Analytical Expressions of Concentration of VOC and Oxygen in Steady-State in Biofilteration Model

Abstract

Mathematical models of steady-state biofilteration are discussed. The theoretical results are much useful for the design of biofilters. This model is based on the system of non-linear reaction/diffusion equations contains a non-linear term related to Monod kinetics, Andrews kinetics, interactive model from Monod kinetics and Andrews kinetics. Analytical expression of concentration of VOC (Volatile organic compounds) and oxygen are derived by solving the system of non-linear equations using Adomian decomposition method (ADM) method. Our analytical results are also compared with the simulation results. Satisfactory agreement is noted.

Cite this paper

M. Sivasankari and L. Rajendran, "Analytical Expressions of Concentration of VOC and Oxygen in Steady-State in Biofilteration Model,"*Applied Mathematics*, Vol. 4 No. 2, 2013, pp. 314-325. doi: 10.4236/am.2013.42048.

M. Sivasankari and L. Rajendran, "Analytical Expressions of Concentration of VOC and Oxygen in Steady-State in Biofilteration Model,"

References

[1] S. P. P Ottengraf, H. J. Rehm and G. Reed, Eds., “Exhaust Gas Purification,” Biotechnology, Vol. 8, 1986, pp. 425-452.

[2] S. P. P. Ottengraf and A. H. C. Van den Oever, “Kinetics of Organic Compound Removal from Waste Gases with a Biological Filter,” Biotechnology and Bioengineering, Vol. 25, No. 12, 1983, pp. 3089-3102.
doi:10.1002/bit.260251222

[3] S. M. Zarook, B. C. Baltzis, Y.-S. Oh and R. Bartha, “Biofiltration of Methanol Vapor,” Biotechnology and Bioengineering, Vol. 41, No. 5, 1993, pp. 512-524.
doi:10.1002/bit.260410503

[4] E. R. Allen and S. Phatak, “Control of Organosulfur Ompound Emissions Using Biofiltration. Methyl Mercaptan,” Proceedings of the 86th, Air and Waste Management Association Annual Meeting and Exhibition, Denver, 13-18 June 1993.

[5] M. A. Deshusses and I. J. Dunn, “Modeling Experiments on the Kinetics of Mixed-Solvent Removal from Waste Gas in a Biofilter,” Proceedings of the 6th European Congress in Iotechnology, Florence, 13-17 June 1993.

[6] S. M. Zarook and B. C. Baltzls, “Biofiltration of Toluene Vapour under Steady State and Transient Conditions,” Chemical Engineering Science, Vol. 49, 1994, pp. 4347-4360. doi:10.1016/S0009-2509(05)80026-0

[7] S. P. P. Ottengraf, R. M. M. Diks, “Biotechniques for Air Pollution Abatement and Odor Control Policies,” Process Technology of Biotechniques, Elsevier Science, New York, 1992, pp. 17-31.

[8] C. Van Lith, S. L. David and R. Marsh, “Design Criteria for Biofilters,” Transactions of the Institution of Chemical Engineers, Vol. 68, 1990, pp. 127-132.

[9] D. S. Hodge and J. S. Devinny, “Modeling Removal of Air Contaminants by Biofiltration,” Journal of Environmental Engineering, Vol. 121, No. 1, 1995, pp. 21-32.
doi:10.1061/(ASCE)0733-9372(1995)121:1(21)

[10] M. A. Deshusses, G. Hamer and I. J. Dunn, “Behavior of Biofilters for Waste Air Biotreatment,” Journal of Environmental Science Technology, Vol. 29, No. 4, 1995, pp. 1048-1068. doi:10.1021/es00004a027

[11] E. Morgenroth, E. D. Schroeder, D. P. Y. Chang and K. M. Scow, “Modeling of a Compost Biofilter Incorporating Microbial Growth,” American Society of Civil Engineers, 1995, pp. 473-480.

