Estimation of Langmuir Adsorption Isotherm Parameters Using Nonlinear Optimization Method

Document Type : Research Article


Chemical Engineering Department, University of Mohaghegh Ardabili, Ardabil, I.R. IRAN


Accurate parameter estimation of non-linear mathematical models is one of the most important calculations in science and engineering. Different methods based on linearization or optimization are applied to find the parameters of the equations. In this article, a new method for parameter estimation in Langmuir adsorption isotherm has been developed. In this method, the structure of the mentioned equation was investigated similarly to the linear curve fitting method and a nonlinear single variable optimization problem was obtained. Results of Methylene blue adsorption by bentonite were used as experimental data sets and the method was compared with other linearization methods. This comparison was based on three statistical methods including Coefficient of determination, Root means square error and Normalized standard deviation, and the Langmuir isotherm parameters were considered. Compared to the linearization nature that makes errorsin mathematical calculations, the proposed nonlinear method provides better results and can be used in other similar equations.


Main Subjects

[1] عی، ح. و م. شیروانی. کاربرد کامپوزیت پلی‌اکریلیک اسید ـ بنتونیت برای جذب کروم از محلول های آبی، نشریه شیمی و مهندسی شیمی ایران، (2) 36: 127 تا 139 (1396).
[2] Bergaya, F. and Lagaly G., "Chapter 1 - General Introduction: Clays, Clay Minerals, and Clay Science", in: "Developments in Clay Science", F. Bergaya and G. Lagaly, (Editors)., Elsevier. p. 1-19 (2013).
[3] Ismadji, S., F.E. Soetaredjo, Ayucitra A., Natural Clay Minerals as Environmental Cleaning Agents, in “Clay Materials for EnvironmentalRemediation”, Springer. p. 5-37 (2015).
[4] Hussin F., Aroua M.K., Daud W.M.A.W., Textural Characteristics, Surface Chemistry and Activation of Bleaching Earth: A Review, Chemical Engineering Journal, 170(1): 90-106 (2011).
[5] Moraes J.D.D., Bertolino S.R.A., Cuffini S.L., Ducart D.F., Bretzke P.E., Leonardi G.R., Clay Minerals: Properties and Applications to Dermocosmetic Products and Perspectives of Natural Raw Materials for Therapeutic Purposes - A Review, International Journal of Pharmaceutics, 534(1): 213-219 (2017).
[6] طهمورسی، م.؛ ا. صرافی، ع.؛ منصوری، ایرج؛ لشکری، ب.؛ جذب یون­های مس، روی و نیکل توسط بنتونیت کلسیمی، نشریه شیمی و مهندسی شیمی ایران، (1)32: 7 تا 16 (1392).
[7] Alaei Shahmirzadi M.A., Hosseini S.S., Luo J., Ortiz I., Significance, Evolution and Recent Advances in Adsorption Technology, Materials and Processes for Desalination, Water Softening and Salt Removal, Journal of Environmental Management, 215: 324-344 (2018).
[8] Cooney D.O., “Adsorption Design for Wastewater Treatment”, CRC Press (1998).
[9] Kumar, K.V., Sivanesan S., Sorption Isotherm for Safranin onto Rice Husk: Comparison of Linear and Non-Linear Methods, Dyes and Pigments, 72(1): 130-133 (2007).
[10] Foo K., Hameed B., Insights into the Modeling of Adsorption Isotherm Systems, Chemical Engineering Journal, 156(1): 2-10 (2010).
[11] Srivastava V.C., Swamy M.M., Mall I.D., Prasad B., Mishra I.M., Adsorptive Removal of Phenol by Bagasse Fly Ash and Activated Carbon: Equilibrium, Kinetics and Thermodynamics, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 272(1): 89-104 (2006).
[13] El-Khaiary M.I., Least-Squares Regression of Adsorption Equilibrium Data: Comparing the Options, Journal of Hazardous Materials, 158(1): 73-87  (2008).
[14] Vijayaraghavan K., Padmesh T., Palanivelu K., Velan M., Biosorption of Nickel (II) Ions onto Sargassum Wightii: Application of Two-Parameter and Three-Parameter Isotherm Models, Journal of Hazardous Materials, 133(1): 304-308 (2006).
[15] Davis T.A., Volesky B., Mucci A., A Review of the Biochemistry of Heavy Metal Biosorption by Brown Algae, Water Research, 37(18): 4311-4330 (2003).
[16] احمدی اسبچین، س.، ا.ع. پوربابایی، و ا. آندره.؛ بررسی فرایند جذب زیستی همزمان دو فلز روی/ نیکل به وسیله جلبک قهوه ای فوکوس سراتوس، نشریه شیمی و مهندسی شیمی ایران، (1)32: 85 تا 91 (1392).
[17] Langmuir I., The Constitution and Fundamental Properties of Solids and Liquids. Part I. Solids, Journal of the American Chemical Society, 38(11): 2221-2295  (1916).
[18] Foo K.Y., Hameed B.H., Insights into the Modeling of Adsorption Isotherm Systems, Chemical Engineering Journal, 156(1): 2-10 (2010).
[19] Heydari A., Fattahi M., Khorasheh F., A New Nonlinear Optimization Method for Parameter Estimation in Enzyme Kinetics, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 37(12): 1275-1281 (2015).
[20] Merikhy A., Heydari A., Eskandari H., Nematollahzadeh A., Revalorization of Spent Bleaching Earth a Waste from Vegetable Oil Refinery Plant by an Efficient Solvent Extraction System, Waste and Biomass Valorization, 1-11 (2018).
[21] Khdour O.M., Bandyopadhyay I., Chowdhury S.R., Visavadiya N.P., Hecht S.M., Lipophilic Methylene Blue Analogues Enhance Mitochondrial Function and Increase Frataxin Levels in a Cellular Model of Friedreich’s Ataxia, Bioorganic & Medicinal Chemistry, 26(12): 3359-3369 (2018).