학술논문
Upscaling coupled heterogeneous diffusion reaction equations in porous media.
Document Type
Journal
Author
Bourbatache, M. K. (F-INSAR-LGC) AMS Author Profile; Millet, O. (F-LARO-SIE) AMS Author Profile; Moyne, C. (F-LOR2-LEM) AMS Author Profile
Source
Subject
35 Partial differential equations -- 35K Parabolic equations and systems
35K57Reaction-diffusion equations
76Fluid mechanics -- 76M Basic methods in fluid mechanics
76M50Homogenization
76Fluid mechanics -- 76R Diffusion and convection
76R50Diffusion
35K57
76
76M50
76
76R50
Language
English
Abstract
Summary: ``In this work, the periodic homogenization method is applied to a system of two equations of diffusion coupled through heterogeneous chemical reactions at the solid-fluid interface. This upscaling is discussed according to the order of magnitude of the Damköhler number. For large values of Damköhler number, a new homogenized diffusion reaction model coupling chemical reaction and diffusion is obtained. The homogenized diffusion and co-diffusion tensors are function of the heterogeneous reaction rate coefficients. The relevance of this homogenized model is analysed with respect to the order of magnitude of the Damköhler number. Some numerical simulations using this homogenized model are carried out and compared to numerical simulations at pore scale.''