Advances in Differential Equations

The dynamics of chemical reactors in porous media

Johannes Bruining, Pablo Castañeda, and Dan Marchesin

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Is ignition or extinction the fate of an exothermic chemical reaction occurring in a bounded region within a heat conductive solid consisting of a porous medium? In the spherical case, the reactor is modeled by a system of reaction-diffusion equations that reduces to a linear heat equation in a shell, coupled at the internal boundary to a nonlinear ODE modeling the reaction region. This ODE can be regarded as a boundary condition. This model allows the complete analysis of the time evolution of the system: there is always a global attractor. We show that, depending on physical parameters, the attractor contains one or three equilibria. The latter case has special physical interest: the two equilibria represent attractors ("extinction" or "ignition") and the third equilibrium is a saddle. The whole system is well approximated by a single ODE, a "reduced" model, justifying the "heat transfer coefficient" approach of Chemical Engineering.

Article information

Adv. Differential Equations, Volume 17, Number 7/8 (2012), 725-746.

First available in Project Euclid: 17 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B38: Critical points 35B40: Asymptotic behavior of solutions 35K55: Nonlinear parabolic equations 35K575 35K60: Nonlinear initial value problems for linear parabolic equations 37L25: Inertial manifolds and other invariant attracting sets


Castañeda, Pablo; Marchesin, Dan; Bruining, Johannes. The dynamics of chemical reactors in porous media. Adv. Differential Equations 17 (2012), no. 7/8, 725--746.

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