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Thermodynamic and Topological Analysis of Phase Diagrams of Quaternary Systems with Internal Singular Points

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Abstract

A review of the literature published in Russia and abroad on the experimental studies of phase equilibria, methods for analyzing and predicting phase diagram structures, and simulating problems of the vapor–liquid equilibrium (VLE) of quaternary systems containing internal singular points is presented. A complete set of parameters that adequately describe the liquid–vapor and liquid–liquid equilibrium is obtained for the following four systems: acetone–chloroform–ethanol–water, acetone–chloroform–propanol-2–water, chloroform–ethanol–cyclohexane–water, and ethyl acetate–methyl ethyl ketone–cyclohexane–propanol-2. The methodology for determining the structure of the VLE diagram and predicting the presence of an internal azeotrope in the systems under study and in a model system that contains binary azeotropes and a quaternary azeotrope is illustrated. Possible ways for evolutionary changes in the structure of the VLE diagram with a variation in the pressure are shown, and the Poincare indices of boundary single azeotropes and a double tangential azeotrope are determined.

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REFERENCES

  1. Yus, D. and Moonyong, L., Distillation design and optimization of quaternary azeotropic mixtures for waste solvent recovery, J. Ind. Eng. Chem. (Amsterdam, Neth.), 2018, vol. 67, p. 255.

  2. Kleimenova, M.N., Komarova, L.F., and Lazutkina, Yu.S., Development of resource-saving technologies in the production of organosilicon enamels based on distillation, Khim. Interesakh Ustoich. Razvit., 2013, vol. 21, p. 211.

    CAS  Google Scholar 

  3. Mujtaba, I.M., Batch Distillation: Design and Operation, London: Imperial College Press, 2004.

    Google Scholar 

  4. Frolkova, A.V., Frolkova, A.K., and Chelyuskina, T.V., Separation of the acetone–chloroform–ethanol–water four-component system by autoextractive heteroazeotropic distillation, Vestn. MITKHT, 2010, vol. 5, no. 6, p. 27.

    Google Scholar 

  5. Toikka, M., Trofimova, D., and Samarov, A., Liquid-liquid equilibrium and critical states for the quaternary system propionic acid–n-butanol–n-butyl propionate–water at 303.15 K, Fluid Phase Equilib., 2018, vol. 460, p. 17.

    CAS  Google Scholar 

  6. Samarov, A., Toikka, M., and Toikka, A., Liquid–liquid equilibrium and critical states for the system acetic acid + n-butanol + n-butyl acetate + water at 308.15 K, Fluid Phase Equilib., 2015, vol. 385, p. 129.

    CAS  Google Scholar 

  7. Xiao, L., Wang, Q., and Wang, H., Isobaric vapor–liquid equilibrium data for the binary system methyl acetate + isopropyl acetate and the quaternary system methyl acetate + methanol + isopropanol + isopropyl acetate at 101.3 kPa, Fluid Phase Equilib., 2013, vol. 344, p. 79.

    CAS  Google Scholar 

  8. Osorio-Viana, W., Duque-Bernal, M., Quintero-Arias, J.D., Dobrosz-Gomez, I., Fontalvo, J., and Gomez-Garcia, M.A., Activity model and consistent thermodynamic features for acetic acid–isoamyl alcohol–isoamyl acetate–water reactive system, Fluid Phase Equilib., 2013, vol. 345, p. 68.

    CAS  Google Scholar 

  9. Harvianto, G.R., Liquid–liquid equilibrium data and correlation for quaternary systems of acetic acid + water + methyl acetate + p-xylene at 313.2 K, J. Ind. Eng. Chem. (Amsterdam, Neth.), 2016, vol. 35, p. 369.

  10. Requejo, P., Comparative study of the LLE of the quaternary and ternary systems involving benzene, n-octane, n-decane and the ionic liquid [BMpyr][NTf2], J. Chem. Thermodyn., 2016, vol. 98, p. 56.

