Theoretical Analysis of Mass Transfer with Chemical Reaction Using Absorption of Carbon Dioxide into Phenyl Glycidyl Ether Solution

Affiliation(s)

District Institute of Education and Training, Pudukkottai, Tamil Nadu, India.

Department of Mathematics, The Madura College, Madurai-625011, Tamil Nadu, India.

District Institute of Education and Training, Pudukkottai, Tamil Nadu, India.

Department of Mathematics, The Madura College, Madurai-625011, Tamil Nadu, India.

ABSTRACT

Theoretical analysis corresponding to the diffusion and reaction kinetics in a chemical reaction between carbon dioxide and phenyl glycidyl ether solution is presented. Analytical expressions pertaining to the concentration of carbon dioxide (CO_{2}), phenyl glycidyl ether solution (PGE) and flux are obtained in terms of reaction rate constants. In this paper, a powerful analytical method, called the Adomian decomposition method (ADM) is used to obtain approximate analytical solutions for nonlinear differential equations. Furthermore, in this work the numerical simulation of the problem is also reported using Scilab/Matlab program. An agreement between analytical and numerical results is noted.

Theoretical analysis corresponding to the diffusion and reaction kinetics in a chemical reaction between carbon dioxide and phenyl glycidyl ether solution is presented. Analytical expressions pertaining to the concentration of carbon dioxide (CO

Cite this paper

M. Subramaniam, I. Krishnaperumal and R. Lakshmanan, "Theoretical Analysis of Mass Transfer with Chemical Reaction Using Absorption of Carbon Dioxide into Phenyl Glycidyl Ether Solution,"*Applied Mathematics*, Vol. 3 No. 10, 2012, pp. 1179-1186. doi: 10.4236/am.2012.310172.

M. Subramaniam, I. Krishnaperumal and R. Lakshmanan, "Theoretical Analysis of Mass Transfer with Chemical Reaction Using Absorption of Carbon Dioxide into Phenyl Glycidyl Ether Solution,"

References

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[2] W. J. Peppel, “Preparation and Properties of the Alkylene Carbonates,” Industrial and Engineering Chemical Research, Vol. 50, No. 5, 1958, pp. 767-770. doi:10.1021/ie50581a030

[3] N. Kihara, N. Hara and T. Endo, “Catalytic Activity of Various Salts in the Reaction of 2,3-Epoxypropyl Phenyl Ether and Carbon Dioxide under Atmospheric Pressure,” The Journal of Organic Chemistry, Vol. 58, No. 23, 1993, pp. 6198-6202. doi:10.1021/jo00075a011

[4] G. Rokicki, “Cyclic Dicarbonates as New Monomers for the Synthesis of Poly(hydroxy ether)s,” Die Makromolekulare Chemie, Vol. 186, No. 2, 1985, pp. 331-337. doi:10.1002/macp.1985.021860212

[5] Y. S. Choe, K. J. Oh, M. C. Kim and S. W. Park, “Chemical Absorption of Carbon Dioxide into Phenyl Glycidyl Ether Solution Containing THA-CP-MS41 Catalyst,” Korean Journal of Chemical Engineering, Vol. 27, No. 6, 2010, pp. 1868-1875. doi:10.1007/s11814-010-0309-1

[6] G. Adomian, “Convergent Series Solution of Nonlinear Equations,” Journal of Computational and Applied Mathematics, Vol. 11, No. 2, 1984, pp. 225-230. doi:10.1016/0377-0427(84)90022-0

[7] A. Patela and S. E. Serrano, “Decomposition Solution of Multidimensional Groundwater Equations,” Journal of Hydrology, Vol. 397, No. 3-4, 2011, pp. 202-209. doi:10.1016/j.jhydrol.2010.11.032

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[9] O. K. Jaradat, “Adomian Decomposition Method for Solving Abelian Differential Equations,” Journal of Applied Sciences, Vol. 8, No. 10, 2008, pp. 1962-1966. doi:10.3923/jas.2008.1962.1966

