid Phase Equilib. 1982, 9, 21) on the basis of the global minimum of TPDF. The preliminary calculation results for three ternary systems showed that the novel branch and bound algorithm can solve the global stability problem effectively.; In this paper, a novel branch and bound algorithm based on the idea of Horst (Math Program. 1976, 10, 312) was developed to minimize the tangent plane distance function (TPDF) of the stability analysis problem where nonideal liquid phases are described by the UNIQUAC activity coefficient equation. Some simple transformations were used to construct the DC (i.e., difference of two convex functions) programming of TPDF that does not rely on any newly introduced parameters except the inner ones of the UNIQUAC equation. A compact partition of the feasible space and a valid underestimation function of the TPDF depending on the linear characteristics of the stability analysis problem were developed to guarantee the new branch and bound algorithm obtaining the epsilon-global convergence to the global solution of the TPDF. In comparison with the algorithms presented by Sun and Seider (Fluid Phase Equilib. 1995, 103, 213) and McDonald and Floudas (AlChE J. 1995, 41, 1798), the novel branch and bound algorithm is slightly slower; however, it can provide complete reliability for solving the phase stability analysis problem. Liquid-liquid equilibrium compositions were then calculated by the Newton-Raphson method (Fluid Phase Equilib. 1982, 9, 21) on the basis of the global minimum of TPDF. The preliminary calculation results for three ternary systems showed that the novel branch and bound algorithm can solve the global stability problem effectively. |
Keyword | Gibbs Free-energy Equal-area Rule Critical-point Calculations Isothermal Flash Problem Fluid-phase Equilibria Chemical-equilibrium Multiphase Equilibria Cubic Equation State Models Optimization |
Subtype | Article |
WOS Headings | Science & Technology ; Technology |
URL | 查看原文 |
Indexed By | SCI |
Language | 英语 |
WOS Keyword | GIBBS FREE-ENERGY ; EQUAL-AREA RULE ; CRITICAL-POINT CALCULATIONS ; ISOTHERMAL FLASH PROBLEM ; FLUID-PHASE EQUILIBRIA ; CHEMICAL-EQUILIBRIUM ; MULTIPHASE EQUILIBRIA ; CUBIC EQUATION ; STATE MODELS ; OPTIMIZATION |
WOS Research Area | Engineering |
WOS Subject | Engineering, Chemical |
WOS ID | WOS:000082525700044 |
Citation statistics | |
Document Type | 期刊论文 |
Version | 出版稿 |
Identifier | http://ir.ipe.ac.cn/handle/122111/5868 |
Collection | 研究所（批量导入） |
Affiliation | Chinese Acad Sci, Inst Chem Met, Beijing 100080, Peoples R China |
Recommended Citation GB/T 7714 | Zhu, YS,Xu, ZH. Calculation of liquid-liquid equilibrium based on the global stability analysis for ternary mixtures by using a novel branch and bound algorithm: Application to UNIQUAC equation[J]. INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH,1999,38(9):3549-3556. |
APA | Zhu, YS,&Xu, ZH.(1999).Calculation of liquid-liquid equilibrium based on the global stability analysis for ternary mixtures by using a novel branch and bound algorithm: Application to UNIQUAC equation.INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH,38(9),3549-3556. |
MLA | Zhu, YS,et al."Calculation of liquid-liquid equilibrium based on the global stability analysis for ternary mixtures by using a novel branch and bound algorithm: Application to UNIQUAC equation".INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 38.9(1999):3549-3556. |
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