{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T01:24:56Z","timestamp":1767835496267,"version":"3.49.0"},"reference-count":83,"publisher":"Springer Science and Business Media LLC","issue":"49","license":[{"start":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T00:00:00Z","timestamp":1730160000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T00:00:00Z","timestamp":1730160000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Guru Gobind Singh Indraprastha University, Delhi","award":["F. No. GGSIPU\/FRGS\/2022\/1223\/35"],"award-info":[{"award-number":["F. No. GGSIPU\/FRGS\/2022\/1223\/35"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Environ Sci Pollut Res"],"DOI":"10.1007\/s11356-024-35257-8","type":"journal-article","created":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T12:03:10Z","timestamp":1730203390000},"page":"28071-28092","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Parameter estimation in vapor\u2013liquid equilibrium modeling of compounds related to biodiesel production using opposite point-based differential evolution algorithm"],"prefix":"10.1007","volume":"32","author":[{"given":"Swati","family":"Yadav","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5009-6594","authenticated-orcid":false,"given":"Rakesh","family":"Angira","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,29]]},"reference":[{"key":"35257_CR1","doi-asserted-by":"publisher","first-page":"116","DOI":"10.1002\/aic.690210115","volume":"21","author":"DS Abrams","year":"1975","unstructured":"Abrams DS, Prausnitz JM (1975) Statistical thermodynamics of liquid mixtures: a new expression for the excess gibbs energy of partly or completely miscible systems. AIChE J 21:116\u2013128. https:\/\/doi.org\/10.1002\/aic.690210115","journal-title":"AIChE J"},{"key":"35257_CR2","doi-asserted-by":"publisher","first-page":"3831","DOI":"10.1016\/j.aej.2021.09.013","volume":"61","author":"MF Ahmad","year":"2022","unstructured":"Ahmad MF, Isa NAM, Lim WH, Ang KM (2022) Differential evolution: a recent review based on state-of-the-art works. Alex Eng J 61:3831\u20133872. https:\/\/doi.org\/10.1016\/j.aej.2021.09.013","journal-title":"Alex Eng J"},{"key":"35257_CR3","doi-asserted-by":"publisher","first-page":"117688","DOI":"10.1016\/j.fuel.2020.117688","volume":"271","author":"AA Albuquerque","year":"2020","unstructured":"Albuquerque AA, Ng FTT, Danielski L, Stragevitch L (2020) Phase equilibrium modeling in biodiesel production by reactive distillation. Fuel 271:117688. https:\/\/doi.org\/10.1016\/j.fuel.2020.117688","journal-title":"Fuel"},{"key":"35257_CR4","doi-asserted-by":"publisher","first-page":"2768","DOI":"10.1109\/tcyb.2016.2617301","volume":"47","author":"MZ Ali","year":"2016","unstructured":"Ali MZ, Awad NZ, Suganthan PN, Reynolds RG (2016) An adaptive multipopulation differential evolution with dynamic population reduction. IEEE Trans Cybern 47:2768\u20132779. https:\/\/doi.org\/10.1109\/tcyb.2016.2617301","journal-title":"IEEE Trans Cybern"},{"key":"35257_CR5","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1002\/aic.690240103","volume":"24","author":"TF Anderson","year":"1978","unstructured":"Anderson TF, Abrams DS, Grens EA II (1978) Evaluation of parameters for thermodynamic models. AIChE J 24:20\u201329. https:\/\/doi.org\/10.1002\/aic.690240103","journal-title":"AIChE J"},{"key":"35257_CR6","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1021\/je00018a036","volume":"40","author":"A Arce","year":"1995","unstructured":"Arce A, Blanco A, Martinez-Ageitos J, Soto A (1995) Isobaric vapor-liquid equilibria of methanol + hexyl acetate and ethanol + hexyl acetate. J Chem Eng Data 40:515\u2013518","journal-title":"J Chem Eng Data"},{"key":"35257_CR7","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1021\/acs.iecr.7b04195","volume":"57","author":"PF Arce","year":"2018","unstructured":"Arce PF, Vieira NF, Igarashi EMS (2018) Thermodynamic modeling and simulation of biodiesel systems at supercritical conditions. Ind Eng Chem Res 57:751\u2013767. https:\/\/doi.org\/10.1021\/acs.iecr.7b04195","journal-title":"Ind Eng Chem Res"},{"key":"35257_CR8","doi-asserted-by":"publisher","first-page":"460","DOI":"10.1016\/j.fuel.2019.04.170","volume":"253","author":"A Asoodeh","year":"2019","unstructured":"Asoodeh A, Eslami F, Sadrameli SM (2019) Liquid-liquid equilibria of systems containing linseed oil biodiesel + methanol + glycerol: Experimental data and modeling. Fuel 