[12] R. S. Cherry and D. N. Thompson, “The Shift from Growth to Nutrient limited Maintenance Kinetics during acclimation of a Biofilter,” Journal of Biotechnology Bioengineering, Vol. 56, No. 3, 1997, pp. 330-339.
doi:10.1002/(SICI)1097-0290(19971105)56:3<330::AID-BIT11>3.0.CO;2-K

[13] S. M. Zarook, A. A. Shaikh and Z. Ansar, “Development, Experimental Validation and Dynamic Analysis of a General Transient Biofilter Model,” Journal of Chemical Engineering Science, Vol. 529, No. 5, 1997, pp. 759-773.
doi:10.1016/S0009-2509(96)00428-9

[14] S. M. Zarook and A. A. Shaikh, “Analysis and Comparison of Biofilter Models,” Chemical Engineering Journal, Vol. 65, No. 1, 1997, pp. 55-61.
doi:10.1016/S1385-8947(96)03101-4

[15] A. Coely, Eds., et al., “Backlund and Darboux Transformation,” American Mathematical Society, Providence, 2001.

[16] M. Wadati, H. Sanuki and K. Konno, “Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws,” Progress of the Theoretical Physics, Vol. 53, No. 2, 1975, pp. 419-436.
doi:10.1143/PTP.53.419

[17] C. S. Gardener, J. M. Green, M. D. Kruskal and R. M. Miura, “Method for Solving the Korteweg-de Vries Equation,” Physical Review Letters, Vol. 19, No. 19, 1967, pp. 1095-1097. doi:10.1103/PhysRevLett.19.1095

[18] R. Hirota, “Exact Solution of the Korteweg-De Vries Equation for Multiple Collisions of Solitons,” Physical Review Letters, Vol. 27, No. 18, 1971, pp. 1192-1194.
doi:10.1103/PhysRevLett.27.1192

[19] W. Malfliet, “Solitary Wave Solutions of Nonlinear Wave Equations Solitons,” American Journal of Physics, Vol. 60, No. 7, 1992, p. 650. doi:10.1119/1.17120

[20] J. H. He, “Approximate Analyticalsolution for Seepage Flow with Fractionalderivatives in Porous Media,” American Computer Methods in Applied Mechanics and Engineering, Vol. 167, No. 1-2, 1998, pp. 57-68.
doi:10.1016/S0045-7825(98)00108-X

[21] J. H. He, “Chaos Solitons Fractals,” Applied Mathematics and Computation, Vol. 26, No. 3, 2005, p. 695.

[22] J. H. He, “Homotopy Perturbation Method for Solving Boundary Value Problems,” Physics Letters A, Vol. 350, No. 1-2, 2006, pp. 87-88.
doi:10.1016/j.physleta.2005.10.005

[23] J. H. He, “A Simple Perturbation Approach to Blasius Equation,” Applied Mathematics and Computation, Vol. 140, No. 2-3, 2003, pp. 217-222.
doi:10.1016/S0096-3003(02)00189-3

[24] D. D. Ganji and M. Rafei, “Solitary Wave Solutions for a Generalized Hirota-Satsuma Coupled KdV Equation by Homotopy Perturbation Method,” Physics Letters A, Vol. 356, No. 2, 2006, pp. 131-137.
doi:10.1016/j.physleta.2006.03.039

[25] P. D. Ariel, “Homotopy Perturbation Method and the Natural Convection Flow of a Third Grade Fluid through a Circular Tube,” Nonlinear Science Letters A, Vol. 1, 2010, pp. 43-52.

[26] B. Jang, “Two-Point Boundary Value Problems by the Extended Adomian Decomposition Method,” Journal of Computational and Applied Mathematics, Vol. 219, No. 1, 2008, pp. 253-262. doi:10.1016/j.cam.2007.07.036

[27] G. Adomian, “Solutions of Nonlinear PDE,” Applied Mathematics, Vol. 11, No. 3, 1998, pp. 121-123.

[28] G. Adomian, “A Global Method for Solution of Complex Systems,” Mathematical Modelling, Vol. 5, No. 4, 1984, pp. 251-263. doi:10.1016/0270-0255(84)90004-6

[29] G. Adomian, “Stochastic Nonlinear Modeling of Fluctuations in a Nuclear Reactor—A New Approach,” Annals of Nuclear Energy, Vol. 8, No. 7, 1981, pp. 329-330.
doi:10.1016/0306-4549(81)90053-0

[30] A. Saufyane and M. Boulmalf, “Solution of Linear and Nonlinear Parabolic Equations by the Decomposition Method,” Applied Mathematics and Computation, Vol. 162, No. 2, 2005, pp. 687-693.
doi:10.1016/j.amc.2004.01.005