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 A modified differential evolution algorithm (MDE) has been used for solving different process related design problems (namely calculation of the NRTL and Two-Suffix Margules activity coefficient models parameters in 20 ternary extraction systems including different ionic liquids and reactor network design problem). The obtained results, in terms of root mean square deviations (rmsd) for these models are satisfactory, with the overall values of 0.0023 and 0.0170 for 169 tie-lines for NRTL and Two-Suffix Margules models, respectively. The results showed that the MDE algorithm results in better solutions compared to the previous work based on genetic algorithm (GA) for correlating liquid-liquid equilibrium (LLE) data in these systems. MDE also outperformed DE algorithm when tested on reactor network design problem with respect to convergence and speed.



NRTL Two-suffix margules Parameter estimation Ionic liquid Optimization.

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Gujarathia, A., Vakili-Nezhaad, G., & Vatani, M. (2016). Optimization of Process Design Problems Using Differential Evolution Algorithm. The Journal of Engineering Research [TJER], 13(1), 89–102.


  1. Alkhaldi KHAE, Al-Tuwaim MS, Fandary MS, Al-Jimaz AS (2011), Separation of propylbenzene and n-alkanes from their mixtures using 4-methyl-N-butylpyridinium tetrafluoroborate as an ionic solvent at several temperatures. Fluid Phase Equilibria 309: 102– 107.
  2. Al-Maamari RS, Vakili-Nezhaad G, Vatani M (2015), Experimental and modeling investigations of the viscosity of crude oil binary blends: New Models Based on the Genetic Algorithm Method. The Journal of Engineering Research 11: 81-91.
  3. Angira R (2006), Evolutionary Computation for Optimization of Selected Non-linear Chemical Processes. Ph.D. Thesis (BITS-Pilani, India).
  4. Angira R, Babu BV (2006), Optimization of process synthesis and design problems: A modified differential evolution approach. Chemical Engineering Science 61: 4707-4721.
  5. Babu BV, Angira R (2006), Modified differential evolution (MDE) for optimization of nonlinea chemical processes. Computers and Chemical Engineering 30: 989-1002.
  6. Colaco MJ, Dulikravich GS, Martin TJ (2004), optimization of wall electrodes for electrohydrodynamic control of natural convection during solidification. Materials and Manufacturing Processes 19: 719–736.
  7. Dománska U, Pobudkowska A, Krolikowski M (2007), Separation of aromatic hydrocarbons from alkanes using ammonium ionic liquid C2NTf2 at T = 298.15 K. Fluid Phase Equilibria 259: 173–179.
  8. Domínguez I, González EJ, González R, Domínguez A (2011), Extraction of benzene from aliphatic compounds using commercial ionic liquids as solvents: study of the liquid– liquid equilibrium at t = 298.15 K. Journal of Chemical and Engineering Data 56: 3376–3383.
  9. Fan HY, Lampinen J (2003), Trigonometric mutation operation to differential evolution. Journal of Global Optimization 27: 105–129.
  10. García J, Fernández A, Torrecilla J, Oliet M, Rodríguez F (2009), Liquid–liquid equilibria for {hexane + benzene + 1-ethyl-3- methylimidazolium ethylsulfate} at (298.2, 313.2 and 328.2) K. Fluid Phase Equilibria 282: 117–120.
  11. García J, Fernández A, Torrecilla J, Oliet M, Rodríguez F (2010a), Ternary liquid−liquid equilibria measurement for hexane and benzene with the ionic liquid 1-Butyl-3- methylimidazolium methylsulfate at T = (298.2, 313.2, and 328.2) K. Journal of Chemical and Engineering Data 55: 258–261.
  12. García J, García S, Torrecilla J, Oliet M, Rodríguez F (2010b), Liquid−liquid equilibria for the ternary systems {Heptane + Toluene + N-Butylpyridinium Tetrafluoroborate or NHexylpyridinium Tetrafluoroborate} at T = 313.2 K. Journal of Chemical and Engineering Data 55: 2862–2865.
