A Singular Perturbation Problem for Steady State Conversion of Methane Oxidation in a Reverse Flow Reactor

Aang Nuryaman, Agus Yodi Gunawan, Kuntjoro Adji Sidarto, Yogi Wibisono Budhi


The governing equations describing methane oxidation in a reverse flow reactor are given by a set of convective-diffusion equations with a nonlinear reaction term, where temperature and methane conversion are dependent variables. In this study, the process is assumed to be a one-dimensional pseudohomogeneous model and takes place with a certain reaction rate in which thewhole process ofthereactor is still workable. Thus, the reaction rate can proceed at a fixed temperature. Under these conditions, we can restrict ourselves to solving the equations for the conversion only. From the available data, it turns out that the ratio of the diffusion term to the reaction term is small. Hence, this ratio is considered as a small parameter in our model and this leads to a singular perturbation problem. Numerical difficulties will be found in the vicinity of a small parameter in front of a higher order term. Here, we present an analytical solutionby means of matched asymptotic expansions. The result shows that, up to and including the first order of approximation, the solution is in agreement with the exact and numerical solutions of the boundary value problem.

Full Text:



Frank-Kamenetskii, D.A., Diffusion and Heat Transfer in Chemical Kinetics, Princeton Univ. Press, Princeton, NJ, 1955.

Matros, Yu. Sh., & Bunimovich, G.A., Reverse-Flow Operation In Fixed Bed Catalytic Reactors, Catalysis Reviews: Science & Engineering, 38, pp. 1-68, 1996.

Garg, L., Luss, D., & Khinast, J.G., Dynamic and Steady-State Features of a Cooled Countercurrent Flow Reactor, AIChE Journal, 46(10), pp. 2030-2040, 2000.

Gosiewski, K., Effective Approach to Cyclic Steady State in the Catalytic Reverse-Flow Combustion of Methane, Chemical Engineering Science, 59, pp. 4095-4101, 2004.

Gosiewski, K. & Warmuzinsky, K., Effect of the Mode of Heat Withdrawal on the Asymmetry of Temperature Profiles in Reverse-Flowreactors, Catalytic Combustion of Methane as A Test Case, Chem. Eng. Sci., 62(10), pp. 2679-2689, 2007.

Khinast, J., Gurumoorthy, A., & Luss, D., Complex Dynamic Features of A Cooled Reverse-Flow Reactor, American Institute of Chemical Engineers Journal, 44(5), p. 1128, 1998.

Khinast, J., Jeong, Y.O. & Luss, D., Dependence of Cooled Reverse-Flow Reactor Dynamics on Reactor Model, A.I.Ch.E. Journal, 45, pp. 299-309, 1999.

Khinast, J. & Luss, D., Efficient Bifurcation Analysis of Periodically- Forced Distributed Parameter System, Computers and Chemical Engineering, 24, pp. 139-152, 2000.

Salinger, A.G. & Eigenberger, G., The Direct Calculations of Periodic States of The Reverse Flow Reactor-I, Methodology and Propane Combustion Results, Chemical Engineering Science, 51, pp. 4903-4913, 1996.

Salinger, A.G. & Eigenberger, G., TheDirect Calculations of Periodic States of The Reverse Flow Reactor-II. Multiplicity and Satability. Chemical Engineering Science, 51, pp. 4915-4922, 1996.

Salomons, S., Hayes, R.E., Poirier, M. & Sapoundjiev, H., Modelling a Reverse Flow Reactor for The Catalytic Combustion of Fugitive Methane Emission, Computer and Chemical Engineering, 28, pp. 1599-1610, 2004.

Holmes, M.H., Introduction to Perturbation Methods, Texts in Applied Mathematics, 20, Springer-Verlag, New York, 1998.

Verhulst, F., Methods and Applications of Singular Perturbations, Texts in Applied Mathematics, 50, Springer-Verlag, New York, 2000.

Van Noorden, T.L., Verduyn Lunel, S.M.V. & Bliek, A., The Efficient Computation of Periodic States of Cyclically Operated Chemical Processes, IMA Journal of Applied Mathematics, 68, pp. 149-166, 2003.

DOI: http://dx.doi.org/10.5614%2Fitbj.sci.2012.44.3.7


  • There are currently no refbacks.

View my Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.