Exploring Nitrogen Release from Urea Fertilizer Coated with Biodegradable Acetylated Lignin Sulfonate: A Numerical Analysis Using the Crank-Nicolson Method

Document Type : Research Article

Authors

Department of Chemical Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, Ardebil, Iran

Abstract
Soil alone cannot provide plants with all the vital nutrients they need. Chemical fertilizers are often used to supplement these nutrients but can introduce harmful contaminants. Fertilizers are coated to prevent wastage, cut costs, and minimize environmental pollution. Utilizing natural and biodegradable polymers is a highly viable option for coating fertilizers and producing slow-release fertilizers. These polymers, such as acetylated lignin sulfonate, offer an ideal solution owing to their natural abundance and efficient utilization. The system's behavior is comprehensively studied by modeling the nitrogen penetration process into the coating. The diffusion coefficient (D), concentration profile, and release rate are generally determined through modeling. Due to the thinness of the membrane, it is impossible to determine the concentration profile experimentally. Therefore, the total mass transferred through the membrane (Mt) is typically measured at specific intervals. The D, a parameter influencing Mt at specific times, is determined differently. This article aims to determine the concentration profile numerically using the Crank–Nicolson method for urea fertilizer coated with acetylated lignin sulfonate. Release charts are generated at various time points by solving Mt. Investigations indicate that at around 3000 seconds, the concentration profile becomes entirely linear and aligns with the concentration profile at 12000 seconds. Furthermore, beyond 3000 seconds, the stability of the concentration profile about time signifies a steady-state system. A comparative analysis between the experimental data and the numerical solution results demonstrates the high accuracy of the numerical solution, with the maximum relative error occurring at 7895 seconds.

Graphical Abstract

Exploring Nitrogen Release from Urea Fertilizer Coated with Biodegradable Acetylated Lignin Sulfonate: A Numerical Analysis Using the Crank-Nicolson Method

