{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T05:26:37Z","timestamp":1743053197091,"version":"3.40.3"},"publisher-location":"Boston, MA","reference-count":34,"publisher":"Springer US","isbn-type":[{"type":"print","value":"9780387747583"},{"type":"electronic","value":"9780387747590"}],"license":[{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008]]},"DOI":"10.1007\/978-0-387-74759-0_471","type":"book-chapter","created":{"date-parts":[[2008,8,25]],"date-time":"2008-08-25T11:10:42Z","timestamp":1219662642000},"page":"2731-2738","source":"Crossref","is-referenced-by-count":0,"title":["Optimality Criteria for Multiphase Chemical Equilibrium"],"prefix":"10.1007","author":[{"given":"William R.","family":"Smith","sequence":"first","affiliation":[]},{"given":"Ronald W.","family":"Missen","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"471_CR1_471","doi-asserted-by":"crossref","first-page":"5979","DOI":"10.1063\/1.459482","volume":"93","author":"R.A. Alberty","year":"1990","unstructured":"Alberty RA (1990) Equilibrium distributions of isomer groups in homologous series of hydrocarbons at a\u00a0specified partial pressure of molecular hydrogen. J\u00a0Chem Phys 93:5979\u20135982","journal-title":"J. Chem. Phys."},{"key":"471_CR2_471","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0010-8545(98)00260-4","volume":"184","author":"L. Alderight","year":"1999","unstructured":"Alderight L, Gans P, Ienco A, Peters D, Sabatini A, Vacca A (1999) Hyperquad simulation and speciation (HySS). A\u00a0utility program for the investigation of equilibria involving soluble and partially soluble species. Coord Chem Rev 184:311\u2013318","journal-title":"Coord. Chem. Rev."},{"key":"471_CR3_471","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195064643.001.0001","volume-title":"Thermodynamics in geochemistry: The equilibrium model","author":"G.M. Anderson","year":"1993","unstructured":"Anderson GM, Crerar DA (1993) Thermodynamics in geochemistry: The equilibrium model. Oxford University Press, Oxford"},{"key":"471_CR4_471","doi-asserted-by":"crossref","first-page":"731","DOI":"10.2118\/9806-PA","volume":"22","author":"L.E. Baker","year":"1982","unstructured":"Baker LE, Pierce AC, Luks KD (1982) Gibbs energy analysis of phase equilibria. Soc Petrol Eng 22:731\u2013742","journal-title":"Soc. Petrol. Engin."},{"key":"471_CR5_471","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1002\/aic.690220324","volume":"22","author":"U. Block","year":"1976","unstructured":"Block U, Hegner B (1976) Development and application of a\u00a0simulation model for three-phase distillation. AIChE J 22:582","journal-title":"AIChE J."},{"key":"471_CR6_471","doi-asserted-by":"crossref","first-page":"2428","DOI":"10.1021\/j100293a044","volume":"91","author":"E.L. Cheluget","year":"1987","unstructured":"Cheluget EL, Missen RW, Smith WR (1987) Computer calculation of ionic equilibria using species- or reaction-related thermodynamic data. J\u00a0Phys Chem 91:2428\u20132432","journal-title":"J. Phys. Chem."},{"key":"471_CR7_471","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1016\/0016-7037(87)90199-2","volume":"51","author":"C.E. Harvie","year":"1987","unstructured":"Harvie CE, Greenberg JP, Weare JH (1987) A\u00a0chemical equilibrium algorithm for highly non-ideal multiphase systems: Free energy minimization. Geochim Cosmochim Acta 51:1045\u20131057","journal-title":"Geochim. Cosmochim. Acta"},{"key":"471_CR8_471","volume-title":"The equilibrium of gaseous systems","author":"R. Holub","year":"1976","unstructured":"Holub R, Vonka P (1976) The equilibrium of gaseous systems. Reidel, London"},{"key":"471_CR9_471","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0378-3812(95)02828-5","volume":"118","author":"Y. Jiang","year":"1996","unstructured":"Jiang Y, Chapman GR, Smith WR (1996) On the geometry of chemical reaction and phase equilibria. Fluid Phase Equilib 118:77\u2013102","journal-title":"Fluid Phase Equilib."},{"key":"471_CR10_471","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1109\/TPS.1985.4316478","volume":"PS-13","author":"P. Kovitya","year":"1985","unstructured":"Kovitya P (1985) Physical properties of high-temperature plasmas of hydrogen and copper in the temperature range 5000\u201360000 K. IEEE Trans Plasma Sci PS-13:587\u2013594","journal-title":"IEEE Trans. Plasma Sci."