    CAS  Google Scholar 

  11. Hongxun, Z., Liquid–liquid phase equilibria of the quaternary system {water (1) + acrylic acid (2) + acetic acid (3) + cyclopentyl methyl ether (4)}: Measurement, correlation, and comparative study, Fluid Phase Equilib., 2015, vol. 403, p. 23.

    Google Scholar 

  12. Toikka, M., Samarov, A., Trofimova, M., Golikova, A., Tsvetov, N., and Toikka, A., Solubility, liquid–liquid equilibrium and critical states for the quaternary system acetic acid–ethanol–ethyl acetate–water at 303.15 K and 313.15 K, Fluid Phase Equilib., 2014, vol. 373, p. 72.

    CAS  Google Scholar 

  13. Toikka, M., Samarov, A., and Toikka, A., Solubility, liquid–liquid equilibrium and critical states for the system acetic acid + n-propanol + n-propyl acetate + water at 293.15 K and 303.15 K, Fluid Phase Equilib., 2014, vol. 375, p. 66.

    CAS  Google Scholar 

  14. Liebergesell, B., Brands, T., Koss, H.-J., and Bardow, A., Quaternary isothermal vapor-liquid equilibrium of the model biofuel 2-butanone + n-heptane + tetrahydrofuran + cyclohexane using Raman spectroscopic characterization, Fluid Phase Equilib., 2018, vol. 472, p. 107.

    CAS  Google Scholar 

  15. Pavlicek, J., Bogdani, G., and Wichterle, I., Vapour–liquid and chemical equilibria in the ethyl ethanoate + ethanol + propyl ethanoate + propanol system accompanied with transesterification reaction, Fluid Phase Equilib., 2012, vol. 328, p. 61.

    CAS  Google Scholar 

  16. Kulov, N.N., Slaikovskaya, N.P., and Lotkhov, V.A., Phase equilibrium in acetone-water-mesityl oxide-diacetone alcohol four-component system, Theor. Found. Chem. Eng., 2012, vol. 46, no. 2, pp. 113–119. https://doi.org/10.1134/S0040579512020066

    Article  CAS  Google Scholar 

  17. Pequenin, A., Asensi, J., and Gomis, V., Vapor–liquid–liquid equilibrium and vapor–liquid equilibrium for the quaternary system water–ethanol–cyclohexane–toluene and the ternary system water–cyclohexane–toluene. Isobaric experimental determination at 101.3 kPa, Fluid Phase Equilib., 2011, vol. 309, p. 62.

    CAS  Google Scholar 

  18. Wisniak, J. and Tamir, A., Vapor-liquid equilibriums in the ternary systems water–formic acid–acetic acid and water–acetic acid–propionic acid, J. Chem. Eng. Data, 1987, vol. 32, p. 291.

    Google Scholar 

  19. Fernandez, J. and Wisniak, J., New computational tool to evaluate experimental VLE and VLLE data of multicomponent systems, Comput. Chem. Eng., 2017, vol. 106, p. 437.

    CAS  Google Scholar 

  20. Sheikholeslamzadeh, E. and Rohani, S., Vapour–liquid and vapour–liquid–liquid equilibrium modeling for binary, ternary, and quaternary systems of solvents, Fluid Phase Equilib., 2012, vol. 333, p. 97.

    CAS  Google Scholar 

  21. Young-Kyu, K. and Dong-Won, P., Liquid–liquid equilibrium for the quaternary system water + tetrahydrofuran + n-heptane + butyl acetate mixture at 25°C and atmospheric pressure, J. Ind. Eng. Chem. (Amsterdam, Neth.), 2008, vol. 14, no. 5, p. 602.

  22. Hussain, A. and Lee, M., Feasibility study of reactive distillation configuration for 2-methoxy – 2-methylheptane, Chem. Eng. Trans., 2018, vol. 69, p. 625.