Keywords

Subjects


[1] S. Moradi, K. Shayesteh, and G. Behbudi, Preparation and characterization of biodegradable lignin-sulfonate nanoparticles using the microemulsion method to enhance the acetylation efficiency of lignin-sulfonate. Int. J. Biol. Macromol., 160 (2020)  632-641.
[2] H. Seddighi, K. Shayesteh, and M. Arjmand, A Review of Slow-release Fertilizers from the Perspective of the Environment and Economy, and its Future in Iran and the World. Sustain. Agric. Sci. Res., 3 (2023)  51-68.
[3] H. Seddighi, K. Shayesteh, and M. Arjmand, A review of drug or fertilizer release mechanism, in 12th International Chemical Engineering Congress & Exhibition. 2023.
[4] H. Seddighi and K. Shayesteh, Slow-Release Fertilizers: A Promising Solution to Environment Pollution. J. Environ. Sci. Stud., 9 (2024)  8407-8417.
[5] H. Seddighi, K. Shayesteh, N. Omrani, and P. Es'haghi, Fertilizers Coating Methods: A Mini Review of Various Techniques. Chem. Res. Technol., 1 (2024)  38-48.
[6] H. Seddighi, K. Shayesteh, and M. Arjmand, An overview of the models presented for drug or fertilizer release based on mathematical and experimental models, in 12th International Chemical Engineering Congress & Exhibition. 2023.
[7] G. Behboudi, K. Shayesteh, M.T. Yaraki, H.A. Ebrahimi, and S. Moradi, Optimized synthesis of lignin sulfonate nanoparticles by solvent shifting method and their application for adsorptive removal of dye pollutant. Chemosphere, 285 (2021)  131576.
[8] S. Moradi, The significance of biot in the modeling of nitrogen release from urea lignin and improving the lignin structure at nanoscale. 2017, University of Mohaghegh Ardabili: Ardabil.
[9] S. Moradi, K. Shayesteh, and S. Lotfiman, The Modelling of the Urea Fertilizer Dissolution Process in Finite/Infinite Volumes of Water. Iran. J. Chem. Chem. Eng., 41 (2022)  1348-1359.
[10] S. Moradi, K. Shayesteh, and Q. Mohammadzadeh, Production of Urea/Acetylated-lignin Sulfonate Matrix as SRFs and an Investigation on the Effect of Hydrodynamic Conditions on Release Rate Using the Biot Number. Recent Innov. Chem. Eng., 15 (2022)  31-46.
[11] K. Shayesteh and G. Mohammadzadeh, Stepwise removal of Lignin sulfonate hydroxyl ion to reduce its solubility in an aqueous environment: As a Coating in slow-release systems or absorbent base. Chem. Rev. Lett., 7 (2024)  253-262.
[12] J. Seifdavati, Q. Mohammadzadeh, K. Shayesteh, and R. Pourbayramian, Investigation of the Bioconversion of Urea with Modified Lignosulfonate Biomass as Slow-Release Urea in Aqueous Medium and Rumen Fluid. (2024).
[13] J.B. Sheppard, B. Hambly, B. Pendley, and E. Lindner, Voltammetric determination of diffusion coefficients in polymer membranes. Anlst, 142 (2017)  930-937.
[14] Q. Chen, A. Engström, and J. Ågren, On negative diagonal elements in the diffusion coefficient matrix of multicomponent systems. Jr. Phase Equilib Diff, 39 (2018)  592-596.
[15] C. Yeom and R. Huang, A new method for determining the diffusion coefficients of penetrants through polymeric membranes from steady state pervaporation experiments. J. Membr. Sci., 68 (1992)  11-20.
[16] R.Y. Huang and J.W. Rhim, Theoretical estimations of diffusion coefficients. J. Appl. Polym. Sci., 41 (1990)  535-546.
[17] T. Walcher and D. Göritz, A method for determining intrinsic diffusion coefficients in the pervaporation process. Macromol. Chem. Phys., 196 (1995)  429-439.
[18] G. Dudek and P. Borys, A simple methodology to estimate the diffusion coefficient in pervaporation-based purification experiments. Polym., 11 (2019)  343.
[19] J. Crank, The mathematics of diffusion. Oxford university press (1979).
[20] H. Bruining, M. Darwish, and A. Rijnks, Computation of the longitudinal and transverse dispersion coefficient in an adsorbing porous medium using homogenization. Transp. Porous Media, 91 (2012)  833-859.
[21] F. Rouholahnejad and M. Tabrizchi, A new method for measuring the diffusion coefficient in a gas phase. J. Phys. Chem. A, 110 (2006)  11208-11213.
[22] M. Hamada and P. de Anna, A method to measure the diffusion coefficient in liquids. Transp. Porous Media, (2021)  1-12.
[23] D. Kouzoudis, T. Baimpos, and G. Samourgkanidis, A new method for the measurement of the diffusion coefficient of adsorbed vapors in thin zeolite films, based on magnetoelastic sensors. Sens., 20 (2020)  3251.
[24] M.R. Payne and K.R. Morison, A multi-component approach to salt and water diffusion in cheese. Int. Dairy J., 9 (1999)  887-894.
[25] J. Floury, S. Jeanson, S. Aly, and S. Lortal, Determination of the diffusion coefficients of small solutes in cheese: a review. Dairy Sci. Technol, 90 (2010)  477-508.
[26] C. Chmelik, J. Caro, D. Freude, J. Haase, R. Valiullin, and J. Kärger, Diffusive spreading of molecules in nanoporous materials, in Diffusive spreading in nature, technology and society. Springer (2023) 179-214.
[27] J. Kärger, D.M. Ruthven, and R. Valiullin, Diffusion in nanopores: inspecting the grounds. Adsorption, 27 (2021)  267-281.
[28] R. Krishna, D. Paschek, and R. Baur, Modeling the occupancy dependence of diffusivities in zeolites. Microporous Mesoporous Mater., 76 (2004)  233-246.
[29] H.A. Daynes, The process of diffusion through a rubber membrane. Proc. R. soc. Lond. Ser. A-Contain. Pap. Math. Phys. Character, 97 (1920)  286-307.
[30] S. Rutherford and D. Do, Review of time lag permeation technique as a method for characterisation of porous media and membranes. Adsorption, 3 (1997)  283-312.
[31] A. Bijani, K. Shayesteh, M.R. Zamanlou, and K. Hashemi Majd, Determination of Nitrogen diffusion coefficent of urea-lignin system by time-lag method. 2018, University of Mohaghegh Ardabili.
[32] H. Wu, J. Thibault, and B. Kruczek, The validity of the time-lag method for the characterization of mixed-matrix membranes. J. Membr. Sci., 618 (2021)  118715.
Volume 7, Issue 6 - Serial Number 6
November and December 2024
Pages 1042-1052

  • Receive Date 22 April 2024
  • Revise Date 27 May 2024
  • Accept Date 31 May 2024