253:460\u2013473. https:\/\/doi.org\/10.1016\/j.fuel.2019.04.170","journal-title":"Fuel"},{"key":"35257_CR9","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1016\/j.eswa.2016.05.009","volume":"60","author":"D Bajer","year":"2016","unstructured":"Bajer D, Martinovic G, Brest J (2016) A population initialization method for evolutionary algorithms based on clustering and Cauchy deviates. Expert Syst Appl 60:294\u2013310. https:\/\/doi.org\/10.1016\/j.eswa.2016.05.009","journal-title":"Expert Syst Appl"},{"key":"35257_CR10","doi-asserted-by":"publisher","first-page":"2402","DOI":"10.1021\/acs.jced.7b00967","volume":"63","author":"IH Bell","year":"2018","unstructured":"Bell IH, Satyro M, Lemmon EW (2018) Consistent Twu parameters for more than 2500 pure fluids from critically evaluated experimental data. J Chem Eng Data 63:2402\u20132409. https:\/\/doi.org\/10.1021\/acs.jced.7b00967","journal-title":"J Chem Eng Data"},{"key":"35257_CR11","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1016\/j.ijrefrig.2019.04.014","volume":"103","author":"IH Bell","year":"2019","unstructured":"Bell IH, Welliquet J, Mondejar ME, Bazyleva A, Quoilin S, Haglind F (2019) Application of the group contribution volume translated Peng-Robinson equation of state to new commercial refrigerant mixtures. Int J Refrig 103:316\u2013328. https:\/\/doi.org\/10.1016\/j.ijrefrig.2019.04.014","journal-title":"Int J Refrig"},{"key":"35257_CR12","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1145\/937503.937505","volume":"35","author":"C Blum","year":"2003","unstructured":"Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35:268\u2013308. https:\/\/doi.org\/10.1145\/937503.937505","journal-title":"ACM Comput Surv"},{"key":"35257_CR13","doi-asserted-by":"publisher","first-page":"1768","DOI":"10.1016\/j.ces.2009.01.003","volume":"64","author":"GM Bollas","year":"2009","unstructured":"Bollas GM, Barton PI, Mitsos A (2009) Bilevel optimization formulation for parameter estimation in vapor-liquid(-liquid) phase equilibrium problems. Chem Eng Sci 64:1768\u20131783. https:\/\/doi.org\/10.1016\/j.ces.2009.01.003","journal-title":"Chem Eng Sci"},{"key":"35257_CR14","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.fluid.2009.09.021","volume":"287","author":"A Bonilla-Petriciolet","year":"2010","unstructured":"Bonilla-Petriciolet A, Rangaiah GP, Segovia-Hernandez JG (2010) Evaluation of stochastic global optimization methods for modelling vapor-liquid equilibrium data. Fluid Ph Equilib 287:111\u2013125. https:\/\/doi.org\/10.1016\/j.fluid.2009.09.021","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR15","doi-asserted-by":"publisher","first-page":"3428","DOI":"10.1135\/cccc19693428","volume":"34","author":"M Broul","year":"1969","unstructured":"Broul M, Hlavaty K, Linek J (1969) Liquid-vapor equilibrium in systems of electrolytic components. V. The system CH3OH-H2O-LiCl at 60\u00b0C. Collect Czech Chem Commun 34:3428\u20133435. https:\/\/doi.org\/10.1135\/cccc19693428","journal-title":"Collect Czech Chem Commun"},{"key":"35257_CR16","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1016\/j.fluid.2018.11.029","volume":"2019","author":"K Carvalho dos Santos","year":"2019","unstructured":"Carvalho dos Santos K, Pedersen Voll AF, Corazza ML (2019) Thermodynamic analysis of biodiesel production systems at supercritical conditions. Fluid Ph Equilib 2019:106\u2013113. https:\/\/doi.org\/10.1016\/j.fluid.2018.11.029","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR17","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/s10765-023-03265-4","volume":"44","author":"F Chalghoum","year":"2023","unstructured":"Chalghoum F, Benziane M, Trache D, Toazi AA, Mokbel I, Jose J (2023) Vapor pressure measurements and predictions for binary systems containing ethyl octanoate or ethyl dodecanoate as biodiesels and n-tetradecane as petrodiesel compound. Int J Thermophys 44:157. https:\/\/doi.org\/10.1007\/s10765-023-03265-4","journal-title":"Int J Thermophys"},{"key":"35257_CR18","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.fuel.2015.08.003","volume":"161","author":"ML Corazza","year":"2015","unstructured":"Corazza ML, Fouad WA, Chapman WG (2015) Application of molecular modeling to the vapor-liquid equilibrium of alkyl esters (biodiesel) and alcohols systems. Fuel 161:34\u201342. https:\/\/doi.org\/10.1016\/j.fuel.2015.08.003","journal-title":"Fuel"},{"key":"35257_CR19","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.fluid.2013.09.019","volume":"362","author":"N Cotabarren","year":"2014","unstructured":"Cotabarren