},{"key":"471_CR11_471","doi-asserted-by":"crossref","first-page":"1183","DOI":"10.1016\/S0098-1354(99)00283-5","volume":"23","author":"Y.P. Lee","year":"1999","unstructured":"Lee YP, Rangaiah GP, Luus R (1999) Phase and chemical equilibrium calculations by direct search optimization. Comput Chem Eng 23:1183\u20131191","journal-title":"Computers Chem. Engin."},{"key":"471_CR12_471","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1021\/i160046a025","volume":"12","author":"W.D. Madeley","year":"1973","unstructured":"Madeley WD, Toguri JM (1973) Computing chemical equilibrium compositions in multiphase systems. Industr Eng Chem Fundam 12:261\u2013262","journal-title":"Industr. Engin. Chem. Fundam."},{"key":"471_CR13_471","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0098-1354(95)00250-2","volume":"21","author":"C.M. McDonald","year":"1997","unstructured":"McDonald CM, Floudas CA (1997) GLOPEQ: A\u00a0new computational tool for the phase and chemical equilibrium problem. Comput Chem Eng 21:1\u201323","journal-title":"Computers Chem. Engin."},{"key":"471_CR14_471","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/978-1-4613-3437-8_23","volume-title":"State of the Art in Global Optimization","author":"K.I.M. McKinnon","year":"1996","unstructured":"McKinnon KIM, Millar C, Mongeau M (1996) Global optimization for the chemical and phase equilibrium problems using interval analysis. State of the Art in Global Optimization. In: Floudas CA, Pardalos PM (eds) Kluwer, Dordrecht, pp\u00a0365\u2013381"},{"key":"471_CR15_471","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0378-3812(82)85001-2","volume":"9","author":"M.L. Michelsen","year":"1982","unstructured":"Michelsen ML (1982) The isothermal flash problem. Part I: Stability. Fluid Phase Equilib 9:1\u201319","journal-title":"Fluid Phase Equilib."},{"key":"471_CR16_471","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1021\/ed067p876","volume":"67","author":"R.W. Missen","year":"1990","unstructured":"Missen RW, Smith WR (1990) The permanganate-peroxide reaction: Illustration of a\u00a0stoichiometric restriction. J\u00a0Chem Educ 67:876\u2013877","journal-title":"J. Chem. Educ."},{"key":"471_CR17_471","doi-asserted-by":"crossref","first-page":"3073","DOI":"10.1039\/a608196g","volume":"93","author":"I. Nezbeda","year":"1997","unstructured":"Nezbeda I, Kolafa J, Smith WR (1997) Global phase diagrams of binary mixtures: Systematic basis for describing types of phase equilibrium phenomena. J\u00a0Chem Soc Faraday Trans 93:3073\u20133080","journal-title":"J. Chem. Soc. Faraday Trans."},{"key":"471_CR18_471","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0378-3812(85)90059-7","volume":"21","author":"L.X. Nghiem","year":"1985","unstructured":"Nghiem LX, Li YK, Heidemann RA (1985) Application of the tangent plane criterion to saturation pressure and temperature computations. Fluid Phase Equilib 21:39\u201360","journal-title":"Fluid Phase Equilib."},{"key":"471_CR19_471","doi-asserted-by":"crossref","first-page":"1884","DOI":"10.1021\/ie00096a022","volume":"28","author":"G.W. Norval","year":"1989","unstructured":"Norval GW, Phillips MJ, Missen RW, Smith WR (1989) Applications of equilibrium sensitivity analysis to aromatization processes. Industr Eng Chem Res 28:1884\u20131887","journal-title":"Industr. Engin. Chem. Res."},{"key":"471_CR20_471","doi-asserted-by":"crossref","first-page":"1184","DOI":"10.1002\/cjce.5450690519","volume":"69","author":"G.W. Norval","year":"1991","unstructured":"Norval GW, Phillips MJ, Missen RW, Smith WR (1991) Constrained chemical equilibrium and incompletely speciied elemental abundance data. Canad J Chem Eng 69:1184\u20131192","journal-title":"Canad. J. Chem. Engin."},{"key":"471_CR21_471","volume-title":"Stoichiometry and thermodynamics of metallurgical processes","author":"Y.K. Rao","year":"1985","unstructured":"Rao YK (1985) Stoichiometry and thermodynamics of metallurgical processes. Cambridge University Press, Cambridge"},{"key":"471_CR22_471","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1023\/A:1019163628470","volume":"22","author":"D. Reynolds","year":"1997","unstructured":"Reynolds D, Mulholland AJ, Gomatam J (1997) Calculation of chemical and phase equilibria via simulated annealing. J\u00a0Math Chem 22:25\u201337","journal-title":"J. Math. Chem."