Laplace transform approach to the rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore

Abstract

In this article, we undertake a rigorous derivation of the upscaled model for reactive flow through a narrow and long two-dimensional pore. The transported and diffused solute particles undergo the infinite adsorption rate reactions at the lateral tube boundary. At the inlet boundary we suppose Danckwerts’ boundary conditions. The transport and reaction parameters are such that we have dominant Peclet number. Our analysis uses the anisotropic singular perturbation technique, the small characteristic parameter ε being the ratio between the thickness and the longitudinal observation length. Our goal is to obtain error estimates for the approximation of the physical solution by the upscaled one. They are presented in the energy norm. They give the approximation error as a power of ε and guarantee the validity of the upscaled model. We use the Laplace transform in time to get better estimates than in our previous article [Mikelić, Rosier, Rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore, Ann Univ Ferrara Sez. VII Sci. Mat. 2007 53, 333–359] and to undertake the study of important Danckwerts' boundary conditions.

Keywords:

• Taylor's dispersion
• large Peclet number
• singular perturbation
• Laplace's transform
• adsorption chemical reaction
• Danckwerts’ boundary conditions

AMS Subject Classifications: :

• 35B25
• 92E20
• 76F25
• 44A10

Acknowledgements

Research of the authors was partially supported by the GDR MOMAS (Modélisation Mathématique et Simulations numériques liées aux problèmes de gestion des déchets nucléaires) (PACEN/CNRS, ANDRA, BRGM, CEA, EDF, IRSN) as a part of the project ‘Modèles de dispersion efficace pour des problèmes de Chimie-Transport: Changement d'échelle dans la modélisation du transport réactif en milieux poreux, en présence des nombres caractéristiques dominants’.