N, Hegel P, Pereda S (2014) Thermodynamic model for process design, simulation and optimization in the production of biodiesel. Fluid Ph Equilib 362:108\u2013112. https:\/\/doi.org\/10.1016\/j.fluid.2013.09.019","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR20","doi-asserted-by":"publisher","first-page":"1855","DOI":"10.3303\/CET1543310","volume":"43","author":"LP Cunico","year":"2015","unstructured":"Cunico LP, Guirardello R (2015) Modeling of phase and chemical equilibria for systems involved in biodiesel production. Chem Eng Trans 43:1855\u20131860. https:\/\/doi.org\/10.3303\/CET1543310","journal-title":"Chem Eng Trans"},{"key":"35257_CR21","doi-asserted-by":"publisher","first-page":"496732","DOI":"10.1155\/2011\/496732","volume":"2011","author":"TT Dao","year":"2011","unstructured":"Dao TT (2011) Investigation on evolutionary computation techniques of a nonlinear system. Model Simul Eng 2011:496732. https:\/\/doi.org\/10.1155\/2011\/496732","journal-title":"Model Simul Eng"},{"key":"35257_CR22","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1109\/TEVC.2010.2059031","volume":"15","author":"S Das","year":"2011","unstructured":"Das S, Suganthan PN (2011) Differential Evolution: a survey of the state-of-the-art. IEEE Trans Evolut Comput 15:4\u201331. https:\/\/doi.org\/10.1109\/TEVC.2010.2059031","journal-title":"IEEE Trans Evolut Comput"},{"key":"35257_CR23","doi-asserted-by":"publisher","first-page":"1697","DOI":"10.1016\/j.enconman.2018.06.108","volume":"171","author":"AA De Jesus","year":"2018","unstructured":"De Jesus AA, De Santana Souza DF, De Oliveira JA, De Deus MS, Da Silva MG, Franceschi E et al (2018) Mathematical modeling and experimental esterification at supercritical conditions for biodiesel production in a tubular reactor. Energy Convers Manag 171:1697\u20131703. https:\/\/doi.org\/10.1016\/j.enconman.2018.06.108","journal-title":"Energy Convers Manag"},{"key":"35257_CR24","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.jct.2017.08.003","volume":"117","author":"IA De Oliveira","year":"2017","unstructured":"De Oliveira IA, Segtovich ISV, Barreto AG, Tavares FW (2017) Accurate thermodynamic description of vapor-liquid and solid-liquid equilibria of THF, water and gas hydrates with a unique set of parameters. J Chem Thermo 117:60\u201367. https:\/\/doi.org\/10.1016\/j.jct.2017.08.003","journal-title":"J Chem Thermo"},{"key":"35257_CR25","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1016\/j.ces.2018.09.015","volume":"193","author":"I D\u00edaz","year":"2019","unstructured":"D\u00edaz I, Rodr\u00edguez M, Gonz\u00e1lez EJ, Gonz\u00e1lez-Miquel M (2019) A simple and reliable procedure to accurately estimate NRTL interaction parameters from liquid-liquid equilibrium data. Chem Eng Sci 193:370\u2013378. https:\/\/doi.org\/10.1016\/j.ces.2018.09.015","journal-title":"Chem Eng Sci"},{"key":"35257_CR26","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1515\/revce-2015-0042","volume":"32","author":"EN Dragoi","year":"2016","unstructured":"Dragoi EN, Curteanu S (2016) The use of differential evolution algorithm for solving chemical engineering problems. Rev Chem Eng 32:149\u2013180. https:\/\/doi.org\/10.1515\/revce-2015-0042","journal-title":"Rev Chem Eng"},{"key":"35257_CR27","volume-title":"Optimization of Chemical Processes","author":"TF Edgar","year":"2001","unstructured":"Edgar TF, Himmelblau DM, Lasdon LS (2001) Optimization of Chemical Processes. McGraw-Hill, New York"},{"key":"35257_CR28","doi-asserted-by":"publisher","first-page":"106684","DOI":"10.1016\/j.compchemeng.2019.106684","volume":"134","author":"P Erodotou","year":"2020","unstructured":"Erodotou P, Voutsas E, Sarimveis H (2020) A genetic algorithm approach for parameter estimation in vapor-liquid thermodynamic modelling problems. Comp Chem Eng 134:106684. https:\/\/doi.org\/10.1016\/j.compchemeng.2019.106684","journal-title":"Comp Chem Eng"},{"key":"35257_CR29","doi-asserted-by":"publisher","first-page":"434","DOI":"10.28991\/HIJ-2023-04-02-014","volume":"4","author":"I Farda","year":"2023","unstructured":"Farda I, Thammano A (2023) An improved differential evolution algorithm for numerical optimization problems. High Tech Innov J 4:434\u2013452. https:\/\/doi.org\/10.28991\/HIJ-2023-04-02-014","journal-title":"High Tech Innov J"},{"key":"35257_CR30","doi-asserted-by":"publisher","first-page":"1086","DOI":"10.1002\/aic.690210607","volume":"21","author":"A Fredenslund","year":"1975","unstructured":"Fredenslund A, Jones