[10] A. M. Siddiquia, M. Hameed, B. M. Siddiquic and Q. K. Ghoric, “Use of Adomian Decomposition Method in the Study of Parallel Plate Flow of a Third Grade Fluid,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 9, 2010, pp. 2388-2399. doi:10.1016/j.cnsns.2009.05.073

[11] K. Indira and L. Rajendran, “Analytical Expression of Non Steady-State Concentration for the CE Mechanism at a Planar Electrode,” Journal of Mathematical Chemistry, Vol. 50, No. 5, 2012 pp. 1277-1288. doi:10.1007/s10910-011-9968-3

[12] M. U. Maheswari and L. Rajendran, “Analytical Solution of Nonlinear Enzyme Reaction Equations Arising in Mathematical Chemistry,” Journal of Mathematical Chemistry, Vol. 49, No. 8, 2011, pp. 1713-1726. doi:10.1007/s10910-011-9853-0

[13] A. Meena and L. Rajendran, “Mathematical Modeling of Amperometric and Potentiometric Biosensors and System of Nonlinear Equations—Homotopy Perturbation Approach,” Journal of Electroanalytical Chemistry, Vol. 644, No. 1, 2010, pp. 50-59. doi:10.1016/j.jelechem.2010.03.027

[14] V. M. PonRani and L. Rajendran, “Mathematical Modelling of Steady-State Concentration in Immobilized Glucose Isomerase of Packed—Bed Reactors,” Journal of Mathematical Chemistry, Vol. 50, No. 5, 2012, pp. 1333-1346. doi:10.1007/s10910-011-9973-6

[15] S. Anitha, A. Subbiah, S. Subramaniam and L. Rajendran, “Analytical Solution of Amperometric Enzymatic Reactions Based on Homotopy Perturbation Method,” Electrochimica Acta, Vol. 56, No. 9, 2011, pp. 3345-3352. doi:10.1016/j.electacta.2011.01.014

[16] S. J. Liao, “The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems,” Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai, 1992.

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[18] S. J. Liao, “Comparison between the Homotopy Analysis Method and Homotopy Perturbation Method,” Applied Mathematics and Computation, Vol. 169, No. 2, 2005, pp. 1186-1194. doi:10.1016/j.amc.2004.10.058

[19] S. J. Liao, “A New Branch of Solutions of BoundaryLayer Flows over an Impermeable Stretched Plate,” International Journal of Heat and Mass Transfer, Vol. 48, No. 12, 2005, pp. 2529-2539. doi:10.1016/j.ijheatmasstransfer.2005.01.005

[20] S. J. Liao, “Beyond Perturbation: Introduction to the Homotopy Analysis Method,” CRC Press, Chapman & Hall, Boca Raton, 2003. doi:10.1201/9780203491164

[21] S. J. Liao, “An Explicit, Totally Analytic Approximation of Blasius Viscous Flow Problems,” International Journal of Non-Linear Mechanics, Vol. 34, No. 4, 1999, pp. 759-778. doi:10.1016/S0020-7462(98)00056-0

[22] A. M. Wazwaza and A. Gorguisb, “An Analytic Study of Fisher’s Equation by Using Adomian Decomposition Method,” Applied Mathematics and Computation, Vol. 154, No. 3, 2004, pp. 609-620. doi:10.1016/S0096-3003(03)00738-0

[23] J. Biazar and R. Islam, “Solution of Wave Equation by Adomian Decomposition Method and the Restrictions of the Method,” Applied Mathematics and Computation, Vol. 149, No. 3, 2004, pp. 807-814. doi:10.1016/S0096-3003(03)00186-3

[24] N. H. Sweilama and M. M. Khaderb, “Approximate Solutions to the Nonlinear Vibrations of Multiwalled Carbon Nanotubes Using Adomian Decomposition Method,” Applied Mathematics and Computation, Vol. 217, No. 2, 2010, pp. 495-505. doi:10.1016/j.amc.2010.05.082

[25] G. Adomian, “Solving the Mathematical Models of Neurosciences and Medicine,” Mathematics and Computers in Simulation, Vol. 40, No. 1-2, 1995, pp. 107-114. doi:10.1016/0378-4754(95)00021-8