    Google Scholar 

  23. Timofeev, V.S., Serafimov, L.A., and Timoshenko, A.V., Printsipy tekhnologii osnovnogo organicheskogo i neftekhimicheskogo sinteza (Principles of the Technology of Basic Organic and Petrochemical Synthesis), Moscow: Vysshaya Shkola, 2010.

  24. Frolkova, A.K., Razdelenie azeotropnykh smesei. Fiziko-khimicheskie osnovy i tekhnologicheskie priemy (Separation of Azeotropic Mixtures: Physicochemical Foundations and Technological Approaches), Moscow: VLADOS, 2010.

  25. Gerbaud, V., Rodriguez-Donis, I., Hegely, L., Lang, P., Denes, F., and You, X.Q., Review of extractive distillation: Process design, operation, optimization and control, Chem. Eng. Res. Des., 2019, vol. 141, p. 229.

    CAS  Google Scholar 

  26. Pequenin, A. and Gomis, V., Quaternary isobaric (vapor + liquid + liquid) equilibrium and (vapor + liquid) equilibrium for the system (water + ethanol + cyclohexane + heptane) at 101.3 kPa, J. Chem. Thermodyn., 2011, vol. 43, no. 8, p. 1097.

    CAS  Google Scholar 

  27. Frolkova, A.K., Maevskii, M.A., Oshanina, I.V., and Frolkova, A.V., Cyclohexanone: The main methods of obtaining and extracting target products from a reaction mixture, Theor. Found. Chem. Eng., 2018, vol. 52, no. 4, pp. 653–660. https://doi.org/10.1134/S0040579518040097

    Article  CAS  Google Scholar 

  28. Frolkova, A.V., Akishina, A.A., Maevskii, M.A., and Ablizin, M.A., Flowsheets of multicomponent multiphase systems separation and material balance calculation features, Theor. Found. Chem. Eng., 2017, vol. 51, no. 3, pp. 313–319. https://doi.org/10.1134/S0040579517030034

    Article  CAS  Google Scholar 

  29. Frolkova, A.V., Balbenov, S.A., Frolkova, A.K., and Akishina, A.A., Phase equilibrium in the system water–acetonitrile–cyclohexene–cyclohexanone, Russ. Chem. Bull., 2015, vol. 64, no. 10, pp. 2330–2336. https://doi.org/10.1007/s11172-015-1160-7

    Article  CAS  Google Scholar 

  30. Safrit, B.T. and Westerberg, A.W., Algorithm for generating the distillation regions for azeotropic multicomponent mixtures, Ind. Eng. Chem. Res., 1997, vol. 36, p. 1827.

    CAS  Google Scholar 

  31. Ahmad, B.S., Zhang, Y., and Barton, P.I., Product sequences in azeotropic batch distillation, AIChE J., 1998, vol. 44, no. 5, p. 1051.

    CAS  Google Scholar 

  32. Rooks, R.E., Doherty, M.F., Malone, M.F., and Julka, V., Structure of distillation regions for multicomponent azeotropic mixtures, AIChE J., 1998, vol. 44, no. 6, p. 1382.

    CAS  Google Scholar 

  33. Blagov, S. and Hasse, H., Topological analysis of vapor–liquid equilibrium diagrams for distillation process design, Phys. Chem. Chem. Phys., 2002, no. 4, p. 896.

  34. Popken, T. and Gmehling, J., Simple method for determining the location of distillation region boundaries in quaternary systems, Ind. Eng. Chem. Res., 2004, vol. 43, p. 777.

    Google Scholar 

  35. Hegely, L. and Lang, P., A new algorithm for the determination of product sequences in azeotropic batch distillation, Ind. Eng. Chem. Res., 2011, vol. 50, no. 22, p. 12757.

    CAS  Google Scholar 

  36. Ogorodnikov, S.K., Lesteva, T.M., and Kogan, V.B., Azeotropnye smesi. Spravochnik (Azeotropic Mixtures: A Handbook), Leningrad: Khimiya, 1971.