RL, Prausnitz JM (1975) Group-contribution estimation of activity coefficients in nonideal liquid mixtures. AIChE J 21:1086\u20131099. https:\/\/doi.org\/10.1002\/aic.690210607","journal-title":"AIChE J"},{"key":"35257_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0378-3812(99)00332-5","volume":"168","author":"CY Gau","year":"2000","unstructured":"Gau CY, Brennecke JF, Stadtherr MA (2000) Reliable nonlinear parameter estimation in VLE modeling. Fluid Ph Equilib 168:1\u201318. https:\/\/doi.org\/10.1016\/S0378-3812(99)00332-5","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2012\/641251","volume":"2012","author":"D Gao","year":"2012","unstructured":"Gao D, Zhang H, Lucking P, Sun H, Si J, Zhu D et al (2012) Computation of isobaric vapor-liquid equilibrium data for binary and ternary mixtures of methanol, water, and ethanoic acid from T, p, x, and HEm measurements. J Therm 2012:1\u201313. https:\/\/doi.org\/10.1155\/2012\/641251","journal-title":"J Therm"},{"key":"35257_CR33","first-page":"315","volume-title":"Chemical thermodynamics for process simulation","author":"J Gmehling","year":"2012","unstructured":"Gmehling J, Barbel K, Kleiber M, Rarey J (2012) Phase equilibria in fluid systems. In: Gmehling J, Barbel K, Kleiber M, Rarey J (eds) Chemical thermodynamics for process simulation, 1st edn. Wiley-VCH, Germany, pp 315\u2013318","edition":"1"},{"key":"35257_CR34","doi-asserted-by":"publisher","unstructured":"Guevara MA, Guevara FA, Belalc\u00e1zar LC (2018) Experimental data and new binary interaction parameters for ethanol-water VLE at low pressures using NRTL and UNIQUAC. TECCIENCIA 13:17\u201326. https:\/\/doi.org\/10.18180\/tecciencia.2017.23.11","DOI":"10.18180\/tecciencia.2017.23.11"},{"key":"35257_CR35","doi-asserted-by":"publisher","first-page":"112581","DOI":"10.1016\/j.molliq.2020.112581","volume":"302","author":"G Kacar","year":"2020","unstructured":"Kacar G, De With G (2020) Parametrizing hydrogen bond interactions in dissipative particle dynamics simulations: The case of water, methanol and their binary mixtures. J Mol Liq 302:112581. https:\/\/doi.org\/10.1016\/j.molliq.2020.112581","journal-title":"J Mol Liq"},{"key":"35257_CR36","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.fluid.2017.10.029","volume":"458","author":"A Khoshsima","year":"2018","unstructured":"Khoshsima A, Shahriari R (2018) Molecular modeling of systems related to the biodiesel production using the PHSC equation of state. Fluid Ph Equilib 458:58\u201383. https:\/\/doi.org\/10.1016\/j.fluid.2017.10.029","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR37","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.cherd.2023.12.013","volume":"202","author":"G Klauck","year":"2024","unstructured":"Klauck G, Dalmolin I, Brusamarello CZ (2024) A comparative study of thermodynamic equations and artificial neural networks in modeling the behavior of glycerol+methanol+CO2 and glycerol+ethanol+CO2 systems in biodiesel production. Chem Eng Res Des 202:92\u2013102. https:\/\/doi.org\/10.1016\/j.cherd.2023.12.013","journal-title":"Chem Eng Res Des"},{"key":"35257_CR38","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1252\/kakoronbunshu1953.32.149","volume":"32","author":"K Kojima","year":"1968","unstructured":"Kojima K, Tochigi K, Seki H, Watase K (1968) Determination of vapor-liquid equilibrium from boiling point curve. Kagaku Kogaku Ronbunshu 32:149\u2013153. https:\/\/doi.org\/10.1252\/kakoronbunshu1953.32.149","journal-title":"Kagaku Kogaku Ronbunshu"},{"key":"35257_CR39","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.molliq.2014.03.031","volume":"196","author":"JA Lazz\u00fas","year":"2014","unstructured":"Lazz\u00fas JA (2014) Hybrid swarm optimization for vapor\u2013liquid equilibrium modeling. J Mol Liq 196:167\u2013177. https:\/\/doi.org\/10.1016\/j.molliq.2014.03.031","journal-title":"J Mol Liq"},{"key":"35257_CR40","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.fluid.2012.12.003","volume":"340","author":"Y Li","year":"2013","unstructured":"Li Y, Bai P, Zhuang Q (2013) Isobaric vapor-liquid equilibrium for binary system of methanol and acetonitrile. Fluid Ph Equilib 340:42\u201345. https:\/\/doi.org\/10.1016\/j.fluid.2012.12.003","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR41","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1016\/j.fluid.2016.06.048","volume":"427","author":"Z Li","year":"2016","unstructured":"Li Z, Li Q, Qiao R, Zhang K, Song X et al (2016) Isobaric vapor-liquid equilibrium for methanol + methyl ethyl ketone + bis(trifluoromethylsulfonyl)imide-based ionic liquids at 101.3 kPa. Fluid Ph Equilib 427:90\u201396. https:\/\/doi.org\/10.1016\/j.fluid.2016.06.048","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR42","doi-asserted-by":"publisher","first-page":"5094","DOI":"10.1109\/TITS.2019.2948596","volume":"21","author":"WL Liu","year":"2020","unstructured":"Liu WL, Gong YJ, Chen WN, Liu Z, Wang H, Zhang J (2020) Coordinated charging scheduling of electric vehicles: a mixed-variable differential evolution approach. IEEE Trans Intell Transport Syst 21:5094\u20135109. https:\/\/doi.org\/10.1109\/TITS.2019.2948596","journal-title":"IEEE Trans Intell Transport Syst"},{"key":"35257_CR43","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.fluid.2006.08.003","volume":"248","author":"JA Lopez","year":"2006","unstructured":"Lopez JA, Trejos VM, Cardona CA (2006) Objective functions analysis in the minimization of binary VLE data for asymmetric mixtures at high pressures. Fluid Ph Equilib 248:147\u2013157. https:\/\/doi.org\/10.1016\/j.fluid.2006.08.003","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR44","doi-asserted-by":"publisher","first-page":"100257","DOI":"10.1016\/j.ceja.2022.100257","volume":"10","author":"JM Lopez","year":"2022","unstructured":"Lopez JM, Perez Flores FJ, Rosales EC, Munoz EO, Hernandez-Anzaldo S, Lima HV et al (2022) A theoretical and experimental study of liquid-liquid equilibrium to refine raw glycerol obtained as a byproduct on the biodiesel production. Chem Eng J Adv 10:100257. https:\/\/doi.org\/10.1016\/j.ceja.2022.100257","journal-title":"Chem Eng J Adv"},{"key":"35257_CR45","doi-asserted-by":"publisher","unstructured":"Luo J, Wang Y, Shi C, Zhang F, Yu Q (2022) Solubility and thermodynamic properties of N-phenylanthranilic acid in Water\u00a0+\u00a0Methanol\/Ethanol\/tert-butanol binary solvents from 283.15\u00a0K to 323.15\u00a0K. J Chem Therm 168:106748. https:\/\/doi.org\/10.1016\/j.jct.2022.106748","DOI":"10.1016\/j.jct.2022.106748"},{"key":"35257_CR46","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1002\/ceat.202300245","volume":"47","author":"K Mamtani","year":"2024","unstructured":"Mamtani K, Da Silveira CL, Farid MM, Shahbaz K (2024) Liquid-liquid phase equilibrium of glycerolysis precursors: experimental and modeling study. Chem Eng Technol 47:208\u2013216. https:\/\/doi.org\/10.1002\/ceat.202300245","journal-title":"Chem Eng Technol"},{"key":"35257_CR47","doi-asserted-by":"publisher","first-page":"1069","DOI":"10.1021\/je400885z","volume":"59","author":"RJ McDougal","year":"2014","unstructured":"McDougal RJ, Jasperson LV, Wilson GM (2014) Vapor-liquid equilibrium for several compounds relevant to the biofuels industry modeled with the wilson equation. J Chem Eng Data 59:1069\u20131085. https:\/\/doi.org\/10.1021\/je400885z","journal-title":"J Chem Eng Data"},{"key":"35257_CR48","doi-asserted-by":"publisher","first-page":"118040","DOI":"10.1016\/j.fuel.2020.118040","volume":"276","author":"HAD Medeiros","year":"2020","unstructured":"Medeiros HAD, Chiavone-Filho O, Rios RB (2020) Influence of estimated physical constants and vapor pressure for esters in the methanol\/ethanol recovery column for biodiesel production. Fuel 276:118040. https:\/\/doi.org\/10.1016\/j.fuel.2020.118040","journal-title":"Fuel"},{"key":"35257_CR49","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1016\/j.ins.2011.12.037","volume":"193","author":"VV Melo","year":"2012","unstructured":"Melo VV, Delbem ACB (2012) Investigating smart sampling as a population initialization method for differential evolution in continuous problems. Inf Sci 193:36\u201353. https:\/\/doi.org\/10.1016\/j.ins.2011.12.037","journal-title":"Inf Sci"},{"key":"35257_CR50","doi-asserted-by":"publisher","first-page":"6361","DOI":"10.1007\/s00500-018-3289-4","volume":"23","author":"D Mustafi","year":"2019","unstructured":"Mustafi D, Sahoo G (2019) A hybrid approach using genetic algorithm and the differential evolution heuristic for enhanced initialization of the k-means algorithm with applications in text clustering. Soft Comput 23:6361\u20136378. https:\/\/doi.org\/10.1007\/s00500-018-3289-4","journal-title":"Soft Comput"},{"key":"35257_CR51","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/978-3-540-39930-8","volume-title":"New Optimization Techniques in Engineering","author":"GC Onwubolu","year":"2004","unstructured":"Onwubolu GC, Babu BV (2004) Differential Evolution. In: Kacprzyk J (ed) New Optimization Techniques