  13. Gujarathi AM, Babu BV (2009a), Improved multi objective differential evolution (MODE) approach for purified terephthalic acid (PTA) Oxidation Process. Materials and Manufacturing Processes 24: 303-319.
  14. Gujarathi AM, Babu BV (2009b), Optimization of adiabatic styrene reactor: A hybrid multi objective differential evolution (H-MODE) Approach. Industrial and Engineering Chemistry Research 48: 11115–11132.
  15. Gujarathi AM, Babu BV (2010a), Advances in optimization and simulation of low density polyethylene (LDPE) tubular reactor. In Handbook of Research on Chemo informatics and Chemical Engineering, Edited by A K Haghi, Nova Science Publishers, USA 109-138.
  16. Gujarathi AM, Babu BV (2010b), Multi-objective optimization of industrial styrene reactor: Adiabatic and pseudo-isothermal operation. Chemical Engineering Science 65: 2009-2026.
  17. Gujarathi AM, Babu BV (2011), Multiobjective optimization of industrial processes using elitist multi objective differential evolution (Elitist-MODE). Materials and Manufacturing Processes 26: 455-463.
  18. Gutierrez JP, Meindersma W, de Haan AB (2011), Binary and ternary (liquid + liquid) equilibrium for {methylcyclohexane (1) + toluene (2) + 1-hexyl-3-methylimidazolium tetracyanoborate (3)/1-butyl-3- methylimidazolium tetracyanoborate (3). The Journal of Chemical Thermodynamics 43: 1672– 1677.
  19. Hansmeier AR, Jongmans M, Meindersma GW, de Haan AB (2010a), LLE data for the ionic liquid 3-methyl-N-butyl pyridinium dicyanamide with several aromatic and aliphatic hydrocarbons. The Journal of Chemical Thermodynamics 42: 484–490.
  20. Hansmeier AR, Minoves Ruiz M, Meindersma GW, de Haan AB (2010b), Liquid−liquid equilibria for the three ternary systems (3- methyl-N-butylpyridinium dicyanamide + Toluene + Heptane), (1-Butyl-3- methylimidazolium Dicyanamide + Toluene + Heptane) and (1-Butyl-3-methylimidazolium Thiocyanate + Toluene + Heptane) at T = (313.15 and 348.15) K and p = 0.1 MPa. Journal of Chemical and Engineering Data 55: 708–713.
  21. Holland JH (1992), Algoritmos geneticos. Investigacion Y Ciencia 192: 38–45.
  22. Kirkpatrick S, Gelatt CD, Vecchi MP (1983), Optimization by simulated annealing. Science 220: 671–680.
  23. Lei Z, Zhang J, Li Q, Chen B (2009), UNIFAC model for ionic liquids. Industrial and Engineering Chemistry Research 48: 2697-2704.
  24. Letcher TM, Deenadayalu N (2003), Ternary liquid–liquid equilibria for mixtures of 1- methyl- 3 – octyl - imidazolium
  25. chlorideþbenzeneþan alkane at T=298.2K and 1 atm. The Journal of Chemical Thermodynamics 35: 67–76.
  26. Letcher TM, Reddy P (2005), Ternary (liquid+liquid) equilibria for mixtures of 1- hexyl-3-methylimidazolium (tetrafluoroborate or hexafluorophosphate)+benzene+alkane at T=298.2 K and p=0.1 MPa. The Journal of Chemical Thermodynamics 37: 415–421.
  27. Maduro RM, Aznar M (2008), Liquid–liquid equilibrium of ternary systems 1-butyl-3- methylimidazolium hexafluorophosphate + aromatic + aliphatic. Fluid Phase Equilibria 265: 129–138.
  28. Maduro RM, Aznar M (2010), Liquid–liquid equilibrium of ternary systems 1-octyl-3- methylimidazolium hexafluorophosphate + aromatic + aliphatic hydrocarbons. Fluid Phase Equilibria 296: 88–94.
  29. Pereiro AB, Rodriguez A (2009), Application of the ionic liquid Ammoeng 102 for
  30. aromatic/aliphatic hydrocarbon separation. The Journal of Chemical Thermodynamics 41: 951–956.
