A Generic Global Optimization Algorithm for the Chemical and Phase Equilibrium Problem
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 mb independent conserved quant...
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| Vydané v: | Journal of global optimization Ročník 12; číslo 4; s. 325 - 351 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Dordrecht
Springer Nature B.V
01.06.1998
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| ISSN: | 0925-5001, 1573-2916 |
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| Abstract | 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 mb independent conserved quantities, where mb=ns when no reaction is possible and mb ≤ 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 tangent-plane 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 mb(ns-1) dimensions) to a finite sequence of local optimization steps inK(ns-1) -space, K ≤ mb, and global optimization steps in (ns-1)-space. The global step uses the tangent-plane criterion to determine whether the current solution is optimal, and, if it is not, it finds an improved feasible solution either with the same number of phases or with one added phase. The global step also determines what class of phase (e.g. liquid or vapour) is to be added, if any phase is to be added. Given a local minimization procedure returning a Kuhn-Tucker point and a global optimization procedure (for a lower-dimensional search space) returning a global minimum, the algorithm is proved to converge to a global minimum in a finite number of the above local and global steps. The theory is supported by encouraging computational results. |
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| AbstractList | 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 mb independent conserved quantities, where mb=ns when no reaction is possible and mb ≤ 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 tangent-plane 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 mb(ns-1) dimensions) to a finite sequence of local optimization steps inK(ns-1) -space, K ≤ mb, and global optimization steps in (ns-1)-space. The global step uses the tangent-plane criterion to determine whether the current solution is optimal, and, if it is not, it finds an improved feasible solution either with the same number of phases or with one added phase. The global step also determines what class of phase (e.g. liquid or vapour) is to be added, if any phase is to be added. Given a local minimization procedure returning a Kuhn-Tucker point and a global optimization procedure (for a lower-dimensional search space) returning a global minimum, the algorithm is proved to converge to a global minimum in a finite number of the above local and global steps. The theory is supported by encouraging computational results. |
| Author | McKinnon, Ken Mongeau, Marcel |
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| CitedBy_id | crossref_primary_10_1007_s13370_013_0181_3 crossref_primary_10_1023_A_1008365206132 crossref_primary_10_1016_j_compchemeng_2014_01_012 crossref_primary_10_1016_S0098_1354_99_80231_2 crossref_primary_10_1016_j_compchemeng_2011_07_009 crossref_primary_10_1016_j_compchemeng_2014_06_009 crossref_primary_10_1016_S0378_3812_01_00528_3 crossref_primary_10_1137_080719613 crossref_primary_10_1016_j_compchemeng_2007_12_001 crossref_primary_10_1023_A_1018968800262 crossref_primary_10_1007_s10589_009_9262_5 crossref_primary_10_1016_S0098_1354_00_00600_1 crossref_primary_10_1016_S1385_8947_00_00276_X crossref_primary_10_1002_aic_11490 crossref_primary_10_1080_00986440701293991 crossref_primary_10_1021_acs_iecr_7b00317 crossref_primary_10_1137_100788458 crossref_primary_10_1016_j_fluid_2008_04_015 crossref_primary_10_1016_j_compchemeng_2005_02_006 crossref_primary_10_1016_j_fluid_2008_08_017 crossref_primary_10_1016_j_geoen_2024_213542 crossref_primary_10_1007_s13370_011_0035_9 crossref_primary_10_1007_s10898_008_9332_8 crossref_primary_10_1016_j_fluid_2010_08_001 |
| Cites_doi | 10.1002/aic.690250610 10.1016/0098-1354(94)00106-5 10.1287/opre.32.1.70 10.1016/0098-1354(81)87005-6 10.1007/BFb0120932 10.1016/0378-3812(82)85001-2 10.1515/9781400862528.561 10.2118/9806-PA 10.1002/cjce.5450670317 10.1137/1.9781611971200 10.1016/0378-3812(84)80013-8 10.1007/BF00934810 10.1016/0098-1354(95)00250-2 10.1002/aic.690390421 10.1007/BF01096454 10.1016/0378-3812(91)80010-S 10.1002/aic.690330606 10.1002/aic.690410715 10.1137/0805039 10.1002/cjce.5450610414 10.1016/0098-1354(90)80020-C 10.1137/0113020 10.1016/0009-2509(87)87051-3 10.1007/BF00939667 10.1023/A:1018968800262 10.1002/aic.690351107 10.1007/978-1-4613-3437-8_23 10.1016/0378-3812(82)85002-4 |
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| Title | A Generic Global Optimization Algorithm for the Chemical and Phase Equilibrium Problem |
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