in Engineering, 1st edn. Springer-Verlag, Berlin, Heidelberg, pp 123\u2013163","edition":"1"},{"key":"35257_CR52","doi-asserted-by":"publisher","first-page":"444","DOI":"10.1021\/je0497350","volume":"50","author":"J Ortega","year":"2005","unstructured":"Ortega J, Espiau F, Postigo M (2005) Vapor-liquid equilibria at 101.32 kPa and excess properties of binary mixtures of butyl esters + tert-butyl alcohol. J Chem Eng Data 50:444\u2013454","journal-title":"J Chem Eng Data"},{"key":"35257_CR53","doi-asserted-by":"publisher","first-page":"4632","DOI":"10.1016\/j.eswa.2009.12.045","volume":"37","author":"AB Ozer","year":"2010","unstructured":"Ozer AB (2010) CIDE: chaotically initialized differential evolution. Expert Syst Appl 37:4632\u20134641. https:\/\/doi.org\/10.1016\/j.eswa.2009.12.045","journal-title":"Expert Syst Appl"},{"key":"35257_CR54","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13068-021-01977-z","volume":"14","author":"MK Pasha","year":"2021","unstructured":"Pasha MK, Dai L, Liu D, Guo M, Du W (2021) An overview to process design, simulation and sustainability evaluation of biodiesel production. Biotechnol Biofuels 14:1\u201323. https:\/\/doi.org\/10.1186\/s13068-021-01977-z","journal-title":"Biotechnol Biofuels"},{"key":"35257_CR55","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1016\/j.supflu.2016.07.025","volume":"118","author":"CG Pereira","year":"2016","unstructured":"Pereira CG, Ferrando N, Lugo R, Mougin P, De Hemptinne JC (2016) Predictive evaluation of phase equilibria in biofuel systems using molecular thermodynamic models. J Supercritical Fluids 118:64\u201378. https:\/\/doi.org\/10.1016\/j.supflu.2016.07.025","journal-title":"J Supercritical Fluids"},{"key":"35257_CR56","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.ins.2014.11.026","volume":"297","author":"I Poikolainen","year":"2015","unstructured":"Poikolainen I, Neri F, Caraffini F (2015) Cluster-based population initialization for differential evolution frameworks. Inf Sci 297:216\u2013235. https:\/\/doi.org\/10.1016\/j.ins.2014.11.026","journal-title":"Inf Sci"},{"key":"35257_CR57","volume-title":"The properties of gases and liquids","author":"BE Poling","year":"2001","unstructured":"Poling BE, Prausnitz JM, O\u2019Connell JP (2001) The properties of gases and liquids. McGraw-Hill, New York"},{"key":"35257_CR58","doi-asserted-by":"publisher","unstructured":"Rahnamayan S, Tizhoosh HR, Salama MMA (2006) Opposition-based differential evolution for optimization of noisy problems. In: 2006 IEEE Int Conf Evol Comput 1865\u20131872. https:\/\/doi.org\/10.1109\/CEC.2006.1688534","DOI":"10.1109\/CEC.2006.1688534"},{"key":"35257_CR59","doi-asserted-by":"publisher","first-page":"1605","DOI":"10.1016\/j.camwa.2006.07.013","volume":"53","author":"S Rahnamayan","year":"2007","unstructured":"Rahnamayan S, Tizhoosh HR, Salama MMA (2007) A novel population initialization method for accelerating evolutionary algorithms. Comput Math Appl 53:1605\u20131614. https:\/\/doi.org\/10.1016\/j.camwa.2006.07.013","journal-title":"Comput Math Appl"},{"key":"35257_CR60","doi-asserted-by":"publisher","first-page":"64","DOI":"10.1109\/TEVC.2007.894200","volume":"12","author":"S Rahnamayan","year":"2008","unstructured":"Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12:64\u201379","journal-title":"IEEE Trans Evol Comput"},{"key":"35257_CR61","volume-title":"The properties of gases and liquids","author":"RC Reid","year":"1987","unstructured":"Reid RC, Prausnitz JM, Poling BE (1987) The properties of gases and liquids. McGraw-Hill, New York"},{"key":"35257_CR62","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1002\/aic.690140124","volume":"14","author":"H Renon","year":"1968","unstructured":"Renon H, Prausnitz JM (1968) Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures. AIChE J 14:135\u2013144","journal-title":"AIChE J"},{"key":"35257_CR63","doi-asserted-by":"publisher","unstructured":"Sajed FT, Shojaeian A, Rasteh M (2023) Thermodynamic modeling of vapor-liquid equilibrium systems including biodiesel in high and low pressures using cubic equations of state.