  37. Serafimov, L.A., Thermodynamic and topological analysis and problems of the separation of multicomponent polyazeotropic mixtures, Teor. Osn. Khim. Tekhnol., 1987, vol. 21, no. 1, p. 74.

    CAS  Google Scholar 

  38. Serafimov, L.A., Thermodynamic and topological analysis of heterogeneous equilibrium diagrams of multicomponent mixtures, Russ. J. Phys. Chem. A, 2002, vol. 76, no. 8, p. 1211.

    Google Scholar 

  39. Serafimov, L.A., State of the art in the thermodynamic and topological analysis of phase diagrams, Theor. Found. Chem. Eng., 2009, vol. 43, no. 3, pp. 268–278. https://doi.org/10.1134/S0040579509030051

    Article  CAS  Google Scholar 

  40. Akishina, A.A., Frolkova, A.K., and Frolkova, A.V., RF Patent 2618273, 2017.

  41. Okhlopkova, E.A., Serafimov, L.A., and Frolkova, A.V., Separation of a multicomponent system formed in epichlorohydrin production, Tonkie Khim. Tekhnol., 2016, vol. 11, no. 6, p. 36.

    CAS  Google Scholar 

  42. Frolkova, A.V. and Frolkova, A.K, The separation of five-component mixture formed in the production of methyl-isobutyl ketone, Proc. 43rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, Slovakia, 2016, p. 502.

  43. Serafimov, L.A., Frolkova, A.V., Medvedev, D.V., and Semin, G.A., Determining the structure of the distillation line diagram from its geometric development for four-component mixtures, Theor. Found. Chem. Eng., 2012, vol. 46, no. 2, pp. 120–127. https://doi.org/10.1134/S0040579512020108

    Article  CAS  Google Scholar 

  44. Serafimov, L.A. and Frolkova, A.V., Determination of vapor-liquid equilibrium diagrams of multicomponent systems, Chem. Pap., 2016, vol. 70, p. 1578.

    CAS  Google Scholar 

  45. Frolkova, A.K., Pavlenko, T.G., Babich, S.V., Beregovykh, V.V., and L’vov, S.V., USSR Inventor’s Certificate no. 1100819, Byull. Izobret., 1984, no. 4.

  46. Blyumberg, E.A., Chizhov, E.B., and Emanuel’, N.M., USSR Inventor’s Certificate no. 136356, Byull. Izobret., 1961, no. 5.

  47. Blyumberg, E.A., Chizhov, E.B., and Gel’perin, N.I., USSR Inventor’s Certificate no. 149772, Byull. Izobret., 1962, no. 17.

  48. Malesinska, B., Quinary heteroazeotrope n-octane tetrachloroethylene–nitromethane–n-propanol–water, Bull. Acad. Pol. Sci., 1964, vol. 12, no. 12, p. 853.

    CAS  Google Scholar 

  49. Engel, K.H., US Patent 2376870, 1945.

  50. Swietoslawski, W. and Galska, A., A method for determining the composition of quaternary heteroazeotropes, Bull. Acad. Pol. Sci., 1954, vol. 2, no. 10, p. 479.

    Google Scholar 

  51. Zieborak, K., On the quaternary azeotropes formed by paraffinic and naphthenic hydrocarbons with benzene, ethanol and water, Rocz. Chem., 1951, vol. 25, no. 3, p. 388.

    CAS  Google Scholar 

  52. Zieborak, K. and Galska, A., A method for determining the composition of quaternary azeotropes and the position of heteroazeotropic lines, Bull. Acad. Pol. Sci., 1955, vol. 3, no. 7, p. 379.