},{"key":"471_CR23_471","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0003-2697(90)90221-T","volume":"191","author":"C.A. Royer","year":"1990","unstructured":"Royer CA, Smith WR, Beecham JM (1990) Analysis of binding in macromolecular complexes: A\u00a0generalized approach. Analyt Biochem 191:287\u2013294","journal-title":"Analyt. Biochem."},{"key":"471_CR24_471","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/S0378-3812(96)90039-4","volume":"123","author":"W.D. Seider","year":"1996","unstructured":"Seider WD, Widagdo S (1996) Multiphase equilibria of reactive systems. Fluid Phase Equilib 123:283\u2013303","journal-title":"Fluid Phase Equilib."},{"key":"471_CR25_471","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1002\/aic.690390421","volume":"39","author":"J.V. Smith","year":"1993","unstructured":"Smith JV, Missen RW, Smith WR (1993) General optimality criteria for multiphase multireaction chemical equilibrium. AIChE J 39:707\u2013710","journal-title":"AIChE J."},{"key":"471_CR26_471","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1002\/cjce.5450470120","volume":"47","author":"W.R. Smith","year":"1969","unstructured":"Smith WR (1969) The effects of changes in problem parameters on chemical equilibrium calculations. Canad J Chem Eng 47:95\u201397","journal-title":"Canad. J. Chem. Engin."},{"key":"471_CR27_471","volume-title":"Chemical reaction equilibrium analysis: Theory and algorithms","author":"W.R. Smith","year":"1982","unstructured":"Smith WR, Missen RW (1982) Chemical reaction equilibrium analysis: Theory and algorithms. Wiley\/Interscience, New York. reprinted with corrections: Krieger, 1991"},{"key":"471_CR28_471","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1002\/cjce.5450660409","volume":"66","author":"W.R. Smith","year":"1988","unstructured":"Smith WR, Missen RW (1988) Strategies for solving the chemical equilibrium problem and an efficient microcomputer-based algorithm. Canad J Chem Eng 66:591\u2013598","journal-title":"Canad. J. Chem. Engin."},{"key":"471_CR29_471","unstructured":"Smith WR, Sikaneta I, Missen RW (1998) Chemical reaction stoichiometry (CRS)"},{"key":"471_CR30_471","doi-asserted-by":"crossref","first-page":"3019","DOI":"10.1063\/1.466443","volume":"100","author":"W.R. Smith","year":"1994","unstructured":"Smith WR, Triska B (1994) The reaction ensemble method for the computer simulation of chemical and phase equilibria. I. Theory and basic examples. J\u00a0Chem Phys 100:3019\u20133027","journal-title":"J. Chem. Phys."},{"key":"471_CR31_471","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/0378-3812(94)02579-P","volume":"103","author":"A.C. Sun","year":"1995","unstructured":"Sun AC, Seider WD (1995) Homotopy-continuation method for stability analysis in the global minimization of the Gibbs free energy. Fluid Phase Equilib 103:213\u2013249","journal-title":"Fluid Phase Equilib."},{"key":"471_CR32_471","first-page":"1","volume":"21","author":"S. Ung","year":"1997","unstructured":"Ung S, Doherty MF (1997) Theory of phase equilibria in multireaction systems. Comput Chem Eng 21:1\u201323","journal-title":"Computers Chem. Engin."},{"key":"471_CR33_471","volume-title":"The computation of chemical equilibria","author":"F. Van Zeggeren","year":"1970","unstructured":"Van Zeggeren F, Storey SH (1970) The computation of chemical equilibria. Cambridge University Press, Cambridge"},{"key":"471_CR34_471","unstructured":"http:\/\/www\/uic.edu\/~mansoori\/_Thermodynamic.Data.and.Property_html. (1999)"}],"container-title":["Encyclopedia of Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-0-387-74759-0_471","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,11]],"date-time":"2024-07-11T10:07:53Z","timestamp":1720692473000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-0-387-74759-0_471"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"ISBN":["9780387747583","9780387747590"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-0-387-74759-0_471","relation":{},"subject":[],"published":{"date-parts":[[2008]]}}}