[26] G. Adomian, “Computation of Solutions to the Generalized Michaelis-Menton Equation,” Applied Mathematics Letters, Vol. 7, No. 4, 1994, pp. 45-48. doi:10.1016/0893-9659(94)90009-4

[27] O. D. Makinde, “Adomian Decomposition Approach to a SIR Epidemic Model with Constant Vaccination Strategy,” Applied Mathematics and Computation, Vol. 184, No. 2, 2007, pp. 842-848. doi:10.1016/j.amc.2006.06.074

[1] S. Inoue, “In Organic and Bioorganic Chemistry of Carbon Dioxide,” In: S. Inoue and N. Amazaki, Eds., Kodansha Ltd., Tokyo, 1982.

[2] W. J. Peppel, “Preparation and Properties of the Alkylene Carbonates,” Industrial and Engineering Chemical Research, Vol. 50, No. 5, 1958, pp. 767-770. doi:10.1021/ie50581a030

[3] N. Kihara, N. Hara and T. Endo, “Catalytic Activity of Various Salts in the Reaction of 2,3-Epoxypropyl Phenyl Ether and Carbon Dioxide under Atmospheric Pressure,” The Journal of Organic Chemistry, Vol. 58, No. 23, 1993, pp. 6198-6202. doi:10.1021/jo00075a011

[4] G. Rokicki, “Cyclic Dicarbonates as New Monomers for the Synthesis of Poly(hydroxy ether)s,” Die Makromolekulare Chemie, Vol. 186, No. 2, 1985, pp. 331-337. doi:10.1002/macp.1985.021860212

[5] Y. S. Choe, K. J. Oh, M. C. Kim and S. W. Park, “Chemical Absorption of Carbon Dioxide into Phenyl Glycidyl Ether Solution Containing THA-CP-MS41 Catalyst,” Korean Journal of Chemical Engineering, Vol. 27, No. 6, 2010, pp. 1868-1875. doi:10.1007/s11814-010-0309-1

[6] G. Adomian, “Convergent Series Solution of Nonlinear Equations,” Journal of Computational and Applied Mathematics, Vol. 11, No. 2, 1984, pp. 225-230. doi:10.1016/0377-0427(84)90022-0

[7] A. Patela and S. E. Serrano, “Decomposition Solution of Multidimensional Groundwater Equations,” Journal of Hydrology, Vol. 397, No. 3-4, 2011, pp. 202-209. doi:10.1016/j.jhydrol.2010.11.032

[8] M. A. Mohamed, “Comparison Differential Transformation Technique with Adomian Decomposition Method for Dispersive Long-Wave Equations in (2+1)-Dimensions,” Applications and Applied Mathematics, Vol. 5, No. 1, 2010, pp. 148-166.

[9] O. K. Jaradat, “Adomian Decomposition Method for Solving Abelian Differential Equations,” Journal of Applied Sciences, Vol. 8, No. 10, 2008, pp. 1962-1966. doi:10.3923/jas.2008.1962.1966

[10] A. M. Siddiquia, M. Hameed, B. M. Siddiquic and Q. K. Ghoric, “Use of Adomian Decomposition Method in the Study of Parallel Plate Flow of a Third Grade Fluid,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 9, 2010, pp. 2388-2399. doi:10.1016/j.cnsns.2009.05.073

[11] K. Indira and L. Rajendran, “Analytical Expression of Non Steady-State Concentration for the CE Mechanism at a Planar Electrode,” Journal of Mathematical Chemistry, Vol. 50, No. 5, 2012 pp. 1277-1288. doi:10.1007/s10910-011-9968-3

[12] M. U. Maheswari and L. Rajendran, “Analytical Solution of Nonlinear Enzyme Reaction Equations Arising in Mathematical Chemistry,” Journal of Mathematical Chemistry, Vol. 49, No. 8, 2011, pp. 1713-1726. doi:10.1007/s10910-011-9853-0