    Google Scholar 

  53. Kominek-Szczepanik, M., Four-component azeotropes, Rocz. Chem., 1959, vol. 33, no. 2, p. 553.

    CAS  Google Scholar 

  54. Kominek-Szczepanik, M., About polyazeotropic toluene systems from a series of homologous paraffin hydrocarbons contained in gasoline boiling at 100-130°C and butanol, Rocz. Chem., 1955, vol. 29, nos 2-3, p. 945.

    CAS  Google Scholar 

  55. Harding, S.T., Maranas, C.D., McDonald, C.M., and Floudas, C.A., Locating all azeotropes in homogeneous azeotropic systems, Comput. Chem. Eng., 1996, vol. 20, p. 413.

    Google Scholar 

  56. Imamura, I., Kutsuwa, Y., and Matsuyama, H., Reduction of the existing region of a quaternary azeotrope by use of a topological condition, Kagaku Kogaku Ronbunshu, 1992, vol. 18, no. 4, p. 535.

    CAS  Google Scholar 

  57. Wang, Q., Yan, X.-H., Chen, G.-H., and Han, S.-J., Measurement and prediction of quaternary azeotropes for cyclohexane + 2-propanol + ethyl acetate + butanone system at elevated pressures, J. Chem. Eng. Data, 2003, vol. 48, p. 66.

    CAS  Google Scholar 

  58. Galska-Krajewska, A. and Zieborak, K., Quaternary positive-negative azeotrope, Rocz. Chem., 1962, vol. 36, no. 1, p. 119.

    CAS  Google Scholar 

  59. Swietoslawski, W., New kinds of azeotropes, Bull. Acad. Pol. Sci., 1955, vol. 7, no. 1, p. 13.

    Google Scholar 

  60. Zieborak, K. and Galska-Krajewska, A., Quaternary positive-negative azeotrope, Bull. Acad. Pol. Sci., 1959, vol. 7, no. 4, p. 253.

    CAS  Google Scholar 

  61. Vahdat, N. and Sather, G.A., Prediction of multicomponent azeotrope composition and temperature, Chem. Eng. J., 1985, vol. 31, no. 2, p. 83.

    CAS  Google Scholar 

  62. Ryland, G.A., Contribution to the study of liquid mixtures of constant boiling-point, Am. Chem. J., 1899, vol. 22, p. 384.

    Google Scholar 

  63. Hanumantha, R.G. and Subbarao, B.V., Isobaric vapor-liquid equilibria: Chloroform + isopropanol, tertiary butanol + toluene, and tertiary butanol + trichloroethylene systems, Indian J. Technol., 1974, vol. 12, pp. 292–295.

    Google Scholar 

  64. Conti, J.J., Othmer, D.F., and Gilmont, R.J., Composition of vapors from boiling binary solutions. Systems containing formic acid, acetic acid, water, J. Chem. Eng. Data, 1960, vol. 5, p. 301.

    CAS  Google Scholar 

  65. Lin, Y.-F. and Tu, C.-H., Isobaric vapor–liquid equilibria for the binary and ternary mixtures of 2-propanol, water, and 1,3-propanediol at P = 101.3 kPa: Effect of the 1,3-propanediol addition, Fluid Phase Equilib., 2014, vol. 368, p. 104.

    CAS  Google Scholar 

  66. Gu, F. and Hou, Y.J., Salt effects on the isobaric vapor-liquid equilibrium for four binary systems, J. Chem. Eng. Data, 2000, vol. 45, p. 467.

    CAS  Google Scholar 

  67. Gultekin, N.J., Vapor-liquid equilibria for binary and ternary systems composed of acetone, 2-propanol, and 1-propanol, J. Chem. Eng. Data, 1989, vol. 34, p. 168.

    CAS  Google Scholar 

  68. Morachevskii, A.G. and Rabinovich, R.Sh., The vapor–liquid equilibrium in the chloroform–ethanol system, Zh. Prikl. Khim., 1959, vol. 32, no. 2, p. 458.