\u00a0Prog Eng Therm Kinet. https:\/\/doi.org\/10.22075\/jpetk.2023.24860.1004","DOI":"10.22075\/jpetk.2023.24860.1004"},{"key":"35257_CR64","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1109\/TEVC.2013.2281528","volume":"18","author":"RA Sarker","year":"2014","unstructured":"Sarker RA, Elsayed SM, Ray T (2014) Differential Evolution with Dynamic Parameters Selection for Optimization Problems. IEEE Trans Evol Comput 18:689\u2013707. https:\/\/doi.org\/10.1109\/TEVC.2013.2281528","journal-title":"IEEE Trans Evol Comput"},{"key":"35257_CR65","doi-asserted-by":"publisher","unstructured":"Sen S (2015) A Survey of Intrusion Detection Systems Using Evolutionary Computation. In: Yang X, Chien SF, Ting TO (ed) Bio-inspired computation in telecommunications, Morgan Kaufmann, Burlington, USA 73\u201394. https:\/\/doi.org\/10.1016\/B978-0-12-801538-4.00004-5","DOI":"10.1016\/B978-0-12-801538-4.00004-5"},{"key":"35257_CR66","volume-title":"Introduction to Chemical Engineering Thermodynamics","author":"JM Smith","year":"2018","unstructured":"Smith JM, Van Ness HC, Abbott MM, Swihart MT (2018) Introduction to Chemical Engineering Thermodynamics, 8th edn. McGraw-Hill, New York","edition":"8"},{"key":"35257_CR67","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1016\/j.jct.2009.11.020","volume":"42","author":"J Soujanya","year":"2010","unstructured":"Soujanya J, Satyavathi B, Vittal Prasad TE (2010) Experimental (vapor + liquid) equilibrium data of (methanol + water), (water + glycerol) and (methanol + glycerol) systems at atmospheric and sub-atmospheric pressures. J Chem Thermodyn 42:621\u2013624. https:\/\/doi.org\/10.1016\/j.jct.2009.11.020","journal-title":"J Chem Thermodyn"},{"key":"35257_CR68","doi-asserted-by":"publisher","first-page":"106444","DOI":"10.1016\/j.jct.2021.106444","volume":"158","author":"GAL Souza","year":"2021","unstructured":"Souza GAL, Silva LYA, Martinez PFM (2021) Vapour-liquid equilibria of systems containing deep eutectic solvent based on choline chloride and glycerol. J Chem Thermodyn 158:106444. https:\/\/doi.org\/10.1016\/j.jct.2021.106444","journal-title":"J Chem Thermodyn"},{"key":"35257_CR69","unstructured":"Storn R, Price K (1995) Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces. ICSI, USA, Tech. Rep. TR-95\u2013012, 12:1\u201316. https:\/\/www.icsi.berkeley.edu\/ftp\/global\/global\/pub\/techreports\/1995\/tr-95-012.pdf"},{"key":"35257_CR70","doi-asserted-by":"publisher","unstructured":"Storn R, (1996) On the usage of differential evolution for function optimization. In: Proceedings of NAFIPS 1996. Berkeley, CA, USA, 519\u2013523.\u00a0https:\/\/doi.org\/10.1109\/NAFIPS.1996.534789","DOI":"10.1109\/NAFIPS.1996.534789"},{"key":"35257_CR71","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1016\/j.fluid.2013.03.008","volume":"347","author":"G Tang","year":"2013","unstructured":"Tang G, Ding H, Hou J, Xu S (2013) Isobaric vapor-liquid equilibrium for binary system of ethyl myristate + ethyl palmitate at 0.5, 1.0 and 1.5 kPa. Fluid Ph Equilib 347:8\u201314. https:\/\/doi.org\/10.1016\/j.fluid.2013.03.008","journal-title":"Fluid Ph Equilib"},{"key":"35257_CR72","doi-asserted-by":"publisher","first-page":"S165","DOI":"10.1134\/S1070363224140172","volume":"94","author":"M Trofimova","year":"2024","unstructured":"Trofimova M, Samarov A, Misikov G, Zaripova S (2024) Vapor-liquid equilibrium in chemically equilibrium systems: the system with reaction of ethyl acetate synthesis. Russ J Gen Chem 94:S165\u2013S176. https:\/\/doi.org\/10.1134\/S1070363224140172","journal-title":"Russ J Gen Chem"},{"key":"35257_CR73","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3390\/molecules27185785","volume":"27","author":"I Tsivintzelis","year":"2022","unstructured":"Tsivintzelis I, Koutsou G, Kontogeorgis GM (2022) Modeling binary and multicomponent systems containing supercritical CO2 with polyethylene glycols and compounds relevant to the biodiesel production. Mol 27:1\u201319. https:\/\/doi.org\/10.3390\/molecules27185785","journal-title":"Mol"},{"key":"35257_CR75","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1021\/ja01056a002","volume":"86","author":"GM Wilson","year":"1964","unstructured":"Wilson GM (1964) Vapor-liquid equilibrium. XI. A new expression for the excess free energy of mixing. J Am Chem Soc 86:127\u2013130. https:\/\/doi.org\/10.1021\/ja01056a002","journal-title":"J Am Chem Soc"},{"key":"35257_CR76","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1016\/j.fuel.2014.07.020","volume":"135","author":"A Woinaroschy","year":"2014","unstructured":"Woinaroschy A (2014) Multiobjective optimal design for biodiesel sustainable production. Fuel 135:393\u2013405. https:\/\/doi.org\/10.1016\/j.fuel.2014.07.020","journal-title":"Fuel"},{"key":"35257_CR77","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1515\/cppm-2022-0044","volume":"6","author":"S Yadav","year":"2023","unstructured":"Yadav