  31. Prausnitz JM, Lichtenthaler RN, Azevedo EG (1999), Molecular thermodynamics of fluid phase equilibria, third ed., Prentice-Hall, New York.
  32. Price KV, Storn RM, Lampinen JA (2005), Differential evolution: A practical approach to global optimization. Springer, Berlin Heidelberg.
  33. Rashtchian D, Ovaysi S, Taghikhani V, Ghotbi C (2007), Application of the genetic algorithm to calculate the interaction parameters for multiphase and multicomponent systems.
  34. Iranian Journal of Chemistry and Chemical Engineering 26: 89-102.
  35. Renon H, Prausnitz J M (1968), Local compositions in thermodynamic excess functions for liquid mixtures. AIChE Journal 14: 135–144.
  36. Revelli AL, Mutelet F, Jaubert JN (2010), Extraction of benzene or thiophene from nheptane using ionic liquids. NMR and thermodynamic study. The Journal of Physical Chemistry B 114: 4600-4608.
  37. Ryoo HS, Sahinidis NV (1995), Global optimization of nonconvex NLPs and MINLPs with applications in process design. Computers and Chemical Engineering 19: 551–566.
  38. Sahoo RK, Banerjee T, Ahmad SA, Khanna A (2006), Improved binary parameters using GA for multi-component aromatic extraction: NRTL model without and with closure equations. Fluid Phase Equilibria 239: 107–119.
  39. Sahoo RK, Banerjee T, Khanna A (2007), UNIQUAC interaction parameters with closure for imidazolium based ionic liquid systems using genetic algorithm. The Canadian Journal of Chemical Engineering 85: 833–853.
  40. Seader JD, Henley E J (2006), Separation process principles, second ed., John Wiley and Sons, Inc., New York.
  41. Selvan MS, McKinley MD, Dubois RH, Atwood JL (2000), Liquid−liquid equilibria for toluene + heptane + 1-Ethyl-3-methylimidazolium triiodide and toluene + heptane + 1-Butyl-3- methylimidazolium triiodide. Journal of Chemical and Engineering Data 45: 841-845.
  42. Singh MK, Banerjee T, Khanna A (2005), Genetic algorithm to estimate interaction parameters of multicomponent systems for liquid–liquid equilibria. Computers and Chemical Engineering 29: 1712–1719.
  43. Stragevitch L, Davila SG (1997), Application of a generalized maximum likelihood method in the reduction of multicomponent liquid-liquid equilibrium data. Brazilian Journal of Chemical Engineering 14: 41–52.
  44. Stumberger G, Dolinar D, Pahner U, Hameyer K (2000), Optimization of radial active magnetic bearings using the finite element technique and the differential evolution algorithm. IEEE Transactions on Magnetics 36: 1009–1013.
  45. Vakili-Nezhaad G, Vatani M, Asghari M (2013), Calculation of the binary interaction and nonrandomness parameters of NRTL, NRTL1, and NRTL2 models using genetic algorithm for ternary ionic liquid systems. Chemical Engineering Communications 200: 1102–1120.
  46. Vakili-Nezhaad G, Vatani M, Gujarathi AM (2014), Application of genetic algorithm to calculation of three-suffix margules parameters in ternary extraction ionic liquid systems. International Journal of Thermodynamics 17: 1-6.
  47. Vatani M, Asghari M, Vakili-Nezhaad G (2012), Application of genetic algorithm to the calculation of parameters for NRTL and twosuffix margules models in ternary extraction ionic liquid systems. Journal of Industrial and Engineering Chemistry 18: 1715– 1720.
  48. Zhou T, Wang Z, Chen L, Ye Y, Qi Z, Freund H, Sundmacher K (2012), Evaluation of the ionic liquids 1-alkyl-3-methylimidazolium hexafluorophosphate as a solvent for the extraction of benzene from cyclohexane: (Liquid + liquid) equilibria. The Journal of Chemical Thermodynamics 48: 145–149.