    CAS  Google Scholar 

  69. Reinders, W.J. and de Minjer, C.H., Vapour-liquid equilibria in ternary systems. vi. the system water-acetone-chloroform, Recl. Trav. Chim., 1947, vol. 66, no. 9, p. 573.

    CAS  Google Scholar 

  70. Henley, E.J. and Seader, J.D., Equilibrium-Stage Separation Operations in Chemical Engineering, New York: Wiley, 1981.

    Google Scholar 

  71. Kudryavtseva, L.S., Kivia, Kh.L., and Susarev, M.P., Calculation of the Composition of Ternary Heteroazeotropes of the Type Hydrocarbon (Halogenoderivative of Hydrocarbon)–Water–Alcohol, Moscow: VINITI, 1971.

    Google Scholar 

  72. Yan, X.H., Wang, Q., and Chen, G., Azeotropes at elevated pressures for systems involving cyclohexane, 2-propanol, ethyl acetate, and butanone, J. Chem. Eng. Data, 2001, vol. 46, p. 1235.

    CAS  Google Scholar 

  73. Stephenson, R.M., Mutual solubilities: Water–ketones, water–ethers, and water–gasoline–alcohols, J. Chem. Eng. Data, 1992, vol. 37, p. 80.

    CAS  Google Scholar 

  74. Budantseva, L.S., Lesteva, T.M., and Nemtsov, M.S., Ravnovesiya zhidkost’-zhidkost’ v sistemakh metanol–voda–parafinovye uglevodorody C7, C8 (Liquid–Liquid Equilibria in Methanol–Water–Paraffin Hydrocarbons C7, C8 Systems), Moscow: Vses. Nauchno-Issled. Inst. Ekon., Organ. Proizvod. i Tekh.-Ekon. Inf. v Gazov. Prom-sti., 1976.

  75. Serafimov, L.A., Azeotropic relationship and classification of multicomponent mixtures: VIII. General patterns of tangential azeotropy, Zh. Fiz. Khim., 1971, vol. 45, no. 5, p. 1140.

    CAS  Google Scholar 

  76. Serafimov, L.A., Azeotropic relationship and classification of multicomponent mixtures: IX. Tangential azeotropy and the general relationship between singular points of different types, Zh. Fiz. Khim., 1971, vol. 45, no. 6, p. 1473.

    CAS  Google Scholar 

  77. Serafimov, L.A., Azeotropic relationship and classification of multicomponent mixtures: X. Doubly tangential azeotropes, Zh. Fiz. Khim., 1971, vol. 45, no. 7, p. 1620.

    CAS  Google Scholar 

  78. Serafimov, L.A., Azeotropic relationship and classification of multicomponent mixtures: XI. Tangential azeotropy in three-component mixtures and chains of topological structures, Zh. Fiz. Khim., 1971, vol. 45, no. 10, p. 2448.

    CAS  Google Scholar 

  79. Bedretdinov, F.N. and Chelyuskina, T.V., Study of various isomanifolds in four-component systems containing biazeotropic binary constituents, Tonkie Khim. Tekhnol., 2018, vol. 13, no. 1, pp. 45–54.

    CAS  Google Scholar 

  80. Zharov, V.T. and Serafimov, L.A., Fiziko-khimicheskie osnovy distillyatsii i rektifikatsii (Physicochemical Fundamentals of Distillation Processes), Leningrad: Khimiya, 1975.

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This work was supported by the Russian Science Foundation (project no. 19-19-00620).

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  1. Lomonosov Institute of Fine Chemical Technology, MIREA – Russian Technological University, 119454, Moscow, Russia

    A. V. Frolkova, T. E. Ososkova & A. K. Frolkova

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  1. A. V. Frolkova
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Frolkova, A.V., Ososkova, T.E. & Frolkova, A.K. Thermodynamic and Topological Analysis of Phase Diagrams of Quaternary Systems with Internal Singular Points. Theor Found Chem Eng 54, 407–419 (2020). https://doi.org/10.1134/S0040579520020049

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