S, Angira R (2023) Parameter estimation in non-linear chemical processes: an opposite point-based differential evolution (OPDE) approach. Chem Prod Process Model 6:1015\u20131037. https:\/\/doi.org\/10.1515\/cppm-2022-0044","journal-title":"Chem Prod Process Model"},{"key":"35257_CR78","doi-asserted-by":"publisher","unstructured":"Yadav S, Angira R (2024) A new method of population initialization for enhancing performance of evolutionary algorithms. In: Das B, Patgiri R, Bandyopadhyay S, Balas VE, Roy S (ed) Modeling, Simulation and Optimization, CoMSO 2022, 1st edn. Springer, Singapore, 51\u201363. https:\/\/doi.org\/10.1007\/978-981-99-6866-4_4","DOI":"10.1007\/978-981-99-6866-4_4"},{"key":"35257_CR79","doi-asserted-by":"publisher","unstructured":"Yadav S, Palak P, Angira R (2024) Swarm intelligence for estimating model parameters in thermodynamic systems. In: Das B, Patgiri R, Bandyopadhyay S, Balas VE, Roy S (ed) Modeling, Simulation and Optimization, CoMSO 2022, 1st edn. Springer, Singapore, 293\u2013304. https:\/\/doi.org\/10.1007\/978-981-99-6866-4_21","DOI":"10.1007\/978-981-99-6866-4_21"},{"key":"35257_CR80","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1016\/j.biombioe.2015.05.015","volume":"81","author":"DM Yancy-Caballero","year":"2015","unstructured":"Yancy-Caballero DM, Guirardello R (2015) Modeling and parameters fitting of chemical and phase equilibria in reactive systems for biodiesel production. Biomass Bioenergy 81:544\u2013555. https:\/\/doi.org\/10.1016\/j.biombioe.2015.05.015","journal-title":"Biomass Bioenergy"},{"key":"35257_CR81","doi-asserted-by":"publisher","first-page":"10047","DOI":"10.1021\/ie200819p","volume":"50","author":"H Zhang","year":"2011","unstructured":"Zhang H, Rangaiah GP, Petriciolet AB (2011) Integrated differential evolution for global optimization and its performance for modeling vapor-liquid equilibrium data. Ind Eng Chem Res 50:10047\u201310061. https:\/\/doi.org\/10.1021\/ie200819p","journal-title":"Ind Eng Chem Res"},{"key":"35257_CR82","doi-asserted-by":"publisher","first-page":"5291","DOI":"10.1109\/tcyb.2020.3025662","volume":"51","author":"F Zhao","year":"2021","unstructured":"Zhao F, He X, Mang L (2021) A two-stage cooperative evolutionary algorithm with problem-specific knowledge for energy-efficient scheduling of no-wait flow-shop problem. IEEE Trans Cybern 51:5291\u20135303. https:\/\/doi.org\/10.1109\/tcyb.2020.3025662","journal-title":"IEEE Trans Cybern"},{"key":"35257_CR83","doi-asserted-by":"publisher","first-page":"1430","DOI":"10.1109\/tcyb.2019.2939219","volume":"51","author":"S Zhou","year":"2021","unstructured":"Zhou S, Xing L, Zheng X, Du N, Wang L, Zhang Q (2021) A self-adaptive differential evolution algorithm for scheduling a single batch-processing machine with arbitrary job sizes and release times. IEEE Trans Cybern 51:1430\u20132144. https:\/\/doi.org\/10.1109\/tcyb.2019.2939219","journal-title":"IEEE Trans Cybern"},{"key":"35257_CR84","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.ins.2012.09.019","volume":"223","author":"W Zhu","year":"2013","unstructured":"Zhu W, Tang Y, Fang JA, Zhang W (2013) Adaptive population tuning scheme for differential evolution. Inf Sci 223:164\u2013191. https:\/\/doi.org\/10.1016\/j.ins.2012.09.019","journal-title":"Inf Sci"}],"container-title":["Environmental Science and Pollution Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11356-024-35257-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11356-024-35257-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11356-024-35257-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T06:28:50Z","timestamp":1765952930000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11356-024-35257-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,29]]},"references-count":83,"journal-issue":{"issue":"49","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["35257"],"URL":"https:\/\/doi.org\/10.1007\/s11356-024-35257-8","relation":{},"ISSN":["1614-7499"],"issn-type":[{"value":"1614-7499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,29]]},"assertion":[{"value":"15 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 October 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 October 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not Applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate:"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication:"}},{"value":"The authors declare that they have no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}]}}