Genetic Algorithm Based Nonlinear Optimization of Adsorption Processes

Abstract

In this study, for different adsorption processes, nonlinear isotherm, kinetic model and thermodynamic parameters were calculated using genetic algorithm-based optimization method. Nonlinear equations were directly used as the model parameters can change to give false results when they are transformed to linear forms. Fifteen isotherms and two kinetic models were considered. All the experimental data was taken from the literature. Methylene green, thiram, and phenol red were used as the adsorbates and silica gel and chemically activated coal mining waste with potassium carbonate (K2CO3) or zinc chloride (ZnCl2) were used as the adsorbents. For three different temperatures, the Root Mean Square Error (RMSE) values were obtained between calculated and the experimental data. The biggest RMSE values were obtained as 5.23 x 10-1 for Freundlich isotherm at 45 °C and the smallest RMSE value was obtained as 3.19 x 10-4 for Halsey isotherm at 35°C. For the kinetic study, Lagergren and Particle Internal Diffusion models were applied to the experimental data for three different initial concentrations and it was shown that Lagergren pseudo-first-order Kinetic Model fits better to experimental data. Thermodynamic calculations were made for two different initial pH values and four different temperatures. The Arrhenius factor (A) and Arrhenius activation energies (Ea) (kJ/mol) were also calculated.

Keywords

• Adsorption
• genetic algorithm
• isotherms
• kinetics
• thermodynamics.

References

1. 1. Yang RT. Adsorbents: fundamentals and applications. Hoboken, N.J: Wiley-Interscience; 2003. 410 p. ISBN: 978-0-471-29741-3.
2. 2. Aarden FF. Adsorption onto heterogeneous porous materials : equilibria and kinetics [Internet] [PhD Thesis]. [Eindhoven, the Netherlands]: Technische Universiteit Eindhoven; 2001 [cited 2021 Nov 25].
3. 3. Thomas WJ, Crittenden BD. Adsorption technology and design. Oxford ; Boston: Butterworth-Heinemann; 1998. 271 p. ISBN: 978-0-7506-1959-2.
4. 4. Topçuoğlu E. Boyar maddelerin çeşitli adsorbanlarla adsorpsiyonunun incelenmesi [MSc Thesis]. [Istanbul, Turkey]: Istanbul University; 2016.
5. 5. Mısırlı T. Kömür Madeni Atıklarından Elde Edilen Adsorbentlerle Boyar Madde ve Pestisit Uzaklaştırılması [MSc Thesis]. [Istanbul, Turkey]: Istanbul University; 2004.
6. 6. Saadi R, Saadi Z, Fazaeli R, Fard NE. Monolayer and multilayer adsorption isotherm models for sorption from aqueous media. Korean J Chem Eng. 2015 May;32(5):787–99.
7. 7. Tóth J, editor. Adsorption: theory, modeling, and analysis. New York: Marcel Dekker; 2002. 878 p. (Surfactant science series). ISBN: 978-0-8247-0747-7.
8. 8. Chattaraj S, Mohanty D, Kumar T, Halder G. Thermodynamics, kinetics and modeling of sorption behaviour of coalbed methane – A review. Journal of Unconventional Oil and Gas Resources. 2016 Dec;16:14–33. .

9. 9. Siddiqui SI, Chaudhry SA. A review on graphene oxide and its composites preparation and their use for the removal of As3+and As5+ from water under the effect of various parameters: Application of isotherm, kinetic and thermodynamics. Process Safety and Environmental Protection. 2018 Oct;119:138–63.
10. 10. Bonilla-Petriciolet A, Mendoza-Castillo DI, Reynel-Ávila HE, editors. Adsorption Processes for Water Treatment and Purification. 1st ed. 2017. Cham: Springer International Publishing : Imprint: Springer; 2017. 1 p. ISBN: 978-3-319-58136-1.
11. 11. Cherkasov N. Liquid-phase adsorption: Common problems and how we could do better. Journal of Molecular Liquids. 2020 Mar;301:112378.
12. 12. Ho YS, McKay G. Pseudo-second order model for sorption processes. Process Biochemistry. 1999 Jul;34(5):451–65.
13. 13. Ghasemi M, Ghasemi N, Zahedi G, Alwi SRW, Goodarzi M, Javadian H. Kinetic and equilibrium study of Ni(II) sorption from aqueous solutions onto Peganum harmala-L. Int J Environ Sci Technol. 2014 Oct;11(7):1835–44.
14. 14. Lin J, Wang L. Comparison between linear and non-linear forms of pseudo-first-order and pseudo-second-order adsorption kinetic models for the removal of methylene blue by activated carbon. Front Environ Sci Eng China. 2009 Sep;3(3):320–4.
15. 15. Doğan M, Alkan M. Adsorption kinetics of methyl violet onto perlite. Chemosphere. 2003 Jan;50(4):517–28.
16. 16. Bhattacharya AK, Venkobachar C. Removal of Cadmium (II) by Low Cost Adsorbents. Journal of Environmental Engineering. 1984 Feb;110(1):110–22.
17. 17. Aljeboree AM, Alshirifi AN, Alkaim AF. Kinetics and equilibrium study for the adsorption of textile dyes on coconut shell activated carbon. Arabian Journal of Chemistry. 2017 May;10:S3381–93.
18. 18. Guo Z, Liu X, Huang H. Kinetics and Thermodynamics of Reserpine Adsorption onto Strong Acidic Cationic Exchange Fiber. Peters M, editor. PLoS ONE. 2015 Sep 30;10(9):e0138619.
19. 19. Idan IJ, Abdullah LC, Choong TS, Jamil SNABM. Equilibrium, kinetics and thermodynamic adsorption studies of acid dyes on adsorbent developed from kenaf core fiber. Adsorption Science & Technology. 2018 Feb;36(1–2):694–712.
20. 20. Hubbe M, Azizian S, Douven S. Implications of apparent pseudo-second-order adsorption kinetics onto cellulosic materials: A review. BioRes. 2019 Aug;14(3):7582–626.
21. 21. Singh SK, Townsend TG, Mazyck D, Boyer TH. Equilibrium and intra-particle diffusion of stabilized landfill leachate onto micro- and meso-porous activated carbon. Water Research. 2012 Feb;46(2):491–9.
22. 22. Abdel Salam M, Burk RC. Thermodynamics and Kinetics Studies of Pentachlorophenol Adsorption from Aqueous Solutions by Multi-Walled Carbon Nanotubes. Water Air Soil Pollut. 2010 Jul;210(1–4):101–11.
23. 23. Chen F, Zhou C, Li G, Peng F. Thermodynamics and kinetics of glyphosate adsorption on resin D301. Arabian Journal of Chemistry. 2016 Nov;9:S1665–9.
24. 24. Hameed BH, Ahmad AA, Aziz N. Isotherms, kinetics and thermodynamics of acid dye adsorption on activated palm ash. Chemical Engineering Journal. 2007 Sep;133(1–3):195–203.
25. 25. Mitchell M. An introduction to genetic algorithms. Cambridge, Mass: MIT Press; 1996. 205 p. (Complex adaptive systems). ISBN: 978-0-262-13316-6.
26. 26. Anonymous. How the Genetic Algorithm Works [Internet]. [cited 2021 Oct 13].
27. 27. Ho YS, Mckay G. Kinetic Models for the Sorption of Dye from Aqueous Solution by Wood. Process Safety and Environmental Protection. 1998 May;76(2):183–91.