Nonlinear Steady-State VOC and Oxygen Modeling in Biofiltration
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Abstract
This paper compares analytical solutions for steady-state volatile organic compounds (VOC) and oxygen concentrations in the context of bio-filtration modeling. Based on a set of nonlinear reaction/diffusion equations, this model consists of the following components:
A nonlinear term from Monod kinetics and Andrew kinetics.
A Monod kinetics, interactive model.
An Andrews kinetics, interactive model.
The theoretical findings are helpful in the design of bio-filters. The ability of two independent strategies, the Akbar Ganji Method (AGM) and the Homotopy perturbation Method (HPM), to forecast steady-state concentrations is tested. The study investigates the advantages and disadvantages of both techniques, shedding insight into their practical usefulness in bio-filtration systems. The outcomes of this study lead to a better understanding of bio-filtration processes. They could influence the design.
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References
- L. Rajendran, R. Swaminathan, M. Chitra Devi, A Closer Look of Nonlinear Reaction-Diffusion Equations, Nova Science Publishers, New York, 2020.
- M.A. Deshusses, I.J. Dunn, Modeling Experiments on the Kinetics of Mixed-Solvent Removal from Waste Gas in a Biofilter, in: Proceedings of the 6th European Congress on Biotechnology, 1191–1198, Elsevier, 1994.
- K. Ranjani, R. Swaminathan, S.G. Karpagavalli, Mathematical Modelling of a Mono-Enzyme Dual Amperometric Biosensor for Enzyme-Catalyzed Reactions Using Homotopy Analysis and Akbari-Ganji Methods, Int. J. Electrochem. Sci. 18 (2023), 100220. https://doi.org/10.1016/j.ijoes.2023.100220.
- D.S. Hodge, J.S. Devinny, Modeling Removal of Air Contaminants by Biofiltration, J. Environ. Eng. 121 (1995), 21–32. https://doi.org/10.1061/(asce)0733-9372(1995)121:1(21).
- K. Ranjani, R. Swaminathan, SG. Karpagavalli, A Theoretical Investigation of Steady-State Concentration Processes at a Carrier-Mediated Transport Model Using Akbari-Ganji and Differential Transform Methods, Part. Diff. Equ. Appl. Math. 8 (2023), 100594. https://doi.org/10.1016/j.padiff.2023.100594.
- S.M. Zarook, A.A. Shaikh, Analysis and Comparison of Biofilter Models, Chem. Eng. J. 65 (1997), 55–61. https://doi.org/10.1016/s1385-8947(96)03101-4.
- J.H. He, Approximate Analytical Solution for Seepage Flow With Fractional Derivatives in Porous Media, Comp. Meth. Appl. Mech. Eng. 167 (1998), 57–68. https://doi.org/10.1016/s0045-7825(98)00108-x.
- A. Reena, SG. Karpagavalli, L. Rajendran, B. Manimegalai, R. Swaminathan, Theoretical Analysis of Putrescine Enzymatic Biosensor With Optical Oxygen Transducer in Sensitive Layer Using Akbari–ganji Method, Int. J. Electrochem. Sci. 18 (2023), 100113. https://doi.org/10.1016/j.ijoes.2023.100113.
- J.H. He, Homotopy Perturbation Method for Solving Boundary Value Problems, Phys. Lett. A 350 (2006), 87–88. https://doi.org/10.1016/j.physleta.2005.10.005.
- A. Reena, SG. Karpagavalli, R. Swaminathan, Theoretical Analysis and Steady-State Responses of the Multienzyme Amperometric Biosensor System for Nonlinear Reaction-Diffusion Equations, Int. J. Electrochem. Sci. 18 (2023), 100293. https://doi.org/10.1016/j.ijoes.2023.100293.
- B. Jang, Two-Point Boundary Value Problems by the Extended Adomian Decomposition Method, J. Comp. Appl. Math. 219 (2008), 253–262. https://doi.org/10.1016/j.cam.2007.07.036.
- A. Uma, R. Swaminathan, Mathematical Analysis of Nonlinear Reaction Diffusion Process at Carbon Dioxide Absorption in Concentrated Mixtures of 2-Amino-2-Methyl-1-Proponal and 1,8-Diamino-p-Methane, Int. J. Anal. Appl. 22 (2024), 110. https://doi.org/10.28924/2291-8639-22-2024-110.
- G. Adomian, Stochastic Nonlinear Modeling of Fluctuations in a Nuclear Reactor-A New Approach, Ann. Nuclear Energy 8 (1981), 329–330. https://doi.org/10.1016/0306-4549(81)90053-0.
- A. Soufyane, M. Boulmalf, Solution of Linear and Nonlinear Parabolic Equations by the Decomposition Method, Appl. Math. Comp. 162 (2005), 687–693. https://doi.org/10.1016/j.amc.2004.01.005.
- R. Raja, R. Swaminathan, Mathematical Analysis of Nonlinear Differential Equations in Polymer Coated Microelectrodes, Contemp. Math. 5 (2024), 2585–2598. https://doi.org/10.37256/cm.5220244426.
- M. Sivasankari, L. Rajendran, Analytical Expressions of Concentration of VOC and Oxygen in Steady-State in Biofilteration Model, Appl. Math. 04 (2013), 314–325. https://doi.org/10.4236/am.2013.42048.
- A. Nebiyal, R. Swaminathan, SG. Karpagavalli, Reaction Kinetics of Amperometric Enzyme Electrode in Various Geometries Using the Akbari-Ganji Method, Int. J. Electrochem. Sci. 18 (2023), 100240. https://doi.org/10.1016/j.ijoes.2023.100240.
- K. Ranjani, R. Swaminathan, SG. Karpagavalli, Mathematical Modelling of Three-Layer Amperometric Biosensor and Analytical Expressions Using Homotopy Perturbation Method, Part. Diff. Equ. Appl. Math. 11 (2024), 100755. https://doi.org/10.1016/j.padiff.2024.100755.
- R. Swaminathan, K.L. Narayanan, V. Mohan, K. Saranya, L. Rajendran, Reaction/Diffusion Equation with MichaelisMenten Kinetics in Microdisk Biosensor: Homotopy Perturbation Method Approach, Int. J. Electrochem. Sci. 14 (2019), 3777–3791. https://doi.org/10.20964/2019.04.13.
- A. Reena, R. Swaminathan, Mathematical Investigation of Non-Linear Reaction-Diffusion Equations on Multiphase Flow Transport in the Entrapped-Cell Photobioreactor Using Asymptotic Methods, Int. J. Anal. Appl. 22 (2024), 74. https://doi.org/10.28924/2291-8639-22-2024-74.
- A. Uma, R. Raja, R. Swaminathan, Analytical Solution of Concentrated Mixtures of Hydrogen Sulfide and Methanol in Steady State in Biofilm Model, Contemp. Math. 5 (2024), 2632–2645. https://doi.org/10.37256/cm.5320244394.