[13] A. Meena and L. Rajendran, “Mathematical Modeling of Amperometric and Potentiometric Biosensors and System of Nonlinear Equations—Homotopy Perturbation Approach,” Journal of Electroanalytical Chemistry, Vol. 644, No. 1, 2010, pp. 50-59. doi:10.1016/j.jelechem.2010.03.027

[14] V. M. PonRani and L. Rajendran, “Mathematical Modelling of Steady-State Concentration in Immobilized Glucose Isomerase of Packed—Bed Reactors,” Journal of Mathematical Chemistry, Vol. 50, No. 5, 2012, pp. 1333-1346. doi:10.1007/s10910-011-9973-6

[15] S. Anitha, A. Subbiah, S. Subramaniam and L. Rajendran, “Analytical Solution of Amperometric Enzymatic Reactions Based on Homotopy Perturbation Method,” Electrochimica Acta, Vol. 56, No. 9, 2011, pp. 3345-3352. doi:10.1016/j.electacta.2011.01.014

[16] S. J. Liao, “The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems,” Ph.D. Thesis, Shanghai Jiao Tong University, Shanghai, 1992.

[17] S. J. Liao, “On the Homotopy Anaylsis Method for Nonlinear Problems,” Applied Mathematics and Computation, Vol. 147, No. 2, 2004, pp. 499-513. doi:10.1016/S0096-3003(02)00790-7

[18] S. J. Liao, “Comparison between the Homotopy Analysis Method and Homotopy Perturbation Method,” Applied Mathematics and Computation, Vol. 169, No. 2, 2005, pp. 1186-1194. doi:10.1016/j.amc.2004.10.058

[19] S. J. Liao, “A New Branch of Solutions of BoundaryLayer Flows over an Impermeable Stretched Plate,” International Journal of Heat and Mass Transfer, Vol. 48, No. 12, 2005, pp. 2529-2539. doi:10.1016/j.ijheatmasstransfer.2005.01.005

[20] S. J. Liao, “Beyond Perturbation: Introduction to the Homotopy Analysis Method,” CRC Press, Chapman & Hall, Boca Raton, 2003. doi:10.1201/9780203491164

[21] S. J. Liao, “An Explicit, Totally Analytic Approximation of Blasius Viscous Flow Problems,” International Journal of Non-Linear Mechanics, Vol. 34, No. 4, 1999, pp. 759-778. doi:10.1016/S0020-7462(98)00056-0

[22] A. M. Wazwaza and A. Gorguisb, “An Analytic Study of Fisher’s Equation by Using Adomian Decomposition Method,” Applied Mathematics and Computation, Vol. 154, No. 3, 2004, pp. 609-620. doi:10.1016/S0096-3003(03)00738-0

[23] J. Biazar and R. Islam, “Solution of Wave Equation by Adomian Decomposition Method and the Restrictions of the Method,” Applied Mathematics and Computation, Vol. 149, No. 3, 2004, pp. 807-814. doi:10.1016/S0096-3003(03)00186-3

[24] N. H. Sweilama and M. M. Khaderb, “Approximate Solutions to the Nonlinear Vibrations of Multiwalled Carbon Nanotubes Using Adomian Decomposition Method,” Applied Mathematics and Computation, Vol. 217, No. 2, 2010, pp. 495-505. doi:10.1016/j.amc.2010.05.082

[25] G. Adomian, “Solving the Mathematical Models of Neurosciences and Medicine,” Mathematics and Computers in Simulation, Vol. 40, No. 1-2, 1995, pp. 107-114. doi:10.1016/0378-4754(95)00021-8

[26] G. Adomian, “Computation of Solutions to the Generalized Michaelis-Menton Equation,” Applied Mathematics Letters, Vol. 7, No. 4, 1994, pp. 45-48. doi:10.1016/0893-9659(94)90009-4

[27] O. D. Makinde, “Adomian Decomposition Approach to a SIR Epidemic Model with Constant Vaccination Strategy,” Applied Mathematics and Computation, Vol. 184, No. 2, 2007, pp. 842-848. doi:10.1016/j.amc.2006.06.074